Properties

Label 725.2.a.d.1.1
Level $725$
Weight $2$
Character 725.1
Self dual yes
Analytic conductor $5.789$
Analytic rank $0$
Dimension $3$
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] = [725,2,Mod(1,725)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(725, 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("725.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 725.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: \(5.78915414654\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 145)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.48119\) of defining polynomial
Character \(\chi\) \(=\) 725.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.67513 q^{2} +0.806063 q^{3} +5.15633 q^{4} -2.15633 q^{6} +4.15633 q^{7} -8.44358 q^{8} -2.35026 q^{9} +O(q^{10})\) \(q-2.67513 q^{2} +0.806063 q^{3} +5.15633 q^{4} -2.15633 q^{6} +4.15633 q^{7} -8.44358 q^{8} -2.35026 q^{9} +2.80606 q^{11} +4.15633 q^{12} -1.35026 q^{13} -11.1187 q^{14} +12.2750 q^{16} +7.11871 q^{17} +6.28726 q^{18} +3.76845 q^{19} +3.35026 q^{21} -7.50659 q^{22} -4.80606 q^{23} -6.80606 q^{24} +3.61213 q^{26} -4.31265 q^{27} +21.4314 q^{28} +1.00000 q^{29} +0.231548 q^{31} -15.9502 q^{32} +2.26187 q^{33} -19.0435 q^{34} -12.1187 q^{36} +5.50659 q^{37} -10.0811 q^{38} -1.08840 q^{39} -6.96239 q^{41} -8.96239 q^{42} +3.19394 q^{43} +14.4690 q^{44} +12.8568 q^{46} -6.41819 q^{47} +9.89446 q^{48} +10.2750 q^{49} +5.73813 q^{51} -6.96239 q^{52} -6.96239 q^{53} +11.5369 q^{54} -35.0943 q^{56} +3.03761 q^{57} -2.67513 q^{58} -2.57452 q^{59} +5.35026 q^{61} -0.619421 q^{62} -9.76845 q^{63} +18.1187 q^{64} -6.05079 q^{66} +3.19394 q^{67} +36.7064 q^{68} -3.87399 q^{69} +11.3503 q^{71} +19.8446 q^{72} +11.2447 q^{73} -14.7308 q^{74} +19.4314 q^{76} +11.6629 q^{77} +2.91160 q^{78} -4.73084 q^{79} +3.57452 q^{81} +18.6253 q^{82} -2.54420 q^{83} +17.2750 q^{84} -8.54420 q^{86} +0.806063 q^{87} -23.6932 q^{88} +14.3127 q^{89} -5.61213 q^{91} -24.7816 q^{92} +0.186642 q^{93} +17.1695 q^{94} -12.8568 q^{96} +1.53102 q^{97} -27.4871 q^{98} -6.59498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + 2 q^{3} + 5 q^{4} + 4 q^{6} + 2 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} + 2 q^{3} + 5 q^{4} + 4 q^{6} + 2 q^{7} - 9 q^{8} + 3 q^{9} + 8 q^{11} + 2 q^{12} + 6 q^{13} - 12 q^{14} + 5 q^{16} + 13 q^{18} - 2 q^{22} - 14 q^{23} - 20 q^{24} + 10 q^{26} + 8 q^{27} + 22 q^{28} + 3 q^{29} + 12 q^{31} - 11 q^{32} + 16 q^{33} - 14 q^{34} - 15 q^{36} - 4 q^{37} + 2 q^{38} + 16 q^{39} - 10 q^{41} - 16 q^{42} + 10 q^{43} + 12 q^{44} + 8 q^{46} - 18 q^{47} + 10 q^{48} - q^{49} + 8 q^{51} - 10 q^{52} - 10 q^{53} + 12 q^{54} - 32 q^{56} + 20 q^{57} - 3 q^{58} + 4 q^{59} + 6 q^{61} - 14 q^{62} - 18 q^{63} + 33 q^{64} + 12 q^{66} + 10 q^{67} + 36 q^{68} - 20 q^{69} + 24 q^{71} + 3 q^{72} + 4 q^{73} - 22 q^{74} + 16 q^{76} + 4 q^{77} + 28 q^{78} + 8 q^{79} - q^{81} + 14 q^{82} + 2 q^{83} + 20 q^{84} - 16 q^{86} + 2 q^{87} - 38 q^{88} + 22 q^{89} - 16 q^{91} - 22 q^{92} - 12 q^{93} - 8 q^{96} + 36 q^{97} - 23 q^{98} + 20 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67513 −1.89160 −0.945802 0.324745i \(-0.894721\pi\)
−0.945802 + 0.324745i \(0.894721\pi\)
\(3\) 0.806063 0.465381 0.232690 0.972551i \(-0.425247\pi\)
0.232690 + 0.972551i \(0.425247\pi\)
\(4\) 5.15633 2.57816
\(5\) 0 0
\(6\) −2.15633 −0.880316
\(7\) 4.15633 1.57094 0.785472 0.618898i \(-0.212420\pi\)
0.785472 + 0.618898i \(0.212420\pi\)
\(8\) −8.44358 −2.98526
\(9\) −2.35026 −0.783421
\(10\) 0 0
\(11\) 2.80606 0.846060 0.423030 0.906116i \(-0.360966\pi\)
0.423030 + 0.906116i \(0.360966\pi\)
\(12\) 4.15633 1.19983
\(13\) −1.35026 −0.374495 −0.187248 0.982313i \(-0.559957\pi\)
−0.187248 + 0.982313i \(0.559957\pi\)
\(14\) −11.1187 −2.97160
\(15\) 0 0
\(16\) 12.2750 3.06876
\(17\) 7.11871 1.72654 0.863271 0.504741i \(-0.168412\pi\)
0.863271 + 0.504741i \(0.168412\pi\)
\(18\) 6.28726 1.48192
\(19\) 3.76845 0.864542 0.432271 0.901744i \(-0.357712\pi\)
0.432271 + 0.901744i \(0.357712\pi\)
\(20\) 0 0
\(21\) 3.35026 0.731087
\(22\) −7.50659 −1.60041
\(23\) −4.80606 −1.00213 −0.501067 0.865409i \(-0.667059\pi\)
−0.501067 + 0.865409i \(0.667059\pi\)
\(24\) −6.80606 −1.38928
\(25\) 0 0
\(26\) 3.61213 0.708396
\(27\) −4.31265 −0.829970
\(28\) 21.4314 4.05015
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 0.231548 0.0415872 0.0207936 0.999784i \(-0.493381\pi\)
0.0207936 + 0.999784i \(0.493381\pi\)
\(32\) −15.9502 −2.81962
\(33\) 2.26187 0.393740
\(34\) −19.0435 −3.26593
\(35\) 0 0
\(36\) −12.1187 −2.01979
\(37\) 5.50659 0.905277 0.452639 0.891694i \(-0.350483\pi\)
0.452639 + 0.891694i \(0.350483\pi\)
\(38\) −10.0811 −1.63537
\(39\) −1.08840 −0.174283
\(40\) 0 0
\(41\) −6.96239 −1.08734 −0.543671 0.839298i \(-0.682966\pi\)
−0.543671 + 0.839298i \(0.682966\pi\)
\(42\) −8.96239 −1.38293
\(43\) 3.19394 0.487071 0.243535 0.969892i \(-0.421693\pi\)
0.243535 + 0.969892i \(0.421693\pi\)
\(44\) 14.4690 2.18128
\(45\) 0 0
\(46\) 12.8568 1.89564
\(47\) −6.41819 −0.936189 −0.468095 0.883678i \(-0.655059\pi\)
−0.468095 + 0.883678i \(0.655059\pi\)
\(48\) 9.89446 1.42814
\(49\) 10.2750 1.46786
\(50\) 0 0
\(51\) 5.73813 0.803500
\(52\) −6.96239 −0.965510
\(53\) −6.96239 −0.956358 −0.478179 0.878263i \(-0.658703\pi\)
−0.478179 + 0.878263i \(0.658703\pi\)
\(54\) 11.5369 1.56997
\(55\) 0 0
\(56\) −35.0943 −4.68967
\(57\) 3.03761 0.402341
\(58\) −2.67513 −0.351262
\(59\) −2.57452 −0.335173 −0.167587 0.985857i \(-0.553597\pi\)
−0.167587 + 0.985857i \(0.553597\pi\)
\(60\) 0 0
\(61\) 5.35026 0.685031 0.342515 0.939512i \(-0.388721\pi\)
0.342515 + 0.939512i \(0.388721\pi\)
\(62\) −0.619421 −0.0786666
\(63\) −9.76845 −1.23071
\(64\) 18.1187 2.26484
\(65\) 0 0
\(66\) −6.05079 −0.744800
\(67\) 3.19394 0.390201 0.195101 0.980783i \(-0.437497\pi\)
0.195101 + 0.980783i \(0.437497\pi\)
\(68\) 36.7064 4.45131
\(69\) −3.87399 −0.466374
\(70\) 0 0
\(71\) 11.3503 1.34703 0.673514 0.739174i \(-0.264784\pi\)
0.673514 + 0.739174i \(0.264784\pi\)
\(72\) 19.8446 2.33871
\(73\) 11.2447 1.31610 0.658048 0.752976i \(-0.271383\pi\)
0.658048 + 0.752976i \(0.271383\pi\)
\(74\) −14.7308 −1.71243
\(75\) 0 0
\(76\) 19.4314 2.22893
\(77\) 11.6629 1.32911
\(78\) 2.91160 0.329674
\(79\) −4.73084 −0.532261 −0.266131 0.963937i \(-0.585745\pi\)
−0.266131 + 0.963937i \(0.585745\pi\)
\(80\) 0 0
\(81\) 3.57452 0.397168
\(82\) 18.6253 2.05682
\(83\) −2.54420 −0.279262 −0.139631 0.990204i \(-0.544592\pi\)
−0.139631 + 0.990204i \(0.544592\pi\)
\(84\) 17.2750 1.88486
\(85\) 0 0
\(86\) −8.54420 −0.921345
\(87\) 0.806063 0.0864191
\(88\) −23.6932 −2.52571
\(89\) 14.3127 1.51714 0.758569 0.651593i \(-0.225899\pi\)
0.758569 + 0.651593i \(0.225899\pi\)
\(90\) 0 0
\(91\) −5.61213 −0.588311
\(92\) −24.7816 −2.58366
\(93\) 0.186642 0.0193539
\(94\) 17.1695 1.77090
\(95\) 0 0
\(96\) −12.8568 −1.31220
\(97\) 1.53102 0.155452 0.0777260 0.996975i \(-0.475234\pi\)
0.0777260 + 0.996975i \(0.475234\pi\)
\(98\) −27.4871 −2.77661
\(99\) −6.59498 −0.662821
\(100\) 0 0
\(101\) 2.83638 0.282230 0.141115 0.989993i \(-0.454931\pi\)
0.141115 + 0.989993i \(0.454931\pi\)
\(102\) −15.3503 −1.51990
\(103\) 9.89446 0.974930 0.487465 0.873142i \(-0.337922\pi\)
0.487465 + 0.873142i \(0.337922\pi\)
\(104\) 11.4010 1.11796
\(105\) 0 0
\(106\) 18.6253 1.80905
\(107\) 11.6932 1.13043 0.565214 0.824945i \(-0.308794\pi\)
0.565214 + 0.824945i \(0.308794\pi\)
\(108\) −22.2374 −2.13980
\(109\) −14.4993 −1.38878 −0.694390 0.719599i \(-0.744326\pi\)
−0.694390 + 0.719599i \(0.744326\pi\)
\(110\) 0 0
\(111\) 4.43866 0.421299
\(112\) 51.0191 4.82085
\(113\) 16.3938 1.54219 0.771097 0.636717i \(-0.219708\pi\)
0.771097 + 0.636717i \(0.219708\pi\)
\(114\) −8.12601 −0.761070
\(115\) 0 0
\(116\) 5.15633 0.478753
\(117\) 3.17347 0.293387
\(118\) 6.88717 0.634015
\(119\) 29.5877 2.71230
\(120\) 0 0
\(121\) −3.12601 −0.284183
\(122\) −14.3127 −1.29581
\(123\) −5.61213 −0.506028
\(124\) 1.19394 0.107219
\(125\) 0 0
\(126\) 26.1319 2.32801
\(127\) −15.3561 −1.36264 −0.681319 0.731987i \(-0.738593\pi\)
−0.681319 + 0.731987i \(0.738593\pi\)
\(128\) −16.5696 −1.46456
\(129\) 2.57452 0.226673
\(130\) 0 0
\(131\) 1.38058 0.120622 0.0603109 0.998180i \(-0.480791\pi\)
0.0603109 + 0.998180i \(0.480791\pi\)
\(132\) 11.6629 1.01513
\(133\) 15.6629 1.35815
\(134\) −8.54420 −0.738106
\(135\) 0 0
\(136\) −60.1075 −5.15417
\(137\) 6.49341 0.554770 0.277385 0.960759i \(-0.410532\pi\)
0.277385 + 0.960759i \(0.410532\pi\)
\(138\) 10.3634 0.882194
\(139\) −19.0132 −1.61268 −0.806338 0.591455i \(-0.798554\pi\)
−0.806338 + 0.591455i \(0.798554\pi\)
\(140\) 0 0
\(141\) −5.17347 −0.435685
\(142\) −30.3634 −2.54804
\(143\) −3.78892 −0.316845
\(144\) −28.8496 −2.40413
\(145\) 0 0
\(146\) −30.0811 −2.48953
\(147\) 8.28233 0.683115
\(148\) 28.3938 2.33395
\(149\) 6.62530 0.542766 0.271383 0.962471i \(-0.412519\pi\)
0.271383 + 0.962471i \(0.412519\pi\)
\(150\) 0 0
\(151\) −9.27504 −0.754792 −0.377396 0.926052i \(-0.623180\pi\)
−0.377396 + 0.926052i \(0.623180\pi\)
\(152\) −31.8192 −2.58088
\(153\) −16.7308 −1.35261
\(154\) −31.1998 −2.51415
\(155\) 0 0
\(156\) −5.61213 −0.449330
\(157\) 5.00729 0.399626 0.199813 0.979834i \(-0.435967\pi\)
0.199813 + 0.979834i \(0.435967\pi\)
\(158\) 12.6556 1.00683
\(159\) −5.61213 −0.445071
\(160\) 0 0
\(161\) −19.9756 −1.57429
\(162\) −9.56230 −0.751285
\(163\) −7.50659 −0.587961 −0.293981 0.955811i \(-0.594980\pi\)
−0.293981 + 0.955811i \(0.594980\pi\)
\(164\) −35.9003 −2.80335
\(165\) 0 0
\(166\) 6.80606 0.528253
\(167\) −21.8945 −1.69424 −0.847122 0.531398i \(-0.821667\pi\)
−0.847122 + 0.531398i \(0.821667\pi\)
\(168\) −28.2882 −2.18248
\(169\) −11.1768 −0.859753
\(170\) 0 0
\(171\) −8.85685 −0.677300
\(172\) 16.4690 1.25575
\(173\) −7.02302 −0.533951 −0.266975 0.963703i \(-0.586024\pi\)
−0.266975 + 0.963703i \(0.586024\pi\)
\(174\) −2.15633 −0.163471
\(175\) 0 0
\(176\) 34.4445 2.59635
\(177\) −2.07522 −0.155983
\(178\) −38.2882 −2.86982
\(179\) 4.77575 0.356956 0.178478 0.983944i \(-0.442883\pi\)
0.178478 + 0.983944i \(0.442883\pi\)
\(180\) 0 0
\(181\) 1.87399 0.139293 0.0696464 0.997572i \(-0.477813\pi\)
0.0696464 + 0.997572i \(0.477813\pi\)
\(182\) 15.0132 1.11285
\(183\) 4.31265 0.318800
\(184\) 40.5804 2.99163
\(185\) 0 0
\(186\) −0.499293 −0.0366099
\(187\) 19.9756 1.46076
\(188\) −33.0943 −2.41365
\(189\) −17.9248 −1.30384
\(190\) 0 0
\(191\) 19.1187 1.38338 0.691691 0.722194i \(-0.256866\pi\)
0.691691 + 0.722194i \(0.256866\pi\)
\(192\) 14.6048 1.05401
\(193\) −19.8945 −1.43203 −0.716017 0.698083i \(-0.754037\pi\)
−0.716017 + 0.698083i \(0.754037\pi\)
\(194\) −4.09569 −0.294053
\(195\) 0 0
\(196\) 52.9814 3.78439
\(197\) 13.5369 0.964464 0.482232 0.876043i \(-0.339826\pi\)
0.482232 + 0.876043i \(0.339826\pi\)
\(198\) 17.6424 1.25379
\(199\) 2.57452 0.182503 0.0912513 0.995828i \(-0.470913\pi\)
0.0912513 + 0.995828i \(0.470913\pi\)
\(200\) 0 0
\(201\) 2.57452 0.181592
\(202\) −7.58769 −0.533868
\(203\) 4.15633 0.291717
\(204\) 29.5877 2.07155
\(205\) 0 0
\(206\) −26.4690 −1.84418
\(207\) 11.2955 0.785092
\(208\) −16.5745 −1.14924
\(209\) 10.5745 0.731455
\(210\) 0 0
\(211\) 11.8945 0.818848 0.409424 0.912344i \(-0.365730\pi\)
0.409424 + 0.912344i \(0.365730\pi\)
\(212\) −35.9003 −2.46565
\(213\) 9.14903 0.626881
\(214\) −31.2809 −2.13832
\(215\) 0 0
\(216\) 36.4142 2.47767
\(217\) 0.962389 0.0653312
\(218\) 38.7875 2.62702
\(219\) 9.06396 0.612486
\(220\) 0 0
\(221\) −9.61213 −0.646582
\(222\) −11.8740 −0.796930
\(223\) 1.11871 0.0749146 0.0374573 0.999298i \(-0.488074\pi\)
0.0374573 + 0.999298i \(0.488074\pi\)
\(224\) −66.2941 −4.42946
\(225\) 0 0
\(226\) −43.8554 −2.91722
\(227\) −0.0303172 −0.00201222 −0.00100611 0.999999i \(-0.500320\pi\)
−0.00100611 + 0.999999i \(0.500320\pi\)
\(228\) 15.6629 1.03730
\(229\) −5.84955 −0.386549 −0.193275 0.981145i \(-0.561911\pi\)
−0.193275 + 0.981145i \(0.561911\pi\)
\(230\) 0 0
\(231\) 9.40105 0.618543
\(232\) −8.44358 −0.554348
\(233\) −26.1016 −1.70997 −0.854985 0.518652i \(-0.826434\pi\)
−0.854985 + 0.518652i \(0.826434\pi\)
\(234\) −8.48944 −0.554972
\(235\) 0 0
\(236\) −13.2750 −0.864131
\(237\) −3.81336 −0.247704
\(238\) −79.1509 −5.13059
\(239\) 1.42548 0.0922069 0.0461035 0.998937i \(-0.485320\pi\)
0.0461035 + 0.998937i \(0.485320\pi\)
\(240\) 0 0
\(241\) −0.0752228 −0.00484553 −0.00242276 0.999997i \(-0.500771\pi\)
−0.00242276 + 0.999997i \(0.500771\pi\)
\(242\) 8.36248 0.537561
\(243\) 15.8192 1.01480
\(244\) 27.5877 1.76612
\(245\) 0 0
\(246\) 15.0132 0.957205
\(247\) −5.08840 −0.323767
\(248\) −1.95509 −0.124149
\(249\) −2.05079 −0.129963
\(250\) 0 0
\(251\) 16.9829 1.07195 0.535974 0.844234i \(-0.319944\pi\)
0.535974 + 0.844234i \(0.319944\pi\)
\(252\) −50.3693 −3.17297
\(253\) −13.4861 −0.847865
\(254\) 41.0797 2.57757
\(255\) 0 0
\(256\) 8.08840 0.505525
\(257\) −25.1998 −1.57192 −0.785961 0.618276i \(-0.787831\pi\)
−0.785961 + 0.618276i \(0.787831\pi\)
\(258\) −6.88717 −0.428776
\(259\) 22.8872 1.42214
\(260\) 0 0
\(261\) −2.35026 −0.145478
\(262\) −3.69323 −0.228168
\(263\) 16.1319 0.994735 0.497367 0.867540i \(-0.334300\pi\)
0.497367 + 0.867540i \(0.334300\pi\)
\(264\) −19.0982 −1.17542
\(265\) 0 0
\(266\) −41.9003 −2.56907
\(267\) 11.5369 0.706047
\(268\) 16.4690 1.00600
\(269\) 5.28963 0.322514 0.161257 0.986912i \(-0.448445\pi\)
0.161257 + 0.986912i \(0.448445\pi\)
\(270\) 0 0
\(271\) 1.13330 0.0688432 0.0344216 0.999407i \(-0.489041\pi\)
0.0344216 + 0.999407i \(0.489041\pi\)
\(272\) 87.3825 5.29834
\(273\) −4.52373 −0.273789
\(274\) −17.3707 −1.04940
\(275\) 0 0
\(276\) −19.9756 −1.20239
\(277\) 16.3634 0.983184 0.491592 0.870826i \(-0.336415\pi\)
0.491592 + 0.870826i \(0.336415\pi\)
\(278\) 50.8627 3.05054
\(279\) −0.544198 −0.0325803
\(280\) 0 0
\(281\) −24.8265 −1.48103 −0.740513 0.672042i \(-0.765418\pi\)
−0.740513 + 0.672042i \(0.765418\pi\)
\(282\) 13.8397 0.824142
\(283\) 4.18076 0.248521 0.124260 0.992250i \(-0.460344\pi\)
0.124260 + 0.992250i \(0.460344\pi\)
\(284\) 58.5256 3.47286
\(285\) 0 0
\(286\) 10.1359 0.599346
\(287\) −28.9380 −1.70815
\(288\) 37.4871 2.20895
\(289\) 33.6761 1.98095
\(290\) 0 0
\(291\) 1.23410 0.0723444
\(292\) 57.9814 3.39311
\(293\) −23.6180 −1.37978 −0.689889 0.723915i \(-0.742341\pi\)
−0.689889 + 0.723915i \(0.742341\pi\)
\(294\) −22.1563 −1.29218
\(295\) 0 0
\(296\) −46.4953 −2.70249
\(297\) −12.1016 −0.702204
\(298\) −17.7235 −1.02670
\(299\) 6.48944 0.375294
\(300\) 0 0
\(301\) 13.2750 0.765161
\(302\) 24.8119 1.42777
\(303\) 2.28630 0.131345
\(304\) 46.2579 2.65307
\(305\) 0 0
\(306\) 44.7572 2.55860
\(307\) −32.5052 −1.85517 −0.927584 0.373614i \(-0.878118\pi\)
−0.927584 + 0.373614i \(0.878118\pi\)
\(308\) 60.1378 3.42667
\(309\) 7.97556 0.453714
\(310\) 0 0
\(311\) −9.31994 −0.528486 −0.264243 0.964456i \(-0.585122\pi\)
−0.264243 + 0.964456i \(0.585122\pi\)
\(312\) 9.18997 0.520279
\(313\) −9.60228 −0.542753 −0.271376 0.962473i \(-0.587479\pi\)
−0.271376 + 0.962473i \(0.587479\pi\)
\(314\) −13.3952 −0.755933
\(315\) 0 0
\(316\) −24.3938 −1.37226
\(317\) −19.3707 −1.08797 −0.543984 0.839095i \(-0.683085\pi\)
−0.543984 + 0.839095i \(0.683085\pi\)
\(318\) 15.0132 0.841897
\(319\) 2.80606 0.157109
\(320\) 0 0
\(321\) 9.42548 0.526079
\(322\) 53.4372 2.97794
\(323\) 26.8265 1.49267
\(324\) 18.4314 1.02396
\(325\) 0 0
\(326\) 20.0811 1.11219
\(327\) −11.6873 −0.646312
\(328\) 58.7875 3.24600
\(329\) −26.6761 −1.47070
\(330\) 0 0
\(331\) −29.5428 −1.62382 −0.811909 0.583784i \(-0.801572\pi\)
−0.811909 + 0.583784i \(0.801572\pi\)
\(332\) −13.1187 −0.719983
\(333\) −12.9419 −0.709213
\(334\) 58.5705 3.20484
\(335\) 0 0
\(336\) 41.1246 2.24353
\(337\) −12.5442 −0.683326 −0.341663 0.939823i \(-0.610990\pi\)
−0.341663 + 0.939823i \(0.610990\pi\)
\(338\) 29.8994 1.62631
\(339\) 13.2144 0.717708
\(340\) 0 0
\(341\) 0.649738 0.0351853
\(342\) 23.6932 1.28118
\(343\) 13.6121 0.734986
\(344\) −26.9683 −1.45403
\(345\) 0 0
\(346\) 18.7875 1.01002
\(347\) 25.0943 1.34713 0.673566 0.739127i \(-0.264762\pi\)
0.673566 + 0.739127i \(0.264762\pi\)
\(348\) 4.15633 0.222802
\(349\) −17.0738 −0.913940 −0.456970 0.889482i \(-0.651065\pi\)
−0.456970 + 0.889482i \(0.651065\pi\)
\(350\) 0 0
\(351\) 5.82321 0.310820
\(352\) −44.7572 −2.38557
\(353\) −5.66291 −0.301406 −0.150703 0.988579i \(-0.548154\pi\)
−0.150703 + 0.988579i \(0.548154\pi\)
\(354\) 5.55149 0.295058
\(355\) 0 0
\(356\) 73.8007 3.91143
\(357\) 23.8496 1.26225
\(358\) −12.7757 −0.675219
\(359\) 0.755278 0.0398621 0.0199310 0.999801i \(-0.493655\pi\)
0.0199310 + 0.999801i \(0.493655\pi\)
\(360\) 0 0
\(361\) −4.79877 −0.252567
\(362\) −5.01317 −0.263487
\(363\) −2.51976 −0.132253
\(364\) −28.9380 −1.51676
\(365\) 0 0
\(366\) −11.5369 −0.603044
\(367\) −11.4460 −0.597474 −0.298737 0.954335i \(-0.596565\pi\)
−0.298737 + 0.954335i \(0.596565\pi\)
\(368\) −58.9946 −3.07531
\(369\) 16.3634 0.851846
\(370\) 0 0
\(371\) −28.9380 −1.50238
\(372\) 0.962389 0.0498975
\(373\) −3.86414 −0.200078 −0.100039 0.994984i \(-0.531897\pi\)
−0.100039 + 0.994984i \(0.531897\pi\)
\(374\) −53.4372 −2.76317
\(375\) 0 0
\(376\) 54.1925 2.79477
\(377\) −1.35026 −0.0695420
\(378\) 47.9511 2.46634
\(379\) 12.1055 0.621820 0.310910 0.950439i \(-0.399366\pi\)
0.310910 + 0.950439i \(0.399366\pi\)
\(380\) 0 0
\(381\) −12.3780 −0.634145
\(382\) −51.1451 −2.61681
\(383\) 10.0205 0.512022 0.256011 0.966674i \(-0.417592\pi\)
0.256011 + 0.966674i \(0.417592\pi\)
\(384\) −13.3561 −0.681578
\(385\) 0 0
\(386\) 53.2203 2.70884
\(387\) −7.50659 −0.381581
\(388\) 7.89446 0.400780
\(389\) −25.6629 −1.30116 −0.650581 0.759437i \(-0.725474\pi\)
−0.650581 + 0.759437i \(0.725474\pi\)
\(390\) 0 0
\(391\) −34.2130 −1.73023
\(392\) −86.7581 −4.38195
\(393\) 1.11283 0.0561351
\(394\) −36.2130 −1.82438
\(395\) 0 0
\(396\) −34.0059 −1.70886
\(397\) −27.7137 −1.39091 −0.695455 0.718569i \(-0.744797\pi\)
−0.695455 + 0.718569i \(0.744797\pi\)
\(398\) −6.88717 −0.345222
\(399\) 12.6253 0.632056
\(400\) 0 0
\(401\) 7.42548 0.370811 0.185406 0.982662i \(-0.440640\pi\)
0.185406 + 0.982662i \(0.440640\pi\)
\(402\) −6.88717 −0.343501
\(403\) −0.312650 −0.0155742
\(404\) 14.6253 0.727636
\(405\) 0 0
\(406\) −11.1187 −0.551812
\(407\) 15.4518 0.765919
\(408\) −48.4504 −2.39865
\(409\) −33.1998 −1.64163 −0.820813 0.571198i \(-0.806479\pi\)
−0.820813 + 0.571198i \(0.806479\pi\)
\(410\) 0 0
\(411\) 5.23410 0.258179
\(412\) 51.0191 2.51353
\(413\) −10.7005 −0.526538
\(414\) −30.2170 −1.48508
\(415\) 0 0
\(416\) 21.5369 1.05593
\(417\) −15.3258 −0.750509
\(418\) −28.2882 −1.38362
\(419\) 16.5599 0.809005 0.404503 0.914537i \(-0.367445\pi\)
0.404503 + 0.914537i \(0.367445\pi\)
\(420\) 0 0
\(421\) −8.82653 −0.430179 −0.215089 0.976594i \(-0.569004\pi\)
−0.215089 + 0.976594i \(0.569004\pi\)
\(422\) −31.8192 −1.54894
\(423\) 15.0844 0.733430
\(424\) 58.7875 2.85497
\(425\) 0 0
\(426\) −24.4749 −1.18581
\(427\) 22.2374 1.07614
\(428\) 60.2941 2.91442
\(429\) −3.05411 −0.147454
\(430\) 0 0
\(431\) 4.25202 0.204812 0.102406 0.994743i \(-0.467346\pi\)
0.102406 + 0.994743i \(0.467346\pi\)
\(432\) −52.9380 −2.54698
\(433\) 1.81924 0.0874270 0.0437135 0.999044i \(-0.486081\pi\)
0.0437135 + 0.999044i \(0.486081\pi\)
\(434\) −2.57452 −0.123581
\(435\) 0 0
\(436\) −74.7631 −3.58050
\(437\) −18.1114 −0.866387
\(438\) −24.2473 −1.15858
\(439\) 14.1114 0.673501 0.336751 0.941594i \(-0.390672\pi\)
0.336751 + 0.941594i \(0.390672\pi\)
\(440\) 0 0
\(441\) −24.1490 −1.14995
\(442\) 25.7137 1.22308
\(443\) 17.2809 0.821041 0.410521 0.911851i \(-0.365347\pi\)
0.410521 + 0.911851i \(0.365347\pi\)
\(444\) 22.8872 1.08618
\(445\) 0 0
\(446\) −2.99271 −0.141709
\(447\) 5.34041 0.252593
\(448\) 75.3073 3.55793
\(449\) 9.35026 0.441266 0.220633 0.975357i \(-0.429188\pi\)
0.220633 + 0.975357i \(0.429188\pi\)
\(450\) 0 0
\(451\) −19.5369 −0.919957
\(452\) 84.5315 3.97603
\(453\) −7.47627 −0.351266
\(454\) 0.0811024 0.00380632
\(455\) 0 0
\(456\) −25.6483 −1.20109
\(457\) 17.6629 0.826236 0.413118 0.910677i \(-0.364440\pi\)
0.413118 + 0.910677i \(0.364440\pi\)
\(458\) 15.6483 0.731198
\(459\) −30.7005 −1.43298
\(460\) 0 0
\(461\) 15.5633 0.724853 0.362426 0.932012i \(-0.381948\pi\)
0.362426 + 0.932012i \(0.381948\pi\)
\(462\) −25.1490 −1.17004
\(463\) −2.98286 −0.138625 −0.0693126 0.997595i \(-0.522081\pi\)
−0.0693126 + 0.997595i \(0.522081\pi\)
\(464\) 12.2750 0.569854
\(465\) 0 0
\(466\) 69.8251 3.23459
\(467\) −34.5804 −1.60019 −0.800095 0.599873i \(-0.795218\pi\)
−0.800095 + 0.599873i \(0.795218\pi\)
\(468\) 16.3634 0.756400
\(469\) 13.2750 0.612984
\(470\) 0 0
\(471\) 4.03620 0.185978
\(472\) 21.7381 1.00058
\(473\) 8.96239 0.412091
\(474\) 10.2012 0.468558
\(475\) 0 0
\(476\) 152.564 6.99275
\(477\) 16.3634 0.749230
\(478\) −3.81336 −0.174419
\(479\) −34.1925 −1.56230 −0.781148 0.624346i \(-0.785366\pi\)
−0.781148 + 0.624346i \(0.785366\pi\)
\(480\) 0 0
\(481\) −7.43533 −0.339022
\(482\) 0.201231 0.00916581
\(483\) −16.1016 −0.732647
\(484\) −16.1187 −0.732669
\(485\) 0 0
\(486\) −42.3185 −1.91961
\(487\) −38.4953 −1.74439 −0.872195 0.489159i \(-0.837304\pi\)
−0.872195 + 0.489159i \(0.837304\pi\)
\(488\) −45.1754 −2.04499
\(489\) −6.05079 −0.273626
\(490\) 0 0
\(491\) −27.4676 −1.23959 −0.619797 0.784762i \(-0.712785\pi\)
−0.619797 + 0.784762i \(0.712785\pi\)
\(492\) −28.9380 −1.30462
\(493\) 7.11871 0.320611
\(494\) 13.6121 0.612439
\(495\) 0 0
\(496\) 2.84226 0.127621
\(497\) 47.1754 2.11610
\(498\) 5.48612 0.245839
\(499\) −32.1016 −1.43706 −0.718532 0.695494i \(-0.755186\pi\)
−0.718532 + 0.695494i \(0.755186\pi\)
\(500\) 0 0
\(501\) −17.6483 −0.788469
\(502\) −45.4314 −2.02770
\(503\) −9.74401 −0.434464 −0.217232 0.976120i \(-0.569703\pi\)
−0.217232 + 0.976120i \(0.569703\pi\)
\(504\) 82.4807 3.67398
\(505\) 0 0
\(506\) 36.0771 1.60382
\(507\) −9.00920 −0.400113
\(508\) −79.1813 −3.51310
\(509\) −8.57452 −0.380059 −0.190029 0.981778i \(-0.560858\pi\)
−0.190029 + 0.981778i \(0.560858\pi\)
\(510\) 0 0
\(511\) 46.7367 2.06751
\(512\) 11.5017 0.508306
\(513\) −16.2520 −0.717544
\(514\) 67.4128 2.97345
\(515\) 0 0
\(516\) 13.2750 0.584401
\(517\) −18.0098 −0.792072
\(518\) −61.2262 −2.69012
\(519\) −5.66100 −0.248490
\(520\) 0 0
\(521\) −37.8251 −1.65715 −0.828574 0.559879i \(-0.810848\pi\)
−0.828574 + 0.559879i \(0.810848\pi\)
\(522\) 6.28726 0.275186
\(523\) 13.5818 0.593891 0.296946 0.954894i \(-0.404032\pi\)
0.296946 + 0.954894i \(0.404032\pi\)
\(524\) 7.11871 0.310982
\(525\) 0 0
\(526\) −43.1549 −1.88164
\(527\) 1.64832 0.0718021
\(528\) 27.7645 1.20829
\(529\) 0.0982457 0.00427155
\(530\) 0 0
\(531\) 6.05079 0.262582
\(532\) 80.7631 3.50152
\(533\) 9.40105 0.407205
\(534\) −30.8627 −1.33556
\(535\) 0 0
\(536\) −26.9683 −1.16485
\(537\) 3.84955 0.166121
\(538\) −14.1504 −0.610069
\(539\) 28.8324 1.24190
\(540\) 0 0
\(541\) 42.3127 1.81916 0.909581 0.415526i \(-0.136402\pi\)
0.909581 + 0.415526i \(0.136402\pi\)
\(542\) −3.03173 −0.130224
\(543\) 1.51056 0.0648242
\(544\) −113.545 −4.86819
\(545\) 0 0
\(546\) 12.1016 0.517899
\(547\) 36.4690 1.55930 0.779650 0.626215i \(-0.215397\pi\)
0.779650 + 0.626215i \(0.215397\pi\)
\(548\) 33.4821 1.43029
\(549\) −12.5745 −0.536667
\(550\) 0 0
\(551\) 3.76845 0.160541
\(552\) 32.7104 1.39225
\(553\) −19.6629 −0.836152
\(554\) −43.7743 −1.85979
\(555\) 0 0
\(556\) −98.0381 −4.15774
\(557\) −19.5223 −0.827187 −0.413594 0.910462i \(-0.635727\pi\)
−0.413594 + 0.910462i \(0.635727\pi\)
\(558\) 1.45580 0.0616290
\(559\) −4.31265 −0.182406
\(560\) 0 0
\(561\) 16.1016 0.679809
\(562\) 66.4142 2.80151
\(563\) 2.94192 0.123987 0.0619936 0.998077i \(-0.480254\pi\)
0.0619936 + 0.998077i \(0.480254\pi\)
\(564\) −26.6761 −1.12327
\(565\) 0 0
\(566\) −11.1841 −0.470102
\(567\) 14.8568 0.623929
\(568\) −95.8369 −4.02123
\(569\) 2.49929 0.104776 0.0523879 0.998627i \(-0.483317\pi\)
0.0523879 + 0.998627i \(0.483317\pi\)
\(570\) 0 0
\(571\) 43.8007 1.83300 0.916501 0.400033i \(-0.131001\pi\)
0.916501 + 0.400033i \(0.131001\pi\)
\(572\) −19.5369 −0.816879
\(573\) 15.4109 0.643799
\(574\) 77.4128 3.23115
\(575\) 0 0
\(576\) −42.5837 −1.77432
\(577\) 23.9062 0.995229 0.497614 0.867398i \(-0.334209\pi\)
0.497614 + 0.867398i \(0.334209\pi\)
\(578\) −90.0879 −3.74716
\(579\) −16.0362 −0.666442
\(580\) 0 0
\(581\) −10.5745 −0.438705
\(582\) −3.30139 −0.136847
\(583\) −19.5369 −0.809136
\(584\) −94.9457 −3.92888
\(585\) 0 0
\(586\) 63.1813 2.60999
\(587\) 3.71767 0.153445 0.0767223 0.997053i \(-0.475555\pi\)
0.0767223 + 0.997053i \(0.475555\pi\)
\(588\) 42.7064 1.76118
\(589\) 0.872577 0.0359539
\(590\) 0 0
\(591\) 10.9116 0.448843
\(592\) 67.5936 2.77808
\(593\) 25.5125 1.04767 0.523836 0.851819i \(-0.324501\pi\)
0.523836 + 0.851819i \(0.324501\pi\)
\(594\) 32.3733 1.32829
\(595\) 0 0
\(596\) 34.1622 1.39934
\(597\) 2.07522 0.0849332
\(598\) −17.3601 −0.709908
\(599\) −15.6834 −0.640806 −0.320403 0.947281i \(-0.603818\pi\)
−0.320403 + 0.947281i \(0.603818\pi\)
\(600\) 0 0
\(601\) 13.1392 0.535958 0.267979 0.963425i \(-0.413644\pi\)
0.267979 + 0.963425i \(0.413644\pi\)
\(602\) −35.5125 −1.44738
\(603\) −7.50659 −0.305692
\(604\) −47.8251 −1.94598
\(605\) 0 0
\(606\) −6.11616 −0.248452
\(607\) −18.1465 −0.736543 −0.368271 0.929718i \(-0.620050\pi\)
−0.368271 + 0.929718i \(0.620050\pi\)
\(608\) −60.1075 −2.43768
\(609\) 3.35026 0.135759
\(610\) 0 0
\(611\) 8.66624 0.350598
\(612\) −86.2697 −3.48724
\(613\) 32.5501 1.31469 0.657343 0.753592i \(-0.271680\pi\)
0.657343 + 0.753592i \(0.271680\pi\)
\(614\) 86.9556 3.50924
\(615\) 0 0
\(616\) −98.4768 −3.96774
\(617\) −20.2433 −0.814965 −0.407482 0.913213i \(-0.633593\pi\)
−0.407482 + 0.913213i \(0.633593\pi\)
\(618\) −21.3357 −0.858247
\(619\) −16.2071 −0.651419 −0.325709 0.945470i \(-0.605603\pi\)
−0.325709 + 0.945470i \(0.605603\pi\)
\(620\) 0 0
\(621\) 20.7269 0.831741
\(622\) 24.9321 0.999685
\(623\) 59.4880 2.38334
\(624\) −13.3601 −0.534832
\(625\) 0 0
\(626\) 25.6873 1.02667
\(627\) 8.52373 0.340405
\(628\) 25.8192 1.03030
\(629\) 39.1998 1.56300
\(630\) 0 0
\(631\) 2.13586 0.0850271 0.0425136 0.999096i \(-0.486463\pi\)
0.0425136 + 0.999096i \(0.486463\pi\)
\(632\) 39.9452 1.58894
\(633\) 9.58769 0.381076
\(634\) 51.8192 2.05800
\(635\) 0 0
\(636\) −28.9380 −1.14746
\(637\) −13.8740 −0.549708
\(638\) −7.50659 −0.297189
\(639\) −26.6761 −1.05529
\(640\) 0 0
\(641\) −14.0362 −0.554396 −0.277198 0.960813i \(-0.589406\pi\)
−0.277198 + 0.960813i \(0.589406\pi\)
\(642\) −25.2144 −0.995133
\(643\) 43.8799 1.73045 0.865227 0.501381i \(-0.167174\pi\)
0.865227 + 0.501381i \(0.167174\pi\)
\(644\) −103.000 −4.05879
\(645\) 0 0
\(646\) −71.7645 −2.82354
\(647\) 22.5560 0.886766 0.443383 0.896332i \(-0.353778\pi\)
0.443383 + 0.896332i \(0.353778\pi\)
\(648\) −30.1817 −1.18565
\(649\) −7.22425 −0.283577
\(650\) 0 0
\(651\) 0.775746 0.0304039
\(652\) −38.7064 −1.51586
\(653\) −27.3054 −1.06854 −0.534271 0.845314i \(-0.679414\pi\)
−0.534271 + 0.845314i \(0.679414\pi\)
\(654\) 31.2652 1.22257
\(655\) 0 0
\(656\) −85.4636 −3.33679
\(657\) −26.4280 −1.03106
\(658\) 71.3620 2.78198
\(659\) 14.0665 0.547954 0.273977 0.961736i \(-0.411661\pi\)
0.273977 + 0.961736i \(0.411661\pi\)
\(660\) 0 0
\(661\) 38.9741 1.51592 0.757959 0.652302i \(-0.226197\pi\)
0.757959 + 0.652302i \(0.226197\pi\)
\(662\) 79.0308 3.07162
\(663\) −7.74798 −0.300907
\(664\) 21.4821 0.833669
\(665\) 0 0
\(666\) 34.6213 1.34155
\(667\) −4.80606 −0.186092
\(668\) −112.895 −4.36804
\(669\) 0.901754 0.0348638
\(670\) 0 0
\(671\) 15.0132 0.579577
\(672\) −53.4372 −2.06139
\(673\) −20.3390 −0.784011 −0.392005 0.919963i \(-0.628219\pi\)
−0.392005 + 0.919963i \(0.628219\pi\)
\(674\) 33.5574 1.29258
\(675\) 0 0
\(676\) −57.6312 −2.21658
\(677\) 19.1841 0.737304 0.368652 0.929567i \(-0.379819\pi\)
0.368652 + 0.929567i \(0.379819\pi\)
\(678\) −35.3503 −1.35762
\(679\) 6.36344 0.244206
\(680\) 0 0
\(681\) −0.0244376 −0.000936449 0
\(682\) −1.73813 −0.0665566
\(683\) 24.1319 0.923381 0.461691 0.887041i \(-0.347243\pi\)
0.461691 + 0.887041i \(0.347243\pi\)
\(684\) −45.6688 −1.74619
\(685\) 0 0
\(686\) −36.4142 −1.39030
\(687\) −4.71511 −0.179893
\(688\) 39.2057 1.49470
\(689\) 9.40105 0.358151
\(690\) 0 0
\(691\) −4.28821 −0.163131 −0.0815657 0.996668i \(-0.525992\pi\)
−0.0815657 + 0.996668i \(0.525992\pi\)
\(692\) −36.2130 −1.37661
\(693\) −27.4109 −1.04125
\(694\) −67.1305 −2.54824
\(695\) 0 0
\(696\) −6.80606 −0.257983
\(697\) −49.5633 −1.87734
\(698\) 45.6747 1.72881
\(699\) −21.0395 −0.795788
\(700\) 0 0
\(701\) −14.1260 −0.533532 −0.266766 0.963761i \(-0.585955\pi\)
−0.266766 + 0.963761i \(0.585955\pi\)
\(702\) −15.5778 −0.587948
\(703\) 20.7513 0.782650
\(704\) 50.8423 1.91619
\(705\) 0 0
\(706\) 15.1490 0.570141
\(707\) 11.7889 0.443368
\(708\) −10.7005 −0.402150
\(709\) 6.75131 0.253551 0.126775 0.991931i \(-0.459537\pi\)
0.126775 + 0.991931i \(0.459537\pi\)
\(710\) 0 0
\(711\) 11.1187 0.416984
\(712\) −120.850 −4.52905
\(713\) −1.11283 −0.0416760
\(714\) −63.8007 −2.38768
\(715\) 0 0
\(716\) 24.6253 0.920291
\(717\) 1.14903 0.0429113
\(718\) −2.02047 −0.0754032
\(719\) −43.8251 −1.63440 −0.817201 0.576353i \(-0.804475\pi\)
−0.817201 + 0.576353i \(0.804475\pi\)
\(720\) 0 0
\(721\) 41.1246 1.53156
\(722\) 12.8373 0.477756
\(723\) −0.0606343 −0.00225502
\(724\) 9.66291 0.359119
\(725\) 0 0
\(726\) 6.74069 0.250170
\(727\) 14.8813 0.551916 0.275958 0.961170i \(-0.411005\pi\)
0.275958 + 0.961170i \(0.411005\pi\)
\(728\) 47.3865 1.75626
\(729\) 2.02776 0.0751023
\(730\) 0 0
\(731\) 22.7367 0.840948
\(732\) 22.2374 0.821919
\(733\) −7.17935 −0.265175 −0.132588 0.991171i \(-0.542329\pi\)
−0.132588 + 0.991171i \(0.542329\pi\)
\(734\) 30.6194 1.13018
\(735\) 0 0
\(736\) 76.6575 2.82563
\(737\) 8.96239 0.330134
\(738\) −43.7743 −1.61136
\(739\) 16.1709 0.594857 0.297428 0.954744i \(-0.403871\pi\)
0.297428 + 0.954744i \(0.403871\pi\)
\(740\) 0 0
\(741\) −4.10157 −0.150675
\(742\) 77.4128 2.84191
\(743\) −27.8192 −1.02059 −0.510294 0.860000i \(-0.670464\pi\)
−0.510294 + 0.860000i \(0.670464\pi\)
\(744\) −1.57593 −0.0577764
\(745\) 0 0
\(746\) 10.3371 0.378468
\(747\) 5.97953 0.218780
\(748\) 103.000 3.76607
\(749\) 48.6009 1.77584
\(750\) 0 0
\(751\) −17.6326 −0.643423 −0.321711 0.946838i \(-0.604258\pi\)
−0.321711 + 0.946838i \(0.604258\pi\)
\(752\) −78.7835 −2.87294
\(753\) 13.6893 0.498864
\(754\) 3.61213 0.131546
\(755\) 0 0
\(756\) −92.4260 −3.36150
\(757\) −1.53102 −0.0556460 −0.0278230 0.999613i \(-0.508857\pi\)
−0.0278230 + 0.999613i \(0.508857\pi\)
\(758\) −32.3839 −1.17624
\(759\) −10.8707 −0.394580
\(760\) 0 0
\(761\) −34.4749 −1.24971 −0.624856 0.780740i \(-0.714842\pi\)
−0.624856 + 0.780740i \(0.714842\pi\)
\(762\) 33.1128 1.19955
\(763\) −60.2638 −2.18170
\(764\) 98.5823 3.56658
\(765\) 0 0
\(766\) −26.8061 −0.968542
\(767\) 3.47627 0.125521
\(768\) 6.51976 0.235262
\(769\) −19.3404 −0.697433 −0.348717 0.937228i \(-0.613382\pi\)
−0.348717 + 0.937228i \(0.613382\pi\)
\(770\) 0 0
\(771\) −20.3127 −0.731542
\(772\) −102.582 −3.69202
\(773\) −36.2677 −1.30446 −0.652230 0.758021i \(-0.726166\pi\)
−0.652230 + 0.758021i \(0.726166\pi\)
\(774\) 20.0811 0.721800
\(775\) 0 0
\(776\) −12.9273 −0.464064
\(777\) 18.4485 0.661837
\(778\) 68.6516 2.46128
\(779\) −26.2374 −0.940053
\(780\) 0 0
\(781\) 31.8496 1.13967
\(782\) 91.5242 3.27290
\(783\) −4.31265 −0.154122
\(784\) 126.127 4.50452
\(785\) 0 0
\(786\) −2.97698 −0.106185
\(787\) −32.0059 −1.14089 −0.570443 0.821337i \(-0.693229\pi\)
−0.570443 + 0.821337i \(0.693229\pi\)
\(788\) 69.8007 2.48655
\(789\) 13.0033 0.462931
\(790\) 0 0
\(791\) 68.1378 2.42270
\(792\) 55.6853 1.97869
\(793\) −7.22425 −0.256541
\(794\) 74.1378 2.63105
\(795\) 0 0
\(796\) 13.2750 0.470521
\(797\) 41.6932 1.47685 0.738425 0.674336i \(-0.235570\pi\)
0.738425 + 0.674336i \(0.235570\pi\)
\(798\) −33.7743 −1.19560
\(799\) −45.6893 −1.61637
\(800\) 0 0
\(801\) −33.6385 −1.18856
\(802\) −19.8641 −0.701427
\(803\) 31.5534 1.11350
\(804\) 13.2750 0.468175
\(805\) 0 0
\(806\) 0.836381 0.0294603
\(807\) 4.26378 0.150092
\(808\) −23.9492 −0.842530
\(809\) 30.6371 1.07714 0.538571 0.842580i \(-0.318964\pi\)
0.538571 + 0.842580i \(0.318964\pi\)
\(810\) 0 0
\(811\) 25.4617 0.894081 0.447040 0.894514i \(-0.352478\pi\)
0.447040 + 0.894514i \(0.352478\pi\)
\(812\) 21.4314 0.752093
\(813\) 0.913513 0.0320383
\(814\) −41.3357 −1.44881
\(815\) 0 0
\(816\) 70.4358 2.46575
\(817\) 12.0362 0.421093
\(818\) 88.8139 3.10530
\(819\) 13.1900 0.460895
\(820\) 0 0
\(821\) −32.7005 −1.14126 −0.570628 0.821209i \(-0.693300\pi\)
−0.570628 + 0.821209i \(0.693300\pi\)
\(822\) −14.0019 −0.488373
\(823\) 31.1041 1.08422 0.542111 0.840307i \(-0.317625\pi\)
0.542111 + 0.840307i \(0.317625\pi\)
\(824\) −83.5447 −2.91042
\(825\) 0 0
\(826\) 28.6253 0.996002
\(827\) 1.58181 0.0550049 0.0275025 0.999622i \(-0.491245\pi\)
0.0275025 + 0.999622i \(0.491245\pi\)
\(828\) 58.2433 2.02409
\(829\) −0.111420 −0.00386976 −0.00193488 0.999998i \(-0.500616\pi\)
−0.00193488 + 0.999998i \(0.500616\pi\)
\(830\) 0 0
\(831\) 13.1900 0.457555
\(832\) −24.4650 −0.848171
\(833\) 73.1451 2.53433
\(834\) 40.9986 1.41966
\(835\) 0 0
\(836\) 54.5256 1.88581
\(837\) −0.998585 −0.0345162
\(838\) −44.3000 −1.53032
\(839\) 28.9829 1.00060 0.500300 0.865852i \(-0.333223\pi\)
0.500300 + 0.865852i \(0.333223\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 23.6121 0.813728
\(843\) −20.0118 −0.689242
\(844\) 61.3317 2.11112
\(845\) 0 0
\(846\) −40.3528 −1.38736
\(847\) −12.9927 −0.446435
\(848\) −85.4636 −2.93483
\(849\) 3.36996 0.115657
\(850\) 0 0
\(851\) −26.4650 −0.907209
\(852\) 47.1754 1.61620
\(853\) 7.77319 0.266149 0.133075 0.991106i \(-0.457515\pi\)
0.133075 + 0.991106i \(0.457515\pi\)
\(854\) −59.4880 −2.03564
\(855\) 0 0
\(856\) −98.7328 −3.37462
\(857\) 13.8740 0.473927 0.236963 0.971519i \(-0.423848\pi\)
0.236963 + 0.971519i \(0.423848\pi\)
\(858\) 8.17014 0.278924
\(859\) −15.2809 −0.521378 −0.260689 0.965423i \(-0.583950\pi\)
−0.260689 + 0.965423i \(0.583950\pi\)
\(860\) 0 0
\(861\) −23.3258 −0.794942
\(862\) −11.3747 −0.387424
\(863\) −31.2301 −1.06309 −0.531543 0.847031i \(-0.678388\pi\)
−0.531543 + 0.847031i \(0.678388\pi\)
\(864\) 68.7875 2.34020
\(865\) 0 0
\(866\) −4.86670 −0.165377
\(867\) 27.1451 0.921895
\(868\) 4.96239 0.168434
\(869\) −13.2750 −0.450325
\(870\) 0 0
\(871\) −4.31265 −0.146129
\(872\) 122.426 4.14587
\(873\) −3.59831 −0.121784
\(874\) 48.4504 1.63886
\(875\) 0 0
\(876\) 46.7367 1.57909
\(877\) 4.26187 0.143913 0.0719565 0.997408i \(-0.477076\pi\)
0.0719565 + 0.997408i \(0.477076\pi\)
\(878\) −37.7499 −1.27400
\(879\) −19.0376 −0.642123
\(880\) 0 0
\(881\) 15.2144 0.512586 0.256293 0.966599i \(-0.417499\pi\)
0.256293 + 0.966599i \(0.417499\pi\)
\(882\) 64.6018 2.17526
\(883\) 13.7078 0.461305 0.230652 0.973036i \(-0.425914\pi\)
0.230652 + 0.973036i \(0.425914\pi\)
\(884\) −49.5633 −1.66699
\(885\) 0 0
\(886\) −46.2287 −1.55308
\(887\) −12.6556 −0.424934 −0.212467 0.977168i \(-0.568150\pi\)
−0.212467 + 0.977168i \(0.568150\pi\)
\(888\) −37.4782 −1.25769
\(889\) −63.8251 −2.14063
\(890\) 0 0
\(891\) 10.0303 0.336028
\(892\) 5.76845 0.193142
\(893\) −24.1866 −0.809375
\(894\) −14.2863 −0.477805
\(895\) 0 0
\(896\) −68.8686 −2.30074
\(897\) 5.23090 0.174655
\(898\) −25.0132 −0.834700
\(899\) 0.231548 0.00772256
\(900\) 0 0
\(901\) −49.5633 −1.65119
\(902\) 52.2638 1.74019
\(903\) 10.7005 0.356091
\(904\) −138.422 −4.60385
\(905\) 0 0
\(906\) 20.0000 0.664455
\(907\) 12.5540 0.416850 0.208425 0.978038i \(-0.433166\pi\)
0.208425 + 0.978038i \(0.433166\pi\)
\(908\) −0.156325 −0.00518783
\(909\) −6.66624 −0.221105
\(910\) 0 0
\(911\) 22.8714 0.757765 0.378882 0.925445i \(-0.376309\pi\)
0.378882 + 0.925445i \(0.376309\pi\)
\(912\) 37.2868 1.23469
\(913\) −7.13918 −0.236272
\(914\) −47.2506 −1.56291
\(915\) 0 0
\(916\) −30.1622 −0.996587
\(917\) 5.73813 0.189490
\(918\) 82.1279 2.71063
\(919\) 9.67750 0.319231 0.159616 0.987179i \(-0.448975\pi\)
0.159616 + 0.987179i \(0.448975\pi\)
\(920\) 0 0
\(921\) −26.2012 −0.863360
\(922\) −41.6337 −1.37113
\(923\) −15.3258 −0.504456
\(924\) 48.4749 1.59471
\(925\) 0 0
\(926\) 7.97953 0.262224
\(927\) −23.2546 −0.763780
\(928\) −15.9502 −0.523590
\(929\) 51.9248 1.70360 0.851798 0.523870i \(-0.175512\pi\)
0.851798 + 0.523870i \(0.175512\pi\)
\(930\) 0 0
\(931\) 38.7210 1.26903
\(932\) −134.588 −4.40858
\(933\) −7.51247 −0.245947
\(934\) 92.5071 3.02692
\(935\) 0 0
\(936\) −26.7954 −0.875837
\(937\) −3.58769 −0.117205 −0.0586024 0.998281i \(-0.518664\pi\)
−0.0586024 + 0.998281i \(0.518664\pi\)
\(938\) −35.5125 −1.15952
\(939\) −7.74004 −0.252587
\(940\) 0 0
\(941\) −18.6253 −0.607167 −0.303584 0.952805i \(-0.598183\pi\)
−0.303584 + 0.952805i \(0.598183\pi\)
\(942\) −10.7974 −0.351797
\(943\) 33.4617 1.08966
\(944\) −31.6023 −1.02857
\(945\) 0 0
\(946\) −23.9756 −0.779513
\(947\) 16.5950 0.539265 0.269632 0.962963i \(-0.413098\pi\)
0.269632 + 0.962963i \(0.413098\pi\)
\(948\) −19.6629 −0.638622
\(949\) −15.1833 −0.492871
\(950\) 0 0
\(951\) −15.6140 −0.506320
\(952\) −249.826 −8.09691
\(953\) 12.7005 0.411410 0.205705 0.978614i \(-0.434051\pi\)
0.205705 + 0.978614i \(0.434051\pi\)
\(954\) −43.7743 −1.41725
\(955\) 0 0
\(956\) 7.35026 0.237724
\(957\) 2.26187 0.0731157
\(958\) 91.4695 2.95524
\(959\) 26.9887 0.871512
\(960\) 0 0
\(961\) −30.9464 −0.998271
\(962\) 19.8905 0.641295
\(963\) −27.4821 −0.885600
\(964\) −0.387873 −0.0124926
\(965\) 0 0
\(966\) 43.0738 1.38588
\(967\) −37.4314 −1.20371 −0.601856 0.798605i \(-0.705572\pi\)
−0.601856 + 0.798605i \(0.705572\pi\)
\(968\) 26.3947 0.848358
\(969\) 21.6239 0.694659
\(970\) 0 0
\(971\) 7.51644 0.241214 0.120607 0.992700i \(-0.461516\pi\)
0.120607 + 0.992700i \(0.461516\pi\)
\(972\) 81.5691 2.61633
\(973\) −79.0249 −2.53342
\(974\) 102.980 3.29969
\(975\) 0 0
\(976\) 65.6747 2.10220
\(977\) 2.52847 0.0808929 0.0404465 0.999182i \(-0.487122\pi\)
0.0404465 + 0.999182i \(0.487122\pi\)
\(978\) 16.1866 0.517592
\(979\) 40.1622 1.28359
\(980\) 0 0
\(981\) 34.0771 1.08800
\(982\) 73.4793 2.34482
\(983\) 9.32979 0.297574 0.148787 0.988869i \(-0.452463\pi\)
0.148787 + 0.988869i \(0.452463\pi\)
\(984\) 47.3865 1.51063
\(985\) 0 0
\(986\) −19.0435 −0.606468
\(987\) −21.5026 −0.684436
\(988\) −26.2374 −0.834724
\(989\) −15.3503 −0.488110
\(990\) 0 0
\(991\) 38.4241 1.22058 0.610290 0.792178i \(-0.291053\pi\)
0.610290 + 0.792178i \(0.291053\pi\)
\(992\) −3.69323 −0.117260
\(993\) −23.8134 −0.755694
\(994\) −126.200 −4.00283
\(995\) 0 0
\(996\) −10.5745 −0.335066
\(997\) 18.8423 0.596740 0.298370 0.954450i \(-0.403557\pi\)
0.298370 + 0.954450i \(0.403557\pi\)
\(998\) 85.8759 2.71835
\(999\) −23.7480 −0.751353
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 725.2.a.d.1.1 3
3.2 odd 2 6525.2.a.bh.1.3 3
5.2 odd 4 725.2.b.d.349.1 6
5.3 odd 4 725.2.b.d.349.6 6
5.4 even 2 145.2.a.d.1.3 3
15.14 odd 2 1305.2.a.o.1.1 3
20.19 odd 2 2320.2.a.s.1.2 3
35.34 odd 2 7105.2.a.p.1.3 3
40.19 odd 2 9280.2.a.bm.1.2 3
40.29 even 2 9280.2.a.bu.1.2 3
145.144 even 2 4205.2.a.e.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
145.2.a.d.1.3 3 5.4 even 2
725.2.a.d.1.1 3 1.1 even 1 trivial
725.2.b.d.349.1 6 5.2 odd 4
725.2.b.d.349.6 6 5.3 odd 4
1305.2.a.o.1.1 3 15.14 odd 2
2320.2.a.s.1.2 3 20.19 odd 2
4205.2.a.e.1.1 3 145.144 even 2
6525.2.a.bh.1.3 3 3.2 odd 2
7105.2.a.p.1.3 3 35.34 odd 2
9280.2.a.bm.1.2 3 40.19 odd 2
9280.2.a.bu.1.2 3 40.29 even 2