Properties

Label 7605.2.a.bm.1.3
Level $7605$
Weight $2$
Character 7605.1
Self dual yes
Analytic conductor $60.726$
Analytic rank $1$
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] = [7605,2,Mod(1,7605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7605, 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("7605.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7605.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: \(60.7262307372\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2535)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.80194\) of defining polynomial
Character \(\chi\) \(=\) 7605.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.04892 q^{2} +2.19806 q^{4} +1.00000 q^{5} -3.04892 q^{7} +0.405813 q^{8} +O(q^{10})\) \(q+2.04892 q^{2} +2.19806 q^{4} +1.00000 q^{5} -3.04892 q^{7} +0.405813 q^{8} +2.04892 q^{10} +1.89008 q^{11} -6.24698 q^{14} -3.56465 q^{16} +4.09783 q^{17} -2.58211 q^{19} +2.19806 q^{20} +3.87263 q^{22} -3.02715 q^{23} +1.00000 q^{25} -6.70171 q^{28} -3.30798 q^{29} -9.31767 q^{31} -8.11529 q^{32} +8.39612 q^{34} -3.04892 q^{35} +10.2959 q^{37} -5.29052 q^{38} +0.405813 q^{40} +0.731250 q^{41} -11.9390 q^{43} +4.15452 q^{44} -6.20237 q^{46} -3.44504 q^{47} +2.29590 q^{49} +2.04892 q^{50} -8.98254 q^{53} +1.89008 q^{55} -1.23729 q^{56} -6.77777 q^{58} -1.11529 q^{59} +5.75302 q^{61} -19.0911 q^{62} -9.49827 q^{64} -10.5211 q^{67} +9.00730 q^{68} -6.24698 q^{70} +7.41789 q^{71} +12.2838 q^{73} +21.0954 q^{74} -5.67563 q^{76} -5.76271 q^{77} -1.71917 q^{79} -3.56465 q^{80} +1.49827 q^{82} -17.8213 q^{83} +4.09783 q^{85} -24.4620 q^{86} +0.767021 q^{88} +1.91185 q^{89} -6.65386 q^{92} -7.05861 q^{94} -2.58211 q^{95} +7.59179 q^{97} +4.70410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + 11 q^{4} + 3 q^{5} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} + 11 q^{4} + 3 q^{5} - 12 q^{8} - 3 q^{10} + 5 q^{11} - 14 q^{14} + 11 q^{16} - 6 q^{17} - 2 q^{19} + 11 q^{20} - 5 q^{22} - 3 q^{23} + 3 q^{25} + 7 q^{28} - 15 q^{29} - 11 q^{31} - 22 q^{32} + 34 q^{34} + 17 q^{37} - 5 q^{38} - 12 q^{40} + 10 q^{41} - 26 q^{43} + 23 q^{44} - 4 q^{46} - 10 q^{47} - 7 q^{49} - 3 q^{50} - 11 q^{53} + 5 q^{55} - 21 q^{56} + 22 q^{58} - q^{59} + 22 q^{61} - 17 q^{62} - 16 q^{67} - 36 q^{68} - 14 q^{70} + 28 q^{71} + 4 q^{73} + 4 q^{74} - 12 q^{76} + 6 q^{79} + 11 q^{80} - 24 q^{82} - 5 q^{83} - 6 q^{85} + 12 q^{86} - 34 q^{88} + 2 q^{89} - 18 q^{92} + 10 q^{94} - 2 q^{95} - 5 q^{97} + 28 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.04892 1.44880 0.724402 0.689378i \(-0.242116\pi\)
0.724402 + 0.689378i \(0.242116\pi\)
\(3\) 0 0
\(4\) 2.19806 1.09903
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −3.04892 −1.15238 −0.576191 0.817315i \(-0.695462\pi\)
−0.576191 + 0.817315i \(0.695462\pi\)
\(8\) 0.405813 0.143477
\(9\) 0 0
\(10\) 2.04892 0.647925
\(11\) 1.89008 0.569882 0.284941 0.958545i \(-0.408026\pi\)
0.284941 + 0.958545i \(0.408026\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −6.24698 −1.66958
\(15\) 0 0
\(16\) −3.56465 −0.891162
\(17\) 4.09783 0.993871 0.496935 0.867788i \(-0.334459\pi\)
0.496935 + 0.867788i \(0.334459\pi\)
\(18\) 0 0
\(19\) −2.58211 −0.592376 −0.296188 0.955130i \(-0.595715\pi\)
−0.296188 + 0.955130i \(0.595715\pi\)
\(20\) 2.19806 0.491502
\(21\) 0 0
\(22\) 3.87263 0.825646
\(23\) −3.02715 −0.631204 −0.315602 0.948892i \(-0.602206\pi\)
−0.315602 + 0.948892i \(0.602206\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) −6.70171 −1.26650
\(29\) −3.30798 −0.614276 −0.307138 0.951665i \(-0.599371\pi\)
−0.307138 + 0.951665i \(0.599371\pi\)
\(30\) 0 0
\(31\) −9.31767 −1.67350 −0.836751 0.547583i \(-0.815548\pi\)
−0.836751 + 0.547583i \(0.815548\pi\)
\(32\) −8.11529 −1.43459
\(33\) 0 0
\(34\) 8.39612 1.43992
\(35\) −3.04892 −0.515361
\(36\) 0 0
\(37\) 10.2959 1.69264 0.846318 0.532679i \(-0.178815\pi\)
0.846318 + 0.532679i \(0.178815\pi\)
\(38\) −5.29052 −0.858236
\(39\) 0 0
\(40\) 0.405813 0.0641647
\(41\) 0.731250 0.114202 0.0571010 0.998368i \(-0.481814\pi\)
0.0571010 + 0.998368i \(0.481814\pi\)
\(42\) 0 0
\(43\) −11.9390 −1.82068 −0.910340 0.413861i \(-0.864180\pi\)
−0.910340 + 0.413861i \(0.864180\pi\)
\(44\) 4.15452 0.626318
\(45\) 0 0
\(46\) −6.20237 −0.914490
\(47\) −3.44504 −0.502511 −0.251256 0.967921i \(-0.580843\pi\)
−0.251256 + 0.967921i \(0.580843\pi\)
\(48\) 0 0
\(49\) 2.29590 0.327985
\(50\) 2.04892 0.289761
\(51\) 0 0
\(52\) 0 0
\(53\) −8.98254 −1.23385 −0.616923 0.787023i \(-0.711621\pi\)
−0.616923 + 0.787023i \(0.711621\pi\)
\(54\) 0 0
\(55\) 1.89008 0.254859
\(56\) −1.23729 −0.165340
\(57\) 0 0
\(58\) −6.77777 −0.889965
\(59\) −1.11529 −0.145199 −0.0725994 0.997361i \(-0.523129\pi\)
−0.0725994 + 0.997361i \(0.523129\pi\)
\(60\) 0 0
\(61\) 5.75302 0.736599 0.368299 0.929707i \(-0.379940\pi\)
0.368299 + 0.929707i \(0.379940\pi\)
\(62\) −19.0911 −2.42458
\(63\) 0 0
\(64\) −9.49827 −1.18728
\(65\) 0 0
\(66\) 0 0
\(67\) −10.5211 −1.28536 −0.642679 0.766136i \(-0.722177\pi\)
−0.642679 + 0.766136i \(0.722177\pi\)
\(68\) 9.00730 1.09230
\(69\) 0 0
\(70\) −6.24698 −0.746657
\(71\) 7.41789 0.880342 0.440171 0.897914i \(-0.354918\pi\)
0.440171 + 0.897914i \(0.354918\pi\)
\(72\) 0 0
\(73\) 12.2838 1.43771 0.718856 0.695159i \(-0.244666\pi\)
0.718856 + 0.695159i \(0.244666\pi\)
\(74\) 21.0954 2.45230
\(75\) 0 0
\(76\) −5.67563 −0.651039
\(77\) −5.76271 −0.656722
\(78\) 0 0
\(79\) −1.71917 −0.193422 −0.0967108 0.995313i \(-0.530832\pi\)
−0.0967108 + 0.995313i \(0.530832\pi\)
\(80\) −3.56465 −0.398540
\(81\) 0 0
\(82\) 1.49827 0.165456
\(83\) −17.8213 −1.95614 −0.978072 0.208268i \(-0.933217\pi\)
−0.978072 + 0.208268i \(0.933217\pi\)
\(84\) 0 0
\(85\) 4.09783 0.444473
\(86\) −24.4620 −2.63781
\(87\) 0 0
\(88\) 0.767021 0.0817647
\(89\) 1.91185 0.202656 0.101328 0.994853i \(-0.467691\pi\)
0.101328 + 0.994853i \(0.467691\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −6.65386 −0.693713
\(93\) 0 0
\(94\) −7.05861 −0.728040
\(95\) −2.58211 −0.264918
\(96\) 0 0
\(97\) 7.59179 0.770830 0.385415 0.922743i \(-0.374058\pi\)
0.385415 + 0.922743i \(0.374058\pi\)
\(98\) 4.70410 0.475186
\(99\) 0 0
\(100\) 2.19806 0.219806
\(101\) −1.67696 −0.166863 −0.0834317 0.996513i \(-0.526588\pi\)
−0.0834317 + 0.996513i \(0.526588\pi\)
\(102\) 0 0
\(103\) −10.4450 −1.02918 −0.514590 0.857436i \(-0.672056\pi\)
−0.514590 + 0.857436i \(0.672056\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −18.4045 −1.78760
\(107\) −15.0194 −1.45198 −0.725989 0.687706i \(-0.758618\pi\)
−0.725989 + 0.687706i \(0.758618\pi\)
\(108\) 0 0
\(109\) 14.1957 1.35970 0.679849 0.733352i \(-0.262045\pi\)
0.679849 + 0.733352i \(0.262045\pi\)
\(110\) 3.87263 0.369240
\(111\) 0 0
\(112\) 10.8683 1.02696
\(113\) 15.8388 1.48999 0.744993 0.667072i \(-0.232453\pi\)
0.744993 + 0.667072i \(0.232453\pi\)
\(114\) 0 0
\(115\) −3.02715 −0.282283
\(116\) −7.27114 −0.675109
\(117\) 0 0
\(118\) −2.28514 −0.210364
\(119\) −12.4940 −1.14532
\(120\) 0 0
\(121\) −7.42758 −0.675235
\(122\) 11.7875 1.06719
\(123\) 0 0
\(124\) −20.4808 −1.83923
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 19.4088 1.72225 0.861126 0.508391i \(-0.169760\pi\)
0.861126 + 0.508391i \(0.169760\pi\)
\(128\) −3.23059 −0.285546
\(129\) 0 0
\(130\) 0 0
\(131\) −21.7168 −1.89740 −0.948702 0.316172i \(-0.897602\pi\)
−0.948702 + 0.316172i \(0.897602\pi\)
\(132\) 0 0
\(133\) 7.87263 0.682643
\(134\) −21.5569 −1.86223
\(135\) 0 0
\(136\) 1.66296 0.142597
\(137\) −12.1806 −1.04066 −0.520330 0.853966i \(-0.674191\pi\)
−0.520330 + 0.853966i \(0.674191\pi\)
\(138\) 0 0
\(139\) −9.46681 −0.802965 −0.401482 0.915867i \(-0.631505\pi\)
−0.401482 + 0.915867i \(0.631505\pi\)
\(140\) −6.70171 −0.566398
\(141\) 0 0
\(142\) 15.1987 1.27544
\(143\) 0 0
\(144\) 0 0
\(145\) −3.30798 −0.274713
\(146\) 25.1685 2.08296
\(147\) 0 0
\(148\) 22.6310 1.86026
\(149\) 3.59850 0.294800 0.147400 0.989077i \(-0.452909\pi\)
0.147400 + 0.989077i \(0.452909\pi\)
\(150\) 0 0
\(151\) −9.52781 −0.775362 −0.387681 0.921794i \(-0.626724\pi\)
−0.387681 + 0.921794i \(0.626724\pi\)
\(152\) −1.04785 −0.0849921
\(153\) 0 0
\(154\) −11.8073 −0.951461
\(155\) −9.31767 −0.748413
\(156\) 0 0
\(157\) −16.4547 −1.31323 −0.656615 0.754226i \(-0.728012\pi\)
−0.656615 + 0.754226i \(0.728012\pi\)
\(158\) −3.52243 −0.280230
\(159\) 0 0
\(160\) −8.11529 −0.641570
\(161\) 9.22952 0.727388
\(162\) 0 0
\(163\) 4.42758 0.346795 0.173398 0.984852i \(-0.444525\pi\)
0.173398 + 0.984852i \(0.444525\pi\)
\(164\) 1.60733 0.125512
\(165\) 0 0
\(166\) −36.5144 −2.83407
\(167\) 19.6896 1.52363 0.761815 0.647795i \(-0.224309\pi\)
0.761815 + 0.647795i \(0.224309\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 8.39612 0.643953
\(171\) 0 0
\(172\) −26.2427 −2.00098
\(173\) −12.3351 −0.937822 −0.468911 0.883245i \(-0.655354\pi\)
−0.468911 + 0.883245i \(0.655354\pi\)
\(174\) 0 0
\(175\) −3.04892 −0.230476
\(176\) −6.73748 −0.507857
\(177\) 0 0
\(178\) 3.91723 0.293609
\(179\) −7.97823 −0.596321 −0.298160 0.954516i \(-0.596373\pi\)
−0.298160 + 0.954516i \(0.596373\pi\)
\(180\) 0 0
\(181\) −13.1860 −0.980106 −0.490053 0.871693i \(-0.663023\pi\)
−0.490053 + 0.871693i \(0.663023\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.22846 −0.0905630
\(185\) 10.2959 0.756969
\(186\) 0 0
\(187\) 7.74525 0.566389
\(188\) −7.57242 −0.552275
\(189\) 0 0
\(190\) −5.29052 −0.383815
\(191\) 1.21446 0.0878749 0.0439375 0.999034i \(-0.486010\pi\)
0.0439375 + 0.999034i \(0.486010\pi\)
\(192\) 0 0
\(193\) 4.32304 0.311180 0.155590 0.987822i \(-0.450272\pi\)
0.155590 + 0.987822i \(0.450272\pi\)
\(194\) 15.5550 1.11678
\(195\) 0 0
\(196\) 5.04652 0.360466
\(197\) −21.0519 −1.49989 −0.749943 0.661503i \(-0.769919\pi\)
−0.749943 + 0.661503i \(0.769919\pi\)
\(198\) 0 0
\(199\) 13.9390 0.988110 0.494055 0.869431i \(-0.335514\pi\)
0.494055 + 0.869431i \(0.335514\pi\)
\(200\) 0.405813 0.0286953
\(201\) 0 0
\(202\) −3.43594 −0.241752
\(203\) 10.0858 0.707881
\(204\) 0 0
\(205\) 0.731250 0.0510727
\(206\) −21.4010 −1.49108
\(207\) 0 0
\(208\) 0 0
\(209\) −4.88040 −0.337584
\(210\) 0 0
\(211\) −1.58748 −0.109287 −0.0546434 0.998506i \(-0.517402\pi\)
−0.0546434 + 0.998506i \(0.517402\pi\)
\(212\) −19.7442 −1.35604
\(213\) 0 0
\(214\) −30.7735 −2.10363
\(215\) −11.9390 −0.814233
\(216\) 0 0
\(217\) 28.4088 1.92851
\(218\) 29.0858 1.96994
\(219\) 0 0
\(220\) 4.15452 0.280098
\(221\) 0 0
\(222\) 0 0
\(223\) −8.97285 −0.600867 −0.300433 0.953803i \(-0.597131\pi\)
−0.300433 + 0.953803i \(0.597131\pi\)
\(224\) 24.7429 1.65320
\(225\) 0 0
\(226\) 32.4523 2.15870
\(227\) −20.5090 −1.36123 −0.680616 0.732640i \(-0.738288\pi\)
−0.680616 + 0.732640i \(0.738288\pi\)
\(228\) 0 0
\(229\) −6.46442 −0.427181 −0.213590 0.976923i \(-0.568516\pi\)
−0.213590 + 0.976923i \(0.568516\pi\)
\(230\) −6.20237 −0.408972
\(231\) 0 0
\(232\) −1.34242 −0.0881343
\(233\) −8.01208 −0.524889 −0.262444 0.964947i \(-0.584529\pi\)
−0.262444 + 0.964947i \(0.584529\pi\)
\(234\) 0 0
\(235\) −3.44504 −0.224730
\(236\) −2.45148 −0.159578
\(237\) 0 0
\(238\) −25.5991 −1.65934
\(239\) −28.3099 −1.83122 −0.915608 0.402073i \(-0.868290\pi\)
−0.915608 + 0.402073i \(0.868290\pi\)
\(240\) 0 0
\(241\) 16.5187 1.06406 0.532032 0.846724i \(-0.321429\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(242\) −15.2185 −0.978283
\(243\) 0 0
\(244\) 12.6455 0.809545
\(245\) 2.29590 0.146679
\(246\) 0 0
\(247\) 0 0
\(248\) −3.78123 −0.240108
\(249\) 0 0
\(250\) 2.04892 0.129585
\(251\) 21.0398 1.32802 0.664011 0.747723i \(-0.268853\pi\)
0.664011 + 0.747723i \(0.268853\pi\)
\(252\) 0 0
\(253\) −5.72156 −0.359711
\(254\) 39.7670 2.49520
\(255\) 0 0
\(256\) 12.3773 0.773584
\(257\) −6.96615 −0.434536 −0.217268 0.976112i \(-0.569715\pi\)
−0.217268 + 0.976112i \(0.569715\pi\)
\(258\) 0 0
\(259\) −31.3913 −1.95056
\(260\) 0 0
\(261\) 0 0
\(262\) −44.4959 −2.74896
\(263\) 16.2543 1.00228 0.501141 0.865366i \(-0.332914\pi\)
0.501141 + 0.865366i \(0.332914\pi\)
\(264\) 0 0
\(265\) −8.98254 −0.551793
\(266\) 16.1304 0.989016
\(267\) 0 0
\(268\) −23.1260 −1.41265
\(269\) −16.6679 −1.01626 −0.508129 0.861281i \(-0.669663\pi\)
−0.508129 + 0.861281i \(0.669663\pi\)
\(270\) 0 0
\(271\) 6.91185 0.419865 0.209933 0.977716i \(-0.432676\pi\)
0.209933 + 0.977716i \(0.432676\pi\)
\(272\) −14.6073 −0.885700
\(273\) 0 0
\(274\) −24.9571 −1.50771
\(275\) 1.89008 0.113976
\(276\) 0 0
\(277\) 11.1400 0.669341 0.334670 0.942335i \(-0.391375\pi\)
0.334670 + 0.942335i \(0.391375\pi\)
\(278\) −19.3967 −1.16334
\(279\) 0 0
\(280\) −1.23729 −0.0739423
\(281\) −0.552565 −0.0329633 −0.0164816 0.999864i \(-0.505247\pi\)
−0.0164816 + 0.999864i \(0.505247\pi\)
\(282\) 0 0
\(283\) 17.2591 1.02594 0.512972 0.858405i \(-0.328544\pi\)
0.512972 + 0.858405i \(0.328544\pi\)
\(284\) 16.3050 0.967523
\(285\) 0 0
\(286\) 0 0
\(287\) −2.22952 −0.131604
\(288\) 0 0
\(289\) −0.207751 −0.0122206
\(290\) −6.77777 −0.398005
\(291\) 0 0
\(292\) 27.0006 1.58009
\(293\) −32.7560 −1.91363 −0.956813 0.290704i \(-0.906111\pi\)
−0.956813 + 0.290704i \(0.906111\pi\)
\(294\) 0 0
\(295\) −1.11529 −0.0649349
\(296\) 4.17821 0.242854
\(297\) 0 0
\(298\) 7.37303 0.427108
\(299\) 0 0
\(300\) 0 0
\(301\) 36.4010 2.09812
\(302\) −19.5217 −1.12335
\(303\) 0 0
\(304\) 9.20429 0.527902
\(305\) 5.75302 0.329417
\(306\) 0 0
\(307\) −7.07069 −0.403545 −0.201773 0.979432i \(-0.564670\pi\)
−0.201773 + 0.979432i \(0.564670\pi\)
\(308\) −12.6668 −0.721758
\(309\) 0 0
\(310\) −19.0911 −1.08430
\(311\) −12.9366 −0.733568 −0.366784 0.930306i \(-0.619541\pi\)
−0.366784 + 0.930306i \(0.619541\pi\)
\(312\) 0 0
\(313\) 25.6353 1.44899 0.724497 0.689278i \(-0.242072\pi\)
0.724497 + 0.689278i \(0.242072\pi\)
\(314\) −33.7144 −1.90261
\(315\) 0 0
\(316\) −3.77884 −0.212576
\(317\) 11.8998 0.668358 0.334179 0.942510i \(-0.391541\pi\)
0.334179 + 0.942510i \(0.391541\pi\)
\(318\) 0 0
\(319\) −6.25236 −0.350065
\(320\) −9.49827 −0.530969
\(321\) 0 0
\(322\) 18.9105 1.05384
\(323\) −10.5810 −0.588745
\(324\) 0 0
\(325\) 0 0
\(326\) 9.07175 0.502438
\(327\) 0 0
\(328\) 0.296751 0.0163853
\(329\) 10.5036 0.579085
\(330\) 0 0
\(331\) 34.2989 1.88524 0.942618 0.333872i \(-0.108355\pi\)
0.942618 + 0.333872i \(0.108355\pi\)
\(332\) −39.1724 −2.14986
\(333\) 0 0
\(334\) 40.3424 2.20744
\(335\) −10.5211 −0.574829
\(336\) 0 0
\(337\) 13.1142 0.714378 0.357189 0.934032i \(-0.383735\pi\)
0.357189 + 0.934032i \(0.383735\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 9.00730 0.488489
\(341\) −17.6112 −0.953698
\(342\) 0 0
\(343\) 14.3424 0.774418
\(344\) −4.84500 −0.261225
\(345\) 0 0
\(346\) −25.2737 −1.35872
\(347\) −2.91723 −0.156605 −0.0783026 0.996930i \(-0.524950\pi\)
−0.0783026 + 0.996930i \(0.524950\pi\)
\(348\) 0 0
\(349\) −9.56465 −0.511984 −0.255992 0.966679i \(-0.582402\pi\)
−0.255992 + 0.966679i \(0.582402\pi\)
\(350\) −6.24698 −0.333915
\(351\) 0 0
\(352\) −15.3386 −0.817549
\(353\) −18.2198 −0.969744 −0.484872 0.874585i \(-0.661134\pi\)
−0.484872 + 0.874585i \(0.661134\pi\)
\(354\) 0 0
\(355\) 7.41789 0.393701
\(356\) 4.20237 0.222725
\(357\) 0 0
\(358\) −16.3467 −0.863952
\(359\) 15.9041 0.839385 0.419693 0.907666i \(-0.362138\pi\)
0.419693 + 0.907666i \(0.362138\pi\)
\(360\) 0 0
\(361\) −12.3327 −0.649091
\(362\) −27.0170 −1.41998
\(363\) 0 0
\(364\) 0 0
\(365\) 12.2838 0.642964
\(366\) 0 0
\(367\) 3.45712 0.180460 0.0902302 0.995921i \(-0.471240\pi\)
0.0902302 + 0.995921i \(0.471240\pi\)
\(368\) 10.7907 0.562505
\(369\) 0 0
\(370\) 21.0954 1.09670
\(371\) 27.3870 1.42186
\(372\) 0 0
\(373\) −17.2731 −0.894365 −0.447183 0.894443i \(-0.647573\pi\)
−0.447183 + 0.894443i \(0.647573\pi\)
\(374\) 15.8694 0.820586
\(375\) 0 0
\(376\) −1.39804 −0.0720986
\(377\) 0 0
\(378\) 0 0
\(379\) 18.9028 0.970969 0.485485 0.874245i \(-0.338643\pi\)
0.485485 + 0.874245i \(0.338643\pi\)
\(380\) −5.67563 −0.291154
\(381\) 0 0
\(382\) 2.48832 0.127313
\(383\) 9.97046 0.509467 0.254733 0.967011i \(-0.418012\pi\)
0.254733 + 0.967011i \(0.418012\pi\)
\(384\) 0 0
\(385\) −5.76271 −0.293695
\(386\) 8.85756 0.450838
\(387\) 0 0
\(388\) 16.6872 0.847166
\(389\) 21.4166 1.08586 0.542932 0.839777i \(-0.317314\pi\)
0.542932 + 0.839777i \(0.317314\pi\)
\(390\) 0 0
\(391\) −12.4047 −0.627335
\(392\) 0.931705 0.0470582
\(393\) 0 0
\(394\) −43.1336 −2.17304
\(395\) −1.71917 −0.0865008
\(396\) 0 0
\(397\) 34.4566 1.72933 0.864665 0.502349i \(-0.167531\pi\)
0.864665 + 0.502349i \(0.167531\pi\)
\(398\) 28.5599 1.43158
\(399\) 0 0
\(400\) −3.56465 −0.178232
\(401\) −0.799545 −0.0399274 −0.0199637 0.999801i \(-0.506355\pi\)
−0.0199637 + 0.999801i \(0.506355\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −3.68605 −0.183388
\(405\) 0 0
\(406\) 20.6649 1.02558
\(407\) 19.4601 0.964602
\(408\) 0 0
\(409\) 33.5351 1.65820 0.829102 0.559097i \(-0.188852\pi\)
0.829102 + 0.559097i \(0.188852\pi\)
\(410\) 1.49827 0.0739943
\(411\) 0 0
\(412\) −22.9589 −1.13110
\(413\) 3.40044 0.167325
\(414\) 0 0
\(415\) −17.8213 −0.874814
\(416\) 0 0
\(417\) 0 0
\(418\) −9.99953 −0.489093
\(419\) 7.98361 0.390025 0.195012 0.980801i \(-0.437525\pi\)
0.195012 + 0.980801i \(0.437525\pi\)
\(420\) 0 0
\(421\) −28.4413 −1.38615 −0.693073 0.720868i \(-0.743743\pi\)
−0.693073 + 0.720868i \(0.743743\pi\)
\(422\) −3.25262 −0.158335
\(423\) 0 0
\(424\) −3.64523 −0.177028
\(425\) 4.09783 0.198774
\(426\) 0 0
\(427\) −17.5405 −0.848843
\(428\) −33.0135 −1.59577
\(429\) 0 0
\(430\) −24.4620 −1.17966
\(431\) 6.27844 0.302422 0.151211 0.988502i \(-0.451683\pi\)
0.151211 + 0.988502i \(0.451683\pi\)
\(432\) 0 0
\(433\) 5.30367 0.254878 0.127439 0.991846i \(-0.459324\pi\)
0.127439 + 0.991846i \(0.459324\pi\)
\(434\) 58.2073 2.79404
\(435\) 0 0
\(436\) 31.2030 1.49435
\(437\) 7.81641 0.373910
\(438\) 0 0
\(439\) 8.52542 0.406896 0.203448 0.979086i \(-0.434785\pi\)
0.203448 + 0.979086i \(0.434785\pi\)
\(440\) 0.767021 0.0365663
\(441\) 0 0
\(442\) 0 0
\(443\) 22.1575 1.05273 0.526367 0.850257i \(-0.323554\pi\)
0.526367 + 0.850257i \(0.323554\pi\)
\(444\) 0 0
\(445\) 1.91185 0.0906306
\(446\) −18.3846 −0.870538
\(447\) 0 0
\(448\) 28.9594 1.36821
\(449\) 21.4873 1.01405 0.507023 0.861932i \(-0.330746\pi\)
0.507023 + 0.861932i \(0.330746\pi\)
\(450\) 0 0
\(451\) 1.38212 0.0650817
\(452\) 34.8146 1.63754
\(453\) 0 0
\(454\) −42.0213 −1.97216
\(455\) 0 0
\(456\) 0 0
\(457\) −26.8267 −1.25490 −0.627450 0.778657i \(-0.715901\pi\)
−0.627450 + 0.778657i \(0.715901\pi\)
\(458\) −13.2451 −0.618901
\(459\) 0 0
\(460\) −6.65386 −0.310238
\(461\) 13.5864 0.632783 0.316391 0.948629i \(-0.397529\pi\)
0.316391 + 0.948629i \(0.397529\pi\)
\(462\) 0 0
\(463\) 13.0664 0.607246 0.303623 0.952792i \(-0.401804\pi\)
0.303623 + 0.952792i \(0.401804\pi\)
\(464\) 11.7918 0.547419
\(465\) 0 0
\(466\) −16.4161 −0.760461
\(467\) −19.4470 −0.899898 −0.449949 0.893054i \(-0.648558\pi\)
−0.449949 + 0.893054i \(0.648558\pi\)
\(468\) 0 0
\(469\) 32.0780 1.48122
\(470\) −7.05861 −0.325589
\(471\) 0 0
\(472\) −0.452601 −0.0208326
\(473\) −22.5657 −1.03757
\(474\) 0 0
\(475\) −2.58211 −0.118475
\(476\) −27.4625 −1.25874
\(477\) 0 0
\(478\) −58.0046 −2.65307
\(479\) 28.2543 1.29097 0.645485 0.763773i \(-0.276655\pi\)
0.645485 + 0.763773i \(0.276655\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 33.8455 1.54162
\(483\) 0 0
\(484\) −16.3263 −0.742104
\(485\) 7.59179 0.344726
\(486\) 0 0
\(487\) −8.38298 −0.379869 −0.189934 0.981797i \(-0.560828\pi\)
−0.189934 + 0.981797i \(0.560828\pi\)
\(488\) 2.33465 0.105685
\(489\) 0 0
\(490\) 4.70410 0.212510
\(491\) −19.5550 −0.882503 −0.441251 0.897384i \(-0.645465\pi\)
−0.441251 + 0.897384i \(0.645465\pi\)
\(492\) 0 0
\(493\) −13.5555 −0.610511
\(494\) 0 0
\(495\) 0 0
\(496\) 33.2142 1.49136
\(497\) −22.6165 −1.01449
\(498\) 0 0
\(499\) 7.90217 0.353750 0.176875 0.984233i \(-0.443401\pi\)
0.176875 + 0.984233i \(0.443401\pi\)
\(500\) 2.19806 0.0983003
\(501\) 0 0
\(502\) 43.1089 1.92404
\(503\) 1.15346 0.0514301 0.0257150 0.999669i \(-0.491814\pi\)
0.0257150 + 0.999669i \(0.491814\pi\)
\(504\) 0 0
\(505\) −1.67696 −0.0746236
\(506\) −11.7230 −0.521151
\(507\) 0 0
\(508\) 42.6617 1.89281
\(509\) 15.0887 0.668797 0.334398 0.942432i \(-0.391467\pi\)
0.334398 + 0.942432i \(0.391467\pi\)
\(510\) 0 0
\(511\) −37.4523 −1.65679
\(512\) 31.8213 1.40632
\(513\) 0 0
\(514\) −14.2731 −0.629558
\(515\) −10.4450 −0.460264
\(516\) 0 0
\(517\) −6.51142 −0.286372
\(518\) −64.3183 −2.82598
\(519\) 0 0
\(520\) 0 0
\(521\) −19.0610 −0.835078 −0.417539 0.908659i \(-0.637107\pi\)
−0.417539 + 0.908659i \(0.637107\pi\)
\(522\) 0 0
\(523\) −21.8984 −0.957552 −0.478776 0.877937i \(-0.658919\pi\)
−0.478776 + 0.877937i \(0.658919\pi\)
\(524\) −47.7348 −2.08531
\(525\) 0 0
\(526\) 33.3037 1.45211
\(527\) −38.1823 −1.66325
\(528\) 0 0
\(529\) −13.8364 −0.601582
\(530\) −18.4045 −0.799440
\(531\) 0 0
\(532\) 17.3045 0.750246
\(533\) 0 0
\(534\) 0 0
\(535\) −15.0194 −0.649344
\(536\) −4.26960 −0.184419
\(537\) 0 0
\(538\) −34.1511 −1.47236
\(539\) 4.33944 0.186913
\(540\) 0 0
\(541\) −27.8345 −1.19670 −0.598348 0.801236i \(-0.704176\pi\)
−0.598348 + 0.801236i \(0.704176\pi\)
\(542\) 14.1618 0.608302
\(543\) 0 0
\(544\) −33.2551 −1.42580
\(545\) 14.1957 0.608076
\(546\) 0 0
\(547\) 43.0810 1.84201 0.921005 0.389552i \(-0.127370\pi\)
0.921005 + 0.389552i \(0.127370\pi\)
\(548\) −26.7737 −1.14372
\(549\) 0 0
\(550\) 3.87263 0.165129
\(551\) 8.54155 0.363882
\(552\) 0 0
\(553\) 5.24160 0.222896
\(554\) 22.8250 0.969743
\(555\) 0 0
\(556\) −20.8086 −0.882483
\(557\) 3.77346 0.159887 0.0799434 0.996799i \(-0.474526\pi\)
0.0799434 + 0.996799i \(0.474526\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 10.8683 0.459270
\(561\) 0 0
\(562\) −1.13216 −0.0477573
\(563\) −37.6708 −1.58764 −0.793818 0.608155i \(-0.791910\pi\)
−0.793818 + 0.608155i \(0.791910\pi\)
\(564\) 0 0
\(565\) 15.8388 0.666342
\(566\) 35.3624 1.48639
\(567\) 0 0
\(568\) 3.01028 0.126309
\(569\) 9.10513 0.381707 0.190853 0.981619i \(-0.438874\pi\)
0.190853 + 0.981619i \(0.438874\pi\)
\(570\) 0 0
\(571\) −21.8334 −0.913699 −0.456850 0.889544i \(-0.651022\pi\)
−0.456850 + 0.889544i \(0.651022\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −4.56810 −0.190669
\(575\) −3.02715 −0.126241
\(576\) 0 0
\(577\) −6.56465 −0.273290 −0.136645 0.990620i \(-0.543632\pi\)
−0.136645 + 0.990620i \(0.543632\pi\)
\(578\) −0.425665 −0.0177053
\(579\) 0 0
\(580\) −7.27114 −0.301918
\(581\) 54.3357 2.25423
\(582\) 0 0
\(583\) −16.9778 −0.703147
\(584\) 4.98493 0.206278
\(585\) 0 0
\(586\) −67.1143 −2.77247
\(587\) 31.8157 1.31317 0.656587 0.754251i \(-0.272000\pi\)
0.656587 + 0.754251i \(0.272000\pi\)
\(588\) 0 0
\(589\) 24.0592 0.991342
\(590\) −2.28514 −0.0940779
\(591\) 0 0
\(592\) −36.7012 −1.50841
\(593\) 14.6752 0.602636 0.301318 0.953524i \(-0.402573\pi\)
0.301318 + 0.953524i \(0.402573\pi\)
\(594\) 0 0
\(595\) −12.4940 −0.512202
\(596\) 7.90972 0.323995
\(597\) 0 0
\(598\) 0 0
\(599\) 15.9705 0.652535 0.326268 0.945277i \(-0.394209\pi\)
0.326268 + 0.945277i \(0.394209\pi\)
\(600\) 0 0
\(601\) 29.9729 1.22262 0.611309 0.791392i \(-0.290643\pi\)
0.611309 + 0.791392i \(0.290643\pi\)
\(602\) 74.5827 3.03976
\(603\) 0 0
\(604\) −20.9427 −0.852147
\(605\) −7.42758 −0.301974
\(606\) 0 0
\(607\) 43.4204 1.76238 0.881190 0.472762i \(-0.156743\pi\)
0.881190 + 0.472762i \(0.156743\pi\)
\(608\) 20.9545 0.849819
\(609\) 0 0
\(610\) 11.7875 0.477260
\(611\) 0 0
\(612\) 0 0
\(613\) −20.2983 −0.819840 −0.409920 0.912121i \(-0.634443\pi\)
−0.409920 + 0.912121i \(0.634443\pi\)
\(614\) −14.4873 −0.584658
\(615\) 0 0
\(616\) −2.33858 −0.0942242
\(617\) 34.8039 1.40115 0.700575 0.713579i \(-0.252927\pi\)
0.700575 + 0.713579i \(0.252927\pi\)
\(618\) 0 0
\(619\) 23.5026 0.944649 0.472324 0.881425i \(-0.343415\pi\)
0.472324 + 0.881425i \(0.343415\pi\)
\(620\) −20.4808 −0.822529
\(621\) 0 0
\(622\) −26.5060 −1.06280
\(623\) −5.82908 −0.233537
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 52.5247 2.09931
\(627\) 0 0
\(628\) −36.1685 −1.44328
\(629\) 42.1909 1.68226
\(630\) 0 0
\(631\) 9.80971 0.390518 0.195259 0.980752i \(-0.437445\pi\)
0.195259 + 0.980752i \(0.437445\pi\)
\(632\) −0.697661 −0.0277515
\(633\) 0 0
\(634\) 24.3817 0.968319
\(635\) 19.4088 0.770215
\(636\) 0 0
\(637\) 0 0
\(638\) −12.8106 −0.507175
\(639\) 0 0
\(640\) −3.23059 −0.127700
\(641\) 1.23968 0.0489646 0.0244823 0.999700i \(-0.492206\pi\)
0.0244823 + 0.999700i \(0.492206\pi\)
\(642\) 0 0
\(643\) 3.61596 0.142599 0.0712997 0.997455i \(-0.477285\pi\)
0.0712997 + 0.997455i \(0.477285\pi\)
\(644\) 20.2871 0.799422
\(645\) 0 0
\(646\) −21.6797 −0.852975
\(647\) 21.5241 0.846199 0.423100 0.906083i \(-0.360942\pi\)
0.423100 + 0.906083i \(0.360942\pi\)
\(648\) 0 0
\(649\) −2.10800 −0.0827461
\(650\) 0 0
\(651\) 0 0
\(652\) 9.73210 0.381139
\(653\) −33.6069 −1.31514 −0.657569 0.753394i \(-0.728415\pi\)
−0.657569 + 0.753394i \(0.728415\pi\)
\(654\) 0 0
\(655\) −21.7168 −0.848545
\(656\) −2.60665 −0.101773
\(657\) 0 0
\(658\) 21.5211 0.838980
\(659\) 20.0441 0.780809 0.390404 0.920644i \(-0.372335\pi\)
0.390404 + 0.920644i \(0.372335\pi\)
\(660\) 0 0
\(661\) 24.1847 0.940674 0.470337 0.882487i \(-0.344132\pi\)
0.470337 + 0.882487i \(0.344132\pi\)
\(662\) 70.2756 2.73134
\(663\) 0 0
\(664\) −7.23213 −0.280661
\(665\) 7.87263 0.305287
\(666\) 0 0
\(667\) 10.0137 0.387733
\(668\) 43.2790 1.67452
\(669\) 0 0
\(670\) −21.5569 −0.832815
\(671\) 10.8737 0.419774
\(672\) 0 0
\(673\) −43.8963 −1.69208 −0.846039 0.533121i \(-0.821019\pi\)
−0.846039 + 0.533121i \(0.821019\pi\)
\(674\) 26.8700 1.03499
\(675\) 0 0
\(676\) 0 0
\(677\) −10.4698 −0.402387 −0.201193 0.979552i \(-0.564482\pi\)
−0.201193 + 0.979552i \(0.564482\pi\)
\(678\) 0 0
\(679\) −23.1468 −0.888291
\(680\) 1.66296 0.0637714
\(681\) 0 0
\(682\) −36.0838 −1.38172
\(683\) 2.15883 0.0826055 0.0413027 0.999147i \(-0.486849\pi\)
0.0413027 + 0.999147i \(0.486849\pi\)
\(684\) 0 0
\(685\) −12.1806 −0.465397
\(686\) 29.3864 1.12198
\(687\) 0 0
\(688\) 42.5583 1.62252
\(689\) 0 0
\(690\) 0 0
\(691\) 3.86294 0.146953 0.0734765 0.997297i \(-0.476591\pi\)
0.0734765 + 0.997297i \(0.476591\pi\)
\(692\) −27.1134 −1.03070
\(693\) 0 0
\(694\) −5.97716 −0.226890
\(695\) −9.46681 −0.359097
\(696\) 0 0
\(697\) 2.99654 0.113502
\(698\) −19.5972 −0.741764
\(699\) 0 0
\(700\) −6.70171 −0.253301
\(701\) 23.5733 0.890350 0.445175 0.895444i \(-0.353141\pi\)
0.445175 + 0.895444i \(0.353141\pi\)
\(702\) 0 0
\(703\) −26.5851 −1.00268
\(704\) −17.9525 −0.676611
\(705\) 0 0
\(706\) −37.3309 −1.40497
\(707\) 5.11290 0.192290
\(708\) 0 0
\(709\) 18.1454 0.681466 0.340733 0.940160i \(-0.389325\pi\)
0.340733 + 0.940160i \(0.389325\pi\)
\(710\) 15.1987 0.570395
\(711\) 0 0
\(712\) 0.775856 0.0290764
\(713\) 28.2059 1.05632
\(714\) 0 0
\(715\) 0 0
\(716\) −17.5366 −0.655375
\(717\) 0 0
\(718\) 32.5862 1.21610
\(719\) 28.7821 1.07339 0.536695 0.843776i \(-0.319672\pi\)
0.536695 + 0.843776i \(0.319672\pi\)
\(720\) 0 0
\(721\) 31.8461 1.18601
\(722\) −25.2687 −0.940405
\(723\) 0 0
\(724\) −28.9836 −1.07717
\(725\) −3.30798 −0.122855
\(726\) 0 0
\(727\) −28.2107 −1.04628 −0.523139 0.852247i \(-0.675239\pi\)
−0.523139 + 0.852247i \(0.675239\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 25.1685 0.931529
\(731\) −48.9241 −1.80952
\(732\) 0 0
\(733\) 1.81833 0.0671616 0.0335808 0.999436i \(-0.489309\pi\)
0.0335808 + 0.999436i \(0.489309\pi\)
\(734\) 7.08336 0.261452
\(735\) 0 0
\(736\) 24.5662 0.905522
\(737\) −19.8858 −0.732502
\(738\) 0 0
\(739\) −14.0707 −0.517599 −0.258799 0.965931i \(-0.583327\pi\)
−0.258799 + 0.965931i \(0.583327\pi\)
\(740\) 22.6310 0.831933
\(741\) 0 0
\(742\) 56.1138 2.06000
\(743\) 48.5599 1.78149 0.890744 0.454505i \(-0.150184\pi\)
0.890744 + 0.454505i \(0.150184\pi\)
\(744\) 0 0
\(745\) 3.59850 0.131839
\(746\) −35.3911 −1.29576
\(747\) 0 0
\(748\) 17.0245 0.622479
\(749\) 45.7928 1.67323
\(750\) 0 0
\(751\) −18.0175 −0.657466 −0.328733 0.944423i \(-0.606622\pi\)
−0.328733 + 0.944423i \(0.606622\pi\)
\(752\) 12.2804 0.447819
\(753\) 0 0
\(754\) 0 0
\(755\) −9.52781 −0.346753
\(756\) 0 0
\(757\) −43.0455 −1.56451 −0.782257 0.622956i \(-0.785932\pi\)
−0.782257 + 0.622956i \(0.785932\pi\)
\(758\) 38.7302 1.40674
\(759\) 0 0
\(760\) −1.04785 −0.0380096
\(761\) 18.7730 0.680520 0.340260 0.940331i \(-0.389485\pi\)
0.340260 + 0.940331i \(0.389485\pi\)
\(762\) 0 0
\(763\) −43.2814 −1.56689
\(764\) 2.66945 0.0965773
\(765\) 0 0
\(766\) 20.4286 0.738117
\(767\) 0 0
\(768\) 0 0
\(769\) 1.57481 0.0567891 0.0283945 0.999597i \(-0.490961\pi\)
0.0283945 + 0.999597i \(0.490961\pi\)
\(770\) −11.8073 −0.425506
\(771\) 0 0
\(772\) 9.50232 0.341996
\(773\) −8.51706 −0.306337 −0.153169 0.988200i \(-0.548948\pi\)
−0.153169 + 0.988200i \(0.548948\pi\)
\(774\) 0 0
\(775\) −9.31767 −0.334700
\(776\) 3.08085 0.110596
\(777\) 0 0
\(778\) 43.8808 1.57320
\(779\) −1.88816 −0.0676505
\(780\) 0 0
\(781\) 14.0204 0.501691
\(782\) −25.4163 −0.908885
\(783\) 0 0
\(784\) −8.18406 −0.292288
\(785\) −16.4547 −0.587295
\(786\) 0 0
\(787\) −16.4421 −0.586096 −0.293048 0.956098i \(-0.594670\pi\)
−0.293048 + 0.956098i \(0.594670\pi\)
\(788\) −46.2734 −1.64842
\(789\) 0 0
\(790\) −3.52243 −0.125323
\(791\) −48.2911 −1.71703
\(792\) 0 0
\(793\) 0 0
\(794\) 70.5988 2.50546
\(795\) 0 0
\(796\) 30.6388 1.08596
\(797\) −6.18359 −0.219034 −0.109517 0.993985i \(-0.534930\pi\)
−0.109517 + 0.993985i \(0.534930\pi\)
\(798\) 0 0
\(799\) −14.1172 −0.499431
\(800\) −8.11529 −0.286919
\(801\) 0 0
\(802\) −1.63820 −0.0578469
\(803\) 23.2174 0.819326
\(804\) 0 0
\(805\) 9.22952 0.325298
\(806\) 0 0
\(807\) 0 0
\(808\) −0.680531 −0.0239410
\(809\) −36.9517 −1.29915 −0.649576 0.760297i \(-0.725053\pi\)
−0.649576 + 0.760297i \(0.725053\pi\)
\(810\) 0 0
\(811\) 4.54958 0.159757 0.0798787 0.996805i \(-0.474547\pi\)
0.0798787 + 0.996805i \(0.474547\pi\)
\(812\) 22.1691 0.777983
\(813\) 0 0
\(814\) 39.8722 1.39752
\(815\) 4.42758 0.155091
\(816\) 0 0
\(817\) 30.8278 1.07853
\(818\) 68.7107 2.40241
\(819\) 0 0
\(820\) 1.60733 0.0561305
\(821\) 46.9288 1.63783 0.818914 0.573916i \(-0.194577\pi\)
0.818914 + 0.573916i \(0.194577\pi\)
\(822\) 0 0
\(823\) 3.07739 0.107271 0.0536356 0.998561i \(-0.482919\pi\)
0.0536356 + 0.998561i \(0.482919\pi\)
\(824\) −4.23874 −0.147663
\(825\) 0 0
\(826\) 6.96721 0.242420
\(827\) 55.1353 1.91724 0.958620 0.284687i \(-0.0918898\pi\)
0.958620 + 0.284687i \(0.0918898\pi\)
\(828\) 0 0
\(829\) 47.0853 1.63534 0.817670 0.575688i \(-0.195266\pi\)
0.817670 + 0.575688i \(0.195266\pi\)
\(830\) −36.5144 −1.26743
\(831\) 0 0
\(832\) 0 0
\(833\) 9.40821 0.325975
\(834\) 0 0
\(835\) 19.6896 0.681388
\(836\) −10.7274 −0.371015
\(837\) 0 0
\(838\) 16.3577 0.565069
\(839\) 40.2127 1.38829 0.694147 0.719833i \(-0.255782\pi\)
0.694147 + 0.719833i \(0.255782\pi\)
\(840\) 0 0
\(841\) −18.0573 −0.622665
\(842\) −58.2739 −2.00825
\(843\) 0 0
\(844\) −3.48938 −0.120110
\(845\) 0 0
\(846\) 0 0
\(847\) 22.6461 0.778129
\(848\) 32.0196 1.09956
\(849\) 0 0
\(850\) 8.39612 0.287985
\(851\) −31.1672 −1.06840
\(852\) 0 0
\(853\) 18.3526 0.628381 0.314190 0.949360i \(-0.398267\pi\)
0.314190 + 0.949360i \(0.398267\pi\)
\(854\) −35.9390 −1.22981
\(855\) 0 0
\(856\) −6.09506 −0.208325
\(857\) −10.1787 −0.347697 −0.173849 0.984772i \(-0.555620\pi\)
−0.173849 + 0.984772i \(0.555620\pi\)
\(858\) 0 0
\(859\) 10.1532 0.346423 0.173211 0.984885i \(-0.444586\pi\)
0.173211 + 0.984885i \(0.444586\pi\)
\(860\) −26.2427 −0.894868
\(861\) 0 0
\(862\) 12.8640 0.438150
\(863\) −28.6088 −0.973854 −0.486927 0.873443i \(-0.661882\pi\)
−0.486927 + 0.873443i \(0.661882\pi\)
\(864\) 0 0
\(865\) −12.3351 −0.419407
\(866\) 10.8668 0.369268
\(867\) 0 0
\(868\) 62.4443 2.11950
\(869\) −3.24937 −0.110227
\(870\) 0 0
\(871\) 0 0
\(872\) 5.76079 0.195085
\(873\) 0 0
\(874\) 16.0152 0.541722
\(875\) −3.04892 −0.103072
\(876\) 0 0
\(877\) −52.0157 −1.75644 −0.878222 0.478253i \(-0.841270\pi\)
−0.878222 + 0.478253i \(0.841270\pi\)
\(878\) 17.4679 0.589512
\(879\) 0 0
\(880\) −6.73748 −0.227120
\(881\) −57.2978 −1.93041 −0.965206 0.261490i \(-0.915786\pi\)
−0.965206 + 0.261490i \(0.915786\pi\)
\(882\) 0 0
\(883\) −21.7730 −0.732719 −0.366360 0.930473i \(-0.619396\pi\)
−0.366360 + 0.930473i \(0.619396\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 45.3989 1.52521
\(887\) 8.35988 0.280697 0.140349 0.990102i \(-0.455178\pi\)
0.140349 + 0.990102i \(0.455178\pi\)
\(888\) 0 0
\(889\) −59.1758 −1.98469
\(890\) 3.91723 0.131306
\(891\) 0 0
\(892\) −19.7229 −0.660371
\(893\) 8.89546 0.297675
\(894\) 0 0
\(895\) −7.97823 −0.266683
\(896\) 9.84979 0.329058
\(897\) 0 0
\(898\) 44.0256 1.46915
\(899\) 30.8226 1.02799
\(900\) 0 0
\(901\) −36.8090 −1.22628
\(902\) 2.83186 0.0942906
\(903\) 0 0
\(904\) 6.42758 0.213778
\(905\) −13.1860 −0.438317
\(906\) 0 0
\(907\) 24.9168 0.827347 0.413674 0.910425i \(-0.364245\pi\)
0.413674 + 0.910425i \(0.364245\pi\)
\(908\) −45.0801 −1.49604
\(909\) 0 0
\(910\) 0 0
\(911\) −27.4064 −0.908015 −0.454007 0.890998i \(-0.650006\pi\)
−0.454007 + 0.890998i \(0.650006\pi\)
\(912\) 0 0
\(913\) −33.6838 −1.11477
\(914\) −54.9657 −1.81810
\(915\) 0 0
\(916\) −14.2092 −0.469485
\(917\) 66.2127 2.18653
\(918\) 0 0
\(919\) 45.7434 1.50894 0.754469 0.656336i \(-0.227895\pi\)
0.754469 + 0.656336i \(0.227895\pi\)
\(920\) −1.22846 −0.0405010
\(921\) 0 0
\(922\) 27.8374 0.916777
\(923\) 0 0
\(924\) 0 0
\(925\) 10.2959 0.338527
\(926\) 26.7719 0.879780
\(927\) 0 0
\(928\) 26.8452 0.881237
\(929\) −15.0301 −0.493123 −0.246561 0.969127i \(-0.579301\pi\)
−0.246561 + 0.969127i \(0.579301\pi\)
\(930\) 0 0
\(931\) −5.92825 −0.194290
\(932\) −17.6111 −0.576869
\(933\) 0 0
\(934\) −39.8452 −1.30378
\(935\) 7.74525 0.253297
\(936\) 0 0
\(937\) −24.1377 −0.788543 −0.394271 0.918994i \(-0.629003\pi\)
−0.394271 + 0.918994i \(0.629003\pi\)
\(938\) 65.7251 2.14600
\(939\) 0 0
\(940\) −7.57242 −0.246985
\(941\) 6.97344 0.227328 0.113664 0.993519i \(-0.463741\pi\)
0.113664 + 0.993519i \(0.463741\pi\)
\(942\) 0 0
\(943\) −2.21360 −0.0720848
\(944\) 3.97563 0.129396
\(945\) 0 0
\(946\) −46.2353 −1.50324
\(947\) −11.3951 −0.370290 −0.185145 0.982711i \(-0.559275\pi\)
−0.185145 + 0.982711i \(0.559275\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −5.29052 −0.171647
\(951\) 0 0
\(952\) −5.07021 −0.164327
\(953\) −30.4198 −0.985394 −0.492697 0.870201i \(-0.663989\pi\)
−0.492697 + 0.870201i \(0.663989\pi\)
\(954\) 0 0
\(955\) 1.21446 0.0392989
\(956\) −62.2269 −2.01256
\(957\) 0 0
\(958\) 57.8907 1.87036
\(959\) 37.1377 1.19924
\(960\) 0 0
\(961\) 55.8189 1.80061
\(962\) 0 0
\(963\) 0 0
\(964\) 36.3092 1.16944
\(965\) 4.32304 0.139164
\(966\) 0 0
\(967\) 31.3019 1.00660 0.503300 0.864112i \(-0.332119\pi\)
0.503300 + 0.864112i \(0.332119\pi\)
\(968\) −3.01421 −0.0968804
\(969\) 0 0
\(970\) 15.5550 0.499440
\(971\) −58.7502 −1.88538 −0.942691 0.333667i \(-0.891714\pi\)
−0.942691 + 0.333667i \(0.891714\pi\)
\(972\) 0 0
\(973\) 28.8635 0.925322
\(974\) −17.1760 −0.550355
\(975\) 0 0
\(976\) −20.5075 −0.656429
\(977\) −60.2737 −1.92832 −0.964162 0.265312i \(-0.914525\pi\)
−0.964162 + 0.265312i \(0.914525\pi\)
\(978\) 0 0
\(979\) 3.61356 0.115490
\(980\) 5.04652 0.161205
\(981\) 0 0
\(982\) −40.0665 −1.27857
\(983\) 10.0030 0.319046 0.159523 0.987194i \(-0.449004\pi\)
0.159523 + 0.987194i \(0.449004\pi\)
\(984\) 0 0
\(985\) −21.0519 −0.670769
\(986\) −27.7742 −0.884511
\(987\) 0 0
\(988\) 0 0
\(989\) 36.1411 1.14922
\(990\) 0 0
\(991\) −37.7178 −1.19815 −0.599073 0.800694i \(-0.704464\pi\)
−0.599073 + 0.800694i \(0.704464\pi\)
\(992\) 75.6156 2.40080
\(993\) 0 0
\(994\) −46.3394 −1.46980
\(995\) 13.9390 0.441896
\(996\) 0 0
\(997\) −17.0388 −0.539623 −0.269811 0.962913i \(-0.586961\pi\)
−0.269811 + 0.962913i \(0.586961\pi\)
\(998\) 16.1909 0.512513
\(999\) 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 7605.2.a.bm.1.3 3
3.2 odd 2 2535.2.a.bh.1.1 yes 3
13.12 even 2 7605.2.a.ce.1.1 3
39.38 odd 2 2535.2.a.t.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2535.2.a.t.1.3 3 39.38 odd 2
2535.2.a.bh.1.1 yes 3 3.2 odd 2
7605.2.a.bm.1.3 3 1.1 even 1 trivial
7605.2.a.ce.1.1 3 13.12 even 2