Properties

Label 241.2.a.a.1.1
Level $241$
Weight $2$
Character 241.1
Self dual yes
Analytic conductor $1.924$
Analytic rank $1$
Dimension $7$
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] = [241,2,Mod(1,241)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(241, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("241.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 241.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: \(1.92439468871\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.31056073.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.60363\) of defining polynomial
Character \(\chi\) \(=\) 241.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.60363 q^{2} +0.980039 q^{3} +4.77887 q^{4} -1.69135 q^{5} -2.55166 q^{6} -1.30586 q^{7} -7.23513 q^{8} -2.03952 q^{9} +O(q^{10})\) \(q-2.60363 q^{2} +0.980039 q^{3} +4.77887 q^{4} -1.69135 q^{5} -2.55166 q^{6} -1.30586 q^{7} -7.23513 q^{8} -2.03952 q^{9} +4.40364 q^{10} -3.27094 q^{11} +4.68348 q^{12} +4.30649 q^{13} +3.39998 q^{14} -1.65759 q^{15} +9.27984 q^{16} -1.02456 q^{17} +5.31016 q^{18} -7.01250 q^{19} -8.08274 q^{20} -1.27980 q^{21} +8.51631 q^{22} +0.835873 q^{23} -7.09071 q^{24} -2.13934 q^{25} -11.2125 q^{26} -4.93893 q^{27} -6.24054 q^{28} -1.11761 q^{29} +4.31574 q^{30} -3.97344 q^{31} -9.69098 q^{32} -3.20565 q^{33} +2.66758 q^{34} +2.20867 q^{35} -9.74661 q^{36} -11.3098 q^{37} +18.2579 q^{38} +4.22053 q^{39} +12.2371 q^{40} +1.22869 q^{41} +3.33211 q^{42} +10.8406 q^{43} -15.6314 q^{44} +3.44955 q^{45} -2.17630 q^{46} -0.151820 q^{47} +9.09461 q^{48} -5.29473 q^{49} +5.57003 q^{50} -1.00411 q^{51} +20.5801 q^{52} +3.02053 q^{53} +12.8591 q^{54} +5.53231 q^{55} +9.44808 q^{56} -6.87252 q^{57} +2.90984 q^{58} -4.15373 q^{59} -7.92140 q^{60} +5.62714 q^{61} +10.3454 q^{62} +2.66334 q^{63} +6.67199 q^{64} -7.28378 q^{65} +8.34632 q^{66} +12.9934 q^{67} -4.89626 q^{68} +0.819188 q^{69} -5.75055 q^{70} -11.2862 q^{71} +14.7562 q^{72} +11.7148 q^{73} +29.4464 q^{74} -2.09663 q^{75} -33.5118 q^{76} +4.27140 q^{77} -10.9887 q^{78} -1.66517 q^{79} -15.6955 q^{80} +1.27823 q^{81} -3.19906 q^{82} -2.34322 q^{83} -6.11597 q^{84} +1.73290 q^{85} -28.2250 q^{86} -1.09530 q^{87} +23.6657 q^{88} +18.1099 q^{89} -8.98133 q^{90} -5.62368 q^{91} +3.99453 q^{92} -3.89413 q^{93} +0.395283 q^{94} +11.8606 q^{95} -9.49754 q^{96} -7.17873 q^{97} +13.7855 q^{98} +6.67116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 4 q^{2} - 3 q^{3} + 2 q^{4} - 8 q^{5} - 5 q^{6} - 7 q^{7} - 6 q^{8} - 2 q^{9} + 3 q^{10} - 18 q^{11} + q^{12} - q^{13} - 6 q^{14} - 11 q^{15} + 4 q^{16} - 2 q^{17} + 8 q^{18} - 6 q^{19} - 8 q^{20} - 2 q^{21} + 10 q^{22} - 22 q^{23} - 3 q^{24} + 5 q^{25} + 8 q^{26} + 3 q^{27} + 9 q^{28} - 16 q^{29} + 29 q^{30} - 18 q^{31} - 6 q^{32} + 4 q^{33} + 11 q^{34} + 7 q^{35} - 7 q^{36} + 8 q^{37} + 16 q^{38} - 9 q^{39} + 14 q^{40} - 15 q^{41} + 19 q^{42} + 14 q^{43} - 4 q^{44} + 3 q^{45} + 11 q^{46} - 10 q^{47} + 31 q^{48} + 6 q^{49} - 4 q^{50} + 13 q^{51} + 27 q^{52} + 15 q^{53} + 16 q^{54} + 29 q^{55} + 13 q^{56} + 14 q^{57} + 17 q^{58} - 18 q^{59} + 15 q^{60} + 4 q^{61} + 13 q^{62} - 16 q^{63} + 2 q^{64} - 7 q^{65} + 16 q^{66} + 18 q^{67} - 15 q^{68} + 26 q^{69} + 8 q^{70} - 50 q^{71} + 30 q^{72} + 10 q^{74} + 16 q^{75} - 20 q^{76} + 17 q^{77} - 32 q^{78} - 15 q^{79} - 11 q^{80} - 9 q^{81} + 45 q^{82} - 24 q^{83} + 6 q^{84} - 2 q^{85} - 23 q^{86} + 12 q^{87} + 8 q^{88} - 13 q^{89} - 39 q^{90} - 12 q^{91} - 10 q^{92} + 14 q^{93} - 32 q^{94} - 41 q^{95} - 15 q^{96} + q^{97} + 9 q^{98} - 20 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60363 −1.84104 −0.920521 0.390694i \(-0.872235\pi\)
−0.920521 + 0.390694i \(0.872235\pi\)
\(3\) 0.980039 0.565826 0.282913 0.959146i \(-0.408699\pi\)
0.282913 + 0.959146i \(0.408699\pi\)
\(4\) 4.77887 2.38943
\(5\) −1.69135 −0.756395 −0.378197 0.925725i \(-0.623456\pi\)
−0.378197 + 0.925725i \(0.623456\pi\)
\(6\) −2.55166 −1.04171
\(7\) −1.30586 −0.493569 −0.246785 0.969070i \(-0.579374\pi\)
−0.246785 + 0.969070i \(0.579374\pi\)
\(8\) −7.23513 −2.55801
\(9\) −2.03952 −0.679841
\(10\) 4.40364 1.39255
\(11\) −3.27094 −0.986226 −0.493113 0.869965i \(-0.664141\pi\)
−0.493113 + 0.869965i \(0.664141\pi\)
\(12\) 4.68348 1.35200
\(13\) 4.30649 1.19441 0.597203 0.802090i \(-0.296279\pi\)
0.597203 + 0.802090i \(0.296279\pi\)
\(14\) 3.39998 0.908682
\(15\) −1.65759 −0.427988
\(16\) 9.27984 2.31996
\(17\) −1.02456 −0.248493 −0.124247 0.992251i \(-0.539651\pi\)
−0.124247 + 0.992251i \(0.539651\pi\)
\(18\) 5.31016 1.25162
\(19\) −7.01250 −1.60878 −0.804388 0.594104i \(-0.797507\pi\)
−0.804388 + 0.594104i \(0.797507\pi\)
\(20\) −8.08274 −1.80736
\(21\) −1.27980 −0.279274
\(22\) 8.51631 1.81568
\(23\) 0.835873 0.174292 0.0871458 0.996196i \(-0.472225\pi\)
0.0871458 + 0.996196i \(0.472225\pi\)
\(24\) −7.09071 −1.44739
\(25\) −2.13934 −0.427867
\(26\) −11.2125 −2.19895
\(27\) −4.93893 −0.950498
\(28\) −6.24054 −1.17935
\(29\) −1.11761 −0.207535 −0.103767 0.994602i \(-0.533090\pi\)
−0.103767 + 0.994602i \(0.533090\pi\)
\(30\) 4.31574 0.787943
\(31\) −3.97344 −0.713652 −0.356826 0.934171i \(-0.616141\pi\)
−0.356826 + 0.934171i \(0.616141\pi\)
\(32\) −9.69098 −1.71314
\(33\) −3.20565 −0.558032
\(34\) 2.66758 0.457486
\(35\) 2.20867 0.373333
\(36\) −9.74661 −1.62444
\(37\) −11.3098 −1.85932 −0.929658 0.368423i \(-0.879898\pi\)
−0.929658 + 0.368423i \(0.879898\pi\)
\(38\) 18.2579 2.96182
\(39\) 4.22053 0.675825
\(40\) 12.2371 1.93486
\(41\) 1.22869 0.191890 0.0959448 0.995387i \(-0.469413\pi\)
0.0959448 + 0.995387i \(0.469413\pi\)
\(42\) 3.33211 0.514156
\(43\) 10.8406 1.65318 0.826591 0.562804i \(-0.190277\pi\)
0.826591 + 0.562804i \(0.190277\pi\)
\(44\) −15.6314 −2.35652
\(45\) 3.44955 0.514228
\(46\) −2.17630 −0.320878
\(47\) −0.151820 −0.0221453 −0.0110726 0.999939i \(-0.503525\pi\)
−0.0110726 + 0.999939i \(0.503525\pi\)
\(48\) 9.09461 1.31269
\(49\) −5.29473 −0.756389
\(50\) 5.57003 0.787721
\(51\) −1.00411 −0.140604
\(52\) 20.5801 2.85395
\(53\) 3.02053 0.414902 0.207451 0.978245i \(-0.433483\pi\)
0.207451 + 0.978245i \(0.433483\pi\)
\(54\) 12.8591 1.74991
\(55\) 5.53231 0.745976
\(56\) 9.44808 1.26255
\(57\) −6.87252 −0.910287
\(58\) 2.90984 0.382080
\(59\) −4.15373 −0.540769 −0.270385 0.962752i \(-0.587151\pi\)
−0.270385 + 0.962752i \(0.587151\pi\)
\(60\) −7.92140 −1.02265
\(61\) 5.62714 0.720482 0.360241 0.932859i \(-0.382694\pi\)
0.360241 + 0.932859i \(0.382694\pi\)
\(62\) 10.3454 1.31386
\(63\) 2.66334 0.335549
\(64\) 6.67199 0.833999
\(65\) −7.28378 −0.903442
\(66\) 8.34632 1.02736
\(67\) 12.9934 1.58740 0.793700 0.608309i \(-0.208152\pi\)
0.793700 + 0.608309i \(0.208152\pi\)
\(68\) −4.89626 −0.593758
\(69\) 0.819188 0.0986187
\(70\) −5.75055 −0.687322
\(71\) −11.2862 −1.33942 −0.669711 0.742622i \(-0.733582\pi\)
−0.669711 + 0.742622i \(0.733582\pi\)
\(72\) 14.7562 1.73904
\(73\) 11.7148 1.37112 0.685560 0.728017i \(-0.259558\pi\)
0.685560 + 0.728017i \(0.259558\pi\)
\(74\) 29.4464 3.42308
\(75\) −2.09663 −0.242098
\(76\) −33.5118 −3.84407
\(77\) 4.27140 0.486771
\(78\) −10.9887 −1.24422
\(79\) −1.66517 −0.187346 −0.0936732 0.995603i \(-0.529861\pi\)
−0.0936732 + 0.995603i \(0.529861\pi\)
\(80\) −15.6955 −1.75481
\(81\) 1.27823 0.142025
\(82\) −3.19906 −0.353277
\(83\) −2.34322 −0.257201 −0.128601 0.991696i \(-0.541049\pi\)
−0.128601 + 0.991696i \(0.541049\pi\)
\(84\) −6.11597 −0.667308
\(85\) 1.73290 0.187959
\(86\) −28.2250 −3.04358
\(87\) −1.09530 −0.117429
\(88\) 23.6657 2.52277
\(89\) 18.1099 1.91965 0.959825 0.280598i \(-0.0905329\pi\)
0.959825 + 0.280598i \(0.0905329\pi\)
\(90\) −8.98133 −0.946715
\(91\) −5.62368 −0.589522
\(92\) 3.99453 0.416458
\(93\) −3.89413 −0.403802
\(94\) 0.395283 0.0407703
\(95\) 11.8606 1.21687
\(96\) −9.49754 −0.969338
\(97\) −7.17873 −0.728890 −0.364445 0.931225i \(-0.618741\pi\)
−0.364445 + 0.931225i \(0.618741\pi\)
\(98\) 13.7855 1.39254
\(99\) 6.67116 0.670477
\(100\) −10.2236 −1.02236
\(101\) −5.48113 −0.545393 −0.272696 0.962100i \(-0.587915\pi\)
−0.272696 + 0.962100i \(0.587915\pi\)
\(102\) 2.61433 0.258858
\(103\) −15.7371 −1.55062 −0.775311 0.631580i \(-0.782407\pi\)
−0.775311 + 0.631580i \(0.782407\pi\)
\(104\) −31.1580 −3.05530
\(105\) 2.16458 0.211242
\(106\) −7.86433 −0.763851
\(107\) −11.1816 −1.08097 −0.540483 0.841355i \(-0.681758\pi\)
−0.540483 + 0.841355i \(0.681758\pi\)
\(108\) −23.6025 −2.27115
\(109\) −0.296424 −0.0283922 −0.0141961 0.999899i \(-0.504519\pi\)
−0.0141961 + 0.999899i \(0.504519\pi\)
\(110\) −14.4041 −1.37337
\(111\) −11.0840 −1.05205
\(112\) −12.1182 −1.14506
\(113\) 10.5881 0.996045 0.498023 0.867164i \(-0.334060\pi\)
0.498023 + 0.867164i \(0.334060\pi\)
\(114\) 17.8935 1.67588
\(115\) −1.41375 −0.131833
\(116\) −5.34091 −0.495891
\(117\) −8.78319 −0.812006
\(118\) 10.8147 0.995578
\(119\) 1.33794 0.122649
\(120\) 11.9929 1.09479
\(121\) −0.300940 −0.0273582
\(122\) −14.6510 −1.32644
\(123\) 1.20417 0.108576
\(124\) −18.9886 −1.70522
\(125\) 12.0751 1.08003
\(126\) −6.93433 −0.617759
\(127\) 14.6989 1.30432 0.652160 0.758081i \(-0.273863\pi\)
0.652160 + 0.758081i \(0.273863\pi\)
\(128\) 2.01059 0.177713
\(129\) 10.6242 0.935413
\(130\) 18.9642 1.66327
\(131\) 9.63853 0.842122 0.421061 0.907032i \(-0.361658\pi\)
0.421061 + 0.907032i \(0.361658\pi\)
\(132\) −15.3194 −1.33338
\(133\) 9.15735 0.794043
\(134\) −33.8300 −2.92247
\(135\) 8.35346 0.718951
\(136\) 7.41286 0.635647
\(137\) 23.2376 1.98532 0.992661 0.120933i \(-0.0385886\pi\)
0.992661 + 0.120933i \(0.0385886\pi\)
\(138\) −2.13286 −0.181561
\(139\) −1.29376 −0.109736 −0.0548678 0.998494i \(-0.517474\pi\)
−0.0548678 + 0.998494i \(0.517474\pi\)
\(140\) 10.5549 0.892055
\(141\) −0.148790 −0.0125304
\(142\) 29.3850 2.46593
\(143\) −14.0863 −1.17795
\(144\) −18.9265 −1.57720
\(145\) 1.89027 0.156978
\(146\) −30.5011 −2.52429
\(147\) −5.18904 −0.427985
\(148\) −54.0480 −4.44271
\(149\) 17.5316 1.43625 0.718123 0.695916i \(-0.245002\pi\)
0.718123 + 0.695916i \(0.245002\pi\)
\(150\) 5.45885 0.445713
\(151\) 5.26990 0.428858 0.214429 0.976740i \(-0.431211\pi\)
0.214429 + 0.976740i \(0.431211\pi\)
\(152\) 50.7363 4.11526
\(153\) 2.08962 0.168936
\(154\) −11.1211 −0.896166
\(155\) 6.72048 0.539802
\(156\) 20.1693 1.61484
\(157\) −14.2165 −1.13460 −0.567299 0.823512i \(-0.692012\pi\)
−0.567299 + 0.823512i \(0.692012\pi\)
\(158\) 4.33548 0.344912
\(159\) 2.96024 0.234762
\(160\) 16.3908 1.29581
\(161\) −1.09153 −0.0860250
\(162\) −3.32802 −0.261474
\(163\) −15.9688 −1.25077 −0.625386 0.780315i \(-0.715059\pi\)
−0.625386 + 0.780315i \(0.715059\pi\)
\(164\) 5.87176 0.458508
\(165\) 5.42188 0.422093
\(166\) 6.10086 0.473518
\(167\) −21.5275 −1.66585 −0.832925 0.553386i \(-0.813335\pi\)
−0.832925 + 0.553386i \(0.813335\pi\)
\(168\) 9.25949 0.714385
\(169\) 5.54585 0.426604
\(170\) −4.51181 −0.346040
\(171\) 14.3021 1.09371
\(172\) 51.8060 3.95017
\(173\) −5.82531 −0.442890 −0.221445 0.975173i \(-0.571077\pi\)
−0.221445 + 0.975173i \(0.571077\pi\)
\(174\) 2.85175 0.216191
\(175\) 2.79368 0.211182
\(176\) −30.3538 −2.28801
\(177\) −4.07081 −0.305981
\(178\) −47.1515 −3.53416
\(179\) −6.03932 −0.451400 −0.225700 0.974197i \(-0.572467\pi\)
−0.225700 + 0.974197i \(0.572467\pi\)
\(180\) 16.4849 1.22871
\(181\) −4.03706 −0.300073 −0.150036 0.988680i \(-0.547939\pi\)
−0.150036 + 0.988680i \(0.547939\pi\)
\(182\) 14.6420 1.08533
\(183\) 5.51482 0.407667
\(184\) −6.04765 −0.445839
\(185\) 19.1288 1.40638
\(186\) 10.1389 0.743417
\(187\) 3.35129 0.245071
\(188\) −0.725529 −0.0529146
\(189\) 6.44956 0.469136
\(190\) −30.8805 −2.24031
\(191\) −16.4803 −1.19247 −0.596235 0.802810i \(-0.703337\pi\)
−0.596235 + 0.802810i \(0.703337\pi\)
\(192\) 6.53881 0.471898
\(193\) −23.0631 −1.66012 −0.830060 0.557674i \(-0.811694\pi\)
−0.830060 + 0.557674i \(0.811694\pi\)
\(194\) 18.6907 1.34192
\(195\) −7.13839 −0.511191
\(196\) −25.3028 −1.80734
\(197\) −13.5540 −0.965680 −0.482840 0.875709i \(-0.660395\pi\)
−0.482840 + 0.875709i \(0.660395\pi\)
\(198\) −17.3692 −1.23438
\(199\) −25.6725 −1.81988 −0.909938 0.414745i \(-0.863871\pi\)
−0.909938 + 0.414745i \(0.863871\pi\)
\(200\) 15.4784 1.09449
\(201\) 12.7341 0.898192
\(202\) 14.2708 1.00409
\(203\) 1.45944 0.102433
\(204\) −4.79852 −0.335964
\(205\) −2.07815 −0.145144
\(206\) 40.9735 2.85476
\(207\) −1.70478 −0.118491
\(208\) 39.9635 2.77097
\(209\) 22.9375 1.58662
\(210\) −5.63576 −0.388905
\(211\) 5.18301 0.356813 0.178407 0.983957i \(-0.442906\pi\)
0.178407 + 0.983957i \(0.442906\pi\)
\(212\) 14.4347 0.991380
\(213\) −11.0609 −0.757879
\(214\) 29.1127 1.99010
\(215\) −18.3353 −1.25046
\(216\) 35.7338 2.43138
\(217\) 5.18877 0.352237
\(218\) 0.771777 0.0522713
\(219\) 11.4810 0.775815
\(220\) 26.4382 1.78246
\(221\) −4.41227 −0.296802
\(222\) 28.8587 1.93687
\(223\) −6.50914 −0.435884 −0.217942 0.975962i \(-0.569934\pi\)
−0.217942 + 0.975962i \(0.569934\pi\)
\(224\) 12.6551 0.845553
\(225\) 4.36323 0.290882
\(226\) −27.5675 −1.83376
\(227\) 11.0460 0.733150 0.366575 0.930389i \(-0.380530\pi\)
0.366575 + 0.930389i \(0.380530\pi\)
\(228\) −32.8429 −2.17507
\(229\) 8.95679 0.591881 0.295941 0.955206i \(-0.404367\pi\)
0.295941 + 0.955206i \(0.404367\pi\)
\(230\) 3.68089 0.242710
\(231\) 4.18614 0.275428
\(232\) 8.08605 0.530875
\(233\) −6.46647 −0.423632 −0.211816 0.977310i \(-0.567938\pi\)
−0.211816 + 0.977310i \(0.567938\pi\)
\(234\) 22.8681 1.49494
\(235\) 0.256781 0.0167506
\(236\) −19.8501 −1.29213
\(237\) −1.63193 −0.106005
\(238\) −3.48349 −0.225801
\(239\) −25.0588 −1.62092 −0.810460 0.585794i \(-0.800783\pi\)
−0.810460 + 0.585794i \(0.800783\pi\)
\(240\) −15.3822 −0.992915
\(241\) −1.00000 −0.0644157
\(242\) 0.783536 0.0503676
\(243\) 16.0695 1.03086
\(244\) 26.8914 1.72154
\(245\) 8.95523 0.572129
\(246\) −3.13520 −0.199893
\(247\) −30.1992 −1.92153
\(248\) 28.7484 1.82552
\(249\) −2.29644 −0.145531
\(250\) −31.4391 −1.98838
\(251\) −12.5611 −0.792847 −0.396424 0.918068i \(-0.629749\pi\)
−0.396424 + 0.918068i \(0.629749\pi\)
\(252\) 12.7277 0.801772
\(253\) −2.73409 −0.171891
\(254\) −38.2706 −2.40131
\(255\) 1.69831 0.106352
\(256\) −18.5788 −1.16117
\(257\) 16.0367 1.00034 0.500171 0.865927i \(-0.333270\pi\)
0.500171 + 0.865927i \(0.333270\pi\)
\(258\) −27.6616 −1.72213
\(259\) 14.7690 0.917702
\(260\) −34.8082 −2.15871
\(261\) 2.27939 0.141091
\(262\) −25.0951 −1.55038
\(263\) 3.33210 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(264\) 23.1933 1.42745
\(265\) −5.10877 −0.313829
\(266\) −23.8423 −1.46187
\(267\) 17.7485 1.08619
\(268\) 62.0939 3.79299
\(269\) −7.44101 −0.453686 −0.226843 0.973931i \(-0.572840\pi\)
−0.226843 + 0.973931i \(0.572840\pi\)
\(270\) −21.7493 −1.32362
\(271\) −20.6031 −1.25155 −0.625774 0.780005i \(-0.715217\pi\)
−0.625774 + 0.780005i \(0.715217\pi\)
\(272\) −9.50779 −0.576495
\(273\) −5.51143 −0.333567
\(274\) −60.5020 −3.65506
\(275\) 6.99764 0.421974
\(276\) 3.91479 0.235643
\(277\) 5.17667 0.311036 0.155518 0.987833i \(-0.450295\pi\)
0.155518 + 0.987833i \(0.450295\pi\)
\(278\) 3.36848 0.202028
\(279\) 8.10393 0.485170
\(280\) −15.9800 −0.954988
\(281\) −14.1821 −0.846031 −0.423015 0.906123i \(-0.639028\pi\)
−0.423015 + 0.906123i \(0.639028\pi\)
\(282\) 0.387393 0.0230689
\(283\) −7.05196 −0.419196 −0.209598 0.977788i \(-0.567215\pi\)
−0.209598 + 0.977788i \(0.567215\pi\)
\(284\) −53.9351 −3.20046
\(285\) 11.6238 0.688537
\(286\) 36.6754 2.16866
\(287\) −1.60450 −0.0947109
\(288\) 19.7650 1.16466
\(289\) −15.9503 −0.938251
\(290\) −4.92155 −0.289004
\(291\) −7.03544 −0.412425
\(292\) 55.9837 3.27620
\(293\) −2.78966 −0.162974 −0.0814869 0.996674i \(-0.525967\pi\)
−0.0814869 + 0.996674i \(0.525967\pi\)
\(294\) 13.5103 0.787937
\(295\) 7.02540 0.409035
\(296\) 81.8278 4.75614
\(297\) 16.1550 0.937405
\(298\) −45.6458 −2.64419
\(299\) 3.59968 0.208175
\(300\) −10.0195 −0.578478
\(301\) −14.1564 −0.815960
\(302\) −13.7208 −0.789546
\(303\) −5.37172 −0.308597
\(304\) −65.0749 −3.73230
\(305\) −9.51747 −0.544969
\(306\) −5.44060 −0.311018
\(307\) 19.8285 1.13167 0.565837 0.824517i \(-0.308553\pi\)
0.565837 + 0.824517i \(0.308553\pi\)
\(308\) 20.4124 1.16311
\(309\) −15.4230 −0.877382
\(310\) −17.4976 −0.993798
\(311\) 33.5109 1.90023 0.950114 0.311902i \(-0.100966\pi\)
0.950114 + 0.311902i \(0.100966\pi\)
\(312\) −30.5361 −1.72877
\(313\) 19.4152 1.09741 0.548705 0.836016i \(-0.315121\pi\)
0.548705 + 0.836016i \(0.315121\pi\)
\(314\) 37.0144 2.08884
\(315\) −4.50463 −0.253807
\(316\) −7.95763 −0.447652
\(317\) −11.7255 −0.658569 −0.329284 0.944231i \(-0.606807\pi\)
−0.329284 + 0.944231i \(0.606807\pi\)
\(318\) −7.70735 −0.432207
\(319\) 3.65564 0.204676
\(320\) −11.2847 −0.630832
\(321\) −10.9584 −0.611638
\(322\) 2.84195 0.158376
\(323\) 7.18475 0.399770
\(324\) 6.10847 0.339359
\(325\) −9.21303 −0.511047
\(326\) 41.5768 2.30272
\(327\) −0.290507 −0.0160651
\(328\) −8.88976 −0.490855
\(329\) 0.198256 0.0109302
\(330\) −14.1165 −0.777090
\(331\) 4.93072 0.271017 0.135509 0.990776i \(-0.456733\pi\)
0.135509 + 0.990776i \(0.456733\pi\)
\(332\) −11.1979 −0.614566
\(333\) 23.0666 1.26404
\(334\) 56.0496 3.06690
\(335\) −21.9764 −1.20070
\(336\) −11.8763 −0.647905
\(337\) 34.4425 1.87620 0.938100 0.346364i \(-0.112584\pi\)
0.938100 + 0.346364i \(0.112584\pi\)
\(338\) −14.4393 −0.785395
\(339\) 10.3768 0.563588
\(340\) 8.28128 0.449116
\(341\) 12.9969 0.703822
\(342\) −37.2374 −2.01357
\(343\) 16.0552 0.866900
\(344\) −78.4334 −4.22885
\(345\) −1.38553 −0.0745946
\(346\) 15.1669 0.815378
\(347\) −23.4553 −1.25915 −0.629574 0.776940i \(-0.716771\pi\)
−0.629574 + 0.776940i \(0.716771\pi\)
\(348\) −5.23430 −0.280588
\(349\) 15.8727 0.849648 0.424824 0.905276i \(-0.360336\pi\)
0.424824 + 0.905276i \(0.360336\pi\)
\(350\) −7.27369 −0.388795
\(351\) −21.2694 −1.13528
\(352\) 31.6986 1.68954
\(353\) −28.4598 −1.51476 −0.757382 0.652972i \(-0.773522\pi\)
−0.757382 + 0.652972i \(0.773522\pi\)
\(354\) 10.5989 0.563324
\(355\) 19.0889 1.01313
\(356\) 86.5450 4.58688
\(357\) 1.31123 0.0693978
\(358\) 15.7241 0.831047
\(359\) −0.772338 −0.0407625 −0.0203812 0.999792i \(-0.506488\pi\)
−0.0203812 + 0.999792i \(0.506488\pi\)
\(360\) −24.9579 −1.31540
\(361\) 30.1751 1.58816
\(362\) 10.5110 0.552446
\(363\) −0.294933 −0.0154800
\(364\) −26.8748 −1.40862
\(365\) −19.8139 −1.03711
\(366\) −14.3585 −0.750532
\(367\) −23.3631 −1.21954 −0.609772 0.792577i \(-0.708739\pi\)
−0.609772 + 0.792577i \(0.708739\pi\)
\(368\) 7.75677 0.404350
\(369\) −2.50595 −0.130454
\(370\) −49.8042 −2.58920
\(371\) −3.94439 −0.204783
\(372\) −18.6095 −0.964859
\(373\) 27.7831 1.43855 0.719277 0.694724i \(-0.244473\pi\)
0.719277 + 0.694724i \(0.244473\pi\)
\(374\) −8.72550 −0.451185
\(375\) 11.8341 0.611109
\(376\) 1.09844 0.0566477
\(377\) −4.81297 −0.247881
\(378\) −16.7922 −0.863700
\(379\) 7.33328 0.376685 0.188343 0.982103i \(-0.439688\pi\)
0.188343 + 0.982103i \(0.439688\pi\)
\(380\) 56.6802 2.90763
\(381\) 14.4055 0.738018
\(382\) 42.9084 2.19539
\(383\) −33.4931 −1.71142 −0.855708 0.517459i \(-0.826878\pi\)
−0.855708 + 0.517459i \(0.826878\pi\)
\(384\) 1.97046 0.100554
\(385\) −7.22443 −0.368191
\(386\) 60.0477 3.05635
\(387\) −22.1097 −1.12390
\(388\) −34.3062 −1.74163
\(389\) 15.6882 0.795425 0.397713 0.917510i \(-0.369804\pi\)
0.397713 + 0.917510i \(0.369804\pi\)
\(390\) 18.5857 0.941123
\(391\) −0.856405 −0.0433103
\(392\) 38.3080 1.93485
\(393\) 9.44613 0.476494
\(394\) 35.2894 1.77786
\(395\) 2.81639 0.141708
\(396\) 31.8806 1.60206
\(397\) 8.34483 0.418815 0.209408 0.977828i \(-0.432846\pi\)
0.209408 + 0.977828i \(0.432846\pi\)
\(398\) 66.8416 3.35047
\(399\) 8.97456 0.449290
\(400\) −19.8527 −0.992635
\(401\) −38.5766 −1.92642 −0.963211 0.268747i \(-0.913391\pi\)
−0.963211 + 0.268747i \(0.913391\pi\)
\(402\) −33.1548 −1.65361
\(403\) −17.1116 −0.852389
\(404\) −26.1936 −1.30318
\(405\) −2.16193 −0.107427
\(406\) −3.79985 −0.188583
\(407\) 36.9936 1.83371
\(408\) 7.26489 0.359666
\(409\) −19.5415 −0.966266 −0.483133 0.875547i \(-0.660501\pi\)
−0.483133 + 0.875547i \(0.660501\pi\)
\(410\) 5.41073 0.267217
\(411\) 22.7737 1.12335
\(412\) −75.2055 −3.70511
\(413\) 5.42419 0.266907
\(414\) 4.43862 0.218146
\(415\) 3.96320 0.194546
\(416\) −41.7341 −2.04618
\(417\) −1.26794 −0.0620912
\(418\) −59.7206 −2.92103
\(419\) −29.7748 −1.45459 −0.727297 0.686323i \(-0.759224\pi\)
−0.727297 + 0.686323i \(0.759224\pi\)
\(420\) 10.3443 0.504748
\(421\) −4.78920 −0.233411 −0.116706 0.993167i \(-0.537233\pi\)
−0.116706 + 0.993167i \(0.537233\pi\)
\(422\) −13.4946 −0.656908
\(423\) 0.309641 0.0150553
\(424\) −21.8539 −1.06132
\(425\) 2.19189 0.106322
\(426\) 28.7984 1.39529
\(427\) −7.34827 −0.355608
\(428\) −53.4354 −2.58290
\(429\) −13.8051 −0.666517
\(430\) 47.7383 2.30214
\(431\) 5.35939 0.258153 0.129076 0.991635i \(-0.458799\pi\)
0.129076 + 0.991635i \(0.458799\pi\)
\(432\) −45.8325 −2.20512
\(433\) 21.5028 1.03336 0.516680 0.856179i \(-0.327168\pi\)
0.516680 + 0.856179i \(0.327168\pi\)
\(434\) −13.5096 −0.648482
\(435\) 1.85254 0.0888224
\(436\) −1.41657 −0.0678414
\(437\) −5.86156 −0.280396
\(438\) −29.8923 −1.42831
\(439\) 4.22306 0.201556 0.100778 0.994909i \(-0.467867\pi\)
0.100778 + 0.994909i \(0.467867\pi\)
\(440\) −40.0270 −1.90821
\(441\) 10.7987 0.514225
\(442\) 11.4879 0.546424
\(443\) 8.34030 0.396260 0.198130 0.980176i \(-0.436513\pi\)
0.198130 + 0.980176i \(0.436513\pi\)
\(444\) −52.9691 −2.51380
\(445\) −30.6303 −1.45201
\(446\) 16.9474 0.802481
\(447\) 17.1817 0.812665
\(448\) −8.71269 −0.411636
\(449\) 15.7796 0.744684 0.372342 0.928096i \(-0.378555\pi\)
0.372342 + 0.928096i \(0.378555\pi\)
\(450\) −11.3602 −0.535525
\(451\) −4.01898 −0.189247
\(452\) 50.5992 2.37998
\(453\) 5.16470 0.242659
\(454\) −28.7597 −1.34976
\(455\) 9.51161 0.445911
\(456\) 49.7236 2.32852
\(457\) −8.71419 −0.407633 −0.203816 0.979009i \(-0.565335\pi\)
−0.203816 + 0.979009i \(0.565335\pi\)
\(458\) −23.3201 −1.08968
\(459\) 5.06025 0.236192
\(460\) −6.75614 −0.315007
\(461\) 24.9140 1.16036 0.580181 0.814487i \(-0.302982\pi\)
0.580181 + 0.814487i \(0.302982\pi\)
\(462\) −10.8991 −0.507074
\(463\) −2.87272 −0.133507 −0.0667534 0.997770i \(-0.521264\pi\)
−0.0667534 + 0.997770i \(0.521264\pi\)
\(464\) −10.3712 −0.481473
\(465\) 6.58634 0.305434
\(466\) 16.8363 0.779925
\(467\) 4.87474 0.225576 0.112788 0.993619i \(-0.464022\pi\)
0.112788 + 0.993619i \(0.464022\pi\)
\(468\) −41.9737 −1.94023
\(469\) −16.9676 −0.783492
\(470\) −0.668562 −0.0308385
\(471\) −13.9327 −0.641985
\(472\) 30.0528 1.38329
\(473\) −35.4591 −1.63041
\(474\) 4.24894 0.195160
\(475\) 15.0021 0.688343
\(476\) 6.39383 0.293061
\(477\) −6.16044 −0.282067
\(478\) 65.2438 2.98418
\(479\) 0.194055 0.00886661 0.00443331 0.999990i \(-0.498589\pi\)
0.00443331 + 0.999990i \(0.498589\pi\)
\(480\) 16.0637 0.733202
\(481\) −48.7055 −2.22078
\(482\) 2.60363 0.118592
\(483\) −1.06975 −0.0486752
\(484\) −1.43815 −0.0653707
\(485\) 12.1417 0.551328
\(486\) −41.8390 −1.89785
\(487\) −30.7592 −1.39383 −0.696915 0.717154i \(-0.745445\pi\)
−0.696915 + 0.717154i \(0.745445\pi\)
\(488\) −40.7131 −1.84300
\(489\) −15.6500 −0.707719
\(490\) −23.3161 −1.05331
\(491\) −21.5528 −0.972663 −0.486332 0.873774i \(-0.661665\pi\)
−0.486332 + 0.873774i \(0.661665\pi\)
\(492\) 5.75456 0.259436
\(493\) 1.14506 0.0515710
\(494\) 78.6275 3.53762
\(495\) −11.2833 −0.507145
\(496\) −36.8729 −1.65564
\(497\) 14.7382 0.661097
\(498\) 5.97908 0.267929
\(499\) 21.8992 0.980341 0.490170 0.871627i \(-0.336935\pi\)
0.490170 + 0.871627i \(0.336935\pi\)
\(500\) 57.7054 2.58066
\(501\) −21.0978 −0.942581
\(502\) 32.7043 1.45966
\(503\) 4.44114 0.198021 0.0990104 0.995086i \(-0.468432\pi\)
0.0990104 + 0.995086i \(0.468432\pi\)
\(504\) −19.2696 −0.858336
\(505\) 9.27050 0.412532
\(506\) 7.11855 0.316458
\(507\) 5.43515 0.241383
\(508\) 70.2443 3.11659
\(509\) 29.6966 1.31628 0.658140 0.752895i \(-0.271343\pi\)
0.658140 + 0.752895i \(0.271343\pi\)
\(510\) −4.42175 −0.195799
\(511\) −15.2980 −0.676742
\(512\) 44.3511 1.96006
\(513\) 34.6342 1.52914
\(514\) −41.7536 −1.84167
\(515\) 26.6169 1.17288
\(516\) 50.7719 2.23511
\(517\) 0.496595 0.0218402
\(518\) −38.4530 −1.68953
\(519\) −5.70903 −0.250598
\(520\) 52.6991 2.31101
\(521\) −32.5336 −1.42532 −0.712661 0.701509i \(-0.752510\pi\)
−0.712661 + 0.701509i \(0.752510\pi\)
\(522\) −5.93468 −0.259754
\(523\) −21.6812 −0.948053 −0.474027 0.880510i \(-0.657200\pi\)
−0.474027 + 0.880510i \(0.657200\pi\)
\(524\) 46.0612 2.01219
\(525\) 2.73791 0.119492
\(526\) −8.67555 −0.378272
\(527\) 4.07105 0.177338
\(528\) −29.7479 −1.29461
\(529\) −22.3013 −0.969622
\(530\) 13.3013 0.577773
\(531\) 8.47162 0.367637
\(532\) 43.7618 1.89731
\(533\) 5.29135 0.229194
\(534\) −46.2103 −1.99972
\(535\) 18.9120 0.817637
\(536\) −94.0092 −4.06058
\(537\) −5.91877 −0.255414
\(538\) 19.3736 0.835255
\(539\) 17.3187 0.745971
\(540\) 39.9201 1.71789
\(541\) 6.08311 0.261533 0.130767 0.991413i \(-0.458256\pi\)
0.130767 + 0.991413i \(0.458256\pi\)
\(542\) 53.6427 2.30415
\(543\) −3.95648 −0.169789
\(544\) 9.92903 0.425703
\(545\) 0.501356 0.0214757
\(546\) 14.3497 0.614110
\(547\) −12.1956 −0.521447 −0.260723 0.965414i \(-0.583961\pi\)
−0.260723 + 0.965414i \(0.583961\pi\)
\(548\) 111.049 4.74379
\(549\) −11.4767 −0.489813
\(550\) −18.2192 −0.776871
\(551\) 7.83723 0.333877
\(552\) −5.92694 −0.252267
\(553\) 2.17448 0.0924684
\(554\) −13.4781 −0.572630
\(555\) 18.7470 0.795765
\(556\) −6.18273 −0.262206
\(557\) −37.5982 −1.59309 −0.796544 0.604581i \(-0.793341\pi\)
−0.796544 + 0.604581i \(0.793341\pi\)
\(558\) −21.0996 −0.893217
\(559\) 46.6851 1.97457
\(560\) 20.4961 0.866118
\(561\) 3.28439 0.138667
\(562\) 36.9248 1.55758
\(563\) 20.6037 0.868342 0.434171 0.900830i \(-0.357041\pi\)
0.434171 + 0.900830i \(0.357041\pi\)
\(564\) −0.711047 −0.0299405
\(565\) −17.9082 −0.753403
\(566\) 18.3607 0.771756
\(567\) −1.66919 −0.0700992
\(568\) 81.6569 3.42625
\(569\) 20.5762 0.862601 0.431301 0.902208i \(-0.358055\pi\)
0.431301 + 0.902208i \(0.358055\pi\)
\(570\) −30.2641 −1.26762
\(571\) 37.1320 1.55392 0.776962 0.629547i \(-0.216760\pi\)
0.776962 + 0.629547i \(0.216760\pi\)
\(572\) −67.3165 −2.81464
\(573\) −16.1513 −0.674730
\(574\) 4.17753 0.174367
\(575\) −1.78821 −0.0745736
\(576\) −13.6077 −0.566986
\(577\) −34.7064 −1.44484 −0.722422 0.691452i \(-0.756971\pi\)
−0.722422 + 0.691452i \(0.756971\pi\)
\(578\) 41.5285 1.72736
\(579\) −22.6028 −0.939339
\(580\) 9.03335 0.375089
\(581\) 3.05992 0.126947
\(582\) 18.3176 0.759291
\(583\) −9.87998 −0.409187
\(584\) −84.7585 −3.50733
\(585\) 14.8554 0.614197
\(586\) 7.26324 0.300042
\(587\) −1.14455 −0.0472405 −0.0236203 0.999721i \(-0.507519\pi\)
−0.0236203 + 0.999721i \(0.507519\pi\)
\(588\) −24.7977 −1.02264
\(589\) 27.8638 1.14811
\(590\) −18.2915 −0.753050
\(591\) −13.2834 −0.546407
\(592\) −104.953 −4.31354
\(593\) 3.60735 0.148136 0.0740680 0.997253i \(-0.476402\pi\)
0.0740680 + 0.997253i \(0.476402\pi\)
\(594\) −42.0615 −1.72580
\(595\) −2.26292 −0.0927708
\(596\) 83.7813 3.43181
\(597\) −25.1601 −1.02973
\(598\) −9.37222 −0.383258
\(599\) −31.6723 −1.29410 −0.647048 0.762449i \(-0.723997\pi\)
−0.647048 + 0.762449i \(0.723997\pi\)
\(600\) 15.1694 0.619289
\(601\) 6.55665 0.267451 0.133726 0.991018i \(-0.457306\pi\)
0.133726 + 0.991018i \(0.457306\pi\)
\(602\) 36.8579 1.50222
\(603\) −26.5004 −1.07918
\(604\) 25.1841 1.02473
\(605\) 0.508996 0.0206936
\(606\) 13.9859 0.568140
\(607\) −9.16648 −0.372056 −0.186028 0.982544i \(-0.559562\pi\)
−0.186028 + 0.982544i \(0.559562\pi\)
\(608\) 67.9579 2.75606
\(609\) 1.43031 0.0579592
\(610\) 24.7799 1.00331
\(611\) −0.653812 −0.0264504
\(612\) 9.98603 0.403661
\(613\) 7.92345 0.320025 0.160012 0.987115i \(-0.448847\pi\)
0.160012 + 0.987115i \(0.448847\pi\)
\(614\) −51.6260 −2.08346
\(615\) −2.03667 −0.0821264
\(616\) −30.9041 −1.24516
\(617\) 16.5959 0.668126 0.334063 0.942551i \(-0.391580\pi\)
0.334063 + 0.942551i \(0.391580\pi\)
\(618\) 40.1556 1.61530
\(619\) 4.49086 0.180503 0.0902514 0.995919i \(-0.471233\pi\)
0.0902514 + 0.995919i \(0.471233\pi\)
\(620\) 32.1163 1.28982
\(621\) −4.12832 −0.165664
\(622\) −87.2498 −3.49840
\(623\) −23.6491 −0.947481
\(624\) 39.1658 1.56789
\(625\) −9.72656 −0.389063
\(626\) −50.5499 −2.02038
\(627\) 22.4796 0.897749
\(628\) −67.9387 −2.71105
\(629\) 11.5876 0.462028
\(630\) 11.7284 0.467270
\(631\) −5.96553 −0.237484 −0.118742 0.992925i \(-0.537886\pi\)
−0.118742 + 0.992925i \(0.537886\pi\)
\(632\) 12.0477 0.479233
\(633\) 5.07955 0.201894
\(634\) 30.5288 1.21245
\(635\) −24.8611 −0.986581
\(636\) 14.1466 0.560949
\(637\) −22.8017 −0.903435
\(638\) −9.51791 −0.376818
\(639\) 23.0184 0.910594
\(640\) −3.40061 −0.134421
\(641\) −1.73375 −0.0684789 −0.0342395 0.999414i \(-0.510901\pi\)
−0.0342395 + 0.999414i \(0.510901\pi\)
\(642\) 28.5316 1.12605
\(643\) 38.3312 1.51163 0.755817 0.654783i \(-0.227240\pi\)
0.755817 + 0.654783i \(0.227240\pi\)
\(644\) −5.21630 −0.205551
\(645\) −17.9693 −0.707541
\(646\) −18.7064 −0.735994
\(647\) 29.2098 1.14836 0.574178 0.818730i \(-0.305322\pi\)
0.574178 + 0.818730i \(0.305322\pi\)
\(648\) −9.24813 −0.363301
\(649\) 13.5866 0.533321
\(650\) 23.9873 0.940858
\(651\) 5.08520 0.199305
\(652\) −76.3127 −2.98864
\(653\) −42.7952 −1.67471 −0.837353 0.546662i \(-0.815898\pi\)
−0.837353 + 0.546662i \(0.815898\pi\)
\(654\) 0.756371 0.0295765
\(655\) −16.3021 −0.636976
\(656\) 11.4021 0.445177
\(657\) −23.8927 −0.932143
\(658\) −0.516185 −0.0201230
\(659\) −23.7004 −0.923238 −0.461619 0.887078i \(-0.652731\pi\)
−0.461619 + 0.887078i \(0.652731\pi\)
\(660\) 25.9104 1.00856
\(661\) 24.1228 0.938268 0.469134 0.883127i \(-0.344566\pi\)
0.469134 + 0.883127i \(0.344566\pi\)
\(662\) −12.8378 −0.498954
\(663\) −4.32420 −0.167938
\(664\) 16.9535 0.657923
\(665\) −15.4883 −0.600610
\(666\) −60.0567 −2.32715
\(667\) −0.934180 −0.0361716
\(668\) −102.877 −3.98044
\(669\) −6.37921 −0.246634
\(670\) 57.2184 2.21054
\(671\) −18.4061 −0.710558
\(672\) 12.4025 0.478436
\(673\) −3.67522 −0.141669 −0.0708346 0.997488i \(-0.522566\pi\)
−0.0708346 + 0.997488i \(0.522566\pi\)
\(674\) −89.6753 −3.45416
\(675\) 10.5660 0.406687
\(676\) 26.5029 1.01934
\(677\) 45.7769 1.75935 0.879675 0.475575i \(-0.157760\pi\)
0.879675 + 0.475575i \(0.157760\pi\)
\(678\) −27.0172 −1.03759
\(679\) 9.37443 0.359758
\(680\) −12.5377 −0.480800
\(681\) 10.8255 0.414835
\(682\) −33.8391 −1.29577
\(683\) −1.52419 −0.0583215 −0.0291608 0.999575i \(-0.509283\pi\)
−0.0291608 + 0.999575i \(0.509283\pi\)
\(684\) 68.3481 2.61335
\(685\) −39.3029 −1.50169
\(686\) −41.8018 −1.59600
\(687\) 8.77800 0.334902
\(688\) 100.599 3.83532
\(689\) 13.0079 0.495561
\(690\) 3.60741 0.137332
\(691\) 20.3036 0.772386 0.386193 0.922418i \(-0.373790\pi\)
0.386193 + 0.922418i \(0.373790\pi\)
\(692\) −27.8384 −1.05826
\(693\) −8.71162 −0.330927
\(694\) 61.0689 2.31814
\(695\) 2.18821 0.0830034
\(696\) 7.92465 0.300383
\(697\) −1.25888 −0.0476833
\(698\) −41.3267 −1.56424
\(699\) −6.33739 −0.239702
\(700\) 13.3506 0.504606
\(701\) −10.3863 −0.392285 −0.196143 0.980575i \(-0.562842\pi\)
−0.196143 + 0.980575i \(0.562842\pi\)
\(702\) 55.3777 2.09010
\(703\) 79.3098 2.99123
\(704\) −21.8237 −0.822511
\(705\) 0.251656 0.00947790
\(706\) 74.0988 2.78874
\(707\) 7.15759 0.269189
\(708\) −19.4539 −0.731122
\(709\) 34.9053 1.31090 0.655448 0.755240i \(-0.272480\pi\)
0.655448 + 0.755240i \(0.272480\pi\)
\(710\) −49.7002 −1.86522
\(711\) 3.39615 0.127366
\(712\) −131.028 −4.91048
\(713\) −3.32129 −0.124383
\(714\) −3.41396 −0.127764
\(715\) 23.8248 0.890998
\(716\) −28.8611 −1.07859
\(717\) −24.5586 −0.917159
\(718\) 2.01088 0.0750454
\(719\) 5.17696 0.193068 0.0965341 0.995330i \(-0.469224\pi\)
0.0965341 + 0.995330i \(0.469224\pi\)
\(720\) 32.0113 1.19299
\(721\) 20.5505 0.765339
\(722\) −78.5646 −2.92387
\(723\) −0.980039 −0.0364480
\(724\) −19.2926 −0.717003
\(725\) 2.39094 0.0887974
\(726\) 0.767896 0.0284993
\(727\) −7.00384 −0.259758 −0.129879 0.991530i \(-0.541459\pi\)
−0.129879 + 0.991530i \(0.541459\pi\)
\(728\) 40.6881 1.50800
\(729\) 11.9141 0.441262
\(730\) 51.5880 1.90936
\(731\) −11.1069 −0.410804
\(732\) 26.3546 0.974094
\(733\) −1.22518 −0.0452530 −0.0226265 0.999744i \(-0.507203\pi\)
−0.0226265 + 0.999744i \(0.507203\pi\)
\(734\) 60.8288 2.24523
\(735\) 8.77648 0.323725
\(736\) −8.10042 −0.298586
\(737\) −42.5008 −1.56554
\(738\) 6.52455 0.240172
\(739\) −31.4569 −1.15716 −0.578580 0.815625i \(-0.696393\pi\)
−0.578580 + 0.815625i \(0.696393\pi\)
\(740\) 91.4140 3.36045
\(741\) −29.5964 −1.08725
\(742\) 10.2697 0.377014
\(743\) 17.5176 0.642659 0.321330 0.946967i \(-0.395870\pi\)
0.321330 + 0.946967i \(0.395870\pi\)
\(744\) 28.1745 1.03293
\(745\) −29.6521 −1.08637
\(746\) −72.3368 −2.64844
\(747\) 4.77904 0.174856
\(748\) 16.0154 0.585580
\(749\) 14.6016 0.533532
\(750\) −30.8115 −1.12508
\(751\) −35.2893 −1.28773 −0.643863 0.765141i \(-0.722669\pi\)
−0.643863 + 0.765141i \(0.722669\pi\)
\(752\) −1.40887 −0.0513761
\(753\) −12.3103 −0.448614
\(754\) 12.5312 0.456359
\(755\) −8.91324 −0.324386
\(756\) 30.8216 1.12097
\(757\) −17.2974 −0.628686 −0.314343 0.949309i \(-0.601784\pi\)
−0.314343 + 0.949309i \(0.601784\pi\)
\(758\) −19.0931 −0.693493
\(759\) −2.67952 −0.0972603
\(760\) −85.8129 −3.11276
\(761\) 9.53250 0.345553 0.172776 0.984961i \(-0.444726\pi\)
0.172776 + 0.984961i \(0.444726\pi\)
\(762\) −37.5066 −1.35872
\(763\) 0.387088 0.0140135
\(764\) −78.7570 −2.84933
\(765\) −3.53428 −0.127782
\(766\) 87.2034 3.15079
\(767\) −17.8880 −0.645897
\(768\) −18.2079 −0.657023
\(769\) −37.0399 −1.33569 −0.667847 0.744299i \(-0.732784\pi\)
−0.667847 + 0.744299i \(0.732784\pi\)
\(770\) 18.8097 0.677855
\(771\) 15.7166 0.566019
\(772\) −110.216 −3.96675
\(773\) −6.97450 −0.250855 −0.125428 0.992103i \(-0.540030\pi\)
−0.125428 + 0.992103i \(0.540030\pi\)
\(774\) 57.5655 2.06915
\(775\) 8.50053 0.305348
\(776\) 51.9391 1.86450
\(777\) 14.4742 0.519259
\(778\) −40.8463 −1.46441
\(779\) −8.61621 −0.308708
\(780\) −34.1134 −1.22146
\(781\) 36.9164 1.32097
\(782\) 2.22976 0.0797360
\(783\) 5.51980 0.197261
\(784\) −49.1342 −1.75479
\(785\) 24.0450 0.858204
\(786\) −24.5942 −0.877246
\(787\) 29.9359 1.06710 0.533550 0.845768i \(-0.320857\pi\)
0.533550 + 0.845768i \(0.320857\pi\)
\(788\) −64.7726 −2.30743
\(789\) 3.26559 0.116258
\(790\) −7.33281 −0.260890
\(791\) −13.8266 −0.491617
\(792\) −48.2667 −1.71508
\(793\) 24.2332 0.860547
\(794\) −21.7268 −0.771056
\(795\) −5.00680 −0.177573
\(796\) −122.685 −4.34847
\(797\) −10.7103 −0.379380 −0.189690 0.981844i \(-0.560748\pi\)
−0.189690 + 0.981844i \(0.560748\pi\)
\(798\) −23.3664 −0.827162
\(799\) 0.155550 0.00550295
\(800\) 20.7323 0.732996
\(801\) −36.9357 −1.30506
\(802\) 100.439 3.54662
\(803\) −38.3186 −1.35223
\(804\) 60.8544 2.14617
\(805\) 1.84617 0.0650688
\(806\) 44.5522 1.56928
\(807\) −7.29248 −0.256707
\(808\) 39.6567 1.39512
\(809\) −30.4625 −1.07100 −0.535502 0.844534i \(-0.679878\pi\)
−0.535502 + 0.844534i \(0.679878\pi\)
\(810\) 5.62885 0.197778
\(811\) −6.38159 −0.224088 −0.112044 0.993703i \(-0.535740\pi\)
−0.112044 + 0.993703i \(0.535740\pi\)
\(812\) 6.97449 0.244757
\(813\) −20.1918 −0.708158
\(814\) −96.3176 −3.37593
\(815\) 27.0088 0.946077
\(816\) −9.31801 −0.326196
\(817\) −76.0199 −2.65960
\(818\) 50.8788 1.77894
\(819\) 11.4696 0.400781
\(820\) −9.93121 −0.346813
\(821\) −31.3814 −1.09522 −0.547609 0.836734i \(-0.684462\pi\)
−0.547609 + 0.836734i \(0.684462\pi\)
\(822\) −59.2943 −2.06813
\(823\) −8.61720 −0.300377 −0.150188 0.988657i \(-0.547988\pi\)
−0.150188 + 0.988657i \(0.547988\pi\)
\(824\) 113.860 3.96650
\(825\) 6.85796 0.238764
\(826\) −14.1226 −0.491387
\(827\) −18.2047 −0.633039 −0.316520 0.948586i \(-0.602514\pi\)
−0.316520 + 0.948586i \(0.602514\pi\)
\(828\) −8.14693 −0.283125
\(829\) 38.0162 1.32036 0.660179 0.751108i \(-0.270480\pi\)
0.660179 + 0.751108i \(0.270480\pi\)
\(830\) −10.3187 −0.358167
\(831\) 5.07334 0.175992
\(832\) 28.7328 0.996132
\(833\) 5.42479 0.187958
\(834\) 3.30124 0.114313
\(835\) 36.4106 1.26004
\(836\) 109.615 3.79112
\(837\) 19.6246 0.678324
\(838\) 77.5224 2.67797
\(839\) 45.6228 1.57507 0.787537 0.616267i \(-0.211356\pi\)
0.787537 + 0.616267i \(0.211356\pi\)
\(840\) −15.6610 −0.540357
\(841\) −27.7509 −0.956929
\(842\) 12.4693 0.429720
\(843\) −13.8990 −0.478706
\(844\) 24.7689 0.852582
\(845\) −9.37997 −0.322681
\(846\) −0.806189 −0.0277174
\(847\) 0.392987 0.0135032
\(848\) 28.0300 0.962556
\(849\) −6.91120 −0.237192
\(850\) −5.70685 −0.195743
\(851\) −9.45354 −0.324063
\(852\) −52.8585 −1.81090
\(853\) 17.2406 0.590307 0.295153 0.955450i \(-0.404629\pi\)
0.295153 + 0.955450i \(0.404629\pi\)
\(854\) 19.1321 0.654689
\(855\) −24.1899 −0.827278
\(856\) 80.9003 2.76512
\(857\) 9.87638 0.337371 0.168685 0.985670i \(-0.446048\pi\)
0.168685 + 0.985670i \(0.446048\pi\)
\(858\) 35.9433 1.22708
\(859\) 25.8904 0.883369 0.441685 0.897170i \(-0.354381\pi\)
0.441685 + 0.897170i \(0.354381\pi\)
\(860\) −87.6220 −2.98789
\(861\) −1.57248 −0.0535899
\(862\) −13.9538 −0.475270
\(863\) −14.8445 −0.505311 −0.252656 0.967556i \(-0.581304\pi\)
−0.252656 + 0.967556i \(0.581304\pi\)
\(864\) 47.8630 1.62833
\(865\) 9.85263 0.334999
\(866\) −55.9853 −1.90246
\(867\) −15.6319 −0.530887
\(868\) 24.7964 0.841646
\(869\) 5.44668 0.184766
\(870\) −4.82331 −0.163526
\(871\) 55.9561 1.89600
\(872\) 2.14467 0.0726275
\(873\) 14.6412 0.495529
\(874\) 15.2613 0.516221
\(875\) −15.7684 −0.533070
\(876\) 54.8662 1.85376
\(877\) 42.0781 1.42088 0.710439 0.703759i \(-0.248497\pi\)
0.710439 + 0.703759i \(0.248497\pi\)
\(878\) −10.9953 −0.371072
\(879\) −2.73398 −0.0922148
\(880\) 51.3389 1.73064
\(881\) −19.0418 −0.641534 −0.320767 0.947158i \(-0.603941\pi\)
−0.320767 + 0.947158i \(0.603941\pi\)
\(882\) −28.1158 −0.946709
\(883\) 6.51087 0.219108 0.109554 0.993981i \(-0.465058\pi\)
0.109554 + 0.993981i \(0.465058\pi\)
\(884\) −21.0857 −0.709188
\(885\) 6.88517 0.231442
\(886\) −21.7150 −0.729531
\(887\) 5.59140 0.187741 0.0938704 0.995584i \(-0.470076\pi\)
0.0938704 + 0.995584i \(0.470076\pi\)
\(888\) 80.1944 2.69115
\(889\) −19.1948 −0.643773
\(890\) 79.7497 2.67322
\(891\) −4.18100 −0.140069
\(892\) −31.1063 −1.04152
\(893\) 1.06464 0.0356268
\(894\) −44.7346 −1.49615
\(895\) 10.2146 0.341437
\(896\) −2.62555 −0.0877135
\(897\) 3.52783 0.117791
\(898\) −41.0841 −1.37099
\(899\) 4.44076 0.148108
\(900\) 20.8513 0.695043
\(901\) −3.09473 −0.103100
\(902\) 10.4639 0.348411
\(903\) −13.8738 −0.461691
\(904\) −76.6063 −2.54789
\(905\) 6.82809 0.226973
\(906\) −13.4470 −0.446745
\(907\) 18.3915 0.610681 0.305340 0.952243i \(-0.401230\pi\)
0.305340 + 0.952243i \(0.401230\pi\)
\(908\) 52.7874 1.75181
\(909\) 11.1789 0.370780
\(910\) −24.7647 −0.820941
\(911\) −38.2665 −1.26783 −0.633913 0.773404i \(-0.718552\pi\)
−0.633913 + 0.773404i \(0.718552\pi\)
\(912\) −63.7759 −2.11183
\(913\) 7.66452 0.253659
\(914\) 22.6885 0.750469
\(915\) −9.32749 −0.308357
\(916\) 42.8033 1.41426
\(917\) −12.5866 −0.415646
\(918\) −13.1750 −0.434840
\(919\) −4.89962 −0.161624 −0.0808118 0.996729i \(-0.525751\pi\)
−0.0808118 + 0.996729i \(0.525751\pi\)
\(920\) 10.2287 0.337230
\(921\) 19.4327 0.640330
\(922\) −64.8669 −2.13628
\(923\) −48.6038 −1.59981
\(924\) 20.0050 0.658116
\(925\) 24.1954 0.795541
\(926\) 7.47949 0.245791
\(927\) 32.0962 1.05418
\(928\) 10.8307 0.355536
\(929\) 17.9381 0.588528 0.294264 0.955724i \(-0.404925\pi\)
0.294264 + 0.955724i \(0.404925\pi\)
\(930\) −17.1484 −0.562317
\(931\) 37.1292 1.21686
\(932\) −30.9024 −1.01224
\(933\) 32.8420 1.07520
\(934\) −12.6920 −0.415295
\(935\) −5.66820 −0.185370
\(936\) 63.5475 2.07712
\(937\) 29.8369 0.974730 0.487365 0.873198i \(-0.337958\pi\)
0.487365 + 0.873198i \(0.337958\pi\)
\(938\) 44.1773 1.44244
\(939\) 19.0276 0.620943
\(940\) 1.22712 0.0400243
\(941\) 26.8047 0.873809 0.436904 0.899508i \(-0.356075\pi\)
0.436904 + 0.899508i \(0.356075\pi\)
\(942\) 36.2755 1.18192
\(943\) 1.02703 0.0334448
\(944\) −38.5459 −1.25456
\(945\) −10.9085 −0.354852
\(946\) 92.3222 3.00165
\(947\) 2.94622 0.0957393 0.0478697 0.998854i \(-0.484757\pi\)
0.0478697 + 0.998854i \(0.484757\pi\)
\(948\) −7.79879 −0.253293
\(949\) 50.4499 1.63767
\(950\) −39.0598 −1.26727
\(951\) −11.4914 −0.372635
\(952\) −9.68017 −0.313736
\(953\) −4.62861 −0.149935 −0.0749676 0.997186i \(-0.523885\pi\)
−0.0749676 + 0.997186i \(0.523885\pi\)
\(954\) 16.0395 0.519297
\(955\) 27.8739 0.901978
\(956\) −119.753 −3.87308
\(957\) 3.58267 0.115811
\(958\) −0.505247 −0.0163238
\(959\) −30.3451 −0.979894
\(960\) −11.0594 −0.356941
\(961\) −15.2117 −0.490702
\(962\) 126.811 4.08854
\(963\) 22.8051 0.734885
\(964\) −4.77887 −0.153917
\(965\) 39.0078 1.25571
\(966\) 2.78522 0.0896130
\(967\) 20.1721 0.648689 0.324345 0.945939i \(-0.394856\pi\)
0.324345 + 0.945939i \(0.394856\pi\)
\(968\) 2.17734 0.0699825
\(969\) 7.04134 0.226200
\(970\) −31.6126 −1.01502
\(971\) 30.0251 0.963550 0.481775 0.876295i \(-0.339992\pi\)
0.481775 + 0.876295i \(0.339992\pi\)
\(972\) 76.7940 2.46317
\(973\) 1.68948 0.0541621
\(974\) 80.0853 2.56610
\(975\) −9.02913 −0.289163
\(976\) 52.2190 1.67149
\(977\) 57.7096 1.84629 0.923147 0.384448i \(-0.125608\pi\)
0.923147 + 0.384448i \(0.125608\pi\)
\(978\) 40.7469 1.30294
\(979\) −59.2366 −1.89321
\(980\) 42.7959 1.36706
\(981\) 0.604563 0.0193022
\(982\) 56.1154 1.79071
\(983\) −3.33817 −0.106471 −0.0532356 0.998582i \(-0.516953\pi\)
−0.0532356 + 0.998582i \(0.516953\pi\)
\(984\) −8.71231 −0.277738
\(985\) 22.9245 0.730435
\(986\) −2.98132 −0.0949444
\(987\) 0.194299 0.00618460
\(988\) −144.318 −4.59137
\(989\) 9.06139 0.288136
\(990\) 29.3774 0.933675
\(991\) 4.48757 0.142552 0.0712762 0.997457i \(-0.477293\pi\)
0.0712762 + 0.997457i \(0.477293\pi\)
\(992\) 38.5065 1.22258
\(993\) 4.83230 0.153349
\(994\) −38.3727 −1.21711
\(995\) 43.4212 1.37654
\(996\) −10.9744 −0.347737
\(997\) −47.4116 −1.50154 −0.750770 0.660564i \(-0.770317\pi\)
−0.750770 + 0.660564i \(0.770317\pi\)
\(998\) −57.0172 −1.80485
\(999\) 55.8582 1.76728
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 241.2.a.a.1.1 7
3.2 odd 2 2169.2.a.e.1.7 7
4.3 odd 2 3856.2.a.j.1.2 7
5.4 even 2 6025.2.a.f.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
241.2.a.a.1.1 7 1.1 even 1 trivial
2169.2.a.e.1.7 7 3.2 odd 2
3856.2.a.j.1.2 7 4.3 odd 2
6025.2.a.f.1.7 7 5.4 even 2