Properties

Label 1205.2.b.c.724.4
Level $1205$
Weight $2$
Character 1205.724
Analytic conductor $9.622$
Analytic rank $0$
Dimension $46$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1205,2,Mod(724,1205)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1205, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1205.724");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.b (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(9.62197344356\)
Analytic rank: \(0\)
Dimension: \(46\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 724.4
Character \(\chi\) \(=\) 1205.724
Dual form 1205.2.b.c.724.43

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.44838i q^{2} -0.992209i q^{3} -3.99457 q^{4} +(0.553587 - 2.16646i) q^{5} -2.42931 q^{6} -0.744704i q^{7} +4.88345i q^{8} +2.01552 q^{9} +O(q^{10})\) \(q-2.44838i q^{2} -0.992209i q^{3} -3.99457 q^{4} +(0.553587 - 2.16646i) q^{5} -2.42931 q^{6} -0.744704i q^{7} +4.88345i q^{8} +2.01552 q^{9} +(-5.30431 - 1.35539i) q^{10} -2.60457 q^{11} +3.96344i q^{12} -4.18428i q^{13} -1.82332 q^{14} +(-2.14958 - 0.549274i) q^{15} +3.96742 q^{16} +0.484012i q^{17} -4.93476i q^{18} -3.30187 q^{19} +(-2.21134 + 8.65406i) q^{20} -0.738902 q^{21} +6.37697i q^{22} +1.44005i q^{23} +4.84541 q^{24} +(-4.38708 - 2.39865i) q^{25} -10.2447 q^{26} -4.97645i q^{27} +2.97477i q^{28} +0.129471 q^{29} +(-1.34483 + 5.26299i) q^{30} +4.43651 q^{31} +0.0531507i q^{32} +2.58428i q^{33} +1.18504 q^{34} +(-1.61337 - 0.412259i) q^{35} -8.05113 q^{36} +4.67172i q^{37} +8.08424i q^{38} -4.15168 q^{39} +(10.5798 + 2.70342i) q^{40} -9.21272 q^{41} +1.80911i q^{42} +7.65578i q^{43} +10.4041 q^{44} +(1.11577 - 4.36654i) q^{45} +3.52579 q^{46} -2.28201i q^{47} -3.93651i q^{48} +6.44542 q^{49} +(-5.87280 + 10.7412i) q^{50} +0.480241 q^{51} +16.7144i q^{52} -12.5450i q^{53} -12.1842 q^{54} +(-1.44186 + 5.64269i) q^{55} +3.63673 q^{56} +3.27615i q^{57} -0.316993i q^{58} +7.30045 q^{59} +(8.58664 + 2.19411i) q^{60} -5.28903 q^{61} -10.8623i q^{62} -1.50097i q^{63} +8.06498 q^{64} +(-9.06508 - 2.31637i) q^{65} +6.32729 q^{66} +5.69391i q^{67} -1.93342i q^{68} +1.42883 q^{69} +(-1.00937 + 3.95014i) q^{70} +2.08218 q^{71} +9.84271i q^{72} -15.5697i q^{73} +11.4381 q^{74} +(-2.37996 + 4.35290i) q^{75} +13.1895 q^{76} +1.93963i q^{77} +10.1649i q^{78} +10.0023 q^{79} +(2.19631 - 8.59526i) q^{80} +1.10889 q^{81} +22.5562i q^{82} +2.71488i q^{83} +2.95159 q^{84} +(1.04859 + 0.267943i) q^{85} +18.7442 q^{86} -0.128462i q^{87} -12.7193i q^{88} +9.86499 q^{89} +(-10.6910 - 2.73182i) q^{90} -3.11605 q^{91} -5.75237i q^{92} -4.40195i q^{93} -5.58723 q^{94} +(-1.82787 + 7.15337i) q^{95} +0.0527366 q^{96} +6.26809i q^{97} -15.7808i q^{98} -5.24956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times\).

\(n\) \(242\) \(971\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.44838i 1.73127i −0.500679 0.865633i \(-0.666916\pi\)
0.500679 0.865633i \(-0.333084\pi\)
\(3\) 0.992209i 0.572852i −0.958102 0.286426i \(-0.907533\pi\)
0.958102 0.286426i \(-0.0924673\pi\)
\(4\) −3.99457 −1.99728
\(5\) 0.553587 2.16646i 0.247572 0.968870i
\(6\) −2.42931 −0.991760
\(7\) 0.744704i 0.281472i −0.990047 0.140736i \(-0.955053\pi\)
0.990047 0.140736i \(-0.0449468\pi\)
\(8\) 4.88345i 1.72656i
\(9\) 2.01552 0.671840
\(10\) −5.30431 1.35539i −1.67737 0.428612i
\(11\) −2.60457 −0.785307 −0.392654 0.919686i \(-0.628443\pi\)
−0.392654 + 0.919686i \(0.628443\pi\)
\(12\) 3.96344i 1.14415i
\(13\) 4.18428i 1.16051i −0.814434 0.580256i \(-0.802953\pi\)
0.814434 0.580256i \(-0.197047\pi\)
\(14\) −1.82332 −0.487302
\(15\) −2.14958 0.549274i −0.555019 0.141822i
\(16\) 3.96742 0.991856
\(17\) 0.484012i 0.117390i 0.998276 + 0.0586950i \(0.0186940\pi\)
−0.998276 + 0.0586950i \(0.981306\pi\)
\(18\) 4.93476i 1.16313i
\(19\) −3.30187 −0.757502 −0.378751 0.925499i \(-0.623646\pi\)
−0.378751 + 0.925499i \(0.623646\pi\)
\(20\) −2.21134 + 8.65406i −0.494471 + 1.93511i
\(21\) −0.738902 −0.161242
\(22\) 6.37697i 1.35958i
\(23\) 1.44005i 0.300271i 0.988665 + 0.150135i \(0.0479710\pi\)
−0.988665 + 0.150135i \(0.952029\pi\)
\(24\) 4.84541 0.989065
\(25\) −4.38708 2.39865i −0.877417 0.479729i
\(26\) −10.2447 −2.00915
\(27\) 4.97645i 0.957717i
\(28\) 2.97477i 0.562179i
\(29\) 0.129471 0.0240421 0.0120210 0.999928i \(-0.496173\pi\)
0.0120210 + 0.999928i \(0.496173\pi\)
\(30\) −1.34483 + 5.26299i −0.245532 + 0.960886i
\(31\) 4.43651 0.796821 0.398410 0.917207i \(-0.369562\pi\)
0.398410 + 0.917207i \(0.369562\pi\)
\(32\) 0.0531507i 0.00939580i
\(33\) 2.58428i 0.449865i
\(34\) 1.18504 0.203234
\(35\) −1.61337 0.412259i −0.272709 0.0696844i
\(36\) −8.05113 −1.34186
\(37\) 4.67172i 0.768026i 0.923328 + 0.384013i \(0.125458\pi\)
−0.923328 + 0.384013i \(0.874542\pi\)
\(38\) 8.08424i 1.31144i
\(39\) −4.15168 −0.664802
\(40\) 10.5798 + 2.70342i 1.67281 + 0.427448i
\(41\) −9.21272 −1.43878 −0.719392 0.694604i \(-0.755580\pi\)
−0.719392 + 0.694604i \(0.755580\pi\)
\(42\) 1.80911i 0.279152i
\(43\) 7.65578i 1.16749i 0.811935 + 0.583747i \(0.198414\pi\)
−0.811935 + 0.583747i \(0.801586\pi\)
\(44\) 10.4041 1.56848
\(45\) 1.11577 4.36654i 0.166329 0.650926i
\(46\) 3.52579 0.519849
\(47\) 2.28201i 0.332865i −0.986053 0.166433i \(-0.946775\pi\)
0.986053 0.166433i \(-0.0532249\pi\)
\(48\) 3.93651i 0.568187i
\(49\) 6.44542 0.920774
\(50\) −5.87280 + 10.7412i −0.830539 + 1.51904i
\(51\) 0.480241 0.0672472
\(52\) 16.7144i 2.31787i
\(53\) 12.5450i 1.72319i −0.507595 0.861596i \(-0.669465\pi\)
0.507595 0.861596i \(-0.330535\pi\)
\(54\) −12.1842 −1.65806
\(55\) −1.44186 + 5.64269i −0.194420 + 0.760860i
\(56\) 3.63673 0.485978
\(57\) 3.27615i 0.433936i
\(58\) 0.316993i 0.0416232i
\(59\) 7.30045 0.950438 0.475219 0.879868i \(-0.342369\pi\)
0.475219 + 0.879868i \(0.342369\pi\)
\(60\) 8.58664 + 2.19411i 1.10853 + 0.283259i
\(61\) −5.28903 −0.677190 −0.338595 0.940932i \(-0.609952\pi\)
−0.338595 + 0.940932i \(0.609952\pi\)
\(62\) 10.8623i 1.37951i
\(63\) 1.50097i 0.189104i
\(64\) 8.06498 1.00812
\(65\) −9.06508 2.31637i −1.12438 0.287310i
\(66\) 6.32729 0.778836
\(67\) 5.69391i 0.695621i 0.937565 + 0.347811i \(0.113075\pi\)
−0.937565 + 0.347811i \(0.886925\pi\)
\(68\) 1.93342i 0.234461i
\(69\) 1.42883 0.172011
\(70\) −1.00937 + 3.95014i −0.120642 + 0.472133i
\(71\) 2.08218 0.247109 0.123555 0.992338i \(-0.460571\pi\)
0.123555 + 0.992338i \(0.460571\pi\)
\(72\) 9.84271i 1.15997i
\(73\) 15.5697i 1.82230i −0.412076 0.911149i \(-0.635196\pi\)
0.412076 0.911149i \(-0.364804\pi\)
\(74\) 11.4381 1.32966
\(75\) −2.37996 + 4.35290i −0.274814 + 0.502630i
\(76\) 13.1895 1.51294
\(77\) 1.93963i 0.221042i
\(78\) 10.1649i 1.15095i
\(79\) 10.0023 1.12534 0.562671 0.826681i \(-0.309774\pi\)
0.562671 + 0.826681i \(0.309774\pi\)
\(80\) 2.19631 8.59526i 0.245555 0.960979i
\(81\) 1.10889 0.123210
\(82\) 22.5562i 2.49092i
\(83\) 2.71488i 0.297997i 0.988837 + 0.148999i \(0.0476050\pi\)
−0.988837 + 0.148999i \(0.952395\pi\)
\(84\) 2.95159 0.322045
\(85\) 1.04859 + 0.267943i 0.113736 + 0.0290625i
\(86\) 18.7442 2.02124
\(87\) 0.128462i 0.0137726i
\(88\) 12.7193i 1.35588i
\(89\) 9.86499 1.04569 0.522843 0.852429i \(-0.324871\pi\)
0.522843 + 0.852429i \(0.324871\pi\)
\(90\) −10.6910 2.73182i −1.12693 0.287959i
\(91\) −3.11605 −0.326651
\(92\) 5.75237i 0.599726i
\(93\) 4.40195i 0.456461i
\(94\) −5.58723 −0.576279
\(95\) −1.82787 + 7.15337i −0.187536 + 0.733920i
\(96\) 0.0527366 0.00538241
\(97\) 6.26809i 0.636428i 0.948019 + 0.318214i \(0.103083\pi\)
−0.948019 + 0.318214i \(0.896917\pi\)
\(98\) 15.7808i 1.59410i
\(99\) −5.24956 −0.527601
\(100\) 17.5245 + 9.58155i 1.75245 + 0.958155i
\(101\) 4.57863 0.455591 0.227796 0.973709i \(-0.426848\pi\)
0.227796 + 0.973709i \(0.426848\pi\)
\(102\) 1.17581i 0.116423i
\(103\) 5.95554i 0.586817i −0.955987 0.293409i \(-0.905210\pi\)
0.955987 0.293409i \(-0.0947896\pi\)
\(104\) 20.4338 2.00369
\(105\) −0.409047 + 1.60080i −0.0399189 + 0.156222i
\(106\) −30.7150 −2.98330
\(107\) 4.83097i 0.467027i 0.972354 + 0.233514i \(0.0750223\pi\)
−0.972354 + 0.233514i \(0.924978\pi\)
\(108\) 19.8787i 1.91283i
\(109\) −9.62741 −0.922138 −0.461069 0.887364i \(-0.652534\pi\)
−0.461069 + 0.887364i \(0.652534\pi\)
\(110\) 13.8154 + 3.53021i 1.31725 + 0.336592i
\(111\) 4.63532 0.439965
\(112\) 2.95456i 0.279179i
\(113\) 4.74825i 0.446677i −0.974741 0.223339i \(-0.928304\pi\)
0.974741 0.223339i \(-0.0716956\pi\)
\(114\) 8.02126 0.751260
\(115\) 3.11981 + 0.797192i 0.290923 + 0.0743386i
\(116\) −0.517179 −0.0480188
\(117\) 8.43351i 0.779678i
\(118\) 17.8743i 1.64546i
\(119\) 0.360446 0.0330420
\(120\) 2.68236 10.4974i 0.244864 0.958275i
\(121\) −4.21622 −0.383293
\(122\) 12.9495i 1.17240i
\(123\) 9.14094i 0.824211i
\(124\) −17.7219 −1.59148
\(125\) −7.62520 + 8.17657i −0.682019 + 0.731335i
\(126\) −3.67494 −0.327389
\(127\) 2.13691i 0.189620i −0.995495 0.0948099i \(-0.969776\pi\)
0.995495 0.0948099i \(-0.0302243\pi\)
\(128\) 19.6398i 1.73593i
\(129\) 7.59613 0.668802
\(130\) −5.67134 + 22.1948i −0.497410 + 1.94661i
\(131\) −15.2770 −1.33476 −0.667378 0.744719i \(-0.732584\pi\)
−0.667378 + 0.744719i \(0.732584\pi\)
\(132\) 10.3231i 0.898507i
\(133\) 2.45892i 0.213215i
\(134\) 13.9408 1.20431
\(135\) −10.7813 2.75490i −0.927903 0.237104i
\(136\) −2.36365 −0.202681
\(137\) 15.6904i 1.34052i −0.742128 0.670259i \(-0.766183\pi\)
0.742128 0.670259i \(-0.233817\pi\)
\(138\) 3.49832i 0.297797i
\(139\) −13.8387 −1.17378 −0.586891 0.809666i \(-0.699648\pi\)
−0.586891 + 0.809666i \(0.699648\pi\)
\(140\) 6.44471 + 1.64679i 0.544678 + 0.139179i
\(141\) −2.26423 −0.190683
\(142\) 5.09797i 0.427812i
\(143\) 10.8983i 0.911358i
\(144\) 7.99642 0.666369
\(145\) 0.0716732 0.280493i 0.00595214 0.0232936i
\(146\) −38.1206 −3.15488
\(147\) 6.39520i 0.527467i
\(148\) 18.6615i 1.53396i
\(149\) 4.70517 0.385463 0.192731 0.981252i \(-0.438265\pi\)
0.192731 + 0.981252i \(0.438265\pi\)
\(150\) 10.6576 + 5.82704i 0.870186 + 0.475776i
\(151\) 15.7760 1.28383 0.641914 0.766776i \(-0.278140\pi\)
0.641914 + 0.766776i \(0.278140\pi\)
\(152\) 16.1245i 1.30787i
\(153\) 0.975536i 0.0788674i
\(154\) 4.74896 0.382682
\(155\) 2.45600 9.61152i 0.197270 0.772016i
\(156\) 16.5842 1.32780
\(157\) 6.26473i 0.499980i −0.968248 0.249990i \(-0.919573\pi\)
0.968248 0.249990i \(-0.0804273\pi\)
\(158\) 24.4893i 1.94827i
\(159\) −12.4473 −0.987134
\(160\) 0.115149 + 0.0294235i 0.00910331 + 0.00232613i
\(161\) 1.07241 0.0845178
\(162\) 2.71498i 0.213309i
\(163\) 22.7092i 1.77872i 0.457204 + 0.889362i \(0.348851\pi\)
−0.457204 + 0.889362i \(0.651149\pi\)
\(164\) 36.8008 2.87366
\(165\) 5.59873 + 1.43062i 0.435860 + 0.111374i
\(166\) 6.64707 0.515913
\(167\) 18.4720i 1.42941i −0.699428 0.714703i \(-0.746562\pi\)
0.699428 0.714703i \(-0.253438\pi\)
\(168\) 3.60840i 0.278394i
\(169\) −4.50823 −0.346787
\(170\) 0.656026 2.56735i 0.0503149 0.196907i
\(171\) −6.65500 −0.508920
\(172\) 30.5815i 2.33182i
\(173\) 11.4775i 0.872615i −0.899798 0.436307i \(-0.856286\pi\)
0.899798 0.436307i \(-0.143714\pi\)
\(174\) −0.314523 −0.0238440
\(175\) −1.78628 + 3.26708i −0.135030 + 0.246968i
\(176\) −10.3334 −0.778911
\(177\) 7.24358i 0.544460i
\(178\) 24.1532i 1.81036i
\(179\) 12.4461 0.930266 0.465133 0.885241i \(-0.346006\pi\)
0.465133 + 0.885241i \(0.346006\pi\)
\(180\) −4.45700 + 17.4424i −0.332205 + 1.30008i
\(181\) −11.1005 −0.825090 −0.412545 0.910937i \(-0.635360\pi\)
−0.412545 + 0.910937i \(0.635360\pi\)
\(182\) 7.62928i 0.565520i
\(183\) 5.24782i 0.387930i
\(184\) −7.03241 −0.518436
\(185\) 10.1211 + 2.58620i 0.744117 + 0.190141i
\(186\) −10.7776 −0.790255
\(187\) 1.26064i 0.0921873i
\(188\) 9.11564i 0.664826i
\(189\) −3.70598 −0.269570
\(190\) 17.5142 + 4.47533i 1.27061 + 0.324675i
\(191\) 5.17318 0.374318 0.187159 0.982330i \(-0.440072\pi\)
0.187159 + 0.982330i \(0.440072\pi\)
\(192\) 8.00214i 0.577505i
\(193\) 14.2338i 1.02457i 0.858816 + 0.512285i \(0.171201\pi\)
−0.858816 + 0.512285i \(0.828799\pi\)
\(194\) 15.3467 1.10183
\(195\) −2.29832 + 8.99445i −0.164586 + 0.644106i
\(196\) −25.7466 −1.83905
\(197\) 6.64124i 0.473169i −0.971611 0.236585i \(-0.923972\pi\)
0.971611 0.236585i \(-0.0760280\pi\)
\(198\) 12.8529i 0.913418i
\(199\) −9.13468 −0.647541 −0.323770 0.946136i \(-0.604950\pi\)
−0.323770 + 0.946136i \(0.604950\pi\)
\(200\) 11.7137 21.4241i 0.828282 1.51491i
\(201\) 5.64954 0.398488
\(202\) 11.2102i 0.788750i
\(203\) 0.0964172i 0.00676716i
\(204\) −1.91835 −0.134312
\(205\) −5.10004 + 19.9590i −0.356202 + 1.39399i
\(206\) −14.5814 −1.01594
\(207\) 2.90245i 0.201734i
\(208\) 16.6008i 1.15106i
\(209\) 8.59996 0.594871
\(210\) 3.91937 + 1.00150i 0.270462 + 0.0691102i
\(211\) −19.5990 −1.34925 −0.674626 0.738160i \(-0.735695\pi\)
−0.674626 + 0.738160i \(0.735695\pi\)
\(212\) 50.1119i 3.44170i
\(213\) 2.06596i 0.141557i
\(214\) 11.8280 0.808548
\(215\) 16.5859 + 4.23814i 1.13115 + 0.289039i
\(216\) 24.3022 1.65356
\(217\) 3.30389i 0.224283i
\(218\) 23.5716i 1.59647i
\(219\) −15.4484 −1.04391
\(220\) 5.75959 22.5401i 0.388311 1.51965i
\(221\) 2.02524 0.136233
\(222\) 11.3490i 0.761697i
\(223\) 4.78461i 0.320401i 0.987085 + 0.160200i \(0.0512141\pi\)
−0.987085 + 0.160200i \(0.948786\pi\)
\(224\) 0.0395815 0.00264465
\(225\) −8.84226 4.83452i −0.589484 0.322302i
\(226\) −11.6255 −0.773318
\(227\) 21.1630i 1.40464i −0.711862 0.702319i \(-0.752148\pi\)
0.711862 0.702319i \(-0.247852\pi\)
\(228\) 13.0868i 0.866694i
\(229\) −22.4594 −1.48416 −0.742080 0.670311i \(-0.766161\pi\)
−0.742080 + 0.670311i \(0.766161\pi\)
\(230\) 1.95183 7.63847i 0.128700 0.503666i
\(231\) 1.92452 0.126624
\(232\) 0.632263i 0.0415101i
\(233\) 11.0004i 0.720658i 0.932825 + 0.360329i \(0.117336\pi\)
−0.932825 + 0.360329i \(0.882664\pi\)
\(234\) −20.6484 −1.34983
\(235\) −4.94388 1.26329i −0.322503 0.0824081i
\(236\) −29.1621 −1.89829
\(237\) 9.92434i 0.644655i
\(238\) 0.882508i 0.0572045i
\(239\) 2.21903 0.143537 0.0717686 0.997421i \(-0.477136\pi\)
0.0717686 + 0.997421i \(0.477136\pi\)
\(240\) −8.52829 2.17920i −0.550499 0.140667i
\(241\) 1.00000 0.0644157
\(242\) 10.3229i 0.663582i
\(243\) 16.0296i 1.02830i
\(244\) 21.1274 1.35254
\(245\) 3.56810 13.9637i 0.227957 0.892110i
\(246\) 22.3805 1.42693
\(247\) 13.8160i 0.879089i
\(248\) 21.6655i 1.37576i
\(249\) 2.69373 0.170708
\(250\) 20.0194 + 18.6694i 1.26614 + 1.18076i
\(251\) 11.1504 0.703807 0.351903 0.936036i \(-0.385535\pi\)
0.351903 + 0.936036i \(0.385535\pi\)
\(252\) 5.99571i 0.377694i
\(253\) 3.75071i 0.235805i
\(254\) −5.23196 −0.328282
\(255\) 0.265855 1.04042i 0.0166485 0.0651537i
\(256\) −31.9558 −1.99724
\(257\) 8.50879i 0.530763i −0.964143 0.265382i \(-0.914502\pi\)
0.964143 0.265382i \(-0.0854980\pi\)
\(258\) 18.5982i 1.15787i
\(259\) 3.47905 0.216177
\(260\) 36.2110 + 9.25287i 2.24571 + 0.573839i
\(261\) 0.260951 0.0161524
\(262\) 37.4039i 2.31082i
\(263\) 10.5798i 0.652377i −0.945305 0.326188i \(-0.894236\pi\)
0.945305 0.326188i \(-0.105764\pi\)
\(264\) −12.6202 −0.776720
\(265\) −27.1783 6.94476i −1.66955 0.426613i
\(266\) 6.02037 0.369132
\(267\) 9.78813i 0.599024i
\(268\) 22.7447i 1.38935i
\(269\) −6.26143 −0.381766 −0.190883 0.981613i \(-0.561135\pi\)
−0.190883 + 0.981613i \(0.561135\pi\)
\(270\) −6.74503 + 26.3966i −0.410490 + 1.60645i
\(271\) 6.22770 0.378306 0.189153 0.981948i \(-0.439426\pi\)
0.189153 + 0.981948i \(0.439426\pi\)
\(272\) 1.92028i 0.116434i
\(273\) 3.09178i 0.187123i
\(274\) −38.4160 −2.32079
\(275\) 11.4265 + 6.24744i 0.689041 + 0.376735i
\(276\) −5.70755 −0.343554
\(277\) 0.195324i 0.0117359i −0.999983 0.00586793i \(-0.998132\pi\)
0.999983 0.00586793i \(-0.00186783\pi\)
\(278\) 33.8824i 2.03213i
\(279\) 8.94188 0.535336
\(280\) 2.01325 7.87882i 0.120314 0.470850i
\(281\) −21.0354 −1.25486 −0.627432 0.778671i \(-0.715894\pi\)
−0.627432 + 0.778671i \(0.715894\pi\)
\(282\) 5.54370i 0.330123i
\(283\) 12.8269i 0.762478i 0.924477 + 0.381239i \(0.124503\pi\)
−0.924477 + 0.381239i \(0.875497\pi\)
\(284\) −8.31740 −0.493547
\(285\) 7.09764 + 1.81363i 0.420428 + 0.107430i
\(286\) 26.6831 1.57780
\(287\) 6.86075i 0.404977i
\(288\) 0.107126i 0.00631248i
\(289\) 16.7657 0.986220
\(290\) −0.686752 0.175483i −0.0403275 0.0103047i
\(291\) 6.21926 0.364579
\(292\) 62.1943i 3.63965i
\(293\) 25.7912i 1.50674i −0.657598 0.753369i \(-0.728427\pi\)
0.657598 0.753369i \(-0.271573\pi\)
\(294\) −15.6579 −0.913186
\(295\) 4.04144 15.8161i 0.235302 0.920850i
\(296\) −22.8141 −1.32604
\(297\) 12.9615i 0.752102i
\(298\) 11.5200i 0.667338i
\(299\) 6.02557 0.348468
\(300\) 9.50690 17.3880i 0.548881 1.00389i
\(301\) 5.70129 0.328617
\(302\) 38.6255i 2.22265i
\(303\) 4.54296i 0.260986i
\(304\) −13.0999 −0.751332
\(305\) −2.92794 + 11.4585i −0.167653 + 0.656109i
\(306\) 2.38848 0.136540
\(307\) 28.5348i 1.62856i −0.580469 0.814282i \(-0.697131\pi\)
0.580469 0.814282i \(-0.302869\pi\)
\(308\) 7.74799i 0.441483i
\(309\) −5.90914 −0.336160
\(310\) −23.5326 6.01321i −1.33656 0.341527i
\(311\) 4.04451 0.229343 0.114672 0.993403i \(-0.463418\pi\)
0.114672 + 0.993403i \(0.463418\pi\)
\(312\) 20.2746i 1.14782i
\(313\) 10.8140i 0.611243i −0.952153 0.305622i \(-0.901136\pi\)
0.952153 0.305622i \(-0.0988643\pi\)
\(314\) −15.3384 −0.865598
\(315\) −3.25178 0.830916i −0.183217 0.0468168i
\(316\) −39.9547 −2.24763
\(317\) 2.62335i 0.147342i −0.997283 0.0736711i \(-0.976528\pi\)
0.997283 0.0736711i \(-0.0234715\pi\)
\(318\) 30.4757i 1.70899i
\(319\) −0.337215 −0.0188804
\(320\) 4.46467 17.4724i 0.249583 0.976739i
\(321\) 4.79333 0.267538
\(322\) 2.62567i 0.146323i
\(323\) 1.59815i 0.0889232i
\(324\) −4.42953 −0.246085
\(325\) −10.0366 + 18.3568i −0.556731 + 1.01825i
\(326\) 55.6008 3.07944
\(327\) 9.55240i 0.528249i
\(328\) 44.9899i 2.48415i
\(329\) −1.69942 −0.0936922
\(330\) 3.50271 13.7078i 0.192818 0.754590i
\(331\) −10.6123 −0.583307 −0.291653 0.956524i \(-0.594205\pi\)
−0.291653 + 0.956524i \(0.594205\pi\)
\(332\) 10.8448i 0.595185i
\(333\) 9.41594i 0.515991i
\(334\) −45.2264 −2.47468
\(335\) 12.3356 + 3.15207i 0.673966 + 0.172216i
\(336\) −2.93154 −0.159928
\(337\) 3.53987i 0.192829i −0.995341 0.0964146i \(-0.969263\pi\)
0.995341 0.0964146i \(-0.0307375\pi\)
\(338\) 11.0379i 0.600381i
\(339\) −4.71125 −0.255880
\(340\) −4.18867 1.07031i −0.227162 0.0580460i
\(341\) −11.5552 −0.625749
\(342\) 16.2940i 0.881076i
\(343\) 10.0129i 0.540643i
\(344\) −37.3866 −2.01575
\(345\) 0.790981 3.09550i 0.0425850 0.166656i
\(346\) −28.1012 −1.51073
\(347\) 13.6131i 0.730791i 0.930852 + 0.365396i \(0.119066\pi\)
−0.930852 + 0.365396i \(0.880934\pi\)
\(348\) 0.513149i 0.0275077i
\(349\) −3.51082 −0.187930 −0.0939649 0.995576i \(-0.529954\pi\)
−0.0939649 + 0.995576i \(0.529954\pi\)
\(350\) 7.99905 + 4.37350i 0.427567 + 0.233773i
\(351\) −20.8229 −1.11144
\(352\) 0.138435i 0.00737859i
\(353\) 10.7398i 0.571621i 0.958286 + 0.285810i \(0.0922627\pi\)
−0.958286 + 0.285810i \(0.907737\pi\)
\(354\) −17.7350 −0.942606
\(355\) 1.15267 4.51095i 0.0611772 0.239417i
\(356\) −39.4063 −2.08853
\(357\) 0.357637i 0.0189282i
\(358\) 30.4728i 1.61054i
\(359\) −12.0903 −0.638099 −0.319050 0.947738i \(-0.603364\pi\)
−0.319050 + 0.947738i \(0.603364\pi\)
\(360\) 21.3238 + 5.44879i 1.12386 + 0.287177i
\(361\) −8.09763 −0.426191
\(362\) 27.1781i 1.42845i
\(363\) 4.18337i 0.219570i
\(364\) 12.4473 0.652415
\(365\) −33.7312 8.61920i −1.76557 0.451150i
\(366\) 12.8487 0.671610
\(367\) 2.89274i 0.151000i −0.997146 0.0754999i \(-0.975945\pi\)
0.997146 0.0754999i \(-0.0240553\pi\)
\(368\) 5.71328i 0.297825i
\(369\) −18.5684 −0.966634
\(370\) 6.33201 24.7803i 0.329185 1.28826i
\(371\) −9.34233 −0.485030
\(372\) 17.5839i 0.911681i
\(373\) 37.8889i 1.96181i 0.194479 + 0.980907i \(0.437698\pi\)
−0.194479 + 0.980907i \(0.562302\pi\)
\(374\) −3.08653 −0.159601
\(375\) 8.11287 + 7.56579i 0.418947 + 0.390696i
\(376\) 11.1441 0.574713
\(377\) 0.541741i 0.0279011i
\(378\) 9.07365i 0.466698i
\(379\) 9.33140 0.479322 0.239661 0.970857i \(-0.422964\pi\)
0.239661 + 0.970857i \(0.422964\pi\)
\(380\) 7.30156 28.5746i 0.374562 1.46585i
\(381\) −2.12026 −0.108624
\(382\) 12.6659i 0.648044i
\(383\) 34.9438i 1.78554i 0.450510 + 0.892771i \(0.351242\pi\)
−0.450510 + 0.892771i \(0.648758\pi\)
\(384\) −19.4868 −0.994433
\(385\) 4.20213 + 1.07376i 0.214161 + 0.0547237i
\(386\) 34.8497 1.77380
\(387\) 15.4304i 0.784370i
\(388\) 25.0383i 1.27113i
\(389\) 22.2652 1.12889 0.564445 0.825470i \(-0.309090\pi\)
0.564445 + 0.825470i \(0.309090\pi\)
\(390\) 22.0218 + 5.62716i 1.11512 + 0.284942i
\(391\) −0.697000 −0.0352488
\(392\) 31.4759i 1.58977i
\(393\) 15.1580i 0.764618i
\(394\) −16.2603 −0.819182
\(395\) 5.53712 21.6695i 0.278603 1.09031i
\(396\) 20.9697 1.05377
\(397\) 18.6917i 0.938110i −0.883169 0.469055i \(-0.844595\pi\)
0.883169 0.469055i \(-0.155405\pi\)
\(398\) 22.3652i 1.12107i
\(399\) 2.43976 0.122141
\(400\) −17.4054 9.51644i −0.870271 0.475822i
\(401\) 30.3420 1.51521 0.757604 0.652715i \(-0.226370\pi\)
0.757604 + 0.652715i \(0.226370\pi\)
\(402\) 13.8322i 0.689889i
\(403\) 18.5636i 0.924720i
\(404\) −18.2897 −0.909944
\(405\) 0.613867 2.40236i 0.0305033 0.119374i
\(406\) −0.236066 −0.0117158
\(407\) 12.1678i 0.603136i
\(408\) 2.34523i 0.116106i
\(409\) −16.1799 −0.800046 −0.400023 0.916505i \(-0.630998\pi\)
−0.400023 + 0.916505i \(0.630998\pi\)
\(410\) 48.8671 + 12.4868i 2.41338 + 0.616681i
\(411\) −15.5681 −0.767918
\(412\) 23.7898i 1.17204i
\(413\) 5.43668i 0.267521i
\(414\) 7.10630 0.349255
\(415\) 5.88168 + 1.50292i 0.288720 + 0.0737757i
\(416\) 0.222398 0.0109039
\(417\) 13.7309i 0.672404i
\(418\) 21.0560i 1.02988i
\(419\) −14.4615 −0.706488 −0.353244 0.935531i \(-0.614921\pi\)
−0.353244 + 0.935531i \(0.614921\pi\)
\(420\) 1.63396 6.39450i 0.0797293 0.312020i
\(421\) 14.6314 0.713093 0.356546 0.934278i \(-0.383954\pi\)
0.356546 + 0.934278i \(0.383954\pi\)
\(422\) 47.9858i 2.33591i
\(423\) 4.59944i 0.223632i
\(424\) 61.2631 2.97520
\(425\) 1.16097 2.12340i 0.0563155 0.103000i
\(426\) −5.05825 −0.245073
\(427\) 3.93876i 0.190610i
\(428\) 19.2976i 0.932785i
\(429\) 10.8133 0.522073
\(430\) 10.3766 40.6086i 0.500403 1.95832i
\(431\) 17.3814 0.837233 0.418616 0.908163i \(-0.362515\pi\)
0.418616 + 0.908163i \(0.362515\pi\)
\(432\) 19.7437i 0.949917i
\(433\) 22.7286i 1.09227i −0.837698 0.546133i \(-0.816099\pi\)
0.837698 0.546133i \(-0.183901\pi\)
\(434\) −8.08917 −0.388293
\(435\) −0.278307 0.0711148i −0.0133438 0.00340969i
\(436\) 38.4573 1.84177
\(437\) 4.75486i 0.227456i
\(438\) 37.8236i 1.80728i
\(439\) 36.3500 1.73489 0.867446 0.497531i \(-0.165760\pi\)
0.867446 + 0.497531i \(0.165760\pi\)
\(440\) −27.5558 7.04124i −1.31367 0.335678i
\(441\) 12.9909 0.618613
\(442\) 4.95856i 0.235855i
\(443\) 41.2429i 1.95951i −0.200201 0.979755i \(-0.564159\pi\)
0.200201 0.979755i \(-0.435841\pi\)
\(444\) −18.5161 −0.878735
\(445\) 5.46113 21.3721i 0.258882 1.01313i
\(446\) 11.7145 0.554699
\(447\) 4.66851i 0.220813i
\(448\) 6.00602i 0.283758i
\(449\) −1.81576 −0.0856909 −0.0428454 0.999082i \(-0.513642\pi\)
−0.0428454 + 0.999082i \(0.513642\pi\)
\(450\) −11.8368 + 21.6492i −0.557990 + 1.02055i
\(451\) 23.9952 1.12989
\(452\) 18.9672i 0.892141i
\(453\) 15.6530i 0.735444i
\(454\) −51.8151 −2.43180
\(455\) −1.72501 + 6.75080i −0.0808696 + 0.316482i
\(456\) −15.9989 −0.749218
\(457\) 9.57207i 0.447763i 0.974616 + 0.223881i \(0.0718728\pi\)
−0.974616 + 0.223881i \(0.928127\pi\)
\(458\) 54.9892i 2.56948i
\(459\) 2.40866 0.112427
\(460\) −12.4623 3.18444i −0.581056 0.148475i
\(461\) −7.96834 −0.371123 −0.185561 0.982633i \(-0.559410\pi\)
−0.185561 + 0.982633i \(0.559410\pi\)
\(462\) 4.71196i 0.219220i
\(463\) 20.5525i 0.955157i −0.878589 0.477579i \(-0.841515\pi\)
0.878589 0.477579i \(-0.158485\pi\)
\(464\) 0.513664 0.0238463
\(465\) −9.53663 2.43686i −0.442251 0.113007i
\(466\) 26.9331 1.24765
\(467\) 15.8957i 0.735567i −0.929912 0.367783i \(-0.880117\pi\)
0.929912 0.367783i \(-0.119883\pi\)
\(468\) 33.6882i 1.55724i
\(469\) 4.24027 0.195798
\(470\) −3.09302 + 12.1045i −0.142670 + 0.558339i
\(471\) −6.21592 −0.286415
\(472\) 35.6514i 1.64099i
\(473\) 19.9400i 0.916842i
\(474\) −24.2985 −1.11607
\(475\) 14.4856 + 7.92003i 0.664644 + 0.363396i
\(476\) −1.43982 −0.0659942
\(477\) 25.2848i 1.15771i
\(478\) 5.43303i 0.248501i
\(479\) 41.6793 1.90437 0.952187 0.305516i \(-0.0988289\pi\)
0.952187 + 0.305516i \(0.0988289\pi\)
\(480\) 0.0291943 0.114252i 0.00133253 0.00521485i
\(481\) 19.5478 0.891303
\(482\) 2.44838i 0.111521i
\(483\) 1.06406i 0.0484162i
\(484\) 16.8420 0.765544
\(485\) 13.5796 + 3.46994i 0.616616 + 0.157562i
\(486\) −39.2465 −1.78026
\(487\) 7.56632i 0.342863i −0.985196 0.171431i \(-0.945161\pi\)
0.985196 0.171431i \(-0.0548392\pi\)
\(488\) 25.8287i 1.16921i
\(489\) 22.5323 1.01895
\(490\) −34.1885 8.73606i −1.54448 0.394655i
\(491\) −26.7723 −1.20822 −0.604108 0.796903i \(-0.706470\pi\)
−0.604108 + 0.796903i \(0.706470\pi\)
\(492\) 36.5141i 1.64618i
\(493\) 0.0626653i 0.00282230i
\(494\) 33.8268 1.52194
\(495\) −2.90609 + 11.3730i −0.130619 + 0.511177i
\(496\) 17.6015 0.790331
\(497\) 1.55061i 0.0695543i
\(498\) 6.59528i 0.295542i
\(499\) 27.0405 1.21050 0.605249 0.796036i \(-0.293074\pi\)
0.605249 + 0.796036i \(0.293074\pi\)
\(500\) 30.4594 32.6619i 1.36218 1.46068i
\(501\) −18.3281 −0.818838
\(502\) 27.3004i 1.21848i
\(503\) 0.950190i 0.0423669i −0.999776 0.0211834i \(-0.993257\pi\)
0.999776 0.0211834i \(-0.00674340\pi\)
\(504\) 7.32990 0.326500
\(505\) 2.53467 9.91942i 0.112791 0.441408i
\(506\) −9.18315 −0.408241
\(507\) 4.47311i 0.198658i
\(508\) 8.53601i 0.378724i
\(509\) 32.8758 1.45719 0.728596 0.684944i \(-0.240173\pi\)
0.728596 + 0.684944i \(0.240173\pi\)
\(510\) −2.54735 0.650914i −0.112798 0.0288230i
\(511\) −11.5948 −0.512926
\(512\) 38.9603i 1.72182i
\(513\) 16.4316i 0.725473i
\(514\) −20.8327 −0.918893
\(515\) −12.9024 3.29691i −0.568549 0.145279i
\(516\) −30.3432 −1.33579
\(517\) 5.94365i 0.261402i
\(518\) 8.51803i 0.374261i
\(519\) −11.3880 −0.499879
\(520\) 11.3119 44.2689i 0.496058 1.94132i
\(521\) −7.96960 −0.349155 −0.174577 0.984643i \(-0.555856\pi\)
−0.174577 + 0.984643i \(0.555856\pi\)
\(522\) 0.638906i 0.0279642i
\(523\) 16.8372i 0.736240i 0.929778 + 0.368120i \(0.119999\pi\)
−0.929778 + 0.368120i \(0.880001\pi\)
\(524\) 61.0249 2.66589
\(525\) 3.24163 + 1.77237i 0.141476 + 0.0773524i
\(526\) −25.9033 −1.12944
\(527\) 2.14732i 0.0935389i
\(528\) 10.2529i 0.446201i
\(529\) 20.9263 0.909837
\(530\) −17.0034 + 66.5428i −0.738582 + 2.89043i
\(531\) 14.7142 0.638543
\(532\) 9.82231i 0.425851i
\(533\) 38.5486i 1.66973i
\(534\) −23.9651 −1.03707
\(535\) 10.4661 + 2.67436i 0.452488 + 0.115623i
\(536\) −27.8059 −1.20103
\(537\) 12.3491i 0.532905i
\(538\) 15.3304i 0.660939i
\(539\) −16.7875 −0.723090
\(540\) 43.0665 + 11.0046i 1.85329 + 0.473563i
\(541\) 22.9397 0.986254 0.493127 0.869957i \(-0.335854\pi\)
0.493127 + 0.869957i \(0.335854\pi\)
\(542\) 15.2478i 0.654948i
\(543\) 11.0140i 0.472655i
\(544\) −0.0257256 −0.00110297
\(545\) −5.32961 + 20.8574i −0.228295 + 0.893432i
\(546\) 7.56984 0.323959
\(547\) 8.56387i 0.366164i 0.983098 + 0.183082i \(0.0586075\pi\)
−0.983098 + 0.183082i \(0.941393\pi\)
\(548\) 62.6761i 2.67739i
\(549\) −10.6601 −0.454964
\(550\) 15.2961 27.9763i 0.652228 1.19291i
\(551\) −0.427495 −0.0182119
\(552\) 6.97762i 0.296987i
\(553\) 7.44873i 0.316752i
\(554\) −0.478227 −0.0203179
\(555\) 2.56605 10.0422i 0.108923 0.426269i
\(556\) 55.2795 2.34437
\(557\) 6.79073i 0.287732i −0.989597 0.143866i \(-0.954046\pi\)
0.989597 0.143866i \(-0.0459535\pi\)
\(558\) 21.8931i 0.926810i
\(559\) 32.0339 1.35489
\(560\) −6.40092 1.63560i −0.270488 0.0691169i
\(561\) −1.25082 −0.0528097
\(562\) 51.5025i 2.17250i
\(563\) 20.2542i 0.853612i 0.904343 + 0.426806i \(0.140361\pi\)
−0.904343 + 0.426806i \(0.859639\pi\)
\(564\) 9.04462 0.380847
\(565\) −10.2869 2.62857i −0.432772 0.110585i
\(566\) 31.4050 1.32005
\(567\) 0.825794i 0.0346801i
\(568\) 10.1682i 0.426649i
\(569\) 31.2543 1.31025 0.655125 0.755521i \(-0.272616\pi\)
0.655125 + 0.755521i \(0.272616\pi\)
\(570\) 4.44046 17.3777i 0.185991 0.727873i
\(571\) −31.1637 −1.30416 −0.652081 0.758149i \(-0.726104\pi\)
−0.652081 + 0.758149i \(0.726104\pi\)
\(572\) 43.5338i 1.82024i
\(573\) 5.13287i 0.214429i
\(574\) 16.7977 0.701123
\(575\) 3.45417 6.31761i 0.144049 0.263463i
\(576\) 16.2551 0.677297
\(577\) 30.7522i 1.28023i −0.768280 0.640114i \(-0.778887\pi\)
0.768280 0.640114i \(-0.221113\pi\)
\(578\) 41.0489i 1.70741i
\(579\) 14.1229 0.586927
\(580\) −0.286303 + 1.12045i −0.0118881 + 0.0465240i
\(581\) 2.02179 0.0838778
\(582\) 15.2271i 0.631184i
\(583\) 32.6744i 1.35323i
\(584\) 76.0341 3.14631
\(585\) −18.2709 4.66868i −0.755407 0.193026i
\(586\) −63.1467 −2.60857
\(587\) 17.7844i 0.734042i −0.930213 0.367021i \(-0.880378\pi\)
0.930213 0.367021i \(-0.119622\pi\)
\(588\) 25.5460i 1.05350i
\(589\) −14.6488 −0.603593
\(590\) −38.7239 9.89497i −1.59424 0.407370i
\(591\) −6.58950 −0.271056
\(592\) 18.5347i 0.761770i
\(593\) 1.96286i 0.0806051i −0.999188 0.0403026i \(-0.987168\pi\)
0.999188 0.0403026i \(-0.0128322\pi\)
\(594\) 31.7347 1.30209
\(595\) 0.199538 0.780890i 0.00818026 0.0320134i
\(596\) −18.7951 −0.769878
\(597\) 9.06352i 0.370945i
\(598\) 14.7529i 0.603291i
\(599\) 26.8177 1.09574 0.547871 0.836563i \(-0.315438\pi\)
0.547871 + 0.836563i \(0.315438\pi\)
\(600\) −21.2572 11.6224i −0.867822 0.474483i
\(601\) 31.3885 1.28036 0.640182 0.768223i \(-0.278859\pi\)
0.640182 + 0.768223i \(0.278859\pi\)
\(602\) 13.9589i 0.568923i
\(603\) 11.4762i 0.467346i
\(604\) −63.0181 −2.56417
\(605\) −2.33405 + 9.13427i −0.0948924 + 0.371361i
\(606\) −11.1229 −0.451837
\(607\) 31.9764i 1.29788i 0.760839 + 0.648941i \(0.224788\pi\)
−0.760839 + 0.648941i \(0.775212\pi\)
\(608\) 0.175497i 0.00711733i
\(609\) −0.0956661 −0.00387658
\(610\) 28.0547 + 7.16870i 1.13590 + 0.290252i
\(611\) −9.54858 −0.386294
\(612\) 3.89684i 0.157521i
\(613\) 19.1393i 0.773028i −0.922283 0.386514i \(-0.873679\pi\)
0.922283 0.386514i \(-0.126321\pi\)
\(614\) −69.8639 −2.81948
\(615\) 19.8035 + 5.06031i 0.798553 + 0.204051i
\(616\) −9.47211 −0.381642
\(617\) 40.5121i 1.63096i −0.578788 0.815478i \(-0.696474\pi\)
0.578788 0.815478i \(-0.303526\pi\)
\(618\) 14.4678i 0.581982i
\(619\) 8.35556 0.335838 0.167919 0.985801i \(-0.446295\pi\)
0.167919 + 0.985801i \(0.446295\pi\)
\(620\) −9.81063 + 38.3938i −0.394005 + 1.54193i
\(621\) 7.16632 0.287575
\(622\) 9.90251i 0.397054i
\(623\) 7.34650i 0.294331i
\(624\) −16.4715 −0.659387
\(625\) 13.4930 + 21.0461i 0.539720 + 0.841845i
\(626\) −26.4768 −1.05822
\(627\) 8.53295i 0.340773i
\(628\) 25.0249i 0.998601i
\(629\) −2.26117 −0.0901586
\(630\) −2.03440 + 7.96160i −0.0810524 + 0.317198i
\(631\) 18.3668 0.731169 0.365585 0.930778i \(-0.380869\pi\)
0.365585 + 0.930778i \(0.380869\pi\)
\(632\) 48.8456i 1.94297i
\(633\) 19.4463i 0.772922i
\(634\) −6.42297 −0.255089
\(635\) −4.62952 1.18296i −0.183717 0.0469445i
\(636\) 49.7215 1.97159
\(637\) 26.9694i 1.06857i
\(638\) 0.825630i 0.0326870i
\(639\) 4.19668 0.166018
\(640\) −42.5489 10.8724i −1.68189 0.429768i
\(641\) −21.6917 −0.856772 −0.428386 0.903596i \(-0.640918\pi\)
−0.428386 + 0.903596i \(0.640918\pi\)
\(642\) 11.7359i 0.463179i
\(643\) 23.2362i 0.916347i 0.888863 + 0.458174i \(0.151496\pi\)
−0.888863 + 0.458174i \(0.848504\pi\)
\(644\) −4.28381 −0.168806
\(645\) 4.20512 16.4567i 0.165576 0.647982i
\(646\) −3.91287 −0.153950
\(647\) 24.4246i 0.960232i 0.877205 + 0.480116i \(0.159405\pi\)
−0.877205 + 0.480116i \(0.840595\pi\)
\(648\) 5.41521i 0.212729i
\(649\) −19.0145 −0.746386
\(650\) 44.9444 + 24.5735i 1.76287 + 0.963850i
\(651\) −3.27815 −0.128481
\(652\) 90.7135i 3.55261i
\(653\) 13.0994i 0.512618i −0.966595 0.256309i \(-0.917494\pi\)
0.966595 0.256309i \(-0.0825064\pi\)
\(654\) 23.3879 0.914540
\(655\) −8.45714 + 33.0970i −0.330448 + 1.29321i
\(656\) −36.5507 −1.42707
\(657\) 31.3811i 1.22429i
\(658\) 4.16083i 0.162206i
\(659\) 37.3844 1.45629 0.728145 0.685423i \(-0.240383\pi\)
0.728145 + 0.685423i \(0.240383\pi\)
\(660\) −22.3645 5.71471i −0.870536 0.222445i
\(661\) 30.5258 1.18731 0.593657 0.804718i \(-0.297683\pi\)
0.593657 + 0.804718i \(0.297683\pi\)
\(662\) 25.9830i 1.00986i
\(663\) 2.00946i 0.0780411i
\(664\) −13.2580 −0.514511
\(665\) 5.32714 + 1.36123i 0.206578 + 0.0527861i
\(666\) 23.0538 0.893317
\(667\) 0.186444i 0.00721913i
\(668\) 73.7876i 2.85493i
\(669\) 4.74733 0.183542
\(670\) 7.71747 30.2023i 0.298152 1.16682i
\(671\) 13.7756 0.531802
\(672\) 0.0392732i 0.00151499i
\(673\) 18.0019i 0.693923i −0.937879 0.346962i \(-0.887213\pi\)
0.937879 0.346962i \(-0.112787\pi\)
\(674\) −8.66696 −0.333839
\(675\) −11.9367 + 21.8321i −0.459445 + 0.840317i
\(676\) 18.0084 0.692632
\(677\) 1.78554i 0.0686239i 0.999411 + 0.0343119i \(0.0109240\pi\)
−0.999411 + 0.0343119i \(0.989076\pi\)
\(678\) 11.5349i 0.442997i
\(679\) 4.66787 0.179137
\(680\) −1.30849 + 5.12075i −0.0501781 + 0.196372i
\(681\) −20.9981 −0.804650
\(682\) 28.2915i 1.08334i
\(683\) 16.9962i 0.650343i 0.945655 + 0.325171i \(0.105422\pi\)
−0.945655 + 0.325171i \(0.894578\pi\)
\(684\) 26.5838 1.01646
\(685\) −33.9925 8.68598i −1.29879 0.331874i
\(686\) −24.5153 −0.935998
\(687\) 22.2844i 0.850205i
\(688\) 30.3737i 1.15799i
\(689\) −52.4919 −1.99978
\(690\) −7.57896 1.93662i −0.288526 0.0737260i
\(691\) −9.73250 −0.370242 −0.185121 0.982716i \(-0.559268\pi\)
−0.185121 + 0.982716i \(0.559268\pi\)
\(692\) 45.8475i 1.74286i
\(693\) 3.90937i 0.148505i
\(694\) 33.3301 1.26519
\(695\) −7.66092 + 29.9809i −0.290595 + 1.13724i
\(696\) 0.627338 0.0237792
\(697\) 4.45906i 0.168899i
\(698\) 8.59582i 0.325356i
\(699\) 10.9147 0.412831
\(700\) 7.13542 13.0506i 0.269694 0.493265i
\(701\) 31.1728 1.17738 0.588690 0.808359i \(-0.299644\pi\)
0.588690 + 0.808359i \(0.299644\pi\)
\(702\) 50.9823i 1.92420i
\(703\) 15.4254i 0.581781i
\(704\) −21.0058 −0.791686
\(705\) −1.25345 + 4.90536i −0.0472076 + 0.184747i
\(706\) 26.2951 0.989627
\(707\) 3.40973i 0.128236i
\(708\) 28.9349i 1.08744i
\(709\) 47.2147 1.77318 0.886592 0.462552i \(-0.153066\pi\)
0.886592 + 0.462552i \(0.153066\pi\)
\(710\) −11.0445 2.82217i −0.414494 0.105914i
\(711\) 20.1598 0.756050
\(712\) 48.1752i 1.80544i
\(713\) 6.38879i 0.239262i
\(714\) −0.875632 −0.0327697
\(715\) 23.6106 + 6.03313i 0.882987 + 0.225626i
\(716\) −49.7168 −1.85801
\(717\) 2.20174i 0.0822256i
\(718\) 29.6015i 1.10472i
\(719\) −10.9829 −0.409592 −0.204796 0.978805i \(-0.565653\pi\)
−0.204796 + 0.978805i \(0.565653\pi\)
\(720\) 4.42672 17.3239i 0.164974 0.645624i
\(721\) −4.43512 −0.165172
\(722\) 19.8261i 0.737851i
\(723\) 0.992209i 0.0369007i
\(724\) 44.3415 1.64794
\(725\) −0.567998 0.310554i −0.0210949 0.0115337i
\(726\) 10.2425 0.380134
\(727\) 4.07723i 0.151216i 0.997138 + 0.0756080i \(0.0240898\pi\)
−0.997138 + 0.0756080i \(0.975910\pi\)
\(728\) 15.2171i 0.563983i
\(729\) −12.5780 −0.465853
\(730\) −21.1031 + 82.5867i −0.781060 + 3.05667i
\(731\) −3.70549 −0.137052
\(732\) 20.9628i 0.774806i
\(733\) 13.3951i 0.494759i 0.968919 + 0.247379i \(0.0795694\pi\)
−0.968919 + 0.247379i \(0.920431\pi\)
\(734\) −7.08253 −0.261421
\(735\) −13.8549 3.54030i −0.511047 0.130586i
\(736\) −0.0765396 −0.00282129
\(737\) 14.8302i 0.546276i
\(738\) 45.4626i 1.67350i
\(739\) −22.3405 −0.821810 −0.410905 0.911678i \(-0.634787\pi\)
−0.410905 + 0.911678i \(0.634787\pi\)
\(740\) −40.4293 10.3308i −1.48621 0.379766i
\(741\) 13.7083 0.503588
\(742\) 22.8736i 0.839716i
\(743\) 36.1839i 1.32746i 0.747973 + 0.663730i \(0.231027\pi\)
−0.747973 + 0.663730i \(0.768973\pi\)
\(744\) 21.4967 0.788107
\(745\) 2.60472 10.1936i 0.0954296 0.373463i
\(746\) 92.7665 3.39642
\(747\) 5.47191i 0.200207i
\(748\) 5.03572i 0.184124i
\(749\) 3.59764 0.131455
\(750\) 18.5239 19.8634i 0.676399 0.725308i
\(751\) −10.1216 −0.369341 −0.184671 0.982800i \(-0.559122\pi\)
−0.184671 + 0.982800i \(0.559122\pi\)
\(752\) 9.05370i 0.330155i
\(753\) 11.0635i 0.403177i
\(754\) −1.32639 −0.0483042
\(755\) 8.73336 34.1779i 0.317840 1.24386i
\(756\) 14.8038 0.538408
\(757\) 32.6680i 1.18734i 0.804709 + 0.593670i \(0.202321\pi\)
−0.804709 + 0.593670i \(0.797679\pi\)
\(758\) 22.8468i 0.829834i
\(759\) −3.72148 −0.135081
\(760\) −34.9332 8.92634i −1.26716 0.323792i
\(761\) 24.2568 0.879309 0.439655 0.898167i \(-0.355101\pi\)
0.439655 + 0.898167i \(0.355101\pi\)
\(762\) 5.19120i 0.188057i
\(763\) 7.16957i 0.259556i
\(764\) −20.6646 −0.747619
\(765\) 2.11346 + 0.540044i 0.0764122 + 0.0195253i
\(766\) 85.5556 3.09125
\(767\) 30.5472i 1.10299i
\(768\) 31.7069i 1.14412i
\(769\) 16.5744 0.597689 0.298845 0.954302i \(-0.403399\pi\)
0.298845 + 0.954302i \(0.403399\pi\)
\(770\) 2.62896 10.2884i 0.0947412 0.370769i
\(771\) −8.44249 −0.304049
\(772\) 56.8578i 2.04636i
\(773\) 37.9826i 1.36614i 0.730353 + 0.683070i \(0.239356\pi\)
−0.730353 + 0.683070i \(0.760644\pi\)
\(774\) 37.7794 1.35795
\(775\) −19.4633 10.6416i −0.699144 0.382258i
\(776\) −30.6099 −1.09883
\(777\) 3.45194i 0.123838i
\(778\) 54.5137i 1.95441i
\(779\) 30.4192 1.08988
\(780\) 9.18079 35.9289i 0.328725 1.28646i
\(781\) −5.42318 −0.194057
\(782\) 1.70652i 0.0610251i
\(783\) 0.644303i 0.0230255i
\(784\) 25.5717 0.913275
\(785\) −13.5723 3.46807i −0.484415 0.123781i
\(786\) 37.1125 1.32376
\(787\) 1.38906i 0.0495146i 0.999693 + 0.0247573i \(0.00788129\pi\)
−0.999693 + 0.0247573i \(0.992119\pi\)
\(788\) 26.5289i 0.945052i
\(789\) −10.4973 −0.373715
\(790\) −53.0551 13.5570i −1.88762 0.482336i
\(791\) −3.53604 −0.125727
\(792\) 25.6360i 0.910936i
\(793\) 22.1308i 0.785887i
\(794\) −45.7644 −1.62412
\(795\) −6.89066 + 26.9665i −0.244386 + 0.956404i
\(796\) 36.4891 1.29332
\(797\) 48.2065i 1.70756i 0.520632 + 0.853781i \(0.325696\pi\)
−0.520632 + 0.853781i \(0.674304\pi\)
\(798\) 5.97346i 0.211458i
\(799\) 1.10452 0.0390751
\(800\) 0.127490 0.233176i 0.00450744 0.00824403i
\(801\) 19.8831 0.702534
\(802\) 74.2888i 2.62323i
\(803\) 40.5524i 1.43106i
\(804\) −22.5675 −0.795893
\(805\) 0.593672 2.32333i 0.0209242 0.0818867i
\(806\) −45.4508 −1.60094
\(807\) 6.21265i 0.218695i
\(808\) 22.3596i 0.786606i
\(809\) −14.6738 −0.515902 −0.257951 0.966158i \(-0.583047\pi\)
−0.257951 + 0.966158i \(0.583047\pi\)
\(810\) −5.88189 1.50298i −0.206669 0.0528093i
\(811\) −19.7745 −0.694377 −0.347189 0.937795i \(-0.612864\pi\)
−0.347189 + 0.937795i \(0.612864\pi\)
\(812\) 0.385145i 0.0135159i
\(813\) 6.17918i 0.216713i
\(814\) −29.7914 −1.04419
\(815\) 49.1986 + 12.5715i 1.72335 + 0.440362i
\(816\) 1.90532 0.0666995
\(817\) 25.2784i 0.884379i
\(818\) 39.6146i 1.38509i
\(819\) −6.28047 −0.219457
\(820\) 20.3725 79.7274i 0.711437 2.78420i
\(821\) −28.5257 −0.995554 −0.497777 0.867305i \(-0.665850\pi\)
−0.497777 + 0.867305i \(0.665850\pi\)
\(822\) 38.1167i 1.32947i
\(823\) 20.1194i 0.701320i −0.936503 0.350660i \(-0.885957\pi\)
0.936503 0.350660i \(-0.114043\pi\)
\(824\) 29.0836 1.01318
\(825\) 6.19877 11.3374i 0.215813 0.394719i
\(826\) −13.3111 −0.463151
\(827\) 25.3763i 0.882421i −0.897404 0.441211i \(-0.854549\pi\)
0.897404 0.441211i \(-0.145451\pi\)
\(828\) 11.5940i 0.402920i
\(829\) −40.5872 −1.40965 −0.704826 0.709380i \(-0.748975\pi\)
−0.704826 + 0.709380i \(0.748975\pi\)
\(830\) 3.67973 14.4006i 0.127725 0.499852i
\(831\) −0.193802 −0.00672291
\(832\) 33.7462i 1.16994i
\(833\) 3.11966i 0.108090i
\(834\) 33.6184 1.16411
\(835\) −40.0188 10.2259i −1.38491 0.353880i
\(836\) −34.3531 −1.18813
\(837\) 22.0781i 0.763129i
\(838\) 35.4071i 1.22312i
\(839\) 16.9800 0.586216 0.293108 0.956079i \(-0.405311\pi\)
0.293108 + 0.956079i \(0.405311\pi\)
\(840\) −7.81744 1.99756i −0.269727 0.0689224i
\(841\) −28.9832 −0.999422
\(842\) 35.8233i 1.23455i
\(843\) 20.8715i 0.718852i
\(844\) 78.2895 2.69484
\(845\) −2.49570 + 9.76689i −0.0858546 + 0.335991i
\(846\) −11.2612 −0.387167
\(847\) 3.13984i 0.107886i
\(848\) 49.7714i 1.70916i
\(849\) 12.7269 0.436787
\(850\) −5.19889 2.84250i −0.178320 0.0974971i
\(851\) −6.72750 −0.230616
\(852\) 8.25260i 0.282729i
\(853\) 3.23644i 0.110814i 0.998464 + 0.0554069i \(0.0176456\pi\)
−0.998464 + 0.0554069i \(0.982354\pi\)
\(854\) 9.64358 0.329997
\(855\) −3.68412 + 14.4178i −0.125994 + 0.493077i
\(856\) −23.5918 −0.806351
\(857\) 1.40877i 0.0481228i 0.999710 + 0.0240614i \(0.00765971\pi\)
−0.999710 + 0.0240614i \(0.992340\pi\)
\(858\) 26.4752i 0.903848i
\(859\) −43.3662 −1.47963 −0.739817 0.672808i \(-0.765088\pi\)
−0.739817 + 0.672808i \(0.765088\pi\)
\(860\) −66.2535 16.9295i −2.25923 0.577292i
\(861\) 6.80730 0.231992
\(862\) 42.5563i 1.44947i
\(863\) 36.3292i 1.23666i −0.785919 0.618329i \(-0.787810\pi\)
0.785919 0.618329i \(-0.212190\pi\)
\(864\) 0.264501 0.00899852
\(865\) −24.8654 6.35377i −0.845450 0.216035i
\(866\) −55.6482 −1.89100
\(867\) 16.6351i 0.564958i
\(868\) 13.1976i 0.447956i
\(869\) −26.0516 −0.883739
\(870\) −0.174116 + 0.681402i −0.00590309 + 0.0231017i
\(871\) 23.8249 0.807276
\(872\) 47.0150i 1.59213i
\(873\) 12.6335i 0.427578i
\(874\) −11.6417 −0.393786
\(875\) 6.08913 + 5.67852i 0.205850 + 0.191969i
\(876\) 61.7097 2.08498
\(877\) 30.8667i 1.04229i −0.853467 0.521147i \(-0.825504\pi\)
0.853467 0.521147i \(-0.174496\pi\)
\(878\) 88.9987i 3.00356i
\(879\) −25.5903 −0.863139
\(880\) −5.72045 + 22.3869i −0.192836 + 0.754663i
\(881\) −34.9920 −1.17891 −0.589456 0.807801i \(-0.700658\pi\)
−0.589456 + 0.807801i \(0.700658\pi\)
\(882\) 31.8066i 1.07098i
\(883\) 44.7518i 1.50602i 0.658011 + 0.753008i \(0.271398\pi\)
−0.658011 + 0.753008i \(0.728602\pi\)
\(884\) −8.08996 −0.272095
\(885\) −15.6929 4.00995i −0.527511 0.134793i
\(886\) −100.978 −3.39243
\(887\) 21.2497i 0.713495i −0.934201 0.356747i \(-0.883886\pi\)
0.934201 0.356747i \(-0.116114\pi\)
\(888\) 22.6364i 0.759627i
\(889\) −1.59136 −0.0533726
\(890\) −52.3270 13.3709i −1.75400 0.448194i
\(891\) −2.88818 −0.0967576
\(892\) 19.1124i 0.639931i
\(893\) 7.53491i 0.252146i
\(894\) −11.4303 −0.382286
\(895\) 6.89001 26.9640i 0.230308 0.901307i
\(896\) −14.6259 −0.488616
\(897\) 5.97863i 0.199621i
\(898\) 4.44566i 0.148354i
\(899\) 0.574397 0.0191572
\(900\) 35.3210 + 19.3118i 1.17737 + 0.643727i
\(901\) 6.07194 0.202286
\(902\) 58.7493i 1.95614i
\(903\) 5.65687i 0.188249i
\(904\) 23.1878 0.771216
\(905\) −6.14507 + 24.0487i −0.204269 + 0.799405i
\(906\) −38.3246 −1.27325
\(907\) 7.07983i 0.235082i −0.993068 0.117541i \(-0.962499\pi\)
0.993068 0.117541i \(-0.0375012\pi\)
\(908\) 84.5370i 2.80546i
\(909\) 9.22833 0.306085
\(910\) 16.5285 + 4.22347i 0.547915 + 0.140007i
\(911\) −40.6767 −1.34768 −0.673840 0.738877i \(-0.735356\pi\)
−0.673840 + 0.738877i \(0.735356\pi\)
\(912\) 12.9979i 0.430402i
\(913\) 7.07110i 0.234019i
\(914\) 23.4361 0.775196
\(915\) 11.3692 + 2.90513i 0.375854 + 0.0960405i
\(916\) 89.7156 2.96429
\(917\) 11.3768i 0.375696i
\(918\) 5.89731i 0.194640i
\(919\) 11.3936 0.375841 0.187920 0.982184i \(-0.439825\pi\)
0.187920 + 0.982184i \(0.439825\pi\)
\(920\) −3.89305 + 15.2354i −0.128350 + 0.502297i
\(921\) −28.3124 −0.932927
\(922\) 19.5095i 0.642512i
\(923\) 8.71243i 0.286773i
\(924\) −7.68763 −0.252904
\(925\) 11.2058 20.4952i 0.368444 0.673878i
\(926\) −50.3204 −1.65363
\(927\) 12.0035i 0.394247i
\(928\) 0.00688145i 0.000225895i
\(929\) 38.5646 1.26526 0.632631 0.774453i \(-0.281975\pi\)
0.632631 + 0.774453i \(0.281975\pi\)
\(930\) −5.96636 + 23.3493i −0.195645 + 0.765654i
\(931\) −21.2819 −0.697488
\(932\) 43.9417i 1.43936i
\(933\) 4.01300i 0.131380i
\(934\) −38.9188 −1.27346
\(935\) −2.73113 0.697875i −0.0893174 0.0228230i
\(936\) 41.1847 1.34616
\(937\) 35.6493i 1.16461i 0.812970 + 0.582306i \(0.197849\pi\)
−0.812970 + 0.582306i \(0.802151\pi\)
\(938\) 10.3818i 0.338978i
\(939\) −10.7297 −0.350152
\(940\) 19.7487 + 5.04630i 0.644130 + 0.164592i
\(941\) −0.459712 −0.0149862 −0.00749308 0.999972i \(-0.502385\pi\)
−0.00749308 + 0.999972i \(0.502385\pi\)
\(942\) 15.2189i 0.495860i
\(943\) 13.2668i 0.432025i
\(944\) 28.9640 0.942697
\(945\) −2.05158 + 8.02885i −0.0667380 + 0.261179i
\(946\) −48.8207 −1.58730
\(947\) 16.4312i 0.533944i −0.963704 0.266972i \(-0.913977\pi\)
0.963704 0.266972i \(-0.0860231\pi\)
\(948\) 39.6434i 1.28756i
\(949\) −65.1482 −2.11480
\(950\) 19.3912 35.4662i 0.629135 1.15068i
\(951\) −2.60291 −0.0844053
\(952\) 1.76022i 0.0570490i
\(953\) 27.4225i 0.888302i −0.895952 0.444151i \(-0.853505\pi\)
0.895952 0.444151i \(-0.146495\pi\)
\(954\) −61.9067 −2.00430
\(955\) 2.86380 11.2075i 0.0926705 0.362665i
\(956\) −8.86406 −0.286684
\(957\) 0.334588i 0.0108157i
\(958\) 102.047i 3.29698i
\(959\) −11.6847 −0.377318
\(960\) −17.3363 4.42988i −0.559527 0.142974i
\(961\) −11.3174 −0.365076
\(962\) 47.8604i 1.54308i
\(963\) 9.73692i 0.313768i
\(964\) −3.99457 −0.128656
\(965\) 30.8369 + 7.87963i 0.992674 + 0.253654i
\(966\) −2.60521 −0.0838213
\(967\) 45.1755i 1.45275i 0.687300 + 0.726373i \(0.258796\pi\)
−0.687300 + 0.726373i \(0.741204\pi\)
\(968\) 20.5897i 0.661779i
\(969\) −1.58569 −0.0509398
\(970\) 8.49572 33.2479i 0.272781 1.06753i
\(971\) 50.1290 1.60872 0.804359 0.594144i \(-0.202509\pi\)
0.804359 + 0.594144i \(0.202509\pi\)
\(972\) 64.0312i 2.05380i
\(973\) 10.3057i 0.330386i
\(974\) −18.5252 −0.593587
\(975\) 18.2138 + 9.95842i 0.583308 + 0.318925i
\(976\) −20.9838 −0.671675
\(977\) 2.05208i 0.0656518i 0.999461 + 0.0328259i \(0.0104507\pi\)
−0.999461 + 0.0328259i \(0.989549\pi\)
\(978\) 55.1676i 1.76407i
\(979\) −25.6940 −0.821185
\(980\) −14.2530 + 55.7790i −0.455296 + 1.78180i
\(981\) −19.4042 −0.619530
\(982\) 65.5487i 2.09174i
\(983\) 48.6503i 1.55170i 0.630915 + 0.775852i \(0.282680\pi\)
−0.630915 + 0.775852i \(0.717320\pi\)
\(984\) −44.6394 −1.42305
\(985\) −14.3880 3.67651i −0.458439 0.117143i
\(986\) 0.153428 0.00488616
\(987\) 1.68618i 0.0536718i
\(988\) 55.1888i 1.75579i
\(989\) −11.0247 −0.350565
\(990\) 27.8453 + 7.11521i 0.884983 + 0.226136i
\(991\) 50.2126 1.59506 0.797528 0.603282i \(-0.206141\pi\)
0.797528 + 0.603282i \(0.206141\pi\)
\(992\) 0.235804i 0.00748677i
\(993\) 10.5297i 0.334149i
\(994\) −3.79648 −0.120417
\(995\) −5.05684 + 19.7899i −0.160313 + 0.627382i
\(996\) −10.7603 −0.340953
\(997\) 21.8288i 0.691325i 0.938359 + 0.345663i \(0.112346\pi\)
−0.938359 + 0.345663i \(0.887654\pi\)
\(998\) 66.2053i 2.09569i
\(999\) 23.2485 0.735551
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 1205.2.b.c.724.4 46
5.2 odd 4 6025.2.a.p.1.43 46
5.3 odd 4 6025.2.a.p.1.4 46
5.4 even 2 inner 1205.2.b.c.724.43 yes 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.4 46 1.1 even 1 trivial
1205.2.b.c.724.43 yes 46 5.4 even 2 inner
6025.2.a.p.1.4 46 5.3 odd 4
6025.2.a.p.1.43 46 5.2 odd 4