Properties

Label 1155.2.i.c.76.13
Level $1155$
Weight $2$
Character 1155.76
Analytic conductor $9.223$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(76,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.i (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: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{16} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.13
Root \(0.0566033 - 1.17421i\) of defining polynomial
Character \(\chi\) \(=\) 1155.76
Dual form 1155.2.i.c.76.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.19849i q^{2} -1.00000i q^{3} -2.83337 q^{4} +1.00000i q^{5} +2.19849 q^{6} +(-2.19849 - 1.47195i) q^{7} -1.83215i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+2.19849i q^{2} -1.00000i q^{3} -2.83337 q^{4} +1.00000i q^{5} +2.19849 q^{6} +(-2.19849 - 1.47195i) q^{7} -1.83215i q^{8} -1.00000 q^{9} -2.19849 q^{10} +(-1.23607 - 3.07768i) q^{11} +2.83337i q^{12} +6.52171 q^{13} +(3.23607 - 4.83337i) q^{14} +1.00000 q^{15} -1.63877 q^{16} +3.82309 q^{17} -2.19849i q^{18} +2.33228 q^{19} -2.83337i q^{20} +(-1.47195 + 2.19849i) q^{21} +(6.76626 - 2.71749i) q^{22} +3.83337 q^{23} -1.83215 q^{24} -1.00000 q^{25} +14.3379i q^{26} +1.00000i q^{27} +(6.22913 + 4.17057i) q^{28} -4.90983i q^{29} +2.19849i q^{30} +7.93290i q^{31} -7.26712i q^{32} +(-3.07768 + 1.23607i) q^{33} +8.40503i q^{34} +(1.47195 - 2.19849i) q^{35} +2.83337 q^{36} -7.93290 q^{37} +5.12749i q^{38} -6.52171i q^{39} +1.83215 q^{40} +10.1860 q^{41} +(-4.83337 - 3.23607i) q^{42} +6.37521i q^{43} +(3.50223 + 8.72020i) q^{44} -1.00000i q^{45} +8.42762i q^{46} -2.06710i q^{47} +1.63877i q^{48} +(2.66673 + 6.47214i) q^{49} -2.19849i q^{50} -3.82309i q^{51} -18.4784 q^{52} +10.0324 q^{53} -2.19849 q^{54} +(3.07768 - 1.23607i) q^{55} +(-2.69683 + 4.02796i) q^{56} -2.33228i q^{57} +10.7942 q^{58} -3.76626i q^{59} -2.83337 q^{60} +9.22033 q^{61} -17.4404 q^{62} +(2.19849 + 1.47195i) q^{63} +12.6992 q^{64} +6.52171i q^{65} +(-2.71749 - 6.76626i) q^{66} -2.13887 q^{67} -10.8322 q^{68} -3.83337i q^{69} +(4.83337 + 3.23607i) q^{70} +8.40503 q^{71} +1.83215i q^{72} +8.34114 q^{73} -17.4404i q^{74} +1.00000i q^{75} -6.60819 q^{76} +(-1.81271 + 8.58569i) q^{77} +14.3379 q^{78} +13.1299i q^{79} -1.63877i q^{80} +1.00000 q^{81} +22.3939i q^{82} -15.3757 q^{83} +(4.17057 - 6.22913i) q^{84} +3.82309i q^{85} -14.0158 q^{86} -4.90983 q^{87} +(-5.63877 + 2.26466i) q^{88} +0.705874i q^{89} +2.19849 q^{90} +(-14.3379 - 9.59963i) q^{91} -10.8613 q^{92} +7.93290 q^{93} +4.54451 q^{94} +2.33228i q^{95} -7.26712 q^{96} -10.0995i q^{97} +(-14.2289 + 5.86279i) q^{98} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 24 q^{4} - 16 q^{9} + 16 q^{11} + 16 q^{14} + 16 q^{15} + 24 q^{16} + 40 q^{23} - 16 q^{25} + 24 q^{36} - 40 q^{37} - 56 q^{42} - 24 q^{44} + 8 q^{53} + 8 q^{56} + 72 q^{58} - 24 q^{60} + 8 q^{64} + 80 q^{67} + 56 q^{70} - 24 q^{71} - 16 q^{78} + 16 q^{81} - 8 q^{86} - 40 q^{88} + 16 q^{91} - 160 q^{92} + 40 q^{93} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.19849i 1.55457i 0.629150 + 0.777284i \(0.283403\pi\)
−0.629150 + 0.777284i \(0.716597\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −2.83337 −1.41668
\(5\) 1.00000i 0.447214i
\(6\) 2.19849 0.897530
\(7\) −2.19849 1.47195i −0.830952 0.556344i
\(8\) 1.83215i 0.647762i
\(9\) −1.00000 −0.333333
\(10\) −2.19849 −0.695224
\(11\) −1.23607 3.07768i −0.372689 0.927957i
\(12\) 2.83337i 0.817922i
\(13\) 6.52171 1.80880 0.904399 0.426689i \(-0.140320\pi\)
0.904399 + 0.426689i \(0.140320\pi\)
\(14\) 3.23607 4.83337i 0.864876 1.29177i
\(15\) 1.00000 0.258199
\(16\) −1.63877 −0.409693
\(17\) 3.82309 0.927236 0.463618 0.886035i \(-0.346551\pi\)
0.463618 + 0.886035i \(0.346551\pi\)
\(18\) 2.19849i 0.518189i
\(19\) 2.33228 0.535061 0.267531 0.963549i \(-0.413792\pi\)
0.267531 + 0.963549i \(0.413792\pi\)
\(20\) 2.83337i 0.633560i
\(21\) −1.47195 + 2.19849i −0.321206 + 0.479750i
\(22\) 6.76626 2.71749i 1.44257 0.579370i
\(23\) 3.83337 0.799312 0.399656 0.916665i \(-0.369130\pi\)
0.399656 + 0.916665i \(0.369130\pi\)
\(24\) −1.83215 −0.373986
\(25\) −1.00000 −0.200000
\(26\) 14.3379i 2.81190i
\(27\) 1.00000i 0.192450i
\(28\) 6.22913 + 4.17057i 1.17720 + 0.788164i
\(29\) 4.90983i 0.911733i −0.890048 0.455866i \(-0.849329\pi\)
0.890048 0.455866i \(-0.150671\pi\)
\(30\) 2.19849i 0.401388i
\(31\) 7.93290i 1.42479i 0.701779 + 0.712395i \(0.252390\pi\)
−0.701779 + 0.712395i \(0.747610\pi\)
\(32\) 7.26712i 1.28466i
\(33\) −3.07768 + 1.23607i −0.535756 + 0.215172i
\(34\) 8.40503i 1.44145i
\(35\) 1.47195 2.19849i 0.248805 0.371613i
\(36\) 2.83337 0.472228
\(37\) −7.93290 −1.30416 −0.652080 0.758150i \(-0.726103\pi\)
−0.652080 + 0.758150i \(0.726103\pi\)
\(38\) 5.12749i 0.831789i
\(39\) 6.52171i 1.04431i
\(40\) 1.83215 0.289688
\(41\) 10.1860 1.59079 0.795393 0.606093i \(-0.207264\pi\)
0.795393 + 0.606093i \(0.207264\pi\)
\(42\) −4.83337 3.23607i −0.745805 0.499336i
\(43\) 6.37521i 0.972210i 0.873900 + 0.486105i \(0.161583\pi\)
−0.873900 + 0.486105i \(0.838417\pi\)
\(44\) 3.50223 + 8.72020i 0.527981 + 1.31462i
\(45\) 1.00000i 0.149071i
\(46\) 8.42762i 1.24259i
\(47\) 2.06710i 0.301518i −0.988571 0.150759i \(-0.951828\pi\)
0.988571 0.150759i \(-0.0481718\pi\)
\(48\) 1.63877i 0.236536i
\(49\) 2.66673 + 6.47214i 0.380962 + 0.924591i
\(50\) 2.19849i 0.310914i
\(51\) 3.82309i 0.535340i
\(52\) −18.4784 −2.56249
\(53\) 10.0324 1.37806 0.689030 0.724733i \(-0.258037\pi\)
0.689030 + 0.724733i \(0.258037\pi\)
\(54\) −2.19849 −0.299177
\(55\) 3.07768 1.23607i 0.414995 0.166671i
\(56\) −2.69683 + 4.02796i −0.360379 + 0.538259i
\(57\) 2.33228i 0.308918i
\(58\) 10.7942 1.41735
\(59\) 3.76626i 0.490326i −0.969482 0.245163i \(-0.921159\pi\)
0.969482 0.245163i \(-0.0788414\pi\)
\(60\) −2.83337 −0.365786
\(61\) 9.22033 1.18054 0.590271 0.807205i \(-0.299021\pi\)
0.590271 + 0.807205i \(0.299021\pi\)
\(62\) −17.4404 −2.21493
\(63\) 2.19849 + 1.47195i 0.276984 + 0.185448i
\(64\) 12.6992 1.58739
\(65\) 6.52171i 0.808919i
\(66\) −2.71749 6.76626i −0.334499 0.832869i
\(67\) −2.13887 −0.261304 −0.130652 0.991428i \(-0.541707\pi\)
−0.130652 + 0.991428i \(0.541707\pi\)
\(68\) −10.8322 −1.31360
\(69\) 3.83337i 0.461483i
\(70\) 4.83337 + 3.23607i 0.577698 + 0.386784i
\(71\) 8.40503 0.997494 0.498747 0.866748i \(-0.333794\pi\)
0.498747 + 0.866748i \(0.333794\pi\)
\(72\) 1.83215i 0.215921i
\(73\) 8.34114 0.976257 0.488128 0.872772i \(-0.337680\pi\)
0.488128 + 0.872772i \(0.337680\pi\)
\(74\) 17.4404i 2.02741i
\(75\) 1.00000i 0.115470i
\(76\) −6.60819 −0.758012
\(77\) −1.81271 + 8.58569i −0.206577 + 0.978430i
\(78\) 14.3379 1.62345
\(79\) 13.1299i 1.47723i 0.674128 + 0.738615i \(0.264520\pi\)
−0.674128 + 0.738615i \(0.735480\pi\)
\(80\) 1.63877i 0.183220i
\(81\) 1.00000 0.111111
\(82\) 22.3939i 2.47299i
\(83\) −15.3757 −1.68770 −0.843851 0.536577i \(-0.819717\pi\)
−0.843851 + 0.536577i \(0.819717\pi\)
\(84\) 4.17057 6.22913i 0.455047 0.679654i
\(85\) 3.82309i 0.414672i
\(86\) −14.0158 −1.51137
\(87\) −4.90983 −0.526389
\(88\) −5.63877 + 2.26466i −0.601095 + 0.241413i
\(89\) 0.705874i 0.0748225i 0.999300 + 0.0374113i \(0.0119112\pi\)
−0.999300 + 0.0374113i \(0.988089\pi\)
\(90\) 2.19849 0.231741
\(91\) −14.3379 9.59963i −1.50302 1.00631i
\(92\) −10.8613 −1.13237
\(93\) 7.93290 0.822603
\(94\) 4.54451 0.468731
\(95\) 2.33228i 0.239287i
\(96\) −7.26712 −0.741697
\(97\) 10.0995i 1.02545i −0.858552 0.512726i \(-0.828636\pi\)
0.858552 0.512726i \(-0.171364\pi\)
\(98\) −14.2289 + 5.86279i −1.43734 + 0.592231i
\(99\) 1.23607 + 3.07768i 0.124230 + 0.309319i
\(100\) 2.83337 0.283337
\(101\) 1.45309 0.144587 0.0722937 0.997383i \(-0.476968\pi\)
0.0722937 + 0.997383i \(0.476968\pi\)
\(102\) 8.40503 0.832222
\(103\) 8.96086i 0.882939i −0.897276 0.441470i \(-0.854457\pi\)
0.897276 0.441470i \(-0.145543\pi\)
\(104\) 11.9487i 1.17167i
\(105\) −2.19849 1.47195i −0.214551 0.143648i
\(106\) 22.0562i 2.14229i
\(107\) 11.6514i 1.12638i −0.826327 0.563191i \(-0.809574\pi\)
0.826327 0.563191i \(-0.190426\pi\)
\(108\) 2.83337i 0.272641i
\(109\) 8.73292i 0.836462i 0.908341 + 0.418231i \(0.137350\pi\)
−0.908341 + 0.418231i \(0.862650\pi\)
\(110\) 2.71749 + 6.76626i 0.259102 + 0.645138i
\(111\) 7.93290i 0.752957i
\(112\) 3.60282 + 2.41219i 0.340435 + 0.227930i
\(113\) 9.36589 0.881069 0.440534 0.897736i \(-0.354789\pi\)
0.440534 + 0.897736i \(0.354789\pi\)
\(114\) 5.12749 0.480234
\(115\) 3.83337i 0.357463i
\(116\) 13.9113i 1.29164i
\(117\) −6.52171 −0.602932
\(118\) 8.28009 0.762245
\(119\) −8.40503 5.62739i −0.770488 0.515862i
\(120\) 1.83215i 0.167251i
\(121\) −7.94427 + 7.60845i −0.722207 + 0.691677i
\(122\) 20.2708i 1.83523i
\(123\) 10.1860i 0.918441i
\(124\) 22.4768i 2.01848i
\(125\) 1.00000i 0.0894427i
\(126\) −3.23607 + 4.83337i −0.288292 + 0.430590i
\(127\) 16.1949i 1.43706i −0.695495 0.718531i \(-0.744815\pi\)
0.695495 0.718531i \(-0.255185\pi\)
\(128\) 13.3848i 1.18306i
\(129\) 6.37521 0.561306
\(130\) −14.3379 −1.25752
\(131\) 12.9824 1.13428 0.567138 0.823623i \(-0.308051\pi\)
0.567138 + 0.823623i \(0.308051\pi\)
\(132\) 8.72020 3.50223i 0.758996 0.304830i
\(133\) −5.12749 3.43299i −0.444610 0.297678i
\(134\) 4.70228i 0.406215i
\(135\) −1.00000 −0.0860663
\(136\) 7.00447i 0.600628i
\(137\) −0.116115 −0.00992041 −0.00496021 0.999988i \(-0.501579\pi\)
−0.00496021 + 0.999988i \(0.501579\pi\)
\(138\) 8.42762 0.717407
\(139\) 2.18577 0.185395 0.0926974 0.995694i \(-0.470451\pi\)
0.0926974 + 0.995694i \(0.470451\pi\)
\(140\) −4.17057 + 6.22913i −0.352478 + 0.526458i
\(141\) −2.06710 −0.174082
\(142\) 18.4784i 1.55067i
\(143\) −8.06128 20.0718i −0.674118 1.67849i
\(144\) 1.63877 0.136564
\(145\) 4.90983 0.407739
\(146\) 18.3379i 1.51766i
\(147\) 6.47214 2.66673i 0.533813 0.219948i
\(148\) 22.4768 1.84758
\(149\) 5.43497i 0.445250i 0.974904 + 0.222625i \(0.0714626\pi\)
−0.974904 + 0.222625i \(0.928537\pi\)
\(150\) −2.19849 −0.179506
\(151\) 22.7176i 1.84873i −0.381506 0.924366i \(-0.624595\pi\)
0.381506 0.924366i \(-0.375405\pi\)
\(152\) 4.27308i 0.346592i
\(153\) −3.82309 −0.309079
\(154\) −18.8756 3.98522i −1.52104 0.321139i
\(155\) −7.93290 −0.637186
\(156\) 18.4784i 1.47946i
\(157\) 6.51147i 0.519672i −0.965653 0.259836i \(-0.916331\pi\)
0.965653 0.259836i \(-0.0836685\pi\)
\(158\) −28.8660 −2.29645
\(159\) 10.0324i 0.795623i
\(160\) 7.26712 0.574516
\(161\) −8.42762 5.64252i −0.664190 0.444693i
\(162\) 2.19849i 0.172730i
\(163\) −10.7942 −0.845469 −0.422734 0.906254i \(-0.638930\pi\)
−0.422734 + 0.906254i \(0.638930\pi\)
\(164\) −28.8607 −2.25364
\(165\) −1.23607 3.07768i −0.0962278 0.239597i
\(166\) 33.8033i 2.62365i
\(167\) −17.4027 −1.34666 −0.673330 0.739342i \(-0.735137\pi\)
−0.673330 + 0.739342i \(0.735137\pi\)
\(168\) 4.02796 + 2.69683i 0.310764 + 0.208065i
\(169\) 29.5327 2.27175
\(170\) −8.40503 −0.644637
\(171\) −2.33228 −0.178354
\(172\) 18.0633i 1.37731i
\(173\) 4.82437 0.366790 0.183395 0.983039i \(-0.441291\pi\)
0.183395 + 0.983039i \(0.441291\pi\)
\(174\) 10.7942i 0.818308i
\(175\) 2.19849 + 1.47195i 0.166190 + 0.111269i
\(176\) 2.02563 + 5.04362i 0.152688 + 0.380177i
\(177\) −3.76626 −0.283090
\(178\) −1.55186 −0.116317
\(179\) −22.3267 −1.66878 −0.834390 0.551175i \(-0.814180\pi\)
−0.834390 + 0.551175i \(0.814180\pi\)
\(180\) 2.83337i 0.211187i
\(181\) 13.2775i 0.986912i 0.869771 + 0.493456i \(0.164267\pi\)
−0.869771 + 0.493456i \(0.835733\pi\)
\(182\) 21.1047 31.5218i 1.56438 2.33655i
\(183\) 9.22033i 0.681587i
\(184\) 7.02329i 0.517764i
\(185\) 7.93290i 0.583238i
\(186\) 17.4404i 1.27879i
\(187\) −4.72560 11.7663i −0.345570 0.860434i
\(188\) 5.85686i 0.427156i
\(189\) 1.47195 2.19849i 0.107069 0.159917i
\(190\) −5.12749 −0.371987
\(191\) −4.52806 −0.327639 −0.163819 0.986490i \(-0.552381\pi\)
−0.163819 + 0.986490i \(0.552381\pi\)
\(192\) 12.6992i 0.916483i
\(193\) 4.39698i 0.316502i −0.987399 0.158251i \(-0.949415\pi\)
0.987399 0.158251i \(-0.0505855\pi\)
\(194\) 22.2037 1.59414
\(195\) 6.52171 0.467029
\(196\) −7.55583 18.3379i −0.539702 1.30985i
\(197\) 22.8254i 1.62624i −0.582097 0.813120i \(-0.697767\pi\)
0.582097 0.813120i \(-0.302233\pi\)
\(198\) −6.76626 + 2.71749i −0.480857 + 0.193123i
\(199\) 17.5325i 1.24285i 0.783475 + 0.621424i \(0.213445\pi\)
−0.783475 + 0.621424i \(0.786555\pi\)
\(200\) 1.83215i 0.129552i
\(201\) 2.13887i 0.150864i
\(202\) 3.19460i 0.224771i
\(203\) −7.22702 + 10.7942i −0.507237 + 0.757606i
\(204\) 10.8322i 0.758407i
\(205\) 10.1860i 0.711422i
\(206\) 19.7004 1.37259
\(207\) −3.83337 −0.266437
\(208\) −10.6876 −0.741051
\(209\) −2.88285 7.17801i −0.199411 0.496513i
\(210\) 3.23607 4.83337i 0.223310 0.333534i
\(211\) 12.9488i 0.891433i 0.895174 + 0.445717i \(0.147051\pi\)
−0.895174 + 0.445717i \(0.852949\pi\)
\(212\) −28.4255 −1.95227
\(213\) 8.40503i 0.575903i
\(214\) 25.6155 1.75104
\(215\) −6.37521 −0.434786
\(216\) 1.83215 0.124662
\(217\) 11.6768 17.4404i 0.792674 1.18393i
\(218\) −19.1993 −1.30034
\(219\) 8.34114i 0.563642i
\(220\) −8.72020 + 3.50223i −0.587916 + 0.236120i
\(221\) 24.9331 1.67718
\(222\) −17.4404 −1.17052
\(223\) 1.62739i 0.108978i −0.998514 0.0544892i \(-0.982647\pi\)
0.998514 0.0544892i \(-0.0173530\pi\)
\(224\) −10.6968 + 15.9767i −0.714712 + 1.06749i
\(225\) 1.00000 0.0666667
\(226\) 20.5908i 1.36968i
\(227\) 15.1336 1.00445 0.502225 0.864737i \(-0.332515\pi\)
0.502225 + 0.864737i \(0.332515\pi\)
\(228\) 6.60819i 0.437638i
\(229\) 4.85442i 0.320789i −0.987053 0.160394i \(-0.948723\pi\)
0.987053 0.160394i \(-0.0512766\pi\)
\(230\) −8.42762 −0.555701
\(231\) 8.58569 + 1.81271i 0.564897 + 0.119267i
\(232\) −8.99553 −0.590586
\(233\) 18.9545i 1.24175i −0.783908 0.620876i \(-0.786777\pi\)
0.783908 0.620876i \(-0.213223\pi\)
\(234\) 14.3379i 0.937300i
\(235\) 2.06710 0.134843
\(236\) 10.6712i 0.694636i
\(237\) 13.1299 0.852879
\(238\) 12.3718 18.4784i 0.801943 1.19778i
\(239\) 8.61185i 0.557055i 0.960428 + 0.278527i \(0.0898463\pi\)
−0.960428 + 0.278527i \(0.910154\pi\)
\(240\) −1.63877 −0.105782
\(241\) −25.0234 −1.61190 −0.805950 0.591983i \(-0.798345\pi\)
−0.805950 + 0.591983i \(0.798345\pi\)
\(242\) −16.7271 17.4654i −1.07526 1.12272i
\(243\) 1.00000i 0.0641500i
\(244\) −26.1246 −1.67245
\(245\) −6.47214 + 2.66673i −0.413490 + 0.170371i
\(246\) 22.3939 1.42778
\(247\) 15.2104 0.967817
\(248\) 14.5342 0.922925
\(249\) 15.3757i 0.974395i
\(250\) 2.19849 0.139045
\(251\) 1.93981i 0.122440i −0.998124 0.0612198i \(-0.980501\pi\)
0.998124 0.0612198i \(-0.0194990\pi\)
\(252\) −6.22913 4.17057i −0.392398 0.262721i
\(253\) −4.73830 11.7979i −0.297894 0.741727i
\(254\) 35.6043 2.23401
\(255\) 3.82309 0.239411
\(256\) −4.02796 −0.251748
\(257\) 27.7987i 1.73403i 0.498278 + 0.867017i \(0.333966\pi\)
−0.498278 + 0.867017i \(0.666034\pi\)
\(258\) 14.0158i 0.872588i
\(259\) 17.4404 + 11.6768i 1.08369 + 0.725562i
\(260\) 18.4784i 1.14598i
\(261\) 4.90983i 0.303911i
\(262\) 28.5416i 1.76331i
\(263\) 2.96933i 0.183097i 0.995801 + 0.0915485i \(0.0291817\pi\)
−0.995801 + 0.0915485i \(0.970818\pi\)
\(264\) 2.26466 + 5.63877i 0.139380 + 0.347042i
\(265\) 10.0324i 0.616287i
\(266\) 7.54741 11.2727i 0.462761 0.691176i
\(267\) 0.705874 0.0431988
\(268\) 6.06019 0.370185
\(269\) 10.2943i 0.627656i −0.949480 0.313828i \(-0.898389\pi\)
0.949480 0.313828i \(-0.101611\pi\)
\(270\) 2.19849i 0.133796i
\(271\) 19.5051 1.18485 0.592426 0.805625i \(-0.298170\pi\)
0.592426 + 0.805625i \(0.298170\pi\)
\(272\) −6.26517 −0.379882
\(273\) −9.59963 + 14.3379i −0.580996 + 0.867771i
\(274\) 0.255279i 0.0154220i
\(275\) 1.23607 + 3.07768i 0.0745377 + 0.185591i
\(276\) 10.8613i 0.653775i
\(277\) 24.0609i 1.44568i 0.691016 + 0.722839i \(0.257163\pi\)
−0.691016 + 0.722839i \(0.742837\pi\)
\(278\) 4.80540i 0.288209i
\(279\) 7.93290i 0.474930i
\(280\) −4.02796 2.69683i −0.240717 0.161166i
\(281\) 2.65089i 0.158139i 0.996869 + 0.0790695i \(0.0251949\pi\)
−0.996869 + 0.0790695i \(0.974805\pi\)
\(282\) 4.54451i 0.270622i
\(283\) 14.1047 0.838439 0.419219 0.907885i \(-0.362304\pi\)
0.419219 + 0.907885i \(0.362304\pi\)
\(284\) −23.8145 −1.41313
\(285\) 2.33228 0.138152
\(286\) 44.1276 17.7227i 2.60932 1.04796i
\(287\) −22.3939 14.9933i −1.32187 0.885026i
\(288\) 7.26712i 0.428219i
\(289\) −2.38398 −0.140234
\(290\) 10.7942i 0.633859i
\(291\) −10.0995 −0.592045
\(292\) −23.6335 −1.38305
\(293\) −1.94262 −0.113489 −0.0567444 0.998389i \(-0.518072\pi\)
−0.0567444 + 0.998389i \(0.518072\pi\)
\(294\) 5.86279 + 14.2289i 0.341925 + 0.829848i
\(295\) 3.76626 0.219280
\(296\) 14.5342i 0.844785i
\(297\) 3.07768 1.23607i 0.178585 0.0717239i
\(298\) −11.9487 −0.692172
\(299\) 25.0001 1.44579
\(300\) 2.83337i 0.163584i
\(301\) 9.38398 14.0158i 0.540884 0.807860i
\(302\) 49.9445 2.87398
\(303\) 1.45309i 0.0834776i
\(304\) −3.82207 −0.219211
\(305\) 9.22033i 0.527955i
\(306\) 8.40503i 0.480484i
\(307\) −8.03584 −0.458630 −0.229315 0.973352i \(-0.573649\pi\)
−0.229315 + 0.973352i \(0.573649\pi\)
\(308\) 5.13607 24.3264i 0.292655 1.38613i
\(309\) −8.96086 −0.509765
\(310\) 17.4404i 0.990548i
\(311\) 12.4949i 0.708520i 0.935147 + 0.354260i \(0.115267\pi\)
−0.935147 + 0.354260i \(0.884733\pi\)
\(312\) −11.9487 −0.676464
\(313\) 4.68778i 0.264969i −0.991185 0.132485i \(-0.957705\pi\)
0.991185 0.132485i \(-0.0422955\pi\)
\(314\) 14.3154 0.807866
\(315\) −1.47195 + 2.19849i −0.0829349 + 0.123871i
\(316\) 37.2018i 2.09277i
\(317\) 17.0604 0.958207 0.479103 0.877758i \(-0.340962\pi\)
0.479103 + 0.877758i \(0.340962\pi\)
\(318\) 22.0562 1.23685
\(319\) −15.1109 + 6.06888i −0.846048 + 0.339792i
\(320\) 12.6992i 0.709904i
\(321\) −11.6514 −0.650317
\(322\) 12.4050 18.5281i 0.691305 1.03253i
\(323\) 8.91650 0.496128
\(324\) −2.83337 −0.157409
\(325\) −6.52171 −0.361759
\(326\) 23.7310i 1.31434i
\(327\) 8.73292 0.482932
\(328\) 18.6623i 1.03045i
\(329\) −3.04267 + 4.54451i −0.167748 + 0.250547i
\(330\) 6.76626 2.71749i 0.372470 0.149593i
\(331\) 17.0507 0.937192 0.468596 0.883413i \(-0.344760\pi\)
0.468596 + 0.883413i \(0.344760\pi\)
\(332\) 43.5650 2.39094
\(333\) 7.93290 0.434720
\(334\) 38.2596i 2.09347i
\(335\) 2.13887i 0.116859i
\(336\) 2.41219 3.60282i 0.131596 0.196550i
\(337\) 7.58616i 0.413244i −0.978421 0.206622i \(-0.933753\pi\)
0.978421 0.206622i \(-0.0662471\pi\)
\(338\) 64.9274i 3.53159i
\(339\) 9.36589i 0.508685i
\(340\) 10.8322i 0.587459i
\(341\) 24.4149 9.80560i 1.32214 0.531003i
\(342\) 5.12749i 0.277263i
\(343\) 3.66387 18.1542i 0.197830 0.980236i
\(344\) 11.6803 0.629761
\(345\) 3.83337 0.206381
\(346\) 10.6063i 0.570201i
\(347\) 28.3235i 1.52048i 0.649640 + 0.760242i \(0.274920\pi\)
−0.649640 + 0.760242i \(0.725080\pi\)
\(348\) 13.9113 0.745726
\(349\) −19.9702 −1.06898 −0.534491 0.845174i \(-0.679497\pi\)
−0.534491 + 0.845174i \(0.679497\pi\)
\(350\) −3.23607 + 4.83337i −0.172975 + 0.258354i
\(351\) 6.52171i 0.348103i
\(352\) −22.3659 + 8.98265i −1.19211 + 0.478777i
\(353\) 15.5098i 0.825502i −0.910844 0.412751i \(-0.864568\pi\)
0.910844 0.412751i \(-0.135432\pi\)
\(354\) 8.28009i 0.440082i
\(355\) 8.40503i 0.446093i
\(356\) 2.00000i 0.106000i
\(357\) −5.62739 + 8.40503i −0.297833 + 0.444841i
\(358\) 49.0852i 2.59423i
\(359\) 25.9068i 1.36731i −0.729806 0.683654i \(-0.760390\pi\)
0.729806 0.683654i \(-0.239610\pi\)
\(360\) −1.83215 −0.0965627
\(361\) −13.5605 −0.713710
\(362\) −29.1906 −1.53422
\(363\) 7.60845 + 7.94427i 0.399340 + 0.416966i
\(364\) 40.6246 + 27.1993i 2.12931 + 1.42563i
\(365\) 8.34114i 0.436595i
\(366\) 20.2708 1.05957
\(367\) 16.2943i 0.850557i 0.905063 + 0.425278i \(0.139824\pi\)
−0.905063 + 0.425278i \(0.860176\pi\)
\(368\) −6.28201 −0.327472
\(369\) −10.1860 −0.530262
\(370\) 17.4404 0.906684
\(371\) −22.0562 14.7672i −1.14510 0.766676i
\(372\) −22.4768 −1.16537
\(373\) 10.6124i 0.549488i −0.961517 0.274744i \(-0.911407\pi\)
0.961517 0.274744i \(-0.0885931\pi\)
\(374\) 25.8680 10.3892i 1.33760 0.537212i
\(375\) −1.00000 −0.0516398
\(376\) −3.78724 −0.195312
\(377\) 32.0205i 1.64914i
\(378\) 4.83337 + 3.23607i 0.248602 + 0.166445i
\(379\) −26.9586 −1.38477 −0.692385 0.721528i \(-0.743440\pi\)
−0.692385 + 0.721528i \(0.743440\pi\)
\(380\) 6.60819i 0.338993i
\(381\) −16.1949 −0.829688
\(382\) 9.95490i 0.509337i
\(383\) 10.2106i 0.521739i −0.965374 0.260869i \(-0.915991\pi\)
0.965374 0.260869i \(-0.0840092\pi\)
\(384\) 13.3848 0.683038
\(385\) −8.58569 1.81271i −0.437567 0.0923842i
\(386\) 9.66673 0.492024
\(387\) 6.37521i 0.324070i
\(388\) 28.6157i 1.45274i
\(389\) 9.57688 0.485567 0.242783 0.970081i \(-0.421940\pi\)
0.242783 + 0.970081i \(0.421940\pi\)
\(390\) 14.3379i 0.726029i
\(391\) 14.6553 0.741151
\(392\) 11.8579 4.88585i 0.598915 0.246772i
\(393\) 12.9824i 0.654874i
\(394\) 50.1814 2.52810
\(395\) −13.1299 −0.660637
\(396\) −3.50223 8.72020i −0.175994 0.438207i
\(397\) 29.9264i 1.50196i 0.660324 + 0.750981i \(0.270419\pi\)
−0.660324 + 0.750981i \(0.729581\pi\)
\(398\) −38.5451 −1.93209
\(399\) −3.43299 + 5.12749i −0.171865 + 0.256696i
\(400\) 1.63877 0.0819385
\(401\) −27.5441 −1.37549 −0.687743 0.725954i \(-0.741398\pi\)
−0.687743 + 0.725954i \(0.741398\pi\)
\(402\) −4.70228 −0.234529
\(403\) 51.7361i 2.57716i
\(404\) −4.11712 −0.204834
\(405\) 1.00000i 0.0496904i
\(406\) −23.7310 15.8885i −1.17775 0.788535i
\(407\) 9.80560 + 24.4149i 0.486045 + 1.21020i
\(408\) −7.00447 −0.346773
\(409\) −4.16714 −0.206052 −0.103026 0.994679i \(-0.532852\pi\)
−0.103026 + 0.994679i \(0.532852\pi\)
\(410\) −22.3939 −1.10595
\(411\) 0.116115i 0.00572755i
\(412\) 25.3894i 1.25085i
\(413\) −5.54375 + 8.28009i −0.272790 + 0.407437i
\(414\) 8.42762i 0.414195i
\(415\) 15.3757i 0.754763i
\(416\) 47.3940i 2.32368i
\(417\) 2.18577i 0.107038i
\(418\) 15.7808 6.33793i 0.771864 0.309998i
\(419\) 11.9005i 0.581376i 0.956818 + 0.290688i \(0.0938842\pi\)
−0.956818 + 0.290688i \(0.906116\pi\)
\(420\) 6.22913 + 4.17057i 0.303950 + 0.203503i
\(421\) −25.9722 −1.26581 −0.632905 0.774230i \(-0.718137\pi\)
−0.632905 + 0.774230i \(0.718137\pi\)
\(422\) −28.4679 −1.38579
\(423\) 2.06710i 0.100506i
\(424\) 18.3809i 0.892655i
\(425\) −3.82309 −0.185447
\(426\) 18.4784 0.895281
\(427\) −20.2708 13.5719i −0.980974 0.656788i
\(428\) 33.0126i 1.59573i
\(429\) −20.0718 + 8.06128i −0.969074 + 0.389202i
\(430\) 14.0158i 0.675904i
\(431\) 19.3963i 0.934289i 0.884181 + 0.467144i \(0.154717\pi\)
−0.884181 + 0.467144i \(0.845283\pi\)
\(432\) 1.63877i 0.0788454i
\(433\) 3.16143i 0.151928i −0.997111 0.0759642i \(-0.975797\pi\)
0.997111 0.0759642i \(-0.0242035\pi\)
\(434\) 38.3426 + 25.6714i 1.84050 + 1.23227i
\(435\) 4.90983i 0.235408i
\(436\) 24.7436i 1.18500i
\(437\) 8.94047 0.427681
\(438\) 18.3379 0.876220
\(439\) 28.0569 1.33908 0.669542 0.742774i \(-0.266490\pi\)
0.669542 + 0.742774i \(0.266490\pi\)
\(440\) −2.26466 5.63877i −0.107963 0.268818i
\(441\) −2.66673 6.47214i −0.126987 0.308197i
\(442\) 54.8152i 2.60729i
\(443\) −32.9489 −1.56545 −0.782725 0.622367i \(-0.786171\pi\)
−0.782725 + 0.622367i \(0.786171\pi\)
\(444\) 22.4768i 1.06670i
\(445\) −0.705874 −0.0334617
\(446\) 3.57781 0.169414
\(447\) 5.43497 0.257065
\(448\) −27.9190 18.6925i −1.31905 0.883138i
\(449\) 28.2106 1.33134 0.665671 0.746245i \(-0.268145\pi\)
0.665671 + 0.746245i \(0.268145\pi\)
\(450\) 2.19849i 0.103638i
\(451\) −12.5906 31.3493i −0.592868 1.47618i
\(452\) −26.5370 −1.24819
\(453\) −22.7176 −1.06737
\(454\) 33.2710i 1.56149i
\(455\) 9.59963 14.3379i 0.450037 0.672172i
\(456\) −4.27308 −0.200105
\(457\) 4.26489i 0.199503i −0.995012 0.0997516i \(-0.968195\pi\)
0.995012 0.0997516i \(-0.0318048\pi\)
\(458\) 10.6724 0.498688
\(459\) 3.82309i 0.178447i
\(460\) 10.8613i 0.506412i
\(461\) 17.6002 0.819724 0.409862 0.912147i \(-0.365577\pi\)
0.409862 + 0.912147i \(0.365577\pi\)
\(462\) −3.98522 + 18.8756i −0.185409 + 0.878171i
\(463\) 7.41641 0.344670 0.172335 0.985038i \(-0.444869\pi\)
0.172335 + 0.985038i \(0.444869\pi\)
\(464\) 8.04609i 0.373530i
\(465\) 7.93290i 0.367879i
\(466\) 41.6714 1.93039
\(467\) 2.27735i 0.105383i −0.998611 0.0526915i \(-0.983220\pi\)
0.998611 0.0526915i \(-0.0167800\pi\)
\(468\) 18.4784 0.854164
\(469\) 4.70228 + 3.14830i 0.217131 + 0.145375i
\(470\) 4.54451i 0.209623i
\(471\) −6.51147 −0.300033
\(472\) −6.90035 −0.317614
\(473\) 19.6209 7.88019i 0.902169 0.362332i
\(474\) 28.8660i 1.32586i
\(475\) −2.33228 −0.107012
\(476\) 23.8145 + 15.9445i 1.09154 + 0.730813i
\(477\) −10.0324 −0.459353
\(478\) −18.9331 −0.865979
\(479\) 13.4221 0.613269 0.306635 0.951827i \(-0.400797\pi\)
0.306635 + 0.951827i \(0.400797\pi\)
\(480\) 7.26712i 0.331697i
\(481\) −51.7361 −2.35896
\(482\) 55.0138i 2.50581i
\(483\) −5.64252 + 8.42762i −0.256744 + 0.383470i
\(484\) 22.5090 21.5575i 1.02314 0.979888i
\(485\) 10.0995 0.458596
\(486\) 2.19849 0.0997256
\(487\) −21.0272 −0.952834 −0.476417 0.879219i \(-0.658065\pi\)
−0.476417 + 0.879219i \(0.658065\pi\)
\(488\) 16.8930i 0.764711i
\(489\) 10.7942i 0.488132i
\(490\) −5.86279 14.2289i −0.264854 0.642798i
\(491\) 29.1814i 1.31694i −0.752608 0.658469i \(-0.771204\pi\)
0.752608 0.658469i \(-0.228796\pi\)
\(492\) 28.8607i 1.30114i
\(493\) 18.7707i 0.845391i
\(494\) 33.4400i 1.50454i
\(495\) −3.07768 + 1.23607i −0.138332 + 0.0555571i
\(496\) 13.0002i 0.583726i
\(497\) −18.4784 12.3718i −0.828869 0.554950i
\(498\) −33.8033 −1.51476
\(499\) −29.1156 −1.30339 −0.651696 0.758480i \(-0.725942\pi\)
−0.651696 + 0.758480i \(0.725942\pi\)
\(500\) 2.83337i 0.126712i
\(501\) 17.4027i 0.777494i
\(502\) 4.26465 0.190341
\(503\) −26.8337 −1.19646 −0.598228 0.801326i \(-0.704128\pi\)
−0.598228 + 0.801326i \(0.704128\pi\)
\(504\) 2.69683 4.02796i 0.120126 0.179420i
\(505\) 1.45309i 0.0646614i
\(506\) 25.9376 10.4171i 1.15306 0.463097i
\(507\) 29.5327i 1.31159i
\(508\) 45.8860i 2.03586i
\(509\) 9.01678i 0.399662i −0.979830 0.199831i \(-0.935961\pi\)
0.979830 0.199831i \(-0.0640393\pi\)
\(510\) 8.40503i 0.372181i
\(511\) −18.3379 12.2777i −0.811222 0.543135i
\(512\) 17.9141i 0.791698i
\(513\) 2.33228i 0.102973i
\(514\) −61.1152 −2.69568
\(515\) 8.96086 0.394863
\(516\) −18.0633 −0.795192
\(517\) −6.36189 + 2.55508i −0.279796 + 0.112372i
\(518\) −25.6714 + 38.3426i −1.12794 + 1.68468i
\(519\) 4.82437i 0.211766i
\(520\) 11.9487 0.523987
\(521\) 28.1829i 1.23471i 0.786683 + 0.617357i \(0.211797\pi\)
−0.786683 + 0.617357i \(0.788203\pi\)
\(522\) −10.7942 −0.472450
\(523\) −32.3643 −1.41519 −0.707596 0.706617i \(-0.750220\pi\)
−0.707596 + 0.706617i \(0.750220\pi\)
\(524\) −36.7838 −1.60691
\(525\) 1.47195 2.19849i 0.0642411 0.0959500i
\(526\) −6.52806 −0.284637
\(527\) 30.3282i 1.32112i
\(528\) 5.04362 2.02563i 0.219495 0.0881543i
\(529\) −8.30531 −0.361100
\(530\) −22.0562 −0.958060
\(531\) 3.76626i 0.163442i
\(532\) 14.5281 + 9.72692i 0.629871 + 0.421716i
\(533\) 66.4302 2.87741
\(534\) 1.55186i 0.0671555i
\(535\) 11.6514 0.503733
\(536\) 3.91872i 0.169263i
\(537\) 22.3267i 0.963470i
\(538\) 22.6320 0.975734
\(539\) 16.6229 16.2074i 0.716000 0.698100i
\(540\) 2.83337 0.121929
\(541\) 4.01749i 0.172726i −0.996264 0.0863628i \(-0.972476\pi\)
0.996264 0.0863628i \(-0.0275244\pi\)
\(542\) 42.8818i 1.84193i
\(543\) 13.2775 0.569794
\(544\) 27.7828i 1.19118i
\(545\) −8.73292 −0.374077
\(546\) −31.5218 21.1047i −1.34901 0.903198i
\(547\) 4.86524i 0.208023i −0.994576 0.104011i \(-0.966832\pi\)
0.994576 0.104011i \(-0.0331679\pi\)
\(548\) 0.328998 0.0140541
\(549\) −9.22033 −0.393514
\(550\) −6.76626 + 2.71749i −0.288514 + 0.115874i
\(551\) 11.4511i 0.487833i
\(552\) −7.02329 −0.298931
\(553\) 19.3266 28.8660i 0.821849 1.22751i
\(554\) −52.8977 −2.24741
\(555\) −7.93290 −0.336733
\(556\) −6.19310 −0.262646
\(557\) 5.35951i 0.227090i 0.993533 + 0.113545i \(0.0362206\pi\)
−0.993533 + 0.113545i \(0.963779\pi\)
\(558\) 17.4404 0.738311
\(559\) 41.5773i 1.75853i
\(560\) −2.41219 + 3.60282i −0.101933 + 0.152247i
\(561\) −11.7663 + 4.72560i −0.496772 + 0.199515i
\(562\) −5.82796 −0.245838
\(563\) −1.65063 −0.0695659 −0.0347829 0.999395i \(-0.511074\pi\)
−0.0347829 + 0.999395i \(0.511074\pi\)
\(564\) 5.85686 0.246618
\(565\) 9.36589i 0.394026i
\(566\) 31.0091i 1.30341i
\(567\) −2.19849 1.47195i −0.0923280 0.0618161i
\(568\) 15.3993i 0.646139i
\(569\) 39.4976i 1.65583i 0.560856 + 0.827914i \(0.310472\pi\)
−0.560856 + 0.827914i \(0.689528\pi\)
\(570\) 5.12749i 0.214767i
\(571\) 9.97531i 0.417454i −0.977974 0.208727i \(-0.933068\pi\)
0.977974 0.208727i \(-0.0669320\pi\)
\(572\) 22.8405 + 56.8706i 0.955011 + 2.37788i
\(573\) 4.52806i 0.189162i
\(574\) 32.9626 49.2327i 1.37583 2.05493i
\(575\) −3.83337 −0.159862
\(576\) −12.6992 −0.529132
\(577\) 42.3245i 1.76199i 0.473124 + 0.880996i \(0.343126\pi\)
−0.473124 + 0.880996i \(0.656874\pi\)
\(578\) 5.24116i 0.218004i
\(579\) −4.39698 −0.182732
\(580\) −13.9113 −0.577637
\(581\) 33.8033 + 22.6322i 1.40240 + 0.938944i
\(582\) 22.2037i 0.920374i
\(583\) −12.4008 30.8766i −0.513587 1.27878i
\(584\) 15.2822i 0.632382i
\(585\) 6.52171i 0.269640i
\(586\) 4.27082i 0.176426i
\(587\) 0.386939i 0.0159707i −0.999968 0.00798535i \(-0.997458\pi\)
0.999968 0.00798535i \(-0.00254184\pi\)
\(588\) −18.3379 + 7.55583i −0.756243 + 0.311597i
\(589\) 18.5017i 0.762350i
\(590\) 8.28009i 0.340886i
\(591\) −22.8254 −0.938910
\(592\) 13.0002 0.534305
\(593\) −7.48636 −0.307428 −0.153714 0.988115i \(-0.549123\pi\)
−0.153714 + 0.988115i \(0.549123\pi\)
\(594\) 2.71749 + 6.76626i 0.111500 + 0.277623i
\(595\) 5.62739 8.40503i 0.230701 0.344573i
\(596\) 15.3993i 0.630778i
\(597\) 17.5325 0.717558
\(598\) 54.9625i 2.24758i
\(599\) 24.3939 0.996706 0.498353 0.866974i \(-0.333938\pi\)
0.498353 + 0.866974i \(0.333938\pi\)
\(600\) 1.83215 0.0747971
\(601\) −17.1086 −0.697876 −0.348938 0.937146i \(-0.613458\pi\)
−0.348938 + 0.937146i \(0.613458\pi\)
\(602\) 30.8137 + 20.6306i 1.25587 + 0.840841i
\(603\) 2.13887 0.0871014
\(604\) 64.3673i 2.61907i
\(605\) −7.60845 7.94427i −0.309328 0.322981i
\(606\) 3.19460 0.129772
\(607\) −32.4398 −1.31669 −0.658345 0.752717i \(-0.728743\pi\)
−0.658345 + 0.752717i \(0.728743\pi\)
\(608\) 16.9489i 0.687370i
\(609\) 10.7942 + 7.22702i 0.437404 + 0.292854i
\(610\) −20.2708 −0.820742
\(611\) 13.4811i 0.545385i
\(612\) 10.8322 0.437866
\(613\) 12.1632i 0.491267i 0.969363 + 0.245634i \(0.0789960\pi\)
−0.969363 + 0.245634i \(0.921004\pi\)
\(614\) 17.6667i 0.712971i
\(615\) 10.1860 0.410739
\(616\) 15.7303 + 3.32115i 0.633790 + 0.133813i
\(617\) −35.0831 −1.41239 −0.706197 0.708015i \(-0.749591\pi\)
−0.706197 + 0.708015i \(0.749591\pi\)
\(618\) 19.7004i 0.792465i
\(619\) 2.89877i 0.116511i 0.998302 + 0.0582557i \(0.0185539\pi\)
−0.998302 + 0.0582557i \(0.981446\pi\)
\(620\) 22.4768 0.902690
\(621\) 3.83337i 0.153828i
\(622\) −27.4699 −1.10144
\(623\) 1.03901 1.55186i 0.0416271 0.0621739i
\(624\) 10.6876i 0.427846i
\(625\) 1.00000 0.0400000
\(626\) 10.3060 0.411913
\(627\) −7.17801 + 2.88285i −0.286662 + 0.115130i
\(628\) 18.4494i 0.736211i
\(629\) −30.3282 −1.20926
\(630\) −4.83337 3.23607i −0.192566 0.128928i
\(631\) 34.8050 1.38557 0.692784 0.721146i \(-0.256384\pi\)
0.692784 + 0.721146i \(0.256384\pi\)
\(632\) 24.0559 0.956893
\(633\) 12.9488 0.514669
\(634\) 37.5071i 1.48960i
\(635\) 16.1949 0.642674
\(636\) 28.4255i 1.12715i
\(637\) 17.3917 + 42.2094i 0.689082 + 1.67240i
\(638\) −13.3424 33.2212i −0.528230 1.31524i
\(639\) −8.40503 −0.332498
\(640\) −13.3848 −0.529079
\(641\) 20.5976 0.813555 0.406778 0.913527i \(-0.366652\pi\)
0.406778 + 0.913527i \(0.366652\pi\)
\(642\) 25.6155i 1.01096i
\(643\) 20.1269i 0.793729i 0.917877 + 0.396865i \(0.129902\pi\)
−0.917877 + 0.396865i \(0.870098\pi\)
\(644\) 23.8785 + 15.9873i 0.940946 + 0.629989i
\(645\) 6.37521i 0.251024i
\(646\) 19.6029i 0.771264i
\(647\) 5.14333i 0.202205i −0.994876 0.101103i \(-0.967763\pi\)
0.994876 0.101103i \(-0.0322370\pi\)
\(648\) 1.83215i 0.0719736i
\(649\) −11.5914 + 4.65536i −0.455001 + 0.182739i
\(650\) 14.3379i 0.562380i
\(651\) −17.4404 11.6768i −0.683543 0.457651i
\(652\) 30.5840 1.19776
\(653\) −30.9118 −1.20967 −0.604837 0.796349i \(-0.706762\pi\)
−0.604837 + 0.796349i \(0.706762\pi\)
\(654\) 19.1993i 0.750750i
\(655\) 12.9824i 0.507263i
\(656\) −16.6925 −0.651734
\(657\) −8.34114 −0.325419
\(658\) −9.99107 6.68929i −0.389492 0.260776i
\(659\) 2.92161i 0.113810i 0.998380 + 0.0569048i \(0.0181231\pi\)
−0.998380 + 0.0569048i \(0.981877\pi\)
\(660\) 3.50223 + 8.72020i 0.136324 + 0.339433i
\(661\) 15.7991i 0.614513i 0.951627 + 0.307256i \(0.0994109\pi\)
−0.951627 + 0.307256i \(0.900589\pi\)
\(662\) 37.4859i 1.45693i
\(663\) 24.9331i 0.968321i
\(664\) 28.1705i 1.09323i
\(665\) 3.43299 5.12749i 0.133126 0.198836i
\(666\) 17.4404i 0.675802i
\(667\) 18.8212i 0.728759i
\(668\) 49.3081 1.90779
\(669\) −1.62739 −0.0629187
\(670\) 4.70228 0.181665
\(671\) −11.3970 28.3773i −0.439975 1.09549i
\(672\) 15.9767 + 10.6968i 0.616315 + 0.412639i
\(673\) 13.1809i 0.508088i 0.967193 + 0.254044i \(0.0817608\pi\)
−0.967193 + 0.254044i \(0.918239\pi\)
\(674\) 16.6781 0.642417
\(675\) 1.00000i 0.0384900i
\(676\) −83.6770 −3.21835
\(677\) −24.6857 −0.948747 −0.474373 0.880324i \(-0.657325\pi\)
−0.474373 + 0.880324i \(0.657325\pi\)
\(678\) 20.5908 0.790786
\(679\) −14.8660 + 22.2037i −0.570505 + 0.852101i
\(680\) 7.00447 0.268609
\(681\) 15.1336i 0.579919i
\(682\) 21.5575 + 53.6760i 0.825480 + 2.05536i
\(683\) 36.4028 1.39291 0.696457 0.717599i \(-0.254759\pi\)
0.696457 + 0.717599i \(0.254759\pi\)
\(684\) 6.60819 0.252671
\(685\) 0.116115i 0.00443654i
\(686\) 39.9119 + 8.05498i 1.52384 + 0.307541i
\(687\) −4.85442 −0.185208
\(688\) 10.4475i 0.398307i
\(689\) 65.4286 2.49263
\(690\) 8.42762i 0.320834i
\(691\) 35.8885i 1.36526i 0.730762 + 0.682632i \(0.239165\pi\)
−0.730762 + 0.682632i \(0.760835\pi\)
\(692\) −13.6692 −0.519626
\(693\) 1.81271 8.58569i 0.0688591 0.326143i
\(694\) −62.2690 −2.36370
\(695\) 2.18577i 0.0829111i
\(696\) 8.99553i 0.340975i
\(697\) 38.9420 1.47503
\(698\) 43.9044i 1.66181i
\(699\) −18.9545 −0.716926
\(700\) −6.22913 4.17057i −0.235439 0.157633i
\(701\) 10.3071i 0.389293i −0.980873 0.194646i \(-0.937644\pi\)
0.980873 0.194646i \(-0.0623559\pi\)
\(702\) −14.3379 −0.541150
\(703\) −18.5017 −0.697805
\(704\) −15.6970 39.0840i −0.591604 1.47303i
\(705\) 2.06710i 0.0778516i
\(706\) 34.0981 1.28330
\(707\) −3.19460 2.13887i −0.120145 0.0804404i
\(708\) 10.6712 0.401048
\(709\) −20.5273 −0.770919 −0.385460 0.922725i \(-0.625957\pi\)
−0.385460 + 0.922725i \(0.625957\pi\)
\(710\) −18.4784 −0.693482
\(711\) 13.1299i 0.492410i
\(712\) 1.29327 0.0484672
\(713\) 30.4097i 1.13885i
\(714\) −18.4784 12.3718i −0.691536 0.463002i
\(715\) 20.0718 8.06128i 0.750641 0.301475i
\(716\) 63.2598 2.36413
\(717\) 8.61185 0.321616
\(718\) 56.9558 2.12557
\(719\) 0.665030i 0.0248014i −0.999923 0.0124007i \(-0.996053\pi\)
0.999923 0.0124007i \(-0.00394737\pi\)
\(720\) 1.63877i 0.0610734i
\(721\) −13.1899 + 19.7004i −0.491219 + 0.733680i
\(722\) 29.8126i 1.10951i
\(723\) 25.0234i 0.930631i
\(724\) 37.6201i 1.39814i
\(725\) 4.90983i 0.182347i
\(726\) −17.4654 + 16.7271i −0.648202 + 0.620802i
\(727\) 32.3592i 1.20014i −0.799949 0.600068i \(-0.795140\pi\)
0.799949 0.600068i \(-0.204860\pi\)
\(728\) −17.5879 + 26.2692i −0.651852 + 0.973601i
\(729\) −1.00000 −0.0370370
\(730\) −18.3379 −0.678717
\(731\) 24.3730i 0.901468i
\(732\) 26.1246i 0.965592i
\(733\) 37.9468 1.40160 0.700799 0.713359i \(-0.252827\pi\)
0.700799 + 0.713359i \(0.252827\pi\)
\(734\) −35.8229 −1.32225
\(735\) 2.66673 + 6.47214i 0.0983639 + 0.238728i
\(736\) 27.8575i 1.02684i
\(737\) 2.64379 + 6.58276i 0.0973851 + 0.242479i
\(738\) 22.3939i 0.824329i
\(739\) 17.3895i 0.639684i 0.947471 + 0.319842i \(0.103630\pi\)
−0.947471 + 0.319842i \(0.896370\pi\)
\(740\) 22.4768i 0.826263i
\(741\) 15.2104i 0.558769i
\(742\) 32.4656 48.4904i 1.19185 1.78014i
\(743\) 11.3236i 0.415423i −0.978190 0.207712i \(-0.933398\pi\)
0.978190 0.207712i \(-0.0666016\pi\)
\(744\) 14.5342i 0.532851i
\(745\) −5.43497 −0.199122
\(746\) 23.3312 0.854216
\(747\) 15.3757 0.562567
\(748\) 13.3894 + 33.3381i 0.489563 + 1.21896i
\(749\) −17.1502 + 25.6155i −0.626656 + 0.935969i
\(750\) 2.19849i 0.0802776i
\(751\) −43.7038 −1.59477 −0.797387 0.603468i \(-0.793785\pi\)
−0.797387 + 0.603468i \(0.793785\pi\)
\(752\) 3.38751i 0.123530i
\(753\) −1.93981 −0.0706905
\(754\) 70.3968 2.56370
\(755\) 22.7176 0.826778
\(756\) −4.17057 + 6.22913i −0.151682 + 0.226551i
\(757\) −51.0654 −1.85600 −0.928002 0.372574i \(-0.878475\pi\)
−0.928002 + 0.372574i \(0.878475\pi\)
\(758\) 59.2683i 2.15272i
\(759\) −11.7979 + 4.73830i −0.428236 + 0.171989i
\(760\) 4.27308 0.155001
\(761\) −43.3228 −1.57045 −0.785226 0.619209i \(-0.787453\pi\)
−0.785226 + 0.619209i \(0.787453\pi\)
\(762\) 35.6043i 1.28981i
\(763\) 12.8544 19.1993i 0.465361 0.695060i
\(764\) 12.8296 0.464160
\(765\) 3.82309i 0.138224i
\(766\) 22.4480 0.811079
\(767\) 24.5625i 0.886899i
\(768\) 4.02796i 0.145347i
\(769\) 27.7894 1.00211 0.501055 0.865415i \(-0.332945\pi\)
0.501055 + 0.865415i \(0.332945\pi\)
\(770\) 3.98522 18.8756i 0.143618 0.680228i
\(771\) 27.7987 1.00115
\(772\) 12.4583i 0.448383i
\(773\) 30.3758i 1.09254i −0.837609 0.546270i \(-0.816047\pi\)
0.837609 0.546270i \(-0.183953\pi\)
\(774\) 14.0158 0.503789
\(775\) 7.93290i 0.284958i
\(776\) −18.5038 −0.664249
\(777\) 11.6768 17.4404i 0.418904 0.625671i
\(778\) 21.0547i 0.754847i
\(779\) 23.7566 0.851168
\(780\) −18.4784 −0.661633
\(781\) −10.3892 25.8680i −0.371754 0.925631i
\(782\) 32.2196i 1.15217i
\(783\) 4.90983 0.175463
\(784\) −4.37016 10.6063i −0.156077 0.378798i
\(785\) 6.51147 0.232404
\(786\) 28.5416 1.01805
\(787\) 11.5972 0.413395 0.206698 0.978405i \(-0.433728\pi\)
0.206698 + 0.978405i \(0.433728\pi\)
\(788\) 64.6726i 2.30387i
\(789\) 2.96933 0.105711
\(790\) 28.8660i 1.02701i
\(791\) −20.5908 13.7861i −0.732126 0.490178i
\(792\) 5.63877 2.26466i 0.200365 0.0804711i
\(793\) 60.1323 2.13536
\(794\) −65.7929 −2.33490
\(795\) 10.0324 0.355813
\(796\) 49.6760i 1.76072i
\(797\) 17.6112i 0.623821i −0.950112 0.311910i \(-0.899031\pi\)
0.950112 0.311910i \(-0.100969\pi\)
\(798\) −11.2727 7.54741i −0.399051 0.267175i
\(799\) 7.90273i 0.279578i
\(800\) 7.26712i 0.256931i
\(801\) 0.705874i 0.0249408i
\(802\) 60.5555i 2.13829i
\(803\) −10.3102 25.6714i −0.363840 0.905924i
\(804\) 6.06019i 0.213727i
\(805\) 5.64252 8.42762i 0.198873 0.297035i
\(806\) −113.741 −4.00637
\(807\) −10.2943 −0.362377
\(808\) 2.66227i 0.0936582i
\(809\) 14.3510i 0.504555i 0.967655 + 0.252278i \(0.0811796\pi\)
−0.967655 + 0.252278i \(0.918820\pi\)
\(810\) −2.19849 −0.0772471
\(811\) 6.31314 0.221684 0.110842 0.993838i \(-0.464645\pi\)
0.110842 + 0.993838i \(0.464645\pi\)
\(812\) 20.4768 30.5840i 0.718595 1.07329i
\(813\) 19.5051i 0.684074i
\(814\) −53.6760 + 21.5575i −1.88134 + 0.755591i
\(815\) 10.7942i 0.378105i
\(816\) 6.26517i 0.219325i
\(817\) 14.8687i 0.520192i
\(818\) 9.16143i 0.320322i
\(819\) 14.3379 + 9.59963i 0.501008 + 0.335438i
\(820\) 28.8607i 1.00786i
\(821\) 51.0311i 1.78100i −0.454986 0.890499i \(-0.650356\pi\)
0.454986 0.890499i \(-0.349644\pi\)
\(822\) −0.255279 −0.00890387
\(823\) 47.7810 1.66554 0.832770 0.553619i \(-0.186754\pi\)
0.832770 + 0.553619i \(0.186754\pi\)
\(824\) −16.4176 −0.571935
\(825\) 3.07768 1.23607i 0.107151 0.0430344i
\(826\) −18.2037 12.1879i −0.633388 0.424071i
\(827\) 3.94416i 0.137152i −0.997646 0.0685759i \(-0.978154\pi\)
0.997646 0.0685759i \(-0.0218455\pi\)
\(828\) 10.8613 0.377457
\(829\) 23.9638i 0.832298i 0.909297 + 0.416149i \(0.136620\pi\)
−0.909297 + 0.416149i \(0.863380\pi\)
\(830\) 33.8033 1.17333
\(831\) 24.0609 0.834663
\(832\) 82.8202 2.87128
\(833\) 10.1952 + 24.7436i 0.353241 + 0.857314i
\(834\) 4.80540 0.166398
\(835\) 17.4027i 0.602244i
\(836\) 8.16818 + 20.3379i 0.282502 + 0.703402i
\(837\) −7.93290 −0.274201
\(838\) −26.1631 −0.903789
\(839\) 23.2339i 0.802124i −0.916051 0.401062i \(-0.868641\pi\)
0.916051 0.401062i \(-0.131359\pi\)
\(840\) −2.69683 + 4.02796i −0.0930494 + 0.138978i
\(841\) 4.89356 0.168743
\(842\) 57.0997i 1.96779i
\(843\) 2.65089 0.0913015
\(844\) 36.6887i 1.26288i
\(845\) 29.5327i 1.01596i
\(846\) −4.54451 −0.156244
\(847\) 28.6647 5.03355i 0.984930 0.172955i
\(848\) −16.4408 −0.564581
\(849\) 14.1047i 0.484073i
\(850\) 8.40503i 0.288290i
\(851\) −30.4097 −1.04243
\(852\) 23.8145i 0.815872i
\(853\) −27.8240 −0.952674 −0.476337 0.879263i \(-0.658036\pi\)
−0.476337 + 0.879263i \(0.658036\pi\)
\(854\) 29.8376 44.5652i 1.02102 1.52499i
\(855\) 2.33228i 0.0797622i
\(856\) −21.3471 −0.729627
\(857\) −3.63200 −0.124067 −0.0620334 0.998074i \(-0.519759\pi\)
−0.0620334 + 0.998074i \(0.519759\pi\)
\(858\) −17.7227 44.1276i −0.605041 1.50649i
\(859\) 23.3644i 0.797182i −0.917129 0.398591i \(-0.869499\pi\)
0.917129 0.398591i \(-0.130501\pi\)
\(860\) 18.0633 0.615953
\(861\) −14.9933 + 22.3939i −0.510970 + 0.763180i
\(862\) −42.6427 −1.45242
\(863\) 7.16683 0.243962 0.121981 0.992532i \(-0.461075\pi\)
0.121981 + 0.992532i \(0.461075\pi\)
\(864\) 7.26712 0.247232
\(865\) 4.82437i 0.164034i
\(866\) 6.95037 0.236183
\(867\) 2.38398i 0.0809643i
\(868\) −33.0847 + 49.4150i −1.12297 + 1.67726i
\(869\) 40.4097 16.2295i 1.37080 0.550547i
\(870\) 10.7942 0.365958
\(871\) −13.9491 −0.472646
\(872\) 16.0000 0.541828
\(873\) 10.0995i 0.341817i
\(874\) 19.6555i 0.664859i
\(875\) −1.47195 + 2.19849i −0.0497610 + 0.0743226i
\(876\) 23.6335i 0.798502i
\(877\) 20.0190i 0.675993i 0.941147 + 0.337997i \(0.109749\pi\)
−0.941147 + 0.337997i \(0.890251\pi\)
\(878\) 61.6830i 2.08170i
\(879\) 1.94262i 0.0655228i
\(880\) −5.04362 + 2.02563i −0.170020 + 0.0682840i
\(881\) 14.0814i 0.474416i 0.971459 + 0.237208i \(0.0762322\pi\)
−0.971459 + 0.237208i \(0.923768\pi\)
\(882\) 14.2289 5.86279i 0.479113 0.197410i
\(883\) −12.1161 −0.407740 −0.203870 0.978998i \(-0.565352\pi\)
−0.203870 + 0.978998i \(0.565352\pi\)
\(884\) −70.6446 −2.37603
\(885\) 3.76626i 0.126602i
\(886\) 72.4380i 2.43360i
\(887\) 1.96381 0.0659384 0.0329692 0.999456i \(-0.489504\pi\)
0.0329692 + 0.999456i \(0.489504\pi\)
\(888\) 14.5342 0.487737
\(889\) −23.8380 + 35.6043i −0.799502 + 1.19413i
\(890\) 1.55186i 0.0520184i
\(891\) −1.23607 3.07768i −0.0414098 0.103106i
\(892\) 4.61100i 0.154388i
\(893\) 4.82106i 0.161331i
\(894\) 11.9487i 0.399626i
\(895\) 22.3267i 0.746301i
\(896\) 19.7017 29.4263i 0.658187 0.983063i
\(897\) 25.0001i 0.834729i
\(898\) 62.0208i 2.06966i
\(899\) 38.9492 1.29903
\(900\) −2.83337 −0.0944455
\(901\) 38.3549 1.27779
\(902\) 68.9212 27.6803i 2.29482 0.921654i
\(903\) −14.0158 9.38398i −0.466418 0.312279i
\(904\) 17.1597i 0.570723i
\(905\) −13.2775 −0.441360
\(906\) 49.9445i 1.65929i
\(907\) 35.5032 1.17887 0.589433 0.807817i \(-0.299351\pi\)
0.589433 + 0.807817i \(0.299351\pi\)
\(908\) −42.8789 −1.42299
\(909\) −1.45309 −0.0481958
\(910\) 31.5218 + 21.1047i 1.04494 + 0.699614i
\(911\) −36.4032 −1.20609 −0.603045 0.797707i \(-0.706046\pi\)
−0.603045 + 0.797707i \(0.706046\pi\)
\(912\) 3.82207i 0.126561i
\(913\) 19.0054 + 47.3215i 0.628987 + 1.56611i
\(914\) 9.37633 0.310141
\(915\) 9.22033 0.304815
\(916\) 13.7543i 0.454456i
\(917\) −28.5416 19.1094i −0.942528 0.631048i
\(918\) −8.40503 −0.277407
\(919\) 43.9423i 1.44952i 0.688999 + 0.724762i \(0.258050\pi\)
−0.688999 + 0.724762i \(0.741950\pi\)
\(920\) 7.02329 0.231551
\(921\) 8.03584i 0.264790i
\(922\) 38.6939i 1.27432i
\(923\) 54.8152 1.80426
\(924\) −24.3264 5.13607i −0.800280 0.168964i
\(925\) 7.93290 0.260832
\(926\) 16.3049i 0.535813i
\(927\) 8.96086i 0.294313i
\(928\) −35.6803 −1.17126
\(929\) 20.4209i 0.669987i −0.942220 0.334994i \(-0.891266\pi\)
0.942220 0.334994i \(-0.108734\pi\)
\(930\) −17.4404 −0.571893
\(931\) 6.21956 + 15.0948i 0.203838 + 0.494713i
\(932\) 53.7051i 1.75917i
\(933\) 12.4949 0.409064
\(934\) 5.00673 0.163825
\(935\) 11.7663 4.72560i 0.384798 0.154544i
\(936\) 11.9487i 0.390557i
\(937\) 24.1831 0.790026 0.395013 0.918676i \(-0.370740\pi\)
0.395013 + 0.918676i \(0.370740\pi\)
\(938\) −6.92152 + 10.3379i −0.225996 + 0.337545i
\(939\) −4.68778 −0.152980
\(940\) −5.85686 −0.191030
\(941\) 10.6236 0.346321 0.173160 0.984894i \(-0.444602\pi\)
0.173160 + 0.984894i \(0.444602\pi\)
\(942\) 14.3154i 0.466422i
\(943\) 39.0467 1.27154
\(944\) 6.17204i 0.200883i
\(945\) 2.19849 + 1.47195i 0.0715169 + 0.0478825i
\(946\) 17.3245 + 43.1363i 0.563269 + 1.40248i
\(947\) −14.1439 −0.459614 −0.229807 0.973236i \(-0.573810\pi\)
−0.229807 + 0.973236i \(0.573810\pi\)
\(948\) −37.2018 −1.20826
\(949\) 54.3985 1.76585
\(950\) 5.12749i 0.166358i
\(951\) 17.0604i 0.553221i
\(952\) −10.3102 + 15.3993i −0.334156 + 0.499093i
\(953\) 27.8095i 0.900840i 0.892817 + 0.450420i \(0.148726\pi\)
−0.892817 + 0.450420i \(0.851274\pi\)
\(954\) 22.0562i 0.714096i
\(955\) 4.52806i 0.146525i
\(956\) 24.4005i 0.789170i
\(957\) 6.06888 + 15.1109i 0.196179 + 0.488466i
\(958\) 29.5083i 0.953369i
\(959\) 0.255279 + 0.170916i 0.00824338 + 0.00551917i
\(960\) 12.6992 0.409864
\(961\) −31.9308 −1.03003
\(962\) 113.741i 3.66717i
\(963\) 11.6514i 0.375461i
\(964\) 70.9005 2.28355
\(965\) 4.39698 0.141544
\(966\) −18.5281 12.4050i −0.596130 0.399125i
\(967\) 11.4103i 0.366930i 0.983026 + 0.183465i \(0.0587313\pi\)
−0.983026 + 0.183465i \(0.941269\pi\)
\(968\) 13.9398 + 14.5551i 0.448042 + 0.467818i
\(969\) 8.91650i 0.286439i
\(970\) 22.2037i 0.712919i
\(971\) 45.1873i 1.45013i 0.688680 + 0.725065i \(0.258190\pi\)
−0.688680 + 0.725065i \(0.741810\pi\)
\(972\) 2.83337i 0.0908802i
\(973\) −4.80540 3.21735i −0.154054 0.103143i
\(974\) 46.2282i 1.48125i
\(975\) 6.52171i 0.208862i
\(976\) −15.1100 −0.483660
\(977\) 49.5094 1.58395 0.791973 0.610556i \(-0.209054\pi\)
0.791973 + 0.610556i \(0.209054\pi\)
\(978\) −23.7310 −0.758834
\(979\) 2.17246 0.872509i 0.0694320 0.0278855i
\(980\) 18.3379 7.55583i 0.585784 0.241362i
\(981\) 8.73292i 0.278821i
\(982\) 64.1551 2.04727
\(983\) 1.65631i 0.0528282i 0.999651 + 0.0264141i \(0.00840884\pi\)
−0.999651 + 0.0264141i \(0.991591\pi\)
\(984\) −18.6623 −0.594931
\(985\) 22.8254 0.727276
\(986\) 41.2673 1.31422
\(987\) 4.54451 + 3.04267i 0.144653 + 0.0968493i
\(988\) −43.0967 −1.37109
\(989\) 24.4385i 0.777099i
\(990\) −2.71749 6.76626i −0.0863673 0.215046i
\(991\) 57.7821 1.83551 0.917754 0.397148i \(-0.130000\pi\)
0.917754 + 0.397148i \(0.130000\pi\)
\(992\) 57.6493 1.83037
\(993\) 17.0507i 0.541088i
\(994\) 27.1993 40.6246i 0.862708 1.28853i
\(995\) −17.5325 −0.555818
\(996\) 43.5650i 1.38041i
\(997\) −49.4028 −1.56460 −0.782300 0.622901i \(-0.785954\pi\)
−0.782300 + 0.622901i \(0.785954\pi\)
\(998\) 64.0103i 2.02621i
\(999\) 7.93290i 0.250986i
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 1155.2.i.c.76.13 yes 16
7.6 odd 2 inner 1155.2.i.c.76.14 yes 16
11.10 odd 2 inner 1155.2.i.c.76.3 16
77.76 even 2 inner 1155.2.i.c.76.4 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.i.c.76.3 16 11.10 odd 2 inner
1155.2.i.c.76.4 yes 16 77.76 even 2 inner
1155.2.i.c.76.13 yes 16 1.1 even 1 trivial
1155.2.i.c.76.14 yes 16 7.6 odd 2 inner