Properties

Label 1110.2.d.j.889.6
Level $1110$
Weight $2$
Character 1110.889
Analytic conductor $8.863$
Analytic rank $0$
Dimension $8$
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] = [1110,2,Mod(889,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1110.889");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.d (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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.57815240704.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 2x^{6} + 89x^{4} - 170x^{3} + 162x^{2} - 72x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 889.6
Root \(-2.15569 - 2.15569i\) of defining polynomial
Character \(\chi\) \(=\) 1110.889
Dual form 1110.2.d.j.889.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.594137 - 2.15569i) q^{5} -1.00000 q^{6} -1.17795i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.594137 - 2.15569i) q^{5} -1.00000 q^{6} -1.17795i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.15569 - 0.594137i) q^{10} -0.822051 q^{11} -1.00000i q^{12} +1.74983i q^{13} +1.17795 q^{14} +(2.15569 - 0.594137i) q^{15} +1.00000 q^{16} +3.94516i q^{17} -1.00000i q^{18} -1.29400 q^{19} +(0.594137 + 2.15569i) q^{20} +1.17795 q^{21} -0.822051i q^{22} +7.68466i q^{23} +1.00000 q^{24} +(-4.29400 + 2.56155i) q^{25} -1.74983 q^{26} -1.00000i q^{27} +1.17795i q^{28} -9.23916 q^{29} +(0.594137 + 2.15569i) q^{30} -9.30433 q^{31} +1.00000i q^{32} -0.822051i q^{33} -3.94516 q^{34} +(-2.53929 + 0.699864i) q^{35} +1.00000 q^{36} -1.00000i q^{37} -1.29400i q^{38} -1.74983 q^{39} +(-2.15569 + 0.594137i) q^{40} -2.50671 q^{41} +1.17795i q^{42} -2.92778i q^{43} +0.822051 q^{44} +(0.594137 + 2.15569i) q^{45} -7.68466 q^{46} -7.18827i q^{47} +1.00000i q^{48} +5.61244 q^{49} +(-2.56155 - 4.29400i) q^{50} -3.94516 q^{51} -1.74983i q^{52} +13.8659i q^{53} +1.00000 q^{54} +(0.488411 + 1.77209i) q^{55} -1.17795 q^{56} -1.29400i q^{57} -9.23916i q^{58} -3.18827 q^{59} +(-2.15569 + 0.594137i) q^{60} +8.78333 q^{61} -9.30433i q^{62} +1.17795i q^{63} -1.00000 q^{64} +(3.77209 - 1.03964i) q^{65} +0.822051 q^{66} +15.2108i q^{67} -3.94516i q^{68} -7.68466 q^{69} +(-0.699864 - 2.53929i) q^{70} -6.65317 q^{71} +1.00000i q^{72} -11.9168i q^{73} +1.00000 q^{74} +(-2.56155 - 4.29400i) q^{75} +1.29400 q^{76} +0.968334i q^{77} -1.74983i q^{78} +0.797618 q^{79} +(-0.594137 - 2.15569i) q^{80} +1.00000 q^{81} -2.50671i q^{82} +7.72918i q^{83} -1.17795 q^{84} +(8.50454 - 2.34397i) q^{85} +2.92778 q^{86} -9.23916i q^{87} +0.822051i q^{88} -14.8729 q^{89} +(-2.15569 + 0.594137i) q^{90} +2.06121 q^{91} -7.68466i q^{92} -9.30433i q^{93} +7.18827 q^{94} +(0.768815 + 2.78947i) q^{95} -1.00000 q^{96} -13.0947i q^{97} +5.61244i q^{98} +0.822051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} - 2 q^{10} - 10 q^{11} + 6 q^{14} - 2 q^{15} + 8 q^{16} + 24 q^{19} + 2 q^{20} + 6 q^{21} + 8 q^{24} + 8 q^{26} - 10 q^{29} + 2 q^{30} - 38 q^{31} - 2 q^{34} + 12 q^{35} + 8 q^{36} + 8 q^{39} + 2 q^{40} + 26 q^{41} + 10 q^{44} + 2 q^{45} - 12 q^{46} - 30 q^{49} - 4 q^{50} - 2 q^{51} + 8 q^{54} + 30 q^{55} - 6 q^{56} - 20 q^{59} + 2 q^{60} - 6 q^{61} - 8 q^{64} + 24 q^{65} + 10 q^{66} - 12 q^{69} + 26 q^{70} - 12 q^{71} + 8 q^{74} - 4 q^{75} - 24 q^{76} + 16 q^{79} - 2 q^{80} + 8 q^{81} - 6 q^{84} + 44 q^{85} - 2 q^{86} - 64 q^{89} + 2 q^{90} - 44 q^{91} + 52 q^{94} - 8 q^{96} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −0.594137 2.15569i −0.265706 0.964054i
\(6\) −1.00000 −0.408248
\(7\) 1.17795i 0.445223i −0.974907 0.222611i \(-0.928542\pi\)
0.974907 0.222611i \(-0.0714581\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 2.15569 0.594137i 0.681689 0.187883i
\(11\) −0.822051 −0.247858 −0.123929 0.992291i \(-0.539549\pi\)
−0.123929 + 0.992291i \(0.539549\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.74983i 0.485315i 0.970112 + 0.242657i \(0.0780191\pi\)
−0.970112 + 0.242657i \(0.921981\pi\)
\(14\) 1.17795 0.314820
\(15\) 2.15569 0.594137i 0.556597 0.153406i
\(16\) 1.00000 0.250000
\(17\) 3.94516i 0.956841i 0.878131 + 0.478420i \(0.158791\pi\)
−0.878131 + 0.478420i \(0.841209\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.29400 −0.296864 −0.148432 0.988923i \(-0.547423\pi\)
−0.148432 + 0.988923i \(0.547423\pi\)
\(20\) 0.594137 + 2.15569i 0.132853 + 0.482027i
\(21\) 1.17795 0.257050
\(22\) 0.822051i 0.175262i
\(23\) 7.68466i 1.60236i 0.598422 + 0.801181i \(0.295795\pi\)
−0.598422 + 0.801181i \(0.704205\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.29400 + 2.56155i −0.858800 + 0.512311i
\(26\) −1.74983 −0.343169
\(27\) 1.00000i 0.192450i
\(28\) 1.17795i 0.222611i
\(29\) −9.23916 −1.71567 −0.857834 0.513926i \(-0.828190\pi\)
−0.857834 + 0.513926i \(0.828190\pi\)
\(30\) 0.594137 + 2.15569i 0.108474 + 0.393573i
\(31\) −9.30433 −1.67111 −0.835553 0.549410i \(-0.814853\pi\)
−0.835553 + 0.549410i \(0.814853\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.822051i 0.143101i
\(34\) −3.94516 −0.676589
\(35\) −2.53929 + 0.699864i −0.429219 + 0.118299i
\(36\) 1.00000 0.166667
\(37\) 1.00000i 0.164399i
\(38\) 1.29400i 0.209915i
\(39\) −1.74983 −0.280197
\(40\) −2.15569 + 0.594137i −0.340845 + 0.0939414i
\(41\) −2.50671 −0.391482 −0.195741 0.980656i \(-0.562711\pi\)
−0.195741 + 0.980656i \(0.562711\pi\)
\(42\) 1.17795i 0.181762i
\(43\) 2.92778i 0.446482i −0.974763 0.223241i \(-0.928336\pi\)
0.974763 0.223241i \(-0.0716637\pi\)
\(44\) 0.822051 0.123929
\(45\) 0.594137 + 2.15569i 0.0885688 + 0.321351i
\(46\) −7.68466 −1.13304
\(47\) 7.18827i 1.04852i −0.851559 0.524259i \(-0.824342\pi\)
0.851559 0.524259i \(-0.175658\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 5.61244 0.801776
\(50\) −2.56155 4.29400i −0.362258 0.607263i
\(51\) −3.94516 −0.552432
\(52\) 1.74983i 0.242657i
\(53\) 13.8659i 1.90463i 0.305124 + 0.952313i \(0.401302\pi\)
−0.305124 + 0.952313i \(0.598698\pi\)
\(54\) 1.00000 0.136083
\(55\) 0.488411 + 1.77209i 0.0658573 + 0.238948i
\(56\) −1.17795 −0.157410
\(57\) 1.29400i 0.171395i
\(58\) 9.23916i 1.21316i
\(59\) −3.18827 −0.415078 −0.207539 0.978227i \(-0.566545\pi\)
−0.207539 + 0.978227i \(0.566545\pi\)
\(60\) −2.15569 + 0.594137i −0.278298 + 0.0767028i
\(61\) 8.78333 1.12459 0.562295 0.826937i \(-0.309918\pi\)
0.562295 + 0.826937i \(0.309918\pi\)
\(62\) 9.30433i 1.18165i
\(63\) 1.17795i 0.148408i
\(64\) −1.00000 −0.125000
\(65\) 3.77209 1.03964i 0.467870 0.128951i
\(66\) 0.822051 0.101187
\(67\) 15.2108i 1.85829i 0.369715 + 0.929145i \(0.379455\pi\)
−0.369715 + 0.929145i \(0.620545\pi\)
\(68\) 3.94516i 0.478420i
\(69\) −7.68466 −0.925124
\(70\) −0.699864 2.53929i −0.0836497 0.303504i
\(71\) −6.65317 −0.789586 −0.394793 0.918770i \(-0.629184\pi\)
−0.394793 + 0.918770i \(0.629184\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 11.9168i 1.39475i −0.716706 0.697376i \(-0.754351\pi\)
0.716706 0.697376i \(-0.245649\pi\)
\(74\) 1.00000 0.116248
\(75\) −2.56155 4.29400i −0.295783 0.495829i
\(76\) 1.29400 0.148432
\(77\) 0.968334i 0.110352i
\(78\) 1.74983i 0.198129i
\(79\) 0.797618 0.0897390 0.0448695 0.998993i \(-0.485713\pi\)
0.0448695 + 0.998993i \(0.485713\pi\)
\(80\) −0.594137 2.15569i −0.0664266 0.241014i
\(81\) 1.00000 0.111111
\(82\) 2.50671i 0.276820i
\(83\) 7.72918i 0.848387i 0.905571 + 0.424194i \(0.139442\pi\)
−0.905571 + 0.424194i \(0.860558\pi\)
\(84\) −1.17795 −0.128525
\(85\) 8.50454 2.34397i 0.922446 0.254239i
\(86\) 2.92778 0.315710
\(87\) 9.23916i 0.990542i
\(88\) 0.822051i 0.0876309i
\(89\) −14.8729 −1.57653 −0.788264 0.615337i \(-0.789020\pi\)
−0.788264 + 0.615337i \(0.789020\pi\)
\(90\) −2.15569 + 0.594137i −0.227230 + 0.0626276i
\(91\) 2.06121 0.216073
\(92\) 7.68466i 0.801181i
\(93\) 9.30433i 0.964814i
\(94\) 7.18827 0.741414
\(95\) 0.768815 + 2.78947i 0.0788787 + 0.286193i
\(96\) −1.00000 −0.102062
\(97\) 13.0947i 1.32957i −0.747036 0.664783i \(-0.768524\pi\)
0.747036 0.664783i \(-0.231476\pi\)
\(98\) 5.61244i 0.566942i
\(99\) 0.822051 0.0826192
\(100\) 4.29400 2.56155i 0.429400 0.256155i
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 3.94516i 0.390629i
\(103\) 19.6666i 1.93781i 0.247439 + 0.968903i \(0.420411\pi\)
−0.247439 + 0.968903i \(0.579589\pi\)
\(104\) 1.74983 0.171585
\(105\) −0.699864 2.53929i −0.0682997 0.247810i
\(106\) −13.8659 −1.34677
\(107\) 10.4964i 1.01472i −0.861733 0.507362i \(-0.830621\pi\)
0.861733 0.507362i \(-0.169379\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 16.0328 1.53567 0.767833 0.640651i \(-0.221335\pi\)
0.767833 + 0.640651i \(0.221335\pi\)
\(110\) −1.77209 + 0.488411i −0.168962 + 0.0465682i
\(111\) 1.00000 0.0949158
\(112\) 1.17795i 0.111306i
\(113\) 3.46288i 0.325760i 0.986646 + 0.162880i \(0.0520784\pi\)
−0.986646 + 0.162880i \(0.947922\pi\)
\(114\) 1.29400 0.121194
\(115\) 16.5657 4.56574i 1.54476 0.425758i
\(116\) 9.23916 0.857834
\(117\) 1.74983i 0.161772i
\(118\) 3.18827i 0.293505i
\(119\) 4.64719 0.426008
\(120\) −0.594137 2.15569i −0.0542371 0.196787i
\(121\) −10.3242 −0.938567
\(122\) 8.78333i 0.795205i
\(123\) 2.50671i 0.226022i
\(124\) 9.30433 0.835553
\(125\) 8.07314 + 7.73462i 0.722084 + 0.691806i
\(126\) −1.17795 −0.104940
\(127\) 17.7498i 1.57504i −0.616287 0.787521i \(-0.711364\pi\)
0.616287 0.787521i \(-0.288636\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 2.92778 0.257776
\(130\) 1.03964 + 3.77209i 0.0911823 + 0.330834i
\(131\) −17.3248 −1.51367 −0.756837 0.653603i \(-0.773257\pi\)
−0.756837 + 0.653603i \(0.773257\pi\)
\(132\) 0.822051i 0.0715503i
\(133\) 1.52427i 0.132171i
\(134\) −15.2108 −1.31401
\(135\) −2.15569 + 0.594137i −0.185532 + 0.0511352i
\(136\) 3.94516 0.338294
\(137\) 1.59958i 0.136662i 0.997663 + 0.0683308i \(0.0217673\pi\)
−0.997663 + 0.0683308i \(0.978233\pi\)
\(138\) 7.68466i 0.654162i
\(139\) −13.5364 −1.14815 −0.574073 0.818804i \(-0.694637\pi\)
−0.574073 + 0.818804i \(0.694637\pi\)
\(140\) 2.53929 0.699864i 0.214609 0.0591493i
\(141\) 7.18827 0.605362
\(142\) 6.65317i 0.558322i
\(143\) 1.43845i 0.120289i
\(144\) −1.00000 −0.0833333
\(145\) 5.48933 + 19.9168i 0.455864 + 1.65400i
\(146\) 11.9168 0.986238
\(147\) 5.61244i 0.462906i
\(148\) 1.00000i 0.0821995i
\(149\) 5.82080 0.476858 0.238429 0.971160i \(-0.423368\pi\)
0.238429 + 0.971160i \(0.423368\pi\)
\(150\) 4.29400 2.56155i 0.350604 0.209150i
\(151\) −6.62672 −0.539275 −0.269638 0.962962i \(-0.586904\pi\)
−0.269638 + 0.962962i \(0.586904\pi\)
\(152\) 1.29400i 0.104957i
\(153\) 3.94516i 0.318947i
\(154\) −0.968334 −0.0780306
\(155\) 5.52805 + 20.0572i 0.444024 + 1.61104i
\(156\) 1.74983 0.140098
\(157\) 13.5505i 1.08145i −0.841199 0.540725i \(-0.818150\pi\)
0.841199 0.540725i \(-0.181850\pi\)
\(158\) 0.797618i 0.0634551i
\(159\) −13.8659 −1.09964
\(160\) 2.15569 0.594137i 0.170422 0.0469707i
\(161\) 9.05214 0.713408
\(162\) 1.00000i 0.0785674i
\(163\) 3.45457i 0.270583i −0.990806 0.135291i \(-0.956803\pi\)
0.990806 0.135291i \(-0.0431971\pi\)
\(164\) 2.50671 0.195741
\(165\) −1.77209 + 0.488411i −0.137957 + 0.0380228i
\(166\) −7.72918 −0.599900
\(167\) 0.294690i 0.0228038i −0.999935 0.0114019i \(-0.996371\pi\)
0.999935 0.0114019i \(-0.00362942\pi\)
\(168\) 1.17795i 0.0908808i
\(169\) 9.93810 0.764469
\(170\) 2.34397 + 8.50454i 0.179774 + 0.652268i
\(171\) 1.29400 0.0989548
\(172\) 2.92778i 0.223241i
\(173\) 12.9542i 0.984892i 0.870343 + 0.492446i \(0.163897\pi\)
−0.870343 + 0.492446i \(0.836103\pi\)
\(174\) 9.23916 0.700419
\(175\) 3.01738 + 5.05812i 0.228092 + 0.382358i
\(176\) −0.822051 −0.0619644
\(177\) 3.18827i 0.239645i
\(178\) 14.8729i 1.11477i
\(179\) −20.4990 −1.53216 −0.766082 0.642742i \(-0.777797\pi\)
−0.766082 + 0.642742i \(0.777797\pi\)
\(180\) −0.594137 2.15569i −0.0442844 0.160676i
\(181\) 20.1449 1.49736 0.748680 0.662932i \(-0.230688\pi\)
0.748680 + 0.662932i \(0.230688\pi\)
\(182\) 2.06121i 0.152787i
\(183\) 8.78333i 0.649283i
\(184\) 7.68466 0.566521
\(185\) −2.15569 + 0.594137i −0.158490 + 0.0436819i
\(186\) 9.30433 0.682226
\(187\) 3.24312i 0.237160i
\(188\) 7.18827i 0.524259i
\(189\) −1.17795 −0.0856832
\(190\) −2.78947 + 0.768815i −0.202369 + 0.0557757i
\(191\) −1.59902 −0.115701 −0.0578504 0.998325i \(-0.518425\pi\)
−0.0578504 + 0.998325i \(0.518425\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 4.53510i 0.326444i −0.986589 0.163222i \(-0.947811\pi\)
0.986589 0.163222i \(-0.0521887\pi\)
\(194\) 13.0947 0.940146
\(195\) 1.03964 + 3.77209i 0.0744500 + 0.270125i
\(196\) −5.61244 −0.400888
\(197\) 3.14956i 0.224397i 0.993686 + 0.112198i \(0.0357892\pi\)
−0.993686 + 0.112198i \(0.964211\pi\)
\(198\) 0.822051i 0.0584206i
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 2.56155 + 4.29400i 0.181129 + 0.303632i
\(201\) −15.2108 −1.07288
\(202\) 2.00000i 0.140720i
\(203\) 10.8833i 0.763855i
\(204\) 3.94516 0.276216
\(205\) 1.48933 + 5.40369i 0.104019 + 0.377410i
\(206\) −19.6666 −1.37024
\(207\) 7.68466i 0.534121i
\(208\) 1.74983i 0.121329i
\(209\) 1.06373 0.0735801
\(210\) 2.53929 0.699864i 0.175228 0.0482952i
\(211\) 0.0954006 0.00656765 0.00328383 0.999995i \(-0.498955\pi\)
0.00328383 + 0.999995i \(0.498955\pi\)
\(212\) 13.8659i 0.952313i
\(213\) 6.65317i 0.455868i
\(214\) 10.4964 0.717518
\(215\) −6.31138 + 1.73950i −0.430433 + 0.118633i
\(216\) −1.00000 −0.0680414
\(217\) 10.9600i 0.744015i
\(218\) 16.0328i 1.08588i
\(219\) 11.9168 0.805260
\(220\) −0.488411 1.77209i −0.0329287 0.119474i
\(221\) −6.90334 −0.464369
\(222\) 1.00000i 0.0671156i
\(223\) 10.5512i 0.706562i 0.935517 + 0.353281i \(0.114934\pi\)
−0.935517 + 0.353281i \(0.885066\pi\)
\(224\) 1.17795 0.0787050
\(225\) 4.29400 2.56155i 0.286267 0.170770i
\(226\) −3.46288 −0.230347
\(227\) 10.1063i 0.670778i 0.942080 + 0.335389i \(0.108868\pi\)
−0.942080 + 0.335389i \(0.891132\pi\)
\(228\) 1.29400i 0.0856973i
\(229\) −4.81173 −0.317968 −0.158984 0.987281i \(-0.550822\pi\)
−0.158984 + 0.987281i \(0.550822\pi\)
\(230\) 4.56574 + 16.5657i 0.301056 + 1.09231i
\(231\) −0.968334 −0.0637117
\(232\) 9.23916i 0.606580i
\(233\) 11.6014i 0.760034i −0.924979 0.380017i \(-0.875918\pi\)
0.924979 0.380017i \(-0.124082\pi\)
\(234\) 1.74983 0.114390
\(235\) −15.4957 + 4.27082i −1.01083 + 0.278598i
\(236\) 3.18827 0.207539
\(237\) 0.797618i 0.0518108i
\(238\) 4.64719i 0.301233i
\(239\) 23.1599 1.49809 0.749044 0.662520i \(-0.230513\pi\)
0.749044 + 0.662520i \(0.230513\pi\)
\(240\) 2.15569 0.594137i 0.139149 0.0383514i
\(241\) −12.7020 −0.818210 −0.409105 0.912487i \(-0.634159\pi\)
−0.409105 + 0.912487i \(0.634159\pi\)
\(242\) 10.3242i 0.663667i
\(243\) 1.00000i 0.0641500i
\(244\) −8.78333 −0.562295
\(245\) −3.33456 12.0987i −0.213037 0.772956i
\(246\) 2.50671 0.159822
\(247\) 2.26428i 0.144073i
\(248\) 9.30433i 0.590825i
\(249\) −7.72918 −0.489817
\(250\) −7.73462 + 8.07314i −0.489180 + 0.510590i
\(251\) −13.5203 −0.853394 −0.426697 0.904395i \(-0.640323\pi\)
−0.426697 + 0.904395i \(0.640323\pi\)
\(252\) 1.17795i 0.0742038i
\(253\) 6.31718i 0.397158i
\(254\) 17.7498 1.11372
\(255\) 2.34397 + 8.50454i 0.146785 + 0.532575i
\(256\) 1.00000 0.0625000
\(257\) 6.07097i 0.378697i 0.981910 + 0.189348i \(0.0606375\pi\)
−0.981910 + 0.189348i \(0.939362\pi\)
\(258\) 2.92778i 0.182275i
\(259\) −1.17795 −0.0731942
\(260\) −3.77209 + 1.03964i −0.233935 + 0.0644756i
\(261\) 9.23916 0.571890
\(262\) 17.3248i 1.07033i
\(263\) 18.0064i 1.11032i 0.831744 + 0.555160i \(0.187343\pi\)
−0.831744 + 0.555160i \(0.812657\pi\)
\(264\) −0.822051 −0.0505937
\(265\) 29.8905 8.23824i 1.83616 0.506071i
\(266\) −1.52427 −0.0934589
\(267\) 14.8729i 0.910209i
\(268\) 15.2108i 0.929145i
\(269\) −6.54745 −0.399205 −0.199602 0.979877i \(-0.563965\pi\)
−0.199602 + 0.979877i \(0.563965\pi\)
\(270\) −0.594137 2.15569i −0.0361581 0.131191i
\(271\) 25.4776 1.54766 0.773828 0.633396i \(-0.218340\pi\)
0.773828 + 0.633396i \(0.218340\pi\)
\(272\) 3.94516i 0.239210i
\(273\) 2.06121i 0.124750i
\(274\) −1.59958 −0.0966344
\(275\) 3.52989 2.10573i 0.212860 0.126980i
\(276\) 7.68466 0.462562
\(277\) 1.74983i 0.105137i 0.998617 + 0.0525685i \(0.0167408\pi\)
−0.998617 + 0.0525685i \(0.983259\pi\)
\(278\) 13.5364i 0.811861i
\(279\) 9.30433 0.557035
\(280\) 0.699864 + 2.53929i 0.0418249 + 0.151752i
\(281\) 21.1927 1.26425 0.632125 0.774866i \(-0.282183\pi\)
0.632125 + 0.774866i \(0.282183\pi\)
\(282\) 7.18827i 0.428056i
\(283\) 29.6420i 1.76203i 0.473086 + 0.881016i \(0.343140\pi\)
−0.473086 + 0.881016i \(0.656860\pi\)
\(284\) 6.65317 0.394793
\(285\) −2.78947 + 0.768815i −0.165234 + 0.0455407i
\(286\) 1.43845 0.0850572
\(287\) 2.95278i 0.174297i
\(288\) 1.00000i 0.0589256i
\(289\) 1.43574 0.0844554
\(290\) −19.9168 + 5.48933i −1.16955 + 0.322345i
\(291\) 13.0947 0.767626
\(292\) 11.9168i 0.697376i
\(293\) 20.7555i 1.21255i 0.795255 + 0.606275i \(0.207337\pi\)
−0.795255 + 0.606275i \(0.792663\pi\)
\(294\) −5.61244 −0.327324
\(295\) 1.89427 + 6.87293i 0.110289 + 0.400158i
\(296\) −1.00000 −0.0581238
\(297\) 0.822051i 0.0477002i
\(298\) 5.82080i 0.337190i
\(299\) −13.4468 −0.777650
\(300\) 2.56155 + 4.29400i 0.147891 + 0.247914i
\(301\) −3.44877 −0.198784
\(302\) 6.62672i 0.381325i
\(303\) 2.00000i 0.114897i
\(304\) −1.29400 −0.0742161
\(305\) −5.21851 18.9341i −0.298811 1.08417i
\(306\) 3.94516 0.225530
\(307\) 17.1315i 0.977746i −0.872355 0.488873i \(-0.837408\pi\)
0.872355 0.488873i \(-0.162592\pi\)
\(308\) 0.968334i 0.0551760i
\(309\) −19.6666 −1.11879
\(310\) −20.0572 + 5.52805i −1.13918 + 0.313972i
\(311\) 29.1740 1.65431 0.827153 0.561977i \(-0.189959\pi\)
0.827153 + 0.561977i \(0.189959\pi\)
\(312\) 1.74983i 0.0990645i
\(313\) 20.0714i 1.13450i −0.823546 0.567250i \(-0.808007\pi\)
0.823546 0.567250i \(-0.191993\pi\)
\(314\) 13.5505 0.764701
\(315\) 2.53929 0.699864i 0.143073 0.0394329i
\(316\) −0.797618 −0.0448695
\(317\) 20.7084i 1.16310i −0.813511 0.581550i \(-0.802447\pi\)
0.813511 0.581550i \(-0.197553\pi\)
\(318\) 13.8659i 0.777560i
\(319\) 7.59506 0.425242
\(320\) 0.594137 + 2.15569i 0.0332133 + 0.120507i
\(321\) 10.4964 0.585851
\(322\) 9.05214i 0.504456i
\(323\) 5.10504i 0.284052i
\(324\) −1.00000 −0.0555556
\(325\) −4.48228 7.51376i −0.248632 0.416789i
\(326\) 3.45457 0.191331
\(327\) 16.0328i 0.886617i
\(328\) 2.50671i 0.138410i
\(329\) −8.46742 −0.466824
\(330\) −0.488411 1.77209i −0.0268861 0.0975502i
\(331\) −18.3339 −1.00772 −0.503860 0.863785i \(-0.668087\pi\)
−0.503860 + 0.863785i \(0.668087\pi\)
\(332\) 7.72918i 0.424194i
\(333\) 1.00000i 0.0547997i
\(334\) 0.294690 0.0161247
\(335\) 32.7897 9.03728i 1.79149 0.493760i
\(336\) 1.17795 0.0642624
\(337\) 32.8607i 1.79003i −0.446032 0.895017i \(-0.647163\pi\)
0.446032 0.895017i \(-0.352837\pi\)
\(338\) 9.93810i 0.540562i
\(339\) −3.46288 −0.188078
\(340\) −8.50454 + 2.34397i −0.461223 + 0.127119i
\(341\) 7.64863 0.414196
\(342\) 1.29400i 0.0699716i
\(343\) 14.8568i 0.802192i
\(344\) −2.92778 −0.157855
\(345\) 4.56574 + 16.5657i 0.245811 + 0.891870i
\(346\) −12.9542 −0.696424
\(347\) 20.5369i 1.10248i 0.834346 + 0.551240i \(0.185845\pi\)
−0.834346 + 0.551240i \(0.814155\pi\)
\(348\) 9.23916i 0.495271i
\(349\) 3.99024 0.213593 0.106796 0.994281i \(-0.465941\pi\)
0.106796 + 0.994281i \(0.465941\pi\)
\(350\) −5.05812 + 3.01738i −0.270368 + 0.161286i
\(351\) 1.74983 0.0933989
\(352\) 0.822051i 0.0438155i
\(353\) 19.2964i 1.02704i −0.858076 0.513522i \(-0.828340\pi\)
0.858076 0.513522i \(-0.171660\pi\)
\(354\) 3.18827 0.169455
\(355\) 3.95290 + 14.3422i 0.209798 + 0.761204i
\(356\) 14.8729 0.788264
\(357\) 4.64719i 0.245956i
\(358\) 20.4990i 1.08340i
\(359\) 8.39904 0.443284 0.221642 0.975128i \(-0.428858\pi\)
0.221642 + 0.975128i \(0.428858\pi\)
\(360\) 2.15569 0.594137i 0.113615 0.0313138i
\(361\) −17.3256 −0.911872
\(362\) 20.1449i 1.05879i
\(363\) 10.3242i 0.541882i
\(364\) −2.06121 −0.108037
\(365\) −25.6888 + 7.08020i −1.34462 + 0.370594i
\(366\) −8.78333 −0.459112
\(367\) 17.5325i 0.915187i 0.889161 + 0.457594i \(0.151289\pi\)
−0.889161 + 0.457594i \(0.848711\pi\)
\(368\) 7.68466i 0.400591i
\(369\) 2.50671 0.130494
\(370\) −0.594137 2.15569i −0.0308877 0.112069i
\(371\) 16.3333 0.847983
\(372\) 9.30433i 0.482407i
\(373\) 26.4479i 1.36942i 0.728815 + 0.684710i \(0.240071\pi\)
−0.728815 + 0.684710i \(0.759929\pi\)
\(374\) 3.24312 0.167698
\(375\) −7.73462 + 8.07314i −0.399414 + 0.416895i
\(376\) −7.18827 −0.370707
\(377\) 16.1669i 0.832639i
\(378\) 1.17795i 0.0605872i
\(379\) −21.3596 −1.09717 −0.548583 0.836096i \(-0.684833\pi\)
−0.548583 + 0.836096i \(0.684833\pi\)
\(380\) −0.768815 2.78947i −0.0394394 0.143097i
\(381\) 17.7498 0.909351
\(382\) 1.59902i 0.0818128i
\(383\) 27.0258i 1.38095i −0.723355 0.690476i \(-0.757401\pi\)
0.723355 0.690476i \(-0.242599\pi\)
\(384\) 1.00000 0.0510310
\(385\) 2.08743 0.575324i 0.106385 0.0293212i
\(386\) 4.53510 0.230831
\(387\) 2.92778i 0.148827i
\(388\) 13.0947i 0.664783i
\(389\) 14.3786 0.729022 0.364511 0.931199i \(-0.381236\pi\)
0.364511 + 0.931199i \(0.381236\pi\)
\(390\) −3.77209 + 1.03964i −0.191007 + 0.0526441i
\(391\) −30.3172 −1.53321
\(392\) 5.61244i 0.283471i
\(393\) 17.3248i 0.873921i
\(394\) −3.14956 −0.158672
\(395\) −0.473895 1.71942i −0.0238442 0.0865133i
\(396\) −0.822051 −0.0413096
\(397\) 28.2383i 1.41724i −0.705591 0.708620i \(-0.749318\pi\)
0.705591 0.708620i \(-0.250682\pi\)
\(398\) 8.00000i 0.401004i
\(399\) −1.52427 −0.0763088
\(400\) −4.29400 + 2.56155i −0.214700 + 0.128078i
\(401\) 9.70096 0.484443 0.242221 0.970221i \(-0.422124\pi\)
0.242221 + 0.970221i \(0.422124\pi\)
\(402\) 15.2108i 0.758644i
\(403\) 16.2810i 0.811013i
\(404\) −2.00000 −0.0995037
\(405\) −0.594137 2.15569i −0.0295229 0.107117i
\(406\) −10.8833 −0.540127
\(407\) 0.822051i 0.0407475i
\(408\) 3.94516i 0.195314i
\(409\) 26.8103 1.32569 0.662843 0.748758i \(-0.269350\pi\)
0.662843 + 0.748758i \(0.269350\pi\)
\(410\) −5.40369 + 1.48933i −0.266869 + 0.0735528i
\(411\) −1.59958 −0.0789016
\(412\) 19.6666i 0.968903i
\(413\) 3.75563i 0.184802i
\(414\) 7.68466 0.377680
\(415\) 16.6617 4.59219i 0.817891 0.225422i
\(416\) −1.74983 −0.0857924
\(417\) 13.5364i 0.662882i
\(418\) 1.06373i 0.0520290i
\(419\) 21.2275 1.03703 0.518514 0.855069i \(-0.326485\pi\)
0.518514 + 0.855069i \(0.326485\pi\)
\(420\) 0.699864 + 2.53929i 0.0341499 + 0.123905i
\(421\) 6.40880 0.312346 0.156173 0.987730i \(-0.450084\pi\)
0.156173 + 0.987730i \(0.450084\pi\)
\(422\) 0.0954006i 0.00464403i
\(423\) 7.18827i 0.349506i
\(424\) 13.8659 0.673387
\(425\) −10.1057 16.9405i −0.490200 0.821735i
\(426\) 6.65317 0.322347
\(427\) 10.3463i 0.500693i
\(428\) 10.4964i 0.507362i
\(429\) 1.43845 0.0694489
\(430\) −1.73950 6.31138i −0.0838862 0.304362i
\(431\) 1.41981 0.0683900 0.0341950 0.999415i \(-0.489113\pi\)
0.0341950 + 0.999415i \(0.489113\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 6.06121i 0.291283i 0.989337 + 0.145642i \(0.0465246\pi\)
−0.989337 + 0.145642i \(0.953475\pi\)
\(434\) −10.9600 −0.526098
\(435\) −19.9168 + 5.48933i −0.954936 + 0.263193i
\(436\) −16.0328 −0.767833
\(437\) 9.94396i 0.475684i
\(438\) 11.9168i 0.569405i
\(439\) −6.54147 −0.312207 −0.156104 0.987741i \(-0.549893\pi\)
−0.156104 + 0.987741i \(0.549893\pi\)
\(440\) 1.77209 0.488411i 0.0844809 0.0232841i
\(441\) −5.61244 −0.267259
\(442\) 6.90334i 0.328359i
\(443\) 4.04887i 0.192367i −0.995364 0.0961837i \(-0.969336\pi\)
0.995364 0.0961837i \(-0.0306636\pi\)
\(444\) −1.00000 −0.0474579
\(445\) 8.83657 + 32.0614i 0.418893 + 1.51986i
\(446\) −10.5512 −0.499615
\(447\) 5.82080i 0.275314i
\(448\) 1.17795i 0.0556529i
\(449\) 2.45148 0.115692 0.0578462 0.998326i \(-0.481577\pi\)
0.0578462 + 0.998326i \(0.481577\pi\)
\(450\) 2.56155 + 4.29400i 0.120753 + 0.202421i
\(451\) 2.06064 0.0970318
\(452\) 3.46288i 0.162880i
\(453\) 6.62672i 0.311351i
\(454\) −10.1063 −0.474312
\(455\) −1.22464 4.44333i −0.0574121 0.208306i
\(456\) −1.29400 −0.0605972
\(457\) 6.87237i 0.321476i 0.986997 + 0.160738i \(0.0513874\pi\)
−0.986997 + 0.160738i \(0.948613\pi\)
\(458\) 4.81173i 0.224837i
\(459\) 3.94516 0.184144
\(460\) −16.5657 + 4.56574i −0.772382 + 0.212879i
\(461\) −1.07222 −0.0499384 −0.0249692 0.999688i \(-0.507949\pi\)
−0.0249692 + 0.999688i \(0.507949\pi\)
\(462\) 0.968334i 0.0450510i
\(463\) 29.3791i 1.36536i 0.730717 + 0.682681i \(0.239186\pi\)
−0.730717 + 0.682681i \(0.760814\pi\)
\(464\) −9.23916 −0.428917
\(465\) −20.0572 + 5.52805i −0.930133 + 0.256357i
\(466\) 11.6014 0.537425
\(467\) 6.56099i 0.303606i 0.988411 + 0.151803i \(0.0485080\pi\)
−0.988411 + 0.151803i \(0.951492\pi\)
\(468\) 1.74983i 0.0808858i
\(469\) 17.9175 0.827354
\(470\) −4.27082 15.4957i −0.196998 0.714763i
\(471\) 13.5505 0.624376
\(472\) 3.18827i 0.146752i
\(473\) 2.40678i 0.110664i
\(474\) −0.797618 −0.0366358
\(475\) 5.55644 3.31465i 0.254947 0.152087i
\(476\) −4.64719 −0.213004
\(477\) 13.8659i 0.634875i
\(478\) 23.1599i 1.05931i
\(479\) −2.93948 −0.134308 −0.0671541 0.997743i \(-0.521392\pi\)
−0.0671541 + 0.997743i \(0.521392\pi\)
\(480\) 0.594137 + 2.15569i 0.0271185 + 0.0983934i
\(481\) 1.74983 0.0797853
\(482\) 12.7020i 0.578562i
\(483\) 9.05214i 0.411887i
\(484\) 10.3242 0.469283
\(485\) −28.2281 + 7.78006i −1.28177 + 0.353274i
\(486\) −1.00000 −0.0453609
\(487\) 31.1217i 1.41026i 0.709078 + 0.705130i \(0.249111\pi\)
−0.709078 + 0.705130i \(0.750889\pi\)
\(488\) 8.78333i 0.397603i
\(489\) 3.45457 0.156221
\(490\) 12.0987 3.33456i 0.546562 0.150640i
\(491\) −4.69373 −0.211825 −0.105913 0.994375i \(-0.533776\pi\)
−0.105913 + 0.994375i \(0.533776\pi\)
\(492\) 2.50671i 0.113011i
\(493\) 36.4499i 1.64162i
\(494\) 2.26428 0.101875
\(495\) −0.488411 1.77209i −0.0219524 0.0796494i
\(496\) −9.30433 −0.417777
\(497\) 7.83710i 0.351542i
\(498\) 7.72918i 0.346353i
\(499\) −8.72527 −0.390597 −0.195298 0.980744i \(-0.562568\pi\)
−0.195298 + 0.980744i \(0.562568\pi\)
\(500\) −8.07314 7.73462i −0.361042 0.345903i
\(501\) 0.294690 0.0131658
\(502\) 13.5203i 0.603441i
\(503\) 1.77444i 0.0791184i 0.999217 + 0.0395592i \(0.0125954\pi\)
−0.999217 + 0.0395592i \(0.987405\pi\)
\(504\) 1.17795 0.0524700
\(505\) −1.18827 4.31138i −0.0528775 0.191854i
\(506\) 6.31718 0.280833
\(507\) 9.93810i 0.441367i
\(508\) 17.7498i 0.787521i
\(509\) −31.1134 −1.37908 −0.689539 0.724249i \(-0.742187\pi\)
−0.689539 + 0.724249i \(0.742187\pi\)
\(510\) −8.50454 + 2.34397i −0.376587 + 0.103793i
\(511\) −14.0373 −0.620975
\(512\) 1.00000i 0.0441942i
\(513\) 1.29400i 0.0571316i
\(514\) −6.07097 −0.267779
\(515\) 42.3951 11.6847i 1.86815 0.514888i
\(516\) −2.92778 −0.128888
\(517\) 5.90913i 0.259883i
\(518\) 1.17795i 0.0517561i
\(519\) −12.9542 −0.568627
\(520\) −1.03964 3.77209i −0.0455912 0.165417i
\(521\) −12.6961 −0.556228 −0.278114 0.960548i \(-0.589709\pi\)
−0.278114 + 0.960548i \(0.589709\pi\)
\(522\) 9.23916i 0.404387i
\(523\) 38.1210i 1.66692i −0.552582 0.833458i \(-0.686358\pi\)
0.552582 0.833458i \(-0.313642\pi\)
\(524\) 17.3248 0.756837
\(525\) −5.05812 + 3.01738i −0.220754 + 0.131689i
\(526\) −18.0064 −0.785115
\(527\) 36.7070i 1.59898i
\(528\) 0.822051i 0.0357752i
\(529\) −36.0540 −1.56756
\(530\) 8.23824 + 29.8905i 0.357846 + 1.29836i
\(531\) 3.18827 0.138359
\(532\) 1.52427i 0.0660854i
\(533\) 4.38631i 0.189992i
\(534\) 14.8729 0.643615
\(535\) −22.6270 + 6.23629i −0.978248 + 0.269619i
\(536\) 15.2108 0.657005
\(537\) 20.4990i 0.884596i
\(538\) 6.54745i 0.282280i
\(539\) −4.61371 −0.198726
\(540\) 2.15569 0.594137i 0.0927661 0.0255676i
\(541\) −26.2770 −1.12974 −0.564868 0.825181i \(-0.691073\pi\)
−0.564868 + 0.825181i \(0.691073\pi\)
\(542\) 25.4776i 1.09436i
\(543\) 20.1449i 0.864501i
\(544\) −3.94516 −0.169147
\(545\) −9.52570 34.5618i −0.408036 1.48046i
\(546\) −2.06121 −0.0882116
\(547\) 6.61244i 0.282727i 0.989958 + 0.141364i \(0.0451487\pi\)
−0.989958 + 0.141364i \(0.954851\pi\)
\(548\) 1.59958i 0.0683308i
\(549\) −8.78333 −0.374863
\(550\) 2.10573 + 3.52989i 0.0897885 + 0.150515i
\(551\) 11.9555 0.509321
\(552\) 7.68466i 0.327081i
\(553\) 0.939553i 0.0399539i
\(554\) −1.74983 −0.0743431
\(555\) −0.594137 2.15569i −0.0252197 0.0915040i
\(556\) 13.5364 0.574073
\(557\) 3.57893i 0.151644i 0.997121 + 0.0758221i \(0.0241581\pi\)
−0.997121 + 0.0758221i \(0.975842\pi\)
\(558\) 9.30433i 0.393884i
\(559\) 5.12311 0.216684
\(560\) −2.53929 + 0.699864i −0.107305 + 0.0295746i
\(561\) 3.24312 0.136925
\(562\) 21.1927i 0.893960i
\(563\) 1.07544i 0.0453243i −0.999743 0.0226622i \(-0.992786\pi\)
0.999743 0.0226622i \(-0.00721421\pi\)
\(564\) −7.18827 −0.302681
\(565\) 7.46490 2.05743i 0.314051 0.0865566i
\(566\) −29.6420 −1.24595
\(567\) 1.17795i 0.0494692i
\(568\) 6.65317i 0.279161i
\(569\) −31.8864 −1.33675 −0.668373 0.743827i \(-0.733009\pi\)
−0.668373 + 0.743827i \(0.733009\pi\)
\(570\) −0.768815 2.78947i −0.0322021 0.116838i
\(571\) −2.21163 −0.0925539 −0.0462770 0.998929i \(-0.514736\pi\)
−0.0462770 + 0.998929i \(0.514736\pi\)
\(572\) 1.43845i 0.0601445i
\(573\) 1.59902i 0.0667999i
\(574\) −2.95278 −0.123246
\(575\) −19.6847 32.9979i −0.820907 1.37611i
\(576\) 1.00000 0.0416667
\(577\) 3.66475i 0.152566i 0.997086 + 0.0762828i \(0.0243052\pi\)
−0.997086 + 0.0762828i \(0.975695\pi\)
\(578\) 1.43574i 0.0597190i
\(579\) 4.53510 0.188472
\(580\) −5.48933 19.9168i −0.227932 0.826999i
\(581\) 9.10458 0.377722
\(582\) 13.0947i 0.542793i
\(583\) 11.3985i 0.472076i
\(584\) −11.9168 −0.493119
\(585\) −3.77209 + 1.03964i −0.155957 + 0.0429838i
\(586\) −20.7555 −0.857402
\(587\) 20.1244i 0.830624i −0.909679 0.415312i \(-0.863672\pi\)
0.909679 0.415312i \(-0.136328\pi\)
\(588\) 5.61244i 0.231453i
\(589\) 12.0398 0.496092
\(590\) −6.87293 + 1.89427i −0.282954 + 0.0779860i
\(591\) −3.14956 −0.129555
\(592\) 1.00000i 0.0410997i
\(593\) 29.7097i 1.22003i −0.792389 0.610016i \(-0.791163\pi\)
0.792389 0.610016i \(-0.208837\pi\)
\(594\) −0.822051 −0.0337291
\(595\) −2.76107 10.0179i −0.113193 0.410694i
\(596\) −5.82080 −0.238429
\(597\) 8.00000i 0.327418i
\(598\) 13.4468i 0.549882i
\(599\) −35.0077 −1.43038 −0.715188 0.698932i \(-0.753659\pi\)
−0.715188 + 0.698932i \(0.753659\pi\)
\(600\) −4.29400 + 2.56155i −0.175302 + 0.104575i
\(601\) 25.1541 1.02606 0.513028 0.858372i \(-0.328524\pi\)
0.513028 + 0.858372i \(0.328524\pi\)
\(602\) 3.44877i 0.140561i
\(603\) 15.2108i 0.619430i
\(604\) 6.62672 0.269638
\(605\) 6.13401 + 22.2558i 0.249383 + 0.904829i
\(606\) −2.00000 −0.0812444
\(607\) 26.6289i 1.08084i 0.841397 + 0.540418i \(0.181734\pi\)
−0.841397 + 0.540418i \(0.818266\pi\)
\(608\) 1.29400i 0.0524787i
\(609\) −10.8833 −0.441012
\(610\) 18.9341 5.21851i 0.766621 0.211291i
\(611\) 12.5782 0.508861
\(612\) 3.94516i 0.159473i
\(613\) 3.71564i 0.150073i −0.997181 0.0750366i \(-0.976093\pi\)
0.997181 0.0750366i \(-0.0239073\pi\)
\(614\) 17.1315 0.691371
\(615\) −5.40369 + 1.48933i −0.217898 + 0.0600556i
\(616\) 0.968334 0.0390153
\(617\) 19.6872i 0.792579i −0.918126 0.396289i \(-0.870298\pi\)
0.918126 0.396289i \(-0.129702\pi\)
\(618\) 19.6666i 0.791106i
\(619\) 13.1708 0.529378 0.264689 0.964334i \(-0.414731\pi\)
0.264689 + 0.964334i \(0.414731\pi\)
\(620\) −5.52805 20.0572i −0.222012 0.805518i
\(621\) 7.68466 0.308375
\(622\) 29.1740i 1.16977i
\(623\) 17.5196i 0.701906i
\(624\) −1.74983 −0.0700492
\(625\) 11.8769 21.9986i 0.475076 0.879945i
\(626\) 20.0714 0.802213
\(627\) 1.06373i 0.0424815i
\(628\) 13.5505i 0.540725i
\(629\) 3.94516 0.157304
\(630\) 0.699864 + 2.53929i 0.0278832 + 0.101168i
\(631\) −12.3398 −0.491239 −0.245619 0.969366i \(-0.578991\pi\)
−0.245619 + 0.969366i \(0.578991\pi\)
\(632\) 0.797618i 0.0317275i
\(633\) 0.0954006i 0.00379184i
\(634\) 20.7084 0.822436
\(635\) −38.2631 + 10.5458i −1.51843 + 0.418499i
\(636\) 13.8659 0.549818
\(637\) 9.82080i 0.389114i
\(638\) 7.59506i 0.300691i
\(639\) 6.65317 0.263195
\(640\) −2.15569 + 0.594137i −0.0852111 + 0.0234853i
\(641\) 22.0715 0.871773 0.435887 0.900002i \(-0.356435\pi\)
0.435887 + 0.900002i \(0.356435\pi\)
\(642\) 10.4964i 0.414259i
\(643\) 22.8858i 0.902530i 0.892390 + 0.451265i \(0.149027\pi\)
−0.892390 + 0.451265i \(0.850973\pi\)
\(644\) −9.05214 −0.356704
\(645\) −1.73950 6.31138i −0.0684928 0.248510i
\(646\) 5.10504 0.200855
\(647\) 17.5402i 0.689577i −0.938680 0.344788i \(-0.887951\pi\)
0.938680 0.344788i \(-0.112049\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 2.62092 0.102880
\(650\) 7.51376 4.48228i 0.294714 0.175809i
\(651\) −10.9600 −0.429557
\(652\) 3.45457i 0.135291i
\(653\) 20.7466i 0.811875i 0.913901 + 0.405938i \(0.133055\pi\)
−0.913901 + 0.405938i \(0.866945\pi\)
\(654\) −16.0328 −0.626933
\(655\) 10.2933 + 37.3469i 0.402193 + 1.45926i
\(656\) −2.50671 −0.0978705
\(657\) 11.9168i 0.464917i
\(658\) 8.46742i 0.330095i
\(659\) −41.8965 −1.63206 −0.816028 0.578012i \(-0.803828\pi\)
−0.816028 + 0.578012i \(0.803828\pi\)
\(660\) 1.77209 0.488411i 0.0689784 0.0190114i
\(661\) −9.30691 −0.361997 −0.180998 0.983483i \(-0.557933\pi\)
−0.180998 + 0.983483i \(0.557933\pi\)
\(662\) 18.3339i 0.712566i
\(663\) 6.90334i 0.268104i
\(664\) 7.72918 0.299950
\(665\) 3.28585 0.905625i 0.127420 0.0351186i
\(666\) −1.00000 −0.0387492
\(667\) 70.9998i 2.74912i
\(668\) 0.294690i 0.0114019i
\(669\) −10.5512 −0.407934
\(670\) 9.03728 + 32.7897i 0.349141 + 1.26678i
\(671\) −7.22034 −0.278738
\(672\) 1.17795i 0.0454404i
\(673\) 8.73825i 0.336835i 0.985716 + 0.168417i \(0.0538656\pi\)
−0.985716 + 0.168417i \(0.946134\pi\)
\(674\) 32.8607 1.26575
\(675\) 2.56155 + 4.29400i 0.0985942 + 0.165276i
\(676\) −9.93810 −0.382235
\(677\) 16.8064i 0.645922i −0.946412 0.322961i \(-0.895322\pi\)
0.946412 0.322961i \(-0.104678\pi\)
\(678\) 3.46288i 0.132991i
\(679\) −15.4249 −0.591954
\(680\) −2.34397 8.50454i −0.0898870 0.326134i
\(681\) −10.1063 −0.387274
\(682\) 7.64863i 0.292881i
\(683\) 30.8058i 1.17875i 0.807859 + 0.589376i \(0.200626\pi\)
−0.807859 + 0.589376i \(0.799374\pi\)
\(684\) −1.29400 −0.0494774
\(685\) 3.44821 0.950373i 0.131749 0.0363119i
\(686\) 14.8568 0.567236
\(687\) 4.81173i 0.183579i
\(688\) 2.92778i 0.111620i
\(689\) −24.2629 −0.924343
\(690\) −16.5657 + 4.56574i −0.630647 + 0.173815i
\(691\) 1.80146 0.0685306 0.0342653 0.999413i \(-0.489091\pi\)
0.0342653 + 0.999413i \(0.489091\pi\)
\(692\) 12.9542i 0.492446i
\(693\) 0.968334i 0.0367840i
\(694\) −20.5369 −0.779572
\(695\) 8.04250 + 29.1804i 0.305069 + 1.10687i
\(696\) −9.23916 −0.350209
\(697\) 9.88936i 0.374586i
\(698\) 3.99024i 0.151033i
\(699\) 11.6014 0.438806
\(700\) −3.01738 5.05812i −0.114046 0.191179i
\(701\) 30.6087 1.15607 0.578036 0.816011i \(-0.303819\pi\)
0.578036 + 0.816011i \(0.303819\pi\)
\(702\) 1.74983i 0.0660430i
\(703\) 1.29400i 0.0488042i
\(704\) 0.822051 0.0309822
\(705\) −4.27082 15.4957i −0.160849 0.583602i
\(706\) 19.2964 0.726230
\(707\) 2.35590i 0.0886027i
\(708\) 3.18827i 0.119823i
\(709\) −17.1845 −0.645377 −0.322689 0.946505i \(-0.604587\pi\)
−0.322689 + 0.946505i \(0.604587\pi\)
\(710\) −14.3422 + 3.95290i −0.538252 + 0.148350i
\(711\) −0.797618 −0.0299130
\(712\) 14.8729i 0.557387i
\(713\) 71.5006i 2.67772i
\(714\) −4.64719 −0.173917
\(715\) −3.10085 + 0.854635i −0.115965 + 0.0319616i
\(716\) 20.4990 0.766082
\(717\) 23.1599i 0.864922i
\(718\) 8.39904i 0.313449i
\(719\) −8.89535 −0.331741 −0.165870 0.986148i \(-0.553043\pi\)
−0.165870 + 0.986148i \(0.553043\pi\)
\(720\) 0.594137 + 2.15569i 0.0221422 + 0.0803378i
\(721\) 23.1662 0.862756
\(722\) 17.3256i 0.644791i
\(723\) 12.7020i 0.472394i
\(724\) −20.1449 −0.748680
\(725\) 39.6730 23.6666i 1.47342 0.878955i
\(726\) 10.3242 0.383168
\(727\) 8.44034i 0.313035i 0.987675 + 0.156517i \(0.0500268\pi\)
−0.987675 + 0.156517i \(0.949973\pi\)
\(728\) 2.06121i 0.0763935i
\(729\) −1.00000 −0.0370370
\(730\) −7.08020 25.6888i −0.262050 0.950787i
\(731\) 11.5505 0.427212
\(732\) 8.78333i 0.324641i
\(733\) 36.7740i 1.35828i 0.734009 + 0.679140i \(0.237647\pi\)
−0.734009 + 0.679140i \(0.762353\pi\)
\(734\) −17.5325 −0.647135
\(735\) 12.0987 3.33456i 0.446266 0.122997i
\(736\) −7.68466 −0.283260
\(737\) 12.5040i 0.460591i
\(738\) 2.50671i 0.0922732i
\(739\) −14.4481 −0.531481 −0.265741 0.964045i \(-0.585616\pi\)
−0.265741 + 0.964045i \(0.585616\pi\)
\(740\) 2.15569 0.594137i 0.0792448 0.0218409i
\(741\) 2.26428 0.0831804
\(742\) 16.3333i 0.599614i
\(743\) 5.29344i 0.194197i −0.995275 0.0970986i \(-0.969044\pi\)
0.995275 0.0970986i \(-0.0309562\pi\)
\(744\) −9.30433 −0.341113
\(745\) −3.45835 12.5478i −0.126704 0.459717i
\(746\) −26.4479 −0.968327
\(747\) 7.72918i 0.282796i
\(748\) 3.24312i 0.118580i
\(749\) −12.3642 −0.451778
\(750\) −8.07314 7.73462i −0.294789 0.282428i
\(751\) −2.79946 −0.102154 −0.0510768 0.998695i \(-0.516265\pi\)
−0.0510768 + 0.998695i \(0.516265\pi\)
\(752\) 7.18827i 0.262129i
\(753\) 13.5203i 0.492707i
\(754\) 16.1669 0.588765
\(755\) 3.93718 + 14.2852i 0.143289 + 0.519890i
\(756\) 1.17795 0.0428416
\(757\) 46.2538i 1.68112i 0.541715 + 0.840562i \(0.317775\pi\)
−0.541715 + 0.840562i \(0.682225\pi\)
\(758\) 21.3596i 0.775814i
\(759\) 6.31718 0.229299
\(760\) 2.78947 0.768815i 0.101185 0.0278878i
\(761\) −9.49764 −0.344289 −0.172145 0.985072i \(-0.555070\pi\)
−0.172145 + 0.985072i \(0.555070\pi\)
\(762\) 17.7498i 0.643008i
\(763\) 18.8858i 0.683713i
\(764\) 1.59902 0.0578504
\(765\) −8.50454 + 2.34397i −0.307482 + 0.0847462i
\(766\) 27.0258 0.976480
\(767\) 5.57893i 0.201444i
\(768\) 1.00000i 0.0360844i
\(769\) −31.5996 −1.13951 −0.569755 0.821815i \(-0.692962\pi\)
−0.569755 + 0.821815i \(0.692962\pi\)
\(770\) 0.575324 + 2.08743i 0.0207332 + 0.0752257i
\(771\) −6.07097 −0.218641
\(772\) 4.53510i 0.163222i
\(773\) 50.6640i 1.82226i −0.412124 0.911128i \(-0.635213\pi\)
0.412124 0.911128i \(-0.364787\pi\)
\(774\) −2.92778 −0.105237
\(775\) 39.9528 23.8335i 1.43515 0.856125i
\(776\) −13.0947 −0.470073
\(777\) 1.17795i 0.0422587i
\(778\) 14.3786i 0.515497i
\(779\) 3.24368 0.116217
\(780\) −1.03964 3.77209i −0.0372250 0.135062i
\(781\) 5.46924 0.195705
\(782\) 30.3172i 1.08414i
\(783\) 9.23916i 0.330181i
\(784\) 5.61244 0.200444
\(785\) −29.2108 + 8.05088i −1.04258 + 0.287348i
\(786\) 17.3248 0.617955
\(787\) 11.8208i 0.421366i 0.977554 + 0.210683i \(0.0675688\pi\)
−0.977554 + 0.210683i \(0.932431\pi\)
\(788\) 3.14956i 0.112198i
\(789\) −18.0064 −0.641044
\(790\) 1.71942 0.473895i 0.0611741 0.0168604i
\(791\) 4.07910 0.145036
\(792\) 0.822051i 0.0292103i
\(793\) 15.3693i 0.545780i
\(794\) 28.2383 1.00214
\(795\) 8.23824 + 29.8905i 0.292180 + 1.06011i
\(796\) −8.00000 −0.283552
\(797\) 29.0645i 1.02952i 0.857335 + 0.514758i \(0.172118\pi\)
−0.857335 + 0.514758i \(0.827882\pi\)
\(798\) 1.52427i 0.0539585i
\(799\) 28.3589 1.00326
\(800\) −2.56155 4.29400i −0.0905646 0.151816i
\(801\) 14.8729 0.525509
\(802\) 9.70096i 0.342553i
\(803\) 9.79618i 0.345700i
\(804\) 15.2108 0.536442
\(805\) −5.37821 19.5136i −0.189557 0.687764i
\(806\) 16.2810 0.573473
\(807\) 6.54745i 0.230481i
\(808\) 2.00000i 0.0703598i
\(809\) −26.4255 −0.929071 −0.464535 0.885555i \(-0.653779\pi\)
−0.464535 + 0.885555i \(0.653779\pi\)
\(810\) 2.15569 0.594137i 0.0757432 0.0208759i
\(811\) −32.7118 −1.14867 −0.574333 0.818622i \(-0.694739\pi\)
−0.574333 + 0.818622i \(0.694739\pi\)
\(812\) 10.8833i 0.381928i
\(813\) 25.4776i 0.893539i
\(814\) −0.822051 −0.0288129
\(815\) −7.44699 + 2.05249i −0.260857 + 0.0718956i
\(816\) −3.94516 −0.138108
\(817\) 3.78855i 0.132544i
\(818\) 26.8103i 0.937402i
\(819\) −2.06121 −0.0720244
\(820\) −1.48933 5.40369i −0.0520097 0.188705i
\(821\) −41.7992 −1.45880 −0.729400 0.684087i \(-0.760201\pi\)
−0.729400 + 0.684087i \(0.760201\pi\)
\(822\) 1.59958i 0.0557919i
\(823\) 24.8303i 0.865528i −0.901507 0.432764i \(-0.857538\pi\)
0.901507 0.432764i \(-0.142462\pi\)
\(824\) 19.6666 0.685118
\(825\) 2.10573 + 3.52989i 0.0733120 + 0.122895i
\(826\) −3.75563 −0.130675
\(827\) 25.6338i 0.891376i 0.895188 + 0.445688i \(0.147041\pi\)
−0.895188 + 0.445688i \(0.852959\pi\)
\(828\) 7.68466i 0.267060i
\(829\) 24.5535 0.852777 0.426388 0.904540i \(-0.359786\pi\)
0.426388 + 0.904540i \(0.359786\pi\)
\(830\) 4.59219 + 16.6617i 0.159397 + 0.578336i
\(831\) −1.74983 −0.0607009
\(832\) 1.74983i 0.0606644i
\(833\) 22.1419i 0.767173i
\(834\) 13.5364 0.468728
\(835\) −0.635261 + 0.175086i −0.0219841 + 0.00605912i
\(836\) −1.06373 −0.0367900
\(837\) 9.30433i 0.321605i
\(838\) 21.2275i 0.733290i
\(839\) 4.60646 0.159033 0.0795163 0.996834i \(-0.474662\pi\)
0.0795163 + 0.996834i \(0.474662\pi\)
\(840\) −2.53929 + 0.699864i −0.0876140 + 0.0241476i
\(841\) 56.3620 1.94352
\(842\) 6.40880i 0.220862i
\(843\) 21.1927i 0.729915i
\(844\) −0.0954006 −0.00328383
\(845\) −5.90460 21.4235i −0.203124 0.736990i
\(846\) −7.18827 −0.247138
\(847\) 12.1614i 0.417871i
\(848\) 13.8659i 0.476156i
\(849\) −29.6420 −1.01731
\(850\) 16.9405 10.1057i 0.581055 0.346624i
\(851\) 7.68466 0.263427
\(852\) 6.65317i 0.227934i
\(853\) 12.5452i 0.429541i −0.976665 0.214771i \(-0.931100\pi\)
0.976665 0.214771i \(-0.0689004\pi\)
\(854\) 10.3463 0.354044
\(855\) −0.768815 2.78947i −0.0262929 0.0953977i
\(856\) −10.4964 −0.358759
\(857\) 29.1700i 0.996429i 0.867054 + 0.498215i \(0.166011\pi\)
−0.867054 + 0.498215i \(0.833989\pi\)
\(858\) 1.43845i 0.0491078i
\(859\) 12.5127 0.426927 0.213464 0.976951i \(-0.431525\pi\)
0.213464 + 0.976951i \(0.431525\pi\)
\(860\) 6.31138 1.73950i 0.215216 0.0593165i
\(861\) −2.95278 −0.100630
\(862\) 1.41981i 0.0483590i
\(863\) 7.92274i 0.269693i 0.990866 + 0.134847i \(0.0430542\pi\)
−0.990866 + 0.134847i \(0.956946\pi\)
\(864\) 1.00000 0.0340207
\(865\) 27.9253 7.69659i 0.949489 0.261692i
\(866\) −6.06121 −0.205968
\(867\) 1.43574i 0.0487603i
\(868\) 10.9600i 0.372007i
\(869\) −0.655682 −0.0222425
\(870\) −5.48933 19.9168i −0.186106 0.675241i
\(871\) −26.6162 −0.901856
\(872\) 16.0328i 0.542940i
\(873\) 13.0947i 0.443189i
\(874\) 9.94396 0.336359
\(875\) 9.11099 9.50975i 0.308008 0.321488i
\(876\) −11.9168 −0.402630
\(877\) 16.0256i 0.541147i 0.962699 + 0.270574i \(0.0872134\pi\)
−0.962699 + 0.270574i \(0.912787\pi\)
\(878\) 6.54147i 0.220764i
\(879\) −20.7555 −0.700066
\(880\) 0.488411 + 1.77209i 0.0164643 + 0.0597370i
\(881\) 45.6110 1.53667 0.768337 0.640046i \(-0.221085\pi\)
0.768337 + 0.640046i \(0.221085\pi\)
\(882\) 5.61244i 0.188981i
\(883\) 54.1737i 1.82309i 0.411201 + 0.911545i \(0.365110\pi\)
−0.411201 + 0.911545i \(0.634890\pi\)
\(884\) 6.90334 0.232185
\(885\) −6.87293 + 1.89427i −0.231031 + 0.0636753i
\(886\) 4.04887 0.136024
\(887\) 57.1933i 1.92036i 0.279379 + 0.960181i \(0.409871\pi\)
−0.279379 + 0.960181i \(0.590129\pi\)
\(888\) 1.00000i 0.0335578i
\(889\) −20.9084 −0.701245
\(890\) −32.0614 + 8.83657i −1.07470 + 0.296202i
\(891\) −0.822051 −0.0275397
\(892\) 10.5512i 0.353281i
\(893\) 9.30164i 0.311267i
\(894\) −5.82080 −0.194677
\(895\) 12.1792 + 44.1894i 0.407106 + 1.47709i
\(896\) −1.17795 −0.0393525
\(897\) 13.4468i 0.448977i
\(898\) 2.45148i 0.0818069i
\(899\) 85.9641 2.86706
\(900\) −4.29400 + 2.56155i −0.143133 + 0.0853851i
\(901\) −54.7031 −1.82242
\(902\) 2.06064i 0.0686119i
\(903\) 3.44877i 0.114768i
\(904\) 3.46288 0.115174
\(905\) −11.9688 43.4262i −0.397858 1.44353i
\(906\) 6.62672 0.220158
\(907\) 15.0011i 0.498103i −0.968490 0.249051i \(-0.919881\pi\)
0.968490 0.249051i \(-0.0801188\pi\)
\(908\) 10.1063i 0.335389i
\(909\) −2.00000 −0.0663358
\(910\) 4.44333 1.22464i 0.147295 0.0405965i
\(911\) 1.75379 0.0581056 0.0290528 0.999578i \(-0.490751\pi\)
0.0290528 + 0.999578i \(0.490751\pi\)
\(912\) 1.29400i 0.0428487i
\(913\) 6.35378i 0.210279i
\(914\) −6.87237 −0.227318
\(915\) 18.9341 5.21851i 0.625943 0.172518i
\(916\) 4.81173 0.158984
\(917\) 20.4077i 0.673923i
\(918\) 3.94516i 0.130210i
\(919\) −14.1735 −0.467540 −0.233770 0.972292i \(-0.575106\pi\)
−0.233770 + 0.972292i \(0.575106\pi\)
\(920\) −4.56574 16.5657i −0.150528 0.546156i
\(921\) 17.1315 0.564502
\(922\) 1.07222i 0.0353118i
\(923\) 11.6419i 0.383198i
\(924\) 0.968334 0.0318559
\(925\) 2.56155 + 4.29400i 0.0842233 + 0.141186i
\(926\) −29.3791 −0.965456
\(927\) 19.6666i 0.645936i
\(928\) 9.23916i 0.303290i
\(929\) 26.9057 0.882749 0.441374 0.897323i \(-0.354491\pi\)
0.441374 + 0.897323i \(0.354491\pi\)
\(930\) −5.52805 20.0572i −0.181272 0.657703i
\(931\) −7.26250 −0.238019
\(932\) 11.6014i 0.380017i
\(933\) 29.1740i 0.955113i
\(934\) −6.56099 −0.214682
\(935\) −6.99116 + 1.92686i −0.228635 + 0.0630150i
\(936\) −1.74983 −0.0571949
\(937\) 43.4635i 1.41989i 0.704256 + 0.709946i \(0.251281\pi\)
−0.704256 + 0.709946i \(0.748719\pi\)
\(938\) 17.9175i 0.585027i
\(939\) 20.0714 0.655004
\(940\) 15.4957 4.27082i 0.505414 0.139299i
\(941\) 54.0784 1.76290 0.881452 0.472274i \(-0.156567\pi\)
0.881452 + 0.472274i \(0.156567\pi\)
\(942\) 13.5505i 0.441500i
\(943\) 19.2632i 0.627296i
\(944\) −3.18827 −0.103770
\(945\) 0.699864 + 2.53929i 0.0227666 + 0.0826032i
\(946\) −2.40678 −0.0782512
\(947\) 43.8801i 1.42591i 0.701210 + 0.712955i \(0.252644\pi\)
−0.701210 + 0.712955i \(0.747356\pi\)
\(948\) 0.797618i 0.0259054i
\(949\) 20.8523 0.676894
\(950\) 3.31465 + 5.55644i 0.107542 + 0.180275i
\(951\) 20.7084 0.671516
\(952\) 4.64719i 0.150616i
\(953\) 55.7604i 1.80626i 0.429370 + 0.903129i \(0.358736\pi\)
−0.429370 + 0.903129i \(0.641264\pi\)
\(954\) 13.8659 0.448924
\(955\) 0.950036 + 3.44699i 0.0307424 + 0.111542i
\(956\) −23.1599 −0.749044
\(957\) 7.59506i 0.245513i
\(958\) 2.93948i 0.0949703i
\(959\) 1.88423 0.0608449
\(960\) −2.15569 + 0.594137i −0.0695746 + 0.0191757i
\(961\) 55.5705 1.79260
\(962\) 1.74983i 0.0564167i
\(963\) 10.4964i 0.338241i
\(964\) 12.7020 0.409105
\(965\) −9.77628 + 2.69447i −0.314710 + 0.0867382i
\(966\) −9.05214 −0.291248
\(967\) 50.3281i 1.61844i −0.587503 0.809222i \(-0.699889\pi\)
0.587503 0.809222i \(-0.300111\pi\)
\(968\) 10.3242i 0.331833i
\(969\) 5.10504 0.163997
\(970\) −7.78006 28.2281i −0.249803 0.906351i
\(971\) −15.1468 −0.486084 −0.243042 0.970016i \(-0.578145\pi\)
−0.243042 + 0.970016i \(0.578145\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 15.9452i 0.511181i
\(974\) −31.1217 −0.997204
\(975\) 7.51376 4.48228i 0.240633 0.143548i
\(976\) 8.78333 0.281148
\(977\) 29.4991i 0.943759i 0.881663 + 0.471880i \(0.156424\pi\)
−0.881663 + 0.471880i \(0.843576\pi\)
\(978\) 3.45457i 0.110465i
\(979\) 12.2263 0.390754
\(980\) 3.33456 + 12.0987i 0.106519 + 0.386478i
\(981\) −16.0328 −0.511888
\(982\) 4.69373i 0.149783i
\(983\) 45.4318i 1.44905i −0.689249 0.724525i \(-0.742059\pi\)
0.689249 0.724525i \(-0.257941\pi\)
\(984\) −2.50671 −0.0799110
\(985\) 6.78947 1.87127i 0.216330 0.0596236i
\(986\) 36.4499 1.16080
\(987\) 8.46742i 0.269521i
\(988\) 2.26428i 0.0720363i
\(989\) 22.4990 0.715426
\(990\) 1.77209 0.488411i 0.0563206 0.0155227i
\(991\) −17.3250 −0.550346 −0.275173 0.961395i \(-0.588735\pi\)
−0.275173 + 0.961395i \(0.588735\pi\)
\(992\) 9.30433i 0.295413i
\(993\) 18.3339i 0.581808i
\(994\) −7.83710 −0.248578
\(995\) −4.75310 17.2455i −0.150683 0.546720i
\(996\) 7.72918 0.244908
\(997\) 20.9077i 0.662153i 0.943604 + 0.331077i \(0.107412\pi\)
−0.943604 + 0.331077i \(0.892588\pi\)
\(998\) 8.72527i 0.276194i
\(999\) −1.00000 −0.0316386
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 1110.2.d.j.889.6 yes 8
3.2 odd 2 3330.2.d.o.1999.3 8
5.2 odd 4 5550.2.a.cl.1.2 4
5.3 odd 4 5550.2.a.cm.1.3 4
5.4 even 2 inner 1110.2.d.j.889.2 8
15.14 odd 2 3330.2.d.o.1999.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.d.j.889.2 8 5.4 even 2 inner
1110.2.d.j.889.6 yes 8 1.1 even 1 trivial
3330.2.d.o.1999.3 8 3.2 odd 2
3330.2.d.o.1999.7 8 15.14 odd 2
5550.2.a.cl.1.2 4 5.2 odd 4
5550.2.a.cm.1.3 4 5.3 odd 4