Properties

Label 1380.2.p.b.91.20
Level $1380$
Weight $2$
Character 1380.91
Analytic conductor $11.019$
Analytic rank $0$
Dimension $48$
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] = [1380,2,Mod(91,1380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1380.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.p (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: \(11.0193554789\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.20
Character \(\chi\) \(=\) 1380.91
Dual form 1380.2.p.b.91.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.651202 + 1.25536i) q^{2} -1.00000i q^{3} +(-1.15187 - 1.63499i) q^{4} +1.00000i q^{5} +(1.25536 + 0.651202i) q^{6} -2.14037 q^{7} +(2.80261 - 0.381312i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.651202 + 1.25536i) q^{2} -1.00000i q^{3} +(-1.15187 - 1.63499i) q^{4} +1.00000i q^{5} +(1.25536 + 0.651202i) q^{6} -2.14037 q^{7} +(2.80261 - 0.381312i) q^{8} -1.00000 q^{9} +(-1.25536 - 0.651202i) q^{10} +3.55021 q^{11} +(-1.63499 + 1.15187i) q^{12} -4.04464 q^{13} +(1.39382 - 2.68695i) q^{14} +1.00000 q^{15} +(-1.34638 + 3.76660i) q^{16} +0.843658i q^{17} +(0.651202 - 1.25536i) q^{18} +5.13553 q^{19} +(1.63499 - 1.15187i) q^{20} +2.14037i q^{21} +(-2.31190 + 4.45680i) q^{22} +(-2.71512 - 3.95324i) q^{23} +(-0.381312 - 2.80261i) q^{24} -1.00000 q^{25} +(2.63388 - 5.07749i) q^{26} +1.00000i q^{27} +(2.46544 + 3.49949i) q^{28} +0.275665 q^{29} +(-0.651202 + 1.25536i) q^{30} +8.41233i q^{31} +(-3.85169 - 4.14301i) q^{32} -3.55021i q^{33} +(-1.05910 - 0.549392i) q^{34} -2.14037i q^{35} +(1.15187 + 1.63499i) q^{36} -2.63854i q^{37} +(-3.34426 + 6.44695i) q^{38} +4.04464i q^{39} +(0.381312 + 2.80261i) q^{40} +7.36818 q^{41} +(-2.68695 - 1.39382i) q^{42} +11.6118 q^{43} +(-4.08939 - 5.80455i) q^{44} -1.00000i q^{45} +(6.73084 - 0.834108i) q^{46} +10.4234i q^{47} +(3.76660 + 1.34638i) q^{48} -2.41880 q^{49} +(0.651202 - 1.25536i) q^{50} +0.843658 q^{51} +(4.65891 + 6.61294i) q^{52} -5.60182i q^{53} +(-1.25536 - 0.651202i) q^{54} +3.55021i q^{55} +(-5.99863 + 0.816150i) q^{56} -5.13553i q^{57} +(-0.179514 + 0.346060i) q^{58} +2.95080i q^{59} +(-1.15187 - 1.63499i) q^{60} +7.05529i q^{61} +(-10.5605 - 5.47812i) q^{62} +2.14037 q^{63} +(7.70920 - 2.13733i) q^{64} -4.04464i q^{65} +(4.45680 + 2.31190i) q^{66} +2.62970 q^{67} +(1.37937 - 0.971787i) q^{68} +(-3.95324 + 2.71512i) q^{69} +(2.68695 + 1.39382i) q^{70} +2.73387i q^{71} +(-2.80261 + 0.381312i) q^{72} +4.84511 q^{73} +(3.31232 + 1.71822i) q^{74} +1.00000i q^{75} +(-5.91548 - 8.39653i) q^{76} -7.59878 q^{77} +(-5.07749 - 2.63388i) q^{78} +16.2338 q^{79} +(-3.76660 - 1.34638i) q^{80} +1.00000 q^{81} +(-4.79817 + 9.24974i) q^{82} +9.45106 q^{83} +(3.49949 - 2.46544i) q^{84} -0.843658 q^{85} +(-7.56161 + 14.5770i) q^{86} -0.275665i q^{87} +(9.94984 - 1.35374i) q^{88} +16.0179i q^{89} +(1.25536 + 0.651202i) q^{90} +8.65705 q^{91} +(-3.33603 + 8.99283i) q^{92} +8.41233 q^{93} +(-13.0851 - 6.78772i) q^{94} +5.13553i q^{95} +(-4.14301 + 3.85169i) q^{96} -0.845087i q^{97} +(1.57512 - 3.03647i) q^{98} -3.55021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(691\) \(1201\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.651202 + 1.25536i −0.460469 + 0.887676i
\(3\) 1.00000i 0.577350i
\(4\) −1.15187 1.63499i −0.575937 0.817494i
\(5\) 1.00000i 0.447214i
\(6\) 1.25536 + 0.651202i 0.512500 + 0.265852i
\(7\) −2.14037 −0.808986 −0.404493 0.914541i \(-0.632552\pi\)
−0.404493 + 0.914541i \(0.632552\pi\)
\(8\) 2.80261 0.381312i 0.990871 0.134814i
\(9\) −1.00000 −0.333333
\(10\) −1.25536 0.651202i −0.396981 0.205928i
\(11\) 3.55021 1.07043 0.535214 0.844716i \(-0.320231\pi\)
0.535214 + 0.844716i \(0.320231\pi\)
\(12\) −1.63499 + 1.15187i −0.471981 + 0.332517i
\(13\) −4.04464 −1.12178 −0.560891 0.827890i \(-0.689541\pi\)
−0.560891 + 0.827890i \(0.689541\pi\)
\(14\) 1.39382 2.68695i 0.372513 0.718117i
\(15\) 1.00000 0.258199
\(16\) −1.34638 + 3.76660i −0.336594 + 0.941650i
\(17\) 0.843658i 0.204617i 0.994753 + 0.102309i \(0.0326229\pi\)
−0.994753 + 0.102309i \(0.967377\pi\)
\(18\) 0.651202 1.25536i 0.153490 0.295892i
\(19\) 5.13553 1.17817 0.589085 0.808071i \(-0.299488\pi\)
0.589085 + 0.808071i \(0.299488\pi\)
\(20\) 1.63499 1.15187i 0.365595 0.257567i
\(21\) 2.14037i 0.467068i
\(22\) −2.31190 + 4.45680i −0.492899 + 0.950193i
\(23\) −2.71512 3.95324i −0.566142 0.824308i
\(24\) −0.381312 2.80261i −0.0778349 0.572080i
\(25\) −1.00000 −0.200000
\(26\) 2.63388 5.07749i 0.516546 0.995778i
\(27\) 1.00000i 0.192450i
\(28\) 2.46544 + 3.49949i 0.465924 + 0.661341i
\(29\) 0.275665 0.0511898 0.0255949 0.999672i \(-0.491852\pi\)
0.0255949 + 0.999672i \(0.491852\pi\)
\(30\) −0.651202 + 1.25536i −0.118893 + 0.229197i
\(31\) 8.41233i 1.51090i 0.655207 + 0.755450i \(0.272581\pi\)
−0.655207 + 0.755450i \(0.727419\pi\)
\(32\) −3.85169 4.14301i −0.680888 0.732387i
\(33\) 3.55021i 0.618012i
\(34\) −1.05910 0.549392i −0.181634 0.0942199i
\(35\) 2.14037i 0.361789i
\(36\) 1.15187 + 1.63499i 0.191979 + 0.272498i
\(37\) 2.63854i 0.433773i −0.976197 0.216886i \(-0.930410\pi\)
0.976197 0.216886i \(-0.0695901\pi\)
\(38\) −3.34426 + 6.44695i −0.542511 + 1.04583i
\(39\) 4.04464i 0.647661i
\(40\) 0.381312 + 2.80261i 0.0602907 + 0.443131i
\(41\) 7.36818 1.15072 0.575358 0.817901i \(-0.304863\pi\)
0.575358 + 0.817901i \(0.304863\pi\)
\(42\) −2.68695 1.39382i −0.414605 0.215070i
\(43\) 11.6118 1.77078 0.885389 0.464850i \(-0.153892\pi\)
0.885389 + 0.464850i \(0.153892\pi\)
\(44\) −4.08939 5.80455i −0.616499 0.875069i
\(45\) 1.00000i 0.149071i
\(46\) 6.73084 0.834108i 0.992409 0.122983i
\(47\) 10.4234i 1.52040i 0.649686 + 0.760202i \(0.274900\pi\)
−0.649686 + 0.760202i \(0.725100\pi\)
\(48\) 3.76660 + 1.34638i 0.543662 + 0.194333i
\(49\) −2.41880 −0.345542
\(50\) 0.651202 1.25536i 0.0920938 0.177535i
\(51\) 0.843658 0.118136
\(52\) 4.65891 + 6.61294i 0.646075 + 0.917050i
\(53\) 5.60182i 0.769470i −0.923027 0.384735i \(-0.874293\pi\)
0.923027 0.384735i \(-0.125707\pi\)
\(54\) −1.25536 0.651202i −0.170833 0.0886173i
\(55\) 3.55021i 0.478710i
\(56\) −5.99863 + 0.816150i −0.801600 + 0.109063i
\(57\) 5.13553i 0.680217i
\(58\) −0.179514 + 0.346060i −0.0235713 + 0.0454399i
\(59\) 2.95080i 0.384162i 0.981379 + 0.192081i \(0.0615236\pi\)
−0.981379 + 0.192081i \(0.938476\pi\)
\(60\) −1.15187 1.63499i −0.148706 0.211076i
\(61\) 7.05529i 0.903338i 0.892186 + 0.451669i \(0.149171\pi\)
−0.892186 + 0.451669i \(0.850829\pi\)
\(62\) −10.5605 5.47812i −1.34119 0.695722i
\(63\) 2.14037 0.269662
\(64\) 7.70920 2.13733i 0.963650 0.267167i
\(65\) 4.04464i 0.501676i
\(66\) 4.45680 + 2.31190i 0.548594 + 0.284575i
\(67\) 2.62970 0.321269 0.160634 0.987014i \(-0.448646\pi\)
0.160634 + 0.987014i \(0.448646\pi\)
\(68\) 1.37937 0.971787i 0.167273 0.117847i
\(69\) −3.95324 + 2.71512i −0.475914 + 0.326862i
\(70\) 2.68695 + 1.39382i 0.321152 + 0.166593i
\(71\) 2.73387i 0.324450i 0.986754 + 0.162225i \(0.0518671\pi\)
−0.986754 + 0.162225i \(0.948133\pi\)
\(72\) −2.80261 + 0.381312i −0.330290 + 0.0449380i
\(73\) 4.84511 0.567077 0.283538 0.958961i \(-0.408492\pi\)
0.283538 + 0.958961i \(0.408492\pi\)
\(74\) 3.31232 + 1.71822i 0.385050 + 0.199739i
\(75\) 1.00000i 0.115470i
\(76\) −5.91548 8.39653i −0.678552 0.963148i
\(77\) −7.59878 −0.865961
\(78\) −5.07749 2.63388i −0.574913 0.298228i
\(79\) 16.2338 1.82645 0.913223 0.407461i \(-0.133586\pi\)
0.913223 + 0.407461i \(0.133586\pi\)
\(80\) −3.76660 1.34638i −0.421119 0.150530i
\(81\) 1.00000 0.111111
\(82\) −4.79817 + 9.24974i −0.529869 + 1.02146i
\(83\) 9.45106 1.03739 0.518694 0.854960i \(-0.326418\pi\)
0.518694 + 0.854960i \(0.326418\pi\)
\(84\) 3.49949 2.46544i 0.381826 0.269002i
\(85\) −0.843658 −0.0915076
\(86\) −7.56161 + 14.5770i −0.815389 + 1.57188i
\(87\) 0.275665i 0.0295544i
\(88\) 9.94984 1.35374i 1.06066 0.144309i
\(89\) 16.0179i 1.69789i 0.528482 + 0.848945i \(0.322762\pi\)
−0.528482 + 0.848945i \(0.677238\pi\)
\(90\) 1.25536 + 0.651202i 0.132327 + 0.0686427i
\(91\) 8.65705 0.907505
\(92\) −3.33603 + 8.99283i −0.347805 + 0.937567i
\(93\) 8.41233 0.872318
\(94\) −13.0851 6.78772i −1.34963 0.700099i
\(95\) 5.13553i 0.526894i
\(96\) −4.14301 + 3.85169i −0.422844 + 0.393111i
\(97\) 0.845087i 0.0858056i −0.999079 0.0429028i \(-0.986339\pi\)
0.999079 0.0429028i \(-0.0136606\pi\)
\(98\) 1.57512 3.03647i 0.159112 0.306730i
\(99\) −3.55021 −0.356810
\(100\) 1.15187 + 1.63499i 0.115187 + 0.163499i
\(101\) 7.04680 0.701182 0.350591 0.936529i \(-0.385981\pi\)
0.350591 + 0.936529i \(0.385981\pi\)
\(102\) −0.549392 + 1.05910i −0.0543979 + 0.104866i
\(103\) 13.7768 1.35747 0.678736 0.734382i \(-0.262528\pi\)
0.678736 + 0.734382i \(0.262528\pi\)
\(104\) −11.3355 + 1.54227i −1.11154 + 0.151232i
\(105\) −2.14037 −0.208879
\(106\) 7.03232 + 3.64792i 0.683040 + 0.354317i
\(107\) −1.44719 −0.139905 −0.0699526 0.997550i \(-0.522285\pi\)
−0.0699526 + 0.997550i \(0.522285\pi\)
\(108\) 1.63499 1.15187i 0.157327 0.110839i
\(109\) 1.02911i 0.0985713i 0.998785 + 0.0492856i \(0.0156945\pi\)
−0.998785 + 0.0492856i \(0.984306\pi\)
\(110\) −4.45680 2.31190i −0.424939 0.220431i
\(111\) −2.63854 −0.250439
\(112\) 2.88175 8.06193i 0.272300 0.761781i
\(113\) 11.0913i 1.04338i 0.853135 + 0.521689i \(0.174698\pi\)
−0.853135 + 0.521689i \(0.825302\pi\)
\(114\) 6.44695 + 3.34426i 0.603812 + 0.313219i
\(115\) 3.95324 2.71512i 0.368642 0.253186i
\(116\) −0.317532 0.450710i −0.0294821 0.0418474i
\(117\) 4.04464 0.373927
\(118\) −3.70433 1.92157i −0.341011 0.176894i
\(119\) 1.80574i 0.165532i
\(120\) 2.80261 0.381312i 0.255842 0.0348088i
\(121\) 1.60399 0.145817
\(122\) −8.85696 4.59442i −0.801871 0.415959i
\(123\) 7.36818i 0.664367i
\(124\) 13.7541 9.68994i 1.23515 0.870182i
\(125\) 1.00000i 0.0894427i
\(126\) −1.39382 + 2.68695i −0.124171 + 0.239372i
\(127\) 20.3834i 1.80873i 0.426758 + 0.904366i \(0.359656\pi\)
−0.426758 + 0.904366i \(0.640344\pi\)
\(128\) −2.33712 + 11.0697i −0.206574 + 0.978431i
\(129\) 11.6118i 1.02236i
\(130\) 5.07749 + 2.63388i 0.445326 + 0.231006i
\(131\) 3.33061i 0.290997i −0.989358 0.145498i \(-0.953521\pi\)
0.989358 0.145498i \(-0.0464786\pi\)
\(132\) −5.80455 + 4.08939i −0.505222 + 0.355936i
\(133\) −10.9920 −0.953123
\(134\) −1.71246 + 3.30123i −0.147934 + 0.285183i
\(135\) −1.00000 −0.0860663
\(136\) 0.321697 + 2.36444i 0.0275853 + 0.202749i
\(137\) 21.9555i 1.87579i −0.346924 0.937893i \(-0.612774\pi\)
0.346924 0.937893i \(-0.387226\pi\)
\(138\) −0.834108 6.73084i −0.0710040 0.572968i
\(139\) 15.4357i 1.30924i 0.755960 + 0.654618i \(0.227170\pi\)
−0.755960 + 0.654618i \(0.772830\pi\)
\(140\) −3.49949 + 2.46544i −0.295761 + 0.208368i
\(141\) 10.4234 0.877806
\(142\) −3.43200 1.78030i −0.288007 0.149399i
\(143\) −14.3593 −1.20079
\(144\) 1.34638 3.76660i 0.112198 0.313883i
\(145\) 0.275665i 0.0228928i
\(146\) −3.15514 + 6.08237i −0.261121 + 0.503380i
\(147\) 2.41880i 0.199499i
\(148\) −4.31398 + 3.03926i −0.354607 + 0.249826i
\(149\) 1.22216i 0.100123i 0.998746 + 0.0500615i \(0.0159417\pi\)
−0.998746 + 0.0500615i \(0.984058\pi\)
\(150\) −1.25536 0.651202i −0.102500 0.0531704i
\(151\) 9.64939i 0.785256i −0.919697 0.392628i \(-0.871566\pi\)
0.919697 0.392628i \(-0.128434\pi\)
\(152\) 14.3929 1.95824i 1.16742 0.158834i
\(153\) 0.843658i 0.0682057i
\(154\) 4.94834 9.53923i 0.398748 0.768693i
\(155\) −8.41233 −0.675695
\(156\) 6.61294 4.65891i 0.529459 0.373012i
\(157\) 15.1421i 1.20847i 0.796807 + 0.604234i \(0.206521\pi\)
−0.796807 + 0.604234i \(0.793479\pi\)
\(158\) −10.5715 + 20.3793i −0.841021 + 1.62129i
\(159\) −5.60182 −0.444254
\(160\) 4.14301 3.85169i 0.327533 0.304503i
\(161\) 5.81138 + 8.46142i 0.458001 + 0.666853i
\(162\) −0.651202 + 1.25536i −0.0511632 + 0.0986306i
\(163\) 6.70557i 0.525221i 0.964902 + 0.262610i \(0.0845833\pi\)
−0.964902 + 0.262610i \(0.915417\pi\)
\(164\) −8.48721 12.0469i −0.662740 0.940705i
\(165\) 3.55021 0.276383
\(166\) −6.15454 + 11.8645i −0.477685 + 0.920865i
\(167\) 22.2534i 1.72202i −0.508589 0.861010i \(-0.669833\pi\)
0.508589 0.861010i \(-0.330167\pi\)
\(168\) 0.816150 + 5.99863i 0.0629673 + 0.462804i
\(169\) 3.35912 0.258394
\(170\) 0.549392 1.05910i 0.0421364 0.0812291i
\(171\) −5.13553 −0.392724
\(172\) −13.3753 18.9851i −1.01986 1.44760i
\(173\) −20.8806 −1.58752 −0.793762 0.608228i \(-0.791881\pi\)
−0.793762 + 0.608228i \(0.791881\pi\)
\(174\) 0.346060 + 0.179514i 0.0262348 + 0.0136089i
\(175\) 2.14037 0.161797
\(176\) −4.77992 + 13.3722i −0.360300 + 1.00797i
\(177\) 2.95080 0.221796
\(178\) −20.1082 10.4309i −1.50718 0.781826i
\(179\) 11.9933i 0.896420i −0.893928 0.448210i \(-0.852062\pi\)
0.893928 0.448210i \(-0.147938\pi\)
\(180\) −1.63499 + 1.15187i −0.121865 + 0.0858555i
\(181\) 11.8382i 0.879927i −0.898016 0.439964i \(-0.854991\pi\)
0.898016 0.439964i \(-0.145009\pi\)
\(182\) −5.63748 + 10.8677i −0.417878 + 0.805570i
\(183\) 7.05529 0.521542
\(184\) −9.11684 10.0441i −0.672102 0.740459i
\(185\) 2.63854 0.193989
\(186\) −5.47812 + 10.5605i −0.401675 + 0.774336i
\(187\) 2.99516i 0.219028i
\(188\) 17.0421 12.0064i 1.24292 0.875657i
\(189\) 2.14037i 0.155689i
\(190\) −6.44695 3.34426i −0.467711 0.242618i
\(191\) −1.29520 −0.0937173 −0.0468587 0.998902i \(-0.514921\pi\)
−0.0468587 + 0.998902i \(0.514921\pi\)
\(192\) −2.13733 7.70920i −0.154249 0.556364i
\(193\) −1.48140 −0.106634 −0.0533169 0.998578i \(-0.516979\pi\)
−0.0533169 + 0.998578i \(0.516979\pi\)
\(194\) 1.06089 + 0.550322i 0.0761675 + 0.0395108i
\(195\) −4.04464 −0.289643
\(196\) 2.78615 + 3.95471i 0.199010 + 0.282479i
\(197\) −13.9422 −0.993338 −0.496669 0.867940i \(-0.665444\pi\)
−0.496669 + 0.867940i \(0.665444\pi\)
\(198\) 2.31190 4.45680i 0.164300 0.316731i
\(199\) −5.33970 −0.378521 −0.189261 0.981927i \(-0.560609\pi\)
−0.189261 + 0.981927i \(0.560609\pi\)
\(200\) −2.80261 + 0.381312i −0.198174 + 0.0269628i
\(201\) 2.62970i 0.185485i
\(202\) −4.58889 + 8.84629i −0.322873 + 0.622423i
\(203\) −0.590027 −0.0414118
\(204\) −0.971787 1.37937i −0.0680387 0.0965753i
\(205\) 7.36818i 0.514616i
\(206\) −8.97150 + 17.2949i −0.625074 + 1.20500i
\(207\) 2.71512 + 3.95324i 0.188714 + 0.274769i
\(208\) 5.44561 15.2345i 0.377585 1.05633i
\(209\) 18.2322 1.26115
\(210\) 1.39382 2.68695i 0.0961824 0.185417i
\(211\) 2.76105i 0.190078i 0.995474 + 0.0950392i \(0.0302976\pi\)
−0.995474 + 0.0950392i \(0.969702\pi\)
\(212\) −9.15892 + 6.45259i −0.629037 + 0.443166i
\(213\) 2.73387 0.187321
\(214\) 0.942413 1.81675i 0.0644220 0.124190i
\(215\) 11.6118i 0.791916i
\(216\) 0.381312 + 2.80261i 0.0259450 + 0.190693i
\(217\) 18.0055i 1.22230i
\(218\) −1.29191 0.670161i −0.0874993 0.0453890i
\(219\) 4.84511i 0.327402i
\(220\) 5.80455 4.08939i 0.391343 0.275707i
\(221\) 3.41229i 0.229536i
\(222\) 1.71822 3.31232i 0.115319 0.222308i
\(223\) 7.40876i 0.496127i 0.968744 + 0.248063i \(0.0797942\pi\)
−0.968744 + 0.248063i \(0.920206\pi\)
\(224\) 8.24405 + 8.86759i 0.550829 + 0.592491i
\(225\) 1.00000 0.0666667
\(226\) −13.9236 7.22265i −0.926182 0.480444i
\(227\) 10.8648 0.721119 0.360560 0.932736i \(-0.382586\pi\)
0.360560 + 0.932736i \(0.382586\pi\)
\(228\) −8.39653 + 5.91548i −0.556074 + 0.391762i
\(229\) 12.6365i 0.835044i 0.908667 + 0.417522i \(0.137101\pi\)
−0.908667 + 0.417522i \(0.862899\pi\)
\(230\) 0.834108 + 6.73084i 0.0549995 + 0.443819i
\(231\) 7.59878i 0.499963i
\(232\) 0.772582 0.105114i 0.0507225 0.00690110i
\(233\) 2.14877 0.140771 0.0703854 0.997520i \(-0.477577\pi\)
0.0703854 + 0.997520i \(0.477577\pi\)
\(234\) −2.63388 + 5.07749i −0.172182 + 0.331926i
\(235\) −10.4234 −0.679946
\(236\) 4.82453 3.39895i 0.314050 0.221253i
\(237\) 16.2338i 1.05450i
\(238\) 2.26687 + 1.17590i 0.146939 + 0.0762225i
\(239\) 15.5046i 1.00291i −0.865183 0.501456i \(-0.832798\pi\)
0.865183 0.501456i \(-0.167202\pi\)
\(240\) −1.34638 + 3.76660i −0.0869083 + 0.243133i
\(241\) 12.5601i 0.809065i 0.914524 + 0.404532i \(0.132566\pi\)
−0.914524 + 0.404532i \(0.867434\pi\)
\(242\) −1.04452 + 2.01359i −0.0671443 + 0.129438i
\(243\) 1.00000i 0.0641500i
\(244\) 11.5353 8.12680i 0.738474 0.520265i
\(245\) 2.41880i 0.154531i
\(246\) 9.24974 + 4.79817i 0.589742 + 0.305920i
\(247\) −20.7714 −1.32165
\(248\) 3.20772 + 23.5764i 0.203690 + 1.49711i
\(249\) 9.45106i 0.598937i
\(250\) 1.25536 + 0.651202i 0.0793961 + 0.0411856i
\(251\) 24.6936 1.55865 0.779323 0.626622i \(-0.215563\pi\)
0.779323 + 0.626622i \(0.215563\pi\)
\(252\) −2.46544 3.49949i −0.155308 0.220447i
\(253\) −9.63925 14.0348i −0.606015 0.882362i
\(254\) −25.5885 13.2737i −1.60557 0.832865i
\(255\) 0.843658i 0.0528319i
\(256\) −12.3745 10.1425i −0.773409 0.633908i
\(257\) −29.0352 −1.81116 −0.905582 0.424171i \(-0.860566\pi\)
−0.905582 + 0.424171i \(0.860566\pi\)
\(258\) 14.5770 + 7.56161i 0.907524 + 0.470765i
\(259\) 5.64746i 0.350916i
\(260\) −6.61294 + 4.65891i −0.410117 + 0.288933i
\(261\) −0.275665 −0.0170633
\(262\) 4.18113 + 2.16890i 0.258311 + 0.133995i
\(263\) −25.0910 −1.54718 −0.773589 0.633688i \(-0.781540\pi\)
−0.773589 + 0.633688i \(0.781540\pi\)
\(264\) −1.35374 9.94984i −0.0833167 0.612370i
\(265\) 5.60182 0.344117
\(266\) 7.15798 13.7989i 0.438884 0.846064i
\(267\) 16.0179 0.980277
\(268\) −3.02908 4.29953i −0.185030 0.262636i
\(269\) 15.8583 0.966900 0.483450 0.875372i \(-0.339384\pi\)
0.483450 + 0.875372i \(0.339384\pi\)
\(270\) 0.651202 1.25536i 0.0396309 0.0763990i
\(271\) 19.2143i 1.16719i −0.812046 0.583594i \(-0.801646\pi\)
0.812046 0.583594i \(-0.198354\pi\)
\(272\) −3.17772 1.13588i −0.192678 0.0688730i
\(273\) 8.65705i 0.523948i
\(274\) 27.5621 + 14.2975i 1.66509 + 0.863741i
\(275\) −3.55021 −0.214086
\(276\) 8.99283 + 3.33603i 0.541305 + 0.200805i
\(277\) 2.32664 0.139794 0.0698972 0.997554i \(-0.477733\pi\)
0.0698972 + 0.997554i \(0.477733\pi\)
\(278\) −19.3774 10.0517i −1.16218 0.602862i
\(279\) 8.41233i 0.503633i
\(280\) −0.816150 5.99863i −0.0487743 0.358487i
\(281\) 2.44660i 0.145952i −0.997334 0.0729758i \(-0.976750\pi\)
0.997334 0.0729758i \(-0.0232496\pi\)
\(282\) −6.78772 + 13.0851i −0.404203 + 0.779207i
\(283\) −9.49613 −0.564486 −0.282243 0.959343i \(-0.591078\pi\)
−0.282243 + 0.959343i \(0.591078\pi\)
\(284\) 4.46984 3.14907i 0.265236 0.186863i
\(285\) 5.13553 0.304202
\(286\) 9.35081 18.0262i 0.552925 1.06591i
\(287\) −15.7707 −0.930913
\(288\) 3.85169 + 4.14301i 0.226963 + 0.244129i
\(289\) 16.2882 0.958132
\(290\) −0.346060 0.179514i −0.0203214 0.0105414i
\(291\) −0.845087 −0.0495399
\(292\) −5.58095 7.92169i −0.326600 0.463582i
\(293\) 16.0874i 0.939836i −0.882710 0.469918i \(-0.844283\pi\)
0.882710 0.469918i \(-0.155717\pi\)
\(294\) −3.03647 1.57512i −0.177090 0.0918631i
\(295\) −2.95080 −0.171802
\(296\) −1.00610 7.39478i −0.0584786 0.429813i
\(297\) 3.55021i 0.206004i
\(298\) −1.53425 0.795871i −0.0888768 0.0461036i
\(299\) 10.9817 + 15.9894i 0.635088 + 0.924693i
\(300\) 1.63499 1.15187i 0.0943961 0.0665034i
\(301\) −24.8535 −1.43253
\(302\) 12.1135 + 6.28370i 0.697053 + 0.361586i
\(303\) 7.04680i 0.404828i
\(304\) −6.91436 + 19.3435i −0.396566 + 1.10942i
\(305\) −7.05529 −0.403985
\(306\) 1.05910 + 0.549392i 0.0605446 + 0.0314066i
\(307\) 1.09550i 0.0625235i −0.999511 0.0312618i \(-0.990047\pi\)
0.999511 0.0312618i \(-0.00995255\pi\)
\(308\) 8.75283 + 12.4239i 0.498739 + 0.707918i
\(309\) 13.7768i 0.783737i
\(310\) 5.47812 10.5605i 0.311136 0.599798i
\(311\) 33.0428i 1.87368i −0.349754 0.936842i \(-0.613735\pi\)
0.349754 0.936842i \(-0.386265\pi\)
\(312\) 1.54227 + 11.3355i 0.0873137 + 0.641748i
\(313\) 17.6117i 0.995472i −0.867329 0.497736i \(-0.834165\pi\)
0.867329 0.497736i \(-0.165835\pi\)
\(314\) −19.0088 9.86053i −1.07273 0.556462i
\(315\) 2.14037i 0.120596i
\(316\) −18.6993 26.5421i −1.05192 1.49311i
\(317\) 11.9669 0.672130 0.336065 0.941839i \(-0.390904\pi\)
0.336065 + 0.941839i \(0.390904\pi\)
\(318\) 3.64792 7.03232i 0.204565 0.394353i
\(319\) 0.978670 0.0547950
\(320\) 2.13733 + 7.70920i 0.119481 + 0.430958i
\(321\) 1.44719i 0.0807743i
\(322\) −14.4065 + 1.78530i −0.802844 + 0.0994911i
\(323\) 4.33263i 0.241074i
\(324\) −1.15187 1.63499i −0.0639929 0.0908327i
\(325\) 4.04464 0.224356
\(326\) −8.41792 4.36668i −0.466226 0.241848i
\(327\) 1.02911 0.0569101
\(328\) 20.6501 2.80957i 1.14021 0.155133i
\(329\) 22.3099i 1.22999i
\(330\) −2.31190 + 4.45680i −0.127266 + 0.245339i
\(331\) 5.36132i 0.294685i −0.989086 0.147343i \(-0.952928\pi\)
0.989086 0.147343i \(-0.0470720\pi\)
\(332\) −10.8864 15.4524i −0.597470 0.848059i
\(333\) 2.63854i 0.144591i
\(334\) 27.9361 + 14.4914i 1.52859 + 0.792937i
\(335\) 2.62970i 0.143676i
\(336\) −8.06193 2.88175i −0.439814 0.157212i
\(337\) 18.1283i 0.987513i 0.869600 + 0.493756i \(0.164377\pi\)
−0.869600 + 0.493756i \(0.835623\pi\)
\(338\) −2.18746 + 4.21691i −0.118982 + 0.229370i
\(339\) 11.0913 0.602395
\(340\) 0.971787 + 1.37937i 0.0527026 + 0.0748069i
\(341\) 29.8655i 1.61731i
\(342\) 3.34426 6.44695i 0.180837 0.348611i
\(343\) 20.1598 1.08852
\(344\) 32.5432 4.42770i 1.75461 0.238726i
\(345\) −2.71512 3.95324i −0.146177 0.212835i
\(346\) 13.5975 26.2128i 0.731006 1.40921i
\(347\) 6.76150i 0.362976i 0.983393 + 0.181488i \(0.0580914\pi\)
−0.983393 + 0.181488i \(0.941909\pi\)
\(348\) −0.450710 + 0.317532i −0.0241606 + 0.0170215i
\(349\) 35.9054 1.92197 0.960987 0.276593i \(-0.0892055\pi\)
0.960987 + 0.276593i \(0.0892055\pi\)
\(350\) −1.39382 + 2.68695i −0.0745026 + 0.143623i
\(351\) 4.04464i 0.215887i
\(352\) −13.6743 14.7085i −0.728842 0.783968i
\(353\) 19.5489 1.04048 0.520240 0.854020i \(-0.325842\pi\)
0.520240 + 0.854020i \(0.325842\pi\)
\(354\) −1.92157 + 3.70433i −0.102130 + 0.196883i
\(355\) −2.73387 −0.145099
\(356\) 26.1890 18.4505i 1.38802 0.977877i
\(357\) −1.80574 −0.0955701
\(358\) 15.0559 + 7.81004i 0.795730 + 0.412774i
\(359\) −28.3999 −1.49889 −0.749446 0.662065i \(-0.769680\pi\)
−0.749446 + 0.662065i \(0.769680\pi\)
\(360\) −0.381312 2.80261i −0.0200969 0.147710i
\(361\) 7.37365 0.388087
\(362\) 14.8613 + 7.70906i 0.781090 + 0.405179i
\(363\) 1.60399i 0.0841876i
\(364\) −9.97182 14.1542i −0.522665 0.741880i
\(365\) 4.84511i 0.253604i
\(366\) −4.59442 + 8.85696i −0.240154 + 0.462961i
\(367\) 17.3687 0.906639 0.453319 0.891348i \(-0.350240\pi\)
0.453319 + 0.891348i \(0.350240\pi\)
\(368\) 18.5459 4.90422i 0.966769 0.255650i
\(369\) −7.36818 −0.383572
\(370\) −1.71822 + 3.31232i −0.0893260 + 0.172199i
\(371\) 11.9900i 0.622490i
\(372\) −9.68994 13.7541i −0.502400 0.713115i
\(373\) 16.4101i 0.849683i 0.905268 + 0.424841i \(0.139670\pi\)
−0.905268 + 0.424841i \(0.860330\pi\)
\(374\) −3.76002 1.95046i −0.194426 0.100856i
\(375\) −1.00000 −0.0516398
\(376\) 3.97455 + 29.2126i 0.204972 + 1.50652i
\(377\) −1.11497 −0.0574237
\(378\) 2.68695 + 1.39382i 0.138202 + 0.0716901i
\(379\) −19.6429 −1.00899 −0.504493 0.863416i \(-0.668321\pi\)
−0.504493 + 0.863416i \(0.668321\pi\)
\(380\) 8.39653 5.91548i 0.430733 0.303458i
\(381\) 20.3834 1.04427
\(382\) 0.843436 1.62594i 0.0431539 0.0831906i
\(383\) 18.4931 0.944955 0.472477 0.881343i \(-0.343360\pi\)
0.472477 + 0.881343i \(0.343360\pi\)
\(384\) 11.0697 + 2.33712i 0.564897 + 0.119266i
\(385\) 7.59878i 0.387270i
\(386\) 0.964692 1.85970i 0.0491015 0.0946562i
\(387\) −11.6118 −0.590260
\(388\) −1.38171 + 0.973433i −0.0701456 + 0.0494186i
\(389\) 18.5928i 0.942690i 0.881949 + 0.471345i \(0.156231\pi\)
−0.881949 + 0.471345i \(0.843769\pi\)
\(390\) 2.63388 5.07749i 0.133372 0.257109i
\(391\) 3.33518 2.29064i 0.168668 0.115842i
\(392\) −6.77893 + 0.922315i −0.342388 + 0.0465839i
\(393\) −3.33061 −0.168007
\(394\) 9.07916 17.5025i 0.457401 0.881762i
\(395\) 16.2338i 0.816811i
\(396\) 4.08939 + 5.80455i 0.205500 + 0.291690i
\(397\) −17.8628 −0.896510 −0.448255 0.893906i \(-0.647954\pi\)
−0.448255 + 0.893906i \(0.647954\pi\)
\(398\) 3.47722 6.70326i 0.174297 0.336004i
\(399\) 10.9920i 0.550286i
\(400\) 1.34638 3.76660i 0.0673189 0.188330i
\(401\) 10.8994i 0.544288i −0.962257 0.272144i \(-0.912267\pi\)
0.962257 0.272144i \(-0.0877327\pi\)
\(402\) 3.30123 + 1.71246i 0.164650 + 0.0854100i
\(403\) 34.0249i 1.69490i
\(404\) −8.11701 11.5214i −0.403837 0.573213i
\(405\) 1.00000i 0.0496904i
\(406\) 0.384227 0.740698i 0.0190688 0.0367602i
\(407\) 9.36736i 0.464323i
\(408\) 2.36444 0.321697i 0.117057 0.0159264i
\(409\) 9.59039 0.474214 0.237107 0.971483i \(-0.423801\pi\)
0.237107 + 0.971483i \(0.423801\pi\)
\(410\) −9.24974 4.79817i −0.456812 0.236965i
\(411\) −21.9555 −1.08299
\(412\) −15.8692 22.5250i −0.781818 1.10973i
\(413\) 6.31582i 0.310781i
\(414\) −6.73084 + 0.834108i −0.330803 + 0.0409942i
\(415\) 9.45106i 0.463934i
\(416\) 15.5787 + 16.7570i 0.763808 + 0.821578i
\(417\) 15.4357 0.755887
\(418\) −11.8728 + 22.8880i −0.580719 + 1.11949i
\(419\) −3.49424 −0.170705 −0.0853525 0.996351i \(-0.527202\pi\)
−0.0853525 + 0.996351i \(0.527202\pi\)
\(420\) 2.46544 + 3.49949i 0.120301 + 0.170758i
\(421\) 19.9196i 0.970823i −0.874286 0.485411i \(-0.838670\pi\)
0.874286 0.485411i \(-0.161330\pi\)
\(422\) −3.46612 1.79800i −0.168728 0.0875252i
\(423\) 10.4234i 0.506802i
\(424\) −2.13604 15.6997i −0.103735 0.762445i
\(425\) 0.843658i 0.0409234i
\(426\) −1.78030 + 3.43200i −0.0862557 + 0.166281i
\(427\) 15.1010i 0.730787i
\(428\) 1.66698 + 2.36614i 0.0805765 + 0.114372i
\(429\) 14.3593i 0.693275i
\(430\) −14.5770 7.56161i −0.702965 0.364653i
\(431\) 1.01045 0.0486715 0.0243358 0.999704i \(-0.492253\pi\)
0.0243358 + 0.999704i \(0.492253\pi\)
\(432\) −3.76660 1.34638i −0.181221 0.0647776i
\(433\) 24.4879i 1.17682i 0.808564 + 0.588408i \(0.200245\pi\)
−0.808564 + 0.588408i \(0.799755\pi\)
\(434\) 22.6035 + 11.7252i 1.08500 + 0.562829i
\(435\) 0.275665 0.0132171
\(436\) 1.68259 1.18541i 0.0805815 0.0567708i
\(437\) −13.9436 20.3020i −0.667012 0.971175i
\(438\) 6.08237 + 3.15514i 0.290627 + 0.150758i
\(439\) 3.96239i 0.189115i 0.995519 + 0.0945573i \(0.0301436\pi\)
−0.995519 + 0.0945573i \(0.969856\pi\)
\(440\) 1.35374 + 9.94984i 0.0645368 + 0.474340i
\(441\) 2.41880 0.115181
\(442\) 4.28367 + 2.22209i 0.203753 + 0.105694i
\(443\) 3.21788i 0.152886i −0.997074 0.0764431i \(-0.975644\pi\)
0.997074 0.0764431i \(-0.0243563\pi\)
\(444\) 3.03926 + 4.31398i 0.144237 + 0.204732i
\(445\) −16.0179 −0.759319
\(446\) −9.30068 4.82459i −0.440400 0.228451i
\(447\) 1.22216 0.0578061
\(448\) −16.5006 + 4.57469i −0.779579 + 0.216134i
\(449\) 3.13859 0.148119 0.0740596 0.997254i \(-0.476404\pi\)
0.0740596 + 0.997254i \(0.476404\pi\)
\(450\) −0.651202 + 1.25536i −0.0306979 + 0.0591784i
\(451\) 26.1586 1.23176
\(452\) 18.1341 12.7757i 0.852956 0.600920i
\(453\) −9.64939 −0.453368
\(454\) −7.07515 + 13.6392i −0.332053 + 0.640120i
\(455\) 8.65705i 0.405849i
\(456\) −1.95824 14.3929i −0.0917028 0.674008i
\(457\) 4.45089i 0.208204i −0.994567 0.104102i \(-0.966803\pi\)
0.994567 0.104102i \(-0.0331968\pi\)
\(458\) −15.8634 8.22892i −0.741248 0.384512i
\(459\) −0.843658 −0.0393786
\(460\) −8.99283 3.33603i −0.419293 0.155543i
\(461\) 18.0299 0.839738 0.419869 0.907585i \(-0.362076\pi\)
0.419869 + 0.907585i \(0.362076\pi\)
\(462\) −9.53923 4.94834i −0.443805 0.230217i
\(463\) 34.3361i 1.59573i −0.602835 0.797866i \(-0.705962\pi\)
0.602835 0.797866i \(-0.294038\pi\)
\(464\) −0.371150 + 1.03832i −0.0172302 + 0.0482028i
\(465\) 8.41233i 0.390112i
\(466\) −1.39929 + 2.69749i −0.0648206 + 0.124959i
\(467\) −36.9009 −1.70757 −0.853786 0.520624i \(-0.825699\pi\)
−0.853786 + 0.520624i \(0.825699\pi\)
\(468\) −4.65891 6.61294i −0.215358 0.305683i
\(469\) −5.62854 −0.259902
\(470\) 6.78772 13.0851i 0.313094 0.603571i
\(471\) 15.1421 0.697709
\(472\) 1.12517 + 8.26993i 0.0517903 + 0.380654i
\(473\) 41.2242 1.89549
\(474\) 20.3793 + 10.5715i 0.936053 + 0.485564i
\(475\) −5.13553 −0.235634
\(476\) −2.95237 + 2.07999i −0.135322 + 0.0953361i
\(477\) 5.60182i 0.256490i
\(478\) 19.4639 + 10.0966i 0.890260 + 0.461810i
\(479\) −36.3522 −1.66098 −0.830488 0.557037i \(-0.811938\pi\)
−0.830488 + 0.557037i \(0.811938\pi\)
\(480\) −3.85169 4.14301i −0.175805 0.189102i
\(481\) 10.6719i 0.486598i
\(482\) −15.7674 8.17913i −0.718187 0.372549i
\(483\) 8.46142 5.81138i 0.385008 0.264427i
\(484\) −1.84759 2.62250i −0.0839814 0.119205i
\(485\) 0.845087 0.0383734
\(486\) 1.25536 + 0.651202i 0.0569444 + 0.0295391i
\(487\) 4.53486i 0.205494i −0.994708 0.102747i \(-0.967237\pi\)
0.994708 0.102747i \(-0.0327632\pi\)
\(488\) 2.69027 + 19.7732i 0.121783 + 0.895091i
\(489\) 6.70557 0.303236
\(490\) 3.03647 + 1.57512i 0.137174 + 0.0711569i
\(491\) 13.4429i 0.606670i −0.952884 0.303335i \(-0.901900\pi\)
0.952884 0.303335i \(-0.0981001\pi\)
\(492\) −12.0469 + 8.48721i −0.543116 + 0.382633i
\(493\) 0.232567i 0.0104743i
\(494\) 13.5263 26.0756i 0.608579 1.17320i
\(495\) 3.55021i 0.159570i
\(496\) −31.6859 11.3262i −1.42274 0.508560i
\(497\) 5.85150i 0.262476i
\(498\) 11.8645 + 6.15454i 0.531661 + 0.275792i
\(499\) 25.2907i 1.13217i 0.824347 + 0.566084i \(0.191542\pi\)
−0.824347 + 0.566084i \(0.808458\pi\)
\(500\) −1.63499 + 1.15187i −0.0731189 + 0.0515133i
\(501\) −22.2534 −0.994208
\(502\) −16.0805 + 30.9994i −0.717708 + 1.38357i
\(503\) 37.8035 1.68557 0.842787 0.538247i \(-0.180913\pi\)
0.842787 + 0.538247i \(0.180913\pi\)
\(504\) 5.99863 0.816150i 0.267200 0.0363542i
\(505\) 7.04680i 0.313578i
\(506\) 23.8959 2.96126i 1.06230 0.131644i
\(507\) 3.35912i 0.149184i
\(508\) 33.3266 23.4791i 1.47863 1.04171i
\(509\) −10.9894 −0.487096 −0.243548 0.969889i \(-0.578311\pi\)
−0.243548 + 0.969889i \(0.578311\pi\)
\(510\) −1.05910 0.549392i −0.0468976 0.0243275i
\(511\) −10.3703 −0.458757
\(512\) 20.7909 8.92971i 0.918835 0.394641i
\(513\) 5.13553i 0.226739i
\(514\) 18.9078 36.4497i 0.833985 1.60773i
\(515\) 13.7768i 0.607080i
\(516\) −18.9851 + 13.3753i −0.835773 + 0.588814i
\(517\) 37.0052i 1.62748i
\(518\) −7.08961 3.67763i −0.311500 0.161586i
\(519\) 20.8806i 0.916558i
\(520\) −1.54227 11.3355i −0.0676329 0.497096i
\(521\) 28.5407i 1.25039i −0.780469 0.625195i \(-0.785019\pi\)
0.780469 0.625195i \(-0.214981\pi\)
\(522\) 0.179514 0.346060i 0.00785710 0.0151466i
\(523\) −14.6277 −0.639625 −0.319813 0.947481i \(-0.603620\pi\)
−0.319813 + 0.947481i \(0.603620\pi\)
\(524\) −5.44551 + 3.83644i −0.237888 + 0.167596i
\(525\) 2.14037i 0.0934136i
\(526\) 16.3393 31.4983i 0.712427 1.37339i
\(527\) −7.09713 −0.309156
\(528\) 13.3722 + 4.77992i 0.581951 + 0.208019i
\(529\) −8.25622 + 21.4671i −0.358966 + 0.933351i
\(530\) −3.64792 + 7.03232i −0.158455 + 0.305465i
\(531\) 2.95080i 0.128054i
\(532\) 12.6613 + 17.9717i 0.548938 + 0.779173i
\(533\) −29.8017 −1.29085
\(534\) −10.4309 + 20.1082i −0.451387 + 0.870168i
\(535\) 1.44719i 0.0625675i
\(536\) 7.37001 1.00273i 0.318336 0.0433115i
\(537\) −11.9933 −0.517548
\(538\) −10.3270 + 19.9080i −0.445227 + 0.858294i
\(539\) −8.58724 −0.369878
\(540\) 1.15187 + 1.63499i 0.0495687 + 0.0703587i
\(541\) −41.9847 −1.80506 −0.902532 0.430623i \(-0.858294\pi\)
−0.902532 + 0.430623i \(0.858294\pi\)
\(542\) 24.1210 + 12.5124i 1.03608 + 0.537453i
\(543\) −11.8382 −0.508026
\(544\) 3.49528 3.24951i 0.149859 0.139321i
\(545\) −1.02911 −0.0440824
\(546\) 10.8677 + 5.63748i 0.465096 + 0.241262i
\(547\) 33.7583i 1.44340i 0.692206 + 0.721700i \(0.256639\pi\)
−0.692206 + 0.721700i \(0.743361\pi\)
\(548\) −35.8970 + 25.2900i −1.53344 + 1.08033i
\(549\) 7.05529i 0.301113i
\(550\) 2.31190 4.45680i 0.0985798 0.190039i
\(551\) 1.41569 0.0603103
\(552\) −10.0441 + 9.11684i −0.427504 + 0.388038i
\(553\) −34.7464 −1.47757
\(554\) −1.51511 + 2.92078i −0.0643710 + 0.124092i
\(555\) 2.63854i 0.112000i
\(556\) 25.2371 17.7799i 1.07029 0.754037i
\(557\) 16.9360i 0.717602i 0.933414 + 0.358801i \(0.116814\pi\)
−0.933414 + 0.358801i \(0.883186\pi\)
\(558\) 10.5605 + 5.47812i 0.447063 + 0.231907i
\(559\) −46.9655 −1.98643
\(560\) 8.06193 + 2.88175i 0.340679 + 0.121776i
\(561\) 2.99516 0.126456
\(562\) 3.07137 + 1.59323i 0.129558 + 0.0672062i
\(563\) −1.63299 −0.0688224 −0.0344112 0.999408i \(-0.510956\pi\)
−0.0344112 + 0.999408i \(0.510956\pi\)
\(564\) −12.0064 17.0421i −0.505561 0.717602i
\(565\) −11.0913 −0.466613
\(566\) 6.18389 11.9211i 0.259928 0.501081i
\(567\) −2.14037 −0.0898873
\(568\) 1.04246 + 7.66195i 0.0437404 + 0.321488i
\(569\) 13.7080i 0.574669i 0.957830 + 0.287334i \(0.0927691\pi\)
−0.957830 + 0.287334i \(0.907231\pi\)
\(570\) −3.34426 + 6.44695i −0.140076 + 0.270033i
\(571\) −47.0402 −1.96857 −0.984285 0.176585i \(-0.943495\pi\)
−0.984285 + 0.176585i \(0.943495\pi\)
\(572\) 16.5401 + 23.4773i 0.691577 + 0.981637i
\(573\) 1.29520i 0.0541077i
\(574\) 10.2699 19.7979i 0.428657 0.826349i
\(575\) 2.71512 + 3.95324i 0.113228 + 0.164862i
\(576\) −7.70920 + 2.13733i −0.321217 + 0.0890555i
\(577\) −3.09943 −0.129031 −0.0645154 0.997917i \(-0.520550\pi\)
−0.0645154 + 0.997917i \(0.520550\pi\)
\(578\) −10.6069 + 20.4477i −0.441190 + 0.850510i
\(579\) 1.48140i 0.0615650i
\(580\) 0.450710 0.317532i 0.0187147 0.0131848i
\(581\) −20.2288 −0.839232
\(582\) 0.550322 1.06089i 0.0228116 0.0439753i
\(583\) 19.8877i 0.823662i
\(584\) 13.5789 1.84749i 0.561900 0.0764499i
\(585\) 4.04464i 0.167225i
\(586\) 20.1955 + 10.4761i 0.834270 + 0.432766i
\(587\) 21.9788i 0.907160i 0.891215 + 0.453580i \(0.149853\pi\)
−0.891215 + 0.453580i \(0.850147\pi\)
\(588\) 3.95471 2.78615i 0.163089 0.114899i
\(589\) 43.2018i 1.78010i
\(590\) 1.92157 3.70433i 0.0791096 0.152505i
\(591\) 13.9422i 0.573504i
\(592\) 9.93831 + 3.55247i 0.408462 + 0.146005i
\(593\) −31.2493 −1.28326 −0.641628 0.767016i \(-0.721741\pi\)
−0.641628 + 0.767016i \(0.721741\pi\)
\(594\) −4.45680 2.31190i −0.182865 0.0948585i
\(595\) 1.80574 0.0740283
\(596\) 1.99821 1.40777i 0.0818500 0.0576645i
\(597\) 5.33970i 0.218539i
\(598\) −27.2238 + 3.37367i −1.11327 + 0.137960i
\(599\) 19.4722i 0.795614i −0.917469 0.397807i \(-0.869771\pi\)
0.917469 0.397807i \(-0.130229\pi\)
\(600\) 0.381312 + 2.80261i 0.0155670 + 0.114416i
\(601\) −27.7862 −1.13342 −0.566711 0.823917i \(-0.691784\pi\)
−0.566711 + 0.823917i \(0.691784\pi\)
\(602\) 16.1847 31.2002i 0.659638 1.27163i
\(603\) −2.62970 −0.107090
\(604\) −15.7766 + 11.1149i −0.641943 + 0.452258i
\(605\) 1.60399i 0.0652114i
\(606\) 8.84629 + 4.58889i 0.359356 + 0.186411i
\(607\) 28.1233i 1.14149i 0.821127 + 0.570745i \(0.193346\pi\)
−0.821127 + 0.570745i \(0.806654\pi\)
\(608\) −19.7804 21.2765i −0.802203 0.862877i
\(609\) 0.590027i 0.0239091i
\(610\) 4.59442 8.85696i 0.186023 0.358608i
\(611\) 42.1588i 1.70556i
\(612\) −1.37937 + 0.971787i −0.0557578 + 0.0392822i
\(613\) 23.6788i 0.956378i 0.878257 + 0.478189i \(0.158707\pi\)
−0.878257 + 0.478189i \(0.841293\pi\)
\(614\) 1.37525 + 0.713391i 0.0555006 + 0.0287901i
\(615\) 7.36818 0.297114
\(616\) −21.2964 + 2.89750i −0.858056 + 0.116744i
\(617\) 0.878056i 0.0353492i −0.999844 0.0176746i \(-0.994374\pi\)
0.999844 0.0176746i \(-0.00562629\pi\)
\(618\) 17.2949 + 8.97150i 0.695705 + 0.360887i
\(619\) 4.28788 0.172344 0.0861722 0.996280i \(-0.472536\pi\)
0.0861722 + 0.996280i \(0.472536\pi\)
\(620\) 9.68994 + 13.7541i 0.389157 + 0.552377i
\(621\) 3.95324 2.71512i 0.158638 0.108954i
\(622\) 41.4807 + 21.5175i 1.66322 + 0.862773i
\(623\) 34.2842i 1.37357i
\(624\) −15.2345 5.44561i −0.609870 0.217999i
\(625\) 1.00000 0.0400000
\(626\) 22.1091 + 11.4688i 0.883656 + 0.458384i
\(627\) 18.2322i 0.728124i
\(628\) 24.7571 17.4417i 0.987916 0.696001i
\(629\) 2.22602 0.0887574
\(630\) −2.68695 1.39382i −0.107051 0.0555309i
\(631\) 39.9346 1.58977 0.794886 0.606759i \(-0.207531\pi\)
0.794886 + 0.606759i \(0.207531\pi\)
\(632\) 45.4969 6.19014i 1.80977 0.246230i
\(633\) 2.76105 0.109742
\(634\) −7.79289 + 15.0228i −0.309495 + 0.596633i
\(635\) −20.3834 −0.808890
\(636\) 6.45259 + 9.15892i 0.255862 + 0.363175i
\(637\) 9.78316 0.387623
\(638\) −0.637311 + 1.22859i −0.0252314 + 0.0486402i
\(639\) 2.73387i 0.108150i
\(640\) −11.0697 2.33712i −0.437568 0.0923827i
\(641\) 20.1012i 0.793951i −0.917829 0.396976i \(-0.870060\pi\)
0.917829 0.396976i \(-0.129940\pi\)
\(642\) −1.81675 0.942413i −0.0717014 0.0371941i
\(643\) 16.2281 0.639976 0.319988 0.947422i \(-0.396321\pi\)
0.319988 + 0.947422i \(0.396321\pi\)
\(644\) 7.14035 19.2480i 0.281369 0.758478i
\(645\) 11.6118 0.457213
\(646\) −5.43902 2.82142i −0.213996 0.111007i
\(647\) 14.3994i 0.566100i 0.959105 + 0.283050i \(0.0913462\pi\)
−0.959105 + 0.283050i \(0.908654\pi\)
\(648\) 2.80261 0.381312i 0.110097 0.0149793i
\(649\) 10.4760i 0.411217i
\(650\) −2.63388 + 5.07749i −0.103309 + 0.199156i
\(651\) −18.0055 −0.705693
\(652\) 10.9635 7.72396i 0.429365 0.302494i
\(653\) −8.13213 −0.318235 −0.159118 0.987260i \(-0.550865\pi\)
−0.159118 + 0.987260i \(0.550865\pi\)
\(654\) −0.670161 + 1.29191i −0.0262054 + 0.0505178i
\(655\) 3.33061 0.130138
\(656\) −9.92035 + 27.7530i −0.387325 + 1.08357i
\(657\) −4.84511 −0.189026
\(658\) 28.0070 + 14.5283i 1.09183 + 0.566370i
\(659\) 50.0704 1.95046 0.975232 0.221183i \(-0.0709919\pi\)
0.975232 + 0.221183i \(0.0709919\pi\)
\(660\) −4.08939 5.80455i −0.159179 0.225942i
\(661\) 34.2686i 1.33290i −0.745552 0.666448i \(-0.767814\pi\)
0.745552 0.666448i \(-0.232186\pi\)
\(662\) 6.73041 + 3.49130i 0.261585 + 0.135693i
\(663\) −3.41229 −0.132523
\(664\) 26.4876 3.60380i 1.02792 0.139854i
\(665\) 10.9920i 0.426250i
\(666\) −3.31232 1.71822i −0.128350 0.0665796i
\(667\) −0.748465 1.08977i −0.0289807 0.0421961i
\(668\) −36.3841 + 25.6331i −1.40774 + 0.991774i
\(669\) 7.40876 0.286439
\(670\) −3.30123 1.71246i −0.127538 0.0661583i
\(671\) 25.0478i 0.966959i
\(672\) 8.86759 8.24405i 0.342075 0.318021i
\(673\) −15.3372 −0.591205 −0.295602 0.955311i \(-0.595520\pi\)
−0.295602 + 0.955311i \(0.595520\pi\)
\(674\) −22.7576 11.8052i −0.876591 0.454719i
\(675\) 1.00000i 0.0384900i
\(676\) −3.86928 5.49212i −0.148818 0.211236i
\(677\) 22.2137i 0.853742i 0.904312 + 0.426871i \(0.140384\pi\)
−0.904312 + 0.426871i \(0.859616\pi\)
\(678\) −7.22265 + 13.9236i −0.277384 + 0.534731i
\(679\) 1.80880i 0.0694155i
\(680\) −2.36444 + 0.321697i −0.0906722 + 0.0123365i
\(681\) 10.8648i 0.416338i
\(682\) −37.4921 19.4485i −1.43565 0.744721i
\(683\) 5.94111i 0.227330i −0.993519 0.113665i \(-0.963741\pi\)
0.993519 0.113665i \(-0.0362591\pi\)
\(684\) 5.91548 + 8.39653i 0.226184 + 0.321049i
\(685\) 21.9555 0.838877
\(686\) −13.1281 + 25.3078i −0.501232 + 0.966257i
\(687\) 12.6365 0.482113
\(688\) −15.6338 + 43.7369i −0.596034 + 1.66745i
\(689\) 22.6574i 0.863177i
\(690\) 6.73084 0.834108i 0.256239 0.0317539i
\(691\) 0.937628i 0.0356690i 0.999841 + 0.0178345i \(0.00567721\pi\)
−0.999841 + 0.0178345i \(0.994323\pi\)
\(692\) 24.0518 + 34.1396i 0.914313 + 1.29779i
\(693\) 7.59878 0.288654
\(694\) −8.48814 4.40310i −0.322205 0.167139i
\(695\) −15.4357 −0.585508
\(696\) −0.105114 0.772582i −0.00398435 0.0292846i
\(697\) 6.21623i 0.235456i
\(698\) −23.3817 + 45.0744i −0.885010 + 1.70609i
\(699\) 2.14877i 0.0812741i
\(700\) −2.46544 3.49949i −0.0931849 0.132268i
\(701\) 36.2643i 1.36968i 0.728692 + 0.684842i \(0.240129\pi\)
−0.728692 + 0.684842i \(0.759871\pi\)
\(702\) 5.07749 + 2.63388i 0.191638 + 0.0994093i
\(703\) 13.5503i 0.511058i
\(704\) 27.3693 7.58798i 1.03152 0.285983i
\(705\) 10.4234i 0.392567i
\(706\) −12.7302 + 24.5409i −0.479109 + 0.923610i
\(707\) −15.0828 −0.567246
\(708\) −3.39895 4.82453i −0.127740 0.181317i
\(709\) 45.9613i 1.72611i 0.505107 + 0.863057i \(0.331453\pi\)
−0.505107 + 0.863057i \(0.668547\pi\)
\(710\) 1.78030 3.43200i 0.0668134 0.128801i
\(711\) −16.2338 −0.608815
\(712\) 6.10779 + 44.8917i 0.228899 + 1.68239i
\(713\) 33.2560 22.8405i 1.24545 0.855384i
\(714\) 1.17590 2.26687i 0.0440071 0.0848353i
\(715\) 14.3593i 0.537008i
\(716\) −19.6089 + 13.8147i −0.732818 + 0.516281i
\(717\) −15.5046 −0.579031
\(718\) 18.4941 35.6522i 0.690193 1.33053i
\(719\) 26.7657i 0.998193i 0.866546 + 0.499097i \(0.166335\pi\)
−0.866546 + 0.499097i \(0.833665\pi\)
\(720\) 3.76660 + 1.34638i 0.140373 + 0.0501765i
\(721\) −29.4876 −1.09818
\(722\) −4.80173 + 9.25660i −0.178702 + 0.344495i
\(723\) 12.5601 0.467114
\(724\) −19.3553 + 13.6361i −0.719336 + 0.506782i
\(725\) −0.275665 −0.0102380
\(726\) 2.01359 + 1.04452i 0.0747313 + 0.0387658i
\(727\) 11.7279 0.434963 0.217482 0.976064i \(-0.430216\pi\)
0.217482 + 0.976064i \(0.430216\pi\)
\(728\) 24.2623 3.30103i 0.899220 0.122344i
\(729\) −1.00000 −0.0370370
\(730\) −6.08237 3.15514i −0.225118 0.116777i
\(731\) 9.79637i 0.362332i
\(732\) −8.12680 11.5353i −0.300375 0.426358i
\(733\) 10.5869i 0.391036i −0.980700 0.195518i \(-0.937361\pi\)
0.980700 0.195518i \(-0.0626389\pi\)
\(734\) −11.3105 + 21.8040i −0.417479 + 0.804801i
\(735\) −2.41880 −0.0892187
\(736\) −5.92050 + 26.4754i −0.218233 + 0.975897i
\(737\) 9.33598 0.343895
\(738\) 4.79817 9.24974i 0.176623 0.340488i
\(739\) 0.174301i 0.00641178i −0.999995 0.00320589i \(-0.998980\pi\)
0.999995 0.00320589i \(-0.00102047\pi\)
\(740\) −3.03926 4.31398i −0.111725 0.158585i
\(741\) 20.7714i 0.763055i
\(742\) −15.0518 7.80791i −0.552569 0.286637i
\(743\) −14.7068 −0.539540 −0.269770 0.962925i \(-0.586948\pi\)
−0.269770 + 0.962925i \(0.586948\pi\)
\(744\) 23.5764 3.20772i 0.864355 0.117601i
\(745\) −1.22216 −0.0447764
\(746\) −20.6006 10.6863i −0.754243 0.391253i
\(747\) −9.45106 −0.345796
\(748\) 4.89706 3.45005i 0.179054 0.126146i
\(749\) 3.09753 0.113181
\(750\) 0.651202 1.25536i 0.0237785 0.0458394i
\(751\) 26.8301 0.979043 0.489522 0.871991i \(-0.337171\pi\)
0.489522 + 0.871991i \(0.337171\pi\)
\(752\) −39.2607 14.0338i −1.43169 0.511760i
\(753\) 24.6936i 0.899885i
\(754\) 0.726069 1.39969i 0.0264419 0.0509737i
\(755\) 9.64939 0.351177
\(756\) −3.49949 + 2.46544i −0.127275 + 0.0896672i
\(757\) 54.6358i 1.98577i 0.119070 + 0.992886i \(0.462009\pi\)
−0.119070 + 0.992886i \(0.537991\pi\)
\(758\) 12.7915 24.6589i 0.464607 0.895653i
\(759\) −14.0348 + 9.63925i −0.509432 + 0.349883i
\(760\) 1.95824 + 14.3929i 0.0710327 + 0.522084i
\(761\) 31.9653 1.15874 0.579370 0.815064i \(-0.303299\pi\)
0.579370 + 0.815064i \(0.303299\pi\)
\(762\) −13.2737 + 25.5885i −0.480855 + 0.926975i
\(763\) 2.20269i 0.0797427i
\(764\) 1.49190 + 2.11764i 0.0539752 + 0.0766134i
\(765\) 0.843658 0.0305025
\(766\) −12.0428 + 23.2156i −0.435122 + 0.838813i
\(767\) 11.9349i 0.430945i
\(768\) −10.1425 + 12.3745i −0.365987 + 0.446528i
\(769\) 4.34029i 0.156515i 0.996933 + 0.0782574i \(0.0249356\pi\)
−0.996933 + 0.0782574i \(0.975064\pi\)
\(770\) 9.53923 + 4.94834i 0.343770 + 0.178326i
\(771\) 29.0352i 1.04568i
\(772\) 1.70639 + 2.42208i 0.0614142 + 0.0871725i
\(773\) 0.809691i 0.0291226i −0.999894 0.0145613i \(-0.995365\pi\)
0.999894 0.0145613i \(-0.00463516\pi\)
\(774\) 7.56161 14.5770i 0.271796 0.523959i
\(775\) 8.41233i 0.302180i
\(776\) −0.322241 2.36845i −0.0115678 0.0850222i
\(777\) 5.64746 0.202601
\(778\) −23.3407 12.1076i −0.836803 0.434080i
\(779\) 37.8395 1.35574
\(780\) 4.65891 + 6.61294i 0.166816 + 0.236781i
\(781\) 9.70580i 0.347301i
\(782\) 0.703702 + 5.67853i 0.0251643 + 0.203064i
\(783\) 0.275665i 0.00985148i
\(784\) 3.25661 9.11064i 0.116308 0.325380i
\(785\) −15.1421 −0.540443
\(786\) 2.16890 4.18113i 0.0773621 0.149136i
\(787\) −30.8746 −1.10056 −0.550280 0.834980i \(-0.685479\pi\)
−0.550280 + 0.834980i \(0.685479\pi\)
\(788\) 16.0596 + 22.7953i 0.572100 + 0.812048i
\(789\) 25.0910i 0.893263i
\(790\) −20.3793 10.5715i −0.725063 0.376116i
\(791\) 23.7395i 0.844078i
\(792\) −9.94984 + 1.35374i −0.353552 + 0.0481029i
\(793\) 28.5361i 1.01335i
\(794\) 11.6323 22.4243i 0.412815 0.795810i
\(795\) 5.60182i 0.198676i
\(796\) 6.15065 + 8.73034i 0.218004 + 0.309439i
\(797\) 39.2460i 1.39016i −0.718931 0.695082i \(-0.755368\pi\)
0.718931 0.695082i \(-0.244632\pi\)
\(798\) −13.7989 7.15798i −0.488475 0.253390i
\(799\) −8.79376 −0.311101
\(800\) 3.85169 + 4.14301i 0.136178 + 0.146477i
\(801\) 16.0179i 0.565963i
\(802\) 13.6826 + 7.09768i 0.483151 + 0.250628i
\(803\) 17.2011 0.607015
\(804\) −4.29953 + 3.02908i −0.151633 + 0.106827i
\(805\) −8.46142 + 5.81138i −0.298226 + 0.204824i
\(806\) 42.7135 + 22.1570i 1.50452 + 0.780448i
\(807\) 15.8583i 0.558240i
\(808\) 19.7494 2.68702i 0.694781 0.0945292i
\(809\) 41.1210 1.44574 0.722869 0.690985i \(-0.242823\pi\)
0.722869 + 0.690985i \(0.242823\pi\)
\(810\) −1.25536 0.651202i −0.0441090 0.0228809i
\(811\) 25.9894i 0.912610i −0.889823 0.456305i \(-0.849173\pi\)
0.889823 0.456305i \(-0.150827\pi\)
\(812\) 0.679636 + 0.964688i 0.0238506 + 0.0338539i
\(813\) −19.2143 −0.673876
\(814\) 11.7594 + 6.10004i 0.412168 + 0.213806i
\(815\) −6.70557 −0.234886
\(816\) −1.13588 + 3.17772i −0.0397638 + 0.111243i
\(817\) 59.6326 2.08628
\(818\) −6.24528 + 12.0394i −0.218361 + 0.420949i
\(819\) −8.65705 −0.302502
\(820\) 12.0469 8.48721i 0.420696 0.296386i
\(821\) −27.7229 −0.967537 −0.483769 0.875196i \(-0.660732\pi\)
−0.483769 + 0.875196i \(0.660732\pi\)
\(822\) 14.2975 27.5621i 0.498681 0.961340i
\(823\) 1.31299i 0.0457679i 0.999738 + 0.0228840i \(0.00728483\pi\)
−0.999738 + 0.0228840i \(0.992715\pi\)
\(824\) 38.6111 5.25327i 1.34508 0.183006i
\(825\) 3.55021i 0.123602i
\(826\) 7.92865 + 4.11287i 0.275873 + 0.143105i
\(827\) 41.1400 1.43058 0.715288 0.698830i \(-0.246295\pi\)
0.715288 + 0.698830i \(0.246295\pi\)
\(828\) 3.33603 8.99283i 0.115935 0.312522i
\(829\) −43.5731 −1.51336 −0.756678 0.653788i \(-0.773179\pi\)
−0.756678 + 0.653788i \(0.773179\pi\)
\(830\) −11.8645 6.15454i −0.411823 0.213627i
\(831\) 2.32664i 0.0807104i
\(832\) −31.1810 + 8.64474i −1.08101 + 0.299702i
\(833\) 2.04064i 0.0707039i
\(834\) −10.0517 + 19.3774i −0.348063 + 0.670983i
\(835\) 22.2534 0.770110
\(836\) −21.0012 29.8094i −0.726341 1.03098i
\(837\) −8.41233 −0.290773
\(838\) 2.27546 4.38654i 0.0786043 0.151531i
\(839\) 24.5721 0.848323 0.424162 0.905586i \(-0.360569\pi\)
0.424162 + 0.905586i \(0.360569\pi\)
\(840\) −5.99863 + 0.816150i −0.206972 + 0.0281598i
\(841\) −28.9240 −0.997380
\(842\) 25.0064 + 12.9717i 0.861776 + 0.447034i
\(843\) −2.44660 −0.0842652
\(844\) 4.51428 3.18038i 0.155388 0.109473i
\(845\) 3.35912i 0.115557i
\(846\) 13.0851 + 6.78772i 0.449876 + 0.233366i
\(847\) −3.43314 −0.117964
\(848\) 21.0998 + 7.54217i 0.724571 + 0.258999i
\(849\) 9.49613i 0.325906i
\(850\) 1.05910 + 0.549392i 0.0363267 + 0.0188440i
\(851\) −10.4308 + 7.16395i −0.357562 + 0.245577i
\(852\) −3.14907 4.46984i −0.107885 0.153134i
\(853\) 18.2241 0.623982 0.311991 0.950085i \(-0.399004\pi\)
0.311991 + 0.950085i \(0.399004\pi\)
\(854\) 18.9572 + 9.83378i 0.648702 + 0.336505i
\(855\) 5.13553i 0.175631i
\(856\) −4.05590 + 0.551830i −0.138628 + 0.0188612i
\(857\) −36.4555 −1.24529 −0.622647 0.782503i \(-0.713943\pi\)
−0.622647 + 0.782503i \(0.713943\pi\)
\(858\) −18.0262 9.35081i −0.615403 0.319232i
\(859\) 8.31770i 0.283796i −0.989881 0.141898i \(-0.954679\pi\)
0.989881 0.141898i \(-0.0453205\pi\)
\(860\) 18.9851 13.3753i 0.647387 0.456094i
\(861\) 15.7707i 0.537463i
\(862\) −0.658005 + 1.26848i −0.0224117 + 0.0432045i
\(863\) 6.91833i 0.235503i −0.993043 0.117751i \(-0.962431\pi\)
0.993043 0.117751i \(-0.0375686\pi\)
\(864\) 4.14301 3.85169i 0.140948 0.131037i
\(865\) 20.8806i 0.709963i
\(866\) −30.7413 15.9466i −1.04463 0.541887i
\(867\) 16.2882i 0.553178i
\(868\) −29.4389 + 20.7401i −0.999220 + 0.703965i
\(869\) 57.6334 1.95508
\(870\) −0.179514 + 0.346060i −0.00608609 + 0.0117325i
\(871\) −10.6362 −0.360394
\(872\) 0.392413 + 2.88420i 0.0132888 + 0.0976714i
\(873\) 0.845087i 0.0286019i
\(874\) 34.5664 4.28358i 1.16923 0.144894i
\(875\) 2.14037i 0.0723579i
\(876\) −7.92169 + 5.58095i −0.267649 + 0.188563i
\(877\) 16.8420 0.568714 0.284357 0.958718i \(-0.408220\pi\)
0.284357 + 0.958718i \(0.408220\pi\)
\(878\) −4.97424 2.58032i −0.167872 0.0870814i
\(879\) −16.0874 −0.542615
\(880\) −13.3722 4.77992i −0.450777 0.161131i
\(881\) 40.7543i 1.37305i −0.727107 0.686524i \(-0.759136\pi\)
0.727107 0.686524i \(-0.240864\pi\)
\(882\) −1.57512 + 3.03647i −0.0530372 + 0.102243i
\(883\) 31.2055i 1.05015i 0.851056 + 0.525075i \(0.175963\pi\)
−0.851056 + 0.525075i \(0.824037\pi\)
\(884\) −5.57906 + 3.93053i −0.187644 + 0.132198i
\(885\) 2.95080i 0.0991901i
\(886\) 4.03961 + 2.09549i 0.135713 + 0.0703993i
\(887\) 1.74524i 0.0585996i 0.999571 + 0.0292998i \(0.00932774\pi\)
−0.999571 + 0.0292998i \(0.990672\pi\)
\(888\) −7.39478 + 1.00610i −0.248153 + 0.0337627i
\(889\) 43.6281i 1.46324i
\(890\) 10.4309 20.1082i 0.349643 0.674029i
\(891\) 3.55021 0.118937
\(892\) 12.1132 8.53395i 0.405581 0.285738i
\(893\) 53.5295i 1.79130i
\(894\) −0.795871 + 1.53425i −0.0266179 + 0.0513130i
\(895\) 11.9933 0.400891
\(896\) 5.00231 23.6933i 0.167115 0.791537i
\(897\) 15.9894 10.9817i 0.533872 0.366668i
\(898\) −2.04385 + 3.94007i −0.0682043 + 0.131482i
\(899\) 2.31899i 0.0773426i
\(900\) −1.15187 1.63499i −0.0383958 0.0544996i
\(901\) 4.72603 0.157447
\(902\) −17.0345 + 32.8385i −0.567187 + 1.09340i
\(903\) 24.8535i 0.827074i
\(904\) 4.22923 + 31.0845i 0.140662 + 1.03385i
\(905\) 11.8382 0.393515
\(906\) 6.28370 12.1135i 0.208762 0.402444i
\(907\) 58.1153 1.92969 0.964844 0.262824i \(-0.0846539\pi\)
0.964844 + 0.262824i \(0.0846539\pi\)
\(908\) −12.5148 17.7638i −0.415319 0.589511i
\(909\) −7.04680 −0.233727
\(910\) −10.8677 5.63748i −0.360262 0.186881i
\(911\) 34.1132 1.13022 0.565110 0.825015i \(-0.308834\pi\)
0.565110 + 0.825015i \(0.308834\pi\)
\(912\) 19.3435 + 6.91436i 0.640526 + 0.228957i
\(913\) 33.5532 1.11045
\(914\) 5.58748 + 2.89843i 0.184818 + 0.0958715i
\(915\) 7.05529i 0.233241i
\(916\) 20.6606 14.5557i 0.682644 0.480932i
\(917\) 7.12876i 0.235412i
\(918\) 0.549392 1.05910i 0.0181326 0.0349554i
\(919\) −24.4239 −0.805669 −0.402834 0.915273i \(-0.631975\pi\)
−0.402834 + 0.915273i \(0.631975\pi\)
\(920\) 10.0441 9.11684i 0.331143 0.300573i
\(921\) −1.09550 −0.0360980
\(922\) −11.7411 + 22.6341i −0.386673 + 0.745415i
\(923\) 11.0575i 0.363962i
\(924\) 12.4239 8.75283i 0.408717 0.287947i
\(925\) 2.63854i 0.0867545i
\(926\) 43.1042 + 22.3597i 1.41649 + 0.734785i
\(927\) −13.7768 −0.452491
\(928\) −1.06178 1.14208i −0.0348545 0.0374907i
\(929\) 30.3665 0.996294 0.498147 0.867093i \(-0.334014\pi\)
0.498147 + 0.867093i \(0.334014\pi\)
\(930\) −10.5605 5.47812i −0.346293 0.179635i
\(931\) −12.4218 −0.407108
\(932\) −2.47512 3.51322i −0.0810751 0.115079i
\(933\) −33.0428 −1.08177
\(934\) 24.0300 46.3241i 0.786284 1.51577i
\(935\) −2.99516 −0.0979523
\(936\) 11.3355 1.54227i 0.370514 0.0504106i
\(937\) 29.6010i 0.967022i −0.875338 0.483511i \(-0.839361\pi\)
0.875338 0.483511i \(-0.160639\pi\)
\(938\) 3.66532 7.06586i 0.119677 0.230709i
\(939\) −17.6117 −0.574736
\(940\) 12.0064 + 17.0421i 0.391606 + 0.555852i
\(941\) 15.9140i 0.518783i 0.965772 + 0.259391i \(0.0835219\pi\)
−0.965772 + 0.259391i \(0.916478\pi\)
\(942\) −9.86053 + 19.0088i −0.321274 + 0.619340i
\(943\) −20.0055 29.1282i −0.651469 0.948545i
\(944\) −11.1145 3.97289i −0.361746 0.129307i
\(945\) 2.14037 0.0696264
\(946\) −26.8453 + 51.7514i −0.872816 + 1.68258i
\(947\) 19.8116i 0.643789i 0.946776 + 0.321894i \(0.104320\pi\)
−0.946776 + 0.321894i \(0.895680\pi\)
\(948\) −26.5421 + 18.6993i −0.862047 + 0.607324i
\(949\) −19.5967 −0.636136
\(950\) 3.34426 6.44695i 0.108502 0.209167i
\(951\) 11.9669i 0.388054i
\(952\) −0.688551 5.06079i −0.0223161 0.164021i
\(953\) 27.1642i 0.879934i 0.898014 + 0.439967i \(0.145010\pi\)
−0.898014 + 0.439967i \(0.854990\pi\)
\(954\) −7.03232 3.64792i −0.227680 0.118106i
\(955\) 1.29520i 0.0419117i
\(956\) −25.3499 + 17.8594i −0.819875 + 0.577613i
\(957\) 0.978670i 0.0316359i
\(958\) 23.6726 45.6352i 0.764828 1.47441i
\(959\) 46.9930i 1.51748i
\(960\) 7.70920 2.13733i 0.248813 0.0689821i
\(961\) −39.7673 −1.28282
\(962\) −13.3972 6.94958i −0.431941 0.224063i
\(963\) 1.44719 0.0466351
\(964\) 20.5356 14.4676i 0.661406 0.465970i
\(965\) 1.48140i 0.0476880i
\(966\) 1.78530 + 14.4065i 0.0574412 + 0.463522i
\(967\) 40.9044i 1.31540i −0.753281 0.657698i \(-0.771530\pi\)
0.753281 0.657698i \(-0.228470\pi\)
\(968\) 4.49535 0.611620i 0.144486 0.0196582i
\(969\) 4.33263 0.139184
\(970\) −0.550322 + 1.06089i −0.0176698 + 0.0340632i
\(971\) −31.1852 −1.00078 −0.500390 0.865800i \(-0.666810\pi\)
−0.500390 + 0.865800i \(0.666810\pi\)
\(972\) −1.63499 + 1.15187i −0.0524423 + 0.0369463i
\(973\) 33.0381i 1.05915i
\(974\) 5.69290 + 2.95311i 0.182412 + 0.0946237i
\(975\) 4.04464i 0.129532i
\(976\) −26.5745 9.49909i −0.850628 0.304058i
\(977\) 43.9246i 1.40527i −0.711549 0.702637i \(-0.752006\pi\)
0.711549 0.702637i \(-0.247994\pi\)
\(978\) −4.36668 + 8.41792i −0.139631 + 0.269175i
\(979\) 56.8668i 1.81747i
\(980\) −3.95471 + 2.78615i −0.126328 + 0.0890002i
\(981\) 1.02911i 0.0328571i
\(982\) 16.8757 + 8.75404i 0.538526 + 0.279353i
\(983\) 37.6723 1.20156 0.600780 0.799414i \(-0.294857\pi\)
0.600780 + 0.799414i \(0.294857\pi\)
\(984\) −2.80957 20.6501i −0.0895659 0.658302i
\(985\) 13.9422i 0.444234i
\(986\) −0.291957 0.151448i −0.00929779 0.00482309i
\(987\) −22.3099 −0.710132
\(988\) 23.9260 + 33.9610i 0.761187 + 1.08044i
\(989\) −31.5274 45.9041i −1.00251 1.45967i
\(990\) 4.45680 + 2.31190i 0.141646 + 0.0734771i
\(991\) 8.15713i 0.259120i −0.991572 0.129560i \(-0.958644\pi\)
0.991572 0.129560i \(-0.0413565\pi\)
\(992\) 34.8523 32.4017i 1.10656 1.02875i
\(993\) −5.36132 −0.170136
\(994\) 7.34576 + 3.81051i 0.232993 + 0.120862i
\(995\) 5.33970i 0.169280i
\(996\) −15.4524 + 10.8864i −0.489627 + 0.344949i
\(997\) 53.7457 1.70214 0.851071 0.525051i \(-0.175954\pi\)
0.851071 + 0.525051i \(0.175954\pi\)
\(998\) −31.7490 16.4694i −1.00500 0.521329i
\(999\) 2.63854 0.0834796
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 1380.2.p.b.91.20 yes 48
4.3 odd 2 1380.2.p.a.91.19 48
23.22 odd 2 1380.2.p.a.91.20 yes 48
92.91 even 2 inner 1380.2.p.b.91.19 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1380.2.p.a.91.19 48 4.3 odd 2
1380.2.p.a.91.20 yes 48 23.22 odd 2
1380.2.p.b.91.19 yes 48 92.91 even 2 inner
1380.2.p.b.91.20 yes 48 1.1 even 1 trivial