Properties

Label 231.2.c.a.76.3
Level $231$
Weight $2$
Character 231.76
Analytic conductor $1.845$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [231,2,Mod(76,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.c (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: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.3
Root \(0.0566033 - 1.17421i\) of defining polynomial
Character \(\chi\) \(=\) 231.76
Dual form 231.2.c.a.76.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.08529i q^{2} -1.00000i q^{3} -2.34841 q^{4} +0.833366i q^{5} -2.08529 q^{6} +(-2.19849 - 1.47195i) q^{7} +0.726543i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-2.08529i q^{2} -1.00000i q^{3} -2.34841 q^{4} +0.833366i q^{5} -2.08529 q^{6} +(-2.19849 - 1.47195i) q^{7} +0.726543i q^{8} -1.00000 q^{9} +1.73781 q^{10} +(-1.23607 - 3.07768i) q^{11} +2.34841i q^{12} -4.54963 q^{13} +(-3.06943 + 4.58448i) q^{14} +0.833366 q^{15} -3.18178 q^{16} +6.38178 q^{17} +2.08529i q^{18} +2.56484 q^{19} -1.95709i q^{20} +(-1.47195 + 2.19849i) q^{21} +(-6.41785 + 2.57755i) q^{22} +9.16896 q^{23} +0.726543 q^{24} +4.30550 q^{25} +9.48728i q^{26} +1.00000i q^{27} +(5.16297 + 3.45675i) q^{28} +0.152649i q^{29} -1.73781i q^{30} -8.36356i q^{31} +8.08800i q^{32} +(-3.07768 + 1.23607i) q^{33} -13.3078i q^{34} +(1.22667 - 1.83215i) q^{35} +2.34841 q^{36} -5.30550 q^{37} -5.34841i q^{38} +4.54963i q^{39} -0.605476 q^{40} -3.21147 q^{41} +(4.58448 + 3.06943i) q^{42} +5.66138i q^{43} +(2.90280 + 7.22768i) q^{44} -0.833366i q^{45} -19.1199i q^{46} -6.00233i q^{47} +3.18178i q^{48} +(2.66673 + 6.47214i) q^{49} -8.97820i q^{50} -6.38178i q^{51} +10.6844 q^{52} +4.69683 q^{53} +2.08529 q^{54} +(2.56484 - 1.03010i) q^{55} +(1.06943 - 1.59730i) q^{56} -2.56484i q^{57} +0.318317 q^{58} -1.05806i q^{59} -1.95709 q^{60} -8.34114 q^{61} -17.4404 q^{62} +(2.19849 + 1.47195i) q^{63} +10.5022 q^{64} -3.79151i q^{65} +(2.57755 + 6.41785i) q^{66} +4.33560 q^{67} -14.9871 q^{68} -9.16896i q^{69} +(-3.82055 - 2.55796i) q^{70} -4.80540 q^{71} -0.726543i q^{72} +10.6673 q^{73} +11.0635i q^{74} -4.30550i q^{75} -6.02330 q^{76} +(-1.81271 + 8.58569i) q^{77} +9.48728 q^{78} +5.70254i q^{79} -2.65159i q^{80} +1.00000 q^{81} +6.69683i q^{82} +10.7533 q^{83} +(3.45675 - 5.16297i) q^{84} +5.31836i q^{85} +11.8056 q^{86} +0.152649 q^{87} +(2.23607 - 0.898056i) q^{88} -8.13887i q^{89} -1.73781 q^{90} +(10.0023 + 6.69683i) q^{91} -21.5325 q^{92} -8.36356 q^{93} -12.5166 q^{94} +2.13745i q^{95} +8.08800 q^{96} +17.7572i q^{97} +(13.4962 - 5.56090i) q^{98} +(1.23607 + 3.07768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{4} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{4} - 16 q^{9} + 16 q^{11} + 8 q^{14} - 8 q^{15} - 4 q^{16} - 20 q^{22} + 24 q^{23} - 24 q^{25} + 12 q^{36} + 8 q^{37} + 12 q^{42} - 32 q^{44} + 24 q^{53} - 40 q^{56} - 12 q^{58} + 36 q^{60} + 88 q^{64} - 32 q^{67} + 36 q^{70} - 48 q^{71} + 12 q^{78} + 16 q^{81} + 32 q^{86} + 16 q^{91} - 128 q^{92} - 40 q^{93} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.08529i 1.47452i −0.675610 0.737260i \(-0.736119\pi\)
0.675610 0.737260i \(-0.263881\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −2.34841 −1.17421
\(5\) 0.833366i 0.372692i 0.982484 + 0.186346i \(0.0596646\pi\)
−0.982484 + 0.186346i \(0.940335\pi\)
\(6\) −2.08529 −0.851314
\(7\) −2.19849 1.47195i −0.830952 0.556344i
\(8\) 0.726543i 0.256872i
\(9\) −1.00000 −0.333333
\(10\) 1.73781 0.549542
\(11\) −1.23607 3.07768i −0.372689 0.927957i
\(12\) 2.34841i 0.677929i
\(13\) −4.54963 −1.26184 −0.630921 0.775847i \(-0.717323\pi\)
−0.630921 + 0.775847i \(0.717323\pi\)
\(14\) −3.06943 + 4.58448i −0.820341 + 1.22525i
\(15\) 0.833366 0.215174
\(16\) −3.18178 −0.795445
\(17\) 6.38178 1.54781 0.773905 0.633302i \(-0.218301\pi\)
0.773905 + 0.633302i \(0.218301\pi\)
\(18\) 2.08529i 0.491506i
\(19\) 2.56484 0.588414 0.294207 0.955742i \(-0.404945\pi\)
0.294207 + 0.955742i \(0.404945\pi\)
\(20\) 1.95709i 0.437618i
\(21\) −1.47195 + 2.19849i −0.321206 + 0.479750i
\(22\) −6.41785 + 2.57755i −1.36829 + 0.549536i
\(23\) 9.16896 1.91186 0.955931 0.293593i \(-0.0948510\pi\)
0.955931 + 0.293593i \(0.0948510\pi\)
\(24\) 0.726543 0.148305
\(25\) 4.30550 0.861100
\(26\) 9.48728i 1.86061i
\(27\) 1.00000i 0.192450i
\(28\) 5.16297 + 3.45675i 0.975709 + 0.653264i
\(29\) 0.152649i 0.0283463i 0.999900 + 0.0141731i \(0.00451160\pi\)
−0.999900 + 0.0141731i \(0.995488\pi\)
\(30\) 1.73781i 0.317278i
\(31\) 8.36356i 1.50214i −0.660223 0.751070i \(-0.729538\pi\)
0.660223 0.751070i \(-0.270462\pi\)
\(32\) 8.08800i 1.42977i
\(33\) −3.07768 + 1.23607i −0.535756 + 0.215172i
\(34\) 13.3078i 2.28227i
\(35\) 1.22667 1.83215i 0.207345 0.309689i
\(36\) 2.34841 0.391402
\(37\) −5.30550 −0.872219 −0.436110 0.899894i \(-0.643644\pi\)
−0.436110 + 0.899894i \(0.643644\pi\)
\(38\) 5.34841i 0.867627i
\(39\) 4.54963i 0.728524i
\(40\) −0.605476 −0.0957341
\(41\) −3.21147 −0.501547 −0.250774 0.968046i \(-0.580685\pi\)
−0.250774 + 0.968046i \(0.580685\pi\)
\(42\) 4.58448 + 3.06943i 0.707401 + 0.473624i
\(43\) 5.66138i 0.863353i 0.902029 + 0.431676i \(0.142078\pi\)
−0.902029 + 0.431676i \(0.857922\pi\)
\(44\) 2.90280 + 7.22768i 0.437613 + 1.08961i
\(45\) 0.833366i 0.124231i
\(46\) 19.1199i 2.81908i
\(47\) 6.00233i 0.875530i −0.899089 0.437765i \(-0.855770\pi\)
0.899089 0.437765i \(-0.144230\pi\)
\(48\) 3.18178i 0.459250i
\(49\) 2.66673 + 6.47214i 0.380962 + 0.924591i
\(50\) 8.97820i 1.26971i
\(51\) 6.38178i 0.893628i
\(52\) 10.6844 1.48166
\(53\) 4.69683 0.645159 0.322579 0.946542i \(-0.395450\pi\)
0.322579 + 0.946542i \(0.395450\pi\)
\(54\) 2.08529 0.283771
\(55\) 2.56484 1.03010i 0.345842 0.138898i
\(56\) 1.06943 1.59730i 0.142909 0.213448i
\(57\) 2.56484i 0.339721i
\(58\) 0.318317 0.0417971
\(59\) 1.05806i 0.137747i −0.997625 0.0688737i \(-0.978059\pi\)
0.997625 0.0688737i \(-0.0219405\pi\)
\(60\) −1.95709 −0.252659
\(61\) −8.34114 −1.06797 −0.533987 0.845493i \(-0.679307\pi\)
−0.533987 + 0.845493i \(0.679307\pi\)
\(62\) −17.4404 −2.21493
\(63\) 2.19849 + 1.47195i 0.276984 + 0.185448i
\(64\) 10.5022 1.31278
\(65\) 3.79151i 0.470279i
\(66\) 2.57755 + 6.41785i 0.317275 + 0.789982i
\(67\) 4.33560 0.529678 0.264839 0.964293i \(-0.414681\pi\)
0.264839 + 0.964293i \(0.414681\pi\)
\(68\) −14.9871 −1.81745
\(69\) 9.16896i 1.10381i
\(70\) −3.82055 2.55796i −0.456643 0.305735i
\(71\) −4.80540 −0.570297 −0.285148 0.958483i \(-0.592043\pi\)
−0.285148 + 0.958483i \(0.592043\pi\)
\(72\) 0.726543i 0.0856239i
\(73\) 10.6673 1.24851 0.624255 0.781221i \(-0.285403\pi\)
0.624255 + 0.781221i \(0.285403\pi\)
\(74\) 11.0635i 1.28610i
\(75\) 4.30550i 0.497157i
\(76\) −6.02330 −0.690919
\(77\) −1.81271 + 8.58569i −0.206577 + 0.978430i
\(78\) 9.48728 1.07422
\(79\) 5.70254i 0.641586i 0.947149 + 0.320793i \(0.103949\pi\)
−0.947149 + 0.320793i \(0.896051\pi\)
\(80\) 2.65159i 0.296456i
\(81\) 1.00000 0.111111
\(82\) 6.69683i 0.739541i
\(83\) 10.7533 1.18033 0.590165 0.807282i \(-0.299062\pi\)
0.590165 + 0.807282i \(0.299062\pi\)
\(84\) 3.45675 5.16297i 0.377162 0.563326i
\(85\) 5.31836i 0.576857i
\(86\) 11.8056 1.27303
\(87\) 0.152649 0.0163657
\(88\) 2.23607 0.898056i 0.238366 0.0957331i
\(89\) 8.13887i 0.862718i −0.902180 0.431359i \(-0.858034\pi\)
0.902180 0.431359i \(-0.141966\pi\)
\(90\) −1.73781 −0.183181
\(91\) 10.0023 + 6.69683i 1.04853 + 0.702018i
\(92\) −21.5325 −2.24492
\(93\) −8.36356 −0.867261
\(94\) −12.5166 −1.29099
\(95\) 2.13745i 0.219297i
\(96\) 8.08800 0.825478
\(97\) 17.7572i 1.80297i 0.432808 + 0.901486i \(0.357523\pi\)
−0.432808 + 0.901486i \(0.642477\pi\)
\(98\) 13.4962 5.56090i 1.36333 0.561735i
\(99\) 1.23607 + 3.07768i 0.124230 + 0.309319i
\(100\) −10.1111 −1.01111
\(101\) −2.10689 −0.209643 −0.104822 0.994491i \(-0.533427\pi\)
−0.104822 + 0.994491i \(0.533427\pi\)
\(102\) −13.3078 −1.31767
\(103\) 10.6110i 1.04553i −0.852476 0.522767i \(-0.824900\pi\)
0.852476 0.522767i \(-0.175100\pi\)
\(104\) 3.30550i 0.324131i
\(105\) −1.83215 1.22667i −0.178799 0.119711i
\(106\) 9.79423i 0.951299i
\(107\) 13.5700i 1.31186i 0.754821 + 0.655931i \(0.227724\pi\)
−0.754821 + 0.655931i \(0.772276\pi\)
\(108\) 2.34841i 0.225976i
\(109\) 6.68708i 0.640506i −0.947332 0.320253i \(-0.896232\pi\)
0.947332 0.320253i \(-0.103768\pi\)
\(110\) −2.14805 5.34841i −0.204808 0.509951i
\(111\) 5.30550i 0.503576i
\(112\) 6.99512 + 4.68342i 0.660976 + 0.442541i
\(113\) −1.33346 −0.125442 −0.0627208 0.998031i \(-0.519978\pi\)
−0.0627208 + 0.998031i \(0.519978\pi\)
\(114\) −5.34841 −0.500925
\(115\) 7.64110i 0.712536i
\(116\) 0.358484i 0.0332844i
\(117\) 4.54963 0.420614
\(118\) −2.20635 −0.203111
\(119\) −14.0303 9.39366i −1.28615 0.861115i
\(120\) 0.605476i 0.0552721i
\(121\) −7.94427 + 7.60845i −0.722207 + 0.691677i
\(122\) 17.3937i 1.57475i
\(123\) 3.21147i 0.289568i
\(124\) 19.6411i 1.76382i
\(125\) 7.75489i 0.693618i
\(126\) 3.06943 4.58448i 0.273447 0.408418i
\(127\) 0.226413i 0.0200909i 0.999950 + 0.0100455i \(0.00319762\pi\)
−0.999950 + 0.0100455i \(0.996802\pi\)
\(128\) 5.72414i 0.505948i
\(129\) 5.66138 0.498457
\(130\) −7.90637 −0.693435
\(131\) −0.305299 −0.0266741 −0.0133370 0.999911i \(-0.504245\pi\)
−0.0133370 + 0.999911i \(0.504245\pi\)
\(132\) 7.22768 2.90280i 0.629088 0.252656i
\(133\) −5.63877 3.77531i −0.488943 0.327361i
\(134\) 9.04096i 0.781020i
\(135\) −0.833366 −0.0717247
\(136\) 4.63663i 0.397588i
\(137\) −11.7572 −1.00449 −0.502243 0.864726i \(-0.667492\pi\)
−0.502243 + 0.864726i \(0.667492\pi\)
\(138\) −19.1199 −1.62759
\(139\) −9.83195 −0.833935 −0.416968 0.908921i \(-0.636907\pi\)
−0.416968 + 0.908921i \(0.636907\pi\)
\(140\) −2.88073 + 4.30264i −0.243466 + 0.363640i
\(141\) −6.00233 −0.505487
\(142\) 10.0206i 0.840913i
\(143\) 5.62366 + 14.0023i 0.470274 + 1.17093i
\(144\) 3.18178 0.265148
\(145\) −0.127213 −0.0105644
\(146\) 22.2443i 1.84095i
\(147\) 6.47214 2.66673i 0.533813 0.219948i
\(148\) 12.4595 1.02417
\(149\) 14.3816i 1.17819i −0.808065 0.589093i \(-0.799485\pi\)
0.808065 0.589093i \(-0.200515\pi\)
\(150\) −8.97820 −0.733067
\(151\) 2.98506i 0.242920i −0.992596 0.121460i \(-0.961242\pi\)
0.992596 0.121460i \(-0.0387577\pi\)
\(152\) 1.86346i 0.151147i
\(153\) −6.38178 −0.515936
\(154\) 17.9036 + 3.78001i 1.44271 + 0.304602i
\(155\) 6.96990 0.559836
\(156\) 10.6844i 0.855438i
\(157\) 17.3983i 1.38854i 0.719716 + 0.694268i \(0.244272\pi\)
−0.719716 + 0.694268i \(0.755728\pi\)
\(158\) 11.8914 0.946031
\(159\) 4.69683i 0.372483i
\(160\) −6.74026 −0.532865
\(161\) −20.1579 13.4962i −1.58866 1.06365i
\(162\) 2.08529i 0.163835i
\(163\) 4.39152 0.343970 0.171985 0.985100i \(-0.444982\pi\)
0.171985 + 0.985100i \(0.444982\pi\)
\(164\) 7.54186 0.588920
\(165\) −1.03010 2.56484i −0.0801929 0.199672i
\(166\) 22.4238i 1.74042i
\(167\) −2.86501 −0.221701 −0.110851 0.993837i \(-0.535358\pi\)
−0.110851 + 0.993837i \(0.535358\pi\)
\(168\) −1.59730 1.06943i −0.123234 0.0825086i
\(169\) 7.69916 0.592243
\(170\) 11.0903 0.850586
\(171\) −2.56484 −0.196138
\(172\) 13.2953i 1.01376i
\(173\) 20.4220 1.55266 0.776329 0.630328i \(-0.217079\pi\)
0.776329 + 0.630328i \(0.217079\pi\)
\(174\) 0.318317i 0.0241316i
\(175\) −9.46561 6.33748i −0.715533 0.479068i
\(176\) 3.93290 + 9.79251i 0.296453 + 0.738138i
\(177\) −1.05806 −0.0795285
\(178\) −16.9719 −1.27209
\(179\) 4.58825 0.342942 0.171471 0.985189i \(-0.445148\pi\)
0.171471 + 0.985189i \(0.445148\pi\)
\(180\) 1.95709i 0.145873i
\(181\) 6.03029i 0.448228i 0.974563 + 0.224114i \(0.0719488\pi\)
−0.974563 + 0.224114i \(0.928051\pi\)
\(182\) 13.9648 20.8577i 1.03514 1.54608i
\(183\) 8.34114i 0.616595i
\(184\) 6.66164i 0.491103i
\(185\) 4.42142i 0.325069i
\(186\) 17.4404i 1.27879i
\(187\) −7.88831 19.6411i −0.576851 1.43630i
\(188\) 14.0960i 1.02805i
\(189\) 1.47195 2.19849i 0.107069 0.159917i
\(190\) 4.45718 0.323358
\(191\) 23.7800 1.72066 0.860329 0.509739i \(-0.170258\pi\)
0.860329 + 0.509739i \(0.170258\pi\)
\(192\) 10.5022i 0.757933i
\(193\) 4.63569i 0.333684i 0.985984 + 0.166842i \(0.0533570\pi\)
−0.985984 + 0.166842i \(0.946643\pi\)
\(194\) 37.0289 2.65852
\(195\) −3.79151 −0.271516
\(196\) −6.26259 15.1993i −0.447328 1.08566i
\(197\) 6.62048i 0.471690i −0.971791 0.235845i \(-0.924214\pi\)
0.971791 0.235845i \(-0.0757858\pi\)
\(198\) 6.41785 2.57755i 0.456097 0.183179i
\(199\) 10.9699i 0.777636i 0.921315 + 0.388818i \(0.127116\pi\)
−0.921315 + 0.388818i \(0.872884\pi\)
\(200\) 3.12813i 0.221192i
\(201\) 4.33560i 0.305810i
\(202\) 4.39346i 0.309123i
\(203\) 0.224692 0.335598i 0.0157703 0.0235544i
\(204\) 14.9871i 1.04930i
\(205\) 2.67633i 0.186923i
\(206\) −22.1270 −1.54166
\(207\) −9.16896 −0.637287
\(208\) 14.4759 1.00373
\(209\) −3.17031 7.89375i −0.219295 0.546022i
\(210\) −2.55796 + 3.82055i −0.176516 + 0.263643i
\(211\) 12.4960i 0.860259i −0.902767 0.430130i \(-0.858468\pi\)
0.902767 0.430130i \(-0.141532\pi\)
\(212\) −11.0301 −0.757550
\(213\) 4.80540i 0.329261i
\(214\) 28.2973 1.93437
\(215\) −4.71800 −0.321765
\(216\) −0.726543 −0.0494350
\(217\) −12.3107 + 18.3872i −0.835707 + 1.24821i
\(218\) −13.9445 −0.944438
\(219\) 10.6673i 0.720827i
\(220\) −6.02330 + 2.41909i −0.406091 + 0.163095i
\(221\) −29.0348 −1.95309
\(222\) 11.0635 0.742532
\(223\) 9.44958i 0.632791i −0.948627 0.316395i \(-0.897527\pi\)
0.948627 0.316395i \(-0.102473\pi\)
\(224\) 11.9051 17.7814i 0.795445 1.18807i
\(225\) −4.30550 −0.287033
\(226\) 2.78065i 0.184966i
\(227\) 5.43497 0.360732 0.180366 0.983600i \(-0.442272\pi\)
0.180366 + 0.983600i \(0.442272\pi\)
\(228\) 6.02330i 0.398903i
\(229\) 18.9746i 1.25387i 0.779070 + 0.626937i \(0.215692\pi\)
−0.779070 + 0.626937i \(0.784308\pi\)
\(230\) 15.9339 1.05065
\(231\) 8.58569 + 1.81271i 0.564897 + 0.119267i
\(232\) −0.110906 −0.00728135
\(233\) 12.5083i 0.819445i 0.912210 + 0.409722i \(0.134374\pi\)
−0.912210 + 0.409722i \(0.865626\pi\)
\(234\) 9.48728i 0.620203i
\(235\) 5.00214 0.326303
\(236\) 2.48476i 0.161744i
\(237\) 5.70254 0.370420
\(238\) −19.5885 + 29.2572i −1.26973 + 1.89646i
\(239\) 6.99955i 0.452763i 0.974039 + 0.226382i \(0.0726896\pi\)
−0.974039 + 0.226382i \(0.927310\pi\)
\(240\) −2.65159 −0.171159
\(241\) −4.24433 −0.273402 −0.136701 0.990612i \(-0.543650\pi\)
−0.136701 + 0.990612i \(0.543650\pi\)
\(242\) 15.8658 + 16.5661i 1.01989 + 1.06491i
\(243\) 1.00000i 0.0641500i
\(244\) 19.5885 1.25402
\(245\) −5.39366 + 2.22236i −0.344588 + 0.141982i
\(246\) 6.69683 0.426974
\(247\) −11.6691 −0.742485
\(248\) 6.07648 0.385857
\(249\) 10.7533i 0.681464i
\(250\) 16.1711 1.02275
\(251\) 24.3403i 1.53634i 0.640244 + 0.768172i \(0.278833\pi\)
−0.640244 + 0.768172i \(0.721167\pi\)
\(252\) −5.16297 3.45675i −0.325236 0.217755i
\(253\) −11.3335 28.2192i −0.712529 1.77412i
\(254\) 0.472136 0.0296244
\(255\) 5.31836 0.333048
\(256\) 9.06799 0.566750
\(257\) 25.1111i 1.56639i −0.621778 0.783194i \(-0.713589\pi\)
0.621778 0.783194i \(-0.286411\pi\)
\(258\) 11.8056i 0.734984i
\(259\) 11.6641 + 7.80943i 0.724772 + 0.485254i
\(260\) 8.90403i 0.552204i
\(261\) 0.152649i 0.00944876i
\(262\) 0.636635i 0.0393314i
\(263\) 11.1167i 0.685483i −0.939430 0.342742i \(-0.888644\pi\)
0.939430 0.342742i \(-0.111356\pi\)
\(264\) −0.898056 2.23607i −0.0552715 0.137620i
\(265\) 3.91418i 0.240446i
\(266\) −7.87259 + 11.7584i −0.482700 + 0.720956i
\(267\) −8.13887 −0.498091
\(268\) −10.1818 −0.621951
\(269\) 12.8054i 0.780759i −0.920654 0.390380i \(-0.872344\pi\)
0.920654 0.390380i \(-0.127656\pi\)
\(270\) 1.73781i 0.105759i
\(271\) 15.5828 0.946589 0.473295 0.880904i \(-0.343065\pi\)
0.473295 + 0.880904i \(0.343065\pi\)
\(272\) −20.3054 −1.23120
\(273\) 6.69683 10.0023i 0.405310 0.605369i
\(274\) 24.5171i 1.48113i
\(275\) −5.32189 13.2510i −0.320922 0.799064i
\(276\) 21.5325i 1.29611i
\(277\) 4.98214i 0.299348i −0.988735 0.149674i \(-0.952178\pi\)
0.988735 0.149674i \(-0.0478224\pi\)
\(278\) 20.5024i 1.22965i
\(279\) 8.36356i 0.500713i
\(280\) 1.33113 + 0.891229i 0.0795504 + 0.0532611i
\(281\) 25.2269i 1.50491i 0.658642 + 0.752457i \(0.271131\pi\)
−0.658642 + 0.752457i \(0.728869\pi\)
\(282\) 12.5166i 0.745351i
\(283\) 20.7634 1.23425 0.617127 0.786864i \(-0.288296\pi\)
0.617127 + 0.786864i \(0.288296\pi\)
\(284\) 11.2851 0.669646
\(285\) 2.13745 0.126611
\(286\) 29.1988 11.7269i 1.72656 0.693428i
\(287\) 7.06039 + 4.72712i 0.416761 + 0.279033i
\(288\) 8.08800i 0.476590i
\(289\) 23.7271 1.39571
\(290\) 0.265275i 0.0155775i
\(291\) 17.7572 1.04095
\(292\) −25.0512 −1.46601
\(293\) −4.37155 −0.255388 −0.127694 0.991814i \(-0.540758\pi\)
−0.127694 + 0.991814i \(0.540758\pi\)
\(294\) −5.56090 13.4962i −0.324318 0.787117i
\(295\) 0.881749 0.0513374
\(296\) 3.85467i 0.224048i
\(297\) 3.07768 1.23607i 0.178585 0.0717239i
\(298\) −29.9897 −1.73726
\(299\) −41.7154 −2.41246
\(300\) 10.1111i 0.583765i
\(301\) 8.33327 12.4465i 0.480322 0.717405i
\(302\) −6.22469 −0.358191
\(303\) 2.10689i 0.121038i
\(304\) −8.16074 −0.468051
\(305\) 6.95122i 0.398026i
\(306\) 13.3078i 0.760758i
\(307\) 4.47930 0.255647 0.127824 0.991797i \(-0.459201\pi\)
0.127824 + 0.991797i \(0.459201\pi\)
\(308\) 4.25699 20.1628i 0.242565 1.14888i
\(309\) −10.6110 −0.603639
\(310\) 14.5342i 0.825489i
\(311\) 22.8841i 1.29764i −0.760943 0.648819i \(-0.775263\pi\)
0.760943 0.648819i \(-0.224737\pi\)
\(312\) −3.30550 −0.187137
\(313\) 5.30317i 0.299753i 0.988705 + 0.149877i \(0.0478876\pi\)
−0.988705 + 0.149877i \(0.952112\pi\)
\(314\) 36.2804 2.04742
\(315\) −1.22667 + 1.83215i −0.0691151 + 0.103230i
\(316\) 13.3919i 0.753355i
\(317\) −22.0951 −1.24099 −0.620493 0.784212i \(-0.713068\pi\)
−0.620493 + 0.784212i \(0.713068\pi\)
\(318\) −9.79423 −0.549233
\(319\) 0.469806 0.188685i 0.0263041 0.0105643i
\(320\) 8.75220i 0.489263i
\(321\) 13.5700 0.757404
\(322\) −28.1435 + 42.0350i −1.56838 + 2.34252i
\(323\) 16.3682 0.910752
\(324\) −2.34841 −0.130467
\(325\) −19.5885 −1.08657
\(326\) 9.15757i 0.507191i
\(327\) −6.68708 −0.369796
\(328\) 2.33327i 0.128833i
\(329\) −8.83512 + 13.1961i −0.487096 + 0.727523i
\(330\) −5.34841 + 2.14805i −0.294421 + 0.118246i
\(331\) −19.7316 −1.08455 −0.542273 0.840202i \(-0.682436\pi\)
−0.542273 + 0.840202i \(0.682436\pi\)
\(332\) −25.2533 −1.38595
\(333\) 5.30550 0.290740
\(334\) 5.97437i 0.326903i
\(335\) 3.61314i 0.197407i
\(336\) 4.68342 6.99512i 0.255501 0.381615i
\(337\) 31.4052i 1.71075i −0.518009 0.855375i \(-0.673327\pi\)
0.518009 0.855375i \(-0.326673\pi\)
\(338\) 16.0549i 0.873274i
\(339\) 1.33346i 0.0724238i
\(340\) 12.4897i 0.677349i
\(341\) −25.7404 + 10.3379i −1.39392 + 0.559830i
\(342\) 5.34841i 0.289209i
\(343\) 3.66387 18.1542i 0.197830 0.980236i
\(344\) −4.11324 −0.221771
\(345\) 7.64110 0.411383
\(346\) 42.5858i 2.28942i
\(347\) 7.14333i 0.383474i 0.981446 + 0.191737i \(0.0614121\pi\)
−0.981446 + 0.191737i \(0.938588\pi\)
\(348\) −0.358484 −0.0192167
\(349\) −12.1326 −0.649446 −0.324723 0.945809i \(-0.605271\pi\)
−0.324723 + 0.945809i \(0.605271\pi\)
\(350\) −13.2155 + 19.7385i −0.706396 + 1.05507i
\(351\) 4.54963i 0.242841i
\(352\) 24.8923 9.99732i 1.32676 0.532859i
\(353\) 14.7173i 0.783320i 0.920110 + 0.391660i \(0.128099\pi\)
−0.920110 + 0.391660i \(0.871901\pi\)
\(354\) 2.20635i 0.117266i
\(355\) 4.00466i 0.212545i
\(356\) 19.1134i 1.01301i
\(357\) −9.39366 + 14.0303i −0.497165 + 0.742562i
\(358\) 9.56781i 0.505675i
\(359\) 6.55732i 0.346082i 0.984915 + 0.173041i \(0.0553593\pi\)
−0.984915 + 0.173041i \(0.944641\pi\)
\(360\) 0.605476 0.0319114
\(361\) −12.4216 −0.653769
\(362\) 12.5749 0.660921
\(363\) 7.60845 + 7.94427i 0.399340 + 0.416966i
\(364\) −23.4896 15.7269i −1.23119 0.824315i
\(365\) 8.88974i 0.465310i
\(366\) 17.3937 0.909181
\(367\) 32.6759i 1.70567i −0.522184 0.852833i \(-0.674883\pi\)
0.522184 0.852833i \(-0.325117\pi\)
\(368\) −29.1736 −1.52078
\(369\) 3.21147 0.167182
\(370\) −9.21993 −0.479321
\(371\) −10.3259 6.91349i −0.536096 0.358931i
\(372\) 19.6411 1.01834
\(373\) 21.9040i 1.13415i 0.823668 + 0.567073i \(0.191924\pi\)
−0.823668 + 0.567073i \(0.808076\pi\)
\(374\) −40.9573 + 16.4494i −2.11785 + 0.850577i
\(375\) 7.75489 0.400461
\(376\) 4.36095 0.224899
\(377\) 0.694498i 0.0357685i
\(378\) −4.58448 3.06943i −0.235800 0.157875i
\(379\) −14.0023 −0.719251 −0.359626 0.933097i \(-0.617096\pi\)
−0.359626 + 0.933097i \(0.617096\pi\)
\(380\) 5.01961i 0.257500i
\(381\) 0.226413 0.0115995
\(382\) 49.5880i 2.53714i
\(383\) 7.05573i 0.360531i 0.983618 + 0.180265i \(0.0576957\pi\)
−0.983618 + 0.180265i \(0.942304\pi\)
\(384\) −5.72414 −0.292109
\(385\) −7.15502 1.51065i −0.364654 0.0769898i
\(386\) 9.66673 0.492024
\(387\) 5.66138i 0.287784i
\(388\) 41.7013i 2.11706i
\(389\) −2.44938 −0.124189 −0.0620944 0.998070i \(-0.519778\pi\)
−0.0620944 + 0.998070i \(0.519778\pi\)
\(390\) 7.90637i 0.400355i
\(391\) 58.5143 2.95920
\(392\) −4.70228 + 1.93749i −0.237501 + 0.0978582i
\(393\) 0.305299i 0.0154003i
\(394\) −13.8056 −0.695516
\(395\) −4.75230 −0.239114
\(396\) −2.90280 7.22768i −0.145871 0.363204i
\(397\) 4.75702i 0.238748i 0.992849 + 0.119374i \(0.0380888\pi\)
−0.992849 + 0.119374i \(0.961911\pi\)
\(398\) 22.8754 1.14664
\(399\) −3.77531 + 5.63877i −0.189002 + 0.282292i
\(400\) −13.6992 −0.684958
\(401\) 18.3682 0.917265 0.458633 0.888626i \(-0.348339\pi\)
0.458633 + 0.888626i \(0.348339\pi\)
\(402\) −9.04096 −0.450922
\(403\) 38.0511i 1.89546i
\(404\) 4.94784 0.246164
\(405\) 0.833366i 0.0414103i
\(406\) −0.699818 0.468547i −0.0347314 0.0232536i
\(407\) 6.55796 + 16.3287i 0.325066 + 0.809381i
\(408\) 4.63663 0.229548
\(409\) 34.7230 1.71694 0.858472 0.512861i \(-0.171414\pi\)
0.858472 + 0.512861i \(0.171414\pi\)
\(410\) −5.58091 −0.275621
\(411\) 11.7572i 0.579941i
\(412\) 24.9190i 1.22767i
\(413\) −1.55741 + 2.32613i −0.0766350 + 0.114461i
\(414\) 19.1199i 0.939692i
\(415\) 8.96145i 0.439900i
\(416\) 36.7974i 1.80414i
\(417\) 9.83195i 0.481473i
\(418\) −16.4607 + 6.61100i −0.805120 + 0.323355i
\(419\) 35.6737i 1.74278i −0.490595 0.871388i \(-0.663221\pi\)
0.490595 0.871388i \(-0.336779\pi\)
\(420\) 4.30264 + 2.88073i 0.209947 + 0.140565i
\(421\) 1.24958 0.0609008 0.0304504 0.999536i \(-0.490306\pi\)
0.0304504 + 0.999536i \(0.490306\pi\)
\(422\) −26.0577 −1.26847
\(423\) 6.00233i 0.291843i
\(424\) 3.41245i 0.165723i
\(425\) 27.4768 1.33282
\(426\) 10.0206 0.485502
\(427\) 18.3379 + 12.2777i 0.887435 + 0.594161i
\(428\) 31.8680i 1.54040i
\(429\) 14.0023 5.62366i 0.676039 0.271513i
\(430\) 9.83838i 0.474449i
\(431\) 31.7177i 1.52779i 0.645343 + 0.763893i \(0.276715\pi\)
−0.645343 + 0.763893i \(0.723285\pi\)
\(432\) 3.18178i 0.153083i
\(433\) 13.7273i 0.659693i −0.944035 0.329846i \(-0.893003\pi\)
0.944035 0.329846i \(-0.106997\pi\)
\(434\) 38.3426 + 25.6714i 1.84050 + 1.23227i
\(435\) 0.127213i 0.00609938i
\(436\) 15.7040i 0.752087i
\(437\) 23.5169 1.12497
\(438\) −22.2443 −1.06287
\(439\) −30.4630 −1.45392 −0.726959 0.686680i \(-0.759067\pi\)
−0.726959 + 0.686680i \(0.759067\pi\)
\(440\) 0.748409 + 1.86346i 0.0356790 + 0.0888371i
\(441\) −2.66673 6.47214i −0.126987 0.308197i
\(442\) 60.5457i 2.87987i
\(443\) −16.8613 −0.801106 −0.400553 0.916274i \(-0.631182\pi\)
−0.400553 + 0.916274i \(0.631182\pi\)
\(444\) 12.4595i 0.591302i
\(445\) 6.78265 0.321529
\(446\) −19.7051 −0.933062
\(447\) −14.3816 −0.680226
\(448\) −23.0891 15.4588i −1.09086 0.730357i
\(449\) 30.0652 1.41887 0.709433 0.704773i \(-0.248951\pi\)
0.709433 + 0.704773i \(0.248951\pi\)
\(450\) 8.97820i 0.423236i
\(451\) 3.96959 + 9.88388i 0.186921 + 0.465414i
\(452\) 3.13152 0.147294
\(453\) −2.98506 −0.140250
\(454\) 11.3335i 0.531906i
\(455\) −5.58091 + 8.33560i −0.261637 + 0.390779i
\(456\) 1.86346 0.0872646
\(457\) 7.39433i 0.345892i 0.984931 + 0.172946i \(0.0553286\pi\)
−0.984931 + 0.172946i \(0.944671\pi\)
\(458\) 39.5674 1.84886
\(459\) 6.38178i 0.297876i
\(460\) 17.9445i 0.836665i
\(461\) 17.1351 0.798062 0.399031 0.916938i \(-0.369347\pi\)
0.399031 + 0.916938i \(0.369347\pi\)
\(462\) 3.78001 17.9036i 0.175862 0.832951i
\(463\) 11.6131 0.539708 0.269854 0.962901i \(-0.413025\pi\)
0.269854 + 0.962901i \(0.413025\pi\)
\(464\) 0.485697i 0.0225479i
\(465\) 6.96990i 0.323222i
\(466\) 26.0833 1.20829
\(467\) 6.99786i 0.323823i 0.986805 + 0.161911i \(0.0517658\pi\)
−0.986805 + 0.161911i \(0.948234\pi\)
\(468\) −10.6844 −0.493888
\(469\) −9.53178 6.38178i −0.440137 0.294683i
\(470\) 10.4309i 0.481141i
\(471\) 17.3983 0.801672
\(472\) 0.768724 0.0353834
\(473\) 17.4239 6.99785i 0.801154 0.321762i
\(474\) 11.8914i 0.546191i
\(475\) 11.0429 0.506683
\(476\) 32.9489 + 22.0602i 1.51021 + 1.01113i
\(477\) −4.69683 −0.215053
\(478\) 14.5961 0.667608
\(479\) −5.70597 −0.260712 −0.130356 0.991467i \(-0.541612\pi\)
−0.130356 + 0.991467i \(0.541612\pi\)
\(480\) 6.74026i 0.307650i
\(481\) 24.1381 1.10060
\(482\) 8.85065i 0.403136i
\(483\) −13.4962 + 20.1579i −0.614101 + 0.917216i
\(484\) 18.6564 17.8678i 0.848020 0.812173i
\(485\) −14.7983 −0.671954
\(486\) −2.08529 −0.0945905
\(487\) −28.3981 −1.28684 −0.643421 0.765513i \(-0.722485\pi\)
−0.643421 + 0.765513i \(0.722485\pi\)
\(488\) 6.06019i 0.274332i
\(489\) 4.39152i 0.198591i
\(490\) 4.63426 + 11.2473i 0.209354 + 0.508102i
\(491\) 10.3585i 0.467475i 0.972300 + 0.233737i \(0.0750956\pi\)
−0.972300 + 0.233737i \(0.924904\pi\)
\(492\) 7.54186i 0.340013i
\(493\) 0.974174i 0.0438746i
\(494\) 24.3333i 1.09481i
\(495\) −2.56484 + 1.03010i −0.115281 + 0.0462994i
\(496\) 26.6110i 1.19487i
\(497\) 10.5646 + 7.07331i 0.473889 + 0.317281i
\(498\) −22.4238 −1.00483
\(499\) −3.88621 −0.173971 −0.0869854 0.996210i \(-0.527723\pi\)
−0.0869854 + 0.996210i \(0.527723\pi\)
\(500\) 18.2117i 0.814451i
\(501\) 2.86501i 0.127999i
\(502\) 50.7564 2.26537
\(503\) 11.7922 0.525787 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(504\) −1.06943 + 1.59730i −0.0476364 + 0.0711493i
\(505\) 1.75581i 0.0781324i
\(506\) −58.8450 + 23.6335i −2.61598 + 1.05064i
\(507\) 7.69916i 0.341932i
\(508\) 0.531712i 0.0235909i
\(509\) 23.6895i 1.05002i 0.851097 + 0.525009i \(0.175938\pi\)
−0.851097 + 0.525009i \(0.824062\pi\)
\(510\) 11.0903i 0.491086i
\(511\) −23.4519 15.7017i −1.03745 0.694601i
\(512\) 30.3576i 1.34163i
\(513\) 2.56484i 0.113240i
\(514\) −52.3638 −2.30967
\(515\) 8.84285 0.389662
\(516\) −13.2953 −0.585292
\(517\) −18.4733 + 7.41929i −0.812454 + 0.326300i
\(518\) 16.2849 24.3230i 0.715517 1.06869i
\(519\) 20.4220i 0.896428i
\(520\) 2.75469 0.120801
\(521\) 20.1109i 0.881075i 0.897734 + 0.440537i \(0.145212\pi\)
−0.897734 + 0.440537i \(0.854788\pi\)
\(522\) −0.318317 −0.0139324
\(523\) −34.8202 −1.52258 −0.761290 0.648411i \(-0.775434\pi\)
−0.761290 + 0.648411i \(0.775434\pi\)
\(524\) 0.716968 0.0313209
\(525\) −6.33748 + 9.46561i −0.276590 + 0.413113i
\(526\) −23.1814 −1.01076
\(527\) 53.3744i 2.32503i
\(528\) 9.79251 3.93290i 0.426164 0.171157i
\(529\) 61.0699 2.65521
\(530\) 8.16217 0.354542
\(531\) 1.05806i 0.0459158i
\(532\) 13.2422 + 8.86599i 0.574121 + 0.384389i
\(533\) 14.6110 0.632873
\(534\) 16.9719i 0.734444i
\(535\) −11.3088 −0.488921
\(536\) 3.15000i 0.136059i
\(537\) 4.58825i 0.197998i
\(538\) −26.7029 −1.15124
\(539\) 16.6229 16.2074i 0.716000 0.698100i
\(540\) 1.95709 0.0842196
\(541\) 38.9979i 1.67665i 0.545169 + 0.838326i \(0.316465\pi\)
−0.545169 + 0.838326i \(0.683535\pi\)
\(542\) 32.4946i 1.39576i
\(543\) 6.03029 0.258785
\(544\) 51.6159i 2.21301i
\(545\) 5.57278 0.238712
\(546\) −20.8577 13.9648i −0.892628 0.597638i
\(547\) 19.6262i 0.839155i 0.907720 + 0.419577i \(0.137822\pi\)
−0.907720 + 0.419577i \(0.862178\pi\)
\(548\) 27.6108 1.17948
\(549\) 8.34114 0.355991
\(550\) −27.6321 + 11.0977i −1.17823 + 0.473206i
\(551\) 0.391520i 0.0166793i
\(552\) 6.66164 0.283538
\(553\) 8.39385 12.5370i 0.356943 0.533127i
\(554\) −10.3892 −0.441394
\(555\) −4.42142 −0.187679
\(556\) 23.0895 0.979213
\(557\) 26.6169i 1.12779i −0.825846 0.563896i \(-0.809302\pi\)
0.825846 0.563896i \(-0.190698\pi\)
\(558\) 17.4404 0.738311
\(559\) 25.7572i 1.08941i
\(560\) −3.90300 + 5.82949i −0.164932 + 0.246341i
\(561\) −19.6411 + 7.88831i −0.829248 + 0.333045i
\(562\) 52.6054 2.21902
\(563\) 13.8173 0.582328 0.291164 0.956673i \(-0.405957\pi\)
0.291164 + 0.956673i \(0.405957\pi\)
\(564\) 14.0960 0.593547
\(565\) 1.11126i 0.0467511i
\(566\) 43.2975i 1.81993i
\(567\) −2.19849 1.47195i −0.0923280 0.0618161i
\(568\) 3.49133i 0.146493i
\(569\) 23.8065i 0.998019i −0.866597 0.499009i \(-0.833697\pi\)
0.866597 0.499009i \(-0.166303\pi\)
\(570\) 4.45718i 0.186691i
\(571\) 47.0206i 1.96775i −0.178852 0.983876i \(-0.557238\pi\)
0.178852 0.983876i \(-0.442762\pi\)
\(572\) −13.2067 32.8833i −0.552199 1.37492i
\(573\) 23.7800i 0.993422i
\(574\) 9.85739 14.7229i 0.411440 0.614523i
\(575\) 39.4770 1.64630
\(576\) −10.5022 −0.437593
\(577\) 25.0301i 1.04202i −0.853552 0.521008i \(-0.825556\pi\)
0.853552 0.521008i \(-0.174444\pi\)
\(578\) 49.4778i 2.05801i
\(579\) 4.63569 0.192653
\(580\) 0.298748 0.0124048
\(581\) −23.6411 15.8284i −0.980798 0.656671i
\(582\) 37.0289i 1.53490i
\(583\) −5.80560 14.4554i −0.240443 0.598679i
\(584\) 7.75023i 0.320707i
\(585\) 3.79151i 0.156760i
\(586\) 9.11592i 0.376575i
\(587\) 18.2754i 0.754307i 0.926151 + 0.377153i \(0.123097\pi\)
−0.926151 + 0.377153i \(0.876903\pi\)
\(588\) −15.1993 + 6.26259i −0.626807 + 0.258265i
\(589\) 21.4512i 0.883880i
\(590\) 1.83870i 0.0756980i
\(591\) −6.62048 −0.272330
\(592\) 16.8809 0.693802
\(593\) 15.6189 0.641390 0.320695 0.947183i \(-0.396084\pi\)
0.320695 + 0.947183i \(0.396084\pi\)
\(594\) −2.57755 6.41785i −0.105758 0.263327i
\(595\) 7.82835 11.6924i 0.320931 0.479340i
\(596\) 33.7739i 1.38343i
\(597\) 10.9699 0.448968
\(598\) 86.9885i 3.55723i
\(599\) −20.9864 −0.857480 −0.428740 0.903428i \(-0.641042\pi\)
−0.428740 + 0.903428i \(0.641042\pi\)
\(600\) 3.12813 0.127705
\(601\) −23.0535 −0.940370 −0.470185 0.882568i \(-0.655813\pi\)
−0.470185 + 0.882568i \(0.655813\pi\)
\(602\) −25.9545 17.3772i −1.05783 0.708243i
\(603\) −4.33560 −0.176559
\(604\) 7.01015i 0.285239i
\(605\) −6.34062 6.62048i −0.257783 0.269161i
\(606\) 4.39346 0.178472
\(607\) 6.14682 0.249492 0.124746 0.992189i \(-0.460188\pi\)
0.124746 + 0.992189i \(0.460188\pi\)
\(608\) 20.7444i 0.841296i
\(609\) −0.335598 0.224692i −0.0135991 0.00910498i
\(610\) −14.4953 −0.586897
\(611\) 27.3084i 1.10478i
\(612\) 14.9871 0.605816
\(613\) 36.4382i 1.47173i 0.677131 + 0.735863i \(0.263223\pi\)
−0.677131 + 0.735863i \(0.736777\pi\)
\(614\) 9.34061i 0.376956i
\(615\) −2.67633 −0.107920
\(616\) −6.23787 1.31701i −0.251331 0.0530638i
\(617\) 13.9441 0.561367 0.280684 0.959800i \(-0.409439\pi\)
0.280684 + 0.959800i \(0.409439\pi\)
\(618\) 22.1270i 0.890077i
\(619\) 18.9140i 0.760217i −0.924942 0.380109i \(-0.875887\pi\)
0.924942 0.380109i \(-0.124113\pi\)
\(620\) −16.3682 −0.657363
\(621\) 9.16896i 0.367938i
\(622\) −47.7198 −1.91339
\(623\) −11.9800 + 17.8932i −0.479969 + 0.716877i
\(624\) 14.4759i 0.579501i
\(625\) 15.0649 0.602594
\(626\) 11.0586 0.441992
\(627\) −7.89375 + 3.17031i −0.315246 + 0.126610i
\(628\) 40.8584i 1.63043i
\(629\) −33.8585 −1.35003
\(630\) 3.82055 + 2.55796i 0.152214 + 0.101912i
\(631\) −45.4030 −1.80746 −0.903732 0.428099i \(-0.859184\pi\)
−0.903732 + 0.428099i \(0.859184\pi\)
\(632\) −4.14314 −0.164805
\(633\) −12.4960 −0.496671
\(634\) 46.0747i 1.82986i
\(635\) −0.188685 −0.00748773
\(636\) 11.0301i 0.437372i
\(637\) −12.1326 29.4458i −0.480713 1.16669i
\(638\) −0.393462 0.979680i −0.0155773 0.0387859i
\(639\) 4.80540 0.190099
\(640\) 4.77030 0.188563
\(641\) 7.70129 0.304183 0.152091 0.988366i \(-0.451399\pi\)
0.152091 + 0.988366i \(0.451399\pi\)
\(642\) 28.2973i 1.11681i
\(643\) 19.5852i 0.772364i −0.922423 0.386182i \(-0.873794\pi\)
0.922423 0.386182i \(-0.126206\pi\)
\(644\) 47.3391 + 31.6948i 1.86542 + 1.24895i
\(645\) 4.71800i 0.185771i
\(646\) 34.1324i 1.34292i
\(647\) 24.7896i 0.974581i 0.873240 + 0.487291i \(0.162015\pi\)
−0.873240 + 0.487291i \(0.837985\pi\)
\(648\) 0.726543i 0.0285413i
\(649\) −3.25637 + 1.30783i −0.127824 + 0.0513369i
\(650\) 40.8475i 1.60217i
\(651\) 18.3872 + 12.3107i 0.720652 + 0.482496i
\(652\) −10.3131 −0.403892
\(653\) 10.2731 0.402017 0.201008 0.979590i \(-0.435578\pi\)
0.201008 + 0.979590i \(0.435578\pi\)
\(654\) 13.9445i 0.545272i
\(655\) 0.254425i 0.00994122i
\(656\) 10.2182 0.398953
\(657\) −10.6673 −0.416170
\(658\) 27.5176 + 18.4238i 1.07275 + 0.718233i
\(659\) 18.6488i 0.726455i −0.931701 0.363227i \(-0.881675\pi\)
0.931701 0.363227i \(-0.118325\pi\)
\(660\) 2.41909 + 6.02330i 0.0941631 + 0.234456i
\(661\) 46.2521i 1.79900i 0.436922 + 0.899499i \(0.356068\pi\)
−0.436922 + 0.899499i \(0.643932\pi\)
\(662\) 41.1460i 1.59918i
\(663\) 29.0348i 1.12762i
\(664\) 7.81275i 0.303193i
\(665\) 3.14621 4.69916i 0.122005 0.182226i
\(666\) 11.0635i 0.428701i
\(667\) 1.39964i 0.0541941i
\(668\) 6.72824 0.260323
\(669\) −9.44958 −0.365342
\(670\) 7.53442 0.291080
\(671\) 10.3102 + 25.6714i 0.398021 + 0.991033i
\(672\) −17.7814 11.9051i −0.685933 0.459250i
\(673\) 24.9823i 0.962996i 0.876447 + 0.481498i \(0.159907\pi\)
−0.876447 + 0.481498i \(0.840093\pi\)
\(674\) −65.4888 −2.52253
\(675\) 4.30550i 0.165719i
\(676\) −18.0808 −0.695416
\(677\) −0.707252 −0.0271819 −0.0135909 0.999908i \(-0.504326\pi\)
−0.0135909 + 0.999908i \(0.504326\pi\)
\(678\) 2.78065 0.106790
\(679\) 26.1377 39.0391i 1.00307 1.49818i
\(680\) −3.86401 −0.148178
\(681\) 5.43497i 0.208269i
\(682\) 21.5575 + 53.6760i 0.825480 + 2.05536i
\(683\) −33.2295 −1.27149 −0.635747 0.771898i \(-0.719308\pi\)
−0.635747 + 0.771898i \(0.719308\pi\)
\(684\) 6.02330 0.230306
\(685\) 9.79806i 0.374365i
\(686\) −37.8567 7.64021i −1.44538 0.291705i
\(687\) 18.9746 0.723925
\(688\) 18.0133i 0.686750i
\(689\) −21.3688 −0.814088
\(690\) 15.9339i 0.606592i
\(691\) 2.11146i 0.0803236i 0.999193 + 0.0401618i \(0.0127873\pi\)
−0.999193 + 0.0401618i \(0.987213\pi\)
\(692\) −47.9594 −1.82314
\(693\) 1.81271 8.58569i 0.0688591 0.326143i
\(694\) 14.8959 0.565440
\(695\) 8.19361i 0.310801i
\(696\) 0.110906i 0.00420389i
\(697\) −20.4949 −0.776299
\(698\) 25.3000i 0.957620i
\(699\) 12.5083 0.473107
\(700\) 22.2292 + 14.8830i 0.840184 + 0.562525i
\(701\) 3.16145i 0.119406i 0.998216 + 0.0597031i \(0.0190154\pi\)
−0.998216 + 0.0597031i \(0.980985\pi\)
\(702\) −9.48728 −0.358074
\(703\) −13.6077 −0.513226
\(704\) −12.9815 32.3225i −0.489258 1.21820i
\(705\) 5.00214i 0.188391i
\(706\) 30.6897 1.15502
\(707\) 4.63198 + 3.10123i 0.174203 + 0.116634i
\(708\) 2.48476 0.0933829
\(709\) −37.2542 −1.39911 −0.699556 0.714578i \(-0.746619\pi\)
−0.699556 + 0.714578i \(0.746619\pi\)
\(710\) −8.35086 −0.313402
\(711\) 5.70254i 0.213862i
\(712\) 5.91323 0.221608
\(713\) 76.6852i 2.87188i
\(714\) 29.2572 + 19.5885i 1.09492 + 0.733079i
\(715\) −11.6691 + 4.68656i −0.436398 + 0.175267i
\(716\) −10.7751 −0.402685
\(717\) 6.99955 0.261403
\(718\) 13.6739 0.510305
\(719\) 21.3405i 0.795865i 0.917415 + 0.397932i \(0.130272\pi\)
−0.917415 + 0.397932i \(0.869728\pi\)
\(720\) 2.65159i 0.0988188i
\(721\) −15.6189 + 23.3282i −0.581677 + 0.868788i
\(722\) 25.9026i 0.963995i
\(723\) 4.24433i 0.157848i
\(724\) 14.1616i 0.526312i
\(725\) 0.657232i 0.0244090i
\(726\) 16.5661 15.8658i 0.614825 0.588835i
\(727\) 13.7013i 0.508153i 0.967184 + 0.254076i \(0.0817715\pi\)
−0.967184 + 0.254076i \(0.918229\pi\)
\(728\) −4.86553 + 7.26712i −0.180329 + 0.269337i
\(729\) −1.00000 −0.0370370
\(730\) 18.5376 0.686109
\(731\) 36.1297i 1.33631i
\(732\) 19.5885i 0.724010i
\(733\) 14.7641 0.545324 0.272662 0.962110i \(-0.412096\pi\)
0.272662 + 0.962110i \(0.412096\pi\)
\(734\) −68.1385 −2.51504
\(735\) 2.22236 + 5.39366i 0.0819731 + 0.198948i
\(736\) 74.1586i 2.73352i
\(737\) −5.35909 13.3436i −0.197405 0.491518i
\(738\) 6.69683i 0.246514i
\(739\) 32.3486i 1.18996i −0.803740 0.594981i \(-0.797160\pi\)
0.803740 0.594981i \(-0.202840\pi\)
\(740\) 10.3833i 0.381699i
\(741\) 11.6691i 0.428674i
\(742\) −14.4166 + 21.5325i −0.529250 + 0.790484i
\(743\) 2.71032i 0.0994318i −0.998763 0.0497159i \(-0.984168\pi\)
0.998763 0.0497159i \(-0.0158316\pi\)
\(744\) 6.07648i 0.222775i
\(745\) 11.9851 0.439101
\(746\) 45.6760 1.67232
\(747\) −10.7533 −0.393444
\(748\) 18.5250 + 46.1254i 0.677342 + 1.68651i
\(749\) 19.9744 29.8336i 0.729848 1.09009i
\(750\) 16.1711i 0.590487i
\(751\) −9.39637 −0.342879 −0.171439 0.985195i \(-0.554842\pi\)
−0.171439 + 0.985195i \(0.554842\pi\)
\(752\) 19.0981i 0.696436i
\(753\) 24.3403 0.887008
\(754\) −1.44823 −0.0527413
\(755\) 2.48764 0.0905346
\(756\) −3.45675 + 5.16297i −0.125721 + 0.187775i
\(757\) 11.9724 0.435145 0.217573 0.976044i \(-0.430186\pi\)
0.217573 + 0.976044i \(0.430186\pi\)
\(758\) 29.1988i 1.06055i
\(759\) −28.2192 + 11.3335i −1.02429 + 0.411379i
\(760\) −1.55295 −0.0563313
\(761\) 15.5977 0.565415 0.282707 0.959206i \(-0.408767\pi\)
0.282707 + 0.959206i \(0.408767\pi\)
\(762\) 0.472136i 0.0171037i
\(763\) −9.84304 + 14.7015i −0.356342 + 0.532230i
\(764\) −55.8452 −2.02041
\(765\) 5.31836i 0.192286i
\(766\) 14.7132 0.531610
\(767\) 4.81377i 0.173815i
\(768\) 9.06799i 0.327213i
\(769\) 15.4093 0.555675 0.277837 0.960628i \(-0.410382\pi\)
0.277837 + 0.960628i \(0.410382\pi\)
\(770\) −3.15013 + 14.9203i −0.113523 + 0.537689i
\(771\) −25.1111 −0.904354
\(772\) 10.8865i 0.391814i
\(773\) 1.78230i 0.0641048i 0.999486 + 0.0320524i \(0.0102043\pi\)
−0.999486 + 0.0320524i \(0.989796\pi\)
\(774\) −11.8056 −0.424343
\(775\) 36.0093i 1.29349i
\(776\) −12.9014 −0.463132
\(777\) 7.80943 11.6641i 0.280162 0.418447i
\(778\) 5.10766i 0.183119i
\(779\) −8.23689 −0.295117
\(780\) 8.90403 0.318815
\(781\) 5.93981 + 14.7895i 0.212543 + 0.529210i
\(782\) 122.019i 4.36339i
\(783\) −0.152649 −0.00545524
\(784\) −8.48495 20.5929i −0.303034 0.735461i
\(785\) −14.4992 −0.517497
\(786\) 0.636635 0.0227080
\(787\) −1.57687 −0.0562093 −0.0281046 0.999605i \(-0.508947\pi\)
−0.0281046 + 0.999605i \(0.508947\pi\)
\(788\) 15.5476i 0.553862i
\(789\) −11.1167 −0.395764
\(790\) 9.90990i 0.352579i
\(791\) 2.93161 + 1.96279i 0.104236 + 0.0697888i
\(792\) −2.23607 + 0.898056i −0.0794552 + 0.0319110i
\(793\) 37.9491 1.34761
\(794\) 9.91975 0.352039
\(795\) 3.91418 0.138821
\(796\) 25.7619i 0.913105i
\(797\) 16.8334i 0.596268i 0.954524 + 0.298134i \(0.0963643\pi\)
−0.954524 + 0.298134i \(0.903636\pi\)
\(798\) 11.7584 + 7.87259i 0.416244 + 0.278687i
\(799\) 38.3055i 1.35515i
\(800\) 34.8229i 1.23118i
\(801\) 8.13887i 0.287573i
\(802\) 38.3030i 1.35252i
\(803\) −13.1855 32.8305i −0.465305 1.15856i
\(804\) 10.1818i 0.359084i
\(805\) 11.2473 16.7989i 0.396416 0.592083i
\(806\) 79.3474 2.79489
\(807\) −12.8054 −0.450772
\(808\) 1.53074i 0.0538514i
\(809\) 22.2453i 0.782104i −0.920369 0.391052i \(-0.872111\pi\)
0.920369 0.391052i \(-0.127889\pi\)
\(810\) 1.73781 0.0610602
\(811\) −44.2460 −1.55369 −0.776843 0.629695i \(-0.783180\pi\)
−0.776843 + 0.629695i \(0.783180\pi\)
\(812\) −0.527670 + 0.788124i −0.0185176 + 0.0276577i
\(813\) 15.5828i 0.546513i
\(814\) 34.0499 13.6752i 1.19345 0.479316i
\(815\) 3.65974i 0.128195i
\(816\) 20.3054i 0.710832i
\(817\) 14.5205i 0.508009i
\(818\) 72.4074i 2.53167i
\(819\) −10.0023 6.69683i −0.349510 0.234006i
\(820\) 6.28513i 0.219486i
\(821\) 1.97420i 0.0689000i 0.999406 + 0.0344500i \(0.0109679\pi\)
−0.999406 + 0.0344500i \(0.989032\pi\)
\(822\) 24.5171 0.855134
\(823\) −2.45171 −0.0854614 −0.0427307 0.999087i \(-0.513606\pi\)
−0.0427307 + 0.999087i \(0.513606\pi\)
\(824\) 7.70935 0.268568
\(825\) −13.2510 + 5.32189i −0.461340 + 0.185285i
\(826\) 4.85065 + 3.24764i 0.168776 + 0.113000i
\(827\) 25.4279i 0.884215i −0.896962 0.442108i \(-0.854231\pi\)
0.896962 0.442108i \(-0.145769\pi\)
\(828\) 21.5325 0.748307
\(829\) 36.0606i 1.25244i 0.779648 + 0.626218i \(0.215398\pi\)
−0.779648 + 0.626218i \(0.784602\pi\)
\(830\) 18.6872 0.648642
\(831\) −4.98214 −0.172829
\(832\) −47.7813 −1.65652
\(833\) 17.0185 + 41.3037i 0.589656 + 1.43109i
\(834\) 20.5024 0.709941
\(835\) 2.38760i 0.0826264i
\(836\) 7.44520 + 18.5378i 0.257498 + 0.641143i
\(837\) 8.36356 0.289087
\(838\) −74.3899 −2.56976
\(839\) 20.1790i 0.696657i 0.937372 + 0.348329i \(0.113251\pi\)
−0.937372 + 0.348329i \(0.886749\pi\)
\(840\) 0.891229 1.33113i 0.0307503 0.0459285i
\(841\) 28.9767 0.999196
\(842\) 2.60573i 0.0897994i
\(843\) 25.2269 0.868862
\(844\) 29.3458i 1.01012i
\(845\) 6.41621i 0.220724i
\(846\) 12.5166 0.430328
\(847\) 28.6647 5.03355i 0.984930 0.172955i
\(848\) −14.9443 −0.513188
\(849\) 20.7634i 0.712597i
\(850\) 57.2969i 1.96527i
\(851\) −48.6460 −1.66756
\(852\) 11.2851i 0.386620i
\(853\) 31.3640 1.07388 0.536942 0.843619i \(-0.319579\pi\)
0.536942 + 0.843619i \(0.319579\pi\)
\(854\) 25.6026 38.2398i 0.876102 1.30854i
\(855\) 2.13745i 0.0730991i
\(856\) −9.85919 −0.336980
\(857\) −6.51959 −0.222705 −0.111353 0.993781i \(-0.535518\pi\)
−0.111353 + 0.993781i \(0.535518\pi\)
\(858\) −11.7269 29.1988i −0.400351 0.996832i
\(859\) 39.4585i 1.34631i 0.739503 + 0.673153i \(0.235061\pi\)
−0.739503 + 0.673153i \(0.764939\pi\)
\(860\) 11.0798 0.377819
\(861\) 4.72712 7.06039i 0.161100 0.240617i
\(862\) 66.1404 2.25275
\(863\) 23.0120 0.783338 0.391669 0.920106i \(-0.371898\pi\)
0.391669 + 0.920106i \(0.371898\pi\)
\(864\) −8.08800 −0.275159
\(865\) 17.0190i 0.578664i
\(866\) −28.6254 −0.972729
\(867\) 23.7271i 0.805815i
\(868\) 28.9107 43.1808i 0.981293 1.46565i
\(869\) 17.5506 7.04873i 0.595364 0.239112i
\(870\) 0.265275 0.00899366
\(871\) −19.7254 −0.668369
\(872\) 4.85845 0.164528
\(873\) 17.7572i 0.600991i
\(874\) 49.0394i 1.65878i
\(875\) 11.4148 17.0491i 0.385891 0.576363i
\(876\) 25.0512i 0.846401i
\(877\) 25.6849i 0.867317i −0.901077 0.433659i \(-0.857222\pi\)
0.901077 0.433659i \(-0.142778\pi\)
\(878\) 63.5240i 2.14383i
\(879\) 4.37155i 0.147449i
\(880\) −8.16074 + 3.27754i −0.275099 + 0.110486i
\(881\) 5.88948i 0.198422i 0.995066 + 0.0992108i \(0.0316318\pi\)
−0.995066 + 0.0992108i \(0.968368\pi\)
\(882\) −13.4962 + 5.56090i −0.454442 + 0.187245i
\(883\) −38.5578 −1.29757 −0.648787 0.760970i \(-0.724723\pi\)
−0.648787 + 0.760970i \(0.724723\pi\)
\(884\) 68.1856 2.29333
\(885\) 0.881749i 0.0296397i
\(886\) 35.1607i 1.18125i
\(887\) −52.9627 −1.77831 −0.889157 0.457602i \(-0.848709\pi\)
−0.889157 + 0.457602i \(0.848709\pi\)
\(888\) −3.85467 −0.129354
\(889\) 0.333269 0.497767i 0.0111775 0.0166946i
\(890\) 14.1438i 0.474100i
\(891\) −1.23607 3.07768i −0.0414098 0.103106i
\(892\) 22.1915i 0.743027i
\(893\) 15.3950i 0.515174i
\(894\) 29.9897i 1.00301i
\(895\) 3.82369i 0.127812i
\(896\) −8.42565 + 12.5845i −0.281481 + 0.420418i
\(897\) 41.7154i 1.39284i
\(898\) 62.6946i 2.09215i
\(899\) 1.27669 0.0425801
\(900\) 10.1111 0.337037
\(901\) 29.9741 0.998583
\(902\) 20.6107 8.27773i 0.686262 0.275618i
\(903\) −12.4465 8.33327i −0.414194 0.277314i
\(904\) 0.968817i 0.0322224i
\(905\) −5.02544 −0.167051
\(906\) 6.22469i 0.206802i
\(907\) 15.7828 0.524061 0.262030 0.965060i \(-0.415608\pi\)
0.262030 + 0.965060i \(0.415608\pi\)
\(908\) −12.7636 −0.423574
\(909\) 2.10689 0.0698811
\(910\) 17.3821 + 11.6378i 0.576211 + 0.385789i
\(911\) −19.9066 −0.659536 −0.329768 0.944062i \(-0.606971\pi\)
−0.329768 + 0.944062i \(0.606971\pi\)
\(912\) 8.16074i 0.270229i
\(913\) −13.2918 33.0953i −0.439896 1.09530i
\(914\) 15.4193 0.510025
\(915\) −6.95122 −0.229800
\(916\) 44.5601i 1.47231i
\(917\) 0.671197 + 0.449384i 0.0221649 + 0.0148400i
\(918\) 13.3078 0.439224
\(919\) 49.7644i 1.64158i 0.571233 + 0.820788i \(0.306465\pi\)
−0.571233 + 0.820788i \(0.693535\pi\)
\(920\) −5.55158 −0.183030
\(921\) 4.47930i 0.147598i
\(922\) 35.7316i 1.17676i
\(923\) 21.8628 0.719624
\(924\) −20.1628 4.25699i −0.663306 0.140045i
\(925\) −22.8428 −0.751068
\(926\) 24.2167i 0.795810i
\(927\) 10.6110i 0.348511i
\(928\) −1.23463 −0.0405287
\(929\) 30.3929i 0.997159i 0.866844 + 0.498580i \(0.166145\pi\)
−0.866844 + 0.498580i \(0.833855\pi\)
\(930\) −14.5342 −0.476596
\(931\) 6.83973 + 16.6000i 0.224163 + 0.544042i
\(932\) 29.3746i 0.962198i
\(933\) −22.8841 −0.749191
\(934\) 14.5925 0.477483
\(935\) 16.3682 6.57385i 0.535298 0.214988i
\(936\) 3.30550i 0.108044i
\(937\) −31.4972 −1.02897 −0.514485 0.857499i \(-0.672017\pi\)
−0.514485 + 0.857499i \(0.672017\pi\)
\(938\) −13.3078 + 19.8765i −0.434516 + 0.648990i
\(939\) 5.30317 0.173062
\(940\) −11.7471 −0.383148
\(941\) 11.1507 0.363501 0.181751 0.983345i \(-0.441824\pi\)
0.181751 + 0.983345i \(0.441824\pi\)
\(942\) 36.2804i 1.18208i
\(943\) −29.4458 −0.958889
\(944\) 3.36651i 0.109570i
\(945\) 1.83215 + 1.22667i 0.0595998 + 0.0399036i
\(946\) −14.5925 36.3339i −0.474444 1.18132i
\(947\) 41.5978 1.35175 0.675873 0.737018i \(-0.263767\pi\)
0.675873 + 0.737018i \(0.263767\pi\)
\(948\) −13.3919 −0.434950
\(949\) −48.5322 −1.57542
\(950\) 23.0276i 0.747114i
\(951\) 22.0951i 0.716484i
\(952\) 6.82489 10.1936i 0.221196 0.330377i
\(953\) 50.6311i 1.64010i 0.572290 + 0.820051i \(0.306055\pi\)
−0.572290 + 0.820051i \(0.693945\pi\)
\(954\) 9.79423i 0.317100i
\(955\) 19.8174i 0.641276i
\(956\) 16.4378i 0.531638i
\(957\) −0.188685 0.469806i −0.00609932 0.0151867i
\(958\) 11.8986i 0.384425i
\(959\) 25.8481 + 17.3060i 0.834680 + 0.558841i
\(960\) 8.75220 0.282476
\(961\) −38.9491 −1.25642
\(962\) 50.3348i 1.62286i
\(963\) 13.5700i 0.437288i
\(964\) 9.96745 0.321030
\(965\) −3.86322 −0.124362
\(966\) 42.0350 + 28.1435i 1.35245 + 0.905503i
\(967\) 42.1819i 1.35648i 0.734841 + 0.678240i \(0.237257\pi\)
−0.734841 + 0.678240i \(0.762743\pi\)
\(968\) −5.52786 5.77185i −0.177672 0.185514i
\(969\) 16.3682i 0.525823i
\(970\) 30.8586i 0.990809i
\(971\) 13.7805i 0.442238i 0.975247 + 0.221119i \(0.0709709\pi\)
−0.975247 + 0.221119i \(0.929029\pi\)
\(972\) 2.34841i 0.0753254i
\(973\) 21.6155 + 14.4721i 0.692960 + 0.463955i
\(974\) 59.2182i 1.89747i
\(975\) 19.5885i 0.627332i
\(976\) 26.5397 0.849514
\(977\) 32.4238 1.03733 0.518664 0.854978i \(-0.326430\pi\)
0.518664 + 0.854978i \(0.326430\pi\)
\(978\) −9.15757 −0.292827
\(979\) −25.0489 + 10.0602i −0.800565 + 0.321525i
\(980\) 12.6665 5.21903i 0.404618 0.166716i
\(981\) 6.68708i 0.213502i
\(982\) 21.6005 0.689300
\(983\) 6.88408i 0.219568i −0.993955 0.109784i \(-0.964984\pi\)
0.993955 0.109784i \(-0.0350159\pi\)
\(984\) −2.33327 −0.0743819
\(985\) 5.51728 0.175795
\(986\) 2.03143 0.0646940
\(987\) 13.1961 + 8.83512i 0.420036 + 0.281225i
\(988\) 27.4038 0.871831
\(989\) 51.9090i 1.65061i
\(990\) 2.14805 + 5.34841i 0.0682694 + 0.169984i
\(991\) −9.45618 −0.300385 −0.150193 0.988657i \(-0.547989\pi\)
−0.150193 + 0.988657i \(0.547989\pi\)
\(992\) 67.6445 2.14771
\(993\) 19.7316i 0.626163i
\(994\) 14.7499 22.0303i 0.467837 0.698758i
\(995\) −9.14194 −0.289819
\(996\) 25.2533i 0.800180i
\(997\) 10.2348 0.324138 0.162069 0.986779i \(-0.448183\pi\)
0.162069 + 0.986779i \(0.448183\pi\)
\(998\) 8.10386i 0.256523i
\(999\) 5.30550i 0.167859i
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 231.2.c.a.76.3 16
3.2 odd 2 693.2.c.e.307.13 16
4.3 odd 2 3696.2.q.e.769.14 16
7.6 odd 2 inner 231.2.c.a.76.4 yes 16
11.10 odd 2 inner 231.2.c.a.76.13 yes 16
21.20 even 2 693.2.c.e.307.14 16
28.27 even 2 3696.2.q.e.769.3 16
33.32 even 2 693.2.c.e.307.3 16
44.43 even 2 3696.2.q.e.769.13 16
77.76 even 2 inner 231.2.c.a.76.14 yes 16
231.230 odd 2 693.2.c.e.307.4 16
308.307 odd 2 3696.2.q.e.769.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.c.a.76.3 16 1.1 even 1 trivial
231.2.c.a.76.4 yes 16 7.6 odd 2 inner
231.2.c.a.76.13 yes 16 11.10 odd 2 inner
231.2.c.a.76.14 yes 16 77.76 even 2 inner
693.2.c.e.307.3 16 33.32 even 2
693.2.c.e.307.4 16 231.230 odd 2
693.2.c.e.307.13 16 3.2 odd 2
693.2.c.e.307.14 16 21.20 even 2
3696.2.q.e.769.3 16 28.27 even 2
3696.2.q.e.769.4 16 308.307 odd 2
3696.2.q.e.769.13 16 44.43 even 2
3696.2.q.e.769.14 16 4.3 odd 2