Properties

Label 93.2.c.a.92.5
Level $93$
Weight $2$
Character 93.92
Analytic conductor $0.743$
Analytic rank $0$
Dimension $8$
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] = [93,2,Mod(92,93)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(93, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("93.92");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 93.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: \(0.742608738798\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.16845963264.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 6x^{6} + 15x^{4} + 8x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 92.5
Root \(1.95007 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 93.92
Dual form 93.2.c.a.92.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.835000i q^{2} +(-0.590434 - 1.62831i) q^{3} +1.30278 q^{4} -2.75782i q^{5} +(1.35964 - 0.493012i) q^{6} -1.00000 q^{7} +2.75782i q^{8} +(-2.30278 + 1.92282i) q^{9} +O(q^{10})\) \(q+0.835000i q^{2} +(-0.590434 - 1.62831i) q^{3} +1.30278 q^{4} -2.75782i q^{5} +(1.35964 - 0.493012i) q^{6} -1.00000 q^{7} +2.75782i q^{8} +(-2.30278 + 1.92282i) q^{9} +2.30278 q^{10} +5.08101 q^{11} +(-0.769203 - 2.12132i) q^{12} +4.24264i q^{13} -0.835000i q^{14} +(-4.49058 + 1.62831i) q^{15} +0.302776 q^{16} -6.61941 q^{17} +(-1.60555 - 1.92282i) q^{18} -3.60555 q^{19} -3.59282i q^{20} +(0.590434 + 1.62831i) q^{21} +4.24264i q^{22} +1.53841 q^{23} +(4.49058 - 1.62831i) q^{24} -2.60555 q^{25} -3.54260 q^{26} +(4.49058 + 2.61433i) q^{27} -1.30278 q^{28} -1.53841 q^{29} +(-1.35964 - 3.74963i) q^{30} +(3.60555 - 4.24264i) q^{31} +5.76845i q^{32} +(-3.00000 - 8.27345i) q^{33} -5.52721i q^{34} +2.75782i q^{35} +(-3.00000 + 2.50500i) q^{36} +5.52721i q^{37} -3.01063i q^{38} +(6.90833 - 2.50500i) q^{39} +7.60555 q^{40} +6.60345i q^{41} +(-1.35964 + 0.493012i) q^{42} -4.24264i q^{43} +6.61941 q^{44} +(5.30278 + 6.35063i) q^{45} +1.28457i q^{46} -3.84563i q^{47} +(-0.178769 - 0.493012i) q^{48} -6.00000 q^{49} -2.17563i q^{50} +(3.90833 + 10.7784i) q^{51} +5.52721i q^{52} +(-2.18297 + 3.74963i) q^{54} -14.0125i q^{55} -2.75782i q^{56} +(2.12884 + 5.87095i) q^{57} -1.28457i q^{58} -2.75782i q^{59} +(-5.85021 + 2.12132i) q^{60} -9.76985i q^{61} +(3.54260 + 3.01063i) q^{62} +(2.30278 - 1.92282i) q^{63} -4.21110 q^{64} +11.7004 q^{65} +(6.90833 - 2.50500i) q^{66} -0.605551 q^{67} -8.62361 q^{68} +(-0.908327 - 2.50500i) q^{69} -2.30278 q^{70} -4.93345i q^{71} +(-5.30278 - 6.35063i) q^{72} -5.52721i q^{73} -4.61522 q^{74} +(1.53841 + 4.24264i) q^{75} -4.69722 q^{76} -5.08101 q^{77} +(2.09167 + 5.76845i) q^{78} +1.28457i q^{79} -0.835000i q^{80} +(1.60555 - 8.85563i) q^{81} -5.51388 q^{82} -10.1620 q^{83} +(0.769203 + 2.12132i) q^{84} +18.2551i q^{85} +3.54260 q^{86} +(0.908327 + 2.50500i) q^{87} +14.0125i q^{88} +6.61941 q^{89} +(-5.30278 + 4.42782i) q^{90} -4.24264i q^{91} +2.00420 q^{92} +(-9.03717 - 3.36595i) q^{93} +3.21110 q^{94} +9.94345i q^{95} +(9.39282 - 3.40589i) q^{96} -8.81665 q^{97} -5.01000i q^{98} +(-11.7004 + 9.76985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{4} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{4} - 8 q^{7} - 4 q^{9} + 4 q^{10} - 12 q^{16} + 16 q^{18} + 8 q^{25} + 4 q^{28} - 24 q^{33} - 24 q^{36} + 12 q^{39} + 32 q^{40} + 28 q^{45} - 48 q^{49} - 12 q^{51} + 4 q^{63} + 24 q^{64} + 12 q^{66} + 24 q^{67} + 36 q^{69} - 4 q^{70} - 28 q^{72} - 52 q^{76} + 60 q^{78} - 16 q^{81} + 28 q^{82} - 36 q^{87} - 28 q^{90} - 12 q^{93} - 32 q^{94} + 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(34\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.835000i 0.590434i 0.955430 + 0.295217i \(0.0953919\pi\)
−0.955430 + 0.295217i \(0.904608\pi\)
\(3\) −0.590434 1.62831i −0.340887 0.940104i
\(4\) 1.30278 0.651388
\(5\) 2.75782i 1.23333i −0.787225 0.616666i \(-0.788483\pi\)
0.787225 0.616666i \(-0.211517\pi\)
\(6\) 1.35964 0.493012i 0.555069 0.201271i
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 2.75782i 0.975035i
\(9\) −2.30278 + 1.92282i −0.767592 + 0.640939i
\(10\) 2.30278 0.728202
\(11\) 5.08101 1.53198 0.765991 0.642851i \(-0.222249\pi\)
0.765991 + 0.642851i \(0.222249\pi\)
\(12\) −0.769203 2.12132i −0.222050 0.612372i
\(13\) 4.24264i 1.17670i 0.808608 + 0.588348i \(0.200222\pi\)
−0.808608 + 0.588348i \(0.799778\pi\)
\(14\) 0.835000i 0.223163i
\(15\) −4.49058 + 1.62831i −1.15946 + 0.420427i
\(16\) 0.302776 0.0756939
\(17\) −6.61941 −1.60544 −0.802722 0.596353i \(-0.796616\pi\)
−0.802722 + 0.596353i \(0.796616\pi\)
\(18\) −1.60555 1.92282i −0.378432 0.453212i
\(19\) −3.60555 −0.827170 −0.413585 0.910465i \(-0.635724\pi\)
−0.413585 + 0.910465i \(0.635724\pi\)
\(20\) 3.59282i 0.803378i
\(21\) 0.590434 + 1.62831i 0.128843 + 0.355326i
\(22\) 4.24264i 0.904534i
\(23\) 1.53841 0.320780 0.160390 0.987054i \(-0.448725\pi\)
0.160390 + 0.987054i \(0.448725\pi\)
\(24\) 4.49058 1.62831i 0.916635 0.332377i
\(25\) −2.60555 −0.521110
\(26\) −3.54260 −0.694762
\(27\) 4.49058 + 2.61433i 0.864212 + 0.503129i
\(28\) −1.30278 −0.246201
\(29\) −1.53841 −0.285675 −0.142837 0.989746i \(-0.545623\pi\)
−0.142837 + 0.989746i \(0.545623\pi\)
\(30\) −1.35964 3.74963i −0.248235 0.684585i
\(31\) 3.60555 4.24264i 0.647576 0.762001i
\(32\) 5.76845i 1.01973i
\(33\) −3.00000 8.27345i −0.522233 1.44022i
\(34\) 5.52721i 0.947909i
\(35\) 2.75782i 0.466156i
\(36\) −3.00000 + 2.50500i −0.500000 + 0.417500i
\(37\) 5.52721i 0.908668i 0.890832 + 0.454334i \(0.150123\pi\)
−0.890832 + 0.454334i \(0.849877\pi\)
\(38\) 3.01063i 0.488389i
\(39\) 6.90833 2.50500i 1.10622 0.401121i
\(40\) 7.60555 1.20254
\(41\) 6.60345i 1.03129i 0.856804 + 0.515643i \(0.172447\pi\)
−0.856804 + 0.515643i \(0.827553\pi\)
\(42\) −1.35964 + 0.493012i −0.209797 + 0.0760734i
\(43\) 4.24264i 0.646997i −0.946229 0.323498i \(-0.895141\pi\)
0.946229 0.323498i \(-0.104859\pi\)
\(44\) 6.61941 0.997914
\(45\) 5.30278 + 6.35063i 0.790491 + 0.946696i
\(46\) 1.28457i 0.189399i
\(47\) 3.84563i 0.560943i −0.959862 0.280472i \(-0.909509\pi\)
0.959862 0.280472i \(-0.0904909\pi\)
\(48\) −0.178769 0.493012i −0.0258031 0.0711602i
\(49\) −6.00000 −0.857143
\(50\) 2.17563i 0.307681i
\(51\) 3.90833 + 10.7784i 0.547275 + 1.50928i
\(52\) 5.52721i 0.766486i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) −2.18297 + 3.74963i −0.297064 + 0.510260i
\(55\) 14.0125i 1.88944i
\(56\) 2.75782i 0.368529i
\(57\) 2.12884 + 5.87095i 0.281972 + 0.777626i
\(58\) 1.28457i 0.168672i
\(59\) 2.75782i 0.359037i −0.983755 0.179519i \(-0.942546\pi\)
0.983755 0.179519i \(-0.0574540\pi\)
\(60\) −5.85021 + 2.12132i −0.755259 + 0.273861i
\(61\) 9.76985i 1.25090i −0.780264 0.625451i \(-0.784915\pi\)
0.780264 0.625451i \(-0.215085\pi\)
\(62\) 3.54260 + 3.01063i 0.449911 + 0.382351i
\(63\) 2.30278 1.92282i 0.290122 0.242252i
\(64\) −4.21110 −0.526388
\(65\) 11.7004 1.45126
\(66\) 6.90833 2.50500i 0.850356 0.308344i
\(67\) −0.605551 −0.0739799 −0.0369899 0.999316i \(-0.511777\pi\)
−0.0369899 + 0.999316i \(0.511777\pi\)
\(68\) −8.62361 −1.04577
\(69\) −0.908327 2.50500i −0.109350 0.301566i
\(70\) −2.30278 −0.275234
\(71\) 4.93345i 0.585493i −0.956190 0.292746i \(-0.905431\pi\)
0.956190 0.292746i \(-0.0945692\pi\)
\(72\) −5.30278 6.35063i −0.624938 0.748429i
\(73\) 5.52721i 0.646911i −0.946243 0.323455i \(-0.895155\pi\)
0.946243 0.323455i \(-0.104845\pi\)
\(74\) −4.61522 −0.536508
\(75\) 1.53841 + 4.24264i 0.177640 + 0.489898i
\(76\) −4.69722 −0.538809
\(77\) −5.08101 −0.579035
\(78\) 2.09167 + 5.76845i 0.236835 + 0.653148i
\(79\) 1.28457i 0.144525i 0.997386 + 0.0722626i \(0.0230220\pi\)
−0.997386 + 0.0722626i \(0.976978\pi\)
\(80\) 0.835000i 0.0933558i
\(81\) 1.60555 8.85563i 0.178395 0.983959i
\(82\) −5.51388 −0.608906
\(83\) −10.1620 −1.11543 −0.557713 0.830034i \(-0.688321\pi\)
−0.557713 + 0.830034i \(0.688321\pi\)
\(84\) 0.769203 + 2.12132i 0.0839269 + 0.231455i
\(85\) 18.2551i 1.98005i
\(86\) 3.54260 0.382009
\(87\) 0.908327 + 2.50500i 0.0973829 + 0.268564i
\(88\) 14.0125i 1.49374i
\(89\) 6.61941 0.701657 0.350828 0.936440i \(-0.385900\pi\)
0.350828 + 0.936440i \(0.385900\pi\)
\(90\) −5.30278 + 4.42782i −0.558962 + 0.466733i
\(91\) 4.24264i 0.444750i
\(92\) 2.00420 0.208952
\(93\) −9.03717 3.36595i −0.937111 0.349033i
\(94\) 3.21110 0.331200
\(95\) 9.94345i 1.02018i
\(96\) 9.39282 3.40589i 0.958650 0.347612i
\(97\) −8.81665 −0.895196 −0.447598 0.894235i \(-0.647720\pi\)
−0.447598 + 0.894235i \(0.647720\pi\)
\(98\) 5.01000i 0.506086i
\(99\) −11.7004 + 9.76985i −1.17594 + 0.981907i
\(100\) −3.39445 −0.339445
\(101\) 11.6134i 1.15558i 0.816185 + 0.577791i \(0.196085\pi\)
−0.816185 + 0.577791i \(0.803915\pi\)
\(102\) −9.00000 + 3.26345i −0.891133 + 0.323130i
\(103\) 16.2111 1.59733 0.798664 0.601778i \(-0.205541\pi\)
0.798664 + 0.601778i \(0.205541\pi\)
\(104\) −11.7004 −1.14732
\(105\) 4.49058 1.62831i 0.438235 0.158907i
\(106\) 0 0
\(107\) 7.76781i 0.750943i −0.926834 0.375471i \(-0.877481\pi\)
0.926834 0.375471i \(-0.122519\pi\)
\(108\) 5.85021 + 3.40589i 0.562937 + 0.327732i
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 11.7004 1.11559
\(111\) 9.00000 3.26345i 0.854242 0.309753i
\(112\) −0.302776 −0.0286096
\(113\) 14.9534i 1.40670i −0.710843 0.703351i \(-0.751686\pi\)
0.710843 0.703351i \(-0.248314\pi\)
\(114\) −4.90224 + 1.77758i −0.459137 + 0.166486i
\(115\) 4.24264i 0.395628i
\(116\) −2.00420 −0.186085
\(117\) −8.15782 9.76985i −0.754191 0.903223i
\(118\) 2.30278 0.211988
\(119\) 6.61941 0.606801
\(120\) −4.49058 12.3842i −0.409932 1.13052i
\(121\) 14.8167 1.34697
\(122\) 8.15782 0.738574
\(123\) 10.7525 3.89890i 0.969516 0.351552i
\(124\) 4.69722 5.52721i 0.421823 0.496358i
\(125\) 6.60345i 0.590631i
\(126\) 1.60555 + 1.92282i 0.143034 + 0.171298i
\(127\) 5.52721i 0.490460i −0.969465 0.245230i \(-0.921136\pi\)
0.969465 0.245230i \(-0.0788636\pi\)
\(128\) 8.02063i 0.708930i
\(129\) −6.90833 + 2.50500i −0.608244 + 0.220553i
\(130\) 9.76985i 0.856872i
\(131\) 12.7013i 1.10971i 0.831946 + 0.554857i \(0.187227\pi\)
−0.831946 + 0.554857i \(0.812773\pi\)
\(132\) −3.90833 10.7784i −0.340176 0.938143i
\(133\) 3.60555 0.312641
\(134\) 0.505635i 0.0436802i
\(135\) 7.20985 12.3842i 0.620525 1.06586i
\(136\) 18.2551i 1.56536i
\(137\) −18.7856 −1.60496 −0.802482 0.596676i \(-0.796488\pi\)
−0.802482 + 0.596676i \(0.796488\pi\)
\(138\) 2.09167 0.758453i 0.178055 0.0645638i
\(139\) 22.4978i 1.90824i 0.299431 + 0.954118i \(0.403203\pi\)
−0.299431 + 0.954118i \(0.596797\pi\)
\(140\) 3.59282i 0.303648i
\(141\) −6.26188 + 2.27059i −0.527345 + 0.191218i
\(142\) 4.11943 0.345695
\(143\) 21.5569i 1.80268i
\(144\) −0.697224 + 0.582182i −0.0581020 + 0.0485152i
\(145\) 4.24264i 0.352332i
\(146\) 4.61522 0.381958
\(147\) 3.54260 + 9.76985i 0.292189 + 0.805804i
\(148\) 7.20071i 0.591895i
\(149\) 8.85563i 0.725482i −0.931890 0.362741i \(-0.881841\pi\)
0.931890 0.362741i \(-0.118159\pi\)
\(150\) −3.54260 + 1.28457i −0.289252 + 0.104885i
\(151\) 4.24264i 0.345261i −0.984987 0.172631i \(-0.944773\pi\)
0.984987 0.172631i \(-0.0552267\pi\)
\(152\) 9.94345i 0.806520i
\(153\) 15.2430 12.7279i 1.23233 1.02899i
\(154\) 4.24264i 0.341882i
\(155\) −11.7004 9.94345i −0.939801 0.798677i
\(156\) 9.00000 3.26345i 0.720577 0.261285i
\(157\) 16.2111 1.29379 0.646893 0.762580i \(-0.276068\pi\)
0.646893 + 0.762580i \(0.276068\pi\)
\(158\) −1.07261 −0.0853326
\(159\) 0 0
\(160\) 15.9083 1.25766
\(161\) −1.53841 −0.121243
\(162\) 7.39445 + 1.34063i 0.580963 + 0.105330i
\(163\) −7.00000 −0.548282 −0.274141 0.961689i \(-0.588394\pi\)
−0.274141 + 0.961689i \(0.588394\pi\)
\(164\) 8.60281i 0.671767i
\(165\) −22.8167 + 8.27345i −1.77627 + 0.644087i
\(166\) 8.48528i 0.658586i
\(167\) 8.15782 0.631271 0.315636 0.948880i \(-0.397782\pi\)
0.315636 + 0.948880i \(0.397782\pi\)
\(168\) −4.49058 + 1.62831i −0.346455 + 0.125627i
\(169\) −5.00000 −0.384615
\(170\) −15.2430 −1.16909
\(171\) 8.30278 6.93281i 0.634929 0.530166i
\(172\) 5.52721i 0.421446i
\(173\) 2.68127i 0.203853i 0.994792 + 0.101927i \(0.0325007\pi\)
−0.994792 + 0.101927i \(0.967499\pi\)
\(174\) −2.09167 + 0.758453i −0.158569 + 0.0574981i
\(175\) 2.60555 0.196961
\(176\) 1.53841 0.115962
\(177\) −4.49058 + 1.62831i −0.337532 + 0.122391i
\(178\) 5.52721i 0.414282i
\(179\) 10.6278 0.794360 0.397180 0.917741i \(-0.369989\pi\)
0.397180 + 0.917741i \(0.369989\pi\)
\(180\) 6.90833 + 8.27345i 0.514916 + 0.616666i
\(181\) 18.2551i 1.35689i 0.734650 + 0.678447i \(0.237347\pi\)
−0.734650 + 0.678447i \(0.762653\pi\)
\(182\) 3.54260 0.262595
\(183\) −15.9083 + 5.76845i −1.17598 + 0.426416i
\(184\) 4.24264i 0.312772i
\(185\) 15.2430 1.12069
\(186\) 2.81057 7.54603i 0.206081 0.553302i
\(187\) −33.6333 −2.45951
\(188\) 5.01000i 0.365392i
\(189\) −4.49058 2.61433i −0.326641 0.190165i
\(190\) −8.30278 −0.602347
\(191\) 8.77908i 0.635232i 0.948219 + 0.317616i \(0.102882\pi\)
−0.948219 + 0.317616i \(0.897118\pi\)
\(192\) 2.48638 + 6.85697i 0.179439 + 0.494859i
\(193\) −1.78890 −0.128768 −0.0643838 0.997925i \(-0.520508\pi\)
−0.0643838 + 0.997925i \(0.520508\pi\)
\(194\) 7.36190i 0.528554i
\(195\) −6.90833 19.0519i −0.494716 1.36433i
\(196\) −7.81665 −0.558332
\(197\) 15.2430 1.08602 0.543010 0.839726i \(-0.317284\pi\)
0.543010 + 0.839726i \(0.317284\pi\)
\(198\) −8.15782 9.76985i −0.579751 0.694313i
\(199\) 5.52721i 0.391813i 0.980623 + 0.195907i \(0.0627650\pi\)
−0.980623 + 0.195907i \(0.937235\pi\)
\(200\) 7.18563i 0.508101i
\(201\) 0.357538 + 0.986024i 0.0252188 + 0.0695488i
\(202\) −9.69722 −0.682294
\(203\) 1.53841 0.107975
\(204\) 5.09167 + 14.0419i 0.356488 + 0.983130i
\(205\) 18.2111 1.27192
\(206\) 13.5363i 0.943116i
\(207\) −3.54260 + 2.95807i −0.246228 + 0.205600i
\(208\) 1.28457i 0.0890688i
\(209\) −18.3198 −1.26721
\(210\) 1.35964 + 3.74963i 0.0938239 + 0.258749i
\(211\) −2.81665 −0.193906 −0.0969532 0.995289i \(-0.530910\pi\)
−0.0969532 + 0.995289i \(0.530910\pi\)
\(212\) 0 0
\(213\) −8.03318 + 2.91288i −0.550424 + 0.199587i
\(214\) 6.48612 0.443382
\(215\) −11.7004 −0.797962
\(216\) −7.20985 + 12.3842i −0.490568 + 0.842637i
\(217\) −3.60555 + 4.24264i −0.244761 + 0.288009i
\(218\) 5.84500i 0.395873i
\(219\) −9.00000 + 3.26345i −0.608164 + 0.220524i
\(220\) 18.2551i 1.23076i
\(221\) 28.0838i 1.88912i
\(222\) 2.72498 + 7.51500i 0.182889 + 0.504374i
\(223\) 14.0125i 0.938346i 0.883106 + 0.469173i \(0.155448\pi\)
−0.883106 + 0.469173i \(0.844552\pi\)
\(224\) 5.76845i 0.385421i
\(225\) 6.00000 5.01000i 0.400000 0.334000i
\(226\) 12.4861 0.830564
\(227\) 25.4025i 1.68603i −0.537894 0.843013i \(-0.680780\pi\)
0.537894 0.843013i \(-0.319220\pi\)
\(228\) 2.77340 + 7.64853i 0.183673 + 0.506536i
\(229\) 11.4434i 0.756198i 0.925765 + 0.378099i \(0.123422\pi\)
−0.925765 + 0.378099i \(0.876578\pi\)
\(230\) 3.54260 0.233592
\(231\) 3.00000 + 8.27345i 0.197386 + 0.544353i
\(232\) 4.24264i 0.278543i
\(233\) 7.26218i 0.475761i 0.971294 + 0.237881i \(0.0764527\pi\)
−0.971294 + 0.237881i \(0.923547\pi\)
\(234\) 8.15782 6.81178i 0.533293 0.445300i
\(235\) −10.6056 −0.691830
\(236\) 3.59282i 0.233872i
\(237\) 2.09167 0.758453i 0.135869 0.0492668i
\(238\) 5.52721i 0.358276i
\(239\) −9.69623 −0.627197 −0.313598 0.949556i \(-0.601535\pi\)
−0.313598 + 0.949556i \(0.601535\pi\)
\(240\) −1.35964 + 0.493012i −0.0877642 + 0.0318238i
\(241\) 22.4978i 1.44921i −0.689165 0.724604i \(-0.742022\pi\)
0.689165 0.724604i \(-0.257978\pi\)
\(242\) 12.3719i 0.795296i
\(243\) −15.3677 + 2.61433i −0.985836 + 0.167710i
\(244\) 12.7279i 0.814822i
\(245\) 16.5469i 1.05714i
\(246\) 3.25558 + 8.97829i 0.207568 + 0.572435i
\(247\) 15.2971i 0.973329i
\(248\) 11.7004 + 9.94345i 0.742978 + 0.631410i
\(249\) 6.00000 + 16.5469i 0.380235 + 1.04862i
\(250\) 5.51388 0.348728
\(251\) −21.8624 −1.37995 −0.689973 0.723836i \(-0.742377\pi\)
−0.689973 + 0.723836i \(0.742377\pi\)
\(252\) 3.00000 2.50500i 0.188982 0.157800i
\(253\) 7.81665 0.491429
\(254\) 4.61522 0.289584
\(255\) 29.7250 10.7784i 1.86145 0.674973i
\(256\) −15.1194 −0.944964
\(257\) 18.7991i 1.17265i 0.810074 + 0.586327i \(0.199427\pi\)
−0.810074 + 0.586327i \(0.800573\pi\)
\(258\) −2.09167 5.76845i −0.130222 0.359128i
\(259\) 5.52721i 0.343444i
\(260\) 15.2430 0.945332
\(261\) 3.54260 2.95807i 0.219282 0.183100i
\(262\) −10.6056 −0.655213
\(263\) 22.9351 1.41424 0.707118 0.707095i \(-0.249995\pi\)
0.707118 + 0.707095i \(0.249995\pi\)
\(264\) 22.8167 8.27345i 1.40427 0.509196i
\(265\) 0 0
\(266\) 3.01063i 0.184594i
\(267\) −3.90833 10.7784i −0.239186 0.659630i
\(268\) −0.788897 −0.0481896
\(269\) 28.4819 1.73657 0.868285 0.496066i \(-0.165223\pi\)
0.868285 + 0.496066i \(0.165223\pi\)
\(270\) 10.3408 + 6.02022i 0.629320 + 0.366379i
\(271\) 7.20071i 0.437412i −0.975791 0.218706i \(-0.929816\pi\)
0.975791 0.218706i \(-0.0701836\pi\)
\(272\) −2.00420 −0.121522
\(273\) −6.90833 + 2.50500i −0.418111 + 0.151609i
\(274\) 15.6860i 0.947626i
\(275\) −13.2388 −0.798331
\(276\) −1.18335 3.26345i −0.0712291 0.196437i
\(277\) 9.76985i 0.587013i −0.955957 0.293507i \(-0.905178\pi\)
0.955957 0.293507i \(-0.0948223\pi\)
\(278\) −18.7856 −1.12669
\(279\) −0.144955 + 16.7027i −0.00867823 + 0.999962i
\(280\) −7.60555 −0.454519
\(281\) 2.25218i 0.134354i 0.997741 + 0.0671769i \(0.0213992\pi\)
−0.997741 + 0.0671769i \(0.978601\pi\)
\(282\) −1.89594 5.22866i −0.112902 0.311362i
\(283\) 3.81665 0.226877 0.113438 0.993545i \(-0.463814\pi\)
0.113438 + 0.993545i \(0.463814\pi\)
\(284\) 6.42718i 0.381383i
\(285\) 16.1910 5.87095i 0.959072 0.347765i
\(286\) −18.0000 −1.06436
\(287\) 6.60345i 0.389789i
\(288\) −11.0917 13.2834i −0.653583 0.782735i
\(289\) 26.8167 1.57745
\(290\) −3.54260 −0.208029
\(291\) 5.20565 + 14.3562i 0.305161 + 0.841577i
\(292\) 7.20071i 0.421390i
\(293\) 12.7013i 0.742016i 0.928630 + 0.371008i \(0.120988\pi\)
−0.928630 + 0.371008i \(0.879012\pi\)
\(294\) −8.15782 + 2.95807i −0.475774 + 0.172518i
\(295\) −7.60555 −0.442812
\(296\) −15.2430 −0.885983
\(297\) 22.8167 + 13.2834i 1.32396 + 0.770784i
\(298\) 7.39445 0.428349
\(299\) 6.52690i 0.377461i
\(300\) 2.00420 + 5.52721i 0.115712 + 0.319114i
\(301\) 4.24264i 0.244542i
\(302\) 3.54260 0.203854
\(303\) 18.9103 6.85697i 1.08637 0.393923i
\(304\) −1.09167 −0.0626117
\(305\) −26.9435 −1.54278
\(306\) 10.6278 + 12.7279i 0.607551 + 0.727607i
\(307\) 14.3944 0.821535 0.410767 0.911740i \(-0.365261\pi\)
0.410767 + 0.911740i \(0.365261\pi\)
\(308\) −6.61941 −0.377176
\(309\) −9.57158 26.3967i −0.544508 1.50165i
\(310\) 8.30278 9.76985i 0.471566 0.554890i
\(311\) 21.4803i 1.21804i −0.793155 0.609019i \(-0.791563\pi\)
0.793155 0.609019i \(-0.208437\pi\)
\(312\) 6.90833 + 19.0519i 0.391107 + 1.07860i
\(313\) 12.3390i 0.697441i 0.937227 + 0.348720i \(0.113384\pi\)
−0.937227 + 0.348720i \(0.886616\pi\)
\(314\) 13.5363i 0.763896i
\(315\) −5.30278 6.35063i −0.298778 0.357818i
\(316\) 1.67350i 0.0941420i
\(317\) 11.6134i 0.652276i 0.945322 + 0.326138i \(0.105747\pi\)
−0.945322 + 0.326138i \(0.894253\pi\)
\(318\) 0 0
\(319\) −7.81665 −0.437649
\(320\) 11.6134i 0.649211i
\(321\) −12.6484 + 4.58638i −0.705965 + 0.255987i
\(322\) 1.28457i 0.0715862i
\(323\) 23.8666 1.32798
\(324\) 2.09167 11.5369i 0.116204 0.640939i
\(325\) 11.0544i 0.613189i
\(326\) 5.84500i 0.323724i
\(327\) 4.13304 + 11.3982i 0.228557 + 0.630320i
\(328\) −18.2111 −1.00554
\(329\) 3.84563i 0.212017i
\(330\) −6.90833 19.0519i −0.380291 1.04877i
\(331\) 2.56914i 0.141213i −0.997504 0.0706063i \(-0.977507\pi\)
0.997504 0.0706063i \(-0.0224934\pi\)
\(332\) −13.2388 −0.726575
\(333\) −10.6278 12.7279i −0.582400 0.697486i
\(334\) 6.81178i 0.372724i
\(335\) 1.67000i 0.0912418i
\(336\) 0.178769 + 0.493012i 0.00975265 + 0.0268960i
\(337\) 20.8243i 1.13437i 0.823590 + 0.567185i \(0.191968\pi\)
−0.823590 + 0.567185i \(0.808032\pi\)
\(338\) 4.17500i 0.227090i
\(339\) −24.3488 + 8.82902i −1.32245 + 0.479527i
\(340\) 23.7823i 1.28978i
\(341\) 18.3198 21.5569i 0.992075 1.16737i
\(342\) 5.78890 + 6.93281i 0.313028 + 0.374884i
\(343\) 13.0000 0.701934
\(344\) 11.7004 0.630845
\(345\) −6.90833 + 2.50500i −0.371932 + 0.134865i
\(346\) −2.23886 −0.120362
\(347\) 1.53841 0.0825859 0.0412930 0.999147i \(-0.486852\pi\)
0.0412930 + 0.999147i \(0.486852\pi\)
\(348\) 1.18335 + 3.26345i 0.0634340 + 0.174939i
\(349\) 1.21110 0.0648288 0.0324144 0.999475i \(-0.489680\pi\)
0.0324144 + 0.999475i \(0.489680\pi\)
\(350\) 2.17563i 0.116293i
\(351\) −11.0917 + 19.0519i −0.592030 + 1.01692i
\(352\) 29.3095i 1.56220i
\(353\) 1.07261 0.0570895 0.0285447 0.999593i \(-0.490913\pi\)
0.0285447 + 0.999593i \(0.490913\pi\)
\(354\) −1.35964 3.74963i −0.0722639 0.199291i
\(355\) −13.6056 −0.722108
\(356\) 8.62361 0.457051
\(357\) −3.90833 10.7784i −0.206851 0.570456i
\(358\) 8.87422i 0.469017i
\(359\) 26.4903i 1.39811i −0.715069 0.699054i \(-0.753605\pi\)
0.715069 0.699054i \(-0.246395\pi\)
\(360\) −17.5139 + 14.6241i −0.923062 + 0.770757i
\(361\) −6.00000 −0.315789
\(362\) −15.2430 −0.801156
\(363\) −8.74825 24.1261i −0.459164 1.26629i
\(364\) 5.52721i 0.289704i
\(365\) −15.2430 −0.797857
\(366\) −4.81665 13.2834i −0.251771 0.694337i
\(367\) 28.0250i 1.46289i −0.681899 0.731446i \(-0.738846\pi\)
0.681899 0.731446i \(-0.261154\pi\)
\(368\) 0.465792 0.0242811
\(369\) −12.6972 15.2063i −0.660991 0.791606i
\(370\) 12.7279i 0.661693i
\(371\) 0 0
\(372\) −11.7734 4.38508i −0.610422 0.227356i
\(373\) 20.6333 1.06835 0.534176 0.845373i \(-0.320622\pi\)
0.534176 + 0.845373i \(0.320622\pi\)
\(374\) 28.0838i 1.45218i
\(375\) −10.7525 + 3.89890i −0.555254 + 0.201338i
\(376\) 10.6056 0.546940
\(377\) 6.52690i 0.336153i
\(378\) 2.18297 3.74963i 0.112280 0.192860i
\(379\) −31.6333 −1.62489 −0.812447 0.583035i \(-0.801865\pi\)
−0.812447 + 0.583035i \(0.801865\pi\)
\(380\) 12.9541i 0.664530i
\(381\) −9.00000 + 3.26345i −0.461084 + 0.167192i
\(382\) −7.33053 −0.375063
\(383\) −3.07681 −0.157218 −0.0786089 0.996906i \(-0.525048\pi\)
−0.0786089 + 0.996906i \(0.525048\pi\)
\(384\) 13.0601 4.73565i 0.666468 0.241665i
\(385\) 14.0125i 0.714143i
\(386\) 1.49373i 0.0760288i
\(387\) 8.15782 + 9.76985i 0.414685 + 0.496629i
\(388\) −11.4861 −0.583119
\(389\) 5.08101 0.257617 0.128809 0.991669i \(-0.458885\pi\)
0.128809 + 0.991669i \(0.458885\pi\)
\(390\) 15.9083 5.76845i 0.805549 0.292097i
\(391\) −10.1833 −0.514994
\(392\) 16.5469i 0.835745i
\(393\) 20.6816 7.49926i 1.04325 0.378287i
\(394\) 12.7279i 0.641223i
\(395\) 3.54260 0.178248
\(396\) −15.2430 + 12.7279i −0.765991 + 0.639602i
\(397\) 34.4500 1.72899 0.864497 0.502638i \(-0.167637\pi\)
0.864497 + 0.502638i \(0.167637\pi\)
\(398\) −4.61522 −0.231340
\(399\) −2.12884 5.87095i −0.106575 0.293915i
\(400\) −0.788897 −0.0394449
\(401\) 18.7856 0.938110 0.469055 0.883169i \(-0.344595\pi\)
0.469055 + 0.883169i \(0.344595\pi\)
\(402\) −0.823330 + 0.298544i −0.0410640 + 0.0148900i
\(403\) 18.0000 + 15.2971i 0.896644 + 0.762001i
\(404\) 15.1297i 0.752732i
\(405\) −24.4222 4.42782i −1.21355 0.220020i
\(406\) 1.28457i 0.0637521i
\(407\) 28.0838i 1.39206i
\(408\) −29.7250 + 10.7784i −1.47161 + 0.533613i
\(409\) 32.2676i 1.59553i −0.602968 0.797766i \(-0.706015\pi\)
0.602968 0.797766i \(-0.293985\pi\)
\(410\) 15.2063i 0.750984i
\(411\) 11.0917 + 30.5888i 0.547112 + 1.50883i
\(412\) 21.1194 1.04048
\(413\) 2.75782i 0.135703i
\(414\) −2.46999 2.95807i −0.121393 0.145381i
\(415\) 28.0250i 1.37569i
\(416\) −24.4735 −1.19991
\(417\) 36.6333 13.2834i 1.79394 0.650493i
\(418\) 15.2971i 0.748204i
\(419\) 34.6872i 1.69458i 0.531128 + 0.847292i \(0.321768\pi\)
−0.531128 + 0.847292i \(0.678232\pi\)
\(420\) 5.85021 2.12132i 0.285461 0.103510i
\(421\) −23.4222 −1.14153 −0.570764 0.821114i \(-0.693353\pi\)
−0.570764 + 0.821114i \(0.693353\pi\)
\(422\) 2.35190i 0.114489i
\(423\) 7.39445 + 8.85563i 0.359530 + 0.430576i
\(424\) 0 0
\(425\) 17.2472 0.836613
\(426\) −2.43225 6.70770i −0.117843 0.324989i
\(427\) 9.76985i 0.472796i
\(428\) 10.1197i 0.489155i
\(429\) 35.1013 12.7279i 1.69471 0.614510i
\(430\) 9.76985i 0.471144i
\(431\) 1.16436i 0.0560854i 0.999607 + 0.0280427i \(0.00892745\pi\)
−0.999607 + 0.0280427i \(0.991073\pi\)
\(432\) 1.35964 + 0.791556i 0.0654156 + 0.0380838i
\(433\) 7.20071i 0.346044i 0.984918 + 0.173022i \(0.0553532\pi\)
−0.984918 + 0.173022i \(0.944647\pi\)
\(434\) −3.54260 3.01063i −0.170050 0.144515i
\(435\) 6.90833 2.50500i 0.331229 0.120106i
\(436\) −9.11943 −0.436741
\(437\) −5.54680 −0.265339
\(438\) −2.72498 7.51500i −0.130205 0.359080i
\(439\) 18.0278 0.860418 0.430209 0.902729i \(-0.358440\pi\)
0.430209 + 0.902729i \(0.358440\pi\)
\(440\) 38.6439 1.84227
\(441\) 13.8167 11.5369i 0.657936 0.549376i
\(442\) 23.4500 1.11540
\(443\) 2.25218i 0.107004i 0.998568 + 0.0535022i \(0.0170384\pi\)
−0.998568 + 0.0535022i \(0.982962\pi\)
\(444\) 11.7250 4.25155i 0.556443 0.201769i
\(445\) 18.2551i 0.865376i
\(446\) −11.7004 −0.554031
\(447\) −14.4197 + 5.22866i −0.682028 + 0.247307i
\(448\) 4.21110 0.198956
\(449\) 2.00420 0.0945839 0.0472920 0.998881i \(-0.484941\pi\)
0.0472920 + 0.998881i \(0.484941\pi\)
\(450\) 4.18335 + 5.01000i 0.197205 + 0.236174i
\(451\) 33.5522i 1.57991i
\(452\) 19.4810i 0.916308i
\(453\) −6.90833 + 2.50500i −0.324582 + 0.117695i
\(454\) 21.2111 0.995486
\(455\) −11.7004 −0.548524
\(456\) −16.1910 + 5.87095i −0.758213 + 0.274932i
\(457\) 22.4978i 1.05240i −0.850360 0.526201i \(-0.823616\pi\)
0.850360 0.526201i \(-0.176384\pi\)
\(458\) −9.55520 −0.446485
\(459\) −29.7250 17.3054i −1.38744 0.807745i
\(460\) 5.52721i 0.257707i
\(461\) −27.4092 −1.27658 −0.638288 0.769798i \(-0.720357\pi\)
−0.638288 + 0.769798i \(0.720357\pi\)
\(462\) −6.90833 + 2.50500i −0.321404 + 0.116543i
\(463\) 8.48528i 0.394344i −0.980369 0.197172i \(-0.936824\pi\)
0.980369 0.197172i \(-0.0631758\pi\)
\(464\) −0.465792 −0.0216238
\(465\) −9.28267 + 24.9228i −0.430474 + 1.15577i
\(466\) −6.06392 −0.280906
\(467\) 1.59345i 0.0737362i 0.999320 + 0.0368681i \(0.0117381\pi\)
−0.999320 + 0.0368681i \(0.988262\pi\)
\(468\) −10.6278 12.7279i −0.491271 0.588348i
\(469\) 0.605551 0.0279618
\(470\) 8.85563i 0.408480i
\(471\) −9.57158 26.3967i −0.441035 1.21629i
\(472\) 7.60555 0.350074
\(473\) 21.5569i 0.991187i
\(474\) 0.633308 + 1.74655i 0.0290888 + 0.0802215i
\(475\) 9.39445 0.431047
\(476\) 8.62361 0.395263
\(477\) 0 0
\(478\) 8.09635i 0.370318i
\(479\) 4.27472i 0.195317i −0.995220 0.0976585i \(-0.968865\pi\)
0.995220 0.0976585i \(-0.0311353\pi\)
\(480\) −9.39282 25.9037i −0.428721 1.18233i
\(481\) −23.4500 −1.06923
\(482\) 18.7856 0.855662
\(483\) 0.908327 + 2.50500i 0.0413303 + 0.113981i
\(484\) 19.3028 0.877399
\(485\) 24.3147i 1.10407i
\(486\) −2.18297 12.8320i −0.0990214 0.582071i
\(487\) 23.7823i 1.07768i −0.842408 0.538840i \(-0.818863\pi\)
0.842408 0.538840i \(-0.181137\pi\)
\(488\) 26.9435 1.21967
\(489\) 4.13304 + 11.3982i 0.186902 + 0.515443i
\(490\) −13.8167 −0.624173
\(491\) 25.4050 1.14651 0.573257 0.819376i \(-0.305680\pi\)
0.573257 + 0.819376i \(0.305680\pi\)
\(492\) 14.0080 5.07939i 0.631531 0.228997i
\(493\) 10.1833 0.458635
\(494\) 12.7730 0.574686
\(495\) 26.9435 + 32.2676i 1.21102 + 1.45032i
\(496\) 1.09167 1.28457i 0.0490176 0.0576788i
\(497\) 4.93345i 0.221296i
\(498\) −13.8167 + 5.01000i −0.619139 + 0.224503i
\(499\) 28.0250i 1.25457i 0.778790 + 0.627285i \(0.215834\pi\)
−0.778790 + 0.627285i \(0.784166\pi\)
\(500\) 8.60281i 0.384730i
\(501\) −4.81665 13.2834i −0.215192 0.593461i
\(502\) 18.2551i 0.814766i
\(503\) 29.3247i 1.30752i −0.756700 0.653762i \(-0.773190\pi\)
0.756700 0.653762i \(-0.226810\pi\)
\(504\) 5.30278 + 6.35063i 0.236204 + 0.282880i
\(505\) 32.0278 1.42522
\(506\) 6.52690i 0.290156i
\(507\) 2.95217 + 8.14154i 0.131110 + 0.361579i
\(508\) 7.20071i 0.319480i
\(509\) −15.7088 −0.696281 −0.348141 0.937442i \(-0.613187\pi\)
−0.348141 + 0.937442i \(0.613187\pi\)
\(510\) 9.00000 + 24.8203i 0.398527 + 1.09906i
\(511\) 5.52721i 0.244509i
\(512\) 3.41655i 0.150991i
\(513\) −16.1910 9.42611i −0.714850 0.416173i
\(514\) −15.6972 −0.692375
\(515\) 44.7072i 1.97004i
\(516\) −9.00000 + 3.26345i −0.396203 + 0.143665i
\(517\) 19.5397i 0.859355i
\(518\) 4.61522 0.202781
\(519\) 4.36593 1.58311i 0.191643 0.0694909i
\(520\) 32.2676i 1.41503i
\(521\) 14.2182i 0.622909i 0.950261 + 0.311455i \(0.100816\pi\)
−0.950261 + 0.311455i \(0.899184\pi\)
\(522\) 2.46999 + 2.95807i 0.108108 + 0.129471i
\(523\) 12.7279i 0.556553i 0.960501 + 0.278277i \(0.0897632\pi\)
−0.960501 + 0.278277i \(0.910237\pi\)
\(524\) 16.5469i 0.722855i
\(525\) −1.53841 4.24264i −0.0671415 0.185164i
\(526\) 19.1508i 0.835013i
\(527\) −23.8666 + 28.0838i −1.03965 + 1.22335i
\(528\) −0.908327 2.50500i −0.0395299 0.109016i
\(529\) −20.6333 −0.897100
\(530\) 0 0
\(531\) 5.30278 + 6.35063i 0.230121 + 0.275594i
\(532\) 4.69722 0.203651
\(533\) −28.0161 −1.21351
\(534\) 9.00000 3.26345i 0.389468 0.141223i
\(535\) −21.4222 −0.926163
\(536\) 1.67000i 0.0721330i
\(537\) −6.27502 17.3054i −0.270787 0.746781i
\(538\) 23.7823i 1.02533i
\(539\) −30.4861 −1.31313
\(540\) 9.39282 16.1338i 0.404202 0.694289i
\(541\) −21.6056 −0.928895 −0.464448 0.885601i \(-0.653747\pi\)
−0.464448 + 0.885601i \(0.653747\pi\)
\(542\) 6.01259 0.258263
\(543\) 29.7250 10.7784i 1.27562 0.462547i
\(544\) 38.1838i 1.63712i
\(545\) 19.3047i 0.826923i
\(546\) −2.09167 5.76845i −0.0895153 0.246867i
\(547\) −15.6056 −0.667245 −0.333623 0.942707i \(-0.608271\pi\)
−0.333623 + 0.942707i \(0.608271\pi\)
\(548\) −24.4735 −1.04545
\(549\) 18.7856 + 22.4978i 0.801751 + 0.960181i
\(550\) 11.0544i 0.471362i
\(551\) 5.54680 0.236302
\(552\) 6.90833 2.50500i 0.294038 0.106620i
\(553\) 1.28457i 0.0546254i
\(554\) 8.15782 0.346593
\(555\) −9.00000 24.8203i −0.382029 1.05357i
\(556\) 29.3095i 1.24300i
\(557\) 2.00420 0.0849206 0.0424603 0.999098i \(-0.486480\pi\)
0.0424603 + 0.999098i \(0.486480\pi\)
\(558\) −13.9467 0.121037i −0.590412 0.00512392i
\(559\) 18.0000 0.761319
\(560\) 0.835000i 0.0352852i
\(561\) 19.8582 + 54.7654i 0.838416 + 2.31220i
\(562\) −1.88057 −0.0793271
\(563\) 0.0765470i 0.00322607i 0.999999 + 0.00161304i \(0.000513445\pi\)
−0.999999 + 0.00161304i \(0.999487\pi\)
\(564\) −8.15782 + 2.95807i −0.343506 + 0.124557i
\(565\) −41.2389 −1.73493
\(566\) 3.18690i 0.133956i
\(567\) −1.60555 + 8.85563i −0.0674268 + 0.371902i
\(568\) 13.6056 0.570876
\(569\) −27.4092 −1.14906 −0.574528 0.818485i \(-0.694814\pi\)
−0.574528 + 0.818485i \(0.694814\pi\)
\(570\) 4.90224 + 13.5195i 0.205332 + 0.566269i
\(571\) 32.2676i 1.35036i −0.737654 0.675179i \(-0.764066\pi\)
0.737654 0.675179i \(-0.235934\pi\)
\(572\) 28.0838i 1.17424i
\(573\) 14.2951 5.18347i 0.597185 0.216543i
\(574\) 5.51388 0.230145
\(575\) −4.00840 −0.167162
\(576\) 9.69722 8.09718i 0.404051 0.337382i
\(577\) −20.4222 −0.850188 −0.425094 0.905149i \(-0.639759\pi\)
−0.425094 + 0.905149i \(0.639759\pi\)
\(578\) 22.3919i 0.931380i
\(579\) 1.05623 + 2.91288i 0.0438952 + 0.121055i
\(580\) 5.52721i 0.229505i
\(581\) 10.1620 0.421592
\(582\) −11.9874 + 4.34672i −0.496896 + 0.180177i
\(583\) 0 0
\(584\) 15.2430 0.630761
\(585\) −26.9435 + 22.4978i −1.11397 + 0.930168i
\(586\) −10.6056 −0.438111
\(587\) 20.3240 0.838863 0.419431 0.907787i \(-0.362229\pi\)
0.419431 + 0.907787i \(0.362229\pi\)
\(588\) 4.61522 + 12.7279i 0.190328 + 0.524891i
\(589\) −13.0000 + 15.2971i −0.535656 + 0.630304i
\(590\) 6.35063i 0.261451i
\(591\) −9.00000 24.8203i −0.370211 1.02097i
\(592\) 1.67350i 0.0687806i
\(593\) 7.76781i 0.318986i −0.987199 0.159493i \(-0.949014\pi\)
0.987199 0.159493i \(-0.0509859\pi\)
\(594\) −11.0917 + 19.0519i −0.455097 + 0.781709i
\(595\) 18.2551i 0.748387i
\(596\) 11.5369i 0.472570i
\(597\) 9.00000 3.26345i 0.368345 0.133564i
\(598\) −5.44996 −0.222865
\(599\) 25.3260i 1.03479i 0.855746 + 0.517396i \(0.173098\pi\)
−0.855746 + 0.517396i \(0.826902\pi\)
\(600\) −11.7004 + 4.24264i −0.477668 + 0.173205i
\(601\) 6.81178i 0.277858i 0.990302 + 0.138929i \(0.0443660\pi\)
−0.990302 + 0.138929i \(0.955634\pi\)
\(602\) −3.54260 −0.144386
\(603\) 1.39445 1.16436i 0.0567863 0.0474166i
\(604\) 5.52721i 0.224899i
\(605\) 40.8616i 1.66126i
\(606\) 5.72557 + 15.7901i 0.232585 + 0.641428i
\(607\) −34.2389 −1.38971 −0.694856 0.719149i \(-0.744532\pi\)
−0.694856 + 0.719149i \(0.744532\pi\)
\(608\) 20.7984i 0.843488i
\(609\) −0.908327 2.50500i −0.0368073 0.101508i
\(610\) 22.4978i 0.910908i
\(611\) 16.3156 0.660060
\(612\) 19.8582 16.5816i 0.802722 0.670273i
\(613\) 25.4558i 1.02815i 0.857745 + 0.514076i \(0.171865\pi\)
−0.857745 + 0.514076i \(0.828135\pi\)
\(614\) 12.0194i 0.485062i
\(615\) −10.7525 29.6533i −0.433581 1.19574i
\(616\) 14.0125i 0.564579i
\(617\) 12.7013i 0.511334i 0.966765 + 0.255667i \(0.0822950\pi\)
−0.966765 + 0.255667i \(0.917705\pi\)
\(618\) 22.0412 7.99227i 0.886628 0.321496i
\(619\) 1.28457i 0.0516312i 0.999667 + 0.0258156i \(0.00821827\pi\)
−0.999667 + 0.0258156i \(0.991782\pi\)
\(620\) −15.2430 12.9541i −0.612175 0.520248i
\(621\) 6.90833 + 4.02190i 0.277222 + 0.161393i
\(622\) 17.9361 0.719171
\(623\) −6.61941 −0.265201
\(624\) 2.09167 0.758453i 0.0837339 0.0303624i
\(625\) −31.2389 −1.24955
\(626\) −10.3030 −0.411793
\(627\) 10.8167 + 29.8303i 0.431976 + 1.19131i
\(628\) 21.1194 0.842757
\(629\) 36.5869i 1.45881i
\(630\) 5.30278 4.42782i 0.211268 0.176408i
\(631\) 11.0544i 0.440069i −0.975492 0.220035i \(-0.929383\pi\)
0.975492 0.220035i \(-0.0706171\pi\)
\(632\) −3.54260 −0.140917
\(633\) 1.66305 + 4.58638i 0.0661002 + 0.182292i
\(634\) −9.69722 −0.385126
\(635\) −15.2430 −0.604901
\(636\) 0 0
\(637\) 25.4558i 1.00860i
\(638\) 6.52690i 0.258403i
\(639\) 9.48612 + 11.3606i 0.375265 + 0.449420i
\(640\) 22.1194 0.874347
\(641\) 37.5713 1.48398 0.741988 0.670413i \(-0.233883\pi\)
0.741988 + 0.670413i \(0.233883\pi\)
\(642\) −3.82963 10.5614i −0.151143 0.416825i
\(643\) 30.5941i 1.20651i −0.797547 0.603257i \(-0.793869\pi\)
0.797547 0.603257i \(-0.206131\pi\)
\(644\) −2.00420 −0.0789764
\(645\) 6.90833 + 19.0519i 0.272015 + 0.750168i
\(646\) 19.9286i 0.784082i
\(647\) 11.2346 0.441679 0.220839 0.975310i \(-0.429120\pi\)
0.220839 + 0.975310i \(0.429120\pi\)
\(648\) 24.4222 + 4.42782i 0.959395 + 0.173941i
\(649\) 14.0125i 0.550038i
\(650\) 9.23043 0.362047
\(651\) 9.03717 + 3.36595i 0.354194 + 0.131922i
\(652\) −9.11943 −0.357144
\(653\) 6.17436i 0.241621i 0.992676 + 0.120811i \(0.0385494\pi\)
−0.992676 + 0.120811i \(0.961451\pi\)
\(654\) −9.51746 + 3.45108i −0.372162 + 0.134948i
\(655\) 35.0278 1.36865
\(656\) 1.99936i 0.0780620i
\(657\) 10.6278 + 12.7279i 0.414630 + 0.496564i
\(658\) −3.21110 −0.125182
\(659\) 2.25218i 0.0877325i 0.999037 + 0.0438663i \(0.0139675\pi\)
−0.999037 + 0.0438663i \(0.986032\pi\)
\(660\) −29.7250 + 10.7784i −1.15704 + 0.419551i
\(661\) 15.1833 0.590564 0.295282 0.955410i \(-0.404586\pi\)
0.295282 + 0.955410i \(0.404586\pi\)
\(662\) 2.14523 0.0833767
\(663\) −45.7291 + 16.5816i −1.77597 + 0.643977i
\(664\) 28.0250i 1.08758i
\(665\) 9.94345i 0.385590i
\(666\) 10.6278 8.87422i 0.411819 0.343869i
\(667\) −2.36669 −0.0916387
\(668\) 10.6278 0.411202
\(669\) 22.8167 8.27345i 0.882143 0.319870i
\(670\) −1.39445 −0.0538723
\(671\) 49.6407i 1.91636i
\(672\) −9.39282 + 3.40589i −0.362336 + 0.131385i
\(673\) 29.6985i 1.14479i −0.819977 0.572396i \(-0.806014\pi\)
0.819977 0.572396i \(-0.193986\pi\)
\(674\) −17.3883 −0.669771
\(675\) −11.7004 6.81178i −0.450350 0.262185i
\(676\) −6.51388 −0.250534
\(677\) 35.5671 1.36695 0.683477 0.729972i \(-0.260467\pi\)
0.683477 + 0.729972i \(0.260467\pi\)
\(678\) −7.37223 20.3313i −0.283129 0.780817i
\(679\) 8.81665 0.338352
\(680\) −50.3443 −1.93062
\(681\) −41.3631 + 14.9985i −1.58504 + 0.574744i
\(682\) 18.0000 + 15.2971i 0.689256 + 0.585755i
\(683\) 50.3760i 1.92758i 0.266657 + 0.963791i \(0.414081\pi\)
−0.266657 + 0.963791i \(0.585919\pi\)
\(684\) 10.8167 9.03190i 0.413585 0.345343i
\(685\) 51.8073i 1.97946i
\(686\) 10.8550i 0.414446i
\(687\) 18.6333 6.75654i 0.710905 0.257778i
\(688\) 1.28457i 0.0489737i
\(689\) 0 0
\(690\) −2.09167 5.76845i −0.0796286 0.219601i
\(691\) −19.0000 −0.722794 −0.361397 0.932412i \(-0.617700\pi\)
−0.361397 + 0.932412i \(0.617700\pi\)
\(692\) 3.49309i 0.132787i
\(693\) 11.7004 9.76985i 0.444462 0.371126i
\(694\) 1.28457i 0.0487615i
\(695\) 62.0447 2.35349
\(696\) −6.90833 + 2.50500i −0.261859 + 0.0949517i
\(697\) 43.7110i 1.65567i
\(698\) 1.01127i 0.0382771i
\(699\) 11.8251 4.28784i 0.447265 0.162181i
\(700\) 3.39445 0.128298
\(701\) 44.7072i 1.68857i 0.535895 + 0.844285i \(0.319974\pi\)
−0.535895 + 0.844285i \(0.680026\pi\)
\(702\) −15.9083 9.26154i −0.600421 0.349554i
\(703\) 19.9286i 0.751623i
\(704\) −21.3967 −0.806417
\(705\) 6.26188 + 17.2691i 0.235836 + 0.650392i
\(706\) 0.895632i 0.0337076i
\(707\) 11.6134i 0.436769i
\(708\) −5.85021 + 2.12132i −0.219864 + 0.0797241i
\(709\) 44.9955i 1.68984i 0.534890 + 0.844922i \(0.320353\pi\)
−0.534890 + 0.844922i \(0.679647\pi\)
\(710\) 11.3606i 0.426357i
\(711\) −2.46999 2.95807i −0.0926318 0.110936i
\(712\) 18.2551i 0.684140i
\(713\) 5.54680 6.52690i 0.207729 0.244434i
\(714\) 9.00000 3.26345i 0.336817 0.122132i
\(715\) 59.4500 2.22330
\(716\) 13.8457 0.517436
\(717\) 5.72498 + 15.7884i 0.213803 + 0.589630i
\(718\) 22.1194 0.825490
\(719\) −6.61941 −0.246863 −0.123431 0.992353i \(-0.539390\pi\)
−0.123431 + 0.992353i \(0.539390\pi\)
\(720\) 1.60555 + 1.92282i 0.0598354 + 0.0716592i
\(721\) −16.2111 −0.603733
\(722\) 5.01000i 0.186453i
\(723\) −36.6333 + 13.2834i −1.36241 + 0.494017i
\(724\) 23.7823i 0.883864i
\(725\) 4.00840 0.148868
\(726\) 20.1453 7.30479i 0.747661 0.271106i
\(727\) 17.0000 0.630495 0.315248 0.949009i \(-0.397912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(728\) 11.7004 0.433647
\(729\) 13.3305 + 23.4797i 0.493723 + 0.869619i
\(730\) 12.7279i 0.471082i
\(731\) 28.0838i 1.03872i
\(732\) −20.7250 + 7.51500i −0.766017 + 0.277762i
\(733\) −1.78890 −0.0660744 −0.0330372 0.999454i \(-0.510518\pi\)
−0.0330372 + 0.999454i \(0.510518\pi\)
\(734\) 23.4008 0.863741
\(735\) 26.9435 9.76985i 0.993824 0.360366i
\(736\) 8.87422i 0.327108i
\(737\) −3.07681 −0.113336
\(738\) 12.6972 10.6022i 0.467391 0.390272i
\(739\) 34.8368i 1.28149i −0.767753 0.640745i \(-0.778625\pi\)
0.767753 0.640745i \(-0.221375\pi\)
\(740\) 19.8582 0.730004
\(741\) −24.9083 + 9.03190i −0.915030 + 0.331795i
\(742\) 0 0
\(743\) −24.9393 −0.914932 −0.457466 0.889227i \(-0.651243\pi\)
−0.457466 + 0.889227i \(0.651243\pi\)
\(744\) 9.28267 24.9228i 0.340319 0.913716i
\(745\) −24.4222 −0.894760
\(746\) 17.2288i 0.630791i
\(747\) 23.4008 19.5397i 0.856192 0.714920i
\(748\) −43.8167 −1.60210
\(749\) 7.76781i 0.283830i
\(750\) −3.25558 8.97829i −0.118877 0.327841i
\(751\) 39.6611 1.44725 0.723626 0.690192i \(-0.242474\pi\)
0.723626 + 0.690192i \(0.242474\pi\)
\(752\) 1.16436i 0.0424600i
\(753\) 12.9083 + 35.5988i 0.470406 + 1.29729i
\(754\) 5.44996 0.198476
\(755\) −11.7004 −0.425822
\(756\) −5.85021 3.40589i −0.212770 0.123871i
\(757\) 23.7823i 0.864384i 0.901782 + 0.432192i \(0.142260\pi\)
−0.901782 + 0.432192i \(0.857740\pi\)
\(758\) 26.4138i 0.959392i
\(759\) −4.61522 12.7279i −0.167522 0.461994i
\(760\) −27.4222 −0.994708
\(761\) −31.5587 −1.14400 −0.572000 0.820253i \(-0.693832\pi\)
−0.572000 + 0.820253i \(0.693832\pi\)
\(762\) −2.72498 7.51500i −0.0987156 0.272240i
\(763\) 7.00000 0.253417
\(764\) 11.4372i 0.413783i
\(765\) −35.1013 42.0375i −1.26909 1.51987i
\(766\) 2.56914i 0.0928267i
\(767\) 11.7004 0.422478
\(768\) 8.92702 + 24.6191i 0.322126 + 0.888365i
\(769\) 0.577795 0.0208358 0.0104179 0.999946i \(-0.496684\pi\)
0.0104179 + 0.999946i \(0.496684\pi\)
\(770\) −11.7004 −0.421654
\(771\) 30.6107 11.0996i 1.10242 0.399743i
\(772\) −2.33053 −0.0838777
\(773\) −35.1013 −1.26251 −0.631253 0.775577i \(-0.717459\pi\)
−0.631253 + 0.775577i \(0.717459\pi\)
\(774\) −8.15782 + 6.81178i −0.293227 + 0.244844i
\(775\) −9.39445 + 11.0544i −0.337459 + 0.397086i
\(776\) 24.3147i 0.872847i
\(777\) −9.00000 + 3.26345i −0.322873 + 0.117076i
\(778\) 4.24264i 0.152106i
\(779\) 23.8091i 0.853049i
\(780\) −9.00000 24.8203i −0.322252 0.888711i
\(781\) 25.0669i 0.896964i
\(782\) 8.50309i 0.304070i
\(783\) −6.90833 4.02190i −0.246883 0.143731i
\(784\) −1.81665 −0.0648805
\(785\) 44.7072i 1.59567i
\(786\) 6.26188 + 17.2691i 0.223354 + 0.615969i
\(787\) 31.8787i 1.13635i 0.822907 + 0.568176i \(0.192351\pi\)
−0.822907 + 0.568176i \(0.807649\pi\)
\(788\) 19.8582 0.707421
\(789\) −13.5416 37.3453i −0.482095 1.32953i
\(790\) 2.95807i 0.105243i
\(791\) 14.9534i 0.531683i
\(792\) −26.9435 32.2676i −0.957394 1.14658i
\(793\) 41.4500 1.47193
\(794\) 28.7657i 1.02086i
\(795\) 0 0
\(796\) 7.20071i 0.255223i
\(797\) 6.15362 0.217973 0.108986 0.994043i \(-0.465240\pi\)
0.108986 + 0.994043i \(0.465240\pi\)
\(798\) 4.90224 1.77758i 0.173537 0.0629257i
\(799\) 25.4558i 0.900563i
\(800\) 15.0300i 0.531391i
\(801\) −15.2430 + 12.7279i −0.538586 + 0.449719i
\(802\) 15.6860i 0.553892i
\(803\) 28.0838i 0.991056i
\(804\) 0.465792 + 1.28457i 0.0164272 + 0.0453032i
\(805\) 4.24264i 0.149533i
\(806\) −12.7730 + 15.0300i −0.449911 + 0.529409i
\(807\) −16.8167 46.3772i −0.591974 1.63256i
\(808\) −32.0278 −1.12673
\(809\) −6.01259 −0.211392 −0.105696 0.994399i \(-0.533707\pi\)
−0.105696 + 0.994399i \(0.533707\pi\)
\(810\) 3.69722 20.3925i 0.129907 0.716521i
\(811\) 21.0278 0.738384 0.369192 0.929353i \(-0.379634\pi\)
0.369192 + 0.929353i \(0.379634\pi\)
\(812\) 2.00420 0.0703335
\(813\) −11.7250 + 4.25155i −0.411213 + 0.149108i
\(814\) −23.4500 −0.821921
\(815\) 19.3047i 0.676215i
\(816\) 1.18335 + 3.26345i 0.0414254 + 0.114244i
\(817\) 15.2971i 0.535176i
\(818\) 26.9435 0.942056
\(819\) 8.15782 + 9.76985i 0.285057 + 0.341386i
\(820\) 23.7250 0.828512
\(821\) −43.2591 −1.50975 −0.754876 0.655867i \(-0.772303\pi\)
−0.754876 + 0.655867i \(0.772303\pi\)
\(822\) −25.5416 + 9.26154i −0.890867 + 0.323033i
\(823\) 35.2257i 1.22789i 0.789349 + 0.613945i \(0.210418\pi\)
−0.789349 + 0.613945i \(0.789582\pi\)
\(824\) 44.7072i 1.55745i
\(825\) 7.81665 + 21.5569i 0.272141 + 0.750515i
\(826\) −2.30278 −0.0801238
\(827\) 4.61522 0.160487 0.0802434 0.996775i \(-0.474430\pi\)
0.0802434 + 0.996775i \(0.474430\pi\)
\(828\) −4.61522 + 3.85370i −0.160390 + 0.133925i
\(829\) 25.4558i 0.884118i 0.896986 + 0.442059i \(0.145752\pi\)
−0.896986 + 0.442059i \(0.854248\pi\)
\(830\) −23.4008 −0.812255
\(831\) −15.9083 + 5.76845i −0.551854 + 0.200105i
\(832\) 17.8662i 0.619399i
\(833\) 39.7165 1.37609
\(834\) 11.0917 + 30.5888i 0.384073 + 1.05920i
\(835\) 22.4978i 0.778567i
\(836\) −23.8666 −0.825445
\(837\) 27.2827 9.62579i 0.943027 0.332716i
\(838\) −28.9638 −1.00054
\(839\) 17.7113i 0.611461i 0.952118 + 0.305730i \(0.0989006\pi\)
−0.952118 + 0.305730i \(0.901099\pi\)
\(840\) 4.49058 + 12.3842i 0.154940 + 0.427295i
\(841\) −26.6333 −0.918390
\(842\) 19.5575i 0.673997i
\(843\) 3.66725 1.32976i 0.126307 0.0457995i
\(844\) −3.66947 −0.126308
\(845\) 13.7891i 0.474359i
\(846\) −7.39445 + 6.17436i −0.254226 + 0.212279i
\(847\) −14.8167 −0.509106
\(848\) 0 0
\(849\) −2.25348 6.21469i −0.0773393 0.213288i
\(850\) 14.4014i 0.493965i
\(851\) 8.50309i 0.291482i
\(852\) −10.4654 + 3.79482i −0.358540 + 0.130009i
\(853\) 19.2111 0.657776 0.328888 0.944369i \(-0.393326\pi\)
0.328888 + 0.944369i \(0.393326\pi\)
\(854\) −8.15782 −0.279155
\(855\) −19.1194 22.8975i −0.653871 0.783079i
\(856\) 21.4222 0.732196
\(857\) 3.84563i 0.131364i −0.997841 0.0656822i \(-0.979078\pi\)
0.997841 0.0656822i \(-0.0209223\pi\)
\(858\) 10.6278 + 29.3095i 0.362827 + 1.00061i
\(859\) 0.388936i 0.0132703i 0.999978 + 0.00663516i \(0.00211205\pi\)
−0.999978 + 0.00663516i \(0.997888\pi\)
\(860\) −15.2430 −0.519783
\(861\) −10.7525 + 3.89890i −0.366443 + 0.132874i
\(862\) −0.972244 −0.0331147
\(863\) −2.61102 −0.0888801 −0.0444401 0.999012i \(-0.514150\pi\)
−0.0444401 + 0.999012i \(0.514150\pi\)
\(864\) −15.0806 + 25.9037i −0.513054 + 0.881260i
\(865\) 7.39445 0.251419
\(866\) −6.01259 −0.204316
\(867\) −15.8335 43.6658i −0.537733 1.48297i
\(868\) −4.69722 + 5.52721i −0.159434 + 0.187606i
\(869\) 6.52690i 0.221410i
\(870\) 2.09167 + 5.76845i 0.0709144 + 0.195569i
\(871\) 2.56914i 0.0870519i
\(872\) 19.3047i 0.653740i
\(873\) 20.3028 16.9528i 0.687145 0.573766i
\(874\) 4.63158i 0.156665i
\(875\) 6.60345i 0.223237i
\(876\) −11.7250 + 4.25155i −0.396150 + 0.143646i
\(877\) 24.0278 0.811360 0.405680 0.914015i \(-0.367035\pi\)
0.405680 + 0.914015i \(0.367035\pi\)
\(878\) 15.0532i 0.508020i
\(879\) 20.6816 7.49926i 0.697572 0.252944i
\(880\) 4.24264i 0.143019i
\(881\) −26.4777 −0.892055 −0.446028 0.895019i \(-0.647162\pi\)
−0.446028 + 0.895019i \(0.647162\pi\)
\(882\) 9.63331 + 11.5369i 0.324370 + 0.388468i
\(883\) 11.0544i 0.372011i 0.982549 + 0.186005i \(0.0595542\pi\)
−0.982549 + 0.186005i \(0.940446\pi\)
\(884\) 36.5869i 1.23055i
\(885\) 4.49058 + 12.3842i 0.150949 + 0.416290i
\(886\) −1.88057 −0.0631790
\(887\) 36.5103i 1.22590i −0.790123 0.612949i \(-0.789983\pi\)
0.790123 0.612949i \(-0.210017\pi\)
\(888\) 9.00000 + 24.8203i 0.302020 + 0.832916i
\(889\) 5.52721i 0.185377i
\(890\) 15.2430 0.510947
\(891\) 8.15782 44.9955i 0.273297 1.50741i
\(892\) 18.2551i 0.611227i
\(893\) 13.8656i 0.463996i
\(894\) −4.36593 12.0404i −0.146019 0.402693i
\(895\) 29.3095i 0.979710i
\(896\) 8.02063i 0.267950i
\(897\) 10.6278 3.85370i 0.354852 0.128671i
\(898\) 1.67350i 0.0558456i
\(899\) −5.54680 + 6.52690i −0.184996 + 0.217684i
\(900\) 7.81665 6.52690i 0.260555 0.217563i
\(901\) 0 0
\(902\) −28.0161 −0.932833
\(903\) 6.90833 2.50500i 0.229895 0.0833611i
\(904\) 41.2389 1.37158
\(905\) 50.3443 1.67350
\(906\) −2.09167 5.76845i −0.0694912 0.191644i
\(907\) 0.0277564 0.000921635 0.000460818 1.00000i \(-0.499853\pi\)
0.000460818 1.00000i \(0.499853\pi\)
\(908\) 33.0938i 1.09826i
\(909\) −22.3305 26.7432i −0.740657 0.887015i
\(910\) 9.76985i 0.323867i
\(911\) −5.54680 −0.183774 −0.0918869 0.995769i \(-0.529290\pi\)
−0.0918869 + 0.995769i \(0.529290\pi\)
\(912\) 0.644561 + 1.77758i 0.0213435 + 0.0588616i
\(913\) −51.6333 −1.70881
\(914\) 18.7856 0.621373
\(915\) 15.9083 + 43.8722i 0.525913 + 1.45037i
\(916\) 14.9081i 0.492578i
\(917\) 12.7013i 0.419433i
\(918\) 14.4500 24.8203i 0.476920 0.819194i
\(919\) −2.42221 −0.0799012 −0.0399506 0.999202i \(-0.512720\pi\)
−0.0399506 + 0.999202i \(0.512720\pi\)
\(920\) 11.7004 0.385752
\(921\) −8.49897 23.4386i −0.280051 0.772328i
\(922\) 22.8867i 0.753734i
\(923\) 20.9309 0.688948
\(924\) 3.90833 + 10.7784i 0.128575 + 0.354585i
\(925\) 14.4014i 0.473516i
\(926\) 7.08521 0.232834
\(927\) −37.3305 + 31.1710i −1.22610 + 1.02379i
\(928\) 8.87422i 0.291310i
\(929\) 5.08101 0.166703 0.0833513 0.996520i \(-0.473438\pi\)
0.0833513 + 0.996520i \(0.473438\pi\)
\(930\) −20.8106 7.75103i −0.682405 0.254166i
\(931\) 21.6333 0.709003
\(932\) 9.46099i 0.309905i
\(933\) −34.9766 + 12.6827i −1.14508 + 0.415214i
\(934\) −1.33053 −0.0435363
\(935\) 92.7545i 3.03340i
\(936\) 26.9435 22.4978i 0.880674 0.735363i
\(937\) 15.5778 0.508904 0.254452 0.967085i \(-0.418105\pi\)
0.254452 + 0.967085i \(0.418105\pi\)
\(938\) 0.505635i 0.0165096i
\(939\) 20.0917 7.28536i 0.655667 0.237749i
\(940\) −13.8167 −0.450650
\(941\) 44.6565 1.45576 0.727880 0.685705i \(-0.240506\pi\)
0.727880 + 0.685705i \(0.240506\pi\)
\(942\) 22.0412 7.99227i 0.718141 0.260402i
\(943\) 10.1588i 0.330816i
\(944\) 0.835000i 0.0271769i
\(945\) −7.20985 + 12.3842i −0.234536 + 0.402857i
\(946\) 18.0000 0.585230
\(947\) −38.6439 −1.25576 −0.627879 0.778311i \(-0.716077\pi\)
−0.627879 + 0.778311i \(0.716077\pi\)
\(948\) 2.72498 0.988094i 0.0885033 0.0320918i
\(949\) 23.4500 0.761218
\(950\) 7.84436i 0.254505i
\(951\) 18.9103 6.85697i 0.613208 0.222353i
\(952\) 18.2551i 0.591652i
\(953\) 29.0887 0.942275 0.471137 0.882060i \(-0.343844\pi\)
0.471137 + 0.882060i \(0.343844\pi\)
\(954\) 0 0
\(955\) 24.2111 0.783453
\(956\) −12.6320 −0.408548
\(957\) 4.61522 + 12.7279i 0.149189 + 0.411435i
\(958\) 3.56939 0.115322
\(959\) 18.7856 0.606620
\(960\) 18.9103 6.85697i 0.610326 0.221308i
\(961\) −5.00000 30.5941i −0.161290 0.986907i
\(962\) 19.5807i 0.631307i
\(963\) 14.9361 + 17.8875i 0.481309 + 0.576418i
\(964\) 29.3095i 0.943997i
\(965\) 4.93345i 0.158813i
\(966\) −2.09167 + 0.758453i −0.0672985 + 0.0244028i
\(967\) 33.5522i 1.07897i 0.841997 + 0.539483i \(0.181380\pi\)
−0.841997 + 0.539483i \(0.818620\pi\)
\(968\) 40.8616i 1.31334i
\(969\) −14.0917 38.8622i −0.452690 1.24844i
\(970\) −20.3028 −0.651883
\(971\) 26.9194i 0.863886i −0.901901 0.431943i \(-0.857828\pi\)
0.901901 0.431943i \(-0.142172\pi\)
\(972\) −20.0206 + 3.40589i −0.642162 + 0.109244i
\(973\) 22.4978i 0.721245i
\(974\) 19.8582 0.636299
\(975\) −18.0000 + 6.52690i −0.576461 + 0.209028i
\(976\) 2.95807i 0.0946856i
\(977\) 43.0372i 1.37688i −0.725292 0.688442i \(-0.758295\pi\)
0.725292 0.688442i \(-0.241705\pi\)
\(978\) −9.51746 + 3.45108i −0.304335 + 0.110354i
\(979\) 33.6333 1.07493
\(980\) 21.5569i 0.688610i
\(981\) 16.1194 13.4597i 0.514654 0.429736i
\(982\) 21.2132i 0.676941i
\(983\) −34.6355 −1.10470 −0.552350 0.833612i \(-0.686269\pi\)
−0.552350 + 0.833612i \(0.686269\pi\)
\(984\) 10.7525 + 29.6533i 0.342776 + 0.945312i
\(985\) 42.0375i 1.33943i
\(986\) 8.50309i 0.270794i
\(987\) 6.26188 2.27059i 0.199318 0.0722738i
\(988\) 19.9286i 0.634014i
\(989\) 6.52690i 0.207543i
\(990\) −26.9435 + 22.4978i −0.856319 + 0.715026i
\(991\) 3.85370i 0.122417i 0.998125 + 0.0612085i \(0.0194955\pi\)
−0.998125 + 0.0612085i \(0.980505\pi\)
\(992\) 24.4735 + 20.7984i 0.777033 + 0.660351i
\(993\) −4.18335 + 1.51691i −0.132754 + 0.0481375i
\(994\) −4.11943 −0.130660
\(995\) 15.2430 0.483236
\(996\) 7.81665 + 21.5569i 0.247680 + 0.683056i
\(997\) −60.4500 −1.91447 −0.957235 0.289312i \(-0.906573\pi\)
−0.957235 + 0.289312i \(0.906573\pi\)
\(998\) −23.4008 −0.740741
\(999\) −14.4500 + 24.8203i −0.457177 + 0.785281i
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 93.2.c.a.92.5 yes 8
3.2 odd 2 inner 93.2.c.a.92.4 yes 8
4.3 odd 2 1488.2.h.e.929.6 8
12.11 even 2 1488.2.h.e.929.4 8
31.30 odd 2 inner 93.2.c.a.92.6 yes 8
93.92 even 2 inner 93.2.c.a.92.3 8
124.123 even 2 1488.2.h.e.929.3 8
372.371 odd 2 1488.2.h.e.929.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
93.2.c.a.92.3 8 93.92 even 2 inner
93.2.c.a.92.4 yes 8 3.2 odd 2 inner
93.2.c.a.92.5 yes 8 1.1 even 1 trivial
93.2.c.a.92.6 yes 8 31.30 odd 2 inner
1488.2.h.e.929.3 8 124.123 even 2
1488.2.h.e.929.4 8 12.11 even 2
1488.2.h.e.929.5 8 372.371 odd 2
1488.2.h.e.929.6 8 4.3 odd 2