Properties

Label 1134.2.k.c.971.7
Level $1134$
Weight $2$
Character 1134.971
Analytic conductor $9.055$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(647,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1134.647");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.k (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + 16903 x^{8} - 23292 x^{7} + 26994 x^{6} - 25716 x^{5} + 19962 x^{4} + \cdots + 225 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 971.7
Root \(0.500000 + 0.0390518i\) of defining polynomial
Character \(\chi\) \(=\) 1134.971
Dual form 1134.2.k.c.647.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.860850 - 1.49104i) q^{5} +(-2.25833 + 1.37838i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.860850 - 1.49104i) q^{5} +(-2.25833 + 1.37838i) q^{7} +1.00000i q^{8} +(1.49104 - 0.860850i) q^{10} +(1.47921 - 0.854023i) q^{11} +1.28315i q^{13} +(-2.64496 + 0.0645439i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.60152 + 4.50597i) q^{17} +(2.39385 + 1.38209i) q^{19} +1.72170 q^{20} +1.70805 q^{22} +(4.71463 + 2.72199i) q^{23} +(1.01787 + 1.76301i) q^{25} +(-0.641574 + 1.11124i) q^{26} +(-2.32288 - 1.26659i) q^{28} +1.44960i q^{29} +(5.82274 - 3.36176i) q^{31} +(-0.866025 + 0.500000i) q^{32} +5.20305i q^{34} +(0.111125 + 4.55384i) q^{35} +(3.75959 - 6.51181i) q^{37} +(1.38209 + 2.39385i) q^{38} +(1.49104 + 0.860850i) q^{40} +8.96434 q^{41} -8.37200 q^{43} +(1.47921 + 0.854023i) q^{44} +(2.72199 + 4.71463i) q^{46} +(-2.61809 + 4.53466i) q^{47} +(3.20014 - 6.22568i) q^{49} +2.03575i q^{50} +(-1.11124 + 0.641574i) q^{52} +(-9.46059 + 5.46207i) q^{53} -2.94074i q^{55} +(-1.37838 - 2.25833i) q^{56} +(-0.724802 + 1.25539i) q^{58} +(2.08655 + 3.61401i) q^{59} +(-2.28575 - 1.31968i) q^{61} +6.72352 q^{62} -1.00000 q^{64} +(1.91322 + 1.10460i) q^{65} +(-4.31994 - 7.48235i) q^{67} +(-2.60152 + 4.50597i) q^{68} +(-2.18068 + 3.99930i) q^{70} -5.07491i q^{71} +(8.18155 - 4.72362i) q^{73} +(6.51181 - 3.75959i) q^{74} +2.76418i q^{76} +(-2.16339 + 3.96758i) q^{77} +(-6.73747 + 11.6696i) q^{79} +(0.860850 + 1.49104i) q^{80} +(7.76335 + 4.48217i) q^{82} -6.07609 q^{83} +8.95809 q^{85} +(-7.25036 - 4.18600i) q^{86} +(0.854023 + 1.47921i) q^{88} +(4.16679 - 7.21709i) q^{89} +(-1.76866 - 2.89778i) q^{91} +5.44399i q^{92} +(-4.53466 + 2.61809i) q^{94} +(4.12150 - 2.37955i) q^{95} -10.0571i q^{97} +(5.88425 - 3.79152i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 8 q^{7} - 12 q^{11} - 12 q^{14} - 8 q^{16} - 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} - 60 q^{35} + 4 q^{37} + 12 q^{38} + 48 q^{41} - 32 q^{43} - 12 q^{44} + 4 q^{49} - 12 q^{52} - 12 q^{56} - 12 q^{58} + 24 q^{59} - 12 q^{61} + 48 q^{62} - 16 q^{64} - 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} - 36 q^{74} - 84 q^{77} + 8 q^{79} + 72 q^{83} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 36 q^{94} - 12 q^{95} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.860850 1.49104i 0.384984 0.666812i −0.606783 0.794868i \(-0.707540\pi\)
0.991767 + 0.128056i \(0.0408736\pi\)
\(6\) 0 0
\(7\) −2.25833 + 1.37838i −0.853570 + 0.520978i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.49104 0.860850i 0.471507 0.272225i
\(11\) 1.47921 0.854023i 0.445999 0.257498i −0.260140 0.965571i \(-0.583769\pi\)
0.706139 + 0.708073i \(0.250435\pi\)
\(12\) 0 0
\(13\) 1.28315i 0.355881i 0.984041 + 0.177941i \(0.0569435\pi\)
−0.984041 + 0.177941i \(0.943056\pi\)
\(14\) −2.64496 + 0.0645439i −0.706896 + 0.0172501i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.60152 + 4.50597i 0.630962 + 1.09286i 0.987355 + 0.158522i \(0.0506729\pi\)
−0.356394 + 0.934336i \(0.615994\pi\)
\(18\) 0 0
\(19\) 2.39385 + 1.38209i 0.549187 + 0.317074i 0.748794 0.662803i \(-0.230633\pi\)
−0.199607 + 0.979876i \(0.563966\pi\)
\(20\) 1.72170 0.384984
\(21\) 0 0
\(22\) 1.70805 0.364157
\(23\) 4.71463 + 2.72199i 0.983069 + 0.567575i 0.903195 0.429230i \(-0.141215\pi\)
0.0798736 + 0.996805i \(0.474548\pi\)
\(24\) 0 0
\(25\) 1.01787 + 1.76301i 0.203575 + 0.352602i
\(26\) −0.641574 + 1.11124i −0.125823 + 0.217932i
\(27\) 0 0
\(28\) −2.32288 1.26659i −0.438983 0.239362i
\(29\) 1.44960i 0.269185i 0.990901 + 0.134592i \(0.0429725\pi\)
−0.990901 + 0.134592i \(0.957028\pi\)
\(30\) 0 0
\(31\) 5.82274 3.36176i 1.04579 0.603790i 0.124325 0.992242i \(-0.460323\pi\)
0.921469 + 0.388452i \(0.126990\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 5.20305i 0.892315i
\(35\) 0.111125 + 4.55384i 0.0187836 + 0.769739i
\(36\) 0 0
\(37\) 3.75959 6.51181i 0.618073 1.07053i −0.371764 0.928327i \(-0.621247\pi\)
0.989837 0.142207i \(-0.0454198\pi\)
\(38\) 1.38209 + 2.39385i 0.224205 + 0.388334i
\(39\) 0 0
\(40\) 1.49104 + 0.860850i 0.235754 + 0.136112i
\(41\) 8.96434 1.39999 0.699997 0.714145i \(-0.253184\pi\)
0.699997 + 0.714145i \(0.253184\pi\)
\(42\) 0 0
\(43\) −8.37200 −1.27672 −0.638359 0.769739i \(-0.720386\pi\)
−0.638359 + 0.769739i \(0.720386\pi\)
\(44\) 1.47921 + 0.854023i 0.222999 + 0.128749i
\(45\) 0 0
\(46\) 2.72199 + 4.71463i 0.401336 + 0.695135i
\(47\) −2.61809 + 4.53466i −0.381887 + 0.661448i −0.991332 0.131381i \(-0.958059\pi\)
0.609445 + 0.792828i \(0.291392\pi\)
\(48\) 0 0
\(49\) 3.20014 6.22568i 0.457164 0.889383i
\(50\) 2.03575i 0.287898i
\(51\) 0 0
\(52\) −1.11124 + 0.641574i −0.154101 + 0.0889703i
\(53\) −9.46059 + 5.46207i −1.29951 + 0.750273i −0.980320 0.197417i \(-0.936745\pi\)
−0.319192 + 0.947690i \(0.603411\pi\)
\(54\) 0 0
\(55\) 2.94074i 0.396530i
\(56\) −1.37838 2.25833i −0.184194 0.301783i
\(57\) 0 0
\(58\) −0.724802 + 1.25539i −0.0951711 + 0.164841i
\(59\) 2.08655 + 3.61401i 0.271646 + 0.470504i 0.969283 0.245946i \(-0.0790987\pi\)
−0.697638 + 0.716451i \(0.745765\pi\)
\(60\) 0 0
\(61\) −2.28575 1.31968i −0.292660 0.168967i 0.346481 0.938057i \(-0.387377\pi\)
−0.639141 + 0.769090i \(0.720710\pi\)
\(62\) 6.72352 0.853888
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.91322 + 1.10460i 0.237306 + 0.137009i
\(66\) 0 0
\(67\) −4.31994 7.48235i −0.527764 0.914115i −0.999476 0.0323619i \(-0.989697\pi\)
0.471712 0.881753i \(-0.343636\pi\)
\(68\) −2.60152 + 4.50597i −0.315481 + 0.546429i
\(69\) 0 0
\(70\) −2.18068 + 3.99930i −0.260641 + 0.478008i
\(71\) 5.07491i 0.602282i −0.953580 0.301141i \(-0.902633\pi\)
0.953580 0.301141i \(-0.0973674\pi\)
\(72\) 0 0
\(73\) 8.18155 4.72362i 0.957578 0.552858i 0.0621516 0.998067i \(-0.480204\pi\)
0.895427 + 0.445209i \(0.146870\pi\)
\(74\) 6.51181 3.75959i 0.756982 0.437044i
\(75\) 0 0
\(76\) 2.76418i 0.317074i
\(77\) −2.16339 + 3.96758i −0.246541 + 0.452148i
\(78\) 0 0
\(79\) −6.73747 + 11.6696i −0.758024 + 1.31294i 0.185833 + 0.982581i \(0.440502\pi\)
−0.943857 + 0.330355i \(0.892832\pi\)
\(80\) 0.860850 + 1.49104i 0.0962460 + 0.166703i
\(81\) 0 0
\(82\) 7.76335 + 4.48217i 0.857318 + 0.494973i
\(83\) −6.07609 −0.666937 −0.333469 0.942761i \(-0.608219\pi\)
−0.333469 + 0.942761i \(0.608219\pi\)
\(84\) 0 0
\(85\) 8.95809 0.971641
\(86\) −7.25036 4.18600i −0.781826 0.451388i
\(87\) 0 0
\(88\) 0.854023 + 1.47921i 0.0910391 + 0.157684i
\(89\) 4.16679 7.21709i 0.441679 0.765010i −0.556136 0.831092i \(-0.687717\pi\)
0.997814 + 0.0660818i \(0.0210498\pi\)
\(90\) 0 0
\(91\) −1.76866 2.89778i −0.185406 0.303770i
\(92\) 5.44399i 0.567575i
\(93\) 0 0
\(94\) −4.53466 + 2.61809i −0.467714 + 0.270035i
\(95\) 4.12150 2.37955i 0.422857 0.244136i
\(96\) 0 0
\(97\) 10.0571i 1.02115i −0.859834 0.510574i \(-0.829433\pi\)
0.859834 0.510574i \(-0.170567\pi\)
\(98\) 5.88425 3.79152i 0.594399 0.383002i
\(99\) 0 0
\(100\) −1.01787 + 1.76301i −0.101787 + 0.176301i
\(101\) 7.90634 + 13.6942i 0.786710 + 1.36262i 0.927972 + 0.372650i \(0.121551\pi\)
−0.141261 + 0.989972i \(0.545116\pi\)
\(102\) 0 0
\(103\) −12.5857 7.26634i −1.24010 0.715973i −0.270988 0.962583i \(-0.587350\pi\)
−0.969115 + 0.246609i \(0.920684\pi\)
\(104\) −1.28315 −0.125823
\(105\) 0 0
\(106\) −10.9241 −1.06105
\(107\) −3.01627 1.74144i −0.291594 0.168352i 0.347067 0.937841i \(-0.387178\pi\)
−0.638660 + 0.769489i \(0.720511\pi\)
\(108\) 0 0
\(109\) −4.53452 7.85401i −0.434328 0.752278i 0.562913 0.826516i \(-0.309681\pi\)
−0.997241 + 0.0742384i \(0.976347\pi\)
\(110\) 1.47037 2.54676i 0.140194 0.242824i
\(111\) 0 0
\(112\) −0.0645439 2.64496i −0.00609883 0.249926i
\(113\) 6.62531i 0.623257i −0.950204 0.311628i \(-0.899126\pi\)
0.950204 0.311628i \(-0.100874\pi\)
\(114\) 0 0
\(115\) 8.11719 4.68646i 0.756931 0.437015i
\(116\) −1.25539 + 0.724802i −0.116560 + 0.0672961i
\(117\) 0 0
\(118\) 4.17310i 0.384165i
\(119\) −12.0860 6.59010i −1.10793 0.604114i
\(120\) 0 0
\(121\) −4.04129 + 6.99972i −0.367390 + 0.636338i
\(122\) −1.31968 2.28575i −0.119478 0.206942i
\(123\) 0 0
\(124\) 5.82274 + 3.36176i 0.522897 + 0.301895i
\(125\) 12.1134 1.08346
\(126\) 0 0
\(127\) −19.4923 −1.72966 −0.864830 0.502065i \(-0.832574\pi\)
−0.864830 + 0.502065i \(0.832574\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 1.10460 + 1.91322i 0.0968797 + 0.167801i
\(131\) −5.31336 + 9.20301i −0.464230 + 0.804071i −0.999166 0.0408220i \(-0.987002\pi\)
0.534936 + 0.844893i \(0.320336\pi\)
\(132\) 0 0
\(133\) −7.31116 + 0.178411i −0.633958 + 0.0154702i
\(134\) 8.63987i 0.746371i
\(135\) 0 0
\(136\) −4.50597 + 2.60152i −0.386384 + 0.223079i
\(137\) 1.76722 1.02030i 0.150984 0.0871704i −0.422605 0.906314i \(-0.638884\pi\)
0.573588 + 0.819144i \(0.305551\pi\)
\(138\) 0 0
\(139\) 17.9136i 1.51941i 0.650266 + 0.759707i \(0.274658\pi\)
−0.650266 + 0.759707i \(0.725342\pi\)
\(140\) −3.88817 + 2.37316i −0.328611 + 0.200568i
\(141\) 0 0
\(142\) 2.53746 4.39500i 0.212939 0.368821i
\(143\) 1.09584 + 1.89805i 0.0916386 + 0.158723i
\(144\) 0 0
\(145\) 2.16141 + 1.24789i 0.179495 + 0.103632i
\(146\) 9.44724 0.781860
\(147\) 0 0
\(148\) 7.51919 0.618073
\(149\) 9.22227 + 5.32448i 0.755518 + 0.436198i 0.827684 0.561194i \(-0.189658\pi\)
−0.0721664 + 0.997393i \(0.522991\pi\)
\(150\) 0 0
\(151\) −5.09396 8.82301i −0.414541 0.718006i 0.580839 0.814018i \(-0.302725\pi\)
−0.995380 + 0.0960123i \(0.969391\pi\)
\(152\) −1.38209 + 2.39385i −0.112102 + 0.194167i
\(153\) 0 0
\(154\) −3.85734 + 2.35433i −0.310833 + 0.189718i
\(155\) 11.5759i 0.929797i
\(156\) 0 0
\(157\) 3.72429 2.15022i 0.297231 0.171606i −0.343967 0.938982i \(-0.611771\pi\)
0.641198 + 0.767375i \(0.278438\pi\)
\(158\) −11.6696 + 6.73747i −0.928386 + 0.536004i
\(159\) 0 0
\(160\) 1.72170i 0.136112i
\(161\) −14.3992 + 0.351376i −1.13481 + 0.0276923i
\(162\) 0 0
\(163\) −4.30789 + 7.46149i −0.337420 + 0.584429i −0.983947 0.178463i \(-0.942888\pi\)
0.646527 + 0.762891i \(0.276221\pi\)
\(164\) 4.48217 + 7.76335i 0.349999 + 0.606216i
\(165\) 0 0
\(166\) −5.26205 3.03804i −0.408414 0.235798i
\(167\) 13.9852 1.08220 0.541102 0.840957i \(-0.318007\pi\)
0.541102 + 0.840957i \(0.318007\pi\)
\(168\) 0 0
\(169\) 11.3535 0.873348
\(170\) 7.75793 + 4.47904i 0.595006 + 0.343527i
\(171\) 0 0
\(172\) −4.18600 7.25036i −0.319179 0.552835i
\(173\) −8.01193 + 13.8771i −0.609135 + 1.05505i 0.382248 + 0.924060i \(0.375150\pi\)
−0.991383 + 0.130994i \(0.958183\pi\)
\(174\) 0 0
\(175\) −4.72879 2.57845i −0.357463 0.194912i
\(176\) 1.70805i 0.128749i
\(177\) 0 0
\(178\) 7.21709 4.16679i 0.540944 0.312314i
\(179\) 3.23826 1.86961i 0.242039 0.139741i −0.374075 0.927399i \(-0.622040\pi\)
0.616113 + 0.787658i \(0.288706\pi\)
\(180\) 0 0
\(181\) 1.07693i 0.0800478i −0.999199 0.0400239i \(-0.987257\pi\)
0.999199 0.0400239i \(-0.0127434\pi\)
\(182\) −0.0828194 3.39388i −0.00613898 0.251571i
\(183\) 0 0
\(184\) −2.72199 + 4.71463i −0.200668 + 0.347567i
\(185\) −6.47289 11.2114i −0.475897 0.824277i
\(186\) 0 0
\(187\) 7.69640 + 4.44352i 0.562817 + 0.324942i
\(188\) −5.23617 −0.381887
\(189\) 0 0
\(190\) 4.75910 0.345261
\(191\) −14.5988 8.42859i −1.05633 0.609872i −0.131914 0.991261i \(-0.542112\pi\)
−0.924414 + 0.381389i \(0.875446\pi\)
\(192\) 0 0
\(193\) −7.11546 12.3243i −0.512182 0.887125i −0.999900 0.0141241i \(-0.995504\pi\)
0.487718 0.873001i \(-0.337829\pi\)
\(194\) 5.02857 8.70974i 0.361030 0.625323i
\(195\) 0 0
\(196\) 6.99167 0.341433i 0.499405 0.0243880i
\(197\) 19.4230i 1.38383i −0.721979 0.691915i \(-0.756767\pi\)
0.721979 0.691915i \(-0.243233\pi\)
\(198\) 0 0
\(199\) 6.99323 4.03754i 0.495737 0.286214i −0.231214 0.972903i \(-0.574270\pi\)
0.726951 + 0.686689i \(0.240937\pi\)
\(200\) −1.76301 + 1.01787i −0.124664 + 0.0719745i
\(201\) 0 0
\(202\) 15.8127i 1.11258i
\(203\) −1.99810 3.27369i −0.140239 0.229768i
\(204\) 0 0
\(205\) 7.71696 13.3662i 0.538976 0.933533i
\(206\) −7.26634 12.5857i −0.506270 0.876885i
\(207\) 0 0
\(208\) −1.11124 0.641574i −0.0770506 0.0444852i
\(209\) 4.72135 0.326583
\(210\) 0 0
\(211\) 19.9133 1.37089 0.685444 0.728125i \(-0.259608\pi\)
0.685444 + 0.728125i \(0.259608\pi\)
\(212\) −9.46059 5.46207i −0.649756 0.375137i
\(213\) 0 0
\(214\) −1.74144 3.01627i −0.119043 0.206188i
\(215\) −7.20703 + 12.4829i −0.491516 + 0.851330i
\(216\) 0 0
\(217\) −8.51591 + 15.6179i −0.578097 + 1.06021i
\(218\) 9.06903i 0.614232i
\(219\) 0 0
\(220\) 2.54676 1.47037i 0.171702 0.0991324i
\(221\) −5.78183 + 3.33814i −0.388928 + 0.224548i
\(222\) 0 0
\(223\) 21.2100i 1.42033i −0.704036 0.710164i \(-0.748621\pi\)
0.704036 0.710164i \(-0.251379\pi\)
\(224\) 1.26659 2.32288i 0.0846273 0.155204i
\(225\) 0 0
\(226\) 3.31266 5.73769i 0.220355 0.381665i
\(227\) −6.79579 11.7707i −0.451053 0.781246i 0.547399 0.836872i \(-0.315618\pi\)
−0.998452 + 0.0556258i \(0.982285\pi\)
\(228\) 0 0
\(229\) −20.8769 12.0533i −1.37959 0.796504i −0.387476 0.921880i \(-0.626653\pi\)
−0.992109 + 0.125376i \(0.959986\pi\)
\(230\) 9.37292 0.618032
\(231\) 0 0
\(232\) −1.44960 −0.0951711
\(233\) −15.9891 9.23129i −1.04748 0.604762i −0.125536 0.992089i \(-0.540065\pi\)
−0.921942 + 0.387327i \(0.873398\pi\)
\(234\) 0 0
\(235\) 4.50756 + 7.80732i 0.294041 + 0.509294i
\(236\) −2.08655 + 3.61401i −0.135823 + 0.235252i
\(237\) 0 0
\(238\) −7.17177 11.7502i −0.464877 0.761653i
\(239\) 23.1917i 1.50015i −0.661355 0.750073i \(-0.730019\pi\)
0.661355 0.750073i \(-0.269981\pi\)
\(240\) 0 0
\(241\) 22.4458 12.9591i 1.44586 0.834770i 0.447632 0.894218i \(-0.352267\pi\)
0.998231 + 0.0594484i \(0.0189342\pi\)
\(242\) −6.99972 + 4.04129i −0.449959 + 0.259784i
\(243\) 0 0
\(244\) 2.63936i 0.168967i
\(245\) −6.52787 10.1309i −0.417050 0.647240i
\(246\) 0 0
\(247\) −1.77343 + 3.07167i −0.112841 + 0.195446i
\(248\) 3.36176 + 5.82274i 0.213472 + 0.369744i
\(249\) 0 0
\(250\) 10.4906 + 6.05672i 0.663481 + 0.383061i
\(251\) 17.9492 1.13295 0.566473 0.824081i \(-0.308308\pi\)
0.566473 + 0.824081i \(0.308308\pi\)
\(252\) 0 0
\(253\) 9.29858 0.584597
\(254\) −16.8808 9.74614i −1.05920 0.611527i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.31001 7.46516i 0.268851 0.465664i −0.699714 0.714423i \(-0.746689\pi\)
0.968565 + 0.248759i \(0.0800226\pi\)
\(258\) 0 0
\(259\) 0.485318 + 19.8880i 0.0301562 + 1.23578i
\(260\) 2.20920i 0.137009i
\(261\) 0 0
\(262\) −9.20301 + 5.31336i −0.568564 + 0.328260i
\(263\) 16.9777 9.80208i 1.04689 0.604422i 0.125113 0.992143i \(-0.460071\pi\)
0.921777 + 0.387720i \(0.126737\pi\)
\(264\) 0 0
\(265\) 18.8081i 1.15537i
\(266\) −6.42086 3.50107i −0.393688 0.214665i
\(267\) 0 0
\(268\) 4.31994 7.48235i 0.263882 0.457057i
\(269\) −6.95328 12.0434i −0.423949 0.734301i 0.572373 0.819994i \(-0.306023\pi\)
−0.996322 + 0.0856923i \(0.972690\pi\)
\(270\) 0 0
\(271\) −1.90381 1.09916i −0.115648 0.0667694i 0.441060 0.897478i \(-0.354603\pi\)
−0.556708 + 0.830708i \(0.687936\pi\)
\(272\) −5.20305 −0.315481
\(273\) 0 0
\(274\) 2.04061 0.123278
\(275\) 3.01130 + 1.73857i 0.181588 + 0.104840i
\(276\) 0 0
\(277\) 0.259978 + 0.450295i 0.0156206 + 0.0270556i 0.873730 0.486411i \(-0.161694\pi\)
−0.858109 + 0.513467i \(0.828361\pi\)
\(278\) −8.95681 + 15.5137i −0.537194 + 0.930447i
\(279\) 0 0
\(280\) −4.55384 + 0.111125i −0.272144 + 0.00664101i
\(281\) 19.7706i 1.17942i −0.807616 0.589709i \(-0.799242\pi\)
0.807616 0.589709i \(-0.200758\pi\)
\(282\) 0 0
\(283\) −28.1815 + 16.2706i −1.67522 + 0.967187i −0.710575 + 0.703621i \(0.751565\pi\)
−0.964641 + 0.263566i \(0.915101\pi\)
\(284\) 4.39500 2.53746i 0.260796 0.150570i
\(285\) 0 0
\(286\) 2.19168i 0.129597i
\(287\) −20.2445 + 12.3563i −1.19499 + 0.729367i
\(288\) 0 0
\(289\) −5.03584 + 8.72233i −0.296226 + 0.513078i
\(290\) 1.24789 + 2.16141i 0.0732787 + 0.126922i
\(291\) 0 0
\(292\) 8.18155 + 4.72362i 0.478789 + 0.276429i
\(293\) −25.5700 −1.49382 −0.746909 0.664927i \(-0.768463\pi\)
−0.746909 + 0.664927i \(0.768463\pi\)
\(294\) 0 0
\(295\) 7.18483 0.418317
\(296\) 6.51181 + 3.75959i 0.378491 + 0.218522i
\(297\) 0 0
\(298\) 5.32448 + 9.22227i 0.308439 + 0.534232i
\(299\) −3.49272 + 6.04957i −0.201989 + 0.349856i
\(300\) 0 0
\(301\) 18.9068 11.5398i 1.08977 0.665142i
\(302\) 10.1879i 0.586249i
\(303\) 0 0
\(304\) −2.39385 + 1.38209i −0.137297 + 0.0792684i
\(305\) −3.93538 + 2.27209i −0.225339 + 0.130100i
\(306\) 0 0
\(307\) 4.85183i 0.276909i 0.990369 + 0.138454i \(0.0442134\pi\)
−0.990369 + 0.138454i \(0.955787\pi\)
\(308\) −4.51772 + 0.110244i −0.257421 + 0.00628173i
\(309\) 0 0
\(310\) 5.78794 10.0250i 0.328733 0.569382i
\(311\) −2.17193 3.76189i −0.123159 0.213317i 0.797853 0.602852i \(-0.205969\pi\)
−0.921012 + 0.389535i \(0.872636\pi\)
\(312\) 0 0
\(313\) 19.5391 + 11.2809i 1.10442 + 0.637635i 0.937378 0.348315i \(-0.113246\pi\)
0.167039 + 0.985950i \(0.446579\pi\)
\(314\) 4.30044 0.242688
\(315\) 0 0
\(316\) −13.4749 −0.758024
\(317\) 29.6293 + 17.1065i 1.66415 + 0.960795i 0.970703 + 0.240282i \(0.0772399\pi\)
0.693442 + 0.720513i \(0.256093\pi\)
\(318\) 0 0
\(319\) 1.23799 + 2.14427i 0.0693144 + 0.120056i
\(320\) −0.860850 + 1.49104i −0.0481230 + 0.0833515i
\(321\) 0 0
\(322\) −12.6457 6.89528i −0.704718 0.384259i
\(323\) 14.3822i 0.800245i
\(324\) 0 0
\(325\) −2.26220 + 1.30608i −0.125484 + 0.0724485i
\(326\) −7.46149 + 4.30789i −0.413254 + 0.238592i
\(327\) 0 0
\(328\) 8.96434i 0.494973i
\(329\) −0.337963 13.8495i −0.0186325 0.763547i
\(330\) 0 0
\(331\) 2.28003 3.94913i 0.125322 0.217064i −0.796537 0.604590i \(-0.793337\pi\)
0.921859 + 0.387526i \(0.126670\pi\)
\(332\) −3.03804 5.26205i −0.166734 0.288792i
\(333\) 0 0
\(334\) 12.1115 + 6.99258i 0.662712 + 0.382617i
\(335\) −14.8753 −0.812723
\(336\) 0 0
\(337\) 30.7531 1.67523 0.837613 0.546264i \(-0.183950\pi\)
0.837613 + 0.546264i \(0.183950\pi\)
\(338\) 9.83245 + 5.67676i 0.534815 + 0.308775i
\(339\) 0 0
\(340\) 4.47904 + 7.75793i 0.242910 + 0.420733i
\(341\) 5.74204 9.94550i 0.310949 0.538579i
\(342\) 0 0
\(343\) 1.35435 + 18.4707i 0.0731278 + 0.997323i
\(344\) 8.37200i 0.451388i
\(345\) 0 0
\(346\) −13.8771 + 8.01193i −0.746035 + 0.430724i
\(347\) −20.6474 + 11.9208i −1.10841 + 0.639940i −0.938417 0.345506i \(-0.887707\pi\)
−0.169992 + 0.985446i \(0.554374\pi\)
\(348\) 0 0
\(349\) 3.14373i 0.168280i −0.996454 0.0841401i \(-0.973186\pi\)
0.996454 0.0841401i \(-0.0268143\pi\)
\(350\) −2.80603 4.59740i −0.149989 0.245741i
\(351\) 0 0
\(352\) −0.854023 + 1.47921i −0.0455196 + 0.0788422i
\(353\) 13.8459 + 23.9818i 0.736944 + 1.27642i 0.953865 + 0.300236i \(0.0970653\pi\)
−0.216921 + 0.976189i \(0.569601\pi\)
\(354\) 0 0
\(355\) −7.56688 4.36874i −0.401608 0.231869i
\(356\) 8.33357 0.441679
\(357\) 0 0
\(358\) 3.73922 0.197624
\(359\) 18.1125 + 10.4572i 0.955940 + 0.551912i 0.894921 0.446225i \(-0.147232\pi\)
0.0610187 + 0.998137i \(0.480565\pi\)
\(360\) 0 0
\(361\) −5.67965 9.83744i −0.298929 0.517760i
\(362\) 0.538466 0.932651i 0.0283012 0.0490190i
\(363\) 0 0
\(364\) 1.62522 2.98060i 0.0851845 0.156226i
\(365\) 16.2653i 0.851366i
\(366\) 0 0
\(367\) −1.01292 + 0.584811i −0.0528741 + 0.0305269i −0.526204 0.850358i \(-0.676385\pi\)
0.473330 + 0.880885i \(0.343052\pi\)
\(368\) −4.71463 + 2.72199i −0.245767 + 0.141894i
\(369\) 0 0
\(370\) 12.9458i 0.673019i
\(371\) 13.8364 25.3755i 0.718348 1.31743i
\(372\) 0 0
\(373\) −4.85503 + 8.40915i −0.251384 + 0.435409i −0.963907 0.266239i \(-0.914219\pi\)
0.712523 + 0.701648i \(0.247552\pi\)
\(374\) 4.44352 + 7.69640i 0.229769 + 0.397971i
\(375\) 0 0
\(376\) −4.53466 2.61809i −0.233857 0.135017i
\(377\) −1.86006 −0.0957978
\(378\) 0 0
\(379\) −15.1452 −0.777958 −0.388979 0.921247i \(-0.627172\pi\)
−0.388979 + 0.921247i \(0.627172\pi\)
\(380\) 4.12150 + 2.37955i 0.211428 + 0.122068i
\(381\) 0 0
\(382\) −8.42859 14.5988i −0.431244 0.746937i
\(383\) −15.9902 + 27.6958i −0.817059 + 1.41519i 0.0907815 + 0.995871i \(0.471064\pi\)
−0.907840 + 0.419316i \(0.862270\pi\)
\(384\) 0 0
\(385\) 4.05346 + 6.64118i 0.206583 + 0.338466i
\(386\) 14.2309i 0.724335i
\(387\) 0 0
\(388\) 8.70974 5.02857i 0.442170 0.255287i
\(389\) −21.6056 + 12.4740i −1.09545 + 0.632457i −0.935021 0.354591i \(-0.884620\pi\)
−0.160426 + 0.987048i \(0.551287\pi\)
\(390\) 0 0
\(391\) 28.3253i 1.43247i
\(392\) 6.22568 + 3.20014i 0.314444 + 0.161632i
\(393\) 0 0
\(394\) 9.71149 16.8208i 0.489258 0.847420i
\(395\) 11.5999 + 20.0916i 0.583654 + 1.01092i
\(396\) 0 0
\(397\) 0.280202 + 0.161774i 0.0140629 + 0.00811923i 0.507015 0.861937i \(-0.330749\pi\)
−0.492952 + 0.870056i \(0.664082\pi\)
\(398\) 8.07509 0.404768
\(399\) 0 0
\(400\) −2.03575 −0.101787
\(401\) −16.4678 9.50768i −0.822362 0.474791i 0.0288684 0.999583i \(-0.490810\pi\)
−0.851230 + 0.524792i \(0.824143\pi\)
\(402\) 0 0
\(403\) 4.31364 + 7.47144i 0.214877 + 0.372179i
\(404\) −7.90634 + 13.6942i −0.393355 + 0.681311i
\(405\) 0 0
\(406\) −0.0935631 3.83415i −0.00464346 0.190286i
\(407\) 12.8431i 0.636609i
\(408\) 0 0
\(409\) 3.90841 2.25652i 0.193258 0.111578i −0.400249 0.916407i \(-0.631076\pi\)
0.593507 + 0.804829i \(0.297743\pi\)
\(410\) 13.3662 7.71696i 0.660108 0.381113i
\(411\) 0 0
\(412\) 14.5327i 0.715973i
\(413\) −9.69361 5.28559i −0.476991 0.260087i
\(414\) 0 0
\(415\) −5.23060 + 9.05967i −0.256760 + 0.444722i
\(416\) −0.641574 1.11124i −0.0314558 0.0544830i
\(417\) 0 0
\(418\) 4.08881 + 2.36068i 0.199990 + 0.115464i
\(419\) 29.2149 1.42724 0.713621 0.700532i \(-0.247054\pi\)
0.713621 + 0.700532i \(0.247054\pi\)
\(420\) 0 0
\(421\) −36.3361 −1.77092 −0.885458 0.464720i \(-0.846155\pi\)
−0.885458 + 0.464720i \(0.846155\pi\)
\(422\) 17.2454 + 9.95665i 0.839494 + 0.484682i
\(423\) 0 0
\(424\) −5.46207 9.46059i −0.265262 0.459447i
\(425\) −5.29604 + 9.17301i −0.256896 + 0.444957i
\(426\) 0 0
\(427\) 6.98100 0.170354i 0.337834 0.00824403i
\(428\) 3.48289i 0.168352i
\(429\) 0 0
\(430\) −12.4829 + 7.20703i −0.601981 + 0.347554i
\(431\) 10.4967 6.06028i 0.505609 0.291913i −0.225418 0.974262i \(-0.572375\pi\)
0.731027 + 0.682349i \(0.239041\pi\)
\(432\) 0 0
\(433\) 31.4160i 1.50976i −0.655864 0.754879i \(-0.727696\pi\)
0.655864 0.754879i \(-0.272304\pi\)
\(434\) −15.1839 + 9.26755i −0.728853 + 0.444857i
\(435\) 0 0
\(436\) 4.53452 7.85401i 0.217164 0.376139i
\(437\) 7.52409 + 13.0321i 0.359926 + 0.623410i
\(438\) 0 0
\(439\) −2.80118 1.61726i −0.133693 0.0771877i 0.431662 0.902036i \(-0.357927\pi\)
−0.565355 + 0.824848i \(0.691261\pi\)
\(440\) 2.94074 0.140194
\(441\) 0 0
\(442\) −6.67628 −0.317558
\(443\) 7.65097 + 4.41729i 0.363509 + 0.209872i 0.670619 0.741802i \(-0.266029\pi\)
−0.307110 + 0.951674i \(0.599362\pi\)
\(444\) 0 0
\(445\) −7.17396 12.4257i −0.340078 0.589033i
\(446\) 10.6050 18.3684i 0.502162 0.869770i
\(447\) 0 0
\(448\) 2.25833 1.37838i 0.106696 0.0651223i
\(449\) 6.83193i 0.322419i −0.986920 0.161209i \(-0.948461\pi\)
0.986920 0.161209i \(-0.0515395\pi\)
\(450\) 0 0
\(451\) 13.2602 7.65575i 0.624396 0.360495i
\(452\) 5.73769 3.31266i 0.269878 0.155814i
\(453\) 0 0
\(454\) 13.5916i 0.637885i
\(455\) −5.84325 + 0.142590i −0.273936 + 0.00668473i
\(456\) 0 0
\(457\) −9.21190 + 15.9555i −0.430915 + 0.746366i −0.996952 0.0780133i \(-0.975142\pi\)
0.566038 + 0.824379i \(0.308476\pi\)
\(458\) −12.0533 20.8769i −0.563213 0.975514i
\(459\) 0 0
\(460\) 8.11719 + 4.68646i 0.378466 + 0.218507i
\(461\) 29.9065 1.39289 0.696443 0.717612i \(-0.254765\pi\)
0.696443 + 0.717612i \(0.254765\pi\)
\(462\) 0 0
\(463\) 1.32509 0.0615821 0.0307911 0.999526i \(-0.490197\pi\)
0.0307911 + 0.999526i \(0.490197\pi\)
\(464\) −1.25539 0.724802i −0.0582802 0.0336481i
\(465\) 0 0
\(466\) −9.23129 15.9891i −0.427631 0.740679i
\(467\) 13.6817 23.6973i 0.633112 1.09658i −0.353800 0.935321i \(-0.615111\pi\)
0.986912 0.161260i \(-0.0515559\pi\)
\(468\) 0 0
\(469\) 20.0694 + 10.9431i 0.926718 + 0.505307i
\(470\) 9.01512i 0.415836i
\(471\) 0 0
\(472\) −3.61401 + 2.08655i −0.166348 + 0.0960413i
\(473\) −12.3839 + 7.14987i −0.569414 + 0.328752i
\(474\) 0 0
\(475\) 5.62718i 0.258193i
\(476\) −0.335825 13.7619i −0.0153925 0.630774i
\(477\) 0 0
\(478\) 11.5958 20.0846i 0.530381 0.918648i
\(479\) −8.41054 14.5675i −0.384287 0.665605i 0.607383 0.794409i \(-0.292219\pi\)
−0.991670 + 0.128804i \(0.958886\pi\)
\(480\) 0 0
\(481\) 8.35561 + 4.82412i 0.380983 + 0.219961i
\(482\) 25.9182 1.18054
\(483\) 0 0
\(484\) −8.08258 −0.367390
\(485\) −14.9956 8.65769i −0.680913 0.393126i
\(486\) 0 0
\(487\) 0.357602 + 0.619385i 0.0162045 + 0.0280670i 0.874014 0.485901i \(-0.161508\pi\)
−0.857809 + 0.513968i \(0.828175\pi\)
\(488\) 1.31968 2.28575i 0.0597390 0.103471i
\(489\) 0 0
\(490\) −0.587845 12.0376i −0.0265561 0.543801i
\(491\) 5.36907i 0.242303i 0.992634 + 0.121151i \(0.0386586\pi\)
−0.992634 + 0.121151i \(0.961341\pi\)
\(492\) 0 0
\(493\) −6.53187 + 3.77118i −0.294181 + 0.169845i
\(494\) −3.07167 + 1.77343i −0.138201 + 0.0797903i
\(495\) 0 0
\(496\) 6.72352i 0.301895i
\(497\) 6.99515 + 11.4609i 0.313776 + 0.514089i
\(498\) 0 0
\(499\) −12.0464 + 20.8649i −0.539269 + 0.934041i 0.459675 + 0.888087i \(0.347966\pi\)
−0.998944 + 0.0459536i \(0.985367\pi\)
\(500\) 6.05672 + 10.4906i 0.270865 + 0.469152i
\(501\) 0 0
\(502\) 15.5445 + 8.97461i 0.693784 + 0.400557i
\(503\) 26.8386 1.19667 0.598336 0.801245i \(-0.295829\pi\)
0.598336 + 0.801245i \(0.295829\pi\)
\(504\) 0 0
\(505\) 27.2247 1.21148
\(506\) 8.05281 + 4.64929i 0.357991 + 0.206686i
\(507\) 0 0
\(508\) −9.74614 16.8808i −0.432415 0.748965i
\(509\) −20.1952 + 34.9791i −0.895137 + 1.55042i −0.0615030 + 0.998107i \(0.519589\pi\)
−0.833634 + 0.552317i \(0.813744\pi\)
\(510\) 0 0
\(511\) −11.9657 + 21.9448i −0.529333 + 0.970781i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 7.46516 4.31001i 0.329274 0.190107i
\(515\) −21.6687 + 12.5105i −0.954839 + 0.551277i
\(516\) 0 0
\(517\) 8.94362i 0.393340i
\(518\) −9.52369 + 17.4661i −0.418447 + 0.767419i
\(519\) 0 0
\(520\) −1.10460 + 1.91322i −0.0484399 + 0.0839003i
\(521\) 15.1983 + 26.3243i 0.665852 + 1.15329i 0.979054 + 0.203602i \(0.0652649\pi\)
−0.313202 + 0.949686i \(0.601402\pi\)
\(522\) 0 0
\(523\) −5.53367 3.19487i −0.241971 0.139702i 0.374112 0.927384i \(-0.377948\pi\)
−0.616082 + 0.787682i \(0.711281\pi\)
\(524\) −10.6267 −0.464230
\(525\) 0 0
\(526\) 19.6042 0.854782
\(527\) 30.2960 + 17.4914i 1.31971 + 0.761937i
\(528\) 0 0
\(529\) 3.31851 + 5.74782i 0.144283 + 0.249905i
\(530\) −9.40405 + 16.2883i −0.408486 + 0.707518i
\(531\) 0 0
\(532\) −3.81009 6.24245i −0.165188 0.270644i
\(533\) 11.5026i 0.498232i
\(534\) 0 0
\(535\) −5.19311 + 2.99825i −0.224518 + 0.129625i
\(536\) 7.48235 4.31994i 0.323188 0.186593i
\(537\) 0 0
\(538\) 13.9066i 0.599555i
\(539\) −0.583182 11.9421i −0.0251194 0.514382i
\(540\) 0 0
\(541\) −0.909263 + 1.57489i −0.0390923 + 0.0677098i −0.884910 0.465763i \(-0.845780\pi\)
0.845817 + 0.533473i \(0.179113\pi\)
\(542\) −1.09916 1.90381i −0.0472131 0.0817755i
\(543\) 0 0
\(544\) −4.50597 2.60152i −0.193192 0.111539i
\(545\) −15.6142 −0.668837
\(546\) 0 0
\(547\) −43.7214 −1.86939 −0.934695 0.355450i \(-0.884327\pi\)
−0.934695 + 0.355450i \(0.884327\pi\)
\(548\) 1.76722 + 1.02030i 0.0754918 + 0.0435852i
\(549\) 0 0
\(550\) 1.73857 + 3.01130i 0.0741331 + 0.128402i
\(551\) −2.00348 + 3.47014i −0.0853513 + 0.147833i
\(552\) 0 0
\(553\) −0.869725 35.6407i −0.0369845 1.51560i
\(554\) 0.519956i 0.0220908i
\(555\) 0 0
\(556\) −15.5137 + 8.95681i −0.657926 + 0.379854i
\(557\) 22.5591 13.0245i 0.955859 0.551865i 0.0609627 0.998140i \(-0.480583\pi\)
0.894896 + 0.446275i \(0.147250\pi\)
\(558\) 0 0
\(559\) 10.7425i 0.454360i
\(560\) −3.99930 2.18068i −0.169001 0.0921506i
\(561\) 0 0
\(562\) 9.88532 17.1219i 0.416987 0.722243i
\(563\) −2.00985 3.48116i −0.0847051 0.146713i 0.820560 0.571560i \(-0.193661\pi\)
−0.905265 + 0.424846i \(0.860328\pi\)
\(564\) 0 0
\(565\) −9.87858 5.70340i −0.415595 0.239944i
\(566\) −32.5412 −1.36781
\(567\) 0 0
\(568\) 5.07491 0.212939
\(569\) −2.17982 1.25852i −0.0913826 0.0527598i 0.453612 0.891199i \(-0.350135\pi\)
−0.544995 + 0.838439i \(0.683468\pi\)
\(570\) 0 0
\(571\) 1.44662 + 2.50561i 0.0605390 + 0.104857i 0.894706 0.446655i \(-0.147385\pi\)
−0.834167 + 0.551511i \(0.814051\pi\)
\(572\) −1.09584 + 1.89805i −0.0458193 + 0.0793613i
\(573\) 0 0
\(574\) −23.7104 + 0.578594i −0.989651 + 0.0241500i
\(575\) 11.0826i 0.462176i
\(576\) 0 0
\(577\) 2.76783 1.59801i 0.115226 0.0665258i −0.441279 0.897370i \(-0.645475\pi\)
0.556505 + 0.830844i \(0.312142\pi\)
\(578\) −8.72233 + 5.03584i −0.362801 + 0.209463i
\(579\) 0 0
\(580\) 2.49578i 0.103632i
\(581\) 13.7218 8.37515i 0.569278 0.347460i
\(582\) 0 0
\(583\) −9.32947 + 16.1591i −0.386387 + 0.669242i
\(584\) 4.72362 + 8.18155i 0.195465 + 0.338555i
\(585\) 0 0
\(586\) −22.1443 12.7850i −0.914772 0.528144i
\(587\) 27.5816 1.13841 0.569207 0.822194i \(-0.307250\pi\)
0.569207 + 0.822194i \(0.307250\pi\)
\(588\) 0 0
\(589\) 18.5850 0.765783
\(590\) 6.22225 + 3.59242i 0.256166 + 0.147897i
\(591\) 0 0
\(592\) 3.75959 + 6.51181i 0.154518 + 0.267634i
\(593\) −15.1199 + 26.1884i −0.620899 + 1.07543i 0.368420 + 0.929660i \(0.379899\pi\)
−0.989319 + 0.145769i \(0.953434\pi\)
\(594\) 0 0
\(595\) −20.2303 + 12.3476i −0.829363 + 0.506204i
\(596\) 10.6490i 0.436198i
\(597\) 0 0
\(598\) −6.04957 + 3.49272i −0.247385 + 0.142828i
\(599\) −2.87629 + 1.66063i −0.117522 + 0.0678515i −0.557609 0.830104i \(-0.688281\pi\)
0.440087 + 0.897955i \(0.354948\pi\)
\(600\) 0 0
\(601\) 10.0946i 0.411766i 0.978577 + 0.205883i \(0.0660067\pi\)
−0.978577 + 0.205883i \(0.933993\pi\)
\(602\) 22.1436 0.540361i 0.902507 0.0220235i
\(603\) 0 0
\(604\) 5.09396 8.82301i 0.207270 0.359003i
\(605\) 6.95789 + 12.0514i 0.282879 + 0.489960i
\(606\) 0 0
\(607\) −18.1038 10.4523i −0.734812 0.424244i 0.0853682 0.996349i \(-0.472793\pi\)
−0.820180 + 0.572106i \(0.806127\pi\)
\(608\) −2.76418 −0.112102
\(609\) 0 0
\(610\) −4.54418 −0.183989
\(611\) −5.81864 3.35939i −0.235397 0.135907i
\(612\) 0 0
\(613\) 2.11525 + 3.66372i 0.0854341 + 0.147976i 0.905576 0.424184i \(-0.139439\pi\)
−0.820142 + 0.572160i \(0.806106\pi\)
\(614\) −2.42592 + 4.20181i −0.0979020 + 0.169571i
\(615\) 0 0
\(616\) −3.96758 2.16339i −0.159858 0.0871653i
\(617\) 6.22012i 0.250412i 0.992131 + 0.125206i \(0.0399593\pi\)
−0.992131 + 0.125206i \(0.960041\pi\)
\(618\) 0 0
\(619\) −23.7546 + 13.7148i −0.954780 + 0.551242i −0.894562 0.446943i \(-0.852513\pi\)
−0.0602173 + 0.998185i \(0.519179\pi\)
\(620\) 10.0250 5.78794i 0.402614 0.232449i
\(621\) 0 0
\(622\) 4.34386i 0.174173i
\(623\) 0.537881 + 22.0420i 0.0215498 + 0.883094i
\(624\) 0 0
\(625\) 5.33850 9.24655i 0.213540 0.369862i
\(626\) 11.2809 + 19.5391i 0.450876 + 0.780941i
\(627\) 0 0
\(628\) 3.72429 + 2.15022i 0.148616 + 0.0858032i
\(629\) 39.1227 1.55992
\(630\) 0 0
\(631\) −15.0610 −0.599570 −0.299785 0.954007i \(-0.596915\pi\)
−0.299785 + 0.954007i \(0.596915\pi\)
\(632\) −11.6696 6.73747i −0.464193 0.268002i
\(633\) 0 0
\(634\) 17.1065 + 29.6293i 0.679384 + 1.17673i
\(635\) −16.7799 + 29.0637i −0.665891 + 1.15336i
\(636\) 0 0
\(637\) 7.98847 + 4.10626i 0.316515 + 0.162696i
\(638\) 2.47599i 0.0980253i
\(639\) 0 0
\(640\) −1.49104 + 0.860850i −0.0589384 + 0.0340281i
\(641\) 21.2390 12.2623i 0.838890 0.484333i −0.0179970 0.999838i \(-0.505729\pi\)
0.856887 + 0.515505i \(0.172396\pi\)
\(642\) 0 0
\(643\) 44.1029i 1.73925i −0.493714 0.869625i \(-0.664361\pi\)
0.493714 0.869625i \(-0.335639\pi\)
\(644\) −7.50388 12.2943i −0.295694 0.484465i
\(645\) 0 0
\(646\) −7.19108 + 12.4553i −0.282929 + 0.490048i
\(647\) 3.67645 + 6.36779i 0.144536 + 0.250344i 0.929200 0.369578i \(-0.120498\pi\)
−0.784664 + 0.619922i \(0.787164\pi\)
\(648\) 0 0
\(649\) 6.17290 + 3.56393i 0.242308 + 0.139896i
\(650\) −2.61217 −0.102458
\(651\) 0 0
\(652\) −8.61578 −0.337420
\(653\) −4.37627 2.52664i −0.171257 0.0988750i 0.411922 0.911219i \(-0.364858\pi\)
−0.583178 + 0.812344i \(0.698191\pi\)
\(654\) 0 0
\(655\) 9.14801 + 15.8448i 0.357442 + 0.619109i
\(656\) −4.48217 + 7.76335i −0.174999 + 0.303108i
\(657\) 0 0
\(658\) 6.63206 12.1630i 0.258545 0.474163i
\(659\) 2.83130i 0.110292i 0.998478 + 0.0551460i \(0.0175624\pi\)
−0.998478 + 0.0551460i \(0.982438\pi\)
\(660\) 0 0
\(661\) 25.5374 14.7440i 0.993290 0.573476i 0.0870338 0.996205i \(-0.472261\pi\)
0.906256 + 0.422729i \(0.138928\pi\)
\(662\) 3.94913 2.28003i 0.153487 0.0886159i
\(663\) 0 0
\(664\) 6.07609i 0.235798i
\(665\) −6.02780 + 11.0548i −0.233748 + 0.428687i
\(666\) 0 0
\(667\) −3.94581 + 6.83435i −0.152782 + 0.264627i
\(668\) 6.99258 + 12.1115i 0.270551 + 0.468608i
\(669\) 0 0
\(670\) −12.8824 7.43764i −0.497689 0.287341i
\(671\) −4.50814 −0.174035
\(672\) 0 0
\(673\) 29.2177 1.12626 0.563130 0.826368i \(-0.309597\pi\)
0.563130 + 0.826368i \(0.309597\pi\)
\(674\) 26.6329 + 15.3765i 1.02586 + 0.592282i
\(675\) 0 0
\(676\) 5.67676 + 9.83245i 0.218337 + 0.378171i
\(677\) −11.4401 + 19.8149i −0.439680 + 0.761548i −0.997665 0.0683033i \(-0.978241\pi\)
0.557985 + 0.829851i \(0.311575\pi\)
\(678\) 0 0
\(679\) 13.8625 + 22.7124i 0.531996 + 0.871621i
\(680\) 8.95809i 0.343527i
\(681\) 0 0
\(682\) 9.94550 5.74204i 0.380833 0.219874i
\(683\) −13.0677 + 7.54464i −0.500021 + 0.288688i −0.728722 0.684809i \(-0.759886\pi\)
0.228701 + 0.973497i \(0.426552\pi\)
\(684\) 0 0
\(685\) 3.51331i 0.134237i
\(686\) −8.06244 + 16.6732i −0.307825 + 0.636587i
\(687\) 0 0
\(688\) 4.18600 7.25036i 0.159590 0.276417i
\(689\) −7.00865 12.1393i −0.267008 0.462472i
\(690\) 0 0
\(691\) −24.1708 13.9550i −0.919499 0.530873i −0.0360240 0.999351i \(-0.511469\pi\)
−0.883475 + 0.468478i \(0.844803\pi\)
\(692\) −16.0239 −0.609135
\(693\) 0 0
\(694\) −23.8415 −0.905012
\(695\) 26.7099 + 15.4210i 1.01316 + 0.584950i
\(696\) 0 0
\(697\) 23.3209 + 40.3930i 0.883343 + 1.53000i
\(698\) 1.57187 2.72255i 0.0594960 0.103050i
\(699\) 0 0
\(700\) −0.131395 5.38448i −0.00496627 0.203514i
\(701\) 27.9911i 1.05721i −0.848868 0.528605i \(-0.822715\pi\)
0.848868 0.528605i \(-0.177285\pi\)
\(702\) 0 0
\(703\) 17.9998 10.3922i 0.678876 0.391949i
\(704\) −1.47921 + 0.854023i −0.0557499 + 0.0321872i
\(705\) 0 0
\(706\) 27.6919i 1.04220i
\(707\) −36.7309 20.0281i −1.38141 0.753235i
\(708\) 0 0
\(709\) −11.5397 + 19.9873i −0.433382 + 0.750640i −0.997162 0.0752852i \(-0.976013\pi\)
0.563780 + 0.825925i \(0.309347\pi\)
\(710\) −4.36874 7.56688i −0.163956 0.283980i
\(711\) 0 0
\(712\) 7.21709 + 4.16679i 0.270472 + 0.156157i
\(713\) 36.6028 1.37078
\(714\) 0 0
\(715\) 3.77341 0.141118
\(716\) 3.23826 + 1.86961i 0.121019 + 0.0698705i
\(717\) 0 0
\(718\) 10.4572 + 18.1125i 0.390261 + 0.675951i
\(719\) 9.45610 16.3784i 0.352653 0.610813i −0.634061 0.773283i \(-0.718613\pi\)
0.986713 + 0.162471i \(0.0519463\pi\)
\(720\) 0 0
\(721\) 38.4384 0.937996i 1.43152 0.0349328i
\(722\) 11.3593i 0.422749i
\(723\) 0 0
\(724\) 0.932651 0.538466i 0.0346617 0.0200119i
\(725\) −2.55566 + 1.47551i −0.0949150 + 0.0547992i
\(726\) 0 0
\(727\) 5.34127i 0.198097i −0.995083 0.0990484i \(-0.968420\pi\)
0.995083 0.0990484i \(-0.0315799\pi\)
\(728\) 2.89778 1.76866i 0.107399 0.0655511i
\(729\) 0 0
\(730\) 8.13266 14.0862i 0.301003 0.521353i
\(731\) −21.7799 37.7240i −0.805560 1.39527i
\(732\) 0 0
\(733\) −44.6896 25.8016i −1.65065 0.953003i −0.976805 0.214129i \(-0.931309\pi\)
−0.673844 0.738874i \(-0.735358\pi\)
\(734\) −1.16962 −0.0431715
\(735\) 0 0
\(736\) −5.44399 −0.200668
\(737\) −12.7802 7.37865i −0.470765 0.271796i
\(738\) 0 0
\(739\) 18.0639 + 31.2875i 0.664490 + 1.15093i 0.979423 + 0.201817i \(0.0646847\pi\)
−0.314933 + 0.949114i \(0.601982\pi\)
\(740\) 6.47289 11.2114i 0.237948 0.412139i
\(741\) 0 0
\(742\) 24.6704 15.0576i 0.905678 0.552782i
\(743\) 3.88507i 0.142529i −0.997457 0.0712647i \(-0.977296\pi\)
0.997457 0.0712647i \(-0.0227035\pi\)
\(744\) 0 0
\(745\) 15.8780 9.16716i 0.581724 0.335859i
\(746\) −8.40915 + 4.85503i −0.307881 + 0.177755i
\(747\) 0 0
\(748\) 8.88704i 0.324942i
\(749\) 9.21212 0.224799i 0.336603 0.00821399i
\(750\) 0 0
\(751\) −1.55761 + 2.69786i −0.0568380 + 0.0984463i −0.893044 0.449969i \(-0.851435\pi\)
0.836206 + 0.548415i \(0.184769\pi\)
\(752\) −2.61809 4.53466i −0.0954718 0.165362i
\(753\) 0 0
\(754\) −1.61086 0.930028i −0.0586639 0.0338696i
\(755\) −17.5406 −0.638366
\(756\) 0 0
\(757\) −1.55505 −0.0565193 −0.0282597 0.999601i \(-0.508997\pi\)
−0.0282597 + 0.999601i \(0.508997\pi\)
\(758\) −13.1161 7.57261i −0.476400 0.275050i
\(759\) 0 0
\(760\) 2.37955 + 4.12150i 0.0863153 + 0.149502i
\(761\) 24.4514 42.3511i 0.886364 1.53523i 0.0422217 0.999108i \(-0.486556\pi\)
0.844142 0.536119i \(-0.180110\pi\)
\(762\) 0 0
\(763\) 21.0663 + 11.4867i 0.762650 + 0.415847i
\(764\) 16.8572i 0.609872i
\(765\) 0 0
\(766\) −27.6958 + 15.9902i −1.00069 + 0.577748i
\(767\) −4.63732 + 2.67736i −0.167444 + 0.0966737i
\(768\) 0 0
\(769\) 19.3089i 0.696298i 0.937439 + 0.348149i \(0.113190\pi\)
−0.937439 + 0.348149i \(0.886810\pi\)
\(770\) 0.189807 + 7.77816i 0.00684017 + 0.280305i
\(771\) 0 0
\(772\) 7.11546 12.3243i 0.256091 0.443563i
\(773\) 21.5416 + 37.3112i 0.774798 + 1.34199i 0.934908 + 0.354890i \(0.115482\pi\)
−0.160110 + 0.987099i \(0.551185\pi\)
\(774\) 0 0
\(775\) 11.8536 + 6.84369i 0.425795 + 0.245833i
\(776\) 10.0571 0.361030
\(777\) 0 0
\(778\) −24.9480 −0.894429
\(779\) 21.4593 + 12.3895i 0.768860 + 0.443901i
\(780\) 0 0
\(781\) −4.33409 7.50687i −0.155086 0.268617i
\(782\) −14.1627 + 24.5304i −0.506456 + 0.877207i
\(783\) 0 0
\(784\) 3.79152 + 5.88425i 0.135412 + 0.210152i
\(785\) 7.40408i 0.264263i
\(786\) 0 0
\(787\) −5.16193 + 2.98024i −0.184003 + 0.106234i −0.589172 0.808008i \(-0.700546\pi\)
0.405169 + 0.914242i \(0.367213\pi\)
\(788\) 16.8208 9.71149i 0.599216 0.345958i
\(789\) 0 0
\(790\) 23.1998i 0.825412i
\(791\) 9.13219 + 14.9622i 0.324703 + 0.531993i
\(792\) 0 0
\(793\) 1.69334 2.93296i 0.0601324 0.104152i
\(794\) 0.161774 + 0.280202i 0.00574116 + 0.00994398i
\(795\) 0 0
\(796\) 6.99323 + 4.03754i 0.247868 + 0.143107i
\(797\) 2.12036 0.0751068 0.0375534 0.999295i \(-0.488044\pi\)
0.0375534 + 0.999295i \(0.488044\pi\)
\(798\) 0 0
\(799\) −27.2440 −0.963825
\(800\) −1.76301 1.01787i −0.0623318 0.0359873i
\(801\) 0 0
\(802\) −9.50768 16.4678i −0.335728 0.581498i
\(803\) 8.06816 13.9745i 0.284719 0.493148i
\(804\) 0 0
\(805\) −11.8716 + 21.7721i −0.418419 + 0.767367i
\(806\) 8.62727i 0.303883i
\(807\) 0 0
\(808\) −13.6942 + 7.90634i −0.481760 + 0.278144i
\(809\) −31.7884 + 18.3530i −1.11762 + 0.645258i −0.940792 0.338983i \(-0.889917\pi\)
−0.176828 + 0.984242i \(0.556584\pi\)
\(810\) 0 0
\(811\) 46.1908i 1.62198i −0.585060 0.810990i \(-0.698929\pi\)
0.585060 0.810990i \(-0.301071\pi\)
\(812\) 1.83605 3.36725i 0.0644326 0.118167i
\(813\) 0 0
\(814\) 6.42156 11.1225i 0.225075 0.389842i
\(815\) 7.41690 + 12.8464i 0.259803 + 0.449991i
\(816\) 0 0
\(817\) −20.0413 11.5709i −0.701157 0.404813i
\(818\) 4.51304 0.157795
\(819\) 0 0
\(820\) 15.4339 0.538976
\(821\) −0.193084 0.111477i −0.00673867 0.00389057i 0.496627 0.867964i \(-0.334572\pi\)
−0.503366 + 0.864074i \(0.667905\pi\)
\(822\) 0 0
\(823\) −12.5354 21.7119i −0.436956 0.756829i 0.560497 0.828156i \(-0.310610\pi\)
−0.997453 + 0.0713268i \(0.977277\pi\)
\(824\) 7.26634 12.5857i 0.253135 0.438442i
\(825\) 0 0
\(826\) −5.75212 9.42426i −0.200142 0.327912i
\(827\) 25.6351i 0.891421i 0.895177 + 0.445711i \(0.147049\pi\)
−0.895177 + 0.445711i \(0.852951\pi\)
\(828\) 0 0
\(829\) −5.72963 + 3.30800i −0.198998 + 0.114892i −0.596188 0.802845i \(-0.703319\pi\)
0.397190 + 0.917736i \(0.369985\pi\)
\(830\) −9.05967 + 5.23060i −0.314466 + 0.181557i
\(831\) 0 0
\(832\) 1.28315i 0.0444852i
\(833\) 36.3780 1.77649i 1.26042 0.0615517i
\(834\) 0 0
\(835\) 12.0391 20.8524i 0.416631 0.721626i
\(836\) 2.36068 + 4.08881i 0.0816457 + 0.141414i
\(837\) 0 0
\(838\) 25.3009 + 14.6075i 0.874004 + 0.504607i
\(839\) −11.4826 −0.396424 −0.198212 0.980159i \(-0.563513\pi\)
−0.198212 + 0.980159i \(0.563513\pi\)
\(840\) 0 0
\(841\) 26.8987 0.927540
\(842\) −31.4680 18.1681i −1.08446 0.626113i
\(843\) 0 0
\(844\) 9.95665 + 17.2454i 0.342722 + 0.593612i
\(845\) 9.77369 16.9285i 0.336225 0.582359i
\(846\) 0 0
\(847\) −0.521681 21.3781i −0.0179252 0.734561i
\(848\) 10.9241i 0.375137i
\(849\) 0 0
\(850\) −9.17301 + 5.29604i −0.314632 + 0.181653i
\(851\) 35.4502 20.4672i 1.21522 0.701606i
\(852\) 0 0
\(853\) 18.0012i 0.616351i −0.951330 0.308175i \(-0.900282\pi\)
0.951330 0.308175i \(-0.0997184\pi\)
\(854\) 6.13090 + 3.34297i 0.209795 + 0.114394i
\(855\) 0 0
\(856\) 1.74144 3.01627i 0.0595213 0.103094i
\(857\) −19.4641 33.7129i −0.664882 1.15161i −0.979317 0.202331i \(-0.935148\pi\)
0.314435 0.949279i \(-0.398185\pi\)
\(858\) 0 0
\(859\) 31.5963 + 18.2421i 1.07805 + 0.622414i 0.930370 0.366621i \(-0.119485\pi\)
0.147682 + 0.989035i \(0.452819\pi\)
\(860\) −14.4141 −0.491516
\(861\) 0 0
\(862\) 12.1206 0.412828
\(863\) −32.9539 19.0259i −1.12176 0.647650i −0.179912 0.983683i \(-0.557581\pi\)
−0.941850 + 0.336033i \(0.890915\pi\)
\(864\) 0 0
\(865\) 13.7941 + 23.8921i 0.469015 + 0.812357i
\(866\) 15.7080 27.2071i 0.533780 0.924534i
\(867\) 0 0
\(868\) −17.7835 + 0.433962i −0.603610 + 0.0147296i
\(869\) 23.0158i 0.780757i
\(870\) 0 0
\(871\) 9.60097 5.54312i 0.325316 0.187822i
\(872\) 7.85401 4.53452i 0.265970 0.153558i
\(873\) 0 0
\(874\) 15.0482i 0.509012i
\(875\) −27.3562 + 16.6969i −0.924809 + 0.564459i
\(876\) 0 0
\(877\) −7.00470 + 12.1325i −0.236532 + 0.409685i −0.959717 0.280969i \(-0.909344\pi\)
0.723185 + 0.690655i \(0.242677\pi\)
\(878\) −1.61726 2.80118i −0.0545799 0.0945352i
\(879\) 0 0
\(880\) 2.54676 + 1.47037i 0.0858512 + 0.0495662i
\(881\) −12.6046 −0.424659 −0.212330 0.977198i \(-0.568105\pi\)
−0.212330 + 0.977198i \(0.568105\pi\)
\(882\) 0 0
\(883\) 7.76793 0.261412 0.130706 0.991421i \(-0.458276\pi\)
0.130706 + 0.991421i \(0.458276\pi\)
\(884\) −5.78183 3.33814i −0.194464 0.112274i
\(885\) 0 0
\(886\) 4.41729 + 7.65097i 0.148402 + 0.257039i
\(887\) −4.55420 + 7.88810i −0.152915 + 0.264857i −0.932298 0.361691i \(-0.882199\pi\)
0.779383 + 0.626548i \(0.215533\pi\)
\(888\) 0 0
\(889\) 44.0201 26.8677i 1.47639 0.901115i
\(890\) 14.3479i 0.480943i
\(891\) 0 0
\(892\) 18.3684 10.6050i 0.615020 0.355082i
\(893\) −12.5346 + 7.23687i −0.419455 + 0.242173i
\(894\) 0 0
\(895\) 6.43781i 0.215192i
\(896\) 2.64496 0.0645439i 0.0883620 0.00215626i
\(897\) 0 0
\(898\) 3.41597 5.91663i 0.113992 0.197440i
\(899\) 4.87322 + 8.44066i 0.162531 + 0.281512i
\(900\) 0 0
\(901\) −49.2239 28.4194i −1.63988 0.946788i
\(902\) 15.3115 0.509817
\(903\) 0 0
\(904\) 6.62531 0.220355
\(905\) −1.60575 0.927078i −0.0533768 0.0308171i
\(906\) 0 0
\(907\) −1.18365 2.05014i −0.0393023 0.0680737i 0.845705 0.533651i \(-0.179180\pi\)
−0.885007 + 0.465577i \(0.845847\pi\)
\(908\) 6.79579 11.7707i 0.225526 0.390623i
\(909\) 0 0
\(910\) −5.13170 2.79814i −0.170114 0.0927573i
\(911\) 6.15544i 0.203939i −0.994788 0.101969i \(-0.967486\pi\)
0.994788 0.101969i \(-0.0325144\pi\)
\(912\) 0 0
\(913\) −8.98782 + 5.18912i −0.297453 + 0.171735i
\(914\) −15.9555 + 9.21190i −0.527760 + 0.304703i
\(915\) 0 0
\(916\) 24.1066i 0.796504i
\(917\) −0.685890 28.1073i −0.0226501 0.928184i
\(918\) 0 0
\(919\) −14.2826 + 24.7382i −0.471140 + 0.816038i −0.999455 0.0330102i \(-0.989491\pi\)
0.528315 + 0.849048i \(0.322824\pi\)
\(920\) 4.68646 + 8.11719i 0.154508 + 0.267616i
\(921\) 0 0
\(922\) 25.8998 + 14.9533i 0.852965 + 0.492460i
\(923\) 6.51187 0.214341
\(924\) 0 0
\(925\) 15.3072 0.503296
\(926\) 1.14756 + 0.662545i 0.0377112 + 0.0217726i
\(927\) 0 0
\(928\) −0.724802 1.25539i −0.0237928 0.0412103i
\(929\) 3.84812 6.66515i 0.126253 0.218676i −0.795969 0.605337i \(-0.793038\pi\)
0.922222 + 0.386661i \(0.126372\pi\)
\(930\) 0 0
\(931\) 16.2651 10.4805i 0.533068 0.343483i
\(932\) 18.4626i 0.604762i
\(933\) 0 0
\(934\) 23.6973 13.6817i 0.775400 0.447677i
\(935\) 13.2509 7.65041i 0.433351 0.250195i
\(936\) 0 0
\(937\) 28.1750i 0.920436i 0.887806 + 0.460218i \(0.152229\pi\)
−0.887806 + 0.460218i \(0.847771\pi\)
\(938\) 11.9090 + 19.5117i 0.388843 + 0.637080i
\(939\) 0 0
\(940\) −4.50756 + 7.80732i −0.147020 + 0.254647i
\(941\) −19.2950 33.4199i −0.628999 1.08946i −0.987753 0.156026i \(-0.950132\pi\)
0.358754 0.933432i \(-0.383202\pi\)
\(942\) 0 0
\(943\) 42.2636 + 24.4009i 1.37629 + 0.794602i
\(944\) −4.17310 −0.135823
\(945\) 0 0
\(946\) −14.2997 −0.464925
\(947\) −19.3980 11.1995i −0.630351 0.363933i 0.150537 0.988604i \(-0.451900\pi\)
−0.780888 + 0.624671i \(0.785233\pi\)
\(948\) 0 0
\(949\) 6.06111 + 10.4981i 0.196752 + 0.340784i
\(950\) −2.81359 + 4.87328i −0.0912849 + 0.158110i
\(951\) 0 0
\(952\) 6.59010 12.0860i 0.213586 0.391711i
\(953\) 38.8771i 1.25935i 0.776858 + 0.629676i \(0.216812\pi\)
−0.776858 + 0.629676i \(0.783188\pi\)
\(954\) 0 0
\(955\) −25.1347 + 14.5115i −0.813339 + 0.469582i
\(956\) 20.0846 11.5958i 0.649582 0.375036i
\(957\) 0 0
\(958\) 16.8211i 0.543464i
\(959\) −2.58460 + 4.74008i −0.0834612 + 0.153065i
\(960\) 0 0
\(961\) 7.10284 12.3025i 0.229124 0.396854i
\(962\) 4.82412 + 8.35561i 0.155536 + 0.269396i
\(963\) 0 0
\(964\) 22.4458 + 12.9591i 0.722932 + 0.417385i
\(965\) −24.5014 −0.788727
\(966\) 0 0
\(967\) −20.5790 −0.661777 −0.330889 0.943670i \(-0.607348\pi\)
−0.330889 + 0.943670i \(0.607348\pi\)
\(968\) −6.99972 4.04129i −0.224980 0.129892i
\(969\) 0 0
\(970\) −8.65769 14.9956i −0.277982 0.481479i
\(971\) 1.02171 1.76966i 0.0327884 0.0567912i −0.849166 0.528127i \(-0.822895\pi\)
0.881954 + 0.471336i \(0.156228\pi\)
\(972\) 0 0
\(973\) −24.6918 40.4550i −0.791581 1.29693i
\(974\) 0.715204i 0.0229166i
\(975\) 0 0
\(976\) 2.28575 1.31968i 0.0731651 0.0422419i
\(977\) 40.0652 23.1317i 1.28180 0.740048i 0.304623 0.952473i \(-0.401469\pi\)
0.977177 + 0.212425i \(0.0681361\pi\)
\(978\) 0 0
\(979\) 14.2341i 0.454925i
\(980\) 5.50969 10.7188i 0.176001 0.342398i
\(981\) 0 0
\(982\) −2.68453 + 4.64975i −0.0856669 + 0.148379i
\(983\) −9.65581 16.7244i −0.307972 0.533424i 0.669946 0.742410i \(-0.266317\pi\)
−0.977919 + 0.208986i \(0.932984\pi\)
\(984\) 0 0
\(985\) −28.9604 16.7203i −0.922754 0.532753i
\(986\) −7.54235 −0.240197
\(987\) 0 0
\(988\) −3.54686 −0.112841
\(989\) −39.4709 22.7885i −1.25510 0.724633i
\(990\) 0 0
\(991\) 0.313252 + 0.542568i 0.00995077 + 0.0172352i 0.870958 0.491358i \(-0.163499\pi\)
−0.861007 + 0.508593i \(0.830166\pi\)
\(992\) −3.36176 + 5.82274i −0.106736 + 0.184872i
\(993\) 0 0
\(994\) 0.327555 + 13.4230i 0.0103894 + 0.425751i
\(995\) 13.9029i 0.440751i
\(996\) 0 0
\(997\) 22.6691 13.0880i 0.717939 0.414502i −0.0960546 0.995376i \(-0.530622\pi\)
0.813994 + 0.580874i \(0.197289\pi\)
\(998\) −20.8649 + 12.0464i −0.660467 + 0.381321i
\(999\) 0 0
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 1134.2.k.c.971.7 yes 16
3.2 odd 2 1134.2.k.d.971.2 yes 16
7.3 odd 6 1134.2.k.d.647.2 yes 16
9.2 odd 6 1134.2.l.g.215.6 16
9.4 even 3 1134.2.t.h.593.2 16
9.5 odd 6 1134.2.t.g.593.7 16
9.7 even 3 1134.2.l.h.215.3 16
21.17 even 6 inner 1134.2.k.c.647.7 16
63.31 odd 6 1134.2.l.g.269.2 16
63.38 even 6 1134.2.t.h.1025.2 16
63.52 odd 6 1134.2.t.g.1025.7 16
63.59 even 6 1134.2.l.h.269.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1134.2.k.c.647.7 16 21.17 even 6 inner
1134.2.k.c.971.7 yes 16 1.1 even 1 trivial
1134.2.k.d.647.2 yes 16 7.3 odd 6
1134.2.k.d.971.2 yes 16 3.2 odd 2
1134.2.l.g.215.6 16 9.2 odd 6
1134.2.l.g.269.2 16 63.31 odd 6
1134.2.l.h.215.3 16 9.7 even 3
1134.2.l.h.269.7 16 63.59 even 6
1134.2.t.g.593.7 16 9.5 odd 6
1134.2.t.g.1025.7 16 63.52 odd 6
1134.2.t.h.593.2 16 9.4 even 3
1134.2.t.h.1025.2 16 63.38 even 6