Properties

Label 1386.2.r.d.89.5
Level $1386$
Weight $2$
Character 1386.89
Analytic conductor $11.067$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1386,2,Mod(89,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1386.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.r (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: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.5
Character \(\chi\) \(=\) 1386.89
Dual form 1386.2.r.d.1277.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.474393 + 0.821673i) q^{5} +(1.41034 + 2.23851i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.474393 + 0.821673i) q^{5} +(1.41034 + 2.23851i) q^{7} -1.00000i q^{8} +(0.821673 - 0.474393i) q^{10} +(0.866025 - 0.500000i) q^{11} -7.03063i q^{13} +(-0.102135 - 2.64378i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.29971 - 3.98321i) q^{17} +(1.93280 + 1.11590i) q^{19} -0.948786 q^{20} -1.00000 q^{22} +(-7.17812 - 4.14429i) q^{23} +(2.04990 + 3.55054i) q^{25} +(-3.51532 + 6.08871i) q^{26} +(-1.23344 + 2.34065i) q^{28} -0.930621i q^{29} +(-2.80537 + 1.61968i) q^{31} +(0.866025 - 0.500000i) q^{32} +4.59942i q^{34} +(-2.50838 + 0.0969044i) q^{35} +(4.57553 - 7.92505i) q^{37} +(-1.11590 - 1.93280i) q^{38} +(0.821673 + 0.474393i) q^{40} +8.54500 q^{41} +12.7269 q^{43} +(0.866025 + 0.500000i) q^{44} +(4.14429 + 7.17812i) q^{46} +(0.251245 - 0.435168i) q^{47} +(-3.02187 + 6.31413i) q^{49} -4.09981i q^{50} +(6.08871 - 3.51532i) q^{52} +(8.22868 - 4.75083i) q^{53} +0.948786i q^{55} +(2.23851 - 1.41034i) q^{56} +(-0.465310 + 0.805941i) q^{58} +(3.94585 + 6.83441i) q^{59} +(-2.02250 - 1.16769i) q^{61} +3.23936 q^{62} -1.00000 q^{64} +(5.77688 + 3.33528i) q^{65} +(-2.94653 - 5.10354i) q^{67} +(2.29971 - 3.98321i) q^{68} +(2.22077 + 1.17027i) q^{70} -12.7563i q^{71} +(4.85471 - 2.80287i) q^{73} +(-7.92505 + 4.57553i) q^{74} +2.23181i q^{76} +(2.34065 + 1.23344i) q^{77} +(-4.16723 + 7.21785i) q^{79} +(-0.474393 - 0.821673i) q^{80} +(-7.40019 - 4.27250i) q^{82} -12.0026 q^{83} +4.36386 q^{85} +(-11.0218 - 6.36346i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-0.441480 + 0.764665i) q^{89} +(15.7382 - 9.91559i) q^{91} -8.28858i q^{92} +(-0.435168 + 0.251245i) q^{94} +(-1.83381 + 1.05875i) q^{95} -12.6315i q^{97} +(5.77409 - 3.95726i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(5\) −0.474393 + 0.821673i −0.212155 + 0.367463i −0.952389 0.304886i \(-0.901381\pi\)
0.740234 + 0.672350i \(0.234715\pi\)
\(6\) 0 0
\(7\) 1.41034 + 2.23851i 0.533059 + 0.846078i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.821673 0.474393i 0.259836 0.150016i
\(11\) 0.866025 0.500000i 0.261116 0.150756i
\(12\) 0 0
\(13\) 7.03063i 1.94995i −0.222322 0.974973i \(-0.571364\pi\)
0.222322 0.974973i \(-0.428636\pi\)
\(14\) −0.102135 2.64378i −0.0272968 0.706580i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.29971 3.98321i −0.557761 0.966071i −0.997683 0.0680349i \(-0.978327\pi\)
0.439922 0.898036i \(-0.355006\pi\)
\(18\) 0 0
\(19\) 1.93280 + 1.11590i 0.443415 + 0.256006i 0.705045 0.709163i \(-0.250927\pi\)
−0.261630 + 0.965168i \(0.584260\pi\)
\(20\) −0.948786 −0.212155
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −7.17812 4.14429i −1.49674 0.864144i −0.496748 0.867895i \(-0.665473\pi\)
−0.999993 + 0.00375054i \(0.998806\pi\)
\(24\) 0 0
\(25\) 2.04990 + 3.55054i 0.409981 + 0.710107i
\(26\) −3.51532 + 6.08871i −0.689410 + 1.19409i
\(27\) 0 0
\(28\) −1.23344 + 2.34065i −0.233098 + 0.442341i
\(29\) 0.930621i 0.172812i −0.996260 0.0864060i \(-0.972462\pi\)
0.996260 0.0864060i \(-0.0275382\pi\)
\(30\) 0 0
\(31\) −2.80537 + 1.61968i −0.503859 + 0.290903i −0.730306 0.683121i \(-0.760622\pi\)
0.226447 + 0.974023i \(0.427289\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 4.59942i 0.788794i
\(35\) −2.50838 + 0.0969044i −0.423994 + 0.0163798i
\(36\) 0 0
\(37\) 4.57553 7.92505i 0.752213 1.30287i −0.194535 0.980895i \(-0.562320\pi\)
0.946748 0.321975i \(-0.104347\pi\)
\(38\) −1.11590 1.93280i −0.181023 0.313542i
\(39\) 0 0
\(40\) 0.821673 + 0.474393i 0.129918 + 0.0750081i
\(41\) 8.54500 1.33450 0.667252 0.744832i \(-0.267470\pi\)
0.667252 + 0.744832i \(0.267470\pi\)
\(42\) 0 0
\(43\) 12.7269 1.94084 0.970418 0.241430i \(-0.0776164\pi\)
0.970418 + 0.241430i \(0.0776164\pi\)
\(44\) 0.866025 + 0.500000i 0.130558 + 0.0753778i
\(45\) 0 0
\(46\) 4.14429 + 7.17812i 0.611042 + 1.05836i
\(47\) 0.251245 0.435168i 0.0366478 0.0634758i −0.847120 0.531402i \(-0.821665\pi\)
0.883768 + 0.467926i \(0.154999\pi\)
\(48\) 0 0
\(49\) −3.02187 + 6.31413i −0.431696 + 0.902019i
\(50\) 4.09981i 0.579800i
\(51\) 0 0
\(52\) 6.08871 3.51532i 0.844352 0.487487i
\(53\) 8.22868 4.75083i 1.13030 0.652577i 0.186287 0.982495i \(-0.440355\pi\)
0.944009 + 0.329919i \(0.107021\pi\)
\(54\) 0 0
\(55\) 0.948786i 0.127934i
\(56\) 2.23851 1.41034i 0.299134 0.188465i
\(57\) 0 0
\(58\) −0.465310 + 0.805941i −0.0610982 + 0.105825i
\(59\) 3.94585 + 6.83441i 0.513706 + 0.889764i 0.999874 + 0.0158990i \(0.00506102\pi\)
−0.486168 + 0.873865i \(0.661606\pi\)
\(60\) 0 0
\(61\) −2.02250 1.16769i −0.258955 0.149508i 0.364903 0.931046i \(-0.381102\pi\)
−0.623858 + 0.781538i \(0.714436\pi\)
\(62\) 3.23936 0.411399
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 5.77688 + 3.33528i 0.716533 + 0.413691i
\(66\) 0 0
\(67\) −2.94653 5.10354i −0.359976 0.623497i 0.627980 0.778229i \(-0.283882\pi\)
−0.987956 + 0.154732i \(0.950548\pi\)
\(68\) 2.29971 3.98321i 0.278881 0.483036i
\(69\) 0 0
\(70\) 2.22077 + 1.17027i 0.265433 + 0.139874i
\(71\) 12.7563i 1.51390i −0.653475 0.756948i \(-0.726689\pi\)
0.653475 0.756948i \(-0.273311\pi\)
\(72\) 0 0
\(73\) 4.85471 2.80287i 0.568201 0.328051i −0.188229 0.982125i \(-0.560275\pi\)
0.756431 + 0.654074i \(0.226942\pi\)
\(74\) −7.92505 + 4.57553i −0.921269 + 0.531895i
\(75\) 0 0
\(76\) 2.23181i 0.256006i
\(77\) 2.34065 + 1.23344i 0.266742 + 0.140563i
\(78\) 0 0
\(79\) −4.16723 + 7.21785i −0.468850 + 0.812072i −0.999366 0.0356031i \(-0.988665\pi\)
0.530516 + 0.847675i \(0.321998\pi\)
\(80\) −0.474393 0.821673i −0.0530387 0.0918658i
\(81\) 0 0
\(82\) −7.40019 4.27250i −0.817214 0.471819i
\(83\) −12.0026 −1.31745 −0.658727 0.752382i \(-0.728905\pi\)
−0.658727 + 0.752382i \(0.728905\pi\)
\(84\) 0 0
\(85\) 4.36386 0.473327
\(86\) −11.0218 6.36346i −1.18851 0.686189i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) −0.441480 + 0.764665i −0.0467968 + 0.0810544i −0.888475 0.458925i \(-0.848235\pi\)
0.841678 + 0.539979i \(0.181568\pi\)
\(90\) 0 0
\(91\) 15.7382 9.91559i 1.64981 1.03944i
\(92\) 8.28858i 0.864144i
\(93\) 0 0
\(94\) −0.435168 + 0.251245i −0.0448842 + 0.0259139i
\(95\) −1.83381 + 1.05875i −0.188145 + 0.108626i
\(96\) 0 0
\(97\) 12.6315i 1.28253i −0.767319 0.641265i \(-0.778410\pi\)
0.767319 0.641265i \(-0.221590\pi\)
\(98\) 5.77409 3.95726i 0.583271 0.399744i
\(99\) 0 0
\(100\) −2.04990 + 3.55054i −0.204990 + 0.355054i
\(101\) −8.03742 13.9212i −0.799754 1.38521i −0.919776 0.392443i \(-0.871630\pi\)
0.120023 0.992771i \(-0.461703\pi\)
\(102\) 0 0
\(103\) 7.42570 + 4.28723i 0.731676 + 0.422433i 0.819035 0.573743i \(-0.194509\pi\)
−0.0873588 + 0.996177i \(0.527843\pi\)
\(104\) −7.03063 −0.689410
\(105\) 0 0
\(106\) −9.50166 −0.922883
\(107\) 12.2507 + 7.07294i 1.18432 + 0.683767i 0.957010 0.290056i \(-0.0936740\pi\)
0.227309 + 0.973823i \(0.427007\pi\)
\(108\) 0 0
\(109\) 3.35840 + 5.81692i 0.321676 + 0.557160i 0.980834 0.194845i \(-0.0624203\pi\)
−0.659158 + 0.752005i \(0.729087\pi\)
\(110\) 0.474393 0.821673i 0.0452316 0.0783434i
\(111\) 0 0
\(112\) −2.64378 + 0.102135i −0.249814 + 0.00965087i
\(113\) 8.39880i 0.790093i 0.918661 + 0.395046i \(0.129271\pi\)
−0.918661 + 0.395046i \(0.870729\pi\)
\(114\) 0 0
\(115\) 6.81050 3.93204i 0.635082 0.366665i
\(116\) 0.805941 0.465310i 0.0748298 0.0432030i
\(117\) 0 0
\(118\) 7.89170i 0.726490i
\(119\) 5.67310 10.7656i 0.520052 0.986882i
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 1.16769 + 2.02250i 0.105718 + 0.183109i
\(123\) 0 0
\(124\) −2.80537 1.61968i −0.251929 0.145451i
\(125\) −8.63377 −0.772227
\(126\) 0 0
\(127\) −7.99819 −0.709724 −0.354862 0.934919i \(-0.615472\pi\)
−0.354862 + 0.934919i \(0.615472\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −3.33528 5.77688i −0.292524 0.506666i
\(131\) −4.37253 + 7.57344i −0.382030 + 0.661695i −0.991352 0.131228i \(-0.958108\pi\)
0.609323 + 0.792922i \(0.291441\pi\)
\(132\) 0 0
\(133\) 0.227946 + 5.90040i 0.0197654 + 0.511630i
\(134\) 5.89306i 0.509083i
\(135\) 0 0
\(136\) −3.98321 + 2.29971i −0.341558 + 0.197198i
\(137\) 0.350664 0.202456i 0.0299592 0.0172970i −0.484946 0.874544i \(-0.661161\pi\)
0.514905 + 0.857247i \(0.327827\pi\)
\(138\) 0 0
\(139\) 17.5997i 1.49278i −0.665506 0.746392i \(-0.731784\pi\)
0.665506 0.746392i \(-0.268216\pi\)
\(140\) −1.33811 2.12387i −0.113091 0.179500i
\(141\) 0 0
\(142\) −6.37816 + 11.0473i −0.535243 + 0.927069i
\(143\) −3.51532 6.08871i −0.293966 0.509163i
\(144\) 0 0
\(145\) 0.764665 + 0.441480i 0.0635020 + 0.0366629i
\(146\) −5.60574 −0.463934
\(147\) 0 0
\(148\) 9.15106 0.752213
\(149\) 17.5141 + 10.1118i 1.43481 + 0.828390i 0.997483 0.0709110i \(-0.0225906\pi\)
0.437331 + 0.899301i \(0.355924\pi\)
\(150\) 0 0
\(151\) −3.93283 6.81186i −0.320049 0.554341i 0.660449 0.750871i \(-0.270366\pi\)
−0.980498 + 0.196530i \(0.937033\pi\)
\(152\) 1.11590 1.93280i 0.0905117 0.156771i
\(153\) 0 0
\(154\) −1.41034 2.23851i −0.113649 0.180384i
\(155\) 3.07346i 0.246866i
\(156\) 0 0
\(157\) −0.300234 + 0.173340i −0.0239613 + 0.0138340i −0.511933 0.859026i \(-0.671070\pi\)
0.487972 + 0.872860i \(0.337737\pi\)
\(158\) 7.21785 4.16723i 0.574221 0.331527i
\(159\) 0 0
\(160\) 0.948786i 0.0750081i
\(161\) −0.846556 21.9132i −0.0667179 1.72700i
\(162\) 0 0
\(163\) −4.00467 + 6.93629i −0.313670 + 0.543292i −0.979154 0.203120i \(-0.934892\pi\)
0.665484 + 0.746412i \(0.268225\pi\)
\(164\) 4.27250 + 7.40019i 0.333626 + 0.577857i
\(165\) 0 0
\(166\) 10.3945 + 6.00129i 0.806772 + 0.465790i
\(167\) 23.3784 1.80907 0.904537 0.426395i \(-0.140217\pi\)
0.904537 + 0.426395i \(0.140217\pi\)
\(168\) 0 0
\(169\) −36.4298 −2.80229
\(170\) −3.77922 2.18193i −0.289853 0.167346i
\(171\) 0 0
\(172\) 6.36346 + 11.0218i 0.485209 + 0.840407i
\(173\) 3.94270 6.82895i 0.299758 0.519196i −0.676323 0.736605i \(-0.736427\pi\)
0.976080 + 0.217410i \(0.0697608\pi\)
\(174\) 0 0
\(175\) −5.05686 + 9.59620i −0.382262 + 0.725405i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) 0.764665 0.441480i 0.0573141 0.0330903i
\(179\) −3.03581 + 1.75273i −0.226907 + 0.131005i −0.609145 0.793059i \(-0.708487\pi\)
0.382237 + 0.924064i \(0.375154\pi\)
\(180\) 0 0
\(181\) 18.4507i 1.37143i −0.727871 0.685714i \(-0.759490\pi\)
0.727871 0.685714i \(-0.240510\pi\)
\(182\) −18.5874 + 0.718075i −1.37779 + 0.0532273i
\(183\) 0 0
\(184\) −4.14429 + 7.17812i −0.305521 + 0.529178i
\(185\) 4.34120 + 7.51918i 0.319171 + 0.552821i
\(186\) 0 0
\(187\) −3.98321 2.29971i −0.291281 0.168171i
\(188\) 0.502489 0.0366478
\(189\) 0 0
\(190\) 2.11750 0.153620
\(191\) 22.4364 + 12.9536i 1.62344 + 0.937293i 0.985991 + 0.166800i \(0.0533436\pi\)
0.637449 + 0.770493i \(0.279990\pi\)
\(192\) 0 0
\(193\) −0.304714 0.527780i −0.0219338 0.0379904i 0.854850 0.518875i \(-0.173649\pi\)
−0.876784 + 0.480884i \(0.840316\pi\)
\(194\) −6.31573 + 10.9392i −0.453443 + 0.785386i
\(195\) 0 0
\(196\) −6.97914 + 0.540046i −0.498510 + 0.0385747i
\(197\) 2.19657i 0.156499i 0.996934 + 0.0782494i \(0.0249330\pi\)
−0.996934 + 0.0782494i \(0.975067\pi\)
\(198\) 0 0
\(199\) 22.9865 13.2713i 1.62947 0.940775i 0.645220 0.763997i \(-0.276766\pi\)
0.984251 0.176778i \(-0.0565675\pi\)
\(200\) 3.55054 2.04990i 0.251061 0.144950i
\(201\) 0 0
\(202\) 16.0748i 1.13102i
\(203\) 2.08321 1.31249i 0.146212 0.0921189i
\(204\) 0 0
\(205\) −4.05369 + 7.02119i −0.283122 + 0.490381i
\(206\) −4.28723 7.42570i −0.298706 0.517373i
\(207\) 0 0
\(208\) 6.08871 + 3.51532i 0.422176 + 0.243743i
\(209\) 2.23181 0.154377
\(210\) 0 0
\(211\) 6.72897 0.463242 0.231621 0.972806i \(-0.425597\pi\)
0.231621 + 0.972806i \(0.425597\pi\)
\(212\) 8.22868 + 4.75083i 0.565148 + 0.326288i
\(213\) 0 0
\(214\) −7.07294 12.2507i −0.483496 0.837440i
\(215\) −6.03756 + 10.4574i −0.411758 + 0.713186i
\(216\) 0 0
\(217\) −7.58219 3.99555i −0.514713 0.271235i
\(218\) 6.71680i 0.454919i
\(219\) 0 0
\(220\) −0.821673 + 0.474393i −0.0553971 + 0.0319836i
\(221\) −28.0045 + 16.1684i −1.88379 + 1.08760i
\(222\) 0 0
\(223\) 24.1105i 1.61456i −0.590168 0.807280i \(-0.700939\pi\)
0.590168 0.807280i \(-0.299061\pi\)
\(224\) 2.34065 + 1.23344i 0.156391 + 0.0824125i
\(225\) 0 0
\(226\) 4.19940 7.27357i 0.279340 0.483831i
\(227\) 4.95825 + 8.58794i 0.329091 + 0.570002i 0.982332 0.187148i \(-0.0599245\pi\)
−0.653241 + 0.757150i \(0.726591\pi\)
\(228\) 0 0
\(229\) −19.6700 11.3565i −1.29983 0.750458i −0.319456 0.947601i \(-0.603500\pi\)
−0.980375 + 0.197144i \(0.936833\pi\)
\(230\) −7.86408 −0.518542
\(231\) 0 0
\(232\) −0.930621 −0.0610982
\(233\) −10.6634 6.15652i −0.698583 0.403327i 0.108237 0.994125i \(-0.465480\pi\)
−0.806819 + 0.590798i \(0.798813\pi\)
\(234\) 0 0
\(235\) 0.238377 + 0.412882i 0.0155500 + 0.0269334i
\(236\) −3.94585 + 6.83441i −0.256853 + 0.444882i
\(237\) 0 0
\(238\) −10.2959 + 6.48675i −0.667381 + 0.420474i
\(239\) 0.355903i 0.0230215i 0.999934 + 0.0115107i \(0.00366406\pi\)
−0.999934 + 0.0115107i \(0.996336\pi\)
\(240\) 0 0
\(241\) −19.3413 + 11.1667i −1.24588 + 0.719311i −0.970286 0.241962i \(-0.922209\pi\)
−0.275597 + 0.961273i \(0.588876\pi\)
\(242\) −0.866025 + 0.500000i −0.0556702 + 0.0321412i
\(243\) 0 0
\(244\) 2.33539i 0.149508i
\(245\) −3.75459 5.47837i −0.239872 0.350000i
\(246\) 0 0
\(247\) 7.84550 13.5888i 0.499197 0.864635i
\(248\) 1.61968 + 2.80537i 0.102850 + 0.178141i
\(249\) 0 0
\(250\) 7.47706 + 4.31688i 0.472891 + 0.273024i
\(251\) 10.8938 0.687612 0.343806 0.939041i \(-0.388284\pi\)
0.343806 + 0.939041i \(0.388284\pi\)
\(252\) 0 0
\(253\) −8.28858 −0.521098
\(254\) 6.92663 + 3.99909i 0.434616 + 0.250925i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.48335 + 7.76538i −0.279663 + 0.484391i −0.971301 0.237853i \(-0.923556\pi\)
0.691638 + 0.722245i \(0.256890\pi\)
\(258\) 0 0
\(259\) 24.1934 0.934646i 1.50330 0.0580761i
\(260\) 6.67056i 0.413691i
\(261\) 0 0
\(262\) 7.57344 4.37253i 0.467889 0.270136i
\(263\) −7.32723 + 4.23038i −0.451817 + 0.260856i −0.708597 0.705613i \(-0.750672\pi\)
0.256781 + 0.966470i \(0.417338\pi\)
\(264\) 0 0
\(265\) 9.01504i 0.553790i
\(266\) 2.75279 5.22387i 0.168785 0.320296i
\(267\) 0 0
\(268\) 2.94653 5.10354i 0.179988 0.311748i
\(269\) 1.61227 + 2.79253i 0.0983017 + 0.170264i 0.910982 0.412447i \(-0.135326\pi\)
−0.812680 + 0.582710i \(0.801992\pi\)
\(270\) 0 0
\(271\) 0.662223 + 0.382335i 0.0402272 + 0.0232252i 0.519979 0.854179i \(-0.325940\pi\)
−0.479752 + 0.877404i \(0.659273\pi\)
\(272\) 4.59942 0.278881
\(273\) 0 0
\(274\) −0.404912 −0.0244616
\(275\) 3.55054 + 2.04990i 0.214105 + 0.123614i
\(276\) 0 0
\(277\) 13.6448 + 23.6334i 0.819834 + 1.41999i 0.905804 + 0.423697i \(0.139268\pi\)
−0.0859699 + 0.996298i \(0.527399\pi\)
\(278\) −8.79984 + 15.2418i −0.527779 + 0.914140i
\(279\) 0 0
\(280\) 0.0969044 + 2.50838i 0.00579115 + 0.149904i
\(281\) 4.36625i 0.260468i −0.991483 0.130234i \(-0.958427\pi\)
0.991483 0.130234i \(-0.0415729\pi\)
\(282\) 0 0
\(283\) −16.5596 + 9.56067i −0.984364 + 0.568323i −0.903585 0.428409i \(-0.859074\pi\)
−0.0807792 + 0.996732i \(0.525741\pi\)
\(284\) 11.0473 6.37816i 0.655537 0.378474i
\(285\) 0 0
\(286\) 7.03063i 0.415730i
\(287\) 12.0514 + 19.1281i 0.711370 + 1.12910i
\(288\) 0 0
\(289\) −2.07732 + 3.59803i −0.122196 + 0.211649i
\(290\) −0.441480 0.764665i −0.0259246 0.0449027i
\(291\) 0 0
\(292\) 4.85471 + 2.80287i 0.284101 + 0.164026i
\(293\) −9.23974 −0.539791 −0.269896 0.962890i \(-0.586989\pi\)
−0.269896 + 0.962890i \(0.586989\pi\)
\(294\) 0 0
\(295\) −7.48753 −0.435941
\(296\) −7.92505 4.57553i −0.460634 0.265947i
\(297\) 0 0
\(298\) −10.1118 17.5141i −0.585760 1.01457i
\(299\) −29.1370 + 50.4667i −1.68503 + 2.91857i
\(300\) 0 0
\(301\) 17.9493 + 28.4894i 1.03458 + 1.64210i
\(302\) 7.86566i 0.452618i
\(303\) 0 0
\(304\) −1.93280 + 1.11590i −0.110854 + 0.0640014i
\(305\) 1.91892 1.10789i 0.109877 0.0634377i
\(306\) 0 0
\(307\) 7.06021i 0.402947i 0.979494 + 0.201474i \(0.0645730\pi\)
−0.979494 + 0.201474i \(0.935427\pi\)
\(308\) 0.102135 + 2.64378i 0.00581969 + 0.150643i
\(309\) 0 0
\(310\) −1.53673 + 2.66169i −0.0872803 + 0.151174i
\(311\) −4.32056 7.48343i −0.244997 0.424346i 0.717134 0.696935i \(-0.245453\pi\)
−0.962131 + 0.272589i \(0.912120\pi\)
\(312\) 0 0
\(313\) −20.6329 11.9124i −1.16624 0.673330i −0.213450 0.976954i \(-0.568470\pi\)
−0.952792 + 0.303624i \(0.901803\pi\)
\(314\) 0.346680 0.0195643
\(315\) 0 0
\(316\) −8.33446 −0.468850
\(317\) 21.9545 + 12.6754i 1.23309 + 0.711923i 0.967672 0.252212i \(-0.0811579\pi\)
0.265414 + 0.964134i \(0.414491\pi\)
\(318\) 0 0
\(319\) −0.465310 0.805941i −0.0260524 0.0451240i
\(320\) 0.474393 0.821673i 0.0265194 0.0459329i
\(321\) 0 0
\(322\) −10.2234 + 19.4006i −0.569730 + 1.08116i
\(323\) 10.2650i 0.571160i
\(324\) 0 0
\(325\) 24.9625 14.4121i 1.38467 0.799440i
\(326\) 6.93629 4.00467i 0.384166 0.221798i
\(327\) 0 0
\(328\) 8.54500i 0.471819i
\(329\) 1.32847 0.0513218i 0.0732410 0.00282946i
\(330\) 0 0
\(331\) −3.86378 + 6.69226i −0.212372 + 0.367840i −0.952457 0.304674i \(-0.901452\pi\)
0.740084 + 0.672514i \(0.234786\pi\)
\(332\) −6.00129 10.3945i −0.329363 0.570474i
\(333\) 0 0
\(334\) −20.2463 11.6892i −1.10783 0.639604i
\(335\) 5.59125 0.305483
\(336\) 0 0
\(337\) 24.9208 1.35752 0.678761 0.734359i \(-0.262517\pi\)
0.678761 + 0.734359i \(0.262517\pi\)
\(338\) 31.5491 + 18.2149i 1.71605 + 0.990760i
\(339\) 0 0
\(340\) 2.18193 + 3.77922i 0.118332 + 0.204957i
\(341\) −1.61968 + 2.80537i −0.0877105 + 0.151919i
\(342\) 0 0
\(343\) −18.3961 + 2.14058i −0.993298 + 0.115580i
\(344\) 12.7269i 0.686189i
\(345\) 0 0
\(346\) −6.82895 + 3.94270i −0.367127 + 0.211961i
\(347\) −11.0204 + 6.36264i −0.591607 + 0.341564i −0.765733 0.643159i \(-0.777623\pi\)
0.174126 + 0.984723i \(0.444290\pi\)
\(348\) 0 0
\(349\) 6.72324i 0.359887i 0.983677 + 0.179943i \(0.0575914\pi\)
−0.983677 + 0.179943i \(0.942409\pi\)
\(350\) 9.17747 5.78213i 0.490556 0.309068i
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −9.54247 16.5280i −0.507895 0.879699i −0.999958 0.00914007i \(-0.997091\pi\)
0.492064 0.870559i \(-0.336243\pi\)
\(354\) 0 0
\(355\) 10.4815 + 6.05151i 0.556301 + 0.321181i
\(356\) −0.882960 −0.0467968
\(357\) 0 0
\(358\) 3.50545 0.185269
\(359\) 11.1639 + 6.44550i 0.589210 + 0.340181i 0.764785 0.644285i \(-0.222845\pi\)
−0.175575 + 0.984466i \(0.556178\pi\)
\(360\) 0 0
\(361\) −7.00952 12.1408i −0.368922 0.638992i
\(362\) −9.22534 + 15.9788i −0.484873 + 0.839825i
\(363\) 0 0
\(364\) 16.4562 + 8.67185i 0.862541 + 0.454528i
\(365\) 5.31865i 0.278391i
\(366\) 0 0
\(367\) −2.21459 + 1.27860i −0.115601 + 0.0667422i −0.556686 0.830723i \(-0.687927\pi\)
0.441085 + 0.897465i \(0.354594\pi\)
\(368\) 7.17812 4.14429i 0.374185 0.216036i
\(369\) 0 0
\(370\) 8.68240i 0.451376i
\(371\) 22.2400 + 11.7197i 1.15465 + 0.608457i
\(372\) 0 0
\(373\) −15.1993 + 26.3259i −0.786989 + 1.36310i 0.140815 + 0.990036i \(0.455028\pi\)
−0.927804 + 0.373069i \(0.878306\pi\)
\(374\) 2.29971 + 3.98321i 0.118915 + 0.205967i
\(375\) 0 0
\(376\) −0.435168 0.251245i −0.0224421 0.0129570i
\(377\) −6.54285 −0.336974
\(378\) 0 0
\(379\) −13.6206 −0.699642 −0.349821 0.936817i \(-0.613758\pi\)
−0.349821 + 0.936817i \(0.613758\pi\)
\(380\) −1.83381 1.05875i −0.0940726 0.0543129i
\(381\) 0 0
\(382\) −12.9536 22.4364i −0.662766 1.14795i
\(383\) −11.4051 + 19.7542i −0.582774 + 1.00939i 0.412375 + 0.911014i \(0.364699\pi\)
−0.995149 + 0.0983803i \(0.968634\pi\)
\(384\) 0 0
\(385\) −2.12387 + 1.33811i −0.108242 + 0.0681965i
\(386\) 0.609428i 0.0310191i
\(387\) 0 0
\(388\) 10.9392 6.31573i 0.555352 0.320633i
\(389\) −1.46953 + 0.848435i −0.0745083 + 0.0430174i −0.536791 0.843715i \(-0.680364\pi\)
0.462283 + 0.886732i \(0.347030\pi\)
\(390\) 0 0
\(391\) 38.1226i 1.92794i
\(392\) 6.31413 + 3.02187i 0.318912 + 0.152628i
\(393\) 0 0
\(394\) 1.09828 1.90228i 0.0553307 0.0958356i
\(395\) −3.95381 6.84819i −0.198938 0.344570i
\(396\) 0 0
\(397\) −21.7326 12.5473i −1.09073 0.629733i −0.156958 0.987605i \(-0.550169\pi\)
−0.933770 + 0.357873i \(0.883502\pi\)
\(398\) −26.5425 −1.33046
\(399\) 0 0
\(400\) −4.09981 −0.204990
\(401\) −18.8176 10.8643i −0.939705 0.542539i −0.0498372 0.998757i \(-0.515870\pi\)
−0.889868 + 0.456218i \(0.849204\pi\)
\(402\) 0 0
\(403\) 11.3874 + 19.7235i 0.567245 + 0.982497i
\(404\) 8.03742 13.9212i 0.399877 0.692607i
\(405\) 0 0
\(406\) −2.46036 + 0.0950491i −0.122105 + 0.00471721i
\(407\) 9.15106i 0.453601i
\(408\) 0 0
\(409\) −4.03930 + 2.33209i −0.199730 + 0.115314i −0.596530 0.802591i \(-0.703454\pi\)
0.396799 + 0.917905i \(0.370121\pi\)
\(410\) 7.02119 4.05369i 0.346752 0.200197i
\(411\) 0 0
\(412\) 8.57446i 0.422433i
\(413\) −9.73392 + 18.4717i −0.478975 + 0.908932i
\(414\) 0 0
\(415\) 5.69394 9.86219i 0.279504 0.484116i
\(416\) −3.51532 6.08871i −0.172353 0.298523i
\(417\) 0 0
\(418\) −1.93280 1.11590i −0.0945363 0.0545806i
\(419\) −36.6109 −1.78856 −0.894281 0.447506i \(-0.852312\pi\)
−0.894281 + 0.447506i \(0.852312\pi\)
\(420\) 0 0
\(421\) −30.4576 −1.48441 −0.742206 0.670172i \(-0.766220\pi\)
−0.742206 + 0.670172i \(0.766220\pi\)
\(422\) −5.82746 3.36449i −0.283676 0.163781i
\(423\) 0 0
\(424\) −4.75083 8.22868i −0.230721 0.399620i
\(425\) 9.42836 16.3304i 0.457343 0.792141i
\(426\) 0 0
\(427\) −0.238525 6.17425i −0.0115430 0.298793i
\(428\) 14.1459i 0.683767i
\(429\) 0 0
\(430\) 10.4574 6.03756i 0.504299 0.291157i
\(431\) −16.1392 + 9.31798i −0.777399 + 0.448832i −0.835508 0.549479i \(-0.814826\pi\)
0.0581087 + 0.998310i \(0.481493\pi\)
\(432\) 0 0
\(433\) 9.69502i 0.465913i 0.972487 + 0.232956i \(0.0748400\pi\)
−0.972487 + 0.232956i \(0.925160\pi\)
\(434\) 4.56860 + 7.25134i 0.219300 + 0.348075i
\(435\) 0 0
\(436\) −3.35840 + 5.81692i −0.160838 + 0.278580i
\(437\) −9.24925 16.0202i −0.442451 0.766348i
\(438\) 0 0
\(439\) 29.0710 + 16.7841i 1.38748 + 0.801063i 0.993031 0.117854i \(-0.0376016\pi\)
0.394450 + 0.918917i \(0.370935\pi\)
\(440\) 0.948786 0.0452316
\(441\) 0 0
\(442\) 32.3368 1.53811
\(443\) 2.64582 + 1.52756i 0.125707 + 0.0725767i 0.561535 0.827453i \(-0.310211\pi\)
−0.435828 + 0.900030i \(0.643544\pi\)
\(444\) 0 0
\(445\) −0.418870 0.725504i −0.0198563 0.0343922i
\(446\) −12.0553 + 20.8803i −0.570833 + 0.988713i
\(447\) 0 0
\(448\) −1.41034 2.23851i −0.0666324 0.105760i
\(449\) 0.355204i 0.0167631i 0.999965 + 0.00838157i \(0.00266797\pi\)
−0.999965 + 0.00838157i \(0.997332\pi\)
\(450\) 0 0
\(451\) 7.40019 4.27250i 0.348461 0.201184i
\(452\) −7.27357 + 4.19940i −0.342120 + 0.197523i
\(453\) 0 0
\(454\) 9.91650i 0.465404i
\(455\) 0.681299 + 17.6355i 0.0319398 + 0.826765i
\(456\) 0 0
\(457\) −4.80324 + 8.31946i −0.224686 + 0.389168i −0.956225 0.292632i \(-0.905469\pi\)
0.731539 + 0.681800i \(0.238802\pi\)
\(458\) 11.3565 + 19.6700i 0.530654 + 0.919119i
\(459\) 0 0
\(460\) 6.81050 + 3.93204i 0.317541 + 0.183332i
\(461\) 38.6120 1.79834 0.899169 0.437602i \(-0.144172\pi\)
0.899169 + 0.437602i \(0.144172\pi\)
\(462\) 0 0
\(463\) 3.61880 0.168180 0.0840899 0.996458i \(-0.473202\pi\)
0.0840899 + 0.996458i \(0.473202\pi\)
\(464\) 0.805941 + 0.465310i 0.0374149 + 0.0216015i
\(465\) 0 0
\(466\) 6.15652 + 10.6634i 0.285195 + 0.493972i
\(467\) 4.07804 7.06337i 0.188709 0.326854i −0.756111 0.654443i \(-0.772903\pi\)
0.944820 + 0.327590i \(0.106236\pi\)
\(468\) 0 0
\(469\) 7.26873 13.7936i 0.335639 0.636928i
\(470\) 0.476755i 0.0219910i
\(471\) 0 0
\(472\) 6.83441 3.94585i 0.314579 0.181622i
\(473\) 11.0218 6.36346i 0.506784 0.292592i
\(474\) 0 0
\(475\) 9.14997i 0.419829i
\(476\) 12.1598 0.469763i 0.557346 0.0215315i
\(477\) 0 0
\(478\) 0.177951 0.308221i 0.00813931 0.0140977i
\(479\) −12.9635 22.4534i −0.592316 1.02592i −0.993920 0.110108i \(-0.964880\pi\)
0.401604 0.915814i \(-0.368453\pi\)
\(480\) 0 0
\(481\) −55.7181 32.1689i −2.54053 1.46677i
\(482\) 22.3334 1.01726
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 10.3789 + 5.99227i 0.471283 + 0.272095i
\(486\) 0 0
\(487\) −1.93103 3.34464i −0.0875032 0.151560i 0.818952 0.573862i \(-0.194555\pi\)
−0.906455 + 0.422302i \(0.861222\pi\)
\(488\) −1.16769 + 2.02250i −0.0528590 + 0.0915545i
\(489\) 0 0
\(490\) 0.512388 + 6.62171i 0.0231473 + 0.299138i
\(491\) 13.5459i 0.611317i 0.952141 + 0.305658i \(0.0988766\pi\)
−0.952141 + 0.305658i \(0.901123\pi\)
\(492\) 0 0
\(493\) −3.70686 + 2.14016i −0.166949 + 0.0963878i
\(494\) −13.5888 + 7.84550i −0.611389 + 0.352986i
\(495\) 0 0
\(496\) 3.23936i 0.145451i
\(497\) 28.5552 17.9908i 1.28088 0.806996i
\(498\) 0 0
\(499\) −5.02599 + 8.70526i −0.224994 + 0.389701i −0.956318 0.292329i \(-0.905570\pi\)
0.731324 + 0.682031i \(0.238903\pi\)
\(500\) −4.31688 7.47706i −0.193057 0.334384i
\(501\) 0 0
\(502\) −9.43433 5.44691i −0.421075 0.243108i
\(503\) −10.4299 −0.465048 −0.232524 0.972591i \(-0.574698\pi\)
−0.232524 + 0.972591i \(0.574698\pi\)
\(504\) 0 0
\(505\) 15.2516 0.678687
\(506\) 7.17812 + 4.14429i 0.319106 + 0.184236i
\(507\) 0 0
\(508\) −3.99909 6.92663i −0.177431 0.307320i
\(509\) 5.46543 9.46640i 0.242251 0.419591i −0.719104 0.694902i \(-0.755448\pi\)
0.961355 + 0.275311i \(0.0887809\pi\)
\(510\) 0 0
\(511\) 13.1211 + 6.91433i 0.580441 + 0.305872i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 7.76538 4.48335i 0.342516 0.197752i
\(515\) −7.04540 + 4.06766i −0.310457 + 0.179243i
\(516\) 0 0
\(517\) 0.502489i 0.0220995i
\(518\) −21.4194 11.2873i −0.941115 0.495934i
\(519\) 0 0
\(520\) 3.33528 5.77688i 0.146262 0.253333i
\(521\) −0.801194 1.38771i −0.0351010 0.0607966i 0.847941 0.530090i \(-0.177842\pi\)
−0.883042 + 0.469294i \(0.844509\pi\)
\(522\) 0 0
\(523\) 18.6963 + 10.7943i 0.817533 + 0.472003i 0.849565 0.527484i \(-0.176865\pi\)
−0.0320322 + 0.999487i \(0.510198\pi\)
\(524\) −8.74506 −0.382030
\(525\) 0 0
\(526\) 8.46076 0.368907
\(527\) 12.9030 + 7.44958i 0.562066 + 0.324509i
\(528\) 0 0
\(529\) 22.8503 + 39.5778i 0.993490 + 1.72077i
\(530\) 4.50752 7.80725i 0.195794 0.339125i
\(531\) 0 0
\(532\) −4.99592 + 3.14761i −0.216601 + 0.136466i
\(533\) 60.0767i 2.60221i
\(534\) 0 0
\(535\) −11.6233 + 6.71070i −0.502518 + 0.290129i
\(536\) −5.10354 + 2.94653i −0.220439 + 0.127271i
\(537\) 0 0
\(538\) 3.22454i 0.139020i
\(539\) 0.540046 + 6.97914i 0.0232614 + 0.300613i
\(540\) 0 0
\(541\) −1.76339 + 3.05429i −0.0758142 + 0.131314i −0.901440 0.432904i \(-0.857489\pi\)
0.825626 + 0.564218i \(0.190822\pi\)
\(542\) −0.382335 0.662223i −0.0164227 0.0284449i
\(543\) 0 0
\(544\) −3.98321 2.29971i −0.170779 0.0985992i
\(545\) −6.37280 −0.272981
\(546\) 0 0
\(547\) 0.548636 0.0234580 0.0117290 0.999931i \(-0.496266\pi\)
0.0117290 + 0.999931i \(0.496266\pi\)
\(548\) 0.350664 + 0.202456i 0.0149796 + 0.00864848i
\(549\) 0 0
\(550\) −2.04990 3.55054i −0.0874082 0.151395i
\(551\) 1.03848 1.79870i 0.0442408 0.0766274i
\(552\) 0 0
\(553\) −22.0345 + 0.851241i −0.937001 + 0.0361985i
\(554\) 27.2895i 1.15942i
\(555\) 0 0
\(556\) 15.2418 8.79984i 0.646395 0.373196i
\(557\) −6.28514 + 3.62873i −0.266310 + 0.153754i −0.627209 0.778851i \(-0.715803\pi\)
0.360900 + 0.932605i \(0.382470\pi\)
\(558\) 0 0
\(559\) 89.4783i 3.78453i
\(560\) 1.17027 2.22077i 0.0494529 0.0938448i
\(561\) 0 0
\(562\) −2.18312 + 3.78128i −0.0920895 + 0.159504i
\(563\) 4.89429 + 8.47715i 0.206270 + 0.357269i 0.950537 0.310613i \(-0.100534\pi\)
−0.744267 + 0.667882i \(0.767201\pi\)
\(564\) 0 0
\(565\) −6.90106 3.98433i −0.290330 0.167622i
\(566\) 19.1213 0.803730
\(567\) 0 0
\(568\) −12.7563 −0.535243
\(569\) −25.5726 14.7644i −1.07206 0.618954i −0.143316 0.989677i \(-0.545777\pi\)
−0.928743 + 0.370723i \(0.879110\pi\)
\(570\) 0 0
\(571\) 16.4562 + 28.5031i 0.688673 + 1.19282i 0.972267 + 0.233872i \(0.0751396\pi\)
−0.283595 + 0.958944i \(0.591527\pi\)
\(572\) 3.51532 6.08871i 0.146983 0.254582i
\(573\) 0 0
\(574\) −0.872745 22.5911i −0.0364277 0.942934i
\(575\) 33.9816i 1.41713i
\(576\) 0 0
\(577\) 14.0259 8.09787i 0.583907 0.337119i −0.178777 0.983890i \(-0.557214\pi\)
0.762685 + 0.646771i \(0.223881\pi\)
\(578\) 3.59803 2.07732i 0.149658 0.0864053i
\(579\) 0 0
\(580\) 0.882960i 0.0366629i
\(581\) −16.9277 26.8679i −0.702281 1.11467i
\(582\) 0 0
\(583\) 4.75083 8.22868i 0.196759 0.340797i
\(584\) −2.80287 4.85471i −0.115984 0.200889i
\(585\) 0 0
\(586\) 8.00185 + 4.61987i 0.330553 + 0.190845i
\(587\) 13.5685 0.560031 0.280016 0.959995i \(-0.409660\pi\)
0.280016 + 0.959995i \(0.409660\pi\)
\(588\) 0 0
\(589\) −7.22961 −0.297891
\(590\) 6.48439 + 3.74376i 0.266958 + 0.154128i
\(591\) 0 0
\(592\) 4.57553 + 7.92505i 0.188053 + 0.325718i
\(593\) −12.5012 + 21.6528i −0.513365 + 0.889174i 0.486515 + 0.873672i \(0.338268\pi\)
−0.999880 + 0.0155014i \(0.995066\pi\)
\(594\) 0 0
\(595\) 6.15454 + 9.76856i 0.252311 + 0.400472i
\(596\) 20.2236i 0.828390i
\(597\) 0 0
\(598\) 50.4667 29.1370i 2.06374 1.19150i
\(599\) −12.1564 + 7.01849i −0.496696 + 0.286768i −0.727348 0.686269i \(-0.759247\pi\)
0.230652 + 0.973036i \(0.425914\pi\)
\(600\) 0 0
\(601\) 15.3598i 0.626540i −0.949664 0.313270i \(-0.898576\pi\)
0.949664 0.313270i \(-0.101424\pi\)
\(602\) −1.29987 33.6472i −0.0529786 1.37136i
\(603\) 0 0
\(604\) 3.93283 6.81186i 0.160025 0.277171i
\(605\) 0.474393 + 0.821673i 0.0192868 + 0.0334057i
\(606\) 0 0
\(607\) 3.15436 + 1.82117i 0.128032 + 0.0739190i 0.562648 0.826697i \(-0.309783\pi\)
−0.434616 + 0.900616i \(0.643116\pi\)
\(608\) 2.23181 0.0905117
\(609\) 0 0
\(610\) −2.21578 −0.0897144
\(611\) −3.05951 1.76641i −0.123774 0.0714612i
\(612\) 0 0
\(613\) −21.4436 37.1414i −0.866099 1.50013i −0.865952 0.500127i \(-0.833287\pi\)
−0.000146529 1.00000i \(-0.500047\pi\)
\(614\) 3.53010 6.11432i 0.142463 0.246754i
\(615\) 0 0
\(616\) 1.23344 2.34065i 0.0496966 0.0943074i
\(617\) 2.97864i 0.119915i −0.998201 0.0599577i \(-0.980903\pi\)
0.998201 0.0599577i \(-0.0190966\pi\)
\(618\) 0 0
\(619\) −14.6085 + 8.43422i −0.587165 + 0.339000i −0.763976 0.645245i \(-0.776755\pi\)
0.176810 + 0.984245i \(0.443422\pi\)
\(620\) 2.66169 1.53673i 0.106896 0.0617165i
\(621\) 0 0
\(622\) 8.64112i 0.346477i
\(623\) −2.33435 + 0.0901812i −0.0935238 + 0.00361304i
\(624\) 0 0
\(625\) −6.15372 + 10.6586i −0.246149 + 0.426342i
\(626\) 11.9124 + 20.6329i 0.476116 + 0.824657i
\(627\) 0 0
\(628\) −0.300234 0.173340i −0.0119806 0.00691702i
\(629\) −42.0896 −1.67822
\(630\) 0 0
\(631\) 26.6847 1.06230 0.531150 0.847278i \(-0.321760\pi\)
0.531150 + 0.847278i \(0.321760\pi\)
\(632\) 7.21785 + 4.16723i 0.287111 + 0.165763i
\(633\) 0 0
\(634\) −12.6754 21.9545i −0.503405 0.871924i
\(635\) 3.79428 6.57189i 0.150572 0.260798i
\(636\) 0 0
\(637\) 44.3923 + 21.2457i 1.75889 + 0.841785i
\(638\) 0.930621i 0.0368436i
\(639\) 0 0
\(640\) −0.821673 + 0.474393i −0.0324795 + 0.0187520i
\(641\) −26.1562 + 15.1013i −1.03311 + 0.596464i −0.917873 0.396874i \(-0.870095\pi\)
−0.115234 + 0.993338i \(0.536762\pi\)
\(642\) 0 0
\(643\) 10.8154i 0.426517i −0.976996 0.213259i \(-0.931592\pi\)
0.976996 0.213259i \(-0.0684077\pi\)
\(644\) 18.5541 11.6897i 0.731133 0.460640i
\(645\) 0 0
\(646\) −5.13250 + 8.88976i −0.201936 + 0.349763i
\(647\) −7.24060 12.5411i −0.284657 0.493041i 0.687869 0.725835i \(-0.258547\pi\)
−0.972526 + 0.232794i \(0.925213\pi\)
\(648\) 0 0
\(649\) 6.83441 + 3.94585i 0.268274 + 0.154888i
\(650\) −28.8242 −1.13058
\(651\) 0 0
\(652\) −8.00934 −0.313670
\(653\) 37.4800 + 21.6391i 1.46671 + 0.846804i 0.999306 0.0372417i \(-0.0118571\pi\)
0.467401 + 0.884045i \(0.345190\pi\)
\(654\) 0 0
\(655\) −4.14859 7.18557i −0.162099 0.280764i
\(656\) −4.27250 + 7.40019i −0.166813 + 0.288929i
\(657\) 0 0
\(658\) −1.17615 0.619789i −0.0458511 0.0241619i
\(659\) 9.95936i 0.387962i 0.981005 + 0.193981i \(0.0621400\pi\)
−0.981005 + 0.193981i \(0.937860\pi\)
\(660\) 0 0
\(661\) −22.1474 + 12.7868i −0.861434 + 0.497349i −0.864492 0.502646i \(-0.832360\pi\)
0.00305800 + 0.999995i \(0.499027\pi\)
\(662\) 6.69226 3.86378i 0.260102 0.150170i
\(663\) 0 0
\(664\) 12.0026i 0.465790i
\(665\) −4.95633 2.61181i −0.192198 0.101282i
\(666\) 0 0
\(667\) −3.85676 + 6.68011i −0.149334 + 0.258655i
\(668\) 11.6892 + 20.2463i 0.452269 + 0.783352i
\(669\) 0 0
\(670\) −4.84217 2.79563i −0.187069 0.108004i
\(671\) −2.33539 −0.0901566
\(672\) 0 0
\(673\) 22.7065 0.875269 0.437635 0.899153i \(-0.355816\pi\)
0.437635 + 0.899153i \(0.355816\pi\)
\(674\) −21.5820 12.4604i −0.831309 0.479957i
\(675\) 0 0
\(676\) −18.2149 31.5491i −0.700573 1.21343i
\(677\) 13.1278 22.7380i 0.504542 0.873893i −0.495444 0.868640i \(-0.664995\pi\)
0.999986 0.00525286i \(-0.00167205\pi\)
\(678\) 0 0
\(679\) 28.2757 17.8147i 1.08512 0.683664i
\(680\) 4.36386i 0.167346i
\(681\) 0 0
\(682\) 2.80537 1.61968i 0.107423 0.0620207i
\(683\) 27.1231 15.6595i 1.03784 0.599194i 0.118616 0.992940i \(-0.462154\pi\)
0.919219 + 0.393746i \(0.128821\pi\)
\(684\) 0 0
\(685\) 0.384174i 0.0146785i
\(686\) 17.0018 + 7.34427i 0.649132 + 0.280406i
\(687\) 0 0
\(688\) −6.36346 + 11.0218i −0.242605 + 0.420203i
\(689\) −33.4013 57.8528i −1.27249 2.20402i
\(690\) 0 0
\(691\) −22.5041 12.9927i −0.856096 0.494267i 0.00660716 0.999978i \(-0.497897\pi\)
−0.862703 + 0.505711i \(0.831230\pi\)
\(692\) 7.88540 0.299758
\(693\) 0 0
\(694\) 12.7253 0.483045
\(695\) 14.4612 + 8.34916i 0.548543 + 0.316702i
\(696\) 0 0
\(697\) −19.6510 34.0366i −0.744335 1.28923i
\(698\) 3.36162 5.82250i 0.127239 0.220385i
\(699\) 0 0
\(700\) −10.8390 + 0.418734i −0.409675 + 0.0158267i
\(701\) 1.46095i 0.0551793i −0.999619 0.0275897i \(-0.991217\pi\)
0.999619 0.0275897i \(-0.00878318\pi\)
\(702\) 0 0
\(703\) 17.6872 10.2117i 0.667084 0.385141i
\(704\) −0.866025 + 0.500000i −0.0326396 + 0.0188445i
\(705\) 0 0
\(706\) 19.0849i 0.718271i
\(707\) 19.8273 37.6256i 0.745683 1.41505i
\(708\) 0 0
\(709\) −7.35318 + 12.7361i −0.276155 + 0.478314i −0.970426 0.241400i \(-0.922394\pi\)
0.694271 + 0.719714i \(0.255727\pi\)
\(710\) −6.05151 10.4815i −0.227109 0.393364i
\(711\) 0 0
\(712\) 0.764665 + 0.441480i 0.0286570 + 0.0165452i
\(713\) 26.8497 1.00553
\(714\) 0 0
\(715\) 6.67056 0.249465
\(716\) −3.03581 1.75273i −0.113454 0.0655025i
\(717\) 0 0
\(718\) −6.44550 11.1639i −0.240544 0.416634i
\(719\) 15.2799 26.4656i 0.569844 0.986999i −0.426737 0.904376i \(-0.640337\pi\)
0.996581 0.0826233i \(-0.0263298\pi\)
\(720\) 0 0
\(721\) 0.875755 + 22.6690i 0.0326148 + 0.844237i
\(722\) 14.0190i 0.521735i
\(723\) 0 0
\(724\) 15.9788 9.22534i 0.593846 0.342857i
\(725\) 3.30420 1.90768i 0.122715 0.0708495i
\(726\) 0 0
\(727\) 23.9985i 0.890056i 0.895517 + 0.445028i \(0.146806\pi\)
−0.895517 + 0.445028i \(0.853194\pi\)
\(728\) −9.91559 15.7382i −0.367496 0.583295i
\(729\) 0 0
\(730\) 2.65932 4.60608i 0.0984259 0.170479i
\(731\) −29.2682 50.6940i −1.08252 1.87499i
\(732\) 0 0
\(733\) 21.1549 + 12.2138i 0.781373 + 0.451126i 0.836917 0.547330i \(-0.184356\pi\)
−0.0555434 + 0.998456i \(0.517689\pi\)
\(734\) 2.55719 0.0943877
\(735\) 0 0
\(736\) −8.28858 −0.305521
\(737\) −5.10354 2.94653i −0.187991 0.108537i
\(738\) 0 0
\(739\) 11.6718 + 20.2161i 0.429354 + 0.743663i 0.996816 0.0797369i \(-0.0254080\pi\)
−0.567462 + 0.823399i \(0.692075\pi\)
\(740\) −4.34120 + 7.51918i −0.159586 + 0.276410i
\(741\) 0 0
\(742\) −13.4006 21.2696i −0.491951 0.780831i
\(743\) 7.04913i 0.258608i −0.991605 0.129304i \(-0.958726\pi\)
0.991605 0.129304i \(-0.0412742\pi\)
\(744\) 0 0
\(745\) −16.6172 + 9.59392i −0.608805 + 0.351494i
\(746\) 26.3259 15.1993i 0.963860 0.556485i
\(747\) 0 0
\(748\) 4.59942i 0.168171i
\(749\) 1.44479 + 37.3986i 0.0527915 + 1.36651i
\(750\) 0 0
\(751\) −0.999206 + 1.73068i −0.0364615 + 0.0631533i −0.883680 0.468091i \(-0.844942\pi\)
0.847219 + 0.531244i \(0.178275\pi\)
\(752\) 0.251245 + 0.435168i 0.00916195 + 0.0158690i
\(753\) 0 0
\(754\) 5.66628 + 3.27143i 0.206354 + 0.119138i
\(755\) 7.46283 0.271600
\(756\) 0 0
\(757\) −39.3860 −1.43151 −0.715753 0.698353i \(-0.753917\pi\)
−0.715753 + 0.698353i \(0.753917\pi\)
\(758\) 11.7958 + 6.81029i 0.428442 + 0.247361i
\(759\) 0 0
\(760\) 1.05875 + 1.83381i 0.0384050 + 0.0665194i
\(761\) −4.01747 + 6.95846i −0.145633 + 0.252244i −0.929609 0.368547i \(-0.879855\pi\)
0.783976 + 0.620791i \(0.213189\pi\)
\(762\) 0 0
\(763\) −8.28476 + 15.7217i −0.299928 + 0.569162i
\(764\) 25.9073i 0.937293i
\(765\) 0 0
\(766\) 19.7542 11.4051i 0.713750 0.412084i
\(767\) 48.0502 27.7418i 1.73499 1.00170i
\(768\) 0 0
\(769\) 1.71938i 0.0620025i −0.999519 0.0310013i \(-0.990130\pi\)
0.999519 0.0310013i \(-0.00986959\pi\)
\(770\) 2.50838 0.0969044i 0.0903957 0.00349219i
\(771\) 0 0
\(772\) 0.304714 0.527780i 0.0109669 0.0189952i
\(773\) 5.05536 + 8.75614i 0.181829 + 0.314936i 0.942503 0.334197i \(-0.108465\pi\)
−0.760675 + 0.649133i \(0.775132\pi\)
\(774\) 0 0
\(775\) −11.5015 6.64037i −0.413144 0.238529i
\(776\) −12.6315 −0.453443
\(777\) 0 0
\(778\) 1.69687 0.0608357
\(779\) 16.5158 + 9.53539i 0.591739 + 0.341641i
\(780\) 0 0
\(781\) −6.37816 11.0473i −0.228229 0.395303i
\(782\) 19.0613 33.0152i 0.681631 1.18062i
\(783\) 0 0
\(784\) −3.95726 5.77409i −0.141331 0.206217i
\(785\) 0.328925i 0.0117398i
\(786\) 0 0
\(787\) 9.25705 5.34456i 0.329978 0.190513i −0.325853 0.945420i \(-0.605652\pi\)
0.655831 + 0.754907i \(0.272318\pi\)
\(788\) −1.90228 + 1.09828i −0.0677660 + 0.0391247i
\(789\) 0 0
\(790\) 7.90761i 0.281340i
\(791\) −18.8008 + 11.8452i −0.668480 + 0.421166i
\(792\) 0 0
\(793\) −8.20962 + 14.2195i −0.291532 + 0.504949i
\(794\) 12.5473 + 21.7326i 0.445288 + 0.771262i
\(795\) 0 0
\(796\) 22.9865 + 13.2713i 0.814735 + 0.470388i
\(797\) −8.76241 −0.310380 −0.155190 0.987885i \(-0.549599\pi\)
−0.155190 + 0.987885i \(0.549599\pi\)
\(798\) 0 0
\(799\) −2.31116 −0.0817629
\(800\) 3.55054 + 2.04990i 0.125530 + 0.0724750i
\(801\) 0 0
\(802\) 10.8643 + 18.8176i 0.383633 + 0.664472i
\(803\) 2.80287 4.85471i 0.0989111 0.171319i
\(804\) 0 0
\(805\) 18.4071 + 9.69986i 0.648763 + 0.341875i
\(806\) 22.7747i 0.802206i
\(807\) 0 0
\(808\) −13.9212 + 8.03742i −0.489747 + 0.282756i
\(809\) −24.4799 + 14.1335i −0.860669 + 0.496908i −0.864236 0.503086i \(-0.832198\pi\)
0.00356720 + 0.999994i \(0.498865\pi\)
\(810\) 0 0
\(811\) 19.6593i 0.690331i 0.938542 + 0.345166i \(0.112177\pi\)
−0.938542 + 0.345166i \(0.887823\pi\)
\(812\) 2.17825 + 1.14786i 0.0764418 + 0.0402821i
\(813\) 0 0
\(814\) −4.57553 + 7.92505i −0.160372 + 0.277773i
\(815\) −3.79957 6.58105i −0.133093 0.230524i
\(816\) 0 0
\(817\) 24.5986 + 14.2020i 0.860596 + 0.496865i
\(818\) 4.66418 0.163079
\(819\) 0 0
\(820\) −8.10737 −0.283122
\(821\) −8.92687 5.15393i −0.311550 0.179873i 0.336070 0.941837i \(-0.390902\pi\)
−0.647620 + 0.761964i \(0.724235\pi\)
\(822\) 0 0
\(823\) −0.561944 0.973316i −0.0195881 0.0339277i 0.856065 0.516868i \(-0.172902\pi\)
−0.875653 + 0.482940i \(0.839569\pi\)
\(824\) 4.28723 7.42570i 0.149353 0.258687i
\(825\) 0 0
\(826\) 17.6657 11.1300i 0.614667 0.387262i
\(827\) 23.9832i 0.833976i 0.908912 + 0.416988i \(0.136914\pi\)
−0.908912 + 0.416988i \(0.863086\pi\)
\(828\) 0 0
\(829\) 5.07807 2.93182i 0.176369 0.101826i −0.409217 0.912437i \(-0.634198\pi\)
0.585585 + 0.810611i \(0.300865\pi\)
\(830\) −9.86219 + 5.69394i −0.342322 + 0.197639i
\(831\) 0 0
\(832\) 7.03063i 0.243743i
\(833\) 32.1000 2.48390i 1.11220 0.0860619i
\(834\) 0 0
\(835\) −11.0905 + 19.2094i −0.383804 + 0.664768i
\(836\) 1.11590 + 1.93280i 0.0385943 + 0.0668473i
\(837\) 0 0
\(838\) 31.7060 + 18.3055i 1.09527 + 0.632352i
\(839\) 14.4962 0.500464 0.250232 0.968186i \(-0.419493\pi\)
0.250232 + 0.968186i \(0.419493\pi\)
\(840\) 0 0
\(841\) 28.1339 0.970136
\(842\) 26.3771 + 15.2288i 0.909013 + 0.524819i
\(843\) 0 0
\(844\) 3.36449 + 5.82746i 0.115810 + 0.200590i
\(845\) 17.2820 29.9334i 0.594520 1.02974i
\(846\) 0 0
\(847\) 2.64378 0.102135i 0.0908413 0.00350941i
\(848\) 9.50166i 0.326288i
\(849\) 0 0
\(850\) −16.3304 + 9.42836i −0.560128 + 0.323390i
\(851\) −65.6874 + 37.9246i −2.25174 + 1.30004i
\(852\) 0 0
\(853\) 22.1687i 0.759042i 0.925183 + 0.379521i \(0.123911\pi\)
−0.925183 + 0.379521i \(0.876089\pi\)
\(854\) −2.88056 + 5.46632i −0.0985706 + 0.187054i
\(855\) 0 0
\(856\) 7.07294 12.2507i 0.241748 0.418720i
\(857\) −8.89302 15.4032i −0.303780 0.526162i 0.673209 0.739452i \(-0.264915\pi\)
−0.976989 + 0.213290i \(0.931582\pi\)
\(858\) 0 0
\(859\) −5.96846 3.44589i −0.203641 0.117572i 0.394712 0.918805i \(-0.370845\pi\)
−0.598353 + 0.801233i \(0.704178\pi\)
\(860\) −12.0751 −0.411758
\(861\) 0 0
\(862\) 18.6360 0.634744
\(863\) 30.7013 + 17.7254i 1.04508 + 0.603380i 0.921269 0.388926i \(-0.127154\pi\)
0.123815 + 0.992305i \(0.460487\pi\)
\(864\) 0 0
\(865\) 3.74078 + 6.47921i 0.127190 + 0.220300i
\(866\) 4.84751 8.39613i 0.164725 0.285312i
\(867\) 0 0
\(868\) −0.330852 8.56414i −0.0112299 0.290686i
\(869\) 8.33446i 0.282727i
\(870\) 0 0
\(871\) −35.8811 + 20.7160i −1.21579 + 0.701934i
\(872\) 5.81692 3.35840i 0.196986 0.113730i
\(873\) 0 0
\(874\) 18.4985i 0.625721i
\(875\) −12.1766 19.3268i −0.411643 0.653365i
\(876\) 0 0
\(877\) 11.5495 20.0042i 0.389997 0.675495i −0.602451 0.798156i \(-0.705809\pi\)
0.992449 + 0.122660i \(0.0391425\pi\)
\(878\) −16.7841 29.0710i −0.566437 0.981097i
\(879\) 0 0
\(880\) −0.821673 0.474393i −0.0276986 0.0159918i
\(881\) 10.9038 0.367360 0.183680 0.982986i \(-0.441199\pi\)
0.183680 + 0.982986i \(0.441199\pi\)
\(882\) 0 0
\(883\) 35.5478 1.19628 0.598140 0.801392i \(-0.295907\pi\)
0.598140 + 0.801392i \(0.295907\pi\)
\(884\) −28.0045 16.1684i −0.941893 0.543802i
\(885\) 0 0
\(886\) −1.52756 2.64582i −0.0513195 0.0888880i
\(887\) 5.61786 9.73042i 0.188629 0.326716i −0.756164 0.654382i \(-0.772929\pi\)
0.944793 + 0.327666i \(0.106262\pi\)
\(888\) 0 0
\(889\) −11.2802 17.9040i −0.378325 0.600482i
\(890\) 0.837739i 0.0280811i
\(891\) 0 0
\(892\) 20.8803 12.0553i 0.699125 0.403640i
\(893\) 0.971211 0.560729i 0.0325003 0.0187641i
\(894\) 0 0
\(895\) 3.32593i 0.111173i
\(896\) 0.102135 + 2.64378i 0.00341210 + 0.0883225i
\(897\) 0 0
\(898\) 0.177602 0.307616i 0.00592666 0.0102653i
\(899\) 1.50731 + 2.61073i 0.0502715 + 0.0870728i
\(900\) 0 0
\(901\) −37.8471 21.8511i −1.26087 0.727964i
\(902\) −8.54500 −0.284517
\(903\) 0 0
\(904\) 8.39880 0.279340
\(905\) 15.1604 + 8.75287i 0.503949 + 0.290955i
\(906\) 0 0
\(907\) 9.85180 + 17.0638i 0.327124 + 0.566595i 0.981940 0.189193i \(-0.0605873\pi\)
−0.654816 + 0.755788i \(0.727254\pi\)
\(908\) −4.95825 + 8.58794i −0.164545 + 0.285001i
\(909\) 0 0
\(910\) 8.22773 15.6134i 0.272746 0.517580i
\(911\) 35.0219i 1.16033i 0.814500 + 0.580164i \(0.197011\pi\)
−0.814500 + 0.580164i \(0.802989\pi\)
\(912\) 0 0
\(913\) −10.3945 + 6.00129i −0.344009 + 0.198614i
\(914\) 8.31946 4.80324i 0.275183 0.158877i
\(915\) 0 0
\(916\) 22.7130i 0.750458i
\(917\) −23.1200 + 0.893178i −0.763490 + 0.0294953i
\(918\) 0 0
\(919\) 18.8411 32.6337i 0.621510 1.07649i −0.367694 0.929947i \(-0.619853\pi\)
0.989205 0.146541i \(-0.0468139\pi\)
\(920\) −3.93204 6.81050i −0.129636 0.224535i
\(921\) 0 0
\(922\) −33.4389 19.3060i −1.10125 0.635808i
\(923\) −89.6850 −2.95202
\(924\) 0 0
\(925\) 37.5176 1.23357
\(926\) −3.13397 1.80940i −0.102989 0.0594605i
\(927\) 0 0
\(928\) −0.465310 0.805941i −0.0152746 0.0264563i
\(929\) −17.5570 + 30.4096i −0.576027 + 0.997707i 0.419903 + 0.907569i \(0.362064\pi\)
−0.995929 + 0.0901382i \(0.971269\pi\)
\(930\) 0 0
\(931\) −12.8866 + 8.83184i −0.422342 + 0.289452i
\(932\) 12.3130i 0.403327i
\(933\) 0 0
\(934\) −7.06337 + 4.07804i −0.231120 + 0.133437i
\(935\) 3.77922 2.18193i 0.123594 0.0713568i
\(936\) 0 0
\(937\) 9.17435i 0.299713i −0.988708 0.149857i \(-0.952119\pi\)
0.988708 0.149857i \(-0.0478812\pi\)
\(938\) −13.1917 + 8.31123i −0.430724 + 0.271371i
\(939\) 0 0
\(940\) −0.238377 + 0.412882i −0.00777501 + 0.0134667i
\(941\) −13.1537 22.7828i −0.428798 0.742699i 0.567969 0.823050i \(-0.307729\pi\)
−0.996767 + 0.0803507i \(0.974396\pi\)
\(942\) 0 0
\(943\) −61.3370 35.4129i −1.99741 1.15320i
\(944\) −7.89170 −0.256853
\(945\) 0 0
\(946\) −12.7269 −0.413788
\(947\) −29.2145 16.8670i −0.949343 0.548103i −0.0564662 0.998405i \(-0.517983\pi\)
−0.892877 + 0.450301i \(0.851317\pi\)
\(948\) 0 0
\(949\) −19.7059 34.1317i −0.639682 1.10796i
\(950\) 4.57498 7.92410i 0.148432 0.257092i
\(951\) 0 0
\(952\) −10.7656 5.67310i −0.348916 0.183866i
\(953\) 26.6703i 0.863937i −0.901889 0.431968i \(-0.857819\pi\)
0.901889 0.431968i \(-0.142181\pi\)
\(954\) 0 0
\(955\) −21.2873 + 12.2902i −0.688841 + 0.397703i
\(956\) −0.308221 + 0.177951i −0.00996858 + 0.00575536i
\(957\) 0 0
\(958\) 25.9269i 0.837661i
\(959\) 0.947755 + 0.499433i 0.0306046 + 0.0161275i
\(960\) 0 0
\(961\) −10.2533 + 17.7592i −0.330751 + 0.572878i
\(962\) 32.1689 + 55.7181i 1.03717 + 1.79642i
\(963\) 0 0
\(964\) −19.3413 11.1667i −0.622942 0.359655i
\(965\) 0.578217 0.0186135
\(966\) 0 0
\(967\) 36.1827 1.16356 0.581779 0.813347i \(-0.302357\pi\)
0.581779 + 0.813347i \(0.302357\pi\)
\(968\) −0.866025 0.500000i −0.0278351 0.0160706i
\(969\) 0 0
\(970\) −5.99227 10.3789i −0.192400 0.333247i
\(971\) −14.3469 + 24.8495i −0.460413 + 0.797459i −0.998981 0.0451229i \(-0.985632\pi\)
0.538568 + 0.842582i \(0.318965\pi\)
\(972\) 0 0
\(973\) 39.3971 24.8215i 1.26301 0.795742i
\(974\) 3.86205i 0.123748i
\(975\) 0 0
\(976\) 2.02250 1.16769i 0.0647388 0.0373770i
\(977\) 40.1239 23.1656i 1.28368 0.741132i 0.306160 0.951980i \(-0.400956\pi\)
0.977519 + 0.210848i \(0.0676226\pi\)
\(978\) 0 0
\(979\) 0.882960i 0.0282195i
\(980\) 2.86711 5.99076i 0.0915865 0.191368i
\(981\) 0 0
\(982\) 6.77294 11.7311i 0.216133 0.374354i
\(983\) −25.0199 43.3357i −0.798009 1.38219i −0.920911 0.389774i \(-0.872553\pi\)
0.122901 0.992419i \(-0.460780\pi\)
\(984\) 0 0
\(985\) −1.80486 1.04203i −0.0575075 0.0332020i
\(986\) 4.28031 0.136313
\(987\) 0 0
\(988\) 15.6910 0.499197
\(989\) −91.3553 52.7440i −2.90493 1.67716i
\(990\) 0 0
\(991\) 8.38422 + 14.5219i 0.266334 + 0.461303i 0.967912 0.251289i \(-0.0808544\pi\)
−0.701579 + 0.712592i \(0.747521\pi\)
\(992\) −1.61968 + 2.80537i −0.0514248 + 0.0890704i
\(993\) 0 0
\(994\) −33.7249 + 1.30287i −1.06969 + 0.0413245i
\(995\) 25.1832i 0.798360i
\(996\) 0 0
\(997\) 4.51546 2.60700i 0.143006 0.0825645i −0.426790 0.904351i \(-0.640356\pi\)
0.569796 + 0.821786i \(0.307022\pi\)
\(998\) 8.70526 5.02599i 0.275560 0.159095i
\(999\) 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 1386.2.r.d.89.5 24
3.2 odd 2 inner 1386.2.r.d.89.8 yes 24
7.3 odd 6 inner 1386.2.r.d.1277.8 yes 24
21.17 even 6 inner 1386.2.r.d.1277.5 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.r.d.89.5 24 1.1 even 1 trivial
1386.2.r.d.89.8 yes 24 3.2 odd 2 inner
1386.2.r.d.1277.5 yes 24 21.17 even 6 inner
1386.2.r.d.1277.8 yes 24 7.3 odd 6 inner