Properties

Label 1386.2.r.d.89.1
Level $1386$
Weight $2$
Character 1386.89
Analytic conductor $11.067$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 89.1
Character \(\chi\) \(=\) 1386.89
Dual form 1386.2.r.d.1277.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.36138 - 2.35797i) q^{5} +(-2.13605 + 1.56119i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.36138 - 2.35797i) q^{5} +(-2.13605 + 1.56119i) q^{7} -1.00000i q^{8} +(-2.35797 + 1.36138i) q^{10} +(0.866025 - 0.500000i) q^{11} +0.193887i q^{13} +(2.63046 - 0.284003i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.07388 + 5.32411i) q^{17} +(0.269276 + 0.155466i) q^{19} +2.72275 q^{20} -1.00000 q^{22} +(4.50799 + 2.60269i) q^{23} +(-1.20669 - 2.09005i) q^{25} +(0.0969436 - 0.167911i) q^{26} +(-2.42005 - 1.06928i) q^{28} -4.17192i q^{29} +(1.38127 - 0.797476i) q^{31} +(0.866025 - 0.500000i) q^{32} -6.14775i q^{34} +(0.773269 + 7.16211i) q^{35} +(2.21011 - 3.82803i) q^{37} +(-0.155466 - 0.269276i) q^{38} +(-2.35797 - 1.36138i) q^{40} +4.29859 q^{41} +4.10271 q^{43} +(0.866025 + 0.500000i) q^{44} +(-2.60269 - 4.50799i) q^{46} +(3.63535 - 6.29661i) q^{47} +(2.12540 - 6.66953i) q^{49} +2.41339i q^{50} +(-0.167911 + 0.0969436i) q^{52} +(-1.04499 + 0.603325i) q^{53} -2.72275i q^{55} +(1.56119 + 2.13605i) q^{56} +(-2.08596 + 3.61299i) q^{58} +(5.43057 + 9.40603i) q^{59} +(-8.20619 - 4.73784i) q^{61} -1.59495 q^{62} -1.00000 q^{64} +(0.457181 + 0.263953i) q^{65} +(2.69458 + 4.66714i) q^{67} +(-3.07388 + 5.32411i) q^{68} +(2.91138 - 6.58920i) q^{70} -9.63462i q^{71} +(-2.50213 + 1.44461i) q^{73} +(-3.82803 + 2.21011i) q^{74} +0.310933i q^{76} +(-1.06928 + 2.42005i) q^{77} +(-7.60345 + 13.1696i) q^{79} +(1.36138 + 2.35797i) q^{80} +(-3.72268 - 2.14929i) q^{82} +10.0883 q^{83} +16.7388 q^{85} +(-3.55305 - 2.05135i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(5.67955 - 9.83727i) q^{89} +(-0.302694 - 0.414152i) q^{91} +5.20538i q^{92} +(-6.29661 + 3.63535i) q^{94} +(0.733171 - 0.423296i) q^{95} -6.77249i q^{97} +(-5.17542 + 4.71329i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) \) 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
\(5\) 1.36138 2.35797i 0.608826 1.05452i −0.382608 0.923911i \(-0.624974\pi\)
0.991434 0.130607i \(-0.0416926\pi\)
\(6\) 0 0
\(7\) −2.13605 + 1.56119i −0.807350 + 0.590073i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −2.35797 + 1.36138i −0.745657 + 0.430505i
\(11\) 0.866025 0.500000i 0.261116 0.150756i
\(12\) 0 0
\(13\) 0.193887i 0.0537746i 0.999638 + 0.0268873i \(0.00855953\pi\)
−0.999638 + 0.0268873i \(0.991440\pi\)
\(14\) 2.63046 0.284003i 0.703021 0.0759029i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.07388 + 5.32411i 0.745524 + 1.29129i 0.949949 + 0.312404i \(0.101134\pi\)
−0.204425 + 0.978882i \(0.565532\pi\)
\(18\) 0 0
\(19\) 0.269276 + 0.155466i 0.0617760 + 0.0356664i 0.530570 0.847641i \(-0.321978\pi\)
−0.468794 + 0.883308i \(0.655311\pi\)
\(20\) 2.72275 0.608826
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 4.50799 + 2.60269i 0.939981 + 0.542698i 0.889954 0.456050i \(-0.150736\pi\)
0.0500264 + 0.998748i \(0.484069\pi\)
\(24\) 0 0
\(25\) −1.20669 2.09005i −0.241339 0.418011i
\(26\) 0.0969436 0.167911i 0.0190122 0.0329301i
\(27\) 0 0
\(28\) −2.42005 1.06928i −0.457347 0.202075i
\(29\) 4.17192i 0.774705i −0.921932 0.387353i \(-0.873390\pi\)
0.921932 0.387353i \(-0.126610\pi\)
\(30\) 0 0
\(31\) 1.38127 0.797476i 0.248083 0.143231i −0.370803 0.928712i \(-0.620918\pi\)
0.618886 + 0.785481i \(0.287584\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 6.14775i 1.05433i
\(35\) 0.773269 + 7.16211i 0.130706 + 1.21062i
\(36\) 0 0
\(37\) 2.21011 3.82803i 0.363340 0.629324i −0.625168 0.780490i \(-0.714970\pi\)
0.988508 + 0.151167i \(0.0483030\pi\)
\(38\) −0.155466 0.269276i −0.0252200 0.0436823i
\(39\) 0 0
\(40\) −2.35797 1.36138i −0.372828 0.215253i
\(41\) 4.29859 0.671326 0.335663 0.941982i \(-0.391040\pi\)
0.335663 + 0.941982i \(0.391040\pi\)
\(42\) 0 0
\(43\) 4.10271 0.625657 0.312829 0.949810i \(-0.398723\pi\)
0.312829 + 0.949810i \(0.398723\pi\)
\(44\) 0.866025 + 0.500000i 0.130558 + 0.0753778i
\(45\) 0 0
\(46\) −2.60269 4.50799i −0.383746 0.664667i
\(47\) 3.63535 6.29661i 0.530270 0.918454i −0.469107 0.883142i \(-0.655424\pi\)
0.999376 0.0353126i \(-0.0112427\pi\)
\(48\) 0 0
\(49\) 2.12540 6.66953i 0.303628 0.952791i
\(50\) 2.41339i 0.341304i
\(51\) 0 0
\(52\) −0.167911 + 0.0969436i −0.0232851 + 0.0134437i
\(53\) −1.04499 + 0.603325i −0.143540 + 0.0828730i −0.570050 0.821610i \(-0.693076\pi\)
0.426510 + 0.904483i \(0.359743\pi\)
\(54\) 0 0
\(55\) 2.72275i 0.367136i
\(56\) 1.56119 + 2.13605i 0.208622 + 0.285441i
\(57\) 0 0
\(58\) −2.08596 + 3.61299i −0.273900 + 0.474408i
\(59\) 5.43057 + 9.40603i 0.707001 + 1.22456i 0.965965 + 0.258674i \(0.0832855\pi\)
−0.258964 + 0.965887i \(0.583381\pi\)
\(60\) 0 0
\(61\) −8.20619 4.73784i −1.05069 0.606619i −0.127851 0.991793i \(-0.540808\pi\)
−0.922844 + 0.385175i \(0.874141\pi\)
\(62\) −1.59495 −0.202559
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.457181 + 0.263953i 0.0567063 + 0.0327394i
\(66\) 0 0
\(67\) 2.69458 + 4.66714i 0.329195 + 0.570182i 0.982352 0.187040i \(-0.0598894\pi\)
−0.653158 + 0.757222i \(0.726556\pi\)
\(68\) −3.07388 + 5.32411i −0.372762 + 0.645643i
\(69\) 0 0
\(70\) 2.91138 6.58920i 0.347977 0.787560i
\(71\) 9.63462i 1.14342i −0.820456 0.571710i \(-0.806280\pi\)
0.820456 0.571710i \(-0.193720\pi\)
\(72\) 0 0
\(73\) −2.50213 + 1.44461i −0.292853 + 0.169079i −0.639228 0.769018i \(-0.720746\pi\)
0.346375 + 0.938096i \(0.387412\pi\)
\(74\) −3.82803 + 2.21011i −0.444999 + 0.256920i
\(75\) 0 0
\(76\) 0.310933i 0.0356664i
\(77\) −1.06928 + 2.42005i −0.121856 + 0.275790i
\(78\) 0 0
\(79\) −7.60345 + 13.1696i −0.855455 + 1.48169i 0.0207679 + 0.999784i \(0.493389\pi\)
−0.876223 + 0.481907i \(0.839944\pi\)
\(80\) 1.36138 + 2.35797i 0.152207 + 0.263629i
\(81\) 0 0
\(82\) −3.72268 2.14929i −0.411102 0.237350i
\(83\) 10.0883 1.10734 0.553668 0.832737i \(-0.313228\pi\)
0.553668 + 0.832737i \(0.313228\pi\)
\(84\) 0 0
\(85\) 16.7388 1.81558
\(86\) −3.55305 2.05135i −0.383135 0.221203i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 5.67955 9.83727i 0.602031 1.04275i −0.390482 0.920610i \(-0.627692\pi\)
0.992513 0.122138i \(-0.0389750\pi\)
\(90\) 0 0
\(91\) −0.302694 0.414152i −0.0317309 0.0434149i
\(92\) 5.20538i 0.542698i
\(93\) 0 0
\(94\) −6.29661 + 3.63535i −0.649445 + 0.374957i
\(95\) 0.733171 0.423296i 0.0752217 0.0434293i
\(96\) 0 0
\(97\) 6.77249i 0.687642i −0.939035 0.343821i \(-0.888279\pi\)
0.939035 0.343821i \(-0.111721\pi\)
\(98\) −5.17542 + 4.71329i −0.522796 + 0.476114i
\(99\) 0 0
\(100\) 1.20669 2.09005i 0.120669 0.209005i
\(101\) −6.35755 11.0116i −0.632600 1.09570i −0.987018 0.160608i \(-0.948654\pi\)
0.354418 0.935087i \(-0.384679\pi\)
\(102\) 0 0
\(103\) 1.88096 + 1.08597i 0.185336 + 0.107004i 0.589797 0.807551i \(-0.299208\pi\)
−0.404461 + 0.914555i \(0.632541\pi\)
\(104\) 0.193887 0.0190122
\(105\) 0 0
\(106\) 1.20665 0.117200
\(107\) 4.39707 + 2.53865i 0.425081 + 0.245421i 0.697249 0.716829i \(-0.254407\pi\)
−0.272168 + 0.962250i \(0.587741\pi\)
\(108\) 0 0
\(109\) 0.813357 + 1.40878i 0.0779054 + 0.134936i 0.902346 0.431012i \(-0.141843\pi\)
−0.824441 + 0.565948i \(0.808510\pi\)
\(110\) −1.36138 + 2.35797i −0.129802 + 0.224824i
\(111\) 0 0
\(112\) −0.284003 2.63046i −0.0268357 0.248556i
\(113\) 9.08122i 0.854290i −0.904183 0.427145i \(-0.859519\pi\)
0.904183 0.427145i \(-0.140481\pi\)
\(114\) 0 0
\(115\) 12.2741 7.08648i 1.14457 0.660818i
\(116\) 3.61299 2.08596i 0.335457 0.193676i
\(117\) 0 0
\(118\) 10.8611i 0.999850i
\(119\) −14.8779 6.57366i −1.36385 0.602606i
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 4.73784 + 8.20619i 0.428944 + 0.742953i
\(123\) 0 0
\(124\) 1.38127 + 0.797476i 0.124042 + 0.0716155i
\(125\) 7.04271 0.629919
\(126\) 0 0
\(127\) 3.00619 0.266756 0.133378 0.991065i \(-0.457418\pi\)
0.133378 + 0.991065i \(0.457418\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −0.263953 0.457181i −0.0231502 0.0400974i
\(131\) 3.10422 5.37666i 0.271217 0.469761i −0.697957 0.716140i \(-0.745907\pi\)
0.969174 + 0.246378i \(0.0792406\pi\)
\(132\) 0 0
\(133\) −0.817897 + 0.0883057i −0.0709207 + 0.00765708i
\(134\) 5.38915i 0.465552i
\(135\) 0 0
\(136\) 5.32411 3.07388i 0.456539 0.263583i
\(137\) 8.22265 4.74735i 0.702508 0.405593i −0.105773 0.994390i \(-0.533732\pi\)
0.808281 + 0.588797i \(0.200398\pi\)
\(138\) 0 0
\(139\) 13.2020i 1.11978i 0.828568 + 0.559888i \(0.189156\pi\)
−0.828568 + 0.559888i \(0.810844\pi\)
\(140\) −5.81593 + 4.25072i −0.491536 + 0.359252i
\(141\) 0 0
\(142\) −4.81731 + 8.34383i −0.404260 + 0.700198i
\(143\) 0.0969436 + 0.167911i 0.00810683 + 0.0140414i
\(144\) 0 0
\(145\) −9.83727 5.67955i −0.816941 0.471661i
\(146\) 2.88921 0.239113
\(147\) 0 0
\(148\) 4.42022 0.363340
\(149\) 11.9136 + 6.87830i 0.975997 + 0.563492i 0.901059 0.433696i \(-0.142791\pi\)
0.0749376 + 0.997188i \(0.476124\pi\)
\(150\) 0 0
\(151\) 10.4182 + 18.0449i 0.847823 + 1.46847i 0.883146 + 0.469097i \(0.155421\pi\)
−0.0353230 + 0.999376i \(0.511246\pi\)
\(152\) 0.155466 0.269276i 0.0126100 0.0218411i
\(153\) 0 0
\(154\) 2.13605 1.56119i 0.172128 0.125804i
\(155\) 4.34266i 0.348811i
\(156\) 0 0
\(157\) 13.5367 7.81541i 1.08034 0.623737i 0.149355 0.988784i \(-0.452280\pi\)
0.930989 + 0.365046i \(0.118947\pi\)
\(158\) 13.1696 7.60345i 1.04771 0.604898i
\(159\) 0 0
\(160\) 2.72275i 0.215253i
\(161\) −13.6926 + 1.47834i −1.07912 + 0.116510i
\(162\) 0 0
\(163\) −2.53891 + 4.39752i −0.198863 + 0.344441i −0.948160 0.317793i \(-0.897058\pi\)
0.749297 + 0.662234i \(0.230392\pi\)
\(164\) 2.14929 + 3.72268i 0.167832 + 0.290693i
\(165\) 0 0
\(166\) −8.73673 5.04416i −0.678102 0.391502i
\(167\) 3.13718 0.242762 0.121381 0.992606i \(-0.461268\pi\)
0.121381 + 0.992606i \(0.461268\pi\)
\(168\) 0 0
\(169\) 12.9624 0.997108
\(170\) −14.4962 8.36940i −1.11181 0.641904i
\(171\) 0 0
\(172\) 2.05135 + 3.55305i 0.156414 + 0.270918i
\(173\) 8.61420 14.9202i 0.654925 1.13436i −0.326987 0.945029i \(-0.606033\pi\)
0.981913 0.189335i \(-0.0606332\pi\)
\(174\) 0 0
\(175\) 5.84051 + 2.58058i 0.441501 + 0.195074i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) −9.83727 + 5.67955i −0.737334 + 0.425700i
\(179\) −10.0700 + 5.81389i −0.752664 + 0.434551i −0.826656 0.562708i \(-0.809759\pi\)
0.0739917 + 0.997259i \(0.476426\pi\)
\(180\) 0 0
\(181\) 10.3940i 0.772577i −0.922378 0.386288i \(-0.873757\pi\)
0.922378 0.386288i \(-0.126243\pi\)
\(182\) 0.0550645 + 0.510013i 0.00408165 + 0.0378047i
\(183\) 0 0
\(184\) 2.60269 4.50799i 0.191873 0.332333i
\(185\) −6.01759 10.4228i −0.442422 0.766297i
\(186\) 0 0
\(187\) 5.32411 + 3.07388i 0.389337 + 0.224784i
\(188\) 7.27069 0.530270
\(189\) 0 0
\(190\) −0.846593 −0.0614183
\(191\) −15.4420 8.91542i −1.11734 0.645097i −0.176620 0.984279i \(-0.556516\pi\)
−0.940721 + 0.339182i \(0.889850\pi\)
\(192\) 0 0
\(193\) −7.66535 13.2768i −0.551764 0.955683i −0.998147 0.0608416i \(-0.980622\pi\)
0.446383 0.894842i \(-0.352712\pi\)
\(194\) −3.38624 + 5.86514i −0.243118 + 0.421093i
\(195\) 0 0
\(196\) 6.83868 1.49412i 0.488477 0.106723i
\(197\) 23.5506i 1.67791i 0.544199 + 0.838956i \(0.316834\pi\)
−0.544199 + 0.838956i \(0.683166\pi\)
\(198\) 0 0
\(199\) −11.4609 + 6.61697i −0.812443 + 0.469064i −0.847804 0.530310i \(-0.822075\pi\)
0.0353603 + 0.999375i \(0.488742\pi\)
\(200\) −2.09005 + 1.20669i −0.147789 + 0.0853260i
\(201\) 0 0
\(202\) 12.7151i 0.894632i
\(203\) 6.51314 + 8.91141i 0.457133 + 0.625458i
\(204\) 0 0
\(205\) 5.85199 10.1360i 0.408721 0.707926i
\(206\) −1.08597 1.88096i −0.0756632 0.131052i
\(207\) 0 0
\(208\) −0.167911 0.0969436i −0.0116425 0.00672183i
\(209\) 0.310933 0.0215077
\(210\) 0 0
\(211\) 0.937344 0.0645294 0.0322647 0.999479i \(-0.489728\pi\)
0.0322647 + 0.999479i \(0.489728\pi\)
\(212\) −1.04499 0.603325i −0.0717702 0.0414365i
\(213\) 0 0
\(214\) −2.53865 4.39707i −0.173539 0.300578i
\(215\) 5.58533 9.67408i 0.380916 0.659767i
\(216\) 0 0
\(217\) −1.70545 + 3.85986i −0.115773 + 0.262025i
\(218\) 1.62671i 0.110175i
\(219\) 0 0
\(220\) 2.35797 1.36138i 0.158975 0.0917840i
\(221\) −1.03228 + 0.595985i −0.0694384 + 0.0400903i
\(222\) 0 0
\(223\) 10.8750i 0.728242i 0.931352 + 0.364121i \(0.118631\pi\)
−0.931352 + 0.364121i \(0.881369\pi\)
\(224\) −1.06928 + 2.42005i −0.0714442 + 0.161696i
\(225\) 0 0
\(226\) −4.54061 + 7.86457i −0.302037 + 0.523143i
\(227\) 3.87060 + 6.70408i 0.256901 + 0.444965i 0.965410 0.260736i \(-0.0839653\pi\)
−0.708509 + 0.705701i \(0.750632\pi\)
\(228\) 0 0
\(229\) 4.44434 + 2.56594i 0.293691 + 0.169562i 0.639605 0.768704i \(-0.279098\pi\)
−0.345914 + 0.938266i \(0.612431\pi\)
\(230\) −14.1730 −0.934537
\(231\) 0 0
\(232\) −4.17192 −0.273900
\(233\) −16.5376 9.54801i −1.08342 0.625511i −0.151600 0.988442i \(-0.548443\pi\)
−0.931816 + 0.362931i \(0.881776\pi\)
\(234\) 0 0
\(235\) −9.89815 17.1441i −0.645684 1.11836i
\(236\) −5.43057 + 9.40603i −0.353500 + 0.612280i
\(237\) 0 0
\(238\) 9.59778 + 13.1319i 0.622132 + 0.851214i
\(239\) 12.4259i 0.803762i −0.915692 0.401881i \(-0.868357\pi\)
0.915692 0.401881i \(-0.131643\pi\)
\(240\) 0 0
\(241\) −19.5847 + 11.3072i −1.26156 + 0.728363i −0.973377 0.229212i \(-0.926385\pi\)
−0.288185 + 0.957575i \(0.593052\pi\)
\(242\) −0.866025 + 0.500000i −0.0556702 + 0.0321412i
\(243\) 0 0
\(244\) 9.47569i 0.606619i
\(245\) −12.8331 14.0914i −0.819878 0.900265i
\(246\) 0 0
\(247\) −0.0301429 + 0.0522091i −0.00191795 + 0.00332198i
\(248\) −0.797476 1.38127i −0.0506398 0.0877107i
\(249\) 0 0
\(250\) −6.09917 3.52136i −0.385745 0.222710i
\(251\) −6.22476 −0.392903 −0.196452 0.980514i \(-0.562942\pi\)
−0.196452 + 0.980514i \(0.562942\pi\)
\(252\) 0 0
\(253\) 5.20538 0.327259
\(254\) −2.60344 1.50310i −0.163354 0.0943126i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −12.6647 + 21.9359i −0.790003 + 1.36832i 0.135962 + 0.990714i \(0.456588\pi\)
−0.925964 + 0.377611i \(0.876746\pi\)
\(258\) 0 0
\(259\) 1.25536 + 11.6272i 0.0780040 + 0.722482i
\(260\) 0.527907i 0.0327394i
\(261\) 0 0
\(262\) −5.37666 + 3.10422i −0.332171 + 0.191779i
\(263\) −20.6740 + 11.9361i −1.27481 + 0.736014i −0.975890 0.218263i \(-0.929961\pi\)
−0.298924 + 0.954277i \(0.596628\pi\)
\(264\) 0 0
\(265\) 3.28541i 0.201821i
\(266\) 0.752472 + 0.332474i 0.0461370 + 0.0203853i
\(267\) 0 0
\(268\) −2.69458 + 4.66714i −0.164597 + 0.285091i
\(269\) −1.06611 1.84656i −0.0650019 0.112587i 0.831693 0.555236i \(-0.187372\pi\)
−0.896695 + 0.442649i \(0.854039\pi\)
\(270\) 0 0
\(271\) −23.5382 13.5898i −1.42984 0.825520i −0.432735 0.901521i \(-0.642451\pi\)
−0.997108 + 0.0760010i \(0.975785\pi\)
\(272\) −6.14775 −0.372762
\(273\) 0 0
\(274\) −9.49469 −0.573595
\(275\) −2.09005 1.20669i −0.126035 0.0727663i
\(276\) 0 0
\(277\) 5.00742 + 8.67311i 0.300867 + 0.521117i 0.976333 0.216275i \(-0.0693907\pi\)
−0.675466 + 0.737391i \(0.736057\pi\)
\(278\) 6.60098 11.4332i 0.395901 0.685720i
\(279\) 0 0
\(280\) 7.16211 0.773269i 0.428018 0.0462117i
\(281\) 28.1787i 1.68100i 0.541813 + 0.840499i \(0.317738\pi\)
−0.541813 + 0.840499i \(0.682262\pi\)
\(282\) 0 0
\(283\) 23.7390 13.7057i 1.41114 0.814721i 0.415642 0.909528i \(-0.363557\pi\)
0.995496 + 0.0948077i \(0.0302236\pi\)
\(284\) 8.34383 4.81731i 0.495115 0.285855i
\(285\) 0 0
\(286\) 0.193887i 0.0114648i
\(287\) −9.18198 + 6.71089i −0.541995 + 0.396131i
\(288\) 0 0
\(289\) −10.3974 + 18.0089i −0.611613 + 1.05934i
\(290\) 5.67955 + 9.83727i 0.333515 + 0.577664i
\(291\) 0 0
\(292\) −2.50213 1.44461i −0.146426 0.0845393i
\(293\) 6.42673 0.375454 0.187727 0.982221i \(-0.439888\pi\)
0.187727 + 0.982221i \(0.439888\pi\)
\(294\) 0 0
\(295\) 29.5722 1.72176
\(296\) −3.82803 2.21011i −0.222499 0.128460i
\(297\) 0 0
\(298\) −6.87830 11.9136i −0.398449 0.690134i
\(299\) −0.504628 + 0.874041i −0.0291834 + 0.0505471i
\(300\) 0 0
\(301\) −8.76358 + 6.40509i −0.505124 + 0.369183i
\(302\) 20.8365i 1.19900i
\(303\) 0 0
\(304\) −0.269276 + 0.155466i −0.0154440 + 0.00891660i
\(305\) −22.3434 + 12.9000i −1.27938 + 0.738651i
\(306\) 0 0
\(307\) 21.7703i 1.24250i 0.783614 + 0.621248i \(0.213374\pi\)
−0.783614 + 0.621248i \(0.786626\pi\)
\(308\) −2.63046 + 0.284003i −0.149885 + 0.0161826i
\(309\) 0 0
\(310\) −2.17133 + 3.76085i −0.123323 + 0.213602i
\(311\) 6.47129 + 11.2086i 0.366953 + 0.635582i 0.989088 0.147329i \(-0.0470676\pi\)
−0.622134 + 0.782910i \(0.713734\pi\)
\(312\) 0 0
\(313\) −1.55581 0.898250i −0.0879398 0.0507721i 0.455385 0.890294i \(-0.349502\pi\)
−0.543325 + 0.839522i \(0.682835\pi\)
\(314\) −15.6308 −0.882098
\(315\) 0 0
\(316\) −15.2069 −0.855455
\(317\) −25.0485 14.4617i −1.40686 0.812252i −0.411777 0.911285i \(-0.635092\pi\)
−0.995084 + 0.0990327i \(0.968425\pi\)
\(318\) 0 0
\(319\) −2.08596 3.61299i −0.116791 0.202288i
\(320\) −1.36138 + 2.35797i −0.0761033 + 0.131815i
\(321\) 0 0
\(322\) 12.5973 + 5.56600i 0.702019 + 0.310181i
\(323\) 1.91154i 0.106361i
\(324\) 0 0
\(325\) 0.405234 0.233962i 0.0224784 0.0129779i
\(326\) 4.39752 2.53891i 0.243556 0.140617i
\(327\) 0 0
\(328\) 4.29859i 0.237350i
\(329\) 2.06490 + 19.1253i 0.113841 + 1.05441i
\(330\) 0 0
\(331\) −17.8278 + 30.8786i −0.979904 + 1.69724i −0.317204 + 0.948357i \(0.602744\pi\)
−0.662700 + 0.748885i \(0.730589\pi\)
\(332\) 5.04416 + 8.73673i 0.276834 + 0.479491i
\(333\) 0 0
\(334\) −2.71688 1.56859i −0.148661 0.0858294i
\(335\) 14.6733 0.801690
\(336\) 0 0
\(337\) 18.6472 1.01578 0.507890 0.861422i \(-0.330426\pi\)
0.507890 + 0.861422i \(0.330426\pi\)
\(338\) −11.2258 6.48120i −0.610602 0.352531i
\(339\) 0 0
\(340\) 8.36940 + 14.4962i 0.453895 + 0.786169i
\(341\) 0.797476 1.38127i 0.0431857 0.0747999i
\(342\) 0 0
\(343\) 5.87243 + 17.5646i 0.317081 + 0.948398i
\(344\) 4.10271i 0.221203i
\(345\) 0 0
\(346\) −14.9202 + 8.61420i −0.802116 + 0.463102i
\(347\) 26.9301 15.5481i 1.44569 0.834667i 0.447465 0.894301i \(-0.352327\pi\)
0.998220 + 0.0596342i \(0.0189934\pi\)
\(348\) 0 0
\(349\) 13.5679i 0.726272i 0.931736 + 0.363136i \(0.118294\pi\)
−0.931736 + 0.363136i \(0.881706\pi\)
\(350\) −3.76774 5.15511i −0.201394 0.275552i
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) 0.975985 + 1.69046i 0.0519465 + 0.0899739i 0.890829 0.454338i \(-0.150124\pi\)
−0.838883 + 0.544312i \(0.816791\pi\)
\(354\) 0 0
\(355\) −22.7182 13.1163i −1.20576 0.696144i
\(356\) 11.3591 0.602031
\(357\) 0 0
\(358\) 11.6278 0.614548
\(359\) −1.05983 0.611893i −0.0559357 0.0322945i 0.471771 0.881721i \(-0.343615\pi\)
−0.527707 + 0.849426i \(0.676948\pi\)
\(360\) 0 0
\(361\) −9.45166 16.3708i −0.497456 0.861619i
\(362\) −5.19698 + 9.00143i −0.273147 + 0.473105i
\(363\) 0 0
\(364\) 0.207319 0.469217i 0.0108665 0.0245936i
\(365\) 7.86662i 0.411758i
\(366\) 0 0
\(367\) 20.6347 11.9134i 1.07712 0.621877i 0.147004 0.989136i \(-0.453037\pi\)
0.930119 + 0.367259i \(0.119704\pi\)
\(368\) −4.50799 + 2.60269i −0.234995 + 0.135675i
\(369\) 0 0
\(370\) 12.0352i 0.625679i
\(371\) 1.29024 2.92015i 0.0669862 0.151607i
\(372\) 0 0
\(373\) −10.5452 + 18.2648i −0.546008 + 0.945714i 0.452535 + 0.891747i \(0.350520\pi\)
−0.998543 + 0.0539668i \(0.982813\pi\)
\(374\) −3.07388 5.32411i −0.158946 0.275303i
\(375\) 0 0
\(376\) −6.29661 3.63535i −0.324723 0.187479i
\(377\) 0.808881 0.0416595
\(378\) 0 0
\(379\) −29.6286 −1.52192 −0.760961 0.648798i \(-0.775272\pi\)
−0.760961 + 0.648798i \(0.775272\pi\)
\(380\) 0.733171 + 0.423296i 0.0376109 + 0.0217146i
\(381\) 0 0
\(382\) 8.91542 + 15.4420i 0.456152 + 0.790079i
\(383\) 2.05855 3.56551i 0.105187 0.182189i −0.808628 0.588321i \(-0.799789\pi\)
0.913815 + 0.406132i \(0.133123\pi\)
\(384\) 0 0
\(385\) 4.25072 + 5.81593i 0.216637 + 0.296407i
\(386\) 15.3307i 0.780312i
\(387\) 0 0
\(388\) 5.86514 3.38624i 0.297758 0.171910i
\(389\) −29.0363 + 16.7641i −1.47220 + 0.849975i −0.999511 0.0312539i \(-0.990050\pi\)
−0.472689 + 0.881229i \(0.656717\pi\)
\(390\) 0 0
\(391\) 32.0014i 1.61838i
\(392\) −6.66953 2.12540i −0.336862 0.107349i
\(393\) 0 0
\(394\) 11.7753 20.3954i 0.593232 1.02751i
\(395\) 20.7023 + 35.8575i 1.04165 + 1.80418i
\(396\) 0 0
\(397\) 1.46549 + 0.846104i 0.0735511 + 0.0424647i 0.536325 0.844012i \(-0.319812\pi\)
−0.462773 + 0.886477i \(0.653146\pi\)
\(398\) 13.2339 0.663357
\(399\) 0 0
\(400\) 2.41339 0.120669
\(401\) −32.1813 18.5799i −1.60706 0.927835i −0.990024 0.140897i \(-0.955001\pi\)
−0.617033 0.786937i \(-0.711665\pi\)
\(402\) 0 0
\(403\) 0.154620 + 0.267810i 0.00770219 + 0.0133406i
\(404\) 6.35755 11.0116i 0.316300 0.547848i
\(405\) 0 0
\(406\) −1.18484 10.9741i −0.0588024 0.544634i
\(407\) 4.42022i 0.219102i
\(408\) 0 0
\(409\) −2.23682 + 1.29143i −0.110604 + 0.0638570i −0.554281 0.832329i \(-0.687007\pi\)
0.443678 + 0.896186i \(0.353673\pi\)
\(410\) −10.1360 + 5.85199i −0.500579 + 0.289009i
\(411\) 0 0
\(412\) 2.17194i 0.107004i
\(413\) −26.2845 11.6136i −1.29338 0.571468i
\(414\) 0 0
\(415\) 13.7340 23.7880i 0.674175 1.16771i
\(416\) 0.0969436 + 0.167911i 0.00475305 + 0.00823252i
\(417\) 0 0
\(418\) −0.269276 0.155466i −0.0131707 0.00760410i
\(419\) 22.0871 1.07903 0.539513 0.841978i \(-0.318609\pi\)
0.539513 + 0.841978i \(0.318609\pi\)
\(420\) 0 0
\(421\) −3.60120 −0.175512 −0.0877559 0.996142i \(-0.527970\pi\)
−0.0877559 + 0.996142i \(0.527970\pi\)
\(422\) −0.811764 0.468672i −0.0395161 0.0228146i
\(423\) 0 0
\(424\) 0.603325 + 1.04499i 0.0293000 + 0.0507492i
\(425\) 7.41845 12.8491i 0.359847 0.623274i
\(426\) 0 0
\(427\) 24.9255 2.69112i 1.20623 0.130232i
\(428\) 5.07730i 0.245421i
\(429\) 0 0
\(430\) −9.67408 + 5.58533i −0.466526 + 0.269349i
\(431\) −2.29763 + 1.32654i −0.110673 + 0.0638970i −0.554315 0.832307i \(-0.687020\pi\)
0.443642 + 0.896204i \(0.353686\pi\)
\(432\) 0 0
\(433\) 21.3112i 1.02415i 0.858940 + 0.512076i \(0.171123\pi\)
−0.858940 + 0.512076i \(0.828877\pi\)
\(434\) 3.40689 2.49002i 0.163536 0.119525i
\(435\) 0 0
\(436\) −0.813357 + 1.40878i −0.0389527 + 0.0674681i
\(437\) 0.809261 + 1.40168i 0.0387122 + 0.0670515i
\(438\) 0 0
\(439\) 11.1839 + 6.45704i 0.533780 + 0.308178i 0.742554 0.669786i \(-0.233614\pi\)
−0.208775 + 0.977964i \(0.566948\pi\)
\(440\) −2.72275 −0.129802
\(441\) 0 0
\(442\) 1.19197 0.0566962
\(443\) 20.9687 + 12.1063i 0.996251 + 0.575186i 0.907137 0.420836i \(-0.138263\pi\)
0.0891141 + 0.996021i \(0.471596\pi\)
\(444\) 0 0
\(445\) −15.4640 26.7845i −0.733064 1.26970i
\(446\) 5.43749 9.41801i 0.257473 0.445956i
\(447\) 0 0
\(448\) 2.13605 1.56119i 0.100919 0.0737591i
\(449\) 6.97436i 0.329140i 0.986365 + 0.164570i \(0.0526237\pi\)
−0.986365 + 0.164570i \(0.947376\pi\)
\(450\) 0 0
\(451\) 3.72268 2.14929i 0.175294 0.101206i
\(452\) 7.86457 4.54061i 0.369918 0.213572i
\(453\) 0 0
\(454\) 7.74120i 0.363312i
\(455\) −1.38864 + 0.149927i −0.0651004 + 0.00702868i
\(456\) 0 0
\(457\) 0.0495834 0.0858810i 0.00231941 0.00401734i −0.864863 0.502007i \(-0.832595\pi\)
0.867183 + 0.497990i \(0.165928\pi\)
\(458\) −2.56594 4.44434i −0.119899 0.207671i
\(459\) 0 0
\(460\) 12.2741 + 7.08648i 0.572285 + 0.330409i
\(461\) 30.2189 1.40744 0.703718 0.710480i \(-0.251522\pi\)
0.703718 + 0.710480i \(0.251522\pi\)
\(462\) 0 0
\(463\) −31.6191 −1.46946 −0.734731 0.678358i \(-0.762692\pi\)
−0.734731 + 0.678358i \(0.762692\pi\)
\(464\) 3.61299 + 2.08596i 0.167729 + 0.0968382i
\(465\) 0 0
\(466\) 9.54801 + 16.5376i 0.442303 + 0.766091i
\(467\) 12.6717 21.9481i 0.586378 1.01564i −0.408324 0.912837i \(-0.633887\pi\)
0.994702 0.102800i \(-0.0327801\pi\)
\(468\) 0 0
\(469\) −13.0420 5.76250i −0.602224 0.266088i
\(470\) 19.7963i 0.913135i
\(471\) 0 0
\(472\) 9.40603 5.43057i 0.432948 0.249962i
\(473\) 3.55305 2.05135i 0.163369 0.0943214i
\(474\) 0 0
\(475\) 0.750400i 0.0344307i
\(476\) −1.74598 16.1714i −0.0800268 0.741217i
\(477\) 0 0
\(478\) −6.21293 + 10.7611i −0.284173 + 0.492202i
\(479\) −16.3051 28.2413i −0.745000 1.29038i −0.950195 0.311657i \(-0.899116\pi\)
0.205194 0.978721i \(-0.434217\pi\)
\(480\) 0 0
\(481\) 0.742205 + 0.428512i 0.0338416 + 0.0195385i
\(482\) 22.6145 1.03006
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −15.9693 9.21990i −0.725130 0.418654i
\(486\) 0 0
\(487\) −2.05532 3.55991i −0.0931353 0.161315i 0.815694 0.578484i \(-0.196356\pi\)
−0.908829 + 0.417169i \(0.863022\pi\)
\(488\) −4.73784 + 8.20619i −0.214472 + 0.371477i
\(489\) 0 0
\(490\) 4.06811 + 18.6201i 0.183779 + 0.841168i
\(491\) 4.57385i 0.206415i −0.994660 0.103207i \(-0.967089\pi\)
0.994660 0.103207i \(-0.0329106\pi\)
\(492\) 0 0
\(493\) 22.2117 12.8240i 1.00037 0.577562i
\(494\) 0.0522091 0.0301429i 0.00234900 0.00135619i
\(495\) 0 0
\(496\) 1.59495i 0.0716155i
\(497\) 15.0414 + 20.5800i 0.674701 + 0.923140i
\(498\) 0 0
\(499\) −18.3034 + 31.7024i −0.819372 + 1.41919i 0.0867728 + 0.996228i \(0.472345\pi\)
−0.906145 + 0.422967i \(0.860989\pi\)
\(500\) 3.52136 + 6.09917i 0.157480 + 0.272763i
\(501\) 0 0
\(502\) 5.39080 + 3.11238i 0.240603 + 0.138912i
\(503\) −17.0391 −0.759738 −0.379869 0.925040i \(-0.624031\pi\)
−0.379869 + 0.925040i \(0.624031\pi\)
\(504\) 0 0
\(505\) −34.6201 −1.54057
\(506\) −4.50799 2.60269i −0.200405 0.115704i
\(507\) 0 0
\(508\) 1.50310 + 2.60344i 0.0666891 + 0.115509i
\(509\) 5.96804 10.3370i 0.264529 0.458177i −0.702911 0.711278i \(-0.748117\pi\)
0.967440 + 0.253100i \(0.0814502\pi\)
\(510\) 0 0
\(511\) 3.08938 6.99205i 0.136666 0.309310i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 21.9359 12.6647i 0.967552 0.558616i
\(515\) 5.12138 2.95683i 0.225675 0.130294i
\(516\) 0 0
\(517\) 7.27069i 0.319765i
\(518\) 4.72645 10.6972i 0.207668 0.470006i
\(519\) 0 0
\(520\) 0.263953 0.457181i 0.0115751 0.0200487i
\(521\) 21.4867 + 37.2161i 0.941350 + 1.63047i 0.762899 + 0.646518i \(0.223775\pi\)
0.178452 + 0.983949i \(0.442891\pi\)
\(522\) 0 0
\(523\) −31.1432 17.9806i −1.36180 0.786235i −0.371935 0.928259i \(-0.621306\pi\)
−0.989863 + 0.142024i \(0.954639\pi\)
\(524\) 6.20844 0.271217
\(525\) 0 0
\(526\) 23.8723 1.04088
\(527\) 8.49170 + 4.90268i 0.369904 + 0.213564i
\(528\) 0 0
\(529\) 2.04798 + 3.54720i 0.0890425 + 0.154226i
\(530\) 1.64270 2.84525i 0.0713545 0.123590i
\(531\) 0 0
\(532\) −0.485424 0.664167i −0.0210458 0.0287953i
\(533\) 0.833440i 0.0361003i
\(534\) 0 0
\(535\) 11.9721 6.91212i 0.517601 0.298837i
\(536\) 4.66714 2.69458i 0.201590 0.116388i
\(537\) 0 0
\(538\) 2.13222i 0.0919266i
\(539\) −1.49412 6.83868i −0.0643562 0.294563i
\(540\) 0 0
\(541\) −1.56847 + 2.71667i −0.0674337 + 0.116799i −0.897771 0.440463i \(-0.854814\pi\)
0.830337 + 0.557261i \(0.188148\pi\)
\(542\) 13.5898 + 23.5382i 0.583731 + 1.01105i
\(543\) 0 0
\(544\) 5.32411 + 3.07388i 0.228269 + 0.131791i
\(545\) 4.42914 0.189723
\(546\) 0 0
\(547\) 1.97672 0.0845184 0.0422592 0.999107i \(-0.486544\pi\)
0.0422592 + 0.999107i \(0.486544\pi\)
\(548\) 8.22265 + 4.74735i 0.351254 + 0.202797i
\(549\) 0 0
\(550\) 1.20669 + 2.09005i 0.0514535 + 0.0891202i
\(551\) 0.648592 1.12339i 0.0276310 0.0478582i
\(552\) 0 0
\(553\) −4.31880 40.0012i −0.183654 1.70102i
\(554\) 10.0148i 0.425490i
\(555\) 0 0
\(556\) −11.4332 + 6.60098i −0.484877 + 0.279944i
\(557\) 12.2471 7.07088i 0.518927 0.299603i −0.217568 0.976045i \(-0.569813\pi\)
0.736496 + 0.676442i \(0.236479\pi\)
\(558\) 0 0
\(559\) 0.795462i 0.0336445i
\(560\) −6.58920 2.91138i −0.278445 0.123028i
\(561\) 0 0
\(562\) 14.0893 24.4034i 0.594323 1.02940i
\(563\) 3.39720 + 5.88412i 0.143175 + 0.247986i 0.928691 0.370856i \(-0.120936\pi\)
−0.785516 + 0.618842i \(0.787602\pi\)
\(564\) 0 0
\(565\) −21.4133 12.3630i −0.900864 0.520114i
\(566\) −27.4114 −1.15219
\(567\) 0 0
\(568\) −9.63462 −0.404260
\(569\) −37.4383 21.6150i −1.56949 0.906147i −0.996228 0.0867776i \(-0.972343\pi\)
−0.573265 0.819370i \(-0.694324\pi\)
\(570\) 0 0
\(571\) −23.3065 40.3680i −0.975346 1.68935i −0.678790 0.734333i \(-0.737495\pi\)
−0.296556 0.955015i \(-0.595838\pi\)
\(572\) −0.0969436 + 0.167911i −0.00405341 + 0.00702072i
\(573\) 0 0
\(574\) 11.3073 1.22081i 0.471957 0.0509556i
\(575\) 12.5626i 0.523896i
\(576\) 0 0
\(577\) 32.6159 18.8308i 1.35782 0.783936i 0.368488 0.929633i \(-0.379876\pi\)
0.989329 + 0.145697i \(0.0465423\pi\)
\(578\) 18.0089 10.3974i 0.749070 0.432476i
\(579\) 0 0
\(580\) 11.3591i 0.471661i
\(581\) −21.5491 + 15.7497i −0.894008 + 0.653409i
\(582\) 0 0
\(583\) −0.603325 + 1.04499i −0.0249872 + 0.0432790i
\(584\) 1.44461 + 2.50213i 0.0597783 + 0.103539i
\(585\) 0 0
\(586\) −5.56571 3.21337i −0.229918 0.132743i
\(587\) −43.9834 −1.81539 −0.907694 0.419632i \(-0.862159\pi\)
−0.907694 + 0.419632i \(0.862159\pi\)
\(588\) 0 0
\(589\) 0.495923 0.0204341
\(590\) −25.6103 14.7861i −1.05436 0.608735i
\(591\) 0 0
\(592\) 2.21011 + 3.82803i 0.0908350 + 0.157331i
\(593\) 9.09719 15.7568i 0.373577 0.647054i −0.616536 0.787327i \(-0.711465\pi\)
0.990113 + 0.140272i \(0.0447978\pi\)
\(594\) 0 0
\(595\) −35.7549 + 26.1324i −1.46581 + 1.07132i
\(596\) 13.7566i 0.563492i
\(597\) 0 0
\(598\) 0.874041 0.504628i 0.0357422 0.0206358i
\(599\) 28.8965 16.6834i 1.18068 0.681665i 0.224507 0.974472i \(-0.427923\pi\)
0.956171 + 0.292807i \(0.0945894\pi\)
\(600\) 0 0
\(601\) 45.3210i 1.84868i −0.381566 0.924341i \(-0.624615\pi\)
0.381566 0.924341i \(-0.375385\pi\)
\(602\) 10.7920 1.16518i 0.439850 0.0474892i
\(603\) 0 0
\(604\) −10.4182 + 18.0449i −0.423912 + 0.734237i
\(605\) −1.36138 2.35797i −0.0553478 0.0958653i
\(606\) 0 0
\(607\) −5.26548 3.04003i −0.213719 0.123391i 0.389319 0.921103i \(-0.372710\pi\)
−0.603039 + 0.797712i \(0.706044\pi\)
\(608\) 0.310933 0.0126100
\(609\) 0 0
\(610\) 25.8000 1.04461
\(611\) 1.22083 + 0.704847i 0.0493895 + 0.0285151i
\(612\) 0 0
\(613\) −11.8152 20.4645i −0.477211 0.826554i 0.522447 0.852671i \(-0.325019\pi\)
−0.999659 + 0.0261170i \(0.991686\pi\)
\(614\) 10.8851 18.8536i 0.439288 0.760870i
\(615\) 0 0
\(616\) 2.42005 + 1.06928i 0.0975066 + 0.0430825i
\(617\) 22.4859i 0.905248i 0.891702 + 0.452624i \(0.149512\pi\)
−0.891702 + 0.452624i \(0.850488\pi\)
\(618\) 0 0
\(619\) 5.68075 3.27978i 0.228329 0.131826i −0.381472 0.924380i \(-0.624583\pi\)
0.609801 + 0.792555i \(0.291249\pi\)
\(620\) 3.76085 2.17133i 0.151040 0.0872027i
\(621\) 0 0
\(622\) 12.9426i 0.518950i
\(623\) 3.22601 + 29.8797i 0.129248 + 1.19710i
\(624\) 0 0
\(625\) 15.6212 27.0568i 0.624850 1.08227i
\(626\) 0.898250 + 1.55581i 0.0359013 + 0.0621828i
\(627\) 0 0
\(628\) 13.5367 + 7.81541i 0.540172 + 0.311869i
\(629\) 27.1744 1.08352
\(630\) 0 0
\(631\) −9.60407 −0.382332 −0.191166 0.981558i \(-0.561227\pi\)
−0.191166 + 0.981558i \(0.561227\pi\)
\(632\) 13.1696 + 7.60345i 0.523857 + 0.302449i
\(633\) 0 0
\(634\) 14.4617 + 25.0485i 0.574349 + 0.994801i
\(635\) 4.09256 7.08852i 0.162408 0.281299i
\(636\) 0 0
\(637\) 1.29314 + 0.412087i 0.0512359 + 0.0163275i
\(638\) 4.17192i 0.165168i
\(639\) 0 0
\(640\) 2.35797 1.36138i 0.0932071 0.0538131i
\(641\) −25.3563 + 14.6395i −1.00151 + 0.578224i −0.908696 0.417459i \(-0.862921\pi\)
−0.0928182 + 0.995683i \(0.529588\pi\)
\(642\) 0 0
\(643\) 16.6438i 0.656368i 0.944614 + 0.328184i \(0.106437\pi\)
−0.944614 + 0.328184i \(0.893563\pi\)
\(644\) −8.12656 11.1189i −0.320231 0.438147i
\(645\) 0 0
\(646\) 0.955768 1.65544i 0.0376042 0.0651324i
\(647\) −20.7616 35.9602i −0.816223 1.41374i −0.908446 0.418001i \(-0.862731\pi\)
0.0922233 0.995738i \(-0.470603\pi\)
\(648\) 0 0
\(649\) 9.40603 + 5.43057i 0.369219 + 0.213169i
\(650\) −0.467924 −0.0183535
\(651\) 0 0
\(652\) −5.07782 −0.198863
\(653\) −30.7284 17.7410i −1.20249 0.694260i −0.241385 0.970429i \(-0.577602\pi\)
−0.961109 + 0.276169i \(0.910935\pi\)
\(654\) 0 0
\(655\) −8.45202 14.6393i −0.330248 0.572006i
\(656\) −2.14929 + 3.72268i −0.0839158 + 0.145346i
\(657\) 0 0
\(658\) 7.77440 17.5954i 0.303078 0.685942i
\(659\) 1.37768i 0.0536668i 0.999640 + 0.0268334i \(0.00854237\pi\)
−0.999640 + 0.0268334i \(0.991458\pi\)
\(660\) 0 0
\(661\) 20.1453 11.6309i 0.783561 0.452389i −0.0541298 0.998534i \(-0.517238\pi\)
0.837691 + 0.546145i \(0.183905\pi\)
\(662\) 30.8786 17.8278i 1.20013 0.692896i
\(663\) 0 0
\(664\) 10.0883i 0.391502i
\(665\) −0.905243 + 2.04880i −0.0351038 + 0.0794489i
\(666\) 0 0
\(667\) 10.8582 18.8070i 0.420431 0.728208i
\(668\) 1.56859 + 2.71688i 0.0606905 + 0.105119i
\(669\) 0 0
\(670\) −12.7075 7.33666i −0.490933 0.283440i
\(671\) −9.47569 −0.365805
\(672\) 0 0
\(673\) −44.3559 −1.70979 −0.854896 0.518799i \(-0.826379\pi\)
−0.854896 + 0.518799i \(0.826379\pi\)
\(674\) −16.1490 9.32362i −0.622036 0.359133i
\(675\) 0 0
\(676\) 6.48120 + 11.2258i 0.249277 + 0.431761i
\(677\) −16.3344 + 28.2920i −0.627781 + 1.08735i 0.360214 + 0.932870i \(0.382704\pi\)
−0.987996 + 0.154480i \(0.950630\pi\)
\(678\) 0 0
\(679\) 10.5731 + 14.4664i 0.405759 + 0.555168i
\(680\) 16.7388i 0.641904i
\(681\) 0 0
\(682\) −1.38127 + 0.797476i −0.0528915 + 0.0305369i
\(683\) 13.7043 7.91217i 0.524380 0.302751i −0.214345 0.976758i \(-0.568762\pi\)
0.738725 + 0.674007i \(0.235428\pi\)
\(684\) 0 0
\(685\) 25.8517i 0.987743i
\(686\) 3.69662 18.1476i 0.141138 0.692878i
\(687\) 0 0
\(688\) −2.05135 + 3.55305i −0.0782072 + 0.135459i
\(689\) −0.116977 0.202610i −0.00445647 0.00771882i
\(690\) 0 0
\(691\) 26.4940 + 15.2963i 1.00788 + 0.581899i 0.910570 0.413355i \(-0.135643\pi\)
0.0973085 + 0.995254i \(0.468977\pi\)
\(692\) 17.2284 0.654925
\(693\) 0 0
\(694\) −31.0962 −1.18040
\(695\) 31.1299 + 17.9729i 1.18082 + 0.681749i
\(696\) 0 0
\(697\) 13.2133 + 22.8861i 0.500490 + 0.866874i
\(698\) 6.78394 11.7501i 0.256776 0.444749i
\(699\) 0 0
\(700\) 0.685408 + 6.34832i 0.0259060 + 0.239944i
\(701\) 6.04929i 0.228479i 0.993453 + 0.114239i \(0.0364431\pi\)
−0.993453 + 0.114239i \(0.963557\pi\)
\(702\) 0 0
\(703\) 1.19026 0.687196i 0.0448914 0.0259181i
\(704\) −0.866025 + 0.500000i −0.0326396 + 0.0188445i
\(705\) 0 0
\(706\) 1.95197i 0.0734634i
\(707\) 30.7712 + 13.5960i 1.15727 + 0.511330i
\(708\) 0 0
\(709\) 6.64611 11.5114i 0.249600 0.432320i −0.713815 0.700334i \(-0.753034\pi\)
0.963415 + 0.268015i \(0.0863675\pi\)
\(710\) 13.1163 + 22.7182i 0.492248 + 0.852598i
\(711\) 0 0
\(712\) −9.83727 5.67955i −0.368667 0.212850i
\(713\) 8.30233 0.310925
\(714\) 0 0
\(715\) 0.527907 0.0197426
\(716\) −10.0700 5.81389i −0.376332 0.217275i
\(717\) 0 0
\(718\) 0.611893 + 1.05983i 0.0228356 + 0.0395525i
\(719\) 5.80479 10.0542i 0.216482 0.374958i −0.737248 0.675622i \(-0.763875\pi\)
0.953730 + 0.300664i \(0.0972084\pi\)
\(720\) 0 0
\(721\) −5.71321 + 0.616837i −0.212771 + 0.0229722i
\(722\) 18.9033i 0.703509i
\(723\) 0 0
\(724\) 9.00143 5.19698i 0.334536 0.193144i
\(725\) −8.71952 + 5.03422i −0.323835 + 0.186966i
\(726\) 0 0
\(727\) 16.0147i 0.593953i −0.954885 0.296977i \(-0.904022\pi\)
0.954885 0.296977i \(-0.0959783\pi\)
\(728\) −0.414152 + 0.302694i −0.0153495 + 0.0112186i
\(729\) 0 0
\(730\) 3.93331 6.81269i 0.145578 0.252149i
\(731\) 12.6112 + 21.8433i 0.466443 + 0.807902i
\(732\) 0 0
\(733\) 17.5271 + 10.1193i 0.647377 + 0.373763i 0.787450 0.616378i \(-0.211401\pi\)
−0.140074 + 0.990141i \(0.544734\pi\)
\(734\) −23.8269 −0.879467
\(735\) 0 0
\(736\) 5.20538 0.191873
\(737\) 4.66714 + 2.69458i 0.171916 + 0.0992560i
\(738\) 0 0
\(739\) −5.78566 10.0211i −0.212829 0.368630i 0.739770 0.672860i \(-0.234934\pi\)
−0.952599 + 0.304229i \(0.901601\pi\)
\(740\) 6.01759 10.4228i 0.221211 0.383149i
\(741\) 0 0
\(742\) −2.57746 + 1.88380i −0.0946216 + 0.0691566i
\(743\) 9.50531i 0.348716i 0.984682 + 0.174358i \(0.0557850\pi\)
−0.984682 + 0.174358i \(0.944215\pi\)
\(744\) 0 0
\(745\) 32.4377 18.7279i 1.18842 0.686137i
\(746\) 18.2648 10.5452i 0.668720 0.386086i
\(747\) 0 0
\(748\) 6.14775i 0.224784i
\(749\) −13.3557 + 1.44197i −0.488005 + 0.0526884i
\(750\) 0 0
\(751\) −13.5445 + 23.4597i −0.494245 + 0.856057i −0.999978 0.00663281i \(-0.997889\pi\)
0.505733 + 0.862690i \(0.331222\pi\)
\(752\) 3.63535 + 6.29661i 0.132567 + 0.229614i
\(753\) 0 0
\(754\) −0.700511 0.404440i −0.0255111 0.0147289i
\(755\) 56.7325 2.06471
\(756\) 0 0
\(757\) 47.9214 1.74173 0.870867 0.491518i \(-0.163558\pi\)
0.870867 + 0.491518i \(0.163558\pi\)
\(758\) 25.6592 + 14.8143i 0.931983 + 0.538081i
\(759\) 0 0
\(760\) −0.423296 0.733171i −0.0153546 0.0265949i
\(761\) −8.27095 + 14.3257i −0.299822 + 0.519306i −0.976095 0.217345i \(-0.930260\pi\)
0.676273 + 0.736651i \(0.263594\pi\)
\(762\) 0 0
\(763\) −3.93673 1.73941i −0.142519 0.0629709i
\(764\) 17.8308i 0.645097i
\(765\) 0 0
\(766\) −3.56551 + 2.05855i −0.128827 + 0.0743783i
\(767\) −1.82371 + 1.05292i −0.0658503 + 0.0380187i
\(768\) 0 0
\(769\) 5.14692i 0.185603i −0.995685 0.0928013i \(-0.970418\pi\)
0.995685 0.0928013i \(-0.0295821\pi\)
\(770\) −0.773269 7.16211i −0.0278667 0.258104i
\(771\) 0 0
\(772\) 7.66535 13.2768i 0.275882 0.477842i
\(773\) 2.10953 + 3.65382i 0.0758746 + 0.131419i 0.901466 0.432849i \(-0.142492\pi\)
−0.825592 + 0.564268i \(0.809158\pi\)
\(774\) 0 0
\(775\) −3.33353 1.92462i −0.119744 0.0691343i
\(776\) −6.77249 −0.243118
\(777\) 0 0
\(778\) 33.5283 1.20205
\(779\) 1.15750 + 0.668285i 0.0414719 + 0.0239438i
\(780\) 0 0
\(781\) −4.81731 8.34383i −0.172377 0.298566i
\(782\) 16.0007 27.7140i 0.572183 0.991050i
\(783\) 0 0
\(784\) 4.71329 + 5.17542i 0.168332 + 0.184836i
\(785\) 42.5588i 1.51899i
\(786\) 0 0
\(787\) −30.2097 + 17.4416i −1.07686 + 0.621724i −0.930047 0.367440i \(-0.880234\pi\)
−0.146811 + 0.989165i \(0.546901\pi\)
\(788\) −20.3954 + 11.7753i −0.726557 + 0.419478i
\(789\) 0 0
\(790\) 41.4046i 1.47311i
\(791\) 14.1775 + 19.3979i 0.504093 + 0.689711i
\(792\) 0 0
\(793\) 0.918607 1.59107i 0.0326207 0.0565007i
\(794\) −0.846104 1.46549i −0.0300271 0.0520085i
\(795\) 0 0
\(796\) −11.4609 6.61697i −0.406222 0.234532i
\(797\) 17.4825 0.619262 0.309631 0.950857i \(-0.399795\pi\)
0.309631 + 0.950857i \(0.399795\pi\)
\(798\) 0 0
\(799\) 44.6984 1.58132
\(800\) −2.09005 1.20669i −0.0738945 0.0426630i
\(801\) 0 0
\(802\) 18.5799 + 32.1813i 0.656078 + 1.13636i
\(803\) −1.44461 + 2.50213i −0.0509791 + 0.0882984i
\(804\) 0 0
\(805\) −15.1548 + 34.2993i −0.534138 + 1.20889i
\(806\) 0.309241i 0.0108925i
\(807\) 0 0
\(808\) −11.0116 + 6.35755i −0.387387 + 0.223658i
\(809\) 22.8674 13.2025i 0.803975 0.464175i −0.0408842 0.999164i \(-0.513017\pi\)
0.844859 + 0.534989i \(0.179684\pi\)
\(810\) 0 0
\(811\) 31.4016i 1.10266i −0.834287 0.551330i \(-0.814121\pi\)
0.834287 0.551330i \(-0.185879\pi\)
\(812\) −4.46094 + 10.0962i −0.156548 + 0.354309i
\(813\) 0 0
\(814\) −2.21011 + 3.82803i −0.0774644 + 0.134172i
\(815\) 6.91283 + 11.9734i 0.242146 + 0.419409i
\(816\) 0 0
\(817\) 1.10476 + 0.637833i 0.0386506 + 0.0223149i
\(818\) 2.58286 0.0903075
\(819\) 0 0
\(820\) 11.7040 0.408721
\(821\) 46.8857 + 27.0695i 1.63632 + 0.944731i 0.982084 + 0.188444i \(0.0603443\pi\)
0.654239 + 0.756288i \(0.272989\pi\)
\(822\) 0 0
\(823\) −13.6961 23.7223i −0.477416 0.826909i 0.522249 0.852793i \(-0.325093\pi\)
−0.999665 + 0.0258842i \(0.991760\pi\)
\(824\) 1.08597 1.88096i 0.0378316 0.0655262i
\(825\) 0 0
\(826\) 16.9563 + 23.1999i 0.589984 + 0.807229i
\(827\) 25.1390i 0.874168i 0.899421 + 0.437084i \(0.143989\pi\)
−0.899421 + 0.437084i \(0.856011\pi\)
\(828\) 0 0
\(829\) −20.4945 + 11.8325i −0.711804 + 0.410960i −0.811729 0.584035i \(-0.801473\pi\)
0.0999244 + 0.994995i \(0.468140\pi\)
\(830\) −23.7880 + 13.7340i −0.825693 + 0.476714i
\(831\) 0 0
\(832\) 0.193887i 0.00672183i
\(833\) 42.0425 9.18547i 1.45669 0.318258i
\(834\) 0 0
\(835\) 4.27088 7.39738i 0.147800 0.255997i
\(836\) 0.155466 + 0.269276i 0.00537691 + 0.00931309i
\(837\) 0 0
\(838\) −19.1280 11.0435i −0.660765 0.381493i
\(839\) 5.46018 0.188506 0.0942532 0.995548i \(-0.469954\pi\)
0.0942532 + 0.995548i \(0.469954\pi\)
\(840\) 0 0
\(841\) 11.5951 0.399832
\(842\) 3.11873 + 1.80060i 0.107479 + 0.0620528i
\(843\) 0 0
\(844\) 0.468672 + 0.811764i 0.0161324 + 0.0279421i
\(845\) 17.6467 30.5650i 0.607066 1.05147i
\(846\) 0 0
\(847\) 0.284003 + 2.63046i 0.00975845 + 0.0903838i
\(848\) 1.20665i 0.0414365i
\(849\) 0 0
\(850\) −12.8491 + 7.41845i −0.440721 + 0.254451i
\(851\) 19.9263 11.5045i 0.683065 0.394368i
\(852\) 0 0
\(853\) 9.29168i 0.318141i −0.987267 0.159071i \(-0.949150\pi\)
0.987267 0.159071i \(-0.0508497\pi\)
\(854\) −22.9316 10.1322i −0.784705 0.346715i
\(855\) 0 0
\(856\) 2.53865 4.39707i 0.0867693 0.150289i
\(857\) 7.51046 + 13.0085i 0.256552 + 0.444362i 0.965316 0.261084i \(-0.0840801\pi\)
−0.708764 + 0.705446i \(0.750747\pi\)
\(858\) 0 0
\(859\) 28.6855 + 16.5616i 0.978737 + 0.565074i 0.901889 0.431969i \(-0.142181\pi\)
0.0768486 + 0.997043i \(0.475514\pi\)
\(860\) 11.1707 0.380916
\(861\) 0 0
\(862\) 2.65307 0.0903640
\(863\) −8.04372 4.64405i −0.273812 0.158085i 0.356807 0.934178i \(-0.383865\pi\)
−0.630619 + 0.776093i \(0.717199\pi\)
\(864\) 0 0
\(865\) −23.4543 40.6241i −0.797471 1.38126i
\(866\) 10.6556 18.4561i 0.362092 0.627162i
\(867\) 0 0
\(868\) −4.19546 + 0.452971i −0.142403 + 0.0153748i
\(869\) 15.2069i 0.515859i
\(870\) 0 0
\(871\) −0.904899 + 0.522443i −0.0306613 + 0.0177023i
\(872\) 1.40878 0.813357i 0.0477071 0.0275437i
\(873\) 0 0
\(874\) 1.61852i 0.0547473i
\(875\) −15.0436 + 10.9950i −0.508566 + 0.371698i
\(876\) 0 0
\(877\) 7.74463 13.4141i 0.261518 0.452962i −0.705128 0.709080i \(-0.749110\pi\)
0.966645 + 0.256118i \(0.0824437\pi\)
\(878\) −6.45704 11.1839i −0.217915 0.377439i
\(879\) 0 0
\(880\) 2.35797 + 1.36138i 0.0794873 + 0.0458920i
\(881\) −33.5368 −1.12988 −0.564942 0.825130i \(-0.691102\pi\)
−0.564942 + 0.825130i \(0.691102\pi\)
\(882\) 0 0
\(883\) 18.5616 0.624648 0.312324 0.949976i \(-0.398893\pi\)
0.312324 + 0.949976i \(0.398893\pi\)
\(884\) −1.03228 0.595985i −0.0347192 0.0200451i
\(885\) 0 0
\(886\) −12.1063 20.9687i −0.406718 0.704456i
\(887\) −11.7850 + 20.4122i −0.395701 + 0.685375i −0.993190 0.116502i \(-0.962832\pi\)
0.597489 + 0.801877i \(0.296165\pi\)
\(888\) 0 0
\(889\) −6.42137 + 4.69322i −0.215366 + 0.157406i
\(890\) 30.9280i 1.03671i
\(891\) 0 0
\(892\) −9.41801 + 5.43749i −0.315338 + 0.182061i
\(893\) 1.95782 1.13035i 0.0655159 0.0378256i
\(894\) 0 0
\(895\) 31.6596i 1.05826i
\(896\) −2.63046 + 0.284003i −0.0878776 + 0.00948787i
\(897\) 0 0
\(898\) 3.48718 6.03997i 0.116369 0.201557i
\(899\) −3.32700 5.76254i −0.110962 0.192191i
\(900\) 0 0
\(901\) −6.42433 3.70909i −0.214026 0.123568i
\(902\) −4.29859 −0.143127
\(903\) 0 0
\(904\) −9.08122 −0.302037
\(905\) −24.5087 14.1501i −0.814696 0.470365i
\(906\) 0 0
\(907\) 25.6867 + 44.4907i 0.852913 + 1.47729i 0.878568 + 0.477618i \(0.158500\pi\)
−0.0256543 + 0.999671i \(0.508167\pi\)
\(908\) −3.87060 + 6.70408i −0.128450 + 0.222483i
\(909\) 0 0
\(910\) 1.27756 + 0.564479i 0.0423507 + 0.0187123i
\(911\) 14.4547i 0.478906i −0.970908 0.239453i \(-0.923032\pi\)
0.970908 0.239453i \(-0.0769681\pi\)
\(912\) 0 0
\(913\) 8.73673 5.04416i 0.289144 0.166937i
\(914\) −0.0858810 + 0.0495834i −0.00284069 + 0.00164007i
\(915\) 0 0
\(916\) 5.13189i 0.169562i
\(917\) 1.76321 + 16.3311i 0.0582264 + 0.539300i
\(918\) 0 0
\(919\) −22.6474 + 39.2265i −0.747070 + 1.29396i 0.202151 + 0.979354i \(0.435207\pi\)
−0.949221 + 0.314609i \(0.898127\pi\)
\(920\) −7.08648 12.2741i −0.233634 0.404666i
\(921\) 0 0
\(922\) −26.1703 15.1095i −0.861874 0.497603i
\(923\) 1.86803 0.0614869
\(924\) 0 0
\(925\) −10.6677 −0.350752
\(926\) 27.3829 + 15.8095i 0.899858 + 0.519533i
\(927\) 0 0
\(928\) −2.08596 3.61299i −0.0684749 0.118602i
\(929\) 29.6524 51.3595i 0.972865 1.68505i 0.286057 0.958212i \(-0.407655\pi\)
0.686808 0.726839i \(-0.259011\pi\)
\(930\) 0 0
\(931\) 1.60921 1.46551i 0.0527396 0.0480303i
\(932\) 19.0960i 0.625511i
\(933\) 0 0
\(934\) −21.9481 + 12.6717i −0.718164 + 0.414632i
\(935\) 14.4962 8.36940i 0.474078 0.273709i
\(936\) 0 0
\(937\) 38.2633i 1.25001i −0.780621 0.625005i \(-0.785097\pi\)
0.780621 0.625005i \(-0.214903\pi\)
\(938\) 8.41346 + 11.5115i 0.274709 + 0.375863i
\(939\) 0 0
\(940\) 9.89815 17.1441i 0.322842 0.559179i
\(941\) −2.04961 3.55002i −0.0668152 0.115727i 0.830683 0.556746i \(-0.187950\pi\)
−0.897498 + 0.441019i \(0.854617\pi\)
\(942\) 0 0
\(943\) 19.3780 + 11.1879i 0.631034 + 0.364328i
\(944\) −10.8611 −0.353500
\(945\) 0 0
\(946\) −4.10271 −0.133391
\(947\) 19.3014 + 11.1437i 0.627211 + 0.362120i 0.779671 0.626189i \(-0.215386\pi\)
−0.152460 + 0.988310i \(0.548720\pi\)
\(948\) 0 0
\(949\) −0.280091 0.485131i −0.00909213 0.0157480i
\(950\) −0.375200 + 0.649866i −0.0121731 + 0.0210844i
\(951\) 0 0
\(952\) −6.57366 + 14.8779i −0.213053 + 0.482194i
\(953\) 6.17864i 0.200146i −0.994980 0.100073i \(-0.968092\pi\)
0.994980 0.100073i \(-0.0319076\pi\)
\(954\) 0 0
\(955\) −42.0446 + 24.2745i −1.36053 + 0.785504i
\(956\) 10.7611 6.21293i 0.348039 0.200941i
\(957\) 0 0
\(958\) 32.6103i 1.05359i
\(959\) −10.1525 + 22.9776i −0.327840 + 0.741987i
\(960\) 0 0
\(961\) −14.2281 + 24.6437i −0.458970 + 0.794959i
\(962\) −0.428512 0.742205i −0.0138158 0.0239296i
\(963\) 0 0
\(964\) −19.5847 11.3072i −0.630781 0.364181i
\(965\) −41.7417 −1.34371
\(966\) 0 0
\(967\) 2.02187 0.0650191 0.0325095 0.999471i \(-0.489650\pi\)
0.0325095 + 0.999471i \(0.489650\pi\)
\(968\) −0.866025 0.500000i −0.0278351 0.0160706i
\(969\) 0 0
\(970\) 9.21990 + 15.9693i 0.296033 + 0.512745i
\(971\) −8.39201 + 14.5354i −0.269313 + 0.466463i −0.968684 0.248295i \(-0.920130\pi\)
0.699372 + 0.714758i \(0.253463\pi\)
\(972\) 0 0
\(973\) −20.6107 28.2000i −0.660750 0.904052i
\(974\) 4.11063i 0.131713i
\(975\) 0 0
\(976\) 8.20619 4.73784i 0.262674 0.151655i
\(977\) −17.2826 + 9.97813i −0.552920 + 0.319229i −0.750299 0.661099i \(-0.770090\pi\)
0.197379 + 0.980327i \(0.436757\pi\)
\(978\) 0 0
\(979\) 11.3591i 0.363038i
\(980\) 5.78693 18.1595i 0.184857 0.580084i
\(981\) 0 0
\(982\) −2.28693 + 3.96107i −0.0729787 + 0.126403i
\(983\) −9.37668 16.2409i −0.299070 0.518004i 0.676854 0.736117i \(-0.263343\pi\)
−0.975923 + 0.218114i \(0.930010\pi\)
\(984\) 0 0
\(985\) 55.5318 + 32.0613i 1.76939 + 1.02156i
\(986\) −25.6479 −0.816796
\(987\) 0 0
\(988\) −0.0602858 −0.00191795
\(989\) 18.4950 + 10.6781i 0.588106 + 0.339543i
\(990\) 0 0
\(991\) −0.643923 1.11531i −0.0204549 0.0354289i 0.855617 0.517610i \(-0.173178\pi\)
−0.876072 + 0.482181i \(0.839845\pi\)
\(992\) 0.797476 1.38127i 0.0253199 0.0438553i
\(993\) 0 0
\(994\) −2.73626 25.3435i −0.0867889 0.803848i
\(995\) 36.0327i 1.14231i
\(996\) 0 0
\(997\) −44.0369 + 25.4247i −1.39466 + 0.805208i −0.993827 0.110942i \(-0.964613\pi\)
−0.400835 + 0.916150i \(0.631280\pi\)
\(998\) 31.7024 18.3034i 1.00352 0.579384i
\(999\) 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.89.1 24
3.2 odd 2 inner 1386.2.r.d.89.12 yes 24
7.3 odd 6 inner 1386.2.r.d.1277.12 yes 24
21.17 even 6 inner 1386.2.r.d.1277.1 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.r.d.89.1 24 1.1 even 1 trivial
1386.2.r.d.89.12 yes 24 3.2 odd 2 inner
1386.2.r.d.1277.1 yes 24 21.17 even 6 inner
1386.2.r.d.1277.12 yes 24 7.3 odd 6 inner