Properties

Label 1134.2.k.c.647.2
Level $1134$
Weight $2$
Character 1134.647
Analytic conductor $9.055$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 647.2
Root \(0.500000 - 0.911095i\) of defining polynomial
Character \(\chi\) \(=\) 1134.647
Dual form 1134.2.k.c.971.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.330211 + 0.571943i) q^{5} +(-2.34953 + 1.21644i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.330211 + 0.571943i) q^{5} +(-2.34953 + 1.21644i) q^{7} +1.00000i q^{8} +(-0.571943 - 0.330211i) q^{10} +(2.25192 + 1.30015i) q^{11} -5.87410i q^{13} +(1.42653 - 2.22823i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.35656 - 4.08169i) q^{17} +(-3.59343 + 2.07467i) q^{19} +0.660423 q^{20} -2.60030 q^{22} +(4.56456 - 2.63535i) q^{23} +(2.28192 - 3.95240i) q^{25} +(2.93705 + 5.08712i) q^{26} +(-0.121294 + 2.64297i) q^{28} +7.43874i q^{29} +(-1.73804 - 1.00346i) q^{31} +(0.866025 + 0.500000i) q^{32} +4.71312i q^{34} +(-1.47157 - 0.942112i) q^{35} +(3.17112 + 5.49254i) q^{37} +(2.07467 - 3.59343i) q^{38} +(-0.571943 + 0.330211i) q^{40} +7.90306 q^{41} -2.66007 q^{43} +(2.25192 - 1.30015i) q^{44} +(-2.63535 + 4.56456i) q^{46} +(0.874572 + 1.51480i) q^{47} +(4.04054 - 5.71612i) q^{49} +4.56384i q^{50} +(-5.08712 - 2.93705i) q^{52} +(7.83672 + 4.52454i) q^{53} +1.71730i q^{55} +(-1.21644 - 2.34953i) q^{56} +(-3.71937 - 6.44214i) q^{58} +(-0.111972 + 0.193941i) q^{59} +(7.78008 - 4.49183i) q^{61} +2.00692 q^{62} -1.00000 q^{64} +(3.35965 - 1.93970i) q^{65} +(5.67037 - 9.82137i) q^{67} +(-2.35656 - 4.08169i) q^{68} +(1.74548 + 0.0801053i) q^{70} -3.89426i q^{71} +(-3.46836 - 2.00246i) q^{73} +(-5.49254 - 3.17112i) q^{74} +4.14934i q^{76} +(-6.87250 - 0.315400i) q^{77} +(5.08602 + 8.80925i) q^{79} +(0.330211 - 0.571943i) q^{80} +(-6.84425 + 3.95153i) q^{82} +12.2888 q^{83} +3.11265 q^{85} +(2.30369 - 1.33003i) q^{86} +(-1.30015 + 2.25192i) q^{88} +(-7.52627 - 13.0359i) q^{89} +(7.14550 + 13.8014i) q^{91} -5.27070i q^{92} +(-1.51480 - 0.874572i) q^{94} +(-2.37318 - 1.37016i) q^{95} +4.33520i q^{97} +(-0.641153 + 6.97058i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 8 q^{7} - 12 q^{11} - 12 q^{14} - 8 q^{16} - 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} - 60 q^{35} + 4 q^{37} + 12 q^{38} + 48 q^{41} - 32 q^{43} - 12 q^{44} + 4 q^{49} - 12 q^{52} - 12 q^{56} - 12 q^{58} + 24 q^{59} - 12 q^{61} + 48 q^{62} - 16 q^{64} - 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} - 36 q^{74} - 84 q^{77} + 8 q^{79} + 72 q^{83} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 36 q^{94} - 12 q^{95} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) 0.330211 + 0.571943i 0.147675 + 0.255781i 0.930368 0.366628i \(-0.119488\pi\)
−0.782693 + 0.622408i \(0.786154\pi\)
\(6\) 0 0
\(7\) −2.34953 + 1.21644i −0.888037 + 0.459772i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.571943 0.330211i −0.180864 0.104422i
\(11\) 2.25192 + 1.30015i 0.678980 + 0.392009i 0.799471 0.600705i \(-0.205113\pi\)
−0.120490 + 0.992714i \(0.538447\pi\)
\(12\) 0 0
\(13\) 5.87410i 1.62918i −0.580035 0.814592i \(-0.696961\pi\)
0.580035 0.814592i \(-0.303039\pi\)
\(14\) 1.42653 2.22823i 0.381256 0.595520i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.35656 4.08169i 0.571550 0.989954i −0.424857 0.905261i \(-0.639676\pi\)
0.996407 0.0846936i \(-0.0269912\pi\)
\(18\) 0 0
\(19\) −3.59343 + 2.07467i −0.824389 + 0.475961i −0.851928 0.523659i \(-0.824566\pi\)
0.0275384 + 0.999621i \(0.491233\pi\)
\(20\) 0.660423 0.147675
\(21\) 0 0
\(22\) −2.60030 −0.554385
\(23\) 4.56456 2.63535i 0.951776 0.549508i 0.0581439 0.998308i \(-0.481482\pi\)
0.893632 + 0.448800i \(0.148148\pi\)
\(24\) 0 0
\(25\) 2.28192 3.95240i 0.456384 0.790481i
\(26\) 2.93705 + 5.08712i 0.576003 + 0.997667i
\(27\) 0 0
\(28\) −0.121294 + 2.64297i −0.0229224 + 0.499474i
\(29\) 7.43874i 1.38134i 0.723170 + 0.690670i \(0.242684\pi\)
−0.723170 + 0.690670i \(0.757316\pi\)
\(30\) 0 0
\(31\) −1.73804 1.00346i −0.312162 0.180227i 0.335732 0.941958i \(-0.391017\pi\)
−0.647894 + 0.761731i \(0.724350\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 4.71312i 0.808294i
\(35\) −1.47157 0.942112i −0.248742 0.159246i
\(36\) 0 0
\(37\) 3.17112 + 5.49254i 0.521329 + 0.902968i 0.999692 + 0.0248059i \(0.00789677\pi\)
−0.478364 + 0.878162i \(0.658770\pi\)
\(38\) 2.07467 3.59343i 0.336556 0.582931i
\(39\) 0 0
\(40\) −0.571943 + 0.330211i −0.0904321 + 0.0522110i
\(41\) 7.90306 1.23425 0.617126 0.786865i \(-0.288297\pi\)
0.617126 + 0.786865i \(0.288297\pi\)
\(42\) 0 0
\(43\) −2.66007 −0.405656 −0.202828 0.979214i \(-0.565013\pi\)
−0.202828 + 0.979214i \(0.565013\pi\)
\(44\) 2.25192 1.30015i 0.339490 0.196005i
\(45\) 0 0
\(46\) −2.63535 + 4.56456i −0.388561 + 0.673007i
\(47\) 0.874572 + 1.51480i 0.127569 + 0.220957i 0.922734 0.385436i \(-0.125949\pi\)
−0.795165 + 0.606393i \(0.792616\pi\)
\(48\) 0 0
\(49\) 4.04054 5.71612i 0.577220 0.816588i
\(50\) 4.56384i 0.645425i
\(51\) 0 0
\(52\) −5.08712 2.93705i −0.705457 0.407296i
\(53\) 7.83672 + 4.52454i 1.07646 + 0.621493i 0.929938 0.367715i \(-0.119860\pi\)
0.146519 + 0.989208i \(0.453193\pi\)
\(54\) 0 0
\(55\) 1.71730i 0.231560i
\(56\) −1.21644 2.34953i −0.162554 0.313969i
\(57\) 0 0
\(58\) −3.71937 6.44214i −0.488377 0.845894i
\(59\) −0.111972 + 0.193941i −0.0145775 + 0.0252490i −0.873222 0.487322i \(-0.837974\pi\)
0.858645 + 0.512571i \(0.171307\pi\)
\(60\) 0 0
\(61\) 7.78008 4.49183i 0.996137 0.575120i 0.0890340 0.996029i \(-0.471622\pi\)
0.907103 + 0.420909i \(0.138289\pi\)
\(62\) 2.00692 0.254879
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.35965 1.93970i 0.416714 0.240590i
\(66\) 0 0
\(67\) 5.67037 9.82137i 0.692746 1.19987i −0.278189 0.960526i \(-0.589734\pi\)
0.970935 0.239345i \(-0.0769326\pi\)
\(68\) −2.35656 4.08169i −0.285775 0.494977i
\(69\) 0 0
\(70\) 1.74548 + 0.0801053i 0.208624 + 0.00957442i
\(71\) 3.89426i 0.462163i −0.972934 0.231082i \(-0.925774\pi\)
0.972934 0.231082i \(-0.0742265\pi\)
\(72\) 0 0
\(73\) −3.46836 2.00246i −0.405940 0.234370i 0.283104 0.959089i \(-0.408636\pi\)
−0.689044 + 0.724720i \(0.741969\pi\)
\(74\) −5.49254 3.17112i −0.638495 0.368635i
\(75\) 0 0
\(76\) 4.14934i 0.475961i
\(77\) −6.87250 0.315400i −0.783195 0.0359432i
\(78\) 0 0
\(79\) 5.08602 + 8.80925i 0.572222 + 0.991118i 0.996337 + 0.0855099i \(0.0272519\pi\)
−0.424115 + 0.905608i \(0.639415\pi\)
\(80\) 0.330211 0.571943i 0.0369188 0.0639452i
\(81\) 0 0
\(82\) −6.84425 + 3.95153i −0.755821 + 0.436374i
\(83\) 12.2888 1.34887 0.674437 0.738332i \(-0.264386\pi\)
0.674437 + 0.738332i \(0.264386\pi\)
\(84\) 0 0
\(85\) 3.11265 0.337615
\(86\) 2.30369 1.33003i 0.248413 0.143421i
\(87\) 0 0
\(88\) −1.30015 + 2.25192i −0.138596 + 0.240056i
\(89\) −7.52627 13.0359i −0.797783 1.38180i −0.921057 0.389428i \(-0.872673\pi\)
0.123274 0.992373i \(-0.460660\pi\)
\(90\) 0 0
\(91\) 7.14550 + 13.8014i 0.749052 + 1.44678i
\(92\) 5.27070i 0.549508i
\(93\) 0 0
\(94\) −1.51480 0.874572i −0.156240 0.0902052i
\(95\) −2.37318 1.37016i −0.243483 0.140575i
\(96\) 0 0
\(97\) 4.33520i 0.440173i 0.975480 + 0.220087i \(0.0706340\pi\)
−0.975480 + 0.220087i \(0.929366\pi\)
\(98\) −0.641153 + 6.97058i −0.0647662 + 0.704134i
\(99\) 0 0
\(100\) −2.28192 3.95240i −0.228192 0.395240i
\(101\) 2.53783 4.39565i 0.252523 0.437384i −0.711696 0.702487i \(-0.752073\pi\)
0.964220 + 0.265104i \(0.0854062\pi\)
\(102\) 0 0
\(103\) 2.48292 1.43352i 0.244649 0.141248i −0.372662 0.927967i \(-0.621555\pi\)
0.617312 + 0.786719i \(0.288222\pi\)
\(104\) 5.87410 0.576003
\(105\) 0 0
\(106\) −9.04907 −0.878923
\(107\) −8.49932 + 4.90709i −0.821660 + 0.474386i −0.850989 0.525184i \(-0.823997\pi\)
0.0293282 + 0.999570i \(0.490663\pi\)
\(108\) 0 0
\(109\) 3.84454 6.65893i 0.368240 0.637810i −0.621051 0.783770i \(-0.713294\pi\)
0.989290 + 0.145961i \(0.0466272\pi\)
\(110\) −0.858648 1.48722i −0.0818688 0.141801i
\(111\) 0 0
\(112\) 2.22823 + 1.42653i 0.210548 + 0.134794i
\(113\) 0.544483i 0.0512207i 0.999672 + 0.0256103i \(0.00815291\pi\)
−0.999672 + 0.0256103i \(0.991847\pi\)
\(114\) 0 0
\(115\) 3.01454 + 1.74044i 0.281107 + 0.162297i
\(116\) 6.44214 + 3.71937i 0.598138 + 0.345335i
\(117\) 0 0
\(118\) 0.223944i 0.0206157i
\(119\) −0.571674 + 12.4566i −0.0524052 + 1.14190i
\(120\) 0 0
\(121\) −2.11923 3.67061i −0.192657 0.333692i
\(122\) −4.49183 + 7.78008i −0.406671 + 0.704375i
\(123\) 0 0
\(124\) −1.73804 + 1.00346i −0.156081 + 0.0901134i
\(125\) 6.31618 0.564936
\(126\) 0 0
\(127\) 19.4512 1.72602 0.863009 0.505189i \(-0.168577\pi\)
0.863009 + 0.505189i \(0.168577\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −1.93970 + 3.35965i −0.170123 + 0.294661i
\(131\) 8.35965 + 14.4793i 0.730386 + 1.26507i 0.956718 + 0.291016i \(0.0939932\pi\)
−0.226332 + 0.974050i \(0.572673\pi\)
\(132\) 0 0
\(133\) 5.91915 9.24568i 0.513255 0.801702i
\(134\) 11.3407i 0.979691i
\(135\) 0 0
\(136\) 4.08169 + 2.35656i 0.350002 + 0.202074i
\(137\) 2.72325 + 1.57227i 0.232663 + 0.134328i 0.611800 0.791013i \(-0.290446\pi\)
−0.379137 + 0.925340i \(0.623779\pi\)
\(138\) 0 0
\(139\) 16.8214i 1.42677i 0.700771 + 0.713386i \(0.252840\pi\)
−0.700771 + 0.713386i \(0.747160\pi\)
\(140\) −1.55168 + 0.803365i −0.131141 + 0.0678968i
\(141\) 0 0
\(142\) 1.94713 + 3.37253i 0.163399 + 0.283016i
\(143\) 7.63721 13.2280i 0.638655 1.10618i
\(144\) 0 0
\(145\) −4.25453 + 2.45636i −0.353320 + 0.203989i
\(146\) 4.00491 0.331449
\(147\) 0 0
\(148\) 6.34224 0.521329
\(149\) −18.0015 + 10.3931i −1.47474 + 0.851439i −0.999595 0.0284697i \(-0.990937\pi\)
−0.475142 + 0.879909i \(0.657603\pi\)
\(150\) 0 0
\(151\) 4.71396 8.16482i 0.383617 0.664443i −0.607960 0.793968i \(-0.708012\pi\)
0.991576 + 0.129525i \(0.0413451\pi\)
\(152\) −2.07467 3.59343i −0.168278 0.291466i
\(153\) 0 0
\(154\) 6.10946 3.16311i 0.492315 0.254890i
\(155\) 1.32542i 0.106460i
\(156\) 0 0
\(157\) 4.00571 + 2.31270i 0.319690 + 0.184573i 0.651254 0.758859i \(-0.274243\pi\)
−0.331564 + 0.943433i \(0.607576\pi\)
\(158\) −8.80925 5.08602i −0.700826 0.404622i
\(159\) 0 0
\(160\) 0.660423i 0.0522110i
\(161\) −7.51880 + 11.7443i −0.592564 + 0.925583i
\(162\) 0 0
\(163\) −5.76907 9.99233i −0.451869 0.782659i 0.546634 0.837372i \(-0.315909\pi\)
−0.998502 + 0.0547126i \(0.982576\pi\)
\(164\) 3.95153 6.84425i 0.308563 0.534446i
\(165\) 0 0
\(166\) −10.6424 + 6.14441i −0.826013 + 0.476899i
\(167\) 19.0063 1.47076 0.735378 0.677658i \(-0.237005\pi\)
0.735378 + 0.677658i \(0.237005\pi\)
\(168\) 0 0
\(169\) −21.5051 −1.65424
\(170\) −2.69564 + 1.55633i −0.206746 + 0.119365i
\(171\) 0 0
\(172\) −1.33003 + 2.30369i −0.101414 + 0.175654i
\(173\) −4.78911 8.29499i −0.364110 0.630656i 0.624523 0.781006i \(-0.285293\pi\)
−0.988633 + 0.150350i \(0.951960\pi\)
\(174\) 0 0
\(175\) −0.553567 + 12.0621i −0.0418457 + 0.911809i
\(176\) 2.60030i 0.196005i
\(177\) 0 0
\(178\) 13.0359 + 7.52627i 0.977080 + 0.564118i
\(179\) −17.6588 10.1953i −1.31988 0.762032i −0.336170 0.941801i \(-0.609132\pi\)
−0.983709 + 0.179769i \(0.942465\pi\)
\(180\) 0 0
\(181\) 23.9866i 1.78291i −0.453107 0.891456i \(-0.649684\pi\)
0.453107 0.891456i \(-0.350316\pi\)
\(182\) −13.0889 8.37958i −0.970211 0.621136i
\(183\) 0 0
\(184\) 2.63535 + 4.56456i 0.194280 + 0.336504i
\(185\) −2.09428 + 3.62740i −0.153974 + 0.266692i
\(186\) 0 0
\(187\) 10.6136 6.12776i 0.776143 0.448106i
\(188\) 1.74914 0.127569
\(189\) 0 0
\(190\) 2.74032 0.198803
\(191\) −4.94699 + 2.85615i −0.357952 + 0.206664i −0.668182 0.743998i \(-0.732927\pi\)
0.310230 + 0.950661i \(0.399594\pi\)
\(192\) 0 0
\(193\) −0.691202 + 1.19720i −0.0497538 + 0.0861761i −0.889830 0.456293i \(-0.849177\pi\)
0.840076 + 0.542469i \(0.182510\pi\)
\(194\) −2.16760 3.75439i −0.155625 0.269550i
\(195\) 0 0
\(196\) −2.93003 6.35727i −0.209288 0.454091i
\(197\) 5.94533i 0.423587i 0.977314 + 0.211794i \(0.0679305\pi\)
−0.977314 + 0.211794i \(0.932069\pi\)
\(198\) 0 0
\(199\) −16.1647 9.33269i −1.14588 0.661577i −0.198003 0.980201i \(-0.563446\pi\)
−0.947881 + 0.318625i \(0.896779\pi\)
\(200\) 3.95240 + 2.28192i 0.279477 + 0.161356i
\(201\) 0 0
\(202\) 5.07566i 0.357122i
\(203\) −9.04879 17.4775i −0.635101 1.22668i
\(204\) 0 0
\(205\) 2.60968 + 4.52010i 0.182268 + 0.315698i
\(206\) −1.43352 + 2.48292i −0.0998777 + 0.172993i
\(207\) 0 0
\(208\) −5.08712 + 2.93705i −0.352729 + 0.203648i
\(209\) −10.7895 −0.746326
\(210\) 0 0
\(211\) −8.17368 −0.562699 −0.281350 0.959605i \(-0.590782\pi\)
−0.281350 + 0.959605i \(0.590782\pi\)
\(212\) 7.83672 4.52454i 0.538228 0.310746i
\(213\) 0 0
\(214\) 4.90709 8.49932i 0.335441 0.581002i
\(215\) −0.878384 1.52141i −0.0599053 0.103759i
\(216\) 0 0
\(217\) 5.30423 + 0.243427i 0.360075 + 0.0165249i
\(218\) 7.68907i 0.520770i
\(219\) 0 0
\(220\) 1.48722 + 0.858648i 0.100268 + 0.0578900i
\(221\) −23.9762 13.8427i −1.61282 0.931160i
\(222\) 0 0
\(223\) 27.1394i 1.81739i 0.417462 + 0.908695i \(0.362920\pi\)
−0.417462 + 0.908695i \(0.637080\pi\)
\(224\) −2.64297 0.121294i −0.176591 0.00810430i
\(225\) 0 0
\(226\) −0.272242 0.471536i −0.0181092 0.0313661i
\(227\) −6.29665 + 10.9061i −0.417924 + 0.723865i −0.995730 0.0923086i \(-0.970575\pi\)
0.577807 + 0.816174i \(0.303909\pi\)
\(228\) 0 0
\(229\) −1.22382 + 0.706571i −0.0808721 + 0.0466916i −0.539891 0.841735i \(-0.681534\pi\)
0.459019 + 0.888427i \(0.348201\pi\)
\(230\) −3.48089 −0.229523
\(231\) 0 0
\(232\) −7.43874 −0.488377
\(233\) 15.5393 8.97160i 1.01801 0.587749i 0.104484 0.994527i \(-0.466681\pi\)
0.913527 + 0.406777i \(0.133348\pi\)
\(234\) 0 0
\(235\) −0.577587 + 1.00041i −0.0376776 + 0.0652596i
\(236\) 0.111972 + 0.193941i 0.00728875 + 0.0126245i
\(237\) 0 0
\(238\) −5.73324 11.0736i −0.371631 0.717795i
\(239\) 25.6164i 1.65699i 0.559997 + 0.828494i \(0.310802\pi\)
−0.559997 + 0.828494i \(0.689198\pi\)
\(240\) 0 0
\(241\) −10.5993 6.11953i −0.682764 0.394194i 0.118132 0.992998i \(-0.462309\pi\)
−0.800896 + 0.598804i \(0.795643\pi\)
\(242\) 3.67061 + 2.11923i 0.235956 + 0.136229i
\(243\) 0 0
\(244\) 8.98366i 0.575120i
\(245\) 4.60353 + 0.423432i 0.294109 + 0.0270521i
\(246\) 0 0
\(247\) 12.1868 + 21.1082i 0.775428 + 1.34308i
\(248\) 1.00346 1.73804i 0.0637198 0.110366i
\(249\) 0 0
\(250\) −5.46997 + 3.15809i −0.345951 + 0.199735i
\(251\) −22.2877 −1.40679 −0.703394 0.710800i \(-0.748333\pi\)
−0.703394 + 0.710800i \(0.748333\pi\)
\(252\) 0 0
\(253\) 13.7054 0.861650
\(254\) −16.8453 + 9.72561i −1.05697 + 0.610239i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −14.1946 24.5858i −0.885436 1.53362i −0.845213 0.534429i \(-0.820527\pi\)
−0.0402224 0.999191i \(-0.512807\pi\)
\(258\) 0 0
\(259\) −14.1320 9.04738i −0.878118 0.562177i
\(260\) 3.87939i 0.240590i
\(261\) 0 0
\(262\) −14.4793 8.35965i −0.894537 0.516461i
\(263\) −24.1449 13.9401i −1.48884 0.859582i −0.488921 0.872328i \(-0.662609\pi\)
−0.999919 + 0.0127465i \(0.995943\pi\)
\(264\) 0 0
\(265\) 5.97621i 0.367116i
\(266\) −0.503290 + 10.9666i −0.0308587 + 0.672403i
\(267\) 0 0
\(268\) −5.67037 9.82137i −0.346373 0.599936i
\(269\) 3.06694 5.31209i 0.186995 0.323884i −0.757252 0.653123i \(-0.773459\pi\)
0.944247 + 0.329238i \(0.106792\pi\)
\(270\) 0 0
\(271\) −2.98593 + 1.72393i −0.181382 + 0.104721i −0.587942 0.808903i \(-0.700062\pi\)
0.406560 + 0.913624i \(0.366728\pi\)
\(272\) −4.71312 −0.285775
\(273\) 0 0
\(274\) −3.14453 −0.189968
\(275\) 10.2774 5.93367i 0.619752 0.357814i
\(276\) 0 0
\(277\) 6.71559 11.6317i 0.403501 0.698884i −0.590645 0.806931i \(-0.701127\pi\)
0.994146 + 0.108048i \(0.0344600\pi\)
\(278\) −8.41070 14.5678i −0.504440 0.873716i
\(279\) 0 0
\(280\) 0.942112 1.47157i 0.0563020 0.0879434i
\(281\) 26.4653i 1.57879i 0.613889 + 0.789393i \(0.289604\pi\)
−0.613889 + 0.789393i \(0.710396\pi\)
\(282\) 0 0
\(283\) −6.64541 3.83673i −0.395029 0.228070i 0.289308 0.957236i \(-0.406575\pi\)
−0.684337 + 0.729166i \(0.739908\pi\)
\(284\) −3.37253 1.94713i −0.200123 0.115541i
\(285\) 0 0
\(286\) 15.2744i 0.903195i
\(287\) −18.5685 + 9.61361i −1.09606 + 0.567474i
\(288\) 0 0
\(289\) −2.60677 4.51506i −0.153340 0.265592i
\(290\) 2.45636 4.25453i 0.144242 0.249835i
\(291\) 0 0
\(292\) −3.46836 + 2.00246i −0.202970 + 0.117185i
\(293\) 3.32948 0.194511 0.0972553 0.995259i \(-0.468994\pi\)
0.0972553 + 0.995259i \(0.468994\pi\)
\(294\) 0 0
\(295\) −0.147898 −0.00861093
\(296\) −5.49254 + 3.17112i −0.319247 + 0.184318i
\(297\) 0 0
\(298\) 10.3931 18.0015i 0.602059 1.04280i
\(299\) −15.4803 26.8127i −0.895250 1.55062i
\(300\) 0 0
\(301\) 6.24990 3.23581i 0.360238 0.186509i
\(302\) 9.42792i 0.542516i
\(303\) 0 0
\(304\) 3.59343 + 2.07467i 0.206097 + 0.118990i
\(305\) 5.13814 + 2.96651i 0.294209 + 0.169862i
\(306\) 0 0
\(307\) 18.5385i 1.05805i −0.848607 0.529024i \(-0.822558\pi\)
0.848607 0.529024i \(-0.177442\pi\)
\(308\) −3.70940 + 5.79406i −0.211363 + 0.330147i
\(309\) 0 0
\(310\) 0.662708 + 1.14784i 0.0376393 + 0.0651932i
\(311\) 10.7758 18.6642i 0.611039 1.05835i −0.380026 0.924976i \(-0.624085\pi\)
0.991066 0.133376i \(-0.0425816\pi\)
\(312\) 0 0
\(313\) 23.5767 13.6120i 1.33263 0.769396i 0.346930 0.937891i \(-0.387224\pi\)
0.985702 + 0.168496i \(0.0538909\pi\)
\(314\) −4.62539 −0.261026
\(315\) 0 0
\(316\) 10.1720 0.572222
\(317\) 19.4249 11.2149i 1.09101 0.629894i 0.157164 0.987573i \(-0.449765\pi\)
0.933845 + 0.357678i \(0.116432\pi\)
\(318\) 0 0
\(319\) −9.67147 + 16.7515i −0.541498 + 0.937902i
\(320\) −0.330211 0.571943i −0.0184594 0.0319726i
\(321\) 0 0
\(322\) 0.639304 13.9303i 0.0356270 0.776305i
\(323\) 19.5563i 1.08814i
\(324\) 0 0
\(325\) −23.2168 13.4042i −1.28784 0.743533i
\(326\) 9.99233 + 5.76907i 0.553424 + 0.319519i
\(327\) 0 0
\(328\) 7.90306i 0.436374i
\(329\) −3.89750 2.49520i −0.214876 0.137565i
\(330\) 0 0
\(331\) −1.46420 2.53608i −0.0804799 0.139395i 0.822976 0.568076i \(-0.192312\pi\)
−0.903456 + 0.428680i \(0.858979\pi\)
\(332\) 6.14441 10.6424i 0.337219 0.584080i
\(333\) 0 0
\(334\) −16.4600 + 9.50317i −0.900650 + 0.519991i
\(335\) 7.48968 0.409205
\(336\) 0 0
\(337\) −24.8418 −1.35322 −0.676610 0.736341i \(-0.736552\pi\)
−0.676610 + 0.736341i \(0.736552\pi\)
\(338\) 18.6240 10.7525i 1.01301 0.584862i
\(339\) 0 0
\(340\) 1.55633 2.69564i 0.0844037 0.146192i
\(341\) −2.60929 4.51943i −0.141301 0.244741i
\(342\) 0 0
\(343\) −2.54004 + 18.3453i −0.137149 + 0.990550i
\(344\) 2.66007i 0.143421i
\(345\) 0 0
\(346\) 8.29499 + 4.78911i 0.445941 + 0.257464i
\(347\) 13.4947 + 7.79117i 0.724433 + 0.418252i 0.816382 0.577512i \(-0.195976\pi\)
−0.0919490 + 0.995764i \(0.529310\pi\)
\(348\) 0 0
\(349\) 16.1238i 0.863085i 0.902093 + 0.431542i \(0.142030\pi\)
−0.902093 + 0.431542i \(0.857970\pi\)
\(350\) −5.55164 10.7229i −0.296748 0.573161i
\(351\) 0 0
\(352\) 1.30015 + 2.25192i 0.0692981 + 0.120028i
\(353\) −10.9701 + 19.0008i −0.583880 + 1.01131i 0.411134 + 0.911575i \(0.365133\pi\)
−0.995014 + 0.0997345i \(0.968201\pi\)
\(354\) 0 0
\(355\) 2.22729 1.28593i 0.118212 0.0682500i
\(356\) −15.0525 −0.797783
\(357\) 0 0
\(358\) 20.3906 1.07768
\(359\) −9.77938 + 5.64613i −0.516136 + 0.297991i −0.735352 0.677685i \(-0.762983\pi\)
0.219216 + 0.975676i \(0.429650\pi\)
\(360\) 0 0
\(361\) −0.891506 + 1.54413i −0.0469214 + 0.0812702i
\(362\) 11.9933 + 20.7730i 0.630355 + 1.09181i
\(363\) 0 0
\(364\) 15.5251 + 0.712494i 0.813735 + 0.0373448i
\(365\) 2.64493i 0.138442i
\(366\) 0 0
\(367\) −10.7901 6.22965i −0.563237 0.325185i 0.191207 0.981550i \(-0.438760\pi\)
−0.754444 + 0.656365i \(0.772093\pi\)
\(368\) −4.56456 2.63535i −0.237944 0.137377i
\(369\) 0 0
\(370\) 4.18856i 0.217753i
\(371\) −23.9164 1.09760i −1.24168 0.0569844i
\(372\) 0 0
\(373\) 9.19719 + 15.9300i 0.476212 + 0.824824i 0.999629 0.0272532i \(-0.00867605\pi\)
−0.523416 + 0.852077i \(0.675343\pi\)
\(374\) −6.12776 + 10.6136i −0.316859 + 0.548816i
\(375\) 0 0
\(376\) −1.51480 + 0.874572i −0.0781200 + 0.0451026i
\(377\) 43.6959 2.25046
\(378\) 0 0
\(379\) −0.285278 −0.0146538 −0.00732688 0.999973i \(-0.502332\pi\)
−0.00732688 + 0.999973i \(0.502332\pi\)
\(380\) −2.37318 + 1.37016i −0.121742 + 0.0702876i
\(381\) 0 0
\(382\) 2.85615 4.94699i 0.146133 0.253110i
\(383\) −1.39732 2.42022i −0.0713996 0.123668i 0.828115 0.560558i \(-0.189413\pi\)
−0.899515 + 0.436890i \(0.856080\pi\)
\(384\) 0 0
\(385\) −2.08899 4.03483i −0.106465 0.205634i
\(386\) 1.38240i 0.0703625i
\(387\) 0 0
\(388\) 3.75439 + 2.16760i 0.190601 + 0.110043i
\(389\) 6.71856 + 3.87896i 0.340645 + 0.196671i 0.660557 0.750776i \(-0.270320\pi\)
−0.319912 + 0.947447i \(0.603653\pi\)
\(390\) 0 0
\(391\) 24.8415i 1.25629i
\(392\) 5.71612 + 4.04054i 0.288708 + 0.204078i
\(393\) 0 0
\(394\) −2.97267 5.14881i −0.149761 0.259393i
\(395\) −3.35893 + 5.81783i −0.169006 + 0.292727i
\(396\) 0 0
\(397\) 5.00629 2.89038i 0.251258 0.145064i −0.369082 0.929397i \(-0.620328\pi\)
0.620340 + 0.784333i \(0.286995\pi\)
\(398\) 18.6654 0.935611
\(399\) 0 0
\(400\) −4.56384 −0.228192
\(401\) −11.8154 + 6.82164i −0.590034 + 0.340656i −0.765111 0.643898i \(-0.777316\pi\)
0.175077 + 0.984555i \(0.443983\pi\)
\(402\) 0 0
\(403\) −5.89443 + 10.2095i −0.293623 + 0.508569i
\(404\) −2.53783 4.39565i −0.126262 0.218692i
\(405\) 0 0
\(406\) 16.5752 + 10.6116i 0.822615 + 0.526644i
\(407\) 16.4917i 0.817463i
\(408\) 0 0
\(409\) −25.3625 14.6431i −1.25410 0.724053i −0.282176 0.959363i \(-0.591056\pi\)
−0.971921 + 0.235309i \(0.924390\pi\)
\(410\) −4.52010 2.60968i −0.223232 0.128883i
\(411\) 0 0
\(412\) 2.86703i 0.141248i
\(413\) 0.0271630 0.591876i 0.00133661 0.0291243i
\(414\) 0 0
\(415\) 4.05791 + 7.02851i 0.199195 + 0.345016i
\(416\) 2.93705 5.08712i 0.144001 0.249417i
\(417\) 0 0
\(418\) 9.34398 5.39475i 0.457029 0.263866i
\(419\) 20.8178 1.01702 0.508509 0.861057i \(-0.330197\pi\)
0.508509 + 0.861057i \(0.330197\pi\)
\(420\) 0 0
\(421\) −38.3993 −1.87147 −0.935734 0.352707i \(-0.885261\pi\)
−0.935734 + 0.352707i \(0.885261\pi\)
\(422\) 7.07862 4.08684i 0.344582 0.198944i
\(423\) 0 0
\(424\) −4.52454 + 7.83672i −0.219731 + 0.380585i
\(425\) −10.7550 18.6282i −0.521693 0.903599i
\(426\) 0 0
\(427\) −12.8154 + 20.0177i −0.620183 + 0.968723i
\(428\) 9.81417i 0.474386i
\(429\) 0 0
\(430\) 1.52141 + 0.878384i 0.0733687 + 0.0423595i
\(431\) 17.2706 + 9.97120i 0.831897 + 0.480296i 0.854502 0.519448i \(-0.173863\pi\)
−0.0226047 + 0.999744i \(0.507196\pi\)
\(432\) 0 0
\(433\) 28.2196i 1.35615i −0.734993 0.678075i \(-0.762815\pi\)
0.734993 0.678075i \(-0.237185\pi\)
\(434\) −4.71531 + 2.44130i −0.226342 + 0.117186i
\(435\) 0 0
\(436\) −3.84454 6.65893i −0.184120 0.318905i
\(437\) −10.9349 + 18.9399i −0.523089 + 0.906017i
\(438\) 0 0
\(439\) −7.91077 + 4.56728i −0.377560 + 0.217985i −0.676756 0.736207i \(-0.736615\pi\)
0.299196 + 0.954192i \(0.403282\pi\)
\(440\) −1.71730 −0.0818688
\(441\) 0 0
\(442\) 27.6854 1.31686
\(443\) 29.2751 16.9020i 1.39090 0.803037i 0.397486 0.917608i \(-0.369883\pi\)
0.993415 + 0.114571i \(0.0365495\pi\)
\(444\) 0 0
\(445\) 4.97052 8.60919i 0.235625 0.408115i
\(446\) −13.5697 23.5034i −0.642544 1.11292i
\(447\) 0 0
\(448\) 2.34953 1.21644i 0.111005 0.0574714i
\(449\) 27.0131i 1.27483i 0.770522 + 0.637413i \(0.219995\pi\)
−0.770522 + 0.637413i \(0.780005\pi\)
\(450\) 0 0
\(451\) 17.7971 + 10.2752i 0.838032 + 0.483838i
\(452\) 0.471536 + 0.272242i 0.0221792 + 0.0128052i
\(453\) 0 0
\(454\) 12.5933i 0.591033i
\(455\) −5.53406 + 8.64418i −0.259441 + 0.405246i
\(456\) 0 0
\(457\) 1.70305 + 2.94976i 0.0796651 + 0.137984i 0.903105 0.429419i \(-0.141282\pi\)
−0.823440 + 0.567403i \(0.807948\pi\)
\(458\) 0.706571 1.22382i 0.0330159 0.0571852i
\(459\) 0 0
\(460\) 3.01454 1.74044i 0.140554 0.0811486i
\(461\) −1.67610 −0.0780639 −0.0390319 0.999238i \(-0.512427\pi\)
−0.0390319 + 0.999238i \(0.512427\pi\)
\(462\) 0 0
\(463\) 16.4467 0.764341 0.382170 0.924092i \(-0.375177\pi\)
0.382170 + 0.924092i \(0.375177\pi\)
\(464\) 6.44214 3.71937i 0.299069 0.172667i
\(465\) 0 0
\(466\) −8.97160 + 15.5393i −0.415601 + 0.719843i
\(467\) −1.83112 3.17159i −0.0847340 0.146764i 0.820544 0.571584i \(-0.193671\pi\)
−0.905278 + 0.424820i \(0.860337\pi\)
\(468\) 0 0
\(469\) −1.37556 + 29.9732i −0.0635176 + 1.38404i
\(470\) 1.15517i 0.0532842i
\(471\) 0 0
\(472\) −0.193941 0.111972i −0.00892686 0.00515392i
\(473\) −5.99027 3.45848i −0.275433 0.159021i
\(474\) 0 0
\(475\) 18.9369i 0.868885i
\(476\) 10.5019 + 6.72341i 0.481355 + 0.308167i
\(477\) 0 0
\(478\) −12.8082 22.1845i −0.585834 1.01469i
\(479\) 14.2133 24.6182i 0.649422 1.12483i −0.333839 0.942630i \(-0.608344\pi\)
0.983261 0.182202i \(-0.0583225\pi\)
\(480\) 0 0
\(481\) 32.2637 18.6275i 1.47110 0.849340i
\(482\) 12.2391 0.557474
\(483\) 0 0
\(484\) −4.23846 −0.192657
\(485\) −2.47949 + 1.43153i −0.112588 + 0.0650026i
\(486\) 0 0
\(487\) −20.0702 + 34.7626i −0.909467 + 1.57524i −0.0946602 + 0.995510i \(0.530176\pi\)
−0.814807 + 0.579733i \(0.803157\pi\)
\(488\) 4.49183 + 7.78008i 0.203336 + 0.352188i
\(489\) 0 0
\(490\) −4.19849 + 1.93506i −0.189668 + 0.0874171i
\(491\) 8.45892i 0.381746i 0.981615 + 0.190873i \(0.0611318\pi\)
−0.981615 + 0.190873i \(0.938868\pi\)
\(492\) 0 0
\(493\) 30.3626 + 17.5299i 1.36746 + 0.789505i
\(494\) −21.1082 12.1868i −0.949702 0.548311i
\(495\) 0 0
\(496\) 2.00692i 0.0901134i
\(497\) 4.73713 + 9.14966i 0.212490 + 0.410418i
\(498\) 0 0
\(499\) −5.74186 9.94519i −0.257041 0.445208i 0.708407 0.705804i \(-0.249414\pi\)
−0.965448 + 0.260596i \(0.916081\pi\)
\(500\) 3.15809 5.46997i 0.141234 0.244625i
\(501\) 0 0
\(502\) 19.3017 11.1439i 0.861478 0.497375i
\(503\) 1.99804 0.0890883 0.0445441 0.999007i \(-0.485816\pi\)
0.0445441 + 0.999007i \(0.485816\pi\)
\(504\) 0 0
\(505\) 3.35208 0.149166
\(506\) −11.8692 + 6.85269i −0.527650 + 0.304639i
\(507\) 0 0
\(508\) 9.72561 16.8453i 0.431504 0.747387i
\(509\) 15.9306 + 27.5926i 0.706112 + 1.22302i 0.966289 + 0.257461i \(0.0828858\pi\)
−0.260177 + 0.965561i \(0.583781\pi\)
\(510\) 0 0
\(511\) 10.5849 + 0.485772i 0.468247 + 0.0214893i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 24.5858 + 14.1946i 1.08443 + 0.626098i
\(515\) 1.63978 + 0.946726i 0.0722572 + 0.0417177i
\(516\) 0 0
\(517\) 4.54829i 0.200034i
\(518\) 16.7623 + 0.769275i 0.736495 + 0.0338000i
\(519\) 0 0
\(520\) 1.93970 + 3.35965i 0.0850613 + 0.147330i
\(521\) 0.864274 1.49697i 0.0378645 0.0655833i −0.846472 0.532433i \(-0.821278\pi\)
0.884337 + 0.466850i \(0.154611\pi\)
\(522\) 0 0
\(523\) −38.4274 + 22.1861i −1.68031 + 0.970130i −0.718864 + 0.695151i \(0.755338\pi\)
−0.961450 + 0.274979i \(0.911329\pi\)
\(524\) 16.7193 0.730386
\(525\) 0 0
\(526\) 27.8801 1.21563
\(527\) −8.19162 + 4.72943i −0.356833 + 0.206017i
\(528\) 0 0
\(529\) 2.39013 4.13982i 0.103919 0.179992i
\(530\) −2.98811 5.17555i −0.129795 0.224812i
\(531\) 0 0
\(532\) −5.04742 9.74897i −0.218834 0.422672i
\(533\) 46.4234i 2.01082i
\(534\) 0 0
\(535\) −5.61315 3.24075i −0.242677 0.140110i
\(536\) 9.82137 + 5.67037i 0.424219 + 0.244923i
\(537\) 0 0
\(538\) 6.13388i 0.264450i
\(539\) 16.5308 7.61896i 0.712032 0.328172i
\(540\) 0 0
\(541\) 15.7052 + 27.2022i 0.675220 + 1.16952i 0.976404 + 0.215950i \(0.0692848\pi\)
−0.301184 + 0.953566i \(0.597382\pi\)
\(542\) 1.72393 2.98593i 0.0740490 0.128257i
\(543\) 0 0
\(544\) 4.08169 2.35656i 0.175001 0.101037i
\(545\) 5.07804 0.217519
\(546\) 0 0
\(547\) −21.6668 −0.926406 −0.463203 0.886252i \(-0.653300\pi\)
−0.463203 + 0.886252i \(0.653300\pi\)
\(548\) 2.72325 1.57227i 0.116331 0.0671639i
\(549\) 0 0
\(550\) −5.93367 + 10.2774i −0.253013 + 0.438231i
\(551\) −15.4329 26.7306i −0.657464 1.13876i
\(552\) 0 0
\(553\) −22.6657 14.5107i −0.963843 0.617058i
\(554\) 13.4312i 0.570636i
\(555\) 0 0
\(556\) 14.5678 + 8.41070i 0.617811 + 0.356693i
\(557\) 7.32110 + 4.22684i 0.310205 + 0.179097i 0.647018 0.762475i \(-0.276016\pi\)
−0.336813 + 0.941571i \(0.609349\pi\)
\(558\) 0 0
\(559\) 15.6255i 0.660889i
\(560\) −0.0801053 + 1.74548i −0.00338507 + 0.0737599i
\(561\) 0 0
\(562\) −13.2326 22.9196i −0.558185 0.966805i
\(563\) 19.9644 34.5794i 0.841400 1.45735i −0.0473118 0.998880i \(-0.515065\pi\)
0.888712 0.458467i \(-0.151601\pi\)
\(564\) 0 0
\(565\) −0.311413 + 0.179795i −0.0131013 + 0.00756401i
\(566\) 7.67346 0.322540
\(567\) 0 0
\(568\) 3.89426 0.163399
\(569\) 17.2519 9.96037i 0.723236 0.417560i −0.0927066 0.995693i \(-0.529552\pi\)
0.815943 + 0.578133i \(0.196219\pi\)
\(570\) 0 0
\(571\) 4.50381 7.80082i 0.188478 0.326454i −0.756265 0.654266i \(-0.772978\pi\)
0.944743 + 0.327812i \(0.106311\pi\)
\(572\) −7.63721 13.2280i −0.319328 0.553092i
\(573\) 0 0
\(574\) 11.2739 17.6099i 0.470565 0.735021i
\(575\) 24.0546i 1.00315i
\(576\) 0 0
\(577\) −17.7359 10.2398i −0.738355 0.426290i 0.0831158 0.996540i \(-0.473513\pi\)
−0.821471 + 0.570250i \(0.806846\pi\)
\(578\) 4.51506 + 2.60677i 0.187802 + 0.108427i
\(579\) 0 0
\(580\) 4.91271i 0.203989i
\(581\) −28.8729 + 14.9486i −1.19785 + 0.620174i
\(582\) 0 0
\(583\) 11.7651 + 20.3778i 0.487262 + 0.843963i
\(584\) 2.00246 3.46836i 0.0828622 0.143522i
\(585\) 0 0
\(586\) −2.88342 + 1.66474i −0.119113 + 0.0687699i
\(587\) 22.2964 0.920270 0.460135 0.887849i \(-0.347801\pi\)
0.460135 + 0.887849i \(0.347801\pi\)
\(588\) 0 0
\(589\) 8.32739 0.343124
\(590\) 0.128083 0.0739488i 0.00527310 0.00304442i
\(591\) 0 0
\(592\) 3.17112 5.49254i 0.130332 0.225742i
\(593\) 18.9090 + 32.7513i 0.776499 + 1.34494i 0.933948 + 0.357409i \(0.116340\pi\)
−0.157449 + 0.987527i \(0.550327\pi\)
\(594\) 0 0
\(595\) −7.31326 + 3.78636i −0.299815 + 0.155226i
\(596\) 20.7863i 0.851439i
\(597\) 0 0
\(598\) 26.8127 + 15.4803i 1.09645 + 0.633037i
\(599\) 5.73495 + 3.31107i 0.234324 + 0.135287i 0.612565 0.790420i \(-0.290138\pi\)
−0.378241 + 0.925707i \(0.623471\pi\)
\(600\) 0 0
\(601\) 29.5837i 1.20674i −0.797460 0.603372i \(-0.793824\pi\)
0.797460 0.603372i \(-0.206176\pi\)
\(602\) −3.79466 + 5.92725i −0.154659 + 0.241577i
\(603\) 0 0
\(604\) −4.71396 8.16482i −0.191808 0.332222i
\(605\) 1.39959 2.42416i 0.0569013 0.0985560i
\(606\) 0 0
\(607\) −9.92423 + 5.72975i −0.402812 + 0.232564i −0.687697 0.725998i \(-0.741378\pi\)
0.284885 + 0.958562i \(0.408045\pi\)
\(608\) −4.14934 −0.168278
\(609\) 0 0
\(610\) −5.93301 −0.240221
\(611\) 8.89811 5.13733i 0.359979 0.207834i
\(612\) 0 0
\(613\) −2.47537 + 4.28746i −0.0999791 + 0.173169i −0.911676 0.410910i \(-0.865211\pi\)
0.811697 + 0.584079i \(0.198544\pi\)
\(614\) 9.26924 + 16.0548i 0.374076 + 0.647919i
\(615\) 0 0
\(616\) 0.315400 6.87250i 0.0127078 0.276901i
\(617\) 10.1338i 0.407970i −0.978974 0.203985i \(-0.934611\pi\)
0.978974 0.203985i \(-0.0653893\pi\)
\(618\) 0 0
\(619\) 22.1612 + 12.7948i 0.890732 + 0.514264i 0.874182 0.485599i \(-0.161398\pi\)
0.0165502 + 0.999863i \(0.494732\pi\)
\(620\) −1.14784 0.662708i −0.0460985 0.0266150i
\(621\) 0 0
\(622\) 21.5516i 0.864140i
\(623\) 33.5405 + 21.4729i 1.34377 + 0.860292i
\(624\) 0 0
\(625\) −9.32393 16.1495i −0.372957 0.645981i
\(626\) −13.6120 + 23.5767i −0.544045 + 0.942313i
\(627\) 0 0
\(628\) 4.00571 2.31270i 0.159845 0.0922866i
\(629\) 29.8918 1.19186
\(630\) 0 0
\(631\) 38.6494 1.53861 0.769305 0.638882i \(-0.220603\pi\)
0.769305 + 0.638882i \(0.220603\pi\)
\(632\) −8.80925 + 5.08602i −0.350413 + 0.202311i
\(633\) 0 0
\(634\) −11.2149 + 19.4249i −0.445403 + 0.771460i
\(635\) 6.42302 + 11.1250i 0.254890 + 0.441482i
\(636\) 0 0
\(637\) −33.5771 23.7346i −1.33037 0.940398i
\(638\) 19.3429i 0.765794i
\(639\) 0 0
\(640\) 0.571943 + 0.330211i 0.0226080 + 0.0130528i
\(641\) −13.2162 7.63037i −0.522008 0.301382i 0.215748 0.976449i \(-0.430781\pi\)
−0.737756 + 0.675068i \(0.764114\pi\)
\(642\) 0 0
\(643\) 0.0876859i 0.00345799i 0.999999 + 0.00172900i \(0.000550357\pi\)
−0.999999 + 0.00172900i \(0.999450\pi\)
\(644\) 6.41149 + 12.3836i 0.252648 + 0.487984i
\(645\) 0 0
\(646\) −9.77817 16.9363i −0.384717 0.666349i
\(647\) −21.1405 + 36.6165i −0.831121 + 1.43954i 0.0660294 + 0.997818i \(0.478967\pi\)
−0.897150 + 0.441726i \(0.854366\pi\)
\(648\) 0 0
\(649\) −0.504304 + 0.291160i −0.0197957 + 0.0114290i
\(650\) 26.8085 1.05152
\(651\) 0 0
\(652\) −11.5381 −0.451869
\(653\) 9.92733 5.73154i 0.388486 0.224293i −0.293018 0.956107i \(-0.594660\pi\)
0.681504 + 0.731814i \(0.261326\pi\)
\(654\) 0 0
\(655\) −5.52090 + 9.56249i −0.215720 + 0.373637i
\(656\) −3.95153 6.84425i −0.154281 0.267223i
\(657\) 0 0
\(658\) 4.62293 + 0.212161i 0.180221 + 0.00827089i
\(659\) 43.1305i 1.68013i 0.542489 + 0.840063i \(0.317482\pi\)
−0.542489 + 0.840063i \(0.682518\pi\)
\(660\) 0 0
\(661\) −1.81381 1.04720i −0.0705491 0.0407315i 0.464311 0.885672i \(-0.346302\pi\)
−0.534860 + 0.844941i \(0.679636\pi\)
\(662\) 2.53608 + 1.46420i 0.0985674 + 0.0569079i
\(663\) 0 0
\(664\) 12.2888i 0.476899i
\(665\) 7.24257 + 0.332384i 0.280855 + 0.0128893i
\(666\) 0 0
\(667\) 19.6037 + 33.9546i 0.759057 + 1.31473i
\(668\) 9.50317 16.4600i 0.367689 0.636856i
\(669\) 0 0
\(670\) −6.48626 + 3.74484i −0.250586 + 0.144676i
\(671\) 23.3602 0.901810
\(672\) 0 0
\(673\) 8.86436 0.341696 0.170848 0.985297i \(-0.445349\pi\)
0.170848 + 0.985297i \(0.445349\pi\)
\(674\) 21.5137 12.4209i 0.828675 0.478436i
\(675\) 0 0
\(676\) −10.7525 + 18.6240i −0.413560 + 0.716306i
\(677\) −2.70881 4.69180i −0.104108 0.180320i 0.809265 0.587443i \(-0.199865\pi\)
−0.913373 + 0.407123i \(0.866532\pi\)
\(678\) 0 0
\(679\) −5.27352 10.1857i −0.202379 0.390890i
\(680\) 3.11265i 0.119365i
\(681\) 0 0
\(682\) 4.51943 + 2.60929i 0.173058 + 0.0999151i
\(683\) −12.5852 7.26604i −0.481558 0.278027i 0.239508 0.970894i \(-0.423014\pi\)
−0.721065 + 0.692867i \(0.756347\pi\)
\(684\) 0 0
\(685\) 2.07672i 0.0793475i
\(686\) −6.97289 17.1575i −0.266226 0.655075i
\(687\) 0 0
\(688\) 1.33003 + 2.30369i 0.0507071 + 0.0878272i
\(689\) 26.5776 46.0337i 1.01253 1.75375i
\(690\) 0 0
\(691\) 3.28158 1.89462i 0.124837 0.0720748i −0.436281 0.899810i \(-0.643705\pi\)
0.561118 + 0.827736i \(0.310371\pi\)
\(692\) −9.57823 −0.364110
\(693\) 0 0
\(694\) −15.5823 −0.591497
\(695\) −9.62088 + 5.55462i −0.364941 + 0.210699i
\(696\) 0 0
\(697\) 18.6241 32.2578i 0.705437 1.22185i
\(698\) −8.06188 13.9636i −0.305147 0.528529i
\(699\) 0 0
\(700\) 10.1693 + 6.51045i 0.384363 + 0.246072i
\(701\) 29.5523i 1.11618i 0.829782 + 0.558088i \(0.188465\pi\)
−0.829782 + 0.558088i \(0.811535\pi\)
\(702\) 0 0
\(703\) −22.7904 13.1580i −0.859556 0.496265i
\(704\) −2.25192 1.30015i −0.0848725 0.0490012i
\(705\) 0 0
\(706\) 21.9402i 0.825730i
\(707\) −0.615647 + 13.4148i −0.0231538 + 0.504516i
\(708\) 0 0
\(709\) 2.27586 + 3.94191i 0.0854718 + 0.148041i 0.905592 0.424150i \(-0.139427\pi\)
−0.820120 + 0.572191i \(0.806094\pi\)
\(710\) −1.28593 + 2.22729i −0.0482600 + 0.0835888i
\(711\) 0 0
\(712\) 13.0359 7.52627i 0.488540 0.282059i
\(713\) −10.5779 −0.396144
\(714\) 0 0
\(715\) 10.0876 0.377254
\(716\) −17.6588 + 10.1953i −0.659939 + 0.381016i
\(717\) 0 0
\(718\) 5.64613 9.77938i 0.210712 0.364963i
\(719\) −14.0142 24.2733i −0.522641 0.905240i −0.999653 0.0263435i \(-0.991614\pi\)
0.477012 0.878897i \(-0.341720\pi\)
\(720\) 0 0
\(721\) −4.08990 + 6.38841i −0.152316 + 0.237917i
\(722\) 1.78301i 0.0663568i
\(723\) 0 0
\(724\) −20.7730 11.9933i −0.772024 0.445728i
\(725\) 29.4009 + 16.9746i 1.09192 + 0.630421i
\(726\) 0 0
\(727\) 18.8842i 0.700374i −0.936680 0.350187i \(-0.886118\pi\)
0.936680 0.350187i \(-0.113882\pi\)
\(728\) −13.8014 + 7.14550i −0.511512 + 0.264830i
\(729\) 0 0
\(730\) 1.32247 + 2.29058i 0.0489467 + 0.0847782i
\(731\) −6.26861 + 10.8576i −0.231853 + 0.401581i
\(732\) 0 0
\(733\) 8.25128 4.76388i 0.304768 0.175958i −0.339815 0.940492i \(-0.610364\pi\)
0.644583 + 0.764534i \(0.277031\pi\)
\(734\) 12.4593 0.459881
\(735\) 0 0
\(736\) 5.27070 0.194280
\(737\) 25.5385 14.7446i 0.940722 0.543126i
\(738\) 0 0
\(739\) 4.87463 8.44311i 0.179316 0.310585i −0.762330 0.647188i \(-0.775945\pi\)
0.941647 + 0.336603i \(0.109278\pi\)
\(740\) 2.09428 + 3.62740i 0.0769872 + 0.133346i
\(741\) 0 0
\(742\) 21.2610 11.0077i 0.780517 0.404104i
\(743\) 33.0765i 1.21346i −0.794908 0.606729i \(-0.792481\pi\)
0.794908 0.606729i \(-0.207519\pi\)
\(744\) 0 0
\(745\) −11.8886 6.86387i −0.435563 0.251473i
\(746\) −15.9300 9.19719i −0.583239 0.336733i
\(747\) 0 0
\(748\) 12.2555i 0.448106i
\(749\) 14.0002 21.8682i 0.511556 0.799048i
\(750\) 0 0
\(751\) 4.18103 + 7.24176i 0.152568 + 0.264256i 0.932171 0.362019i \(-0.117912\pi\)
−0.779603 + 0.626274i \(0.784579\pi\)
\(752\) 0.874572 1.51480i 0.0318924 0.0552392i
\(753\) 0 0
\(754\) −37.8418 + 21.8480i −1.37812 + 0.795656i
\(755\) 6.22641 0.226602
\(756\) 0 0
\(757\) −18.1472 −0.659572 −0.329786 0.944056i \(-0.606977\pi\)
−0.329786 + 0.944056i \(0.606977\pi\)
\(758\) 0.247058 0.142639i 0.00897356 0.00518089i
\(759\) 0 0
\(760\) 1.37016 2.37318i 0.0497009 0.0860844i
\(761\) −4.08474 7.07498i −0.148072 0.256468i 0.782443 0.622722i \(-0.213973\pi\)
−0.930515 + 0.366254i \(0.880640\pi\)
\(762\) 0 0
\(763\) −0.932638 + 20.3220i −0.0337638 + 0.735705i
\(764\) 5.71230i 0.206664i
\(765\) 0 0
\(766\) 2.42022 + 1.39732i 0.0874463 + 0.0504871i
\(767\) 1.13923 + 0.657734i 0.0411352 + 0.0237494i
\(768\) 0 0
\(769\) 21.6670i 0.781333i −0.920532 0.390667i \(-0.872245\pi\)
0.920532 0.390667i \(-0.127755\pi\)
\(770\) 3.82653 + 2.44977i 0.137899 + 0.0882836i
\(771\) 0 0
\(772\) 0.691202 + 1.19720i 0.0248769 + 0.0430881i
\(773\) 5.35259 9.27095i 0.192519 0.333453i −0.753565 0.657373i \(-0.771668\pi\)
0.946084 + 0.323920i \(0.105001\pi\)
\(774\) 0 0
\(775\) −7.93216 + 4.57964i −0.284932 + 0.164505i
\(776\) −4.33520 −0.155625
\(777\) 0 0
\(778\) −7.75793 −0.278135
\(779\) −28.3991 + 16.3962i −1.01750 + 0.587456i
\(780\) 0 0
\(781\) 5.06311 8.76957i 0.181172 0.313800i
\(782\) 12.4207 + 21.5133i 0.444164 + 0.769315i
\(783\) 0 0
\(784\) −6.97058 0.641153i −0.248949 0.0228983i
\(785\) 3.05471i 0.109027i
\(786\) 0 0
\(787\) 21.4355 + 12.3758i 0.764093 + 0.441149i 0.830763 0.556626i \(-0.187904\pi\)
−0.0666702 + 0.997775i \(0.521238\pi\)
\(788\) 5.14881 + 2.97267i 0.183419 + 0.105897i
\(789\) 0 0
\(790\) 6.71785i 0.239010i
\(791\) −0.662332 1.27928i −0.0235498 0.0454859i
\(792\) 0 0
\(793\) −26.3855 45.7010i −0.936976 1.62289i
\(794\) −2.89038 + 5.00629i −0.102576 + 0.177666i
\(795\) 0 0
\(796\) −16.1647 + 9.33269i −0.572942 + 0.330788i
\(797\) −54.4419 −1.92843 −0.964215 0.265122i \(-0.914588\pi\)
−0.964215 + 0.265122i \(0.914588\pi\)
\(798\) 0 0
\(799\) 8.24393 0.291649
\(800\) 3.95240 2.28192i 0.139739 0.0806781i
\(801\) 0 0
\(802\) 6.82164 11.8154i 0.240881 0.417217i
\(803\) −5.20698 9.01875i −0.183750 0.318265i
\(804\) 0 0
\(805\) −9.19988 0.422211i −0.324253 0.0148810i
\(806\) 11.7889i 0.415245i
\(807\) 0 0
\(808\) 4.39565 + 2.53783i 0.154638 + 0.0892805i
\(809\) −24.6546 14.2343i −0.866809 0.500452i −0.000522376 1.00000i \(-0.500166\pi\)
−0.866286 + 0.499548i \(0.833500\pi\)
\(810\) 0 0
\(811\) 34.3732i 1.20701i −0.797361 0.603503i \(-0.793771\pi\)
0.797361 0.603503i \(-0.206229\pi\)
\(812\) −19.6604 0.902275i −0.689944 0.0316636i
\(813\) 0 0
\(814\) −8.24585 14.2822i −0.289017 0.500592i
\(815\) 3.81003 6.59916i 0.133459 0.231158i
\(816\) 0 0
\(817\) 9.55877 5.51876i 0.334419 0.193077i
\(818\) 29.2861 1.02397
\(819\) 0 0
\(820\) 5.21936 0.182268
\(821\) −0.957060 + 0.552559i −0.0334016 + 0.0192844i −0.516608 0.856222i \(-0.672805\pi\)
0.483206 + 0.875507i \(0.339472\pi\)
\(822\) 0 0
\(823\) −17.4396 + 30.2063i −0.607908 + 1.05293i 0.383677 + 0.923467i \(0.374658\pi\)
−0.991585 + 0.129460i \(0.958676\pi\)
\(824\) 1.43352 + 2.48292i 0.0499389 + 0.0864967i
\(825\) 0 0
\(826\) 0.272414 + 0.526162i 0.00947851 + 0.0183075i
\(827\) 17.3806i 0.604382i 0.953247 + 0.302191i \(0.0977181\pi\)
−0.953247 + 0.302191i \(0.902282\pi\)
\(828\) 0 0
\(829\) 45.2612 + 26.1315i 1.57199 + 0.907586i 0.995926 + 0.0901786i \(0.0287438\pi\)
0.576060 + 0.817408i \(0.304590\pi\)
\(830\) −7.02851 4.05791i −0.243963 0.140852i
\(831\) 0 0
\(832\) 5.87410i 0.203648i
\(833\) −13.8096 29.9626i −0.478475 1.03814i
\(834\) 0 0
\(835\) 6.27611 + 10.8705i 0.217194 + 0.376191i
\(836\) −5.39475 + 9.34398i −0.186581 + 0.323168i
\(837\) 0 0
\(838\) −18.0288 + 10.4089i −0.622794 + 0.359570i
\(839\) −28.2310 −0.974644 −0.487322 0.873222i \(-0.662026\pi\)
−0.487322 + 0.873222i \(0.662026\pi\)
\(840\) 0 0
\(841\) −26.3349 −0.908099
\(842\) 33.2548 19.1997i 1.14604 0.661664i
\(843\) 0 0
\(844\) −4.08684 + 7.07862i −0.140675 + 0.243656i
\(845\) −7.10123 12.2997i −0.244290 0.423122i
\(846\) 0 0
\(847\) 9.44427 + 6.04628i 0.324509 + 0.207753i
\(848\) 9.04907i 0.310746i
\(849\) 0 0
\(850\) 18.6282 + 10.7550i 0.638941 + 0.368893i
\(851\) 28.9495 + 16.7140i 0.992376 + 0.572949i
\(852\) 0 0
\(853\) 32.5436i 1.11427i 0.830422 + 0.557135i \(0.188099\pi\)
−0.830422 + 0.557135i \(0.811901\pi\)
\(854\) 1.08966 23.7435i 0.0372875 0.812487i
\(855\) 0 0
\(856\) −4.90709 8.49932i −0.167721 0.290501i
\(857\) −23.6268 + 40.9228i −0.807075 + 1.39789i 0.107807 + 0.994172i \(0.465617\pi\)
−0.914881 + 0.403723i \(0.867716\pi\)
\(858\) 0 0
\(859\) −3.48645 + 2.01290i −0.118956 + 0.0686794i −0.558297 0.829641i \(-0.688545\pi\)
0.439341 + 0.898320i \(0.355212\pi\)
\(860\) −1.75677 −0.0599053
\(861\) 0 0
\(862\) −19.9424 −0.679241
\(863\) −19.4653 + 11.2383i −0.662605 + 0.382555i −0.793269 0.608871i \(-0.791623\pi\)
0.130664 + 0.991427i \(0.458289\pi\)
\(864\) 0 0
\(865\) 3.16284 5.47820i 0.107540 0.186264i
\(866\) 14.1098 + 24.4389i 0.479471 + 0.830469i
\(867\) 0 0
\(868\) 2.86293 4.47189i 0.0971742 0.151786i
\(869\) 26.4503i 0.897266i
\(870\) 0 0
\(871\) −57.6917 33.3083i −1.95481 1.12861i
\(872\) 6.65893 + 3.84454i 0.225500 + 0.130192i
\(873\) 0 0
\(874\) 21.8699i 0.739760i
\(875\) −14.8400 + 7.68326i −0.501684 + 0.259742i
\(876\) 0 0
\(877\) 6.82567 + 11.8224i 0.230487 + 0.399214i 0.957951 0.286931i \(-0.0926349\pi\)
−0.727465 + 0.686145i \(0.759302\pi\)
\(878\) 4.56728 7.91077i 0.154138 0.266975i
\(879\) 0 0
\(880\) 1.48722 0.858648i 0.0501342 0.0289450i
\(881\) −11.6865 −0.393727 −0.196863 0.980431i \(-0.563076\pi\)
−0.196863 + 0.980431i \(0.563076\pi\)
\(882\) 0 0
\(883\) −26.6602 −0.897187 −0.448593 0.893736i \(-0.648075\pi\)
−0.448593 + 0.893736i \(0.648075\pi\)
\(884\) −23.9762 + 13.8427i −0.806408 + 0.465580i
\(885\) 0 0
\(886\) −16.9020 + 29.2751i −0.567833 + 0.983515i
\(887\) 6.50026 + 11.2588i 0.218257 + 0.378033i 0.954275 0.298929i \(-0.0966294\pi\)
−0.736018 + 0.676962i \(0.763296\pi\)
\(888\) 0 0
\(889\) −45.7012 + 23.6613i −1.53277 + 0.793574i
\(890\) 9.94104i 0.333224i
\(891\) 0 0
\(892\) 23.5034 + 13.5697i 0.786953 + 0.454347i
\(893\) −6.28543 3.62889i −0.210334 0.121436i
\(894\) 0 0
\(895\) 13.4664i 0.450133i
\(896\) −1.42653 + 2.22823i −0.0476570 + 0.0744400i
\(897\) 0 0
\(898\) −13.5065 23.3940i −0.450719 0.780668i
\(899\) 7.46448 12.9289i 0.248954 0.431202i
\(900\) 0 0
\(901\) 36.9355 21.3247i 1.23050 0.710429i
\(902\) −20.5503 −0.684250
\(903\) 0 0
\(904\) −0.544483 −0.0181092
\(905\) 13.7190 7.92066i 0.456034 0.263292i
\(906\) 0 0
\(907\) −13.5506 + 23.4703i −0.449940 + 0.779319i −0.998382 0.0568698i \(-0.981888\pi\)
0.548441 + 0.836189i \(0.315221\pi\)
\(908\) 6.29665 + 10.9061i 0.208962 + 0.361932i
\(909\) 0 0
\(910\) 0.470547 10.2531i 0.0155985 0.339887i
\(911\) 37.3223i 1.23654i 0.785964 + 0.618272i \(0.212167\pi\)
−0.785964 + 0.618272i \(0.787833\pi\)
\(912\) 0 0
\(913\) 27.6735 + 15.9773i 0.915859 + 0.528771i
\(914\) −2.94976 1.70305i −0.0975694 0.0563317i
\(915\) 0 0
\(916\) 1.41314i 0.0466916i
\(917\) −37.2545 23.8506i −1.23025 0.787615i
\(918\) 0 0
\(919\) −6.00814 10.4064i −0.198190 0.343276i 0.749751 0.661720i \(-0.230173\pi\)
−0.947942 + 0.318444i \(0.896840\pi\)
\(920\) −1.74044 + 3.01454i −0.0573807 + 0.0993864i
\(921\) 0 0
\(922\) 1.45155 0.838051i 0.0478042 0.0275997i
\(923\) −22.8753 −0.752949
\(924\) 0 0
\(925\) 28.9450 0.951705
\(926\) −14.2432 + 8.22333i −0.468061 + 0.270235i
\(927\) 0 0
\(928\) −3.71937 + 6.44214i −0.122094 + 0.211474i
\(929\) 16.7460 + 29.0050i 0.549419 + 0.951622i 0.998314 + 0.0580375i \(0.0184843\pi\)
−0.448895 + 0.893584i \(0.648182\pi\)
\(930\) 0 0
\(931\) −2.66036 + 28.9233i −0.0871897 + 0.947922i
\(932\) 17.9432i 0.587749i
\(933\) 0 0
\(934\) 3.17159 + 1.83112i 0.103778 + 0.0599160i
\(935\) 7.00946 + 4.04691i 0.229234 + 0.132348i
\(936\) 0 0
\(937\) 28.5256i 0.931891i 0.884813 + 0.465946i \(0.154286\pi\)
−0.884813 + 0.465946i \(0.845714\pi\)
\(938\) −13.7953 26.6454i −0.450434 0.870002i
\(939\) 0 0
\(940\) 0.577587 + 1.00041i 0.0188388 + 0.0326298i
\(941\) 4.05703 7.02698i 0.132255 0.229073i −0.792290 0.610144i \(-0.791111\pi\)
0.924546 + 0.381071i \(0.124445\pi\)
\(942\) 0 0
\(943\) 36.0740 20.8273i 1.17473 0.678231i
\(944\) 0.223944 0.00728875
\(945\) 0 0
\(946\) 6.91696 0.224890
\(947\) 27.5208 15.8892i 0.894307 0.516329i 0.0189584 0.999820i \(-0.493965\pi\)
0.875349 + 0.483492i \(0.160632\pi\)
\(948\) 0 0
\(949\) −11.7626 + 20.3735i −0.381831 + 0.661351i
\(950\) −9.46846 16.3998i −0.307197 0.532081i
\(951\) 0 0
\(952\) −12.4566 0.571674i −0.403722 0.0185281i
\(953\) 4.07356i 0.131956i −0.997821 0.0659778i \(-0.978983\pi\)
0.997821 0.0659778i \(-0.0210166\pi\)
\(954\) 0 0
\(955\) −3.26711 1.88627i −0.105721 0.0610381i
\(956\) 22.1845 + 12.8082i 0.717497 + 0.414247i
\(957\) 0 0
\(958\) 28.4266i 0.918422i
\(959\) −8.31091 0.381413i −0.268373 0.0123165i
\(960\) 0 0
\(961\) −13.4861 23.3587i −0.435037 0.753505i
\(962\) −18.6275 + 32.2637i −0.600574 + 1.04022i
\(963\) 0 0
\(964\) −10.5993 + 6.11953i −0.341382 + 0.197097i
\(965\) −0.912971 −0.0293896
\(966\) 0 0
\(967\) −37.7138 −1.21279 −0.606397 0.795162i \(-0.707386\pi\)
−0.606397 + 0.795162i \(0.707386\pi\)
\(968\) 3.67061 2.11923i 0.117978 0.0681146i
\(969\) 0 0
\(970\) 1.43153 2.47949i 0.0459638 0.0796116i
\(971\) 26.7525 + 46.3368i 0.858530 + 1.48702i 0.873331 + 0.487127i \(0.161955\pi\)
−0.0148008 + 0.999890i \(0.504711\pi\)
\(972\) 0 0
\(973\) −20.4622 39.5223i −0.655989 1.26703i
\(974\) 40.1404i 1.28618i
\(975\) 0 0
\(976\) −7.78008 4.49183i −0.249034 0.143780i
\(977\) 4.43220 + 2.55893i 0.141799 + 0.0818675i 0.569221 0.822185i \(-0.307245\pi\)
−0.427422 + 0.904052i \(0.640578\pi\)
\(978\) 0 0
\(979\) 39.1411i 1.25095i
\(980\) 2.66847 3.77506i 0.0852410 0.120590i
\(981\) 0 0
\(982\) −4.22946 7.32564i −0.134967 0.233770i
\(983\) 9.18953 15.9167i 0.293100 0.507665i −0.681441 0.731873i \(-0.738646\pi\)
0.974541 + 0.224208i \(0.0719797\pi\)
\(984\) 0 0
\(985\) −3.40039 + 1.96322i −0.108345 + 0.0625533i
\(986\) −35.0597 −1.11653
\(987\) 0 0
\(988\) 24.3736 0.775428
\(989\) −12.1420 + 7.01020i −0.386094 + 0.222912i
\(990\) 0 0
\(991\) 11.8103 20.4561i 0.375168 0.649810i −0.615184 0.788383i \(-0.710918\pi\)
0.990352 + 0.138574i \(0.0442517\pi\)
\(992\) −1.00346 1.73804i −0.0318599 0.0551830i
\(993\) 0 0
\(994\) −8.67731 5.55527i −0.275227 0.176202i
\(995\) 12.3270i 0.390793i
\(996\) 0 0
\(997\) 32.3902 + 18.7005i 1.02581 + 0.592250i 0.915781 0.401678i \(-0.131573\pi\)
0.110027 + 0.993929i \(0.464906\pi\)
\(998\) 9.94519 + 5.74186i 0.314809 + 0.181755i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1134.2.k.c.647.2 16
3.2 odd 2 1134.2.k.d.647.7 yes 16
7.5 odd 6 1134.2.k.d.971.7 yes 16
9.2 odd 6 1134.2.t.g.1025.2 16
9.4 even 3 1134.2.l.h.269.2 16
9.5 odd 6 1134.2.l.g.269.7 16
9.7 even 3 1134.2.t.h.1025.7 16
21.5 even 6 inner 1134.2.k.c.971.2 yes 16
63.5 even 6 1134.2.t.h.593.7 16
63.40 odd 6 1134.2.t.g.593.2 16
63.47 even 6 1134.2.l.h.215.6 16
63.61 odd 6 1134.2.l.g.215.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1134.2.k.c.647.2 16 1.1 even 1 trivial
1134.2.k.c.971.2 yes 16 21.5 even 6 inner
1134.2.k.d.647.7 yes 16 3.2 odd 2
1134.2.k.d.971.7 yes 16 7.5 odd 6
1134.2.l.g.215.3 16 63.61 odd 6
1134.2.l.g.269.7 16 9.5 odd 6
1134.2.l.h.215.6 16 63.47 even 6
1134.2.l.h.269.2 16 9.4 even 3
1134.2.t.g.593.2 16 63.40 odd 6
1134.2.t.g.1025.2 16 9.2 odd 6
1134.2.t.h.593.7 16 63.5 even 6
1134.2.t.h.1025.7 16 9.7 even 3