Properties

Label 855.2.k.k.676.4
Level $855$
Weight $2$
Character 855.676
Analytic conductor $6.827$
Analytic rank $0$
Dimension $12$
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] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + 14 x^{3} + 46 x^{2} + 12 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 676.4
Root \(-0.156312 + 0.270740i\) of defining polynomial
Character \(\chi\) \(=\) 855.676
Dual form 855.2.k.k.406.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.656312 - 1.13677i) q^{2} +(0.138510 + 0.239907i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.11486 q^{7} +2.98887 q^{8} +O(q^{10})\) \(q+(0.656312 - 1.13677i) q^{2} +(0.138510 + 0.239907i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.11486 q^{7} +2.98887 q^{8} +(-0.656312 - 1.13677i) q^{10} -0.692973 q^{11} +(2.07262 + 3.58988i) q^{13} +(2.04432 - 3.54086i) q^{14} +(1.68461 - 2.91783i) q^{16} +(-1.40392 + 2.43165i) q^{17} +(-1.62820 + 4.04339i) q^{19} +0.277020 q^{20} +(-0.454806 + 0.787748i) q^{22} +(-1.51519 - 2.62438i) q^{23} +(-0.500000 - 0.866025i) q^{25} +5.44113 q^{26} +(0.431440 + 0.747275i) q^{28} +(-1.93613 - 3.35348i) q^{29} +0.374753 q^{31} +(0.777612 + 1.34686i) q^{32} +(1.84281 + 3.19185i) q^{34} +(1.55743 - 2.69755i) q^{35} -1.34678 q^{37} +(3.52778 + 4.50460i) q^{38} +(1.49443 - 2.58844i) q^{40} +(4.77223 - 8.26575i) q^{41} +(2.32486 - 4.02677i) q^{43} +(-0.0959838 - 0.166249i) q^{44} -3.97774 q^{46} +(-0.0650711 - 0.112706i) q^{47} +2.70235 q^{49} -1.31262 q^{50} +(-0.574157 + 0.994469i) q^{52} +(-0.442770 - 0.766900i) q^{53} +(-0.346487 + 0.600132i) q^{55} +9.30991 q^{56} -5.08282 q^{58} +(-0.719490 + 1.24619i) q^{59} +(-1.63574 - 2.83319i) q^{61} +(0.245955 - 0.426007i) q^{62} +8.77986 q^{64} +4.14523 q^{65} +(-5.44562 - 9.43209i) q^{67} -0.777826 q^{68} +(-2.04432 - 3.54086i) q^{70} +(5.75724 - 9.97184i) q^{71} +(-2.37964 + 4.12166i) q^{73} +(-0.883908 + 1.53097i) q^{74} +(-1.19556 + 0.169435i) q^{76} -2.15851 q^{77} +(-5.37760 + 9.31428i) q^{79} +(-1.68461 - 2.91783i) q^{80} +(-6.26414 - 10.8498i) q^{82} -0.386145 q^{83} +(1.40392 + 2.43165i) q^{85} +(-3.05166 - 5.28564i) q^{86} -2.07121 q^{88} +(3.37096 + 5.83867i) q^{89} +(6.45591 + 11.1820i) q^{91} +(0.419737 - 0.727006i) q^{92} -0.170828 q^{94} +(2.68758 + 3.43175i) q^{95} +(2.16484 - 3.74962i) q^{97} +(1.77359 - 3.07194i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 3 q^{10} - 8 q^{13} + 10 q^{14} - 3 q^{16} + 4 q^{17} - 6 q^{19} - 10 q^{20} - 2 q^{23} - 6 q^{25} - 40 q^{26} - 26 q^{28} + 4 q^{29} + 24 q^{31} + 15 q^{32} + 7 q^{34} + 2 q^{35} - 29 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} + 6 q^{44} + 48 q^{46} + 6 q^{47} + 32 q^{49} - 6 q^{50} - 20 q^{52} + 26 q^{53} - 44 q^{56} - 20 q^{58} + 16 q^{59} + 20 q^{61} - 25 q^{62} + 28 q^{64} - 16 q^{65} - 12 q^{67} + 54 q^{68} - 10 q^{70} - 8 q^{71} - 4 q^{73} - 16 q^{74} - 66 q^{76} + 48 q^{77} - 12 q^{79} + 3 q^{80} + 26 q^{82} - 44 q^{83} - 4 q^{85} - 44 q^{86} - 32 q^{88} - 8 q^{89} + 2 q^{91} + 36 q^{92} - 14 q^{94} - 6 q^{95} + 30 q^{97} + 49 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.656312 1.13677i 0.464082 0.803814i −0.535077 0.844803i \(-0.679717\pi\)
0.999160 + 0.0409889i \(0.0130508\pi\)
\(3\) 0 0
\(4\) 0.138510 + 0.239907i 0.0692550 + 0.119953i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 3.11486 1.17731 0.588653 0.808386i \(-0.299658\pi\)
0.588653 + 0.808386i \(0.299658\pi\)
\(8\) 2.98887 1.05672
\(9\) 0 0
\(10\) −0.656312 1.13677i −0.207544 0.359477i
\(11\) −0.692973 −0.208939 −0.104470 0.994528i \(-0.533314\pi\)
−0.104470 + 0.994528i \(0.533314\pi\)
\(12\) 0 0
\(13\) 2.07262 + 3.58988i 0.574841 + 0.995653i 0.996059 + 0.0886938i \(0.0282693\pi\)
−0.421218 + 0.906959i \(0.638397\pi\)
\(14\) 2.04432 3.54086i 0.546367 0.946336i
\(15\) 0 0
\(16\) 1.68461 2.91783i 0.421152 0.729457i
\(17\) −1.40392 + 2.43165i −0.340500 + 0.589763i −0.984526 0.175241i \(-0.943930\pi\)
0.644026 + 0.765004i \(0.277263\pi\)
\(18\) 0 0
\(19\) −1.62820 + 4.04339i −0.373534 + 0.927616i
\(20\) 0.277020 0.0619436
\(21\) 0 0
\(22\) −0.454806 + 0.787748i −0.0969650 + 0.167948i
\(23\) −1.51519 2.62438i −0.315938 0.547221i 0.663698 0.748000i \(-0.268986\pi\)
−0.979637 + 0.200779i \(0.935653\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 5.44113 1.06709
\(27\) 0 0
\(28\) 0.431440 + 0.747275i 0.0815344 + 0.141222i
\(29\) −1.93613 3.35348i −0.359530 0.622725i 0.628352 0.777929i \(-0.283730\pi\)
−0.987882 + 0.155204i \(0.950396\pi\)
\(30\) 0 0
\(31\) 0.374753 0.0673077 0.0336539 0.999434i \(-0.489286\pi\)
0.0336539 + 0.999434i \(0.489286\pi\)
\(32\) 0.777612 + 1.34686i 0.137464 + 0.238094i
\(33\) 0 0
\(34\) 1.84281 + 3.19185i 0.316040 + 0.547397i
\(35\) 1.55743 2.69755i 0.263254 0.455969i
\(36\) 0 0
\(37\) −1.34678 −0.221410 −0.110705 0.993853i \(-0.535311\pi\)
−0.110705 + 0.993853i \(0.535311\pi\)
\(38\) 3.52778 + 4.50460i 0.572281 + 0.730742i
\(39\) 0 0
\(40\) 1.49443 2.58844i 0.236291 0.409268i
\(41\) 4.77223 8.26575i 0.745297 1.29089i −0.204759 0.978812i \(-0.565641\pi\)
0.950056 0.312080i \(-0.101026\pi\)
\(42\) 0 0
\(43\) 2.32486 4.02677i 0.354538 0.614077i −0.632501 0.774560i \(-0.717972\pi\)
0.987039 + 0.160482i \(0.0513049\pi\)
\(44\) −0.0959838 0.166249i −0.0144701 0.0250629i
\(45\) 0 0
\(46\) −3.97774 −0.586486
\(47\) −0.0650711 0.112706i −0.00949159 0.0164399i 0.861241 0.508197i \(-0.169688\pi\)
−0.870732 + 0.491758i \(0.836355\pi\)
\(48\) 0 0
\(49\) 2.70235 0.386051
\(50\) −1.31262 −0.185633
\(51\) 0 0
\(52\) −0.574157 + 0.994469i −0.0796212 + 0.137908i
\(53\) −0.442770 0.766900i −0.0608191 0.105342i 0.834013 0.551745i \(-0.186038\pi\)
−0.894832 + 0.446403i \(0.852705\pi\)
\(54\) 0 0
\(55\) −0.346487 + 0.600132i −0.0467202 + 0.0809218i
\(56\) 9.30991 1.24409
\(57\) 0 0
\(58\) −5.08282 −0.667407
\(59\) −0.719490 + 1.24619i −0.0936697 + 0.162241i −0.909053 0.416681i \(-0.863193\pi\)
0.815383 + 0.578922i \(0.196526\pi\)
\(60\) 0 0
\(61\) −1.63574 2.83319i −0.209435 0.362753i 0.742101 0.670288i \(-0.233829\pi\)
−0.951537 + 0.307535i \(0.900496\pi\)
\(62\) 0.245955 0.426007i 0.0312363 0.0541029i
\(63\) 0 0
\(64\) 8.77986 1.09748
\(65\) 4.14523 0.514153
\(66\) 0 0
\(67\) −5.44562 9.43209i −0.665288 1.15231i −0.979207 0.202864i \(-0.934975\pi\)
0.313919 0.949450i \(-0.398358\pi\)
\(68\) −0.777826 −0.0943253
\(69\) 0 0
\(70\) −2.04432 3.54086i −0.244343 0.423214i
\(71\) 5.75724 9.97184i 0.683259 1.18344i −0.290721 0.956808i \(-0.593895\pi\)
0.973981 0.226632i \(-0.0727714\pi\)
\(72\) 0 0
\(73\) −2.37964 + 4.12166i −0.278516 + 0.482404i −0.971016 0.239014i \(-0.923176\pi\)
0.692500 + 0.721418i \(0.256509\pi\)
\(74\) −0.883908 + 1.53097i −0.102752 + 0.177972i
\(75\) 0 0
\(76\) −1.19556 + 0.169435i −0.137140 + 0.0194355i
\(77\) −2.15851 −0.245986
\(78\) 0 0
\(79\) −5.37760 + 9.31428i −0.605027 + 1.04794i 0.387020 + 0.922071i \(0.373504\pi\)
−0.992047 + 0.125867i \(0.959829\pi\)
\(80\) −1.68461 2.91783i −0.188345 0.326223i
\(81\) 0 0
\(82\) −6.26414 10.8498i −0.691759 1.19816i
\(83\) −0.386145 −0.0423850 −0.0211925 0.999775i \(-0.506746\pi\)
−0.0211925 + 0.999775i \(0.506746\pi\)
\(84\) 0 0
\(85\) 1.40392 + 2.43165i 0.152276 + 0.263750i
\(86\) −3.05166 5.28564i −0.329069 0.569965i
\(87\) 0 0
\(88\) −2.07121 −0.220791
\(89\) 3.37096 + 5.83867i 0.357321 + 0.618898i 0.987512 0.157542i \(-0.0503569\pi\)
−0.630191 + 0.776440i \(0.717024\pi\)
\(90\) 0 0
\(91\) 6.45591 + 11.1820i 0.676763 + 1.17219i
\(92\) 0.419737 0.727006i 0.0437606 0.0757957i
\(93\) 0 0
\(94\) −0.170828 −0.0176195
\(95\) 2.68758 + 3.43175i 0.275740 + 0.352090i
\(96\) 0 0
\(97\) 2.16484 3.74962i 0.219807 0.380716i −0.734942 0.678130i \(-0.762791\pi\)
0.954749 + 0.297414i \(0.0961240\pi\)
\(98\) 1.77359 3.07194i 0.179159 0.310313i
\(99\) 0 0
\(100\) 0.138510 0.239907i 0.0138510 0.0239907i
\(101\) −0.498699 0.863773i −0.0496224 0.0859486i 0.840147 0.542358i \(-0.182468\pi\)
−0.889770 + 0.456410i \(0.849135\pi\)
\(102\) 0 0
\(103\) −4.52737 −0.446095 −0.223047 0.974808i \(-0.571600\pi\)
−0.223047 + 0.974808i \(0.571600\pi\)
\(104\) 6.19478 + 10.7297i 0.607448 + 1.05213i
\(105\) 0 0
\(106\) −1.16238 −0.112900
\(107\) −18.6472 −1.80270 −0.901348 0.433096i \(-0.857421\pi\)
−0.901348 + 0.433096i \(0.857421\pi\)
\(108\) 0 0
\(109\) −5.72633 + 9.91830i −0.548483 + 0.950000i 0.449896 + 0.893081i \(0.351461\pi\)
−0.998379 + 0.0569194i \(0.981872\pi\)
\(110\) 0.454806 + 0.787748i 0.0433641 + 0.0751088i
\(111\) 0 0
\(112\) 5.24732 9.08863i 0.495825 0.858795i
\(113\) −18.2976 −1.72130 −0.860649 0.509199i \(-0.829942\pi\)
−0.860649 + 0.509199i \(0.829942\pi\)
\(114\) 0 0
\(115\) −3.03037 −0.282584
\(116\) 0.536347 0.928980i 0.0497986 0.0862537i
\(117\) 0 0
\(118\) 0.944420 + 1.63578i 0.0869409 + 0.150586i
\(119\) −4.37300 + 7.57427i −0.400873 + 0.694332i
\(120\) 0 0
\(121\) −10.5198 −0.956344
\(122\) −4.29423 −0.388781
\(123\) 0 0
\(124\) 0.0519071 + 0.0899058i 0.00466140 + 0.00807378i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −5.94672 10.3000i −0.527686 0.913979i −0.999479 0.0322694i \(-0.989727\pi\)
0.471793 0.881709i \(-0.343607\pi\)
\(128\) 4.20710 7.28691i 0.371859 0.644078i
\(129\) 0 0
\(130\) 2.72057 4.71216i 0.238609 0.413284i
\(131\) −6.09045 + 10.5490i −0.532125 + 0.921668i 0.467172 + 0.884167i \(0.345273\pi\)
−0.999297 + 0.0375009i \(0.988060\pi\)
\(132\) 0 0
\(133\) −5.07161 + 12.5946i −0.439764 + 1.09209i
\(134\) −14.2961 −1.23499
\(135\) 0 0
\(136\) −4.19612 + 7.26790i −0.359815 + 0.623217i
\(137\) 8.40697 + 14.5613i 0.718256 + 1.24406i 0.961690 + 0.274138i \(0.0883925\pi\)
−0.243435 + 0.969917i \(0.578274\pi\)
\(138\) 0 0
\(139\) −0.952762 1.65023i −0.0808122 0.139971i 0.822787 0.568350i \(-0.192418\pi\)
−0.903599 + 0.428379i \(0.859085\pi\)
\(140\) 0.862879 0.0729266
\(141\) 0 0
\(142\) −7.55709 13.0893i −0.634177 1.09843i
\(143\) −1.43627 2.48769i −0.120107 0.208031i
\(144\) 0 0
\(145\) −3.87226 −0.321574
\(146\) 3.12358 + 5.41019i 0.258509 + 0.447751i
\(147\) 0 0
\(148\) −0.186543 0.323102i −0.0153337 0.0265588i
\(149\) −0.145728 + 0.252409i −0.0119385 + 0.0206782i −0.871933 0.489625i \(-0.837134\pi\)
0.859994 + 0.510303i \(0.170467\pi\)
\(150\) 0 0
\(151\) 18.5750 1.51161 0.755807 0.654794i \(-0.227245\pi\)
0.755807 + 0.654794i \(0.227245\pi\)
\(152\) −4.86647 + 12.0852i −0.394723 + 0.980236i
\(153\) 0 0
\(154\) −1.41666 + 2.45372i −0.114158 + 0.197727i
\(155\) 0.187377 0.324546i 0.0150505 0.0260682i
\(156\) 0 0
\(157\) 9.88718 17.1251i 0.789083 1.36673i −0.137446 0.990509i \(-0.543890\pi\)
0.926529 0.376222i \(-0.122777\pi\)
\(158\) 7.05876 + 12.2261i 0.561565 + 0.972659i
\(159\) 0 0
\(160\) 1.55522 0.122951
\(161\) −4.71960 8.17458i −0.371956 0.644247i
\(162\) 0 0
\(163\) 15.7513 1.23374 0.616868 0.787066i \(-0.288401\pi\)
0.616868 + 0.787066i \(0.288401\pi\)
\(164\) 2.64401 0.206462
\(165\) 0 0
\(166\) −0.253432 + 0.438957i −0.0196701 + 0.0340696i
\(167\) −1.83465 3.17771i −0.141970 0.245898i 0.786269 0.617885i \(-0.212010\pi\)
−0.928238 + 0.371986i \(0.878677\pi\)
\(168\) 0 0
\(169\) −2.09148 + 3.62255i −0.160883 + 0.278658i
\(170\) 3.68563 0.282675
\(171\) 0 0
\(172\) 1.28807 0.0982141
\(173\) 3.50081 6.06357i 0.266161 0.461005i −0.701706 0.712467i \(-0.747578\pi\)
0.967867 + 0.251462i \(0.0809113\pi\)
\(174\) 0 0
\(175\) −1.55743 2.69755i −0.117731 0.203915i
\(176\) −1.16739 + 2.02198i −0.0879953 + 0.152412i
\(177\) 0 0
\(178\) 8.84960 0.663305
\(179\) −18.4828 −1.38147 −0.690735 0.723108i \(-0.742713\pi\)
−0.690735 + 0.723108i \(0.742713\pi\)
\(180\) 0 0
\(181\) 7.77997 + 13.4753i 0.578281 + 1.00161i 0.995677 + 0.0928869i \(0.0296095\pi\)
−0.417396 + 0.908725i \(0.637057\pi\)
\(182\) 16.9484 1.25630
\(183\) 0 0
\(184\) −4.52870 7.84393i −0.333860 0.578262i
\(185\) −0.673391 + 1.16635i −0.0495087 + 0.0857515i
\(186\) 0 0
\(187\) 0.972876 1.68507i 0.0711438 0.123225i
\(188\) 0.0180260 0.0312220i 0.00131468 0.00227710i
\(189\) 0 0
\(190\) 5.66499 0.802844i 0.410981 0.0582444i
\(191\) 6.07892 0.439855 0.219928 0.975516i \(-0.429418\pi\)
0.219928 + 0.975516i \(0.429418\pi\)
\(192\) 0 0
\(193\) −6.37309 + 11.0385i −0.458745 + 0.794570i −0.998895 0.0469988i \(-0.985034\pi\)
0.540150 + 0.841569i \(0.318368\pi\)
\(194\) −2.84162 4.92184i −0.204017 0.353367i
\(195\) 0 0
\(196\) 0.374303 + 0.648312i 0.0267359 + 0.0463080i
\(197\) −26.8916 −1.91595 −0.957975 0.286851i \(-0.907391\pi\)
−0.957975 + 0.286851i \(0.907391\pi\)
\(198\) 0 0
\(199\) 11.7248 + 20.3079i 0.831148 + 1.43959i 0.897129 + 0.441769i \(0.145649\pi\)
−0.0659811 + 0.997821i \(0.521018\pi\)
\(200\) −1.49443 2.58844i −0.105672 0.183030i
\(201\) 0 0
\(202\) −1.30921 −0.0921156
\(203\) −6.03077 10.4456i −0.423277 0.733138i
\(204\) 0 0
\(205\) −4.77223 8.26575i −0.333307 0.577305i
\(206\) −2.97136 + 5.14655i −0.207025 + 0.358577i
\(207\) 0 0
\(208\) 13.9662 0.968382
\(209\) 1.12830 2.80196i 0.0780459 0.193815i
\(210\) 0 0
\(211\) 4.77527 8.27101i 0.328743 0.569400i −0.653520 0.756910i \(-0.726708\pi\)
0.982263 + 0.187510i \(0.0600416\pi\)
\(212\) 0.122656 0.212447i 0.00842406 0.0145909i
\(213\) 0 0
\(214\) −12.2384 + 21.1975i −0.836599 + 1.44903i
\(215\) −2.32486 4.02677i −0.158554 0.274624i
\(216\) 0 0
\(217\) 1.16730 0.0792418
\(218\) 7.51651 + 13.0190i 0.509083 + 0.881757i
\(219\) 0 0
\(220\) −0.191968 −0.0129424
\(221\) −11.6391 −0.782932
\(222\) 0 0
\(223\) 6.59965 11.4309i 0.441945 0.765471i −0.555889 0.831257i \(-0.687622\pi\)
0.997834 + 0.0657855i \(0.0209553\pi\)
\(224\) 2.42215 + 4.19529i 0.161837 + 0.280310i
\(225\) 0 0
\(226\) −12.0090 + 20.8001i −0.798824 + 1.38360i
\(227\) −8.69848 −0.577339 −0.288669 0.957429i \(-0.593213\pi\)
−0.288669 + 0.957429i \(0.593213\pi\)
\(228\) 0 0
\(229\) 19.6107 1.29591 0.647955 0.761679i \(-0.275624\pi\)
0.647955 + 0.761679i \(0.275624\pi\)
\(230\) −1.98887 + 3.44482i −0.131142 + 0.227145i
\(231\) 0 0
\(232\) −5.78684 10.0231i −0.379925 0.658049i
\(233\) −13.9062 + 24.0863i −0.911027 + 1.57795i −0.0984108 + 0.995146i \(0.531376\pi\)
−0.812616 + 0.582799i \(0.801957\pi\)
\(234\) 0 0
\(235\) −0.130142 −0.00848954
\(236\) −0.398627 −0.0259484
\(237\) 0 0
\(238\) 5.74011 + 9.94216i 0.372076 + 0.644454i
\(239\) 23.5071 1.52055 0.760275 0.649601i \(-0.225064\pi\)
0.760275 + 0.649601i \(0.225064\pi\)
\(240\) 0 0
\(241\) −12.2817 21.2725i −0.791132 1.37028i −0.925266 0.379318i \(-0.876159\pi\)
0.134134 0.990963i \(-0.457175\pi\)
\(242\) −6.90426 + 11.9585i −0.443823 + 0.768723i
\(243\) 0 0
\(244\) 0.453134 0.784851i 0.0290089 0.0502449i
\(245\) 1.35118 2.34031i 0.0863235 0.149517i
\(246\) 0 0
\(247\) −17.8899 + 2.53536i −1.13831 + 0.161321i
\(248\) 1.12009 0.0711257
\(249\) 0 0
\(250\) −0.656312 + 1.13677i −0.0415088 + 0.0718953i
\(251\) −5.17195 8.95808i −0.326451 0.565429i 0.655354 0.755322i \(-0.272519\pi\)
−0.981805 + 0.189893i \(0.939186\pi\)
\(252\) 0 0
\(253\) 1.04998 + 1.81863i 0.0660119 + 0.114336i
\(254\) −15.6116 −0.979559
\(255\) 0 0
\(256\) 3.25752 + 5.64219i 0.203595 + 0.352637i
\(257\) 1.34568 + 2.33079i 0.0839413 + 0.145391i 0.904940 0.425540i \(-0.139916\pi\)
−0.820998 + 0.570931i \(0.806583\pi\)
\(258\) 0 0
\(259\) −4.19504 −0.260667
\(260\) 0.574157 + 0.994469i 0.0356077 + 0.0616743i
\(261\) 0 0
\(262\) 7.99447 + 13.8468i 0.493900 + 0.855459i
\(263\) −7.57261 + 13.1161i −0.466947 + 0.808776i −0.999287 0.0377547i \(-0.987979\pi\)
0.532340 + 0.846531i \(0.321313\pi\)
\(264\) 0 0
\(265\) −0.885540 −0.0543983
\(266\) 10.9885 + 14.0312i 0.673750 + 0.860308i
\(267\) 0 0
\(268\) 1.50855 2.61288i 0.0921492 0.159607i
\(269\) −5.03811 + 8.72626i −0.307179 + 0.532050i −0.977744 0.209801i \(-0.932718\pi\)
0.670565 + 0.741851i \(0.266052\pi\)
\(270\) 0 0
\(271\) 9.60942 16.6440i 0.583730 1.01105i −0.411302 0.911499i \(-0.634926\pi\)
0.995032 0.0995516i \(-0.0317408\pi\)
\(272\) 4.73010 + 8.19278i 0.286805 + 0.496760i
\(273\) 0 0
\(274\) 22.0704 1.33332
\(275\) 0.346487 + 0.600132i 0.0208939 + 0.0361893i
\(276\) 0 0
\(277\) 14.3594 0.862771 0.431386 0.902168i \(-0.358025\pi\)
0.431386 + 0.902168i \(0.358025\pi\)
\(278\) −2.50123 −0.150014
\(279\) 0 0
\(280\) 4.65496 8.06262i 0.278187 0.481834i
\(281\) 9.65362 + 16.7206i 0.575887 + 0.997465i 0.995945 + 0.0899676i \(0.0286764\pi\)
−0.420058 + 0.907497i \(0.637990\pi\)
\(282\) 0 0
\(283\) −16.2313 + 28.1134i −0.964850 + 1.67117i −0.254831 + 0.966986i \(0.582020\pi\)
−0.710018 + 0.704183i \(0.751313\pi\)
\(284\) 3.18975 0.189277
\(285\) 0 0
\(286\) −3.77056 −0.222958
\(287\) 14.8648 25.7466i 0.877443 1.51978i
\(288\) 0 0
\(289\) 4.55804 + 7.89475i 0.268120 + 0.464397i
\(290\) −2.54141 + 4.40185i −0.149237 + 0.258486i
\(291\) 0 0
\(292\) −1.31842 −0.0771546
\(293\) −7.22833 −0.422283 −0.211142 0.977455i \(-0.567718\pi\)
−0.211142 + 0.977455i \(0.567718\pi\)
\(294\) 0 0
\(295\) 0.719490 + 1.24619i 0.0418904 + 0.0725562i
\(296\) −4.02535 −0.233969
\(297\) 0 0
\(298\) 0.191287 + 0.331318i 0.0110809 + 0.0191927i
\(299\) 6.28080 10.8787i 0.363228 0.629130i
\(300\) 0 0
\(301\) 7.24161 12.5428i 0.417400 0.722957i
\(302\) 12.1910 21.1155i 0.701514 1.21506i
\(303\) 0 0
\(304\) 9.05504 + 11.5623i 0.519342 + 0.663145i
\(305\) −3.27149 −0.187325
\(306\) 0 0
\(307\) 6.69667 11.5990i 0.382199 0.661989i −0.609177 0.793034i \(-0.708500\pi\)
0.991376 + 0.131046i \(0.0418334\pi\)
\(308\) −0.298976 0.517842i −0.0170357 0.0295068i
\(309\) 0 0
\(310\) −0.245955 0.426007i −0.0139693 0.0241956i
\(311\) −19.0587 −1.08072 −0.540361 0.841433i \(-0.681712\pi\)
−0.540361 + 0.841433i \(0.681712\pi\)
\(312\) 0 0
\(313\) −5.47738 9.48711i −0.309600 0.536243i 0.668675 0.743555i \(-0.266862\pi\)
−0.978275 + 0.207312i \(0.933528\pi\)
\(314\) −12.9781 22.4788i −0.732399 1.26855i
\(315\) 0 0
\(316\) −2.97941 −0.167605
\(317\) 5.04659 + 8.74096i 0.283445 + 0.490941i 0.972231 0.234024i \(-0.0751893\pi\)
−0.688786 + 0.724965i \(0.741856\pi\)
\(318\) 0 0
\(319\) 1.34169 + 2.32387i 0.0751200 + 0.130112i
\(320\) 4.38993 7.60358i 0.245405 0.425053i
\(321\) 0 0
\(322\) −12.3901 −0.690473
\(323\) −7.54627 9.63579i −0.419886 0.536150i
\(324\) 0 0
\(325\) 2.07262 3.58988i 0.114968 0.199131i
\(326\) 10.3378 17.9055i 0.572556 0.991695i
\(327\) 0 0
\(328\) 14.2636 24.7052i 0.787574 1.36412i
\(329\) −0.202687 0.351065i −0.0111745 0.0193548i
\(330\) 0 0
\(331\) −1.50229 −0.0825736 −0.0412868 0.999147i \(-0.513146\pi\)
−0.0412868 + 0.999147i \(0.513146\pi\)
\(332\) −0.0534850 0.0926388i −0.00293537 0.00508421i
\(333\) 0 0
\(334\) −4.81641 −0.263542
\(335\) −10.8912 −0.595052
\(336\) 0 0
\(337\) 1.46673 2.54045i 0.0798980 0.138387i −0.823308 0.567595i \(-0.807874\pi\)
0.903206 + 0.429208i \(0.141207\pi\)
\(338\) 2.74533 + 4.75505i 0.149326 + 0.258641i
\(339\) 0 0
\(340\) −0.388913 + 0.673617i −0.0210918 + 0.0365320i
\(341\) −0.259694 −0.0140632
\(342\) 0 0
\(343\) −13.3866 −0.722807
\(344\) 6.94870 12.0355i 0.374649 0.648911i
\(345\) 0 0
\(346\) −4.59524 7.95919i −0.247042 0.427889i
\(347\) 4.86657 8.42915i 0.261251 0.452501i −0.705323 0.708886i \(-0.749198\pi\)
0.966575 + 0.256385i \(0.0825315\pi\)
\(348\) 0 0
\(349\) 12.0493 0.644987 0.322493 0.946572i \(-0.395479\pi\)
0.322493 + 0.946572i \(0.395479\pi\)
\(350\) −4.08864 −0.218547
\(351\) 0 0
\(352\) −0.538864 0.933340i −0.0287215 0.0497472i
\(353\) 26.1484 1.39174 0.695870 0.718168i \(-0.255019\pi\)
0.695870 + 0.718168i \(0.255019\pi\)
\(354\) 0 0
\(355\) −5.75724 9.97184i −0.305563 0.529250i
\(356\) −0.933824 + 1.61743i −0.0494926 + 0.0857236i
\(357\) 0 0
\(358\) −12.1305 + 21.0106i −0.641116 + 1.11045i
\(359\) 16.6763 28.8843i 0.880144 1.52445i 0.0289631 0.999580i \(-0.490779\pi\)
0.851181 0.524873i \(-0.175887\pi\)
\(360\) 0 0
\(361\) −13.6979 13.1669i −0.720945 0.692993i
\(362\) 20.4243 1.07348
\(363\) 0 0
\(364\) −1.78842 + 3.09763i −0.0937386 + 0.162360i
\(365\) 2.37964 + 4.12166i 0.124556 + 0.215738i
\(366\) 0 0
\(367\) −6.49560 11.2507i −0.339068 0.587283i 0.645190 0.764022i \(-0.276778\pi\)
−0.984258 + 0.176740i \(0.943445\pi\)
\(368\) −10.2100 −0.532233
\(369\) 0 0
\(370\) 0.883908 + 1.53097i 0.0459522 + 0.0795916i
\(371\) −1.37917 2.38879i −0.0716028 0.124020i
\(372\) 0 0
\(373\) −36.5438 −1.89216 −0.946082 0.323926i \(-0.894997\pi\)
−0.946082 + 0.323926i \(0.894997\pi\)
\(374\) −1.27702 2.21186i −0.0660331 0.114373i
\(375\) 0 0
\(376\) −0.194489 0.336865i −0.0100300 0.0173725i
\(377\) 8.02571 13.9009i 0.413345 0.715935i
\(378\) 0 0
\(379\) −32.7622 −1.68288 −0.841441 0.540350i \(-0.818292\pi\)
−0.841441 + 0.540350i \(0.818292\pi\)
\(380\) −0.451043 + 1.12010i −0.0231380 + 0.0574599i
\(381\) 0 0
\(382\) 3.98967 6.91030i 0.204129 0.353562i
\(383\) 19.3221 33.4669i 0.987315 1.71008i 0.356153 0.934428i \(-0.384088\pi\)
0.631162 0.775651i \(-0.282578\pi\)
\(384\) 0 0
\(385\) −1.07926 + 1.86933i −0.0550040 + 0.0952698i
\(386\) 8.36547 + 14.4894i 0.425791 + 0.737492i
\(387\) 0 0
\(388\) 1.19941 0.0608909
\(389\) 17.7295 + 30.7085i 0.898923 + 1.55698i 0.828873 + 0.559437i \(0.188983\pi\)
0.0700500 + 0.997543i \(0.477684\pi\)
\(390\) 0 0
\(391\) 8.50878 0.430308
\(392\) 8.07698 0.407949
\(393\) 0 0
\(394\) −17.6493 + 30.5695i −0.889159 + 1.54007i
\(395\) 5.37760 + 9.31428i 0.270576 + 0.468652i
\(396\) 0 0
\(397\) −6.08814 + 10.5450i −0.305555 + 0.529237i −0.977385 0.211469i \(-0.932175\pi\)
0.671830 + 0.740706i \(0.265509\pi\)
\(398\) 30.7804 1.54288
\(399\) 0 0
\(400\) −3.36922 −0.168461
\(401\) −15.4557 + 26.7701i −0.771822 + 1.33684i 0.164741 + 0.986337i \(0.447321\pi\)
−0.936563 + 0.350498i \(0.886012\pi\)
\(402\) 0 0
\(403\) 0.776720 + 1.34532i 0.0386912 + 0.0670151i
\(404\) 0.138150 0.239282i 0.00687321 0.0119047i
\(405\) 0 0
\(406\) −15.8323 −0.785742
\(407\) 0.933283 0.0462611
\(408\) 0 0
\(409\) −6.96184 12.0583i −0.344241 0.596243i 0.640975 0.767562i \(-0.278530\pi\)
−0.985216 + 0.171319i \(0.945197\pi\)
\(410\) −12.5283 −0.618728
\(411\) 0 0
\(412\) −0.627086 1.08614i −0.0308943 0.0535105i
\(413\) −2.24111 + 3.88172i −0.110278 + 0.191007i
\(414\) 0 0
\(415\) −0.193073 + 0.334412i −0.00947757 + 0.0164156i
\(416\) −3.22338 + 5.58306i −0.158039 + 0.273732i
\(417\) 0 0
\(418\) −2.44465 3.12157i −0.119572 0.152681i
\(419\) 19.7638 0.965525 0.482763 0.875751i \(-0.339633\pi\)
0.482763 + 0.875751i \(0.339633\pi\)
\(420\) 0 0
\(421\) 1.07302 1.85853i 0.0522959 0.0905791i −0.838692 0.544605i \(-0.816679\pi\)
0.890988 + 0.454026i \(0.150013\pi\)
\(422\) −6.26813 10.8567i −0.305128 0.528497i
\(423\) 0 0
\(424\) −1.32338 2.29216i −0.0642691 0.111317i
\(425\) 2.80783 0.136200
\(426\) 0 0
\(427\) −5.09511 8.82499i −0.246570 0.427071i
\(428\) −2.58283 4.47359i −0.124846 0.216239i
\(429\) 0 0
\(430\) −6.10333 −0.294329
\(431\) −14.0250 24.2920i −0.675559 1.17010i −0.976305 0.216398i \(-0.930569\pi\)
0.300746 0.953704i \(-0.402764\pi\)
\(432\) 0 0
\(433\) 5.38799 + 9.33227i 0.258930 + 0.448480i 0.965956 0.258708i \(-0.0832967\pi\)
−0.707025 + 0.707188i \(0.749963\pi\)
\(434\) 0.766116 1.32695i 0.0367747 0.0636957i
\(435\) 0 0
\(436\) −3.17262 −0.151941
\(437\) 13.0784 1.85348i 0.625625 0.0886638i
\(438\) 0 0
\(439\) 9.03536 15.6497i 0.431234 0.746920i −0.565745 0.824580i \(-0.691412\pi\)
0.996980 + 0.0776600i \(0.0247449\pi\)
\(440\) −1.03560 + 1.79372i −0.0493704 + 0.0855121i
\(441\) 0 0
\(442\) −7.63889 + 13.2310i −0.363345 + 0.629332i
\(443\) 1.78684 + 3.09491i 0.0848956 + 0.147043i 0.905347 0.424673i \(-0.139611\pi\)
−0.820451 + 0.571717i \(0.806278\pi\)
\(444\) 0 0
\(445\) 6.74192 0.319598
\(446\) −8.66285 15.0045i −0.410198 0.710483i
\(447\) 0 0
\(448\) 27.3480 1.29207
\(449\) 12.7199 0.600291 0.300145 0.953893i \(-0.402965\pi\)
0.300145 + 0.953893i \(0.402965\pi\)
\(450\) 0 0
\(451\) −3.30703 + 5.72794i −0.155722 + 0.269718i
\(452\) −2.53441 4.38972i −0.119209 0.206475i
\(453\) 0 0
\(454\) −5.70892 + 9.88813i −0.267933 + 0.464073i
\(455\) 12.9118 0.605316
\(456\) 0 0
\(457\) 29.7579 1.39202 0.696008 0.718034i \(-0.254958\pi\)
0.696008 + 0.718034i \(0.254958\pi\)
\(458\) 12.8707 22.2927i 0.601409 1.04167i
\(459\) 0 0
\(460\) −0.419737 0.727006i −0.0195704 0.0338969i
\(461\) −17.2888 + 29.9450i −0.805218 + 1.39468i 0.110926 + 0.993829i \(0.464618\pi\)
−0.916144 + 0.400850i \(0.868715\pi\)
\(462\) 0 0
\(463\) 0.783874 0.0364297 0.0182149 0.999834i \(-0.494202\pi\)
0.0182149 + 0.999834i \(0.494202\pi\)
\(464\) −13.0465 −0.605668
\(465\) 0 0
\(466\) 18.2536 + 31.6162i 0.845583 + 1.46459i
\(467\) 14.2134 0.657720 0.328860 0.944379i \(-0.393336\pi\)
0.328860 + 0.944379i \(0.393336\pi\)
\(468\) 0 0
\(469\) −16.9623 29.3796i −0.783248 1.35663i
\(470\) −0.0854138 + 0.147941i −0.00393985 + 0.00682401i
\(471\) 0 0
\(472\) −2.15046 + 3.72471i −0.0989831 + 0.171444i
\(473\) −1.61107 + 2.79045i −0.0740769 + 0.128305i
\(474\) 0 0
\(475\) 4.31577 0.611633i 0.198021 0.0280637i
\(476\) −2.42282 −0.111050
\(477\) 0 0
\(478\) 15.4280 26.7221i 0.705660 1.22224i
\(479\) −9.33951 16.1765i −0.426733 0.739123i 0.569848 0.821750i \(-0.307002\pi\)
−0.996581 + 0.0826272i \(0.973669\pi\)
\(480\) 0 0
\(481\) −2.79136 4.83478i −0.127275 0.220447i
\(482\) −32.2424 −1.46860
\(483\) 0 0
\(484\) −1.45710 2.52377i −0.0662317 0.114717i
\(485\) −2.16484 3.74962i −0.0983005 0.170261i
\(486\) 0 0
\(487\) −14.6054 −0.661833 −0.330916 0.943660i \(-0.607358\pi\)
−0.330916 + 0.943660i \(0.607358\pi\)
\(488\) −4.88902 8.46804i −0.221316 0.383330i
\(489\) 0 0
\(490\) −1.77359 3.07194i −0.0801225 0.138776i
\(491\) 1.65767 2.87116i 0.0748094 0.129574i −0.826194 0.563386i \(-0.809499\pi\)
0.901003 + 0.433812i \(0.142832\pi\)
\(492\) 0 0
\(493\) 10.8727 0.489680
\(494\) −8.85923 + 22.0006i −0.398596 + 0.989854i
\(495\) 0 0
\(496\) 0.631313 1.09347i 0.0283468 0.0490981i
\(497\) 17.9330 31.0609i 0.804405 1.39327i
\(498\) 0 0
\(499\) 4.63324 8.02501i 0.207412 0.359249i −0.743486 0.668751i \(-0.766829\pi\)
0.950899 + 0.309502i \(0.100162\pi\)
\(500\) −0.138510 0.239907i −0.00619436 0.0107289i
\(501\) 0 0
\(502\) −13.5776 −0.606000
\(503\) −16.6005 28.7530i −0.740181 1.28203i −0.952413 0.304812i \(-0.901406\pi\)
0.212231 0.977219i \(-0.431927\pi\)
\(504\) 0 0
\(505\) −0.997399 −0.0443837
\(506\) 2.75647 0.122540
\(507\) 0 0
\(508\) 1.64736 2.85331i 0.0730898 0.126595i
\(509\) 18.3832 + 31.8406i 0.814820 + 1.41131i 0.909457 + 0.415798i \(0.136498\pi\)
−0.0946365 + 0.995512i \(0.530169\pi\)
\(510\) 0 0
\(511\) −7.41226 + 12.8384i −0.327899 + 0.567938i
\(512\) 25.3802 1.12166
\(513\) 0 0
\(514\) 3.53274 0.155823
\(515\) −2.26368 + 3.92081i −0.0997498 + 0.172772i
\(516\) 0 0
\(517\) 0.0450925 + 0.0781025i 0.00198317 + 0.00343495i
\(518\) −2.75325 + 4.76877i −0.120971 + 0.209528i
\(519\) 0 0
\(520\) 12.3896 0.543318
\(521\) 5.40142 0.236640 0.118320 0.992975i \(-0.462249\pi\)
0.118320 + 0.992975i \(0.462249\pi\)
\(522\) 0 0
\(523\) −5.04334 8.73533i −0.220530 0.381969i 0.734439 0.678675i \(-0.237445\pi\)
−0.954969 + 0.296705i \(0.904112\pi\)
\(524\) −3.37435 −0.147409
\(525\) 0 0
\(526\) 9.93998 + 17.2166i 0.433404 + 0.750677i
\(527\) −0.526123 + 0.911271i −0.0229183 + 0.0396956i
\(528\) 0 0
\(529\) 6.90842 11.9657i 0.300366 0.520249i
\(530\) −0.581190 + 1.00665i −0.0252453 + 0.0437261i
\(531\) 0 0
\(532\) −3.72399 + 0.527765i −0.161455 + 0.0228815i
\(533\) 39.5640 1.71371
\(534\) 0 0
\(535\) −9.32362 + 16.1490i −0.403095 + 0.698181i
\(536\) −16.2763 28.1913i −0.703027 1.21768i
\(537\) 0 0
\(538\) 6.61314 + 11.4543i 0.285113 + 0.493830i
\(539\) −1.87266 −0.0806611
\(540\) 0 0
\(541\) −4.85048 8.40128i −0.208538 0.361199i 0.742716 0.669607i \(-0.233537\pi\)
−0.951254 + 0.308407i \(0.900204\pi\)
\(542\) −12.6135 21.8473i −0.541798 0.938422i
\(543\) 0 0
\(544\) −4.36681 −0.187225
\(545\) 5.72633 + 9.91830i 0.245289 + 0.424853i
\(546\) 0 0
\(547\) −2.05849 3.56540i −0.0880145 0.152446i 0.818657 0.574282i \(-0.194719\pi\)
−0.906672 + 0.421837i \(0.861386\pi\)
\(548\) −2.32890 + 4.03377i −0.0994857 + 0.172314i
\(549\) 0 0
\(550\) 0.909613 0.0387860
\(551\) 16.7118 2.36840i 0.711947 0.100897i
\(552\) 0 0
\(553\) −16.7505 + 29.0127i −0.712302 + 1.23374i
\(554\) 9.42422 16.3232i 0.400397 0.693508i
\(555\) 0 0
\(556\) 0.263934 0.457147i 0.0111933 0.0193874i
\(557\) 16.8094 + 29.1147i 0.712237 + 1.23363i 0.964016 + 0.265846i \(0.0856512\pi\)
−0.251779 + 0.967785i \(0.581015\pi\)
\(558\) 0 0
\(559\) 19.2742 0.815211
\(560\) −5.24732 9.08863i −0.221740 0.384065i
\(561\) 0 0
\(562\) 25.3431 1.06904
\(563\) −34.8168 −1.46735 −0.733677 0.679498i \(-0.762198\pi\)
−0.733677 + 0.679498i \(0.762198\pi\)
\(564\) 0 0
\(565\) −9.14882 + 15.8462i −0.384894 + 0.666656i
\(566\) 21.3056 + 36.9023i 0.895539 + 1.55112i
\(567\) 0 0
\(568\) 17.2076 29.8045i 0.722017 1.25057i
\(569\) 35.0377 1.46886 0.734429 0.678686i \(-0.237450\pi\)
0.734429 + 0.678686i \(0.237450\pi\)
\(570\) 0 0
\(571\) 35.7203 1.49485 0.747424 0.664347i \(-0.231290\pi\)
0.747424 + 0.664347i \(0.231290\pi\)
\(572\) 0.397875 0.689140i 0.0166360 0.0288144i
\(573\) 0 0
\(574\) −19.5119 33.7956i −0.814412 1.41060i
\(575\) −1.51519 + 2.62438i −0.0631877 + 0.109444i
\(576\) 0 0
\(577\) 28.5678 1.18929 0.594647 0.803987i \(-0.297292\pi\)
0.594647 + 0.803987i \(0.297292\pi\)
\(578\) 11.9660 0.497719
\(579\) 0 0
\(580\) −0.536347 0.928980i −0.0222706 0.0385738i
\(581\) −1.20279 −0.0499001
\(582\) 0 0
\(583\) 0.306828 + 0.531441i 0.0127075 + 0.0220100i
\(584\) −7.11245 + 12.3191i −0.294315 + 0.509769i
\(585\) 0 0
\(586\) −4.74404 + 8.21691i −0.195974 + 0.339437i
\(587\) 10.8661 18.8206i 0.448492 0.776811i −0.549796 0.835299i \(-0.685295\pi\)
0.998288 + 0.0584879i \(0.0186279\pi\)
\(588\) 0 0
\(589\) −0.610173 + 1.51527i −0.0251417 + 0.0624357i
\(590\) 1.88884 0.0777623
\(591\) 0 0
\(592\) −2.26880 + 3.92968i −0.0932472 + 0.161509i
\(593\) −4.15459 7.19595i −0.170608 0.295502i 0.768024 0.640421i \(-0.221240\pi\)
−0.938633 + 0.344918i \(0.887907\pi\)
\(594\) 0 0
\(595\) 4.37300 + 7.57427i 0.179276 + 0.310515i
\(596\) −0.0807395 −0.00330722
\(597\) 0 0
\(598\) −8.24433 14.2796i −0.337136 0.583936i
\(599\) −7.98082 13.8232i −0.326087 0.564800i 0.655644 0.755070i \(-0.272397\pi\)
−0.981732 + 0.190270i \(0.939064\pi\)
\(600\) 0 0
\(601\) 10.2096 0.416457 0.208228 0.978080i \(-0.433230\pi\)
0.208228 + 0.978080i \(0.433230\pi\)
\(602\) −9.50551 16.4640i −0.387416 0.671024i
\(603\) 0 0
\(604\) 2.57283 + 4.45627i 0.104687 + 0.181323i
\(605\) −5.25989 + 9.11040i −0.213845 + 0.370391i
\(606\) 0 0
\(607\) −11.4506 −0.464764 −0.232382 0.972625i \(-0.574652\pi\)
−0.232382 + 0.972625i \(0.574652\pi\)
\(608\) −6.71199 + 0.951226i −0.272207 + 0.0385773i
\(609\) 0 0
\(610\) −2.14711 + 3.71891i −0.0869341 + 0.150574i
\(611\) 0.269735 0.467195i 0.0109123 0.0189007i
\(612\) 0 0
\(613\) 13.0849 22.6637i 0.528494 0.915378i −0.470954 0.882158i \(-0.656090\pi\)
0.999448 0.0332202i \(-0.0105763\pi\)
\(614\) −8.79021 15.2251i −0.354744 0.614435i
\(615\) 0 0
\(616\) −6.45152 −0.259939
\(617\) 15.2975 + 26.4961i 0.615854 + 1.06669i 0.990234 + 0.139416i \(0.0445224\pi\)
−0.374379 + 0.927276i \(0.622144\pi\)
\(618\) 0 0
\(619\) 28.4931 1.14523 0.572616 0.819823i \(-0.305928\pi\)
0.572616 + 0.819823i \(0.305928\pi\)
\(620\) 0.103814 0.00416928
\(621\) 0 0
\(622\) −12.5085 + 21.6653i −0.501544 + 0.868700i
\(623\) 10.5001 + 18.1866i 0.420676 + 0.728633i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −14.3795 −0.574720
\(627\) 0 0
\(628\) 5.47790 0.218592
\(629\) 1.89077 3.27491i 0.0753899 0.130579i
\(630\) 0 0
\(631\) 5.50411 + 9.53340i 0.219115 + 0.379518i 0.954538 0.298090i \(-0.0963496\pi\)
−0.735423 + 0.677609i \(0.763016\pi\)
\(632\) −16.0729 + 27.8392i −0.639347 + 1.10738i
\(633\) 0 0
\(634\) 13.2486 0.526167
\(635\) −11.8934 −0.471976
\(636\) 0 0
\(637\) 5.60094 + 9.70112i 0.221918 + 0.384372i
\(638\) 3.52226 0.139447
\(639\) 0 0
\(640\) −4.20710 7.28691i −0.166300 0.288041i
\(641\) 11.0021 19.0562i 0.434557 0.752675i −0.562702 0.826660i \(-0.690238\pi\)
0.997259 + 0.0739847i \(0.0235716\pi\)
\(642\) 0 0
\(643\) −23.4637 + 40.6403i −0.925319 + 1.60270i −0.134271 + 0.990945i \(0.542869\pi\)
−0.791048 + 0.611754i \(0.790464\pi\)
\(644\) 1.30742 2.26452i 0.0515197 0.0892347i
\(645\) 0 0
\(646\) −15.9063 + 2.25425i −0.625826 + 0.0886924i
\(647\) 0.973639 0.0382777 0.0191389 0.999817i \(-0.493908\pi\)
0.0191389 + 0.999817i \(0.493908\pi\)
\(648\) 0 0
\(649\) 0.498588 0.863579i 0.0195713 0.0338984i
\(650\) −2.72057 4.71216i −0.106709 0.184826i
\(651\) 0 0
\(652\) 2.18171 + 3.77884i 0.0854425 + 0.147991i
\(653\) −43.3819 −1.69766 −0.848832 0.528662i \(-0.822694\pi\)
−0.848832 + 0.528662i \(0.822694\pi\)
\(654\) 0 0
\(655\) 6.09045 + 10.5490i 0.237974 + 0.412182i
\(656\) −16.0787 27.8491i −0.627767 1.08733i
\(657\) 0 0
\(658\) −0.532104 −0.0207436
\(659\) −1.95482 3.38584i −0.0761489 0.131894i 0.825436 0.564495i \(-0.190929\pi\)
−0.901585 + 0.432601i \(0.857596\pi\)
\(660\) 0 0
\(661\) 19.3249 + 33.4717i 0.751652 + 1.30190i 0.947022 + 0.321169i \(0.104076\pi\)
−0.195370 + 0.980730i \(0.562591\pi\)
\(662\) −0.985973 + 1.70776i −0.0383209 + 0.0663738i
\(663\) 0 0
\(664\) −1.15414 −0.0447892
\(665\) 8.37143 + 10.6894i 0.324630 + 0.414518i
\(666\) 0 0
\(667\) −5.86720 + 10.1623i −0.227179 + 0.393485i
\(668\) 0.508235 0.880289i 0.0196642 0.0340594i
\(669\) 0 0
\(670\) −7.14805 + 12.3808i −0.276153 + 0.478311i
\(671\) 1.13353 + 1.96332i 0.0437593 + 0.0757933i
\(672\) 0 0
\(673\) −19.0257 −0.733387 −0.366693 0.930342i \(-0.619510\pi\)
−0.366693 + 0.930342i \(0.619510\pi\)
\(674\) −1.92527 3.33466i −0.0741585 0.128446i
\(675\) 0 0
\(676\) −1.15877 −0.0445679
\(677\) 3.39483 0.130474 0.0652369 0.997870i \(-0.479220\pi\)
0.0652369 + 0.997870i \(0.479220\pi\)
\(678\) 0 0
\(679\) 6.74319 11.6795i 0.258780 0.448220i
\(680\) 4.19612 + 7.26790i 0.160914 + 0.278711i
\(681\) 0 0
\(682\) −0.170440 + 0.295211i −0.00652649 + 0.0113042i
\(683\) −6.42057 −0.245676 −0.122838 0.992427i \(-0.539200\pi\)
−0.122838 + 0.992427i \(0.539200\pi\)
\(684\) 0 0
\(685\) 16.8139 0.642427
\(686\) −8.78576 + 15.2174i −0.335442 + 0.581002i
\(687\) 0 0
\(688\) −7.83296 13.5671i −0.298629 0.517240i
\(689\) 1.83539 3.17898i 0.0699226 0.121110i
\(690\) 0 0
\(691\) 9.32092 0.354584 0.177292 0.984158i \(-0.443266\pi\)
0.177292 + 0.984158i \(0.443266\pi\)
\(692\) 1.93959 0.0737321
\(693\) 0 0
\(694\) −6.38798 11.0643i −0.242484 0.419995i
\(695\) −1.90552 −0.0722806
\(696\) 0 0
\(697\) 13.3996 + 23.2088i 0.507547 + 0.879097i
\(698\) 7.90813 13.6973i 0.299327 0.518450i
\(699\) 0 0
\(700\) 0.431440 0.747275i 0.0163069 0.0282443i
\(701\) −12.1943 + 21.1211i −0.460572 + 0.797735i −0.998990 0.0449438i \(-0.985689\pi\)
0.538417 + 0.842678i \(0.319022\pi\)
\(702\) 0 0
\(703\) 2.19283 5.44556i 0.0827040 0.205383i
\(704\) −6.08421 −0.229307
\(705\) 0 0
\(706\) 17.1615 29.7246i 0.645882 1.11870i
\(707\) −1.55338 2.69053i −0.0584208 0.101188i
\(708\) 0 0
\(709\) −8.78866 15.2224i −0.330065 0.571689i 0.652459 0.757824i \(-0.273737\pi\)
−0.982524 + 0.186135i \(0.940404\pi\)
\(710\) −15.1142 −0.567225
\(711\) 0 0
\(712\) 10.0754 + 17.4510i 0.377590 + 0.654005i
\(713\) −0.567822 0.983496i −0.0212651 0.0368322i
\(714\) 0 0
\(715\) −2.87254 −0.107427
\(716\) −2.56006 4.43415i −0.0956738 0.165712i
\(717\) 0 0
\(718\) −21.8898 37.9142i −0.816918 1.41494i
\(719\) 9.54695 16.5358i 0.356041 0.616681i −0.631255 0.775576i \(-0.717460\pi\)
0.987296 + 0.158895i \(0.0507930\pi\)
\(720\) 0 0
\(721\) −14.1021 −0.525190
\(722\) −23.9577 + 6.92979i −0.891615 + 0.257900i
\(723\) 0 0
\(724\) −2.15521 + 3.73293i −0.0800977 + 0.138733i
\(725\) −1.93613 + 3.35348i −0.0719061 + 0.124545i
\(726\) 0 0
\(727\) −0.846286 + 1.46581i −0.0313870 + 0.0543639i −0.881292 0.472572i \(-0.843326\pi\)
0.849905 + 0.526936i \(0.176659\pi\)
\(728\) 19.2959 + 33.4214i 0.715153 + 1.23868i
\(729\) 0 0
\(730\) 6.24715 0.231217
\(731\) 6.52782 + 11.3065i 0.241440 + 0.418186i
\(732\) 0 0
\(733\) −18.4707 −0.682233 −0.341116 0.940021i \(-0.610805\pi\)
−0.341116 + 0.940021i \(0.610805\pi\)
\(734\) −17.0526 −0.629422
\(735\) 0 0
\(736\) 2.35645 4.08150i 0.0868601 0.150446i
\(737\) 3.77367 + 6.53619i 0.139005 + 0.240763i
\(738\) 0 0
\(739\) 8.97295 15.5416i 0.330075 0.571707i −0.652451 0.757831i \(-0.726259\pi\)
0.982526 + 0.186124i \(0.0595925\pi\)
\(740\) −0.373086 −0.0137149
\(741\) 0 0
\(742\) −3.62065 −0.132918
\(743\) −15.3279 + 26.5486i −0.562324 + 0.973975i 0.434969 + 0.900446i \(0.356759\pi\)
−0.997293 + 0.0735289i \(0.976574\pi\)
\(744\) 0 0
\(745\) 0.145728 + 0.252409i 0.00533908 + 0.00924756i
\(746\) −23.9841 + 41.5417i −0.878120 + 1.52095i
\(747\) 0 0
\(748\) 0.539013 0.0197083
\(749\) −58.0835 −2.12233
\(750\) 0 0
\(751\) −13.8978 24.0717i −0.507139 0.878390i −0.999966 0.00826290i \(-0.997370\pi\)
0.492827 0.870127i \(-0.335964\pi\)
\(752\) −0.438478 −0.0159896
\(753\) 0 0
\(754\) −10.5347 18.2467i −0.383652 0.664506i
\(755\) 9.28752 16.0865i 0.338007 0.585446i
\(756\) 0 0
\(757\) 3.66800 6.35317i 0.133316 0.230910i −0.791637 0.610992i \(-0.790771\pi\)
0.924953 + 0.380082i \(0.124104\pi\)
\(758\) −21.5022 + 37.2429i −0.780996 + 1.35272i
\(759\) 0 0
\(760\) 8.03282 + 10.2571i 0.291381 + 0.372063i
\(761\) 32.6306 1.18286 0.591430 0.806356i \(-0.298564\pi\)
0.591430 + 0.806356i \(0.298564\pi\)
\(762\) 0 0
\(763\) −17.8367 + 30.8941i −0.645733 + 1.11844i
\(764\) 0.841992 + 1.45837i 0.0304622 + 0.0527621i
\(765\) 0 0
\(766\) −25.3627 43.9294i −0.916391 1.58724i
\(767\) −5.96491 −0.215381
\(768\) 0 0
\(769\) 15.2386 + 26.3941i 0.549519 + 0.951796i 0.998307 + 0.0581573i \(0.0185225\pi\)
−0.448788 + 0.893638i \(0.648144\pi\)
\(770\) 1.41666 + 2.45372i 0.0510528 + 0.0884261i
\(771\) 0 0
\(772\) −3.53095 −0.127082
\(773\) 19.9777 + 34.6024i 0.718548 + 1.24456i 0.961575 + 0.274542i \(0.0885263\pi\)
−0.243027 + 0.970020i \(0.578140\pi\)
\(774\) 0 0
\(775\) −0.187377 0.324546i −0.00673077 0.0116580i
\(776\) 6.47044 11.2071i 0.232275 0.402312i
\(777\) 0 0
\(778\) 46.5444 1.66870
\(779\) 25.6515 + 32.7542i 0.919059 + 1.17354i
\(780\) 0 0
\(781\) −3.98961 + 6.91022i −0.142760 + 0.247267i
\(782\) 5.58441 9.67249i 0.199698 0.345888i
\(783\) 0 0
\(784\) 4.55241 7.88501i 0.162586 0.281607i
\(785\) −9.88718 17.1251i −0.352889 0.611221i
\(786\) 0 0
\(787\) 23.4665 0.836492 0.418246 0.908334i \(-0.362645\pi\)
0.418246 + 0.908334i \(0.362645\pi\)
\(788\) −3.72476 6.45148i −0.132689 0.229824i
\(789\) 0 0
\(790\) 14.1175 0.502279
\(791\) −56.9946 −2.02650
\(792\) 0 0
\(793\) 6.78054 11.7442i 0.240784 0.417050i
\(794\) 7.99143 + 13.8416i 0.283605 + 0.491219i
\(795\) 0 0
\(796\) −3.24800 + 5.62570i −0.115122 + 0.199398i
\(797\) −29.1427 −1.03229 −0.516145 0.856502i \(-0.672633\pi\)
−0.516145 + 0.856502i \(0.672633\pi\)
\(798\) 0 0
\(799\) 0.365418 0.0129275
\(800\) 0.777612 1.34686i 0.0274927 0.0476188i
\(801\) 0 0
\(802\) 20.2875 + 35.1391i 0.716378 + 1.24080i
\(803\) 1.64903 2.85620i 0.0581930 0.100793i
\(804\) 0 0
\(805\) −9.43919 −0.332688
\(806\) 2.03908 0.0718236
\(807\) 0 0
\(808\) −1.49055 2.58170i −0.0524373 0.0908240i
\(809\) −29.6241 −1.04153 −0.520765 0.853700i \(-0.674353\pi\)
−0.520765 + 0.853700i \(0.674353\pi\)
\(810\) 0 0
\(811\) 7.40989 + 12.8343i 0.260196 + 0.450673i 0.966294 0.257441i \(-0.0828793\pi\)
−0.706098 + 0.708115i \(0.749546\pi\)
\(812\) 1.67065 2.89364i 0.0586282 0.101547i
\(813\) 0 0
\(814\) 0.612525 1.06092i 0.0214690 0.0371854i
\(815\) 7.87565 13.6410i 0.275872 0.477824i
\(816\) 0 0
\(817\) 12.4965 + 15.9567i 0.437196 + 0.558254i
\(818\) −18.2766 −0.639025
\(819\) 0 0
\(820\) 1.32200 2.28978i 0.0461664 0.0799625i
\(821\) 13.1421 + 22.7628i 0.458663 + 0.794427i 0.998891 0.0470915i \(-0.0149952\pi\)
−0.540228 + 0.841519i \(0.681662\pi\)
\(822\) 0 0
\(823\) 9.43263 + 16.3378i 0.328801 + 0.569500i 0.982274 0.187450i \(-0.0600222\pi\)
−0.653473 + 0.756950i \(0.726689\pi\)
\(824\) −13.5317 −0.471399
\(825\) 0 0
\(826\) 2.94174 + 5.09524i 0.102356 + 0.177286i
\(827\) −11.0170 19.0820i −0.383098 0.663546i 0.608405 0.793627i \(-0.291810\pi\)
−0.991503 + 0.130081i \(0.958476\pi\)
\(828\) 0 0
\(829\) −22.6976 −0.788320 −0.394160 0.919042i \(-0.628964\pi\)
−0.394160 + 0.919042i \(0.628964\pi\)
\(830\) 0.253432 + 0.438957i 0.00879674 + 0.0152364i
\(831\) 0 0
\(832\) 18.1973 + 31.5186i 0.630878 + 1.09271i
\(833\) −3.79388 + 6.57119i −0.131450 + 0.227678i
\(834\) 0 0
\(835\) −3.66930 −0.126981
\(836\) 0.828488 0.117414i 0.0286539 0.00406084i
\(837\) 0 0
\(838\) 12.9712 22.4668i 0.448083 0.776103i
\(839\) −14.7891 + 25.6155i −0.510577 + 0.884345i 0.489348 + 0.872089i \(0.337235\pi\)
−0.999925 + 0.0122566i \(0.996099\pi\)
\(840\) 0 0
\(841\) 7.00280 12.1292i 0.241476 0.418249i
\(842\) −1.40847 2.43955i −0.0485392 0.0840723i
\(843\) 0 0
\(844\) 2.64569 0.0910685
\(845\) 2.09148 + 3.62255i 0.0719492 + 0.124620i
\(846\) 0 0
\(847\) −32.7677 −1.12591
\(848\) −2.98358 −0.102457
\(849\) 0 0
\(850\) 1.84281 3.19185i 0.0632080 0.109479i
\(851\) 2.04063 + 3.53447i 0.0699518 + 0.121160i
\(852\) 0 0
\(853\) 7.21421 12.4954i 0.247010 0.427834i −0.715685 0.698423i \(-0.753885\pi\)
0.962695 + 0.270590i \(0.0872187\pi\)
\(854\) −13.3759 −0.457715
\(855\) 0 0
\(856\) −55.7341 −1.90495
\(857\) −3.93716 + 6.81937i −0.134491 + 0.232945i −0.925403 0.378985i \(-0.876273\pi\)
0.790912 + 0.611930i \(0.209607\pi\)
\(858\) 0 0
\(859\) 0.789249 + 1.36702i 0.0269288 + 0.0466421i 0.879176 0.476498i \(-0.158094\pi\)
−0.852247 + 0.523140i \(0.824761\pi\)
\(860\) 0.644033 1.11550i 0.0219613 0.0380382i
\(861\) 0 0
\(862\) −36.8190 −1.25406
\(863\) 24.2826 0.826591 0.413295 0.910597i \(-0.364378\pi\)
0.413295 + 0.910597i \(0.364378\pi\)
\(864\) 0 0
\(865\) −3.50081 6.06357i −0.119031 0.206168i
\(866\) 14.1448 0.480660
\(867\) 0 0
\(868\) 0.161683 + 0.280044i 0.00548789 + 0.00950531i
\(869\) 3.72653 6.45454i 0.126414 0.218955i
\(870\) 0 0
\(871\) 22.5734 39.0982i 0.764870 1.32479i
\(872\) −17.1153 + 29.6445i −0.579596 + 1.00389i
\(873\) 0 0
\(874\) 6.47654 16.0835i 0.219072 0.544034i
\(875\) −3.11486 −0.105301
\(876\) 0 0
\(877\) −15.1997 + 26.3266i −0.513256 + 0.888986i 0.486625 + 0.873611i \(0.338228\pi\)
−0.999882 + 0.0153754i \(0.995106\pi\)
\(878\) −11.8600 20.5422i −0.400257 0.693265i
\(879\) 0 0
\(880\) 1.16739 + 2.02198i 0.0393527 + 0.0681608i
\(881\) −3.60055 −0.121306 −0.0606529 0.998159i \(-0.519318\pi\)
−0.0606529 + 0.998159i \(0.519318\pi\)
\(882\) 0 0
\(883\) −8.99273 15.5759i −0.302630 0.524170i 0.674101 0.738639i \(-0.264531\pi\)
−0.976731 + 0.214469i \(0.931198\pi\)
\(884\) −1.61214 2.79230i −0.0542220 0.0939153i
\(885\) 0 0
\(886\) 4.69091 0.157594
\(887\) 7.74011 + 13.4063i 0.259888 + 0.450138i 0.966212 0.257750i \(-0.0829812\pi\)
−0.706324 + 0.707889i \(0.749648\pi\)
\(888\) 0 0
\(889\) −18.5232 32.0831i −0.621248 1.07603i
\(890\) 4.42480 7.66398i 0.148320 0.256897i
\(891\) 0 0
\(892\) 3.65647 0.122428
\(893\) 0.561664 0.0795993i 0.0187954 0.00266369i
\(894\) 0 0
\(895\) −9.24141 + 16.0066i −0.308906 + 0.535041i
\(896\) 13.1045 22.6977i 0.437792 0.758278i
\(897\) 0 0
\(898\) 8.34824 14.4596i 0.278584 0.482522i
\(899\) −0.725571 1.25673i −0.0241992 0.0419142i
\(900\) 0 0
\(901\) 2.48645 0.0828356
\(902\) 4.34088 + 7.51863i 0.144536 + 0.250343i
\(903\) 0 0
\(904\) −54.6893 −1.81894
\(905\) 15.5599 0.517230
\(906\) 0 0
\(907\) 9.40551 16.2908i 0.312305 0.540928i −0.666556 0.745455i \(-0.732232\pi\)
0.978861 + 0.204527i \(0.0655657\pi\)
\(908\) −1.20483 2.08682i −0.0399836 0.0692537i
\(909\) 0 0
\(910\) 8.47418 14.6777i 0.280916 0.486561i
\(911\) 12.4666 0.413038 0.206519 0.978443i \(-0.433786\pi\)
0.206519 + 0.978443i \(0.433786\pi\)
\(912\) 0 0
\(913\) 0.267588 0.00885588
\(914\) 19.5305 33.8278i 0.646011 1.11892i
\(915\) 0 0
\(916\) 2.71628 + 4.70473i 0.0897483 + 0.155449i
\(917\) −18.9709 + 32.8586i −0.626474 + 1.08509i
\(918\) 0 0
\(919\) −12.4751 −0.411515 −0.205757 0.978603i \(-0.565966\pi\)
−0.205757 + 0.978603i \(0.565966\pi\)
\(920\) −9.05739 −0.298613
\(921\) 0 0
\(922\) 22.6936 + 39.3065i 0.747375 + 1.29449i
\(923\) 47.7302 1.57106
\(924\) 0 0
\(925\) 0.673391 + 1.16635i 0.0221410 + 0.0383493i
\(926\) 0.514466 0.891081i 0.0169064 0.0292827i
\(927\) 0 0
\(928\) 3.01111 5.21540i 0.0988447 0.171204i
\(929\) 26.5510 45.9876i 0.871109 1.50880i 0.0102579 0.999947i \(-0.496735\pi\)
0.860851 0.508857i \(-0.169932\pi\)
\(930\) 0 0
\(931\) −4.39996 + 10.9267i −0.144203 + 0.358107i
\(932\) −7.70461 −0.252373
\(933\) 0 0
\(934\) 9.32845 16.1573i 0.305236 0.528685i
\(935\) −0.972876 1.68507i −0.0318165 0.0551077i
\(936\) 0 0
\(937\) 3.04507 + 5.27422i 0.0994782 + 0.172301i 0.911469 0.411369i \(-0.134949\pi\)
−0.811991 + 0.583671i \(0.801616\pi\)
\(938\) −44.5303 −1.45397
\(939\) 0 0
\(940\) −0.0180260 0.0312220i −0.000587943 0.00101835i
\(941\) 7.55084 + 13.0784i 0.246150 + 0.426345i 0.962454 0.271443i \(-0.0875010\pi\)
−0.716304 + 0.697788i \(0.754168\pi\)
\(942\) 0 0
\(943\) −28.9233 −0.941872
\(944\) 2.42412 + 4.19870i 0.0788984 + 0.136656i
\(945\) 0 0
\(946\) 2.11472 + 3.66281i 0.0687555 + 0.119088i
\(947\) −19.0664 + 33.0240i −0.619576 + 1.07314i 0.369988 + 0.929037i \(0.379362\pi\)
−0.989563 + 0.144100i \(0.953971\pi\)
\(948\) 0 0
\(949\) −19.7284 −0.640410
\(950\) 2.13721 5.30744i 0.0693402 0.172196i
\(951\) 0 0
\(952\) −13.0703 + 22.6385i −0.423612 + 0.733718i
\(953\) 23.0367 39.9008i 0.746233 1.29251i −0.203383 0.979099i \(-0.565194\pi\)
0.949616 0.313415i \(-0.101473\pi\)
\(954\) 0 0
\(955\) 3.03946 5.26450i 0.0983546 0.170355i
\(956\) 3.25597 + 5.63951i 0.105306 + 0.182395i
\(957\) 0 0
\(958\) −24.5185 −0.792157
\(959\) 26.1865 + 45.3564i 0.845607 + 1.46463i
\(960\) 0 0
\(961\) −30.8596 −0.995470
\(962\) −7.32802 −0.236265
\(963\) 0 0
\(964\) 3.40227 5.89291i 0.109580 0.189798i
\(965\) 6.37309 + 11.0385i 0.205157 + 0.355343i
\(966\) 0 0
\(967\) −27.8881 + 48.3036i −0.896821 + 1.55334i −0.0652862 + 0.997867i \(0.520796\pi\)
−0.831535 + 0.555473i \(0.812537\pi\)
\(968\) −31.4423 −1.01059
\(969\) 0 0
\(970\) −5.68325 −0.182478
\(971\) 20.9238 36.2410i 0.671476 1.16303i −0.306010 0.952028i \(-0.598994\pi\)
0.977486 0.211002i \(-0.0676725\pi\)
\(972\) 0 0
\(973\) −2.96772 5.14024i −0.0951407 0.164789i
\(974\) −9.58568 + 16.6029i −0.307145 + 0.531991i
\(975\) 0 0
\(976\) −11.0224 −0.352817
\(977\) −35.9635 −1.15057 −0.575287 0.817952i \(-0.695110\pi\)
−0.575287 + 0.817952i \(0.695110\pi\)
\(978\) 0 0
\(979\) −2.33598 4.04604i −0.0746584 0.129312i
\(980\) 0.748607 0.0239134
\(981\) 0 0
\(982\) −2.17589 3.76875i −0.0694354 0.120266i
\(983\) 1.03321 1.78956i 0.0329541 0.0570782i −0.849078 0.528268i \(-0.822842\pi\)
0.882032 + 0.471189i \(0.156175\pi\)
\(984\) 0 0
\(985\) −13.4458 + 23.2888i −0.428419 + 0.742044i
\(986\) 7.13585 12.3597i 0.227252 0.393612i
\(987\) 0 0
\(988\) −3.08618 3.94073i −0.0981845 0.125371i
\(989\) −14.0904 −0.448048
\(990\) 0 0
\(991\) 13.9425 24.1491i 0.442898 0.767121i −0.555006 0.831847i \(-0.687284\pi\)
0.997903 + 0.0647256i \(0.0206172\pi\)
\(992\) 0.291413 + 0.504742i 0.00925236 + 0.0160256i
\(993\) 0 0
\(994\) −23.5393 40.7712i −0.746621 1.29319i
\(995\) 23.4496 0.743401
\(996\) 0 0
\(997\) 28.6627 + 49.6453i 0.907758 + 1.57228i 0.817171 + 0.576395i \(0.195541\pi\)
0.0905868 + 0.995889i \(0.471126\pi\)
\(998\) −6.08170 10.5338i −0.192513 0.333442i
\(999\) 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 855.2.k.k.676.4 yes 12
3.2 odd 2 855.2.k.j.676.3 yes 12
19.7 even 3 inner 855.2.k.k.406.4 yes 12
57.26 odd 6 855.2.k.j.406.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
855.2.k.j.406.3 12 57.26 odd 6
855.2.k.j.676.3 yes 12 3.2 odd 2
855.2.k.k.406.4 yes 12 19.7 even 3 inner
855.2.k.k.676.4 yes 12 1.1 even 1 trivial