Properties

Label 567.2.e.e.487.2
Level $567$
Weight $2$
Character 567.487
Analytic conductor $4.528$
Analytic rank $0$
Dimension $10$
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] = [567,2,Mod(163,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("567.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.e (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: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 487.2
Root \(0.920620 + 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 567.487
Dual form 567.2.e.e.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.920620 - 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +(0.667377 + 1.15593i) q^{5} +(0.640804 - 2.56698i) q^{7} -1.12285 q^{8} +O(q^{10})\) \(q+(-0.920620 - 1.59456i) q^{2} +(-0.695084 + 1.20392i) q^{4} +(0.667377 + 1.15593i) q^{5} +(0.640804 - 2.56698i) q^{7} -1.12285 q^{8} +(1.22880 - 2.12835i) q^{10} +(0.756508 - 1.31031i) q^{11} +5.17599 q^{13} +(-4.68314 + 1.34141i) q^{14} +(2.42388 + 4.19829i) q^{16} +(-0.774463 + 1.34141i) q^{17} +(-1.25211 - 2.16872i) q^{19} -1.85553 q^{20} -2.78583 q^{22} +(-3.68039 - 6.37463i) q^{23} +(1.60922 - 2.78725i) q^{25} +(-4.76513 - 8.25344i) q^{26} +(2.64502 + 2.55574i) q^{28} -0.0619427 q^{29} +(1.92388 - 3.33227i) q^{31} +(3.34011 - 5.78523i) q^{32} +2.85195 q^{34} +(3.39490 - 0.972416i) q^{35} +(-0.281608 - 0.487760i) q^{37} +(-2.30543 + 3.99313i) q^{38} +(-0.749363 - 1.29794i) q^{40} +9.02376 q^{41} -10.1998 q^{43} +(1.05167 + 1.82155i) q^{44} +(-6.77649 + 11.7372i) q^{46} +(-4.75925 - 8.24327i) q^{47} +(-6.17874 - 3.28986i) q^{49} -5.92591 q^{50} +(-3.59775 + 6.23148i) q^{52} +(-0.755374 + 1.30835i) q^{53} +2.01950 q^{55} +(-0.719526 + 2.88233i) q^{56} +(0.0570257 + 0.0987714i) q^{58} +(-4.22166 + 7.31212i) q^{59} +(-1.61958 - 2.80520i) q^{61} -7.08467 q^{62} -2.60434 q^{64} +(3.45434 + 5.98309i) q^{65} +(-3.46670 + 6.00449i) q^{67} +(-1.07663 - 1.86478i) q^{68} +(-4.67599 - 4.51816i) q^{70} +12.3304 q^{71} +(-1.37936 + 2.38912i) q^{73} +(-0.518508 + 0.898083i) q^{74} +3.48128 q^{76} +(-2.87876 - 2.78159i) q^{77} +(2.95969 + 5.12633i) q^{79} +(-3.23529 + 5.60368i) q^{80} +(-8.30746 - 14.3889i) q^{82} +5.60222 q^{83} -2.06744 q^{85} +(9.39010 + 16.2641i) q^{86} +(-0.849444 + 1.47128i) q^{88} +(-0.703287 - 1.21813i) q^{89} +(3.31680 - 13.2867i) q^{91} +10.2327 q^{92} +(-8.76293 + 15.1778i) q^{94} +(1.67126 - 2.89470i) q^{95} +12.1943 q^{97} +(0.442393 + 12.8811i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} + 16 q^{13} - 4 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} + 10 q^{20} + 2 q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} + 14 q^{29} - 3 q^{31} + 2 q^{32} - 6 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} + 10 q^{41} + 14 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} - 17 q^{49} + 38 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 27 q^{56} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} - 11 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} - 10 q^{76} - 20 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} + 18 q^{83} + 12 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} + 54 q^{92} - 3 q^{94} + 14 q^{95} + 24 q^{97} - 59 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.920620 1.59456i −0.650977 1.12753i −0.982886 0.184214i \(-0.941026\pi\)
0.331909 0.943311i \(-0.392307\pi\)
\(3\) 0 0
\(4\) −0.695084 + 1.20392i −0.347542 + 0.601960i
\(5\) 0.667377 + 1.15593i 0.298460 + 0.516948i 0.975784 0.218737i \(-0.0701937\pi\)
−0.677324 + 0.735685i \(0.736860\pi\)
\(6\) 0 0
\(7\) 0.640804 2.56698i 0.242201 0.970226i
\(8\) −1.12285 −0.396987
\(9\) 0 0
\(10\) 1.22880 2.12835i 0.388581 0.673042i
\(11\) 0.756508 1.31031i 0.228096 0.395073i −0.729148 0.684356i \(-0.760083\pi\)
0.957244 + 0.289283i \(0.0934167\pi\)
\(12\) 0 0
\(13\) 5.17599 1.43556 0.717781 0.696269i \(-0.245158\pi\)
0.717781 + 0.696269i \(0.245158\pi\)
\(14\) −4.68314 + 1.34141i −1.25162 + 0.358507i
\(15\) 0 0
\(16\) 2.42388 + 4.19829i 0.605971 + 1.04957i
\(17\) −0.774463 + 1.34141i −0.187835 + 0.325340i −0.944528 0.328430i \(-0.893480\pi\)
0.756693 + 0.653770i \(0.226814\pi\)
\(18\) 0 0
\(19\) −1.25211 2.16872i −0.287254 0.497538i 0.685900 0.727696i \(-0.259409\pi\)
−0.973153 + 0.230158i \(0.926076\pi\)
\(20\) −1.85553 −0.414909
\(21\) 0 0
\(22\) −2.78583 −0.593940
\(23\) −3.68039 6.37463i −0.767415 1.32920i −0.938960 0.344025i \(-0.888209\pi\)
0.171545 0.985176i \(-0.445124\pi\)
\(24\) 0 0
\(25\) 1.60922 2.78725i 0.321843 0.557449i
\(26\) −4.76513 8.25344i −0.934518 1.61863i
\(27\) 0 0
\(28\) 2.64502 + 2.55574i 0.499862 + 0.482990i
\(29\) −0.0619427 −0.0115025 −0.00575123 0.999983i \(-0.501831\pi\)
−0.00575123 + 0.999983i \(0.501831\pi\)
\(30\) 0 0
\(31\) 1.92388 3.33227i 0.345540 0.598493i −0.639912 0.768448i \(-0.721029\pi\)
0.985452 + 0.169956i \(0.0543625\pi\)
\(32\) 3.34011 5.78523i 0.590453 1.02269i
\(33\) 0 0
\(34\) 2.85195 0.489105
\(35\) 3.39490 0.972416i 0.573844 0.164368i
\(36\) 0 0
\(37\) −0.281608 0.487760i −0.0462961 0.0801872i 0.841949 0.539557i \(-0.181408\pi\)
−0.888245 + 0.459370i \(0.848075\pi\)
\(38\) −2.30543 + 3.99313i −0.373991 + 0.647771i
\(39\) 0 0
\(40\) −0.749363 1.29794i −0.118485 0.205222i
\(41\) 9.02376 1.40928 0.704638 0.709567i \(-0.251110\pi\)
0.704638 + 0.709567i \(0.251110\pi\)
\(42\) 0 0
\(43\) −10.1998 −1.55545 −0.777724 0.628606i \(-0.783626\pi\)
−0.777724 + 0.628606i \(0.783626\pi\)
\(44\) 1.05167 + 1.82155i 0.158546 + 0.274609i
\(45\) 0 0
\(46\) −6.77649 + 11.7372i −0.999139 + 1.73056i
\(47\) −4.75925 8.24327i −0.694209 1.20240i −0.970447 0.241315i \(-0.922421\pi\)
0.276238 0.961089i \(-0.410912\pi\)
\(48\) 0 0
\(49\) −6.17874 3.28986i −0.882677 0.469980i
\(50\) −5.92591 −0.838050
\(51\) 0 0
\(52\) −3.59775 + 6.23148i −0.498918 + 0.864151i
\(53\) −0.755374 + 1.30835i −0.103759 + 0.179715i −0.913230 0.407444i \(-0.866420\pi\)
0.809472 + 0.587159i \(0.199754\pi\)
\(54\) 0 0
\(55\) 2.01950 0.272310
\(56\) −0.719526 + 2.88233i −0.0961507 + 0.385167i
\(57\) 0 0
\(58\) 0.0570257 + 0.0987714i 0.00748784 + 0.0129693i
\(59\) −4.22166 + 7.31212i −0.549613 + 0.951957i 0.448688 + 0.893688i \(0.351891\pi\)
−0.998301 + 0.0582689i \(0.981442\pi\)
\(60\) 0 0
\(61\) −1.61958 2.80520i −0.207367 0.359169i 0.743518 0.668716i \(-0.233156\pi\)
−0.950884 + 0.309547i \(0.899823\pi\)
\(62\) −7.08467 −0.899754
\(63\) 0 0
\(64\) −2.60434 −0.325543
\(65\) 3.45434 + 5.98309i 0.428458 + 0.742111i
\(66\) 0 0
\(67\) −3.46670 + 6.00449i −0.423524 + 0.733566i −0.996281 0.0861595i \(-0.972541\pi\)
0.572757 + 0.819725i \(0.305874\pi\)
\(68\) −1.07663 1.86478i −0.130561 0.226138i
\(69\) 0 0
\(70\) −4.67599 4.51816i −0.558888 0.540023i
\(71\) 12.3304 1.46335 0.731673 0.681656i \(-0.238740\pi\)
0.731673 + 0.681656i \(0.238740\pi\)
\(72\) 0 0
\(73\) −1.37936 + 2.38912i −0.161442 + 0.279625i −0.935386 0.353629i \(-0.884948\pi\)
0.773944 + 0.633254i \(0.218281\pi\)
\(74\) −0.518508 + 0.898083i −0.0602754 + 0.104400i
\(75\) 0 0
\(76\) 3.48128 0.399331
\(77\) −2.87876 2.78159i −0.328065 0.316992i
\(78\) 0 0
\(79\) 2.95969 + 5.12633i 0.332991 + 0.576758i 0.983097 0.183086i \(-0.0586087\pi\)
−0.650106 + 0.759844i \(0.725275\pi\)
\(80\) −3.23529 + 5.60368i −0.361716 + 0.626511i
\(81\) 0 0
\(82\) −8.30746 14.3889i −0.917406 1.58899i
\(83\) 5.60222 0.614924 0.307462 0.951560i \(-0.400520\pi\)
0.307462 + 0.951560i \(0.400520\pi\)
\(84\) 0 0
\(85\) −2.06744 −0.224245
\(86\) 9.39010 + 16.2641i 1.01256 + 1.75381i
\(87\) 0 0
\(88\) −0.849444 + 1.47128i −0.0905511 + 0.156839i
\(89\) −0.703287 1.21813i −0.0745483 0.129121i 0.826341 0.563169i \(-0.190418\pi\)
−0.900890 + 0.434048i \(0.857085\pi\)
\(90\) 0 0
\(91\) 3.31680 13.2867i 0.347695 1.39282i
\(92\) 10.2327 1.06684
\(93\) 0 0
\(94\) −8.76293 + 15.1778i −0.903827 + 1.56548i
\(95\) 1.67126 2.89470i 0.171467 0.296990i
\(96\) 0 0
\(97\) 12.1943 1.23814 0.619070 0.785336i \(-0.287510\pi\)
0.619070 + 0.785336i \(0.287510\pi\)
\(98\) 0.442393 + 12.8811i 0.0446885 + 1.30119i
\(99\) 0 0
\(100\) 2.23708 + 3.87474i 0.223708 + 0.387474i
\(101\) 0.559336 0.968798i 0.0556560 0.0963990i −0.836855 0.547425i \(-0.815608\pi\)
0.892511 + 0.451025i \(0.148942\pi\)
\(102\) 0 0
\(103\) −0.965224 1.67182i −0.0951063 0.164729i 0.814547 0.580098i \(-0.196986\pi\)
−0.909653 + 0.415369i \(0.863652\pi\)
\(104\) −5.81186 −0.569900
\(105\) 0 0
\(106\) 2.78165 0.270178
\(107\) −2.88969 5.00509i −0.279357 0.483860i 0.691868 0.722024i \(-0.256788\pi\)
−0.971225 + 0.238163i \(0.923455\pi\)
\(108\) 0 0
\(109\) −4.12106 + 7.13788i −0.394726 + 0.683685i −0.993066 0.117557i \(-0.962494\pi\)
0.598340 + 0.801242i \(0.295827\pi\)
\(110\) −1.85920 3.22022i −0.177267 0.307036i
\(111\) 0 0
\(112\) 12.3302 3.53177i 1.16509 0.333721i
\(113\) 14.5021 1.36424 0.682121 0.731239i \(-0.261058\pi\)
0.682121 + 0.731239i \(0.261058\pi\)
\(114\) 0 0
\(115\) 4.91242 8.50856i 0.458085 0.793427i
\(116\) 0.0430553 0.0745740i 0.00399759 0.00692403i
\(117\) 0 0
\(118\) 15.5462 1.43114
\(119\) 2.94709 + 2.84761i 0.270159 + 0.261040i
\(120\) 0 0
\(121\) 4.35539 + 7.54376i 0.395945 + 0.685796i
\(122\) −2.98204 + 5.16505i −0.269982 + 0.467622i
\(123\) 0 0
\(124\) 2.67452 + 4.63241i 0.240179 + 0.416002i
\(125\) 10.9696 0.981149
\(126\) 0 0
\(127\) 8.50004 0.754257 0.377128 0.926161i \(-0.376912\pi\)
0.377128 + 0.926161i \(0.376912\pi\)
\(128\) −4.28260 7.41769i −0.378532 0.655637i
\(129\) 0 0
\(130\) 6.36027 11.0163i 0.557832 0.966194i
\(131\) −1.00673 1.74371i −0.0879585 0.152349i 0.818690 0.574236i \(-0.194701\pi\)
−0.906648 + 0.421888i \(0.861368\pi\)
\(132\) 0 0
\(133\) −6.36940 + 1.82441i −0.552297 + 0.158197i
\(134\) 12.7660 1.10282
\(135\) 0 0
\(136\) 0.869605 1.50620i 0.0745680 0.129156i
\(137\) 1.10870 1.92032i 0.0947225 0.164064i −0.814770 0.579784i \(-0.803137\pi\)
0.909493 + 0.415720i \(0.136470\pi\)
\(138\) 0 0
\(139\) −0.755339 −0.0640670 −0.0320335 0.999487i \(-0.510198\pi\)
−0.0320335 + 0.999487i \(0.510198\pi\)
\(140\) −1.18903 + 4.76310i −0.100492 + 0.402556i
\(141\) 0 0
\(142\) −11.3516 19.6615i −0.952604 1.64996i
\(143\) 3.91568 6.78216i 0.327446 0.567153i
\(144\) 0 0
\(145\) −0.0413391 0.0716014i −0.00343303 0.00594618i
\(146\) 5.07946 0.420379
\(147\) 0 0
\(148\) 0.782965 0.0643593
\(149\) 3.29249 + 5.70277i 0.269732 + 0.467189i 0.968792 0.247873i \(-0.0797317\pi\)
−0.699061 + 0.715062i \(0.746398\pi\)
\(150\) 0 0
\(151\) −6.33356 + 10.9700i −0.515417 + 0.892729i 0.484422 + 0.874834i \(0.339030\pi\)
−0.999840 + 0.0178950i \(0.994304\pi\)
\(152\) 1.40593 + 2.43514i 0.114036 + 0.197516i
\(153\) 0 0
\(154\) −1.78517 + 7.15115i −0.143853 + 0.576256i
\(155\) 5.13582 0.412519
\(156\) 0 0
\(157\) 8.65372 14.9887i 0.690642 1.19623i −0.280986 0.959712i \(-0.590662\pi\)
0.971628 0.236515i \(-0.0760052\pi\)
\(158\) 5.44950 9.43882i 0.433539 0.750912i
\(159\) 0 0
\(160\) 8.91644 0.704906
\(161\) −18.7219 + 5.36260i −1.47549 + 0.422632i
\(162\) 0 0
\(163\) 6.10963 + 10.5822i 0.478543 + 0.828861i 0.999697 0.0246014i \(-0.00783167\pi\)
−0.521154 + 0.853463i \(0.674498\pi\)
\(164\) −6.27227 + 10.8639i −0.489782 + 0.848327i
\(165\) 0 0
\(166\) −5.15752 8.93309i −0.400301 0.693342i
\(167\) 3.52495 0.272769 0.136385 0.990656i \(-0.456452\pi\)
0.136385 + 0.990656i \(0.456452\pi\)
\(168\) 0 0
\(169\) 13.7909 1.06084
\(170\) 1.90332 + 3.29665i 0.145978 + 0.252842i
\(171\) 0 0
\(172\) 7.08968 12.2797i 0.540583 0.936318i
\(173\) 5.07046 + 8.78229i 0.385500 + 0.667705i 0.991838 0.127502i \(-0.0406958\pi\)
−0.606339 + 0.795206i \(0.707362\pi\)
\(174\) 0 0
\(175\) −6.12360 5.91690i −0.462901 0.447276i
\(176\) 7.33475 0.552878
\(177\) 0 0
\(178\) −1.29492 + 2.24287i −0.0970584 + 0.168110i
\(179\) −0.850579 + 1.47325i −0.0635752 + 0.110116i −0.896061 0.443931i \(-0.853584\pi\)
0.832486 + 0.554046i \(0.186917\pi\)
\(180\) 0 0
\(181\) −16.9941 −1.26316 −0.631581 0.775310i \(-0.717594\pi\)
−0.631581 + 0.775310i \(0.717594\pi\)
\(182\) −24.2399 + 6.94313i −1.79678 + 0.514659i
\(183\) 0 0
\(184\) 4.13252 + 7.15774i 0.304654 + 0.527676i
\(185\) 0.375877 0.651039i 0.0276351 0.0478653i
\(186\) 0 0
\(187\) 1.17178 + 2.02957i 0.0856887 + 0.148417i
\(188\) 13.2323 0.965066
\(189\) 0 0
\(190\) −6.15437 −0.446485
\(191\) 11.3470 + 19.6535i 0.821038 + 1.42208i 0.904910 + 0.425603i \(0.139938\pi\)
−0.0838717 + 0.996477i \(0.526729\pi\)
\(192\) 0 0
\(193\) −3.09349 + 5.35808i −0.222674 + 0.385683i −0.955619 0.294605i \(-0.904812\pi\)
0.732945 + 0.680288i \(0.238145\pi\)
\(194\) −11.2263 19.4445i −0.806001 1.39603i
\(195\) 0 0
\(196\) 8.25547 5.15198i 0.589676 0.367999i
\(197\) −9.77010 −0.696091 −0.348045 0.937478i \(-0.613154\pi\)
−0.348045 + 0.937478i \(0.613154\pi\)
\(198\) 0 0
\(199\) −4.33973 + 7.51664i −0.307636 + 0.532840i −0.977845 0.209332i \(-0.932871\pi\)
0.670209 + 0.742172i \(0.266204\pi\)
\(200\) −1.80691 + 3.12965i −0.127768 + 0.221300i
\(201\) 0 0
\(202\) −2.05974 −0.144923
\(203\) −0.0396931 + 0.159005i −0.00278591 + 0.0111600i
\(204\) 0 0
\(205\) 6.02225 + 10.4308i 0.420612 + 0.728522i
\(206\) −1.77721 + 3.07822i −0.123824 + 0.214470i
\(207\) 0 0
\(208\) 12.5460 + 21.7303i 0.869909 + 1.50673i
\(209\) −3.78892 −0.262085
\(210\) 0 0
\(211\) 5.68439 0.391330 0.195665 0.980671i \(-0.437314\pi\)
0.195665 + 0.980671i \(0.437314\pi\)
\(212\) −1.05010 1.81882i −0.0721209 0.124917i
\(213\) 0 0
\(214\) −5.32062 + 9.21558i −0.363710 + 0.629964i
\(215\) −6.80708 11.7902i −0.464239 0.804086i
\(216\) 0 0
\(217\) −7.32102 7.07390i −0.496983 0.480207i
\(218\) 15.1757 1.02783
\(219\) 0 0
\(220\) −1.40372 + 2.43132i −0.0946390 + 0.163920i
\(221\) −4.00862 + 6.94313i −0.269649 + 0.467045i
\(222\) 0 0
\(223\) −11.7227 −0.785007 −0.392503 0.919751i \(-0.628391\pi\)
−0.392503 + 0.919751i \(0.628391\pi\)
\(224\) −12.7102 12.2812i −0.849236 0.820571i
\(225\) 0 0
\(226\) −13.3509 23.1245i −0.888091 1.53822i
\(227\) 5.59154 9.68482i 0.371123 0.642804i −0.618615 0.785694i \(-0.712306\pi\)
0.989739 + 0.142890i \(0.0456394\pi\)
\(228\) 0 0
\(229\) 4.82824 + 8.36275i 0.319059 + 0.552626i 0.980292 0.197554i \(-0.0632999\pi\)
−0.661233 + 0.750181i \(0.729967\pi\)
\(230\) −18.0899 −1.19281
\(231\) 0 0
\(232\) 0.0695523 0.00456633
\(233\) 9.64492 + 16.7055i 0.631860 + 1.09441i 0.987171 + 0.159666i \(0.0510416\pi\)
−0.355311 + 0.934748i \(0.615625\pi\)
\(234\) 0 0
\(235\) 6.35243 11.0027i 0.414387 0.717739i
\(236\) −5.86881 10.1651i −0.382027 0.661690i
\(237\) 0 0
\(238\) 1.82754 7.32088i 0.118462 0.474542i
\(239\) −0.389282 −0.0251806 −0.0125903 0.999921i \(-0.504008\pi\)
−0.0125903 + 0.999921i \(0.504008\pi\)
\(240\) 0 0
\(241\) −5.31807 + 9.21117i −0.342567 + 0.593344i −0.984909 0.173075i \(-0.944630\pi\)
0.642342 + 0.766419i \(0.277963\pi\)
\(242\) 8.01932 13.8899i 0.515502 0.892875i
\(243\) 0 0
\(244\) 4.50299 0.288274
\(245\) −0.320700 9.33777i −0.0204888 0.596568i
\(246\) 0 0
\(247\) −6.48091 11.2253i −0.412370 0.714247i
\(248\) −2.16023 + 3.74163i −0.137175 + 0.237594i
\(249\) 0 0
\(250\) −10.0988 17.4917i −0.638705 1.10627i
\(251\) 3.26628 0.206166 0.103083 0.994673i \(-0.467129\pi\)
0.103083 + 0.994673i \(0.467129\pi\)
\(252\) 0 0
\(253\) −11.1370 −0.700176
\(254\) −7.82531 13.5538i −0.491004 0.850443i
\(255\) 0 0
\(256\) −10.4896 + 18.1686i −0.655603 + 1.13554i
\(257\) −2.34787 4.06663i −0.146456 0.253669i 0.783459 0.621443i \(-0.213453\pi\)
−0.929915 + 0.367774i \(0.880120\pi\)
\(258\) 0 0
\(259\) −1.43252 + 0.410323i −0.0890127 + 0.0254962i
\(260\) −9.60421 −0.595628
\(261\) 0 0
\(262\) −1.85363 + 3.21059i −0.114518 + 0.198351i
\(263\) 9.77491 16.9306i 0.602747 1.04399i −0.389656 0.920960i \(-0.627406\pi\)
0.992403 0.123028i \(-0.0392605\pi\)
\(264\) 0 0
\(265\) −2.01648 −0.123871
\(266\) 8.77294 + 8.47681i 0.537903 + 0.519747i
\(267\) 0 0
\(268\) −4.81929 8.34725i −0.294385 0.509890i
\(269\) −7.88365 + 13.6549i −0.480675 + 0.832553i −0.999754 0.0221730i \(-0.992942\pi\)
0.519079 + 0.854726i \(0.326275\pi\)
\(270\) 0 0
\(271\) 7.39882 + 12.8151i 0.449446 + 0.778464i 0.998350 0.0574218i \(-0.0182880\pi\)
−0.548904 + 0.835886i \(0.684955\pi\)
\(272\) −7.50884 −0.455290
\(273\) 0 0
\(274\) −4.08276 −0.246649
\(275\) −2.43477 4.21715i −0.146822 0.254304i
\(276\) 0 0
\(277\) 3.72561 6.45295i 0.223850 0.387720i −0.732124 0.681172i \(-0.761471\pi\)
0.955974 + 0.293452i \(0.0948040\pi\)
\(278\) 0.695380 + 1.20443i 0.0417061 + 0.0722371i
\(279\) 0 0
\(280\) −3.81196 + 1.09188i −0.227808 + 0.0652521i
\(281\) −25.9876 −1.55029 −0.775146 0.631782i \(-0.782324\pi\)
−0.775146 + 0.631782i \(0.782324\pi\)
\(282\) 0 0
\(283\) −9.37768 + 16.2426i −0.557445 + 0.965524i 0.440263 + 0.897869i \(0.354885\pi\)
−0.997709 + 0.0676550i \(0.978448\pi\)
\(284\) −8.57064 + 14.8448i −0.508574 + 0.880876i
\(285\) 0 0
\(286\) −14.4194 −0.852638
\(287\) 5.78246 23.1638i 0.341328 1.36732i
\(288\) 0 0
\(289\) 7.30041 + 12.6447i 0.429436 + 0.743805i
\(290\) −0.0761152 + 0.131835i −0.00446964 + 0.00774165i
\(291\) 0 0
\(292\) −1.91754 3.32127i −0.112215 0.194363i
\(293\) −2.46178 −0.143819 −0.0719093 0.997411i \(-0.522909\pi\)
−0.0719093 + 0.997411i \(0.522909\pi\)
\(294\) 0 0
\(295\) −11.2697 −0.656150
\(296\) 0.316203 + 0.547680i 0.0183790 + 0.0318333i
\(297\) 0 0
\(298\) 6.06227 10.5002i 0.351178 0.608258i
\(299\) −19.0497 32.9950i −1.10167 1.90815i
\(300\) 0 0
\(301\) −6.53605 + 26.1825i −0.376731 + 1.50914i
\(302\) 23.3232 1.34210
\(303\) 0 0
\(304\) 6.06994 10.5134i 0.348135 0.602987i
\(305\) 2.16175 3.74425i 0.123781 0.214395i
\(306\) 0 0
\(307\) −4.66277 −0.266118 −0.133059 0.991108i \(-0.542480\pi\)
−0.133059 + 0.991108i \(0.542480\pi\)
\(308\) 5.34979 1.53236i 0.304833 0.0873145i
\(309\) 0 0
\(310\) −4.72814 8.18938i −0.268541 0.465126i
\(311\) 13.7410 23.8002i 0.779183 1.34958i −0.153231 0.988190i \(-0.548968\pi\)
0.932413 0.361393i \(-0.117699\pi\)
\(312\) 0 0
\(313\) −2.74666 4.75735i −0.155250 0.268901i 0.777900 0.628388i \(-0.216285\pi\)
−0.933150 + 0.359487i \(0.882952\pi\)
\(314\) −31.8671 −1.79837
\(315\) 0 0
\(316\) −8.22893 −0.462914
\(317\) 4.93879 + 8.55424i 0.277390 + 0.480454i 0.970735 0.240152i \(-0.0771972\pi\)
−0.693345 + 0.720606i \(0.743864\pi\)
\(318\) 0 0
\(319\) −0.0468601 + 0.0811641i −0.00262366 + 0.00454432i
\(320\) −1.73808 3.01044i −0.0971614 0.168288i
\(321\) 0 0
\(322\) 25.7868 + 24.9164i 1.43704 + 1.38853i
\(323\) 3.87885 0.215825
\(324\) 0 0
\(325\) 8.32930 14.4268i 0.462026 0.800253i
\(326\) 11.2493 19.4844i 0.623041 1.07914i
\(327\) 0 0
\(328\) −10.1323 −0.559464
\(329\) −24.2100 + 6.93457i −1.33474 + 0.382315i
\(330\) 0 0
\(331\) 10.3471 + 17.9217i 0.568729 + 0.985067i 0.996692 + 0.0812710i \(0.0258979\pi\)
−0.427963 + 0.903796i \(0.640769\pi\)
\(332\) −3.89401 + 6.74463i −0.213712 + 0.370160i
\(333\) 0 0
\(334\) −3.24514 5.62076i −0.177566 0.307554i
\(335\) −9.25437 −0.505620
\(336\) 0 0
\(337\) −1.49749 −0.0815737 −0.0407869 0.999168i \(-0.512986\pi\)
−0.0407869 + 0.999168i \(0.512986\pi\)
\(338\) −12.6962 21.9905i −0.690582 1.19612i
\(339\) 0 0
\(340\) 1.43704 2.48903i 0.0779344 0.134986i
\(341\) −2.91087 5.04177i −0.157632 0.273027i
\(342\) 0 0
\(343\) −12.4044 + 13.7525i −0.669772 + 0.742567i
\(344\) 11.4528 0.617493
\(345\) 0 0
\(346\) 9.33593 16.1703i 0.501903 0.869321i
\(347\) −14.7694 + 25.5813i −0.792862 + 1.37328i 0.131326 + 0.991339i \(0.458077\pi\)
−0.924188 + 0.381938i \(0.875257\pi\)
\(348\) 0 0
\(349\) −36.0013 −1.92710 −0.963551 0.267523i \(-0.913795\pi\)
−0.963551 + 0.267523i \(0.913795\pi\)
\(350\) −3.79735 + 15.2117i −0.202977 + 0.813098i
\(351\) 0 0
\(352\) −5.05363 8.75315i −0.269360 0.466545i
\(353\) −14.7465 + 25.5417i −0.784877 + 1.35945i 0.144196 + 0.989549i \(0.453940\pi\)
−0.929073 + 0.369897i \(0.879393\pi\)
\(354\) 0 0
\(355\) 8.22900 + 14.2530i 0.436750 + 0.756473i
\(356\) 1.95537 0.103635
\(357\) 0 0
\(358\) 3.13224 0.165544
\(359\) −2.70535 4.68580i −0.142783 0.247307i 0.785761 0.618531i \(-0.212272\pi\)
−0.928544 + 0.371224i \(0.878938\pi\)
\(360\) 0 0
\(361\) 6.36444 11.0235i 0.334971 0.580186i
\(362\) 15.6451 + 27.0981i 0.822289 + 1.42425i
\(363\) 0 0
\(364\) 13.6906 + 13.2285i 0.717584 + 0.693362i
\(365\) −3.68220 −0.192735
\(366\) 0 0
\(367\) 11.5422 19.9916i 0.602496 1.04355i −0.389946 0.920838i \(-0.627506\pi\)
0.992442 0.122715i \(-0.0391602\pi\)
\(368\) 17.8417 30.9027i 0.930063 1.61092i
\(369\) 0 0
\(370\) −1.38416 −0.0719591
\(371\) 2.87445 + 2.77742i 0.149234 + 0.144196i
\(372\) 0 0
\(373\) −10.7515 18.6222i −0.556692 0.964219i −0.997770 0.0667498i \(-0.978737\pi\)
0.441078 0.897469i \(-0.354596\pi\)
\(374\) 2.15752 3.73694i 0.111563 0.193232i
\(375\) 0 0
\(376\) 5.34392 + 9.25595i 0.275592 + 0.477339i
\(377\) −0.320615 −0.0165125
\(378\) 0 0
\(379\) 5.72168 0.293903 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(380\) 2.32333 + 4.02412i 0.119184 + 0.206433i
\(381\) 0 0
\(382\) 20.8925 36.1869i 1.06895 1.85148i
\(383\) −17.4604 30.2424i −0.892187 1.54531i −0.837248 0.546823i \(-0.815837\pi\)
−0.0549390 0.998490i \(-0.517496\pi\)
\(384\) 0 0
\(385\) 1.29411 5.18402i 0.0659538 0.264202i
\(386\) 11.3917 0.579823
\(387\) 0 0
\(388\) −8.47603 + 14.6809i −0.430305 + 0.745311i
\(389\) −14.4411 + 25.0127i −0.732192 + 1.26819i 0.223752 + 0.974646i \(0.428169\pi\)
−0.955944 + 0.293548i \(0.905164\pi\)
\(390\) 0 0
\(391\) 11.4013 0.576589
\(392\) 6.93779 + 3.69401i 0.350411 + 0.186576i
\(393\) 0 0
\(394\) 8.99455 + 15.5790i 0.453139 + 0.784860i
\(395\) −3.95046 + 6.84239i −0.198769 + 0.344278i
\(396\) 0 0
\(397\) 5.59226 + 9.68607i 0.280667 + 0.486130i 0.971549 0.236838i \(-0.0761109\pi\)
−0.690882 + 0.722968i \(0.742778\pi\)
\(398\) 15.9810 0.801055
\(399\) 0 0
\(400\) 15.6022 0.780111
\(401\) −0.541061 0.937146i −0.0270193 0.0467988i 0.852200 0.523217i \(-0.175268\pi\)
−0.879219 + 0.476418i \(0.841935\pi\)
\(402\) 0 0
\(403\) 9.95802 17.2478i 0.496044 0.859174i
\(404\) 0.777570 + 1.34679i 0.0386856 + 0.0670054i
\(405\) 0 0
\(406\) 0.290086 0.0830905i 0.0143967 0.00412371i
\(407\) −0.852155 −0.0422398
\(408\) 0 0
\(409\) 10.8674 18.8229i 0.537360 0.930735i −0.461685 0.887044i \(-0.652755\pi\)
0.999045 0.0436908i \(-0.0139116\pi\)
\(410\) 11.0884 19.2057i 0.547618 0.948501i
\(411\) 0 0
\(412\) 2.68365 0.132214
\(413\) 16.0648 + 15.5225i 0.790497 + 0.763814i
\(414\) 0 0
\(415\) 3.73879 + 6.47578i 0.183530 + 0.317884i
\(416\) 17.2884 29.9443i 0.847632 1.46814i
\(417\) 0 0
\(418\) 3.48816 + 6.04167i 0.170611 + 0.295508i
\(419\) 25.1811 1.23018 0.615090 0.788457i \(-0.289120\pi\)
0.615090 + 0.788457i \(0.289120\pi\)
\(420\) 0 0
\(421\) 29.6607 1.44558 0.722788 0.691070i \(-0.242860\pi\)
0.722788 + 0.691070i \(0.242860\pi\)
\(422\) −5.23316 9.06411i −0.254746 0.441234i
\(423\) 0 0
\(424\) 0.848171 1.46907i 0.0411908 0.0713446i
\(425\) 2.49256 + 4.31724i 0.120907 + 0.209417i
\(426\) 0 0
\(427\) −8.23873 + 2.35985i −0.398700 + 0.114201i
\(428\) 8.03431 0.388353
\(429\) 0 0
\(430\) −12.5335 + 21.7086i −0.604418 + 1.04688i
\(431\) −2.44517 + 4.23516i −0.117780 + 0.204000i −0.918887 0.394520i \(-0.870911\pi\)
0.801108 + 0.598520i \(0.204244\pi\)
\(432\) 0 0
\(433\) 9.71430 0.466839 0.233420 0.972376i \(-0.425008\pi\)
0.233420 + 0.972376i \(0.425008\pi\)
\(434\) −4.53989 + 18.1862i −0.217921 + 0.872965i
\(435\) 0 0
\(436\) −5.72896 9.92285i −0.274367 0.475218i
\(437\) −9.21651 + 15.9635i −0.440885 + 0.763636i
\(438\) 0 0
\(439\) 7.41176 + 12.8375i 0.353744 + 0.612703i 0.986902 0.161320i \(-0.0515751\pi\)
−0.633158 + 0.774022i \(0.718242\pi\)
\(440\) −2.26760 −0.108103
\(441\) 0 0
\(442\) 14.7617 0.702141
\(443\) −10.9510 18.9676i −0.520297 0.901180i −0.999722 0.0235972i \(-0.992488\pi\)
0.479425 0.877583i \(-0.340845\pi\)
\(444\) 0 0
\(445\) 0.938715 1.62590i 0.0444994 0.0770751i
\(446\) 10.7921 + 18.6925i 0.511021 + 0.885115i
\(447\) 0 0
\(448\) −1.66887 + 6.68528i −0.0788468 + 0.315850i
\(449\) −21.4952 −1.01442 −0.507212 0.861822i \(-0.669324\pi\)
−0.507212 + 0.861822i \(0.669324\pi\)
\(450\) 0 0
\(451\) 6.82655 11.8239i 0.321450 0.556767i
\(452\) −10.0802 + 17.4594i −0.474131 + 0.821220i
\(453\) 0 0
\(454\) −20.5907 −0.966371
\(455\) 17.5720 5.03322i 0.823788 0.235961i
\(456\) 0 0
\(457\) −20.3128 35.1827i −0.950190 1.64578i −0.745009 0.667054i \(-0.767555\pi\)
−0.205181 0.978724i \(-0.565778\pi\)
\(458\) 8.88995 15.3978i 0.415400 0.719494i
\(459\) 0 0
\(460\) 6.82908 + 11.8283i 0.318408 + 0.551498i
\(461\) 2.83081 0.131844 0.0659220 0.997825i \(-0.479001\pi\)
0.0659220 + 0.997825i \(0.479001\pi\)
\(462\) 0 0
\(463\) 27.8648 1.29499 0.647494 0.762070i \(-0.275817\pi\)
0.647494 + 0.762070i \(0.275817\pi\)
\(464\) −0.150142 0.260053i −0.00697016 0.0120727i
\(465\) 0 0
\(466\) 17.7586 30.7588i 0.822653 1.42488i
\(467\) 13.3219 + 23.0742i 0.616464 + 1.06775i 0.990126 + 0.140182i \(0.0447689\pi\)
−0.373661 + 0.927565i \(0.621898\pi\)
\(468\) 0 0
\(469\) 13.1919 + 12.7466i 0.609146 + 0.588585i
\(470\) −23.3927 −1.07903
\(471\) 0 0
\(472\) 4.74028 8.21041i 0.218189 0.377915i
\(473\) −7.71620 + 13.3648i −0.354791 + 0.614516i
\(474\) 0 0
\(475\) −8.05966 −0.369803
\(476\) −5.47677 + 1.56873i −0.251027 + 0.0719027i
\(477\) 0 0
\(478\) 0.358381 + 0.620734i 0.0163920 + 0.0283917i
\(479\) −15.7895 + 27.3483i −0.721443 + 1.24958i 0.238979 + 0.971025i \(0.423187\pi\)
−0.960422 + 0.278551i \(0.910146\pi\)
\(480\) 0 0
\(481\) −1.45760 2.52464i −0.0664609 0.115114i
\(482\) 19.5837 0.892013
\(483\) 0 0
\(484\) −12.1094 −0.550429
\(485\) 8.13817 + 14.0957i 0.369535 + 0.640054i
\(486\) 0 0
\(487\) −0.153087 + 0.265154i −0.00693703 + 0.0120153i −0.869473 0.493980i \(-0.835541\pi\)
0.862536 + 0.505996i \(0.168875\pi\)
\(488\) 1.81855 + 3.14982i 0.0823218 + 0.142586i
\(489\) 0 0
\(490\) −14.5944 + 9.10792i −0.659308 + 0.411454i
\(491\) −18.1396 −0.818629 −0.409315 0.912393i \(-0.634232\pi\)
−0.409315 + 0.912393i \(0.634232\pi\)
\(492\) 0 0
\(493\) 0.0479723 0.0830905i 0.00216057 0.00374221i
\(494\) −11.9329 + 20.6684i −0.536887 + 0.929916i
\(495\) 0 0
\(496\) 18.6531 0.837549
\(497\) 7.90135 31.6518i 0.354424 1.41978i
\(498\) 0 0
\(499\) 10.6546 + 18.4543i 0.476964 + 0.826126i 0.999652 0.0263983i \(-0.00840381\pi\)
−0.522687 + 0.852524i \(0.675070\pi\)
\(500\) −7.62478 + 13.2065i −0.340990 + 0.590613i
\(501\) 0 0
\(502\) −3.00701 5.20829i −0.134209 0.232457i
\(503\) 17.0738 0.761285 0.380642 0.924722i \(-0.375703\pi\)
0.380642 + 0.924722i \(0.375703\pi\)
\(504\) 0 0
\(505\) 1.49315 0.0664443
\(506\) 10.2529 + 17.7586i 0.455799 + 0.789466i
\(507\) 0 0
\(508\) −5.90824 + 10.2334i −0.262136 + 0.454032i
\(509\) 18.3868 + 31.8468i 0.814979 + 1.41159i 0.909343 + 0.416048i \(0.136585\pi\)
−0.0943635 + 0.995538i \(0.530082\pi\)
\(510\) 0 0
\(511\) 5.24891 + 5.07173i 0.232198 + 0.224360i
\(512\) 21.4975 0.950065
\(513\) 0 0
\(514\) −4.32299 + 7.48764i −0.190679 + 0.330265i
\(515\) 1.28834 2.23146i 0.0567709 0.0983300i
\(516\) 0 0
\(517\) −14.4017 −0.633384
\(518\) 1.97310 + 1.90649i 0.0866929 + 0.0837666i
\(519\) 0 0
\(520\) −3.87870 6.71810i −0.170092 0.294608i
\(521\) 9.57535 16.5850i 0.419504 0.726602i −0.576386 0.817178i \(-0.695537\pi\)
0.995890 + 0.0905758i \(0.0288707\pi\)
\(522\) 0 0
\(523\) −20.9715 36.3236i −0.917018 1.58832i −0.803920 0.594737i \(-0.797256\pi\)
−0.113097 0.993584i \(-0.536077\pi\)
\(524\) 2.79905 0.122277
\(525\) 0 0
\(526\) −35.9959 −1.56950
\(527\) 2.97996 + 5.16144i 0.129809 + 0.224836i
\(528\) 0 0
\(529\) −15.5906 + 27.0037i −0.677851 + 1.17407i
\(530\) 1.85641 + 3.21539i 0.0806372 + 0.139668i
\(531\) 0 0
\(532\) 2.23082 8.93637i 0.0967183 0.387441i
\(533\) 46.7069 2.02310
\(534\) 0 0
\(535\) 3.85702 6.68056i 0.166754 0.288826i
\(536\) 3.89258 6.74214i 0.168134 0.291216i
\(537\) 0 0
\(538\) 29.0314 1.25163
\(539\) −8.98500 + 5.60726i −0.387011 + 0.241522i
\(540\) 0 0
\(541\) −1.44272 2.49886i −0.0620273 0.107434i 0.833344 0.552754i \(-0.186423\pi\)
−0.895371 + 0.445320i \(0.853090\pi\)
\(542\) 13.6230 23.5957i 0.585158 1.01352i
\(543\) 0 0
\(544\) 5.17358 + 8.96090i 0.221815 + 0.384196i
\(545\) −11.0012 −0.471239
\(546\) 0 0
\(547\) −2.77476 −0.118640 −0.0593201 0.998239i \(-0.518893\pi\)
−0.0593201 + 0.998239i \(0.518893\pi\)
\(548\) 1.54128 + 2.66957i 0.0658401 + 0.114038i
\(549\) 0 0
\(550\) −4.48300 + 7.76478i −0.191156 + 0.331091i
\(551\) 0.0775590 + 0.134336i 0.00330413 + 0.00572291i
\(552\) 0 0
\(553\) 15.0558 4.31248i 0.640236 0.183385i
\(554\) −13.7195 −0.582886
\(555\) 0 0
\(556\) 0.525024 0.909368i 0.0222660 0.0385658i
\(557\) −15.5344 + 26.9064i −0.658214 + 1.14006i 0.322864 + 0.946445i \(0.395354\pi\)
−0.981078 + 0.193614i \(0.937979\pi\)
\(558\) 0 0
\(559\) −52.7939 −2.23294
\(560\) 12.3113 + 11.8958i 0.520249 + 0.502688i
\(561\) 0 0
\(562\) 23.9248 + 41.4389i 1.00920 + 1.74799i
\(563\) 0.144020 0.249451i 0.00606973 0.0105131i −0.862975 0.505247i \(-0.831401\pi\)
0.869044 + 0.494734i \(0.164735\pi\)
\(564\) 0 0
\(565\) 9.67836 + 16.7634i 0.407172 + 0.705242i
\(566\) 34.5331 1.45154
\(567\) 0 0
\(568\) −13.8451 −0.580929
\(569\) −8.04004 13.9258i −0.337056 0.583798i 0.646821 0.762641i \(-0.276098\pi\)
−0.983878 + 0.178843i \(0.942765\pi\)
\(570\) 0 0
\(571\) 7.64289 13.2379i 0.319845 0.553988i −0.660610 0.750729i \(-0.729702\pi\)
0.980456 + 0.196741i \(0.0630358\pi\)
\(572\) 5.44345 + 9.42834i 0.227602 + 0.394218i
\(573\) 0 0
\(574\) −42.2595 + 12.1046i −1.76388 + 0.505235i
\(575\) −23.6902 −0.987950
\(576\) 0 0
\(577\) 12.0812 20.9253i 0.502949 0.871133i −0.497045 0.867725i \(-0.665582\pi\)
0.999994 0.00340833i \(-0.00108491\pi\)
\(578\) 13.4418 23.2819i 0.559106 0.968400i
\(579\) 0 0
\(580\) 0.114937 0.00477248
\(581\) 3.58993 14.3808i 0.148935 0.596615i
\(582\) 0 0
\(583\) 1.14289 + 1.97955i 0.0473338 + 0.0819845i
\(584\) 1.54881 2.68262i 0.0640902 0.111007i
\(585\) 0 0
\(586\) 2.26636 + 3.92546i 0.0936226 + 0.162159i
\(587\) 36.0289 1.48707 0.743537 0.668695i \(-0.233147\pi\)
0.743537 + 0.668695i \(0.233147\pi\)
\(588\) 0 0
\(589\) −9.63566 −0.397030
\(590\) 10.3752 + 17.9703i 0.427138 + 0.739825i
\(591\) 0 0
\(592\) 1.36517 2.36455i 0.0561082 0.0971823i
\(593\) −12.4668 21.5932i −0.511951 0.886726i −0.999904 0.0138558i \(-0.995589\pi\)
0.487953 0.872870i \(-0.337744\pi\)
\(594\) 0 0
\(595\) −1.32482 + 5.30706i −0.0543124 + 0.217568i
\(596\) −9.15424 −0.374972
\(597\) 0 0
\(598\) −35.0751 + 60.7518i −1.43433 + 2.48433i
\(599\) 19.7642 34.2325i 0.807542 1.39870i −0.107019 0.994257i \(-0.534131\pi\)
0.914561 0.404447i \(-0.132536\pi\)
\(600\) 0 0
\(601\) −3.72895 −0.152107 −0.0760534 0.997104i \(-0.524232\pi\)
−0.0760534 + 0.997104i \(0.524232\pi\)
\(602\) 47.7669 13.6821i 1.94683 0.557639i
\(603\) 0 0
\(604\) −8.80470 15.2502i −0.358258 0.620521i
\(605\) −5.81337 + 10.0691i −0.236347 + 0.409365i
\(606\) 0 0
\(607\) −11.8264 20.4839i −0.480018 0.831415i 0.519719 0.854337i \(-0.326036\pi\)
−0.999737 + 0.0229218i \(0.992703\pi\)
\(608\) −16.7287 −0.678439
\(609\) 0 0
\(610\) −7.96059 −0.322315
\(611\) −24.6339 42.6671i −0.996580 1.72613i
\(612\) 0 0
\(613\) 1.89952 3.29006i 0.0767208 0.132884i −0.825113 0.564968i \(-0.808888\pi\)
0.901833 + 0.432084i \(0.142222\pi\)
\(614\) 4.29264 + 7.43507i 0.173237 + 0.300055i
\(615\) 0 0
\(616\) 3.23242 + 3.12331i 0.130238 + 0.125842i
\(617\) −35.1230 −1.41400 −0.706999 0.707214i \(-0.749952\pi\)
−0.706999 + 0.707214i \(0.749952\pi\)
\(618\) 0 0
\(619\) 10.5816 18.3279i 0.425311 0.736660i −0.571138 0.820854i \(-0.693498\pi\)
0.996449 + 0.0841934i \(0.0268314\pi\)
\(620\) −3.56983 + 6.18312i −0.143368 + 0.248320i
\(621\) 0 0
\(622\) −50.6011 −2.02892
\(623\) −3.57758 + 1.02474i −0.143333 + 0.0410553i
\(624\) 0 0
\(625\) −0.725240 1.25615i −0.0290096 0.0502461i
\(626\) −5.05726 + 8.75943i −0.202129 + 0.350097i
\(627\) 0 0
\(628\) 12.0301 + 20.8368i 0.480054 + 0.831477i
\(629\) 0.872381 0.0347841
\(630\) 0 0
\(631\) 4.74845 0.189033 0.0945164 0.995523i \(-0.469870\pi\)
0.0945164 + 0.995523i \(0.469870\pi\)
\(632\) −3.32329 5.75610i −0.132193 0.228965i
\(633\) 0 0
\(634\) 9.09350 15.7504i 0.361149 0.625529i
\(635\) 5.67273 + 9.82546i 0.225115 + 0.389911i
\(636\) 0 0
\(637\) −31.9811 17.0283i −1.26714 0.674685i
\(638\) 0.172562 0.00683178
\(639\) 0 0
\(640\) 5.71622 9.90078i 0.225953 0.391363i
\(641\) −4.93735 + 8.55174i −0.195013 + 0.337773i −0.946905 0.321514i \(-0.895808\pi\)
0.751891 + 0.659287i \(0.229142\pi\)
\(642\) 0 0
\(643\) −43.9496 −1.73320 −0.866602 0.499000i \(-0.833701\pi\)
−0.866602 + 0.499000i \(0.833701\pi\)
\(644\) 6.55717 26.2672i 0.258389 1.03507i
\(645\) 0 0
\(646\) −3.57095 6.18507i −0.140497 0.243348i
\(647\) −22.1936 + 38.4404i −0.872521 + 1.51125i −0.0131398 + 0.999914i \(0.504183\pi\)
−0.859381 + 0.511336i \(0.829151\pi\)
\(648\) 0 0
\(649\) 6.38743 + 11.0634i 0.250729 + 0.434275i
\(650\) −30.6725 −1.20307
\(651\) 0 0
\(652\) −16.9868 −0.665255
\(653\) 20.9956 + 36.3655i 0.821622 + 1.42309i 0.904474 + 0.426529i \(0.140264\pi\)
−0.0828523 + 0.996562i \(0.526403\pi\)
\(654\) 0 0
\(655\) 1.34374 2.32742i 0.0525042 0.0909399i
\(656\) 21.8726 + 37.8844i 0.853980 + 1.47914i
\(657\) 0 0
\(658\) 33.3459 + 32.2203i 1.29996 + 1.25608i
\(659\) −39.2729 −1.52986 −0.764928 0.644115i \(-0.777226\pi\)
−0.764928 + 0.644115i \(0.777226\pi\)
\(660\) 0 0
\(661\) 0.0933694 0.161721i 0.00363165 0.00629020i −0.864204 0.503142i \(-0.832177\pi\)
0.867836 + 0.496852i \(0.165511\pi\)
\(662\) 19.0515 32.9982i 0.740459 1.28251i
\(663\) 0 0
\(664\) −6.29045 −0.244117
\(665\) −6.35969 6.14502i −0.246618 0.238293i
\(666\) 0 0
\(667\) 0.227973 + 0.394862i 0.00882717 + 0.0152891i
\(668\) −2.45014 + 4.24376i −0.0947987 + 0.164196i
\(669\) 0 0
\(670\) 8.51976 + 14.7567i 0.329147 + 0.570099i
\(671\) −4.90091 −0.189198
\(672\) 0 0
\(673\) 10.8676 0.418917 0.209458 0.977818i \(-0.432830\pi\)
0.209458 + 0.977818i \(0.432830\pi\)
\(674\) 1.37862 + 2.38785i 0.0531026 + 0.0919764i
\(675\) 0 0
\(676\) −9.58584 + 16.6032i −0.368686 + 0.638583i
\(677\) 14.1950 + 24.5865i 0.545560 + 0.944937i 0.998571 + 0.0534326i \(0.0170162\pi\)
−0.453012 + 0.891505i \(0.649650\pi\)
\(678\) 0 0
\(679\) 7.81414 31.3024i 0.299879 1.20128i
\(680\) 2.32142 0.0890223
\(681\) 0 0
\(682\) −5.35961 + 9.28312i −0.205230 + 0.355469i
\(683\) −5.92034 + 10.2543i −0.226536 + 0.392371i −0.956779 0.290816i \(-0.906073\pi\)
0.730243 + 0.683187i \(0.239407\pi\)
\(684\) 0 0
\(685\) 2.95968 0.113083
\(686\) 33.3489 + 7.11864i 1.27327 + 0.271791i
\(687\) 0 0
\(688\) −24.7230 42.8216i −0.942557 1.63256i
\(689\) −3.90981 + 6.77199i −0.148952 + 0.257992i
\(690\) 0 0
\(691\) −5.95416 10.3129i −0.226507 0.392321i 0.730264 0.683165i \(-0.239397\pi\)
−0.956770 + 0.290844i \(0.906064\pi\)
\(692\) −14.0976 −0.535909
\(693\) 0 0
\(694\) 54.3880 2.06454
\(695\) −0.504096 0.873119i −0.0191214 0.0331193i
\(696\) 0 0
\(697\) −6.98857 + 12.1046i −0.264711 + 0.458493i
\(698\) 33.1435 + 57.4062i 1.25450 + 2.17286i
\(699\) 0 0
\(700\) 11.3799 3.25959i 0.430119 0.123201i
\(701\) 31.3902 1.18559 0.592795 0.805353i \(-0.298024\pi\)
0.592795 + 0.805353i \(0.298024\pi\)
\(702\) 0 0
\(703\) −0.705208 + 1.22146i −0.0265974 + 0.0460681i
\(704\) −1.97020 + 3.41249i −0.0742549 + 0.128613i
\(705\) 0 0
\(706\) 54.3037 2.04375
\(707\) −2.12846 2.05661i −0.0800489 0.0773469i
\(708\) 0 0
\(709\) −0.312609 0.541455i −0.0117403 0.0203348i 0.860096 0.510133i \(-0.170404\pi\)
−0.871836 + 0.489798i \(0.837070\pi\)
\(710\) 15.1516 26.2433i 0.568628 0.984893i
\(711\) 0 0
\(712\) 0.789685 + 1.36777i 0.0295947 + 0.0512595i
\(713\) −28.3226 −1.06069
\(714\) 0 0
\(715\) 10.4529 0.390918
\(716\) −1.18245 2.04806i −0.0441901 0.0765395i
\(717\) 0 0
\(718\) −4.98119 + 8.62768i −0.185897 + 0.321982i
\(719\) −12.1969 21.1257i −0.454869 0.787857i 0.543811 0.839208i \(-0.316981\pi\)
−0.998681 + 0.0513506i \(0.983647\pi\)
\(720\) 0 0
\(721\) −4.91003 + 1.40640i −0.182859 + 0.0523771i
\(722\) −23.4369 −0.872233
\(723\) 0 0
\(724\) 11.8123 20.4595i 0.439002 0.760373i
\(725\) −0.0996792 + 0.172649i −0.00370199 + 0.00641204i
\(726\) 0 0
\(727\) 37.8506 1.40380 0.701900 0.712275i \(-0.252335\pi\)
0.701900 + 0.712275i \(0.252335\pi\)
\(728\) −3.72426 + 14.9189i −0.138030 + 0.552932i
\(729\) 0 0
\(730\) 3.38991 + 5.87150i 0.125466 + 0.217314i
\(731\) 7.89934 13.6821i 0.292168 0.506049i
\(732\) 0 0
\(733\) −1.20077 2.07980i −0.0443516 0.0768193i 0.842997 0.537918i \(-0.180789\pi\)
−0.887349 + 0.461098i \(0.847456\pi\)
\(734\) −42.5038 −1.56884
\(735\) 0 0
\(736\) −49.1716 −1.81249
\(737\) 5.24517 + 9.08490i 0.193208 + 0.334646i
\(738\) 0 0
\(739\) −15.1940 + 26.3167i −0.558920 + 0.968077i 0.438667 + 0.898650i \(0.355451\pi\)
−0.997587 + 0.0694277i \(0.977883\pi\)
\(740\) 0.522533 + 0.905053i 0.0192087 + 0.0332704i
\(741\) 0 0
\(742\) 1.78249 7.14043i 0.0654374 0.262133i
\(743\) −5.09570 −0.186943 −0.0934715 0.995622i \(-0.529796\pi\)
−0.0934715 + 0.995622i \(0.529796\pi\)
\(744\) 0 0
\(745\) −4.39467 + 7.61179i −0.161008 + 0.278874i
\(746\) −19.7961 + 34.2879i −0.724787 + 1.25537i
\(747\) 0 0
\(748\) −3.25793 −0.119122
\(749\) −14.6997 + 4.21049i −0.537115 + 0.153848i
\(750\) 0 0
\(751\) 0.487506 + 0.844384i 0.0177893 + 0.0308120i 0.874783 0.484515i \(-0.161004\pi\)
−0.856994 + 0.515327i \(0.827671\pi\)
\(752\) 23.0718 39.9615i 0.841341 1.45724i
\(753\) 0 0
\(754\) 0.295165 + 0.511240i 0.0107493 + 0.0186183i
\(755\) −16.9075 −0.615326
\(756\) 0 0
\(757\) 11.6346 0.422865 0.211433 0.977393i \(-0.432187\pi\)
0.211433 + 0.977393i \(0.432187\pi\)
\(758\) −5.26750 9.12357i −0.191324 0.331383i
\(759\) 0 0
\(760\) −1.87657 + 3.25031i −0.0680703 + 0.117901i
\(761\) −27.0875 46.9169i −0.981920 1.70073i −0.654897 0.755718i \(-0.727288\pi\)
−0.327023 0.945016i \(-0.606045\pi\)
\(762\) 0 0
\(763\) 15.6820 + 15.1526i 0.567726 + 0.548562i
\(764\) −31.5484 −1.14138
\(765\) 0 0
\(766\) −32.1489 + 55.6835i −1.16159 + 2.01193i
\(767\) −21.8513 + 37.8475i −0.789004 + 1.36659i
\(768\) 0 0
\(769\) 20.8652 0.752417 0.376208 0.926535i \(-0.377228\pi\)
0.376208 + 0.926535i \(0.377228\pi\)
\(770\) −9.45762 + 2.70898i −0.340829 + 0.0976249i
\(771\) 0 0
\(772\) −4.30047 7.44863i −0.154777 0.268082i
\(773\) 27.4972 47.6266i 0.989007 1.71301i 0.366447 0.930439i \(-0.380574\pi\)
0.622561 0.782572i \(-0.286092\pi\)
\(774\) 0 0
\(775\) −6.19189 10.7247i −0.222419 0.385242i
\(776\) −13.6923 −0.491526
\(777\) 0 0
\(778\) 53.1790 1.90656
\(779\) −11.2987 19.5700i −0.404819 0.701168i
\(780\) 0 0
\(781\) 9.32802 16.1566i 0.333783 0.578129i
\(782\) −10.4963 18.1801i −0.375346 0.650119i
\(783\) 0 0
\(784\) −1.16477 33.9144i −0.0415989 1.21123i
\(785\) 23.1012 0.824516
\(786\) 0 0
\(787\) −4.59475 + 7.95833i −0.163785 + 0.283684i −0.936223 0.351406i \(-0.885704\pi\)
0.772438 + 0.635090i \(0.219037\pi\)
\(788\) 6.79103 11.7624i 0.241921 0.419019i
\(789\) 0 0
\(790\) 14.5475 0.517576
\(791\) 9.29301 37.2266i 0.330421 1.32362i
\(792\) 0 0
\(793\) −8.38296 14.5197i −0.297688 0.515610i
\(794\) 10.2967 17.8344i 0.365416 0.632919i
\(795\) 0 0
\(796\) −6.03296 10.4494i −0.213832 0.370369i
\(797\) 7.07547 0.250626 0.125313 0.992117i \(-0.460006\pi\)
0.125313 + 0.992117i \(0.460006\pi\)
\(798\) 0 0
\(799\) 14.7435 0.521586
\(800\) −10.7499 18.6194i −0.380067 0.658295i
\(801\) 0 0
\(802\) −0.996224 + 1.72551i −0.0351779 + 0.0609299i
\(803\) 2.08699 + 3.61477i 0.0736483 + 0.127563i
\(804\) 0 0
\(805\) −18.6934 18.0624i −0.658855 0.636615i
\(806\) −36.6702 −1.29165
\(807\) 0 0
\(808\) −0.628050 + 1.08781i −0.0220947 + 0.0382692i
\(809\) 2.97060 5.14522i 0.104441 0.180896i −0.809069 0.587714i \(-0.800028\pi\)
0.913510 + 0.406817i \(0.133361\pi\)
\(810\) 0 0
\(811\) 44.4139 1.55958 0.779791 0.626039i \(-0.215325\pi\)
0.779791 + 0.626039i \(0.215325\pi\)
\(812\) −0.163840 0.158309i −0.00574965 0.00555557i
\(813\) 0 0
\(814\) 0.784512 + 1.35881i 0.0274971 + 0.0476264i
\(815\) −8.15485 + 14.1246i −0.285652 + 0.494764i
\(816\) 0 0
\(817\) 12.7712 + 22.1204i 0.446808 + 0.773894i
\(818\) −40.0191 −1.39924
\(819\) 0 0
\(820\) −16.7439 −0.584721
\(821\) 3.17761 + 5.50378i 0.110899 + 0.192083i 0.916133 0.400874i \(-0.131294\pi\)
−0.805234 + 0.592958i \(0.797960\pi\)
\(822\) 0 0
\(823\) 4.73216 8.19635i 0.164953 0.285707i −0.771686 0.636004i \(-0.780586\pi\)
0.936639 + 0.350297i \(0.113919\pi\)
\(824\) 1.08380 + 1.87720i 0.0377560 + 0.0653953i
\(825\) 0 0
\(826\) 9.96205 39.9067i 0.346624 1.38853i
\(827\) 4.86261 0.169090 0.0845448 0.996420i \(-0.473056\pi\)
0.0845448 + 0.996420i \(0.473056\pi\)
\(828\) 0 0
\(829\) 20.3926 35.3211i 0.708266 1.22675i −0.257234 0.966349i \(-0.582811\pi\)
0.965500 0.260403i \(-0.0838555\pi\)
\(830\) 6.88402 11.9235i 0.238948 0.413870i
\(831\) 0 0
\(832\) −13.4801 −0.467337
\(833\) 9.19826 5.74035i 0.318701 0.198891i
\(834\) 0 0
\(835\) 2.35247 + 4.07460i 0.0814107 + 0.141007i
\(836\) 2.63362 4.56156i 0.0910856 0.157765i
\(837\) 0 0
\(838\) −23.1823 40.1529i −0.800818 1.38706i
\(839\) 19.2034 0.662976 0.331488 0.943459i \(-0.392449\pi\)
0.331488 + 0.943459i \(0.392449\pi\)
\(840\) 0 0
\(841\) −28.9962 −0.999868
\(842\) −27.3063 47.2959i −0.941036 1.62992i
\(843\) 0 0
\(844\) −3.95113 + 6.84355i −0.136003 + 0.235565i
\(845\) 9.20374 + 15.9413i 0.316618 + 0.548399i
\(846\) 0 0
\(847\) 22.1556 6.34612i 0.761276 0.218055i
\(848\) −7.32376 −0.251499
\(849\) 0 0
\(850\) 4.58940 7.94907i 0.157415 0.272651i
\(851\) −2.07286 + 3.59029i −0.0710566 + 0.123074i
\(852\) 0 0
\(853\) 13.9011 0.475965 0.237982 0.971269i \(-0.423514\pi\)
0.237982 + 0.971269i \(0.423514\pi\)
\(854\) 11.3477 + 10.9646i 0.388309 + 0.375202i
\(855\) 0 0
\(856\) 3.24469 + 5.61996i 0.110901 + 0.192086i
\(857\) 28.4919 49.3494i 0.973265 1.68574i 0.287718 0.957715i \(-0.407103\pi\)
0.685547 0.728029i \(-0.259563\pi\)
\(858\) 0 0
\(859\) 10.0501 + 17.4073i 0.342905 + 0.593929i 0.984971 0.172721i \(-0.0552557\pi\)
−0.642066 + 0.766650i \(0.721922\pi\)
\(860\) 18.9260 0.645370
\(861\) 0 0
\(862\) 9.00429 0.306687
\(863\) 3.08893 + 5.35018i 0.105148 + 0.182122i 0.913799 0.406167i \(-0.133135\pi\)
−0.808650 + 0.588289i \(0.799802\pi\)
\(864\) 0 0
\(865\) −6.76781 + 11.7222i −0.230112 + 0.398566i
\(866\) −8.94318 15.4900i −0.303902 0.526373i
\(867\) 0 0
\(868\) 13.6051 3.89697i 0.461788 0.132272i
\(869\) 8.95612 0.303816
\(870\) 0 0
\(871\) −17.9436 + 31.0792i −0.607996 + 1.05308i
\(872\) 4.62732 8.01476i 0.156701 0.271414i
\(873\) 0 0
\(874\) 33.9396 1.14802
\(875\) 7.02935 28.1587i 0.237636 0.951937i
\(876\) 0 0
\(877\) 18.6287 + 32.2658i 0.629046 + 1.08954i 0.987743 + 0.156086i \(0.0498877\pi\)
−0.358697 + 0.933454i \(0.616779\pi\)
\(878\) 13.6468 23.6370i 0.460558 0.797710i
\(879\) 0 0
\(880\) 4.89504 + 8.47846i 0.165012 + 0.285809i
\(881\) 11.7848 0.397041 0.198520 0.980097i \(-0.436386\pi\)
0.198520 + 0.980097i \(0.436386\pi\)
\(882\) 0 0
\(883\) −29.2308 −0.983693 −0.491847 0.870682i \(-0.663678\pi\)
−0.491847 + 0.870682i \(0.663678\pi\)
\(884\) −5.57265 9.65211i −0.187428 0.324636i
\(885\) 0 0
\(886\) −20.1634 + 34.9240i −0.677402 + 1.17329i
\(887\) 14.2581 + 24.6957i 0.478739 + 0.829201i 0.999703 0.0243782i \(-0.00776058\pi\)
−0.520964 + 0.853579i \(0.674427\pi\)
\(888\) 0 0
\(889\) 5.44686 21.8194i 0.182682 0.731800i
\(890\) −3.45680 −0.115872
\(891\) 0 0
\(892\) 8.14822 14.1131i 0.272823 0.472543i
\(893\) −11.9182 + 20.6430i −0.398828 + 0.690790i
\(894\) 0 0
\(895\) −2.27063 −0.0758986
\(896\) −21.7853 + 6.24006i −0.727797 + 0.208466i
\(897\) 0 0
\(898\) 19.7890 + 34.2755i 0.660366 + 1.14379i
\(899\) −0.119171 + 0.206410i −0.00397456 + 0.00688414i
\(900\) 0 0
\(901\) −1.17002 2.02653i −0.0389790 0.0675135i
\(902\) −25.1386 −0.837025
\(903\) 0 0
\(904\) −16.2837 −0.541587
\(905\) −11.3415 19.6440i −0.377003 0.652989i
\(906\) 0 0
\(907\) 3.94577 6.83428i 0.131017 0.226929i −0.793052 0.609154i \(-0.791509\pi\)
0.924069 + 0.382226i \(0.124842\pi\)
\(908\) 7.77317 + 13.4635i 0.257962 + 0.446803i
\(909\) 0 0
\(910\) −24.2029 23.3860i −0.802319 0.775237i
\(911\) −28.4412 −0.942299 −0.471150 0.882053i \(-0.656161\pi\)
−0.471150 + 0.882053i \(0.656161\pi\)
\(912\) 0 0
\(913\) 4.23813 7.34065i 0.140262 0.242940i
\(914\) −37.4007 + 64.7798i −1.23710 + 2.14273i
\(915\) 0 0
\(916\) −13.4241 −0.443545
\(917\) −5.12118 + 1.46688i −0.169116 + 0.0484406i
\(918\) 0 0
\(919\) 3.99271 + 6.91558i 0.131707 + 0.228124i 0.924335 0.381582i \(-0.124621\pi\)
−0.792627 + 0.609706i \(0.791287\pi\)
\(920\) −5.51590 + 9.55382i −0.181854 + 0.314980i
\(921\) 0 0
\(922\) −2.60610 4.51390i −0.0858274 0.148657i
\(923\) 63.8219 2.10072
\(924\) 0 0
\(925\) −1.81267 −0.0596004
\(926\) −25.6529 44.4322i −0.843008 1.46013i
\(927\) 0 0
\(928\) −0.206895 + 0.358353i −0.00679167 + 0.0117635i
\(929\) 9.40031 + 16.2818i 0.308414 + 0.534189i 0.978016 0.208531i \(-0.0668684\pi\)
−0.669601 + 0.742721i \(0.733535\pi\)
\(930\) 0 0
\(931\) 0.601686 + 17.5192i 0.0197195 + 0.574169i
\(932\) −26.8161 −0.878391
\(933\) 0 0
\(934\) 24.5288 42.4852i 0.802608 1.39016i
\(935\) −1.56403 + 2.70898i −0.0511493 + 0.0885932i
\(936\) 0 0
\(937\) 48.5788 1.58700 0.793500 0.608570i \(-0.208256\pi\)
0.793500 + 0.608570i \(0.208256\pi\)
\(938\) 8.18053 32.7701i 0.267104 1.06998i
\(939\) 0 0
\(940\) 8.83094 + 15.2956i 0.288034 + 0.498889i
\(941\) 10.2425 17.7406i 0.333898 0.578328i −0.649375 0.760468i \(-0.724969\pi\)
0.983272 + 0.182141i \(0.0583027\pi\)
\(942\) 0 0
\(943\) −33.2110 57.5231i −1.08150 1.87321i
\(944\) −40.9312 −1.33220
\(945\) 0 0
\(946\) 28.4148 0.923843
\(947\) −7.42524 12.8609i −0.241288 0.417923i 0.719793 0.694188i \(-0.244236\pi\)
−0.961081 + 0.276265i \(0.910903\pi\)
\(948\) 0 0
\(949\) −7.13954 + 12.3661i −0.231759 + 0.401419i
\(950\) 7.41989 + 12.8516i 0.240733 + 0.416962i
\(951\) 0 0
\(952\) −3.30914 3.19744i −0.107250 0.103629i
\(953\) −46.4678 −1.50524 −0.752620 0.658456i \(-0.771210\pi\)
−0.752620 + 0.658456i \(0.771210\pi\)
\(954\) 0 0
\(955\) −15.1454 + 26.2326i −0.490094 + 0.848868i
\(956\) 0.270584 0.468665i 0.00875130 0.0151577i
\(957\) 0 0
\(958\) 58.1447 1.87857
\(959\) −4.21896 4.07655i −0.136237 0.131639i
\(960\) 0 0
\(961\) 8.09733 + 14.0250i 0.261204 + 0.452419i
\(962\) −2.68380 + 4.64847i −0.0865291 + 0.149873i
\(963\) 0 0
\(964\) −7.39301 12.8051i −0.238113 0.412423i
\(965\) −8.25809 −0.265837
\(966\) 0 0
\(967\) −1.72734 −0.0555475 −0.0277738 0.999614i \(-0.508842\pi\)
−0.0277738 + 0.999614i \(0.508842\pi\)
\(968\) −4.89045 8.47050i −0.157185 0.272252i
\(969\) 0 0
\(970\) 14.9843 25.9536i 0.481118 0.833320i
\(971\) 3.78085 + 6.54863i 0.121333 + 0.210156i 0.920294 0.391228i \(-0.127950\pi\)
−0.798960 + 0.601384i \(0.794616\pi\)
\(972\) 0 0
\(973\) −0.484024 + 1.93894i −0.0155171 + 0.0621595i
\(974\) 0.563740 0.0180634
\(975\) 0 0
\(976\) 7.85137 13.5990i 0.251316 0.435293i
\(977\) −28.3101 + 49.0345i −0.905721 + 1.56875i −0.0857737 + 0.996315i \(0.527336\pi\)
−0.819947 + 0.572440i \(0.805997\pi\)
\(978\) 0 0
\(979\) −2.12817 −0.0680166
\(980\) 11.4648 + 6.10443i 0.366231 + 0.194999i
\(981\) 0 0
\(982\) 16.6997 + 28.9247i 0.532909 + 0.923025i
\(983\) 16.1486 27.9702i 0.515061 0.892112i −0.484786 0.874633i \(-0.661103\pi\)
0.999847 0.0174790i \(-0.00556402\pi\)
\(984\) 0 0
\(985\) −6.52033 11.2936i −0.207755 0.359842i
\(986\) −0.176657 −0.00562591
\(987\) 0 0
\(988\) 18.0191 0.573264
\(989\) 37.5391 + 65.0197i 1.19367 + 2.06750i
\(990\) 0 0
\(991\) −7.15502 + 12.3929i −0.227287 + 0.393672i −0.957003 0.290078i \(-0.906319\pi\)
0.729716 + 0.683750i \(0.239652\pi\)
\(992\) −12.8520 22.2602i −0.408050 0.706764i
\(993\) 0 0
\(994\) −57.7448 + 16.5401i −1.83155 + 0.524619i
\(995\) −11.5849 −0.367268
\(996\) 0 0
\(997\) −28.1262 + 48.7160i −0.890765 + 1.54285i −0.0518058 + 0.998657i \(0.516498\pi\)
−0.838960 + 0.544194i \(0.816836\pi\)
\(998\) 19.6176 33.9787i 0.620985 1.07558i
\(999\) 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 567.2.e.e.487.2 10
3.2 odd 2 567.2.e.f.487.4 10
7.2 even 3 inner 567.2.e.e.163.2 10
7.3 odd 6 3969.2.a.bb.1.4 5
7.4 even 3 3969.2.a.bc.1.4 5
9.2 odd 6 63.2.g.b.4.4 10
9.4 even 3 189.2.h.b.46.4 10
9.5 odd 6 63.2.h.b.25.2 yes 10
9.7 even 3 189.2.g.b.172.2 10
21.2 odd 6 567.2.e.f.163.4 10
21.11 odd 6 3969.2.a.z.1.2 5
21.17 even 6 3969.2.a.ba.1.2 5
36.7 odd 6 3024.2.t.i.1873.2 10
36.11 even 6 1008.2.t.i.193.5 10
36.23 even 6 1008.2.q.i.529.2 10
36.31 odd 6 3024.2.q.i.2881.4 10
63.2 odd 6 63.2.h.b.58.2 yes 10
63.4 even 3 1323.2.f.e.883.2 10
63.5 even 6 441.2.g.f.79.4 10
63.11 odd 6 441.2.f.e.148.4 10
63.13 odd 6 1323.2.h.f.802.4 10
63.16 even 3 189.2.h.b.37.4 10
63.20 even 6 441.2.g.f.67.4 10
63.23 odd 6 63.2.g.b.16.4 yes 10
63.25 even 3 1323.2.f.e.442.2 10
63.31 odd 6 1323.2.f.f.883.2 10
63.32 odd 6 441.2.f.e.295.4 10
63.34 odd 6 1323.2.g.f.361.2 10
63.38 even 6 441.2.f.f.148.4 10
63.40 odd 6 1323.2.g.f.667.2 10
63.41 even 6 441.2.h.f.214.2 10
63.47 even 6 441.2.h.f.373.2 10
63.52 odd 6 1323.2.f.f.442.2 10
63.58 even 3 189.2.g.b.100.2 10
63.59 even 6 441.2.f.f.295.4 10
63.61 odd 6 1323.2.h.f.226.4 10
252.23 even 6 1008.2.t.i.961.5 10
252.79 odd 6 3024.2.q.i.2305.4 10
252.191 even 6 1008.2.q.i.625.2 10
252.247 odd 6 3024.2.t.i.289.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.4 10 9.2 odd 6
63.2.g.b.16.4 yes 10 63.23 odd 6
63.2.h.b.25.2 yes 10 9.5 odd 6
63.2.h.b.58.2 yes 10 63.2 odd 6
189.2.g.b.100.2 10 63.58 even 3
189.2.g.b.172.2 10 9.7 even 3
189.2.h.b.37.4 10 63.16 even 3
189.2.h.b.46.4 10 9.4 even 3
441.2.f.e.148.4 10 63.11 odd 6
441.2.f.e.295.4 10 63.32 odd 6
441.2.f.f.148.4 10 63.38 even 6
441.2.f.f.295.4 10 63.59 even 6
441.2.g.f.67.4 10 63.20 even 6
441.2.g.f.79.4 10 63.5 even 6
441.2.h.f.214.2 10 63.41 even 6
441.2.h.f.373.2 10 63.47 even 6
567.2.e.e.163.2 10 7.2 even 3 inner
567.2.e.e.487.2 10 1.1 even 1 trivial
567.2.e.f.163.4 10 21.2 odd 6
567.2.e.f.487.4 10 3.2 odd 2
1008.2.q.i.529.2 10 36.23 even 6
1008.2.q.i.625.2 10 252.191 even 6
1008.2.t.i.193.5 10 36.11 even 6
1008.2.t.i.961.5 10 252.23 even 6
1323.2.f.e.442.2 10 63.25 even 3
1323.2.f.e.883.2 10 63.4 even 3
1323.2.f.f.442.2 10 63.52 odd 6
1323.2.f.f.883.2 10 63.31 odd 6
1323.2.g.f.361.2 10 63.34 odd 6
1323.2.g.f.667.2 10 63.40 odd 6
1323.2.h.f.226.4 10 63.61 odd 6
1323.2.h.f.802.4 10 63.13 odd 6
3024.2.q.i.2305.4 10 252.79 odd 6
3024.2.q.i.2881.4 10 36.31 odd 6
3024.2.t.i.289.2 10 252.247 odd 6
3024.2.t.i.1873.2 10 36.7 odd 6
3969.2.a.z.1.2 5 21.11 odd 6
3969.2.a.ba.1.2 5 21.17 even 6
3969.2.a.bb.1.4 5 7.3 odd 6
3969.2.a.bc.1.4 5 7.4 even 3