Properties

Label 644.2.y.a.261.7
Level $644$
Weight $2$
Character 644.261
Analytic conductor $5.142$
Analytic rank $0$
Dimension $320$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [644,2,Mod(9,644)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(644, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([0, 22, 30]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("644.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 644.y (of order \(33\), degree \(20\), 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: \(5.14236589017\)
Analytic rank: \(0\)
Dimension: \(320\)
Relative dimension: \(16\) over \(\Q(\zeta_{33})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 261.7
Character \(\chi\) \(=\) 644.261
Dual form 644.2.y.a.417.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.197213 + 0.276947i) q^{3} +(1.19919 - 0.231125i) q^{5} +(2.50207 + 0.860036i) q^{7} +(0.943397 + 2.72577i) q^{9} +O(q^{10})\) \(q+(-0.197213 + 0.276947i) q^{3} +(1.19919 - 0.231125i) q^{5} +(2.50207 + 0.860036i) q^{7} +(0.943397 + 2.72577i) q^{9} +(-2.76318 + 2.17299i) q^{11} +(-3.06291 + 1.96841i) q^{13} +(-0.172486 + 0.377692i) q^{15} +(1.05715 + 1.00799i) q^{17} +(2.83097 - 2.69932i) q^{19} +(-0.731623 + 0.523329i) q^{21} +(4.64971 - 1.17480i) q^{23} +(-3.25720 + 1.30399i) q^{25} +(-1.91959 - 0.563643i) q^{27} +(-3.72259 + 1.09305i) q^{29} +(7.59757 - 0.725480i) q^{31} +(-0.0568675 - 1.19380i) q^{33} +(3.19923 + 0.453056i) q^{35} +(-2.05309 - 5.93201i) q^{37} +(0.0588998 - 1.23646i) q^{39} +(7.13579 + 8.23515i) q^{41} +(2.85154 + 6.24400i) q^{43} +(1.76130 + 3.05067i) q^{45} +(-4.11529 + 7.12788i) q^{47} +(5.52068 + 4.30373i) q^{49} +(-0.487641 + 0.0939851i) q^{51} +(-0.200219 + 4.20312i) q^{53} +(-2.81135 + 3.24447i) q^{55} +(0.189265 + 1.31637i) q^{57} +(-3.86859 - 1.99440i) q^{59} +(-3.19051 - 4.48044i) q^{61} +(0.0161860 + 7.63141i) q^{63} +(-3.21806 + 3.06841i) q^{65} +(9.04338 - 3.62042i) q^{67} +(-0.591626 + 1.51941i) q^{69} +(2.02254 - 14.0671i) q^{71} +(-1.95769 - 8.06970i) q^{73} +(0.281227 - 1.15923i) q^{75} +(-8.78252 + 3.06054i) q^{77} +(-0.576761 - 12.1077i) q^{79} +(-6.26723 + 4.92860i) q^{81} +(4.97214 - 5.73815i) q^{83} +(1.50069 + 0.964434i) q^{85} +(0.431425 - 1.24652i) q^{87} +(-6.78039 - 0.647449i) q^{89} +(-9.35651 + 2.29089i) q^{91} +(-1.29742 + 2.24719i) q^{93} +(2.77099 - 3.89131i) q^{95} +(-3.18666 - 3.67761i) q^{97} +(-8.52985 - 5.48180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/644\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\) \(323\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{11}\right)\) \(1\)

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 0
\(3\) −0.197213 + 0.276947i −0.113861 + 0.159895i −0.867574 0.497309i \(-0.834322\pi\)
0.753713 + 0.657204i \(0.228261\pi\)
\(4\) 0 0
\(5\) 1.19919 0.231125i 0.536294 0.103362i 0.0860889 0.996287i \(-0.472563\pi\)
0.450205 + 0.892925i \(0.351351\pi\)
\(6\) 0 0
\(7\) 2.50207 + 0.860036i 0.945692 + 0.325063i
\(8\) 0 0
\(9\) 0.943397 + 2.72577i 0.314466 + 0.908589i
\(10\) 0 0
\(11\) −2.76318 + 2.17299i −0.833132 + 0.655182i −0.940784 0.339007i \(-0.889909\pi\)
0.107652 + 0.994189i \(0.465667\pi\)
\(12\) 0 0
\(13\) −3.06291 + 1.96841i −0.849498 + 0.545939i −0.891418 0.453182i \(-0.850289\pi\)
0.0419200 + 0.999121i \(0.486653\pi\)
\(14\) 0 0
\(15\) −0.172486 + 0.377692i −0.0445357 + 0.0975196i
\(16\) 0 0
\(17\) 1.05715 + 1.00799i 0.256395 + 0.244473i 0.807364 0.590053i \(-0.200893\pi\)
−0.550969 + 0.834526i \(0.685742\pi\)
\(18\) 0 0
\(19\) 2.83097 2.69932i 0.649469 0.619268i −0.291979 0.956425i \(-0.594314\pi\)
0.941448 + 0.337157i \(0.109465\pi\)
\(20\) 0 0
\(21\) −0.731623 + 0.523329i −0.159653 + 0.114200i
\(22\) 0 0
\(23\) 4.64971 1.17480i 0.969532 0.244963i
\(24\) 0 0
\(25\) −3.25720 + 1.30399i −0.651441 + 0.260798i
\(26\) 0 0
\(27\) −1.91959 0.563643i −0.369426 0.108473i
\(28\) 0 0
\(29\) −3.72259 + 1.09305i −0.691267 + 0.202974i −0.608452 0.793590i \(-0.708209\pi\)
−0.0828152 + 0.996565i \(0.526391\pi\)
\(30\) 0 0
\(31\) 7.59757 0.725480i 1.36456 0.130300i 0.613064 0.790033i \(-0.289937\pi\)
0.751500 + 0.659733i \(0.229331\pi\)
\(32\) 0 0
\(33\) −0.0568675 1.19380i −0.00989936 0.207813i
\(34\) 0 0
\(35\) 3.19923 + 0.453056i 0.540768 + 0.0765804i
\(36\) 0 0
\(37\) −2.05309 5.93201i −0.337526 0.975217i −0.978247 0.207443i \(-0.933486\pi\)
0.640721 0.767774i \(-0.278635\pi\)
\(38\) 0 0
\(39\) 0.0588998 1.23646i 0.00943151 0.197992i
\(40\) 0 0
\(41\) 7.13579 + 8.23515i 1.11442 + 1.28611i 0.954245 + 0.299026i \(0.0966616\pi\)
0.160179 + 0.987088i \(0.448793\pi\)
\(42\) 0 0
\(43\) 2.85154 + 6.24400i 0.434856 + 0.952201i 0.992514 + 0.122130i \(0.0389726\pi\)
−0.557659 + 0.830070i \(0.688300\pi\)
\(44\) 0 0
\(45\) 1.76130 + 3.05067i 0.262560 + 0.454767i
\(46\) 0 0
\(47\) −4.11529 + 7.12788i −0.600276 + 1.03971i 0.392503 + 0.919751i \(0.371609\pi\)
−0.992779 + 0.119958i \(0.961724\pi\)
\(48\) 0 0
\(49\) 5.52068 + 4.30373i 0.788668 + 0.614819i
\(50\) 0 0
\(51\) −0.487641 + 0.0939851i −0.0682834 + 0.0131605i
\(52\) 0 0
\(53\) −0.200219 + 4.20312i −0.0275022 + 0.577342i 0.942494 + 0.334223i \(0.108474\pi\)
−0.969996 + 0.243120i \(0.921829\pi\)
\(54\) 0 0
\(55\) −2.81135 + 3.24447i −0.379082 + 0.437484i
\(56\) 0 0
\(57\) 0.189265 + 1.31637i 0.0250688 + 0.174357i
\(58\) 0 0
\(59\) −3.86859 1.99440i −0.503647 0.259648i 0.187627 0.982240i \(-0.439920\pi\)
−0.691275 + 0.722592i \(0.742951\pi\)
\(60\) 0 0
\(61\) −3.19051 4.48044i −0.408503 0.573662i 0.558154 0.829737i \(-0.311510\pi\)
−0.966657 + 0.256075i \(0.917570\pi\)
\(62\) 0 0
\(63\) 0.0161860 + 7.63141i 0.00203925 + 0.961467i
\(64\) 0 0
\(65\) −3.21806 + 3.06841i −0.399151 + 0.380590i
\(66\) 0 0
\(67\) 9.04338 3.62042i 1.10482 0.442305i 0.253708 0.967281i \(-0.418350\pi\)
0.851117 + 0.524976i \(0.175926\pi\)
\(68\) 0 0
\(69\) −0.591626 + 1.51941i −0.0712234 + 0.182915i
\(70\) 0 0
\(71\) 2.02254 14.0671i 0.240032 1.66946i −0.411939 0.911212i \(-0.635148\pi\)
0.651970 0.758245i \(-0.273943\pi\)
\(72\) 0 0
\(73\) −1.95769 8.06970i −0.229130 0.944487i −0.963920 0.266192i \(-0.914234\pi\)
0.734790 0.678295i \(-0.237281\pi\)
\(74\) 0 0
\(75\) 0.281227 1.15923i 0.0324733 0.133857i
\(76\) 0 0
\(77\) −8.78252 + 3.06054i −1.00086 + 0.348780i
\(78\) 0 0
\(79\) −0.576761 12.1077i −0.0648907 1.36222i −0.763077 0.646308i \(-0.776312\pi\)
0.698186 0.715916i \(-0.253991\pi\)
\(80\) 0 0
\(81\) −6.26723 + 4.92860i −0.696358 + 0.547622i
\(82\) 0 0
\(83\) 4.97214 5.73815i 0.545763 0.629844i −0.414128 0.910219i \(-0.635913\pi\)
0.959891 + 0.280375i \(0.0904587\pi\)
\(84\) 0 0
\(85\) 1.50069 + 0.964434i 0.162772 + 0.104608i
\(86\) 0 0
\(87\) 0.431425 1.24652i 0.0462537 0.133641i
\(88\) 0 0
\(89\) −6.78039 0.647449i −0.718720 0.0686294i −0.270714 0.962660i \(-0.587260\pi\)
−0.448006 + 0.894031i \(0.647866\pi\)
\(90\) 0 0
\(91\) −9.35651 + 2.29089i −0.980829 + 0.240150i
\(92\) 0 0
\(93\) −1.29742 + 2.24719i −0.134536 + 0.233023i
\(94\) 0 0
\(95\) 2.77099 3.89131i 0.284297 0.399240i
\(96\) 0 0
\(97\) −3.18666 3.67761i −0.323557 0.373404i 0.570546 0.821265i \(-0.306731\pi\)
−0.894103 + 0.447861i \(0.852186\pi\)
\(98\) 0 0
\(99\) −8.52985 5.48180i −0.857283 0.550942i
\(100\) 0 0
\(101\) 17.2520 + 3.32504i 1.71663 + 0.330854i 0.950240 0.311518i \(-0.100837\pi\)
0.766393 + 0.642372i \(0.222049\pi\)
\(102\) 0 0
\(103\) 14.1042 + 5.64646i 1.38973 + 0.556362i 0.941334 0.337475i \(-0.109573\pi\)
0.448391 + 0.893837i \(0.351997\pi\)
\(104\) 0 0
\(105\) −0.756400 + 0.796666i −0.0738171 + 0.0777467i
\(106\) 0 0
\(107\) −4.11307 5.77600i −0.397626 0.558387i 0.566422 0.824115i \(-0.308327\pi\)
−0.964048 + 0.265728i \(0.914388\pi\)
\(108\) 0 0
\(109\) −5.95518 5.67826i −0.570403 0.543878i 0.349037 0.937109i \(-0.386509\pi\)
−0.919440 + 0.393231i \(0.871357\pi\)
\(110\) 0 0
\(111\) 2.04775 + 0.601272i 0.194363 + 0.0570702i
\(112\) 0 0
\(113\) 1.15111 8.00612i 0.108287 0.753152i −0.861245 0.508189i \(-0.830315\pi\)
0.969532 0.244963i \(-0.0787759\pi\)
\(114\) 0 0
\(115\) 5.30436 2.48347i 0.494634 0.231585i
\(116\) 0 0
\(117\) −8.25498 6.49178i −0.763173 0.600166i
\(118\) 0 0
\(119\) 1.77814 + 3.43123i 0.163002 + 0.314541i
\(120\) 0 0
\(121\) 0.319946 1.31883i 0.0290860 0.119894i
\(122\) 0 0
\(123\) −3.68796 + 0.352158i −0.332533 + 0.0317530i
\(124\) 0 0
\(125\) −8.74156 + 5.61786i −0.781869 + 0.502477i
\(126\) 0 0
\(127\) −1.92999 13.4234i −0.171259 1.19113i −0.876230 0.481894i \(-0.839949\pi\)
0.704971 0.709236i \(-0.250960\pi\)
\(128\) 0 0
\(129\) −2.29161 0.441672i −0.201765 0.0388871i
\(130\) 0 0
\(131\) −9.75237 + 5.02770i −0.852069 + 0.439272i −0.828193 0.560443i \(-0.810631\pi\)
−0.0238757 + 0.999715i \(0.507601\pi\)
\(132\) 0 0
\(133\) 9.40479 4.31916i 0.815499 0.374518i
\(134\) 0 0
\(135\) −2.43223 0.232249i −0.209333 0.0199888i
\(136\) 0 0
\(137\) 4.13517 + 7.16233i 0.353292 + 0.611919i 0.986824 0.161797i \(-0.0517289\pi\)
−0.633532 + 0.773716i \(0.718396\pi\)
\(138\) 0 0
\(139\) 9.31077 0.789729 0.394864 0.918739i \(-0.370792\pi\)
0.394864 + 0.918739i \(0.370792\pi\)
\(140\) 0 0
\(141\) −1.16246 2.54542i −0.0978964 0.214363i
\(142\) 0 0
\(143\) 4.18604 12.0948i 0.350054 1.01142i
\(144\) 0 0
\(145\) −4.21146 + 2.17116i −0.349742 + 0.180305i
\(146\) 0 0
\(147\) −2.28065 + 0.680181i −0.188105 + 0.0561004i
\(148\) 0 0
\(149\) −15.9743 6.39514i −1.30866 0.523910i −0.390679 0.920527i \(-0.627760\pi\)
−0.917984 + 0.396617i \(0.870184\pi\)
\(150\) 0 0
\(151\) −3.50907 1.80905i −0.285564 0.147219i 0.309493 0.950902i \(-0.399841\pi\)
−0.595058 + 0.803683i \(0.702871\pi\)
\(152\) 0 0
\(153\) −1.75023 + 3.83246i −0.141498 + 0.309836i
\(154\) 0 0
\(155\) 8.94324 2.62597i 0.718339 0.210923i
\(156\) 0 0
\(157\) 1.04802 + 4.32002i 0.0836415 + 0.344775i 0.998220 0.0596326i \(-0.0189929\pi\)
−0.914579 + 0.404407i \(0.867478\pi\)
\(158\) 0 0
\(159\) −1.12455 0.884358i −0.0891828 0.0701341i
\(160\) 0 0
\(161\) 12.6443 + 1.05949i 0.996508 + 0.0834995i
\(162\) 0 0
\(163\) −16.8321 13.2369i −1.31839 1.03680i −0.995922 0.0902156i \(-0.971244\pi\)
−0.322470 0.946580i \(-0.604513\pi\)
\(164\) 0 0
\(165\) −0.344111 1.41844i −0.0267890 0.110426i
\(166\) 0 0
\(167\) −10.9660 + 3.21990i −0.848573 + 0.249163i −0.676977 0.736004i \(-0.736710\pi\)
−0.171596 + 0.985167i \(0.554892\pi\)
\(168\) 0 0
\(169\) 0.106372 0.232923i 0.00818249 0.0179171i
\(170\) 0 0
\(171\) 10.0285 + 5.17003i 0.766896 + 0.395362i
\(172\) 0 0
\(173\) −2.89309 1.15822i −0.219958 0.0880578i 0.259066 0.965859i \(-0.416585\pi\)
−0.479024 + 0.877802i \(0.659009\pi\)
\(174\) 0 0
\(175\) −9.27122 + 0.461353i −0.700838 + 0.0348750i
\(176\) 0 0
\(177\) 1.31528 0.678072i 0.0988622 0.0509670i
\(178\) 0 0
\(179\) 3.64749 10.5387i 0.272626 0.787702i −0.722703 0.691159i \(-0.757100\pi\)
0.995329 0.0965427i \(-0.0307784\pi\)
\(180\) 0 0
\(181\) 0.765806 + 1.67688i 0.0569219 + 0.124642i 0.935956 0.352118i \(-0.114538\pi\)
−0.879034 + 0.476760i \(0.841811\pi\)
\(182\) 0 0
\(183\) 1.87005 0.138238
\(184\) 0 0
\(185\) −3.83308 6.63908i −0.281813 0.488115i
\(186\) 0 0
\(187\) −5.11144 0.488083i −0.373785 0.0356922i
\(188\) 0 0
\(189\) −4.31819 3.06119i −0.314102 0.222669i
\(190\) 0 0
\(191\) −11.0775 + 5.71086i −0.801541 + 0.413223i −0.809773 0.586743i \(-0.800410\pi\)
0.00823231 + 0.999966i \(0.497380\pi\)
\(192\) 0 0
\(193\) −17.1329 3.30209i −1.23325 0.237690i −0.469344 0.883015i \(-0.655510\pi\)
−0.763908 + 0.645326i \(0.776722\pi\)
\(194\) 0 0
\(195\) −0.215144 1.49636i −0.0154068 0.107157i
\(196\) 0 0
\(197\) 7.90439 5.07984i 0.563165 0.361924i −0.227874 0.973691i \(-0.573177\pi\)
0.791038 + 0.611767i \(0.209541\pi\)
\(198\) 0 0
\(199\) 24.3286 2.32310i 1.72461 0.164680i 0.814809 0.579730i \(-0.196842\pi\)
0.909799 + 0.415050i \(0.136236\pi\)
\(200\) 0 0
\(201\) −0.780806 + 3.21853i −0.0550738 + 0.227017i
\(202\) 0 0
\(203\) −10.2542 0.466673i −0.719706 0.0327540i
\(204\) 0 0
\(205\) 10.4605 + 8.22624i 0.730594 + 0.574545i
\(206\) 0 0
\(207\) 7.58876 + 11.5657i 0.527455 + 0.803874i
\(208\) 0 0
\(209\) −1.95688 + 13.6104i −0.135360 + 0.941452i
\(210\) 0 0
\(211\) 10.6625 + 3.13078i 0.734033 + 0.215532i 0.627324 0.778759i \(-0.284150\pi\)
0.106710 + 0.994290i \(0.465968\pi\)
\(212\) 0 0
\(213\) 3.49696 + 3.33434i 0.239608 + 0.228466i
\(214\) 0 0
\(215\) 4.86268 + 6.82867i 0.331632 + 0.465712i
\(216\) 0 0
\(217\) 19.6336 + 4.71898i 1.33281 + 0.320345i
\(218\) 0 0
\(219\) 2.62096 + 1.04927i 0.177108 + 0.0709032i
\(220\) 0 0
\(221\) −5.22207 1.00647i −0.351275 0.0677027i
\(222\) 0 0
\(223\) −12.2722 7.88690i −0.821811 0.528146i 0.0608553 0.998147i \(-0.480617\pi\)
−0.882666 + 0.470001i \(0.844254\pi\)
\(224\) 0 0
\(225\) −6.62721 7.64820i −0.441814 0.509880i
\(226\) 0 0
\(227\) −0.563984 + 0.792005i −0.0374330 + 0.0525672i −0.832868 0.553471i \(-0.813303\pi\)
0.795435 + 0.606038i \(0.207242\pi\)
\(228\) 0 0
\(229\) 8.68120 15.0363i 0.573670 0.993625i −0.422515 0.906356i \(-0.638853\pi\)
0.996185 0.0872690i \(-0.0278140\pi\)
\(230\) 0 0
\(231\) 0.884421 3.03587i 0.0581906 0.199745i
\(232\) 0 0
\(233\) −26.6366 2.54349i −1.74502 0.166629i −0.826747 0.562573i \(-0.809811\pi\)
−0.918275 + 0.395944i \(0.870417\pi\)
\(234\) 0 0
\(235\) −3.28757 + 9.49882i −0.214458 + 0.619635i
\(236\) 0 0
\(237\) 3.46693 + 2.22806i 0.225202 + 0.144728i
\(238\) 0 0
\(239\) −5.68332 + 6.55890i −0.367624 + 0.424260i −0.909179 0.416405i \(-0.863290\pi\)
0.541556 + 0.840665i \(0.317835\pi\)
\(240\) 0 0
\(241\) 7.41213 5.82896i 0.477457 0.375476i −0.350232 0.936663i \(-0.613897\pi\)
0.827689 + 0.561187i \(0.189655\pi\)
\(242\) 0 0
\(243\) −0.414564 8.70277i −0.0265943 0.558283i
\(244\) 0 0
\(245\) 7.61503 + 3.88502i 0.486507 + 0.248205i
\(246\) 0 0
\(247\) −3.35762 + 13.8403i −0.213640 + 0.880638i
\(248\) 0 0
\(249\) 0.608593 + 2.50865i 0.0385680 + 0.158979i
\(250\) 0 0
\(251\) −1.79439 + 12.4802i −0.113261 + 0.787745i 0.851450 + 0.524435i \(0.175723\pi\)
−0.964711 + 0.263310i \(0.915186\pi\)
\(252\) 0 0
\(253\) −10.2952 + 13.3500i −0.647253 + 0.839306i
\(254\) 0 0
\(255\) −0.563051 + 0.225412i −0.0352596 + 0.0141158i
\(256\) 0 0
\(257\) 14.0370 13.3843i 0.875607 0.834889i −0.111696 0.993742i \(-0.535628\pi\)
0.987302 + 0.158853i \(0.0507797\pi\)
\(258\) 0 0
\(259\) −0.0352252 16.6080i −0.00218879 1.03197i
\(260\) 0 0
\(261\) −6.49128 9.11573i −0.401800 0.564250i
\(262\) 0 0
\(263\) −9.03647 4.65862i −0.557213 0.287263i 0.156528 0.987674i \(-0.449970\pi\)
−0.713740 + 0.700411i \(0.753000\pi\)
\(264\) 0 0
\(265\) 0.731344 + 5.08661i 0.0449261 + 0.312468i
\(266\) 0 0
\(267\) 1.51649 1.75012i 0.0928075 0.107106i
\(268\) 0 0
\(269\) −1.30077 + 27.3066i −0.0793097 + 1.66491i 0.512388 + 0.858754i \(0.328761\pi\)
−0.591697 + 0.806160i \(0.701542\pi\)
\(270\) 0 0
\(271\) 31.5630 6.08326i 1.91731 0.369532i 0.917699 0.397277i \(-0.130045\pi\)
0.999615 + 0.0277456i \(0.00883283\pi\)
\(272\) 0 0
\(273\) 1.21077 3.04304i 0.0732791 0.184173i
\(274\) 0 0
\(275\) 6.16670 10.6810i 0.371866 0.644091i
\(276\) 0 0
\(277\) 5.34566 + 9.25896i 0.321190 + 0.556317i 0.980734 0.195349i \(-0.0625840\pi\)
−0.659544 + 0.751666i \(0.729251\pi\)
\(278\) 0 0
\(279\) 9.14502 + 20.0248i 0.547498 + 1.19885i
\(280\) 0 0
\(281\) 7.82872 + 9.03482i 0.467022 + 0.538972i 0.939581 0.342327i \(-0.111215\pi\)
−0.472559 + 0.881299i \(0.656670\pi\)
\(282\) 0 0
\(283\) 0.684220 14.3636i 0.0406727 0.853825i −0.882704 0.469929i \(-0.844279\pi\)
0.923377 0.383895i \(-0.125418\pi\)
\(284\) 0 0
\(285\) 0.531210 + 1.53483i 0.0314662 + 0.0909155i
\(286\) 0 0
\(287\) 10.7717 + 26.7419i 0.635834 + 1.57853i
\(288\) 0 0
\(289\) −0.707372 14.8496i −0.0416101 0.873504i
\(290\) 0 0
\(291\) 1.64695 0.157265i 0.0965460 0.00921902i
\(292\) 0 0
\(293\) −16.8794 + 4.95625i −0.986107 + 0.289547i −0.734743 0.678345i \(-0.762697\pi\)
−0.251364 + 0.967893i \(0.580879\pi\)
\(294\) 0 0
\(295\) −5.10012 1.49753i −0.296941 0.0871896i
\(296\) 0 0
\(297\) 6.52898 2.61381i 0.378850 0.151669i
\(298\) 0 0
\(299\) −11.9292 + 12.7509i −0.689881 + 0.737402i
\(300\) 0 0
\(301\) 1.76468 + 18.0753i 0.101714 + 1.04184i
\(302\) 0 0
\(303\) −4.32316 + 4.12213i −0.248359 + 0.236810i
\(304\) 0 0
\(305\) −4.86157 4.63549i −0.278372 0.265428i
\(306\) 0 0
\(307\) −1.67747 + 3.67315i −0.0957382 + 0.209637i −0.951442 0.307829i \(-0.900398\pi\)
0.855703 + 0.517467i \(0.173125\pi\)
\(308\) 0 0
\(309\) −4.34529 + 2.79255i −0.247195 + 0.158863i
\(310\) 0 0
\(311\) −1.26415 + 0.994138i −0.0716833 + 0.0563724i −0.653358 0.757049i \(-0.726640\pi\)
0.581674 + 0.813422i \(0.302398\pi\)
\(312\) 0 0
\(313\) −8.72307 25.2037i −0.493057 1.42460i −0.867543 0.497363i \(-0.834302\pi\)
0.374486 0.927233i \(-0.377819\pi\)
\(314\) 0 0
\(315\) 1.78322 + 9.14776i 0.100473 + 0.515418i
\(316\) 0 0
\(317\) 27.7228 5.34312i 1.55707 0.300100i 0.663203 0.748440i \(-0.269197\pi\)
0.893863 + 0.448340i \(0.147985\pi\)
\(318\) 0 0
\(319\) 7.91101 11.1095i 0.442932 0.622010i
\(320\) 0 0
\(321\) 2.41079 0.134557
\(322\) 0 0
\(323\) 5.71363 0.317915
\(324\) 0 0
\(325\) 7.40974 10.4055i 0.411018 0.577194i
\(326\) 0 0
\(327\) 2.74701 0.529443i 0.151910 0.0292783i
\(328\) 0 0
\(329\) −16.4270 + 14.2951i −0.905647 + 0.788117i
\(330\) 0 0
\(331\) −3.61273 10.4383i −0.198573 0.573740i 0.801120 0.598504i \(-0.204238\pi\)
−0.999693 + 0.0247637i \(0.992117\pi\)
\(332\) 0 0
\(333\) 14.2324 11.1925i 0.779931 0.613345i
\(334\) 0 0
\(335\) 10.0080 6.43172i 0.546793 0.351402i
\(336\) 0 0
\(337\) −10.1557 + 22.2379i −0.553216 + 1.21137i 0.402048 + 0.915619i \(0.368299\pi\)
−0.955264 + 0.295755i \(0.904429\pi\)
\(338\) 0 0
\(339\) 1.99025 + 1.89770i 0.108096 + 0.103069i
\(340\) 0 0
\(341\) −19.4170 + 18.5141i −1.05149 + 1.00259i
\(342\) 0 0
\(343\) 10.1117 + 15.5162i 0.545983 + 0.837796i
\(344\) 0 0
\(345\) −0.358298 + 1.95880i −0.0192901 + 0.105458i
\(346\) 0 0
\(347\) −18.0919 + 7.24290i −0.971224 + 0.388819i −0.802373 0.596822i \(-0.796430\pi\)
−0.168850 + 0.985642i \(0.554005\pi\)
\(348\) 0 0
\(349\) 23.7677 + 6.97883i 1.27226 + 0.373568i 0.847043 0.531525i \(-0.178381\pi\)
0.425213 + 0.905093i \(0.360199\pi\)
\(350\) 0 0
\(351\) 6.98902 2.05216i 0.373046 0.109536i
\(352\) 0 0
\(353\) 7.50007 0.716170i 0.399188 0.0381179i 0.106468 0.994316i \(-0.466046\pi\)
0.292720 + 0.956198i \(0.405440\pi\)
\(354\) 0 0
\(355\) −0.825842 17.3366i −0.0438311 0.920129i
\(356\) 0 0
\(357\) −1.30094 0.184232i −0.0688531 0.00975057i
\(358\) 0 0
\(359\) 4.46238 + 12.8932i 0.235515 + 0.680476i 0.999384 + 0.0351045i \(0.0111764\pi\)
−0.763868 + 0.645372i \(0.776702\pi\)
\(360\) 0 0
\(361\) −0.176018 + 3.69506i −0.00926408 + 0.194477i
\(362\) 0 0
\(363\) 0.302149 + 0.348699i 0.0158587 + 0.0183019i
\(364\) 0 0
\(365\) −4.21274 9.22462i −0.220505 0.482839i
\(366\) 0 0
\(367\) 3.54068 + 6.13264i 0.184822 + 0.320121i 0.943517 0.331325i \(-0.107496\pi\)
−0.758694 + 0.651447i \(0.774162\pi\)
\(368\) 0 0
\(369\) −15.7152 + 27.2195i −0.818101 + 1.41699i
\(370\) 0 0
\(371\) −4.11579 + 10.3443i −0.213681 + 0.537048i
\(372\) 0 0
\(373\) 23.7968 4.58645i 1.23215 0.237477i 0.468708 0.883353i \(-0.344720\pi\)
0.763442 + 0.645876i \(0.223508\pi\)
\(374\) 0 0
\(375\) 0.168100 3.52886i 0.00868066 0.182229i
\(376\) 0 0
\(377\) 9.25038 10.6755i 0.476419 0.549817i
\(378\) 0 0
\(379\) −2.36344 16.4381i −0.121402 0.844369i −0.955970 0.293464i \(-0.905192\pi\)
0.834568 0.550905i \(-0.185717\pi\)
\(380\) 0 0
\(381\) 4.09817 + 2.11275i 0.209956 + 0.108240i
\(382\) 0 0
\(383\) 11.6031 + 16.2943i 0.592892 + 0.832600i 0.996609 0.0822836i \(-0.0262213\pi\)
−0.403717 + 0.914884i \(0.632282\pi\)
\(384\) 0 0
\(385\) −9.82454 + 5.70002i −0.500705 + 0.290500i
\(386\) 0 0
\(387\) −14.3296 + 13.6632i −0.728412 + 0.694540i
\(388\) 0 0
\(389\) 5.94310 2.37926i 0.301327 0.120633i −0.216072 0.976377i \(-0.569325\pi\)
0.517399 + 0.855744i \(0.326900\pi\)
\(390\) 0 0
\(391\) 6.09961 + 3.44491i 0.308470 + 0.174217i
\(392\) 0 0
\(393\) 0.530889 3.69241i 0.0267798 0.186258i
\(394\) 0 0
\(395\) −3.49004 14.3861i −0.175603 0.723845i
\(396\) 0 0
\(397\) 4.38298 18.0669i 0.219975 0.906750i −0.749587 0.661906i \(-0.769748\pi\)
0.969562 0.244845i \(-0.0787369\pi\)
\(398\) 0 0
\(399\) −0.658570 + 3.45642i −0.0329697 + 0.173037i
\(400\) 0 0
\(401\) 0.182279 + 3.82650i 0.00910256 + 0.191086i 0.998839 + 0.0481794i \(0.0153419\pi\)
−0.989736 + 0.142907i \(0.954355\pi\)
\(402\) 0 0
\(403\) −21.8426 + 17.1772i −1.08806 + 0.855659i
\(404\) 0 0
\(405\) −6.37647 + 7.35884i −0.316849 + 0.365663i
\(406\) 0 0
\(407\) 18.5633 + 11.9299i 0.920148 + 0.591343i
\(408\) 0 0
\(409\) 2.84950 8.23309i 0.140899 0.407100i −0.852369 0.522941i \(-0.824835\pi\)
0.993268 + 0.115840i \(0.0369561\pi\)
\(410\) 0 0
\(411\) −2.79909 0.267281i −0.138069 0.0131840i
\(412\) 0 0
\(413\) −7.96421 8.31723i −0.391893 0.409264i
\(414\) 0 0
\(415\) 4.63630 8.03031i 0.227587 0.394193i
\(416\) 0 0
\(417\) −1.83620 + 2.57858i −0.0899192 + 0.126274i
\(418\) 0 0
\(419\) 3.05886 + 3.53012i 0.149435 + 0.172457i 0.825532 0.564356i \(-0.190875\pi\)
−0.676097 + 0.736813i \(0.736330\pi\)
\(420\) 0 0
\(421\) 26.3366 + 16.9255i 1.28357 + 0.824898i 0.991323 0.131446i \(-0.0419620\pi\)
0.292243 + 0.956344i \(0.405598\pi\)
\(422\) 0 0
\(423\) −23.3113 4.49289i −1.13343 0.218452i
\(424\) 0 0
\(425\) −4.75774 1.90471i −0.230784 0.0923921i
\(426\) 0 0
\(427\) −4.12953 13.9543i −0.199842 0.675297i
\(428\) 0 0
\(429\) 2.52406 + 3.54455i 0.121863 + 0.171133i
\(430\) 0 0
\(431\) 16.2425 + 15.4872i 0.782372 + 0.745990i 0.971775 0.235909i \(-0.0758067\pi\)
−0.189403 + 0.981899i \(0.560655\pi\)
\(432\) 0 0
\(433\) −7.77776 2.28376i −0.373775 0.109750i 0.0894491 0.995991i \(-0.471489\pi\)
−0.463224 + 0.886241i \(0.653308\pi\)
\(434\) 0 0
\(435\) 0.229259 1.59453i 0.0109921 0.0764518i
\(436\) 0 0
\(437\) 9.99203 15.8769i 0.477984 0.759496i
\(438\) 0 0
\(439\) 17.5163 + 13.7750i 0.836007 + 0.657443i 0.941513 0.336976i \(-0.109404\pi\)
−0.105507 + 0.994419i \(0.533646\pi\)
\(440\) 0 0
\(441\) −6.52278 + 19.1082i −0.310609 + 0.909915i
\(442\) 0 0
\(443\) 5.66075 23.3339i 0.268950 1.10863i −0.663744 0.747960i \(-0.731034\pi\)
0.932694 0.360668i \(-0.117451\pi\)
\(444\) 0 0
\(445\) −8.28061 + 0.790702i −0.392539 + 0.0374829i
\(446\) 0 0
\(447\) 4.92144 3.16282i 0.232776 0.149596i
\(448\) 0 0
\(449\) −0.0453443 0.315377i −0.00213993 0.0148835i 0.988724 0.149753i \(-0.0478477\pi\)
−0.990863 + 0.134869i \(0.956939\pi\)
\(450\) 0 0
\(451\) −37.6124 7.24920i −1.77110 0.341352i
\(452\) 0 0
\(453\) 1.19304 0.615057i 0.0560541 0.0288979i
\(454\) 0 0
\(455\) −10.6907 + 4.90973i −0.501190 + 0.230172i
\(456\) 0 0
\(457\) 28.8383 + 2.75373i 1.34900 + 0.128814i 0.744410 0.667723i \(-0.232731\pi\)
0.604590 + 0.796537i \(0.293337\pi\)
\(458\) 0 0
\(459\) −1.46114 2.53077i −0.0682003 0.118126i
\(460\) 0 0
\(461\) −21.3530 −0.994507 −0.497254 0.867605i \(-0.665658\pi\)
−0.497254 + 0.867605i \(0.665658\pi\)
\(462\) 0 0
\(463\) −5.62685 12.3211i −0.261502 0.572609i 0.732649 0.680606i \(-0.238283\pi\)
−0.994151 + 0.107997i \(0.965556\pi\)
\(464\) 0 0
\(465\) −1.03647 + 2.99468i −0.0480650 + 0.138875i
\(466\) 0 0
\(467\) −12.6884 + 6.54135i −0.587151 + 0.302698i −0.726086 0.687604i \(-0.758663\pi\)
0.138935 + 0.990302i \(0.455632\pi\)
\(468\) 0 0
\(469\) 25.7408 1.28091i 1.18860 0.0591470i
\(470\) 0 0
\(471\) −1.40310 0.561715i −0.0646513 0.0258825i
\(472\) 0 0
\(473\) −21.4475 11.0569i −0.986157 0.508399i
\(474\) 0 0
\(475\) −5.70116 + 12.4838i −0.261587 + 0.572796i
\(476\) 0 0
\(477\) −11.6456 + 3.41946i −0.533216 + 0.156566i
\(478\) 0 0
\(479\) 6.35010 + 26.1755i 0.290144 + 1.19599i 0.911114 + 0.412154i \(0.135224\pi\)
−0.620970 + 0.783834i \(0.713261\pi\)
\(480\) 0 0
\(481\) 17.9651 + 14.1279i 0.819137 + 0.644176i
\(482\) 0 0
\(483\) −2.78703 + 3.29284i −0.126814 + 0.149829i
\(484\) 0 0
\(485\) −4.67140 3.67363i −0.212117 0.166811i
\(486\) 0 0
\(487\) −0.272194 1.12200i −0.0123343 0.0508426i 0.965312 0.261100i \(-0.0840851\pi\)
−0.977646 + 0.210257i \(0.932570\pi\)
\(488\) 0 0
\(489\) 6.98542 2.05111i 0.315892 0.0927542i
\(490\) 0 0
\(491\) 8.28629 18.1445i 0.373955 0.818848i −0.625305 0.780381i \(-0.715025\pi\)
0.999260 0.0384669i \(-0.0122474\pi\)
\(492\) 0 0
\(493\) −5.03710 2.59681i −0.226860 0.116954i
\(494\) 0 0
\(495\) −11.4959 4.60226i −0.516702 0.206856i
\(496\) 0 0
\(497\) 17.1587 33.4573i 0.769674 1.50077i
\(498\) 0 0
\(499\) −30.3138 + 15.6278i −1.35703 + 0.699599i −0.974509 0.224348i \(-0.927975\pi\)
−0.382523 + 0.923946i \(0.624945\pi\)
\(500\) 0 0
\(501\) 1.27089 3.67200i 0.0567792 0.164053i
\(502\) 0 0
\(503\) 4.85207 + 10.6245i 0.216343 + 0.473725i 0.986423 0.164222i \(-0.0525113\pi\)
−0.770081 + 0.637947i \(0.779784\pi\)
\(504\) 0 0
\(505\) 21.4569 0.954817
\(506\) 0 0
\(507\) 0.0435292 + 0.0753948i 0.00193320 + 0.00334840i
\(508\) 0 0
\(509\) −19.2215 1.83543i −0.851979 0.0813542i −0.340077 0.940398i \(-0.610453\pi\)
−0.511903 + 0.859043i \(0.671059\pi\)
\(510\) 0 0
\(511\) 2.04196 21.8746i 0.0903311 0.967675i
\(512\) 0 0
\(513\) −6.95576 + 3.58594i −0.307104 + 0.158323i
\(514\) 0 0
\(515\) 18.2186 + 3.51135i 0.802808 + 0.154729i
\(516\) 0 0
\(517\) −4.11754 28.6381i −0.181089 1.25950i
\(518\) 0 0
\(519\) 0.891319 0.572816i 0.0391246 0.0251438i
\(520\) 0 0
\(521\) 44.1931 4.21993i 1.93614 0.184879i 0.945918 0.324407i \(-0.105165\pi\)
0.990218 + 0.139528i \(0.0445587\pi\)
\(522\) 0 0
\(523\) −2.25024 + 9.27560i −0.0983959 + 0.405593i −0.999614 0.0277718i \(-0.991159\pi\)
0.901218 + 0.433365i \(0.142674\pi\)
\(524\) 0 0
\(525\) 1.70063 2.65862i 0.0742217 0.116032i
\(526\) 0 0
\(527\) 8.76301 + 6.89131i 0.381723 + 0.300190i
\(528\) 0 0
\(529\) 20.2397 10.9250i 0.879986 0.474999i
\(530\) 0 0
\(531\) 1.78664 12.4264i 0.0775337 0.539259i
\(532\) 0 0
\(533\) −38.0665 11.1773i −1.64884 0.484143i
\(534\) 0 0
\(535\) −6.26733 5.97589i −0.270960 0.258360i
\(536\) 0 0
\(537\) 2.19933 + 3.08853i 0.0949083 + 0.133280i
\(538\) 0 0
\(539\) −24.6066 + 0.104381i −1.05988 + 0.00449599i
\(540\) 0 0
\(541\) −22.2510 8.90797i −0.956646 0.382983i −0.159789 0.987151i \(-0.551081\pi\)
−0.796857 + 0.604168i \(0.793506\pi\)
\(542\) 0 0
\(543\) −0.615433 0.118615i −0.0264108 0.00509026i
\(544\) 0 0
\(545\) −8.45377 5.43291i −0.362120 0.232720i
\(546\) 0 0
\(547\) −17.5454 20.2484i −0.750185 0.865760i 0.244401 0.969674i \(-0.421409\pi\)
−0.994586 + 0.103914i \(0.966863\pi\)
\(548\) 0 0
\(549\) 9.20273 12.9234i 0.392763 0.551558i
\(550\) 0 0
\(551\) −7.58804 + 13.1429i −0.323261 + 0.559905i
\(552\) 0 0
\(553\) 8.96997 30.7903i 0.381442 1.30934i
\(554\) 0 0
\(555\) 2.59460 + 0.247755i 0.110135 + 0.0105166i
\(556\) 0 0
\(557\) 11.0358 31.8859i 0.467602 1.35105i −0.427028 0.904239i \(-0.640439\pi\)
0.894630 0.446808i \(-0.147439\pi\)
\(558\) 0 0
\(559\) −21.0248 13.5118i −0.889253 0.571488i
\(560\) 0 0
\(561\) 1.14321 1.31934i 0.0482665 0.0557025i
\(562\) 0 0
\(563\) −19.0242 + 14.9608i −0.801775 + 0.630523i −0.932612 0.360881i \(-0.882476\pi\)
0.130837 + 0.991404i \(0.458234\pi\)
\(564\) 0 0
\(565\) −0.470018 9.86690i −0.0197738 0.415104i
\(566\) 0 0
\(567\) −19.9198 + 6.94165i −0.836553 + 0.291522i
\(568\) 0 0
\(569\) −4.49737 + 18.5384i −0.188540 + 0.777171i 0.796471 + 0.604677i \(0.206698\pi\)
−0.985011 + 0.172494i \(0.944817\pi\)
\(570\) 0 0
\(571\) 9.54208 + 39.3330i 0.399323 + 1.64603i 0.716441 + 0.697648i \(0.245770\pi\)
−0.317118 + 0.948386i \(0.602715\pi\)
\(572\) 0 0
\(573\) 0.603025 4.19413i 0.0251917 0.175212i
\(574\) 0 0
\(575\) −13.6131 + 9.88974i −0.567707 + 0.412431i
\(576\) 0 0
\(577\) −10.3189 + 4.13107i −0.429582 + 0.171979i −0.576369 0.817189i \(-0.695531\pi\)
0.146787 + 0.989168i \(0.453107\pi\)
\(578\) 0 0
\(579\) 4.29332 4.09368i 0.178424 0.170127i
\(580\) 0 0
\(581\) 17.3756 10.0810i 0.720863 0.418232i
\(582\) 0 0
\(583\) −8.58010 12.0491i −0.355351 0.499021i
\(584\) 0 0
\(585\) −11.3997 5.87695i −0.471319 0.242982i
\(586\) 0 0
\(587\) −2.73095 18.9942i −0.112718 0.783973i −0.965256 0.261307i \(-0.915847\pi\)
0.852538 0.522666i \(-0.175062\pi\)
\(588\) 0 0
\(589\) 19.5502 22.5621i 0.805551 0.929656i
\(590\) 0 0
\(591\) −0.152001 + 3.19090i −0.00625251 + 0.131256i
\(592\) 0 0
\(593\) 16.1804 3.11852i 0.664451 0.128062i 0.154136 0.988050i \(-0.450741\pi\)
0.510316 + 0.859987i \(0.329529\pi\)
\(594\) 0 0
\(595\) 2.92537 + 3.70372i 0.119929 + 0.151838i
\(596\) 0 0
\(597\) −4.15453 + 7.19586i −0.170034 + 0.294507i
\(598\) 0 0
\(599\) 10.3249 + 17.8833i 0.421865 + 0.730691i 0.996122 0.0879837i \(-0.0280423\pi\)
−0.574257 + 0.818675i \(0.694709\pi\)
\(600\) 0 0
\(601\) −12.4170 27.1895i −0.506501 1.10908i −0.974301 0.225248i \(-0.927681\pi\)
0.467801 0.883834i \(-0.345047\pi\)
\(602\) 0 0
\(603\) 18.3999 + 21.2347i 0.749303 + 0.864742i
\(604\) 0 0
\(605\) 0.0788601 1.65548i 0.00320612 0.0673048i
\(606\) 0 0
\(607\) 6.22214 + 17.9777i 0.252549 + 0.729692i 0.998005 + 0.0631373i \(0.0201106\pi\)
−0.745456 + 0.666555i \(0.767768\pi\)
\(608\) 0 0
\(609\) 2.15151 2.74784i 0.0871835 0.111348i
\(610\) 0 0
\(611\) −1.42587 29.9326i −0.0576844 1.21094i
\(612\) 0 0
\(613\) −10.4232 + 0.995299i −0.420991 + 0.0401997i −0.303402 0.952863i \(-0.598123\pi\)
−0.117589 + 0.993062i \(0.537516\pi\)
\(614\) 0 0
\(615\) −4.34117 + 1.27468i −0.175053 + 0.0514002i
\(616\) 0 0
\(617\) −13.6190 3.99889i −0.548279 0.160989i −0.00415104 0.999991i \(-0.501321\pi\)
−0.544128 + 0.839002i \(0.683140\pi\)
\(618\) 0 0
\(619\) −23.8986 + 9.56755i −0.960565 + 0.384552i −0.798344 0.602202i \(-0.794290\pi\)
−0.162222 + 0.986754i \(0.551866\pi\)
\(620\) 0 0
\(621\) −9.58772 0.365641i −0.384742 0.0146727i
\(622\) 0 0
\(623\) −16.4082 7.45134i −0.657379 0.298531i
\(624\) 0 0
\(625\) 3.51185 3.34854i 0.140474 0.133942i
\(626\) 0 0
\(627\) −3.38343 3.22610i −0.135121 0.128838i
\(628\) 0 0
\(629\) 3.80897 8.34049i 0.151874 0.332557i
\(630\) 0 0
\(631\) 15.7418 10.1167i 0.626673 0.402738i −0.188403 0.982092i \(-0.560331\pi\)
0.815076 + 0.579353i \(0.196695\pi\)
\(632\) 0 0
\(633\) −2.96983 + 2.33550i −0.118040 + 0.0928278i
\(634\) 0 0
\(635\) −5.41689 15.6511i −0.214963 0.621094i
\(636\) 0 0
\(637\) −25.3809 2.31498i −1.00563 0.0917227i
\(638\) 0 0
\(639\) 40.2517 7.75787i 1.59233 0.306897i
\(640\) 0 0
\(641\) −8.72045 + 12.2462i −0.344437 + 0.483694i −0.950064 0.312054i \(-0.898983\pi\)
0.605627 + 0.795748i \(0.292922\pi\)
\(642\) 0 0
\(643\) −43.6845 −1.72275 −0.861375 0.507970i \(-0.830396\pi\)
−0.861375 + 0.507970i \(0.830396\pi\)
\(644\) 0 0
\(645\) −2.85016 −0.112225
\(646\) 0 0
\(647\) −8.71930 + 12.2445i −0.342791 + 0.481383i −0.949600 0.313465i \(-0.898510\pi\)
0.606809 + 0.794848i \(0.292449\pi\)
\(648\) 0 0
\(649\) 15.0234 2.89553i 0.589721 0.113659i
\(650\) 0 0
\(651\) −5.17889 + 4.50680i −0.202977 + 0.176636i
\(652\) 0 0
\(653\) 9.76375 + 28.2105i 0.382085 + 1.10396i 0.958078 + 0.286508i \(0.0924945\pi\)
−0.575993 + 0.817455i \(0.695384\pi\)
\(654\) 0 0
\(655\) −10.5329 + 8.28317i −0.411555 + 0.323650i
\(656\) 0 0
\(657\) 20.1492 12.9491i 0.786097 0.505194i
\(658\) 0 0
\(659\) 1.89965 4.15966i 0.0739999 0.162037i −0.869017 0.494783i \(-0.835248\pi\)
0.943017 + 0.332745i \(0.107975\pi\)
\(660\) 0 0
\(661\) 31.2430 + 29.7901i 1.21521 + 1.15870i 0.982521 + 0.186151i \(0.0596014\pi\)
0.232691 + 0.972551i \(0.425247\pi\)
\(662\) 0 0
\(663\) 1.30860 1.24775i 0.0508218 0.0484584i
\(664\) 0 0
\(665\) 10.2799 7.35316i 0.398636 0.285143i
\(666\) 0 0
\(667\) −16.0249 + 9.45568i −0.620485 + 0.366125i
\(668\) 0 0
\(669\) 4.60449 1.84336i 0.178020 0.0712684i
\(670\) 0 0
\(671\) 18.5519 + 5.44734i 0.716190 + 0.210292i
\(672\) 0 0
\(673\) −34.4721 + 10.1219i −1.32880 + 0.390171i −0.867661 0.497156i \(-0.834378\pi\)
−0.461140 + 0.887327i \(0.652559\pi\)
\(674\) 0 0
\(675\) 6.98749 0.667224i 0.268948 0.0256815i
\(676\) 0 0
\(677\) −2.00494 42.0890i −0.0770563 1.61761i −0.624677 0.780883i \(-0.714769\pi\)
0.547621 0.836727i \(-0.315534\pi\)
\(678\) 0 0
\(679\) −4.81037 11.9423i −0.184605 0.458302i
\(680\) 0 0
\(681\) −0.108118 0.312387i −0.00414310 0.0119707i
\(682\) 0 0
\(683\) 2.06173 43.2810i 0.0788898 1.65610i −0.519186 0.854662i \(-0.673765\pi\)
0.598075 0.801440i \(-0.295932\pi\)
\(684\) 0 0
\(685\) 6.61425 + 7.63325i 0.252717 + 0.291651i
\(686\) 0 0
\(687\) 2.45220 + 5.36957i 0.0935573 + 0.204862i
\(688\) 0 0
\(689\) −7.66021 13.2679i −0.291831 0.505466i
\(690\) 0 0
\(691\) −10.3472 + 17.9219i −0.393628 + 0.681783i −0.992925 0.118743i \(-0.962113\pi\)
0.599297 + 0.800527i \(0.295447\pi\)
\(692\) 0 0
\(693\) −16.6277 21.0518i −0.631635 0.799693i
\(694\) 0 0
\(695\) 11.1654 2.15195i 0.423527 0.0816281i
\(696\) 0 0
\(697\) −0.757340 + 15.8985i −0.0286863 + 0.602200i
\(698\) 0 0
\(699\) 5.95749 6.87531i 0.225333 0.260048i
\(700\) 0 0
\(701\) 5.62714 + 39.1376i 0.212534 + 1.47821i 0.764654 + 0.644441i \(0.222910\pi\)
−0.552120 + 0.833765i \(0.686181\pi\)
\(702\) 0 0
\(703\) −21.8247 11.2514i −0.823133 0.424354i
\(704\) 0 0
\(705\) −1.98231 2.78377i −0.0746583 0.104843i
\(706\) 0 0
\(707\) 40.3059 + 23.1568i 1.51586 + 0.870900i
\(708\) 0 0
\(709\) −10.9939 + 10.4827i −0.412885 + 0.393685i −0.867852 0.496823i \(-0.834500\pi\)
0.454967 + 0.890509i \(0.349651\pi\)
\(710\) 0 0
\(711\) 32.4587 12.9945i 1.21730 0.487332i
\(712\) 0 0
\(713\) 34.4742 12.2989i 1.29107 0.460598i
\(714\) 0 0
\(715\) 2.22445 15.4714i 0.0831898 0.578598i
\(716\) 0 0
\(717\) −0.695642 2.86748i −0.0259792 0.107088i
\(718\) 0 0
\(719\) 9.28072 38.2557i 0.346112 1.42670i −0.486908 0.873453i \(-0.661875\pi\)
0.833021 0.553242i \(-0.186609\pi\)
\(720\) 0 0
\(721\) 30.4334 + 26.2579i 1.13340 + 0.977896i
\(722\) 0 0
\(723\) 0.152545 + 3.20231i 0.00567320 + 0.119095i
\(724\) 0 0
\(725\) 10.6999 8.41450i 0.397385 0.312507i
\(726\) 0 0
\(727\) 6.43934 7.43139i 0.238822 0.275615i −0.623668 0.781689i \(-0.714358\pi\)
0.862490 + 0.506074i \(0.168904\pi\)
\(728\) 0 0
\(729\) −17.6301 11.3302i −0.652965 0.419635i
\(730\) 0 0
\(731\) −3.27937 + 9.47513i −0.121292 + 0.350450i
\(732\) 0 0
\(733\) −22.3162 2.13094i −0.824268 0.0787081i −0.325607 0.945505i \(-0.605569\pi\)
−0.498661 + 0.866797i \(0.666175\pi\)
\(734\) 0 0
\(735\) −2.57773 + 1.34278i −0.0950808 + 0.0495292i
\(736\) 0 0
\(737\) −17.1214 + 29.6551i −0.630674 + 1.09236i
\(738\) 0 0
\(739\) −14.3171 + 20.1056i −0.526664 + 0.739596i −0.989130 0.147041i \(-0.953025\pi\)
0.462467 + 0.886637i \(0.346964\pi\)
\(740\) 0 0
\(741\) −3.17086 3.65937i −0.116484 0.134430i
\(742\) 0 0
\(743\) −8.46111 5.43763i −0.310408 0.199487i 0.376156 0.926556i \(-0.377246\pi\)
−0.686564 + 0.727069i \(0.740882\pi\)
\(744\) 0 0
\(745\) −20.6343 3.97693i −0.755980 0.145703i
\(746\) 0 0
\(747\) 20.3316 + 8.13954i 0.743893 + 0.297810i
\(748\) 0 0
\(749\) −5.32362 17.9893i −0.194521 0.657316i
\(750\) 0 0
\(751\) 15.9297 + 22.3701i 0.581283 + 0.816298i 0.995587 0.0938405i \(-0.0299144\pi\)
−0.414304 + 0.910139i \(0.635975\pi\)
\(752\) 0 0
\(753\) −3.10248 2.95821i −0.113061 0.107803i
\(754\) 0 0
\(755\) −4.62616 1.35836i −0.168363 0.0494359i
\(756\) 0 0
\(757\) −3.24023 + 22.5363i −0.117768 + 0.819096i 0.842236 + 0.539109i \(0.181239\pi\)
−0.960004 + 0.279986i \(0.909670\pi\)
\(758\) 0 0
\(759\) −1.66689 5.48400i −0.0605043 0.199057i
\(760\) 0 0
\(761\) −35.8795 28.2160i −1.30063 1.02283i −0.997557 0.0698614i \(-0.977744\pi\)
−0.303075 0.952967i \(-0.598013\pi\)
\(762\) 0 0
\(763\) −10.0168 19.3290i −0.362631 0.699758i
\(764\) 0 0
\(765\) −1.21308 + 5.00037i −0.0438589 + 0.180789i
\(766\) 0 0
\(767\) 15.7749 1.50632i 0.569600 0.0543902i
\(768\) 0 0
\(769\) −11.8285 + 7.60174i −0.426548 + 0.274126i −0.736252 0.676707i \(-0.763406\pi\)
0.309704 + 0.950833i \(0.399770\pi\)
\(770\) 0 0
\(771\) 0.938450 + 6.52706i 0.0337974 + 0.235066i
\(772\) 0 0
\(773\) −29.8801 5.75892i −1.07471 0.207134i −0.378958 0.925414i \(-0.623718\pi\)
−0.695754 + 0.718280i \(0.744930\pi\)
\(774\) 0 0
\(775\) −23.8008 + 12.2702i −0.854950 + 0.440758i
\(776\) 0 0
\(777\) 4.60648 + 3.26556i 0.165257 + 0.117151i
\(778\) 0 0
\(779\) 42.4306 + 4.05163i 1.52023 + 0.145165i
\(780\) 0 0
\(781\) 24.9790 + 43.2649i 0.893820 + 1.54814i
\(782\) 0 0
\(783\) 7.76194 0.277389
\(784\) 0 0
\(785\) 2.25524 + 4.93829i 0.0804930 + 0.176255i
\(786\) 0 0
\(787\) −7.76090 + 22.4236i −0.276646 + 0.799316i 0.718006 + 0.696037i \(0.245055\pi\)
−0.994652 + 0.103280i \(0.967066\pi\)
\(788\) 0 0
\(789\) 3.07230 1.58388i 0.109377 0.0563876i
\(790\) 0 0
\(791\) 9.76569 19.0419i 0.347228 0.677050i
\(792\) 0 0
\(793\) 18.5916 + 7.44296i 0.660207 + 0.264307i
\(794\) 0 0
\(795\) −1.55295 0.800600i −0.0550774 0.0283944i
\(796\) 0 0
\(797\) −4.43931 + 9.72074i −0.157249 + 0.344326i −0.971815 0.235743i \(-0.924247\pi\)
0.814567 + 0.580070i \(0.196975\pi\)
\(798\) 0 0
\(799\) −11.5353 + 3.38706i −0.408088 + 0.119826i
\(800\) 0 0
\(801\) −4.63181 19.0926i −0.163657 0.674603i
\(802\) 0 0
\(803\) 22.9448 + 18.0440i 0.809706 + 0.636760i
\(804\) 0 0
\(805\) 15.4077 1.65187i 0.543051 0.0582209i
\(806\) 0 0
\(807\) −7.30595 5.74546i −0.257181 0.202250i
\(808\) 0 0
\(809\) −9.80106 40.4005i −0.344587 1.42041i −0.835640 0.549277i \(-0.814903\pi\)
0.491054 0.871129i \(-0.336612\pi\)
\(810\) 0 0
\(811\) 12.3815 3.63552i 0.434772 0.127660i −0.0570207 0.998373i \(-0.518160\pi\)
0.491792 + 0.870713i \(0.336342\pi\)
\(812\) 0 0
\(813\) −4.53988 + 9.94095i −0.159221 + 0.348644i
\(814\) 0 0
\(815\) −23.2443 11.9832i −0.814211 0.419755i
\(816\) 0 0
\(817\) 24.9272 + 9.97935i 0.872092 + 0.349133i
\(818\) 0 0
\(819\) −15.0713 23.3425i −0.526635 0.815651i
\(820\) 0 0
\(821\) −3.39055 + 1.74795i −0.118331 + 0.0610038i −0.516376 0.856362i \(-0.672719\pi\)
0.398045 + 0.917366i \(0.369689\pi\)
\(822\) 0 0
\(823\) 15.5416 44.9045i 0.541746 1.56527i −0.258757 0.965942i \(-0.583313\pi\)
0.800503 0.599329i \(-0.204566\pi\)
\(824\) 0 0
\(825\) 1.74192 + 3.81428i 0.0606460 + 0.132796i
\(826\) 0 0
\(827\) −23.2050 −0.806919 −0.403459 0.914998i \(-0.632192\pi\)
−0.403459 + 0.914998i \(0.632192\pi\)
\(828\) 0 0
\(829\) 7.79548 + 13.5022i 0.270748 + 0.468949i 0.969054 0.246850i \(-0.0793956\pi\)
−0.698305 + 0.715800i \(0.746062\pi\)
\(830\) 0 0
\(831\) −3.61847 0.345522i −0.125523 0.0119860i
\(832\) 0 0
\(833\) 1.49806 + 10.1144i 0.0519046 + 0.350445i
\(834\) 0 0
\(835\) −12.4061 + 6.39578i −0.429330 + 0.221335i
\(836\) 0 0
\(837\) −14.9931 2.88969i −0.518239 0.0998823i
\(838\) 0 0
\(839\) −1.74101 12.1090i −0.0601063 0.418049i −0.997553 0.0699189i \(-0.977726\pi\)
0.937446 0.348130i \(-0.113183\pi\)
\(840\) 0 0
\(841\) −11.7334 + 7.54062i −0.404601 + 0.260022i
\(842\) 0 0
\(843\) −4.04609 + 0.386354i −0.139355 + 0.0133067i
\(844\) 0 0
\(845\) 0.0737263 0.303904i 0.00253626 0.0104546i
\(846\) 0 0
\(847\) 1.93477 3.02465i 0.0664795 0.103928i
\(848\) 0 0
\(849\) 3.84300 + 3.02217i 0.131891 + 0.103721i
\(850\) 0 0
\(851\) −16.5152 25.1702i −0.566134 0.862823i
\(852\) 0 0
\(853\) 3.10485 21.5947i 0.106308 0.739388i −0.865036 0.501710i \(-0.832705\pi\)
0.971344 0.237678i \(-0.0763864\pi\)
\(854\) 0 0
\(855\) 13.2209 + 3.88202i 0.452147 + 0.132762i
\(856\) 0 0
\(857\) 12.0557 + 11.4951i 0.411816 + 0.392666i 0.867469 0.497492i \(-0.165746\pi\)
−0.455653 + 0.890158i \(0.650594\pi\)
\(858\) 0 0
\(859\) −4.17218 5.85900i −0.142353 0.199907i 0.737244 0.675627i \(-0.236127\pi\)
−0.879597 + 0.475720i \(0.842187\pi\)
\(860\) 0 0
\(861\) −9.53040 2.29066i −0.324795 0.0780654i
\(862\) 0 0
\(863\) 11.4492 + 4.58356i 0.389735 + 0.156026i 0.558250 0.829673i \(-0.311473\pi\)
−0.168515 + 0.985699i \(0.553897\pi\)
\(864\) 0 0
\(865\) −3.73706 0.720259i −0.127064 0.0244895i
\(866\) 0 0
\(867\) 4.25204 + 2.73262i 0.144407 + 0.0928046i
\(868\) 0 0
\(869\) 27.9037 + 32.2025i 0.946567 + 1.09240i
\(870\) 0 0
\(871\) −20.5726 + 28.8901i −0.697075 + 0.978905i
\(872\) 0 0
\(873\) 7.01801 12.1556i 0.237524 0.411403i
\(874\) 0 0
\(875\) −26.7035 + 6.53821i −0.902744 + 0.221032i
\(876\) 0 0
\(877\) 9.13649 + 0.872429i 0.308517 + 0.0294598i 0.248166 0.968717i \(-0.420172\pi\)
0.0603508 + 0.998177i \(0.480778\pi\)
\(878\) 0 0
\(879\) 1.95622 5.65214i 0.0659818 0.190642i
\(880\) 0 0
\(881\) 16.8294 + 10.8156i 0.566997 + 0.364387i 0.792515 0.609852i \(-0.208771\pi\)
−0.225519 + 0.974239i \(0.572408\pi\)
\(882\) 0 0
\(883\) −11.1697 + 12.8905i −0.375889 + 0.433799i −0.911900 0.410412i \(-0.865385\pi\)
0.536012 + 0.844211i \(0.319930\pi\)
\(884\) 0 0
\(885\) 1.42054 1.11713i 0.0477511 0.0375519i
\(886\) 0 0
\(887\) 1.49935 + 31.4752i 0.0503431 + 1.05683i 0.872823 + 0.488038i \(0.162287\pi\)
−0.822479 + 0.568795i \(0.807410\pi\)
\(888\) 0 0
\(889\) 6.71561 35.2460i 0.225234 1.18211i
\(890\) 0 0
\(891\) 6.60769 27.2373i 0.221366 0.912483i
\(892\) 0 0
\(893\) 7.59022 + 31.2873i 0.253997 + 1.04699i
\(894\) 0 0
\(895\) 1.93827 13.4810i 0.0647892 0.450619i
\(896\) 0 0
\(897\) −1.17873 5.81837i −0.0393565 0.194270i
\(898\) 0 0
\(899\) −27.4896 + 11.0052i −0.916831 + 0.367044i
\(900\) 0 0
\(901\) −4.44834 + 4.24149i −0.148196 + 0.141304i
\(902\) 0 0
\(903\) −5.35392 3.07596i −0.178167 0.102362i
\(904\) 0 0
\(905\) 1.30591 + 1.83390i 0.0434101 + 0.0609609i
\(906\) 0 0
\(907\) 20.6753 + 10.6589i 0.686513 + 0.353922i 0.765934 0.642919i \(-0.222277\pi\)
−0.0794209 + 0.996841i \(0.525307\pi\)
\(908\) 0 0
\(909\) 7.21216 + 50.1617i 0.239212 + 1.66376i
\(910\) 0 0
\(911\) −8.45323 + 9.75555i −0.280068 + 0.323216i −0.878302 0.478105i \(-0.841324\pi\)
0.598234 + 0.801321i \(0.295869\pi\)
\(912\) 0 0
\(913\) −1.26997 + 26.6600i −0.0420299 + 0.882317i
\(914\) 0 0
\(915\) 2.24255 0.432215i 0.0741363 0.0142886i
\(916\) 0 0
\(917\) −28.7251 + 4.19225i −0.948586 + 0.138440i
\(918\) 0 0
\(919\) −0.888045 + 1.53814i −0.0292939 + 0.0507385i −0.880301 0.474416i \(-0.842659\pi\)
0.851007 + 0.525155i \(0.175993\pi\)
\(920\) 0 0
\(921\) −0.686446 1.18896i −0.0226192 0.0391776i
\(922\) 0 0
\(923\) 21.4950 + 47.0674i 0.707515 + 1.54924i
\(924\) 0 0
\(925\) 14.4226 + 16.6446i 0.474212 + 0.547270i
\(926\) 0 0
\(927\) −2.08510 + 43.7716i −0.0684835 + 1.43765i
\(928\) 0 0
\(929\) 13.5421 + 39.1272i 0.444301 + 1.28372i 0.915721 + 0.401814i \(0.131620\pi\)
−0.471420 + 0.881909i \(0.656258\pi\)
\(930\) 0 0
\(931\) 27.2460 2.71836i 0.892953 0.0890907i
\(932\) 0 0
\(933\) −0.0260167 0.546158i −0.000851750 0.0178804i
\(934\) 0 0
\(935\) −6.24239 + 0.596076i −0.204148 + 0.0194938i
\(936\) 0 0
\(937\) 27.1391 7.96876i 0.886596 0.260328i 0.193437 0.981113i \(-0.438036\pi\)
0.693159 + 0.720785i \(0.256218\pi\)
\(938\) 0 0
\(939\) 8.70037 + 2.55466i 0.283926 + 0.0833681i
\(940\) 0 0
\(941\) 19.1817 7.67918i 0.625305 0.250334i −0.0372994 0.999304i \(-0.511876\pi\)
0.662604 + 0.748970i \(0.269451\pi\)
\(942\) 0 0
\(943\) 42.8541 + 29.9079i 1.39552 + 0.973936i
\(944\) 0 0
\(945\) −5.88585 2.67290i −0.191467 0.0869496i
\(946\) 0 0
\(947\) 1.39585 1.33094i 0.0453592 0.0432499i −0.667061 0.745004i \(-0.732448\pi\)
0.712420 + 0.701754i \(0.247599\pi\)
\(948\) 0 0
\(949\) 21.8807 + 20.8632i 0.710278 + 0.677249i
\(950\) 0 0
\(951\) −3.98752 + 8.73145i −0.129304 + 0.283137i
\(952\) 0 0
\(953\) −22.2587 + 14.3048i −0.721031 + 0.463379i −0.848995 0.528400i \(-0.822792\pi\)
0.127964 + 0.991779i \(0.459156\pi\)
\(954\) 0 0
\(955\) −11.9641 + 9.40868i −0.387150 + 0.304458i
\(956\) 0 0
\(957\) 1.51657 + 4.38185i 0.0490239 + 0.141645i
\(958\) 0 0
\(959\) 4.18662 + 21.4770i 0.135193 + 0.693530i
\(960\) 0 0
\(961\) 26.7569 5.15698i 0.863127 0.166354i
\(962\) 0 0
\(963\) 11.8638 16.6604i 0.382305 0.536872i
\(964\) 0 0
\(965\) −21.3088 −0.685953
\(966\) 0 0
\(967\) 8.87739 0.285478 0.142739 0.989760i \(-0.454409\pi\)
0.142739 + 0.989760i \(0.454409\pi\)
\(968\) 0 0
\(969\) −1.12680 + 1.58237i −0.0361980 + 0.0508330i
\(970\) 0 0
\(971\) 3.08930 0.595414i 0.0991404 0.0191078i −0.139440 0.990231i \(-0.544530\pi\)
0.238580 + 0.971123i \(0.423318\pi\)
\(972\) 0 0
\(973\) 23.2962 + 8.00759i 0.746841 + 0.256712i
\(974\) 0 0
\(975\) 1.42048 + 4.10420i 0.0454917 + 0.131440i
\(976\) 0 0
\(977\) −15.0122 + 11.8058i −0.480284 + 0.377699i −0.828747 0.559623i \(-0.810946\pi\)
0.348463 + 0.937322i \(0.386704\pi\)
\(978\) 0 0
\(979\) 20.1424 12.9447i 0.643753 0.413715i
\(980\) 0 0
\(981\) 9.85950 21.5893i 0.314790 0.689293i
\(982\) 0 0
\(983\) −13.6529 13.0180i −0.435459 0.415209i 0.440381 0.897811i \(-0.354843\pi\)
−0.875840 + 0.482602i \(0.839692\pi\)
\(984\) 0 0
\(985\) 8.30478 7.91859i 0.264612 0.252307i
\(986\) 0 0
\(987\) −0.719388 7.36857i −0.0228984 0.234544i
\(988\) 0 0
\(989\) 20.5943 + 25.6828i 0.654860 + 0.816666i
\(990\) 0 0
\(991\) 5.06273 2.02681i 0.160823 0.0643838i −0.289854 0.957071i \(-0.593607\pi\)
0.450677 + 0.892687i \(0.351183\pi\)
\(992\) 0 0
\(993\) 3.60332 + 1.05803i 0.114348 + 0.0335756i
\(994\) 0 0
\(995\) 28.6376 8.40877i 0.907874 0.266576i
\(996\) 0 0
\(997\) −59.4691 + 5.67861i −1.88341 + 0.179843i −0.972520 0.232818i \(-0.925205\pi\)
−0.910885 + 0.412661i \(0.864599\pi\)
\(998\) 0 0
\(999\) 0.597556 + 12.5443i 0.0189058 + 0.396883i
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 644.2.y.a.261.7 yes 320
7.4 even 3 inner 644.2.y.a.445.10 yes 320
23.3 even 11 inner 644.2.y.a.233.10 320
161.95 even 33 inner 644.2.y.a.417.7 yes 320
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
644.2.y.a.233.10 320 23.3 even 11 inner
644.2.y.a.261.7 yes 320 1.1 even 1 trivial
644.2.y.a.417.7 yes 320 161.95 even 33 inner
644.2.y.a.445.10 yes 320 7.4 even 3 inner