Properties

Label 369.2.u.a.46.3
Level $369$
Weight $2$
Character 369.46
Analytic conductor $2.946$
Analytic rank $0$
Dimension $24$
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] = [369,2,Mod(46,369)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(369, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("369.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 369 = 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 369.u (of order \(20\), degree \(8\), 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: \(2.94647983459\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 41)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 46.3
Character \(\chi\) \(=\) 369.46
Dual form 369.2.u.a.361.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00762 + 1.38687i) q^{2} +(-0.290083 + 0.892782i) q^{4} +(2.57687 + 0.837277i) q^{5} +(-0.252316 - 1.59306i) q^{7} +(1.73027 - 0.562198i) q^{8} +O(q^{10})\) \(q+(1.00762 + 1.38687i) q^{2} +(-0.290083 + 0.892782i) q^{4} +(2.57687 + 0.837277i) q^{5} +(-0.252316 - 1.59306i) q^{7} +(1.73027 - 0.562198i) q^{8} +(1.43532 + 4.41746i) q^{10} +(-0.314590 + 0.617417i) q^{11} +(-1.50733 - 0.238738i) q^{13} +(1.95513 - 1.95513i) q^{14} +(4.04205 + 2.93672i) q^{16} +(-0.942631 - 0.480295i) q^{17} +(-0.126968 + 0.0201098i) q^{19} +(-1.49501 + 2.05771i) q^{20} +(-1.17327 + 0.185828i) q^{22} +(-1.52374 + 1.10707i) q^{23} +(1.89416 + 1.37619i) q^{25} +(-1.18772 - 2.33104i) q^{26} +(1.49545 + 0.236856i) q^{28} +(-7.39222 + 3.76652i) q^{29} +(0.373094 + 1.14827i) q^{31} +4.92630i q^{32} +(-0.283709 - 1.79127i) q^{34} +(0.683646 - 4.31637i) q^{35} +(-1.86889 + 5.75186i) q^{37} +(-0.155826 - 0.155826i) q^{38} +4.92939 q^{40} +(-5.96866 + 2.31844i) q^{41} +(-6.21829 - 8.55874i) q^{43} +(-0.459962 - 0.459962i) q^{44} +(-3.07072 - 0.997738i) q^{46} +(0.991818 - 6.26210i) q^{47} +(4.18322 - 1.35921i) q^{49} +4.01364i q^{50} +(0.650391 - 1.27646i) q^{52} +(11.1289 - 5.67046i) q^{53} +(-1.32761 + 1.32761i) q^{55} +(-1.33219 - 2.61457i) q^{56} +(-12.6723 - 6.45684i) q^{58} +(6.61738 - 4.80781i) q^{59} +(-1.54768 + 2.13021i) q^{61} +(-1.21656 + 1.67445i) q^{62} +(1.25193 - 0.909582i) q^{64} +(-3.68431 - 1.87725i) q^{65} +(-3.85439 - 7.56467i) q^{67} +(0.702239 - 0.702239i) q^{68} +(6.67512 - 3.40115i) q^{70} +(-1.94789 + 3.82296i) q^{71} +12.1957i q^{73} +(-9.86025 + 3.20379i) q^{74} +(0.0188776 - 0.119188i) q^{76} +(1.06296 + 0.345376i) q^{77} +(-8.14191 - 8.14191i) q^{79} +(7.95700 + 10.9519i) q^{80} +(-9.22954 - 5.94167i) q^{82} -6.49090 q^{83} +(-2.02690 - 2.02690i) q^{85} +(5.60421 - 17.2480i) q^{86} +(-0.197214 + 1.24516i) q^{88} +(-0.451128 - 2.84831i) q^{89} +2.46150i q^{91} +(-0.546357 - 1.68151i) q^{92} +(9.68412 - 4.93431i) q^{94} +(-0.344018 - 0.0544871i) q^{95} +(0.548878 + 1.07723i) q^{97} +(6.10017 + 4.43203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/369\mathbb{Z}\right)^\times\).

\(n\) \(83\) \(334\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{20}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00762 + 1.38687i 0.712497 + 0.980669i 0.999740 + 0.0228107i \(0.00726149\pi\)
−0.287242 + 0.957858i \(0.592739\pi\)
\(3\) 0 0
\(4\) −0.290083 + 0.892782i −0.145041 + 0.446391i
\(5\) 2.57687 + 0.837277i 1.15241 + 0.374442i 0.822052 0.569413i \(-0.192829\pi\)
0.330361 + 0.943855i \(0.392829\pi\)
\(6\) 0 0
\(7\) −0.252316 1.59306i −0.0953664 0.602120i −0.988370 0.152070i \(-0.951406\pi\)
0.893003 0.450050i \(-0.148594\pi\)
\(8\) 1.73027 0.562198i 0.611742 0.198767i
\(9\) 0 0
\(10\) 1.43532 + 4.41746i 0.453888 + 1.39692i
\(11\) −0.314590 + 0.617417i −0.0948524 + 0.186158i −0.933558 0.358427i \(-0.883313\pi\)
0.838705 + 0.544586i \(0.183313\pi\)
\(12\) 0 0
\(13\) −1.50733 0.238738i −0.418058 0.0662139i −0.0561381 0.998423i \(-0.517879\pi\)
−0.361920 + 0.932209i \(0.617879\pi\)
\(14\) 1.95513 1.95513i 0.522532 0.522532i
\(15\) 0 0
\(16\) 4.04205 + 2.93672i 1.01051 + 0.734180i
\(17\) −0.942631 0.480295i −0.228622 0.116489i 0.335928 0.941888i \(-0.390950\pi\)
−0.564550 + 0.825399i \(0.690950\pi\)
\(18\) 0 0
\(19\) −0.126968 + 0.0201098i −0.0291285 + 0.00461350i −0.170982 0.985274i \(-0.554694\pi\)
0.141853 + 0.989888i \(0.454694\pi\)
\(20\) −1.49501 + 2.05771i −0.334295 + 0.460117i
\(21\) 0 0
\(22\) −1.17327 + 0.185828i −0.250142 + 0.0396186i
\(23\) −1.52374 + 1.10707i −0.317723 + 0.230839i −0.735203 0.677847i \(-0.762913\pi\)
0.417480 + 0.908686i \(0.362913\pi\)
\(24\) 0 0
\(25\) 1.89416 + 1.37619i 0.378831 + 0.275237i
\(26\) −1.18772 2.33104i −0.232932 0.457154i
\(27\) 0 0
\(28\) 1.49545 + 0.236856i 0.282613 + 0.0447615i
\(29\) −7.39222 + 3.76652i −1.37270 + 0.699426i −0.975847 0.218456i \(-0.929898\pi\)
−0.396853 + 0.917882i \(0.629898\pi\)
\(30\) 0 0
\(31\) 0.373094 + 1.14827i 0.0670097 + 0.206235i 0.978955 0.204078i \(-0.0654196\pi\)
−0.911945 + 0.410313i \(0.865420\pi\)
\(32\) 4.92630i 0.870855i
\(33\) 0 0
\(34\) −0.283709 1.79127i −0.0486557 0.307200i
\(35\) 0.683646 4.31637i 0.115557 0.729600i
\(36\) 0 0
\(37\) −1.86889 + 5.75186i −0.307244 + 0.945600i 0.671586 + 0.740926i \(0.265613\pi\)
−0.978830 + 0.204673i \(0.934387\pi\)
\(38\) −0.155826 0.155826i −0.0252783 0.0252783i
\(39\) 0 0
\(40\) 4.92939 0.779405
\(41\) −5.96866 + 2.31844i −0.932147 + 0.362079i
\(42\) 0 0
\(43\) −6.21829 8.55874i −0.948280 1.30520i −0.952287 0.305204i \(-0.901276\pi\)
0.00400713 0.999992i \(-0.498724\pi\)
\(44\) −0.459962 0.459962i −0.0693419 0.0693419i
\(45\) 0 0
\(46\) −3.07072 0.997738i −0.452753 0.147108i
\(47\) 0.991818 6.26210i 0.144672 0.913421i −0.803418 0.595416i \(-0.796987\pi\)
0.948089 0.318005i \(-0.103013\pi\)
\(48\) 0 0
\(49\) 4.18322 1.35921i 0.597603 0.194173i
\(50\) 4.01364i 0.567614i
\(51\) 0 0
\(52\) 0.650391 1.27646i 0.0901930 0.177014i
\(53\) 11.1289 5.67046i 1.52867 0.778898i 0.531020 0.847359i \(-0.321809\pi\)
0.997654 + 0.0684612i \(0.0218089\pi\)
\(54\) 0 0
\(55\) −1.32761 + 1.32761i −0.179015 + 0.179015i
\(56\) −1.33219 2.61457i −0.178021 0.349386i
\(57\) 0 0
\(58\) −12.6723 6.45684i −1.66395 0.847825i
\(59\) 6.61738 4.80781i 0.861509 0.625923i −0.0667860 0.997767i \(-0.521274\pi\)
0.928295 + 0.371844i \(0.121274\pi\)
\(60\) 0 0
\(61\) −1.54768 + 2.13021i −0.198161 + 0.272745i −0.896521 0.443002i \(-0.853913\pi\)
0.698360 + 0.715747i \(0.253913\pi\)
\(62\) −1.21656 + 1.67445i −0.154504 + 0.212656i
\(63\) 0 0
\(64\) 1.25193 0.909582i 0.156491 0.113698i
\(65\) −3.68431 1.87725i −0.456982 0.232844i
\(66\) 0 0
\(67\) −3.85439 7.56467i −0.470889 0.924172i −0.997264 0.0739193i \(-0.976449\pi\)
0.526375 0.850252i \(-0.323551\pi\)
\(68\) 0.702239 0.702239i 0.0851590 0.0851590i
\(69\) 0 0
\(70\) 6.67512 3.40115i 0.797830 0.406515i
\(71\) −1.94789 + 3.82296i −0.231172 + 0.453701i −0.977231 0.212179i \(-0.931944\pi\)
0.746058 + 0.665881i \(0.231944\pi\)
\(72\) 0 0
\(73\) 12.1957i 1.42739i 0.700455 + 0.713697i \(0.252981\pi\)
−0.700455 + 0.713697i \(0.747019\pi\)
\(74\) −9.86025 + 3.20379i −1.14623 + 0.372433i
\(75\) 0 0
\(76\) 0.0188776 0.119188i 0.00216541 0.0136718i
\(77\) 1.06296 + 0.345376i 0.121135 + 0.0393593i
\(78\) 0 0
\(79\) −8.14191 8.14191i −0.916037 0.916037i 0.0807015 0.996738i \(-0.474284\pi\)
−0.996738 + 0.0807015i \(0.974284\pi\)
\(80\) 7.95700 + 10.9519i 0.889619 + 1.22446i
\(81\) 0 0
\(82\) −9.22954 5.94167i −1.01923 0.656147i
\(83\) −6.49090 −0.712469 −0.356235 0.934397i \(-0.615940\pi\)
−0.356235 + 0.934397i \(0.615940\pi\)
\(84\) 0 0
\(85\) −2.02690 2.02690i −0.219848 0.219848i
\(86\) 5.60421 17.2480i 0.604317 1.85990i
\(87\) 0 0
\(88\) −0.197214 + 1.24516i −0.0210231 + 0.132734i
\(89\) −0.451128 2.84831i −0.0478195 0.301920i 0.952174 0.305557i \(-0.0988425\pi\)
−0.999993 + 0.00363635i \(0.998843\pi\)
\(90\) 0 0
\(91\) 2.46150i 0.258036i
\(92\) −0.546357 1.68151i −0.0569616 0.175310i
\(93\) 0 0
\(94\) 9.68412 4.93431i 0.998841 0.508935i
\(95\) −0.344018 0.0544871i −0.0352955 0.00559026i
\(96\) 0 0
\(97\) 0.548878 + 1.07723i 0.0557301 + 0.109377i 0.917192 0.398446i \(-0.130450\pi\)
−0.861462 + 0.507823i \(0.830450\pi\)
\(98\) 6.10017 + 4.43203i 0.616210 + 0.447703i
\(99\) 0 0
\(100\) −1.77810 + 1.29186i −0.177810 + 0.129186i
\(101\) 5.23645 0.829373i 0.521047 0.0825257i 0.109629 0.993973i \(-0.465034\pi\)
0.411418 + 0.911447i \(0.365034\pi\)
\(102\) 0 0
\(103\) 8.15642 11.2264i 0.803676 1.10617i −0.188592 0.982055i \(-0.560392\pi\)
0.992268 0.124110i \(-0.0396075\pi\)
\(104\) −2.74230 + 0.434338i −0.268905 + 0.0425903i
\(105\) 0 0
\(106\) 19.0780 + 9.72072i 1.85302 + 0.944159i
\(107\) 7.71269 + 5.60360i 0.745614 + 0.541720i 0.894464 0.447139i \(-0.147557\pi\)
−0.148850 + 0.988860i \(0.547557\pi\)
\(108\) 0 0
\(109\) −1.66630 + 1.66630i −0.159603 + 0.159603i −0.782391 0.622788i \(-0.786000\pi\)
0.622788 + 0.782391i \(0.286000\pi\)
\(110\) −3.17895 0.503497i −0.303101 0.0480065i
\(111\) 0 0
\(112\) 3.65850 7.18020i 0.345695 0.678465i
\(113\) 2.37239 + 7.30147i 0.223176 + 0.686865i 0.998472 + 0.0552663i \(0.0176008\pi\)
−0.775296 + 0.631598i \(0.782399\pi\)
\(114\) 0 0
\(115\) −4.85342 + 1.57697i −0.452583 + 0.147053i
\(116\) −1.21833 7.69224i −0.113119 0.714207i
\(117\) 0 0
\(118\) 13.3356 + 4.33302i 1.22765 + 0.398886i
\(119\) −0.527297 + 1.62285i −0.0483372 + 0.148767i
\(120\) 0 0
\(121\) 6.18340 + 8.51072i 0.562127 + 0.773702i
\(122\) −4.51381 −0.408661
\(123\) 0 0
\(124\) −1.13338 −0.101781
\(125\) −4.23422 5.82791i −0.378720 0.521264i
\(126\) 0 0
\(127\) −1.92578 + 5.92695i −0.170886 + 0.525932i −0.999422 0.0340038i \(-0.989174\pi\)
0.828536 + 0.559936i \(0.189174\pi\)
\(128\) 11.8933 + 3.86438i 1.05123 + 0.341566i
\(129\) 0 0
\(130\) −1.10889 7.00124i −0.0972558 0.614049i
\(131\) −0.689839 + 0.224142i −0.0602715 + 0.0195834i −0.338998 0.940787i \(-0.610088\pi\)
0.278726 + 0.960371i \(0.410088\pi\)
\(132\) 0 0
\(133\) 0.0640721 + 0.197194i 0.00555576 + 0.0170989i
\(134\) 6.60748 12.9679i 0.570799 1.12026i
\(135\) 0 0
\(136\) −1.90102 0.301093i −0.163011 0.0258185i
\(137\) −13.1949 + 13.1949i −1.12731 + 1.12731i −0.136700 + 0.990612i \(0.543650\pi\)
−0.990612 + 0.136700i \(0.956350\pi\)
\(138\) 0 0
\(139\) −5.13170 3.72840i −0.435265 0.316239i 0.348486 0.937314i \(-0.386696\pi\)
−0.783751 + 0.621075i \(0.786696\pi\)
\(140\) 3.65527 + 1.86245i 0.308926 + 0.157406i
\(141\) 0 0
\(142\) −7.26470 + 1.15062i −0.609640 + 0.0965576i
\(143\) 0.621592 0.855548i 0.0519801 0.0715445i
\(144\) 0 0
\(145\) −22.2024 + 3.51652i −1.84381 + 0.292031i
\(146\) −16.9139 + 12.2886i −1.39980 + 1.01701i
\(147\) 0 0
\(148\) −4.59302 3.33703i −0.377544 0.274302i
\(149\) −5.86949 11.5195i −0.480848 0.943717i −0.996230 0.0867562i \(-0.972350\pi\)
0.515382 0.856961i \(-0.327650\pi\)
\(150\) 0 0
\(151\) −1.37899 0.218411i −0.112221 0.0177740i 0.100071 0.994980i \(-0.468093\pi\)
−0.212292 + 0.977206i \(0.568093\pi\)
\(152\) −0.208383 + 0.106176i −0.0169021 + 0.00861205i
\(153\) 0 0
\(154\) 0.592069 + 1.82220i 0.0477102 + 0.146837i
\(155\) 3.27132i 0.262759i
\(156\) 0 0
\(157\) 2.74716 + 17.3449i 0.219247 + 1.38427i 0.814234 + 0.580537i \(0.197157\pi\)
−0.594987 + 0.803735i \(0.702843\pi\)
\(158\) 3.08783 19.4958i 0.245655 1.55100i
\(159\) 0 0
\(160\) −4.12468 + 12.6945i −0.326084 + 1.00358i
\(161\) 2.14809 + 2.14809i 0.169293 + 0.169293i
\(162\) 0 0
\(163\) 17.6081 1.37918 0.689588 0.724202i \(-0.257792\pi\)
0.689588 + 0.724202i \(0.257792\pi\)
\(164\) −0.338458 6.00125i −0.0264291 0.468619i
\(165\) 0 0
\(166\) −6.54039 9.00207i −0.507632 0.698696i
\(167\) 1.96297 + 1.96297i 0.151899 + 0.151899i 0.778966 0.627066i \(-0.215745\pi\)
−0.627066 + 0.778966i \(0.715745\pi\)
\(168\) 0 0
\(169\) −10.1487 3.29751i −0.780668 0.253654i
\(170\) 0.768705 4.85341i 0.0589570 0.372240i
\(171\) 0 0
\(172\) 9.44491 3.06884i 0.720168 0.233997i
\(173\) 11.7096i 0.890265i 0.895465 + 0.445132i \(0.146843\pi\)
−0.895465 + 0.445132i \(0.853157\pi\)
\(174\) 0 0
\(175\) 1.71442 3.36474i 0.129598 0.254350i
\(176\) −3.08477 + 1.57177i −0.232523 + 0.118476i
\(177\) 0 0
\(178\) 3.49568 3.49568i 0.262012 0.262012i
\(179\) −1.93111 3.79002i −0.144338 0.283279i 0.807508 0.589857i \(-0.200816\pi\)
−0.951846 + 0.306578i \(0.900816\pi\)
\(180\) 0 0
\(181\) 4.13089 + 2.10479i 0.307047 + 0.156448i 0.600724 0.799457i \(-0.294879\pi\)
−0.293677 + 0.955905i \(0.594879\pi\)
\(182\) −3.41380 + 2.48027i −0.253048 + 0.183850i
\(183\) 0 0
\(184\) −2.01409 + 2.77216i −0.148481 + 0.204367i
\(185\) −9.63179 + 13.2570i −0.708144 + 0.974676i
\(186\) 0 0
\(187\) 0.593084 0.430901i 0.0433706 0.0315106i
\(188\) 5.30298 + 2.70200i 0.386760 + 0.197064i
\(189\) 0 0
\(190\) −0.271074 0.532013i −0.0196658 0.0385963i
\(191\) −15.8171 + 15.8171i −1.14449 + 1.14449i −0.156869 + 0.987619i \(0.550140\pi\)
−0.987619 + 0.156869i \(0.949860\pi\)
\(192\) 0 0
\(193\) 12.9855 6.61647i 0.934720 0.476264i 0.0808362 0.996727i \(-0.474241\pi\)
0.853884 + 0.520464i \(0.174241\pi\)
\(194\) −0.940926 + 1.84667i −0.0675546 + 0.132583i
\(195\) 0 0
\(196\) 4.12899i 0.294928i
\(197\) −0.885009 + 0.287557i −0.0630543 + 0.0204876i −0.340374 0.940290i \(-0.610554\pi\)
0.277320 + 0.960778i \(0.410554\pi\)
\(198\) 0 0
\(199\) 0.0644895 0.407171i 0.00457154 0.0288636i −0.985297 0.170850i \(-0.945349\pi\)
0.989869 + 0.141986i \(0.0453488\pi\)
\(200\) 4.05109 + 1.31628i 0.286455 + 0.0930749i
\(201\) 0 0
\(202\) 6.42661 + 6.42661i 0.452175 + 0.452175i
\(203\) 7.86547 + 10.8259i 0.552048 + 0.759828i
\(204\) 0 0
\(205\) −17.3216 + 0.976904i −1.20980 + 0.0682299i
\(206\) 23.7881 1.65740
\(207\) 0 0
\(208\) −5.39160 5.39160i −0.373840 0.373840i
\(209\) 0.0275268 0.0847187i 0.00190407 0.00586011i
\(210\) 0 0
\(211\) −3.50778 + 22.1473i −0.241486 + 1.52468i 0.507243 + 0.861803i \(0.330665\pi\)
−0.748728 + 0.662877i \(0.769335\pi\)
\(212\) 1.83419 + 11.5806i 0.125972 + 0.795359i
\(213\) 0 0
\(214\) 16.3429i 1.11717i
\(215\) −8.85770 27.2612i −0.604090 1.85920i
\(216\) 0 0
\(217\) 1.73512 0.884087i 0.117788 0.0600157i
\(218\) −3.98995 0.631946i −0.270234 0.0428008i
\(219\) 0 0
\(220\) −0.800149 1.57038i −0.0539460 0.105875i
\(221\) 1.30619 + 0.949004i 0.0878640 + 0.0638369i
\(222\) 0 0
\(223\) 3.29767 2.39590i 0.220829 0.160441i −0.471871 0.881668i \(-0.656421\pi\)
0.692700 + 0.721226i \(0.256421\pi\)
\(224\) 7.84789 1.24298i 0.524359 0.0830504i
\(225\) 0 0
\(226\) −7.73575 + 10.6473i −0.514574 + 0.708251i
\(227\) 21.3270 3.37787i 1.41552 0.224197i 0.598649 0.801012i \(-0.295705\pi\)
0.816875 + 0.576815i \(0.195705\pi\)
\(228\) 0 0
\(229\) 8.82761 + 4.49789i 0.583345 + 0.297229i 0.720649 0.693300i \(-0.243844\pi\)
−0.137304 + 0.990529i \(0.543844\pi\)
\(230\) −7.07748 5.14209i −0.466675 0.339059i
\(231\) 0 0
\(232\) −10.6730 + 10.6730i −0.700715 + 0.700715i
\(233\) 1.27079 + 0.201273i 0.0832521 + 0.0131858i 0.197922 0.980218i \(-0.436581\pi\)
−0.114669 + 0.993404i \(0.536581\pi\)
\(234\) 0 0
\(235\) 7.79890 15.3062i 0.508744 0.998466i
\(236\) 2.37274 + 7.30254i 0.154452 + 0.475355i
\(237\) 0 0
\(238\) −2.78201 + 0.903930i −0.180331 + 0.0585931i
\(239\) 1.11016 + 7.00929i 0.0718104 + 0.453393i 0.997226 + 0.0744383i \(0.0237164\pi\)
−0.925415 + 0.378955i \(0.876284\pi\)
\(240\) 0 0
\(241\) 10.2597 + 3.33359i 0.660888 + 0.214735i 0.620209 0.784437i \(-0.287048\pi\)
0.0406791 + 0.999172i \(0.487048\pi\)
\(242\) −5.57276 + 17.1512i −0.358231 + 1.10252i
\(243\) 0 0
\(244\) −1.45285 1.99968i −0.0930094 0.128016i
\(245\) 11.9177 0.761391
\(246\) 0 0
\(247\) 0.196184 0.0124829
\(248\) 1.29111 + 1.77705i 0.0819853 + 0.112843i
\(249\) 0 0
\(250\) 3.81608 11.7447i 0.241350 0.742798i
\(251\) −5.35009 1.73835i −0.337695 0.109724i 0.135261 0.990810i \(-0.456813\pi\)
−0.472955 + 0.881086i \(0.656813\pi\)
\(252\) 0 0
\(253\) −0.204167 1.28906i −0.0128359 0.0810424i
\(254\) −10.1604 + 3.30132i −0.637520 + 0.207143i
\(255\) 0 0
\(256\) 5.66820 + 17.4449i 0.354263 + 1.09031i
\(257\) 9.98071 19.5882i 0.622580 1.22188i −0.337281 0.941404i \(-0.609507\pi\)
0.959861 0.280477i \(-0.0904927\pi\)
\(258\) 0 0
\(259\) 9.63460 + 1.52597i 0.598665 + 0.0948192i
\(260\) 2.74473 2.74473i 0.170221 0.170221i
\(261\) 0 0
\(262\) −1.00596 0.730869i −0.0621481 0.0451533i
\(263\) −5.22227 2.66088i −0.322019 0.164077i 0.285507 0.958377i \(-0.407838\pi\)
−0.607526 + 0.794300i \(0.707838\pi\)
\(264\) 0 0
\(265\) 33.4255 5.29409i 2.05331 0.325213i
\(266\) −0.208922 + 0.287557i −0.0128099 + 0.0176313i
\(267\) 0 0
\(268\) 7.87170 1.24675i 0.480840 0.0761576i
\(269\) 11.1080 8.07042i 0.677265 0.492062i −0.195184 0.980767i \(-0.562530\pi\)
0.872449 + 0.488705i \(0.162530\pi\)
\(270\) 0 0
\(271\) 12.8738 + 9.35335i 0.782026 + 0.568175i 0.905586 0.424162i \(-0.139431\pi\)
−0.123560 + 0.992337i \(0.539431\pi\)
\(272\) −2.39967 4.70962i −0.145501 0.285562i
\(273\) 0 0
\(274\) −31.5951 5.00417i −1.90873 0.302313i
\(275\) −1.44556 + 0.736551i −0.0871708 + 0.0444157i
\(276\) 0 0
\(277\) −5.93200 18.2568i −0.356420 1.09695i −0.955182 0.296020i \(-0.904341\pi\)
0.598762 0.800927i \(-0.295659\pi\)
\(278\) 10.8738i 0.652170i
\(279\) 0 0
\(280\) −1.24376 7.85282i −0.0743291 0.469296i
\(281\) 0.226991 1.43316i 0.0135411 0.0854954i −0.979992 0.199036i \(-0.936219\pi\)
0.993533 + 0.113540i \(0.0362191\pi\)
\(282\) 0 0
\(283\) −2.91195 + 8.96207i −0.173098 + 0.532740i −0.999541 0.0302793i \(-0.990360\pi\)
0.826444 + 0.563019i \(0.190360\pi\)
\(284\) −2.84802 2.84802i −0.168999 0.168999i
\(285\) 0 0
\(286\) 1.81287 0.107197
\(287\) 5.19940 + 8.92345i 0.306911 + 0.526734i
\(288\) 0 0
\(289\) −9.33448 12.8478i −0.549087 0.755753i
\(290\) −27.2487 27.2487i −1.60010 1.60010i
\(291\) 0 0
\(292\) −10.8881 3.53775i −0.637176 0.207031i
\(293\) −0.169720 + 1.07157i −0.00991512 + 0.0626016i −0.992150 0.125055i \(-0.960089\pi\)
0.982235 + 0.187657i \(0.0600892\pi\)
\(294\) 0 0
\(295\) 21.0776 6.84853i 1.22719 0.398737i
\(296\) 11.0029i 0.639533i
\(297\) 0 0
\(298\) 10.0619 19.7476i 0.582871 1.14395i
\(299\) 2.56108 1.30494i 0.148111 0.0754665i
\(300\) 0 0
\(301\) −12.0656 + 12.0656i −0.695450 + 0.695450i
\(302\) −1.08660 2.13256i −0.0625266 0.122715i
\(303\) 0 0
\(304\) −0.572268 0.291585i −0.0328218 0.0167236i
\(305\) −5.77176 + 4.19343i −0.330490 + 0.240115i
\(306\) 0 0
\(307\) 17.4258 23.9845i 0.994542 1.36887i 0.0659270 0.997824i \(-0.479000\pi\)
0.928615 0.371045i \(-0.121000\pi\)
\(308\) −0.616692 + 0.848803i −0.0351393 + 0.0483650i
\(309\) 0 0
\(310\) −4.53691 + 3.29626i −0.257679 + 0.187215i
\(311\) 15.3673 + 7.83002i 0.871399 + 0.444000i 0.831709 0.555212i \(-0.187363\pi\)
0.0396900 + 0.999212i \(0.487363\pi\)
\(312\) 0 0
\(313\) −0.736533 1.44553i −0.0416313 0.0817060i 0.869254 0.494366i \(-0.164600\pi\)
−0.910885 + 0.412660i \(0.864600\pi\)
\(314\) −21.2871 + 21.2871i −1.20130 + 1.20130i
\(315\) 0 0
\(316\) 9.63078 4.90713i 0.541774 0.276048i
\(317\) 7.39686 14.5172i 0.415449 0.815364i −0.584543 0.811363i \(-0.698726\pi\)
0.999992 0.00400175i \(-0.00127380\pi\)
\(318\) 0 0
\(319\) 5.74899i 0.321882i
\(320\) 3.98764 1.29566i 0.222916 0.0724298i
\(321\) 0 0
\(322\) −0.814664 + 5.14359i −0.0453995 + 0.286641i
\(323\) 0.129343 + 0.0420260i 0.00719682 + 0.00233839i
\(324\) 0 0
\(325\) −2.52657 2.52657i −0.140149 0.140149i
\(326\) 17.7424 + 24.4203i 0.982660 + 1.35251i
\(327\) 0 0
\(328\) −9.02395 + 7.36708i −0.498264 + 0.406779i
\(329\) −10.2261 −0.563786
\(330\) 0 0
\(331\) −17.9285 17.9285i −0.985441 0.985441i 0.0144544 0.999896i \(-0.495399\pi\)
−0.999896 + 0.0144544i \(0.995399\pi\)
\(332\) 1.88290 5.79496i 0.103337 0.318040i
\(333\) 0 0
\(334\) −0.744460 + 4.70034i −0.0407350 + 0.257191i
\(335\) −3.59856 22.7204i −0.196610 1.24135i
\(336\) 0 0
\(337\) 26.2434i 1.42957i 0.699344 + 0.714785i \(0.253475\pi\)
−0.699344 + 0.714785i \(0.746525\pi\)
\(338\) −5.65282 17.3976i −0.307473 0.946305i
\(339\) 0 0
\(340\) 2.39755 1.22161i 0.130025 0.0662513i
\(341\) −0.826331 0.130878i −0.0447483 0.00708744i
\(342\) 0 0
\(343\) −8.34654 16.3810i −0.450671 0.884491i
\(344\) −15.5710 11.3130i −0.839532 0.609956i
\(345\) 0 0
\(346\) −16.2398 + 11.7989i −0.873055 + 0.634311i
\(347\) 16.4622 2.60735i 0.883735 0.139970i 0.301961 0.953320i \(-0.402359\pi\)
0.581774 + 0.813351i \(0.302359\pi\)
\(348\) 0 0
\(349\) 5.08471 6.99851i 0.272178 0.374622i −0.650945 0.759125i \(-0.725627\pi\)
0.923124 + 0.384503i \(0.125627\pi\)
\(350\) 6.39396 1.01270i 0.341772 0.0541313i
\(351\) 0 0
\(352\) −3.04158 1.54976i −0.162117 0.0826027i
\(353\) 11.1586 + 8.10719i 0.593912 + 0.431502i 0.843713 0.536795i \(-0.180365\pi\)
−0.249801 + 0.968297i \(0.580365\pi\)
\(354\) 0 0
\(355\) −8.22035 + 8.22035i −0.436291 + 0.436291i
\(356\) 2.67379 + 0.423486i 0.141710 + 0.0224447i
\(357\) 0 0
\(358\) 3.31045 6.49712i 0.174962 0.343383i
\(359\) 5.59785 + 17.2284i 0.295443 + 0.909281i 0.983072 + 0.183219i \(0.0586517\pi\)
−0.687629 + 0.726062i \(0.741348\pi\)
\(360\) 0 0
\(361\) −18.0544 + 5.86622i −0.950229 + 0.308748i
\(362\) 1.24330 + 7.84987i 0.0653462 + 0.412580i
\(363\) 0 0
\(364\) −2.19759 0.714040i −0.115185 0.0374258i
\(365\) −10.2111 + 31.4267i −0.534476 + 1.64495i
\(366\) 0 0
\(367\) 13.5735 + 18.6823i 0.708531 + 0.975210i 0.999827 + 0.0185766i \(0.00591347\pi\)
−0.291296 + 0.956633i \(0.594087\pi\)
\(368\) −9.41019 −0.490540
\(369\) 0 0
\(370\) −28.0911 −1.46038
\(371\) −11.8414 16.2983i −0.614774 0.846164i
\(372\) 0 0
\(373\) 4.36956 13.4481i 0.226247 0.696317i −0.771915 0.635725i \(-0.780701\pi\)
0.998163 0.0605920i \(-0.0192989\pi\)
\(374\) 1.19521 + 0.388348i 0.0618029 + 0.0200810i
\(375\) 0 0
\(376\) −1.80443 11.3927i −0.0930561 0.587533i
\(377\) 12.0417 3.91259i 0.620180 0.201509i
\(378\) 0 0
\(379\) −11.4876 35.3552i −0.590079 1.81608i −0.577840 0.816150i \(-0.696104\pi\)
−0.0122385 0.999925i \(-0.503896\pi\)
\(380\) 0.148439 0.291328i 0.00761475 0.0149448i
\(381\) 0 0
\(382\) −37.8741 5.99867i −1.93781 0.306919i
\(383\) 4.89444 4.89444i 0.250094 0.250094i −0.570915 0.821009i \(-0.693411\pi\)
0.821009 + 0.570915i \(0.193411\pi\)
\(384\) 0 0
\(385\) 2.44993 + 1.77998i 0.124860 + 0.0907162i
\(386\) 22.2607 + 11.3424i 1.13304 + 0.577314i
\(387\) 0 0
\(388\) −1.12096 + 0.177542i −0.0569079 + 0.00901333i
\(389\) −1.39142 + 1.91513i −0.0705480 + 0.0971010i −0.842833 0.538175i \(-0.819114\pi\)
0.772285 + 0.635276i \(0.219114\pi\)
\(390\) 0 0
\(391\) 1.96805 0.311708i 0.0995284 0.0157637i
\(392\) 6.47394 4.70359i 0.326983 0.237567i
\(393\) 0 0
\(394\) −1.29056 0.937648i −0.0650176 0.0472380i
\(395\) −14.1636 27.7977i −0.712650 1.39865i
\(396\) 0 0
\(397\) 15.9514 + 2.52646i 0.800580 + 0.126799i 0.543301 0.839538i \(-0.317174\pi\)
0.257278 + 0.966337i \(0.417174\pi\)
\(398\) 0.629676 0.320836i 0.0315628 0.0160820i
\(399\) 0 0
\(400\) 3.61480 + 11.1252i 0.180740 + 0.556261i
\(401\) 4.77242i 0.238323i 0.992875 + 0.119162i \(0.0380207\pi\)
−0.992875 + 0.119162i \(0.961979\pi\)
\(402\) 0 0
\(403\) −0.288242 1.81989i −0.0143584 0.0906551i
\(404\) −0.778554 + 4.91560i −0.0387345 + 0.244560i
\(405\) 0 0
\(406\) −7.08872 + 21.8168i −0.351807 + 1.08275i
\(407\) −2.96336 2.96336i −0.146888 0.146888i
\(408\) 0 0
\(409\) −9.57331 −0.473370 −0.236685 0.971586i \(-0.576061\pi\)
−0.236685 + 0.971586i \(0.576061\pi\)
\(410\) −18.8085 23.0386i −0.928887 1.13780i
\(411\) 0 0
\(412\) 7.65665 + 10.5385i 0.377216 + 0.519194i
\(413\) −9.32879 9.32879i −0.459040 0.459040i
\(414\) 0 0
\(415\) −16.7262 5.43468i −0.821058 0.266778i
\(416\) 1.17609 7.42556i 0.0576627 0.364068i
\(417\) 0 0
\(418\) 0.145231 0.0471883i 0.00710347 0.00230806i
\(419\) 8.06247i 0.393878i −0.980416 0.196939i \(-0.936900\pi\)
0.980416 0.196939i \(-0.0631000\pi\)
\(420\) 0 0
\(421\) −8.01644 + 15.7331i −0.390697 + 0.766787i −0.999651 0.0264191i \(-0.991590\pi\)
0.608954 + 0.793206i \(0.291590\pi\)
\(422\) −34.2500 + 17.4512i −1.66726 + 0.849513i
\(423\) 0 0
\(424\) 16.0681 16.0681i 0.780334 0.780334i
\(425\) −1.12452 2.20699i −0.0545471 0.107055i
\(426\) 0 0
\(427\) 3.78405 + 1.92807i 0.183123 + 0.0933058i
\(428\) −7.24011 + 5.26025i −0.349964 + 0.254264i
\(429\) 0 0
\(430\) 28.8827 39.7536i 1.39285 1.91709i
\(431\) 5.96805 8.21431i 0.287471 0.395670i −0.640720 0.767775i \(-0.721364\pi\)
0.928191 + 0.372105i \(0.121364\pi\)
\(432\) 0 0
\(433\) 26.8766 19.5270i 1.29161 0.938406i 0.291769 0.956489i \(-0.405756\pi\)
0.999837 + 0.0180823i \(0.00575610\pi\)
\(434\) 2.97446 + 1.51557i 0.142779 + 0.0727495i
\(435\) 0 0
\(436\) −1.00428 1.97101i −0.0480962 0.0943941i
\(437\) 0.171204 0.171204i 0.00818981 0.00818981i
\(438\) 0 0
\(439\) −32.8349 + 16.7302i −1.56713 + 0.798490i −0.999689 0.0249274i \(-0.992065\pi\)
−0.567436 + 0.823418i \(0.692065\pi\)
\(440\) −1.55074 + 3.04349i −0.0739285 + 0.145093i
\(441\) 0 0
\(442\) 2.76776i 0.131649i
\(443\) −29.3333 + 9.53097i −1.39367 + 0.452830i −0.907138 0.420834i \(-0.861738\pi\)
−0.486530 + 0.873664i \(0.661738\pi\)
\(444\) 0 0
\(445\) 1.22232 7.71745i 0.0579437 0.365842i
\(446\) 6.64563 + 2.15930i 0.314680 + 0.102246i
\(447\) 0 0
\(448\) −1.76490 1.76490i −0.0833837 0.0833837i
\(449\) −17.4190 23.9753i −0.822055 1.13146i −0.989350 0.145555i \(-0.953503\pi\)
0.167295 0.985907i \(-0.446497\pi\)
\(450\) 0 0
\(451\) 0.446235 4.41451i 0.0210124 0.207871i
\(452\) −7.20681 −0.338980
\(453\) 0 0
\(454\) 26.1743 + 26.1743i 1.22842 + 1.22842i
\(455\) −2.06096 + 6.34298i −0.0966193 + 0.297364i
\(456\) 0 0
\(457\) −1.18792 + 7.50026i −0.0555688 + 0.350847i 0.944201 + 0.329371i \(0.106837\pi\)
−0.999769 + 0.0214764i \(0.993163\pi\)
\(458\) 2.65689 + 16.7750i 0.124149 + 0.783843i
\(459\) 0 0
\(460\) 4.79050i 0.223358i
\(461\) 7.81323 + 24.0467i 0.363898 + 1.11996i 0.950668 + 0.310210i \(0.100399\pi\)
−0.586770 + 0.809754i \(0.699601\pi\)
\(462\) 0 0
\(463\) 13.1377 6.69397i 0.610559 0.311095i −0.121233 0.992624i \(-0.538685\pi\)
0.731791 + 0.681529i \(0.238685\pi\)
\(464\) −40.9409 6.48440i −1.90063 0.301031i
\(465\) 0 0
\(466\) 1.00134 + 1.96523i 0.0463860 + 0.0910376i
\(467\) −17.8981 13.0037i −0.828226 0.601742i 0.0908306 0.995866i \(-0.471048\pi\)
−0.919057 + 0.394125i \(0.871048\pi\)
\(468\) 0 0
\(469\) −11.0784 + 8.04896i −0.511555 + 0.371667i
\(470\) 29.0861 4.60679i 1.34164 0.212495i
\(471\) 0 0
\(472\) 8.74689 12.0391i 0.402608 0.554143i
\(473\) 7.24052 1.14679i 0.332920 0.0527293i
\(474\) 0 0
\(475\) −0.268172 0.136641i −0.0123046 0.00626950i
\(476\) −1.29590 0.941523i −0.0593973 0.0431546i
\(477\) 0 0
\(478\) −8.60238 + 8.60238i −0.393464 + 0.393464i
\(479\) 15.6892 + 2.48493i 0.716859 + 0.113539i 0.504200 0.863587i \(-0.331787\pi\)
0.212660 + 0.977126i \(0.431787\pi\)
\(480\) 0 0
\(481\) 4.19022 8.22377i 0.191058 0.374972i
\(482\) 5.71468 + 17.5880i 0.260297 + 0.801110i
\(483\) 0 0
\(484\) −9.39192 + 3.05162i −0.426905 + 0.138710i
\(485\) 0.512446 + 3.23546i 0.0232690 + 0.146915i
\(486\) 0 0
\(487\) 20.0083 + 6.50110i 0.906664 + 0.294593i 0.724985 0.688765i \(-0.241847\pi\)
0.181679 + 0.983358i \(0.441847\pi\)
\(488\) −1.48031 + 4.55593i −0.0670105 + 0.206237i
\(489\) 0 0
\(490\) 12.0085 + 16.5283i 0.542489 + 0.746673i
\(491\) 0.0541126 0.00244207 0.00122103 0.999999i \(-0.499611\pi\)
0.00122103 + 0.999999i \(0.499611\pi\)
\(492\) 0 0
\(493\) 8.77717 0.395304
\(494\) 0.197680 + 0.272083i 0.00889402 + 0.0122416i
\(495\) 0 0
\(496\) −1.86407 + 5.73702i −0.0836992 + 0.257600i
\(497\) 6.58168 + 2.13852i 0.295229 + 0.0959256i
\(498\) 0 0
\(499\) 5.08470 + 32.1035i 0.227623 + 1.43715i 0.791437 + 0.611251i \(0.209333\pi\)
−0.563815 + 0.825901i \(0.690667\pi\)
\(500\) 6.43133 2.08966i 0.287618 0.0934526i
\(501\) 0 0
\(502\) −2.98001 9.17151i −0.133004 0.409345i
\(503\) 14.6571 28.7662i 0.653529 1.28262i −0.291793 0.956482i \(-0.594252\pi\)
0.945321 0.326140i \(-0.105748\pi\)
\(504\) 0 0
\(505\) 14.1881 + 2.24717i 0.631362 + 0.0999979i
\(506\) 1.58204 1.58204i 0.0703302 0.0703302i
\(507\) 0 0
\(508\) −4.73284 3.43861i −0.209986 0.152564i
\(509\) 25.7195 + 13.1047i 1.14000 + 0.580857i 0.918938 0.394403i \(-0.129049\pi\)
0.221059 + 0.975260i \(0.429049\pi\)
\(510\) 0 0
\(511\) 19.4284 3.07716i 0.859462 0.136125i
\(512\) −3.78156 + 5.20487i −0.167123 + 0.230025i
\(513\) 0 0
\(514\) 37.2232 5.89558i 1.64185 0.260043i
\(515\) 30.4176 22.0997i 1.34036 0.973829i
\(516\) 0 0
\(517\) 3.55431 + 2.58236i 0.156318 + 0.113572i
\(518\) 7.59172 + 14.8996i 0.333561 + 0.654650i
\(519\) 0 0
\(520\) −7.43022 1.17683i −0.325837 0.0516075i
\(521\) −15.6014 + 7.94931i −0.683509 + 0.348265i −0.761022 0.648726i \(-0.775302\pi\)
0.0775127 + 0.996991i \(0.475302\pi\)
\(522\) 0 0
\(523\) 2.25075 + 6.92710i 0.0984185 + 0.302901i 0.988130 0.153623i \(-0.0490942\pi\)
−0.889711 + 0.456524i \(0.849094\pi\)
\(524\) 0.680896i 0.0297451i
\(525\) 0 0
\(526\) −1.57178 9.92380i −0.0685327 0.432698i
\(527\) 0.199816 1.26159i 0.00870411 0.0549556i
\(528\) 0 0
\(529\) −6.01119 + 18.5005i −0.261356 + 0.804371i
\(530\) 41.0226 + 41.0226i 1.78191 + 1.78191i
\(531\) 0 0
\(532\) −0.194637 −0.00843860
\(533\) 9.55023 2.06971i 0.413667 0.0896491i
\(534\) 0 0
\(535\) 15.1829 + 20.8974i 0.656413 + 0.903474i
\(536\) −10.9220 10.9220i −0.471757 0.471757i
\(537\) 0 0
\(538\) 22.3853 + 7.27343i 0.965100 + 0.313580i
\(539\) −0.476798 + 3.01039i −0.0205372 + 0.129667i
\(540\) 0 0
\(541\) −28.9790 + 9.41585i −1.24590 + 0.404819i −0.856451 0.516228i \(-0.827336\pi\)
−0.389453 + 0.921046i \(0.627336\pi\)
\(542\) 27.2790i 1.17173i
\(543\) 0 0
\(544\) 2.36608 4.64368i 0.101445 0.199096i
\(545\) −5.68900 + 2.89869i −0.243690 + 0.124166i
\(546\) 0 0
\(547\) −22.9755 + 22.9755i −0.982360 + 0.982360i −0.999847 0.0174867i \(-0.994434\pi\)
0.0174867 + 0.999847i \(0.494434\pi\)
\(548\) −7.95254 15.6077i −0.339716 0.666729i
\(549\) 0 0
\(550\) −2.47809 1.26265i −0.105666 0.0538395i
\(551\) 0.862832 0.626884i 0.0367579 0.0267062i
\(552\) 0 0
\(553\) −10.9162 + 15.0249i −0.464205 + 0.638923i
\(554\) 19.3427 26.6230i 0.821793 1.13110i
\(555\) 0 0
\(556\) 4.81727 3.49995i 0.204298 0.148431i
\(557\) 22.1309 + 11.2762i 0.937716 + 0.477790i 0.854910 0.518776i \(-0.173612\pi\)
0.0828053 + 0.996566i \(0.473612\pi\)
\(558\) 0 0
\(559\) 7.32972 + 14.3854i 0.310014 + 0.608437i
\(560\) 15.4393 15.4393i 0.652429 0.652429i
\(561\) 0 0
\(562\) 2.21634 1.12928i 0.0934907 0.0476359i
\(563\) −11.3113 + 22.1997i −0.476716 + 0.935608i 0.519964 + 0.854188i \(0.325945\pi\)
−0.996680 + 0.0814196i \(0.974055\pi\)
\(564\) 0 0
\(565\) 20.8013i 0.875118i
\(566\) −15.3634 + 4.99188i −0.645773 + 0.209824i
\(567\) 0 0
\(568\) −1.22112 + 7.70983i −0.0512370 + 0.323497i
\(569\) 13.3652 + 4.34260i 0.560297 + 0.182051i 0.575455 0.817834i \(-0.304825\pi\)
−0.0151580 + 0.999885i \(0.504825\pi\)
\(570\) 0 0
\(571\) −21.7176 21.7176i −0.908854 0.908854i 0.0873260 0.996180i \(-0.472168\pi\)
−0.996180 + 0.0873260i \(0.972168\pi\)
\(572\) 0.583505 + 0.803126i 0.0243976 + 0.0335804i
\(573\) 0 0
\(574\) −7.13667 + 16.2024i −0.297879 + 0.676274i
\(575\) −4.40974 −0.183899
\(576\) 0 0
\(577\) 0.105596 + 0.105596i 0.00439603 + 0.00439603i 0.709301 0.704905i \(-0.249011\pi\)
−0.704905 + 0.709301i \(0.749011\pi\)
\(578\) 8.41266 25.8915i 0.349921 1.07694i
\(579\) 0 0
\(580\) 3.30105 20.8420i 0.137069 0.865418i
\(581\) 1.63776 + 10.3404i 0.0679456 + 0.428992i
\(582\) 0 0
\(583\) 8.65505i 0.358456i
\(584\) 6.85637 + 21.1017i 0.283719 + 0.873196i
\(585\) 0 0
\(586\) −1.65714 + 0.844356i −0.0684559 + 0.0348800i
\(587\) −15.8079 2.50372i −0.652460 0.103339i −0.178575 0.983926i \(-0.557149\pi\)
−0.473885 + 0.880587i \(0.657149\pi\)
\(588\) 0 0
\(589\) −0.0704625 0.138290i −0.00290335 0.00569815i
\(590\) 30.7363 + 22.3313i 1.26540 + 0.919363i
\(591\) 0 0
\(592\) −24.4457 + 17.7609i −1.00471 + 0.729967i
\(593\) −1.94396 + 0.307893i −0.0798289 + 0.0126436i −0.196221 0.980560i \(-0.562867\pi\)
0.116392 + 0.993203i \(0.462867\pi\)
\(594\) 0 0
\(595\) −2.71756 + 3.74039i −0.111409 + 0.153341i
\(596\) 11.9871 1.89857i 0.491010 0.0777683i
\(597\) 0 0
\(598\) 4.39039 + 2.23702i 0.179537 + 0.0914785i
\(599\) −15.0623 10.9434i −0.615429 0.447136i 0.235893 0.971779i \(-0.424199\pi\)
−0.851322 + 0.524644i \(0.824199\pi\)
\(600\) 0 0
\(601\) 7.07160 7.07160i 0.288456 0.288456i −0.548013 0.836470i \(-0.684616\pi\)
0.836470 + 0.548013i \(0.184616\pi\)
\(602\) −28.8911 4.57590i −1.17751 0.186500i
\(603\) 0 0
\(604\) 0.595015 1.16778i 0.0242108 0.0475164i
\(605\) 8.80801 + 27.1083i 0.358096 + 1.10211i
\(606\) 0 0
\(607\) 36.0725 11.7207i 1.46414 0.475727i 0.534806 0.844975i \(-0.320385\pi\)
0.929331 + 0.369248i \(0.120385\pi\)
\(608\) −0.0990668 0.625483i −0.00401769 0.0253667i
\(609\) 0 0
\(610\) −11.6315 3.77931i −0.470946 0.153020i
\(611\) −2.99000 + 9.20226i −0.120962 + 0.372284i
\(612\) 0 0
\(613\) −15.8786 21.8550i −0.641331 0.882717i 0.357354 0.933969i \(-0.383679\pi\)
−0.998686 + 0.0512520i \(0.983679\pi\)
\(614\) 50.8222 2.05102
\(615\) 0 0
\(616\) 2.03337 0.0819269
\(617\) 5.89230 + 8.11005i 0.237215 + 0.326498i 0.910983 0.412445i \(-0.135325\pi\)
−0.673768 + 0.738943i \(0.735325\pi\)
\(618\) 0 0
\(619\) 10.2987 31.6960i 0.413938 1.27397i −0.499259 0.866453i \(-0.666394\pi\)
0.913197 0.407518i \(-0.133606\pi\)
\(620\) −2.92058 0.948953i −0.117293 0.0381109i
\(621\) 0 0
\(622\) 4.62518 + 29.2022i 0.185453 + 1.17090i
\(623\) −4.42370 + 1.43735i −0.177232 + 0.0575861i
\(624\) 0 0
\(625\) −9.64900 29.6966i −0.385960 1.18786i
\(626\) 1.26262 2.47803i 0.0504643 0.0990418i
\(627\) 0 0
\(628\) −16.2821 2.57883i −0.649727 0.102907i
\(629\) 4.52426 4.52426i 0.180394 0.180394i
\(630\) 0 0
\(631\) 8.52090 + 6.19080i 0.339212 + 0.246452i 0.744329 0.667813i \(-0.232769\pi\)
−0.405117 + 0.914265i \(0.632769\pi\)
\(632\) −18.6650 9.51032i −0.742456 0.378300i
\(633\) 0 0
\(634\) 27.5867 4.36931i 1.09561 0.173527i
\(635\) −9.92500 + 13.6606i −0.393862 + 0.542104i
\(636\) 0 0
\(637\) −6.62999 + 1.05009i −0.262690 + 0.0416060i
\(638\) 7.97313 5.79282i 0.315659 0.229340i
\(639\) 0 0
\(640\) 27.4121 + 19.9160i 1.08356 + 0.787250i
\(641\) 2.10778 + 4.13674i 0.0832521 + 0.163391i 0.928879 0.370382i \(-0.120773\pi\)
−0.845627 + 0.533774i \(0.820773\pi\)
\(642\) 0 0
\(643\) −29.6739 4.69989i −1.17023 0.185346i −0.459083 0.888393i \(-0.651822\pi\)
−0.711143 + 0.703048i \(0.751822\pi\)
\(644\) −2.54090 + 1.29465i −0.100125 + 0.0510164i
\(645\) 0 0
\(646\) 0.0720440 + 0.221729i 0.00283453 + 0.00872379i
\(647\) 16.4853i 0.648104i 0.946039 + 0.324052i \(0.105045\pi\)
−0.946039 + 0.324052i \(0.894955\pi\)
\(648\) 0 0
\(649\) 0.886663 + 5.59817i 0.0348046 + 0.219747i
\(650\) 0.958206 6.04988i 0.0375839 0.237296i
\(651\) 0 0
\(652\) −5.10782 + 15.7202i −0.200038 + 0.615652i
\(653\) −23.6145 23.6145i −0.924105 0.924105i 0.0732110 0.997316i \(-0.476675\pi\)
−0.997316 + 0.0732110i \(0.976675\pi\)
\(654\) 0 0
\(655\) −1.96530 −0.0767905
\(656\) −30.9342 8.15703i −1.20778 0.318478i
\(657\) 0 0
\(658\) −10.3041 14.1824i −0.401696 0.552887i
\(659\) 3.37421 + 3.37421i 0.131441 + 0.131441i 0.769766 0.638326i \(-0.220373\pi\)
−0.638326 + 0.769766i \(0.720373\pi\)
\(660\) 0 0
\(661\) 12.2982 + 3.99593i 0.478345 + 0.155424i 0.538258 0.842780i \(-0.319082\pi\)
−0.0599133 + 0.998204i \(0.519082\pi\)
\(662\) 6.79942 42.9298i 0.264267 1.66852i
\(663\) 0 0
\(664\) −11.2310 + 3.64917i −0.435847 + 0.141615i
\(665\) 0.561789i 0.0217853i
\(666\) 0 0
\(667\) 7.09406 13.9229i 0.274683 0.539096i
\(668\) −2.32193 + 1.18308i −0.0898383 + 0.0457749i
\(669\) 0 0
\(670\) 27.8843 27.8843i 1.07727 1.07727i
\(671\) −0.828340 1.62571i −0.0319777 0.0627598i
\(672\) 0 0
\(673\) 5.66568 + 2.88681i 0.218396 + 0.111278i 0.559766 0.828651i \(-0.310891\pi\)
−0.341370 + 0.939929i \(0.610891\pi\)
\(674\) −36.3963 + 26.4435i −1.40193 + 1.01856i
\(675\) 0 0
\(676\) 5.88791 8.10402i 0.226458 0.311693i
\(677\) 20.5198 28.2431i 0.788642 1.08547i −0.205634 0.978629i \(-0.565926\pi\)
0.994276 0.106843i \(-0.0340743\pi\)
\(678\) 0 0
\(679\) 1.57761 1.14620i 0.0605430 0.0439871i
\(680\) −4.64660 2.36756i −0.178189 0.0907918i
\(681\) 0 0
\(682\) −0.651119 1.27789i −0.0249326 0.0489331i
\(683\) −17.6969 + 17.6969i −0.677154 + 0.677154i −0.959355 0.282201i \(-0.908935\pi\)
0.282201 + 0.959355i \(0.408935\pi\)
\(684\) 0 0
\(685\) −45.0492 + 22.9537i −1.72124 + 0.877017i
\(686\) 14.3082 28.0815i 0.546291 1.07216i
\(687\) 0 0
\(688\) 52.8562i 2.01512i
\(689\) −18.1287 + 5.89037i −0.690649 + 0.224405i
\(690\) 0 0
\(691\) 4.16500 26.2968i 0.158444 1.00038i −0.772446 0.635080i \(-0.780967\pi\)
0.930891 0.365298i \(-0.119033\pi\)
\(692\) −10.4541 3.39675i −0.397406 0.129125i
\(693\) 0 0
\(694\) 20.2037 + 20.2037i 0.766923 + 0.766923i
\(695\) −10.1020 13.9043i −0.383192 0.527419i
\(696\) 0 0
\(697\) 6.73977 + 0.681281i 0.255287 + 0.0258053i
\(698\) 14.8295 0.561306
\(699\) 0 0
\(700\) 2.50666 + 2.50666i 0.0947427 + 0.0947427i
\(701\) −6.42667 + 19.7793i −0.242732 + 0.747052i 0.753269 + 0.657712i \(0.228476\pi\)
−0.996001 + 0.0893399i \(0.971524\pi\)
\(702\) 0 0
\(703\) 0.121621 0.767886i 0.00458703 0.0289614i
\(704\) 0.167746 + 1.05911i 0.00632218 + 0.0399167i
\(705\) 0 0
\(706\) 23.6446i 0.889874i
\(707\) −2.64248 8.13272i −0.0993807 0.305862i
\(708\) 0 0
\(709\) 7.83436 3.99181i 0.294226 0.149915i −0.300647 0.953736i \(-0.597203\pi\)
0.594872 + 0.803820i \(0.297203\pi\)
\(710\) −19.6836 3.11758i −0.738712 0.117001i
\(711\) 0 0
\(712\) −2.38188 4.67471i −0.0892649 0.175192i
\(713\) −1.83971 1.33662i −0.0688975 0.0500570i
\(714\) 0 0
\(715\) 2.31809 1.68419i 0.0866918 0.0629852i
\(716\) 3.94384 0.624643i 0.147388 0.0233440i
\(717\) 0 0
\(718\) −18.2531 + 25.1233i −0.681201 + 0.937593i
\(719\) −12.8945 + 2.04229i −0.480885 + 0.0761647i −0.392171 0.919892i \(-0.628276\pi\)
−0.0887143 + 0.996057i \(0.528276\pi\)
\(720\) 0 0
\(721\) −19.9422 10.1611i −0.742688 0.378418i
\(722\) −26.3277 19.1282i −0.979816 0.711878i
\(723\) 0 0
\(724\) −3.07742 + 3.07742i −0.114371 + 0.114371i
\(725\) −19.1855 3.03868i −0.712530 0.112854i
\(726\) 0 0
\(727\) −12.5723 + 24.6746i −0.466282 + 0.915131i 0.531402 + 0.847120i \(0.321665\pi\)
−0.997685 + 0.0680111i \(0.978335\pi\)
\(728\) 1.38385 + 4.25906i 0.0512890 + 0.157851i
\(729\) 0 0
\(730\) −53.8738 + 17.5047i −1.99396 + 0.647877i
\(731\) 1.75084 + 11.0543i 0.0647570 + 0.408860i
\(732\) 0 0
\(733\) −23.2536 7.55554i −0.858890 0.279070i −0.153725 0.988114i \(-0.549127\pi\)
−0.705165 + 0.709043i \(0.749127\pi\)
\(734\) −12.2331 + 37.6495i −0.451531 + 1.38967i
\(735\) 0 0
\(736\) −5.45374 7.50643i −0.201027 0.276690i
\(737\) 5.88311 0.216707
\(738\) 0 0
\(739\) −35.1342 −1.29243 −0.646215 0.763155i \(-0.723649\pi\)
−0.646215 + 0.763155i \(0.723649\pi\)
\(740\) −9.04162 12.4447i −0.332377 0.457477i
\(741\) 0 0
\(742\) 10.6720 32.8450i 0.391782 1.20578i
\(743\) −5.44093 1.76787i −0.199608 0.0648567i 0.207507 0.978234i \(-0.433465\pi\)
−0.407115 + 0.913377i \(0.633465\pi\)
\(744\) 0 0
\(745\) −5.47991 34.5988i −0.200768 1.26760i
\(746\) 23.0537 7.49061i 0.844057 0.274251i
\(747\) 0 0
\(748\) 0.212657 + 0.654492i 0.00777552 + 0.0239306i
\(749\) 6.98083 13.7007i 0.255074 0.500611i
\(750\) 0 0
\(751\) −11.5290 1.82601i −0.420699 0.0666322i −0.0575040 0.998345i \(-0.518314\pi\)
−0.363195 + 0.931713i \(0.618314\pi\)
\(752\) 22.3990 22.3990i 0.816807 0.816807i
\(753\) 0 0
\(754\) 17.5598 + 12.7579i 0.639490 + 0.464617i
\(755\) −3.37062 1.71741i −0.122669 0.0625031i
\(756\) 0 0
\(757\) 37.9100 6.00436i 1.37786 0.218232i 0.576836 0.816860i \(-0.304287\pi\)
0.801027 + 0.598628i \(0.204287\pi\)
\(758\) 37.4581 51.5566i 1.36054 1.87262i
\(759\) 0 0
\(760\) −0.625876 + 0.0991290i −0.0227029 + 0.00359579i
\(761\) −39.0623 + 28.3804i −1.41601 + 1.02879i −0.423591 + 0.905854i \(0.639231\pi\)
−0.992415 + 0.122935i \(0.960769\pi\)
\(762\) 0 0
\(763\) 3.07495 + 2.23408i 0.111321 + 0.0808792i
\(764\) −9.53299 18.7095i −0.344891 0.676887i
\(765\) 0 0
\(766\) 11.7197 + 1.85622i 0.423451 + 0.0670680i
\(767\) −11.1224 + 5.66713i −0.401606 + 0.204628i
\(768\) 0 0
\(769\) 1.21277 + 3.73252i 0.0437336 + 0.134598i 0.970539 0.240943i \(-0.0774568\pi\)
−0.926806 + 0.375541i \(0.877457\pi\)
\(770\) 5.19130i 0.187082i
\(771\) 0 0
\(772\) 2.14018 + 13.5126i 0.0770269 + 0.486329i
\(773\) 5.21943 32.9542i 0.187730 1.18528i −0.696265 0.717784i \(-0.745156\pi\)
0.883995 0.467496i \(-0.154844\pi\)
\(774\) 0 0
\(775\) −0.873528 + 2.68844i −0.0313781 + 0.0965717i
\(776\) 1.55532 + 1.55532i 0.0558329 + 0.0558329i
\(777\) 0 0
\(778\) −4.05808 −0.145489
\(779\) 0.711206 0.414396i 0.0254816 0.0148473i
\(780\) 0 0
\(781\) −1.74757 2.40533i −0.0625330 0.0860693i
\(782\) 2.41535 + 2.41535i 0.0863727 + 0.0863727i
\(783\) 0 0
\(784\) 20.9004 + 6.79095i 0.746443 + 0.242534i
\(785\) −7.44338 + 46.9957i −0.265666 + 1.67735i
\(786\) 0 0
\(787\) −10.7260 + 3.48510i −0.382342 + 0.124230i −0.493881 0.869530i \(-0.664422\pi\)
0.111539 + 0.993760i \(0.464422\pi\)
\(788\) 0.873536i 0.0311184i
\(789\) 0 0
\(790\) 24.2803 47.6528i 0.863855 1.69541i
\(791\) 11.0331 5.62164i 0.392291 0.199882i
\(792\) 0 0
\(793\) 2.84143 2.84143i 0.100902 0.100902i
\(794\) 12.5692 + 24.6684i 0.446063 + 0.875447i
\(795\) 0 0
\(796\) 0.344807 + 0.175688i 0.0122214 + 0.00622710i
\(797\) −23.1041 + 16.7861i −0.818391 + 0.594596i −0.916251 0.400604i \(-0.868800\pi\)
0.0978602 + 0.995200i \(0.468800\pi\)
\(798\) 0 0
\(799\) −3.94257 + 5.42648i −0.139478 + 0.191975i
\(800\) −6.77951 + 9.33119i −0.239692 + 0.329907i
\(801\) 0 0
\(802\) −6.61875 + 4.80880i −0.233716 + 0.169805i
\(803\) −7.52981 3.83663i −0.265721 0.135392i
\(804\) 0 0
\(805\) 3.73680 + 7.33389i 0.131705 + 0.258486i
\(806\) 2.23352 2.23352i 0.0786723 0.0786723i
\(807\) 0 0
\(808\) 8.59419 4.37896i 0.302343 0.154051i
\(809\) −4.83865 + 9.49639i −0.170118 + 0.333875i −0.960287 0.279013i \(-0.909993\pi\)
0.790169 + 0.612889i \(0.209993\pi\)
\(810\) 0 0
\(811\) 33.8780i 1.18962i 0.803867 + 0.594809i \(0.202772\pi\)
−0.803867 + 0.594809i \(0.797228\pi\)
\(812\) −11.9468 + 3.88175i −0.419250 + 0.136223i
\(813\) 0 0
\(814\) 1.12386 7.09577i 0.0393912 0.248706i
\(815\) 45.3739 + 14.7429i 1.58938 + 0.516421i
\(816\) 0 0
\(817\) 0.961639 + 0.961639i 0.0336435 + 0.0336435i
\(818\) −9.64629 13.2770i −0.337275 0.464219i
\(819\) 0 0
\(820\) 4.15254 15.7478i 0.145013 0.549938i
\(821\) −50.1853 −1.75148 −0.875739 0.482785i \(-0.839625\pi\)
−0.875739 + 0.482785i \(0.839625\pi\)
\(822\) 0 0
\(823\) −31.8583 31.8583i −1.11051 1.11051i −0.993081 0.117431i \(-0.962534\pi\)
−0.117431 0.993081i \(-0.537466\pi\)
\(824\) 7.80136 24.0101i 0.271773 0.836432i
\(825\) 0 0
\(826\) 3.53796 22.3378i 0.123101 0.777231i
\(827\) 0.559901 + 3.53508i 0.0194697 + 0.122927i 0.995509 0.0946679i \(-0.0301789\pi\)
−0.976039 + 0.217595i \(0.930179\pi\)
\(828\) 0 0
\(829\) 18.5904i 0.645672i 0.946455 + 0.322836i \(0.104636\pi\)
−0.946455 + 0.322836i \(0.895364\pi\)
\(830\) −9.31652 28.6733i −0.323381 0.995265i
\(831\) 0 0
\(832\) −2.10423 + 1.07216i −0.0729509 + 0.0371703i
\(833\) −4.59605 0.727944i −0.159244 0.0252217i
\(834\) 0 0
\(835\) 3.41478 + 6.70188i 0.118173 + 0.231928i
\(836\) 0.0676503 + 0.0491508i 0.00233973 + 0.00169992i
\(837\) 0 0
\(838\) 11.1816 8.12394i 0.386263 0.280637i
\(839\) 35.8357 5.67582i 1.23719 0.195951i 0.496640 0.867957i \(-0.334567\pi\)
0.740546 + 0.672006i \(0.234567\pi\)
\(840\) 0 0
\(841\) 23.4124 32.2244i 0.807324 1.11119i
\(842\) −29.8975 + 4.73529i −1.03033 + 0.163189i
\(843\) 0 0
\(844\) −18.7551 9.55622i −0.645578 0.328939i
\(845\) −23.3909 16.9945i −0.804673 0.584629i
\(846\) 0 0
\(847\) 11.9979 11.9979i 0.412253 0.412253i
\(848\) 61.6362 + 9.76221i 2.11659 + 0.335236i
\(849\) 0 0
\(850\) 1.92773 3.78338i 0.0661205 0.129769i
\(851\) −3.51997 10.8333i −0.120663 0.371362i
\(852\) 0 0
\(853\) −15.2753 + 4.96325i −0.523017 + 0.169939i −0.558614 0.829428i \(-0.688667\pi\)
0.0355971 + 0.999366i \(0.488667\pi\)
\(854\) 1.13891 + 7.19077i 0.0389726 + 0.246063i
\(855\) 0 0
\(856\) 16.4953 + 5.35966i 0.563799 + 0.183190i
\(857\) 4.88329 15.0292i 0.166810 0.513389i −0.832355 0.554243i \(-0.813008\pi\)
0.999165 + 0.0408542i \(0.0130079\pi\)
\(858\) 0 0
\(859\) −11.8857 16.3593i −0.405535 0.558171i 0.556587 0.830789i \(-0.312110\pi\)
−0.962122 + 0.272618i \(0.912110\pi\)
\(860\) 26.9078 0.917548
\(861\) 0 0
\(862\) 17.4058 0.592843
\(863\) 6.30383 + 8.67648i 0.214585 + 0.295351i 0.902717 0.430234i \(-0.141569\pi\)
−0.688132 + 0.725585i \(0.741569\pi\)
\(864\) 0 0
\(865\) −9.80418 + 30.1742i −0.333352 + 1.02595i
\(866\) 54.1629 + 17.5986i 1.84053 + 0.598025i
\(867\) 0 0
\(868\) 0.285970 + 1.80554i 0.00970644 + 0.0612841i
\(869\) 7.58832 2.46560i 0.257416 0.0836396i
\(870\) 0 0
\(871\) 4.00387 + 12.3226i 0.135666 + 0.417537i
\(872\) −1.94635 + 3.81993i −0.0659118 + 0.129359i
\(873\) 0 0
\(874\) 0.409948 + 0.0649294i 0.0138667 + 0.00219627i
\(875\) −8.21584 + 8.21584i −0.277746 + 0.277746i
\(876\) 0 0
\(877\) 9.77788 + 7.10405i 0.330176 + 0.239887i 0.740505 0.672051i \(-0.234586\pi\)
−0.410330 + 0.911937i \(0.634586\pi\)
\(878\) −56.2880 28.6802i −1.89963 0.967908i
\(879\) 0 0
\(880\) −9.26506 + 1.46744i −0.312325 + 0.0494674i
\(881\) −5.54253 + 7.62863i −0.186732 + 0.257015i −0.892112 0.451815i \(-0.850777\pi\)
0.705379 + 0.708830i \(0.250777\pi\)
\(882\) 0 0
\(883\) −23.2136 + 3.67668i −0.781200 + 0.123730i −0.534282 0.845306i \(-0.679418\pi\)
−0.246918 + 0.969036i \(0.579418\pi\)
\(884\) −1.22616 + 0.890856i −0.0412402 + 0.0299627i
\(885\) 0 0
\(886\) −42.7752 31.0780i −1.43706 1.04409i
\(887\) 22.0210 + 43.2187i 0.739394 + 1.45114i 0.886842 + 0.462073i \(0.152894\pi\)
−0.147448 + 0.989070i \(0.547106\pi\)
\(888\) 0 0
\(889\) 9.92789 + 1.57242i 0.332971 + 0.0527374i
\(890\) 11.9348 6.08107i 0.400055 0.203838i
\(891\) 0 0
\(892\) 1.18242 + 3.63912i 0.0395904 + 0.121847i
\(893\) 0.815032i 0.0272740i
\(894\) 0 0
\(895\) −1.80293 11.3833i −0.0602654 0.380500i
\(896\) 3.15531 19.9218i 0.105411 0.665542i
\(897\) 0 0
\(898\) 15.6988 48.3161i 0.523877 1.61233i
\(899\) −7.08296 7.08296i −0.236230 0.236230i
\(900\) 0 0
\(901\) −13.2140 −0.440221
\(902\) 6.57201 3.82929i 0.218824 0.127501i
\(903\) 0 0
\(904\) 8.20974 + 11.2997i 0.273052 + 0.375824i
\(905\) 8.88248 + 8.88248i 0.295264 + 0.295264i
\(906\) 0 0
\(907\) −8.16520 2.65304i −0.271121 0.0880926i 0.170301 0.985392i \(-0.445526\pi\)
−0.441422 + 0.897299i \(0.645526\pi\)
\(908\) −3.17090 + 20.0202i −0.105230 + 0.664395i
\(909\) 0 0
\(910\) −10.8736 + 3.53305i −0.360456 + 0.117119i
\(911\) 21.0427i 0.697176i 0.937276 + 0.348588i \(0.113339\pi\)
−0.937276 + 0.348588i \(0.886661\pi\)
\(912\) 0 0
\(913\) 2.04197 4.00760i 0.0675794 0.132632i
\(914\) −11.5989 + 5.90994i −0.383658 + 0.195483i
\(915\) 0 0
\(916\) −6.57638 + 6.57638i −0.217290 + 0.217290i
\(917\) 0.531129 + 1.04240i 0.0175394 + 0.0344231i
\(918\) 0 0
\(919\) 42.6461 + 21.7293i 1.40676 + 0.716782i 0.982063 0.188552i \(-0.0603794\pi\)
0.424700 + 0.905334i \(0.360379\pi\)
\(920\) −7.51114 + 5.45716i −0.247635 + 0.179917i
\(921\) 0 0
\(922\) −25.4769 + 35.0659i −0.839037 + 1.15484i
\(923\) 3.84880 5.29742i 0.126685 0.174367i
\(924\) 0 0
\(925\) −11.4556 + 8.32298i −0.376658 + 0.273658i
\(926\) 22.5215 + 11.4753i 0.740103 + 0.377101i
\(927\) 0 0
\(928\) −18.5550 36.4163i −0.609099 1.19542i
\(929\) 36.8866 36.8866i 1.21021 1.21021i 0.239254 0.970957i \(-0.423097\pi\)
0.970957 0.239254i \(-0.0769028\pi\)
\(930\) 0 0
\(931\) −0.503802 + 0.256700i −0.0165115 + 0.00841300i
\(932\) −0.548327 + 1.07615i −0.0179610 + 0.0352505i
\(933\) 0 0
\(934\) 37.9253i 1.24096i
\(935\) 1.88909 0.613801i 0.0617797 0.0200735i
\(936\) 0 0
\(937\) 2.38729 15.0727i 0.0779893 0.492405i −0.917516 0.397699i \(-0.869809\pi\)
0.995505 0.0947061i \(-0.0301911\pi\)
\(938\) −22.3258 7.25409i −0.728963 0.236855i
\(939\) 0 0
\(940\) 11.4028 + 11.4028i 0.371918 + 0.371918i
\(941\) −32.5243 44.7658i −1.06026 1.45932i −0.879561 0.475787i \(-0.842163\pi\)
−0.180701 0.983538i \(-0.557837\pi\)
\(942\) 0 0
\(943\) 6.52804 10.1404i 0.212582 0.330217i
\(944\) 40.8669 1.33011
\(945\) 0 0
\(946\) 8.88617 + 8.88617i 0.288914 + 0.288914i
\(947\) 0.485672 1.49474i 0.0157822 0.0485727i −0.942855 0.333203i \(-0.891871\pi\)
0.958637 + 0.284630i \(0.0918707\pi\)
\(948\) 0 0
\(949\) 2.91156 18.3829i 0.0945133 0.596734i
\(950\) −0.0807133 0.509604i −0.00261869 0.0165337i
\(951\) 0 0
\(952\) 3.10441i 0.100615i
\(953\) −13.1845 40.5778i −0.427089 1.31444i −0.900980 0.433861i \(-0.857151\pi\)
0.473891 0.880584i \(-0.342849\pi\)
\(954\) 0 0
\(955\) −54.0021 + 27.5154i −1.74747 + 0.890379i
\(956\) −6.57981 1.04214i −0.212806 0.0337052i
\(957\) 0 0
\(958\) 12.3626 + 24.2629i 0.399416 + 0.783898i
\(959\) 24.3495 + 17.6909i 0.786285 + 0.571270i
\(960\) 0 0
\(961\) 23.9002 17.3645i 0.770975 0.560146i
\(962\) 15.6275 2.47515i 0.503851 0.0798022i
\(963\) 0 0
\(964\) −5.95234 + 8.19270i −0.191712 + 0.263869i
\(965\) 39.0019 6.17730i 1.25552 0.198854i
\(966\) 0 0
\(967\) 3.68798 + 1.87912i 0.118597 + 0.0604284i 0.512283 0.858817i \(-0.328800\pi\)
−0.393685 + 0.919245i \(0.628800\pi\)
\(968\) 15.4836 + 11.2495i 0.497663 + 0.361573i
\(969\) 0 0
\(970\) −3.97082 + 3.97082i −0.127495 + 0.127495i
\(971\) −15.8383 2.50854i −0.508276 0.0805030i −0.102971 0.994684i \(-0.532835\pi\)
−0.405305 + 0.914181i \(0.632835\pi\)
\(972\) 0 0
\(973\) −4.64475 + 9.11584i −0.148904 + 0.292240i
\(974\) 11.1447 + 34.2997i 0.357098 + 1.09903i
\(975\) 0 0
\(976\) −12.5116 + 4.06528i −0.400488 + 0.130126i
\(977\) −6.69308 42.2584i −0.214131 1.35197i −0.827187 0.561927i \(-0.810060\pi\)
0.613056 0.790039i \(-0.289940\pi\)
\(978\) 0 0
\(979\) 1.90052 + 0.617515i 0.0607408 + 0.0197359i
\(980\) −3.45711 + 10.6399i −0.110433 + 0.339878i
\(981\) 0 0
\(982\) 0.0545251 + 0.0750473i 0.00173997 + 0.00239486i
\(983\) 31.6046 1.00803 0.504015 0.863695i \(-0.331856\pi\)
0.504015 + 0.863695i \(0.331856\pi\)
\(984\) 0 0
\(985\) −2.52132 −0.0803360
\(986\) 8.84409 + 12.1728i 0.281653 + 0.387662i
\(987\) 0 0
\(988\) −0.0569095 + 0.175150i −0.00181053 + 0.00557225i
\(989\) 18.9502 + 6.15728i 0.602580 + 0.195790i
\(990\) 0 0
\(991\) 4.28861 + 27.0772i 0.136232 + 0.860137i 0.957256 + 0.289242i \(0.0934034\pi\)
−0.821024 + 0.570894i \(0.806597\pi\)
\(992\) −5.65670 + 1.83797i −0.179601 + 0.0583558i
\(993\) 0 0
\(994\) 3.66600 + 11.2828i 0.116278 + 0.357868i
\(995\) 0.507096 0.995231i 0.0160760 0.0315510i
\(996\) 0 0
\(997\) 24.5211 + 3.88375i 0.776590 + 0.123000i 0.532133 0.846661i \(-0.321391\pi\)
0.244456 + 0.969660i \(0.421391\pi\)
\(998\) −39.4001 + 39.4001i −1.24719 + 1.24719i
\(999\) 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 369.2.u.a.46.3 24
3.2 odd 2 41.2.g.a.5.1 24
12.11 even 2 656.2.bs.d.497.1 24
41.33 even 20 inner 369.2.u.a.361.3 24
123.74 odd 20 41.2.g.a.33.1 yes 24
123.101 even 40 1681.2.a.m.1.3 24
123.104 even 40 1681.2.a.m.1.4 24
492.443 even 20 656.2.bs.d.33.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
41.2.g.a.5.1 24 3.2 odd 2
41.2.g.a.33.1 yes 24 123.74 odd 20
369.2.u.a.46.3 24 1.1 even 1 trivial
369.2.u.a.361.3 24 41.33 even 20 inner
656.2.bs.d.33.1 24 492.443 even 20
656.2.bs.d.497.1 24 12.11 even 2
1681.2.a.m.1.3 24 123.101 even 40
1681.2.a.m.1.4 24 123.104 even 40