Properties

Label 432.2.l.b.107.13
Level $432$
Weight $2$
Character 432.107
Analytic conductor $3.450$
Analytic rank $0$
Dimension $32$
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] = [432,2,Mod(107,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.13
Character \(\chi\) \(=\) 432.107
Dual form 432.2.l.b.323.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.12975 + 0.850687i) q^{2} +(0.552664 + 1.92212i) q^{4} +(1.26575 - 1.26575i) q^{5} +1.47880 q^{7} +(-1.01076 + 2.64166i) q^{8} +O(q^{10})\) \(q+(1.12975 + 0.850687i) q^{2} +(0.552664 + 1.92212i) q^{4} +(1.26575 - 1.26575i) q^{5} +1.47880 q^{7} +(-1.01076 + 2.64166i) q^{8} +(2.50674 - 0.353222i) q^{10} +(1.16753 + 1.16753i) q^{11} +(-0.842585 + 0.842585i) q^{13} +(1.67068 + 1.25800i) q^{14} +(-3.38913 + 2.12458i) q^{16} -4.56781i q^{17} +(2.78873 + 2.78873i) q^{19} +(3.13246 + 1.73340i) q^{20} +(0.325812 + 2.31221i) q^{22} -5.13786i q^{23} +1.79575i q^{25} +(-1.66869 + 0.235133i) q^{26} +(0.817282 + 2.84245i) q^{28} +(-0.161370 - 0.161370i) q^{29} +9.34223i q^{31} +(-5.63621 - 0.482847i) q^{32} +(3.88578 - 5.16048i) q^{34} +(1.87180 - 1.87180i) q^{35} +(-6.53108 - 6.53108i) q^{37} +(0.778227 + 5.52290i) q^{38} +(2.06432 + 4.62305i) q^{40} -9.35455 q^{41} +(3.98100 - 3.98100i) q^{43} +(-1.59888 + 2.88939i) q^{44} +(4.37071 - 5.80449i) q^{46} -5.75824 q^{47} -4.81314 q^{49} +(-1.52762 + 2.02875i) q^{50} +(-2.08522 - 1.15389i) q^{52} +(7.87488 - 7.87488i) q^{53} +2.95560 q^{55} +(-1.49471 + 3.90650i) q^{56} +(-0.0450322 - 0.319583i) q^{58} +(-1.12227 - 1.12227i) q^{59} +(0.396250 - 0.396250i) q^{61} +(-7.94732 + 10.5544i) q^{62} +(-5.95675 - 5.34015i) q^{64} +2.13300i q^{65} +(6.11749 + 6.11749i) q^{67} +(8.77991 - 2.52446i) q^{68} +(3.70697 - 0.522347i) q^{70} -15.9291i q^{71} -12.6493i q^{73} +(-1.82257 - 12.9344i) q^{74} +(-3.81905 + 6.90151i) q^{76} +(1.72655 + 1.72655i) q^{77} -4.38560i q^{79} +(-1.60060 + 6.97897i) q^{80} +(-10.5683 - 7.95779i) q^{82} +(-4.10414 + 4.10414i) q^{83} +(-5.78171 - 5.78171i) q^{85} +(7.88412 - 1.11095i) q^{86} +(-4.26430 + 1.90413i) q^{88} +0.815713 q^{89} +(-1.24602 + 1.24602i) q^{91} +(9.87561 - 2.83951i) q^{92} +(-6.50536 - 4.89846i) q^{94} +7.05966 q^{95} -12.3377 q^{97} +(-5.43763 - 4.09447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.12975 + 0.850687i 0.798853 + 0.601526i
\(3\) 0 0
\(4\) 0.552664 + 1.92212i 0.276332 + 0.961062i
\(5\) 1.26575 1.26575i 0.566061 0.566061i −0.364962 0.931022i \(-0.618918\pi\)
0.931022 + 0.364962i \(0.118918\pi\)
\(6\) 0 0
\(7\) 1.47880 0.558936 0.279468 0.960155i \(-0.409842\pi\)
0.279468 + 0.960155i \(0.409842\pi\)
\(8\) −1.01076 + 2.64166i −0.357356 + 0.933968i
\(9\) 0 0
\(10\) 2.50674 0.353222i 0.792700 0.111699i
\(11\) 1.16753 + 1.16753i 0.352023 + 0.352023i 0.860862 0.508839i \(-0.169925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(12\) 0 0
\(13\) −0.842585 + 0.842585i −0.233691 + 0.233691i −0.814231 0.580540i \(-0.802841\pi\)
0.580540 + 0.814231i \(0.302841\pi\)
\(14\) 1.67068 + 1.25800i 0.446507 + 0.336215i
\(15\) 0 0
\(16\) −3.38913 + 2.12458i −0.847281 + 0.531144i
\(17\) 4.56781i 1.10786i −0.832564 0.553929i \(-0.813128\pi\)
0.832564 0.553929i \(-0.186872\pi\)
\(18\) 0 0
\(19\) 2.78873 + 2.78873i 0.639778 + 0.639778i 0.950501 0.310723i \(-0.100571\pi\)
−0.310723 + 0.950501i \(0.600571\pi\)
\(20\) 3.13246 + 1.73340i 0.700440 + 0.387599i
\(21\) 0 0
\(22\) 0.325812 + 2.31221i 0.0694634 + 0.492966i
\(23\) 5.13786i 1.07132i −0.844434 0.535659i \(-0.820063\pi\)
0.844434 0.535659i \(-0.179937\pi\)
\(24\) 0 0
\(25\) 1.79575i 0.359151i
\(26\) −1.66869 + 0.235133i −0.327256 + 0.0461134i
\(27\) 0 0
\(28\) 0.817282 + 2.84245i 0.154452 + 0.537172i
\(29\) −0.161370 0.161370i −0.0299657 0.0299657i 0.691965 0.721931i \(-0.256745\pi\)
−0.721931 + 0.691965i \(0.756745\pi\)
\(30\) 0 0
\(31\) 9.34223i 1.67791i 0.544197 + 0.838957i \(0.316834\pi\)
−0.544197 + 0.838957i \(0.683166\pi\)
\(32\) −5.63621 0.482847i −0.996351 0.0853562i
\(33\) 0 0
\(34\) 3.88578 5.16048i 0.666406 0.885015i
\(35\) 1.87180 1.87180i 0.316391 0.316391i
\(36\) 0 0
\(37\) −6.53108 6.53108i −1.07370 1.07370i −0.997059 0.0766437i \(-0.975580\pi\)
−0.0766437 0.997059i \(-0.524420\pi\)
\(38\) 0.778227 + 5.52290i 0.126245 + 0.895932i
\(39\) 0 0
\(40\) 2.06432 + 4.62305i 0.326398 + 0.730968i
\(41\) −9.35455 −1.46094 −0.730468 0.682947i \(-0.760698\pi\)
−0.730468 + 0.682947i \(0.760698\pi\)
\(42\) 0 0
\(43\) 3.98100 3.98100i 0.607097 0.607097i −0.335089 0.942186i \(-0.608766\pi\)
0.942186 + 0.335089i \(0.108766\pi\)
\(44\) −1.59888 + 2.88939i −0.241041 + 0.435591i
\(45\) 0 0
\(46\) 4.37071 5.80449i 0.644426 0.855826i
\(47\) −5.75824 −0.839925 −0.419963 0.907541i \(-0.637957\pi\)
−0.419963 + 0.907541i \(0.637957\pi\)
\(48\) 0 0
\(49\) −4.81314 −0.687591
\(50\) −1.52762 + 2.02875i −0.216039 + 0.286909i
\(51\) 0 0
\(52\) −2.08522 1.15389i −0.289168 0.160015i
\(53\) 7.87488 7.87488i 1.08170 1.08170i 0.0853469 0.996351i \(-0.472800\pi\)
0.996351 0.0853469i \(-0.0271998\pi\)
\(54\) 0 0
\(55\) 2.95560 0.398533
\(56\) −1.49471 + 3.90650i −0.199739 + 0.522028i
\(57\) 0 0
\(58\) −0.0450322 0.319583i −0.00591302 0.0419633i
\(59\) −1.12227 1.12227i −0.146107 0.146107i 0.630269 0.776377i \(-0.282944\pi\)
−0.776377 + 0.630269i \(0.782944\pi\)
\(60\) 0 0
\(61\) 0.396250 0.396250i 0.0507346 0.0507346i −0.681284 0.732019i \(-0.738578\pi\)
0.732019 + 0.681284i \(0.238578\pi\)
\(62\) −7.94732 + 10.5544i −1.00931 + 1.34041i
\(63\) 0 0
\(64\) −5.95675 5.34015i −0.744593 0.667518i
\(65\) 2.13300i 0.264567i
\(66\) 0 0
\(67\) 6.11749 + 6.11749i 0.747370 + 0.747370i 0.973985 0.226614i \(-0.0727657\pi\)
−0.226614 + 0.973985i \(0.572766\pi\)
\(68\) 8.77991 2.52446i 1.06472 0.306136i
\(69\) 0 0
\(70\) 3.70697 0.522347i 0.443068 0.0624324i
\(71\) 15.9291i 1.89043i −0.326444 0.945216i \(-0.605851\pi\)
0.326444 0.945216i \(-0.394149\pi\)
\(72\) 0 0
\(73\) 12.6493i 1.48048i −0.672340 0.740242i \(-0.734711\pi\)
0.672340 0.740242i \(-0.265289\pi\)
\(74\) −1.82257 12.9344i −0.211870 1.50359i
\(75\) 0 0
\(76\) −3.81905 + 6.90151i −0.438076 + 0.791658i
\(77\) 1.72655 + 1.72655i 0.196758 + 0.196758i
\(78\) 0 0
\(79\) 4.38560i 0.493419i −0.969090 0.246709i \(-0.920651\pi\)
0.969090 0.246709i \(-0.0793493\pi\)
\(80\) −1.60060 + 6.97897i −0.178953 + 0.780272i
\(81\) 0 0
\(82\) −10.5683 7.95779i −1.16707 0.878791i
\(83\) −4.10414 + 4.10414i −0.450488 + 0.450488i −0.895516 0.445029i \(-0.853193\pi\)
0.445029 + 0.895516i \(0.353193\pi\)
\(84\) 0 0
\(85\) −5.78171 5.78171i −0.627114 0.627114i
\(86\) 7.88412 1.11095i 0.850166 0.119796i
\(87\) 0 0
\(88\) −4.26430 + 1.90413i −0.454576 + 0.202981i
\(89\) 0.815713 0.0864654 0.0432327 0.999065i \(-0.486234\pi\)
0.0432327 + 0.999065i \(0.486234\pi\)
\(90\) 0 0
\(91\) −1.24602 + 1.24602i −0.130618 + 0.130618i
\(92\) 9.87561 2.83951i 1.02960 0.296039i
\(93\) 0 0
\(94\) −6.50536 4.89846i −0.670977 0.505237i
\(95\) 7.05966 0.724306
\(96\) 0 0
\(97\) −12.3377 −1.25270 −0.626350 0.779542i \(-0.715452\pi\)
−0.626350 + 0.779542i \(0.715452\pi\)
\(98\) −5.43763 4.09447i −0.549284 0.413604i
\(99\) 0 0
\(100\) −3.45166 + 0.992448i −0.345166 + 0.0992448i
\(101\) −0.195337 + 0.195337i −0.0194367 + 0.0194367i −0.716758 0.697322i \(-0.754375\pi\)
0.697322 + 0.716758i \(0.254375\pi\)
\(102\) 0 0
\(103\) 7.40614 0.729749 0.364874 0.931057i \(-0.381112\pi\)
0.364874 + 0.931057i \(0.381112\pi\)
\(104\) −1.37418 3.07747i −0.134749 0.301771i
\(105\) 0 0
\(106\) 15.5957 2.19758i 1.51479 0.213448i
\(107\) 12.0499 + 12.0499i 1.16491 + 1.16491i 0.983387 + 0.181519i \(0.0581013\pi\)
0.181519 + 0.983387i \(0.441899\pi\)
\(108\) 0 0
\(109\) −2.33845 + 2.33845i −0.223983 + 0.223983i −0.810173 0.586190i \(-0.800627\pi\)
0.586190 + 0.810173i \(0.300627\pi\)
\(110\) 3.33908 + 2.51429i 0.318369 + 0.239728i
\(111\) 0 0
\(112\) −5.01186 + 3.14183i −0.473576 + 0.296875i
\(113\) 17.6709i 1.66234i 0.556021 + 0.831168i \(0.312328\pi\)
−0.556021 + 0.831168i \(0.687672\pi\)
\(114\) 0 0
\(115\) −6.50325 6.50325i −0.606431 0.606431i
\(116\) 0.220990 0.399357i 0.0205184 0.0370793i
\(117\) 0 0
\(118\) −0.313183 2.22259i −0.0288308 0.204606i
\(119\) 6.75490i 0.619221i
\(120\) 0 0
\(121\) 8.27376i 0.752160i
\(122\) 0.784748 0.110578i 0.0710477 0.0100113i
\(123\) 0 0
\(124\) −17.9569 + 5.16311i −1.61258 + 0.463661i
\(125\) 8.60173 + 8.60173i 0.769362 + 0.769362i
\(126\) 0 0
\(127\) 2.51234i 0.222934i −0.993768 0.111467i \(-0.964445\pi\)
0.993768 0.111467i \(-0.0355550\pi\)
\(128\) −2.18683 11.1003i −0.193291 0.981142i
\(129\) 0 0
\(130\) −1.81452 + 2.40976i −0.159144 + 0.211350i
\(131\) −12.9471 + 12.9471i −1.13119 + 1.13119i −0.141209 + 0.989980i \(0.545099\pi\)
−0.989980 + 0.141209i \(0.954901\pi\)
\(132\) 0 0
\(133\) 4.12398 + 4.12398i 0.357595 + 0.357595i
\(134\) 1.70716 + 12.1153i 0.147476 + 1.04660i
\(135\) 0 0
\(136\) 12.0666 + 4.61694i 1.03470 + 0.395899i
\(137\) −18.2869 −1.56235 −0.781176 0.624310i \(-0.785380\pi\)
−0.781176 + 0.624310i \(0.785380\pi\)
\(138\) 0 0
\(139\) −9.14289 + 9.14289i −0.775490 + 0.775490i −0.979060 0.203570i \(-0.934745\pi\)
0.203570 + 0.979060i \(0.434745\pi\)
\(140\) 4.63230 + 2.56335i 0.391501 + 0.216643i
\(141\) 0 0
\(142\) 13.5507 17.9958i 1.13715 1.51018i
\(143\) −1.96748 −0.164529
\(144\) 0 0
\(145\) −0.408508 −0.0339248
\(146\) 10.7606 14.2905i 0.890550 1.18269i
\(147\) 0 0
\(148\) 8.94405 16.1630i 0.735197 1.32859i
\(149\) 15.0435 15.0435i 1.23241 1.23241i 0.269381 0.963034i \(-0.413181\pi\)
0.963034 0.269381i \(-0.0868190\pi\)
\(150\) 0 0
\(151\) 1.62721 0.132421 0.0662104 0.997806i \(-0.478909\pi\)
0.0662104 + 0.997806i \(0.478909\pi\)
\(152\) −10.1856 + 4.54815i −0.826161 + 0.368904i
\(153\) 0 0
\(154\) 0.481813 + 3.41931i 0.0388256 + 0.275536i
\(155\) 11.8249 + 11.8249i 0.949802 + 0.949802i
\(156\) 0 0
\(157\) 8.31389 8.31389i 0.663521 0.663521i −0.292688 0.956208i \(-0.594550\pi\)
0.956208 + 0.292688i \(0.0945496\pi\)
\(158\) 3.73077 4.95463i 0.296804 0.394169i
\(159\) 0 0
\(160\) −7.74520 + 6.52287i −0.612312 + 0.515678i
\(161\) 7.59789i 0.598798i
\(162\) 0 0
\(163\) 10.0962 + 10.0962i 0.790797 + 0.790797i 0.981624 0.190827i \(-0.0611170\pi\)
−0.190827 + 0.981624i \(0.561117\pi\)
\(164\) −5.16992 17.9806i −0.403703 1.40405i
\(165\) 0 0
\(166\) −8.12798 + 1.14531i −0.630854 + 0.0888931i
\(167\) 13.3585i 1.03371i 0.856073 + 0.516856i \(0.172898\pi\)
−0.856073 + 0.516856i \(0.827102\pi\)
\(168\) 0 0
\(169\) 11.5801i 0.890777i
\(170\) −1.61345 11.4503i −0.123746 0.878198i
\(171\) 0 0
\(172\) 9.85214 + 5.45183i 0.751219 + 0.415698i
\(173\) 4.10881 + 4.10881i 0.312387 + 0.312387i 0.845834 0.533447i \(-0.179104\pi\)
−0.533447 + 0.845834i \(0.679104\pi\)
\(174\) 0 0
\(175\) 2.65557i 0.200742i
\(176\) −6.43740 1.47640i −0.485238 0.111288i
\(177\) 0 0
\(178\) 0.921551 + 0.693917i 0.0690732 + 0.0520112i
\(179\) 0.0730717 0.0730717i 0.00546164 0.00546164i −0.704371 0.709832i \(-0.748771\pi\)
0.709832 + 0.704371i \(0.248771\pi\)
\(180\) 0 0
\(181\) 4.05639 + 4.05639i 0.301509 + 0.301509i 0.841604 0.540095i \(-0.181612\pi\)
−0.540095 + 0.841604i \(0.681612\pi\)
\(182\) −2.46766 + 0.347716i −0.182915 + 0.0257744i
\(183\) 0 0
\(184\) 13.5725 + 5.19312i 1.00058 + 0.382842i
\(185\) −16.5334 −1.21556
\(186\) 0 0
\(187\) 5.33305 5.33305i 0.389991 0.389991i
\(188\) −3.18237 11.0681i −0.232098 0.807221i
\(189\) 0 0
\(190\) 7.97565 + 6.00556i 0.578614 + 0.435689i
\(191\) −14.2421 −1.03052 −0.515261 0.857033i \(-0.672305\pi\)
−0.515261 + 0.857033i \(0.672305\pi\)
\(192\) 0 0
\(193\) −2.49549 −0.179630 −0.0898148 0.995958i \(-0.528628\pi\)
−0.0898148 + 0.995958i \(0.528628\pi\)
\(194\) −13.9385 10.4955i −1.00072 0.753533i
\(195\) 0 0
\(196\) −2.66005 9.25145i −0.190003 0.660818i
\(197\) −7.01941 + 7.01941i −0.500113 + 0.500113i −0.911473 0.411360i \(-0.865054\pi\)
0.411360 + 0.911473i \(0.365054\pi\)
\(198\) 0 0
\(199\) 0.00885227 0.000627521 0.000313760 1.00000i \(-0.499900\pi\)
0.000313760 1.00000i \(0.499900\pi\)
\(200\) −4.74377 1.81507i −0.335435 0.128345i
\(201\) 0 0
\(202\) −0.386852 + 0.0545110i −0.0272188 + 0.00383538i
\(203\) −0.238635 0.238635i −0.0167489 0.0167489i
\(204\) 0 0
\(205\) −11.8405 + 11.8405i −0.826978 + 0.826978i
\(206\) 8.36707 + 6.30030i 0.582962 + 0.438963i
\(207\) 0 0
\(208\) 1.06549 4.64576i 0.0738785 0.322126i
\(209\) 6.51184i 0.450433i
\(210\) 0 0
\(211\) 5.34136 + 5.34136i 0.367714 + 0.367714i 0.866643 0.498929i \(-0.166273\pi\)
−0.498929 + 0.866643i \(0.666273\pi\)
\(212\) 19.4887 + 10.7843i 1.33849 + 0.740672i
\(213\) 0 0
\(214\) 3.36266 + 23.8640i 0.229867 + 1.63131i
\(215\) 10.0779i 0.687308i
\(216\) 0 0
\(217\) 13.8153i 0.937847i
\(218\) −4.63116 + 0.652573i −0.313662 + 0.0441978i
\(219\) 0 0
\(220\) 1.63345 + 5.68103i 0.110127 + 0.383015i
\(221\) 3.84877 + 3.84877i 0.258896 + 0.258896i
\(222\) 0 0
\(223\) 9.03492i 0.605023i −0.953146 0.302512i \(-0.902175\pi\)
0.953146 0.302512i \(-0.0978251\pi\)
\(224\) −8.33485 0.714037i −0.556896 0.0477086i
\(225\) 0 0
\(226\) −15.0324 + 19.9637i −0.999940 + 1.32796i
\(227\) −8.78561 + 8.78561i −0.583121 + 0.583121i −0.935760 0.352638i \(-0.885285\pi\)
0.352638 + 0.935760i \(0.385285\pi\)
\(228\) 0 0
\(229\) −3.05241 3.05241i −0.201709 0.201709i 0.599023 0.800732i \(-0.295556\pi\)
−0.800732 + 0.599023i \(0.795556\pi\)
\(230\) −1.81481 12.8793i −0.119665 0.849234i
\(231\) 0 0
\(232\) 0.589391 0.263179i 0.0386954 0.0172786i
\(233\) 0.628345 0.0411642 0.0205821 0.999788i \(-0.493448\pi\)
0.0205821 + 0.999788i \(0.493448\pi\)
\(234\) 0 0
\(235\) −7.28849 + 7.28849i −0.475449 + 0.475449i
\(236\) 1.53691 2.77738i 0.100044 0.180792i
\(237\) 0 0
\(238\) 5.74631 7.63134i 0.372478 0.494666i
\(239\) 2.31962 0.150043 0.0750217 0.997182i \(-0.476097\pi\)
0.0750217 + 0.997182i \(0.476097\pi\)
\(240\) 0 0
\(241\) 24.8731 1.60222 0.801109 0.598518i \(-0.204244\pi\)
0.801109 + 0.598518i \(0.204244\pi\)
\(242\) 7.03838 9.34726i 0.452444 0.600865i
\(243\) 0 0
\(244\) 0.980635 + 0.542649i 0.0627787 + 0.0347395i
\(245\) −6.09223 + 6.09223i −0.389218 + 0.389218i
\(246\) 0 0
\(247\) −4.69948 −0.299021
\(248\) −24.6790 9.44271i −1.56712 0.599613i
\(249\) 0 0
\(250\) 2.40041 + 17.0352i 0.151815 + 1.07740i
\(251\) 15.2526 + 15.2526i 0.962737 + 0.962737i 0.999330 0.0365936i \(-0.0116507\pi\)
−0.0365936 + 0.999330i \(0.511651\pi\)
\(252\) 0 0
\(253\) 5.99860 5.99860i 0.377129 0.377129i
\(254\) 2.13722 2.83832i 0.134101 0.178092i
\(255\) 0 0
\(256\) 6.97235 14.4009i 0.435772 0.900057i
\(257\) 11.8747i 0.740722i 0.928888 + 0.370361i \(0.120766\pi\)
−0.928888 + 0.370361i \(0.879234\pi\)
\(258\) 0 0
\(259\) −9.65819 9.65819i −0.600131 0.600131i
\(260\) −4.09990 + 1.17883i −0.254265 + 0.0731082i
\(261\) 0 0
\(262\) −25.6408 + 3.61303i −1.58409 + 0.223213i
\(263\) 7.44522i 0.459092i −0.973298 0.229546i \(-0.926276\pi\)
0.973298 0.229546i \(-0.0737241\pi\)
\(264\) 0 0
\(265\) 19.9353i 1.22461i
\(266\) 1.15085 + 8.16728i 0.0705629 + 0.500768i
\(267\) 0 0
\(268\) −8.37766 + 15.1395i −0.511747 + 0.924792i
\(269\) −0.822509 0.822509i −0.0501492 0.0501492i 0.681587 0.731737i \(-0.261290\pi\)
−0.731737 + 0.681587i \(0.761290\pi\)
\(270\) 0 0
\(271\) 13.8535i 0.841543i 0.907167 + 0.420771i \(0.138241\pi\)
−0.907167 + 0.420771i \(0.861759\pi\)
\(272\) 9.70467 + 15.4809i 0.588432 + 0.938667i
\(273\) 0 0
\(274\) −20.6596 15.5564i −1.24809 0.939797i
\(275\) −2.09659 + 2.09659i −0.126429 + 0.126429i
\(276\) 0 0
\(277\) 22.7763 + 22.7763i 1.36849 + 1.36849i 0.862589 + 0.505906i \(0.168842\pi\)
0.505906 + 0.862589i \(0.331158\pi\)
\(278\) −18.1069 + 2.55143i −1.08598 + 0.153025i
\(279\) 0 0
\(280\) 3.05273 + 6.83658i 0.182435 + 0.408564i
\(281\) 8.02293 0.478608 0.239304 0.970945i \(-0.423081\pi\)
0.239304 + 0.970945i \(0.423081\pi\)
\(282\) 0 0
\(283\) 9.94633 9.94633i 0.591248 0.591248i −0.346721 0.937968i \(-0.612705\pi\)
0.937968 + 0.346721i \(0.112705\pi\)
\(284\) 30.6177 8.80342i 1.81682 0.522387i
\(285\) 0 0
\(286\) −2.22276 1.67371i −0.131435 0.0989687i
\(287\) −13.8336 −0.816569
\(288\) 0 0
\(289\) −3.86492 −0.227348
\(290\) −0.461512 0.347513i −0.0271009 0.0204066i
\(291\) 0 0
\(292\) 24.3135 6.99079i 1.42284 0.409105i
\(293\) 17.8928 17.8928i 1.04531 1.04531i 0.0463831 0.998924i \(-0.485231\pi\)
0.998924 0.0463831i \(-0.0147695\pi\)
\(294\) 0 0
\(295\) −2.84103 −0.165411
\(296\) 23.8542 10.6516i 1.38650 0.619110i
\(297\) 0 0
\(298\) 29.7928 4.19807i 1.72585 0.243188i
\(299\) 4.32909 + 4.32909i 0.250358 + 0.250358i
\(300\) 0 0
\(301\) 5.88713 5.88713i 0.339328 0.339328i
\(302\) 1.83834 + 1.38425i 0.105785 + 0.0796547i
\(303\) 0 0
\(304\) −15.3762 3.52648i −0.881886 0.202258i
\(305\) 1.00311i 0.0574377i
\(306\) 0 0
\(307\) −11.9244 11.9244i −0.680562 0.680562i 0.279565 0.960127i \(-0.409810\pi\)
−0.960127 + 0.279565i \(0.909810\pi\)
\(308\) −2.36444 + 4.27284i −0.134726 + 0.243467i
\(309\) 0 0
\(310\) 3.29989 + 23.4185i 0.187421 + 1.33008i
\(311\) 0.125339i 0.00710734i −0.999994 0.00355367i \(-0.998869\pi\)
0.999994 0.00355367i \(-0.00113117\pi\)
\(312\) 0 0
\(313\) 28.8410i 1.63019i 0.579329 + 0.815094i \(0.303315\pi\)
−0.579329 + 0.815094i \(0.696685\pi\)
\(314\) 16.4651 2.32009i 0.929180 0.130930i
\(315\) 0 0
\(316\) 8.42967 2.42376i 0.474206 0.136347i
\(317\) 18.4600 + 18.4600i 1.03682 + 1.03682i 0.999296 + 0.0375227i \(0.0119467\pi\)
0.0375227 + 0.999296i \(0.488053\pi\)
\(318\) 0 0
\(319\) 0.376808i 0.0210972i
\(320\) −14.2990 + 0.780464i −0.799341 + 0.0436292i
\(321\) 0 0
\(322\) 6.46343 8.58371i 0.360193 0.478351i
\(323\) 12.7384 12.7384i 0.708783 0.708783i
\(324\) 0 0
\(325\) −1.51308 1.51308i −0.0839303 0.0839303i
\(326\) 2.81747 + 19.9949i 0.156045 + 1.10742i
\(327\) 0 0
\(328\) 9.45516 24.7116i 0.522074 1.36447i
\(329\) −8.51531 −0.469464
\(330\) 0 0
\(331\) 4.25015 4.25015i 0.233609 0.233609i −0.580588 0.814197i \(-0.697177\pi\)
0.814197 + 0.580588i \(0.197177\pi\)
\(332\) −10.1569 5.62046i −0.557431 0.308463i
\(333\) 0 0
\(334\) −11.3639 + 15.0917i −0.621805 + 0.825783i
\(335\) 15.4864 0.846114
\(336\) 0 0
\(337\) 12.7546 0.694789 0.347394 0.937719i \(-0.387067\pi\)
0.347394 + 0.937719i \(0.387067\pi\)
\(338\) −9.85104 + 13.0826i −0.535826 + 0.711600i
\(339\) 0 0
\(340\) 7.91783 14.3085i 0.429404 0.775988i
\(341\) −10.9073 + 10.9073i −0.590665 + 0.590665i
\(342\) 0 0
\(343\) −17.4693 −0.943255
\(344\) 6.49264 + 14.5403i 0.350060 + 0.783959i
\(345\) 0 0
\(346\) 1.14661 + 8.13723i 0.0616422 + 0.437460i
\(347\) −24.3745 24.3745i −1.30849 1.30849i −0.922504 0.385988i \(-0.873861\pi\)
−0.385988 0.922504i \(-0.626139\pi\)
\(348\) 0 0
\(349\) −5.14223 + 5.14223i −0.275257 + 0.275257i −0.831212 0.555955i \(-0.812353\pi\)
0.555955 + 0.831212i \(0.312353\pi\)
\(350\) −2.25906 + 3.00013i −0.120752 + 0.160363i
\(351\) 0 0
\(352\) −6.01670 7.14417i −0.320691 0.380786i
\(353\) 22.1829i 1.18068i −0.807156 0.590338i \(-0.798995\pi\)
0.807156 0.590338i \(-0.201005\pi\)
\(354\) 0 0
\(355\) −20.1622 20.1622i −1.07010 1.07010i
\(356\) 0.450815 + 1.56790i 0.0238932 + 0.0830987i
\(357\) 0 0
\(358\) 0.144714 0.0203915i 0.00764836 0.00107772i
\(359\) 8.55209i 0.451362i −0.974201 0.225681i \(-0.927539\pi\)
0.974201 0.225681i \(-0.0724607\pi\)
\(360\) 0 0
\(361\) 3.44599i 0.181368i
\(362\) 1.13198 + 8.03343i 0.0594958 + 0.422228i
\(363\) 0 0
\(364\) −3.08363 1.70637i −0.161626 0.0894383i
\(365\) −16.0108 16.0108i −0.838044 0.838044i
\(366\) 0 0
\(367\) 27.9033i 1.45654i −0.685291 0.728270i \(-0.740325\pi\)
0.685291 0.728270i \(-0.259675\pi\)
\(368\) 10.9158 + 17.4129i 0.569024 + 0.907708i
\(369\) 0 0
\(370\) −18.6786 14.0648i −0.971055 0.731192i
\(371\) 11.6454 11.6454i 0.604600 0.604600i
\(372\) 0 0
\(373\) 2.32666 + 2.32666i 0.120470 + 0.120470i 0.764771 0.644302i \(-0.222852\pi\)
−0.644302 + 0.764771i \(0.722852\pi\)
\(374\) 10.5618 1.48825i 0.546136 0.0769556i
\(375\) 0 0
\(376\) 5.82017 15.2113i 0.300152 0.784464i
\(377\) 0.271936 0.0140054
\(378\) 0 0
\(379\) −0.522727 + 0.522727i −0.0268507 + 0.0268507i −0.720405 0.693554i \(-0.756044\pi\)
0.693554 + 0.720405i \(0.256044\pi\)
\(380\) 3.90162 + 13.5696i 0.200149 + 0.696103i
\(381\) 0 0
\(382\) −16.0900 12.1156i −0.823235 0.619886i
\(383\) 25.8856 1.32269 0.661346 0.750081i \(-0.269985\pi\)
0.661346 + 0.750081i \(0.269985\pi\)
\(384\) 0 0
\(385\) 4.37075 0.222754
\(386\) −2.81928 2.12288i −0.143498 0.108052i
\(387\) 0 0
\(388\) −6.81858 23.7145i −0.346161 1.20392i
\(389\) 1.95484 1.95484i 0.0991144 0.0991144i −0.655811 0.754925i \(-0.727673\pi\)
0.754925 + 0.655811i \(0.227673\pi\)
\(390\) 0 0
\(391\) −23.4688 −1.18687
\(392\) 4.86490 12.7147i 0.245715 0.642188i
\(393\) 0 0
\(394\) −13.9015 + 1.95885i −0.700347 + 0.0986854i
\(395\) −5.55107 5.55107i −0.279305 0.279305i
\(396\) 0 0
\(397\) −3.86800 + 3.86800i −0.194129 + 0.194129i −0.797478 0.603348i \(-0.793833\pi\)
0.603348 + 0.797478i \(0.293833\pi\)
\(398\) 0.0100008 + 0.00753051i 0.000501297 + 0.000377470i
\(399\) 0 0
\(400\) −3.81522 6.08603i −0.190761 0.304302i
\(401\) 16.1774i 0.807863i 0.914789 + 0.403931i \(0.132357\pi\)
−0.914789 + 0.403931i \(0.867643\pi\)
\(402\) 0 0
\(403\) −7.87163 7.87163i −0.392114 0.392114i
\(404\) −0.483417 0.267506i −0.0240509 0.0133089i
\(405\) 0 0
\(406\) −0.0665938 0.472601i −0.00330500 0.0234548i
\(407\) 15.2504i 0.755936i
\(408\) 0 0
\(409\) 15.1738i 0.750295i 0.926965 + 0.375148i \(0.122408\pi\)
−0.926965 + 0.375148i \(0.877592\pi\)
\(410\) −23.4494 + 3.30424i −1.15808 + 0.163185i
\(411\) 0 0
\(412\) 4.09310 + 14.2355i 0.201653 + 0.701334i
\(413\) −1.65962 1.65962i −0.0816646 0.0816646i
\(414\) 0 0
\(415\) 10.3896i 0.510007i
\(416\) 5.15583 4.34215i 0.252785 0.212891i
\(417\) 0 0
\(418\) −5.53953 + 7.35674i −0.270947 + 0.359830i
\(419\) 6.32294 6.32294i 0.308896 0.308896i −0.535585 0.844481i \(-0.679909\pi\)
0.844481 + 0.535585i \(0.179909\pi\)
\(420\) 0 0
\(421\) −18.1865 18.1865i −0.886356 0.886356i 0.107815 0.994171i \(-0.465615\pi\)
−0.994171 + 0.107815i \(0.965615\pi\)
\(422\) 1.49057 + 10.5782i 0.0725597 + 0.514939i
\(423\) 0 0
\(424\) 12.8432 + 28.7623i 0.623720 + 1.39682i
\(425\) 8.20267 0.397888
\(426\) 0 0
\(427\) 0.585976 0.585976i 0.0283574 0.0283574i
\(428\) −16.5018 + 29.8209i −0.797647 + 1.44145i
\(429\) 0 0
\(430\) 8.57315 11.3855i 0.413434 0.549058i
\(431\) −33.2536 −1.60177 −0.800884 0.598820i \(-0.795637\pi\)
−0.800884 + 0.598820i \(0.795637\pi\)
\(432\) 0 0
\(433\) 21.2087 1.01922 0.509612 0.860404i \(-0.329789\pi\)
0.509612 + 0.860404i \(0.329789\pi\)
\(434\) −11.7525 + 15.6079i −0.564139 + 0.749201i
\(435\) 0 0
\(436\) −5.78718 3.20242i −0.277156 0.153368i
\(437\) 14.3281 14.3281i 0.685406 0.685406i
\(438\) 0 0
\(439\) −34.3580 −1.63982 −0.819908 0.572495i \(-0.805976\pi\)
−0.819908 + 0.572495i \(0.805976\pi\)
\(440\) −2.98739 + 7.80769i −0.142418 + 0.372217i
\(441\) 0 0
\(442\) 1.07404 + 7.62224i 0.0510871 + 0.362553i
\(443\) 6.79175 + 6.79175i 0.322686 + 0.322686i 0.849797 0.527111i \(-0.176725\pi\)
−0.527111 + 0.849797i \(0.676725\pi\)
\(444\) 0 0
\(445\) 1.03249 1.03249i 0.0489447 0.0489447i
\(446\) 7.68589 10.2072i 0.363937 0.483324i
\(447\) 0 0
\(448\) −8.80887 7.89703i −0.416180 0.373100i
\(449\) 24.1062i 1.13764i −0.822461 0.568821i \(-0.807400\pi\)
0.822461 0.568821i \(-0.192600\pi\)
\(450\) 0 0
\(451\) −10.9217 10.9217i −0.514283 0.514283i
\(452\) −33.9656 + 9.76605i −1.59761 + 0.459357i
\(453\) 0 0
\(454\) −17.3993 + 2.45173i −0.816591 + 0.115065i
\(455\) 3.15430i 0.147876i
\(456\) 0 0
\(457\) 1.51672i 0.0709493i 0.999371 + 0.0354746i \(0.0112943\pi\)
−0.999371 + 0.0354746i \(0.988706\pi\)
\(458\) −0.851811 6.04511i −0.0398025 0.282469i
\(459\) 0 0
\(460\) 8.90595 16.0942i 0.415242 0.750394i
\(461\) −23.6025 23.6025i −1.09928 1.09928i −0.994495 0.104783i \(-0.966585\pi\)
−0.104783 0.994495i \(-0.533415\pi\)
\(462\) 0 0
\(463\) 15.2915i 0.710655i −0.934742 0.355328i \(-0.884369\pi\)
0.934742 0.355328i \(-0.115631\pi\)
\(464\) 0.889746 + 0.204060i 0.0413054 + 0.00947326i
\(465\) 0 0
\(466\) 0.709872 + 0.534525i 0.0328842 + 0.0247614i
\(467\) −24.2269 + 24.2269i −1.12109 + 1.12109i −0.129507 + 0.991579i \(0.541339\pi\)
−0.991579 + 0.129507i \(0.958661\pi\)
\(468\) 0 0
\(469\) 9.04657 + 9.04657i 0.417732 + 0.417732i
\(470\) −14.4344 + 2.03394i −0.665809 + 0.0938186i
\(471\) 0 0
\(472\) 4.09900 1.83032i 0.188672 0.0842473i
\(473\) 9.29587 0.427424
\(474\) 0 0
\(475\) −5.00787 + 5.00787i −0.229777 + 0.229777i
\(476\) 12.9838 3.73319i 0.595110 0.171110i
\(477\) 0 0
\(478\) 2.62058 + 1.97327i 0.119863 + 0.0902551i
\(479\) −10.7866 −0.492852 −0.246426 0.969162i \(-0.579256\pi\)
−0.246426 + 0.969162i \(0.579256\pi\)
\(480\) 0 0
\(481\) 11.0060 0.501829
\(482\) 28.1004 + 21.1592i 1.27994 + 0.963777i
\(483\) 0 0
\(484\) 15.9032 4.57260i 0.722872 0.207846i
\(485\) −15.6164 + 15.6164i −0.709105 + 0.709105i
\(486\) 0 0
\(487\) 19.6195 0.889044 0.444522 0.895768i \(-0.353374\pi\)
0.444522 + 0.895768i \(0.353374\pi\)
\(488\) 0.646247 + 1.44727i 0.0292542 + 0.0655148i
\(489\) 0 0
\(490\) −12.0653 + 1.70011i −0.545053 + 0.0768030i
\(491\) −25.7673 25.7673i −1.16286 1.16286i −0.983846 0.179017i \(-0.942708\pi\)
−0.179017 0.983846i \(-0.557292\pi\)
\(492\) 0 0
\(493\) −0.737108 + 0.737108i −0.0331977 + 0.0331977i
\(494\) −5.30923 3.99779i −0.238874 0.179869i
\(495\) 0 0
\(496\) −19.8483 31.6620i −0.891215 1.42167i
\(497\) 23.5560i 1.05663i
\(498\) 0 0
\(499\) 16.7571 + 16.7571i 0.750152 + 0.750152i 0.974507 0.224355i \(-0.0720275\pi\)
−0.224355 + 0.974507i \(0.572028\pi\)
\(500\) −11.7797 + 21.2874i −0.526805 + 0.952004i
\(501\) 0 0
\(502\) 4.25642 + 30.2068i 0.189973 + 1.34820i
\(503\) 27.0368i 1.20551i 0.797926 + 0.602755i \(0.205930\pi\)
−0.797926 + 0.602755i \(0.794070\pi\)
\(504\) 0 0
\(505\) 0.494495i 0.0220047i
\(506\) 11.8798 1.67398i 0.528123 0.0744174i
\(507\) 0 0
\(508\) 4.82904 1.38848i 0.214254 0.0616039i
\(509\) −17.4927 17.4927i −0.775351 0.775351i 0.203685 0.979036i \(-0.434708\pi\)
−0.979036 + 0.203685i \(0.934708\pi\)
\(510\) 0 0
\(511\) 18.7058i 0.827495i
\(512\) 20.1277 10.3381i 0.889526 0.456885i
\(513\) 0 0
\(514\) −10.1016 + 13.4154i −0.445564 + 0.591728i
\(515\) 9.37432 9.37432i 0.413082 0.413082i
\(516\) 0 0
\(517\) −6.72291 6.72291i −0.295673 0.295673i
\(518\) −2.69523 19.1274i −0.118422 0.840410i
\(519\) 0 0
\(520\) −5.63468 2.15595i −0.247097 0.0945445i
\(521\) 15.8879 0.696063 0.348032 0.937483i \(-0.386850\pi\)
0.348032 + 0.937483i \(0.386850\pi\)
\(522\) 0 0
\(523\) 15.6815 15.6815i 0.685703 0.685703i −0.275576 0.961279i \(-0.588869\pi\)
0.961279 + 0.275576i \(0.0888687\pi\)
\(524\) −32.0412 17.7305i −1.39973 0.774560i
\(525\) 0 0
\(526\) 6.33355 8.41122i 0.276156 0.366747i
\(527\) 42.6736 1.85889
\(528\) 0 0
\(529\) −3.39762 −0.147723
\(530\) 16.9587 22.5218i 0.736637 0.978286i
\(531\) 0 0
\(532\) −5.64764 + 10.2060i −0.244856 + 0.442486i
\(533\) 7.88201 7.88201i 0.341408 0.341408i
\(534\) 0 0
\(535\) 30.5043 1.31882
\(536\) −22.3436 + 9.97705i −0.965097 + 0.430943i
\(537\) 0 0
\(538\) −0.229531 1.62893i −0.00989577 0.0702280i
\(539\) −5.61947 5.61947i −0.242048 0.242048i
\(540\) 0 0
\(541\) 28.8331 28.8331i 1.23963 1.23963i 0.279482 0.960151i \(-0.409837\pi\)
0.960151 0.279482i \(-0.0901627\pi\)
\(542\) −11.7850 + 15.6510i −0.506210 + 0.672269i
\(543\) 0 0
\(544\) −2.20556 + 25.7452i −0.0945625 + 1.10381i
\(545\) 5.91980i 0.253576i
\(546\) 0 0
\(547\) 7.25520 + 7.25520i 0.310210 + 0.310210i 0.844991 0.534781i \(-0.179606\pi\)
−0.534781 + 0.844991i \(0.679606\pi\)
\(548\) −10.1065 35.1496i −0.431728 1.50152i
\(549\) 0 0
\(550\) −4.15217 + 0.585079i −0.177049 + 0.0249478i
\(551\) 0.900034i 0.0383427i
\(552\) 0 0
\(553\) 6.48545i 0.275789i
\(554\) 6.35599 + 45.1070i 0.270040 + 1.91641i
\(555\) 0 0
\(556\) −22.6267 12.5208i −0.959587 0.531002i
\(557\) −2.08325 2.08325i −0.0882703 0.0882703i 0.661593 0.749863i \(-0.269881\pi\)
−0.749863 + 0.661593i \(0.769881\pi\)
\(558\) 0 0
\(559\) 6.70867i 0.283746i
\(560\) −2.36698 + 10.3205i −0.100023 + 0.436122i
\(561\) 0 0
\(562\) 9.06390 + 6.82501i 0.382338 + 0.287895i
\(563\) 18.1884 18.1884i 0.766549 0.766549i −0.210948 0.977497i \(-0.567655\pi\)
0.977497 + 0.210948i \(0.0676552\pi\)
\(564\) 0 0
\(565\) 22.3669 + 22.3669i 0.940983 + 0.940983i
\(566\) 19.6981 2.77564i 0.827971 0.116669i
\(567\) 0 0
\(568\) 42.0792 + 16.1004i 1.76560 + 0.675557i
\(569\) 24.1971 1.01440 0.507198 0.861829i \(-0.330681\pi\)
0.507198 + 0.861829i \(0.330681\pi\)
\(570\) 0 0
\(571\) −24.4026 + 24.4026i −1.02122 + 1.02122i −0.0214492 + 0.999770i \(0.506828\pi\)
−0.999770 + 0.0214492i \(0.993172\pi\)
\(572\) −1.08736 3.78175i −0.0454647 0.158123i
\(573\) 0 0
\(574\) −15.6284 11.7680i −0.652318 0.491188i
\(575\) 9.22633 0.384765
\(576\) 0 0
\(577\) −44.9453 −1.87110 −0.935548 0.353200i \(-0.885094\pi\)
−0.935548 + 0.353200i \(0.885094\pi\)
\(578\) −4.36638 3.28783i −0.181618 0.136756i
\(579\) 0 0
\(580\) −0.225768 0.785204i −0.00937449 0.0326038i
\(581\) −6.06922 + 6.06922i −0.251794 + 0.251794i
\(582\) 0 0
\(583\) 18.3883 0.761565
\(584\) 33.4151 + 12.7853i 1.38273 + 0.529060i
\(585\) 0 0
\(586\) 35.4355 4.99319i 1.46383 0.206267i
\(587\) −15.6677 15.6677i −0.646676 0.646676i 0.305512 0.952188i \(-0.401172\pi\)
−0.952188 + 0.305512i \(0.901172\pi\)
\(588\) 0 0
\(589\) −26.0529 + 26.0529i −1.07349 + 1.07349i
\(590\) −3.20965 2.41683i −0.132139 0.0994992i
\(591\) 0 0
\(592\) 36.0104 + 8.25887i 1.48002 + 0.339437i
\(593\) 0.259633i 0.0106618i −0.999986 0.00533092i \(-0.998303\pi\)
0.999986 0.00533092i \(-0.00169689\pi\)
\(594\) 0 0
\(595\) −8.55002 8.55002i −0.350517 0.350517i
\(596\) 37.2296 + 20.6015i 1.52498 + 0.843872i
\(597\) 0 0
\(598\) 1.20808 + 8.57348i 0.0494021 + 0.350596i
\(599\) 33.6422i 1.37458i 0.726382 + 0.687291i \(0.241200\pi\)
−0.726382 + 0.687291i \(0.758800\pi\)
\(600\) 0 0
\(601\) 21.8534i 0.891419i −0.895178 0.445710i \(-0.852951\pi\)
0.895178 0.445710i \(-0.147049\pi\)
\(602\) 11.6591 1.64287i 0.475188 0.0669584i
\(603\) 0 0
\(604\) 0.899302 + 3.12771i 0.0365921 + 0.127265i
\(605\) −10.4725 10.4725i −0.425768 0.425768i
\(606\) 0 0
\(607\) 19.4186i 0.788177i 0.919073 + 0.394088i \(0.128940\pi\)
−0.919073 + 0.394088i \(0.871060\pi\)
\(608\) −14.3713 17.0644i −0.582834 0.692052i
\(609\) 0 0
\(610\) 0.853330 1.13326i 0.0345503 0.0458843i
\(611\) 4.85181 4.85181i 0.196283 0.196283i
\(612\) 0 0
\(613\) 11.1127 + 11.1127i 0.448839 + 0.448839i 0.894968 0.446129i \(-0.147198\pi\)
−0.446129 + 0.894968i \(0.647198\pi\)
\(614\) −3.32764 23.6155i −0.134293 0.953044i
\(615\) 0 0
\(616\) −6.30607 + 2.81583i −0.254079 + 0.113453i
\(617\) 4.27564 0.172131 0.0860654 0.996289i \(-0.472571\pi\)
0.0860654 + 0.996289i \(0.472571\pi\)
\(618\) 0 0
\(619\) −6.85100 + 6.85100i −0.275365 + 0.275365i −0.831255 0.555891i \(-0.812377\pi\)
0.555891 + 0.831255i \(0.312377\pi\)
\(620\) −16.1938 + 29.2642i −0.650358 + 1.17528i
\(621\) 0 0
\(622\) 0.106625 0.141602i 0.00427525 0.00567772i
\(623\) 1.20628 0.0483286
\(624\) 0 0
\(625\) 12.7965 0.511860
\(626\) −24.5346 + 32.5830i −0.980601 + 1.30228i
\(627\) 0 0
\(628\) 20.5751 + 11.3855i 0.821036 + 0.454333i
\(629\) −29.8327 + 29.8327i −1.18951 + 1.18951i
\(630\) 0 0
\(631\) −1.73528 −0.0690802 −0.0345401 0.999403i \(-0.510997\pi\)
−0.0345401 + 0.999403i \(0.510997\pi\)
\(632\) 11.5853 + 4.43277i 0.460837 + 0.176326i
\(633\) 0 0
\(634\) 5.15149 + 36.5589i 0.204592 + 1.45194i
\(635\) −3.18000 3.18000i −0.126194 0.126194i
\(636\) 0 0
\(637\) 4.05548 4.05548i 0.160684 0.160684i
\(638\) 0.320546 0.425698i 0.0126905 0.0168536i
\(639\) 0 0
\(640\) −16.8183 11.2823i −0.664800 0.445971i
\(641\) 3.07469i 0.121443i −0.998155 0.0607214i \(-0.980660\pi\)
0.998155 0.0607214i \(-0.0193401\pi\)
\(642\) 0 0
\(643\) 7.18763 + 7.18763i 0.283452 + 0.283452i 0.834484 0.551032i \(-0.185766\pi\)
−0.551032 + 0.834484i \(0.685766\pi\)
\(644\) 14.6041 4.19908i 0.575482 0.165467i
\(645\) 0 0
\(646\) 25.2276 3.55480i 0.992565 0.139862i
\(647\) 11.1585i 0.438685i 0.975648 + 0.219342i \(0.0703912\pi\)
−0.975648 + 0.219342i \(0.929609\pi\)
\(648\) 0 0
\(649\) 2.62057i 0.102866i
\(650\) −0.422241 2.99655i −0.0165617 0.117534i
\(651\) 0 0
\(652\) −13.8264 + 24.9860i −0.541483 + 0.978527i
\(653\) 24.1318 + 24.1318i 0.944349 + 0.944349i 0.998531 0.0541822i \(-0.0172552\pi\)
−0.0541822 + 0.998531i \(0.517255\pi\)
\(654\) 0 0
\(655\) 32.7755i 1.28064i
\(656\) 31.7037 19.8745i 1.23782 0.775967i
\(657\) 0 0
\(658\) −9.62016 7.24386i −0.375033 0.282395i
\(659\) 14.1846 14.1846i 0.552552 0.552552i −0.374625 0.927177i \(-0.622228\pi\)
0.927177 + 0.374625i \(0.122228\pi\)
\(660\) 0 0
\(661\) 21.3432 + 21.3432i 0.830153 + 0.830153i 0.987537 0.157385i \(-0.0503062\pi\)
−0.157385 + 0.987537i \(0.550306\pi\)
\(662\) 8.41715 1.18605i 0.327142 0.0460973i
\(663\) 0 0
\(664\) −6.69346 14.9900i −0.259757 0.581726i
\(665\) 10.4399 0.404841
\(666\) 0 0
\(667\) −0.829097 + 0.829097i −0.0321028 + 0.0321028i
\(668\) −25.6767 + 7.38275i −0.993461 + 0.285647i
\(669\) 0 0
\(670\) 17.4958 + 13.1741i 0.675920 + 0.508960i
\(671\) 0.925266 0.0357195
\(672\) 0 0
\(673\) −13.7772 −0.531071 −0.265536 0.964101i \(-0.585549\pi\)
−0.265536 + 0.964101i \(0.585549\pi\)
\(674\) 14.4095 + 10.8502i 0.555034 + 0.417934i
\(675\) 0 0
\(676\) −22.2584 + 6.39990i −0.856092 + 0.246150i
\(677\) −18.7732 + 18.7732i −0.721514 + 0.721514i −0.968914 0.247400i \(-0.920424\pi\)
0.247400 + 0.968914i \(0.420424\pi\)
\(678\) 0 0
\(679\) −18.2450 −0.700179
\(680\) 21.1172 9.42942i 0.809808 0.361602i
\(681\) 0 0
\(682\) −21.6012 + 3.04382i −0.827155 + 0.116554i
\(683\) 32.0134 + 32.0134i 1.22496 + 1.22496i 0.965847 + 0.259112i \(0.0834298\pi\)
0.259112 + 0.965847i \(0.416570\pi\)
\(684\) 0 0
\(685\) −23.1466 + 23.1466i −0.884386 + 0.884386i
\(686\) −19.7359 14.8609i −0.753522 0.567393i
\(687\) 0 0
\(688\) −5.03417 + 21.9501i −0.191926 + 0.836838i
\(689\) 13.2705i 0.505566i
\(690\) 0 0
\(691\) 16.3176 + 16.3176i 0.620752 + 0.620752i 0.945724 0.324972i \(-0.105355\pi\)
−0.324972 + 0.945724i \(0.605355\pi\)
\(692\) −5.62685 + 10.1684i −0.213901 + 0.386546i
\(693\) 0 0
\(694\) −6.80199 48.2721i −0.258200 1.83238i
\(695\) 23.1452i 0.877949i
\(696\) 0 0
\(697\) 42.7298i 1.61851i
\(698\) −10.1839 + 1.43500i −0.385464 + 0.0543155i
\(699\) 0 0
\(700\) −5.10433 + 1.46764i −0.192926 + 0.0554714i
\(701\) −4.92514 4.92514i −0.186020 0.186020i 0.607953 0.793973i \(-0.291991\pi\)
−0.793973 + 0.607953i \(0.791991\pi\)
\(702\) 0 0
\(703\) 36.4268i 1.37386i
\(704\) −0.719900 13.1894i −0.0271323 0.497096i
\(705\) 0 0
\(706\) 18.8707 25.0611i 0.710207 0.943186i
\(707\) −0.288865 + 0.288865i −0.0108639 + 0.0108639i
\(708\) 0 0
\(709\) −17.8267 17.8267i −0.669497 0.669497i 0.288103 0.957599i \(-0.406976\pi\)
−0.957599 + 0.288103i \(0.906976\pi\)
\(710\) −5.62650 39.9300i −0.211159 1.49855i
\(711\) 0 0
\(712\) −0.824487 + 2.15484i −0.0308989 + 0.0807560i
\(713\) 47.9991 1.79758
\(714\) 0 0
\(715\) −2.49034 + 2.49034i −0.0931336 + 0.0931336i
\(716\) 0.180837 + 0.100069i 0.00675820 + 0.00373975i
\(717\) 0 0
\(718\) 7.27515 9.66171i 0.271506 0.360572i
\(719\) −39.2431 −1.46352 −0.731761 0.681561i \(-0.761301\pi\)
−0.731761 + 0.681561i \(0.761301\pi\)
\(720\) 0 0
\(721\) 10.9522 0.407882
\(722\) 2.93146 3.89311i 0.109098 0.144886i
\(723\) 0 0
\(724\) −5.55507 + 10.0387i −0.206453 + 0.373086i
\(725\) 0.289781 0.289781i 0.0107622 0.0107622i
\(726\) 0 0
\(727\) 39.9286 1.48087 0.740435 0.672128i \(-0.234620\pi\)
0.740435 + 0.672128i \(0.234620\pi\)
\(728\) −2.03214 4.55098i −0.0753161 0.168671i
\(729\) 0 0
\(730\) −4.46800 31.7084i −0.165368 1.17358i
\(731\) −18.1845 18.1845i −0.672577 0.672577i
\(732\) 0 0
\(733\) 15.5110 15.5110i 0.572912 0.572912i −0.360029 0.932941i \(-0.617233\pi\)
0.932941 + 0.360029i \(0.117233\pi\)
\(734\) 23.7370 31.5237i 0.876147 1.16356i
\(735\) 0 0
\(736\) −2.48080 + 28.9581i −0.0914436 + 1.06741i
\(737\) 14.2847i 0.526183i
\(738\) 0 0
\(739\) 21.9310 + 21.9310i 0.806744 + 0.806744i 0.984140 0.177396i \(-0.0567673\pi\)
−0.177396 + 0.984140i \(0.556767\pi\)
\(740\) −9.13742 31.7793i −0.335898 1.16823i
\(741\) 0 0
\(742\) 23.0630 3.24979i 0.846669 0.119303i
\(743\) 16.0670i 0.589439i 0.955584 + 0.294720i \(0.0952263\pi\)
−0.955584 + 0.294720i \(0.904774\pi\)
\(744\) 0 0
\(745\) 38.0827i 1.39524i
\(746\) 0.649281 + 4.60779i 0.0237718 + 0.168703i
\(747\) 0 0
\(748\) 13.1982 + 7.30340i 0.482573 + 0.267039i
\(749\) 17.8194 + 17.8194i 0.651108 + 0.651108i
\(750\) 0 0
\(751\) 2.33565i 0.0852289i 0.999092 + 0.0426145i \(0.0135687\pi\)
−0.999092 + 0.0426145i \(0.986431\pi\)
\(752\) 19.5154 12.2338i 0.711653 0.446121i
\(753\) 0 0
\(754\) 0.307219 + 0.231332i 0.0111883 + 0.00842463i
\(755\) 2.05965 2.05965i 0.0749582 0.0749582i
\(756\) 0 0
\(757\) −9.89049 9.89049i −0.359476 0.359476i 0.504144 0.863620i \(-0.331808\pi\)
−0.863620 + 0.504144i \(0.831808\pi\)
\(758\) −1.03523 + 0.145873i −0.0376011 + 0.00529835i
\(759\) 0 0
\(760\) −7.13559 + 18.6492i −0.258835 + 0.676479i
\(761\) −5.73919 −0.208045 −0.104023 0.994575i \(-0.533171\pi\)
−0.104023 + 0.994575i \(0.533171\pi\)
\(762\) 0 0
\(763\) −3.45812 + 3.45812i −0.125192 + 0.125192i
\(764\) −7.87109 27.3751i −0.284766 0.990396i
\(765\) 0 0
\(766\) 29.2442 + 22.0205i 1.05664 + 0.795634i
\(767\) 1.89122 0.0682880
\(768\) 0 0
\(769\) −53.0430 −1.91278 −0.956391 0.292091i \(-0.905649\pi\)
−0.956391 + 0.292091i \(0.905649\pi\)
\(770\) 4.93785 + 3.71814i 0.177948 + 0.133993i
\(771\) 0 0
\(772\) −1.37917 4.79665i −0.0496374 0.172635i
\(773\) −23.4184 + 23.4184i −0.842300 + 0.842300i −0.989158 0.146858i \(-0.953084\pi\)
0.146858 + 0.989158i \(0.453084\pi\)
\(774\) 0 0
\(775\) −16.7764 −0.602624
\(776\) 12.4704 32.5919i 0.447660 1.16998i
\(777\) 0 0
\(778\) 3.87144 0.545522i 0.138798 0.0195579i
\(779\) −26.0873 26.0873i −0.934674 0.934674i
\(780\) 0 0
\(781\) 18.5976 18.5976i 0.665476 0.665476i
\(782\) −26.5138 19.9646i −0.948133 0.713932i
\(783\) 0 0
\(784\) 16.3123 10.2259i 0.582583 0.365210i
\(785\) 21.0466i 0.751186i
\(786\) 0 0
\(787\) −0.858162 0.858162i −0.0305902 0.0305902i 0.691646 0.722236i \(-0.256886\pi\)
−0.722236 + 0.691646i \(0.756886\pi\)
\(788\) −17.3716 9.61281i −0.618836 0.342442i
\(789\) 0 0
\(790\) −1.54909 10.9935i −0.0551142 0.391133i
\(791\) 26.1318i 0.929139i
\(792\) 0 0
\(793\) 0.667749i 0.0237125i
\(794\) −7.66032 + 1.07941i −0.271855 + 0.0383068i
\(795\) 0 0
\(796\) 0.00489233 + 0.0170152i 0.000173404 + 0.000603087i
\(797\) −5.26955 5.26955i −0.186657 0.186657i 0.607592 0.794249i \(-0.292136\pi\)
−0.794249 + 0.607592i \(0.792136\pi\)
\(798\) 0 0
\(799\) 26.3026i 0.930518i
\(800\) 0.867075 10.1212i 0.0306557 0.357840i
\(801\) 0 0
\(802\) −13.7619 + 18.2764i −0.485951 + 0.645364i
\(803\) 14.7684 14.7684i 0.521165 0.521165i
\(804\) 0 0
\(805\) −9.61704 9.61704i −0.338956 0.338956i
\(806\) −2.19667 15.5893i −0.0773744 0.549108i
\(807\) 0 0
\(808\) −0.318576 0.713451i −0.0112075 0.0250991i
\(809\) −7.20874 −0.253446 −0.126723 0.991938i \(-0.540446\pi\)
−0.126723 + 0.991938i \(0.540446\pi\)
\(810\) 0 0
\(811\) 5.72509 5.72509i 0.201035 0.201035i −0.599408 0.800443i \(-0.704597\pi\)
0.800443 + 0.599408i \(0.204597\pi\)
\(812\) 0.326801 0.590571i 0.0114685 0.0207250i
\(813\) 0 0
\(814\) 12.9733 17.2292i 0.454715 0.603882i
\(815\) 25.5586 0.895278
\(816\) 0 0
\(817\) 22.2039 0.776815
\(818\) −12.9081 + 17.1426i −0.451322 + 0.599376i
\(819\) 0 0
\(820\) −29.3028 16.2151i −1.02330 0.566257i
\(821\) −28.9487 + 28.9487i −1.01032 + 1.01032i −0.0103699 + 0.999946i \(0.503301\pi\)
−0.999946 + 0.0103699i \(0.996699\pi\)
\(822\) 0 0
\(823\) 23.9244 0.833953 0.416976 0.908917i \(-0.363090\pi\)
0.416976 + 0.908917i \(0.363090\pi\)
\(824\) −7.48579 + 19.5645i −0.260780 + 0.681562i
\(825\) 0 0
\(826\) −0.463136 3.28677i −0.0161146 0.114361i
\(827\) −29.2738 29.2738i −1.01795 1.01795i −0.999836 0.0181126i \(-0.994234\pi\)
−0.0181126 0.999836i \(-0.505766\pi\)
\(828\) 0 0
\(829\) 4.28147 4.28147i 0.148702 0.148702i −0.628836 0.777538i \(-0.716468\pi\)
0.777538 + 0.628836i \(0.216468\pi\)
\(830\) −8.83832 + 11.7377i −0.306782 + 0.407420i
\(831\) 0 0
\(832\) 9.51860 0.519540i 0.329998 0.0180118i
\(833\) 21.9855i 0.761753i
\(834\) 0 0
\(835\) 16.9085 + 16.9085i 0.585143 + 0.585143i
\(836\) −12.5166 + 3.59886i −0.432894 + 0.124469i
\(837\) 0 0
\(838\) 12.5222 1.76449i 0.432572 0.0609533i
\(839\) 41.0260i 1.41638i 0.706024 + 0.708188i \(0.250487\pi\)
−0.706024 + 0.708188i \(0.749513\pi\)
\(840\) 0 0
\(841\) 28.9479i 0.998204i
\(842\) −5.07515 36.0172i −0.174901 1.24123i
\(843\) 0 0
\(844\) −7.31478 + 13.2187i −0.251785 + 0.455007i
\(845\) 14.6575 + 14.6575i 0.504234 + 0.504234i
\(846\) 0 0
\(847\) 12.2353i 0.420409i
\(848\) −9.95817 + 43.4198i −0.341965 + 1.49104i
\(849\) 0 0
\(850\) 9.26695 + 6.97790i 0.317854 + 0.239340i
\(851\) −33.5558 + 33.5558i −1.15028 + 1.15028i
\(852\) 0 0
\(853\) −35.5411 35.5411i −1.21690 1.21690i −0.968711 0.248193i \(-0.920163\pi\)
−0.248193 0.968711i \(-0.579837\pi\)
\(854\) 1.16049 0.163524i 0.0397111 0.00559566i
\(855\) 0 0
\(856\) −44.0112 + 19.6522i −1.50427 + 0.671699i
\(857\) −8.85223 −0.302386 −0.151193 0.988504i \(-0.548312\pi\)
−0.151193 + 0.988504i \(0.548312\pi\)
\(858\) 0 0
\(859\) 31.1164 31.1164i 1.06168 1.06168i 0.0637080 0.997969i \(-0.479707\pi\)
0.997969 0.0637080i \(-0.0202926\pi\)
\(860\) 19.3710 5.56969i 0.660546 0.189925i
\(861\) 0 0
\(862\) −37.5682 28.2884i −1.27958 0.963506i
\(863\) 11.6345 0.396043 0.198022 0.980198i \(-0.436548\pi\)
0.198022 + 0.980198i \(0.436548\pi\)
\(864\) 0 0
\(865\) 10.4014 0.353660
\(866\) 23.9605 + 18.0420i 0.814210 + 0.613091i
\(867\) 0 0
\(868\) −26.5548 + 7.63524i −0.901329 + 0.259157i
\(869\) 5.12031 5.12031i 0.173695 0.173695i
\(870\) 0 0
\(871\) −10.3090 −0.349308
\(872\) −3.81380 8.54101i −0.129152 0.289235i
\(873\) 0 0
\(874\) 28.3759 3.99842i 0.959828 0.135249i
\(875\) 12.7203 + 12.7203i 0.430024 + 0.430024i
\(876\) 0 0
\(877\) −27.8544 + 27.8544i −0.940576 + 0.940576i −0.998331 0.0577553i \(-0.981606\pi\)
0.0577553 + 0.998331i \(0.481606\pi\)
\(878\) −38.8159 29.2279i −1.30997 0.986393i
\(879\) 0 0
\(880\) −10.0169 + 6.27939i −0.337669 + 0.211678i
\(881\) 18.4567i 0.621823i −0.950439 0.310912i \(-0.899366\pi\)
0.950439 0.310912i \(-0.100634\pi\)
\(882\) 0 0
\(883\) −2.68187 2.68187i −0.0902521 0.0902521i 0.660539 0.750791i \(-0.270328\pi\)
−0.750791 + 0.660539i \(0.770328\pi\)
\(884\) −5.27074 + 9.52489i −0.177274 + 0.320357i
\(885\) 0 0
\(886\) 1.89532 + 13.4506i 0.0636744 + 0.451882i
\(887\) 0.308340i 0.0103531i 0.999987 + 0.00517653i \(0.00164775\pi\)
−0.999987 + 0.00517653i \(0.998352\pi\)
\(888\) 0 0
\(889\) 3.71526i 0.124606i
\(890\) 2.04478 0.288128i 0.0685411 0.00965808i
\(891\) 0 0
\(892\) 17.3662 4.99327i 0.581465 0.167187i
\(893\) −16.0582 16.0582i −0.537366 0.537366i
\(894\) 0 0
\(895\) 0.184981i 0.00618323i
\(896\) −3.23390 16.4153i −0.108037 0.548395i
\(897\) 0 0
\(898\) 20.5068 27.2340i 0.684322 0.908809i
\(899\) 1.50756 1.50756i 0.0502798 0.0502798i
\(900\) 0 0
\(901\) −35.9710 35.9710i −1.19837 1.19837i
\(902\) −3.04783 21.6297i −0.101482 0.720191i
\(903\) 0 0
\(904\) −46.6805 17.8609i −1.55257 0.594046i
\(905\) 10.2688 0.341345
\(906\) 0 0
\(907\) 11.5311 11.5311i 0.382882 0.382882i −0.489257 0.872140i \(-0.662732\pi\)
0.872140 + 0.489257i \(0.162732\pi\)
\(908\) −21.7425 12.0315i −0.721551 0.399281i
\(909\) 0 0
\(910\) −2.68332 + 3.56356i −0.0889512 + 0.118131i
\(911\) −4.72201 −0.156447 −0.0782236 0.996936i \(-0.524925\pi\)
−0.0782236 + 0.996936i \(0.524925\pi\)
\(912\) 0 0
\(913\) −9.58339 −0.317164
\(914\) −1.29026 + 1.71351i −0.0426779 + 0.0566780i
\(915\) 0 0
\(916\) 4.18016 7.55407i 0.138116 0.249594i
\(917\) −19.1462 + 19.1462i −0.632262 + 0.632262i
\(918\) 0 0
\(919\) 35.4646 1.16987 0.584935 0.811080i \(-0.301120\pi\)
0.584935 + 0.811080i \(0.301120\pi\)
\(920\) 23.7526 10.6062i 0.783099 0.349676i
\(921\) 0 0
\(922\) −6.58655 46.7432i −0.216917 1.53941i
\(923\) 13.4216 + 13.4216i 0.441777 + 0.441777i
\(924\) 0 0
\(925\) 11.7282 11.7282i 0.385621 0.385621i
\(926\) 13.0083 17.2755i 0.427478 0.567709i
\(927\) 0 0
\(928\) 0.831598 + 0.987432i 0.0272985 + 0.0324141i
\(929\) 59.4380i 1.95010i 0.221993 + 0.975048i \(0.428744\pi\)
−0.221993 + 0.975048i \(0.571256\pi\)
\(930\) 0 0
\(931\) −13.4225 13.4225i −0.439906 0.439906i
\(932\) 0.347263 + 1.20776i 0.0113750 + 0.0395614i
\(933\) 0 0
\(934\) −47.9797 + 6.76079i −1.56994 + 0.221220i
\(935\) 13.5006i 0.441517i
\(936\) 0 0
\(937\) 20.2422i 0.661283i −0.943756 0.330642i \(-0.892735\pi\)
0.943756 0.330642i \(-0.107265\pi\)
\(938\) 2.52455 + 17.9162i 0.0824295 + 0.584983i
\(939\) 0 0
\(940\) −18.0375 9.98130i −0.588317 0.325554i
\(941\) −26.7386 26.7386i −0.871654 0.871654i 0.120999 0.992653i \(-0.461390\pi\)
−0.992653 + 0.120999i \(0.961390\pi\)
\(942\) 0 0
\(943\) 48.0624i 1.56513i
\(944\) 6.18787 + 1.41917i 0.201398 + 0.0461900i
\(945\) 0 0
\(946\) 10.5020 + 7.90787i 0.341449 + 0.257107i
\(947\) 5.67631 5.67631i 0.184455 0.184455i −0.608839 0.793294i \(-0.708364\pi\)
0.793294 + 0.608839i \(0.208364\pi\)
\(948\) 0 0
\(949\) 10.6581 + 10.6581i 0.345976 + 0.345976i
\(950\) −9.91776 + 1.39750i −0.321775 + 0.0453410i
\(951\) 0 0
\(952\) 17.8442 + 6.82755i 0.578333 + 0.221282i
\(953\) 57.8320 1.87336 0.936680 0.350185i \(-0.113881\pi\)
0.936680 + 0.350185i \(0.113881\pi\)
\(954\) 0 0
\(955\) −18.0269 + 18.0269i −0.583338 + 0.583338i
\(956\) 1.28197 + 4.45859i 0.0414618 + 0.144201i
\(957\) 0 0
\(958\) −12.1861 9.17602i −0.393717 0.296464i
\(959\) −27.0427 −0.873255
\(960\) 0 0
\(961\) −56.2773 −1.81540
\(962\) 12.4340 + 9.36264i 0.400888 + 0.301864i
\(963\) 0 0
\(964\) 13.7465 + 47.8092i 0.442744 + 1.53983i
\(965\) −3.15867 + 3.15867i −0.101681 + 0.101681i
\(966\) 0 0
\(967\) −19.5761 −0.629526 −0.314763 0.949170i \(-0.601925\pi\)
−0.314763 + 0.949170i \(0.601925\pi\)
\(968\) 21.8565 + 8.36274i 0.702493 + 0.268789i
\(969\) 0 0
\(970\) −30.9273 + 4.35794i −0.993015 + 0.139925i
\(971\) −2.78950 2.78950i −0.0895194 0.0895194i 0.660929 0.750448i \(-0.270162\pi\)
−0.750448 + 0.660929i \(0.770162\pi\)
\(972\) 0 0
\(973\) −13.5206 + 13.5206i −0.433449 + 0.433449i
\(974\) 22.1651 + 16.6900i 0.710215 + 0.534783i
\(975\) 0 0
\(976\) −0.501078 + 2.18480i −0.0160391 + 0.0699339i
\(977\) 38.5087i 1.23200i −0.787745 0.616001i \(-0.788752\pi\)
0.787745 0.616001i \(-0.211248\pi\)
\(978\) 0 0
\(979\) 0.952368 + 0.952368i 0.0304378 + 0.0304378i
\(980\) −15.0770 8.34307i −0.481616 0.266510i
\(981\) 0 0
\(982\) −7.19067 51.0305i −0.229464 1.62845i
\(983\) 1.26237i 0.0402634i 0.999797 + 0.0201317i \(0.00640855\pi\)
−0.999797 + 0.0201317i \(0.993591\pi\)
\(984\) 0 0
\(985\) 17.7696i 0.566188i
\(986\) −1.45979 + 0.205699i −0.0464893 + 0.00655078i
\(987\) 0 0
\(988\) −2.59723 9.03299i −0.0826290 0.287378i
\(989\) −20.4538 20.4538i −0.650394 0.650394i
\(990\) 0 0
\(991\) 7.56646i 0.240357i 0.992752 + 0.120178i \(0.0383466\pi\)
−0.992752 + 0.120178i \(0.961653\pi\)
\(992\) 4.51087 52.6548i 0.143220 1.67179i
\(993\) 0 0
\(994\) 20.0388 26.6123i 0.635591 0.844092i
\(995\) 0.0112048 0.0112048i 0.000355215 0.000355215i
\(996\) 0 0
\(997\) −32.4462 32.4462i −1.02758 1.02758i −0.999609 0.0279715i \(-0.991095\pi\)
−0.0279715 0.999609i \(-0.508905\pi\)
\(998\) 4.67627 + 33.1864i 0.148025 + 1.05050i
\(999\) 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 432.2.l.b.107.13 yes 32
3.2 odd 2 inner 432.2.l.b.107.4 32
4.3 odd 2 1728.2.l.b.1295.11 32
12.11 even 2 1728.2.l.b.1295.6 32
16.3 odd 4 inner 432.2.l.b.323.4 yes 32
16.13 even 4 1728.2.l.b.431.6 32
48.29 odd 4 1728.2.l.b.431.11 32
48.35 even 4 inner 432.2.l.b.323.13 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
432.2.l.b.107.4 32 3.2 odd 2 inner
432.2.l.b.107.13 yes 32 1.1 even 1 trivial
432.2.l.b.323.4 yes 32 16.3 odd 4 inner
432.2.l.b.323.13 yes 32 48.35 even 4 inner
1728.2.l.b.431.6 32 16.13 even 4
1728.2.l.b.431.11 32 48.29 odd 4
1728.2.l.b.1295.6 32 12.11 even 2
1728.2.l.b.1295.11 32 4.3 odd 2