Properties

Label 351.2.ba.a.89.9
Level $351$
Weight $2$
Character 351.89
Analytic conductor $2.803$
Analytic rank $0$
Dimension $48$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [351,2,Mod(71,351)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(351, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("351.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 351 = 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 351.ba (of order \(12\), degree \(4\), not 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: \(2.80274911095\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 117)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 89.9
Character \(\chi\) \(=\) 351.89
Dual form 351.2.ba.a.71.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.841634 - 0.841634i) q^{2} +0.583303i q^{4} +(2.77680 + 0.744040i) q^{5} +(-1.42554 - 0.381973i) q^{7} +(2.17420 + 2.17420i) q^{8} +O(q^{10})\) \(q+(0.841634 - 0.841634i) q^{2} +0.583303i q^{4} +(2.77680 + 0.744040i) q^{5} +(-1.42554 - 0.381973i) q^{7} +(2.17420 + 2.17420i) q^{8} +(2.96326 - 1.71084i) q^{10} +(1.23230 + 1.23230i) q^{11} +(-3.60363 + 0.117561i) q^{13} +(-1.52127 + 0.878303i) q^{14} +2.49315 q^{16} +(-0.939625 + 1.62748i) q^{17} +(4.34907 - 1.16533i) q^{19} +(-0.434001 + 1.61971i) q^{20} +2.07429 q^{22} +(2.82588 - 4.89457i) q^{23} +(2.82688 + 1.63210i) q^{25} +(-2.93400 + 3.13189i) q^{26} +(0.222806 - 0.831522i) q^{28} -6.70089i q^{29} +(0.676611 - 2.52515i) q^{31} +(-2.25007 + 2.25007i) q^{32} +(0.578921 + 2.16056i) q^{34} +(-3.67424 - 2.12132i) q^{35} +(-11.1775 - 2.99499i) q^{37} +(2.67955 - 4.64111i) q^{38} +(4.41961 + 7.65499i) q^{40} +(-0.168067 - 0.627234i) q^{41} +(1.78065 - 1.02806i) q^{43} +(-0.718802 + 0.718802i) q^{44} +(-1.74108 - 6.49779i) q^{46} +(-2.31288 + 0.619735i) q^{47} +(-4.17591 - 2.41096i) q^{49} +(3.75283 - 1.00557i) q^{50} +(-0.0685738 - 2.10201i) q^{52} +11.5633i q^{53} +(2.50496 + 4.33872i) q^{55} +(-2.26892 - 3.92989i) q^{56} +(-5.63970 - 5.63970i) q^{58} +(9.15908 + 9.15908i) q^{59} +(-5.24278 - 9.08077i) q^{61} +(-1.55579 - 2.69471i) q^{62} +8.77378i q^{64} +(-10.0940 - 2.35481i) q^{65} +(3.50643 - 0.939544i) q^{67} +(-0.949313 - 0.548086i) q^{68} +(-4.87774 + 1.30699i) q^{70} +(-2.99663 - 11.1836i) q^{71} +(-8.97423 + 8.97423i) q^{73} +(-11.9280 + 6.88665i) q^{74} +(0.679740 + 2.53683i) q^{76} +(-1.28599 - 2.22739i) q^{77} +(-4.85927 + 8.41651i) q^{79} +(6.92298 + 1.85501i) q^{80} +(-0.669352 - 0.386451i) q^{82} +(-0.712145 - 2.65776i) q^{83} +(-3.82006 + 3.82006i) q^{85} +(0.633407 - 2.36391i) q^{86} +5.35851i q^{88} +(1.57286 - 5.86998i) q^{89} +(5.18203 + 1.20890i) q^{91} +(2.85501 + 1.64834i) q^{92} +(-1.42501 + 2.46819i) q^{94} +12.9435 q^{95} +(-1.35706 + 5.06463i) q^{97} +(-5.54374 + 1.48544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 6 q^{2} + 6 q^{5} - 4 q^{7} - 30 q^{8} - 12 q^{10} + 6 q^{11} - 2 q^{13} + 12 q^{14} - 28 q^{16} - 4 q^{19} + 18 q^{20} - 4 q^{22} + 6 q^{23} + 48 q^{26} - 18 q^{31} - 54 q^{32} + 6 q^{34} - 6 q^{35} - 6 q^{37} - 36 q^{38} - 12 q^{40} - 18 q^{41} - 30 q^{43} - 12 q^{44} - 12 q^{46} + 36 q^{47} - 6 q^{49} + 60 q^{50} + 56 q^{52} - 4 q^{55} + 6 q^{56} + 50 q^{58} + 6 q^{59} + 2 q^{61} - 18 q^{62} - 72 q^{65} + 26 q^{67} - 42 q^{68} - 16 q^{70} + 48 q^{71} - 22 q^{73} - 30 q^{74} + 6 q^{76} - 72 q^{77} + 8 q^{79} + 54 q^{80} - 12 q^{82} - 54 q^{83} - 24 q^{85} + 54 q^{86} - 16 q^{91} - 120 q^{92} + 26 q^{94} + 12 q^{95} - 24 q^{97} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(326\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.841634 0.841634i 0.595125 0.595125i −0.343886 0.939011i \(-0.611743\pi\)
0.939011 + 0.343886i \(0.111743\pi\)
\(3\) 0 0
\(4\) 0.583303i 0.291651i
\(5\) 2.77680 + 0.744040i 1.24182 + 0.332745i 0.819172 0.573548i \(-0.194433\pi\)
0.422650 + 0.906293i \(0.361100\pi\)
\(6\) 0 0
\(7\) −1.42554 0.381973i −0.538804 0.144372i −0.0208532 0.999783i \(-0.506638\pi\)
−0.517951 + 0.855410i \(0.673305\pi\)
\(8\) 2.17420 + 2.17420i 0.768695 + 0.768695i
\(9\) 0 0
\(10\) 2.96326 1.71084i 0.937065 0.541014i
\(11\) 1.23230 + 1.23230i 0.371552 + 0.371552i 0.868042 0.496491i \(-0.165378\pi\)
−0.496491 + 0.868042i \(0.665378\pi\)
\(12\) 0 0
\(13\) −3.60363 + 0.117561i −0.999468 + 0.0326056i
\(14\) −1.52127 + 0.878303i −0.406575 + 0.234736i
\(15\) 0 0
\(16\) 2.49315 0.623288
\(17\) −0.939625 + 1.62748i −0.227893 + 0.394722i −0.957183 0.289482i \(-0.906517\pi\)
0.729291 + 0.684204i \(0.239850\pi\)
\(18\) 0 0
\(19\) 4.34907 1.16533i 0.997745 0.267345i 0.277245 0.960799i \(-0.410579\pi\)
0.720501 + 0.693454i \(0.243912\pi\)
\(20\) −0.434001 + 1.61971i −0.0970455 + 0.362179i
\(21\) 0 0
\(22\) 2.07429 0.442240
\(23\) 2.82588 4.89457i 0.589237 1.02059i −0.405096 0.914274i \(-0.632762\pi\)
0.994333 0.106314i \(-0.0339048\pi\)
\(24\) 0 0
\(25\) 2.82688 + 1.63210i 0.565376 + 0.326420i
\(26\) −2.93400 + 3.13189i −0.575405 + 0.614213i
\(27\) 0 0
\(28\) 0.222806 0.831522i 0.0421063 0.157143i
\(29\) 6.70089i 1.24432i −0.782888 0.622162i \(-0.786254\pi\)
0.782888 0.622162i \(-0.213746\pi\)
\(30\) 0 0
\(31\) 0.676611 2.52515i 0.121523 0.453530i −0.878169 0.478350i \(-0.841235\pi\)
0.999692 + 0.0248208i \(0.00790153\pi\)
\(32\) −2.25007 + 2.25007i −0.397760 + 0.397760i
\(33\) 0 0
\(34\) 0.578921 + 2.16056i 0.0992842 + 0.370534i
\(35\) −3.67424 2.12132i −0.621059 0.358569i
\(36\) 0 0
\(37\) −11.1775 2.99499i −1.83756 0.492374i −0.838912 0.544267i \(-0.816808\pi\)
−0.998653 + 0.0518927i \(0.983475\pi\)
\(38\) 2.67955 4.64111i 0.434680 0.752888i
\(39\) 0 0
\(40\) 4.41961 + 7.65499i 0.698802 + 1.21036i
\(41\) −0.168067 0.627234i −0.0262476 0.0979574i 0.951559 0.307465i \(-0.0994806\pi\)
−0.977807 + 0.209507i \(0.932814\pi\)
\(42\) 0 0
\(43\) 1.78065 1.02806i 0.271547 0.156778i −0.358044 0.933705i \(-0.616556\pi\)
0.629590 + 0.776927i \(0.283223\pi\)
\(44\) −0.718802 + 0.718802i −0.108364 + 0.108364i
\(45\) 0 0
\(46\) −1.74108 6.49779i −0.256708 0.958048i
\(47\) −2.31288 + 0.619735i −0.337369 + 0.0903977i −0.423526 0.905884i \(-0.639208\pi\)
0.0861575 + 0.996282i \(0.472541\pi\)
\(48\) 0 0
\(49\) −4.17591 2.41096i −0.596559 0.344424i
\(50\) 3.75283 1.00557i 0.530730 0.142209i
\(51\) 0 0
\(52\) −0.0685738 2.10201i −0.00950947 0.291496i
\(53\) 11.5633i 1.58834i 0.607698 + 0.794168i \(0.292093\pi\)
−0.607698 + 0.794168i \(0.707907\pi\)
\(54\) 0 0
\(55\) 2.50496 + 4.33872i 0.337769 + 0.585033i
\(56\) −2.26892 3.92989i −0.303198 0.525154i
\(57\) 0 0
\(58\) −5.63970 5.63970i −0.740529 0.740529i
\(59\) 9.15908 + 9.15908i 1.19241 + 1.19241i 0.976388 + 0.216023i \(0.0693086\pi\)
0.216023 + 0.976388i \(0.430691\pi\)
\(60\) 0 0
\(61\) −5.24278 9.08077i −0.671269 1.16267i −0.977544 0.210730i \(-0.932416\pi\)
0.306275 0.951943i \(-0.400917\pi\)
\(62\) −1.55579 2.69471i −0.197586 0.342228i
\(63\) 0 0
\(64\) 8.77378i 1.09672i
\(65\) −10.0940 2.35481i −1.25201 0.292078i
\(66\) 0 0
\(67\) 3.50643 0.939544i 0.428378 0.114784i −0.0381866 0.999271i \(-0.512158\pi\)
0.466565 + 0.884487i \(0.345491\pi\)
\(68\) −0.949313 0.548086i −0.115121 0.0664652i
\(69\) 0 0
\(70\) −4.87774 + 1.30699i −0.583001 + 0.156215i
\(71\) −2.99663 11.1836i −0.355635 1.32725i −0.879684 0.475559i \(-0.842246\pi\)
0.524049 0.851688i \(-0.324421\pi\)
\(72\) 0 0
\(73\) −8.97423 + 8.97423i −1.05035 + 1.05035i −0.0516906 + 0.998663i \(0.516461\pi\)
−0.998663 + 0.0516906i \(0.983539\pi\)
\(74\) −11.9280 + 6.88665i −1.38661 + 0.800557i
\(75\) 0 0
\(76\) 0.679740 + 2.53683i 0.0779716 + 0.290994i
\(77\) −1.28599 2.22739i −0.146552 0.253835i
\(78\) 0 0
\(79\) −4.85927 + 8.41651i −0.546711 + 0.946931i 0.451786 + 0.892126i \(0.350787\pi\)
−0.998497 + 0.0548048i \(0.982546\pi\)
\(80\) 6.92298 + 1.85501i 0.774012 + 0.207396i
\(81\) 0 0
\(82\) −0.669352 0.386451i −0.0739176 0.0426763i
\(83\) −0.712145 2.65776i −0.0781681 0.291727i 0.915765 0.401715i \(-0.131586\pi\)
−0.993933 + 0.109987i \(0.964919\pi\)
\(84\) 0 0
\(85\) −3.82006 + 3.82006i −0.414344 + 0.414344i
\(86\) 0.633407 2.36391i 0.0683020 0.254907i
\(87\) 0 0
\(88\) 5.35851i 0.571219i
\(89\) 1.57286 5.86998i 0.166722 0.622217i −0.831092 0.556135i \(-0.812284\pi\)
0.997814 0.0660814i \(-0.0210497\pi\)
\(90\) 0 0
\(91\) 5.18203 + 1.20890i 0.543225 + 0.126727i
\(92\) 2.85501 + 1.64834i 0.297656 + 0.171852i
\(93\) 0 0
\(94\) −1.42501 + 2.46819i −0.146979 + 0.254575i
\(95\) 12.9435 1.32798
\(96\) 0 0
\(97\) −1.35706 + 5.06463i −0.137789 + 0.514235i 0.862182 + 0.506599i \(0.169097\pi\)
−0.999971 + 0.00763623i \(0.997569\pi\)
\(98\) −5.54374 + 1.48544i −0.560003 + 0.150052i
\(99\) 0 0
\(100\) −0.952008 + 1.64893i −0.0952008 + 0.164893i
\(101\) 3.02851 0.301348 0.150674 0.988584i \(-0.451856\pi\)
0.150674 + 0.988584i \(0.451856\pi\)
\(102\) 0 0
\(103\) 15.9431 9.20475i 1.57092 0.906971i 0.574864 0.818249i \(-0.305055\pi\)
0.996056 0.0887220i \(-0.0282783\pi\)
\(104\) −8.09061 7.57941i −0.793350 0.743222i
\(105\) 0 0
\(106\) 9.73204 + 9.73204i 0.945259 + 0.945259i
\(107\) −3.97340 + 2.29404i −0.384123 + 0.221774i −0.679611 0.733573i \(-0.737851\pi\)
0.295487 + 0.955347i \(0.404518\pi\)
\(108\) 0 0
\(109\) 0.138592 + 0.138592i 0.0132747 + 0.0132747i 0.713713 0.700438i \(-0.247012\pi\)
−0.700438 + 0.713713i \(0.747012\pi\)
\(110\) 5.75988 + 1.54335i 0.549183 + 0.147153i
\(111\) 0 0
\(112\) −3.55409 0.952316i −0.335830 0.0899854i
\(113\) 7.46794i 0.702524i 0.936277 + 0.351262i \(0.114247\pi\)
−0.936277 + 0.351262i \(0.885753\pi\)
\(114\) 0 0
\(115\) 11.4887 11.4887i 1.07132 1.07132i
\(116\) 3.90865 0.362909
\(117\) 0 0
\(118\) 15.4172 1.41927
\(119\) 1.96113 1.96113i 0.179776 0.179776i
\(120\) 0 0
\(121\) 7.96289i 0.723899i
\(122\) −12.0552 3.23018i −1.09143 0.292447i
\(123\) 0 0
\(124\) 1.47292 + 0.394669i 0.132273 + 0.0354423i
\(125\) −3.52846 3.52846i −0.315595 0.315595i
\(126\) 0 0
\(127\) −9.37062 + 5.41013i −0.831508 + 0.480071i −0.854369 0.519667i \(-0.826056\pi\)
0.0228608 + 0.999739i \(0.492723\pi\)
\(128\) 2.88417 + 2.88417i 0.254927 + 0.254927i
\(129\) 0 0
\(130\) −10.4774 + 6.51360i −0.918926 + 0.571280i
\(131\) −6.84566 + 3.95234i −0.598108 + 0.345318i −0.768297 0.640094i \(-0.778896\pi\)
0.170189 + 0.985411i \(0.445562\pi\)
\(132\) 0 0
\(133\) −6.64490 −0.576186
\(134\) 2.16038 3.74188i 0.186628 0.323249i
\(135\) 0 0
\(136\) −5.58139 + 1.49553i −0.478600 + 0.128241i
\(137\) 2.19061 8.17545i 0.187156 0.698476i −0.807003 0.590548i \(-0.798912\pi\)
0.994159 0.107928i \(-0.0344216\pi\)
\(138\) 0 0
\(139\) 0.469919 0.0398580 0.0199290 0.999801i \(-0.493656\pi\)
0.0199290 + 0.999801i \(0.493656\pi\)
\(140\) 1.23737 2.14319i 0.104577 0.181133i
\(141\) 0 0
\(142\) −11.9346 6.89042i −1.00153 0.578231i
\(143\) −4.58562 4.29588i −0.383469 0.359239i
\(144\) 0 0
\(145\) 4.98574 18.6070i 0.414043 1.54523i
\(146\) 15.1060i 1.25018i
\(147\) 0 0
\(148\) 1.74699 6.51985i 0.143602 0.535928i
\(149\) 3.83653 3.83653i 0.314301 0.314301i −0.532272 0.846573i \(-0.678662\pi\)
0.846573 + 0.532272i \(0.178662\pi\)
\(150\) 0 0
\(151\) −5.12016 19.1087i −0.416673 1.55504i −0.781462 0.623953i \(-0.785525\pi\)
0.364789 0.931090i \(-0.381141\pi\)
\(152\) 11.9894 + 6.92208i 0.972468 + 0.561455i
\(153\) 0 0
\(154\) −2.95698 0.792321i −0.238280 0.0638470i
\(155\) 3.75762 6.50839i 0.301819 0.522767i
\(156\) 0 0
\(157\) 11.5326 + 19.9750i 0.920401 + 1.59418i 0.798796 + 0.601602i \(0.205471\pi\)
0.121605 + 0.992579i \(0.461196\pi\)
\(158\) 2.99389 + 11.1734i 0.238181 + 0.888904i
\(159\) 0 0
\(160\) −7.92213 + 4.57384i −0.626300 + 0.361594i
\(161\) −5.89800 + 5.89800i −0.464827 + 0.464827i
\(162\) 0 0
\(163\) 1.15428 + 4.30782i 0.0904100 + 0.337415i 0.996284 0.0861334i \(-0.0274511\pi\)
−0.905874 + 0.423548i \(0.860784\pi\)
\(164\) 0.365867 0.0980338i 0.0285694 0.00765515i
\(165\) 0 0
\(166\) −2.83623 1.63750i −0.220134 0.127095i
\(167\) −0.344237 + 0.0922379i −0.0266378 + 0.00713759i −0.272113 0.962265i \(-0.587723\pi\)
0.245476 + 0.969403i \(0.421056\pi\)
\(168\) 0 0
\(169\) 12.9724 0.847295i 0.997874 0.0651766i
\(170\) 6.43019i 0.493173i
\(171\) 0 0
\(172\) 0.599670 + 1.03866i 0.0457244 + 0.0791970i
\(173\) 5.94881 + 10.3036i 0.452280 + 0.783371i 0.998527 0.0542525i \(-0.0172776\pi\)
−0.546248 + 0.837624i \(0.683944\pi\)
\(174\) 0 0
\(175\) −3.40641 3.40641i −0.257501 0.257501i
\(176\) 3.07230 + 3.07230i 0.231584 + 0.231584i
\(177\) 0 0
\(178\) −3.61661 6.26415i −0.271076 0.469518i
\(179\) 2.92970 + 5.07439i 0.218976 + 0.379278i 0.954495 0.298226i \(-0.0963950\pi\)
−0.735519 + 0.677504i \(0.763062\pi\)
\(180\) 0 0
\(181\) 8.29778i 0.616769i −0.951262 0.308384i \(-0.900212\pi\)
0.951262 0.308384i \(-0.0997883\pi\)
\(182\) 5.37883 3.34393i 0.398705 0.247868i
\(183\) 0 0
\(184\) 16.7858 4.49773i 1.23746 0.331577i
\(185\) −28.8092 16.6330i −2.11809 1.22288i
\(186\) 0 0
\(187\) −3.16344 + 0.847640i −0.231333 + 0.0619856i
\(188\) −0.361493 1.34911i −0.0263646 0.0983940i
\(189\) 0 0
\(190\) 10.8937 10.8937i 0.790314 0.790314i
\(191\) 6.20085 3.58006i 0.448678 0.259044i −0.258594 0.965986i \(-0.583259\pi\)
0.707272 + 0.706942i \(0.249926\pi\)
\(192\) 0 0
\(193\) −0.709019 2.64609i −0.0510363 0.190470i 0.935701 0.352793i \(-0.114768\pi\)
−0.986738 + 0.162323i \(0.948101\pi\)
\(194\) 3.12041 + 5.40471i 0.224033 + 0.388036i
\(195\) 0 0
\(196\) 1.40632 2.43582i 0.100452 0.173987i
\(197\) 23.1428 + 6.20110i 1.64886 + 0.441810i 0.959292 0.282414i \(-0.0911353\pi\)
0.689564 + 0.724224i \(0.257802\pi\)
\(198\) 0 0
\(199\) 8.08608 + 4.66850i 0.573207 + 0.330941i 0.758429 0.651755i \(-0.225967\pi\)
−0.185222 + 0.982697i \(0.559300\pi\)
\(200\) 2.59768 + 9.69469i 0.183684 + 0.685518i
\(201\) 0 0
\(202\) 2.54890 2.54890i 0.179340 0.179340i
\(203\) −2.55956 + 9.55240i −0.179646 + 0.670447i
\(204\) 0 0
\(205\) 1.86675i 0.130379i
\(206\) 5.67122 21.1653i 0.395133 1.47466i
\(207\) 0 0
\(208\) −8.98441 + 0.293098i −0.622957 + 0.0203227i
\(209\) 6.79538 + 3.92332i 0.470046 + 0.271381i
\(210\) 0 0
\(211\) −2.60557 + 4.51298i −0.179375 + 0.310687i −0.941667 0.336547i \(-0.890741\pi\)
0.762292 + 0.647234i \(0.224074\pi\)
\(212\) −6.74488 −0.463240
\(213\) 0 0
\(214\) −1.41341 + 5.27490i −0.0966184 + 0.360585i
\(215\) 5.70942 1.52984i 0.389379 0.104334i
\(216\) 0 0
\(217\) −1.92907 + 3.34125i −0.130954 + 0.226819i
\(218\) 0.233287 0.0158002
\(219\) 0 0
\(220\) −2.53079 + 1.46115i −0.170626 + 0.0985107i
\(221\) 3.19474 5.97530i 0.214901 0.401942i
\(222\) 0 0
\(223\) 4.83926 + 4.83926i 0.324061 + 0.324061i 0.850323 0.526262i \(-0.176407\pi\)
−0.526262 + 0.850323i \(0.676407\pi\)
\(224\) 4.06703 2.34810i 0.271740 0.156889i
\(225\) 0 0
\(226\) 6.28527 + 6.28527i 0.418090 + 0.418090i
\(227\) 12.3360 + 3.30542i 0.818769 + 0.219389i 0.643808 0.765187i \(-0.277353\pi\)
0.174961 + 0.984575i \(0.444020\pi\)
\(228\) 0 0
\(229\) 17.6101 + 4.71861i 1.16371 + 0.311815i 0.788446 0.615104i \(-0.210886\pi\)
0.375263 + 0.926919i \(0.377553\pi\)
\(230\) 19.3385i 1.27514i
\(231\) 0 0
\(232\) 14.5691 14.5691i 0.956506 0.956506i
\(233\) −4.27048 −0.279769 −0.139884 0.990168i \(-0.544673\pi\)
−0.139884 + 0.990168i \(0.544673\pi\)
\(234\) 0 0
\(235\) −6.88351 −0.449031
\(236\) −5.34252 + 5.34252i −0.347768 + 0.347768i
\(237\) 0 0
\(238\) 3.30110i 0.213979i
\(239\) 1.08816 + 0.291572i 0.0703874 + 0.0188603i 0.293841 0.955854i \(-0.405066\pi\)
−0.223453 + 0.974715i \(0.571733\pi\)
\(240\) 0 0
\(241\) 8.52710 + 2.28483i 0.549279 + 0.147179i 0.522776 0.852470i \(-0.324896\pi\)
0.0265026 + 0.999649i \(0.491563\pi\)
\(242\) −6.70184 6.70184i −0.430811 0.430811i
\(243\) 0 0
\(244\) 5.29684 3.05813i 0.339095 0.195777i
\(245\) −9.80181 9.80181i −0.626215 0.626215i
\(246\) 0 0
\(247\) −15.5355 + 4.71071i −0.988498 + 0.299735i
\(248\) 6.96125 4.01908i 0.442040 0.255212i
\(249\) 0 0
\(250\) −5.93935 −0.375638
\(251\) −8.72352 + 15.1096i −0.550624 + 0.953708i 0.447606 + 0.894231i \(0.352277\pi\)
−0.998230 + 0.0594773i \(0.981057\pi\)
\(252\) 0 0
\(253\) 9.51388 2.54924i 0.598133 0.160269i
\(254\) −3.33328 + 12.4400i −0.209149 + 0.780554i
\(255\) 0 0
\(256\) −12.6927 −0.793295
\(257\) −1.62517 + 2.81488i −0.101376 + 0.175588i −0.912252 0.409630i \(-0.865658\pi\)
0.810876 + 0.585218i \(0.198991\pi\)
\(258\) 0 0
\(259\) 14.7899 + 8.53897i 0.919002 + 0.530586i
\(260\) 1.37356 5.88788i 0.0851849 0.365151i
\(261\) 0 0
\(262\) −2.43511 + 9.08797i −0.150442 + 0.561457i
\(263\) 18.0770i 1.11467i 0.830286 + 0.557337i \(0.188177\pi\)
−0.830286 + 0.557337i \(0.811823\pi\)
\(264\) 0 0
\(265\) −8.60353 + 32.1088i −0.528511 + 1.97243i
\(266\) −5.59258 + 5.59258i −0.342903 + 0.342903i
\(267\) 0 0
\(268\) 0.548039 + 2.04531i 0.0334768 + 0.124937i
\(269\) 0.992035 + 0.572752i 0.0604854 + 0.0349213i 0.529938 0.848037i \(-0.322215\pi\)
−0.469452 + 0.882958i \(0.655549\pi\)
\(270\) 0 0
\(271\) −8.64641 2.31680i −0.525232 0.140736i −0.0135464 0.999908i \(-0.504312\pi\)
−0.511686 + 0.859173i \(0.670979\pi\)
\(272\) −2.34263 + 4.05755i −0.142043 + 0.246025i
\(273\) 0 0
\(274\) −5.03705 8.72443i −0.304299 0.527062i
\(275\) 1.47232 + 5.49478i 0.0887844 + 0.331348i
\(276\) 0 0
\(277\) −22.2593 + 12.8514i −1.33743 + 0.772165i −0.986426 0.164209i \(-0.947493\pi\)
−0.351003 + 0.936374i \(0.614159\pi\)
\(278\) 0.395500 0.395500i 0.0237205 0.0237205i
\(279\) 0 0
\(280\) −3.37634 12.6007i −0.201775 0.753035i
\(281\) −0.868838 + 0.232804i −0.0518305 + 0.0138879i −0.284641 0.958634i \(-0.591874\pi\)
0.232811 + 0.972522i \(0.425208\pi\)
\(282\) 0 0
\(283\) −15.7574 9.09752i −0.936678 0.540791i −0.0477608 0.998859i \(-0.515209\pi\)
−0.888917 + 0.458067i \(0.848542\pi\)
\(284\) 6.52341 1.74794i 0.387093 0.103721i
\(285\) 0 0
\(286\) −7.47497 + 0.243856i −0.442004 + 0.0144195i
\(287\) 0.958344i 0.0565693i
\(288\) 0 0
\(289\) 6.73421 + 11.6640i 0.396130 + 0.686117i
\(290\) −11.4641 19.8565i −0.673198 1.16601i
\(291\) 0 0
\(292\) −5.23469 5.23469i −0.306337 0.306337i
\(293\) 3.24724 + 3.24724i 0.189706 + 0.189706i 0.795569 0.605863i \(-0.207172\pi\)
−0.605863 + 0.795569i \(0.707172\pi\)
\(294\) 0 0
\(295\) 18.6182 + 32.2476i 1.08399 + 1.87753i
\(296\) −17.7903 30.8137i −1.03404 1.79101i
\(297\) 0 0
\(298\) 6.45792i 0.374097i
\(299\) −9.60803 + 17.9704i −0.555646 + 1.03926i
\(300\) 0 0
\(301\) −2.93108 + 0.785381i −0.168945 + 0.0452686i
\(302\) −20.3918 11.7732i −1.17342 0.677474i
\(303\) 0 0
\(304\) 10.8429 2.90535i 0.621883 0.166633i
\(305\) −7.80168 29.1163i −0.446723 1.66719i
\(306\) 0 0
\(307\) 3.93098 3.93098i 0.224353 0.224353i −0.585976 0.810329i \(-0.699289\pi\)
0.810329 + 0.585976i \(0.199289\pi\)
\(308\) 1.29925 0.750119i 0.0740314 0.0427420i
\(309\) 0 0
\(310\) −2.31514 8.64023i −0.131491 0.490732i
\(311\) 10.9466 + 18.9600i 0.620724 + 1.07513i 0.989351 + 0.145548i \(0.0464945\pi\)
−0.368627 + 0.929577i \(0.620172\pi\)
\(312\) 0 0
\(313\) −3.78444 + 6.55485i −0.213909 + 0.370502i −0.952935 0.303176i \(-0.901953\pi\)
0.739025 + 0.673678i \(0.235286\pi\)
\(314\) 26.5179 + 7.10545i 1.49649 + 0.400984i
\(315\) 0 0
\(316\) −4.90937 2.83443i −0.276174 0.159449i
\(317\) −7.64018 28.5136i −0.429116 1.60148i −0.754768 0.655992i \(-0.772251\pi\)
0.325653 0.945489i \(-0.394416\pi\)
\(318\) 0 0
\(319\) 8.25749 8.25749i 0.462331 0.462331i
\(320\) −6.52805 + 24.3630i −0.364929 + 1.36193i
\(321\) 0 0
\(322\) 9.92792i 0.553261i
\(323\) −2.18995 + 8.17300i −0.121852 + 0.454758i
\(324\) 0 0
\(325\) −10.3789 5.54916i −0.575718 0.307812i
\(326\) 4.59709 + 2.65413i 0.254609 + 0.146999i
\(327\) 0 0
\(328\) 0.998319 1.72914i 0.0551230 0.0954758i
\(329\) 3.53383 0.194826
\(330\) 0 0
\(331\) 4.98513 18.6048i 0.274008 1.02261i −0.682496 0.730890i \(-0.739105\pi\)
0.956503 0.291721i \(-0.0942280\pi\)
\(332\) 1.55028 0.415396i 0.0850827 0.0227978i
\(333\) 0 0
\(334\) −0.212091 + 0.367352i −0.0116051 + 0.0201006i
\(335\) 10.4357 0.570163
\(336\) 0 0
\(337\) −15.6291 + 9.02348i −0.851373 + 0.491541i −0.861114 0.508412i \(-0.830233\pi\)
0.00974077 + 0.999953i \(0.496899\pi\)
\(338\) 10.2049 11.6311i 0.555072 0.632648i
\(339\) 0 0
\(340\) −2.22825 2.22825i −0.120844 0.120844i
\(341\) 3.94552 2.27794i 0.213662 0.123358i
\(342\) 0 0
\(343\) 12.3370 + 12.3370i 0.666135 + 0.666135i
\(344\) 6.10669 + 1.63628i 0.329251 + 0.0882224i
\(345\) 0 0
\(346\) 13.6786 + 3.66518i 0.735367 + 0.197041i
\(347\) 25.1292i 1.34901i −0.738272 0.674503i \(-0.764358\pi\)
0.738272 0.674503i \(-0.235642\pi\)
\(348\) 0 0
\(349\) −16.5014 + 16.5014i −0.883300 + 0.883300i −0.993868 0.110569i \(-0.964733\pi\)
0.110569 + 0.993868i \(0.464733\pi\)
\(350\) −5.73391 −0.306490
\(351\) 0 0
\(352\) −5.54551 −0.295577
\(353\) −14.1500 + 14.1500i −0.753127 + 0.753127i −0.975061 0.221935i \(-0.928763\pi\)
0.221935 + 0.975061i \(0.428763\pi\)
\(354\) 0 0
\(355\) 33.2841i 1.76654i
\(356\) 3.42398 + 0.917452i 0.181470 + 0.0486248i
\(357\) 0 0
\(358\) 6.73652 + 1.80504i 0.356036 + 0.0953996i
\(359\) 1.97346 + 1.97346i 0.104155 + 0.104155i 0.757264 0.653109i \(-0.226536\pi\)
−0.653109 + 0.757264i \(0.726536\pi\)
\(360\) 0 0
\(361\) 1.10195 0.636209i 0.0579972 0.0334847i
\(362\) −6.98370 6.98370i −0.367055 0.367055i
\(363\) 0 0
\(364\) −0.705155 + 3.02269i −0.0369602 + 0.158432i
\(365\) −31.5968 + 18.2424i −1.65385 + 0.954852i
\(366\) 0 0
\(367\) −32.9892 −1.72202 −0.861011 0.508587i \(-0.830168\pi\)
−0.861011 + 0.508587i \(0.830168\pi\)
\(368\) 7.04535 12.2029i 0.367264 0.636120i
\(369\) 0 0
\(370\) −38.2457 + 10.2479i −1.98830 + 0.532763i
\(371\) 4.41685 16.4839i 0.229311 0.855802i
\(372\) 0 0
\(373\) −4.70461 −0.243596 −0.121798 0.992555i \(-0.538866\pi\)
−0.121798 + 0.992555i \(0.538866\pi\)
\(374\) −1.94905 + 3.37586i −0.100783 + 0.174562i
\(375\) 0 0
\(376\) −6.37609 3.68124i −0.328822 0.189845i
\(377\) 0.787765 + 24.1476i 0.0405720 + 1.24366i
\(378\) 0 0
\(379\) 5.09903 19.0299i 0.261920 0.977498i −0.702189 0.711991i \(-0.747794\pi\)
0.964109 0.265507i \(-0.0855394\pi\)
\(380\) 7.55000i 0.387307i
\(381\) 0 0
\(382\) 2.20574 8.23195i 0.112856 0.421183i
\(383\) −4.04582 + 4.04582i −0.206732 + 0.206732i −0.802877 0.596145i \(-0.796698\pi\)
0.596145 + 0.802877i \(0.296698\pi\)
\(384\) 0 0
\(385\) −1.91365 7.14185i −0.0975287 0.363982i
\(386\) −2.82378 1.63031i −0.143727 0.0829806i
\(387\) 0 0
\(388\) −2.95421 0.791578i −0.149977 0.0401863i
\(389\) −8.59884 + 14.8936i −0.435978 + 0.755137i −0.997375 0.0724102i \(-0.976931\pi\)
0.561397 + 0.827547i \(0.310264\pi\)
\(390\) 0 0
\(391\) 5.31054 + 9.19812i 0.268565 + 0.465169i
\(392\) −3.83735 14.3212i −0.193815 0.723328i
\(393\) 0 0
\(394\) 24.6968 14.2587i 1.24421 0.718344i
\(395\) −19.7554 + 19.7554i −0.994004 + 0.994004i
\(396\) 0 0
\(397\) −0.701121 2.61662i −0.0351882 0.131324i 0.946097 0.323882i \(-0.104988\pi\)
−0.981286 + 0.192558i \(0.938322\pi\)
\(398\) 10.7347 2.87635i 0.538082 0.144179i
\(399\) 0 0
\(400\) 7.04784 + 4.06907i 0.352392 + 0.203454i
\(401\) −7.48577 + 2.00581i −0.373822 + 0.100165i −0.440838 0.897587i \(-0.645319\pi\)
0.0670163 + 0.997752i \(0.478652\pi\)
\(402\) 0 0
\(403\) −2.14140 + 9.17925i −0.106671 + 0.457251i
\(404\) 1.76654i 0.0878886i
\(405\) 0 0
\(406\) 5.88542 + 10.1938i 0.292088 + 0.505912i
\(407\) −10.0832 17.4647i −0.499808 0.865692i
\(408\) 0 0
\(409\) −5.60298 5.60298i −0.277050 0.277050i 0.554880 0.831930i \(-0.312764\pi\)
−0.831930 + 0.554880i \(0.812764\pi\)
\(410\) −1.57112 1.57112i −0.0775921 0.0775921i
\(411\) 0 0
\(412\) 5.36916 + 9.29965i 0.264519 + 0.458161i
\(413\) −9.55813 16.5552i −0.470325 0.814627i
\(414\) 0 0
\(415\) 7.90993i 0.388283i
\(416\) 7.84391 8.37295i 0.384579 0.410518i
\(417\) 0 0
\(418\) 9.02123 2.41723i 0.441243 0.118231i
\(419\) 26.4028 + 15.2436i 1.28986 + 0.744700i 0.978629 0.205634i \(-0.0659257\pi\)
0.311230 + 0.950335i \(0.399259\pi\)
\(420\) 0 0
\(421\) −7.53981 + 2.02029i −0.367468 + 0.0984628i −0.437828 0.899059i \(-0.644252\pi\)
0.0703596 + 0.997522i \(0.477585\pi\)
\(422\) 1.60534 + 5.99122i 0.0781469 + 0.291648i
\(423\) 0 0
\(424\) −25.1408 + 25.1408i −1.22095 + 1.22095i
\(425\) −5.31241 + 3.06712i −0.257690 + 0.148777i
\(426\) 0 0
\(427\) 4.00520 + 14.9476i 0.193825 + 0.723365i
\(428\) −1.33812 2.31770i −0.0646806 0.112030i
\(429\) 0 0
\(430\) 3.51769 6.09281i 0.169638 0.293821i
\(431\) −30.9395 8.29022i −1.49030 0.399326i −0.580465 0.814285i \(-0.697129\pi\)
−0.909840 + 0.414960i \(0.863796\pi\)
\(432\) 0 0
\(433\) 19.6303 + 11.3335i 0.943371 + 0.544655i 0.891015 0.453973i \(-0.149994\pi\)
0.0523555 + 0.998629i \(0.483327\pi\)
\(434\) 1.18854 + 4.43569i 0.0570517 + 0.212920i
\(435\) 0 0
\(436\) −0.0808408 + 0.0808408i −0.00387157 + 0.00387157i
\(437\) 6.58617 24.5799i 0.315059 1.17582i
\(438\) 0 0
\(439\) 32.3810i 1.54546i −0.634735 0.772730i \(-0.718891\pi\)
0.634735 0.772730i \(-0.281109\pi\)
\(440\) −3.98695 + 14.8795i −0.190070 + 0.709352i
\(441\) 0 0
\(442\) −2.34022 7.71782i −0.111313 0.367099i
\(443\) −21.0067 12.1282i −0.998059 0.576230i −0.0903854 0.995907i \(-0.528810\pi\)
−0.907673 + 0.419677i \(0.862143\pi\)
\(444\) 0 0
\(445\) 8.73501 15.1295i 0.414079 0.717206i
\(446\) 8.14578 0.385714
\(447\) 0 0
\(448\) 3.35134 12.5074i 0.158336 0.590918i
\(449\) 10.4048 2.78796i 0.491032 0.131572i −0.00480262 0.999988i \(-0.501529\pi\)
0.495835 + 0.868417i \(0.334862\pi\)
\(450\) 0 0
\(451\) 0.565830 0.980046i 0.0266439 0.0461486i
\(452\) −4.35607 −0.204892
\(453\) 0 0
\(454\) 13.1644 7.60045i 0.617834 0.356707i
\(455\) 13.4900 + 7.21252i 0.632420 + 0.338128i
\(456\) 0 0
\(457\) −17.0357 17.0357i −0.796895 0.796895i 0.185710 0.982605i \(-0.440541\pi\)
−0.982605 + 0.185710i \(0.940541\pi\)
\(458\) 18.7926 10.8499i 0.878122 0.506984i
\(459\) 0 0
\(460\) 6.70136 + 6.70136i 0.312453 + 0.312453i
\(461\) −2.85339 0.764563i −0.132896 0.0356092i 0.191758 0.981442i \(-0.438581\pi\)
−0.324654 + 0.945833i \(0.605248\pi\)
\(462\) 0 0
\(463\) 1.79433 + 0.480789i 0.0833896 + 0.0223442i 0.300273 0.953853i \(-0.402922\pi\)
−0.216883 + 0.976198i \(0.569589\pi\)
\(464\) 16.7064i 0.775573i
\(465\) 0 0
\(466\) −3.59419 + 3.59419i −0.166497 + 0.166497i
\(467\) 16.0374 0.742122 0.371061 0.928608i \(-0.378994\pi\)
0.371061 + 0.928608i \(0.378994\pi\)
\(468\) 0 0
\(469\) −5.35743 −0.247383
\(470\) −5.79340 + 5.79340i −0.267230 + 0.267230i
\(471\) 0 0
\(472\) 39.8273i 1.83320i
\(473\) 3.46117 + 0.927416i 0.159145 + 0.0426427i
\(474\) 0 0
\(475\) 14.1962 + 3.80387i 0.651368 + 0.174533i
\(476\) 1.14393 + 1.14393i 0.0524320 + 0.0524320i
\(477\) 0 0
\(478\) 1.16123 0.670438i 0.0531136 0.0306651i
\(479\) 26.1930 + 26.1930i 1.19679 + 1.19679i 0.975123 + 0.221664i \(0.0711489\pi\)
0.221664 + 0.975123i \(0.428851\pi\)
\(480\) 0 0
\(481\) 40.6316 + 9.47883i 1.85264 + 0.432197i
\(482\) 9.09969 5.25371i 0.414480 0.239300i
\(483\) 0 0
\(484\) 4.64477 0.211126
\(485\) −7.53657 + 13.0537i −0.342218 + 0.592739i
\(486\) 0 0
\(487\) 19.5635 5.24201i 0.886505 0.237538i 0.213293 0.976988i \(-0.431581\pi\)
0.673212 + 0.739450i \(0.264914\pi\)
\(488\) 8.34453 31.1422i 0.377739 1.40974i
\(489\) 0 0
\(490\) −16.4991 −0.745352
\(491\) −5.66933 + 9.81958i −0.255854 + 0.443151i −0.965127 0.261782i \(-0.915690\pi\)
0.709273 + 0.704933i \(0.249023\pi\)
\(492\) 0 0
\(493\) 10.9056 + 6.29633i 0.491162 + 0.283572i
\(494\) −9.11049 + 17.0399i −0.409900 + 0.766660i
\(495\) 0 0
\(496\) 1.68689 6.29557i 0.0757438 0.282680i
\(497\) 17.0873i 0.766469i
\(498\) 0 0
\(499\) −1.32264 + 4.93618i −0.0592097 + 0.220974i −0.989191 0.146634i \(-0.953156\pi\)
0.929981 + 0.367607i \(0.119823\pi\)
\(500\) 2.05816 2.05816i 0.0920438 0.0920438i
\(501\) 0 0
\(502\) 5.37473 + 20.0588i 0.239886 + 0.895266i
\(503\) 16.1644 + 9.33251i 0.720734 + 0.416116i 0.815023 0.579429i \(-0.196724\pi\)
−0.0942889 + 0.995545i \(0.530058\pi\)
\(504\) 0 0
\(505\) 8.40956 + 2.25333i 0.374220 + 0.100272i
\(506\) 5.86169 10.1527i 0.260584 0.451344i
\(507\) 0 0
\(508\) −3.15574 5.46591i −0.140013 0.242510i
\(509\) −0.836359 3.12134i −0.0370710 0.138351i 0.944910 0.327330i \(-0.106149\pi\)
−0.981981 + 0.188979i \(0.939482\pi\)
\(510\) 0 0
\(511\) 16.2210 9.36522i 0.717576 0.414293i
\(512\) −16.4510 + 16.4510i −0.727037 + 0.727037i
\(513\) 0 0
\(514\) 1.00130 + 3.73691i 0.0441655 + 0.164828i
\(515\) 51.1195 13.6974i 2.25259 0.603580i
\(516\) 0 0
\(517\) −3.61386 2.08646i −0.158937 0.0917625i
\(518\) 19.6344 5.26103i 0.862687 0.231156i
\(519\) 0 0
\(520\) −16.8266 27.0662i −0.737895 1.18693i
\(521\) 21.9128i 0.960018i 0.877263 + 0.480009i \(0.159367\pi\)
−0.877263 + 0.480009i \(0.840633\pi\)
\(522\) 0 0
\(523\) 9.66002 + 16.7316i 0.422403 + 0.731624i 0.996174 0.0873922i \(-0.0278533\pi\)
−0.573771 + 0.819016i \(0.694520\pi\)
\(524\) −2.30541 3.99309i −0.100712 0.174439i
\(525\) 0 0
\(526\) 15.2142 + 15.2142i 0.663371 + 0.663371i
\(527\) 3.47386 + 3.47386i 0.151324 + 0.151324i
\(528\) 0 0
\(529\) −4.47119 7.74433i −0.194400 0.336710i
\(530\) 19.7829 + 34.2649i 0.859313 + 1.48837i
\(531\) 0 0
\(532\) 3.87599i 0.168046i
\(533\) 0.679389 + 2.24056i 0.0294276 + 0.0970495i
\(534\) 0 0
\(535\) −12.7402 + 3.41372i −0.550807 + 0.147588i
\(536\) 9.66641 + 5.58091i 0.417525 + 0.241058i
\(537\) 0 0
\(538\) 1.31698 0.352883i 0.0567790 0.0152139i
\(539\) −2.17494 8.11699i −0.0936814 0.349624i
\(540\) 0 0
\(541\) −1.88126 + 1.88126i −0.0808815 + 0.0808815i −0.746390 0.665509i \(-0.768215\pi\)
0.665509 + 0.746390i \(0.268215\pi\)
\(542\) −9.22702 + 5.32722i −0.396334 + 0.228824i
\(543\) 0 0
\(544\) −1.54772 5.77617i −0.0663579 0.247651i
\(545\) 0.281723 + 0.487958i 0.0120677 + 0.0209018i
\(546\) 0 0
\(547\) 14.0438 24.3246i 0.600469 1.04004i −0.392281 0.919846i \(-0.628314\pi\)
0.992750 0.120198i \(-0.0383529\pi\)
\(548\) 4.76876 + 1.27779i 0.203711 + 0.0545843i
\(549\) 0 0
\(550\) 5.86376 + 3.38544i 0.250031 + 0.144356i
\(551\) −7.80876 29.1427i −0.332664 1.24152i
\(552\) 0 0
\(553\) 10.1420 10.1420i 0.431280 0.431280i
\(554\) −7.91798 + 29.5503i −0.336403 + 1.25547i
\(555\) 0 0
\(556\) 0.274105i 0.0116246i
\(557\) 3.91190 14.5994i 0.165753 0.618597i −0.832190 0.554490i \(-0.812913\pi\)
0.997943 0.0641073i \(-0.0204200\pi\)
\(558\) 0 0
\(559\) −6.29595 + 3.91408i −0.266290 + 0.165548i
\(560\) −9.16043 5.28878i −0.387099 0.223492i
\(561\) 0 0
\(562\) −0.535308 + 0.927180i −0.0225806 + 0.0391107i
\(563\) 25.4105 1.07093 0.535463 0.844558i \(-0.320137\pi\)
0.535463 + 0.844558i \(0.320137\pi\)
\(564\) 0 0
\(565\) −5.55645 + 20.7369i −0.233762 + 0.872410i
\(566\) −20.9187 + 5.60516i −0.879280 + 0.235602i
\(567\) 0 0
\(568\) 17.8000 30.8306i 0.746873 1.29362i
\(569\) −25.0364 −1.04958 −0.524789 0.851232i \(-0.675856\pi\)
−0.524789 + 0.851232i \(0.675856\pi\)
\(570\) 0 0
\(571\) −23.2909 + 13.4470i −0.974693 + 0.562739i −0.900664 0.434517i \(-0.856919\pi\)
−0.0740294 + 0.997256i \(0.523586\pi\)
\(572\) 2.50580 2.67480i 0.104773 0.111839i
\(573\) 0 0
\(574\) 0.806576 + 0.806576i 0.0336658 + 0.0336658i
\(575\) 15.9768 9.22423i 0.666280 0.384677i
\(576\) 0 0
\(577\) −12.8490 12.8490i −0.534912 0.534912i 0.387118 0.922030i \(-0.373470\pi\)
−0.922030 + 0.387118i \(0.873470\pi\)
\(578\) 15.4846 + 4.14907i 0.644073 + 0.172579i
\(579\) 0 0
\(580\) 10.8535 + 2.90819i 0.450668 + 0.120756i
\(581\) 4.06077i 0.168469i
\(582\) 0 0
\(583\) −14.2494 + 14.2494i −0.590149 + 0.590149i
\(584\) −39.0235 −1.61480
\(585\) 0 0
\(586\) 5.46598 0.225797
\(587\) 10.0666 10.0666i 0.415495 0.415495i −0.468153 0.883648i \(-0.655080\pi\)
0.883648 + 0.468153i \(0.155080\pi\)
\(588\) 0 0
\(589\) 11.7705i 0.484996i
\(590\) 42.8104 + 11.4710i 1.76248 + 0.472255i
\(591\) 0 0
\(592\) −27.8671 7.46698i −1.14533 0.306891i
\(593\) 14.8629 + 14.8629i 0.610345 + 0.610345i 0.943036 0.332691i \(-0.107957\pi\)
−0.332691 + 0.943036i \(0.607957\pi\)
\(594\) 0 0
\(595\) 6.90481 3.98649i 0.283070 0.163430i
\(596\) 2.23786 + 2.23786i 0.0916664 + 0.0916664i
\(597\) 0 0
\(598\) 7.03810 + 23.2110i 0.287809 + 0.949168i
\(599\) 29.6012 17.0903i 1.20947 0.698289i 0.246828 0.969059i \(-0.420612\pi\)
0.962644 + 0.270770i \(0.0872783\pi\)
\(600\) 0 0
\(601\) 8.94270 0.364780 0.182390 0.983226i \(-0.441617\pi\)
0.182390 + 0.983226i \(0.441617\pi\)
\(602\) −1.80590 + 3.12790i −0.0736028 + 0.127484i
\(603\) 0 0
\(604\) 11.1462 2.98660i 0.453531 0.121523i
\(605\) 5.92471 22.1113i 0.240874 0.898953i
\(606\) 0 0
\(607\) 9.16628 0.372048 0.186024 0.982545i \(-0.440440\pi\)
0.186024 + 0.982545i \(0.440440\pi\)
\(608\) −7.16364 + 12.4078i −0.290524 + 0.503202i
\(609\) 0 0
\(610\) −31.0714 17.9391i −1.25805 0.726333i
\(611\) 8.26193 2.50520i 0.334242 0.101350i
\(612\) 0 0
\(613\) −0.197913 + 0.738622i −0.00799364 + 0.0298327i −0.969807 0.243872i \(-0.921582\pi\)
0.961814 + 0.273705i \(0.0882490\pi\)
\(614\) 6.61690i 0.267037i
\(615\) 0 0
\(616\) 2.04680 7.63878i 0.0824681 0.307775i
\(617\) −11.7973 + 11.7973i −0.474940 + 0.474940i −0.903509 0.428569i \(-0.859018\pi\)
0.428569 + 0.903509i \(0.359018\pi\)
\(618\) 0 0
\(619\) −0.995076 3.71367i −0.0399955 0.149265i 0.943041 0.332678i \(-0.107952\pi\)
−0.983036 + 0.183413i \(0.941286\pi\)
\(620\) 3.79636 + 2.19183i 0.152466 + 0.0880261i
\(621\) 0 0
\(622\) 25.1704 + 6.74440i 1.00924 + 0.270426i
\(623\) −4.48434 + 7.76711i −0.179661 + 0.311183i
\(624\) 0 0
\(625\) −15.3330 26.5575i −0.613320 1.06230i
\(626\) 2.33167 + 8.70190i 0.0931922 + 0.347798i
\(627\) 0 0
\(628\) −11.6515 + 6.72699i −0.464945 + 0.268436i
\(629\) 15.3769 15.3769i 0.613118 0.613118i
\(630\) 0 0
\(631\) 3.46710 + 12.9394i 0.138023 + 0.515110i 0.999967 + 0.00810607i \(0.00258027\pi\)
−0.861944 + 0.507004i \(0.830753\pi\)
\(632\) −28.8642 + 7.73413i −1.14815 + 0.307647i
\(633\) 0 0
\(634\) −30.4282 17.5678i −1.20846 0.697705i
\(635\) −30.0457 + 8.05071i −1.19233 + 0.319483i
\(636\) 0 0
\(637\) 15.3319 + 8.19731i 0.607472 + 0.324789i
\(638\) 13.8996i 0.550290i
\(639\) 0 0
\(640\) 5.86282 + 10.1547i 0.231748 + 0.401400i
\(641\) 12.7444 + 22.0740i 0.503375 + 0.871870i 0.999992 + 0.00390095i \(0.00124172\pi\)
−0.496618 + 0.867969i \(0.665425\pi\)
\(642\) 0 0
\(643\) −3.94884 3.94884i −0.155727 0.155727i 0.624943 0.780670i \(-0.285122\pi\)
−0.780670 + 0.624943i \(0.785122\pi\)
\(644\) −3.44032 3.44032i −0.135568 0.135568i
\(645\) 0 0
\(646\) 5.03554 + 8.72181i 0.198121 + 0.343155i
\(647\) −1.23117 2.13245i −0.0484024 0.0838354i 0.840809 0.541332i \(-0.182080\pi\)
−0.889212 + 0.457496i \(0.848746\pi\)
\(648\) 0 0
\(649\) 22.5734i 0.886085i
\(650\) −13.4056 + 4.06488i −0.525811 + 0.159438i
\(651\) 0 0
\(652\) −2.51276 + 0.673293i −0.0984075 + 0.0263682i
\(653\) −27.7948 16.0473i −1.08769 0.627981i −0.154733 0.987956i \(-0.549452\pi\)
−0.932962 + 0.359975i \(0.882785\pi\)
\(654\) 0 0
\(655\) −21.9497 + 5.88141i −0.857646 + 0.229806i
\(656\) −0.419016 1.56379i −0.0163598 0.0610557i
\(657\) 0 0
\(658\) 2.97419 2.97419i 0.115946 0.115946i
\(659\) −4.60604 + 2.65930i −0.179426 + 0.103591i −0.587023 0.809570i \(-0.699700\pi\)
0.407597 + 0.913162i \(0.366367\pi\)
\(660\) 0 0
\(661\) −5.92362 22.1073i −0.230402 0.859872i −0.980168 0.198169i \(-0.936500\pi\)
0.749766 0.661703i \(-0.230166\pi\)
\(662\) −11.4628 19.8541i −0.445513 0.771651i
\(663\) 0 0
\(664\) 4.23015 7.32684i 0.164162 0.284337i
\(665\) −18.4516 4.94408i −0.715520 0.191723i
\(666\) 0 0
\(667\) −32.7980 18.9359i −1.26994 0.733202i
\(668\) −0.0538026 0.200794i −0.00208169 0.00776896i
\(669\) 0 0
\(670\) 8.78304 8.78304i 0.339318 0.339318i
\(671\) 4.72954 17.6509i 0.182582 0.681404i
\(672\) 0 0
\(673\) 28.4168i 1.09539i 0.836679 + 0.547693i \(0.184494\pi\)
−0.836679 + 0.547693i \(0.815506\pi\)
\(674\) −5.55954 + 20.7485i −0.214146 + 0.799202i
\(675\) 0 0
\(676\) 0.494230 + 7.56681i 0.0190088 + 0.291031i
\(677\) −19.5004 11.2586i −0.749461 0.432701i 0.0760383 0.997105i \(-0.475773\pi\)
−0.825499 + 0.564404i \(0.809106\pi\)
\(678\) 0 0
\(679\) 3.86910 6.70147i 0.148482 0.257179i
\(680\) −16.6111 −0.637007
\(681\) 0 0
\(682\) 1.40349 5.23788i 0.0537422 0.200569i
\(683\) −38.9958 + 10.4489i −1.49213 + 0.399816i −0.910457 0.413604i \(-0.864270\pi\)
−0.581677 + 0.813420i \(0.697603\pi\)
\(684\) 0 0
\(685\) 12.1657 21.0717i 0.464829 0.805107i
\(686\) 20.7665 0.792868
\(687\) 0 0
\(688\) 4.43943 2.56311i 0.169252 0.0977176i
\(689\) −1.35939 41.6698i −0.0517887 1.58749i
\(690\) 0 0
\(691\) 23.7637 + 23.7637i 0.904015 + 0.904015i 0.995781 0.0917661i \(-0.0292512\pi\)
−0.0917661 + 0.995781i \(0.529251\pi\)
\(692\) −6.01014 + 3.46996i −0.228471 + 0.131908i
\(693\) 0 0
\(694\) −21.1496 21.1496i −0.802828 0.802828i
\(695\) 1.30487 + 0.349639i 0.0494965 + 0.0132625i
\(696\) 0 0
\(697\) 1.17873 + 0.315840i 0.0446476 + 0.0119633i
\(698\) 27.7763i 1.05135i
\(699\) 0 0
\(700\) 1.98697 1.98697i 0.0751004 0.0751004i
\(701\) 34.8493 1.31624 0.658120 0.752913i \(-0.271352\pi\)
0.658120 + 0.752913i \(0.271352\pi\)
\(702\) 0 0
\(703\) −52.1018 −1.96506
\(704\) −10.8119 + 10.8119i −0.407489 + 0.407489i
\(705\) 0 0
\(706\) 23.8182i 0.896410i
\(707\) −4.31727 1.15681i −0.162367 0.0435062i
\(708\) 0 0
\(709\) 8.53384 + 2.28664i 0.320495 + 0.0858764i 0.415480 0.909602i \(-0.363614\pi\)
−0.0949849 + 0.995479i \(0.530280\pi\)
\(710\) −28.0131 28.0131i −1.05131 1.05131i
\(711\) 0 0
\(712\) 16.1822 9.34279i 0.606453 0.350136i
\(713\) −10.4475 10.4475i −0.391261 0.391261i
\(714\) 0 0
\(715\) −9.53702 15.3407i −0.356664 0.573708i
\(716\) −2.95991 + 1.70890i −0.110617 + 0.0638647i
\(717\) 0 0
\(718\) 3.32187 0.123971
\(719\) −12.4677 + 21.5947i −0.464966 + 0.805345i −0.999200 0.0399915i \(-0.987267\pi\)
0.534234 + 0.845337i \(0.320600\pi\)
\(720\) 0 0
\(721\) −26.2435 + 7.03193i −0.977359 + 0.261883i
\(722\) 0.391981 1.46289i 0.0145880 0.0544432i
\(723\) 0 0
\(724\) 4.84012 0.179882
\(725\) 10.9365 18.9426i 0.406172 0.703511i
\(726\) 0 0
\(727\) 15.7972 + 9.12055i 0.585888 + 0.338262i 0.763470 0.645844i \(-0.223494\pi\)
−0.177582 + 0.984106i \(0.556828\pi\)
\(728\) 8.63837 + 13.8951i 0.320159 + 0.514989i
\(729\) 0 0
\(730\) −11.2395 + 41.9464i −0.415993 + 1.55251i
\(731\) 3.86396i 0.142914i
\(732\) 0 0
\(733\) 5.98357 22.3310i 0.221008 0.824814i −0.762956 0.646450i \(-0.776253\pi\)
0.983965 0.178364i \(-0.0570805\pi\)
\(734\) −27.7648 + 27.7648i −1.02482 + 1.02482i
\(735\) 0 0
\(736\) 4.65469 + 17.3715i 0.171574 + 0.640324i
\(737\) 5.47876 + 3.16316i 0.201813 + 0.116517i
\(738\) 0 0
\(739\) 11.4323 + 3.06326i 0.420542 + 0.112684i 0.462883 0.886419i \(-0.346815\pi\)
−0.0423409 + 0.999103i \(0.513482\pi\)
\(740\) 9.70206 16.8045i 0.356655 0.617745i
\(741\) 0 0
\(742\) −10.1560 17.5908i −0.372840 0.645778i
\(743\) −11.3842 42.4865i −0.417647 1.55868i −0.779474 0.626434i \(-0.784514\pi\)
0.361827 0.932245i \(-0.382153\pi\)
\(744\) 0 0
\(745\) 13.5078 7.79874i 0.494888 0.285724i
\(746\) −3.95957 + 3.95957i −0.144970 + 0.144970i
\(747\) 0 0
\(748\) −0.494431 1.84524i −0.0180782 0.0674687i
\(749\) 6.54051 1.75252i 0.238985 0.0640358i
\(750\) 0 0
\(751\) 32.0454 + 18.5014i 1.16935 + 0.675126i 0.953528 0.301306i \(-0.0974225\pi\)
0.215825 + 0.976432i \(0.430756\pi\)
\(752\) −5.76637 + 1.54509i −0.210278 + 0.0563438i
\(753\) 0 0
\(754\) 20.9864 + 19.6604i 0.764281 + 0.715990i
\(755\) 56.8706i 2.06973i
\(756\) 0 0
\(757\) −23.2842 40.3294i −0.846278 1.46580i −0.884507 0.466527i \(-0.845505\pi\)
0.0382287 0.999269i \(-0.487828\pi\)
\(758\) −11.7247 20.3077i −0.425859 0.737609i
\(759\) 0 0
\(760\) 28.1418 + 28.1418i 1.02081 + 1.02081i
\(761\) 21.4108 + 21.4108i 0.776142 + 0.776142i 0.979172 0.203031i \(-0.0650792\pi\)
−0.203031 + 0.979172i \(0.565079\pi\)
\(762\) 0 0
\(763\) −0.144630 0.250506i −0.00523595 0.00906893i
\(764\) 2.08826 + 3.61697i 0.0755506 + 0.130857i
\(765\) 0 0
\(766\) 6.81020i 0.246062i
\(767\) −34.0827 31.9292i −1.23066 1.15290i
\(768\) 0 0
\(769\) −50.7997 + 13.6117i −1.83188 + 0.490852i −0.998121 0.0612700i \(-0.980485\pi\)
−0.833763 + 0.552122i \(0.813818\pi\)
\(770\) −7.62142 4.40023i −0.274657 0.158573i
\(771\) 0 0
\(772\) 1.54347 0.413573i 0.0555508 0.0148848i
\(773\) −5.09988 19.0330i −0.183430 0.684570i −0.994961 0.100261i \(-0.968032\pi\)
0.811531 0.584309i \(-0.198634\pi\)
\(774\) 0 0
\(775\) 6.03398 6.03398i 0.216747 0.216747i
\(776\) −13.9620 + 8.06097i −0.501207 + 0.289372i
\(777\) 0 0
\(778\) 5.29791 + 19.7721i 0.189939 + 0.708863i
\(779\) −1.46187 2.53203i −0.0523769 0.0907194i
\(780\) 0 0
\(781\) 10.0888 17.4742i 0.361004 0.625277i
\(782\) 12.2110 + 3.27192i 0.436664 + 0.117004i
\(783\) 0 0
\(784\) −10.4112 6.01090i −0.371828 0.214675i
\(785\) 17.1614 + 64.0473i 0.612517 + 2.28595i
\(786\) 0 0
\(787\) −7.17503 + 7.17503i −0.255762 + 0.255762i −0.823328 0.567566i \(-0.807885\pi\)
0.567566 + 0.823328i \(0.307885\pi\)
\(788\) −3.61712 + 13.4993i −0.128854 + 0.480891i
\(789\) 0 0
\(790\) 33.2537i 1.18311i
\(791\) 2.85255 10.6459i 0.101425 0.378523i
\(792\) 0 0
\(793\) 19.9606 + 32.1074i 0.708822 + 1.14017i
\(794\) −2.79232 1.61215i −0.0990958 0.0572130i
\(795\) 0 0
\(796\) −2.72315 + 4.71663i −0.0965195 + 0.167177i
\(797\) 41.2377 1.46072 0.730358 0.683065i \(-0.239353\pi\)
0.730358 + 0.683065i \(0.239353\pi\)
\(798\) 0 0
\(799\) 1.16464 4.34649i 0.0412019 0.153768i
\(800\) −10.0330 + 2.68834i −0.354720 + 0.0950471i
\(801\) 0 0
\(802\) −4.61213 + 7.98844i −0.162860 + 0.282082i
\(803\) −22.1178 −0.780521
\(804\) 0 0
\(805\) −20.7659 + 11.9892i −0.731902 + 0.422564i
\(806\) 5.92330 + 9.52785i 0.208639 + 0.335604i
\(807\) 0 0
\(808\) 6.58458 + 6.58458i 0.231645 + 0.231645i
\(809\) 22.9401 13.2445i 0.806532 0.465651i −0.0392184 0.999231i \(-0.512487\pi\)
0.845750 + 0.533579i \(0.179153\pi\)
\(810\) 0 0
\(811\) −27.7759 27.7759i −0.975343 0.975343i 0.0243602 0.999703i \(-0.492245\pi\)
−0.999703 + 0.0243602i \(0.992245\pi\)
\(812\) −5.57194 1.49300i −0.195537 0.0523939i
\(813\) 0 0
\(814\) −23.1853 6.21248i −0.812644 0.217747i
\(815\) 12.8208i 0.449092i
\(816\) 0 0
\(817\) 6.54615 6.54615i 0.229021 0.229021i
\(818\) −9.43133 −0.329759
\(819\) 0 0
\(820\) 1.08888 0.0380253
\(821\) 20.0159 20.0159i 0.698561 0.698561i −0.265539 0.964100i \(-0.585550\pi\)
0.964100 + 0.265539i \(0.0855501\pi\)
\(822\) 0 0
\(823\) 3.18802i 0.111127i 0.998455 + 0.0555636i \(0.0176956\pi\)
−0.998455 + 0.0555636i \(0.982304\pi\)
\(824\) 54.6764 + 14.6505i 1.90474 + 0.510374i
\(825\) 0 0
\(826\) −21.9779 5.88895i −0.764707 0.204903i
\(827\) −40.4226 40.4226i −1.40563 1.40563i −0.780603 0.625027i \(-0.785088\pi\)
−0.625027 0.780603i \(-0.714912\pi\)
\(828\) 0 0
\(829\) 0.372721 0.215190i 0.0129451 0.00747387i −0.493513 0.869738i \(-0.664288\pi\)
0.506459 + 0.862264i \(0.330954\pi\)
\(830\) −6.65727 6.65727i −0.231077 0.231077i
\(831\) 0 0
\(832\) −1.03146 31.6175i −0.0357593 1.09614i
\(833\) 7.84759 4.53081i 0.271903 0.156983i
\(834\) 0 0
\(835\) −1.02450 −0.0354544
\(836\) −2.28848 + 3.96376i −0.0791488 + 0.137090i
\(837\) 0 0
\(838\) 35.0510 9.39190i 1.21082 0.324438i
\(839\) −1.25045 + 4.66673i −0.0431702 + 0.161113i −0.984146 0.177361i \(-0.943244\pi\)
0.940976 + 0.338474i \(0.109911\pi\)
\(840\) 0 0
\(841\) −15.9020 −0.548345
\(842\) −4.64542 + 8.04611i −0.160092 + 0.277287i
\(843\) 0 0
\(844\) −2.63244 1.51984i −0.0906122 0.0523150i
\(845\) 36.6520 + 7.29919i 1.26087 + 0.251100i
\(846\) 0 0
\(847\) −3.04160 + 11.3514i −0.104511 + 0.390040i
\(848\) 28.8290i 0.989991i
\(849\) 0 0
\(850\) −1.88971 + 7.05251i −0.0648166 + 0.241899i
\(851\) −46.2454 + 46.2454i −1.58527 + 1.58527i
\(852\) 0 0
\(853\) −11.5603 43.1437i −0.395818 1.47721i −0.820383 0.571815i \(-0.806240\pi\)
0.424565 0.905397i \(-0.360427\pi\)
\(854\) 15.9513 + 9.20951i 0.545843 + 0.315143i
\(855\) 0 0
\(856\) −13.6267 3.65125i −0.465750 0.124797i
\(857\) −25.1388 + 43.5417i −0.858725 + 1.48736i 0.0144207 + 0.999896i \(0.495410\pi\)
−0.873146 + 0.487459i \(0.837924\pi\)
\(858\) 0 0
\(859\) 25.1679 + 43.5920i 0.858717 + 1.48734i 0.873153 + 0.487445i \(0.162071\pi\)
−0.0144366 + 0.999896i \(0.504595\pi\)
\(860\) 0.892357 + 3.33032i 0.0304291 + 0.113563i
\(861\) 0 0
\(862\) −33.0171 + 19.0624i −1.12457 + 0.649269i
\(863\) 29.3689 29.3689i 0.999728 0.999728i −0.000272025 1.00000i \(-0.500087\pi\)
1.00000 0.000272025i \(8.65883e-5\pi\)
\(864\) 0 0
\(865\) 8.85231 + 33.0373i 0.300988 + 1.12330i
\(866\) 26.0602 6.98281i 0.885562 0.237286i
\(867\) 0 0
\(868\) −1.94896 1.12523i −0.0661521 0.0381929i
\(869\) −16.3597 + 4.38357i −0.554965 + 0.148702i
\(870\) 0 0
\(871\) −12.5254 + 3.79799i −0.424408 + 0.128690i
\(872\) 0.602650i 0.0204083i
\(873\) 0 0
\(874\) −15.1442 26.2304i −0.512259 0.887258i
\(875\) 3.68219 + 6.37775i 0.124481 + 0.215607i
\(876\) 0 0
\(877\) −12.4238 12.4238i −0.419523 0.419523i 0.465516 0.885039i \(-0.345869\pi\)
−0.885039 + 0.465516i \(0.845869\pi\)
\(878\) −27.2529 27.2529i −0.919742 0.919742i
\(879\) 0 0
\(880\) 6.24525 + 10.8171i 0.210527 + 0.364644i
\(881\) 11.7668 + 20.3807i 0.396434 + 0.686644i 0.993283 0.115710i \(-0.0369142\pi\)
−0.596849 + 0.802354i \(0.703581\pi\)
\(882\) 0 0
\(883\) 5.09275i 0.171385i 0.996322 + 0.0856923i \(0.0273102\pi\)
−0.996322 + 0.0856923i \(0.972690\pi\)
\(884\) 3.48541 + 1.86350i 0.117227 + 0.0626763i
\(885\) 0 0
\(886\) −27.8875 + 7.47243i −0.936899 + 0.251041i
\(887\) −11.4511 6.61127i −0.384489 0.221985i 0.295281 0.955411i \(-0.404587\pi\)
−0.679769 + 0.733426i \(0.737920\pi\)
\(888\) 0 0
\(889\) 15.4247 4.13304i 0.517329 0.138618i
\(890\) −5.38181 20.0852i −0.180399 0.673256i
\(891\) 0 0
\(892\) −2.82276 + 2.82276i −0.0945129 + 0.0945129i
\(893\) −9.33670 + 5.39054i −0.312441 + 0.180388i
\(894\) 0 0
\(895\) 4.35963 + 16.2704i 0.145726 + 0.543858i
\(896\) −3.00983 5.21318i −0.100551 0.174160i
\(897\) 0 0
\(898\) 6.41059 11.1035i 0.213924 0.370528i
\(899\) −16.9207 4.53390i −0.564338 0.151214i
\(900\) 0 0
\(901\) −18.8190 10.8651i −0.626951 0.361970i
\(902\) −0.348619 1.30106i −0.0116077 0.0433207i
\(903\) 0 0
\(904\) −16.2368 + 16.2368i −0.540027 + 0.540027i
\(905\) 6.17388 23.0412i 0.205227 0.765917i
\(906\) 0 0
\(907\) 9.89130i 0.328435i −0.986424 0.164218i \(-0.947490\pi\)
0.986424 0.164218i \(-0.0525099\pi\)
\(908\) −1.92806 + 7.19562i −0.0639850 + 0.238795i
\(909\) 0 0
\(910\) 17.4239 5.28333i 0.577598 0.175141i
\(911\) 10.2559 + 5.92123i 0.339792 + 0.196179i 0.660180 0.751107i \(-0.270480\pi\)
−0.320388 + 0.947286i \(0.603813\pi\)
\(912\) 0 0
\(913\) 2.39758 4.15273i 0.0793483 0.137435i
\(914\) −28.6756 −0.948504
\(915\) 0 0
\(916\) −2.75238 + 10.2720i −0.0909412 + 0.339397i
\(917\) 11.2685 3.01937i 0.372117 0.0997085i
\(918\) 0 0
\(919\) −1.00599 + 1.74243i −0.0331846 + 0.0574775i −0.882141 0.470986i \(-0.843898\pi\)
0.848956 + 0.528463i \(0.177232\pi\)
\(920\) 49.9572 1.64704
\(921\) 0 0
\(922\) −3.04499 + 1.75803i −0.100281 + 0.0578975i
\(923\) 12.1135 + 39.9492i 0.398721 + 1.31495i
\(924\) 0 0
\(925\) −26.7092 26.7092i −0.878194 0.878194i
\(926\) 1.91482 1.10552i 0.0629248 0.0363297i
\(927\) 0 0
\(928\) 15.0775 + 15.0775i 0.494943 + 0.494943i
\(929\) 40.2389 + 10.7820i 1.32019 + 0.353745i 0.849051 0.528311i \(-0.177175\pi\)
0.471144 + 0.882056i \(0.343841\pi\)
\(930\) 0 0
\(931\) −20.9709 5.61914i −0.687294 0.184160i
\(932\) 2.49098i 0.0815949i
\(933\) 0 0
\(934\) 13.4976 13.4976i 0.441656 0.441656i
\(935\) −9.41490 −0.307900
\(936\) 0 0
\(937\) 47.9819 1.56750 0.783750 0.621077i \(-0.213304\pi\)
0.783750 + 0.621077i \(0.213304\pi\)
\(938\) −4.50900 + 4.50900i −0.147224 + 0.147224i
\(939\) 0 0
\(940\) 4.01517i 0.130960i
\(941\) −23.7536 6.36477i −0.774346 0.207485i −0.150056 0.988678i \(-0.547945\pi\)
−0.624291 + 0.781192i \(0.714612\pi\)
\(942\) 0 0
\(943\) −3.54497 0.949873i −0.115440 0.0309321i
\(944\) 22.8350 + 22.8350i 0.743216 + 0.743216i
\(945\) 0 0
\(946\) 3.69358 2.13249i 0.120089 0.0693332i
\(947\) 29.5660 + 29.5660i 0.960767 + 0.960767i 0.999259 0.0384921i \(-0.0122554\pi\)
−0.0384921 + 0.999259i \(0.512255\pi\)
\(948\) 0 0
\(949\) 31.2848 33.3949i 1.01555 1.08404i
\(950\) 15.1495 8.74657i 0.491515 0.283776i
\(951\) 0 0
\(952\) 8.52775 0.276386
\(953\) 3.67150 6.35923i 0.118932 0.205996i −0.800413 0.599449i \(-0.795386\pi\)
0.919345 + 0.393453i \(0.128720\pi\)
\(954\) 0 0
\(955\) 19.8822 5.32742i 0.643373 0.172391i
\(956\) −0.170075 + 0.634729i −0.00550062 + 0.0205286i
\(957\) 0 0
\(958\) 44.0898 1.42448
\(959\) −6.24560 + 10.8177i −0.201681 + 0.349321i
\(960\) 0 0
\(961\) 20.9282 + 12.0829i 0.675104 + 0.389772i
\(962\) 42.1747 26.2193i 1.35977 0.845343i
\(963\) 0 0
\(964\) −1.33275 + 4.97388i −0.0429249 + 0.160198i
\(965\) 7.87520i 0.253512i
\(966\) 0 0
\(967\) 6.78898 25.3368i 0.218319 0.814778i −0.766653 0.642062i \(-0.778079\pi\)
0.984972 0.172716i \(-0.0552542\pi\)
\(968\) 17.3129 17.3129i 0.556457 0.556457i
\(969\) 0 0
\(970\) 4.64343 + 17.3295i 0.149091 + 0.556417i
\(971\) 11.1860 + 6.45823i 0.358975 + 0.207255i 0.668631 0.743594i \(-0.266880\pi\)
−0.309656 + 0.950849i \(0.600214\pi\)
\(972\) 0 0
\(973\) −0.669888 0.179496i −0.0214756 0.00575438i
\(974\) 12.0534 20.8771i 0.386217 0.668947i
\(975\) 0 0
\(976\) −13.0711 22.6397i −0.418394 0.724680i
\(977\) −8.97618 33.4996i −0.287174 1.07175i −0.947236 0.320536i \(-0.896137\pi\)
0.660063 0.751210i \(-0.270530\pi\)
\(978\) 0 0
\(979\) 9.17179 5.29533i 0.293132 0.169240i
\(980\) 5.71742 5.71742i 0.182636 0.182636i
\(981\) 0 0
\(982\) 3.49299 + 13.0360i 0.111466 + 0.415996i
\(983\) −27.3813 + 7.33678i −0.873326 + 0.234007i −0.667526 0.744587i \(-0.732647\pi\)
−0.205801 + 0.978594i \(0.565980\pi\)
\(984\) 0 0
\(985\) 59.6490 + 34.4384i 1.90058 + 1.09730i
\(986\) 14.4777 3.87929i 0.461064 0.123542i
\(987\) 0 0
\(988\) −2.74777 9.06188i −0.0874181 0.288297i
\(989\) 11.6207i 0.369516i
\(990\) 0 0
\(991\) 0.249119 + 0.431486i 0.00791352 + 0.0137066i 0.869955 0.493131i \(-0.164148\pi\)
−0.862042 + 0.506838i \(0.830814\pi\)
\(992\) 4.15933 + 7.20418i 0.132059 + 0.228733i
\(993\) 0 0
\(994\) 14.3812 + 14.3812i 0.456145 + 0.456145i
\(995\) 18.9798 + 18.9798i 0.601702 + 0.601702i
\(996\) 0 0
\(997\) −19.9952 34.6328i −0.633255 1.09683i −0.986882 0.161444i \(-0.948385\pi\)
0.353626 0.935387i \(-0.384948\pi\)
\(998\) 3.04127 + 5.26764i 0.0962698 + 0.166744i
\(999\) 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 351.2.ba.a.89.9 48
3.2 odd 2 117.2.x.a.11.4 48
9.4 even 3 117.2.bc.a.50.9 yes 48
9.5 odd 6 351.2.bf.a.206.4 48
13.6 odd 12 351.2.bf.a.305.4 48
39.32 even 12 117.2.bc.a.110.9 yes 48
117.32 even 12 inner 351.2.ba.a.71.9 48
117.58 odd 12 117.2.x.a.32.4 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.2.x.a.11.4 48 3.2 odd 2
117.2.x.a.32.4 yes 48 117.58 odd 12
117.2.bc.a.50.9 yes 48 9.4 even 3
117.2.bc.a.110.9 yes 48 39.32 even 12
351.2.ba.a.71.9 48 117.32 even 12 inner
351.2.ba.a.89.9 48 1.1 even 1 trivial
351.2.bf.a.206.4 48 9.5 odd 6
351.2.bf.a.305.4 48 13.6 odd 12