Properties

Label 363.2.f.f.239.1
Level $363$
Weight $2$
Character 363.239
Analytic conductor $2.899$
Analytic rank $0$
Dimension $8$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,2,Mod(161,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("363.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.f (of order \(10\), 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: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.64000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 239.1
Root \(-1.34500 - 0.437016i\) of defining polynomial
Character \(\chi\) \(=\) 363.239
Dual form 363.2.f.f.161.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(-1.03598 + 1.38807i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.66251 - 2.28825i) q^{5} +(-0.0222369 + 1.73191i) q^{6} +(1.34500 + 0.437016i) q^{7} +(0.927051 + 2.85317i) q^{8} +(-0.853491 - 2.87603i) q^{9} -2.82843i q^{10} +(-1.00000 - 1.41421i) q^{12} +(2.49376 + 3.43237i) q^{13} +(1.34500 - 0.437016i) q^{14} +(1.45393 + 4.67826i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.85410 + 3.52671i) q^{17} +(-2.38098 - 1.82509i) q^{18} +(-4.03499 + 1.31105i) q^{19} +(1.66251 + 2.28825i) q^{20} +(-2.00000 + 1.41421i) q^{21} +(-4.92081 - 1.66901i) q^{24} +(-0.927051 - 2.85317i) q^{25} +(4.03499 + 1.31105i) q^{26} +(4.87634 + 1.79480i) q^{27} +(-0.831254 + 1.14412i) q^{28} +(0.618034 - 1.90211i) q^{29} +(3.92606 + 2.93019i) q^{30} +(1.61803 - 1.17557i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(3.23607 - 2.35114i) q^{35} +(2.99901 + 0.0770245i) q^{36} +(2.47214 - 7.60845i) q^{37} +(-2.49376 + 3.43237i) q^{38} +(-7.34786 - 0.0943431i) q^{39} +(8.06998 + 2.62210i) q^{40} +(-1.85410 - 5.70634i) q^{41} +(-0.786780 + 2.31969i) q^{42} +4.24264i q^{43} +(-8.00000 - 2.82843i) q^{45} +(-2.68999 + 0.874032i) q^{47} +(-1.65401 + 0.514040i) q^{48} +(-4.04508 - 2.93893i) q^{49} +(-2.42705 - 1.76336i) q^{50} +(-9.92408 + 3.08424i) q^{51} +(-4.03499 + 1.31105i) q^{52} +(-3.32502 - 4.57649i) q^{53} +(5.00000 - 1.41421i) q^{54} +4.24264i q^{56} +(2.36034 - 6.95908i) q^{57} +(-0.618034 - 1.90211i) q^{58} +(-10.7600 - 3.49613i) q^{59} +(-4.89858 - 0.0628954i) q^{60} +(5.81878 - 8.00886i) q^{61} +(0.618034 - 1.90211i) q^{62} +(0.108929 - 4.24124i) q^{63} +(-5.66312 + 4.11450i) q^{64} +12.0000 q^{65} +2.00000 q^{67} +(-4.85410 + 3.52671i) q^{68} +(1.23607 - 3.80423i) q^{70} +(1.66251 - 2.28825i) q^{71} +(7.41457 - 5.10138i) q^{72} +(1.34500 + 0.437016i) q^{73} +(-2.47214 - 7.60845i) q^{74} +(4.92081 + 1.66901i) q^{75} -4.24264i q^{76} +(-6.00000 + 4.24264i) q^{78} +(2.49376 + 3.43237i) q^{79} +(2.68999 - 0.874032i) q^{80} +(-7.54311 + 4.90933i) q^{81} +(-4.85410 - 3.52671i) q^{82} +(-12.9443 - 9.40456i) q^{83} +(-0.726963 - 2.33913i) q^{84} +(16.1400 - 5.24419i) q^{85} +(2.49376 + 3.43237i) q^{86} +(2.00000 + 2.82843i) q^{87} +(-8.13464 + 2.41404i) q^{90} +(1.85410 + 5.70634i) q^{91} +(-0.0444738 + 3.46382i) q^{93} +(-1.66251 + 2.28825i) q^{94} +(-3.70820 + 11.4127i) q^{95} +(5.17990 - 6.94036i) q^{96} +(1.61803 - 1.17557i) q^{97} -5.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 6 q^{8} + 2 q^{9} - 8 q^{12} + 8 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} - 16 q^{21} - 6 q^{24} + 6 q^{25} + 10 q^{27} - 4 q^{29} - 8 q^{30} + 4 q^{31} - 40 q^{32}+ \cdots - 40 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.572061 0.415627i −0.263792 0.964580i \(-0.584973\pi\)
0.835853 + 0.548953i \(0.184973\pi\)
\(3\) −1.03598 + 1.38807i −0.598123 + 0.801404i
\(4\) −0.309017 + 0.951057i −0.154508 + 0.475528i
\(5\) 1.66251 2.28825i 0.743496 1.02333i −0.254914 0.966964i \(-0.582047\pi\)
0.998410 0.0563708i \(-0.0179529\pi\)
\(6\) −0.0222369 + 1.73191i −0.00907817 + 0.707049i
\(7\) 1.34500 + 0.437016i 0.508361 + 0.165177i 0.551957 0.833873i \(-0.313881\pi\)
−0.0435957 + 0.999049i \(0.513881\pi\)
\(8\) 0.927051 + 2.85317i 0.327762 + 1.00875i
\(9\) −0.853491 2.87603i −0.284497 0.958677i
\(10\) 2.82843i 0.894427i
\(11\) 0 0
\(12\) −1.00000 1.41421i −0.288675 0.408248i
\(13\) 2.49376 + 3.43237i 0.691645 + 0.951968i 1.00000 0.000696272i \(0.000221630\pi\)
−0.308355 + 0.951271i \(0.599778\pi\)
\(14\) 1.34500 0.437016i 0.359466 0.116797i
\(15\) 1.45393 + 4.67826i 0.375402 + 1.20792i
\(16\) 0.809017 + 0.587785i 0.202254 + 0.146946i
\(17\) 4.85410 + 3.52671i 1.17729 + 0.855353i 0.991864 0.127304i \(-0.0406325\pi\)
0.185429 + 0.982658i \(0.440633\pi\)
\(18\) −2.38098 1.82509i −0.561202 0.430178i
\(19\) −4.03499 + 1.31105i −0.925690 + 0.300775i −0.732799 0.680445i \(-0.761786\pi\)
−0.192891 + 0.981220i \(0.561786\pi\)
\(20\) 1.66251 + 2.28825i 0.371748 + 0.511667i
\(21\) −2.00000 + 1.41421i −0.436436 + 0.308607i
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −4.92081 1.66901i −1.00446 0.340686i
\(25\) −0.927051 2.85317i −0.185410 0.570634i
\(26\) 4.03499 + 1.31105i 0.791327 + 0.257118i
\(27\) 4.87634 + 1.79480i 0.938452 + 0.345410i
\(28\) −0.831254 + 1.14412i −0.157092 + 0.216219i
\(29\) 0.618034 1.90211i 0.114766 0.353214i −0.877132 0.480249i \(-0.840546\pi\)
0.991898 + 0.127036i \(0.0405463\pi\)
\(30\) 3.92606 + 2.93019i 0.716798 + 0.534978i
\(31\) 1.61803 1.17557i 0.290607 0.211139i −0.432923 0.901431i \(-0.642518\pi\)
0.723531 + 0.690292i \(0.242518\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 3.23607 2.35114i 0.546995 0.397415i
\(36\) 2.99901 + 0.0770245i 0.499835 + 0.0128374i
\(37\) 2.47214 7.60845i 0.406417 1.25082i −0.513290 0.858215i \(-0.671573\pi\)
0.919707 0.392607i \(-0.128427\pi\)
\(38\) −2.49376 + 3.43237i −0.404542 + 0.556804i
\(39\) −7.34786 0.0943431i −1.17660 0.0151070i
\(40\) 8.06998 + 2.62210i 1.27598 + 0.414590i
\(41\) −1.85410 5.70634i −0.289562 0.891180i −0.984994 0.172588i \(-0.944787\pi\)
0.695432 0.718592i \(-0.255213\pi\)
\(42\) −0.786780 + 2.31969i −0.121403 + 0.357936i
\(43\) 4.24264i 0.646997i 0.946229 + 0.323498i \(0.104859\pi\)
−0.946229 + 0.323498i \(0.895141\pi\)
\(44\) 0 0
\(45\) −8.00000 2.82843i −1.19257 0.421637i
\(46\) 0 0
\(47\) −2.68999 + 0.874032i −0.392376 + 0.127491i −0.498559 0.866856i \(-0.666137\pi\)
0.106183 + 0.994347i \(0.466137\pi\)
\(48\) −1.65401 + 0.514040i −0.238736 + 0.0741954i
\(49\) −4.04508 2.93893i −0.577869 0.419847i
\(50\) −2.42705 1.76336i −0.343237 0.249376i
\(51\) −9.92408 + 3.08424i −1.38965 + 0.431880i
\(52\) −4.03499 + 1.31105i −0.559553 + 0.181810i
\(53\) −3.32502 4.57649i −0.456726 0.628629i 0.517100 0.855925i \(-0.327012\pi\)
−0.973826 + 0.227296i \(0.927012\pi\)
\(54\) 5.00000 1.41421i 0.680414 0.192450i
\(55\) 0 0
\(56\) 4.24264i 0.566947i
\(57\) 2.36034 6.95908i 0.312635 0.921753i
\(58\) −0.618034 1.90211i −0.0811518 0.249760i
\(59\) −10.7600 3.49613i −1.40083 0.455157i −0.491371 0.870951i \(-0.663504\pi\)
−0.909459 + 0.415794i \(0.863504\pi\)
\(60\) −4.89858 0.0628954i −0.632403 0.00811976i
\(61\) 5.81878 8.00886i 0.745018 1.02543i −0.253296 0.967389i \(-0.581515\pi\)
0.998314 0.0580406i \(-0.0184853\pi\)
\(62\) 0.618034 1.90211i 0.0784904 0.241569i
\(63\) 0.108929 4.24124i 0.0137238 0.534346i
\(64\) −5.66312 + 4.11450i −0.707890 + 0.514312i
\(65\) 12.0000 1.48842
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) −4.85410 + 3.52671i −0.588646 + 0.427677i
\(69\) 0 0
\(70\) 1.23607 3.80423i 0.147738 0.454692i
\(71\) 1.66251 2.28825i 0.197303 0.271565i −0.698889 0.715230i \(-0.746322\pi\)
0.896193 + 0.443665i \(0.146322\pi\)
\(72\) 7.41457 5.10138i 0.873816 0.601204i
\(73\) 1.34500 + 0.437016i 0.157420 + 0.0511489i 0.386667 0.922219i \(-0.373626\pi\)
−0.229247 + 0.973368i \(0.573626\pi\)
\(74\) −2.47214 7.60845i −0.287380 0.884465i
\(75\) 4.92081 + 1.66901i 0.568206 + 0.192721i
\(76\) 4.24264i 0.486664i
\(77\) 0 0
\(78\) −6.00000 + 4.24264i −0.679366 + 0.480384i
\(79\) 2.49376 + 3.43237i 0.280570 + 0.386172i 0.925923 0.377713i \(-0.123290\pi\)
−0.645353 + 0.763885i \(0.723290\pi\)
\(80\) 2.68999 0.874032i 0.300750 0.0977198i
\(81\) −7.54311 + 4.90933i −0.838123 + 0.545481i
\(82\) −4.85410 3.52671i −0.536046 0.389460i
\(83\) −12.9443 9.40456i −1.42082 1.03229i −0.991636 0.129067i \(-0.958802\pi\)
−0.429183 0.903218i \(-0.641198\pi\)
\(84\) −0.726963 2.33913i −0.0793182 0.255220i
\(85\) 16.1400 5.24419i 1.75062 0.568813i
\(86\) 2.49376 + 3.43237i 0.268909 + 0.370122i
\(87\) 2.00000 + 2.82843i 0.214423 + 0.303239i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −8.13464 + 2.41404i −0.857467 + 0.254462i
\(91\) 1.85410 + 5.70634i 0.194363 + 0.598187i
\(92\) 0 0
\(93\) −0.0444738 + 3.46382i −0.00461171 + 0.359181i
\(94\) −1.66251 + 2.28825i −0.171475 + 0.236015i
\(95\) −3.70820 + 11.4127i −0.380454 + 1.17092i
\(96\) 5.17990 6.94036i 0.528671 0.708348i
\(97\) 1.61803 1.17557i 0.164286 0.119361i −0.502604 0.864517i \(-0.667625\pi\)
0.666891 + 0.745155i \(0.267625\pi\)
\(98\) −5.00000 −0.505076
\(99\) 0 0
\(100\) 3.00000 0.300000
\(101\) −8.09017 + 5.87785i −0.805002 + 0.584868i −0.912377 0.409350i \(-0.865755\pi\)
0.107375 + 0.994219i \(0.465755\pi\)
\(102\) −6.21588 + 8.32844i −0.615464 + 0.824638i
\(103\) 2.47214 7.60845i 0.243587 0.749683i −0.752279 0.658845i \(-0.771045\pi\)
0.995866 0.0908382i \(-0.0289546\pi\)
\(104\) −7.48128 + 10.2971i −0.733600 + 1.00971i
\(105\) −0.0889475 + 6.92763i −0.00868039 + 0.676068i
\(106\) −5.37999 1.74806i −0.522551 0.169787i
\(107\) 4.94427 + 15.2169i 0.477981 + 1.47107i 0.841895 + 0.539641i \(0.181440\pi\)
−0.363914 + 0.931432i \(0.618560\pi\)
\(108\) −3.21383 + 4.08305i −0.309251 + 0.392892i
\(109\) 4.24264i 0.406371i 0.979140 + 0.203186i \(0.0651295\pi\)
−0.979140 + 0.203186i \(0.934871\pi\)
\(110\) 0 0
\(111\) 8.00000 + 11.3137i 0.759326 + 1.07385i
\(112\) 0.831254 + 1.14412i 0.0785461 + 0.108109i
\(113\) −2.68999 + 0.874032i −0.253053 + 0.0822220i −0.432797 0.901492i \(-0.642473\pi\)
0.179743 + 0.983714i \(0.442473\pi\)
\(114\) −2.18089 7.01739i −0.204259 0.657239i
\(115\) 0 0
\(116\) 1.61803 + 1.17557i 0.150231 + 0.109149i
\(117\) 7.74320 10.1016i 0.715859 0.933896i
\(118\) −10.7600 + 3.49613i −0.990536 + 0.321845i
\(119\) 4.98752 + 6.86474i 0.457206 + 0.629289i
\(120\) −12.0000 + 8.48528i −1.09545 + 0.774597i
\(121\) 0 0
\(122\) 9.89949i 0.896258i
\(123\) 9.84163 + 3.33803i 0.887389 + 0.300980i
\(124\) 0.618034 + 1.90211i 0.0555011 + 0.170815i
\(125\) 5.37999 + 1.74806i 0.481201 + 0.156352i
\(126\) −2.40481 3.49526i −0.214238 0.311383i
\(127\) 5.81878 8.00886i 0.516333 0.710671i −0.468638 0.883390i \(-0.655255\pi\)
0.984971 + 0.172719i \(0.0552552\pi\)
\(128\) 0.927051 2.85317i 0.0819405 0.252187i
\(129\) −5.88909 4.39529i −0.518506 0.386984i
\(130\) 9.70820 7.05342i 0.851466 0.618626i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 1.61803 1.17557i 0.139777 0.101554i
\(135\) 12.2139 8.17439i 1.05121 0.703539i
\(136\) −5.56231 + 17.1190i −0.476964 + 1.46794i
\(137\) 1.66251 2.28825i 0.142038 0.195498i −0.732071 0.681228i \(-0.761446\pi\)
0.874109 + 0.485730i \(0.161446\pi\)
\(138\) 0 0
\(139\) 1.34500 + 0.437016i 0.114081 + 0.0370672i 0.365501 0.930811i \(-0.380898\pi\)
−0.251420 + 0.967878i \(0.580898\pi\)
\(140\) 1.23607 + 3.80423i 0.104467 + 0.321516i
\(141\) 1.57356 4.63939i 0.132518 0.390707i
\(142\) 2.82843i 0.237356i
\(143\) 0 0
\(144\) 1.00000 2.82843i 0.0833333 0.235702i
\(145\) −3.32502 4.57649i −0.276128 0.380057i
\(146\) 1.34500 0.437016i 0.111313 0.0361677i
\(147\) 8.27007 2.57020i 0.682104 0.211987i
\(148\) 6.47214 + 4.70228i 0.532006 + 0.386525i
\(149\) 4.85410 + 3.52671i 0.397664 + 0.288919i 0.768589 0.639743i \(-0.220959\pi\)
−0.370925 + 0.928663i \(0.620959\pi\)
\(150\) 4.96204 1.54212i 0.405149 0.125914i
\(151\) −4.03499 + 1.31105i −0.328363 + 0.106692i −0.468559 0.883432i \(-0.655227\pi\)
0.140196 + 0.990124i \(0.455227\pi\)
\(152\) −7.48128 10.2971i −0.606812 0.835206i
\(153\) 6.00000 16.9706i 0.485071 1.37199i
\(154\) 0 0
\(155\) 5.65685i 0.454369i
\(156\) 2.36034 6.95908i 0.188978 0.557172i
\(157\) −6.18034 19.0211i −0.493245 1.51805i −0.819674 0.572830i \(-0.805846\pi\)
0.326429 0.945222i \(-0.394154\pi\)
\(158\) 4.03499 + 1.31105i 0.321007 + 0.104301i
\(159\) 9.79715 + 0.125791i 0.776965 + 0.00997586i
\(160\) −8.31254 + 11.4412i −0.657164 + 0.904508i
\(161\) 0 0
\(162\) −3.21687 + 8.40546i −0.252741 + 0.660395i
\(163\) −16.1803 + 11.7557i −1.26734 + 0.920778i −0.999093 0.0425718i \(-0.986445\pi\)
−0.268249 + 0.963350i \(0.586445\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −16.0000 −1.24184
\(167\) 9.70820 7.05342i 0.751243 0.545810i −0.144969 0.989436i \(-0.546308\pi\)
0.896212 + 0.443626i \(0.146308\pi\)
\(168\) −5.88909 4.39529i −0.454353 0.339104i
\(169\) −1.54508 + 4.75528i −0.118853 + 0.365791i
\(170\) 9.97505 13.7295i 0.765051 1.05300i
\(171\) 7.21444 + 10.4858i 0.551702 + 0.801869i
\(172\) −4.03499 1.31105i −0.307665 0.0999665i
\(173\) −1.85410 5.70634i −0.140965 0.433845i 0.855505 0.517794i \(-0.173247\pi\)
−0.996470 + 0.0839492i \(0.973247\pi\)
\(174\) 3.28054 + 1.11268i 0.248697 + 0.0843517i
\(175\) 4.24264i 0.320713i
\(176\) 0 0
\(177\) 16.0000 11.3137i 1.20263 0.850390i
\(178\) 0 0
\(179\) −2.68999 + 0.874032i −0.201060 + 0.0653282i −0.407816 0.913064i \(-0.633709\pi\)
0.206756 + 0.978393i \(0.433709\pi\)
\(180\) 5.16213 6.73442i 0.384762 0.501954i
\(181\) 8.09017 + 5.87785i 0.601338 + 0.436897i 0.846353 0.532622i \(-0.178793\pi\)
−0.245016 + 0.969519i \(0.578793\pi\)
\(182\) 4.85410 + 3.52671i 0.359810 + 0.261417i
\(183\) 5.08874 + 16.3739i 0.376171 + 1.21039i
\(184\) 0 0
\(185\) −13.3001 18.3060i −0.977840 1.34588i
\(186\) 2.00000 + 2.82843i 0.146647 + 0.207390i
\(187\) 0 0
\(188\) 2.82843i 0.206284i
\(189\) 5.77430 + 4.54504i 0.420019 + 0.330603i
\(190\) 3.70820 + 11.4127i 0.269021 + 0.827963i
\(191\) 18.8300 + 6.11822i 1.36249 + 0.442699i 0.896873 0.442288i \(-0.145833\pi\)
0.465615 + 0.884987i \(0.345833\pi\)
\(192\) 0.155658 12.1234i 0.0112337 0.874928i
\(193\) −12.4688 + 17.1618i −0.897524 + 1.23534i 0.0737265 + 0.997278i \(0.476511\pi\)
−0.971251 + 0.238058i \(0.923489\pi\)
\(194\) 0.618034 1.90211i 0.0443723 0.136564i
\(195\) −12.4318 + 16.6569i −0.890257 + 1.19282i
\(196\) 4.04508 2.93893i 0.288935 0.209923i
\(197\) −22.0000 −1.56744 −0.783718 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) 7.28115 5.29007i 0.514855 0.374064i
\(201\) −2.07196 + 2.77615i −0.146145 + 0.195814i
\(202\) −3.09017 + 9.51057i −0.217424 + 0.669161i
\(203\) 1.66251 2.28825i 0.116685 0.160603i
\(204\) 0.133421 10.3914i 0.00934136 0.727547i
\(205\) −16.1400 5.24419i −1.12726 0.366270i
\(206\) −2.47214 7.60845i −0.172242 0.530106i
\(207\) 0 0
\(208\) 4.24264i 0.294174i
\(209\) 0 0
\(210\) 4.00000 + 5.65685i 0.276026 + 0.390360i
\(211\) −15.7938 21.7383i −1.08729 1.49653i −0.851232 0.524790i \(-0.824144\pi\)
−0.236060 0.971738i \(-0.575856\pi\)
\(212\) 5.37999 1.74806i 0.369499 0.120058i
\(213\) 1.45393 + 4.67826i 0.0996214 + 0.320549i
\(214\) 12.9443 + 9.40456i 0.884852 + 0.642883i
\(215\) 9.70820 + 7.05342i 0.662094 + 0.481039i
\(216\) −0.600264 + 15.5769i −0.0408428 + 1.05987i
\(217\) 2.68999 0.874032i 0.182609 0.0593332i
\(218\) 2.49376 + 3.43237i 0.168899 + 0.232469i
\(219\) −2.00000 + 1.41421i −0.135147 + 0.0955637i
\(220\) 0 0
\(221\) 25.4558i 1.71235i
\(222\) 13.1222 + 4.45070i 0.880702 + 0.298711i
\(223\) 7.41641 + 22.8254i 0.496639 + 1.52850i 0.814386 + 0.580323i \(0.197074\pi\)
−0.317747 + 0.948176i \(0.602926\pi\)
\(224\) −6.72499 2.18508i −0.449332 0.145997i
\(225\) −7.41457 + 5.10138i −0.494305 + 0.340092i
\(226\) −1.66251 + 2.28825i −0.110588 + 0.152212i
\(227\) 7.41641 22.8254i 0.492244 1.51497i −0.328963 0.944343i \(-0.606699\pi\)
0.821208 0.570629i \(-0.193301\pi\)
\(228\) 5.88909 + 4.39529i 0.390015 + 0.291085i
\(229\) 19.4164 14.1068i 1.28307 0.932207i 0.283431 0.958993i \(-0.408527\pi\)
0.999641 + 0.0267860i \(0.00852726\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) −8.09017 + 5.87785i −0.530005 + 0.385071i −0.820360 0.571848i \(-0.806227\pi\)
0.290355 + 0.956919i \(0.406227\pi\)
\(234\) 0.326787 12.7237i 0.0213627 0.831776i
\(235\) −2.47214 + 7.60845i −0.161264 + 0.496321i
\(236\) 6.65003 9.15298i 0.432880 0.595808i
\(237\) −7.34786 0.0943431i −0.477295 0.00612824i
\(238\) 8.06998 + 2.62210i 0.523099 + 0.169965i
\(239\) 4.94427 + 15.2169i 0.319818 + 0.984300i 0.973726 + 0.227725i \(0.0731287\pi\)
−0.653907 + 0.756575i \(0.726871\pi\)
\(240\) −1.57356 + 4.63939i −0.101573 + 0.299471i
\(241\) 4.24264i 0.273293i 0.990620 + 0.136646i \(0.0436324\pi\)
−0.990620 + 0.136646i \(0.956368\pi\)
\(242\) 0 0
\(243\) 1.00000 15.5563i 0.0641500 0.997940i
\(244\) 5.81878 + 8.00886i 0.372509 + 0.512715i
\(245\) −13.4500 + 4.37016i −0.859287 + 0.279199i
\(246\) 9.92408 3.08424i 0.632736 0.196644i
\(247\) −14.5623 10.5801i −0.926577 0.673198i
\(248\) 4.85410 + 3.52671i 0.308236 + 0.223946i
\(249\) 26.4642 8.22465i 1.67710 0.521216i
\(250\) 5.37999 1.74806i 0.340260 0.110557i
\(251\) 14.9626 + 20.5942i 0.944429 + 1.29990i 0.953958 + 0.299940i \(0.0969668\pi\)
−0.00952890 + 0.999955i \(0.503033\pi\)
\(252\) 4.00000 + 1.41421i 0.251976 + 0.0890871i
\(253\) 0 0
\(254\) 9.89949i 0.621150i
\(255\) −9.44136 + 27.8363i −0.591241 + 1.74318i
\(256\) −5.25329 16.1680i −0.328331 1.01050i
\(257\) −10.7600 3.49613i −0.671189 0.218082i −0.0464552 0.998920i \(-0.514792\pi\)
−0.624734 + 0.780838i \(0.714792\pi\)
\(258\) −7.34786 0.0943431i −0.457458 0.00587354i
\(259\) 6.65003 9.15298i 0.413213 0.568739i
\(260\) −3.70820 + 11.4127i −0.229973 + 0.707784i
\(261\) −5.99802 0.154049i −0.371268 0.00953539i
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −16.0000 −0.982872
\(266\) −4.85410 + 3.52671i −0.297624 + 0.216237i
\(267\) 0 0
\(268\) −0.618034 + 1.90211i −0.0377524 + 0.116190i
\(269\) −16.6251 + 22.8825i −1.01365 + 1.39517i −0.0970866 + 0.995276i \(0.530952\pi\)
−0.916562 + 0.399892i \(0.869048\pi\)
\(270\) 5.07647 13.7924i 0.308944 0.839377i
\(271\) −28.2449 9.17734i −1.71576 0.557483i −0.724483 0.689293i \(-0.757921\pi\)
−0.991275 + 0.131809i \(0.957921\pi\)
\(272\) 1.85410 + 5.70634i 0.112421 + 0.345998i
\(273\) −9.84163 3.33803i −0.595642 0.202026i
\(274\) 2.82843i 0.170872i
\(275\) 0 0
\(276\) 0 0
\(277\) 2.49376 + 3.43237i 0.149836 + 0.206231i 0.877336 0.479876i \(-0.159318\pi\)
−0.727501 + 0.686107i \(0.759318\pi\)
\(278\) 1.34500 0.437016i 0.0806676 0.0262105i
\(279\) −4.76195 3.65018i −0.285091 0.218530i
\(280\) 9.70820 + 7.05342i 0.580176 + 0.421523i
\(281\) 4.85410 + 3.52671i 0.289571 + 0.210386i 0.723081 0.690763i \(-0.242725\pi\)
−0.433510 + 0.901149i \(0.642725\pi\)
\(282\) −1.45393 4.67826i −0.0865800 0.278586i
\(283\) 25.5549 8.30330i 1.51908 0.493580i 0.573568 0.819158i \(-0.305559\pi\)
0.945515 + 0.325577i \(0.105559\pi\)
\(284\) 1.66251 + 2.28825i 0.0986517 + 0.135782i
\(285\) −12.0000 16.9706i −0.710819 1.00525i
\(286\) 0 0
\(287\) 8.48528i 0.500870i
\(288\) 4.26745 + 14.3802i 0.251462 + 0.847359i
\(289\) 5.87132 + 18.0701i 0.345372 + 1.06295i
\(290\) −5.37999 1.74806i −0.315924 0.102650i
\(291\) −0.0444738 + 3.46382i −0.00260710 + 0.203052i
\(292\) −0.831254 + 1.14412i −0.0486455 + 0.0669547i
\(293\) 0.618034 1.90211i 0.0361059 0.111123i −0.931379 0.364051i \(-0.881394\pi\)
0.967485 + 0.252928i \(0.0813935\pi\)
\(294\) 5.17990 6.94036i 0.302098 0.404770i
\(295\) −25.8885 + 18.8091i −1.50729 + 1.09511i
\(296\) 24.0000 1.39497
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) −3.10794 + 4.16422i −0.179437 + 0.240421i
\(301\) −1.85410 + 5.70634i −0.106869 + 0.328908i
\(302\) −2.49376 + 3.43237i −0.143500 + 0.197511i
\(303\) 0.222369 17.3191i 0.0127748 0.994955i
\(304\) −4.03499 1.31105i −0.231423 0.0751938i
\(305\) −8.65248 26.6296i −0.495439 1.52481i
\(306\) −5.12094 17.2562i −0.292745 0.986470i
\(307\) 4.24264i 0.242140i 0.992644 + 0.121070i \(0.0386326\pi\)
−0.992644 + 0.121070i \(0.961367\pi\)
\(308\) 0 0
\(309\) 8.00000 + 11.3137i 0.455104 + 0.643614i
\(310\) −3.32502 4.57649i −0.188848 0.259927i
\(311\) 26.8999 8.74032i 1.52536 0.495618i 0.578064 0.815991i \(-0.303808\pi\)
0.947291 + 0.320373i \(0.103808\pi\)
\(312\) −6.54267 21.0522i −0.370406 1.19184i
\(313\) −9.70820 7.05342i −0.548740 0.398683i 0.278581 0.960413i \(-0.410136\pi\)
−0.827321 + 0.561730i \(0.810136\pi\)
\(314\) −16.1803 11.7557i −0.913109 0.663413i
\(315\) −9.52391 7.30035i −0.536611 0.411328i
\(316\) −4.03499 + 1.31105i −0.226986 + 0.0737522i
\(317\) 14.9626 + 20.5942i 0.840382 + 1.15669i 0.985901 + 0.167331i \(0.0535147\pi\)
−0.145519 + 0.989355i \(0.546485\pi\)
\(318\) 8.00000 5.65685i 0.448618 0.317221i
\(319\) 0 0
\(320\) 19.7990i 1.10680i
\(321\) −26.2443 8.90140i −1.46482 0.496828i
\(322\) 0 0
\(323\) −24.2099 7.86629i −1.34708 0.437692i
\(324\) −2.33810 8.69099i −0.129895 0.482833i
\(325\) 7.48128 10.2971i 0.414987 0.571181i
\(326\) −6.18034 + 19.0211i −0.342297 + 1.05348i
\(327\) −5.88909 4.39529i −0.325668 0.243060i
\(328\) 14.5623 10.5801i 0.804069 0.584190i
\(329\) −4.00000 −0.220527
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 12.9443 9.40456i 0.710409 0.516143i
\(333\) −23.9921 0.616196i −1.31476 0.0337673i
\(334\) 3.70820 11.4127i 0.202904 0.624474i
\(335\) 3.32502 4.57649i 0.181665 0.250040i
\(336\) −2.44929 0.0314477i −0.133620 0.00171561i
\(337\) 30.9349 + 10.0514i 1.68513 + 0.547533i 0.985896 0.167357i \(-0.0535233\pi\)
0.699237 + 0.714890i \(0.253523\pi\)
\(338\) 1.54508 + 4.75528i 0.0840415 + 0.258653i
\(339\) 1.57356 4.63939i 0.0854641 0.251977i
\(340\) 16.9706i 0.920358i
\(341\) 0 0
\(342\) 12.0000 + 4.24264i 0.648886 + 0.229416i
\(343\) −9.97505 13.7295i −0.538602 0.741322i
\(344\) −12.1050 + 3.93314i −0.652656 + 0.212061i
\(345\) 0 0
\(346\) −4.85410 3.52671i −0.260958 0.189597i
\(347\) −12.9443 9.40456i −0.694885 0.504863i 0.183377 0.983043i \(-0.441297\pi\)
−0.878262 + 0.478179i \(0.841297\pi\)
\(348\) −3.30803 + 1.02808i −0.177329 + 0.0551109i
\(349\) −4.03499 + 1.31105i −0.215988 + 0.0701788i −0.415012 0.909816i \(-0.636223\pi\)
0.199024 + 0.979995i \(0.436223\pi\)
\(350\) −2.49376 3.43237i −0.133297 0.183468i
\(351\) 6.00000 + 21.2132i 0.320256 + 1.13228i
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 6.29424 18.5575i 0.334535 0.986322i
\(355\) −2.47214 7.60845i −0.131207 0.403815i
\(356\) 0 0
\(357\) −14.6957 0.188686i −0.777780 0.00998633i
\(358\) −1.66251 + 2.28825i −0.0878663 + 0.120938i
\(359\) −6.18034 + 19.0211i −0.326186 + 1.00390i 0.644717 + 0.764422i \(0.276975\pi\)
−0.970902 + 0.239475i \(0.923025\pi\)
\(360\) 0.653574 25.4475i 0.0344464 1.34120i
\(361\) −0.809017 + 0.587785i −0.0425798 + 0.0309361i
\(362\) 10.0000 0.525588
\(363\) 0 0
\(364\) −6.00000 −0.314485
\(365\) 3.23607 2.35114i 0.169384 0.123064i
\(366\) 13.7412 + 10.2557i 0.718265 + 0.536073i
\(367\) 2.47214 7.60845i 0.129044 0.397158i −0.865572 0.500785i \(-0.833045\pi\)
0.994616 + 0.103627i \(0.0330448\pi\)
\(368\) 0 0
\(369\) −14.8291 + 10.2028i −0.771975 + 0.531135i
\(370\) −21.5200 6.99226i −1.11877 0.363510i
\(371\) −2.47214 7.60845i −0.128347 0.395011i
\(372\) −3.28054 1.11268i −0.170088 0.0576895i
\(373\) 4.24264i 0.219676i 0.993950 + 0.109838i \(0.0350331\pi\)
−0.993950 + 0.109838i \(0.964967\pi\)
\(374\) 0 0
\(375\) −8.00000 + 5.65685i −0.413118 + 0.292119i
\(376\) −4.98752 6.86474i −0.257212 0.354022i
\(377\) 8.06998 2.62210i 0.415625 0.135045i
\(378\) 7.34302 + 0.282967i 0.377684 + 0.0145543i
\(379\) −9.70820 7.05342i −0.498677 0.362310i 0.309834 0.950791i \(-0.399726\pi\)
−0.808511 + 0.588481i \(0.799726\pi\)
\(380\) −9.70820 7.05342i −0.498020 0.361833i
\(381\) 5.08874 + 16.3739i 0.260704 + 0.838860i
\(382\) 18.8300 6.11822i 0.963424 0.313036i
\(383\) −3.32502 4.57649i −0.169900 0.233848i 0.715573 0.698538i \(-0.246166\pi\)
−0.885473 + 0.464690i \(0.846166\pi\)
\(384\) 3.00000 + 4.24264i 0.153093 + 0.216506i
\(385\) 0 0
\(386\) 21.2132i 1.07972i
\(387\) 12.2020 3.62105i 0.620261 0.184069i
\(388\) 0.618034 + 1.90211i 0.0313759 + 0.0965652i
\(389\) 18.8300 + 6.11822i 0.954717 + 0.310206i 0.744631 0.667477i \(-0.232626\pi\)
0.210086 + 0.977683i \(0.432626\pi\)
\(390\) −0.266843 + 20.7829i −0.0135121 + 1.05238i
\(391\) 0 0
\(392\) 4.63525 14.2658i 0.234116 0.720534i
\(393\) 0 0
\(394\) −17.7984 + 12.9313i −0.896669 + 0.651468i
\(395\) 12.0000 0.603786
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 1.61803 1.17557i 0.0811047 0.0589260i
\(399\) 6.21588 8.32844i 0.311183 0.416943i
\(400\) 0.927051 2.85317i 0.0463525 0.142658i
\(401\) 1.66251 2.28825i 0.0830217 0.114270i −0.765486 0.643452i \(-0.777501\pi\)
0.848508 + 0.529183i \(0.177501\pi\)
\(402\) −0.0444738 + 3.46382i −0.00221815 + 0.172759i
\(403\) 8.06998 + 2.62210i 0.401994 + 0.130616i
\(404\) −3.09017 9.51057i −0.153742 0.473168i
\(405\) −1.30672 + 25.4223i −0.0649313 + 1.26324i
\(406\) 2.82843i 0.140372i
\(407\) 0 0
\(408\) −18.0000 25.4558i −0.891133 1.26025i
\(409\) 2.49376 + 3.43237i 0.123309 + 0.169720i 0.866208 0.499683i \(-0.166550\pi\)
−0.742900 + 0.669403i \(0.766550\pi\)
\(410\) −16.1400 + 5.24419i −0.797096 + 0.258992i
\(411\) 1.45393 + 4.67826i 0.0717169 + 0.230761i
\(412\) 6.47214 + 4.70228i 0.318859 + 0.231665i
\(413\) −12.9443 9.40456i −0.636946 0.462768i
\(414\) 0 0
\(415\) −43.0399 + 13.9845i −2.11275 + 0.686473i
\(416\) −12.4688 17.1618i −0.611334 0.841429i
\(417\) −2.00000 + 1.41421i −0.0979404 + 0.0692543i
\(418\) 0 0
\(419\) 31.1127i 1.51995i −0.649950 0.759977i \(-0.725210\pi\)
0.649950 0.759977i \(-0.274790\pi\)
\(420\) −6.56108 2.22535i −0.320148 0.108586i
\(421\) −6.18034 19.0211i −0.301211 0.927033i −0.981064 0.193684i \(-0.937956\pi\)
0.679853 0.733349i \(-0.262044\pi\)
\(422\) −25.5549 8.30330i −1.24400 0.404199i
\(423\) 4.80963 + 6.99053i 0.233852 + 0.339891i
\(424\) 9.97505 13.7295i 0.484431 0.666762i
\(425\) 5.56231 17.1190i 0.269811 0.830394i
\(426\) 3.92606 + 2.93019i 0.190218 + 0.141968i
\(427\) 11.3262 8.22899i 0.548115 0.398229i
\(428\) −16.0000 −0.773389
\(429\) 0 0
\(430\) 12.0000 0.578691
\(431\) −25.8885 + 18.8091i −1.24701 + 0.906004i −0.998044 0.0625092i \(-0.980090\pi\)
−0.248963 + 0.968513i \(0.580090\pi\)
\(432\) 2.89008 + 4.31827i 0.139049 + 0.207763i
\(433\) 9.27051 28.5317i 0.445512 1.37115i −0.436409 0.899749i \(-0.643750\pi\)
0.881921 0.471397i \(-0.156250\pi\)
\(434\) 1.66251 2.28825i 0.0798029 0.109839i
\(435\) 9.79715 + 0.125791i 0.469737 + 0.00603121i
\(436\) −4.03499 1.31105i −0.193241 0.0627878i
\(437\) 0 0
\(438\) −0.786780 + 2.31969i −0.0375938 + 0.110839i
\(439\) 26.8701i 1.28244i −0.767358 0.641219i \(-0.778429\pi\)
0.767358 0.641219i \(-0.221571\pi\)
\(440\) 0 0
\(441\) −5.00000 + 14.1421i −0.238095 + 0.673435i
\(442\) 14.9626 + 20.5942i 0.711697 + 0.979567i
\(443\) 26.8999 8.74032i 1.27805 0.415265i 0.410160 0.912014i \(-0.365473\pi\)
0.867895 + 0.496748i \(0.165473\pi\)
\(444\) −13.2321 + 4.11232i −0.627968 + 0.195162i
\(445\) 0 0
\(446\) 19.4164 + 14.1068i 0.919394 + 0.667979i
\(447\) −9.92408 + 3.08424i −0.469393 + 0.145880i
\(448\) −9.41498 + 3.05911i −0.444816 + 0.144529i
\(449\) −3.32502 4.57649i −0.156917 0.215978i 0.723319 0.690514i \(-0.242616\pi\)
−0.880236 + 0.474536i \(0.842616\pi\)
\(450\) −3.00000 + 8.48528i −0.141421 + 0.400000i
\(451\) 0 0
\(452\) 2.82843i 0.133038i
\(453\) 2.36034 6.95908i 0.110898 0.326966i
\(454\) −7.41641 22.8254i −0.348069 1.07125i
\(455\) 16.1400 + 5.24419i 0.756653 + 0.245852i
\(456\) 22.0436 + 0.283029i 1.03229 + 0.0132541i
\(457\) 5.81878 8.00886i 0.272191 0.374639i −0.650937 0.759132i \(-0.725624\pi\)
0.923128 + 0.384493i \(0.125624\pi\)
\(458\) 7.41641 22.8254i 0.346546 1.06656i
\(459\) 17.3405 + 25.9096i 0.809385 + 1.20936i
\(460\) 0 0
\(461\) −22.0000 −1.02464 −0.512321 0.858794i \(-0.671214\pi\)
−0.512321 + 0.858794i \(0.671214\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 1.61803 1.17557i 0.0751153 0.0545745i
\(465\) 7.85212 + 5.86039i 0.364134 + 0.271769i
\(466\) −3.09017 + 9.51057i −0.143149 + 0.440568i
\(467\) −16.6251 + 22.8825i −0.769317 + 1.05887i 0.227065 + 0.973880i \(0.427087\pi\)
−0.996381 + 0.0849941i \(0.972913\pi\)
\(468\) 7.21444 + 10.4858i 0.333488 + 0.484706i
\(469\) 2.68999 + 0.874032i 0.124212 + 0.0403591i
\(470\) 2.47214 + 7.60845i 0.114031 + 0.350952i
\(471\) 32.8054 + 11.1268i 1.51159 + 0.512694i
\(472\) 33.9411i 1.56227i
\(473\) 0 0
\(474\) −6.00000 + 4.24264i −0.275589 + 0.194871i
\(475\) 7.48128 + 10.2971i 0.343265 + 0.472464i
\(476\) −8.06998 + 2.62210i −0.369887 + 0.120184i
\(477\) −10.3243 + 13.4688i −0.472715 + 0.616696i
\(478\) 12.9443 + 9.40456i 0.592057 + 0.430155i
\(479\) 22.6525 + 16.4580i 1.03502 + 0.751985i 0.969307 0.245854i \(-0.0790684\pi\)
0.0657112 + 0.997839i \(0.479068\pi\)
\(480\) −7.26963 23.3913i −0.331812 1.06766i
\(481\) 32.2799 10.4884i 1.47184 0.478229i
\(482\) 2.49376 + 3.43237i 0.113588 + 0.156340i
\(483\) 0 0
\(484\) 0 0
\(485\) 5.65685i 0.256865i
\(486\) −8.33478 13.1731i −0.378073 0.597546i
\(487\) 0.618034 + 1.90211i 0.0280058 + 0.0861930i 0.964082 0.265603i \(-0.0855711\pi\)
−0.936077 + 0.351796i \(0.885571\pi\)
\(488\) 28.2449 + 9.17734i 1.27859 + 0.415439i
\(489\) 0.444738 34.6382i 0.0201117 1.56639i
\(490\) −8.31254 + 11.4412i −0.375522 + 0.516862i
\(491\) −6.18034 + 19.0211i −0.278915 + 0.858412i 0.709242 + 0.704965i \(0.249037\pi\)
−0.988157 + 0.153447i \(0.950963\pi\)
\(492\) −6.21588 + 8.32844i −0.280234 + 0.375475i
\(493\) 9.70820 7.05342i 0.437236 0.317670i
\(494\) −18.0000 −0.809858
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 3.23607 2.35114i 0.145157 0.105463i
\(498\) 16.5757 22.2092i 0.742774 0.995216i
\(499\) −4.32624 + 13.3148i −0.193669 + 0.596052i 0.806321 + 0.591479i \(0.201456\pi\)
−0.999990 + 0.00457310i \(0.998544\pi\)
\(500\) −3.32502 + 4.57649i −0.148699 + 0.204667i
\(501\) −0.266843 + 20.7829i −0.0119216 + 0.928511i
\(502\) 24.2099 + 7.86629i 1.08054 + 0.351090i
\(503\) 4.94427 + 15.2169i 0.220454 + 0.678488i 0.998721 + 0.0505549i \(0.0160990\pi\)
−0.778267 + 0.627933i \(0.783901\pi\)
\(504\) 12.2020 3.62105i 0.543519 0.161295i
\(505\) 28.2843i 1.25863i
\(506\) 0 0
\(507\) −5.00000 7.07107i −0.222058 0.314037i
\(508\) 5.81878 + 8.00886i 0.258166 + 0.355336i
\(509\) −32.2799 + 10.4884i −1.43078 + 0.464889i −0.919011 0.394232i \(-0.871011\pi\)
−0.511772 + 0.859121i \(0.671011\pi\)
\(510\) 8.72356 + 28.0695i 0.386286 + 1.24294i
\(511\) 1.61803 + 1.17557i 0.0715776 + 0.0520042i
\(512\) −8.89919 6.46564i −0.393292 0.285744i
\(513\) −22.0291 0.848901i −0.972607 0.0374799i
\(514\) −10.7600 + 3.49613i −0.474602 + 0.154208i
\(515\) −13.3001 18.3060i −0.586071 0.806657i
\(516\) 6.00000 4.24264i 0.264135 0.186772i
\(517\) 0 0
\(518\) 11.3137i 0.497096i
\(519\) 9.84163 + 3.33803i 0.431999 + 0.146523i
\(520\) 11.1246 + 34.2380i 0.487846 + 1.50144i
\(521\) 18.8300 + 6.11822i 0.824955 + 0.268044i 0.690919 0.722932i \(-0.257206\pi\)
0.134036 + 0.990976i \(0.457206\pi\)
\(522\) −4.94305 + 3.40092i −0.216351 + 0.148854i
\(523\) −12.4688 + 17.1618i −0.545223 + 0.750435i −0.989354 0.145527i \(-0.953512\pi\)
0.444131 + 0.895962i \(0.353512\pi\)
\(524\) 0 0
\(525\) 5.88909 + 4.39529i 0.257021 + 0.191826i
\(526\) 0 0
\(527\) 12.0000 0.522728
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) −12.9443 + 9.40456i −0.562263 + 0.408508i
\(531\) −0.871432 + 33.9299i −0.0378169 + 1.47243i
\(532\) 1.85410 5.70634i 0.0803855 0.247401i
\(533\) 14.9626 20.5942i 0.648101 0.892034i
\(534\) 0 0
\(535\) 43.0399 + 13.9845i 1.86078 + 0.604603i
\(536\) 1.85410 + 5.70634i 0.0800850 + 0.246476i
\(537\) 1.57356 4.63939i 0.0679041 0.200204i
\(538\) 28.2843i 1.21942i
\(539\) 0 0
\(540\) 4.00000 + 14.1421i 0.172133 + 0.608581i
\(541\) 20.7813 + 28.6031i 0.893460 + 1.22974i 0.972508 + 0.232871i \(0.0748121\pi\)
−0.0790477 + 0.996871i \(0.525188\pi\)
\(542\) −28.2449 + 9.17734i −1.21322 + 0.394200i
\(543\) −16.5401 + 5.14040i −0.709805 + 0.220596i
\(544\) −24.2705 17.6336i −1.04059 0.756033i
\(545\) 9.70820 + 7.05342i 0.415854 + 0.302135i
\(546\) −9.92408 + 3.08424i −0.424712 + 0.131993i
\(547\) −33.6249 + 10.9254i −1.43770 + 0.467136i −0.921179 0.389139i \(-0.872772\pi\)
−0.516519 + 0.856276i \(0.672772\pi\)
\(548\) 1.66251 + 2.28825i 0.0710188 + 0.0977490i
\(549\) −28.0000 9.89949i −1.19501 0.422500i
\(550\) 0 0
\(551\) 8.48528i 0.361485i
\(552\) 0 0
\(553\) 1.85410 + 5.70634i 0.0788444 + 0.242658i
\(554\) 4.03499 + 1.31105i 0.171430 + 0.0557011i
\(555\) 39.1886 + 0.503163i 1.66346 + 0.0213581i
\(556\) −0.831254 + 1.14412i −0.0352530 + 0.0485216i
\(557\) 0.618034 1.90211i 0.0261869 0.0805951i −0.937109 0.349037i \(-0.886509\pi\)
0.963296 + 0.268442i \(0.0865087\pi\)
\(558\) −5.99802 0.154049i −0.253917 0.00652141i
\(559\) −14.5623 + 10.5801i −0.615920 + 0.447492i
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 9.70820 7.05342i 0.409152 0.297266i −0.364106 0.931357i \(-0.618626\pi\)
0.773258 + 0.634091i \(0.218626\pi\)
\(564\) 3.92606 + 2.93019i 0.165317 + 0.123383i
\(565\) −2.47214 + 7.60845i −0.104004 + 0.320090i
\(566\) 15.7938 21.7383i 0.663864 0.913730i
\(567\) −12.2909 + 3.30658i −0.516170 + 0.138863i
\(568\) 8.06998 + 2.62210i 0.338609 + 0.110021i
\(569\) 11.7426 + 36.1401i 0.492277 + 1.51507i 0.821157 + 0.570702i \(0.193329\pi\)
−0.328880 + 0.944372i \(0.606671\pi\)
\(570\) −19.6833 6.67605i −0.824441 0.279629i
\(571\) 26.8701i 1.12448i −0.826975 0.562238i \(-0.809940\pi\)
0.826975 0.562238i \(-0.190060\pi\)
\(572\) 0 0
\(573\) −28.0000 + 19.7990i −1.16972 + 0.827115i
\(574\) −4.98752 6.86474i −0.208175 0.286529i
\(575\) 0 0
\(576\) 16.6668 + 12.7756i 0.694452 + 0.532317i
\(577\) 25.8885 + 18.8091i 1.07775 + 0.783034i 0.977290 0.211906i \(-0.0679672\pi\)
0.100464 + 0.994941i \(0.467967\pi\)
\(578\) 15.3713 + 11.1679i 0.639363 + 0.464524i
\(579\) −10.9044 35.0869i −0.453173 1.45816i
\(580\) 5.37999 1.74806i 0.223392 0.0725844i
\(581\) −13.3001 18.3060i −0.551780 0.759459i
\(582\) 2.00000 + 2.82843i 0.0829027 + 0.117242i
\(583\) 0 0
\(584\) 4.24264i 0.175562i
\(585\) −10.2419 34.5124i −0.423450 1.42691i
\(586\) −0.618034 1.90211i −0.0255307 0.0785756i
\(587\) −10.7600 3.49613i −0.444112 0.144301i 0.0784201 0.996920i \(-0.475012\pi\)
−0.522532 + 0.852620i \(0.675012\pi\)
\(588\) −0.111184 + 8.65954i −0.00458517 + 0.357113i
\(589\) −4.98752 + 6.86474i −0.205507 + 0.282857i
\(590\) −9.88854 + 30.4338i −0.407105 + 1.25294i
\(591\) 22.7916 30.5376i 0.937520 1.25615i
\(592\) 6.47214 4.70228i 0.266003 0.193263i
\(593\) 22.0000 0.903432 0.451716 0.892162i \(-0.350812\pi\)
0.451716 + 0.892162i \(0.350812\pi\)
\(594\) 0 0
\(595\) 24.0000 0.983904
\(596\) −4.85410 + 3.52671i −0.198832 + 0.144460i
\(597\) −2.07196 + 2.77615i −0.0847997 + 0.113620i
\(598\) 0 0
\(599\) 19.9501 27.4589i 0.815139 1.12194i −0.175371 0.984502i \(-0.556113\pi\)
0.990510 0.137440i \(-0.0438874\pi\)
\(600\) −0.200132 + 15.5872i −0.00817035 + 0.636344i
\(601\) −28.2449 9.17734i −1.15214 0.374351i −0.330188 0.943915i \(-0.607112\pi\)
−0.821947 + 0.569564i \(0.807112\pi\)
\(602\) 1.85410 + 5.70634i 0.0755676 + 0.232573i
\(603\) −1.70698 5.75206i −0.0695137 0.234242i
\(604\) 4.24264i 0.172631i
\(605\) 0 0
\(606\) −10.0000 14.1421i −0.406222 0.574485i
\(607\) 2.49376 + 3.43237i 0.101219 + 0.139316i 0.856622 0.515945i \(-0.172559\pi\)
−0.755403 + 0.655260i \(0.772559\pi\)
\(608\) 20.1750 6.55524i 0.818202 0.265850i
\(609\) 1.45393 + 4.67826i 0.0589161 + 0.189573i
\(610\) −22.6525 16.4580i −0.917172 0.666364i
\(611\) −9.70820 7.05342i −0.392752 0.285351i
\(612\) 14.2859 + 10.9505i 0.577472 + 0.442649i
\(613\) −4.03499 + 1.31105i −0.162972 + 0.0529527i −0.389367 0.921083i \(-0.627306\pi\)
0.226395 + 0.974036i \(0.427306\pi\)
\(614\) 2.49376 + 3.43237i 0.100640 + 0.138519i
\(615\) 24.0000 16.9706i 0.967773 0.684319i
\(616\) 0 0
\(617\) 31.1127i 1.25255i −0.779602 0.626275i \(-0.784579\pi\)
0.779602 0.626275i \(-0.215421\pi\)
\(618\) 13.1222 + 4.45070i 0.527851 + 0.179033i
\(619\) −6.18034 19.0211i −0.248409 0.764524i −0.995057 0.0993047i \(-0.968338\pi\)
0.746648 0.665219i \(-0.231662\pi\)
\(620\) 5.37999 + 1.74806i 0.216066 + 0.0702039i
\(621\) 0 0
\(622\) 16.6251 22.8825i 0.666605 0.917503i
\(623\) 0 0
\(624\) −5.88909 4.39529i −0.235752 0.175952i
\(625\) 25.0795 18.2213i 1.00318 0.728854i
\(626\) −12.0000 −0.479616
\(627\) 0 0
\(628\) 20.0000 0.798087
\(629\) 38.8328 28.2137i 1.54837 1.12495i
\(630\) −11.9960 0.308098i −0.477934 0.0122749i
\(631\) −4.32624 + 13.3148i −0.172225 + 0.530053i −0.999496 0.0317495i \(-0.989892\pi\)
0.827271 + 0.561803i \(0.189892\pi\)
\(632\) −7.48128 + 10.2971i −0.297590 + 0.409597i
\(633\) 46.5365 + 0.597506i 1.84966 + 0.0237487i
\(634\) 24.2099 + 7.86629i 0.961500 + 0.312410i
\(635\) −8.65248 26.6296i −0.343363 1.05676i
\(636\) −3.14712 + 9.27877i −0.124791 + 0.367927i
\(637\) 21.2132i 0.840498i
\(638\) 0 0
\(639\) −8.00000 2.82843i −0.316475 0.111891i
\(640\) −4.98752 6.86474i −0.197149 0.271353i
\(641\) 26.8999 8.74032i 1.06248 0.345222i 0.274928 0.961465i \(-0.411346\pi\)
0.787556 + 0.616243i \(0.211346\pi\)
\(642\) −26.4642 + 8.22465i −1.04446 + 0.324601i
\(643\) −9.70820 7.05342i −0.382854 0.278160i 0.379667 0.925123i \(-0.376039\pi\)
−0.762521 + 0.646963i \(0.776039\pi\)
\(644\) 0 0
\(645\) −19.8482 + 6.16849i −0.781521 + 0.242884i
\(646\) −24.2099 + 7.86629i −0.952528 + 0.309495i
\(647\) −3.32502 4.57649i −0.130720 0.179920i 0.738640 0.674100i \(-0.235468\pi\)
−0.869360 + 0.494180i \(0.835468\pi\)
\(648\) −21.0000 16.9706i −0.824958 0.666667i
\(649\) 0 0
\(650\) 12.7279i 0.499230i
\(651\) −1.57356 + 4.63939i −0.0616727 + 0.181832i
\(652\) −6.18034 19.0211i −0.242041 0.744925i
\(653\) −10.7600 3.49613i −0.421070 0.136814i 0.0908151 0.995868i \(-0.471053\pi\)
−0.511885 + 0.859054i \(0.671053\pi\)
\(654\) −7.34786 0.0943431i −0.287324 0.00368911i
\(655\) 0 0
\(656\) 1.85410 5.70634i 0.0723905 0.222795i
\(657\) 0.108929 4.24124i 0.00424973 0.165467i
\(658\) −3.23607 + 2.35114i −0.126155 + 0.0916570i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −20.0000 −0.777910 −0.388955 0.921257i \(-0.627164\pi\)
−0.388955 + 0.921257i \(0.627164\pi\)
\(662\) −16.1803 + 11.7557i −0.628867 + 0.456898i
\(663\) −35.3346 26.3717i −1.37228 1.02419i
\(664\) 14.8328 45.6507i 0.575625 1.77159i
\(665\) −9.97505 + 13.7295i −0.386816 + 0.532406i
\(666\) −19.7722 + 13.6037i −0.766157 + 0.527132i
\(667\) 0 0
\(668\) 3.70820 + 11.4127i 0.143475 + 0.441570i
\(669\) −39.3665 13.3521i −1.52200 0.516222i
\(670\) 5.65685i 0.218543i
\(671\) 0 0
\(672\) 10.0000 7.07107i 0.385758 0.272772i
\(673\) 2.49376 + 3.43237i 0.0961274 + 0.132308i 0.854371 0.519663i \(-0.173942\pi\)
−0.758244 + 0.651971i \(0.773942\pi\)
\(674\) 30.9349 10.0514i 1.19157 0.387164i
\(675\) 0.600264 15.5769i 0.0231042 0.599555i
\(676\) −4.04508 2.93893i −0.155580 0.113036i
\(677\) −30.7426 22.3358i −1.18154 0.858436i −0.189192 0.981940i \(-0.560587\pi\)
−0.992344 + 0.123504i \(0.960587\pi\)
\(678\) −1.45393 4.67826i −0.0558377 0.179667i
\(679\) 2.68999 0.874032i 0.103232 0.0335423i
\(680\) 29.9251 + 41.1884i 1.14758 + 1.57950i
\(681\) 24.0000 + 33.9411i 0.919682 + 1.30063i
\(682\) 0 0
\(683\) 31.1127i 1.19049i 0.803543 + 0.595247i \(0.202946\pi\)
−0.803543 + 0.595247i \(0.797054\pi\)
\(684\) −12.2020 + 3.62105i −0.466554 + 0.138454i
\(685\) −2.47214 7.60845i −0.0944555 0.290704i
\(686\) −16.1400 5.24419i −0.616227 0.200224i
\(687\) −0.533685 + 41.5658i −0.0203614 + 1.58583i
\(688\) −2.49376 + 3.43237i −0.0950738 + 0.130858i
\(689\) 7.41641 22.8254i 0.282543 0.869577i
\(690\) 0 0
\(691\) −16.1803 + 11.7557i −0.615529 + 0.447208i −0.851357 0.524587i \(-0.824220\pi\)
0.235828 + 0.971795i \(0.424220\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) 3.23607 2.35114i 0.122751 0.0891839i
\(696\) −6.21588 + 8.32844i −0.235612 + 0.315689i
\(697\) 11.1246 34.2380i 0.421375 1.29686i
\(698\) −2.49376 + 3.43237i −0.0943903 + 0.129917i
\(699\) 0.222369 17.3191i 0.00841076 0.655068i
\(700\) 4.03499 + 1.31105i 0.152508 + 0.0495530i
\(701\) −1.85410 5.70634i −0.0700285 0.215525i 0.909917 0.414790i \(-0.136145\pi\)
−0.979946 + 0.199264i \(0.936145\pi\)
\(702\) 17.3229 + 13.6351i 0.653811 + 0.514625i
\(703\) 33.9411i 1.28011i
\(704\) 0 0
\(705\) −8.00000 11.3137i −0.301297 0.426099i
\(706\) 0 0
\(707\) −13.4500 + 4.37016i −0.505838 + 0.164357i
\(708\) 5.81570 + 18.7130i 0.218568 + 0.703279i
\(709\) 25.8885 + 18.8091i 0.972265 + 0.706392i 0.955967 0.293476i \(-0.0948119\pi\)
0.0162981 + 0.999867i \(0.494812\pi\)
\(710\) −6.47214 4.70228i −0.242895 0.176473i
\(711\) 7.74320 10.1016i 0.290393 0.378841i
\(712\) 0 0
\(713\) 0 0
\(714\) −12.0000 + 8.48528i −0.449089 + 0.317554i
\(715\) 0 0
\(716\) 2.82843i 0.105703i
\(717\) −26.2443 8.90140i −0.980113 0.332429i
\(718\) 6.18034 + 19.0211i 0.230648 + 0.709862i
\(719\) 18.8300 + 6.11822i 0.702239 + 0.228171i 0.638306 0.769783i \(-0.279636\pi\)
0.0639332 + 0.997954i \(0.479636\pi\)
\(720\) −4.80963 6.99053i −0.179244 0.260522i
\(721\) 6.65003 9.15298i 0.247660 0.340875i
\(722\) −0.309017 + 0.951057i −0.0115004 + 0.0353947i
\(723\) −5.88909 4.39529i −0.219018 0.163463i
\(724\) −8.09017 + 5.87785i −0.300669 + 0.218449i
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 2.00000 0.0741759 0.0370879 0.999312i \(-0.488192\pi\)
0.0370879 + 0.999312i \(0.488192\pi\)
\(728\) −14.5623 + 10.5801i −0.539715 + 0.392126i
\(729\) 20.5574 + 17.5041i 0.761384 + 0.648301i
\(730\) 1.23607 3.80423i 0.0457489 0.140801i
\(731\) −14.9626 + 20.5942i −0.553411 + 0.761704i
\(732\) −17.1450 0.220134i −0.633698 0.00813638i
\(733\) 1.34500 + 0.437016i 0.0496786 + 0.0161416i 0.333751 0.942661i \(-0.391686\pi\)
−0.284072 + 0.958803i \(0.591686\pi\)
\(734\) −2.47214 7.60845i −0.0912482 0.280833i
\(735\) 7.86780 23.1969i 0.290208 0.855632i
\(736\) 0 0
\(737\) 0 0
\(738\) −6.00000 + 16.9706i −0.220863 + 0.624695i
\(739\) 2.49376 + 3.43237i 0.0917345 + 0.126262i 0.852417 0.522862i \(-0.175136\pi\)
−0.760683 + 0.649124i \(0.775136\pi\)
\(740\) 21.5200 6.99226i 0.791089 0.257040i
\(741\) 29.7723 9.25273i 1.09371 0.339907i
\(742\) −6.47214 4.70228i −0.237600 0.172626i
\(743\) −12.9443 9.40456i −0.474879 0.345020i 0.324461 0.945899i \(-0.394817\pi\)
−0.799340 + 0.600879i \(0.794817\pi\)
\(744\) −9.92408 + 3.08424i −0.363835 + 0.113074i
\(745\) 16.1400 5.24419i 0.591323 0.192132i
\(746\) 2.49376 + 3.43237i 0.0913031 + 0.125668i
\(747\) −16.0000 + 45.2548i −0.585409 + 1.65579i
\(748\) 0 0
\(749\) 22.6274i 0.826788i
\(750\) −3.14712 + 9.27877i −0.114917 + 0.338813i
\(751\) 0.618034 + 1.90211i 0.0225524 + 0.0694091i 0.961699 0.274107i \(-0.0883821\pi\)
−0.939147 + 0.343516i \(0.888382\pi\)
\(752\) −2.68999 0.874032i −0.0980940 0.0318727i
\(753\) −44.0872 0.566059i −1.60663 0.0206283i
\(754\) 4.98752 6.86474i 0.181635 0.249999i
\(755\) −3.70820 + 11.4127i −0.134955 + 0.415350i
\(756\) −6.10695 + 4.08719i −0.222108 + 0.148650i
\(757\) −16.1803 + 11.7557i −0.588084 + 0.427268i −0.841630 0.540055i \(-0.818403\pi\)
0.253545 + 0.967324i \(0.418403\pi\)
\(758\) −12.0000 −0.435860
\(759\) 0 0
\(760\) −36.0000 −1.30586
\(761\) −8.09017 + 5.87785i −0.293268 + 0.213072i −0.724684 0.689081i \(-0.758014\pi\)
0.431416 + 0.902153i \(0.358014\pi\)
\(762\) 13.7412 + 10.2557i 0.497792 + 0.371524i
\(763\) −1.85410 + 5.70634i −0.0671230 + 0.206583i
\(764\) −11.6376 + 16.0177i −0.421032 + 0.579501i
\(765\) −28.8578 41.9432i −1.04335 1.51646i
\(766\) −5.37999 1.74806i −0.194387 0.0631601i
\(767\) −14.8328 45.6507i −0.535582 1.64835i
\(768\) 27.8846 + 9.45774i 1.00620 + 0.341277i
\(769\) 35.3553i 1.27495i 0.770473 + 0.637473i \(0.220020\pi\)
−0.770473 + 0.637473i \(0.779980\pi\)
\(770\) 0 0
\(771\) 16.0000 11.3137i 0.576226 0.407453i
\(772\) −12.4688 17.1618i −0.448762 0.617668i
\(773\) −32.2799 + 10.4884i −1.16103 + 0.377241i −0.825287 0.564713i \(-0.808987\pi\)
−0.335741 + 0.941954i \(0.608987\pi\)
\(774\) 7.74320 10.1016i 0.278323 0.363096i
\(775\) −4.85410 3.52671i −0.174364 0.126683i
\(776\) 4.85410 + 3.52671i 0.174252 + 0.126602i
\(777\) 5.81570 + 18.7130i 0.208637 + 0.671326i
\(778\) 18.8300 6.11822i 0.675087 0.219349i
\(779\) 14.9626 + 20.5942i 0.536090 + 0.737864i
\(780\) −12.0000 16.9706i −0.429669 0.607644i
\(781\) 0 0
\(782\) 0 0
\(783\) 6.42766 8.16610i 0.229706 0.291833i
\(784\) −1.54508 4.75528i −0.0551816 0.169832i
\(785\) −53.7999 17.4806i −1.92020 0.623911i
\(786\) 0 0
\(787\) −12.4688 + 17.1618i −0.444465 + 0.611754i −0.971197 0.238278i \(-0.923417\pi\)
0.526732 + 0.850031i \(0.323417\pi\)
\(788\) 6.79837 20.9232i 0.242182 0.745360i
\(789\) 0 0
\(790\) 9.70820 7.05342i 0.345402 0.250950i
\(791\) −4.00000 −0.142224
\(792\) 0 0
\(793\) 42.0000 1.49146
\(794\) 1.61803 1.17557i 0.0574219 0.0417194i
\(795\) 16.5757 22.2092i 0.587879 0.787678i
\(796\) −0.618034 + 1.90211i −0.0219056 + 0.0674186i
\(797\) 1.66251 2.28825i 0.0588890 0.0810538i −0.778557 0.627574i \(-0.784048\pi\)
0.837446 + 0.546520i \(0.184048\pi\)
\(798\) 0.133421 10.3914i 0.00472306 0.367853i
\(799\) −16.1400 5.24419i −0.570991 0.185526i
\(800\) 4.63525 + 14.2658i 0.163881 + 0.504374i
\(801\) 0 0
\(802\) 2.82843i 0.0998752i
\(803\) 0 0
\(804\) −2.00000 2.82843i −0.0705346 0.0997509i
\(805\) 0 0
\(806\) 8.06998 2.62210i 0.284253 0.0923594i
\(807\) −14.5393 46.7826i −0.511806 1.64682i
\(808\) −24.2705 17.6336i −0.853834 0.620346i
\(809\) 40.4508 + 29.3893i 1.42218 + 1.03327i 0.991408 + 0.130809i \(0.0417575\pi\)
0.430769 + 0.902462i \(0.358243\pi\)
\(810\) 13.8857 + 21.3351i 0.487893 + 0.749640i
\(811\) 25.5549 8.30330i 0.897355 0.291568i 0.176210 0.984353i \(-0.443616\pi\)
0.721145 + 0.692784i \(0.243616\pi\)
\(812\) 1.66251 + 2.28825i 0.0583426 + 0.0803017i
\(813\) 42.0000 29.6985i 1.47300 1.04157i
\(814\) 0 0
\(815\) 56.5685i 1.98151i
\(816\) −9.84163 3.33803i −0.344526 0.116854i
\(817\) −5.56231 17.1190i −0.194600 0.598919i
\(818\) 4.03499 + 1.31105i 0.141080 + 0.0458397i
\(819\) 14.8291 10.2028i 0.518172 0.356513i
\(820\) 9.97505 13.7295i 0.348344 0.479454i
\(821\) −12.9787 + 39.9444i −0.452960 + 1.39407i 0.420553 + 0.907268i \(0.361836\pi\)
−0.873513 + 0.486800i \(0.838164\pi\)
\(822\) 3.92606 + 2.93019i 0.136937 + 0.102202i
\(823\) 19.4164 14.1068i 0.676813 0.491734i −0.195486 0.980707i \(-0.562628\pi\)
0.872299 + 0.488973i \(0.162628\pi\)
\(824\) 24.0000 0.836080
\(825\) 0 0
\(826\) −16.0000 −0.556711
\(827\) 9.70820 7.05342i 0.337587 0.245272i −0.406056 0.913848i \(-0.633096\pi\)
0.743643 + 0.668577i \(0.233096\pi\)
\(828\) 0 0
\(829\) −4.32624 + 13.3148i −0.150256 + 0.462442i −0.997649 0.0685244i \(-0.978171\pi\)
0.847393 + 0.530966i \(0.178171\pi\)
\(830\) −26.6001 + 36.6119i −0.923304 + 1.27082i
\(831\) −7.34786 0.0943431i −0.254895 0.00327273i
\(832\) −28.2449 9.17734i −0.979217 0.318167i
\(833\) −9.27051 28.5317i −0.321204 0.988565i
\(834\) −0.786780 + 2.31969i −0.0272440 + 0.0803244i
\(835\) 33.9411i 1.17458i
\(836\) 0 0
\(837\) 10.0000 2.82843i 0.345651 0.0977647i
\(838\) −18.2876 25.1707i −0.631734 0.869507i
\(839\) −32.2799 + 10.4884i −1.11443 + 0.362099i −0.807638 0.589678i \(-0.799255\pi\)
−0.306789 + 0.951778i \(0.599255\pi\)
\(840\) −19.8482 + 6.16849i −0.684827 + 0.212833i
\(841\) 20.2254 + 14.6946i 0.697428 + 0.506711i
\(842\) −16.1803 11.7557i −0.557611 0.405128i
\(843\) −9.92408 + 3.08424i −0.341804 + 0.106227i
\(844\) 25.5549 8.30330i 0.879637 0.285812i
\(845\) 8.31254 + 11.4412i 0.285960 + 0.393590i
\(846\) 8.00000 + 2.82843i 0.275046 + 0.0972433i
\(847\) 0 0
\(848\) 5.65685i 0.194257i
\(849\) −14.9488 + 44.0742i −0.513042 + 1.51262i
\(850\) −5.56231 17.1190i −0.190786 0.587177i
\(851\) 0 0
\(852\) −4.89858 0.0628954i −0.167822 0.00215476i
\(853\) 24.1064 33.1796i 0.825386 1.13605i −0.163378 0.986564i \(-0.552239\pi\)
0.988764 0.149483i \(-0.0477609\pi\)
\(854\) 4.32624 13.3148i 0.148041 0.455623i
\(855\) 35.9881 + 0.924294i 1.23077 + 0.0316102i
\(856\) −38.8328 + 28.2137i −1.32728 + 0.964324i
\(857\) 22.0000 0.751506 0.375753 0.926720i \(-0.377384\pi\)
0.375753 + 0.926720i \(0.377384\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) −9.70820 + 7.05342i −0.331047 + 0.240520i
\(861\) 11.7782 + 8.79058i 0.401400 + 0.299582i
\(862\) −9.88854 + 30.4338i −0.336805 + 1.03658i
\(863\) 19.9501 27.4589i 0.679109 0.934713i −0.320814 0.947142i \(-0.603956\pi\)
0.999923 + 0.0124289i \(0.00395634\pi\)
\(864\) −24.3817 8.97402i −0.829482 0.305302i
\(865\) −16.1400 5.24419i −0.548775 0.178308i
\(866\) −9.27051 28.5317i −0.315025 0.969546i
\(867\) −31.1651 10.5704i −1.05842 0.358990i
\(868\) 2.82843i 0.0960031i
\(869\) 0 0
\(870\) 8.00000 5.65685i 0.271225 0.191785i
\(871\) 4.98752 + 6.86474i 0.168996 + 0.232603i
\(872\) −12.1050 + 3.93314i −0.409926 + 0.133193i
\(873\) −4.76195 3.65018i −0.161168 0.123540i
\(874\) 0 0
\(875\) 6.47214 + 4.70228i 0.218798 + 0.158966i
\(876\) −0.726963 2.33913i −0.0245618 0.0790318i
\(877\) −33.6249 + 10.9254i −1.13543 + 0.368925i −0.815638 0.578562i \(-0.803614\pi\)
−0.319795 + 0.947487i \(0.603614\pi\)
\(878\) −15.7938 21.7383i −0.533016 0.733633i
\(879\) 2.00000 + 2.82843i 0.0674583 + 0.0954005i
\(880\) 0 0
\(881\) 31.1127i 1.04821i −0.851653 0.524107i \(-0.824399\pi\)
0.851653 0.524107i \(-0.175601\pi\)
\(882\) 4.26745 + 14.3802i 0.143693 + 0.484205i
\(883\) 14.2148 + 43.7486i 0.478365 + 1.47226i 0.841365 + 0.540468i \(0.181753\pi\)
−0.362999 + 0.931790i \(0.618247\pi\)
\(884\) −24.2099 7.86629i −0.814269 0.264572i
\(885\) 0.711580 55.4211i 0.0239195 1.86296i
\(886\) 16.6251 22.8825i 0.558530 0.768751i
\(887\) 7.41641 22.8254i 0.249019 0.766400i −0.745931 0.666023i \(-0.767995\pi\)
0.994949 0.100377i \(-0.0320049\pi\)
\(888\) −24.8635 + 33.3137i −0.834365 + 1.11794i
\(889\) 11.3262 8.22899i 0.379870 0.275992i
\(890\) 0 0
\(891\) 0 0
\(892\) −24.0000 −0.803579
\(893\) 9.70820 7.05342i 0.324873 0.236034i
\(894\) −6.21588 + 8.32844i −0.207890 + 0.278545i
\(895\) −2.47214 + 7.60845i −0.0826344 + 0.254323i
\(896\) 2.49376 3.43237i 0.0833107 0.114667i
\(897\) 0 0
\(898\) −5.37999 1.74806i −0.179533 0.0583337i
\(899\) −1.23607 3.80423i −0.0412252 0.126878i
\(900\) −2.56047 8.62809i −0.0853491 0.287603i
\(901\) 33.9411i 1.13074i
\(902\) 0 0
\(903\) −6.00000 8.48528i −0.199667 0.282372i
\(904\) −4.98752 6.86474i −0.165883 0.228318i
\(905\) 26.8999 8.74032i 0.894184 0.290538i
\(906\) −2.18089 7.01739i −0.0724552 0.233137i
\(907\) −9.70820 7.05342i −0.322356 0.234205i 0.414824 0.909902i \(-0.363843\pi\)
−0.737180 + 0.675696i \(0.763843\pi\)
\(908\) 19.4164 + 14.1068i 0.644356 + 0.468152i
\(909\) 23.8098 + 18.2509i 0.789720 + 0.605344i
\(910\) 16.1400 5.24419i 0.535035 0.173843i
\(911\) −21.6126 29.7472i −0.716057 0.985568i −0.999646 0.0266223i \(-0.991525\pi\)
0.283588 0.958946i \(-0.408475\pi\)
\(912\) 6.00000 4.24264i 0.198680 0.140488i
\(913\) 0 0
\(914\) 9.89949i 0.327446i
\(915\) 45.9276 + 15.5775i 1.51832 + 0.514975i
\(916\) 7.41641 + 22.8254i 0.245045 + 0.754171i
\(917\) 0 0
\(918\) 29.2580 + 10.7688i 0.965659 + 0.355424i
\(919\) −12.4688 + 17.1618i −0.411308 + 0.566117i −0.963537 0.267576i \(-0.913777\pi\)
0.552229 + 0.833693i \(0.313777\pi\)
\(920\) 0 0
\(921\) −5.88909 4.39529i −0.194052 0.144830i
\(922\) −17.7984 + 12.9313i −0.586158 + 0.425869i
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) −24.0000 −0.789115
\(926\) 19.4164 14.1068i 0.638063 0.463580i
\(927\) −23.9921 0.616196i −0.788004 0.0202385i
\(928\) −3.09017 + 9.51057i −0.101440 + 0.312200i
\(929\) 1.66251 2.28825i 0.0545451 0.0750749i −0.780873 0.624690i \(-0.785225\pi\)
0.835418 + 0.549615i \(0.185225\pi\)
\(930\) 9.79715 + 0.125791i 0.321261 + 0.00412484i
\(931\) 20.1750 + 6.55524i 0.661207 + 0.214839i
\(932\) −3.09017 9.51057i −0.101222 0.311529i
\(933\) −15.7356 + 46.3939i −0.515160 + 1.51887i
\(934\) 28.2843i 0.925490i
\(935\) 0 0
\(936\) 36.0000 + 12.7279i 1.17670 + 0.416025i
\(937\) 20.7813 + 28.6031i 0.678897 + 0.934422i 0.999920 0.0126498i \(-0.00402667\pi\)
−0.321023 + 0.947071i \(0.604027\pi\)
\(938\) 2.68999 0.874032i 0.0878314 0.0285382i
\(939\) 19.8482 6.16849i 0.647720 0.201301i
\(940\) −6.47214 4.70228i −0.211098 0.153372i
\(941\) −30.7426 22.3358i −1.00218 0.728128i −0.0396268 0.999215i \(-0.512617\pi\)
−0.962555 + 0.271087i \(0.912617\pi\)
\(942\) 33.0803 10.2808i 1.07781 0.334967i
\(943\) 0 0
\(944\) −6.65003 9.15298i −0.216440 0.297904i
\(945\) 20.0000 5.65685i 0.650600 0.184017i
\(946\) 0 0
\(947\) 31.1127i 1.01103i 0.862819 + 0.505513i \(0.168697\pi\)
−0.862819 + 0.505513i \(0.831303\pi\)
\(948\) 2.36034 6.95908i 0.0766603 0.226020i
\(949\) 1.85410 + 5.70634i 0.0601867 + 0.185236i
\(950\) 12.1050 + 3.93314i 0.392737 + 0.127608i
\(951\) −44.0872 0.566059i −1.42962 0.0183557i
\(952\) −14.9626 + 20.5942i −0.484940 + 0.667462i
\(953\) 0.618034 1.90211i 0.0200201 0.0616155i −0.940547 0.339663i \(-0.889687\pi\)
0.960567 + 0.278047i \(0.0896871\pi\)
\(954\) −0.435716 + 16.9650i −0.0141068 + 0.549261i
\(955\) 45.3050 32.9160i 1.46603 1.06514i
\(956\) −16.0000 −0.517477
\(957\) 0 0
\(958\) 28.0000 0.904639
\(959\) 3.23607 2.35114i 0.104498 0.0759223i
\(960\) −27.4824 20.5114i −0.886992 0.662001i
\(961\) −8.34346 + 25.6785i −0.269144 + 0.828340i
\(962\) 19.9501 27.4589i 0.643217 0.885312i
\(963\) 39.5444 27.2074i 1.27430 0.876745i
\(964\) −4.03499 1.31105i −0.129958 0.0422260i
\(965\) 18.5410 + 57.0634i 0.596857 + 1.83694i
\(966\) 0 0
\(967\) 4.24264i 0.136434i 0.997671 + 0.0682171i \(0.0217310\pi\)
−0.997671 + 0.0682171i \(0.978269\pi\)
\(968\) 0 0
\(969\) 36.0000 25.4558i 1.15649 0.817760i
\(970\) −3.32502 4.57649i −0.106760 0.146942i
\(971\) −32.2799 + 10.4884i −1.03591 + 0.336588i −0.777125 0.629346i \(-0.783323\pi\)
−0.258787 + 0.965934i \(0.583323\pi\)
\(972\) 14.4860 + 5.75823i 0.464637 + 0.184695i
\(973\) 1.61803 + 1.17557i 0.0518718 + 0.0376871i
\(974\) 1.61803 + 1.17557i 0.0518452 + 0.0376677i
\(975\) 6.54267 + 21.0522i 0.209533 + 0.674209i
\(976\) 9.41498 3.05911i 0.301366 0.0979198i
\(977\) 14.9626 + 20.5942i 0.478695 + 0.658867i 0.978253 0.207413i \(-0.0665044\pi\)
−0.499558 + 0.866280i \(0.666504\pi\)
\(978\) −20.0000 28.2843i −0.639529 0.904431i
\(979\) 0 0
\(980\) 14.1421i 0.451754i
\(981\) 12.2020 3.62105i 0.389579 0.115611i
\(982\) 6.18034 + 19.0211i 0.197223 + 0.606989i
\(983\) −10.7600 3.49613i −0.343190 0.111509i 0.132351 0.991203i \(-0.457748\pi\)
−0.475541 + 0.879694i \(0.657748\pi\)
\(984\) −0.400264 + 31.1743i −0.0127599 + 0.993802i
\(985\) −36.5752 + 50.3414i −1.16538 + 1.60401i
\(986\) 3.70820 11.4127i 0.118093 0.363454i
\(987\) 4.14392 5.55229i 0.131902 0.176731i
\(988\) 14.5623 10.5801i 0.463289 0.336599i
\(989\) 0 0
\(990\) 0 0
\(991\) −42.0000 −1.33417 −0.667087 0.744980i \(-0.732459\pi\)
−0.667087 + 0.744980i \(0.732459\pi\)
\(992\) −8.09017 + 5.87785i −0.256863 + 0.186622i
\(993\) 20.7196 27.7615i 0.657517 0.880983i
\(994\) 1.23607 3.80423i 0.0392057 0.120663i
\(995\) 3.32502 4.57649i 0.105410 0.145085i
\(996\) −0.355790 + 27.7105i −0.0112736 + 0.878042i
\(997\) −28.2449 9.17734i −0.894526 0.290649i −0.174550 0.984648i \(-0.555847\pi\)
−0.719976 + 0.693999i \(0.755847\pi\)
\(998\) 4.32624 + 13.3148i 0.136945 + 0.421472i
\(999\) 25.7106 32.6644i 0.813449 1.03346i
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 363.2.f.f.239.1 8
3.2 odd 2 363.2.f.a.239.2 8
11.2 odd 10 363.2.d.b.362.2 yes 2
11.3 even 5 inner 363.2.f.f.215.2 8
11.4 even 5 inner 363.2.f.f.161.2 8
11.5 even 5 inner 363.2.f.f.233.1 8
11.6 odd 10 363.2.f.a.233.1 8
11.7 odd 10 363.2.f.a.161.2 8
11.8 odd 10 363.2.f.a.215.2 8
11.9 even 5 363.2.d.a.362.2 yes 2
11.10 odd 2 363.2.f.a.239.1 8
33.2 even 10 363.2.d.a.362.1 2
33.5 odd 10 363.2.f.a.233.2 8
33.8 even 10 inner 363.2.f.f.215.1 8
33.14 odd 10 363.2.f.a.215.1 8
33.17 even 10 inner 363.2.f.f.233.2 8
33.20 odd 10 363.2.d.b.362.1 yes 2
33.26 odd 10 363.2.f.a.161.1 8
33.29 even 10 inner 363.2.f.f.161.1 8
33.32 even 2 inner 363.2.f.f.239.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.2.d.a.362.1 2 33.2 even 10
363.2.d.a.362.2 yes 2 11.9 even 5
363.2.d.b.362.1 yes 2 33.20 odd 10
363.2.d.b.362.2 yes 2 11.2 odd 10
363.2.f.a.161.1 8 33.26 odd 10
363.2.f.a.161.2 8 11.7 odd 10
363.2.f.a.215.1 8 33.14 odd 10
363.2.f.a.215.2 8 11.8 odd 10
363.2.f.a.233.1 8 11.6 odd 10
363.2.f.a.233.2 8 33.5 odd 10
363.2.f.a.239.1 8 11.10 odd 2
363.2.f.a.239.2 8 3.2 odd 2
363.2.f.f.161.1 8 33.29 even 10 inner
363.2.f.f.161.2 8 11.4 even 5 inner
363.2.f.f.215.1 8 33.8 even 10 inner
363.2.f.f.215.2 8 11.3 even 5 inner
363.2.f.f.233.1 8 11.5 even 5 inner
363.2.f.f.233.2 8 33.17 even 10 inner
363.2.f.f.239.1 8 1.1 even 1 trivial
363.2.f.f.239.2 8 33.32 even 2 inner