Properties

Label 363.2.f.f.239.2
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 239.2
Root \(1.34500 + 0.437016i\) of defining polynomial
Character \(\chi\) \(=\) 363.239
Dual form 363.2.f.f.161.2

$q$-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} +(1.65401 + 0.514040i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.66251 + 2.28825i) q^{5} +(1.64027 - 0.556338i) q^{6} +(-1.34500 - 0.437016i) q^{7} +(0.927051 + 2.85317i) q^{8} +(2.47152 + 1.70046i) q^{9} +2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} +(-2.49376 - 3.43237i) q^{13} +(-1.34500 + 0.437016i) q^{14} +(-3.92606 + 2.93019i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.85410 + 3.52671i) q^{17} +(2.99901 - 0.0770245i) q^{18} +(4.03499 - 1.31105i) q^{19} +(-1.66251 - 2.28825i) q^{20} +(-2.00000 - 1.41421i) q^{21} +(0.0667106 + 5.19572i) q^{24} +(-0.927051 - 2.85317i) q^{25} +(-4.03499 - 1.31105i) q^{26} +(3.21383 + 4.08305i) q^{27} +(0.831254 - 1.14412i) q^{28} +(0.618034 - 1.90211i) q^{29} +(-1.45393 + 4.67826i) q^{30} +(1.61803 - 1.17557i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(3.23607 - 2.35114i) q^{35} +(-2.38098 + 1.82509i) q^{36} +(2.47214 - 7.60845i) q^{37} +(2.49376 - 3.43237i) q^{38} +(-2.36034 - 6.95908i) q^{39} +(-8.06998 - 2.62210i) q^{40} +(-1.85410 - 5.70634i) q^{41} +(-2.44929 + 0.0314477i) q^{42} -4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} +(2.68999 - 0.874032i) q^{47} +(1.03598 + 1.38807i) q^{48} +(-4.04508 - 2.93893i) q^{49} +(-2.42705 - 1.76336i) q^{50} +(6.21588 + 8.32844i) q^{51} +(4.03499 - 1.31105i) q^{52} +(3.32502 + 4.57649i) q^{53} +(5.00000 + 1.41421i) q^{54} -4.24264i q^{56} +(7.34786 - 0.0943431i) q^{57} +(-0.618034 - 1.90211i) q^{58} +(10.7600 + 3.49613i) q^{59} +(-1.57356 - 4.63939i) q^{60} +(-5.81878 + 8.00886i) q^{61} +(0.618034 - 1.90211i) q^{62} +(-2.58107 - 3.36721i) 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} +(-2.56047 + 8.62809i) q^{72} +(-1.34500 - 0.437016i) q^{73} +(-2.47214 - 7.60845i) q^{74} +(-0.0667106 - 5.19572i) q^{75} +4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} +(-2.49376 - 3.43237i) q^{79} +(-2.68999 + 0.874032i) q^{80} +(3.21687 + 8.40546i) q^{81} +(-4.85410 - 3.52671i) q^{82} +(-12.9443 - 9.40456i) q^{83} +(1.96303 - 1.46510i) q^{84} +(-16.1400 + 5.24419i) q^{85} +(-2.49376 - 3.43237i) q^{86} +(2.00000 - 2.82843i) q^{87} +(-4.80963 + 6.99053i) q^{90} +(1.85410 + 5.70634i) q^{91} +(3.28054 - 1.11268i) q^{93} +(1.66251 - 2.28825i) q^{94} +(-3.70820 + 11.4127i) q^{95} +(-8.27007 - 2.57020i) 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 \(0.184973\pi\)
\(3\) 1.65401 + 0.514040i 0.954945 + 0.296781i
\(4\) −0.309017 + 0.951057i −0.154508 + 0.475528i
\(5\) −1.66251 + 2.28825i −0.743496 + 1.02333i 0.254914 + 0.966964i \(0.417953\pi\)
−0.998410 + 0.0563708i \(0.982047\pi\)
\(6\) 1.64027 0.556338i 0.669638 0.227124i
\(7\) −1.34500 0.437016i −0.508361 0.165177i 0.0435957 0.999049i \(-0.486119\pi\)
−0.551957 + 0.833873i \(0.686119\pi\)
\(8\) 0.927051 + 2.85317i 0.327762 + 1.00875i
\(9\) 2.47152 + 1.70046i 0.823842 + 0.566820i
\(10\) 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 \(-0.999778\pi\)
0.308355 0.951271i \(-0.400222\pi\)
\(14\) −1.34500 + 0.437016i −0.359466 + 0.116797i
\(15\) −3.92606 + 2.93019i −1.01370 + 0.756573i
\(16\) 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 \(0.440633\pi\)
\(18\) 2.99901 0.0770245i 0.706874 0.0181548i
\(19\) 4.03499 1.31105i 0.925690 0.300775i 0.192891 0.981220i \(-0.438214\pi\)
0.732799 + 0.680445i \(0.238214\pi\)
\(20\) −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 \(\pi\)
\(24\) 0.0667106 + 5.19572i 0.0136173 + 1.06057i
\(25\) −0.927051 2.85317i −0.185410 0.570634i
\(26\) −4.03499 1.31105i −0.791327 0.257118i
\(27\) 3.21383 + 4.08305i 0.618502 + 0.785783i
\(28\) 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 \(0.0405463\pi\)
\(30\) −1.45393 + 4.67826i −0.265449 + 0.854129i
\(31\) 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
\(36\) −2.38098 + 1.82509i −0.396830 + 0.304181i
\(37\) 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
\(39\) −2.36034 6.95908i −0.377957 1.11434i
\(40\) −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 \(-0.255213\pi\)
\(42\) −2.44929 + 0.0314477i −0.377933 + 0.00485249i
\(43\) 4.24264i 0.646997i −0.946229 0.323498i \(-0.895141\pi\)
0.946229 0.323498i \(-0.104859\pi\)
\(44\) 0 0
\(45\) −8.00000 + 2.82843i −1.19257 + 0.421637i
\(46\) 0 0
\(47\) 2.68999 0.874032i 0.392376 0.127491i −0.106183 0.994347i \(-0.533863\pi\)
0.498559 + 0.866856i \(0.333863\pi\)
\(48\) 1.03598 + 1.38807i 0.149531 + 0.200351i
\(49\) −4.04508 2.93893i −0.577869 0.419847i
\(50\) −2.42705 1.76336i −0.343237 0.249376i
\(51\) 6.21588 + 8.32844i 0.870397 + 1.16621i
\(52\) 4.03499 1.31105i 0.559553 0.181810i
\(53\) 3.32502 + 4.57649i 0.456726 + 0.628629i 0.973826 0.227296i \(-0.0729884\pi\)
−0.517100 + 0.855925i \(0.672988\pi\)
\(54\) 5.00000 + 1.41421i 0.680414 + 0.192450i
\(55\) 0 0
\(56\) 4.24264i 0.566947i
\(57\) 7.34786 0.0943431i 0.973248 0.0124960i
\(58\) −0.618034 1.90211i −0.0811518 0.249760i
\(59\) 10.7600 + 3.49613i 1.40083 + 0.455157i 0.909459 0.415794i \(-0.136496\pi\)
0.491371 + 0.870951i \(0.336496\pi\)
\(60\) −1.57356 4.63939i −0.203146 0.598942i
\(61\) −5.81878 + 8.00886i −0.745018 + 1.02543i 0.253296 + 0.967389i \(0.418485\pi\)
−0.998314 + 0.0580406i \(0.981515\pi\)
\(62\) 0.618034 1.90211i 0.0784904 0.241569i
\(63\) −2.58107 3.36721i −0.325184 0.424229i
\(64\) −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 −0.896193 0.443665i \(-0.853678\pi\)
0.698889 + 0.715230i \(0.253678\pi\)
\(72\) −2.56047 + 8.62809i −0.301755 + 1.01683i
\(73\) −1.34500 0.437016i −0.157420 0.0511489i 0.229247 0.973368i \(-0.426374\pi\)
−0.386667 + 0.922219i \(0.626374\pi\)
\(74\) −2.47214 7.60845i −0.287380 0.884465i
\(75\) −0.0667106 5.19572i −0.00770308 0.599951i
\(76\) 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 0.645353 0.763885i \(-0.276710\pi\)
−0.925923 + 0.377713i \(0.876710\pi\)
\(80\) −2.68999 + 0.874032i −0.300750 + 0.0977198i
\(81\) 3.21687 + 8.40546i 0.357430 + 0.933940i
\(82\) −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 \(-0.641198\pi\)
\(84\) 1.96303 1.46510i 0.214184 0.159855i
\(85\) −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 \(\pi\)
\(90\) −4.80963 + 6.99053i −0.506979 + 0.736866i
\(91\) 1.85410 + 5.70634i 0.194363 + 0.598187i
\(92\) 0 0
\(93\) 3.28054 1.11268i 0.340176 0.115379i
\(94\) 1.66251 2.28825i 0.171475 0.236015i
\(95\) −3.70820 + 11.4127i −0.380454 + 1.17092i
\(96\) −8.27007 2.57020i −0.844060 0.262320i
\(97\) 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 \(0.465755\pi\)
\(102\) 9.92408 + 3.08424i 0.982631 + 0.305386i
\(103\) 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
\(105\) 6.56108 2.22535i 0.640296 0.217172i
\(106\) 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 \(0.618560\pi\)
\(108\) −4.87634 + 1.79480i −0.469226 + 0.172705i
\(109\) 4.24264i 0.406371i −0.979140 0.203186i \(-0.934871\pi\)
0.979140 0.203186i \(-0.0651295\pi\)
\(110\) 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 −0.179743 0.983714i \(-0.557527\pi\)
0.432797 + 0.901492i \(0.357527\pi\)
\(114\) 5.88909 4.39529i 0.551564 0.411657i
\(115\) 0 0
\(116\) 1.61803 + 1.17557i 0.150231 + 0.109149i
\(117\) −0.326787 12.7237i −0.0302115 1.17631i
\(118\) 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
\(123\) −0.133421 10.3914i −0.0120302 0.936965i
\(124\) 0.618034 + 1.90211i 0.0555011 + 0.170815i
\(125\) −5.37999 1.74806i −0.481201 0.156352i
\(126\) −4.06732 1.20702i −0.362346 0.107530i
\(127\) −5.81878 + 8.00886i −0.516333 + 0.710671i −0.984971 0.172719i \(-0.944745\pi\)
0.468638 + 0.883390i \(0.344745\pi\)
\(128\) 0.927051 2.85317i 0.0819405 0.252187i
\(129\) 2.18089 7.01739i 0.192017 0.617846i
\(130\) 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
\(135\) −14.6860 + 0.565934i −1.26397 + 0.0487079i
\(136\) −5.56231 + 17.1190i −0.476964 + 1.46794i
\(137\) −1.66251 + 2.28825i −0.142038 + 0.195498i −0.874109 0.485730i \(-0.838554\pi\)
0.732071 + 0.681228i \(0.238554\pi\)
\(138\) 0 0
\(139\) −1.34500 0.437016i −0.114081 0.0370672i 0.251420 0.967878i \(-0.419102\pi\)
−0.365501 + 0.930811i \(0.619102\pi\)
\(140\) 1.23607 + 3.80423i 0.104467 + 0.321516i
\(141\) 4.89858 0.0628954i 0.412534 0.00529675i
\(142\) 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
\(147\) −5.17990 6.94036i −0.427231 0.572431i
\(148\) 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 \(0.620959\pi\)
\(150\) −3.10794 4.16422i −0.253762 0.340007i
\(151\) 4.03499 1.31105i 0.328363 0.106692i −0.140196 0.990124i \(-0.544773\pi\)
0.468559 + 0.883432i \(0.344773\pi\)
\(152\) 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
\(156\) 7.34786 0.0943431i 0.588300 0.00755349i
\(157\) −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
\(159\) 3.14712 + 9.27877i 0.249583 + 0.735855i
\(160\) 8.31254 11.4412i 0.657164 0.904508i
\(161\) 0 0
\(162\) 7.54311 + 4.90933i 0.592642 + 0.385714i
\(163\) −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 \(0.146308\pi\)
\(168\) 2.18089 7.01739i 0.168259 0.541403i
\(169\) −1.54508 + 4.75528i −0.118853 + 0.365791i
\(170\) −9.97505 + 13.7295i −0.765051 + 1.05300i
\(171\) 12.2020 + 3.62105i 0.933108 + 0.276909i
\(172\) 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 \(0.973247\pi\)
\(174\) −0.0444738 3.46382i −0.00337155 0.262591i
\(175\) 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 −0.206756 0.978393i \(-0.566291\pi\)
0.407816 + 0.913064i \(0.366291\pi\)
\(180\) −0.217858 8.48248i −0.0162382 0.632247i
\(181\) 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
\(183\) −13.7412 + 10.2557i −1.01578 + 0.758122i
\(184\) 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
\(189\) −2.53824 6.89618i −0.184629 0.501624i
\(190\) 3.70820 + 11.4127i 0.269021 + 0.827963i
\(191\) −18.8300 6.11822i −1.36249 0.442699i −0.465615 0.884987i \(-0.654167\pi\)
−0.896873 + 0.442288i \(0.854167\pi\)
\(192\) −11.4819 + 3.89436i −0.828634 + 0.281051i
\(193\) 12.4688 17.1618i 0.897524 1.23534i −0.0737265 0.997278i \(-0.523489\pi\)
0.971251 0.238058i \(-0.0765108\pi\)
\(194\) 0.618034 1.90211i 0.0443723 0.136564i
\(195\) 19.8482 + 6.16849i 1.42136 + 0.441734i
\(196\) 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
\(201\) 3.30803 + 1.02808i 0.233330 + 0.0725152i
\(202\) −3.09017 + 9.51057i −0.217424 + 0.669161i
\(203\) −1.66251 + 2.28825i −0.116685 + 0.160603i
\(204\) −9.84163 + 3.33803i −0.689052 + 0.233709i
\(205\) 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 \(0.175856\pi\)
0.236060 + 0.971738i \(0.424144\pi\)
\(212\) −5.37999 + 1.74806i −0.369499 + 0.120058i
\(213\) −3.92606 + 2.93019i −0.269009 + 0.200774i
\(214\) 12.9443 + 9.40456i 0.884852 + 0.642883i
\(215\) 9.70820 + 7.05342i 0.662094 + 0.481039i
\(216\) −8.67025 + 12.9548i −0.589936 + 0.881462i
\(217\) −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
\(222\) −0.177895 13.8553i −0.0119395 0.929904i
\(223\) 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
\(225\) 2.56047 8.62809i 0.170698 0.575206i
\(226\) 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 \(-0.193301\pi\)
\(228\) −2.18089 + 7.01739i −0.144433 + 0.464738i
\(229\) 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 \(0.406227\pi\)
\(234\) −7.74320 10.1016i −0.506188 0.660364i
\(235\) −2.47214 + 7.60845i −0.161264 + 0.496321i
\(236\) −6.65003 + 9.15298i −0.432880 + 0.595808i
\(237\) −2.36034 6.95908i −0.153321 0.452041i
\(238\) −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 \(0.726871\pi\)
\(240\) −4.89858 + 0.0628954i −0.316202 + 0.00405988i
\(241\) 4.24264i 0.273293i −0.990620 0.136646i \(-0.956368\pi\)
0.990620 0.136646i \(-0.0436324\pi\)
\(242\) 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
\(246\) −6.21588 8.32844i −0.396310 0.531002i
\(247\) −14.5623 10.5801i −0.926577 0.673198i
\(248\) 4.85410 + 3.52671i 0.308236 + 0.223946i
\(249\) −16.5757 22.2092i −1.05044 1.40745i
\(250\) −5.37999 + 1.74806i −0.340260 + 0.110557i
\(251\) −14.9626 20.5942i −0.944429 1.29990i −0.953958 0.299940i \(-0.903033\pi\)
0.00952890 0.999955i \(-0.496967\pi\)
\(252\) 4.00000 1.41421i 0.251976 0.0890871i
\(253\) 0 0
\(254\) 9.89949i 0.621150i
\(255\) −29.3915 + 0.377372i −1.84056 + 0.0236320i
\(256\) −5.25329 16.1680i −0.328331 1.01050i
\(257\) 10.7600 + 3.49613i 0.671189 + 0.218082i 0.624734 0.780838i \(-0.285208\pi\)
0.0464552 + 0.998920i \(0.485208\pi\)
\(258\) −2.36034 6.95908i −0.146948 0.433253i
\(259\) −6.65003 + 9.15298i −0.413213 + 0.568739i
\(260\) −3.70820 + 11.4127i −0.229973 + 0.707784i
\(261\) 4.76195 3.65018i 0.294758 0.225940i
\(262\) 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 \(-0.469048\pi\)
0.916562 0.399892i \(-0.130952\pi\)
\(270\) −11.5486 + 9.09009i −0.702826 + 0.553205i
\(271\) 28.2449 + 9.17734i 1.71576 + 0.557483i 0.991275 0.131809i \(-0.0420787\pi\)
0.724483 + 0.689293i \(0.242079\pi\)
\(272\) 1.85410 + 5.70634i 0.112421 + 0.345998i
\(273\) 0.133421 + 10.3914i 0.00807502 + 0.628919i
\(274\) 2.82843i 0.170872i
\(275\) 0 0
\(276\) 0 0
\(277\) −2.49376 3.43237i −0.149836 0.206231i 0.727501 0.686107i \(-0.240682\pi\)
−0.877336 + 0.479876i \(0.840682\pi\)
\(278\) −1.34500 + 0.437016i −0.0806676 + 0.0262105i
\(279\) 5.99802 0.154049i 0.359092 0.00922267i
\(280\) 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 \(0.642725\pi\)
\(282\) 3.92606 2.93019i 0.233794 0.174491i
\(283\) −25.5549 + 8.30330i −1.51908 + 0.493580i −0.945515 0.325577i \(-0.894441\pi\)
−0.573568 + 0.819158i \(0.694441\pi\)
\(284\) −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
\(288\) −12.3576 8.50230i −0.728180 0.501003i
\(289\) 5.87132 + 18.0701i 0.345372 + 1.06295i
\(290\) 5.37999 + 1.74806i 0.315924 + 0.102650i
\(291\) 3.28054 1.11268i 0.192309 0.0652262i
\(292\) 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 \(0.0813935\pi\)
\(294\) −8.27007 2.57020i −0.482320 0.149897i
\(295\) −25.8885 + 18.8091i −1.50729 + 1.09511i
\(296\) 24.0000 1.39497
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 4.96204 + 1.54212i 0.286484 + 0.0890344i
\(301\) −1.85410 + 5.70634i −0.106869 + 0.328908i
\(302\) 2.49376 3.43237i 0.143500 0.197511i
\(303\) −16.4027 + 5.56338i −0.942311 + 0.319608i
\(304\) 4.03499 + 1.31105i 0.231423 + 0.0751938i
\(305\) −8.65248 26.6296i −0.495439 1.52481i
\(306\) 14.8291 + 10.2028i 0.847726 + 0.583253i
\(307\) 4.24264i 0.242140i −0.992644 0.121070i \(-0.961367\pi\)
0.992644 0.121070i \(-0.0386326\pi\)
\(308\) 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 −0.947291 0.320373i \(-0.896192\pi\)
−0.578064 + 0.815991i \(0.696192\pi\)
\(312\) 17.6673 13.1859i 1.00021 0.746503i
\(313\) −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
\(315\) 11.9960 0.308098i 0.675901 0.0173593i
\(316\) 4.03499 1.31105i 0.226986 0.0737522i
\(317\) −14.9626 20.5942i −0.840382 1.15669i −0.985901 0.167331i \(-0.946485\pi\)
0.145519 0.989355i \(-0.453515\pi\)
\(318\) 8.00000 + 5.65685i 0.448618 + 0.317221i
\(319\) 0 0
\(320\) 19.7990i 1.10680i
\(321\) 0.355790 + 27.7105i 0.0198583 + 1.54665i
\(322\) 0 0
\(323\) 24.2099 + 7.86629i 1.34708 + 0.437692i
\(324\) −8.98813 + 0.461994i −0.499341 + 0.0256664i
\(325\) −7.48128 + 10.2971i −0.414987 + 0.571181i
\(326\) −6.18034 + 19.0211i −0.342297 + 1.05348i
\(327\) 2.18089 7.01739i 0.120603 0.388062i
\(328\) 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
\(333\) 19.0478 14.6007i 1.04381 0.800114i
\(334\) 3.70820 11.4127i 0.202904 0.624474i
\(335\) −3.32502 + 4.57649i −0.181665 + 0.250040i
\(336\) −0.786780 2.31969i −0.0429224 0.126550i
\(337\) −30.9349 10.0514i −1.68513 0.547533i −0.699237 0.714890i \(-0.746477\pi\)
−0.985896 + 0.167357i \(0.946477\pi\)
\(338\) 1.54508 + 4.75528i 0.0840415 + 0.258653i
\(339\) 4.89858 0.0628954i 0.266054 0.00341601i
\(340\) 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 \(0.841297\pi\)
\(348\) 2.07196 + 2.77615i 0.111069 + 0.148817i
\(349\) 4.03499 1.31105i 0.215988 0.0701788i −0.199024 0.979995i \(-0.563777\pi\)
0.415012 + 0.909816i \(0.363777\pi\)
\(350\) 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 \(\pi\)
\(354\) 19.5943 0.251582i 1.04143 0.0133714i
\(355\) −2.47214 7.60845i −0.131207 0.403815i
\(356\) 0 0
\(357\) −4.72068 13.9182i −0.249845 0.736627i
\(358\) 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 \(0.923025\pi\)
\(360\) −15.4864 20.2033i −0.816204 1.06481i
\(361\) −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
\(366\) −5.08874 + 16.3739i −0.265993 + 0.855878i
\(367\) 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
\(369\) 5.12094 17.2562i 0.266586 0.898321i
\(370\) 21.5200 + 6.99226i 1.11877 + 0.363510i
\(371\) −2.47214 7.60845i −0.128347 0.395011i
\(372\) 0.0444738 + 3.46382i 0.00230586 + 0.179590i
\(373\) 4.24264i 0.219676i −0.993950 0.109838i \(-0.964967\pi\)
0.993950 0.109838i \(-0.0350331\pi\)
\(374\) 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
\(378\) −6.10695 4.08719i −0.314108 0.210223i
\(379\) −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
\(381\) −13.7412 + 10.2557i −0.703984 + 0.525414i
\(382\) −18.8300 + 6.11822i −0.963424 + 0.313036i
\(383\) 3.32502 + 4.57649i 0.169900 + 0.233848i 0.885473 0.464690i \(-0.153834\pi\)
−0.715573 + 0.698538i \(0.753834\pi\)
\(384\) 3.00000 4.24264i 0.153093 0.216506i
\(385\) 0 0
\(386\) 21.2132i 1.07972i
\(387\) 7.21444 10.4858i 0.366731 0.533023i
\(388\) 0.618034 + 1.90211i 0.0313759 + 0.0965652i
\(389\) −18.8300 6.11822i −0.954717 0.310206i −0.210086 0.977683i \(-0.567374\pi\)
−0.744631 + 0.667477i \(0.767374\pi\)
\(390\) 19.6833 6.67605i 0.996700 0.338055i
\(391\) 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
\(399\) −9.92408 3.08424i −0.496826 0.154405i
\(400\) 0.927051 2.85317i 0.0463525 0.142658i
\(401\) −1.66251 + 2.28825i −0.0830217 + 0.114270i −0.848508 0.529183i \(-0.822499\pi\)
0.765486 + 0.643452i \(0.222499\pi\)
\(402\) 3.28054 1.11268i 0.163619 0.0554952i
\(403\) −8.06998 2.62210i −0.401994 0.130616i
\(404\) −3.09017 9.51057i −0.153742 0.473168i
\(405\) −24.5818 6.61316i −1.22148 0.328610i
\(406\) 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 0.742900 0.669403i \(-0.233450\pi\)
−0.866208 + 0.499683i \(0.833450\pi\)
\(410\) 16.1400 5.24419i 0.797096 0.258992i
\(411\) −3.92606 + 2.93019i −0.193658 + 0.144536i
\(412\) 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 \(0.274790\pi\)
−0.649950 + 0.759977i \(0.725210\pi\)
\(420\) 0.0889475 + 6.92763i 0.00434019 + 0.338034i
\(421\) −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
\(423\) 8.13464 + 2.41404i 0.395520 + 0.117374i
\(424\) −9.97505 + 13.7295i −0.484431 + 0.666762i
\(425\) 5.56231 17.1190i 0.269811 0.830394i
\(426\) −1.45393 + 4.67826i −0.0704429 + 0.226662i
\(427\) 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 \(0.580090\pi\)
\(432\) 0.200088 + 5.19230i 0.00962674 + 0.249815i
\(433\) 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
\(435\) 3.14712 + 9.27877i 0.150893 + 0.444883i
\(436\) 4.03499 + 1.31105i 0.193241 + 0.0627878i
\(437\) 0 0
\(438\) −2.44929 + 0.0314477i −0.117032 + 0.00150263i
\(439\) 26.8701i 1.28244i 0.767358 + 0.641219i \(0.221571\pi\)
−0.767358 + 0.641219i \(0.778429\pi\)
\(440\) 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 −0.867895 0.496748i \(-0.834527\pi\)
−0.410160 + 0.912014i \(0.634527\pi\)
\(444\) 8.28784 + 11.1046i 0.393323 + 0.527000i
\(445\) 0 0
\(446\) 19.4164 + 14.1068i 0.919394 + 0.667979i
\(447\) 6.21588 + 8.32844i 0.294001 + 0.393921i
\(448\) 9.41498 3.05911i 0.444816 0.144529i
\(449\) 3.32502 + 4.57649i 0.156917 + 0.215978i 0.880236 0.474536i \(-0.157384\pi\)
−0.723319 + 0.690514i \(0.757384\pi\)
\(450\) −3.00000 8.48528i −0.141421 0.400000i
\(451\) 0 0
\(452\) 2.82843i 0.133038i
\(453\) 7.34786 0.0943431i 0.345233 0.00443263i
\(454\) −7.41641 22.8254i −0.348069 1.07125i
\(455\) −16.1400 5.24419i −0.756653 0.245852i
\(456\) 7.08102 + 20.8772i 0.331599 + 0.977666i
\(457\) −5.81878 + 8.00886i −0.272191 + 0.374639i −0.923128 0.384493i \(-0.874376\pi\)
0.650937 + 0.759132i \(0.274376\pi\)
\(458\) 7.41641 22.8254i 0.346546 1.06656i
\(459\) 1.20053 + 31.1538i 0.0560358 + 1.45413i
\(460\) 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
\(465\) −2.90785 + 9.35652i −0.134848 + 0.433898i
\(466\) −3.09017 + 9.51057i −0.143149 + 0.440568i
\(467\) 16.6251 22.8825i 0.769317 1.05887i −0.227065 0.973880i \(-0.572913\pi\)
0.996381 0.0849941i \(-0.0270871\pi\)
\(468\) 12.2020 + 3.62105i 0.564036 + 0.167383i
\(469\) −2.68999 0.874032i −0.124212 0.0403591i
\(470\) 2.47214 + 7.60845i 0.114031 + 0.350952i
\(471\) −0.444738 34.6382i −0.0204924 1.59604i
\(472\) 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
\(477\) 0.435716 + 16.9650i 0.0199501 + 0.776773i
\(478\) 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 \(0.479068\pi\)
\(480\) 19.6303 14.6510i 0.895997 0.668722i
\(481\) −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
\(486\) 9.95281 + 11.9976i 0.451469 + 0.544221i
\(487\) 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
\(489\) −32.8054 + 11.1268i −1.48351 + 0.503169i
\(490\) 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 \(0.950963\pi\)
\(492\) 9.92408 + 3.08424i 0.447412 + 0.139048i
\(493\) 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
\(498\) −26.4642 8.22465i −1.18589 0.368555i
\(499\) −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
\(501\) 19.6833 6.67605i 0.879383 0.298264i
\(502\) −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 \(0.783901\pi\)
\(504\) 7.21444 10.4858i 0.321357 0.467074i
\(505\) 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 0.511772 0.859121i \(-0.328989\pi\)
0.919011 + 0.394232i \(0.128989\pi\)
\(510\) −23.5564 + 17.5812i −1.04309 + 0.778507i
\(511\) 1.61803 + 1.17557i 0.0715776 + 0.0520042i
\(512\) −8.89919 6.46564i −0.393292 0.285744i
\(513\) 18.3209 + 12.2616i 0.808885 + 0.541362i
\(514\) 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
\(519\) −0.133421 10.3914i −0.00585654 0.456134i
\(520\) 11.1246 + 34.2380i 0.487846 + 1.50144i
\(521\) −18.8300 6.11822i −0.824955 0.268044i −0.134036 0.990976i \(-0.542794\pi\)
−0.690919 + 0.722932i \(0.742794\pi\)
\(522\) 1.70698 5.75206i 0.0747126 0.251761i
\(523\) 12.4688 17.1618i 0.545223 0.750435i −0.444131 0.895962i \(-0.646488\pi\)
0.989354 + 0.145527i \(0.0464877\pi\)
\(524\) 0 0
\(525\) −2.18089 + 7.01739i −0.0951818 + 0.306264i
\(526\) 0 0
\(527\) 12.0000 0.522728
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) −12.9443 + 9.40456i −0.562263 + 0.408508i
\(531\) 20.6485 + 26.9377i 0.896069 + 1.16900i
\(532\) 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
\(537\) 4.89858 0.0628954i 0.211389 0.00271414i
\(538\) 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 \(-0.925188\pi\)
0.0790477 0.996871i \(-0.474812\pi\)
\(542\) 28.2449 9.17734i 1.21322 0.394200i
\(543\) 10.3598 + 13.8807i 0.444582 + 0.595679i
\(544\) −24.2705 17.6336i −1.04059 0.756033i
\(545\) 9.70820 + 7.05342i 0.415854 + 0.302135i
\(546\) 6.21588 + 8.32844i 0.266015 + 0.356424i
\(547\) 33.6249 10.9254i 1.43770 0.467136i 0.516519 0.856276i \(-0.327228\pi\)
0.921179 + 0.389139i \(0.127228\pi\)
\(548\) −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
\(555\) 12.5885 + 37.1151i 0.534351 + 1.57545i
\(556\) 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 \(0.0865087\pi\)
\(558\) 4.76195 3.65018i 0.201590 0.154524i
\(559\) −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 \(0.218626\pi\)
\(564\) −1.45393 + 4.67826i −0.0612213 + 0.196990i
\(565\) −2.47214 + 7.60845i −0.104004 + 0.320090i
\(566\) −15.7938 + 21.7383i −0.663864 + 0.913730i
\(567\) −0.653359 12.7111i −0.0274385 0.533818i
\(568\) −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 \(0.606671\pi\)
\(570\) 0.266843 + 20.7829i 0.0111768 + 0.870500i
\(571\) 26.8701i 1.12448i 0.826975 + 0.562238i \(0.190060\pi\)
−0.826975 + 0.562238i \(0.809940\pi\)
\(572\) 0 0
\(573\) −28.0000 19.7990i −1.16972 0.827115i
\(574\) 4.98752 + 6.86474i 0.208175 + 0.286529i
\(575\) 0 0
\(576\) −20.9931 + 0.539171i −0.874712 + 0.0224655i
\(577\) 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
\(579\) 29.4455 21.9765i 1.22371 0.913310i
\(580\) −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
\(585\) 29.6583 + 20.4055i 1.22622 + 0.843665i
\(586\) −0.618034 1.90211i −0.0255307 0.0785756i
\(587\) 10.7600 + 3.49613i 0.444112 + 0.144301i 0.522532 0.852620i \(-0.324988\pi\)
−0.0784201 + 0.996920i \(0.524988\pi\)
\(588\) 8.20135 2.78169i 0.338218 0.114715i
\(589\) 4.98752 6.86474i 0.205507 0.282857i
\(590\) −9.88854 + 30.4338i −0.407105 + 1.25294i
\(591\) −36.3883 11.3089i −1.49681 0.465186i
\(592\) 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
\(597\) 3.30803 + 1.02808i 0.135389 + 0.0420766i
\(598\) 0 0
\(599\) −19.9501 + 27.4589i −0.815139 + 1.12194i 0.175371 + 0.984502i \(0.443887\pi\)
−0.990510 + 0.137440i \(0.956113\pi\)
\(600\) 14.7624 5.00704i 0.602674 0.204411i
\(601\) 28.2449 + 9.17734i 1.15214 + 0.374351i 0.821947 0.569564i \(-0.192888\pi\)
0.330188 + 0.943915i \(0.392888\pi\)
\(602\) 1.85410 + 5.70634i 0.0755676 + 0.232573i
\(603\) 4.94305 + 3.40092i 0.201297 + 0.138496i
\(604\) 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 0.755403 0.655260i \(-0.227441\pi\)
−0.856622 + 0.515945i \(0.827441\pi\)
\(608\) −20.1750 + 6.55524i −0.818202 + 0.265850i
\(609\) −3.92606 + 2.93019i −0.159092 + 0.118737i
\(610\) −22.6525 16.4580i −0.917172 0.666364i
\(611\) −9.70820 7.05342i −0.392752 0.285351i
\(612\) −17.9941 + 0.462147i −0.727367 + 0.0186812i
\(613\) 4.03499 1.31105i 0.162972 0.0529527i −0.226395 0.974036i \(-0.572694\pi\)
0.389367 + 0.921083i \(0.372694\pi\)
\(614\) −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 \(0.215421\pi\)
−0.779602 + 0.626275i \(0.784579\pi\)
\(618\) −0.177895 13.8553i −0.00715599 0.557340i
\(619\) −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
\(624\) 2.18089 7.01739i 0.0873054 0.280920i
\(625\) 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
\(630\) 9.52391 7.30035i 0.379442 0.290853i
\(631\) −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
\(633\) 14.9488 + 44.0742i 0.594162 + 1.75179i
\(634\) −24.2099 7.86629i −0.961500 0.312410i
\(635\) −8.65248 26.6296i −0.343363 1.05676i
\(636\) −9.79715 + 0.125791i −0.388482 + 0.00498793i
\(637\) 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 −0.787556 0.616243i \(-0.788654\pi\)
−0.274928 + 0.961465i \(0.588654\pi\)
\(642\) 16.5757 + 22.2092i 0.654190 + 0.876526i
\(643\) −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
\(645\) 12.4318 + 16.6569i 0.489500 + 0.655864i
\(646\) 24.2099 7.86629i 0.952528 0.309495i
\(647\) 3.32502 + 4.57649i 0.130720 + 0.179920i 0.869360 0.494180i \(-0.164532\pi\)
−0.738640 + 0.674100i \(0.764532\pi\)
\(648\) −21.0000 + 16.9706i −0.824958 + 0.666667i
\(649\) 0 0
\(650\) 12.7279i 0.499230i
\(651\) −4.89858 + 0.0628954i −0.191990 + 0.00246506i
\(652\) −6.18034 19.0211i −0.242041 0.744925i
\(653\) 10.7600 + 3.49613i 0.421070 + 0.136814i 0.511885 0.859054i \(-0.328947\pi\)
−0.0908151 + 0.995868i \(0.528947\pi\)
\(654\) −2.36034 6.95908i −0.0922966 0.272122i
\(655\) 0 0
\(656\) 1.85410 5.70634i 0.0723905 0.222795i
\(657\) −2.58107 3.36721i −0.100697 0.131367i
\(658\) −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
\(663\) 13.0853 42.1043i 0.508192 1.63520i
\(664\) 14.8328 45.6507i 0.575625 1.77159i
\(665\) 9.97505 13.7295i 0.386816 0.532406i
\(666\) 6.82793 23.0082i 0.264577 0.891551i
\(667\) 0 0
\(668\) 3.70820 + 11.4127i 0.143475 + 0.441570i
\(669\) 0.533685 + 41.5658i 0.0206335 + 1.60703i
\(670\) 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 0.758244 0.651971i \(-0.226058\pi\)
−0.854371 + 0.519663i \(0.826058\pi\)
\(674\) −30.9349 + 10.0514i −1.19157 + 0.387164i
\(675\) 8.67025 12.9548i 0.333718 0.498630i
\(676\) −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 \(0.960587\pi\)
\(678\) 3.92606 2.93019i 0.150780 0.112533i
\(679\) −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 \(-0.797054\pi\)
0.803543 0.595247i \(-0.202946\pi\)
\(684\) −7.21444 + 10.4858i −0.275851 + 0.400934i
\(685\) −2.47214 7.60845i −0.0944555 0.290704i
\(686\) 16.1400 + 5.24419i 0.616227 + 0.200224i
\(687\) 39.3665 13.3521i 1.50193 0.509414i
\(688\) 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
\(696\) 9.92408 + 3.08424i 0.376171 + 0.116908i
\(697\) 11.1246 34.2380i 0.421375 1.29686i
\(698\) 2.49376 3.43237i 0.0943903 0.129917i
\(699\) −16.4027 + 5.56338i −0.620407 + 0.210426i
\(700\) −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 \(0.936145\pi\)
\(702\) −7.61471 20.6886i −0.287399 0.780839i
\(703\) 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
\(708\) −15.7042 + 11.7208i −0.590202 + 0.440494i
\(709\) 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
\(711\) −0.326787 12.7237i −0.0122555 0.477177i
\(712\) 0 0
\(713\) 0 0
\(714\) −12.0000 8.48528i −0.449089 0.317554i
\(715\) 0 0
\(716\) 2.82843i 0.105703i
\(717\) 0.355790 + 27.7105i 0.0132872 + 1.03487i
\(718\) 6.18034 + 19.0211i 0.230648 + 0.709862i
\(719\) −18.8300 6.11822i −0.702239 0.228171i −0.0639332 0.997954i \(-0.520364\pi\)
−0.638306 + 0.769783i \(0.720364\pi\)
\(720\) −8.13464 2.41404i −0.303160 0.0899658i
\(721\) −6.65003 + 9.15298i −0.247660 + 0.340875i
\(722\) −0.309017 + 0.951057i −0.0115004 + 0.0353947i
\(723\) 2.18089 7.01739i 0.0811081 0.260979i
\(724\) −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
\(729\) −6.34258 + 26.2445i −0.234910 + 0.972017i
\(730\) 1.23607 3.80423i 0.0457489 0.140801i
\(731\) 14.9626 20.5942i 0.553411 0.761704i
\(732\) −5.50746 16.2379i −0.203562 0.600168i
\(733\) −1.34500 0.437016i −0.0496786 0.0161416i 0.284072 0.958803i \(-0.408314\pi\)
−0.333751 + 0.942661i \(0.608314\pi\)
\(734\) −2.47214 7.60845i −0.0912482 0.280833i
\(735\) 24.4929 0.314477i 0.903433 0.0115997i
\(736\) 0 0
\(737\) 0 0
\(738\) −6.00000 16.9706i −0.220863 0.624695i
\(739\) −2.49376 3.43237i −0.0917345 0.126262i 0.760683 0.649124i \(-0.224864\pi\)
−0.852417 + 0.522862i \(0.824864\pi\)
\(740\) −21.5200 + 6.99226i −0.791089 + 0.257040i
\(741\) −18.6476 24.9853i −0.685038 0.917858i
\(742\) −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 \(0.794817\pi\)
\(744\) 6.21588 + 8.32844i 0.227885 + 0.305335i
\(745\) −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
\(750\) −9.79715 + 0.125791i −0.357741 + 0.00459323i
\(751\) 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
\(753\) −14.1620 41.7545i −0.516094 1.52162i
\(754\) −4.98752 + 6.86474i −0.181635 + 0.249999i
\(755\) −3.70820 + 11.4127i −0.134955 + 0.415350i
\(756\) 7.34302 0.282967i 0.267063 0.0102914i
\(757\) −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 \(0.358014\pi\)
\(762\) −5.08874 + 16.3739i −0.184346 + 0.593164i
\(763\) −1.85410 + 5.70634i −0.0671230 + 0.206583i
\(764\) 11.6376 16.0177i 0.421032 0.579501i
\(765\) −48.8079 14.4842i −1.76465 0.523678i
\(766\) 5.37999 + 1.74806i 0.194387 + 0.0631601i
\(767\) −14.8328 45.6507i −0.535582 1.64835i
\(768\) −0.378027 29.4424i −0.0136409 1.06241i
\(769\) 35.3553i 1.27495i −0.770473 0.637473i \(-0.779980\pi\)
0.770473 0.637473i \(-0.220020\pi\)
\(770\) 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 0.335741 0.941954i \(-0.391013\pi\)
0.825287 + 0.564713i \(0.191013\pi\)
\(774\) −0.326787 12.7237i −0.0117461 0.457345i
\(775\) −4.85410 3.52671i −0.174364 0.126683i
\(776\) 4.85410 + 3.52671i 0.174252 + 0.126602i
\(777\) −15.7042 + 11.7208i −0.563387 + 0.420480i
\(778\) −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
\(783\) 9.75268 3.58961i 0.348532 0.128282i
\(784\) −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 −0.526732 0.850031i \(-0.676583\pi\)
0.971197 + 0.238278i \(0.0765829\pi\)
\(788\) 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
\(795\) −26.4642 8.22465i −0.938589 0.291698i
\(796\) −0.618034 + 1.90211i −0.0219056 + 0.0674186i
\(797\) −1.66251 + 2.28825i −0.0588890 + 0.0810538i −0.837446 0.546520i \(-0.815952\pi\)
0.778557 + 0.627574i \(0.215952\pi\)
\(798\) −9.84163 + 3.33803i −0.348390 + 0.118165i
\(799\) 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
\(807\) 39.2606 29.3019i 1.38204 1.03148i
\(808\) −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 \(0.358243\pi\)
\(810\) −23.7742 + 9.09868i −0.835341 + 0.319695i
\(811\) −25.5549 + 8.30330i −0.897355 + 0.291568i −0.721145 0.692784i \(-0.756384\pi\)
−0.176210 + 0.984353i \(0.556384\pi\)
\(812\) −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
\(816\) 0.133421 + 10.3914i 0.00467068 + 0.363773i
\(817\) −5.56231 17.1190i −0.194600 0.598919i
\(818\) −4.03499 1.31105i −0.141080 0.0458397i
\(819\) −5.12094 + 17.2562i −0.178940 + 0.602980i
\(820\) −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 \(0.838164\pi\)
\(822\) −1.45393 + 4.67826i −0.0507115 + 0.163173i
\(823\) 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
\(831\) −2.36034 6.95908i −0.0818793 0.241408i
\(832\) 28.2449 + 9.17734i 0.979217 + 0.318167i
\(833\) −9.27051 28.5317i −0.321204 0.988565i
\(834\) −2.44929 + 0.0314477i −0.0848119 + 0.00108894i
\(835\) 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 0.306789 0.951778i \(-0.400745\pi\)
0.807638 + 0.589678i \(0.200745\pi\)
\(840\) 12.4318 + 16.6569i 0.428936 + 0.574717i
\(841\) 20.2254 + 14.6946i 0.697428 + 0.506711i
\(842\) −16.1803 11.7557i −0.557611 0.405128i
\(843\) 6.21588 + 8.32844i 0.214086 + 0.286847i
\(844\) −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
\(849\) −46.5365 + 0.597506i −1.59713 + 0.0205064i
\(850\) −5.56231 17.1190i −0.190786 0.587177i
\(851\) 0 0
\(852\) −1.57356 4.63939i −0.0539093 0.158943i
\(853\) −24.1064 + 33.1796i −0.825386 + 1.13605i 0.163378 + 0.986564i \(0.447761\pi\)
−0.988764 + 0.149483i \(0.952239\pi\)
\(854\) 4.32624 13.3148i 0.148041 0.455623i
\(855\) −28.5717 + 21.9011i −0.977132 + 0.749001i
\(856\) −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
\(861\) −4.36178 + 14.0348i −0.148649 + 0.478304i
\(862\) −9.88854 + 30.4338i −0.336805 + 1.03658i
\(863\) −19.9501 + 27.4589i −0.679109 + 0.934713i −0.999923 0.0124289i \(-0.996044\pi\)
0.320814 + 0.947142i \(0.396044\pi\)
\(864\) −16.0692 20.4152i −0.546684 0.694541i
\(865\) 16.1400 + 5.24419i 0.548775 + 0.178308i
\(866\) −9.27051 28.5317i −0.315025 0.969546i
\(867\) 0.422501 + 32.9063i 0.0143489 + 1.11755i
\(868\) 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
\(873\) 5.99802 0.154049i 0.203002 0.00521377i
\(874\) 0 0
\(875\) 6.47214 + 4.70228i 0.218798 + 0.158966i
\(876\) 1.96303 1.46510i 0.0663247 0.0495010i
\(877\) 33.6249 10.9254i 1.13543 0.368925i 0.319795 0.947487i \(-0.396386\pi\)
0.815638 + 0.578562i \(0.196386\pi\)
\(878\) 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 \(0.175601\pi\)
−0.851653 + 0.524107i \(0.824399\pi\)
\(882\) −12.3576 8.50230i −0.416103 0.286287i
\(883\) 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
\(885\) −52.4887 + 17.8028i −1.76439 + 0.598435i
\(886\) −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 \(-0.0320049\pi\)
\(888\) 39.6963 + 12.3370i 1.33212 + 0.414002i
\(889\) 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
\(894\) 9.92408 + 3.08424i 0.331911 + 0.103153i
\(895\) −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
\(900\) 7.41457 + 5.10138i 0.247152 + 0.170046i
\(901\) 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
\(906\) 5.88909 4.39529i 0.195652 0.146024i
\(907\) −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
\(909\) −29.9901 + 0.770245i −0.994709 + 0.0255474i
\(910\) −16.1400 + 5.24419i −0.535035 + 0.173843i
\(911\) 21.6126 + 29.7472i 0.716057 + 0.985568i 0.999646 + 0.0266223i \(0.00847514\pi\)
−0.283588 + 0.958946i \(0.591525\pi\)
\(912\) 6.00000 + 4.24264i 0.198680 + 0.140488i
\(913\) 0 0
\(914\) 9.89949i 0.327446i
\(915\) −0.622633 48.4934i −0.0205836 1.60314i
\(916\) 7.41641 + 22.8254i 0.245045 + 0.754171i
\(917\) 0 0
\(918\) 19.2830 + 24.4983i 0.636433 + 0.808564i
\(919\) 12.4688 17.1618i 0.411308 0.566117i −0.552229 0.833693i \(-0.686223\pi\)
0.963537 + 0.267576i \(0.0862225\pi\)
\(920\) 0 0
\(921\) 2.18089 7.01739i 0.0718627 0.231231i
\(922\) −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
\(927\) 19.0478 14.6007i 0.625612 0.479550i
\(928\) −3.09017 + 9.51057i −0.101440 + 0.312200i
\(929\) −1.66251 + 2.28825i −0.0545451 + 0.0750749i −0.835418 0.549615i \(-0.814775\pi\)
0.780873 + 0.624690i \(0.214775\pi\)
\(930\) 3.14712 + 9.27877i 0.103198 + 0.304263i
\(931\) −20.1750 6.55524i −0.661207 0.214839i
\(932\) −3.09017 9.51057i −0.101222 0.311529i
\(933\) −48.9858 + 0.628954i −1.60372 + 0.0205910i
\(934\) 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 0.321023 0.947071i \(-0.395973\pi\)
−0.999920 + 0.0126498i \(0.995973\pi\)
\(938\) −2.68999 + 0.874032i −0.0878314 + 0.0285382i
\(939\) −12.4318 16.6569i −0.405695 0.543576i
\(940\) −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 \(0.912617\pi\)
\(942\) −20.7196 27.7615i −0.675081 0.904517i
\(943\) 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 \(-0.831303\pi\)
0.862819 0.505513i \(-0.168697\pi\)
\(948\) 7.34786 0.0943431i 0.238648 0.00306412i
\(949\) 1.85410 + 5.70634i 0.0601867 + 0.185236i
\(950\) −12.1050 3.93314i −0.392737 0.127608i
\(951\) −14.1620 41.7545i −0.459236 1.35398i
\(952\) 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 \(0.0896871\pi\)
\(954\) 10.3243 + 13.4688i 0.334260 + 0.436070i
\(955\) 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
\(960\) 10.1775 32.7478i 0.328477 1.05693i
\(961\) −8.34346 + 25.6785i −0.269144 + 0.828340i
\(962\) −19.9501 + 27.4589i −0.643217 + 0.885312i
\(963\) −13.6559 + 46.0165i −0.440054 + 1.48286i
\(964\) 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 \(-0.978269\pi\)
0.997671 0.0682171i \(-0.0217310\pi\)
\(968\) 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 0.258787 0.965934i \(-0.416677\pi\)
0.777125 + 0.629346i \(0.216677\pi\)
\(972\) −15.1040 3.85612i −0.484461 0.123685i
\(973\) 1.61803 + 1.17557i 0.0518718 + 0.0376871i
\(974\) 1.61803 + 1.17557i 0.0518452 + 0.0376677i
\(975\) −17.6673 + 13.1859i −0.565806 + 0.422286i
\(976\) −9.41498 + 3.05911i −0.301366 + 0.0979198i
\(977\) −14.9626 20.5942i −0.478695 0.658867i 0.499558 0.866280i \(-0.333496\pi\)
−0.978253 + 0.207413i \(0.933496\pi\)
\(978\) −20.0000 + 28.2843i −0.639529 + 0.904431i
\(979\) 0 0
\(980\) 14.1421i 0.451754i
\(981\) 7.21444 10.4858i 0.230339 0.334786i
\(982\) 6.18034 + 19.0211i 0.197223 + 0.606989i
\(983\) 10.7600 + 3.49613i 0.343190 + 0.111509i 0.475541 0.879694i \(-0.342252\pi\)
−0.132351 + 0.991203i \(0.542252\pi\)
\(984\) 29.5249 10.0141i 0.941219 0.319237i
\(985\) 36.5752 50.3414i 1.16538 1.60401i
\(986\) 3.70820 11.4127i 0.118093 0.363454i
\(987\) −6.61606 2.05616i −0.210591 0.0654484i
\(988\) 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
\(993\) −33.0803 10.2808i −1.04977 0.326252i
\(994\) 1.23607 3.80423i 0.0392057 0.120663i
\(995\) −3.32502 + 4.57649i −0.105410 + 0.145085i
\(996\) 26.2443 8.90140i 0.831584 0.282052i
\(997\) 28.2449 + 9.17734i 0.894526 + 0.290649i 0.719976 0.693999i \(-0.244153\pi\)
0.174550 + 0.984648i \(0.444153\pi\)
\(998\) 4.32624 + 13.3148i 0.136945 + 0.421472i
\(999\) 39.0107 14.3584i 1.23424 0.454281i
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.239.2 8
3.2 odd 2 363.2.f.a.239.1 8
11.2 odd 10 363.2.d.b.362.1 yes 2
11.3 even 5 inner 363.2.f.f.215.1 8
11.4 even 5 inner 363.2.f.f.161.1 8
11.5 even 5 inner 363.2.f.f.233.2 8
11.6 odd 10 363.2.f.a.233.2 8
11.7 odd 10 363.2.f.a.161.1 8
11.8 odd 10 363.2.f.a.215.1 8
11.9 even 5 363.2.d.a.362.1 2
11.10 odd 2 363.2.f.a.239.2 8
33.2 even 10 363.2.d.a.362.2 yes 2
33.5 odd 10 363.2.f.a.233.1 8
33.8 even 10 inner 363.2.f.f.215.2 8
33.14 odd 10 363.2.f.a.215.2 8
33.17 even 10 inner 363.2.f.f.233.1 8
33.20 odd 10 363.2.d.b.362.2 yes 2
33.26 odd 10 363.2.f.a.161.2 8
33.29 even 10 inner 363.2.f.f.161.2 8
33.32 even 2 inner 363.2.f.f.239.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.2.d.a.362.1 2 11.9 even 5
363.2.d.a.362.2 yes 2 33.2 even 10
363.2.d.b.362.1 yes 2 11.2 odd 10
363.2.d.b.362.2 yes 2 33.20 odd 10
363.2.f.a.161.1 8 11.7 odd 10
363.2.f.a.161.2 8 33.26 odd 10
363.2.f.a.215.1 8 11.8 odd 10
363.2.f.a.215.2 8 33.14 odd 10
363.2.f.a.233.1 8 33.5 odd 10
363.2.f.a.233.2 8 11.6 odd 10
363.2.f.a.239.1 8 3.2 odd 2
363.2.f.a.239.2 8 11.10 odd 2
363.2.f.f.161.1 8 11.4 even 5 inner
363.2.f.f.161.2 8 33.29 even 10 inner
363.2.f.f.215.1 8 11.3 even 5 inner
363.2.f.f.215.2 8 33.8 even 10 inner
363.2.f.f.233.1 8 33.17 even 10 inner
363.2.f.f.233.2 8 11.5 even 5 inner
363.2.f.f.239.1 8 33.32 even 2 inner
363.2.f.f.239.2 8 1.1 even 1 trivial