Properties

Label 363.2.f.f.233.2
Level $363$
Weight $2$
Character 363.233
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 233.2
Root \(0.831254 - 1.14412i\) of defining polynomial
Character \(\chi\) \(=\) 363.233
Dual form 363.2.f.f.215.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.0222369 + 1.73191i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.68999 - 0.874032i) q^{5} +(-1.65401 - 0.514040i) q^{6} +(-0.831254 + 1.14412i) q^{7} +(-2.42705 + 1.76336i) q^{8} +(-2.99901 + 0.0770245i) q^{9} +2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} +(4.03499 + 1.31105i) q^{13} +(-0.831254 - 1.14412i) q^{14} +(1.57356 + 4.63939i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-1.85410 - 5.70634i) q^{17} +(0.853491 - 2.87603i) q^{18} +(2.49376 + 3.43237i) q^{19} +(2.68999 + 0.874032i) q^{20} +(-2.00000 - 1.41421i) q^{21} +(-3.10794 - 4.16422i) q^{24} +(2.42705 - 1.76336i) q^{25} +(-2.49376 + 3.43237i) q^{26} +(-0.200088 - 5.19230i) q^{27} +(-1.34500 + 0.437016i) q^{28} +(-1.61803 - 1.17557i) q^{29} +(-4.89858 + 0.0628954i) q^{30} +(-0.618034 + 1.90211i) q^{31} -5.00000 q^{32} +6.00000 q^{34} +(-1.23607 + 3.80423i) q^{35} +(-2.47152 - 1.70046i) q^{36} +(-6.47214 - 4.70228i) q^{37} +(-4.03499 + 1.31105i) q^{38} +(-2.18089 + 7.01739i) q^{39} +(-4.98752 + 6.86474i) q^{40} +(4.85410 - 3.52671i) q^{41} +(1.96303 - 1.46510i) q^{42} -4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} +(1.66251 + 2.28825i) q^{47} +(1.64027 - 0.556338i) q^{48} +(1.54508 + 4.75528i) q^{49} +(0.927051 + 2.85317i) q^{50} +(9.84163 - 3.33803i) q^{51} +(2.49376 + 3.43237i) q^{52} +(-5.37999 - 1.74806i) q^{53} +(5.00000 + 1.41421i) q^{54} -4.24264i q^{56} +(-5.88909 + 4.39529i) q^{57} +(1.61803 - 1.17557i) q^{58} +(6.65003 - 9.15298i) q^{59} +(-1.45393 + 4.67826i) q^{60} +(9.41498 - 3.05911i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(2.40481 - 3.49526i) q^{63} +(2.16312 - 6.65740i) q^{64} +12.0000 q^{65} +2.00000 q^{67} +(1.85410 - 5.70634i) q^{68} +(-3.23607 - 2.35114i) q^{70} +(2.68999 - 0.874032i) q^{71} +(7.14293 - 5.47527i) q^{72} +(-0.831254 + 1.14412i) q^{73} +(6.47214 - 4.70228i) q^{74} +(3.10794 + 4.16422i) q^{75} +4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} +(4.03499 + 1.31105i) q^{79} +(-1.66251 - 2.28825i) q^{80} +(8.98813 - 0.461994i) q^{81} +(1.85410 + 5.70634i) q^{82} +(4.94427 + 15.2169i) q^{83} +(-0.786780 - 2.31969i) q^{84} +(-9.97505 - 13.7295i) q^{85} +(4.03499 + 1.31105i) q^{86} +(2.00000 - 2.82843i) q^{87} +(-0.217858 - 8.48248i) q^{90} +(-4.85410 + 3.52671i) q^{91} +(-3.30803 - 1.02808i) q^{93} +(-2.68999 + 0.874032i) q^{94} +(9.70820 + 7.05342i) q^{95} +(-0.111184 - 8.65954i) q^{96} +(-0.618034 + 1.90211i) 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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i 0.780378 + 0.625308i \(0.215027\pi\)
−0.998886 + 0.0471903i \(0.984973\pi\)
\(3\) 0.0222369 + 1.73191i 0.0128385 + 0.999918i
\(4\) 0.809017 + 0.587785i 0.404508 + 0.293893i
\(5\) 2.68999 0.874032i 1.20300 0.390879i 0.362137 0.932125i \(-0.382047\pi\)
0.840864 + 0.541246i \(0.182047\pi\)
\(6\) −1.65401 0.514040i −0.675248 0.209856i
\(7\) −0.831254 + 1.14412i −0.314184 + 0.432438i −0.936680 0.350185i \(-0.886119\pi\)
0.622496 + 0.782623i \(0.286119\pi\)
\(8\) −2.42705 + 1.76336i −0.858092 + 0.623440i
\(9\) −2.99901 + 0.0770245i −0.999670 + 0.0256748i
\(10\) 2.82843i 0.894427i
\(11\) 0 0
\(12\) −1.00000 + 1.41421i −0.288675 + 0.408248i
\(13\) 4.03499 + 1.31105i 1.11911 + 0.363619i 0.809426 0.587222i \(-0.199778\pi\)
0.309679 + 0.950841i \(0.399778\pi\)
\(14\) −0.831254 1.14412i −0.222162 0.305780i
\(15\) 1.57356 + 4.63939i 0.406292 + 1.19788i
\(16\) −0.309017 0.951057i −0.0772542 0.237764i
\(17\) −1.85410 5.70634i −0.449686 1.38399i −0.877262 0.480011i \(-0.840633\pi\)
0.427576 0.903979i \(-0.359367\pi\)
\(18\) 0.853491 2.87603i 0.201170 0.677887i
\(19\) 2.49376 + 3.43237i 0.572108 + 0.787439i 0.992802 0.119763i \(-0.0382135\pi\)
−0.420694 + 0.907202i \(0.638214\pi\)
\(20\) 2.68999 + 0.874032i 0.601501 + 0.195440i
\(21\) −2.00000 1.41421i −0.436436 0.308607i
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −3.10794 4.16422i −0.634406 0.850017i
\(25\) 2.42705 1.76336i 0.485410 0.352671i
\(26\) −2.49376 + 3.43237i −0.489067 + 0.673143i
\(27\) −0.200088 5.19230i −0.0385069 0.999258i
\(28\) −1.34500 + 0.437016i −0.254181 + 0.0825883i
\(29\) −1.61803 1.17557i −0.300461 0.218298i 0.427331 0.904095i \(-0.359454\pi\)
−0.727793 + 0.685797i \(0.759454\pi\)
\(30\) −4.89858 + 0.0628954i −0.894353 + 0.0114831i
\(31\) −0.618034 + 1.90211i −0.111002 + 0.341630i −0.991092 0.133177i \(-0.957482\pi\)
0.880090 + 0.474807i \(0.157482\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) −1.23607 + 3.80423i −0.208934 + 0.643032i
\(36\) −2.47152 1.70046i −0.411921 0.283410i
\(37\) −6.47214 4.70228i −1.06401 0.773050i −0.0891861 0.996015i \(-0.528427\pi\)
−0.974827 + 0.222965i \(0.928427\pi\)
\(38\) −4.03499 + 1.31105i −0.654562 + 0.212680i
\(39\) −2.18089 + 7.01739i −0.349222 + 1.12368i
\(40\) −4.98752 + 6.86474i −0.788597 + 1.08541i
\(41\) 4.85410 3.52671i 0.758083 0.550780i −0.140238 0.990118i \(-0.544787\pi\)
0.898322 + 0.439338i \(0.144787\pi\)
\(42\) 1.96303 1.46510i 0.302902 0.226069i
\(43\) 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
\(47\) 1.66251 + 2.28825i 0.242502 + 0.333775i 0.912868 0.408256i \(-0.133863\pi\)
−0.670366 + 0.742031i \(0.733863\pi\)
\(48\) 1.64027 0.556338i 0.236753 0.0803004i
\(49\) 1.54508 + 4.75528i 0.220726 + 0.679326i
\(50\) 0.927051 + 2.85317i 0.131105 + 0.403499i
\(51\) 9.84163 3.33803i 1.37810 0.467417i
\(52\) 2.49376 + 3.43237i 0.345823 + 0.475984i
\(53\) −5.37999 1.74806i −0.738998 0.240115i −0.0847577 0.996402i \(-0.527012\pi\)
−0.654241 + 0.756287i \(0.727012\pi\)
\(54\) 5.00000 + 1.41421i 0.680414 + 0.192450i
\(55\) 0 0
\(56\) 4.24264i 0.566947i
\(57\) −5.88909 + 4.39529i −0.780029 + 0.582171i
\(58\) 1.61803 1.17557i 0.212458 0.154360i
\(59\) 6.65003 9.15298i 0.865760 1.19162i −0.114405 0.993434i \(-0.536496\pi\)
0.980165 0.198183i \(-0.0635039\pi\)
\(60\) −1.45393 + 4.67826i −0.187701 + 0.603961i
\(61\) 9.41498 3.05911i 1.20546 0.391679i 0.363696 0.931518i \(-0.381515\pi\)
0.841769 + 0.539839i \(0.181515\pi\)
\(62\) −1.61803 1.17557i −0.205491 0.149298i
\(63\) 2.40481 3.49526i 0.302978 0.440362i
\(64\) 2.16312 6.65740i 0.270390 0.832174i
\(65\) 12.0000 1.48842
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 1.85410 5.70634i 0.224843 0.691995i
\(69\) 0 0
\(70\) −3.23607 2.35114i −0.386784 0.281015i
\(71\) 2.68999 0.874032i 0.319244 0.103729i −0.145012 0.989430i \(-0.546322\pi\)
0.464255 + 0.885701i \(0.346322\pi\)
\(72\) 7.14293 5.47527i 0.841803 0.645266i
\(73\) −0.831254 + 1.14412i −0.0972909 + 0.133909i −0.854887 0.518814i \(-0.826374\pi\)
0.757596 + 0.652724i \(0.226374\pi\)
\(74\) 6.47214 4.70228i 0.752371 0.546629i
\(75\) 3.10794 + 4.16422i 0.358874 + 0.480842i
\(76\) 4.24264i 0.486664i
\(77\) 0 0
\(78\) −6.00000 4.24264i −0.679366 0.480384i
\(79\) 4.03499 + 1.31105i 0.453972 + 0.147504i 0.527073 0.849820i \(-0.323290\pi\)
−0.0731009 + 0.997325i \(0.523290\pi\)
\(80\) −1.66251 2.28825i −0.185874 0.255834i
\(81\) 8.98813 0.461994i 0.998682 0.0513327i
\(82\) 1.85410 + 5.70634i 0.204751 + 0.630160i
\(83\) 4.94427 + 15.2169i 0.542704 + 1.67027i 0.726386 + 0.687287i \(0.241198\pi\)
−0.183682 + 0.982986i \(0.558802\pi\)
\(84\) −0.786780 2.31969i −0.0858447 0.253099i
\(85\) −9.97505 13.7295i −1.08195 1.48917i
\(86\) 4.03499 + 1.31105i 0.435104 + 0.141374i
\(87\) 2.00000 2.82843i 0.214423 0.303239i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −0.217858 8.48248i −0.0229643 0.894132i
\(91\) −4.85410 + 3.52671i −0.508848 + 0.369700i
\(92\) 0 0
\(93\) −3.30803 1.02808i −0.343027 0.106607i
\(94\) −2.68999 + 0.874032i −0.277452 + 0.0901495i
\(95\) 9.70820 + 7.05342i 0.996041 + 0.723666i
\(96\) −0.111184 8.65954i −0.0113477 0.883811i
\(97\) −0.618034 + 1.90211i −0.0627518 + 0.193130i −0.977517 0.210855i \(-0.932375\pi\)
0.914766 + 0.403985i \(0.132375\pi\)
\(98\) −5.00000 −0.505076
\(99\) 0 0
\(100\) 3.00000 0.300000
\(101\) 3.09017 9.51057i 0.307483 0.946337i −0.671255 0.741226i \(-0.734245\pi\)
0.978739 0.205110i \(-0.0657554\pi\)
\(102\) 0.133421 + 10.3914i 0.0132107 + 1.02891i
\(103\) −6.47214 4.70228i −0.637719 0.463330i 0.221347 0.975195i \(-0.428955\pi\)
−0.859066 + 0.511865i \(0.828955\pi\)
\(104\) −12.1050 + 3.93314i −1.18699 + 0.385677i
\(105\) −6.61606 2.05616i −0.645661 0.200661i
\(106\) 3.32502 4.57649i 0.322954 0.444508i
\(107\) −12.9443 + 9.40456i −1.25137 + 0.909174i −0.998301 0.0582746i \(-0.981440\pi\)
−0.253069 + 0.967448i \(0.581440\pi\)
\(108\) 2.89008 4.31827i 0.278098 0.415525i
\(109\) 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
\(112\) 1.34500 + 0.437016i 0.127090 + 0.0412941i
\(113\) 1.66251 + 2.28825i 0.156396 + 0.215260i 0.880023 0.474930i \(-0.157527\pi\)
−0.723628 + 0.690190i \(0.757527\pi\)
\(114\) −2.36034 6.95908i −0.221066 0.651778i
\(115\) 0 0
\(116\) −0.618034 1.90211i −0.0573830 0.176607i
\(117\) −12.2020 3.62105i −1.12807 0.334767i
\(118\) 6.65003 + 9.15298i 0.612185 + 0.842600i
\(119\) 8.06998 + 2.62210i 0.739774 + 0.240367i
\(120\) −12.0000 8.48528i −1.09545 0.774597i
\(121\) 0 0
\(122\) 9.89949i 0.896258i
\(123\) 6.21588 + 8.32844i 0.560467 + 0.750950i
\(124\) −1.61803 + 1.17557i −0.145304 + 0.105569i
\(125\) −3.32502 + 4.57649i −0.297398 + 0.409334i
\(126\) 2.58107 + 3.36721i 0.229940 + 0.299975i
\(127\) 9.41498 3.05911i 0.835444 0.271452i 0.140107 0.990136i \(-0.455255\pi\)
0.695337 + 0.718684i \(0.255255\pi\)
\(128\) −2.42705 1.76336i −0.214523 0.155860i
\(129\) 7.34786 0.0943431i 0.646943 0.00830645i
\(130\) −3.70820 + 11.4127i −0.325231 + 1.00096i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) −0.618034 + 1.90211i −0.0533900 + 0.164318i
\(135\) −5.07647 13.7924i −0.436913 1.18706i
\(136\) 14.5623 + 10.5801i 1.24871 + 0.907239i
\(137\) 2.68999 0.874032i 0.229822 0.0746736i −0.191842 0.981426i \(-0.561446\pi\)
0.421664 + 0.906752i \(0.361446\pi\)
\(138\) 0 0
\(139\) −0.831254 + 1.14412i −0.0705060 + 0.0970432i −0.842814 0.538206i \(-0.819102\pi\)
0.772308 + 0.635249i \(0.219102\pi\)
\(140\) −3.23607 + 2.35114i −0.273498 + 0.198708i
\(141\) −3.92606 + 2.93019i −0.330634 + 0.246767i
\(142\) 2.82843i 0.237356i
\(143\) 0 0
\(144\) 1.00000 + 2.82843i 0.0833333 + 0.235702i
\(145\) −5.37999 1.74806i −0.446784 0.145169i
\(146\) −0.831254 1.14412i −0.0687951 0.0946883i
\(147\) −8.20135 + 2.78169i −0.676436 + 0.229430i
\(148\) −2.47214 7.60845i −0.203208 0.625411i
\(149\) −1.85410 5.70634i −0.151894 0.467482i 0.845939 0.533280i \(-0.179041\pi\)
−0.997833 + 0.0657982i \(0.979041\pi\)
\(150\) −4.92081 + 1.66901i −0.401783 + 0.136274i
\(151\) 2.49376 + 3.43237i 0.202939 + 0.279322i 0.898341 0.439300i \(-0.144773\pi\)
−0.695401 + 0.718622i \(0.744773\pi\)
\(152\) −12.1050 3.93314i −0.981843 0.319020i
\(153\) 6.00000 + 16.9706i 0.485071 + 1.37199i
\(154\) 0 0
\(155\) 5.65685i 0.454369i
\(156\) −5.88909 + 4.39529i −0.471505 + 0.351905i
\(157\) 16.1803 11.7557i 1.29133 0.938207i 0.291500 0.956571i \(-0.405846\pi\)
0.999831 + 0.0183633i \(0.00584556\pi\)
\(158\) −2.49376 + 3.43237i −0.198393 + 0.273065i
\(159\) 2.90785 9.35652i 0.230608 0.742020i
\(160\) −13.4500 + 4.37016i −1.06331 + 0.345492i
\(161\) 0 0
\(162\) −2.33810 + 8.69099i −0.183699 + 0.682829i
\(163\) 6.18034 19.0211i 0.484082 1.48985i −0.349225 0.937039i \(-0.613555\pi\)
0.833307 0.552811i \(-0.186445\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −16.0000 −1.24184
\(167\) −3.70820 + 11.4127i −0.286949 + 0.883140i 0.698858 + 0.715260i \(0.253692\pi\)
−0.985808 + 0.167879i \(0.946308\pi\)
\(168\) 7.34786 0.0943431i 0.566900 0.00727873i
\(169\) 4.04508 + 2.93893i 0.311160 + 0.226071i
\(170\) 16.1400 5.24419i 1.23788 0.402211i
\(171\) −7.74320 10.1016i −0.592137 0.772491i
\(172\) 2.49376 3.43237i 0.190148 0.261716i
\(173\) 4.85410 3.52671i 0.369051 0.268131i −0.387767 0.921758i \(-0.626753\pi\)
0.756817 + 0.653627i \(0.226753\pi\)
\(174\) 2.07196 + 2.77615i 0.157075 + 0.210459i
\(175\) 4.24264i 0.320713i
\(176\) 0 0
\(177\) 16.0000 + 11.3137i 1.20263 + 0.850390i
\(178\) 0 0
\(179\) 1.66251 + 2.28825i 0.124262 + 0.171032i 0.866615 0.498977i \(-0.166291\pi\)
−0.742354 + 0.670008i \(0.766291\pi\)
\(180\) −8.13464 2.41404i −0.606321 0.179932i
\(181\) −3.09017 9.51057i −0.229691 0.706915i −0.997781 0.0665740i \(-0.978793\pi\)
0.768091 0.640341i \(-0.221207\pi\)
\(182\) −1.85410 5.70634i −0.137435 0.422982i
\(183\) 5.50746 + 16.2379i 0.407123 + 1.20034i
\(184\) 0 0
\(185\) −21.5200 6.99226i −1.58218 0.514081i
\(186\) 2.00000 2.82843i 0.146647 0.207390i
\(187\) 0 0
\(188\) 2.82843i 0.206284i
\(189\) 6.10695 + 4.08719i 0.444215 + 0.297300i
\(190\) −9.70820 + 7.05342i −0.704307 + 0.511709i
\(191\) −11.6376 + 16.0177i −0.842064 + 1.15900i 0.143492 + 0.989651i \(0.454167\pi\)
−0.985556 + 0.169350i \(0.945833\pi\)
\(192\) 11.5781 + 3.59828i 0.835577 + 0.259684i
\(193\) −20.1750 + 6.55524i −1.45223 + 0.471857i −0.925685 0.378294i \(-0.876511\pi\)
−0.526540 + 0.850151i \(0.676511\pi\)
\(194\) −1.61803 1.17557i −0.116168 0.0844010i
\(195\) 0.266843 + 20.7829i 0.0191090 + 1.48829i
\(196\) −1.54508 + 4.75528i −0.110363 + 0.339663i
\(197\) −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 \(0.477417\pi\)
\(200\) −2.78115 + 8.55951i −0.196657 + 0.605249i
\(201\) 0.0444738 + 3.46382i 0.00313694 + 0.244319i
\(202\) 8.09017 + 5.87785i 0.569222 + 0.413564i
\(203\) 2.68999 0.874032i 0.188801 0.0613450i
\(204\) 9.92408 + 3.08424i 0.694825 + 0.215940i
\(205\) 9.97505 13.7295i 0.696687 0.958908i
\(206\) 6.47214 4.70228i 0.450935 0.327624i
\(207\) 0 0
\(208\) 4.24264i 0.294174i
\(209\) 0 0
\(210\) 4.00000 5.65685i 0.276026 0.390360i
\(211\) −25.5549 8.30330i −1.75927 0.571623i −0.762150 0.647400i \(-0.775856\pi\)
−0.997125 + 0.0757773i \(0.975856\pi\)
\(212\) −3.32502 4.57649i −0.228363 0.314315i
\(213\) 1.57356 + 4.63939i 0.107819 + 0.317886i
\(214\) −4.94427 15.2169i −0.337983 1.04021i
\(215\) −3.70820 11.4127i −0.252897 0.778338i
\(216\) 9.64149 + 12.2491i 0.656021 + 0.833449i
\(217\) −1.66251 2.28825i −0.112858 0.155336i
\(218\) 4.03499 + 1.31105i 0.273284 + 0.0887954i
\(219\) −2.00000 1.41421i −0.135147 0.0955637i
\(220\) 0 0
\(221\) 25.4558i 1.71235i
\(222\) 8.28784 + 11.1046i 0.556243 + 0.745291i
\(223\) −19.4164 + 14.1068i −1.30022 + 0.944664i −0.999958 0.00919277i \(-0.997074\pi\)
−0.300261 + 0.953857i \(0.597074\pi\)
\(224\) 4.15627 5.72061i 0.277702 0.382225i
\(225\) −7.14293 + 5.47527i −0.476195 + 0.365018i
\(226\) −2.68999 + 0.874032i −0.178936 + 0.0581397i
\(227\) −19.4164 14.1068i −1.28871 0.936304i −0.288934 0.957349i \(-0.593301\pi\)
−0.999779 + 0.0210448i \(0.993301\pi\)
\(228\) −7.34786 + 0.0943431i −0.486624 + 0.00624802i
\(229\) −7.41641 + 22.8254i −0.490090 + 1.50834i 0.334381 + 0.942438i \(0.391473\pi\)
−0.824471 + 0.565904i \(0.808527\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 3.09017 9.51057i 0.202444 0.623058i −0.797365 0.603497i \(-0.793773\pi\)
0.999809 0.0195604i \(-0.00622666\pi\)
\(234\) 7.21444 10.4858i 0.471623 0.685478i
\(235\) 6.47214 + 4.70228i 0.422196 + 0.306743i
\(236\) 10.7600 3.49613i 0.700415 0.227579i
\(237\) −2.18089 + 7.01739i −0.141664 + 0.455828i
\(238\) −4.98752 + 6.86474i −0.323293 + 0.444975i
\(239\) −12.9443 + 9.40456i −0.837295 + 0.608331i −0.921614 0.388108i \(-0.873129\pi\)
0.0843185 + 0.996439i \(0.473129\pi\)
\(240\) 3.92606 2.93019i 0.253426 0.189143i
\(241\) 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
\(244\) 9.41498 + 3.05911i 0.602732 + 0.195840i
\(245\) 8.31254 + 11.4412i 0.531069 + 0.730953i
\(246\) −9.84163 + 3.33803i −0.627479 + 0.212825i
\(247\) 5.56231 + 17.1190i 0.353921 + 1.08926i
\(248\) −1.85410 5.70634i −0.117736 0.362353i
\(249\) −26.2443 + 8.90140i −1.66317 + 0.564103i
\(250\) −3.32502 4.57649i −0.210292 0.289443i
\(251\) 24.2099 + 7.86629i 1.52812 + 0.496516i 0.948069 0.318065i \(-0.103033\pi\)
0.580050 + 0.814581i \(0.303033\pi\)
\(252\) 4.00000 1.41421i 0.251976 0.0890871i
\(253\) 0 0
\(254\) 9.89949i 0.621150i
\(255\) 23.5564 17.5812i 1.47516 1.10098i
\(256\) 13.7533 9.99235i 0.859581 0.624522i
\(257\) 6.65003 9.15298i 0.414818 0.570947i −0.549568 0.835449i \(-0.685208\pi\)
0.964385 + 0.264502i \(0.0852075\pi\)
\(258\) −2.18089 + 7.01739i −0.135776 + 0.436883i
\(259\) 10.7600 3.49613i 0.668592 0.217239i
\(260\) 9.70820 + 7.05342i 0.602077 + 0.437435i
\(261\) 4.94305 + 3.40092i 0.305967 + 0.210512i
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −16.0000 −0.982872
\(266\) 1.85410 5.70634i 0.113682 0.349878i
\(267\) 0 0
\(268\) 1.61803 + 1.17557i 0.0988372 + 0.0718094i
\(269\) −26.8999 + 8.74032i −1.64012 + 0.532907i −0.976565 0.215222i \(-0.930952\pi\)
−0.663553 + 0.748129i \(0.730952\pi\)
\(270\) 14.6860 0.565934i 0.893764 0.0344417i
\(271\) 17.4563 24.0266i 1.06040 1.45951i 0.180963 0.983490i \(-0.442079\pi\)
0.879434 0.476021i \(-0.157921\pi\)
\(272\) −4.85410 + 3.52671i −0.294323 + 0.213838i
\(273\) −6.21588 8.32844i −0.376202 0.504060i
\(274\) 2.82843i 0.170872i
\(275\) 0 0
\(276\) 0 0
\(277\) 4.03499 + 1.31105i 0.242439 + 0.0787732i 0.427716 0.903913i \(-0.359318\pi\)
−0.185277 + 0.982686i \(0.559318\pi\)
\(278\) −0.831254 1.14412i −0.0498553 0.0686199i
\(279\) 1.70698 5.75206i 0.102194 0.344367i
\(280\) −3.70820 11.4127i −0.221608 0.682038i
\(281\) −1.85410 5.70634i −0.110606 0.340412i 0.880399 0.474234i \(-0.157275\pi\)
−0.991005 + 0.133822i \(0.957275\pi\)
\(282\) −1.57356 4.63939i −0.0937041 0.276271i
\(283\) −15.7938 21.7383i −0.938845 1.29221i −0.956308 0.292362i \(-0.905559\pi\)
0.0174623 0.999848i \(-0.494441\pi\)
\(284\) 2.68999 + 0.874032i 0.159622 + 0.0518643i
\(285\) −12.0000 + 16.9706i −0.710819 + 1.00525i
\(286\) 0 0
\(287\) 8.48528i 0.500870i
\(288\) 14.9951 0.385122i 0.883592 0.0226936i
\(289\) −15.3713 + 11.1679i −0.904195 + 0.656936i
\(290\) 3.32502 4.57649i 0.195252 0.268741i
\(291\) −3.30803 1.02808i −0.193920 0.0602672i
\(292\) −1.34500 + 0.437016i −0.0787100 + 0.0255744i
\(293\) −1.61803 1.17557i −0.0945266 0.0686776i 0.539518 0.841974i \(-0.318606\pi\)
−0.634045 + 0.773296i \(0.718606\pi\)
\(294\) −0.111184 8.65954i −0.00648441 0.505035i
\(295\) 9.88854 30.4338i 0.575733 1.77192i
\(296\) 24.0000 1.39497
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 0.0667106 + 5.19572i 0.00385154 + 0.299975i
\(301\) 4.85410 + 3.52671i 0.279786 + 0.203276i
\(302\) −4.03499 + 1.31105i −0.232188 + 0.0754423i
\(303\) 16.5401 + 5.14040i 0.950206 + 0.295309i
\(304\) 2.49376 3.43237i 0.143027 0.196860i
\(305\) 22.6525 16.4580i 1.29708 0.942382i
\(306\) −17.9941 + 0.462147i −1.02865 + 0.0264192i
\(307\) 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
\(310\) −5.37999 1.74806i −0.305563 0.0992834i
\(311\) −16.6251 22.8825i −0.942722 1.29755i −0.954685 0.297617i \(-0.903808\pi\)
0.0119638 0.999928i \(-0.496192\pi\)
\(312\) −7.08102 20.8772i −0.400884 1.18194i
\(313\) 3.70820 + 11.4127i 0.209600 + 0.645083i 0.999493 + 0.0318380i \(0.0101361\pi\)
−0.789893 + 0.613245i \(0.789864\pi\)
\(314\) 6.18034 + 19.0211i 0.348777 + 1.07342i
\(315\) 3.41396 11.5041i 0.192355 0.648184i
\(316\) 2.49376 + 3.43237i 0.140285 + 0.193086i
\(317\) 24.2099 + 7.86629i 1.35977 + 0.441815i 0.895965 0.444125i \(-0.146485\pi\)
0.463801 + 0.885939i \(0.346485\pi\)
\(318\) 8.00000 + 5.65685i 0.448618 + 0.317221i
\(319\) 0 0
\(320\) 19.7990i 1.10680i
\(321\) −16.5757 22.2092i −0.925164 1.23959i
\(322\) 0 0
\(323\) 14.9626 20.5942i 0.832540 1.14589i
\(324\) 7.54311 + 4.90933i 0.419062 + 0.272741i
\(325\) 12.1050 3.93314i 0.671463 0.218172i
\(326\) 16.1803 + 11.7557i 0.896146 + 0.651088i
\(327\) 7.34786 0.0943431i 0.406338 0.00521719i
\(328\) −5.56231 + 17.1190i −0.307127 + 0.945240i
\(329\) −4.00000 −0.220527
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) −4.94427 + 15.2169i −0.271352 + 0.835136i
\(333\) 19.7722 + 13.6037i 1.08351 + 0.745477i
\(334\) −9.70820 7.05342i −0.531209 0.385946i
\(335\) 5.37999 1.74806i 0.293940 0.0955069i
\(336\) −0.726963 + 2.33913i −0.0396591 + 0.127610i
\(337\) −19.1188 + 26.3148i −1.04147 + 1.43346i −0.145493 + 0.989359i \(0.546477\pi\)
−0.895977 + 0.444100i \(0.853523\pi\)
\(338\) −4.04508 + 2.93893i −0.220024 + 0.159857i
\(339\) −3.92606 + 2.93019i −0.213234 + 0.159146i
\(340\) 16.9706i 0.920358i
\(341\) 0 0
\(342\) 12.0000 4.24264i 0.648886 0.229416i
\(343\) −16.1400 5.24419i −0.871476 0.283160i
\(344\) 7.48128 + 10.2971i 0.403364 + 0.555183i
\(345\) 0 0
\(346\) 1.85410 + 5.70634i 0.0996771 + 0.306775i
\(347\) 4.94427 + 15.2169i 0.265422 + 0.816886i 0.991596 + 0.129375i \(0.0412970\pi\)
−0.726173 + 0.687512i \(0.758703\pi\)
\(348\) 3.28054 1.11268i 0.175855 0.0596456i
\(349\) 2.49376 + 3.43237i 0.133488 + 0.183730i 0.870528 0.492118i \(-0.163777\pi\)
−0.737040 + 0.675849i \(0.763777\pi\)
\(350\) −4.03499 1.31105i −0.215679 0.0700785i
\(351\) 6.00000 21.2132i 0.320256 1.13228i
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) −15.7042 + 11.7208i −0.834671 + 0.622952i
\(355\) 6.47214 4.70228i 0.343505 0.249571i
\(356\) 0 0
\(357\) −4.36178 + 14.0348i −0.230850 + 0.742799i
\(358\) −2.68999 + 0.874032i −0.142171 + 0.0461940i
\(359\) 16.1803 + 11.7557i 0.853966 + 0.620442i 0.926237 0.376943i \(-0.123025\pi\)
−0.0722709 + 0.997385i \(0.523025\pi\)
\(360\) 14.4289 20.9716i 0.760469 1.10530i
\(361\) 0.309017 0.951057i 0.0162641 0.0500556i
\(362\) 10.0000 0.525588
\(363\) 0 0
\(364\) −6.00000 −0.314485
\(365\) −1.23607 + 3.80423i −0.0646988 + 0.199122i
\(366\) −17.1450 + 0.220134i −0.896184 + 0.0115066i
\(367\) −6.47214 4.70228i −0.337843 0.245457i 0.405908 0.913914i \(-0.366955\pi\)
−0.743751 + 0.668457i \(0.766955\pi\)
\(368\) 0 0
\(369\) −14.2859 + 10.9505i −0.743692 + 0.570062i
\(370\) 13.3001 18.3060i 0.691437 0.951682i
\(371\) 6.47214 4.70228i 0.336017 0.244130i
\(372\) −2.07196 2.77615i −0.107426 0.143936i
\(373\) 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
\(376\) −8.06998 2.62210i −0.416178 0.135224i
\(377\) −4.98752 6.86474i −0.256871 0.353552i
\(378\) −5.77430 + 4.54504i −0.296998 + 0.233772i
\(379\) 3.70820 + 11.4127i 0.190478 + 0.586230i 1.00000 0.000859657i \(-0.000273637\pi\)
−0.809522 + 0.587090i \(0.800274\pi\)
\(380\) 3.70820 + 11.4127i 0.190227 + 0.585458i
\(381\) 5.50746 + 16.2379i 0.282156 + 0.831890i
\(382\) −11.6376 16.0177i −0.595429 0.819538i
\(383\) −5.37999 1.74806i −0.274905 0.0893219i 0.168320 0.985732i \(-0.446166\pi\)
−0.443225 + 0.896410i \(0.646166\pi\)
\(384\) 3.00000 4.24264i 0.153093 0.216506i
\(385\) 0 0
\(386\) 21.2132i 1.07972i
\(387\) 0.326787 + 12.7237i 0.0166115 + 0.646783i
\(388\) −1.61803 + 1.17557i −0.0821432 + 0.0596806i
\(389\) −11.6376 + 16.0177i −0.590047 + 0.812131i −0.994752 0.102317i \(-0.967374\pi\)
0.404704 + 0.914448i \(0.367374\pi\)
\(390\) −19.8482 6.16849i −1.00505 0.312353i
\(391\) 0 0
\(392\) −12.1353 8.81678i −0.612923 0.445315i
\(393\) 0 0
\(394\) 6.79837 20.9232i 0.342497 1.05410i
\(395\) 12.0000 0.603786
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) −0.618034 + 1.90211i −0.0309792 + 0.0953443i
\(399\) −0.133421 10.3914i −0.00667942 0.520223i
\(400\) −2.42705 1.76336i −0.121353 0.0881678i
\(401\) 2.68999 0.874032i 0.134332 0.0436471i −0.241079 0.970505i \(-0.577501\pi\)
0.375411 + 0.926858i \(0.377501\pi\)
\(402\) −3.30803 1.02808i −0.164989 0.0512760i
\(403\) −4.98752 + 6.86474i −0.248446 + 0.341957i
\(404\) 8.09017 5.87785i 0.402501 0.292434i
\(405\) 23.7742 9.09868i 1.18135 0.452117i
\(406\) 2.82843i 0.140372i
\(407\) 0 0
\(408\) −18.0000 + 25.4558i −0.891133 + 1.26025i
\(409\) 4.03499 + 1.31105i 0.199517 + 0.0648272i 0.407071 0.913396i \(-0.366550\pi\)
−0.207554 + 0.978224i \(0.566550\pi\)
\(410\) 9.97505 + 13.7295i 0.492632 + 0.678050i
\(411\) 1.57356 + 4.63939i 0.0776180 + 0.228844i
\(412\) −2.47214 7.60845i −0.121793 0.374842i
\(413\) 4.94427 + 15.2169i 0.243292 + 0.748775i
\(414\) 0 0
\(415\) 26.6001 + 36.6119i 1.30575 + 1.79721i
\(416\) −20.1750 6.55524i −0.989159 0.321397i
\(417\) −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 \(0.725210\pi\)
\(420\) −4.14392 5.55229i −0.202203 0.270924i
\(421\) 16.1803 11.7557i 0.788582 0.572938i −0.118961 0.992899i \(-0.537956\pi\)
0.907542 + 0.419961i \(0.137956\pi\)
\(422\) 15.7938 21.7383i 0.768831 1.05821i
\(423\) −5.16213 6.73442i −0.250991 0.327439i
\(424\) 16.1400 5.24419i 0.783826 0.254680i
\(425\) −14.5623 10.5801i −0.706376 0.513212i
\(426\) −4.89858 + 0.0628954i −0.237337 + 0.00304729i
\(427\) −4.32624 + 13.3148i −0.209361 + 0.644348i
\(428\) −16.0000 −0.773389
\(429\) 0 0
\(430\) 12.0000 0.578691
\(431\) 9.88854 30.4338i 0.476314 1.46594i −0.367862 0.929880i \(-0.619910\pi\)
0.844177 0.536065i \(-0.180090\pi\)
\(432\) −4.87634 + 1.79480i −0.234613 + 0.0863525i
\(433\) −24.2705 17.6336i −1.16637 0.847415i −0.175797 0.984426i \(-0.556250\pi\)
−0.990569 + 0.137012i \(0.956250\pi\)
\(434\) 2.68999 0.874032i 0.129124 0.0419549i
\(435\) 2.90785 9.35652i 0.139421 0.448611i
\(436\) 2.49376 3.43237i 0.119430 0.164381i
\(437\) 0 0
\(438\) 1.96303 1.46510i 0.0937972 0.0700050i
\(439\) 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
\(442\) 24.2099 + 7.86629i 1.15155 + 0.374161i
\(443\) −16.6251 22.8825i −0.789881 1.08718i −0.994123 0.108258i \(-0.965473\pi\)
0.204242 0.978921i \(-0.434527\pi\)
\(444\) 13.1222 4.45070i 0.622750 0.211221i
\(445\) 0 0
\(446\) −7.41641 22.8254i −0.351177 1.08081i
\(447\) 9.84163 3.33803i 0.465493 0.157883i
\(448\) 5.81878 + 8.00886i 0.274911 + 0.378383i
\(449\) −5.37999 1.74806i −0.253897 0.0824962i 0.179303 0.983794i \(-0.442616\pi\)
−0.433200 + 0.901298i \(0.642616\pi\)
\(450\) −3.00000 8.48528i −0.141421 0.400000i
\(451\) 0 0
\(452\) 2.82843i 0.133038i
\(453\) −5.88909 + 4.39529i −0.276694 + 0.206509i
\(454\) 19.4164 14.1068i 0.911257 0.662067i
\(455\) −9.97505 + 13.7295i −0.467637 + 0.643648i
\(456\) 6.54267 21.0522i 0.306388 0.985858i
\(457\) 9.41498 3.05911i 0.440414 0.143099i −0.0804125 0.996762i \(-0.525624\pi\)
0.520827 + 0.853662i \(0.325624\pi\)
\(458\) −19.4164 14.1068i −0.907269 0.659170i
\(459\) −29.2580 + 10.7688i −1.36565 + 0.502646i
\(460\) 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 \(0.311689\pi\)
\(464\) −0.618034 + 1.90211i −0.0286915 + 0.0883034i
\(465\) −9.79715 + 0.125791i −0.454332 + 0.00583341i
\(466\) 8.09017 + 5.87785i 0.374770 + 0.272286i
\(467\) −26.8999 + 8.74032i −1.24478 + 0.404454i −0.856048 0.516897i \(-0.827087\pi\)
−0.388733 + 0.921350i \(0.627087\pi\)
\(468\) −7.74320 10.1016i −0.357929 0.466948i
\(469\) −1.66251 + 2.28825i −0.0767675 + 0.105661i
\(470\) −6.47214 + 4.70228i −0.298537 + 0.216900i
\(471\) 20.7196 + 27.7615i 0.954709 + 1.27918i
\(472\) 33.9411i 1.56227i
\(473\) 0 0
\(474\) −6.00000 4.24264i −0.275589 0.194871i
\(475\) 12.1050 + 3.93314i 0.555414 + 0.180465i
\(476\) 4.98752 + 6.86474i 0.228603 + 0.314645i
\(477\) 16.2693 + 4.82807i 0.744919 + 0.221062i
\(478\) −4.94427 15.2169i −0.226146 0.696005i
\(479\) −8.65248 26.6296i −0.395342 1.21674i −0.928695 0.370844i \(-0.879068\pi\)
0.533353 0.845893i \(-0.320932\pi\)
\(480\) −7.86780 23.1969i −0.359114 1.05879i
\(481\) −19.9501 27.4589i −0.909646 1.25202i
\(482\) 4.03499 + 1.31105i 0.183789 + 0.0597166i
\(483\) 0 0
\(484\) 0 0
\(485\) 5.65685i 0.256865i
\(486\) −15.1040 3.85612i −0.685131 0.174917i
\(487\) −1.61803 + 1.17557i −0.0733201 + 0.0532702i −0.623842 0.781551i \(-0.714429\pi\)
0.550521 + 0.834821i \(0.314429\pi\)
\(488\) −17.4563 + 24.0266i −0.790211 + 1.08763i
\(489\) 33.0803 + 10.2808i 1.49594 + 0.464914i
\(490\) −13.4500 + 4.37016i −0.607608 + 0.197424i
\(491\) 16.1803 + 11.7557i 0.730209 + 0.530528i 0.889629 0.456683i \(-0.150963\pi\)
−0.159421 + 0.987211i \(0.550963\pi\)
\(492\) 0.133421 + 10.3914i 0.00601510 + 0.468483i
\(493\) −3.70820 + 11.4127i −0.167009 + 0.514001i
\(494\) −18.0000 −0.809858
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) −1.23607 + 3.80423i −0.0554452 + 0.170643i
\(498\) −0.355790 27.7105i −0.0159433 1.24174i
\(499\) 11.3262 + 8.22899i 0.507032 + 0.368380i 0.811697 0.584079i \(-0.198544\pi\)
−0.304664 + 0.952460i \(0.598544\pi\)
\(500\) −5.37999 + 1.74806i −0.240600 + 0.0781758i
\(501\) −19.8482 6.16849i −0.886751 0.275588i
\(502\) −14.9626 + 20.5942i −0.667812 + 0.919165i
\(503\) −12.9443 + 9.40456i −0.577157 + 0.419329i −0.837698 0.546134i \(-0.816099\pi\)
0.260541 + 0.965463i \(0.416099\pi\)
\(504\) 0.326787 + 12.7237i 0.0145563 + 0.566760i
\(505\) 28.2843i 1.25863i
\(506\) 0 0
\(507\) −5.00000 + 7.07107i −0.222058 + 0.314037i
\(508\) 9.41498 + 3.05911i 0.417722 + 0.135726i
\(509\) 19.9501 + 27.4589i 0.884272 + 1.21710i 0.975219 + 0.221241i \(0.0710106\pi\)
−0.0909469 + 0.995856i \(0.528989\pi\)
\(510\) 9.44136 + 27.8363i 0.418071 + 1.23261i
\(511\) −0.618034 1.90211i −0.0273402 0.0841445i
\(512\) 3.39919 + 10.4616i 0.150224 + 0.462343i
\(513\) 17.3229 13.6351i 0.764825 0.602006i
\(514\) 6.65003 + 9.15298i 0.293320 + 0.403721i
\(515\) −21.5200 6.99226i −0.948282 0.308116i
\(516\) 6.00000 + 4.24264i 0.264135 + 0.186772i
\(517\) 0 0
\(518\) 11.3137i 0.497096i
\(519\) 6.21588 + 8.32844i 0.272847 + 0.365578i
\(520\) −29.1246 + 21.1603i −1.27720 + 0.927939i
\(521\) −11.6376 + 16.0177i −0.509851 + 0.701749i −0.983894 0.178752i \(-0.942794\pi\)
0.474044 + 0.880501i \(0.342794\pi\)
\(522\) −4.76195 + 3.65018i −0.208425 + 0.159764i
\(523\) −20.1750 + 6.55524i −0.882189 + 0.286641i −0.714866 0.699261i \(-0.753512\pi\)
−0.167323 + 0.985902i \(0.553512\pi\)
\(524\) 0 0
\(525\) −7.34786 + 0.0943431i −0.320687 + 0.00411747i
\(526\) 0 0
\(527\) 12.0000 0.522728
\(528\) 0 0
\(529\) 23.0000 1.00000
\(530\) 4.94427 15.2169i 0.214765 0.660980i
\(531\) −19.2385 + 27.9621i −0.834880 + 1.21345i
\(532\) −4.85410 3.52671i −0.210452 0.152902i
\(533\) 24.2099 7.86629i 1.04865 0.340727i
\(534\) 0 0
\(535\) −26.6001 + 36.6119i −1.15002 + 1.58287i
\(536\) −4.85410 + 3.52671i −0.209665 + 0.152331i
\(537\) −3.92606 + 2.93019i −0.169422 + 0.126447i
\(538\) 28.2843i 1.21942i
\(539\) 0 0
\(540\) 4.00000 14.1421i 0.172133 0.608581i
\(541\) 33.6249 + 10.9254i 1.44565 + 0.469720i 0.923653 0.383229i \(-0.125188\pi\)
0.521995 + 0.852949i \(0.325188\pi\)
\(542\) 17.4563 + 24.0266i 0.749814 + 1.03203i
\(543\) 16.4027 5.56338i 0.703908 0.238747i
\(544\) 9.27051 + 28.5317i 0.397470 + 1.22329i
\(545\) −3.70820 11.4127i −0.158842 0.488865i
\(546\) 9.84163 3.33803i 0.421183 0.142854i
\(547\) 20.7813 + 28.6031i 0.888546 + 1.22298i 0.973980 + 0.226635i \(0.0727725\pi\)
−0.0854335 + 0.996344i \(0.527228\pi\)
\(548\) 2.68999 + 0.874032i 0.114911 + 0.0373368i
\(549\) −28.0000 + 9.89949i −1.19501 + 0.422500i
\(550\) 0 0
\(551\) 8.48528i 0.361485i
\(552\) 0 0
\(553\) −4.85410 + 3.52671i −0.206417 + 0.149971i
\(554\) −2.49376 + 3.43237i −0.105950 + 0.145827i
\(555\) 11.6314 37.4261i 0.493726 1.58865i
\(556\) −1.34500 + 0.437016i −0.0570406 + 0.0185336i
\(557\) −1.61803 1.17557i −0.0685583 0.0498105i 0.552978 0.833196i \(-0.313491\pi\)
−0.621537 + 0.783385i \(0.713491\pi\)
\(558\) 4.94305 + 3.40092i 0.209256 + 0.143972i
\(559\) 5.56231 17.1190i 0.235260 0.724057i
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −3.70820 + 11.4127i −0.156282 + 0.480987i −0.998289 0.0584805i \(-0.981374\pi\)
0.842006 + 0.539468i \(0.181374\pi\)
\(564\) −4.89858 + 0.0628954i −0.206267 + 0.00264837i
\(565\) 6.47214 + 4.70228i 0.272285 + 0.197826i
\(566\) 25.5549 8.30330i 1.07415 0.349014i
\(567\) −6.94284 + 10.6676i −0.291572 + 0.447996i
\(568\) −4.98752 + 6.86474i −0.209272 + 0.288038i
\(569\) −30.7426 + 22.3358i −1.28880 + 0.936367i −0.999780 0.0209564i \(-0.993329\pi\)
−0.289018 + 0.957324i \(0.593329\pi\)
\(570\) −12.4318 16.6569i −0.520709 0.697680i
\(571\) 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
\(574\) −8.06998 2.62210i −0.336835 0.109444i
\(575\) 0 0
\(576\) −5.97444 + 20.1322i −0.248935 + 0.838842i
\(577\) −9.88854 30.4338i −0.411665 1.26698i −0.915200 0.403001i \(-0.867967\pi\)
0.503534 0.863975i \(-0.332033\pi\)
\(578\) −5.87132 18.0701i −0.244215 0.751616i
\(579\) −11.8017 34.7954i −0.490462 1.44605i
\(580\) −3.32502 4.57649i −0.138064 0.190028i
\(581\) −21.5200 6.99226i −0.892798 0.290088i
\(582\) 2.00000 2.82843i 0.0829027 0.117242i
\(583\) 0 0
\(584\) 4.24264i 0.175562i
\(585\) −35.9881 + 0.924294i −1.48793 + 0.0382148i
\(586\) 1.61803 1.17557i 0.0668404 0.0485624i
\(587\) 6.65003 9.15298i 0.274476 0.377784i −0.649418 0.760431i \(-0.724988\pi\)
0.923894 + 0.382647i \(0.124988\pi\)
\(588\) −8.27007 2.57020i −0.341052 0.105993i
\(589\) −8.06998 + 2.62210i −0.332518 + 0.108042i
\(590\) 25.8885 + 18.8091i 1.06581 + 0.774360i
\(591\) −0.489211 38.1020i −0.0201235 1.56731i
\(592\) −2.47214 + 7.60845i −0.101604 + 0.312705i
\(593\) 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
\(596\) 1.85410 5.70634i 0.0759470 0.233741i
\(597\) 0.0444738 + 3.46382i 0.00182019 + 0.141765i
\(598\) 0 0
\(599\) 32.2799 10.4884i 1.31892 0.428544i 0.436798 0.899560i \(-0.356113\pi\)
0.882125 + 0.471016i \(0.156113\pi\)
\(600\) −14.8861 4.62636i −0.607724 0.188871i
\(601\) 17.4563 24.0266i 0.712059 0.980065i −0.287692 0.957723i \(-0.592888\pi\)
0.999750 0.0223415i \(-0.00711213\pi\)
\(602\) −4.85410 + 3.52671i −0.197838 + 0.143738i
\(603\) −5.99802 + 0.154049i −0.244258 + 0.00627336i
\(604\) 4.24264i 0.172631i
\(605\) 0 0
\(606\) −10.0000 + 14.1421i −0.406222 + 0.574485i
\(607\) 4.03499 + 1.31105i 0.163775 + 0.0532138i 0.389757 0.920918i \(-0.372559\pi\)
−0.225982 + 0.974132i \(0.572559\pi\)
\(608\) −12.4688 17.1618i −0.505677 0.696005i
\(609\) 1.57356 + 4.63939i 0.0637639 + 0.187997i
\(610\) 8.65248 + 26.6296i 0.350329 + 1.07820i
\(611\) 3.70820 + 11.4127i 0.150018 + 0.461708i
\(612\) −5.12094 + 17.2562i −0.207002 + 0.697540i
\(613\) 2.49376 + 3.43237i 0.100722 + 0.138632i 0.856403 0.516308i \(-0.172694\pi\)
−0.755681 + 0.654940i \(0.772694\pi\)
\(614\) 4.03499 + 1.31105i 0.162839 + 0.0529096i
\(615\) 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 \(0.784579\pi\)
\(618\) 8.28784 + 11.1046i 0.333386 + 0.446692i
\(619\) 16.1803 11.7557i 0.650343 0.472502i −0.213045 0.977042i \(-0.568338\pi\)
0.863388 + 0.504541i \(0.168338\pi\)
\(620\) −3.32502 + 4.57649i −0.133536 + 0.183796i
\(621\) 0 0
\(622\) 26.8999 8.74032i 1.07859 0.350455i
\(623\) 0 0
\(624\) 7.34786 0.0943431i 0.294150 0.00377675i
\(625\) −9.57953 + 29.4828i −0.383181 + 1.17931i
\(626\) −12.0000 −0.479616
\(627\) 0 0
\(628\) 20.0000 0.798087
\(629\) −14.8328 + 45.6507i −0.591423 + 1.82021i
\(630\) 9.88610 + 6.80184i 0.393872 + 0.270992i
\(631\) 11.3262 + 8.22899i 0.450890 + 0.327591i 0.789947 0.613175i \(-0.210108\pi\)
−0.339057 + 0.940766i \(0.610108\pi\)
\(632\) −12.1050 + 3.93314i −0.481510 + 0.156452i
\(633\) 13.8123 44.4435i 0.548990 1.76647i
\(634\) −14.9626 + 20.5942i −0.594240 + 0.817901i
\(635\) 22.6525 16.4580i 0.898936 0.653115i
\(636\) 7.85212 5.86039i 0.311357 0.232380i
\(637\) 21.2132i 0.840498i
\(638\) 0 0
\(639\) −8.00000 + 2.82843i −0.316475 + 0.111891i
\(640\) −8.06998 2.62210i −0.318994 0.103647i
\(641\) −16.6251 22.8825i −0.656651 0.903803i 0.342714 0.939440i \(-0.388654\pi\)
−0.999365 + 0.0356372i \(0.988654\pi\)
\(642\) 26.2443 8.90140i 1.03578 0.351310i
\(643\) 3.70820 + 11.4127i 0.146237 + 0.450072i 0.997168 0.0752058i \(-0.0239614\pi\)
−0.850931 + 0.525278i \(0.823961\pi\)
\(644\) 0 0
\(645\) 19.6833 6.67605i 0.775027 0.262869i
\(646\) 14.9626 + 20.5942i 0.588694 + 0.810268i
\(647\) −5.37999 1.74806i −0.211509 0.0687235i 0.201346 0.979520i \(-0.435468\pi\)
−0.412855 + 0.910797i \(0.635468\pi\)
\(648\) −21.0000 + 16.9706i −0.824958 + 0.666667i
\(649\) 0 0
\(650\) 12.7279i 0.499230i
\(651\) 3.92606 2.93019i 0.153875 0.114843i
\(652\) 16.1803 11.7557i 0.633671 0.460389i
\(653\) 6.65003 9.15298i 0.260236 0.358184i −0.658827 0.752294i \(-0.728947\pi\)
0.919063 + 0.394110i \(0.128947\pi\)
\(654\) −2.18089 + 7.01739i −0.0852795 + 0.274402i
\(655\) 0 0
\(656\) −4.85410 3.52671i −0.189521 0.137695i
\(657\) 2.40481 3.49526i 0.0938207 0.136363i
\(658\) 1.23607 3.80423i 0.0481869 0.148304i
\(659\) 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 \(0.627164\pi\)
\(662\) 6.18034 19.0211i 0.240206 0.739277i
\(663\) 44.0872 0.566059i 1.71220 0.0219839i
\(664\) −38.8328 28.2137i −1.50701 1.09490i
\(665\) −16.1400 + 5.24419i −0.625881 + 0.203361i
\(666\) −19.0478 + 14.6007i −0.738088 + 0.565766i
\(667\) 0 0
\(668\) −9.70820 + 7.05342i −0.375622 + 0.272905i
\(669\) −24.8635 33.3137i −0.961279 1.28798i
\(670\) 5.65685i 0.218543i
\(671\) 0 0
\(672\) 10.0000 + 7.07107i 0.385758 + 0.272772i
\(673\) 4.03499 + 1.31105i 0.155537 + 0.0505372i 0.385751 0.922603i \(-0.373942\pi\)
−0.230213 + 0.973140i \(0.573942\pi\)
\(674\) −19.1188 26.3148i −0.736430 1.01361i
\(675\) −9.64149 12.2491i −0.371101 0.471470i
\(676\) 1.54508 + 4.75528i 0.0594263 + 0.182895i
\(677\) 11.7426 + 36.1401i 0.451307 + 1.38898i 0.875417 + 0.483368i \(0.160587\pi\)
−0.424111 + 0.905610i \(0.639413\pi\)
\(678\) −1.57356 4.63939i −0.0604322 0.178175i
\(679\) −1.66251 2.28825i −0.0638012 0.0878148i
\(680\) 48.4199 + 15.7326i 1.85682 + 0.603317i
\(681\) 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 \(-0.202946\pi\)
\(684\) −0.326787 12.7237i −0.0124950 0.486504i
\(685\) 6.47214 4.70228i 0.247288 0.179665i
\(686\) 9.97505 13.7295i 0.380849 0.524194i
\(687\) −39.6963 12.3370i −1.51451 0.470685i
\(688\) −4.03499 + 1.31105i −0.153833 + 0.0499832i
\(689\) −19.4164 14.1068i −0.739706 0.537428i
\(690\) 0 0
\(691\) 6.18034 19.0211i 0.235111 0.723598i −0.761995 0.647582i \(-0.775780\pi\)
0.997107 0.0760155i \(-0.0242198\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) −1.23607 + 3.80423i −0.0468867 + 0.144303i
\(696\) 0.133421 + 10.3914i 0.00505732 + 0.393887i
\(697\) −29.1246 21.1603i −1.10317 0.801502i
\(698\) −4.03499 + 1.31105i −0.152727 + 0.0496239i
\(699\) 16.5401 + 5.14040i 0.625606 + 0.194428i
\(700\) −2.49376 + 3.43237i −0.0942553 + 0.129731i
\(701\) 4.85410 3.52671i 0.183337 0.133202i −0.492331 0.870408i \(-0.663855\pi\)
0.675668 + 0.737206i \(0.263855\pi\)
\(702\) 18.3209 + 12.2616i 0.691476 + 0.462783i
\(703\) 33.9411i 1.28011i
\(704\) 0 0
\(705\) −8.00000 + 11.3137i −0.301297 + 0.426099i
\(706\) 0 0
\(707\) 8.31254 + 11.4412i 0.312625 + 0.430292i
\(708\) 6.29424 + 18.5575i 0.236552 + 0.697435i
\(709\) −9.88854 30.4338i −0.371372 1.14297i −0.945894 0.324476i \(-0.894812\pi\)
0.574522 0.818489i \(-0.305188\pi\)
\(710\) 2.47214 + 7.60845i 0.0927776 + 0.285540i
\(711\) −12.2020 3.62105i −0.457609 0.135800i
\(712\) 0 0
\(713\) 0 0
\(714\) −12.0000 8.48528i −0.449089 0.317554i
\(715\) 0 0
\(716\) 2.82843i 0.105703i
\(717\) −16.5757 22.2092i −0.619030 0.829416i
\(718\) −16.1803 + 11.7557i −0.603845 + 0.438719i
\(719\) −11.6376 + 16.0177i −0.434008 + 0.597360i −0.968867 0.247581i \(-0.920364\pi\)
0.534860 + 0.844941i \(0.320364\pi\)
\(720\) 5.16213 + 6.73442i 0.192381 + 0.250977i
\(721\) 10.7600 3.49613i 0.400722 0.130203i
\(722\) 0.809017 + 0.587785i 0.0301085 + 0.0218751i
\(723\) 7.34786 0.0943431i 0.273270 0.00350866i
\(724\) 3.09017 9.51057i 0.114845 0.353457i
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 2.00000 0.0741759 0.0370879 0.999312i \(-0.488192\pi\)
0.0370879 + 0.999312i \(0.488192\pi\)
\(728\) 5.56231 17.1190i 0.206153 0.634473i
\(729\) −26.9199 + 2.07783i −0.997034 + 0.0769568i
\(730\) −3.23607 2.35114i −0.119772 0.0870196i
\(731\) −24.2099 + 7.86629i −0.895437 + 0.290945i
\(732\) −5.08874 + 16.3739i −0.188085 + 0.605197i
\(733\) −0.831254 + 1.14412i −0.0307031 + 0.0422591i −0.824093 0.566455i \(-0.808314\pi\)
0.793389 + 0.608714i \(0.208314\pi\)
\(734\) 6.47214 4.70228i 0.238891 0.173564i
\(735\) −19.6303 + 14.6510i −0.724075 + 0.540409i
\(736\) 0 0
\(737\) 0 0
\(738\) −6.00000 16.9706i −0.220863 0.624695i
\(739\) 4.03499 + 1.31105i 0.148430 + 0.0482277i 0.382289 0.924043i \(-0.375136\pi\)
−0.233860 + 0.972270i \(0.575136\pi\)
\(740\) −13.3001 18.3060i −0.488920 0.672941i
\(741\) −29.5249 + 10.0141i −1.08462 + 0.367876i
\(742\) 2.47214 + 7.60845i 0.0907550 + 0.279315i
\(743\) 4.94427 + 15.2169i 0.181388 + 0.558254i 0.999867 0.0162814i \(-0.00518275\pi\)
−0.818480 + 0.574535i \(0.805183\pi\)
\(744\) 9.84163 3.33803i 0.360811 0.122378i
\(745\) −9.97505 13.7295i −0.365457 0.503009i
\(746\) 4.03499 + 1.31105i 0.147732 + 0.0480009i
\(747\) −16.0000 45.2548i −0.585409 1.65579i
\(748\) 0 0
\(749\) 22.6274i 0.826788i
\(750\) 7.85212 5.86039i 0.286719 0.213991i
\(751\) −1.61803 + 1.17557i −0.0590429 + 0.0428972i −0.616915 0.787030i \(-0.711618\pi\)
0.557872 + 0.829927i \(0.311618\pi\)
\(752\) 1.66251 2.28825i 0.0606254 0.0834437i
\(753\) −13.0853 + 42.1043i −0.476856 + 1.53437i
\(754\) 8.06998 2.62210i 0.293891 0.0954911i
\(755\) 9.70820 + 7.05342i 0.353318 + 0.256700i
\(756\) 2.53824 + 6.89618i 0.0923147 + 0.250812i
\(757\) 6.18034 19.0211i 0.224628 0.691335i −0.773701 0.633551i \(-0.781597\pi\)
0.998329 0.0577836i \(-0.0184034\pi\)
\(758\) −12.0000 −0.435860
\(759\) 0 0
\(760\) −36.0000 −1.30586
\(761\) 3.09017 9.51057i 0.112019 0.344758i −0.879295 0.476278i \(-0.841986\pi\)
0.991314 + 0.131520i \(0.0419857\pi\)
\(762\) −17.1450 + 0.220134i −0.621098 + 0.00797461i
\(763\) 4.85410 + 3.52671i 0.175730 + 0.127676i
\(764\) −18.8300 + 6.11822i −0.681244 + 0.221350i
\(765\) 30.9728 + 40.4065i 1.11982 + 1.46090i
\(766\) 3.32502 4.57649i 0.120138 0.165355i
\(767\) 38.8328 28.2137i 1.40217 1.01874i
\(768\) 17.6117 + 23.5972i 0.635506 + 0.851492i
\(769\) 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
\(772\) −20.1750 6.55524i −0.726113 0.235928i
\(773\) 19.9501 + 27.4589i 0.717555 + 0.987630i 0.999601 + 0.0282290i \(0.00898675\pi\)
−0.282047 + 0.959401i \(0.591013\pi\)
\(774\) −12.2020 3.62105i −0.438591 0.130156i
\(775\) 1.85410 + 5.70634i 0.0666013 + 0.204978i
\(776\) −1.85410 5.70634i −0.0665584 0.204846i
\(777\) 6.29424 + 18.5575i 0.225805 + 0.665748i
\(778\) −11.6376 16.0177i −0.417227 0.574263i
\(779\) 24.2099 + 7.86629i 0.867411 + 0.281839i
\(780\) −12.0000 + 16.9706i −0.429669 + 0.607644i
\(781\) 0 0
\(782\) 0 0
\(783\) −5.78016 + 8.63653i −0.206566 + 0.308645i
\(784\) 4.04508 2.93893i 0.144467 0.104962i
\(785\) 33.2502 45.7649i 1.18675 1.63342i
\(786\) 0 0
\(787\) −20.1750 + 6.55524i −0.719159 + 0.233669i −0.645659 0.763626i \(-0.723417\pi\)
−0.0735007 + 0.997295i \(0.523417\pi\)
\(788\) −17.7984 12.9313i −0.634041 0.460658i
\(789\) 0 0
\(790\) −3.70820 + 11.4127i −0.131932 + 0.406045i
\(791\) −4.00000 −0.142224
\(792\) 0 0
\(793\) 42.0000 1.49146
\(794\) −0.618034 + 1.90211i −0.0219332 + 0.0675035i
\(795\) −0.355790 27.7105i −0.0126186 0.982791i
\(796\) 1.61803 + 1.17557i 0.0573497 + 0.0416670i
\(797\) 2.68999 0.874032i 0.0952845 0.0309598i −0.260987 0.965342i \(-0.584048\pi\)
0.356271 + 0.934383i \(0.384048\pi\)
\(798\) 9.92408 + 3.08424i 0.351309 + 0.109181i
\(799\) 9.97505 13.7295i 0.352892 0.485714i
\(800\) −12.1353 + 8.81678i −0.429046 + 0.311720i
\(801\) 0 0
\(802\) 2.82843i 0.0998752i
\(803\) 0 0
\(804\) −2.00000 + 2.82843i −0.0705346 + 0.0997509i
\(805\) 0 0
\(806\) −4.98752 6.86474i −0.175678 0.241800i
\(807\) −15.7356 46.3939i −0.553919 1.63314i
\(808\) 9.27051 + 28.5317i 0.326135 + 1.00374i
\(809\) −15.4508 47.5528i −0.543223 1.67187i −0.725178 0.688561i \(-0.758243\pi\)
0.181955 0.983307i \(-0.441757\pi\)
\(810\) 1.30672 + 25.4223i 0.0459134 + 0.893248i
\(811\) −15.7938 21.7383i −0.554596 0.763336i 0.436031 0.899932i \(-0.356384\pi\)
−0.990627 + 0.136596i \(0.956384\pi\)
\(812\) 2.68999 + 0.874032i 0.0944003 + 0.0306725i
\(813\) 42.0000 + 29.6985i 1.47300 + 1.04157i
\(814\) 0 0
\(815\) 56.5685i 1.98151i
\(816\) −6.21588 8.32844i −0.217599 0.291554i
\(817\) 14.5623 10.5801i 0.509471 0.370152i
\(818\) −2.49376 + 3.43237i −0.0871923 + 0.120010i
\(819\) 14.2859 10.9505i 0.499188 0.382643i
\(820\) 16.1400 5.24419i 0.563632 0.183135i
\(821\) 33.9787 + 24.6870i 1.18587 + 0.861582i 0.992821 0.119609i \(-0.0381639\pi\)
0.193044 + 0.981190i \(0.438164\pi\)
\(822\) −4.89858 + 0.0628954i −0.170857 + 0.00219373i
\(823\) −7.41641 + 22.8254i −0.258520 + 0.795642i 0.734596 + 0.678505i \(0.237372\pi\)
−0.993116 + 0.117137i \(0.962628\pi\)
\(824\) 24.0000 0.836080
\(825\) 0 0
\(826\) −16.0000 −0.556711
\(827\) −3.70820 + 11.4127i −0.128947 + 0.396858i −0.994600 0.103787i \(-0.966904\pi\)
0.865653 + 0.500645i \(0.166904\pi\)
\(828\) 0 0
\(829\) 11.3262 + 8.22899i 0.393377 + 0.285805i 0.766838 0.641841i \(-0.221829\pi\)
−0.373461 + 0.927646i \(0.621829\pi\)
\(830\) −43.0399 + 13.9845i −1.49394 + 0.485410i
\(831\) −2.18089 + 7.01739i −0.0756542 + 0.243430i
\(832\) 17.4563 24.0266i 0.605189 0.832972i
\(833\) 24.2705 17.6336i 0.840923 0.610967i
\(834\) 1.96303 1.46510i 0.0679742 0.0507322i
\(835\) 33.9411i 1.17458i
\(836\) 0 0
\(837\) 10.0000 + 2.82843i 0.345651 + 0.0977647i
\(838\) −29.5899 9.61435i −1.02217 0.332122i
\(839\) 19.9501 + 27.4589i 0.688754 + 0.947988i 0.999997 0.00234204i \(-0.000745495\pi\)
−0.311244 + 0.950330i \(0.600745\pi\)
\(840\) 19.6833 6.67605i 0.679137 0.230346i
\(841\) −7.72542 23.7764i −0.266394 0.819876i
\(842\) 6.18034 + 19.0211i 0.212989 + 0.655511i
\(843\) 9.84163 3.33803i 0.338964 0.114968i
\(844\) −15.7938 21.7383i −0.543646 0.748264i
\(845\) 13.4500 + 4.37016i 0.462693 + 0.150338i
\(846\) 8.00000 2.82843i 0.275046 0.0972433i
\(847\) 0 0
\(848\) 5.65685i 0.194257i
\(849\) 37.2976 27.8368i 1.28005 0.955358i
\(850\) 14.5623 10.5801i 0.499483 0.362896i
\(851\) 0 0
\(852\) −1.45393 + 4.67826i −0.0498107 + 0.160274i
\(853\) 39.0049 12.6735i 1.33550 0.433931i 0.447712 0.894178i \(-0.352239\pi\)
0.887791 + 0.460247i \(0.152239\pi\)
\(854\) −11.3262 8.22899i −0.387576 0.281590i
\(855\) −29.6583 20.4055i −1.01429 0.697854i
\(856\) 14.8328 45.6507i 0.506975 1.56031i
\(857\) 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 \(0.610832\pi\)
\(860\) 3.70820 11.4127i 0.126449 0.389169i
\(861\) −14.6957 + 0.188686i −0.500829 + 0.00643041i
\(862\) 25.8885 + 18.8091i 0.881767 + 0.640641i
\(863\) 32.2799 10.4884i 1.09882 0.357029i 0.297173 0.954824i \(-0.403956\pi\)
0.801649 + 0.597795i \(0.203956\pi\)
\(864\) 1.00044 + 25.9615i 0.0340357 + 0.883228i
\(865\) 9.97505 13.7295i 0.339162 0.466816i
\(866\) 24.2705 17.6336i 0.824745 0.599213i
\(867\) −19.6836 26.3734i −0.668491 0.895687i
\(868\) 2.82843i 0.0960031i
\(869\) 0 0
\(870\) 8.00000 + 5.65685i 0.271225 + 0.191785i
\(871\) 8.06998 + 2.62210i 0.273441 + 0.0888463i
\(872\) 7.48128 + 10.2971i 0.253348 + 0.348704i
\(873\) 1.70698 5.75206i 0.0577726 0.194678i
\(874\) 0 0
\(875\) −2.47214 7.60845i −0.0835734 0.257213i
\(876\) −0.786780 2.31969i −0.0265828 0.0783752i
\(877\) 20.7813 + 28.6031i 0.701736 + 0.965857i 0.999936 + 0.0113534i \(0.00361399\pi\)
−0.298199 + 0.954504i \(0.596386\pi\)
\(878\) −25.5549 8.30330i −0.862438 0.280223i
\(879\) 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 \(0.824399\pi\)
\(882\) 14.9951 0.385122i 0.504910 0.0129677i
\(883\) −37.2148 + 27.0381i −1.25238 + 0.909905i −0.998357 0.0572938i \(-0.981753\pi\)
−0.254020 + 0.967199i \(0.581753\pi\)
\(884\) 14.9626 20.5942i 0.503246 0.692658i
\(885\) 52.9284 + 16.4493i 1.77917 + 0.552937i
\(886\) 26.8999 8.74032i 0.903721 0.293637i
\(887\) −19.4164 14.1068i −0.651939 0.473662i 0.211992 0.977271i \(-0.432005\pi\)
−0.863931 + 0.503610i \(0.832005\pi\)
\(888\) 0.533685 + 41.5658i 0.0179093 + 1.39486i
\(889\) −4.32624 + 13.3148i −0.145097 + 0.446564i
\(890\) 0 0
\(891\) 0 0
\(892\) −24.0000 −0.803579
\(893\) −3.70820 + 11.4127i −0.124090 + 0.381911i
\(894\) 0.133421 + 10.3914i 0.00446228 + 0.347542i
\(895\) 6.47214 + 4.70228i 0.216340 + 0.157180i
\(896\) 4.03499 1.31105i 0.134800 0.0437990i
\(897\) 0 0
\(898\) 3.32502 4.57649i 0.110957 0.152719i
\(899\) 3.23607 2.35114i 0.107929 0.0784149i
\(900\) −8.99703 + 0.231073i −0.299901 + 0.00770245i
\(901\) 33.9411i 1.13074i
\(902\) 0 0
\(903\) −6.00000 + 8.48528i −0.199667 + 0.282372i
\(904\) −8.06998 2.62210i −0.268404 0.0872096i
\(905\) −16.6251 22.8825i −0.552636 0.760639i
\(906\) −2.36034 6.95908i −0.0784171 0.231200i
\(907\) 3.70820 + 11.4127i 0.123129 + 0.378952i 0.993556 0.113346i \(-0.0361570\pi\)
−0.870427 + 0.492298i \(0.836157\pi\)
\(908\) −7.41641 22.8254i −0.246122 0.757486i
\(909\) −8.53491 + 28.7603i −0.283085 + 0.953919i
\(910\) −9.97505 13.7295i −0.330670 0.455128i
\(911\) −34.9699 11.3624i −1.15861 0.376454i −0.334227 0.942493i \(-0.608475\pi\)
−0.824378 + 0.566039i \(0.808475\pi\)
\(912\) 6.00000 + 4.24264i 0.198680 + 0.140488i
\(913\) 0 0
\(914\) 9.89949i 0.327446i
\(915\) 29.0074 + 38.8660i 0.958956 + 1.28487i
\(916\) −19.4164 + 14.1068i −0.641536 + 0.466103i
\(917\) 0 0
\(918\) −1.20053 31.1538i −0.0396233 1.02823i
\(919\) −20.1750 + 6.55524i −0.665510 + 0.216237i −0.622241 0.782826i \(-0.713777\pi\)
−0.0432697 + 0.999063i \(0.513777\pi\)
\(920\) 0 0
\(921\) 7.34786 0.0943431i 0.242120 0.00310871i
\(922\) 6.79837 20.9232i 0.223893 0.689070i
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) −24.0000 −0.789115
\(926\) −7.41641 + 22.8254i −0.243718 + 0.750088i
\(927\) 19.7722 + 13.6037i 0.649404 + 0.446804i
\(928\) 8.09017 + 5.87785i 0.265573 + 0.192950i
\(929\) 2.68999 0.874032i 0.0882558 0.0286761i −0.264556 0.964370i \(-0.585225\pi\)
0.352812 + 0.935694i \(0.385225\pi\)
\(930\) 2.90785 9.35652i 0.0953522 0.306812i
\(931\) −12.4688 + 17.1618i −0.408649 + 0.562457i
\(932\) 8.09017 5.87785i 0.265002 0.192535i
\(933\) 39.2606 29.3019i 1.28534 0.959302i
\(934\) 28.2843i 0.925490i
\(935\) 0 0
\(936\) 36.0000 12.7279i 1.17670 0.416025i
\(937\) 33.6249 + 10.9254i 1.09848 + 0.356917i 0.801517 0.597972i \(-0.204027\pi\)
0.296962 + 0.954889i \(0.404027\pi\)
\(938\) −1.66251 2.28825i −0.0542828 0.0747139i
\(939\) −19.6833 + 6.67605i −0.642339 + 0.217865i
\(940\) 2.47214 + 7.60845i 0.0806322 + 0.248160i
\(941\) 11.7426 + 36.1401i 0.382799 + 1.17814i 0.938064 + 0.346462i \(0.112617\pi\)
−0.555265 + 0.831674i \(0.687383\pi\)
\(942\) −32.8054 + 11.1268i −1.06886 + 0.362529i
\(943\) 0 0
\(944\) −10.7600 3.49613i −0.350207 0.113789i
\(945\) 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 \(-0.168697\pi\)
\(948\) −5.88909 + 4.39529i −0.191269 + 0.142752i
\(949\) −4.85410 + 3.52671i −0.157571 + 0.114482i
\(950\) −7.48128 + 10.2971i −0.242725 + 0.334082i
\(951\) −13.0853 + 42.1043i −0.424321 + 1.36533i
\(952\) −24.2099 + 7.86629i −0.784649 + 0.254948i
\(953\) −1.61803 1.17557i −0.0524133 0.0380805i 0.561270 0.827633i \(-0.310313\pi\)
−0.613683 + 0.789552i \(0.710313\pi\)
\(954\) −9.61926 + 13.9811i −0.311435 + 0.452653i
\(955\) −17.3050 + 53.2592i −0.559975 + 1.72343i
\(956\) −16.0000 −0.517477
\(957\) 0 0
\(958\) 28.0000 0.904639
\(959\) −1.23607 + 3.80423i −0.0399147 + 0.122845i
\(960\) 34.2900 0.440268i 1.10671 0.0142096i
\(961\) 21.8435 + 15.8702i 0.704628 + 0.511942i
\(962\) 32.2799 10.4884i 1.04075 0.338159i
\(963\) 38.0956 29.2014i 1.22761 0.941003i
\(964\) 2.49376 3.43237i 0.0803187 0.110549i
\(965\) −48.5410 + 35.2671i −1.56259 + 1.13529i
\(966\) 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
\(970\) −5.37999 1.74806i −0.172741 0.0561270i
\(971\) 19.9501 + 27.4589i 0.640229 + 0.881200i 0.998628 0.0523690i \(-0.0166772\pi\)
−0.358399 + 0.933569i \(0.616677\pi\)
\(972\) −8.33478 + 13.1731i −0.267338 + 0.422529i
\(973\) −0.618034 1.90211i −0.0198133 0.0609789i
\(974\) −0.618034 1.90211i −0.0198031 0.0609476i
\(975\) 7.08102 + 20.8772i 0.226774 + 0.668607i
\(976\) −5.81878 8.00886i −0.186255 0.256357i
\(977\) 24.2099 + 7.86629i 0.774545 + 0.251665i 0.669509 0.742804i \(-0.266504\pi\)
0.105035 + 0.994468i \(0.466504\pi\)
\(978\) −20.0000 + 28.2843i −0.639529 + 0.904431i
\(979\) 0 0
\(980\) 14.1421i 0.451754i
\(981\) 0.326787 + 12.7237i 0.0104335 + 0.406237i
\(982\) −16.1803 + 11.7557i −0.516335 + 0.375140i
\(983\) 6.65003 9.15298i 0.212103 0.291935i −0.689688 0.724106i \(-0.742252\pi\)
0.901791 + 0.432171i \(0.142252\pi\)
\(984\) −29.7723 9.25273i −0.949105 0.294966i
\(985\) −59.1799 + 19.2287i −1.88563 + 0.612677i
\(986\) −9.70820 7.05342i −0.309172 0.224627i
\(987\) −0.0889475 6.92763i −0.00283123 0.220509i
\(988\) −5.56231 + 17.1190i −0.176961 + 0.544628i
\(989\) 0 0
\(990\) 0 0
\(991\) −42.0000 −1.33417 −0.667087 0.744980i \(-0.732459\pi\)
−0.667087 + 0.744980i \(0.732459\pi\)
\(992\) 3.09017 9.51057i 0.0981130 0.301961i
\(993\) −0.444738 34.6382i −0.0141133 1.09921i
\(994\) −3.23607 2.35114i −0.102642 0.0745737i
\(995\) 5.37999 1.74806i 0.170557 0.0554174i
\(996\) −26.4642 8.22465i −0.838551 0.260608i
\(997\) 17.4563 24.0266i 0.552848 0.760929i −0.437548 0.899195i \(-0.644153\pi\)
0.990395 + 0.138266i \(0.0441528\pi\)
\(998\) −11.3262 + 8.22899i −0.358526 + 0.260484i
\(999\) −23.1207 + 34.5461i −0.731505 + 1.09299i
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.233.2 8
3.2 odd 2 363.2.f.a.233.1 8
11.2 odd 10 363.2.f.a.239.2 8
11.3 even 5 inner 363.2.f.f.161.1 8
11.4 even 5 363.2.d.a.362.1 2
11.5 even 5 inner 363.2.f.f.215.1 8
11.6 odd 10 363.2.f.a.215.1 8
11.7 odd 10 363.2.d.b.362.1 yes 2
11.8 odd 10 363.2.f.a.161.1 8
11.9 even 5 inner 363.2.f.f.239.2 8
11.10 odd 2 363.2.f.a.233.2 8
33.2 even 10 inner 363.2.f.f.239.1 8
33.5 odd 10 363.2.f.a.215.2 8
33.8 even 10 inner 363.2.f.f.161.2 8
33.14 odd 10 363.2.f.a.161.2 8
33.17 even 10 inner 363.2.f.f.215.2 8
33.20 odd 10 363.2.f.a.239.1 8
33.26 odd 10 363.2.d.b.362.2 yes 2
33.29 even 10 363.2.d.a.362.2 yes 2
33.32 even 2 inner 363.2.f.f.233.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.2.d.a.362.1 2 11.4 even 5
363.2.d.a.362.2 yes 2 33.29 even 10
363.2.d.b.362.1 yes 2 11.7 odd 10
363.2.d.b.362.2 yes 2 33.26 odd 10
363.2.f.a.161.1 8 11.8 odd 10
363.2.f.a.161.2 8 33.14 odd 10
363.2.f.a.215.1 8 11.6 odd 10
363.2.f.a.215.2 8 33.5 odd 10
363.2.f.a.233.1 8 3.2 odd 2
363.2.f.a.233.2 8 11.10 odd 2
363.2.f.a.239.1 8 33.20 odd 10
363.2.f.a.239.2 8 11.2 odd 10
363.2.f.f.161.1 8 11.3 even 5 inner
363.2.f.f.161.2 8 33.8 even 10 inner
363.2.f.f.215.1 8 11.5 even 5 inner
363.2.f.f.215.2 8 33.17 even 10 inner
363.2.f.f.233.1 8 33.32 even 2 inner
363.2.f.f.233.2 8 1.1 even 1 trivial
363.2.f.f.239.1 8 33.2 even 10 inner
363.2.f.f.239.2 8 11.9 even 5 inner