Properties

Label 375.2.i.c.199.4
Level $375$
Weight $2$
Character 375.199
Analytic conductor $2.994$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [375,2,Mod(49,375)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(375, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("375.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.i (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: \(2.99439007580\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 199.4
Root \(1.53767i\) of defining polynomial
Character \(\chi\) \(=\) 375.199
Dual form 375.2.i.c.49.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.903822 + 1.24400i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.112618 + 0.346603i) q^{4} +(0.475167 + 1.46241i) q^{6} +1.68601i q^{7} +(2.39187 - 0.777165i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(0.903822 + 1.24400i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.112618 + 0.346603i) q^{4} +(0.475167 + 1.46241i) q^{6} +1.68601i q^{7} +(2.39187 - 0.777165i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.40891 - 1.75017i) q^{11} +(-0.214212 + 0.294838i) q^{12} +(-0.136890 + 0.188414i) q^{13} +(-2.09740 + 1.52385i) q^{14} +(3.71829 + 2.70150i) q^{16} +(-7.09394 + 2.30496i) q^{17} +1.53767i q^{18} +(-0.232853 - 0.716646i) q^{19} +(-0.521005 + 1.60349i) q^{21} +(4.35444 + 1.41484i) q^{22} +(0.512972 + 0.706046i) q^{23} +2.51496 q^{24} -0.358112 q^{26} +(0.587785 + 0.809017i) q^{27} +(-0.584375 - 0.189875i) q^{28} +(-2.12444 + 6.53835i) q^{29} +(-3.03433 - 9.33870i) q^{31} +2.03733i q^{32} +(2.83184 - 0.920120i) q^{33} +(-9.27904 - 6.74162i) q^{34} +(-0.294838 + 0.214212i) q^{36} +(5.95259 - 8.19304i) q^{37} +(0.681054 - 0.937390i) q^{38} +(-0.188414 + 0.136890i) q^{39} +(-3.07210 - 2.23201i) q^{41} +(-2.46564 + 0.801135i) q^{42} +5.27322i q^{43} +(0.335328 + 1.03203i) q^{44} +(-0.414688 + 1.27628i) q^{46} +(-8.14814 - 2.64749i) q^{47} +(2.70150 + 3.71829i) q^{48} +4.15738 q^{49} -7.45901 q^{51} +(-0.0498883 - 0.0686654i) q^{52} +(-5.68614 - 1.84754i) q^{53} +(-0.475167 + 1.46241i) q^{54} +(1.31031 + 4.03270i) q^{56} -0.753527i q^{57} +(-10.0538 + 3.26669i) q^{58} +(-3.11564 - 2.26365i) q^{59} +(3.55679 - 2.58416i) q^{61} +(8.87488 - 12.2152i) q^{62} +(-0.991010 + 1.36401i) q^{63} +(4.90214 - 3.56161i) q^{64} +(3.70411 + 2.69119i) q^{66} +(-1.70508 + 0.554013i) q^{67} -2.71836i q^{68} +(0.269686 + 0.830007i) q^{69} +(-1.35179 + 4.16039i) q^{71} +(2.39187 + 0.777165i) q^{72} +(-8.84783 - 12.1780i) q^{73} +15.5723 q^{74} +0.274615 q^{76} +(2.95080 + 4.06143i) q^{77} +(-0.340585 - 0.110663i) q^{78} +(-2.27926 + 7.01484i) q^{79} +(0.309017 + 0.951057i) q^{81} -5.83904i q^{82} +(4.13188 - 1.34253i) q^{83} +(-0.497099 - 0.361163i) q^{84} +(-6.55991 + 4.76605i) q^{86} +(-4.04092 + 5.56185i) q^{87} +(4.40161 - 6.05830i) q^{88} +(9.79170 - 7.11409i) q^{89} +(-0.317667 - 0.230798i) q^{91} +(-0.302487 + 0.0982841i) q^{92} -9.81929i q^{93} +(-4.07098 - 12.5292i) q^{94} +(-0.629569 + 1.93761i) q^{96} +(9.01055 + 2.92771i) q^{97} +(3.75753 + 5.17180i) q^{98} +2.97757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.903822 + 1.24400i 0.639099 + 0.879644i 0.998567 0.0535136i \(-0.0170420\pi\)
−0.359469 + 0.933157i \(0.617042\pi\)
\(3\) 0.951057 + 0.309017i 0.549093 + 0.178411i
\(4\) −0.112618 + 0.346603i −0.0563090 + 0.173301i
\(5\) 0 0
\(6\) 0.475167 + 1.46241i 0.193986 + 0.597028i
\(7\) 1.68601i 0.637251i 0.947881 + 0.318625i \(0.103221\pi\)
−0.947881 + 0.318625i \(0.896779\pi\)
\(8\) 2.39187 0.777165i 0.845653 0.274769i
\(9\) 0.809017 + 0.587785i 0.269672 + 0.195928i
\(10\) 0 0
\(11\) 2.40891 1.75017i 0.726312 0.527697i −0.162082 0.986777i \(-0.551821\pi\)
0.888395 + 0.459080i \(0.151821\pi\)
\(12\) −0.214212 + 0.294838i −0.0618377 + 0.0851123i
\(13\) −0.136890 + 0.188414i −0.0379666 + 0.0522565i −0.827578 0.561350i \(-0.810282\pi\)
0.789612 + 0.613607i \(0.210282\pi\)
\(14\) −2.09740 + 1.52385i −0.560554 + 0.407266i
\(15\) 0 0
\(16\) 3.71829 + 2.70150i 0.929573 + 0.675375i
\(17\) −7.09394 + 2.30496i −1.72053 + 0.559035i −0.992030 0.126005i \(-0.959784\pi\)
−0.728505 + 0.685041i \(0.759784\pi\)
\(18\) 1.53767i 0.362433i
\(19\) −0.232853 0.716646i −0.0534200 0.164410i 0.920787 0.390065i \(-0.127548\pi\)
−0.974207 + 0.225656i \(0.927548\pi\)
\(20\) 0 0
\(21\) −0.521005 + 1.60349i −0.113693 + 0.349910i
\(22\) 4.35444 + 1.41484i 0.928370 + 0.301646i
\(23\) 0.512972 + 0.706046i 0.106962 + 0.147221i 0.859142 0.511737i \(-0.170998\pi\)
−0.752180 + 0.658958i \(0.770998\pi\)
\(24\) 2.51496 0.513364
\(25\) 0 0
\(26\) −0.358112 −0.0702315
\(27\) 0.587785 + 0.809017i 0.113119 + 0.155695i
\(28\) −0.584375 0.189875i −0.110436 0.0358830i
\(29\) −2.12444 + 6.53835i −0.394498 + 1.21414i 0.534854 + 0.844945i \(0.320367\pi\)
−0.929352 + 0.369195i \(0.879633\pi\)
\(30\) 0 0
\(31\) −3.03433 9.33870i −0.544981 1.67728i −0.721035 0.692899i \(-0.756333\pi\)
0.176054 0.984381i \(-0.443667\pi\)
\(32\) 2.03733i 0.360152i
\(33\) 2.83184 0.920120i 0.492960 0.160172i
\(34\) −9.27904 6.74162i −1.59134 1.15618i
\(35\) 0 0
\(36\) −0.294838 + 0.214212i −0.0491396 + 0.0357020i
\(37\) 5.95259 8.19304i 0.978600 1.34693i 0.0410198 0.999158i \(-0.486939\pi\)
0.937580 0.347769i \(-0.113061\pi\)
\(38\) 0.681054 0.937390i 0.110482 0.152065i
\(39\) −0.188414 + 0.136890i −0.0301703 + 0.0219200i
\(40\) 0 0
\(41\) −3.07210 2.23201i −0.479781 0.348581i 0.321460 0.946923i \(-0.395826\pi\)
−0.801241 + 0.598342i \(0.795826\pi\)
\(42\) −2.46564 + 0.801135i −0.380457 + 0.123618i
\(43\) 5.27322i 0.804159i 0.915605 + 0.402079i \(0.131712\pi\)
−0.915605 + 0.402079i \(0.868288\pi\)
\(44\) 0.335328 + 1.03203i 0.0505526 + 0.155585i
\(45\) 0 0
\(46\) −0.414688 + 1.27628i −0.0611425 + 0.188177i
\(47\) −8.14814 2.64749i −1.18853 0.386176i −0.353000 0.935623i \(-0.614839\pi\)
−0.835529 + 0.549447i \(0.814839\pi\)
\(48\) 2.70150 + 3.71829i 0.389928 + 0.536689i
\(49\) 4.15738 0.593911
\(50\) 0 0
\(51\) −7.45901 −1.04447
\(52\) −0.0498883 0.0686654i −0.00691826 0.00952217i
\(53\) −5.68614 1.84754i −0.781051 0.253779i −0.108762 0.994068i \(-0.534689\pi\)
−0.672289 + 0.740289i \(0.734689\pi\)
\(54\) −0.475167 + 1.46241i −0.0646621 + 0.199009i
\(55\) 0 0
\(56\) 1.31031 + 4.03270i 0.175097 + 0.538893i
\(57\) 0.753527i 0.0998070i
\(58\) −10.0538 + 3.26669i −1.32013 + 0.428937i
\(59\) −3.11564 2.26365i −0.405622 0.294702i 0.366205 0.930534i \(-0.380657\pi\)
−0.771827 + 0.635833i \(0.780657\pi\)
\(60\) 0 0
\(61\) 3.55679 2.58416i 0.455400 0.330867i −0.336324 0.941746i \(-0.609184\pi\)
0.791724 + 0.610879i \(0.209184\pi\)
\(62\) 8.87488 12.2152i 1.12711 1.55134i
\(63\) −0.991010 + 1.36401i −0.124856 + 0.171849i
\(64\) 4.90214 3.56161i 0.612768 0.445202i
\(65\) 0 0
\(66\) 3.70411 + 2.69119i 0.455944 + 0.331263i
\(67\) −1.70508 + 0.554013i −0.208308 + 0.0676835i −0.411312 0.911494i \(-0.634930\pi\)
0.203004 + 0.979178i \(0.434930\pi\)
\(68\) 2.71836i 0.329650i
\(69\) 0.269686 + 0.830007i 0.0324663 + 0.0999211i
\(70\) 0 0
\(71\) −1.35179 + 4.16039i −0.160428 + 0.493748i −0.998670 0.0515506i \(-0.983584\pi\)
0.838242 + 0.545298i \(0.183584\pi\)
\(72\) 2.39187 + 0.777165i 0.281884 + 0.0915897i
\(73\) −8.84783 12.1780i −1.03556 1.42533i −0.900690 0.434463i \(-0.856938\pi\)
−0.134870 0.990863i \(-0.543062\pi\)
\(74\) 15.5723 1.81024
\(75\) 0 0
\(76\) 0.274615 0.0315005
\(77\) 2.95080 + 4.06143i 0.336275 + 0.462843i
\(78\) −0.340585 0.110663i −0.0385636 0.0125301i
\(79\) −2.27926 + 7.01484i −0.256437 + 0.789232i 0.737106 + 0.675777i \(0.236192\pi\)
−0.993543 + 0.113455i \(0.963808\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 5.83904i 0.644814i
\(83\) 4.13188 1.34253i 0.453532 0.147362i −0.0733383 0.997307i \(-0.523365\pi\)
0.526871 + 0.849946i \(0.323365\pi\)
\(84\) −0.497099 0.361163i −0.0542379 0.0394061i
\(85\) 0 0
\(86\) −6.55991 + 4.76605i −0.707373 + 0.513937i
\(87\) −4.04092 + 5.56185i −0.433232 + 0.596293i
\(88\) 4.40161 6.05830i 0.469213 0.645817i
\(89\) 9.79170 7.11409i 1.03792 0.754092i 0.0680399 0.997683i \(-0.478325\pi\)
0.969878 + 0.243591i \(0.0783255\pi\)
\(90\) 0 0
\(91\) −0.317667 0.230798i −0.0333005 0.0241942i
\(92\) −0.302487 + 0.0982841i −0.0315365 + 0.0102468i
\(93\) 9.81929i 1.01821i
\(94\) −4.07098 12.5292i −0.419889 1.29229i
\(95\) 0 0
\(96\) −0.629569 + 1.93761i −0.0642551 + 0.197757i
\(97\) 9.01055 + 2.92771i 0.914883 + 0.297264i 0.728366 0.685188i \(-0.240280\pi\)
0.186517 + 0.982452i \(0.440280\pi\)
\(98\) 3.75753 + 5.17180i 0.379568 + 0.522430i
\(99\) 2.97757 0.299257
\(100\) 0 0
\(101\) −6.54468 −0.651220 −0.325610 0.945504i \(-0.605570\pi\)
−0.325610 + 0.945504i \(0.605570\pi\)
\(102\) −6.74162 9.27904i −0.667520 0.918762i
\(103\) 0.666504 + 0.216560i 0.0656726 + 0.0213383i 0.341669 0.939820i \(-0.389008\pi\)
−0.275996 + 0.961159i \(0.589008\pi\)
\(104\) −0.180995 + 0.557047i −0.0177481 + 0.0546229i
\(105\) 0 0
\(106\) −2.84091 8.74342i −0.275934 0.849236i
\(107\) 12.5288i 1.21120i 0.795768 + 0.605602i \(0.207067\pi\)
−0.795768 + 0.605602i \(0.792933\pi\)
\(108\) −0.346603 + 0.112618i −0.0333519 + 0.0108367i
\(109\) 3.46541 + 2.51776i 0.331926 + 0.241158i 0.741247 0.671232i \(-0.234235\pi\)
−0.409322 + 0.912390i \(0.634235\pi\)
\(110\) 0 0
\(111\) 8.19304 5.95259i 0.777649 0.564995i
\(112\) −4.55474 + 6.26907i −0.430383 + 0.592371i
\(113\) −4.83607 + 6.65628i −0.454939 + 0.626170i −0.973450 0.228901i \(-0.926487\pi\)
0.518511 + 0.855071i \(0.326487\pi\)
\(114\) 0.937390 0.681054i 0.0877946 0.0637865i
\(115\) 0 0
\(116\) −2.02696 1.47267i −0.188198 0.136734i
\(117\) −0.221493 + 0.0719676i −0.0204771 + 0.00665340i
\(118\) 5.92180i 0.545146i
\(119\) −3.88618 11.9604i −0.356246 1.09641i
\(120\) 0 0
\(121\) −0.659464 + 2.02962i −0.0599512 + 0.184511i
\(122\) 6.42940 + 2.08904i 0.582091 + 0.189133i
\(123\) −2.23201 3.07210i −0.201253 0.277002i
\(124\) 3.57854 0.321362
\(125\) 0 0
\(126\) −2.59253 −0.230961
\(127\) −7.02296 9.66627i −0.623187 0.857743i 0.374393 0.927270i \(-0.377851\pi\)
−0.997580 + 0.0695269i \(0.977851\pi\)
\(128\) 12.7366 + 4.13836i 1.12576 + 0.365783i
\(129\) −1.62951 + 5.01513i −0.143471 + 0.441558i
\(130\) 0 0
\(131\) 6.63068 + 20.4071i 0.579326 + 1.78298i 0.620953 + 0.783848i \(0.286746\pi\)
−0.0416276 + 0.999133i \(0.513254\pi\)
\(132\) 1.08514i 0.0944497i
\(133\) 1.20827 0.392591i 0.104770 0.0340420i
\(134\) −2.23028 1.62039i −0.192667 0.139981i
\(135\) 0 0
\(136\) −15.1764 + 11.0263i −1.30137 + 0.945500i
\(137\) 5.88914 8.10570i 0.503143 0.692517i −0.479601 0.877487i \(-0.659219\pi\)
0.982744 + 0.184970i \(0.0592187\pi\)
\(138\) −0.788784 + 1.08567i −0.0671458 + 0.0924182i
\(139\) −5.31902 + 3.86450i −0.451154 + 0.327782i −0.790051 0.613041i \(-0.789946\pi\)
0.338897 + 0.940823i \(0.389946\pi\)
\(140\) 0 0
\(141\) −6.93123 5.03583i −0.583714 0.424093i
\(142\) −6.39733 + 2.07862i −0.536852 + 0.174434i
\(143\) 0.693452i 0.0579894i
\(144\) 1.42026 + 4.37112i 0.118355 + 0.364260i
\(145\) 0 0
\(146\) 7.15261 22.0135i 0.591954 1.82185i
\(147\) 3.95390 + 1.28470i 0.326112 + 0.105960i
\(148\) 2.16936 + 2.98587i 0.178320 + 0.245437i
\(149\) −10.9143 −0.894132 −0.447066 0.894501i \(-0.647531\pi\)
−0.447066 + 0.894501i \(0.647531\pi\)
\(150\) 0 0
\(151\) 20.4128 1.66117 0.830584 0.556894i \(-0.188007\pi\)
0.830584 + 0.556894i \(0.188007\pi\)
\(152\) −1.11390 1.53316i −0.0903496 0.124356i
\(153\) −7.09394 2.30496i −0.573511 0.186345i
\(154\) −2.38544 + 7.34162i −0.192224 + 0.591605i
\(155\) 0 0
\(156\) −0.0262278 0.0807210i −0.00209991 0.00646285i
\(157\) 3.49944i 0.279286i 0.990202 + 0.139643i \(0.0445954\pi\)
−0.990202 + 0.139643i \(0.955405\pi\)
\(158\) −10.7865 + 3.50476i −0.858131 + 0.278824i
\(159\) −4.83692 3.51423i −0.383592 0.278696i
\(160\) 0 0
\(161\) −1.19040 + 0.864875i −0.0938165 + 0.0681617i
\(162\) −0.903822 + 1.24400i −0.0710109 + 0.0977382i
\(163\) −3.51118 + 4.83272i −0.275017 + 0.378528i −0.924075 0.382210i \(-0.875163\pi\)
0.649059 + 0.760738i \(0.275163\pi\)
\(164\) 1.11959 0.813432i 0.0874256 0.0635184i
\(165\) 0 0
\(166\) 5.40459 + 3.92666i 0.419477 + 0.304768i
\(167\) 2.22326 0.722381i 0.172041 0.0558995i −0.221730 0.975108i \(-0.571170\pi\)
0.393771 + 0.919209i \(0.371170\pi\)
\(168\) 4.24024i 0.327141i
\(169\) 4.00046 + 12.3122i 0.307728 + 0.947089i
\(170\) 0 0
\(171\) 0.232853 0.716646i 0.0178067 0.0548033i
\(172\) −1.82771 0.593860i −0.139362 0.0452814i
\(173\) 3.56844 + 4.91154i 0.271303 + 0.373417i 0.922829 0.385209i \(-0.125871\pi\)
−0.651526 + 0.758626i \(0.725871\pi\)
\(174\) −10.5712 −0.801403
\(175\) 0 0
\(176\) 13.6851 1.03155
\(177\) −2.26365 3.11564i −0.170146 0.234186i
\(178\) 17.6999 + 5.75105i 1.32666 + 0.431059i
\(179\) −3.53007 + 10.8644i −0.263850 + 0.812045i 0.728107 + 0.685464i \(0.240401\pi\)
−0.991956 + 0.126581i \(0.959599\pi\)
\(180\) 0 0
\(181\) −2.42581 7.46586i −0.180309 0.554933i 0.819527 0.573040i \(-0.194236\pi\)
−0.999836 + 0.0181070i \(0.994236\pi\)
\(182\) 0.603779i 0.0447551i
\(183\) 4.18125 1.35857i 0.309087 0.100428i
\(184\) 1.77568 + 1.29010i 0.130905 + 0.0951077i
\(185\) 0 0
\(186\) 12.2152 8.87488i 0.895664 0.650738i
\(187\) −13.0546 + 17.9681i −0.954644 + 1.31395i
\(188\) 1.83526 2.52601i 0.133850 0.184228i
\(189\) −1.36401 + 0.991010i −0.0992170 + 0.0720854i
\(190\) 0 0
\(191\) −10.1646 7.38502i −0.735485 0.534361i 0.155809 0.987787i \(-0.450202\pi\)
−0.891294 + 0.453426i \(0.850202\pi\)
\(192\) 5.76281 1.87245i 0.415895 0.135133i
\(193\) 10.1437i 0.730161i 0.930976 + 0.365081i \(0.118959\pi\)
−0.930976 + 0.365081i \(0.881041\pi\)
\(194\) 4.50186 + 13.8553i 0.323214 + 0.994752i
\(195\) 0 0
\(196\) −0.468196 + 1.44096i −0.0334426 + 0.102926i
\(197\) −1.94684 0.632566i −0.138706 0.0450685i 0.238841 0.971059i \(-0.423233\pi\)
−0.377547 + 0.925990i \(0.623233\pi\)
\(198\) 2.69119 + 3.70411i 0.191255 + 0.263240i
\(199\) −3.57125 −0.253159 −0.126580 0.991956i \(-0.540400\pi\)
−0.126580 + 0.991956i \(0.540400\pi\)
\(200\) 0 0
\(201\) −1.79282 −0.126456
\(202\) −5.91522 8.14161i −0.416194 0.572842i
\(203\) −11.0237 3.58182i −0.773712 0.251394i
\(204\) 0.840020 2.58531i 0.0588131 0.181008i
\(205\) 0 0
\(206\) 0.332999 + 1.02487i 0.0232011 + 0.0714058i
\(207\) 0.872721i 0.0606583i
\(208\) −1.01800 + 0.330767i −0.0705854 + 0.0229346i
\(209\) −1.81517 1.31880i −0.125558 0.0912234i
\(210\) 0 0
\(211\) −3.01474 + 2.19034i −0.207543 + 0.150789i −0.686701 0.726940i \(-0.740942\pi\)
0.479158 + 0.877729i \(0.340942\pi\)
\(212\) 1.28072 1.76276i 0.0879604 0.121067i
\(213\) −2.57126 + 3.53904i −0.176180 + 0.242491i
\(214\) −15.5859 + 11.3238i −1.06543 + 0.774078i
\(215\) 0 0
\(216\) 2.03464 + 1.47826i 0.138440 + 0.100583i
\(217\) 15.7451 5.11590i 1.06885 0.347290i
\(218\) 6.58659i 0.446100i
\(219\) −4.65158 14.3161i −0.314325 0.967391i
\(220\) 0 0
\(221\) 0.536807 1.65212i 0.0361096 0.111134i
\(222\) 14.8101 + 4.81209i 0.993988 + 0.322966i
\(223\) 15.4287 + 21.2357i 1.03318 + 1.42205i 0.902533 + 0.430622i \(0.141706\pi\)
0.130647 + 0.991429i \(0.458294\pi\)
\(224\) −3.43495 −0.229507
\(225\) 0 0
\(226\) −12.6514 −0.841557
\(227\) 2.63981 + 3.63338i 0.175210 + 0.241156i 0.887586 0.460642i \(-0.152381\pi\)
−0.712376 + 0.701798i \(0.752381\pi\)
\(228\) 0.261174 + 0.0848607i 0.0172967 + 0.00562004i
\(229\) 2.32979 7.17035i 0.153957 0.473830i −0.844097 0.536191i \(-0.819863\pi\)
0.998054 + 0.0623605i \(0.0198629\pi\)
\(230\) 0 0
\(231\) 1.55133 + 4.77450i 0.102070 + 0.314139i
\(232\) 17.2899i 1.13514i
\(233\) 9.85679 3.20266i 0.645740 0.209814i 0.0322049 0.999481i \(-0.489747\pi\)
0.613535 + 0.789668i \(0.289747\pi\)
\(234\) −0.289719 0.210493i −0.0189395 0.0137603i
\(235\) 0 0
\(236\) 1.13546 0.824962i 0.0739124 0.0537005i
\(237\) −4.33541 + 5.96718i −0.281615 + 0.387610i
\(238\) 11.3664 15.6445i 0.736775 1.01408i
\(239\) −15.0265 + 10.9174i −0.971985 + 0.706188i −0.955903 0.293683i \(-0.905119\pi\)
−0.0160815 + 0.999871i \(0.505119\pi\)
\(240\) 0 0
\(241\) 4.39735 + 3.19486i 0.283258 + 0.205799i 0.720337 0.693624i \(-0.243987\pi\)
−0.437079 + 0.899423i \(0.643987\pi\)
\(242\) −3.12089 + 1.01404i −0.200619 + 0.0651849i
\(243\) 1.00000i 0.0641500i
\(244\) 0.495117 + 1.52381i 0.0316966 + 0.0975522i
\(245\) 0 0
\(246\) 1.80436 5.55325i 0.115042 0.354063i
\(247\) 0.166901 + 0.0542295i 0.0106197 + 0.00345054i
\(248\) −14.5154 19.9787i −0.921729 1.26865i
\(249\) 4.34451 0.275322
\(250\) 0 0
\(251\) 23.3577 1.47432 0.737162 0.675716i \(-0.236166\pi\)
0.737162 + 0.675716i \(0.236166\pi\)
\(252\) −0.361163 0.497099i −0.0227511 0.0313143i
\(253\) 2.47140 + 0.803008i 0.155376 + 0.0504847i
\(254\) 5.67738 17.4732i 0.356230 1.09636i
\(255\) 0 0
\(256\) 2.61854 + 8.05903i 0.163659 + 0.503690i
\(257\) 4.48380i 0.279692i 0.990173 + 0.139846i \(0.0446607\pi\)
−0.990173 + 0.139846i \(0.955339\pi\)
\(258\) −7.71163 + 2.50566i −0.480105 + 0.155996i
\(259\) 13.8135 + 10.0361i 0.858330 + 0.623614i
\(260\) 0 0
\(261\) −5.56185 + 4.04092i −0.344270 + 0.250127i
\(262\) −19.3936 + 26.6930i −1.19814 + 1.64910i
\(263\) 4.54093 6.25006i 0.280006 0.385395i −0.645730 0.763566i \(-0.723447\pi\)
0.925736 + 0.378171i \(0.123447\pi\)
\(264\) 6.05830 4.40161i 0.372862 0.270900i
\(265\) 0 0
\(266\) 1.58045 + 1.14826i 0.0969034 + 0.0704044i
\(267\) 11.5108 3.74010i 0.704451 0.228890i
\(268\) 0.653376i 0.0399113i
\(269\) −3.31865 10.2138i −0.202342 0.622743i −0.999812 0.0193855i \(-0.993829\pi\)
0.797470 0.603358i \(-0.206171\pi\)
\(270\) 0 0
\(271\) −7.94563 + 24.4541i −0.482662 + 1.48548i 0.352676 + 0.935746i \(0.385272\pi\)
−0.835338 + 0.549737i \(0.814728\pi\)
\(272\) −32.6042 10.5938i −1.97692 0.642341i
\(273\) −0.230798 0.317667i −0.0139685 0.0192261i
\(274\) 15.4063 0.930726
\(275\) 0 0
\(276\) −0.318054 −0.0191446
\(277\) −5.65712 7.78635i −0.339903 0.467837i 0.604510 0.796598i \(-0.293369\pi\)
−0.944413 + 0.328761i \(0.893369\pi\)
\(278\) −9.61490 3.12407i −0.576663 0.187369i
\(279\) 3.03433 9.33870i 0.181660 0.559093i
\(280\) 0 0
\(281\) −0.875368 2.69411i −0.0522201 0.160717i 0.921545 0.388270i \(-0.126927\pi\)
−0.973766 + 0.227553i \(0.926927\pi\)
\(282\) 13.1740i 0.784498i
\(283\) 22.5052 7.31238i 1.33780 0.434676i 0.449226 0.893418i \(-0.351700\pi\)
0.888569 + 0.458742i \(0.151700\pi\)
\(284\) −1.28977 0.937071i −0.0765336 0.0556049i
\(285\) 0 0
\(286\) −0.862658 + 0.626757i −0.0510100 + 0.0370609i
\(287\) 3.76318 5.17958i 0.222134 0.305741i
\(288\) −1.19751 + 1.64823i −0.0705640 + 0.0971231i
\(289\) 31.2579 22.7102i 1.83870 1.33589i
\(290\) 0 0
\(291\) 7.66483 + 5.56883i 0.449321 + 0.326450i
\(292\) 5.21735 1.69522i 0.305322 0.0992052i
\(293\) 23.2376i 1.35755i −0.734345 0.678777i \(-0.762510\pi\)
0.734345 0.678777i \(-0.237490\pi\)
\(294\) 1.97545 + 6.07981i 0.115211 + 0.354582i
\(295\) 0 0
\(296\) 7.87047 24.2228i 0.457462 1.40792i
\(297\) 2.83184 + 0.920120i 0.164320 + 0.0533908i
\(298\) −9.86455 13.5774i −0.571438 0.786517i
\(299\) −0.203250 −0.0117542
\(300\) 0 0
\(301\) −8.89069 −0.512451
\(302\) 18.4495 + 25.3936i 1.06165 + 1.46124i
\(303\) −6.22436 2.02242i −0.357580 0.116185i
\(304\) 1.07020 3.29375i 0.0613805 0.188910i
\(305\) 0 0
\(306\) −3.54428 10.9082i −0.202613 0.623579i
\(307\) 21.8131i 1.24494i −0.782643 0.622470i \(-0.786129\pi\)
0.782643 0.622470i \(-0.213871\pi\)
\(308\) −1.74002 + 0.565366i −0.0991467 + 0.0322147i
\(309\) 0.566962 + 0.411922i 0.0322533 + 0.0234334i
\(310\) 0 0
\(311\) −8.12364 + 5.90217i −0.460649 + 0.334681i −0.793786 0.608197i \(-0.791893\pi\)
0.333137 + 0.942879i \(0.391893\pi\)
\(312\) −0.344274 + 0.473852i −0.0194907 + 0.0268266i
\(313\) −3.55825 + 4.89752i −0.201124 + 0.276824i −0.897651 0.440707i \(-0.854728\pi\)
0.696527 + 0.717531i \(0.254728\pi\)
\(314\) −4.35332 + 3.16287i −0.245672 + 0.178491i
\(315\) 0 0
\(316\) −2.17468 1.58000i −0.122335 0.0888817i
\(317\) 8.08309 2.62636i 0.453992 0.147511i −0.0730902 0.997325i \(-0.523286\pi\)
0.527082 + 0.849814i \(0.323286\pi\)
\(318\) 9.19338i 0.515539i
\(319\) 6.32566 + 19.4684i 0.354169 + 1.09002i
\(320\) 0 0
\(321\) −3.87161 + 11.9156i −0.216092 + 0.665063i
\(322\) −2.15182 0.699167i −0.119916 0.0389631i
\(323\) 3.30369 + 4.54713i 0.183822 + 0.253009i
\(324\) −0.364440 −0.0202466
\(325\) 0 0
\(326\) −9.18540 −0.508733
\(327\) 2.51776 + 3.46541i 0.139233 + 0.191637i
\(328\) −9.08268 2.95114i −0.501507 0.162950i
\(329\) 4.46369 13.7378i 0.246091 0.757391i
\(330\) 0 0
\(331\) 5.03526 + 15.4969i 0.276763 + 0.851789i 0.988748 + 0.149594i \(0.0477966\pi\)
−0.711984 + 0.702195i \(0.752203\pi\)
\(332\) 1.58331i 0.0868955i
\(333\) 9.63150 3.12946i 0.527803 0.171493i
\(334\) 2.90808 + 2.11284i 0.159123 + 0.115610i
\(335\) 0 0
\(336\) −6.26907 + 4.55474i −0.342006 + 0.248482i
\(337\) 14.5161 19.9796i 0.790740 1.08836i −0.203275 0.979122i \(-0.565159\pi\)
0.994015 0.109239i \(-0.0348414\pi\)
\(338\) −11.7007 + 16.1046i −0.636432 + 0.875974i
\(339\) −6.65628 + 4.83607i −0.361519 + 0.262659i
\(340\) 0 0
\(341\) −23.6537 17.1854i −1.28092 0.930644i
\(342\) 1.10197 0.358051i 0.0595876 0.0193612i
\(343\) 18.8114i 1.01572i
\(344\) 4.09816 + 12.6128i 0.220958 + 0.680039i
\(345\) 0 0
\(346\) −2.88474 + 8.87831i −0.155084 + 0.477301i
\(347\) −13.2640 4.30975i −0.712051 0.231359i −0.0694775 0.997584i \(-0.522133\pi\)
−0.642573 + 0.766224i \(0.722133\pi\)
\(348\) −1.47267 2.02696i −0.0789435 0.108656i
\(349\) −18.4966 −0.990099 −0.495049 0.868865i \(-0.664850\pi\)
−0.495049 + 0.868865i \(0.664850\pi\)
\(350\) 0 0
\(351\) −0.232892 −0.0124309
\(352\) 3.56568 + 4.90773i 0.190051 + 0.261583i
\(353\) 0.420113 + 0.136503i 0.0223604 + 0.00726532i 0.320176 0.947358i \(-0.396258\pi\)
−0.297815 + 0.954623i \(0.596258\pi\)
\(354\) 1.82994 5.63197i 0.0972601 0.299336i
\(355\) 0 0
\(356\) 1.36304 + 4.19500i 0.0722409 + 0.222335i
\(357\) 12.5760i 0.665590i
\(358\) −16.7059 + 5.42809i −0.882936 + 0.286883i
\(359\) 3.73869 + 2.71631i 0.197320 + 0.143362i 0.682058 0.731298i \(-0.261085\pi\)
−0.484738 + 0.874659i \(0.661085\pi\)
\(360\) 0 0
\(361\) 14.9120 10.8342i 0.784840 0.570220i
\(362\) 7.09506 9.76552i 0.372908 0.513264i
\(363\) −1.25437 + 1.72650i −0.0658376 + 0.0906176i
\(364\) 0.115770 0.0841120i 0.00606801 0.00440867i
\(365\) 0 0
\(366\) 5.46917 + 3.97359i 0.285878 + 0.207703i
\(367\) −8.34738 + 2.71223i −0.435730 + 0.141577i −0.518665 0.854978i \(-0.673571\pi\)
0.0829348 + 0.996555i \(0.473571\pi\)
\(368\) 4.01108i 0.209092i
\(369\) −1.17344 3.61147i −0.0610867 0.188005i
\(370\) 0 0
\(371\) 3.11496 9.58687i 0.161721 0.497725i
\(372\) 3.40339 + 1.10583i 0.176458 + 0.0573345i
\(373\) −9.10804 12.5361i −0.471596 0.649097i 0.505266 0.862963i \(-0.331394\pi\)
−0.976863 + 0.213867i \(0.931394\pi\)
\(374\) −34.1513 −1.76592
\(375\) 0 0
\(376\) −21.5468 −1.11119
\(377\) −0.941098 1.29531i −0.0484690 0.0667118i
\(378\) −2.46564 0.801135i −0.126819 0.0412060i
\(379\) 8.43404 25.9573i 0.433227 1.33334i −0.461665 0.887054i \(-0.652748\pi\)
0.894892 0.446282i \(-0.147252\pi\)
\(380\) 0 0
\(381\) −3.69219 11.3634i −0.189157 0.582164i
\(382\) 19.3196i 0.988474i
\(383\) −12.4628 + 4.04941i −0.636820 + 0.206915i −0.609594 0.792714i \(-0.708667\pi\)
−0.0272261 + 0.999629i \(0.508667\pi\)
\(384\) 10.8344 + 7.87162i 0.552889 + 0.401697i
\(385\) 0 0
\(386\) −12.6188 + 9.16812i −0.642282 + 0.466645i
\(387\) −3.09952 + 4.26612i −0.157558 + 0.216859i
\(388\) −2.02950 + 2.79337i −0.103032 + 0.141812i
\(389\) 13.6769 9.93685i 0.693447 0.503818i −0.184345 0.982862i \(-0.559016\pi\)
0.877791 + 0.479043i \(0.159016\pi\)
\(390\) 0 0
\(391\) −5.26641 3.82627i −0.266334 0.193503i
\(392\) 9.94390 3.23097i 0.502243 0.163189i
\(393\) 21.4573i 1.08238i
\(394\) −0.972680 2.99360i −0.0490029 0.150815i
\(395\) 0 0
\(396\) −0.335328 + 1.03203i −0.0168509 + 0.0518617i
\(397\) 9.89842 + 3.21619i 0.496787 + 0.161416i 0.546685 0.837338i \(-0.315890\pi\)
−0.0498977 + 0.998754i \(0.515890\pi\)
\(398\) −3.22778 4.44265i −0.161794 0.222690i
\(399\) 1.27045 0.0636021
\(400\) 0 0
\(401\) −0.694800 −0.0346967 −0.0173483 0.999850i \(-0.505522\pi\)
−0.0173483 + 0.999850i \(0.505522\pi\)
\(402\) −1.62039 2.23028i −0.0808179 0.111236i
\(403\) 2.17491 + 0.706670i 0.108340 + 0.0352017i
\(404\) 0.737049 2.26840i 0.0366696 0.112857i
\(405\) 0 0
\(406\) −5.50766 16.9508i −0.273341 0.841256i
\(407\) 30.1543i 1.49469i
\(408\) −17.8410 + 5.79688i −0.883260 + 0.286988i
\(409\) −0.962002 0.698936i −0.0475680 0.0345601i 0.563747 0.825947i \(-0.309359\pi\)
−0.611315 + 0.791387i \(0.709359\pi\)
\(410\) 0 0
\(411\) 8.10570 5.88914i 0.399825 0.290490i
\(412\) −0.150121 + 0.206623i −0.00739592 + 0.0101796i
\(413\) 3.81652 5.25299i 0.187799 0.258483i
\(414\) −1.08567 + 0.788784i −0.0533577 + 0.0387666i
\(415\) 0 0
\(416\) −0.383860 0.278891i −0.0188203 0.0136737i
\(417\) −6.25289 + 2.03169i −0.306205 + 0.0994921i
\(418\) 3.45005i 0.168747i
\(419\) −0.611361 1.88158i −0.0298670 0.0919210i 0.935012 0.354616i \(-0.115389\pi\)
−0.964879 + 0.262695i \(0.915389\pi\)
\(420\) 0 0
\(421\) 3.42467 10.5400i 0.166908 0.513690i −0.832264 0.554380i \(-0.812955\pi\)
0.999172 + 0.0406895i \(0.0129554\pi\)
\(422\) −5.44958 1.77068i −0.265281 0.0861951i
\(423\) −5.03583 6.93123i −0.244850 0.337008i
\(424\) −15.0363 −0.730229
\(425\) 0 0
\(426\) −6.72655 −0.325902
\(427\) 4.35690 + 5.99677i 0.210845 + 0.290204i
\(428\) −4.34251 1.41097i −0.209903 0.0682017i
\(429\) −0.214289 + 0.659512i −0.0103460 + 0.0318416i
\(430\) 0 0
\(431\) −3.21800 9.90398i −0.155005 0.477058i 0.843156 0.537669i \(-0.180695\pi\)
−0.998161 + 0.0606112i \(0.980695\pi\)
\(432\) 4.59606i 0.221128i
\(433\) 9.76195 3.17185i 0.469129 0.152429i −0.0649063 0.997891i \(-0.520675\pi\)
0.534035 + 0.845462i \(0.320675\pi\)
\(434\) 20.5950 + 14.9631i 0.988590 + 0.718253i
\(435\) 0 0
\(436\) −1.26293 + 0.917573i −0.0604834 + 0.0439438i
\(437\) 0.386538 0.532024i 0.0184906 0.0254502i
\(438\) 13.6051 18.7258i 0.650075 0.894752i
\(439\) −19.9920 + 14.5251i −0.954168 + 0.693244i −0.951789 0.306753i \(-0.900757\pi\)
−0.00237925 + 0.999997i \(0.500757\pi\)
\(440\) 0 0
\(441\) 3.36339 + 2.44365i 0.160161 + 0.116364i
\(442\) 2.54043 0.825434i 0.120836 0.0392619i
\(443\) 7.52935i 0.357730i 0.983874 + 0.178865i \(0.0572426\pi\)
−0.983874 + 0.178865i \(0.942757\pi\)
\(444\) 1.14050 + 3.51010i 0.0541257 + 0.166582i
\(445\) 0 0
\(446\) −12.4726 + 38.3867i −0.590594 + 1.81766i
\(447\) −10.3801 3.37269i −0.490961 0.159523i
\(448\) 6.00491 + 8.26505i 0.283705 + 0.390487i
\(449\) 31.6627 1.49426 0.747128 0.664681i \(-0.231432\pi\)
0.747128 + 0.664681i \(0.231432\pi\)
\(450\) 0 0
\(451\) −11.3068 −0.532416
\(452\) −1.76245 2.42581i −0.0828989 0.114101i
\(453\) 19.4137 + 6.30789i 0.912135 + 0.296371i
\(454\) −2.13403 + 6.56786i −0.100155 + 0.308245i
\(455\) 0 0
\(456\) −0.585614 1.80234i −0.0274239 0.0844021i
\(457\) 2.95742i 0.138342i −0.997605 0.0691712i \(-0.977965\pi\)
0.997605 0.0691712i \(-0.0220355\pi\)
\(458\) 11.0257 3.58245i 0.515195 0.167397i
\(459\) −6.03447 4.38430i −0.281665 0.204642i
\(460\) 0 0
\(461\) 14.2396 10.3457i 0.663204 0.481846i −0.204539 0.978858i \(-0.565570\pi\)
0.867743 + 0.497012i \(0.165570\pi\)
\(462\) −4.53737 + 6.24516i −0.211098 + 0.290551i
\(463\) −15.4835 + 21.3112i −0.719578 + 0.990414i 0.279960 + 0.960012i \(0.409679\pi\)
−0.999538 + 0.0304024i \(0.990321\pi\)
\(464\) −25.5626 + 18.5723i −1.18671 + 0.862198i
\(465\) 0 0
\(466\) 12.8929 + 9.36724i 0.597252 + 0.433929i
\(467\) −6.99888 + 2.27408i −0.323870 + 0.105232i −0.466439 0.884553i \(-0.654463\pi\)
0.142570 + 0.989785i \(0.454463\pi\)
\(468\) 0.0848751i 0.00392335i
\(469\) −0.934070 2.87477i −0.0431313 0.132745i
\(470\) 0 0
\(471\) −1.08139 + 3.32816i −0.0498276 + 0.153354i
\(472\) −9.21143 2.99297i −0.423990 0.137763i
\(473\) 9.22905 + 12.7027i 0.424352 + 0.584070i
\(474\) −11.3416 −0.520939
\(475\) 0 0
\(476\) 4.58317 0.210069
\(477\) −3.51423 4.83692i −0.160905 0.221467i
\(478\) −27.1626 8.82566i −1.24239 0.403676i
\(479\) 8.79679 27.0737i 0.401936 1.23703i −0.521491 0.853257i \(-0.674624\pi\)
0.923427 0.383774i \(-0.125376\pi\)
\(480\) 0 0
\(481\) 0.728827 + 2.24310i 0.0332316 + 0.102276i
\(482\) 8.35791i 0.380692i
\(483\) −1.39940 + 0.454692i −0.0636748 + 0.0206892i
\(484\) −0.629204 0.457144i −0.0286002 0.0207793i
\(485\) 0 0
\(486\) −1.24400 + 0.903822i −0.0564292 + 0.0409982i
\(487\) 1.40132 1.92875i 0.0634998 0.0873999i −0.776086 0.630627i \(-0.782798\pi\)
0.839586 + 0.543227i \(0.182798\pi\)
\(488\) 6.49904 8.94516i 0.294198 0.404929i
\(489\) −4.83272 + 3.51118i −0.218543 + 0.158781i
\(490\) 0 0
\(491\) 20.8105 + 15.1197i 0.939163 + 0.682342i 0.948219 0.317617i \(-0.102883\pi\)
−0.00905626 + 0.999959i \(0.502883\pi\)
\(492\) 1.31616 0.427647i 0.0593371 0.0192798i
\(493\) 51.2794i 2.30951i
\(494\) 0.0833872 + 0.256640i 0.00375177 + 0.0115468i
\(495\) 0 0
\(496\) 13.9460 42.9212i 0.626192 1.92722i
\(497\) −7.01445 2.27913i −0.314641 0.102233i
\(498\) 3.92666 + 5.40459i 0.175958 + 0.242185i
\(499\) −29.9989 −1.34293 −0.671467 0.741035i \(-0.734335\pi\)
−0.671467 + 0.741035i \(0.734335\pi\)
\(500\) 0 0
\(501\) 2.33767 0.104440
\(502\) 21.1112 + 29.0570i 0.942238 + 1.29688i
\(503\) 13.1483 + 4.27216i 0.586256 + 0.190486i 0.587101 0.809514i \(-0.300269\pi\)
−0.000845408 1.00000i \(0.500269\pi\)
\(504\) −1.31031 + 4.03270i −0.0583656 + 0.179631i
\(505\) 0 0
\(506\) 1.23476 + 3.80021i 0.0548920 + 0.168940i
\(507\) 12.9458i 0.574941i
\(508\) 4.14127 1.34558i 0.183739 0.0597004i
\(509\) 25.8511 + 18.7819i 1.14583 + 0.832493i 0.987921 0.154960i \(-0.0495250\pi\)
0.157908 + 0.987454i \(0.449525\pi\)
\(510\) 0 0
\(511\) 20.5322 14.9175i 0.908290 0.659911i
\(512\) 8.08447 11.1273i 0.357286 0.491763i
\(513\) 0.442912 0.609616i 0.0195550 0.0269152i
\(514\) −5.57787 + 4.05256i −0.246029 + 0.178751i
\(515\) 0 0
\(516\) −1.55474 1.12959i −0.0684438 0.0497273i
\(517\) −24.2617 + 7.88310i −1.06703 + 0.346698i
\(518\) 26.2549i 1.15358i
\(519\) 1.87604 + 5.77386i 0.0823490 + 0.253444i
\(520\) 0 0
\(521\) −11.9889 + 36.8979i −0.525242 + 1.61653i 0.238595 + 0.971119i \(0.423313\pi\)
−0.763837 + 0.645409i \(0.776687\pi\)
\(522\) −10.0538 3.26669i −0.440045 0.142979i
\(523\) 13.9389 + 19.1853i 0.609507 + 0.838914i 0.996537 0.0831532i \(-0.0264991\pi\)
−0.387030 + 0.922067i \(0.626499\pi\)
\(524\) −7.81991 −0.341614
\(525\) 0 0
\(526\) 11.8793 0.517962
\(527\) 43.0507 + 59.2542i 1.87532 + 2.58115i
\(528\) 13.0153 + 4.22893i 0.566419 + 0.184041i
\(529\) 6.87203 21.1499i 0.298784 0.919562i
\(530\) 0 0
\(531\) −1.19007 3.66266i −0.0516446 0.158946i
\(532\) 0.463003i 0.0200737i
\(533\) 0.841081 0.273284i 0.0364313 0.0118372i
\(534\) 15.0564 + 10.9391i 0.651556 + 0.473383i
\(535\) 0 0
\(536\) −3.64776 + 2.65025i −0.157559 + 0.114473i
\(537\) −6.71458 + 9.24183i −0.289756 + 0.398815i
\(538\) 9.70648 13.3598i 0.418476 0.575983i
\(539\) 10.0147 7.27613i 0.431365 0.313405i
\(540\) 0 0
\(541\) −2.27953 1.65618i −0.0980046 0.0712045i 0.537704 0.843134i \(-0.319292\pi\)
−0.635708 + 0.771929i \(0.719292\pi\)
\(542\) −37.6025 + 12.2178i −1.61516 + 0.524799i
\(543\) 7.85007i 0.336879i
\(544\) −4.69597 14.4527i −0.201338 0.619654i
\(545\) 0 0
\(546\) 0.186578 0.574228i 0.00798480 0.0245747i
\(547\) −4.20728 1.36703i −0.179890 0.0584499i 0.217687 0.976019i \(-0.430149\pi\)
−0.397577 + 0.917569i \(0.630149\pi\)
\(548\) 2.14623 + 2.95404i 0.0916826 + 0.126190i
\(549\) 4.39643 0.187635
\(550\) 0 0
\(551\) 5.18036 0.220691
\(552\) 1.29010 + 1.77568i 0.0549105 + 0.0755778i
\(553\) −11.8271 3.84285i −0.502938 0.163415i
\(554\) 4.57323 14.0749i 0.194298 0.597987i
\(555\) 0 0
\(556\) −0.740427 2.27880i −0.0314011 0.0966426i
\(557\) 7.20182i 0.305151i 0.988292 + 0.152575i \(0.0487567\pi\)
−0.988292 + 0.152575i \(0.951243\pi\)
\(558\) 14.3599 4.66580i 0.607902 0.197519i
\(559\) −0.993546 0.721854i −0.0420225 0.0305312i
\(560\) 0 0
\(561\) −17.9681 + 13.0546i −0.758612 + 0.551164i
\(562\) 2.56030 3.52395i 0.108000 0.148649i
\(563\) 13.6665 18.8103i 0.575975 0.792761i −0.417272 0.908782i \(-0.637014\pi\)
0.993247 + 0.116020i \(0.0370137\pi\)
\(564\) 2.52601 1.83526i 0.106364 0.0772782i
\(565\) 0 0
\(566\) 29.4373 + 21.3875i 1.23734 + 0.898982i
\(567\) −1.60349 + 0.521005i −0.0673402 + 0.0218801i
\(568\) 11.0017i 0.461620i
\(569\) 6.37307 + 19.6143i 0.267173 + 0.822273i 0.991185 + 0.132486i \(0.0422960\pi\)
−0.724012 + 0.689787i \(0.757704\pi\)
\(570\) 0 0
\(571\) 0.557381 1.71544i 0.0233257 0.0717890i −0.938716 0.344691i \(-0.887984\pi\)
0.962042 + 0.272902i \(0.0879836\pi\)
\(572\) −0.240352 0.0780952i −0.0100496 0.00326533i
\(573\) −7.38502 10.1646i −0.308514 0.424633i
\(574\) 9.84466 0.410908
\(575\) 0 0
\(576\) 6.05938 0.252474
\(577\) 9.69043 + 13.3377i 0.403418 + 0.555257i 0.961598 0.274463i \(-0.0885001\pi\)
−0.558180 + 0.829720i \(0.688500\pi\)
\(578\) 56.5032 + 18.3590i 2.35022 + 0.763633i
\(579\) −3.13458 + 9.64725i −0.130269 + 0.400926i
\(580\) 0 0
\(581\) 2.26351 + 6.96637i 0.0939063 + 0.289014i
\(582\) 14.5683i 0.603876i
\(583\) −16.9309 + 5.50118i −0.701205 + 0.227835i
\(584\) −30.6271 22.2519i −1.26736 0.920791i
\(585\) 0 0
\(586\) 28.9076 21.0026i 1.19416 0.867610i
\(587\) −4.27415 + 5.88286i −0.176413 + 0.242811i −0.888062 0.459723i \(-0.847949\pi\)
0.711649 + 0.702535i \(0.247949\pi\)
\(588\) −0.890562 + 1.22575i −0.0367261 + 0.0505492i
\(589\) −5.98599 + 4.34908i −0.246649 + 0.179201i
\(590\) 0 0
\(591\) −1.65608 1.20321i −0.0681220 0.0494935i
\(592\) 44.2670 14.3832i 1.81936 0.591146i
\(593\) 2.47898i 0.101800i −0.998704 0.0508998i \(-0.983791\pi\)
0.998704 0.0508998i \(-0.0162089\pi\)
\(594\) 1.41484 + 4.35444i 0.0580518 + 0.178665i
\(595\) 0 0
\(596\) 1.22914 3.78291i 0.0503477 0.154954i
\(597\) −3.39646 1.10358i −0.139008 0.0451664i
\(598\) −0.183701 0.252843i −0.00751211 0.0103395i
\(599\) −30.2951 −1.23782 −0.618912 0.785460i \(-0.712426\pi\)
−0.618912 + 0.785460i \(0.712426\pi\)
\(600\) 0 0
\(601\) 4.46130 0.181980 0.0909900 0.995852i \(-0.470997\pi\)
0.0909900 + 0.995852i \(0.470997\pi\)
\(602\) −8.03560 11.0600i −0.327506 0.450774i
\(603\) −1.70508 0.554013i −0.0694361 0.0225612i
\(604\) −2.29885 + 7.07512i −0.0935387 + 0.287882i
\(605\) 0 0
\(606\) −3.10982 9.57103i −0.126328 0.388797i
\(607\) 17.2931i 0.701906i 0.936393 + 0.350953i \(0.114142\pi\)
−0.936393 + 0.350953i \(0.885858\pi\)
\(608\) 1.46004 0.474397i 0.0592126 0.0192393i
\(609\) −9.37732 6.81302i −0.379988 0.276077i
\(610\) 0 0
\(611\) 1.61423 1.17280i 0.0653046 0.0474466i
\(612\) 1.59781 2.19920i 0.0645877 0.0888974i
\(613\) −8.41293 + 11.5794i −0.339795 + 0.467688i −0.944382 0.328852i \(-0.893338\pi\)
0.604587 + 0.796539i \(0.293338\pi\)
\(614\) 27.1356 19.7152i 1.09510 0.795640i
\(615\) 0 0
\(616\) 10.2143 + 7.42115i 0.411547 + 0.299006i
\(617\) 25.0669 8.14472i 1.00915 0.327894i 0.242637 0.970117i \(-0.421988\pi\)
0.766518 + 0.642223i \(0.221988\pi\)
\(618\) 1.07761i 0.0433477i
\(619\) 0.864708 + 2.66130i 0.0347555 + 0.106967i 0.966929 0.255045i \(-0.0820902\pi\)
−0.932174 + 0.362011i \(0.882090\pi\)
\(620\) 0 0
\(621\) −0.269686 + 0.830007i −0.0108221 + 0.0333070i
\(622\) −14.6846 4.77133i −0.588800 0.191313i
\(623\) 11.9944 + 16.5089i 0.480545 + 0.661414i
\(624\) −1.07039 −0.0428497
\(625\) 0 0
\(626\) −9.30856 −0.372045
\(627\) −1.31880 1.81517i −0.0526679 0.0724911i
\(628\) −1.21291 0.394100i −0.0484006 0.0157263i
\(629\) −23.3427 + 71.8415i −0.930735 + 2.86451i
\(630\) 0 0
\(631\) 10.9403 + 33.6707i 0.435526 + 1.34041i 0.892547 + 0.450955i \(0.148916\pi\)
−0.457021 + 0.889456i \(0.651084\pi\)
\(632\) 18.5499i 0.737877i
\(633\) −3.54404 + 1.15153i −0.140863 + 0.0457692i
\(634\) 10.5729 + 7.68164i 0.419902 + 0.305077i
\(635\) 0 0
\(636\) 1.76276 1.28072i 0.0698981 0.0507840i
\(637\) −0.569106 + 0.783307i −0.0225488 + 0.0310357i
\(638\) −18.5015 + 25.4651i −0.732481 + 1.00817i
\(639\) −3.53904 + 2.57126i −0.140002 + 0.101718i
\(640\) 0 0
\(641\) −13.6994 9.95321i −0.541094 0.393128i 0.283397 0.959003i \(-0.408539\pi\)
−0.824491 + 0.565875i \(0.808539\pi\)
\(642\) −18.3223 + 5.95327i −0.723122 + 0.234957i
\(643\) 25.9118i 1.02186i −0.859622 0.510931i \(-0.829301\pi\)
0.859622 0.510931i \(-0.170699\pi\)
\(644\) −0.165708 0.509996i −0.00652980 0.0200966i
\(645\) 0 0
\(646\) −2.67071 + 8.21960i −0.105078 + 0.323396i
\(647\) 10.3911 + 3.37629i 0.408518 + 0.132736i 0.506065 0.862495i \(-0.331100\pi\)
−0.0975468 + 0.995231i \(0.531100\pi\)
\(648\) 1.47826 + 2.03464i 0.0580713 + 0.0799283i
\(649\) −11.4671 −0.450121
\(650\) 0 0
\(651\) 16.5554 0.648857
\(652\) −1.27961 1.76124i −0.0501135 0.0689753i
\(653\) −13.5602 4.40596i −0.530650 0.172419i 0.0314233 0.999506i \(-0.489996\pi\)
−0.562073 + 0.827088i \(0.689996\pi\)
\(654\) −2.03537 + 6.26422i −0.0795892 + 0.244950i
\(655\) 0 0
\(656\) −5.39319 16.5985i −0.210569 0.648063i
\(657\) 15.0528i 0.587267i
\(658\) 21.1243 6.86370i 0.823511 0.267575i
\(659\) 18.5179 + 13.4540i 0.721355 + 0.524095i 0.886817 0.462121i \(-0.152912\pi\)
−0.165462 + 0.986216i \(0.552912\pi\)
\(660\) 0 0
\(661\) 32.2838 23.4556i 1.25570 0.912316i 0.257158 0.966369i \(-0.417214\pi\)
0.998538 + 0.0540529i \(0.0172140\pi\)
\(662\) −14.7273 + 20.2704i −0.572392 + 0.787830i
\(663\) 1.02107 1.40538i 0.0396550 0.0545804i
\(664\) 8.83953 6.42230i 0.343040 0.249233i
\(665\) 0 0
\(666\) 12.5982 + 9.15314i 0.488171 + 0.354677i
\(667\) −5.70615 + 1.85404i −0.220943 + 0.0717887i
\(668\) 0.851941i 0.0329626i
\(669\) 8.11133 + 24.9641i 0.313602 + 0.965168i
\(670\) 0 0
\(671\) 4.04524 12.4500i 0.156165 0.480626i
\(672\) −3.26683 1.06146i −0.126021 0.0409466i
\(673\) −1.26872 1.74624i −0.0489054 0.0673126i 0.783864 0.620933i \(-0.213246\pi\)
−0.832769 + 0.553620i \(0.813246\pi\)
\(674\) 37.9747 1.46273
\(675\) 0 0
\(676\) −4.71795 −0.181460
\(677\) −24.6717 33.9577i −0.948210 1.30510i −0.952318 0.305108i \(-0.901307\pi\)
0.00410738 0.999992i \(-0.498693\pi\)
\(678\) −12.0322 3.90949i −0.462093 0.150143i
\(679\) −4.93613 + 15.1919i −0.189431 + 0.583010i
\(680\) 0 0
\(681\) 1.38783 + 4.27129i 0.0531817 + 0.163676i
\(682\) 44.9579i 1.72153i
\(683\) −27.7767 + 9.02521i −1.06285 + 0.345340i −0.787698 0.616061i \(-0.788727\pi\)
−0.275149 + 0.961401i \(0.588727\pi\)
\(684\) 0.222168 + 0.161415i 0.00849481 + 0.00617184i
\(685\) 0 0
\(686\) −23.4015 + 17.0022i −0.893473 + 0.649146i
\(687\) 4.43152 6.09946i 0.169073 0.232709i
\(688\) −14.2456 + 19.6074i −0.543108 + 0.747524i
\(689\) 1.12648 0.818435i 0.0429154 0.0311799i
\(690\) 0 0
\(691\) −36.0221 26.1716i −1.37034 0.995614i −0.997710 0.0676353i \(-0.978455\pi\)
−0.372634 0.927978i \(-0.621545\pi\)
\(692\) −2.10422 + 0.683703i −0.0799905 + 0.0259905i
\(693\) 5.02021i 0.190702i
\(694\) −6.62698 20.3958i −0.251557 0.774212i
\(695\) 0 0
\(696\) −5.34287 + 16.4437i −0.202521 + 0.623295i
\(697\) 26.9380 + 8.75268i 1.02035 + 0.331531i
\(698\) −16.7176 23.0098i −0.632771 0.870934i
\(699\) 10.3640 0.392004
\(700\) 0 0
\(701\) −4.50567 −0.170177 −0.0850884 0.996373i \(-0.527117\pi\)
−0.0850884 + 0.996373i \(0.527117\pi\)
\(702\) −0.210493 0.289719i −0.00794454 0.0109347i
\(703\) −7.25759 2.35813i −0.273725 0.0889387i
\(704\) 5.57536 17.1592i 0.210129 0.646711i
\(705\) 0 0
\(706\) 0.209897 + 0.645997i 0.00789958 + 0.0243124i
\(707\) 11.0344i 0.414990i
\(708\) 1.33482 0.433708i 0.0501655 0.0162998i
\(709\) −41.4788 30.1361i −1.55777 1.13178i −0.937809 0.347151i \(-0.887149\pi\)
−0.619959 0.784634i \(-0.712851\pi\)
\(710\) 0 0
\(711\) −5.96718 + 4.33541i −0.223787 + 0.162591i
\(712\) 17.8916 24.6257i 0.670517 0.922887i
\(713\) 5.03702 6.93287i 0.188638 0.259638i
\(714\) 15.6445 11.3664i 0.585482 0.425378i
\(715\) 0 0
\(716\) −3.36809 2.44706i −0.125871 0.0914509i
\(717\) −17.6647 + 5.73962i −0.659701 + 0.214350i
\(718\) 7.10600i 0.265194i
\(719\) −10.8976 33.5393i −0.406411 1.25080i −0.919712 0.392595i \(-0.871578\pi\)
0.513301 0.858209i \(-0.328422\pi\)
\(720\) 0 0
\(721\) −0.365122 + 1.12373i −0.0135979 + 0.0418499i
\(722\) 26.9555 + 8.75838i 1.00318 + 0.325953i
\(723\) 3.19486 + 4.39735i 0.118818 + 0.163539i
\(724\) 2.86088 0.106324
\(725\) 0 0
\(726\) −3.28150 −0.121788
\(727\) −25.8648 35.5998i −0.959271 1.32032i −0.947284 0.320396i \(-0.896184\pi\)
−0.0119876 0.999928i \(-0.503816\pi\)
\(728\) −0.939184 0.305160i −0.0348085 0.0113100i
\(729\) −0.309017 + 0.951057i −0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) −12.1546 37.4079i −0.449553 1.38358i
\(732\) 1.60223i 0.0592202i
\(733\) −26.5098 + 8.61356i −0.979162 + 0.318149i −0.754509 0.656290i \(-0.772125\pi\)
−0.224653 + 0.974439i \(0.572125\pi\)
\(734\) −10.9186 7.93281i −0.403012 0.292805i
\(735\) 0 0
\(736\) −1.43845 + 1.04509i −0.0530219 + 0.0385226i
\(737\) −3.13775 + 4.31874i −0.115581 + 0.159083i
\(738\) 3.43210 4.72388i 0.126337 0.173888i
\(739\) −26.2456 + 19.0685i −0.965459 + 0.701447i −0.954412 0.298492i \(-0.903516\pi\)
−0.0110469 + 0.999939i \(0.503516\pi\)
\(740\) 0 0
\(741\) 0.141975 + 0.103151i 0.00521557 + 0.00378933i
\(742\) 14.7415 4.78979i 0.541176 0.175839i
\(743\) 9.09256i 0.333574i −0.985993 0.166787i \(-0.946661\pi\)
0.985993 0.166787i \(-0.0533392\pi\)
\(744\) −7.63120 23.4864i −0.279773 0.861054i
\(745\) 0 0
\(746\) 7.36297 22.6609i 0.269577 0.829674i
\(747\) 4.13188 + 1.34253i 0.151177 + 0.0491205i
\(748\) −4.75760 6.54827i −0.173955 0.239429i
\(749\) −21.1236 −0.771840
\(750\) 0 0
\(751\) −49.8861 −1.82037 −0.910185 0.414202i \(-0.864061\pi\)
−0.910185 + 0.414202i \(0.864061\pi\)
\(752\) −23.1450 31.8563i −0.844011 1.16168i
\(753\) 22.2145 + 7.21792i 0.809540 + 0.263036i
\(754\) 0.760786 2.34146i 0.0277062 0.0852709i
\(755\) 0 0
\(756\) −0.189875 0.584375i −0.00690568 0.0212535i
\(757\) 31.1239i 1.13122i 0.824674 + 0.565608i \(0.191358\pi\)
−0.824674 + 0.565608i \(0.808642\pi\)
\(758\) 39.9138 12.9688i 1.44974 0.471048i
\(759\) 2.10230 + 1.52741i 0.0763087 + 0.0554415i
\(760\) 0 0
\(761\) −31.6544 + 22.9982i −1.14747 + 0.833686i −0.988142 0.153540i \(-0.950933\pi\)
−0.159327 + 0.987226i \(0.550933\pi\)
\(762\) 10.7990 14.8636i 0.391207 0.538450i
\(763\) −4.24497 + 5.84270i −0.153678 + 0.211520i
\(764\) 3.70438 2.69139i 0.134020 0.0973712i
\(765\) 0 0
\(766\) −16.3016 11.8438i −0.589002 0.427935i
\(767\) 0.853003 0.277158i 0.0308002 0.0100076i
\(768\) 8.47377i 0.305771i
\(769\) −4.43076 13.6365i −0.159777 0.491744i 0.838836 0.544384i \(-0.183236\pi\)
−0.998614 + 0.0526398i \(0.983236\pi\)
\(770\) 0 0
\(771\) −1.38557 + 4.26435i −0.0499001 + 0.153577i
\(772\) −3.51584 1.14237i −0.126538 0.0411146i
\(773\) −2.49807 3.43830i −0.0898493 0.123667i 0.761726 0.647899i \(-0.224352\pi\)
−0.851575 + 0.524232i \(0.824352\pi\)
\(774\) −8.10849 −0.291454
\(775\) 0 0
\(776\) 23.8274 0.855352
\(777\) 10.0361 + 13.8135i 0.360043 + 0.495557i
\(778\) 24.7230 + 8.03298i 0.886361 + 0.287996i
\(779\) −0.884215 + 2.72134i −0.0316803 + 0.0975020i
\(780\) 0 0
\(781\) 4.02506 + 12.3879i 0.144028 + 0.443273i
\(782\) 10.0097i 0.357946i
\(783\) −6.53835 + 2.12444i −0.233661 + 0.0759212i
\(784\) 15.4584 + 11.2312i 0.552084 + 0.401113i
\(785\) 0 0
\(786\) −26.6930 + 19.3936i −0.952109 + 0.691747i
\(787\) −15.9464 + 21.9483i −0.568428 + 0.782374i −0.992367 0.123317i \(-0.960647\pi\)
0.423940 + 0.905690i \(0.360647\pi\)
\(788\) 0.438498 0.603541i 0.0156208 0.0215002i
\(789\) 6.25006 4.54093i 0.222508 0.161662i
\(790\) 0 0
\(791\) −11.2225 8.15364i −0.399027 0.289910i
\(792\) 7.12195 2.31406i 0.253068 0.0822267i
\(793\) 1.02389i 0.0363595i
\(794\) 4.94545 + 15.2205i 0.175507 + 0.540156i
\(795\) 0 0
\(796\) 0.402187 1.23781i 0.0142552 0.0438729i
\(797\) −12.0000 3.89902i −0.425060 0.138111i 0.0886722 0.996061i \(-0.471738\pi\)
−0.513733 + 0.857950i \(0.671738\pi\)
\(798\) 1.14826 + 1.58045i 0.0406480 + 0.0559472i
\(799\) 63.9049 2.26079
\(800\) 0 0
\(801\) 12.1032 0.427646
\(802\) −0.627976 0.864334i −0.0221746 0.0305207i
\(803\) −42.6272 13.8504i −1.50428 0.488770i
\(804\) 0.201904 0.621398i 0.00712062 0.0219150i
\(805\) 0 0
\(806\) 1.08663 + 3.34430i 0.0382748 + 0.117798i
\(807\) 10.7394i 0.378044i
\(808\) −15.6540 + 5.08629i −0.550706 + 0.178935i
\(809\) −30.2684 21.9913i −1.06418 0.773172i −0.0893229 0.996003i \(-0.528470\pi\)
−0.974857 + 0.222831i \(0.928470\pi\)
\(810\) 0 0
\(811\) −30.0948 + 21.8651i −1.05677 + 0.767789i −0.973488 0.228737i \(-0.926540\pi\)
−0.0832825 + 0.996526i \(0.526540\pi\)
\(812\) 2.48293 3.41747i 0.0871339 0.119930i
\(813\) −15.1135 + 20.8019i −0.530053 + 0.729555i
\(814\) 37.5121 27.2541i 1.31480 0.955257i
\(815\) 0 0
\(816\) −27.7348 20.1505i −0.970912 0.705409i
\(817\) 3.77903 1.22788i 0.132212 0.0429582i
\(818\) 1.82845i 0.0639302i
\(819\) −0.121338 0.373439i −0.00423989 0.0130490i
\(820\) 0 0
\(821\) 8.48994 26.1294i 0.296301 0.911921i −0.686480 0.727148i \(-0.740845\pi\)
0.982781 0.184772i \(-0.0591548\pi\)
\(822\) 14.6522 + 4.76080i 0.511055 + 0.166052i
\(823\) −13.7698 18.9526i −0.479987 0.660645i 0.498516 0.866881i \(-0.333879\pi\)
−0.978502 + 0.206236i \(0.933879\pi\)
\(824\) 1.76249 0.0613993
\(825\) 0 0
\(826\) 9.98420 0.347395
\(827\) −19.0778 26.2583i −0.663399 0.913090i 0.336189 0.941794i \(-0.390862\pi\)
−0.999588 + 0.0287047i \(0.990862\pi\)
\(828\) −0.302487 0.0982841i −0.0105122 0.00341561i
\(829\) 0.0476213 0.146563i 0.00165395 0.00509035i −0.950226 0.311561i \(-0.899148\pi\)
0.951880 + 0.306471i \(0.0991482\pi\)
\(830\) 0 0
\(831\) −2.97412 9.15340i −0.103171 0.317528i
\(832\) 1.41118i 0.0489239i
\(833\) −29.4922 + 9.58260i −1.02185 + 0.332018i
\(834\) −8.17892 5.94233i −0.283213 0.205766i
\(835\) 0 0
\(836\) 0.661522 0.480624i 0.0228792 0.0166227i
\(837\) 5.77163 7.94397i 0.199497 0.274584i
\(838\) 1.78813 2.46115i 0.0617698 0.0850189i
\(839\) −28.6568 + 20.8204i −0.989342 + 0.718799i −0.959777 0.280764i \(-0.909412\pi\)
−0.0295652 + 0.999563i \(0.509412\pi\)
\(840\) 0 0
\(841\) −14.7752 10.7348i −0.509491 0.370167i
\(842\) 16.2072 5.26602i 0.558535 0.181479i
\(843\) 2.83275i 0.0975651i
\(844\) −0.419663 1.29159i −0.0144454 0.0444583i
\(845\) 0 0
\(846\) 4.07098 12.5292i 0.139963 0.430762i
\(847\) −3.42195 1.11186i −0.117580 0.0382040i
\(848\) −16.1516 22.2308i −0.554648 0.763408i
\(849\) 23.6634 0.812125
\(850\) 0 0
\(851\) 8.83818 0.302969
\(852\) −0.937071 1.28977i −0.0321035 0.0441867i
\(853\) −34.8150 11.3121i −1.19204 0.387318i −0.355215 0.934785i \(-0.615592\pi\)
−0.836828 + 0.547467i \(0.815592\pi\)
\(854\) −3.52213 + 10.8400i −0.120525 + 0.370938i
\(855\) 0 0
\(856\) 9.73693 + 29.9672i 0.332801 + 1.02426i
\(857\) 2.04867i 0.0699813i 0.999388 + 0.0349907i \(0.0111402\pi\)
−0.999388 + 0.0349907i \(0.988860\pi\)
\(858\) −1.01411 + 0.329506i −0.0346213 + 0.0112491i
\(859\) 11.4736 + 8.33605i 0.391474 + 0.284422i 0.766059 0.642770i \(-0.222215\pi\)
−0.374585 + 0.927192i \(0.622215\pi\)
\(860\) 0 0
\(861\) 5.17958 3.76318i 0.176519 0.128249i
\(862\) 9.41209 12.9546i 0.320577 0.441237i
\(863\) 25.3546 34.8976i 0.863081 1.18793i −0.117745 0.993044i \(-0.537567\pi\)
0.980826 0.194885i \(-0.0624333\pi\)
\(864\) −1.64823 + 1.19751i −0.0560740 + 0.0407402i
\(865\) 0 0
\(866\) 12.7689 + 9.27711i 0.433903 + 0.315249i
\(867\) 36.7459 11.9395i 1.24796 0.405485i
\(868\) 6.03344i 0.204788i
\(869\) 6.78666 + 20.8872i 0.230222 + 0.708550i
\(870\) 0 0
\(871\) 0.129025 0.397099i 0.00437185 0.0134552i
\(872\) 10.2455 + 3.32897i 0.346957 + 0.112733i
\(873\) 5.56883 + 7.66483i 0.188476 + 0.259415i
\(874\) 1.01120 0.0342044
\(875\) 0 0
\(876\) 5.48584 0.185350
\(877\) −3.96567 5.45827i −0.133911 0.184313i 0.736795 0.676116i \(-0.236338\pi\)
−0.870707 + 0.491803i \(0.836338\pi\)
\(878\) −36.1385 11.7421i −1.21962 0.396277i
\(879\) 7.18080 22.1002i 0.242202 0.745423i
\(880\) 0 0
\(881\) 5.30839 + 16.3375i 0.178844 + 0.550426i 0.999788 0.0205829i \(-0.00655221\pi\)
−0.820944 + 0.571009i \(0.806552\pi\)
\(882\) 6.39269i 0.215253i
\(883\) 54.0787 17.5712i 1.81989 0.591319i 0.820075 0.572257i \(-0.193932\pi\)
0.999818 0.0190624i \(-0.00606811\pi\)
\(884\) 0.512176 + 0.372118i 0.0172263 + 0.0125157i
\(885\) 0 0
\(886\) −9.36654 + 6.80519i −0.314675 + 0.228625i
\(887\) −21.7067 + 29.8768i −0.728841 + 1.00316i 0.270342 + 0.962764i \(0.412863\pi\)
−0.999184 + 0.0403995i \(0.987137\pi\)
\(888\) 14.9705 20.6051i 0.502378 0.691463i
\(889\) 16.2974 11.8408i 0.546597 0.397126i
\(890\) 0 0
\(891\) 2.40891 + 1.75017i 0.0807014 + 0.0586330i
\(892\) −9.09791 + 2.95609i −0.304621 + 0.0989772i
\(893\) 6.45581i 0.216036i
\(894\) −5.18610 15.9612i −0.173449 0.533822i
\(895\) 0 0
\(896\) −6.97730 + 21.4739i −0.233095 + 0.717393i
\(897\) −0.193302 0.0628076i −0.00645416 0.00209708i
\(898\) 28.6174 + 39.3885i 0.954976 + 1.31441i
\(899\) 67.5058 2.25145
\(900\) 0 0
\(901\) 44.5956 1.48570
\(902\) −10.2193 14.0657i −0.340266 0.468336i
\(903\) −8.45555 2.74737i −0.281383 0.0914269i
\(904\) −6.39421 + 19.6793i −0.212668 + 0.654525i
\(905\) 0 0
\(906\) 9.69948 + 29.8519i 0.322244 + 0.991764i
\(907\) 25.7833i 0.856120i 0.903750 + 0.428060i \(0.140803\pi\)
−0.903750 + 0.428060i \(0.859197\pi\)
\(908\) −1.55663 + 0.505779i −0.0516585 + 0.0167849i
\(909\) −5.29476 3.84687i −0.175616 0.127593i
\(910\) 0 0
\(911\) 21.8488 15.8741i 0.723882 0.525931i −0.163740 0.986504i \(-0.552356\pi\)
0.887622 + 0.460572i \(0.152356\pi\)
\(912\) 2.03565 2.80183i 0.0674071 0.0927780i
\(913\) 7.60364 10.4655i 0.251644 0.346358i
\(914\) 3.67905 2.67298i 0.121692 0.0884145i
\(915\) 0 0
\(916\) 2.22289 + 1.61502i 0.0734462 + 0.0533618i
\(917\) −34.4066 + 11.1794i −1.13621 + 0.369176i
\(918\) 11.4695i 0.378551i
\(919\) 8.01412 + 24.6649i 0.264362 + 0.813621i 0.991840 + 0.127490i \(0.0406922\pi\)
−0.727478 + 0.686131i \(0.759308\pi\)
\(920\) 0 0
\(921\) 6.74062 20.7455i 0.222111 0.683588i
\(922\) 25.7401 + 8.36347i 0.847705 + 0.275436i
\(923\) −0.598827 0.824214i −0.0197106 0.0271293i
\(924\) −1.82956 −0.0601882
\(925\) 0 0
\(926\) −40.5055 −1.33109
\(927\) 0.411922 + 0.566962i 0.0135293 + 0.0186215i
\(928\) −13.3208 4.32818i −0.437275 0.142079i
\(929\) −4.66201 + 14.3482i −0.152955 + 0.470749i −0.997948 0.0640296i \(-0.979605\pi\)
0.844993 + 0.534778i \(0.179605\pi\)
\(930\) 0 0
\(931\) −0.968057 2.97937i −0.0317268 0.0976450i
\(932\) 3.77707i 0.123722i
\(933\) −9.54991 + 3.10295i −0.312650 + 0.101586i
\(934\) −9.15470 6.65128i −0.299551 0.217637i
\(935\) 0 0
\(936\) −0.473852 + 0.344274i −0.0154883 + 0.0112529i
\(937\) −0.385330 + 0.530361i −0.0125882 + 0.0173262i −0.815265 0.579088i \(-0.803409\pi\)
0.802677 + 0.596415i \(0.203409\pi\)
\(938\) 2.73199 3.76027i 0.0892028 0.122777i
\(939\) −4.89752 + 3.55825i −0.159824 + 0.116119i
\(940\) 0 0
\(941\) 29.4596 + 21.4036i 0.960354 + 0.697738i 0.953233 0.302237i \(-0.0977333\pi\)
0.00712112 + 0.999975i \(0.497733\pi\)
\(942\) −5.11763 + 1.66282i −0.166741 + 0.0541776i
\(943\) 3.31400i 0.107919i
\(944\) −5.46963 16.8338i −0.178021 0.547893i
\(945\) 0 0
\(946\) −7.46079 + 22.9619i −0.242571 + 0.746557i
\(947\) 43.1901 + 14.0333i 1.40349 + 0.456021i 0.910317 0.413911i \(-0.135838\pi\)
0.493171 + 0.869932i \(0.335838\pi\)
\(948\) −1.58000 2.17468i −0.0513159 0.0706302i
\(949\) 3.50568 0.113799
\(950\) 0 0
\(951\) 8.49907 0.275601
\(952\) −18.5905 25.5876i −0.602520 0.829298i
\(953\) 43.9898 + 14.2932i 1.42497 + 0.463001i 0.917178 0.398478i \(-0.130462\pi\)
0.507793 + 0.861479i \(0.330462\pi\)
\(954\) 2.84091 8.74342i 0.0919779 0.283079i
\(955\) 0 0
\(956\) −2.09174 6.43773i −0.0676518 0.208211i
\(957\) 20.4703i 0.661710i
\(958\) 41.6306 13.5266i 1.34502 0.437024i
\(959\) 13.6663 + 9.92913i 0.441307 + 0.320628i
\(960\) 0 0
\(961\) −52.9246 + 38.4520i −1.70724 + 1.24039i
\(962\) −2.13169 + 2.93402i −0.0687285 + 0.0945967i
\(963\) −7.36423 + 10.1360i −0.237309 + 0.326628i
\(964\) −1.60257 + 1.16433i −0.0516153 + 0.0375007i
\(965\) 0 0
\(966\) −1.83044 1.32990i −0.0588936 0.0427887i
\(967\) 2.77461 0.901526i 0.0892255 0.0289911i −0.264064 0.964505i \(-0.585063\pi\)
0.353290 + 0.935514i \(0.385063\pi\)
\(968\) 5.36709i 0.172505i
\(969\) 1.73685 + 5.34548i 0.0557957 + 0.171721i
\(970\) 0 0
\(971\) −0.376445 + 1.15858i −0.0120807 + 0.0371806i −0.956915 0.290368i \(-0.906222\pi\)
0.944834 + 0.327548i \(0.106222\pi\)
\(972\) −0.346603 0.112618i −0.0111173 0.00361222i
\(973\) −6.51557 8.96791i −0.208879 0.287498i
\(974\) 3.66591 0.117463
\(975\) 0 0
\(976\) 20.2063 0.646787
\(977\) −26.2575 36.1404i −0.840053 1.15623i −0.985968 0.166936i \(-0.946613\pi\)
0.145915 0.989297i \(-0.453387\pi\)
\(978\) −8.73584 2.83845i −0.279341 0.0907635i
\(979\) 11.1364 34.2743i 0.355921 1.09541i
\(980\) 0 0
\(981\) 1.32367 + 4.07383i 0.0422614 + 0.130067i
\(982\) 39.5538i 1.26221i
\(983\) −34.3627 + 11.1651i −1.09600 + 0.356112i −0.800561 0.599251i \(-0.795465\pi\)
−0.295437 + 0.955362i \(0.595465\pi\)
\(984\) −7.72619 5.61341i −0.246302 0.178949i
\(985\) 0 0
\(986\) 63.7918 46.3474i 2.03154 1.47600i
\(987\) 8.49044 11.6861i 0.270254 0.371972i
\(988\) −0.0375922 + 0.0517412i −0.00119597 + 0.00164611i
\(989\) −3.72314 + 2.70502i −0.118389 + 0.0860145i
\(990\) 0 0
\(991\) 32.3765 + 23.5229i 1.02847 + 0.747229i 0.968002 0.250941i \(-0.0807399\pi\)
0.0604705 + 0.998170i \(0.480740\pi\)
\(992\) 19.0260 6.18192i 0.604076 0.196276i
\(993\) 16.2945i 0.517089i
\(994\) −3.50456 10.7859i −0.111158 0.342109i
\(995\) 0 0
\(996\) −0.489270 + 1.50582i −0.0155031 + 0.0477137i
\(997\) 3.08464 + 1.00226i 0.0976915 + 0.0317419i 0.357455 0.933930i \(-0.383645\pi\)
−0.259763 + 0.965672i \(0.583645\pi\)
\(998\) −27.1136 37.3187i −0.858267 1.18130i
\(999\) 10.1272 0.320409
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 375.2.i.c.199.4 16
5.2 odd 4 375.2.g.e.301.1 16
5.3 odd 4 375.2.g.d.301.4 16
5.4 even 2 75.2.i.a.64.1 yes 16
15.14 odd 2 225.2.m.b.64.4 16
25.3 odd 20 1875.2.a.p.1.1 8
25.4 even 10 1875.2.b.h.1249.14 16
25.9 even 10 inner 375.2.i.c.49.4 16
25.12 odd 20 375.2.g.e.76.1 16
25.13 odd 20 375.2.g.d.76.4 16
25.16 even 5 75.2.i.a.34.1 16
25.21 even 5 1875.2.b.h.1249.3 16
25.22 odd 20 1875.2.a.m.1.8 8
75.41 odd 10 225.2.m.b.109.4 16
75.47 even 20 5625.2.a.bd.1.1 8
75.53 even 20 5625.2.a.t.1.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.i.a.34.1 16 25.16 even 5
75.2.i.a.64.1 yes 16 5.4 even 2
225.2.m.b.64.4 16 15.14 odd 2
225.2.m.b.109.4 16 75.41 odd 10
375.2.g.d.76.4 16 25.13 odd 20
375.2.g.d.301.4 16 5.3 odd 4
375.2.g.e.76.1 16 25.12 odd 20
375.2.g.e.301.1 16 5.2 odd 4
375.2.i.c.49.4 16 25.9 even 10 inner
375.2.i.c.199.4 16 1.1 even 1 trivial
1875.2.a.m.1.8 8 25.22 odd 20
1875.2.a.p.1.1 8 25.3 odd 20
1875.2.b.h.1249.3 16 25.21 even 5
1875.2.b.h.1249.14 16 25.4 even 10
5625.2.a.t.1.8 8 75.53 even 20
5625.2.a.bd.1.1 8 75.47 even 20