Properties

Label 250.2.d.a.51.1
Level $250$
Weight $2$
Character 250.51
Analytic conductor $1.996$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [250,2,Mod(51,250)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(250, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("250.51");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 250 = 2 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 250.d (of order \(5\), 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: \(1.99626005053\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 51.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 250.51
Dual form 250.2.d.a.201.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 - 2.48990i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 2.48990i) q^{6} +3.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.11803 - 2.26538i) q^{9} +O(q^{10})\) \(q+(-0.809017 + 0.587785i) q^{2} +(0.809017 - 2.48990i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 2.48990i) q^{6} +3.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.11803 - 2.26538i) q^{9} +(0.190983 - 0.138757i) q^{11} +(-2.11803 - 1.53884i) q^{12} +(0.809017 + 0.587785i) q^{13} +(-2.42705 + 1.76336i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-2.42705 - 7.46969i) q^{17} +3.85410 q^{18} +(-0.263932 - 0.812299i) q^{19} +(2.42705 - 7.46969i) q^{21} +(-0.0729490 + 0.224514i) q^{22} +(-5.04508 + 3.66547i) q^{23} +2.61803 q^{24} -1.00000 q^{26} +(-1.80902 + 1.31433i) q^{27} +(0.927051 - 2.85317i) q^{28} +(-0.163119 + 0.502029i) q^{29} +(1.30902 + 4.02874i) q^{31} +1.00000 q^{32} +(-0.190983 - 0.587785i) q^{33} +(6.35410 + 4.61653i) q^{34} +(-3.11803 + 2.26538i) q^{36} +(5.92705 + 4.30625i) q^{37} +(0.690983 + 0.502029i) q^{38} +(2.11803 - 1.53884i) q^{39} +(6.04508 + 4.39201i) q^{41} +(2.42705 + 7.46969i) q^{42} +1.76393 q^{43} +(-0.0729490 - 0.224514i) q^{44} +(1.92705 - 5.93085i) q^{46} +(-1.83688 + 5.65334i) q^{47} +(-2.11803 + 1.53884i) q^{48} +2.00000 q^{49} -20.5623 q^{51} +(0.809017 - 0.587785i) q^{52} +(-0.472136 + 1.45309i) q^{53} +(0.690983 - 2.12663i) q^{54} +(0.927051 + 2.85317i) q^{56} -2.23607 q^{57} +(-0.163119 - 0.502029i) q^{58} +(-3.61803 - 2.62866i) q^{59} +(1.73607 - 1.26133i) q^{61} +(-3.42705 - 2.48990i) q^{62} +(-9.35410 - 6.79615i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.500000 + 0.363271i) q^{66} +(1.78115 + 5.48183i) q^{67} -7.85410 q^{68} +(5.04508 + 15.5272i) q^{69} +(-0.927051 + 2.85317i) q^{71} +(1.19098 - 3.66547i) q^{72} +(-4.61803 + 3.35520i) q^{73} -7.32624 q^{74} -0.854102 q^{76} +(0.572949 - 0.416272i) q^{77} +(-0.809017 + 2.48990i) q^{78} +(-0.854102 + 2.62866i) q^{79} +(-1.76393 - 5.42882i) q^{81} -7.47214 q^{82} +(4.16312 + 12.8128i) q^{83} +(-6.35410 - 4.61653i) q^{84} +(-1.42705 + 1.03681i) q^{86} +(1.11803 + 0.812299i) q^{87} +(0.190983 + 0.138757i) q^{88} +(3.61803 - 2.62866i) q^{89} +(2.42705 + 1.76336i) q^{91} +(1.92705 + 5.93085i) q^{92} +11.0902 q^{93} +(-1.83688 - 5.65334i) q^{94} +(0.809017 - 2.48990i) q^{96} +(3.26393 - 10.0453i) q^{97} +(-1.61803 + 1.17557i) q^{98} -0.909830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + q^{3} - q^{4} + q^{6} + 12 q^{7} - q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} + q^{3} - q^{4} + q^{6} + 12 q^{7} - q^{8} - 8 q^{9} + 3 q^{11} - 4 q^{12} + q^{13} - 3 q^{14} - q^{16} - 3 q^{17} + 2 q^{18} - 10 q^{19} + 3 q^{21} - 7 q^{22} - 9 q^{23} + 6 q^{24} - 4 q^{26} - 5 q^{27} - 3 q^{28} + 15 q^{29} + 3 q^{31} + 4 q^{32} - 3 q^{33} + 12 q^{34} - 8 q^{36} + 17 q^{37} + 5 q^{38} + 4 q^{39} + 13 q^{41} + 3 q^{42} + 16 q^{43} - 7 q^{44} + q^{46} - 23 q^{47} - 4 q^{48} + 8 q^{49} - 42 q^{51} + q^{52} + 16 q^{53} + 5 q^{54} - 3 q^{56} + 15 q^{58} - 10 q^{59} - 2 q^{61} - 7 q^{62} - 24 q^{63} - q^{64} + 2 q^{66} - 13 q^{67} - 18 q^{68} + 9 q^{69} + 3 q^{71} + 7 q^{72} - 14 q^{73} + 2 q^{74} + 10 q^{76} + 9 q^{77} - q^{78} + 10 q^{79} - 16 q^{81} - 12 q^{82} + q^{83} - 12 q^{84} + q^{86} + 3 q^{88} + 10 q^{89} + 3 q^{91} + q^{92} + 22 q^{93} - 23 q^{94} + q^{96} + 22 q^{97} - 2 q^{98} - 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/250\mathbb{Z}\right)^\times\).

\(n\) \(127\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.809017 + 0.587785i −0.572061 + 0.415627i
\(3\) 0.809017 2.48990i 0.467086 1.43754i −0.389254 0.921131i \(-0.627267\pi\)
0.856340 0.516413i \(-0.172733\pi\)
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 0 0
\(6\) 0.809017 + 2.48990i 0.330280 + 1.01650i
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 0.309017 + 0.951057i 0.109254 + 0.336249i
\(9\) −3.11803 2.26538i −1.03934 0.755128i
\(10\) 0 0
\(11\) 0.190983 0.138757i 0.0575835 0.0418369i −0.558621 0.829423i \(-0.688669\pi\)
0.616205 + 0.787586i \(0.288669\pi\)
\(12\) −2.11803 1.53884i −0.611424 0.444225i
\(13\) 0.809017 + 0.587785i 0.224381 + 0.163022i 0.694297 0.719689i \(-0.255716\pi\)
−0.469916 + 0.882711i \(0.655716\pi\)
\(14\) −2.42705 + 1.76336i −0.648657 + 0.471277i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) −2.42705 7.46969i −0.588646 1.81167i −0.584106 0.811677i \(-0.698555\pi\)
−0.00454037 0.999990i \(-0.501445\pi\)
\(18\) 3.85410 0.908421
\(19\) −0.263932 0.812299i −0.0605502 0.186354i 0.916206 0.400707i \(-0.131236\pi\)
−0.976756 + 0.214353i \(0.931236\pi\)
\(20\) 0 0
\(21\) 2.42705 7.46969i 0.529626 1.63002i
\(22\) −0.0729490 + 0.224514i −0.0155528 + 0.0478665i
\(23\) −5.04508 + 3.66547i −1.05197 + 0.764303i −0.972587 0.232541i \(-0.925296\pi\)
−0.0793863 + 0.996844i \(0.525296\pi\)
\(24\) 2.61803 0.534404
\(25\) 0 0
\(26\) −1.00000 −0.196116
\(27\) −1.80902 + 1.31433i −0.348145 + 0.252942i
\(28\) 0.927051 2.85317i 0.175196 0.539198i
\(29\) −0.163119 + 0.502029i −0.0302904 + 0.0932244i −0.965059 0.262033i \(-0.915607\pi\)
0.934768 + 0.355258i \(0.115607\pi\)
\(30\) 0 0
\(31\) 1.30902 + 4.02874i 0.235106 + 0.723583i 0.997107 + 0.0760071i \(0.0242172\pi\)
−0.762001 + 0.647576i \(0.775783\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.190983 0.587785i −0.0332459 0.102320i
\(34\) 6.35410 + 4.61653i 1.08972 + 0.791728i
\(35\) 0 0
\(36\) −3.11803 + 2.26538i −0.519672 + 0.377564i
\(37\) 5.92705 + 4.30625i 0.974401 + 0.707944i 0.956450 0.291895i \(-0.0942858\pi\)
0.0179508 + 0.999839i \(0.494286\pi\)
\(38\) 0.690983 + 0.502029i 0.112092 + 0.0814398i
\(39\) 2.11803 1.53884i 0.339157 0.246412i
\(40\) 0 0
\(41\) 6.04508 + 4.39201i 0.944084 + 0.685917i 0.949400 0.314069i \(-0.101692\pi\)
−0.00531652 + 0.999986i \(0.501692\pi\)
\(42\) 2.42705 + 7.46969i 0.374502 + 1.15260i
\(43\) 1.76393 0.268997 0.134499 0.990914i \(-0.457058\pi\)
0.134499 + 0.990914i \(0.457058\pi\)
\(44\) −0.0729490 0.224514i −0.0109975 0.0338468i
\(45\) 0 0
\(46\) 1.92705 5.93085i 0.284128 0.874457i
\(47\) −1.83688 + 5.65334i −0.267937 + 0.824624i 0.723066 + 0.690779i \(0.242732\pi\)
−0.991002 + 0.133845i \(0.957268\pi\)
\(48\) −2.11803 + 1.53884i −0.305712 + 0.222113i
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) −20.5623 −2.87930
\(52\) 0.809017 0.587785i 0.112190 0.0815111i
\(53\) −0.472136 + 1.45309i −0.0648529 + 0.199597i −0.978232 0.207513i \(-0.933463\pi\)
0.913379 + 0.407109i \(0.133463\pi\)
\(54\) 0.690983 2.12663i 0.0940309 0.289397i
\(55\) 0 0
\(56\) 0.927051 + 2.85317i 0.123882 + 0.381271i
\(57\) −2.23607 −0.296174
\(58\) −0.163119 0.502029i −0.0214186 0.0659196i
\(59\) −3.61803 2.62866i −0.471028 0.342222i 0.326814 0.945089i \(-0.394025\pi\)
−0.797842 + 0.602867i \(0.794025\pi\)
\(60\) 0 0
\(61\) 1.73607 1.26133i 0.222281 0.161496i −0.471072 0.882095i \(-0.656133\pi\)
0.693353 + 0.720598i \(0.256133\pi\)
\(62\) −3.42705 2.48990i −0.435236 0.316217i
\(63\) −9.35410 6.79615i −1.17851 0.856235i
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) 0 0
\(66\) 0.500000 + 0.363271i 0.0615457 + 0.0447156i
\(67\) 1.78115 + 5.48183i 0.217602 + 0.669712i 0.998959 + 0.0456261i \(0.0145283\pi\)
−0.781356 + 0.624085i \(0.785472\pi\)
\(68\) −7.85410 −0.952450
\(69\) 5.04508 + 15.5272i 0.607357 + 1.86925i
\(70\) 0 0
\(71\) −0.927051 + 2.85317i −0.110021 + 0.338609i −0.990876 0.134777i \(-0.956968\pi\)
0.880855 + 0.473386i \(0.156968\pi\)
\(72\) 1.19098 3.66547i 0.140359 0.431980i
\(73\) −4.61803 + 3.35520i −0.540500 + 0.392696i −0.824271 0.566196i \(-0.808415\pi\)
0.283771 + 0.958892i \(0.408415\pi\)
\(74\) −7.32624 −0.851658
\(75\) 0 0
\(76\) −0.854102 −0.0979722
\(77\) 0.572949 0.416272i 0.0652936 0.0474386i
\(78\) −0.809017 + 2.48990i −0.0916031 + 0.281925i
\(79\) −0.854102 + 2.62866i −0.0960940 + 0.295747i −0.987537 0.157385i \(-0.949693\pi\)
0.891443 + 0.453132i \(0.149693\pi\)
\(80\) 0 0
\(81\) −1.76393 5.42882i −0.195992 0.603203i
\(82\) −7.47214 −0.825159
\(83\) 4.16312 + 12.8128i 0.456962 + 1.40638i 0.868817 + 0.495134i \(0.164881\pi\)
−0.411855 + 0.911249i \(0.635119\pi\)
\(84\) −6.35410 4.61653i −0.693289 0.503704i
\(85\) 0 0
\(86\) −1.42705 + 1.03681i −0.153883 + 0.111802i
\(87\) 1.11803 + 0.812299i 0.119866 + 0.0870876i
\(88\) 0.190983 + 0.138757i 0.0203589 + 0.0147916i
\(89\) 3.61803 2.62866i 0.383511 0.278637i −0.379280 0.925282i \(-0.623828\pi\)
0.762791 + 0.646645i \(0.223828\pi\)
\(90\) 0 0
\(91\) 2.42705 + 1.76336i 0.254424 + 0.184850i
\(92\) 1.92705 + 5.93085i 0.200909 + 0.618334i
\(93\) 11.0902 1.15000
\(94\) −1.83688 5.65334i −0.189460 0.583097i
\(95\) 0 0
\(96\) 0.809017 2.48990i 0.0825700 0.254124i
\(97\) 3.26393 10.0453i 0.331402 1.01995i −0.637065 0.770810i \(-0.719852\pi\)
0.968467 0.249141i \(-0.0801482\pi\)
\(98\) −1.61803 + 1.17557i −0.163446 + 0.118751i
\(99\) −0.909830 −0.0914414
\(100\) 0 0
\(101\) −1.61803 −0.161000 −0.0805002 0.996755i \(-0.525652\pi\)
−0.0805002 + 0.996755i \(0.525652\pi\)
\(102\) 16.6353 12.0862i 1.64714 1.19671i
\(103\) 6.13525 18.8824i 0.604525 1.86054i 0.104499 0.994525i \(-0.466676\pi\)
0.500026 0.866010i \(-0.333324\pi\)
\(104\) −0.309017 + 0.951057i −0.0303016 + 0.0932588i
\(105\) 0 0
\(106\) −0.472136 1.45309i −0.0458579 0.141136i
\(107\) −10.0902 −0.975454 −0.487727 0.872996i \(-0.662174\pi\)
−0.487727 + 0.872996i \(0.662174\pi\)
\(108\) 0.690983 + 2.12663i 0.0664899 + 0.204635i
\(109\) 12.1353 + 8.81678i 1.16235 + 0.844494i 0.990073 0.140555i \(-0.0448886\pi\)
0.172274 + 0.985049i \(0.444889\pi\)
\(110\) 0 0
\(111\) 15.5172 11.2739i 1.47283 1.07007i
\(112\) −2.42705 1.76336i −0.229335 0.166621i
\(113\) 6.66312 + 4.84104i 0.626814 + 0.455407i 0.855295 0.518142i \(-0.173376\pi\)
−0.228481 + 0.973548i \(0.573376\pi\)
\(114\) 1.80902 1.31433i 0.169430 0.123098i
\(115\) 0 0
\(116\) 0.427051 + 0.310271i 0.0396507 + 0.0288079i
\(117\) −1.19098 3.66547i −0.110106 0.338873i
\(118\) 4.47214 0.411693
\(119\) −7.28115 22.4091i −0.667462 2.05424i
\(120\) 0 0
\(121\) −3.38197 + 10.4086i −0.307451 + 0.946238i
\(122\) −0.663119 + 2.04087i −0.0600360 + 0.184772i
\(123\) 15.8262 11.4984i 1.42700 1.03678i
\(124\) 4.23607 0.380410
\(125\) 0 0
\(126\) 11.5623 1.03005
\(127\) −10.0902 + 7.33094i −0.895358 + 0.650516i −0.937269 0.348606i \(-0.886655\pi\)
0.0419116 + 0.999121i \(0.486655\pi\)
\(128\) 0.309017 0.951057i 0.0273135 0.0840623i
\(129\) 1.42705 4.39201i 0.125645 0.386695i
\(130\) 0 0
\(131\) 3.21885 + 9.90659i 0.281232 + 0.865543i 0.987503 + 0.157601i \(0.0503761\pi\)
−0.706271 + 0.707942i \(0.749624\pi\)
\(132\) −0.618034 −0.0537930
\(133\) −0.791796 2.43690i −0.0686574 0.211306i
\(134\) −4.66312 3.38795i −0.402832 0.292675i
\(135\) 0 0
\(136\) 6.35410 4.61653i 0.544860 0.395864i
\(137\) −4.92705 3.57971i −0.420946 0.305835i 0.357072 0.934077i \(-0.383775\pi\)
−0.778018 + 0.628241i \(0.783775\pi\)
\(138\) −13.2082 9.59632i −1.12436 0.816893i
\(139\) −8.35410 + 6.06961i −0.708586 + 0.514818i −0.882717 0.469905i \(-0.844288\pi\)
0.174131 + 0.984722i \(0.444288\pi\)
\(140\) 0 0
\(141\) 12.5902 + 9.14729i 1.06028 + 0.770341i
\(142\) −0.927051 2.85317i −0.0777964 0.239433i
\(143\) 0.236068 0.0197410
\(144\) 1.19098 + 3.66547i 0.0992486 + 0.305456i
\(145\) 0 0
\(146\) 1.76393 5.42882i 0.145984 0.449293i
\(147\) 1.61803 4.97980i 0.133453 0.410727i
\(148\) 5.92705 4.30625i 0.487201 0.353972i
\(149\) −2.23607 −0.183186 −0.0915929 0.995797i \(-0.529196\pi\)
−0.0915929 + 0.995797i \(0.529196\pi\)
\(150\) 0 0
\(151\) 3.70820 0.301769 0.150885 0.988551i \(-0.451788\pi\)
0.150885 + 0.988551i \(0.451788\pi\)
\(152\) 0.690983 0.502029i 0.0560461 0.0407199i
\(153\) −9.35410 + 28.7890i −0.756234 + 2.32745i
\(154\) −0.218847 + 0.673542i −0.0176352 + 0.0542756i
\(155\) 0 0
\(156\) −0.809017 2.48990i −0.0647732 0.199351i
\(157\) 15.5623 1.24201 0.621004 0.783808i \(-0.286725\pi\)
0.621004 + 0.783808i \(0.286725\pi\)
\(158\) −0.854102 2.62866i −0.0679487 0.209125i
\(159\) 3.23607 + 2.35114i 0.256637 + 0.186458i
\(160\) 0 0
\(161\) −15.1353 + 10.9964i −1.19283 + 0.866638i
\(162\) 4.61803 + 3.35520i 0.362827 + 0.263609i
\(163\) −3.92705 2.85317i −0.307590 0.223477i 0.423271 0.906003i \(-0.360882\pi\)
−0.730862 + 0.682525i \(0.760882\pi\)
\(164\) 6.04508 4.39201i 0.472042 0.342958i
\(165\) 0 0
\(166\) −10.8992 7.91872i −0.845941 0.614612i
\(167\) −4.82624 14.8536i −0.373466 1.14941i −0.944508 0.328488i \(-0.893461\pi\)
0.571043 0.820920i \(-0.306539\pi\)
\(168\) 7.85410 0.605957
\(169\) −3.70820 11.4127i −0.285246 0.877898i
\(170\) 0 0
\(171\) −1.01722 + 3.13068i −0.0777888 + 0.239409i
\(172\) 0.545085 1.67760i 0.0415623 0.127916i
\(173\) 2.61803 1.90211i 0.199045 0.144615i −0.483798 0.875180i \(-0.660743\pi\)
0.682843 + 0.730565i \(0.260743\pi\)
\(174\) −1.38197 −0.104767
\(175\) 0 0
\(176\) −0.236068 −0.0177943
\(177\) −9.47214 + 6.88191i −0.711969 + 0.517276i
\(178\) −1.38197 + 4.25325i −0.103583 + 0.318795i
\(179\) −3.45492 + 10.6331i −0.258232 + 0.794758i 0.734943 + 0.678129i \(0.237209\pi\)
−0.993176 + 0.116629i \(0.962791\pi\)
\(180\) 0 0
\(181\) −6.61803 20.3682i −0.491915 1.51396i −0.821710 0.569905i \(-0.806980\pi\)
0.329796 0.944052i \(-0.393020\pi\)
\(182\) −3.00000 −0.222375
\(183\) −1.73607 5.34307i −0.128334 0.394971i
\(184\) −5.04508 3.66547i −0.371929 0.270222i
\(185\) 0 0
\(186\) −8.97214 + 6.51864i −0.657869 + 0.477970i
\(187\) −1.50000 1.08981i −0.109691 0.0796951i
\(188\) 4.80902 + 3.49396i 0.350734 + 0.254823i
\(189\) −5.42705 + 3.94298i −0.394760 + 0.286810i
\(190\) 0 0
\(191\) −14.2812 10.3759i −1.03335 0.750771i −0.0643719 0.997926i \(-0.520504\pi\)
−0.968976 + 0.247155i \(0.920504\pi\)
\(192\) 0.809017 + 2.48990i 0.0583858 + 0.179693i
\(193\) −16.6525 −1.19867 −0.599336 0.800498i \(-0.704569\pi\)
−0.599336 + 0.800498i \(0.704569\pi\)
\(194\) 3.26393 + 10.0453i 0.234337 + 0.721214i
\(195\) 0 0
\(196\) 0.618034 1.90211i 0.0441453 0.135865i
\(197\) −3.70820 + 11.4127i −0.264199 + 0.813120i 0.727678 + 0.685919i \(0.240599\pi\)
−0.991877 + 0.127201i \(0.959401\pi\)
\(198\) 0.736068 0.534785i 0.0523101 0.0380055i
\(199\) −17.5623 −1.24496 −0.622479 0.782636i \(-0.713875\pi\)
−0.622479 + 0.782636i \(0.713875\pi\)
\(200\) 0 0
\(201\) 15.0902 1.06438
\(202\) 1.30902 0.951057i 0.0921021 0.0669161i
\(203\) −0.489357 + 1.50609i −0.0343461 + 0.105706i
\(204\) −6.35410 + 19.5559i −0.444876 + 1.36919i
\(205\) 0 0
\(206\) 6.13525 + 18.8824i 0.427463 + 1.31560i
\(207\) 24.0344 1.67051
\(208\) −0.309017 0.951057i −0.0214265 0.0659439i
\(209\) −0.163119 0.118513i −0.0112832 0.00819771i
\(210\) 0 0
\(211\) −9.11803 + 6.62464i −0.627711 + 0.456059i −0.855607 0.517627i \(-0.826816\pi\)
0.227895 + 0.973686i \(0.426816\pi\)
\(212\) 1.23607 + 0.898056i 0.0848935 + 0.0616787i
\(213\) 6.35410 + 4.61653i 0.435376 + 0.316319i
\(214\) 8.16312 5.93085i 0.558019 0.405425i
\(215\) 0 0
\(216\) −1.80902 1.31433i −0.123088 0.0894287i
\(217\) 3.92705 + 12.0862i 0.266586 + 0.820466i
\(218\) −15.0000 −1.01593
\(219\) 4.61803 + 14.2128i 0.312058 + 0.960415i
\(220\) 0 0
\(221\) 2.42705 7.46969i 0.163261 0.502466i
\(222\) −5.92705 + 18.2416i −0.397798 + 1.22430i
\(223\) −7.28115 + 5.29007i −0.487582 + 0.354249i −0.804254 0.594286i \(-0.797435\pi\)
0.316672 + 0.948535i \(0.397435\pi\)
\(224\) 3.00000 0.200446
\(225\) 0 0
\(226\) −8.23607 −0.547855
\(227\) −12.4271 + 9.02878i −0.824812 + 0.599261i −0.918087 0.396379i \(-0.870267\pi\)
0.0932746 + 0.995640i \(0.470267\pi\)
\(228\) −0.690983 + 2.12663i −0.0457615 + 0.140839i
\(229\) 5.42705 16.7027i 0.358630 1.10375i −0.595245 0.803544i \(-0.702945\pi\)
0.953875 0.300204i \(-0.0970549\pi\)
\(230\) 0 0
\(231\) −0.572949 1.76336i −0.0376973 0.116020i
\(232\) −0.527864 −0.0346560
\(233\) −8.56231 26.3521i −0.560935 1.72638i −0.679730 0.733463i \(-0.737903\pi\)
0.118795 0.992919i \(-0.462097\pi\)
\(234\) 3.11803 + 2.26538i 0.203832 + 0.148093i
\(235\) 0 0
\(236\) −3.61803 + 2.62866i −0.235514 + 0.171111i
\(237\) 5.85410 + 4.25325i 0.380265 + 0.276279i
\(238\) 19.0623 + 13.8496i 1.23563 + 0.897735i
\(239\) 14.6353 10.6331i 0.946676 0.687800i −0.00334240 0.999994i \(-0.501064\pi\)
0.950018 + 0.312194i \(0.101064\pi\)
\(240\) 0 0
\(241\) −10.8262 7.86572i −0.697379 0.506676i 0.181698 0.983354i \(-0.441841\pi\)
−0.879078 + 0.476679i \(0.841841\pi\)
\(242\) −3.38197 10.4086i −0.217401 0.669092i
\(243\) −21.6525 −1.38901
\(244\) −0.663119 2.04087i −0.0424518 0.130653i
\(245\) 0 0
\(246\) −6.04508 + 18.6049i −0.385421 + 1.18620i
\(247\) 0.263932 0.812299i 0.0167936 0.0516854i
\(248\) −3.42705 + 2.48990i −0.217618 + 0.158109i
\(249\) 35.2705 2.23518
\(250\) 0 0
\(251\) 23.1803 1.46313 0.731565 0.681772i \(-0.238790\pi\)
0.731565 + 0.681772i \(0.238790\pi\)
\(252\) −9.35410 + 6.79615i −0.589253 + 0.428117i
\(253\) −0.454915 + 1.40008i −0.0286003 + 0.0880226i
\(254\) 3.85410 11.8617i 0.241828 0.744270i
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 16.7426 1.04438 0.522189 0.852830i \(-0.325116\pi\)
0.522189 + 0.852830i \(0.325116\pi\)
\(258\) 1.42705 + 4.39201i 0.0888443 + 0.273435i
\(259\) 17.7812 + 12.9188i 1.10487 + 0.802733i
\(260\) 0 0
\(261\) 1.64590 1.19581i 0.101879 0.0740191i
\(262\) −8.42705 6.12261i −0.520625 0.378256i
\(263\) 1.92705 + 1.40008i 0.118827 + 0.0863329i 0.645612 0.763666i \(-0.276603\pi\)
−0.526785 + 0.849999i \(0.676603\pi\)
\(264\) 0.500000 0.363271i 0.0307729 0.0223578i
\(265\) 0 0
\(266\) 2.07295 + 1.50609i 0.127101 + 0.0923440i
\(267\) −3.61803 11.1352i −0.221420 0.681461i
\(268\) 5.76393 0.352088
\(269\) 4.04508 + 12.4495i 0.246633 + 0.759059i 0.995364 + 0.0961842i \(0.0306638\pi\)
−0.748730 + 0.662875i \(0.769336\pi\)
\(270\) 0 0
\(271\) −2.93769 + 9.04129i −0.178452 + 0.549219i −0.999774 0.0212453i \(-0.993237\pi\)
0.821322 + 0.570465i \(0.193237\pi\)
\(272\) −2.42705 + 7.46969i −0.147162 + 0.452917i
\(273\) 6.35410 4.61653i 0.384568 0.279405i
\(274\) 6.09017 0.367921
\(275\) 0 0
\(276\) 16.3262 0.982724
\(277\) 11.0902 8.05748i 0.666344 0.484127i −0.202456 0.979291i \(-0.564892\pi\)
0.868799 + 0.495164i \(0.164892\pi\)
\(278\) 3.19098 9.82084i 0.191382 0.589015i
\(279\) 5.04508 15.5272i 0.302041 0.929588i
\(280\) 0 0
\(281\) −5.92705 18.2416i −0.353578 1.08820i −0.956829 0.290651i \(-0.906128\pi\)
0.603251 0.797551i \(-0.293872\pi\)
\(282\) −15.5623 −0.926722
\(283\) 7.94427 + 24.4500i 0.472238 + 1.45340i 0.849647 + 0.527352i \(0.176815\pi\)
−0.377409 + 0.926047i \(0.623185\pi\)
\(284\) 2.42705 + 1.76336i 0.144019 + 0.104636i
\(285\) 0 0
\(286\) −0.190983 + 0.138757i −0.0112931 + 0.00820489i
\(287\) 18.1353 + 13.1760i 1.07049 + 0.777757i
\(288\) −3.11803 2.26538i −0.183732 0.133489i
\(289\) −36.1525 + 26.2663i −2.12662 + 1.54508i
\(290\) 0 0
\(291\) −22.3713 16.2537i −1.31143 0.952810i
\(292\) 1.76393 + 5.42882i 0.103226 + 0.317698i
\(293\) 11.5623 0.675477 0.337739 0.941240i \(-0.390338\pi\)
0.337739 + 0.941240i \(0.390338\pi\)
\(294\) 1.61803 + 4.97980i 0.0943657 + 0.290428i
\(295\) 0 0
\(296\) −2.26393 + 6.96767i −0.131588 + 0.404987i
\(297\) −0.163119 + 0.502029i −0.00946512 + 0.0291307i
\(298\) 1.80902 1.31433i 0.104794 0.0761370i
\(299\) −6.23607 −0.360641
\(300\) 0 0
\(301\) 5.29180 0.305014
\(302\) −3.00000 + 2.17963i −0.172631 + 0.125423i
\(303\) −1.30902 + 4.02874i −0.0752011 + 0.231445i
\(304\) −0.263932 + 0.812299i −0.0151375 + 0.0465886i
\(305\) 0 0
\(306\) −9.35410 28.7890i −0.534738 1.64576i
\(307\) −17.1246 −0.977353 −0.488677 0.872465i \(-0.662520\pi\)
−0.488677 + 0.872465i \(0.662520\pi\)
\(308\) −0.218847 0.673542i −0.0124700 0.0383786i
\(309\) −42.0517 30.5523i −2.39224 1.73806i
\(310\) 0 0
\(311\) 17.0623 12.3965i 0.967515 0.702941i 0.0126308 0.999920i \(-0.495979\pi\)
0.954884 + 0.296980i \(0.0959794\pi\)
\(312\) 2.11803 + 1.53884i 0.119910 + 0.0871198i
\(313\) 2.88197 + 2.09387i 0.162898 + 0.118353i 0.666248 0.745730i \(-0.267899\pi\)
−0.503350 + 0.864083i \(0.667899\pi\)
\(314\) −12.5902 + 9.14729i −0.710504 + 0.516212i
\(315\) 0 0
\(316\) 2.23607 + 1.62460i 0.125789 + 0.0913908i
\(317\) −3.28115 10.0984i −0.184288 0.567180i 0.815647 0.578549i \(-0.196381\pi\)
−0.999935 + 0.0113694i \(0.996381\pi\)
\(318\) −4.00000 −0.224309
\(319\) 0.0385072 + 0.118513i 0.00215599 + 0.00663545i
\(320\) 0 0
\(321\) −8.16312 + 25.1235i −0.455621 + 1.40226i
\(322\) 5.78115 17.7926i 0.322171 0.991541i
\(323\) −5.42705 + 3.94298i −0.301969 + 0.219393i
\(324\) −5.70820 −0.317122
\(325\) 0 0
\(326\) 4.85410 0.268844
\(327\) 31.7705 23.0826i 1.75691 1.27647i
\(328\) −2.30902 + 7.10642i −0.127494 + 0.392387i
\(329\) −5.51064 + 16.9600i −0.303812 + 0.935036i
\(330\) 0 0
\(331\) 1.40983 + 4.33901i 0.0774913 + 0.238494i 0.982297 0.187332i \(-0.0599839\pi\)
−0.904805 + 0.425825i \(0.859984\pi\)
\(332\) 13.4721 0.739380
\(333\) −8.72542 26.8541i −0.478150 1.47160i
\(334\) 12.6353 + 9.18005i 0.691370 + 0.502310i
\(335\) 0 0
\(336\) −6.35410 + 4.61653i −0.346645 + 0.251852i
\(337\) −25.4164 18.4661i −1.38452 1.00591i −0.996442 0.0842863i \(-0.973139\pi\)
−0.388078 0.921626i \(-0.626861\pi\)
\(338\) 9.70820 + 7.05342i 0.528057 + 0.383656i
\(339\) 17.4443 12.6740i 0.947443 0.688357i
\(340\) 0 0
\(341\) 0.809017 + 0.587785i 0.0438107 + 0.0318304i
\(342\) −1.01722 3.13068i −0.0550050 0.169288i
\(343\) −15.0000 −0.809924
\(344\) 0.545085 + 1.67760i 0.0293890 + 0.0904501i
\(345\) 0 0
\(346\) −1.00000 + 3.07768i −0.0537603 + 0.165457i
\(347\) 3.06231 9.42481i 0.164393 0.505950i −0.834598 0.550860i \(-0.814300\pi\)
0.998991 + 0.0449095i \(0.0142999\pi\)
\(348\) 1.11803 0.812299i 0.0599329 0.0435438i
\(349\) −22.2361 −1.19027 −0.595135 0.803626i \(-0.702901\pi\)
−0.595135 + 0.803626i \(0.702901\pi\)
\(350\) 0 0
\(351\) −2.23607 −0.119352
\(352\) 0.190983 0.138757i 0.0101794 0.00739579i
\(353\) 5.18034 15.9434i 0.275722 0.848584i −0.713306 0.700853i \(-0.752803\pi\)
0.989028 0.147731i \(-0.0471970\pi\)
\(354\) 3.61803 11.1352i 0.192296 0.591827i
\(355\) 0 0
\(356\) −1.38197 4.25325i −0.0732441 0.225422i
\(357\) −61.6869 −3.26482
\(358\) −3.45492 10.6331i −0.182598 0.561979i
\(359\) −2.50000 1.81636i −0.131945 0.0958636i 0.519855 0.854254i \(-0.325986\pi\)
−0.651800 + 0.758391i \(0.725986\pi\)
\(360\) 0 0
\(361\) 14.7812 10.7391i 0.777955 0.565218i
\(362\) 17.3262 + 12.5882i 0.910647 + 0.661624i
\(363\) 23.1803 + 16.8415i 1.21665 + 0.883950i
\(364\) 2.42705 1.76336i 0.127212 0.0924250i
\(365\) 0 0
\(366\) 4.54508 + 3.30220i 0.237575 + 0.172609i
\(367\) 9.74671 + 29.9973i 0.508774 + 1.56585i 0.794332 + 0.607484i \(0.207821\pi\)
−0.285557 + 0.958362i \(0.592179\pi\)
\(368\) 6.23607 0.325078
\(369\) −8.89919 27.3889i −0.463273 1.42581i
\(370\) 0 0
\(371\) −1.41641 + 4.35926i −0.0735362 + 0.226321i
\(372\) 3.42705 10.5474i 0.177684 0.546856i
\(373\) −13.1353 + 9.54332i −0.680118 + 0.494134i −0.873397 0.487009i \(-0.838088\pi\)
0.193279 + 0.981144i \(0.438088\pi\)
\(374\) 1.85410 0.0958733
\(375\) 0 0
\(376\) −5.94427 −0.306552
\(377\) −0.427051 + 0.310271i −0.0219942 + 0.0159798i
\(378\) 2.07295 6.37988i 0.106621 0.328146i
\(379\) 0.163119 0.502029i 0.00837886 0.0257875i −0.946780 0.321882i \(-0.895684\pi\)
0.955159 + 0.296095i \(0.0956845\pi\)
\(380\) 0 0
\(381\) 10.0902 + 31.0543i 0.516935 + 1.59096i
\(382\) 17.6525 0.903179
\(383\) 1.33688 + 4.11450i 0.0683114 + 0.210241i 0.979385 0.202003i \(-0.0647451\pi\)
−0.911073 + 0.412244i \(0.864745\pi\)
\(384\) −2.11803 1.53884i −0.108085 0.0785287i
\(385\) 0 0
\(386\) 13.4721 9.78808i 0.685714 0.498200i
\(387\) −5.50000 3.99598i −0.279581 0.203127i
\(388\) −8.54508 6.20837i −0.433811 0.315182i
\(389\) 26.8713 19.5232i 1.36243 0.989863i 0.364144 0.931343i \(-0.381362\pi\)
0.998286 0.0585208i \(-0.0186384\pi\)
\(390\) 0 0
\(391\) 39.6246 + 28.7890i 2.00390 + 1.45592i
\(392\) 0.618034 + 1.90211i 0.0312154 + 0.0960712i
\(393\) 27.2705 1.37562
\(394\) −3.70820 11.4127i −0.186817 0.574962i
\(395\) 0 0
\(396\) −0.281153 + 0.865300i −0.0141285 + 0.0434830i
\(397\) 1.78115 5.48183i 0.0893935 0.275125i −0.896359 0.443330i \(-0.853797\pi\)
0.985752 + 0.168205i \(0.0537970\pi\)
\(398\) 14.2082 10.3229i 0.712193 0.517438i
\(399\) −6.70820 −0.335830
\(400\) 0 0
\(401\) 8.18034 0.408507 0.204253 0.978918i \(-0.434523\pi\)
0.204253 + 0.978918i \(0.434523\pi\)
\(402\) −12.2082 + 8.86978i −0.608890 + 0.442384i
\(403\) −1.30902 + 4.02874i −0.0652068 + 0.200686i
\(404\) −0.500000 + 1.53884i −0.0248759 + 0.0765602i
\(405\) 0 0
\(406\) −0.489357 1.50609i −0.0242864 0.0747458i
\(407\) 1.72949 0.0857276
\(408\) −6.35410 19.5559i −0.314575 0.968162i
\(409\) −5.42705 3.94298i −0.268350 0.194968i 0.445470 0.895297i \(-0.353037\pi\)
−0.713820 + 0.700329i \(0.753037\pi\)
\(410\) 0 0
\(411\) −12.8992 + 9.37181i −0.636270 + 0.462277i
\(412\) −16.0623 11.6699i −0.791333 0.574937i
\(413\) −10.8541 7.88597i −0.534095 0.388043i
\(414\) −19.4443 + 14.1271i −0.955634 + 0.694309i
\(415\) 0 0
\(416\) 0.809017 + 0.587785i 0.0396653 + 0.0288185i
\(417\) 8.35410 + 25.7113i 0.409102 + 1.25909i
\(418\) 0.201626 0.00986186
\(419\) 8.41641 + 25.9030i 0.411168 + 1.26545i 0.915633 + 0.402014i \(0.131690\pi\)
−0.504465 + 0.863432i \(0.668310\pi\)
\(420\) 0 0
\(421\) −3.79180 + 11.6699i −0.184801 + 0.568758i −0.999945 0.0104998i \(-0.996658\pi\)
0.815144 + 0.579258i \(0.196658\pi\)
\(422\) 3.48278 10.7189i 0.169539 0.521787i
\(423\) 18.5344 13.4661i 0.901175 0.654742i
\(424\) −1.52786 −0.0741996
\(425\) 0 0
\(426\) −7.85410 −0.380532
\(427\) 5.20820 3.78398i 0.252043 0.183120i
\(428\) −3.11803 + 9.59632i −0.150716 + 0.463856i
\(429\) 0.190983 0.587785i 0.00922075 0.0283785i
\(430\) 0 0
\(431\) −9.90983 30.4993i −0.477340 1.46910i −0.842776 0.538264i \(-0.819080\pi\)
0.365436 0.930836i \(-0.380920\pi\)
\(432\) 2.23607 0.107583
\(433\) −7.21885 22.2173i −0.346916 1.06770i −0.960550 0.278106i \(-0.910293\pi\)
0.613635 0.789590i \(-0.289707\pi\)
\(434\) −10.2812 7.46969i −0.493511 0.358557i
\(435\) 0 0
\(436\) 12.1353 8.81678i 0.581173 0.422247i
\(437\) 4.30902 + 3.13068i 0.206128 + 0.149761i
\(438\) −12.0902 8.78402i −0.577691 0.419717i
\(439\) 4.57295 3.32244i 0.218255 0.158572i −0.473286 0.880909i \(-0.656932\pi\)
0.691541 + 0.722337i \(0.256932\pi\)
\(440\) 0 0
\(441\) −6.23607 4.53077i −0.296956 0.215751i
\(442\) 2.42705 + 7.46969i 0.115443 + 0.355297i
\(443\) 7.41641 0.352364 0.176182 0.984358i \(-0.443625\pi\)
0.176182 + 0.984358i \(0.443625\pi\)
\(444\) −5.92705 18.2416i −0.281285 0.865707i
\(445\) 0 0
\(446\) 2.78115 8.55951i 0.131691 0.405304i
\(447\) −1.80902 + 5.56758i −0.0855636 + 0.263338i
\(448\) −2.42705 + 1.76336i −0.114667 + 0.0833107i
\(449\) 13.9443 0.658071 0.329035 0.944318i \(-0.393276\pi\)
0.329035 + 0.944318i \(0.393276\pi\)
\(450\) 0 0
\(451\) 1.76393 0.0830603
\(452\) 6.66312 4.84104i 0.313407 0.227703i
\(453\) 3.00000 9.23305i 0.140952 0.433807i
\(454\) 4.74671 14.6089i 0.222774 0.685628i
\(455\) 0 0
\(456\) −0.690983 2.12663i −0.0323582 0.0995884i
\(457\) 11.2148 0.524605 0.262303 0.964986i \(-0.415518\pi\)
0.262303 + 0.964986i \(0.415518\pi\)
\(458\) 5.42705 + 16.7027i 0.253589 + 0.780468i
\(459\) 14.2082 + 10.3229i 0.663182 + 0.481830i
\(460\) 0 0
\(461\) −22.7984 + 16.5640i −1.06183 + 0.771462i −0.974425 0.224711i \(-0.927856\pi\)
−0.0874008 + 0.996173i \(0.527856\pi\)
\(462\) 1.50000 + 1.08981i 0.0697863 + 0.0507027i
\(463\) 9.69098 + 7.04091i 0.450378 + 0.327219i 0.789745 0.613435i \(-0.210213\pi\)
−0.339367 + 0.940654i \(0.610213\pi\)
\(464\) 0.427051 0.310271i 0.0198253 0.0144040i
\(465\) 0 0
\(466\) 22.4164 + 16.2865i 1.03842 + 0.754456i
\(467\) −0.982779 3.02468i −0.0454776 0.139966i 0.925739 0.378162i \(-0.123444\pi\)
−0.971217 + 0.238196i \(0.923444\pi\)
\(468\) −3.85410 −0.178156
\(469\) 5.34346 + 16.4455i 0.246738 + 0.759381i
\(470\) 0 0
\(471\) 12.5902 38.7486i 0.580124 1.78544i
\(472\) 1.38197 4.25325i 0.0636101 0.195772i
\(473\) 0.336881 0.244758i 0.0154898 0.0112540i
\(474\) −7.23607 −0.332364
\(475\) 0 0
\(476\) −23.5623 −1.07998
\(477\) 4.76393 3.46120i 0.218125 0.158477i
\(478\) −5.59017 + 17.2048i −0.255688 + 0.786928i
\(479\) −12.2984 + 37.8505i −0.561927 + 1.72943i 0.114983 + 0.993368i \(0.463319\pi\)
−0.676910 + 0.736066i \(0.736681\pi\)
\(480\) 0 0
\(481\) 2.26393 + 6.96767i 0.103226 + 0.317698i
\(482\) 13.3820 0.609532
\(483\) 15.1353 + 46.5815i 0.688678 + 2.11953i
\(484\) 8.85410 + 6.43288i 0.402459 + 0.292404i
\(485\) 0 0
\(486\) 17.5172 12.7270i 0.794597 0.577309i
\(487\) −14.6631 10.6534i −0.664449 0.482751i 0.203713 0.979031i \(-0.434699\pi\)
−0.868163 + 0.496280i \(0.834699\pi\)
\(488\) 1.73607 + 1.26133i 0.0785881 + 0.0570976i
\(489\) −10.2812 + 7.46969i −0.464930 + 0.337791i
\(490\) 0 0
\(491\) −11.9443 8.67802i −0.539037 0.391634i 0.284690 0.958620i \(-0.408109\pi\)
−0.823727 + 0.566986i \(0.808109\pi\)
\(492\) −6.04508 18.6049i −0.272533 0.838772i
\(493\) 4.14590 0.186722
\(494\) 0.263932 + 0.812299i 0.0118749 + 0.0365471i
\(495\) 0 0
\(496\) 1.30902 4.02874i 0.0587766 0.180896i
\(497\) −2.78115 + 8.55951i −0.124752 + 0.383946i
\(498\) −28.5344 + 20.7315i −1.27866 + 0.929000i
\(499\) 40.8541 1.82888 0.914440 0.404721i \(-0.132631\pi\)
0.914440 + 0.404721i \(0.132631\pi\)
\(500\) 0 0
\(501\) −40.8885 −1.82677
\(502\) −18.7533 + 13.6251i −0.837000 + 0.608116i
\(503\) −2.31966 + 7.13918i −0.103429 + 0.318320i −0.989358 0.145499i \(-0.953521\pi\)
0.885930 + 0.463819i \(0.153521\pi\)
\(504\) 3.57295 10.9964i 0.159152 0.489819i
\(505\) 0 0
\(506\) −0.454915 1.40008i −0.0202234 0.0622413i
\(507\) −31.4164 −1.39525
\(508\) 3.85410 + 11.8617i 0.170998 + 0.526278i
\(509\) 10.5902 + 7.69421i 0.469401 + 0.341040i 0.797208 0.603705i \(-0.206310\pi\)
−0.327807 + 0.944745i \(0.606310\pi\)
\(510\) 0 0
\(511\) −13.8541 + 10.0656i −0.612869 + 0.445276i
\(512\) −0.809017 0.587785i −0.0357538 0.0259767i
\(513\) 1.54508 + 1.12257i 0.0682172 + 0.0495627i
\(514\) −13.5451 + 9.84108i −0.597448 + 0.434071i
\(515\) 0 0
\(516\) −3.73607 2.71441i −0.164471 0.119495i
\(517\) 0.433629 + 1.33457i 0.0190710 + 0.0586944i
\(518\) −21.9787 −0.965689
\(519\) −2.61803 8.05748i −0.114919 0.353684i
\(520\) 0 0
\(521\) 10.0279 30.8626i 0.439329 1.35211i −0.449256 0.893403i \(-0.648311\pi\)
0.888585 0.458712i \(-0.151689\pi\)
\(522\) −0.628677 + 1.93487i −0.0275164 + 0.0846869i
\(523\) 21.5623 15.6659i 0.942854 0.685023i −0.00625211 0.999980i \(-0.501990\pi\)
0.949106 + 0.314957i \(0.101990\pi\)
\(524\) 10.4164 0.455043
\(525\) 0 0
\(526\) −2.38197 −0.103859
\(527\) 26.9164 19.5559i 1.17250 0.851869i
\(528\) −0.190983 + 0.587785i −0.00831147 + 0.0255801i
\(529\) 4.90983 15.1109i 0.213471 0.656996i
\(530\) 0 0
\(531\) 5.32624 + 16.3925i 0.231139 + 0.711373i
\(532\) −2.56231 −0.111090
\(533\) 2.30902 + 7.10642i 0.100015 + 0.307813i
\(534\) 9.47214 + 6.88191i 0.409899 + 0.297809i
\(535\) 0 0
\(536\) −4.66312 + 3.38795i −0.201416 + 0.146337i
\(537\) 23.6803 + 17.2048i 1.02188 + 0.742441i
\(538\) −10.5902 7.69421i −0.456575 0.331721i
\(539\) 0.381966 0.277515i 0.0164524 0.0119534i
\(540\) 0 0
\(541\) −23.2254 16.8743i −0.998539 0.725481i −0.0367646 0.999324i \(-0.511705\pi\)
−0.961774 + 0.273843i \(0.911705\pi\)
\(542\) −2.93769 9.04129i −0.126185 0.388357i
\(543\) −56.0689 −2.40615
\(544\) −2.42705 7.46969i −0.104059 0.320261i
\(545\) 0 0
\(546\) −2.42705 + 7.46969i −0.103868 + 0.319673i
\(547\) −3.28115 + 10.0984i −0.140292 + 0.431774i −0.996376 0.0850631i \(-0.972891\pi\)
0.856084 + 0.516837i \(0.172891\pi\)
\(548\) −4.92705 + 3.57971i −0.210473 + 0.152918i
\(549\) −8.27051 −0.352977
\(550\) 0 0
\(551\) 0.450850 0.0192068
\(552\) −13.2082 + 9.59632i −0.562178 + 0.408447i
\(553\) −2.56231 + 7.88597i −0.108960 + 0.335345i
\(554\) −4.23607 + 13.0373i −0.179973 + 0.553901i
\(555\) 0 0
\(556\) 3.19098 + 9.82084i 0.135328 + 0.416496i
\(557\) 10.8885 0.461362 0.230681 0.973029i \(-0.425905\pi\)
0.230681 + 0.973029i \(0.425905\pi\)
\(558\) 5.04508 + 15.5272i 0.213575 + 0.657318i
\(559\) 1.42705 + 1.03681i 0.0603578 + 0.0438525i
\(560\) 0 0
\(561\) −3.92705 + 2.85317i −0.165800 + 0.120461i
\(562\) 15.5172 + 11.2739i 0.654554 + 0.475562i
\(563\) −28.1976 20.4867i −1.18839 0.863413i −0.195293 0.980745i \(-0.562566\pi\)
−0.993093 + 0.117332i \(0.962566\pi\)
\(564\) 12.5902 9.14729i 0.530142 0.385171i
\(565\) 0 0
\(566\) −20.7984 15.1109i −0.874221 0.635159i
\(567\) −5.29180 16.2865i −0.222235 0.683968i
\(568\) −3.00000 −0.125877
\(569\) 6.87132 + 21.1478i 0.288061 + 0.886560i 0.985464 + 0.169882i \(0.0543385\pi\)
−0.697404 + 0.716679i \(0.745661\pi\)
\(570\) 0 0
\(571\) 0.517221 1.59184i 0.0216450 0.0666165i −0.939651 0.342136i \(-0.888850\pi\)
0.961296 + 0.275519i \(0.0888497\pi\)
\(572\) 0.0729490 0.224514i 0.00305015 0.00938740i
\(573\) −37.3885 + 27.1644i −1.56193 + 1.13481i
\(574\) −22.4164 −0.935643
\(575\) 0 0
\(576\) 3.85410 0.160588
\(577\) −34.7877 + 25.2748i −1.44823 + 1.05220i −0.461992 + 0.886884i \(0.652865\pi\)
−0.986240 + 0.165318i \(0.947135\pi\)
\(578\) 13.8090 42.4998i 0.574379 1.76776i
\(579\) −13.4721 + 41.4630i −0.559883 + 1.72314i
\(580\) 0 0
\(581\) 12.4894 + 38.4383i 0.518146 + 1.59469i
\(582\) 27.6525 1.14623
\(583\) 0.111456 + 0.343027i 0.00461604 + 0.0142067i
\(584\) −4.61803 3.35520i −0.191096 0.138839i
\(585\) 0 0
\(586\) −9.35410 + 6.79615i −0.386414 + 0.280746i
\(587\) −9.56231 6.94742i −0.394679 0.286751i 0.372691 0.927955i \(-0.378435\pi\)
−0.767370 + 0.641205i \(0.778435\pi\)
\(588\) −4.23607 3.07768i −0.174692 0.126922i
\(589\) 2.92705 2.12663i 0.120607 0.0876261i
\(590\) 0 0
\(591\) 25.4164 + 18.4661i 1.04549 + 0.759594i
\(592\) −2.26393 6.96767i −0.0930470 0.286369i
\(593\) 47.0132 1.93060 0.965299 0.261145i \(-0.0841002\pi\)
0.965299 + 0.261145i \(0.0841002\pi\)
\(594\) −0.163119 0.502029i −0.00669285 0.0205985i
\(595\) 0 0
\(596\) −0.690983 + 2.12663i −0.0283038 + 0.0871100i
\(597\) −14.2082 + 43.7284i −0.581503 + 1.78968i
\(598\) 5.04508 3.66547i 0.206309 0.149892i
\(599\) −8.94427 −0.365453 −0.182727 0.983164i \(-0.558492\pi\)
−0.182727 + 0.983164i \(0.558492\pi\)
\(600\) 0 0
\(601\) −14.8328 −0.605043 −0.302522 0.953143i \(-0.597828\pi\)
−0.302522 + 0.953143i \(0.597828\pi\)
\(602\) −4.28115 + 3.11044i −0.174487 + 0.126772i
\(603\) 6.86475 21.1275i 0.279554 0.860379i
\(604\) 1.14590 3.52671i 0.0466259 0.143500i
\(605\) 0 0
\(606\) −1.30902 4.02874i −0.0531752 0.163656i
\(607\) 27.1459 1.10182 0.550909 0.834565i \(-0.314281\pi\)
0.550909 + 0.834565i \(0.314281\pi\)
\(608\) −0.263932 0.812299i −0.0107039 0.0329431i
\(609\) 3.35410 + 2.43690i 0.135915 + 0.0987481i
\(610\) 0 0
\(611\) −4.80902 + 3.49396i −0.194552 + 0.141350i
\(612\) 24.4894 + 17.7926i 0.989924 + 0.719222i
\(613\) −33.6246 24.4297i −1.35809 0.986707i −0.998564 0.0535698i \(-0.982940\pi\)
−0.359521 0.933137i \(-0.617060\pi\)
\(614\) 13.8541 10.0656i 0.559106 0.406214i
\(615\) 0 0
\(616\) 0.572949 + 0.416272i 0.0230848 + 0.0167721i
\(617\) 9.38197 + 28.8747i 0.377704 + 1.16245i 0.941636 + 0.336632i \(0.109288\pi\)
−0.563933 + 0.825821i \(0.690712\pi\)
\(618\) 51.9787 2.09089
\(619\) −14.5106 44.6592i −0.583232 1.79500i −0.606257 0.795269i \(-0.707330\pi\)
0.0230252 0.999735i \(-0.492670\pi\)
\(620\) 0 0
\(621\) 4.30902 13.2618i 0.172915 0.532177i
\(622\) −6.51722 + 20.0579i −0.261317 + 0.804250i
\(623\) 10.8541 7.88597i 0.434860 0.315945i
\(624\) −2.61803 −0.104805
\(625\) 0 0
\(626\) −3.56231 −0.142378
\(627\) −0.427051 + 0.310271i −0.0170548 + 0.0123910i
\(628\) 4.80902 14.8006i 0.191901 0.590610i
\(629\) 17.7812 54.7248i 0.708981 2.18202i
\(630\) 0 0
\(631\) 2.72949 + 8.40051i 0.108659 + 0.334419i 0.990572 0.136994i \(-0.0437441\pi\)
−0.881913 + 0.471413i \(0.843744\pi\)
\(632\) −2.76393 −0.109943
\(633\) 9.11803 + 28.0624i 0.362409 + 1.11538i
\(634\) 8.59017 + 6.24112i 0.341159 + 0.247867i
\(635\) 0 0
\(636\) 3.23607 2.35114i 0.128318 0.0932288i
\(637\) 1.61803 + 1.17557i 0.0641088 + 0.0465778i
\(638\) −0.100813 0.0732450i −0.00399123 0.00289980i
\(639\) 9.35410 6.79615i 0.370043 0.268852i
\(640\) 0 0
\(641\) −11.6180 8.44100i −0.458885 0.333399i 0.334209 0.942499i \(-0.391531\pi\)
−0.793094 + 0.609100i \(0.791531\pi\)
\(642\) −8.16312 25.1235i −0.322173 0.991545i
\(643\) 36.2361 1.42901 0.714506 0.699630i \(-0.246652\pi\)
0.714506 + 0.699630i \(0.246652\pi\)
\(644\) 5.78115 + 17.7926i 0.227809 + 0.701125i
\(645\) 0 0
\(646\) 2.07295 6.37988i 0.0815591 0.251013i
\(647\) −2.36475 + 7.27794i −0.0929677 + 0.286125i −0.986719 0.162438i \(-0.948064\pi\)
0.893751 + 0.448563i \(0.148064\pi\)
\(648\) 4.61803 3.35520i 0.181414 0.131805i
\(649\) −1.05573 −0.0414410
\(650\) 0 0
\(651\) 33.2705 1.30397
\(652\) −3.92705 + 2.85317i −0.153795 + 0.111739i
\(653\) −12.5451 + 38.6098i −0.490927 + 1.51092i 0.332282 + 0.943180i \(0.392181\pi\)
−0.823209 + 0.567738i \(0.807819\pi\)
\(654\) −12.1353 + 37.3485i −0.474526 + 1.46044i
\(655\) 0 0
\(656\) −2.30902 7.10642i −0.0901520 0.277459i
\(657\) 22.0000 0.858302
\(658\) −5.51064 16.9600i −0.214827 0.661170i
\(659\) −4.57295 3.32244i −0.178137 0.129424i 0.495144 0.868811i \(-0.335115\pi\)
−0.673281 + 0.739387i \(0.735115\pi\)
\(660\) 0 0
\(661\) −5.07295 + 3.68571i −0.197315 + 0.143358i −0.682056 0.731300i \(-0.738914\pi\)
0.484741 + 0.874658i \(0.338914\pi\)
\(662\) −3.69098 2.68166i −0.143454 0.104226i
\(663\) −16.6353 12.0862i −0.646060 0.469390i
\(664\) −10.8992 + 7.91872i −0.422970 + 0.307306i
\(665\) 0 0
\(666\) 22.8435 + 16.5967i 0.885166 + 0.643111i
\(667\) −1.01722 3.13068i −0.0393870 0.121221i
\(668\) −15.6180 −0.604280
\(669\) 7.28115 + 22.4091i 0.281506 + 0.866385i
\(670\) 0 0
\(671\) 0.156541 0.481784i 0.00604320 0.0185991i
\(672\) 2.42705 7.46969i 0.0936255 0.288150i
\(673\) −1.00000 + 0.726543i −0.0385472 + 0.0280062i −0.606892 0.794784i \(-0.707584\pi\)
0.568345 + 0.822790i \(0.307584\pi\)
\(674\) 31.4164 1.21011
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 8.59017 6.24112i 0.330147 0.239866i −0.410346 0.911930i \(-0.634592\pi\)
0.740493 + 0.672064i \(0.234592\pi\)
\(678\) −6.66312 + 20.5070i −0.255896 + 0.787565i
\(679\) 9.79180 30.1360i 0.375775 1.15652i
\(680\) 0 0
\(681\) 12.4271 + 38.2465i 0.476206 + 1.46561i
\(682\) −1.00000 −0.0382920
\(683\) −10.3090 31.7279i −0.394464 1.21403i −0.929379 0.369128i \(-0.879656\pi\)
0.534915 0.844906i \(-0.320344\pi\)
\(684\) 2.66312 + 1.93487i 0.101827 + 0.0739816i
\(685\) 0 0
\(686\) 12.1353 8.81678i 0.463326 0.336626i
\(687\) −37.1976 27.0256i −1.41918 1.03109i
\(688\) −1.42705 1.03681i −0.0544058 0.0395281i
\(689\) −1.23607 + 0.898056i −0.0470904 + 0.0342132i
\(690\) 0 0
\(691\) −1.02786 0.746787i −0.0391018 0.0284091i 0.568063 0.822985i \(-0.307693\pi\)
−0.607164 + 0.794576i \(0.707693\pi\)
\(692\) −1.00000 3.07768i −0.0380143 0.116996i
\(693\) −2.72949 −0.103685
\(694\) 3.06231 + 9.42481i 0.116244 + 0.357761i
\(695\) 0 0
\(696\) −0.427051 + 1.31433i −0.0161873 + 0.0498195i
\(697\) 18.1353 55.8146i 0.686922 2.11413i
\(698\) 17.9894 13.0700i 0.680907 0.494708i
\(699\) −72.5410 −2.74375
\(700\) 0 0
\(701\) −4.18034 −0.157889 −0.0789446 0.996879i \(-0.525155\pi\)
−0.0789446 + 0.996879i \(0.525155\pi\)
\(702\) 1.80902 1.31433i 0.0682769 0.0496061i
\(703\) 1.93363 5.95110i 0.0729282 0.224450i
\(704\) −0.0729490 + 0.224514i −0.00274937 + 0.00846169i
\(705\) 0 0
\(706\) 5.18034 + 15.9434i 0.194965 + 0.600040i
\(707\) −4.85410 −0.182557
\(708\) 3.61803 + 11.1352i 0.135974 + 0.418485i
\(709\) −6.28115 4.56352i −0.235894 0.171387i 0.463558 0.886066i \(-0.346572\pi\)
−0.699452 + 0.714680i \(0.746572\pi\)
\(710\) 0 0
\(711\) 8.61803 6.26137i 0.323202 0.234820i
\(712\) 3.61803 + 2.62866i 0.135592 + 0.0985130i
\(713\) −21.3713 15.5272i −0.800362 0.581497i
\(714\) 49.9058 36.2587i 1.86768 1.35695i
\(715\) 0 0
\(716\) 9.04508 + 6.57164i 0.338031 + 0.245594i
\(717\) −14.6353 45.0427i −0.546564 1.68215i
\(718\) 3.09017 0.115324
\(719\) −8.19098 25.2093i −0.305472 0.940147i −0.979501 0.201441i \(-0.935438\pi\)
0.674028 0.738705i \(-0.264562\pi\)
\(720\) 0 0
\(721\) 18.4058 56.6471i 0.685466 2.10965i
\(722\) −5.64590 + 17.3763i −0.210119 + 0.646678i
\(723\) −28.3435 + 20.5927i −1.05410 + 0.765852i
\(724\) −21.4164 −0.795935
\(725\) 0 0
\(726\) −28.6525 −1.06339
\(727\) −23.1803 + 16.8415i −0.859711 + 0.624617i −0.927806 0.373062i \(-0.878308\pi\)
0.0680952 + 0.997679i \(0.478308\pi\)
\(728\) −0.927051 + 2.85317i −0.0343588 + 0.105745i
\(729\) −12.2254 + 37.6260i −0.452794 + 1.39356i
\(730\) 0 0
\(731\) −4.28115 13.1760i −0.158344 0.487333i
\(732\) −5.61803 −0.207649
\(733\) 12.2918 + 37.8303i 0.454008 + 1.39729i 0.872296 + 0.488978i \(0.162630\pi\)
−0.418288 + 0.908314i \(0.637370\pi\)
\(734\) −25.5172 18.5393i −0.941858 0.684300i
\(735\) 0 0
\(736\) −5.04508 + 3.66547i −0.185964 + 0.135111i
\(737\) 1.10081 + 0.799788i 0.0405490 + 0.0294606i
\(738\) 23.2984 + 16.9273i 0.857625 + 0.623101i
\(739\) −24.2705 + 17.6336i −0.892805 + 0.648661i −0.936608 0.350379i \(-0.886053\pi\)
0.0438028 + 0.999040i \(0.486053\pi\)
\(740\) 0 0
\(741\) −1.80902 1.31433i −0.0664559 0.0482830i
\(742\) −1.41641 4.35926i −0.0519980 0.160033i
\(743\) 18.2705 0.670280 0.335140 0.942168i \(-0.391216\pi\)
0.335140 + 0.942168i \(0.391216\pi\)
\(744\) 3.42705 + 10.5474i 0.125642 + 0.386686i
\(745\) 0 0
\(746\) 5.01722 15.4414i 0.183694 0.565350i
\(747\) 16.0451 49.3817i 0.587059 1.80678i
\(748\) −1.50000 + 1.08981i −0.0548454 + 0.0398475i
\(749\) −30.2705 −1.10606
\(750\) 0 0
\(751\) 1.14590 0.0418144 0.0209072 0.999781i \(-0.493345\pi\)
0.0209072 + 0.999781i \(0.493345\pi\)
\(752\) 4.80902 3.49396i 0.175367 0.127411i
\(753\) 18.7533 57.7167i 0.683408 2.10331i
\(754\) 0.163119 0.502029i 0.00594044 0.0182828i
\(755\) 0 0
\(756\) 2.07295 + 6.37988i 0.0753924 + 0.232034i
\(757\) −10.4164 −0.378591 −0.189295 0.981920i \(-0.560620\pi\)
−0.189295 + 0.981920i \(0.560620\pi\)
\(758\) 0.163119 + 0.502029i 0.00592475 + 0.0182345i
\(759\) 3.11803 + 2.26538i 0.113177 + 0.0822282i
\(760\) 0 0
\(761\) 30.6803 22.2906i 1.11216 0.808033i 0.129159 0.991624i \(-0.458772\pi\)
0.983003 + 0.183591i \(0.0587723\pi\)
\(762\) −26.4164 19.1926i −0.956965 0.695276i
\(763\) 36.4058 + 26.4503i 1.31798 + 0.957566i
\(764\) −14.2812 + 10.3759i −0.516674 + 0.375386i
\(765\) 0 0
\(766\) −3.50000 2.54290i −0.126460 0.0918787i
\(767\) −1.38197 4.25325i −0.0498999 0.153576i
\(768\) 2.61803 0.0944702
\(769\) −7.23607 22.2703i −0.260939 0.803089i −0.992601 0.121421i \(-0.961255\pi\)
0.731662 0.681668i \(-0.238745\pi\)
\(770\) 0 0
\(771\) 13.5451 41.6875i 0.487814 1.50134i
\(772\) −5.14590 + 15.8374i −0.185205 + 0.570002i
\(773\) 5.01722 3.64522i 0.180457 0.131110i −0.493890 0.869525i \(-0.664425\pi\)
0.674347 + 0.738415i \(0.264425\pi\)
\(774\) 6.79837 0.244363
\(775\) 0 0
\(776\) 10.5623 0.379165
\(777\) 46.5517 33.8218i 1.67003 1.21335i
\(778\) −10.2639 + 31.5891i −0.367980 + 1.13253i
\(779\) 1.97214 6.06961i 0.0706591 0.217466i
\(780\) 0 0
\(781\) 0.218847 + 0.673542i 0.00783096 + 0.0241012i
\(782\) −48.9787 −1.75148
\(783\) −0.364745 1.12257i −0.0130349 0.0401174i
\(784\) −1.61803 1.17557i −0.0577869 0.0419847i
\(785\) 0 0
\(786\) −22.0623 + 16.0292i −0.786936 + 0.571743i
\(787\) 12.4721 + 9.06154i 0.444584 + 0.323009i 0.787454 0.616374i \(-0.211399\pi\)
−0.342870 + 0.939383i \(0.611399\pi\)
\(788\) 9.70820 + 7.05342i 0.345840 + 0.251268i
\(789\) 5.04508 3.66547i 0.179610 0.130494i
\(790\) 0 0
\(791\) 19.9894 + 14.5231i 0.710740 + 0.516383i
\(792\) −0.281153 0.865300i −0.00999034 0.0307471i
\(793\) 2.14590 0.0762031
\(794\) 1.78115 + 5.48183i 0.0632108 + 0.194543i
\(795\) 0 0
\(796\) −5.42705 + 16.7027i −0.192357 + 0.592013i
\(797\) −1.04508 + 3.21644i −0.0370188 + 0.113932i −0.967858 0.251496i \(-0.919077\pi\)
0.930840 + 0.365428i \(0.119077\pi\)
\(798\) 5.42705 3.94298i 0.192116 0.139580i
\(799\) 46.6869 1.65166
\(800\) 0 0
\(801\) −17.2361 −0.609007
\(802\) −6.61803 + 4.80828i −0.233691 + 0.169786i
\(803\) −0.416408 + 1.28157i −0.0146947 + 0.0452257i
\(804\) 4.66312 14.3516i 0.164456 0.506142i
\(805\) 0 0
\(806\) −1.30902 4.02874i −0.0461082 0.141906i
\(807\) 34.2705 1.20638
\(808\) −0.500000 1.53884i −0.0175899 0.0541363i
\(809\) −1.80902 1.31433i −0.0636017 0.0462093i 0.555530 0.831496i \(-0.312515\pi\)
−0.619132 + 0.785287i \(0.712515\pi\)
\(810\) 0 0
\(811\) −18.6525 + 13.5518i −0.654977 + 0.475869i −0.864963 0.501836i \(-0.832658\pi\)
0.209986 + 0.977704i \(0.432658\pi\)
\(812\) 1.28115 + 0.930812i 0.0449597 + 0.0326651i
\(813\) 20.1353 + 14.6291i 0.706174 + 0.513066i
\(814\) −1.39919 + 1.01657i −0.0490415 + 0.0356307i
\(815\) 0 0
\(816\) 16.6353 + 12.0862i 0.582350 + 0.423102i
\(817\) −0.465558 1.43284i −0.0162878 0.0501287i
\(818\) 6.70820 0.234547
\(819\) −3.57295 10.9964i −0.124849 0.384246i
\(820\) 0 0
\(821\) −9.31966 + 28.6830i −0.325258 + 1.00104i 0.646065 + 0.763282i \(0.276413\pi\)
−0.971324 + 0.237760i \(0.923587\pi\)
\(822\) 4.92705 15.1639i 0.171851 0.528902i
\(823\) 26.5623 19.2986i 0.925904 0.672708i −0.0190827 0.999818i \(-0.506075\pi\)
0.944986 + 0.327109i \(0.106075\pi\)
\(824\) 19.8541 0.691650
\(825\) 0 0
\(826\) 13.4164 0.466817
\(827\) 19.4443 14.1271i 0.676144 0.491247i −0.195932 0.980617i \(-0.562773\pi\)
0.872076 + 0.489370i \(0.162773\pi\)
\(828\) 7.42705 22.8581i 0.258108 0.794374i
\(829\) 8.21478 25.2825i 0.285311 0.878097i −0.700994 0.713167i \(-0.747260\pi\)
0.986305 0.164930i \(-0.0527399\pi\)
\(830\) 0 0
\(831\) −11.0902 34.1320i −0.384714 1.18403i
\(832\) −1.00000 −0.0346688
\(833\) −4.85410 14.9394i −0.168185 0.517619i
\(834\) −21.8713 15.8904i −0.757342 0.550241i
\(835\) 0 0
\(836\) −0.163119 + 0.118513i −0.00564159 + 0.00409885i
\(837\) −7.66312 5.56758i −0.264876 0.192444i
\(838\) −22.0344 16.0090i −0.761167 0.553020i
\(839\) −20.4271 + 14.8411i −0.705220 + 0.512372i −0.881628 0.471945i \(-0.843552\pi\)
0.176408 + 0.984317i \(0.443552\pi\)
\(840\) 0 0
\(841\) 23.2361 + 16.8820i 0.801244 + 0.582138i
\(842\) −3.79180 11.6699i −0.130674 0.402173i
\(843\) −50.2148 −1.72949
\(844\) 3.48278 + 10.7189i 0.119882 + 0.368959i
\(845\) 0 0
\(846\) −7.07953 + 21.7885i −0.243399 + 0.749106i
\(847\) −10.1459 + 31.2259i −0.348617 + 1.07293i
\(848\) 1.23607 0.898056i 0.0424467 0.0308394i
\(849\) 67.3050 2.30990
\(850\) 0 0
\(851\) −45.6869 −1.56613
\(852\) 6.35410 4.61653i 0.217688 0.158160i
\(853\) 7.68034 23.6377i 0.262970 0.809338i −0.729184 0.684317i \(-0.760100\pi\)
0.992154 0.125021i \(-0.0398997\pi\)
\(854\) −1.98936 + 6.12261i −0.0680744 + 0.209511i
\(855\) 0 0
\(856\) −3.11803 9.59632i −0.106572 0.327996i
\(857\) −35.3394 −1.20717 −0.603585 0.797298i \(-0.706262\pi\)
−0.603585 + 0.797298i \(0.706262\pi\)
\(858\) 0.190983 + 0.587785i 0.00652005 + 0.0200667i
\(859\) 31.8713 + 23.1559i 1.08744 + 0.790068i 0.978964 0.204031i \(-0.0654045\pi\)
0.108471 + 0.994100i \(0.465404\pi\)
\(860\) 0 0
\(861\) 47.4787 34.4953i 1.61807 1.17560i
\(862\) 25.9443 + 18.8496i 0.883665 + 0.642020i
\(863\) −5.47214 3.97574i −0.186274 0.135336i 0.490740 0.871306i \(-0.336726\pi\)
−0.677014 + 0.735970i \(0.736726\pi\)
\(864\) −1.80902 + 1.31433i −0.0615440 + 0.0447143i
\(865\) 0 0
\(866\) 18.8992 + 13.7311i 0.642221 + 0.466601i
\(867\) 36.1525 + 111.266i 1.22780 + 3.77879i
\(868\) 12.7082 0.431345
\(869\) 0.201626 + 0.620541i 0.00683970 + 0.0210504i
\(870\) 0 0
\(871\) −1.78115 + 5.48183i −0.0603521 + 0.185745i
\(872\) −4.63525 + 14.2658i −0.156970 + 0.483103i
\(873\) −32.9336 + 23.9277i −1.11463 + 0.809829i
\(874\) −5.32624 −0.180163
\(875\) 0 0
\(876\) 14.9443 0.504920
\(877\) 19.8713 14.4374i 0.671007 0.487515i −0.199355 0.979927i \(-0.563885\pi\)
0.870362 + 0.492412i \(0.163885\pi\)
\(878\) −1.74671 + 5.37582i −0.0589486 + 0.181425i
\(879\) 9.35410 28.7890i 0.315506 0.971028i
\(880\) 0 0
\(881\) 4.88854 + 15.0454i 0.164699 + 0.506892i 0.999014 0.0443963i \(-0.0141364\pi\)
−0.834315 + 0.551288i \(0.814136\pi\)
\(882\) 7.70820 0.259549
\(883\) −5.77458 17.7723i −0.194330 0.598086i −0.999984 0.00569940i \(-0.998186\pi\)
0.805654 0.592387i \(-0.201814\pi\)
\(884\) −6.35410 4.61653i −0.213712 0.155271i
\(885\) 0 0
\(886\) −6.00000 + 4.35926i −0.201574 + 0.146452i
\(887\) 8.75329 + 6.35964i 0.293907 + 0.213536i 0.724960 0.688791i \(-0.241858\pi\)
−0.431054 + 0.902326i \(0.641858\pi\)
\(888\) 15.5172 + 11.2739i 0.520724 + 0.378328i
\(889\) −30.2705 + 21.9928i −1.01524 + 0.737615i
\(890\) 0 0
\(891\) −1.09017 0.792055i −0.0365221 0.0265348i
\(892\) 2.78115 + 8.55951i 0.0931199 + 0.286594i
\(893\) 5.07701 0.169896
\(894\) −1.80902 5.56758i −0.0605026 0.186208i
\(895\) 0 0
\(896\) 0.927051 2.85317i 0.0309706 0.0953177i
\(897\) −5.04508 + 15.5272i −0.168450 + 0.518437i
\(898\) −11.2812 + 8.19624i −0.376457 + 0.273512i
\(899\) −2.23607 −0.0745770
\(900\) 0 0
\(901\) 12.0000 0.399778
\(902\) −1.42705 + 1.03681i −0.0475156 + 0.0345221i
\(903\) 4.28115 13.1760i 0.142468 0.438471i
\(904\) −2.54508 + 7.83297i −0.0846483 + 0.260521i
\(905\) 0 0
\(906\) 3.00000 + 9.23305i 0.0996683 + 0.306748i
\(907\) −23.3820 −0.776385 −0.388193 0.921578i \(-0.626901\pi\)
−0.388193 + 0.921578i \(0.626901\pi\)
\(908\) 4.74671 + 14.6089i 0.157525 + 0.484813i
\(909\) 5.04508 + 3.66547i 0.167335 + 0.121576i
\(910\) 0 0
\(911\) −8.42705 + 6.12261i −0.279201 + 0.202851i −0.718569 0.695456i \(-0.755202\pi\)
0.439368 + 0.898307i \(0.355202\pi\)
\(912\) 1.80902 + 1.31433i 0.0599025 + 0.0435217i
\(913\) 2.57295 + 1.86936i 0.0851522 + 0.0618667i
\(914\) −9.07295 + 6.59188i −0.300106 + 0.218040i
\(915\) 0 0
\(916\) −14.2082 10.3229i −0.469452 0.341077i
\(917\) 9.65654 + 29.7198i 0.318887 + 0.981434i
\(918\) −17.5623 −0.579642
\(919\) 7.92705 + 24.3970i 0.261489 + 0.804781i 0.992481 + 0.122395i \(0.0390576\pi\)
−0.730992 + 0.682386i \(0.760942\pi\)
\(920\) 0 0
\(921\) −13.8541 + 42.6385i −0.456508 + 1.40499i
\(922\) 8.70820 26.8011i 0.286789 0.882647i
\(923\) −2.42705 + 1.76336i −0.0798874 + 0.0580416i
\(924\) −1.85410 −0.0609955
\(925\) 0 0
\(926\) −11.9787 −0.393645
\(927\) −61.9058 + 44.9772i −2.03325 + 1.47724i
\(928\) −0.163119 + 0.502029i −0.00535464 + 0.0164799i
\(929\) −5.28773 + 16.2740i −0.173485 + 0.533931i −0.999561 0.0296271i \(-0.990568\pi\)
0.826076 + 0.563558i \(0.190568\pi\)
\(930\) 0 0
\(931\) −0.527864 1.62460i −0.0173000 0.0532441i
\(932\) −27.7082 −0.907612
\(933\) −17.0623 52.5124i −0.558595 1.71918i
\(934\) 2.57295 + 1.86936i 0.0841895 + 0.0611672i
\(935\) 0 0
\(936\) 3.11803 2.26538i 0.101916 0.0740464i
\(937\) −18.5451 13.4738i −0.605842 0.440170i 0.242106 0.970250i \(-0.422162\pi\)
−0.847948 + 0.530080i \(0.822162\pi\)
\(938\) −13.9894 10.1639i −0.456769 0.331862i
\(939\) 7.54508 5.48183i 0.246225 0.178893i
\(940\) 0 0
\(941\) 9.39919 + 6.82891i 0.306405 + 0.222616i 0.730352 0.683071i \(-0.239356\pi\)
−0.423948 + 0.905687i \(0.639356\pi\)
\(942\) 12.5902 + 38.7486i 0.410210 + 1.26250i
\(943\) −46.5967 −1.51740
\(944\) 1.38197 + 4.25325i 0.0449792 + 0.138432i
\(945\) 0 0
\(946\) −0.128677 + 0.396027i −0.00418365 + 0.0128760i
\(947\) 12.8607 39.5811i 0.417916 1.28621i −0.491701 0.870764i \(-0.663625\pi\)
0.909617 0.415449i \(-0.136375\pi\)
\(948\) 5.85410 4.25325i 0.190132 0.138139i
\(949\) −5.70820 −0.185296
\(950\) 0 0
\(951\) −27.7984 −0.901424
\(952\) 19.0623 13.8496i 0.617813 0.448867i
\(953\) −13.0967 + 40.3076i −0.424245 + 1.30569i 0.479470 + 0.877558i \(0.340829\pi\)
−0.903715 + 0.428134i \(0.859171\pi\)
\(954\) −1.81966 + 5.60034i −0.0589137 + 0.181318i
\(955\) 0 0
\(956\) −5.59017 17.2048i −0.180799 0.556442i
\(957\) 0.326238 0.0105458
\(958\) −12.2984 37.8505i −0.397342 1.22289i
\(959\) −14.7812 10.7391i −0.477308 0.346785i
\(960\) 0 0
\(961\) 10.5623 7.67396i 0.340720 0.247547i
\(962\) −5.92705 4.30625i −0.191096 0.138839i
\(963\) 31.4615 + 22.8581i 1.01383 + 0.736592i
\(964\) −10.8262 + 7.86572i −0.348690 + 0.253338i
\(965\) 0 0
\(966\) −39.6246 28.7890i −1.27490 0.926270i
\(967\) −8.38197 25.7970i −0.269546 0.829577i −0.990611 0.136710i \(-0.956347\pi\)
0.721065 0.692867i \(-0.243653\pi\)
\(968\) −10.9443 −0.351762
\(969\) 5.42705 + 16.7027i 0.174342 + 0.536569i
\(970\) 0 0
\(971\) −16.0902 + 49.5205i −0.516358 + 1.58919i 0.264439 + 0.964402i \(0.414813\pi\)
−0.780797 + 0.624785i \(0.785187\pi\)
\(972\) −6.69098 + 20.5927i −0.214613 + 0.660512i
\(973\) −25.0623 + 18.2088i −0.803461 + 0.583748i
\(974\) 18.1246 0.580750
\(975\) 0 0
\(976\) −2.14590 −0.0686885
\(977\) −21.0451 + 15.2901i −0.673292 + 0.489175i −0.871126 0.491060i \(-0.836609\pi\)
0.197834 + 0.980236i \(0.436609\pi\)
\(978\) 3.92705 12.0862i 0.125573 0.386475i
\(979\) 0.326238 1.00406i 0.0104266 0.0320898i
\(980\) 0 0
\(981\) −17.8647 54.9820i −0.570377 1.75544i
\(982\) 14.7639 0.471136
\(983\) 14.3647 + 44.2101i 0.458164 + 1.41008i 0.867380 + 0.497647i \(0.165802\pi\)
−0.409216 + 0.912438i \(0.634198\pi\)
\(984\) 15.8262 + 11.4984i 0.504522 + 0.366557i
\(985\) 0 0
\(986\) −3.35410 + 2.43690i −0.106816 + 0.0776066i
\(987\) 37.7705 + 27.4419i 1.20225 + 0.873485i
\(988\) −0.690983 0.502029i −0.0219831 0.0159717i
\(989\) −8.89919 + 6.46564i −0.282978 + 0.205595i
\(990\) 0 0
\(991\) −42.4336 30.8298i −1.34795 0.979342i −0.999111 0.0421589i \(-0.986576\pi\)
−0.348838 0.937183i \(-0.613424\pi\)
\(992\) 1.30902 + 4.02874i 0.0415613 + 0.127913i
\(993\) 11.9443 0.379040
\(994\) −2.78115 8.55951i −0.0882128 0.271491i
\(995\) 0 0
\(996\) 10.8992 33.5442i 0.345354 1.06289i
\(997\) 16.4549 50.6430i 0.521132 1.60388i −0.250707 0.968063i \(-0.580663\pi\)
0.771839 0.635818i \(-0.219337\pi\)
\(998\) −33.0517 + 24.0134i −1.04623 + 0.760132i
\(999\) −16.3820 −0.518302
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 250.2.d.a.51.1 4
5.2 odd 4 250.2.e.b.199.1 8
5.3 odd 4 250.2.e.b.199.2 8
5.4 even 2 50.2.d.a.11.1 4
15.14 odd 2 450.2.h.a.361.1 4
20.19 odd 2 400.2.u.c.161.1 4
25.3 odd 20 1250.2.b.b.1249.2 4
25.4 even 10 1250.2.a.a.1.1 2
25.9 even 10 50.2.d.a.41.1 yes 4
25.12 odd 20 250.2.e.b.49.2 8
25.13 odd 20 250.2.e.b.49.1 8
25.16 even 5 inner 250.2.d.a.201.1 4
25.21 even 5 1250.2.a.d.1.2 2
25.22 odd 20 1250.2.b.b.1249.3 4
75.59 odd 10 450.2.h.a.91.1 4
100.59 odd 10 400.2.u.c.241.1 4
100.71 odd 10 10000.2.a.a.1.1 2
100.79 odd 10 10000.2.a.n.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.2.d.a.11.1 4 5.4 even 2
50.2.d.a.41.1 yes 4 25.9 even 10
250.2.d.a.51.1 4 1.1 even 1 trivial
250.2.d.a.201.1 4 25.16 even 5 inner
250.2.e.b.49.1 8 25.13 odd 20
250.2.e.b.49.2 8 25.12 odd 20
250.2.e.b.199.1 8 5.2 odd 4
250.2.e.b.199.2 8 5.3 odd 4
400.2.u.c.161.1 4 20.19 odd 2
400.2.u.c.241.1 4 100.59 odd 10
450.2.h.a.91.1 4 75.59 odd 10
450.2.h.a.361.1 4 15.14 odd 2
1250.2.a.a.1.1 2 25.4 even 10
1250.2.a.d.1.2 2 25.21 even 5
1250.2.b.b.1249.2 4 25.3 odd 20
1250.2.b.b.1249.3 4 25.22 odd 20
10000.2.a.a.1.1 2 100.71 odd 10
10000.2.a.n.1.2 2 100.79 odd 10