Properties

Label 250.2.e.b.199.2
Level $250$
Weight $2$
Character 250.199
Analytic conductor $1.996$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [250,2,Mod(49,250)]
 
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([7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("250.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 250 = 2 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 250.e (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: \(1.99626005053\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) 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: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 199.2
Root \(0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 250.199
Dual form 250.2.e.b.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.587785 + 0.809017i) q^{2} +(2.48990 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.809017 + 2.48990i) q^{6} -3.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(3.11803 + 2.26538i) q^{9} +O(q^{10})\) \(q+(0.587785 + 0.809017i) q^{2} +(2.48990 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.809017 + 2.48990i) q^{6} -3.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(3.11803 + 2.26538i) q^{9} +(0.190983 - 0.138757i) q^{11} +(-1.53884 + 2.11803i) q^{12} +(-0.587785 + 0.809017i) q^{13} +(2.42705 - 1.76336i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-7.46969 + 2.42705i) q^{17} +3.85410i q^{18} +(0.263932 + 0.812299i) q^{19} +(2.42705 - 7.46969i) q^{21} +(0.224514 + 0.0729490i) q^{22} +(-3.66547 - 5.04508i) q^{23} -2.61803 q^{24} -1.00000 q^{26} +(1.31433 + 1.80902i) q^{27} +(2.85317 + 0.927051i) q^{28} +(0.163119 - 0.502029i) q^{29} +(1.30902 + 4.02874i) q^{31} -1.00000i q^{32} +(0.587785 - 0.190983i) q^{33} +(-6.35410 - 4.61653i) q^{34} +(-3.11803 + 2.26538i) q^{36} +(4.30625 - 5.92705i) q^{37} +(-0.502029 + 0.690983i) q^{38} +(-2.11803 + 1.53884i) q^{39} +(6.04508 + 4.39201i) q^{41} +(7.46969 - 2.42705i) q^{42} +1.76393i q^{43} +(0.0729490 + 0.224514i) q^{44} +(1.92705 - 5.93085i) q^{46} +(5.65334 + 1.83688i) q^{47} +(-1.53884 - 2.11803i) q^{48} -2.00000 q^{49} -20.5623 q^{51} +(-0.587785 - 0.809017i) q^{52} +(-1.45309 - 0.472136i) q^{53} +(-0.690983 + 2.12663i) q^{54} +(0.927051 + 2.85317i) q^{56} +2.23607i q^{57} +(0.502029 - 0.163119i) q^{58} +(3.61803 + 2.62866i) q^{59} +(1.73607 - 1.26133i) q^{61} +(-2.48990 + 3.42705i) q^{62} +(6.79615 - 9.35410i) q^{63} +(0.809017 - 0.587785i) q^{64} +(0.500000 + 0.363271i) q^{66} +(5.48183 - 1.78115i) q^{67} -7.85410i q^{68} +(-5.04508 - 15.5272i) q^{69} +(-0.927051 + 2.85317i) q^{71} +(-3.66547 - 1.19098i) q^{72} +(-3.35520 - 4.61803i) q^{73} +7.32624 q^{74} -0.854102 q^{76} +(-0.416272 - 0.572949i) q^{77} +(-2.48990 - 0.809017i) q^{78} +(0.854102 - 2.62866i) q^{79} +(-1.76393 - 5.42882i) q^{81} +7.47214i q^{82} +(-12.8128 + 4.16312i) q^{83} +(6.35410 + 4.61653i) q^{84} +(-1.42705 + 1.03681i) q^{86} +(0.812299 - 1.11803i) q^{87} +(-0.138757 + 0.190983i) q^{88} +(-3.61803 + 2.62866i) q^{89} +(2.42705 + 1.76336i) q^{91} +(5.93085 - 1.92705i) q^{92} +11.0902i q^{93} +(1.83688 + 5.65334i) q^{94} +(0.809017 - 2.48990i) q^{96} +(-10.0453 - 3.26393i) q^{97} +(-1.17557 - 1.61803i) q^{98} +0.909830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} + 2 q^{6} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{4} + 2 q^{6} + 16 q^{9} + 6 q^{11} + 6 q^{14} - 2 q^{16} + 20 q^{19} + 6 q^{21} - 12 q^{24} - 8 q^{26} - 30 q^{29} + 6 q^{31} - 24 q^{34} - 16 q^{36} - 8 q^{39} + 26 q^{41} + 14 q^{44} + 2 q^{46} - 16 q^{49} - 84 q^{51} - 10 q^{54} - 6 q^{56} + 20 q^{59} - 4 q^{61} + 2 q^{64} + 4 q^{66} - 18 q^{69} + 6 q^{71} - 4 q^{74} + 20 q^{76} - 20 q^{79} - 32 q^{81} + 24 q^{84} + 2 q^{86} - 20 q^{89} + 6 q^{91} + 46 q^{94} + 2 q^{96} + 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.587785 + 0.809017i 0.415627 + 0.572061i
\(3\) 2.48990 + 0.809017i 1.43754 + 0.467086i 0.921131 0.389254i \(-0.127267\pi\)
0.516413 + 0.856340i \(0.327267\pi\)
\(4\) −0.309017 + 0.951057i −0.154508 + 0.475528i
\(5\) 0 0
\(6\) 0.809017 + 2.48990i 0.330280 + 1.01650i
\(7\) 3.00000i 1.13389i −0.823754 0.566947i \(-0.808125\pi\)
0.823754 0.566947i \(-0.191875\pi\)
\(8\) −0.951057 + 0.309017i −0.336249 + 0.109254i
\(9\) 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 \(0.288669\pi\)
\(12\) −1.53884 + 2.11803i −0.444225 + 0.611424i
\(13\) −0.587785 + 0.809017i −0.163022 + 0.224381i −0.882711 0.469916i \(-0.844284\pi\)
0.719689 + 0.694297i \(0.244284\pi\)
\(14\) 2.42705 1.76336i 0.648657 0.471277i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) −7.46969 + 2.42705i −1.81167 + 0.588646i −0.811677 + 0.584106i \(0.801445\pi\)
−0.999990 + 0.00454037i \(0.998555\pi\)
\(18\) 3.85410i 0.908421i
\(19\) 0.263932 + 0.812299i 0.0605502 + 0.186354i 0.976756 0.214353i \(-0.0687644\pi\)
−0.916206 + 0.400707i \(0.868764\pi\)
\(20\) 0 0
\(21\) 2.42705 7.46969i 0.529626 1.63002i
\(22\) 0.224514 + 0.0729490i 0.0478665 + 0.0155528i
\(23\) −3.66547 5.04508i −0.764303 1.05197i −0.996844 0.0793863i \(-0.974704\pi\)
0.232541 0.972587i \(-0.425296\pi\)
\(24\) −2.61803 −0.534404
\(25\) 0 0
\(26\) −1.00000 −0.196116
\(27\) 1.31433 + 1.80902i 0.252942 + 0.348145i
\(28\) 2.85317 + 0.927051i 0.539198 + 0.175196i
\(29\) 0.163119 0.502029i 0.0302904 0.0932244i −0.934768 0.355258i \(-0.884393\pi\)
0.965059 + 0.262033i \(0.0843931\pi\)
\(30\) 0 0
\(31\) 1.30902 + 4.02874i 0.235106 + 0.723583i 0.997107 + 0.0760071i \(0.0242172\pi\)
−0.762001 + 0.647576i \(0.775783\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.587785 0.190983i 0.102320 0.0332459i
\(34\) −6.35410 4.61653i −1.08972 0.791728i
\(35\) 0 0
\(36\) −3.11803 + 2.26538i −0.519672 + 0.377564i
\(37\) 4.30625 5.92705i 0.707944 0.974401i −0.291895 0.956450i \(-0.594286\pi\)
0.999839 0.0179508i \(-0.00571422\pi\)
\(38\) −0.502029 + 0.690983i −0.0814398 + 0.112092i
\(39\) −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 \(0.501692\pi\)
\(42\) 7.46969 2.42705i 1.15260 0.374502i
\(43\) 1.76393i 0.268997i 0.990914 + 0.134499i \(0.0429424\pi\)
−0.990914 + 0.134499i \(0.957058\pi\)
\(44\) 0.0729490 + 0.224514i 0.0109975 + 0.0338468i
\(45\) 0 0
\(46\) 1.92705 5.93085i 0.284128 0.874457i
\(47\) 5.65334 + 1.83688i 0.824624 + 0.267937i 0.690779 0.723066i \(-0.257268\pi\)
0.133845 + 0.991002i \(0.457268\pi\)
\(48\) −1.53884 2.11803i −0.222113 0.305712i
\(49\) −2.00000 −0.285714
\(50\) 0 0
\(51\) −20.5623 −2.87930
\(52\) −0.587785 0.809017i −0.0815111 0.112190i
\(53\) −1.45309 0.472136i −0.199597 0.0648529i 0.207513 0.978232i \(-0.433463\pi\)
−0.407109 + 0.913379i \(0.633463\pi\)
\(54\) −0.690983 + 2.12663i −0.0940309 + 0.289397i
\(55\) 0 0
\(56\) 0.927051 + 2.85317i 0.123882 + 0.381271i
\(57\) 2.23607i 0.296174i
\(58\) 0.502029 0.163119i 0.0659196 0.0214186i
\(59\) 3.61803 + 2.62866i 0.471028 + 0.342222i 0.797842 0.602867i \(-0.205975\pi\)
−0.326814 + 0.945089i \(0.605975\pi\)
\(60\) 0 0
\(61\) 1.73607 1.26133i 0.222281 0.161496i −0.471072 0.882095i \(-0.656133\pi\)
0.693353 + 0.720598i \(0.256133\pi\)
\(62\) −2.48990 + 3.42705i −0.316217 + 0.435236i
\(63\) 6.79615 9.35410i 0.856235 1.17851i
\(64\) 0.809017 0.587785i 0.101127 0.0734732i
\(65\) 0 0
\(66\) 0.500000 + 0.363271i 0.0615457 + 0.0447156i
\(67\) 5.48183 1.78115i 0.669712 0.217602i 0.0456261 0.998959i \(-0.485472\pi\)
0.624085 + 0.781356i \(0.285472\pi\)
\(68\) 7.85410i 0.952450i
\(69\) −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 \(0.156968\pi\)
\(72\) −3.66547 1.19098i −0.431980 0.140359i
\(73\) −3.35520 4.61803i −0.392696 0.540500i 0.566196 0.824271i \(-0.308415\pi\)
−0.958892 + 0.283771i \(0.908415\pi\)
\(74\) 7.32624 0.851658
\(75\) 0 0
\(76\) −0.854102 −0.0979722
\(77\) −0.416272 0.572949i −0.0474386 0.0652936i
\(78\) −2.48990 0.809017i −0.281925 0.0916031i
\(79\) 0.854102 2.62866i 0.0960940 0.295747i −0.891443 0.453132i \(-0.850307\pi\)
0.987537 + 0.157385i \(0.0503065\pi\)
\(80\) 0 0
\(81\) −1.76393 5.42882i −0.195992 0.603203i
\(82\) 7.47214i 0.825159i
\(83\) −12.8128 + 4.16312i −1.40638 + 0.456962i −0.911249 0.411855i \(-0.864881\pi\)
−0.495134 + 0.868817i \(0.664881\pi\)
\(84\) 6.35410 + 4.61653i 0.693289 + 0.503704i
\(85\) 0 0
\(86\) −1.42705 + 1.03681i −0.153883 + 0.111802i
\(87\) 0.812299 1.11803i 0.0870876 0.119866i
\(88\) −0.138757 + 0.190983i −0.0147916 + 0.0203589i
\(89\) −3.61803 + 2.62866i −0.383511 + 0.278637i −0.762791 0.646645i \(-0.776172\pi\)
0.379280 + 0.925282i \(0.376172\pi\)
\(90\) 0 0
\(91\) 2.42705 + 1.76336i 0.254424 + 0.184850i
\(92\) 5.93085 1.92705i 0.618334 0.200909i
\(93\) 11.0902i 1.15000i
\(94\) 1.83688 + 5.65334i 0.189460 + 0.583097i
\(95\) 0 0
\(96\) 0.809017 2.48990i 0.0825700 0.254124i
\(97\) −10.0453 3.26393i −1.01995 0.331402i −0.249141 0.968467i \(-0.580148\pi\)
−0.770810 + 0.637065i \(0.780148\pi\)
\(98\) −1.17557 1.61803i −0.118751 0.163446i
\(99\) 0.909830 0.0914414
\(100\) 0 0
\(101\) −1.61803 −0.161000 −0.0805002 0.996755i \(-0.525652\pi\)
−0.0805002 + 0.996755i \(0.525652\pi\)
\(102\) −12.0862 16.6353i −1.19671 1.64714i
\(103\) 18.8824 + 6.13525i 1.86054 + 0.604525i 0.994525 + 0.104499i \(0.0333238\pi\)
0.866010 + 0.500026i \(0.166676\pi\)
\(104\) 0.309017 0.951057i 0.0303016 0.0932588i
\(105\) 0 0
\(106\) −0.472136 1.45309i −0.0458579 0.141136i
\(107\) 10.0902i 0.975454i 0.872996 + 0.487727i \(0.162174\pi\)
−0.872996 + 0.487727i \(0.837826\pi\)
\(108\) −2.12663 + 0.690983i −0.204635 + 0.0664899i
\(109\) −12.1353 8.81678i −1.16235 0.844494i −0.172274 0.985049i \(-0.555111\pi\)
−0.990073 + 0.140555i \(0.955111\pi\)
\(110\) 0 0
\(111\) 15.5172 11.2739i 1.47283 1.07007i
\(112\) −1.76336 + 2.42705i −0.166621 + 0.229335i
\(113\) −4.84104 + 6.66312i −0.455407 + 0.626814i −0.973548 0.228481i \(-0.926624\pi\)
0.518142 + 0.855295i \(0.326624\pi\)
\(114\) −1.80902 + 1.31433i −0.169430 + 0.123098i
\(115\) 0 0
\(116\) 0.427051 + 0.310271i 0.0396507 + 0.0288079i
\(117\) −3.66547 + 1.19098i −0.338873 + 0.110106i
\(118\) 4.47214i 0.411693i
\(119\) 7.28115 + 22.4091i 0.667462 + 2.05424i
\(120\) 0 0
\(121\) −3.38197 + 10.4086i −0.307451 + 0.946238i
\(122\) 2.04087 + 0.663119i 0.184772 + 0.0600360i
\(123\) 11.4984 + 15.8262i 1.03678 + 1.42700i
\(124\) −4.23607 −0.380410
\(125\) 0 0
\(126\) 11.5623 1.03005
\(127\) 7.33094 + 10.0902i 0.650516 + 0.895358i 0.999121 0.0419116i \(-0.0133448\pi\)
−0.348606 + 0.937269i \(0.613345\pi\)
\(128\) 0.951057 + 0.309017i 0.0840623 + 0.0273135i
\(129\) −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 \(0.749624\pi\)
\(132\) 0.618034i 0.0537930i
\(133\) 2.43690 0.791796i 0.211306 0.0686574i
\(134\) 4.66312 + 3.38795i 0.402832 + 0.292675i
\(135\) 0 0
\(136\) 6.35410 4.61653i 0.544860 0.395864i
\(137\) −3.57971 + 4.92705i −0.305835 + 0.420946i −0.934077 0.357072i \(-0.883775\pi\)
0.628241 + 0.778018i \(0.283775\pi\)
\(138\) 9.59632 13.2082i 0.816893 1.12436i
\(139\) 8.35410 6.06961i 0.708586 0.514818i −0.174131 0.984722i \(-0.555712\pi\)
0.882717 + 0.469905i \(0.155712\pi\)
\(140\) 0 0
\(141\) 12.5902 + 9.14729i 1.06028 + 0.770341i
\(142\) −2.85317 + 0.927051i −0.239433 + 0.0777964i
\(143\) 0.236068i 0.0197410i
\(144\) −1.19098 3.66547i −0.0992486 0.305456i
\(145\) 0 0
\(146\) 1.76393 5.42882i 0.145984 0.449293i
\(147\) −4.97980 1.61803i −0.410727 0.133453i
\(148\) 4.30625 + 5.92705i 0.353972 + 0.487201i
\(149\) 2.23607 0.183186 0.0915929 0.995797i \(-0.470804\pi\)
0.0915929 + 0.995797i \(0.470804\pi\)
\(150\) 0 0
\(151\) 3.70820 0.301769 0.150885 0.988551i \(-0.451788\pi\)
0.150885 + 0.988551i \(0.451788\pi\)
\(152\) −0.502029 0.690983i −0.0407199 0.0560461i
\(153\) −28.7890 9.35410i −2.32745 0.756234i
\(154\) 0.218847 0.673542i 0.0176352 0.0542756i
\(155\) 0 0
\(156\) −0.809017 2.48990i −0.0647732 0.199351i
\(157\) 15.5623i 1.24201i −0.783808 0.621004i \(-0.786725\pi\)
0.783808 0.621004i \(-0.213275\pi\)
\(158\) 2.62866 0.854102i 0.209125 0.0679487i
\(159\) −3.23607 2.35114i −0.256637 0.186458i
\(160\) 0 0
\(161\) −15.1353 + 10.9964i −1.19283 + 0.866638i
\(162\) 3.35520 4.61803i 0.263609 0.362827i
\(163\) 2.85317 3.92705i 0.223477 0.307590i −0.682525 0.730862i \(-0.739118\pi\)
0.906003 + 0.423271i \(0.139118\pi\)
\(164\) −6.04508 + 4.39201i −0.472042 + 0.342958i
\(165\) 0 0
\(166\) −10.8992 7.91872i −0.845941 0.614612i
\(167\) −14.8536 + 4.82624i −1.14941 + 0.373466i −0.820920 0.571043i \(-0.806539\pi\)
−0.328488 + 0.944508i \(0.606539\pi\)
\(168\) 7.85410i 0.605957i
\(169\) 3.70820 + 11.4127i 0.285246 + 0.877898i
\(170\) 0 0
\(171\) −1.01722 + 3.13068i −0.0777888 + 0.239409i
\(172\) −1.67760 0.545085i −0.127916 0.0415623i
\(173\) 1.90211 + 2.61803i 0.144615 + 0.199045i 0.875180 0.483798i \(-0.160743\pi\)
−0.730565 + 0.682843i \(0.760743\pi\)
\(174\) 1.38197 0.104767
\(175\) 0 0
\(176\) −0.236068 −0.0177943
\(177\) 6.88191 + 9.47214i 0.517276 + 0.711969i
\(178\) −4.25325 1.38197i −0.318795 0.103583i
\(179\) 3.45492 10.6331i 0.258232 0.794758i −0.734943 0.678129i \(-0.762791\pi\)
0.993176 0.116629i \(-0.0372089\pi\)
\(180\) 0 0
\(181\) −6.61803 20.3682i −0.491915 1.51396i −0.821710 0.569905i \(-0.806980\pi\)
0.329796 0.944052i \(-0.393020\pi\)
\(182\) 3.00000i 0.222375i
\(183\) 5.34307 1.73607i 0.394971 0.128334i
\(184\) 5.04508 + 3.66547i 0.371929 + 0.270222i
\(185\) 0 0
\(186\) −8.97214 + 6.51864i −0.657869 + 0.477970i
\(187\) −1.08981 + 1.50000i −0.0796951 + 0.109691i
\(188\) −3.49396 + 4.80902i −0.254823 + 0.350734i
\(189\) 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 \(0.920504\pi\)
\(192\) 2.48990 0.809017i 0.179693 0.0583858i
\(193\) 16.6525i 1.19867i −0.800498 0.599336i \(-0.795431\pi\)
0.800498 0.599336i \(-0.204569\pi\)
\(194\) −3.26393 10.0453i −0.234337 0.721214i
\(195\) 0 0
\(196\) 0.618034 1.90211i 0.0441453 0.135865i
\(197\) 11.4127 + 3.70820i 0.813120 + 0.264199i 0.685919 0.727678i \(-0.259401\pi\)
0.127201 + 0.991877i \(0.459401\pi\)
\(198\) 0.534785 + 0.736068i 0.0380055 + 0.0523101i
\(199\) 17.5623 1.24496 0.622479 0.782636i \(-0.286125\pi\)
0.622479 + 0.782636i \(0.286125\pi\)
\(200\) 0 0
\(201\) 15.0902 1.06438
\(202\) −0.951057 1.30902i −0.0669161 0.0921021i
\(203\) −1.50609 0.489357i −0.105706 0.0343461i
\(204\) 6.35410 19.5559i 0.444876 1.36919i
\(205\) 0 0
\(206\) 6.13525 + 18.8824i 0.427463 + 1.31560i
\(207\) 24.0344i 1.67051i
\(208\) 0.951057 0.309017i 0.0659439 0.0214265i
\(209\) 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 \(0.426816\pi\)
\(212\) 0.898056 1.23607i 0.0616787 0.0848935i
\(213\) −4.61653 + 6.35410i −0.316319 + 0.435376i
\(214\) −8.16312 + 5.93085i −0.558019 + 0.405425i
\(215\) 0 0
\(216\) −1.80902 1.31433i −0.123088 0.0894287i
\(217\) 12.0862 3.92705i 0.820466 0.266586i
\(218\) 15.0000i 1.01593i
\(219\) −4.61803 14.2128i −0.312058 0.960415i
\(220\) 0 0
\(221\) 2.42705 7.46969i 0.163261 0.502466i
\(222\) 18.2416 + 5.92705i 1.22430 + 0.397798i
\(223\) −5.29007 7.28115i −0.354249 0.487582i 0.594286 0.804254i \(-0.297435\pi\)
−0.948535 + 0.316672i \(0.897435\pi\)
\(224\) −3.00000 −0.200446
\(225\) 0 0
\(226\) −8.23607 −0.547855
\(227\) 9.02878 + 12.4271i 0.599261 + 0.824812i 0.995640 0.0932746i \(-0.0297334\pi\)
−0.396379 + 0.918087i \(0.629733\pi\)
\(228\) −2.12663 0.690983i −0.140839 0.0457615i
\(229\) −5.42705 + 16.7027i −0.358630 + 1.10375i 0.595245 + 0.803544i \(0.297055\pi\)
−0.953875 + 0.300204i \(0.902945\pi\)
\(230\) 0 0
\(231\) −0.572949 1.76336i −0.0376973 0.116020i
\(232\) 0.527864i 0.0346560i
\(233\) 26.3521 8.56231i 1.72638 0.560935i 0.733463 0.679730i \(-0.237903\pi\)
0.992919 + 0.118795i \(0.0379030\pi\)
\(234\) −3.11803 2.26538i −0.203832 0.148093i
\(235\) 0 0
\(236\) −3.61803 + 2.62866i −0.235514 + 0.171111i
\(237\) 4.25325 5.85410i 0.276279 0.380265i
\(238\) −13.8496 + 19.0623i −0.897735 + 1.23563i
\(239\) −14.6353 + 10.6331i −0.946676 + 0.687800i −0.950018 0.312194i \(-0.898936\pi\)
0.00334240 + 0.999994i \(0.498936\pi\)
\(240\) 0 0
\(241\) −10.8262 7.86572i −0.697379 0.506676i 0.181698 0.983354i \(-0.441841\pi\)
−0.879078 + 0.476679i \(0.841841\pi\)
\(242\) −10.4086 + 3.38197i −0.669092 + 0.217401i
\(243\) 21.6525i 1.38901i
\(244\) 0.663119 + 2.04087i 0.0424518 + 0.130653i
\(245\) 0 0
\(246\) −6.04508 + 18.6049i −0.385421 + 1.18620i
\(247\) −0.812299 0.263932i −0.0516854 0.0167936i
\(248\) −2.48990 3.42705i −0.158109 0.217618i
\(249\) −35.2705 −2.23518
\(250\) 0 0
\(251\) 23.1803 1.46313 0.731565 0.681772i \(-0.238790\pi\)
0.731565 + 0.681772i \(0.238790\pi\)
\(252\) 6.79615 + 9.35410i 0.428117 + 0.589253i
\(253\) −1.40008 0.454915i −0.0880226 0.0286003i
\(254\) −3.85410 + 11.8617i −0.241828 + 0.744270i
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 16.7426i 1.04438i −0.852830 0.522189i \(-0.825116\pi\)
0.852830 0.522189i \(-0.174884\pi\)
\(258\) −4.39201 + 1.42705i −0.273435 + 0.0888443i
\(259\) −17.7812 12.9188i −1.10487 0.802733i
\(260\) 0 0
\(261\) 1.64590 1.19581i 0.101879 0.0740191i
\(262\) −6.12261 + 8.42705i −0.378256 + 0.520625i
\(263\) −1.40008 + 1.92705i −0.0863329 + 0.118827i −0.849999 0.526785i \(-0.823397\pi\)
0.763666 + 0.645612i \(0.223397\pi\)
\(264\) −0.500000 + 0.363271i −0.0307729 + 0.0223578i
\(265\) 0 0
\(266\) 2.07295 + 1.50609i 0.127101 + 0.0923440i
\(267\) −11.1352 + 3.61803i −0.681461 + 0.221420i
\(268\) 5.76393i 0.352088i
\(269\) −4.04508 12.4495i −0.246633 0.759059i −0.995364 0.0961842i \(-0.969336\pi\)
0.748730 0.662875i \(-0.230664\pi\)
\(270\) 0 0
\(271\) −2.93769 + 9.04129i −0.178452 + 0.549219i −0.999774 0.0212453i \(-0.993237\pi\)
0.821322 + 0.570465i \(0.193237\pi\)
\(272\) 7.46969 + 2.42705i 0.452917 + 0.147162i
\(273\) 4.61653 + 6.35410i 0.279405 + 0.384568i
\(274\) −6.09017 −0.367921
\(275\) 0 0
\(276\) 16.3262 0.982724
\(277\) −8.05748 11.0902i −0.484127 0.666344i 0.495164 0.868799i \(-0.335108\pi\)
−0.979291 + 0.202456i \(0.935108\pi\)
\(278\) 9.82084 + 3.19098i 0.589015 + 0.191382i
\(279\) −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 \(-0.293872\pi\)
\(282\) 15.5623i 0.926722i
\(283\) −24.4500 + 7.94427i −1.45340 + 0.472238i −0.926047 0.377409i \(-0.876815\pi\)
−0.527352 + 0.849647i \(0.676815\pi\)
\(284\) −2.42705 1.76336i −0.144019 0.104636i
\(285\) 0 0
\(286\) −0.190983 + 0.138757i −0.0112931 + 0.00820489i
\(287\) 13.1760 18.1353i 0.777757 1.07049i
\(288\) 2.26538 3.11803i 0.133489 0.183732i
\(289\) 36.1525 26.2663i 2.12662 1.54508i
\(290\) 0 0
\(291\) −22.3713 16.2537i −1.31143 0.952810i
\(292\) 5.42882 1.76393i 0.317698 0.103226i
\(293\) 11.5623i 0.675477i 0.941240 + 0.337739i \(0.109662\pi\)
−0.941240 + 0.337739i \(0.890338\pi\)
\(294\) −1.61803 4.97980i −0.0943657 0.290428i
\(295\) 0 0
\(296\) −2.26393 + 6.96767i −0.131588 + 0.404987i
\(297\) 0.502029 + 0.163119i 0.0291307 + 0.00946512i
\(298\) 1.31433 + 1.80902i 0.0761370 + 0.104794i
\(299\) 6.23607 0.360641
\(300\) 0 0
\(301\) 5.29180 0.305014
\(302\) 2.17963 + 3.00000i 0.125423 + 0.172631i
\(303\) −4.02874 1.30902i −0.231445 0.0752011i
\(304\) 0.263932 0.812299i 0.0151375 0.0465886i
\(305\) 0 0
\(306\) −9.35410 28.7890i −0.534738 1.64576i
\(307\) 17.1246i 0.977353i 0.872465 + 0.488677i \(0.162520\pi\)
−0.872465 + 0.488677i \(0.837480\pi\)
\(308\) 0.673542 0.218847i 0.0383786 0.0124700i
\(309\) 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 \(0.0959794\pi\)
\(312\) 1.53884 2.11803i 0.0871198 0.119910i
\(313\) −2.09387 + 2.88197i −0.118353 + 0.162898i −0.864083 0.503350i \(-0.832101\pi\)
0.745730 + 0.666248i \(0.232101\pi\)
\(314\) 12.5902 9.14729i 0.710504 0.516212i
\(315\) 0 0
\(316\) 2.23607 + 1.62460i 0.125789 + 0.0913908i
\(317\) −10.0984 + 3.28115i −0.567180 + 0.184288i −0.578549 0.815647i \(-0.696381\pi\)
0.0113694 + 0.999935i \(0.496381\pi\)
\(318\) 4.00000i 0.224309i
\(319\) −0.0385072 0.118513i −0.00215599 0.00663545i
\(320\) 0 0
\(321\) −8.16312 + 25.1235i −0.455621 + 1.40226i
\(322\) −17.7926 5.78115i −0.991541 0.322171i
\(323\) −3.94298 5.42705i −0.219393 0.301969i
\(324\) 5.70820 0.317122
\(325\) 0 0
\(326\) 4.85410 0.268844
\(327\) −23.0826 31.7705i −1.27647 1.75691i
\(328\) −7.10642 2.30902i −0.392387 0.127494i
\(329\) 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 \(0.859984\pi\)
\(332\) 13.4721i 0.739380i
\(333\) 26.8541 8.72542i 1.47160 0.478150i
\(334\) −12.6353 9.18005i −0.691370 0.502310i
\(335\) 0 0
\(336\) −6.35410 + 4.61653i −0.346645 + 0.251852i
\(337\) −18.4661 + 25.4164i −1.00591 + 1.38452i −0.0842863 + 0.996442i \(0.526861\pi\)
−0.921626 + 0.388078i \(0.873139\pi\)
\(338\) −7.05342 + 9.70820i −0.383656 + 0.528057i
\(339\) −17.4443 + 12.6740i −0.947443 + 0.688357i
\(340\) 0 0
\(341\) 0.809017 + 0.587785i 0.0438107 + 0.0318304i
\(342\) −3.13068 + 1.01722i −0.169288 + 0.0550050i
\(343\) 15.0000i 0.809924i
\(344\) −0.545085 1.67760i −0.0293890 0.0904501i
\(345\) 0 0
\(346\) −1.00000 + 3.07768i −0.0537603 + 0.165457i
\(347\) −9.42481 3.06231i −0.505950 0.164393i 0.0449095 0.998991i \(-0.485700\pi\)
−0.550860 + 0.834598i \(0.685700\pi\)
\(348\) 0.812299 + 1.11803i 0.0435438 + 0.0599329i
\(349\) 22.2361 1.19027 0.595135 0.803626i \(-0.297099\pi\)
0.595135 + 0.803626i \(0.297099\pi\)
\(350\) 0 0
\(351\) −2.23607 −0.119352
\(352\) −0.138757 0.190983i −0.00739579 0.0101794i
\(353\) 15.9434 + 5.18034i 0.848584 + 0.275722i 0.700853 0.713306i \(-0.252803\pi\)
0.147731 + 0.989028i \(0.452803\pi\)
\(354\) −3.61803 + 11.1352i −0.192296 + 0.591827i
\(355\) 0 0
\(356\) −1.38197 4.25325i −0.0732441 0.225422i
\(357\) 61.6869i 3.26482i
\(358\) 10.6331 3.45492i 0.561979 0.182598i
\(359\) 2.50000 + 1.81636i 0.131945 + 0.0958636i 0.651800 0.758391i \(-0.274014\pi\)
−0.519855 + 0.854254i \(0.674014\pi\)
\(360\) 0 0
\(361\) 14.7812 10.7391i 0.777955 0.565218i
\(362\) 12.5882 17.3262i 0.661624 0.910647i
\(363\) −16.8415 + 23.1803i −0.883950 + 1.21665i
\(364\) −2.42705 + 1.76336i −0.127212 + 0.0924250i
\(365\) 0 0
\(366\) 4.54508 + 3.30220i 0.237575 + 0.172609i
\(367\) 29.9973 9.74671i 1.56585 0.508774i 0.607484 0.794332i \(-0.292179\pi\)
0.958362 + 0.285557i \(0.0921788\pi\)
\(368\) 6.23607i 0.325078i
\(369\) 8.89919 + 27.3889i 0.463273 + 1.42581i
\(370\) 0 0
\(371\) −1.41641 + 4.35926i −0.0735362 + 0.226321i
\(372\) −10.5474 3.42705i −0.546856 0.177684i
\(373\) −9.54332 13.1353i −0.494134 0.680118i 0.487009 0.873397i \(-0.338088\pi\)
−0.981144 + 0.193279i \(0.938088\pi\)
\(374\) −1.85410 −0.0958733
\(375\) 0 0
\(376\) −5.94427 −0.306552
\(377\) 0.310271 + 0.427051i 0.0159798 + 0.0219942i
\(378\) 6.37988 + 2.07295i 0.328146 + 0.106621i
\(379\) −0.163119 + 0.502029i −0.00837886 + 0.0257875i −0.955159 0.296095i \(-0.904316\pi\)
0.946780 + 0.321882i \(0.104316\pi\)
\(380\) 0 0
\(381\) 10.0902 + 31.0543i 0.516935 + 1.59096i
\(382\) 17.6525i 0.903179i
\(383\) −4.11450 + 1.33688i −0.210241 + 0.0683114i −0.412244 0.911073i \(-0.635255\pi\)
0.202003 + 0.979385i \(0.435255\pi\)
\(384\) 2.11803 + 1.53884i 0.108085 + 0.0785287i
\(385\) 0 0
\(386\) 13.4721 9.78808i 0.685714 0.498200i
\(387\) −3.99598 + 5.50000i −0.203127 + 0.279581i
\(388\) 6.20837 8.54508i 0.315182 0.433811i
\(389\) −26.8713 + 19.5232i −1.36243 + 0.989863i −0.364144 + 0.931343i \(0.618638\pi\)
−0.998286 + 0.0585208i \(0.981362\pi\)
\(390\) 0 0
\(391\) 39.6246 + 28.7890i 2.00390 + 1.45592i
\(392\) 1.90211 0.618034i 0.0960712 0.0312154i
\(393\) 27.2705i 1.37562i
\(394\) 3.70820 + 11.4127i 0.186817 + 0.574962i
\(395\) 0 0
\(396\) −0.281153 + 0.865300i −0.0141285 + 0.0434830i
\(397\) −5.48183 1.78115i −0.275125 0.0893935i 0.168205 0.985752i \(-0.446203\pi\)
−0.443330 + 0.896359i \(0.646203\pi\)
\(398\) 10.3229 + 14.2082i 0.517438 + 0.712193i
\(399\) 6.70820 0.335830
\(400\) 0 0
\(401\) 8.18034 0.408507 0.204253 0.978918i \(-0.434523\pi\)
0.204253 + 0.978918i \(0.434523\pi\)
\(402\) 8.86978 + 12.2082i 0.442384 + 0.608890i
\(403\) −4.02874 1.30902i −0.200686 0.0652068i
\(404\) 0.500000 1.53884i 0.0248759 0.0765602i
\(405\) 0 0
\(406\) −0.489357 1.50609i −0.0242864 0.0747458i
\(407\) 1.72949i 0.0857276i
\(408\) 19.5559 6.35410i 0.968162 0.314575i
\(409\) 5.42705 + 3.94298i 0.268350 + 0.194968i 0.713820 0.700329i \(-0.246963\pi\)
−0.445470 + 0.895297i \(0.646963\pi\)
\(410\) 0 0
\(411\) −12.8992 + 9.37181i −0.636270 + 0.462277i
\(412\) −11.6699 + 16.0623i −0.574937 + 0.791333i
\(413\) 7.88597 10.8541i 0.388043 0.534095i
\(414\) 19.4443 14.1271i 0.955634 0.694309i
\(415\) 0 0
\(416\) 0.809017 + 0.587785i 0.0396653 + 0.0288185i
\(417\) 25.7113 8.35410i 1.25909 0.409102i
\(418\) 0.201626i 0.00986186i
\(419\) −8.41641 25.9030i −0.411168 1.26545i −0.915633 0.402014i \(-0.868310\pi\)
0.504465 0.863432i \(-0.331690\pi\)
\(420\) 0 0
\(421\) −3.79180 + 11.6699i −0.184801 + 0.568758i −0.999945 0.0104998i \(-0.996658\pi\)
0.815144 + 0.579258i \(0.196658\pi\)
\(422\) −10.7189 3.48278i −0.521787 0.169539i
\(423\) 13.4661 + 18.5344i 0.654742 + 0.901175i
\(424\) 1.52786 0.0741996
\(425\) 0 0
\(426\) −7.85410 −0.380532
\(427\) −3.78398 5.20820i −0.183120 0.252043i
\(428\) −9.59632 3.11803i −0.463856 0.150716i
\(429\) −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 \(-0.380920\pi\)
\(432\) 2.23607i 0.107583i
\(433\) 22.2173 7.21885i 1.06770 0.346916i 0.278106 0.960550i \(-0.410293\pi\)
0.789590 + 0.613635i \(0.210293\pi\)
\(434\) 10.2812 + 7.46969i 0.493511 + 0.358557i
\(435\) 0 0
\(436\) 12.1353 8.81678i 0.581173 0.422247i
\(437\) 3.13068 4.30902i 0.149761 0.206128i
\(438\) 8.78402 12.0902i 0.419717 0.577691i
\(439\) −4.57295 + 3.32244i −0.218255 + 0.158572i −0.691541 0.722337i \(-0.743068\pi\)
0.473286 + 0.880909i \(0.343068\pi\)
\(440\) 0 0
\(441\) −6.23607 4.53077i −0.296956 0.215751i
\(442\) 7.46969 2.42705i 0.355297 0.115443i
\(443\) 7.41641i 0.352364i 0.984358 + 0.176182i \(0.0563748\pi\)
−0.984358 + 0.176182i \(0.943625\pi\)
\(444\) 5.92705 + 18.2416i 0.281285 + 0.865707i
\(445\) 0 0
\(446\) 2.78115 8.55951i 0.131691 0.405304i
\(447\) 5.56758 + 1.80902i 0.263338 + 0.0855636i
\(448\) −1.76336 2.42705i −0.0833107 0.114667i
\(449\) −13.9443 −0.658071 −0.329035 0.944318i \(-0.606724\pi\)
−0.329035 + 0.944318i \(0.606724\pi\)
\(450\) 0 0
\(451\) 1.76393 0.0830603
\(452\) −4.84104 6.66312i −0.227703 0.313407i
\(453\) 9.23305 + 3.00000i 0.433807 + 0.140952i
\(454\) −4.74671 + 14.6089i −0.222774 + 0.685628i
\(455\) 0 0
\(456\) −0.690983 2.12663i −0.0323582 0.0995884i
\(457\) 11.2148i 0.524605i −0.964986 0.262303i \(-0.915518\pi\)
0.964986 0.262303i \(-0.0844819\pi\)
\(458\) −16.7027 + 5.42705i −0.780468 + 0.253589i
\(459\) −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 \(0.527856\pi\)
\(462\) 1.08981 1.50000i 0.0507027 0.0697863i
\(463\) −7.04091 + 9.69098i −0.327219 + 0.450378i −0.940654 0.339367i \(-0.889787\pi\)
0.613435 + 0.789745i \(0.289787\pi\)
\(464\) −0.427051 + 0.310271i −0.0198253 + 0.0144040i
\(465\) 0 0
\(466\) 22.4164 + 16.2865i 1.03842 + 0.754456i
\(467\) −3.02468 + 0.982779i −0.139966 + 0.0454776i −0.378162 0.925739i \(-0.623444\pi\)
0.238196 + 0.971217i \(0.423444\pi\)
\(468\) 3.85410i 0.178156i
\(469\) −5.34346 16.4455i −0.246738 0.759381i
\(470\) 0 0
\(471\) 12.5902 38.7486i 0.580124 1.78544i
\(472\) −4.25325 1.38197i −0.195772 0.0636101i
\(473\) 0.244758 + 0.336881i 0.0112540 + 0.0154898i
\(474\) 7.23607 0.332364
\(475\) 0 0
\(476\) −23.5623 −1.07998
\(477\) −3.46120 4.76393i −0.158477 0.218125i
\(478\) −17.2048 5.59017i −0.786928 0.255688i
\(479\) 12.2984 37.8505i 0.561927 1.72943i −0.114983 0.993368i \(-0.536681\pi\)
0.676910 0.736066i \(-0.263319\pi\)
\(480\) 0 0
\(481\) 2.26393 + 6.96767i 0.103226 + 0.317698i
\(482\) 13.3820i 0.609532i
\(483\) −46.5815 + 15.1353i −2.11953 + 0.688678i
\(484\) −8.85410 6.43288i −0.402459 0.292404i
\(485\) 0 0
\(486\) 17.5172 12.7270i 0.794597 0.577309i
\(487\) −10.6534 + 14.6631i −0.482751 + 0.664449i −0.979031 0.203713i \(-0.934699\pi\)
0.496280 + 0.868163i \(0.334699\pi\)
\(488\) −1.26133 + 1.73607i −0.0570976 + 0.0785881i
\(489\) 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 \(0.808109\pi\)
\(492\) −18.6049 + 6.04508i −0.838772 + 0.272533i
\(493\) 4.14590i 0.186722i
\(494\) −0.263932 0.812299i −0.0118749 0.0365471i
\(495\) 0 0
\(496\) 1.30902 4.02874i 0.0587766 0.180896i
\(497\) 8.55951 + 2.78115i 0.383946 + 0.124752i
\(498\) −20.7315 28.5344i −0.929000 1.27866i
\(499\) −40.8541 −1.82888 −0.914440 0.404721i \(-0.867369\pi\)
−0.914440 + 0.404721i \(0.867369\pi\)
\(500\) 0 0
\(501\) −40.8885 −1.82677
\(502\) 13.6251 + 18.7533i 0.608116 + 0.837000i
\(503\) −7.13918 2.31966i −0.318320 0.103429i 0.145499 0.989358i \(-0.453521\pi\)
−0.463819 + 0.885930i \(0.653521\pi\)
\(504\) −3.57295 + 10.9964i −0.159152 + 0.489819i
\(505\) 0 0
\(506\) −0.454915 1.40008i −0.0202234 0.0622413i
\(507\) 31.4164i 1.39525i
\(508\) −11.8617 + 3.85410i −0.526278 + 0.170998i
\(509\) −10.5902 7.69421i −0.469401 0.341040i 0.327807 0.944745i \(-0.393690\pi\)
−0.797208 + 0.603705i \(0.793690\pi\)
\(510\) 0 0
\(511\) −13.8541 + 10.0656i −0.612869 + 0.445276i
\(512\) −0.587785 + 0.809017i −0.0259767 + 0.0357538i
\(513\) −1.12257 + 1.54508i −0.0495627 + 0.0682172i
\(514\) 13.5451 9.84108i 0.597448 0.434071i
\(515\) 0 0
\(516\) −3.73607 2.71441i −0.164471 0.119495i
\(517\) 1.33457 0.433629i 0.0586944 0.0190710i
\(518\) 21.9787i 0.965689i
\(519\) 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 \(-0.151689\pi\)
\(522\) 1.93487 + 0.628677i 0.0846869 + 0.0275164i
\(523\) 15.6659 + 21.5623i 0.685023 + 0.942854i 0.999980 0.00625211i \(-0.00199012\pi\)
−0.314957 + 0.949106i \(0.601990\pi\)
\(524\) −10.4164 −0.455043
\(525\) 0 0
\(526\) −2.38197 −0.103859
\(527\) −19.5559 26.9164i −0.851869 1.17250i
\(528\) −0.587785 0.190983i −0.0255801 0.00831147i
\(529\) −4.90983 + 15.1109i −0.213471 + 0.656996i
\(530\) 0 0
\(531\) 5.32624 + 16.3925i 0.231139 + 0.711373i
\(532\) 2.56231i 0.111090i
\(533\) −7.10642 + 2.30902i −0.307813 + 0.100015i
\(534\) −9.47214 6.88191i −0.409899 0.297809i
\(535\) 0 0
\(536\) −4.66312 + 3.38795i −0.201416 + 0.146337i
\(537\) 17.2048 23.6803i 0.742441 1.02188i
\(538\) 7.69421 10.5902i 0.331721 0.456575i
\(539\) −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 \(0.911705\pi\)
\(542\) −9.04129 + 2.93769i −0.388357 + 0.126185i
\(543\) 56.0689i 2.40615i
\(544\) 2.42705 + 7.46969i 0.104059 + 0.320261i
\(545\) 0 0
\(546\) −2.42705 + 7.46969i −0.103868 + 0.319673i
\(547\) 10.0984 + 3.28115i 0.431774 + 0.140292i 0.516837 0.856084i \(-0.327109\pi\)
−0.0850631 + 0.996376i \(0.527109\pi\)
\(548\) −3.57971 4.92705i −0.152918 0.210473i
\(549\) 8.27051 0.352977
\(550\) 0 0
\(551\) 0.450850 0.0192068
\(552\) 9.59632 + 13.2082i 0.408447 + 0.562178i
\(553\) −7.88597 2.56231i −0.335345 0.108960i
\(554\) 4.23607 13.0373i 0.179973 0.553901i
\(555\) 0 0
\(556\) 3.19098 + 9.82084i 0.135328 + 0.416496i
\(557\) 10.8885i 0.461362i −0.973029 0.230681i \(-0.925905\pi\)
0.973029 0.230681i \(-0.0740954\pi\)
\(558\) −15.5272 + 5.04508i −0.657318 + 0.213575i
\(559\) −1.42705 1.03681i −0.0603578 0.0438525i
\(560\) 0 0
\(561\) −3.92705 + 2.85317i −0.165800 + 0.120461i
\(562\) 11.2739 15.5172i 0.475562 0.654554i
\(563\) 20.4867 28.1976i 0.863413 1.18839i −0.117332 0.993093i \(-0.537434\pi\)
0.980745 0.195293i \(-0.0625657\pi\)
\(564\) −12.5902 + 9.14729i −0.530142 + 0.385171i
\(565\) 0 0
\(566\) −20.7984 15.1109i −0.874221 0.635159i
\(567\) −16.2865 + 5.29180i −0.683968 + 0.222235i
\(568\) 3.00000i 0.125877i
\(569\) −6.87132 21.1478i −0.288061 0.886560i −0.985464 0.169882i \(-0.945661\pi\)
0.697404 0.716679i \(-0.254339\pi\)
\(570\) 0 0
\(571\) 0.517221 1.59184i 0.0216450 0.0666165i −0.939651 0.342136i \(-0.888850\pi\)
0.961296 + 0.275519i \(0.0888497\pi\)
\(572\) −0.224514 0.0729490i −0.00938740 0.00305015i
\(573\) −27.1644 37.3885i −1.13481 1.56193i
\(574\) 22.4164 0.935643
\(575\) 0 0
\(576\) 3.85410 0.160588
\(577\) 25.2748 + 34.7877i 1.05220 + 1.44823i 0.886884 + 0.461992i \(0.152865\pi\)
0.165318 + 0.986240i \(0.447135\pi\)
\(578\) 42.4998 + 13.8090i 1.76776 + 0.574379i
\(579\) 13.4721 41.4630i 0.559883 1.72314i
\(580\) 0 0
\(581\) 12.4894 + 38.4383i 0.518146 + 1.59469i
\(582\) 27.6525i 1.14623i
\(583\) −0.343027 + 0.111456i −0.0142067 + 0.00461604i
\(584\) 4.61803 + 3.35520i 0.191096 + 0.138839i
\(585\) 0 0
\(586\) −9.35410 + 6.79615i −0.386414 + 0.280746i
\(587\) −6.94742 + 9.56231i −0.286751 + 0.394679i −0.927955 0.372691i \(-0.878435\pi\)
0.641205 + 0.767370i \(0.278435\pi\)
\(588\) 3.07768 4.23607i 0.126922 0.174692i
\(589\) −2.92705 + 2.12663i −0.120607 + 0.0876261i
\(590\) 0 0
\(591\) 25.4164 + 18.4661i 1.04549 + 0.759594i
\(592\) −6.96767 + 2.26393i −0.286369 + 0.0930470i
\(593\) 47.0132i 1.93060i 0.261145 + 0.965299i \(0.415900\pi\)
−0.261145 + 0.965299i \(0.584100\pi\)
\(594\) 0.163119 + 0.502029i 0.00669285 + 0.0205985i
\(595\) 0 0
\(596\) −0.690983 + 2.12663i −0.0283038 + 0.0871100i
\(597\) 43.7284 + 14.2082i 1.78968 + 0.581503i
\(598\) 3.66547 + 5.04508i 0.149892 + 0.206309i
\(599\) 8.94427 0.365453 0.182727 0.983164i \(-0.441508\pi\)
0.182727 + 0.983164i \(0.441508\pi\)
\(600\) 0 0
\(601\) −14.8328 −0.605043 −0.302522 0.953143i \(-0.597828\pi\)
−0.302522 + 0.953143i \(0.597828\pi\)
\(602\) 3.11044 + 4.28115i 0.126772 + 0.174487i
\(603\) 21.1275 + 6.86475i 0.860379 + 0.279554i
\(604\) −1.14590 + 3.52671i −0.0466259 + 0.143500i
\(605\) 0 0
\(606\) −1.30902 4.02874i −0.0531752 0.163656i
\(607\) 27.1459i 1.10182i −0.834565 0.550909i \(-0.814281\pi\)
0.834565 0.550909i \(-0.185719\pi\)
\(608\) 0.812299 0.263932i 0.0329431 0.0107039i
\(609\) −3.35410 2.43690i −0.135915 0.0987481i
\(610\) 0 0
\(611\) −4.80902 + 3.49396i −0.194552 + 0.141350i
\(612\) 17.7926 24.4894i 0.719222 0.989924i
\(613\) 24.4297 33.6246i 0.986707 1.35809i 0.0535698 0.998564i \(-0.482940\pi\)
0.933137 0.359521i \(-0.117060\pi\)
\(614\) −13.8541 + 10.0656i −0.559106 + 0.406214i
\(615\) 0 0
\(616\) 0.572949 + 0.416272i 0.0230848 + 0.0167721i
\(617\) 28.8747 9.38197i 1.16245 0.377704i 0.336632 0.941636i \(-0.390712\pi\)
0.825821 + 0.563933i \(0.190712\pi\)
\(618\) 51.9787i 2.09089i
\(619\) 14.5106 + 44.6592i 0.583232 + 1.79500i 0.606257 + 0.795269i \(0.292670\pi\)
−0.0230252 + 0.999735i \(0.507330\pi\)
\(620\) 0 0
\(621\) 4.30902 13.2618i 0.172915 0.532177i
\(622\) 20.0579 + 6.51722i 0.804250 + 0.261317i
\(623\) 7.88597 + 10.8541i 0.315945 + 0.434860i
\(624\) 2.61803 0.104805
\(625\) 0 0
\(626\) −3.56231 −0.142378
\(627\) 0.310271 + 0.427051i 0.0123910 + 0.0170548i
\(628\) 14.8006 + 4.80902i 0.590610 + 0.191901i
\(629\) −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 \(0.843744\pi\)
\(632\) 2.76393i 0.109943i
\(633\) −28.0624 + 9.11803i −1.11538 + 0.362409i
\(634\) −8.59017 6.24112i −0.341159 0.247867i
\(635\) 0 0
\(636\) 3.23607 2.35114i 0.128318 0.0932288i
\(637\) 1.17557 1.61803i 0.0465778 0.0641088i
\(638\) 0.0732450 0.100813i 0.00289980 0.00399123i
\(639\) −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 \(0.791531\pi\)
\(642\) −25.1235 + 8.16312i −0.991545 + 0.322173i
\(643\) 36.2361i 1.42901i 0.699630 + 0.714506i \(0.253348\pi\)
−0.699630 + 0.714506i \(0.746652\pi\)
\(644\) −5.78115 17.7926i −0.227809 0.701125i
\(645\) 0 0
\(646\) 2.07295 6.37988i 0.0815591 0.251013i
\(647\) 7.27794 + 2.36475i 0.286125 + 0.0929677i 0.448563 0.893751i \(-0.351936\pi\)
−0.162438 + 0.986719i \(0.551936\pi\)
\(648\) 3.35520 + 4.61803i 0.131805 + 0.181414i
\(649\) 1.05573 0.0414410
\(650\) 0 0
\(651\) 33.2705 1.30397
\(652\) 2.85317 + 3.92705i 0.111739 + 0.153795i
\(653\) −38.6098 12.5451i −1.51092 0.490927i −0.567738 0.823209i \(-0.692181\pi\)
−0.943180 + 0.332282i \(0.892181\pi\)
\(654\) 12.1353 37.3485i 0.474526 1.46044i
\(655\) 0 0
\(656\) −2.30902 7.10642i −0.0901520 0.277459i
\(657\) 22.0000i 0.858302i
\(658\) 16.9600 5.51064i 0.661170 0.214827i
\(659\) 4.57295 + 3.32244i 0.178137 + 0.129424i 0.673281 0.739387i \(-0.264885\pi\)
−0.495144 + 0.868811i \(0.664885\pi\)
\(660\) 0 0
\(661\) −5.07295 + 3.68571i −0.197315 + 0.143358i −0.682056 0.731300i \(-0.738914\pi\)
0.484741 + 0.874658i \(0.338914\pi\)
\(662\) −2.68166 + 3.69098i −0.104226 + 0.143454i
\(663\) 12.0862 16.6353i 0.469390 0.646060i
\(664\) 10.8992 7.91872i 0.422970 0.307306i
\(665\) 0 0
\(666\) 22.8435 + 16.5967i 0.885166 + 0.643111i
\(667\) −3.13068 + 1.01722i −0.121221 + 0.0393870i
\(668\) 15.6180i 0.604280i
\(669\) −7.28115 22.4091i −0.281506 0.866385i
\(670\) 0 0
\(671\) 0.156541 0.481784i 0.00604320 0.0185991i
\(672\) −7.46969 2.42705i −0.288150 0.0936255i
\(673\) −0.726543 1.00000i −0.0280062 0.0385472i 0.794784 0.606892i \(-0.207584\pi\)
−0.822790 + 0.568345i \(0.807584\pi\)
\(674\) −31.4164 −1.21011
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) −6.24112 8.59017i −0.239866 0.330147i 0.672064 0.740493i \(-0.265408\pi\)
−0.911930 + 0.410346i \(0.865408\pi\)
\(678\) −20.5070 6.66312i −0.787565 0.255896i
\(679\) −9.79180 + 30.1360i −0.375775 + 1.15652i
\(680\) 0 0
\(681\) 12.4271 + 38.2465i 0.476206 + 1.46561i
\(682\) 1.00000i 0.0382920i
\(683\) 31.7279 10.3090i 1.21403 0.394464i 0.369128 0.929379i \(-0.379656\pi\)
0.844906 + 0.534915i \(0.179656\pi\)
\(684\) −2.66312 1.93487i −0.101827 0.0739816i
\(685\) 0 0
\(686\) 12.1353 8.81678i 0.463326 0.336626i
\(687\) −27.0256 + 37.1976i −1.03109 + 1.41918i
\(688\) 1.03681 1.42705i 0.0395281 0.0544058i
\(689\) 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 \(0.707693\pi\)
\(692\) −3.07768 + 1.00000i −0.116996 + 0.0380143i
\(693\) 2.72949i 0.103685i
\(694\) −3.06231 9.42481i −0.116244 0.357761i
\(695\) 0 0
\(696\) −0.427051 + 1.31433i −0.0161873 + 0.0498195i
\(697\) −55.8146 18.1353i −2.11413 0.686922i
\(698\) 13.0700 + 17.9894i 0.494708 + 0.680907i
\(699\) 72.5410 2.74375
\(700\) 0 0
\(701\) −4.18034 −0.157889 −0.0789446 0.996879i \(-0.525155\pi\)
−0.0789446 + 0.996879i \(0.525155\pi\)
\(702\) −1.31433 1.80902i −0.0496061 0.0682769i
\(703\) 5.95110 + 1.93363i 0.224450 + 0.0729282i
\(704\) 0.0729490 0.224514i 0.00274937 0.00846169i
\(705\) 0 0
\(706\) 5.18034 + 15.9434i 0.194965 + 0.600040i
\(707\) 4.85410i 0.182557i
\(708\) −11.1352 + 3.61803i −0.418485 + 0.135974i
\(709\) 6.28115 + 4.56352i 0.235894 + 0.171387i 0.699452 0.714680i \(-0.253428\pi\)
−0.463558 + 0.886066i \(0.653428\pi\)
\(710\) 0 0
\(711\) 8.61803 6.26137i 0.323202 0.234820i
\(712\) 2.62866 3.61803i 0.0985130 0.135592i
\(713\) 15.5272 21.3713i 0.581497 0.800362i
\(714\) −49.9058 + 36.2587i −1.86768 + 1.35695i
\(715\) 0 0
\(716\) 9.04508 + 6.57164i 0.338031 + 0.245594i
\(717\) −45.0427 + 14.6353i −1.68215 + 0.546564i
\(718\) 3.09017i 0.115324i
\(719\) 8.19098 + 25.2093i 0.305472 + 0.940147i 0.979501 + 0.201441i \(0.0645625\pi\)
−0.674028 + 0.738705i \(0.735438\pi\)
\(720\) 0 0
\(721\) 18.4058 56.6471i 0.685466 2.10965i
\(722\) 17.3763 + 5.64590i 0.646678 + 0.210119i
\(723\) −20.5927 28.3435i −0.765852 1.05410i
\(724\) 21.4164 0.795935
\(725\) 0 0
\(726\) −28.6525 −1.06339
\(727\) 16.8415 + 23.1803i 0.624617 + 0.859711i 0.997679 0.0680952i \(-0.0216922\pi\)
−0.373062 + 0.927806i \(0.621692\pi\)
\(728\) −2.85317 0.927051i −0.105745 0.0343588i
\(729\) 12.2254 37.6260i 0.452794 1.39356i
\(730\) 0 0
\(731\) −4.28115 13.1760i −0.158344 0.487333i
\(732\) 5.61803i 0.207649i
\(733\) −37.8303 + 12.2918i −1.39729 + 0.454008i −0.908314 0.418288i \(-0.862630\pi\)
−0.488978 + 0.872296i \(0.662630\pi\)
\(734\) 25.5172 + 18.5393i 0.941858 + 0.684300i
\(735\) 0 0
\(736\) −5.04508 + 3.66547i −0.185964 + 0.135111i
\(737\) 0.799788 1.10081i 0.0294606 0.0405490i
\(738\) −16.9273 + 23.2984i −0.623101 + 0.857625i
\(739\) 24.2705 17.6336i 0.892805 0.648661i −0.0438028 0.999040i \(-0.513947\pi\)
0.936608 + 0.350379i \(0.113947\pi\)
\(740\) 0 0
\(741\) −1.80902 1.31433i −0.0664559 0.0482830i
\(742\) −4.35926 + 1.41641i −0.160033 + 0.0519980i
\(743\) 18.2705i 0.670280i 0.942168 + 0.335140i \(0.108784\pi\)
−0.942168 + 0.335140i \(0.891216\pi\)
\(744\) −3.42705 10.5474i −0.125642 0.386686i
\(745\) 0 0
\(746\) 5.01722 15.4414i 0.183694 0.565350i
\(747\) −49.3817 16.0451i −1.80678 0.587059i
\(748\) −1.08981 1.50000i −0.0398475 0.0548454i
\(749\) 30.2705 1.10606
\(750\) 0 0
\(751\) 1.14590 0.0418144 0.0209072 0.999781i \(-0.493345\pi\)
0.0209072 + 0.999781i \(0.493345\pi\)
\(752\) −3.49396 4.80902i −0.127411 0.175367i
\(753\) 57.7167 + 18.7533i 2.10331 + 0.683408i
\(754\) −0.163119 + 0.502029i −0.00594044 + 0.0182828i
\(755\) 0 0
\(756\) 2.07295 + 6.37988i 0.0753924 + 0.232034i
\(757\) 10.4164i 0.378591i 0.981920 + 0.189295i \(0.0606204\pi\)
−0.981920 + 0.189295i \(0.939380\pi\)
\(758\) −0.502029 + 0.163119i −0.0182345 + 0.00592475i
\(759\) −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 \(0.0587723\pi\)
\(762\) −19.1926 + 26.4164i −0.695276 + 0.956965i
\(763\) −26.4503 + 36.4058i −0.957566 + 1.31798i
\(764\) 14.2812 10.3759i 0.516674 0.375386i
\(765\) 0 0
\(766\) −3.50000 2.54290i −0.126460 0.0918787i
\(767\) −4.25325 + 1.38197i −0.153576 + 0.0498999i
\(768\) 2.61803i 0.0944702i
\(769\) 7.23607 + 22.2703i 0.260939 + 0.803089i 0.992601 + 0.121421i \(0.0387450\pi\)
−0.731662 + 0.681668i \(0.761255\pi\)
\(770\) 0 0
\(771\) 13.5451 41.6875i 0.487814 1.50134i
\(772\) 15.8374 + 5.14590i 0.570002 + 0.185205i
\(773\) 3.64522 + 5.01722i 0.131110 + 0.180457i 0.869525 0.493890i \(-0.164425\pi\)
−0.738415 + 0.674347i \(0.764425\pi\)
\(774\) −6.79837 −0.244363
\(775\) 0 0
\(776\) 10.5623 0.379165
\(777\) −33.8218 46.5517i −1.21335 1.67003i
\(778\) −31.5891 10.2639i −1.13253 0.367980i
\(779\) −1.97214 + 6.06961i −0.0706591 + 0.217466i
\(780\) 0 0
\(781\) 0.218847 + 0.673542i 0.00783096 + 0.0241012i
\(782\) 48.9787i 1.75148i
\(783\) 1.12257 0.364745i 0.0401174 0.0130349i
\(784\) 1.61803 + 1.17557i 0.0577869 + 0.0419847i
\(785\) 0 0
\(786\) −22.0623 + 16.0292i −0.786936 + 0.571743i
\(787\) 9.06154 12.4721i 0.323009 0.444584i −0.616374 0.787454i \(-0.711399\pi\)
0.939383 + 0.342870i \(0.111399\pi\)
\(788\) −7.05342 + 9.70820i −0.251268 + 0.345840i
\(789\) −5.04508 + 3.66547i −0.179610 + 0.130494i
\(790\) 0 0
\(791\) 19.9894 + 14.5231i 0.710740 + 0.516383i
\(792\) −0.865300 + 0.281153i −0.0307471 + 0.00999034i
\(793\) 2.14590i 0.0762031i
\(794\) −1.78115 5.48183i −0.0632108 0.194543i
\(795\) 0 0
\(796\) −5.42705 + 16.7027i −0.192357 + 0.592013i
\(797\) 3.21644 + 1.04508i 0.113932 + 0.0370188i 0.365428 0.930840i \(-0.380923\pi\)
−0.251496 + 0.967858i \(0.580923\pi\)
\(798\) 3.94298 + 5.42705i 0.139580 + 0.192116i
\(799\) −46.6869 −1.65166
\(800\) 0 0
\(801\) −17.2361 −0.609007
\(802\) 4.80828 + 6.61803i 0.169786 + 0.233691i
\(803\) −1.28157 0.416408i −0.0452257 0.0146947i
\(804\) −4.66312 + 14.3516i −0.164456 + 0.506142i
\(805\) 0 0
\(806\) −1.30902 4.02874i −0.0461082 0.141906i
\(807\) 34.2705i 1.20638i
\(808\) 1.53884 0.500000i 0.0541363 0.0175899i
\(809\) 1.80902 + 1.31433i 0.0636017 + 0.0462093i 0.619132 0.785287i \(-0.287485\pi\)
−0.555530 + 0.831496i \(0.687485\pi\)
\(810\) 0 0
\(811\) −18.6525 + 13.5518i −0.654977 + 0.475869i −0.864963 0.501836i \(-0.832658\pi\)
0.209986 + 0.977704i \(0.432658\pi\)
\(812\) 0.930812 1.28115i 0.0326651 0.0449597i
\(813\) −14.6291 + 20.1353i −0.513066 + 0.706174i
\(814\) 1.39919 1.01657i 0.0490415 0.0356307i
\(815\) 0 0
\(816\) 16.6353 + 12.0862i 0.582350 + 0.423102i
\(817\) −1.43284 + 0.465558i −0.0501287 + 0.0162878i
\(818\) 6.70820i 0.234547i
\(819\) 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 \(0.923587\pi\)
\(822\) −15.1639 4.92705i −0.528902 0.171851i
\(823\) 19.2986 + 26.5623i 0.672708 + 0.925904i 0.999818 0.0190827i \(-0.00607458\pi\)
−0.327109 + 0.944986i \(0.606075\pi\)
\(824\) −19.8541 −0.691650
\(825\) 0 0
\(826\) 13.4164 0.466817
\(827\) −14.1271 19.4443i −0.491247 0.676144i 0.489370 0.872076i \(-0.337227\pi\)
−0.980617 + 0.195932i \(0.937227\pi\)
\(828\) 22.8581 + 7.42705i 0.794374 + 0.258108i
\(829\) −8.21478 + 25.2825i −0.285311 + 0.878097i 0.700994 + 0.713167i \(0.252740\pi\)
−0.986305 + 0.164930i \(0.947260\pi\)
\(830\) 0 0
\(831\) −11.0902 34.1320i −0.384714 1.18403i
\(832\) 1.00000i 0.0346688i
\(833\) 14.9394 4.85410i 0.517619 0.168185i
\(834\) 21.8713 + 15.8904i 0.757342 + 0.550241i
\(835\) 0 0
\(836\) −0.163119 + 0.118513i −0.00564159 + 0.00409885i
\(837\) −5.56758 + 7.66312i −0.192444 + 0.264876i
\(838\) 16.0090 22.0344i 0.553020 0.761167i
\(839\) 20.4271 14.8411i 0.705220 0.512372i −0.176408 0.984317i \(-0.556448\pi\)
0.881628 + 0.471945i \(0.156448\pi\)
\(840\) 0 0
\(841\) 23.2361 + 16.8820i 0.801244 + 0.582138i
\(842\) −11.6699 + 3.79180i −0.402173 + 0.130674i
\(843\) 50.2148i 1.72949i
\(844\) −3.48278 10.7189i −0.119882 0.368959i
\(845\) 0 0
\(846\) −7.07953 + 21.7885i −0.243399 + 0.749106i
\(847\) 31.2259 + 10.1459i 1.07293 + 0.348617i
\(848\) 0.898056 + 1.23607i 0.0308394 + 0.0424467i
\(849\) −67.3050 −2.30990
\(850\) 0 0
\(851\) −45.6869 −1.56613
\(852\) −4.61653 6.35410i −0.158160 0.217688i
\(853\) 23.6377 + 7.68034i 0.809338 + 0.262970i 0.684317 0.729184i \(-0.260100\pi\)
0.125021 + 0.992154i \(0.460100\pi\)
\(854\) 1.98936 6.12261i 0.0680744 0.209511i
\(855\) 0 0
\(856\) −3.11803 9.59632i −0.106572 0.327996i
\(857\) 35.3394i 1.20717i 0.797298 + 0.603585i \(0.206262\pi\)
−0.797298 + 0.603585i \(0.793738\pi\)
\(858\) −0.587785 + 0.190983i −0.0200667 + 0.00652005i
\(859\) −31.8713 23.1559i −1.08744 0.790068i −0.108471 0.994100i \(-0.534596\pi\)
−0.978964 + 0.204031i \(0.934596\pi\)
\(860\) 0 0
\(861\) 47.4787 34.4953i 1.61807 1.17560i
\(862\) 18.8496 25.9443i 0.642020 0.883665i
\(863\) 3.97574 5.47214i 0.135336 0.186274i −0.735970 0.677014i \(-0.763274\pi\)
0.871306 + 0.490740i \(0.163274\pi\)
\(864\) 1.80902 1.31433i 0.0615440 0.0447143i
\(865\) 0 0
\(866\) 18.8992 + 13.7311i 0.642221 + 0.466601i
\(867\) 111.266 36.1525i 3.77879 1.22780i
\(868\) 12.7082i 0.431345i
\(869\) −0.201626 0.620541i −0.00683970 0.0210504i
\(870\) 0 0
\(871\) −1.78115 + 5.48183i −0.0603521 + 0.185745i
\(872\) 14.2658 + 4.63525i 0.483103 + 0.156970i
\(873\) −23.9277 32.9336i −0.809829 1.11463i
\(874\) 5.32624 0.180163
\(875\) 0 0
\(876\) 14.9443 0.504920
\(877\) −14.4374 19.8713i −0.487515 0.671007i 0.492412 0.870362i \(-0.336115\pi\)
−0.979927 + 0.199355i \(0.936115\pi\)
\(878\) −5.37582 1.74671i −0.181425 0.0589486i
\(879\) −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 \(0.814136\pi\)
\(882\) 7.70820i 0.259549i
\(883\) 17.7723 5.77458i 0.598086 0.194330i 0.00569940 0.999984i \(-0.498186\pi\)
0.592387 + 0.805654i \(0.298186\pi\)
\(884\) 6.35410 + 4.61653i 0.213712 + 0.155271i
\(885\) 0 0
\(886\) −6.00000 + 4.35926i −0.201574 + 0.146452i
\(887\) 6.35964 8.75329i 0.213536 0.293907i −0.688791 0.724960i \(-0.741858\pi\)
0.902326 + 0.431054i \(0.141858\pi\)
\(888\) −11.2739 + 15.5172i −0.378328 + 0.520724i
\(889\) 30.2705 21.9928i 1.01524 0.737615i
\(890\) 0 0
\(891\) −1.09017 0.792055i −0.0365221 0.0265348i
\(892\) 8.55951 2.78115i 0.286594 0.0931199i
\(893\) 5.07701i 0.169896i
\(894\) 1.80902 + 5.56758i 0.0605026 + 0.186208i
\(895\) 0 0
\(896\) 0.927051 2.85317i 0.0309706 0.0953177i
\(897\) 15.5272 + 5.04508i 0.518437 + 0.168450i
\(898\) −8.19624 11.2812i −0.273512 0.376457i
\(899\) 2.23607 0.0745770
\(900\) 0 0
\(901\) 12.0000 0.399778
\(902\) 1.03681 + 1.42705i 0.0345221 + 0.0475156i
\(903\) 13.1760 + 4.28115i 0.438471 + 0.142468i
\(904\) 2.54508 7.83297i 0.0846483 0.260521i
\(905\) 0 0
\(906\) 3.00000 + 9.23305i 0.0996683 + 0.306748i
\(907\) 23.3820i 0.776385i 0.921578 + 0.388193i \(0.126901\pi\)
−0.921578 + 0.388193i \(0.873099\pi\)
\(908\) −14.6089 + 4.74671i −0.484813 + 0.157525i
\(909\) −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 \(0.355202\pi\)
\(912\) 1.31433 1.80902i 0.0435217 0.0599025i
\(913\) −1.86936 + 2.57295i −0.0618667 + 0.0851522i
\(914\) 9.07295 6.59188i 0.300106 0.218040i
\(915\) 0 0
\(916\) −14.2082 10.3229i −0.469452 0.341077i
\(917\) 29.7198 9.65654i 0.981434 0.318887i
\(918\) 17.5623i 0.579642i
\(919\) −7.92705 24.3970i −0.261489 0.804781i −0.992481 0.122395i \(-0.960942\pi\)
0.730992 0.682386i \(-0.239058\pi\)
\(920\) 0 0
\(921\) −13.8541 + 42.6385i −0.456508 + 1.40499i
\(922\) −26.8011 8.70820i −0.882647 0.286789i
\(923\) −1.76336 2.42705i −0.0580416 0.0798874i
\(924\) 1.85410 0.0609955
\(925\) 0 0
\(926\) −11.9787 −0.393645
\(927\) 44.9772 + 61.9058i 1.47724 + 2.03325i
\(928\) −0.502029 0.163119i −0.0164799 0.00535464i
\(929\) 5.28773 16.2740i 0.173485 0.533931i −0.826076 0.563558i \(-0.809432\pi\)
0.999561 + 0.0296271i \(0.00943197\pi\)
\(930\) 0 0
\(931\) −0.527864 1.62460i −0.0173000 0.0532441i
\(932\) 27.7082i 0.907612i
\(933\) 52.5124 17.0623i 1.71918 0.558595i
\(934\) −2.57295 1.86936i −0.0841895 0.0611672i
\(935\) 0 0
\(936\) 3.11803 2.26538i 0.101916 0.0740464i
\(937\) −13.4738 + 18.5451i −0.440170 + 0.605842i −0.970250 0.242106i \(-0.922162\pi\)
0.530080 + 0.847948i \(0.322162\pi\)
\(938\) 10.1639 13.9894i 0.331862 0.456769i
\(939\) −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 \(0.639356\pi\)
\(942\) 38.7486 12.5902i 1.26250 0.410210i
\(943\) 46.5967i 1.51740i
\(944\) −1.38197 4.25325i −0.0449792 0.138432i
\(945\) 0 0
\(946\) −0.128677 + 0.396027i −0.00418365 + 0.0128760i
\(947\) −39.5811 12.8607i −1.28621 0.417916i −0.415449 0.909617i \(-0.636375\pi\)
−0.870764 + 0.491701i \(0.836375\pi\)
\(948\) 4.25325 + 5.85410i 0.138139 + 0.190132i
\(949\) 5.70820 0.185296
\(950\) 0 0
\(951\) −27.7984 −0.901424
\(952\) −13.8496 19.0623i −0.448867 0.617813i
\(953\) −40.3076 13.0967i −1.30569 0.424245i −0.428134 0.903715i \(-0.640829\pi\)
−0.877558 + 0.479470i \(0.840829\pi\)
\(954\) 1.81966 5.60034i 0.0589137 0.181318i
\(955\) 0 0
\(956\) −5.59017 17.2048i −0.180799 0.556442i
\(957\) 0.326238i 0.0105458i
\(958\) 37.8505 12.2984i 1.22289 0.397342i
\(959\) 14.7812 + 10.7391i 0.477308 + 0.346785i
\(960\) 0 0
\(961\) 10.5623 7.67396i 0.340720 0.247547i
\(962\) −4.30625 + 5.92705i −0.138839 + 0.191096i
\(963\) −22.8581 + 31.4615i −0.736592 + 1.01383i
\(964\) 10.8262 7.86572i 0.348690 0.253338i
\(965\) 0 0
\(966\) −39.6246 28.7890i −1.27490 0.926270i
\(967\) −25.7970 + 8.38197i −0.829577 + 0.269546i −0.692867 0.721065i \(-0.743653\pi\)
−0.136710 + 0.990611i \(0.543653\pi\)
\(968\) 10.9443i 0.351762i
\(969\) −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 \(0.785187\pi\)
\(972\) 20.5927 + 6.69098i 0.660512 + 0.214613i
\(973\) −18.2088 25.0623i −0.583748 0.803461i
\(974\) −18.1246 −0.580750
\(975\) 0 0
\(976\) −2.14590 −0.0686885
\(977\) 15.2901 + 21.0451i 0.489175 + 0.673292i 0.980236 0.197834i \(-0.0633906\pi\)
−0.491060 + 0.871126i \(0.663391\pi\)
\(978\) 12.0862 + 3.92705i 0.386475 + 0.125573i
\(979\) −0.326238 + 1.00406i −0.0104266 + 0.0320898i
\(980\) 0 0
\(981\) −17.8647 54.9820i −0.570377 1.75544i
\(982\) 14.7639i 0.471136i
\(983\) −44.2101 + 14.3647i −1.41008 + 0.458164i −0.912438 0.409216i \(-0.865802\pi\)
−0.497647 + 0.867380i \(0.665802\pi\)
\(984\) −15.8262 11.4984i −0.504522 0.366557i
\(985\) 0 0
\(986\) −3.35410 + 2.43690i −0.106816 + 0.0776066i
\(987\) 27.4419 37.7705i 0.873485 1.20225i
\(988\) 0.502029 0.690983i 0.0159717 0.0219831i
\(989\) 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 \(-0.613424\pi\)
\(992\) 4.02874 1.30902i 0.127913 0.0415613i
\(993\) 11.9443i 0.379040i
\(994\) 2.78115 + 8.55951i 0.0882128 + 0.271491i
\(995\) 0 0
\(996\) 10.8992 33.5442i 0.345354 1.06289i
\(997\) −50.6430 16.4549i −1.60388 0.521132i −0.635818 0.771839i \(-0.719337\pi\)
−0.968063 + 0.250707i \(0.919337\pi\)
\(998\) −24.0134 33.0517i −0.760132 1.04623i
\(999\) 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.e.b.199.2 8
5.2 odd 4 250.2.d.a.51.1 4
5.3 odd 4 50.2.d.a.11.1 4
5.4 even 2 inner 250.2.e.b.199.1 8
15.8 even 4 450.2.h.a.361.1 4
20.3 even 4 400.2.u.c.161.1 4
25.3 odd 20 1250.2.a.a.1.1 2
25.4 even 10 1250.2.b.b.1249.3 4
25.9 even 10 inner 250.2.e.b.49.2 8
25.12 odd 20 250.2.d.a.201.1 4
25.13 odd 20 50.2.d.a.41.1 yes 4
25.16 even 5 inner 250.2.e.b.49.1 8
25.21 even 5 1250.2.b.b.1249.2 4
25.22 odd 20 1250.2.a.d.1.2 2
75.38 even 20 450.2.h.a.91.1 4
100.3 even 20 10000.2.a.n.1.2 2
100.47 even 20 10000.2.a.a.1.1 2
100.63 even 20 400.2.u.c.241.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.2.d.a.11.1 4 5.3 odd 4
50.2.d.a.41.1 yes 4 25.13 odd 20
250.2.d.a.51.1 4 5.2 odd 4
250.2.d.a.201.1 4 25.12 odd 20
250.2.e.b.49.1 8 25.16 even 5 inner
250.2.e.b.49.2 8 25.9 even 10 inner
250.2.e.b.199.1 8 5.4 even 2 inner
250.2.e.b.199.2 8 1.1 even 1 trivial
400.2.u.c.161.1 4 20.3 even 4
400.2.u.c.241.1 4 100.63 even 20
450.2.h.a.91.1 4 75.38 even 20
450.2.h.a.361.1 4 15.8 even 4
1250.2.a.a.1.1 2 25.3 odd 20
1250.2.a.d.1.2 2 25.22 odd 20
1250.2.b.b.1249.2 4 25.21 even 5
1250.2.b.b.1249.3 4 25.4 even 10
10000.2.a.a.1.1 2 100.47 even 20
10000.2.a.n.1.2 2 100.3 even 20