Properties

Label 462.2.u.a.349.4
Level $462$
Weight $2$
Character 462.349
Analytic conductor $3.689$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [462,2,Mod(13,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.u (of order \(10\), degree \(4\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 349.4
Character \(\chi\) \(=\) 462.349
Dual form 462.2.u.a.139.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.12216 - 1.54452i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.488107 + 2.60034i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.12216 - 1.54452i) q^{5} +(0.809017 + 0.587785i) q^{6} +(0.488107 + 2.60034i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} -1.90913 q^{10} +(-0.215110 + 3.30964i) q^{11} -1.00000i q^{12} +(-2.19973 + 1.59820i) q^{13} +(1.81681 - 1.92333i) q^{14} +(-0.589954 + 1.81569i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-3.34007 - 2.42671i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(1.23236 + 3.79280i) q^{19} +(1.12216 + 1.54452i) q^{20} +(-1.26777 - 2.32223i) q^{21} +(2.80399 - 1.77133i) q^{22} +6.88157 q^{23} +(-0.809017 + 0.587785i) q^{24} +(0.418787 + 1.28889i) q^{25} +(2.58594 + 0.840221i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-2.62390 - 0.339331i) q^{28} +(6.78796 + 2.20554i) q^{29} +(1.81569 - 0.589954i) q^{30} +(1.61579 + 2.22395i) q^{31} +1.00000i q^{32} +(-0.818154 - 3.21413i) q^{33} +4.12856i q^{34} +(4.56400 + 2.16410i) q^{35} +(0.309017 + 0.951057i) q^{36} +(0.321233 - 0.988653i) q^{37} +(2.34408 - 3.22635i) q^{38} +(1.59820 - 2.19973i) q^{39} +(0.589954 - 1.81569i) q^{40} +(2.51353 + 7.73587i) q^{41} +(-1.13355 + 2.39062i) q^{42} +1.21706i q^{43} +(-3.08118 - 1.22732i) q^{44} -1.90913i q^{45} +(-4.04489 - 5.56731i) q^{46} +(7.21926 - 2.34568i) q^{47} +(0.951057 + 0.309017i) q^{48} +(-6.52350 + 2.53848i) q^{49} +(0.796579 - 1.09640i) q^{50} +(3.92649 + 1.27579i) q^{51} +(-0.840221 - 2.58594i) q^{52} +(-3.96828 + 2.88312i) q^{53} +1.00000 q^{54} +(4.87042 + 4.04618i) q^{55} +(1.26777 + 2.32223i) q^{56} +(-2.34408 - 3.22635i) q^{57} +(-2.20554 - 6.78796i) q^{58} +(3.13164 + 1.01753i) q^{59} +(-1.54452 - 1.12216i) q^{60} +(-6.21098 - 4.51254i) q^{61} +(0.849472 - 2.61440i) q^{62} +(1.92333 + 1.81681i) q^{63} +(0.809017 - 0.587785i) q^{64} +5.19095i q^{65} +(-2.11939 + 2.55112i) q^{66} +1.75788 q^{67} +(3.34007 - 2.42671i) q^{68} +(-6.54476 + 2.12652i) q^{69} +(-0.931859 - 4.96438i) q^{70} +(-10.1359 - 7.36420i) q^{71} +(0.587785 - 0.809017i) q^{72} +(2.13629 - 6.57482i) q^{73} +(-0.988653 + 0.321233i) q^{74} +(-0.796579 - 1.09640i) q^{75} -3.98799 q^{76} +(-8.71118 + 1.05610i) q^{77} -2.71901 q^{78} +(-1.00449 - 1.38256i) q^{79} +(-1.81569 + 0.589954i) q^{80} +(0.309017 - 0.951057i) q^{81} +(4.78103 - 6.58052i) q^{82} +(1.15480 + 0.839010i) q^{83} +(2.60034 - 0.488107i) q^{84} +(-7.49618 + 2.43566i) q^{85} +(0.984619 - 0.715368i) q^{86} -7.13729 q^{87} +(0.818154 + 3.21413i) q^{88} -7.07430i q^{89} +(-1.54452 + 1.12216i) q^{90} +(-5.22955 - 4.93994i) q^{91} +(-2.12652 + 6.54476i) q^{92} +(-2.22395 - 1.61579i) q^{93} +(-6.14107 - 4.46175i) q^{94} +(7.24095 + 2.35273i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(3.78817 + 5.21398i) q^{97} +(5.88810 + 3.78554i) q^{98} +(1.77133 + 2.80399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{10}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587785 0.809017i −0.415627 0.572061i
\(3\) −0.951057 + 0.309017i −0.549093 + 0.178411i
\(4\) −0.309017 + 0.951057i −0.154508 + 0.475528i
\(5\) 1.12216 1.54452i 0.501845 0.690730i −0.480673 0.876900i \(-0.659608\pi\)
0.982518 + 0.186170i \(0.0596076\pi\)
\(6\) 0.809017 + 0.587785i 0.330280 + 0.239962i
\(7\) 0.488107 + 2.60034i 0.184487 + 0.982835i
\(8\) 0.951057 0.309017i 0.336249 0.109254i
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) −1.90913 −0.603720
\(11\) −0.215110 + 3.30964i −0.0648581 + 0.997894i
\(12\) 1.00000i 0.288675i
\(13\) −2.19973 + 1.59820i −0.610095 + 0.443260i −0.849448 0.527673i \(-0.823065\pi\)
0.239353 + 0.970933i \(0.423065\pi\)
\(14\) 1.81681 1.92333i 0.485564 0.514031i
\(15\) −0.589954 + 1.81569i −0.152325 + 0.468809i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) −3.34007 2.42671i −0.810087 0.588563i 0.103769 0.994601i \(-0.466910\pi\)
−0.913856 + 0.406039i \(0.866910\pi\)
\(18\) −0.951057 0.309017i −0.224166 0.0728360i
\(19\) 1.23236 + 3.79280i 0.282722 + 0.870128i 0.987072 + 0.160276i \(0.0512384\pi\)
−0.704350 + 0.709852i \(0.748762\pi\)
\(20\) 1.12216 + 1.54452i 0.250922 + 0.345365i
\(21\) −1.26777 2.32223i −0.276649 0.506753i
\(22\) 2.80399 1.77133i 0.597814 0.377649i
\(23\) 6.88157 1.43491 0.717453 0.696607i \(-0.245308\pi\)
0.717453 + 0.696607i \(0.245308\pi\)
\(24\) −0.809017 + 0.587785i −0.165140 + 0.119981i
\(25\) 0.418787 + 1.28889i 0.0837573 + 0.257778i
\(26\) 2.58594 + 0.840221i 0.507144 + 0.164781i
\(27\) −0.587785 + 0.809017i −0.113119 + 0.155695i
\(28\) −2.62390 0.339331i −0.495871 0.0641276i
\(29\) 6.78796 + 2.20554i 1.26049 + 0.409559i 0.861670 0.507469i \(-0.169419\pi\)
0.398823 + 0.917028i \(0.369419\pi\)
\(30\) 1.81569 0.589954i 0.331498 0.107710i
\(31\) 1.61579 + 2.22395i 0.290205 + 0.399432i 0.929081 0.369877i \(-0.120600\pi\)
−0.638876 + 0.769310i \(0.720600\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.818154 3.21413i −0.142422 0.559508i
\(34\) 4.12856i 0.708042i
\(35\) 4.56400 + 2.16410i 0.771457 + 0.365800i
\(36\) 0.309017 + 0.951057i 0.0515028 + 0.158509i
\(37\) 0.321233 0.988653i 0.0528104 0.162534i −0.921173 0.389154i \(-0.872768\pi\)
0.973983 + 0.226620i \(0.0727675\pi\)
\(38\) 2.34408 3.22635i 0.380260 0.523383i
\(39\) 1.59820 2.19973i 0.255916 0.352238i
\(40\) 0.589954 1.81569i 0.0932799 0.287086i
\(41\) 2.51353 + 7.73587i 0.392548 + 1.20814i 0.930855 + 0.365390i \(0.119064\pi\)
−0.538306 + 0.842749i \(0.680936\pi\)
\(42\) −1.13355 + 2.39062i −0.174911 + 0.368880i
\(43\) 1.21706i 0.185599i 0.995685 + 0.0927997i \(0.0295816\pi\)
−0.995685 + 0.0927997i \(0.970418\pi\)
\(44\) −3.08118 1.22732i −0.464506 0.185025i
\(45\) 1.90913i 0.284596i
\(46\) −4.04489 5.56731i −0.596386 0.820855i
\(47\) 7.21926 2.34568i 1.05304 0.342152i 0.269177 0.963091i \(-0.413248\pi\)
0.783859 + 0.620938i \(0.213248\pi\)
\(48\) 0.951057 + 0.309017i 0.137273 + 0.0446028i
\(49\) −6.52350 + 2.53848i −0.931929 + 0.362641i
\(50\) 0.796579 1.09640i 0.112653 0.155054i
\(51\) 3.92649 + 1.27579i 0.549819 + 0.178647i
\(52\) −0.840221 2.58594i −0.116518 0.358605i
\(53\) −3.96828 + 2.88312i −0.545085 + 0.396027i −0.825970 0.563714i \(-0.809372\pi\)
0.280885 + 0.959741i \(0.409372\pi\)
\(54\) 1.00000 0.136083
\(55\) 4.87042 + 4.04618i 0.656727 + 0.545587i
\(56\) 1.26777 + 2.32223i 0.169412 + 0.310322i
\(57\) −2.34408 3.22635i −0.310481 0.427340i
\(58\) −2.20554 6.78796i −0.289602 0.891303i
\(59\) 3.13164 + 1.01753i 0.407705 + 0.132471i 0.505687 0.862717i \(-0.331239\pi\)
−0.0979824 + 0.995188i \(0.531239\pi\)
\(60\) −1.54452 1.12216i −0.199397 0.144870i
\(61\) −6.21098 4.51254i −0.795234 0.577771i 0.114278 0.993449i \(-0.463545\pi\)
−0.909512 + 0.415677i \(0.863545\pi\)
\(62\) 0.849472 2.61440i 0.107883 0.332030i
\(63\) 1.92333 + 1.81681i 0.242316 + 0.228897i
\(64\) 0.809017 0.587785i 0.101127 0.0734732i
\(65\) 5.19095i 0.643858i
\(66\) −2.11939 + 2.55112i −0.260878 + 0.314021i
\(67\) 1.75788 0.214759 0.107379 0.994218i \(-0.465754\pi\)
0.107379 + 0.994218i \(0.465754\pi\)
\(68\) 3.34007 2.42671i 0.405043 0.294281i
\(69\) −6.54476 + 2.12652i −0.787897 + 0.256003i
\(70\) −0.931859 4.96438i −0.111378 0.593357i
\(71\) −10.1359 7.36420i −1.20292 0.873969i −0.208347 0.978055i \(-0.566808\pi\)
−0.994568 + 0.104086i \(0.966808\pi\)
\(72\) 0.587785 0.809017i 0.0692712 0.0953436i
\(73\) 2.13629 6.57482i 0.250033 0.769524i −0.744734 0.667361i \(-0.767424\pi\)
0.994768 0.102163i \(-0.0325763\pi\)
\(74\) −0.988653 + 0.321233i −0.114929 + 0.0373426i
\(75\) −0.796579 1.09640i −0.0919811 0.126601i
\(76\) −3.98799 −0.457454
\(77\) −8.71118 + 1.05610i −0.992731 + 0.120354i
\(78\) −2.71901 −0.307868
\(79\) −1.00449 1.38256i −0.113014 0.155551i 0.748763 0.662838i \(-0.230648\pi\)
−0.861777 + 0.507287i \(0.830648\pi\)
\(80\) −1.81569 + 0.589954i −0.203000 + 0.0659588i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 4.78103 6.58052i 0.527976 0.726697i
\(83\) 1.15480 + 0.839010i 0.126756 + 0.0920933i 0.649357 0.760484i \(-0.275038\pi\)
−0.522601 + 0.852577i \(0.675038\pi\)
\(84\) 2.60034 0.488107i 0.283720 0.0532568i
\(85\) −7.49618 + 2.43566i −0.813075 + 0.264184i
\(86\) 0.984619 0.715368i 0.106174 0.0771401i
\(87\) −7.13729 −0.765197
\(88\) 0.818154 + 3.21413i 0.0872155 + 0.342627i
\(89\) 7.07430i 0.749874i −0.927050 0.374937i \(-0.877664\pi\)
0.927050 0.374937i \(-0.122336\pi\)
\(90\) −1.54452 + 1.12216i −0.162807 + 0.118286i
\(91\) −5.22955 4.93994i −0.548206 0.517847i
\(92\) −2.12652 + 6.54476i −0.221705 + 0.682339i
\(93\) −2.22395 1.61579i −0.230612 0.167550i
\(94\) −6.14107 4.46175i −0.633403 0.460194i
\(95\) 7.24095 + 2.35273i 0.742906 + 0.241385i
\(96\) −0.309017 0.951057i −0.0315389 0.0970668i
\(97\) 3.78817 + 5.21398i 0.384631 + 0.529399i 0.956804 0.290734i \(-0.0938994\pi\)
−0.572173 + 0.820133i \(0.693899\pi\)
\(98\) 5.88810 + 3.78554i 0.594787 + 0.382397i
\(99\) 1.77133 + 2.80399i 0.178025 + 0.281812i
\(100\) −1.35522 −0.135522
\(101\) 8.75254 6.35909i 0.870910 0.632753i −0.0599210 0.998203i \(-0.519085\pi\)
0.930831 + 0.365450i \(0.119085\pi\)
\(102\) −1.27579 3.92649i −0.126322 0.388781i
\(103\) −10.3277 3.35566i −1.01761 0.330643i −0.247732 0.968829i \(-0.579685\pi\)
−0.769883 + 0.638186i \(0.779685\pi\)
\(104\) −1.59820 + 2.19973i −0.156716 + 0.215701i
\(105\) −5.00937 0.647827i −0.488864 0.0632215i
\(106\) 4.66499 + 1.51575i 0.453104 + 0.147222i
\(107\) −9.02140 + 2.93123i −0.872132 + 0.283373i −0.710686 0.703509i \(-0.751616\pi\)
−0.161445 + 0.986882i \(0.551616\pi\)
\(108\) −0.587785 0.809017i −0.0565597 0.0778477i
\(109\) 18.9852i 1.81846i 0.416298 + 0.909228i \(0.363327\pi\)
−0.416298 + 0.909228i \(0.636673\pi\)
\(110\) 0.410673 6.31854i 0.0391562 0.602449i
\(111\) 1.03953i 0.0986680i
\(112\) 1.13355 2.39062i 0.107111 0.225892i
\(113\) −3.93992 12.1258i −0.370636 1.14070i −0.946376 0.323068i \(-0.895286\pi\)
0.575740 0.817633i \(-0.304714\pi\)
\(114\) −1.23236 + 3.79280i −0.115421 + 0.355228i
\(115\) 7.72221 10.6287i 0.720100 0.991133i
\(116\) −4.19519 + 5.77419i −0.389514 + 0.536120i
\(117\) −0.840221 + 2.58594i −0.0776785 + 0.239070i
\(118\) −1.01753 3.13164i −0.0936714 0.288291i
\(119\) 4.67994 9.86981i 0.429009 0.904764i
\(120\) 1.90913i 0.174279i
\(121\) −10.9075 1.42387i −0.991587 0.129443i
\(122\) 7.67719i 0.695060i
\(123\) −4.78103 6.58052i −0.431091 0.593345i
\(124\) −2.61440 + 0.849472i −0.234780 + 0.0762848i
\(125\) 11.5391 + 3.74929i 1.03209 + 0.335346i
\(126\) 0.339331 2.62390i 0.0302300 0.233756i
\(127\) −7.38628 + 10.1663i −0.655426 + 0.902117i −0.999319 0.0368922i \(-0.988254\pi\)
0.343893 + 0.939009i \(0.388254\pi\)
\(128\) −0.951057 0.309017i −0.0840623 0.0273135i
\(129\) −0.376091 1.15749i −0.0331130 0.101911i
\(130\) 4.19957 3.05116i 0.368326 0.267605i
\(131\) 0.710341 0.0620628 0.0310314 0.999518i \(-0.490121\pi\)
0.0310314 + 0.999518i \(0.490121\pi\)
\(132\) 3.30964 + 0.215110i 0.288067 + 0.0187229i
\(133\) −9.26104 + 5.05583i −0.803034 + 0.438396i
\(134\) −1.03325 1.42215i −0.0892596 0.122855i
\(135\) 0.589954 + 1.81569i 0.0507751 + 0.156270i
\(136\) −3.92649 1.27579i −0.336694 0.109398i
\(137\) −14.7546 10.7198i −1.26057 0.915858i −0.261785 0.965126i \(-0.584311\pi\)
−0.998786 + 0.0492679i \(0.984311\pi\)
\(138\) 5.56731 + 4.04489i 0.473921 + 0.344324i
\(139\) −6.36306 + 19.5835i −0.539708 + 1.66105i 0.193544 + 0.981092i \(0.438002\pi\)
−0.733251 + 0.679958i \(0.761998\pi\)
\(140\) −3.46854 + 3.67188i −0.293145 + 0.310331i
\(141\) −6.14107 + 4.46175i −0.517171 + 0.375747i
\(142\) 12.5287i 1.05139i
\(143\) −4.81627 7.62410i −0.402757 0.637559i
\(144\) −1.00000 −0.0833333
\(145\) 11.0237 8.00917i 0.915466 0.665125i
\(146\) −6.57482 + 2.13629i −0.544136 + 0.176800i
\(147\) 5.41979 4.43012i 0.447016 0.365390i
\(148\) 0.840999 + 0.611021i 0.0691297 + 0.0502257i
\(149\) −11.0994 + 15.2771i −0.909301 + 1.25155i 0.0581031 + 0.998311i \(0.481495\pi\)
−0.967405 + 0.253236i \(0.918505\pi\)
\(150\) −0.418787 + 1.28889i −0.0341938 + 0.105238i
\(151\) 15.5959 5.06741i 1.26918 0.412380i 0.404420 0.914573i \(-0.367473\pi\)
0.864755 + 0.502193i \(0.167473\pi\)
\(152\) 2.34408 + 3.22635i 0.190130 + 0.261692i
\(153\) −4.12856 −0.333774
\(154\) 5.97471 + 6.42673i 0.481455 + 0.517881i
\(155\) 5.24810 0.421537
\(156\) 1.59820 + 2.19973i 0.127958 + 0.176119i
\(157\) 12.6177 4.09974i 1.00700 0.327195i 0.241343 0.970440i \(-0.422412\pi\)
0.765661 + 0.643245i \(0.222412\pi\)
\(158\) −0.528092 + 1.62530i −0.0420128 + 0.129302i
\(159\) 2.88312 3.96828i 0.228646 0.314705i
\(160\) 1.54452 + 1.12216i 0.122105 + 0.0887144i
\(161\) 3.35894 + 17.8944i 0.264722 + 1.41028i
\(162\) −0.951057 + 0.309017i −0.0747221 + 0.0242787i
\(163\) 11.8632 8.61911i 0.929196 0.675101i −0.0165995 0.999862i \(-0.505284\pi\)
0.945796 + 0.324762i \(0.105284\pi\)
\(164\) −8.13397 −0.635156
\(165\) −5.88238 2.34311i −0.457943 0.182411i
\(166\) 1.42741i 0.110788i
\(167\) −0.813770 + 0.591239i −0.0629714 + 0.0457514i −0.618826 0.785528i \(-0.712391\pi\)
0.555854 + 0.831280i \(0.312391\pi\)
\(168\) −1.92333 1.81681i −0.148388 0.140170i
\(169\) −1.73265 + 5.33254i −0.133281 + 0.410195i
\(170\) 6.37664 + 4.63290i 0.489066 + 0.355327i
\(171\) 3.22635 + 2.34408i 0.246725 + 0.179256i
\(172\) −1.15749 0.376091i −0.0882577 0.0286767i
\(173\) −5.63370 17.3388i −0.428322 1.31824i −0.899777 0.436350i \(-0.856271\pi\)
0.471454 0.881890i \(-0.343729\pi\)
\(174\) 4.19519 + 5.77419i 0.318037 + 0.437740i
\(175\) −3.14714 + 1.71810i −0.237902 + 0.129876i
\(176\) 2.11939 2.55112i 0.159755 0.192298i
\(177\) −3.29280 −0.247502
\(178\) −5.72323 + 4.15817i −0.428974 + 0.311668i
\(179\) 1.25932 + 3.87579i 0.0941259 + 0.289690i 0.987025 0.160567i \(-0.0513323\pi\)
−0.892899 + 0.450257i \(0.851332\pi\)
\(180\) 1.81569 + 0.589954i 0.135334 + 0.0439726i
\(181\) 9.68475 13.3299i 0.719862 0.990805i −0.279667 0.960097i \(-0.590224\pi\)
0.999528 0.0307077i \(-0.00977610\pi\)
\(182\) −0.922646 + 7.13442i −0.0683911 + 0.528839i
\(183\) 7.30144 + 2.37238i 0.539738 + 0.175372i
\(184\) 6.54476 2.12652i 0.482486 0.156769i
\(185\) −1.16652 1.60558i −0.0857642 0.118044i
\(186\) 2.74895i 0.201563i
\(187\) 8.75001 10.5324i 0.639864 0.770208i
\(188\) 7.59077i 0.553614i
\(189\) −2.39062 1.13355i −0.173892 0.0824539i
\(190\) −2.35273 7.24095i −0.170685 0.525314i
\(191\) 8.03783 24.7379i 0.581597 1.78997i −0.0309311 0.999522i \(-0.509847\pi\)
0.612528 0.790449i \(-0.290153\pi\)
\(192\) −0.587785 + 0.809017i −0.0424197 + 0.0583858i
\(193\) 13.2069 18.1777i 0.950654 1.30846i −0.000582623 1.00000i \(-0.500185\pi\)
0.951236 0.308463i \(-0.0998145\pi\)
\(194\) 1.99156 6.12940i 0.142986 0.440065i
\(195\) −1.60409 4.93689i −0.114871 0.353538i
\(196\) −0.398368 6.98866i −0.0284549 0.499190i
\(197\) 18.1214i 1.29109i −0.763720 0.645547i \(-0.776629\pi\)
0.763720 0.645547i \(-0.223371\pi\)
\(198\) 1.22732 3.08118i 0.0872216 0.218970i
\(199\) 0.713487i 0.0505778i 0.999680 + 0.0252889i \(0.00805056\pi\)
−0.999680 + 0.0252889i \(0.991949\pi\)
\(200\) 0.796579 + 1.09640i 0.0563267 + 0.0775270i
\(201\) −1.67184 + 0.543214i −0.117923 + 0.0383154i
\(202\) −10.2892 3.34317i −0.723947 0.235225i
\(203\) −2.42190 + 18.7275i −0.169984 + 1.31441i
\(204\) −2.42671 + 3.34007i −0.169903 + 0.233852i
\(205\) 14.7688 + 4.79867i 1.03150 + 0.335153i
\(206\) 3.35566 + 10.3277i 0.233800 + 0.719562i
\(207\) 5.56731 4.04489i 0.386955 0.281139i
\(208\) 2.71901 0.188530
\(209\) −12.8179 + 3.26279i −0.886633 + 0.225692i
\(210\) 2.42033 + 4.43345i 0.167019 + 0.305937i
\(211\) −1.62246 2.23313i −0.111695 0.153735i 0.749510 0.661994i \(-0.230289\pi\)
−0.861204 + 0.508259i \(0.830289\pi\)
\(212\) −1.51575 4.66499i −0.104102 0.320393i
\(213\) 11.9155 + 3.87159i 0.816438 + 0.265277i
\(214\) 7.67406 + 5.57553i 0.524588 + 0.381136i
\(215\) 1.87977 + 1.36573i 0.128199 + 0.0931420i
\(216\) −0.309017 + 0.951057i −0.0210259 + 0.0647112i
\(217\) −4.99433 + 5.28712i −0.339037 + 0.358913i
\(218\) 15.3594 11.1592i 1.04027 0.755800i
\(219\) 6.91317i 0.467149i
\(220\) −5.35319 + 3.38170i −0.360912 + 0.227994i
\(221\) 11.2256 0.755116
\(222\) 0.840999 0.611021i 0.0564441 0.0410091i
\(223\) 3.49261 1.13482i 0.233883 0.0759931i −0.189731 0.981836i \(-0.560762\pi\)
0.423613 + 0.905843i \(0.360762\pi\)
\(224\) −2.60034 + 0.488107i −0.173742 + 0.0326130i
\(225\) 1.09640 + 0.796579i 0.0730932 + 0.0531053i
\(226\) −7.49417 + 10.3148i −0.498505 + 0.686133i
\(227\) 0.199367 0.613587i 0.0132324 0.0407252i −0.944222 0.329309i \(-0.893184\pi\)
0.957455 + 0.288584i \(0.0931843\pi\)
\(228\) 3.79280 1.23236i 0.251184 0.0816148i
\(229\) 1.63099 + 2.24486i 0.107779 + 0.148345i 0.859499 0.511137i \(-0.170776\pi\)
−0.751720 + 0.659482i \(0.770776\pi\)
\(230\) −13.1378 −0.866282
\(231\) 7.95847 3.69631i 0.523629 0.243200i
\(232\) 7.13729 0.468586
\(233\) −8.21976 11.3135i −0.538495 0.741174i 0.449901 0.893079i \(-0.351459\pi\)
−0.988395 + 0.151904i \(0.951459\pi\)
\(234\) 2.58594 0.840221i 0.169048 0.0549270i
\(235\) 4.47821 13.7825i 0.292126 0.899071i
\(236\) −1.93546 + 2.66393i −0.125988 + 0.173407i
\(237\) 1.38256 + 1.00449i 0.0898072 + 0.0652487i
\(238\) −10.7356 + 2.01518i −0.695888 + 0.130625i
\(239\) 3.05379 0.992237i 0.197533 0.0641824i −0.208580 0.978005i \(-0.566884\pi\)
0.406113 + 0.913823i \(0.366884\pi\)
\(240\) 1.54452 1.12216i 0.0996983 0.0724350i
\(241\) 24.4115 1.57248 0.786242 0.617919i \(-0.212024\pi\)
0.786242 + 0.617919i \(0.212024\pi\)
\(242\) 5.25930 + 9.66125i 0.338081 + 0.621049i
\(243\) 1.00000i 0.0641500i
\(244\) 6.21098 4.51254i 0.397617 0.288886i
\(245\) −3.39967 + 12.9243i −0.217197 + 0.825700i
\(246\) −2.51353 + 7.73587i −0.160257 + 0.493221i
\(247\) −8.77249 6.37359i −0.558180 0.405542i
\(248\) 2.22395 + 1.61579i 0.141221 + 0.102603i
\(249\) −1.35755 0.441094i −0.0860310 0.0279532i
\(250\) −3.74929 11.5391i −0.237126 0.729798i
\(251\) 3.43611 + 4.72940i 0.216885 + 0.298517i 0.903572 0.428437i \(-0.140935\pi\)
−0.686686 + 0.726954i \(0.740935\pi\)
\(252\) −2.32223 + 1.26777i −0.146287 + 0.0798617i
\(253\) −1.48030 + 22.7755i −0.0930654 + 1.43189i
\(254\) 12.5663 0.788479
\(255\) 6.37664 4.63290i 0.399320 0.290123i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −17.5661 5.70759i −1.09575 0.356030i −0.295282 0.955410i \(-0.595414\pi\)
−0.800464 + 0.599381i \(0.795414\pi\)
\(258\) −0.715368 + 0.984619i −0.0445368 + 0.0612997i
\(259\) 2.72763 + 0.352746i 0.169487 + 0.0219185i
\(260\) −4.93689 1.60409i −0.306173 0.0994816i
\(261\) 6.78796 2.20554i 0.420164 0.136520i
\(262\) −0.417528 0.574678i −0.0257950 0.0355037i
\(263\) 9.05216i 0.558180i 0.960265 + 0.279090i \(0.0900328\pi\)
−0.960265 + 0.279090i \(0.909967\pi\)
\(264\) −1.77133 2.80399i −0.109018 0.172574i
\(265\) 9.36439i 0.575250i
\(266\) 9.53376 + 4.52060i 0.584552 + 0.277176i
\(267\) 2.18608 + 6.72806i 0.133786 + 0.411750i
\(268\) −0.543214 + 1.67184i −0.0331821 + 0.102124i
\(269\) −13.8793 + 19.1032i −0.846236 + 1.16474i 0.138444 + 0.990370i \(0.455790\pi\)
−0.984680 + 0.174374i \(0.944210\pi\)
\(270\) 1.12216 1.54452i 0.0682924 0.0939964i
\(271\) −9.94012 + 30.5925i −0.603819 + 1.85836i −0.0991078 + 0.995077i \(0.531599\pi\)
−0.504711 + 0.863288i \(0.668401\pi\)
\(272\) 1.27579 + 3.92649i 0.0773564 + 0.238079i
\(273\) 6.50012 + 3.08215i 0.393405 + 0.186540i
\(274\) 18.2377i 1.10178i
\(275\) −4.35586 + 1.10878i −0.262668 + 0.0668619i
\(276\) 6.88157i 0.414222i
\(277\) −8.40015 11.5618i −0.504716 0.694682i 0.478301 0.878196i \(-0.341253\pi\)
−0.983017 + 0.183514i \(0.941253\pi\)
\(278\) 19.5835 6.36306i 1.17454 0.381631i
\(279\) 2.61440 + 0.849472i 0.156520 + 0.0508565i
\(280\) 5.00937 + 0.647827i 0.299367 + 0.0387151i
\(281\) 13.0935 18.0216i 0.781090 1.07508i −0.214071 0.976818i \(-0.568672\pi\)
0.995161 0.0982601i \(-0.0313277\pi\)
\(282\) 7.21926 + 2.34568i 0.429900 + 0.139683i
\(283\) 7.19759 + 22.1519i 0.427852 + 1.31679i 0.900236 + 0.435401i \(0.143393\pi\)
−0.472384 + 0.881393i \(0.656607\pi\)
\(284\) 10.1359 7.36420i 0.601458 0.436985i
\(285\) −7.61359 −0.450990
\(286\) −3.33709 + 8.37778i −0.197326 + 0.495389i
\(287\) −18.8890 + 10.3120i −1.11498 + 0.608696i
\(288\) 0.587785 + 0.809017i 0.0346356 + 0.0476718i
\(289\) 0.0139034 + 0.0427904i 0.000817849 + 0.00251708i
\(290\) −12.9591 4.21067i −0.760985 0.247259i
\(291\) −5.21398 3.78817i −0.305649 0.222067i
\(292\) 5.59287 + 4.06346i 0.327298 + 0.237796i
\(293\) 0.0227379 0.0699800i 0.00132836 0.00408828i −0.950390 0.311060i \(-0.899316\pi\)
0.951719 + 0.306972i \(0.0993158\pi\)
\(294\) −6.76971 1.78074i −0.394817 0.103855i
\(295\) 5.08580 3.69505i 0.296107 0.215134i
\(296\) 1.03953i 0.0604216i
\(297\) −2.55112 2.11939i −0.148031 0.122979i
\(298\) 18.8835 1.09389
\(299\) −15.1376 + 10.9981i −0.875429 + 0.636037i
\(300\) 1.28889 0.418787i 0.0744142 0.0241787i
\(301\) −3.16476 + 0.594053i −0.182414 + 0.0342407i
\(302\) −13.2667 9.63879i −0.763410 0.554650i
\(303\) −6.35909 + 8.75254i −0.365320 + 0.502820i
\(304\) 1.23236 3.79280i 0.0706805 0.217532i
\(305\) −13.9394 + 4.52919i −0.798168 + 0.259340i
\(306\) 2.42671 + 3.34007i 0.138726 + 0.190939i
\(307\) −13.2297 −0.755059 −0.377530 0.925998i \(-0.623226\pi\)
−0.377530 + 0.925998i \(0.623226\pi\)
\(308\) 1.68749 8.61118i 0.0961538 0.490667i
\(309\) 10.8591 0.617755
\(310\) −3.08476 4.24580i −0.175202 0.241145i
\(311\) 30.0805 9.77374i 1.70571 0.554218i 0.716098 0.698000i \(-0.245926\pi\)
0.989609 + 0.143782i \(0.0459263\pi\)
\(312\) 0.840221 2.58594i 0.0475682 0.146400i
\(313\) 19.2646 26.5154i 1.08890 1.49874i 0.239565 0.970880i \(-0.422995\pi\)
0.849332 0.527859i \(-0.177005\pi\)
\(314\) −10.7333 7.79818i −0.605713 0.440076i
\(315\) 4.96438 0.931859i 0.279711 0.0525043i
\(316\) 1.62530 0.528092i 0.0914303 0.0297075i
\(317\) −2.61599 + 1.90063i −0.146928 + 0.106750i −0.658821 0.752300i \(-0.728945\pi\)
0.511893 + 0.859049i \(0.328945\pi\)
\(318\) −4.90506 −0.275062
\(319\) −8.75972 + 21.9913i −0.490450 + 1.23128i
\(320\) 1.90913i 0.106724i
\(321\) 7.67406 5.57553i 0.428324 0.311196i
\(322\) 12.5025 13.2355i 0.696739 0.737586i
\(323\) 5.08785 15.6588i 0.283096 0.871279i
\(324\) 0.809017 + 0.587785i 0.0449454 + 0.0326547i
\(325\) −2.98112 2.16591i −0.165363 0.120143i
\(326\) −13.9460 4.53133i −0.772398 0.250967i
\(327\) −5.86676 18.0560i −0.324433 0.998501i
\(328\) 4.78103 + 6.58052i 0.263988 + 0.363348i
\(329\) 9.62332 + 17.6276i 0.530551 + 0.971839i
\(330\) 1.56196 + 6.13619i 0.0859832 + 0.337786i
\(331\) −15.9912 −0.878954 −0.439477 0.898254i \(-0.644836\pi\)
−0.439477 + 0.898254i \(0.644836\pi\)
\(332\) −1.15480 + 0.839010i −0.0633778 + 0.0460466i
\(333\) −0.321233 0.988653i −0.0176035 0.0541779i
\(334\) 0.956645 + 0.310833i 0.0523453 + 0.0170080i
\(335\) 1.97262 2.71507i 0.107776 0.148340i
\(336\) −0.339331 + 2.62390i −0.0185120 + 0.143146i
\(337\) 8.65290 + 2.81150i 0.471354 + 0.153152i 0.535055 0.844817i \(-0.320291\pi\)
−0.0637019 + 0.997969i \(0.520291\pi\)
\(338\) 5.33254 1.73265i 0.290052 0.0942436i
\(339\) 7.49417 + 10.3148i 0.407027 + 0.560225i
\(340\) 7.88196i 0.427459i
\(341\) −7.70804 + 4.86930i −0.417414 + 0.263687i
\(342\) 3.98799i 0.215646i
\(343\) −9.78508 15.7243i −0.528345 0.849030i
\(344\) 0.376091 + 1.15749i 0.0202775 + 0.0624076i
\(345\) −4.05981 + 12.4948i −0.218573 + 0.672698i
\(346\) −10.7159 + 14.7492i −0.576092 + 0.792923i
\(347\) −1.31526 + 1.81030i −0.0706068 + 0.0971819i −0.842860 0.538133i \(-0.819130\pi\)
0.772253 + 0.635315i \(0.219130\pi\)
\(348\) 2.20554 6.78796i 0.118229 0.363873i
\(349\) −10.8651 33.4393i −0.581595 1.78997i −0.612535 0.790444i \(-0.709850\pi\)
0.0309397 0.999521i \(-0.490150\pi\)
\(350\) 3.23982 + 1.53622i 0.173176 + 0.0821142i
\(351\) 2.71901i 0.145130i
\(352\) −3.30964 0.215110i −0.176404 0.0114654i
\(353\) 25.2151i 1.34206i −0.741429 0.671031i \(-0.765852\pi\)
0.741429 0.671031i \(-0.234148\pi\)
\(354\) 1.93546 + 2.66393i 0.102869 + 0.141586i
\(355\) −22.7483 + 7.39136i −1.20735 + 0.392293i
\(356\) 6.72806 + 2.18608i 0.356586 + 0.115862i
\(357\) −1.40095 + 10.8329i −0.0741461 + 0.573339i
\(358\) 2.39537 3.29694i 0.126599 0.174249i
\(359\) 24.0137 + 7.80253i 1.26740 + 0.411802i 0.864124 0.503279i \(-0.167873\pi\)
0.403271 + 0.915080i \(0.367873\pi\)
\(360\) −0.589954 1.81569i −0.0310933 0.0956953i
\(361\) 2.50468 1.81976i 0.131825 0.0957766i
\(362\) −16.4767 −0.865995
\(363\) 10.8136 2.01640i 0.567567 0.105834i
\(364\) 6.31419 3.44707i 0.330953 0.180676i
\(365\) −7.75767 10.6775i −0.406055 0.558887i
\(366\) −2.37238 7.30144i −0.124006 0.381652i
\(367\) 5.12799 + 1.66619i 0.267679 + 0.0869742i 0.439781 0.898105i \(-0.355056\pi\)
−0.172102 + 0.985079i \(0.555056\pi\)
\(368\) −5.56731 4.04489i −0.290216 0.210854i
\(369\) 6.58052 + 4.78103i 0.342568 + 0.248890i
\(370\) −0.613276 + 1.88747i −0.0318827 + 0.0981248i
\(371\) −9.43403 8.91158i −0.489790 0.462666i
\(372\) 2.22395 1.61579i 0.115306 0.0837749i
\(373\) 6.68899i 0.346343i 0.984892 + 0.173171i \(0.0554014\pi\)
−0.984892 + 0.173171i \(0.944599\pi\)
\(374\) −13.6640 0.888095i −0.706551 0.0459223i
\(375\) −12.1329 −0.626543
\(376\) 6.14107 4.46175i 0.316701 0.230097i
\(377\) −18.4566 + 5.99690i −0.950561 + 0.308856i
\(378\) 0.488107 + 2.60034i 0.0251055 + 0.133747i
\(379\) 18.8923 + 13.7260i 0.970431 + 0.705060i 0.955550 0.294830i \(-0.0952629\pi\)
0.0148815 + 0.999889i \(0.495263\pi\)
\(380\) −4.47515 + 6.15952i −0.229571 + 0.315977i
\(381\) 3.88320 11.9512i 0.198942 0.612281i
\(382\) −24.7379 + 8.03783i −1.26570 + 0.411251i
\(383\) 8.32573 + 11.4594i 0.425425 + 0.585547i 0.966896 0.255173i \(-0.0821323\pi\)
−0.541471 + 0.840720i \(0.682132\pi\)
\(384\) 1.00000 0.0510310
\(385\) −8.14416 + 14.6397i −0.415065 + 0.746108i
\(386\) −22.4689 −1.14364
\(387\) 0.715368 + 0.984619i 0.0363642 + 0.0500510i
\(388\) −6.12940 + 1.99156i −0.311173 + 0.101106i
\(389\) −8.15943 + 25.1121i −0.413699 + 1.27324i 0.499709 + 0.866193i \(0.333440\pi\)
−0.913409 + 0.407043i \(0.866560\pi\)
\(390\) −3.05116 + 4.19957i −0.154502 + 0.212653i
\(391\) −22.9850 16.6995i −1.16240 0.844532i
\(392\) −5.41979 + 4.43012i −0.273741 + 0.223755i
\(393\) −0.675575 + 0.219507i −0.0340782 + 0.0110727i
\(394\) −14.6605 + 10.6515i −0.738585 + 0.536614i
\(395\) −3.26259 −0.164159
\(396\) −3.21413 + 0.818154i −0.161516 + 0.0411138i
\(397\) 8.98173i 0.450780i −0.974269 0.225390i \(-0.927634\pi\)
0.974269 0.225390i \(-0.0723656\pi\)
\(398\) 0.577223 0.419377i 0.0289336 0.0210215i
\(399\) 7.24544 7.67020i 0.362725 0.383990i
\(400\) 0.418787 1.28889i 0.0209393 0.0644446i
\(401\) −18.3662 13.3438i −0.917164 0.666358i 0.0256527 0.999671i \(-0.491834\pi\)
−0.942816 + 0.333312i \(0.891834\pi\)
\(402\) 1.42215 + 1.03325i 0.0709305 + 0.0515340i
\(403\) −7.10860 2.30972i −0.354105 0.115056i
\(404\) 3.34317 + 10.2892i 0.166329 + 0.511908i
\(405\) −1.12216 1.54452i −0.0557605 0.0767478i
\(406\) 16.5744 9.04840i 0.822576 0.449065i
\(407\) 3.20299 + 1.27584i 0.158766 + 0.0632408i
\(408\) 4.12856 0.204394
\(409\) −20.7446 + 15.0718i −1.02575 + 0.745254i −0.967455 0.253045i \(-0.918568\pi\)
−0.0582999 + 0.998299i \(0.518568\pi\)
\(410\) −4.79867 14.7688i −0.236989 0.729378i
\(411\) 17.3451 + 5.63576i 0.855569 + 0.277991i
\(412\) 6.38285 8.78523i 0.314460 0.432817i
\(413\) −1.11735 + 8.63999i −0.0549812 + 0.425146i
\(414\) −6.54476 2.12652i −0.321658 0.104513i
\(415\) 2.59173 0.842105i 0.127223 0.0413373i
\(416\) −1.59820 2.19973i −0.0783580 0.107851i
\(417\) 20.5913i 1.00836i
\(418\) 10.1738 + 8.45209i 0.497618 + 0.413405i
\(419\) 31.0233i 1.51559i −0.652494 0.757794i \(-0.726277\pi\)
0.652494 0.757794i \(-0.273723\pi\)
\(420\) 2.16410 4.56400i 0.105597 0.222701i
\(421\) 8.37167 + 25.7654i 0.408010 + 1.25573i 0.918355 + 0.395757i \(0.129518\pi\)
−0.510345 + 0.859970i \(0.670482\pi\)
\(422\) −0.852979 + 2.62520i −0.0415224 + 0.127793i
\(423\) 4.46175 6.14107i 0.216937 0.298589i
\(424\) −2.88312 + 3.96828i −0.140017 + 0.192716i
\(425\) 1.72898 5.32127i 0.0838681 0.258119i
\(426\) −3.87159 11.9155i −0.187579 0.577309i
\(427\) 8.70250 18.3532i 0.421144 0.888175i
\(428\) 9.48566i 0.458507i
\(429\) 6.93652 + 5.76264i 0.334899 + 0.278223i
\(430\) 2.32352i 0.112050i
\(431\) 5.33158 + 7.33829i 0.256813 + 0.353473i 0.917883 0.396852i \(-0.129897\pi\)
−0.661070 + 0.750325i \(0.729897\pi\)
\(432\) 0.951057 0.309017i 0.0457577 0.0148676i
\(433\) 22.3025 + 7.24653i 1.07179 + 0.348246i 0.791185 0.611577i \(-0.209464\pi\)
0.280606 + 0.959823i \(0.409464\pi\)
\(434\) 7.21297 + 0.932804i 0.346233 + 0.0447760i
\(435\) −8.00917 + 11.0237i −0.384010 + 0.528545i
\(436\) −18.0560 5.86676i −0.864727 0.280967i
\(437\) 8.48055 + 26.1004i 0.405679 + 1.24855i
\(438\) 5.59287 4.06346i 0.267238 0.194160i
\(439\) 22.9690 1.09625 0.548125 0.836396i \(-0.315342\pi\)
0.548125 + 0.836396i \(0.315342\pi\)
\(440\) 5.88238 + 2.34311i 0.280431 + 0.111703i
\(441\) −3.78554 + 5.88810i −0.180264 + 0.280386i
\(442\) −6.59825 9.08171i −0.313847 0.431973i
\(443\) −0.592518 1.82358i −0.0281514 0.0866411i 0.935994 0.352017i \(-0.114504\pi\)
−0.964145 + 0.265376i \(0.914504\pi\)
\(444\) −0.988653 0.321233i −0.0469194 0.0152450i
\(445\) −10.9264 7.93848i −0.517960 0.376320i
\(446\) −2.97099 2.15855i −0.140681 0.102210i
\(447\) 5.83532 17.9593i 0.276001 0.849444i
\(448\) 1.92333 + 1.81681i 0.0908686 + 0.0858364i
\(449\) 14.3703 10.4406i 0.678176 0.492724i −0.194576 0.980887i \(-0.562333\pi\)
0.872752 + 0.488164i \(0.162333\pi\)
\(450\) 1.35522i 0.0638858i
\(451\) −26.1436 + 6.65484i −1.23106 + 0.313364i
\(452\) 12.7498 0.599702
\(453\) −13.2667 + 9.63879i −0.623322 + 0.452870i
\(454\) −0.613587 + 0.199367i −0.0287971 + 0.00935673i
\(455\) −13.4982 + 2.53374i −0.632806 + 0.118783i
\(456\) −3.22635 2.34408i −0.151088 0.109772i
\(457\) 11.7566 16.1816i 0.549952 0.756944i −0.440054 0.897971i \(-0.645041\pi\)
0.990006 + 0.141027i \(0.0450406\pi\)
\(458\) 0.857462 2.63900i 0.0400666 0.123312i
\(459\) 3.92649 1.27579i 0.183273 0.0595490i
\(460\) 7.72221 + 10.6287i 0.360050 + 0.495566i
\(461\) −16.3460 −0.761308 −0.380654 0.924717i \(-0.624301\pi\)
−0.380654 + 0.924717i \(0.624301\pi\)
\(462\) −7.66825 4.26590i −0.356759 0.198468i
\(463\) −26.7178 −1.24168 −0.620841 0.783937i \(-0.713209\pi\)
−0.620841 + 0.783937i \(0.713209\pi\)
\(464\) −4.19519 5.77419i −0.194757 0.268060i
\(465\) −4.99124 + 1.62175i −0.231463 + 0.0752069i
\(466\) −4.32139 + 13.2999i −0.200184 + 0.616104i
\(467\) −11.6965 + 16.0988i −0.541247 + 0.744963i −0.988792 0.149299i \(-0.952298\pi\)
0.447545 + 0.894261i \(0.352298\pi\)
\(468\) −2.19973 1.59820i −0.101682 0.0738766i
\(469\) 0.858032 + 4.57107i 0.0396202 + 0.211073i
\(470\) −13.7825 + 4.47821i −0.635739 + 0.206564i
\(471\) −10.7333 + 7.79818i −0.494563 + 0.359321i
\(472\) 3.29280 0.151564
\(473\) −4.02802 0.261801i −0.185209 0.0120376i
\(474\) 1.70894i 0.0784944i
\(475\) −4.37242 + 3.17675i −0.200620 + 0.145759i
\(476\) 7.94056 + 7.50083i 0.363955 + 0.343800i
\(477\) −1.51575 + 4.66499i −0.0694013 + 0.213595i
\(478\) −2.59771 1.88735i −0.118816 0.0863252i
\(479\) 2.22341 + 1.61540i 0.101590 + 0.0738095i 0.637421 0.770516i \(-0.280001\pi\)
−0.535831 + 0.844326i \(0.680001\pi\)
\(480\) −1.81569 0.589954i −0.0828746 0.0269276i
\(481\) 0.873437 + 2.68816i 0.0398253 + 0.122570i
\(482\) −14.3487 19.7493i −0.653566 0.899557i
\(483\) −8.72422 15.9806i −0.396966 0.727143i
\(484\) 4.72477 9.93360i 0.214762 0.451527i
\(485\) 12.3040 0.558697
\(486\) 0.809017 0.587785i 0.0366978 0.0266625i
\(487\) 7.61161 + 23.4261i 0.344915 + 1.06154i 0.961629 + 0.274352i \(0.0884635\pi\)
−0.616714 + 0.787187i \(0.711537\pi\)
\(488\) −7.30144 2.37238i −0.330521 0.107393i
\(489\) −8.61911 + 11.8632i −0.389770 + 0.536472i
\(490\) 12.4542 4.84630i 0.562624 0.218933i
\(491\) −7.19483 2.33774i −0.324698 0.105501i 0.142132 0.989848i \(-0.454604\pi\)
−0.466830 + 0.884347i \(0.654604\pi\)
\(492\) 7.73587 2.51353i 0.348760 0.113319i
\(493\) −17.3201 23.8391i −0.780058 1.07366i
\(494\) 10.8434i 0.487867i
\(495\) 6.31854 + 0.410673i 0.283997 + 0.0184584i
\(496\) 2.74895i 0.123431i
\(497\) 14.2020 29.9514i 0.637045 1.34350i
\(498\) 0.441094 + 1.35755i 0.0197659 + 0.0608331i
\(499\) 1.75709 5.40777i 0.0786581 0.242085i −0.903993 0.427546i \(-0.859378\pi\)
0.982652 + 0.185462i \(0.0593780\pi\)
\(500\) −7.13157 + 9.81576i −0.318933 + 0.438974i
\(501\) 0.591239 0.813770i 0.0264146 0.0363566i
\(502\) 1.80647 5.55975i 0.0806267 0.248144i
\(503\) −11.3574 34.9546i −0.506404 1.55855i −0.798398 0.602130i \(-0.794319\pi\)
0.291994 0.956420i \(-0.405681\pi\)
\(504\) 2.39062 + 1.13355i 0.106487 + 0.0504925i
\(505\) 20.6544i 0.919107i
\(506\) 19.2959 12.1895i 0.857807 0.541891i
\(507\) 5.60696i 0.249014i
\(508\) −7.38628 10.1663i −0.327713 0.451058i
\(509\) −7.52368 + 2.44459i −0.333481 + 0.108355i −0.470971 0.882148i \(-0.656096\pi\)
0.137490 + 0.990503i \(0.456096\pi\)
\(510\) −7.49618 2.43566i −0.331937 0.107853i
\(511\) 18.1395 + 2.34585i 0.802443 + 0.103774i
\(512\) 0.587785 0.809017i 0.0259767 0.0357538i
\(513\) −3.79280 1.23236i −0.167456 0.0544098i
\(514\) 5.70759 + 17.5661i 0.251751 + 0.774810i
\(515\) −16.7722 + 12.1857i −0.739069 + 0.536965i
\(516\) 1.21706 0.0535779
\(517\) 6.21042 + 24.3977i 0.273134 + 1.07301i
\(518\) −1.31788 2.41404i −0.0579044 0.106067i
\(519\) 10.7159 + 14.7492i 0.470377 + 0.647419i
\(520\) 1.60409 + 4.93689i 0.0703441 + 0.216497i
\(521\) 9.78679 + 3.17992i 0.428767 + 0.139315i 0.515447 0.856921i \(-0.327626\pi\)
−0.0866802 + 0.996236i \(0.527626\pi\)
\(522\) −5.77419 4.19519i −0.252729 0.183619i
\(523\) −3.62725 2.63535i −0.158609 0.115236i 0.505650 0.862739i \(-0.331253\pi\)
−0.664259 + 0.747503i \(0.731253\pi\)
\(524\) −0.219507 + 0.675575i −0.00958923 + 0.0295126i
\(525\) 2.46219 2.60653i 0.107459 0.113758i
\(526\) 7.32335 5.32073i 0.319313 0.231995i
\(527\) 11.3492i 0.494379i
\(528\) −1.22732 + 3.08118i −0.0534121 + 0.134091i
\(529\) 24.3560 1.05896
\(530\) 7.57595 5.50425i 0.329078 0.239089i
\(531\) 3.13164 1.01753i 0.135902 0.0441571i
\(532\) −1.94656 10.3701i −0.0843942 0.449601i
\(533\) −17.8925 12.9997i −0.775011 0.563079i
\(534\) 4.15817 5.72323i 0.179942 0.247668i
\(535\) −5.59610 + 17.2230i −0.241941 + 0.744617i
\(536\) 1.67184 0.543214i 0.0722125 0.0234633i
\(537\) −2.39537 3.29694i −0.103368 0.142273i
\(538\) 23.6129 1.01802
\(539\) −6.99820 22.1365i −0.301434 0.953487i
\(540\) −1.90913 −0.0821559
\(541\) 8.63926 + 11.8909i 0.371431 + 0.511231i 0.953289 0.302059i \(-0.0976741\pi\)
−0.581858 + 0.813290i \(0.697674\pi\)
\(542\) 30.5925 9.94012i 1.31406 0.426965i
\(543\) −5.09158 + 15.6703i −0.218500 + 0.672475i
\(544\) 2.42671 3.34007i 0.104044 0.143204i
\(545\) 29.3231 + 21.3045i 1.25606 + 0.912583i
\(546\) −1.32717 7.07035i −0.0567976 0.302583i
\(547\) −17.9817 + 5.84260i −0.768840 + 0.249811i −0.667069 0.744996i \(-0.732451\pi\)
−0.101772 + 0.994808i \(0.532451\pi\)
\(548\) 14.7546 10.7198i 0.630285 0.457929i
\(549\) −7.67719 −0.327654
\(550\) 3.45733 + 2.87224i 0.147421 + 0.122473i
\(551\) 28.4634i 1.21258i
\(552\) −5.56731 + 4.04489i −0.236960 + 0.172162i
\(553\) 3.10483 3.28686i 0.132031 0.139771i
\(554\) −4.41622 + 13.5917i −0.187627 + 0.577457i
\(555\) 1.60558 + 1.16652i 0.0681529 + 0.0495160i
\(556\) −16.6587 12.1033i −0.706486 0.513292i
\(557\) 19.3654 + 6.29221i 0.820539 + 0.266609i 0.689055 0.724709i \(-0.258026\pi\)
0.131484 + 0.991318i \(0.458026\pi\)
\(558\) −0.849472 2.61440i −0.0359610 0.110677i
\(559\) −1.94509 2.67719i −0.0822687 0.113233i
\(560\) −2.42033 4.43345i −0.102278 0.187347i
\(561\) −5.06705 + 12.7208i −0.213931 + 0.537075i
\(562\) −22.2759 −0.939653
\(563\) 14.5310 10.5574i 0.612411 0.444942i −0.237852 0.971301i \(-0.576443\pi\)
0.850262 + 0.526359i \(0.176443\pi\)
\(564\) −2.34568 7.21926i −0.0987709 0.303985i
\(565\) −23.1498 7.52181i −0.973918 0.316445i
\(566\) 13.6906 18.8435i 0.575460 0.792053i
\(567\) 2.62390 + 0.339331i 0.110193 + 0.0142506i
\(568\) −11.9155 3.87159i −0.499964 0.162448i
\(569\) 21.5381 6.99814i 0.902922 0.293377i 0.179480 0.983762i \(-0.442559\pi\)
0.723443 + 0.690384i \(0.242559\pi\)
\(570\) 4.47515 + 6.15952i 0.187444 + 0.257994i
\(571\) 27.7551i 1.16151i −0.814077 0.580757i \(-0.802757\pi\)
0.814077 0.580757i \(-0.197243\pi\)
\(572\) 8.73926 2.22457i 0.365407 0.0930140i
\(573\) 26.0110i 1.08662i
\(574\) 19.4452 + 9.22029i 0.811628 + 0.384847i
\(575\) 2.88191 + 8.86960i 0.120184 + 0.369888i
\(576\) 0.309017 0.951057i 0.0128757 0.0396274i
\(577\) 21.3210 29.3458i 0.887605 1.22168i −0.0866511 0.996239i \(-0.527617\pi\)
0.974256 0.225445i \(-0.0723835\pi\)
\(578\) 0.0264459 0.0363997i 0.00110000 0.00151403i
\(579\) −6.94328 + 21.3692i −0.288553 + 0.888074i
\(580\) 4.21067 + 12.9591i 0.174838 + 0.538098i
\(581\) −1.61804 + 3.41239i −0.0671278 + 0.141570i
\(582\) 6.44483i 0.267147i
\(583\) −8.68848 13.7538i −0.359840 0.569622i
\(584\) 6.91317i 0.286069i
\(585\) 3.05116 + 4.19957i 0.126150 + 0.173631i
\(586\) −0.0699800 + 0.0227379i −0.00289085 + 0.000939294i
\(587\) 41.9338 + 13.6251i 1.73079 + 0.562368i 0.993564 0.113275i \(-0.0361341\pi\)
0.737229 + 0.675643i \(0.236134\pi\)
\(588\) 2.53848 + 6.52350i 0.104685 + 0.269025i
\(589\) −6.44375 + 8.86907i −0.265510 + 0.365444i
\(590\) −5.97871 1.94260i −0.246140 0.0799756i
\(591\) 5.59981 + 17.2345i 0.230346 + 0.708931i
\(592\) −0.840999 + 0.611021i −0.0345648 + 0.0251128i
\(593\) 10.1642 0.417396 0.208698 0.977980i \(-0.433077\pi\)
0.208698 + 0.977980i \(0.433077\pi\)
\(594\) −0.215110 + 3.30964i −0.00882608 + 0.135796i
\(595\) −9.99247 18.3037i −0.409651 0.750380i
\(596\) −11.0994 15.2771i −0.454651 0.625773i
\(597\) −0.220480 0.678566i −0.00902363 0.0277719i
\(598\) 17.7953 + 5.78204i 0.727704 + 0.236445i
\(599\) 23.5283 + 17.0943i 0.961341 + 0.698455i 0.953462 0.301514i \(-0.0974919\pi\)
0.00787939 + 0.999969i \(0.497492\pi\)
\(600\) −1.09640 0.796579i −0.0447602 0.0325202i
\(601\) 5.99331 18.4455i 0.244472 0.752408i −0.751250 0.660017i \(-0.770549\pi\)
0.995723 0.0923912i \(-0.0294510\pi\)
\(602\) 2.34080 + 2.21117i 0.0954037 + 0.0901204i
\(603\) 1.42215 1.03325i 0.0579145 0.0420774i
\(604\) 16.3985i 0.667245i
\(605\) −14.4391 + 15.2490i −0.587033 + 0.619958i
\(606\) 10.8187 0.439481
\(607\) −38.3875 + 27.8902i −1.55810 + 1.13203i −0.620559 + 0.784160i \(0.713094\pi\)
−0.937544 + 0.347868i \(0.886906\pi\)
\(608\) −3.79280 + 1.23236i −0.153818 + 0.0499786i
\(609\) −3.48376 18.5593i −0.141169 0.752063i
\(610\) 11.8576 + 8.61502i 0.480099 + 0.348812i
\(611\) −12.1315 + 16.6976i −0.490790 + 0.675514i
\(612\) 1.27579 3.92649i 0.0515709 0.158719i
\(613\) −8.33984 + 2.70978i −0.336843 + 0.109447i −0.472554 0.881302i \(-0.656668\pi\)
0.135712 + 0.990748i \(0.456668\pi\)
\(614\) 7.77622 + 10.7031i 0.313823 + 0.431940i
\(615\) −15.5288 −0.626182
\(616\) −7.95847 + 3.69631i −0.320656 + 0.148929i
\(617\) −13.0687 −0.526124 −0.263062 0.964779i \(-0.584732\pi\)
−0.263062 + 0.964779i \(0.584732\pi\)
\(618\) −6.38285 8.78523i −0.256756 0.353394i
\(619\) −4.54010 + 1.47517i −0.182482 + 0.0592920i −0.398833 0.917024i \(-0.630585\pi\)
0.216351 + 0.976316i \(0.430585\pi\)
\(620\) −1.62175 + 4.99124i −0.0651311 + 0.200453i
\(621\) −4.04489 + 5.56731i −0.162316 + 0.223408i
\(622\) −25.5880 18.5908i −1.02598 0.745422i
\(623\) 18.3956 3.45301i 0.737002 0.138342i
\(624\) −2.58594 + 0.840221i −0.103520 + 0.0336358i
\(625\) 13.2576 9.63219i 0.530303 0.385288i
\(626\) −32.7748 −1.30995
\(627\) 11.1823 7.06405i 0.446578 0.282111i
\(628\) 13.2670i 0.529413i
\(629\) −3.47211 + 2.52264i −0.138442 + 0.100584i
\(630\) −3.67188 3.46854i −0.146291 0.138190i
\(631\) 6.04031 18.5902i 0.240461 0.740062i −0.755889 0.654700i \(-0.772795\pi\)
0.996350 0.0853628i \(-0.0272049\pi\)
\(632\) −1.38256 1.00449i −0.0549954 0.0399565i
\(633\) 2.23313 + 1.62246i 0.0887589 + 0.0644871i
\(634\) 3.07528 + 0.999218i 0.122135 + 0.0396840i
\(635\) 7.41353 + 22.8165i 0.294197 + 0.905445i
\(636\) 2.88312 + 3.96828i 0.114323 + 0.157352i
\(637\) 10.2929 16.0098i 0.407821 0.634332i
\(638\) 22.9402 5.83940i 0.908210 0.231184i
\(639\) −12.5287 −0.495629
\(640\) −1.54452 + 1.12216i −0.0610525 + 0.0443572i
\(641\) 8.97699 + 27.6283i 0.354570 + 1.09125i 0.956259 + 0.292523i \(0.0944947\pi\)
−0.601689 + 0.798731i \(0.705505\pi\)
\(642\) −9.02140 2.93123i −0.356046 0.115686i
\(643\) 28.1940 38.8057i 1.11186 1.53035i 0.293221 0.956045i \(-0.405273\pi\)
0.818642 0.574304i \(-0.194727\pi\)
\(644\) −18.0566 2.33513i −0.711528 0.0920171i
\(645\) −2.20980 0.718007i −0.0870107 0.0282715i
\(646\) −15.6588 + 5.08785i −0.616087 + 0.200179i
\(647\) 18.6901 + 25.7248i 0.734785 + 1.01134i 0.998902 + 0.0468537i \(0.0149195\pi\)
−0.264117 + 0.964491i \(0.585081\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −4.04131 + 10.1457i −0.158635 + 0.398255i
\(650\) 3.68487i 0.144532i
\(651\) 3.11608 6.57169i 0.122129 0.257565i
\(652\) 4.53133 + 13.9460i 0.177461 + 0.546168i
\(653\) −2.68238 + 8.25550i −0.104969 + 0.323063i −0.989723 0.142996i \(-0.954326\pi\)
0.884754 + 0.466059i \(0.154326\pi\)
\(654\) −11.1592 + 15.3594i −0.436361 + 0.600599i
\(655\) 0.797115 1.09714i 0.0311459 0.0428686i
\(656\) 2.51353 7.73587i 0.0981371 0.302035i
\(657\) −2.13629 6.57482i −0.0833445 0.256508i
\(658\) 8.60455 18.1466i 0.335440 0.707430i
\(659\) 8.85864i 0.345084i −0.985002 0.172542i \(-0.944802\pi\)
0.985002 0.172542i \(-0.0551980\pi\)
\(660\) 4.04618 4.87042i 0.157498 0.189581i
\(661\) 13.7111i 0.533299i −0.963794 0.266649i \(-0.914083\pi\)
0.963794 0.266649i \(-0.0859165\pi\)
\(662\) 9.39937 + 12.9371i 0.365317 + 0.502816i
\(663\) −10.6762 + 3.46890i −0.414629 + 0.134721i
\(664\) 1.35755 + 0.441094i 0.0526830 + 0.0171177i
\(665\) −2.58353 + 19.9773i −0.100185 + 0.774686i
\(666\) −0.611021 + 0.840999i −0.0236766 + 0.0325880i
\(667\) 46.7118 + 15.1776i 1.80869 + 0.587679i
\(668\) −0.310833 0.956645i −0.0120265 0.0370137i
\(669\) −2.97099 + 2.15855i −0.114865 + 0.0834545i
\(670\) −3.35602 −0.129654
\(671\) 16.2709 19.5854i 0.628132 0.756087i
\(672\) 2.32223 1.26777i 0.0895821 0.0489051i
\(673\) 24.7380 + 34.0490i 0.953580 + 1.31249i 0.949919 + 0.312497i \(0.101166\pi\)
0.00366159 + 0.999993i \(0.498834\pi\)
\(674\) −2.81150 8.65290i −0.108295 0.333297i
\(675\) −1.28889 0.418787i −0.0496095 0.0161191i
\(676\) −4.53613 3.29569i −0.174467 0.126757i
\(677\) 18.5546 + 13.4807i 0.713113 + 0.518107i 0.884176 0.467153i \(-0.154720\pi\)
−0.171064 + 0.985260i \(0.554720\pi\)
\(678\) 3.93992 12.1258i 0.151312 0.465689i
\(679\) −11.7091 + 12.3955i −0.449352 + 0.475696i
\(680\) −6.37664 + 4.63290i −0.244533 + 0.177663i
\(681\) 0.645164i 0.0247227i
\(682\) 8.47001 + 3.37383i 0.324334 + 0.129191i
\(683\) −32.6961 −1.25108 −0.625541 0.780191i \(-0.715122\pi\)
−0.625541 + 0.780191i \(0.715122\pi\)
\(684\) −3.22635 + 2.34408i −0.123363 + 0.0896282i
\(685\) −33.1140 + 10.7594i −1.26522 + 0.411095i
\(686\) −6.96967 + 17.1588i −0.266103 + 0.655125i
\(687\) −2.24486 1.63099i −0.0856469 0.0622261i
\(688\) 0.715368 0.984619i 0.0272731 0.0375383i
\(689\) 4.12133 12.6842i 0.157010 0.483228i
\(690\) 12.4948 4.05981i 0.475669 0.154554i
\(691\) −6.99712 9.63071i −0.266183 0.366369i 0.654914 0.755704i \(-0.272705\pi\)
−0.921096 + 0.389334i \(0.872705\pi\)
\(692\) 18.2310 0.693040
\(693\) −6.42673 + 5.97471i −0.244131 + 0.226960i
\(694\) 2.23765 0.0849401
\(695\) 23.1067 + 31.8036i 0.876487 + 1.20638i
\(696\) −6.78796 + 2.20554i −0.257297 + 0.0836009i
\(697\) 10.3773 31.9380i 0.393067 1.20974i
\(698\) −20.6666 + 28.4452i −0.782243 + 1.07667i
\(699\) 11.3135 + 8.21976i 0.427917 + 0.310900i
\(700\) −0.661493 3.52403i −0.0250021 0.133196i
\(701\) 18.3841 5.97334i 0.694356 0.225610i 0.0594865 0.998229i \(-0.481054\pi\)
0.634870 + 0.772619i \(0.281054\pi\)
\(702\) −2.19973 + 1.59820i −0.0830234 + 0.0603200i
\(703\) 4.14564 0.156356
\(704\) 1.77133 + 2.80399i 0.0667595 + 0.105680i
\(705\) 14.4918i 0.545792i
\(706\) −20.3994 + 14.8210i −0.767742 + 0.557797i
\(707\) 20.8080 + 19.6556i 0.782564 + 0.739226i
\(708\) 1.01753 3.13164i 0.0382412 0.117694i
\(709\) 28.6813 + 20.8382i 1.07715 + 0.782595i 0.977184 0.212396i \(-0.0681267\pi\)
0.0999656 + 0.994991i \(0.468127\pi\)
\(710\) 19.3508 + 14.0592i 0.726224 + 0.527633i
\(711\) −1.62530 0.528092i −0.0609536 0.0198050i
\(712\) −2.18608 6.72806i −0.0819267 0.252145i
\(713\) 11.1192 + 15.3042i 0.416417 + 0.573148i
\(714\) 9.58748 5.23404i 0.358802 0.195879i
\(715\) −17.1802 1.11663i −0.642503 0.0417595i
\(716\) −4.07524 −0.152299
\(717\) −2.59771 + 1.88735i −0.0970132 + 0.0704842i
\(718\) −7.80253 24.0137i −0.291188 0.896184i
\(719\) −34.1264 11.0883i −1.27270 0.413525i −0.406696 0.913564i \(-0.633319\pi\)
−0.866003 + 0.500039i \(0.833319\pi\)
\(720\) −1.12216 + 1.54452i −0.0418204 + 0.0575608i
\(721\) 3.68485 28.4933i 0.137231 1.06115i
\(722\) −2.94443 0.956702i −0.109580 0.0356048i
\(723\) −23.2167 + 7.54357i −0.863439 + 0.280548i
\(724\) 9.68475 + 13.3299i 0.359931 + 0.495402i
\(725\) 9.67260i 0.359232i
\(726\) −7.98738 7.56318i −0.296440 0.280696i
\(727\) 5.33422i 0.197835i 0.995096 + 0.0989176i \(0.0315380\pi\)
−0.995096 + 0.0989176i \(0.968462\pi\)
\(728\) −6.50012 3.08215i −0.240911 0.114232i
\(729\) −0.309017 0.951057i −0.0114451 0.0352243i
\(730\) −4.07845 + 12.5522i −0.150950 + 0.464577i
\(731\) 2.95344 4.06506i 0.109237 0.150352i
\(732\) −4.51254 + 6.21098i −0.166788 + 0.229564i
\(733\) −11.6517 + 35.8604i −0.430367 + 1.32453i 0.467394 + 0.884049i \(0.345193\pi\)
−0.897761 + 0.440484i \(0.854807\pi\)
\(734\) −1.66619 5.12799i −0.0615001 0.189278i
\(735\) −0.760537 13.3423i −0.0280528 0.492136i
\(736\) 6.88157i 0.253658i
\(737\) −0.378137 + 5.81794i −0.0139289 + 0.214307i
\(738\) 8.13397i 0.299416i
\(739\) −13.3796 18.4155i −0.492178 0.677425i 0.488610 0.872502i \(-0.337504\pi\)
−0.980788 + 0.195078i \(0.937504\pi\)
\(740\) 1.88747 0.613276i 0.0693847 0.0225445i
\(741\) 10.3127 + 3.35079i 0.378846 + 0.123094i
\(742\) −1.66444 + 12.8704i −0.0611035 + 0.472487i
\(743\) −1.73681 + 2.39052i −0.0637174 + 0.0876995i −0.839686 0.543071i \(-0.817261\pi\)
0.775969 + 0.630771i \(0.217261\pi\)
\(744\) −2.61440 0.849472i −0.0958487 0.0311431i
\(745\) 11.1404 + 34.2866i 0.408152 + 1.25616i
\(746\) 5.41150 3.93169i 0.198129 0.143949i
\(747\) 1.42741 0.0522262
\(748\) 7.31304 + 11.5765i 0.267391 + 0.423277i
\(749\) −12.0256 22.0279i −0.439406 0.804883i
\(750\) 7.13157 + 9.81576i 0.260408 + 0.358421i
\(751\) −12.3752 38.0871i −0.451579 1.38982i −0.875105 0.483933i \(-0.839208\pi\)
0.423527 0.905884i \(-0.360792\pi\)
\(752\) −7.21926 2.34568i −0.263259 0.0855381i
\(753\) −4.72940 3.43611i −0.172349 0.125219i
\(754\) 15.7001 + 11.4068i 0.571764 + 0.415411i
\(755\) 9.67435 29.7746i 0.352085 1.08361i
\(756\) 1.81681 1.92333i 0.0660769 0.0699507i
\(757\) −5.01663 + 3.64480i −0.182333 + 0.132472i −0.675208 0.737628i \(-0.735946\pi\)
0.492875 + 0.870100i \(0.335946\pi\)
\(758\) 23.3521i 0.848188i
\(759\) −5.63018 22.1183i −0.204363 0.802842i
\(760\) 7.61359 0.276174
\(761\) 25.4521 18.4921i 0.922639 0.670336i −0.0215405 0.999768i \(-0.506857\pi\)
0.944179 + 0.329432i \(0.106857\pi\)
\(762\) −11.9512 + 3.88320i −0.432948 + 0.140673i
\(763\) −49.3680 + 9.26683i −1.78724 + 0.335482i
\(764\) 21.0433 + 15.2889i 0.761320 + 0.553131i
\(765\) −4.63290 + 6.37664i −0.167503 + 0.230548i
\(766\) 4.37710 13.4713i 0.158151 0.486738i
\(767\) −8.51498 + 2.76668i −0.307458 + 0.0998992i
\(768\) −0.587785 0.809017i −0.0212099 0.0291929i
\(769\) 9.26308 0.334035 0.167018 0.985954i \(-0.446586\pi\)
0.167018 + 0.985954i \(0.446586\pi\)
\(770\) 16.6308 2.01623i 0.599332 0.0726599i
\(771\) 18.4701 0.665186
\(772\) 13.2069 + 18.1777i 0.475327 + 0.654231i
\(773\) −36.0597 + 11.7165i −1.29698 + 0.421413i −0.874529 0.484974i \(-0.838829\pi\)
−0.422448 + 0.906387i \(0.638829\pi\)
\(774\) 0.376091 1.15749i 0.0135183 0.0416051i
\(775\) −2.18975 + 3.01394i −0.0786583 + 0.108264i
\(776\) 5.21398 + 3.78817i 0.187171 + 0.135988i
\(777\) −2.70313 + 0.507402i −0.0969744 + 0.0182030i
\(778\) 25.1121 8.15943i 0.900314 0.292530i
\(779\) −26.2430 + 19.0667i −0.940254 + 0.683135i
\(780\) 5.19095 0.185866
\(781\) 26.5532 31.9622i 0.950148 1.14370i
\(782\) 28.4110i 1.01597i
\(783\) −5.77419 + 4.19519i −0.206353 + 0.149924i
\(784\) 6.76971 + 1.78074i 0.241775 + 0.0635980i
\(785\) 7.82694 24.0889i 0.279356 0.859768i
\(786\) 0.574678 + 0.417528i 0.0204981 + 0.0148927i
\(787\) −20.9772 15.2408i −0.747757 0.543277i 0.147374 0.989081i \(-0.452918\pi\)
−0.895131 + 0.445804i \(0.852918\pi\)
\(788\) 17.2345 + 5.59981i 0.613952 + 0.199485i
\(789\) −2.79727 8.60912i −0.0995855 0.306493i
\(790\) 1.91771 + 2.63949i 0.0682289 + 0.0939090i
\(791\) 29.6081 16.1638i 1.05274 0.574719i
\(792\) 2.55112 + 2.11939i 0.0906500 + 0.0753091i
\(793\) 20.8744 0.741271
\(794\) −7.26637 + 5.27933i −0.257874 + 0.187356i
\(795\) −2.89376 8.90607i −0.102631 0.315866i
\(796\) −0.678566 0.220480i −0.0240512 0.00781469i
\(797\) −4.17131 + 5.74131i −0.147755 + 0.203368i −0.876479 0.481440i \(-0.840114\pi\)
0.728724 + 0.684808i \(0.240114\pi\)
\(798\) −10.4641 1.35325i −0.370425 0.0479045i
\(799\) −29.8051 9.68427i −1.05443 0.342605i
\(800\) −1.28889 + 0.418787i −0.0455692 + 0.0148063i
\(801\) −4.15817 5.72323i −0.146922 0.202220i
\(802\) 22.7019i 0.801631i
\(803\) 21.3007 + 8.48465i 0.751687 + 0.299417i
\(804\) 1.75788i 0.0619956i
\(805\) 31.4075 + 14.8924i 1.10697 + 0.524888i
\(806\) 2.30972 + 7.10860i 0.0813566 + 0.250390i
\(807\) 7.29678 22.4572i 0.256859 0.790530i
\(808\) 6.35909 8.75254i 0.223712 0.307913i
\(809\) 23.8566 32.8358i 0.838753 1.15444i −0.147477 0.989065i \(-0.547115\pi\)
0.986230 0.165379i \(-0.0528847\pi\)
\(810\) −0.589954 + 1.81569i −0.0207289 + 0.0637969i
\(811\) −7.43785 22.8914i −0.261178 0.803824i −0.992549 0.121844i \(-0.961119\pi\)
0.731371 0.681980i \(-0.238881\pi\)
\(812\) −17.0625 8.09049i −0.598777 0.283921i
\(813\) 32.1669i 1.12814i
\(814\) −0.850497 3.34119i −0.0298099 0.117109i
\(815\) 27.9949i 0.980619i
\(816\) −2.42671 3.34007i −0.0849517 0.116926i
\(817\) −4.61605 + 1.49985i −0.161495 + 0.0524730i
\(818\) 24.3867 + 7.92373i 0.852662 + 0.277047i
\(819\) −7.13442 0.922646i −0.249297 0.0322399i
\(820\) −9.12760 + 12.5631i −0.318750 + 0.438721i
\(821\) −31.5692 10.2574i −1.10177 0.357987i −0.298987 0.954257i \(-0.596649\pi\)
−0.802784 + 0.596270i \(0.796649\pi\)
\(822\) −5.63576 17.3451i −0.196570 0.604979i
\(823\) −35.2052 + 25.5781i −1.22718 + 0.891596i −0.996675 0.0814755i \(-0.974037\pi\)
−0.230502 + 0.973072i \(0.574037\pi\)
\(824\) −10.8591 −0.378296
\(825\) 3.80003 2.40055i 0.132300 0.0835763i
\(826\) 7.64666 4.17450i 0.266061 0.145249i
\(827\) 3.67801 + 5.06235i 0.127897 + 0.176035i 0.868163 0.496279i \(-0.165301\pi\)
−0.740266 + 0.672314i \(0.765301\pi\)
\(828\) 2.12652 + 6.54476i 0.0739018 + 0.227446i
\(829\) 2.02371 + 0.657543i 0.0702863 + 0.0228374i 0.343949 0.938988i \(-0.388235\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(830\) −2.20466 1.60178i −0.0765249 0.0555986i
\(831\) 11.5618 + 8.40015i 0.401075 + 0.291398i
\(832\) −0.840221 + 2.58594i −0.0291294 + 0.0896512i
\(833\) 27.9491 + 7.35190i 0.968380 + 0.254728i
\(834\) −16.6587 + 12.1033i −0.576844 + 0.419102i
\(835\) 1.92035i 0.0664564i
\(836\) 0.857857 13.1988i 0.0296696 0.456490i
\(837\) −2.74895 −0.0950175
\(838\) −25.0984 + 18.2350i −0.867009 + 0.629919i
\(839\) −42.1193 + 13.6854i −1.45412 + 0.472472i −0.926269 0.376864i \(-0.877002\pi\)
−0.527852 + 0.849337i \(0.677002\pi\)
\(840\) −4.96438 + 0.931859i −0.171287 + 0.0321522i
\(841\) 17.7505 + 12.8965i 0.612087 + 0.444707i
\(842\) 15.9239 21.9173i 0.548773 0.755321i
\(843\) −6.88364 + 21.1857i −0.237085 + 0.729673i
\(844\) 2.62520 0.852979i 0.0903631 0.0293607i
\(845\) 6.29190 + 8.66006i 0.216448 + 0.297915i
\(846\) −7.59077 −0.260976
\(847\) −1.62145 29.0581i −0.0557136 0.998447i
\(848\) 4.90506 0.168440
\(849\) −13.6906 18.8435i −0.469861 0.646708i
\(850\) −5.32127 + 1.72898i −0.182518 + 0.0593037i
\(851\) 2.21059 6.80349i 0.0757780 0.233221i
\(852\) −7.36420 + 10.1359i −0.252293 + 0.347252i
\(853\) 15.3618 + 11.1610i 0.525977 + 0.382145i 0.818851 0.574007i \(-0.194612\pi\)
−0.292874 + 0.956151i \(0.594612\pi\)
\(854\) −19.9633 + 3.74729i −0.683129 + 0.128230i
\(855\) 7.24095 2.35273i 0.247635 0.0804616i
\(856\) −7.67406 + 5.57553i −0.262294 + 0.190568i
\(857\) 34.1118 1.16524 0.582619 0.812746i \(-0.302028\pi\)
0.582619 + 0.812746i \(0.302028\pi\)
\(858\) 0.584887 8.99896i 0.0199677 0.307219i
\(859\) 16.6970i 0.569694i 0.958573 + 0.284847i \(0.0919429\pi\)
−0.958573 + 0.284847i \(0.908057\pi\)
\(860\) −1.87977 + 1.36573i −0.0640995 + 0.0465710i
\(861\) 14.7779 15.6443i 0.503630 0.533156i
\(862\) 2.80298 8.62668i 0.0954698 0.293826i
\(863\) −16.4968 11.9856i −0.561556 0.407994i 0.270472 0.962728i \(-0.412820\pi\)
−0.832028 + 0.554733i \(0.812820\pi\)
\(864\) −0.809017 0.587785i −0.0275233 0.0199969i
\(865\) −33.1019 10.7555i −1.12550 0.365697i
\(866\) −7.24653 22.3025i −0.246247 0.757871i
\(867\) −0.0264459 0.0363997i −0.000898150 0.00123620i
\(868\) −3.48502 6.38370i −0.118289 0.216677i
\(869\) 4.79187 3.02710i 0.162553 0.102687i
\(870\) 13.6260 0.461965
\(871\) −3.86685 + 2.80943i −0.131023 + 0.0951940i
\(872\) 5.86676 + 18.0560i 0.198674 + 0.611455i
\(873\) 6.12940 + 1.99156i 0.207449 + 0.0674041i
\(874\) 16.1310 22.2024i 0.545638 0.751006i
\(875\) −4.11709 + 31.8356i −0.139183 + 1.07624i
\(876\) −6.57482 2.13629i −0.222142 0.0721785i
\(877\) 10.3046 3.34816i 0.347961 0.113059i −0.129822 0.991537i \(-0.541441\pi\)
0.477783 + 0.878478i \(0.341441\pi\)
\(878\) −13.5008 18.5823i −0.455631 0.627123i
\(879\) 0.0735814i 0.00248184i
\(880\) −1.56196 6.13619i −0.0526537 0.206851i
\(881\) 5.09128i 0.171530i 0.996315 + 0.0857648i \(0.0273334\pi\)
−0.996315 + 0.0857648i \(0.972667\pi\)
\(882\) 6.98866 0.398368i 0.235320 0.0134138i
\(883\) −13.9190 42.8382i −0.468410 1.44162i −0.854642 0.519217i \(-0.826224\pi\)
0.386232 0.922402i \(-0.373776\pi\)
\(884\) −3.46890 + 10.6762i −0.116672 + 0.359079i
\(885\) −3.69505 + 5.08580i −0.124208 + 0.170957i
\(886\) −1.12704 + 1.55123i −0.0378635 + 0.0521147i
\(887\) 2.99211 9.20876i 0.100465 0.309200i −0.888174 0.459507i \(-0.848026\pi\)
0.988639 + 0.150307i \(0.0480262\pi\)
\(888\) 0.321233 + 0.988653i 0.0107799 + 0.0331770i
\(889\) −30.0412 14.2446i −1.00755 0.477747i
\(890\) 13.5058i 0.452714i
\(891\) 3.08118 + 1.22732i 0.103224 + 0.0411167i
\(892\) 3.67235i 0.122959i
\(893\) 17.7934 + 24.4905i 0.595433 + 0.819543i
\(894\) −17.9593 + 5.83532i −0.600648 + 0.195162i
\(895\) 7.39938 + 2.40420i 0.247334 + 0.0803637i
\(896\) 0.339331 2.62390i 0.0113363 0.0876584i
\(897\) 10.9981 15.1376i 0.367216 0.505429i
\(898\) −16.8933 5.48896i −0.563736 0.183169i
\(899\) 6.06292 + 18.6598i 0.202210 + 0.622338i
\(900\) −1.09640 + 0.796579i −0.0365466 + 0.0265526i
\(901\) 20.2508 0.674653
\(902\) 20.7507 + 17.2390i 0.690923 + 0.573997i
\(903\) 2.82629 1.54294i 0.0940530 0.0513459i
\(904\) −7.49417 10.3148i −0.249252 0.343066i
\(905\) −9.72048 29.9166i −0.323120 0.994460i
\(906\) 15.5959 + 5.06741i 0.518139 + 0.168353i
\(907\) 31.1086 + 22.6017i 1.03294 + 0.750478i 0.968896 0.247469i \(-0.0795988\pi\)
0.0640482 + 0.997947i \(0.479599\pi\)
\(908\) 0.521948 + 0.379218i 0.0173215 + 0.0125848i
\(909\) 3.34317 10.2892i 0.110886 0.341272i
\(910\) 9.98389 + 9.43100i 0.330963 + 0.312635i
\(911\) −1.74791 + 1.26993i −0.0579108 + 0.0420746i −0.616364 0.787461i \(-0.711395\pi\)
0.558453 + 0.829536i \(0.311395\pi\)
\(912\) 3.98799i 0.132055i
\(913\) −3.02523 + 3.64149i −0.100121 + 0.120516i
\(914\) −20.0016 −0.661593
\(915\) 11.8576 8.61502i 0.391999 0.284804i
\(916\) −2.63900 + 0.857462i −0.0871949 + 0.0283313i
\(917\) 0.346722 + 1.84713i 0.0114498 + 0.0609975i
\(918\) −3.34007 2.42671i −0.110239 0.0800932i
\(919\) 17.8319 24.5435i 0.588220 0.809616i −0.406346 0.913719i \(-0.633197\pi\)
0.994566 + 0.104103i \(0.0331972\pi\)
\(920\) 4.05981 12.4948i 0.133848 0.411942i
\(921\) 12.5822 4.08820i 0.414597 0.134711i
\(922\) 9.60793 + 13.2242i 0.316420 + 0.435515i
\(923\) 34.0658 1.12129
\(924\) 1.05610 + 8.71118i 0.0347431 + 0.286577i
\(925\) 1.40880 0.0463209
\(926\) 15.7043 + 21.6152i 0.516076 + 0.710318i
\(927\) −10.3277 + 3.35566i −0.339205 + 0.110214i
\(928\) −2.20554 + 6.78796i −0.0724005 + 0.222826i
\(929\) 6.02613 8.29426i 0.197711 0.272126i −0.698638 0.715476i \(-0.746210\pi\)
0.896349 + 0.443350i \(0.146210\pi\)
\(930\) 4.24580 + 3.08476i 0.139225 + 0.101153i
\(931\) −17.6672 21.6140i −0.579021 0.708372i
\(932\) 13.2999 4.32139i 0.435651 0.141552i
\(933\) −25.5880 + 18.5908i −0.837713 + 0.608634i
\(934\) 19.8992 0.651121
\(935\) −6.44865 25.3336i −0.210893 0.828498i
\(936\) 2.71901i 0.0888737i
\(937\) −6.04418 + 4.39135i −0.197455 + 0.143459i −0.682119 0.731241i \(-0.738942\pi\)
0.484665 + 0.874700i \(0.338942\pi\)
\(938\) 3.19374 3.38097i 0.104279 0.110393i
\(939\) −10.1280 + 31.1707i −0.330514 + 1.01722i
\(940\) 11.7241 + 8.51805i 0.382398 + 0.277828i
\(941\) −6.90963 5.02014i −0.225247 0.163652i 0.469438 0.882965i \(-0.344456\pi\)
−0.694686 + 0.719314i \(0.744456\pi\)
\(942\) 12.6177 + 4.09974i 0.411107 + 0.133577i
\(943\) 17.2971 + 53.2349i 0.563270 + 1.73357i
\(944\) −1.93546 2.66393i −0.0629939 0.0867037i
\(945\) −4.43345 + 2.42033i −0.144220 + 0.0787333i
\(946\) 2.15581 + 3.41262i 0.0700914 + 0.110954i
\(947\) 14.3206 0.465358 0.232679 0.972554i \(-0.425251\pi\)
0.232679 + 0.972554i \(0.425251\pi\)
\(948\) −1.38256 + 1.00449i −0.0449036 + 0.0326244i
\(949\) 5.80859 + 17.8770i 0.188555 + 0.580312i
\(950\) 5.14009 + 1.67012i 0.166766 + 0.0541857i
\(951\) 1.90063 2.61599i 0.0616320 0.0848292i
\(952\) 1.40095 10.8329i 0.0454050 0.351097i
\(953\) −24.9335 8.10139i −0.807676 0.262430i −0.124063 0.992274i \(-0.539592\pi\)
−0.683613 + 0.729844i \(0.739592\pi\)
\(954\) 4.66499 1.51575i 0.151035 0.0490741i
\(955\) −29.1884 40.1744i −0.944515 1.30001i
\(956\) 3.21094i 0.103849i
\(957\) 1.53530 23.6219i 0.0496293 0.763586i
\(958\) 2.74828i 0.0887929i
\(959\) 20.6734 43.5994i 0.667579 1.40790i
\(960\) 0.589954 + 1.81569i 0.0190407 + 0.0586012i
\(961\) 7.24437 22.2959i 0.233689 0.719222i
\(962\) 1.66138 2.28669i 0.0535649 0.0737258i
\(963\) −5.57553 + 7.67406i −0.179669 + 0.247293i
\(964\) −7.54357 + 23.2167i −0.242962 + 0.747760i
\(965\) −13.2556 40.7966i −0.426714 1.31329i
\(966\) −7.80063 + 16.4512i −0.250981 + 0.529309i
\(967\) 7.95189i 0.255715i −0.991793 0.127858i \(-0.959190\pi\)
0.991793 0.127858i \(-0.0408101\pi\)
\(968\) −10.8136 + 2.01640i −0.347563 + 0.0648097i
\(969\) 16.4646i 0.528920i
\(970\) −7.23212 9.95416i −0.232209 0.319609i
\(971\) −3.14087 + 1.02053i −0.100795 + 0.0327504i −0.358980 0.933345i \(-0.616876\pi\)
0.258185 + 0.966095i \(0.416876\pi\)
\(972\) −0.951057 0.309017i −0.0305052 0.00991172i
\(973\) −54.0295 6.98727i −1.73211 0.224002i
\(974\) 14.4781 19.9275i 0.463910 0.638517i
\(975\) 3.50452 + 1.13869i 0.112234 + 0.0364671i
\(976\) 2.37238 + 7.30144i 0.0759381 + 0.233713i
\(977\) −12.0874 + 8.78203i −0.386711 + 0.280962i −0.764106 0.645090i \(-0.776820\pi\)
0.377395 + 0.926052i \(0.376820\pi\)
\(978\) 14.6637 0.468894
\(979\) 23.4134 + 1.52175i 0.748295 + 0.0486354i
\(980\) −11.2411 7.22709i −0.359085 0.230861i
\(981\) 11.1592 + 15.3594i 0.356287 + 0.490387i
\(982\) 2.33774 + 7.19483i 0.0746003 + 0.229596i
\(983\) −4.67661 1.51952i −0.149161 0.0484652i 0.233485 0.972360i \(-0.424987\pi\)
−0.382646 + 0.923895i \(0.624987\pi\)
\(984\) −6.58052 4.78103i −0.209779 0.152414i
\(985\) −27.9888 20.3351i −0.891797 0.647929i
\(986\) −9.10571 + 28.0245i −0.289985 + 0.892482i
\(987\) −14.5995 13.7910i −0.464708 0.438973i
\(988\) 8.77249 6.37359i 0.279090 0.202771i
\(989\) 8.37526i 0.266318i
\(990\) −3.38170 5.35319i −0.107478 0.170136i
\(991\) −45.0334 −1.43053 −0.715266 0.698852i \(-0.753695\pi\)
−0.715266 + 0.698852i \(0.753695\pi\)
\(992\) −2.22395 + 1.61579i −0.0706103 + 0.0513014i
\(993\) 15.2085 4.94154i 0.482627 0.156815i
\(994\) −32.5789 + 6.11535i −1.03334 + 0.193967i
\(995\) 1.10199 + 0.800646i 0.0349356 + 0.0253822i
\(996\) 0.839010 1.15480i 0.0265850 0.0365912i
\(997\) 6.69325 20.5997i 0.211977 0.652399i −0.787377 0.616472i \(-0.788561\pi\)
0.999354 0.0359275i \(-0.0114385\pi\)
\(998\) −5.40777 + 1.75709i −0.171180 + 0.0556197i
\(999\) 0.611021 + 0.840999i 0.0193319 + 0.0266080i
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 462.2.u.a.349.4 yes 32
7.6 odd 2 462.2.u.b.349.1 yes 32
11.7 odd 10 462.2.u.b.139.1 yes 32
77.62 even 10 inner 462.2.u.a.139.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.u.a.139.4 32 77.62 even 10 inner
462.2.u.a.349.4 yes 32 1.1 even 1 trivial
462.2.u.b.139.1 yes 32 11.7 odd 10
462.2.u.b.349.1 yes 32 7.6 odd 2