Properties

Label 930.2.o.e.491.11
Level $930$
Weight $2$
Character 930.491
Analytic conductor $7.426$
Analytic rank $0$
Dimension $40$
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] = [930,2,Mod(161,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.o (of order \(6\), degree \(2\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 491.11
Character \(\chi\) \(=\) 930.491
Dual form 930.2.o.e.161.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-1.67328 + 0.447368i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.447368 - 1.67328i) q^{6} +(-1.32225 + 2.29021i) q^{7} -1.00000i q^{8} +(2.59972 - 1.49714i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-1.67328 + 0.447368i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.447368 - 1.67328i) q^{6} +(-1.32225 + 2.29021i) q^{7} -1.00000i q^{8} +(2.59972 - 1.49714i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-1.35563 - 2.34802i) q^{11} +(1.67328 - 0.447368i) q^{12} +(3.49868 - 2.01996i) q^{13} +(-2.29021 - 1.32225i) q^{14} +(-1.22542 + 1.22407i) q^{15} +1.00000 q^{16} +(0.370882 - 0.642386i) q^{17} +(1.49714 + 2.59972i) q^{18} +(1.17674 - 2.03818i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(1.18793 - 4.42369i) q^{21} +(2.34802 - 1.35563i) q^{22} -3.17723 q^{23} +(0.447368 + 1.67328i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.01996 + 3.49868i) q^{26} +(-3.68029 + 3.66817i) q^{27} +(1.32225 - 2.29021i) q^{28} +1.11630 q^{29} +(-1.22407 - 1.22542i) q^{30} +(4.10522 - 3.76128i) q^{31} +1.00000i q^{32} +(3.31878 + 3.32243i) q^{33} +(0.642386 + 0.370882i) q^{34} +2.64450i q^{35} +(-2.59972 + 1.49714i) q^{36} +(8.66260 + 5.00135i) q^{37} +(2.03818 + 1.17674i) q^{38} +(-4.95060 + 4.94516i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(4.56104 - 2.63332i) q^{41} +(4.42369 + 1.18793i) q^{42} +(4.20794 + 2.42945i) q^{43} +(1.35563 + 2.34802i) q^{44} +(1.50285 - 2.59643i) q^{45} -3.17723i q^{46} +3.29156i q^{47} +(-1.67328 + 0.447368i) q^{48} +(0.00329675 + 0.00571013i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-0.333205 + 1.24081i) q^{51} +(-3.49868 + 2.01996i) q^{52} +(0.432136 + 0.748481i) q^{53} +(-3.66817 - 3.68029i) q^{54} +(-2.34802 - 1.35563i) q^{55} +(2.29021 + 1.32225i) q^{56} +(-1.05720 + 3.93687i) q^{57} +1.11630i q^{58} +(-0.0673682 - 0.0388951i) q^{59} +(1.22542 - 1.22407i) q^{60} +8.21375i q^{61} +(3.76128 + 4.10522i) q^{62} +(-0.00871827 + 7.93351i) q^{63} -1.00000 q^{64} +(2.01996 - 3.49868i) q^{65} +(-3.32243 + 3.31878i) q^{66} +(4.09060 + 7.08512i) q^{67} +(-0.370882 + 0.642386i) q^{68} +(5.31639 - 1.42139i) q^{69} -2.64450 q^{70} +(11.6252 - 6.71183i) q^{71} +(-1.49714 - 2.59972i) q^{72} +(9.24020 - 5.33483i) q^{73} +(-5.00135 + 8.66260i) q^{74} +(-0.449207 + 1.67279i) q^{75} +(-1.17674 + 2.03818i) q^{76} +7.16994 q^{77} +(-4.94516 - 4.95060i) q^{78} +(-10.5492 - 6.09057i) q^{79} +(0.866025 - 0.500000i) q^{80} +(4.51712 - 7.78432i) q^{81} +(2.63332 + 4.56104i) q^{82} +(-2.44932 - 4.24235i) q^{83} +(-1.18793 + 4.42369i) q^{84} -0.741764i q^{85} +(-2.42945 + 4.20794i) q^{86} +(-1.86788 + 0.499398i) q^{87} +(-2.34802 + 1.35563i) q^{88} -17.1663 q^{89} +(2.59643 + 1.50285i) q^{90} +10.6836i q^{91} +3.17723 q^{92} +(-5.18650 + 8.13021i) q^{93} -3.29156 q^{94} -2.35348i q^{95} +(-0.447368 - 1.67328i) q^{96} +12.4034 q^{97} +(-0.00571013 + 0.00329675i) q^{98} +(-7.03959 - 4.07463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.67328 + 0.447368i −0.966068 + 0.258288i
\(4\) −1.00000 −0.500000
\(5\) 0.866025 0.500000i 0.387298 0.223607i
\(6\) −0.447368 1.67328i −0.182637 0.683113i
\(7\) −1.32225 + 2.29021i −0.499764 + 0.865617i −1.00000 0.000271954i \(-0.999913\pi\)
0.500236 + 0.865889i \(0.333247\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 2.59972 1.49714i 0.866574 0.499048i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −1.35563 2.34802i −0.408738 0.707955i 0.586011 0.810303i \(-0.300698\pi\)
−0.994749 + 0.102348i \(0.967364\pi\)
\(12\) 1.67328 0.447368i 0.483034 0.129144i
\(13\) 3.49868 2.01996i 0.970359 0.560237i 0.0710136 0.997475i \(-0.477377\pi\)
0.899346 + 0.437238i \(0.144043\pi\)
\(14\) −2.29021 1.32225i −0.612084 0.353387i
\(15\) −1.22542 + 1.22407i −0.316401 + 0.316054i
\(16\) 1.00000 0.250000
\(17\) 0.370882 0.642386i 0.0899521 0.155802i −0.817539 0.575874i \(-0.804662\pi\)
0.907491 + 0.420072i \(0.137995\pi\)
\(18\) 1.49714 + 2.59972i 0.352880 + 0.612761i
\(19\) 1.17674 2.03818i 0.269963 0.467590i −0.698889 0.715230i \(-0.746322\pi\)
0.968852 + 0.247641i \(0.0796552\pi\)
\(20\) −0.866025 + 0.500000i −0.193649 + 0.111803i
\(21\) 1.18793 4.42369i 0.259228 0.965329i
\(22\) 2.34802 1.35563i 0.500600 0.289021i
\(23\) −3.17723 −0.662498 −0.331249 0.943543i \(-0.607470\pi\)
−0.331249 + 0.943543i \(0.607470\pi\)
\(24\) 0.447368 + 1.67328i 0.0913187 + 0.341557i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 2.01996 + 3.49868i 0.396148 + 0.686148i
\(27\) −3.68029 + 3.66817i −0.708271 + 0.705940i
\(28\) 1.32225 2.29021i 0.249882 0.432809i
\(29\) 1.11630 0.207292 0.103646 0.994614i \(-0.466949\pi\)
0.103646 + 0.994614i \(0.466949\pi\)
\(30\) −1.22407 1.22542i −0.223484 0.223730i
\(31\) 4.10522 3.76128i 0.737319 0.675545i
\(32\) 1.00000i 0.176777i
\(33\) 3.31878 + 3.32243i 0.577725 + 0.578360i
\(34\) 0.642386 + 0.370882i 0.110168 + 0.0636057i
\(35\) 2.64450i 0.447003i
\(36\) −2.59972 + 1.49714i −0.433287 + 0.249524i
\(37\) 8.66260 + 5.00135i 1.42412 + 0.822218i 0.996648 0.0818097i \(-0.0260700\pi\)
0.427475 + 0.904027i \(0.359403\pi\)
\(38\) 2.03818 + 1.17674i 0.330636 + 0.190893i
\(39\) −4.95060 + 4.94516i −0.792730 + 0.791860i
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) 4.56104 2.63332i 0.712315 0.411255i −0.0996025 0.995027i \(-0.531757\pi\)
0.811918 + 0.583772i \(0.198424\pi\)
\(42\) 4.42369 + 1.18793i 0.682590 + 0.183302i
\(43\) 4.20794 + 2.42945i 0.641704 + 0.370488i 0.785271 0.619153i \(-0.212524\pi\)
−0.143567 + 0.989641i \(0.545857\pi\)
\(44\) 1.35563 + 2.34802i 0.204369 + 0.353978i
\(45\) 1.50285 2.59643i 0.224032 0.387052i
\(46\) 3.17723i 0.468457i
\(47\) 3.29156i 0.480123i 0.970758 + 0.240061i \(0.0771676\pi\)
−0.970758 + 0.240061i \(0.922832\pi\)
\(48\) −1.67328 + 0.447368i −0.241517 + 0.0645721i
\(49\) 0.00329675 + 0.00571013i 0.000470964 + 0.000815734i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) −0.333205 + 1.24081i −0.0466581 + 0.173748i
\(52\) −3.49868 + 2.01996i −0.485180 + 0.280119i
\(53\) 0.432136 + 0.748481i 0.0593584 + 0.102812i 0.894178 0.447712i \(-0.147761\pi\)
−0.834819 + 0.550524i \(0.814428\pi\)
\(54\) −3.66817 3.68029i −0.499175 0.500824i
\(55\) −2.34802 1.35563i −0.316607 0.182793i
\(56\) 2.29021 + 1.32225i 0.306042 + 0.176693i
\(57\) −1.05720 + 3.93687i −0.140030 + 0.521452i
\(58\) 1.11630i 0.146577i
\(59\) −0.0673682 0.0388951i −0.00877060 0.00506371i 0.495608 0.868546i \(-0.334945\pi\)
−0.504379 + 0.863482i \(0.668279\pi\)
\(60\) 1.22542 1.22407i 0.158201 0.158027i
\(61\) 8.21375i 1.05166i 0.850589 + 0.525832i \(0.176246\pi\)
−0.850589 + 0.525832i \(0.823754\pi\)
\(62\) 3.76128 + 4.10522i 0.477682 + 0.521363i
\(63\) −0.00871827 + 7.93351i −0.00109840 + 0.999528i
\(64\) −1.00000 −0.125000
\(65\) 2.01996 3.49868i 0.250546 0.433958i
\(66\) −3.32243 + 3.31878i −0.408963 + 0.408513i
\(67\) 4.09060 + 7.08512i 0.499746 + 0.865586i 1.00000 0.000293150i \(-9.33126e-5\pi\)
−0.500254 + 0.865879i \(0.666760\pi\)
\(68\) −0.370882 + 0.642386i −0.0449760 + 0.0779008i
\(69\) 5.31639 1.42139i 0.640018 0.171115i
\(70\) −2.64450 −0.316079
\(71\) 11.6252 6.71183i 1.37966 0.796548i 0.387543 0.921852i \(-0.373324\pi\)
0.992118 + 0.125304i \(0.0399906\pi\)
\(72\) −1.49714 2.59972i −0.176440 0.306380i
\(73\) 9.24020 5.33483i 1.08148 0.624395i 0.150188 0.988657i \(-0.452012\pi\)
0.931296 + 0.364262i \(0.118679\pi\)
\(74\) −5.00135 + 8.66260i −0.581396 + 1.00701i
\(75\) −0.449207 + 1.67279i −0.0518699 + 0.193157i
\(76\) −1.17674 + 2.03818i −0.134982 + 0.233795i
\(77\) 7.16994 0.817091
\(78\) −4.94516 4.95060i −0.559929 0.560545i
\(79\) −10.5492 6.09057i −1.18688 0.685243i −0.229280 0.973360i \(-0.573637\pi\)
−0.957595 + 0.288118i \(0.906971\pi\)
\(80\) 0.866025 0.500000i 0.0968246 0.0559017i
\(81\) 4.51712 7.78432i 0.501902 0.864924i
\(82\) 2.63332 + 4.56104i 0.290801 + 0.503683i
\(83\) −2.44932 4.24235i −0.268848 0.465659i 0.699716 0.714421i \(-0.253310\pi\)
−0.968565 + 0.248762i \(0.919976\pi\)
\(84\) −1.18793 + 4.42369i −0.129614 + 0.482664i
\(85\) 0.741764i 0.0804556i
\(86\) −2.42945 + 4.20794i −0.261975 + 0.453753i
\(87\) −1.86788 + 0.499398i −0.200258 + 0.0535410i
\(88\) −2.34802 + 1.35563i −0.250300 + 0.144511i
\(89\) −17.1663 −1.81962 −0.909811 0.415022i \(-0.863774\pi\)
−0.909811 + 0.415022i \(0.863774\pi\)
\(90\) 2.59643 + 1.50285i 0.273687 + 0.158415i
\(91\) 10.6836i 1.11995i
\(92\) 3.17723 0.331249
\(93\) −5.18650 + 8.13021i −0.537815 + 0.843063i
\(94\) −3.29156 −0.339498
\(95\) 2.35348i 0.241462i
\(96\) −0.447368 1.67328i −0.0456593 0.170778i
\(97\) 12.4034 1.25938 0.629689 0.776847i \(-0.283182\pi\)
0.629689 + 0.776847i \(0.283182\pi\)
\(98\) −0.00571013 + 0.00329675i −0.000576811 + 0.000333022i
\(99\) −7.03959 4.07463i −0.707505 0.409516i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 0.291018i 0.0289574i 0.999895 + 0.0144787i \(0.00460888\pi\)
−0.999895 + 0.0144787i \(0.995391\pi\)
\(102\) −1.24081 0.333205i −0.122859 0.0329923i
\(103\) 3.02724 + 5.24333i 0.298283 + 0.516641i 0.975743 0.218918i \(-0.0702528\pi\)
−0.677460 + 0.735559i \(0.736919\pi\)
\(104\) −2.01996 3.49868i −0.198074 0.343074i
\(105\) −1.18307 4.42499i −0.115456 0.431835i
\(106\) −0.748481 + 0.432136i −0.0726989 + 0.0419727i
\(107\) 4.83678 + 2.79252i 0.467590 + 0.269963i 0.715230 0.698889i \(-0.246322\pi\)
−0.247641 + 0.968852i \(0.579655\pi\)
\(108\) 3.68029 3.66817i 0.354136 0.352970i
\(109\) 7.74239 0.741587 0.370793 0.928715i \(-0.379086\pi\)
0.370793 + 0.928715i \(0.379086\pi\)
\(110\) 1.35563 2.34802i 0.129254 0.223875i
\(111\) −16.7324 4.49329i −1.58817 0.426484i
\(112\) −1.32225 + 2.29021i −0.124941 + 0.216404i
\(113\) −5.97390 + 3.44903i −0.561978 + 0.324458i −0.753939 0.656945i \(-0.771849\pi\)
0.191961 + 0.981402i \(0.438515\pi\)
\(114\) −3.93687 1.05720i −0.368722 0.0990159i
\(115\) −2.75156 + 1.58861i −0.256584 + 0.148139i
\(116\) −1.11630 −0.103646
\(117\) 6.07142 10.4894i 0.561303 0.969743i
\(118\) 0.0388951 0.0673682i 0.00358058 0.00620175i
\(119\) 0.980799 + 1.69879i 0.0899097 + 0.155728i
\(120\) 1.22407 + 1.22542i 0.111742 + 0.111865i
\(121\) 1.82453 3.16018i 0.165866 0.287289i
\(122\) −8.21375 −0.743638
\(123\) −6.45383 + 6.44674i −0.581922 + 0.581283i
\(124\) −4.10522 + 3.76128i −0.368659 + 0.337772i
\(125\) 1.00000i 0.0894427i
\(126\) −7.93351 0.00871827i −0.706773 0.000776685i
\(127\) 6.24347 + 3.60467i 0.554019 + 0.319863i 0.750741 0.660596i \(-0.229696\pi\)
−0.196723 + 0.980459i \(0.563030\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −8.12791 2.18265i −0.715623 0.192172i
\(130\) 3.49868 + 2.01996i 0.306855 + 0.177163i
\(131\) 13.4418 + 7.76065i 1.17442 + 0.678051i 0.954717 0.297516i \(-0.0961580\pi\)
0.219702 + 0.975567i \(0.429491\pi\)
\(132\) −3.31878 3.32243i −0.288863 0.289180i
\(133\) 3.11190 + 5.38997i 0.269836 + 0.467369i
\(134\) −7.08512 + 4.09060i −0.612061 + 0.353374i
\(135\) −1.35313 + 5.01687i −0.116459 + 0.431784i
\(136\) −0.642386 0.370882i −0.0550842 0.0318029i
\(137\) −9.07490 15.7182i −0.775321 1.34290i −0.934614 0.355664i \(-0.884255\pi\)
0.159293 0.987231i \(-0.449079\pi\)
\(138\) 1.42139 + 5.31639i 0.120997 + 0.452561i
\(139\) 20.3716i 1.72789i −0.503583 0.863947i \(-0.667985\pi\)
0.503583 0.863947i \(-0.332015\pi\)
\(140\) 2.64450i 0.223501i
\(141\) −1.47254 5.50769i −0.124010 0.463831i
\(142\) 6.71183 + 11.6252i 0.563244 + 0.975568i
\(143\) −9.48584 5.47665i −0.793246 0.457981i
\(144\) 2.59972 1.49714i 0.216644 0.124762i
\(145\) 0.966745 0.558150i 0.0802838 0.0463519i
\(146\) 5.33483 + 9.24020i 0.441514 + 0.764725i
\(147\) −0.00807091 0.00807979i −0.000665678 0.000666410i
\(148\) −8.66260 5.00135i −0.712061 0.411109i
\(149\) −6.93481 4.00381i −0.568122 0.328005i 0.188277 0.982116i \(-0.439710\pi\)
−0.756399 + 0.654111i \(0.773043\pi\)
\(150\) −1.67279 0.449207i −0.136582 0.0366776i
\(151\) 7.40096i 0.602282i 0.953580 + 0.301141i \(0.0973674\pi\)
−0.953580 + 0.301141i \(0.902633\pi\)
\(152\) −2.03818 1.17674i −0.165318 0.0954463i
\(153\) 0.00244541 2.22529i 0.000197700 0.179904i
\(154\) 7.16994i 0.577771i
\(155\) 1.67459 5.30997i 0.134506 0.426507i
\(156\) 4.95060 4.94516i 0.396365 0.395930i
\(157\) 2.41698 0.192896 0.0964482 0.995338i \(-0.469252\pi\)
0.0964482 + 0.995338i \(0.469252\pi\)
\(158\) 6.09057 10.5492i 0.484540 0.839247i
\(159\) −1.05793 1.05909i −0.0838993 0.0839916i
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 4.20110 7.27652i 0.331093 0.573470i
\(162\) 7.78432 + 4.51712i 0.611594 + 0.354898i
\(163\) −25.1648 −1.97106 −0.985532 0.169492i \(-0.945787\pi\)
−0.985532 + 0.169492i \(0.945787\pi\)
\(164\) −4.56104 + 2.63332i −0.356158 + 0.205628i
\(165\) 4.53536 + 1.21792i 0.353077 + 0.0948147i
\(166\) 4.24235 2.44932i 0.329270 0.190104i
\(167\) 11.2639 19.5096i 0.871624 1.50970i 0.0113086 0.999936i \(-0.496400\pi\)
0.860316 0.509762i \(-0.170266\pi\)
\(168\) −4.42369 1.18793i −0.341295 0.0916508i
\(169\) 1.66051 2.87609i 0.127731 0.221237i
\(170\) 0.741764 0.0568907
\(171\) 0.00775884 7.06044i 0.000593333 0.539926i
\(172\) −4.20794 2.42945i −0.320852 0.185244i
\(173\) −7.33403 + 4.23431i −0.557596 + 0.321928i −0.752180 0.658958i \(-0.770998\pi\)
0.194584 + 0.980886i \(0.437664\pi\)
\(174\) −0.499398 1.86788i −0.0378592 0.141604i
\(175\) 1.32225 + 2.29021i 0.0999529 + 0.173123i
\(176\) −1.35563 2.34802i −0.102185 0.176989i
\(177\) 0.130126 + 0.0349439i 0.00978089 + 0.00262654i
\(178\) 17.1663i 1.28667i
\(179\) 8.32290 14.4157i 0.622083 1.07748i −0.367014 0.930215i \(-0.619620\pi\)
0.989097 0.147264i \(-0.0470466\pi\)
\(180\) −1.50285 + 2.59643i −0.112016 + 0.193526i
\(181\) −2.86960 + 1.65676i −0.213296 + 0.123146i −0.602842 0.797861i \(-0.705965\pi\)
0.389547 + 0.921007i \(0.372632\pi\)
\(182\) −10.6836 −0.791922
\(183\) −3.67457 13.7439i −0.271632 1.01598i
\(184\) 3.17723i 0.234228i
\(185\) 10.0027 0.735414
\(186\) −8.13021 5.18650i −0.596136 0.380292i
\(187\) −2.01112 −0.147067
\(188\) 3.29156i 0.240061i
\(189\) −3.53461 13.2789i −0.257105 0.965896i
\(190\) 2.35348 0.170740
\(191\) 2.56932 1.48340i 0.185909 0.107335i −0.404157 0.914690i \(-0.632435\pi\)
0.590066 + 0.807355i \(0.299102\pi\)
\(192\) 1.67328 0.447368i 0.120758 0.0322860i
\(193\) 6.42312 11.1252i 0.462346 0.800807i −0.536731 0.843753i \(-0.680341\pi\)
0.999077 + 0.0429465i \(0.0136745\pi\)
\(194\) 12.4034i 0.890515i
\(195\) −1.81476 + 6.75794i −0.129958 + 0.483946i
\(196\) −0.00329675 0.00571013i −0.000235482 0.000407867i
\(197\) −6.44071 11.1556i −0.458881 0.794806i 0.540021 0.841652i \(-0.318416\pi\)
−0.998902 + 0.0468458i \(0.985083\pi\)
\(198\) 4.07463 7.03959i 0.289571 0.500282i
\(199\) 8.97201 5.17999i 0.636009 0.367200i −0.147067 0.989127i \(-0.546983\pi\)
0.783075 + 0.621927i \(0.213650\pi\)
\(200\) −0.866025 0.500000i −0.0612372 0.0353553i
\(201\) −10.0144 10.0254i −0.706359 0.707136i
\(202\) −0.291018 −0.0204760
\(203\) −1.47603 + 2.55656i −0.103597 + 0.179435i
\(204\) 0.333205 1.24081i 0.0233290 0.0868742i
\(205\) 2.63332 4.56104i 0.183919 0.318557i
\(206\) −5.24333 + 3.02724i −0.365320 + 0.210918i
\(207\) −8.25991 + 4.75677i −0.574104 + 0.330618i
\(208\) 3.49868 2.01996i 0.242590 0.140059i
\(209\) −6.38091 −0.441377
\(210\) 4.42499 1.18307i 0.305354 0.0816394i
\(211\) 2.42025 4.19199i 0.166617 0.288588i −0.770612 0.637305i \(-0.780049\pi\)
0.937228 + 0.348717i \(0.113382\pi\)
\(212\) −0.432136 0.748481i −0.0296792 0.0514059i
\(213\) −16.4496 + 16.4315i −1.12711 + 1.12587i
\(214\) −2.79252 + 4.83678i −0.190893 + 0.330636i
\(215\) 4.85891 0.331375
\(216\) 3.66817 + 3.68029i 0.249588 + 0.250412i
\(217\) 3.18597 + 14.3752i 0.216278 + 0.975849i
\(218\) 7.74239i 0.524381i
\(219\) −13.0748 + 13.0604i −0.883513 + 0.882543i
\(220\) 2.34802 + 1.35563i 0.158304 + 0.0913966i
\(221\) 2.99667i 0.201578i
\(222\) 4.49329 16.7324i 0.301570 1.12300i
\(223\) 7.55204 + 4.36017i 0.505722 + 0.291979i 0.731073 0.682299i \(-0.239020\pi\)
−0.225351 + 0.974278i \(0.572353\pi\)
\(224\) −2.29021 1.32225i −0.153021 0.0883467i
\(225\) 0.00329675 3.00000i 0.000219783 0.200000i
\(226\) −3.44903 5.97390i −0.229426 0.397378i
\(227\) −11.0216 + 6.36331i −0.731528 + 0.422348i −0.818981 0.573821i \(-0.805461\pi\)
0.0874527 + 0.996169i \(0.472127\pi\)
\(228\) 1.05720 3.93687i 0.0700148 0.260726i
\(229\) −0.300311 0.173385i −0.0198451 0.0114576i 0.490045 0.871697i \(-0.336980\pi\)
−0.509890 + 0.860240i \(0.670314\pi\)
\(230\) −1.58861 2.75156i −0.104750 0.181433i
\(231\) −11.9973 + 3.20761i −0.789365 + 0.211045i
\(232\) 1.11630i 0.0732887i
\(233\) 3.05182i 0.199931i 0.994991 + 0.0999657i \(0.0318733\pi\)
−0.994991 + 0.0999657i \(0.968127\pi\)
\(234\) 10.4894 + 6.07142i 0.685712 + 0.396901i
\(235\) 1.64578 + 2.85057i 0.107359 + 0.185951i
\(236\) 0.0673682 + 0.0388951i 0.00438530 + 0.00253185i
\(237\) 20.3764 + 5.47185i 1.32359 + 0.355435i
\(238\) −1.69879 + 0.980799i −0.110116 + 0.0635758i
\(239\) 6.34019 + 10.9815i 0.410113 + 0.710336i 0.994902 0.100850i \(-0.0321561\pi\)
−0.584789 + 0.811185i \(0.698823\pi\)
\(240\) −1.22542 + 1.22407i −0.0791004 + 0.0790135i
\(241\) −17.6091 10.1666i −1.13430 0.654890i −0.189289 0.981921i \(-0.560618\pi\)
−0.945013 + 0.327032i \(0.893952\pi\)
\(242\) 3.16018 + 1.82453i 0.203144 + 0.117285i
\(243\) −4.07594 + 15.0462i −0.261472 + 0.965211i
\(244\) 8.21375i 0.525832i
\(245\) 0.00571013 + 0.00329675i 0.000364807 + 0.000210621i
\(246\) −6.44674 6.45383i −0.411029 0.411481i
\(247\) 9.50790i 0.604973i
\(248\) −3.76128 4.10522i −0.238841 0.260682i
\(249\) 5.99630 + 6.00289i 0.380000 + 0.380418i
\(250\) 1.00000 0.0632456
\(251\) 8.05449 13.9508i 0.508395 0.880565i −0.491558 0.870845i \(-0.663572\pi\)
0.999953 0.00972062i \(-0.00309422\pi\)
\(252\) 0.00871827 7.93351i 0.000549199 0.499764i
\(253\) 4.30715 + 7.46020i 0.270788 + 0.469019i
\(254\) −3.60467 + 6.24347i −0.226177 + 0.391750i
\(255\) 0.331842 + 1.24118i 0.0207807 + 0.0777255i
\(256\) 1.00000 0.0625000
\(257\) 17.9053 10.3376i 1.11690 0.644843i 0.176293 0.984338i \(-0.443589\pi\)
0.940608 + 0.339494i \(0.110256\pi\)
\(258\) 2.18265 8.12791i 0.135886 0.506022i
\(259\) −22.9083 + 13.2261i −1.42345 + 0.821830i
\(260\) −2.01996 + 3.49868i −0.125273 + 0.216979i
\(261\) 2.90207 1.67126i 0.179634 0.103449i
\(262\) −7.76065 + 13.4418i −0.479455 + 0.830440i
\(263\) 16.8210 1.03723 0.518613 0.855009i \(-0.326449\pi\)
0.518613 + 0.855009i \(0.326449\pi\)
\(264\) 3.32243 3.31878i 0.204481 0.204257i
\(265\) 0.748481 + 0.432136i 0.0459788 + 0.0265459i
\(266\) −5.38997 + 3.11190i −0.330480 + 0.190803i
\(267\) 28.7240 7.67965i 1.75788 0.469987i
\(268\) −4.09060 7.08512i −0.249873 0.432793i
\(269\) −3.65752 6.33501i −0.223003 0.386252i 0.732716 0.680535i \(-0.238253\pi\)
−0.955718 + 0.294283i \(0.904919\pi\)
\(270\) −5.01687 1.35313i −0.305317 0.0823492i
\(271\) 4.32372i 0.262647i 0.991340 + 0.131324i \(0.0419227\pi\)
−0.991340 + 0.131324i \(0.958077\pi\)
\(272\) 0.370882 0.642386i 0.0224880 0.0389504i
\(273\) −4.77951 17.8767i −0.289269 1.08194i
\(274\) 15.7182 9.07490i 0.949570 0.548235i
\(275\) −2.71126 −0.163495
\(276\) −5.31639 + 1.42139i −0.320009 + 0.0855577i
\(277\) 12.3568i 0.742447i 0.928544 + 0.371223i \(0.121062\pi\)
−0.928544 + 0.371223i \(0.878938\pi\)
\(278\) 20.3716 1.22181
\(279\) 5.04126 15.9244i 0.301812 0.953367i
\(280\) 2.64450 0.158039
\(281\) 2.26737i 0.135260i −0.997710 0.0676300i \(-0.978456\pi\)
0.997710 0.0676300i \(-0.0215437\pi\)
\(282\) 5.50769 1.47254i 0.327978 0.0876884i
\(283\) 4.78042 0.284166 0.142083 0.989855i \(-0.454620\pi\)
0.142083 + 0.989855i \(0.454620\pi\)
\(284\) −11.6252 + 6.71183i −0.689831 + 0.398274i
\(285\) 1.05287 + 3.93803i 0.0623669 + 0.233269i
\(286\) 5.47665 9.48584i 0.323841 0.560909i
\(287\) 13.9277i 0.822123i
\(288\) 1.49714 + 2.59972i 0.0882201 + 0.153190i
\(289\) 8.22489 + 14.2459i 0.483817 + 0.837996i
\(290\) 0.558150 + 0.966745i 0.0327757 + 0.0567692i
\(291\) −20.7544 + 5.54891i −1.21665 + 0.325283i
\(292\) −9.24020 + 5.33483i −0.540742 + 0.312198i
\(293\) 16.4722 + 9.51024i 0.962318 + 0.555594i 0.896886 0.442263i \(-0.145824\pi\)
0.0654320 + 0.997857i \(0.479157\pi\)
\(294\) 0.00807979 0.00807091i 0.000471223 0.000470705i
\(295\) −0.0777901 −0.00452912
\(296\) 5.00135 8.66260i 0.290698 0.503503i
\(297\) 13.6021 + 3.66870i 0.789271 + 0.212880i
\(298\) 4.00381 6.93481i 0.231935 0.401723i
\(299\) −11.1161 + 6.41789i −0.642861 + 0.371156i
\(300\) 0.449207 1.67279i 0.0259350 0.0965783i
\(301\) −11.1279 + 6.42470i −0.641402 + 0.370314i
\(302\) −7.40096 −0.425877
\(303\) −0.130192 0.486955i −0.00747936 0.0279748i
\(304\) 1.17674 2.03818i 0.0674908 0.116897i
\(305\) 4.10688 + 7.11332i 0.235159 + 0.407308i
\(306\) 2.22529 + 0.00244541i 0.127211 + 0.000139795i
\(307\) −14.0713 + 24.3721i −0.803089 + 1.39099i 0.114485 + 0.993425i \(0.463478\pi\)
−0.917574 + 0.397566i \(0.869855\pi\)
\(308\) −7.16994 −0.408546
\(309\) −7.41112 7.41927i −0.421604 0.422067i
\(310\) 5.30997 + 1.67459i 0.301586 + 0.0951100i
\(311\) 34.7697i 1.97161i 0.167895 + 0.985805i \(0.446303\pi\)
−0.167895 + 0.985805i \(0.553697\pi\)
\(312\) 4.94516 + 4.95060i 0.279965 + 0.280272i
\(313\) −13.4245 7.75065i −0.758799 0.438093i 0.0700654 0.997542i \(-0.477679\pi\)
−0.828864 + 0.559450i \(0.811013\pi\)
\(314\) 2.41698i 0.136398i
\(315\) 3.95920 + 6.87498i 0.223076 + 0.387361i
\(316\) 10.5492 + 6.09057i 0.593438 + 0.342621i
\(317\) −4.29014 2.47691i −0.240958 0.139117i 0.374659 0.927163i \(-0.377760\pi\)
−0.615617 + 0.788045i \(0.711093\pi\)
\(318\) 1.05909 1.05793i 0.0593910 0.0593258i
\(319\) −1.51329 2.62110i −0.0847281 0.146753i
\(320\) −0.866025 + 0.500000i −0.0484123 + 0.0279508i
\(321\) −9.34257 2.50884i −0.521452 0.140030i
\(322\) 7.27652 + 4.20110i 0.405504 + 0.234118i
\(323\) −0.872864 1.51185i −0.0485675 0.0841213i
\(324\) −4.51712 + 7.78432i −0.250951 + 0.432462i
\(325\) 4.03993i 0.224095i
\(326\) 25.1648i 1.39375i
\(327\) −12.9552 + 3.46370i −0.716423 + 0.191543i
\(328\) −2.63332 4.56104i −0.145401 0.251841i
\(329\) −7.53835 4.35227i −0.415603 0.239948i
\(330\) −1.21792 + 4.53536i −0.0670442 + 0.249663i
\(331\) −1.63849 + 0.945983i −0.0900596 + 0.0519959i −0.544353 0.838856i \(-0.683225\pi\)
0.454294 + 0.890852i \(0.349892\pi\)
\(332\) 2.44932 + 4.24235i 0.134424 + 0.232829i
\(333\) 30.0081 + 0.0329764i 1.64443 + 0.00180710i
\(334\) 19.5096 + 11.2639i 1.06752 + 0.616331i
\(335\) 7.08512 + 4.09060i 0.387102 + 0.223493i
\(336\) 1.18793 4.42369i 0.0648069 0.241332i
\(337\) 27.5245i 1.49936i −0.661802 0.749678i \(-0.730208\pi\)
0.661802 0.749678i \(-0.269792\pi\)
\(338\) 2.87609 + 1.66051i 0.156438 + 0.0903198i
\(339\) 8.45302 8.44373i 0.459105 0.458601i
\(340\) 0.741764i 0.0402278i
\(341\) −14.3967 4.54024i −0.779626 0.245868i
\(342\) 7.06044 + 0.00775884i 0.381785 + 0.000419550i
\(343\) −18.5290 −1.00047
\(344\) 2.42945 4.20794i 0.130987 0.226877i
\(345\) 3.89343 3.88916i 0.209615 0.209385i
\(346\) −4.23431 7.33403i −0.227638 0.394280i
\(347\) −12.1983 + 21.1281i −0.654841 + 1.13422i 0.327092 + 0.944992i \(0.393931\pi\)
−0.981934 + 0.189226i \(0.939402\pi\)
\(348\) 1.86788 0.499398i 0.100129 0.0267705i
\(349\) −7.97476 −0.426879 −0.213440 0.976956i \(-0.568467\pi\)
−0.213440 + 0.976956i \(0.568467\pi\)
\(350\) −2.29021 + 1.32225i −0.122417 + 0.0706774i
\(351\) −5.46657 + 20.2678i −0.291784 + 1.08182i
\(352\) 2.34802 1.35563i 0.125150 0.0722554i
\(353\) −17.7462 + 30.7372i −0.944533 + 1.63598i −0.187848 + 0.982198i \(0.560151\pi\)
−0.756684 + 0.653781i \(0.773182\pi\)
\(354\) −0.0349439 + 0.130126i −0.00185725 + 0.00691613i
\(355\) 6.71183 11.6252i 0.356227 0.617003i
\(356\) 17.1663 0.909811
\(357\) −2.40114 2.40378i −0.127082 0.127221i
\(358\) 14.4157 + 8.32290i 0.761893 + 0.439879i
\(359\) 8.61779 4.97548i 0.454830 0.262596i −0.255038 0.966931i \(-0.582088\pi\)
0.709868 + 0.704335i \(0.248755\pi\)
\(360\) −2.59643 1.50285i −0.136844 0.0792074i
\(361\) 6.73056 + 11.6577i 0.354240 + 0.613562i
\(362\) −1.65676 2.86960i −0.0870775 0.150823i
\(363\) −1.63918 + 6.10410i −0.0860348 + 0.320382i
\(364\) 10.6836i 0.559973i
\(365\) 5.33483 9.24020i 0.279238 0.483654i
\(366\) 13.7439 3.67457i 0.718405 0.192073i
\(367\) 4.15155 2.39690i 0.216709 0.125117i −0.387716 0.921779i \(-0.626736\pi\)
0.604426 + 0.796662i \(0.293403\pi\)
\(368\) −3.17723 −0.165624
\(369\) 7.91499 13.6744i 0.412038 0.711863i
\(370\) 10.0027i 0.520016i
\(371\) −2.28557 −0.118661
\(372\) 5.18650 8.13021i 0.268907 0.421532i
\(373\) −23.1098 −1.19658 −0.598289 0.801280i \(-0.704153\pi\)
−0.598289 + 0.801280i \(0.704153\pi\)
\(374\) 2.01112i 0.103992i
\(375\) 0.447368 + 1.67328i 0.0231020 + 0.0864077i
\(376\) 3.29156 0.169749
\(377\) 3.90558 2.25489i 0.201148 0.116133i
\(378\) 13.2789 3.53461i 0.682992 0.181801i
\(379\) −0.565702 + 0.979824i −0.0290582 + 0.0503302i −0.880189 0.474624i \(-0.842584\pi\)
0.851131 + 0.524954i \(0.175917\pi\)
\(380\) 2.35348i 0.120731i
\(381\) −12.0597 3.23849i −0.617837 0.165913i
\(382\) 1.48340 + 2.56932i 0.0758971 + 0.131458i
\(383\) −1.85664 3.21579i −0.0948697 0.164319i 0.814685 0.579904i \(-0.196910\pi\)
−0.909554 + 0.415585i \(0.863577\pi\)
\(384\) 0.447368 + 1.67328i 0.0228297 + 0.0853891i
\(385\) 6.20935 3.58497i 0.316458 0.182707i
\(386\) 11.1252 + 6.42312i 0.566256 + 0.326928i
\(387\) 14.5767 + 0.0160186i 0.740976 + 0.000814271i
\(388\) −12.4034 −0.629689
\(389\) −4.87542 + 8.44448i −0.247194 + 0.428152i −0.962746 0.270407i \(-0.912842\pi\)
0.715552 + 0.698559i \(0.246175\pi\)
\(390\) −6.75794 1.81476i −0.342201 0.0918941i
\(391\) −1.17838 + 2.04101i −0.0595931 + 0.103218i
\(392\) 0.00571013 0.00329675i 0.000288405 0.000166511i
\(393\) −25.9638 6.97228i −1.30970 0.351705i
\(394\) 11.1556 6.44071i 0.562013 0.324478i
\(395\) −12.1811 −0.612900
\(396\) 7.03959 + 4.07463i 0.353753 + 0.204758i
\(397\) −5.53921 + 9.59420i −0.278005 + 0.481519i −0.970889 0.239530i \(-0.923007\pi\)
0.692884 + 0.721049i \(0.256340\pi\)
\(398\) 5.17999 + 8.97201i 0.259650 + 0.449726i
\(399\) −7.61837 7.62675i −0.381396 0.381815i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −0.963613 −0.0481205 −0.0240603 0.999711i \(-0.507659\pi\)
−0.0240603 + 0.999711i \(0.507659\pi\)
\(402\) 10.0254 10.0144i 0.500021 0.499471i
\(403\) 6.76520 21.4519i 0.336999 1.06859i
\(404\) 0.291018i 0.0144787i
\(405\) 0.0197805 8.99998i 0.000982900 0.447213i
\(406\) −2.55656 1.47603i −0.126880 0.0732542i
\(407\) 27.1200i 1.34429i
\(408\) 1.24081 + 0.333205i 0.0614294 + 0.0164961i
\(409\) −3.39020 1.95733i −0.167635 0.0967838i 0.413835 0.910352i \(-0.364189\pi\)
−0.581470 + 0.813568i \(0.697522\pi\)
\(410\) 4.56104 + 2.63332i 0.225254 + 0.130050i
\(411\) 22.2167 + 22.2411i 1.09587 + 1.09707i
\(412\) −3.02724 5.24333i −0.149141 0.258321i
\(413\) 0.178156 0.102858i 0.00876647 0.00506132i
\(414\) −4.75677 8.25991i −0.233782 0.405953i
\(415\) −4.24235 2.44932i −0.208249 0.120233i
\(416\) 2.01996 + 3.49868i 0.0990369 + 0.171537i
\(417\) 9.11360 + 34.0873i 0.446295 + 1.66926i
\(418\) 6.38091i 0.312100i
\(419\) 6.12859i 0.299401i 0.988731 + 0.149701i \(0.0478310\pi\)
−0.988731 + 0.149701i \(0.952169\pi\)
\(420\) 1.18307 + 4.42499i 0.0577278 + 0.215918i
\(421\) −6.31725 10.9418i −0.307884 0.533271i 0.670015 0.742347i \(-0.266288\pi\)
−0.977899 + 0.209077i \(0.932954\pi\)
\(422\) 4.19199 + 2.42025i 0.204063 + 0.117816i
\(423\) 4.92794 + 8.55714i 0.239604 + 0.416062i
\(424\) 0.748481 0.432136i 0.0363495 0.0209864i
\(425\) −0.370882 0.642386i −0.0179904 0.0311603i
\(426\) −16.4315 16.4496i −0.796110 0.796985i
\(427\) −18.8112 10.8607i −0.910338 0.525584i
\(428\) −4.83678 2.79252i −0.233795 0.134982i
\(429\) 18.3225 + 4.92030i 0.884620 + 0.237554i
\(430\) 4.85891i 0.234317i
\(431\) −24.8975 14.3746i −1.19927 0.692399i −0.238878 0.971050i \(-0.576780\pi\)
−0.960393 + 0.278650i \(0.910113\pi\)
\(432\) −3.68029 + 3.66817i −0.177068 + 0.176485i
\(433\) 7.12270i 0.342295i 0.985245 + 0.171148i \(0.0547475\pi\)
−0.985245 + 0.171148i \(0.945252\pi\)
\(434\) −14.3752 + 3.18597i −0.690030 + 0.152931i
\(435\) −1.36793 + 1.36643i −0.0655874 + 0.0655154i
\(436\) −7.74239 −0.370793
\(437\) −3.73878 + 6.47575i −0.178850 + 0.309777i
\(438\) −13.0604 13.0748i −0.624052 0.624738i
\(439\) 16.5785 + 28.7148i 0.791248 + 1.37048i 0.925194 + 0.379494i \(0.123902\pi\)
−0.133946 + 0.990989i \(0.542765\pi\)
\(440\) −1.35563 + 2.34802i −0.0646272 + 0.111938i
\(441\) 0.0171195 + 0.00990906i 0.000815215 + 0.000471860i
\(442\) 2.99667 0.142537
\(443\) −23.1960 + 13.3922i −1.10207 + 0.636283i −0.936765 0.349959i \(-0.886196\pi\)
−0.165310 + 0.986242i \(0.552862\pi\)
\(444\) 16.7324 + 4.49329i 0.794084 + 0.213242i
\(445\) −14.8664 + 8.58314i −0.704737 + 0.406880i
\(446\) −4.36017 + 7.55204i −0.206460 + 0.357599i
\(447\) 13.3951 + 3.59708i 0.633564 + 0.170136i
\(448\) 1.32225 2.29021i 0.0624706 0.108202i
\(449\) 24.5175 1.15705 0.578527 0.815663i \(-0.303628\pi\)
0.578527 + 0.815663i \(0.303628\pi\)
\(450\) 3.00000 + 0.00329675i 0.141421 + 0.000155410i
\(451\) −12.3662 7.13962i −0.582301 0.336191i
\(452\) 5.97390 3.44903i 0.280989 0.162229i
\(453\) −3.31096 12.3839i −0.155562 0.581845i
\(454\) −6.36331 11.0216i −0.298645 0.517269i
\(455\) 5.34180 + 9.25228i 0.250428 + 0.433753i
\(456\) 3.93687 + 1.05720i 0.184361 + 0.0495080i
\(457\) 8.46145i 0.395810i −0.980221 0.197905i \(-0.936586\pi\)
0.980221 0.197905i \(-0.0634137\pi\)
\(458\) 0.173385 0.300311i 0.00810174 0.0140326i
\(459\) 0.991433 + 3.72462i 0.0462761 + 0.173851i
\(460\) 2.75156 1.58861i 0.128292 0.0740695i
\(461\) −10.2584 −0.477779 −0.238890 0.971047i \(-0.576783\pi\)
−0.238890 + 0.971047i \(0.576783\pi\)
\(462\) −3.20761 11.9973i −0.149231 0.558166i
\(463\) 16.4580i 0.764870i −0.923982 0.382435i \(-0.875086\pi\)
0.923982 0.382435i \(-0.124914\pi\)
\(464\) 1.11630 0.0518230
\(465\) −0.426535 + 9.63421i −0.0197801 + 0.446776i
\(466\) −3.05182 −0.141373
\(467\) 21.7403i 1.00602i 0.864281 + 0.503010i \(0.167774\pi\)
−0.864281 + 0.503010i \(0.832226\pi\)
\(468\) −6.07142 + 10.4894i −0.280652 + 0.484872i
\(469\) −21.6352 −0.999021
\(470\) −2.85057 + 1.64578i −0.131487 + 0.0759141i
\(471\) −4.04429 + 1.08128i −0.186351 + 0.0498229i
\(472\) −0.0388951 + 0.0673682i −0.00179029 + 0.00310087i
\(473\) 13.1738i 0.605730i
\(474\) −5.47185 + 20.3764i −0.251331 + 0.935921i
\(475\) −1.17674 2.03818i −0.0539926 0.0935179i
\(476\) −0.980799 1.69879i −0.0449548 0.0778641i
\(477\) 2.24402 + 1.29887i 0.102747 + 0.0594714i
\(478\) −10.9815 + 6.34019i −0.502283 + 0.289993i
\(479\) −16.4488 9.49670i −0.751563 0.433915i 0.0746954 0.997206i \(-0.476202\pi\)
−0.826258 + 0.563291i \(0.809535\pi\)
\(480\) −1.22407 1.22542i −0.0558710 0.0559324i
\(481\) 40.4102 1.84255
\(482\) 10.1666 17.6091i 0.463077 0.802073i
\(483\) −3.77432 + 14.0551i −0.171738 + 0.639528i
\(484\) −1.82453 + 3.16018i −0.0829332 + 0.143645i
\(485\) 10.7417 6.20172i 0.487755 0.281606i
\(486\) −15.0462 4.07594i −0.682507 0.184888i
\(487\) 21.3554 12.3295i 0.967704 0.558704i 0.0691683 0.997605i \(-0.477965\pi\)
0.898535 + 0.438901i \(0.144632\pi\)
\(488\) 8.21375 0.371819
\(489\) 42.1078 11.2580i 1.90418 0.509102i
\(490\) −0.00329675 + 0.00571013i −0.000148932 + 0.000257958i
\(491\) 13.0832 + 22.6608i 0.590438 + 1.02267i 0.994173 + 0.107793i \(0.0343784\pi\)
−0.403735 + 0.914876i \(0.632288\pi\)
\(492\) 6.45383 6.44674i 0.290961 0.290642i
\(493\) 0.414016 0.717096i 0.0186463 0.0322964i
\(494\) 9.50790 0.427781
\(495\) −8.13378 0.00893835i −0.365586 0.000401749i
\(496\) 4.10522 3.76128i 0.184330 0.168886i
\(497\) 35.4989i 1.59235i
\(498\) −6.00289 + 5.99630i −0.268996 + 0.268700i
\(499\) −25.4093 14.6701i −1.13748 0.656722i −0.191672 0.981459i \(-0.561391\pi\)
−0.945804 + 0.324737i \(0.894724\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) −10.1196 + 37.6841i −0.452111 + 1.68360i
\(502\) 13.9508 + 8.05449i 0.622654 + 0.359489i
\(503\) −6.14219 3.54620i −0.273867 0.158117i 0.356777 0.934190i \(-0.383876\pi\)
−0.630644 + 0.776073i \(0.717209\pi\)
\(504\) 7.93351 + 0.00871827i 0.353387 + 0.000388342i
\(505\) 0.145509 + 0.252029i 0.00647508 + 0.0112152i
\(506\) −7.46020 + 4.30715i −0.331646 + 0.191476i
\(507\) −1.49182 + 5.55535i −0.0662543 + 0.246722i
\(508\) −6.24347 3.60467i −0.277009 0.159931i
\(509\) 11.2332 + 19.4565i 0.497903 + 0.862393i 0.999997 0.00241974i \(-0.000770229\pi\)
−0.502094 + 0.864813i \(0.667437\pi\)
\(510\) −1.24118 + 0.331842i −0.0549603 + 0.0146942i
\(511\) 28.2160i 1.24820i
\(512\) 1.00000i 0.0441942i
\(513\) 3.14564 + 11.8176i 0.138883 + 0.521758i
\(514\) 10.3376 + 17.9053i 0.455973 + 0.789769i
\(515\) 5.24333 + 3.02724i 0.231049 + 0.133396i
\(516\) 8.12791 + 2.18265i 0.357811 + 0.0960860i
\(517\) 7.72865 4.46214i 0.339905 0.196245i
\(518\) −13.2261 22.9083i −0.581122 1.00653i
\(519\) 10.3776 10.3662i 0.455525 0.455025i
\(520\) −3.49868 2.01996i −0.153427 0.0885813i
\(521\) 24.2738 + 14.0145i 1.06346 + 0.613986i 0.926386 0.376575i \(-0.122898\pi\)
0.137069 + 0.990561i \(0.456232\pi\)
\(522\) 1.67126 + 2.90207i 0.0731492 + 0.127020i
\(523\) 22.8974i 1.00123i 0.865669 + 0.500617i \(0.166893\pi\)
−0.865669 + 0.500617i \(0.833107\pi\)
\(524\) −13.4418 7.76065i −0.587210 0.339026i
\(525\) −3.23706 3.24062i −0.141277 0.141432i
\(526\) 16.8210i 0.733429i
\(527\) −0.893641 4.03212i −0.0389276 0.175642i
\(528\) 3.31878 + 3.32243i 0.144431 + 0.144590i
\(529\) −12.9052 −0.561097
\(530\) −0.432136 + 0.748481i −0.0187708 + 0.0325119i
\(531\) −0.233370 0.000256455i −0.0101274 1.11292e-5i
\(532\) −3.11190 5.38997i −0.134918 0.233685i
\(533\) 10.6384 18.4263i 0.460801 0.798131i
\(534\) 7.67965 + 28.7240i 0.332331 + 1.24301i
\(535\) 5.58504 0.241462
\(536\) 7.08512 4.09060i 0.306031 0.176687i
\(537\) −7.47741 + 27.8449i −0.322674 + 1.20159i
\(538\) 6.33501 3.65752i 0.273122 0.157687i
\(539\) 0.00893835 0.0154817i 0.000385002 0.000666843i
\(540\) 1.35313 5.01687i 0.0582296 0.215892i
\(541\) −6.55194 + 11.3483i −0.281690 + 0.487901i −0.971801 0.235802i \(-0.924228\pi\)
0.690111 + 0.723703i \(0.257562\pi\)
\(542\) −4.32372 −0.185720
\(543\) 4.06045 4.05599i 0.174251 0.174059i
\(544\) 0.642386 + 0.370882i 0.0275421 + 0.0159014i
\(545\) 6.70511 3.87120i 0.287215 0.165824i
\(546\) 17.8767 4.77951i 0.765050 0.204544i
\(547\) −23.1238 40.0517i −0.988704 1.71249i −0.624153 0.781302i \(-0.714556\pi\)
−0.364552 0.931183i \(-0.618778\pi\)
\(548\) 9.07490 + 15.7182i 0.387661 + 0.671448i
\(549\) 12.2972 + 21.3535i 0.524831 + 0.911345i
\(550\) 2.71126i 0.115609i
\(551\) 1.31360 2.27522i 0.0559611 0.0969275i
\(552\) −1.42139 5.31639i −0.0604984 0.226281i
\(553\) 27.8974 16.1065i 1.18632 0.684920i
\(554\) −12.3568 −0.524989
\(555\) −16.7373 + 4.47490i −0.710460 + 0.189949i
\(556\) 20.3716i 0.863947i
\(557\) −36.3726 −1.54116 −0.770579 0.637345i \(-0.780033\pi\)
−0.770579 + 0.637345i \(0.780033\pi\)
\(558\) 15.9244 + 5.04126i 0.674133 + 0.213413i
\(559\) 19.6296 0.830245
\(560\) 2.64450i 0.111751i
\(561\) 3.36516 0.899710i 0.142077 0.0379858i
\(562\) 2.26737 0.0956432
\(563\) −19.8508 + 11.4609i −0.836613 + 0.483019i −0.856112 0.516791i \(-0.827126\pi\)
0.0194982 + 0.999810i \(0.493793\pi\)
\(564\) 1.47254 + 5.50769i 0.0620051 + 0.231916i
\(565\) −3.44903 + 5.97390i −0.145102 + 0.251324i
\(566\) 4.78042i 0.200936i
\(567\) 11.8549 + 20.6380i 0.497861 + 0.866714i
\(568\) −6.71183 11.6252i −0.281622 0.487784i
\(569\) 6.04836 + 10.4761i 0.253561 + 0.439180i 0.964504 0.264070i \(-0.0850649\pi\)
−0.710943 + 0.703250i \(0.751732\pi\)
\(570\) −3.93803 + 1.05287i −0.164946 + 0.0441000i
\(571\) 32.0896 18.5270i 1.34291 0.775329i 0.355676 0.934609i \(-0.384251\pi\)
0.987233 + 0.159281i \(0.0509175\pi\)
\(572\) 9.48584 + 5.47665i 0.396623 + 0.228990i
\(573\) −3.63556 + 3.63157i −0.151878 + 0.151711i
\(574\) −13.9277 −0.581329
\(575\) −1.58861 + 2.75156i −0.0662498 + 0.114748i
\(576\) −2.59972 + 1.49714i −0.108322 + 0.0623810i
\(577\) 10.8409 18.7769i 0.451311 0.781693i −0.547157 0.837030i \(-0.684290\pi\)
0.998468 + 0.0553370i \(0.0176233\pi\)
\(578\) −14.2459 + 8.22489i −0.592553 + 0.342110i
\(579\) −5.77062 + 21.4890i −0.239819 + 0.893052i
\(580\) −0.966745 + 0.558150i −0.0401419 + 0.0231759i
\(581\) 12.9545 0.537443
\(582\) −5.54891 20.7544i −0.230010 0.860298i
\(583\) 1.17163 2.02933i 0.0485241 0.0840462i
\(584\) −5.33483 9.24020i −0.220757 0.382362i
\(585\) 0.0133186 12.1198i 0.000550657 0.501091i
\(586\) −9.51024 + 16.4722i −0.392864 + 0.680461i
\(587\) 34.2190 1.41237 0.706185 0.708027i \(-0.250415\pi\)
0.706185 + 0.708027i \(0.250415\pi\)
\(588\) 0.00807091 + 0.00807979i 0.000332839 + 0.000333205i
\(589\) −2.83536 12.7932i −0.116829 0.527135i
\(590\) 0.0777901i 0.00320257i
\(591\) 15.7678 + 15.7851i 0.648600 + 0.649313i
\(592\) 8.66260 + 5.00135i 0.356031 + 0.205554i
\(593\) 22.8931i 0.940105i 0.882638 + 0.470053i \(0.155765\pi\)
−0.882638 + 0.470053i \(0.844235\pi\)
\(594\) −3.66870 + 13.6021i −0.150529 + 0.558099i
\(595\) 1.69879 + 0.980799i 0.0696437 + 0.0402088i
\(596\) 6.93481 + 4.00381i 0.284061 + 0.164003i
\(597\) −12.6953 + 12.6814i −0.519584 + 0.519014i
\(598\) −6.41789 11.1161i −0.262447 0.454571i
\(599\) 34.1667 19.7261i 1.39601 0.805988i 0.402041 0.915622i \(-0.368301\pi\)
0.993972 + 0.109634i \(0.0349677\pi\)
\(600\) 1.67279 + 0.449207i 0.0682912 + 0.0183388i
\(601\) 28.0179 + 16.1761i 1.14287 + 0.659838i 0.947140 0.320820i \(-0.103958\pi\)
0.195732 + 0.980657i \(0.437292\pi\)
\(602\) −6.42470 11.1279i −0.261851 0.453540i
\(603\) 21.2419 + 12.2951i 0.865036 + 0.500697i
\(604\) 7.40096i 0.301141i
\(605\) 3.64906i 0.148355i
\(606\) 0.486955 0.130192i 0.0197812 0.00528871i
\(607\) −7.33156 12.6986i −0.297579 0.515422i 0.678002 0.735060i \(-0.262846\pi\)
−0.975582 + 0.219638i \(0.929513\pi\)
\(608\) 2.03818 + 1.17674i 0.0826590 + 0.0477232i
\(609\) 1.32609 4.93817i 0.0537358 0.200105i
\(610\) −7.11332 + 4.10688i −0.288010 + 0.166283i
\(611\) 6.64883 + 11.5161i 0.268983 + 0.465892i
\(612\) −0.00244541 + 2.22529i −9.88498e−5 + 0.0899520i
\(613\) −9.31317 5.37696i −0.376155 0.217173i 0.299989 0.953943i \(-0.403017\pi\)
−0.676144 + 0.736769i \(0.736350\pi\)
\(614\) −24.3721 14.0713i −0.983579 0.567870i
\(615\) −2.36581 + 8.80996i −0.0953987 + 0.355252i
\(616\) 7.16994i 0.288885i
\(617\) −38.3757 22.1562i −1.54495 0.891975i −0.998515 0.0544716i \(-0.982653\pi\)
−0.546431 0.837504i \(-0.684014\pi\)
\(618\) 7.41927 7.41112i 0.298447 0.298119i
\(619\) 31.8706i 1.28099i −0.767963 0.640495i \(-0.778729\pi\)
0.767963 0.640495i \(-0.221271\pi\)
\(620\) −1.67459 + 5.30997i −0.0672530 + 0.213253i
\(621\) 11.6931 11.6546i 0.469228 0.467684i
\(622\) −34.7697 −1.39414
\(623\) 22.6982 39.3144i 0.909383 1.57510i
\(624\) −4.95060 + 4.94516i −0.198183 + 0.197965i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 7.75065 13.4245i 0.309778 0.536552i
\(627\) 10.6770 2.85462i 0.426400 0.114002i
\(628\) −2.41698 −0.0964482
\(629\) 6.42560 3.70982i 0.256206 0.147920i
\(630\) −6.87498 + 3.95920i −0.273906 + 0.157738i
\(631\) −30.4987 + 17.6084i −1.21413 + 0.700980i −0.963657 0.267143i \(-0.913920\pi\)
−0.250476 + 0.968123i \(0.580587\pi\)
\(632\) −6.09057 + 10.5492i −0.242270 + 0.419624i
\(633\) −2.17438 + 8.09711i −0.0864240 + 0.321831i
\(634\) 2.47691 4.29014i 0.0983708 0.170383i
\(635\) 7.20934 0.286094
\(636\) 1.05793 + 1.05909i 0.0419497 + 0.0419958i
\(637\) 0.0230685 + 0.0133186i 0.000914009 + 0.000527703i
\(638\) 2.62110 1.51329i 0.103770 0.0599118i
\(639\) 20.1738 34.8536i 0.798064 1.37879i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 2.24960 + 3.89643i 0.0888540 + 0.153900i 0.907027 0.421073i \(-0.138346\pi\)
−0.818173 + 0.574972i \(0.805013\pi\)
\(642\) 2.50884 9.34257i 0.0990159 0.368722i
\(643\) 7.11918i 0.280753i −0.990098 0.140376i \(-0.955169\pi\)
0.990098 0.140376i \(-0.0448313\pi\)
\(644\) −4.20110 + 7.27652i −0.165546 + 0.286735i
\(645\) −8.13030 + 2.17372i −0.320130 + 0.0855902i
\(646\) 1.51185 0.872864i 0.0594827 0.0343424i
\(647\) −38.1767 −1.50088 −0.750441 0.660937i \(-0.770159\pi\)
−0.750441 + 0.660937i \(0.770159\pi\)
\(648\) −7.78432 4.51712i −0.305797 0.177449i
\(649\) 0.210909i 0.00827892i
\(650\) 4.03993 0.158459
\(651\) −11.7620 22.6283i −0.460989 0.886875i
\(652\) 25.1648 0.985532
\(653\) 31.6623i 1.23904i −0.784981 0.619520i \(-0.787327\pi\)
0.784981 0.619520i \(-0.212673\pi\)
\(654\) −3.46370 12.9552i −0.135441 0.506588i
\(655\) 15.5213 0.606468
\(656\) 4.56104 2.63332i 0.178079 0.102814i
\(657\) 16.0350 27.7030i 0.625583 1.08080i
\(658\) 4.35227 7.53835i 0.169669 0.293876i
\(659\) 23.6853i 0.922648i −0.887232 0.461324i \(-0.847375\pi\)
0.887232 0.461324i \(-0.152625\pi\)
\(660\) −4.53536 1.21792i −0.176539 0.0474074i
\(661\) 4.12220 + 7.13985i 0.160335 + 0.277708i 0.934989 0.354677i \(-0.115409\pi\)
−0.774654 + 0.632385i \(0.782076\pi\)
\(662\) −0.945983 1.63849i −0.0367667 0.0636818i
\(663\) 1.34062 + 5.01427i 0.0520652 + 0.194738i
\(664\) −4.24235 + 2.44932i −0.164635 + 0.0950522i
\(665\) 5.38997 + 3.11190i 0.209014 + 0.120674i
\(666\) −0.0329764 + 30.0081i −0.00127781 + 1.16279i
\(667\) −3.54674 −0.137330
\(668\) −11.2639 + 19.5096i −0.435812 + 0.754849i
\(669\) −14.5873 3.91724i −0.563976 0.151449i
\(670\) −4.09060 + 7.08512i −0.158034 + 0.273722i
\(671\) 19.2861 11.1348i 0.744531 0.429855i
\(672\) 4.42369 + 1.18793i 0.170648 + 0.0458254i
\(673\) 9.26140 5.34707i 0.357001 0.206114i −0.310764 0.950487i \(-0.600585\pi\)
0.667764 + 0.744373i \(0.267251\pi\)
\(674\) 27.5245 1.06021
\(675\) 1.33659 + 5.02131i 0.0514453 + 0.193270i
\(676\) −1.66051 + 2.87609i −0.0638657 + 0.110619i
\(677\) −7.89992 13.6831i −0.303619 0.525883i 0.673334 0.739338i \(-0.264862\pi\)
−0.976953 + 0.213455i \(0.931528\pi\)
\(678\) 8.44373 + 8.45302i 0.324280 + 0.324636i
\(679\) −16.4005 + 28.4065i −0.629393 + 1.09014i
\(680\) −0.741764 −0.0284453
\(681\) 15.5954 15.5783i 0.597618 0.596962i
\(682\) 4.54024 14.3967i 0.173855 0.551279i
\(683\) 34.5090i 1.32045i 0.751068 + 0.660224i \(0.229539\pi\)
−0.751068 + 0.660224i \(0.770461\pi\)
\(684\) −0.00775884 + 7.06044i −0.000296667 + 0.269963i
\(685\) −15.7182 9.07490i −0.600561 0.346734i
\(686\) 18.5290i 0.707439i
\(687\) 0.580071 + 0.155771i 0.0221311 + 0.00594305i
\(688\) 4.20794 + 2.42945i 0.160426 + 0.0926220i
\(689\) 3.02381 + 1.74580i 0.115198 + 0.0665096i
\(690\) 3.88916 + 3.89343i 0.148058 + 0.148220i
\(691\) 8.69755 + 15.0646i 0.330870 + 0.573084i 0.982683 0.185296i \(-0.0593244\pi\)
−0.651813 + 0.758380i \(0.725991\pi\)
\(692\) 7.33403 4.23431i 0.278798 0.160964i
\(693\) 18.6399 10.7344i 0.708070 0.407768i
\(694\) −21.1281 12.1983i −0.802013 0.463043i
\(695\) −10.1858 17.6423i −0.386369 0.669210i
\(696\) 0.499398 + 1.86788i 0.0189296 + 0.0708019i
\(697\) 3.90660i 0.147973i
\(698\) 7.97476i 0.301849i
\(699\) −1.36529 5.10655i −0.0516399 0.193147i
\(700\) −1.32225 2.29021i −0.0499764 0.0865617i
\(701\) 14.1135 + 8.14843i 0.533060 + 0.307762i 0.742261 0.670110i \(-0.233753\pi\)
−0.209202 + 0.977872i \(0.567087\pi\)
\(702\) −20.2678 5.46657i −0.764959 0.206322i
\(703\) 20.3873 11.7706i 0.768921 0.443937i
\(704\) 1.35563 + 2.34802i 0.0510923 + 0.0884944i
\(705\) −4.02910 4.03353i −0.151745 0.151912i
\(706\) −30.7372 17.7462i −1.15681 0.667885i
\(707\) −0.666493 0.384800i −0.0250660 0.0144719i
\(708\) −0.130126 0.0349439i −0.00489044 0.00131327i
\(709\) 34.3386i 1.28961i −0.764346 0.644807i \(-0.776938\pi\)
0.764346 0.644807i \(-0.223062\pi\)
\(710\) 11.6252 + 6.71183i 0.436287 + 0.251891i
\(711\) −36.5434 0.0401581i −1.37048 0.00150605i
\(712\) 17.1663i 0.643334i
\(713\) −13.0432 + 11.9504i −0.488472 + 0.447547i
\(714\) 2.40378 2.40114i 0.0899591 0.0898603i
\(715\) −10.9533 −0.409630
\(716\) −8.32290 + 14.4157i −0.311041 + 0.538739i
\(717\) −15.5217 15.5388i −0.579668 0.580305i
\(718\) 4.97548 + 8.61779i 0.185683 + 0.321613i
\(719\) 12.9598 22.4470i 0.483319 0.837133i −0.516497 0.856289i \(-0.672764\pi\)
0.999817 + 0.0191556i \(0.00609778\pi\)
\(720\) 1.50285 2.59643i 0.0560081 0.0967631i
\(721\) −16.0111 −0.596285
\(722\) −11.6577 + 6.73056i −0.433854 + 0.250485i
\(723\) 34.0132 + 9.13384i 1.26496 + 0.339691i
\(724\) 2.86960 1.65676i 0.106648 0.0615731i
\(725\) 0.558150 0.966745i 0.0207292 0.0359040i
\(726\) −6.10410 1.63918i −0.226544 0.0608358i
\(727\) −5.51137 + 9.54597i −0.204405 + 0.354040i −0.949943 0.312423i \(-0.898859\pi\)
0.745538 + 0.666463i \(0.232193\pi\)
\(728\) 10.6836 0.395961
\(729\) 0.0890120 26.9999i 0.00329674 0.999995i
\(730\) 9.24020 + 5.33483i 0.341995 + 0.197451i
\(731\) 3.12129 1.80208i 0.115445 0.0666523i
\(732\) 3.67457 + 13.7439i 0.135816 + 0.507989i
\(733\) 23.9907 + 41.5531i 0.886116 + 1.53480i 0.844429 + 0.535667i \(0.179940\pi\)
0.0416867 + 0.999131i \(0.486727\pi\)
\(734\) 2.39690 + 4.15155i 0.0884711 + 0.153236i
\(735\) −0.0110295 0.00296184i −0.000406830 0.000109249i
\(736\) 3.17723i 0.117114i
\(737\) 11.0907 19.2096i 0.408531 0.707596i
\(738\) 13.6744 + 7.91499i 0.503363 + 0.291355i
\(739\) 27.7681 16.0319i 1.02147 0.589745i 0.106939 0.994266i \(-0.465895\pi\)
0.914529 + 0.404521i \(0.132562\pi\)
\(740\) −10.0027 −0.367707
\(741\) 4.25353 + 15.9094i 0.156258 + 0.584445i
\(742\) 2.28557i 0.0839059i
\(743\) 25.3947 0.931641 0.465821 0.884879i \(-0.345759\pi\)
0.465821 + 0.884879i \(0.345759\pi\)
\(744\) 8.13021 + 5.18650i 0.298068 + 0.190146i
\(745\) −8.00763 −0.293377
\(746\) 23.1098i 0.846109i
\(747\) −12.7190 7.36195i −0.465363 0.269360i
\(748\) 2.01112 0.0735337
\(749\) −12.7909 + 7.38483i −0.467369 + 0.269836i
\(750\) −1.67328 + 0.447368i −0.0610995 + 0.0163356i
\(751\) 9.23056 15.9878i 0.336828 0.583403i −0.647006 0.762485i \(-0.723979\pi\)
0.983834 + 0.179082i \(0.0573126\pi\)
\(752\) 3.29156i 0.120031i
\(753\) −7.23626 + 26.9469i −0.263704 + 0.981998i
\(754\) 2.25489 + 3.90558i 0.0821181 + 0.142233i
\(755\) 3.70048 + 6.40942i 0.134674 + 0.233263i
\(756\) 3.53461 + 13.2789i 0.128553 + 0.482948i
\(757\) −36.5554 + 21.1053i −1.32863 + 0.767084i −0.985088 0.172053i \(-0.944960\pi\)
−0.343541 + 0.939138i \(0.611627\pi\)
\(758\) −0.979824 0.565702i −0.0355888 0.0205472i
\(759\) −10.5445 10.5561i −0.382742 0.383163i
\(760\) −2.35348 −0.0853698
\(761\) 0.562411 0.974124i 0.0203874 0.0353120i −0.855652 0.517552i \(-0.826843\pi\)
0.876039 + 0.482240i \(0.160177\pi\)
\(762\) 3.23849 12.0597i 0.117318 0.436876i
\(763\) −10.2374 + 17.7317i −0.370619 + 0.641930i
\(764\) −2.56932 + 1.48340i −0.0929546 + 0.0536674i
\(765\) −1.11053 1.92838i −0.0401512 0.0697207i
\(766\) 3.21579 1.85664i 0.116191 0.0670830i
\(767\) −0.314267 −0.0113475
\(768\) −1.67328 + 0.447368i −0.0603792 + 0.0161430i
\(769\) −18.7708 + 32.5120i −0.676892 + 1.17241i 0.299020 + 0.954247i \(0.403340\pi\)
−0.975912 + 0.218165i \(0.929993\pi\)
\(770\) 3.58497 + 6.20935i 0.129193 + 0.223770i
\(771\) −25.3358 + 25.3080i −0.912447 + 0.911445i
\(772\) −6.42312 + 11.1252i −0.231173 + 0.400403i
\(773\) 13.0451 0.469198 0.234599 0.972092i \(-0.424622\pi\)
0.234599 + 0.972092i \(0.424622\pi\)
\(774\) −0.0160186 + 14.5767i −0.000575776 + 0.523949i
\(775\) −1.20475 5.43586i −0.0432759 0.195262i
\(776\) 12.4034i 0.445258i
\(777\) 32.4150 32.3794i 1.16288 1.16160i
\(778\) −8.44448 4.87542i −0.302749 0.174792i
\(779\) 12.3949i 0.444095i
\(780\) 1.81476 6.75794i 0.0649790 0.241973i
\(781\) −31.5190 18.1975i −1.12784 0.651159i
\(782\) −2.04101 1.17838i −0.0729863 0.0421387i
\(783\) −4.10831 + 4.09478i −0.146819 + 0.146336i
\(784\) 0.00329675 + 0.00571013i 0.000117741 + 0.000203933i
\(785\) 2.09317 1.20849i 0.0747084 0.0431329i
\(786\) 6.97228 25.9638i 0.248693 0.926099i
\(787\) −1.98975 1.14878i −0.0709269 0.0409497i 0.464117 0.885774i \(-0.346372\pi\)
−0.535044 + 0.844824i \(0.679705\pi\)
\(788\) 6.44071 + 11.1556i 0.229441 + 0.397403i
\(789\) −28.1462 + 7.52517i −1.00203 + 0.267903i
\(790\) 12.1811i 0.433386i
\(791\) 18.2420i 0.648610i
\(792\) −4.07463 + 7.03959i −0.144786 + 0.250141i
\(793\) 16.5915 + 28.7373i 0.589181 + 1.02049i
\(794\) −9.59420 5.53921i −0.340485 0.196579i
\(795\) −1.44574 0.388237i −0.0512752 0.0137693i
\(796\) −8.97201 + 5.17999i −0.318004 + 0.183600i
\(797\) −5.95313 10.3111i −0.210871 0.365239i 0.741116 0.671376i \(-0.234297\pi\)
−0.951987 + 0.306137i \(0.900963\pi\)
\(798\) 7.62675 7.61837i 0.269984 0.269688i
\(799\) 2.11445 + 1.22078i 0.0748039 + 0.0431881i
\(800\) 0.866025 + 0.500000i 0.0306186 + 0.0176777i
\(801\) −44.6276 + 25.7004i −1.57684 + 0.908079i
\(802\) 0.963613i 0.0340264i
\(803\) −25.0526 14.4641i −0.884087 0.510428i
\(804\) 10.0144 + 10.0254i 0.353180 + 0.353568i
\(805\) 8.40220i 0.296138i
\(806\) 21.4519 + 6.76520i 0.755611 + 0.238294i
\(807\) 8.95413 + 8.96398i 0.315200 + 0.315547i
\(808\) 0.291018 0.0102380
\(809\) −11.3601 + 19.6762i −0.399398 + 0.691778i −0.993652 0.112500i \(-0.964114\pi\)
0.594254 + 0.804278i \(0.297448\pi\)
\(810\) 8.99998 + 0.0197805i 0.316227 + 0.000695015i
\(811\) 7.53102 + 13.0441i 0.264450 + 0.458041i 0.967419 0.253179i \(-0.0814763\pi\)
−0.702969 + 0.711220i \(0.748143\pi\)
\(812\) 1.47603 2.55656i 0.0517985 0.0897177i
\(813\) −1.93430 7.23479i −0.0678388 0.253735i
\(814\) 27.1200 0.950554
\(815\) −21.7934 + 12.5824i −0.763389 + 0.440743i
\(816\) −0.333205 + 1.24081i −0.0116645 + 0.0434371i
\(817\) 9.90330 5.71768i 0.346473 0.200036i
\(818\) 1.95733 3.39020i 0.0684365 0.118535i
\(819\) 15.9949 + 27.7744i 0.558907 + 0.970517i
\(820\) −2.63332 + 4.56104i −0.0919595 + 0.159279i
\(821\) 56.1246 1.95876 0.979382 0.202018i \(-0.0647500\pi\)
0.979382 + 0.202018i \(0.0647500\pi\)
\(822\) −22.2411 + 22.2167i −0.775747 + 0.774895i
\(823\) −32.8353 18.9575i −1.14457 0.660816i −0.197010 0.980401i \(-0.563123\pi\)
−0.947558 + 0.319585i \(0.896457\pi\)
\(824\) 5.24333 3.02724i 0.182660 0.105459i
\(825\) 4.53670 1.21293i 0.157947 0.0422289i
\(826\) 0.102858 + 0.178156i 0.00357890 + 0.00619883i
\(827\) 3.95780 + 6.85511i 0.137626 + 0.238375i 0.926598 0.376054i \(-0.122719\pi\)
−0.788971 + 0.614430i \(0.789386\pi\)
\(828\) 8.25991 4.75677i 0.287052 0.165309i
\(829\) 13.2824i 0.461318i 0.973035 + 0.230659i \(0.0740881\pi\)
−0.973035 + 0.230659i \(0.925912\pi\)
\(830\) 2.44932 4.24235i 0.0850173 0.147254i
\(831\) −5.52803 20.6763i −0.191765 0.717254i
\(832\) −3.49868 + 2.01996i −0.121295 + 0.0700297i
\(833\) 0.00489082 0.000169457
\(834\) −34.0873 + 9.11360i −1.18035 + 0.315578i
\(835\) 22.5277i 0.779604i
\(836\) 6.38091 0.220688
\(837\) −1.31137 + 28.9012i −0.0453275 + 0.998972i
\(838\) −6.12859 −0.211709
\(839\) 40.0948i 1.38423i −0.721789 0.692113i \(-0.756680\pi\)
0.721789 0.692113i \(-0.243320\pi\)
\(840\) −4.42499 + 1.18307i −0.152677 + 0.0408197i
\(841\) −27.7539 −0.957030
\(842\) 10.9418 6.31725i 0.377079 0.217707i
\(843\) 1.01435 + 3.79394i 0.0349361 + 0.130670i
\(844\) −2.42025 + 4.19199i −0.0833083 + 0.144294i
\(845\) 3.32102i 0.114247i
\(846\) −8.55714 + 4.92794i −0.294200 + 0.169426i
\(847\) 4.82498 + 8.35711i 0.165788 + 0.287154i
\(848\) 0.432136 + 0.748481i 0.0148396 + 0.0257030i
\(849\) −7.99897 + 2.13861i −0.274524 + 0.0733968i
\(850\) 0.642386 0.370882i 0.0220337 0.0127211i
\(851\) −27.5231 15.8904i −0.943478 0.544717i
\(852\) 16.4496 16.4315i 0.563554 0.562935i
\(853\) 8.66750 0.296769 0.148385 0.988930i \(-0.452593\pi\)
0.148385 + 0.988930i \(0.452593\pi\)
\(854\) 10.8607 18.8112i 0.371644 0.643706i
\(855\) −3.52350 6.11840i −0.120501 0.209245i
\(856\) 2.79252 4.83678i 0.0954463 0.165318i
\(857\) −13.4362 + 7.75737i −0.458970 + 0.264987i −0.711611 0.702574i \(-0.752034\pi\)
0.252641 + 0.967560i \(0.418701\pi\)
\(858\) −4.92030 + 18.3225i −0.167976 + 0.625521i
\(859\) −31.0933 + 17.9517i −1.06089 + 0.612504i −0.925678 0.378313i \(-0.876504\pi\)
−0.135211 + 0.990817i \(0.543171\pi\)
\(860\) −4.85891 −0.165687
\(861\) −6.23079 23.3048i −0.212345 0.794227i
\(862\) 14.3746 24.8975i 0.489600 0.848012i
\(863\) −16.5186 28.6110i −0.562299 0.973930i −0.997295 0.0734982i \(-0.976584\pi\)
0.434996 0.900432i \(-0.356750\pi\)
\(864\) −3.66817 3.68029i −0.124794 0.125206i
\(865\) −4.23431 + 7.33403i −0.143971 + 0.249365i
\(866\) −7.12270 −0.242039
\(867\) −20.1357 20.1579i −0.683845 0.684597i
\(868\) −3.18597 14.3752i −0.108139 0.487925i
\(869\) 33.0263i 1.12034i
\(870\) −1.36643 1.36793i −0.0463264 0.0463773i
\(871\) 28.6234 + 16.5257i 0.969867 + 0.559953i
\(872\) 7.74239i 0.262191i
\(873\) 32.2455 18.5697i 1.09135 0.628490i
\(874\) −6.47575 3.73878i −0.219046 0.126466i
\(875\) 2.29021 + 1.32225i 0.0774232 + 0.0447003i
\(876\) 13.0748 13.0604i 0.441757 0.441271i
\(877\) −19.1990 33.2536i −0.648303 1.12289i −0.983528 0.180755i \(-0.942146\pi\)
0.335225 0.942138i \(-0.391188\pi\)
\(878\) −28.7148 + 16.5785i −0.969077 + 0.559497i
\(879\) −31.8172 8.54413i −1.07317 0.288186i
\(880\) −2.34802 1.35563i −0.0791518 0.0456983i
\(881\) −18.3245 31.7390i −0.617369 1.06932i −0.989964 0.141321i \(-0.954865\pi\)
0.372594 0.927994i \(-0.378468\pi\)
\(882\) −0.00990906 + 0.0171195i −0.000333655 + 0.000576444i
\(883\) 28.7912i 0.968901i 0.874819 + 0.484451i \(0.160980\pi\)
−0.874819 + 0.484451i \(0.839020\pi\)
\(884\) 2.99667i 0.100789i
\(885\) 0.130165 0.0348009i 0.00437544 0.00116982i
\(886\) −13.3922 23.1960i −0.449920 0.779285i
\(887\) −10.4123 6.01154i −0.349611 0.201848i 0.314903 0.949124i \(-0.398028\pi\)
−0.664514 + 0.747276i \(0.731361\pi\)
\(888\) −4.49329 + 16.7324i −0.150785 + 0.561502i
\(889\) −16.5109 + 9.53257i −0.553758 + 0.319712i
\(890\) −8.58314 14.8664i −0.287708 0.498324i
\(891\) −24.4013 0.0536300i −0.817474 0.00179667i
\(892\) −7.55204 4.36017i −0.252861 0.145989i
\(893\) 6.70877 + 3.87331i 0.224501 + 0.129615i
\(894\) −3.59708 + 13.3951i −0.120304 + 0.447998i
\(895\) 16.6458i 0.556408i
\(896\) 2.29021 + 1.32225i 0.0765105 + 0.0441734i
\(897\) 15.7292 15.7119i 0.525182 0.524605i
\(898\) 24.5175i 0.818161i
\(899\) 4.58266 4.19871i 0.152840 0.140035i
\(900\) −0.00329675 + 3.00000i −0.000109892 + 0.0999999i
\(901\) 0.641085 0.0213577
\(902\) 7.13962 12.3662i 0.237723 0.411749i
\(903\) 15.7459 15.7286i 0.523990 0.523415i
\(904\) 3.44903 + 5.97390i 0.114713 + 0.198689i
\(905\) −1.65676 + 2.86960i −0.0550727 + 0.0953886i
\(906\) 12.3839 3.31096i 0.411427 0.109999i
\(907\) −55.4236 −1.84031 −0.920155 0.391554i \(-0.871938\pi\)
−0.920155 + 0.391554i \(0.871938\pi\)
\(908\) 11.0216 6.36331i 0.365764 0.211174i
\(909\) 0.435697 + 0.756567i 0.0144511 + 0.0250938i
\(910\) −9.25228 + 5.34180i −0.306710 + 0.177079i
\(911\) −21.2928 + 36.8802i −0.705462 + 1.22190i 0.261062 + 0.965322i \(0.415927\pi\)
−0.966524 + 0.256574i \(0.917406\pi\)
\(912\) −1.05720 + 3.93687i −0.0350074 + 0.130363i
\(913\) −6.64076 + 11.5021i −0.219777 + 0.380665i
\(914\) 8.46145 0.279880
\(915\) −10.0542 10.0653i −0.332382 0.332748i
\(916\) 0.300311 + 0.173385i 0.00992256 + 0.00572880i
\(917\) −35.5470 + 20.5231i −1.17387 + 0.677732i
\(918\) −3.72462 + 0.991433i −0.122931 + 0.0327222i
\(919\) −1.62944 2.82227i −0.0537502 0.0930980i 0.837898 0.545826i \(-0.183784\pi\)
−0.891649 + 0.452728i \(0.850451\pi\)
\(920\) 1.58861 + 2.75156i 0.0523751 + 0.0907163i
\(921\) 12.6418 47.0764i 0.416562 1.55122i
\(922\) 10.2584i 0.337841i
\(923\) 27.1153 46.9651i 0.892512 1.54588i
\(924\) 11.9973 3.20761i 0.394683 0.105523i
\(925\) 8.66260 5.00135i 0.284825 0.164444i
\(926\) 16.4580 0.540845
\(927\) 15.7200 + 9.09900i 0.516313 + 0.298850i
\(928\) 1.11630i 0.0366444i
\(929\) −26.9297 −0.883535 −0.441767 0.897130i \(-0.645648\pi\)
−0.441767 + 0.897130i \(0.645648\pi\)
\(930\) −9.63421 0.426535i −0.315918 0.0139866i
\(931\) 0.0155177 0.000508571
\(932\) 3.05182i 0.0999657i
\(933\) −15.5549 58.1794i −0.509244 1.90471i
\(934\) −21.7403 −0.711363
\(935\) −1.74168 + 1.00556i −0.0569589 + 0.0328853i
\(936\) −10.4894 6.07142i −0.342856 0.198451i
\(937\) 21.0825 36.5160i 0.688735 1.19292i −0.283512 0.958969i \(-0.591500\pi\)
0.972247 0.233956i \(-0.0751670\pi\)
\(938\) 21.6352i 0.706415i
\(939\) 25.9304 + 6.96329i 0.846205 + 0.227238i
\(940\) −1.64578 2.85057i −0.0536794 0.0929754i
\(941\) 7.15865 + 12.3992i 0.233365 + 0.404201i 0.958796 0.284094i \(-0.0916928\pi\)
−0.725431 + 0.688295i \(0.758359\pi\)
\(942\) −1.08128 4.04429i −0.0352301 0.131770i
\(943\) −14.4915 + 8.36666i −0.471907 + 0.272456i
\(944\) −0.0673682 0.0388951i −0.00219265 0.00126593i
\(945\) −9.70050 9.73253i −0.315557 0.316599i
\(946\) 13.1738 0.428316
\(947\) −4.56614 + 7.90879i −0.148380 + 0.257001i −0.930629 0.365965i \(-0.880739\pi\)
0.782249 + 0.622966i \(0.214072\pi\)
\(948\) −20.3764 5.47185i −0.661796 0.177718i
\(949\) 21.5523 37.3298i 0.699619 1.21178i
\(950\) 2.03818 1.17674i 0.0661272 0.0381785i
\(951\) 8.28669 + 2.22529i 0.268714 + 0.0721601i
\(952\) 1.69879 0.980799i 0.0550582 0.0317879i
\(953\) −37.8957 −1.22756 −0.613781 0.789476i \(-0.710352\pi\)
−0.613781 + 0.789476i \(0.710352\pi\)
\(954\) −1.29887 + 2.24402i −0.0420526 + 0.0726528i
\(955\) 1.48340 2.56932i 0.0480016 0.0831412i
\(956\) −6.34019 10.9815i −0.205056 0.355168i
\(957\) 3.70475 + 3.70883i 0.119758 + 0.119889i
\(958\) 9.49670 16.4488i 0.306824 0.531435i
\(959\) 47.9972 1.54991
\(960\) 1.22542 1.22407i 0.0395502 0.0395067i
\(961\) 2.70562 30.8817i 0.0872781 0.996184i
\(962\) 40.4102i 1.30288i
\(963\) 16.7551 + 0.0184125i 0.539926 + 0.000593333i
\(964\) 17.6091 + 10.1666i 0.567151 + 0.327445i
\(965\) 12.8462i 0.413535i
\(966\) −14.0551 3.77432i −0.452215 0.121437i
\(967\) −22.3015 12.8758i −0.717169 0.414058i 0.0965407 0.995329i \(-0.469222\pi\)
−0.813710 + 0.581271i \(0.802556\pi\)
\(968\) −3.16018 1.82453i −0.101572 0.0586426i
\(969\) 2.13690 + 2.13925i 0.0686470 + 0.0687225i
\(970\) 6.20172 + 10.7417i 0.199125 + 0.344895i
\(971\) −4.80189 + 2.77237i −0.154100 + 0.0889697i −0.575067 0.818106i \(-0.695024\pi\)
0.420967 + 0.907076i \(0.361691\pi\)
\(972\) 4.07594 15.0462i 0.130736 0.482606i
\(973\) 46.6551 + 26.9364i 1.49570 + 0.863540i
\(974\) 12.3295 + 21.3554i 0.395063 + 0.684270i
\(975\) 1.80734 + 6.75993i 0.0578811 + 0.216491i
\(976\) 8.21375i 0.262916i
\(977\) 12.3135i 0.393945i 0.980409 + 0.196972i \(0.0631110\pi\)
−0.980409 + 0.196972i \(0.936889\pi\)
\(978\) 11.2580 + 42.1078i 0.359990 + 1.34646i
\(979\) 23.2711 + 40.3068i 0.743749 + 1.28821i
\(980\) −0.00571013 0.00329675i −0.000182404 0.000105311i
\(981\) 20.1281 11.5915i 0.642640 0.370087i
\(982\) −22.6608 + 13.0832i −0.723136 + 0.417503i
\(983\) 14.8812 + 25.7750i 0.474636 + 0.822094i 0.999578 0.0290441i \(-0.00924631\pi\)
−0.524942 + 0.851138i \(0.675913\pi\)
\(984\) 6.44674 + 6.45383i 0.205515 + 0.205741i
\(985\) −11.1556 6.44071i −0.355448 0.205218i
\(986\) 0.717096 + 0.414016i 0.0228370 + 0.0131849i
\(987\) 14.5608 + 3.91014i 0.463476 + 0.124461i
\(988\) 9.50790i 0.302487i
\(989\) −13.3696 7.71893i −0.425128 0.245448i
\(990\) 0.00893835 8.13378i 0.000284079 0.258508i
\(991\) 0.499587i 0.0158699i 0.999969 + 0.00793495i \(0.00252580\pi\)
−0.999969 + 0.00793495i \(0.997474\pi\)
\(992\) 3.76128 + 4.10522i 0.119421 + 0.130341i
\(993\) 2.31845 2.31590i 0.0735738 0.0734930i
\(994\) −35.4989 −1.12596
\(995\) 5.17999 8.97201i 0.164217 0.284432i
\(996\) −5.99630 6.00289i −0.190000 0.190209i
\(997\) 23.2105 + 40.2018i 0.735085 + 1.27320i 0.954686 + 0.297615i \(0.0961910\pi\)
−0.219601 + 0.975590i \(0.570476\pi\)
\(998\) 14.6701 25.4093i 0.464373 0.804317i
\(999\) −50.2267 + 13.3695i −1.58910 + 0.422992i
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 930.2.o.e.491.11 yes 40
3.2 odd 2 inner 930.2.o.e.491.4 yes 40
31.6 odd 6 inner 930.2.o.e.161.14 yes 40
93.68 even 6 inner 930.2.o.e.161.1 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.o.e.161.1 40 93.68 even 6 inner
930.2.o.e.161.14 yes 40 31.6 odd 6 inner
930.2.o.e.491.4 yes 40 3.2 odd 2 inner
930.2.o.e.491.11 yes 40 1.1 even 1 trivial