Properties

Label 930.2.bg.i.421.3
Level $930$
Weight $2$
Character 930.421
Analytic conductor $7.426$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(121,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bg (of order \(15\), degree \(8\), 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: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 421.3
Character \(\chi\) \(=\) 930.421
Dual form 930.2.bg.i.391.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.17471 + 1.30465i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.17471 + 1.30465i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(2.60047 - 0.552747i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(-0.429483 + 4.08626i) q^{13} +(1.71721 + 0.365004i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.56069 + 0.544291i) q^{17} +(0.104528 - 0.994522i) q^{18} +(-0.494568 - 4.70550i) q^{19} +(0.978148 - 0.207912i) q^{20} +(1.60380 + 0.714056i) q^{21} +(1.77893 - 1.97570i) q^{22} +(0.937331 + 2.88481i) q^{23} +(-0.669131 - 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.05438 + 3.55830i) q^{26} +(0.309017 - 0.951057i) q^{27} +(1.60380 - 0.714056i) q^{28} +(-0.912652 + 0.663081i) q^{29} +1.00000 q^{30} +(3.41847 - 4.39478i) q^{31} -1.00000 q^{32} +(2.15083 - 1.56267i) q^{33} +(2.39157 - 1.06479i) q^{34} +(-0.542502 + 1.66965i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.01166 + 3.48430i) q^{37} +(-3.16594 - 3.51613i) q^{38} +(1.26968 + 3.90767i) q^{39} +(0.669131 - 0.743145i) q^{40} +(-4.47475 - 1.99229i) q^{41} +(1.71721 - 0.365004i) q^{42} +(-0.639276 - 6.08230i) q^{43} +(0.277896 - 2.64400i) q^{44} +(0.978148 + 0.207912i) q^{45} +(2.45396 + 1.78291i) q^{46} +(1.96458 + 1.42735i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(0.409539 - 3.89650i) q^{49} +(0.104528 + 0.994522i) q^{50} +(2.56069 - 0.544291i) q^{51} +(3.75355 + 1.67119i) q^{52} +(2.35411 - 2.61450i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(1.77893 + 1.97570i) q^{55} +(0.877787 - 1.52037i) q^{56} +(-2.36571 - 4.09753i) q^{57} +(-0.348602 + 1.07289i) q^{58} +(-12.1313 + 5.40121i) q^{59} +(0.809017 - 0.587785i) q^{60} +2.77777 q^{61} +(0.182418 - 5.56478i) q^{62} +1.75557 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-3.75355 + 1.67119i) q^{65} +(0.821543 - 2.52845i) q^{66} +(1.91497 + 3.31682i) q^{67} +(1.30895 - 2.26716i) q^{68} +(2.02965 + 2.25416i) q^{69} +(0.542502 + 1.66965i) q^{70} +(-0.453372 + 0.503520i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-3.03533 + 0.645180i) q^{73} +(0.420552 + 4.00128i) q^{74} +(-0.104528 + 0.994522i) q^{75} +(-4.62803 - 0.983718i) q^{76} +(3.77593 + 2.74338i) q^{77} +(3.32406 + 2.41507i) q^{78} +(-0.829909 - 0.176403i) q^{79} +(0.104528 - 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-4.79118 + 1.01840i) q^{82} +(-7.09977 - 3.16102i) q^{83} +(1.17471 - 1.30465i) q^{84} +(0.808974 + 2.48977i) q^{85} +(-4.09227 - 4.54493i) q^{86} +(-0.564050 + 0.976963i) q^{87} +(-1.32928 - 2.30239i) q^{88} +(0.0570948 - 0.175720i) q^{89} +(0.913545 - 0.406737i) q^{90} +(-5.83564 + 4.23984i) q^{91} +3.03327 q^{92} +(1.33541 - 5.40524i) q^{93} +2.42836 q^{94} +(3.82780 - 2.78106i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(2.90264 - 8.93340i) q^{97} +(-1.95898 - 3.39306i) q^{98} +(1.32928 - 2.30239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{13}{15}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.572061 0.415627i
\(3\) 0.913545 0.406737i 0.527436 0.234830i
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) 1.17471 + 1.30465i 0.443998 + 0.493109i 0.923052 0.384676i \(-0.125687\pi\)
−0.479054 + 0.877785i \(0.659020\pi\)
\(8\) −0.309017 0.951057i −0.109254 0.336249i
\(9\) 0.669131 0.743145i 0.223044 0.247715i
\(10\) 0.913545 + 0.406737i 0.288888 + 0.128621i
\(11\) 2.60047 0.552747i 0.784072 0.166660i 0.201554 0.979477i \(-0.435401\pi\)
0.582518 + 0.812818i \(0.302068\pi\)
\(12\) −0.104528 0.994522i −0.0301748 0.287094i
\(13\) −0.429483 + 4.08626i −0.119117 + 1.13332i 0.757734 + 0.652563i \(0.226306\pi\)
−0.876851 + 0.480761i \(0.840360\pi\)
\(14\) 1.71721 + 0.365004i 0.458944 + 0.0975515i
\(15\) 0.809017 + 0.587785i 0.208887 + 0.151765i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 2.56069 + 0.544291i 0.621058 + 0.132010i 0.507685 0.861543i \(-0.330501\pi\)
0.113373 + 0.993553i \(0.463835\pi\)
\(18\) 0.104528 0.994522i 0.0246376 0.234411i
\(19\) −0.494568 4.70550i −0.113462 1.07952i −0.892036 0.451964i \(-0.850724\pi\)
0.778575 0.627552i \(-0.215943\pi\)
\(20\) 0.978148 0.207912i 0.218720 0.0464905i
\(21\) 1.60380 + 0.714056i 0.349977 + 0.155820i
\(22\) 1.77893 1.97570i 0.379269 0.421221i
\(23\) 0.937331 + 2.88481i 0.195447 + 0.601524i 0.999971 + 0.00760400i \(0.00242045\pi\)
−0.804524 + 0.593920i \(0.797580\pi\)
\(24\) −0.669131 0.743145i −0.136586 0.151694i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 2.05438 + 3.55830i 0.402898 + 0.697840i
\(27\) 0.309017 0.951057i 0.0594703 0.183031i
\(28\) 1.60380 0.714056i 0.303089 0.134944i
\(29\) −0.912652 + 0.663081i −0.169475 + 0.123131i −0.669290 0.743002i \(-0.733402\pi\)
0.499815 + 0.866132i \(0.333402\pi\)
\(30\) 1.00000 0.182574
\(31\) 3.41847 4.39478i 0.613976 0.789325i
\(32\) −1.00000 −0.176777
\(33\) 2.15083 1.56267i 0.374411 0.272025i
\(34\) 2.39157 1.06479i 0.410150 0.182611i
\(35\) −0.542502 + 1.66965i −0.0916996 + 0.282222i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −2.01166 + 3.48430i −0.330715 + 0.572815i −0.982652 0.185458i \(-0.940623\pi\)
0.651937 + 0.758273i \(0.273957\pi\)
\(38\) −3.16594 3.51613i −0.513583 0.570392i
\(39\) 1.26968 + 3.90767i 0.203311 + 0.625728i
\(40\) 0.669131 0.743145i 0.105799 0.117502i
\(41\) −4.47475 1.99229i −0.698838 0.311143i 0.0263896 0.999652i \(-0.491599\pi\)
−0.725228 + 0.688509i \(0.758266\pi\)
\(42\) 1.71721 0.365004i 0.264971 0.0563214i
\(43\) −0.639276 6.08230i −0.0974886 0.927542i −0.928511 0.371304i \(-0.878911\pi\)
0.831023 0.556238i \(-0.187756\pi\)
\(44\) 0.277896 2.64400i 0.0418944 0.398599i
\(45\) 0.978148 + 0.207912i 0.145814 + 0.0309936i
\(46\) 2.45396 + 1.78291i 0.361817 + 0.262876i
\(47\) 1.96458 + 1.42735i 0.286564 + 0.208201i 0.721775 0.692127i \(-0.243326\pi\)
−0.435211 + 0.900328i \(0.643326\pi\)
\(48\) −0.978148 0.207912i −0.141183 0.0300095i
\(49\) 0.409539 3.89650i 0.0585055 0.556643i
\(50\) 0.104528 + 0.994522i 0.0147826 + 0.140647i
\(51\) 2.56069 0.544291i 0.358568 0.0762160i
\(52\) 3.75355 + 1.67119i 0.520523 + 0.231752i
\(53\) 2.35411 2.61450i 0.323361 0.359129i −0.559444 0.828868i \(-0.688985\pi\)
0.882805 + 0.469739i \(0.155652\pi\)
\(54\) −0.309017 0.951057i −0.0420519 0.129422i
\(55\) 1.77893 + 1.97570i 0.239871 + 0.266404i
\(56\) 0.877787 1.52037i 0.117299 0.203168i
\(57\) −2.36571 4.09753i −0.313346 0.542731i
\(58\) −0.348602 + 1.07289i −0.0457737 + 0.140877i
\(59\) −12.1313 + 5.40121i −1.57936 + 0.703177i −0.994181 0.107726i \(-0.965643\pi\)
−0.585181 + 0.810903i \(0.698976\pi\)
\(60\) 0.809017 0.587785i 0.104444 0.0758827i
\(61\) 2.77777 0.355657 0.177828 0.984062i \(-0.443093\pi\)
0.177828 + 0.984062i \(0.443093\pi\)
\(62\) 0.182418 5.56478i 0.0231671 0.706727i
\(63\) 1.75557 0.221181
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −3.75355 + 1.67119i −0.465570 + 0.207285i
\(66\) 0.821543 2.52845i 0.101125 0.311231i
\(67\) 1.91497 + 3.31682i 0.233951 + 0.405214i 0.958967 0.283517i \(-0.0915012\pi\)
−0.725017 + 0.688731i \(0.758168\pi\)
\(68\) 1.30895 2.26716i 0.158733 0.274934i
\(69\) 2.02965 + 2.25416i 0.244341 + 0.271369i
\(70\) 0.542502 + 1.66965i 0.0648414 + 0.199561i
\(71\) −0.453372 + 0.503520i −0.0538053 + 0.0597569i −0.769447 0.638711i \(-0.779468\pi\)
0.715641 + 0.698468i \(0.246135\pi\)
\(72\) −0.913545 0.406737i −0.107662 0.0479344i
\(73\) −3.03533 + 0.645180i −0.355259 + 0.0755126i −0.382084 0.924127i \(-0.624794\pi\)
0.0268252 + 0.999640i \(0.491460\pi\)
\(74\) 0.420552 + 4.00128i 0.0488881 + 0.465140i
\(75\) −0.104528 + 0.994522i −0.0120699 + 0.114837i
\(76\) −4.62803 0.983718i −0.530871 0.112840i
\(77\) 3.77593 + 2.74338i 0.430308 + 0.312637i
\(78\) 3.32406 + 2.41507i 0.376376 + 0.273453i
\(79\) −0.829909 0.176403i −0.0933721 0.0198468i 0.160989 0.986956i \(-0.448532\pi\)
−0.254361 + 0.967109i \(0.581865\pi\)
\(80\) 0.104528 0.994522i 0.0116866 0.111191i
\(81\) −0.104528 0.994522i −0.0116143 0.110502i
\(82\) −4.79118 + 1.01840i −0.529098 + 0.112463i
\(83\) −7.09977 3.16102i −0.779301 0.346967i −0.0217674 0.999763i \(-0.506929\pi\)
−0.757534 + 0.652796i \(0.773596\pi\)
\(84\) 1.17471 1.30465i 0.128171 0.142348i
\(85\) 0.808974 + 2.48977i 0.0877455 + 0.270053i
\(86\) −4.09227 4.54493i −0.441281 0.490092i
\(87\) −0.564050 + 0.976963i −0.0604725 + 0.104741i
\(88\) −1.32928 2.30239i −0.141702 0.245435i
\(89\) 0.0570948 0.175720i 0.00605204 0.0186263i −0.947985 0.318315i \(-0.896883\pi\)
0.954037 + 0.299689i \(0.0968829\pi\)
\(90\) 0.913545 0.406737i 0.0962961 0.0428738i
\(91\) −5.83564 + 4.23984i −0.611741 + 0.444456i
\(92\) 3.03327 0.316240
\(93\) 1.33541 5.40524i 0.138476 0.560498i
\(94\) 2.42836 0.250466
\(95\) 3.82780 2.78106i 0.392724 0.285331i
\(96\) −0.913545 + 0.406737i −0.0932383 + 0.0415124i
\(97\) 2.90264 8.93340i 0.294718 0.907050i −0.688598 0.725144i \(-0.741773\pi\)
0.983316 0.181906i \(-0.0582267\pi\)
\(98\) −1.95898 3.39306i −0.197887 0.342750i
\(99\) 1.32928 2.30239i 0.133598 0.231399i
\(100\) 0.669131 + 0.743145i 0.0669131 + 0.0743145i
\(101\) 4.51025 + 13.8811i 0.448786 + 1.38122i 0.878277 + 0.478151i \(0.158693\pi\)
−0.429491 + 0.903071i \(0.641307\pi\)
\(102\) 1.75171 1.94547i 0.173445 0.192631i
\(103\) −9.78227 4.35535i −0.963875 0.429145i −0.136404 0.990653i \(-0.543555\pi\)
−0.827471 + 0.561508i \(0.810221\pi\)
\(104\) 4.01898 0.854261i 0.394094 0.0837672i
\(105\) 0.183507 + 1.74596i 0.0179085 + 0.170388i
\(106\) 0.367748 3.49888i 0.0357188 0.339842i
\(107\) −2.82122 0.599669i −0.272738 0.0579721i 0.0695125 0.997581i \(-0.477856\pi\)
−0.342250 + 0.939609i \(0.611189\pi\)
\(108\) −0.809017 0.587785i −0.0778477 0.0565597i
\(109\) −14.5040 10.5378i −1.38923 1.00934i −0.995949 0.0899217i \(-0.971338\pi\)
−0.393286 0.919416i \(-0.628662\pi\)
\(110\) 2.60047 + 0.552747i 0.247945 + 0.0527024i
\(111\) −0.420552 + 4.00128i −0.0399170 + 0.379785i
\(112\) −0.183507 1.74596i −0.0173398 0.164977i
\(113\) −15.4972 + 3.29404i −1.45786 + 0.309877i −0.867569 0.497316i \(-0.834319\pi\)
−0.590287 + 0.807193i \(0.700986\pi\)
\(114\) −4.32237 1.92444i −0.404827 0.180241i
\(115\) −2.02965 + 2.25416i −0.189266 + 0.210201i
\(116\) 0.348602 + 1.07289i 0.0323669 + 0.0996150i
\(117\) 2.74930 + 3.05341i 0.254173 + 0.282288i
\(118\) −6.63968 + 11.5003i −0.611232 + 1.05869i
\(119\) 2.29795 + 3.98017i 0.210653 + 0.364862i
\(120\) 0.309017 0.951057i 0.0282093 0.0868192i
\(121\) −3.59207 + 1.59929i −0.326552 + 0.145390i
\(122\) 2.24726 1.63273i 0.203458 0.147821i
\(123\) −4.89822 −0.441658
\(124\) −3.12331 4.60922i −0.280482 0.413920i
\(125\) −1.00000 −0.0894427
\(126\) 1.42029 1.03190i 0.126529 0.0919290i
\(127\) 16.7816 7.47164i 1.48912 0.663001i 0.508888 0.860833i \(-0.330057\pi\)
0.980236 + 0.197832i \(0.0633900\pi\)
\(128\) −0.309017 + 0.951057i −0.0273135 + 0.0840623i
\(129\) −3.05790 5.29644i −0.269233 0.466326i
\(130\) −2.05438 + 3.55830i −0.180181 + 0.312083i
\(131\) 8.72301 + 9.68789i 0.762133 + 0.846435i 0.991928 0.126805i \(-0.0404721\pi\)
−0.229795 + 0.973239i \(0.573805\pi\)
\(132\) −0.821543 2.52845i −0.0715061 0.220073i
\(133\) 5.55804 6.17282i 0.481943 0.535252i
\(134\) 3.49882 + 1.55778i 0.302252 + 0.134571i
\(135\) 0.978148 0.207912i 0.0841855 0.0178942i
\(136\) −0.273645 2.60355i −0.0234648 0.223253i
\(137\) −0.949954 + 9.03821i −0.0811600 + 0.772186i 0.875938 + 0.482423i \(0.160243\pi\)
−0.957098 + 0.289763i \(0.906423\pi\)
\(138\) 2.96698 + 0.630652i 0.252566 + 0.0536846i
\(139\) 2.80318 + 2.03663i 0.237763 + 0.172745i 0.700286 0.713863i \(-0.253056\pi\)
−0.462523 + 0.886607i \(0.653056\pi\)
\(140\) 1.42029 + 1.03190i 0.120036 + 0.0872115i
\(141\) 2.37529 + 0.504884i 0.200036 + 0.0425189i
\(142\) −0.0708236 + 0.673842i −0.00594339 + 0.0565475i
\(143\) 1.14181 + 10.8636i 0.0954830 + 0.908460i
\(144\) −0.978148 + 0.207912i −0.0815123 + 0.0173260i
\(145\) −1.03057 0.458840i −0.0855842 0.0381046i
\(146\) −2.07641 + 2.30609i −0.171845 + 0.190853i
\(147\) −1.21072 3.72620i −0.0998583 0.307332i
\(148\) 2.69213 + 2.98991i 0.221292 + 0.245769i
\(149\) −8.78994 + 15.2246i −0.720100 + 1.24725i 0.240859 + 0.970560i \(0.422571\pi\)
−0.960959 + 0.276690i \(0.910763\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) −2.65969 + 8.18568i −0.216442 + 0.666141i 0.782606 + 0.622518i \(0.213890\pi\)
−0.999048 + 0.0436235i \(0.986110\pi\)
\(152\) −4.32237 + 1.92444i −0.350590 + 0.156093i
\(153\) 2.11792 1.53876i 0.171224 0.124401i
\(154\) 4.66731 0.376103
\(155\) 5.51522 + 0.763096i 0.442993 + 0.0612933i
\(156\) 4.10877 0.328965
\(157\) 4.53923 3.29794i 0.362270 0.263204i −0.391728 0.920081i \(-0.628123\pi\)
0.753998 + 0.656876i \(0.228123\pi\)
\(158\) −0.775097 + 0.345096i −0.0616634 + 0.0274543i
\(159\) 1.08717 3.34597i 0.0862182 0.265352i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −2.66256 + 4.61169i −0.209839 + 0.363452i
\(162\) −0.669131 0.743145i −0.0525719 0.0583870i
\(163\) 4.15869 + 12.7991i 0.325734 + 1.00251i 0.971108 + 0.238640i \(0.0767015\pi\)
−0.645374 + 0.763867i \(0.723299\pi\)
\(164\) −3.27755 + 3.64009i −0.255934 + 0.284243i
\(165\) 2.42872 + 1.08134i 0.189076 + 0.0841820i
\(166\) −7.60184 + 1.61582i −0.590017 + 0.125412i
\(167\) 0.880827 + 8.38051i 0.0681605 + 0.648503i 0.974258 + 0.225435i \(0.0723803\pi\)
−0.906098 + 0.423068i \(0.860953\pi\)
\(168\) 0.183507 1.74596i 0.0141579 0.134703i
\(169\) −3.79715 0.807109i −0.292088 0.0620853i
\(170\) 2.11792 + 1.53876i 0.162437 + 0.118017i
\(171\) −3.82780 2.78106i −0.292719 0.212673i
\(172\) −5.98216 1.27155i −0.456135 0.0969546i
\(173\) 0.800487 7.61613i 0.0608599 0.579044i −0.921017 0.389523i \(-0.872640\pi\)
0.981877 0.189521i \(-0.0606934\pi\)
\(174\) 0.117919 + 1.12192i 0.00893938 + 0.0850525i
\(175\) −1.71721 + 0.365004i −0.129809 + 0.0275917i
\(176\) −2.42872 1.08134i −0.183072 0.0815089i
\(177\) −8.88563 + 9.86849i −0.667885 + 0.741761i
\(178\) −0.0570948 0.175720i −0.00427944 0.0131708i
\(179\) −16.1129 17.8952i −1.20433 1.33755i −0.926212 0.377004i \(-0.876954\pi\)
−0.278123 0.960545i \(-0.589712\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) −8.66018 14.9999i −0.643706 1.11493i −0.984599 0.174830i \(-0.944063\pi\)
0.340893 0.940102i \(-0.389271\pi\)
\(182\) −2.22901 + 6.86020i −0.165226 + 0.508512i
\(183\) 2.53762 1.12982i 0.187586 0.0835187i
\(184\) 2.45396 1.78291i 0.180909 0.131438i
\(185\) −4.02332 −0.295801
\(186\) −2.09675 5.15787i −0.153741 0.378193i
\(187\) 6.95985 0.508955
\(188\) 1.96458 1.42735i 0.143282 0.104101i
\(189\) 1.60380 0.714056i 0.116659 0.0519399i
\(190\) 1.46209 4.49985i 0.106071 0.326453i
\(191\) 7.15860 + 12.3991i 0.517978 + 0.897165i 0.999782 + 0.0208856i \(0.00664858\pi\)
−0.481803 + 0.876279i \(0.660018\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −0.909083 1.00964i −0.0654373 0.0726754i 0.709537 0.704668i \(-0.248904\pi\)
−0.774975 + 0.631992i \(0.782237\pi\)
\(194\) −2.90264 8.93340i −0.208397 0.641381i
\(195\) −2.74930 + 3.05341i −0.196882 + 0.218659i
\(196\) −3.57924 1.59358i −0.255660 0.113827i
\(197\) −10.0055 + 2.12674i −0.712863 + 0.151524i −0.550048 0.835133i \(-0.685391\pi\)
−0.162815 + 0.986657i \(0.552057\pi\)
\(198\) −0.277896 2.64400i −0.0197492 0.187901i
\(199\) −0.321575 + 3.05958i −0.0227958 + 0.216888i 0.977194 + 0.212349i \(0.0681114\pi\)
−0.999990 + 0.00453872i \(0.998555\pi\)
\(200\) 0.978148 + 0.207912i 0.0691655 + 0.0147016i
\(201\) 3.09848 + 2.25118i 0.218550 + 0.158786i
\(202\) 11.8080 + 8.57900i 0.830807 + 0.603616i
\(203\) −1.93718 0.411761i −0.135964 0.0289000i
\(204\) 0.273645 2.60355i 0.0191589 0.182285i
\(205\) −0.512004 4.87139i −0.0357599 0.340233i
\(206\) −10.4740 + 2.22632i −0.729760 + 0.155115i
\(207\) 2.77103 + 1.23374i 0.192600 + 0.0857509i
\(208\) 2.74930 3.05341i 0.190630 0.211716i
\(209\) −3.88706 11.9632i −0.268874 0.827509i
\(210\) 1.17471 + 1.30465i 0.0810625 + 0.0900291i
\(211\) −1.88914 + 3.27208i −0.130054 + 0.225260i −0.923697 0.383124i \(-0.874848\pi\)
0.793643 + 0.608383i \(0.208182\pi\)
\(212\) −1.75908 3.04681i −0.120814 0.209256i
\(213\) −0.209376 + 0.644392i −0.0143462 + 0.0441530i
\(214\) −2.63489 + 1.17313i −0.180117 + 0.0801934i
\(215\) 4.94779 3.59478i 0.337436 0.245162i
\(216\) −1.00000 −0.0680414
\(217\) 9.74933 0.702684i 0.661827 0.0477013i
\(218\) −17.9280 −1.21424
\(219\) −2.51050 + 1.82398i −0.169644 + 0.123253i
\(220\) 2.42872 1.08134i 0.163744 0.0729037i
\(221\) −3.32389 + 10.2299i −0.223589 + 0.688136i
\(222\) 2.01166 + 3.48430i 0.135014 + 0.233851i
\(223\) 9.12528 15.8054i 0.611074 1.05841i −0.379986 0.924992i \(-0.624071\pi\)
0.991060 0.133419i \(-0.0425955\pi\)
\(224\) −1.17471 1.30465i −0.0784885 0.0871703i
\(225\) 0.309017 + 0.951057i 0.0206011 + 0.0634038i
\(226\) −10.6013 + 11.7740i −0.705190 + 0.783193i
\(227\) 24.6802 + 10.9883i 1.63808 + 0.729321i 0.999200 0.0399849i \(-0.0127310\pi\)
0.638881 + 0.769306i \(0.279398\pi\)
\(228\) −4.62803 + 0.983718i −0.306499 + 0.0651483i
\(229\) −0.587564 5.59030i −0.0388274 0.369418i −0.996632 0.0819990i \(-0.973870\pi\)
0.957805 0.287419i \(-0.0927971\pi\)
\(230\) −0.317063 + 3.01665i −0.0209065 + 0.198912i
\(231\) 4.56532 + 0.970389i 0.300376 + 0.0638469i
\(232\) 0.912652 + 0.663081i 0.0599185 + 0.0435334i
\(233\) 2.62021 + 1.90369i 0.171656 + 0.124715i 0.670296 0.742094i \(-0.266167\pi\)
−0.498640 + 0.866809i \(0.666167\pi\)
\(234\) 4.01898 + 0.854261i 0.262729 + 0.0558448i
\(235\) −0.253833 + 2.41506i −0.0165582 + 0.157541i
\(236\) 1.38807 + 13.2066i 0.0903558 + 0.859678i
\(237\) −0.829909 + 0.176403i −0.0539084 + 0.0114586i
\(238\) 4.19857 + 1.86932i 0.272153 + 0.121170i
\(239\) −15.6382 + 17.3679i −1.01155 + 1.12344i −0.0192192 + 0.999815i \(0.506118\pi\)
−0.992329 + 0.123623i \(0.960549\pi\)
\(240\) −0.309017 0.951057i −0.0199470 0.0613904i
\(241\) −16.0434 17.8180i −1.03345 1.14776i −0.988874 0.148754i \(-0.952474\pi\)
−0.0445739 0.999006i \(-0.514193\pi\)
\(242\) −1.96601 + 3.40522i −0.126380 + 0.218896i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0.858378 2.64181i 0.0549520 0.169125i
\(245\) 3.57924 1.59358i 0.228669 0.101810i
\(246\) −3.96275 + 2.87910i −0.252655 + 0.183565i
\(247\) 19.4403 1.23696
\(248\) −5.23605 1.89310i −0.332489 0.120212i
\(249\) −7.77167 −0.492510
\(250\) −0.809017 + 0.587785i −0.0511667 + 0.0371748i
\(251\) 11.1289 4.95491i 0.702451 0.312751i −0.0242495 0.999706i \(-0.507720\pi\)
0.726700 + 0.686955i \(0.241053\pi\)
\(252\) 0.542502 1.66965i 0.0341744 0.105178i
\(253\) 4.03207 + 6.98376i 0.253494 + 0.439065i
\(254\) 9.18486 15.9086i 0.576309 0.998197i
\(255\) 1.75171 + 1.94547i 0.109697 + 0.121830i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −6.16889 + 6.85125i −0.384805 + 0.427369i −0.904163 0.427188i \(-0.859504\pi\)
0.519358 + 0.854557i \(0.326171\pi\)
\(258\) −5.58707 2.48752i −0.347836 0.154866i
\(259\) −6.90889 + 1.46853i −0.429297 + 0.0912500i
\(260\) 0.429483 + 4.08626i 0.0266354 + 0.253419i
\(261\) −0.117919 + 1.12192i −0.00729898 + 0.0694451i
\(262\) 12.7515 + 2.71041i 0.787788 + 0.167449i
\(263\) −21.1043 15.3332i −1.30135 0.945483i −0.301377 0.953505i \(-0.597446\pi\)
−0.999968 + 0.00802228i \(0.997446\pi\)
\(264\) −2.15083 1.56267i −0.132374 0.0961755i
\(265\) 3.44128 + 0.731466i 0.211396 + 0.0449336i
\(266\) 0.868250 8.26085i 0.0532358 0.506505i
\(267\) −0.0193130 0.183751i −0.00118193 0.0112454i
\(268\) 3.74624 0.796289i 0.228838 0.0486411i
\(269\) −5.56186 2.47630i −0.339112 0.150983i 0.230113 0.973164i \(-0.426090\pi\)
−0.569226 + 0.822181i \(0.692757\pi\)
\(270\) 0.669131 0.743145i 0.0407220 0.0452264i
\(271\) 3.35492 + 10.3254i 0.203797 + 0.627223i 0.999761 + 0.0218785i \(0.00696468\pi\)
−0.795964 + 0.605345i \(0.793035\pi\)
\(272\) −1.75171 1.94547i −0.106213 0.117962i
\(273\) −3.60662 + 6.24685i −0.218283 + 0.378077i
\(274\) 4.54400 + 7.87043i 0.274513 + 0.475470i
\(275\) −0.821543 + 2.52845i −0.0495409 + 0.152471i
\(276\) 2.77103 1.23374i 0.166796 0.0742625i
\(277\) −15.0746 + 10.9523i −0.905743 + 0.658061i −0.939935 0.341354i \(-0.889114\pi\)
0.0341915 + 0.999415i \(0.489114\pi\)
\(278\) 3.46492 0.207812
\(279\) −0.978551 5.48110i −0.0585843 0.328145i
\(280\) 1.75557 0.104916
\(281\) 3.33636 2.42401i 0.199030 0.144604i −0.483806 0.875175i \(-0.660746\pi\)
0.682837 + 0.730571i \(0.260746\pi\)
\(282\) 2.21842 0.987703i 0.132105 0.0588169i
\(283\) −1.52542 + 4.69475i −0.0906766 + 0.279074i −0.986103 0.166136i \(-0.946871\pi\)
0.895426 + 0.445210i \(0.146871\pi\)
\(284\) 0.338777 + 0.586779i 0.0201027 + 0.0348189i
\(285\) 2.36571 4.09753i 0.140133 0.242717i
\(286\) 7.30921 + 8.11770i 0.432203 + 0.480010i
\(287\) −2.65729 8.17831i −0.156855 0.482751i
\(288\) −0.669131 + 0.743145i −0.0394289 + 0.0437902i
\(289\) −9.26941 4.12701i −0.545259 0.242765i
\(290\) −1.10345 + 0.234545i −0.0647967 + 0.0137730i
\(291\) −0.981850 9.34168i −0.0575571 0.547619i
\(292\) −0.324367 + 3.08615i −0.0189821 + 0.180603i
\(293\) −1.62370 0.345127i −0.0948573 0.0201625i 0.160238 0.987078i \(-0.448774\pi\)
−0.255096 + 0.966916i \(0.582107\pi\)
\(294\) −3.16970 2.30292i −0.184861 0.134309i
\(295\) −10.7432 7.80542i −0.625495 0.454449i
\(296\) 3.93540 + 0.836496i 0.228741 + 0.0486203i
\(297\) 0.277896 2.64400i 0.0161252 0.153421i
\(298\) 1.83760 + 17.4836i 0.106449 + 1.01280i
\(299\) −12.1906 + 2.59120i −0.705003 + 0.149853i
\(300\) 0.913545 + 0.406737i 0.0527436 + 0.0234830i
\(301\) 7.18428 7.97895i 0.414095 0.459899i
\(302\) 2.65969 + 8.18568i 0.153048 + 0.471033i
\(303\) 9.76627 + 10.8465i 0.561058 + 0.623118i
\(304\) −2.36571 + 4.09753i −0.135683 + 0.235009i
\(305\) 1.38888 + 2.40562i 0.0795273 + 0.137745i
\(306\) 0.808974 2.48977i 0.0462460 0.142330i
\(307\) 18.5146 8.24324i 1.05668 0.470466i 0.196529 0.980498i \(-0.437033\pi\)
0.860156 + 0.510032i \(0.170366\pi\)
\(308\) 3.77593 2.74338i 0.215154 0.156318i
\(309\) −10.7080 −0.609158
\(310\) 4.91045 2.62441i 0.278895 0.149056i
\(311\) 5.90148 0.334642 0.167321 0.985902i \(-0.446488\pi\)
0.167321 + 0.985902i \(0.446488\pi\)
\(312\) 3.32406 2.41507i 0.188188 0.136727i
\(313\) −1.62322 + 0.722704i −0.0917499 + 0.0408497i −0.452098 0.891968i \(-0.649324\pi\)
0.360349 + 0.932818i \(0.382658\pi\)
\(314\) 1.73383 5.33618i 0.0978457 0.301138i
\(315\) 0.877787 + 1.52037i 0.0494577 + 0.0856632i
\(316\) −0.424225 + 0.734779i −0.0238645 + 0.0413345i
\(317\) 5.74016 + 6.37509i 0.322399 + 0.358061i 0.882457 0.470393i \(-0.155888\pi\)
−0.560058 + 0.828454i \(0.689221\pi\)
\(318\) −1.08717 3.34597i −0.0609655 0.187633i
\(319\) −2.00681 + 2.22879i −0.112360 + 0.124788i
\(320\) −0.913545 0.406737i −0.0510687 0.0227373i
\(321\) −2.82122 + 0.599669i −0.157465 + 0.0334702i
\(322\) 0.556627 + 5.29595i 0.0310196 + 0.295132i
\(323\) 1.29473 12.3185i 0.0720405 0.685420i
\(324\) −0.978148 0.207912i −0.0543415 0.0115506i
\(325\) −3.32406 2.41507i −0.184386 0.133964i
\(326\) 10.8876 + 7.91031i 0.603008 + 0.438111i
\(327\) −17.5362 3.72744i −0.969754 0.206128i
\(328\) −0.512004 + 4.87139i −0.0282707 + 0.268977i
\(329\) 0.445622 + 4.23981i 0.0245679 + 0.233748i
\(330\) 2.60047 0.552747i 0.143151 0.0304277i
\(331\) −12.9702 5.77470i −0.712907 0.317406i 0.0180436 0.999837i \(-0.494256\pi\)
−0.730950 + 0.682431i \(0.760923\pi\)
\(332\) −5.20026 + 5.77548i −0.285401 + 0.316970i
\(333\) 1.24327 + 3.82641i 0.0681310 + 0.209686i
\(334\) 5.63854 + 6.26224i 0.308527 + 0.342654i
\(335\) −1.91497 + 3.31682i −0.104626 + 0.181217i
\(336\) −0.877787 1.52037i −0.0478872 0.0829430i
\(337\) 0.562733 1.73191i 0.0306540 0.0943434i −0.934559 0.355808i \(-0.884206\pi\)
0.965213 + 0.261465i \(0.0842056\pi\)
\(338\) −3.54637 + 1.57894i −0.192897 + 0.0858832i
\(339\) −12.8176 + 9.31254i −0.696157 + 0.505788i
\(340\) 2.61789 0.141975
\(341\) 6.46044 13.3180i 0.349852 0.721213i
\(342\) −4.73142 −0.255846
\(343\) 15.5067 11.2662i 0.837281 0.608320i
\(344\) −5.58707 + 2.48752i −0.301234 + 0.134118i
\(345\) −0.937331 + 2.88481i −0.0504642 + 0.155313i
\(346\) −3.82904 6.63209i −0.205850 0.356543i
\(347\) 1.21602 2.10621i 0.0652795 0.113067i −0.831538 0.555467i \(-0.812539\pi\)
0.896818 + 0.442400i \(0.145873\pi\)
\(348\) 0.754846 + 0.838342i 0.0404640 + 0.0449398i
\(349\) −6.63332 20.4153i −0.355074 1.09280i −0.955967 0.293475i \(-0.905188\pi\)
0.600893 0.799329i \(-0.294812\pi\)
\(350\) −1.17471 + 1.30465i −0.0627908 + 0.0697362i
\(351\) 3.75355 + 1.67119i 0.200350 + 0.0892014i
\(352\) −2.60047 + 0.552747i −0.138606 + 0.0294615i
\(353\) −0.722585 6.87494i −0.0384593 0.365916i −0.996778 0.0802137i \(-0.974440\pi\)
0.958318 0.285703i \(-0.0922269\pi\)
\(354\) −1.38807 + 13.2066i −0.0737752 + 0.701924i
\(355\) −0.662747 0.140871i −0.0351750 0.00747667i
\(356\) −0.149476 0.108601i −0.00792223 0.00575583i
\(357\) 3.71817 + 2.70141i 0.196786 + 0.142974i
\(358\) −23.5541 5.00659i −1.24487 0.264606i
\(359\) 0.0774854 0.737224i 0.00408952 0.0389092i −0.992287 0.123963i \(-0.960440\pi\)
0.996376 + 0.0850539i \(0.0271062\pi\)
\(360\) −0.104528 0.994522i −0.00550913 0.0524159i
\(361\) −3.31234 + 0.704059i −0.174334 + 0.0370557i
\(362\) −15.8229 7.04483i −0.831635 0.370268i
\(363\) −2.63103 + 2.92206i −0.138093 + 0.153368i
\(364\) 2.22901 + 6.86020i 0.116832 + 0.359572i
\(365\) −2.07641 2.30609i −0.108684 0.120706i
\(366\) 1.38888 2.40562i 0.0725981 0.125744i
\(367\) 11.6377 + 20.1570i 0.607480 + 1.05219i 0.991654 + 0.128926i \(0.0411530\pi\)
−0.384174 + 0.923261i \(0.625514\pi\)
\(368\) 0.937331 2.88481i 0.0488618 0.150381i
\(369\) −4.47475 + 1.99229i −0.232946 + 0.103714i
\(370\) −3.25494 + 2.36485i −0.169216 + 0.122943i
\(371\) 6.17638 0.320662
\(372\) −4.72803 2.94037i −0.245137 0.152451i
\(373\) 15.3830 0.796500 0.398250 0.917277i \(-0.369618\pi\)
0.398250 + 0.917277i \(0.369618\pi\)
\(374\) 5.63064 4.09090i 0.291153 0.211535i
\(375\) −0.913545 + 0.406737i −0.0471753 + 0.0210038i
\(376\) 0.750405 2.30951i 0.0386992 0.119104i
\(377\) −2.31755 4.01412i −0.119360 0.206737i
\(378\) 0.877787 1.52037i 0.0451485 0.0781994i
\(379\) 11.1287 + 12.3597i 0.571645 + 0.634876i 0.957758 0.287576i \(-0.0928493\pi\)
−0.386113 + 0.922451i \(0.626183\pi\)
\(380\) −1.46209 4.49985i −0.0750036 0.230837i
\(381\) 12.2917 13.6514i 0.629725 0.699381i
\(382\) 13.0794 + 5.82333i 0.669201 + 0.297948i
\(383\) 22.5650 4.79633i 1.15302 0.245081i 0.408547 0.912737i \(-0.366036\pi\)
0.744470 + 0.667656i \(0.232702\pi\)
\(384\) 0.104528 + 0.994522i 0.00533420 + 0.0507515i
\(385\) −0.487867 + 4.64174i −0.0248640 + 0.236565i
\(386\) −1.32892 0.282470i −0.0676400 0.0143773i
\(387\) −4.94779 3.59478i −0.251510 0.182733i
\(388\) −7.59921 5.52115i −0.385791 0.280294i
\(389\) −2.29014 0.486784i −0.116115 0.0246809i 0.149488 0.988764i \(-0.452238\pi\)
−0.265602 + 0.964083i \(0.585571\pi\)
\(390\) −0.429483 + 4.08626i −0.0217477 + 0.206916i
\(391\) 0.830037 + 7.89727i 0.0419768 + 0.399382i
\(392\) −3.83235 + 0.814590i −0.193563 + 0.0411430i
\(393\) 11.9093 + 5.30236i 0.600744 + 0.267468i
\(394\) −6.84456 + 7.60166i −0.344824 + 0.382966i
\(395\) −0.262185 0.806924i −0.0131920 0.0406007i
\(396\) −1.77893 1.97570i −0.0893946 0.0992827i
\(397\) −1.29235 + 2.23842i −0.0648613 + 0.112343i −0.896632 0.442776i \(-0.853994\pi\)
0.831771 + 0.555119i \(0.187327\pi\)
\(398\) 1.53822 + 2.66427i 0.0771038 + 0.133548i
\(399\) 2.56680 7.89981i 0.128501 0.395485i
\(400\) 0.913545 0.406737i 0.0456773 0.0203368i
\(401\) 13.8605 10.0702i 0.692160 0.502884i −0.185209 0.982699i \(-0.559296\pi\)
0.877370 + 0.479815i \(0.159296\pi\)
\(402\) 3.82994 0.191020
\(403\) 16.4900 + 15.8562i 0.821426 + 0.789856i
\(404\) 14.5955 0.726152
\(405\) 0.809017 0.587785i 0.0402004 0.0292073i
\(406\) −1.80924 + 0.805526i −0.0897912 + 0.0399776i
\(407\) −3.30533 + 10.1728i −0.163839 + 0.504245i
\(408\) −1.30895 2.26716i −0.0648026 0.112241i
\(409\) 17.1447 29.6955i 0.847752 1.46835i −0.0354568 0.999371i \(-0.511289\pi\)
0.883209 0.468979i \(-0.155378\pi\)
\(410\) −3.27755 3.64009i −0.161867 0.179771i
\(411\) 2.80834 + 8.64320i 0.138525 + 0.426337i
\(412\) −7.16507 + 7.95761i −0.352997 + 0.392043i
\(413\) −21.2974 9.48221i −1.04798 0.466589i
\(414\) 2.96698 0.630652i 0.145819 0.0309948i
\(415\) −0.812361 7.72910i −0.0398772 0.379406i
\(416\) 0.429483 4.08626i 0.0210572 0.200345i
\(417\) 3.38920 + 0.720397i 0.165970 + 0.0352780i
\(418\) −10.1765 7.39364i −0.497747 0.361635i
\(419\) −16.6847 12.1221i −0.815101 0.592205i 0.100204 0.994967i \(-0.468050\pi\)
−0.915305 + 0.402762i \(0.868050\pi\)
\(420\) 1.71721 + 0.365004i 0.0837912 + 0.0178104i
\(421\) 0.951845 9.05620i 0.0463901 0.441372i −0.946532 0.322609i \(-0.895440\pi\)
0.992923 0.118764i \(-0.0378931\pi\)
\(422\) 0.394938 + 3.75758i 0.0192253 + 0.182916i
\(423\) 2.37529 0.504884i 0.115491 0.0245483i
\(424\) −3.21400 1.43096i −0.156085 0.0694937i
\(425\) −1.75171 + 1.94547i −0.0849706 + 0.0943694i
\(426\) 0.209376 + 0.644392i 0.0101443 + 0.0312209i
\(427\) 3.26307 + 3.62400i 0.157911 + 0.175378i
\(428\) −1.44212 + 2.49783i −0.0697077 + 0.120737i
\(429\) 5.46172 + 9.45998i 0.263694 + 0.456732i
\(430\) 1.88989 5.81648i 0.0911385 0.280495i
\(431\) 19.4024 8.63852i 0.934583 0.416103i 0.117793 0.993038i \(-0.462418\pi\)
0.816790 + 0.576935i \(0.195751\pi\)
\(432\) −0.809017 + 0.587785i −0.0389238 + 0.0282798i
\(433\) 16.9307 0.813637 0.406818 0.913509i \(-0.366638\pi\)
0.406818 + 0.913509i \(0.366638\pi\)
\(434\) 7.47434 6.29899i 0.358780 0.302361i
\(435\) −1.12810 −0.0540883
\(436\) −14.5040 + 10.5378i −0.694617 + 0.504669i
\(437\) 13.1109 5.83735i 0.627179 0.279238i
\(438\) −0.958925 + 2.95127i −0.0458192 + 0.141017i
\(439\) −5.54939 9.61183i −0.264858 0.458748i 0.702668 0.711518i \(-0.251992\pi\)
−0.967526 + 0.252770i \(0.918658\pi\)
\(440\) 1.32928 2.30239i 0.0633711 0.109762i
\(441\) −2.62163 2.91161i −0.124839 0.138648i
\(442\) 3.32389 + 10.2299i 0.158101 + 0.486585i
\(443\) −10.4449 + 11.6003i −0.496253 + 0.551145i −0.938289 0.345852i \(-0.887590\pi\)
0.442036 + 0.896998i \(0.354257\pi\)
\(444\) 3.67549 + 1.63643i 0.174431 + 0.0776617i
\(445\) 0.180725 0.0384143i 0.00856720 0.00182101i
\(446\) −1.90770 18.1506i −0.0903323 0.859455i
\(447\) −1.83760 + 17.4836i −0.0869154 + 0.826945i
\(448\) −1.71721 0.365004i −0.0811305 0.0172448i
\(449\) 6.11441 + 4.44238i 0.288557 + 0.209649i 0.722641 0.691223i \(-0.242928\pi\)
−0.434084 + 0.900872i \(0.642928\pi\)
\(450\) 0.809017 + 0.587785i 0.0381374 + 0.0277085i
\(451\) −12.7377 2.70748i −0.599795 0.127490i
\(452\) −1.65609 + 15.7567i −0.0778960 + 0.741131i
\(453\) 0.899670 + 8.55979i 0.0422702 + 0.402174i
\(454\) 26.4255 5.61691i 1.24021 0.263614i
\(455\) −6.58963 2.93389i −0.308926 0.137543i
\(456\) −3.16594 + 3.51613i −0.148259 + 0.164658i
\(457\) −7.15083 22.0080i −0.334502 1.02949i −0.966967 0.254901i \(-0.917957\pi\)
0.632465 0.774589i \(-0.282043\pi\)
\(458\) −3.76125 4.17729i −0.175752 0.195192i
\(459\) 1.30895 2.26716i 0.0610964 0.105822i
\(460\) 1.51663 + 2.62689i 0.0707134 + 0.122479i
\(461\) 12.2208 37.6117i 0.569179 1.75175i −0.0860154 0.996294i \(-0.527413\pi\)
0.655195 0.755460i \(-0.272587\pi\)
\(462\) 4.26380 1.89837i 0.198370 0.0883200i
\(463\) 29.5516 21.4705i 1.37338 0.997819i 0.375916 0.926654i \(-0.377328\pi\)
0.997465 0.0711657i \(-0.0226719\pi\)
\(464\) 1.12810 0.0523707
\(465\) 5.34879 1.54612i 0.248044 0.0716996i
\(466\) 3.23876 0.150032
\(467\) 18.0090 13.0843i 0.833355 0.605468i −0.0871512 0.996195i \(-0.527776\pi\)
0.920507 + 0.390727i \(0.127776\pi\)
\(468\) 3.75355 1.67119i 0.173508 0.0772506i
\(469\) −2.07775 + 6.39465i −0.0959415 + 0.295278i
\(470\) 1.21418 + 2.10302i 0.0560060 + 0.0970052i
\(471\) 2.80540 4.85909i 0.129266 0.223895i
\(472\) 8.88563 + 9.86849i 0.408994 + 0.454234i
\(473\) −5.02440 15.4635i −0.231022 0.711013i
\(474\) −0.567724 + 0.630521i −0.0260764 + 0.0289608i
\(475\) 4.32237 + 1.92444i 0.198324 + 0.0882995i
\(476\) 4.49547 0.955542i 0.206050 0.0437972i
\(477\) −0.367748 3.49888i −0.0168380 0.160203i
\(478\) −2.44292 + 23.2428i −0.111737 + 1.06310i
\(479\) −28.3510 6.02618i −1.29539 0.275343i −0.491894 0.870655i \(-0.663695\pi\)
−0.803495 + 0.595312i \(0.797028\pi\)
\(480\) −0.809017 0.587785i −0.0369264 0.0268286i
\(481\) −13.3738 9.71662i −0.609792 0.443040i
\(482\) −23.4526 4.98500i −1.06824 0.227061i
\(483\) −0.556627 + 5.29595i −0.0253274 + 0.240974i
\(484\) 0.411007 + 3.91047i 0.0186821 + 0.177749i
\(485\) 9.18788 1.95294i 0.417200 0.0886786i
\(486\) −0.913545 0.406737i −0.0414393 0.0184499i
\(487\) 11.0090 12.2267i 0.498866 0.554047i −0.440148 0.897925i \(-0.645074\pi\)
0.939014 + 0.343879i \(0.111741\pi\)
\(488\) −0.858378 2.64181i −0.0388569 0.119589i
\(489\) 9.00504 + 10.0011i 0.407222 + 0.452266i
\(490\) 1.95898 3.39306i 0.0884978 0.153283i
\(491\) 10.3646 + 17.9520i 0.467747 + 0.810162i 0.999321 0.0368504i \(-0.0117325\pi\)
−0.531574 + 0.847012i \(0.678399\pi\)
\(492\) −1.51363 + 4.65849i −0.0682399 + 0.210021i
\(493\) −2.69793 + 1.20119i −0.121508 + 0.0540990i
\(494\) 15.7275 11.4267i 0.707616 0.514113i
\(495\) 2.65857 0.119494
\(496\) −5.34879 + 1.54612i −0.240168 + 0.0694229i
\(497\) −1.18949 −0.0533561
\(498\) −6.28741 + 4.56807i −0.281746 + 0.204700i
\(499\) −4.31925 + 1.92305i −0.193356 + 0.0860877i −0.501131 0.865372i \(-0.667082\pi\)
0.307775 + 0.951459i \(0.400416\pi\)
\(500\) −0.309017 + 0.951057i −0.0138197 + 0.0425325i
\(501\) 4.21334 + 7.29771i 0.188238 + 0.326038i
\(502\) 6.09106 10.5500i 0.271857 0.470870i
\(503\) 23.5005 + 26.0999i 1.04783 + 1.16374i 0.986186 + 0.165640i \(0.0529689\pi\)
0.0616480 + 0.998098i \(0.480364\pi\)
\(504\) −0.542502 1.66965i −0.0241650 0.0743721i
\(505\) −9.76627 + 10.8465i −0.434593 + 0.482665i
\(506\) 7.36696 + 3.27998i 0.327502 + 0.145813i
\(507\) −3.79715 + 0.807109i −0.168637 + 0.0358450i
\(508\) −1.92016 18.2691i −0.0851933 0.810560i
\(509\) 0.169190 1.60974i 0.00749922 0.0713503i −0.990132 0.140136i \(-0.955246\pi\)
0.997631 + 0.0687860i \(0.0219126\pi\)
\(510\) 2.56069 + 0.544291i 0.113389 + 0.0241016i
\(511\) −4.40736 3.20214i −0.194970 0.141654i
\(512\) 0.809017 + 0.587785i 0.0357538 + 0.0259767i
\(513\) −4.62803 0.983718i −0.204332 0.0434322i
\(514\) −0.963675 + 9.16876i −0.0425059 + 0.404416i
\(515\) −1.11929 10.6494i −0.0493220 0.469267i
\(516\) −5.98216 + 1.27155i −0.263350 + 0.0559768i
\(517\) 5.89781 + 2.62588i 0.259386 + 0.115486i
\(518\) −4.72623 + 5.24901i −0.207659 + 0.230628i
\(519\) −2.36648 7.28327i −0.103877 0.319700i
\(520\) 2.74930 + 3.05341i 0.120565 + 0.133901i
\(521\) −3.14177 + 5.44171i −0.137644 + 0.238406i −0.926604 0.376038i \(-0.877286\pi\)
0.788961 + 0.614444i \(0.210620\pi\)
\(522\) 0.564050 + 0.976963i 0.0246878 + 0.0427605i
\(523\) −2.59324 + 7.98117i −0.113394 + 0.348992i −0.991609 0.129275i \(-0.958735\pi\)
0.878214 + 0.478267i \(0.158735\pi\)
\(524\) 11.9093 5.30236i 0.520260 0.231634i
\(525\) −1.42029 + 1.03190i −0.0619865 + 0.0450358i
\(526\) −26.0863 −1.13742
\(527\) 11.1457 9.39300i 0.485513 0.409166i
\(528\) −2.65857 −0.115699
\(529\) 11.1639 8.11102i 0.485385 0.352653i
\(530\) 3.21400 1.43096i 0.139607 0.0621571i
\(531\) −4.10355 + 12.6294i −0.178079 + 0.548071i
\(532\) −4.15318 7.19351i −0.180063 0.311878i
\(533\) 10.0628 17.4293i 0.435870 0.754948i
\(534\) −0.123630 0.137306i −0.00535001 0.00594179i
\(535\) −0.891281 2.74308i −0.0385334 0.118594i
\(536\) 2.56273 2.84620i 0.110693 0.122937i
\(537\) −21.9985 9.79436i −0.949305 0.422658i
\(538\) −5.95517 + 1.26581i −0.256746 + 0.0545729i
\(539\) −1.08879 10.3591i −0.0468974 0.446199i
\(540\) 0.104528 0.994522i 0.00449819 0.0427974i
\(541\) −34.3603 7.30351i −1.47726 0.314002i −0.602332 0.798246i \(-0.705762\pi\)
−0.874933 + 0.484244i \(0.839095\pi\)
\(542\) 8.78331 + 6.38144i 0.377275 + 0.274107i
\(543\) −14.0125 10.1807i −0.601333 0.436894i
\(544\) −2.56069 0.544291i −0.109789 0.0233363i
\(545\) 1.87398 17.8298i 0.0802726 0.763743i
\(546\) 0.753989 + 7.17373i 0.0322678 + 0.307007i
\(547\) −17.7390 + 3.77054i −0.758464 + 0.161217i −0.570882 0.821032i \(-0.693399\pi\)
−0.187582 + 0.982249i \(0.560065\pi\)
\(548\) 8.30230 + 3.69642i 0.354656 + 0.157903i
\(549\) 1.85869 2.06428i 0.0793270 0.0881015i
\(550\) 0.821543 + 2.52845i 0.0350307 + 0.107813i
\(551\) 3.57149 + 3.96655i 0.152151 + 0.168981i
\(552\) 1.51663 2.62689i 0.0645522 0.111808i
\(553\) −0.744758 1.28996i −0.0316703 0.0548546i
\(554\) −5.75797 + 17.7212i −0.244633 + 0.752903i
\(555\) −3.67549 + 1.63643i −0.156016 + 0.0694627i
\(556\) 2.80318 2.03663i 0.118881 0.0863723i
\(557\) 24.6871 1.04602 0.523012 0.852325i \(-0.324808\pi\)
0.523012 + 0.852325i \(0.324808\pi\)
\(558\) −4.01337 3.85912i −0.169900 0.163370i
\(559\) 25.1284 1.06282
\(560\) 1.42029 1.03190i 0.0600181 0.0436057i
\(561\) 6.35814 2.83083i 0.268441 0.119518i
\(562\) 1.27438 3.92213i 0.0537563 0.165445i
\(563\) 9.95166 + 17.2368i 0.419413 + 0.726444i 0.995880 0.0906759i \(-0.0289027\pi\)
−0.576468 + 0.817120i \(0.695569\pi\)
\(564\) 1.21418 2.10302i 0.0511262 0.0885532i
\(565\) −10.6013 11.7740i −0.446002 0.495335i
\(566\) 1.52542 + 4.69475i 0.0641180 + 0.197335i
\(567\) 1.17471 1.30465i 0.0493331 0.0547899i
\(568\) 0.618976 + 0.275586i 0.0259717 + 0.0115633i
\(569\) 13.5219 2.87418i 0.566869 0.120492i 0.0844427 0.996428i \(-0.473089\pi\)
0.482426 + 0.875937i \(0.339756\pi\)
\(570\) −0.494568 4.70550i −0.0207152 0.197092i
\(571\) −0.877582 + 8.34963i −0.0367256 + 0.349421i 0.960693 + 0.277613i \(0.0895435\pi\)
−0.997418 + 0.0718077i \(0.977123\pi\)
\(572\) 10.6847 + 2.27111i 0.446751 + 0.0949599i
\(573\) 11.5829 + 8.41544i 0.483881 + 0.351560i
\(574\) −6.95689 5.05448i −0.290375 0.210970i
\(575\) −2.96698 0.630652i −0.123732 0.0263000i
\(576\) −0.104528 + 0.994522i −0.00435535 + 0.0414384i
\(577\) 3.92398 + 37.3342i 0.163358 + 1.55424i 0.702288 + 0.711893i \(0.252162\pi\)
−0.538931 + 0.842350i \(0.681171\pi\)
\(578\) −9.92490 + 2.10960i −0.412821 + 0.0877479i
\(579\) −1.24115 0.552594i −0.0515803 0.0229650i
\(580\) −0.754846 + 0.838342i −0.0313433 + 0.0348102i
\(581\) −4.21615 12.9760i −0.174915 0.538334i
\(582\) −6.28524 6.98046i −0.260531 0.289349i
\(583\) 4.67663 8.10016i 0.193686 0.335475i
\(584\) 1.55157 + 2.68740i 0.0642045 + 0.111206i
\(585\) −1.26968 + 3.90767i −0.0524948 + 0.161562i
\(586\) −1.51646 + 0.675170i −0.0626443 + 0.0278910i
\(587\) 15.7907 11.4726i 0.651752 0.473526i −0.212116 0.977245i \(-0.568035\pi\)
0.863868 + 0.503719i \(0.168035\pi\)
\(588\) −3.91796 −0.161574
\(589\) −22.3703 13.9121i −0.921752 0.573238i
\(590\) −13.2794 −0.546703
\(591\) −8.27547 + 6.01248i −0.340407 + 0.247320i
\(592\) 3.67549 1.63643i 0.151062 0.0672570i
\(593\) 1.92563 5.92649i 0.0790763 0.243372i −0.903701 0.428163i \(-0.859161\pi\)
0.982778 + 0.184791i \(0.0591609\pi\)
\(594\) −1.32928 2.30239i −0.0545412 0.0944681i
\(595\) −2.29795 + 3.98017i −0.0942069 + 0.163171i
\(596\) 11.7632 + 13.0644i 0.481841 + 0.535138i
\(597\) 0.950670 + 2.92586i 0.0389083 + 0.119748i
\(598\) −8.33937 + 9.26181i −0.341022 + 0.378743i
\(599\) 26.8370 + 11.9486i 1.09653 + 0.488206i 0.873608 0.486630i \(-0.161774\pi\)
0.222921 + 0.974837i \(0.428441\pi\)
\(600\) 0.978148 0.207912i 0.0399327 0.00848796i
\(601\) −4.46149 42.4483i −0.181988 1.73150i −0.580432 0.814309i \(-0.697116\pi\)
0.398444 0.917193i \(-0.369550\pi\)
\(602\) 1.12230 10.6779i 0.0457413 0.435200i
\(603\) 3.74624 + 0.796289i 0.152559 + 0.0324274i
\(604\) 6.96316 + 5.05903i 0.283327 + 0.205849i
\(605\) −3.18107 2.31118i −0.129329 0.0939628i
\(606\) 14.2765 + 3.03457i 0.579944 + 0.123271i
\(607\) −2.35186 + 22.3764i −0.0954590 + 0.908232i 0.837060 + 0.547111i \(0.184272\pi\)
−0.932519 + 0.361121i \(0.882394\pi\)
\(608\) 0.494568 + 4.70550i 0.0200574 + 0.190833i
\(609\) −1.93718 + 0.411761i −0.0784987 + 0.0166854i
\(610\) 2.53762 + 1.12982i 0.102745 + 0.0457451i
\(611\) −6.67630 + 7.41478i −0.270094 + 0.299970i
\(612\) −0.808974 2.48977i −0.0327008 0.100643i
\(613\) −8.58413 9.53365i −0.346710 0.385060i 0.544417 0.838815i \(-0.316751\pi\)
−0.891127 + 0.453754i \(0.850084\pi\)
\(614\) 10.1334 17.5515i 0.408950 0.708322i
\(615\) −2.44911 4.24198i −0.0987577 0.171053i
\(616\) 1.44228 4.43888i 0.0581111 0.178847i
\(617\) 5.77574 2.57153i 0.232523 0.103526i −0.287168 0.957880i \(-0.592714\pi\)
0.519691 + 0.854354i \(0.326047\pi\)
\(618\) −8.66297 + 6.29402i −0.348476 + 0.253183i
\(619\) 39.6231 1.59259 0.796293 0.604911i \(-0.206791\pi\)
0.796293 + 0.604911i \(0.206791\pi\)
\(620\) 2.43004 5.00948i 0.0975929 0.201186i
\(621\) 3.03327 0.121721
\(622\) 4.77440 3.46880i 0.191436 0.139086i
\(623\) 0.296322 0.131931i 0.0118719 0.00528570i
\(624\) 1.26968 3.90767i 0.0508279 0.156432i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −0.888418 + 1.53879i −0.0355083 + 0.0615022i
\(627\) −8.41686 9.34787i −0.336137 0.373318i
\(628\) −1.73383 5.33618i −0.0691874 0.212937i
\(629\) −7.04771 + 7.82727i −0.281011 + 0.312094i
\(630\) 1.60380 + 0.714056i 0.0638968 + 0.0284487i
\(631\) −36.0787 + 7.66876i −1.43627 + 0.305289i −0.859298 0.511475i \(-0.829099\pi\)
−0.576972 + 0.816764i \(0.695766\pi\)
\(632\) 0.0886871 + 0.843802i 0.00352778 + 0.0335646i
\(633\) −0.394938 + 3.75758i −0.0156974 + 0.149350i
\(634\) 8.39107 + 1.78358i 0.333252 + 0.0708349i
\(635\) 14.8614 + 10.7975i 0.589757 + 0.428484i
\(636\) −2.84625 2.06792i −0.112861 0.0819984i
\(637\) 15.7462 + 3.34696i 0.623888 + 0.132612i
\(638\) −0.313495 + 2.98270i −0.0124114 + 0.118086i
\(639\) 0.0708236 + 0.673842i 0.00280174 + 0.0266568i
\(640\) −0.978148 + 0.207912i −0.0386647 + 0.00821843i
\(641\) −6.38768 2.84398i −0.252298 0.112330i 0.276691 0.960959i \(-0.410762\pi\)
−0.528989 + 0.848629i \(0.677429\pi\)
\(642\) −1.92994 + 2.14341i −0.0761686 + 0.0845938i
\(643\) 5.14222 + 15.8261i 0.202789 + 0.624121i 0.999797 + 0.0201520i \(0.00641503\pi\)
−0.797008 + 0.603969i \(0.793585\pi\)
\(644\) 3.56320 + 3.95734i 0.140410 + 0.155941i
\(645\) 3.05790 5.29644i 0.120405 0.208547i
\(646\) −6.19318 10.7269i −0.243667 0.422044i
\(647\) 11.1926 34.4474i 0.440028 1.35427i −0.447818 0.894125i \(-0.647799\pi\)
0.887846 0.460141i \(-0.152201\pi\)
\(648\) −0.913545 + 0.406737i −0.0358875 + 0.0159781i
\(649\) −28.5616 + 20.7512i −1.12114 + 0.814557i
\(650\) −4.10877 −0.161159
\(651\) 8.62065 4.60734i 0.337870 0.180576i
\(652\) 13.4578 0.527049
\(653\) 19.4763 14.1504i 0.762166 0.553746i −0.137408 0.990515i \(-0.543877\pi\)
0.899574 + 0.436768i \(0.143877\pi\)
\(654\) −16.3780 + 7.29196i −0.640431 + 0.285138i
\(655\) −4.02845 + 12.3983i −0.157405 + 0.484441i
\(656\) 2.44911 + 4.24198i 0.0956217 + 0.165622i
\(657\) −1.55157 + 2.68740i −0.0605326 + 0.104846i
\(658\) 2.85261 + 3.16815i 0.111206 + 0.123507i
\(659\) 6.41778 + 19.7519i 0.250001 + 0.769424i 0.994774 + 0.102106i \(0.0325580\pi\)
−0.744773 + 0.667318i \(0.767442\pi\)
\(660\) 1.77893 1.97570i 0.0692447 0.0769041i
\(661\) −5.21935 2.32380i −0.203009 0.0903855i 0.302714 0.953082i \(-0.402107\pi\)
−0.505723 + 0.862696i \(0.668774\pi\)
\(662\) −13.8874 + 2.95186i −0.539749 + 0.114727i
\(663\) 1.12434 + 10.6974i 0.0436658 + 0.415453i
\(664\) −0.812361 + 7.72910i −0.0315257 + 0.299947i
\(665\) 8.12484 + 1.72699i 0.315068 + 0.0669697i
\(666\) 3.25494 + 2.36485i 0.126126 + 0.0916361i
\(667\) −2.76832 2.01130i −0.107190 0.0778778i
\(668\) 8.24253 + 1.75200i 0.318913 + 0.0677871i
\(669\) 1.90770 18.1506i 0.0737560 0.701742i
\(670\) 0.400338 + 3.80896i 0.0154664 + 0.147153i
\(671\) 7.22351 1.53540i 0.278861 0.0592736i
\(672\) −1.60380 0.714056i −0.0618678 0.0275453i
\(673\) −1.07592 + 1.19493i −0.0414738 + 0.0460613i −0.763525 0.645779i \(-0.776533\pi\)
0.722051 + 0.691840i \(0.243200\pi\)
\(674\) −0.562733 1.73191i −0.0216757 0.0667108i
\(675\) 0.669131 + 0.743145i 0.0257548 + 0.0286037i
\(676\) −1.94099 + 3.36189i −0.0746535 + 0.129304i
\(677\) −2.84997 4.93629i −0.109533 0.189717i 0.806048 0.591850i \(-0.201602\pi\)
−0.915581 + 0.402133i \(0.868269\pi\)
\(678\) −4.89589 + 15.0680i −0.188026 + 0.578684i
\(679\) 15.0647 6.70723i 0.578129 0.257400i
\(680\) 2.11792 1.53876i 0.0812186 0.0590087i
\(681\) 27.0158 1.03525
\(682\) −2.60154 14.5719i −0.0996183 0.557986i
\(683\) −16.7176 −0.639682 −0.319841 0.947471i \(-0.603630\pi\)
−0.319841 + 0.947471i \(0.603630\pi\)
\(684\) −3.82780 + 2.78106i −0.146360 + 0.106336i
\(685\) −8.30230 + 3.69642i −0.317214 + 0.141233i
\(686\) 5.92302 18.2292i 0.226142 0.695993i
\(687\) −2.81055 4.86801i −0.107229 0.185726i
\(688\) −3.05790 + 5.29644i −0.116581 + 0.201925i
\(689\) 9.67248 + 10.7424i 0.368492 + 0.409252i
\(690\) 0.937331 + 2.88481i 0.0356836 + 0.109823i
\(691\) 6.53204 7.25456i 0.248490 0.275976i −0.605976 0.795483i \(-0.707217\pi\)
0.854467 + 0.519506i \(0.173884\pi\)
\(692\) −6.99600 3.11482i −0.265948 0.118408i
\(693\) 4.56532 0.970389i 0.173422 0.0368620i
\(694\) −0.254218 2.41872i −0.00964998 0.0918134i
\(695\) −0.362183 + 3.44594i −0.0137384 + 0.130712i
\(696\) 1.10345 + 0.234545i 0.0418261 + 0.00889041i
\(697\) −10.3740 7.53719i −0.392945 0.285491i
\(698\) −17.3663 12.6173i −0.657323 0.477573i
\(699\) 3.16798 + 0.673375i 0.119824 + 0.0254694i
\(700\) −0.183507 + 1.74596i −0.00693593 + 0.0659909i
\(701\) −0.133001 1.26542i −0.00502337 0.0477941i 0.991723 0.128395i \(-0.0409826\pi\)
−0.996746 + 0.0806012i \(0.974316\pi\)
\(702\) 4.01898 0.854261i 0.151687 0.0322420i
\(703\) 17.3903 + 7.74265i 0.655887 + 0.292020i
\(704\) −1.77893 + 1.97570i −0.0670459 + 0.0744621i
\(705\) 0.750405 + 2.30951i 0.0282619 + 0.0869811i
\(706\) −4.62557 5.13722i −0.174086 0.193342i
\(707\) −12.8117 + 22.1905i −0.481834 + 0.834560i
\(708\) 6.63968 + 11.5003i 0.249535 + 0.432207i
\(709\) −8.34803 + 25.6926i −0.313517 + 0.964906i 0.662844 + 0.748758i \(0.269349\pi\)
−0.976361 + 0.216148i \(0.930651\pi\)
\(710\) −0.618976 + 0.275586i −0.0232298 + 0.0103426i
\(711\) −0.686410 + 0.498706i −0.0257424 + 0.0187029i
\(712\) −0.184763 −0.00692428
\(713\) 15.8823 + 5.74228i 0.594798 + 0.215050i
\(714\) 4.59591 0.171997
\(715\) −8.83725 + 6.42064i −0.330494 + 0.240118i
\(716\) −21.9985 + 9.79436i −0.822122 + 0.366032i
\(717\) −7.22199 + 22.2270i −0.269710 + 0.830083i
\(718\) −0.370643 0.641972i −0.0138323 0.0239582i
\(719\) 14.9657 25.9213i 0.558125 0.966701i −0.439528 0.898229i \(-0.644854\pi\)
0.997653 0.0684720i \(-0.0218124\pi\)
\(720\) −0.669131 0.743145i −0.0249370 0.0276954i
\(721\) −5.80912 17.8786i −0.216343 0.665835i
\(722\) −2.26590 + 2.51654i −0.0843281 + 0.0936559i
\(723\) −21.9036 9.75213i −0.814605 0.362686i
\(724\) −16.9419 + 3.60111i −0.629640 + 0.133834i
\(725\) −0.117919 1.12192i −0.00437939 0.0416671i
\(726\) −0.411007 + 3.91047i −0.0152539 + 0.145131i
\(727\) −9.71327 2.06462i −0.360245 0.0765725i 0.0242335 0.999706i \(-0.492285\pi\)
−0.384479 + 0.923134i \(0.625619\pi\)
\(728\) 5.83564 + 4.23984i 0.216283 + 0.157139i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) −3.03533 0.645180i −0.112343 0.0238792i
\(731\) 1.67356 15.9228i 0.0618987 0.588927i
\(732\) −0.290356 2.76255i −0.0107319 0.102107i
\(733\) −52.3335 + 11.1238i −1.93298 + 0.410868i −0.934489 + 0.355992i \(0.884143\pi\)
−0.998493 + 0.0548763i \(0.982524\pi\)
\(734\) 21.2630 + 9.46692i 0.784833 + 0.349430i
\(735\) 2.62163 2.91161i 0.0967002 0.107397i
\(736\) −0.937331 2.88481i −0.0345505 0.106335i
\(737\) 6.81319 + 7.56681i 0.250967 + 0.278727i
\(738\) −2.44911 + 4.24198i −0.0901530 + 0.156150i
\(739\) 24.2644 + 42.0272i 0.892581 + 1.54599i 0.836771 + 0.547553i \(0.184441\pi\)
0.0558099 + 0.998441i \(0.482226\pi\)
\(740\) −1.24327 + 3.82641i −0.0457037 + 0.140662i
\(741\) 17.7596 7.90709i 0.652416 0.290474i
\(742\) 4.99680 3.63039i 0.183438 0.133276i
\(743\) 17.5424 0.643570 0.321785 0.946813i \(-0.395717\pi\)
0.321785 + 0.946813i \(0.395717\pi\)
\(744\) −5.55336 + 0.400259i −0.203596 + 0.0146742i
\(745\) −17.5799 −0.644077
\(746\) 12.4451 9.04188i 0.455647 0.331047i
\(747\) −7.09977 + 3.16102i −0.259767 + 0.115656i
\(748\) 2.15071 6.61921i 0.0786378 0.242022i
\(749\) −2.53175 4.38512i −0.0925082 0.160229i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 8.09398 + 8.98928i 0.295354 + 0.328024i 0.872497 0.488619i \(-0.162499\pi\)
−0.577143 + 0.816643i \(0.695833\pi\)
\(752\) −0.750405 2.30951i −0.0273644 0.0842191i
\(753\) 8.15142 9.05307i 0.297054 0.329912i
\(754\) −4.23438 1.88527i −0.154207 0.0686573i
\(755\) −8.41885 + 1.78948i −0.306393 + 0.0651259i
\(756\) −0.183507 1.74596i −0.00667410 0.0634998i
\(757\) −4.76774 + 45.3621i −0.173287 + 1.64871i 0.469694 + 0.882829i \(0.344364\pi\)
−0.642980 + 0.765883i \(0.722302\pi\)
\(758\) 16.2682 + 3.45791i 0.590887 + 0.125597i
\(759\) 6.52403 + 4.73999i 0.236807 + 0.172051i
\(760\) −3.82780 2.78106i −0.138849 0.100880i
\(761\) −11.0358 2.34572i −0.400046 0.0850324i 0.00349519 0.999994i \(-0.498887\pi\)
−0.403541 + 0.914961i \(0.632221\pi\)
\(762\) 1.92016 18.2691i 0.0695600 0.661819i
\(763\) −3.28991 31.3014i −0.119103 1.13319i
\(764\) 14.0043 2.97671i 0.506659 0.107694i
\(765\) 2.39157 + 1.06479i 0.0864672 + 0.0384977i
\(766\) 15.4362 17.1437i 0.557734 0.619426i
\(767\) −16.8605 51.8914i −0.608799 1.87369i
\(768\) 0.669131 + 0.743145i 0.0241452 + 0.0268159i
\(769\) −23.9159 + 41.4236i −0.862431 + 1.49377i 0.00714425 + 0.999974i \(0.497726\pi\)
−0.869575 + 0.493800i \(0.835607\pi\)
\(770\) 2.33366 + 4.04201i 0.0840991 + 0.145664i
\(771\) −2.84891 + 8.76804i −0.102601 + 0.315773i
\(772\) −1.24115 + 0.552594i −0.0446698 + 0.0198883i
\(773\) −13.2118 + 9.59891i −0.475194 + 0.345249i −0.799462 0.600717i \(-0.794882\pi\)
0.324268 + 0.945965i \(0.394882\pi\)
\(774\) −6.11581 −0.219828
\(775\) 2.09675 + 5.15787i 0.0753175 + 0.185276i
\(776\) −9.39314 −0.337194
\(777\) −5.71428 + 4.15167i −0.204999 + 0.148940i
\(778\) −2.13888 + 0.952293i −0.0766827 + 0.0341414i
\(779\) −7.16164 + 22.0413i −0.256592 + 0.789710i
\(780\) 2.05438 + 3.55830i 0.0735588 + 0.127408i
\(781\) −0.900661 + 1.55999i −0.0322282 + 0.0558209i
\(782\) 5.31341 + 5.90114i 0.190007 + 0.211024i
\(783\) 0.348602 + 1.07289i 0.0124580 + 0.0383418i
\(784\) −2.62163 + 2.91161i −0.0936296 + 0.103986i
\(785\) 5.12572 + 2.28212i 0.182945 + 0.0814522i
\(786\) 12.7515 2.71041i 0.454830 0.0966770i
\(787\) −0.832822 7.92377i −0.0296869 0.282452i −0.999287 0.0377568i \(-0.987979\pi\)
0.969600 0.244695i \(-0.0786879\pi\)
\(788\) −1.06923 + 10.1730i −0.0380896 + 0.362398i
\(789\) −25.5163 5.42365i −0.908403 0.193087i
\(790\) −0.686410 0.498706i −0.0244214 0.0177432i
\(791\) −22.5023 16.3489i −0.800088 0.581298i
\(792\) −2.60047 0.552747i −0.0924038 0.0196410i
\(793\) −1.19301 + 11.3507i −0.0423649 + 0.403075i
\(794\) 0.270175 + 2.57055i 0.00958816 + 0.0912253i
\(795\) 3.44128 0.731466i 0.122050 0.0259424i
\(796\) 2.81046 + 1.25130i 0.0996141 + 0.0443511i
\(797\) 10.4520 11.6081i 0.370227 0.411179i −0.529027 0.848605i \(-0.677443\pi\)
0.899254 + 0.437426i \(0.144110\pi\)
\(798\) −2.56680 7.89981i −0.0908639 0.279650i
\(799\) 4.25379 + 4.72431i 0.150488 + 0.167134i
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) −0.0923814 0.160009i −0.00326414 0.00565365i
\(802\) 5.29424 16.2940i 0.186946 0.575361i
\(803\) −7.53668 + 3.35555i −0.265964 + 0.118415i
\(804\) 3.09848 2.25118i 0.109275 0.0793930i
\(805\) −5.32512 −0.187686
\(806\) 22.6608 + 3.13538i 0.798192 + 0.110439i
\(807\) −6.08821 −0.214315
\(808\) 11.8080 8.57900i 0.415403 0.301808i
\(809\) 17.7773 7.91498i 0.625018 0.278276i −0.0696889 0.997569i \(-0.522201\pi\)
0.694707 + 0.719293i \(0.255534\pi\)
\(810\) 0.309017 0.951057i 0.0108578 0.0334167i
\(811\) 27.2776 + 47.2461i 0.957845 + 1.65904i 0.727719 + 0.685875i \(0.240580\pi\)
0.230126 + 0.973161i \(0.426086\pi\)
\(812\) −0.990231 + 1.71513i −0.0347503 + 0.0601893i
\(813\) 7.26459 + 8.06815i 0.254780 + 0.282962i
\(814\) 3.30533 + 10.1728i 0.115852 + 0.356555i
\(815\) −9.00504 + 10.0011i −0.315433 + 0.350323i
\(816\) −2.39157 1.06479i −0.0837216 0.0372752i
\(817\) −28.3041 + 6.01623i −0.990236 + 0.210481i
\(818\) −3.58423 34.1016i −0.125319 1.19234i
\(819\) −0.753989 + 7.17373i −0.0263465 + 0.250670i
\(820\) −4.79118 1.01840i −0.167315 0.0355640i
\(821\) 30.9566 + 22.4913i 1.08039 + 0.784950i 0.977751 0.209768i \(-0.0672709\pi\)
0.102640 + 0.994719i \(0.467271\pi\)
\(822\) 7.35234 + 5.34179i 0.256442 + 0.186316i
\(823\) −8.60558 1.82917i −0.299972 0.0637610i 0.0554671 0.998461i \(-0.482335\pi\)
−0.355439 + 0.934700i \(0.615669\pi\)
\(824\) −1.11929 + 10.6494i −0.0389924 + 0.370988i
\(825\) 0.277896 + 2.64400i 0.00967510 + 0.0920524i
\(826\) −22.8035 + 4.84702i −0.793434 + 0.168650i
\(827\) −28.7111 12.7830i −0.998383 0.444509i −0.158549 0.987351i \(-0.550681\pi\)
−0.839835 + 0.542842i \(0.817348\pi\)
\(828\) 2.02965 2.25416i 0.0705353 0.0783373i
\(829\) 16.3542 + 50.3331i 0.568005 + 1.74814i 0.658849 + 0.752275i \(0.271043\pi\)
−0.0908443 + 0.995865i \(0.528957\pi\)
\(830\) −5.20026 5.77548i −0.180504 0.200470i
\(831\) −9.31660 + 16.1368i −0.323189 + 0.559780i
\(832\) −2.05438 3.55830i −0.0712230 0.123362i
\(833\) 3.16953 9.75481i 0.109818 0.337984i
\(834\) 3.16536 1.40931i 0.109607 0.0488004i
\(835\) −6.81732 + 4.95307i −0.235923 + 0.171408i
\(836\) −12.5788 −0.435047
\(837\) −3.12331 4.60922i −0.107958 0.159318i
\(838\) −20.6234 −0.712424
\(839\) −21.4817 + 15.6074i −0.741631 + 0.538826i −0.893221 0.449617i \(-0.851560\pi\)
0.151591 + 0.988443i \(0.451560\pi\)
\(840\) 1.60380 0.714056i 0.0553362 0.0246373i
\(841\) −8.56823 + 26.3703i −0.295456 + 0.909321i
\(842\) −4.55304 7.88610i −0.156908 0.271773i
\(843\) 2.06198 3.57146i 0.0710185 0.123008i
\(844\) 2.52816 + 2.80781i 0.0870229 + 0.0966487i
\(845\) −1.19960 3.69198i −0.0412674 0.127008i
\(846\) 1.62489 1.80462i 0.0558649 0.0620442i
\(847\) −6.30615 2.80768i −0.216682 0.0964729i
\(848\) −3.44128 + 0.731466i −0.118174 + 0.0251186i
\(849\) 0.515989 + 4.90931i 0.0177087 + 0.168487i
\(850\) −0.273645 + 2.60355i −0.00938593 + 0.0893012i
\(851\) −11.9371 2.53731i −0.409199 0.0869780i
\(852\) 0.548152 + 0.398256i 0.0187794 + 0.0136440i
\(853\) 26.6130 + 19.3355i 0.911212 + 0.662034i 0.941321 0.337512i \(-0.109586\pi\)
−0.0301092 + 0.999547i \(0.509586\pi\)
\(854\) 4.77001 + 1.01390i 0.163226 + 0.0346948i
\(855\) 0.494568 4.70550i 0.0169139 0.160925i
\(856\) 0.301486 + 2.86845i 0.0103046 + 0.0980415i
\(857\) −51.4329 + 10.9324i −1.75691 + 0.373443i −0.969902 0.243496i \(-0.921706\pi\)
−0.787011 + 0.616939i \(0.788372\pi\)
\(858\) 9.97906 + 4.44296i 0.340680 + 0.151680i
\(859\) −11.3051 + 12.5556i −0.385726 + 0.428392i −0.904470 0.426537i \(-0.859733\pi\)
0.518744 + 0.854930i \(0.326400\pi\)
\(860\) −1.88989 5.81648i −0.0644446 0.198340i
\(861\) −5.75398 6.39044i −0.196095 0.217786i
\(862\) 10.6193 18.3932i 0.361695 0.626474i
\(863\) 16.4172 + 28.4353i 0.558846 + 0.967950i 0.997593 + 0.0693395i \(0.0220892\pi\)
−0.438747 + 0.898611i \(0.644577\pi\)
\(864\) −0.309017 + 0.951057i −0.0105130 + 0.0323556i
\(865\) 6.99600 3.11482i 0.237871 0.105907i
\(866\) 13.6972 9.95160i 0.465450 0.338169i
\(867\) −10.1466 −0.344598
\(868\) 2.34442 9.48930i 0.0795746 0.322088i
\(869\) −2.25566 −0.0765181
\(870\) −0.912652 + 0.663081i −0.0309418 + 0.0224805i
\(871\) −14.3759 + 6.40054i −0.487107 + 0.216874i
\(872\) −5.54005 + 17.0505i −0.187610 + 0.577403i
\(873\) −4.69657 8.13470i −0.158955 0.275318i
\(874\) 7.17583 12.4289i 0.242726 0.420414i
\(875\) −1.17471 1.30465i −0.0397124 0.0441051i
\(876\) 0.958925 + 2.95127i 0.0323991 + 0.0997141i
\(877\) −26.9811 + 29.9656i −0.911089 + 1.01187i 0.0887863 + 0.996051i \(0.471701\pi\)
−0.999875 + 0.0158157i \(0.994965\pi\)
\(878\) −10.1392 4.51428i −0.342183 0.152350i
\(879\) −1.62370 + 0.345127i −0.0547659 + 0.0116408i
\(880\) −0.277896 2.64400i −0.00936788 0.0891294i
\(881\) −0.580362 + 5.52177i −0.0195529 + 0.186033i −0.999939 0.0110536i \(-0.996481\pi\)
0.980386 + 0.197087i \(0.0631481\pi\)
\(882\) −3.83235 0.814590i −0.129042 0.0274287i
\(883\) 14.3415 + 10.4197i 0.482631 + 0.350652i 0.802343 0.596863i \(-0.203586\pi\)
−0.319712 + 0.947515i \(0.603586\pi\)
\(884\) 8.70205 + 6.32241i 0.292682 + 0.212646i
\(885\) −12.9892 2.76094i −0.436627 0.0928078i
\(886\) −1.63166 + 15.5242i −0.0548166 + 0.521545i
\(887\) −3.44633 32.7896i −0.115716 1.10097i −0.886134 0.463428i \(-0.846619\pi\)
0.770418 0.637539i \(-0.220048\pi\)
\(888\) 3.93540 0.836496i 0.132063 0.0280710i
\(889\) 29.4613 + 13.1170i 0.988100 + 0.439930i
\(890\) 0.123630 0.137306i 0.00414410 0.00460249i
\(891\) −0.821543 2.52845i −0.0275227 0.0847062i
\(892\) −12.2120 13.5628i −0.408888 0.454116i
\(893\) 5.74480 9.95028i 0.192242 0.332973i
\(894\) 8.78994 + 15.2246i 0.293980 + 0.509187i
\(895\) 7.44124 22.9018i 0.248733 0.765522i
\(896\) −1.60380 + 0.714056i −0.0535791 + 0.0238549i
\(897\) −10.0828 + 7.32556i −0.336654 + 0.244593i
\(898\) 7.55783 0.252208
\(899\) −0.205785 + 6.27762i −0.00686332 + 0.209370i
\(900\) 1.00000 0.0333333
\(901\) 7.45118 5.41360i 0.248235 0.180353i
\(902\) −11.8964 + 5.29663i −0.396108 + 0.176358i
\(903\) 3.31784 10.2112i 0.110411 0.339809i
\(904\) 7.92172 + 13.7208i 0.263473 + 0.456348i
\(905\) 8.66018 14.9999i 0.287874 0.498613i
\(906\) 5.75916 + 6.39620i 0.191335 + 0.212499i
\(907\) −14.8019 45.5556i −0.491489 1.51265i −0.822357 0.568971i \(-0.807342\pi\)
0.330868 0.943677i \(-0.392658\pi\)
\(908\) 18.0771 20.0767i 0.599910 0.666268i
\(909\) 13.3336 + 5.93651i 0.442248 + 0.196902i
\(910\) −7.05562 + 1.49972i −0.233891 + 0.0497152i
\(911\) 1.42225 + 13.5318i 0.0471213 + 0.448330i 0.992490 + 0.122326i \(0.0390354\pi\)
−0.945369 + 0.326003i \(0.894298\pi\)
\(912\) −0.494568 + 4.70550i −0.0163768 + 0.155815i
\(913\) −20.2100 4.29577i −0.668854 0.142169i
\(914\) −18.7211 13.6017i −0.619239 0.449904i
\(915\) 2.24726 + 1.63273i 0.0742922 + 0.0539764i
\(916\) −5.49826 1.16869i −0.181668 0.0386147i
\(917\) −2.39226 + 22.7609i −0.0789995 + 0.751630i
\(918\) −0.273645 2.60355i −0.00903161 0.0859301i
\(919\) 32.9532 7.00442i 1.08703 0.231055i 0.370653 0.928771i \(-0.379134\pi\)
0.716374 + 0.697717i \(0.245801\pi\)
\(920\) 2.77103 + 1.23374i 0.0913580 + 0.0406752i
\(921\) 13.5611 15.0611i 0.446854 0.496282i
\(922\) −12.2208 37.6117i −0.402471 1.23868i
\(923\) −1.86280 2.06885i −0.0613148 0.0680970i
\(924\) 2.33366 4.04201i 0.0767716 0.132972i
\(925\) −2.01166 3.48430i −0.0661430 0.114563i
\(926\) 11.2877 34.7400i 0.370937 1.14163i
\(927\) −9.78227 + 4.35535i −0.321292 + 0.143048i
\(928\) 0.912652 0.663081i 0.0299593 0.0217667i
\(929\) −58.1840 −1.90895 −0.954477 0.298284i \(-0.903586\pi\)
−0.954477 + 0.298284i \(0.903586\pi\)
\(930\) 3.41847 4.39478i 0.112096 0.144110i
\(931\) −18.5375 −0.607543
\(932\) 2.62021 1.90369i 0.0858278 0.0623575i
\(933\) 5.39127 2.40035i 0.176502 0.0785839i
\(934\) 6.87881 21.1708i 0.225082 0.692730i
\(935\) 3.47993 + 6.02741i 0.113806 + 0.197117i
\(936\) 2.05438 3.55830i 0.0671497 0.116307i
\(937\) 6.82705 + 7.58220i 0.223030 + 0.247700i 0.844267 0.535923i \(-0.180036\pi\)
−0.621237 + 0.783623i \(0.713370\pi\)
\(938\) 2.07775 + 6.39465i 0.0678409 + 0.208793i
\(939\) −1.18894 + 1.32045i −0.0387994 + 0.0430911i
\(940\) 2.21842 + 0.987703i 0.0723568 + 0.0322153i
\(941\) 5.78057 1.22870i 0.188441 0.0400544i −0.112724 0.993626i \(-0.535958\pi\)
0.301165 + 0.953572i \(0.402624\pi\)
\(942\) −0.586488 5.58006i −0.0191088 0.181808i
\(943\) 1.55304 14.7762i 0.0505741 0.481180i
\(944\) 12.9892 + 2.76094i 0.422762 + 0.0898608i
\(945\) 1.42029 + 1.03190i 0.0462020 + 0.0335677i
\(946\) −13.1540 9.55697i −0.427675 0.310724i
\(947\) −53.2388 11.3162i −1.73003 0.367729i −0.767951 0.640509i \(-0.778723\pi\)
−0.962076 + 0.272780i \(0.912057\pi\)
\(948\) −0.0886871 + 0.843802i −0.00288042 + 0.0274054i
\(949\) −1.33275 12.6803i −0.0432629 0.411619i
\(950\) 4.62803 0.983718i 0.150153 0.0319160i
\(951\) 7.83688 + 3.48920i 0.254128 + 0.113145i
\(952\) 3.07526 3.41542i 0.0996698 0.110695i
\(953\) 8.78626 + 27.0413i 0.284615 + 0.875955i 0.986514 + 0.163678i \(0.0523359\pi\)
−0.701899 + 0.712277i \(0.747664\pi\)
\(954\) −2.35411 2.61450i −0.0762170 0.0846476i
\(955\) −7.15860 + 12.3991i −0.231647 + 0.401224i
\(956\) 11.6854 + 20.2398i 0.377934 + 0.654601i
\(957\) −0.926782 + 2.85234i −0.0299586 + 0.0922032i
\(958\) −26.4785 + 11.7890i −0.855482 + 0.380885i
\(959\) −12.9076 + 9.37790i −0.416807 + 0.302828i
\(960\) −1.00000 −0.0322749
\(961\) −7.62810 30.0468i −0.246068 0.969253i
\(962\) −16.5309 −0.532978
\(963\) −2.33340 + 1.69532i −0.0751929 + 0.0546308i
\(964\) −21.9036 + 9.75213i −0.705469 + 0.314095i
\(965\) 0.419832 1.29211i 0.0135149 0.0415945i
\(966\) 2.66256 + 4.61169i 0.0856665 + 0.148379i
\(967\) 5.63591 9.76168i 0.181239 0.313914i −0.761064 0.648677i \(-0.775323\pi\)
0.942303 + 0.334762i \(0.108656\pi\)
\(968\) 2.63103 + 2.92206i 0.0845645 + 0.0939184i
\(969\) −3.82760 11.7801i −0.122960 0.378432i
\(970\) 6.28524 6.98046i 0.201807 0.224129i
\(971\) −45.8715 20.4233i −1.47209 0.655416i −0.495124 0.868822i \(-0.664877\pi\)
−0.976963 + 0.213407i \(0.931544\pi\)
\(972\) −0.978148 + 0.207912i −0.0313741 + 0.00666877i
\(973\) 0.635838 + 6.04960i 0.0203840 + 0.193941i
\(974\) 1.71978 16.3626i 0.0551052 0.524291i
\(975\) −4.01898 0.854261i −0.128710 0.0273582i
\(976\) −2.24726 1.63273i −0.0719331 0.0522625i
\(977\) −21.6307 15.7156i −0.692028 0.502788i 0.185298 0.982682i \(-0.440675\pi\)
−0.877326 + 0.479894i \(0.840675\pi\)
\(978\) 13.1637 + 2.79804i 0.420930 + 0.0894714i
\(979\) 0.0513449 0.488514i 0.00164099 0.0156130i
\(980\) −0.409539 3.89650i −0.0130822 0.124469i
\(981\) −17.5362 + 3.72744i −0.559888 + 0.119008i
\(982\) 18.9370 + 8.43131i 0.604305 + 0.269054i
\(983\) 5.21985 5.79723i 0.166487 0.184903i −0.654128 0.756384i \(-0.726964\pi\)
0.820615 + 0.571481i \(0.193631\pi\)
\(984\) 1.51363 + 4.65849i 0.0482529 + 0.148507i
\(985\) −6.84456 7.60166i −0.218086 0.242209i
\(986\) −1.47662 + 2.55759i −0.0470253 + 0.0814502i
\(987\) 2.13158 + 3.69201i 0.0678490 + 0.117518i
\(988\) 6.00739 18.4888i 0.191120 0.588208i
\(989\) 16.9471 7.54532i 0.538885 0.239927i
\(990\) 2.15083 1.56267i 0.0683578 0.0496648i
\(991\) 25.2253 0.801309 0.400654 0.916229i \(-0.368783\pi\)
0.400654 + 0.916229i \(0.368783\pi\)
\(992\) −3.41847 + 4.39478i −0.108537 + 0.139534i
\(993\) −14.1977 −0.450549
\(994\) −0.962321 + 0.699167i −0.0305230 + 0.0221762i
\(995\) −2.81046 + 1.25130i −0.0890976 + 0.0396688i
\(996\) −2.40158 + 7.39130i −0.0760969 + 0.234202i
\(997\) −21.5008 37.2405i −0.680938 1.17942i −0.974695 0.223539i \(-0.928239\pi\)
0.293757 0.955880i \(-0.405094\pi\)
\(998\) −2.36400 + 4.09457i −0.0748312 + 0.129611i
\(999\) 2.69213 + 2.98991i 0.0851752 + 0.0945966i
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.bg.i.421.3 yes 24
31.19 even 15 inner 930.2.bg.i.391.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.i.391.3 24 31.19 even 15 inner
930.2.bg.i.421.3 yes 24 1.1 even 1 trivial