Properties

Label 81.2.g.a.40.3
Level 8181
Weight 22
Character 81.40
Analytic conductor 0.6470.647
Analytic rank 00
Dimension 144144
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 81=34 81 = 3^{4}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 81.g (of order 2727, degree 1818, 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: 0.6467882563720.646788256372
Analytic rank: 00
Dimension: 144144
Relative dimension: 88 over Q(ζ27)\Q(\zeta_{27})
Twist minimal: yes
Sato-Tate group: SU(2)[C27]\mathrm{SU}(2)[C_{27}]

Embedding invariants

Embedding label 40.3
Character χ\chi == 81.40
Dual form 81.2.g.a.79.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.08833421.51664i)q2+(0.961557+1.44063i)q3+(0.305915+0.0357564i)q4+(0.07746020.0183584i)q5+(2.099971.58559i)q6+(0.510276+0.685420i)q7+(0.4463642.53145i)q8+(1.15082+2.77049i)q9+(0.0210007+0.119101i)q10+(2.740142.90438i)q11+(0.3456670.406328i)q12+(1.81277+0.910408i)q13+(1.08461+0.713359i)q14+(0.04803480.129244i)q15+(4.39927+1.04265i)q16+(1.92609+0.701038i)q17+(4.30349+1.50064i)q18+(5.26032+1.91460i)q19+(0.0243527+0.00284642i)q20+(1.478100.0760476i)q21+(4.16285+4.41236i)q22+(4.48100+6.01902i)q23+(3.217683.07718i)q24+(4.462502.24115i)q25+(1.54089+2.66890i)q26+(5.09782+1.00609i)q27+(0.1315930.227926i)q28+(0.928490+0.610677i)q29+(0.191773+0.0842682i)q30+(2.373515.50241i)q31+(0.495463+1.65496i)q32+(1.549336.74025i)q33+(1.23336+2.85925i)q34+(0.05210940.0437249i)q35+(0.2529890.888685i)q36+(0.7822740.656406i)q37+(2.439098.14713i)q38+(3.054641.73612i)q39+(0.0118980+0.204282i)q40+(0.2545284.37008i)q41+(0.0152296+2.24845i)q42+(3.4440211.5038i)q43+(0.942101+0.790516i)q44+(0.1400040.193476i)q45+(8.732867.32774i)q46+(2.03795+4.72449i)q47+(5.732215.33514i)q48+(1.79820+6.00642i)q49+(3.00483+6.96597i)q50+(2.861982.10068i)q51+(0.5220020.343326i)q52+(5.16096+8.93905i)q53+(1.97619+7.64268i)q54+(0.158932+0.275278i)q55+(1.96288+0.985795i)q56+(2.29987+9.41916i)q57+(1.00819+1.35424i)q58+(7.517587.96817i)q59+(0.0193159+0.0378202i)q60+(10.5595+1.23423i)q61+(8.554833.11370i)q62+(1.311722.20251i)q63+(6.03074+2.19501i)q64+(0.1571310.0372408i)q65+(10.35941.75438i)q66+(3.83910+2.52502i)q67+(0.5641520.283328i)q68+(4.36244+12.2431i)q69+(0.07091800.0751687i)q70+(0.963622+5.46497i)q71+(7.52705+1.67659i)q72+(0.267464+1.51686i)q73+(0.926430+1.24441i)q74+(1.062288.58380i)q75+(1.677670.397615i)q76+(3.388950.396111i)q77+(2.36324+4.78615i)q78+(0.79384613.6298i)q79+0.359909q80+(6.351256.37665i)q816.65031q82+(0.365349+6.27280i)q83+(0.4548910.0295872i)q84+(0.1620650.0189427i)q85+(17.75144.20715i)q86+(1.772550.750407i)q87+(6.12920+8.23295i)q88+(1.7952010.1811i)q89+(0.3058000.195245i)q90+(0.3010021.70707i)q91+(1.586021.68109i)q92+(10.20921.87154i)q93+(6.985333.50817i)q94+(0.3723170.244876i)q95+(1.90777+2.30512i)q96+(13.3681+3.16829i)q97+(8.950733.25780i)q98+(11.20004.24913i)q99+O(q100)q+(-0.0883342 - 1.51664i) q^{2} +(0.961557 + 1.44063i) q^{3} +(-0.305915 + 0.0357564i) q^{4} +(-0.0774602 - 0.0183584i) q^{5} +(2.09997 - 1.58559i) q^{6} +(-0.510276 + 0.685420i) q^{7} +(-0.446364 - 2.53145i) q^{8} +(-1.15082 + 2.77049i) q^{9} +(-0.0210007 + 0.119101i) q^{10} +(-2.74014 - 2.90438i) q^{11} +(-0.345667 - 0.406328i) q^{12} +(-1.81277 + 0.910408i) q^{13} +(1.08461 + 0.713359i) q^{14} +(-0.0480348 - 0.129244i) q^{15} +(-4.39927 + 1.04265i) q^{16} +(-1.92609 + 0.701038i) q^{17} +(4.30349 + 1.50064i) q^{18} +(5.26032 + 1.91460i) q^{19} +(0.0243527 + 0.00284642i) q^{20} +(-1.47810 - 0.0760476i) q^{21} +(-4.16285 + 4.41236i) q^{22} +(4.48100 + 6.01902i) q^{23} +(3.21768 - 3.07718i) q^{24} +(-4.46250 - 2.24115i) q^{25} +(1.54089 + 2.66890i) q^{26} +(-5.09782 + 1.00609i) q^{27} +(0.131593 - 0.227926i) q^{28} +(-0.928490 + 0.610677i) q^{29} +(-0.191773 + 0.0842682i) q^{30} +(2.37351 - 5.50241i) q^{31} +(0.495463 + 1.65496i) q^{32} +(1.54933 - 6.74025i) q^{33} +(1.23336 + 2.85925i) q^{34} +(0.0521094 - 0.0437249i) q^{35} +(0.252989 - 0.888685i) q^{36} +(-0.782274 - 0.656406i) q^{37} +(2.43909 - 8.14713i) q^{38} +(-3.05464 - 1.73612i) q^{39} +(-0.0118980 + 0.204282i) q^{40} +(0.254528 - 4.37008i) q^{41} +(0.0152296 + 2.24845i) q^{42} +(3.44402 - 11.5038i) q^{43} +(0.942101 + 0.790516i) q^{44} +(0.140004 - 0.193476i) q^{45} +(8.73286 - 7.32774i) q^{46} +(2.03795 + 4.72449i) q^{47} +(-5.73221 - 5.33514i) q^{48} +(1.79820 + 6.00642i) q^{49} +(-3.00483 + 6.96597i) q^{50} +(-2.86198 - 2.10068i) q^{51} +(0.522002 - 0.343326i) q^{52} +(-5.16096 + 8.93905i) q^{53} +(1.97619 + 7.64268i) q^{54} +(0.158932 + 0.275278i) q^{55} +(1.96288 + 0.985795i) q^{56} +(2.29987 + 9.41916i) q^{57} +(1.00819 + 1.35424i) q^{58} +(7.51758 - 7.96817i) q^{59} +(0.0193159 + 0.0378202i) q^{60} +(10.5595 + 1.23423i) q^{61} +(-8.55483 - 3.11370i) q^{62} +(-1.31172 - 2.20251i) q^{63} +(-6.03074 + 2.19501i) q^{64} +(0.157131 - 0.0372408i) q^{65} +(-10.3594 - 1.75438i) q^{66} +(3.83910 + 2.52502i) q^{67} +(0.564152 - 0.283328i) q^{68} +(-4.36244 + 12.2431i) q^{69} +(-0.0709180 - 0.0751687i) q^{70} +(-0.963622 + 5.46497i) q^{71} +(7.52705 + 1.67659i) q^{72} +(0.267464 + 1.51686i) q^{73} +(-0.926430 + 1.24441i) q^{74} +(-1.06228 - 8.58380i) q^{75} +(-1.67767 - 0.397615i) q^{76} +(3.38895 - 0.396111i) q^{77} +(-2.36324 + 4.78615i) q^{78} +(-0.793846 - 13.6298i) q^{79} +0.359909 q^{80} +(-6.35125 - 6.37665i) q^{81} -6.65031 q^{82} +(0.365349 + 6.27280i) q^{83} +(0.454891 - 0.0295872i) q^{84} +(0.162065 - 0.0189427i) q^{85} +(-17.7514 - 4.20715i) q^{86} +(-1.77255 - 0.750407i) q^{87} +(-6.12920 + 8.23295i) q^{88} +(-1.79520 - 10.1811i) q^{89} +(-0.305800 - 0.195245i) q^{90} +(0.301002 - 1.70707i) q^{91} +(-1.58602 - 1.68109i) q^{92} +(10.2092 - 1.87154i) q^{93} +(6.98533 - 3.50817i) q^{94} +(-0.372317 - 0.244876i) q^{95} +(-1.90777 + 2.30512i) q^{96} +(-13.3681 + 3.16829i) q^{97} +(8.95073 - 3.25780i) q^{98} +(11.2000 - 4.24913i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 144q18q218q318q418q518q618q718q818q918q1018q1118q1218q1318q1418q1518q1618q179q1818q19++54q99+O(q100) 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/81Z)×\left(\mathbb{Z}/81\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(1327)e\left(\frac{13}{27}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.0883342 1.51664i −0.0624617 1.07243i −0.873309 0.487168i 0.838030π-0.838030\pi
0.810847 0.585258i 0.199007π-0.199007\pi
33 0.961557 + 1.44063i 0.555155 + 0.831747i
44 −0.305915 + 0.0357564i −0.152958 + 0.0178782i
55 −0.0774602 0.0183584i −0.0346413 0.00821013i 0.213259 0.976996i 0.431592π-0.431592\pi
−0.247900 + 0.968786i 0.579740π0.579740\pi
66 2.09997 1.58559i 0.857311 0.647315i
77 −0.510276 + 0.685420i −0.192866 + 0.259064i −0.888028 0.459789i 0.847925π-0.847925\pi
0.695162 + 0.718853i 0.255333π0.255333\pi
88 −0.446364 2.53145i −0.157813 0.895004i
99 −1.15082 + 2.77049i −0.383605 + 0.923497i
1010 −0.0210007 + 0.119101i −0.00664101 + 0.0376630i
1111 −2.74014 2.90438i −0.826183 0.875703i 0.167734 0.985832i 0.446355π-0.446355\pi
−0.993917 + 0.110129i 0.964874π0.964874\pi
1212 −0.345667 0.406328i −0.0997854 0.117297i
1313 −1.81277 + 0.910408i −0.502772 + 0.252502i −0.682062 0.731295i 0.738916π-0.738916\pi
0.179289 + 0.983796i 0.442620π0.442620\pi
1414 1.08461 + 0.713359i 0.289874 + 0.190653i
1515 −0.0480348 0.129244i −0.0124025 0.0333707i
1616 −4.39927 + 1.04265i −1.09982 + 0.260661i
1717 −1.92609 + 0.701038i −0.467144 + 0.170027i −0.564858 0.825188i 0.691069π-0.691069\pi
0.0977140 + 0.995215i 0.468847π0.468847\pi
1818 4.30349 + 1.50064i 1.01434 + 0.353705i
1919 5.26032 + 1.91460i 1.20680 + 0.439239i 0.865593 0.500749i 0.166942π-0.166942\pi
0.341207 + 0.939988i 0.389164π0.389164\pi
2020 0.0243527 + 0.00284642i 0.00544543 + 0.000636479i
2121 −1.47810 0.0760476i −0.322547 0.0165949i
2222 −4.16285 + 4.41236i −0.887522 + 0.940718i
2323 4.48100 + 6.01902i 0.934352 + 1.25505i 0.966788 + 0.255579i 0.0822661π0.0822661\pi
−0.0324361 + 0.999474i 0.510327π0.510327\pi
2424 3.21768 3.07718i 0.656806 0.628127i
2525 −4.46250 2.24115i −0.892500 0.448230i
2626 1.54089 + 2.66890i 0.302193 + 0.523414i
2727 −5.09782 + 1.00609i −0.981076 + 0.193622i
2828 0.131593 0.227926i 0.0248688 0.0430740i
2929 −0.928490 + 0.610677i −0.172416 + 0.113400i −0.632784 0.774328i 0.718088π-0.718088\pi
0.460368 + 0.887728i 0.347718π0.347718\pi
3030 −0.191773 + 0.0842682i −0.0350129 + 0.0153852i
3131 2.37351 5.50241i 0.426294 0.988262i −0.560775 0.827968i 0.689497π-0.689497\pi
0.987069 0.160293i 0.0512440π-0.0512440\pi
3232 0.495463 + 1.65496i 0.0875863 + 0.292559i
3333 1.54933 6.74025i 0.269703 1.17333i
3434 1.23336 + 2.85925i 0.211520 + 0.490357i
3535 0.0521094 0.0437249i 0.00880809 0.00739086i
3636 0.252989 0.888685i 0.0421649 0.148114i
3737 −0.782274 0.656406i −0.128605 0.107913i 0.576216 0.817297i 0.304529π-0.304529\pi
−0.704822 + 0.709385i 0.748973π0.748973\pi
3838 2.43909 8.14713i 0.395673 1.32164i
3939 −3.05464 1.73612i −0.489134 0.278002i
4040 −0.0118980 + 0.204282i −0.00188125 + 0.0322998i
4141 0.254528 4.37008i 0.0397506 0.682491i −0.918299 0.395888i 0.870437π-0.870437\pi
0.958049 0.286603i 0.0925262π-0.0925262\pi
4242 0.0152296 + 2.24845i 0.00234997 + 0.346944i
4343 3.44402 11.5038i 0.525208 1.75432i −0.122543 0.992463i 0.539105π-0.539105\pi
0.647751 0.761852i 0.275710π-0.275710\pi
4444 0.942101 + 0.790516i 0.142027 + 0.119175i
4545 0.140004 0.193476i 0.0208706 0.0288417i
4646 8.73286 7.32774i 1.28759 1.08042i
4747 2.03795 + 4.72449i 0.297265 + 0.689138i 0.999745 0.0225650i 0.00718327π-0.00718327\pi
−0.702480 + 0.711703i 0.747924π0.747924\pi
4848 −5.73221 5.33514i −0.827373 0.770061i
4949 1.79820 + 6.00642i 0.256886 + 0.858060i
5050 −3.00483 + 6.96597i −0.424947 + 0.985137i
5151 −2.86198 2.10068i −0.400757 0.294155i
5252 0.522002 0.343326i 0.0723886 0.0476107i
5353 −5.16096 + 8.93905i −0.708913 + 1.22787i 0.256348 + 0.966584i 0.417481π0.417481\pi
−0.965261 + 0.261288i 0.915853π0.915853\pi
5454 1.97619 + 7.64268i 0.268925 + 1.04004i
5555 0.158932 + 0.275278i 0.0214304 + 0.0371185i
5656 1.96288 + 0.985795i 0.262301 + 0.131732i
5757 2.29987 + 9.41916i 0.304626 + 1.24760i
5858 1.00819 + 1.35424i 0.132382 + 0.177820i
5959 7.51758 7.96817i 0.978705 1.03737i −0.0205882 0.999788i 0.506554π-0.506554\pi
0.999294 0.0375792i 0.0119646π-0.0119646\pi
6060 0.0193159 + 0.0378202i 0.00249367 + 0.00488256i
6161 10.5595 + 1.23423i 1.35201 + 0.158027i 0.761060 0.648681i 0.224679π-0.224679\pi
0.590950 + 0.806708i 0.298753π0.298753\pi
6262 −8.55483 3.11370i −1.08646 0.395441i
6363 −1.31172 2.20251i −0.165261 0.277490i
6464 −6.03074 + 2.19501i −0.753842 + 0.274376i
6565 0.157131 0.0372408i 0.0194897 0.00461915i
6666 −10.3594 1.75438i −1.27515 0.215949i
6767 3.83910 + 2.52502i 0.469021 + 0.308480i 0.761929 0.647661i 0.224253π-0.224253\pi
−0.292908 + 0.956141i 0.594623π0.594623\pi
6868 0.564152 0.283328i 0.0684135 0.0343586i
6969 −4.36244 + 12.2431i −0.525175 + 1.47389i
7070 −0.0709180 0.0751687i −0.00847632 0.00898438i
7171 −0.963622 + 5.46497i −0.114361 + 0.648573i 0.872704 + 0.488250i 0.162365π0.162365\pi
−0.987065 + 0.160323i 0.948746π0.948746\pi
7272 7.52705 + 1.67659i 0.887072 + 0.197588i
7373 0.267464 + 1.51686i 0.0313043 + 0.177536i 0.996451 0.0841735i 0.0268250π-0.0268250\pi
−0.965147 + 0.261709i 0.915714π0.915714\pi
7474 −0.926430 + 1.24441i −0.107695 + 0.144660i
7575 −1.06228 8.58380i −0.122662 0.991171i
7676 −1.67767 0.397615i −0.192442 0.0456096i
7777 3.38895 0.396111i 0.386206 0.0451411i
7878 −2.36324 + 4.78615i −0.267584 + 0.541925i
7979 −0.793846 13.6298i −0.0893146 1.53347i −0.683981 0.729500i 0.739753π-0.739753\pi
0.594666 0.803973i 0.297284π-0.297284\pi
8080 0.359909 0.0402391
8181 −6.35125 6.37665i −0.705694 0.708517i
8282 −6.65031 −0.734404
8383 0.365349 + 6.27280i 0.0401022 + 0.688529i 0.957122 + 0.289686i 0.0935510π0.0935510\pi
−0.917019 + 0.398843i 0.869412π0.869412\pi
8484 0.454891 0.0295872i 0.0496327 0.00322823i
8585 0.162065 0.0189427i 0.0175784 0.00205462i
8686 −17.7514 4.20715i −1.91418 0.453669i
8787 −1.77255 0.750407i −0.190038 0.0804521i
8888 −6.12920 + 8.23295i −0.653375 + 0.877635i
8989 −1.79520 10.1811i −0.190291 1.07919i −0.918967 0.394334i 0.870975π-0.870975\pi
0.728676 0.684858i 0.240136π-0.240136\pi
9090 −0.305800 0.195245i −0.0322342 0.0205807i
9191 0.301002 1.70707i 0.0315536 0.178950i
9292 −1.58602 1.68109i −0.165354 0.175265i
9393 10.2092 1.87154i 1.05864 0.194070i
9494 6.98533 3.50817i 0.720482 0.361840i
9595 −0.372317 0.244876i −0.0381989 0.0251238i
9696 −1.90777 + 2.30512i −0.194711 + 0.235265i
9797 −13.3681 + 3.16829i −1.35732 + 0.321691i −0.843926 0.536460i 0.819761π-0.819761\pi
−0.513397 + 0.858151i 0.671613π0.671613\pi
9898 8.95073 3.25780i 0.904160 0.329087i
9999 11.2000 4.24913i 1.12564 0.427054i
100100 1.44528 + 0.526040i 0.144528 + 0.0526040i
101101 8.47927 + 0.991085i 0.843719 + 0.0986166i 0.526961 0.849890i 0.323331π-0.323331\pi
0.316758 + 0.948506i 0.397406π0.397406\pi
102102 −2.93317 + 4.52615i −0.290427 + 0.448155i
103103 −5.64758 + 5.98608i −0.556472 + 0.589826i −0.943141 0.332393i 0.892144π-0.892144\pi
0.386669 + 0.922219i 0.373626π0.373626\pi
104104 3.11381 + 4.18257i 0.305334 + 0.410135i
105105 0.113097 + 0.0330261i 0.0110372 + 0.00322302i
106106 14.0132 + 7.03769i 1.36108 + 0.683561i
107107 2.93755 + 5.08798i 0.283984 + 0.491874i 0.972362 0.233478i 0.0750106π-0.0750106\pi
−0.688379 + 0.725352i 0.741677π0.741677\pi
108108 1.52353 0.490058i 0.146601 0.0471558i
109109 −5.21293 + 9.02906i −0.499308 + 0.864827i −1.00000 0.000798944i 0.999746π-0.999746\pi
0.500692 + 0.865626i 0.333079π0.333079\pi
110110 0.403459 0.265359i 0.0384683 0.0253010i
111111 0.193435 1.75814i 0.0183601 0.166875i
112112 1.53019 3.54738i 0.144589 0.335196i
113113 0.795419 + 2.65689i 0.0748268 + 0.249939i 0.987217 0.159383i 0.0509505π-0.0509505\pi
−0.912390 + 0.409322i 0.865765π0.865765\pi
114114 14.0823 4.32011i 1.31893 0.404615i
115115 −0.236599 0.548499i −0.0220630 0.0511478i
116116 0.262204 0.220015i 0.0243450 0.0204279i
117117 −0.436112 6.06998i −0.0403186 0.561170i
118118 −12.7489 10.6976i −1.17363 0.984793i
119119 0.502330 1.67790i 0.0460486 0.153813i
120120 −0.305734 + 0.179288i −0.0279096 + 0.0163667i
121121 −0.287455 + 4.93541i −0.0261323 + 0.448674i
122122 0.939118 16.1240i 0.0850238 1.45980i
123123 6.54040 3.83540i 0.589728 0.345826i
124124 −0.529346 + 1.76814i −0.0475367 + 0.158784i
125125 0.609431 + 0.511373i 0.0545092 + 0.0457386i
126126 −3.22454 + 2.18396i −0.287265 + 0.194562i
127127 −8.52362 + 7.15216i −0.756349 + 0.634652i −0.937174 0.348863i 0.886568π-0.886568\pi
0.180825 + 0.983515i 0.442123π0.442123\pi
128128 5.23024 + 12.1251i 0.462292 + 1.07171i
129129 19.8843 6.10003i 1.75072 0.537078i
130130 −0.0703610 0.235022i −0.00617106 0.0206128i
131131 3.93336 9.11855i 0.343659 0.796691i −0.655480 0.755212i 0.727534π-0.727534\pi
0.999139 0.0414790i 0.0132070π-0.0132070\pi
132132 −0.232956 + 2.11734i −0.0202762 + 0.184291i
133133 −3.99652 + 2.62855i −0.346542 + 0.227925i
134134 3.49042 6.04558i 0.301526 0.522259i
135135 0.413349 + 0.0156560i 0.0355754 + 0.00134745i
136136 2.63438 + 4.56288i 0.225896 + 0.391264i
137137 −14.3691 7.21646i −1.22764 0.616543i −0.287646 0.957737i 0.592873π-0.592873\pi
−0.939993 + 0.341193i 0.889169π0.889169\pi
138138 18.9537 + 5.53476i 1.61345 + 0.471150i
139139 −12.1194 16.2791i −1.02795 1.38078i −0.922344 0.386370i 0.873729π-0.873729\pi
−0.105607 0.994408i 0.533679π-0.533679\pi
140140 −0.0143776 + 0.0152394i −0.00121513 + 0.00128796i
141141 −4.84663 + 7.47880i −0.408160 + 0.629828i
142142 8.37351 + 0.978723i 0.702690 + 0.0821326i
143143 7.61142 + 2.77033i 0.636499 + 0.231667i
144144 2.17410 13.3880i 0.181175 1.11567i
145145 0.0831321 0.0302576i 0.00690375 0.00251276i
146146 2.27691 0.539638i 0.188438 0.0446607i
147147 −6.92394 + 8.36606i −0.571077 + 0.690021i
148148 0.262780 + 0.172833i 0.0216004 + 0.0142068i
149149 −4.56885 + 2.29456i −0.374295 + 0.187978i −0.625995 0.779827i 0.715307π-0.715307\pi
0.251700 + 0.967805i 0.419010π0.419010\pi
150150 −12.9247 + 2.36934i −1.05530 + 0.193456i
151151 12.1904 + 12.9211i 0.992044 + 1.05150i 0.998672 + 0.0515269i 0.0164088π0.0164088\pi
−0.00662782 + 0.999978i 0.502110π0.502110\pi
152152 2.49871 14.1709i 0.202672 1.14941i
153153 0.274350 6.14297i 0.0221799 0.496629i
154154 −0.900118 5.10482i −0.0725336 0.411358i
155155 −0.284868 + 0.382644i −0.0228811 + 0.0307347i
156156 0.996539 + 0.421882i 0.0797870 + 0.0337776i
157157 −7.02249 1.66436i −0.560456 0.132830i −0.0593825 0.998235i 0.518913π-0.518913\pi
−0.501073 + 0.865405i 0.667061π0.667061\pi
158158 −20.6014 + 2.40796i −1.63896 + 0.191567i
159159 −17.8404 + 1.16038i −1.41484 + 0.0920243i
160160 −0.00799621 0.137290i −0.000632156 0.0108537i
161161 −6.41210 −0.505345
162162 −9.11005 + 10.1958i −0.715753 + 0.801060i
163163 4.94597 0.387398 0.193699 0.981061i 0.437951π-0.437951\pi
0.193699 + 0.981061i 0.437951π0.437951\pi
164164 0.0783941 + 1.34597i 0.00612155 + 0.105103i
165165 −0.243751 + 0.493658i −0.0189760 + 0.0384312i
166166 9.48130 1.10820i 0.735891 0.0860134i
167167 −17.4390 4.13312i −1.34947 0.319831i −0.508571 0.861020i 0.669826π-0.669826\pi
−0.840901 + 0.541190i 0.817974π0.817974\pi
168168 0.467257 + 3.77567i 0.0360497 + 0.291300i
169169 −5.30576 + 7.12688i −0.408136 + 0.548221i
170170 −0.0430451 0.244121i −0.00330141 0.0187232i
171171 −11.3580 + 12.3703i −0.868571 + 0.945982i
172172 −0.642242 + 3.64234i −0.0489705 + 0.277726i
173173 −1.18242 1.25329i −0.0898978 0.0952861i 0.680863 0.732411i 0.261605π-0.261605\pi
−0.770761 + 0.637125i 0.780124π0.780124\pi
174174 −0.981519 + 2.75461i −0.0744088 + 0.208827i
175175 3.81324 1.91508i 0.288254 0.144766i
176176 15.0828 + 9.92014i 1.13691 + 0.747759i
177177 18.7077 + 3.16818i 1.40616 + 0.238135i
178178 −15.2824 + 3.62201i −1.14547 + 0.271481i
179179 11.6071 4.22465i 0.867558 0.315765i 0.130380 0.991464i 0.458380π-0.458380\pi
0.737178 + 0.675699i 0.236158π0.236158\pi
180180 −0.0359115 + 0.0641932i −0.00267668 + 0.00478468i
181181 −0.0341083 0.0124144i −0.00253525 0.000922757i 0.340752 0.940153i 0.389318π-0.389318\pi
−0.343287 + 0.939230i 0.611541π0.611541\pi
182182 −2.61560 0.305720i −0.193881 0.0226614i
183183 8.37553 + 16.3991i 0.619137 + 1.21226i
184184 13.2367 14.0301i 0.975824 1.03431i
185185 0.0485446 + 0.0652067i 0.00356907 + 0.00479409i
186186 −3.74027 15.3183i −0.274250 1.12319i
187187 7.31382 + 3.67314i 0.534840 + 0.268607i
188188 −0.792370 1.37243i −0.0577895 0.100094i
189189 1.91170 4.00753i 0.139056 0.291505i
190190 −0.338501 + 0.586301i −0.0245574 + 0.0425347i
191191 −22.1875 + 14.5930i −1.60543 + 1.05591i −0.650325 + 0.759656i 0.725367π0.725367\pi
−0.955109 + 0.296255i 0.904262π0.904262\pi
192192 −8.96109 6.57742i −0.646711 0.474684i
193193 −0.0179151 + 0.0415320i −0.00128956 + 0.00298954i −0.918860 0.394584i 0.870889π-0.870889\pi
0.917570 + 0.397574i 0.130148π0.130148\pi
194194 5.98602 + 19.9947i 0.429771 + 1.43553i
195195 0.204741 + 0.190559i 0.0146618 + 0.0136462i
196196 −0.764866 1.77316i −0.0546333 0.126654i
197197 9.33211 7.83057i 0.664885 0.557905i −0.246661 0.969102i 0.579334π-0.579334\pi
0.911547 + 0.411197i 0.134889π0.134889\pi
198198 −7.43374 16.6109i −0.528293 1.18049i
199199 9.63166 + 8.08192i 0.682770 + 0.572912i 0.916814 0.399314i 0.130752π-0.130752\pi
−0.234044 + 0.972226i 0.575196π0.575196\pi
200200 −3.68148 + 12.2970i −0.260320 + 0.869528i
201201 0.0539068 + 7.95867i 0.00380229 + 0.561361i
202202 0.754109 12.9475i 0.0530589 0.910986i
203203 0.0552159 0.948020i 0.00387539 0.0665379i
204204 0.950635 + 0.540297i 0.0665577 + 0.0378284i
205205 −0.0999435 + 0.333834i −0.00698036 + 0.0233160i
206206 9.57760 + 8.03656i 0.667303 + 0.559934i
207207 −21.8324 + 5.48778i −1.51746 + 0.381427i
208208 7.02563 5.89520i 0.487140 0.408759i
209209 −8.85329 20.5242i −0.612395 1.41969i
210210 0.0400984 0.174445i 0.00276705 0.0120379i
211211 −3.93645 13.1487i −0.270997 0.905192i −0.979833 0.199819i 0.935965π-0.935965\pi
0.708836 0.705373i 0.249221π-0.249221\pi
212212 1.25919 2.91913i 0.0864815 0.200487i
213213 −8.79957 + 3.86666i −0.602936 + 0.264939i
214214 7.45715 4.90464i 0.509760 0.335275i
215215 −0.477966 + 0.827862i −0.0325970 + 0.0564597i
216216 4.82235 + 12.4558i 0.328119 + 0.847511i
217217 2.56032 + 4.43460i 0.173806 + 0.301040i
218218 14.1543 + 7.10856i 0.958650 + 0.481452i
219219 −1.92806 + 1.84387i −0.130286 + 0.124597i
220220 −0.0584627 0.0785291i −0.00394156 0.00529443i
221221 2.85332 3.02434i 0.191935 0.203439i
222222 −2.68355 0.138068i −0.180108 0.00926651i
223223 2.91741 + 0.340996i 0.195364 + 0.0228348i 0.213212 0.977006i 0.431607π-0.431607\pi
−0.0178480 + 0.999841i 0.505681π0.505681\pi
224224 −1.38717 0.504888i −0.0926840 0.0337342i
225225 11.3446 9.78417i 0.756307 0.652278i
226226 3.95927 1.44106i 0.263367 0.0958578i
227227 3.85911 0.914626i 0.256138 0.0607059i −0.100541 0.994933i 0.532057π-0.532057\pi
0.356679 + 0.934227i 0.383909π0.383909\pi
228228 −1.04036 2.79923i −0.0688996 0.185383i
229229 8.53681 + 5.61475i 0.564128 + 0.371033i 0.799310 0.600918i 0.205198π-0.205198\pi
−0.235182 + 0.971951i 0.575569π0.575569\pi
230230 −0.810975 + 0.407287i −0.0534741 + 0.0268557i
231231 3.82932 + 4.50133i 0.251950 + 0.296166i
232232 1.96035 + 2.07785i 0.128703 + 0.136417i
233233 0.443423 2.51478i 0.0290496 0.164748i −0.966832 0.255414i 0.917788π-0.917788\pi
0.995881 + 0.0906654i 0.0288994π0.0288994\pi
234234 −9.16745 + 1.19761i −0.599295 + 0.0782903i
235235 −0.0711257 0.403374i −0.00463973 0.0263132i
236236 −2.01483 + 2.70639i −0.131154 + 0.176171i
237237 18.8721 14.2495i 1.22588 0.925603i
238238 −2.58914 0.613638i −0.167829 0.0397763i
239239 4.63024 0.541197i 0.299505 0.0350071i 0.0349867 0.999388i 0.488861π-0.488861\pi
0.264518 + 0.964381i 0.414787π0.414787\pi
240240 0.346074 + 0.518495i 0.0223389 + 0.0334687i
241241 −0.0882797 1.51570i −0.00568660 0.0976351i 0.994271 0.106893i 0.0340902π-0.0340902\pi
−0.999957 + 0.00925773i 0.997053π0.997053\pi
242242 7.51064 0.482802
243243 3.07929 15.2813i 0.197537 0.980296i
244244 −3.27446 −0.209626
245245 −0.0290210 0.498271i −0.00185408 0.0318334i
246246 −6.39466 9.58063i −0.407708 0.610838i
247247 −11.2788 + 1.31831i −0.717654 + 0.0838818i
248248 −14.9885 3.55235i −0.951773 0.225574i
249249 −8.68546 + 6.55798i −0.550419 + 0.415595i
250250 0.721735 0.969459i 0.0456466 0.0613140i
251251 3.80000 + 21.5509i 0.239854 + 1.36028i 0.832146 + 0.554556i 0.187112π0.187112\pi
−0.592293 + 0.805723i 0.701777π0.701777\pi
252252 0.480028 + 0.626879i 0.0302389 + 0.0394897i
253253 5.20296 29.5075i 0.327107 1.85512i
254254 11.6002 + 12.2955i 0.727860 + 0.771486i
255255 0.183124 + 0.215261i 0.0114677 + 0.0134802i
256256 6.45707 3.24286i 0.403567 0.202679i
257257 5.94694 + 3.91136i 0.370960 + 0.243984i 0.721277 0.692647i 0.243556π-0.243556\pi
−0.350317 + 0.936631i 0.613926π0.613926\pi
258258 −11.0080 29.6185i −0.685329 1.84397i
259259 0.849090 0.201238i 0.0527599 0.0125043i
260260 −0.0467373 + 0.0170110i −0.00289852 + 0.00105498i
261261 −0.623356 3.27515i −0.0385848 0.202727i
262262 −14.1770 5.16001i −0.875858 0.318786i
263263 16.6763 + 1.94919i 1.02831 + 0.120192i 0.613482 0.789709i 0.289768π-0.289768\pi
0.414826 + 0.909901i 0.363843π0.363843\pi
264264 −17.7542 0.913448i −1.09269 0.0562188i
265265 0.563876 0.597674i 0.0346386 0.0367148i
266266 4.33960 + 5.82909i 0.266078 + 0.357405i
267267 12.9410 12.3759i 0.791974 0.757393i
268268 −1.26473 0.635169i −0.0772554 0.0387991i
269269 −10.3000 17.8402i −0.628003 1.08773i −0.987952 0.154762i 0.950539π-0.950539\pi
0.359948 0.932972i 0.382794π-0.382794\pi
270270 −0.0127683 0.628284i −0.000777054 0.0382361i
271271 −1.75375 + 3.03758i −0.106533 + 0.184520i −0.914363 0.404895i 0.867308π-0.867308\pi
0.807831 + 0.589414i 0.200641π0.200641\pi
272272 7.74243 5.09227i 0.469454 0.308764i
273273 2.74868 1.20781i 0.166358 0.0731001i
274274 −9.67548 + 22.4303i −0.584517 + 1.35506i
275275 5.71872 + 19.1019i 0.344852 + 1.15189i
276276 0.896767 3.90133i 0.0539791 0.234832i
277277 −6.43374 14.9151i −0.386566 0.896160i −0.994747 0.102362i 0.967360π-0.967360\pi
0.608181 0.793798i 0.291899π-0.291899\pi
278278 −23.6190 + 19.8187i −1.41657 + 1.18865i
279279 12.5129 + 12.9080i 0.749128 + 0.772784i
280280 −0.133947 0.112395i −0.00800489 0.00671690i
281281 0.116738 0.389931i 0.00696398 0.0232613i −0.954437 0.298413i 0.903543π-0.903543\pi
0.961401 + 0.275151i 0.0887280π0.0887280\pi
282282 11.7708 + 6.68996i 0.700939 + 0.398381i
283283 −1.08676 + 18.6589i −0.0646011 + 1.10916i 0.797797 + 0.602927i 0.205999π0.205999\pi
−0.862398 + 0.506231i 0.831038π0.831038\pi
284284 0.0993791 1.70627i 0.00589707 0.101249i
285285 −0.00522788 0.771832i −0.000309673 0.0457194i
286286 3.52924 11.7885i 0.208688 0.697068i
287287 2.86546 + 2.40441i 0.169143 + 0.141928i
288288 −5.15525 0.531880i −0.303776 0.0313413i
289289 −9.80441 + 8.22687i −0.576730 + 0.483934i
290290 −0.0532333 0.123409i −0.00312597 0.00724681i
291291 −17.4185 16.2119i −1.02109 0.950360i
292292 −0.136059 0.454469i −0.00796225 0.0265958i
293293 5.10071 11.8248i 0.297987 0.690810i −0.701781 0.712393i 0.747611π-0.747611\pi
0.999767 + 0.0215828i 0.00687056π0.00687056\pi
294294 13.2999 + 9.76211i 0.775667 + 0.569338i
295295 −0.728596 + 0.479205i −0.0424205 + 0.0279004i
296296 −1.31248 + 2.27329i −0.0762865 + 0.132132i
297297 16.8908 + 12.0492i 0.980104 + 0.699164i
298298 3.88361 + 6.72661i 0.224972 + 0.389662i
299299 −13.6028 6.83158i −0.786669 0.395080i
300300 0.631894 + 2.58793i 0.0364824 + 0.149414i
301301 6.12755 + 8.23072i 0.353186 + 0.474411i
302302 18.5198 19.6299i 1.06570 1.12957i
303303 6.72552 + 13.1685i 0.386371 + 0.756508i
304304 −25.1378 2.93819i −1.44175 0.168517i
305305 −0.795286 0.289460i −0.0455379 0.0165745i
306306 −9.34090 + 0.126544i −0.533984 + 0.00723404i
307307 8.20971 2.98809i 0.468553 0.170539i −0.0969439 0.995290i 0.530907π-0.530907\pi
0.565497 + 0.824751i 0.308685π0.308685\pi
308308 −1.02257 + 0.242353i −0.0582662 + 0.0138093i
309309 −14.0542 2.38009i −0.799514 0.135399i
310310 0.605497 + 0.398241i 0.0343899 + 0.0226186i
311311 −16.6117 + 8.34269i −0.941961 + 0.473071i −0.852388 0.522909i 0.824847π-0.824847\pi
−0.0895731 + 0.995980i 0.528550π0.528550\pi
312312 −3.03142 + 8.50763i −0.171621 + 0.481650i
313313 14.4377 + 15.3030i 0.816065 + 0.864979i 0.992862 0.119269i 0.0380550π-0.0380550\pi
−0.176797 + 0.984247i 0.556574π0.556574\pi
314314 −1.90391 + 10.7976i −0.107444 + 0.609344i
315315 0.0611713 + 0.194688i 0.00344661 + 0.0109694i
316316 0.730202 + 4.14118i 0.0410771 + 0.232960i
317317 9.67477 12.9955i 0.543389 0.729898i −0.442598 0.896720i 0.645943π-0.645943\pi
0.985987 + 0.166822i 0.0533505π0.0533505\pi
318318 3.33580 + 26.9549i 0.187062 + 1.51156i
319319 4.31783 + 1.02334i 0.241752 + 0.0572963i
320320 0.507439 0.0593111i 0.0283667 0.00331559i
321321 −4.50527 + 9.12430i −0.251460 + 0.509269i
322322 0.566408 + 9.72485i 0.0315647 + 0.541945i
323323 −11.4740 −0.638432
324324 2.17095 + 1.72362i 0.120608 + 0.0957565i
325325 10.1299 0.561903
326326 −0.436898 7.50125i −0.0241976 0.415456i
327327 −18.0200 + 1.17207i −0.996510 + 0.0648154i
328328 −11.1763 + 1.30632i −0.617106 + 0.0721293i
329329 −4.27818 1.01395i −0.235864 0.0559007i
330330 0.770233 + 0.326076i 0.0423999 + 0.0179499i
331331 11.3784 15.2839i 0.625414 0.840077i −0.370645 0.928775i 0.620863π-0.620863\pi
0.996059 + 0.0886981i 0.0282706π0.0282706\pi
332332 −0.336058 1.90588i −0.0184436 0.104599i
333333 2.71882 1.41188i 0.148990 0.0773707i
334334 −4.72799 + 26.8138i −0.258704 + 1.46719i
335335 −0.251023 0.266068i −0.0137148 0.0145369i
336336 6.58182 1.20657i 0.359068 0.0658241i
337337 −9.76843 + 4.90589i −0.532120 + 0.267241i −0.694507 0.719486i 0.744377π-0.744377\pi
0.162386 + 0.986727i 0.448081π0.448081\pi
338338 11.2776 + 7.41738i 0.613420 + 0.403453i
339339 −3.06274 + 3.70065i −0.166345 + 0.200992i
340340 −0.0489008 + 0.0115897i −0.00265202 + 0.000628540i
341341 −22.4848 + 8.18380i −1.21762 + 0.443178i
342342 19.7646 + 16.1333i 1.06875 + 0.872390i
343343 −10.6553 3.87822i −0.575333 0.209404i
344344 −30.6587 3.58348i −1.65300 0.193208i
345345 0.562679 0.868264i 0.0302936 0.0467458i
346346 −1.79635 + 1.90401i −0.0965721 + 0.102360i
347347 −13.3267 17.9008i −0.715413 0.960966i −0.999997 0.00231546i 0.999263π-0.999263\pi
0.284584 0.958651i 0.408144π-0.408144\pi
348348 0.569083 + 0.166181i 0.0305061 + 0.00890823i
349349 −20.8909 10.4918i −1.11826 0.561613i −0.209034 0.977908i 0.567032π-0.567032\pi
−0.909229 + 0.416295i 0.863328π0.863328\pi
350350 −3.24133 5.61414i −0.173256 0.300088i
351351 8.32523 6.46491i 0.444368 0.345071i
352352 3.44900 5.97384i 0.183832 0.318407i
353353 26.6369 17.5193i 1.41774 0.932461i 0.418026 0.908435i 0.362722π-0.362722\pi
0.999711 0.0240257i 0.00764835π-0.00764835\pi
354354 3.15246 28.6528i 0.167551 1.52288i
355355 0.174971 0.405627i 0.00928648 0.0215285i
356356 0.913217 + 3.05036i 0.0484004 + 0.161669i
357357 2.90025 0.889726i 0.153497 0.0470893i
358358 −7.43258 17.2307i −0.392824 0.910669i
359359 8.66761 7.27299i 0.457459 0.383854i −0.384736 0.923027i 0.625708π-0.625708\pi
0.842195 + 0.539173i 0.181263π0.181263\pi
360360 −0.552268 0.268054i −0.0291071 0.0141277i
361361 9.45042 + 7.92984i 0.497391 + 0.417360i
362362 −0.0158153 + 0.0528267i −0.000831232 + 0.00277651i
363363 −7.38650 + 4.33157i −0.387691 + 0.227348i
364364 −0.0310426 + 0.532981i −0.00162708 + 0.0279358i
365365 0.00712939 0.122407i 0.000373169 0.00640707i
366366 24.1317 14.1513i 1.26139 0.739698i
367367 0.194561 0.649881i 0.0101560 0.0339235i −0.952761 0.303720i 0.901771π-0.901771\pi
0.962917 + 0.269797i 0.0869564π0.0869564\pi
368368 −25.9888 21.8072i −1.35476 1.13678i
369369 11.8143 + 5.73432i 0.615030 + 0.298517i
370370 0.0946069 0.0793846i 0.00491838 0.00412701i
371371 −3.49349 8.09881i −0.181373 0.420469i
372372 −3.05623 + 0.937576i −0.158458 + 0.0486110i
373373 3.19886 + 10.6849i 0.165630 + 0.553244i 0.999998 + 0.00203573i 0.000647993π0.000647993\pi
−0.834367 + 0.551209i 0.814167π0.814167\pi
374374 4.92477 11.4169i 0.254654 0.590353i
375375 −0.150696 + 1.36968i −0.00778190 + 0.0707299i
376376 11.0502 7.26782i 0.569869 0.374809i
377377 1.12717 1.95232i 0.0580524 0.100550i
378378 −6.24685 2.54536i −0.321303 0.130919i
379379 −9.99112 17.3051i −0.513209 0.888905i −0.999883 0.0153206i 0.995123π-0.995123\pi
0.486673 0.873584i 0.338210π-0.338210\pi
380380 0.122653 + 0.0615988i 0.00629198 + 0.00315995i
381381 −18.4995 5.40214i −0.947761 0.276760i
382382 24.0922 + 32.3614i 1.23266 + 1.65576i
383383 16.1583 17.1268i 0.825651 0.875139i −0.168212 0.985751i 0.553799π-0.553799\pi
0.993864 + 0.110611i 0.0352809π0.0352809\pi
384384 −12.4385 + 19.1938i −0.634751 + 0.979478i
385385 −0.269781 0.0315328i −0.0137493 0.00160706i
386386 0.0645715 + 0.0235021i 0.00328660 + 0.00119623i
387387 27.9078 + 22.7804i 1.41863 + 1.15799i
388388 3.97621 1.44722i 0.201862 0.0734716i
389389 −6.07680 + 1.44023i −0.308106 + 0.0730225i −0.381760 0.924261i 0.624682π-0.624682\pi
0.0736542 + 0.997284i 0.476534π0.476534\pi
390390 0.270923 0.327351i 0.0137187 0.0165761i
391391 −12.8503 8.45180i −0.649870 0.427426i
392392 14.4023 7.23312i 0.727427 0.365328i
393393 16.9186 3.10150i 0.853429 0.156450i
394394 −12.7005 13.4617i −0.639842 0.678192i
395395 −0.188730 + 1.07034i −0.00949604 + 0.0538547i
396396 −3.27430 + 1.70034i −0.164540 + 0.0854455i
397397 −0.194836 1.10497i −0.00977853 0.0554568i 0.979528 0.201308i 0.0645191π-0.0645191\pi
−0.989307 + 0.145851i 0.953408π0.953408\pi
398398 11.4066 15.3217i 0.571759 0.768006i
399399 −7.62965 3.22999i −0.381960 0.161702i
400400 21.9684 + 5.20662i 1.09842 + 0.260331i
401401 −4.20990 + 0.492067i −0.210232 + 0.0245726i −0.220557 0.975374i 0.570788π-0.570788\pi
0.0103248 + 0.999947i 0.496713π0.496713\pi
402402 12.0657 0.784780i 0.601781 0.0391412i
403403 0.706810 + 12.1355i 0.0352087 + 0.604511i
404404 −2.62938 −0.130816
405405 0.374904 + 0.610536i 0.0186291 + 0.0303378i
406406 −1.44268 −0.0715991
407407 0.237089 + 4.07067i 0.0117521 + 0.201775i
408408 −4.04030 + 8.18263i −0.200025 + 0.405100i
409409 1.89802 0.221846i 0.0938509 0.0109696i −0.0690378 0.997614i 0.521993π-0.521993\pi
0.162889 + 0.986644i 0.447919π0.447919\pi
410410 0.515135 + 0.122089i 0.0254407 + 0.00602956i
411411 −3.42053 27.6396i −0.168722 1.36336i
412412 1.51364 2.03317i 0.0745717 0.100167i
413413 1.62550 + 9.21867i 0.0799856 + 0.453621i
414414 10.2515 + 32.6272i 0.503835 + 1.60354i
415415 0.0868586 0.492600i 0.00426372 0.0241808i
416416 −2.40485 2.54899i −0.117908 0.124975i
417417 11.7987 33.1128i 0.577785 1.62154i
418418 −30.3458 + 15.2402i −1.48426 + 0.745424i
419419 −2.07357 1.36381i −0.101300 0.0666263i 0.497848 0.867264i 0.334124π-0.334124\pi
−0.599148 + 0.800638i 0.704494π0.704494\pi
420420 −0.0357791 0.00605925i −0.00174584 0.000295661i
421421 16.9944 4.02774i 0.828255 0.196300i 0.205440 0.978670i 0.434137π-0.434137\pi
0.622814 + 0.782370i 0.285989π0.285989\pi
422422 −19.5941 + 7.13166i −0.953825 + 0.347164i
423423 −15.4345 + 0.209096i −0.750450 + 0.0101666i
424424 24.9325 + 9.07467i 1.21083 + 0.440705i
425425 10.1663 + 1.18827i 0.493137 + 0.0576395i
426426 6.64164 + 13.0042i 0.321788 + 0.630056i
427427 −6.23425 + 6.60792i −0.301697 + 0.319780i
428428 −1.08057 1.45146i −0.0522313 0.0701588i
429429 3.32780 + 13.6290i 0.160668 + 0.658016i
430430 1.29779 + 0.651774i 0.0625849 + 0.0314313i
431431 11.6850 + 20.2390i 0.562845 + 0.974877i 0.997247 + 0.0741572i 0.0236267π0.0236267\pi
−0.434401 + 0.900719i 0.643040π0.643040\pi
432432 21.3777 9.74127i 1.02853 0.468677i
433433 15.2874 26.4785i 0.734664 1.27247i −0.220207 0.975453i 0.570673π-0.570673\pi
0.954871 0.297021i 0.0959933π-0.0959933\pi
434434 6.49952 4.27480i 0.311987 0.205197i
435435 0.123526 + 0.0906680i 0.00592263 + 0.00434720i
436436 1.27187 2.94852i 0.0609114 0.141209i
437437 12.0474 + 40.2413i 0.576308 + 1.92500i
438438 2.96680 + 2.76129i 0.141759 + 0.131939i
439439 4.91463 + 11.3934i 0.234563 + 0.543777i 0.994320 0.106429i 0.0339417π-0.0339417\pi
−0.759758 + 0.650206i 0.774682π0.774682\pi
440440 0.625913 0.525204i 0.0298392 0.0250381i
441441 −18.7101 1.93037i −0.890959 0.0919225i
442442 −4.83889 4.06031i −0.230162 0.193129i
443443 −0.994767 + 3.32275i −0.0472628 + 0.157869i −0.978363 0.206894i 0.933665π-0.933665\pi
0.931101 + 0.364762i 0.118850π0.118850\pi
444444 0.00368983 + 0.544758i 0.000175112 + 0.0258531i
445445 −0.0478519 + 0.821586i −0.00226840 + 0.0389469i
446446 0.259462 4.45478i 0.0122859 0.210940i
447447 −7.69882 4.37566i −0.364142 0.206962i
448448 1.57284 5.25365i 0.0743097 0.248212i
449449 2.37761 + 1.99505i 0.112206 + 0.0941523i 0.697165 0.716911i 0.254445π-0.254445\pi
−0.584958 + 0.811063i 0.698889π0.698889\pi
450450 −15.8412 16.3414i −0.746760 0.770341i
451451 −13.3898 + 11.2354i −0.630501 + 0.529053i
452452 −0.338331 0.784341i −0.0159138 0.0368923i
453453 −6.89270 + 29.9863i −0.323847 + 1.40888i
454454 −1.72805 5.77209i −0.0811014 0.270897i
455455 −0.0546548 + 0.126704i −0.00256226 + 0.00593998i
456456 22.8176 10.0264i 1.06853 0.469529i
457457 −29.6424 + 19.4961i −1.38662 + 0.911991i −0.999948 0.0102280i 0.996744π-0.996744\pi
−0.386668 + 0.922219i 0.626374π0.626374\pi
458458 7.76145 13.4432i 0.362669 0.628161i
459459 9.11353 5.51158i 0.425383 0.257258i
460460 0.0919917 + 0.159334i 0.00428913 + 0.00742900i
461461 22.7764 + 11.4387i 1.06080 + 0.532754i 0.891598 0.452827i 0.149584π-0.149584\pi
0.169203 + 0.985581i 0.445881π0.445881\pi
462462 6.48863 6.20531i 0.301878 0.288697i
463463 −5.56359 7.47319i −0.258562 0.347309i 0.653819 0.756651i 0.273166π-0.273166\pi
−0.912381 + 0.409342i 0.865758π0.865758\pi
464464 3.44795 3.65462i 0.160067 0.169661i
465465 −0.825164 0.0424545i −0.0382661 0.00196878i
466466 −3.85318 0.450372i −0.178495 0.0208631i
467467 11.6612 + 4.24434i 0.539617 + 0.196404i 0.597427 0.801923i 0.296190π-0.296190\pi
−0.0578105 + 0.998328i 0.518412π0.518412\pi
468468 0.350454 + 1.84131i 0.0161997 + 0.0851144i
469469 −3.68970 + 1.34294i −0.170375 + 0.0620113i
470470 −0.605490 + 0.143504i −0.0279292 + 0.00661934i
471471 −4.35480 11.7172i −0.200659 0.539899i
472472 −23.5266 15.4737i −1.08290 0.712235i
473473 −42.8485 + 21.5193i −1.97018 + 0.989460i
474474 −23.2784 27.3635i −1.06921 1.25685i
475475 −19.1833 20.3331i −0.880189 0.932945i
476476 −0.0936749 + 0.531257i −0.00429358 + 0.0243501i
477477 −18.8262 24.5856i −0.861994 1.12570i
478478 −1.22981 6.97459i −0.0562501 0.319010i
479479 −20.7600 + 27.8855i −0.948548 + 1.27412i 0.0131220 + 0.999914i 0.495823π0.495823\pi
−0.961670 + 0.274208i 0.911584π0.911584\pi
480480 0.190094 0.143531i 0.00867659 0.00655128i
481481 2.01568 + 0.477725i 0.0919072 + 0.0217824i
482482 −2.29098 + 0.267777i −0.104351 + 0.0121969i
483483 −6.16561 9.23746i −0.280545 0.420319i
484484 −0.0885356 1.52010i −0.00402434 0.0690953i
485485 1.09366 0.0496605
486486 −23.4482 3.32031i −1.06363 0.150612i
487487 4.53564 0.205529 0.102765 0.994706i 0.467231π-0.467231\pi
0.102765 + 0.994706i 0.467231π0.467231\pi
488488 −1.58899 27.2819i −0.0719302 1.23499i
489489 4.75583 + 7.12530i 0.215066 + 0.322217i
490490 −0.753134 + 0.0880287i −0.0340231 + 0.00397673i
491491 29.1460 + 6.90774i 1.31534 + 0.311742i 0.827636 0.561266i 0.189685π-0.189685\pi
0.487707 + 0.873008i 0.337834π0.337834\pi
492492 −1.86367 + 1.40717i −0.0840206 + 0.0634400i
493493 1.36024 1.82712i 0.0612622 0.0822895i
494494 2.99570 + 16.9895i 0.134783 + 0.764392i
495495 −0.945558 + 0.123525i −0.0424997 + 0.00555205i
496496 −4.70463 + 26.6813i −0.211244 + 1.19802i
497497 −3.25409 3.44913i −0.145966 0.154715i
498498 10.7133 + 12.5934i 0.480075 + 0.564324i
499499 6.09867 3.06287i 0.273014 0.137113i −0.307025 0.951701i 0.599334π-0.599334\pi
0.580039 + 0.814589i 0.303037π0.303037\pi
500500 −0.204719 0.134646i −0.00915532 0.00602155i
501501 −10.8143 29.0974i −0.483148 1.29997i
502502 32.3492 7.66691i 1.44382 0.342191i
503503 −5.01364 + 1.82482i −0.223547 + 0.0813646i −0.451366 0.892339i 0.649063π-0.649063\pi
0.227818 + 0.973704i 0.426841π0.426841\pi
504504 −4.99005 + 4.30367i −0.222274 + 0.191701i
505505 −0.638612 0.232436i −0.0284179 0.0103433i
506506 −45.2118 5.28450i −2.00991 0.234925i
507507 −15.3690 0.790730i −0.682560 0.0351175i
508508 2.35177 2.49273i 0.104343 0.110597i
509509 26.6991 + 35.8631i 1.18342 + 1.58960i 0.699839 + 0.714301i 0.253255π0.253255\pi
0.483577 + 0.875302i 0.339337π0.339337\pi
510510 0.310297 0.296748i 0.0137402 0.0131402i
511511 −1.17617 0.590695i −0.0520307 0.0261308i
512512 7.71639 + 13.3652i 0.341019 + 0.590663i
513513 −28.7424 4.46794i −1.26901 0.197264i
514514 5.40681 9.36487i 0.238484 0.413067i
515515 0.547358 0.360003i 0.0241195 0.0158636i
516516 −5.86481 + 2.57708i −0.258184 + 0.113450i
517517 8.13746 18.8647i 0.357885 0.829671i
518518 −0.380209 1.26999i −0.0167054 0.0558000i
519519 0.668563 2.90854i 0.0293467 0.127671i
520520 −0.164411 0.381148i −0.00720991 0.0167144i
521521 7.56500 6.34779i 0.331429 0.278102i −0.461853 0.886956i 0.652815π-0.652815\pi
0.793282 + 0.608855i 0.208371π0.208371\pi
522522 −4.91216 + 1.23471i −0.214999 + 0.0540420i
523523 29.0347 + 24.3630i 1.26960 + 1.06532i 0.994590 + 0.103880i 0.0331258π0.0331258\pi
0.275010 + 0.961441i 0.411319π0.411319\pi
524524 −0.877228 + 2.93015i −0.0383219 + 0.128004i
525525 6.42557 + 3.65200i 0.280435 + 0.159386i
526526 1.48312 25.4642i 0.0646671 1.11029i
527527 −0.714181 + 12.2620i −0.0311102 + 0.534142i
528528 0.211786 + 31.2675i 0.00921679 + 1.36074i
529529 −9.55282 + 31.9087i −0.415340 + 1.38733i
530530 −0.956265 0.802402i −0.0415375 0.0348541i
531531 13.4244 + 29.9973i 0.582569 + 1.30177i
532532 1.12861 0.947016i 0.0489314 0.0410583i
533533 3.51715 + 8.15367i 0.152345 + 0.353175i
534534 −19.9129 18.5335i −0.861716 0.802025i
535535 −0.134136 0.448045i −0.00579920 0.0193707i
536536 4.67833 10.8456i 0.202073 0.468458i
537537 17.2471 + 12.6593i 0.744266 + 0.546290i
538538 −26.1472 + 17.1973i −1.12729 + 0.741429i
539539 12.5176 21.6811i 0.539171 0.933871i
540540 −0.127009 + 0.00999044i −0.00546562 + 0.000429920i
541541 −22.1922 38.4380i −0.954116 1.65258i −0.736378 0.676570i 0.763466π-0.763466\pi
−0.217737 0.976007i 0.569868π-0.569868\pi
542542 4.76183 + 2.39148i 0.204538 + 0.102723i
543543 −0.0149126 0.0610746i −0.000639959 0.00262096i
544544 −2.11449 2.84026i −0.0906582 0.121775i
545545 0.569554 0.603692i 0.0243970 0.0258593i
546546 −2.07462 4.06207i −0.0887855 0.173841i
547547 −3.16949 0.370461i −0.135518 0.0158398i 0.0480635 0.998844i 0.484695π-0.484695\pi
−0.183581 + 0.983005i 0.558769π0.558769\pi
548548 4.65378 + 1.69384i 0.198799 + 0.0723571i
549549 −15.5715 + 27.8347i −0.664576 + 1.18796i
550550 28.4655 10.3606i 1.21377 0.441777i
551551 −6.05335 + 1.43467i −0.257882 + 0.0611191i
552552 32.9400 + 5.57844i 1.40202 + 0.237434i
553553 9.74723 + 6.41085i 0.414494 + 0.272617i
554554 −22.0525 + 11.0752i −0.936920 + 0.470539i
555555 −0.0472602 + 0.132635i −0.00200608 + 0.00563003i
556556 4.28958 + 4.54669i 0.181919 + 0.192823i
557557 −4.44633 + 25.2164i −0.188397 + 1.06845i 0.733116 + 0.680104i 0.238065π0.238065\pi
−0.921513 + 0.388348i 0.873046π0.873046\pi
558558 18.4715 20.1178i 0.781962 0.851654i
559559 4.22995 + 23.9892i 0.178908 + 1.01464i
560560 −0.183653 + 0.246689i −0.00776077 + 0.0104245i
561561 1.74103 + 14.0684i 0.0735064 + 0.593969i
562562 −0.601696 0.142605i −0.0253810 0.00601541i
563563 −15.1734 + 1.77351i −0.639481 + 0.0747446i −0.429653 0.902994i 0.641364π-0.641364\pi
−0.209827 + 0.977738i 0.567290π0.567290\pi
564564 1.21524 2.46118i 0.0511710 0.103634i
565565 −0.0128372 0.220406i −0.000540064 0.00927253i
566566 28.3949 1.19352
567567 7.61158 1.09942i 0.319656 0.0461712i
568568 14.2645 0.598523
569569 0.935369 + 16.0597i 0.0392127 + 0.673256i 0.959447 + 0.281889i 0.0909609π0.0909609\pi
−0.920234 + 0.391368i 0.872002π0.872002\pi
570570 −1.17013 + 0.0761080i −0.0490113 + 0.00318781i
571571 18.1635 2.12301i 0.760119 0.0888451i 0.272802 0.962070i 0.412050π-0.412050\pi
0.487317 + 0.873225i 0.337976π0.337976\pi
572572 −2.42751 0.575329i −0.101499 0.0240557i
573573 −42.3576 17.9320i −1.76952 0.749120i
574574 3.39350 4.55826i 0.141642 0.190258i
575575 −6.50690 36.9025i −0.271357 1.53894i
576576 0.859013 19.2342i 0.0357922 0.801423i
577577 1.90472 10.8022i 0.0792945 0.449702i −0.919148 0.393912i 0.871121π-0.871121\pi
0.998443 0.0557894i 0.0177675π-0.0177675\pi
578578 13.3433 + 14.1430i 0.555007 + 0.588273i
579579 −0.0770585 + 0.0141263i −0.00320244 + 0.000587069i
580580 −0.0243495 + 0.0122288i −0.00101106 + 0.000507772i
581581 −4.48593 2.95044i −0.186108 0.122405i
582582 −23.0490 + 27.8497i −0.955412 + 1.15441i
583583 40.1041 9.50485i 1.66094 0.393651i
584584 3.72049 1.35415i 0.153955 0.0560350i
585585 −0.0776539 + 0.478188i −0.00321059 + 0.0197707i
586586 −18.3845 6.69140i −0.759456 0.276419i
587587 15.5791 + 1.82094i 0.643019 + 0.0751581i 0.431352 0.902184i 0.358037π-0.358037\pi
0.211667 + 0.977342i 0.432111π0.432111\pi
588588 1.81900 2.80688i 0.0750142 0.115754i
589589 23.0203 24.4001i 0.948535 1.00539i
590590 0.791142 + 1.06269i 0.0325708 + 0.0437502i
591591 20.2543 + 5.91455i 0.833150 + 0.243292i
592592 4.12583 + 2.07207i 0.169571 + 0.0851616i
593593 −20.4416 35.4058i −0.839434 1.45394i −0.890369 0.455240i 0.849553π-0.849553\pi
0.0509346 0.998702i 0.483780π-0.483780\pi
594594 16.7822 26.6816i 0.688583 1.09476i
595595 −0.0697142 + 0.120749i −0.00285800 + 0.00495021i
596596 1.31564 0.865308i 0.0538906 0.0354444i
597597 −2.38165 + 21.6469i −0.0974744 + 0.885947i
598598 −9.15945 + 21.2340i −0.374558 + 0.868322i
599599 −7.75749 25.9118i −0.316962 1.05873i −0.956928 0.290325i 0.906237π-0.906237\pi
0.639966 0.768403i 0.278948π-0.278948\pi
600600 −21.2553 + 6.52062i −0.867745 + 0.266203i
601601 6.61392 + 15.3328i 0.269788 + 0.625438i 0.998217 0.0596825i 0.0190088π-0.0190088\pi
−0.728430 + 0.685120i 0.759750π0.759750\pi
602602 11.9418 10.0203i 0.486710 0.408398i
603603 −11.4136 + 7.73037i −0.464799 + 0.314805i
604604 −4.19125 3.51688i −0.170540 0.143100i
605605 0.112873 0.377021i 0.00458893 0.0153281i
606606 19.3777 11.3634i 0.787166 0.461607i
607607 2.65408 45.5688i 0.107726 1.84958i −0.322143 0.946691i 0.604403π-0.604403\pi
0.429869 0.902891i 0.358560π-0.358560\pi
608608 −0.562296 + 9.65424i −0.0228041 + 0.391531i
609609 1.41884 0.832030i 0.0574942 0.0337155i
610610 −0.368756 + 1.23173i −0.0149305 + 0.0498713i
611611 −7.99555 6.70906i −0.323465 0.271420i
612612 0.135722 + 1.88904i 0.00548625 + 0.0763598i
613613 30.0949 25.2526i 1.21552 1.01994i 0.216476 0.976288i 0.430544π-0.430544\pi
0.999047 0.0436562i 0.0139006π-0.0139006\pi
614614 −5.25705 12.1872i −0.212157 0.491836i
615615 −0.577033 + 0.177020i −0.0232682 + 0.00713812i
616616 −2.51544 8.40216i −0.101350 0.338533i
617617 −1.00511 + 2.33010i −0.0404640 + 0.0938061i −0.937249 0.348660i 0.886637π-0.886637\pi
0.896785 + 0.442466i 0.145896π0.145896\pi
618618 −2.36828 + 21.5254i −0.0952662 + 0.865877i
619619 10.2465 6.73923i 0.411841 0.270872i −0.326637 0.945150i 0.605915π-0.605915\pi
0.738478 + 0.674278i 0.235545π0.235545\pi
620620 0.0734635 0.127242i 0.00295036 0.00511018i
621621 −28.8990 26.1756i −1.15968 1.05039i
622622 14.1202 + 24.4570i 0.566170 + 0.980635i
623623 7.89436 + 3.96470i 0.316281 + 0.158842i
624624 15.2483 + 4.45274i 0.610422 + 0.178252i
625625 14.8722 + 19.9769i 0.594889 + 0.799075i
626626 21.9338 23.2485i 0.876653 0.929198i
627627 21.0548 32.4895i 0.840849 1.29751i
628628 2.20780 + 0.258055i 0.0881008 + 0.0102975i
629629 1.96689 + 0.715890i 0.0784251 + 0.0285444i
630630 0.289868 0.109972i 0.0115486 0.00438141i
631631 −38.1004 + 13.8674i −1.51675 + 0.552053i −0.960335 0.278848i 0.910047π-0.910047\pi
−0.556419 + 0.830902i 0.687825π0.687825\pi
632632 −34.1489 + 8.09344i −1.35837 + 0.321940i
633633 15.1572 18.3142i 0.602445 0.727923i
634634 −20.5641 13.5252i −0.816703 0.537154i
635635 0.791544 0.397528i 0.0314115 0.0157754i
636636 5.41616 0.992886i 0.214765 0.0393705i
637637 −8.72802 9.25117i −0.345817 0.366545i
638638 1.17063 6.63899i 0.0463458 0.262840i
639639 −14.0317 8.95888i −0.555086 0.354408i
640640 −0.182539 1.03523i −0.00721548 0.0409210i
641641 −18.0299 + 24.2184i −0.712140 + 0.956570i −0.999999 0.00110272i 0.999649π-0.999649\pi
0.287859 + 0.957673i 0.407056π0.407056\pi
642642 14.2362 + 6.02688i 0.561860 + 0.237862i
643643 −0.432548 0.102516i −0.0170580 0.00404283i 0.222078 0.975029i 0.428716π-0.428716\pi
−0.239136 + 0.970986i 0.576864π0.576864\pi
644644 1.96156 0.229274i 0.0772963 0.00903464i
645645 −1.65223 + 0.107465i −0.0650566 + 0.00423143i
646646 1.01355 + 17.4020i 0.0398775 + 0.684671i
647647 38.0107 1.49436 0.747178 0.664624i 0.231408π-0.231408\pi
0.747178 + 0.664624i 0.231408π0.231408\pi
648648 −13.3072 + 18.9242i −0.522757 + 0.743413i
649649 −43.7418 −1.71702
650650 −0.894812 15.3633i −0.0350974 0.602600i
651651 −3.92671 + 7.95258i −0.153900 + 0.311686i
652652 −1.51305 + 0.176850i −0.0592555 + 0.00692598i
653653 −13.1542 3.11759i −0.514762 0.122001i −0.0349790 0.999388i 0.511136π-0.511136\pi
−0.479783 + 0.877387i 0.659285π0.659285\pi
654654 3.36939 + 27.2264i 0.131753 + 1.06463i
655655 −0.472081 + 0.634115i −0.0184457 + 0.0247769i
656656 3.43670 + 19.4905i 0.134181 + 0.760977i
657657 −4.51026 1.00462i −0.175962 0.0391941i
658658 −1.15988 + 6.57802i −0.0452169 + 0.256438i
659659 −17.8731 18.9443i −0.696235 0.737966i 0.278719 0.960373i 0.410090π-0.410090\pi
−0.974954 + 0.222407i 0.928609π0.928609\pi
660660 0.0569159 0.159733i 0.00221545 0.00621761i
661661 2.14977 1.07965i 0.0836162 0.0419936i −0.406500 0.913651i 0.633251π-0.633251\pi
0.490116 + 0.871657i 0.336954π0.336954\pi
662662 −24.1852 15.9069i −0.939984 0.618237i
663663 7.10059 + 1.20249i 0.275764 + 0.0467010i
664664 15.7162 3.72481i 0.609908 0.144551i
665665 0.357828 0.130239i 0.0138760 0.00505044i
666666 −2.38148 3.99875i −0.0922805 0.154949i
667667 −7.83624 2.85216i −0.303420 0.110436i
668668 5.48265 + 0.640829i 0.212130 + 0.0247944i
669669 2.31401 + 4.53079i 0.0894647 + 0.175170i
670670 −0.381356 + 0.404214i −0.0147331 + 0.0156161i
671671 −25.3499 34.0509i −0.978623 1.31452i
672672 −0.606486 2.48387i −0.0233957 0.0958174i
673673 −11.7838 5.91802i −0.454230 0.228123i 0.206948 0.978352i 0.433647π-0.433647\pi
−0.661178 + 0.750229i 0.729943π0.729943\pi
674674 8.30335 + 14.3818i 0.319833 + 0.553967i
675675 25.0038 + 6.93532i 0.962398 + 0.266941i
676676 1.36828 2.36994i 0.0526263 0.0911514i
677677 9.64188 6.34156i 0.370568 0.243726i −0.350542 0.936547i 0.614003π-0.614003\pi
0.721110 + 0.692821i 0.243632π0.243632\pi
678678 5.88310 + 4.31818i 0.225939 + 0.165839i
679679 4.64980 10.7795i 0.178443 0.413678i
680680 −0.120292 0.401805i −0.00461300 0.0154085i
681681 5.02839 + 4.68008i 0.192688 + 0.179341i
682682 14.3981 + 33.3784i 0.551330 + 1.27813i
683683 −7.16633 + 6.01327i −0.274212 + 0.230091i −0.769514 0.638629i 0.779502π-0.779502\pi
0.495302 + 0.868721i 0.335057π0.335057\pi
684684 3.03228 4.19039i 0.115942 0.160224i
685685 0.980555 + 0.822783i 0.0374651 + 0.0314369i
686686 −4.94063 + 16.5029i −0.188634 + 0.630082i
687687 0.119870 + 17.6973i 0.00457331 + 0.675193i
688688 −3.15674 + 54.1992i −0.120350 + 2.06633i
689689 1.21746 20.9030i 0.0463816 0.796342i
690690 −1.36655 0.776683i −0.0520236 0.0295678i
691691 −4.30869 + 14.3920i −0.163910 + 0.547498i −0.999999 0.00109520i 0.999651π-0.999651\pi
0.836089 + 0.548594i 0.184837π0.184837\pi
692692 0.406534 + 0.341122i 0.0154541 + 0.0129675i
693693 −2.80263 + 9.84490i −0.106463 + 0.373977i
694694 −25.9719 + 21.7930i −0.985880 + 0.827251i
695695 0.639910 + 1.48348i 0.0242732 + 0.0562715i
696696 −1.10842 + 4.82210i −0.0420144 + 0.182781i
697697 2.57335 + 8.59557i 0.0974724 + 0.325581i
698698 −14.0669 + 32.6107i −0.532440 + 1.23433i
699699 4.04923 1.77929i 0.153156 0.0672991i
700700 −1.09805 + 0.722200i −0.0415025 + 0.0272966i
701701 −8.41328 + 14.5722i −0.317765 + 0.550385i −0.980021 0.198892i 0.936266π-0.936266\pi
0.662256 + 0.749277i 0.269599π0.269599\pi
702702 −10.5403 12.0553i −0.397819 0.454998i
703703 −2.85826 4.95065i −0.107801 0.186717i
704704 22.9002 + 11.5009i 0.863084 + 0.433457i
705705 0.512720 0.490333i 0.0193102 0.0184670i
706706 −28.9235 38.8510i −1.08855 1.46218i
707707 −5.00608 + 5.30614i −0.188273 + 0.199558i
708708 −5.83627 0.300274i −0.219340 0.0112850i
709709 −9.55304 1.11659i −0.358772 0.0419344i −0.0652022 0.997872i 0.520769π-0.520769\pi
−0.293570 + 0.955938i 0.594843π0.594843\pi
710710 −0.630647 0.229537i −0.0236677 0.00861435i
711711 38.6748 + 13.4861i 1.45042 + 0.505766i
712712 −24.9716 + 9.08893i −0.935851 + 0.340622i
713713 43.7548 10.3701i 1.63863 0.388362i
714714 −1.60558 4.32004i −0.0600875 0.161673i
715715 −0.538723 0.354324i −0.0201471 0.0132510i
716716 −3.39974 + 1.70741i −0.127054 + 0.0638091i
717717 5.23190 + 6.15005i 0.195389 + 0.229678i
718718 −11.7961 12.5032i −0.440228 0.466615i
719719 3.87901 21.9989i 0.144663 0.820422i −0.822975 0.568078i 0.807687π-0.807687\pi
0.967638 0.252344i 0.0812016π-0.0812016\pi
720720 −0.414189 + 0.997126i −0.0154359 + 0.0371607i
721721 −1.22116 6.92552i −0.0454782 0.257920i
722722 11.1919 15.0334i 0.416520 0.559484i
723723 2.09868 1.58461i 0.0780507 0.0589324i
724724 0.0108782 + 0.00257817i 0.000404283 + 9.58169e-5i
725725 5.51201 0.644261i 0.204711 0.0239273i
726726 7.22191 + 10.8200i 0.268030 + 0.401569i
727727 2.37548 + 40.7855i 0.0881018 + 1.51265i 0.695658 + 0.718373i 0.255113π0.255113\pi
−0.607556 + 0.794277i 0.707850π0.707850\pi
728728 −4.45573 −0.165140
729729 24.9756 10.2577i 0.925021 0.379916i
730730 −0.186277 −0.00689442
731731 1.43114 + 24.5717i 0.0529326 + 0.908818i
732732 −3.14858 4.71727i −0.116375 0.174355i
733733 27.1610 3.17467i 1.00321 0.117259i 0.401407 0.915900i 0.368521π-0.368521\pi
0.601808 + 0.798641i 0.294447π0.294447\pi
734734 −1.00282 0.237673i −0.0370148 0.00877267i
735735 0.689917 0.520924i 0.0254480 0.0192146i
736736 −7.74108 + 10.3981i −0.285340 + 0.383278i
737737 −3.18607 18.0691i −0.117360 0.665584i
738738 7.65329 18.4246i 0.281721 0.678220i
739739 −1.54918 + 8.78585i −0.0569876 + 0.323193i −0.999953 0.00969806i 0.996913π-0.996913\pi
0.942965 + 0.332891i 0.108024π0.108024\pi
740740 −0.0171821 0.0182119i −0.000631626 0.000669485i
741741 −12.7444 14.9810i −0.468178 0.550339i
742742 −11.9744 + 6.01376i −0.439593 + 0.220772i
743743 −12.8882 8.47670i −0.472822 0.310980i 0.290640 0.956832i 0.406132π-0.406132\pi
−0.763462 + 0.645852i 0.776502π0.776502\pi
744744 −9.29473 25.0087i −0.340761 0.916863i
745745 0.396029 0.0938606i 0.0145094 0.00343879i
746746 15.9226 5.79536i 0.582968 0.212183i
747747 −17.7992 6.20664i −0.651238 0.227089i
748748 −2.36875 0.862154i −0.0866100 0.0315235i
749749 −4.98637 0.582823i −0.182198 0.0212959i
750750 2.09062 + 0.107562i 0.0763386 + 0.00392760i
751751 −20.0965 + 21.3010i −0.733332 + 0.777286i −0.981506 0.191429i 0.938688π-0.938688\pi
0.248175 + 0.968715i 0.420169π0.420169\pi
752752 −13.8914 18.6594i −0.506569 0.680440i
753753 −27.3929 + 26.1968i −0.998251 + 0.954664i
754754 −3.06054 1.53706i −0.111458 0.0559764i
755755 −0.707063 1.22467i −0.0257327 0.0445703i
756756 −0.441525 + 1.29432i −0.0160581 + 0.0470740i
757757 −16.6330 + 28.8091i −0.604536 + 1.04709i 0.387589 + 0.921832i 0.373308π0.373308\pi
−0.992125 + 0.125254i 0.960025π0.960025\pi
758758 −25.3631 + 16.6816i −0.921228 + 0.605901i
759759 47.5122 20.8776i 1.72458 0.757808i
760760 −0.453705 + 1.05181i −0.0164576 + 0.0381530i
761761 −0.0917864 0.306588i −0.00332726 0.0111138i 0.956310 0.292355i 0.0944390π-0.0944390\pi
−0.959637 + 0.281242i 0.909254π0.909254\pi
762762 −6.55896 + 28.5343i −0.237606 + 1.03369i
763763 −3.52866 8.18036i −0.127746 0.296149i
764764 6.26572 5.25756i 0.226686 0.190212i
765765 −0.134026 + 0.470799i −0.00484573 + 0.0170218i
766766 −27.4025 22.9935i −0.990094 0.830787i
767767 −6.37337 + 21.2885i −0.230129 + 0.768684i
768768 10.8806 + 6.18404i 0.392620 + 0.223147i
769769 −0.120845 + 2.07483i −0.00435778 + 0.0748202i −0.999786 0.0206939i 0.993412π-0.993412\pi
0.995428 + 0.0955141i 0.0304495π0.0304495\pi
770770 −0.0239931 + 0.411945i −0.000864651 + 0.0148455i
771771 0.0835039 + 12.3283i 0.00300732 + 0.443994i
772772 0.00399548 0.0133458i 0.000143801 0.000480327i
773773 5.06191 + 4.24745i 0.182064 + 0.152770i 0.729265 0.684231i 0.239862π-0.239862\pi
−0.547201 + 0.837001i 0.684307π0.684307\pi
774774 32.0844 44.3383i 1.15325 1.59371i
775775 −22.9235 + 19.2351i −0.823437 + 0.690945i
776776 13.9874 + 32.4265i 0.502119 + 1.16404i
777777 1.10636 + 1.02972i 0.0396904 + 0.0369410i
778778 2.72110 + 9.08910i 0.0975561 + 0.325860i
779779 9.70585 22.5007i 0.347748 0.806171i
780780 −0.0694471 0.0509740i −0.00248660 0.00182516i
781781 18.5128 12.1761i 0.662440 0.435694i
782782 −11.6832 + 20.2359i −0.417791 + 0.723635i
783783 4.11888 4.04727i 0.147197 0.144638i
784784 −14.1733 24.5489i −0.506191 0.876748i
785785 0.513409 + 0.257844i 0.0183243 + 0.00920283i
786786 −6.19835 25.3854i −0.221088 0.905468i
787787 1.88656 + 2.53409i 0.0672487 + 0.0903306i 0.834475 0.551046i 0.185771π-0.185771\pi
−0.767226 + 0.641377i 0.778364π0.778364\pi
788788 −2.57484 + 2.72917i −0.0917249 + 0.0972228i
789789 13.2272 + 25.8987i 0.470901 + 0.922017i
790790 1.63999 + 0.191688i 0.0583484 + 0.00681995i
791791 −2.22697 0.810550i −0.0791818 0.0288198i
792792 −15.7557 26.4555i −0.559855 0.940055i
793793 −20.2657 + 7.37611i −0.719656 + 0.261933i
794794 −1.65863 + 0.393102i −0.0588626 + 0.0139507i
795795 1.40322 + 0.237638i 0.0497672 + 0.00842815i
796796 −3.23545 2.12799i −0.114678 0.0754246i
797797 41.8410 21.0134i 1.48209 0.744331i 0.490217 0.871600i 0.336918π-0.336918\pi
0.991868 + 0.127269i 0.0406213π0.0406213\pi
798798 −4.22478 + 11.8567i −0.149556 + 0.419724i
799799 −7.23731 7.67110i −0.256038 0.271384i
800800 1.49802 8.49568i 0.0529629 0.300368i
801801 30.2725 + 6.74296i 1.06963 + 0.238251i
802802 1.11817 + 6.34143i 0.0394838 + 0.223924i
803803 3.67266 4.93324i 0.129605 0.174090i
804804 −0.301064 2.43275i −0.0106177 0.0857965i
805805 0.496683 + 0.117716i 0.0175058 + 0.00414895i
806806 18.3427 2.14395i 0.646094 0.0755175i
807807 15.7970 31.9928i 0.556080 1.12620i
808808 −1.27595 21.9073i −0.0448879 0.770695i
809809 −47.8251 −1.68144 −0.840721 0.541468i 0.817869π-0.817869\pi
−0.840721 + 0.541468i 0.817869π0.817869\pi
810810 0.892846 0.622525i 0.0313714 0.0218733i
811811 11.3948 0.400124 0.200062 0.979783i 0.435886π-0.435886\pi
0.200062 + 0.979783i 0.435886π0.435886\pi
812812 0.0170064 + 0.291988i 0.000596807 + 0.0102468i
813813 −6.06235 + 0.394309i −0.212616 + 0.0138290i
814814 6.15279 0.719158i 0.215655 0.0252065i
815815 −0.383116 0.0908002i −0.0134200 0.00318059i
816816 14.7809 + 6.25744i 0.517433 + 0.219054i
817817 40.1418 53.9198i 1.40438 1.88642i
818818 −0.504121 2.85901i −0.0176262 0.0999630i
819819 4.38302 + 2.79845i 0.153155 + 0.0977857i
820820 0.0186375 0.105699i 0.000650851 0.00369116i
821821 10.9406 + 11.5964i 0.381830 + 0.404716i 0.889573 0.456792i 0.151002π-0.151002\pi
−0.507744 + 0.861508i 0.669520π0.669520\pi
822822 −41.6172 + 7.62923i −1.45157 + 0.266100i
823823 34.5077 17.3304i 1.20286 0.604100i 0.269488 0.963004i 0.413146π-0.413146\pi
0.933375 + 0.358904i 0.116849π0.116849\pi
824824 17.6744 + 11.6246i 0.615716 + 0.404963i
825825 −22.0198 + 26.6061i −0.766631 + 0.926305i
826826 13.8378 3.27962i 0.481479 0.114113i
827827 −32.7798 + 11.9309i −1.13986 + 0.414877i −0.841865 0.539689i 0.818542π-0.818542\pi
−0.298000 + 0.954566i 0.596320π0.596320\pi
828828 6.48266 2.45944i 0.225288 0.0854716i
829829 25.8256 + 9.39976i 0.896961 + 0.326467i 0.749034 0.662531i 0.230518π-0.230518\pi
0.147927 + 0.988998i 0.452740π0.452740\pi
830830 −0.754768 0.0882198i −0.0261984 0.00306215i
831831 15.3007 23.6103i 0.530774 0.819033i
832832 8.93399 9.46948i 0.309730 0.328295i
833833 −7.67422 10.3083i −0.265896 0.357160i
834834 −51.2624 14.9694i −1.77507 0.518348i
835835 1.27495 + 0.640305i 0.0441216 + 0.0221587i
836836 3.44223 + 5.96211i 0.119052 + 0.206204i
837837 −6.56380 + 30.4383i −0.226878 + 1.05210i
838838 −1.88524 + 3.26532i −0.0651244 + 0.112799i
839839 19.1139 12.5714i 0.659884 0.434013i −0.174903 0.984586i 0.555961π-0.555961\pi
0.834787 + 0.550573i 0.185591π0.185591\pi
840840 0.0331216 0.301043i 0.00114280 0.0103870i
841841 −10.9971 + 25.4943i −0.379212 + 0.879112i
842842 −7.60981 25.4185i −0.262251 0.875981i
843843 0.673995 0.206765i 0.0232136 0.00712138i
844844 1.67437 + 3.88163i 0.0576342 + 0.133611i
845845 0.541824 0.454644i 0.0186393 0.0156402i
846846 1.68051 + 23.3901i 0.0577773 + 0.804167i
847847 −3.23615 2.71545i −0.111195 0.0933041i
848848 13.3842 44.7063i 0.459615 1.53522i
849849 −27.9255 + 16.3760i −0.958402 + 0.562023i
850850 0.904144 15.5236i 0.0310119 0.532454i
851851 0.445555 7.64988i 0.0152734 0.262234i
852852 2.55366 1.49751i 0.0874871 0.0513039i
853853 −15.1823 + 50.7124i −0.519832 + 1.73636i 0.145064 + 0.989422i 0.453661π0.453661\pi
−0.664896 + 0.746936i 0.731524π0.731524\pi
854854 10.5725 + 8.87141i 0.361785 + 0.303573i
855855 1.10690 0.749692i 0.0378550 0.0256389i
856856 11.5688 9.70736i 0.395413 0.331791i
857857 −6.23293 14.4496i −0.212913 0.493588i 0.777972 0.628299i 0.216249π-0.216249\pi
−0.990885 + 0.134711i 0.956989π0.956989\pi
858858 20.3764 6.25098i 0.695638 0.213405i
859859 5.14494 + 17.1853i 0.175543 + 0.586355i 0.999797 + 0.0201350i 0.00640959π0.00640959\pi
−0.824254 + 0.566220i 0.808405π0.808405\pi
860860 0.116616 0.270346i 0.00397657 0.00921872i
861861 −0.708550 + 6.44003i −0.0241473 + 0.219476i
862862 29.6630 19.5097i 1.01033 0.664502i
863863 24.9816 43.2695i 0.850385 1.47291i −0.0304761 0.999535i 0.509702π-0.509702\pi
0.880861 0.473375i 0.156964π-0.156964\pi
864864 −4.19082 7.93822i −0.142575 0.270064i
865865 0.0685821 + 0.118788i 0.00233186 + 0.00403890i
866866 −41.5087 20.8465i −1.41052 0.708391i
867867 −21.2794 6.21389i −0.722685 0.211035i
868868 −0.941805 1.26506i −0.0319669 0.0429391i
869869 −37.4109 + 39.6532i −1.26908 + 1.34514i
870870 0.126599 0.195354i 0.00429211 0.00662311i
871871 −9.25821 1.08213i −0.313703 0.0366666i
872872 25.1835 + 9.16605i 0.852821 + 0.310401i
873873 6.60647 40.6823i 0.223595 1.37689i
874874 59.9673 21.8263i 2.02842 0.738286i
875875 −0.661484 + 0.156775i −0.0223622 + 0.00529995i
876876 0.523892 0.633008i 0.0177007 0.0213874i
877877 6.84275 + 4.50055i 0.231063 + 0.151973i 0.659762 0.751475i 0.270657π-0.270657\pi
−0.428698 + 0.903448i 0.641028π0.641028\pi
878878 16.8455 8.46015i 0.568510 0.285516i
879879 21.9397 4.02197i 0.740008 0.135658i
880880 −0.986202 1.04531i −0.0332449 0.0352375i
881881 −2.64591 + 15.0057i −0.0891429 + 0.505555i 0.907243 + 0.420608i 0.138183π0.138183\pi
−0.996385 + 0.0849468i 0.972928π0.972928\pi
882882 −1.27493 + 28.5470i −0.0429293 + 0.961229i
883883 −5.32760 30.2143i −0.179288 1.01679i −0.933077 0.359677i 0.882887π-0.882887\pi
0.753789 0.657117i 0.228224π-0.228224\pi
884884 −0.764735 + 1.02722i −0.0257208 + 0.0345491i
885885 −1.39094 0.588853i −0.0467561 0.0197941i
886886 5.12729 + 1.21519i 0.172255 + 0.0408251i
887887 −23.6129 + 2.75996i −0.792845 + 0.0926702i −0.502868 0.864363i 0.667722π-0.667722\pi
−0.289977 + 0.957034i 0.593648π0.593648\pi
888888 −4.53699 + 0.295096i −0.152251 + 0.00990279i
889889 −0.552837 9.49184i −0.0185415 0.318346i
890890 1.25028 0.0419094
891891 −1.11690 + 35.9193i −0.0374176 + 1.20334i
892892 −0.904673 −0.0302907
893893 1.67474 + 28.7542i 0.0560431 + 0.962223i
894894 −5.95623 + 12.0629i −0.199206 + 0.403442i
895895 −0.976650 + 0.114154i −0.0326458 + 0.00381575i
896896 −10.9796 2.60222i −0.366804 0.0869341i
897897 −3.23810 26.1655i −0.108117 0.873641i
898898 2.81575 3.78221i 0.0939628 0.126214i
899899 1.15642 + 6.55838i 0.0385687 + 0.218734i
900900 −3.12064 + 3.39877i −0.104021 + 0.113292i
901901 3.67384 20.8354i 0.122393 0.694128i
902902 18.2228 + 19.3150i 0.606753 + 0.643120i
903903 −5.96542 + 16.7418i −0.198517 + 0.557133i
904904 6.37074 3.19950i 0.211888 0.106414i
905905 0.00241413 + 0.00158780i 8.02484e−5 + 5.27802e-5i
906906 46.0872 + 7.80493i 1.53115 + 0.259302i
907907 −33.6177 + 7.96755i −1.11626 + 0.264558i −0.747037 0.664783i 0.768524π-0.768524\pi
−0.369222 + 0.929341i 0.620376π0.620376\pi
908908 −1.14786 + 0.417786i −0.0380930 + 0.0138647i
909909 −12.5039 + 22.3512i −0.414727 + 0.741343i
910910 0.196992 + 0.0716993i 0.00653023 + 0.00237681i
911911 49.7468 + 5.81456i 1.64818 + 0.192645i 0.888896 0.458110i 0.151473π-0.151473\pi
0.759288 + 0.650755i 0.225547π0.225547\pi
912912 −19.9386 39.0394i −0.660233 1.29272i
913913 17.2175 18.2494i 0.569815 0.603969i
914914 32.1871 + 43.2347i 1.06465 + 1.43008i
915915 −0.347708 1.42404i −0.0114949 0.0470774i
916916 −2.81230 1.41239i −0.0929211 0.0466667i
917917 4.24294 + 7.34898i 0.140114 + 0.242685i
918918 −9.16411 13.3351i −0.302461 0.440123i
919919 1.41443 2.44986i 0.0466577 0.0808136i −0.841753 0.539862i 0.818476π-0.818476\pi
0.888411 + 0.459049i 0.151810π0.151810\pi
920920 −1.28289 + 0.843770i −0.0422956 + 0.0278183i
921921 12.1988 + 8.95391i 0.401965 + 0.295041i
922922 15.3365 35.5540i 0.505080 1.17091i
923923 −3.22853 10.7840i −0.106268 0.354961i
924924 −1.33240 1.24010i −0.0438327 0.0407964i
925925 2.01979 + 4.68241i 0.0664104 + 0.153957i
926926 −10.8427 + 9.09809i −0.356313 + 0.298982i
927927 −10.0851 22.5354i −0.331237 0.740161i
928928 −1.47068 1.23405i −0.0482774 0.0405096i
929929 −3.54186 + 11.8306i −0.116205 + 0.388150i −0.996227 0.0867811i 0.972342π-0.972342\pi
0.880023 + 0.474931i 0.157527π0.157527\pi
930930 0.00850208 + 1.25523i 0.000278794 + 0.0411605i
931931 −2.04076 + 35.0385i −0.0668833 + 1.14834i
932932 −0.0457306 + 0.785164i −0.00149795 + 0.0257189i
933933 −27.9918 15.9093i −0.916410 0.520846i
934934 5.40704 18.0608i 0.176924 0.590967i
935935 −0.499097 0.418792i −0.0163222 0.0136960i
936936 −15.1712 + 3.81342i −0.495887 + 0.124645i
937937 −4.94841 + 4.15221i −0.161658 + 0.135647i −0.720028 0.693945i 0.755871π-0.755871\pi
0.558371 + 0.829592i 0.311427π0.311427\pi
938938 2.36269 + 5.47732i 0.0771444 + 0.178841i
939939 −8.16333 + 35.5140i −0.266400 + 1.15896i
940940 0.0361816 + 0.120855i 0.00118011 + 0.00394186i
941941 −4.95563 + 11.4885i −0.161549 + 0.374513i −0.979694 0.200500i 0.935743π-0.935743\pi
0.818145 + 0.575012i 0.195003π0.195003\pi
942942 −17.3860 + 7.63969i −0.566468 + 0.248915i
943943 27.4441 18.0503i 0.893704 0.587798i
944944 −24.7639 + 42.8923i −0.805995 + 1.39602i
945945 −0.221653 + 0.275329i −0.00721037 + 0.00895644i
946946 36.4221 + 63.0849i 1.18418 + 2.05107i
947947 −43.0350 21.6130i −1.39845 0.702328i −0.419752 0.907639i 0.637883π-0.637883\pi
−0.978697 + 0.205311i 0.934179π0.934179\pi
948948 −5.26377 + 5.03393i −0.170959 + 0.163494i
949949 −1.86582 2.50623i −0.0605670 0.0813556i
950950 −29.1434 + 30.8902i −0.945537 + 1.00221i
951951 28.0245 + 1.44185i 0.908756 + 0.0467552i
952952 −4.47175 0.522673i −0.144930 0.0169399i
953953 −23.6434 8.60549i −0.765884 0.278759i −0.0706105 0.997504i 0.522495π-0.522495\pi
−0.695274 + 0.718745i 0.744717π0.744717\pi
954954 −35.6245 + 30.7244i −1.15339 + 0.994738i
955955 1.98656 0.723047i 0.0642834 0.0233973i
956956 −1.39711 + 0.331121i −0.0451857 + 0.0107092i
957957 2.67758 + 7.20439i 0.0865539 + 0.232885i
958958 44.1261 + 29.0222i 1.42565 + 0.937664i
959959 12.2785 6.16651i 0.396495 0.199127i
960960 0.573377 + 0.674000i 0.0185057 + 0.0217533i
961961 −3.36946 3.57142i −0.108692 0.115207i
962962 0.546484 3.09926i 0.0176193 0.0999242i
963963 −17.4768 + 2.28312i −0.563182 + 0.0735726i
964964 0.0812022 + 0.460520i 0.00261535 + 0.0148324i
965965 0.00215017 0.00288818i 6.92165e−5 9.29739e-5i
966966 −13.4653 + 10.1670i −0.433237 + 0.327117i
967967 −45.8988 10.8782i −1.47601 0.349820i −0.587704 0.809076i 0.699968π-0.699968\pi
−0.888304 + 0.459256i 0.848116π0.848116\pi
968968 12.6221 1.47531i 0.405689 0.0474183i
969969 −11.0329 16.5298i −0.354429 0.531014i
970970 −0.0966075 1.65869i −0.00310188 0.0532572i
971971 −26.3271 −0.844876 −0.422438 0.906392i 0.638826π-0.638826\pi
−0.422438 + 0.906392i 0.638826π0.638826\pi
972972 −0.395599 + 4.78489i −0.0126888 + 0.153475i
973973 17.3423 0.555968
974974 −0.400652 6.87893i −0.0128377 0.220415i
975975 9.74043 + 14.5933i 0.311944 + 0.467361i
976976 −47.7411 + 5.58013i −1.52815 + 0.178616i
977977 17.0061 + 4.03051i 0.544072 + 0.128947i 0.493456 0.869771i 0.335733π-0.335733\pi
0.0506160 + 0.998718i 0.483882π0.483882\pi
978978 10.3864 7.84229i 0.332121 0.250769i
979979 −24.6506 + 33.1115i −0.787837 + 1.05825i
980980 0.0266943 + 0.151391i 0.000852719 + 0.00483601i
981981 −19.0158 24.8332i −0.607128 0.792862i
982982 7.90196 44.8142i 0.252162 1.43008i
983983 −27.2676 28.9020i −0.869701 0.921830i 0.127848 0.991794i 0.459193π-0.459193\pi
−0.997550 + 0.0699641i 0.977712π0.977712\pi
984984 −12.6285 14.8447i −0.402583 0.473233i
985985 −0.866624 + 0.435235i −0.0276129 + 0.0138677i
986986 −2.89124 1.90160i −0.0920759 0.0605593i
987987 −2.65299 7.13823i −0.0844458 0.227212i
988988 3.40323 0.806579i 0.108271 0.0256607i
989989 84.6743 30.8189i 2.69249 0.979985i
990990 0.270868 + 1.42316i 0.00860876 + 0.0452310i
991991 −11.5059 4.18780i −0.365497 0.133030i 0.152742 0.988266i 0.451190π-0.451190\pi
−0.518238 + 0.855236i 0.673412π0.673412\pi
992992 10.2823 + 1.20182i 0.326462 + 0.0381580i
993993 32.9593 + 1.69575i 1.04593 + 0.0538130i
994994 −4.94364 + 5.23995i −0.156803 + 0.166201i
995995 −0.597699 0.802850i −0.0189483 0.0254520i
996996 2.42252 2.31675i 0.0767606 0.0734090i
997997 −7.48521 3.75921i −0.237059 0.119056i 0.326304 0.945265i 0.394197π-0.394197\pi
−0.563363 + 0.826209i 0.690493π0.690493\pi
998998 −5.18398 8.97892i −0.164096 0.284223i
999999 4.64830 + 2.55920i 0.147066 + 0.0809696i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 81.2.g.a.40.3 144
3.2 odd 2 243.2.g.a.91.6 144
9.2 odd 6 729.2.g.a.28.6 144
9.4 even 3 729.2.g.c.271.6 144
9.5 odd 6 729.2.g.b.271.3 144
9.7 even 3 729.2.g.d.28.3 144
81.2 odd 54 243.2.g.a.235.6 144
81.22 even 27 6561.2.a.c.1.55 72
81.25 even 27 729.2.g.d.703.3 144
81.29 odd 54 729.2.g.b.460.3 144
81.52 even 27 729.2.g.c.460.6 144
81.56 odd 54 729.2.g.a.703.6 144
81.59 odd 54 6561.2.a.d.1.18 72
81.79 even 27 inner 81.2.g.a.79.3 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.40.3 144 1.1 even 1 trivial
81.2.g.a.79.3 yes 144 81.79 even 27 inner
243.2.g.a.91.6 144 3.2 odd 2
243.2.g.a.235.6 144 81.2 odd 54
729.2.g.a.28.6 144 9.2 odd 6
729.2.g.a.703.6 144 81.56 odd 54
729.2.g.b.271.3 144 9.5 odd 6
729.2.g.b.460.3 144 81.29 odd 54
729.2.g.c.271.6 144 9.4 even 3
729.2.g.c.460.6 144 81.52 even 27
729.2.g.d.28.3 144 9.7 even 3
729.2.g.d.703.3 144 81.25 even 27
6561.2.a.c.1.55 72 81.22 even 27
6561.2.a.d.1.18 72 81.59 odd 54