Properties

Label 128.2.k.a.109.8
Level 128128
Weight 22
Character 128.109
Analytic conductor 1.0221.022
Analytic rank 00
Dimension 240240
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [128,2,Mod(5,128)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(128, base_ring=CyclotomicField(32))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("128.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 128=27 128 = 2^{7}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 128.k (of order 3232, degree 1616, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.022085145871.02208514587
Analytic rank: 00
Dimension: 240240
Relative dimension: 1515 over Q(ζ32)\Q(\zeta_{32})
Twist minimal: yes
Sato-Tate group: SU(2)[C32]\mathrm{SU}(2)[C_{32}]

Embedding invariants

Embedding label 109.8
Character χ\chi == 128.109
Dual form 128.2.k.a.101.8

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+(0.3991841.35671i)q2+(0.1356340.0724978i)q3+(1.68130+1.08315i)q4+(2.129422.59470i)q5+(0.0442153+0.212955i)q6+(1.110600.742082i)q7+(2.14067+1.84866i)q8+(1.653572.47474i)q9+(4.370281.85323i)q10+(0.1814970.0550566i)q11+(0.3065680.0250213i)q12+(0.3741370.307046i)q13+(0.563451+1.80299i)q14+(0.476932+0.197552i)q15+(1.653563.64222i)q16+(1.79255+0.742500i)q17+(2.69742+3.23129i)q18+(0.487163+4.94625i)q19+(0.769739+6.66897i)q20+(0.0968362+0.181168i)q21+(0.00224473+0.268216i)q22+(5.40603+1.07533i)q23+(0.1563240.405934i)q24+(1.222616.14649i)q25+(0.5659210.385026i)q26+(0.0900899+0.914698i)q27+(2.67105+0.0447117i)q28+(2.45765+8.10178i)q29+(0.458403+0.568197i)q30+(3.302973.30297i)q31+(5.601490.789483i)q32+(0.0206257+0.0206257i)q33+(0.2917952.72836i)q34+(4.29042+1.30149i)q35+(5.46068+2.36973i)q36+(8.327890.820226i)q37+(6.905081.31353i)q38+(0.0730059+0.0145218i)q39+(9.355101.61784i)q40+(0.5801682.91670i)q41+(0.2071360.203698i)q42+(8.36535+4.47137i)q43+(0.3647870.104022i)q44+(9.942370.979238i)q45+(0.6991027.76365i)q46+(3.57155+8.62250i)q47+(0.488332+0.374128i)q48+(1.996034.81884i)q49+(7.85094+4.11231i)q50+(0.1893010.230664i)q51+(0.296460+0.921485i)q52+(3.12341+10.2965i)q53+(1.205010.487359i)q54+(0.529339+0.353693i)q55+(1.005583.64168i)q56+(0.4246680.635561i)q57+(10.01076.56841i)q58+(10.84838.90293i)q59+(0.5878880.848734i)q60+(0.3398500.635815i)q61+(5.799663.16267i)q62+3.97554iq63+(1.16493+7.91473i)q641.62460iq65+(0.01974950.0362165i)q66+(0.0570291+0.106694i)q67+(3.81807+0.693240i)q68+(0.6552830.537776i)q69+(3.47840+5.30131i)q70+(8.8139913.1911i)q71+(1.035208.35449i)q72+(1.93431+1.29247i)q73+(4.4371710.9711i)q74+(0.279780+0.922310i)q75+(4.538488.84383i)q76+(0.160715+0.195832i)q77+(0.0488446+0.0932506i)q78+(3.114047.51796i)q79+(5.9293412.0463i)q80+(3.36290+8.11876i)q81+(4.18870+0.377184i)q82+(14.1505+1.39370i)q83+(0.3590430.199710i)q84+(5.743663.07005i)q85+(9.40566+9.56442i)q86+(0.2540211.27705i)q87+(0.2867450.453384i)q88+(1.57448+0.313183i)q89+(2.64030+13.8798i)q90+(0.643371+0.0633666i)q91+(10.2539+4.04761i)q92+(0.687453+0.208537i)q93+(13.1239+1.40358i)q94+(11.7967+11.7967i)q95+(0.702516+0.513177i)q96+(11.0877+11.0877i)q97+(5.74097+4.63163i)q98+(0.163868+0.540199i)q99+O(q100)q+(-0.399184 - 1.35671i) q^{2} +(-0.135634 - 0.0724978i) q^{3} +(-1.68130 + 1.08315i) q^{4} +(2.12942 - 2.59470i) q^{5} +(-0.0442153 + 0.212955i) q^{6} +(-1.11060 - 0.742082i) q^{7} +(2.14067 + 1.84866i) q^{8} +(-1.65357 - 2.47474i) q^{9} +(-4.37028 - 1.85323i) q^{10} +(-0.181497 - 0.0550566i) q^{11} +(0.306568 - 0.0250213i) q^{12} +(0.374137 - 0.307046i) q^{13} +(-0.563451 + 1.80299i) q^{14} +(-0.476932 + 0.197552i) q^{15} +(1.65356 - 3.64222i) q^{16} +(1.79255 + 0.742500i) q^{17} +(-2.69742 + 3.23129i) q^{18} +(-0.487163 + 4.94625i) q^{19} +(-0.769739 + 6.66897i) q^{20} +(0.0968362 + 0.181168i) q^{21} +(-0.00224473 + 0.268216i) q^{22} +(5.40603 + 1.07533i) q^{23} +(-0.156324 - 0.405934i) q^{24} +(-1.22261 - 6.14649i) q^{25} +(-0.565921 - 0.385026i) q^{26} +(0.0900899 + 0.914698i) q^{27} +(2.67105 + 0.0447117i) q^{28} +(2.45765 + 8.10178i) q^{29} +(0.458403 + 0.568197i) q^{30} +(3.30297 - 3.30297i) q^{31} +(-5.60149 - 0.789483i) q^{32} +(0.0206257 + 0.0206257i) q^{33} +(0.291795 - 2.72836i) q^{34} +(-4.29042 + 1.30149i) q^{35} +(5.46068 + 2.36973i) q^{36} +(8.32789 - 0.820226i) q^{37} +(6.90508 - 1.31353i) q^{38} +(-0.0730059 + 0.0145218i) q^{39} +(9.35510 - 1.61784i) q^{40} +(0.580168 - 2.91670i) q^{41} +(0.207136 - 0.203698i) q^{42} +(-8.36535 + 4.47137i) q^{43} +(0.364787 - 0.104022i) q^{44} +(-9.94237 - 0.979238i) q^{45} +(-0.699102 - 7.76365i) q^{46} +(-3.57155 + 8.62250i) q^{47} +(-0.488332 + 0.374128i) q^{48} +(-1.99603 - 4.81884i) q^{49} +(-7.85094 + 4.11231i) q^{50} +(-0.189301 - 0.230664i) q^{51} +(-0.296460 + 0.921485i) q^{52} +(-3.12341 + 10.2965i) q^{53} +(1.20501 - 0.487359i) q^{54} +(-0.529339 + 0.353693i) q^{55} +(-1.00558 - 3.64168i) q^{56} +(0.424668 - 0.635561i) q^{57} +(10.0107 - 6.56841i) q^{58} +(-10.8483 - 8.90293i) q^{59} +(0.587888 - 0.848734i) q^{60} +(0.339850 - 0.635815i) q^{61} +(-5.79966 - 3.16267i) q^{62} +3.97554i q^{63} +(1.16493 + 7.91473i) q^{64} -1.62460i q^{65} +(0.0197495 - 0.0362165i) q^{66} +(-0.0570291 + 0.106694i) q^{67} +(-3.81807 + 0.693240i) q^{68} +(-0.655283 - 0.537776i) q^{69} +(3.47840 + 5.30131i) q^{70} +(8.81399 - 13.1911i) q^{71} +(1.03520 - 8.35449i) q^{72} +(-1.93431 + 1.29247i) q^{73} +(-4.43717 - 10.9711i) q^{74} +(-0.279780 + 0.922310i) q^{75} +(-4.53848 - 8.84383i) q^{76} +(0.160715 + 0.195832i) q^{77} +(0.0488446 + 0.0932506i) q^{78} +(-3.11404 - 7.51796i) q^{79} +(-5.92934 - 12.0463i) q^{80} +(-3.36290 + 8.11876i) q^{81} +(-4.18870 + 0.377184i) q^{82} +(14.1505 + 1.39370i) q^{83} +(-0.359043 - 0.199710i) q^{84} +(5.74366 - 3.07005i) q^{85} +(9.40566 + 9.56442i) q^{86} +(0.254021 - 1.27705i) q^{87} +(-0.286745 - 0.453384i) q^{88} +(-1.57448 + 0.313183i) q^{89} +(2.64030 + 13.8798i) q^{90} +(-0.643371 + 0.0633666i) q^{91} +(-10.2539 + 4.04761i) q^{92} +(-0.687453 + 0.208537i) q^{93} +(13.1239 + 1.40358i) q^{94} +(11.7967 + 11.7967i) q^{95} +(0.702516 + 0.513177i) q^{96} +(-11.0877 + 11.0877i) q^{97} +(-5.74097 + 4.63163i) q^{98} +(0.163868 + 0.540199i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 240q16q216q316q416q516q616q716q816q916q1016q1116q1216q1316q1416q1516q1616q1716q18+16q99+O(q100) 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/128Z)×\left(\mathbb{Z}/128\mathbb{Z}\right)^\times.

nn 55 127127
χ(n)\chi(n) e(2332)e\left(\frac{23}{32}\right) 11

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 −0.399184 1.35671i −0.282266 0.959336i
33 −0.135634 0.0724978i −0.0783083 0.0418566i 0.431778 0.901980i 0.357886π-0.357886\pi
−0.510086 + 0.860123i 0.670386π0.670386\pi
44 −1.68130 + 1.08315i −0.840652 + 0.541576i
55 2.12942 2.59470i 0.952305 1.16039i −0.0346516 0.999399i 0.511032π-0.511032\pi
0.986956 0.160987i 0.0514678π-0.0514678\pi
66 −0.0442153 + 0.212955i −0.0180508 + 0.0869387i
77 −1.11060 0.742082i −0.419769 0.280480i 0.327694 0.944784i 0.393728π-0.393728\pi
−0.747463 + 0.664303i 0.768728π0.768728\pi
88 2.14067 + 1.84866i 0.756841 + 0.653599i
99 −1.65357 2.47474i −0.551190 0.824914i
1010 −4.37028 1.85323i −1.38200 0.586043i
1111 −0.181497 0.0550566i −0.0547235 0.0166002i 0.262804 0.964849i 0.415353π-0.415353\pi
−0.317528 + 0.948249i 0.602853π0.602853\pi
1212 0.306568 0.0250213i 0.0884985 0.00722303i
1313 0.374137 0.307046i 0.103767 0.0851593i −0.581079 0.813847i 0.697369π-0.697369\pi
0.684846 + 0.728688i 0.259869π0.259869\pi
1414 −0.563451 + 1.80299i −0.150589 + 0.481869i
1515 −0.476932 + 0.197552i −0.123143 + 0.0510076i
1616 1.65356 3.64222i 0.413391 0.910554i
1717 1.79255 + 0.742500i 0.434758 + 0.180083i 0.589319 0.807901i 0.299396π-0.299396\pi
−0.154561 + 0.987983i 0.549396π0.549396\pi
1818 −2.69742 + 3.23129i −0.635788 + 0.761622i
1919 −0.487163 + 4.94625i −0.111763 + 1.13475i 0.761724 + 0.647901i 0.224353π0.224353\pi
−0.873487 + 0.486847i 0.838147π0.838147\pi
2020 −0.769739 + 6.66897i −0.172119 + 1.49123i
2121 0.0968362 + 0.181168i 0.0211314 + 0.0395340i
2222 −0.00224473 + 0.268216i −0.000478577 + 0.0571839i
2323 5.40603 + 1.07533i 1.12724 + 0.224221i 0.723278 0.690557i 0.242634π-0.242634\pi
0.403958 + 0.914778i 0.367634π0.367634\pi
2424 −0.156324 0.405934i −0.0319094 0.0828610i
2525 −1.22261 6.14649i −0.244523 1.22930i
2626 −0.565921 0.385026i −0.110986 0.0755098i
2727 0.0900899 + 0.914698i 0.0173378 + 0.176034i
2828 2.67105 + 0.0447117i 0.504781 + 0.00844971i
2929 2.45765 + 8.10178i 0.456374 + 1.50446i 0.819695 + 0.572800i 0.194143π0.194143\pi
−0.363321 + 0.931664i 0.618357π0.618357\pi
3030 0.458403 + 0.568197i 0.0836926 + 0.103738i
3131 3.30297 3.30297i 0.593232 0.593232i −0.345271 0.938503i 0.612213π-0.612213\pi
0.938503 + 0.345271i 0.112213π0.112213\pi
3232 −5.60149 0.789483i −0.990213 0.139562i
3333 0.0206257 + 0.0206257i 0.00359047 + 0.00359047i
3434 0.291795 2.72836i 0.0500424 0.467910i
3535 −4.29042 + 1.30149i −0.725214 + 0.219991i
3636 5.46068 + 2.36973i 0.910113 + 0.394954i
3737 8.32789 0.820226i 1.36910 0.134844i 0.613404 0.789770i 0.289800π-0.289800\pi
0.755694 + 0.654925i 0.227300π0.227300\pi
3838 6.90508 1.31353i 1.12015 0.213083i
3939 −0.0730059 + 0.0145218i −0.0116903 + 0.00232534i
4040 9.35510 1.61784i 1.47917 0.255803i
4141 0.580168 2.91670i 0.0906070 0.455512i −0.908671 0.417513i 0.862902π-0.862902\pi
0.999278 0.0379988i 0.0120983π-0.0120983\pi
4242 0.207136 0.203698i 0.0319618 0.0314312i
4343 −8.36535 + 4.47137i −1.27570 + 0.681878i −0.963391 0.268101i 0.913604π-0.913604\pi
−0.312313 + 0.949979i 0.601104π0.601104\pi
4444 0.364787 0.104022i 0.0549937 0.0156820i
4545 −9.94237 0.979238i −1.48212 0.145976i
4646 −0.699102 7.76365i −0.103077 1.14469i
4747 −3.57155 + 8.62250i −0.520965 + 1.25772i 0.416340 + 0.909209i 0.363313π0.363313\pi
−0.937305 + 0.348511i 0.886687π0.886687\pi
4848 −0.488332 + 0.374128i −0.0704846 + 0.0540007i
4949 −1.99603 4.81884i −0.285147 0.688406i
5050 −7.85094 + 4.11231i −1.11029 + 0.581569i
5151 −0.189301 0.230664i −0.0265075 0.0322995i
5252 −0.296460 + 0.921485i −0.0411116 + 0.127787i
5353 −3.12341 + 10.2965i −0.429033 + 1.41433i 0.430194 + 0.902737i 0.358445π0.358445\pi
−0.859227 + 0.511595i 0.829055π0.829055\pi
5454 1.20501 0.487359i 0.163982 0.0663212i
5555 −0.529339 + 0.353693i −0.0713761 + 0.0476920i
5656 −1.00558 3.64168i −0.134376 0.486640i
5757 0.424668 0.635561i 0.0562487 0.0841822i
5858 10.0107 6.56841i 1.31447 0.862475i
5959 −10.8483 8.90293i −1.41232 1.15906i −0.964227 0.265077i 0.914603π-0.914603\pi
−0.448095 0.893986i 0.647897π-0.647897\pi
6060 0.587888 0.848734i 0.0758961 0.109571i
6161 0.339850 0.635815i 0.0435134 0.0814078i −0.859225 0.511598i 0.829054π-0.829054\pi
0.902738 + 0.430190i 0.141554π0.141554\pi
6262 −5.79966 3.16267i −0.736558 0.401659i
6363 3.97554i 0.500871i
6464 1.16493 + 7.91473i 0.145617 + 0.989341i
6565 1.62460i 0.201507i
6666 0.0197495 0.0362165i 0.00243100 0.00445794i
6767 −0.0570291 + 0.106694i −0.00696721 + 0.0130347i −0.885381 0.464866i 0.846102π-0.846102\pi
0.878414 + 0.477901i 0.158602π0.158602\pi
6868 −3.81807 + 0.693240i −0.463009 + 0.0840677i
6969 −0.655283 0.537776i −0.0788867 0.0647407i
7070 3.47840 + 5.30131i 0.415749 + 0.633628i
7171 8.81399 13.1911i 1.04603 1.56549i 0.242567 0.970135i 0.422011π-0.422011\pi
0.803461 0.595357i 0.202989π-0.202989\pi
7272 1.03520 8.35449i 0.122000 0.984586i
7373 −1.93431 + 1.29247i −0.226394 + 0.151272i −0.663595 0.748092i 0.730970π-0.730970\pi
0.437200 + 0.899364i 0.355970π0.355970\pi
7474 −4.43717 10.9711i −0.515811 1.27536i
7575 −0.279780 + 0.922310i −0.0323062 + 0.106499i
7676 −4.53848 8.84383i −0.520599 1.01446i
7777 0.160715 + 0.195832i 0.0183152 + 0.0223171i
7878 0.0488446 + 0.0932506i 0.00553056 + 0.0105586i
7979 −3.11404 7.51796i −0.350357 0.845837i −0.996576 0.0826847i 0.973651π-0.973651\pi
0.646219 0.763152i 0.276349π-0.276349\pi
8080 −5.92934 12.0463i −0.662921 1.34682i
8181 −3.36290 + 8.11876i −0.373656 + 0.902085i
8282 −4.18870 + 0.377184i −0.462565 + 0.0416530i
8383 14.1505 + 1.39370i 1.55322 + 0.152979i 0.837903 0.545820i 0.183782π-0.183782\pi
0.715318 + 0.698799i 0.246282π0.246282\pi
8484 −0.359043 0.199710i −0.0391748 0.0217901i
8585 5.74366 3.07005i 0.622988 0.332994i
8686 9.40566 + 9.56442i 1.01424 + 1.03136i
8787 0.254021 1.27705i 0.0272339 0.136914i
8888 −0.286745 0.453384i −0.0305671 0.0483309i
8989 −1.57448 + 0.313183i −0.166894 + 0.0331974i −0.277830 0.960630i 0.589615π-0.589615\pi
0.110936 + 0.993828i 0.464615π0.464615\pi
9090 2.64030 + 13.8798i 0.278312 + 1.46306i
9191 −0.643371 + 0.0633666i −0.0674437 + 0.00664262i
9292 −10.2539 + 4.04761i −1.06905 + 0.421992i
9393 −0.687453 + 0.208537i −0.0712856 + 0.0216243i
9494 13.1239 + 1.40358i 1.35363 + 0.144769i
9595 11.7967 + 11.7967i 1.21031 + 1.21031i
9696 0.702516 + 0.513177i 0.0717003 + 0.0523759i
9797 −11.0877 + 11.0877i −1.12578 + 1.12578i −0.134927 + 0.990856i 0.543080π0.543080\pi
−0.990856 + 0.134927i 0.956920π0.956920\pi
9898 −5.74097 + 4.63163i −0.579925 + 0.467865i
9999 0.163868 + 0.540199i 0.0164693 + 0.0542920i
100100 8.71317 + 9.00984i 0.871317 + 0.900984i
101101 0.150952 + 1.53264i 0.0150203 + 0.152504i 0.999769 0.0214772i 0.00683695π-0.00683695\pi
−0.984749 + 0.173981i 0.944337π0.944337\pi
102102 −0.237378 + 0.348904i −0.0235039 + 0.0345466i
103103 −2.60627 13.1026i −0.256804 1.29104i −0.866808 0.498642i 0.833832π-0.833832\pi
0.610004 0.792398i 0.291168π-0.291168\pi
104104 1.36853 + 0.0343664i 0.134195 + 0.00336991i
105105 0.676281 + 0.134521i 0.0659983 + 0.0131279i
106106 15.2161 + 0.127345i 1.47792 + 0.0123689i
107107 2.08456 + 3.89993i 0.201522 + 0.377021i 0.962300 0.271992i 0.0876823π-0.0876823\pi
−0.760778 + 0.649012i 0.775182π0.775182\pi
108108 −1.14223 1.44030i −0.109911 0.138593i
109109 −0.181097 + 1.83871i −0.0173459 + 0.176116i −0.999954 0.00957465i 0.996952π-0.996952\pi
0.982608 + 0.185691i 0.0594522π0.0594522\pi
110110 0.691162 + 0.576969i 0.0658997 + 0.0550118i
111111 −1.18901 0.492504i −0.112856 0.0467464i
112112 −4.53927 + 2.81798i −0.428921 + 0.266274i
113113 3.84674 1.59337i 0.361871 0.149892i −0.194337 0.980935i 0.562256π-0.562256\pi
0.556208 + 0.831043i 0.312256π0.312256\pi
114114 −1.03179 0.322444i −0.0966361 0.0301997i
115115 14.3019 11.7372i 1.33366 1.09450i
116116 −12.9075 10.9595i −1.19843 1.01757i
117117 −1.37852 0.418170i −0.127444 0.0386599i
118118 −7.74821 + 18.2718i −0.713280 + 1.68206i
119119 −1.43982 2.15484i −0.131988 0.197534i
120120 −1.38616 0.458791i −0.126538 0.0418817i
121121 −9.11626 6.09129i −0.828751 0.553753i
122122 −0.998278 0.207270i −0.0903798 0.0187653i
123123 −0.290145 + 0.353543i −0.0261615 + 0.0318779i
124124 −1.97568 + 9.13092i −0.177421 + 0.819981i
125125 −3.75040 2.00463i −0.335446 0.179300i
126126 5.39364 1.58697i 0.480504 0.141379i
127127 −8.79384 −0.780328 −0.390164 0.920745i 0.627582π-0.627582\pi
−0.390164 + 0.920745i 0.627582π0.627582\pi
128128 10.2729 4.73991i 0.908008 0.418953i
129129 1.45879 0.128439
130130 −2.20411 + 0.648517i −0.193313 + 0.0568787i
131131 12.3982 + 6.62696i 1.08323 + 0.579000i 0.913644 0.406515i 0.133256π-0.133256\pi
0.169589 + 0.985515i 0.445756π0.445756\pi
132132 −0.0570188 0.0123373i −0.00496285 0.00107382i
133133 4.21157 5.13181i 0.365189 0.444985i
134134 0.167517 + 0.0347811i 0.0144713 + 0.00300463i
135135 2.56521 + 1.71402i 0.220778 + 0.147519i
136136 2.46464 + 4.90326i 0.211341 + 0.420451i
137137 5.95510 + 8.91243i 0.508778 + 0.761440i 0.993574 0.113187i 0.0361060π-0.0361060\pi
−0.484796 + 0.874628i 0.661106π0.661106\pi
138138 −0.468026 + 1.10370i −0.0398410 + 0.0939530i
139139 −0.316667 0.0960600i −0.0268594 0.00814770i 0.276826 0.960920i 0.410717π-0.410717\pi
−0.303686 + 0.952772i 0.598217π0.598217\pi
140140 5.80379 6.83537i 0.490510 0.577694i
141141 1.10954 0.910573i 0.0934398 0.0766840i
142142 −21.4148 6.69232i −1.79709 0.561607i
143143 −0.0848098 + 0.0351294i −0.00709215 + 0.00293766i
144144 −11.7478 + 1.93052i −0.978986 + 0.160876i
145145 26.2551 + 10.8752i 2.18037 + 0.903137i
146146 2.52565 + 2.10836i 0.209024 + 0.174489i
147147 −0.0786262 + 0.798306i −0.00648498 + 0.0658431i
148148 −13.1133 + 10.3994i −1.07791 + 0.854827i
149149 0.739789 + 1.38405i 0.0606059 + 0.113386i 0.910400 0.413729i 0.135774π-0.135774\pi
−0.849794 + 0.527115i 0.823274π0.823274\pi
150150 1.36299 + 0.0114070i 0.111287 + 0.000931375i
151151 −12.0809 2.40303i −0.983126 0.195556i −0.322745 0.946486i 0.604606π-0.604606\pi
−0.660382 + 0.750930i 0.729606π0.729606\pi
152152 −10.1868 + 9.68770i −0.826257 + 0.785776i
153153 −1.12662 5.66388i −0.0910815 0.457898i
154154 0.201531 0.296216i 0.0162399 0.0238698i
155155 −1.53683 15.6036i −0.123441 1.25332i
156156 0.107016 0.103492i 0.00856811 0.00828599i
157157 2.19799 + 7.24581i 0.175419 + 0.578278i 0.999923 + 0.0124222i 0.00395422π0.00395422\pi
−0.824504 + 0.565856i 0.808546π0.808546\pi
158158 −8.95659 + 7.22590i −0.712548 + 0.574861i
159159 1.17011 1.17011i 0.0927960 0.0927960i
160160 −13.9764 + 12.8531i −1.10493 + 1.01612i
161161 −5.20598 5.20598i −0.410289 0.410289i
162162 12.3572 + 1.32159i 0.970873 + 0.103834i
163163 −15.2055 + 4.61255i −1.19099 + 0.361283i −0.822726 0.568439i 0.807548π-0.807548\pi
−0.368264 + 0.929721i 0.620048π0.620048\pi
164164 2.18379 + 5.53227i 0.170526 + 0.431998i
165165 0.0974383 0.00959683i 0.00758556 0.000747113i
166166 −3.75782 19.7544i −0.291663 1.53324i
167167 14.9692 2.97756i 1.15835 0.230410i 0.421733 0.906720i 0.361422π-0.361422\pi
0.736618 + 0.676310i 0.236422π0.236422\pi
168168 −0.127623 + 0.566837i −0.00984632 + 0.0437324i
169169 −2.49047 + 12.5205i −0.191575 + 0.963112i
170170 −6.45794 6.56695i −0.495301 0.503662i
171171 13.0463 6.97337i 0.997673 0.533267i
172172 9.22152 16.5787i 0.703134 1.26411i
173173 −15.3857 1.51536i −1.16975 0.115210i −0.505572 0.862784i 0.668719π-0.668719\pi
−0.664179 + 0.747574i 0.731219π0.731219\pi
174174 −1.83398 + 0.165147i −0.139034 + 0.0125197i
175175 −3.20336 + 7.73360i −0.242151 + 0.584605i
176176 −0.500645 + 0.570012i −0.0377375 + 0.0429663i
177177 0.825948 + 1.99401i 0.0620820 + 0.149879i
178178 1.05341 + 2.01109i 0.0789561 + 0.150737i
179179 −8.70051 10.6016i −0.650307 0.792401i 0.338601 0.940930i 0.390046π-0.390046\pi
−0.988908 + 0.148529i 0.952546π0.952546\pi
180180 17.7768 9.12270i 1.32500 0.679966i
181181 2.43393 8.02359i 0.180913 0.596389i −0.818837 0.574026i 0.805381π-0.805381\pi
0.999750 0.0223633i 0.00711904π-0.00711904\pi
182182 0.342794 + 0.847571i 0.0254096 + 0.0628261i
183183 −0.0921905 + 0.0615997i −0.00681492 + 0.00455358i
184184 9.58462 + 12.2958i 0.706588 + 0.906460i
185185 15.6053 23.3550i 1.14733 1.71710i
186186 0.557344 + 0.849428i 0.0408664 + 0.0622831i
187187 −0.284464 0.233454i −0.0208021 0.0170718i
188188 −3.33461 18.3656i −0.243201 1.33945i
189189 0.578727 1.08272i 0.0420962 0.0787564i
190190 11.2956 20.7137i 0.819468 1.50273i
191191 5.63943i 0.408055i 0.978965 + 0.204027i 0.0654032π0.0654032\pi
−0.978965 + 0.204027i 0.934597π0.934597\pi
192192 0.415796 1.15796i 0.0300075 0.0835686i
193193 2.21104i 0.159154i 0.996829 + 0.0795769i 0.0253569π0.0253569\pi
−0.996829 + 0.0795769i 0.974643π0.974643\pi
194194 19.4687 + 10.6167i 1.39777 + 0.762234i
195195 −0.117780 + 0.220351i −0.00843442 + 0.0157797i
196196 8.57547 + 5.93993i 0.612533 + 0.424281i
197197 −6.53350 5.36190i −0.465493 0.382020i 0.372208 0.928149i 0.378601π-0.378601\pi
−0.837701 + 0.546129i 0.816101π0.816101\pi
198198 0.667478 0.437959i 0.0474356 0.0311244i
199199 −7.32240 + 10.9587i −0.519071 + 0.776845i −0.994702 0.102800i 0.967220π-0.967220\pi
0.475631 + 0.879645i 0.342220π0.342220\pi
200200 8.74555 15.4178i 0.618404 1.09020i
201201 0.0154701 0.0103368i 0.00109118 0.000729103i
202202 2.01909 0.816604i 0.142062 0.0574561i
203203 3.28271 10.8216i 0.230401 0.759531i
204204 0.568118 + 0.182775i 0.0397762 + 0.0127968i
205205 −6.33255 7.71624i −0.442285 0.538926i
206206 −16.7360 + 8.76631i −1.16605 + 0.610778i
207207 −6.27810 15.1567i −0.436358 1.05346i
208208 −0.499670 1.87041i −0.0346459 0.129689i
209209 0.360743 0.870910i 0.0249531 0.0602421i
210210 −0.0874559 0.971214i −0.00603503 0.0670201i
211211 −5.77547 0.568835i −0.397600 0.0391602i −0.102758 0.994706i 0.532767π-0.532767\pi
−0.294842 + 0.955546i 0.595267π0.595267\pi
212212 −5.90127 20.6947i −0.405301 1.42131i
213213 −2.15180 + 1.15016i −0.147439 + 0.0788077i
214214 4.45894 4.38492i 0.304807 0.299747i
215215 −6.21144 + 31.2270i −0.423617 + 2.12967i
216216 −1.49811 + 2.12461i −0.101934 + 0.144562i
217217 −6.11937 + 1.21722i −0.415410 + 0.0826302i
218218 2.56687 0.488288i 0.173851 0.0330710i
219219 0.356060 0.0350688i 0.0240603 0.00236973i
220220 0.506876 1.16802i 0.0341736 0.0787479i
221221 0.898642 0.272600i 0.0604492 0.0183371i
222222 −0.193549 + 1.80974i −0.0129901 + 0.121462i
223223 1.95160 + 1.95160i 0.130689 + 0.130689i 0.769425 0.638737i 0.220543π-0.220543\pi
−0.638737 + 0.769425i 0.720543π0.720543\pi
224224 5.63518 + 5.03357i 0.376516 + 0.336319i
225225 −13.1893 + 13.1893i −0.879287 + 0.879287i
226226 −3.69730 4.58285i −0.245941 0.304847i
227227 4.38810 + 14.4656i 0.291248 + 0.960117i 0.973440 + 0.228944i 0.0735271π0.0735271\pi
−0.682191 + 0.731174i 0.738973π0.738973\pi
228228 −0.0255870 + 1.52855i −0.00169454 + 0.101231i
229229 0.0144057 + 0.146264i 0.000951955 + 0.00966536i 0.995649 0.0931833i 0.0297043π-0.0297043\pi
−0.994697 + 0.102849i 0.967204π0.967204\pi
230230 −21.6331 14.7181i −1.42644 0.970483i
231231 −0.00760102 0.0382129i −0.000500111 0.00251423i
232232 −9.71641 + 21.8866i −0.637913 + 1.43693i
233233 −20.2728 4.03251i −1.32811 0.264178i −0.520486 0.853870i 0.674249π-0.674249\pi
−0.807628 + 0.589692i 0.799249π0.799249\pi
234234 −0.0170493 + 2.03718i −0.00111455 + 0.133174i
235235 14.7675 + 27.6280i 0.963325 + 1.80225i
236236 27.8824 + 3.21822i 1.81499 + 0.209488i
237237 −0.122666 + 1.24545i −0.00796803 + 0.0809008i
238238 −2.34874 + 2.81359i −0.152246 + 0.182378i
239239 −12.4323 5.14962i −0.804177 0.333101i −0.0575490 0.998343i 0.518329π-0.518329\pi
−0.746628 + 0.665242i 0.768329π0.768329\pi
240240 −0.0691112 + 2.06375i −0.00446111 + 0.133215i
241241 16.5636 6.86086i 1.06695 0.441947i 0.221039 0.975265i 0.429055π-0.429055\pi
0.845915 + 0.533318i 0.179055π0.179055\pi
242242 −4.62502 + 14.7996i −0.297308 + 0.951356i
243243 3.17619 2.60664i 0.203753 0.167216i
244244 0.117293 + 1.43711i 0.00750892 + 0.0920014i
245245 −16.7538 5.08222i −1.07036 0.324691i
246246 0.595475 + 0.252513i 0.0379661 + 0.0160996i
247247 1.33646 + 2.00016i 0.0850371 + 0.127267i
248248 13.1766 0.964509i 0.836717 0.0612464i
249249 −1.81825 1.21492i −0.115227 0.0769921i
250250 −1.22259 + 5.88841i −0.0773236 + 0.372416i
251251 −10.4175 + 12.6937i −0.657546 + 0.801222i −0.989875 0.141941i 0.954666π-0.954666\pi
0.332329 + 0.943164i 0.392166π0.392166\pi
252252 −4.30612 6.68409i −0.271260 0.421058i
253253 −0.921976 0.492807i −0.0579642 0.0309825i
254254 3.51037 + 11.9307i 0.220260 + 0.748596i
255255 −1.00161 −0.0627231
256256 −10.5315 12.0453i −0.658216 0.752829i
257257 4.49360 0.280303 0.140152 0.990130i 0.455241π-0.455241\pi
0.140152 + 0.990130i 0.455241π0.455241\pi
258258 −0.582326 1.97915i −0.0362541 0.123216i
259259 −9.85766 5.26903i −0.612525 0.327402i
260260 1.75969 + 2.73145i 0.109132 + 0.169398i
261261 15.9859 19.4789i 0.989504 1.20571i
262262 4.04168 19.4660i 0.249696 1.20262i
263263 14.2440 + 9.51756i 0.878325 + 0.586878i 0.910916 0.412591i 0.135376π-0.135376\pi
−0.0325916 + 0.999469i 0.510376π0.510376\pi
264264 0.00602296 + 0.0822826i 0.000370687 + 0.00506415i
265265 20.0653 + 30.0299i 1.23260 + 1.84472i
266266 −8.64355 3.66532i −0.529970 0.224735i
267267 0.236258 + 0.0716680i 0.0144587 + 0.00438601i
268268 −0.0196825 0.241156i −0.00120230 0.0147309i
269269 11.4987 9.43672i 0.701087 0.575367i −0.214870 0.976643i 0.568933π-0.568933\pi
0.915957 + 0.401275i 0.131433π0.131433\pi
270270 1.30143 4.16445i 0.0792024 0.253440i
271271 −11.5173 + 4.77061i −0.699624 + 0.289794i −0.704003 0.710197i 0.748606π-0.748606\pi
0.00437943 + 0.999990i 0.498606π0.498606\pi
272272 5.66844 5.30109i 0.343700 0.321426i
273273 0.0918569 + 0.0380484i 0.00555943 + 0.00230279i
274274 9.71437 11.6370i 0.586866 0.703018i
275275 −0.116504 + 1.18288i −0.00702545 + 0.0713306i
276276 1.68422 + 0.194395i 0.101378 + 0.0117012i
277277 5.09008 + 9.52286i 0.305833 + 0.572173i 0.987146 0.159819i 0.0510909π-0.0510909\pi
−0.681313 + 0.731992i 0.738591π0.738591\pi
278278 −0.00391649 + 0.467970i −0.000234895 + 0.0280670i
279279 −13.6357 2.71231i −0.816348 0.162382i
280280 −11.5904 5.14547i −0.692657 0.307501i
281281 5.00511 + 25.1624i 0.298580 + 1.50106i 0.780671 + 0.624942i 0.214877π0.214877\pi
−0.482091 + 0.876121i 0.660123π0.660123\pi
282282 −1.67829 1.14183i −0.0999407 0.0679949i
283283 −1.47858 15.0123i −0.0878928 0.892390i −0.933498 0.358582i 0.883260π-0.883260\pi
0.845606 0.533808i 0.179240π-0.179240\pi
284284 −0.531058 + 31.7251i −0.0315125 + 1.88254i
285285 −0.744796 2.45526i −0.0441179 0.145437i
286286 0.0815150 + 0.101039i 0.00482008 + 0.00597455i
287287 −2.80877 + 2.80877i −0.165796 + 0.165796i
288288 7.30869 + 15.1677i 0.430669 + 0.893766i
289289 −9.35887 9.35887i −0.550522 0.550522i
290290 4.27385 39.9617i 0.250969 2.34663i
291291 2.30770 0.700032i 0.135280 0.0410366i
292292 1.85223 4.26819i 0.108394 0.249777i
293293 0.107888 0.0106261i 0.00630290 0.000620782i −0.0948652 0.995490i 0.530242π-0.530242\pi
0.101168 + 0.994869i 0.467742π0.467742\pi
294294 1.11445 0.211999i 0.0649962 0.0123640i
295295 −46.2009 + 9.18994i −2.68992 + 0.535059i
296296 19.3436 + 13.6396i 1.12432 + 0.792785i
297297 0.0340091 0.170975i 0.00197341 0.00992099i
298298 1.58244 1.55617i 0.0916680 0.0901464i
299299 2.35277 1.25758i 0.136064 0.0727279i
300300 −0.528607 1.85373i −0.0305192 0.107025i
301301 12.6087 + 1.24185i 0.726754 + 0.0715790i
302302 1.56228 + 17.3494i 0.0898993 + 0.998348i
303303 0.0906390 0.218822i 0.00520707 0.0125710i
304304 17.2098 + 9.95329i 0.987048 + 0.570861i
305305 −0.926069 2.23573i −0.0530266 0.128017i
306306 −7.23450 + 3.78942i −0.413569 + 0.216627i
307307 11.1702 + 13.6110i 0.637518 + 0.776818i 0.987103 0.160087i 0.0511773π-0.0511773\pi
−0.349585 + 0.936905i 0.613677π0.613677\pi
308308 −0.482326 0.155174i −0.0274831 0.00884185i
309309 −0.596413 + 1.96611i −0.0339287 + 0.111848i
310310 −20.5561 + 8.31376i −1.16751 + 0.472190i
311311 18.5250 12.3780i 1.05045 0.701891i 0.0945355 0.995521i 0.469863π-0.469863\pi
0.955919 + 0.293630i 0.0948634π0.0948634\pi
312312 −0.183127 0.103877i −0.0103675 0.00588085i
313313 8.47932 12.6902i 0.479279 0.717292i −0.510503 0.859876i 0.670541π-0.670541\pi
0.989783 + 0.142583i 0.0455409π0.0455409\pi
314314 8.95303 5.87444i 0.505249 0.331514i
315315 10.3154 + 8.46559i 0.581204 + 0.476982i
316316 13.3788 + 9.26700i 0.752614 + 0.521309i
317317 0.174406 0.326290i 0.00979561 0.0183263i −0.876976 0.480534i 0.840443π-0.840443\pi
0.886771 + 0.462208i 0.152943π0.152943\pi
318318 −2.05459 1.12041i −0.115216 0.0628294i
319319 1.60576i 0.0899054i
320320 23.0170 + 13.8311i 1.28669 + 0.773183i
321321 0.680089i 0.0379589i
322322 −4.98484 + 9.14113i −0.277794 + 0.509415i
323323 −4.54586 + 8.50470i −0.252938 + 0.473214i
324324 −3.13980 17.2926i −0.174433 0.960702i
325325 −2.34468 1.92423i −0.130060 0.106737i
326326 12.3277 + 18.7882i 0.682767 + 1.04058i
327327 0.157865 0.236262i 0.00872995 0.0130653i
328328 6.63393 5.17116i 0.366297 0.285530i
329329 10.3652 6.92579i 0.571451 0.381831i
330330 −0.0519159 0.128364i −0.00285788 0.00706622i
331331 −2.83863 + 9.35771i −0.156025 + 0.514346i −0.999748 0.0224324i 0.992859π-0.992859\pi
0.843723 + 0.536779i 0.180359π0.180359\pi
332332 −25.3009 + 12.9839i −1.38857 + 0.712585i
333333 −15.8006 19.2531i −0.865868 1.05506i
334334 −10.0151 19.1202i −0.548004 1.04621i
335335 0.155400 + 0.375169i 0.00849042 + 0.0204977i
336336 0.819977 0.0531260i 0.0447334 0.00289826i
337337 1.79808 4.34094i 0.0979475 0.236466i −0.867309 0.497770i 0.834152π-0.834152\pi
0.965257 + 0.261304i 0.0841524π0.0841524\pi
338338 17.9807 1.61913i 0.978023 0.0880691i
339339 −0.637265 0.0627651i −0.0346115 0.00340893i
340340 −6.33151 + 11.3829i −0.343374 + 0.617327i
341341 −0.781331 + 0.417630i −0.0423114 + 0.0226159i
342342 −14.6687 14.9163i −0.793192 0.806580i
343343 −3.18327 + 16.0034i −0.171880 + 0.864100i
344344 −26.1735 5.89293i −1.41118 0.317726i
345345 −2.79074 + 0.555113i −0.150248 + 0.0298863i
346346 4.08583 + 21.4787i 0.219656 + 1.15470i
347347 20.0724 1.97696i 1.07754 0.106129i 0.456360 0.889795i 0.349153π-0.349153\pi
0.621182 + 0.783666i 0.286653π0.286653\pi
348348 0.956154 + 2.42225i 0.0512552 + 0.129846i
349349 27.5367 8.35317i 1.47401 0.447135i 0.551847 0.833946i 0.313923π-0.313923\pi
0.922159 + 0.386811i 0.126423π0.126423\pi
350350 11.7710 + 1.25889i 0.629184 + 0.0672904i
351351 0.314561 + 0.314561i 0.0167900 + 0.0167900i
352352 0.973189 + 0.451688i 0.0518712 + 0.0240751i
353353 12.0137 12.0137i 0.639425 0.639425i −0.310989 0.950414i 0.600660π-0.600660\pi
0.950414 + 0.310989i 0.100660π0.100660\pi
354354 2.37559 1.91655i 0.126261 0.101863i
355355 −15.4582 50.9590i −0.820438 2.70462i
356356 2.30795 2.23196i 0.122321 0.118293i
357357 0.0390670 + 0.396654i 0.00206764 + 0.0209931i
358358 −10.9102 + 16.0360i −0.576619 + 0.847531i
359359 −6.61583 33.2600i −0.349170 1.75540i −0.612290 0.790633i 0.709752π-0.709752\pi
0.263120 0.964763i 0.415248π-0.415248\pi
360360 −19.4730 20.4763i −1.02632 1.07919i
361361 −5.59318 1.11255i −0.294378 0.0585554i
362362 −11.8572 0.0992344i −0.623203 0.00521565i
363363 0.794868 + 1.48709i 0.0417198 + 0.0780522i
364364 1.01307 0.803408i 0.0530991 0.0421100i
365365 −0.765394 + 7.77117i −0.0400625 + 0.406762i
366366 0.120374 + 0.100486i 0.00629203 + 0.00525247i
367367 22.3629 + 9.26301i 1.16733 + 0.483525i 0.880310 0.474399i 0.157334π-0.157334\pi
0.287023 + 0.957924i 0.407334π0.407334\pi
368368 12.8558 17.9118i 0.670154 0.933718i
369369 −8.17743 + 3.38720i −0.425700 + 0.176331i
370370 −37.9153 11.8489i −1.97112 0.615994i
371371 11.1097 9.11750i 0.576787 0.473357i
372372 0.929941 1.09523i 0.0482152 0.0567850i
373373 −31.7137 9.62025i −1.64207 0.498118i −0.671923 0.740621i 0.734532π-0.734532\pi
−0.970151 + 0.242503i 0.922032π0.922032\pi
374374 −0.203174 + 0.479125i −0.0105059 + 0.0247750i
375375 0.363350 + 0.543792i 0.0187633 + 0.0280813i
376376 −23.5856 + 11.8553i −1.21633 + 0.611392i
377377 3.40712 + 2.27657i 0.175476 + 0.117249i
378378 −1.69995 0.352956i −0.0874362 0.0181541i
379379 −3.38631 + 4.12623i −0.173943 + 0.211950i −0.852683 0.522428i 0.825026π-0.825026\pi
0.678740 + 0.734379i 0.262526π0.262526\pi
380380 −32.6114 7.05620i −1.67293 0.361976i
381381 1.19274 + 0.637535i 0.0611061 + 0.0326619i
382382 7.65105 2.25117i 0.391462 0.115180i
383383 13.1180 0.670298 0.335149 0.942165i 0.391213π-0.391213\pi
0.335149 + 0.942165i 0.391213π0.391213\pi
384384 −1.73699 0.101874i −0.0886405 0.00519871i
385385 0.850355 0.0433381
386386 2.99973 0.882611i 0.152682 0.0449237i
387387 24.8982 + 13.3084i 1.26565 + 0.676502i
388388 6.63211 30.6514i 0.336694 1.55609i
389389 −0.145657 + 0.177483i −0.00738509 + 0.00899876i −0.776690 0.629883i 0.783103π-0.783103\pi
0.769305 + 0.638882i 0.220603π0.220603\pi
390390 0.345968 + 0.0718324i 0.0175188 + 0.00363737i
391391 8.89217 + 5.94156i 0.449697 + 0.300478i
392392 4.63555 14.0055i 0.234130 0.707385i
393393 −1.20117 1.79768i −0.0605911 0.0906810i
394394 −4.66646 + 11.0044i −0.235093 + 0.554395i
395395 −26.1380 7.92887i −1.31515 0.398945i
396396 −0.860629 0.730745i −0.0432482 0.0367213i
397397 14.6428 12.0170i 0.734899 0.603116i −0.190688 0.981651i 0.561072π-0.561072\pi
0.925587 + 0.378535i 0.123572π0.123572\pi
398398 17.7908 + 5.55978i 0.891771 + 0.278687i
399399 −0.943277 + 0.390718i −0.0472229 + 0.0195604i
400400 −24.4085 5.71059i −1.22043 0.285530i
401401 −31.8230 13.1815i −1.58917 0.658254i −0.599334 0.800499i 0.704568π-0.704568\pi
−0.989831 + 0.142245i 0.954568π0.954568\pi
402402 −0.0201995 0.0168621i −0.00100746 0.000841007i
403403 0.221599 2.24993i 0.0110386 0.112077i
404404 −1.91388 2.41333i −0.0952191 0.120068i
405405 13.9048 + 26.0140i 0.690933 + 1.29265i
406406 −15.9922 0.133840i −0.793680 0.00664238i
407407 −1.55665 0.309637i −0.0771602 0.0153481i
408408 0.0211877 0.843729i 0.00104895 0.0417708i
409409 5.18514 + 26.0675i 0.256389 + 1.28895i 0.867511 + 0.497418i 0.165718π0.165718\pi
−0.611122 + 0.791536i 0.709282π0.709282\pi
410410 −7.94081 + 11.6716i −0.392169 + 0.576420i
411411 −0.161581 1.64056i −0.00797020 0.0809228i
412412 18.5741 + 19.2065i 0.915079 + 0.946236i
413413 5.44141 + 17.9379i 0.267754 + 0.882667i
414414 −18.0570 + 14.5678i −0.887455 + 0.715970i
415415 33.7486 33.7486i 1.65665 1.65665i
416416 −2.33813 + 1.42454i −0.114636 + 0.0698440i
417417 0.0359867 + 0.0359867i 0.00176228 + 0.00176228i
418418 −1.32557 0.141768i −0.0648358 0.00693410i
419419 −21.7315 + 6.59218i −1.06165 + 0.322049i −0.772356 0.635190i 0.780922π-0.780922\pi
−0.289298 + 0.957239i 0.593422π0.593422\pi
420420 −1.28274 + 0.506345i −0.0625913 + 0.0247071i
421421 −29.7632 + 2.93141i −1.45057 + 0.142868i −0.792399 0.610003i 0.791168π-0.791168\pi
−0.658168 + 0.752871i 0.728668π0.728668\pi
422422 1.53374 + 8.06269i 0.0746612 + 0.392486i
423423 27.2443 5.41922i 1.32466 0.263492i
424424 −25.7209 + 16.2673i −1.24912 + 0.790009i
425425 2.37217 11.9257i 0.115067 0.578482i
426426 2.41940 + 2.46023i 0.117220 + 0.119199i
427427 −0.849266 + 0.453942i −0.0410989 + 0.0219678i
428428 −7.72899 4.29908i −0.373595 0.207804i
429429 0.0140499 + 0.00138379i 0.000678335 + 6.68101e-5i
430430 44.8454 4.03824i 2.16264 0.194741i
431431 5.85086 14.1252i 0.281826 0.680388i −0.718052 0.695989i 0.754966π-0.754966\pi
0.999878 + 0.0156011i 0.00496618π0.00496618\pi
432432 3.48050 + 1.18438i 0.167456 + 0.0569837i
433433 −11.6465 28.1171i −0.559694 1.35122i −0.910009 0.414589i 0.863925π-0.863925\pi
0.350315 0.936632i 0.386075π-0.386075\pi
434434 4.09417 + 7.81629i 0.196526 + 0.375194i
435435 −2.77265 3.37848i −0.132938 0.161986i
436436 −1.68712 3.28758i −0.0807984 0.157446i
437437 −7.95246 + 26.2158i −0.380418 + 1.25407i
438438 −0.189712 0.469069i −0.00906477 0.0224130i
439439 1.85148 1.23712i 0.0883664 0.0590445i −0.510602 0.859817i 0.670577π-0.670577\pi
0.598968 + 0.800773i 0.295577π0.295577\pi
440440 −1.78700 0.221427i −0.0851918 0.0105561i
441441 −8.62481 + 12.9079i −0.410705 + 0.614664i
442442 −0.728563 1.11038i −0.0346542 0.0528152i
443443 −16.0609 13.1808i −0.763075 0.626239i 0.170197 0.985410i 0.445560π-0.445560\pi
−0.933272 + 0.359171i 0.883060π0.883060\pi
444444 2.53254 0.459830i 0.120189 0.0218225i
445445 −2.54011 + 4.75221i −0.120413 + 0.225276i
446446 1.86870 3.42679i 0.0884854 0.162263i
447447 0.241357i 0.0114158i
448448 4.57960 9.65460i 0.216366 0.456137i
449449 12.0240i 0.567447i −0.958906 0.283724i 0.908430π-0.908430\pi
0.958906 0.283724i 0.0915698π-0.0915698\pi
450450 23.1590 + 12.6291i 1.09173 + 0.595339i
451451 −0.265882 + 0.497431i −0.0125199 + 0.0234231i
452452 −4.74168 + 6.84555i −0.223030 + 0.321988i
453453 1.46436 + 1.20177i 0.0688016 + 0.0564640i
454454 17.8739 11.7278i 0.838866 0.550414i
455455 −1.20559 + 1.80429i −0.0565189 + 0.0845865i
456456 2.08401 0.575460i 0.0975927 0.0269484i
457457 9.55723 6.38594i 0.447068 0.298722i −0.311582 0.950219i 0.600859π-0.600859\pi
0.758651 + 0.651498i 0.225859π0.225859\pi
458458 0.192686 0.0779304i 0.00900363 0.00364145i
459459 −0.517672 + 1.70654i −0.0241629 + 0.0796543i
460460 −11.3326 + 35.2249i −0.528383 + 1.64237i
461461 8.79720 + 10.7194i 0.409727 + 0.499253i 0.936459 0.350778i 0.114083π-0.114083\pi
−0.526732 + 0.850031i 0.676583π0.676583\pi
462462 −0.0488095 + 0.0255664i −0.00227082 + 0.00118945i
463463 −3.77259 9.10783i −0.175327 0.423277i 0.811649 0.584146i 0.198570π-0.198570\pi
−0.986976 + 0.160869i 0.948570π0.948570\pi
464464 33.5723 + 4.44552i 1.55856 + 0.206378i
465465 −0.922785 + 2.22780i −0.0427931 + 0.103312i
466466 2.62165 + 29.1139i 0.121446 + 1.34868i
467467 −29.6180 2.91712i −1.37056 0.134988i −0.614202 0.789149i 0.710522π-0.710522\pi
−0.756356 + 0.654161i 0.773022π0.773022\pi
468468 2.77066 0.790079i 0.128074 0.0365214i
469469 0.142512 0.0761744i 0.00658060 0.00351741i
470470 31.5882 31.0638i 1.45705 1.43287i
471471 0.227183 1.14213i 0.0104680 0.0526264i
472472 −6.76406 39.1129i −0.311341 1.80032i
473473 1.76447 0.350974i 0.0811303 0.0161378i
474474 1.73868 0.330743i 0.0798602 0.0151915i
475475 30.9977 3.05301i 1.42227 0.140082i
476476 4.75480 + 2.06340i 0.217936 + 0.0945759i
477477 30.6459 9.29634i 1.40318 0.425650i
478478 −2.02375 + 18.9226i −0.0925640 + 0.865499i
479479 −1.25772 1.25772i −0.0574668 0.0574668i 0.677789 0.735256i 0.262938π-0.262938\pi
−0.735256 + 0.677789i 0.762938π0.762938\pi
480480 2.82749 0.730054i 0.129057 0.0333223i
481481 2.86393 2.86393i 0.130584 0.130584i
482482 −15.9201 19.7332i −0.725141 0.898821i
483483 0.328685 + 1.08353i 0.0149557 + 0.0493023i
484484 21.9250 + 0.367010i 0.996590 + 0.0166823i
485485 5.15893 + 52.3795i 0.234255 + 2.37843i
486486 −4.80433 3.26863i −0.217929 0.148268i
487487 2.68056 + 13.4761i 0.121468 + 0.610661i 0.992782 + 0.119935i 0.0382685π0.0382685\pi
−0.871314 + 0.490726i 0.836732π0.836732\pi
488488 1.90291 0.732804i 0.0861408 0.0331725i
489489 2.39679 + 0.476750i 0.108386 + 0.0215594i
490490 −0.207209 + 24.7588i −0.00936073 + 1.11849i
491491 14.1771 + 26.5235i 0.639804 + 1.19699i 0.967659 + 0.252261i 0.0811740π0.0811740\pi
−0.327856 + 0.944728i 0.606326π0.606326\pi
492492 0.104881 0.908683i 0.00472841 0.0409666i
493493 −1.61011 + 16.3477i −0.0725155 + 0.736263i
494494 2.18013 2.61162i 0.0980888 0.117502i
495495 1.75060 + 0.725122i 0.0786836 + 0.0325918i
496496 −6.56847 17.4918i −0.294933 0.785406i
497497 −19.5777 + 8.10935i −0.878180 + 0.363754i
498498 −0.922466 + 2.95180i −0.0413367 + 0.132274i
499499 −3.93306 + 3.22778i −0.176068 + 0.144495i −0.718300 0.695734i 0.755079π-0.755079\pi
0.542232 + 0.840229i 0.317579π0.317579\pi
500500 8.47689 0.691862i 0.379098 0.0309410i
501501 −2.24620 0.681376i −0.100353 0.0304416i
502502 21.3802 + 9.06632i 0.954244 + 0.404650i
503503 8.17711 + 12.2379i 0.364599 + 0.545661i 0.967733 0.251979i 0.0810814π-0.0810814\pi
−0.603134 + 0.797640i 0.706081π0.706081\pi
504504 −7.34941 + 8.51032i −0.327369 + 0.379080i
505505 4.29819 + 2.87196i 0.191267 + 0.127800i
506506 −0.300555 + 1.44757i −0.0133613 + 0.0643524i
507507 1.24550 1.51764i 0.0553145 0.0674009i
508508 14.7851 9.52507i 0.655984 0.422607i
509509 −14.7190 7.86746i −0.652407 0.348719i 0.111762 0.993735i 0.464351π-0.464351\pi
−0.764169 + 0.645016i 0.776851π0.776851\pi
510510 0.399826 + 1.35889i 0.0177046 + 0.0601725i
511511 3.10737 0.137462
512512 −12.1379 + 19.0964i −0.536424 + 0.843949i
513513 −4.56822 −0.201692
514514 −1.79378 6.09650i −0.0791200 0.268905i
515515 −39.5473 21.1385i −1.74266 0.931472i
516516 −2.45267 + 1.58009i −0.107973 + 0.0695596i
517517 1.12295 1.36832i 0.0493874 0.0601787i
518518 −3.21350 + 15.4773i −0.141193 + 0.680032i
519519 1.97696 + 1.32096i 0.0867789 + 0.0579838i
520520 3.00334 3.47774i 0.131705 0.152509i
521521 −5.06833 7.58529i −0.222047 0.332317i 0.703674 0.710523i 0.251541π-0.251541\pi
−0.925722 + 0.378205i 0.876541π0.876541\pi
522522 −32.8085 13.9125i −1.43599 0.608935i
523523 1.12932 + 0.342577i 0.0493819 + 0.0149798i 0.314879 0.949132i 0.398036π-0.398036\pi
−0.265497 + 0.964112i 0.585536π0.585536\pi
524524 −28.0231 + 2.28717i −1.22419 + 0.0999156i
525525 0.995153 0.816701i 0.0434320 0.0356438i
526526 7.22653 23.1242i 0.315092 1.00826i
527527 8.37321 3.46830i 0.364743 0.151081i
528528 0.109229 0.0410173i 0.00475359 0.00178505i
529529 6.81964 + 2.82479i 0.296506 + 0.122817i
530530 32.7319 39.2102i 1.42178 1.70318i
531531 −4.09412 + 41.5683i −0.177669 + 1.80391i
532532 −1.52239 + 13.1899i −0.0660041 + 0.571855i
533533 −0.678500 1.26938i −0.0293891 0.0549831i
534534 0.00292200 0.349141i 0.000126447 0.0151088i
535535 14.5581 + 2.89578i 0.629400 + 0.125195i
536536 −0.319321 + 0.122969i −0.0137926 + 0.00531146i
537537 0.411491 + 2.06870i 0.0177571 + 0.0892712i
538538 −17.3930 11.8333i −0.749864 0.510171i
539539 0.0969649 + 0.984501i 0.00417657 + 0.0424054i
540540 −6.16944 0.103273i −0.265490 0.00444414i
541541 5.23802 + 17.2674i 0.225200 + 0.742386i 0.994615 + 0.103636i 0.0330478π0.0330478\pi
−0.769415 + 0.638749i 0.779452π0.779452\pi
542542 11.0698 + 13.7212i 0.475490 + 0.589376i
543543 −0.911816 + 0.911816i −0.0391298 + 0.0391298i
544544 −9.45478 5.57430i −0.405370 0.238996i
545545 4.38527 + 4.38527i 0.187844 + 0.187844i
546546 0.0149526 0.139811i 0.000639913 0.00598337i
547547 0.760300 0.230635i 0.0325081 0.00986122i −0.273989 0.961733i 0.588343π-0.588343\pi
0.306497 + 0.951872i 0.400843π0.400843\pi
548548 −19.6658 8.53423i −0.840083 0.364564i
549549 −2.13545 + 0.210323i −0.0911386 + 0.00897637i
550550 1.65133 0.314128i 0.0704131 0.0133944i
551551 −41.2708 + 8.20926i −1.75819 + 0.349726i
552552 −0.408579 2.36259i −0.0173903 0.100559i
553553 −2.12048 + 10.6604i −0.0901718 + 0.453324i
554554 10.8878 10.7071i 0.462580 0.454902i
555555 −3.80980 + 2.03638i −0.161717 + 0.0864395i
556556 0.636462 0.181493i 0.0269920 0.00769702i
557557 −18.2234 1.79485i −0.772152 0.0760504i −0.295735 0.955270i 0.595565π-0.595565\pi
−0.476417 + 0.879220i 0.658065π0.658065\pi
558558 1.76335 + 19.5824i 0.0746487 + 0.828987i
559559 −1.75687 + 4.24146i −0.0743076 + 0.179395i
560560 −2.35419 + 17.7787i −0.0994828 + 0.751288i
561561 0.0216581 + 0.0522872i 0.000914405 + 0.00220757i
562562 32.1400 16.8349i 1.35574 0.710138i
563563 −9.14512 11.1434i −0.385421 0.469637i 0.543771 0.839233i 0.316996π-0.316996\pi
−0.929192 + 0.369597i 0.879496π0.879496\pi
564564 −0.879178 + 2.73275i −0.0370201 + 0.115069i
565565 4.05700 13.3741i 0.170679 0.562654i
566566 −19.7771 + 7.99869i −0.831293 + 0.336210i
567567 9.75964 6.52118i 0.409866 0.273864i
568568 43.2536 11.9437i 1.81488 0.501145i
569569 0.0300548 0.0449802i 0.00125996 0.00188567i −0.830839 0.556513i 0.812139π-0.812139\pi
0.832099 + 0.554627i 0.187139π0.187139\pi
570570 −3.03376 + 1.99057i −0.127070 + 0.0833760i
571571 19.2334 + 15.7845i 0.804893 + 0.660559i 0.944083 0.329707i 0.106950π-0.106950\pi
−0.139190 + 0.990266i 0.544450π0.544450\pi
572572 0.104541 0.150925i 0.00437106 0.00631049i
573573 0.408846 0.764898i 0.0170798 0.0319541i
574574 4.93189 + 2.68945i 0.205853 + 0.112256i
575575 34.5429i 1.44054i
576576 17.6606 15.9705i 0.735859 0.665436i
577577 8.94718i 0.372476i −0.982505 0.186238i 0.940370π-0.940370\pi
0.982505 0.186238i 0.0596295π-0.0596295\pi
578578 −8.96133 + 16.4332i −0.372742 + 0.683529i
579579 0.160295 0.299891i 0.00666164 0.0124631i
580580 −55.9223 + 10.1537i −2.32205 + 0.421610i
581581 −14.6814 12.0487i −0.609086 0.499864i
582582 −1.87093 2.85142i −0.0775527 0.118195i
583583 1.13378 1.69682i 0.0469563 0.0702751i
584584 −6.53005 0.809138i −0.270216 0.0334824i
585585 −4.02048 + 2.68640i −0.166226 + 0.111069i
586586 −0.0574838 0.142131i −0.00237463 0.00587138i
587587 7.89764 26.0350i 0.325971 1.07458i −0.628882 0.777501i 0.716487π-0.716487\pi
0.954853 0.297080i 0.0960128π-0.0960128\pi
588588 −0.732492 1.42736i −0.0302075 0.0588633i
589589 14.7283 + 17.9464i 0.606867 + 0.739470i
590590 30.9107 + 59.0126i 1.27258 + 2.42951i
591591 0.497438 + 1.20092i 0.0204618 + 0.0493993i
592592 10.7833 31.6883i 0.443189 1.30238i
593593 −1.82052 + 4.39513i −0.0747599 + 0.180486i −0.956841 0.290610i 0.906142π-0.906142\pi
0.882082 + 0.471097i 0.156142π0.156142\pi
594594 −0.245539 + 0.0221103i −0.0100746 + 0.000907198i
595595 −8.65716 0.852656i −0.354909 0.0349555i
596596 −2.74295 1.52570i −0.112355 0.0624952i
597597 1.78765 0.955519i 0.0731637 0.0391068i
598598 −2.64536 2.69001i −0.108177 0.110003i
599599 −2.80655 + 14.1095i −0.114672 + 0.576497i 0.880135 + 0.474723i 0.157452π0.157452\pi
−0.994808 + 0.101774i 0.967548π0.967548\pi
600600 −2.30395 + 1.45714i −0.0940584 + 0.0594876i
601601 −42.4056 + 8.43499i −1.72976 + 0.344070i −0.956880 0.290483i 0.906184π-0.906184\pi
−0.772879 + 0.634554i 0.781184π0.781184\pi
602602 −3.34838 17.6020i −0.136470 0.717406i
603603 0.358341 0.0352936i 0.0145928 0.00143726i
604604 22.9144 9.04518i 0.932375 0.368043i
605605 −35.2174 + 10.6831i −1.43179 + 0.434329i
606606 −0.333059 0.0356202i −0.0135296 0.00144697i
607607 −16.1357 16.1357i −0.654930 0.654930i 0.299246 0.954176i 0.403265π-0.403265\pi
−0.954176 + 0.299246i 0.903265π0.903265\pi
608608 6.63383 27.3218i 0.269037 1.10805i
609609 −1.22979 + 1.22979i −0.0498337 + 0.0498337i
610610 −2.66355 + 2.14887i −0.107844 + 0.0870053i
611611 1.31125 + 4.32263i 0.0530477 + 0.174875i
612612 8.02903 + 8.30241i 0.324554 + 0.335605i
613613 −0.498594 5.06231i −0.0201380 0.204465i −0.999989 0.00473379i 0.998493π-0.998493\pi
0.979851 0.199731i 0.0640068π-0.0640068\pi
614614 14.0071 20.5880i 0.565280 0.830864i
615615 0.299498 + 1.50568i 0.0120769 + 0.0607149i
616616 −0.0179882 + 0.716318i −0.000724764 + 0.0288613i
617617 −29.6709 5.90191i −1.19451 0.237602i −0.442506 0.896766i 0.645910π-0.645910\pi
−0.752000 + 0.659164i 0.770910π0.770910\pi
618618 2.90551 + 0.0243165i 0.116877 + 0.000978153i
619619 −8.63894 16.1623i −0.347228 0.649618i 0.646315 0.763071i 0.276309π-0.276309\pi
−0.993543 + 0.113452i 0.963809π0.963809\pi
620620 19.4850 + 24.5699i 0.782536 + 0.986749i
621621 −0.496571 + 5.04177i −0.0199267 + 0.202319i
622622 −24.1882 20.1918i −0.969857 0.809619i
623623 1.98103 + 0.820570i 0.0793683 + 0.0328754i
624624 −0.0678284 + 0.289916i −0.00271531 + 0.0116059i
625625 15.7617 6.52873i 0.630470 0.261149i
626626 −20.6017 6.43822i −0.823409 0.257323i
627627 −0.112068 + 0.0919718i −0.00447556 + 0.00367300i
628628 −11.5438 9.80164i −0.460648 0.391128i
629629 15.5372 + 4.71316i 0.619509 + 0.187926i
630630 7.36759 17.3742i 0.293532 0.692206i
631631 −18.9104 28.3014i −0.752812 1.12666i −0.987961 0.154703i 0.950558π-0.950558\pi
0.235149 0.971959i 0.424442π-0.424442\pi
632632 7.23200 21.8503i 0.287674 0.869157i
633633 0.742111 + 0.495863i 0.0294963 + 0.0197088i
634634 −0.512300 0.106367i −0.0203460 0.00422439i
635635 −18.7258 + 22.8174i −0.743110 + 0.905482i
636636 −0.699905 + 3.23473i −0.0277530 + 0.128265i
637637 −2.22640 1.19003i −0.0882130 0.0471508i
638638 −2.17855 + 0.640995i −0.0862495 + 0.0253772i
639639 −47.2190 −1.86796
640640 9.57673 36.7485i 0.378553 1.45261i
641641 11.0097 0.434858 0.217429 0.976076i 0.430233π-0.430233\pi
0.217429 + 0.976076i 0.430233π0.430233\pi
642642 −0.922681 + 0.271481i −0.0364153 + 0.0107145i
643643 42.0290 + 22.4650i 1.65746 + 0.885932i 0.989964 + 0.141321i 0.0451348π0.0451348\pi
0.667498 + 0.744611i 0.267365π0.267365\pi
644644 14.3917 + 3.11396i 0.567112 + 0.122707i
645645 3.10637 3.78513i 0.122313 0.149039i
646646 13.3530 + 2.77245i 0.525368 + 0.109081i
647647 29.4587 + 19.6837i 1.15814 + 0.773846i 0.977755 0.209750i 0.0672650π-0.0672650\pi
0.180387 + 0.983596i 0.442265π0.442265\pi
648648 −22.2077 + 11.1627i −0.872400 + 0.438514i
649649 1.47876 + 2.21313i 0.0580465 + 0.0868728i
650650 −1.67466 + 3.94917i −0.0656854 + 0.154899i
651651 0.918240 + 0.278545i 0.0359886 + 0.0109170i
652652 20.5690 24.2250i 0.805545 0.948724i
653653 3.90577 3.20538i 0.152844 0.125436i −0.554863 0.831942i 0.687229π-0.687229\pi
0.707708 + 0.706505i 0.249729π0.249729\pi
654654 −0.383555 0.119864i −0.0149982 0.00468707i
655655 43.5959 18.0580i 1.70343 0.705584i
656656 −9.66391 6.93604i −0.377312 0.270807i
657657 6.39705 + 2.64974i 0.249573 + 0.103376i
658658 −13.5339 11.2978i −0.527606 0.440435i
659659 2.04620 20.7754i 0.0797086 0.809295i −0.869350 0.494197i 0.835462π-0.835462\pi
0.949059 0.315099i 0.102038π-0.102038\pi
660660 −0.153429 + 0.121676i −0.00597220 + 0.00473622i
661661 −17.0403 31.8801i −0.662789 1.23999i −0.958603 0.284746i 0.908091π-0.908091\pi
0.295813 0.955246i 0.404409π-0.404409\pi
662662 13.8288 + 0.115735i 0.537471 + 0.00449815i
663663 −0.141649 0.0281758i −0.00550120 0.00109426i
664664 27.7151 + 29.1429i 1.07555 + 1.13096i
665665 −4.34734 21.8555i −0.168583 0.847522i
666666 −19.8134 + 29.1223i −0.767755 + 1.12847i
667667 4.57407 + 46.4413i 0.177109 + 1.79821i
668668 −21.9426 + 21.2201i −0.848985 + 0.821030i
669669 −0.123216 0.406189i −0.00476381 0.0157042i
670670 0.446961 0.360594i 0.0172676 0.0139310i
671671 −0.0966877 + 0.0966877i −0.00373259 + 0.00373259i
672672 −0.399398 1.09126i −0.0154071 0.0420963i
673673 −18.7729 18.7729i −0.723642 0.723642i 0.245703 0.969345i 0.420981π-0.420981\pi
−0.969345 + 0.245703i 0.920981π0.920981\pi
674674 −6.60715 0.706626i −0.254498 0.0272182i
675675 5.51204 1.67206i 0.212159 0.0643576i
676676 −9.37432 23.7482i −0.360551 0.913394i
677677 27.0517 2.66436i 1.03968 0.102400i 0.436259 0.899821i 0.356303π-0.356303\pi
0.603423 + 0.797421i 0.293803π0.293803\pi
678678 0.169232 + 0.889636i 0.00649933 + 0.0341663i
679679 20.5420 4.08605i 0.788328 0.156808i
680680 17.9708 + 4.04610i 0.689147 + 0.155161i
681681 0.453551 2.28016i 0.0173801 0.0873758i
682682 0.878497 + 0.893325i 0.0336394 + 0.0342072i
683683 8.04037 4.29767i 0.307656 0.164446i −0.310342 0.950625i 0.600444π-0.600444\pi
0.617999 + 0.786179i 0.287944π0.287944\pi
684684 −14.3815 + 25.8554i −0.549891 + 0.988608i
685685 35.8060 + 3.52658i 1.36808 + 0.134744i
686686 22.9826 2.06954i 0.877479 0.0790153i
687687 0.00864988 0.0208827i 0.000330014 0.000796724i
688688 2.45307 + 37.8621i 0.0935224 + 1.44348i
689689 1.99292 + 4.81133i 0.0759241 + 0.183297i
690690 1.86715 + 3.56462i 0.0710810 + 0.135703i
691691 −24.5094 29.8648i −0.932382 1.13611i −0.990460 0.137798i 0.955997π-0.955997\pi
0.0580785 0.998312i 0.481503π-0.481503\pi
692692 27.5093 14.1173i 1.04575 0.536657i
693693 0.218880 0.721550i 0.00831456 0.0274094i
694694 −10.6947 26.4432i −0.405967 1.00377i
695695 −0.923565 + 0.617106i −0.0350328 + 0.0234082i
696696 2.90460 2.26415i 0.110099 0.0858222i
697697 3.20563 4.79757i 0.121422 0.181721i
698698 −22.3250 34.0248i −0.845014 1.28786i
699699 2.45733 + 2.01668i 0.0929447 + 0.0762778i
700700 −2.99084 16.4722i −0.113043 0.622593i
701701 14.6991 27.5000i 0.555176 1.03866i −0.435210 0.900329i 0.643326π-0.643326\pi
0.990386 0.138332i 0.0441740π-0.0441740\pi
702702 0.301199 0.552334i 0.0113680 0.0208465i
703703 41.5915i 1.56865i
704704 0.224326 1.50064i 0.00845460 0.0565574i
705705 4.81791i 0.181453i
706706 −21.0947 11.5034i −0.793911 0.432935i
707707 0.969697 1.81418i 0.0364692 0.0682291i
708708 −3.54849 2.45792i −0.133360 0.0923741i
709709 2.31868 + 1.90289i 0.0870797 + 0.0714645i 0.676926 0.736051i 0.263312π-0.263312\pi
−0.589846 + 0.807516i 0.700812π0.700812\pi
710710 −62.9657 + 41.3143i −2.36306 + 1.55050i
711711 −13.4557 + 20.1379i −0.504630 + 0.755232i
712712 −3.94941 2.24025i −0.148010 0.0839569i
713713 21.4078 14.3042i 0.801727 0.535697i
714714 0.522548 0.211340i 0.0195559 0.00790922i
715715 −0.0894452 + 0.294861i −0.00334506 + 0.0110272i
716716 26.1113 + 8.40054i 0.975827 + 0.313943i
717717 1.31290 + 1.59978i 0.0490312 + 0.0597447i
718718 −42.4831 + 22.2526i −1.58546 + 0.830460i
719719 −6.09932 14.7251i −0.227466 0.549152i 0.768401 0.639968i 0.221052π-0.221052\pi
−0.995868 + 0.0908161i 0.971052π0.971052\pi
720720 −20.0069 + 34.5930i −0.745614 + 1.28921i
721721 −6.82868 + 16.4859i −0.254313 + 0.613967i
722722 0.723303 + 8.03241i 0.0269186 + 0.298935i
723723 −2.74398 0.270259i −0.102050 0.0100510i
724724 4.59860 + 16.1264i 0.170905 + 0.599333i
725725 46.7928 25.0113i 1.73784 0.928895i
726726 1.70025 1.67203i 0.0631022 0.0620548i
727727 6.02809 30.3052i 0.223569 1.12396i −0.692031 0.721868i 0.743284π-0.743284\pi
0.915600 0.402091i 0.131716π-0.131716\pi
728728 −1.49439 1.05373i −0.0553857 0.0390537i
729729 25.2367 5.01990i 0.934694 0.185922i
730730 10.8487 2.06372i 0.401530 0.0763816i
731731 −18.3153 + 1.80390i −0.677417 + 0.0667197i
732732 0.0882783 0.203424i 0.00326286 0.00751877i
733733 −16.5818 + 5.03003i −0.612463 + 0.185789i −0.581251 0.813724i 0.697437π-0.697437\pi
−0.0312116 + 0.999513i 0.509937π0.509937\pi
734734 3.64027 34.0375i 0.134365 1.25635i
735735 1.90394 + 1.90394i 0.0702278 + 0.0702278i
736736 −29.4329 10.2914i −1.08491 0.379346i
737737 0.0162248 0.0162248i 0.000597649 0.000597649i
738738 7.85974 + 9.74225i 0.289321 + 0.358617i
739739 5.77788 + 19.0471i 0.212543 + 0.700660i 0.996779 + 0.0801974i 0.0255551π0.0255551\pi
−0.784236 + 0.620462i 0.786945π0.786945\pi
740740 −0.940247 + 56.1698i −0.0345642 + 2.06484i
741741 −0.0362626 0.368180i −0.00133214 0.0135254i
742742 −16.8046 11.4330i −0.616916 0.419720i
743743 7.74710 + 38.9473i 0.284213 + 1.42884i 0.814078 + 0.580755i 0.197243π0.197243\pi
−0.529865 + 0.848082i 0.677757π0.677757\pi
744744 −1.85712 0.824458i −0.0680855 0.0302261i
745745 5.16652 + 1.02768i 0.189287 + 0.0376514i
746746 −0.392230 + 46.8664i −0.0143606 + 1.71590i
747747 −19.9498 37.3235i −0.729925 1.36559i
748748 0.731136 + 0.0843885i 0.0267330 + 0.00308555i
749749 0.578951 5.87819i 0.0211544 0.214784i
750750 0.592722 0.710033i 0.0216432 0.0259267i
751751 30.2032 + 12.5106i 1.10213 + 0.456518i 0.858221 0.513280i 0.171570π-0.171570\pi
0.243910 + 0.969798i 0.421570π0.421570\pi
752752 25.4992 + 27.2662i 0.929860 + 0.994296i
753753 2.33323 0.966457i 0.0850278 0.0352196i
754754 1.72856 5.53123i 0.0629505 0.201436i
755755 −31.9604 + 26.2292i −1.16316 + 0.954578i
756756 0.199737 + 2.44723i 0.00726436 + 0.0890050i
757757 17.5361 + 5.31953i 0.637362 + 0.193342i 0.592396 0.805647i 0.298182π-0.298182\pi
0.0449660 + 0.998989i 0.485682π0.485682\pi
758758 6.94985 + 2.94710i 0.252430 + 0.107044i
759759 0.0893238 + 0.133683i 0.00324225 + 0.00485237i
760760 3.44478 + 47.0608i 0.124955 + 1.70708i
761761 10.7889 + 7.20891i 0.391097 + 0.261323i 0.735536 0.677486i 0.236931π-0.236931\pi
−0.344438 + 0.938809i 0.611931π0.611931\pi
762762 0.388822 1.87270i 0.0140856 0.0678406i
763763 1.56560 1.90768i 0.0566784 0.0690628i
764764 −6.10836 9.48159i −0.220993 0.343032i
765765 −17.0951 9.13754i −0.618076 0.330368i
766766 −5.23650 17.7973i −0.189202 0.643041i
767767 −6.79235 −0.245257
768768 0.555168 + 2.39725i 0.0200329 + 0.0865034i
769769 55.4296 1.99884 0.999422 0.0339985i 0.0108241π-0.0108241\pi
0.999422 + 0.0339985i 0.0108241π0.0108241\pi
770770 −0.339449 1.15368i −0.0122329 0.0415758i
771771 −0.609484 0.325776i −0.0219500 0.0117325i
772772 −2.39489 3.71742i −0.0861939 0.133793i
773773 −29.5336 + 35.9867i −1.06225 + 1.29435i −0.108386 + 0.994109i 0.534568π0.534568\pi
−0.953862 + 0.300244i 0.902932π0.902932\pi
774774 8.11656 39.0920i 0.291744 1.40513i
775775 −24.3400 16.2634i −0.874317 0.584200i
776776 −44.2324 + 3.23774i −1.58785 + 0.116228i
777777 0.955040 + 1.42932i 0.0342619 + 0.0512765i
778778 0.298937 + 0.126765i 0.0107174 + 0.00454474i
779779 14.1441 + 4.29057i 0.506765 + 0.153726i
780780 −0.0406497 0.498052i −0.00145549 0.0178331i
781781 −2.32597 + 1.90887i −0.0832297 + 0.0683049i
782782 4.51133 14.4358i 0.161325 0.516225i
783783 −7.18928 + 2.97790i −0.256924 + 0.106421i
784784 −20.8518 0.698288i −0.744707 0.0249389i
785785 23.4812 + 9.72622i 0.838079 + 0.347144i
786786 −1.95943 + 2.34724i −0.0698907 + 0.0837234i
787787 −2.46437 + 25.0212i −0.0878455 + 0.891910i 0.845750 + 0.533580i 0.179154π0.179154\pi
−0.933595 + 0.358330i 0.883346π0.883346\pi
788788 16.7926 + 1.93821i 0.598210 + 0.0690460i
789789 −1.24197 2.32357i −0.0442154 0.0827211i
790790 −0.323270 + 38.6267i −0.0115014 + 1.37427i
791791 −5.45462 1.08499i −0.193944 0.0385779i
792792 −0.647856 + 1.45932i −0.0230206 + 0.0518548i
793793 −0.0680742 0.342232i −0.00241738 0.0121530i
794794 −22.1487 15.0689i −0.786028 0.534776i
795795 −0.544437 5.52776i −0.0193092 0.196049i
796796 0.441187 26.3562i 0.0156375 0.934172i
797797 −6.23492 20.5538i −0.220852 0.728052i −0.995423 0.0955650i 0.969534π-0.969534\pi
0.774571 0.632487i 0.217966π-0.217966\pi
798798 0.906631 + 1.12378i 0.0320944 + 0.0397814i
799799 −12.8044 + 12.8044i −0.452987 + 0.452987i
800800 1.99591 + 35.3948i 0.0705660 + 1.25139i
801801 3.37856 + 3.37856i 0.119376 + 0.119376i
802802 −5.18020 + 48.4363i −0.182919 + 1.71035i
803803 0.422231 0.128082i 0.0149002 0.00451993i
804804 −0.0148137 + 0.0341359i −0.000522438 + 0.00120388i
805805 −24.5937 + 2.42227i −0.866814 + 0.0853737i
806806 −3.14095 + 0.597493i −0.110635 + 0.0210458i
807807 −2.24375 + 0.446310i −0.0789838 + 0.0157109i
808808 −2.51019 + 3.55994i −0.0883082 + 0.125238i
809809 7.10502 35.7193i 0.249799 1.25582i −0.628537 0.777780i 0.716346π-0.716346\pi
0.878336 0.478045i 0.158654π-0.158654\pi
810810 29.7428 29.2491i 1.04505 1.02771i
811811 −5.53266 + 2.95727i −0.194278 + 0.103844i −0.565667 0.824633i 0.691381π-0.691381\pi
0.371390 + 0.928477i 0.378881π0.378881\pi
812812 6.20226 + 21.7501i 0.217657 + 0.763281i
813813 1.90799 + 0.187921i 0.0669161 + 0.00659066i
814814 0.201304 + 2.23552i 0.00705570 + 0.0783548i
815815 −20.4107 + 49.2759i −0.714957 + 1.72606i
816816 −1.15315 + 0.308058i −0.0403684 + 0.0107842i
817817 −18.0413 43.5554i −0.631183 1.52381i
818818 33.2961 17.4405i 1.16417 0.609791i
819819 1.22068 + 1.48740i 0.0426539 + 0.0519739i
820820 19.0048 + 6.11422i 0.663677 + 0.213518i
821821 8.45214 27.8630i 0.294982 0.972424i −0.676725 0.736235i 0.736602π-0.736602\pi
0.971707 0.236189i 0.0758984π-0.0758984\pi
822822 −2.16126 + 0.874104i −0.0753825 + 0.0304879i
823823 −11.9092 + 7.95748i −0.415129 + 0.277380i −0.745545 0.666455i 0.767811π-0.767811\pi
0.330416 + 0.943835i 0.392811π0.392811\pi
824824 18.6431 32.8665i 0.649463 1.14496i
825825 0.101558 0.151993i 0.00353581 0.00529171i
826826 22.1644 14.5429i 0.771197 0.506013i
827827 −22.9146 18.8055i −0.796819 0.653933i 0.145234 0.989397i 0.453607π-0.453607\pi
−0.942053 + 0.335465i 0.891107π0.891107\pi
828828 26.9724 + 18.6828i 0.937355 + 0.649273i
829829 8.94431 16.7336i 0.310649 0.581183i −0.677347 0.735664i 0.736870π-0.736870\pi
0.987996 + 0.154481i 0.0493705π0.0493705\pi
830830 −59.2589 32.3150i −2.05691 1.12167i
831831 1.66064i 0.0576070i
832832 2.86603 + 2.60351i 0.0993618 + 0.0902603i
833833 10.1201i 0.350640i
834834 0.0344580 0.0631887i 0.00119318 0.00218805i
835835 24.1498 45.1811i 0.835738 1.56356i
836836 0.336810 + 1.85500i 0.0116488 + 0.0641566i
837837 3.31879 + 2.72366i 0.114714 + 0.0941435i
838838 17.6185 + 26.8518i 0.608622 + 0.927579i
839839 7.42607 11.1139i 0.256376 0.383694i −0.680846 0.732427i 0.738388π-0.738388\pi
0.937222 + 0.348732i 0.113388π0.113388\pi
840840 1.19901 + 1.53818i 0.0413699 + 0.0530721i
841841 −35.4862 + 23.7111i −1.22366 + 0.817626i
842842 15.8581 + 39.2097i 0.546505 + 1.35125i
843843 1.14536 3.77573i 0.0394482 0.130043i
844844 10.3265 5.29933i 0.355451 0.182411i
845845 27.1836 + 33.1233i 0.935145 + 1.13948i
846846 −18.2278 34.7992i −0.626684 1.19642i
847847 5.60431 + 13.5300i 0.192567 + 0.464897i
848848 32.3373 + 28.4020i 1.11047 + 0.975329i
849849 −0.887815 + 2.14337i −0.0304697 + 0.0735604i
850850 −17.1266 + 1.54222i −0.587438 + 0.0528977i
851851 45.9029 + 4.52104i 1.57353 + 0.154979i
852852 2.37203 4.26450i 0.0812644 0.146099i
853853 −11.2584 + 6.01773i −0.385479 + 0.206043i −0.652741 0.757581i 0.726381π-0.726381\pi
0.267262 + 0.963624i 0.413881π0.413881\pi
854854 0.954880 + 0.970998i 0.0326753 + 0.0332269i
855855 9.68711 48.7004i 0.331292 1.66552i
856856 −2.74729 + 12.2021i −0.0939004 + 0.417059i
857857 36.9270 7.34524i 1.26140 0.250909i 0.481298 0.876557i 0.340166π-0.340166\pi
0.780105 + 0.625649i 0.215166π0.215166\pi
858858 −0.00373109 0.0196139i −0.000127377 0.000669609i
859859 −14.8740 + 1.46496i −0.507494 + 0.0499838i −0.348524 0.937300i 0.613317π-0.613317\pi
−0.158970 + 0.987283i 0.550817π0.550817\pi
860860 −23.3803 59.2301i −0.797262 2.01973i
861861 0.584593 0.177334i 0.0199229 0.00604354i
862862 −21.4993 2.29933i −0.732271 0.0783154i
863863 38.0460 + 38.0460i 1.29510 + 1.29510i 0.931590 + 0.363511i 0.118422π0.118422\pi
0.363511 + 0.931590i 0.381578π0.381578\pi
864864 0.217501 5.19480i 0.00739953 0.176731i
865865 −36.6944 + 36.6944i −1.24765 + 1.24765i
866866 −33.4975 + 27.0248i −1.13829 + 0.918338i
867867 0.590882 + 1.94788i 0.0200674 + 0.0661534i
868868 8.97009 8.67472i 0.304465 0.294439i
869869 0.151277 + 1.53594i 0.00513171 + 0.0521031i
870870 −3.47681 + 5.11031i −0.117875 + 0.173256i
871871 0.0114233 + 0.0574287i 0.000387063 + 0.00194590i
872872 −3.78680 + 3.60128i −0.128237 + 0.121955i
873873 45.7734 + 9.10489i 1.54919 + 0.308154i
874874 38.7416 + 0.324232i 1.31045 + 0.0109673i
875875 2.67761 + 5.00946i 0.0905198 + 0.169351i
876876 −0.560659 + 0.444628i −0.0189429 + 0.0150226i
877877 0.261117 2.65116i 0.00881729 0.0895234i −0.989769 0.142680i 0.954428π-0.954428\pi
0.998586 + 0.0531562i 0.0169281π0.0169281\pi
878878 −2.41749 2.01808i −0.0815864 0.0681068i
879879 −0.0154037 0.00638041i −0.000519553 0.000215206i
880880 0.412931 + 2.51282i 0.0139199 + 0.0847072i
881881 −20.2346 + 8.38144i −0.681720 + 0.282378i −0.696546 0.717512i 0.745281π-0.745281\pi
0.0148256 + 0.999890i 0.495281π0.495281\pi
882882 20.9552 + 6.54869i 0.705598 + 0.220506i
883883 11.5623 9.48892i 0.389102 0.319328i −0.419422 0.907792i 0.637767π-0.637767\pi
0.808523 + 0.588464i 0.200267π0.200267\pi
884884 −1.21562 + 1.43169i −0.0408858 + 0.0481530i
885885 6.93266 + 2.10300i 0.233039 + 0.0706916i
886886 −11.4712 + 27.0515i −0.385384 + 0.908811i
887887 3.14343 + 4.70448i 0.105546 + 0.157961i 0.880483 0.474078i 0.157218π-0.157218\pi
−0.774937 + 0.632039i 0.782218π0.782218\pi
888888 −1.63481 3.25236i −0.0548605 0.109142i
889889 9.76648 + 6.52575i 0.327557 + 0.218867i
890890 7.46132 + 1.54917i 0.250104 + 0.0519284i
891891 1.05735 1.28838i 0.0354225 0.0431625i
892892 −5.39511 1.16735i −0.180642 0.0390858i
893893 −40.9091 21.8664i −1.36897 0.731730i
894894 −0.327451 + 0.0963460i −0.0109516 + 0.00322229i
895895 −46.0350 −1.53878
896896 −14.9266 2.35920i −0.498661 0.0788153i
897897 −0.410288 −0.0136991
898898 −16.3130 + 4.79979i −0.544373 + 0.160171i
899899 34.8775 + 18.6424i 1.16323 + 0.621760i
900900 7.88920 36.4613i 0.262973 1.21538i
901901 −13.2440 + 16.1379i −0.441222 + 0.537631i
902902 0.781004 + 0.162158i 0.0260046 + 0.00539926i
903903 −1.62014 1.08254i −0.0539148 0.0360247i
904904 11.1802 + 3.70043i 0.371848 + 0.123074i
905905 −15.6360 23.4009i −0.519758 0.777873i
906906 1.04590 2.46643i 0.0347476 0.0819417i
907907 6.34426 + 1.92451i 0.210658 + 0.0639023i 0.393850 0.919175i 0.371143π-0.371143\pi
−0.183192 + 0.983077i 0.558643π0.558643\pi
908908 −23.0462 19.5681i −0.764815 0.649391i
909909 3.54328 2.90790i 0.117523 0.0964489i
910910 2.92915 + 0.915385i 0.0971003 + 0.0303447i
911911 8.63355 3.57614i 0.286042 0.118483i −0.235049 0.971984i 0.575525π-0.575525\pi
0.521091 + 0.853501i 0.325525π0.325525\pi
912912 −1.61263 2.59767i −0.0533997 0.0860176i
913913 −2.49155 1.03203i −0.0824582 0.0341553i
914914 −12.4789 10.4172i −0.412767 0.344570i
915915 −0.0364791 + 0.370378i −0.00120596 + 0.0122443i
916916 −0.182646 0.230310i −0.00603479 0.00760965i
917917 −8.85170 16.5604i −0.292309 0.546872i
918918 2.52192 + 0.0211062i 0.0832357 + 0.000696607i
919919 −9.57985 1.90555i −0.316010 0.0628583i 0.0345370 0.999403i 0.489004π-0.489004\pi
−0.350547 + 0.936545i 0.614004π0.614004\pi
920920 52.3137 + 1.31370i 1.72473 + 0.0433114i
921921 −0.528296 2.65592i −0.0174079 0.0875156i
922922 11.0314 16.2142i 0.363300 0.533988i
923923 −0.752629 7.64157i −0.0247731 0.251525i
924924 0.0541700 + 0.0560145i 0.00178206 + 0.00184274i
925925 −15.2233 50.1845i −0.500539 1.65006i
926926 −10.8507 + 8.75399i −0.356576 + 0.287674i
927927 −28.1160 + 28.1160i −0.923450 + 0.923450i
928928 −7.37028 47.3224i −0.241941 1.55343i
929929 39.9272 + 39.9272i 1.30997 + 1.30997i 0.921434 + 0.388534i 0.127018π0.127018\pi
0.388534 + 0.921434i 0.372982π0.372982\pi
930930 3.39083 + 0.362645i 0.111190 + 0.0118916i
931931 24.8076 7.52530i 0.813036 0.246632i
932932 38.4525 15.1786i 1.25955 0.497193i
933933 −3.40999 + 0.335855i −0.111638 + 0.0109954i
934934 7.86537 + 41.3474i 0.257363 + 1.35293i
935935 −1.21149 + 0.240979i −0.0396198 + 0.00788087i
936936 −2.17791 3.44358i −0.0711871 0.112557i
937937 −1.71770 + 8.63545i −0.0561147 + 0.282108i −0.998647 0.0520083i 0.983438π-0.983438\pi
0.942532 + 0.334116i 0.108438π0.108438\pi
938938 −0.160235 0.162940i −0.00523186 0.00532017i
939939 −2.07009 + 1.10649i −0.0675550 + 0.0361089i
940940 −54.7540 30.4557i −1.78588 0.993354i
941941 −25.7216 2.53336i −0.838502 0.0825852i −0.330356 0.943856i 0.607169π-0.607169\pi
−0.508146 + 0.861271i 0.669669π0.669669\pi
942942 −1.64022 + 0.147698i −0.0534412 + 0.00481228i
943943 6.27281 15.1439i 0.204271 0.493154i
944944 −50.3647 + 24.7901i −1.63923 + 0.806850i
945945 −1.57699 3.80719i −0.0512995 0.123848i
946946 −1.18052 2.25376i −0.0383819 0.0732760i
947947 −3.75302 4.57307i −0.121957 0.148605i 0.708453 0.705758i 0.249393π-0.249393\pi
−0.830410 + 0.557154i 0.811893π0.811893\pi
948948 −1.14277 2.22685i −0.0371156 0.0723247i
949949 −0.326851 + 1.07748i −0.0106100 + 0.0349766i
950950 −16.5158 40.8361i −0.535845 1.32490i
951951 −0.0473107 + 0.0316120i −0.00153415 + 0.00102509i
952952 0.901388 7.27454i 0.0292141 0.235769i
953953 −11.0052 + 16.4704i −0.356492 + 0.533528i −0.965760 0.259436i 0.916463π-0.916463\pi
0.609268 + 0.792964i 0.291463π0.291463\pi
954954 −24.8458 37.8666i −0.804412 1.22598i
955955 14.6326 + 12.0087i 0.473501 + 0.388593i
956956 26.4803 4.80798i 0.856433 0.155501i
957957 −0.116414 + 0.217796i −0.00376314 + 0.00704033i
958958 −1.20430 + 2.20842i −0.0389090 + 0.0713509i
959959 14.3173i 0.462331i
960960 −2.11916 3.54465i −0.0683956 0.114403i
961961 9.18073i 0.296153i
962962 −5.02874 2.74227i −0.162133 0.0884144i
963963 6.20437 11.6076i 0.199933 0.374048i
964964 −20.4171 + 29.4761i −0.657589 + 0.949360i
965965 5.73698 + 4.70822i 0.184680 + 0.151563i
966966 1.33883 0.878457i 0.0430760 0.0282639i
967967 −7.85147 + 11.7506i −0.252486 + 0.377872i −0.935962 0.352101i 0.885467π-0.885467\pi
0.683476 + 0.729973i 0.260467π0.260467\pi
968968 −8.25419 29.8923i −0.265300 0.960774i
969969 1.23315 0.823961i 0.0396143 0.0264694i
970970 69.0043 27.9083i 2.21559 0.896080i
971971 4.95320 16.3285i 0.158956 0.524007i −0.840897 0.541196i 0.817972π-0.817972\pi
0.999852 + 0.0171891i 0.00547172π0.00547172\pi
972972 −2.51676 + 7.82285i −0.0807252 + 0.250918i
973973 0.280408 + 0.341678i 0.00898946 + 0.0109537i
974974 17.2131 9.01619i 0.551543 0.288897i
975975 0.178516 + 0.430975i 0.00571708 + 0.0138023i
976976 −1.75381 2.28917i −0.0561382 0.0732745i
977977 −15.1737 + 36.6326i −0.485450 + 1.17198i 0.471536 + 0.881847i 0.343700π0.343700\pi
−0.956986 + 0.290133i 0.906300π0.906300\pi
978978 −0.309950 3.44205i −0.00991109 0.110064i
979979 0.303006 + 0.0298435i 0.00968413 + 0.000953804i
980980 33.6731 9.60220i 1.07565 0.306731i
981981 4.84978 2.59226i 0.154842 0.0827645i
982982 30.3253 29.8219i 0.967719 0.951656i
983983 1.18564 5.96062i 0.0378161 0.190114i −0.957260 0.289229i 0.906601π-0.906601\pi
0.995076 + 0.0991147i 0.0316011π0.0316011\pi
984984 −1.27468 + 0.220439i −0.0406354 + 0.00702735i
985985 −27.8251 + 5.53476i −0.886582 + 0.176352i
986986 22.8217 4.34130i 0.726792 0.138255i
987987 −1.90797 + 0.187919i −0.0607315 + 0.00598153i
988988 −4.41348 1.91528i −0.140411 0.0609332i
989989 −50.0316 + 15.1769i −1.59091 + 0.482598i
990990 0.284965 2.66451i 0.00905679 0.0846835i
991991 −15.6471 15.6471i −0.497048 0.497048i 0.413470 0.910518i 0.364317π-0.364317\pi
−0.910518 + 0.413470i 0.864317π0.864317\pi
992992 −21.1092 + 15.8939i −0.670218 + 0.504633i
993993 1.06343 1.06343i 0.0337469 0.0337469i
994994 18.8171 + 23.3241i 0.596843 + 0.739794i
995995 12.8422 + 42.3352i 0.407127 + 1.34212i
996996 4.37297 + 0.0732007i 0.138563 + 0.00231945i
997997 −4.19514 42.5940i −0.132861 1.34896i −0.798186 0.602411i 0.794207π-0.794207\pi
0.665325 0.746554i 0.268293π-0.268293\pi
998998 5.94916 + 4.04752i 0.188317 + 0.128122i
999999 1.50052 + 7.54362i 0.0474743 + 0.238669i
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 128.2.k.a.109.8 yes 240
4.3 odd 2 512.2.k.a.273.8 240
128.27 odd 32 512.2.k.a.497.8 240
128.101 even 32 inner 128.2.k.a.101.8 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.2.k.a.101.8 240 128.101 even 32 inner
128.2.k.a.109.8 yes 240 1.1 even 1 trivial
512.2.k.a.273.8 240 4.3 odd 2
512.2.k.a.497.8 240 128.27 odd 32