Properties

Label 825.2.n.p.526.2
Level 825825
Weight 22
Character 825.526
Analytic conductor 6.5886.588
Analytic rank 00
Dimension 2424
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(301,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.301");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 825=35211 825 = 3 \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 825.n (of order 55, degree 44, 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: 6.587658166766.58765816676
Analytic rank: 00
Dimension: 2424
Relative dimension: 66 over Q(ζ5)\Q(\zeta_{5})
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 526.2
Character χ\chi == 825.526
Dual form 825.2.n.p.676.2

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+(0.650947+2.00341i)q2+(0.809017+0.587785i)q3+(1.971881.43266i)q4+(0.6509472.00341i)q6+(2.682961.94929i)q7+(0.7453860.541555i)q8+(0.3090170.951057i)q9+(3.312670.162019i)q11+2.43738q12+(0.772198+2.37658i)q13+(5.651694.10619i)q14+(0.9066362.79034i)q16+(2.104466.47687i)q17+(1.70420+1.23818i)q18+(0.9285030.674597i)q19+3.31633q21+(1.83178+6.74209i)q22+5.89026q23+(0.284712+0.876254i)q24+(4.258613.09406i)q26+(0.309017+0.951057i)q27+(2.49783+7.68753i)q28+(0.908175+0.659827i)q29+(0.338908+1.04305i)q31+8.02306q32+(2.58477+2.07821i)q33+14.3457q34+(1.97188+1.43266i)q36+(9.33514+6.78238i)q37+(0.747087+2.29930i)q38+(0.7721982.37658i)q39+(0.7544630.548149i)q41+(2.15875+6.64396i)q42+0.552188q43+(6.764314.42643i)q44+(3.83425+11.8006i)q46+(1.726661.25449i)q47+(2.37360+1.72452i)q48+(1.23546+3.80234i)q49+(5.50956+4.00293i)q51+(4.927513.58005i)q52+(3.5956011.0661i)q532.10651q543.05549q56+(0.354657+1.09152i)q57+(1.91308+1.38993i)q58+(6.794434.93644i)q59+(2.538007.81115i)q61+(1.869051.35794i)q62+(2.68296+1.94929i)q63+(3.40931+10.4928i)q64+(2.480966.53116i)q664.15419q67+(5.12938+15.7866i)q68+(4.76532+3.46221i)q69+(3.87323+11.9206i)q71+(0.2847120.876254i)q72+(4.64182+3.37248i)q73+(19.6646+14.2871i)q742.79736q76+(9.203586.02265i)q77+5.26393q78+(1.19514+3.67825i)q79+(0.8090170.587785i)q81+(0.607052+1.86831i)q82+(1.878995.78295i)q83+(6.539414.75116i)q84+(0.359446+1.10626i)q861.12257q87+(2.381471.91476i)q88+12.5950q89+(6.704424.87105i)q91+(11.61498.43872i)q92+(0.3389081.04305i)q93+(1.38930+4.27582i)q94+(6.49079+4.71583i)q96+(0.886486+2.72832i)q978.42187q98+(0.8695813.20060i)q99+O(q100)q+(-0.650947 + 2.00341i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.97188 - 1.43266i) q^{4} +(-0.650947 - 2.00341i) q^{6} +(-2.68296 - 1.94929i) q^{7} +(0.745386 - 0.541555i) q^{8} +(0.309017 - 0.951057i) q^{9} +(3.31267 - 0.162019i) q^{11} +2.43738 q^{12} +(-0.772198 + 2.37658i) q^{13} +(5.65169 - 4.10619i) q^{14} +(-0.906636 - 2.79034i) q^{16} +(-2.10446 - 6.47687i) q^{17} +(1.70420 + 1.23818i) q^{18} +(0.928503 - 0.674597i) q^{19} +3.31633 q^{21} +(-1.83178 + 6.74209i) q^{22} +5.89026 q^{23} +(-0.284712 + 0.876254i) q^{24} +(-4.25861 - 3.09406i) q^{26} +(0.309017 + 0.951057i) q^{27} +(2.49783 + 7.68753i) q^{28} +(0.908175 + 0.659827i) q^{29} +(-0.338908 + 1.04305i) q^{31} +8.02306 q^{32} +(-2.58477 + 2.07821i) q^{33} +14.3457 q^{34} +(-1.97188 + 1.43266i) q^{36} +(9.33514 + 6.78238i) q^{37} +(0.747087 + 2.29930i) q^{38} +(-0.772198 - 2.37658i) q^{39} +(0.754463 - 0.548149i) q^{41} +(-2.15875 + 6.64396i) q^{42} +0.552188 q^{43} +(-6.76431 - 4.42643i) q^{44} +(-3.83425 + 11.8006i) q^{46} +(1.72666 - 1.25449i) q^{47} +(2.37360 + 1.72452i) q^{48} +(1.23546 + 3.80234i) q^{49} +(5.50956 + 4.00293i) q^{51} +(4.92751 - 3.58005i) q^{52} +(3.59560 - 11.0661i) q^{53} -2.10651 q^{54} -3.05549 q^{56} +(-0.354657 + 1.09152i) q^{57} +(-1.91308 + 1.38993i) q^{58} +(-6.79443 - 4.93644i) q^{59} +(-2.53800 - 7.81115i) q^{61} +(-1.86905 - 1.35794i) q^{62} +(-2.68296 + 1.94929i) q^{63} +(-3.40931 + 10.4928i) q^{64} +(-2.48096 - 6.53116i) q^{66} -4.15419 q^{67} +(-5.12938 + 15.7866i) q^{68} +(-4.76532 + 3.46221i) q^{69} +(3.87323 + 11.9206i) q^{71} +(-0.284712 - 0.876254i) q^{72} +(4.64182 + 3.37248i) q^{73} +(-19.6646 + 14.2871i) q^{74} -2.79736 q^{76} +(-9.20358 - 6.02265i) q^{77} +5.26393 q^{78} +(-1.19514 + 3.67825i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.607052 + 1.86831i) q^{82} +(-1.87899 - 5.78295i) q^{83} +(-6.53941 - 4.75116i) q^{84} +(-0.359446 + 1.10626i) q^{86} -1.12257 q^{87} +(2.38147 - 1.91476i) q^{88} +12.5950 q^{89} +(6.70442 - 4.87105i) q^{91} +(-11.6149 - 8.43872i) q^{92} +(-0.338908 - 1.04305i) q^{93} +(1.38930 + 4.27582i) q^{94} +(-6.49079 + 4.71583i) q^{96} +(-0.886486 + 2.72832i) q^{97} -8.42187 q^{98} +(0.869581 - 3.20060i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+2q26q36q4+2q6+4q7+6q86q9+24q12+4q13+2q1422q16+4q17+2q18+8q1916q214q22+6q2438q266q27+120q98+O(q100) 24 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 2 q^{6} + 4 q^{7} + 6 q^{8} - 6 q^{9} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 22 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 16 q^{21} - 4 q^{22} + 6 q^{24} - 38 q^{26} - 6 q^{27}+ \cdots - 120 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/825Z)×\left(\mathbb{Z}/825\mathbb{Z}\right)^\times.

nn 376376 551551 727727
χ(n)\chi(n) e(35)e\left(\frac{3}{5}\right) 11 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 −0.650947 + 2.00341i −0.460289 + 1.41662i 0.404523 + 0.914528i 0.367438π0.367438\pi
−0.864812 + 0.502096i 0.832562π0.832562\pi
33 −0.809017 + 0.587785i −0.467086 + 0.339358i
44 −1.97188 1.43266i −0.985942 0.716328i
55 0 0
66 −0.650947 2.00341i −0.265748 0.817888i
77 −2.68296 1.94929i −1.01407 0.736761i −0.0490073 0.998798i 0.515606π-0.515606\pi
−0.965058 + 0.262037i 0.915606π0.915606\pi
88 0.745386 0.541555i 0.263534 0.191469i
99 0.309017 0.951057i 0.103006 0.317019i
1010 0 0
1111 3.31267 0.162019i 0.998806 0.0488505i
1212 2.43738 0.703611
1313 −0.772198 + 2.37658i −0.214169 + 0.659145i 0.785042 + 0.619442i 0.212641π0.212641\pi
−0.999212 + 0.0397029i 0.987359π0.987359\pi
1414 5.65169 4.10619i 1.51048 1.09743i
1515 0 0
1616 −0.906636 2.79034i −0.226659 0.697584i
1717 −2.10446 6.47687i −0.510408 1.57087i −0.791486 0.611188i 0.790692π-0.790692\pi
0.281078 0.959685i 0.409308π-0.409308\pi
1818 1.70420 + 1.23818i 0.401684 + 0.291841i
1919 0.928503 0.674597i 0.213013 0.154763i −0.476163 0.879357i 0.657973π-0.657973\pi
0.689176 + 0.724594i 0.257973π0.257973\pi
2020 0 0
2121 3.31633 0.723682
2222 −1.83178 + 6.74209i −0.390537 + 1.43742i
2323 5.89026 1.22820 0.614102 0.789226i 0.289518π-0.289518\pi
0.614102 + 0.789226i 0.289518π0.289518\pi
2424 −0.284712 + 0.876254i −0.0581167 + 0.178865i
2525 0 0
2626 −4.25861 3.09406i −0.835181 0.606795i
2727 0.309017 + 0.951057i 0.0594703 + 0.183031i
2828 2.49783 + 7.68753i 0.472046 + 1.45281i
2929 0.908175 + 0.659827i 0.168644 + 0.122527i 0.668906 0.743347i 0.266763π-0.266763\pi
−0.500262 + 0.865874i 0.666763π0.666763\pi
3030 0 0
3131 −0.338908 + 1.04305i −0.0608697 + 0.187338i −0.976867 0.213846i 0.931401π-0.931401\pi
0.915998 + 0.401183i 0.131401π0.131401\pi
3232 8.02306 1.41829
3333 −2.58477 + 2.07821i −0.449951 + 0.361770i
3434 14.3457 2.46027
3535 0 0
3636 −1.97188 + 1.43266i −0.328647 + 0.238776i
3737 9.33514 + 6.78238i 1.53469 + 1.11502i 0.953560 + 0.301203i 0.0973883π0.0973883\pi
0.581128 + 0.813812i 0.302612π0.302612\pi
3838 0.747087 + 2.29930i 0.121194 + 0.372995i
3939 −0.772198 2.37658i −0.123651 0.380558i
4040 0 0
4141 0.754463 0.548149i 0.117827 0.0856066i −0.527311 0.849672i 0.676800π-0.676800\pi
0.645138 + 0.764066i 0.276800π0.276800\pi
4242 −2.15875 + 6.64396i −0.333103 + 1.02519i
4343 0.552188 0.0842079 0.0421040 0.999113i 0.486594π-0.486594\pi
0.0421040 + 0.999113i 0.486594π0.486594\pi
4444 −6.76431 4.42643i −1.01976 0.667309i
4545 0 0
4646 −3.83425 + 11.8006i −0.565329 + 1.73990i
4747 1.72666 1.25449i 0.251860 0.182987i −0.454691 0.890649i 0.650250π-0.650250\pi
0.706551 + 0.707663i 0.250250π0.250250\pi
4848 2.37360 + 1.72452i 0.342600 + 0.248913i
4949 1.23546 + 3.80234i 0.176494 + 0.543192i
5050 0 0
5151 5.50956 + 4.00293i 0.771493 + 0.560522i
5252 4.92751 3.58005i 0.683323 0.496463i
5353 3.59560 11.0661i 0.493893 1.52005i −0.324781 0.945789i 0.605291π-0.605291\pi
0.818674 0.574258i 0.194709π-0.194709\pi
5454 −2.10651 −0.286660
5555 0 0
5656 −3.05549 −0.408307
5757 −0.354657 + 1.09152i −0.0469754 + 0.144575i
5858 −1.91308 + 1.38993i −0.251199 + 0.182507i
5959 −6.79443 4.93644i −0.884559 0.642670i 0.0498947 0.998754i 0.484111π-0.484111\pi
−0.934454 + 0.356085i 0.884111π0.884111\pi
6060 0 0
6161 −2.53800 7.81115i −0.324957 1.00012i −0.971460 0.237204i 0.923769π-0.923769\pi
0.646503 0.762912i 0.276231π-0.276231\pi
6262 −1.86905 1.35794i −0.237369 0.172459i
6363 −2.68296 + 1.94929i −0.338022 + 0.245587i
6464 −3.40931 + 10.4928i −0.426164 + 1.31160i
6565 0 0
6666 −2.48096 6.53116i −0.305385 0.803930i
6767 −4.15419 −0.507515 −0.253757 0.967268i 0.581666π-0.581666\pi
−0.253757 + 0.967268i 0.581666π0.581666\pi
6868 −5.12938 + 15.7866i −0.622029 + 1.91441i
6969 −4.76532 + 3.46221i −0.573677 + 0.416801i
7070 0 0
7171 3.87323 + 11.9206i 0.459668 + 1.41471i 0.865566 + 0.500795i 0.166959π0.166959\pi
−0.405897 + 0.913919i 0.633041π0.633041\pi
7272 −0.284712 0.876254i −0.0335537 0.103268i
7373 4.64182 + 3.37248i 0.543284 + 0.394719i 0.825303 0.564690i 0.191004π-0.191004\pi
−0.282019 + 0.959409i 0.591004π0.591004\pi
7474 −19.6646 + 14.2871i −2.28596 + 1.66085i
7575 0 0
7676 −2.79736 −0.320880
7777 −9.20358 6.02265i −1.04885 0.686344i
7878 5.26393 0.596022
7979 −1.19514 + 3.67825i −0.134463 + 0.413835i −0.995506 0.0946970i 0.969812π-0.969812\pi
0.861043 + 0.508532i 0.169812π0.169812\pi
8080 0 0
8181 −0.809017 0.587785i −0.0898908 0.0653095i
8282 0.607052 + 1.86831i 0.0670377 + 0.206321i
8383 −1.87899 5.78295i −0.206246 0.634761i −0.999660 0.0260781i 0.991698π-0.991698\pi
0.793414 0.608683i 0.208302π-0.208302\pi
8484 −6.53941 4.75116i −0.713508 0.518394i
8585 0 0
8686 −0.359446 + 1.10626i −0.0387600 + 0.119291i
8787 −1.12257 −0.120352
8888 2.38147 1.91476i 0.253866 0.204114i
8989 12.5950 1.33506 0.667531 0.744582i 0.267351π-0.267351\pi
0.667531 + 0.744582i 0.267351π0.267351\pi
9090 0 0
9191 6.70442 4.87105i 0.702814 0.510624i
9292 −11.6149 8.43872i −1.21094 0.879798i
9393 −0.338908 1.04305i −0.0351431 0.108159i
9494 1.38930 + 4.27582i 0.143295 + 0.441017i
9595 0 0
9696 −6.49079 + 4.71583i −0.662463 + 0.481308i
9797 −0.886486 + 2.72832i −0.0900090 + 0.277019i −0.985921 0.167213i 0.946523π-0.946523\pi
0.895912 + 0.444232i 0.146523π0.146523\pi
9898 −8.42187 −0.850737
9999 0.869581 3.20060i 0.0873962 0.321672i
100100 0 0
101101 3.05000 9.38694i 0.303487 0.934036i −0.676751 0.736212i 0.736613π-0.736613\pi
0.980238 0.197824i 0.0633873π-0.0633873\pi
102102 −11.6059 + 8.43221i −1.14916 + 0.834913i
103103 −6.24523 4.53743i −0.615361 0.447086i 0.235937 0.971768i 0.424184π-0.424184\pi
−0.851298 + 0.524682i 0.824184π0.824184\pi
104104 0.711463 + 2.18966i 0.0697647 + 0.214714i
105105 0 0
106106 19.8294 + 14.4069i 1.92600 + 1.39932i
107107 12.5490 9.11737i 1.21316 0.881409i 0.217642 0.976029i 0.430163π-0.430163\pi
0.995514 + 0.0946194i 0.0301634π0.0301634\pi
108108 0.753192 2.31809i 0.0724760 0.223058i
109109 6.79834 0.651163 0.325581 0.945514i 0.394440π-0.394440\pi
0.325581 + 0.945514i 0.394440π0.394440\pi
110110 0 0
111111 −11.5389 −1.09522
112112 −3.00670 + 9.25367i −0.284106 + 0.874390i
113113 0.243910 0.177211i 0.0229451 0.0166706i −0.576254 0.817271i 0.695486π-0.695486\pi
0.599199 + 0.800600i 0.295486π0.295486\pi
114114 −1.95590 1.42104i −0.183187 0.133093i
115115 0 0
116116 −0.845508 2.60221i −0.0785034 0.241609i
117117 2.02164 + 1.46881i 0.186901 + 0.135791i
118118 14.3125 10.3987i 1.31757 0.957274i
119119 −6.97909 + 21.4794i −0.639772 + 1.96902i
120120 0 0
121121 10.9475 1.07343i 0.995227 0.0975844i
122122 17.3010 1.56636
123123 −0.288179 + 0.886924i −0.0259842 + 0.0799713i
124124 2.16262 1.57124i 0.194209 0.141101i
125125 0 0
126126 −2.15875 6.64396i −0.192317 0.591891i
127127 −2.07208 6.37720i −0.183867 0.565885i 0.816060 0.577968i 0.196154π-0.196154\pi
−0.999927 + 0.0120823i 0.996154π0.996154\pi
128128 −5.82050 4.22884i −0.514464 0.373780i
129129 −0.446730 + 0.324568i −0.0393324 + 0.0285766i
130130 0 0
131131 −8.07729 −0.705716 −0.352858 0.935677i 0.614790π-0.614790\pi
−0.352858 + 0.935677i 0.614790π0.614790\pi
132132 8.07423 0.394902i 0.702771 0.0343718i
133133 −3.80612 −0.330033
134134 2.70416 8.32254i 0.233604 0.718958i
135135 0 0
136136 −5.07622 3.68809i −0.435282 0.316251i
137137 −1.98939 6.12273i −0.169965 0.523100i 0.829402 0.558652i 0.188681π-0.188681\pi
−0.999368 + 0.0355519i 0.988681π0.988681\pi
138138 −3.83425 11.8006i −0.326393 1.00453i
139139 −5.64344 4.10020i −0.478670 0.347774i 0.322140 0.946692i 0.395598π-0.395598\pi
−0.800811 + 0.598918i 0.795598π0.795598\pi
140140 0 0
141141 −0.659526 + 2.02981i −0.0555421 + 0.170941i
142142 −26.4031 −2.21570
143143 −2.17298 + 7.99793i −0.181714 + 0.668820i
144144 −2.93393 −0.244495
145145 0 0
146146 −9.77805 + 7.10417i −0.809237 + 0.587945i
147147 −3.23447 2.34998i −0.266774 0.193823i
148148 −8.69099 26.7481i −0.714395 2.19868i
149149 −5.87766 18.0896i −0.481516 1.48196i −0.836963 0.547259i 0.815671π-0.815671\pi
0.355447 0.934696i 0.384329π-0.384329\pi
150150 0 0
151151 −3.15582 + 2.29284i −0.256817 + 0.186589i −0.708743 0.705467i 0.750737π-0.750737\pi
0.451925 + 0.892056i 0.350737π0.350737\pi
152152 0.326762 1.00567i 0.0265039 0.0815707i
153153 −6.81019 −0.550571
154154 18.0569 14.5181i 1.45506 1.16990i
155155 0 0
156156 −1.88214 + 5.79264i −0.150692 + 0.463782i
157157 14.8732 10.8060i 1.18701 0.862413i 0.194065 0.980989i 0.437833π-0.437833\pi
0.992945 + 0.118575i 0.0378327π0.0378327\pi
158158 −6.59107 4.78869i −0.524357 0.380968i
159159 3.59560 + 11.0661i 0.285149 + 0.877600i
160160 0 0
161161 −15.8034 11.4818i −1.24548 0.904894i
162162 1.70420 1.23818i 0.133895 0.0972802i
163163 −5.43005 + 16.7120i −0.425314 + 1.30898i 0.477379 + 0.878698i 0.341587π0.341587\pi
−0.902693 + 0.430285i 0.858413π0.858413\pi
164164 −2.27302 −0.177493
165165 0 0
166166 12.8087 0.994151
167167 −3.73220 + 11.4865i −0.288807 + 0.888855i 0.696425 + 0.717629i 0.254773π0.254773\pi
−0.985232 + 0.171226i 0.945227π0.945227\pi
168168 2.47194 1.79597i 0.190715 0.138562i
169169 5.46537 + 3.97083i 0.420413 + 0.305448i
170170 0 0
171171 −0.354657 1.09152i −0.0271213 0.0834707i
172172 −1.08885 0.791097i −0.0830241 0.0603206i
173173 19.6135 14.2500i 1.49119 1.08341i 0.517454 0.855711i 0.326880π-0.326880\pi
0.973732 0.227698i 0.0731200π-0.0731200\pi
174174 0.730731 2.24896i 0.0553966 0.170493i
175175 0 0
176176 −3.45547 9.09656i −0.260466 0.685679i
177177 8.39837 0.631260
178178 −8.19865 + 25.2329i −0.614515 + 1.89128i
179179 16.1310 11.7198i 1.20569 0.875982i 0.210854 0.977517i 0.432375π-0.432375\pi
0.994832 + 0.101535i 0.0323754π0.0323754\pi
180180 0 0
181181 −1.58615 4.88168i −0.117898 0.362852i 0.874643 0.484768i 0.161096π-0.161096\pi
−0.992540 + 0.121916i 0.961096π0.961096\pi
182182 5.39448 + 16.6025i 0.399865 + 1.23066i
183183 6.64456 + 4.82756i 0.491180 + 0.356863i
184184 4.39052 3.18990i 0.323674 0.235163i
185185 0 0
186186 2.31027 0.169397
187187 −8.02076 21.1148i −0.586536 1.54406i
188188 −5.20204 −0.379397
189189 1.02480 3.15401i 0.0745433 0.229421i
190190 0 0
191191 2.27606 + 1.65365i 0.164690 + 0.119654i 0.667078 0.744988i 0.267545π-0.267545\pi
−0.502388 + 0.864642i 0.667545π0.667545\pi
192192 −3.40931 10.4928i −0.246046 0.757252i
193193 −5.96502 18.3584i −0.429371 1.32147i −0.898746 0.438470i 0.855520π-0.855520\pi
0.469374 0.882999i 0.344480π-0.344480\pi
194194 −4.88889 3.55199i −0.351002 0.255018i
195195 0 0
196196 3.01128 9.26776i 0.215091 0.661983i
197197 3.57956 0.255033 0.127516 0.991836i 0.459299π-0.459299\pi
0.127516 + 0.991836i 0.459299π0.459299\pi
198198 5.84606 + 3.82555i 0.415461 + 0.271870i
199199 12.7087 0.900893 0.450447 0.892803i 0.351265π-0.351265\pi
0.450447 + 0.892803i 0.351265π0.351265\pi
200200 0 0
201201 3.36081 2.44177i 0.237053 0.172229i
202202 16.8205 + 12.2208i 1.18349 + 0.859853i
203203 −1.15041 3.54059i −0.0807427 0.248500i
204204 −5.12938 15.7866i −0.359129 1.10528i
205205 0 0
206206 13.1556 9.55813i 0.916597 0.665947i
207207 1.82019 5.60197i 0.126512 0.389364i
208208 7.33157 0.508353
209209 2.96652 2.38515i 0.205199 0.164984i
210210 0 0
211211 −1.08007 + 3.32412i −0.0743552 + 0.228842i −0.981326 0.192352i 0.938389π-0.938389\pi
0.906971 + 0.421193i 0.138389π0.138389\pi
212212 −22.9440 + 16.6698i −1.57580 + 1.14489i
213213 −10.1403 7.36733i −0.694799 0.504801i
214214 10.0971 + 31.0757i 0.690223 + 2.12429i
215215 0 0
216216 0.745386 + 0.541555i 0.0507171 + 0.0368481i
217217 2.94249 2.13784i 0.199749 0.145126i
218218 −4.42536 + 13.6199i −0.299723 + 0.922453i
219219 −5.73761 −0.387712
220220 0 0
221221 17.0179 1.14475
222222 7.51119 23.1171i 0.504118 1.55152i
223223 4.21140 3.05976i 0.282016 0.204897i −0.437780 0.899082i 0.644235π-0.644235\pi
0.719796 + 0.694185i 0.244235π0.244235\pi
224224 −21.5256 15.6392i −1.43824 1.04494i
225225 0 0
226226 0.196253 + 0.604005i 0.0130546 + 0.0401778i
227227 7.84944 + 5.70295i 0.520985 + 0.378518i 0.816975 0.576673i 0.195649π-0.195649\pi
−0.295990 + 0.955191i 0.595649π0.595649\pi
228228 2.26312 1.64425i 0.149878 0.108893i
229229 5.71715 17.5956i 0.377800 1.16275i −0.563770 0.825932i 0.690650π-0.690650\pi
0.941570 0.336817i 0.109350π-0.109350\pi
230230 0 0
231231 10.9859 0.537307i 0.722818 0.0353522i
232232 1.03427 0.0679034
233233 4.62115 14.2224i 0.302741 0.931742i −0.677769 0.735275i 0.737053π-0.737053\pi
0.980510 0.196467i 0.0629469π-0.0629469\pi
234234 −4.25861 + 3.09406i −0.278394 + 0.202265i
235235 0 0
236236 6.32559 + 19.4682i 0.411761 + 1.26727i
237237 −1.19514 3.67825i −0.0776324 0.238928i
238238 −38.4891 27.9639i −2.49488 1.81263i
239239 1.21932 0.885887i 0.0788712 0.0573033i −0.547651 0.836707i 0.684478π-0.684478\pi
0.626522 + 0.779404i 0.284478π0.284478\pi
240240 0 0
241241 −7.09571 −0.457075 −0.228537 0.973535i 0.573394π-0.573394\pi
−0.228537 + 0.973535i 0.573394π0.573394\pi
242242 −4.97573 + 22.6311i −0.319852 + 1.45478i
243243 1.00000 0.0641500
244244 −6.18607 + 19.0388i −0.396022 + 1.21883i
245245 0 0
246246 −1.58928 1.15468i −0.101329 0.0736198i
247247 0.886246 + 2.72758i 0.0563905 + 0.173552i
248248 0.312252 + 0.961014i 0.0198280 + 0.0610244i
249249 4.91927 + 3.57406i 0.311746 + 0.226497i
250250 0 0
251251 −4.22692 + 13.0091i −0.266801 + 0.821129i 0.724472 + 0.689304i 0.242084π0.242084\pi
−0.991273 + 0.131825i 0.957916π0.957916\pi
252252 8.08315 0.509191
253253 19.5125 0.954333i 1.22674 0.0599984i
254254 14.1250 0.886279
255255 0 0
256256 −5.59047 + 4.06172i −0.349405 + 0.253857i
257257 −6.71817 4.88104i −0.419068 0.304471i 0.358195 0.933647i 0.383392π-0.383392\pi
−0.777263 + 0.629176i 0.783392π0.783392\pi
258258 −0.359446 1.10626i −0.0223781 0.0688727i
259259 −11.8250 36.3937i −0.734773 2.26140i
260260 0 0
261261 0.908175 0.659827i 0.0562146 0.0408423i
262262 5.25789 16.1821i 0.324834 0.999735i
263263 −11.1345 −0.686582 −0.343291 0.939229i 0.611542π-0.611542\pi
−0.343291 + 0.939229i 0.611542π0.611542\pi
264264 −0.801187 + 2.94887i −0.0493096 + 0.181490i
265265 0 0
266266 2.47759 7.62522i 0.151910 0.467532i
267267 −10.1895 + 7.40313i −0.623589 + 0.453064i
268268 8.19157 + 5.95153i 0.500380 + 0.363547i
269269 7.03209 + 21.6426i 0.428754 + 1.31957i 0.899353 + 0.437223i 0.144038π0.144038\pi
−0.470599 + 0.882347i 0.655962π0.655962\pi
270270 0 0
271271 −6.30586 4.58148i −0.383054 0.278305i 0.379549 0.925172i 0.376079π-0.376079\pi
−0.762603 + 0.646867i 0.776079π0.776079\pi
272272 −16.1647 + 11.7443i −0.980128 + 0.712105i
273273 −2.56086 + 7.88152i −0.154990 + 0.477011i
274274 13.5613 0.819269
275275 0 0
276276 14.3568 0.864179
277277 −2.92552 + 9.00383i −0.175778 + 0.540988i −0.999668 0.0257612i 0.991799π-0.991799\pi
0.823891 + 0.566749i 0.191799π0.191799\pi
278278 11.8880 8.63711i 0.712992 0.518019i
279279 0.887273 + 0.644641i 0.0531196 + 0.0385937i
280280 0 0
281281 9.67271 + 29.7696i 0.577026 + 1.77590i 0.629175 + 0.777263i 0.283393π0.283393\pi
−0.0521495 + 0.998639i 0.516607π0.516607\pi
282282 −3.63723 2.64260i −0.216594 0.157365i
283283 −19.7500 + 14.3492i −1.17402 + 0.852972i −0.991484 0.130228i 0.958429π-0.958429\pi
−0.182531 + 0.983200i 0.558429π0.558429\pi
284284 9.44055 29.0550i 0.560194 1.72410i
285285 0 0
286286 −14.6086 9.55960i −0.863826 0.565271i
287287 −3.09270 −0.182556
288288 2.47926 7.63038i 0.146092 0.449624i
289289 −23.7678 + 17.2684i −1.39811 + 1.01579i
290290 0 0
291291 −0.886486 2.72832i −0.0519667 0.159937i
292292 −4.32152 13.3003i −0.252898 0.778340i
293293 9.56230 + 6.94742i 0.558636 + 0.405873i 0.830959 0.556333i 0.187792π-0.187792\pi
−0.272324 + 0.962206i 0.587792π0.587792\pi
294294 6.81343 4.95025i 0.397367 0.288704i
295295 0 0
296296 10.6313 0.617933
297297 1.17776 + 3.10047i 0.0683405 + 0.179907i
298298 40.0669 2.32101
299299 −4.54845 + 13.9987i −0.263044 + 0.809565i
300300 0 0
301301 −1.48150 1.07637i −0.0853923 0.0620412i
302302 −2.53922 7.81492i −0.146116 0.449698i
303303 3.05000 + 9.38694i 0.175218 + 0.539266i
304304 −2.72417 1.97922i −0.156242 0.113516i
305305 0 0
306306 4.43307 13.6436i 0.253422 0.779952i
307307 −22.3217 −1.27396 −0.636982 0.770878i 0.719818π-0.719818\pi
−0.636982 + 0.770878i 0.719818π0.719818\pi
308308 9.52000 + 25.0615i 0.542453 + 1.42801i
309309 7.71953 0.439149
310310 0 0
311311 15.7624 11.4521i 0.893804 0.649386i −0.0430633 0.999072i 0.513712π-0.513712\pi
0.936867 + 0.349686i 0.113712π0.113712\pi
312312 −1.86264 1.35328i −0.105451 0.0766146i
313313 −5.36228 16.5034i −0.303094 0.932827i −0.980382 0.197109i 0.936845π-0.936845\pi
0.677288 0.735718i 0.263155π-0.263155\pi
314314 11.9672 + 36.8312i 0.675348 + 2.07851i
315315 0 0
316316 7.62634 5.54086i 0.429015 0.311698i
317317 −0.256706 + 0.790059i −0.0144180 + 0.0443741i −0.958007 0.286746i 0.907426π-0.907426\pi
0.943589 + 0.331120i 0.107426π0.107426\pi
318318 −24.5105 −1.37448
319319 3.11538 + 2.03865i 0.174428 + 0.114142i
320320 0 0
321321 −4.79328 + 14.7522i −0.267535 + 0.823388i
322322 33.2899 24.1865i 1.85518 1.34786i
323323 −6.32328 4.59413i −0.351837 0.255624i
324324 0.753192 + 2.31809i 0.0418440 + 0.128783i
325325 0 0
326326 −29.9462 21.7572i −1.65857 1.20502i
327327 −5.49997 + 3.99596i −0.304149 + 0.220977i
328328 0.265513 0.817166i 0.0146605 0.0451205i
329329 −7.07794 −0.390220
330330 0 0
331331 −31.5311 −1.73311 −0.866554 0.499084i 0.833670π-0.833670\pi
−0.866554 + 0.499084i 0.833670π0.833670\pi
332332 −4.57982 + 14.0953i −0.251351 + 0.773577i
333333 9.33514 6.78238i 0.511563 0.371672i
334334 −20.5828 14.9543i −1.12624 0.818261i
335335 0 0
336336 −3.00670 9.25367i −0.164029 0.504829i
337337 −13.1335 9.54207i −0.715429 0.519790i 0.169491 0.985532i 0.445788π-0.445788\pi
−0.884921 + 0.465742i 0.845788π0.845788\pi
338338 −11.5129 + 8.36458i −0.626217 + 0.454973i
339339 −0.0931652 + 0.286733i −0.00506004 + 0.0155732i
340340 0 0
341341 −0.953695 + 3.51019i −0.0516455 + 0.190087i
342342 2.41763 0.130730
343343 −3.07643 + 9.46829i −0.166112 + 0.511239i
344344 0.411594 0.299040i 0.0221916 0.0161232i
345345 0 0
346346 15.7813 + 48.5698i 0.848408 + 2.61113i
347347 3.84726 + 11.8406i 0.206532 + 0.635639i 0.999647 + 0.0265674i 0.00845767π0.00845767\pi
−0.793115 + 0.609071i 0.791542π0.791542\pi
348348 2.21357 + 1.60825i 0.118660 + 0.0862113i
349349 −26.3980 + 19.1793i −1.41305 + 1.02664i −0.420182 + 0.907440i 0.638034π0.638034\pi
−0.992870 + 0.119203i 0.961966π0.961966\pi
350350 0 0
351351 −2.49889 −0.133381
352352 26.5777 1.29989i 1.41660 0.0692842i
353353 15.7921 0.840530 0.420265 0.907402i 0.361937π-0.361937\pi
0.420265 + 0.907402i 0.361937π0.361937\pi
354354 −5.46690 + 16.8254i −0.290562 + 0.894259i
355355 0 0
356356 −24.8358 18.0443i −1.31629 0.956343i
357357 −6.97909 21.4794i −0.369373 1.13681i
358358 12.9792 + 39.9460i 0.685974 + 2.11121i
359359 −14.6935 10.6755i −0.775494 0.563429i 0.128129 0.991757i 0.459103π-0.459103\pi
−0.903623 + 0.428328i 0.859103π0.859103\pi
360360 0 0
361361 −5.46429 + 16.8173i −0.287594 + 0.885123i
362362 10.8125 0.568292
363363 −8.22577 + 7.30320i −0.431741 + 0.383319i
364364 −20.1989 −1.05871
365365 0 0
366366 −13.9968 + 10.1693i −0.731626 + 0.531558i
367367 −0.381893 0.277462i −0.0199347 0.0144834i 0.577773 0.816197i 0.303922π-0.303922\pi
−0.597708 + 0.801714i 0.703922π0.703922\pi
368368 −5.34032 16.4358i −0.278383 0.856776i
369369 −0.288179 0.886924i −0.0150020 0.0461714i
370370 0 0
371371 −31.2179 + 22.6811i −1.62075 + 1.17755i
372372 −0.826048 + 2.54231i −0.0428286 + 0.131813i
373373 −15.4102 −0.797910 −0.398955 0.916970i 0.630627π-0.630627\pi
−0.398955 + 0.916970i 0.630627π0.630627\pi
374374 47.5226 2.32428i 2.45733 0.120186i
375375 0 0
376376 0.607653 1.87017i 0.0313373 0.0964464i
377377 −2.26942 + 1.64883i −0.116881 + 0.0849192i
378378 5.65169 + 4.10619i 0.290692 + 0.211200i
379379 −5.95617 18.3312i −0.305948 0.941611i −0.979322 0.202309i 0.935156π-0.935156\pi
0.673374 0.739302i 0.264844π-0.264844\pi
380380 0 0
381381 5.42477 + 3.94133i 0.277920 + 0.201920i
382382 −4.79454 + 3.48344i −0.245310 + 0.178228i
383383 2.30163 7.08369i 0.117608 0.361960i −0.874874 0.484350i 0.839056π-0.839056\pi
0.992482 + 0.122390i 0.0390560π0.0390560\pi
384384 7.19453 0.367144
385385 0 0
386386 40.6624 2.06966
387387 0.170636 0.525162i 0.00867390 0.0266955i
388388 5.65680 4.10990i 0.287180 0.208649i
389389 0.577492 + 0.419572i 0.0292800 + 0.0212732i 0.602329 0.798248i 0.294240π-0.294240\pi
−0.573049 + 0.819521i 0.694240π0.694240\pi
390390 0 0
391391 −12.3958 38.1505i −0.626885 1.92935i
392392 2.98007 + 2.16515i 0.150516 + 0.109356i
393393 6.53467 4.74771i 0.329630 0.239490i
394394 −2.33010 + 7.17132i −0.117389 + 0.361286i
395395 0 0
396396 −6.30007 + 5.06539i −0.316590 + 0.254546i
397397 0.764171 0.0383526 0.0191763 0.999816i 0.493896π-0.493896\pi
0.0191763 + 0.999816i 0.493896π0.493896\pi
398398 −8.27267 + 25.4607i −0.414672 + 1.27623i
399399 3.07922 2.23718i 0.154154 0.111999i
400400 0 0
401401 −4.86839 14.9834i −0.243116 0.748234i −0.995941 0.0900128i 0.971309π-0.971309\pi
0.752825 0.658221i 0.228691π-0.228691\pi
402402 2.70416 + 8.32254i 0.134871 + 0.415091i
403403 −2.21719 1.61089i −0.110446 0.0802439i
404404 −19.4625 + 14.1403i −0.968296 + 0.703508i
405405 0 0
406406 7.84210 0.389197
407407 32.0231 + 20.9553i 1.58732 + 1.03871i
408408 6.27456 0.310637
409409 −0.809935 + 2.49272i −0.0400487 + 0.123257i −0.969082 0.246739i 0.920641π-0.920641\pi
0.929033 + 0.369996i 0.120641π0.120641\pi
410410 0 0
411411 5.20830 + 3.78405i 0.256907 + 0.186654i
412412 5.81429 + 17.8945i 0.286450 + 0.881601i
413413 8.60666 + 26.4886i 0.423506 + 1.30342i
414414 10.0382 + 7.29318i 0.493350 + 0.358440i
415415 0 0
416416 −6.19539 + 19.0674i −0.303754 + 0.934858i
417417 6.97567 0.341600
418418 2.84738 + 7.49576i 0.139270 + 0.366630i
419419 −18.0078 −0.879737 −0.439868 0.898062i 0.644975π-0.644975\pi
−0.439868 + 0.898062i 0.644975π0.644975\pi
420420 0 0
421421 −0.947495 + 0.688395i −0.0461781 + 0.0335503i −0.610635 0.791912i 0.709086π-0.709086\pi
0.564457 + 0.825463i 0.309086π0.309086\pi
422422 −5.95650 4.32765i −0.289958 0.210667i
423423 −0.659526 2.02981i −0.0320673 0.0986929i
424424 −3.31280 10.1957i −0.160884 0.495149i
425425 0 0
426426 21.3606 15.5193i 1.03492 0.751915i
427427 −8.41683 + 25.9043i −0.407319 + 1.25360i
428428 −37.8072 −1.82748
429429 −2.94308 7.74771i −0.142093 0.374063i
430430 0 0
431431 10.8441 33.3746i 0.522340 1.60760i −0.247177 0.968970i 0.579503π-0.579503\pi
0.769517 0.638626i 0.220497π-0.220497\pi
432432 2.37360 1.72452i 0.114200 0.0829712i
433433 14.7452 + 10.7130i 0.708608 + 0.514834i 0.882724 0.469891i 0.155707π-0.155707\pi
−0.174116 + 0.984725i 0.555707π0.555707\pi
434434 2.36757 + 7.28663i 0.113647 + 0.349769i
435435 0 0
436436 −13.4055 9.73969i −0.642009 0.466446i
437437 5.46912 3.97355i 0.261624 0.190081i
438438 3.73488 11.4948i 0.178460 0.549242i
439439 −19.8155 −0.945743 −0.472871 0.881131i 0.656782π-0.656782\pi
−0.472871 + 0.881131i 0.656782π0.656782\pi
440440 0 0
441441 3.99802 0.190382
442442 −11.0777 + 34.0938i −0.526914 + 1.62168i
443443 −13.5012 + 9.80922i −0.641463 + 0.466050i −0.860352 0.509700i 0.829757π-0.829757\pi
0.218890 + 0.975750i 0.429757π0.429757\pi
444444 22.7533 + 16.5312i 1.07982 + 0.784538i
445445 0 0
446446 3.38856 + 10.4289i 0.160453 + 0.493823i
447447 15.3879 + 11.1800i 0.727823 + 0.528794i
448448 29.6005 21.5061i 1.39849 1.01607i
449449 −4.07811 + 12.5511i −0.192458 + 0.592325i 0.807539 + 0.589815i 0.200799π0.200799\pi
−0.999997 + 0.00251063i 0.999201π0.999201\pi
450450 0 0
451451 2.41047 1.93807i 0.113505 0.0912603i
452452 −0.734843 −0.0345641
453453 1.20542 3.70989i 0.0566354 0.174306i
454454 −16.5349 + 12.0133i −0.776022 + 0.563813i
455455 0 0
456456 0.326762 + 1.00567i 0.0153020 + 0.0470948i
457457 6.57194 + 20.2264i 0.307423 + 0.946149i 0.978762 + 0.204999i 0.0657192π0.0657192\pi
−0.671340 + 0.741150i 0.734281π0.734281\pi
458458 31.5296 + 22.9076i 1.47328 + 1.07040i
459459 5.50956 4.00293i 0.257164 0.186841i
460460 0 0
461461 −20.0772 −0.935086 −0.467543 0.883970i 0.654861π-0.654861\pi
−0.467543 + 0.883970i 0.654861π0.654861\pi
462462 −6.07478 + 22.3590i −0.282624 + 1.04023i
463463 −0.962526 −0.0447324 −0.0223662 0.999750i 0.507120π-0.507120\pi
−0.0223662 + 0.999750i 0.507120π0.507120\pi
464464 1.01776 3.13234i 0.0472482 0.145415i
465465 0 0
466466 25.4852 + 18.5161i 1.18058 + 0.857742i
467467 −4.60838 14.1831i −0.213250 0.656317i −0.999273 0.0381194i 0.987863π-0.987863\pi
0.786023 0.618197i 0.212137π-0.212137\pi
468468 −1.88214 5.79264i −0.0870020 0.267765i
469469 11.1455 + 8.09771i 0.514653 + 0.373917i
470470 0 0
471471 −5.68106 + 17.4845i −0.261769 + 0.805643i
472472 −7.73783 −0.356162
473473 1.82922 0.0894649i 0.0841074 0.00411360i
474474 8.14701 0.374204
475475 0 0
476476 44.5346 32.3563i 2.04124 1.48305i
477477 −9.41340 6.83923i −0.431010 0.313147i
478478 0.981082 + 3.01946i 0.0448737 + 0.138107i
479479 −0.146946 0.452253i −0.00671413 0.0206640i 0.947643 0.319331i 0.103458π-0.103458\pi
−0.954357 + 0.298667i 0.903458π0.903458\pi
480480 0 0
481481 −23.3274 + 16.9484i −1.06364 + 0.772780i
482482 4.61893 14.2156i 0.210387 0.647503i
483483 19.5340 0.888829
484484 −23.1250 13.5673i −1.05114 0.616697i
485485 0 0
486486 −0.650947 + 2.00341i −0.0295276 + 0.0908765i
487487 28.6011 20.7799i 1.29604 0.941629i 0.296132 0.955147i 0.404303π-0.404303\pi
0.999909 + 0.0135183i 0.00430313π0.00430313\pi
488488 −6.12196 4.44786i −0.277128 0.201345i
489489 −5.43005 16.7120i −0.245555 0.755741i
490490 0 0
491491 24.3779 + 17.7116i 1.10016 + 0.799314i 0.981086 0.193572i 0.0620072π-0.0620072\pi
0.119075 + 0.992885i 0.462007π0.462007\pi
492492 1.83891 1.33605i 0.0829047 0.0602338i
493493 2.36240 7.27072i 0.106397 0.327457i
494494 −6.04137 −0.271814
495495 0 0
496496 3.21773 0.144480
497497 12.8449 39.5326i 0.576173 1.77328i
498498 −10.3625 + 7.52879i −0.464354 + 0.337373i
499499 29.5127 + 21.4422i 1.32117 + 0.959887i 0.999917 + 0.0128935i 0.00410424π0.00410424\pi
0.321254 + 0.946993i 0.395896π0.395896\pi
500500 0 0
501501 −3.73220 11.4865i −0.166743 0.513181i
502502 −23.3111 16.9365i −1.04043 0.755914i
503503 −12.4792 + 9.06666i −0.556420 + 0.404262i −0.830147 0.557545i 0.811743π-0.811743\pi
0.273727 + 0.961807i 0.411743π0.411743\pi
504504 −0.944199 + 2.90595i −0.0420580 + 0.129441i
505505 0 0
506506 −10.7897 + 39.7127i −0.479659 + 1.76544i
507507 −6.75557 −0.300025
508508 −5.05045 + 15.5437i −0.224077 + 0.689639i
509509 −10.2238 + 7.42806i −0.453164 + 0.329243i −0.790844 0.612018i 0.790358π-0.790358\pi
0.337680 + 0.941261i 0.390358π0.390358\pi
510510 0 0
511511 −5.87991 18.0965i −0.260112 0.800542i
512512 −8.94464 27.5288i −0.395301 1.21661i
513513 0.928503 + 0.674597i 0.0409944 + 0.0297842i
514514 14.1519 10.2819i 0.624213 0.453517i
515515 0 0
516516 1.34589 0.0592497
517517 5.51660 4.43547i 0.242620 0.195072i
518518 80.6091 3.54176
519519 −7.49168 + 23.0570i −0.328848 + 1.01209i
520520 0 0
521521 7.43033 + 5.39845i 0.325529 + 0.236510i 0.738531 0.674220i 0.235520π-0.235520\pi
−0.413002 + 0.910730i 0.635520π0.635520\pi
522522 0.730731 + 2.24896i 0.0319832 + 0.0984342i
523523 10.3781 + 31.9404i 0.453801 + 1.39665i 0.872537 + 0.488547i 0.162473π0.162473\pi
−0.418737 + 0.908108i 0.637527π0.637527\pi
524524 15.9275 + 11.5720i 0.695795 + 0.505525i
525525 0 0
526526 7.24796 22.3069i 0.316026 0.972629i
527527 7.46893 0.325352
528528 8.14236 + 5.32820i 0.354351 + 0.231880i
529529 11.6952 0.508486
530530 0 0
531531 −6.79443 + 4.93644i −0.294853 + 0.214223i
532532 7.50523 + 5.45287i 0.325393 + 0.236412i
533533 0.720127 + 2.21632i 0.0311922 + 0.0959996i
534534 −8.19865 25.2329i −0.354790 1.09193i
535535 0 0
536536 −3.09648 + 2.24972i −0.133747 + 0.0971731i
537537 −6.16149 + 18.9631i −0.265888 + 0.818319i
538538 −47.9364 −2.06669
539539 4.70870 + 12.3957i 0.202818 + 0.533921i
540540 0 0
541541 13.7829 42.4194i 0.592573 1.82375i 0.0261178 0.999659i 0.491685π-0.491685\pi
0.566455 0.824093i 0.308315π-0.308315\pi
542542 13.2834 9.65093i 0.570569 0.414543i
543543 4.15260 + 3.01704i 0.178205 + 0.129474i
544544 −16.8842 51.9643i −0.723906 2.22795i
545545 0 0
546546 −14.1229 10.2609i −0.604405 0.439126i
547547 −15.5582 + 11.3037i −0.665219 + 0.483310i −0.868421 0.495827i 0.834865π-0.834865\pi
0.203202 + 0.979137i 0.434865π0.434865\pi
548548 −4.84891 + 14.9234i −0.207135 + 0.637497i
549549 −8.21313 −0.350528
550550 0 0
551551 1.28836 0.0548860
552552 −1.67703 + 5.16137i −0.0713791 + 0.219682i
553553 10.3765 7.53895i 0.441252 0.320589i
554554 −16.1340 11.7220i −0.685468 0.498022i
555555 0 0
556556 5.25402 + 16.1702i 0.222820 + 0.685770i
557557 26.9944 + 19.6126i 1.14379 + 0.831011i 0.987643 0.156723i 0.0500931π-0.0500931\pi
0.156145 + 0.987734i 0.450093π0.450093\pi
558558 −1.86905 + 1.35794i −0.0791231 + 0.0574863i
559559 −0.426399 + 1.31232i −0.0180348 + 0.0555053i
560560 0 0
561561 18.8999 + 12.3677i 0.797953 + 0.522165i
562562 −65.9370 −2.78139
563563 −0.646509 + 1.98975i −0.0272471 + 0.0838580i −0.963755 0.266788i 0.914038π-0.914038\pi
0.936508 + 0.350646i 0.114038π0.114038\pi
564564 4.20853 3.05768i 0.177211 0.128752i
565565 0 0
566566 −15.8911 48.9079i −0.667955 2.05575i
567567 1.02480 + 3.15401i 0.0430376 + 0.132456i
568568 9.34271 + 6.78788i 0.392011 + 0.284813i
569569 7.53693 5.47590i 0.315964 0.229562i −0.418487 0.908223i 0.637439π-0.637439\pi
0.734452 + 0.678661i 0.237439π0.237439\pi
570570 0 0
571571 2.32989 0.0975029 0.0487514 0.998811i 0.484476π-0.484476\pi
0.0487514 + 0.998811i 0.484476π0.484476\pi
572572 15.7432 12.6578i 0.658254 0.529251i
573573 −2.81336 −0.117530
574574 2.01318 6.19594i 0.0840286 0.258614i
575575 0 0
576576 8.92570 + 6.48490i 0.371904 + 0.270204i
577577 9.10449 + 28.0207i 0.379025 + 1.16652i 0.940723 + 0.339176i 0.110148π0.110148\pi
−0.561698 + 0.827342i 0.689852π0.689852\pi
578578 −19.1240 58.8575i −0.795452 2.44815i
579579 15.6166 + 11.3461i 0.649005 + 0.471530i
580580 0 0
581581 −6.23136 + 19.1781i −0.258520 + 0.795643i
582582 6.04300 0.250491
583583 10.1181 37.2409i 0.419049 1.54236i
584584 5.28634 0.218750
585585 0 0
586586 −20.1431 + 14.6348i −0.832103 + 0.604558i
587587 −33.5877 24.4029i −1.38631 1.00722i −0.996258 0.0864248i 0.972456π-0.972456\pi
−0.390056 0.920791i 0.627544π-0.627544\pi
588588 3.01128 + 9.26776i 0.124183 + 0.382196i
589589 0.388962 + 1.19710i 0.0160269 + 0.0493258i
590590 0 0
591591 −2.89592 + 2.10401i −0.119122 + 0.0865475i
592592 10.4615 32.1973i 0.429967 1.32330i
593593 9.36964 0.384765 0.192383 0.981320i 0.438379π-0.438379\pi
0.192383 + 0.981320i 0.438379π0.438379\pi
594594 −6.97816 + 0.341294i −0.286317 + 0.0140035i
595595 0 0
596596 −14.3261 + 44.0912i −0.586820 + 1.80605i
597597 −10.2815 + 7.46997i −0.420795 + 0.305725i
598598 −25.0843 18.2248i −1.02577 0.745268i
599599 0.406983 + 1.25256i 0.0166289 + 0.0511784i 0.959027 0.283316i 0.0914345π-0.0914345\pi
−0.942398 + 0.334494i 0.891434π0.891434\pi
600600 0 0
601601 −12.6422 9.18512i −0.515688 0.374669i 0.299289 0.954162i 0.403250π-0.403250\pi
−0.814977 + 0.579493i 0.803250π0.803250\pi
602602 3.12080 2.26739i 0.127194 0.0924120i
603603 −1.28371 + 3.95087i −0.0522769 + 0.160892i
604604 9.50777 0.386866
605605 0 0
606606 −20.7913 −0.844588
607607 −7.48201 + 23.0273i −0.303685 + 0.934647i 0.676479 + 0.736462i 0.263505π0.263505\pi
−0.980165 + 0.198186i 0.936495π0.936495\pi
608608 7.44943 5.41233i 0.302114 0.219499i
609609 3.01180 + 2.18820i 0.122044 + 0.0886705i
610610 0 0
611611 1.64808 + 5.07227i 0.0666742 + 0.205202i
612612 13.4289 + 9.75666i 0.542831 + 0.394390i
613613 3.30589 2.40187i 0.133524 0.0970105i −0.519019 0.854763i 0.673702π-0.673702\pi
0.652542 + 0.757752i 0.273702π0.273702\pi
614614 14.5302 44.7194i 0.586392 1.80473i
615615 0 0
616616 −10.1218 + 0.495047i −0.407820 + 0.0199460i
617617 −16.9835 −0.683731 −0.341866 0.939749i 0.611059π-0.611059\pi
−0.341866 + 0.939749i 0.611059π0.611059\pi
618618 −5.02501 + 15.4654i −0.202135 + 0.622109i
619619 25.9942 18.8859i 1.04480 0.759089i 0.0735802 0.997289i 0.476558π-0.476558\pi
0.971216 + 0.238200i 0.0765575π0.0765575\pi
620620 0 0
621621 1.82019 + 5.60197i 0.0730417 + 0.224799i
622622 12.6827 + 39.0332i 0.508528 + 1.56509i
623623 −33.7918 24.5512i −1.35384 0.983623i
624624 −5.93136 + 4.30939i −0.237444 + 0.172514i
625625 0 0
626626 36.5536 1.46098
627627 −0.998011 + 3.67330i −0.0398567 + 0.146698i
628628 −44.8095 −1.78809
629629 24.2831 74.7358i 0.968232 2.97991i
630630 0 0
631631 5.10947 + 3.71225i 0.203405 + 0.147782i 0.684825 0.728708i 0.259879π-0.259879\pi
−0.481420 + 0.876490i 0.659879π0.659879\pi
632632 1.10114 + 3.38895i 0.0438008 + 0.134805i
633633 −1.08007 3.32412i −0.0429290 0.132122i
634634 −1.41571 1.02857i −0.0562250 0.0408499i
635635 0 0
636636 8.76384 26.9723i 0.347509 1.06952i
637637 −9.99059 −0.395842
638638 −6.11219 + 4.91434i −0.241984 + 0.194560i
639639 12.5340 0.495839
640640 0 0
641641 −11.8814 + 8.63236i −0.469288 + 0.340958i −0.797164 0.603763i 0.793667π-0.793667\pi
0.327876 + 0.944721i 0.393667π0.393667\pi
642642 −26.4345 19.2058i −1.04329 0.757993i
643643 4.99093 + 15.3605i 0.196823 + 0.605759i 0.999950 + 0.00995196i 0.00316786π0.00316786\pi
−0.803127 + 0.595807i 0.796832π0.796832\pi
644644 14.7129 + 45.2816i 0.579769 + 1.78434i
645645 0 0
646646 13.3200 9.67758i 0.524070 0.380759i
647647 −8.58676 + 26.4273i −0.337581 + 1.03897i 0.627856 + 0.778329i 0.283933π0.283933\pi
−0.965437 + 0.260637i 0.916067π0.916067\pi
648648 −0.921348 −0.0361940
649649 −23.3075 15.2519i −0.914898 0.598691i
650650 0 0
651651 −1.12393 + 3.45910i −0.0440503 + 0.135573i
652652 34.6499 25.1747i 1.35700 0.985916i
653653 −27.5595 20.0232i −1.07849 0.783568i −0.101070 0.994879i 0.532227π-0.532227\pi
−0.977419 + 0.211312i 0.932227π0.932227\pi
654654 −4.42536 13.6199i −0.173045 0.532579i
655655 0 0
656656 −2.21354 1.60823i −0.0864244 0.0627910i
657657 4.64182 3.37248i 0.181095 0.131573i
658658 4.60737 14.1800i 0.179614 0.552795i
659659 14.4196 0.561709 0.280855 0.959750i 0.409382π-0.409382\pi
0.280855 + 0.959750i 0.409382π0.409382\pi
660660 0 0
661661 26.4275 1.02791 0.513956 0.857817i 0.328179π-0.328179\pi
0.513956 + 0.857817i 0.328179π0.328179\pi
662662 20.5251 63.1697i 0.797730 2.45516i
663663 −13.7678 + 10.0029i −0.534695 + 0.388479i
664664 −4.53236 3.29295i −0.175890 0.127791i
665665 0 0
666666 7.51119 + 23.1171i 0.291053 + 0.895769i
667667 5.34939 + 3.88656i 0.207129 + 0.150488i
668668 23.8157 17.3032i 0.921459 0.669479i
669669 −1.60861 + 4.95080i −0.0621925 + 0.191409i
670670 0 0
671671 −9.67309 25.4645i −0.373426 0.983047i
672672 26.6071 1.02639
673673 −11.2213 + 34.5357i −0.432550 + 1.33125i 0.463026 + 0.886345i 0.346764π0.346764\pi
−0.895576 + 0.444908i 0.853236π0.853236\pi
674674 27.6659 20.1005i 1.06565 0.774241i
675675 0 0
676676 −5.08824 15.6600i −0.195702 0.602308i
677677 −3.50556 10.7890i −0.134730 0.414655i 0.860818 0.508913i 0.169952π-0.169952\pi
−0.995548 + 0.0942574i 0.969952π0.969952\pi
678678 −0.513798 0.373296i −0.0197323 0.0143363i
679679 7.69669 5.59198i 0.295372 0.214600i
680680 0 0
681681 −9.70244 −0.371798
682682 −6.41154 4.19559i −0.245511 0.160657i
683683 −39.4269 −1.50863 −0.754314 0.656514i 0.772030π-0.772030\pi
−0.754314 + 0.656514i 0.772030π0.772030\pi
684684 −0.864433 + 2.66045i −0.0330524 + 0.101725i
685685 0 0
686686 −16.9663 12.3267i −0.647775 0.470636i
687687 5.71715 + 17.5956i 0.218123 + 0.671313i
688688 −0.500634 1.54079i −0.0190865 0.0587421i
689689 23.5230 + 17.0905i 0.896155 + 0.651095i
690690 0 0
691691 4.56613 14.0531i 0.173704 0.534606i −0.825868 0.563864i 0.809314π-0.809314\pi
0.999572 + 0.0292578i 0.00931437π0.00931437\pi
692692 −59.0909 −2.24630
693693 −8.57194 + 6.89203i −0.325621 + 0.261806i
694694 −26.2260 −0.995526
695695 0 0
696696 −0.836745 + 0.607931i −0.0317167 + 0.0230436i
697697 −5.13804 3.73300i −0.194617 0.141398i
698698 −21.2402 65.3707i −0.803954 2.47432i
699699 4.62115 + 14.2224i 0.174788 + 0.537942i
700700 0 0
701701 5.76774 4.19051i 0.217845 0.158273i −0.473511 0.880788i 0.657014π-0.657014\pi
0.691356 + 0.722514i 0.257014π0.257014\pi
702702 1.62664 5.00629i 0.0613937 0.188950i
703703 13.2431 0.499472
704704 −9.59389 + 35.3115i −0.361583 + 1.33085i
705705 0 0
706706 −10.2798 + 31.6381i −0.386887 + 1.19071i
707707 −26.4809 + 19.2395i −0.995917 + 0.723576i
708708 −16.5606 12.0320i −0.622386 0.452190i
709709 −1.65473 5.09274i −0.0621447 0.191262i 0.915164 0.403082i 0.132061π-0.132061\pi
−0.977309 + 0.211820i 0.932061π0.932061\pi
710710 0 0
711711 3.12890 + 2.27328i 0.117343 + 0.0852548i
712712 9.38811 6.82086i 0.351834 0.255623i
713713 −1.99626 + 6.14385i −0.0747604 + 0.230089i
714714 47.5751 1.78045
715715 0 0
716716 −48.5989 −1.81623
717717 −0.465738 + 1.43340i −0.0173933 + 0.0535311i
718718 30.9520 22.4880i 1.15512 0.839243i
719719 32.9940 + 23.9716i 1.23047 + 0.893989i 0.996925 0.0783569i 0.0249674π-0.0249674\pi
0.233545 + 0.972346i 0.424967π0.424967\pi
720720 0 0
721721 7.91098 + 24.3475i 0.294620 + 0.906749i
722722 −30.1351 21.8944i −1.12151 0.814825i
723723 5.74055 4.17075i 0.213493 0.155112i
724724 −3.86606 + 11.8985i −0.143681 + 0.442204i
725725 0 0
726726 −9.27676 21.2336i −0.344293 0.788052i
727727 28.6101 1.06109 0.530546 0.847656i 0.321987π-0.321987\pi
0.530546 + 0.847656i 0.321987π0.321987\pi
728728 2.35944 7.26162i 0.0874468 0.269134i
729729 −0.809017 + 0.587785i −0.0299636 + 0.0217698i
730730 0 0
731731 −1.16206 3.57646i −0.0429804 0.132280i
732732 −6.18607 19.0388i −0.228644 0.703693i
733733 3.55653 + 2.58397i 0.131364 + 0.0954412i 0.651527 0.758626i 0.274129π-0.274129\pi
−0.520163 + 0.854067i 0.674129π0.674129\pi
734734 0.804462 0.584476i 0.0296932 0.0215734i
735735 0 0
736736 47.2579 1.74195
737737 −13.7614 + 0.673056i −0.506909 + 0.0247924i
738738 1.96446 0.0723129
739739 −3.25000 + 10.0025i −0.119553 + 0.367947i −0.992869 0.119207i 0.961965π-0.961965\pi
0.873316 + 0.487154i 0.161965π0.161965\pi
740740 0 0
741741 −2.32022 1.68574i −0.0852355 0.0619272i
742742 −25.1184 77.3064i −0.922125 2.83801i
743743 10.6580 + 32.8020i 0.391005 + 1.20339i 0.932030 + 0.362382i 0.118036π0.118036\pi
−0.541025 + 0.841007i 0.681964π0.681964\pi
744744 −0.817487 0.593939i −0.0299705 0.0217749i
745745 0 0
746746 10.0312 30.8729i 0.367269 1.13034i
747747 −6.08055 −0.222476
748748 −14.4342 + 53.1268i −0.527766 + 1.94251i
749749 −51.4408 −1.87961
750750 0 0
751751 1.92630 1.39954i 0.0702918 0.0510700i −0.552084 0.833788i 0.686167π-0.686167\pi
0.622376 + 0.782718i 0.286167π0.286167\pi
752752 −5.06591 3.68060i −0.184735 0.134218i
753753 −4.22692 13.0091i −0.154038 0.474079i
754754 −1.82601 5.61989i −0.0664995 0.204664i
755755 0 0
756756 −6.53941 + 4.75116i −0.237836 + 0.172798i
757757 2.59435 7.98459i 0.0942932 0.290205i −0.892776 0.450502i 0.851245π-0.851245\pi
0.987069 + 0.160297i 0.0512452π0.0512452\pi
758758 40.6021 1.47473
759759 −15.2250 + 12.2412i −0.552631 + 0.444328i
760760 0 0
761761 3.23481 9.95573i 0.117262 0.360895i −0.875150 0.483851i 0.839238π-0.839238\pi
0.992412 + 0.122956i 0.0392375π0.0392375\pi
762762 −11.4273 + 8.30245i −0.413969 + 0.300766i
763763 −18.2397 13.2519i −0.660322 0.479752i
764764 −2.11900 6.52162i −0.0766628 0.235944i
765765 0 0
766766 12.6933 + 9.22222i 0.458627 + 0.333212i
767767 16.9785 12.3356i 0.613058 0.445413i
768768 2.13537 6.57200i 0.0770536 0.237146i
769769 −9.70799 −0.350079 −0.175040 0.984561i 0.556005π-0.556005\pi
−0.175040 + 0.984561i 0.556005π0.556005\pi
770770 0 0
771771 8.30411 0.299065
772772 −14.5390 + 44.7465i −0.523271 + 1.61046i
773773 25.8560 18.7855i 0.929977 0.675668i −0.0160101 0.999872i 0.505096π-0.505096\pi
0.945987 + 0.324204i 0.105096π0.105096\pi
774774 0.941041 + 0.683706i 0.0338250 + 0.0245753i
775775 0 0
776776 0.816762 + 2.51374i 0.0293201 + 0.0902378i
777777 30.9584 + 22.4926i 1.11063 + 0.806917i
778778 −1.21649 + 0.883833i −0.0436133 + 0.0316869i
779779 0.330741 1.01792i 0.0118500 0.0364706i
780780 0 0
781781 14.7621 + 38.8614i 0.528229 + 1.39057i
782782 84.5001 3.02172
783783 −0.346892 + 1.06762i −0.0123969 + 0.0381537i
784784 9.48971 6.89468i 0.338918 0.246239i
785785 0 0
786786 5.25789 + 16.1821i 0.187543 + 0.577197i
787787 14.3605 + 44.1971i 0.511896 + 1.57545i 0.788859 + 0.614574i 0.210672π0.210672\pi
−0.276963 + 0.960881i 0.589328π0.589328\pi
788788 −7.05847 5.12828i −0.251448 0.182687i
789789 9.00799 6.54469i 0.320693 0.232997i
790790 0 0
791791 −0.999835 −0.0355500
792792 −1.08513 2.85661i −0.0385583 0.101505i
793793 20.5237 0.728817
794794 −0.497435 + 1.53095i −0.0176533 + 0.0543313i
795795 0 0
796796 −25.0600 18.2072i −0.888228 0.645336i
797797 9.96126 + 30.6576i 0.352846 + 1.08595i 0.957248 + 0.289269i 0.0934121π0.0934121\pi
−0.604402 + 0.796680i 0.706588π0.706588\pi
798798 2.47759 + 7.62522i 0.0877056 + 0.269930i
799799 −11.7589 8.54334i −0.416000 0.302242i
800800 0 0
801801 3.89206 11.9785i 0.137519 0.423240i
802802 33.1869 1.17187
803803 15.9232 + 10.4198i 0.561918 + 0.367708i
804804 −10.1253 −0.357093
805805 0 0
806806 4.67054 3.39334i 0.164513 0.119525i
807807 −18.4103 13.3758i −0.648072 0.470852i
808808 −2.81011 8.64864i −0.0988595 0.304258i
809809 6.55046 + 20.1603i 0.230302 + 0.708797i 0.997710 + 0.0676376i 0.0215462π0.0215462\pi
−0.767408 + 0.641159i 0.778454π0.778454\pi
810810 0 0
811811 19.0967 13.8746i 0.670578 0.487203i −0.199641 0.979869i 0.563978π-0.563978\pi
0.870218 + 0.492666i 0.163978π0.163978\pi
812812 −2.80398 + 8.62976i −0.0984004 + 0.302845i
813813 7.79448 0.273364
814814 −62.8273 + 50.5145i −2.20210 + 1.77053i
815815 0 0
816816 6.17436 19.0027i 0.216146 0.665228i
817817 0.512709 0.372505i 0.0179374 0.0130323i
818818 −4.46672 3.24526i −0.156175 0.113468i
819819 −2.56086 7.88152i −0.0894837 0.275403i
820820 0 0
821821 36.0153 + 26.1667i 1.25694 + 0.913223i 0.998603 0.0528314i 0.0168246π-0.0168246\pi
0.258340 + 0.966054i 0.416825π0.416825\pi
822822 −10.9713 + 7.97114i −0.382669 + 0.278026i
823823 0.0421588 0.129751i 0.00146956 0.00452285i −0.950319 0.311278i 0.899243π-0.899243\pi
0.951789 + 0.306755i 0.0992431π0.0992431\pi
824824 −7.11238 −0.247771
825825 0 0
826826 −58.6700 −2.04139
827827 −3.63750 + 11.1951i −0.126488 + 0.389291i −0.994169 0.107830i 0.965610π-0.965610\pi
0.867681 + 0.497121i 0.165610π0.165610\pi
828828 −11.6149 + 8.43872i −0.403646 + 0.293266i
829829 −8.92262 6.48266i −0.309895 0.225152i 0.421956 0.906616i 0.361344π-0.361344\pi
−0.731852 + 0.681464i 0.761344π0.761344\pi
830830 0 0
831831 −2.92552 9.00383i −0.101485 0.312339i
832832 −22.3043 16.2050i −0.773263 0.561808i
833833 22.0273 16.0038i 0.763202 0.554498i
834834 −4.54080 + 13.9751i −0.157235 + 0.483919i
835835 0 0
836836 −9.26673 + 0.453226i −0.320497 + 0.0156751i
837837 −1.09673 −0.0379085
838838 11.7221 36.0769i 0.404933 1.24626i
839839 8.56769 6.22479i 0.295790 0.214904i −0.429985 0.902836i 0.641481π-0.641481\pi
0.725775 + 0.687932i 0.241481π0.241481\pi
840840 0 0
841841 −8.57208 26.3822i −0.295589 0.909730i
842842 −0.762368 2.34633i −0.0262730 0.0808598i
843843 −25.3235 18.3986i −0.872188 0.633681i
844844 6.89209 5.00740i 0.237236 0.172362i
845845 0 0
846846 4.49586 0.154571
847847 −31.4642 18.4599i −1.08112 0.634288i
848848 −34.1381 −1.17231
849849 7.54383 23.2175i 0.258903 0.796823i
850850 0 0
851851 54.9864 + 39.9500i 1.88491 + 1.36947i
852852 9.44055 + 29.0550i 0.323428 + 0.995409i
853853 −13.7763 42.3992i −0.471693 1.45172i −0.850367 0.526190i 0.823620π-0.823620\pi
0.378674 0.925530i 0.376380π-0.376380\pi
854854 −46.4181 33.7247i −1.58839 1.15404i
855855 0 0
856856 4.41628 13.5919i 0.150945 0.464562i
857857 −24.3105 −0.830430 −0.415215 0.909723i 0.636294π-0.636294\pi
−0.415215 + 0.909723i 0.636294π0.636294\pi
858858 17.4376 0.852855i 0.595311 0.0291160i
859859 −35.5045 −1.21140 −0.605699 0.795694i 0.707107π-0.707107\pi
−0.605699 + 0.795694i 0.707107π0.707107\pi
860860 0 0
861861 2.50205 1.81784i 0.0852695 0.0619519i
862862 59.8040 + 43.4502i 2.03693 + 1.47992i
863863 3.60684 + 11.1007i 0.122778 + 0.377873i 0.993490 0.113921i 0.0363412π-0.0363412\pi
−0.870711 + 0.491794i 0.836341π0.836341\pi
864864 2.47926 + 7.63038i 0.0843462 + 0.259591i
865865 0 0
866866 −31.0609 + 22.5670i −1.05549 + 0.766859i
867867 9.07851 27.9408i 0.308322 0.948919i
868868 −8.86503 −0.300899
869869 −3.36314 + 12.3784i −0.114087 + 0.419910i
870870 0 0
871871 3.20786 9.87276i 0.108694 0.334526i
872872 5.06739 3.68167i 0.171603 0.124677i
873873 2.32085 + 1.68620i 0.0785489 + 0.0570691i
874874 4.40054 + 13.5435i 0.148850 + 0.458115i
875875 0 0
876876 11.3139 + 8.22003i 0.382261 + 0.277729i
877877 21.4243 15.5657i 0.723447 0.525615i −0.164036 0.986454i 0.552451π-0.552451\pi
0.887484 + 0.460839i 0.152451π0.152451\pi
878878 12.8989 39.6986i 0.435315 1.33976i
879879 −11.8197 −0.398667
880880 0 0
881881 10.3488 0.348658 0.174329 0.984687i 0.444224π-0.444224\pi
0.174329 + 0.984687i 0.444224π0.444224\pi
882882 −2.60250 + 8.00967i −0.0876307 + 0.269700i
883883 2.19364 1.59377i 0.0738217 0.0536346i −0.550262 0.834992i 0.685472π-0.685472\pi
0.624084 + 0.781357i 0.285472π0.285472\pi
884884 −33.5573 24.3808i −1.12865 0.820015i
885885 0 0
886886 −10.8633 33.4338i −0.364959 1.12323i
887887 −0.0992445 0.0721054i −0.00333230 0.00242106i 0.586118 0.810226i 0.300656π-0.300656\pi
−0.589450 + 0.807805i 0.700656π0.700656\pi
888888 −8.60092 + 6.24893i −0.288628 + 0.209700i
889889 −6.87169 + 21.1489i −0.230469 + 0.709311i
890890 0 0
891891 −2.77523 1.81606i −0.0929739 0.0608403i
892892 −12.6880 −0.424825
893893 0.756933 2.32960i 0.0253298 0.0779571i
894894 −32.4148 + 23.5507i −1.08411 + 0.787654i
895895 0 0
896896 7.37296 + 22.6916i 0.246313 + 0.758075i
897897 −4.54845 13.9987i −0.151868 0.467403i
898898 −22.4904 16.3403i −0.750516 0.545282i
899899 −0.996022 + 0.723652i −0.0332192 + 0.0241352i
900900 0 0
901901 −79.2406 −2.63989
902902 2.31366 + 6.09075i 0.0770365 + 0.202800i
903903 1.83124 0.0609398
904904 0.0858376 0.264181i 0.00285491 0.00878652i
905905 0 0
906906 6.64777 + 4.82989i 0.220857 + 0.160462i
907907 −4.27023 13.1424i −0.141791 0.436387i 0.854794 0.518968i 0.173684π-0.173684\pi
−0.996584 + 0.0825812i 0.973684π0.973684\pi
908908 −7.30780 22.4911i −0.242518 0.746393i
909909 −7.98501 5.80145i −0.264846 0.192422i
910910 0 0
911911 7.18645 22.1176i 0.238098 0.732790i −0.758598 0.651559i 0.774115π-0.774115\pi
0.996695 0.0812302i 0.0258849π-0.0258849\pi
912912 3.36725 0.111501
913913 −7.16142 18.8525i −0.237009 0.623928i
914914 −44.7997 −1.48184
915915 0 0
916916 −36.4820 + 26.5057i −1.20540 + 0.875773i
917917 21.6711 + 15.7450i 0.715642 + 0.519945i
918918 4.43307 + 13.6436i 0.146313 + 0.450306i
919919 8.16663 + 25.1343i 0.269392 + 0.829104i 0.990649 + 0.136436i 0.0435648π0.0435648\pi
−0.721257 + 0.692668i 0.756435π0.756435\pi
920920 0 0
921921 18.0586 13.1203i 0.595051 0.432330i
922922 13.0692 40.2228i 0.430410 1.32467i
923923 −31.3212 −1.03095
924924 −22.4326 14.6795i −0.737980 0.482920i
925925 0 0
926926 0.626554 1.92833i 0.0205898 0.0633690i
927927 −6.24523 + 4.53743i −0.205120 + 0.149029i
928928 7.28634 + 5.29383i 0.239186 + 0.173779i
929929 −2.48284 7.64138i −0.0814592 0.250706i 0.902030 0.431674i 0.142077π-0.142077\pi
−0.983489 + 0.180968i 0.942077π0.942077\pi
930930 0 0
931931 3.71217 + 2.69705i 0.121662 + 0.0883923i
932932 −29.4882 + 21.4244i −0.965919 + 0.701781i
933933 −6.02070 + 18.5298i −0.197109 + 0.606639i
934934 31.4144 1.02791
935935 0 0
936936 2.30234 0.0752545
937937 4.16903 12.8309i 0.136196 0.419169i −0.859578 0.511005i 0.829274π-0.829274\pi
0.995774 + 0.0918359i 0.0292735π0.0292735\pi
938938 −23.4782 + 17.0579i −0.766590 + 0.556960i
939939 14.0386 + 10.1997i 0.458133 + 0.332853i
940940 0 0
941941 −9.85889 30.3425i −0.321391 0.989138i −0.973044 0.230621i 0.925924π-0.925924\pi
0.651653 0.758517i 0.274076π-0.274076\pi
942942 −31.3305 22.7630i −1.02080 0.741657i
943943 4.44398 3.22874i 0.144716 0.105142i
944944 −7.61426 + 23.4343i −0.247823 + 0.762721i
945945 0 0
946946 −1.01149 + 3.72290i −0.0328863 + 0.121042i
947947 −10.2719 −0.333793 −0.166896 0.985974i 0.553375π-0.553375\pi
−0.166896 + 0.985974i 0.553375π0.553375\pi
948948 −2.91300 + 8.96529i −0.0946099 + 0.291179i
949949 −11.5994 + 8.42745i −0.376532 + 0.273567i
950950 0 0
951951 −0.256706 0.790059i −0.00832425 0.0256194i
952952 6.43017 + 19.7900i 0.208403 + 0.641399i
953953 7.95608 + 5.78043i 0.257723 + 0.187247i 0.709143 0.705065i 0.249082π-0.249082\pi
−0.451420 + 0.892312i 0.649082π0.649082\pi
954954 19.8294 14.4069i 0.642001 0.466441i
955955 0 0
956956 −3.67353 −0.118810
957957 −3.71868 + 0.181877i −0.120208 + 0.00587924i
958958 1.00170 0.0323635
959959 −6.59748 + 20.3050i −0.213044 + 0.655681i
960960 0 0
961961 24.1064 + 17.5143i 0.777627 + 0.564979i
962962 −18.7696 57.7669i −0.605157 1.86248i
963963 −4.79328 14.7522i −0.154461 0.475383i
964964 13.9919 + 10.1657i 0.450649 + 0.327416i
965965 0 0
966966 −12.7156 + 39.1347i −0.409118 + 1.25914i
967967 3.85001 0.123808 0.0619041 0.998082i 0.480283π-0.480283\pi
0.0619041 + 0.998082i 0.480283π0.480283\pi
968968 7.57880 6.72879i 0.243592 0.216272i
969969 7.81600 0.251086
970970 0 0
971971 −17.3065 + 12.5739i −0.555392 + 0.403516i −0.829769 0.558106i 0.811528π-0.811528\pi
0.274378 + 0.961622i 0.411528π0.411528\pi
972972 −1.97188 1.43266i −0.0632482 0.0459525i
973973 7.14868 + 22.0014i 0.229176 + 0.705332i
974974 23.0129 + 70.8264i 0.737381 + 2.26942i
975975 0 0
976976 −19.4947 + 14.1637i −0.624011 + 0.453370i
977977 5.15071 15.8523i 0.164786 0.507159i −0.834235 0.551410i 0.814090π-0.814090\pi
0.999020 + 0.0442509i 0.0140901π0.0140901\pi
978978 37.0156 1.18363
979979 41.7229 2.04062i 1.33347 0.0652185i
980980 0 0
981981 2.10080 6.46561i 0.0670735 0.206431i
982982 −51.3524 + 37.3097i −1.63872 + 1.19060i
983983 41.9532 + 30.4808i 1.33810 + 0.972186i 0.999512 + 0.0312510i 0.00994913π0.00994913\pi
0.338588 + 0.940935i 0.390051π0.390051\pi
984984 0.265513 + 0.817166i 0.00846426 + 0.0260503i
985985 0 0
986986 13.0284 + 9.46570i 0.414910 + 0.301449i
987987 5.72618 4.16031i 0.182266 0.132424i
988988 2.16012 6.64816i 0.0687226 0.211506i
989989 3.25253 0.103425
990990 0 0
991991 19.8195 0.629588 0.314794 0.949160i 0.398065π-0.398065\pi
0.314794 + 0.949160i 0.398065π0.398065\pi
992992 −2.71908 + 8.36846i −0.0863308 + 0.265699i
993993 25.5092 18.5335i 0.809510 0.588144i
994994 70.8386 + 51.4672i 2.24686 + 1.63244i
995995 0 0
996996 −4.57982 14.0953i −0.145117 0.446625i
997997 −41.7934 30.3647i −1.32361 0.961658i −0.999880 0.0155088i 0.995063π-0.995063\pi
−0.323730 0.946150i 0.604937π-0.604937\pi
998998 −62.1688 + 45.1683i −1.96792 + 1.42978i
999999 −3.56571 + 10.9741i −0.112814 + 0.347206i
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 825.2.n.p.526.2 24
5.2 odd 4 165.2.s.a.64.3 yes 48
5.3 odd 4 165.2.s.a.64.10 yes 48
5.4 even 2 825.2.n.o.526.5 24
11.4 even 5 9075.2.a.dy.1.3 12
11.5 even 5 inner 825.2.n.p.676.2 24
11.7 odd 10 9075.2.a.ea.1.10 12
15.2 even 4 495.2.ba.c.64.10 48
15.8 even 4 495.2.ba.c.64.3 48
55.4 even 10 9075.2.a.dz.1.10 12
55.7 even 20 1815.2.c.k.364.20 24
55.18 even 20 1815.2.c.k.364.5 24
55.27 odd 20 165.2.s.a.49.10 yes 48
55.29 odd 10 9075.2.a.dx.1.3 12
55.37 odd 20 1815.2.c.j.364.5 24
55.38 odd 20 165.2.s.a.49.3 48
55.48 odd 20 1815.2.c.j.364.20 24
55.49 even 10 825.2.n.o.676.5 24
165.38 even 20 495.2.ba.c.379.10 48
165.137 even 20 495.2.ba.c.379.3 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.s.a.49.3 48 55.38 odd 20
165.2.s.a.49.10 yes 48 55.27 odd 20
165.2.s.a.64.3 yes 48 5.2 odd 4
165.2.s.a.64.10 yes 48 5.3 odd 4
495.2.ba.c.64.3 48 15.8 even 4
495.2.ba.c.64.10 48 15.2 even 4
495.2.ba.c.379.3 48 165.137 even 20
495.2.ba.c.379.10 48 165.38 even 20
825.2.n.o.526.5 24 5.4 even 2
825.2.n.o.676.5 24 55.49 even 10
825.2.n.p.526.2 24 1.1 even 1 trivial
825.2.n.p.676.2 24 11.5 even 5 inner
1815.2.c.j.364.5 24 55.37 odd 20
1815.2.c.j.364.20 24 55.48 odd 20
1815.2.c.k.364.5 24 55.18 even 20
1815.2.c.k.364.20 24 55.7 even 20
9075.2.a.dx.1.3 12 55.29 odd 10
9075.2.a.dy.1.3 12 11.4 even 5
9075.2.a.dz.1.10 12 55.4 even 10
9075.2.a.ea.1.10 12 11.7 odd 10