Properties

Label 483.2.u.a.113.9
Level 483483
Weight 22
Character 483.113
Analytic conductor 3.8573.857
Analytic rank 00
Dimension 480480
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,2,Mod(113,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 0, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.113");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 483=3723 483 = 3 \cdot 7 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 483.u (of order 2222, degree 1010, 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: 3.856774417633.85677441763
Analytic rank: 00
Dimension: 480480
Relative dimension: 4848 over Q(ζ22)\Q(\zeta_{22})
Twist minimal: yes
Sato-Tate group: SU(2)[C22]\mathrm{SU}(2)[C_{22}]

Embedding invariants

Embedding label 113.9
Character χ\chi == 483.113
Dual form 483.2.u.a.218.9

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+(1.07812+1.67759i)q2+(1.587070.693695i)q3+(0.8211241.79801i)q4+(1.957720.574839i)q5+(0.547316+3.41033i)q6+(0.7557500.654861i)q7+(0.04611730.00663067i)q8+(2.037572.20188i)q9+(3.075002.66450i)q10+(3.31421+2.12992i)q11+(2.550452.28396i)q12+(3.279623.78489i)q13+(1.913370.561817i)q14+(3.50580+0.445753i)q15+(2.649693.05790i)q16+(0.964591+2.11216i)q17+(1.49710+5.79210i)q18+(1.91527+0.874676i)q19+(0.573966+3.99202i)q20+(1.653700.515049i)q217.85618iq22+(3.252533.52435i)q23+(0.0777911+0.0214680i)q24+(0.7040350.452456i)q25+(9.885301.42129i)q26+(1.706334.90800i)q27+(0.556883+1.89657i)q28+(9.410514.29763i)q29+(3.031886.36186i)q30+(0.3543022.46423i)q31+(2.24696+7.65245i)q32+(3.78237+5.67938i)q33+(2.503383.89534i)q34+(1.10311+1.71647i)q35+(5.632111.85556i)q36+(0.623786+2.12442i)q37+(0.5975494.15604i)q38+(7.830553.73182i)q39+(0.0864733+0.0394910i)q40+(1.97370+6.72182i)q41+(2.646922.21894i)q42+(3.55611+0.511291i)q43+(6.55100+4.21007i)q44+(5.25473+3.13940i)q45+(2.40578+9.25607i)q466.97798iq47+(2.083986.69117i)q48+(0.142315+0.989821i)q49+(1.518070.693278i)q50+(0.0656770+4.02127i)q51+(4.11229+9.00466i)q52+(2.429092.80331i)q53+(6.39396+8.15393i)q54+(7.712672.26464i)q55+(0.0305110+0.0352116i)q56+(2.43291+2.71679i)q57+(17.355311.1536i)q58+(4.835864.19029i)q59+(3.68017+5.93745i)q60+(11.3602+1.63335i)q61+(3.75197+3.25110i)q62+(2.98182+0.329746i)q63+(7.495572.20090i)q64+(4.24489+9.29501i)q65+(5.4498012.4683i)q66+(1.682712.61835i)q67+4.58973q68+(2.717177.84965i)q694.06881q70+(7.74611+12.0532i)q71+(0.108567+0.0880345i)q72+(2.63075+5.76055i)q73+(4.236411.24392i)q74+(1.431220.229693i)q75+(3.14535+2.72547i)q76+(3.89951+0.560666i)q77+(14.70279.11307i)q78+(3.71086+3.21547i)q79+(6.94515+4.46337i)q80+(0.6965858.97300i)q81+(9.1485410.5580i)q82+(11.39633.34627i)q83+(0.431829+3.39629i)q84+(3.102553.58053i)q85+(2.976176.51691i)q86+(17.91640.292617i)q87+(0.1669660.0762506i)q88+(0.6752744.69663i)q89+(0.39861412.1999i)q90+5.00812iq91+(9.007552.95417i)q92+(1.147124.15667i)q93+(11.7062+7.52310i)q94+(4.252370.611398i)q95+(8.87455+10.5863i)q96+(3.95894+13.4829i)q97+(1.813940.828400i)q98+(2.06313+11.6374i)q99+O(q100)q+(-1.07812 + 1.67759i) q^{2} +(1.58707 - 0.693695i) q^{3} +(-0.821124 - 1.79801i) q^{4} +(-1.95772 - 0.574839i) q^{5} +(-0.547316 + 3.41033i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.0461173 - 0.00663067i) q^{8} +(2.03757 - 2.20188i) q^{9} +(3.07500 - 2.66450i) q^{10} +(-3.31421 + 2.12992i) q^{11} +(-2.55045 - 2.28396i) q^{12} +(-3.27962 - 3.78489i) q^{13} +(1.91337 - 0.561817i) q^{14} +(-3.50580 + 0.445753i) q^{15} +(2.64969 - 3.05790i) q^{16} +(-0.964591 + 2.11216i) q^{17} +(1.49710 + 5.79210i) q^{18} +(-1.91527 + 0.874676i) q^{19} +(0.573966 + 3.99202i) q^{20} +(-1.65370 - 0.515049i) q^{21} -7.85618i q^{22} +(3.25253 - 3.52435i) q^{23} +(-0.0777911 + 0.0214680i) q^{24} +(-0.704035 - 0.452456i) q^{25} +(9.88530 - 1.42129i) q^{26} +(1.70633 - 4.90800i) q^{27} +(-0.556883 + 1.89657i) q^{28} +(-9.41051 - 4.29763i) q^{29} +(3.03188 - 6.36186i) q^{30} +(0.354302 - 2.46423i) q^{31} +(2.24696 + 7.65245i) q^{32} +(-3.78237 + 5.67938i) q^{33} +(-2.50338 - 3.89534i) q^{34} +(1.10311 + 1.71647i) q^{35} +(-5.63211 - 1.85556i) q^{36} +(0.623786 + 2.12442i) q^{37} +(0.597549 - 4.15604i) q^{38} +(-7.83055 - 3.73182i) q^{39} +(0.0864733 + 0.0394910i) q^{40} +(-1.97370 + 6.72182i) q^{41} +(2.64692 - 2.21894i) q^{42} +(-3.55611 + 0.511291i) q^{43} +(6.55100 + 4.21007i) q^{44} +(-5.25473 + 3.13940i) q^{45} +(2.40578 + 9.25607i) q^{46} -6.97798i q^{47} +(2.08398 - 6.69117i) q^{48} +(0.142315 + 0.989821i) q^{49} +(1.51807 - 0.693278i) q^{50} +(-0.0656770 + 4.02127i) q^{51} +(-4.11229 + 9.00466i) q^{52} +(2.42909 - 2.80331i) q^{53} +(6.39396 + 8.15393i) q^{54} +(7.71267 - 2.26464i) q^{55} +(0.0305110 + 0.0352116i) q^{56} +(-2.43291 + 2.71679i) q^{57} +(17.3553 - 11.1536i) q^{58} +(4.83586 - 4.19029i) q^{59} +(3.68017 + 5.93745i) q^{60} +(11.3602 + 1.63335i) q^{61} +(3.75197 + 3.25110i) q^{62} +(-2.98182 + 0.329746i) q^{63} +(-7.49557 - 2.20090i) q^{64} +(4.24489 + 9.29501i) q^{65} +(-5.44980 - 12.4683i) q^{66} +(1.68271 - 2.61835i) q^{67} +4.58973 q^{68} +(2.71717 - 7.84965i) q^{69} -4.06881 q^{70} +(-7.74611 + 12.0532i) q^{71} +(-0.108567 + 0.0880345i) q^{72} +(2.63075 + 5.76055i) q^{73} +(-4.23641 - 1.24392i) q^{74} +(-1.43122 - 0.229693i) q^{75} +(3.14535 + 2.72547i) q^{76} +(3.89951 + 0.560666i) q^{77} +(14.7027 - 9.11307i) q^{78} +(-3.71086 + 3.21547i) q^{79} +(-6.94515 + 4.46337i) q^{80} +(-0.696585 - 8.97300i) q^{81} +(-9.14854 - 10.5580i) q^{82} +(11.3963 - 3.34627i) q^{83} +(0.431829 + 3.39629i) q^{84} +(3.10255 - 3.58053i) q^{85} +(2.97617 - 6.51691i) q^{86} +(-17.9164 - 0.292617i) q^{87} +(0.166966 - 0.0762506i) q^{88} +(-0.675274 - 4.69663i) q^{89} +(0.398614 - 12.1999i) q^{90} +5.00812i q^{91} +(-9.00755 - 2.95417i) q^{92} +(-1.14712 - 4.15667i) q^{93} +(11.7062 + 7.52310i) q^{94} +(4.25237 - 0.611398i) q^{95} +(8.87455 + 10.5863i) q^{96} +(-3.95894 + 13.4829i) q^{97} +(-1.81394 - 0.828400i) q^{98} +(-2.06313 + 11.6374i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 480q+4q3+40q46q64q922q12+8q1322q1524q1630q18120q2488q25+16q2744q30+8q3122q3344q34+10q36+132q97+O(q100) 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/483Z)×\left(\mathbb{Z}/483\mathbb{Z}\right)^\times.

nn 323323 346346 442442
χ(n)\chi(n) 1-1 11 e(1322)e\left(\frac{13}{22}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.07812 + 1.67759i −0.762345 + 1.18623i 0.215418 + 0.976522i 0.430889π0.430889\pi
−0.977764 + 0.209711i 0.932748π0.932748\pi
33 1.58707 0.693695i 0.916295 0.400505i
44 −0.821124 1.79801i −0.410562 0.899006i
55 −1.95772 0.574839i −0.875520 0.257076i −0.187058 0.982349i 0.559895π-0.559895\pi
−0.688461 + 0.725273i 0.741713π0.741713\pi
66 −0.547316 + 3.41033i −0.223441 + 1.39226i
77 −0.755750 0.654861i −0.285646 0.247514i
88 −0.0461173 0.00663067i −0.0163049 0.00234430i
99 2.03757 2.20188i 0.679191 0.733961i
1010 3.07500 2.66450i 0.972400 0.842589i
1111 −3.31421 + 2.12992i −0.999273 + 0.642194i −0.934596 0.355712i 0.884238π-0.884238\pi
−0.0646778 + 0.997906i 0.520602π0.520602\pi
1212 −2.55045 2.28396i −0.736252 0.659322i
1313 −3.27962 3.78489i −0.909604 1.04974i −0.998557 0.0537031i 0.982898π-0.982898\pi
0.0889530 0.996036i 0.471648π-0.471648\pi
1414 1.91337 0.561817i 0.511371 0.150152i
1515 −3.50580 + 0.445753i −0.905194 + 0.115093i
1616 2.64969 3.05790i 0.662421 0.764475i
1717 −0.964591 + 2.11216i −0.233948 + 0.512274i −0.989799 0.142469i 0.954496π-0.954496\pi
0.755852 + 0.654743i 0.227223π0.227223\pi
1818 1.49710 + 5.79210i 0.352870 + 1.36521i
1919 −1.91527 + 0.874676i −0.439394 + 0.200664i −0.622814 0.782370i 0.714011π-0.714011\pi
0.183420 + 0.983035i 0.441283π0.441283\pi
2020 0.573966 + 3.99202i 0.128343 + 0.892643i
2121 −1.65370 0.515049i −0.360867 0.112393i
2222 7.85618i 1.67494i
2323 3.25253 3.52435i 0.678200 0.734877i
2424 −0.0777911 + 0.0214680i −0.0158790 + 0.00438215i
2525 −0.704035 0.452456i −0.140807 0.0904912i
2626 9.88530 1.42129i 1.93867 0.278738i
2727 1.70633 4.90800i 0.328384 0.944544i
2828 −0.556883 + 1.89657i −0.105241 + 0.358418i
2929 −9.41051 4.29763i −1.74749 0.798051i −0.989279 0.146039i 0.953348π-0.953348\pi
−0.758208 0.652012i 0.773925π-0.773925\pi
3030 3.03188 6.36186i 0.553543 1.16151i
3131 0.354302 2.46423i 0.0636346 0.442588i −0.932950 0.360007i 0.882774π-0.882774\pi
0.996584 0.0825815i 0.0263165π-0.0263165\pi
3232 2.24696 + 7.65245i 0.397210 + 1.35277i
3333 −3.78237 + 5.67938i −0.658427 + 0.988653i
3434 −2.50338 3.89534i −0.429327 0.668046i
3535 1.10311 + 1.71647i 0.186459 + 0.290136i
3636 −5.63211 1.85556i −0.938686 0.309260i
3737 0.623786 + 2.12442i 0.102550 + 0.349252i 0.994743 0.102401i 0.0326525π-0.0326525\pi
−0.892193 + 0.451653i 0.850834π0.850834\pi
3838 0.597549 4.15604i 0.0969352 0.674199i
3939 −7.83055 3.73182i −1.25389 0.597569i
4040 0.0864733 + 0.0394910i 0.0136726 + 0.00624408i
4141 −1.97370 + 6.72182i −0.308241 + 1.04977i 0.649074 + 0.760725i 0.275156π0.275156\pi
−0.957315 + 0.289047i 0.906662π0.906662\pi
4242 2.64692 2.21894i 0.408429 0.342390i
4343 −3.55611 + 0.511291i −0.542302 + 0.0779712i −0.408022 0.912972i 0.633781π-0.633781\pi
−0.134280 + 0.990943i 0.542872π0.542872\pi
4444 6.55100 + 4.21007i 0.987600 + 0.634692i
4545 −5.25473 + 3.13940i −0.783329 + 0.467994i
4646 2.40578 + 9.25607i 0.354712 + 1.36473i
4747 6.97798i 1.01784i −0.860813 0.508922i 0.830044π-0.830044\pi
0.860813 0.508922i 0.169956π-0.169956\pi
4848 2.08398 6.69117i 0.300797 0.965788i
4949 0.142315 + 0.989821i 0.0203307 + 0.141403i
5050 1.51807 0.693278i 0.214687 0.0980444i
5151 −0.0656770 + 4.02127i −0.00919663 + 0.563091i
5252 −4.11229 + 9.00466i −0.570272 + 1.24872i
5353 2.42909 2.80331i 0.333661 0.385065i −0.563983 0.825786i 0.690732π-0.690732\pi
0.897644 + 0.440721i 0.145277π0.145277\pi
5454 6.39396 + 8.15393i 0.870107 + 1.10961i
5555 7.71267 2.26464i 1.03998 0.305364i
5656 0.0305110 + 0.0352116i 0.00407720 + 0.00470534i
5757 −2.43291 + 2.71679i −0.322247 + 0.359847i
5858 17.3553 11.1536i 2.27886 1.46454i
5959 4.83586 4.19029i 0.629575 0.545530i −0.280563 0.959836i 0.590521π-0.590521\pi
0.910138 + 0.414306i 0.135976π0.135976\pi
6060 3.68017 + 5.93745i 0.475108 + 0.766522i
6161 11.3602 + 1.63335i 1.45453 + 0.209129i 0.823802 0.566878i 0.191849π-0.191849\pi
0.630724 + 0.776007i 0.282758π0.282758\pi
6262 3.75197 + 3.25110i 0.476501 + 0.412890i
6363 −2.98182 + 0.329746i −0.375674 + 0.0415441i
6464 −7.49557 2.20090i −0.936946 0.275112i
6565 4.24489 + 9.29501i 0.526514 + 1.15290i
6666 −5.44980 12.4683i −0.670824 1.53474i
6767 1.68271 2.61835i 0.205576 0.319882i −0.723122 0.690721i 0.757293π-0.757293\pi
0.928697 + 0.370839i 0.120930π0.120930\pi
6868 4.58973 0.556587
6969 2.71717 7.84965i 0.327109 0.944987i
7070 −4.06881 −0.486315
7171 −7.74611 + 12.0532i −0.919294 + 1.43045i −0.0167455 + 0.999860i 0.505331π0.505331\pi
−0.902548 + 0.430589i 0.858306π0.858306\pi
7272 −0.108567 + 0.0880345i −0.0127948 + 0.0103750i
7373 2.63075 + 5.76055i 0.307907 + 0.674221i 0.998812 0.0487236i 0.0155153π-0.0155153\pi
−0.690906 + 0.722945i 0.742788π0.742788\pi
7474 −4.23641 1.24392i −0.492473 0.144603i
7575 −1.43122 0.229693i −0.165263 0.0265226i
7676 3.14535 + 2.72547i 0.360797 + 0.312632i
7777 3.89951 + 0.560666i 0.444391 + 0.0638938i
7878 14.7027 9.11307i 1.66475 1.03185i
7979 −3.71086 + 3.21547i −0.417504 + 0.361769i −0.838135 0.545463i 0.816354π-0.816354\pi
0.420631 + 0.907232i 0.361809π0.361809\pi
8080 −6.94515 + 4.46337i −0.776491 + 0.499020i
8181 −0.696585 8.97300i −0.0773984 0.997000i
8282 −9.14854 10.5580i −1.01029 1.16593i
8383 11.3963 3.34627i 1.25091 0.367301i 0.411807 0.911271i 0.364898π-0.364898\pi
0.839105 + 0.543970i 0.183080π0.183080\pi
8484 0.431829 + 3.39629i 0.0471164 + 0.370566i
8585 3.10255 3.58053i 0.336519 0.388363i
8686 2.97617 6.51691i 0.320929 0.702737i
8787 −17.9164 0.292617i −1.92084 0.0313719i
8888 0.166966 0.0762506i 0.0177986 0.00812834i
8989 −0.675274 4.69663i −0.0715789 0.497842i −0.993800 0.111180i 0.964537π-0.964537\pi
0.922221 0.386662i 0.126372π-0.126372\pi
9090 0.398614 12.1999i 0.0420176 1.28598i
9191 5.00812i 0.524994i
9292 −9.00755 2.95417i −0.939102 0.307993i
9393 −1.14712 4.15667i −0.118951 0.431027i
9494 11.7062 + 7.52310i 1.20740 + 0.775948i
9595 4.25237 0.611398i 0.436284 0.0627282i
9696 8.87455 + 10.5863i 0.905755 + 1.08046i
9797 −3.95894 + 13.4829i −0.401969 + 1.36898i 0.471399 + 0.881920i 0.343749π0.343749\pi
−0.873368 + 0.487061i 0.838069π0.838069\pi
9898 −1.81394 0.828400i −0.183236 0.0836810i
9999 −2.06313 + 11.6374i −0.207352 + 1.16960i
100100 −0.235421 + 1.63739i −0.0235421 + 0.163739i
101101 −2.94293 10.0227i −0.292833 0.997296i −0.966158 0.257950i 0.916953π-0.916953\pi
0.673326 0.739346i 0.264865π-0.264865\pi
102102 −6.67522 4.44559i −0.660946 0.440179i
103103 8.63200 + 13.4316i 0.850536 + 1.32346i 0.944711 + 0.327904i 0.106342π0.106342\pi
−0.0941751 + 0.995556i 0.530021π0.530021\pi
104104 0.126151 + 0.196295i 0.0123701 + 0.0192483i
105105 2.94141 + 1.95893i 0.287053 + 0.191172i
106106 2.08396 + 7.09731i 0.202412 + 0.689351i
107107 0.930543 6.47207i 0.0899590 0.625679i −0.894104 0.447859i 0.852187π-0.852187\pi
0.984063 0.177819i 0.0569043π-0.0569043\pi
108108 −10.2257 + 0.962068i −0.983973 + 0.0925750i
109109 −12.1313 5.54020i −1.16197 0.530655i −0.261344 0.965246i 0.584166π-0.584166\pi
−0.900628 + 0.434591i 0.856893π0.856893\pi
110110 −4.51604 + 15.3802i −0.430587 + 1.46645i
111111 2.46369 + 2.93888i 0.233843 + 0.278946i
112112 −4.00500 + 0.575832i −0.378437 + 0.0544110i
113113 −10.6364 6.83559i −1.00059 0.643038i −0.0656464 0.997843i 0.520911π-0.520911\pi
−0.934940 + 0.354805i 0.884547π0.884547\pi
114114 −1.93468 7.01044i −0.181199 0.656588i
115115 −8.39349 + 5.03001i −0.782697 + 0.469050i
116116 20.4491i 1.89865i
117117 −15.0164 0.490637i −1.38826 0.0453594i
118118 1.81595 + 12.6302i 0.167172 + 1.16270i
119119 2.11216 0.964591i 0.193621 0.0884239i
120120 0.164634 + 0.00268887i 0.0150289 + 0.000245459i
121121 1.87791 4.11205i 0.170719 0.373823i
122122 −14.9877 + 17.2968i −1.35693 + 1.56598i
123123 1.53049 + 12.0371i 0.138000 + 1.08535i
124124 −4.72163 + 1.38640i −0.424015 + 0.124502i
125125 7.79901 + 9.00054i 0.697564 + 0.805032i
126126 2.66158 5.35777i 0.237113 0.477308i
127127 −8.75277 + 5.62506i −0.776683 + 0.499144i −0.867931 0.496684i 0.834551π-0.834551\pi
0.0912484 + 0.995828i 0.470914π0.470914\pi
128128 −0.281673 + 0.244071i −0.0248966 + 0.0215731i
129129 −5.28911 + 3.27831i −0.465680 + 0.288639i
130130 −20.1697 2.89996i −1.76900 0.254343i
131131 −4.90847 4.25322i −0.428855 0.371605i 0.413521 0.910494i 0.364299π-0.364299\pi
−0.842377 + 0.538889i 0.818844π0.818844\pi
132132 13.3174 + 2.13727i 1.15913 + 0.186026i
133133 2.02026 + 0.593201i 0.175179 + 0.0514371i
134134 2.57834 + 5.64578i 0.222735 + 0.487721i
135135 −6.16183 + 8.62762i −0.530326 + 0.742547i
136136 0.0584894 0.0910113i 0.00501542 0.00780415i
137137 −14.1447 −1.20846 −0.604231 0.796809i 0.706520π-0.706520\pi
−0.604231 + 0.796809i 0.706520π0.706520\pi
138138 10.2390 + 13.0211i 0.871604 + 1.10843i
139139 −17.7832 −1.50835 −0.754175 0.656673i 0.771963π-0.771963\pi
−0.754175 + 0.656673i 0.771963π0.771963\pi
140140 2.18044 3.39283i 0.184281 0.286747i
141141 −4.84059 11.0745i −0.407652 0.932644i
142142 −11.8690 25.9895i −0.996026 2.18099i
143143 18.9309 + 5.55861i 1.58308 + 0.464834i
144144 −1.33421 12.0650i −0.111184 1.00542i
145145 15.9527 + 13.8231i 1.32480 + 1.14795i
146146 −12.5001 1.79724i −1.03451 0.148741i
147147 0.912498 + 1.47219i 0.0752616 + 0.121424i
148148 3.30752 2.86599i 0.271877 0.235583i
149149 5.66513 3.64076i 0.464106 0.298263i −0.287613 0.957747i 0.592862π-0.592862\pi
0.751719 + 0.659484i 0.229225π0.229225\pi
150150 1.92835 2.15336i 0.157449 0.175821i
151151 −6.22379 7.18264i −0.506485 0.584515i 0.443710 0.896170i 0.353662π-0.353662\pi
−0.950195 + 0.311656i 0.899116π0.899116\pi
152152 0.0941270 0.0276382i 0.00763471 0.00224175i
153153 2.68530 + 6.42760i 0.217094 + 0.519640i
154154 −5.14471 + 5.93731i −0.414572 + 0.478442i
155155 −2.11016 + 4.62060i −0.169492 + 0.371136i
156156 −0.279998 + 17.1437i −0.0224178 + 1.37259i
157157 17.2378 7.87223i 1.37572 0.628272i 0.416039 0.909347i 0.363418π-0.363418\pi
0.959686 + 0.281075i 0.0906908π0.0906908\pi
158158 −1.39349 9.69194i −0.110860 0.771050i
159159 1.91048 6.13410i 0.151511 0.486466i
160160 16.2730i 1.28649i
161161 −4.76606 + 0.533567i −0.375618 + 0.0420510i
162162 15.8040 + 8.50538i 1.24168 + 0.668246i
163163 5.66759 + 3.64234i 0.443920 + 0.285290i 0.743443 0.668799i 0.233191π-0.233191\pi
−0.299524 + 0.954089i 0.596828π0.596828\pi
164164 13.7066 1.97071i 1.07030 0.153886i
165165 10.6696 8.94438i 0.830624 0.696319i
166166 −6.67297 + 22.7260i −0.517923 + 1.76388i
167167 2.38105 + 1.08739i 0.184251 + 0.0841448i 0.505405 0.862882i 0.331343π-0.331343\pi
−0.321153 + 0.947027i 0.604070π0.604070\pi
168168 0.0728491 + 0.0347178i 0.00562043 + 0.00267854i
169169 −1.71935 + 11.9583i −0.132258 + 0.919872i
170170 2.66173 + 9.06504i 0.204146 + 0.695257i
171171 −1.97658 + 5.99943i −0.151153 + 0.458788i
172172 3.83931 + 5.97409i 0.292745 + 0.455520i
173173 −0.285707 0.444569i −0.0217219 0.0337999i 0.830223 0.557432i 0.188213π-0.188213\pi
−0.851945 + 0.523632i 0.824577π0.824577\pi
174174 19.8069 29.7408i 1.50156 2.25464i
175175 0.235779 + 0.802988i 0.0178232 + 0.0607002i
176176 −2.26856 + 15.7781i −0.170999 + 1.18932i
177177 4.76805 10.0049i 0.358389 0.752014i
178178 8.60703 + 3.93070i 0.645124 + 0.294618i
179179 1.75878 5.98984i 0.131457 0.447702i −0.867287 0.497809i 0.834138π-0.834138\pi
0.998744 + 0.0501070i 0.0159562π0.0159562\pi
180180 9.95946 + 6.87023i 0.742334 + 0.512077i
181181 6.47822 0.931428i 0.481523 0.0692325i 0.102721 0.994710i 0.467245π-0.467245\pi
0.378802 + 0.925478i 0.376336π0.376336\pi
182182 −8.40156 5.39935i −0.622765 0.400227i
183183 19.1625 5.28828i 1.41653 0.390921i
184184 −0.173367 + 0.140967i −0.0127808 + 0.0103922i
185185 4.51760i 0.332140i
186186 8.20991 + 2.55700i 0.601980 + 0.187488i
187187 −1.30186 9.05464i −0.0952015 0.662141i
188188 −12.5465 + 5.72979i −0.915047 + 0.417888i
189189 −4.50361 + 2.59181i −0.327590 + 0.188526i
190190 −3.55889 + 7.79288i −0.258189 + 0.565355i
191191 −1.57583 + 1.81860i −0.114023 + 0.131590i −0.809892 0.586580i 0.800474π-0.800474\pi
0.695869 + 0.718169i 0.255020π0.255020\pi
192192 −13.4227 + 1.70666i −0.968702 + 0.123168i
193193 −14.7952 + 4.34427i −1.06498 + 0.312707i −0.766856 0.641819i 0.778180π-0.778180\pi
−0.298127 + 0.954526i 0.596362π0.596362\pi
194194 −18.3505 21.1776i −1.31749 1.52047i
195195 13.1848 + 11.8072i 0.944185 + 0.845528i
196196 1.66285 1.06865i 0.118775 0.0763321i
197197 18.8558 16.3387i 1.34342 1.16408i 0.371594 0.928395i 0.378811π-0.378811\pi
0.971829 0.235687i 0.0757340π-0.0757340\pi
198198 −17.2984 16.0076i −1.22934 1.13761i
199199 −0.930788 0.133827i −0.0659818 0.00948675i 0.109245 0.994015i 0.465157π-0.465157\pi
−0.175227 + 0.984528i 0.556066π0.556066\pi
200200 0.0294681 + 0.0255343i 0.00208371 + 0.00180555i
201201 0.854241 5.32279i 0.0602535 0.375440i
202202 19.9868 + 5.86865i 1.40626 + 0.412917i
203203 4.29763 + 9.41051i 0.301635 + 0.660488i
204204 7.28422 3.18388i 0.509998 0.222916i
205205 7.72792 12.0249i 0.539742 0.839854i
206206 −31.8391 −2.21833
207207 −1.13292 14.3428i −0.0787437 0.996895i
208208 −20.2638 −1.40504
209209 4.48464 6.97824i 0.310209 0.482695i
210210 −6.45747 + 2.82251i −0.445608 + 0.194772i
211211 −8.53249 18.6836i −0.587401 1.28623i −0.937000 0.349330i 0.886409π-0.886409\pi
0.349599 0.936900i 0.386318π-0.386318\pi
212212 −7.03497 2.06565i −0.483164 0.141870i
213213 −3.93237 + 24.5027i −0.269442 + 1.67889i
214214 9.85422 + 8.53873i 0.673620 + 0.583695i
215215 7.25578 + 1.04322i 0.494840 + 0.0711473i
216216 −0.111235 + 0.215030i −0.00756857 + 0.0146309i
217217 −1.88149 + 1.63032i −0.127724 + 0.110673i
218218 22.3732 14.3784i 1.51530 0.973826i
219219 8.17125 + 7.31744i 0.552162 + 0.494467i
220220 −10.4049 12.0079i −0.701499 0.809573i
221221 11.1578 3.27622i 0.750553 0.220382i
222222 −7.58638 + 0.964588i −0.509164 + 0.0647389i
223223 9.12603 10.5320i 0.611124 0.705275i −0.362872 0.931839i 0.618204π-0.618204\pi
0.973996 + 0.226564i 0.0727492π0.0727492\pi
224224 3.31315 7.25478i 0.221369 0.484731i
225225 −2.43078 + 0.628291i −0.162052 + 0.0418861i
226226 22.9346 10.4739i 1.52559 0.696712i
227227 2.00213 + 13.9251i 0.132886 + 0.924244i 0.941766 + 0.336270i 0.109165π0.109165\pi
−0.808879 + 0.587974i 0.799926π0.799926\pi
228228 6.88254 + 2.14358i 0.455807 + 0.141962i
229229 21.6847i 1.43297i −0.697604 0.716483i 0.745751π-0.745751\pi
0.697604 0.716483i 0.254249π-0.254249\pi
230230 0.610910 19.5037i 0.0402822 1.28604i
231231 6.57773 1.81526i 0.432783 0.119435i
232232 0.405491 + 0.260593i 0.0266218 + 0.0171088i
233233 28.4352 4.08836i 1.86285 0.267837i 0.883266 0.468872i 0.155339π-0.155339\pi
0.979584 + 0.201034i 0.0644302π0.0644302\pi
234234 17.0125 24.6623i 1.11214 1.61222i
235235 −4.01122 + 13.6609i −0.261663 + 0.891142i
236236 −11.5050 5.25417i −0.748914 0.342018i
237237 −3.65882 + 7.67738i −0.237666 + 0.498699i
238238 −0.658975 + 4.58327i −0.0427150 + 0.297089i
239239 −4.72877 16.1047i −0.305879 1.04173i −0.958748 0.284257i 0.908253π-0.908253\pi
0.652869 0.757471i 0.273565π-0.273565\pi
240240 −7.92620 + 11.9015i −0.511634 + 0.768238i
241241 6.04221 + 9.40186i 0.389213 + 0.605627i 0.979470 0.201588i 0.0646102π-0.0646102\pi
−0.590258 + 0.807215i 0.700974π0.700974\pi
242242 4.87371 + 7.58363i 0.313294 + 0.487494i
243243 −7.33006 13.7576i −0.470223 0.882547i
244244 −6.39136 21.7670i −0.409165 1.39349i
245245 0.290375 2.01960i 0.0185514 0.129028i
246246 −21.8434 10.4099i −1.39268 0.663713i
247247 9.59193 + 4.38049i 0.610320 + 0.278724i
248248 −0.0326790 + 0.111294i −0.00207512 + 0.00706720i
249249 15.7655 13.2164i 0.999098 0.837552i
250250 −23.5074 + 3.37986i −1.48674 + 0.213761i
251251 −23.3438 15.0021i −1.47345 0.946926i −0.997731 0.0673270i 0.978553π-0.978553\pi
−0.475715 0.879599i 0.657811π-0.657811\pi
252252 3.04133 + 5.09059i 0.191586 + 0.320677i
253253 −3.27303 + 18.6081i −0.205774 + 1.16988i
254254 20.7480i 1.30185i
255255 2.44016 7.83478i 0.152809 0.490633i
256256 −2.32930 16.2007i −0.145581 1.01254i
257257 −9.22692 + 4.21379i −0.575560 + 0.262849i −0.681857 0.731485i 0.738828π-0.738828\pi
0.106298 + 0.994334i 0.466100π0.466100\pi
258258 0.202642 12.4073i 0.0126159 0.772448i
259259 0.919773 2.01402i 0.0571519 0.125145i
260260 13.2269 15.2647i 0.820301 0.946677i
261261 −28.6375 + 11.9641i −1.77262 + 0.740559i
262262 12.4271 3.64891i 0.767746 0.225431i
263263 −2.41205 2.78365i −0.148733 0.171647i 0.676494 0.736448i 0.263498π-0.263498\pi
−0.825227 + 0.564801i 0.808953π0.808953\pi
264264 0.212091 0.236838i 0.0130533 0.0145764i
265265 −6.36693 + 4.09177i −0.391117 + 0.251356i
266266 −3.17323 + 2.74962i −0.194563 + 0.168590i
267267 −4.32974 6.98544i −0.264976 0.427502i
268268 −6.08953 0.875543i −0.371978 0.0534823i
269269 16.7393 + 14.5047i 1.02061 + 0.884367i 0.993335 0.115261i 0.0367703π-0.0367703\pi
0.0272790 + 0.999628i 0.491316π0.491316\pi
270270 −7.83039 19.6386i −0.476542 1.19517i
271271 −17.9666 5.27547i −1.09139 0.320462i −0.313966 0.949434i 0.601658π-0.601658\pi
−0.777428 + 0.628972i 0.783476π0.783476\pi
272272 3.90291 + 8.54618i 0.236649 + 0.518188i
273273 3.47411 + 7.94824i 0.210263 + 0.481049i
274274 15.2497 23.7289i 0.921265 1.43352i
275275 3.29702 0.198818
276276 −16.3449 + 1.56003i −0.983847 + 0.0939027i
277277 12.1422 0.729555 0.364777 0.931095i 0.381145π-0.381145\pi
0.364777 + 0.931095i 0.381145π0.381145\pi
278278 19.1724 29.8328i 1.14988 1.78925i
279279 −4.70402 5.80118i −0.281623 0.347307i
280280 −0.0394910 0.0864733i −0.00236004 0.00516777i
281281 24.1583 + 7.09352i 1.44116 + 0.423164i 0.906610 0.421970i 0.138661π-0.138661\pi
0.534555 + 0.845134i 0.320479π0.320479\pi
282282 23.7972 + 3.81916i 1.41710 + 0.227428i
283283 −1.76062 1.52559i −0.104658 0.0906867i 0.600960 0.799279i 0.294785π-0.294785\pi
−0.705618 + 0.708592i 0.749331π0.749331\pi
284284 28.0323 + 4.03043i 1.66341 + 0.239162i
285285 6.32468 3.92018i 0.374642 0.232211i
286286 −29.7348 + 25.7653i −1.75825 + 1.52354i
287287 5.89348 3.78751i 0.347881 0.223570i
288288 21.4282 + 10.6449i 1.26267 + 0.627256i
289289 7.60185 + 8.77301i 0.447168 + 0.516059i
290290 −40.3883 + 11.8591i −2.37169 + 0.696390i
291291 3.06992 + 24.1446i 0.179962 + 1.41538i
292292 8.19736 9.46025i 0.479714 0.553619i
293293 −4.32941 + 9.48009i −0.252927 + 0.553833i −0.992920 0.118781i 0.962101π-0.962101\pi
0.739993 + 0.672614i 0.234829π0.234829\pi
294294 −3.45351 0.0564041i −0.201413 0.00328955i
295295 −11.8760 + 5.42359i −0.691448 + 0.315774i
296296 −0.0146810 0.102109i −0.000853317 0.00593495i
297297 4.79847 + 19.9005i 0.278435 + 1.15474i
298298 13.4289i 0.777917i
299299 −24.0063 0.751944i −1.38832 0.0434861i
300300 0.762218 + 2.76195i 0.0440067 + 0.159461i
301301 3.02235 + 1.94235i 0.174205 + 0.111955i
302302 18.7595 2.69721i 1.07949 0.155207i
303303 −11.6233 13.8652i −0.667743 0.796536i
304304 −2.40020 + 8.17433i −0.137661 + 0.468830i
305305 −21.3012 9.72793i −1.21970 0.557020i
306306 −13.6779 2.42489i −0.781915 0.138621i
307307 1.96867 13.6924i 0.112358 0.781467i −0.853257 0.521491i 0.825376π-0.825376\pi
0.965615 0.259976i 0.0837147π-0.0837147\pi
308308 −2.19390 7.47175i −0.125009 0.425742i
309309 23.0170 + 15.3290i 1.30939 + 0.872035i
310310 −5.47646 8.52153i −0.311042 0.483990i
311311 −0.750569 1.16791i −0.0425609 0.0662260i 0.819321 0.573335i 0.194351π-0.194351\pi
−0.861882 + 0.507109i 0.830714π0.830714\pi
312312 0.336380 + 0.224023i 0.0190437 + 0.0126828i
313313 2.21091 + 7.52966i 0.124968 + 0.425602i 0.998081 0.0619154i 0.0197209π-0.0197209\pi
−0.873114 + 0.487517i 0.837903π0.837903\pi
314314 −5.37804 + 37.4051i −0.303500 + 2.11089i
315315 6.02713 + 1.06852i 0.339590 + 0.0602041i
316316 8.82853 + 4.03186i 0.496644 + 0.226810i
317317 −1.88321 + 6.41362i −0.105772 + 0.360225i −0.995322 0.0966119i 0.969199π-0.969199\pi
0.889551 + 0.456837i 0.151018π0.151018\pi
318318 8.23075 + 9.81828i 0.461558 + 0.550582i
319319 40.3420 5.80031i 2.25872 0.324755i
320320 13.4091 + 8.61749i 0.749590 + 0.481732i
321321 −3.01281 10.9171i −0.168159 0.609335i
322322 4.24327 8.57072i 0.236468 0.477628i
323323 4.88907i 0.272035i
324324 −15.5616 + 8.62042i −0.864532 + 0.478912i
325325 0.596476 + 4.14858i 0.0330865 + 0.230122i
326326 −12.2207 + 5.58099i −0.676840 + 0.309103i
327327 −23.0965 0.377221i −1.27724 0.0208604i
328328 0.135592 0.296905i 0.00748682 0.0163939i
329329 −4.56961 + 5.27361i −0.251931 + 0.290743i
330330 3.50192 + 27.5422i 0.192774 + 1.51615i
331331 19.4350 5.70663i 1.06824 0.313665i 0.300077 0.953915i 0.402987π-0.402987\pi
0.768167 + 0.640250i 0.221169π0.221169\pi
332332 −15.3744 17.7431i −0.843783 0.973777i
333333 5.94873 + 2.95516i 0.325989 + 0.161942i
334334 −4.39125 + 2.82208i −0.240278 + 0.154418i
335335 −4.79941 + 4.15871i −0.262220 + 0.227215i
336336 −5.95676 + 3.69213i −0.324968 + 0.201422i
337337 −9.70171 1.39490i −0.528486 0.0759848i −0.127093 0.991891i 0.540565π-0.540565\pi
−0.401393 + 0.915906i 0.631474π0.631474\pi
338338 −18.2075 15.7769i −0.990356 0.858148i
339339 −21.6225 3.47014i −1.17437 0.188472i
340340 −8.98542 2.63836i −0.487303 0.143085i
341341 4.07436 + 8.92161i 0.220639 + 0.483132i
342342 −7.93357 9.78397i −0.428998 0.529057i
343343 0.540641 0.841254i 0.0291919 0.0454234i
344344 0.167388 0.00902498
345345 −9.83175 + 13.8055i −0.529324 + 0.743262i
346346 1.05383 0.0566542
347347 0.248919 0.387326i 0.0133627 0.0207927i −0.834508 0.550996i 0.814248π-0.814248\pi
0.847871 + 0.530203i 0.177884π0.177884\pi
348348 14.1854 + 32.4541i 0.760419 + 1.73972i
349349 −6.14218 13.4495i −0.328783 0.719935i 0.670985 0.741471i 0.265872π-0.265872\pi
−0.999768 + 0.0215362i 0.993144π0.993144\pi
350350 −1.60128 0.470178i −0.0855920 0.0251321i
351351 −24.1723 + 9.63810i −1.29022 + 0.514444i
352352 −23.7460 20.5760i −1.26567 1.09671i
353353 7.03252 + 1.01112i 0.374303 + 0.0538167i 0.326900 0.945059i 0.393996π-0.393996\pi
0.0474039 + 0.998876i 0.484905π0.484905\pi
354354 11.6435 + 18.7853i 0.618848 + 0.998427i
355355 22.0933 19.1440i 1.17259 1.01606i
356356 −7.89011 + 5.07067i −0.418175 + 0.268745i
357357 2.68301 2.99607i 0.142000 0.158569i
358358 8.15231 + 9.40827i 0.430863 + 0.497242i
359359 −26.8739 + 7.89088i −1.41835 + 0.416465i −0.898944 0.438064i 0.855664π-0.855664\pi
−0.519405 + 0.854528i 0.673846π0.673846\pi
360360 0.263150 0.109938i 0.0138692 0.00579426i
361361 −9.53914 + 11.0088i −0.502060 + 0.579408i
362362 −5.42175 + 11.8720i −0.284961 + 0.623977i
363363 0.127863 7.82880i 0.00671107 0.410905i
364364 9.00466 4.11229i 0.471973 0.215543i
365365 −1.83890 12.7898i −0.0962523 0.669449i
366366 −11.7879 + 37.8481i −0.616163 + 1.97835i
367367 19.5190i 1.01888i −0.860506 0.509441i 0.829852π-0.829852\pi
0.860506 0.509441i 0.170148π-0.170148\pi
368368 −2.15891 19.2843i −0.112541 1.00527i
369369 10.7791 + 18.0421i 0.561137 + 0.939233i
370370 7.57866 + 4.87051i 0.393996 + 0.253206i
371371 −3.67156 + 0.527891i −0.190618 + 0.0274067i
372372 −6.53182 + 5.47568i −0.338659 + 0.283901i
373373 10.7111 36.4787i 0.554600 1.88880i 0.107772 0.994176i 0.465628π-0.465628\pi
0.446829 0.894620i 0.352553π-0.352553\pi
374374 16.5935 + 7.57800i 0.858030 + 0.391849i
375375 18.6212 + 8.87433i 0.961594 + 0.458269i
376376 −0.0462687 + 0.321806i −0.00238613 + 0.0165959i
377377 14.5969 + 49.7123i 0.751776 + 2.56032i
378378 0.507456 10.3495i 0.0261007 0.532320i
379379 −2.22140 3.45657i −0.114106 0.177552i 0.779503 0.626398i 0.215472π-0.215472\pi
−0.893609 + 0.448846i 0.851835π0.851835\pi
380380 −4.59102 7.14377i −0.235515 0.366468i
381381 −9.98917 + 14.9991i −0.511761 + 0.768428i
382382 −1.35193 4.60426i −0.0691709 0.235575i
383383 3.22390 22.4227i 0.164733 1.14575i −0.724828 0.688930i 0.758081π-0.758081\pi
0.889561 0.456816i 0.151010π-0.151010\pi
384384 −0.277724 + 0.582753i −0.0141725 + 0.0297385i
385385 −7.31187 3.33922i −0.372647 0.170182i
386386 8.66312 29.5039i 0.440941 1.50171i
387387 −6.12003 + 8.87193i −0.311099 + 0.450986i
388388 27.4932 3.95292i 1.39576 0.200679i
389389 1.29734 + 0.833752i 0.0657779 + 0.0422729i 0.573116 0.819474i 0.305734π-0.305734\pi
−0.507339 + 0.861747i 0.669371π0.669371\pi
390390 −34.0223 + 9.38917i −1.72279 + 0.475439i
391391 4.30662 + 10.2694i 0.217795 + 0.519347i
392392 0.0465916i 0.00235323i
393393 −10.7405 3.34516i −0.541788 0.168741i
394394 7.08070 + 49.2473i 0.356720 + 2.48104i
395395 9.11320 4.16186i 0.458535 0.209406i
396396 22.6182 5.84620i 1.13661 0.293783i
397397 3.63173 7.95239i 0.182272 0.399119i −0.796336 0.604854i 0.793231π-0.793231\pi
0.978608 + 0.205735i 0.0659586π0.0659586\pi
398398 1.22801 1.41720i 0.0615544 0.0710376i
399399 3.61779 0.459992i 0.181116 0.0230284i
400400 −3.24904 + 0.954004i −0.162452 + 0.0477002i
401401 −16.5453 19.0943i −0.826231 0.953522i 0.173277 0.984873i 0.444564π-0.444564\pi
−0.999508 + 0.0313513i 0.990019π0.990019\pi
402402 8.00846 + 7.17166i 0.399426 + 0.357690i
403403 −10.4888 + 6.74074i −0.522484 + 0.335780i
404404 −15.6044 + 13.5213i −0.776349 + 0.672710i
405405 −3.79431 + 17.9671i −0.188541 + 0.892790i
406406 −20.4203 2.93600i −1.01344 0.145711i
407407 −6.59220 5.71217i −0.326763 0.283142i
408408 0.0296926 0.185015i 0.00147000 0.00915960i
409409 −9.39280 2.75798i −0.464444 0.136373i 0.0411345 0.999154i 0.486903π-0.486903\pi
−0.505579 + 0.862781i 0.668721π0.668721\pi
410410 11.8412 + 25.9285i 0.584793 + 1.28052i
411411 −22.4486 + 9.81210i −1.10731 + 0.483995i
412412 17.0623 26.5495i 0.840600 1.30800i
413413 −6.39876 −0.314862
414414 25.2827 + 13.5627i 1.24258 + 0.666570i
415415 −24.2344 −1.18962
416416 21.5945 33.6016i 1.05876 1.64746i
417417 −28.2231 + 12.3361i −1.38209 + 0.604102i
418418 6.87162 + 15.0467i 0.336102 + 0.735960i
419419 −11.5518 3.39191i −0.564341 0.165705i −0.0128962 0.999917i 0.504105π-0.504105\pi
−0.551445 + 0.834211i 0.685923π0.685923\pi
420420 1.10692 6.89722i 0.0540121 0.336550i
421421 −8.86143 7.67847i −0.431880 0.374226i 0.411620 0.911356i 0.364963π-0.364963\pi
−0.843500 + 0.537130i 0.819509π0.819509\pi
422422 40.5423 + 5.82911i 1.97357 + 0.283756i
423423 −15.3647 14.2182i −0.747058 0.691310i
424424 −0.130611 + 0.113175i −0.00634302 + 0.00549626i
425425 1.63476 1.05060i 0.0792977 0.0509616i
426426 −36.8657 33.0137i −1.78615 1.59952i
427427 −7.51585 8.67376i −0.363718 0.419753i
428428 −12.4009 + 3.64125i −0.599422 + 0.176006i
429429 33.9006 4.31037i 1.63673 0.208106i
430430 −9.57269 + 11.0475i −0.461636 + 0.532757i
431431 −6.47755 + 14.1838i −0.312012 + 0.683212i −0.999058 0.0434028i 0.986180π-0.986180\pi
0.687045 + 0.726615i 0.258907π0.258907\pi
432432 −10.4869 18.2224i −0.504552 0.876728i
433433 −0.917931 + 0.419205i −0.0441129 + 0.0201457i −0.437349 0.899292i 0.644083π-0.644083\pi
0.393236 + 0.919437i 0.371355π0.371355\pi
434434 −0.706532 4.91404i −0.0339146 0.235881i
435435 34.9070 + 10.8719i 1.67366 + 0.521267i
436436 26.3615i 1.26249i
437437 −3.14683 + 9.59500i −0.150533 + 0.458991i
438438 −21.0852 + 5.81890i −1.00749 + 0.278038i
439439 31.1556 + 20.0225i 1.48698 + 0.955623i 0.996449 + 0.0841977i 0.0268327π0.0268327\pi
0.490529 + 0.871425i 0.336804π0.336804\pi
440440 −0.370704 + 0.0532992i −0.0176726 + 0.00254094i
441441 2.46945 + 1.70347i 0.117593 + 0.0811178i
442442 −6.53327 + 22.2503i −0.310756 + 1.05834i
443443 −14.2004 6.48509i −0.674680 0.308116i 0.0484523 0.998825i 0.484571π-0.484571\pi
−0.723132 + 0.690709i 0.757298π0.757298\pi
444444 3.26115 6.84293i 0.154767 0.324751i
445445 −1.37781 + 9.58287i −0.0653144 + 0.454271i
446446 7.82939 + 26.6645i 0.370732 + 1.26260i
447447 6.46538 9.70801i 0.305802 0.459173i
448448 4.22349 + 6.57188i 0.199541 + 0.310492i
449449 0.478552 + 0.744641i 0.0225843 + 0.0351418i 0.852362 0.522952i 0.175169π-0.175169\pi
−0.829778 + 0.558094i 0.811533π0.811533\pi
450450 1.56666 4.75521i 0.0738529 0.224163i
451451 −7.77563 26.4814i −0.366140 1.24696i
452452 −3.55667 + 24.7372i −0.167292 + 1.16354i
453453 −14.8601 7.08192i −0.698190 0.332738i
454454 −25.5192 11.6542i −1.19767 0.546959i
455455 2.87886 9.80451i 0.134963 0.459643i
456456 0.130214 0.109159i 0.00609781 0.00511185i
457457 17.6177 2.53305i 0.824122 0.118491i 0.282664 0.959219i 0.408782π-0.408782\pi
0.541458 + 0.840728i 0.317873π0.317873\pi
458458 36.3780 + 23.3787i 1.69983 + 1.09242i
459459 8.72055 + 8.33825i 0.407041 + 0.389196i
460460 15.9361 + 10.9613i 0.743025 + 0.511074i
461461 4.55078i 0.211951i 0.994369 + 0.105975i 0.0337965π0.0337965\pi
−0.994369 + 0.105975i 0.966204π0.966204\pi
462462 −4.04632 + 12.9918i −0.188252 + 0.604432i
463463 −3.48582 24.2444i −0.162000 1.12673i −0.894857 0.446352i 0.852723π-0.852723\pi
0.732857 0.680382i 0.238186π-0.238186\pi
464464 −38.0766 + 17.3890i −1.76766 + 0.807265i
465465 −0.143676 + 8.79702i −0.00666284 + 0.407952i
466466 −23.7979 + 52.1102i −1.10242 + 2.41396i
467467 −7.23406 + 8.34855i −0.334752 + 0.386325i −0.898024 0.439947i 0.854997π-0.854997\pi
0.563271 + 0.826272i 0.309543π0.309543\pi
468468 11.4481 + 27.4025i 0.529190 + 1.26668i
469469 −2.98636 + 0.876875i −0.137897 + 0.0404903i
470470 −18.5928 21.4573i −0.857624 0.989751i
471471 21.8966 24.4515i 1.00894 1.12667i
472472 −0.250801 + 0.161180i −0.0115441 + 0.00741892i
473473 10.6967 9.26874i 0.491835 0.426177i
474474 −8.93482 14.4151i −0.410390 0.662108i
475475 1.74417 + 0.250774i 0.0800281 + 0.0115063i
476476 −3.46869 3.00564i −0.158987 0.137763i
477477 −1.22313 11.0605i −0.0560033 0.506427i
478478 32.1152 + 9.42988i 1.46892 + 0.431313i
479479 −12.3064 26.9473i −0.562295 1.23126i −0.950799 0.309808i 0.899735π-0.899735\pi
0.388504 0.921447i 0.372992π-0.372992\pi
480480 −11.2885 25.8264i −0.515247 1.17881i
481481 5.99491 9.32826i 0.273344 0.425332i
482482 −22.2866 −1.01513
483483 −7.19393 + 4.15300i −0.327335 + 0.188968i
484484 −8.93551 −0.406159
485485 15.5010 24.1200i 0.703864 1.09523i
486486 30.9822 + 2.53548i 1.40538 + 0.115012i
487487 −10.2794 22.5087i −0.465803 1.01997i −0.986126 0.165998i 0.946916π-0.946916\pi
0.520323 0.853970i 0.325812π-0.325812\pi
488488 −0.513072 0.150652i −0.0232257 0.00681968i
489489 11.5215 + 1.84906i 0.521021 + 0.0836174i
490490 3.07500 + 2.66450i 0.138914 + 0.120370i
491491 14.6840 + 2.11123i 0.662677 + 0.0952786i 0.465443 0.885078i 0.345895π-0.345895\pi
0.197234 + 0.980356i 0.436804π0.436804\pi
492492 20.3862 12.6358i 0.919080 0.569667i
493493 18.1546 15.7310i 0.817641 0.708490i
494494 −17.6899 + 11.3686i −0.795905 + 0.511497i
495495 10.7286 21.5968i 0.482217 0.970703i
496496 −6.59657 7.61285i −0.296195 0.341827i
497497 13.7473 4.03656i 0.616649 0.181065i
498498 5.17449 + 40.6968i 0.231874 + 1.82367i
499499 −11.1397 + 12.8559i −0.498681 + 0.575508i −0.948164 0.317780i 0.897063π-0.897063\pi
0.449484 + 0.893289i 0.351608π0.351608\pi
500500 9.77911 21.4133i 0.437335 0.957630i
501501 4.53321 + 0.0740382i 0.202529 + 0.00330778i
502502 50.3347 22.9871i 2.24655 1.02596i
503503 −0.348565 2.42432i −0.0155417 0.108095i 0.980574 0.196150i 0.0628440π-0.0628440\pi
−0.996116 + 0.0880549i 0.971935π0.971935\pi
504504 0.139700 + 0.00456450i 0.00622274 + 0.000203319i
505505 21.3134i 0.948433i
506506 −27.6879 25.5525i −1.23088 1.13595i
507507 5.56671 + 20.1714i 0.247226 + 0.895843i
508508 17.3010 + 11.1187i 0.767610 + 0.493313i
509509 −0.105490 + 0.0151672i −0.00467578 + 0.000672275i −0.144652 0.989483i 0.546206π-0.546206\pi
0.139977 + 0.990155i 0.455297π0.455297\pi
510510 10.5127 + 12.5404i 0.465511 + 0.555298i
511511 1.78417 6.07631i 0.0789268 0.268800i
512512 29.0112 + 13.2490i 1.28213 + 0.585527i
513513 1.02481 + 10.8926i 0.0452466 + 0.480922i
514514 2.87872 20.0219i 0.126975 0.883129i
515515 −9.17801 31.2574i −0.404431 1.37737i
516516 10.2375 + 6.81798i 0.450679 + 0.300145i
517517 14.8625 + 23.1265i 0.653653 + 1.01710i
518518 2.38707 + 3.71435i 0.104882 + 0.163199i
519519 −0.761832 0.507367i −0.0334407 0.0222710i
520520 −0.134131 0.456808i −0.00588202 0.0200323i
521521 −0.411643 + 2.86304i −0.0180344 + 0.125432i −0.996850 0.0793129i 0.974727π-0.974727\pi
0.978815 + 0.204745i 0.0656365π0.0656365\pi
522522 10.8038 60.9406i 0.472871 2.66730i
523523 8.82493 + 4.03021i 0.385887 + 0.176229i 0.598906 0.800819i 0.295602π-0.295602\pi
−0.213019 + 0.977048i 0.568330π0.568330\pi
524524 −3.61686 + 12.3179i −0.158003 + 0.538110i
525525 0.931226 + 1.11084i 0.0406420 + 0.0484810i
526526 7.27029 1.04531i 0.317000 0.0455777i
527527 4.86308 + 3.12531i 0.211839 + 0.136141i
528528 7.34487 + 26.6147i 0.319645 + 1.15826i
529529 −1.84204 22.9261i −0.0800888 0.996788i
530530 15.0925i 0.655576i
531531 0.626875 19.1860i 0.0272041 0.832603i
532532 −0.592300 4.11954i −0.0256795 0.178605i
533533 31.9143 14.5748i 1.38236 0.631304i
534534 16.3867 + 0.267633i 0.709120 + 0.0115816i
535535 −5.54214 + 12.1356i −0.239608 + 0.524667i
536536 −0.0949635 + 0.109594i −0.00410180 + 0.00473373i
537537 −1.36383 10.7263i −0.0588535 0.462876i
538538 −42.3799 + 12.4439i −1.82713 + 0.536493i
539539 −2.57990 2.97736i −0.111124 0.128244i
540540 20.5722 + 3.99469i 0.885286 + 0.171904i
541541 −26.0957 + 16.7707i −1.12194 + 0.721027i −0.963863 0.266399i 0.914166π-0.914166\pi
−0.158078 + 0.987427i 0.550530π0.550530\pi
542542 28.2202 24.4529i 1.21216 1.05034i
543543 9.63526 5.97215i 0.413489 0.256290i
544544 −18.3306 2.63554i −0.785917 0.112998i
545545 20.5651 + 17.8197i 0.880910 + 0.763313i
546546 −17.0794 2.74102i −0.730929 0.117305i
547547 −0.0906448 0.0266157i −0.00387569 0.00113801i 0.279794 0.960060i 0.409734π-0.409734\pi
−0.283670 + 0.958922i 0.591552π0.591552\pi
548548 11.6145 + 25.4323i 0.496149 + 1.08641i
549549 26.7437 21.6858i 1.14139 0.925527i
550550 −3.55458 + 5.53103i −0.151568 + 0.235844i
551551 21.7827 0.927976
552552 −0.177357 + 0.343988i −0.00754882 + 0.0146411i
553553 4.91016 0.208801
554554 −13.0907 + 20.3696i −0.556172 + 0.865421i
555555 −3.13384 7.16974i −0.133024 0.304338i
556556 14.6022 + 31.9744i 0.619272 + 1.35602i
557557 −10.2906 3.02161i −0.436029 0.128030i 0.0563492 0.998411i 0.482054π-0.482054\pi
−0.492378 + 0.870382i 0.663872π0.663872\pi
558558 14.8035 1.63705i 0.626681 0.0693017i
559559 13.5979 + 11.7826i 0.575129 + 0.498352i
560560 8.17168 + 1.17491i 0.345316 + 0.0496490i
561561 −8.34731 13.4672i −0.352424 0.568588i
562562 −37.9455 + 32.8800i −1.60064 + 1.38696i
563563 −21.4288 + 13.7715i −0.903116 + 0.580397i −0.907713 0.419592i 0.862173π-0.862173\pi
0.00459679 + 0.999989i 0.498537π0.498537\pi
564564 −15.9374 + 17.7970i −0.671086 + 0.749390i
565565 16.8937 + 19.4964i 0.710724 + 0.820219i
566566 4.45746 1.30883i 0.187361 0.0550142i
567567 −5.34962 + 7.23751i −0.224663 + 0.303947i
568568 0.437150 0.504499i 0.0183424 0.0211683i
569569 8.76558 19.1939i 0.367472 0.804652i −0.632085 0.774899i 0.717801π-0.717801\pi
0.999557 0.0297530i 0.00947208π-0.00947208\pi
570570 −0.242318 + 14.8366i −0.0101496 + 0.621437i
571571 −22.4759 + 10.2644i −0.940588 + 0.429552i −0.825879 0.563847i 0.809321π-0.809321\pi
−0.114709 + 0.993399i 0.536593π0.536593\pi
572572 −5.55016 38.6022i −0.232064 1.61404i
573573 −1.23939 + 3.97940i −0.0517764 + 0.166242i
574574 13.9702i 0.583105i
575575 −3.88451 + 1.00964i −0.161995 + 0.0421047i
576576 −20.1189 + 12.0199i −0.838287 + 0.500828i
577577 17.4832 + 11.2358i 0.727835 + 0.467751i 0.851355 0.524591i 0.175782π-0.175782\pi
−0.123519 + 0.992342i 0.539418π0.539418\pi
578578 −22.9132 + 3.29442i −0.953062 + 0.137030i
579579 −20.4674 + 17.1580i −0.850597 + 0.713063i
580580 11.7549 40.0336i 0.488097 1.66231i
581581 −10.8041 4.93408i −0.448231 0.204700i
582582 −43.8144 20.8807i −1.81616 0.865533i
583583 −2.07969 + 14.4645i −0.0861318 + 0.599060i
584584 −0.0831271 0.283105i −0.00343982 0.0117150i
585585 29.1158 + 9.59252i 1.20379 + 0.396602i
586586 −11.2360 17.4836i −0.464157 0.722242i
587587 −12.0193 18.7024i −0.496089 0.771930i 0.499444 0.866346i 0.333538π-0.333538\pi
−0.995533 + 0.0944167i 0.969901π0.969901\pi
588588 1.89774 2.84953i 0.0782616 0.117513i
589589 1.47681 + 5.02957i 0.0608511 + 0.207240i
590590 3.70521 25.7703i 0.152541 1.06095i
591591 18.5914 39.0108i 0.764750 1.60469i
592592 8.14910 + 3.72157i 0.334926 + 0.152956i
593593 −2.78151 + 9.47295i −0.114223 + 0.389007i −0.996683 0.0813794i 0.974067π-0.974067\pi
0.882460 + 0.470387i 0.155886π0.155886\pi
594594 −38.5581 13.4053i −1.58206 0.550025i
595595 −4.68950 + 0.674249i −0.192251 + 0.0276415i
596596 −11.1979 7.19646i −0.458684 0.294778i
597597 −1.57006 + 0.433290i −0.0642582 + 0.0177334i
598598 27.1431 39.4620i 1.10997 1.61372i
599599 30.4875i 1.24569i −0.782347 0.622843i 0.785978π-0.785978\pi
0.782347 0.622843i 0.214022π-0.214022\pi
600600 0.0644810 + 0.0200828i 0.00263243 + 0.000819876i
601601 4.84771 + 33.7166i 0.197742 + 1.37533i 0.810816 + 0.585302i 0.199024π0.199024\pi
−0.613073 + 0.790026i 0.710067π0.710067\pi
602602 −6.51691 + 2.97617i −0.265609 + 0.121300i
603603 −2.33665 9.04021i −0.0951559 0.368146i
604604 −7.80396 + 17.0883i −0.317538 + 0.695312i
605605 −6.04019 + 6.97075i −0.245569 + 0.283401i
606606 35.7914 4.55079i 1.45393 0.184863i
607607 −15.0514 + 4.41948i −0.610916 + 0.179381i −0.572533 0.819882i 0.694039π-0.694039\pi
−0.0383836 + 0.999263i 0.512221π0.512221\pi
608608 −10.9970 12.6912i −0.445986 0.514695i
609609 13.3487 + 11.9539i 0.540915 + 0.484395i
610610 39.2847 25.2467i 1.59059 1.02221i
611611 −26.4109 + 22.8852i −1.06847 + 0.925835i
612612 9.35192 10.1061i 0.378029 0.408513i
613613 18.4313 + 2.65003i 0.744435 + 0.107034i 0.504087 0.863653i 0.331829π-0.331829\pi
0.240348 + 0.970687i 0.422738π0.422738\pi
614614 20.8477 + 18.0647i 0.841346 + 0.729030i
615615 3.92314 24.4451i 0.158196 0.985723i
616616 −0.176118 0.0517128i −0.00709598 0.00208357i
617617 15.4717 + 33.8783i 0.622867 + 1.36389i 0.913415 + 0.407029i 0.133435π0.133435\pi
−0.290548 + 0.956860i 0.593838π0.593838\pi
618618 −50.5308 + 22.0866i −2.03265 + 0.888454i
619619 −9.85067 + 15.3279i −0.395932 + 0.616082i −0.980793 0.195051i 0.937513π-0.937513\pi
0.584861 + 0.811133i 0.301149π0.301149\pi
620620 10.0406 0.403240
621621 −11.7476 21.9771i −0.471414 0.881912i
622622 2.76847 0.111005
623623 −2.56530 + 3.99169i −0.102777 + 0.159924i
624624 −32.1600 + 14.0569i −1.28743 + 0.562726i
625625 −8.35615 18.2974i −0.334246 0.731896i
626626 −15.0153 4.40888i −0.600131 0.176214i
627627 2.27666 14.1859i 0.0909212 0.566531i
628628 −28.3087 24.5296i −1.12964 0.978839i
629629 −5.08881 0.731660i −0.202904 0.0291732i
630630 −8.29049 + 8.95904i −0.330301 + 0.356937i
631631 −34.0394 + 29.4953i −1.35509 + 1.17419i −0.387438 + 0.921896i 0.626640π0.626640\pi
−0.967650 + 0.252295i 0.918815π0.918815\pi
632632 0.192456 0.123684i 0.00765547 0.00491987i
633633 −26.5023 23.7331i −1.05337 0.943307i
634634 −8.72907 10.0739i −0.346676 0.400085i
635635 20.3690 5.98087i 0.808319 0.237344i
636636 −12.5979 + 1.60179i −0.499540 + 0.0635152i
637637 3.27962 3.78489i 0.129943 0.149963i
638638 −33.7630 + 73.9307i −1.33669 + 2.92694i
639639 10.7564 + 41.6153i 0.425518 + 1.64627i
640640 0.691739 0.315907i 0.0273434 0.0124873i
641641 1.41590 + 9.84783i 0.0559249 + 0.388966i 0.998490 + 0.0549423i 0.0174975π0.0174975\pi
−0.942565 + 0.334024i 0.891593π0.891593\pi
642642 21.5626 + 6.71572i 0.851008 + 0.265048i
643643 30.3507i 1.19691i −0.801155 0.598457i 0.795781π-0.795781\pi
0.801155 0.598457i 0.204219π-0.204219\pi
644644 4.87288 + 8.13130i 0.192019 + 0.320418i
645645 12.2391 3.37763i 0.481914 0.132994i
646646 8.20183 + 5.27100i 0.322697 + 0.207385i
647647 42.4731 6.10671i 1.66979 0.240079i 0.758449 0.651733i 0.225958π-0.225958\pi
0.911341 + 0.411653i 0.135049π0.135049\pi
648648 −0.0273724 + 0.418430i −0.00107529 + 0.0164375i
649649 −7.10209 + 24.1875i −0.278782 + 0.949443i
650650 −7.60267 3.47202i −0.298201 0.136184i
651651 −1.85511 + 3.89261i −0.0727074 + 0.152563i
652652 1.89517 13.1812i 0.0742206 0.516216i
653653 −2.32030 7.90223i −0.0908005 0.309238i 0.901553 0.432669i 0.142428π-0.142428\pi
−0.992353 + 0.123431i 0.960610π0.960610\pi
654654 25.5336 38.3396i 0.998442 1.49920i
655655 7.16451 + 11.1482i 0.279941 + 0.435596i
656656 15.3250 + 23.8461i 0.598339 + 0.931034i
657657 18.0444 + 5.94493i 0.703980 + 0.231934i
658658 −3.92035 13.3515i −0.152831 0.520495i
659659 −6.62502 + 46.0780i −0.258074 + 1.79495i 0.288442 + 0.957497i 0.406863π0.406863\pi
−0.546516 + 0.837448i 0.684046π0.684046\pi
660660 −24.8431 11.8395i −0.967018 0.460853i
661661 −41.3008 18.8615i −1.60642 0.733626i −0.608226 0.793764i 0.708119π-0.708119\pi
−0.998190 + 0.0601382i 0.980846π0.980846\pi
662662 −11.3799 + 38.7563i −0.442292 + 1.50631i
663663 15.4355 12.9397i 0.599464 0.502536i
664664 −0.547757 + 0.0787556i −0.0212571 + 0.00305631i
665665 −3.61411 2.32265i −0.140149 0.0900683i
666666 −11.3710 + 6.79350i −0.440616 + 0.263243i
667667 −45.7544 + 19.1877i −1.77162 + 0.742950i
668668 5.17404i 0.200190i
669669 7.17764 23.0457i 0.277504 0.890998i
670670 −1.80226 12.5350i −0.0696274 0.484269i
671671 −41.1291 + 18.7830i −1.58777 + 0.725110i
672672 0.225586 13.8122i 0.00870216 0.532815i
673673 20.8970 45.7580i 0.805520 1.76384i 0.179948 0.983676i 0.442407π-0.442407\pi
0.625572 0.780167i 0.284866π-0.284866\pi
674674 12.7997 14.7716i 0.493024 0.568980i
675675 −3.42197 + 2.68336i −0.131712 + 0.103283i
676676 22.9130 6.72787i 0.881270 0.258764i
677677 23.4837 + 27.1016i 0.902551 + 1.04160i 0.998930 + 0.0462544i 0.0147285π0.0147285\pi
−0.0963789 + 0.995345i 0.530726π0.530726\pi
678678 29.1331 32.5324i 1.11885 1.24940i
679679 11.8214 7.59715i 0.453663 0.291552i
680680 −0.166823 + 0.144553i −0.00639736 + 0.00554334i
681681 12.8373 + 20.7113i 0.491927 + 0.793658i
682682 −19.3594 2.78346i −0.741310 0.106584i
683683 −2.25542 1.95434i −0.0863014 0.0747806i 0.610642 0.791907i 0.290912π-0.290912\pi
−0.696943 + 0.717126i 0.745457π0.745457\pi
684684 12.4101 1.37237i 0.474510 0.0524738i
685685 27.6913 + 8.13091i 1.05803 + 0.310666i
686686 0.828400 + 1.81394i 0.0316285 + 0.0692567i
687687 −15.0426 34.4151i −0.573910 1.31302i
688688 −7.85909 + 12.2290i −0.299625 + 0.466226i
689689 −18.5767 −0.707716
690690 −12.5601 31.3776i −0.478155 1.19452i
691691 9.28661 0.353279 0.176640 0.984276i 0.443477π-0.443477\pi
0.176640 + 0.984276i 0.443477π0.443477\pi
692692 −0.564739 + 0.878750i −0.0214681 + 0.0334051i
693693 9.18007 7.44388i 0.348722 0.282770i
694694 0.381408 + 0.835166i 0.0144780 + 0.0317025i
695695 34.8145 + 10.2225i 1.32059 + 0.387760i
696696 0.824315 + 0.132292i 0.0312456 + 0.00501453i
697697 −12.2937 10.6526i −0.465658 0.403495i
698698 29.1847 + 4.19612i 1.10466 + 0.158826i
699699 42.2925 26.2139i 1.59965 0.991499i
700700 1.25018 1.08329i 0.0472523 0.0409444i
701701 −34.8594 + 22.4028i −1.31662 + 0.846142i −0.994917 0.100698i 0.967892π-0.967892\pi
−0.321705 + 0.946840i 0.604256π0.604256\pi
702702 9.89192 50.9422i 0.373347 1.92269i
703703 −3.05290 3.52323i −0.115142 0.132881i
704704 29.5296 8.67069i 1.11294 0.326789i
705705 3.11046 + 24.4634i 0.117147 + 0.921346i
706706 −9.27815 + 10.7076i −0.349188 + 0.402984i
707707 −4.33936 + 9.50186i −0.163198 + 0.357354i
708708 −21.9041 0.357746i −0.823206 0.0134449i
709709 −29.5183 + 13.4805i −1.10858 + 0.506272i −0.883672 0.468108i 0.844936π-0.844936\pi
−0.224910 + 0.974380i 0.572209π0.572209\pi
710710 8.29644 + 57.7030i 0.311360 + 2.16556i
711711 −0.481040 + 14.7226i −0.0180404 + 0.552142i
712712 0.221074i 0.00828509i
713713 −7.53241 9.26366i −0.282091 0.346927i
714714 2.13356 + 7.73109i 0.0798463 + 0.289329i
715715 −33.8661 21.7644i −1.26652 0.813942i
716716 −12.2140 + 1.75611i −0.456458 + 0.0656287i
717717 −18.6767 22.2790i −0.697493 0.832023i
718718 15.7356 53.5905i 0.587247 1.99998i
719719 19.3685 + 8.84530i 0.722323 + 0.329874i 0.742430 0.669924i 0.233673π-0.233673\pi
−0.0201065 + 0.999798i 0.506401π0.506401\pi
720720 −4.32342 + 24.3869i −0.161124 + 0.908845i
721721 2.27223 15.8037i 0.0846223 0.588561i
722722 −8.18380 27.8715i −0.304570 1.03727i
723723 16.1114 + 10.7299i 0.599190 + 0.399051i
724724 −6.99415 10.8831i −0.259935 0.404467i
725725 4.68084 + 7.28353i 0.173842 + 0.270503i
726726 12.9956 + 8.65488i 0.482313 + 0.321213i
727727 8.28640 + 28.2209i 0.307326 + 1.04666i 0.957874 + 0.287190i 0.0927211π0.0927211\pi
−0.650548 + 0.759465i 0.725461π0.725461\pi
728728 0.0332072 0.230961i 0.00123074 0.00856000i
729729 −21.1769 16.7494i −0.784328 0.620346i
730730 23.4386 + 10.7040i 0.867500 + 0.396174i
731731 2.35026 8.00425i 0.0869275 0.296048i
732732 −25.2432 30.1120i −0.933014 1.11297i
733733 2.22315 0.319641i 0.0821141 0.0118062i −0.101135 0.994873i 0.532248π-0.532248\pi
0.183249 + 0.983066i 0.441338π0.441338\pi
734734 32.7447 + 21.0438i 1.20863 + 0.776740i
735735 −0.940144 3.40668i −0.0346777 0.125657i
736736 34.2782 + 16.9708i 1.26351 + 0.625551i
737737 12.2618i 0.451669i
738738 −41.8883 1.36864i −1.54193 0.0503802i
739739 −1.34493 9.35420i −0.0494741 0.344100i −0.999491 0.0319015i 0.989844π-0.989844\pi
0.950017 0.312198i 0.101065π-0.101065\pi
740740 −8.12269 + 3.70951i −0.298596 + 0.136364i
741741 18.2618 + 0.298259i 0.670863 + 0.0109568i
742742 3.07280 6.72849i 0.112806 0.247011i
743743 34.0709 39.3199i 1.24994 1.44251i 0.399246 0.916844i 0.369272π-0.369272\pi
0.850693 0.525662i 0.176182π-0.176182\pi
744744 0.0253406 + 0.199301i 0.000929031 + 0.00730673i
745745 −13.1836 + 3.87106i −0.483010 + 0.141824i
746746 49.6483 + 57.2972i 1.81775 + 2.09780i
747747 15.8528 31.9117i 0.580024 1.16759i
748748 −15.2114 + 9.77575i −0.556182 + 0.357437i
749749 −4.94156 + 4.28189i −0.180561 + 0.156457i
750750 −34.9633 + 21.6711i −1.27668 + 0.791315i
751751 2.62425 + 0.377310i 0.0957602 + 0.0137682i 0.190028 0.981779i 0.439142π-0.439142\pi
−0.0942681 + 0.995547i 0.530051π0.530051\pi
752752 −21.3380 18.4895i −0.778116 0.674241i
753753 −47.4551 7.61595i −1.72936 0.277541i
754754 −99.1339 29.1083i −3.61024 1.06006i
755755 8.05559 + 17.6393i 0.293173 + 0.641959i
756756 8.35812 + 5.96936i 0.303982 + 0.217103i
757757 −18.0261 + 28.0491i −0.655169 + 1.01946i 0.341655 + 0.939826i 0.389013π0.389013\pi
−0.996824 + 0.0796377i 0.974624π0.974624\pi
758758 8.19364 0.297606
759759 7.71380 + 31.8028i 0.279993 + 1.15437i
760760 −0.200162 −0.00726064
761761 21.1719 32.9441i 0.767479 1.19422i −0.208853 0.977947i 0.566973π-0.566973\pi
0.976333 0.216274i 0.0693905π-0.0693905\pi
762762 −14.3928 32.9285i −0.521396 1.19287i
763763 5.54020 + 12.1313i 0.200569 + 0.439184i
764764 4.56382 + 1.34006i 0.165113 + 0.0484816i
765765 −1.56224 14.1271i −0.0564831 0.510765i
766766 34.1402 + 29.5827i 1.23354 + 1.06887i
767767 −31.7196 4.56059i −1.14533 0.164673i
768768 −14.9351 24.0957i −0.538923 0.869480i
769769 −25.2008 + 21.8366i −0.908765 + 0.787450i −0.977664 0.210174i 0.932597π-0.932597\pi
0.0688987 + 0.997624i 0.478051π0.478051\pi
770770 13.4849 8.66622i 0.485962 0.312309i
771771 −11.7207 + 13.0883i −0.422110 + 0.471362i
772772 19.9597 + 23.0348i 0.718367 + 0.829040i
773773 −9.72357 + 2.85510i −0.349733 + 0.102691i −0.451881 0.892078i 0.649247π-0.649247\pi
0.102148 + 0.994769i 0.467428π0.467428\pi
774774 −8.28531 19.8319i −0.297809 0.712842i
775775 −1.36440 + 1.57460i −0.0490105 + 0.0565612i
776776 0.271976 0.595545i 0.00976339 0.0213788i
777777 0.0626255 3.83443i 0.00224668 0.137560i
778778 −2.79738 + 1.27752i −0.100291 + 0.0458013i
779779 −2.09923 14.6005i −0.0752128 0.523116i
780780 10.4030 33.4016i 0.372488 1.19597i
781781 56.4454i 2.01977i
782782 −21.8709 3.84694i −0.782101 0.137566i
783783 −37.1502 + 38.8535i −1.32764 + 1.38851i
784784 3.40387 + 2.18753i 0.121567 + 0.0781261i
785785 −38.2720 + 5.50269i −1.36599 + 0.196399i
786786 17.1914 14.4117i 0.613195 0.514047i
787787 −1.20570 + 4.10625i −0.0429787 + 0.146372i −0.978187 0.207726i 0.933394π-0.933394\pi
0.935208 + 0.354098i 0.115212π0.115212\pi
788788 −44.8601 20.4869i −1.59808 0.729816i
789789 −5.75909 2.74462i −0.205029 0.0977111i
790790 −2.84324 + 19.7752i −0.101158 + 0.703568i
791791 3.56208 + 12.1313i 0.126653 + 0.431341i
792792 0.172310 0.523005i 0.00612276 0.0185842i
793793 −31.0752 48.3539i −1.10351 1.71710i
794794 9.42538 + 14.6662i 0.334494 + 0.520483i
795795 −7.26630 + 10.9106i −0.257709 + 0.386960i
796796 0.523670 + 1.78346i 0.0185610 + 0.0632129i
797797 −4.05851 + 28.2276i −0.143760 + 0.999872i 0.782410 + 0.622764i 0.213990π0.213990\pi
−0.926169 + 0.377107i 0.876919π0.876919\pi
798798 −3.12873 + 6.56508i −0.110756 + 0.232401i
799799 14.7386 + 6.73090i 0.521415 + 0.238122i
800800 1.88046 6.40425i 0.0664842 0.226424i
801801 −11.7174 8.08286i −0.414012 0.285594i
802802 49.8700 7.17023i 1.76097 0.253190i
803803 −20.9884 13.4884i −0.740664 0.475996i
804804 −10.2719 + 2.83473i −0.362261 + 0.0999734i
805805 9.63733 + 1.69514i 0.339671 + 0.0597458i
806806 24.8632i 0.875768i
807807 36.6283 + 11.4080i 1.28938 + 0.401580i
808808 0.0692629 + 0.481734i 0.00243666 + 0.0169473i
809809 6.77283 3.09305i 0.238120 0.108746i −0.292781 0.956179i 0.594581π-0.594581\pi
0.530901 + 0.847434i 0.321854π0.321854\pi
810810 −26.0506 25.7359i −0.915324 0.904268i
811811 6.55486 14.3531i 0.230172 0.504007i −0.758942 0.651159i 0.774283π-0.774283\pi
0.989114 + 0.147152i 0.0470105π0.0470105\pi
812812 13.3913 15.4544i 0.469943 0.542343i
813813 −32.1738 + 4.09081i −1.12838 + 0.143471i
814814 16.6898 4.90058i 0.584978 0.171765i
815815 −9.00180 10.3886i −0.315319 0.363898i
816816 12.1226 + 10.8559i 0.424377 + 0.380034i
817817 6.36371 4.08971i 0.222638 0.143081i
818818 14.7533 12.7838i 0.515837 0.446975i
819819 11.0273 + 10.2044i 0.385325 + 0.356571i
820820 −27.9665 4.02097i −0.976631 0.140418i
821821 24.9163 + 21.5901i 0.869586 + 0.753501i 0.970425 0.241402i 0.0776073π-0.0776073\pi
−0.100839 + 0.994903i 0.532153π0.532153\pi
822822 7.74161 48.2380i 0.270019 1.68249i
823823 −16.2548 4.77284i −0.566607 0.166371i −0.0141317 0.999900i 0.504498π-0.504498\pi
−0.552475 + 0.833529i 0.686317π0.686317\pi
824824 −0.309024 0.676668i −0.0107654 0.0235728i
825825 5.23259 2.28713i 0.182176 0.0796275i
826826 6.89862 10.7345i 0.240034 0.373500i
827827 −8.25538 −0.287068 −0.143534 0.989645i 0.545847π-0.545847\pi
−0.143534 + 0.989645i 0.545847π0.545847\pi
828828 −24.8583 + 13.8142i −0.863885 + 0.480078i
829829 −5.22695 −0.181540 −0.0907698 0.995872i 0.528933π-0.528933\pi
−0.0907698 + 0.995872i 0.528933π0.528933\pi
830830 26.1276 40.6554i 0.906903 1.41117i
831831 19.2705 8.42299i 0.668487 0.292190i
832832 16.2525 + 35.5880i 0.563454 + 1.23379i
833833 −2.22794 0.654181i −0.0771934 0.0226660i
834834 9.73302 60.6466i 0.337027 2.10002i
835835 −4.03636 3.49753i −0.139684 0.121037i
836836 −16.2294 2.33343i −0.561305 0.0807035i
837837 −11.4899 5.94371i −0.397148 0.205445i
838838 18.1444 15.7222i 0.626788 0.543115i
839839 −7.14641 + 4.59272i −0.246721 + 0.158558i −0.658157 0.752880i 0.728664π-0.728664\pi
0.411436 + 0.911439i 0.365027π0.365027\pi
840840 −0.122661 0.109844i −0.00423221 0.00378999i
841841 51.0970 + 58.9691i 1.76197 + 2.03342i
842842 22.4350 6.58750i 0.773160 0.227020i
843843 43.2617 5.50060i 1.49001 0.189451i
844844 −26.5870 + 30.6830i −0.915162 + 1.05615i
845845 10.2401 22.4227i 0.352271 0.771365i
846846 40.4172 10.4468i 1.38957 0.359167i
847847 −4.11205 + 1.87791i −0.141292 + 0.0645257i
848848 −2.13594 14.8558i −0.0733486 0.510150i
849849 −3.85252 1.19988i −0.132218 0.0411797i
850850 3.87513i 0.132916i
851851 9.51608 + 4.71131i 0.326207 + 0.161502i
852852 47.2850 13.0493i 1.61996 0.447061i
853853 −15.4856 9.95199i −0.530217 0.340750i 0.247985 0.968764i 0.420232π-0.420232\pi
−0.778202 + 0.628014i 0.783868π0.783868\pi
854854 22.6540 3.25715i 0.775203 0.111457i
855855 7.31829 10.6090i 0.250280 0.362820i
856856 −0.0858283 + 0.292304i −0.00293355 + 0.00999076i
857857 47.2292 + 21.5689i 1.61332 + 0.736778i 0.998647 0.0520038i 0.0165608π-0.0165608\pi
0.614673 + 0.788782i 0.289288π0.289288\pi
858858 −29.3178 + 61.5182i −1.00089 + 2.10020i
859859 −0.251497 + 1.74920i −0.00858097 + 0.0596819i −0.993662 0.112409i 0.964143π-0.964143\pi
0.985081 + 0.172091i 0.0550524π0.0550524\pi
860860 −4.08217 13.9026i −0.139201 0.474074i
861861 6.72598 10.0993i 0.229221 0.344184i
862862 −16.8111 26.1585i −0.572587 0.890963i
863863 −0.157206 0.244617i −0.00535135 0.00832687i 0.838568 0.544798i 0.183394π-0.183394\pi
−0.843919 + 0.536471i 0.819757π0.819757\pi
864864 41.3923 + 2.02955i 1.40819 + 0.0690467i
865865 0.303779 + 1.03458i 0.0103288 + 0.0351767i
866866 0.286386 1.99186i 0.00973180 0.0676862i
867867 18.1505 + 8.64999i 0.616422 + 0.293769i
868868 4.47627 + 2.04424i 0.151934 + 0.0693861i
869869 5.44988 18.5606i 0.184874 0.629625i
870870 −55.8725 + 46.8384i −1.89425 + 1.58797i
871871 −15.4288 + 2.21833i −0.522785 + 0.0751652i
872872 0.522730 + 0.335938i 0.0177019 + 0.0113763i
873873 21.6212 + 36.1895i 0.731766 + 1.22483i
874874 −12.7038 15.6236i −0.429712 0.528477i
875875 11.9094i 0.402612i
876876 6.44723 20.7005i 0.217832 0.699406i
877877 0.368646 + 2.56399i 0.0124483 + 0.0865798i 0.995098 0.0988887i 0.0315288π-0.0315288\pi
−0.982650 + 0.185469i 0.940620π0.940620\pi
878878 −67.1790 + 30.6796i −2.26718 + 1.03539i
879879 −0.294781 + 18.0488i −0.00994272 + 0.608773i
880880 13.5111 29.5852i 0.455459 0.997316i
881881 14.8277 17.1120i 0.499556 0.576519i −0.448838 0.893613i 0.648162π-0.648162\pi
0.948394 + 0.317095i 0.102707π0.102707\pi
882882 −5.52008 + 2.30617i −0.185871 + 0.0776526i
883883 −17.1515 + 5.03613i −0.577193 + 0.169479i −0.557283 0.830323i 0.688156π-0.688156\pi
−0.0199100 + 0.999802i 0.506338π0.506338\pi
884884 −15.0526 17.3716i −0.506274 0.584271i
885885 −15.0857 + 16.8459i −0.507101 + 0.566270i
886886 26.1890 16.8306i 0.879837 0.565437i
887887 −10.4215 + 9.03027i −0.349919 + 0.303207i −0.812030 0.583615i 0.801638π-0.801638\pi
0.462111 + 0.886822i 0.347092π0.347092\pi
888888 −0.0941321 0.151869i −0.00315887 0.00509640i
889889 10.2985 + 1.48071i 0.345402 + 0.0496613i
890890 −14.5906 12.6429i −0.489079 0.423790i
891891 21.4204 + 28.2548i 0.717610 + 0.946571i
892892 −26.4303 7.76063i −0.884951 0.259845i
893893 6.10348 + 13.3647i 0.204245 + 0.447234i
894894 9.31558 + 21.3126i 0.311560 + 0.712801i
895895 −6.88639 + 10.7154i −0.230187 + 0.358177i
896896 0.372707 0.0124513
897897 −38.6213 + 15.4597i −1.28953 + 0.516184i
898898 −1.76514 −0.0589033
899899 −13.9245 + 21.6670i −0.464408 + 0.722634i
900900 3.12565 + 3.85466i 0.104188 + 0.128489i
901901 3.57797 + 7.83466i 0.119200 + 0.261011i
902902 52.8078 + 15.5058i 1.75831 + 0.516286i
903903 6.14408 + 0.986048i 0.204462 + 0.0328136i
904904 0.445197 + 0.385766i 0.0148070 + 0.0128304i
905905 −13.2180 1.90046i −0.439380 0.0631734i
906906 27.9015 17.2940i 0.926967 0.574555i
907907 7.75137 6.71660i 0.257380 0.223021i −0.516607 0.856223i 0.672805π-0.672805\pi
0.773987 + 0.633202i 0.218260π0.218260\pi
908908 23.3936 15.0341i 0.776343 0.498925i
909909 −28.0653 13.9420i −0.930866 0.462427i
910910 13.3442 + 15.4000i 0.442354 + 0.510504i
911911 −33.9316 + 9.96322i −1.12420 + 0.330096i −0.790427 0.612556i 0.790141π-0.790141\pi
−0.333777 + 0.942652i 0.608323π0.608323\pi
912912 1.86121 + 14.6382i 0.0616309 + 0.484720i
913913 −30.6427 + 35.3635i −1.01412 + 1.17036i
914914 −14.7446 + 32.2862i −0.487708 + 1.06793i
915915 −40.5547 0.662356i −1.34070 0.0218968i
916916 −38.9894 + 17.8058i −1.28824 + 0.588322i
917917 0.924312 + 6.42873i 0.0305235 + 0.212295i
918918 −23.3899 + 5.63985i −0.771983 + 0.186143i
919919 43.3277i 1.42925i −0.699509 0.714624i 0.746598π-0.746598\pi
0.699509 0.714624i 0.253402π-0.253402\pi
920920 0.420438 0.176316i 0.0138614 0.00581297i
921921 −6.37394 23.0964i −0.210028 0.761054i
922922 −7.63432 4.90628i −0.251423 0.161580i
923923 71.0242 10.2117i 2.33779 0.336124i
924924 −8.66499 10.3363i −0.285057 0.340039i
925925 0.522039 1.77790i 0.0171645 0.0584571i
926926 44.4303 + 20.2906i 1.46007 + 0.666791i
927927 47.1633 + 8.36132i 1.54904 + 0.274622i
928928 11.7424 81.6700i 0.385463 2.68095i
929929 −5.64730 19.2329i −0.185282 0.631012i −0.998777 0.0494403i 0.984256π-0.984256\pi
0.813495 0.581571i 0.197562π-0.197562\pi
930930 −14.6029 9.72526i −0.478846 0.318904i
931931 −1.13835 1.77130i −0.0373078 0.0580520i
932932 −30.6997 47.7697i −1.00560 1.56475i
933933 −2.00138 1.33288i −0.0655221 0.0436367i
934934 −6.20624 21.1365i −0.203074 0.691607i
935935 −2.65628 + 18.4748i −0.0868696 + 0.604192i
936936 0.689261 + 0.122195i 0.0225292 + 0.00399408i
937937 51.5865 + 23.5587i 1.68526 + 0.769631i 0.999111 + 0.0421662i 0.0134259π0.0134259\pi
0.686145 + 0.727464i 0.259301π0.259301\pi
938938 1.74862 5.95525i 0.0570945 0.194446i
939939 8.73215 + 10.4164i 0.284963 + 0.339926i
940940 27.8562 4.00512i 0.908570 0.130633i
941941 −29.4403 18.9201i −0.959726 0.616779i −0.0358041 0.999359i 0.511399π-0.511399\pi
−0.923922 + 0.382580i 0.875036π0.875036\pi
942942 17.4124 + 63.0951i 0.567327 + 2.05575i
943943 17.2705 + 28.8190i 0.562404 + 0.938475i
944944 25.8905i 0.842665i
945945 10.3067 2.48518i 0.335277 0.0808429i
946946 4.01680 + 27.9374i 0.130597 + 0.908325i
947947 24.1037 11.0078i 0.783266 0.357706i 0.0166913 0.999861i 0.494687π-0.494687\pi
0.766575 + 0.642155i 0.221959π0.221959\pi
948948 16.8084 + 0.274521i 0.545910 + 0.00891603i
949949 13.1751 28.8495i 0.427683 0.936496i
950950 −2.30112 + 2.65564i −0.0746582 + 0.0861602i
951951 1.46032 + 11.4852i 0.0473540 + 0.372434i
952952 −0.103803 + 0.0304793i −0.00336428 + 0.000987840i
953953 −8.18986 9.45160i −0.265296 0.306167i 0.607435 0.794369i 0.292198π-0.292198\pi
−0.872731 + 0.488202i 0.837653π0.837653\pi
954954 19.8737 + 9.87265i 0.643434 + 0.319639i
955955 4.13044 2.65447i 0.133658 0.0858967i
956956 −25.0736 + 21.7264i −0.810937 + 0.702681i
957957 60.0019 37.1906i 1.93959 1.20220i
958958 58.4743 + 8.40733i 1.88922 + 0.271629i
959959 10.6898 + 9.26280i 0.345193 + 0.299111i
960960 27.2590 + 4.37473i 0.879781 + 0.141194i
961961 23.7974 + 6.98755i 0.767658 + 0.225405i
962962 9.18573 + 20.1139i 0.296160 + 0.648499i
963963 −12.3547 15.2363i −0.398124 0.490982i
964964 11.9432 18.5841i 0.384666 0.598552i
965965 31.4621 1.01280
966966 0.788899 16.5459i 0.0253824 0.532354i
967967 −32.0005 −1.02907 −0.514534 0.857470i 0.672035π-0.672035\pi
−0.514534 + 0.857470i 0.672035π0.672035\pi
968968 −0.113870 + 0.177185i −0.00365992 + 0.00569494i
969969 −3.39152 7.75928i −0.108951 0.249264i
970970 23.7515 + 52.0085i 0.762614 + 1.66989i
971971 26.0493 + 7.64876i 0.835962 + 0.245460i 0.671576 0.740936i 0.265618π-0.265618\pi
0.164386 + 0.986396i 0.447436π0.447436\pi
972972 −18.7173 + 24.4762i −0.600359 + 0.785074i
973973 13.4396 + 11.6455i 0.430855 + 0.373338i
974974 48.8427 + 7.02252i 1.56502 + 0.225016i
975975 3.82450 + 6.17031i 0.122482 + 0.197608i
976976 35.0956 30.4105i 1.12338 0.973417i
977977 −25.4835 + 16.3773i −0.815290 + 0.523955i −0.880572 0.473912i 0.842842π-0.842842\pi
0.0652823 + 0.997867i 0.479205π0.479205\pi
978978 −15.5235 + 17.3348i −0.496388 + 0.554307i
979979 12.2414 + 14.1274i 0.391238 + 0.451513i
980980 −3.86970 + 1.13625i −0.123613 + 0.0362961i
981981 −36.9174 + 15.4232i −1.17868 + 0.492426i
982982 −19.3728 + 22.3574i −0.618212 + 0.713454i
983983 −11.8628 + 25.9758i −0.378363 + 0.828500i 0.620650 + 0.784088i 0.286869π0.286869\pi
−0.999013 + 0.0444124i 0.985858π0.985858\pi
984984 0.00923220 0.565269i 0.000294312 0.0180201i
985985 −46.3066 + 21.1475i −1.47545 + 0.673815i
986986 6.81736 + 47.4158i 0.217109 + 1.51003i
987987 −3.59400 + 11.5395i −0.114398 + 0.367306i
988988 20.8433i 0.663114i
989989 −9.76440 + 14.1960i −0.310490 + 0.451405i
990990 24.6637 + 41.2821i 0.783864 + 1.31203i
991991 −21.0500 13.5280i −0.668674 0.429731i 0.161773 0.986828i 0.448279π-0.448279\pi
−0.830447 + 0.557097i 0.811915π0.811915\pi
992992 19.6535 2.82574i 0.623998 0.0897174i
993993 26.8860 22.5388i 0.853202 0.715246i
994994 −8.04951 + 27.4141i −0.255315 + 0.869523i
995995 1.74529 + 0.797049i 0.0553295 + 0.0252682i
996996 −36.7086 17.4943i −1.16316 0.554327i
997997 8.75982 60.9259i 0.277426 1.92954i −0.0825609 0.996586i 0.526310π-0.526310\pi
0.359987 0.932957i 0.382781π-0.382781\pi
998998 −9.55694 32.5479i −0.302520 1.03029i
999999 11.4910 + 0.563429i 0.363560 + 0.0178261i
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 483.2.u.a.113.9 480
3.2 odd 2 inner 483.2.u.a.113.40 yes 480
23.11 odd 22 inner 483.2.u.a.218.40 yes 480
69.11 even 22 inner 483.2.u.a.218.9 yes 480
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.u.a.113.9 480 1.1 even 1 trivial
483.2.u.a.113.40 yes 480 3.2 odd 2 inner
483.2.u.a.218.9 yes 480 69.11 even 22 inner
483.2.u.a.218.40 yes 480 23.11 odd 22 inner