Properties

Label 980.2.x.n.263.18
Level 980980
Weight 22
Character 980.263
Analytic conductor 7.8257.825
Analytic rank 00
Dimension 112112
Inner twists 1616

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 980=22572 980 = 2^{2} \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 980.x (of order 1212, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [112,4,0,0,0,0,0,-32,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.825339398097.82533939809
Analytic rank: 00
Dimension: 112112
Relative dimension: 2828 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 263.18
Character χ\chi == 980.263
Dual form 980.2.x.n.667.18

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.604271+1.27862i)q2+(0.844627+3.15219i)q3+(1.26971+1.54526i)q4+(1.793321.33567i)q5+(3.52006+2.98473i)q6+(2.743040.689718i)q8+(6.62484+3.82485i)q9+(0.6241593.10007i)q10+(1.968751.13666i)q11+(5.943392.69721i)q12+(1.38240+1.38240i)q13+(2.695616.78102i)q15+(0.7756573.92407i)q16+(0.0499069+0.186255i)q17+(8.893716.15937i)q18+(3.45645+5.98675i)q19+(4.340961.07522i)q20+(0.2636903.20413i)q22+(3.234870.866782i)q23+(0.1427259.22915i)q24+(1.43197+4.79056i)q25+(0.932215+2.60291i)q26+(10.729510.7295i)q277.33156iq29+(10.29920.650933i)q30+(0.430790+0.248717i)q31+(4.548673.36297i)q32+(1.920117.16594i)q33+(0.207991+0.176360i)q34+(2.5012515.0936i)q36+(3.376050.904610i)q37+(5.56612+8.03710i)q38+(3.18998+5.52522i)q39+(3.99791+4.90069i)q40+3.22939q41+(2.91165+2.91165i)q43+(4.256181.59900i)q44+(16.9892+1.98943i)q45+(0.8464604.65993i)q46+(0.6457252.40988i)q47+(11.71435.75940i)q48+(5.25998+4.72573i)q50+(0.544959+0.314632i)q51+(3.89143+0.380917i)q52+(6.98469+1.87154i)q53+(7.2353720.2024i)q54+(2.01239+4.66799i)q55+(15.9520+15.9520i)q57+(9.374244.43025i)q58+(2.61146+4.52318i)q59+(7.05580+12.7754i)q60+(5.00922+8.67623i)q61+(0.0576991+0.701107i)q62+(7.04858+3.78386i)q64+(0.6326524.32552i)q65+(10.32271.87509i)q66+(12.0126+3.21877i)q67+(0.3511800.159371i)q6810.9290iq69+3.60061iq71+(20.81035.92247i)q72+(12.6457+3.38841i)q73+(0.8834014.86330i)q74+(13.8913+8.56008i)q75+(13.63982.26034i)q76+(8.992240.740035i)q78+(5.66954+9.81994i)q79+(3.85027+8.07313i)q80+(13.284423.0093i)q81+(1.95143+4.12915i)q82+(0.591847+0.591847i)q83+(0.1592770.400674i)q85+(5.482311.96345i)q86+(23.11056.19243i)q87+(4.61640+4.47579i)q88+(3.45672+1.99574i)q89+(7.72235+22.9248i)q90+(5.446763.89816i)q92+(0.420146+1.56801i)q93+(3.471500.630586i)q94+(1.7978115.3528i)q95+(14.4427+11.4978i)q96+(1.09368+1.09368i)q97+17.3902q99+O(q100)q+(0.604271 + 1.27862i) q^{2} +(0.844627 + 3.15219i) q^{3} +(-1.26971 + 1.54526i) q^{4} +(-1.79332 - 1.33567i) q^{5} +(-3.52006 + 2.98473i) q^{6} +(-2.74304 - 0.689718i) q^{8} +(-6.62484 + 3.82485i) q^{9} +(0.624159 - 3.10007i) q^{10} +(-1.96875 - 1.13666i) q^{11} +(-5.94339 - 2.69721i) q^{12} +(1.38240 + 1.38240i) q^{13} +(2.69561 - 6.78102i) q^{15} +(-0.775657 - 3.92407i) q^{16} +(0.0499069 + 0.186255i) q^{17} +(-8.89371 - 6.15937i) q^{18} +(3.45645 + 5.98675i) q^{19} +(4.34096 - 1.07522i) q^{20} +(0.263690 - 3.20413i) q^{22} +(-3.23487 - 0.866782i) q^{23} +(-0.142725 - 9.22915i) q^{24} +(1.43197 + 4.79056i) q^{25} +(-0.932215 + 2.60291i) q^{26} +(-10.7295 - 10.7295i) q^{27} -7.33156i q^{29} +(10.2992 - 0.650933i) q^{30} +(0.430790 + 0.248717i) q^{31} +(4.54867 - 3.36297i) q^{32} +(1.92011 - 7.16594i) q^{33} +(-0.207991 + 0.176360i) q^{34} +(2.50125 - 15.0936i) q^{36} +(-3.37605 - 0.904610i) q^{37} +(-5.56612 + 8.03710i) q^{38} +(-3.18998 + 5.52522i) q^{39} +(3.99791 + 4.90069i) q^{40} +3.22939 q^{41} +(-2.91165 + 2.91165i) q^{43} +(4.25618 - 1.59900i) q^{44} +(16.9892 + 1.98943i) q^{45} +(-0.846460 - 4.65993i) q^{46} +(0.645725 - 2.40988i) q^{47} +(11.7143 - 5.75940i) q^{48} +(-5.25998 + 4.72573i) q^{50} +(-0.544959 + 0.314632i) q^{51} +(-3.89143 + 0.380917i) q^{52} +(-6.98469 + 1.87154i) q^{53} +(7.23537 - 20.2024i) q^{54} +(2.01239 + 4.66799i) q^{55} +(-15.9520 + 15.9520i) q^{57} +(9.37424 - 4.43025i) q^{58} +(-2.61146 + 4.52318i) q^{59} +(7.05580 + 12.7754i) q^{60} +(5.00922 + 8.67623i) q^{61} +(-0.0576991 + 0.701107i) q^{62} +(7.04858 + 3.78386i) q^{64} +(-0.632652 - 4.32552i) q^{65} +(10.3227 - 1.87509i) q^{66} +(-12.0126 + 3.21877i) q^{67} +(-0.351180 - 0.159371i) q^{68} -10.9290i q^{69} +3.60061i q^{71} +(20.8103 - 5.92247i) q^{72} +(-12.6457 + 3.38841i) q^{73} +(-0.883401 - 4.86330i) q^{74} +(-13.8913 + 8.56008i) q^{75} +(-13.6398 - 2.26034i) q^{76} +(-8.99224 - 0.740035i) q^{78} +(5.66954 + 9.81994i) q^{79} +(-3.85027 + 8.07313i) q^{80} +(13.2844 - 23.0093i) q^{81} +(1.95143 + 4.12915i) q^{82} +(-0.591847 + 0.591847i) q^{83} +(0.159277 - 0.400674i) q^{85} +(-5.48231 - 1.96345i) q^{86} +(23.1105 - 6.19243i) q^{87} +(4.61640 + 4.47579i) q^{88} +(-3.45672 + 1.99574i) q^{89} +(7.72235 + 22.9248i) q^{90} +(5.44676 - 3.89816i) q^{92} +(-0.420146 + 1.56801i) q^{93} +(3.47150 - 0.630586i) q^{94} +(1.79781 - 15.3528i) q^{95} +(14.4427 + 11.4978i) q^{96} +(-1.09368 + 1.09368i) q^{97} +17.3902 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 112q+4q232q832q16+40q2232q25+28q30+64q32+32q36+8q37+184q4624q5096q5316q57124q588q60+120q65+80q72++176q93+O(q100) 112 q + 4 q^{2} - 32 q^{8} - 32 q^{16} + 40 q^{22} - 32 q^{25} + 28 q^{30} + 64 q^{32} + 32 q^{36} + 8 q^{37} + 184 q^{46} - 24 q^{50} - 96 q^{53} - 16 q^{57} - 124 q^{58} - 8 q^{60} + 120 q^{65} + 80 q^{72}+ \cdots + 176 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/980Z)×\left(\mathbb{Z}/980\mathbb{Z}\right)^\times.

nn 101101 197197 491491
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) e(34)e\left(\frac{3}{4}\right) 1-1

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 0.604271 + 1.27862i 0.427284 + 0.904117i
33 0.844627 + 3.15219i 0.487646 + 1.81992i 0.567839 + 0.823139i 0.307779π0.307779\pi
−0.0801936 + 0.996779i 0.525554π0.525554\pi
44 −1.26971 + 1.54526i −0.634857 + 0.772630i
55 −1.79332 1.33567i −0.801996 0.597330i
66 −3.52006 + 2.98473i −1.43706 + 1.21851i
77 0 0
88 −2.74304 0.689718i −0.969812 0.243852i
99 −6.62484 + 3.82485i −2.20828 + 1.27495i
1010 0.624159 3.10007i 0.197376 0.980328i
1111 −1.96875 1.13666i −0.593601 0.342716i 0.172919 0.984936i 0.444680π-0.444680\pi
−0.766520 + 0.642220i 0.778013π0.778013\pi
1212 −5.94339 2.69721i −1.71571 0.778618i
1313 1.38240 + 1.38240i 0.383410 + 0.383410i 0.872329 0.488919i 0.162609π-0.162609\pi
−0.488919 + 0.872329i 0.662609π0.662609\pi
1414 0 0
1515 2.69561 6.78102i 0.696002 1.75085i
1616 −0.775657 3.92407i −0.193914 0.981018i
1717 0.0499069 + 0.186255i 0.0121042 + 0.0451735i 0.971714 0.236162i 0.0758894π-0.0758894\pi
−0.959610 + 0.281335i 0.909223π0.909223\pi
1818 −8.89371 6.15937i −2.09627 1.45178i
1919 3.45645 + 5.98675i 0.792965 + 1.37346i 0.924123 + 0.382094i 0.124797π0.124797\pi
−0.131158 + 0.991361i 0.541870π0.541870\pi
2020 4.34096 1.07522i 0.970667 0.240427i
2121 0 0
2222 0.263690 3.20413i 0.0562189 0.683122i
2323 −3.23487 0.866782i −0.674518 0.180736i −0.0947286 0.995503i 0.530198π-0.530198\pi
−0.579789 + 0.814767i 0.696865π0.696865\pi
2424 −0.142725 9.22915i −0.0291336 1.88389i
2525 1.43197 + 4.79056i 0.286394 + 0.958112i
2626 −0.932215 + 2.60291i −0.182822 + 0.510472i
2727 −10.7295 10.7295i −2.06489 2.06489i
2828 0 0
2929 7.33156i 1.36144i −0.732546 0.680718i 0.761668π-0.761668\pi
0.732546 0.680718i 0.238332π-0.238332\pi
3030 10.2992 0.650933i 1.88037 0.118844i
3131 0.430790 + 0.248717i 0.0773722 + 0.0446709i 0.538187 0.842825i 0.319109π-0.319109\pi
−0.460815 + 0.887496i 0.652443π0.652443\pi
3232 4.54867 3.36297i 0.804099 0.594495i
3333 1.92011 7.16594i 0.334248 1.24743i
3434 −0.207991 + 0.176360i −0.0356702 + 0.0302455i
3535 0 0
3636 2.50125 15.0936i 0.416876 2.51559i
3737 −3.37605 0.904610i −0.555019 0.148717i −0.0296020 0.999562i 0.509424π-0.509424\pi
−0.525417 + 0.850845i 0.676091π0.676091\pi
3838 −5.56612 + 8.03710i −0.902944 + 1.30379i
3939 −3.18998 + 5.52522i −0.510806 + 0.884743i
4040 3.99791 + 4.90069i 0.632125 + 0.774866i
4141 3.22939 0.504346 0.252173 0.967682i 0.418855π-0.418855\pi
0.252173 + 0.967682i 0.418855π0.418855\pi
4242 0 0
4343 −2.91165 + 2.91165i −0.444022 + 0.444022i −0.893361 0.449339i 0.851660π-0.851660\pi
0.449339 + 0.893361i 0.351660π0.351660\pi
4444 4.25618 1.59900i 0.641644 0.241059i
4545 16.9892 + 1.98943i 2.53260 + 0.296567i
4646 −0.846460 4.65993i −0.124804 0.687069i
4747 0.645725 2.40988i 0.0941887 0.351517i −0.902707 0.430257i 0.858423π-0.858423\pi
0.996895 + 0.0787399i 0.0250897π0.0250897\pi
4848 11.7143 5.75940i 1.69081 0.831298i
4949 0 0
5050 −5.25998 + 4.72573i −0.743874 + 0.668320i
5151 −0.544959 + 0.314632i −0.0763095 + 0.0440573i
5252 −3.89143 + 0.380917i −0.539644 + 0.0528237i
5353 −6.98469 + 1.87154i −0.959421 + 0.257076i −0.704355 0.709847i 0.748764π-0.748764\pi
−0.255066 + 0.966924i 0.582097π0.582097\pi
5454 7.23537 20.2024i 0.984610 2.74920i
5555 2.01239 + 4.66799i 0.271351 + 0.629432i
5656 0 0
5757 −15.9520 + 15.9520i −2.11289 + 2.11289i
5858 9.37424 4.43025i 1.23090 0.581720i
5959 −2.61146 + 4.52318i −0.339983 + 0.588868i −0.984429 0.175782i 0.943755π-0.943755\pi
0.644446 + 0.764650i 0.277088π0.277088\pi
6060 7.05580 + 12.7754i 0.910899 + 1.64929i
6161 5.00922 + 8.67623i 0.641365 + 1.11088i 0.985128 + 0.171821i 0.0549649π0.0549649\pi
−0.343763 + 0.939056i 0.611702π0.611702\pi
6262 −0.0576991 + 0.701107i −0.00732779 + 0.0890407i
6363 0 0
6464 7.04858 + 3.78386i 0.881072 + 0.472982i
6565 −0.632652 4.32552i −0.0784708 0.536515i
6666 10.3227 1.87509i 1.27064 0.230808i
6767 −12.0126 + 3.21877i −1.46757 + 0.393235i −0.902098 0.431531i 0.857974π-0.857974\pi
−0.565474 + 0.824766i 0.691307π0.691307\pi
6868 −0.351180 0.159371i −0.0425868 0.0193266i
6969 10.9290i 1.31570i
7070 0 0
7171 3.60061i 0.427314i 0.976909 + 0.213657i 0.0685375π0.0685375\pi
−0.976909 + 0.213657i 0.931462π0.931462\pi
7272 20.8103 5.92247i 2.45252 0.697969i
7373 −12.6457 + 3.38841i −1.48007 + 0.396584i −0.906371 0.422482i 0.861159π-0.861159\pi
−0.573700 + 0.819066i 0.694492π0.694492\pi
7474 −0.883401 4.86330i −0.102693 0.565347i
7575 −13.8913 + 8.56008i −1.60403 + 0.988433i
7676 −13.6398 2.26034i −1.56459 0.259279i
7777 0 0
7878 −8.99224 0.740035i −1.01817 0.0837925i
7979 5.66954 + 9.81994i 0.637874 + 1.10483i 0.985899 + 0.167344i 0.0535191π0.0535191\pi
−0.348025 + 0.937485i 0.613148π0.613148\pi
8080 −3.85027 + 8.07313i −0.430473 + 0.902603i
8181 13.2844 23.0093i 1.47605 2.55659i
8282 1.95143 + 4.12915i 0.215499 + 0.455988i
8383 −0.591847 + 0.591847i −0.0649636 + 0.0649636i −0.738842 0.673879i 0.764627π-0.764627\pi
0.673879 + 0.738842i 0.264627π0.264627\pi
8484 0 0
8585 0.159277 0.400674i 0.0172760 0.0434592i
8686 −5.48231 1.96345i −0.591172 0.211725i
8787 23.1105 6.19243i 2.47770 0.663898i
8888 4.61640 + 4.47579i 0.492110 + 0.477121i
8989 −3.45672 + 1.99574i −0.366412 + 0.211548i −0.671890 0.740651i 0.734517π-0.734517\pi
0.305478 + 0.952199i 0.401184π0.401184\pi
9090 7.72235 + 22.9248i 0.814008 + 2.41648i
9191 0 0
9292 5.44676 3.89816i 0.567864 0.406411i
9393 −0.420146 + 1.56801i −0.0435671 + 0.162595i
9494 3.47150 0.630586i 0.358058 0.0650400i
9595 1.79781 15.3528i 0.184452 1.57517i
9696 14.4427 + 11.4978i 1.47405 + 1.17349i
9797 −1.09368 + 1.09368i −0.111047 + 0.111047i −0.760447 0.649400i 0.775020π-0.775020\pi
0.649400 + 0.760447i 0.275020π0.275020\pi
9898 0 0
9999 17.3902 1.74778
100100 −9.22085 3.86987i −0.922085 0.386987i
101101 −2.49645 + 4.32397i −0.248406 + 0.430251i −0.963084 0.269202i 0.913240π-0.913240\pi
0.714678 + 0.699454i 0.246573π0.246573\pi
102102 −0.731597 0.506670i −0.0724389 0.0501678i
103103 10.0333 + 2.68842i 0.988612 + 0.264898i 0.716667 0.697415i 0.245667π-0.245667\pi
0.271945 + 0.962313i 0.412333π0.412333\pi
104104 −2.83852 4.74546i −0.278340 0.465331i
105105 0 0
106106 −6.61363 7.79981i −0.642373 0.757585i
107107 0.553575 2.06597i 0.0535161 0.199725i −0.933992 0.357295i 0.883699π-0.883699\pi
0.987508 + 0.157570i 0.0503659π0.0503659\pi
108108 30.2033 2.95648i 2.90631 0.284488i
109109 −8.19415 4.73090i −0.784857 0.453138i 0.0532916 0.998579i 0.483029π-0.483029\pi
−0.838149 + 0.545441i 0.816362π0.816362\pi
110110 −4.75254 + 5.39381i −0.453137 + 0.514280i
111111 11.4060i 1.08261i
112112 0 0
113113 12.1490 + 12.1490i 1.14289 + 1.14289i 0.987920 + 0.154967i 0.0495270π0.0495270\pi
0.154967 + 0.987920i 0.450473π0.450473\pi
114114 −30.0358 10.7571i −2.81311 1.00750i
115115 4.64342 + 5.87514i 0.433001 + 0.547859i
116116 11.3292 + 9.30897i 1.05189 + 0.864316i
117117 −14.4457 3.87071i −1.33550 0.357847i
118118 −7.36144 0.605825i −0.677676 0.0557707i
119119 0 0
120120 −12.0712 + 16.7414i −1.10194 + 1.52828i
121121 −2.91601 5.05068i −0.265092 0.459153i
122122 −8.06663 + 11.6477i −0.730318 + 1.05453i
123123 2.72763 + 10.1797i 0.245942 + 0.917869i
124124 −0.931312 + 0.349884i −0.0836343 + 0.0314205i
125125 3.83064 10.5036i 0.342622 0.939473i
126126 0 0
127127 −2.01009 2.01009i −0.178367 0.178367i 0.612277 0.790643i 0.290254π-0.290254\pi
−0.790643 + 0.612277i 0.790254π0.790254\pi
128128 −0.578844 + 11.2989i −0.0511630 + 0.998690i
129129 −11.6373 6.71882i −1.02461 0.591559i
130130 5.14838 3.42271i 0.451543 0.300191i
131131 −5.65370 + 3.26417i −0.493966 + 0.285191i −0.726218 0.687464i 0.758724π-0.758724\pi
0.232252 + 0.972656i 0.425391π0.425391\pi
132132 8.63525 + 12.0657i 0.751602 + 1.05019i
133133 0 0
134134 −11.3744 13.4145i −0.982601 1.15883i
135135 4.91031 + 33.5725i 0.422613 + 2.88946i
136136 −0.00843325 0.545328i −0.000723145 0.0467615i
137137 1.52380 + 5.68690i 0.130187 + 0.485865i 0.999971 0.00756731i 0.00240877π-0.00240877\pi
−0.869784 + 0.493432i 0.835742π0.835742\pi
138138 13.9740 6.60411i 1.18955 0.562179i
139139 −6.55194 −0.555729 −0.277864 0.960620i 0.589627π-0.589627\pi
−0.277864 + 0.960620i 0.589627π0.589627\pi
140140 0 0
141141 8.14180 0.685663
142142 −4.60380 + 2.17575i −0.386342 + 0.182585i
143143 −1.15029 4.29293i −0.0961919 0.358993i
144144 20.1476 + 23.0296i 1.67897 + 1.91913i
145145 −9.79254 + 13.1478i −0.813226 + 1.09187i
146146 −11.9739 14.1215i −0.990969 1.16870i
147147 0 0
148148 5.68447 4.06828i 0.467261 0.334410i
149149 12.4603 7.19395i 1.02079 0.589352i 0.106455 0.994318i 0.466050π-0.466050\pi
0.914332 + 0.404966i 0.132717π0.132717\pi
150150 −19.3391 12.5890i −1.57903 1.02789i
151151 6.33365 + 3.65673i 0.515425 + 0.297581i 0.735061 0.678001i 0.237154π-0.237154\pi
−0.219636 + 0.975582i 0.570487π0.570487\pi
152152 −5.35203 18.8059i −0.434107 1.52536i
153153 −1.04302 1.04302i −0.0843235 0.0843235i
154154 0 0
155155 −0.440339 1.02142i −0.0353689 0.0820426i
156156 −4.48753 11.9448i −0.359290 0.956349i
157157 −5.19817 19.3998i −0.414859 1.54828i −0.785117 0.619347i 0.787397π-0.787397\pi
0.370258 0.928929i 0.379269π-0.379269\pi
158158 −9.12998 + 13.1831i −0.726342 + 1.04879i
159159 −11.7989 20.4363i −0.935715 1.62071i
160160 −12.6490 0.0446550i −0.999994 0.00353029i
161161 0 0
162162 37.4475 + 3.08182i 2.94215 + 0.242131i
163163 12.8941 + 3.45495i 1.00994 + 0.270613i 0.725604 0.688112i 0.241560π-0.241560\pi
0.284336 + 0.958725i 0.408227π0.408227\pi
164164 −4.10040 + 4.99025i −0.320187 + 0.389673i
165165 −13.0147 + 10.2862i −1.01319 + 0.800777i
166166 −1.11438 0.399108i −0.0864927 0.0309768i
167167 4.21040 + 4.21040i 0.325811 + 0.325811i 0.850991 0.525180i 0.176002π-0.176002\pi
−0.525180 + 0.850991i 0.676002π0.676002\pi
168168 0 0
169169 9.17792i 0.705994i
170170 0.608553 0.0384620i 0.0466739 0.00294990i
171171 −45.7969 26.4409i −3.50218 2.02198i
172172 −0.802296 8.19622i −0.0611745 0.624956i
173173 −5.25823 + 19.6240i −0.399776 + 1.49198i 0.413715 + 0.910406i 0.364231π0.364231\pi
−0.813491 + 0.581578i 0.802436π0.802436\pi
174174 21.8827 + 25.8075i 1.65892 + 1.95646i
175175 0 0
176176 −2.93326 + 8.60719i −0.221103 + 0.648791i
177177 −16.4637 4.41142i −1.23748 0.331583i
178178 −4.64058 3.21385i −0.347826 0.240888i
179179 1.59053 2.75487i 0.118881 0.205909i −0.800443 0.599409i 0.795402π-0.795402\pi
0.919325 + 0.393500i 0.128736π0.128736\pi
180180 −24.6456 + 23.7267i −1.83697 + 1.76848i
181181 9.22913 0.685996 0.342998 0.939336i 0.388558π-0.388558\pi
0.342998 + 0.939336i 0.388558π0.388558\pi
182182 0 0
183183 −23.1182 + 23.1182i −1.70895 + 1.70895i
184184 8.27556 + 4.60877i 0.610083 + 0.339763i
185185 4.84606 + 6.13154i 0.356290 + 0.450800i
186186 −2.25876 + 0.410296i −0.165620 + 0.0300843i
187187 0.113454 0.423417i 0.00829660 0.0309633i
188188 2.90400 + 4.05767i 0.211796 + 0.295936i
189189 0 0
190190 20.7167 6.97856i 1.50295 0.506278i
191191 −12.7944 + 7.38687i −0.925773 + 0.534495i −0.885472 0.464692i 0.846165π-0.846165\pi
−0.0403006 + 0.999188i 0.512832π0.512832\pi
192192 −5.97402 + 25.4144i −0.431138 + 1.83413i
193193 −2.95127 + 0.790790i −0.212437 + 0.0569223i −0.363468 0.931607i 0.618407π-0.618407\pi
0.151031 + 0.988529i 0.451741π0.451741\pi
194194 −2.05928 0.737520i −0.147848 0.0529508i
195195 13.1005 5.64769i 0.938148 0.404440i
196196 0 0
197197 6.45634 6.45634i 0.459995 0.459995i −0.438658 0.898654i 0.644546π-0.644546\pi
0.898654 + 0.438658i 0.144546π0.144546\pi
198198 10.5084 + 22.2354i 0.746800 + 1.58020i
199199 7.48432 12.9632i 0.530549 0.918939i −0.468815 0.883296i 0.655319π-0.655319\pi
0.999365 0.0356423i 0.0113477π-0.0113477\pi
200200 −0.623816 14.1284i −0.0441105 0.999027i
201201 −20.2923 35.1474i −1.43131 2.47910i
202202 −7.03722 0.579143i −0.495137 0.0407484i
203203 0 0
204204 0.205753 1.24160i 0.0144056 0.0869291i
205205 −5.79132 4.31340i −0.404483 0.301261i
206206 2.62539 + 14.4533i 0.182920 + 1.00701i
207207 24.7458 6.63062i 1.71995 0.460860i
208208 4.35238 6.49692i 0.301783 0.450481i
209209 15.7152i 1.08705i
210210 0 0
211211 16.6114i 1.14358i 0.820401 + 0.571789i 0.193750π0.193750\pi
−0.820401 + 0.571789i 0.806250π0.806250\pi
212212 5.97654 13.1695i 0.410470 0.904484i
213213 −11.3498 + 3.04118i −0.777677 + 0.208378i
214214 2.97609 0.540596i 0.203441 0.0369544i
215215 9.11052 1.33251i 0.621332 0.0908761i
216216 22.0312 + 36.8318i 1.49903 + 2.50609i
217217 0 0
218218 1.09751 13.3359i 0.0743325 0.903222i
219219 −21.3619 36.9998i −1.44350 2.50022i
220220 −9.76843 2.81734i −0.658587 0.189945i
221221 −0.188488 + 0.326471i −0.0126791 + 0.0219608i
222222 14.5839 6.89232i 0.978807 0.462582i
223223 −10.5774 + 10.5774i −0.708318 + 0.708318i −0.966181 0.257863i 0.916982π-0.916982\pi
0.257863 + 0.966181i 0.416982π0.416982\pi
224224 0 0
225225 −27.8098 26.2596i −1.85398 1.75064i
226226 −8.19264 + 22.8753i −0.544966 + 1.52164i
227227 −8.10649 + 2.17213i −0.538047 + 0.144169i −0.517602 0.855622i 0.673175π-0.673175\pi
−0.0204453 + 0.999791i 0.506508π0.506508\pi
228228 −4.39552 44.9044i −0.291100 2.97387i
229229 8.28192 4.78157i 0.547285 0.315975i −0.200741 0.979644i 0.564335π-0.564335\pi
0.748026 + 0.663669i 0.231002π0.231002\pi
230230 −4.70616 + 9.48732i −0.310315 + 0.625575i
231231 0 0
232232 −5.05671 + 20.1108i −0.331989 + 1.32034i
233233 2.57959 9.62717i 0.168995 0.630697i −0.828502 0.559986i 0.810807π-0.810807\pi
0.997497 0.0707108i 0.0225268π-0.0225268\pi
234234 −3.77996 20.8094i −0.247104 1.36036i
235235 −4.37679 + 3.45920i −0.285511 + 0.225653i
236236 −3.67369 9.77853i −0.239137 0.636528i
237237 −26.1657 + 26.1657i −1.69964 + 1.69964i
238238 0 0
239239 19.5170 1.26245 0.631225 0.775600i 0.282552π-0.282552\pi
0.631225 + 0.775600i 0.282552π0.282552\pi
240240 −28.7001 5.31800i −1.85258 0.343276i
241241 4.81231 8.33517i 0.309988 0.536915i −0.668371 0.743828i 0.733008π-0.733008\pi
0.978359 + 0.206913i 0.0663416π0.0663416\pi
242242 4.69581 6.78043i 0.301858 0.435863i
243243 39.7800 + 10.6590i 2.55189 + 0.683776i
244244 −19.7673 3.27577i −1.26547 0.209710i
245245 0 0
246246 −11.3676 + 9.63886i −0.724774 + 0.614551i
247247 −3.49790 + 13.0543i −0.222566 + 0.830627i
248248 −1.01013 0.979365i −0.0641434 0.0621897i
249249 −2.36550 1.36572i −0.149908 0.0865493i
250250 15.7448 1.44913i 0.995791 0.0916511i
251251 27.2830i 1.72209i 0.508532 + 0.861043i 0.330188π0.330188\pi
−0.508532 + 0.861043i 0.669812π0.669812\pi
252252 0 0
253253 5.38343 + 5.38343i 0.338453 + 0.338453i
254254 1.35549 3.78477i 0.0850511 0.237477i
255255 1.39753 + 0.163650i 0.0875167 + 0.0102482i
256256 −14.7967 + 6.08747i −0.924794 + 0.380467i
257257 27.8738 + 7.46875i 1.73872 + 0.465888i 0.982161 0.188041i 0.0602136π-0.0602136\pi
0.756556 + 0.653929i 0.226880π0.226880\pi
258258 1.55868 18.9397i 0.0970391 1.17913i
259259 0 0
260260 7.48734 + 4.51456i 0.464345 + 0.279981i
261261 28.0421 + 48.5704i 1.73576 + 3.00643i
262262 −7.58998 5.25647i −0.468910 0.324746i
263263 −1.35037 5.03964i −0.0832672 0.310757i 0.911713 0.410827i 0.134760π-0.134760\pi
−0.994980 + 0.100070i 0.968093π0.968093\pi
264264 −10.2094 + 18.3321i −0.628346 + 1.12827i
265265 15.0255 + 5.97298i 0.923011 + 0.366917i
266266 0 0
267267 −9.21059 9.21059i −0.563679 0.563679i
268268 10.2787 22.6495i 0.627873 1.38354i
269269 11.0061 + 6.35438i 0.671054 + 0.387433i 0.796476 0.604670i 0.206695π-0.206695\pi
−0.125422 + 0.992104i 0.540028π0.540028\pi
270270 −39.9591 + 26.5653i −2.43183 + 1.61671i
271271 −25.0351 + 14.4540i −1.52078 + 0.878021i −0.521077 + 0.853510i 0.674470π0.674470\pi
−0.999700 + 0.0245112i 0.992197π0.992197\pi
272272 0.692168 0.340309i 0.0419689 0.0206342i
273273 0 0
274274 −6.35057 + 5.38479i −0.383652 + 0.325307i
275275 2.62604 11.0591i 0.158356 0.666888i
276276 16.8882 + 13.8768i 1.01655 + 0.835282i
277277 5.66377 + 21.1375i 0.340303 + 1.27003i 0.898004 + 0.439987i 0.145017π0.145017\pi
−0.557701 + 0.830042i 0.688316π0.688316\pi
278278 −3.95915 8.37741i −0.237454 0.502444i
279279 −3.80522 −0.227813
280280 0 0
281281 6.96882 0.415725 0.207862 0.978158i 0.433349π-0.433349\pi
0.207862 + 0.978158i 0.433349π0.433349\pi
282282 4.91985 + 10.4102i 0.292973 + 0.619920i
283283 6.97386 + 26.0268i 0.414553 + 1.54713i 0.785729 + 0.618570i 0.212288π0.212288\pi
−0.371176 + 0.928562i 0.621046π0.621046\pi
284284 −5.56389 4.57175i −0.330156 0.271283i
285285 49.9135 7.30036i 2.95662 0.432436i
286286 4.79392 4.06487i 0.283471 0.240361i
287287 0 0
288288 −17.2714 + 39.6772i −1.01772 + 2.33800i
289289 14.6902 8.48141i 0.864131 0.498906i
290290 −22.7283 4.57606i −1.33465 0.268715i
291291 −4.37126 2.52375i −0.256248 0.147945i
292292 10.8205 23.8433i 0.633220 1.39532i
293293 9.60083 + 9.60083i 0.560886 + 0.560886i 0.929559 0.368673i 0.120188π-0.120188\pi
−0.368673 + 0.929559i 0.620188π0.620188\pi
294294 0 0
295295 10.7247 4.62345i 0.624414 0.269188i
296296 8.63672 + 4.80991i 0.501999 + 0.279570i
297297 8.92794 + 33.3195i 0.518051 + 1.93339i
298298 16.7277 + 11.5848i 0.969009 + 0.671091i
299299 −3.27366 5.67014i −0.189320 0.327913i
300300 4.41040 32.3345i 0.254634 1.86683i
301301 0 0
302302 −0.848314 + 10.3080i −0.0488150 + 0.593156i
303303 −15.7386 4.21713i −0.904156 0.242268i
304304 20.8114 18.2071i 1.19362 1.04425i
305305 2.60546 22.2499i 0.149188 1.27402i
306306 0.703357 1.96390i 0.0402082 0.112268i
307307 −9.95915 9.95915i −0.568399 0.568399i 0.363281 0.931680i 0.381657π-0.381657\pi
−0.931680 + 0.363281i 0.881657π0.881657\pi
308308 0 0
309309 33.8977i 1.92837i
310310 1.03992 1.18024i 0.0590635 0.0670331i
311311 7.83321 + 4.52251i 0.444181 + 0.256448i 0.705369 0.708840i 0.250781π-0.250781\pi
−0.261189 + 0.965288i 0.584114π0.584114\pi
312312 12.5611 12.9557i 0.711133 0.733473i
313313 4.12250 15.3854i 0.233018 0.869634i −0.746015 0.665929i 0.768035π-0.768035\pi
0.979032 0.203704i 0.0652981π-0.0652981\pi
314314 21.6638 18.3692i 1.22256 1.03664i
315315 0 0
316316 −22.3731 3.70758i −1.25858 0.208568i
317317 −11.8007 3.16198i −0.662792 0.177595i −0.0882865 0.996095i 0.528139π-0.528139\pi
−0.574506 + 0.818500i 0.694806π0.694806\pi
318318 19.0005 27.4354i 1.06549 1.53850i
319319 −8.33348 + 14.4340i −0.466585 + 0.808150i
320320 −7.58635 16.2002i −0.424090 0.905620i
321321 6.97990 0.389580
322322 0 0
323323 −0.942563 + 0.942563i −0.0524456 + 0.0524456i
324324 18.6880 + 49.7432i 1.03822 + 2.76351i
325325 −4.64293 + 8.60204i −0.257543 + 0.477156i
326326 3.37395 + 18.5743i 0.186866 + 1.02873i
327327 7.99169 29.8254i 0.441941 1.64935i
328328 −8.85836 2.22737i −0.489121 0.122986i
329329 0 0
330330 −21.0164 10.4251i −1.15692 0.573886i
331331 25.1183 14.5020i 1.38062 0.797104i 0.388392 0.921494i 0.373031π-0.373031\pi
0.992233 + 0.124390i 0.0396975π0.0396975\pi
332332 −0.163082 1.66603i −0.00895027 0.0914355i
333333 25.8258 6.92000i 1.41524 0.379214i
334334 −2.83926 + 7.92771i −0.155357 + 0.433785i
335335 25.8416 + 10.2726i 1.41188 + 0.561252i
336336 0 0
337337 0.436142 0.436142i 0.0237582 0.0237582i −0.695128 0.718886i 0.744652π-0.744652\pi
0.718886 + 0.695128i 0.244652π0.244652\pi
338338 11.7350 5.54595i 0.638301 0.301660i
339339 −28.0347 + 48.5575i −1.52264 + 2.63728i
340340 0.416909 + 0.754864i 0.0226101 + 0.0409383i
341341 −0.565413 0.979324i −0.0306188 0.0530333i
342342 6.13394 74.5341i 0.331685 4.03034i
343343 0 0
344344 9.99500 5.97856i 0.538894 0.322343i
345345 −14.5976 + 19.5992i −0.785909 + 1.05519i
346346 −28.2689 + 5.13495i −1.51975 + 0.276057i
347347 −20.0808 + 5.38063i −1.07799 + 0.288847i −0.753773 0.657135i 0.771768π-0.771768\pi
−0.324219 + 0.945982i 0.605102π0.605102\pi
348348 −19.7747 + 43.5743i −1.06004 + 2.33583i
349349 11.4922i 0.615164i 0.951522 + 0.307582i 0.0995198π0.0995198\pi
−0.951522 + 0.307582i 0.900480π0.900480\pi
350350 0 0
351351 29.6650i 1.58340i
352352 −12.7778 + 1.45056i −0.681057 + 0.0773154i
353353 17.5453 4.70125i 0.933843 0.250222i 0.240350 0.970686i 0.422738π-0.422738\pi
0.693493 + 0.720464i 0.256071π0.256071\pi
354354 −4.30800 23.7164i −0.228967 1.26051i
355355 4.80923 6.45704i 0.255248 0.342704i
356356 1.30511 7.87555i 0.0691706 0.417403i
357357 0 0
358358 4.48353 + 0.368981i 0.236962 + 0.0195013i
359359 −11.2339 19.4577i −0.592902 1.02694i −0.993839 0.110831i 0.964649π-0.964649\pi
0.400938 0.916105i 0.368684π-0.368684\pi
360360 −45.2299 17.1748i −2.38383 0.905194i
361361 −14.3942 + 24.9314i −0.757587 + 1.31218i
362362 5.57689 + 11.8005i 0.293115 + 0.620221i
363363 13.4578 13.4578i 0.706349 0.706349i
364364 0 0
365365 27.2036 + 10.8140i 1.42390 + 0.566032i
366366 −43.5289 15.5896i −2.27529 0.814883i
367367 10.3023 2.76049i 0.537776 0.144097i 0.0202990 0.999794i 0.493538π-0.493538\pi
0.517476 + 0.855697i 0.326872π0.326872\pi
368368 −0.892162 + 13.3662i −0.0465071 + 0.696762i
369369 −21.3942 + 12.3519i −1.11374 + 0.643016i
370370 −4.91154 + 9.90136i −0.255339 + 0.514747i
371371 0 0
372372 −1.88951 2.64015i −0.0979667 0.136886i
373373 −5.01170 + 18.7039i −0.259496 + 0.968452i 0.706038 + 0.708174i 0.250481π0.250481\pi
−0.965534 + 0.260278i 0.916186π0.916186\pi
374374 0.609945 0.110794i 0.0315395 0.00572904i
375375 36.3449 + 3.20325i 1.87684 + 0.165415i
376376 −3.43339 + 6.16503i −0.177064 + 0.317937i
377377 10.1352 10.1352i 0.521988 0.521988i
378378 0 0
379379 11.3167 0.581298 0.290649 0.956830i 0.406129π-0.406129\pi
0.290649 + 0.956830i 0.406129π0.406129\pi
380380 21.4414 + 22.2718i 1.09992 + 1.14252i
381381 4.63841 8.03396i 0.237633 0.411592i
382382 −17.1763 11.8955i −0.878814 0.608626i
383383 4.31792 + 1.15698i 0.220635 + 0.0591191i 0.367443 0.930046i 0.380233π-0.380233\pi
−0.146808 + 0.989165i 0.546900π0.546900\pi
384384 −36.1052 + 7.71872i −1.84248 + 0.393894i
385385 0 0
386386 −2.79448 3.29568i −0.142235 0.167746i
387387 8.15258 30.4259i 0.414419 1.54663i
388388 −0.301361 3.07869i −0.0152993 0.156297i
389389 23.3678 + 13.4914i 1.18480 + 0.684043i 0.957119 0.289694i 0.0935535π-0.0935535\pi
0.227677 + 0.973737i 0.426887π0.426887\pi
390390 15.1375 + 13.3378i 0.766517 + 0.675385i
391391 0.645770i 0.0326580i
392392 0 0
393393 −15.0645 15.0645i −0.759906 0.759906i
394394 12.1566 + 4.35380i 0.612439 + 0.219341i
395395 2.94891 25.1829i 0.148376 1.26709i
396396 −22.0806 + 26.8724i −1.10959 + 1.35039i
397397 8.72496 + 2.33785i 0.437893 + 0.117333i 0.471029 0.882118i 0.343883π-0.343883\pi
−0.0331358 + 0.999451i 0.510549π0.510549\pi
398398 21.0975 + 1.73627i 1.05752 + 0.0870311i
399399 0 0
400400 17.6878 9.33499i 0.884390 0.466749i
401401 −3.01957 5.23005i −0.150790 0.261176i 0.780728 0.624871i 0.214848π-0.214848\pi
−0.931518 + 0.363695i 0.881515π0.881515\pi
402402 32.6779 47.1846i 1.62982 2.35335i
403403 0.251699 + 0.939353i 0.0125380 + 0.0467925i
404404 −3.51189 9.34786i −0.174723 0.465073i
405405 −54.5561 + 23.5194i −2.71092 + 1.16869i
406406 0 0
407407 5.61837 + 5.61837i 0.278492 + 0.278492i
408408 1.71185 0.487182i 0.0847494 0.0241191i
409409 18.5956 + 10.7362i 0.919493 + 0.530869i 0.883473 0.468482i 0.155199π-0.155199\pi
0.0360194 + 0.999351i 0.488532π0.488532\pi
410410 2.01565 10.0113i 0.0995460 0.494424i
411411 −16.6392 + 9.60663i −0.820749 + 0.473860i
412412 −16.8937 + 12.0906i −0.832295 + 0.595659i
413413 0 0
414414 23.4312 + 27.6337i 1.15158 + 1.35812i
415415 1.85188 0.270857i 0.0909053 0.0132958i
416416 10.9371 + 1.63912i 0.536235 + 0.0803643i
417417 −5.53395 20.6530i −0.270999 1.01138i
418418 20.0938 9.49627i 0.982817 0.464478i
419419 −12.1274 −0.592464 −0.296232 0.955116i 0.595730π-0.595730\pi
−0.296232 + 0.955116i 0.595730π0.595730\pi
420420 0 0
421421 −30.9496 −1.50839 −0.754196 0.656649i 0.771973π-0.771973\pi
−0.754196 + 0.656649i 0.771973π0.771973\pi
422422 −21.2396 + 10.0378i −1.03393 + 0.488633i
423423 4.93961 + 18.4349i 0.240172 + 0.896334i
424424 20.4502 0.316252i 0.993147 0.0153586i
425425 −0.820801 + 0.505794i −0.0398147 + 0.0245346i
426426 −10.7469 12.6744i −0.520687 0.614075i
427427 0 0
428428 2.48958 + 3.47861i 0.120338 + 0.168145i
429429 12.5606 7.25185i 0.606430 0.350123i
430430 7.20898 + 10.8436i 0.347648 + 0.522927i
431431 −19.5042 11.2608i −0.939486 0.542413i −0.0496870 0.998765i 0.515822π-0.515822\pi
−0.889799 + 0.456352i 0.849156π0.849156\pi
432432 −33.7809 + 50.4258i −1.62529 + 2.42611i
433433 −14.7279 14.7279i −0.707779 0.707779i 0.258289 0.966068i 0.416841π-0.416841\pi
−0.966068 + 0.258289i 0.916841π0.916841\pi
434434 0 0
435435 −49.7154 19.7630i −2.38367 0.947562i
436436 17.7147 6.65522i 0.848380 0.318727i
437437 −5.99198 22.3624i −0.286635 1.06974i
438438 34.4002 49.6715i 1.64370 2.37340i
439439 16.3149 + 28.2582i 0.778666 + 1.34869i 0.932711 + 0.360625i 0.117437π0.117437\pi
−0.154045 + 0.988064i 0.549230π0.549230\pi
440440 −2.30048 14.1925i −0.109671 0.676601i
441441 0 0
442442 −0.531329 0.0437268i −0.0252727 0.00207987i
443443 −35.4675 9.50348i −1.68511 0.451524i −0.715989 0.698111i 0.754024π-0.754024\pi
−0.969120 + 0.246588i 0.920691π0.920691\pi
444444 17.6253 + 14.4824i 0.836457 + 0.687302i
445445 8.86465 + 1.03805i 0.420225 + 0.0492082i
446446 −19.9161 7.13284i −0.943056 0.337750i
447447 33.2010 + 33.2010i 1.57035 + 1.57035i
448448 0 0
449449 29.6263i 1.39815i −0.715047 0.699077i 0.753595π-0.753595\pi
0.715047 0.699077i 0.246405π-0.246405\pi
450450 16.7713 51.4259i 0.790608 2.42424i
451451 −6.35787 3.67072i −0.299380 0.172847i
452452 −34.1992 + 3.34763i −1.60860 + 0.157459i
453453 −6.17715 + 23.0534i −0.290228 + 1.08315i
454454 −7.67584 9.05253i −0.360245 0.424856i
455455 0 0
456456 54.7594 32.7546i 2.56434 1.53387i
457457 5.76995 + 1.54605i 0.269907 + 0.0723213i 0.391234 0.920291i 0.372048π-0.372048\pi
−0.121327 + 0.992613i 0.538715π0.538715\pi
458458 11.1183 + 7.70002i 0.519525 + 0.359799i
459459 1.46295 2.53390i 0.0682846 0.118272i
460460 −14.9744 0.284453i −0.698186 0.0132627i
461461 −6.73072 −0.313481 −0.156740 0.987640i 0.550099π-0.550099\pi
−0.156740 + 0.987640i 0.550099π0.550099\pi
462462 0 0
463463 −0.122270 + 0.122270i −0.00568238 + 0.00568238i −0.709942 0.704260i 0.751279π-0.751279\pi
0.704260 + 0.709942i 0.251279π0.251279\pi
464464 −28.7696 + 5.68678i −1.33559 + 0.264002i
465465 2.84779 2.25076i 0.132063 0.104376i
466466 13.8682 2.51911i 0.642433 0.116696i
467467 −1.25037 + 4.66643i −0.0578601 + 0.215937i −0.988803 0.149229i 0.952321π-0.952321\pi
0.930943 + 0.365165i 0.118988π0.118988\pi
468468 24.3231 17.4077i 1.12434 0.804669i
469469 0 0
470470 −7.06775 3.50594i −0.326011 0.161717i
471471 56.7615 32.7713i 2.61543 1.51002i
472472 10.2831 10.6061i 0.473317 0.488186i
473473 9.04187 2.42276i 0.415746 0.111399i
474474 −49.2670 17.6447i −2.26291 0.810447i
475475 −23.7304 + 25.1312i −1.08882 + 1.15310i
476476 0 0
477477 39.1141 39.1141i 1.79091 1.79091i
478478 11.7936 + 24.9547i 0.539425 + 1.14140i
479479 15.7076 27.2063i 0.717697 1.24309i −0.244214 0.969721i 0.578530π-0.578530\pi
0.961910 0.273365i 0.0881368π-0.0881368\pi
480480 −10.5430 39.9099i −0.481218 1.82163i
481481 −3.41653 5.91760i −0.155780 0.269819i
482482 13.5654 + 1.11639i 0.617888 + 0.0508503i
483483 0 0
484484 11.5071 + 1.90692i 0.523050 + 0.0866781i
485485 3.42212 0.500521i 0.155391 0.0227275i
486486 10.4091 + 57.3042i 0.472167 + 2.59937i
487487 −5.63804 + 1.51071i −0.255484 + 0.0684568i −0.384288 0.923213i 0.625553π-0.625553\pi
0.128804 + 0.991670i 0.458886π0.458886\pi
488488 −7.75636 27.2542i −0.351114 1.23374i
489489 43.5627i 1.96997i
490490 0 0
491491 4.53656i 0.204732i 0.994747 + 0.102366i 0.0326413π0.0326413\pi
−0.994747 + 0.102366i 0.967359π0.967359\pi
492492 −19.1935 8.71034i −0.865311 0.392693i
493493 1.36554 0.365895i 0.0615008 0.0164791i
494494 −18.8051 + 3.41589i −0.846083 + 0.153688i
495495 −31.1862 23.2276i −1.40171 1.04400i
496496 0.641838 1.88337i 0.0288194 0.0845659i
497497 0 0
498498 0.316830 3.84984i 0.0141975 0.172515i
499499 16.1667 + 28.0016i 0.723722 + 1.25352i 0.959498 + 0.281716i 0.0909036π0.0909036\pi
−0.235776 + 0.971808i 0.575763π0.575763\pi
500500 11.3670 + 19.2559i 0.508349 + 0.861151i
501501 −9.71578 + 16.8282i −0.434069 + 0.751829i
502502 −34.8844 + 16.4863i −1.55697 + 0.735820i
503503 19.0966 19.0966i 0.851475 0.851475i −0.138840 0.990315i 0.544337π-0.544337\pi
0.990315 + 0.138840i 0.0443373π0.0443373\pi
504504 0 0
505505 10.2523 4.41982i 0.456222 0.196679i
506506 −3.63028 + 10.1364i −0.161386 + 0.450617i
507507 28.9306 7.75192i 1.28485 0.344275i
508508 5.65835 0.553874i 0.251049 0.0245742i
509509 −25.4928 + 14.7183i −1.12995 + 0.652377i −0.943922 0.330167i 0.892895π-0.892895\pi
−0.186028 + 0.982544i 0.559561π0.559561\pi
510510 0.635240 + 1.88579i 0.0281289 + 0.0835042i
511511 0 0
512512 −16.7248 15.2408i −0.739137 0.673555i
513513 27.1489 101.321i 1.19865 4.47343i
514514 7.29365 + 40.1530i 0.321709 + 1.77107i
515515 −14.4021 18.2224i −0.634631 0.802975i
516516 25.1584 9.45174i 1.10754 0.416090i
517517 −4.01048 + 4.01048i −0.176381 + 0.176381i
518518 0 0
519519 −66.2998 −2.91024
520520 −1.24800 + 12.3014i −0.0547285 + 0.539454i
521521 19.2144 33.2803i 0.841798 1.45804i −0.0465748 0.998915i 0.514831π-0.514831\pi
0.888373 0.459122i 0.151836π-0.151836\pi
522522 −45.1578 + 65.2048i −1.97650 + 2.85393i
523523 −40.8579 10.9478i −1.78659 0.478716i −0.794831 0.606830i 0.792441π-0.792441\pi
−0.991759 + 0.128115i 0.959107π0.959107\pi
524524 2.13459 12.8810i 0.0932501 0.562709i
525525 0 0
526526 5.62777 4.77191i 0.245382 0.208065i
527527 −0.0248254 + 0.0926496i −0.00108141 + 0.00403588i
528528 −29.6090 1.97633i −1.28857 0.0860087i
529529 −10.2055 5.89214i −0.443717 0.256180i
530530 1.44235 + 22.8212i 0.0626518 + 0.991288i
531531 39.9538i 1.73385i
532532 0 0
533533 4.46432 + 4.46432i 0.193371 + 0.193371i
534534 6.21111 17.3425i 0.268781 0.750483i
535535 −3.75219 + 2.96554i −0.162221 + 0.128212i
536536 35.1711 0.543906i 1.51916 0.0234931i
537537 10.0273 + 2.68680i 0.432709 + 0.115944i
538538 −1.47413 + 17.9123i −0.0635544 + 0.772256i
539539 0 0
540540 −58.1129 35.0397i −2.50078 1.50787i
541541 12.8616 + 22.2770i 0.552964 + 0.957762i 0.998059 + 0.0622786i 0.0198367π0.0198367\pi
−0.445095 + 0.895484i 0.646830π0.646830\pi
542542 −33.6092 23.2762i −1.44364 0.999796i
543543 7.79517 + 29.0920i 0.334523 + 1.24846i
544544 0.853381 + 0.679378i 0.0365884 + 0.0291281i
545545 8.37579 + 19.4287i 0.358779 + 0.832233i
546546 0 0
547547 14.6703 + 14.6703i 0.627257 + 0.627257i 0.947377 0.320120i 0.103723π-0.103723\pi
−0.320120 + 0.947377i 0.603723π0.603723\pi
548548 −10.7225 4.86607i −0.458044 0.207868i
549549 −66.3706 38.3191i −2.83263 1.63542i
550550 15.7272 3.32499i 0.670608 0.141778i
551551 43.8922 25.3412i 1.86987 1.07957i
552552 −7.53796 + 29.9788i −0.320837 + 1.27598i
553553 0 0
554554 −23.6043 + 20.0146i −1.00285 + 0.850337i
555555 −15.2347 + 20.4546i −0.646676 + 0.868249i
556556 8.31909 10.1245i 0.352808 0.429373i
557557 0.0844516 + 0.315178i 0.00357833 + 0.0133545i 0.967692 0.252136i 0.0811329π-0.0811329\pi
−0.964114 + 0.265490i 0.914466π0.914466\pi
558558 −2.29939 4.86541i −0.0973407 0.205969i
559559 −8.05015 −0.340485
560560 0 0
561561 1.43052 0.0603966
562562 4.21106 + 8.91044i 0.177633 + 0.375864i
563563 3.98515 + 14.8728i 0.167954 + 0.626812i 0.997645 + 0.0685896i 0.0218499π0.0218499\pi
−0.829691 + 0.558223i 0.811483π0.811483\pi
564564 −10.3377 + 12.5812i −0.435298 + 0.529764i
565565 −5.55997 38.0142i −0.233910 1.59927i
566566 −29.0642 + 24.6441i −1.22166 + 1.03587i
567567 0 0
568568 2.48341 9.87664i 0.104202 0.414415i
569569 −6.11191 + 3.52871i −0.256224 + 0.147931i −0.622611 0.782531i 0.713928π-0.713928\pi
0.366387 + 0.930463i 0.380595π0.380595\pi
570570 39.4957 + 59.4088i 1.65429 + 2.48836i
571571 12.6951 + 7.32953i 0.531274 + 0.306731i 0.741535 0.670914i 0.234098π-0.234098\pi
−0.210261 + 0.977645i 0.567431π0.567431\pi
572572 8.09423 + 3.67330i 0.338437 + 0.153588i
573573 −34.0914 34.0914i −1.42419 1.42419i
574574 0 0
575575 −0.479869 16.7381i −0.0200119 0.698025i
576576 −61.1684 + 1.89234i −2.54868 + 0.0788473i
577577 1.01912 + 3.80340i 0.0424265 + 0.158338i 0.983889 0.178779i 0.0572148π-0.0572148\pi
−0.941463 + 0.337117i 0.890548π0.890548\pi
578578 19.7213 + 13.6581i 0.820300 + 0.568101i
579579 −4.98544 8.63504i −0.207188 0.358860i
580580 −7.88305 31.8260i −0.327326 1.32150i
581581 0 0
582582 0.585477 7.11418i 0.0242688 0.294892i
583583 15.8784 + 4.25461i 0.657618 + 0.176208i
584584 37.0248 0.572573i 1.53210 0.0236932i
585585 20.7357 + 26.2361i 0.857316 + 1.08473i
586586 −6.47426 + 18.0773i −0.267449 + 0.746765i
587587 10.0254 + 10.0254i 0.413791 + 0.413791i 0.883057 0.469266i 0.155481π-0.155481\pi
−0.469266 + 0.883057i 0.655481π0.655481\pi
588588 0 0
589589 3.43871i 0.141690i
590590 12.3922 + 10.9189i 0.510179 + 0.449524i
591591 25.8048 + 14.8984i 1.06147 + 0.612839i
592592 −0.931097 + 13.9495i −0.0382679 + 0.573322i
593593 −3.54698 + 13.2375i −0.145657 + 0.543599i 0.854068 + 0.520161i 0.174128π0.174128\pi
−0.999725 + 0.0234382i 0.992539π0.992539\pi
594594 −37.2079 + 31.5494i −1.52666 + 1.29449i
595595 0 0
596596 −4.70447 + 28.3886i −0.192702 + 1.16284i
597597 47.1840 + 12.6429i 1.93111 + 0.517440i
598598 5.27175 7.61205i 0.215578 0.311280i
599599 21.0392 36.4409i 0.859637 1.48893i −0.0126393 0.999920i 0.504023π-0.504023\pi
0.872276 0.489014i 0.162643π-0.162643\pi
600600 44.0084 13.8996i 1.79664 0.567449i
601601 35.4599 1.44644 0.723220 0.690618i 0.242661π-0.242661\pi
0.723220 + 0.690618i 0.242661π0.242661\pi
602602 0 0
603603 67.2702 67.2702i 2.73946 2.73946i
604604 −13.6925 + 5.14413i −0.557141 + 0.209312i
605605 −1.51671 + 12.9523i −0.0616631 + 0.526586i
606606 −4.11826 22.6718i −0.167293 0.920981i
607607 4.60061 17.1697i 0.186733 0.696898i −0.807520 0.589841i 0.799191π-0.799191\pi
0.994253 0.107057i 0.0341428π-0.0341428\pi
608608 35.8556 + 15.6078i 1.45414 + 0.632981i
609609 0 0
610610 30.0234 10.1136i 1.21561 0.409487i
611611 4.22408 2.43877i 0.170888 0.0986622i
612612 2.93608 0.287402i 0.118684 0.0116175i
613613 −34.1959 + 9.16276i −1.38116 + 0.370080i −0.871542 0.490321i 0.836880π-0.836880\pi
−0.509617 + 0.860401i 0.670213π0.670213\pi
614614 6.71589 18.7519i 0.271031 0.756767i
615615 8.70516 21.8986i 0.351026 0.883035i
616616 0 0
617617 −20.4594 + 20.4594i −0.823663 + 0.823663i −0.986631 0.162968i 0.947893π-0.947893\pi
0.162968 + 0.986631i 0.447893π0.447893\pi
618618 −43.3420 + 20.4834i −1.74347 + 0.823962i
619619 −0.816411 + 1.41407i −0.0328143 + 0.0568361i −0.881966 0.471313i 0.843780π-0.843780\pi
0.849152 + 0.528149i 0.177114π0.177114\pi
620620 2.13747 + 0.616473i 0.0858427 + 0.0247582i
621621 25.4084 + 44.0087i 1.01961 + 1.76601i
622622 −1.04916 + 12.7485i −0.0420676 + 0.511168i
623623 0 0
624624 24.1557 + 8.23206i 0.967002 + 0.329546i
625625 −20.8989 + 13.7199i −0.835957 + 0.548795i
626626 22.1631 4.02585i 0.885816 0.160905i
627627 49.5375 13.2735i 1.97834 0.530094i
628628 36.5780 + 16.5997i 1.45962 + 0.662400i
629629 0.673953i 0.0268723i
630630 0 0
631631 41.6810i 1.65929i −0.558289 0.829647i 0.688542π-0.688542\pi
0.558289 0.829647i 0.311458π-0.311458\pi
632632 −8.77882 30.8469i −0.349203 1.22702i
633633 −52.3624 + 14.0305i −2.08122 + 0.557661i
634634 −3.08785 16.9992i −0.122634 0.675126i
635635 0.919910 + 6.28954i 0.0365055 + 0.249593i
636636 46.5607 + 7.71588i 1.84625 + 0.305954i
637637 0 0
638638 −23.4912 1.93326i −0.930027 0.0765385i
639639 −13.7718 23.8535i −0.544805 0.943630i
640640 16.1296 19.4893i 0.637580 0.770384i
641641 9.61057 16.6460i 0.379595 0.657477i −0.611408 0.791315i 0.709397π-0.709397\pi
0.991003 + 0.133838i 0.0427301π0.0427301\pi
642642 4.21775 + 8.92460i 0.166461 + 0.352226i
643643 9.73498 9.73498i 0.383910 0.383910i −0.488599 0.872509i 0.662492π-0.662492\pi
0.872509 + 0.488599i 0.162492π0.162492\pi
644644 0 0
645645 11.8953 + 27.5926i 0.468377 + 1.08646i
646646 −1.77474 0.635612i −0.0698261 0.0250078i
647647 −41.9129 + 11.2305i −1.64777 + 0.441518i −0.958986 0.283452i 0.908520π-0.908520\pi
−0.688780 + 0.724970i 0.741854π0.741854\pi
648648 −52.3098 + 53.9531i −2.05492 + 2.11948i
649649 10.2826 5.93668i 0.403629 0.233035i
650650 −13.8043 0.738550i −0.541449 0.0289683i
651651 0 0
652652 −21.7105 + 15.5379i −0.850251 + 0.608510i
653653 −9.62651 + 35.9266i −0.376714 + 1.40592i 0.474109 + 0.880466i 0.342770π0.342770\pi
−0.850824 + 0.525451i 0.823897π0.823897\pi
654654 42.9643 7.80432i 1.68004 0.305173i
655655 14.4987 + 1.69780i 0.566512 + 0.0663385i
656656 −2.50490 12.6724i −0.0977999 0.494773i
657657 70.8158 70.8158i 2.76279 2.76279i
658658 0 0
659659 −31.4251 −1.22415 −0.612074 0.790800i 0.709665π-0.709665\pi
−0.612074 + 0.790800i 0.709665π0.709665\pi
660660 0.630124 33.1716i 0.0245275 1.29120i
661661 1.81769 3.14833i 0.0707000 0.122456i −0.828508 0.559977i 0.810810π-0.810810\pi
0.899208 + 0.437521i 0.144143π0.144143\pi
662662 33.7208 + 23.3534i 1.31059 + 0.907657i
663663 −1.18830 0.318405i −0.0461498 0.0123658i
664664 2.03167 1.21525i 0.0788441 0.0471610i
665665 0 0
666666 24.4538 + 28.8397i 0.947565 + 1.11752i
667667 −6.35486 + 23.7166i −0.246061 + 0.918312i
668668 −11.8522 + 1.16016i −0.458574 + 0.0448881i
669669 −42.2761 24.4081i −1.63449 0.943673i
670670 2.48062 + 39.2489i 0.0958348 + 1.51632i
671671 22.7751i 0.879224i
672672 0 0
673673 7.66159 + 7.66159i 0.295333 + 0.295333i 0.839183 0.543850i 0.183034π-0.183034\pi
−0.543850 + 0.839183i 0.683034π0.683034\pi
674674 0.821205 + 0.294110i 0.0316317 + 0.0113287i
675675 36.0360 66.7646i 1.38703 2.56977i
676676 14.1823 + 11.6533i 0.545472 + 0.448205i
677677 0.273888 + 0.0733880i 0.0105264 + 0.00282053i 0.264078 0.964501i 0.414932π-0.414932\pi
−0.253552 + 0.967322i 0.581599π0.581599\pi
678678 −79.0270 6.50369i −3.03501 0.249773i
679679 0 0
680680 −0.713255 + 0.989209i −0.0273521 + 0.0379344i
681681 −13.6939 23.7186i −0.524753 0.908898i
682682 0.910515 1.31472i 0.0348654 0.0503433i
683683 −11.1511 41.6163i −0.426683 1.59240i −0.760220 0.649666i 0.774909π-0.774909\pi
0.333536 0.942737i 0.391758π-0.391758\pi
684684 99.0070 37.1958i 3.78563 1.42222i
685685 4.86317 12.2337i 0.185812 0.467426i
686686 0 0
687687 22.0676 + 22.0676i 0.841930 + 0.841930i
688688 13.6840 + 9.16709i 0.521697 + 0.349492i
689689 −12.2429 7.06844i −0.466417 0.269286i
690690 −33.8808 6.82146i −1.28982 0.259689i
691691 2.91753 1.68444i 0.110988 0.0640791i −0.443478 0.896285i 0.646256π-0.646256\pi
0.554467 + 0.832206i 0.312922π0.312922\pi
692692 −23.6477 33.0422i −0.898951 1.25607i
693693 0 0
694694 −19.0140 22.4242i −0.721761 0.851212i
695695 11.7497 + 8.75124i 0.445692 + 0.331953i
696696 −67.6641 + 1.04639i −2.56480 + 0.0396635i
697697 0.161169 + 0.601490i 0.00610471 + 0.0227831i
698698 −14.6941 + 6.94441i −0.556180 + 0.262850i
699699 32.5255 1.23023
700700 0 0
701701 −20.4918 −0.773966 −0.386983 0.922087i 0.626483π-0.626483\pi
−0.386983 + 0.922087i 0.626483π0.626483\pi
702702 37.9301 17.9257i 1.43158 0.676562i
703703 −6.25348 23.3383i −0.235855 0.880221i
704704 −9.57595 15.4613i −0.360907 0.582720i
705705 −14.6008 10.8748i −0.549899 0.409567i
706706 16.6132 + 19.5929i 0.625247 + 0.737387i
707707 0 0
708708 27.7209 19.8394i 1.04182 0.745610i
709709 24.0284 13.8728i 0.902407 0.521005i 0.0244266 0.999702i 0.492224π-0.492224\pi
0.877980 + 0.478697i 0.158891π0.158891\pi
710710 11.1622 + 2.24736i 0.418908 + 0.0843418i
711711 −75.1197 43.3704i −2.81721 1.62652i
712712 10.8584 3.09024i 0.406937 0.115811i
713713 −1.17797 1.17797i −0.0441153 0.0441153i
714714 0 0
715715 −3.67111 + 9.23499i −0.137292 + 0.345369i
716716 2.23748 + 5.95567i 0.0836186 + 0.222574i
717717 16.4846 + 61.5213i 0.615628 + 2.29756i
718718 18.0905 26.1215i 0.675133 0.974846i
719719 8.96044 + 15.5199i 0.334168 + 0.578796i 0.983325 0.181859i 0.0582114π-0.0582114\pi
−0.649157 + 0.760655i 0.724878π0.724878\pi
720720 −5.37111 68.2099i −0.200170 2.54203i
721721 0 0
722722 −40.5756 3.33926i −1.51007 0.124274i
723723 30.3387 + 8.12922i 1.12831 + 0.302329i
724724 −11.7183 + 14.2614i −0.435509 + 0.530021i
725725 35.1223 10.4986i 1.30441 0.389907i
726726 25.3394 + 9.07516i 0.940435 + 0.336811i
727727 −12.7173 12.7173i −0.471659 0.471659i 0.430792 0.902451i 0.358234π-0.358234\pi
−0.902451 + 0.430792i 0.858234π0.858234\pi
728728 0 0
729729 54.6902i 2.02556i
730730 2.61137 + 41.3175i 0.0966510 + 1.52923i
731731 −0.687621 0.396998i −0.0254326 0.0146835i
732732 −6.37015 65.0771i −0.235448 2.40532i
733733 8.28399 30.9163i 0.305976 1.14192i −0.626126 0.779722i 0.715360π-0.715360\pi
0.932102 0.362196i 0.117973π-0.117973\pi
734734 9.75499 + 11.5046i 0.360063 + 0.424642i
735735 0 0
736736 −17.6293 + 6.93608i −0.649826 + 0.255667i
737737 27.3085 + 7.31728i 1.00592 + 0.269536i
738738 −28.7213 19.8910i −1.05724 0.732198i
739739 −17.8879 + 30.9827i −0.658016 + 1.13972i 0.323112 + 0.946361i 0.395271π0.395271\pi
−0.981128 + 0.193357i 0.938062π0.938062\pi
740740 −15.6279 0.296867i −0.574494 0.0109130i
741741 −44.1041 −1.62021
742742 0 0
743743 −1.03957 + 1.03957i −0.0381381 + 0.0381381i −0.725919 0.687781i 0.758585π-0.758585\pi
0.687781 + 0.725919i 0.258585π0.258585\pi
744744 2.23396 4.01133i 0.0819010 0.147062i
745745 −31.9540 3.74181i −1.17070 0.137089i
746746 −26.9435 + 4.89420i −0.986473 + 0.179189i
747747 1.65716 6.18462i 0.0606325 0.226283i
748748 0.510235 + 0.712935i 0.0186561 + 0.0260675i
749749 0 0
750750 17.8665 + 48.4068i 0.652391 + 1.76757i
751751 −2.97538 + 1.71784i −0.108573 + 0.0626847i −0.553303 0.832980i 0.686633π-0.686633\pi
0.444730 + 0.895665i 0.353300π0.353300\pi
752752 −9.95740 0.664633i −0.363109 0.0242367i
753753 −86.0012 + 23.0439i −3.13406 + 0.839768i
754754 19.0834 + 6.83459i 0.694975 + 0.248901i
755755 −6.47404 15.0173i −0.235615 0.546537i
756756 0 0
757757 21.8519 21.8519i 0.794220 0.794220i −0.187957 0.982177i 0.560187π-0.560187\pi
0.982177 + 0.187957i 0.0601866π0.0601866\pi
758758 6.83833 + 14.4697i 0.248379 + 0.525562i
759759 −12.4226 + 21.5166i −0.450912 + 0.781002i
760760 −15.5206 + 40.8735i −0.562992 + 1.48264i
761761 3.32790 + 5.76410i 0.120636 + 0.208948i 0.920019 0.391874i 0.128173π-0.128173\pi
−0.799382 + 0.600823i 0.794840π0.794840\pi
762762 13.0752 + 1.07605i 0.473665 + 0.0389812i
763763 0 0
764764 4.83062 29.1499i 0.174766 1.05461i
765765 0.477336 + 3.26361i 0.0172581 + 0.117996i
766766 1.12986 + 6.22009i 0.0408234 + 0.224741i
767767 −9.86296 + 2.64277i −0.356131 + 0.0954249i
768768 −31.6866 41.5004i −1.14339 1.49752i
769769 10.3364i 0.372740i 0.982480 + 0.186370i 0.0596723π0.0596723\pi
−0.982480 + 0.186370i 0.940328π0.940328\pi
770770 0 0
771771 94.1718i 3.39151i
772772 2.52529 5.56455i 0.0908871 0.200273i
773773 24.1755 6.47780i 0.869531 0.232990i 0.203646 0.979045i 0.434721π-0.434721\pi
0.665885 + 0.746054i 0.268054π0.268054\pi
774774 43.8293 7.96145i 1.57541 0.286168i
775775 −0.574615 + 2.41988i −0.0206408 + 0.0869247i
776776 3.75436 2.24569i 0.134774 0.0806156i
777777 0 0
778778 −3.12984 + 38.0310i −0.112210 + 1.36348i
779779 11.1622 + 19.3336i 0.399929 + 0.692697i
780780 −7.90675 + 27.4147i −0.283107 + 0.981602i
781781 4.09267 7.08872i 0.146447 0.253654i
782782 0.825691 0.390220i 0.0295267 0.0139542i
783783 −78.6639 + 78.6639i −2.81122 + 2.81122i
784784 0 0
785785 −16.5898 + 41.7331i −0.592116 + 1.48952i
786786 10.1587 28.3648i 0.362348 1.01174i
787787 4.13231 1.10725i 0.147301 0.0394692i −0.184415 0.982848i 0.559039π-0.559039\pi
0.331716 + 0.943379i 0.392372π0.392372\pi
788788 1.77903 + 18.1744i 0.0633752 + 0.647437i
789789 14.7453 8.51323i 0.524948 0.303079i
790790 33.9812 11.4468i 1.20900 0.407258i
791791 0 0
792792 −47.7021 11.9944i −1.69502 0.426201i
793793 −5.06928 + 18.9188i −0.180015 + 0.671827i
794794 2.28304 + 12.5686i 0.0810219 + 0.446041i
795795 −6.13700 + 52.4083i −0.217657 + 1.85873i
796796 10.5286 + 28.0248i 0.373177 + 0.993313i
797797 −27.3364 + 27.3364i −0.968306 + 0.968306i −0.999513 0.0312066i 0.990065π-0.990065\pi
0.0312066 + 0.999513i 0.490065π0.490065\pi
798798 0 0
799799 0.481078 0.0170193
800800 22.6241 + 16.9750i 0.799882 + 0.600158i
801801 15.2668 26.4429i 0.539427 0.934314i
802802 4.86258 7.02123i 0.171704 0.247928i
803803 28.7478 + 7.70294i 1.01449 + 0.271831i
804804 80.0773 + 13.2701i 2.82411 + 0.468001i
805805 0 0
806806 −1.04898 + 0.889450i −0.0369486 + 0.0313295i
807807 −10.7342 + 40.0604i −0.377860 + 1.41019i
808808 9.83018 10.1390i 0.345825 0.356689i
809809 12.5601 + 7.25159i 0.441590 + 0.254952i 0.704272 0.709930i 0.251274π-0.251274\pi
−0.262682 + 0.964883i 0.584607π0.584607\pi
810810 −63.0389 55.5442i −2.21496 1.95162i
811811 24.8308i 0.871927i 0.899964 + 0.435964i 0.143592π0.143592\pi
−0.899964 + 0.435964i 0.856408π0.856408\pi
812812 0 0
813813 −66.7073 66.7073i −2.33953 2.33953i
814814 −3.78871 + 10.5788i −0.132794 + 0.370785i
815815 −18.5084 23.4180i −0.648323 0.820298i
816816 1.65734 + 1.89441i 0.0580186 + 0.0663177i
817817 −27.4953 7.36735i −0.961939 0.257751i
818818 −2.49065 + 30.2642i −0.0870836 + 1.05816i
819819 0 0
820820 14.0186 3.47231i 0.489552 0.121258i
821821 −22.4803 38.9370i −0.784567 1.35891i −0.929257 0.369434i 0.879552π-0.879552\pi
0.144690 0.989477i 0.453782π-0.453782\pi
822822 −22.3377 15.4701i −0.779118 0.539581i
823823 4.23553 + 15.8072i 0.147641 + 0.551005i 0.999624 + 0.0274346i 0.00873379π0.00873379\pi
−0.851982 + 0.523571i 0.824600π0.824600\pi
824824 −25.6676 14.2946i −0.894172 0.497977i
825825 37.0784 1.06301i 1.29090 0.0370093i
826826 0 0
827827 −15.3869 15.3869i −0.535056 0.535056i 0.387017 0.922073i 0.373506π-0.373506\pi
−0.922073 + 0.387017i 0.873506π0.873506\pi
828828 −21.1741 + 46.6577i −0.735850 + 1.62147i
829829 34.9273 + 20.1653i 1.21307 + 0.700369i 0.963428 0.267968i 0.0863521π-0.0863521\pi
0.249647 + 0.968337i 0.419685π0.419685\pi
830830 1.46536 + 2.20417i 0.0508634 + 0.0765080i
831831 −61.8456 + 35.7066i −2.14540 + 1.23865i
832832 4.51316 + 14.9748i 0.156466 + 0.519157i
833833 0 0
834834 23.0632 19.5558i 0.798614 0.677162i
835835 −1.92688 13.1743i −0.0666823 0.455915i
836836 24.2841 + 19.9539i 0.839885 + 0.690118i
837837 −1.95356 7.29077i −0.0675248 0.252006i
838838 −7.32826 15.5063i −0.253151 0.535657i
839839 −19.9919 −0.690195 −0.345098 0.938567i 0.612154π-0.612154\pi
−0.345098 + 0.938567i 0.612154π0.612154\pi
840840 0 0
841841 −24.7517 −0.853507
842842 −18.7020 39.5727i −0.644512 1.36376i
843843 5.88605 + 21.9671i 0.202726 + 0.756586i
844844 −25.6690 21.0918i −0.883563 0.726008i
845845 −12.2587 + 16.4589i −0.421711 + 0.566204i
846846 −20.5862 + 17.4555i −0.707769 + 0.600133i
847847 0 0
848848 12.7618 + 25.9568i 0.438242 + 0.891359i
849849 −76.1512 + 43.9659i −2.61350 + 1.50891i
850850 −1.14270 0.743852i −0.0391943 0.0255139i
851851 10.1370 + 5.85259i 0.347492 + 0.200624i
852852 9.71161 21.3999i 0.332714 0.733147i
853853 −4.67428 4.67428i −0.160044 0.160044i 0.622542 0.782586i 0.286100π-0.286100\pi
−0.782586 + 0.622542i 0.786100π0.786100\pi
854854 0 0
855855 46.8121 + 108.586i 1.60094 + 3.71358i
856856 −2.94342 + 5.28523i −0.100604 + 0.180646i
857857 4.28833 + 16.0043i 0.146487 + 0.546695i 0.999685 + 0.0251084i 0.00799311π0.00799311\pi
−0.853198 + 0.521587i 0.825340π0.825340\pi
858858 16.8623 + 11.6781i 0.575670 + 0.398682i
859859 −2.05099 3.55242i −0.0699788 0.121207i 0.828913 0.559378i 0.188960π-0.188960\pi
−0.898892 + 0.438171i 0.855627π0.855627\pi
860860 −9.50867 + 15.7700i −0.324243 + 0.537753i
861861 0 0
862862 2.61235 31.7430i 0.0889771 1.08117i
863863 −47.9390 12.8452i −1.63186 0.437257i −0.677408 0.735608i 0.736897π-0.736897\pi
−0.954456 + 0.298351i 0.903563π0.903563\pi
864864 −84.8880 12.7220i −2.88795 0.432811i
865865 35.6409 28.1688i 1.21183 0.957766i
866866 9.93169 27.7310i 0.337493 0.942338i
867867 39.1428 + 39.1428i 1.32936 + 1.32936i
868868 0 0
869869 25.7774i 0.874437i
870870 −4.77235 75.5091i −0.161798 2.56000i
871871 −21.0559 12.1566i −0.713452 0.411912i
872872 19.2139 + 18.6287i 0.650666 + 0.630848i
873873 3.06230 11.4287i 0.103643 0.386802i
874874 24.9721 21.1744i 0.844694 0.716234i
875875 0 0
876876 84.2978 + 13.9695i 2.84816 + 0.471987i
877877 9.43608 + 2.52839i 0.318634 + 0.0853776i 0.414591 0.910008i 0.363925π-0.363925\pi
−0.0959575 + 0.995385i 0.530591π0.530591\pi
878878 −26.2727 + 37.9360i −0.886661 + 1.28028i
879879 −22.1545 + 38.3728i −0.747254 + 1.29428i
880880 16.7566 11.5175i 0.564866 0.388256i
881881 −14.9131 −0.502435 −0.251217 0.967931i 0.580831π-0.580831\pi
−0.251217 + 0.967931i 0.580831π0.580831\pi
882882 0 0
883883 −19.0557 + 19.0557i −0.641277 + 0.641277i −0.950869 0.309592i 0.899807π-0.899807\pi
0.309592 + 0.950869i 0.399807π0.399807\pi
884884 −0.265157 0.705788i −0.00891819 0.0237382i
885885 23.6323 + 29.9011i 0.794392 + 1.00511i
886886 −9.28067 51.0919i −0.311790 1.71647i
887887 −13.8347 + 51.6318i −0.464524 + 1.73363i 0.193941 + 0.981013i 0.437873π0.437873\pi
−0.658464 + 0.752612i 0.728794π0.728794\pi
888888 −7.86694 + 31.2872i −0.263997 + 1.04993i
889889 0 0
890890 4.02938 + 11.9617i 0.135065 + 0.400958i
891891 −52.3076 + 30.1998i −1.75237 + 1.01173i
892892 −2.91458 29.7752i −0.0975874 0.996948i
893893 16.6593 4.46384i 0.557481 0.149377i
894894 −22.3889 + 62.5137i −0.748797 + 2.09077i
895895 −6.53192 + 2.81594i −0.218338 + 0.0941265i
896896 0 0
897897 15.1083 15.1083i 0.504453 0.504453i
898898 37.8807 17.9023i 1.26409 0.597409i
899899 1.82348 3.15836i 0.0608165 0.105337i
900900 75.8884 9.63112i 2.52961 0.321037i
901901 −0.697169 1.20753i −0.0232261 0.0402287i
902902 0.851558 10.3474i 0.0283538 0.344530i
903903 0 0
904904 −24.9459 41.7048i −0.829690 1.38708i
905905 −16.5507 12.3271i −0.550165 0.409766i
906906 −33.2092 + 6.03233i −1.10330 + 0.200411i
907907 44.2268 11.8505i 1.46853 0.393490i 0.566100 0.824336i 0.308451π-0.308451\pi
0.902425 + 0.430846i 0.141785π0.141785\pi
908908 6.93642 15.2846i 0.230193 0.507238i
909909 38.1942i 1.26682i
910910 0 0
911911 56.0047i 1.85552i −0.373181 0.927758i 0.621733π-0.621733\pi
0.373181 0.927758i 0.378267π-0.378267\pi
912912 74.9700 + 50.2235i 2.48251 + 1.66307i
913913 1.83793 0.492471i 0.0608265 0.0162984i
914914 1.50981 + 8.31178i 0.0499399 + 0.274929i
915915 72.3366 10.5800i 2.39137 0.349763i
916916 −3.12689 + 18.8689i −0.103316 + 0.623447i
917917 0 0
918918 4.12390 + 0.339385i 0.136109 + 0.0112014i
919919 −19.2225 33.2943i −0.634091 1.09828i −0.986707 0.162509i 0.948041π-0.948041\pi
0.352616 0.935768i 0.385292π-0.385292\pi
920920 −8.68490 19.3184i −0.286333 0.636909i
921921 22.9814 39.8049i 0.757262 1.31162i
922922 −4.06718 8.60600i −0.133945 0.283423i
923923 −4.97750 + 4.97750i −0.163836 + 0.163836i
924924 0 0
925925 −0.500811 17.4685i −0.0164666 0.574362i
926926 −0.230221 0.0824521i −0.00756552 0.00270955i
927927 −76.7519 + 20.5656i −2.52086 + 0.675464i
928928 −24.6558 33.3488i −0.809367 1.09473i
929929 26.9022 15.5320i 0.882632 0.509588i 0.0111066 0.999938i 0.496465π-0.496465\pi
0.871525 + 0.490351i 0.163131π0.163131\pi
930930 4.59869 + 2.28117i 0.150797 + 0.0748024i
931931 0 0
932932 11.6011 + 16.2099i 0.380008 + 0.530972i
933933 −7.63967 + 28.5116i −0.250111 + 0.933429i
934934 −6.72213 + 1.22105i −0.219955 + 0.0399540i
935935 −0.769005 + 0.607784i −0.0251492 + 0.0198767i
936936 36.9555 + 20.5810i 1.20793 + 0.672711i
937937 −30.6258 + 30.6258i −1.00050 + 1.00050i −0.000502083 1.00000i 0.500160π0.500160\pi
−1.00000 0.000502083i 0.999840π0.999840\pi
938938 0 0
939939 51.9797 1.69629
940940 0.211908 11.1555i 0.00691169 0.363852i
941941 20.8453 36.1052i 0.679539 1.17700i −0.295581 0.955318i 0.595513π-0.595513\pi
0.975120 0.221678i 0.0711535π-0.0711535\pi
942942 76.2012 + 52.7734i 2.48277 + 1.71945i
943943 −10.4467 2.79918i −0.340190 0.0911537i
944944 19.7749 + 6.73913i 0.643618 + 0.219340i
945945 0 0
946946 8.56152 + 10.0971i 0.278359 + 0.328284i
947947 −2.35220 + 8.77852i −0.0764362 + 0.285264i −0.993555 0.113350i 0.963842π-0.963842\pi
0.917119 + 0.398614i 0.130509π0.130509\pi
948948 −7.20987 73.6557i −0.234166 2.39223i
949949 −22.1657 12.7973i −0.719528 0.415419i
950950 −46.4727 15.1560i −1.50777 0.491724i
951951 39.8687i 1.29283i
952952 0 0
953953 16.5153 + 16.5153i 0.534984 + 0.534984i 0.922051 0.387068i 0.126512π-0.126512\pi
−0.387068 + 0.922051i 0.626512π0.626512\pi
954954 73.6474 + 26.3764i 2.38442 + 0.853966i
955955 32.8109 + 3.84215i 1.06174 + 0.124329i
956956 −24.7810 + 30.1588i −0.801475 + 0.975407i
957957 −52.5375 14.0774i −1.69830 0.455057i
958958 44.2780 + 3.64395i 1.43056 + 0.117731i
959959 0 0
960960 44.6586 37.5968i 1.44135 1.21343i
961961 −15.3763 26.6325i −0.496009 0.859113i
962962 5.50182 7.94425i 0.177386 0.256133i
963963 4.23469 + 15.8041i 0.136461 + 0.509279i
964964 6.76975 + 18.0195i 0.218039 + 0.580370i
965965 6.34879 + 2.52378i 0.204375 + 0.0812435i
966966 0 0
967967 28.7327 + 28.7327i 0.923981 + 0.923981i 0.997308 0.0733272i 0.0233617π-0.0233617\pi
−0.0733272 + 0.997308i 0.523362π0.523362\pi
968968 4.51520 + 15.8655i 0.145124 + 0.509935i
969969 −3.76725 2.17502i −0.121022 0.0698718i
970970 2.70786 + 4.07313i 0.0869443 + 0.130780i
971971 18.8837 10.9025i 0.606006 0.349878i −0.165394 0.986227i 0.552890π-0.552890\pi
0.771401 + 0.636350i 0.219556π0.219556\pi
972972 −66.9801 + 47.9365i −2.14839 + 1.53756i
973973 0 0
974974 −5.33852 6.29601i −0.171057 0.201737i
975975 −31.0368 7.36988i −0.993974 0.236025i
976976 30.1607 26.3863i 0.965421 0.844606i
977977 5.90126 + 22.0238i 0.188798 + 0.704604i 0.993785 + 0.111312i 0.0355053π0.0355053\pi
−0.804987 + 0.593292i 0.797828π0.797828\pi
978978 −55.6999 + 26.3237i −1.78109 + 0.841738i
979979 9.07390 0.290003
980980 0 0
981981 72.3799 2.31091
982982 −5.80051 + 2.74131i −0.185102 + 0.0874787i
983983 2.51085 + 9.37063i 0.0800838 + 0.298877i 0.994338 0.106264i 0.0338890π-0.0338890\pi
−0.914254 + 0.405141i 0.867222π0.867222\pi
984984 −0.460914 29.8045i −0.0146934 0.950134i
985985 −20.2018 + 2.95472i −0.643683 + 0.0941452i
986986 1.29300 + 1.52490i 0.0411774 + 0.0485627i
987987 0 0
988988 −15.7310 21.9804i −0.500470 0.699290i
989989 11.9426 6.89505i 0.379752 0.219250i
990990 10.8543 53.9109i 0.344971 1.71340i
991991 21.7531 + 12.5591i 0.691009 + 0.398954i 0.803990 0.594643i 0.202707π-0.202707\pi
−0.112981 + 0.993597i 0.536040π0.536040\pi
992992 2.79595 0.317404i 0.0887715 0.0100776i
993993 66.9288 + 66.9288i 2.12392 + 2.12392i
994994 0 0
995995 −30.7364 + 13.2506i −0.974408 + 0.420072i
996996 5.11391 1.92124i 0.162041 0.0608769i
997997 −1.72506 6.43800i −0.0546331 0.203894i 0.933214 0.359320i 0.116991π-0.116991\pi
−0.987847 + 0.155427i 0.950325π0.950325\pi
998998 −26.0342 + 37.5916i −0.824098 + 1.18994i
999999 26.5173 + 45.9293i 0.838970 + 1.45314i
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 980.2.x.n.263.18 112
4.3 odd 2 inner 980.2.x.n.263.23 112
5.2 odd 4 inner 980.2.x.n.67.6 112
7.2 even 3 inner 980.2.x.n.863.21 112
7.3 odd 6 980.2.k.m.883.1 yes 56
7.4 even 3 980.2.k.m.883.2 yes 56
7.5 odd 6 inner 980.2.x.n.863.22 112
7.6 odd 2 inner 980.2.x.n.263.17 112
20.7 even 4 inner 980.2.x.n.67.21 112
28.3 even 6 980.2.k.m.883.18 yes 56
28.11 odd 6 980.2.k.m.883.17 yes 56
28.19 even 6 inner 980.2.x.n.863.5 112
28.23 odd 6 inner 980.2.x.n.863.6 112
28.27 even 2 inner 980.2.x.n.263.24 112
35.2 odd 12 inner 980.2.x.n.667.23 112
35.12 even 12 inner 980.2.x.n.667.24 112
35.17 even 12 980.2.k.m.687.18 yes 56
35.27 even 4 inner 980.2.x.n.67.5 112
35.32 odd 12 980.2.k.m.687.17 yes 56
140.27 odd 4 inner 980.2.x.n.67.22 112
140.47 odd 12 inner 980.2.x.n.667.17 112
140.67 even 12 980.2.k.m.687.2 yes 56
140.87 odd 12 980.2.k.m.687.1 56
140.107 even 12 inner 980.2.x.n.667.18 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
980.2.k.m.687.1 56 140.87 odd 12
980.2.k.m.687.2 yes 56 140.67 even 12
980.2.k.m.687.17 yes 56 35.32 odd 12
980.2.k.m.687.18 yes 56 35.17 even 12
980.2.k.m.883.1 yes 56 7.3 odd 6
980.2.k.m.883.2 yes 56 7.4 even 3
980.2.k.m.883.17 yes 56 28.11 odd 6
980.2.k.m.883.18 yes 56 28.3 even 6
980.2.x.n.67.5 112 35.27 even 4 inner
980.2.x.n.67.6 112 5.2 odd 4 inner
980.2.x.n.67.21 112 20.7 even 4 inner
980.2.x.n.67.22 112 140.27 odd 4 inner
980.2.x.n.263.17 112 7.6 odd 2 inner
980.2.x.n.263.18 112 1.1 even 1 trivial
980.2.x.n.263.23 112 4.3 odd 2 inner
980.2.x.n.263.24 112 28.27 even 2 inner
980.2.x.n.667.17 112 140.47 odd 12 inner
980.2.x.n.667.18 112 140.107 even 12 inner
980.2.x.n.667.23 112 35.2 odd 12 inner
980.2.x.n.667.24 112 35.12 even 12 inner
980.2.x.n.863.5 112 28.19 even 6 inner
980.2.x.n.863.6 112 28.23 odd 6 inner
980.2.x.n.863.21 112 7.2 even 3 inner
980.2.x.n.863.22 112 7.5 odd 6 inner