Properties

Label 261.2.o.b.154.1
Level 261261
Weight 22
Character 261.154
Analytic conductor 2.0842.084
Analytic rank 00
Dimension 2424
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [261,2,Mod(64,261)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(261, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("261.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 261=3229 261 = 3^{2} \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 261.o (of order 1414, degree 66, 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: 2.084095492762.08409549276
Analytic rank: 00
Dimension: 2424
Relative dimension: 44 over Q(ζ14)\Q(\zeta_{14})
Twist minimal: no (minimal twist has level 87)
Sato-Tate group: SU(2)[C14]\mathrm{SU}(2)[C_{14}]

Embedding invariants

Embedding label 154.1
Character χ\chi == 261.154
Dual form 261.2.o.b.100.1

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+(1.006952.09096i)q2+(2.11117+2.64732i)q4+(1.71239+0.824646i)q5+(2.132592.67418i)q7+(3.13608+0.715791i)q8+(3.44860+2.75017i)q10+(0.806696+0.184123i)q11+(1.20608+5.28419i)q13+(3.44418+7.15191i)q14+(0.1542630.675869i)q16+6.71892iq17+(3.451462.75245i)q19+(1.432056.27423i)q20+(1.19730+1.50136i)q22+(0.139227+0.0670480i)q23+(0.865194+1.08492i)q25+(9.834567.84280i)q26+11.5817q28+(5.066761.82425i)q29+(2.487815.16599i)q31+(3.772013.00808i)q32+(14.04906.76563i)q34+(5.85708+2.82062i)q35+(9.490712.16619i)q37+(2.27980+9.98844i)q38+(5.96049+1.36044i)q405.43514iq41+(1.93772+4.02372i)q43+(1.215642.52430i)q440.358631iq46+(1.186720.270862i)q47+(1.04566+4.58133i)q49+(3.13973+0.716622i)q50+(16.53527.96294i)q52+(0.4199090.202218i)q53+(1.229550.980530i)q55+(4.773829.91293i)q56+(1.28756+12.4313i)q5811.5925q59+(8.771896.99535i)q61+(8.29676+10.4038i)q62+(11.33725.45970i)q64+(6.422888.05404i)q65+(2.88159+12.6251i)q67+(17.787114.1848i)q6815.0871iq70+(0.7505853.28853i)q71+(0.425383+0.883317i)q73+(5.02727+22.0259i)q74+(14.57323.32625i)q76+(2.21273+1.76459i)q77+(4.74548+1.08313i)q79+(0.821511+1.03014i)q80+(11.3647+5.47293i)q82+(4.818476.04218i)q83+(5.5407311.5054i)q85+10.3646q862.66166q88+(2.020754.19613i)q89+(11.558814.4943i)q91+(0.471429+0.227028i)q92+(1.761332.20864i)q94+(8.18006+1.86705i)q95+(7.82946+6.24379i)q97+(10.63232.42675i)q98+O(q100)q+(-1.00695 - 2.09096i) q^{2} +(-2.11117 + 2.64732i) q^{4} +(-1.71239 + 0.824646i) q^{5} +(-2.13259 - 2.67418i) q^{7} +(3.13608 + 0.715791i) q^{8} +(3.44860 + 2.75017i) q^{10} +(-0.806696 + 0.184123i) q^{11} +(1.20608 + 5.28419i) q^{13} +(-3.44418 + 7.15191i) q^{14} +(-0.154263 - 0.675869i) q^{16} +6.71892i q^{17} +(-3.45146 - 2.75245i) q^{19} +(1.43205 - 6.27423i) q^{20} +(1.19730 + 1.50136i) q^{22} +(0.139227 + 0.0670480i) q^{23} +(-0.865194 + 1.08492i) q^{25} +(9.83456 - 7.84280i) q^{26} +11.5817 q^{28} +(-5.06676 - 1.82425i) q^{29} +(-2.48781 - 5.16599i) q^{31} +(3.77201 - 3.00808i) q^{32} +(14.0490 - 6.76563i) q^{34} +(5.85708 + 2.82062i) q^{35} +(-9.49071 - 2.16619i) q^{37} +(-2.27980 + 9.98844i) q^{38} +(-5.96049 + 1.36044i) q^{40} -5.43514i q^{41} +(-1.93772 + 4.02372i) q^{43} +(1.21564 - 2.52430i) q^{44} -0.358631i q^{46} +(1.18672 - 0.270862i) q^{47} +(-1.04566 + 4.58133i) q^{49} +(3.13973 + 0.716622i) q^{50} +(-16.5352 - 7.96294i) q^{52} +(0.419909 - 0.202218i) q^{53} +(1.22955 - 0.980530i) q^{55} +(-4.77382 - 9.91293i) q^{56} +(1.28756 + 12.4313i) q^{58} -11.5925 q^{59} +(8.77189 - 6.99535i) q^{61} +(-8.29676 + 10.4038i) q^{62} +(-11.3372 - 5.45970i) q^{64} +(-6.42288 - 8.05404i) q^{65} +(-2.88159 + 12.6251i) q^{67} +(-17.7871 - 14.1848i) q^{68} -15.0871i q^{70} +(-0.750585 - 3.28853i) q^{71} +(-0.425383 + 0.883317i) q^{73} +(5.02727 + 22.0259i) q^{74} +(14.5732 - 3.32625i) q^{76} +(2.21273 + 1.76459i) q^{77} +(4.74548 + 1.08313i) q^{79} +(0.821511 + 1.03014i) q^{80} +(-11.3647 + 5.47293i) q^{82} +(4.81847 - 6.04218i) q^{83} +(-5.54073 - 11.5054i) q^{85} +10.3646 q^{86} -2.66166 q^{88} +(-2.02075 - 4.19613i) q^{89} +(11.5588 - 14.4943i) q^{91} +(-0.471429 + 0.227028i) q^{92} +(-1.76133 - 2.20864i) q^{94} +(8.18006 + 1.86705i) q^{95} +(7.82946 + 6.24379i) q^{97} +(10.6323 - 2.42675i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q2q4+4q5+8q7+28q1110q1322q16+20q20+4q2218q2318q2528q26+8q2828q29+28q31+14q32+34q3428q37+4q38++42q98+O(q100) 24 q - 2 q^{4} + 4 q^{5} + 8 q^{7} + 28 q^{11} - 10 q^{13} - 22 q^{16} + 20 q^{20} + 4 q^{22} - 18 q^{23} - 18 q^{25} - 28 q^{26} + 8 q^{28} - 28 q^{29} + 28 q^{31} + 14 q^{32} + 34 q^{34} - 28 q^{37} + 4 q^{38}+ \cdots + 42 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/261Z)×\left(\mathbb{Z}/261\mathbb{Z}\right)^\times.

nn 118118 146146
χ(n)\chi(n) e(514)e\left(\frac{5}{14}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.00695 2.09096i −0.712022 1.47853i −0.871018 0.491251i 0.836540π-0.836540\pi
0.158996 0.987279i 0.449174π-0.449174\pi
33 0 0
44 −2.11117 + 2.64732i −1.05558 + 1.32366i
55 −1.71239 + 0.824646i −0.765806 + 0.368793i −0.775654 0.631159i 0.782580π-0.782580\pi
0.00984749 + 0.999952i 0.496865π0.496865\pi
66 0 0
77 −2.13259 2.67418i −0.806042 1.01074i −0.999560 0.0296476i 0.990561π-0.990561\pi
0.193519 0.981097i 0.438010π-0.438010\pi
88 3.13608 + 0.715791i 1.10877 + 0.253070i
99 0 0
1010 3.44860 + 2.75017i 1.09054 + 0.869679i
1111 −0.806696 + 0.184123i −0.243228 + 0.0555152i −0.342397 0.939555i 0.611239π-0.611239\pi
0.0991689 + 0.995071i 0.468382π0.468382\pi
1212 0 0
1313 1.20608 + 5.28419i 0.334507 + 1.46557i 0.810301 + 0.586015i 0.199304π0.199304\pi
−0.475793 + 0.879557i 0.657839π0.657839\pi
1414 −3.44418 + 7.15191i −0.920496 + 1.91143i
1515 0 0
1616 −0.154263 0.675869i −0.0385657 0.168967i
1717 6.71892i 1.62958i 0.579758 + 0.814788i 0.303147π0.303147\pi
−0.579758 + 0.814788i 0.696853π0.696853\pi
1818 0 0
1919 −3.45146 2.75245i −0.791819 0.631455i 0.141729 0.989905i 0.454734π-0.454734\pi
−0.933549 + 0.358451i 0.883305π0.883305\pi
2020 1.43205 6.27423i 0.320217 1.40296i
2121 0 0
2222 1.19730 + 1.50136i 0.255265 + 0.320092i
2323 0.139227 + 0.0670480i 0.0290308 + 0.0139805i 0.448343 0.893862i 0.352014π-0.352014\pi
−0.419312 + 0.907842i 0.637729π0.637729\pi
2424 0 0
2525 −0.865194 + 1.08492i −0.173039 + 0.216984i
2626 9.83456 7.84280i 1.92871 1.53810i
2727 0 0
2828 11.5817 2.18873
2929 −5.06676 1.82425i −0.940875 0.338755i
3030 0 0
3131 −2.48781 5.16599i −0.446824 0.927840i −0.995761 0.0919761i 0.970682π-0.970682\pi
0.548937 0.835864i 0.315033π-0.315033\pi
3232 3.77201 3.00808i 0.666804 0.531758i
3333 0 0
3434 14.0490 6.76563i 2.40938 1.16030i
3535 5.85708 + 2.82062i 0.990027 + 0.476772i
3636 0 0
3737 −9.49071 2.16619i −1.56026 0.356120i −0.646677 0.762764i 0.723842π-0.723842\pi
−0.913587 + 0.406644i 0.866699π0.866699\pi
3838 −2.27980 + 9.98844i −0.369832 + 1.62034i
3939 0 0
4040 −5.96049 + 1.36044i −0.942436 + 0.215105i
4141 5.43514i 0.848827i −0.905469 0.424413i 0.860480π-0.860480\pi
0.905469 0.424413i 0.139520π-0.139520\pi
4242 0 0
4343 −1.93772 + 4.02372i −0.295500 + 0.613612i −0.994872 0.101146i 0.967749π-0.967749\pi
0.699372 + 0.714758i 0.253463π0.253463\pi
4444 1.21564 2.52430i 0.183264 0.380553i
4545 0 0
4646 0.358631i 0.0528772i
4747 1.18672 0.270862i 0.173101 0.0395092i −0.135092 0.990833i 0.543133π-0.543133\pi
0.308193 + 0.951324i 0.400276π0.400276\pi
4848 0 0
4949 −1.04566 + 4.58133i −0.149380 + 0.654476i
5050 3.13973 + 0.716622i 0.444024 + 0.101346i
5151 0 0
5252 −16.5352 7.96294i −2.29302 1.10426i
5353 0.419909 0.202218i 0.0576790 0.0277767i −0.404822 0.914396i 0.632666π-0.632666\pi
0.462501 + 0.886619i 0.346952π0.346952\pi
5454 0 0
5555 1.22955 0.980530i 0.165792 0.132215i
5656 −4.77382 9.91293i −0.637928 1.32467i
5757 0 0
5858 1.28756 + 12.4313i 0.169064 + 1.63231i
5959 −11.5925 −1.50921 −0.754605 0.656179i 0.772172π-0.772172\pi
−0.754605 + 0.656179i 0.772172π0.772172\pi
6060 0 0
6161 8.77189 6.99535i 1.12312 0.895662i 0.127757 0.991805i 0.459222π-0.459222\pi
0.995368 + 0.0961432i 0.0306507π0.0306507\pi
6262 −8.29676 + 10.4038i −1.05369 + 1.32129i
6363 0 0
6464 −11.3372 5.45970i −1.41715 0.682463i
6565 −6.42288 8.05404i −0.796660 0.998980i
6666 0 0
6767 −2.88159 + 12.6251i −0.352042 + 1.54240i 0.420415 + 0.907332i 0.361885π0.361885\pi
−0.772457 + 0.635067i 0.780973π0.780973\pi
6868 −17.7871 14.1848i −2.15701 1.72016i
6969 0 0
7070 15.0871i 1.80326i
7171 −0.750585 3.28853i −0.0890780 0.390276i 0.910660 0.413156i 0.135574π-0.135574\pi
−0.999738 + 0.0228799i 0.992716π0.992716\pi
7272 0 0
7373 −0.425383 + 0.883317i −0.0497873 + 0.103384i −0.924378 0.381477i 0.875416π-0.875416\pi
0.874591 + 0.484861i 0.161130π0.161130\pi
7474 5.02727 + 22.0259i 0.584409 + 2.56046i
7575 0 0
7676 14.5732 3.32625i 1.67167 0.381547i
7777 2.21273 + 1.76459i 0.252164 + 0.201094i
7878 0 0
7979 4.74548 + 1.08313i 0.533909 + 0.121861i 0.480971 0.876737i 0.340284π-0.340284\pi
0.0529379 + 0.998598i 0.483141π0.483141\pi
8080 0.821511 + 1.03014i 0.0918477 + 0.115173i
8181 0 0
8282 −11.3647 + 5.47293i −1.25502 + 0.604384i
8383 4.81847 6.04218i 0.528896 0.663215i −0.443575 0.896237i 0.646290π-0.646290\pi
0.972471 + 0.233022i 0.0748615π0.0748615\pi
8484 0 0
8585 −5.54073 11.5054i −0.600976 1.24794i
8686 10.3646 1.11765
8787 0 0
8888 −2.66166 −0.283734
8989 −2.02075 4.19613i −0.214199 0.444789i 0.765990 0.642852i 0.222249π-0.222249\pi
−0.980189 + 0.198063i 0.936535π0.936535\pi
9090 0 0
9191 11.5588 14.4943i 1.21169 1.51941i
9292 −0.471429 + 0.227028i −0.0491498 + 0.0236693i
9393 0 0
9494 −1.76133 2.20864i −0.181668 0.227804i
9595 8.18006 + 1.86705i 0.839256 + 0.191555i
9696 0 0
9797 7.82946 + 6.24379i 0.794961 + 0.633960i 0.934382 0.356273i 0.115953π-0.115953\pi
−0.139421 + 0.990233i 0.544524π0.544524\pi
9898 10.6323 2.42675i 1.07402 0.245139i
9999 0 0
100100 −1.04556 4.58089i −0.104556 0.458089i
101101 −6.58733 + 13.6787i −0.655463 + 1.36108i 0.262698 + 0.964878i 0.415388π0.415388\pi
−0.918162 + 0.396206i 0.870327π0.870327\pi
102102 0 0
103103 −0.0464759 0.203624i −0.00457941 0.0200637i 0.972587 0.232541i 0.0747040π-0.0747040\pi
−0.977166 + 0.212477i 0.931847π0.931847\pi
104104 17.4350i 1.70964i
105105 0 0
106106 −0.845657 0.674389i −0.0821375 0.0655025i
107107 −0.572801 + 2.50960i −0.0553747 + 0.242613i −0.995039 0.0994854i 0.968280π-0.968280\pi
0.939664 + 0.342098i 0.111137π0.111137\pi
108108 0 0
109109 0.718366 + 0.900802i 0.0688070 + 0.0862812i 0.815044 0.579399i 0.196713π-0.196713\pi
−0.746237 + 0.665681i 0.768141π0.768141\pi
110110 −3.28834 1.58358i −0.313531 0.150988i
111111 0 0
112112 −1.47841 + 1.85387i −0.139697 + 0.175175i
113113 −3.40029 + 2.71164i −0.319872 + 0.255089i −0.770241 0.637753i 0.779864π-0.779864\pi
0.450369 + 0.892843i 0.351293π0.351293\pi
114114 0 0
115115 −0.293702 −0.0273878
116116 15.5262 9.56206i 1.44157 0.887815i
117117 0 0
118118 11.6731 + 24.2393i 1.07459 + 2.23141i
119119 17.9676 14.3287i 1.64709 1.31351i
120120 0 0
121121 −9.29380 + 4.47566i −0.844891 + 0.406878i
122122 −23.4598 11.2977i −2.12395 1.02284i
123123 0 0
124124 18.9282 + 4.32025i 1.69981 + 0.387970i
125125 2.70151 11.8361i 0.241631 1.05865i
126126 0 0
127127 0.379767 0.0866794i 0.0336989 0.00769155i −0.205638 0.978628i 0.565927π-0.565927\pi
0.239337 + 0.970937i 0.423070π0.423070\pi
128128 19.5541i 1.72835i
129129 0 0
130130 −10.3731 + 21.5400i −0.909782 + 1.88918i
131131 0.329927 0.685100i 0.0288258 0.0598575i −0.886059 0.463573i 0.846567π-0.846567\pi
0.914885 + 0.403716i 0.132281π0.132281\pi
132132 0 0
133133 15.0997i 1.30931i
134134 29.3001 6.68756i 2.53114 0.577717i
135135 0 0
136136 −4.80934 + 21.0711i −0.412397 + 1.80683i
137137 14.5588 + 3.32295i 1.24384 + 0.283899i 0.793285 0.608850i 0.208369π-0.208369\pi
0.450555 + 0.892749i 0.351226π0.351226\pi
138138 0 0
139139 −3.29720 1.58785i −0.279665 0.134679i 0.288794 0.957391i 0.406746π-0.406746\pi
−0.568459 + 0.822712i 0.692460π0.692460\pi
140140 −19.8324 + 9.55077i −1.67614 + 0.807187i
141141 0 0
142142 −6.12036 + 4.88083i −0.513609 + 0.409590i
143143 −1.94588 4.04067i −0.162723 0.337898i
144144 0 0
145145 10.1807 1.05445i 0.845458 0.0875671i
146146 2.27532 0.188307
147147 0 0
148148 25.7711 20.5518i 2.11837 1.68935i
149149 −9.67852 + 12.1365i −0.792896 + 0.994260i 0.206978 + 0.978346i 0.433637π0.433637\pi
−0.999873 + 0.0159140i 0.994934π0.994934\pi
150150 0 0
151151 5.93334 + 2.85734i 0.482848 + 0.232527i 0.659441 0.751757i 0.270793π-0.270793\pi
−0.176593 + 0.984284i 0.556507π0.556507\pi
152152 −8.85390 11.1024i −0.718146 0.900526i
153153 0 0
154154 1.46157 6.40357i 0.117777 0.516015i
155155 8.52023 + 6.79466i 0.684361 + 0.545760i
156156 0 0
157157 10.0667i 0.803407i −0.915770 0.401704i 0.868418π-0.868418\pi
0.915770 0.401704i 0.131582π-0.131582\pi
158158 −2.51370 11.0133i −0.199980 0.876168i
159159 0 0
160160 −3.97857 + 8.26159i −0.314534 + 0.653136i
161161 −0.117614 0.515302i −0.00926931 0.0406115i
162162 0 0
163163 1.44138 0.328985i 0.112897 0.0257681i −0.165699 0.986176i 0.552988π-0.552988\pi
0.278596 + 0.960408i 0.410131π0.410131\pi
164164 14.3886 + 11.4745i 1.12356 + 0.896009i
165165 0 0
166166 −17.4859 3.99104i −1.35717 0.309765i
167167 7.77867 + 9.75414i 0.601931 + 0.754798i 0.985678 0.168640i 0.0539377π-0.0539377\pi
−0.383746 + 0.923439i 0.625366π0.625366\pi
168168 0 0
169169 −14.7555 + 7.10586i −1.13504 + 0.546605i
170170 −18.4781 + 23.1708i −1.41721 + 1.77712i
171171 0 0
172172 −6.56123 13.6245i −0.500289 1.03886i
173173 2.64519 0.201110 0.100555 0.994931i 0.467938π-0.467938\pi
0.100555 + 0.994931i 0.467938π0.467938\pi
174174 0 0
175175 4.74636 0.358791
176176 0.248886 + 0.516817i 0.0187605 + 0.0389566i
177177 0 0
178178 −6.73914 + 8.45061i −0.505120 + 0.633400i
179179 −5.72859 + 2.75874i −0.428175 + 0.206198i −0.635544 0.772065i 0.719224π-0.719224\pi
0.207369 + 0.978263i 0.433510π0.433510\pi
180180 0 0
181181 −10.7455 13.4744i −0.798705 1.00154i −0.999759 0.0219643i 0.993008π-0.993008\pi
0.201054 0.979580i 0.435563π-0.435563\pi
182182 −41.9461 9.57391i −3.10925 0.709666i
183183 0 0
184184 0.388634 + 0.309925i 0.0286505 + 0.0228480i
185185 18.0382 4.11710i 1.32619 0.302695i
186186 0 0
187187 −1.23711 5.42012i −0.0904663 0.396359i
188188 −1.78831 + 3.71347i −0.130426 + 0.270833i
189189 0 0
190190 −4.33301 18.9842i −0.314350 1.37726i
191191 16.4482i 1.19015i −0.803671 0.595074i 0.797123π-0.797123\pi
0.803671 0.595074i 0.202877π-0.202877\pi
192192 0 0
193193 −9.77612 7.79620i −0.703701 0.561183i 0.204933 0.978776i 0.434302π-0.434302\pi
−0.908634 + 0.417593i 0.862874π0.862874\pi
194194 5.17160 22.6583i 0.371299 1.62677i
195195 0 0
196196 −9.92070 12.4402i −0.708621 0.888583i
197197 −12.7451 6.13771i −0.908050 0.437294i −0.0792604 0.996854i 0.525256π-0.525256\pi
−0.828790 + 0.559560i 0.810970π0.810970\pi
198198 0 0
199199 8.05509 10.1008i 0.571010 0.716024i −0.409540 0.912292i 0.634311π-0.634311\pi
0.980550 + 0.196268i 0.0628822π0.0628822\pi
200200 −3.48989 + 2.78310i −0.246773 + 0.196795i
201201 0 0
202202 35.2347 2.47911
203203 5.92694 + 17.4398i 0.415989 + 1.22403i
204204 0 0
205205 4.48207 + 9.30711i 0.313041 + 0.650037i
206206 −0.378970 + 0.302219i −0.0264041 + 0.0210566i
207207 0 0
208208 3.38537 1.63031i 0.234733 0.113041i
209209 3.29107 + 1.58490i 0.227648 + 0.109629i
210210 0 0
211211 13.4042 + 3.05943i 0.922787 + 0.210620i 0.657417 0.753527i 0.271649π-0.271649\pi
0.265369 + 0.964147i 0.414506π0.414506\pi
212212 −0.351164 + 1.53855i −0.0241181 + 0.105668i
213213 0 0
214214 5.82426 1.32935i 0.398138 0.0908724i
215215 8.48813i 0.578886i
216216 0 0
217217 −8.50931 + 17.6698i −0.577650 + 1.19950i
218218 1.16018 2.40914i 0.0785772 0.163167i
219219 0 0
220220 5.32507i 0.359016i
221221 −35.5041 + 8.10357i −2.38826 + 0.545105i
222222 0 0
223223 3.00379 13.1605i 0.201149 0.881291i −0.769090 0.639141i 0.779290π-0.779290\pi
0.970239 0.242150i 0.0778527π-0.0778527\pi
224224 −16.0883 3.67204i −1.07494 0.245349i
225225 0 0
226226 9.09384 + 4.37936i 0.604913 + 0.291311i
227227 −24.2997 + 11.7021i −1.61283 + 0.776698i −0.999910 0.0134459i 0.995720π-0.995720\pi
−0.612921 + 0.790144i 0.710006π0.710006\pi
228228 0 0
229229 8.53536 6.80672i 0.564032 0.449801i −0.299499 0.954097i 0.596819π-0.596819\pi
0.863531 + 0.504296i 0.168248π0.168248\pi
230230 0.295744 + 0.614118i 0.0195008 + 0.0404937i
231231 0 0
232232 −14.5840 9.34775i −0.957488 0.613710i
233233 5.48306 0.359207 0.179604 0.983739i 0.442518π-0.442518\pi
0.179604 + 0.983739i 0.442518π0.442518\pi
234234 0 0
235235 −1.80877 + 1.44245i −0.117991 + 0.0940949i
236236 24.4737 30.6890i 1.59310 1.99768i
237237 0 0
238238 −48.0531 23.1412i −3.11482 1.50002i
239239 0.474367 + 0.594838i 0.0306843 + 0.0384769i 0.796937 0.604063i 0.206452π-0.206452\pi
−0.766253 + 0.642539i 0.777881π0.777881\pi
240240 0 0
241241 −5.57063 + 24.4065i −0.358836 + 1.57216i 0.397263 + 0.917705i 0.369960π0.369960\pi
−0.756098 + 0.654458i 0.772897π0.772897\pi
242242 18.7168 + 14.9262i 1.20316 + 0.959490i
243243 0 0
244244 37.9904i 2.43208i
245245 −1.98739 8.70734i −0.126970 0.556292i
246246 0 0
247247 10.3817 21.5579i 0.660573 1.37169i
248248 −4.10422 17.9817i −0.260618 1.14184i
249249 0 0
250250 −27.4691 + 6.26964i −1.73730 + 0.396527i
251251 8.20753 + 6.54528i 0.518054 + 0.413135i 0.847304 0.531108i 0.178224π-0.178224\pi
−0.329249 + 0.944243i 0.606796π0.606796\pi
252252 0 0
253253 −0.124659 0.0284525i −0.00783722 0.00178879i
254254 −0.563650 0.706795i −0.0353666 0.0443483i
255255 0 0
256256 18.2123 8.77060i 1.13827 0.548162i
257257 0.169465 0.212503i 0.0105710 0.0132556i −0.776518 0.630095i 0.783016π-0.783016\pi
0.787089 + 0.616840i 0.211587π0.211587\pi
258258 0 0
259259 14.4470 + 29.9995i 0.897691 + 1.86408i
260260 34.8814 2.16325
261261 0 0
262262 −1.76474 −0.109026
263263 −3.18585 6.61549i −0.196448 0.407929i 0.779354 0.626584i 0.215547π-0.215547\pi
−0.975802 + 0.218655i 0.929833π0.929833\pi
264264 0 0
265265 −0.552293 + 0.692553i −0.0339271 + 0.0425432i
266266 31.5727 15.2046i 1.93585 0.932255i
267267 0 0
268268 −27.3391 34.2822i −1.67000 2.09412i
269269 29.2703 + 6.68076i 1.78464 + 0.407333i 0.981962 0.189077i 0.0605495π-0.0605495\pi
0.802680 + 0.596410i 0.203407π0.203407\pi
270270 0 0
271271 −0.137209 0.109421i −0.00833488 0.00664684i 0.619314 0.785144i 0.287411π-0.287411\pi
−0.627648 + 0.778497i 0.715982π0.715982\pi
272272 4.54111 1.03648i 0.275345 0.0628457i
273273 0 0
274274 −7.71185 33.7878i −0.465890 2.04120i
275275 0.498190 1.03450i 0.0300420 0.0623828i
276276 0 0
277277 −0.652185 2.85741i −0.0391860 0.171685i 0.951548 0.307499i 0.0994922π-0.0994922\pi
−0.990734 + 0.135814i 0.956635π0.956635\pi
278278 8.49318i 0.509387i
279279 0 0
280280 16.3493 + 13.0381i 0.977059 + 0.779178i
281281 −2.26831 + 9.93812i −0.135316 + 0.592858i 0.861112 + 0.508415i 0.169768π0.169768\pi
−0.996428 + 0.0844434i 0.973089π0.973089\pi
282282 0 0
283283 11.9907 + 15.0359i 0.712773 + 0.893789i 0.997905 0.0646996i 0.0206089π-0.0206089\pi
−0.285132 + 0.958488i 0.592038π0.592038\pi
284284 10.2904 + 4.95560i 0.610623 + 0.294061i
285285 0 0
286286 −6.48946 + 8.13752i −0.383730 + 0.481182i
287287 −14.5345 + 11.5909i −0.857947 + 0.684190i
288288 0 0
289289 −28.1439 −1.65552
290290 −12.4562 20.2256i −0.731456 1.18769i
291291 0 0
292292 −1.44037 2.99096i −0.0842912 0.175033i
293293 −8.69694 + 6.93558i −0.508081 + 0.405181i −0.843699 0.536817i 0.819626π-0.819626\pi
0.335618 + 0.941998i 0.391055π0.391055\pi
294294 0 0
295295 19.8509 9.55968i 1.15576 0.556586i
296296 −28.2131 13.5867i −1.63986 0.789713i
297297 0 0
298298 35.1227 + 8.01652i 2.03460 + 0.464385i
299299 −0.186376 + 0.816566i −0.0107784 + 0.0472232i
300300 0 0
301301 14.8925 3.39912i 0.858390 0.195922i
302302 15.2836i 0.879470i
303303 0 0
304304 −1.32786 + 2.75733i −0.0761581 + 0.158144i
305305 −9.25225 + 19.2125i −0.529782 + 1.10010i
306306 0 0
307307 3.09566i 0.176678i −0.996090 0.0883392i 0.971844π-0.971844\pi
0.996090 0.0883392i 0.0281559π-0.0281559\pi
308308 −9.34288 + 2.13245i −0.532360 + 0.121508i
309309 0 0
310310 5.62787 24.6573i 0.319642 1.40044i
311311 14.2761 + 3.25843i 0.809523 + 0.184768i 0.607199 0.794550i 0.292293π-0.292293\pi
0.202325 + 0.979318i 0.435150π0.435150\pi
312312 0 0
313313 6.02573 + 2.90184i 0.340594 + 0.164022i 0.596360 0.802717i 0.296613π-0.296613\pi
−0.255765 + 0.966739i 0.582327π0.582327\pi
314314 −21.0490 + 10.1366i −1.18786 + 0.572044i
315315 0 0
316316 −12.8859 + 10.2762i −0.724889 + 0.578080i
317317 2.41609 + 5.01705i 0.135701 + 0.281786i 0.957735 0.287653i 0.0928749π-0.0928749\pi
−0.822034 + 0.569439i 0.807161π0.807161\pi
318318 0 0
319319 4.42323 + 0.538708i 0.247653 + 0.0301619i
320320 23.9161 1.33695
321321 0 0
322322 −0.959043 + 0.764811i −0.0534454 + 0.0426213i
323323 18.4935 23.1901i 1.02900 1.29033i
324324 0 0
325325 −6.77641 3.26335i −0.375888 0.181018i
326326 −2.13929 2.68259i −0.118484 0.148575i
327327 0 0
328328 3.89043 17.0451i 0.214813 0.941157i
329329 −3.25512 2.59587i −0.179461 0.143115i
330330 0 0
331331 34.6315i 1.90352i 0.306847 + 0.951759i 0.400726π0.400726\pi
−0.306847 + 0.951759i 0.599274π0.599274\pi
332332 5.82297 + 25.5121i 0.319577 + 1.40016i
333333 0 0
334334 12.5627 26.0868i 0.687403 1.42741i
335335 −5.47680 23.9954i −0.299229 1.31101i
336336 0 0
337337 8.60703 1.96450i 0.468855 0.107013i 0.0184351 0.999830i 0.494132π-0.494132\pi
0.450419 + 0.892817i 0.351274π0.351274\pi
338338 29.7161 + 23.6978i 1.61634 + 1.28899i
339339 0 0
340340 42.1560 + 9.62184i 2.28623 + 0.521818i
341341 2.95809 + 3.70932i 0.160189 + 0.200871i
342342 0 0
343343 −7.09048 + 3.41460i −0.382850 + 0.184371i
344344 −8.95700 + 11.2317i −0.482929 + 0.605574i
345345 0 0
346346 −2.66358 5.53098i −0.143195 0.297347i
347347 −16.3136 −0.875759 −0.437880 0.899034i 0.644270π-0.644270\pi
−0.437880 + 0.899034i 0.644270π0.644270\pi
348348 0 0
349349 −9.44632 −0.505650 −0.252825 0.967512i 0.581360π-0.581360\pi
−0.252825 + 0.967512i 0.581360π0.581360\pi
350350 −4.77936 9.92444i −0.255468 0.530484i
351351 0 0
352352 −2.48901 + 3.12112i −0.132665 + 0.166356i
353353 13.4827 6.49294i 0.717613 0.345584i −0.0391859 0.999232i 0.512476π-0.512476\pi
0.756799 + 0.653648i 0.226762π0.226762\pi
354354 0 0
355355 3.99717 + 5.01229i 0.212148 + 0.266025i
356356 15.3747 + 3.50917i 0.814856 + 0.185986i
357357 0 0
358358 11.5368 + 9.20031i 0.609740 + 0.486252i
359359 −15.0352 + 3.43168i −0.793527 + 0.181117i −0.600024 0.799982i 0.704842π-0.704842\pi
−0.193503 + 0.981100i 0.561985π0.561985\pi
360360 0 0
361361 0.108713 + 0.476304i 0.00572175 + 0.0250686i
362362 −17.3542 + 36.0364i −0.912118 + 1.89403i
363363 0 0
364364 13.9684 + 61.1997i 0.732145 + 3.20774i
365365 1.86338i 0.0975336i
366366 0 0
367367 −26.0706 20.7906i −1.36088 1.08526i −0.987506 0.157580i 0.949631π-0.949631\pi
−0.373370 0.927683i 0.621798π-0.621798\pi
368368 0.0238382 0.104442i 0.00124265 0.00544441i
369369 0 0
370370 −26.7723 33.5714i −1.39182 1.74529i
371371 −1.43626 0.691666i −0.0745668 0.0359095i
372372 0 0
373373 −2.02994 + 2.54547i −0.105106 + 0.131799i −0.831602 0.555371i 0.812576π-0.812576\pi
0.726496 + 0.687171i 0.241148π0.241148\pi
374374 −10.0875 + 8.04454i −0.521614 + 0.415973i
375375 0 0
376376 3.91554 0.201929
377377 3.52876 28.9740i 0.181741 1.49224i
378378 0 0
379379 −11.2522 23.3653i −0.577984 1.20020i −0.961024 0.276465i 0.910837π-0.910837\pi
0.383040 0.923732i 0.374877π-0.374877\pi
380380 −22.2122 + 17.7136i −1.13946 + 0.908689i
381381 0 0
382382 −34.3924 + 16.5625i −1.75967 + 0.847412i
383383 −26.6637 12.8406i −1.36245 0.656123i −0.397272 0.917701i 0.630043π-0.630043\pi
−0.965182 + 0.261578i 0.915757π0.915757\pi
384384 0 0
385385 −5.24422 1.19696i −0.267270 0.0610027i
386386 −6.45743 + 28.2918i −0.328675 + 1.44002i
387387 0 0
388388 −33.0586 + 7.54542i −1.67830 + 0.383061i
389389 11.6584i 0.591103i 0.955327 + 0.295551i 0.0955033π0.0955033\pi
−0.955327 + 0.295551i 0.904497π0.904497\pi
390390 0 0
391391 −0.450490 + 0.935452i −0.0227823 + 0.0473078i
392392 −6.55855 + 13.6190i −0.331257 + 0.687862i
393393 0 0
394394 32.8298i 1.65394i
395395 −9.01934 + 2.05861i −0.453812 + 0.103580i
396396 0 0
397397 −4.79777 + 21.0204i −0.240793 + 1.05498i 0.699504 + 0.714628i 0.253404π0.253404\pi
−0.940297 + 0.340354i 0.889453π0.889453\pi
398398 −29.2314 6.67187i −1.46524 0.334430i
399399 0 0
400400 0.866730 + 0.417395i 0.0433365 + 0.0208697i
401401 18.0240 8.67991i 0.900077 0.433454i 0.0741601 0.997246i 0.476372π-0.476372\pi
0.825917 + 0.563792i 0.190658π0.190658\pi
402402 0 0
403403 24.2976 19.3767i 1.21035 0.965222i
404404 −22.3050 46.3169i −1.10972 2.30435i
405405 0 0
406406 30.4977 29.9540i 1.51358 1.48659i
407407 8.05497 0.399270
408408 0 0
409409 −22.2527 + 17.7460i −1.10033 + 0.877482i −0.993160 0.116759i 0.962749π-0.962749\pi
−0.107167 + 0.994241i 0.534178π0.534178\pi
410410 14.9475 18.7436i 0.738207 0.925682i
411411 0 0
412412 0.637178 + 0.306849i 0.0313915 + 0.0151173i
413413 24.7219 + 31.0003i 1.21649 + 1.52543i
414414 0 0
415415 −3.26848 + 14.3201i −0.160443 + 0.702947i
416416 20.4446 + 16.3040i 1.00238 + 0.799372i
417417 0 0
418418 8.47740i 0.414643i
419419 −2.46307 10.7914i −0.120329 0.527196i −0.998781 0.0493649i 0.984280π-0.984280\pi
0.878452 0.477831i 0.158577π-0.158577\pi
420420 0 0
421421 −11.6154 + 24.1196i −0.566099 + 1.17552i 0.399802 + 0.916602i 0.369079π0.369079\pi
−0.965900 + 0.258914i 0.916635π0.916635\pi
422422 −7.10029 31.1084i −0.345637 1.51433i
423423 0 0
424424 1.46162 0.333605i 0.0709824 0.0162013i
425425 −7.28948 5.81316i −0.353592 0.281980i
426426 0 0
427427 −37.4136 8.53941i −1.81057 0.413251i
428428 −5.43445 6.81459i −0.262684 0.329396i
429429 0 0
430430 −17.7483 + 8.54714i −0.855900 + 0.412180i
431431 −20.6592 + 25.9059i −0.995120 + 1.24784i −0.0264091 + 0.999651i 0.508407π0.508407\pi
−0.968711 + 0.248190i 0.920164π0.920164\pi
432432 0 0
433433 −2.30859 4.79384i −0.110944 0.230377i 0.838103 0.545512i 0.183665π-0.183665\pi
−0.949047 + 0.315135i 0.897950π0.897950\pi
434434 45.5152 2.18480
435435 0 0
436436 −3.90131 −0.186839
437437 −0.295989 0.614628i −0.0141591 0.0294016i
438438 0 0
439439 19.4239 24.3568i 0.927053 1.16249i −0.0593651 0.998236i 0.518908π-0.518908\pi
0.986418 0.164252i 0.0525210π-0.0525210\pi
440440 4.55781 2.19493i 0.217285 0.104639i
441441 0 0
442442 52.6951 + 66.0776i 2.50645 + 3.14299i
443443 12.5788 + 2.87103i 0.597636 + 0.136407i 0.510629 0.859801i 0.329413π-0.329413\pi
0.0870071 + 0.996208i 0.472270π0.472270\pi
444444 0 0
445445 6.92065 + 5.51903i 0.328070 + 0.261627i
446446 −30.5427 + 6.97117i −1.44624 + 0.330094i
447447 0 0
448448 9.57731 + 41.9609i 0.452485 + 1.98247i
449449 14.6872 30.4983i 0.693132 1.43930i −0.195509 0.980702i 0.562636π-0.562636\pi
0.888642 0.458602i 0.151650π-0.151650\pi
450450 0 0
451451 1.00074 + 4.38451i 0.0471228 + 0.206458i
452452 14.7264i 0.692671i
453453 0 0
454454 48.9373 + 39.0262i 2.29674 + 1.83159i
455455 −7.84058 + 34.3518i −0.367572 + 1.61044i
456456 0 0
457457 4.76027 + 5.96919i 0.222676 + 0.279227i 0.880603 0.473855i 0.157138π-0.157138\pi
−0.657927 + 0.753082i 0.728566π0.728566\pi
458458 −22.8273 10.9930i −1.06665 0.513670i
459459 0 0
460460 0.620054 0.777523i 0.0289102 0.0362522i
461461 13.2633 10.5771i 0.617731 0.492624i −0.263908 0.964548i 0.585012π-0.585012\pi
0.881639 + 0.471924i 0.156440π0.156440\pi
462462 0 0
463463 −9.31660 −0.432979 −0.216490 0.976285i 0.569461π-0.569461\pi
−0.216490 + 0.976285i 0.569461π0.569461\pi
464464 −0.451342 + 3.70588i −0.0209530 + 0.172041i
465465 0 0
466466 −5.52118 11.4648i −0.255764 0.531099i
467467 19.8211 15.8068i 0.917212 0.731452i −0.0463531 0.998925i 0.514760π-0.514760\pi
0.963565 + 0.267473i 0.0861885π0.0861885\pi
468468 0 0
469469 39.9069 19.2182i 1.84273 0.887413i
470470 4.83744 + 2.32959i 0.223135 + 0.107456i
471471 0 0
472472 −36.3550 8.29778i −1.67337 0.381936i
473473 0.822293 3.60270i 0.0378091 0.165652i
474474 0 0
475475 5.97236 1.36315i 0.274031 0.0625458i
476476 77.8162i 3.56670i
477477 0 0
478478 0.766115 1.59086i 0.0350413 0.0727640i
479479 9.99005 20.7446i 0.456457 0.947843i −0.538024 0.842929i 0.680829π-0.680829\pi
0.994481 0.104914i 0.0334566π-0.0334566\pi
480480 0 0
481481 52.7634i 2.40580i
482482 56.6424 12.9282i 2.57999 0.588866i
483483 0 0
484484 7.77228 34.0526i 0.353285 1.54784i
485485 −18.5560 4.23530i −0.842586 0.192315i
486486 0 0
487487 −1.38231 0.665685i −0.0626384 0.0301651i 0.402302 0.915507i 0.368210π-0.368210\pi
−0.464941 + 0.885342i 0.653924π0.653924\pi
488488 32.5166 15.6592i 1.47196 0.708857i
489489 0 0
490490 −16.2055 + 12.9234i −0.732089 + 0.583821i
491491 8.74266 + 18.1543i 0.394551 + 0.819293i 0.999731 + 0.0232042i 0.00738680π0.00738680\pi
−0.605180 + 0.796089i 0.706899π0.706899\pi
492492 0 0
493493 12.2570 34.0432i 0.552027 1.53323i
494494 −55.5305 −2.49843
495495 0 0
496496 −3.10776 + 2.47835i −0.139542 + 0.111281i
497497 −7.19342 + 9.02026i −0.322669 + 0.404614i
498498 0 0
499499 31.2688 + 15.0583i 1.39978 + 0.674100i 0.973117 0.230309i 0.0739738π-0.0739738\pi
0.426666 + 0.904409i 0.359688π0.359688\pi
500500 25.6306 + 32.1398i 1.14624 + 1.43734i
501501 0 0
502502 5.42132 23.7524i 0.241966 1.06012i
503503 −22.5450 17.9790i −1.00523 0.801646i −0.0250384 0.999686i 0.507971π-0.507971\pi
−0.980194 + 0.198041i 0.936542π0.936542\pi
504504 0 0
505505 28.8556i 1.28406i
506506 0.0660322 + 0.289306i 0.00293549 + 0.0128612i
507507 0 0
508508 −0.572285 + 1.18836i −0.0253910 + 0.0527250i
509509 −0.690039 3.02326i −0.0305854 0.134004i 0.957330 0.288997i 0.0933216π-0.0933216\pi
−0.987916 + 0.154993i 0.950464π0.950464\pi
510510 0 0
511511 3.26931 0.746199i 0.144626 0.0330099i
512512 −6.10192 4.86612i −0.269669 0.215054i
513513 0 0
514514 −0.614978 0.140365i −0.0271255 0.00619122i
515515 0.247503 + 0.310359i 0.0109063 + 0.0136760i
516516 0 0
517517 −0.907452 + 0.437006i −0.0399097 + 0.0192195i
518518 48.1802 60.4160i 2.11691 2.65453i
519519 0 0
520520 −14.3777 29.8556i −0.630503 1.30925i
521521 −33.4475 −1.46536 −0.732680 0.680573i 0.761731π-0.761731\pi
−0.732680 + 0.680573i 0.761731π0.761731\pi
522522 0 0
523523 −23.5081 −1.02794 −0.513969 0.857809i 0.671825π-0.671825\pi
−0.513969 + 0.857809i 0.671825π0.671825\pi
524524 1.11715 + 2.31979i 0.0488029 + 0.101340i
525525 0 0
526526 −10.6247 + 13.3230i −0.463259 + 0.580909i
527527 34.7099 16.7154i 1.51199 0.728134i
528528 0 0
529529 −14.3254 17.9635i −0.622842 0.781020i
530530 2.00423 + 0.457453i 0.0870582 + 0.0198705i
531531 0 0
532532 −39.9737 31.8779i −1.73308 1.38208i
533533 28.7204 6.55523i 1.24402 0.283939i
534534 0 0
535535 −1.08867 4.76979i −0.0470675 0.206216i
536536 −18.0738 + 37.5307i −0.780671 + 1.62108i
537537 0 0
538538 −15.5046 67.9302i −0.668452 2.92868i
539539 3.88827i 0.167480i
540540 0 0
541541 25.6227 + 20.4334i 1.10161 + 0.878501i 0.993294 0.115616i 0.0368841π-0.0368841\pi
0.108312 + 0.994117i 0.465456π0.465456\pi
542542 −0.0906310 + 0.397081i −0.00389294 + 0.0170561i
543543 0 0
544544 20.2110 + 25.3438i 0.866541 + 1.08661i
545545 −1.97297 0.950132i −0.0845127 0.0406992i
546546 0 0
547547 −17.5465 + 22.0026i −0.750235 + 0.940765i −0.999618 0.0276401i 0.991201π-0.991201\pi
0.249383 + 0.968405i 0.419772π0.419772\pi
548548 −39.5330 + 31.5265i −1.68876 + 1.34675i
549549 0 0
550550 −2.66475 −0.113625
551551 12.4666 + 20.2423i 0.531094 + 0.862353i
552552 0 0
553553 −7.22368 15.0001i −0.307182 0.637870i
554554 −5.31800 + 4.24097i −0.225940 + 0.180181i
555555 0 0
556556 11.1645 5.37653i 0.473480 0.228016i
557557 11.9640 + 5.76157i 0.506932 + 0.244125i 0.669826 0.742518i 0.266369π-0.266369\pi
−0.162894 + 0.986644i 0.552083π0.552083\pi
558558 0 0
559559 −23.5992 5.38636i −0.998139 0.227819i
560560 1.00284 4.39373i 0.0423778 0.185669i
561561 0 0
562562 23.0643 5.26426i 0.972907 0.222060i
563563 12.5201i 0.527658i 0.964569 + 0.263829i 0.0849855π0.0849855\pi
−0.964569 + 0.263829i 0.915014π0.915014\pi
564564 0 0
565565 3.58649 7.44743i 0.150885 0.313316i
566566 19.3653 40.2124i 0.813983 1.69025i
567567 0 0
568568 10.8504i 0.455271i
569569 −12.6153 + 2.87936i −0.528860 + 0.120709i −0.478610 0.878028i 0.658859π-0.658859\pi
−0.0502506 + 0.998737i 0.516002π0.516002\pi
570570 0 0
571571 −4.56081 + 19.9822i −0.190864 + 0.836229i 0.785286 + 0.619133i 0.212516π0.212516\pi
−0.976150 + 0.217096i 0.930341π0.930341\pi
572572 14.8051 + 3.37916i 0.619030 + 0.141290i
573573 0 0
574574 38.8717 + 18.7196i 1.62247 + 0.781342i
575575 −0.193200 + 0.0930400i −0.00805698 + 0.00388004i
576576 0 0
577577 1.84202 1.46896i 0.0766841 0.0611536i −0.584398 0.811468i 0.698669π-0.698669\pi
0.661082 + 0.750314i 0.270098π0.270098\pi
578578 28.3395 + 58.8476i 1.17877 + 2.44774i
579579 0 0
580580 −18.7016 + 29.1776i −0.776544 + 1.21153i
581581 −26.4337 −1.09665
582582 0 0
583583 −0.301506 + 0.240443i −0.0124871 + 0.00995814i
584584 −1.96631 + 2.46567i −0.0813663 + 0.102030i
585585 0 0
586586 23.2594 + 11.2011i 0.960837 + 0.462715i
587587 −5.07686 6.36618i −0.209544 0.262760i 0.665942 0.746004i 0.268030π-0.268030\pi
−0.875486 + 0.483244i 0.839459π0.839459\pi
588588 0 0
589589 −5.63255 + 24.6778i −0.232085 + 1.01683i
590590 −39.9778 31.8812i −1.64586 1.31253i
591591 0 0
592592 6.74864i 0.277367i
593593 7.80289 + 34.1867i 0.320426 + 1.40388i 0.836797 + 0.547514i 0.184426π0.184426\pi
−0.516370 + 0.856365i 0.672717π0.672717\pi
594594 0 0
595595 −18.9515 + 39.3532i −0.776936 + 1.61333i
596596 −11.6962 51.2444i −0.479095 2.09905i
597597 0 0
598598 1.89508 0.432539i 0.0774954 0.0176878i
599599 −20.1222 16.0469i −0.822171 0.655659i 0.119261 0.992863i 0.461948π-0.461948\pi
−0.941432 + 0.337204i 0.890519π0.890519\pi
600600 0 0
601601 0.871592 + 0.198935i 0.0355530 + 0.00811473i 0.240260 0.970708i 0.422767π-0.422767\pi
−0.204707 + 0.978823i 0.565624π0.565624\pi
602602 −22.1034 27.7168i −0.900869 1.12965i
603603 0 0
604604 −20.0906 + 9.67512i −0.817475 + 0.393675i
605605 12.2238 15.3282i 0.496969 0.623180i
606606 0 0
607607 −1.84678 3.83488i −0.0749585 0.155653i 0.860122 0.510088i 0.170387π-0.170387\pi
−0.935080 + 0.354436i 0.884673π0.884673\pi
608608 −21.2985 −0.863769
609609 0 0
610610 49.4891 2.00375
611611 2.86257 + 5.94419i 0.115807 + 0.240476i
612612 0 0
613613 8.60900 10.7953i 0.347714 0.436020i −0.576964 0.816770i 0.695763π-0.695763\pi
0.924678 + 0.380750i 0.124334π0.124334\pi
614614 −6.47288 + 3.11718i −0.261224 + 0.125799i
615615 0 0
616616 5.67622 + 7.11775i 0.228701 + 0.286782i
617617 −4.99156 1.13929i −0.200953 0.0458662i 0.120860 0.992670i 0.461435π-0.461435\pi
−0.321812 + 0.946803i 0.604292π0.604292\pi
618618 0 0
619619 −31.5229 25.1387i −1.26701 1.01041i −0.998894 0.0470219i 0.985027π-0.985027\pi
−0.268118 0.963386i 0.586402π-0.586402\pi
620620 −35.9753 + 8.21113i −1.44480 + 0.329767i
621621 0 0
622622 −7.56212 33.1318i −0.303213 1.32846i
623623 −6.91178 + 14.3525i −0.276915 + 0.575019i
624624 0 0
625625 3.59062 + 15.7315i 0.143625 + 0.629261i
626626 15.5216i 0.620366i
627627 0 0
628628 26.6497 + 21.2524i 1.06344 + 0.848064i
629629 14.5545 63.7673i 0.580325 2.54257i
630630 0 0
631631 1.53439 + 1.92407i 0.0610832 + 0.0765959i 0.811434 0.584443i 0.198687π-0.198687\pi
−0.750351 + 0.661039i 0.770116π0.770116\pi
632632 14.1069 + 6.79355i 0.561144 + 0.270233i
633633 0 0
634634 8.05756 10.1039i 0.320007 0.401276i
635635 −0.578832 + 0.461603i −0.0229702 + 0.0183182i
636636 0 0
637637 −25.4698 −1.00915
638638 −3.32756 9.79123i −0.131739 0.387638i
639639 0 0
640640 −16.1252 33.4843i −0.637404 1.32358i
641641 −13.3801 + 10.6703i −0.528482 + 0.421450i −0.851041 0.525099i 0.824028π-0.824028\pi
0.322559 + 0.946549i 0.395457π0.395457\pi
642642 0 0
643643 −36.0341 + 17.3531i −1.42105 + 0.684340i −0.977309 0.211816i 0.932062π-0.932062\pi
−0.443738 + 0.896157i 0.646348π0.646348\pi
644644 1.61248 + 0.776527i 0.0635404 + 0.0305995i
645645 0 0
646646 −67.1115 15.3178i −2.64047 0.602669i
647647 −1.67703 + 7.34755i −0.0659308 + 0.288862i −0.997136 0.0756346i 0.975902π-0.975902\pi
0.931205 + 0.364496i 0.118759π0.118759\pi
648648 0 0
649649 9.35160 2.13444i 0.367082 0.0837841i
650650 17.4552i 0.684650i
651651 0 0
652652 −2.17206 + 4.51033i −0.0850645 + 0.176638i
653653 −17.3043 + 35.9328i −0.677170 + 1.40616i 0.224820 + 0.974400i 0.427821π0.427821\pi
−0.901990 + 0.431757i 0.857894π0.857894\pi
654654 0 0
655655 1.44524i 0.0564700i
656656 −3.67344 + 0.838440i −0.143424 + 0.0327356i
657657 0 0
658658 −2.15011 + 9.42023i −0.0838199 + 0.367239i
659659 −8.75482 1.99823i −0.341039 0.0778400i 0.0485712 0.998820i 0.484533π-0.484533\pi
−0.389610 + 0.920980i 0.627390π0.627390\pi
660660 0 0
661661 −22.0949 10.6403i −0.859390 0.413860i −0.0483357 0.998831i 0.515392π-0.515392\pi
−0.811054 + 0.584971i 0.801106π0.801106\pi
662662 72.4129 34.8722i 2.81441 1.35535i
663663 0 0
664664 19.4361 15.4998i 0.754266 0.601507i
665665 −12.4519 25.8566i −0.482863 1.00267i
666666 0 0
667667 −0.583116 0.593701i −0.0225783 0.0229882i
668668 −42.2444 −1.63449
669669 0 0
670670 −44.6585 + 35.6140i −1.72531 + 1.37589i
671671 −5.78824 + 7.25822i −0.223453 + 0.280201i
672672 0 0
673673 19.2378 + 9.26446i 0.741564 + 0.357119i 0.766221 0.642577i 0.222135π-0.222135\pi
−0.0246564 + 0.999696i 0.507849π0.507849\pi
674674 −12.7745 16.0188i −0.492057 0.617020i
675675 0 0
676676 12.3398 54.0642i 0.474608 2.07939i
677677 6.90970 + 5.51030i 0.265561 + 0.211778i 0.747213 0.664585i 0.231392π-0.231392\pi
−0.481652 + 0.876363i 0.659963π0.659963\pi
678678 0 0
679679 34.2528i 1.31450i
680680 −9.14070 40.0480i −0.350530 1.53577i
681681 0 0
682682 4.77738 9.92034i 0.182935 0.379869i
683683 7.09180 + 31.0712i 0.271360 + 1.18891i 0.908409 + 0.418083i 0.137298π0.137298\pi
−0.637049 + 0.770823i 0.719845π0.719845\pi
684684 0 0
685685 −27.6706 + 6.31564i −1.05724 + 0.241308i
686686 14.2795 + 11.3876i 0.545196 + 0.434779i
687687 0 0
688688 3.01843 + 0.688936i 0.115076 + 0.0262654i
689689 1.57500 + 1.97499i 0.0600028 + 0.0752412i
690690 0 0
691691 6.23726 3.00371i 0.237277 0.114266i −0.311467 0.950257i 0.600820π-0.600820\pi
0.548744 + 0.835990i 0.315106π0.315106\pi
692692 −5.58445 + 7.00267i −0.212289 + 0.266202i
693693 0 0
694694 16.4270 + 34.1110i 0.623560 + 1.29484i
695695 6.95551 0.263838
696696 0 0
697697 36.5183 1.38323
698698 9.51199 + 19.7518i 0.360034 + 0.747618i
699699 0 0
700700 −10.0204 + 12.5652i −0.378735 + 0.474918i
701701 −40.3171 + 19.4157i −1.52276 + 0.733321i −0.993359 0.115052i 0.963296π-0.963296\pi
−0.529398 + 0.848374i 0.677582π0.677582\pi
702702 0 0
703703 26.7945 + 33.5992i 1.01057 + 1.26722i
704704 10.1509 + 2.31688i 0.382577 + 0.0873208i
705705 0 0
706706 −27.1529 21.6537i −1.02191 0.814949i
707707 50.6274 11.5554i 1.90404 0.434584i
708708 0 0
709709 1.40825 + 6.16993i 0.0528878 + 0.231717i 0.994463 0.105086i 0.0335117π-0.0335117\pi
−0.941575 + 0.336802i 0.890655π0.890655\pi
710710 6.45552 13.4050i 0.242272 0.503082i
711711 0 0
712712 −3.33369 14.6059i −0.124935 0.547378i
713713 0.886046i 0.0331827i
714714 0 0
715715 6.66424 + 5.31456i 0.249229 + 0.198753i
716716 4.79074 20.9896i 0.179038 0.784418i
717717 0 0
718718 22.3152 + 27.9824i 0.832797 + 1.04429i
719719 41.6772 + 20.0707i 1.55430 + 0.748511i 0.996667 0.0815773i 0.0259958π-0.0259958\pi
0.557632 + 0.830088i 0.311710π0.311710\pi
720720 0 0
721721 −0.445413 + 0.558531i −0.0165881 + 0.0208008i
722722 0.886461 0.706929i 0.0329907 0.0263092i
723723 0 0
724724 58.3566 2.16881
725725 6.36290 3.91870i 0.236312 0.145537i
726726 0 0
727727 −9.14331 18.9863i −0.339107 0.704162i 0.659774 0.751464i 0.270652π-0.270652\pi
−0.998881 + 0.0473020i 0.984938π0.984938\pi
728728 46.6242 37.1816i 1.72801 1.37804i
729729 0 0
730730 −3.89624 + 1.87633i −0.144206 + 0.0694461i
731731 −27.0351 13.0194i −0.999928 0.481540i
732732 0 0
733733 30.5332 + 6.96900i 1.12777 + 0.257406i 0.745409 0.666607i 0.232254π-0.232254\pi
0.382360 + 0.924013i 0.375111π0.375111\pi
734734 −17.2205 + 75.4477i −0.635619 + 2.78483i
735735 0 0
736736 0.726850 0.165899i 0.0267920 0.00611511i
737737 10.7152i 0.394698i
738738 0 0
739739 20.2629 42.0764i 0.745383 1.54780i −0.0886328 0.996064i 0.528250π-0.528250\pi
0.834016 0.551740i 0.186036π-0.186036\pi
740740 −27.1824 + 56.4448i −0.999245 + 2.07495i
741741 0 0
742742 3.69963i 0.135818i
743743 7.43840 1.69777i 0.272889 0.0622850i −0.0838866 0.996475i 0.526733π-0.526733\pi
0.356775 + 0.934190i 0.383876π0.383876\pi
744744 0 0
745745 6.56515 28.7638i 0.240529 1.05382i
746746 7.36652 + 1.68136i 0.269707 + 0.0615590i
747747 0 0
748748 16.9606 + 8.16778i 0.620140 + 0.298643i
749749 7.93267 3.82017i 0.289854 0.139586i
750750 0 0
751751 −41.1510 + 32.8168i −1.50162 + 1.19750i −0.576923 + 0.816799i 0.695747π0.695747\pi
−0.924697 + 0.380703i 0.875682π0.875682\pi
752752 −0.366134 0.760285i −0.0133515 0.0277247i
753753 0 0
754754 −64.1366 + 21.7969i −2.33572 + 0.793796i
755755 −12.5165 −0.455522
756756 0 0
757757 13.7753 10.9854i 0.500671 0.399272i −0.340329 0.940306i 0.610539π-0.610539\pi
0.841000 + 0.541034i 0.181967π0.181967\pi
758758 −37.5255 + 47.0555i −1.36299 + 1.70913i
759759 0 0
760760 24.3169 + 11.7104i 0.882068 + 0.424782i
761761 0.853678 + 1.07048i 0.0309458 + 0.0388048i 0.797064 0.603895i 0.206386π-0.206386\pi
−0.766118 + 0.642700i 0.777814π0.777814\pi
762762 0 0
763763 0.876929 3.84208i 0.0317469 0.139092i
764764 43.5436 + 34.7249i 1.57535 + 1.25630i
765765 0 0
766766 68.6826i 2.48160i
767767 −13.9815 61.2568i −0.504842 2.21186i
768768 0 0
769769 −6.94776 + 14.4272i −0.250543 + 0.520257i −0.987871 0.155278i 0.950373π-0.950373\pi
0.737328 + 0.675535i 0.236087π0.236087\pi
770770 2.77789 + 12.1707i 0.100108 + 0.438602i
771771 0 0
772772 41.2781 9.42146i 1.48563 0.339086i
773773 −26.5907 21.2053i −0.956399 0.762703i 0.0150656 0.999887i 0.495204π-0.495204\pi
−0.971465 + 0.237184i 0.923776π0.923776\pi
774774 0 0
775775 7.75712 + 1.77051i 0.278644 + 0.0635987i
776776 20.0846 + 25.1853i 0.720995 + 0.904099i
777777 0 0
778778 24.3771 11.7394i 0.873963 0.420878i
779779 −14.9600 + 18.7592i −0.535996 + 0.672118i
780780 0 0
781781 1.21099 + 2.51464i 0.0433325 + 0.0899809i
782782 2.40961 0.0861675
783783 0 0
784784 3.25768 0.116346
785785 8.30143 + 17.2381i 0.296291 + 0.615254i
786786 0 0
787787 −31.1762 + 39.0937i −1.11131 + 1.39354i −0.201014 + 0.979588i 0.564424π0.564424\pi
−0.910298 + 0.413953i 0.864148π0.864148\pi
788788 43.1556 20.7826i 1.53735 0.740350i
789789 0 0
790790 13.3865 + 16.7861i 0.476270 + 0.597224i
791791 14.5028 + 3.31017i 0.515660 + 0.117696i
792792 0 0
793793 47.5444 + 37.9154i 1.68835 + 1.34641i
794794 48.7838 11.1346i 1.73127 0.395152i
795795 0 0
796796 9.73433 + 42.6489i 0.345024 + 1.51165i
797797 −9.48100 + 19.6875i −0.335834 + 0.697367i −0.998679 0.0513901i 0.983635π-0.983635\pi
0.662844 + 0.748757i 0.269349π0.269349\pi
798798 0 0
799799 1.81990 + 7.97349i 0.0643833 + 0.282082i
800800 6.69490i 0.236700i
801801 0 0
802802 −36.2986 28.9472i −1.28175 1.02216i
803803 0.180516 0.790891i 0.00637026 0.0279099i
804804 0 0
805805 0.626344 + 0.785411i 0.0220757 + 0.0276821i
806806 −64.9823 31.2938i −2.28891 1.10228i
807807 0 0
808808 −30.4495 + 38.1825i −1.07121 + 1.34325i
809809 −3.61100 + 2.87968i −0.126956 + 0.101244i −0.684909 0.728628i 0.740158π-0.740158\pi
0.557953 + 0.829872i 0.311587π0.311587\pi
810810 0 0
811811 −5.86604 −0.205985 −0.102992 0.994682i 0.532842π-0.532842\pi
−0.102992 + 0.994682i 0.532842π0.532842\pi
812812 −58.6816 21.1279i −2.05932 0.741443i
813813 0 0
814814 −8.11096 16.8426i −0.284289 0.590332i
815815 −2.19691 + 1.75198i −0.0769544 + 0.0613691i
816816 0 0
817817 17.7631 8.55424i 0.621451 0.299275i
818818 59.5135 + 28.6602i 2.08084 + 1.00208i
819819 0 0
820820 −34.1013 7.78341i −1.19087 0.271808i
821821 2.65143 11.6167i 0.0925354 0.405424i −0.907353 0.420370i 0.861900π-0.861900\pi
0.999888 + 0.0149456i 0.00475750π0.00475750\pi
822822 0 0
823823 9.13650 2.08535i 0.318478 0.0726906i −0.0602935 0.998181i 0.519204π-0.519204\pi
0.378772 + 0.925490i 0.376347π0.376347\pi
824824 0.671850i 0.0234050i
825825 0 0
826826 39.9265 82.9083i 1.38922 2.88475i
827827 −16.9637 + 35.2256i −0.589887 + 1.22491i 0.365845 + 0.930676i 0.380780π0.380780\pi
−0.955732 + 0.294238i 0.904934π0.904934\pi
828828 0 0
829829 6.57154i 0.228239i 0.993467 + 0.114119i 0.0364047π0.0364047\pi
−0.993467 + 0.114119i 0.963595π0.963595\pi
830830 33.2340 7.58544i 1.15357 0.263294i
831831 0 0
832832 15.1765 66.4928i 0.526152 2.30522i
833833 −30.7816 7.02569i −1.06652 0.243426i
834834 0 0
835835 −21.3639 10.2883i −0.739327 0.356041i
836836 −11.1437 + 5.36654i −0.385414 + 0.185606i
837837 0 0
838838 −20.0842 + 16.0166i −0.693798 + 0.553285i
839839 −8.06762 16.7526i −0.278525 0.578363i 0.714036 0.700109i 0.246865π-0.246865\pi
−0.992561 + 0.121745i 0.961151π0.961151\pi
840840 0 0
841841 22.3442 + 18.4861i 0.770490 + 0.637452i
842842 62.1291 2.14111
843843 0 0
844844 −36.3979 + 29.0264i −1.25287 + 0.999130i
845845 19.4074 24.3361i 0.667634 0.837187i
846846 0 0
847847 31.7885 + 15.3085i 1.09227 + 0.526008i
848848 −0.201449 0.252609i −0.00691779 0.00867463i
849849 0 0
850850 −4.81492 + 21.0956i −0.165151 + 0.723572i
851851 −1.17612 0.937925i −0.0403169 0.0321517i
852852 0 0
853853 15.0581i 0.515578i −0.966201 0.257789i 0.917006π-0.917006\pi
0.966201 0.257789i 0.0829939π-0.0829939\pi
854854 19.8181 + 86.8290i 0.678163 + 2.97123i
855855 0 0
856856 −3.59270 + 7.46032i −0.122796 + 0.254989i
857857 1.46838 + 6.43339i 0.0501589 + 0.219760i 0.993795 0.111223i 0.0354767π-0.0354767\pi
−0.943637 + 0.330983i 0.892620π0.892620\pi
858858 0 0
859859 −10.3600 + 2.36460i −0.353479 + 0.0806792i −0.395573 0.918434i 0.629454π-0.629454\pi
0.0420946 + 0.999114i 0.486597π0.486597\pi
860860 22.4708 + 17.9199i 0.766249 + 0.611063i
861861 0 0
862862 74.9709 + 17.1116i 2.55352 + 0.582824i
863863 25.7393 + 32.2760i 0.876175 + 1.09869i 0.994398 + 0.105701i 0.0337088π0.0337088\pi
−0.118223 + 0.992987i 0.537720π0.537720\pi
864864 0 0
865865 −4.52961 + 2.18135i −0.154011 + 0.0741680i
866866 −7.69907 + 9.65433i −0.261625 + 0.328067i
867867 0 0
868868 −28.8130 59.8308i −0.977977 2.03079i
869869 −4.02759 −0.136627
870870 0 0
871871 −70.1888 −2.37826
872872 1.60807 + 3.33919i 0.0544561 + 0.113079i
873873 0 0
874874 −0.987113 + 1.23780i −0.0333896 + 0.0418692i
875875 −37.4130 + 18.0172i −1.26479 + 0.609092i
876876 0 0
877877 15.2676 + 19.1450i 0.515550 + 0.646479i 0.969657 0.244468i 0.0786132π-0.0786132\pi
−0.454107 + 0.890947i 0.650042π0.650042\pi
878878 −70.4880 16.0884i −2.37886 0.542958i
879879 0 0
880880 −0.852383 0.679752i −0.0287338 0.0229144i
881881 −12.0649 + 2.75373i −0.406476 + 0.0927755i −0.420870 0.907121i 0.638275π-0.638275\pi
0.0143941 + 0.999896i 0.495418π0.495418\pi
882882 0 0
883883 6.42165 + 28.1351i 0.216106 + 0.946822i 0.960324 + 0.278885i 0.0899650π0.0899650\pi
−0.744218 + 0.667936i 0.767178π0.767178\pi
884884 53.5023 111.099i 1.79948 3.73666i
885885 0 0
886886 −6.66304 29.1927i −0.223849 0.980747i
887887 46.9153i 1.57526i 0.616147 + 0.787631i 0.288693π0.288693\pi
−0.616147 + 0.787631i 0.711307π0.711307\pi
888888 0 0
889889 −1.04168 0.830714i −0.0349369 0.0278613i
890890 4.57130 20.0282i 0.153230 0.671346i
891891 0 0
892892 28.4985 + 35.7360i 0.954201 + 1.19653i
893893 −4.84146 2.33152i −0.162013 0.0780215i
894894 0 0
895895 7.53462 9.44812i 0.251855 0.315816i
896896 52.2911 41.7007i 1.74692 1.39312i
897897 0 0
898898 −78.5600 −2.62158
899899 3.18108 + 30.7133i 0.106095 + 1.02434i
900900 0 0
901901 1.35868 + 2.82134i 0.0452643 + 0.0939924i
902902 8.16013 6.50748i 0.271703 0.216676i
903903 0 0
904904 −12.6045 + 6.07003i −0.419221 + 0.201886i
905905 29.5121 + 14.2123i 0.981016 + 0.472432i
906906 0 0
907907 20.6912 + 4.72262i 0.687039 + 0.156812i 0.551769 0.833997i 0.313953π-0.313953\pi
0.135270 + 0.990809i 0.456810π0.456810\pi
908908 20.3215 89.0345i 0.674394 2.95471i
909909 0 0
910910 79.7233 18.1963i 2.64280 0.603202i
911911 46.1944i 1.53049i −0.643739 0.765245i 0.722618π-0.722618\pi
0.643739 0.765245i 0.277382π-0.277382\pi
912912 0 0
913913 −2.77454 + 5.76139i −0.0918239 + 0.190674i
914914 7.68796 15.9642i 0.254295 0.528049i
915915 0 0
916916 36.9660i 1.22139i
917917 −2.53568 + 0.578752i −0.0837354 + 0.0191121i
918918 0 0
919919 11.0939 48.6055i 0.365954 1.60335i −0.371824 0.928303i 0.621267π-0.621267\pi
0.737777 0.675044i 0.235876π-0.235876\pi
920920 −0.921074 0.210229i −0.0303669 0.00693105i
921921 0 0
922922 −35.4717 17.0823i −1.16820 0.562575i
923923 16.4719 7.93247i 0.542180 0.261100i
924924 0 0
925925 10.5614 8.42247i 0.347258 0.276929i
926926 9.38137 + 19.4806i 0.308291 + 0.640173i
927927 0 0
928928 −24.5994 + 8.36013i −0.807514 + 0.274435i
929929 −16.6870 −0.547484 −0.273742 0.961803i 0.588261π-0.588261\pi
−0.273742 + 0.961803i 0.588261π0.588261\pi
930930 0 0
931931 16.2189 12.9342i 0.531554 0.423900i
932932 −11.5757 + 14.5154i −0.379174 + 0.475469i
933933 0 0
934934 −53.0103 25.5284i −1.73455 0.835315i
935935 6.58810 + 8.26122i 0.215454 + 0.270171i
936936 0 0
937937 5.03903 22.0775i 0.164618 0.721239i −0.823471 0.567358i 0.807966π-0.807966\pi
0.988089 0.153881i 0.0491772π-0.0491772\pi
938938 −80.3687 64.0919i −2.62413 2.09268i
939939 0 0
940940 7.83366i 0.255506i
941941 −0.897147 3.93066i −0.0292461 0.128136i 0.958197 0.286108i 0.0923615π-0.0923615\pi
−0.987444 + 0.157972i 0.949504π0.949504\pi
942942 0 0
943943 0.364416 0.756717i 0.0118670 0.0246421i
944944 1.78828 + 7.83499i 0.0582037 + 0.255007i
945945 0 0
946946 −8.36110 + 1.90837i −0.271843 + 0.0620463i
947947 −22.0167 17.5577i −0.715446 0.570549i 0.196676 0.980469i 0.436985π-0.436985\pi
−0.912122 + 0.409919i 0.865557π0.865557\pi
948948 0 0
949949 −5.18066 1.18245i −0.168171 0.0383840i
950950 −8.86418 11.1153i −0.287592 0.360629i
951951 0 0
952952 66.6042 32.0749i 2.15865 1.03955i
953953 −20.2660 + 25.4128i −0.656482 + 0.823202i −0.992955 0.118491i 0.962194π-0.962194\pi
0.336473 + 0.941693i 0.390766π0.390766\pi
954954 0 0
955955 13.5639 + 28.1658i 0.438918 + 0.911423i
956956 −2.57620 −0.0833202
957957 0 0
958958 −53.4355 −1.72642
959959 −22.1617 46.0192i −0.715639 1.48604i
960960 0 0
961961 −1.17010 + 1.46726i −0.0377451 + 0.0473309i
962962 −110.326 + 53.1302i −3.55705 + 1.71299i
963963 0 0
964964 −52.8514 66.2736i −1.70223 2.13453i
965965 23.1697 + 5.28833i 0.745859 + 0.170237i
966966 0 0
967967 1.03303 + 0.823813i 0.0332200 + 0.0264920i 0.639959 0.768409i 0.278951π-0.278951\pi
−0.606739 + 0.794901i 0.707523π0.707523\pi
968968 −32.3498 + 7.38363i −1.03976 + 0.237319i
969969 0 0
970970 9.82922 + 43.0646i 0.315597 + 1.38272i
971971 17.1222 35.5546i 0.549478 1.14100i −0.422594 0.906319i 0.638880π-0.638880\pi
0.972072 0.234684i 0.0754054π-0.0754054\pi
972972 0 0
973973 2.78537 + 12.2035i 0.0892949 + 0.391227i
974974 3.56066i 0.114091i
975975 0 0
976976 −6.08111 4.84952i −0.194652 0.155229i
977977 4.16227 18.2361i 0.133163 0.583424i −0.863681 0.504038i 0.831847π-0.831847\pi
0.996844 0.0793858i 0.0252959π-0.0252959\pi
978978 0 0
979979 2.40274 + 3.01294i 0.0767918 + 0.0962939i
980980 27.2469 + 13.1214i 0.870370 + 0.419148i
981981 0 0
982982 29.1565 36.5610i 0.930420 1.16671i
983983 6.29633 5.02115i 0.200822 0.160150i −0.517916 0.855432i 0.673292π-0.673292\pi
0.718737 + 0.695282i 0.244720π0.244720\pi
984984 0 0
985985 26.8861 0.856662
986986 −83.5250 + 8.65098i −2.65998 + 0.275503i
987987 0 0
988988 35.1531 + 72.9961i 1.11837 + 2.32231i
989989 −0.539565 + 0.430289i −0.0171572 + 0.0136824i
990990 0 0
991991 −54.5016 + 26.2466i −1.73130 + 0.833751i −0.745359 + 0.666663i 0.767722π0.767722\pi
−0.985942 + 0.167087i 0.946564π0.946564\pi
992992 −24.9238 12.0027i −0.791330 0.381085i
993993 0 0
994994 26.1044 + 5.95816i 0.827981 + 0.188981i
995995 −5.46394 + 23.9391i −0.173219 + 0.758921i
996996 0 0
997997 2.89082 0.659811i 0.0915532 0.0208964i −0.176499 0.984301i 0.556477π-0.556477\pi
0.268052 + 0.963404i 0.413620π0.413620\pi
998998 80.5446i 2.54960i
999999 0 0
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 261.2.o.b.154.1 24
3.2 odd 2 87.2.i.a.67.4 yes 24
29.10 odd 28 7569.2.a.bn.1.2 12
29.13 even 14 inner 261.2.o.b.100.1 24
29.19 odd 28 7569.2.a.bt.1.11 12
87.68 even 28 2523.2.a.v.1.11 12
87.71 odd 14 87.2.i.a.13.4 24
87.77 even 28 2523.2.a.s.1.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
87.2.i.a.13.4 24 87.71 odd 14
87.2.i.a.67.4 yes 24 3.2 odd 2
261.2.o.b.100.1 24 29.13 even 14 inner
261.2.o.b.154.1 24 1.1 even 1 trivial
2523.2.a.s.1.2 12 87.77 even 28
2523.2.a.v.1.11 12 87.68 even 28
7569.2.a.bn.1.2 12 29.10 odd 28
7569.2.a.bt.1.11 12 29.19 odd 28