Properties

Label 605.2.b.g.364.3
Level 605605
Weight 22
Character 605.364
Analytic conductor 4.8314.831
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(364,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 605=5112 605 = 5 \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 605.b (of order 22, degree 11, 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: 4.830949322294.83094932229
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.1480160000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+9x6+27x4+31x2+11 x^{8} + 9x^{6} + 27x^{4} + 31x^{2} + 11 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 364.3
Root 1.23399i-1.23399i of defining polynomial
Character χ\chi == 605.364
Dual form 605.2.b.g.364.6

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) == q1.23399iq20.363982iq3+0.477260q4+(1.294961.82293i)q50.449152q62.58558iq73.05692iq8+2.86752q9+(2.249481.59798i)q100.173714iq12+2.75929iq133.19059q14+(0.6635140.471344i)q152.81770q16+3.85124iq173.53850iq18+0.277591q19+(0.6180340.870011i)q200.941105q21+8.40180iq231.11267q24+(1.646144.72125i)q25+3.40495q262.13567iq271.23399iq283.32307q29+(0.581635+0.818772i)q30+0.564263q312.63682iq32+4.75241q34+(4.713333.34823i)q35+1.36855q360.522583iq370.342546iq38+1.00433q39+(5.572553.95860i)q405.11188q41+1.16132iq422.54457iq43+(3.713335.22728i)q45+10.3678q464.92477iq47+1.02559iq48+0.314780q49+(5.82599+2.03133i)q50+1.40178q51+1.31690iq52+8.72086iq532.63541q547.90392q560.101038iq57+4.10065iq587.50726q59+(0.3166690.224953i)q60+14.1791q610.696297iq627.41419iq638.88922q64+(5.03000+3.57318i)q65+3.20618iq67+1.83804iq68+3.05810q69+(4.13169+5.81622i)q708.40099q718.76578iq72+13.0353iq730.644864q74+(1.71845+0.599167i)q75+0.132483q761.23934iq789.70425q79+(3.64882+5.13647i)q80+7.82520q81+6.30802iq823.29699iq830.449152q84+(7.02054+4.98721i)q853.13998q86+1.20954iq872.48823q89+(6.450434.58222i)q90+7.13437q91+4.00984iq920.205382iq936.07713q94+(0.3594700.506029i)q950.959755q9610.9014iq970.388437iq98+O(q100)q-1.23399i q^{2} -0.363982i q^{3} +0.477260 q^{4} +(1.29496 - 1.82293i) q^{5} -0.449152 q^{6} -2.58558i q^{7} -3.05692i q^{8} +2.86752 q^{9} +(-2.24948 - 1.59798i) q^{10} -0.173714i q^{12} +2.75929i q^{13} -3.19059 q^{14} +(-0.663514 - 0.471344i) q^{15} -2.81770 q^{16} +3.85124i q^{17} -3.53850i q^{18} +0.277591 q^{19} +(0.618034 - 0.870011i) q^{20} -0.941105 q^{21} +8.40180i q^{23} -1.11267 q^{24} +(-1.64614 - 4.72125i) q^{25} +3.40495 q^{26} -2.13567i q^{27} -1.23399i q^{28} -3.32307 q^{29} +(-0.581635 + 0.818772i) q^{30} +0.564263 q^{31} -2.63682i q^{32} +4.75241 q^{34} +(-4.71333 - 3.34823i) q^{35} +1.36855 q^{36} -0.522583i q^{37} -0.342546i q^{38} +1.00433 q^{39} +(-5.57255 - 3.95860i) q^{40} -5.11188 q^{41} +1.16132i q^{42} -2.54457i q^{43} +(3.71333 - 5.22728i) q^{45} +10.3678 q^{46} -4.92477i q^{47} +1.02559i q^{48} +0.314780 q^{49} +(-5.82599 + 2.03133i) q^{50} +1.40178 q^{51} +1.31690i q^{52} +8.72086i q^{53} -2.63541 q^{54} -7.90392 q^{56} -0.101038i q^{57} +4.10065i q^{58} -7.50726 q^{59} +(-0.316669 - 0.224953i) q^{60} +14.1791 q^{61} -0.696297i q^{62} -7.41419i q^{63} -8.88922 q^{64} +(5.03000 + 3.57318i) q^{65} +3.20618i q^{67} +1.83804i q^{68} +3.05810 q^{69} +(-4.13169 + 5.81622i) q^{70} -8.40099 q^{71} -8.76578i q^{72} +13.0353i q^{73} -0.644864 q^{74} +(-1.71845 + 0.599167i) q^{75} +0.132483 q^{76} -1.23934i q^{78} -9.70425 q^{79} +(-3.64882 + 5.13647i) q^{80} +7.82520 q^{81} +6.30802i q^{82} -3.29699i q^{83} -0.449152 q^{84} +(7.02054 + 4.98721i) q^{85} -3.13998 q^{86} +1.20954i q^{87} -2.48823 q^{89} +(-6.45043 - 4.58222i) q^{90} +7.13437 q^{91} +4.00984i q^{92} -0.205382i q^{93} -6.07713 q^{94} +(0.359470 - 0.506029i) q^{95} -0.959755 q^{96} -10.9014i q^{97} -0.388437i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q2q4+4q5+6q64q9+4q148q1522q1612q194q20+4q212q248q25+10q2624q2922q30+14q318q3414q35+8q96+O(q100) 8 q - 2 q^{4} + 4 q^{5} + 6 q^{6} - 4 q^{9} + 4 q^{14} - 8 q^{15} - 22 q^{16} - 12 q^{19} - 4 q^{20} + 4 q^{21} - 2 q^{24} - 8 q^{25} + 10 q^{26} - 24 q^{29} - 22 q^{30} + 14 q^{31} - 8 q^{34} - 14 q^{35}+ \cdots - 8 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/605Z)×\left(\mathbb{Z}/605\mathbb{Z}\right)^\times.

nn 122122 486486
χ(n)\chi(n) 1-1 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 1.23399i 0.872565i −0.899810 0.436283i 0.856295π-0.856295\pi
0.899810 0.436283i 0.143705π-0.143705\pi
33 0.363982i 0.210145i −0.994465 0.105073i 0.966492π-0.966492\pi
0.994465 0.105073i 0.0335075π-0.0335075\pi
44 0.477260 0.238630
55 1.29496 1.82293i 0.579125 0.815239i
66 −0.449152 −0.183365
77 2.58558i 0.977257i −0.872492 0.488629i 0.837497π-0.837497\pi
0.872492 0.488629i 0.162503π-0.162503\pi
88 3.05692i 1.08079i
99 2.86752 0.955839
1010 −2.24948 1.59798i −0.711349 0.505324i
1111 0 0
1212 0.173714i 0.0501470i
1313 2.75929i 0.765290i 0.923895 + 0.382645i 0.124987π0.124987\pi
−0.923895 + 0.382645i 0.875013π0.875013\pi
1414 −3.19059 −0.852721
1515 −0.663514 0.471344i −0.171319 0.121700i
1616 −2.81770 −0.704426
1717 3.85124i 0.934063i 0.884241 + 0.467031i 0.154677π0.154677\pi
−0.884241 + 0.467031i 0.845323π0.845323\pi
1818 3.53850i 0.834032i
1919 0.277591 0.0636838 0.0318419 0.999493i 0.489863π-0.489863\pi
0.0318419 + 0.999493i 0.489863π0.489863\pi
2020 0.618034 0.870011i 0.138197 0.194540i
2121 −0.941105 −0.205366
2222 0 0
2323 8.40180i 1.75190i 0.482406 + 0.875948i 0.339763π0.339763\pi
−0.482406 + 0.875948i 0.660237π0.660237\pi
2424 −1.11267 −0.227122
2525 −1.64614 4.72125i −0.329228 0.944250i
2626 3.40495 0.667766
2727 2.13567i 0.411010i
2828 1.23399i 0.233203i
2929 −3.32307 −0.617079 −0.308539 0.951212i 0.599840π-0.599840\pi
−0.308539 + 0.951212i 0.599840π0.599840\pi
3030 −0.581635 + 0.818772i −0.106192 + 0.149487i
3131 0.564263 0.101345 0.0506723 0.998715i 0.483864π-0.483864\pi
0.0506723 + 0.998715i 0.483864π0.483864\pi
3232 2.63682i 0.466128i
3333 0 0
3434 4.75241 0.815031
3535 −4.71333 3.34823i −0.796698 0.565954i
3636 1.36855 0.228092
3737 0.522583i 0.0859121i −0.999077 0.0429560i 0.986322π-0.986322\pi
0.999077 0.0429560i 0.0136775π-0.0136775\pi
3838 0.342546i 0.0555682i
3939 1.00433 0.160822
4040 −5.57255 3.95860i −0.881098 0.625910i
4141 −5.11188 −0.798341 −0.399170 0.916877i 0.630702π-0.630702\pi
−0.399170 + 0.916877i 0.630702π0.630702\pi
4242 1.16132i 0.179195i
4343 2.54457i 0.388043i −0.980997 0.194022i 0.937847π-0.937847\pi
0.980997 0.194022i 0.0621532π-0.0621532\pi
4444 0 0
4545 3.71333 5.22728i 0.553550 0.779237i
4646 10.3678 1.52864
4747 4.92477i 0.718351i −0.933270 0.359176i 0.883058π-0.883058\pi
0.933270 0.359176i 0.116942π-0.116942\pi
4848 1.02559i 0.148032i
4949 0.314780 0.0449686
5050 −5.82599 + 2.03133i −0.823920 + 0.287273i
5151 1.40178 0.196289
5252 1.31690i 0.182621i
5353 8.72086i 1.19790i 0.800786 + 0.598951i 0.204416π0.204416\pi
−0.800786 + 0.598951i 0.795584π0.795584\pi
5454 −2.63541 −0.358633
5555 0 0
5656 −7.90392 −1.05621
5757 0.101038i 0.0133828i
5858 4.10065i 0.538441i
5959 −7.50726 −0.977362 −0.488681 0.872463i 0.662522π-0.662522\pi
−0.488681 + 0.872463i 0.662522π0.662522\pi
6060 −0.316669 0.224953i −0.0408818 0.0290414i
6161 14.1791 1.81544 0.907721 0.419573i 0.137820π-0.137820\pi
0.907721 + 0.419573i 0.137820π0.137820\pi
6262 0.696297i 0.0884298i
6363 7.41419i 0.934100i
6464 −8.88922 −1.11115
6565 5.03000 + 3.57318i 0.623894 + 0.443199i
6666 0 0
6767 3.20618i 0.391698i 0.980634 + 0.195849i 0.0627462π0.0627462\pi
−0.980634 + 0.195849i 0.937254π0.937254\pi
6868 1.83804i 0.222895i
6969 3.05810 0.368153
7070 −4.13169 + 5.81622i −0.493832 + 0.695171i
7171 −8.40099 −0.997014 −0.498507 0.866886i 0.666118π-0.666118\pi
−0.498507 + 0.866886i 0.666118π0.666118\pi
7272 8.76578i 1.03306i
7373 13.0353i 1.52566i 0.646598 + 0.762831i 0.276191π0.276191\pi
−0.646598 + 0.762831i 0.723809π0.723809\pi
7474 −0.644864 −0.0749639
7575 −1.71845 + 0.599167i −0.198430 + 0.0691858i
7676 0.132483 0.0151969
7777 0 0
7878 1.23934i 0.140328i
7979 −9.70425 −1.09181 −0.545907 0.837846i 0.683815π-0.683815\pi
−0.545907 + 0.837846i 0.683815π0.683815\pi
8080 −3.64882 + 5.13647i −0.407951 + 0.574275i
8181 7.82520 0.869467
8282 6.30802i 0.696604i
8383 3.29699i 0.361892i −0.983493 0.180946i 0.942084π-0.942084\pi
0.983493 0.180946i 0.0579159π-0.0579159\pi
8484 −0.449152 −0.0490065
8585 7.02054 + 4.98721i 0.761484 + 0.540939i
8686 −3.13998 −0.338593
8787 1.20954i 0.129676i
8888 0 0
8989 −2.48823 −0.263752 −0.131876 0.991266i 0.542100π-0.542100\pi
−0.131876 + 0.991266i 0.542100π0.542100\pi
9090 −6.45043 4.58222i −0.679935 0.483009i
9191 7.13437 0.747885
9292 4.00984i 0.418055i
9393 0.205382i 0.0212971i
9494 −6.07713 −0.626808
9595 0.359470 0.506029i 0.0368809 0.0519175i
9696 −0.959755 −0.0979546
9797 10.9014i 1.10687i −0.832891 0.553437i 0.813316π-0.813316\pi
0.832891 0.553437i 0.186684π-0.186684\pi
9898 0.388437i 0.0392380i
9999 0 0
100100 −0.785638 2.25326i −0.0785638 0.225326i
101101 13.8382 1.37696 0.688478 0.725257i 0.258279π-0.258279\pi
0.688478 + 0.725257i 0.258279π0.258279\pi
102102 1.72979i 0.171275i
103103 13.3899i 1.31935i −0.751553 0.659673i 0.770695π-0.770695\pi
0.751553 0.659673i 0.229305π-0.229305\pi
104104 8.43495 0.827115
105105 −1.21870 + 1.71557i −0.118933 + 0.167422i
106106 10.7615 1.04525
107107 10.2594i 0.991815i 0.868375 + 0.495907i 0.165164π0.165164\pi
−0.868375 + 0.495907i 0.834836π0.834836\pi
108108 1.01927i 0.0980794i
109109 4.94262 0.473417 0.236708 0.971581i 0.423931π-0.423931\pi
0.236708 + 0.971581i 0.423931π0.423931\pi
110110 0 0
111111 −0.190211 −0.0180540
112112 7.28539i 0.688405i
113113 9.92408i 0.933579i 0.884369 + 0.466789i 0.154589π0.154589\pi
−0.884369 + 0.466789i 0.845411π0.845411\pi
114114 −0.124681 −0.0116774
115115 15.3159 + 10.8800i 1.42821 + 1.01457i
116116 −1.58597 −0.147254
117117 7.91232i 0.731494i
118118 9.26391i 0.852812i
119119 9.95769 0.912820
120120 −1.44086 + 2.02831i −0.131532 + 0.185159i
121121 0 0
122122 17.4969i 1.58409i
123123 1.86063i 0.167768i
124124 0.269300 0.0241839
125125 −10.7382 3.11304i −0.960454 0.278439i
126126 −9.14906 −0.815063
127127 11.1357i 0.988138i 0.869423 + 0.494069i 0.164491π0.164491\pi
−0.869423 + 0.494069i 0.835509π0.835509\pi
128128 5.69561i 0.503425i
129129 −0.926179 −0.0815455
130130 4.40928 6.20698i 0.386720 0.544388i
131131 10.1649 0.888114 0.444057 0.895999i 0.353539π-0.353539\pi
0.444057 + 0.895999i 0.353539π0.353539\pi
132132 0 0
133133 0.717734i 0.0622354i
134134 3.95641 0.341782
135135 −3.89318 2.76562i −0.335072 0.238026i
136136 11.7729 1.00952
137137 4.34606i 0.371309i −0.982615 0.185655i 0.940559π-0.940559\pi
0.982615 0.185655i 0.0594406π-0.0594406\pi
138138 3.77368i 0.321237i
139139 8.30246 0.704206 0.352103 0.935961i 0.385467π-0.385467\pi
0.352103 + 0.935961i 0.385467π0.385467\pi
140140 −2.24948 1.59798i −0.190116 0.135054i
141141 −1.79253 −0.150958
142142 10.3668i 0.869960i
143143 0 0
144144 −8.07981 −0.673318
145145 −4.30325 + 6.05772i −0.357366 + 0.503067i
146146 16.0854 1.33124
147147 0.114574i 0.00944994i
148148 0.249408i 0.0205012i
149149 −8.46690 −0.693636 −0.346818 0.937933i 0.612738π-0.612738\pi
−0.346818 + 0.937933i 0.612738π0.612738\pi
150150 0.739368 + 2.12056i 0.0603691 + 0.173143i
151151 11.1023 0.903493 0.451746 0.892146i 0.350801π-0.350801\pi
0.451746 + 0.892146i 0.350801π0.350801\pi
152152 0.848575i 0.0688285i
153153 11.0435i 0.892814i
154154 0 0
155155 0.730700 1.02861i 0.0586912 0.0826201i
156156 0.479328 0.0383770
157157 13.7662i 1.09867i 0.835604 + 0.549333i 0.185118π0.185118\pi
−0.835604 + 0.549333i 0.814882π0.814882\pi
158158 11.9750i 0.952678i
159159 3.17424 0.251734
160160 −4.80673 3.41458i −0.380006 0.269946i
161161 21.7235 1.71205
162162 9.65625i 0.758667i
163163 8.94093i 0.700308i −0.936692 0.350154i 0.886129π-0.886129\pi
0.936692 0.350154i 0.113871π-0.113871\pi
164164 −2.43969 −0.190508
165165 0 0
166166 −4.06846 −0.315774
167167 16.9182i 1.30917i −0.755990 0.654583i 0.772844π-0.772844\pi
0.755990 0.654583i 0.227156π-0.227156\pi
168168 2.87689i 0.221957i
169169 5.38630 0.414331
170170 6.15419 8.66330i 0.472005 0.664445i
171171 0.795997 0.0608714
172172 1.21442i 0.0925988i
173173 3.37990i 0.256969i −0.991712 0.128484i 0.958989π-0.958989\pi
0.991712 0.128484i 0.0410112π-0.0410112\pi
174174 1.49256 0.113151
175175 −12.2072 + 4.25623i −0.922775 + 0.321741i
176176 0 0
177177 2.73251i 0.205388i
178178 3.07046i 0.230141i
179179 −13.8239 −1.03325 −0.516624 0.856212i 0.672812π-0.672812\pi
−0.516624 + 0.856212i 0.672812π0.672812\pi
180180 1.77222 2.49477i 0.132094 0.185949i
181181 −2.59901 −0.193183 −0.0965913 0.995324i 0.530794π-0.530794\pi
−0.0965913 + 0.995324i 0.530794π0.530794\pi
182182 8.80377i 0.652579i
183183 5.16093i 0.381507i
184184 25.6836 1.89342
185185 −0.952632 0.676725i −0.0700389 0.0497538i
186186 −0.253440 −0.0185831
187187 0 0
188188 2.35039i 0.171420i
189189 −5.52195 −0.401663
190190 −0.624436 0.443584i −0.0453014 0.0321810i
191191 2.21832 0.160512 0.0802560 0.996774i 0.474426π-0.474426\pi
0.0802560 + 0.996774i 0.474426π0.474426\pi
192192 3.23552i 0.233504i
193193 10.4765i 0.754112i 0.926190 + 0.377056i 0.123064π0.123064\pi
−0.926190 + 0.377056i 0.876936π0.876936\pi
194194 −13.4523 −0.965820
195195 1.30058 1.83083i 0.0931361 0.131108i
196196 0.150232 0.0107309
197197 1.32667i 0.0945210i −0.998883 0.0472605i 0.984951π-0.984951\pi
0.998883 0.0472605i 0.0150491π-0.0150491\pi
198198 0 0
199199 5.20321 0.368846 0.184423 0.982847i 0.440958π-0.440958\pi
0.184423 + 0.982847i 0.440958π0.440958\pi
200200 −14.4325 + 5.03213i −1.02053 + 0.355825i
201201 1.16699 0.0823134
202202 17.0763i 1.20148i
203203 8.59206i 0.603045i
204204 0.669015 0.0468404
205205 −6.61969 + 9.31859i −0.462339 + 0.650838i
206206 −16.5230 −1.15122
207207 24.0923i 1.67453i
208208 7.77487i 0.539090i
209209 0 0
210210 2.11700 + 1.50386i 0.146087 + 0.103776i
211211 18.9165 1.30227 0.651134 0.758963i 0.274294π-0.274294\pi
0.651134 + 0.758963i 0.274294π0.274294\pi
212212 4.16212i 0.285855i
213213 3.05781i 0.209518i
214214 12.6600 0.865423
215215 −4.63857 3.29512i −0.316348 0.224726i
216216 −6.52859 −0.444214
217217 1.45895i 0.0990398i
218218 6.09916i 0.413087i
219219 4.74460 0.320611
220220 0 0
221221 −10.6267 −0.714829
222222 0.234719i 0.0157533i
223223 21.8723i 1.46468i −0.680942 0.732338i 0.738429π-0.738429\pi
0.680942 0.732338i 0.261571π-0.261571\pi
224224 −6.81770 −0.455527
225225 −4.72034 13.5383i −0.314689 0.902551i
226226 12.2462 0.814608
227227 2.43865i 0.161859i −0.996720 0.0809294i 0.974211π-0.974211\pi
0.996720 0.0809294i 0.0257888π-0.0257888\pi
228228 0.0482215i 0.00319355i
229229 −7.30119 −0.482476 −0.241238 0.970466i 0.577553π-0.577553\pi
−0.241238 + 0.970466i 0.577553π0.577553\pi
230230 13.4259 18.8997i 0.885275 1.24621i
231231 0 0
232232 10.1584i 0.666930i
233233 4.45831i 0.292073i −0.989279 0.146037i 0.953348π-0.953348\pi
0.989279 0.146037i 0.0466518π-0.0466518\pi
234234 9.76375 0.638276
235235 −8.97750 6.37739i −0.585628 0.416015i
236236 −3.58291 −0.233228
237237 3.53217i 0.229439i
238238 12.2877i 0.796495i
239239 −24.1747 −1.56373 −0.781867 0.623446i 0.785732π-0.785732\pi
−0.781867 + 0.623446i 0.785732π0.785732\pi
240240 1.86959 + 1.32811i 0.120681 + 0.0857289i
241241 −12.0393 −0.775522 −0.387761 0.921760i 0.626751π-0.626751\pi
−0.387761 + 0.921760i 0.626751π0.626751\pi
242242 0 0
243243 9.25525i 0.593725i
244244 6.76710 0.433219
245245 0.407629 0.573822i 0.0260424 0.0366601i
246246 2.29601 0.146388
247247 0.765955i 0.0487366i
248248 1.72491i 0.109532i
249249 −1.20005 −0.0760498
250250 −3.84148 + 13.2509i −0.242956 + 0.838059i
251251 −0.536388 −0.0338565 −0.0169283 0.999857i 0.505389π-0.505389\pi
−0.0169283 + 0.999857i 0.505389π0.505389\pi
252252 3.53850i 0.222904i
253253 0 0
254254 13.7414 0.862214
255255 1.81526 2.55535i 0.113676 0.160022i
256256 −10.7501 −0.671882
257257 23.7199i 1.47961i 0.672822 + 0.739805i 0.265082π0.265082\pi
−0.672822 + 0.739805i 0.734918π0.734918\pi
258258 1.14290i 0.0711538i
259259 −1.35118 −0.0839582
260260 2.40062 + 1.70534i 0.148880 + 0.105761i
261261 −9.52896 −0.589828
262262 12.5435i 0.774937i
263263 4.97643i 0.306860i 0.988160 + 0.153430i 0.0490320π0.0490320\pi
−0.988160 + 0.153430i 0.950968π0.950968\pi
264264 0 0
265265 15.8975 + 11.2932i 0.976576 + 0.693735i
266266 −0.885679 −0.0543044
267267 0.905671i 0.0554262i
268268 1.53018i 0.0934708i
269269 −28.8046 −1.75625 −0.878124 0.478434i 0.841205π-0.841205\pi
−0.878124 + 0.478434i 0.841205π0.841205\pi
270270 −3.41275 + 4.80416i −0.207694 + 0.292372i
271271 −16.0762 −0.976559 −0.488280 0.872687i 0.662375π-0.662375\pi
−0.488280 + 0.872687i 0.662375π0.662375\pi
272272 10.8517i 0.657978i
273273 2.59679i 0.157165i
274274 −5.36301 −0.323992
275275 0 0
276276 1.45951 0.0878522
277277 18.0038i 1.08174i 0.841105 + 0.540871i 0.181905π0.181905\pi
−0.841105 + 0.540871i 0.818095π0.818095\pi
278278 10.2452i 0.614465i
279279 1.61803 0.0968692
280280 −10.2353 + 14.4083i −0.611675 + 0.861059i
281281 13.7150 0.818167 0.409084 0.912497i 0.365848π-0.365848\pi
0.409084 + 0.912497i 0.365848π0.365848\pi
282282 2.21197i 0.131721i
283283 20.5044i 1.21886i 0.792839 + 0.609431i 0.208602π0.208602\pi
−0.792839 + 0.609431i 0.791398π0.791398\pi
284284 −4.00946 −0.237918
285285 −0.184186 0.130841i −0.0109102 0.00775034i
286286 0 0
287287 13.2172i 0.780184i
288288 7.56112i 0.445543i
289289 2.16795 0.127526
290290 7.47519 + 5.31019i 0.438958 + 0.311825i
291291 −3.96793 −0.232604
292292 6.22121i 0.364069i
293293 22.4133i 1.30940i −0.755890 0.654699i 0.772796π-0.772796\pi
0.755890 0.654699i 0.227204π-0.227204\pi
294294 −0.141384 −0.00824569
295295 −9.72162 + 13.6852i −0.566015 + 0.796783i
296296 −1.59750 −0.0928525
297297 0 0
298298 10.4481i 0.605242i
299299 −23.1830 −1.34071
300300 −0.820148 + 0.285958i −0.0473513 + 0.0165098i
301301 −6.57919 −0.379218
302302 13.7002i 0.788356i
303303 5.03688i 0.289361i
304304 −0.782169 −0.0448605
305305 18.3614 25.8474i 1.05137 1.48002i
306306 13.6276 0.779038
307307 20.3044i 1.15883i −0.815032 0.579416i 0.803281π-0.803281\pi
0.815032 0.579416i 0.196719π-0.196719\pi
308308 0 0
309309 −4.87369 −0.277254
310310 −1.26930 0.901679i −0.0720914 0.0512119i
311311 −8.75881 −0.496666 −0.248333 0.968675i 0.579883π-0.579883\pi
−0.248333 + 0.968675i 0.579883π0.579883\pi
312312 3.07017i 0.173814i
313313 1.73123i 0.0978550i −0.998802 0.0489275i 0.984420π-0.984420\pi
0.998802 0.0489275i 0.0155803π-0.0155803\pi
314314 16.9875 0.958657
315315 −13.5155 9.60110i −0.761515 0.540961i
316316 −4.63145 −0.260539
317317 17.4764i 0.981573i 0.871280 + 0.490786i 0.163290π0.163290\pi
−0.871280 + 0.490786i 0.836710π0.836710\pi
318318 3.91699i 0.219654i
319319 0 0
320320 −11.5112 + 16.2044i −0.643496 + 0.905855i
321321 3.73424 0.208425
322322 26.8067i 1.49388i
323323 1.06907i 0.0594846i
324324 3.73466 0.207481
325325 13.0273 4.54219i 0.722626 0.251955i
326326 −11.0331 −0.611064
327327 1.79902i 0.0994863i
328328 15.6266i 0.862835i
329329 −12.7334 −0.702014
330330 0 0
331331 12.6193 0.693620 0.346810 0.937935i 0.387265π-0.387265\pi
0.346810 + 0.937935i 0.387265π0.387265\pi
332332 1.57352i 0.0863582i
333333 1.49852i 0.0821181i
334334 −20.8769 −1.14233
335335 5.84464 + 4.15189i 0.319327 + 0.226842i
336336 2.65175 0.144665
337337 11.8599i 0.646047i −0.946391 0.323024i 0.895301π-0.895301\pi
0.946391 0.323024i 0.104699π-0.104699\pi
338338 6.64666i 0.361531i
339339 3.61219 0.196187
340340 3.35062 + 2.38020i 0.181713 + 0.129084i
341341 0 0
342342 0.982255i 0.0531143i
343343 18.9129i 1.02120i
344344 −7.77856 −0.419392
345345 3.96013 5.57471i 0.213206 0.300132i
346346 −4.17077 −0.224222
347347 22.3040i 1.19734i −0.800994 0.598672i 0.795695π-0.795695\pi
0.800994 0.598672i 0.204305π-0.204305\pi
348348 0.577265i 0.0309446i
349349 −15.9679 −0.854740 −0.427370 0.904077i 0.640560π-0.640560\pi
−0.427370 + 0.904077i 0.640560π0.640560\pi
350350 5.25216 + 15.0636i 0.280740 + 0.805182i
351351 5.89295 0.314542
352352 0 0
353353 24.1406i 1.28488i −0.766337 0.642439i 0.777923π-0.777923\pi
0.766337 0.642439i 0.222077π-0.222077\pi
354354 3.37190 0.179214
355355 −10.8790 + 15.3144i −0.577396 + 0.812805i
356356 −1.18753 −0.0629391
357357 3.62442i 0.191825i
358358 17.0586i 0.901577i
359359 −20.3784 −1.07553 −0.537764 0.843095i 0.680731π-0.680731\pi
−0.537764 + 0.843095i 0.680731π0.680731\pi
360360 −15.9794 11.3514i −0.842188 0.598269i
361361 −18.9229 −0.995944
362362 3.20716i 0.168564i
363363 0 0
364364 3.40495 0.178468
365365 23.7624 + 16.8802i 1.24378 + 0.883549i
366366 −6.36855 −0.332889
367367 5.40430i 0.282102i −0.990002 0.141051i 0.954952π-0.954952\pi
0.990002 0.141051i 0.0450482π-0.0450482\pi
368368 23.6738i 1.23408i
369369 −14.6584 −0.763085
370370 −0.835075 + 1.17554i −0.0434135 + 0.0611135i
371371 22.5485 1.17066
372372 0.0980205i 0.00508213i
373373 17.0982i 0.885311i −0.896692 0.442656i 0.854036π-0.854036\pi
0.896692 0.442656i 0.145964π-0.145964\pi
374374 0 0
375375 −1.13309 + 3.90852i −0.0585127 + 0.201835i
376376 −15.0546 −0.776384
377377 9.16933i 0.472244i
378378 6.81405i 0.350477i
379379 8.59196 0.441339 0.220670 0.975349i 0.429176π-0.429176\pi
0.220670 + 0.975349i 0.429176π0.429176\pi
380380 0.171561 0.241507i 0.00880088 0.0123891i
381381 4.05321 0.207652
382382 2.73739i 0.140057i
383383 9.66958i 0.494093i −0.969004 0.247046i 0.920540π-0.920540\pi
0.969004 0.247046i 0.0794600π-0.0794600\pi
384384 2.07310 0.105792
385385 0 0
386386 12.9279 0.658012
387387 7.29660i 0.370907i
388388 5.20283i 0.264133i
389389 27.3693 1.38768 0.693841 0.720129i 0.255917π-0.255917\pi
0.693841 + 0.720129i 0.255917π0.255917\pi
390390 −2.25923 1.60490i −0.114401 0.0812673i
391391 −32.3573 −1.63638
392392 0.962259i 0.0486014i
393393 3.69985i 0.186633i
394394 −1.63710 −0.0824758
395395 −12.5666 + 17.6902i −0.632296 + 0.890088i
396396 0 0
397397 10.6518i 0.534596i 0.963614 + 0.267298i 0.0861308π0.0861308\pi
−0.963614 + 0.267298i 0.913869π0.913869\pi
398398 6.42073i 0.321842i
399399 −0.261242 −0.0130785
400400 4.63834 + 13.3031i 0.231917 + 0.665154i
401401 13.7146 0.684875 0.342437 0.939541i 0.388748π-0.388748\pi
0.342437 + 0.939541i 0.388748π0.388748\pi
402402 1.44006i 0.0718238i
403403 1.55697i 0.0775581i
404404 6.60444 0.328583
405405 10.1333 14.2648i 0.503530 0.708823i
406406 10.6026 0.526196
407407 0 0
408408 4.28514i 0.212146i
409409 22.3083 1.10308 0.551538 0.834150i 0.314041π-0.314041\pi
0.551538 + 0.834150i 0.314041π0.314041\pi
410410 11.4991 + 8.16865i 0.567899 + 0.403421i
411411 −1.58189 −0.0780289
412412 6.39046i 0.314836i
413413 19.4106i 0.955134i
414414 29.7297 1.46114
415415 −6.01018 4.26948i −0.295028 0.209581i
416416 7.27576 0.356723
417417 3.02195i 0.147986i
418418 0 0
419419 0.510725 0.0249506 0.0124753 0.999922i 0.496029π-0.496029\pi
0.0124753 + 0.999922i 0.496029π0.496029\pi
420420 −0.581635 + 0.818772i −0.0283809 + 0.0399520i
421421 13.2150 0.644058 0.322029 0.946730i 0.395635π-0.395635\pi
0.322029 + 0.946730i 0.395635π0.395635\pi
422422 23.3429i 1.13631i
423423 14.1219i 0.686628i
424424 26.6590 1.29468
425425 18.1827 6.33969i 0.881989 0.307520i
426426 3.77332 0.182818
427427 36.6611i 1.77415i
428428 4.89641i 0.236677i
429429 0 0
430430 −4.06616 + 5.72397i −0.196088 + 0.276034i
431431 −29.4064 −1.41645 −0.708227 0.705985i 0.750505π-0.750505\pi
−0.708227 + 0.705985i 0.750505π0.750505\pi
432432 6.01769i 0.289526i
433433 10.2165i 0.490975i 0.969400 + 0.245488i 0.0789481π0.0789481\pi
−0.969400 + 0.245488i 0.921052π0.921052\pi
434434 −1.80033 −0.0864187
435435 2.20490 + 1.56631i 0.105717 + 0.0750987i
436436 2.35891 0.112971
437437 2.33226i 0.111567i
438438 5.85481i 0.279754i
439439 1.53306 0.0731691 0.0365846 0.999331i 0.488352π-0.488352\pi
0.0365846 + 0.999331i 0.488352π0.488352\pi
440440 0 0
441441 0.902638 0.0429827
442442 13.1133i 0.623735i
443443 3.39254i 0.161185i −0.996747 0.0805923i 0.974319π-0.974319\pi
0.996747 0.0805923i 0.0256812π-0.0256812\pi
444444 −0.0907801 −0.00430823
445445 −3.22216 + 4.53587i −0.152745 + 0.215021i
446446 −26.9902 −1.27802
447447 3.08180i 0.145764i
448448 22.9838i 1.08588i
449449 32.3501 1.52669 0.763347 0.645989i 0.223555π-0.223555\pi
0.763347 + 0.645989i 0.223555π0.223555\pi
450450 −16.7061 + 5.82487i −0.787535 + 0.274587i
451451 0 0
452452 4.73637i 0.222780i
453453 4.04104i 0.189865i
454454 −3.00928 −0.141232
455455 9.23875 13.0055i 0.433119 0.609705i
456456 −0.308866 −0.0144640
457457 12.1730i 0.569427i 0.958613 + 0.284714i 0.0918985π0.0918985\pi
−0.958613 + 0.284714i 0.908101π0.908101\pi
458458 9.00962i 0.420992i
459459 8.22499 0.383910
460460 7.30966 + 5.19260i 0.340814 + 0.242106i
461461 −16.5699 −0.771739 −0.385869 0.922553i 0.626098π-0.626098\pi
−0.385869 + 0.922553i 0.626098π0.626098\pi
462462 0 0
463463 14.6302i 0.679924i −0.940439 0.339962i 0.889586π-0.889586\pi
0.940439 0.339962i 0.110414π-0.110414\pi
464464 9.36343 0.434686
465465 −0.374396 0.265962i −0.0173622 0.0123337i
466466 −5.50152 −0.254853
467467 30.4853i 1.41069i 0.708862 + 0.705347i 0.249209π0.249209\pi
−0.708862 + 0.705347i 0.750791π0.750791\pi
468468 3.77623i 0.174556i
469469 8.28984 0.382789
470470 −7.86966 + 11.0782i −0.363000 + 0.510998i
471471 5.01067 0.230879
472472 22.9491i 1.05632i
473473 0 0
474474 4.35868 0.200201
475475 −0.456954 1.31058i −0.0209665 0.0601334i
476476 4.75241 0.217826
477477 25.0072i 1.14500i
478478 29.8315i 1.36446i
479479 −13.9993 −0.639643 −0.319822 0.947478i 0.603623π-0.603623\pi
−0.319822 + 0.947478i 0.603623π0.603623\pi
480480 −1.24285 + 1.74957i −0.0567280 + 0.0798564i
481481 1.44196 0.0657477
482482 14.8565i 0.676693i
483483 7.90697i 0.359780i
484484 0 0
485485 −19.8726 14.1170i −0.902367 0.641019i
486486 −11.4209 −0.518064
487487 34.1311i 1.54663i 0.634024 + 0.773313i 0.281402π0.281402\pi
−0.634024 + 0.773313i 0.718598π0.718598\pi
488488 43.3443i 1.96210i
489489 −3.25434 −0.147166
490490 −0.708093 0.503011i −0.0319884 0.0227237i
491491 −3.19431 −0.144157 −0.0720786 0.997399i 0.522963π-0.522963\pi
−0.0720786 + 0.997399i 0.522963π0.522963\pi
492492 0.888005i 0.0400344i
493493 12.7979i 0.576390i
494494 0.945184 0.0425258
495495 0 0
496496 −1.58993 −0.0713898
497497 21.7214i 0.974339i
498498 1.48085i 0.0663584i
499499 −6.52850 −0.292256 −0.146128 0.989266i 0.546681π-0.546681\pi
−0.146128 + 0.989266i 0.546681π0.546681\pi
500500 −5.12491 1.48573i −0.229193 0.0664439i
501501 −6.15791 −0.275115
502502 0.661899i 0.0295420i
503503 1.00387i 0.0447603i −0.999750 0.0223802i 0.992876π-0.992876\pi
0.999750 0.0223802i 0.00712442π-0.00712442\pi
504504 −22.6646 −1.00956
505505 17.9200 25.2261i 0.797430 1.12255i
506506 0 0
507507 1.96052i 0.0870697i
508508 5.31465i 0.235799i
509509 4.27401 0.189442 0.0947211 0.995504i 0.469804π-0.469804\pi
0.0947211 + 0.995504i 0.469804π0.469804\pi
510510 −3.15329 2.24002i −0.139630 0.0991896i
511511 33.7037 1.49096
512512 24.6568i 1.08969i
513513 0.592844i 0.0261747i
514514 29.2703 1.29106
515515 −24.4088 17.3394i −1.07558 0.764066i
516516 −0.442028 −0.0194592
517517 0 0
518518 1.66735i 0.0732590i
519519 −1.23022 −0.0540008
520520 10.9229 15.3763i 0.479003 0.674296i
521521 −9.88817 −0.433208 −0.216604 0.976259i 0.569498π-0.569498\pi
−0.216604 + 0.976259i 0.569498π0.569498\pi
522522 11.7587i 0.514663i
523523 44.1670i 1.93129i −0.259870 0.965644i 0.583680π-0.583680\pi
0.259870 0.965644i 0.416320π-0.416320\pi
524524 4.85131 0.211931
525525 1.54919 + 4.44319i 0.0676123 + 0.193917i
526526 6.14089 0.267755
527527 2.17311i 0.0946623i
528528 0 0
529529 −47.5902 −2.06914
530530 13.9357 19.6174i 0.605329 0.852127i
531531 −21.5272 −0.934200
532532 0.342546i 0.0148512i
533533 14.1052i 0.610963i
534534 1.11759 0.0483630
535535 18.7022 + 13.2856i 0.808566 + 0.574385i
536536 9.80105 0.423341
537537 5.03166i 0.217132i
538538 35.5447i 1.53244i
539539 0 0
540540 −1.85806 1.31992i −0.0799581 0.0568002i
541541 −21.2695 −0.914449 −0.457224 0.889351i 0.651156π-0.651156\pi
−0.457224 + 0.889351i 0.651156π0.651156\pi
542542 19.8379i 0.852112i
543543 0.945992i 0.0405964i
544544 10.1550 0.435393
545545 6.40050 9.01004i 0.274168 0.385948i
546546 −3.20442 −0.137136
547547 4.13393i 0.176754i 0.996087 + 0.0883771i 0.0281681π0.0281681\pi
−0.996087 + 0.0883771i 0.971832π0.971832\pi
548548 2.07420i 0.0886055i
549549 40.6587 1.73527
550550 0 0
551551 −0.922455 −0.0392979
552552 9.34839i 0.397894i
553553 25.0911i 1.06698i
554554 22.2166 0.943891
555555 −0.246316 + 0.346741i −0.0104555 + 0.0147183i
556556 3.96243 0.168045
557557 31.6671i 1.34178i 0.741557 + 0.670890i 0.234088π0.234088\pi
−0.741557 + 0.670890i 0.765912π0.765912\pi
558558 1.99664i 0.0845247i
559559 7.02122 0.296966
560560 13.2808 + 9.43431i 0.561214 + 0.398673i
561561 0 0
562562 16.9242i 0.713904i
563563 12.7467i 0.537210i 0.963250 + 0.268605i 0.0865626π0.0865626\pi
−0.963250 + 0.268605i 0.913437π0.913437\pi
564564 −0.855502 −0.0360231
565565 18.0909 + 12.8513i 0.761090 + 0.540659i
566566 25.3023 1.06354
567567 20.2327i 0.849693i
568568 25.6812i 1.07756i
569569 −15.6352 −0.655461 −0.327730 0.944771i 0.606284π-0.606284\pi
−0.327730 + 0.944771i 0.606284π0.606284\pi
570570 −0.161457 + 0.227284i −0.00676268 + 0.00951987i
571571 −3.61999 −0.151492 −0.0757460 0.997127i 0.524134π-0.524134\pi
−0.0757460 + 0.997127i 0.524134π0.524134\pi
572572 0 0
573573 0.807429i 0.0337308i
574574 16.3099 0.680762
575575 39.6670 13.8305i 1.65423 0.576774i
576576 −25.4900 −1.06208
577577 23.8352i 0.992273i −0.868245 0.496136i 0.834752π-0.834752\pi
0.868245 0.496136i 0.165248π-0.165248\pi
578578 2.67523i 0.111275i
579579 3.81325 0.158473
580580 −2.05377 + 2.89111i −0.0852782 + 0.120047i
581581 −8.52463 −0.353661
582582 4.89641i 0.202963i
583583 0 0
584584 39.8478 1.64891
585585 14.4236 + 10.2462i 0.596342 + 0.423627i
586586 −27.6578 −1.14253
587587 1.24698i 0.0514684i −0.999669 0.0257342i 0.991808π-0.991808\pi
0.999669 0.0257342i 0.00819235π-0.00819235\pi
588588 0.0546818i 0.00225504i
589589 0.156634 0.00645401
590590 16.8874 + 11.9964i 0.695245 + 0.493885i
591591 −0.482883 −0.0198631
592592 1.47248i 0.0605187i
593593 18.5288i 0.760886i 0.924804 + 0.380443i 0.124228π0.124228\pi
−0.924804 + 0.380443i 0.875772π0.875772\pi
594594 0 0
595595 12.8948 18.1522i 0.528637 0.744166i
596596 −4.04091 −0.165522
597597 1.89388i 0.0775112i
598598 28.6077i 1.16986i
599599 −33.8359 −1.38250 −0.691248 0.722617i 0.742939π-0.742939\pi
−0.691248 + 0.722617i 0.742939π0.742939\pi
600600 1.83161 + 5.25318i 0.0747750 + 0.214460i
601601 −21.3026 −0.868951 −0.434475 0.900684i 0.643066π-0.643066\pi
−0.434475 + 0.900684i 0.643066π0.643066\pi
602602 8.11868i 0.330893i
603603 9.19378i 0.374400i
604604 5.29869 0.215601
605605 0 0
606606 −6.21547 −0.252486
607607 37.4601i 1.52046i −0.649654 0.760230i 0.725086π-0.725086\pi
0.649654 0.760230i 0.274914π-0.274914\pi
608608 0.731957i 0.0296848i
609609 3.12736 0.126727
610610 −31.8956 22.6578i −1.29141 0.917387i
611611 13.5889 0.549747
612612 5.27062i 0.213052i
613613 20.0047i 0.807983i −0.914763 0.403991i 0.867623π-0.867623\pi
0.914763 0.403991i 0.132377π-0.132377\pi
614614 −25.0555 −1.01116
615615 3.39180 + 2.40945i 0.136771 + 0.0971584i
616616 0 0
617617 34.7932i 1.40072i −0.713790 0.700360i 0.753023π-0.753023\pi
0.713790 0.700360i 0.246977π-0.246977\pi
618618 6.01410i 0.241922i
619619 46.0840 1.85227 0.926136 0.377189i 0.123109π-0.123109\pi
0.926136 + 0.377189i 0.123109π0.123109\pi
620620 0.348734 0.490915i 0.0140055 0.0197156i
621621 17.9435 0.720047
622622 10.8083i 0.433374i
623623 6.43351i 0.257753i
624624 −2.82991 −0.113287
625625 −19.5804 + 15.5437i −0.783217 + 0.621748i
626626 −2.13633 −0.0853849
627627 0 0
628628 6.57008i 0.262175i
629629 2.01259 0.0802473
630630 −11.8477 + 16.6781i −0.472024 + 0.664471i
631631 −20.5380 −0.817604 −0.408802 0.912623i 0.634053π-0.634053\pi
−0.408802 + 0.912623i 0.634053π0.634053\pi
632632 29.6651i 1.18002i
633633 6.88529i 0.273666i
634634 21.5658 0.856486
635635 20.2997 + 14.4204i 0.805568 + 0.572255i
636636 1.51494 0.0600712
637637 0.868571i 0.0344140i
638638 0 0
639639 −24.0900 −0.952985
640640 10.3827 + 7.37560i 0.410412 + 0.291546i
641641 15.9095 0.628389 0.314194 0.949359i 0.398266π-0.398266\pi
0.314194 + 0.949359i 0.398266π0.398266\pi
642642 4.60803i 0.181865i
643643 42.3039i 1.66830i 0.551536 + 0.834151i 0.314042π0.314042\pi
−0.551536 + 0.834151i 0.685958π0.685958\pi
644644 10.3678 0.408547
645645 −1.19937 + 1.68836i −0.0472250 + 0.0664790i
646646 1.31923 0.0519042
647647 7.48891i 0.294419i 0.989105 + 0.147210i 0.0470292π0.0470292\pi
−0.989105 + 0.147210i 0.952971π0.952971\pi
648648 23.9210i 0.939707i
649649 0 0
650650 −5.60503 16.0756i −0.219847 0.630538i
651651 −0.531031 −0.0208127
652652 4.26715i 0.167114i
653653 16.4702i 0.644531i 0.946649 + 0.322265i 0.104444π0.104444\pi
−0.946649 + 0.322265i 0.895556π0.895556\pi
654654 −2.21999 −0.0868083
655655 13.1632 18.5299i 0.514329 0.724025i
656656 14.4037 0.562372
657657 37.3788i 1.45829i
658658 15.7129i 0.612553i
659659 −23.7359 −0.924619 −0.462310 0.886719i 0.652979π-0.652979\pi
−0.462310 + 0.886719i 0.652979π0.652979\pi
660660 0 0
661661 13.4183 0.521911 0.260956 0.965351i 0.415962π-0.415962\pi
0.260956 + 0.965351i 0.415962π0.415962\pi
662662 15.5721i 0.605229i
663663 3.86793i 0.150218i
664664 −10.0786 −0.391127
665665 −1.30838 0.929439i −0.0507367 0.0360421i
666666 −1.84916 −0.0716534
667667 27.9198i 1.08106i
668668 8.07436i 0.312407i
669669 −7.96112 −0.307795
670670 5.12340 7.21225i 0.197934 0.278634i
671671 0 0
672672 2.48152i 0.0957268i
673673 48.2870i 1.86133i 0.365875 + 0.930664i 0.380770π0.380770\pi
−0.365875 + 0.930664i 0.619230π0.619230\pi
674674 −14.6350 −0.563718
675675 −10.0830 + 3.51562i −0.388097 + 0.135316i
676676 2.57067 0.0988718
677677 24.3637i 0.936374i −0.883629 0.468187i 0.844907π-0.844907\pi
0.883629 0.468187i 0.155093π-0.155093\pi
678678 4.45742i 0.171186i
679679 −28.1866 −1.08170
680680 15.2455 21.4612i 0.584639 0.823001i
681681 −0.887625 −0.0340139
682682 0 0
683683 38.9856i 1.49174i 0.666090 + 0.745871i 0.267966π0.267966\pi
−0.666090 + 0.745871i 0.732034π0.732034\pi
684684 0.379898 0.0145257
685685 −7.92257 5.62799i −0.302706 0.215034i
686686 −23.3384 −0.891066
687687 2.65750i 0.101390i
688688 7.16984i 0.273348i
689689 −24.0634 −0.916743
690690 −6.87915 4.88678i −0.261885 0.186036i
691691 5.91854 0.225152 0.112576 0.993643i 0.464090π-0.464090\pi
0.112576 + 0.993643i 0.464090π0.464090\pi
692692 1.61309i 0.0613205i
693693 0 0
694694 −27.5230 −1.04476
695695 10.7514 15.1348i 0.407823 0.574096i
696696 3.69747 0.140152
697697 19.6871i 0.745701i
698698 19.7042i 0.745817i
699699 −1.62275 −0.0613779
700700 −5.82599 + 2.03133i −0.220202 + 0.0767770i
701701 11.9672 0.451996 0.225998 0.974128i 0.427436π-0.427436\pi
0.225998 + 0.974128i 0.427436π0.427436\pi
702702 7.27186i 0.274459i
703703 0.145064i 0.00547120i
704704 0 0
705705 −2.32126 + 3.26765i −0.0874236 + 0.123067i
706706 −29.7894 −1.12114
707707 35.7799i 1.34564i
708708 1.30412i 0.0490117i
709709 −6.80850 −0.255699 −0.127849 0.991794i 0.540807π-0.540807\pi
−0.127849 + 0.991794i 0.540807π0.540807\pi
710710 18.8979 + 13.4246i 0.709225 + 0.503816i
711711 −27.8271 −1.04360
712712 7.60633i 0.285059i
713713 4.74082i 0.177545i
714714 −4.47251 −0.167380
715715 0 0
716716 −6.59761 −0.246564
717717 8.79917i 0.328611i
718718 25.1468i 0.938469i
719719 9.26411 0.345493 0.172746 0.984966i 0.444736π-0.444736\pi
0.172746 + 0.984966i 0.444736π0.444736\pi
720720 −10.4631 + 14.7289i −0.389935 + 0.548915i
721721 −34.6206 −1.28934
722722 23.3508i 0.869026i
723723 4.38210i 0.162972i
724724 −1.24040 −0.0460992
725725 5.47025 + 15.6891i 0.203160 + 0.582677i
726726 0 0
727727 19.4121i 0.719956i −0.932961 0.359978i 0.882784π-0.882784\pi
0.932961 0.359978i 0.117216π-0.117216\pi
728728 21.8092i 0.808304i
729729 20.1069 0.744699
730730 20.8300 29.3226i 0.770954 1.08528i
731731 9.79975 0.362457
732732 2.46310i 0.0910390i
733733 11.5620i 0.427054i 0.976937 + 0.213527i 0.0684951π0.0684951\pi
−0.976937 + 0.213527i 0.931505π0.931505\pi
734734 −6.66887 −0.246153
735735 −0.208861 0.148370i −0.00770396 0.00547270i
736736 22.1540 0.816608
737737 0 0
738738 18.0884i 0.665842i
739739 −9.10736 −0.335020 −0.167510 0.985870i 0.553573π-0.553573\pi
−0.167510 + 0.985870i 0.553573π0.553573\pi
740740 −0.454653 0.322974i −0.0167134 0.0118728i
741741 0.278794 0.0102418
742742 27.8247i 1.02148i
743743 0.0731008i 0.00268181i 0.999999 + 0.00134090i 0.000426823π0.000426823\pi
−0.999999 + 0.00134090i 0.999573π0.999573\pi
744744 −0.627836 −0.0230176
745745 −10.9643 + 15.4346i −0.401702 + 0.565479i
746746 −21.0991 −0.772492
747747 9.45417i 0.345910i
748748 0 0
749749 26.5265 0.969258
750750 4.82308 + 1.39823i 0.176114 + 0.0510561i
751751 −38.5239 −1.40576 −0.702878 0.711310i 0.748102π-0.748102\pi
−0.702878 + 0.711310i 0.748102π0.748102\pi
752752 13.8765i 0.506025i
753753 0.195236i 0.00711479i
754754 −11.3149 −0.412064
755755 14.3771 20.2387i 0.523235 0.736562i
756756 −2.63541 −0.0958488
757757 28.1617i 1.02355i −0.859118 0.511777i 0.828987π-0.828987\pi
0.859118 0.511777i 0.171013π-0.171013\pi
758758 10.6024i 0.385097i
759759 0 0
760760 −1.54689 1.09887i −0.0561116 0.0398603i
761761 −29.4894 −1.06899 −0.534496 0.845171i 0.679498π-0.679498\pi
−0.534496 + 0.845171i 0.679498π0.679498\pi
762762 5.00164i 0.181190i
763763 12.7795i 0.462650i
764764 1.05871 0.0383030
765765 20.1315 + 14.3009i 0.727856 + 0.517051i
766766 −11.9322 −0.431128
767767 20.7147i 0.747965i
768768 3.91285i 0.141193i
769769 −8.42410 −0.303781 −0.151890 0.988397i 0.548536π-0.548536\pi
−0.151890 + 0.988397i 0.548536π0.548536\pi
770770 0 0
771771 8.63364 0.310933
772772 5.00000i 0.179954i
773773 0.897483i 0.0322802i 0.999870 + 0.0161401i 0.00513778π0.00513778\pi
−0.999870 + 0.0161401i 0.994862π0.994862\pi
774774 −9.00396 −0.323641
775775 −0.928857 2.66403i −0.0333655 0.0956947i
776776 −33.3249 −1.19629
777777 0.491805i 0.0176434i
778778 33.7736i 1.21084i
779779 −1.41901 −0.0508413
780780 0.620713 0.873782i 0.0222251 0.0312864i
781781 0 0
782782 39.9287i 1.42785i
783783 7.09699i 0.253626i
784784 −0.886957 −0.0316770
785785 25.0949 + 17.8268i 0.895675 + 0.636265i
786786 −4.56559 −0.162849
787787 37.8007i 1.34745i 0.738983 + 0.673724i 0.235306π0.235306\pi
−0.738983 + 0.673724i 0.764694π0.764694\pi
788788 0.633165i 0.0225556i
789789 1.81133 0.0644852
790790 21.8295 + 15.5072i 0.776660 + 0.551720i
791791 25.6595 0.912346
792792 0 0
793793 39.1242i 1.38934i
794794 13.1442 0.466470
795795 4.11052 5.78641i 0.145785 0.205223i
796796 2.48329 0.0880177
797797 15.1906i 0.538078i −0.963129 0.269039i 0.913294π-0.913294\pi
0.963129 0.269039i 0.0867061π-0.0867061\pi
798798 0.322371i 0.0114118i
799799 18.9665 0.670985
800800 −12.4491 + 4.34058i −0.440142 + 0.153463i
801801 −7.13504 −0.252104
802802 16.9237i 0.597598i
803803 0 0
804804 0.556959 0.0196424
805805 28.1311 39.6004i 0.991492 1.39573i
806806 1.92129 0.0676745
807807 10.4844i 0.369067i
808808 42.3024i 1.48819i
809809 39.7109 1.39616 0.698080 0.716020i 0.254038π-0.254038\pi
0.698080 + 0.716020i 0.254038π0.254038\pi
810810 −17.6027 12.5045i −0.618494 0.439363i
811811 8.81679 0.309599 0.154800 0.987946i 0.450527π-0.450527\pi
0.154800 + 0.987946i 0.450527π0.450527\pi
812812 4.10065i 0.143905i
813813 5.85145i 0.205219i
814814 0 0
815815 −16.2987 11.5782i −0.570918 0.405566i
816816 −3.94981 −0.138271
817817 0.706350i 0.0247121i
818818 27.5283i 0.962506i
819819 20.4579 0.714858
820820 −3.15931 + 4.44739i −0.110328 + 0.155310i
821821 −8.42070 −0.293884 −0.146942 0.989145i 0.546943π-0.546943\pi
−0.146942 + 0.989145i 0.546943π0.546943\pi
822822 1.95204i 0.0680853i
823823 23.9040i 0.833241i 0.909080 + 0.416621i 0.136786π0.136786\pi
−0.909080 + 0.416621i 0.863214π0.863214\pi
824824 −40.9319 −1.42593
825825 0 0
826826 23.9526 0.833416
827827 47.5118i 1.65215i 0.563561 + 0.826074i 0.309431π0.309431\pi
−0.563561 + 0.826074i 0.690569π0.690569\pi
828828 11.4983i 0.399593i
829829 28.2003 0.979437 0.489718 0.871881i 0.337100π-0.337100\pi
0.489718 + 0.871881i 0.337100π0.337100\pi
830830 −5.26851 + 7.41652i −0.182873 + 0.257431i
831831 6.55306 0.227323
832832 24.5280i 0.850354i
833833 1.21229i 0.0420035i
834834 −3.72907 −0.129127
835835 −30.8406 21.9084i −1.06728 0.758171i
836836 0 0
837837 1.20508i 0.0416537i
838838 0.630232i 0.0217710i
839839 −22.3406 −0.771284 −0.385642 0.922648i 0.626020π-0.626020\pi
−0.385642 + 0.922648i 0.626020π0.626020\pi
840840 5.24436 + 3.72546i 0.180948 + 0.128541i
841841 −17.9572 −0.619214
842842 16.3072i 0.561983i
843843 4.99201i 0.171934i
844844 9.02811 0.310760
845845 6.97506 9.81884i 0.239949 0.337778i
846846 −17.4263 −0.599128
847847 0 0
848848 24.5728i 0.843833i
849849 7.46325 0.256138
850850 −7.82314 22.4373i −0.268331 0.769593i
851851 4.39063 0.150509
852852 1.45937i 0.0499973i
853853 8.15265i 0.279141i −0.990212 0.139571i 0.955428π-0.955428\pi
0.990212 0.139571i 0.0445723π-0.0445723\pi
854854 −45.2395 −1.54807
855855 1.03079 1.45105i 0.0352522 0.0496247i
856856 31.3622 1.07194
857857 4.42433i 0.151132i −0.997141 0.0755662i 0.975924π-0.975924\pi
0.997141 0.0755662i 0.0240764π-0.0240764\pi
858858 0 0
859859 −2.90501 −0.0991176 −0.0495588 0.998771i 0.515782π-0.515782\pi
−0.0495588 + 0.998771i 0.515782π0.515782\pi
860860 −2.21381 1.57263i −0.0754901 0.0536263i
861861 4.81081 0.163952
862862 36.2873i 1.23595i
863863 17.7101i 0.602858i −0.953489 0.301429i 0.902536π-0.902536\pi
0.953489 0.301429i 0.0974636π-0.0974636\pi
864864 −5.63138 −0.191583
865865 −6.16131 4.37684i −0.209491 0.148817i
866866 12.6071 0.428408
867867 0.789095i 0.0267991i
868868 0.696297i 0.0236339i
869869 0 0
870870 1.93281 2.72084i 0.0655285 0.0922450i
871871 −8.84680 −0.299762
872872 15.1092i 0.511662i
873873 31.2601i 1.05799i
874874 2.87800 0.0973497
875875 −8.04902 + 27.7645i −0.272107 + 0.938610i
876876 2.26441 0.0765073
877877 51.3798i 1.73497i −0.497461 0.867487i 0.665734π-0.665734\pi
0.497461 0.867487i 0.334266π-0.334266\pi
878878 1.89179i 0.0638448i
879879 −8.15803 −0.275164
880880 0 0
881881 33.6727 1.13446 0.567231 0.823559i 0.308015π-0.308015\pi
0.567231 + 0.823559i 0.308015π0.308015\pi
882882 1.11385i 0.0375052i
883883 13.9106i 0.468128i −0.972221 0.234064i 0.924797π-0.924797\pi
0.972221 0.234064i 0.0752026π-0.0752026\pi
884884 −5.07170 −0.170580
885885 4.98117 + 3.53850i 0.167440 + 0.118945i
886886 −4.18638 −0.140644
887887 44.7006i 1.50090i −0.660927 0.750450i 0.729837π-0.729837\pi
0.660927 0.750450i 0.270163π-0.270163\pi
888888 0.581460i 0.0195125i
889889 28.7923 0.965664
890890 5.59723 + 3.97613i 0.187620 + 0.133280i
891891 0 0
892892 10.4388i 0.349516i
893893 1.36707i 0.0457473i
894894 3.80292 0.127189
895895 −17.9015 + 25.2000i −0.598380 + 0.842344i
896896 14.7264 0.491976
897897 8.43821i 0.281744i
898898 39.9198i 1.33214i
899899 −1.87509 −0.0625376
900900 −2.25283 6.46127i −0.0750943 0.215376i
901901 −33.5861 −1.11892
902902 0 0
903903 2.39471i 0.0796909i
904904 30.3371 1.00900
905905 −3.36562 + 4.73781i −0.111877 + 0.157490i
906906 −4.98662 −0.165669
907907 22.7980i 0.756994i −0.925602 0.378497i 0.876441π-0.876441\pi
0.925602 0.378497i 0.123559π-0.123559\pi
908908 1.16387i 0.0386244i
909909 39.6814 1.31615
910910 −16.0486 11.4006i −0.532007 0.377925i
911911 37.5625 1.24450 0.622250 0.782819i 0.286219π-0.286219\pi
0.622250 + 0.782819i 0.286219π0.286219\pi
912912 0.284696i 0.00942722i
913913 0 0
914914 15.0214 0.496863
915915 −9.40801 6.68321i −0.311019 0.220940i
916916 −3.48456 −0.115133
917917 26.2822i 0.867915i
918918 10.1496i 0.334986i
919919 −39.7124 −1.30999 −0.654996 0.755632i 0.727330π-0.727330\pi
−0.654996 + 0.755632i 0.727330π0.727330\pi
920920 33.2594 46.8195i 1.09653 1.54359i
921921 −7.39044 −0.243523
922922 20.4472i 0.673392i
923923 23.1808i 0.763005i
924924 0 0
925925 −2.46724 + 0.860246i −0.0811225 + 0.0282847i
926926 −18.0536 −0.593278
927927 38.3958i 1.26108i
928928 8.76234i 0.287638i
929929 −20.7298 −0.680123 −0.340061 0.940403i 0.610448π-0.610448\pi
−0.340061 + 0.940403i 0.610448π0.610448\pi
930930 −0.328195 + 0.462003i −0.0107619 + 0.0151497i
931931 0.0873802 0.00286377
932932 2.12777i 0.0696975i
933933 3.18805i 0.104372i
934934 37.6187 1.23092
935935 0 0
936936 24.1874 0.790588
937937 55.8506i 1.82456i −0.409568 0.912280i 0.634320π-0.634320\pi
0.409568 0.912280i 0.365680π-0.365680\pi
938938 10.2296i 0.334009i
939939 −0.630138 −0.0205638
940940 −4.28460 3.04367i −0.139748 0.0992737i
941941 −13.3644 −0.435667 −0.217834 0.975986i 0.569899π-0.569899\pi
−0.217834 + 0.975986i 0.569899π0.569899\pi
942942 6.18313i 0.201457i
943943 42.9489i 1.39861i
944944 21.1532 0.688479
945945 −7.15072 + 10.0661i −0.232613 + 0.327451i
946946 0 0
947947 42.2245i 1.37211i 0.727550 + 0.686055i 0.240659π0.240659\pi
−0.727550 + 0.686055i 0.759341π0.759341\pi
948948 1.68577i 0.0547511i
949949 −35.9681 −1.16757
950950 −1.61724 + 0.563879i −0.0524703 + 0.0182946i
951951 6.36110 0.206273
952952 30.4399i 0.986562i
953953 14.7188i 0.476790i 0.971168 + 0.238395i 0.0766213π0.0766213\pi
−0.971168 + 0.238395i 0.923379π0.923379\pi
954954 30.8587 0.999089
955955 2.87264 4.04384i 0.0929565 0.130856i
956956 −11.5376 −0.373154
957957 0 0
958958 17.2750i 0.558131i
959959 −11.2371 −0.362865
960960 5.89812 + 4.18988i 0.190361 + 0.135228i
961961 −30.6816 −0.989729
962962 1.77937i 0.0573691i
963963 29.4190i 0.948015i
964964 −5.74589 −0.185063
965965 19.0979 + 13.5666i 0.614782 + 0.436725i
966966 −9.75715 −0.313931
967967 32.2786i 1.03801i 0.854771 + 0.519005i 0.173697π0.173697\pi
−0.854771 + 0.519005i 0.826303π0.826303\pi
968968 0 0
969969 0.389123 0.0125004
970970 −17.4203 + 24.5226i −0.559331 + 0.787374i
971971 −42.8008 −1.37354 −0.686771 0.726874i 0.740973π-0.740973\pi
−0.686771 + 0.726874i 0.740973π0.740973\pi
972972 4.41716i 0.141681i
973973 21.4667i 0.688190i
974974 42.1175 1.34953
975975 −1.65328 4.74171i −0.0529472 0.151856i
976976 −39.9524 −1.27884
977977 12.1972i 0.390222i −0.980781 0.195111i 0.937493π-0.937493\pi
0.980781 0.195111i 0.0625067π-0.0625067\pi
978978 4.01584i 0.128412i
979979 0 0
980980 0.194545 0.273862i 0.00621451 0.00874821i
981981 14.1730 0.452510
982982 3.94176i 0.125787i
983983 14.0671i 0.448670i 0.974512 + 0.224335i 0.0720211π0.0720211\pi
−0.974512 + 0.224335i 0.927979π0.927979\pi
984984 5.68781 0.181321
985985 −2.41842 1.71798i −0.0770572 0.0547395i
986986 −15.7926 −0.502938
987987 4.63472i 0.147525i
988988 0.365560i 0.0116300i
989989 21.3790 0.679811
990990 0 0
991991 −22.9455 −0.728887 −0.364444 0.931225i 0.618741π-0.618741\pi
−0.364444 + 0.931225i 0.618741π0.618741\pi
992992 1.48786i 0.0472396i
993993 4.59321i 0.145761i
994994 26.8041 0.850175
995995 6.73797 9.48509i 0.213608 0.300698i
996996 −0.572734 −0.0181478
997997 3.63447i 0.115105i −0.998342 0.0575525i 0.981670π-0.981670\pi
0.998342 0.0575525i 0.0183297π-0.0183297\pi
998998 8.05612i 0.255012i
999999 −1.11607 −0.0353108
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 605.2.b.g.364.3 8
5.2 odd 4 3025.2.a.bl.1.6 8
5.3 odd 4 3025.2.a.bl.1.3 8
5.4 even 2 inner 605.2.b.g.364.6 8
11.2 odd 10 605.2.j.d.444.3 16
11.3 even 5 605.2.j.h.9.2 16
11.4 even 5 605.2.j.h.269.3 16
11.5 even 5 55.2.j.a.14.3 yes 16
11.6 odd 10 605.2.j.d.124.2 16
11.7 odd 10 605.2.j.g.269.2 16
11.8 odd 10 605.2.j.g.9.3 16
11.9 even 5 55.2.j.a.4.2 16
11.10 odd 2 605.2.b.f.364.6 8
33.5 odd 10 495.2.ba.a.289.2 16
33.20 odd 10 495.2.ba.a.334.3 16
44.27 odd 10 880.2.cd.c.289.2 16
44.31 odd 10 880.2.cd.c.609.3 16
55.4 even 10 605.2.j.h.269.2 16
55.9 even 10 55.2.j.a.4.3 yes 16
55.14 even 10 605.2.j.h.9.3 16
55.19 odd 10 605.2.j.g.9.2 16
55.24 odd 10 605.2.j.d.444.2 16
55.27 odd 20 275.2.h.d.201.2 16
55.29 odd 10 605.2.j.g.269.3 16
55.32 even 4 3025.2.a.bk.1.3 8
55.38 odd 20 275.2.h.d.201.3 16
55.39 odd 10 605.2.j.d.124.3 16
55.42 odd 20 275.2.h.d.26.2 16
55.43 even 4 3025.2.a.bk.1.6 8
55.49 even 10 55.2.j.a.14.2 yes 16
55.53 odd 20 275.2.h.d.26.3 16
55.54 odd 2 605.2.b.f.364.3 8
165.104 odd 10 495.2.ba.a.289.3 16
165.119 odd 10 495.2.ba.a.334.2 16
220.119 odd 10 880.2.cd.c.609.2 16
220.159 odd 10 880.2.cd.c.289.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.j.a.4.2 16 11.9 even 5
55.2.j.a.4.3 yes 16 55.9 even 10
55.2.j.a.14.2 yes 16 55.49 even 10
55.2.j.a.14.3 yes 16 11.5 even 5
275.2.h.d.26.2 16 55.42 odd 20
275.2.h.d.26.3 16 55.53 odd 20
275.2.h.d.201.2 16 55.27 odd 20
275.2.h.d.201.3 16 55.38 odd 20
495.2.ba.a.289.2 16 33.5 odd 10
495.2.ba.a.289.3 16 165.104 odd 10
495.2.ba.a.334.2 16 165.119 odd 10
495.2.ba.a.334.3 16 33.20 odd 10
605.2.b.f.364.3 8 55.54 odd 2
605.2.b.f.364.6 8 11.10 odd 2
605.2.b.g.364.3 8 1.1 even 1 trivial
605.2.b.g.364.6 8 5.4 even 2 inner
605.2.j.d.124.2 16 11.6 odd 10
605.2.j.d.124.3 16 55.39 odd 10
605.2.j.d.444.2 16 55.24 odd 10
605.2.j.d.444.3 16 11.2 odd 10
605.2.j.g.9.2 16 55.19 odd 10
605.2.j.g.9.3 16 11.8 odd 10
605.2.j.g.269.2 16 11.7 odd 10
605.2.j.g.269.3 16 55.29 odd 10
605.2.j.h.9.2 16 11.3 even 5
605.2.j.h.9.3 16 55.14 even 10
605.2.j.h.269.2 16 55.4 even 10
605.2.j.h.269.3 16 11.4 even 5
880.2.cd.c.289.2 16 44.27 odd 10
880.2.cd.c.289.3 16 220.159 odd 10
880.2.cd.c.609.2 16 220.119 odd 10
880.2.cd.c.609.3 16 44.31 odd 10
3025.2.a.bk.1.3 8 55.32 even 4
3025.2.a.bk.1.6 8 55.43 even 4
3025.2.a.bl.1.3 8 5.3 odd 4
3025.2.a.bl.1.6 8 5.2 odd 4