Properties

Label 784.2.i.k.177.2
Level 784784
Weight 22
Character 784.177
Analytic conductor 6.2606.260
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(177,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.177");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 784=2472 784 = 2^{4} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 784.i (of order 33, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.260271518476.26027151847
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(2,3)\Q(\sqrt{2}, \sqrt{-3})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+2x2+4 x^{4} + 2x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 392)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 177.2
Root 0.707107+1.22474i0.707107 + 1.22474i of defining polynomial
Character χ\chi == 784.177
Dual form 784.2.i.k.753.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.41421+2.44949i)q3+(1.41421+2.44949i)q5+(2.50000+4.33013i)q9+(2.000003.46410i)q112.82843q138.00000q15+(2.82843+4.89898i)q17+(1.41421+2.44949i)q19+(1.500002.59808i)q255.65685q27+2.00000q29+(2.828434.89898i)q31+(5.656859.79796i)q33+(5.00000+8.66025i)q37+(4.000006.92820i)q39+5.65685q41+4.00000q43+(7.0710712.2474i)q45+(2.828434.89898i)q47+(8.00000+13.8564i)q51+(3.000005.19615i)q53+11.3137q558.00000q57+(1.414212.44949i)q59+(7.07107+12.2474i)q61+(4.000006.92820i)q65+(6.00000+10.3923i)q67+(4.242647.34847i)q75+(4.000006.92820i)q79+(0.5000000.866025i)q81+14.1421q8316.0000q85+(2.82843+4.89898i)q87+(8.0000013.8564i)q93+(4.000006.92820i)q95+5.65685q97+20.0000q99+O(q100)q+(1.41421 + 2.44949i) q^{3} +(-1.41421 + 2.44949i) q^{5} +(-2.50000 + 4.33013i) q^{9} +(-2.00000 - 3.46410i) q^{11} -2.82843 q^{13} -8.00000 q^{15} +(2.82843 + 4.89898i) q^{17} +(-1.41421 + 2.44949i) q^{19} +(-1.50000 - 2.59808i) q^{25} -5.65685 q^{27} +2.00000 q^{29} +(-2.82843 - 4.89898i) q^{31} +(5.65685 - 9.79796i) q^{33} +(-5.00000 + 8.66025i) q^{37} +(-4.00000 - 6.92820i) q^{39} +5.65685 q^{41} +4.00000 q^{43} +(-7.07107 - 12.2474i) q^{45} +(2.82843 - 4.89898i) q^{47} +(-8.00000 + 13.8564i) q^{51} +(-3.00000 - 5.19615i) q^{53} +11.3137 q^{55} -8.00000 q^{57} +(-1.41421 - 2.44949i) q^{59} +(-7.07107 + 12.2474i) q^{61} +(4.00000 - 6.92820i) q^{65} +(6.00000 + 10.3923i) q^{67} +(4.24264 - 7.34847i) q^{75} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +14.1421 q^{83} -16.0000 q^{85} +(2.82843 + 4.89898i) q^{87} +(8.00000 - 13.8564i) q^{93} +(-4.00000 - 6.92820i) q^{95} +5.65685 q^{97} +20.0000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q10q98q1132q156q25+8q2920q3716q39+16q4332q5112q5332q57+16q65+24q67+16q792q8164q85+32q93++80q99+O(q100) 4 q - 10 q^{9} - 8 q^{11} - 32 q^{15} - 6 q^{25} + 8 q^{29} - 20 q^{37} - 16 q^{39} + 16 q^{43} - 32 q^{51} - 12 q^{53} - 32 q^{57} + 16 q^{65} + 24 q^{67} + 16 q^{79} - 2 q^{81} - 64 q^{85} + 32 q^{93}+ \cdots + 80 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/784Z)×\left(\mathbb{Z}/784\mathbb{Z}\right)^\times.

nn 197197 687687 689689
χ(n)\chi(n) 11 11 e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 1.41421 + 2.44949i 0.816497 + 1.41421i 0.908248 + 0.418432i 0.137420π0.137420\pi
−0.0917517 + 0.995782i 0.529247π0.529247\pi
44 0 0
55 −1.41421 + 2.44949i −0.632456 + 1.09545i 0.354593 + 0.935021i 0.384620π0.384620\pi
−0.987048 + 0.160424i 0.948714π0.948714\pi
66 0 0
77 0 0
88 0 0
99 −2.50000 + 4.33013i −0.833333 + 1.44338i
1010 0 0
1111 −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i 0.960630π-0.960630\pi
0.389338 0.921095i 0.372704π-0.372704\pi
1212 0 0
1313 −2.82843 −0.784465 −0.392232 0.919866i 0.628297π-0.628297\pi
−0.392232 + 0.919866i 0.628297π0.628297\pi
1414 0 0
1515 −8.00000 −2.06559
1616 0 0
1717 2.82843 + 4.89898i 0.685994 + 1.18818i 0.973123 + 0.230285i 0.0739659π0.0739659\pi
−0.287129 + 0.957892i 0.592701π0.592701\pi
1818 0 0
1919 −1.41421 + 2.44949i −0.324443 + 0.561951i −0.981399 0.191977i 0.938510π-0.938510\pi
0.656957 + 0.753928i 0.271843π0.271843\pi
2020 0 0
2121 0 0
2222 0 0
2323 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
2424 0 0
2525 −1.50000 2.59808i −0.300000 0.519615i
2626 0 0
2727 −5.65685 −1.08866
2828 0 0
2929 2.00000 0.371391 0.185695 0.982607i 0.440546π-0.440546\pi
0.185695 + 0.982607i 0.440546π0.440546\pi
3030 0 0
3131 −2.82843 4.89898i −0.508001 0.879883i −0.999957 0.00926296i 0.997051π-0.997051\pi
0.491957 0.870620i 0.336282π-0.336282\pi
3232 0 0
3333 5.65685 9.79796i 0.984732 1.70561i
3434 0 0
3535 0 0
3636 0 0
3737 −5.00000 + 8.66025i −0.821995 + 1.42374i 0.0821995 + 0.996616i 0.473806π0.473806\pi
−0.904194 + 0.427121i 0.859528π0.859528\pi
3838 0 0
3939 −4.00000 6.92820i −0.640513 1.10940i
4040 0 0
4141 5.65685 0.883452 0.441726 0.897150i 0.354366π-0.354366\pi
0.441726 + 0.897150i 0.354366π0.354366\pi
4242 0 0
4343 4.00000 0.609994 0.304997 0.952353i 0.401344π-0.401344\pi
0.304997 + 0.952353i 0.401344π0.401344\pi
4444 0 0
4545 −7.07107 12.2474i −1.05409 1.82574i
4646 0 0
4747 2.82843 4.89898i 0.412568 0.714590i −0.582601 0.812758i 0.697965π-0.697965\pi
0.995170 + 0.0981685i 0.0312984π0.0312984\pi
4848 0 0
4949 0 0
5050 0 0
5151 −8.00000 + 13.8564i −1.12022 + 1.94029i
5252 0 0
5353 −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i 0.301865π-0.301865\pi
−0.995117 + 0.0987002i 0.968532π0.968532\pi
5454 0 0
5555 11.3137 1.52554
5656 0 0
5757 −8.00000 −1.05963
5858 0 0
5959 −1.41421 2.44949i −0.184115 0.318896i 0.759163 0.650901i 0.225609π-0.225609\pi
−0.943278 + 0.332004i 0.892275π0.892275\pi
6060 0 0
6161 −7.07107 + 12.2474i −0.905357 + 1.56813i −0.0849208 + 0.996388i 0.527064π0.527064\pi
−0.820437 + 0.571737i 0.806270π0.806270\pi
6262 0 0
6363 0 0
6464 0 0
6565 4.00000 6.92820i 0.496139 0.859338i
6666 0 0
6767 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i 0.0952216π0.0952216\pi
−0.222571 + 0.974916i 0.571445π0.571445\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
7474 0 0
7575 4.24264 7.34847i 0.489898 0.848528i
7676 0 0
7777 0 0
7878 0 0
7979 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i 0.684745π-0.684745\pi
0.998388 + 0.0567635i 0.0180781π0.0180781\pi
8080 0 0
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 0 0
8383 14.1421 1.55230 0.776151 0.630548i 0.217170π-0.217170\pi
0.776151 + 0.630548i 0.217170π0.217170\pi
8484 0 0
8585 −16.0000 −1.73544
8686 0 0
8787 2.82843 + 4.89898i 0.303239 + 0.525226i
8888 0 0
8989 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
9090 0 0
9191 0 0
9292 0 0
9393 8.00000 13.8564i 0.829561 1.43684i
9494 0 0
9595 −4.00000 6.92820i −0.410391 0.710819i
9696 0 0
9797 5.65685 0.574367 0.287183 0.957876i 0.407281π-0.407281\pi
0.287183 + 0.957876i 0.407281π0.407281\pi
9898 0 0
9999 20.0000 2.01008
100100 0 0
101101 4.24264 + 7.34847i 0.422159 + 0.731200i 0.996150 0.0876610i 0.0279392π-0.0279392\pi
−0.573992 + 0.818861i 0.694606π0.694606\pi
102102 0 0
103103 −8.48528 + 14.6969i −0.836080 + 1.44813i 0.0570688 + 0.998370i 0.481825π0.481825\pi
−0.893148 + 0.449762i 0.851509π0.851509\pi
104104 0 0
105105 0 0
106106 0 0
107107 −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i 0.363630π0.363630\pi
−0.995474 + 0.0950377i 0.969703π0.969703\pi
108108 0 0
109109 −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i 0.197202π-0.197202\pi
−0.909935 + 0.414751i 0.863869π0.863869\pi
110110 0 0
111111 −28.2843 −2.68462
112112 0 0
113113 10.0000 0.940721 0.470360 0.882474i 0.344124π-0.344124\pi
0.470360 + 0.882474i 0.344124π0.344124\pi
114114 0 0
115115 0 0
116116 0 0
117117 7.07107 12.2474i 0.653720 1.13228i
118118 0 0
119119 0 0
120120 0 0
121121 −2.50000 + 4.33013i −0.227273 + 0.393648i
122122 0 0
123123 8.00000 + 13.8564i 0.721336 + 1.24939i
124124 0 0
125125 −5.65685 −0.505964
126126 0 0
127127 −8.00000 −0.709885 −0.354943 0.934888i 0.615500π-0.615500\pi
−0.354943 + 0.934888i 0.615500π0.615500\pi
128128 0 0
129129 5.65685 + 9.79796i 0.498058 + 0.862662i
130130 0 0
131131 −7.07107 + 12.2474i −0.617802 + 1.07006i 0.372084 + 0.928199i 0.378643π0.378643\pi
−0.989886 + 0.141865i 0.954690π0.954690\pi
132132 0 0
133133 0 0
134134 0 0
135135 8.00000 13.8564i 0.688530 1.19257i
136136 0 0
137137 5.00000 + 8.66025i 0.427179 + 0.739895i 0.996621 0.0821359i 0.0261741π-0.0261741\pi
−0.569442 + 0.822031i 0.692841π0.692841\pi
138138 0 0
139139 −14.1421 −1.19952 −0.599760 0.800180i 0.704737π-0.704737\pi
−0.599760 + 0.800180i 0.704737π0.704737\pi
140140 0 0
141141 16.0000 1.34744
142142 0 0
143143 5.65685 + 9.79796i 0.473050 + 0.819346i
144144 0 0
145145 −2.82843 + 4.89898i −0.234888 + 0.406838i
146146 0 0
147147 0 0
148148 0 0
149149 5.00000 8.66025i 0.409616 0.709476i −0.585231 0.810867i 0.698996π-0.698996\pi
0.994847 + 0.101391i 0.0323294π0.0323294\pi
150150 0 0
151151 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i 0.0589965π0.0589965\pi
−0.331842 + 0.943335i 0.607670π0.607670\pi
152152 0 0
153153 −28.2843 −2.28665
154154 0 0
155155 16.0000 1.28515
156156 0 0
157157 7.07107 + 12.2474i 0.564333 + 0.977453i 0.997111 + 0.0759527i 0.0241998π0.0241998\pi
−0.432779 + 0.901500i 0.642467π0.642467\pi
158158 0 0
159159 8.48528 14.6969i 0.672927 1.16554i
160160 0 0
161161 0 0
162162 0 0
163163 10.0000 17.3205i 0.783260 1.35665i −0.146772 0.989170i 0.546888π-0.546888\pi
0.930033 0.367477i 0.119778π-0.119778\pi
164164 0 0
165165 16.0000 + 27.7128i 1.24560 + 2.15744i
166166 0 0
167167 5.65685 0.437741 0.218870 0.975754i 0.429763π-0.429763\pi
0.218870 + 0.975754i 0.429763π0.429763\pi
168168 0 0
169169 −5.00000 −0.384615
170170 0 0
171171 −7.07107 12.2474i −0.540738 0.936586i
172172 0 0
173173 1.41421 2.44949i 0.107521 0.186231i −0.807245 0.590217i 0.799042π-0.799042\pi
0.914765 + 0.403986i 0.132375π0.132375\pi
174174 0 0
175175 0 0
176176 0 0
177177 4.00000 6.92820i 0.300658 0.520756i
178178 0 0
179179 −10.0000 17.3205i −0.747435 1.29460i −0.949048 0.315130i 0.897952π-0.897952\pi
0.201613 0.979465i 0.435382π-0.435382\pi
180180 0 0
181181 8.48528 0.630706 0.315353 0.948974i 0.397877π-0.397877\pi
0.315353 + 0.948974i 0.397877π0.397877\pi
182182 0 0
183183 −40.0000 −2.95689
184184 0 0
185185 −14.1421 24.4949i −1.03975 1.80090i
186186 0 0
187187 11.3137 19.5959i 0.827340 1.43300i
188188 0 0
189189 0 0
190190 0 0
191191 12.0000 20.7846i 0.868290 1.50392i 0.00454614 0.999990i 0.498553π-0.498553\pi
0.863743 0.503932i 0.168114π-0.168114\pi
192192 0 0
193193 −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i 0.283859π-0.283859\pi
−0.987945 + 0.154805i 0.950525π0.950525\pi
194194 0 0
195195 22.6274 1.62038
196196 0 0
197197 22.0000 1.56744 0.783718 0.621117i 0.213321π-0.213321\pi
0.783718 + 0.621117i 0.213321π0.213321\pi
198198 0 0
199199 8.48528 + 14.6969i 0.601506 + 1.04184i 0.992593 + 0.121485i 0.0387656π0.0387656\pi
−0.391088 + 0.920353i 0.627901π0.627901\pi
200200 0 0
201201 −16.9706 + 29.3939i −1.19701 + 2.07328i
202202 0 0
203203 0 0
204204 0 0
205205 −8.00000 + 13.8564i −0.558744 + 0.967773i
206206 0 0
207207 0 0
208208 0 0
209209 11.3137 0.782586
210210 0 0
211211 4.00000 0.275371 0.137686 0.990476i 0.456034π-0.456034\pi
0.137686 + 0.990476i 0.456034π0.456034\pi
212212 0 0
213213 0 0
214214 0 0
215215 −5.65685 + 9.79796i −0.385794 + 0.668215i
216216 0 0
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 −8.00000 13.8564i −0.538138 0.932083i
222222 0 0
223223 11.3137 0.757622 0.378811 0.925474i 0.376333π-0.376333\pi
0.378811 + 0.925474i 0.376333π0.376333\pi
224224 0 0
225225 15.0000 1.00000
226226 0 0
227227 4.24264 + 7.34847i 0.281594 + 0.487735i 0.971778 0.235899i 0.0758036π-0.0758036\pi
−0.690184 + 0.723634i 0.742470π0.742470\pi
228228 0 0
229229 12.7279 22.0454i 0.841085 1.45680i −0.0478936 0.998852i 0.515251π-0.515251\pi
0.888978 0.457949i 0.151416π-0.151416\pi
230230 0 0
231231 0 0
232232 0 0
233233 5.00000 8.66025i 0.327561 0.567352i −0.654466 0.756091i 0.727107π-0.727107\pi
0.982027 + 0.188739i 0.0604400π0.0604400\pi
234234 0 0
235235 8.00000 + 13.8564i 0.521862 + 0.903892i
236236 0 0
237237 22.6274 1.46981
238238 0 0
239239 8.00000 0.517477 0.258738 0.965947i 0.416693π-0.416693\pi
0.258738 + 0.965947i 0.416693π0.416693\pi
240240 0 0
241241 −14.1421 24.4949i −0.910975 1.57786i −0.812690 0.582697i 0.801998π-0.801998\pi
−0.0982854 0.995158i 0.531336π-0.531336\pi
242242 0 0
243243 −7.07107 + 12.2474i −0.453609 + 0.785674i
244244 0 0
245245 0 0
246246 0 0
247247 4.00000 6.92820i 0.254514 0.440831i
248248 0 0
249249 20.0000 + 34.6410i 1.26745 + 2.19529i
250250 0 0
251251 −14.1421 −0.892644 −0.446322 0.894873i 0.647266π-0.647266\pi
−0.446322 + 0.894873i 0.647266π0.647266\pi
252252 0 0
253253 0 0
254254 0 0
255255 −22.6274 39.1918i −1.41698 2.45429i
256256 0 0
257257 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
258258 0 0
259259 0 0
260260 0 0
261261 −5.00000 + 8.66025i −0.309492 + 0.536056i
262262 0 0
263263 −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i 0.330877π-0.330877\pi
−0.999970 + 0.00771799i 0.997543π0.997543\pi
264264 0 0
265265 16.9706 1.04249
266266 0 0
267267 0 0
268268 0 0
269269 7.07107 + 12.2474i 0.431131 + 0.746740i 0.996971 0.0777747i 0.0247815π-0.0247815\pi
−0.565840 + 0.824515i 0.691448π0.691448\pi
270270 0 0
271271 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
272272 0 0
273273 0 0
274274 0 0
275275 −6.00000 + 10.3923i −0.361814 + 0.626680i
276276 0 0
277277 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i 0.0695395π-0.0695395\pi
−0.675810 + 0.737075i 0.736206π0.736206\pi
278278 0 0
279279 28.2843 1.69334
280280 0 0
281281 6.00000 0.357930 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
282282 0 0
283283 −1.41421 2.44949i −0.0840663 0.145607i 0.820927 0.571034i 0.193457π-0.193457\pi
−0.904993 + 0.425427i 0.860124π0.860124\pi
284284 0 0
285285 11.3137 19.5959i 0.670166 1.16076i
286286 0 0
287287 0 0
288288 0 0
289289 −7.50000 + 12.9904i −0.441176 + 0.764140i
290290 0 0
291291 8.00000 + 13.8564i 0.468968 + 0.812277i
292292 0 0
293293 2.82843 0.165238 0.0826192 0.996581i 0.473671π-0.473671\pi
0.0826192 + 0.996581i 0.473671π0.473671\pi
294294 0 0
295295 8.00000 0.465778
296296 0 0
297297 11.3137 + 19.5959i 0.656488 + 1.13707i
298298 0 0
299299 0 0
300300 0 0
301301 0 0
302302 0 0
303303 −12.0000 + 20.7846i −0.689382 + 1.19404i
304304 0 0
305305 −20.0000 34.6410i −1.14520 1.98354i
306306 0 0
307307 −8.48528 −0.484281 −0.242140 0.970241i 0.577849π-0.577849\pi
−0.242140 + 0.970241i 0.577849π0.577849\pi
308308 0 0
309309 −48.0000 −2.73062
310310 0 0
311311 −11.3137 19.5959i −0.641542 1.11118i −0.985089 0.172047i 0.944962π-0.944962\pi
0.343547 0.939135i 0.388371π-0.388371\pi
312312 0 0
313313 8.48528 14.6969i 0.479616 0.830720i −0.520110 0.854099i 0.674109π-0.674109\pi
0.999727 + 0.0233791i 0.00744247π0.00744247\pi
314314 0 0
315315 0 0
316316 0 0
317317 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i 0.664645π-0.664645\pi
0.999980 0.00635137i 0.00202172π-0.00202172\pi
318318 0 0
319319 −4.00000 6.92820i −0.223957 0.387905i
320320 0 0
321321 −33.9411 −1.89441
322322 0 0
323323 −16.0000 −0.890264
324324 0 0
325325 4.24264 + 7.34847i 0.235339 + 0.407620i
326326 0 0
327327 2.82843 4.89898i 0.156412 0.270914i
328328 0 0
329329 0 0
330330 0 0
331331 −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i 0.351905π0.351905\pi
−0.998298 + 0.0583130i 0.981428π0.981428\pi
332332 0 0
333333 −25.0000 43.3013i −1.36999 2.37289i
334334 0 0
335335 −33.9411 −1.85440
336336 0 0
337337 −10.0000 −0.544735 −0.272367 0.962193i 0.587807π-0.587807\pi
−0.272367 + 0.962193i 0.587807π0.587807\pi
338338 0 0
339339 14.1421 + 24.4949i 0.768095 + 1.33038i
340340 0 0
341341 −11.3137 + 19.5959i −0.612672 + 1.06118i
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 −10.0000 17.3205i −0.536828 0.929814i −0.999072 0.0430610i 0.986289π-0.986289\pi
0.462244 0.886753i 0.347044π-0.347044\pi
348348 0 0
349349 −25.4558 −1.36262 −0.681310 0.731995i 0.738589π-0.738589\pi
−0.681310 + 0.731995i 0.738589π0.738589\pi
350350 0 0
351351 16.0000 0.854017
352352 0 0
353353 −5.65685 9.79796i −0.301084 0.521493i 0.675298 0.737545i 0.264015π-0.264015\pi
−0.976382 + 0.216052i 0.930682π0.930682\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
360360 0 0
361361 5.50000 + 9.52628i 0.289474 + 0.501383i
362362 0 0
363363 −14.1421 −0.742270
364364 0 0
365365 0 0
366366 0 0
367367 16.9706 + 29.3939i 0.885856 + 1.53435i 0.844729 + 0.535194i 0.179761π0.179761\pi
0.0411270 + 0.999154i 0.486905π0.486905\pi
368368 0 0
369369 −14.1421 + 24.4949i −0.736210 + 1.27515i
370370 0 0
371371 0 0
372372 0 0
373373 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i 0.749977π-0.749977\pi
0.965945 + 0.258748i 0.0833099π0.0833099\pi
374374 0 0
375375 −8.00000 13.8564i −0.413118 0.715542i
376376 0 0
377377 −5.65685 −0.291343
378378 0 0
379379 4.00000 0.205466 0.102733 0.994709i 0.467241π-0.467241\pi
0.102733 + 0.994709i 0.467241π0.467241\pi
380380 0 0
381381 −11.3137 19.5959i −0.579619 1.00393i
382382 0 0
383383 14.1421 24.4949i 0.722629 1.25163i −0.237313 0.971433i 0.576267π-0.576267\pi
0.959942 0.280198i 0.0904000π-0.0904000\pi
384384 0 0
385385 0 0
386386 0 0
387387 −10.0000 + 17.3205i −0.508329 + 0.880451i
388388 0 0
389389 11.0000 + 19.0526i 0.557722 + 0.966003i 0.997686 + 0.0679877i 0.0216579π0.0216579\pi
−0.439964 + 0.898015i 0.645009π0.645009\pi
390390 0 0
391391 0 0
392392 0 0
393393 −40.0000 −2.01773
394394 0 0
395395 11.3137 + 19.5959i 0.569254 + 0.985978i
396396 0 0
397397 −4.24264 + 7.34847i −0.212932 + 0.368809i −0.952631 0.304129i 0.901635π-0.901635\pi
0.739699 + 0.672938i 0.234968π0.234968\pi
398398 0 0
399399 0 0
400400 0 0
401401 −3.00000 + 5.19615i −0.149813 + 0.259483i −0.931158 0.364615i 0.881200π-0.881200\pi
0.781345 + 0.624099i 0.214534π0.214534\pi
402402 0 0
403403 8.00000 + 13.8564i 0.398508 + 0.690237i
404404 0 0
405405 2.82843 0.140546
406406 0 0
407407 40.0000 1.98273
408408 0 0
409409 8.48528 + 14.6969i 0.419570 + 0.726717i 0.995896 0.0905030i 0.0288475π-0.0288475\pi
−0.576326 + 0.817220i 0.695514π0.695514\pi
410410 0 0
411411 −14.1421 + 24.4949i −0.697580 + 1.20824i
412412 0 0
413413 0 0
414414 0 0
415415 −20.0000 + 34.6410i −0.981761 + 1.70046i
416416 0 0
417417 −20.0000 34.6410i −0.979404 1.69638i
418418 0 0
419419 −2.82843 −0.138178 −0.0690889 0.997611i 0.522009π-0.522009\pi
−0.0690889 + 0.997611i 0.522009π0.522009\pi
420420 0 0
421421 6.00000 0.292422 0.146211 0.989253i 0.453292π-0.453292\pi
0.146211 + 0.989253i 0.453292π0.453292\pi
422422 0 0
423423 14.1421 + 24.4949i 0.687614 + 1.19098i
424424 0 0
425425 8.48528 14.6969i 0.411597 0.712906i
426426 0 0
427427 0 0
428428 0 0
429429 −16.0000 + 27.7128i −0.772487 + 1.33799i
430430 0 0
431431 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i 0.0295076π0.0295076\pi
−0.417687 + 0.908591i 0.637159π0.637159\pi
432432 0 0
433433 5.65685 0.271851 0.135926 0.990719i 0.456599π-0.456599\pi
0.135926 + 0.990719i 0.456599π0.456599\pi
434434 0 0
435435 −16.0000 −0.767141
436436 0 0
437437 0 0
438438 0 0
439439 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
440440 0 0
441441 0 0
442442 0 0
443443 2.00000 3.46410i 0.0950229 0.164584i −0.814595 0.580030i 0.803041π-0.803041\pi
0.909618 + 0.415445i 0.136374π0.136374\pi
444444 0 0
445445 0 0
446446 0 0
447447 28.2843 1.33780
448448 0 0
449449 2.00000 0.0943858 0.0471929 0.998886i 0.484972π-0.484972\pi
0.0471929 + 0.998886i 0.484972π0.484972\pi
450450 0 0
451451 −11.3137 19.5959i −0.532742 0.922736i
452452 0 0
453453 −22.6274 + 39.1918i −1.06313 + 1.84139i
454454 0 0
455455 0 0
456456 0 0
457457 −9.00000 + 15.5885i −0.421002 + 0.729197i −0.996038 0.0889312i 0.971655π-0.971655\pi
0.575036 + 0.818128i 0.304988π0.304988\pi
458458 0 0
459459 −16.0000 27.7128i −0.746816 1.29352i
460460 0 0
461461 −14.1421 −0.658665 −0.329332 0.944214i 0.606824π-0.606824\pi
−0.329332 + 0.944214i 0.606824π0.606824\pi
462462 0 0
463463 −40.0000 −1.85896 −0.929479 0.368875i 0.879743π-0.879743\pi
−0.929479 + 0.368875i 0.879743π0.879743\pi
464464 0 0
465465 22.6274 + 39.1918i 1.04932 + 1.81748i
466466 0 0
467467 4.24264 7.34847i 0.196326 0.340047i −0.751008 0.660293i 0.770432π-0.770432\pi
0.947334 + 0.320246i 0.103766π0.103766\pi
468468 0 0
469469 0 0
470470 0 0
471471 −20.0000 + 34.6410i −0.921551 + 1.59617i
472472 0 0
473473 −8.00000 13.8564i −0.367840 0.637118i
474474 0 0
475475 8.48528 0.389331
476476 0 0
477477 30.0000 1.37361
478478 0 0
479479 −14.1421 24.4949i −0.646171 1.11920i −0.984030 0.178004i 0.943036π-0.943036\pi
0.337859 0.941197i 0.390297π-0.390297\pi
480480 0 0
481481 14.1421 24.4949i 0.644826 1.11687i
482482 0 0
483483 0 0
484484 0 0
485485 −8.00000 + 13.8564i −0.363261 + 0.629187i
486486 0 0
487487 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
488488 0 0
489489 56.5685 2.55812
490490 0 0
491491 −4.00000 −0.180517 −0.0902587 0.995918i 0.528769π-0.528769\pi
−0.0902587 + 0.995918i 0.528769π0.528769\pi
492492 0 0
493493 5.65685 + 9.79796i 0.254772 + 0.441278i
494494 0 0
495495 −28.2843 + 48.9898i −1.27128 + 2.20193i
496496 0 0
497497 0 0
498498 0 0
499499 14.0000 24.2487i 0.626726 1.08552i −0.361478 0.932381i 0.617728π-0.617728\pi
0.988204 0.153141i 0.0489388π-0.0489388\pi
500500 0 0
501501 8.00000 + 13.8564i 0.357414 + 0.619059i
502502 0 0
503503 −11.3137 −0.504453 −0.252227 0.967668i 0.581163π-0.581163\pi
−0.252227 + 0.967668i 0.581163π0.581163\pi
504504 0 0
505505 −24.0000 −1.06799
506506 0 0
507507 −7.07107 12.2474i −0.314037 0.543928i
508508 0 0
509509 7.07107 12.2474i 0.313420 0.542859i −0.665681 0.746237i 0.731859π-0.731859\pi
0.979100 + 0.203378i 0.0651920π0.0651920\pi
510510 0 0
511511 0 0
512512 0 0
513513 8.00000 13.8564i 0.353209 0.611775i
514514 0 0
515515 −24.0000 41.5692i −1.05757 1.83176i
516516 0 0
517517 −22.6274 −0.995153
518518 0 0
519519 8.00000 0.351161
520520 0 0
521521 2.82843 + 4.89898i 0.123916 + 0.214628i 0.921309 0.388832i 0.127121π-0.127121\pi
−0.797393 + 0.603460i 0.793788π0.793788\pi
522522 0 0
523523 9.89949 17.1464i 0.432875 0.749761i −0.564245 0.825608i 0.690833π-0.690833\pi
0.997119 + 0.0758466i 0.0241659π0.0241659\pi
524524 0 0
525525 0 0
526526 0 0
527527 16.0000 27.7128i 0.696971 1.20719i
528528 0 0
529529 11.5000 + 19.9186i 0.500000 + 0.866025i
530530 0 0
531531 14.1421 0.613716
532532 0 0
533533 −16.0000 −0.693037
534534 0 0
535535 −16.9706 29.3939i −0.733701 1.27081i
536536 0 0
537537 28.2843 48.9898i 1.22056 2.11407i
538538 0 0
539539 0 0
540540 0 0
541541 17.0000 29.4449i 0.730887 1.26593i −0.225617 0.974216i 0.572440π-0.572440\pi
0.956504 0.291718i 0.0942267π-0.0942267\pi
542542 0 0
543543 12.0000 + 20.7846i 0.514969 + 0.891953i
544544 0 0
545545 5.65685 0.242313
546546 0 0
547547 −20.0000 −0.855138 −0.427569 0.903983i 0.640630π-0.640630\pi
−0.427569 + 0.903983i 0.640630π0.640630\pi
548548 0 0
549549 −35.3553 61.2372i −1.50893 2.61354i
550550 0 0
551551 −2.82843 + 4.89898i −0.120495 + 0.208704i
552552 0 0
553553 0 0
554554 0 0
555555 40.0000 69.2820i 1.69791 2.94086i
556556 0 0
557557 −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i 0.947432π-0.947432\pi
0.350824 0.936442i 0.385902π-0.385902\pi
558558 0 0
559559 −11.3137 −0.478519
560560 0 0
561561 64.0000 2.70208
562562 0 0
563563 −21.2132 36.7423i −0.894030 1.54851i −0.835001 0.550249i 0.814533π-0.814533\pi
−0.0590293 0.998256i 0.518801π-0.518801\pi
564564 0 0
565565 −14.1421 + 24.4949i −0.594964 + 1.03051i
566566 0 0
567567 0 0
568568 0 0
569569 −15.0000 + 25.9808i −0.628833 + 1.08917i 0.358954 + 0.933355i 0.383134π0.383134\pi
−0.987786 + 0.155815i 0.950200π0.950200\pi
570570 0 0
571571 −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i 0.304106π-0.304106\pi
−0.995788 + 0.0916910i 0.970773π0.970773\pi
572572 0 0
573573 67.8823 2.83582
574574 0 0
575575 0 0
576576 0 0
577577 −16.9706 29.3939i −0.706494 1.22368i −0.966150 0.257982i 0.916942π-0.916942\pi
0.259656 0.965701i 0.416391π-0.416391\pi
578578 0 0
579579 14.1421 24.4949i 0.587727 1.01797i
580580 0 0
581581 0 0
582582 0 0
583583 −12.0000 + 20.7846i −0.496989 + 0.860811i
584584 0 0
585585 20.0000 + 34.6410i 0.826898 + 1.43223i
586586 0 0
587587 42.4264 1.75113 0.875563 0.483105i 0.160491π-0.160491\pi
0.875563 + 0.483105i 0.160491π0.160491\pi
588588 0 0
589589 16.0000 0.659269
590590 0 0
591591 31.1127 + 53.8888i 1.27981 + 2.21669i
592592 0 0
593593 5.65685 9.79796i 0.232299 0.402354i −0.726185 0.687499i 0.758708π-0.758708\pi
0.958484 + 0.285145i 0.0920418π0.0920418\pi
594594 0 0
595595 0 0
596596 0 0
597597 −24.0000 + 41.5692i −0.982255 + 1.70131i
598598 0 0
599599 16.0000 + 27.7128i 0.653742 + 1.13231i 0.982208 + 0.187799i 0.0601353π0.0601353\pi
−0.328465 + 0.944516i 0.606531π0.606531\pi
600600 0 0
601601 −22.6274 −0.922992 −0.461496 0.887142i 0.652687π-0.652687\pi
−0.461496 + 0.887142i 0.652687π0.652687\pi
602602 0 0
603603 −60.0000 −2.44339
604604 0 0
605605 −7.07107 12.2474i −0.287480 0.497930i
606606 0 0
607607 11.3137 19.5959i 0.459209 0.795374i −0.539710 0.841851i 0.681466π-0.681466\pi
0.998919 + 0.0464772i 0.0147995π0.0147995\pi
608608 0 0
609609 0 0
610610 0 0
611611 −8.00000 + 13.8564i −0.323645 + 0.560570i
612612 0 0
613613 3.00000 + 5.19615i 0.121169 + 0.209871i 0.920229 0.391381i 0.128002π-0.128002\pi
−0.799060 + 0.601251i 0.794669π0.794669\pi
614614 0 0
615615 −45.2548 −1.82485
616616 0 0
617617 30.0000 1.20775 0.603877 0.797077i 0.293622π-0.293622\pi
0.603877 + 0.797077i 0.293622π0.293622\pi
618618 0 0
619619 −7.07107 12.2474i −0.284210 0.492267i 0.688207 0.725514i 0.258398π-0.258398\pi
−0.972417 + 0.233248i 0.925065π0.925065\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 15.5000 26.8468i 0.620000 1.07387i
626626 0 0
627627 16.0000 + 27.7128i 0.638978 + 1.10674i
628628 0 0
629629 −56.5685 −2.25554
630630 0 0
631631 16.0000 0.636950 0.318475 0.947931i 0.396829π-0.396829\pi
0.318475 + 0.947931i 0.396829π0.396829\pi
632632 0 0
633633 5.65685 + 9.79796i 0.224840 + 0.389434i
634634 0 0
635635 11.3137 19.5959i 0.448971 0.777640i
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 5.00000 + 8.66025i 0.197488 + 0.342059i 0.947713 0.319123i 0.103388π-0.103388\pi
−0.750225 + 0.661182i 0.770055π0.770055\pi
642642 0 0
643643 −25.4558 −1.00388 −0.501940 0.864902i 0.667380π-0.667380\pi
−0.501940 + 0.864902i 0.667380π0.667380\pi
644644 0 0
645645 −32.0000 −1.26000
646646 0 0
647647 8.48528 + 14.6969i 0.333591 + 0.577796i 0.983213 0.182461i 0.0584063π-0.0584063\pi
−0.649622 + 0.760257i 0.725073π0.725073\pi
648648 0 0
649649 −5.65685 + 9.79796i −0.222051 + 0.384604i
650650 0 0
651651 0 0
652652 0 0
653653 7.00000 12.1244i 0.273931 0.474463i −0.695934 0.718106i 0.745009π-0.745009\pi
0.969865 + 0.243643i 0.0783426π0.0783426\pi
654654 0 0
655655 −20.0000 34.6410i −0.781465 1.35354i
656656 0 0
657657 0 0
658658 0 0
659659 12.0000 0.467454 0.233727 0.972302i 0.424908π-0.424908\pi
0.233727 + 0.972302i 0.424908π0.424908\pi
660660 0 0
661661 −7.07107 12.2474i −0.275033 0.476371i 0.695111 0.718903i 0.255355π-0.255355\pi
−0.970143 + 0.242532i 0.922022π0.922022\pi
662662 0 0
663663 22.6274 39.1918i 0.878776 1.52208i
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 16.0000 + 27.7128i 0.618596 + 1.07144i
670670 0 0
671671 56.5685 2.18380
672672 0 0
673673 30.0000 1.15642 0.578208 0.815890i 0.303752π-0.303752\pi
0.578208 + 0.815890i 0.303752π0.303752\pi
674674 0 0
675675 8.48528 + 14.6969i 0.326599 + 0.565685i
676676 0 0
677677 −4.24264 + 7.34847i −0.163058 + 0.282425i −0.935964 0.352096i 0.885469π-0.885469\pi
0.772906 + 0.634521i 0.218802π0.218802\pi
678678 0 0
679679 0 0
680680 0 0
681681 −12.0000 + 20.7846i −0.459841 + 0.796468i
682682 0 0
683683 10.0000 + 17.3205i 0.382639 + 0.662751i 0.991439 0.130573i 0.0416818π-0.0416818\pi
−0.608799 + 0.793324i 0.708349π0.708349\pi
684684 0 0
685685 −28.2843 −1.08069
686686 0 0
687687 72.0000 2.74697
688688 0 0
689689 8.48528 + 14.6969i 0.323263 + 0.559909i
690690 0 0
691691 −7.07107 + 12.2474i −0.268996 + 0.465915i −0.968603 0.248613i 0.920025π-0.920025\pi
0.699607 + 0.714528i 0.253359π0.253359\pi
692692 0 0
693693 0 0
694694 0 0
695695 20.0000 34.6410i 0.758643 1.31401i
696696 0 0
697697 16.0000 + 27.7128i 0.606043 + 1.04970i
698698 0 0
699699 28.2843 1.06981
700700 0 0
701701 34.0000 1.28416 0.642081 0.766637i 0.278071π-0.278071\pi
0.642081 + 0.766637i 0.278071π0.278071\pi
702702 0 0
703703 −14.1421 24.4949i −0.533381 0.923843i
704704 0 0
705705 −22.6274 + 39.1918i −0.852198 + 1.47605i
706706 0 0
707707 0 0
708708 0 0
709709 11.0000 19.0526i 0.413114 0.715534i −0.582115 0.813107i 0.697775π-0.697775\pi
0.995228 + 0.0975728i 0.0311079π0.0311079\pi
710710 0 0
711711 20.0000 + 34.6410i 0.750059 + 1.29914i
712712 0 0
713713 0 0
714714 0 0
715715 −32.0000 −1.19673
716716 0 0
717717 11.3137 + 19.5959i 0.422518 + 0.731823i
718718 0 0
719719 −14.1421 + 24.4949i −0.527413 + 0.913506i 0.472077 + 0.881557i 0.343504π0.343504\pi
−0.999490 + 0.0319481i 0.989829π0.989829\pi
720720 0 0
721721 0 0
722722 0 0
723723 40.0000 69.2820i 1.48762 2.57663i
724724 0 0
725725 −3.00000 5.19615i −0.111417 0.192980i
726726 0 0
727727 −28.2843 −1.04901 −0.524503 0.851409i 0.675749π-0.675749\pi
−0.524503 + 0.851409i 0.675749π0.675749\pi
728728 0 0
729729 −43.0000 −1.59259
730730 0 0
731731 11.3137 + 19.5959i 0.418453 + 0.724781i
732732 0 0
733733 −12.7279 + 22.0454i −0.470117 + 0.814266i −0.999416 0.0341693i 0.989121π-0.989121\pi
0.529300 + 0.848435i 0.322455π0.322455\pi
734734 0 0
735735 0 0
736736 0 0
737737 24.0000 41.5692i 0.884051 1.53122i
738738 0 0
739739 −6.00000 10.3923i −0.220714 0.382287i 0.734311 0.678813i 0.237505π-0.237505\pi
−0.955025 + 0.296526i 0.904172π0.904172\pi
740740 0 0
741741 22.6274 0.831239
742742 0 0
743743 16.0000 0.586983 0.293492 0.955962i 0.405183π-0.405183\pi
0.293492 + 0.955962i 0.405183π0.405183\pi
744744 0 0
745745 14.1421 + 24.4949i 0.518128 + 0.897424i
746746 0 0
747747 −35.3553 + 61.2372i −1.29358 + 2.24055i
748748 0 0
749749 0 0
750750 0 0
751751 −12.0000 + 20.7846i −0.437886 + 0.758441i −0.997526 0.0702946i 0.977606π-0.977606\pi
0.559640 + 0.828736i 0.310939π0.310939\pi
752752 0 0
753753 −20.0000 34.6410i −0.728841 1.26239i
754754 0 0
755755 −45.2548 −1.64699
756756 0 0
757757 10.0000 0.363456 0.181728 0.983349i 0.441831π-0.441831\pi
0.181728 + 0.983349i 0.441831π0.441831\pi
758758 0 0
759759 0 0
760760 0 0
761761 14.1421 24.4949i 0.512652 0.887939i −0.487240 0.873268i 0.661996π-0.661996\pi
0.999892 0.0146714i 0.00467023π-0.00467023\pi
762762 0 0
763763 0 0
764764 0 0
765765 40.0000 69.2820i 1.44620 2.50490i
766766 0 0
767767 4.00000 + 6.92820i 0.144432 + 0.250163i
768768 0 0
769769 16.9706 0.611974 0.305987 0.952036i 0.401014π-0.401014\pi
0.305987 + 0.952036i 0.401014π0.401014\pi
770770 0 0
771771 0 0
772772 0 0
773773 26.8701 + 46.5403i 0.966449 + 1.67394i 0.705671 + 0.708540i 0.250646π0.250646\pi
0.260778 + 0.965399i 0.416021π0.416021\pi
774774 0 0
775775 −8.48528 + 14.6969i −0.304800 + 0.527930i
776776 0 0
777777 0 0
778778 0 0
779779 −8.00000 + 13.8564i −0.286630 + 0.496457i
780780 0 0
781781 0 0
782782 0 0
783783 −11.3137 −0.404319
784784 0 0
785785 −40.0000 −1.42766
786786 0 0
787787 4.24264 + 7.34847i 0.151234 + 0.261945i 0.931681 0.363277i 0.118342π-0.118342\pi
−0.780447 + 0.625221i 0.785009π0.785009\pi
788788 0 0
789789 22.6274 39.1918i 0.805557 1.39527i
790790 0 0
791791 0 0
792792 0 0
793793 20.0000 34.6410i 0.710221 1.23014i
794794 0 0
795795 24.0000 + 41.5692i 0.851192 + 1.47431i
796796 0 0
797797 8.48528 0.300564 0.150282 0.988643i 0.451982π-0.451982\pi
0.150282 + 0.988643i 0.451982π0.451982\pi
798798 0 0
799799 32.0000 1.13208
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 −20.0000 + 34.6410i −0.704033 + 1.21942i
808808 0 0
809809 −9.00000 15.5885i −0.316423 0.548061i 0.663316 0.748340i 0.269149π-0.269149\pi
−0.979739 + 0.200279i 0.935815π0.935815\pi
810810 0 0
811811 14.1421 0.496598 0.248299 0.968683i 0.420129π-0.420129\pi
0.248299 + 0.968683i 0.420129π0.420129\pi
812812 0 0
813813 0 0
814814 0 0
815815 28.2843 + 48.9898i 0.990755 + 1.71604i
816816 0 0
817817 −5.65685 + 9.79796i −0.197908 + 0.342787i
818818 0 0
819819 0 0
820820 0 0
821821 −27.0000 + 46.7654i −0.942306 + 1.63212i −0.181250 + 0.983437i 0.558014π0.558014\pi
−0.761056 + 0.648686i 0.775319π0.775319\pi
822822 0 0
823823 −8.00000 13.8564i −0.278862 0.483004i 0.692240 0.721668i 0.256624π-0.256624\pi
−0.971102 + 0.238664i 0.923291π0.923291\pi
824824 0 0
825825 −33.9411 −1.18168
826826 0 0
827827 −20.0000 −0.695468 −0.347734 0.937593i 0.613049π-0.613049\pi
−0.347734 + 0.937593i 0.613049π0.613049\pi
828828 0 0
829829 15.5563 + 26.9444i 0.540294 + 0.935817i 0.998887 + 0.0471706i 0.0150204π0.0150204\pi
−0.458593 + 0.888647i 0.651646π0.651646\pi
830830 0 0
831831 −14.1421 + 24.4949i −0.490585 + 0.849719i
832832 0 0
833833 0 0
834834 0 0
835835 −8.00000 + 13.8564i −0.276851 + 0.479521i
836836 0 0
837837 16.0000 + 27.7128i 0.553041 + 0.957895i
838838 0 0
839839 −28.2843 −0.976481 −0.488241 0.872709i 0.662361π-0.662361\pi
−0.488241 + 0.872709i 0.662361π0.662361\pi
840840 0 0
841841 −25.0000 −0.862069
842842 0 0
843843 8.48528 + 14.6969i 0.292249 + 0.506189i
844844 0 0
845845 7.07107 12.2474i 0.243252 0.421325i
846846 0 0
847847 0 0
848848 0 0
849849 4.00000 6.92820i 0.137280 0.237775i
850850 0 0
851851 0 0
852852 0 0
853853 42.4264 1.45265 0.726326 0.687350i 0.241226π-0.241226\pi
0.726326 + 0.687350i 0.241226π0.241226\pi
854854 0 0
855855 40.0000 1.36797
856856 0 0
857857 −14.1421 24.4949i −0.483086 0.836730i 0.516725 0.856151i 0.327151π-0.327151\pi
−0.999811 + 0.0194215i 0.993818π0.993818\pi
858858 0 0
859859 −21.2132 + 36.7423i −0.723785 + 1.25363i 0.235687 + 0.971829i 0.424266π0.424266\pi
−0.959472 + 0.281804i 0.909067π0.909067\pi
860860 0 0
861861 0 0
862862 0 0
863863 12.0000 20.7846i 0.408485 0.707516i −0.586235 0.810141i 0.699391π-0.699391\pi
0.994720 + 0.102624i 0.0327240π0.0327240\pi
864864 0 0
865865 4.00000 + 6.92820i 0.136004 + 0.235566i
866866 0 0
867867 −42.4264 −1.44088
868868 0 0
869869 −32.0000 −1.08553
870870 0 0
871871 −16.9706 29.3939i −0.575026 0.995974i
872872 0 0
873873 −14.1421 + 24.4949i −0.478639 + 0.829027i
874874 0 0
875875 0 0
876876 0 0
877877 −1.00000 + 1.73205i −0.0337676 + 0.0584872i −0.882415 0.470471i 0.844084π-0.844084\pi
0.848648 + 0.528958i 0.177417π0.177417\pi
878878 0 0
879879 4.00000 + 6.92820i 0.134917 + 0.233682i
880880 0 0
881881 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
882882 0 0
883883 20.0000 0.673054 0.336527 0.941674i 0.390748π-0.390748\pi
0.336527 + 0.941674i 0.390748π0.390748\pi
884884 0 0
885885 11.3137 + 19.5959i 0.380306 + 0.658710i
886886 0 0
887887 14.1421 24.4949i 0.474846 0.822458i −0.524739 0.851263i 0.675837π-0.675837\pi
0.999585 + 0.0288053i 0.00917026π0.00917026\pi
888888 0 0
889889 0 0
890890 0 0
891891 −2.00000 + 3.46410i −0.0670025 + 0.116052i
892892 0 0
893893 8.00000 + 13.8564i 0.267710 + 0.463687i
894894 0 0
895895 56.5685 1.89088
896896 0 0
897897 0 0
898898 0 0
899899 −5.65685 9.79796i −0.188667 0.326780i
900900 0 0
901901 16.9706 29.3939i 0.565371 0.979252i
902902 0 0
903903 0 0
904904 0 0
905905 −12.0000 + 20.7846i −0.398893 + 0.690904i
906906 0 0
907907 10.0000 + 17.3205i 0.332045 + 0.575118i 0.982913 0.184073i 0.0589282π-0.0589282\pi
−0.650868 + 0.759191i 0.725595π0.725595\pi
908908 0 0
909909 −42.4264 −1.40720
910910 0 0
911911 40.0000 1.32526 0.662630 0.748947i 0.269440π-0.269440\pi
0.662630 + 0.748947i 0.269440π0.269440\pi
912912 0 0
913913 −28.2843 48.9898i −0.936073 1.62133i
914914 0 0
915915 56.5685 97.9796i 1.87010 3.23911i
916916 0 0
917917 0 0
918918 0 0
919919 −16.0000 + 27.7128i −0.527791 + 0.914161i 0.471684 + 0.881768i 0.343646π0.343646\pi
−0.999475 + 0.0323936i 0.989687π0.989687\pi
920920 0 0
921921 −12.0000 20.7846i −0.395413 0.684876i
922922 0 0
923923 0 0
924924 0 0
925925 30.0000 0.986394
926926 0 0
927927 −42.4264 73.4847i −1.39347 2.41355i
928928 0 0
929929 −19.7990 + 34.2929i −0.649584 + 1.12511i 0.333639 + 0.942701i 0.391723π0.391723\pi
−0.983222 + 0.182411i 0.941610π0.941610\pi
930930 0 0
931931 0 0
932932 0 0
933933 32.0000 55.4256i 1.04763 1.81455i
934934 0 0
935935 32.0000 + 55.4256i 1.04651 + 1.81261i
936936 0 0
937937 −22.6274 −0.739205 −0.369603 0.929190i 0.620506π-0.620506\pi
−0.369603 + 0.929190i 0.620506π0.620506\pi
938938 0 0
939939 48.0000 1.56642
940940 0 0
941941 −7.07107 12.2474i −0.230510 0.399255i 0.727448 0.686163i 0.240706π-0.240706\pi
−0.957958 + 0.286907i 0.907373π0.907373\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 −6.00000 + 10.3923i −0.194974 + 0.337705i −0.946892 0.321552i 0.895796π-0.895796\pi
0.751918 + 0.659256i 0.229129π0.229129\pi
948948 0 0
949949 0 0
950950 0 0
951951 50.9117 1.65092
952952 0 0
953953 −6.00000 −0.194359 −0.0971795 0.995267i 0.530982π-0.530982\pi
−0.0971795 + 0.995267i 0.530982π0.530982\pi
954954 0 0
955955 33.9411 + 58.7878i 1.09831 + 1.90233i
956956 0 0
957957 11.3137 19.5959i 0.365720 0.633446i
958958 0 0
959959 0 0
960960 0 0
961961 −0.500000 + 0.866025i −0.0161290 + 0.0279363i
962962 0 0
963963 −30.0000 51.9615i −0.966736 1.67444i
964964 0 0
965965 28.2843 0.910503
966966 0 0
967967 −48.0000 −1.54358 −0.771788 0.635880i 0.780637π-0.780637\pi
−0.771788 + 0.635880i 0.780637π0.780637\pi
968968 0 0
969969 −22.6274 39.1918i −0.726897 1.25902i
970970 0 0
971971 9.89949 17.1464i 0.317690 0.550255i −0.662316 0.749225i 0.730426π-0.730426\pi
0.980006 + 0.198970i 0.0637596π0.0637596\pi
972972 0 0
973973 0 0
974974 0 0
975975 −12.0000 + 20.7846i −0.384308 + 0.665640i
976976 0 0
977977 9.00000 + 15.5885i 0.287936 + 0.498719i 0.973317 0.229465i 0.0736978π-0.0736978\pi
−0.685381 + 0.728184i 0.740364π0.740364\pi
978978 0 0
979979 0 0
980980 0 0
981981 10.0000 0.319275
982982 0 0
983983 −19.7990 34.2929i −0.631490 1.09377i −0.987247 0.159194i 0.949110π-0.949110\pi
0.355758 0.934578i 0.384223π-0.384223\pi
984984 0 0
985985 −31.1127 + 53.8888i −0.991333 + 1.71704i
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 4.00000 + 6.92820i 0.127064 + 0.220082i 0.922538 0.385906i 0.126111π-0.126111\pi
−0.795474 + 0.605988i 0.792778π0.792778\pi
992992 0 0
993993 −56.5685 −1.79515
994994 0 0
995995 −48.0000 −1.52170
996996 0 0
997997 −18.3848 31.8434i −0.582252 1.00849i −0.995212 0.0977405i 0.968838π-0.968838\pi
0.412960 0.910749i 0.364495π-0.364495\pi
998998 0 0
999999 28.2843 48.9898i 0.894875 1.54997i
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 784.2.i.k.177.2 4
4.3 odd 2 392.2.i.g.177.1 4
7.2 even 3 784.2.a.n.1.1 2
7.3 odd 6 inner 784.2.i.k.753.1 4
7.4 even 3 inner 784.2.i.k.753.2 4
7.5 odd 6 784.2.a.n.1.2 2
7.6 odd 2 inner 784.2.i.k.177.1 4
12.11 even 2 3528.2.s.be.3313.2 4
21.2 odd 6 7056.2.a.cj.1.1 2
21.5 even 6 7056.2.a.cj.1.2 2
28.3 even 6 392.2.i.g.361.2 4
28.11 odd 6 392.2.i.g.361.1 4
28.19 even 6 392.2.a.h.1.1 2
28.23 odd 6 392.2.a.h.1.2 yes 2
28.27 even 2 392.2.i.g.177.2 4
56.5 odd 6 3136.2.a.bq.1.1 2
56.19 even 6 3136.2.a.bt.1.2 2
56.37 even 6 3136.2.a.bq.1.2 2
56.51 odd 6 3136.2.a.bt.1.1 2
84.11 even 6 3528.2.s.be.361.2 4
84.23 even 6 3528.2.a.bj.1.1 2
84.47 odd 6 3528.2.a.bj.1.2 2
84.59 odd 6 3528.2.s.be.361.1 4
84.83 odd 2 3528.2.s.be.3313.1 4
140.19 even 6 9800.2.a.bw.1.2 2
140.79 odd 6 9800.2.a.bw.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
392.2.a.h.1.1 2 28.19 even 6
392.2.a.h.1.2 yes 2 28.23 odd 6
392.2.i.g.177.1 4 4.3 odd 2
392.2.i.g.177.2 4 28.27 even 2
392.2.i.g.361.1 4 28.11 odd 6
392.2.i.g.361.2 4 28.3 even 6
784.2.a.n.1.1 2 7.2 even 3
784.2.a.n.1.2 2 7.5 odd 6
784.2.i.k.177.1 4 7.6 odd 2 inner
784.2.i.k.177.2 4 1.1 even 1 trivial
784.2.i.k.753.1 4 7.3 odd 6 inner
784.2.i.k.753.2 4 7.4 even 3 inner
3136.2.a.bq.1.1 2 56.5 odd 6
3136.2.a.bq.1.2 2 56.37 even 6
3136.2.a.bt.1.1 2 56.51 odd 6
3136.2.a.bt.1.2 2 56.19 even 6
3528.2.a.bj.1.1 2 84.23 even 6
3528.2.a.bj.1.2 2 84.47 odd 6
3528.2.s.be.361.1 4 84.59 odd 6
3528.2.s.be.361.2 4 84.11 even 6
3528.2.s.be.3313.1 4 84.83 odd 2
3528.2.s.be.3313.2 4 12.11 even 2
7056.2.a.cj.1.1 2 21.2 odd 6
7056.2.a.cj.1.2 2 21.5 even 6
9800.2.a.bw.1.1 2 140.79 odd 6
9800.2.a.bw.1.2 2 140.19 even 6