Properties

Label 1620.2.i.h.541.1
Level 16201620
Weight 22
Character 1620.541
Analytic conductor 12.93612.936
Analytic rank 11
Dimension 22
Inner twists 22

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1620,2,Mod(541,1620)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1620.541");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1620=22345 1620 = 2^{2} \cdot 3^{4} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1620.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: 12.935765127412.9357651274
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 541.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 1620.541
Dual form 1620.2.i.h.1081.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.500000+0.866025i)q5+(1.00000+1.73205i)q7+(1.000001.73205i)q136.00000q174.00000q19+(3.000005.19615i)q23+(0.500000+0.866025i)q25+(3.00000+5.19615i)q29+(2.00000+3.46410i)q312.00000q35+2.00000q37+(3.000005.19615i)q41+(5.000008.66025i)q43+(3.000005.19615i)q47+(1.50000+2.59808i)q496.00000q53+(6.0000010.3923i)q59+(1.00000+1.73205i)q61+(1.000001.73205i)q65+(1.000001.73205i)q6712.0000q71+2.00000q73+(4.00000+6.92820i)q79+(3.00000+5.19615i)q83+(3.000005.19615i)q856.00000q89+4.00000q91+(2.000003.46410i)q95+(1.00000+1.73205i)q97+O(q100)q+(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{7} +(-1.00000 - 1.73205i) q^{13} -6.00000 q^{17} -4.00000 q^{19} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} -2.00000 q^{35} +2.00000 q^{37} +(-3.00000 - 5.19615i) q^{41} +(5.00000 - 8.66025i) q^{43} +(3.00000 - 5.19615i) q^{47} +(1.50000 + 2.59808i) q^{49} -6.00000 q^{53} +(-6.00000 - 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(1.00000 - 1.73205i) q^{65} +(-1.00000 - 1.73205i) q^{67} -12.0000 q^{71} +2.00000 q^{73} +(-4.00000 + 6.92820i) q^{79} +(-3.00000 + 5.19615i) q^{83} +(-3.00000 - 5.19615i) q^{85} -6.00000 q^{89} +4.00000 q^{91} +(-2.00000 - 3.46410i) q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q52q72q1312q178q196q23q256q29+4q314q35+4q376q41+10q43+6q47+3q4912q5312q592q61+2q97+O(q100) 2 q + q^{5} - 2 q^{7} - 2 q^{13} - 12 q^{17} - 8 q^{19} - 6 q^{23} - q^{25} - 6 q^{29} + 4 q^{31} - 4 q^{35} + 4 q^{37} - 6 q^{41} + 10 q^{43} + 6 q^{47} + 3 q^{49} - 12 q^{53} - 12 q^{59} - 2 q^{61}+ \cdots - 2 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1620Z)×\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times.

nn 811811 12971297 15411541
χ(n)\chi(n) 11 11 e(23)e\left(\frac{2}{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 0 0
44 0 0
55 0.500000 + 0.866025i 0.223607 + 0.387298i
66 0 0
77 −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i 0.956709π-0.956709\pi
0.612801 + 0.790237i 0.290043π0.290043\pi
88 0 0
99 0 0
1010 0 0
1111 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
1212 0 0
1313 −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i 0.256123π-0.256123\pi
−0.970725 + 0.240192i 0.922790π0.922790\pi
1414 0 0
1515 0 0
1616 0 0
1717 −6.00000 −1.45521 −0.727607 0.685994i 0.759367π-0.759367\pi
−0.727607 + 0.685994i 0.759367π0.759367\pi
1818 0 0
1919 −4.00000 −0.917663 −0.458831 0.888523i 0.651732π-0.651732\pi
−0.458831 + 0.888523i 0.651732π0.651732\pi
2020 0 0
2121 0 0
2222 0 0
2323 −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i 0.951544π-0.951544\pi
0.362892 0.931831i 0.381789π-0.381789\pi
2424 0 0
2525 −0.500000 + 0.866025i −0.100000 + 0.173205i
2626 0 0
2727 0 0
2828 0 0
2929 −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i 0.354747π0.354747\pi
−0.997738 + 0.0672232i 0.978586π0.978586\pi
3030 0 0
3131 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i 0.0497126π-0.0497126\pi
−0.628619 + 0.777714i 0.716379π0.716379\pi
3232 0 0
3333 0 0
3434 0 0
3535 −2.00000 −0.338062
3636 0 0
3737 2.00000 0.328798 0.164399 0.986394i 0.447432π-0.447432\pi
0.164399 + 0.986394i 0.447432π0.447432\pi
3838 0 0
3939 0 0
4040 0 0
4141 −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i 0.321880π-0.321880\pi
−0.999353 + 0.0359748i 0.988546π0.988546\pi
4242 0 0
4343 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i 0.557309π-0.557309\pi
0.941562 0.336840i 0.109358π-0.109358\pi
4444 0 0
4545 0 0
4646 0 0
4747 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i 0.689164π-0.689164\pi
0.997503 + 0.0706177i 0.0224970π0.0224970\pi
4848 0 0
4949 1.50000 + 2.59808i 0.214286 + 0.371154i
5050 0 0
5151 0 0
5252 0 0
5353 −6.00000 −0.824163 −0.412082 0.911147i 0.635198π-0.635198\pi
−0.412082 + 0.911147i 0.635198π0.635198\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i 0.881308π-0.881308\pi
0.150148 0.988663i 0.452025π-0.452025\pi
6060 0 0
6161 −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i 0.874201π-0.874201\pi
0.794879 + 0.606768i 0.207534π0.207534\pi
6262 0 0
6363 0 0
6464 0 0
6565 1.00000 1.73205i 0.124035 0.214834i
6666 0 0
6767 −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i 0.205652π-0.205652\pi
−0.920623 + 0.390453i 0.872318π0.872318\pi
6868 0 0
6969 0 0
7070 0 0
7171 −12.0000 −1.42414 −0.712069 0.702109i 0.752242π-0.752242\pi
−0.712069 + 0.702109i 0.752242π0.752242\pi
7272 0 0
7373 2.00000 0.234082 0.117041 0.993127i 0.462659π-0.462659\pi
0.117041 + 0.993127i 0.462659π0.462659\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i 0.981922π-0.981922\pi
0.548352 + 0.836247i 0.315255π0.315255\pi
8080 0 0
8181 0 0
8282 0 0
8383 −3.00000 + 5.19615i −0.329293 + 0.570352i −0.982372 0.186938i 0.940144π-0.940144\pi
0.653079 + 0.757290i 0.273477π0.273477\pi
8484 0 0
8585 −3.00000 5.19615i −0.325396 0.563602i
8686 0 0
8787 0 0
8888 0 0
8989 −6.00000 −0.635999 −0.317999 0.948091i 0.603011π-0.603011\pi
−0.317999 + 0.948091i 0.603011π0.603011\pi
9090 0 0
9191 4.00000 0.419314
9292 0 0
9393 0 0
9494 0 0
9595 −2.00000 3.46410i −0.205196 0.355409i
9696 0 0
9797 −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i 0.865709π-0.865709\pi
0.810782 + 0.585348i 0.199042π0.199042\pi
9898 0 0
9999 0 0
100100 0 0
101101 −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i 0.929823π-0.929823\pi
0.677284 + 0.735721i 0.263157π0.263157\pi
102102 0 0
103103 −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i 0.924396π-0.924396\pi
0.282194 0.959357i 0.408938π-0.408938\pi
104104 0 0
105105 0 0
106106 0 0
107107 −6.00000 −0.580042 −0.290021 0.957020i 0.593662π-0.593662\pi
−0.290021 + 0.957020i 0.593662π0.593662\pi
108108 0 0
109109 2.00000 0.191565 0.0957826 0.995402i 0.469465π-0.469465\pi
0.0957826 + 0.995402i 0.469465π0.469465\pi
110110 0 0
111111 0 0
112112 0 0
113113 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i 0.0755971π-0.0755971\pi
−0.689714 + 0.724082i 0.742264π0.742264\pi
114114 0 0
115115 3.00000 5.19615i 0.279751 0.484544i
116116 0 0
117117 0 0
118118 0 0
119119 6.00000 10.3923i 0.550019 0.952661i
120120 0 0
121121 5.50000 + 9.52628i 0.500000 + 0.866025i
122122 0 0
123123 0 0
124124 0 0
125125 −1.00000 −0.0894427
126126 0 0
127127 2.00000 0.177471 0.0887357 0.996055i 0.471717π-0.471717\pi
0.0887357 + 0.996055i 0.471717π0.471717\pi
128128 0 0
129129 0 0
130130 0 0
131131 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
132132 0 0
133133 4.00000 6.92820i 0.346844 0.600751i
134134 0 0
135135 0 0
136136 0 0
137137 −9.00000 + 15.5885i −0.768922 + 1.33181i 0.169226 + 0.985577i 0.445873π0.445873\pi
−0.938148 + 0.346235i 0.887460π0.887460\pi
138138 0 0
139139 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i 0.112407π-0.112407\pi
−0.768655 + 0.639664i 0.779074π0.779074\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 0 0
145145 −6.00000 −0.498273
146146 0 0
147147 0 0
148148 0 0
149149 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i 0.0876260π-0.0876260\pi
−0.716578 + 0.697507i 0.754293π0.754293\pi
150150 0 0
151151 −10.0000 + 17.3205i −0.813788 + 1.40952i 0.0964061 + 0.995342i 0.469265π0.469265\pi
−0.910195 + 0.414181i 0.864068π0.864068\pi
152152 0 0
153153 0 0
154154 0 0
155155 −2.00000 + 3.46410i −0.160644 + 0.278243i
156156 0 0
157157 11.0000 + 19.0526i 0.877896 + 1.52056i 0.853646 + 0.520854i 0.174386π0.174386\pi
0.0242497 + 0.999706i 0.492280π0.492280\pi
158158 0 0
159159 0 0
160160 0 0
161161 12.0000 0.945732
162162 0 0
163163 −10.0000 −0.783260 −0.391630 0.920123i 0.628089π-0.628089\pi
−0.391630 + 0.920123i 0.628089π0.628089\pi
164164 0 0
165165 0 0
166166 0 0
167167 −9.00000 15.5885i −0.696441 1.20627i −0.969693 0.244328i 0.921432π-0.921432\pi
0.273252 0.961943i 0.411901π-0.411901\pi
168168 0 0
169169 4.50000 7.79423i 0.346154 0.599556i
170170 0 0
171171 0 0
172172 0 0
173173 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i 0.760087π-0.760087\pi
0.957241 + 0.289292i 0.0934200π0.0934200\pi
174174 0 0
175175 −1.00000 1.73205i −0.0755929 0.130931i
176176 0 0
177177 0 0
178178 0 0
179179 −12.0000 −0.896922 −0.448461 0.893802i 0.648028π-0.648028\pi
−0.448461 + 0.893802i 0.648028π0.648028\pi
180180 0 0
181181 −10.0000 −0.743294 −0.371647 0.928374i 0.621207π-0.621207\pi
−0.371647 + 0.928374i 0.621207π0.621207\pi
182182 0 0
183183 0 0
184184 0 0
185185 1.00000 + 1.73205i 0.0735215 + 0.127343i
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i 0.690384π-0.690384\pi
0.997225 + 0.0744412i 0.0237173π0.0237173\pi
192192 0 0
193193 −13.0000 22.5167i −0.935760 1.62078i −0.773272 0.634074i 0.781381π-0.781381\pi
−0.162488 0.986710i 0.551952π-0.551952\pi
194194 0 0
195195 0 0
196196 0 0
197197 18.0000 1.28245 0.641223 0.767354i 0.278427π-0.278427\pi
0.641223 + 0.767354i 0.278427π0.278427\pi
198198 0 0
199199 8.00000 0.567105 0.283552 0.958957i 0.408487π-0.408487\pi
0.283552 + 0.958957i 0.408487π0.408487\pi
200200 0 0
201201 0 0
202202 0 0
203203 −6.00000 10.3923i −0.421117 0.729397i
204204 0 0
205205 3.00000 5.19615i 0.209529 0.362915i
206206 0 0
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i 0.0189888π0.0189888\pi
−0.447478 + 0.894295i 0.647678π0.647678\pi
212212 0 0
213213 0 0
214214 0 0
215215 10.0000 0.681994
216216 0 0
217217 −8.00000 −0.543075
218218 0 0
219219 0 0
220220 0 0
221221 6.00000 + 10.3923i 0.403604 + 0.699062i
222222 0 0
223223 5.00000 8.66025i 0.334825 0.579934i −0.648626 0.761107i 0.724656π-0.724656\pi
0.983451 + 0.181173i 0.0579895π0.0579895\pi
224224 0 0
225225 0 0
226226 0 0
227227 3.00000 5.19615i 0.199117 0.344881i −0.749125 0.662428i 0.769526π-0.769526\pi
0.948242 + 0.317547i 0.102859π0.102859\pi
228228 0 0
229229 −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i 0.319740π-0.319740\pi
−0.999088 + 0.0426906i 0.986407π0.986407\pi
230230 0 0
231231 0 0
232232 0 0
233233 −6.00000 −0.393073 −0.196537 0.980497i 0.562969π-0.562969\pi
−0.196537 + 0.980497i 0.562969π0.562969\pi
234234 0 0
235235 6.00000 0.391397
236236 0 0
237237 0 0
238238 0 0
239239 12.0000 + 20.7846i 0.776215 + 1.34444i 0.934109 + 0.356988i 0.116196π0.116196\pi
−0.157893 + 0.987456i 0.550470π0.550470\pi
240240 0 0
241241 −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i 0.982234π-0.982234\pi
0.547533 + 0.836784i 0.315567π0.315567\pi
242242 0 0
243243 0 0
244244 0 0
245245 −1.50000 + 2.59808i −0.0958315 + 0.165985i
246246 0 0
247247 4.00000 + 6.92820i 0.254514 + 0.440831i
248248 0 0
249249 0 0
250250 0 0
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0 0
257257 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i 0.106747π-0.106747\pi
−0.757159 + 0.653231i 0.773413π0.773413\pi
258258 0 0
259259 −2.00000 + 3.46410i −0.124274 + 0.215249i
260260 0 0
261261 0 0
262262 0 0
263263 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i 0.646065π-0.646065\pi
0.997906 0.0646755i 0.0206012π-0.0206012\pi
264264 0 0
265265 −3.00000 5.19615i −0.184289 0.319197i
266266 0 0
267267 0 0
268268 0 0
269269 18.0000 1.09748 0.548740 0.835993i 0.315108π-0.315108\pi
0.548740 + 0.835993i 0.315108π0.315108\pi
270270 0 0
271271 20.0000 1.21491 0.607457 0.794353i 0.292190π-0.292190\pi
0.607457 + 0.794353i 0.292190π0.292190\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 −13.0000 + 22.5167i −0.781094 + 1.35290i 0.150210 + 0.988654i 0.452005π0.452005\pi
−0.931305 + 0.364241i 0.881328π0.881328\pi
278278 0 0
279279 0 0
280280 0 0
281281 −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i 0.890608π-0.890608\pi
0.762561 + 0.646916i 0.223942π0.223942\pi
282282 0 0
283283 −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i 0.303272π-0.303272\pi
−0.995544 + 0.0942988i 0.969939π0.969939\pi
284284 0 0
285285 0 0
286286 0 0
287287 12.0000 0.708338
288288 0 0
289289 19.0000 1.11765
290290 0 0
291291 0 0
292292 0 0
293293 15.0000 + 25.9808i 0.876309 + 1.51781i 0.855361 + 0.518032i 0.173335π0.173335\pi
0.0209480 + 0.999781i 0.493332π0.493332\pi
294294 0 0
295295 6.00000 10.3923i 0.349334 0.605063i
296296 0 0
297297 0 0
298298 0 0
299299 −6.00000 + 10.3923i −0.346989 + 0.601003i
300300 0 0
301301 10.0000 + 17.3205i 0.576390 + 0.998337i
302302 0 0
303303 0 0
304304 0 0
305305 −2.00000 −0.114520
306306 0 0
307307 2.00000 0.114146 0.0570730 0.998370i 0.481823π-0.481823\pi
0.0570730 + 0.998370i 0.481823π0.481823\pi
308308 0 0
309309 0 0
310310 0 0
311311 −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i 0.277171π-0.277171\pi
−0.984475 + 0.175525i 0.943838π0.943838\pi
312312 0 0
313313 11.0000 19.0526i 0.621757 1.07691i −0.367402 0.930062i 0.619753π-0.619753\pi
0.989158 0.146852i 0.0469141π-0.0469141\pi
314314 0 0
315315 0 0
316316 0 0
317317 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i 0.779442π-0.779442\pi
0.937892 + 0.346929i 0.112775π0.112775\pi
318318 0 0
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 24.0000 1.33540
324324 0 0
325325 2.00000 0.110940
326326 0 0
327327 0 0
328328 0 0
329329 6.00000 + 10.3923i 0.330791 + 0.572946i
330330 0 0
331331 −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i 0.903893π-0.903893\pi
0.734905 + 0.678170i 0.237227π0.237227\pi
332332 0 0
333333 0 0
334334 0 0
335335 1.00000 1.73205i 0.0546358 0.0946320i
336336 0 0
337337 −1.00000 1.73205i −0.0544735 0.0943508i 0.837503 0.546433i 0.184015π-0.184015\pi
−0.891976 + 0.452082i 0.850681π0.850681\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 −20.0000 −1.07990
344344 0 0
345345 0 0
346346 0 0
347347 15.0000 + 25.9808i 0.805242 + 1.39472i 0.916127 + 0.400887i 0.131298π0.131298\pi
−0.110885 + 0.993833i 0.535369π0.535369\pi
348348 0 0
349349 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i 0.747088π-0.747088\pi
0.968253 + 0.249973i 0.0804216π0.0804216\pi
350350 0 0
351351 0 0
352352 0 0
353353 −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i 0.992342π-0.992342\pi
0.520689 + 0.853746i 0.325675π0.325675\pi
354354 0 0
355355 −6.00000 10.3923i −0.318447 0.551566i
356356 0 0
357357 0 0
358358 0 0
359359 24.0000 1.26667 0.633336 0.773877i 0.281685π-0.281685\pi
0.633336 + 0.773877i 0.281685π0.281685\pi
360360 0 0
361361 −3.00000 −0.157895
362362 0 0
363363 0 0
364364 0 0
365365 1.00000 + 1.73205i 0.0523424 + 0.0906597i
366366 0 0
367367 11.0000 19.0526i 0.574195 0.994535i −0.421933 0.906627i 0.638648π-0.638648\pi
0.996129 0.0879086i 0.0280183π-0.0280183\pi
368368 0 0
369369 0 0
370370 0 0
371371 6.00000 10.3923i 0.311504 0.539542i
372372 0 0
373373 −13.0000 22.5167i −0.673114 1.16587i −0.977016 0.213165i 0.931623π-0.931623\pi
0.303902 0.952703i 0.401711π-0.401711\pi
374374 0 0
375375 0 0
376376 0 0
377377 12.0000 0.618031
378378 0 0
379379 −28.0000 −1.43826 −0.719132 0.694874i 0.755460π-0.755460\pi
−0.719132 + 0.694874i 0.755460π0.755460\pi
380380 0 0
381381 0 0
382382 0 0
383383 −3.00000 5.19615i −0.153293 0.265511i 0.779143 0.626846i 0.215654π-0.215654\pi
−0.932436 + 0.361335i 0.882321π0.882321\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i 0.784728π-0.784728\pi
0.932002 + 0.362454i 0.118061π0.118061\pi
390390 0 0
391391 18.0000 + 31.1769i 0.910299 + 1.57668i
392392 0 0
393393 0 0
394394 0 0
395395 −8.00000 −0.402524
396396 0 0
397397 2.00000 0.100377 0.0501886 0.998740i 0.484018π-0.484018\pi
0.0501886 + 0.998740i 0.484018π0.484018\pi
398398 0 0
399399 0 0
400400 0 0
401401 15.0000 + 25.9808i 0.749064 + 1.29742i 0.948272 + 0.317460i 0.102830π0.102830\pi
−0.199207 + 0.979957i 0.563837π0.563837\pi
402402 0 0
403403 4.00000 6.92820i 0.199254 0.345118i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 17.0000 + 29.4449i 0.840596 + 1.45595i 0.889392 + 0.457146i 0.151128π0.151128\pi
−0.0487958 + 0.998809i 0.515538π0.515538\pi
410410 0 0
411411 0 0
412412 0 0
413413 24.0000 1.18096
414414 0 0
415415 −6.00000 −0.294528
416416 0 0
417417 0 0
418418 0 0
419419 −18.0000 31.1769i −0.879358 1.52309i −0.852047 0.523465i 0.824639π-0.824639\pi
−0.0273103 0.999627i 0.508694π-0.508694\pi
420420 0 0
421421 −13.0000 + 22.5167i −0.633581 + 1.09739i 0.353233 + 0.935536i 0.385082π0.385082\pi
−0.986814 + 0.161859i 0.948251π0.948251\pi
422422 0 0
423423 0 0
424424 0 0
425425 3.00000 5.19615i 0.145521 0.252050i
426426 0 0
427427 −2.00000 3.46410i −0.0967868 0.167640i
428428 0 0
429429 0 0
430430 0 0
431431 36.0000 1.73406 0.867029 0.498257i 0.166026π-0.166026\pi
0.867029 + 0.498257i 0.166026π0.166026\pi
432432 0 0
433433 2.00000 0.0961139 0.0480569 0.998845i 0.484697π-0.484697\pi
0.0480569 + 0.998845i 0.484697π0.484697\pi
434434 0 0
435435 0 0
436436 0 0
437437 12.0000 + 20.7846i 0.574038 + 0.994263i
438438 0 0
439439 −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i 0.894477π-0.894477\pi
0.754642 + 0.656136i 0.227810π0.227810\pi
440440 0 0
441441 0 0
442442 0 0
443443 −3.00000 + 5.19615i −0.142534 + 0.246877i −0.928450 0.371457i 0.878858π-0.878858\pi
0.785916 + 0.618333i 0.212192π0.212192\pi
444444 0 0
445445 −3.00000 5.19615i −0.142214 0.246321i
446446 0 0
447447 0 0
448448 0 0
449449 6.00000 0.283158 0.141579 0.989927i 0.454782π-0.454782\pi
0.141579 + 0.989927i 0.454782π0.454782\pi
450450 0 0
451451 0 0
452452 0 0
453453 0 0
454454 0 0
455455 2.00000 + 3.46410i 0.0937614 + 0.162400i
456456 0 0
457457 −13.0000 + 22.5167i −0.608114 + 1.05328i 0.383437 + 0.923567i 0.374740π0.374740\pi
−0.991551 + 0.129718i 0.958593π0.958593\pi
458458 0 0
459459 0 0
460460 0 0
461461 −15.0000 + 25.9808i −0.698620 + 1.21004i 0.270326 + 0.962769i 0.412869π0.412869\pi
−0.968945 + 0.247276i 0.920465π0.920465\pi
462462 0 0
463463 −7.00000 12.1244i −0.325318 0.563467i 0.656259 0.754536i 0.272138π-0.272138\pi
−0.981577 + 0.191069i 0.938805π0.938805\pi
464464 0 0
465465 0 0
466466 0 0
467467 −30.0000 −1.38823 −0.694117 0.719862i 0.744205π-0.744205\pi
−0.694117 + 0.719862i 0.744205π0.744205\pi
468468 0 0
469469 4.00000 0.184703
470470 0 0
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 2.00000 3.46410i 0.0917663 0.158944i
476476 0 0
477477 0 0
478478 0 0
479479 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i 0.648611π-0.648611\pi
0.998392 0.0566937i 0.0180558π-0.0180558\pi
480480 0 0
481481 −2.00000 3.46410i −0.0911922 0.157949i
482482 0 0
483483 0 0
484484 0 0
485485 −2.00000 −0.0908153
486486 0 0
487487 26.0000 1.17817 0.589086 0.808070i 0.299488π-0.299488\pi
0.589086 + 0.808070i 0.299488π0.299488\pi
488488 0 0
489489 0 0
490490 0 0
491491 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
492492 0 0
493493 18.0000 31.1769i 0.810679 1.40414i
494494 0 0
495495 0 0
496496 0 0
497497 12.0000 20.7846i 0.538274 0.932317i
498498 0 0
499499 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i 0.138129π-0.138129\pi
−0.817781 + 0.575529i 0.804796π0.804796\pi
500500 0 0
501501 0 0
502502 0 0
503503 −18.0000 −0.802580 −0.401290 0.915951i 0.631438π-0.631438\pi
−0.401290 + 0.915951i 0.631438π0.631438\pi
504504 0 0
505505 −6.00000 −0.266996
506506 0 0
507507 0 0
508508 0 0
509509 −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i 0.209119π-0.209119\pi
−0.924821 + 0.380402i 0.875786π0.875786\pi
510510 0 0
511511 −2.00000 + 3.46410i −0.0884748 + 0.153243i
512512 0 0
513513 0 0
514514 0 0
515515 7.00000 12.1244i 0.308457 0.534263i
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 −6.00000 −0.262865 −0.131432 0.991325i 0.541958π-0.541958\pi
−0.131432 + 0.991325i 0.541958π0.541958\pi
522522 0 0
523523 14.0000 0.612177 0.306089 0.952003i 0.400980π-0.400980\pi
0.306089 + 0.952003i 0.400980π0.400980\pi
524524 0 0
525525 0 0
526526 0 0
527527 −12.0000 20.7846i −0.522728 0.905392i
528528 0 0
529529 −6.50000 + 11.2583i −0.282609 + 0.489493i
530530 0 0
531531 0 0
532532 0 0
533533 −6.00000 + 10.3923i −0.259889 + 0.450141i
534534 0 0
535535 −3.00000 5.19615i −0.129701 0.224649i
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 14.0000 0.601907 0.300954 0.953639i 0.402695π-0.402695\pi
0.300954 + 0.953639i 0.402695π0.402695\pi
542542 0 0
543543 0 0
544544 0 0
545545 1.00000 + 1.73205i 0.0428353 + 0.0741929i
546546 0 0
547547 −13.0000 + 22.5167i −0.555840 + 0.962743i 0.441998 + 0.897016i 0.354270π0.354270\pi
−0.997838 + 0.0657267i 0.979063π0.979063\pi
548548 0 0
549549 0 0
550550 0 0
551551 12.0000 20.7846i 0.511217 0.885454i
552552 0 0
553553 −8.00000 13.8564i −0.340195 0.589234i
554554 0 0
555555 0 0
556556 0 0
557557 −30.0000 −1.27114 −0.635570 0.772043i 0.719235π-0.719235\pi
−0.635570 + 0.772043i 0.719235π0.719235\pi
558558 0 0
559559 −20.0000 −0.845910
560560 0 0
561561 0 0
562562 0 0
563563 9.00000 + 15.5885i 0.379305 + 0.656975i 0.990961 0.134148i 0.0428299π-0.0428299\pi
−0.611656 + 0.791123i 0.709497π0.709497\pi
564564 0 0
565565 −3.00000 + 5.19615i −0.126211 + 0.218604i
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 −4.00000 6.92820i −0.167395 0.289936i 0.770108 0.637913i 0.220202π-0.220202\pi
−0.937503 + 0.347977i 0.886869π0.886869\pi
572572 0 0
573573 0 0
574574 0 0
575575 6.00000 0.250217
576576 0 0
577577 −22.0000 −0.915872 −0.457936 0.888985i 0.651411π-0.651411\pi
−0.457936 + 0.888985i 0.651411π0.651411\pi
578578 0 0
579579 0 0
580580 0 0
581581 −6.00000 10.3923i −0.248922 0.431145i
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 3.00000 5.19615i 0.123823 0.214468i −0.797449 0.603386i 0.793818π-0.793818\pi
0.921272 + 0.388918i 0.127151π0.127151\pi
588588 0 0
589589 −8.00000 13.8564i −0.329634 0.570943i
590590 0 0
591591 0 0
592592 0 0
593593 18.0000 0.739171 0.369586 0.929197i 0.379500π-0.379500\pi
0.369586 + 0.929197i 0.379500π0.379500\pi
594594 0 0
595595 12.0000 0.491952
596596 0 0
597597 0 0
598598 0 0
599599 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
600600 0 0
601601 5.00000 8.66025i 0.203954 0.353259i −0.745845 0.666120i 0.767954π-0.767954\pi
0.949799 + 0.312861i 0.101287π0.101287\pi
602602 0 0
603603 0 0
604604 0 0
605605 −5.50000 + 9.52628i −0.223607 + 0.387298i
606606 0 0
607607 11.0000 + 19.0526i 0.446476 + 0.773320i 0.998154 0.0607380i 0.0193454π-0.0193454\pi
−0.551678 + 0.834058i 0.686012π0.686012\pi
608608 0 0
609609 0 0
610610 0 0
611611 −12.0000 −0.485468
612612 0 0
613613 2.00000 0.0807792 0.0403896 0.999184i 0.487140π-0.487140\pi
0.0403896 + 0.999184i 0.487140π0.487140\pi
614614 0 0
615615 0 0
616616 0 0
617617 3.00000 + 5.19615i 0.120775 + 0.209189i 0.920074 0.391745i 0.128129π-0.128129\pi
−0.799298 + 0.600935i 0.794795π0.794795\pi
618618 0 0
619619 −10.0000 + 17.3205i −0.401934 + 0.696170i −0.993959 0.109749i 0.964995π-0.964995\pi
0.592025 + 0.805919i 0.298329π0.298329\pi
620620 0 0
621621 0 0
622622 0 0
623623 6.00000 10.3923i 0.240385 0.416359i
624624 0 0
625625 −0.500000 0.866025i −0.0200000 0.0346410i
626626 0 0
627627 0 0
628628 0 0
629629 −12.0000 −0.478471
630630 0 0
631631 −28.0000 −1.11466 −0.557331 0.830290i 0.688175π-0.688175\pi
−0.557331 + 0.830290i 0.688175π0.688175\pi
632632 0 0
633633 0 0
634634 0 0
635635 1.00000 + 1.73205i 0.0396838 + 0.0687343i
636636 0 0
637637 3.00000 5.19615i 0.118864 0.205879i
638638 0 0
639639 0 0
640640 0 0
641641 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i 0.717651π-0.717651\pi
0.987200 + 0.159489i 0.0509845π0.0509845\pi
642642 0 0
643643 −7.00000 12.1244i −0.276053 0.478138i 0.694347 0.719640i 0.255693π-0.255693\pi
−0.970400 + 0.241502i 0.922360π0.922360\pi
644644 0 0
645645 0 0
646646 0 0
647647 42.0000 1.65119 0.825595 0.564263i 0.190840π-0.190840\pi
0.825595 + 0.564263i 0.190840π0.190840\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 −21.0000 36.3731i −0.821794 1.42339i −0.904345 0.426801i 0.859640π-0.859640\pi
0.0825519 0.996587i 0.473693π-0.473693\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i 0.414010π0.414010\pi
−0.968052 + 0.250748i 0.919323π0.919323\pi
660660 0 0
661661 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i 0.0259377π-0.0259377\pi
−0.568831 + 0.822454i 0.692604π0.692604\pi
662662 0 0
663663 0 0
664664 0 0
665665 8.00000 0.310227
666666 0 0
667667 36.0000 1.39393
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 23.0000 39.8372i 0.886585 1.53561i 0.0426985 0.999088i 0.486405π-0.486405\pi
0.843886 0.536522i 0.180262π-0.180262\pi
674674 0 0
675675 0 0
676676 0 0
677677 −9.00000 + 15.5885i −0.345898 + 0.599113i −0.985517 0.169580i 0.945759π-0.945759\pi
0.639618 + 0.768693i 0.279092π0.279092\pi
678678 0 0
679679 −2.00000 3.46410i −0.0767530 0.132940i
680680 0 0
681681 0 0
682682 0 0
683683 −42.0000 −1.60709 −0.803543 0.595247i 0.797054π-0.797054\pi
−0.803543 + 0.595247i 0.797054π0.797054\pi
684684 0 0
685685 −18.0000 −0.687745
686686 0 0
687687 0 0
688688 0 0
689689 6.00000 + 10.3923i 0.228582 + 0.395915i
690690 0 0
691691 −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i 0.881959π-0.881959\pi
0.779857 + 0.625958i 0.215292π0.215292\pi
692692 0 0
693693 0 0
694694 0 0
695695 −2.00000 + 3.46410i −0.0758643 + 0.131401i
696696 0 0
697697 18.0000 + 31.1769i 0.681799 + 1.18091i
698698 0 0
699699 0 0
700700 0 0
701701 −30.0000 −1.13308 −0.566542 0.824033i 0.691719π-0.691719\pi
−0.566542 + 0.824033i 0.691719π0.691719\pi
702702 0 0
703703 −8.00000 −0.301726
704704 0 0
705705 0 0
706706 0 0
707707 −6.00000 10.3923i −0.225653 0.390843i
708708 0 0
709709 17.0000 29.4449i 0.638448 1.10583i −0.347325 0.937745i 0.612910π-0.612910\pi
0.985773 0.168080i 0.0537568π-0.0537568\pi
710710 0 0
711711 0 0
712712 0 0
713713 12.0000 20.7846i 0.449404 0.778390i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 −24.0000 −0.895049 −0.447524 0.894272i 0.647694π-0.647694\pi
−0.447524 + 0.894272i 0.647694π0.647694\pi
720720 0 0
721721 28.0000 1.04277
722722 0 0
723723 0 0
724724 0 0
725725 −3.00000 5.19615i −0.111417 0.192980i
726726 0 0
727727 23.0000 39.8372i 0.853023 1.47748i −0.0254445 0.999676i 0.508100π-0.508100\pi
0.878467 0.477803i 0.158567π-0.158567\pi
728728 0 0
729729 0 0
730730 0 0
731731 −30.0000 + 51.9615i −1.10959 + 1.92187i
732732 0 0
733733 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i 0.0334875π-0.0334875\pi
−0.588177 + 0.808732i 0.700154π0.700154\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 20.0000 0.735712 0.367856 0.929883i 0.380092π-0.380092\pi
0.367856 + 0.929883i 0.380092π0.380092\pi
740740 0 0
741741 0 0
742742 0 0
743743 −3.00000 5.19615i −0.110059 0.190628i 0.805735 0.592277i 0.201771π-0.201771\pi
−0.915794 + 0.401648i 0.868437π0.868437\pi
744744 0 0
745745 −3.00000 + 5.19615i −0.109911 + 0.190372i
746746 0 0
747747 0 0
748748 0 0
749749 6.00000 10.3923i 0.219235 0.379727i
750750 0 0
751751 2.00000 + 3.46410i 0.0729810 + 0.126407i 0.900207 0.435463i 0.143415π-0.143415\pi
−0.827225 + 0.561870i 0.810082π0.810082\pi
752752 0 0
753753 0 0
754754 0 0
755755 −20.0000 −0.727875
756756 0 0
757757 −22.0000 −0.799604 −0.399802 0.916602i 0.630921π-0.630921\pi
−0.399802 + 0.916602i 0.630921π0.630921\pi
758758 0 0
759759 0 0
760760 0 0
761761 −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i 0.891253π-0.891253\pi
0.180957 0.983491i 0.442080π-0.442080\pi
762762 0 0
763763 −2.00000 + 3.46410i −0.0724049 + 0.125409i
764764 0 0
765765 0 0
766766 0 0
767767 −12.0000 + 20.7846i −0.433295 + 0.750489i
768768 0 0
769769 −1.00000 1.73205i −0.0360609 0.0624593i 0.847432 0.530904i 0.178148π-0.178148\pi
−0.883493 + 0.468445i 0.844814π0.844814\pi
770770 0 0
771771 0 0
772772 0 0
773773 −30.0000 −1.07903 −0.539513 0.841978i 0.681391π-0.681391\pi
−0.539513 + 0.841978i 0.681391π0.681391\pi
774774 0 0
775775 −4.00000 −0.143684
776776 0 0
777777 0 0
778778 0 0
779779 12.0000 + 20.7846i 0.429945 + 0.744686i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0 0
785785 −11.0000 + 19.0526i −0.392607 + 0.680015i
786786 0 0
787787 −13.0000 22.5167i −0.463400 0.802632i 0.535728 0.844391i 0.320037π-0.320037\pi
−0.999128 + 0.0417585i 0.986704π0.986704\pi
788788 0 0
789789 0 0
790790 0 0
791791 −12.0000 −0.426671
792792 0 0
793793 4.00000 0.142044
794794 0 0
795795 0 0
796796 0 0
797797 −21.0000 36.3731i −0.743858 1.28840i −0.950726 0.310031i 0.899660π-0.899660\pi
0.206868 0.978369i 0.433673π-0.433673\pi
798798 0 0
799799 −18.0000 + 31.1769i −0.636794 + 1.10296i
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 0 0
805805 6.00000 + 10.3923i 0.211472 + 0.366281i
806806 0 0
807807 0 0
808808 0 0
809809 −6.00000 −0.210949 −0.105474 0.994422i 0.533636π-0.533636\pi
−0.105474 + 0.994422i 0.533636π0.533636\pi
810810 0 0
811811 −16.0000 −0.561836 −0.280918 0.959732i 0.590639π-0.590639\pi
−0.280918 + 0.959732i 0.590639π0.590639\pi
812812 0 0
813813 0 0
814814 0 0
815815 −5.00000 8.66025i −0.175142 0.303355i
816816 0 0
817817 −20.0000 + 34.6410i −0.699711 + 1.21194i
818818 0 0
819819 0 0
820820 0 0
821821 27.0000 46.7654i 0.942306 1.63212i 0.181250 0.983437i 0.441986π-0.441986\pi
0.761056 0.648686i 0.224681π-0.224681\pi
822822 0 0
823823 −19.0000 32.9090i −0.662298 1.14713i −0.980010 0.198947i 0.936248π-0.936248\pi
0.317712 0.948187i 0.397086π-0.397086\pi
824824 0 0
825825 0 0
826826 0 0
827827 −30.0000 −1.04320 −0.521601 0.853189i 0.674665π-0.674665\pi
−0.521601 + 0.853189i 0.674665π0.674665\pi
828828 0 0
829829 2.00000 0.0694629 0.0347314 0.999397i 0.488942π-0.488942\pi
0.0347314 + 0.999397i 0.488942π0.488942\pi
830830 0 0
831831 0 0
832832 0 0
833833 −9.00000 15.5885i −0.311832 0.540108i
834834 0 0
835835 9.00000 15.5885i 0.311458 0.539461i
836836 0 0
837837 0 0
838838 0 0
839839 24.0000 41.5692i 0.828572 1.43513i −0.0705865 0.997506i 0.522487π-0.522487\pi
0.899158 0.437623i 0.144180π-0.144180\pi
840840 0 0
841841 −3.50000 6.06218i −0.120690 0.209041i
842842 0 0
843843 0 0
844844 0 0
845845 9.00000 0.309609
846846 0 0
847847 −22.0000 −0.755929
848848 0 0
849849 0 0
850850 0 0
851851 −6.00000 10.3923i −0.205677 0.356244i
852852 0 0
853853 −25.0000 + 43.3013i −0.855984 + 1.48261i 0.0197457 + 0.999805i 0.493714π0.493714\pi
−0.875729 + 0.482802i 0.839619π0.839619\pi
854854 0 0
855855 0 0
856856 0 0
857857 −9.00000 + 15.5885i −0.307434 + 0.532492i −0.977800 0.209539i 0.932804π-0.932804\pi
0.670366 + 0.742030i 0.266137π0.266137\pi
858858 0 0
859859 2.00000 + 3.46410i 0.0682391 + 0.118194i 0.898126 0.439738i 0.144929π-0.144929\pi
−0.829887 + 0.557931i 0.811595π0.811595\pi
860860 0 0
861861 0 0
862862 0 0
863863 6.00000 0.204242 0.102121 0.994772i 0.467437π-0.467437\pi
0.102121 + 0.994772i 0.467437π0.467437\pi
864864 0 0
865865 6.00000 0.204006
866866 0 0
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 −2.00000 + 3.46410i −0.0677674 + 0.117377i
872872 0 0
873873 0 0
874874 0 0
875875 1.00000 1.73205i 0.0338062 0.0585540i
876876 0 0
877877 −13.0000 22.5167i −0.438979 0.760334i 0.558632 0.829416i 0.311326π-0.311326\pi
−0.997611 + 0.0690819i 0.977993π0.977993\pi
878878 0 0
879879 0 0
880880 0 0
881881 −18.0000 −0.606435 −0.303218 0.952921i 0.598061π-0.598061\pi
−0.303218 + 0.952921i 0.598061π0.598061\pi
882882 0 0
883883 14.0000 0.471138 0.235569 0.971858i 0.424305π-0.424305\pi
0.235569 + 0.971858i 0.424305π0.424305\pi
884884 0 0
885885 0 0
886886 0 0
887887 −9.00000 15.5885i −0.302190 0.523409i 0.674441 0.738328i 0.264385π-0.264385\pi
−0.976632 + 0.214919i 0.931051π0.931051\pi
888888 0 0
889889 −2.00000 + 3.46410i −0.0670778 + 0.116182i
890890 0 0
891891 0 0
892892 0 0
893893 −12.0000 + 20.7846i −0.401565 + 0.695530i
894894 0 0
895895 −6.00000 10.3923i −0.200558 0.347376i
896896 0 0
897897 0 0
898898 0 0
899899 −24.0000 −0.800445
900900 0 0
901901 36.0000 1.19933
902902 0 0
903903 0 0
904904 0 0
905905 −5.00000 8.66025i −0.166206 0.287877i
906906 0 0
907907 23.0000 39.8372i 0.763702 1.32277i −0.177227 0.984170i 0.556713π-0.556713\pi
0.940930 0.338602i 0.109954π-0.109954\pi
908908 0 0
909909 0 0
910910 0 0
911911 −6.00000 + 10.3923i −0.198789 + 0.344312i −0.948136 0.317865i 0.897034π-0.897034\pi
0.749347 + 0.662177i 0.230367π0.230367\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 −16.0000 −0.527791 −0.263896 0.964551i 0.585007π-0.585007\pi
−0.263896 + 0.964551i 0.585007π0.585007\pi
920920 0 0
921921 0 0
922922 0 0
923923 12.0000 + 20.7846i 0.394985 + 0.684134i
924924 0 0
925925 −1.00000 + 1.73205i −0.0328798 + 0.0569495i
926926 0 0
927927 0 0
928928 0 0
929929 21.0000 36.3731i 0.688988 1.19336i −0.283178 0.959067i 0.591389π-0.591389\pi
0.972166 0.234294i 0.0752779π-0.0752779\pi
930930 0 0
931931 −6.00000 10.3923i −0.196642 0.340594i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 −22.0000 −0.718709 −0.359354 0.933201i 0.617003π-0.617003\pi
−0.359354 + 0.933201i 0.617003π0.617003\pi
938938 0 0
939939 0 0
940940 0 0
941941 9.00000 + 15.5885i 0.293392 + 0.508169i 0.974609 0.223912i 0.0718827π-0.0718827\pi
−0.681218 + 0.732081i 0.738549π0.738549\pi
942942 0 0
943943 −18.0000 + 31.1769i −0.586161 + 1.01526i
944944 0 0
945945 0 0
946946 0 0
947947 −9.00000 + 15.5885i −0.292461 + 0.506557i −0.974391 0.224860i 0.927807π-0.927807\pi
0.681930 + 0.731417i 0.261141π0.261141\pi
948948 0 0
949949 −2.00000 3.46410i −0.0649227 0.112449i
950950 0 0
951951 0 0
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 12.0000 0.388311
956956 0 0
957957 0 0
958958 0 0
959959 −18.0000 31.1769i −0.581250 1.00676i
960960 0 0
961961 7.50000 12.9904i 0.241935 0.419045i
962962 0 0
963963 0 0
964964 0 0
965965 13.0000 22.5167i 0.418485 0.724837i
966966 0 0
967967 11.0000 + 19.0526i 0.353736 + 0.612689i 0.986901 0.161328i 0.0515777π-0.0515777\pi
−0.633165 + 0.774017i 0.718244π0.718244\pi
968968 0 0
969969 0 0
970970 0 0
971971 −24.0000 −0.770197 −0.385098 0.922876i 0.625832π-0.625832\pi
−0.385098 + 0.922876i 0.625832π0.625832\pi
972972 0 0
973973 −8.00000 −0.256468
974974 0 0
975975 0 0
976976 0 0
977977 −9.00000 15.5885i −0.287936 0.498719i 0.685381 0.728184i 0.259636π-0.259636\pi
−0.973317 + 0.229465i 0.926302π0.926302\pi
978978 0 0
979979 0 0
980980 0 0
981981 0 0
982982 0 0
983983 9.00000 15.5885i 0.287055 0.497195i −0.686050 0.727554i 0.740657π-0.740657\pi
0.973106 + 0.230360i 0.0739903π0.0739903\pi
984984 0 0
985985 9.00000 + 15.5885i 0.286764 + 0.496690i
986986 0 0
987987 0 0
988988 0 0
989989 −60.0000 −1.90789
990990 0 0
991991 −4.00000 −0.127064 −0.0635321 0.997980i 0.520237π-0.520237\pi
−0.0635321 + 0.997980i 0.520237π0.520237\pi
992992 0 0
993993 0 0
994994 0 0
995995 4.00000 + 6.92820i 0.126809 + 0.219639i
996996 0 0
997997 −13.0000 + 22.5167i −0.411714 + 0.713110i −0.995077 0.0991016i 0.968403π-0.968403\pi
0.583363 + 0.812211i 0.301736π0.301736\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1620.2.i.h.541.1 2
3.2 odd 2 1620.2.i.b.541.1 2
9.2 odd 6 180.2.a.a.1.1 1
9.4 even 3 inner 1620.2.i.h.1081.1 2
9.5 odd 6 1620.2.i.b.1081.1 2
9.7 even 3 20.2.a.a.1.1 1
36.7 odd 6 80.2.a.b.1.1 1
36.11 even 6 720.2.a.h.1.1 1
45.2 even 12 900.2.d.c.649.2 2
45.7 odd 12 100.2.c.a.49.2 2
45.29 odd 6 900.2.a.b.1.1 1
45.34 even 6 100.2.a.a.1.1 1
45.38 even 12 900.2.d.c.649.1 2
45.43 odd 12 100.2.c.a.49.1 2
63.16 even 3 980.2.i.i.361.1 2
63.20 even 6 8820.2.a.g.1.1 1
63.25 even 3 980.2.i.i.961.1 2
63.34 odd 6 980.2.a.h.1.1 1
63.52 odd 6 980.2.i.c.961.1 2
63.61 odd 6 980.2.i.c.361.1 2
72.11 even 6 2880.2.a.f.1.1 1
72.29 odd 6 2880.2.a.m.1.1 1
72.43 odd 6 320.2.a.a.1.1 1
72.61 even 6 320.2.a.f.1.1 1
99.43 odd 6 2420.2.a.a.1.1 1
117.25 even 6 3380.2.a.c.1.1 1
117.34 odd 12 3380.2.f.b.3041.1 2
117.70 odd 12 3380.2.f.b.3041.2 2
144.43 odd 12 1280.2.d.g.641.1 2
144.61 even 12 1280.2.d.c.641.1 2
144.115 odd 12 1280.2.d.g.641.2 2
144.133 even 12 1280.2.d.c.641.2 2
153.16 even 6 5780.2.a.f.1.1 1
153.106 even 12 5780.2.c.a.5201.2 2
153.115 even 12 5780.2.c.a.5201.1 2
171.151 odd 6 7220.2.a.f.1.1 1
180.7 even 12 400.2.c.b.49.1 2
180.43 even 12 400.2.c.b.49.2 2
180.47 odd 12 3600.2.f.j.2449.1 2
180.79 odd 6 400.2.a.c.1.1 1
180.83 odd 12 3600.2.f.j.2449.2 2
180.119 even 6 3600.2.a.be.1.1 1
252.223 even 6 3920.2.a.h.1.1 1
315.34 odd 6 4900.2.a.e.1.1 1
315.97 even 12 4900.2.e.f.2549.1 2
315.223 even 12 4900.2.e.f.2549.2 2
360.43 even 12 1600.2.c.e.449.1 2
360.133 odd 12 1600.2.c.d.449.2 2
360.187 even 12 1600.2.c.e.449.2 2
360.259 odd 6 1600.2.a.w.1.1 1
360.277 odd 12 1600.2.c.d.449.1 2
360.349 even 6 1600.2.a.c.1.1 1
396.43 even 6 9680.2.a.ba.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.2.a.a.1.1 1 9.7 even 3
80.2.a.b.1.1 1 36.7 odd 6
100.2.a.a.1.1 1 45.34 even 6
100.2.c.a.49.1 2 45.43 odd 12
100.2.c.a.49.2 2 45.7 odd 12
180.2.a.a.1.1 1 9.2 odd 6
320.2.a.a.1.1 1 72.43 odd 6
320.2.a.f.1.1 1 72.61 even 6
400.2.a.c.1.1 1 180.79 odd 6
400.2.c.b.49.1 2 180.7 even 12
400.2.c.b.49.2 2 180.43 even 12
720.2.a.h.1.1 1 36.11 even 6
900.2.a.b.1.1 1 45.29 odd 6
900.2.d.c.649.1 2 45.38 even 12
900.2.d.c.649.2 2 45.2 even 12
980.2.a.h.1.1 1 63.34 odd 6
980.2.i.c.361.1 2 63.61 odd 6
980.2.i.c.961.1 2 63.52 odd 6
980.2.i.i.361.1 2 63.16 even 3
980.2.i.i.961.1 2 63.25 even 3
1280.2.d.c.641.1 2 144.61 even 12
1280.2.d.c.641.2 2 144.133 even 12
1280.2.d.g.641.1 2 144.43 odd 12
1280.2.d.g.641.2 2 144.115 odd 12
1600.2.a.c.1.1 1 360.349 even 6
1600.2.a.w.1.1 1 360.259 odd 6
1600.2.c.d.449.1 2 360.277 odd 12
1600.2.c.d.449.2 2 360.133 odd 12
1600.2.c.e.449.1 2 360.43 even 12
1600.2.c.e.449.2 2 360.187 even 12
1620.2.i.b.541.1 2 3.2 odd 2
1620.2.i.b.1081.1 2 9.5 odd 6
1620.2.i.h.541.1 2 1.1 even 1 trivial
1620.2.i.h.1081.1 2 9.4 even 3 inner
2420.2.a.a.1.1 1 99.43 odd 6
2880.2.a.f.1.1 1 72.11 even 6
2880.2.a.m.1.1 1 72.29 odd 6
3380.2.a.c.1.1 1 117.25 even 6
3380.2.f.b.3041.1 2 117.34 odd 12
3380.2.f.b.3041.2 2 117.70 odd 12
3600.2.a.be.1.1 1 180.119 even 6
3600.2.f.j.2449.1 2 180.47 odd 12
3600.2.f.j.2449.2 2 180.83 odd 12
3920.2.a.h.1.1 1 252.223 even 6
4900.2.a.e.1.1 1 315.34 odd 6
4900.2.e.f.2549.1 2 315.97 even 12
4900.2.e.f.2549.2 2 315.223 even 12
5780.2.a.f.1.1 1 153.16 even 6
5780.2.c.a.5201.1 2 153.115 even 12
5780.2.c.a.5201.2 2 153.106 even 12
7220.2.a.f.1.1 1 171.151 odd 6
8820.2.a.g.1.1 1 63.20 even 6
9680.2.a.ba.1.1 1 396.43 even 6