Properties

Label 1440.2.x.j.703.1
Level 14401440
Weight 22
Character 1440.703
Analytic conductor 11.49811.498
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1440,2,Mod(127,1440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1440, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 0, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1440.127"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1440=25325 1440 = 2^{5} \cdot 3^{2} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1440.x (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,0,4,0,4,0,0,0,0,0,-2,0,0,0,10,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 11.498457891111.4984578911
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 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 160)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 703.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 1440.703
Dual form 1440.2.x.j.127.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(2.00000+1.00000i)q5+(2.00000+2.00000i)q7+(1.000001.00000i)q13+(5.000005.00000i)q17+4.00000q19+(2.00000+2.00000i)q23+(3.00000+4.00000i)q254.00000iq29+4.00000iq31+(2.00000+6.00000i)q35+(1.000001.00000i)q37+(6.00000+6.00000i)q43+(2.00000+2.00000i)q47+1.00000iq49+(7.00000+7.00000i)q534.00000q594.00000q61+(1.000003.00000i)q65+(10.000010.0000i)q67+12.0000iq71+(3.000003.00000i)q73+16.0000q79+(2.000002.00000i)q83+(15.00005.00000i)q854.00000iq91+(8.00000+4.00000i)q95+(3.00000+3.00000i)q97+O(q100)q+(2.00000 + 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-1.00000 - 1.00000i) q^{13} +(5.00000 - 5.00000i) q^{17} +4.00000 q^{19} +(-2.00000 + 2.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} -4.00000i q^{29} +4.00000i q^{31} +(2.00000 + 6.00000i) q^{35} +(1.00000 - 1.00000i) q^{37} +(-6.00000 + 6.00000i) q^{43} +(2.00000 + 2.00000i) q^{47} +1.00000i q^{49} +(7.00000 + 7.00000i) q^{53} -4.00000 q^{59} -4.00000 q^{61} +(-1.00000 - 3.00000i) q^{65} +(-10.0000 - 10.0000i) q^{67} +12.0000i q^{71} +(-3.00000 - 3.00000i) q^{73} +16.0000 q^{79} +(2.00000 - 2.00000i) q^{83} +(15.0000 - 5.00000i) q^{85} -4.00000i q^{91} +(8.00000 + 4.00000i) q^{95} +(-3.00000 + 3.00000i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+4q5+4q72q13+10q17+8q194q23+6q25+4q35+2q3712q43+4q47+14q538q598q612q6520q676q73+32q79+6q97+O(q100) 2 q + 4 q^{5} + 4 q^{7} - 2 q^{13} + 10 q^{17} + 8 q^{19} - 4 q^{23} + 6 q^{25} + 4 q^{35} + 2 q^{37} - 12 q^{43} + 4 q^{47} + 14 q^{53} - 8 q^{59} - 8 q^{61} - 2 q^{65} - 20 q^{67} - 6 q^{73} + 32 q^{79}+ \cdots - 6 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1440Z)×\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times.

nn 577577 641641 901901 991991
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 11 11 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0 0
44 0 0
55 2.00000 + 1.00000i 0.894427 + 0.447214i
66 0 0
77 2.00000 + 2.00000i 0.755929 + 0.755929i 0.975579 0.219650i 0.0704915π-0.0704915\pi
−0.219650 + 0.975579i 0.570491π0.570491\pi
88 0 0
99 0 0
1010 0 0
1111 0 0 1.00000 00
−1.00000 π\pi
1212 0 0
1313 −1.00000 1.00000i −0.277350 0.277350i 0.554700 0.832050i 0.312833π-0.312833\pi
−0.832050 + 0.554700i 0.812833π0.812833\pi
1414 0 0
1515 0 0
1616 0 0
1717 5.00000 5.00000i 1.21268 1.21268i 0.242536 0.970143i 0.422021π-0.422021\pi
0.970143 0.242536i 0.0779791π-0.0779791\pi
1818 0 0
1919 4.00000 0.917663 0.458831 0.888523i 0.348268π-0.348268\pi
0.458831 + 0.888523i 0.348268π0.348268\pi
2020 0 0
2121 0 0
2222 0 0
2323 −2.00000 + 2.00000i −0.417029 + 0.417029i −0.884178 0.467150i 0.845281π-0.845281\pi
0.467150 + 0.884178i 0.345281π0.345281\pi
2424 0 0
2525 3.00000 + 4.00000i 0.600000 + 0.800000i
2626 0 0
2727 0 0
2828 0 0
2929 4.00000i 0.742781i −0.928477 0.371391i 0.878881π-0.878881\pi
0.928477 0.371391i 0.121119π-0.121119\pi
3030 0 0
3131 4.00000i 0.718421i 0.933257 + 0.359211i 0.116954π0.116954\pi
−0.933257 + 0.359211i 0.883046π0.883046\pi
3232 0 0
3333 0 0
3434 0 0
3535 2.00000 + 6.00000i 0.338062 + 1.01419i
3636 0 0
3737 1.00000 1.00000i 0.164399 0.164399i −0.620113 0.784512i 0.712913π-0.712913\pi
0.784512 + 0.620113i 0.212913π0.212913\pi
3838 0 0
3939 0 0
4040 0 0
4141 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4242 0 0
4343 −6.00000 + 6.00000i −0.914991 + 0.914991i −0.996660 0.0816682i 0.973975π-0.973975\pi
0.0816682 + 0.996660i 0.473975π0.473975\pi
4444 0 0
4545 0 0
4646 0 0
4747 2.00000 + 2.00000i 0.291730 + 0.291730i 0.837763 0.546033i 0.183863π-0.183863\pi
−0.546033 + 0.837763i 0.683863π0.683863\pi
4848 0 0
4949 1.00000i 0.142857i
5050 0 0
5151 0 0
5252 0 0
5353 7.00000 + 7.00000i 0.961524 + 0.961524i 0.999287 0.0377628i 0.0120231π-0.0120231\pi
−0.0377628 + 0.999287i 0.512023π0.512023\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 −4.00000 −0.520756 −0.260378 0.965507i 0.583847π-0.583847\pi
−0.260378 + 0.965507i 0.583847π0.583847\pi
6060 0 0
6161 −4.00000 −0.512148 −0.256074 0.966657i 0.582429π-0.582429\pi
−0.256074 + 0.966657i 0.582429π0.582429\pi
6262 0 0
6363 0 0
6464 0 0
6565 −1.00000 3.00000i −0.124035 0.372104i
6666 0 0
6767 −10.0000 10.0000i −1.22169 1.22169i −0.967029 0.254665i 0.918035π-0.918035\pi
−0.254665 0.967029i 0.581965π-0.581965\pi
6868 0 0
6969 0 0
7070 0 0
7171 12.0000i 1.42414i 0.702109 + 0.712069i 0.252242π0.252242\pi
−0.702109 + 0.712069i 0.747758π0.747758\pi
7272 0 0
7373 −3.00000 3.00000i −0.351123 0.351123i 0.509404 0.860527i 0.329866π-0.329866\pi
−0.860527 + 0.509404i 0.829866π0.829866\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 16.0000 1.80014 0.900070 0.435745i 0.143515π-0.143515\pi
0.900070 + 0.435745i 0.143515π0.143515\pi
8080 0 0
8181 0 0
8282 0 0
8383 2.00000 2.00000i 0.219529 0.219529i −0.588771 0.808300i 0.700388π-0.700388\pi
0.808300 + 0.588771i 0.200388π0.200388\pi
8484 0 0
8585 15.0000 5.00000i 1.62698 0.542326i
8686 0 0
8787 0 0
8888 0 0
8989 0 0 1.00000 00
−1.00000 π\pi
9090 0 0
9191 4.00000i 0.419314i
9292 0 0
9393 0 0
9494 0 0
9595 8.00000 + 4.00000i 0.820783 + 0.410391i
9696 0 0
9797 −3.00000 + 3.00000i −0.304604 + 0.304604i −0.842812 0.538208i 0.819101π-0.819101\pi
0.538208 + 0.842812i 0.319101π0.319101\pi
9898 0 0
9999 0 0
100100 0 0
101101 6.00000 0.597022 0.298511 0.954406i 0.403510π-0.403510\pi
0.298511 + 0.954406i 0.403510π0.403510\pi
102102 0 0
103103 −6.00000 + 6.00000i −0.591198 + 0.591198i −0.937955 0.346757i 0.887283π-0.887283\pi
0.346757 + 0.937955i 0.387283π0.387283\pi
104104 0 0
105105 0 0
106106 0 0
107107 −6.00000 6.00000i −0.580042 0.580042i 0.354873 0.934915i 0.384524π-0.384524\pi
−0.934915 + 0.354873i 0.884524π0.884524\pi
108108 0 0
109109 10.0000i 0.957826i −0.877862 0.478913i 0.841031π-0.841031\pi
0.877862 0.478913i 0.158969π-0.158969\pi
110110 0 0
111111 0 0
112112 0 0
113113 9.00000 + 9.00000i 0.846649 + 0.846649i 0.989713 0.143065i 0.0456957π-0.0456957\pi
−0.143065 + 0.989713i 0.545696π0.545696\pi
114114 0 0
115115 −6.00000 + 2.00000i −0.559503 + 0.186501i
116116 0 0
117117 0 0
118118 0 0
119119 20.0000 1.83340
120120 0 0
121121 11.0000 1.00000
122122 0 0
123123 0 0
124124 0 0
125125 2.00000 + 11.0000i 0.178885 + 0.983870i
126126 0 0
127127 10.0000 + 10.0000i 0.887357 + 0.887357i 0.994268 0.106912i 0.0340963π-0.0340963\pi
−0.106912 + 0.994268i 0.534096π0.534096\pi
128128 0 0
129129 0 0
130130 0 0
131131 8.00000i 0.698963i 0.936943 + 0.349482i 0.113642π0.113642\pi
−0.936943 + 0.349482i 0.886358π0.886358\pi
132132 0 0
133133 8.00000 + 8.00000i 0.693688 + 0.693688i
134134 0 0
135135 0 0
136136 0 0
137137 −1.00000 + 1.00000i −0.0854358 + 0.0854358i −0.748533 0.663097i 0.769242π-0.769242\pi
0.663097 + 0.748533i 0.269242π0.269242\pi
138138 0 0
139139 −12.0000 −1.01783 −0.508913 0.860818i 0.669953π-0.669953\pi
−0.508913 + 0.860818i 0.669953π0.669953\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 0 0
145145 4.00000 8.00000i 0.332182 0.664364i
146146 0 0
147147 0 0
148148 0 0
149149 18.0000i 1.47462i −0.675556 0.737309i 0.736096π-0.736096\pi
0.675556 0.737309i 0.263904π-0.263904\pi
150150 0 0
151151 12.0000i 0.976546i −0.872691 0.488273i 0.837627π-0.837627\pi
0.872691 0.488273i 0.162373π-0.162373\pi
152152 0 0
153153 0 0
154154 0 0
155155 −4.00000 + 8.00000i −0.321288 + 0.642575i
156156 0 0
157157 −9.00000 + 9.00000i −0.718278 + 0.718278i −0.968252 0.249974i 0.919578π-0.919578\pi
0.249974 + 0.968252i 0.419578π0.419578\pi
158158 0 0
159159 0 0
160160 0 0
161161 −8.00000 −0.630488
162162 0 0
163163 2.00000 2.00000i 0.156652 0.156652i −0.624429 0.781081i 0.714668π-0.714668\pi
0.781081 + 0.624429i 0.214668π0.214668\pi
164164 0 0
165165 0 0
166166 0 0
167167 2.00000 + 2.00000i 0.154765 + 0.154765i 0.780242 0.625478i 0.215096π-0.215096\pi
−0.625478 + 0.780242i 0.715096π0.715096\pi
168168 0 0
169169 11.0000i 0.846154i
170170 0 0
171171 0 0
172172 0 0
173173 −13.0000 13.0000i −0.988372 0.988372i 0.0115615 0.999933i 0.496320π-0.496320\pi
−0.999933 + 0.0115615i 0.996320π0.996320\pi
174174 0 0
175175 −2.00000 + 14.0000i −0.151186 + 1.05830i
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 3.00000 1.00000i 0.220564 0.0735215i
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 20.0000i 1.44715i −0.690246 0.723575i 0.742498π-0.742498\pi
0.690246 0.723575i 0.257502π-0.257502\pi
192192 0 0
193193 −5.00000 5.00000i −0.359908 0.359908i 0.503871 0.863779i 0.331909π-0.331909\pi
−0.863779 + 0.503871i 0.831909π0.831909\pi
194194 0 0
195195 0 0
196196 0 0
197197 −5.00000 + 5.00000i −0.356235 + 0.356235i −0.862423 0.506188i 0.831054π-0.831054\pi
0.506188 + 0.862423i 0.331054π0.331054\pi
198198 0 0
199199 24.0000 1.70131 0.850657 0.525720i 0.176204π-0.176204\pi
0.850657 + 0.525720i 0.176204π0.176204\pi
200200 0 0
201201 0 0
202202 0 0
203203 8.00000 8.00000i 0.561490 0.561490i
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 16.0000i 1.10149i −0.834675 0.550743i 0.814345π-0.814345\pi
0.834675 0.550743i 0.185655π-0.185655\pi
212212 0 0
213213 0 0
214214 0 0
215215 −18.0000 + 6.00000i −1.22759 + 0.409197i
216216 0 0
217217 −8.00000 + 8.00000i −0.543075 + 0.543075i
218218 0 0
219219 0 0
220220 0 0
221221 −10.0000 −0.672673
222222 0 0
223223 −10.0000 + 10.0000i −0.669650 + 0.669650i −0.957635 0.287985i 0.907015π-0.907015\pi
0.287985 + 0.957635i 0.407015π0.407015\pi
224224 0 0
225225 0 0
226226 0 0
227227 −10.0000 10.0000i −0.663723 0.663723i 0.292532 0.956256i 0.405502π-0.405502\pi
−0.956256 + 0.292532i 0.905502π0.905502\pi
228228 0 0
229229 20.0000i 1.32164i 0.750546 + 0.660819i 0.229791π0.229791\pi
−0.750546 + 0.660819i 0.770209π0.770209\pi
230230 0 0
231231 0 0
232232 0 0
233233 5.00000 + 5.00000i 0.327561 + 0.327561i 0.851658 0.524097i 0.175597π-0.175597\pi
−0.524097 + 0.851658i 0.675597π0.675597\pi
234234 0 0
235235 2.00000 + 6.00000i 0.130466 + 0.391397i
236236 0 0
237237 0 0
238238 0 0
239239 −8.00000 −0.517477 −0.258738 0.965947i 0.583307π-0.583307\pi
−0.258738 + 0.965947i 0.583307π0.583307\pi
240240 0 0
241241 −16.0000 −1.03065 −0.515325 0.856995i 0.672329π-0.672329\pi
−0.515325 + 0.856995i 0.672329π0.672329\pi
242242 0 0
243243 0 0
244244 0 0
245245 −1.00000 + 2.00000i −0.0638877 + 0.127775i
246246 0 0
247247 −4.00000 4.00000i −0.254514 0.254514i
248248 0 0
249249 0 0
250250 0 0
251251 24.0000i 1.51487i −0.652913 0.757433i 0.726453π-0.726453\pi
0.652913 0.757433i 0.273547π-0.273547\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0 0
257257 −7.00000 + 7.00000i −0.436648 + 0.436648i −0.890882 0.454234i 0.849913π-0.849913\pi
0.454234 + 0.890882i 0.349913π0.349913\pi
258258 0 0
259259 4.00000 0.248548
260260 0 0
261261 0 0
262262 0 0
263263 −6.00000 + 6.00000i −0.369976 + 0.369976i −0.867468 0.497492i 0.834254π-0.834254\pi
0.497492 + 0.867468i 0.334254π0.334254\pi
264264 0 0
265265 7.00000 + 21.0000i 0.430007 + 1.29002i
266266 0 0
267267 0 0
268268 0 0
269269 10.0000i 0.609711i −0.952399 0.304855i 0.901392π-0.901392\pi
0.952399 0.304855i 0.0986081π-0.0986081\pi
270270 0 0
271271 20.0000i 1.21491i −0.794353 0.607457i 0.792190π-0.792190\pi
0.794353 0.607457i 0.207810π-0.207810\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 −9.00000 + 9.00000i −0.540758 + 0.540758i −0.923751 0.382993i 0.874893π-0.874893\pi
0.382993 + 0.923751i 0.374893π0.374893\pi
278278 0 0
279279 0 0
280280 0 0
281281 −8.00000 −0.477240 −0.238620 0.971113i 0.576695π-0.576695\pi
−0.238620 + 0.971113i 0.576695π0.576695\pi
282282 0 0
283283 6.00000 6.00000i 0.356663 0.356663i −0.505918 0.862581i 0.668846π-0.668846\pi
0.862581 + 0.505918i 0.168846π0.168846\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 33.0000i 1.94118i
290290 0 0
291291 0 0
292292 0 0
293293 5.00000 + 5.00000i 0.292103 + 0.292103i 0.837911 0.545807i 0.183777π-0.183777\pi
−0.545807 + 0.837911i 0.683777π0.683777\pi
294294 0 0
295295 −8.00000 4.00000i −0.465778 0.232889i
296296 0 0
297297 0 0
298298 0 0
299299 4.00000 0.231326
300300 0 0
301301 −24.0000 −1.38334
302302 0 0
303303 0 0
304304 0 0
305305 −8.00000 4.00000i −0.458079 0.229039i
306306 0 0
307307 −10.0000 10.0000i −0.570730 0.570730i 0.361602 0.932332i 0.382230π-0.382230\pi
−0.932332 + 0.361602i 0.882230π0.882230\pi
308308 0 0
309309 0 0
310310 0 0
311311 28.0000i 1.58773i −0.608091 0.793867i 0.708065π-0.708065\pi
0.608091 0.793867i 0.291935π-0.291935\pi
312312 0 0
313313 15.0000 + 15.0000i 0.847850 + 0.847850i 0.989865 0.142014i 0.0453579π-0.0453579\pi
−0.142014 + 0.989865i 0.545358π0.545358\pi
314314 0 0
315315 0 0
316316 0 0
317317 −11.0000 + 11.0000i −0.617822 + 0.617822i −0.944972 0.327151i 0.893912π-0.893912\pi
0.327151 + 0.944972i 0.393912π0.393912\pi
318318 0 0
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 20.0000 20.0000i 1.11283 1.11283i
324324 0 0
325325 1.00000 7.00000i 0.0554700 0.388290i
326326 0 0
327327 0 0
328328 0 0
329329 8.00000i 0.441054i
330330 0 0
331331 0 0 1.00000 00
−1.00000 π\pi
332332 0 0
333333 0 0
334334 0 0
335335 −10.0000 30.0000i −0.546358 1.63908i
336336 0 0
337337 −23.0000 + 23.0000i −1.25289 + 1.25289i −0.298471 + 0.954419i 0.596477π0.596477\pi
−0.954419 + 0.298471i 0.903523π0.903523\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 12.0000 12.0000i 0.647939 0.647939i
344344 0 0
345345 0 0
346346 0 0
347347 −18.0000 18.0000i −0.966291 0.966291i 0.0331594 0.999450i 0.489443π-0.489443\pi
−0.999450 + 0.0331594i 0.989443π0.989443\pi
348348 0 0
349349 20.0000i 1.07058i −0.844670 0.535288i 0.820203π-0.820203\pi
0.844670 0.535288i 0.179797π-0.179797\pi
350350 0 0
351351 0 0
352352 0 0
353353 −9.00000 9.00000i −0.479022 0.479022i 0.425797 0.904819i 0.359994π-0.359994\pi
−0.904819 + 0.425797i 0.859994π0.859994\pi
354354 0 0
355355 −12.0000 + 24.0000i −0.636894 + 1.27379i
356356 0 0
357357 0 0
358358 0 0
359359 16.0000 0.844448 0.422224 0.906492i 0.361250π-0.361250\pi
0.422224 + 0.906492i 0.361250π0.361250\pi
360360 0 0
361361 −3.00000 −0.157895
362362 0 0
363363 0 0
364364 0 0
365365 −3.00000 9.00000i −0.157027 0.471082i
366366 0 0
367367 −22.0000 22.0000i −1.14839 1.14839i −0.986869 0.161521i 0.948360π-0.948360\pi
−0.161521 0.986869i 0.551640π-0.551640\pi
368368 0 0
369369 0 0
370370 0 0
371371 28.0000i 1.45369i
372372 0 0
373373 21.0000 + 21.0000i 1.08734 + 1.08734i 0.995802 + 0.0915371i 0.0291780π0.0291780\pi
0.0915371 + 0.995802i 0.470822π0.470822\pi
374374 0 0
375375 0 0
376376 0 0
377377 −4.00000 + 4.00000i −0.206010 + 0.206010i
378378 0 0
379379 28.0000 1.43826 0.719132 0.694874i 0.244540π-0.244540\pi
0.719132 + 0.694874i 0.244540π0.244540\pi
380380 0 0
381381 0 0
382382 0 0
383383 −22.0000 + 22.0000i −1.12415 + 1.12415i −0.133036 + 0.991111i 0.542473π0.542473\pi
−0.991111 + 0.133036i 0.957527π0.957527\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 18.0000i 0.912636i 0.889817 + 0.456318i 0.150832π0.150832\pi
−0.889817 + 0.456318i 0.849168π0.849168\pi
390390 0 0
391391 20.0000i 1.01144i
392392 0 0
393393 0 0
394394 0 0
395395 32.0000 + 16.0000i 1.61009 + 0.805047i
396396 0 0
397397 13.0000 13.0000i 0.652451 0.652451i −0.301131 0.953583i 0.597364π-0.597364\pi
0.953583 + 0.301131i 0.0973643π0.0973643\pi
398398 0 0
399399 0 0
400400 0 0
401401 −34.0000 −1.69788 −0.848939 0.528490i 0.822758π-0.822758\pi
−0.848939 + 0.528490i 0.822758π0.822758\pi
402402 0 0
403403 4.00000 4.00000i 0.199254 0.199254i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 2.00000i 0.0988936i −0.998777 0.0494468i 0.984254π-0.984254\pi
0.998777 0.0494468i 0.0157458π-0.0157458\pi
410410 0 0
411411 0 0
412412 0 0
413413 −8.00000 8.00000i −0.393654 0.393654i
414414 0 0
415415 6.00000 2.00000i 0.294528 0.0981761i
416416 0 0
417417 0 0
418418 0 0
419419 12.0000 0.586238 0.293119 0.956076i 0.405307π-0.405307\pi
0.293119 + 0.956076i 0.405307π0.405307\pi
420420 0 0
421421 20.0000 0.974740 0.487370 0.873195i 0.337956π-0.337956\pi
0.487370 + 0.873195i 0.337956π0.337956\pi
422422 0 0
423423 0 0
424424 0 0
425425 35.0000 + 5.00000i 1.69775 + 0.242536i
426426 0 0
427427 −8.00000 8.00000i −0.387147 0.387147i
428428 0 0
429429 0 0
430430 0 0
431431 4.00000i 0.192673i 0.995349 + 0.0963366i 0.0307125π0.0307125\pi
−0.995349 + 0.0963366i 0.969287π0.969287\pi
432432 0 0
433433 −19.0000 19.0000i −0.913082 0.913082i 0.0834318 0.996513i 0.473412π-0.473412\pi
−0.996513 + 0.0834318i 0.973412π0.973412\pi
434434 0 0
435435 0 0
436436 0 0
437437 −8.00000 + 8.00000i −0.382692 + 0.382692i
438438 0 0
439439 −16.0000 −0.763638 −0.381819 0.924237i 0.624702π-0.624702\pi
−0.381819 + 0.924237i 0.624702π0.624702\pi
440440 0 0
441441 0 0
442442 0 0
443443 −22.0000 + 22.0000i −1.04525 + 1.04525i −0.0463251 + 0.998926i 0.514751π0.514751\pi
−0.998926 + 0.0463251i 0.985249π0.985249\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 26.0000i 1.22702i −0.789689 0.613508i 0.789758π-0.789758\pi
0.789689 0.613508i 0.210242π-0.210242\pi
450450 0 0
451451 0 0
452452 0 0
453453 0 0
454454 0 0
455455 4.00000 8.00000i 0.187523 0.375046i
456456 0 0
457457 15.0000 15.0000i 0.701670 0.701670i −0.263099 0.964769i 0.584744π-0.584744\pi
0.964769 + 0.263099i 0.0847444π0.0847444\pi
458458 0 0
459459 0 0
460460 0 0
461461 14.0000 0.652045 0.326023 0.945362i 0.394291π-0.394291\pi
0.326023 + 0.945362i 0.394291π0.394291\pi
462462 0 0
463463 −22.0000 + 22.0000i −1.02243 + 1.02243i −0.0226840 + 0.999743i 0.507221π0.507221\pi
−0.999743 + 0.0226840i 0.992779π0.992779\pi
464464 0 0
465465 0 0
466466 0 0
467467 −2.00000 2.00000i −0.0925490 0.0925490i 0.659317 0.751865i 0.270846π-0.270846\pi
−0.751865 + 0.659317i 0.770846π0.770846\pi
468468 0 0
469469 40.0000i 1.84703i
470470 0 0
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 12.0000 + 16.0000i 0.550598 + 0.734130i
476476 0 0
477477 0 0
478478 0 0
479479 24.0000 1.09659 0.548294 0.836286i 0.315277π-0.315277\pi
0.548294 + 0.836286i 0.315277π0.315277\pi
480480 0 0
481481 −2.00000 −0.0911922
482482 0 0
483483 0 0
484484 0 0
485485 −9.00000 + 3.00000i −0.408669 + 0.136223i
486486 0 0
487487 −6.00000 6.00000i −0.271886 0.271886i 0.557973 0.829859i 0.311579π-0.311579\pi
−0.829859 + 0.557973i 0.811579π0.811579\pi
488488 0 0
489489 0 0
490490 0 0
491491 16.0000i 0.722070i −0.932552 0.361035i 0.882424π-0.882424\pi
0.932552 0.361035i 0.117576π-0.117576\pi
492492 0 0
493493 −20.0000 20.0000i −0.900755 0.900755i
494494 0 0
495495 0 0
496496 0 0
497497 −24.0000 + 24.0000i −1.07655 + 1.07655i
498498 0 0
499499 4.00000 0.179065 0.0895323 0.995984i 0.471463π-0.471463\pi
0.0895323 + 0.995984i 0.471463π0.471463\pi
500500 0 0
501501 0 0
502502 0 0
503503 −10.0000 + 10.0000i −0.445878 + 0.445878i −0.893982 0.448104i 0.852100π-0.852100\pi
0.448104 + 0.893982i 0.352100π0.352100\pi
504504 0 0
505505 12.0000 + 6.00000i 0.533993 + 0.266996i
506506 0 0
507507 0 0
508508 0 0
509509 36.0000i 1.59567i 0.602875 + 0.797836i 0.294022π0.294022\pi
−0.602875 + 0.797836i 0.705978π0.705978\pi
510510 0 0
511511 12.0000i 0.530849i
512512 0 0
513513 0 0
514514 0 0
515515 −18.0000 + 6.00000i −0.793175 + 0.264392i
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 14.0000i 0.612177 0.612177i −0.331336 0.943513i 0.607499π-0.607499\pi
0.943513 + 0.331336i 0.107499π0.107499\pi
524524 0 0
525525 0 0
526526 0 0
527527 20.0000 + 20.0000i 0.871214 + 0.871214i
528528 0 0
529529 15.0000i 0.652174i
530530 0 0
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 −6.00000 18.0000i −0.259403 0.778208i
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 −30.0000 −1.28980 −0.644900 0.764267i 0.723101π-0.723101\pi
−0.644900 + 0.764267i 0.723101π0.723101\pi
542542 0 0
543543 0 0
544544 0 0
545545 10.0000 20.0000i 0.428353 0.856706i
546546 0 0
547547 −6.00000 6.00000i −0.256541 0.256541i 0.567104 0.823646i 0.308064π-0.308064\pi
−0.823646 + 0.567104i 0.808064π0.808064\pi
548548 0 0
549549 0 0
550550 0 0
551551 16.0000i 0.681623i
552552 0 0
553553 32.0000 + 32.0000i 1.36078 + 1.36078i
554554 0 0
555555 0 0
556556 0 0
557557 15.0000 15.0000i 0.635570 0.635570i −0.313889 0.949460i 0.601632π-0.601632\pi
0.949460 + 0.313889i 0.101632π0.101632\pi
558558 0 0
559559 12.0000 0.507546
560560 0 0
561561 0 0
562562 0 0
563563 6.00000 6.00000i 0.252870 0.252870i −0.569276 0.822146i 0.692777π-0.692777\pi
0.822146 + 0.569276i 0.192777π0.192777\pi
564564 0 0
565565 9.00000 + 27.0000i 0.378633 + 1.13590i
566566 0 0
567567 0 0
568568 0 0
569569 2.00000i 0.0838444i −0.999121 0.0419222i 0.986652π-0.986652\pi
0.999121 0.0419222i 0.0133482π-0.0133482\pi
570570 0 0
571571 16.0000i 0.669579i 0.942293 + 0.334790i 0.108665π0.108665\pi
−0.942293 + 0.334790i 0.891335π0.891335\pi
572572 0 0
573573 0 0
574574 0 0
575575 −14.0000 2.00000i −0.583840 0.0834058i
576576 0 0
577577 15.0000 15.0000i 0.624458 0.624458i −0.322210 0.946668i 0.604426π-0.604426\pi
0.946668 + 0.322210i 0.104426π0.104426\pi
578578 0 0
579579 0 0
580580 0 0
581581 8.00000 0.331896
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 14.0000 + 14.0000i 0.577842 + 0.577842i 0.934308 0.356466i 0.116019π-0.116019\pi
−0.356466 + 0.934308i 0.616019π0.616019\pi
588588 0 0
589589 16.0000i 0.659269i
590590 0 0
591591 0 0
592592 0 0
593593 −1.00000 1.00000i −0.0410651 0.0410651i 0.686276 0.727341i 0.259244π-0.259244\pi
−0.727341 + 0.686276i 0.759244π0.759244\pi
594594 0 0
595595 40.0000 + 20.0000i 1.63984 + 0.819920i
596596 0 0
597597 0 0
598598 0 0
599599 8.00000 0.326871 0.163436 0.986554i 0.447742π-0.447742\pi
0.163436 + 0.986554i 0.447742π0.447742\pi
600600 0 0
601601 −8.00000 −0.326327 −0.163163 0.986599i 0.552170π-0.552170\pi
−0.163163 + 0.986599i 0.552170π0.552170\pi
602602 0 0
603603 0 0
604604 0 0
605605 22.0000 + 11.0000i 0.894427 + 0.447214i
606606 0 0
607607 −18.0000 18.0000i −0.730597 0.730597i 0.240141 0.970738i 0.422806π-0.422806\pi
−0.970738 + 0.240141i 0.922806π0.922806\pi
608608 0 0
609609 0 0
610610 0 0
611611 4.00000i 0.161823i
612612 0 0
613613 −9.00000 9.00000i −0.363507 0.363507i 0.501596 0.865102i 0.332747π-0.332747\pi
−0.865102 + 0.501596i 0.832747π0.832747\pi
614614 0 0
615615 0 0
616616 0 0
617617 29.0000 29.0000i 1.16750 1.16750i 0.184701 0.982795i 0.440868π-0.440868\pi
0.982795 0.184701i 0.0591318π-0.0591318\pi
618618 0 0
619619 −28.0000 −1.12542 −0.562708 0.826656i 0.690240π-0.690240\pi
−0.562708 + 0.826656i 0.690240π0.690240\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −7.00000 + 24.0000i −0.280000 + 0.960000i
626626 0 0
627627 0 0
628628 0 0
629629 10.0000i 0.398726i
630630 0 0
631631 4.00000i 0.159237i −0.996825 0.0796187i 0.974630π-0.974630\pi
0.996825 0.0796187i 0.0253703π-0.0253703\pi
632632 0 0
633633 0 0
634634 0 0
635635 10.0000 + 30.0000i 0.396838 + 1.19051i
636636 0 0
637637 1.00000 1.00000i 0.0396214 0.0396214i
638638 0 0
639639 0 0
640640 0 0
641641 48.0000 1.89589 0.947943 0.318440i 0.103159π-0.103159\pi
0.947943 + 0.318440i 0.103159π0.103159\pi
642642 0 0
643643 −10.0000 + 10.0000i −0.394362 + 0.394362i −0.876239 0.481877i 0.839955π-0.839955\pi
0.481877 + 0.876239i 0.339955π0.339955\pi
644644 0 0
645645 0 0
646646 0 0
647647 −10.0000 10.0000i −0.393141 0.393141i 0.482665 0.875805i 0.339669π-0.339669\pi
−0.875805 + 0.482665i 0.839669π0.839669\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 −1.00000 1.00000i −0.0391330 0.0391330i 0.687270 0.726403i 0.258809π-0.258809\pi
−0.726403 + 0.687270i 0.758809π0.758809\pi
654654 0 0
655655 −8.00000 + 16.0000i −0.312586 + 0.625172i
656656 0 0
657657 0 0
658658 0 0
659659 −20.0000 −0.779089 −0.389545 0.921008i 0.627368π-0.627368\pi
−0.389545 + 0.921008i 0.627368π0.627368\pi
660660 0 0
661661 12.0000 0.466746 0.233373 0.972387i 0.425024π-0.425024\pi
0.233373 + 0.972387i 0.425024π0.425024\pi
662662 0 0
663663 0 0
664664 0 0
665665 8.00000 + 24.0000i 0.310227 + 0.930680i
666666 0 0
667667 8.00000 + 8.00000i 0.309761 + 0.309761i
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 5.00000 + 5.00000i 0.192736 + 0.192736i 0.796877 0.604141i 0.206484π-0.206484\pi
−0.604141 + 0.796877i 0.706484π0.706484\pi
674674 0 0
675675 0 0
676676 0 0
677677 3.00000 3.00000i 0.115299 0.115299i −0.647103 0.762402i 0.724020π-0.724020\pi
0.762402 + 0.647103i 0.224020π0.224020\pi
678678 0 0
679679 −12.0000 −0.460518
680680 0 0
681681 0 0
682682 0 0
683683 22.0000 22.0000i 0.841807 0.841807i −0.147287 0.989094i 0.547054π-0.547054\pi
0.989094 + 0.147287i 0.0470541π0.0470541\pi
684684 0 0
685685 −3.00000 + 1.00000i −0.114624 + 0.0382080i
686686 0 0
687687 0 0
688688 0 0
689689 14.0000i 0.533358i
690690 0 0
691691 32.0000i 1.21734i 0.793424 + 0.608669i 0.208296π0.208296\pi
−0.793424 + 0.608669i 0.791704π0.791704\pi
692692 0 0
693693 0 0
694694 0 0
695695 −24.0000 12.0000i −0.910372 0.455186i
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 0 0
701701 −20.0000 −0.755390 −0.377695 0.925930i 0.623283π-0.623283\pi
−0.377695 + 0.925930i 0.623283π0.623283\pi
702702 0 0
703703 4.00000 4.00000i 0.150863 0.150863i
704704 0 0
705705 0 0
706706 0 0
707707 12.0000 + 12.0000i 0.451306 + 0.451306i
708708 0 0
709709 12.0000i 0.450669i 0.974281 + 0.225335i 0.0723476π0.0723476\pi
−0.974281 + 0.225335i 0.927652π0.927652\pi
710710 0 0
711711 0 0
712712 0 0
713713 −8.00000 8.00000i −0.299602 0.299602i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 −8.00000 −0.298350 −0.149175 0.988811i 0.547662π-0.547662\pi
−0.149175 + 0.988811i 0.547662π0.547662\pi
720720 0 0
721721 −24.0000 −0.893807
722722 0 0
723723 0 0
724724 0 0
725725 16.0000 12.0000i 0.594225 0.445669i
726726 0 0
727727 18.0000 + 18.0000i 0.667583 + 0.667583i 0.957156 0.289573i 0.0935133π-0.0935133\pi
−0.289573 + 0.957156i 0.593513π0.593513\pi
728728 0 0
729729 0 0
730730 0 0
731731 60.0000i 2.21918i
732732 0 0
733733 21.0000 + 21.0000i 0.775653 + 0.775653i 0.979088 0.203436i 0.0652108π-0.0652108\pi
−0.203436 + 0.979088i 0.565211π0.565211\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 44.0000 1.61857 0.809283 0.587419i 0.199856π-0.199856\pi
0.809283 + 0.587419i 0.199856π0.199856\pi
740740 0 0
741741 0 0
742742 0 0
743743 −30.0000 + 30.0000i −1.10059 + 1.10059i −0.106254 + 0.994339i 0.533886π0.533886\pi
−0.994339 + 0.106254i 0.966114π0.966114\pi
744744 0 0
745745 18.0000 36.0000i 0.659469 1.31894i
746746 0 0
747747 0 0
748748 0 0
749749 24.0000i 0.876941i
750750 0 0
751751 44.0000i 1.60558i −0.596260 0.802791i 0.703347π-0.703347\pi
0.596260 0.802791i 0.296653π-0.296653\pi
752752 0 0
753753 0 0
754754 0 0
755755 12.0000 24.0000i 0.436725 0.873449i
756756 0 0
757757 −1.00000 + 1.00000i −0.0363456 + 0.0363456i −0.725046 0.688700i 0.758182π-0.758182\pi
0.688700 + 0.725046i 0.258182π0.258182\pi
758758 0 0
759759 0 0
760760 0 0
761761 22.0000 0.797499 0.398750 0.917060i 0.369444π-0.369444\pi
0.398750 + 0.917060i 0.369444π0.369444\pi
762762 0 0
763763 20.0000 20.0000i 0.724049 0.724049i
764764 0 0
765765 0 0
766766 0 0
767767 4.00000 + 4.00000i 0.144432 + 0.144432i
768768 0 0
769769 40.0000i 1.44244i −0.692708 0.721218i 0.743582π-0.743582\pi
0.692708 0.721218i 0.256418π-0.256418\pi
770770 0 0
771771 0 0
772772 0 0
773773 1.00000 + 1.00000i 0.0359675 + 0.0359675i 0.724862 0.688894i 0.241904π-0.241904\pi
−0.688894 + 0.724862i 0.741904π0.741904\pi
774774 0 0
775775 −16.0000 + 12.0000i −0.574737 + 0.431053i
776776 0 0
777777 0 0
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0 0
785785 −27.0000 + 9.00000i −0.963671 + 0.321224i
786786 0 0
787787 30.0000 + 30.0000i 1.06938 + 1.06938i 0.997406 + 0.0719783i 0.0229312π0.0229312\pi
0.0719783 + 0.997406i 0.477069π0.477069\pi
788788 0 0
789789 0 0
790790 0 0
791791 36.0000i 1.28001i
792792 0 0
793793 4.00000 + 4.00000i 0.142044 + 0.142044i
794794 0 0
795795 0 0
796796 0 0
797797 29.0000 29.0000i 1.02723 1.02723i 0.0276140 0.999619i 0.491209π-0.491209\pi
0.999619 0.0276140i 0.00879094π-0.00879094\pi
798798 0 0
799799 20.0000 0.707549
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 0 0
805805 −16.0000 8.00000i −0.563926 0.281963i
806806 0 0
807807 0 0
808808 0 0
809809 24.0000i 0.843795i 0.906644 + 0.421898i 0.138636π0.138636\pi
−0.906644 + 0.421898i 0.861364π0.861364\pi
810810 0 0
811811 24.0000i 0.842754i 0.906886 + 0.421377i 0.138453π0.138453\pi
−0.906886 + 0.421377i 0.861547π0.861547\pi
812812 0 0
813813 0 0
814814 0 0
815815 6.00000 2.00000i 0.210171 0.0700569i
816816 0 0
817817 −24.0000 + 24.0000i −0.839654 + 0.839654i
818818 0 0
819819 0 0
820820 0 0
821821 28.0000 0.977207 0.488603 0.872506i 0.337507π-0.337507\pi
0.488603 + 0.872506i 0.337507π0.337507\pi
822822 0 0
823823 −30.0000 + 30.0000i −1.04573 + 1.04573i −0.0468315 + 0.998903i 0.514912π0.514912\pi
−0.998903 + 0.0468315i 0.985088π0.985088\pi
824824 0 0
825825 0 0
826826 0 0
827827 −2.00000 2.00000i −0.0695468 0.0695468i 0.671478 0.741025i 0.265660π-0.265660\pi
−0.741025 + 0.671478i 0.765660π0.765660\pi
828828 0 0
829829 6.00000i 0.208389i −0.994557 0.104194i 0.966774π-0.966774\pi
0.994557 0.104194i 0.0332264π-0.0332264\pi
830830 0 0
831831 0 0
832832 0 0
833833 5.00000 + 5.00000i 0.173240 + 0.173240i
834834 0 0
835835 2.00000 + 6.00000i 0.0692129 + 0.207639i
836836 0 0
837837 0 0
838838 0 0
839839 24.0000 0.828572 0.414286 0.910147i 0.364031π-0.364031\pi
0.414286 + 0.910147i 0.364031π0.364031\pi
840840 0 0
841841 13.0000 0.448276
842842 0 0
843843 0 0
844844 0 0
845845 11.0000 22.0000i 0.378412 0.756823i
846846 0 0
847847 22.0000 + 22.0000i 0.755929 + 0.755929i
848848 0 0
849849 0 0
850850 0 0
851851 4.00000i 0.137118i
852852 0 0
853853 15.0000 + 15.0000i 0.513590 + 0.513590i 0.915625 0.402034i 0.131697π-0.131697\pi
−0.402034 + 0.915625i 0.631697π0.631697\pi
854854 0 0
855855 0 0
856856 0 0
857857 7.00000 7.00000i 0.239115 0.239115i −0.577368 0.816484i 0.695920π-0.695920\pi
0.816484 + 0.577368i 0.195920π0.195920\pi
858858 0 0
859859 −28.0000 −0.955348 −0.477674 0.878537i 0.658520π-0.658520\pi
−0.477674 + 0.878537i 0.658520π0.658520\pi
860860 0 0
861861 0 0
862862 0 0
863863 −34.0000 + 34.0000i −1.15737 + 1.15737i −0.172335 + 0.985038i 0.555131π0.555131\pi
−0.985038 + 0.172335i 0.944869π0.944869\pi
864864 0 0
865865 −13.0000 39.0000i −0.442013 1.32604i
866866 0 0
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 20.0000i 0.677674i
872872 0 0
873873 0 0
874874 0 0
875875 −18.0000 + 26.0000i −0.608511 + 0.878960i
876876 0 0
877877 15.0000 15.0000i 0.506514 0.506514i −0.406941 0.913455i 0.633404π-0.633404\pi
0.913455 + 0.406941i 0.133404π0.133404\pi
878878 0 0
879879 0 0
880880 0 0
881881 40.0000 1.34763 0.673817 0.738898i 0.264654π-0.264654\pi
0.673817 + 0.738898i 0.264654π0.264654\pi
882882 0 0
883883 10.0000 10.0000i 0.336527 0.336527i −0.518532 0.855058i 0.673521π-0.673521\pi
0.855058 + 0.518532i 0.173521π0.173521\pi
884884 0 0
885885 0 0
886886 0 0
887887 −10.0000 10.0000i −0.335767 0.335767i 0.519004 0.854772i 0.326303π-0.326303\pi
−0.854772 + 0.519004i 0.826303π0.826303\pi
888888 0 0
889889 40.0000i 1.34156i
890890 0 0
891891 0 0
892892 0 0
893893 8.00000 + 8.00000i 0.267710 + 0.267710i
894894 0 0
895895 −24.0000 12.0000i −0.802232 0.401116i
896896 0 0
897897 0 0
898898 0 0
899899 16.0000 0.533630
900900 0 0
901901 70.0000 2.33204
902902 0 0
903903 0 0
904904 0 0
905905 −20.0000 10.0000i −0.664822 0.332411i
906906 0 0
907907 6.00000 + 6.00000i 0.199227 + 0.199227i 0.799668 0.600442i 0.205009π-0.205009\pi
−0.600442 + 0.799668i 0.705009π0.705009\pi
908908 0 0
909909 0 0
910910 0 0
911911 4.00000i 0.132526i −0.997802 0.0662630i 0.978892π-0.978892\pi
0.997802 0.0662630i 0.0211076π-0.0211076\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0 0
917917 −16.0000 + 16.0000i −0.528367 + 0.528367i
918918 0 0
919919 −24.0000 −0.791687 −0.395843 0.918318i 0.629548π-0.629548\pi
−0.395843 + 0.918318i 0.629548π0.629548\pi
920920 0 0
921921 0 0
922922 0 0
923923 12.0000 12.0000i 0.394985 0.394985i
924924 0 0
925925 7.00000 + 1.00000i 0.230159 + 0.0328798i
926926 0 0
927927 0 0
928928 0 0
929929 6.00000i 0.196854i −0.995144 0.0984268i 0.968619π-0.968619\pi
0.995144 0.0984268i 0.0313810π-0.0313810\pi
930930 0 0
931931 4.00000i 0.131095i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 27.0000 27.0000i 0.882052 0.882052i −0.111691 0.993743i 0.535627π-0.535627\pi
0.993743 + 0.111691i 0.0356268π0.0356268\pi
938938 0 0
939939 0 0
940940 0 0
941941 −46.0000 −1.49956 −0.749779 0.661689i 0.769840π-0.769840\pi
−0.749779 + 0.661689i 0.769840π0.769840\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 10.0000 + 10.0000i 0.324956 + 0.324956i 0.850665 0.525708i 0.176200π-0.176200\pi
−0.525708 + 0.850665i 0.676200π0.676200\pi
948948 0 0
949949 6.00000i 0.194768i
950950 0 0
951951 0 0
952952 0 0
953953 9.00000 + 9.00000i 0.291539 + 0.291539i 0.837688 0.546149i 0.183907π-0.183907\pi
−0.546149 + 0.837688i 0.683907π0.683907\pi
954954 0 0
955955 20.0000 40.0000i 0.647185 1.29437i
956956 0 0
957957 0 0
958958 0 0
959959 −4.00000 −0.129167
960960 0 0
961961 15.0000 0.483871
962962 0 0
963963 0 0
964964 0 0
965965 −5.00000 15.0000i −0.160956 0.482867i
966966 0 0
967967 −10.0000 10.0000i −0.321578 0.321578i 0.527794 0.849372i 0.323019π-0.323019\pi
−0.849372 + 0.527794i 0.823019π0.823019\pi
968968 0 0
969969 0 0
970970 0 0
971971 8.00000i 0.256732i 0.991727 + 0.128366i 0.0409733π0.0409733\pi
−0.991727 + 0.128366i 0.959027π0.959027\pi
972972 0 0
973973 −24.0000 24.0000i −0.769405 0.769405i
974974 0 0
975975 0 0
976976 0 0
977977 −21.0000 + 21.0000i −0.671850 + 0.671850i −0.958142 0.286293i 0.907577π-0.907577\pi
0.286293 + 0.958142i 0.407577π0.407577\pi
978978 0 0
979979 0 0
980980 0 0
981981 0 0
982982 0 0
983983 34.0000 34.0000i 1.08443 1.08443i 0.0883413 0.996090i 0.471843π-0.471843\pi
0.996090 0.0883413i 0.0281566π-0.0281566\pi
984984 0 0
985985 −15.0000 + 5.00000i −0.477940 + 0.159313i
986986 0 0
987987 0 0
988988 0 0
989989 24.0000i 0.763156i
990990 0 0
991991 4.00000i 0.127064i −0.997980 0.0635321i 0.979763π-0.979763\pi
0.997980 0.0635321i 0.0202365π-0.0202365\pi
992992 0 0
993993 0 0
994994 0 0
995995 48.0000 + 24.0000i 1.52170 + 0.760851i
996996 0 0
997997 −21.0000 + 21.0000i −0.665077 + 0.665077i −0.956572 0.291496i 0.905847π-0.905847\pi
0.291496 + 0.956572i 0.405847π0.405847\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 1440.2.x.j.703.1 2
3.2 odd 2 160.2.n.f.63.1 yes 2
4.3 odd 2 1440.2.x.i.703.1 2
5.2 odd 4 1440.2.x.i.127.1 2
12.11 even 2 160.2.n.a.63.1 2
15.2 even 4 160.2.n.a.127.1 yes 2
15.8 even 4 800.2.n.j.607.1 2
15.14 odd 2 800.2.n.a.543.1 2
20.7 even 4 inner 1440.2.x.j.127.1 2
24.5 odd 2 320.2.n.a.63.1 2
24.11 even 2 320.2.n.h.63.1 2
48.5 odd 4 1280.2.o.b.383.1 2
48.11 even 4 1280.2.o.p.383.1 2
48.29 odd 4 1280.2.o.o.383.1 2
48.35 even 4 1280.2.o.a.383.1 2
60.23 odd 4 800.2.n.a.607.1 2
60.47 odd 4 160.2.n.f.127.1 yes 2
60.59 even 2 800.2.n.j.543.1 2
120.29 odd 2 1600.2.n.n.1343.1 2
120.53 even 4 1600.2.n.a.1407.1 2
120.59 even 2 1600.2.n.a.1343.1 2
120.77 even 4 320.2.n.h.127.1 2
120.83 odd 4 1600.2.n.n.1407.1 2
120.107 odd 4 320.2.n.a.127.1 2
240.77 even 4 1280.2.o.p.127.1 2
240.107 odd 4 1280.2.o.o.127.1 2
240.197 even 4 1280.2.o.a.127.1 2
240.227 odd 4 1280.2.o.b.127.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.n.a.63.1 2 12.11 even 2
160.2.n.a.127.1 yes 2 15.2 even 4
160.2.n.f.63.1 yes 2 3.2 odd 2
160.2.n.f.127.1 yes 2 60.47 odd 4
320.2.n.a.63.1 2 24.5 odd 2
320.2.n.a.127.1 2 120.107 odd 4
320.2.n.h.63.1 2 24.11 even 2
320.2.n.h.127.1 2 120.77 even 4
800.2.n.a.543.1 2 15.14 odd 2
800.2.n.a.607.1 2 60.23 odd 4
800.2.n.j.543.1 2 60.59 even 2
800.2.n.j.607.1 2 15.8 even 4
1280.2.o.a.127.1 2 240.197 even 4
1280.2.o.a.383.1 2 48.35 even 4
1280.2.o.b.127.1 2 240.227 odd 4
1280.2.o.b.383.1 2 48.5 odd 4
1280.2.o.o.127.1 2 240.107 odd 4
1280.2.o.o.383.1 2 48.29 odd 4
1280.2.o.p.127.1 2 240.77 even 4
1280.2.o.p.383.1 2 48.11 even 4
1440.2.x.i.127.1 2 5.2 odd 4
1440.2.x.i.703.1 2 4.3 odd 2
1440.2.x.j.127.1 2 20.7 even 4 inner
1440.2.x.j.703.1 2 1.1 even 1 trivial
1600.2.n.a.1343.1 2 120.59 even 2
1600.2.n.a.1407.1 2 120.53 even 4
1600.2.n.n.1343.1 2 120.29 odd 2
1600.2.n.n.1407.1 2 120.83 odd 4