Properties

Label 3200.2.f.i.449.1
Level 32003200
Weight 22
Character 3200.449
Analytic conductor 25.55225.552
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] = [3200,2,Mod(449,3200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3200.449");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3200=2752 3200 = 2^{7} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3200.f (of order 22, degree 11, 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: 25.552128646825.5521286468
Analytic rank: 00
Dimension: 44
Coefficient field: Q(ζ8)\Q(\zeta_{8})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+1 x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 640)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 449.1
Root 0.707107+0.707107i0.707107 + 0.707107i of defining polynomial
Character χ\chi == 3200.449
Dual form 3200.2.f.i.449.2

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) == q1.41421q34.24264iq71.00000q95.65685iq112.00000q136.00000iq17+2.82843iq19+6.00000iq217.07107iq23+5.65685q274.00000iq29+2.82843q31+8.00000iq33+2.00000q37+2.82843q398.00000q411.41421q431.41421iq4711.0000q49+8.48528iq51+2.00000q534.00000iq57+2.82843iq59+14.0000iq61+4.24264iq634.24264q67+10.0000iq692.82843q716.00000iq7324.0000q77+16.9706q795.00000q81+12.7279q83+5.65685iq87+6.00000q89+8.48528iq914.00000q9310.0000iq97+5.65685iq99+O(q100)q-1.41421 q^{3} -4.24264i q^{7} -1.00000 q^{9} -5.65685i q^{11} -2.00000 q^{13} -6.00000i q^{17} +2.82843i q^{19} +6.00000i q^{21} -7.07107i q^{23} +5.65685 q^{27} -4.00000i q^{29} +2.82843 q^{31} +8.00000i q^{33} +2.00000 q^{37} +2.82843 q^{39} -8.00000 q^{41} -1.41421 q^{43} -1.41421i q^{47} -11.0000 q^{49} +8.48528i q^{51} +2.00000 q^{53} -4.00000i q^{57} +2.82843i q^{59} +14.0000i q^{61} +4.24264i q^{63} -4.24264 q^{67} +10.0000i q^{69} -2.82843 q^{71} -6.00000i q^{73} -24.0000 q^{77} +16.9706 q^{79} -5.00000 q^{81} +12.7279 q^{83} +5.65685i q^{87} +6.00000 q^{89} +8.48528i q^{91} -4.00000 q^{93} -10.0000i q^{97} +5.65685i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q98q13+8q3732q4144q49+8q5396q7720q81+24q8916q93+O(q100) 4 q - 4 q^{9} - 8 q^{13} + 8 q^{37} - 32 q^{41} - 44 q^{49} + 8 q^{53} - 96 q^{77} - 20 q^{81} + 24 q^{89} - 16 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3200Z)×\left(\mathbb{Z}/3200\mathbb{Z}\right)^\times.

nn 901901 11511151 21772177
χ(n)\chi(n) 1-1 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 −1.41421 −0.816497 −0.408248 0.912871i 0.633860π-0.633860\pi
−0.408248 + 0.912871i 0.633860π0.633860\pi
44 0 0
55 0 0
66 0 0
77 − 4.24264i − 1.60357i −0.597614 0.801784i 0.703885π-0.703885\pi
0.597614 0.801784i 0.296115π-0.296115\pi
88 0 0
99 −1.00000 −0.333333
1010 0 0
1111 − 5.65685i − 1.70561i −0.522233 0.852803i 0.674901π-0.674901\pi
0.522233 0.852803i 0.325099π-0.325099\pi
1212 0 0
1313 −2.00000 −0.554700 −0.277350 0.960769i 0.589456π-0.589456\pi
−0.277350 + 0.960769i 0.589456π0.589456\pi
1414 0 0
1515 0 0
1616 0 0
1717 − 6.00000i − 1.45521i −0.685994 0.727607i 0.740633π-0.740633\pi
0.685994 0.727607i 0.259367π-0.259367\pi
1818 0 0
1919 2.82843i 0.648886i 0.945905 + 0.324443i 0.105177π0.105177\pi
−0.945905 + 0.324443i 0.894823π0.894823\pi
2020 0 0
2121 6.00000i 1.30931i
2222 0 0
2323 − 7.07107i − 1.47442i −0.675664 0.737210i 0.736143π-0.736143\pi
0.675664 0.737210i 0.263857π-0.263857\pi
2424 0 0
2525 0 0
2626 0 0
2727 5.65685 1.08866
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 2.82843 0.508001 0.254000 0.967204i 0.418254π-0.418254\pi
0.254000 + 0.967204i 0.418254π0.418254\pi
3232 0 0
3333 8.00000i 1.39262i
3434 0 0
3535 0 0
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 2.82843 0.452911
4040 0 0
4141 −8.00000 −1.24939 −0.624695 0.780869i 0.714777π-0.714777\pi
−0.624695 + 0.780869i 0.714777π0.714777\pi
4242 0 0
4343 −1.41421 −0.215666 −0.107833 0.994169i 0.534391π-0.534391\pi
−0.107833 + 0.994169i 0.534391π0.534391\pi
4444 0 0
4545 0 0
4646 0 0
4747 − 1.41421i − 0.206284i −0.994667 0.103142i 0.967110π-0.967110\pi
0.994667 0.103142i 0.0328896π-0.0328896\pi
4848 0 0
4949 −11.0000 −1.57143
5050 0 0
5151 8.48528i 1.18818i
5252 0 0
5353 2.00000 0.274721 0.137361 0.990521i 0.456138π-0.456138\pi
0.137361 + 0.990521i 0.456138π0.456138\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 4.00000i − 0.529813i
5858 0 0
5959 2.82843i 0.368230i 0.982905 + 0.184115i 0.0589419π0.0589419\pi
−0.982905 + 0.184115i 0.941058π0.941058\pi
6060 0 0
6161 14.0000i 1.79252i 0.443533 + 0.896258i 0.353725π0.353725\pi
−0.443533 + 0.896258i 0.646275π0.646275\pi
6262 0 0
6363 4.24264i 0.534522i
6464 0 0
6565 0 0
6666 0 0
6767 −4.24264 −0.518321 −0.259161 0.965834i 0.583446π-0.583446\pi
−0.259161 + 0.965834i 0.583446π0.583446\pi
6868 0 0
6969 10.0000i 1.20386i
7070 0 0
7171 −2.82843 −0.335673 −0.167836 0.985815i 0.553678π-0.553678\pi
−0.167836 + 0.985815i 0.553678π0.553678\pi
7272 0 0
7373 − 6.00000i − 0.702247i −0.936329 0.351123i 0.885800π-0.885800\pi
0.936329 0.351123i 0.114200π-0.114200\pi
7474 0 0
7575 0 0
7676 0 0
7777 −24.0000 −2.73505
7878 0 0
7979 16.9706 1.90934 0.954669 0.297670i 0.0962096π-0.0962096\pi
0.954669 + 0.297670i 0.0962096π0.0962096\pi
8080 0 0
8181 −5.00000 −0.555556
8282 0 0
8383 12.7279 1.39707 0.698535 0.715575i 0.253835π-0.253835\pi
0.698535 + 0.715575i 0.253835π0.253835\pi
8484 0 0
8585 0 0
8686 0 0
8787 5.65685i 0.606478i
8888 0 0
8989 6.00000 0.635999 0.317999 0.948091i 0.396989π-0.396989\pi
0.317999 + 0.948091i 0.396989π0.396989\pi
9090 0 0
9191 8.48528i 0.889499i
9292 0 0
9393 −4.00000 −0.414781
9494 0 0
9595 0 0
9696 0 0
9797 − 10.0000i − 1.01535i −0.861550 0.507673i 0.830506π-0.830506\pi
0.861550 0.507673i 0.169494π-0.169494\pi
9898 0 0
9999 5.65685i 0.568535i
100100 0 0
101101 0 0 1.00000 00
−1.00000 π\pi
102102 0 0
103103 9.89949i 0.975426i 0.873004 + 0.487713i 0.162169π0.162169\pi
−0.873004 + 0.487713i 0.837831π0.837831\pi
104104 0 0
105105 0 0
106106 0 0
107107 7.07107 0.683586 0.341793 0.939775i 0.388966π-0.388966\pi
0.341793 + 0.939775i 0.388966π0.388966\pi
108108 0 0
109109 6.00000i 0.574696i 0.957826 + 0.287348i 0.0927736π0.0927736\pi
−0.957826 + 0.287348i 0.907226π0.907226\pi
110110 0 0
111111 −2.82843 −0.268462
112112 0 0
113113 − 10.0000i − 0.940721i −0.882474 0.470360i 0.844124π-0.844124\pi
0.882474 0.470360i 0.155876π-0.155876\pi
114114 0 0
115115 0 0
116116 0 0
117117 2.00000 0.184900
118118 0 0
119119 −25.4558 −2.33353
120120 0 0
121121 −21.0000 −1.90909
122122 0 0
123123 11.3137 1.02012
124124 0 0
125125 0 0
126126 0 0
127127 − 9.89949i − 0.878438i −0.898380 0.439219i 0.855255π-0.855255\pi
0.898380 0.439219i 0.144745π-0.144745\pi
128128 0 0
129129 2.00000 0.176090
130130 0 0
131131 − 11.3137i − 0.988483i −0.869325 0.494242i 0.835446π-0.835446\pi
0.869325 0.494242i 0.164554π-0.164554\pi
132132 0 0
133133 12.0000 1.04053
134134 0 0
135135 0 0
136136 0 0
137137 − 2.00000i − 0.170872i −0.996344 0.0854358i 0.972772π-0.972772\pi
0.996344 0.0854358i 0.0272282π-0.0272282\pi
138138 0 0
139139 − 8.48528i − 0.719712i −0.933008 0.359856i 0.882826π-0.882826\pi
0.933008 0.359856i 0.117174π-0.117174\pi
140140 0 0
141141 2.00000i 0.168430i
142142 0 0
143143 11.3137i 0.946100i
144144 0 0
145145 0 0
146146 0 0
147147 15.5563 1.28307
148148 0 0
149149 22.0000i 1.80231i 0.433497 + 0.901155i 0.357280π0.357280\pi
−0.433497 + 0.901155i 0.642720π0.642720\pi
150150 0 0
151151 −14.1421 −1.15087 −0.575435 0.817847i 0.695167π-0.695167\pi
−0.575435 + 0.817847i 0.695167π0.695167\pi
152152 0 0
153153 6.00000i 0.485071i
154154 0 0
155155 0 0
156156 0 0
157157 −18.0000 −1.43656 −0.718278 0.695756i 0.755069π-0.755069\pi
−0.718278 + 0.695756i 0.755069π0.755069\pi
158158 0 0
159159 −2.82843 −0.224309
160160 0 0
161161 −30.0000 −2.36433
162162 0 0
163163 −18.3848 −1.44001 −0.720003 0.693971i 0.755860π-0.755860\pi
−0.720003 + 0.693971i 0.755860π0.755860\pi
164164 0 0
165165 0 0
166166 0 0
167167 9.89949i 0.766046i 0.923739 + 0.383023i 0.125117π0.125117\pi
−0.923739 + 0.383023i 0.874883π0.874883\pi
168168 0 0
169169 −9.00000 −0.692308
170170 0 0
171171 − 2.82843i − 0.216295i
172172 0 0
173173 18.0000 1.36851 0.684257 0.729241i 0.260127π-0.260127\pi
0.684257 + 0.729241i 0.260127π0.260127\pi
174174 0 0
175175 0 0
176176 0 0
177177 − 4.00000i − 0.300658i
178178 0 0
179179 − 19.7990i − 1.47985i −0.672692 0.739923i 0.734862π-0.734862\pi
0.672692 0.739923i 0.265138π-0.265138\pi
180180 0 0
181181 16.0000i 1.18927i 0.803996 + 0.594635i 0.202704π0.202704\pi
−0.803996 + 0.594635i 0.797296π0.797296\pi
182182 0 0
183183 − 19.7990i − 1.46358i
184184 0 0
185185 0 0
186186 0 0
187187 −33.9411 −2.48202
188188 0 0
189189 − 24.0000i − 1.74574i
190190 0 0
191191 −2.82843 −0.204658 −0.102329 0.994751i 0.532629π-0.532629\pi
−0.102329 + 0.994751i 0.532629π0.532629\pi
192192 0 0
193193 6.00000i 0.431889i 0.976406 + 0.215945i 0.0692831π0.0692831\pi
−0.976406 + 0.215945i 0.930717π0.930717\pi
194194 0 0
195195 0 0
196196 0 0
197197 −6.00000 −0.427482 −0.213741 0.976890i 0.568565π-0.568565\pi
−0.213741 + 0.976890i 0.568565π0.568565\pi
198198 0 0
199199 11.3137 0.802008 0.401004 0.916076i 0.368661π-0.368661\pi
0.401004 + 0.916076i 0.368661π0.368661\pi
200200 0 0
201201 6.00000 0.423207
202202 0 0
203203 −16.9706 −1.19110
204204 0 0
205205 0 0
206206 0 0
207207 7.07107i 0.491473i
208208 0 0
209209 16.0000 1.10674
210210 0 0
211211 − 16.9706i − 1.16830i −0.811645 0.584151i 0.801428π-0.801428\pi
0.811645 0.584151i 0.198572π-0.198572\pi
212212 0 0
213213 4.00000 0.274075
214214 0 0
215215 0 0
216216 0 0
217217 − 12.0000i − 0.814613i
218218 0 0
219219 8.48528i 0.573382i
220220 0 0
221221 12.0000i 0.807207i
222222 0 0
223223 − 15.5563i − 1.04173i −0.853639 0.520865i 0.825609π-0.825609\pi
0.853639 0.520865i 0.174391π-0.174391\pi
224224 0 0
225225 0 0
226226 0 0
227227 −7.07107 −0.469323 −0.234662 0.972077i 0.575398π-0.575398\pi
−0.234662 + 0.972077i 0.575398π0.575398\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 33.9411 2.23316
232232 0 0
233233 6.00000i 0.393073i 0.980497 + 0.196537i 0.0629694π0.0629694\pi
−0.980497 + 0.196537i 0.937031π0.937031\pi
234234 0 0
235235 0 0
236236 0 0
237237 −24.0000 −1.55897
238238 0 0
239239 −11.3137 −0.731823 −0.365911 0.930650i 0.619243π-0.619243\pi
−0.365911 + 0.930650i 0.619243π0.619243\pi
240240 0 0
241241 8.00000 0.515325 0.257663 0.966235i 0.417048π-0.417048\pi
0.257663 + 0.966235i 0.417048π0.417048\pi
242242 0 0
243243 −9.89949 −0.635053
244244 0 0
245245 0 0
246246 0 0
247247 − 5.65685i − 0.359937i
248248 0 0
249249 −18.0000 −1.14070
250250 0 0
251251 22.6274i 1.42823i 0.700028 + 0.714115i 0.253171π0.253171\pi
−0.700028 + 0.714115i 0.746829π0.746829\pi
252252 0 0
253253 −40.0000 −2.51478
254254 0 0
255255 0 0
256256 0 0
257257 18.0000i 1.12281i 0.827541 + 0.561405i 0.189739π0.189739\pi
−0.827541 + 0.561405i 0.810261π0.810261\pi
258258 0 0
259259 − 8.48528i − 0.527250i
260260 0 0
261261 4.00000i 0.247594i
262262 0 0
263263 7.07107i 0.436021i 0.975946 + 0.218010i 0.0699567π0.0699567\pi
−0.975946 + 0.218010i 0.930043π0.930043\pi
264264 0 0
265265 0 0
266266 0 0
267267 −8.48528 −0.519291
268268 0 0
269269 − 6.00000i − 0.365826i −0.983129 0.182913i 0.941447π-0.941447\pi
0.983129 0.182913i 0.0585527π-0.0585527\pi
270270 0 0
271271 25.4558 1.54633 0.773166 0.634203i 0.218672π-0.218672\pi
0.773166 + 0.634203i 0.218672π0.218672\pi
272272 0 0
273273 − 12.0000i − 0.726273i
274274 0 0
275275 0 0
276276 0 0
277277 30.0000 1.80253 0.901263 0.433273i 0.142641π-0.142641\pi
0.901263 + 0.433273i 0.142641π0.142641\pi
278278 0 0
279279 −2.82843 −0.169334
280280 0 0
281281 8.00000 0.477240 0.238620 0.971113i 0.423305π-0.423305\pi
0.238620 + 0.971113i 0.423305π0.423305\pi
282282 0 0
283283 −9.89949 −0.588464 −0.294232 0.955734i 0.595064π-0.595064\pi
−0.294232 + 0.955734i 0.595064π0.595064\pi
284284 0 0
285285 0 0
286286 0 0
287287 33.9411i 2.00348i
288288 0 0
289289 −19.0000 −1.11765
290290 0 0
291291 14.1421i 0.829027i
292292 0 0
293293 6.00000 0.350524 0.175262 0.984522i 0.443923π-0.443923\pi
0.175262 + 0.984522i 0.443923π0.443923\pi
294294 0 0
295295 0 0
296296 0 0
297297 − 32.0000i − 1.85683i
298298 0 0
299299 14.1421i 0.817861i
300300 0 0
301301 6.00000i 0.345834i
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 0 0
307307 −15.5563 −0.887848 −0.443924 0.896065i 0.646414π-0.646414\pi
−0.443924 + 0.896065i 0.646414π0.646414\pi
308308 0 0
309309 − 14.0000i − 0.796432i
310310 0 0
311311 −2.82843 −0.160385 −0.0801927 0.996779i 0.525554π-0.525554\pi
−0.0801927 + 0.996779i 0.525554π0.525554\pi
312312 0 0
313313 6.00000i 0.339140i 0.985518 + 0.169570i 0.0542379π0.0542379\pi
−0.985518 + 0.169570i 0.945762π0.945762\pi
314314 0 0
315315 0 0
316316 0 0
317317 −2.00000 −0.112331 −0.0561656 0.998421i 0.517887π-0.517887\pi
−0.0561656 + 0.998421i 0.517887π0.517887\pi
318318 0 0
319319 −22.6274 −1.26689
320320 0 0
321321 −10.0000 −0.558146
322322 0 0
323323 16.9706 0.944267
324324 0 0
325325 0 0
326326 0 0
327327 − 8.48528i − 0.469237i
328328 0 0
329329 −6.00000 −0.330791
330330 0 0
331331 − 22.6274i − 1.24372i −0.783130 0.621858i 0.786378π-0.786378\pi
0.783130 0.621858i 0.213622π-0.213622\pi
332332 0 0
333333 −2.00000 −0.109599
334334 0 0
335335 0 0
336336 0 0
337337 − 18.0000i − 0.980522i −0.871576 0.490261i 0.836901π-0.836901\pi
0.871576 0.490261i 0.163099π-0.163099\pi
338338 0 0
339339 14.1421i 0.768095i
340340 0 0
341341 − 16.0000i − 0.866449i
342342 0 0
343343 16.9706i 0.916324i
344344 0 0
345345 0 0
346346 0 0
347347 4.24264 0.227757 0.113878 0.993495i 0.463673π-0.463673\pi
0.113878 + 0.993495i 0.463673π0.463673\pi
348348 0 0
349349 − 12.0000i − 0.642345i −0.947021 0.321173i 0.895923π-0.895923\pi
0.947021 0.321173i 0.104077π-0.104077\pi
350350 0 0
351351 −11.3137 −0.603881
352352 0 0
353353 10.0000i 0.532246i 0.963939 + 0.266123i 0.0857428π0.0857428\pi
−0.963939 + 0.266123i 0.914257π0.914257\pi
354354 0 0
355355 0 0
356356 0 0
357357 36.0000 1.90532
358358 0 0
359359 28.2843 1.49279 0.746393 0.665505i 0.231784π-0.231784\pi
0.746393 + 0.665505i 0.231784π0.231784\pi
360360 0 0
361361 11.0000 0.578947
362362 0 0
363363 29.6985 1.55877
364364 0 0
365365 0 0
366366 0 0
367367 − 4.24264i − 0.221464i −0.993850 0.110732i 0.964680π-0.964680\pi
0.993850 0.110732i 0.0353195π-0.0353195\pi
368368 0 0
369369 8.00000 0.416463
370370 0 0
371371 − 8.48528i − 0.440534i
372372 0 0
373373 −14.0000 −0.724893 −0.362446 0.932005i 0.618058π-0.618058\pi
−0.362446 + 0.932005i 0.618058π0.618058\pi
374374 0 0
375375 0 0
376376 0 0
377377 8.00000i 0.412021i
378378 0 0
379379 − 31.1127i − 1.59815i −0.601230 0.799076i 0.705322π-0.705322\pi
0.601230 0.799076i 0.294678π-0.294678\pi
380380 0 0
381381 14.0000i 0.717242i
382382 0 0
383383 7.07107i 0.361315i 0.983546 + 0.180657i 0.0578225π0.0578225\pi
−0.983546 + 0.180657i 0.942177π0.942177\pi
384384 0 0
385385 0 0
386386 0 0
387387 1.41421 0.0718885
388388 0 0
389389 14.0000i 0.709828i 0.934899 + 0.354914i 0.115490π0.115490\pi
−0.934899 + 0.354914i 0.884510π0.884510\pi
390390 0 0
391391 −42.4264 −2.14560
392392 0 0
393393 16.0000i 0.807093i
394394 0 0
395395 0 0
396396 0 0
397397 −14.0000 −0.702640 −0.351320 0.936255i 0.614267π-0.614267\pi
−0.351320 + 0.936255i 0.614267π0.614267\pi
398398 0 0
399399 −16.9706 −0.849591
400400 0 0
401401 18.0000 0.898877 0.449439 0.893311i 0.351624π-0.351624\pi
0.449439 + 0.893311i 0.351624π0.351624\pi
402402 0 0
403403 −5.65685 −0.281788
404404 0 0
405405 0 0
406406 0 0
407407 − 11.3137i − 0.560800i
408408 0 0
409409 −4.00000 −0.197787 −0.0988936 0.995098i 0.531530π-0.531530\pi
−0.0988936 + 0.995098i 0.531530π0.531530\pi
410410 0 0
411411 2.82843i 0.139516i
412412 0 0
413413 12.0000 0.590481
414414 0 0
415415 0 0
416416 0 0
417417 12.0000i 0.587643i
418418 0 0
419419 8.48528i 0.414533i 0.978285 + 0.207267i 0.0664567π0.0664567\pi
−0.978285 + 0.207267i 0.933543π0.933543\pi
420420 0 0
421421 10.0000i 0.487370i 0.969854 + 0.243685i 0.0783563π0.0783563\pi
−0.969854 + 0.243685i 0.921644π0.921644\pi
422422 0 0
423423 1.41421i 0.0687614i
424424 0 0
425425 0 0
426426 0 0
427427 59.3970 2.87442
428428 0 0
429429 − 16.0000i − 0.772487i
430430 0 0
431431 −31.1127 −1.49865 −0.749323 0.662205i 0.769621π-0.769621\pi
−0.749323 + 0.662205i 0.769621π0.769621\pi
432432 0 0
433433 − 14.0000i − 0.672797i −0.941720 0.336399i 0.890791π-0.890791\pi
0.941720 0.336399i 0.109209π-0.109209\pi
434434 0 0
435435 0 0
436436 0 0
437437 20.0000 0.956730
438438 0 0
439439 16.9706 0.809961 0.404980 0.914325i 0.367278π-0.367278\pi
0.404980 + 0.914325i 0.367278π0.367278\pi
440440 0 0
441441 11.0000 0.523810
442442 0 0
443443 −15.5563 −0.739104 −0.369552 0.929210i 0.620489π-0.620489\pi
−0.369552 + 0.929210i 0.620489π0.620489\pi
444444 0 0
445445 0 0
446446 0 0
447447 − 31.1127i − 1.47158i
448448 0 0
449449 20.0000 0.943858 0.471929 0.881636i 0.343558π-0.343558\pi
0.471929 + 0.881636i 0.343558π0.343558\pi
450450 0 0
451451 45.2548i 2.13097i
452452 0 0
453453 20.0000 0.939682
454454 0 0
455455 0 0
456456 0 0
457457 34.0000i 1.59045i 0.606313 + 0.795226i 0.292648π0.292648\pi
−0.606313 + 0.795226i 0.707352π0.707352\pi
458458 0 0
459459 − 33.9411i − 1.58424i
460460 0 0
461461 − 24.0000i − 1.11779i −0.829238 0.558896i 0.811225π-0.811225\pi
0.829238 0.558896i 0.188775π-0.188775\pi
462462 0 0
463463 − 7.07107i − 0.328620i −0.986409 0.164310i 0.947460π-0.947460\pi
0.986409 0.164310i 0.0525398π-0.0525398\pi
464464 0 0
465465 0 0
466466 0 0
467467 9.89949 0.458094 0.229047 0.973415i 0.426439π-0.426439\pi
0.229047 + 0.973415i 0.426439π0.426439\pi
468468 0 0
469469 18.0000i 0.831163i
470470 0 0
471471 25.4558 1.17294
472472 0 0
473473 8.00000i 0.367840i
474474 0 0
475475 0 0
476476 0 0
477477 −2.00000 −0.0915737
478478 0 0
479479 33.9411 1.55081 0.775405 0.631464i 0.217546π-0.217546\pi
0.775405 + 0.631464i 0.217546π0.217546\pi
480480 0 0
481481 −4.00000 −0.182384
482482 0 0
483483 42.4264 1.93047
484484 0 0
485485 0 0
486486 0 0
487487 12.7279i 0.576757i 0.957516 + 0.288379i 0.0931162π0.0931162\pi
−0.957516 + 0.288379i 0.906884π0.906884\pi
488488 0 0
489489 26.0000 1.17576
490490 0 0
491491 − 16.9706i − 0.765871i −0.923775 0.382935i 0.874913π-0.874913\pi
0.923775 0.382935i 0.125087π-0.125087\pi
492492 0 0
493493 −24.0000 −1.08091
494494 0 0
495495 0 0
496496 0 0
497497 12.0000i 0.538274i
498498 0 0
499499 25.4558i 1.13956i 0.821797 + 0.569780i 0.192972π0.192972\pi
−0.821797 + 0.569780i 0.807028π0.807028\pi
500500 0 0
501501 − 14.0000i − 0.625474i
502502 0 0
503503 32.5269i 1.45030i 0.688589 + 0.725152i 0.258230π0.258230\pi
−0.688589 + 0.725152i 0.741770π0.741770\pi
504504 0 0
505505 0 0
506506 0 0
507507 12.7279 0.565267
508508 0 0
509509 − 20.0000i − 0.886484i −0.896402 0.443242i 0.853828π-0.853828\pi
0.896402 0.443242i 0.146172π-0.146172\pi
510510 0 0
511511 −25.4558 −1.12610
512512 0 0
513513 16.0000i 0.706417i
514514 0 0
515515 0 0
516516 0 0
517517 −8.00000 −0.351840
518518 0 0
519519 −25.4558 −1.11739
520520 0 0
521521 18.0000 0.788594 0.394297 0.918983i 0.370988π-0.370988\pi
0.394297 + 0.918983i 0.370988π0.370988\pi
522522 0 0
523523 12.7279 0.556553 0.278277 0.960501i 0.410237π-0.410237\pi
0.278277 + 0.960501i 0.410237π0.410237\pi
524524 0 0
525525 0 0
526526 0 0
527527 − 16.9706i − 0.739249i
528528 0 0
529529 −27.0000 −1.17391
530530 0 0
531531 − 2.82843i − 0.122743i
532532 0 0
533533 16.0000 0.693037
534534 0 0
535535 0 0
536536 0 0
537537 28.0000i 1.20829i
538538 0 0
539539 62.2254i 2.68024i
540540 0 0
541541 − 40.0000i − 1.71973i −0.510518 0.859867i 0.670546π-0.670546\pi
0.510518 0.859867i 0.329454π-0.329454\pi
542542 0 0
543543 − 22.6274i − 0.971035i
544544 0 0
545545 0 0
546546 0 0
547547 4.24264 0.181402 0.0907011 0.995878i 0.471089π-0.471089\pi
0.0907011 + 0.995878i 0.471089π0.471089\pi
548548 0 0
549549 − 14.0000i − 0.597505i
550550 0 0
551551 11.3137 0.481980
552552 0 0
553553 − 72.0000i − 3.06175i
554554 0 0
555555 0 0
556556 0 0
557557 18.0000 0.762684 0.381342 0.924434i 0.375462π-0.375462\pi
0.381342 + 0.924434i 0.375462π0.375462\pi
558558 0 0
559559 2.82843 0.119630
560560 0 0
561561 48.0000 2.02656
562562 0 0
563563 −35.3553 −1.49005 −0.745025 0.667037i 0.767562π-0.767562\pi
−0.745025 + 0.667037i 0.767562π0.767562\pi
564564 0 0
565565 0 0
566566 0 0
567567 21.2132i 0.890871i
568568 0 0
569569 28.0000 1.17382 0.586911 0.809652i 0.300344π-0.300344\pi
0.586911 + 0.809652i 0.300344π0.300344\pi
570570 0 0
571571 − 22.6274i − 0.946928i −0.880813 0.473464i 0.843003π-0.843003\pi
0.880813 0.473464i 0.156997π-0.156997\pi
572572 0 0
573573 4.00000 0.167102
574574 0 0
575575 0 0
576576 0 0
577577 10.0000i 0.416305i 0.978096 + 0.208153i 0.0667451π0.0667451\pi
−0.978096 + 0.208153i 0.933255π0.933255\pi
578578 0 0
579579 − 8.48528i − 0.352636i
580580 0 0
581581 − 54.0000i − 2.24030i
582582 0 0
583583 − 11.3137i − 0.468566i
584584 0 0
585585 0 0
586586 0 0
587587 −12.7279 −0.525338 −0.262669 0.964886i 0.584603π-0.584603\pi
−0.262669 + 0.964886i 0.584603π0.584603\pi
588588 0 0
589589 8.00000i 0.329634i
590590 0 0
591591 8.48528 0.349038
592592 0 0
593593 − 30.0000i − 1.23195i −0.787765 0.615976i 0.788762π-0.788762\pi
0.787765 0.615976i 0.211238π-0.211238\pi
594594 0 0
595595 0 0
596596 0 0
597597 −16.0000 −0.654836
598598 0 0
599599 39.5980 1.61793 0.808965 0.587857i 0.200028π-0.200028\pi
0.808965 + 0.587857i 0.200028π0.200028\pi
600600 0 0
601601 −32.0000 −1.30531 −0.652654 0.757656i 0.726344π-0.726344\pi
−0.652654 + 0.757656i 0.726344π0.726344\pi
602602 0 0
603603 4.24264 0.172774
604604 0 0
605605 0 0
606606 0 0
607607 9.89949i 0.401808i 0.979611 + 0.200904i 0.0643879π0.0643879\pi
−0.979611 + 0.200904i 0.935612π0.935612\pi
608608 0 0
609609 24.0000 0.972529
610610 0 0
611611 2.82843i 0.114426i
612612 0 0
613613 −26.0000 −1.05013 −0.525065 0.851062i 0.675959π-0.675959\pi
−0.525065 + 0.851062i 0.675959π0.675959\pi
614614 0 0
615615 0 0
616616 0 0
617617 2.00000i 0.0805170i 0.999189 + 0.0402585i 0.0128181π0.0128181\pi
−0.999189 + 0.0402585i 0.987182π0.987182\pi
618618 0 0
619619 19.7990i 0.795789i 0.917431 + 0.397894i 0.130259π0.130259\pi
−0.917431 + 0.397894i 0.869741π0.869741\pi
620620 0 0
621621 − 40.0000i − 1.60514i
622622 0 0
623623 − 25.4558i − 1.01987i
624624 0 0
625625 0 0
626626 0 0
627627 −22.6274 −0.903652
628628 0 0
629629 − 12.0000i − 0.478471i
630630 0 0
631631 36.7696 1.46377 0.731886 0.681427i 0.238640π-0.238640\pi
0.731886 + 0.681427i 0.238640π0.238640\pi
632632 0 0
633633 24.0000i 0.953914i
634634 0 0
635635 0 0
636636 0 0
637637 22.0000 0.871672
638638 0 0
639639 2.82843 0.111891
640640 0 0
641641 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
642642 0 0
643643 7.07107 0.278856 0.139428 0.990232i 0.455474π-0.455474\pi
0.139428 + 0.990232i 0.455474π0.455474\pi
644644 0 0
645645 0 0
646646 0 0
647647 − 32.5269i − 1.27876i −0.768889 0.639382i 0.779190π-0.779190\pi
0.768889 0.639382i 0.220810π-0.220810\pi
648648 0 0
649649 16.0000 0.628055
650650 0 0
651651 16.9706i 0.665129i
652652 0 0
653653 18.0000 0.704394 0.352197 0.935926i 0.385435π-0.385435\pi
0.352197 + 0.935926i 0.385435π0.385435\pi
654654 0 0
655655 0 0
656656 0 0
657657 6.00000i 0.234082i
658658 0 0
659659 − 25.4558i − 0.991619i −0.868431 0.495809i 0.834871π-0.834871\pi
0.868431 0.495809i 0.165129π-0.165129\pi
660660 0 0
661661 − 10.0000i − 0.388955i −0.980907 0.194477i 0.937699π-0.937699\pi
0.980907 0.194477i 0.0623011π-0.0623011\pi
662662 0 0
663663 − 16.9706i − 0.659082i
664664 0 0
665665 0 0
666666 0 0
667667 −28.2843 −1.09517
668668 0 0
669669 22.0000i 0.850569i
670670 0 0
671671 79.1960 3.05733
672672 0 0
673673 50.0000i 1.92736i 0.267063 + 0.963679i 0.413947π0.413947\pi
−0.267063 + 0.963679i 0.586053π0.586053\pi
674674 0 0
675675 0 0
676676 0 0
677677 10.0000 0.384331 0.192166 0.981363i 0.438449π-0.438449\pi
0.192166 + 0.981363i 0.438449π0.438449\pi
678678 0 0
679679 −42.4264 −1.62818
680680 0 0
681681 10.0000 0.383201
682682 0 0
683683 −35.3553 −1.35283 −0.676417 0.736519i 0.736468π-0.736468\pi
−0.676417 + 0.736519i 0.736468π0.736468\pi
684684 0 0
685685 0 0
686686 0 0
687687 − 28.2843i − 1.07911i
688688 0 0
689689 −4.00000 −0.152388
690690 0 0
691691 − 22.6274i − 0.860788i −0.902641 0.430394i 0.858375π-0.858375\pi
0.902641 0.430394i 0.141625π-0.141625\pi
692692 0 0
693693 24.0000 0.911685
694694 0 0
695695 0 0
696696 0 0
697697 48.0000i 1.81813i
698698 0 0
699699 − 8.48528i − 0.320943i
700700 0 0
701701 18.0000i 0.679851i 0.940452 + 0.339925i 0.110402π0.110402\pi
−0.940452 + 0.339925i 0.889598π0.889598\pi
702702 0 0
703703 5.65685i 0.213352i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 28.0000i 1.05156i 0.850620 + 0.525781i 0.176227π0.176227\pi
−0.850620 + 0.525781i 0.823773π0.823773\pi
710710 0 0
711711 −16.9706 −0.636446
712712 0 0
713713 − 20.0000i − 0.749006i
714714 0 0
715715 0 0
716716 0 0
717717 16.0000 0.597531
718718 0 0
719719 −11.3137 −0.421930 −0.210965 0.977494i 0.567661π-0.567661\pi
−0.210965 + 0.977494i 0.567661π0.567661\pi
720720 0 0
721721 42.0000 1.56416
722722 0 0
723723 −11.3137 −0.420761
724724 0 0
725725 0 0
726726 0 0
727727 − 4.24264i − 0.157351i −0.996900 0.0786754i 0.974931π-0.974931\pi
0.996900 0.0786754i 0.0250691π-0.0250691\pi
728728 0 0
729729 29.0000 1.07407
730730 0 0
731731 8.48528i 0.313839i
732732 0 0
733733 34.0000 1.25582 0.627909 0.778287i 0.283911π-0.283911\pi
0.627909 + 0.778287i 0.283911π0.283911\pi
734734 0 0
735735 0 0
736736 0 0
737737 24.0000i 0.884051i
738738 0 0
739739 25.4558i 0.936408i 0.883620 + 0.468204i 0.155099π0.155099\pi
−0.883620 + 0.468204i 0.844901π0.844901\pi
740740 0 0
741741 8.00000i 0.293887i
742742 0 0
743743 − 32.5269i − 1.19330i −0.802503 0.596648i 0.796499π-0.796499\pi
0.802503 0.596648i 0.203501π-0.203501\pi
744744 0 0
745745 0 0
746746 0 0
747747 −12.7279 −0.465690
748748 0 0
749749 − 30.0000i − 1.09618i
750750 0 0
751751 −8.48528 −0.309632 −0.154816 0.987943i 0.549479π-0.549479\pi
−0.154816 + 0.987943i 0.549479π0.549479\pi
752752 0 0
753753 − 32.0000i − 1.16614i
754754 0 0
755755 0 0
756756 0 0
757757 46.0000 1.67190 0.835949 0.548807i 0.184918π-0.184918\pi
0.835949 + 0.548807i 0.184918π0.184918\pi
758758 0 0
759759 56.5685 2.05331
760760 0 0
761761 14.0000 0.507500 0.253750 0.967270i 0.418336π-0.418336\pi
0.253750 + 0.967270i 0.418336π0.418336\pi
762762 0 0
763763 25.4558 0.921563
764764 0 0
765765 0 0
766766 0 0
767767 − 5.65685i − 0.204257i
768768 0 0
769769 −14.0000 −0.504853 −0.252426 0.967616i 0.581229π-0.581229\pi
−0.252426 + 0.967616i 0.581229π0.581229\pi
770770 0 0
771771 − 25.4558i − 0.916770i
772772 0 0
773773 −26.0000 −0.935155 −0.467578 0.883952i 0.654873π-0.654873\pi
−0.467578 + 0.883952i 0.654873π0.654873\pi
774774 0 0
775775 0 0
776776 0 0
777777 12.0000i 0.430498i
778778 0 0
779779 − 22.6274i − 0.810711i
780780 0 0
781781 16.0000i 0.572525i
782782 0 0
783783 − 22.6274i − 0.808638i
784784 0 0
785785 0 0
786786 0 0
787787 46.6690 1.66357 0.831786 0.555097i 0.187319π-0.187319\pi
0.831786 + 0.555097i 0.187319π0.187319\pi
788788 0 0
789789 − 10.0000i − 0.356009i
790790 0 0
791791 −42.4264 −1.50851
792792 0 0
793793 − 28.0000i − 0.994309i
794794 0 0
795795 0 0
796796 0 0
797797 −10.0000 −0.354218 −0.177109 0.984191i 0.556675π-0.556675\pi
−0.177109 + 0.984191i 0.556675π0.556675\pi
798798 0 0
799799 −8.48528 −0.300188
800800 0 0
801801 −6.00000 −0.212000
802802 0 0
803803 −33.9411 −1.19776
804804 0 0
805805 0 0
806806 0 0
807807 8.48528i 0.298696i
808808 0 0
809809 −10.0000 −0.351581 −0.175791 0.984428i 0.556248π-0.556248\pi
−0.175791 + 0.984428i 0.556248π0.556248\pi
810810 0 0
811811 0 0 1.00000 00
−1.00000 π\pi
812812 0 0
813813 −36.0000 −1.26258
814814 0 0
815815 0 0
816816 0 0
817817 − 4.00000i − 0.139942i
818818 0 0
819819 − 8.48528i − 0.296500i
820820 0 0
821821 − 26.0000i − 0.907406i −0.891153 0.453703i 0.850103π-0.850103\pi
0.891153 0.453703i 0.149897π-0.149897\pi
822822 0 0
823823 26.8701i 0.936631i 0.883561 + 0.468316i 0.155139π0.155139\pi
−0.883561 + 0.468316i 0.844861π0.844861\pi
824824 0 0
825825 0 0
826826 0 0
827827 −7.07107 −0.245885 −0.122943 0.992414i 0.539233π-0.539233\pi
−0.122943 + 0.992414i 0.539233π0.539233\pi
828828 0 0
829829 26.0000i 0.903017i 0.892267 + 0.451509i 0.149114π0.149114\pi
−0.892267 + 0.451509i 0.850886π0.850886\pi
830830 0 0
831831 −42.4264 −1.47176
832832 0 0
833833 66.0000i 2.28676i
834834 0 0
835835 0 0
836836 0 0
837837 16.0000 0.553041
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 13.0000 0.448276
842842 0 0
843843 −11.3137 −0.389665
844844 0 0
845845 0 0
846846 0 0
847847 89.0955i 3.06136i
848848 0 0
849849 14.0000 0.480479
850850 0 0
851851 − 14.1421i − 0.484786i
852852 0 0
853853 −26.0000 −0.890223 −0.445112 0.895475i 0.646836π-0.646836\pi
−0.445112 + 0.895475i 0.646836π0.646836\pi
854854 0 0
855855 0 0
856856 0 0
857857 − 18.0000i − 0.614868i −0.951569 0.307434i 0.900530π-0.900530\pi
0.951569 0.307434i 0.0994704π-0.0994704\pi
858858 0 0
859859 2.82843i 0.0965047i 0.998835 + 0.0482523i 0.0153652π0.0153652\pi
−0.998835 + 0.0482523i 0.984635π0.984635\pi
860860 0 0
861861 − 48.0000i − 1.63584i
862862 0 0
863863 55.1543i 1.87748i 0.344633 + 0.938738i 0.388003π0.388003\pi
−0.344633 + 0.938738i 0.611997π0.611997\pi
864864 0 0
865865 0 0
866866 0 0
867867 26.8701 0.912555
868868 0 0
869869 − 96.0000i − 3.25658i
870870 0 0
871871 8.48528 0.287513
872872 0 0
873873 10.0000i 0.338449i
874874 0 0
875875 0 0
876876 0 0
877877 38.0000 1.28317 0.641584 0.767052i 0.278277π-0.278277\pi
0.641584 + 0.767052i 0.278277π0.278277\pi
878878 0 0
879879 −8.48528 −0.286201
880880 0 0
881881 48.0000 1.61716 0.808581 0.588386i 0.200236π-0.200236\pi
0.808581 + 0.588386i 0.200236π0.200236\pi
882882 0 0
883883 21.2132 0.713881 0.356941 0.934127i 0.383820π-0.383820\pi
0.356941 + 0.934127i 0.383820π0.383820\pi
884884 0 0
885885 0 0
886886 0 0
887887 − 26.8701i − 0.902208i −0.892471 0.451104i 0.851030π-0.851030\pi
0.892471 0.451104i 0.148970π-0.148970\pi
888888 0 0
889889 −42.0000 −1.40863
890890 0 0
891891 28.2843i 0.947559i
892892 0 0
893893 4.00000 0.133855
894894 0 0
895895 0 0
896896 0 0
897897 − 20.0000i − 0.667781i
898898 0 0
899899 − 11.3137i − 0.377333i
900900 0 0
901901 − 12.0000i − 0.399778i
902902 0 0
903903 − 8.48528i − 0.282372i
904904 0 0
905905 0 0
906906 0 0
907907 1.41421 0.0469582 0.0234791 0.999724i 0.492526π-0.492526\pi
0.0234791 + 0.999724i 0.492526π0.492526\pi
908908 0 0
909909 0 0
910910 0 0
911911 −31.1127 −1.03081 −0.515405 0.856947i 0.672358π-0.672358\pi
−0.515405 + 0.856947i 0.672358π0.672358\pi
912912 0 0
913913 − 72.0000i − 2.38285i
914914 0 0
915915 0 0
916916 0 0
917917 −48.0000 −1.58510
918918 0 0
919919 −39.5980 −1.30622 −0.653108 0.757264i 0.726535π-0.726535\pi
−0.653108 + 0.757264i 0.726535π0.726535\pi
920920 0 0
921921 22.0000 0.724925
922922 0 0
923923 5.65685 0.186198
924924 0 0
925925 0 0
926926 0 0
927927 − 9.89949i − 0.325142i
928928 0 0
929929 28.0000 0.918650 0.459325 0.888268i 0.348091π-0.348091\pi
0.459325 + 0.888268i 0.348091π0.348091\pi
930930 0 0
931931 − 31.1127i − 1.01968i
932932 0 0
933933 4.00000 0.130954
934934 0 0
935935 0 0
936936 0 0
937937 2.00000i 0.0653372i 0.999466 + 0.0326686i 0.0104006π0.0104006\pi
−0.999466 + 0.0326686i 0.989599π0.989599\pi
938938 0 0
939939 − 8.48528i − 0.276907i
940940 0 0
941941 48.0000i 1.56476i 0.622804 + 0.782378i 0.285993π0.285993\pi
−0.622804 + 0.782378i 0.714007π0.714007\pi
942942 0 0
943943 56.5685i 1.84213i
944944 0 0
945945 0 0
946946 0 0
947947 −15.5563 −0.505513 −0.252757 0.967530i 0.581337π-0.581337\pi
−0.252757 + 0.967530i 0.581337π0.581337\pi
948948 0 0
949949 12.0000i 0.389536i
950950 0 0
951951 2.82843 0.0917180
952952 0 0
953953 54.0000i 1.74923i 0.484817 + 0.874616i 0.338886π0.338886\pi
−0.484817 + 0.874616i 0.661114π0.661114\pi
954954 0 0
955955 0 0
956956 0 0
957957 32.0000 1.03441
958958 0 0
959959 −8.48528 −0.274004
960960 0 0
961961 −23.0000 −0.741935
962962 0 0
963963 −7.07107 −0.227862
964964 0 0
965965 0 0
966966 0 0
967967 4.24264i 0.136434i 0.997671 + 0.0682171i 0.0217310π0.0217310\pi
−0.997671 + 0.0682171i 0.978269π0.978269\pi
968968 0 0
969969 −24.0000 −0.770991
970970 0 0
971971 28.2843i 0.907685i 0.891082 + 0.453843i 0.149947π0.149947\pi
−0.891082 + 0.453843i 0.850053π0.850053\pi
972972 0 0
973973 −36.0000 −1.15411
974974 0 0
975975 0 0
976976 0 0
977977 − 42.0000i − 1.34370i −0.740688 0.671850i 0.765500π-0.765500\pi
0.740688 0.671850i 0.234500π-0.234500\pi
978978 0 0
979979 − 33.9411i − 1.08476i
980980 0 0
981981 − 6.00000i − 0.191565i
982982 0 0
983983 18.3848i 0.586383i 0.956054 + 0.293192i 0.0947174π0.0947174\pi
−0.956054 + 0.293192i 0.905283π0.905283\pi
984984 0 0
985985 0 0
986986 0 0
987987 8.48528 0.270089
988988 0 0
989989 10.0000i 0.317982i
990990 0 0
991991 8.48528 0.269544 0.134772 0.990877i 0.456970π-0.456970\pi
0.134772 + 0.990877i 0.456970π0.456970\pi
992992 0 0
993993 32.0000i 1.01549i
994994 0 0
995995 0 0
996996 0 0
997997 −10.0000 −0.316703 −0.158352 0.987383i 0.550618π-0.550618\pi
−0.158352 + 0.987383i 0.550618π0.550618\pi
998998 0 0
999999 11.3137 0.357950
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 3200.2.f.i.449.1 4
4.3 odd 2 inner 3200.2.f.i.449.4 4
5.2 odd 4 640.2.d.d.321.4 yes 4
5.3 odd 4 3200.2.d.s.1601.1 4
5.4 even 2 3200.2.f.j.449.4 4
8.3 odd 2 3200.2.f.j.449.2 4
8.5 even 2 3200.2.f.j.449.3 4
15.2 even 4 5760.2.k.o.2881.2 4
20.3 even 4 3200.2.d.s.1601.4 4
20.7 even 4 640.2.d.d.321.2 yes 4
20.19 odd 2 3200.2.f.j.449.1 4
40.3 even 4 3200.2.d.s.1601.2 4
40.13 odd 4 3200.2.d.s.1601.3 4
40.19 odd 2 inner 3200.2.f.i.449.3 4
40.27 even 4 640.2.d.d.321.3 yes 4
40.29 even 2 inner 3200.2.f.i.449.2 4
40.37 odd 4 640.2.d.d.321.1 4
60.47 odd 4 5760.2.k.o.2881.1 4
80.3 even 4 6400.2.a.bn.1.1 2
80.13 odd 4 6400.2.a.bn.1.2 2
80.27 even 4 1280.2.a.f.1.1 2
80.37 odd 4 1280.2.a.f.1.2 2
80.43 even 4 6400.2.a.bl.1.2 2
80.53 odd 4 6400.2.a.bl.1.1 2
80.67 even 4 1280.2.a.j.1.2 2
80.77 odd 4 1280.2.a.j.1.1 2
120.77 even 4 5760.2.k.o.2881.4 4
120.107 odd 4 5760.2.k.o.2881.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.d.d.321.1 4 40.37 odd 4
640.2.d.d.321.2 yes 4 20.7 even 4
640.2.d.d.321.3 yes 4 40.27 even 4
640.2.d.d.321.4 yes 4 5.2 odd 4
1280.2.a.f.1.1 2 80.27 even 4
1280.2.a.f.1.2 2 80.37 odd 4
1280.2.a.j.1.1 2 80.77 odd 4
1280.2.a.j.1.2 2 80.67 even 4
3200.2.d.s.1601.1 4 5.3 odd 4
3200.2.d.s.1601.2 4 40.3 even 4
3200.2.d.s.1601.3 4 40.13 odd 4
3200.2.d.s.1601.4 4 20.3 even 4
3200.2.f.i.449.1 4 1.1 even 1 trivial
3200.2.f.i.449.2 4 40.29 even 2 inner
3200.2.f.i.449.3 4 40.19 odd 2 inner
3200.2.f.i.449.4 4 4.3 odd 2 inner
3200.2.f.j.449.1 4 20.19 odd 2
3200.2.f.j.449.2 4 8.3 odd 2
3200.2.f.j.449.3 4 8.5 even 2
3200.2.f.j.449.4 4 5.4 even 2
5760.2.k.o.2881.1 4 60.47 odd 4
5760.2.k.o.2881.2 4 15.2 even 4
5760.2.k.o.2881.3 4 120.107 odd 4
5760.2.k.o.2881.4 4 120.77 even 4
6400.2.a.bl.1.1 2 80.53 odd 4
6400.2.a.bl.1.2 2 80.43 even 4
6400.2.a.bn.1.1 2 80.3 even 4
6400.2.a.bn.1.2 2 80.13 odd 4