Properties

Label 3200.2.d.s.1601.1
Level 32003200
Weight 22
Character 3200.1601
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(1601,3200)]
 
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, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3200.1601");
 
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.d (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 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,,a13]\Z[a_1, \ldots, a_{13}]
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 1601.1
Root 0.7071070.707107i-0.707107 - 0.707107i of defining polynomial
Character χ\chi == 3200.1601
Dual form 3200.2.d.s.1601.3

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) == q1.41421iq34.24264q7+1.00000q95.65685iq112.00000iq136.00000q172.82843iq19+6.00000iq21+7.07107q235.65685iq27+4.00000iq29+2.82843q318.00000q332.00000iq372.82843q398.00000q411.41421iq431.41421q47+11.0000q49+8.48528iq51+2.00000iq534.00000q572.82843iq59+14.0000iq614.24264q63+4.24264iq6710.0000iq692.82843q71+6.00000q73+24.0000iq7716.9706q795.00000q81+12.7279iq83+5.65685q876.00000q89+8.48528iq914.00000iq9310.0000q975.65685iq99+O(q100)q-1.41421i q^{3} -4.24264 q^{7} +1.00000 q^{9} -5.65685i q^{11} -2.00000i q^{13} -6.00000 q^{17} -2.82843i q^{19} +6.00000i q^{21} +7.07107 q^{23} -5.65685i q^{27} +4.00000i q^{29} +2.82843 q^{31} -8.00000 q^{33} -2.00000i q^{37} -2.82843 q^{39} -8.00000 q^{41} -1.41421i q^{43} -1.41421 q^{47} +11.0000 q^{49} +8.48528i q^{51} +2.00000i q^{53} -4.00000 q^{57} -2.82843i q^{59} +14.0000i q^{61} -4.24264 q^{63} +4.24264i q^{67} -10.0000i q^{69} -2.82843 q^{71} +6.00000 q^{73} +24.0000i q^{77} -16.9706 q^{79} -5.00000 q^{81} +12.7279i q^{83} +5.65685 q^{87} -6.00000 q^{89} +8.48528i q^{91} -4.00000i q^{93} -10.0000 q^{97} -5.65685i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q924q1732q3332q41+44q4916q57+24q7320q8124q8940q97+O(q100) 4 q + 4 q^{9} - 24 q^{17} - 32 q^{33} - 32 q^{41} + 44 q^{49} - 16 q^{57} + 24 q^{73} - 20 q^{81} - 24 q^{89} - 40 q^{97}+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 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 − 1.41421i − 0.816497i −0.912871 0.408248i 0.866140π-0.866140\pi
0.912871 0.408248i 0.133860π-0.133860\pi
44 0 0
55 0 0
66 0 0
77 −4.24264 −1.60357 −0.801784 0.597614i 0.796115π-0.796115\pi
−0.801784 + 0.597614i 0.796115π0.796115\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 − 2.00000i − 0.554700i −0.960769 0.277350i 0.910544π-0.910544\pi
0.960769 0.277350i 0.0894562π-0.0894562\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 − 2.82843i − 0.648886i −0.945905 0.324443i 0.894823π-0.894823\pi
0.945905 0.324443i 0.105177π-0.105177\pi
2020 0 0
2121 6.00000i 1.30931i
2222 0 0
2323 7.07107 1.47442 0.737210 0.675664i 0.236143π-0.236143\pi
0.737210 + 0.675664i 0.236143π0.236143\pi
2424 0 0
2525 0 0
2626 0 0
2727 − 5.65685i − 1.08866i
2828 0 0
2929 4.00000i 0.742781i 0.928477 + 0.371391i 0.121119π0.121119\pi
−0.928477 + 0.371391i 0.878881π0.878881\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 −8.00000 −1.39262
3434 0 0
3535 0 0
3636 0 0
3737 − 2.00000i − 0.328798i −0.986394 0.164399i 0.947432π-0.947432\pi
0.986394 0.164399i 0.0525685π-0.0525685\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 − 1.41421i − 0.215666i −0.994169 0.107833i 0.965609π-0.965609\pi
0.994169 0.107833i 0.0343911π-0.0343911\pi
4444 0 0
4545 0 0
4646 0 0
4747 −1.41421 −0.206284 −0.103142 0.994667i 0.532890π-0.532890\pi
−0.103142 + 0.994667i 0.532890π0.532890\pi
4848 0 0
4949 11.0000 1.57143
5050 0 0
5151 8.48528i 1.18818i
5252 0 0
5353 2.00000i 0.274721i 0.990521 + 0.137361i 0.0438619π0.0438619\pi
−0.990521 + 0.137361i 0.956138π0.956138\pi
5454 0 0
5555 0 0
5656 0 0
5757 −4.00000 −0.529813
5858 0 0
5959 − 2.82843i − 0.368230i −0.982905 0.184115i 0.941058π-0.941058\pi
0.982905 0.184115i 0.0589419π-0.0589419\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 −4.24264 −0.534522
6464 0 0
6565 0 0
6666 0 0
6767 4.24264i 0.518321i 0.965834 + 0.259161i 0.0834459π0.0834459\pi
−0.965834 + 0.259161i 0.916554π0.916554\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 6.00000 0.702247 0.351123 0.936329i 0.385800π-0.385800\pi
0.351123 + 0.936329i 0.385800π0.385800\pi
7474 0 0
7575 0 0
7676 0 0
7777 24.0000i 2.73505i
7878 0 0
7979 −16.9706 −1.90934 −0.954669 0.297670i 0.903790π-0.903790\pi
−0.954669 + 0.297670i 0.903790π0.903790\pi
8080 0 0
8181 −5.00000 −0.555556
8282 0 0
8383 12.7279i 1.39707i 0.715575 + 0.698535i 0.246165π0.246165\pi
−0.715575 + 0.698535i 0.753835π0.753835\pi
8484 0 0
8585 0 0
8686 0 0
8787 5.65685 0.606478
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 8.48528i 0.889499i
9292 0 0
9393 − 4.00000i − 0.414781i
9494 0 0
9595 0 0
9696 0 0
9797 −10.0000 −1.01535 −0.507673 0.861550i 0.669494π-0.669494\pi
−0.507673 + 0.861550i 0.669494π0.669494\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 −9.89949 −0.975426 −0.487713 0.873004i 0.662169π-0.662169\pi
−0.487713 + 0.873004i 0.662169π0.662169\pi
104104 0 0
105105 0 0
106106 0 0
107107 − 7.07107i − 0.683586i −0.939775 0.341793i 0.888966π-0.888966\pi
0.939775 0.341793i 0.111034π-0.111034\pi
108108 0 0
109109 − 6.00000i − 0.574696i −0.957826 0.287348i 0.907226π-0.907226\pi
0.957826 0.287348i 0.0927736π-0.0927736\pi
110110 0 0
111111 −2.82843 −0.268462
112112 0 0
113113 10.0000 0.940721 0.470360 0.882474i 0.344124π-0.344124\pi
0.470360 + 0.882474i 0.344124π0.344124\pi
114114 0 0
115115 0 0
116116 0 0
117117 − 2.00000i − 0.184900i
118118 0 0
119119 25.4558 2.33353
120120 0 0
121121 −21.0000 −1.90909
122122 0 0
123123 11.3137i 1.02012i
124124 0 0
125125 0 0
126126 0 0
127127 −9.89949 −0.878438 −0.439219 0.898380i 0.644745π-0.644745\pi
−0.439219 + 0.898380i 0.644745π0.644745\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 12.0000i 1.04053i
134134 0 0
135135 0 0
136136 0 0
137137 −2.00000 −0.170872 −0.0854358 0.996344i 0.527228π-0.527228\pi
−0.0854358 + 0.996344i 0.527228π0.527228\pi
138138 0 0
139139 8.48528i 0.719712i 0.933008 + 0.359856i 0.117174π0.117174\pi
−0.933008 + 0.359856i 0.882826π0.882826\pi
140140 0 0
141141 2.00000i 0.168430i
142142 0 0
143143 −11.3137 −0.946100
144144 0 0
145145 0 0
146146 0 0
147147 − 15.5563i − 1.28307i
148148 0 0
149149 − 22.0000i − 1.80231i −0.433497 0.901155i 0.642720π-0.642720\pi
0.433497 0.901155i 0.357280π-0.357280\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 −6.00000 −0.485071
154154 0 0
155155 0 0
156156 0 0
157157 18.0000i 1.43656i 0.695756 + 0.718278i 0.255069π0.255069\pi
−0.695756 + 0.718278i 0.744931π0.744931\pi
158158 0 0
159159 2.82843 0.224309
160160 0 0
161161 −30.0000 −2.36433
162162 0 0
163163 − 18.3848i − 1.44001i −0.693971 0.720003i 0.744140π-0.744140\pi
0.693971 0.720003i 0.255860π-0.255860\pi
164164 0 0
165165 0 0
166166 0 0
167167 9.89949 0.766046 0.383023 0.923739i 0.374883π-0.374883\pi
0.383023 + 0.923739i 0.374883π0.374883\pi
168168 0 0
169169 9.00000 0.692308
170170 0 0
171171 − 2.82843i − 0.216295i
172172 0 0
173173 18.0000i 1.36851i 0.729241 + 0.684257i 0.239873π0.239873\pi
−0.729241 + 0.684257i 0.760127π0.760127\pi
174174 0 0
175175 0 0
176176 0 0
177177 −4.00000 −0.300658
178178 0 0
179179 19.7990i 1.47985i 0.672692 + 0.739923i 0.265138π0.265138\pi
−0.672692 + 0.739923i 0.734862π0.734862\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 19.7990 1.46358
184184 0 0
185185 0 0
186186 0 0
187187 33.9411i 2.48202i
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 −6.00000 −0.431889 −0.215945 0.976406i 0.569283π-0.569283\pi
−0.215945 + 0.976406i 0.569283π0.569283\pi
194194 0 0
195195 0 0
196196 0 0
197197 6.00000i 0.427482i 0.976890 + 0.213741i 0.0685649π0.0685649\pi
−0.976890 + 0.213741i 0.931435π0.931435\pi
198198 0 0
199199 −11.3137 −0.802008 −0.401004 0.916076i 0.631339π-0.631339\pi
−0.401004 + 0.916076i 0.631339π0.631339\pi
200200 0 0
201201 6.00000 0.423207
202202 0 0
203203 − 16.9706i − 1.19110i
204204 0 0
205205 0 0
206206 0 0
207207 7.07107 0.491473
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 4.00000i 0.274075i
214214 0 0
215215 0 0
216216 0 0
217217 −12.0000 −0.814613
218218 0 0
219219 − 8.48528i − 0.573382i
220220 0 0
221221 12.0000i 0.807207i
222222 0 0
223223 15.5563 1.04173 0.520865 0.853639i 0.325609π-0.325609\pi
0.520865 + 0.853639i 0.325609π0.325609\pi
224224 0 0
225225 0 0
226226 0 0
227227 7.07107i 0.469323i 0.972077 + 0.234662i 0.0753982π0.0753982\pi
−0.972077 + 0.234662i 0.924602π0.924602\pi
228228 0 0
229229 − 20.0000i − 1.32164i −0.750546 0.660819i 0.770209π-0.770209\pi
0.750546 0.660819i 0.229791π-0.229791\pi
230230 0 0
231231 33.9411 2.23316
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 0 0
236236 0 0
237237 24.0000i 1.55897i
238238 0 0
239239 11.3137 0.731823 0.365911 0.930650i 0.380757π-0.380757\pi
0.365911 + 0.930650i 0.380757π0.380757\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 − 9.89949i − 0.635053i
244244 0 0
245245 0 0
246246 0 0
247247 −5.65685 −0.359937
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 − 40.0000i − 2.51478i
254254 0 0
255255 0 0
256256 0 0
257257 18.0000 1.12281 0.561405 0.827541i 0.310261π-0.310261\pi
0.561405 + 0.827541i 0.310261π0.310261\pi
258258 0 0
259259 8.48528i 0.527250i
260260 0 0
261261 4.00000i 0.247594i
262262 0 0
263263 −7.07107 −0.436021 −0.218010 0.975946i 0.569957π-0.569957\pi
−0.218010 + 0.975946i 0.569957π0.569957\pi
264264 0 0
265265 0 0
266266 0 0
267267 8.48528i 0.519291i
268268 0 0
269269 6.00000i 0.365826i 0.983129 + 0.182913i 0.0585527π0.0585527\pi
−0.983129 + 0.182913i 0.941447π0.941447\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 12.0000 0.726273
274274 0 0
275275 0 0
276276 0 0
277277 − 30.0000i − 1.80253i −0.433273 0.901263i 0.642641π-0.642641\pi
0.433273 0.901263i 0.357359π-0.357359\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 − 9.89949i − 0.588464i −0.955734 0.294232i 0.904936π-0.904936\pi
0.955734 0.294232i 0.0950638π-0.0950638\pi
284284 0 0
285285 0 0
286286 0 0
287287 33.9411 2.00348
288288 0 0
289289 19.0000 1.11765
290290 0 0
291291 14.1421i 0.829027i
292292 0 0
293293 6.00000i 0.350524i 0.984522 + 0.175262i 0.0560772π0.0560772\pi
−0.984522 + 0.175262i 0.943923π0.943923\pi
294294 0 0
295295 0 0
296296 0 0
297297 −32.0000 −1.85683
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 15.5563i 0.887848i 0.896065 + 0.443924i 0.146414π0.146414\pi
−0.896065 + 0.443924i 0.853586π0.853586\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 −6.00000 −0.339140 −0.169570 0.985518i 0.554238π-0.554238\pi
−0.169570 + 0.985518i 0.554238π0.554238\pi
314314 0 0
315315 0 0
316316 0 0
317317 2.00000i 0.112331i 0.998421 + 0.0561656i 0.0178875π0.0178875\pi
−0.998421 + 0.0561656i 0.982113π0.982113\pi
318318 0 0
319319 22.6274 1.26689
320320 0 0
321321 −10.0000 −0.558146
322322 0 0
323323 16.9706i 0.944267i
324324 0 0
325325 0 0
326326 0 0
327327 −8.48528 −0.469237
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 − 2.00000i − 0.109599i
334334 0 0
335335 0 0
336336 0 0
337337 −18.0000 −0.980522 −0.490261 0.871576i 0.663099π-0.663099\pi
−0.490261 + 0.871576i 0.663099π0.663099\pi
338338 0 0
339339 − 14.1421i − 0.768095i
340340 0 0
341341 − 16.0000i − 0.866449i
342342 0 0
343343 −16.9706 −0.916324
344344 0 0
345345 0 0
346346 0 0
347347 − 4.24264i − 0.227757i −0.993495 0.113878i 0.963673π-0.963673\pi
0.993495 0.113878i 0.0363274π-0.0363274\pi
348348 0 0
349349 12.0000i 0.642345i 0.947021 + 0.321173i 0.104077π0.104077\pi
−0.947021 + 0.321173i 0.895923π0.895923\pi
350350 0 0
351351 −11.3137 −0.603881
352352 0 0
353353 −10.0000 −0.532246 −0.266123 0.963939i 0.585743π-0.585743\pi
−0.266123 + 0.963939i 0.585743π0.585743\pi
354354 0 0
355355 0 0
356356 0 0
357357 − 36.0000i − 1.90532i
358358 0 0
359359 −28.2843 −1.49279 −0.746393 0.665505i 0.768216π-0.768216\pi
−0.746393 + 0.665505i 0.768216π0.768216\pi
360360 0 0
361361 11.0000 0.578947
362362 0 0
363363 29.6985i 1.55877i
364364 0 0
365365 0 0
366366 0 0
367367 −4.24264 −0.221464 −0.110732 0.993850i 0.535320π-0.535320\pi
−0.110732 + 0.993850i 0.535320π0.535320\pi
368368 0 0
369369 −8.00000 −0.416463
370370 0 0
371371 − 8.48528i − 0.440534i
372372 0 0
373373 − 14.0000i − 0.724893i −0.932005 0.362446i 0.881942π-0.881942\pi
0.932005 0.362446i 0.118058π-0.118058\pi
374374 0 0
375375 0 0
376376 0 0
377377 8.00000 0.412021
378378 0 0
379379 31.1127i 1.59815i 0.601230 + 0.799076i 0.294678π0.294678\pi
−0.601230 + 0.799076i 0.705322π0.705322\pi
380380 0 0
381381 14.0000i 0.717242i
382382 0 0
383383 −7.07107 −0.361315 −0.180657 0.983546i 0.557823π-0.557823\pi
−0.180657 + 0.983546i 0.557823π0.557823\pi
384384 0 0
385385 0 0
386386 0 0
387387 − 1.41421i − 0.0718885i
388388 0 0
389389 − 14.0000i − 0.709828i −0.934899 0.354914i 0.884510π-0.884510\pi
0.934899 0.354914i 0.115490π-0.115490\pi
390390 0 0
391391 −42.4264 −2.14560
392392 0 0
393393 −16.0000 −0.807093
394394 0 0
395395 0 0
396396 0 0
397397 14.0000i 0.702640i 0.936255 + 0.351320i 0.114267π0.114267\pi
−0.936255 + 0.351320i 0.885733π0.885733\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 − 5.65685i − 0.281788i
404404 0 0
405405 0 0
406406 0 0
407407 −11.3137 −0.560800
408408 0 0
409409 4.00000 0.197787 0.0988936 0.995098i 0.468470π-0.468470\pi
0.0988936 + 0.995098i 0.468470π0.468470\pi
410410 0 0
411411 2.82843i 0.139516i
412412 0 0
413413 12.0000i 0.590481i
414414 0 0
415415 0 0
416416 0 0
417417 12.0000 0.587643
418418 0 0
419419 − 8.48528i − 0.414533i −0.978285 0.207267i 0.933543π-0.933543\pi
0.978285 0.207267i 0.0664567π-0.0664567\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 −1.41421 −0.0687614
424424 0 0
425425 0 0
426426 0 0
427427 − 59.3970i − 2.87442i
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 14.0000 0.672797 0.336399 0.941720i 0.390791π-0.390791\pi
0.336399 + 0.941720i 0.390791π0.390791\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 20.0000i − 0.956730i
438438 0 0
439439 −16.9706 −0.809961 −0.404980 0.914325i 0.632722π-0.632722\pi
−0.404980 + 0.914325i 0.632722π0.632722\pi
440440 0 0
441441 11.0000 0.523810
442442 0 0
443443 − 15.5563i − 0.739104i −0.929210 0.369552i 0.879511π-0.879511\pi
0.929210 0.369552i 0.120489π-0.120489\pi
444444 0 0
445445 0 0
446446 0 0
447447 −31.1127 −1.47158
448448 0 0
449449 −20.0000 −0.943858 −0.471929 0.881636i 0.656442π-0.656442\pi
−0.471929 + 0.881636i 0.656442π0.656442\pi
450450 0 0
451451 45.2548i 2.13097i
452452 0 0
453453 20.0000i 0.939682i
454454 0 0
455455 0 0
456456 0 0
457457 34.0000 1.59045 0.795226 0.606313i 0.207352π-0.207352\pi
0.795226 + 0.606313i 0.207352π0.207352\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 7.07107 0.328620 0.164310 0.986409i 0.447460π-0.447460\pi
0.164310 + 0.986409i 0.447460π0.447460\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 9.89949i − 0.458094i −0.973415 0.229047i 0.926439π-0.926439\pi
0.973415 0.229047i 0.0735609π-0.0735609\pi
468468 0 0
469469 − 18.0000i − 0.831163i
470470 0 0
471471 25.4558 1.17294
472472 0 0
473473 −8.00000 −0.367840
474474 0 0
475475 0 0
476476 0 0
477477 2.00000i 0.0915737i
478478 0 0
479479 −33.9411 −1.55081 −0.775405 0.631464i 0.782454π-0.782454\pi
−0.775405 + 0.631464i 0.782454π0.782454\pi
480480 0 0
481481 −4.00000 −0.182384
482482 0 0
483483 42.4264i 1.93047i
484484 0 0
485485 0 0
486486 0 0
487487 12.7279 0.576757 0.288379 0.957516i 0.406884π-0.406884\pi
0.288379 + 0.957516i 0.406884π0.406884\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 − 24.0000i − 1.08091i
494494 0 0
495495 0 0
496496 0 0
497497 12.0000 0.538274
498498 0 0
499499 − 25.4558i − 1.13956i −0.821797 0.569780i 0.807028π-0.807028\pi
0.821797 0.569780i 0.192972π-0.192972\pi
500500 0 0
501501 − 14.0000i − 0.625474i
502502 0 0
503503 −32.5269 −1.45030 −0.725152 0.688589i 0.758230π-0.758230\pi
−0.725152 + 0.688589i 0.758230π0.758230\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 12.7279i − 0.565267i
508508 0 0
509509 20.0000i 0.886484i 0.896402 + 0.443242i 0.146172π0.146172\pi
−0.896402 + 0.443242i 0.853828π0.853828\pi
510510 0 0
511511 −25.4558 −1.12610
512512 0 0
513513 −16.0000 −0.706417
514514 0 0
515515 0 0
516516 0 0
517517 8.00000i 0.351840i
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 12.7279i 0.556553i 0.960501 + 0.278277i 0.0897632π0.0897632\pi
−0.960501 + 0.278277i 0.910237π0.910237\pi
524524 0 0
525525 0 0
526526 0 0
527527 −16.9706 −0.739249
528528 0 0
529529 27.0000 1.17391
530530 0 0
531531 − 2.82843i − 0.122743i
532532 0 0
533533 16.0000i 0.693037i
534534 0 0
535535 0 0
536536 0 0
537537 28.0000 1.20829
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 22.6274 0.971035
544544 0 0
545545 0 0
546546 0 0
547547 − 4.24264i − 0.181402i −0.995878 0.0907011i 0.971089π-0.971089\pi
0.995878 0.0907011i 0.0289108π-0.0289108\pi
548548 0 0
549549 14.0000i 0.597505i
550550 0 0
551551 11.3137 0.481980
552552 0 0
553553 72.0000 3.06175
554554 0 0
555555 0 0
556556 0 0
557557 − 18.0000i − 0.762684i −0.924434 0.381342i 0.875462π-0.875462\pi
0.924434 0.381342i 0.124538π-0.124538\pi
558558 0 0
559559 −2.82843 −0.119630
560560 0 0
561561 48.0000 2.02656
562562 0 0
563563 − 35.3553i − 1.49005i −0.667037 0.745025i 0.732438π-0.732438\pi
0.667037 0.745025i 0.267562π-0.267562\pi
564564 0 0
565565 0 0
566566 0 0
567567 21.2132 0.890871
568568 0 0
569569 −28.0000 −1.17382 −0.586911 0.809652i 0.699656π-0.699656\pi
−0.586911 + 0.809652i 0.699656π0.699656\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 4.00000i 0.167102i
574574 0 0
575575 0 0
576576 0 0
577577 10.0000 0.416305 0.208153 0.978096i 0.433255π-0.433255\pi
0.208153 + 0.978096i 0.433255π0.433255\pi
578578 0 0
579579 8.48528i 0.352636i
580580 0 0
581581 − 54.0000i − 2.24030i
582582 0 0
583583 11.3137 0.468566
584584 0 0
585585 0 0
586586 0 0
587587 12.7279i 0.525338i 0.964886 + 0.262669i 0.0846027π0.0846027\pi
−0.964886 + 0.262669i 0.915397π0.915397\pi
588588 0 0
589589 − 8.00000i − 0.329634i
590590 0 0
591591 8.48528 0.349038
592592 0 0
593593 30.0000 1.23195 0.615976 0.787765i 0.288762π-0.288762\pi
0.615976 + 0.787765i 0.288762π0.288762\pi
594594 0 0
595595 0 0
596596 0 0
597597 16.0000i 0.654836i
598598 0 0
599599 −39.5980 −1.61793 −0.808965 0.587857i 0.799972π-0.799972\pi
−0.808965 + 0.587857i 0.799972π0.799972\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 4.24264i 0.172774i
604604 0 0
605605 0 0
606606 0 0
607607 9.89949 0.401808 0.200904 0.979611i 0.435612π-0.435612\pi
0.200904 + 0.979611i 0.435612π0.435612\pi
608608 0 0
609609 −24.0000 −0.972529
610610 0 0
611611 2.82843i 0.114426i
612612 0 0
613613 − 26.0000i − 1.05013i −0.851062 0.525065i 0.824041π-0.824041\pi
0.851062 0.525065i 0.175959π-0.175959\pi
614614 0 0
615615 0 0
616616 0 0
617617 2.00000 0.0805170 0.0402585 0.999189i 0.487182π-0.487182\pi
0.0402585 + 0.999189i 0.487182π0.487182\pi
618618 0 0
619619 − 19.7990i − 0.795789i −0.917431 0.397894i 0.869741π-0.869741\pi
0.917431 0.397894i 0.130259π-0.130259\pi
620620 0 0
621621 − 40.0000i − 1.60514i
622622 0 0
623623 25.4558 1.01987
624624 0 0
625625 0 0
626626 0 0
627627 22.6274i 0.903652i
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 −24.0000 −0.953914
634634 0 0
635635 0 0
636636 0 0
637637 − 22.0000i − 0.871672i
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 7.07107i 0.278856i 0.990232 + 0.139428i 0.0445263π0.0445263\pi
−0.990232 + 0.139428i 0.955474π0.955474\pi
644644 0 0
645645 0 0
646646 0 0
647647 −32.5269 −1.27876 −0.639382 0.768889i 0.720810π-0.720810\pi
−0.639382 + 0.768889i 0.720810π0.720810\pi
648648 0 0
649649 −16.0000 −0.628055
650650 0 0
651651 16.9706i 0.665129i
652652 0 0
653653 18.0000i 0.704394i 0.935926 + 0.352197i 0.114565π0.114565\pi
−0.935926 + 0.352197i 0.885435π0.885435\pi
654654 0 0
655655 0 0
656656 0 0
657657 6.00000 0.234082
658658 0 0
659659 25.4558i 0.991619i 0.868431 + 0.495809i 0.165129π0.165129\pi
−0.868431 + 0.495809i 0.834871π0.834871\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 16.9706 0.659082
664664 0 0
665665 0 0
666666 0 0
667667 28.2843i 1.09517i
668668 0 0
669669 − 22.0000i − 0.850569i
670670 0 0
671671 79.1960 3.05733
672672 0 0
673673 −50.0000 −1.92736 −0.963679 0.267063i 0.913947π-0.913947\pi
−0.963679 + 0.267063i 0.913947π0.913947\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 10.0000i − 0.384331i −0.981363 0.192166i 0.938449π-0.938449\pi
0.981363 0.192166i 0.0615511π-0.0615511\pi
678678 0 0
679679 42.4264 1.62818
680680 0 0
681681 10.0000 0.383201
682682 0 0
683683 − 35.3553i − 1.35283i −0.736519 0.676417i 0.763532π-0.763532\pi
0.736519 0.676417i 0.236468π-0.236468\pi
684684 0 0
685685 0 0
686686 0 0
687687 −28.2843 −1.07911
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 24.0000i 0.911685i
694694 0 0
695695 0 0
696696 0 0
697697 48.0000 1.81813
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 −5.65685 −0.213352
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 − 28.0000i − 1.05156i −0.850620 0.525781i 0.823773π-0.823773\pi
0.850620 0.525781i 0.176227π-0.176227\pi
710710 0 0
711711 −16.9706 −0.636446
712712 0 0
713713 20.0000 0.749006
714714 0 0
715715 0 0
716716 0 0
717717 − 16.0000i − 0.597531i
718718 0 0
719719 11.3137 0.421930 0.210965 0.977494i 0.432339π-0.432339\pi
0.210965 + 0.977494i 0.432339π0.432339\pi
720720 0 0
721721 42.0000 1.56416
722722 0 0
723723 − 11.3137i − 0.420761i
724724 0 0
725725 0 0
726726 0 0
727727 −4.24264 −0.157351 −0.0786754 0.996900i 0.525069π-0.525069\pi
−0.0786754 + 0.996900i 0.525069π0.525069\pi
728728 0 0
729729 −29.0000 −1.07407
730730 0 0
731731 8.48528i 0.313839i
732732 0 0
733733 34.0000i 1.25582i 0.778287 + 0.627909i 0.216089π0.216089\pi
−0.778287 + 0.627909i 0.783911π0.783911\pi
734734 0 0
735735 0 0
736736 0 0
737737 24.0000 0.884051
738738 0 0
739739 − 25.4558i − 0.936408i −0.883620 0.468204i 0.844901π-0.844901\pi
0.883620 0.468204i 0.155099π-0.155099\pi
740740 0 0
741741 8.00000i 0.293887i
742742 0 0
743743 32.5269 1.19330 0.596648 0.802503i 0.296499π-0.296499\pi
0.596648 + 0.802503i 0.296499π0.296499\pi
744744 0 0
745745 0 0
746746 0 0
747747 12.7279i 0.465690i
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 32.0000 1.16614
754754 0 0
755755 0 0
756756 0 0
757757 − 46.0000i − 1.67190i −0.548807 0.835949i 0.684918π-0.684918\pi
0.548807 0.835949i 0.315082π-0.315082\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 25.4558i 0.921563i
764764 0 0
765765 0 0
766766 0 0
767767 −5.65685 −0.204257
768768 0 0
769769 14.0000 0.504853 0.252426 0.967616i 0.418771π-0.418771\pi
0.252426 + 0.967616i 0.418771π0.418771\pi
770770 0 0
771771 − 25.4558i − 0.916770i
772772 0 0
773773 − 26.0000i − 0.935155i −0.883952 0.467578i 0.845127π-0.845127\pi
0.883952 0.467578i 0.154873π-0.154873\pi
774774 0 0
775775 0 0
776776 0 0
777777 12.0000 0.430498
778778 0 0
779779 22.6274i 0.810711i
780780 0 0
781781 16.0000i 0.572525i
782782 0 0
783783 22.6274 0.808638
784784 0 0
785785 0 0
786786 0 0
787787 − 46.6690i − 1.66357i −0.555097 0.831786i 0.687319π-0.687319\pi
0.555097 0.831786i 0.312681π-0.312681\pi
788788 0 0
789789 10.0000i 0.356009i
790790 0 0
791791 −42.4264 −1.50851
792792 0 0
793793 28.0000 0.994309
794794 0 0
795795 0 0
796796 0 0
797797 10.0000i 0.354218i 0.984191 + 0.177109i 0.0566745π0.0566745\pi
−0.984191 + 0.177109i 0.943325π0.943325\pi
798798 0 0
799799 8.48528 0.300188
800800 0 0
801801 −6.00000 −0.212000
802802 0 0
803803 − 33.9411i − 1.19776i
804804 0 0
805805 0 0
806806 0 0
807807 8.48528 0.298696
808808 0 0
809809 10.0000 0.351581 0.175791 0.984428i 0.443752π-0.443752\pi
0.175791 + 0.984428i 0.443752π0.443752\pi
810810 0 0
811811 0 0 1.00000 00
−1.00000 π\pi
812812 0 0
813813 − 36.0000i − 1.26258i
814814 0 0
815815 0 0
816816 0 0
817817 −4.00000 −0.139942
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 −26.8701 −0.936631 −0.468316 0.883561i 0.655139π-0.655139\pi
−0.468316 + 0.883561i 0.655139π0.655139\pi
824824 0 0
825825 0 0
826826 0 0
827827 7.07107i 0.245885i 0.992414 + 0.122943i 0.0392331π0.0392331\pi
−0.992414 + 0.122943i 0.960767π0.960767\pi
828828 0 0
829829 − 26.0000i − 0.903017i −0.892267 0.451509i 0.850886π-0.850886\pi
0.892267 0.451509i 0.149114π-0.149114\pi
830830 0 0
831831 −42.4264 −1.47176
832832 0 0
833833 −66.0000 −2.28676
834834 0 0
835835 0 0
836836 0 0
837837 − 16.0000i − 0.553041i
838838 0 0
839839 28.2843 0.976481 0.488241 0.872709i 0.337639π-0.337639\pi
0.488241 + 0.872709i 0.337639π0.337639\pi
840840 0 0
841841 13.0000 0.448276
842842 0 0
843843 − 11.3137i − 0.389665i
844844 0 0
845845 0 0
846846 0 0
847847 89.0955 3.06136
848848 0 0
849849 −14.0000 −0.480479
850850 0 0
851851 − 14.1421i − 0.484786i
852852 0 0
853853 − 26.0000i − 0.890223i −0.895475 0.445112i 0.853164π-0.853164\pi
0.895475 0.445112i 0.146836π-0.146836\pi
854854 0 0
855855 0 0
856856 0 0
857857 −18.0000 −0.614868 −0.307434 0.951569i 0.599470π-0.599470\pi
−0.307434 + 0.951569i 0.599470π0.599470\pi
858858 0 0
859859 − 2.82843i − 0.0965047i −0.998835 0.0482523i 0.984635π-0.984635\pi
0.998835 0.0482523i 0.0153652π-0.0153652\pi
860860 0 0
861861 − 48.0000i − 1.63584i
862862 0 0
863863 −55.1543 −1.87748 −0.938738 0.344633i 0.888003π-0.888003\pi
−0.938738 + 0.344633i 0.888003π0.888003\pi
864864 0 0
865865 0 0
866866 0 0
867867 − 26.8701i − 0.912555i
868868 0 0
869869 96.0000i 3.25658i
870870 0 0
871871 8.48528 0.287513
872872 0 0
873873 −10.0000 −0.338449
874874 0 0
875875 0 0
876876 0 0
877877 − 38.0000i − 1.28317i −0.767052 0.641584i 0.778277π-0.778277\pi
0.767052 0.641584i 0.221723π-0.221723\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 21.2132i 0.713881i 0.934127 + 0.356941i 0.116180π0.116180\pi
−0.934127 + 0.356941i 0.883820π0.883820\pi
884884 0 0
885885 0 0
886886 0 0
887887 −26.8701 −0.902208 −0.451104 0.892471i 0.648970π-0.648970\pi
−0.451104 + 0.892471i 0.648970π0.648970\pi
888888 0 0
889889 42.0000 1.40863
890890 0 0
891891 28.2843i 0.947559i
892892 0 0
893893 4.00000i 0.133855i
894894 0 0
895895 0 0
896896 0 0
897897 −20.0000 −0.667781
898898 0 0
899899 11.3137i 0.377333i
900900 0 0
901901 − 12.0000i − 0.399778i
902902 0 0
903903 8.48528 0.282372
904904 0 0
905905 0 0
906906 0 0
907907 − 1.41421i − 0.0469582i −0.999724 0.0234791i 0.992526π-0.992526\pi
0.999724 0.0234791i 0.00747431π-0.00747431\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 72.0000 2.38285
914914 0 0
915915 0 0
916916 0 0
917917 48.0000i 1.58510i
918918 0 0
919919 39.5980 1.30622 0.653108 0.757264i 0.273465π-0.273465\pi
0.653108 + 0.757264i 0.273465π0.273465\pi
920920 0 0
921921 22.0000 0.724925
922922 0 0
923923 5.65685i 0.186198i
924924 0 0
925925 0 0
926926 0 0
927927 −9.89949 −0.325142
928928 0 0
929929 −28.0000 −0.918650 −0.459325 0.888268i 0.651909π-0.651909\pi
−0.459325 + 0.888268i 0.651909π0.651909\pi
930930 0 0
931931 − 31.1127i − 1.01968i
932932 0 0
933933 4.00000i 0.130954i
934934 0 0
935935 0 0
936936 0 0
937937 2.00000 0.0653372 0.0326686 0.999466i 0.489599π-0.489599\pi
0.0326686 + 0.999466i 0.489599π0.489599\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 −56.5685 −1.84213
944944 0 0
945945 0 0
946946 0 0
947947 15.5563i 0.505513i 0.967530 + 0.252757i 0.0813372π0.0813372\pi
−0.967530 + 0.252757i 0.918663π0.918663\pi
948948 0 0
949949 − 12.0000i − 0.389536i
950950 0 0
951951 2.82843 0.0917180
952952 0 0
953953 −54.0000 −1.74923 −0.874616 0.484817i 0.838886π-0.838886\pi
−0.874616 + 0.484817i 0.838886π0.838886\pi
954954 0 0
955955 0 0
956956 0 0
957957 − 32.0000i − 1.03441i
958958 0 0
959959 8.48528 0.274004
960960 0 0
961961 −23.0000 −0.741935
962962 0 0
963963 − 7.07107i − 0.227862i
964964 0 0
965965 0 0
966966 0 0
967967 4.24264 0.136434 0.0682171 0.997671i 0.478269π-0.478269\pi
0.0682171 + 0.997671i 0.478269π0.478269\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 − 36.0000i − 1.15411i
974974 0 0
975975 0 0
976976 0 0
977977 −42.0000 −1.34370 −0.671850 0.740688i 0.734500π-0.734500\pi
−0.671850 + 0.740688i 0.734500π0.734500\pi
978978 0 0
979979 33.9411i 1.08476i
980980 0 0
981981 − 6.00000i − 0.191565i
982982 0 0
983983 −18.3848 −0.586383 −0.293192 0.956054i 0.594717π-0.594717\pi
−0.293192 + 0.956054i 0.594717π0.594717\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 8.48528i − 0.270089i
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 −32.0000 −1.01549
994994 0 0
995995 0 0
996996 0 0
997997 10.0000i 0.316703i 0.987383 + 0.158352i 0.0506179π0.0506179\pi
−0.987383 + 0.158352i 0.949382π0.949382\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.d.s.1601.1 4
4.3 odd 2 inner 3200.2.d.s.1601.4 4
5.2 odd 4 3200.2.f.i.449.1 4
5.3 odd 4 3200.2.f.j.449.4 4
5.4 even 2 640.2.d.d.321.4 yes 4
8.3 odd 2 inner 3200.2.d.s.1601.2 4
8.5 even 2 inner 3200.2.d.s.1601.3 4
15.14 odd 2 5760.2.k.o.2881.2 4
16.3 odd 4 6400.2.a.bn.1.1 2
16.5 even 4 6400.2.a.bl.1.1 2
16.11 odd 4 6400.2.a.bl.1.2 2
16.13 even 4 6400.2.a.bn.1.2 2
20.3 even 4 3200.2.f.j.449.1 4
20.7 even 4 3200.2.f.i.449.4 4
20.19 odd 2 640.2.d.d.321.2 yes 4
40.3 even 4 3200.2.f.i.449.3 4
40.13 odd 4 3200.2.f.i.449.2 4
40.19 odd 2 640.2.d.d.321.3 yes 4
40.27 even 4 3200.2.f.j.449.2 4
40.29 even 2 640.2.d.d.321.1 4
40.37 odd 4 3200.2.f.j.449.3 4
60.59 even 2 5760.2.k.o.2881.1 4
80.19 odd 4 1280.2.a.j.1.2 2
80.29 even 4 1280.2.a.j.1.1 2
80.59 odd 4 1280.2.a.f.1.1 2
80.69 even 4 1280.2.a.f.1.2 2
120.29 odd 2 5760.2.k.o.2881.4 4
120.59 even 2 5760.2.k.o.2881.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.d.d.321.1 4 40.29 even 2
640.2.d.d.321.2 yes 4 20.19 odd 2
640.2.d.d.321.3 yes 4 40.19 odd 2
640.2.d.d.321.4 yes 4 5.4 even 2
1280.2.a.f.1.1 2 80.59 odd 4
1280.2.a.f.1.2 2 80.69 even 4
1280.2.a.j.1.1 2 80.29 even 4
1280.2.a.j.1.2 2 80.19 odd 4
3200.2.d.s.1601.1 4 1.1 even 1 trivial
3200.2.d.s.1601.2 4 8.3 odd 2 inner
3200.2.d.s.1601.3 4 8.5 even 2 inner
3200.2.d.s.1601.4 4 4.3 odd 2 inner
3200.2.f.i.449.1 4 5.2 odd 4
3200.2.f.i.449.2 4 40.13 odd 4
3200.2.f.i.449.3 4 40.3 even 4
3200.2.f.i.449.4 4 20.7 even 4
3200.2.f.j.449.1 4 20.3 even 4
3200.2.f.j.449.2 4 40.27 even 4
3200.2.f.j.449.3 4 40.37 odd 4
3200.2.f.j.449.4 4 5.3 odd 4
5760.2.k.o.2881.1 4 60.59 even 2
5760.2.k.o.2881.2 4 15.14 odd 2
5760.2.k.o.2881.3 4 120.59 even 2
5760.2.k.o.2881.4 4 120.29 odd 2
6400.2.a.bl.1.1 2 16.5 even 4
6400.2.a.bl.1.2 2 16.11 odd 4
6400.2.a.bn.1.1 2 16.3 odd 4
6400.2.a.bn.1.2 2 16.13 even 4