Properties

Label 3200.2.c.w.2049.3
Level 32003200
Weight 22
Character 3200.2049
Analytic conductor 25.55225.552
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3200,2,Mod(2049,3200)]
 
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, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3200.2049");
 
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.c (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(i,5)\Q(i, \sqrt{5})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+3x2+1 x^{4} + 3x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 640)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 2049.3
Root 0.618034i0.618034i of defining polynomial
Character χ\chi == 3200.2049
Dual form 3200.2.c.w.2049.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+1.23607iq3+3.23607iq7+1.47214q9+2.00000q11+4.47214iq13+4.47214iq174.47214q194.00000q214.76393iq23+5.52786iq27+2.00000q296.47214q31+2.47214iq33+6.94427iq375.52786q39+12.4721q417.70820iq43+7.23607iq473.47214q495.52786q510.472136iq535.52786iq578.47214q596.00000q61+4.76393iq637.70820iq67+5.88854q69+2.47214q714.47214iq73+6.47214iq77+12.9443q792.41641q813.70820iq83+2.47214iq87+14.9443q8914.4721q918.00000iq9316.4721iq97+2.94427q99+O(q100)q+1.23607i q^{3} +3.23607i q^{7} +1.47214 q^{9} +2.00000 q^{11} +4.47214i q^{13} +4.47214i q^{17} -4.47214 q^{19} -4.00000 q^{21} -4.76393i q^{23} +5.52786i q^{27} +2.00000 q^{29} -6.47214 q^{31} +2.47214i q^{33} +6.94427i q^{37} -5.52786 q^{39} +12.4721 q^{41} -7.70820i q^{43} +7.23607i q^{47} -3.47214 q^{49} -5.52786 q^{51} -0.472136i q^{53} -5.52786i q^{57} -8.47214 q^{59} -6.00000 q^{61} +4.76393i q^{63} -7.70820i q^{67} +5.88854 q^{69} +2.47214 q^{71} -4.47214i q^{73} +6.47214i q^{77} +12.9443 q^{79} -2.41641 q^{81} -3.70820i q^{83} +2.47214i q^{87} +14.9443 q^{89} -14.4721 q^{91} -8.00000i q^{93} -16.4721i q^{97} +2.94427 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q12q9+8q1116q21+8q298q3140q39+32q41+4q4940q5116q5924q6148q698q71+16q79+44q81+24q8940q91+24q99+O(q100) 4 q - 12 q^{9} + 8 q^{11} - 16 q^{21} + 8 q^{29} - 8 q^{31} - 40 q^{39} + 32 q^{41} + 4 q^{49} - 40 q^{51} - 16 q^{59} - 24 q^{61} - 48 q^{69} - 8 q^{71} + 16 q^{79} + 44 q^{81} + 24 q^{89} - 40 q^{91}+ \cdots - 24 q^{99}+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) 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 1.23607i 0.713644i 0.934172 + 0.356822i 0.116140π0.116140\pi
−0.934172 + 0.356822i 0.883860π0.883860\pi
44 0 0
55 0 0
66 0 0
77 3.23607i 1.22312i 0.791199 + 0.611559i 0.209457π0.209457\pi
−0.791199 + 0.611559i 0.790543π0.790543\pi
88 0 0
99 1.47214 0.490712
1010 0 0
1111 2.00000 0.603023 0.301511 0.953463i 0.402509π-0.402509\pi
0.301511 + 0.953463i 0.402509π0.402509\pi
1212 0 0
1313 4.47214i 1.24035i 0.784465 + 0.620174i 0.212938π0.212938\pi
−0.784465 + 0.620174i 0.787062π0.787062\pi
1414 0 0
1515 0 0
1616 0 0
1717 4.47214i 1.08465i 0.840168 + 0.542326i 0.182456π0.182456\pi
−0.840168 + 0.542326i 0.817544π0.817544\pi
1818 0 0
1919 −4.47214 −1.02598 −0.512989 0.858395i 0.671462π-0.671462\pi
−0.512989 + 0.858395i 0.671462π0.671462\pi
2020 0 0
2121 −4.00000 −0.872872
2222 0 0
2323 − 4.76393i − 0.993348i −0.867937 0.496674i 0.834554π-0.834554\pi
0.867937 0.496674i 0.165446π-0.165446\pi
2424 0 0
2525 0 0
2626 0 0
2727 5.52786i 1.06384i
2828 0 0
2929 2.00000 0.371391 0.185695 0.982607i 0.440546π-0.440546\pi
0.185695 + 0.982607i 0.440546π0.440546\pi
3030 0 0
3131 −6.47214 −1.16243 −0.581215 0.813750i 0.697422π-0.697422\pi
−0.581215 + 0.813750i 0.697422π0.697422\pi
3232 0 0
3333 2.47214i 0.430344i
3434 0 0
3535 0 0
3636 0 0
3737 6.94427i 1.14163i 0.821078 + 0.570816i 0.193373π0.193373\pi
−0.821078 + 0.570816i 0.806627π0.806627\pi
3838 0 0
3939 −5.52786 −0.885167
4040 0 0
4141 12.4721 1.94782 0.973910 0.226934i 0.0728701π-0.0728701\pi
0.973910 + 0.226934i 0.0728701π0.0728701\pi
4242 0 0
4343 − 7.70820i − 1.17549i −0.809046 0.587745i 0.800016π-0.800016\pi
0.809046 0.587745i 0.199984π-0.199984\pi
4444 0 0
4545 0 0
4646 0 0
4747 7.23607i 1.05549i 0.849403 + 0.527744i 0.176962π0.176962\pi
−0.849403 + 0.527744i 0.823038π0.823038\pi
4848 0 0
4949 −3.47214 −0.496019
5050 0 0
5151 −5.52786 −0.774056
5252 0 0
5353 − 0.472136i − 0.0648529i −0.999474 0.0324264i 0.989677π-0.989677\pi
0.999474 0.0324264i 0.0103235π-0.0103235\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 5.52786i − 0.732183i
5858 0 0
5959 −8.47214 −1.10298 −0.551489 0.834182i 0.685940π-0.685940\pi
−0.551489 + 0.834182i 0.685940π0.685940\pi
6060 0 0
6161 −6.00000 −0.768221 −0.384111 0.923287i 0.625492π-0.625492\pi
−0.384111 + 0.923287i 0.625492π0.625492\pi
6262 0 0
6363 4.76393i 0.600199i
6464 0 0
6565 0 0
6666 0 0
6767 − 7.70820i − 0.941707i −0.882211 0.470853i 0.843946π-0.843946\pi
0.882211 0.470853i 0.156054π-0.156054\pi
6868 0 0
6969 5.88854 0.708897
7070 0 0
7171 2.47214 0.293389 0.146694 0.989182i 0.453137π-0.453137\pi
0.146694 + 0.989182i 0.453137π0.453137\pi
7272 0 0
7373 − 4.47214i − 0.523424i −0.965146 0.261712i 0.915713π-0.915713\pi
0.965146 0.261712i 0.0842870π-0.0842870\pi
7474 0 0
7575 0 0
7676 0 0
7777 6.47214i 0.737568i
7878 0 0
7979 12.9443 1.45634 0.728172 0.685394i 0.240370π-0.240370\pi
0.728172 + 0.685394i 0.240370π0.240370\pi
8080 0 0
8181 −2.41641 −0.268490
8282 0 0
8383 − 3.70820i − 0.407028i −0.979072 0.203514i 0.934764π-0.934764\pi
0.979072 0.203514i 0.0652363π-0.0652363\pi
8484 0 0
8585 0 0
8686 0 0
8787 2.47214i 0.265041i
8888 0 0
8989 14.9443 1.58409 0.792045 0.610463i 0.209017π-0.209017\pi
0.792045 + 0.610463i 0.209017π0.209017\pi
9090 0 0
9191 −14.4721 −1.51709
9292 0 0
9393 − 8.00000i − 0.829561i
9494 0 0
9595 0 0
9696 0 0
9797 − 16.4721i − 1.67249i −0.548354 0.836246i 0.684746π-0.684746\pi
0.548354 0.836246i 0.315254π-0.315254\pi
9898 0 0
9999 2.94427 0.295910
100100 0 0
101101 −10.0000 −0.995037 −0.497519 0.867453i 0.665755π-0.665755\pi
−0.497519 + 0.867453i 0.665755π0.665755\pi
102102 0 0
103103 3.23607i 0.318859i 0.987209 + 0.159430i 0.0509655π0.0509655\pi
−0.987209 + 0.159430i 0.949034π0.949034\pi
104104 0 0
105105 0 0
106106 0 0
107107 17.2361i 1.66627i 0.553067 + 0.833137i 0.313457π0.313457\pi
−0.553067 + 0.833137i 0.686543π0.686543\pi
108108 0 0
109109 −14.9443 −1.43140 −0.715701 0.698407i 0.753893π-0.753893\pi
−0.715701 + 0.698407i 0.753893π0.753893\pi
110110 0 0
111111 −8.58359 −0.814719
112112 0 0
113113 2.94427i 0.276974i 0.990364 + 0.138487i 0.0442239π0.0442239\pi
−0.990364 + 0.138487i 0.955776π0.955776\pi
114114 0 0
115115 0 0
116116 0 0
117117 6.58359i 0.608653i
118118 0 0
119119 −14.4721 −1.32666
120120 0 0
121121 −7.00000 −0.636364
122122 0 0
123123 15.4164i 1.39005i
124124 0 0
125125 0 0
126126 0 0
127127 20.1803i 1.79072i 0.445348 + 0.895358i 0.353080π0.353080\pi
−0.445348 + 0.895358i 0.646920π0.646920\pi
128128 0 0
129129 9.52786 0.838882
130130 0 0
131131 −14.9443 −1.30569 −0.652844 0.757493i 0.726424π-0.726424\pi
−0.652844 + 0.757493i 0.726424π0.726424\pi
132132 0 0
133133 − 14.4721i − 1.25489i
134134 0 0
135135 0 0
136136 0 0
137137 2.00000i 0.170872i 0.996344 + 0.0854358i 0.0272282π0.0272282\pi
−0.996344 + 0.0854358i 0.972772π0.972772\pi
138138 0 0
139139 20.4721 1.73642 0.868212 0.496194i 0.165269π-0.165269\pi
0.868212 + 0.496194i 0.165269π0.165269\pi
140140 0 0
141141 −8.94427 −0.753244
142142 0 0
143143 8.94427i 0.747958i
144144 0 0
145145 0 0
146146 0 0
147147 − 4.29180i − 0.353981i
148148 0 0
149149 −6.94427 −0.568897 −0.284448 0.958691i 0.591810π-0.591810\pi
−0.284448 + 0.958691i 0.591810π0.591810\pi
150150 0 0
151151 −23.4164 −1.90560 −0.952800 0.303598i 0.901812π-0.901812\pi
−0.952800 + 0.303598i 0.901812π0.901812\pi
152152 0 0
153153 6.58359i 0.532252i
154154 0 0
155155 0 0
156156 0 0
157157 5.05573i 0.403491i 0.979438 + 0.201746i 0.0646614π0.0646614\pi
−0.979438 + 0.201746i 0.935339π0.935339\pi
158158 0 0
159159 0.583592 0.0462819
160160 0 0
161161 15.4164 1.21498
162162 0 0
163163 − 11.7082i − 0.917057i −0.888680 0.458529i 0.848377π-0.848377\pi
0.888680 0.458529i 0.151623π-0.151623\pi
164164 0 0
165165 0 0
166166 0 0
167167 − 14.6525i − 1.13384i −0.823772 0.566921i 0.808134π-0.808134\pi
0.823772 0.566921i 0.191866π-0.191866\pi
168168 0 0
169169 −7.00000 −0.538462
170170 0 0
171171 −6.58359 −0.503460
172172 0 0
173173 10.9443i 0.832078i 0.909347 + 0.416039i 0.136582π0.136582\pi
−0.909347 + 0.416039i 0.863418π0.863418\pi
174174 0 0
175175 0 0
176176 0 0
177177 − 10.4721i − 0.787134i
178178 0 0
179179 −20.4721 −1.53016 −0.765080 0.643936i 0.777300π-0.777300\pi
−0.765080 + 0.643936i 0.777300π0.777300\pi
180180 0 0
181181 10.9443 0.813481 0.406741 0.913544i 0.366665π-0.366665\pi
0.406741 + 0.913544i 0.366665π0.366665\pi
182182 0 0
183183 − 7.41641i − 0.548237i
184184 0 0
185185 0 0
186186 0 0
187187 8.94427i 0.654070i
188188 0 0
189189 −17.8885 −1.30120
190190 0 0
191191 −11.4164 −0.826062 −0.413031 0.910717i 0.635530π-0.635530\pi
−0.413031 + 0.910717i 0.635530π0.635530\pi
192192 0 0
193193 11.5279i 0.829794i 0.909868 + 0.414897i 0.136182π0.136182\pi
−0.909868 + 0.414897i 0.863818π0.863818\pi
194194 0 0
195195 0 0
196196 0 0
197197 0.472136i 0.0336383i 0.999859 + 0.0168191i 0.00535395π0.00535395\pi
−0.999859 + 0.0168191i 0.994646π0.994646\pi
198198 0 0
199199 −0.944272 −0.0669377 −0.0334688 0.999440i 0.510655π-0.510655\pi
−0.0334688 + 0.999440i 0.510655π0.510655\pi
200200 0 0
201201 9.52786 0.672044
202202 0 0
203203 6.47214i 0.454255i
204204 0 0
205205 0 0
206206 0 0
207207 − 7.01316i − 0.487448i
208208 0 0
209209 −8.94427 −0.618688
210210 0 0
211211 1.05573 0.0726793 0.0363397 0.999339i 0.488430π-0.488430\pi
0.0363397 + 0.999339i 0.488430π0.488430\pi
212212 0 0
213213 3.05573i 0.209375i
214214 0 0
215215 0 0
216216 0 0
217217 − 20.9443i − 1.42179i
218218 0 0
219219 5.52786 0.373538
220220 0 0
221221 −20.0000 −1.34535
222222 0 0
223223 − 8.76393i − 0.586876i −0.955978 0.293438i 0.905201π-0.905201\pi
0.955978 0.293438i 0.0947995π-0.0947995\pi
224224 0 0
225225 0 0
226226 0 0
227227 10.1803i 0.675693i 0.941201 + 0.337846i 0.109698π0.109698\pi
−0.941201 + 0.337846i 0.890302π0.890302\pi
228228 0 0
229229 −2.94427 −0.194563 −0.0972815 0.995257i 0.531015π-0.531015\pi
−0.0972815 + 0.995257i 0.531015π0.531015\pi
230230 0 0
231231 −8.00000 −0.526361
232232 0 0
233233 − 15.5279i − 1.01726i −0.860984 0.508632i 0.830151π-0.830151\pi
0.860984 0.508632i 0.169849π-0.169849\pi
234234 0 0
235235 0 0
236236 0 0
237237 16.0000i 1.03931i
238238 0 0
239239 −12.9443 −0.837295 −0.418648 0.908149i 0.637496π-0.637496\pi
−0.418648 + 0.908149i 0.637496π0.637496\pi
240240 0 0
241241 26.3607 1.69804 0.849020 0.528360i 0.177193π-0.177193\pi
0.849020 + 0.528360i 0.177193π0.177193\pi
242242 0 0
243243 13.5967i 0.872232i
244244 0 0
245245 0 0
246246 0 0
247247 − 20.0000i − 1.27257i
248248 0 0
249249 4.58359 0.290473
250250 0 0
251251 2.00000 0.126239 0.0631194 0.998006i 0.479895π-0.479895\pi
0.0631194 + 0.998006i 0.479895π0.479895\pi
252252 0 0
253253 − 9.52786i − 0.599012i
254254 0 0
255255 0 0
256256 0 0
257257 − 2.94427i − 0.183659i −0.995775 0.0918293i 0.970729π-0.970729\pi
0.995775 0.0918293i 0.0292714π-0.0292714\pi
258258 0 0
259259 −22.4721 −1.39635
260260 0 0
261261 2.94427 0.182246
262262 0 0
263263 − 17.7082i − 1.09193i −0.837806 0.545967i 0.816162π-0.816162\pi
0.837806 0.545967i 0.183838π-0.183838\pi
264264 0 0
265265 0 0
266266 0 0
267267 18.4721i 1.13048i
268268 0 0
269269 23.8885 1.45651 0.728255 0.685306i 0.240332π-0.240332\pi
0.728255 + 0.685306i 0.240332π0.240332\pi
270270 0 0
271271 24.3607 1.47981 0.739903 0.672714i 0.234871π-0.234871\pi
0.739903 + 0.672714i 0.234871π0.234871\pi
272272 0 0
273273 − 17.8885i − 1.08266i
274274 0 0
275275 0 0
276276 0 0
277277 − 10.9443i − 0.657578i −0.944403 0.328789i 0.893360π-0.893360\pi
0.944403 0.328789i 0.106640π-0.106640\pi
278278 0 0
279279 −9.52786 −0.570418
280280 0 0
281281 3.52786 0.210455 0.105227 0.994448i 0.466443π-0.466443\pi
0.105227 + 0.994448i 0.466443π0.466443\pi
282282 0 0
283283 8.29180i 0.492896i 0.969156 + 0.246448i 0.0792635π0.0792635\pi
−0.969156 + 0.246448i 0.920737π0.920737\pi
284284 0 0
285285 0 0
286286 0 0
287287 40.3607i 2.38242i
288288 0 0
289289 −3.00000 −0.176471
290290 0 0
291291 20.3607 1.19356
292292 0 0
293293 23.8885i 1.39558i 0.716301 + 0.697792i 0.245834π0.245834\pi
−0.716301 + 0.697792i 0.754166π0.754166\pi
294294 0 0
295295 0 0
296296 0 0
297297 11.0557i 0.641518i
298298 0 0
299299 21.3050 1.23210
300300 0 0
301301 24.9443 1.43776
302302 0 0
303303 − 12.3607i − 0.710102i
304304 0 0
305305 0 0
306306 0 0
307307 0.291796i 0.0166537i 0.999965 + 0.00832684i 0.00265055π0.00265055\pi
−0.999965 + 0.00832684i 0.997349π0.997349\pi
308308 0 0
309309 −4.00000 −0.227552
310310 0 0
311311 15.4164 0.874184 0.437092 0.899417i 0.356008π-0.356008\pi
0.437092 + 0.899417i 0.356008π0.356008\pi
312312 0 0
313313 28.8328i 1.62973i 0.579653 + 0.814864i 0.303188π0.303188\pi
−0.579653 + 0.814864i 0.696812π0.696812\pi
314314 0 0
315315 0 0
316316 0 0
317317 − 20.4721i − 1.14983i −0.818213 0.574915i 0.805035π-0.805035\pi
0.818213 0.574915i 0.194965π-0.194965\pi
318318 0 0
319319 4.00000 0.223957
320320 0 0
321321 −21.3050 −1.18913
322322 0 0
323323 − 20.0000i − 1.11283i
324324 0 0
325325 0 0
326326 0 0
327327 − 18.4721i − 1.02151i
328328 0 0
329329 −23.4164 −1.29099
330330 0 0
331331 −15.8885 −0.873313 −0.436657 0.899628i 0.643838π-0.643838\pi
−0.436657 + 0.899628i 0.643838π0.643838\pi
332332 0 0
333333 10.2229i 0.560212i
334334 0 0
335335 0 0
336336 0 0
337337 5.05573i 0.275403i 0.990474 + 0.137702i 0.0439715π0.0439715\pi
−0.990474 + 0.137702i 0.956029π0.956029\pi
338338 0 0
339339 −3.63932 −0.197661
340340 0 0
341341 −12.9443 −0.700972
342342 0 0
343343 11.4164i 0.616428i
344344 0 0
345345 0 0
346346 0 0
347347 17.2361i 0.925281i 0.886546 + 0.462640i 0.153098π0.153098\pi
−0.886546 + 0.462640i 0.846902π0.846902\pi
348348 0 0
349349 14.9443 0.799949 0.399974 0.916526i 0.369019π-0.369019\pi
0.399974 + 0.916526i 0.369019π0.369019\pi
350350 0 0
351351 −24.7214 −1.31953
352352 0 0
353353 − 5.05573i − 0.269089i −0.990908 0.134545i 0.957043π-0.957043\pi
0.990908 0.134545i 0.0429572π-0.0429572\pi
354354 0 0
355355 0 0
356356 0 0
357357 − 17.8885i − 0.946762i
358358 0 0
359359 −15.0557 −0.794611 −0.397305 0.917686i 0.630055π-0.630055\pi
−0.397305 + 0.917686i 0.630055π0.630055\pi
360360 0 0
361361 1.00000 0.0526316
362362 0 0
363363 − 8.65248i − 0.454137i
364364 0 0
365365 0 0
366366 0 0
367367 18.2918i 0.954824i 0.878680 + 0.477412i 0.158425π0.158425\pi
−0.878680 + 0.477412i 0.841575π0.841575\pi
368368 0 0
369369 18.3607 0.955819
370370 0 0
371371 1.52786 0.0793227
372372 0 0
373373 − 5.05573i − 0.261776i −0.991397 0.130888i 0.958217π-0.958217\pi
0.991397 0.130888i 0.0417828π-0.0417828\pi
374374 0 0
375375 0 0
376376 0 0
377377 8.94427i 0.460653i
378378 0 0
379379 15.5279 0.797613 0.398806 0.917035i 0.369425π-0.369425\pi
0.398806 + 0.917035i 0.369425π0.369425\pi
380380 0 0
381381 −24.9443 −1.27793
382382 0 0
383383 10.2918i 0.525886i 0.964811 + 0.262943i 0.0846932π0.0846932\pi
−0.964811 + 0.262943i 0.915307π0.915307\pi
384384 0 0
385385 0 0
386386 0 0
387387 − 11.3475i − 0.576827i
388388 0 0
389389 −11.8885 −0.602773 −0.301387 0.953502i 0.597449π-0.597449\pi
−0.301387 + 0.953502i 0.597449π0.597449\pi
390390 0 0
391391 21.3050 1.07744
392392 0 0
393393 − 18.4721i − 0.931796i
394394 0 0
395395 0 0
396396 0 0
397397 − 12.4721i − 0.625959i −0.949760 0.312979i 0.898673π-0.898673\pi
0.949760 0.312979i 0.101327π-0.101327\pi
398398 0 0
399399 17.8885 0.895547
400400 0 0
401401 −2.00000 −0.0998752 −0.0499376 0.998752i 0.515902π-0.515902\pi
−0.0499376 + 0.998752i 0.515902π0.515902\pi
402402 0 0
403403 − 28.9443i − 1.44182i
404404 0 0
405405 0 0
406406 0 0
407407 13.8885i 0.688430i
408408 0 0
409409 −17.4164 −0.861186 −0.430593 0.902546i 0.641696π-0.641696\pi
−0.430593 + 0.902546i 0.641696π0.641696\pi
410410 0 0
411411 −2.47214 −0.121941
412412 0 0
413413 − 27.4164i − 1.34907i
414414 0 0
415415 0 0
416416 0 0
417417 25.3050i 1.23919i
418418 0 0
419419 −4.47214 −0.218478 −0.109239 0.994016i 0.534841π-0.534841\pi
−0.109239 + 0.994016i 0.534841π0.534841\pi
420420 0 0
421421 −28.8328 −1.40523 −0.702613 0.711572i 0.747983π-0.747983\pi
−0.702613 + 0.711572i 0.747983π0.747983\pi
422422 0 0
423423 10.6525i 0.517941i
424424 0 0
425425 0 0
426426 0 0
427427 − 19.4164i − 0.939626i
428428 0 0
429429 −11.0557 −0.533776
430430 0 0
431431 24.3607 1.17341 0.586706 0.809800i 0.300424π-0.300424\pi
0.586706 + 0.809800i 0.300424π0.300424\pi
432432 0 0
433433 0.472136i 0.0226894i 0.999936 + 0.0113447i 0.00361121π0.00361121\pi
−0.999936 + 0.0113447i 0.996389π0.996389\pi
434434 0 0
435435 0 0
436436 0 0
437437 21.3050i 1.01915i
438438 0 0
439439 15.0557 0.718571 0.359285 0.933228i 0.383020π-0.383020\pi
0.359285 + 0.933228i 0.383020π0.383020\pi
440440 0 0
441441 −5.11146 −0.243403
442442 0 0
443443 − 4.65248i − 0.221046i −0.993874 0.110523i 0.964747π-0.964747\pi
0.993874 0.110523i 0.0352526π-0.0352526\pi
444444 0 0
445445 0 0
446446 0 0
447447 − 8.58359i − 0.405990i
448448 0 0
449449 1.41641 0.0668444 0.0334222 0.999441i 0.489359π-0.489359\pi
0.0334222 + 0.999441i 0.489359π0.489359\pi
450450 0 0
451451 24.9443 1.17458
452452 0 0
453453 − 28.9443i − 1.35992i
454454 0 0
455455 0 0
456456 0 0
457457 3.88854i 0.181898i 0.995856 + 0.0909492i 0.0289901π0.0289901\pi
−0.995856 + 0.0909492i 0.971010π0.971010\pi
458458 0 0
459459 −24.7214 −1.15389
460460 0 0
461461 41.7771 1.94575 0.972876 0.231325i 0.0743061π-0.0743061\pi
0.972876 + 0.231325i 0.0743061π0.0743061\pi
462462 0 0
463463 1.12461i 0.0522651i 0.999658 + 0.0261326i 0.00831920π0.00831920\pi
−0.999658 + 0.0261326i 0.991681π0.991681\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 41.5967i − 1.92487i −0.271516 0.962434i 0.587525π-0.587525\pi
0.271516 0.962434i 0.412475π-0.412475\pi
468468 0 0
469469 24.9443 1.15182
470470 0 0
471471 −6.24922 −0.287949
472472 0 0
473473 − 15.4164i − 0.708847i
474474 0 0
475475 0 0
476476 0 0
477477 − 0.695048i − 0.0318241i
478478 0 0
479479 12.9443 0.591439 0.295719 0.955275i 0.404441π-0.404441\pi
0.295719 + 0.955275i 0.404441π0.404441\pi
480480 0 0
481481 −31.0557 −1.41602
482482 0 0
483483 19.0557i 0.867066i
484484 0 0
485485 0 0
486486 0 0
487487 − 12.7639i − 0.578389i −0.957270 0.289194i 0.906613π-0.906613\pi
0.957270 0.289194i 0.0933874π-0.0933874\pi
488488 0 0
489489 14.4721 0.654453
490490 0 0
491491 21.0557 0.950232 0.475116 0.879923i 0.342406π-0.342406\pi
0.475116 + 0.879923i 0.342406π0.342406\pi
492492 0 0
493493 8.94427i 0.402830i
494494 0 0
495495 0 0
496496 0 0
497497 8.00000i 0.358849i
498498 0 0
499499 14.5836 0.652851 0.326426 0.945223i 0.394156π-0.394156\pi
0.326426 + 0.945223i 0.394156π0.394156\pi
500500 0 0
501501 18.1115 0.809160
502502 0 0
503503 5.12461i 0.228495i 0.993452 + 0.114248i 0.0364457π0.0364457\pi
−0.993452 + 0.114248i 0.963554π0.963554\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 8.65248i − 0.384270i
508508 0 0
509509 16.8328 0.746101 0.373051 0.927811i 0.378312π-0.378312\pi
0.373051 + 0.927811i 0.378312π0.378312\pi
510510 0 0
511511 14.4721 0.640210
512512 0 0
513513 − 24.7214i − 1.09147i
514514 0 0
515515 0 0
516516 0 0
517517 14.4721i 0.636484i
518518 0 0
519519 −13.5279 −0.593807
520520 0 0
521521 −15.8885 −0.696090 −0.348045 0.937478i 0.613154π-0.613154\pi
−0.348045 + 0.937478i 0.613154π0.613154\pi
522522 0 0
523523 20.0689i 0.877551i 0.898597 + 0.438776i 0.144588π0.144588\pi
−0.898597 + 0.438776i 0.855412π0.855412\pi
524524 0 0
525525 0 0
526526 0 0
527527 − 28.9443i − 1.26083i
528528 0 0
529529 0.304952 0.0132588
530530 0 0
531531 −12.4721 −0.541245
532532 0 0
533533 55.7771i 2.41597i
534534 0 0
535535 0 0
536536 0 0
537537 − 25.3050i − 1.09199i
538538 0 0
539539 −6.94427 −0.299111
540540 0 0
541541 23.8885 1.02705 0.513524 0.858075i 0.328340π-0.328340\pi
0.513524 + 0.858075i 0.328340π0.328340\pi
542542 0 0
543543 13.5279i 0.580536i
544544 0 0
545545 0 0
546546 0 0
547547 − 20.6525i − 0.883036i −0.897252 0.441518i 0.854440π-0.854440\pi
0.897252 0.441518i 0.145560π-0.145560\pi
548548 0 0
549549 −8.83282 −0.376975
550550 0 0
551551 −8.94427 −0.381039
552552 0 0
553553 41.8885i 1.78128i
554554 0 0
555555 0 0
556556 0 0
557557 13.0557i 0.553189i 0.960987 + 0.276594i 0.0892059π0.0892059\pi
−0.960987 + 0.276594i 0.910794π0.910794\pi
558558 0 0
559559 34.4721 1.45802
560560 0 0
561561 −11.0557 −0.466773
562562 0 0
563563 4.29180i 0.180878i 0.995902 + 0.0904388i 0.0288270π0.0288270\pi
−0.995902 + 0.0904388i 0.971173π0.971173\pi
564564 0 0
565565 0 0
566566 0 0
567567 − 7.81966i − 0.328395i
568568 0 0
569569 34.3607 1.44047 0.720237 0.693728i 0.244033π-0.244033\pi
0.720237 + 0.693728i 0.244033π0.244033\pi
570570 0 0
571571 16.8328 0.704431 0.352216 0.935919i 0.385428π-0.385428\pi
0.352216 + 0.935919i 0.385428π0.385428\pi
572572 0 0
573573 − 14.1115i − 0.589515i
574574 0 0
575575 0 0
576576 0 0
577577 19.8885i 0.827971i 0.910283 + 0.413985i 0.135864π0.135864\pi
−0.910283 + 0.413985i 0.864136π0.864136\pi
578578 0 0
579579 −14.2492 −0.592178
580580 0 0
581581 12.0000 0.497844
582582 0 0
583583 − 0.944272i − 0.0391077i
584584 0 0
585585 0 0
586586 0 0
587587 − 8.65248i − 0.357126i −0.983928 0.178563i 0.942855π-0.942855\pi
0.983928 0.178563i 0.0571448π-0.0571448\pi
588588 0 0
589589 28.9443 1.19263
590590 0 0
591591 −0.583592 −0.0240058
592592 0 0
593593 14.0000i 0.574911i 0.957794 + 0.287456i 0.0928094π0.0928094\pi
−0.957794 + 0.287456i 0.907191π0.907191\pi
594594 0 0
595595 0 0
596596 0 0
597597 − 1.16718i − 0.0477697i
598598 0 0
599599 −21.8885 −0.894342 −0.447171 0.894449i 0.647568π-0.647568\pi
−0.447171 + 0.894449i 0.647568π0.647568\pi
600600 0 0
601601 −22.3607 −0.912111 −0.456056 0.889951i 0.650738π-0.650738\pi
−0.456056 + 0.889951i 0.650738π0.650738\pi
602602 0 0
603603 − 11.3475i − 0.462107i
604604 0 0
605605 0 0
606606 0 0
607607 − 6.87539i − 0.279063i −0.990218 0.139532i 0.955440π-0.955440\pi
0.990218 0.139532i 0.0445597π-0.0445597\pi
608608 0 0
609609 −8.00000 −0.324176
610610 0 0
611611 −32.3607 −1.30917
612612 0 0
613613 − 19.5279i − 0.788723i −0.918955 0.394362i 0.870966π-0.870966\pi
0.918955 0.394362i 0.129034π-0.129034\pi
614614 0 0
615615 0 0
616616 0 0
617617 25.4164i 1.02323i 0.859216 + 0.511613i 0.170952π0.170952\pi
−0.859216 + 0.511613i 0.829048π0.829048\pi
618618 0 0
619619 20.4721 0.822845 0.411422 0.911445i 0.365032π-0.365032\pi
0.411422 + 0.911445i 0.365032π0.365032\pi
620620 0 0
621621 26.3344 1.05676
622622 0 0
623623 48.3607i 1.93753i
624624 0 0
625625 0 0
626626 0 0
627627 − 11.0557i − 0.441523i
628628 0 0
629629 −31.0557 −1.23827
630630 0 0
631631 34.4721 1.37231 0.686157 0.727453i 0.259296π-0.259296\pi
0.686157 + 0.727453i 0.259296π0.259296\pi
632632 0 0
633633 1.30495i 0.0518672i
634634 0 0
635635 0 0
636636 0 0
637637 − 15.5279i − 0.615236i
638638 0 0
639639 3.63932 0.143969
640640 0 0
641641 0.472136 0.0186482 0.00932412 0.999957i 0.497032π-0.497032\pi
0.00932412 + 0.999957i 0.497032π0.497032\pi
642642 0 0
643643 22.1803i 0.874707i 0.899290 + 0.437354i 0.144084π0.144084\pi
−0.899290 + 0.437354i 0.855916π0.855916\pi
644644 0 0
645645 0 0
646646 0 0
647647 − 12.7639i − 0.501802i −0.968013 0.250901i 0.919273π-0.919273\pi
0.968013 0.250901i 0.0807269π-0.0807269\pi
648648 0 0
649649 −16.9443 −0.665121
650650 0 0
651651 25.8885 1.01465
652652 0 0
653653 49.4164i 1.93381i 0.255130 + 0.966907i 0.417882π0.417882\pi
−0.255130 + 0.966907i 0.582118π0.582118\pi
654654 0 0
655655 0 0
656656 0 0
657657 − 6.58359i − 0.256850i
658658 0 0
659659 21.4164 0.834265 0.417132 0.908846i 0.363035π-0.363035\pi
0.417132 + 0.908846i 0.363035π0.363035\pi
660660 0 0
661661 35.8885 1.39590 0.697951 0.716145i 0.254095π-0.254095\pi
0.697951 + 0.716145i 0.254095π0.254095\pi
662662 0 0
663663 − 24.7214i − 0.960098i
664664 0 0
665665 0 0
666666 0 0
667667 − 9.52786i − 0.368920i
668668 0 0
669669 10.8328 0.418821
670670 0 0
671671 −12.0000 −0.463255
672672 0 0
673673 23.3050i 0.898340i 0.893446 + 0.449170i 0.148280π0.148280\pi
−0.893446 + 0.449170i 0.851720π0.851720\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 30.3607i − 1.16686i −0.812165 0.583428i 0.801711π-0.801711\pi
0.812165 0.583428i 0.198289π-0.198289\pi
678678 0 0
679679 53.3050 2.04566
680680 0 0
681681 −12.5836 −0.482204
682682 0 0
683683 24.2918i 0.929500i 0.885442 + 0.464750i 0.153856π0.153856\pi
−0.885442 + 0.464750i 0.846144π0.846144\pi
684684 0 0
685685 0 0
686686 0 0
687687 − 3.63932i − 0.138849i
688688 0 0
689689 2.11146 0.0804401
690690 0 0
691691 30.0000 1.14125 0.570627 0.821209i 0.306700π-0.306700\pi
0.570627 + 0.821209i 0.306700π0.306700\pi
692692 0 0
693693 9.52786i 0.361934i
694694 0 0
695695 0 0
696696 0 0
697697 55.7771i 2.11271i
698698 0 0
699699 19.1935 0.725965
700700 0 0
701701 −9.05573 −0.342030 −0.171015 0.985268i 0.554705π-0.554705\pi
−0.171015 + 0.985268i 0.554705π0.554705\pi
702702 0 0
703703 − 31.0557i − 1.17129i
704704 0 0
705705 0 0
706706 0 0
707707 − 32.3607i − 1.21705i
708708 0 0
709709 18.0000 0.676004 0.338002 0.941145i 0.390249π-0.390249\pi
0.338002 + 0.941145i 0.390249π0.390249\pi
710710 0 0
711711 19.0557 0.714646
712712 0 0
713713 30.8328i 1.15470i
714714 0 0
715715 0 0
716716 0 0
717717 − 16.0000i − 0.597531i
718718 0 0
719719 22.8328 0.851520 0.425760 0.904836i 0.360007π-0.360007\pi
0.425760 + 0.904836i 0.360007π0.360007\pi
720720 0 0
721721 −10.4721 −0.390003
722722 0 0
723723 32.5836i 1.21180i
724724 0 0
725725 0 0
726726 0 0
727727 − 1.70820i − 0.0633538i −0.999498 0.0316769i 0.989915π-0.989915\pi
0.999498 0.0316769i 0.0100848π-0.0100848\pi
728728 0 0
729729 −24.0557 −0.890953
730730 0 0
731731 34.4721 1.27500
732732 0 0
733733 − 51.8885i − 1.91655i −0.285853 0.958274i 0.592277π-0.592277\pi
0.285853 0.958274i 0.407723π-0.407723\pi
734734 0 0
735735 0 0
736736 0 0
737737 − 15.4164i − 0.567871i
738738 0 0
739739 49.1935 1.80961 0.904806 0.425824i 0.140016π-0.140016\pi
0.904806 + 0.425824i 0.140016π0.140016\pi
740740 0 0
741741 24.7214 0.908162
742742 0 0
743743 − 30.6525i − 1.12453i −0.826957 0.562265i 0.809930π-0.809930\pi
0.826957 0.562265i 0.190070π-0.190070\pi
744744 0 0
745745 0 0
746746 0 0
747747 − 5.45898i − 0.199734i
748748 0 0
749749 −55.7771 −2.03805
750750 0 0
751751 −16.3607 −0.597010 −0.298505 0.954408i 0.596488π-0.596488\pi
−0.298505 + 0.954408i 0.596488π0.596488\pi
752752 0 0
753753 2.47214i 0.0900896i
754754 0 0
755755 0 0
756756 0 0
757757 19.8885i 0.722861i 0.932399 + 0.361431i 0.117712π0.117712\pi
−0.932399 + 0.361431i 0.882288π0.882288\pi
758758 0 0
759759 11.7771 0.427481
760760 0 0
761761 3.88854 0.140960 0.0704798 0.997513i 0.477547π-0.477547\pi
0.0704798 + 0.997513i 0.477547π0.477547\pi
762762 0 0
763763 − 48.3607i − 1.75077i
764764 0 0
765765 0 0
766766 0 0
767767 − 37.8885i − 1.36808i
768768 0 0
769769 14.9443 0.538904 0.269452 0.963014i 0.413157π-0.413157\pi
0.269452 + 0.963014i 0.413157π0.413157\pi
770770 0 0
771771 3.63932 0.131067
772772 0 0
773773 − 18.3607i − 0.660388i −0.943913 0.330194i 0.892886π-0.892886\pi
0.943913 0.330194i 0.107114π-0.107114\pi
774774 0 0
775775 0 0
776776 0 0
777777 − 27.7771i − 0.996497i
778778 0 0
779779 −55.7771 −1.99842
780780 0 0
781781 4.94427 0.176920
782782 0 0
783783 11.0557i 0.395099i
784784 0 0
785785 0 0
786786 0 0
787787 44.0689i 1.57089i 0.618934 + 0.785443i 0.287565π0.287565\pi
−0.618934 + 0.785443i 0.712435π0.712435\pi
788788 0 0
789789 21.8885 0.779253
790790 0 0
791791 −9.52786 −0.338772
792792 0 0
793793 − 26.8328i − 0.952861i
794794 0 0
795795 0 0
796796 0 0
797797 − 25.4164i − 0.900295i −0.892954 0.450148i 0.851371π-0.851371\pi
0.892954 0.450148i 0.148629π-0.148629\pi
798798 0 0
799799 −32.3607 −1.14484
800800 0 0
801801 22.0000 0.777332
802802 0 0
803803 − 8.94427i − 0.315637i
804804 0 0
805805 0 0
806806 0 0
807807 29.5279i 1.03943i
808808 0 0
809809 12.1115 0.425816 0.212908 0.977072i 0.431707π-0.431707\pi
0.212908 + 0.977072i 0.431707π0.431707\pi
810810 0 0
811811 2.00000 0.0702295 0.0351147 0.999383i 0.488820π-0.488820\pi
0.0351147 + 0.999383i 0.488820π0.488820\pi
812812 0 0
813813 30.1115i 1.05605i
814814 0 0
815815 0 0
816816 0 0
817817 34.4721i 1.20603i
818818 0 0
819819 −21.3050 −0.744455
820820 0 0
821821 21.0557 0.734850 0.367425 0.930053i 0.380239π-0.380239\pi
0.367425 + 0.930053i 0.380239π0.380239\pi
822822 0 0
823823 − 1.70820i − 0.0595442i −0.999557 0.0297721i 0.990522π-0.990522\pi
0.999557 0.0297721i 0.00947816π-0.00947816\pi
824824 0 0
825825 0 0
826826 0 0
827827 6.18034i 0.214911i 0.994210 + 0.107456i 0.0342704π0.0342704\pi
−0.994210 + 0.107456i 0.965730π0.965730\pi
828828 0 0
829829 38.0000 1.31979 0.659897 0.751356i 0.270600π-0.270600\pi
0.659897 + 0.751356i 0.270600π0.270600\pi
830830 0 0
831831 13.5279 0.469276
832832 0 0
833833 − 15.5279i − 0.538009i
834834 0 0
835835 0 0
836836 0 0
837837 − 35.7771i − 1.23664i
838838 0 0
839839 4.00000 0.138095 0.0690477 0.997613i 0.478004π-0.478004\pi
0.0690477 + 0.997613i 0.478004π0.478004\pi
840840 0 0
841841 −25.0000 −0.862069
842842 0 0
843843 4.36068i 0.150190i
844844 0 0
845845 0 0
846846 0 0
847847 − 22.6525i − 0.778348i
848848 0 0
849849 −10.2492 −0.351752
850850 0 0
851851 33.0820 1.13404
852852 0 0
853853 7.52786i 0.257749i 0.991661 + 0.128875i 0.0411365π0.0411365\pi
−0.991661 + 0.128875i 0.958864π0.958864\pi
854854 0 0
855855 0 0
856856 0 0
857857 24.8328i 0.848273i 0.905598 + 0.424136i 0.139422π0.139422\pi
−0.905598 + 0.424136i 0.860578π0.860578\pi
858858 0 0
859859 49.4164 1.68607 0.843033 0.537862i 0.180768π-0.180768\pi
0.843033 + 0.537862i 0.180768π0.180768\pi
860860 0 0
861861 −49.8885 −1.70020
862862 0 0
863863 18.2918i 0.622660i 0.950302 + 0.311330i 0.100774π0.100774\pi
−0.950302 + 0.311330i 0.899226π0.899226\pi
864864 0 0
865865 0 0
866866 0 0
867867 − 3.70820i − 0.125937i
868868 0 0
869869 25.8885 0.878209
870870 0 0
871871 34.4721 1.16804
872872 0 0
873873 − 24.2492i − 0.820712i
874874 0 0
875875 0 0
876876 0 0
877877 51.8885i 1.75215i 0.482173 + 0.876076i 0.339848π0.339848\pi
−0.482173 + 0.876076i 0.660152π0.660152\pi
878878 0 0
879879 −29.5279 −0.995950
880880 0 0
881881 −24.4721 −0.824487 −0.412244 0.911074i 0.635255π-0.635255\pi
−0.412244 + 0.911074i 0.635255π0.635255\pi
882882 0 0
883883 − 27.7082i − 0.932455i −0.884665 0.466228i 0.845613π-0.845613\pi
0.884665 0.466228i 0.154387π-0.154387\pi
884884 0 0
885885 0 0
886886 0 0
887887 − 11.5967i − 0.389381i −0.980865 0.194690i 0.937630π-0.937630\pi
0.980865 0.194690i 0.0623702π-0.0623702\pi
888888 0 0
889889 −65.3050 −2.19026
890890 0 0
891891 −4.83282 −0.161905
892892 0 0
893893 − 32.3607i − 1.08291i
894894 0 0
895895 0 0
896896 0 0
897897 26.3344i 0.879279i
898898 0 0
899899 −12.9443 −0.431716
900900 0 0
901901 2.11146 0.0703428
902902 0 0
903903 30.8328i 1.02605i
904904 0 0
905905 0 0
906906 0 0
907907 9.23607i 0.306679i 0.988174 + 0.153339i 0.0490027π0.0490027\pi
−0.988174 + 0.153339i 0.950997π0.950997\pi
908908 0 0
909909 −14.7214 −0.488277
910910 0 0
911911 53.3050 1.76607 0.883036 0.469305i 0.155496π-0.155496\pi
0.883036 + 0.469305i 0.155496π0.155496\pi
912912 0 0
913913 − 7.41641i − 0.245447i
914914 0 0
915915 0 0
916916 0 0
917917 − 48.3607i − 1.59701i
918918 0 0
919919 −5.88854 −0.194245 −0.0971226 0.995272i 0.530964π-0.530964\pi
−0.0971226 + 0.995272i 0.530964π0.530964\pi
920920 0 0
921921 −0.360680 −0.0118848
922922 0 0
923923 11.0557i 0.363904i
924924 0 0
925925 0 0
926926 0 0
927927 4.76393i 0.156468i
928928 0 0
929929 −24.4721 −0.802905 −0.401452 0.915880i 0.631494π-0.631494\pi
−0.401452 + 0.915880i 0.631494π0.631494\pi
930930 0 0
931931 15.5279 0.508905
932932 0 0
933933 19.0557i 0.623857i
934934 0 0
935935 0 0
936936 0 0
937937 − 3.52786i − 0.115250i −0.998338 0.0576251i 0.981647π-0.981647\pi
0.998338 0.0576251i 0.0183528π-0.0183528\pi
938938 0 0
939939 −35.6393 −1.16305
940940 0 0
941941 44.8328 1.46151 0.730754 0.682641i 0.239169π-0.239169\pi
0.730754 + 0.682641i 0.239169π0.239169\pi
942942 0 0
943943 − 59.4164i − 1.93486i
944944 0 0
945945 0 0
946946 0 0
947947 − 21.8197i − 0.709044i −0.935048 0.354522i 0.884644π-0.884644\pi
0.935048 0.354522i 0.115356π-0.115356\pi
948948 0 0
949949 20.0000 0.649227
950950 0 0
951951 25.3050 0.820569
952952 0 0
953953 − 45.7771i − 1.48287i −0.671027 0.741433i 0.734147π-0.734147\pi
0.671027 0.741433i 0.265853π-0.265853\pi
954954 0 0
955955 0 0
956956 0 0
957957 4.94427i 0.159826i
958958 0 0
959959 −6.47214 −0.208996
960960 0 0
961961 10.8885 0.351243
962962 0 0
963963 25.3738i 0.817660i
964964 0 0
965965 0 0
966966 0 0
967967 1.34752i 0.0433335i 0.999765 + 0.0216667i 0.00689727π0.00689727\pi
−0.999765 + 0.0216667i 0.993103π0.993103\pi
968968 0 0
969969 24.7214 0.794164
970970 0 0
971971 −23.8885 −0.766620 −0.383310 0.923620i 0.625216π-0.625216\pi
−0.383310 + 0.923620i 0.625216π0.625216\pi
972972 0 0
973973 66.2492i 2.12385i
974974 0 0
975975 0 0
976976 0 0
977977 − 39.3050i − 1.25748i −0.777617 0.628738i 0.783572π-0.783572\pi
0.777617 0.628738i 0.216428π-0.216428\pi
978978 0 0
979979 29.8885 0.955242
980980 0 0
981981 −22.0000 −0.702406
982982 0 0
983983 39.0132i 1.24433i 0.782888 + 0.622163i 0.213746π0.213746\pi
−0.782888 + 0.622163i 0.786254π0.786254\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 28.9443i − 0.921306i
988988 0 0
989989 −36.7214 −1.16767
990990 0 0
991991 17.5279 0.556791 0.278395 0.960467i 0.410197π-0.410197\pi
0.278395 + 0.960467i 0.410197π0.410197\pi
992992 0 0
993993 − 19.6393i − 0.623235i
994994 0 0
995995 0 0
996996 0 0
997997 − 34.5836i − 1.09527i −0.836716 0.547637i 0.815528π-0.815528\pi
0.836716 0.547637i 0.184472π-0.184472\pi
998998 0 0
999999 −38.3870 −1.21451
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.c.w.2049.3 4
4.3 odd 2 3200.2.c.u.2049.2 4
5.2 odd 4 3200.2.a.be.1.2 2
5.3 odd 4 640.2.a.k.1.1 yes 2
5.4 even 2 inner 3200.2.c.w.2049.2 4
8.3 odd 2 3200.2.c.x.2049.3 4
8.5 even 2 3200.2.c.v.2049.2 4
15.8 even 4 5760.2.a.ci.1.2 2
20.3 even 4 640.2.a.i.1.2 2
20.7 even 4 3200.2.a.bl.1.1 2
20.19 odd 2 3200.2.c.u.2049.3 4
40.3 even 4 640.2.a.l.1.1 yes 2
40.13 odd 4 640.2.a.j.1.2 yes 2
40.19 odd 2 3200.2.c.x.2049.2 4
40.27 even 4 3200.2.a.bf.1.2 2
40.29 even 2 3200.2.c.v.2049.3 4
40.37 odd 4 3200.2.a.bk.1.1 2
60.23 odd 4 5760.2.a.ch.1.1 2
80.3 even 4 1280.2.d.m.641.3 4
80.13 odd 4 1280.2.d.k.641.2 4
80.43 even 4 1280.2.d.m.641.2 4
80.53 odd 4 1280.2.d.k.641.3 4
120.53 even 4 5760.2.a.cd.1.2 2
120.83 odd 4 5760.2.a.bw.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.a.i.1.2 2 20.3 even 4
640.2.a.j.1.2 yes 2 40.13 odd 4
640.2.a.k.1.1 yes 2 5.3 odd 4
640.2.a.l.1.1 yes 2 40.3 even 4
1280.2.d.k.641.2 4 80.13 odd 4
1280.2.d.k.641.3 4 80.53 odd 4
1280.2.d.m.641.2 4 80.43 even 4
1280.2.d.m.641.3 4 80.3 even 4
3200.2.a.be.1.2 2 5.2 odd 4
3200.2.a.bf.1.2 2 40.27 even 4
3200.2.a.bk.1.1 2 40.37 odd 4
3200.2.a.bl.1.1 2 20.7 even 4
3200.2.c.u.2049.2 4 4.3 odd 2
3200.2.c.u.2049.3 4 20.19 odd 2
3200.2.c.v.2049.2 4 8.5 even 2
3200.2.c.v.2049.3 4 40.29 even 2
3200.2.c.w.2049.2 4 5.4 even 2 inner
3200.2.c.w.2049.3 4 1.1 even 1 trivial
3200.2.c.x.2049.2 4 40.19 odd 2
3200.2.c.x.2049.3 4 8.3 odd 2
5760.2.a.bw.1.1 2 120.83 odd 4
5760.2.a.cd.1.2 2 120.53 even 4
5760.2.a.ch.1.1 2 60.23 odd 4
5760.2.a.ci.1.2 2 15.8 even 4