Properties

Label 3800.2.d.m.3649.5
Level 38003800
Weight 22
Character 3800.3649
Analytic conductor 30.34330.343
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [3800,2,Mod(3649,3800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3800, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3800.3649"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 3800=235219 3800 = 2^{3} \cdot 5^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3800.d (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,0,0,0,0,0,0,-2,0,-6,0,0,0,0,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 30.343152768130.3431527681
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.4227136.2
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x6+9x4+22x2+9 x^{6} + 9x^{4} + 22x^{2} + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a23]\Z[a_1, \ldots, a_{23}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 3649.5
Root 2.19869i-2.19869i of defining polynomial
Character χ\chi == 3800.3649
Dual form 3800.2.d.m.3649.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.83424iq3+1.83424iq70.364448q9+0.834243q112.19869iq132.56314iq17+1.00000q193.36445q21+0.635552iq23+4.83424iq27+9.62901q296.59607q31+1.53020iq33+5.23163iq37+4.03293q39+4.43032q41+7.06587iq43+9.86718iq47+3.63555q49+4.70142q510.668486iq53+1.83424iq570.397382q59+2.26456q610.668486iq63+2.43686iq671.16576q69+4.12628q71+9.49073iq73+1.53020iq772.62901q799.96052q8110.8277iq83+17.6619iq87+5.97252q89+4.03293q9112.0988iq9310.5961iq970.304038q99+O(q100)q+1.83424i q^{3} +1.83424i q^{7} -0.364448 q^{9} +0.834243 q^{11} -2.19869i q^{13} -2.56314i q^{17} +1.00000 q^{19} -3.36445 q^{21} +0.635552i q^{23} +4.83424i q^{27} +9.62901 q^{29} -6.59607 q^{31} +1.53020i q^{33} +5.23163i q^{37} +4.03293 q^{39} +4.43032 q^{41} +7.06587i q^{43} +9.86718i q^{47} +3.63555 q^{49} +4.70142 q^{51} -0.668486i q^{53} +1.83424i q^{57} -0.397382 q^{59} +2.26456 q^{61} -0.668486i q^{63} +2.43686i q^{67} -1.16576 q^{69} +4.12628 q^{71} +9.49073i q^{73} +1.53020i q^{77} -2.62901 q^{79} -9.96052 q^{81} -10.8277i q^{83} +17.6619i q^{87} +5.97252 q^{89} +4.03293 q^{91} -12.0988i q^{93} -10.5961i q^{97} -0.304038 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q2q96q11+6q1920q21+2q296q31+2q3918q41+22q4916q51+20q5942q6118q69+2q71+40q7926q818q89+2q91++20q99+O(q100) 6 q - 2 q^{9} - 6 q^{11} + 6 q^{19} - 20 q^{21} + 2 q^{29} - 6 q^{31} + 2 q^{39} - 18 q^{41} + 22 q^{49} - 16 q^{51} + 20 q^{59} - 42 q^{61} - 18 q^{69} + 2 q^{71} + 40 q^{79} - 26 q^{81} - 8 q^{89} + 2 q^{91}+ \cdots + 20 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3800Z)×\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times.

nn 401401 951951 19011901 19771977
χ(n)\chi(n) 11 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 1.83424i 1.05900i 0.848310 + 0.529500i 0.177621π0.177621\pi
−0.848310 + 0.529500i 0.822379π0.822379\pi
44 0 0
55 0 0
66 0 0
77 1.83424i 0.693279i 0.937998 + 0.346639i 0.112677π0.112677\pi
−0.937998 + 0.346639i 0.887323π0.887323\pi
88 0 0
99 −0.364448 −0.121483
1010 0 0
1111 0.834243 0.251534 0.125767 0.992060i 0.459861π-0.459861\pi
0.125767 + 0.992060i 0.459861π0.459861\pi
1212 0 0
1313 − 2.19869i − 0.609807i −0.952383 0.304904i 0.901376π-0.901376\pi
0.952383 0.304904i 0.0986243π-0.0986243\pi
1414 0 0
1515 0 0
1616 0 0
1717 − 2.56314i − 0.621653i −0.950467 0.310826i 0.899394π-0.899394\pi
0.950467 0.310826i 0.100606π-0.100606\pi
1818 0 0
1919 1.00000 0.229416
2020 0 0
2121 −3.36445 −0.734183
2222 0 0
2323 0.635552i 0.132522i 0.997802 + 0.0662609i 0.0211070π0.0211070\pi
−0.997802 + 0.0662609i 0.978893π0.978893\pi
2424 0 0
2525 0 0
2626 0 0
2727 4.83424i 0.930351i
2828 0 0
2929 9.62901 1.78806 0.894031 0.448005i 0.147865π-0.147865\pi
0.894031 + 0.448005i 0.147865π0.147865\pi
3030 0 0
3131 −6.59607 −1.18469 −0.592345 0.805684i 0.701798π-0.701798\pi
−0.592345 + 0.805684i 0.701798π0.701798\pi
3232 0 0
3333 1.53020i 0.266374i
3434 0 0
3535 0 0
3636 0 0
3737 5.23163i 0.860074i 0.902811 + 0.430037i 0.141499π0.141499\pi
−0.902811 + 0.430037i 0.858501π0.858501\pi
3838 0 0
3939 4.03293 0.645786
4040 0 0
4141 4.43032 0.691899 0.345950 0.938253i 0.387557π-0.387557\pi
0.345950 + 0.938253i 0.387557π0.387557\pi
4242 0 0
4343 7.06587i 1.07753i 0.842455 + 0.538767i 0.181110π0.181110\pi
−0.842455 + 0.538767i 0.818890π0.818890\pi
4444 0 0
4545 0 0
4646 0 0
4747 9.86718i 1.43928i 0.694350 + 0.719638i 0.255692π0.255692\pi
−0.694350 + 0.719638i 0.744308π0.744308\pi
4848 0 0
4949 3.63555 0.519365
5050 0 0
5151 4.70142 0.658331
5252 0 0
5353 − 0.668486i − 0.0918237i −0.998945 0.0459118i 0.985381π-0.985381\pi
0.998945 0.0459118i 0.0146193π-0.0146193\pi
5454 0 0
5555 0 0
5656 0 0
5757 1.83424i 0.242951i
5858 0 0
5959 −0.397382 −0.0517348 −0.0258674 0.999665i 0.508235π-0.508235\pi
−0.0258674 + 0.999665i 0.508235π0.508235\pi
6060 0 0
6161 2.26456 0.289947 0.144974 0.989436i 0.453690π-0.453690\pi
0.144974 + 0.989436i 0.453690π0.453690\pi
6262 0 0
6363 − 0.668486i − 0.0842214i
6464 0 0
6565 0 0
6666 0 0
6767 2.43686i 0.297710i 0.988859 + 0.148855i 0.0475588π0.0475588\pi
−0.988859 + 0.148855i 0.952441π0.952441\pi
6868 0 0
6969 −1.16576 −0.140341
7070 0 0
7171 4.12628 0.489699 0.244850 0.969561i 0.421261π-0.421261\pi
0.244850 + 0.969561i 0.421261π0.421261\pi
7272 0 0
7373 9.49073i 1.11081i 0.831581 + 0.555403i 0.187436π0.187436\pi
−0.831581 + 0.555403i 0.812564π0.812564\pi
7474 0 0
7575 0 0
7676 0 0
7777 1.53020i 0.174383i
7878 0 0
7979 −2.62901 −0.295787 −0.147893 0.989003i 0.547249π-0.547249\pi
−0.147893 + 0.989003i 0.547249π0.547249\pi
8080 0 0
8181 −9.96052 −1.10672
8282 0 0
8383 − 10.8277i − 1.18849i −0.804282 0.594247i 0.797450π-0.797450\pi
0.804282 0.594247i 0.202550π-0.202550\pi
8484 0 0
8585 0 0
8686 0 0
8787 17.6619i 1.89356i
8888 0 0
8989 5.97252 0.633086 0.316543 0.948578i 0.397478π-0.397478\pi
0.316543 + 0.948578i 0.397478π0.397478\pi
9090 0 0
9191 4.03293 0.422766
9292 0 0
9393 − 12.0988i − 1.25459i
9494 0 0
9595 0 0
9696 0 0
9797 − 10.5961i − 1.07587i −0.842987 0.537934i 0.819205π-0.819205\pi
0.842987 0.537934i 0.180795π-0.180795\pi
9898 0 0
9999 −0.304038 −0.0305570
100100 0 0
101101 −14.6290 −1.45564 −0.727820 0.685768i 0.759467π-0.759467\pi
−0.727820 + 0.685768i 0.759467π0.759467\pi
102102 0 0
103103 7.50273i 0.739266i 0.929178 + 0.369633i 0.120517π0.120517\pi
−0.929178 + 0.369633i 0.879483π0.879483\pi
104104 0 0
105105 0 0
106106 0 0
107107 14.7014i 1.42124i 0.703576 + 0.710620i 0.251585π0.251585\pi
−0.703576 + 0.710620i 0.748415π0.748415\pi
108108 0 0
109109 1.30404 0.124904 0.0624521 0.998048i 0.480108π-0.480108\pi
0.0624521 + 0.998048i 0.480108π0.480108\pi
110110 0 0
111111 −9.59607 −0.910819
112112 0 0
113113 1.13282i 0.106567i 0.998579 + 0.0532835i 0.0169687π0.0169687\pi
−0.998579 + 0.0532835i 0.983031π0.983031\pi
114114 0 0
115115 0 0
116116 0 0
117117 0.801309i 0.0740810i
118118 0 0
119119 4.70142 0.430979
120120 0 0
121121 −10.3040 −0.936731
122122 0 0
123123 8.12628i 0.732722i
124124 0 0
125125 0 0
126126 0 0
127127 − 4.88811i − 0.433750i −0.976199 0.216875i 0.930414π-0.930414\pi
0.976199 0.216875i 0.0695863π-0.0695863\pi
128128 0 0
129129 −12.9605 −1.14111
130130 0 0
131131 −1.96707 −0.171863 −0.0859317 0.996301i 0.527387π-0.527387\pi
−0.0859317 + 0.996301i 0.527387π0.527387\pi
132132 0 0
133133 1.83424i 0.159049i
134134 0 0
135135 0 0
136136 0 0
137137 3.49073i 0.298233i 0.988820 + 0.149116i 0.0476429π0.0476429\pi
−0.988820 + 0.149116i 0.952357π0.952357\pi
138138 0 0
139139 15.2526 1.29371 0.646853 0.762615i 0.276085π-0.276085\pi
0.646853 + 0.762615i 0.276085π0.276085\pi
140140 0 0
141141 −18.0988 −1.52419
142142 0 0
143143 − 1.83424i − 0.153387i
144144 0 0
145145 0 0
146146 0 0
147147 6.66849i 0.550007i
148148 0 0
149149 −1.70142 −0.139386 −0.0696929 0.997568i 0.522202π-0.522202\pi
−0.0696929 + 0.997568i 0.522202π0.522202\pi
150150 0 0
151151 −4.80131 −0.390725 −0.195362 0.980731i 0.562588π-0.562588\pi
−0.195362 + 0.980731i 0.562588π0.562588\pi
152152 0 0
153153 0.934131i 0.0755200i
154154 0 0
155155 0 0
156156 0 0
157157 1.55114i 0.123794i 0.998083 + 0.0618971i 0.0197151π0.0197151\pi
−0.998083 + 0.0618971i 0.980285π0.980285\pi
158158 0 0
159159 1.22617 0.0972413
160160 0 0
161161 −1.16576 −0.0918745
162162 0 0
163163 − 5.25910i − 0.411925i −0.978560 0.205962i 0.933968π-0.933968\pi
0.978560 0.205962i 0.0660324π-0.0660324\pi
164164 0 0
165165 0 0
166166 0 0
167167 3.56968i 0.276230i 0.990416 + 0.138115i 0.0441044π0.0441044\pi
−0.990416 + 0.138115i 0.955896π0.955896\pi
168168 0 0
169169 8.16576 0.628135
170170 0 0
171171 −0.364448 −0.0278700
172172 0 0
173173 19.9660i 1.51799i 0.651099 + 0.758993i 0.274308π0.274308\pi
−0.651099 + 0.758993i 0.725692π0.725692\pi
174174 0 0
175175 0 0
176176 0 0
177177 − 0.728896i − 0.0547872i
178178 0 0
179179 −16.1921 −1.21026 −0.605129 0.796127i 0.706878π-0.706878\pi
−0.605129 + 0.796127i 0.706878π0.706878\pi
180180 0 0
181181 −13.2107 −0.981943 −0.490972 0.871176i 0.663358π-0.663358\pi
−0.490972 + 0.871176i 0.663358π0.663358\pi
182182 0 0
183183 4.15375i 0.307054i
184184 0 0
185185 0 0
186186 0 0
187187 − 2.13828i − 0.156367i
188188 0 0
189189 −8.86718 −0.644992
190190 0 0
191191 −1.37645 −0.0995965 −0.0497982 0.998759i 0.515858π-0.515858\pi
−0.0497982 + 0.998759i 0.515858π0.515858\pi
192192 0 0
193193 − 2.21962i − 0.159772i −0.996804 0.0798860i 0.974544π-0.974544\pi
0.996804 0.0798860i 0.0254556π-0.0254556\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 16.0264i − 1.14183i −0.821008 0.570917i 0.806588π-0.806588\pi
0.821008 0.570917i 0.193412π-0.193412\pi
198198 0 0
199199 7.56314 0.536137 0.268068 0.963400i 0.413615π-0.413615\pi
0.268068 + 0.963400i 0.413615π0.413615\pi
200200 0 0
201201 −4.46980 −0.315275
202202 0 0
203203 17.6619i 1.23963i
204204 0 0
205205 0 0
206206 0 0
207207 − 0.231626i − 0.0160991i
208208 0 0
209209 0.834243 0.0577058
210210 0 0
211211 −7.18669 −0.494752 −0.247376 0.968920i 0.579568π-0.579568\pi
−0.247376 + 0.968920i 0.579568π0.579568\pi
212212 0 0
213213 7.56860i 0.518592i
214214 0 0
215215 0 0
216216 0 0
217217 − 12.0988i − 0.821320i
218218 0 0
219219 −17.4083 −1.17634
220220 0 0
221221 −5.63555 −0.379088
222222 0 0
223223 17.6739i 1.18353i 0.806109 + 0.591767i 0.201570π0.201570\pi
−0.806109 + 0.591767i 0.798430π0.798430\pi
224224 0 0
225225 0 0
226226 0 0
227227 10.7618i 0.714288i 0.934049 + 0.357144i 0.116249π0.116249\pi
−0.934049 + 0.357144i 0.883751π0.883751\pi
228228 0 0
229229 7.66194 0.506315 0.253158 0.967425i 0.418531π-0.418531\pi
0.253158 + 0.967425i 0.418531π0.418531\pi
230230 0 0
231231 −2.80677 −0.184672
232232 0 0
233233 8.03948i 0.526684i 0.964703 + 0.263342i 0.0848247π0.0848247\pi
−0.964703 + 0.263342i 0.915175π0.915175\pi
234234 0 0
235235 0 0
236236 0 0
237237 − 4.82224i − 0.313238i
238238 0 0
239239 24.3304 1.57380 0.786902 0.617078i 0.211684π-0.211684\pi
0.786902 + 0.617078i 0.211684π0.211684\pi
240240 0 0
241241 5.15921 0.332334 0.166167 0.986098i 0.446861π-0.446861\pi
0.166167 + 0.986098i 0.446861π0.446861\pi
242242 0 0
243243 − 3.76729i − 0.241672i
244244 0 0
245245 0 0
246246 0 0
247247 − 2.19869i − 0.139899i
248248 0 0
249249 19.8606 1.25862
250250 0 0
251251 7.95159 0.501900 0.250950 0.968000i 0.419257π-0.419257\pi
0.250950 + 0.968000i 0.419257π0.419257\pi
252252 0 0
253253 0.530205i 0.0333337i
254254 0 0
255255 0 0
256256 0 0
257257 7.02639i 0.438294i 0.975692 + 0.219147i 0.0703275π0.0703275\pi
−0.975692 + 0.219147i 0.929673π0.929673\pi
258258 0 0
259259 −9.59607 −0.596271
260260 0 0
261261 −3.50927 −0.217219
262262 0 0
263263 1.20415i 0.0742511i 0.999311 + 0.0371255i 0.0118201π0.0118201\pi
−0.999311 + 0.0371255i 0.988180π0.988180\pi
264264 0 0
265265 0 0
266266 0 0
267267 10.9551i 0.670439i
268268 0 0
269269 −9.74090 −0.593913 −0.296957 0.954891i 0.595972π-0.595972\pi
−0.296957 + 0.954891i 0.595972π0.595972\pi
270270 0 0
271271 −16.2371 −0.986333 −0.493166 0.869935i 0.664161π-0.664161\pi
−0.493166 + 0.869935i 0.664161π0.664161\pi
272272 0 0
273273 7.39738i 0.447710i
274274 0 0
275275 0 0
276276 0 0
277277 − 19.6739i − 1.18209i −0.806638 0.591046i 0.798715π-0.798715\pi
0.806638 0.591046i 0.201285π-0.201285\pi
278278 0 0
279279 2.40393 0.143919
280280 0 0
281281 −12.5841 −0.750703 −0.375351 0.926883i 0.622478π-0.622478\pi
−0.375351 + 0.926883i 0.622478π0.622478\pi
282282 0 0
283283 − 14.0329i − 0.834171i −0.908867 0.417086i 0.863051π-0.863051\pi
0.908867 0.417086i 0.136949π-0.136949\pi
284284 0 0
285285 0 0
286286 0 0
287287 8.12628i 0.479679i
288288 0 0
289289 10.4303 0.613548
290290 0 0
291291 19.4358 1.13935
292292 0 0
293293 17.3095i 1.01123i 0.862759 + 0.505616i 0.168735π0.168735\pi
−0.862759 + 0.505616i 0.831265π0.831265\pi
294294 0 0
295295 0 0
296296 0 0
297297 4.03293i 0.234015i
298298 0 0
299299 1.39738 0.0808127
300300 0 0
301301 −12.9605 −0.747032
302302 0 0
303303 − 26.8332i − 1.54152i
304304 0 0
305305 0 0
306306 0 0
307307 − 16.0384i − 0.915359i −0.889117 0.457680i 0.848681π-0.848681\pi
0.889117 0.457680i 0.151319π-0.151319\pi
308308 0 0
309309 −13.7618 −0.782883
310310 0 0
311311 −20.5411 −1.16478 −0.582390 0.812909i 0.697882π-0.697882\pi
−0.582390 + 0.812909i 0.697882π0.697882\pi
312312 0 0
313313 9.44232i 0.533711i 0.963736 + 0.266856i 0.0859847π0.0859847\pi
−0.963736 + 0.266856i 0.914015π0.914015\pi
314314 0 0
315315 0 0
316316 0 0
317317 0.0329344i 0.00184978i 1.00000 0.000924891i 0.000294402π0.000294402\pi
−1.00000 0.000924891i 0.999706π0.999706\pi
318318 0 0
319319 8.03293 0.449758
320320 0 0
321321 −26.9660 −1.50509
322322 0 0
323323 − 2.56314i − 0.142617i
324324 0 0
325325 0 0
326326 0 0
327327 2.39192i 0.132274i
328328 0 0
329329 −18.0988 −0.997819
330330 0 0
331331 32.5226 1.78760 0.893801 0.448463i 0.148029π-0.148029\pi
0.893801 + 0.448463i 0.148029π0.148029\pi
332332 0 0
333333 − 1.90666i − 0.104484i
334334 0 0
335335 0 0
336336 0 0
337337 − 29.1252i − 1.58655i −0.608863 0.793275i 0.708374π-0.708374\pi
0.608863 0.793275i 0.291626π-0.291626\pi
338338 0 0
339339 −2.07787 −0.112855
340340 0 0
341341 −5.50273 −0.297990
342342 0 0
343343 19.5082i 1.05334i
344344 0 0
345345 0 0
346346 0 0
347347 − 15.8266i − 0.849617i −0.905283 0.424809i 0.860341π-0.860341\pi
0.905283 0.424809i 0.139659π-0.139659\pi
348348 0 0
349349 −34.1911 −1.83021 −0.915103 0.403221i 0.867891π-0.867891\pi
−0.915103 + 0.403221i 0.867891π0.867891\pi
350350 0 0
351351 10.6290 0.567334
352352 0 0
353353 26.9330i 1.43350i 0.697329 + 0.716751i 0.254371π0.254371\pi
−0.697329 + 0.716751i 0.745629π0.745629\pi
354354 0 0
355355 0 0
356356 0 0
357357 8.62355i 0.456407i
358358 0 0
359359 8.22270 0.433977 0.216989 0.976174i 0.430377π-0.430377\pi
0.216989 + 0.976174i 0.430377π0.430377\pi
360360 0 0
361361 1.00000 0.0526316
362362 0 0
363363 − 18.9001i − 0.991999i
364364 0 0
365365 0 0
366366 0 0
367367 30.3514i 1.58433i 0.610308 + 0.792164i 0.291046π0.291046\pi
−0.610308 + 0.792164i 0.708954π0.708954\pi
368368 0 0
369369 −1.61462 −0.0840538
370370 0 0
371371 1.22617 0.0636594
372372 0 0
373373 − 29.4018i − 1.52237i −0.648538 0.761183i 0.724619π-0.724619\pi
0.648538 0.761183i 0.275381π-0.275381\pi
374374 0 0
375375 0 0
376376 0 0
377377 − 21.1712i − 1.09037i
378378 0 0
379379 13.8013 0.708926 0.354463 0.935070i 0.384664π-0.384664\pi
0.354463 + 0.935070i 0.384664π0.384664\pi
380380 0 0
381381 8.96598 0.459341
382382 0 0
383383 10.5961i 0.541434i 0.962659 + 0.270717i 0.0872608π0.0872608\pi
−0.962659 + 0.270717i 0.912739π0.912739\pi
384384 0 0
385385 0 0
386386 0 0
387387 − 2.57514i − 0.130902i
388388 0 0
389389 −1.84972 −0.0937843 −0.0468922 0.998900i 0.514932π-0.514932\pi
−0.0468922 + 0.998900i 0.514932π0.514932\pi
390390 0 0
391391 1.62901 0.0823825
392392 0 0
393393 − 3.60808i − 0.182003i
394394 0 0
395395 0 0
396396 0 0
397397 0.998915i 0.0501341i 0.999686 + 0.0250671i 0.00797993π0.00797993\pi
−0.999686 + 0.0250671i 0.992020π0.992020\pi
398398 0 0
399399 −3.36445 −0.168433
400400 0 0
401401 17.2371 0.860779 0.430389 0.902643i 0.358376π-0.358376\pi
0.430389 + 0.902643i 0.358376π0.358376\pi
402402 0 0
403403 14.5027i 0.722432i
404404 0 0
405405 0 0
406406 0 0
407407 4.36445i 0.216338i
408408 0 0
409409 −8.43578 −0.417122 −0.208561 0.978009i 0.566878π-0.566878\pi
−0.208561 + 0.978009i 0.566878π0.566878\pi
410410 0 0
411411 −6.40284 −0.315829
412412 0 0
413413 − 0.728896i − 0.0358666i
414414 0 0
415415 0 0
416416 0 0
417417 27.9769i 1.37003i
418418 0 0
419419 −7.38538 −0.360799 −0.180400 0.983593i 0.557739π-0.557739\pi
−0.180400 + 0.983593i 0.557739π0.557739\pi
420420 0 0
421421 −32.7278 −1.59506 −0.797528 0.603282i 0.793859π-0.793859\pi
−0.797528 + 0.603282i 0.793859π0.793859\pi
422422 0 0
423423 − 3.59607i − 0.174847i
424424 0 0
425425 0 0
426426 0 0
427427 4.15375i 0.201014i
428428 0 0
429429 3.36445 0.162437
430430 0 0
431431 −18.2789 −0.880466 −0.440233 0.897884i 0.645104π-0.645104\pi
−0.440233 + 0.897884i 0.645104π0.645104\pi
432432 0 0
433433 19.4172i 0.933132i 0.884486 + 0.466566i 0.154509π0.154509\pi
−0.884486 + 0.466566i 0.845491π0.845491\pi
434434 0 0
435435 0 0
436436 0 0
437437 0.635552i 0.0304026i
438438 0 0
439439 21.4423 1.02339 0.511693 0.859168i 0.329019π-0.329019\pi
0.511693 + 0.859168i 0.329019π0.329019\pi
440440 0 0
441441 −1.32497 −0.0630938
442442 0 0
443443 11.4118i 0.542190i 0.962553 + 0.271095i 0.0873857π0.0873857\pi
−0.962553 + 0.271095i 0.912614π0.912614\pi
444444 0 0
445445 0 0
446446 0 0
447447 − 3.12082i − 0.147610i
448448 0 0
449449 −31.8122 −1.50131 −0.750656 0.660693i 0.770262π-0.770262\pi
−0.750656 + 0.660693i 0.770262π0.770262\pi
450450 0 0
451451 3.69596 0.174036
452452 0 0
453453 − 8.80677i − 0.413778i
454454 0 0
455455 0 0
456456 0 0
457457 − 19.5357i − 0.913840i −0.889508 0.456920i 0.848953π-0.848953\pi
0.889508 0.456920i 0.151047π-0.151047\pi
458458 0 0
459459 12.3908 0.578355
460460 0 0
461461 36.7333 1.71084 0.855419 0.517936i 0.173299π-0.173299\pi
0.855419 + 0.517936i 0.173299π0.173299\pi
462462 0 0
463463 − 6.00654i − 0.279148i −0.990212 0.139574i 0.955427π-0.955427\pi
0.990212 0.139574i 0.0445733π-0.0445733\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 33.4776i − 1.54916i −0.632476 0.774580i 0.717961π-0.717961\pi
0.632476 0.774580i 0.282039π-0.282039\pi
468468 0 0
469469 −4.46980 −0.206396
470470 0 0
471471 −2.84516 −0.131098
472472 0 0
473473 5.89465i 0.271036i
474474 0 0
475475 0 0
476476 0 0
477477 0.243629i 0.0111550i
478478 0 0
479479 30.6609 1.40093 0.700465 0.713687i 0.252976π-0.252976\pi
0.700465 + 0.713687i 0.252976π0.252976\pi
480480 0 0
481481 11.5027 0.524479
482482 0 0
483483 − 2.13828i − 0.0972952i
484484 0 0
485485 0 0
486486 0 0
487487 9.11735i 0.413147i 0.978431 + 0.206573i 0.0662312π0.0662312\pi
−0.978431 + 0.206573i 0.933769π0.933769\pi
488488 0 0
489489 9.64647 0.436228
490490 0 0
491491 7.36991 0.332599 0.166300 0.986075i 0.446818π-0.446818\pi
0.166300 + 0.986075i 0.446818π0.446818\pi
492492 0 0
493493 − 24.6805i − 1.11155i
494494 0 0
495495 0 0
496496 0 0
497497 7.56860i 0.339498i
498498 0 0
499499 13.1712 0.589625 0.294812 0.955555i 0.404743π-0.404743\pi
0.294812 + 0.955555i 0.404743π0.404743\pi
500500 0 0
501501 −6.54767 −0.292528
502502 0 0
503503 − 17.0024i − 0.758099i −0.925376 0.379049i 0.876251π-0.876251\pi
0.925376 0.379049i 0.123749π-0.123749\pi
504504 0 0
505505 0 0
506506 0 0
507507 14.9780i 0.665196i
508508 0 0
509509 −21.4489 −0.950704 −0.475352 0.879796i 0.657679π-0.657679\pi
−0.475352 + 0.879796i 0.657679π0.657679\pi
510510 0 0
511511 −17.4083 −0.770098
512512 0 0
513513 4.83424i 0.213437i
514514 0 0
515515 0 0
516516 0 0
517517 8.23163i 0.362026i
518518 0 0
519519 −36.6225 −1.60755
520520 0 0
521521 12.5182 0.548432 0.274216 0.961668i 0.411582π-0.411582\pi
0.274216 + 0.961668i 0.411582π0.411582\pi
522522 0 0
523523 − 31.5136i − 1.37800i −0.724763 0.688998i 0.758051π-0.758051\pi
0.724763 0.688998i 0.241949π-0.241949\pi
524524 0 0
525525 0 0
526526 0 0
527527 16.9067i 0.736465i
528528 0 0
529529 22.5961 0.982438
530530 0 0
531531 0.144825 0.00628488
532532 0 0
533533 − 9.74090i − 0.421925i
534534 0 0
535535 0 0
536536 0 0
537537 − 29.7003i − 1.28166i
538538 0 0
539539 3.03293 0.130638
540540 0 0
541541 13.7189 0.589821 0.294910 0.955525i 0.404710π-0.404710\pi
0.294910 + 0.955525i 0.404710π0.404710\pi
542542 0 0
543543 − 24.2316i − 1.03988i
544544 0 0
545545 0 0
546546 0 0
547547 4.12519i 0.176381i 0.996104 + 0.0881903i 0.0281084π0.0281084\pi
−0.996104 + 0.0881903i 0.971892π0.971892\pi
548548 0 0
549549 −0.825315 −0.0352236
550550 0 0
551551 9.62901 0.410210
552552 0 0
553553 − 4.82224i − 0.205063i
554554 0 0
555555 0 0
556556 0 0
557557 7.10535i 0.301063i 0.988605 + 0.150532i 0.0480985π0.0480985\pi
−0.988605 + 0.150532i 0.951901π0.951901\pi
558558 0 0
559559 15.5357 0.657089
560560 0 0
561561 3.92213 0.165592
562562 0 0
563563 − 37.7058i − 1.58911i −0.607192 0.794555i 0.707704π-0.707704\pi
0.607192 0.794555i 0.292296π-0.292296\pi
564564 0 0
565565 0 0
566566 0 0
567567 − 18.2700i − 0.767269i
568568 0 0
569569 7.72344 0.323783 0.161892 0.986809i 0.448240π-0.448240\pi
0.161892 + 0.986809i 0.448240π0.448240\pi
570570 0 0
571571 −14.5621 −0.609403 −0.304702 0.952448i 0.598557π-0.598557\pi
−0.304702 + 0.952448i 0.598557π0.598557\pi
572572 0 0
573573 − 2.52475i − 0.105473i
574574 0 0
575575 0 0
576576 0 0
577577 18.0318i 0.750676i 0.926888 + 0.375338i 0.122473π0.122473\pi
−0.926888 + 0.375338i 0.877527π0.877527\pi
578578 0 0
579579 4.07133 0.169199
580580 0 0
581581 19.8606 0.823958
582582 0 0
583583 − 0.557680i − 0.0230968i
584584 0 0
585585 0 0
586586 0 0
587587 16.0923i 0.664199i 0.943244 + 0.332099i 0.107757π0.107757\pi
−0.943244 + 0.332099i 0.892243π0.892243\pi
588588 0 0
589589 −6.59607 −0.271786
590590 0 0
591591 29.3963 1.20920
592592 0 0
593593 31.0833i 1.27644i 0.769854 + 0.638220i 0.220329π0.220329\pi
−0.769854 + 0.638220i 0.779671π0.779671\pi
594594 0 0
595595 0 0
596596 0 0
597597 13.8726i 0.567769i
598598 0 0
599599 −28.5686 −1.16728 −0.583641 0.812012i 0.698372π-0.698372\pi
−0.583641 + 0.812012i 0.698372π0.698372\pi
600600 0 0
601601 32.8277 1.33907 0.669535 0.742781i 0.266493π-0.266493\pi
0.669535 + 0.742781i 0.266493π0.266493\pi
602602 0 0
603603 − 0.888109i − 0.0361666i
604604 0 0
605605 0 0
606606 0 0
607607 1.18322i 0.0480254i 0.999712 + 0.0240127i 0.00764421π0.00764421\pi
−0.999712 + 0.0240127i 0.992356π0.992356\pi
608608 0 0
609609 −32.3963 −1.31276
610610 0 0
611611 21.6949 0.877681
612612 0 0
613613 11.9385i 0.482192i 0.970501 + 0.241096i 0.0775068π0.0775068\pi
−0.970501 + 0.241096i 0.922493π0.922493\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 11.8552i − 0.477271i −0.971109 0.238636i 0.923300π-0.923300\pi
0.971109 0.238636i 0.0767002π-0.0767002\pi
618618 0 0
619619 5.38299 0.216361 0.108180 0.994131i 0.465498π-0.465498\pi
0.108180 + 0.994131i 0.465498π0.465498\pi
620620 0 0
621621 −3.07241 −0.123292
622622 0 0
623623 10.9551i 0.438905i
624624 0 0
625625 0 0
626626 0 0
627627 1.53020i 0.0611105i
628628 0 0
629629 13.4094 0.534667
630630 0 0
631631 25.4598 1.01354 0.506769 0.862082i 0.330840π-0.330840\pi
0.506769 + 0.862082i 0.330840π0.330840\pi
632632 0 0
633633 − 13.1821i − 0.523943i
634634 0 0
635635 0 0
636636 0 0
637637 − 7.99346i − 0.316712i
638638 0 0
639639 −1.50381 −0.0594900
640640 0 0
641641 29.0899 1.14898 0.574490 0.818511i 0.305200π-0.305200\pi
0.574490 + 0.818511i 0.305200π0.305200\pi
642642 0 0
643643 − 30.7948i − 1.21443i −0.794539 0.607213i 0.792287π-0.792287\pi
0.794539 0.607213i 0.207713π-0.207713\pi
644644 0 0
645645 0 0
646646 0 0
647647 7.77275i 0.305578i 0.988259 + 0.152789i 0.0488255π0.0488255\pi
−0.988259 + 0.152789i 0.951174π0.951174\pi
648648 0 0
649649 −0.331514 −0.0130130
650650 0 0
651651 22.1921 0.869779
652652 0 0
653653 − 29.1647i − 1.14130i −0.821193 0.570651i 0.806691π-0.806691\pi
0.821193 0.570651i 0.193309π-0.193309\pi
654654 0 0
655655 0 0
656656 0 0
657657 − 3.45888i − 0.134944i
658658 0 0
659659 46.2569 1.80191 0.900957 0.433908i 0.142866π-0.142866\pi
0.900957 + 0.433908i 0.142866π0.142866\pi
660660 0 0
661661 −14.1143 −0.548982 −0.274491 0.961590i 0.588509π-0.588509\pi
−0.274491 + 0.961590i 0.588509π0.588509\pi
662662 0 0
663663 − 10.3370i − 0.401455i
664664 0 0
665665 0 0
666666 0 0
667667 6.11973i 0.236957i
668668 0 0
669669 −32.4183 −1.25336
670670 0 0
671671 1.88919 0.0729315
672672 0 0
673673 10.6596i 0.410896i 0.978668 + 0.205448i 0.0658651π0.0658651\pi
−0.978668 + 0.205448i 0.934135π0.934135\pi
674674 0 0
675675 0 0
676676 0 0
677677 28.5686i 1.09798i 0.835829 + 0.548990i 0.184988π0.184988\pi
−0.835829 + 0.548990i 0.815012π0.815012\pi
678678 0 0
679679 19.4358 0.745877
680680 0 0
681681 −19.7398 −0.756431
682682 0 0
683683 − 41.4478i − 1.58596i −0.609251 0.792978i 0.708530π-0.708530\pi
0.609251 0.792978i 0.291470π-0.291470\pi
684684 0 0
685685 0 0
686686 0 0
687687 14.0539i 0.536188i
688688 0 0
689689 −1.46980 −0.0559947
690690 0 0
691691 −2.79476 −0.106318 −0.0531589 0.998586i 0.516929π-0.516929\pi
−0.0531589 + 0.998586i 0.516929π0.516929\pi
692692 0 0
693693 − 0.557680i − 0.0211845i
694694 0 0
695695 0 0
696696 0 0
697697 − 11.3555i − 0.430121i
698698 0 0
699699 −14.7464 −0.557758
700700 0 0
701701 50.3468 1.90157 0.950786 0.309847i 0.100278π-0.100278\pi
0.950786 + 0.309847i 0.100278π0.100278\pi
702702 0 0
703703 5.23163i 0.197314i
704704 0 0
705705 0 0
706706 0 0
707707 − 26.8332i − 1.00916i
708708 0 0
709709 2.54112 0.0954339 0.0477169 0.998861i 0.484805π-0.484805\pi
0.0477169 + 0.998861i 0.484805π0.484805\pi
710710 0 0
711711 0.958137 0.0359329
712712 0 0
713713 − 4.19215i − 0.156997i
714714 0 0
715715 0 0
716716 0 0
717717 44.6279i 1.66666i
718718 0 0
719719 −1.13828 −0.0424507 −0.0212254 0.999775i 0.506757π-0.506757\pi
−0.0212254 + 0.999775i 0.506757π0.506757\pi
720720 0 0
721721 −13.7618 −0.512517
722722 0 0
723723 9.46325i 0.351942i
724724 0 0
725725 0 0
726726 0 0
727727 19.1581i 0.710536i 0.934765 + 0.355268i 0.115610π0.115610\pi
−0.934765 + 0.355268i 0.884390π0.884390\pi
728728 0 0
729729 −22.9714 −0.850794
730730 0 0
731731 18.1108 0.669852
732732 0 0
733733 − 25.3974i − 0.938074i −0.883179 0.469037i 0.844601π-0.844601\pi
0.883179 0.469037i 0.155399π-0.155399\pi
734734 0 0
735735 0 0
736736 0 0
737737 2.03293i 0.0748841i
738738 0 0
739739 42.8122 1.57487 0.787437 0.616396i 0.211408π-0.211408\pi
0.787437 + 0.616396i 0.211408π0.211408\pi
740740 0 0
741741 4.03293 0.148154
742742 0 0
743743 46.9518i 1.72249i 0.508186 + 0.861247i 0.330316π0.330316\pi
−0.508186 + 0.861247i 0.669684π0.669684\pi
744744 0 0
745745 0 0
746746 0 0
747747 3.94613i 0.144381i
748748 0 0
749749 −26.9660 −0.985315
750750 0 0
751751 −10.6356 −0.388097 −0.194048 0.980992i 0.562162π-0.562162\pi
−0.194048 + 0.980992i 0.562162π0.562162\pi
752752 0 0
753753 14.5852i 0.531513i
754754 0 0
755755 0 0
756756 0 0
757757 − 35.0329i − 1.27329i −0.771156 0.636647i 0.780321π-0.780321\pi
0.771156 0.636647i 0.219679π-0.219679\pi
758758 0 0
759759 −0.972525 −0.0353004
760760 0 0
761761 23.8462 0.864426 0.432213 0.901772i 0.357733π-0.357733\pi
0.432213 + 0.901772i 0.357733π0.357733\pi
762762 0 0
763763 2.39192i 0.0865934i
764764 0 0
765765 0 0
766766 0 0
767767 0.873721i 0.0315483i
768768 0 0
769769 38.1976 1.37744 0.688720 0.725027i 0.258173π-0.258173\pi
0.688720 + 0.725027i 0.258173π0.258173\pi
770770 0 0
771771 −12.8881 −0.464154
772772 0 0
773773 − 0.835328i − 0.0300447i −0.999887 0.0150223i 0.995218π-0.995218\pi
0.999887 0.0150223i 0.00478194π-0.00478194\pi
774774 0 0
775775 0 0
776776 0 0
777777 − 17.6015i − 0.631451i
778778 0 0
779779 4.43032 0.158733
780780 0 0
781781 3.44232 0.123176
782782 0 0
783783 46.5490i 1.66352i
784784 0 0
785785 0 0
786786 0 0
787787 − 50.7806i − 1.81013i −0.425270 0.905066i 0.639821π-0.639821\pi
0.425270 0.905066i 0.360179π-0.360179\pi
788788 0 0
789789 −2.20870 −0.0786320
790790 0 0
791791 −2.07787 −0.0738806
792792 0 0
793793 − 4.97907i − 0.176812i
794794 0 0
795795 0 0
796796 0 0
797797 − 27.2011i − 0.963512i −0.876306 0.481756i 0.839999π-0.839999\pi
0.876306 0.481756i 0.160001π-0.160001\pi
798798 0 0
799799 25.2910 0.894730
800800 0 0
801801 −2.17668 −0.0769090
802802 0 0
803803 7.91757i 0.279405i
804804 0 0
805805 0 0
806806 0 0
807807 − 17.8672i − 0.628954i
808808 0 0
809809 36.3304 1.27731 0.638655 0.769493i 0.279491π-0.279491\pi
0.638655 + 0.769493i 0.279491π0.279491\pi
810810 0 0
811811 54.3778 1.90946 0.954731 0.297472i 0.0961435π-0.0961435\pi
0.954731 + 0.297472i 0.0961435π0.0961435\pi
812812 0 0
813813 − 29.7828i − 1.04453i
814814 0 0
815815 0 0
816816 0 0
817817 7.06587i 0.247203i
818818 0 0
819819 −1.46980 −0.0513588
820820 0 0
821821 −13.6225 −0.475427 −0.237714 0.971335i 0.576398π-0.576398\pi
−0.237714 + 0.971335i 0.576398π0.576398\pi
822822 0 0
823823 − 35.1725i − 1.22604i −0.790069 0.613018i 0.789955π-0.789955\pi
0.790069 0.613018i 0.210045π-0.210045\pi
824824 0 0
825825 0 0
826826 0 0
827827 9.86172i 0.342926i 0.985191 + 0.171463i 0.0548493π0.0548493\pi
−0.985191 + 0.171463i 0.945151π0.945151\pi
828828 0 0
829829 −38.4873 −1.33672 −0.668359 0.743839i 0.733003π-0.733003\pi
−0.668359 + 0.743839i 0.733003π0.733003\pi
830830 0 0
831831 36.0868 1.25184
832832 0 0
833833 − 9.31843i − 0.322864i
834834 0 0
835835 0 0
836836 0 0
837837 − 31.8870i − 1.10218i
838838 0 0
839839 −27.3908 −0.945637 −0.472818 0.881160i 0.656763π-0.656763\pi
−0.472818 + 0.881160i 0.656763π0.656763\pi
840840 0 0
841841 63.7178 2.19717
842842 0 0
843843 − 23.0822i − 0.794995i
844844 0 0
845845 0 0
846846 0 0
847847 − 18.9001i − 0.649416i
848848 0 0
849849 25.7398 0.883388
850850 0 0
851851 −3.32497 −0.113978
852852 0 0
853853 − 47.7738i − 1.63574i −0.575400 0.817872i 0.695153π-0.695153\pi
0.575400 0.817872i 0.304847π-0.304847\pi
854854 0 0
855855 0 0
856856 0 0
857857 − 20.9571i − 0.715879i −0.933745 0.357940i 0.883479π-0.883479\pi
0.933745 0.357940i 0.116521π-0.116521\pi
858858 0 0
859859 −2.59300 −0.0884720 −0.0442360 0.999021i 0.514085π-0.514085\pi
−0.0442360 + 0.999021i 0.514085π0.514085\pi
860860 0 0
861861 −14.9056 −0.507981
862862 0 0
863863 − 9.87372i − 0.336105i −0.985778 0.168053i 0.946252π-0.946252\pi
0.985778 0.168053i 0.0537479π-0.0537479\pi
864864 0 0
865865 0 0
866866 0 0
867867 19.1317i 0.649748i
868868 0 0
869869 −2.19323 −0.0744003
870870 0 0
871871 5.35790 0.181546
872872 0 0
873873 3.86172i 0.130699i
874874 0 0
875875 0 0
876876 0 0
877877 − 19.8421i − 0.670020i −0.942215 0.335010i 0.891260π-0.891260\pi
0.942215 0.335010i 0.108740π-0.108740\pi
878878 0 0
879879 −31.7498 −1.07090
880880 0 0
881881 13.9485 0.469938 0.234969 0.972003i 0.424501π-0.424501\pi
0.234969 + 0.972003i 0.424501π0.424501\pi
882882 0 0
883883 41.4766i 1.39580i 0.716197 + 0.697899i 0.245881π0.245881\pi
−0.716197 + 0.697899i 0.754119π0.754119\pi
884884 0 0
885885 0 0
886886 0 0
887887 13.1581i 0.441807i 0.975296 + 0.220903i 0.0709005π0.0709005\pi
−0.975296 + 0.220903i 0.929099π0.929099\pi
888888 0 0
889889 8.96598 0.300709
890890 0 0
891891 −8.30950 −0.278379
892892 0 0
893893 9.86718i 0.330193i
894894 0 0
895895 0 0
896896 0 0
897897 2.56314i 0.0855807i
898898 0 0
899899 −63.5136 −2.11830
900900 0 0
901901 −1.71342 −0.0570824
902902 0 0
903903 − 23.7727i − 0.791108i
904904 0 0
905905 0 0
906906 0 0
907907 − 5.23271i − 0.173749i −0.996219 0.0868746i 0.972312π-0.972312\pi
0.996219 0.0868746i 0.0276880π-0.0276880\pi
908908 0 0
909909 5.33151 0.176835
910910 0 0
911911 25.6434 0.849604 0.424802 0.905286i 0.360344π-0.360344\pi
0.424802 + 0.905286i 0.360344π0.360344\pi
912912 0 0
913913 − 9.03293i − 0.298946i
914914 0 0
915915 0 0
916916 0 0
917917 − 3.60808i − 0.119149i
918918 0 0
919919 19.2406 0.634687 0.317344 0.948311i 0.397209π-0.397209\pi
0.317344 + 0.948311i 0.397209π0.397209\pi
920920 0 0
921921 29.4183 0.969366
922922 0 0
923923 − 9.07241i − 0.298622i
924924 0 0
925925 0 0
926926 0 0
927927 − 2.73436i − 0.0898080i
928928 0 0
929929 −29.1570 −0.956612 −0.478306 0.878193i 0.658749π-0.658749\pi
−0.478306 + 0.878193i 0.658749π0.658749\pi
930930 0 0
931931 3.63555 0.119150
932932 0 0
933933 − 37.6774i − 1.23350i
934934 0 0
935935 0 0
936936 0 0
937937 2.23163i 0.0729040i 0.999335 + 0.0364520i 0.0116056π0.0116056\pi
−0.999335 + 0.0364520i 0.988394π0.988394\pi
938938 0 0
939939 −17.3195 −0.565201
940940 0 0
941941 −49.8859 −1.62624 −0.813118 0.582099i 0.802231π-0.802231\pi
−0.813118 + 0.582099i 0.802231π0.802231\pi
942942 0 0
943943 2.81570i 0.0916917i
944944 0 0
945945 0 0
946946 0 0
947947 − 11.8648i − 0.385554i −0.981243 0.192777i 0.938251π-0.938251\pi
0.981243 0.192777i 0.0617494π-0.0617494\pi
948948 0 0
949949 20.8672 0.677377
950950 0 0
951951 −0.0604097 −0.00195892
952952 0 0
953953 46.4041i 1.50318i 0.659632 + 0.751589i 0.270712π0.270712\pi
−0.659632 + 0.751589i 0.729288π0.729288\pi
954954 0 0
955955 0 0
956956 0 0
957957 14.7344i 0.476294i
958958 0 0
959959 −6.40284 −0.206759
960960 0 0
961961 12.5082 0.403490
962962 0 0
963963 − 5.35790i − 0.172656i
964964 0 0
965965 0 0
966966 0 0
967967 − 36.2591i − 1.16601i −0.812467 0.583007i 0.801876π-0.801876\pi
0.812467 0.583007i 0.198124π-0.198124\pi
968968 0 0
969969 4.70142 0.151031
970970 0 0
971971 6.18669 0.198540 0.0992701 0.995061i 0.468349π-0.468349\pi
0.0992701 + 0.995061i 0.468349π0.468349\pi
972972 0 0
973973 27.9769i 0.896898i
974974 0 0
975975 0 0
976976 0 0
977977 54.0277i 1.72850i 0.503063 + 0.864249i 0.332206π0.332206\pi
−0.503063 + 0.864249i 0.667794π0.667794\pi
978978 0 0
979979 4.98254 0.159243
980980 0 0
981981 −0.475254 −0.0151737
982982 0 0
983983 − 0.765300i − 0.0244093i −0.999926 0.0122046i 0.996115π-0.996115\pi
0.999926 0.0122046i 0.00388495π-0.00388495\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 33.1976i − 1.05669i
988988 0 0
989989 −4.49073 −0.142797
990990 0 0
991991 17.1173 0.543751 0.271875 0.962332i 0.412356π-0.412356\pi
0.271875 + 0.962332i 0.412356π0.412356\pi
992992 0 0
993993 59.6543i 1.89307i
994994 0 0
995995 0 0
996996 0 0
997997 10.7673i 0.341003i 0.985357 + 0.170502i 0.0545388π0.0545388\pi
−0.985357 + 0.170502i 0.945461π0.945461\pi
998998 0 0
999999 −25.2910 −0.800170
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 3800.2.d.m.3649.5 6
5.2 odd 4 3800.2.a.u.1.3 3
5.3 odd 4 3800.2.a.v.1.1 yes 3
5.4 even 2 inner 3800.2.d.m.3649.2 6
20.3 even 4 7600.2.a.bu.1.3 3
20.7 even 4 7600.2.a.bt.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3800.2.a.u.1.3 3 5.2 odd 4
3800.2.a.v.1.1 yes 3 5.3 odd 4
3800.2.d.m.3649.2 6 5.4 even 2 inner
3800.2.d.m.3649.5 6 1.1 even 1 trivial
7600.2.a.bt.1.1 3 20.7 even 4
7600.2.a.bu.1.3 3 20.3 even 4