Properties

Label 3072.2.d.f.1537.7
Level 30723072
Weight 22
Character 3072.1537
Analytic conductor 24.53024.530
Analytic rank 00
Dimension 88
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] = [3072,2,Mod(1537,3072)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3072.1537"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3072, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 3072=2103 3072 = 2^{10} \cdot 3
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3072.d (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,0,0,0,0,-8,0,-8,0,0,0,0,0,8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 24.530043500924.5300435009
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.18939904.2
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x84x7+14x628x5+43x444x3+30x212x+2 x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 26 2^{6}
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1537.7
Root 0.500000+0.0297061i0.500000 + 0.0297061i of defining polynomial
Character χ\chi == 3072.1537
Dual form 3072.2.d.f.1537.2

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+1.00000iq3+0.473626iq54.55765q71.00000q93.49824iq110.0840215iq130.473626q153.61706q17+3.61706iq194.55765iq212.82843q23+4.77568q251.00000iq27+7.30205iq290.557647q31+3.49824q332.15862iq356.20285iq37+0.0840215q39+9.27391q412.27744iq430.473626iq452.82843q47+13.7721q493.61706iq510.697947iq53+1.65685q553.61706q575.65685iq593.85970iq61+4.55765q63+0.0397948q655.33962iq672.82843iq69+9.11529q71+0.541560q73+4.77568iq75+15.9437iq77+10.9937q79+1.00000q8115.0496iq831.71313iq857.30205q87+14.6533q89+0.382941iq910.557647iq931.71313q95+4.31724q97+3.49824iq99+O(q100)q+1.00000i q^{3} +0.473626i q^{5} -4.55765 q^{7} -1.00000 q^{9} -3.49824i q^{11} -0.0840215i q^{13} -0.473626 q^{15} -3.61706 q^{17} +3.61706i q^{19} -4.55765i q^{21} -2.82843 q^{23} +4.77568 q^{25} -1.00000i q^{27} +7.30205i q^{29} -0.557647 q^{31} +3.49824 q^{33} -2.15862i q^{35} -6.20285i q^{37} +0.0840215 q^{39} +9.27391 q^{41} -2.27744i q^{43} -0.473626i q^{45} -2.82843 q^{47} +13.7721 q^{49} -3.61706i q^{51} -0.697947i q^{53} +1.65685 q^{55} -3.61706 q^{57} -5.65685i q^{59} -3.85970i q^{61} +4.55765 q^{63} +0.0397948 q^{65} -5.33962i q^{67} -2.82843i q^{69} +9.11529 q^{71} +0.541560 q^{73} +4.77568i q^{75} +15.9437i q^{77} +10.9937 q^{79} +1.00000 q^{81} -15.0496i q^{83} -1.71313i q^{85} -7.30205 q^{87} +14.6533 q^{89} +0.382941i q^{91} -0.557647i q^{93} -1.71313 q^{95} +4.31724 q^{97} +3.49824i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q8q78q9+8q158q25+24q3116q39+8q4932q55+8q6316q65+16q71+16q73+24q79+8q8124q87+16q8948q95+O(q100) 8 q - 8 q^{7} - 8 q^{9} + 8 q^{15} - 8 q^{25} + 24 q^{31} - 16 q^{39} + 8 q^{49} - 32 q^{55} + 8 q^{63} - 16 q^{65} + 16 q^{71} + 16 q^{73} + 24 q^{79} + 8 q^{81} - 24 q^{87} + 16 q^{89} - 48 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3072Z)×\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times.

nn 10251025 20472047 20532053
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 1.00000i 0.577350i
44 0 0
55 0.473626i 0.211812i 0.994376 + 0.105906i 0.0337742π0.0337742\pi
−0.994376 + 0.105906i 0.966226π0.966226\pi
66 0 0
77 −4.55765 −1.72263 −0.861314 0.508072i 0.830358π-0.830358\pi
−0.861314 + 0.508072i 0.830358π0.830358\pi
88 0 0
99 −1.00000 −0.333333
1010 0 0
1111 − 3.49824i − 1.05476i −0.849630 0.527379i 0.823175π-0.823175\pi
0.849630 0.527379i 0.176825π-0.176825\pi
1212 0 0
1313 − 0.0840215i − 0.0233034i −0.999932 0.0116517i 0.996291π-0.996291\pi
0.999932 0.0116517i 0.00370893π-0.00370893\pi
1414 0 0
1515 −0.473626 −0.122290
1616 0 0
1717 −3.61706 −0.877266 −0.438633 0.898666i 0.644537π-0.644537\pi
−0.438633 + 0.898666i 0.644537π0.644537\pi
1818 0 0
1919 3.61706i 0.829810i 0.909865 + 0.414905i 0.136185π0.136185\pi
−0.909865 + 0.414905i 0.863815π0.863815\pi
2020 0 0
2121 − 4.55765i − 0.994560i
2222 0 0
2323 −2.82843 −0.589768 −0.294884 0.955533i 0.595281π-0.595281\pi
−0.294884 + 0.955533i 0.595281π0.595281\pi
2424 0 0
2525 4.77568 0.955136
2626 0 0
2727 − 1.00000i − 0.192450i
2828 0 0
2929 7.30205i 1.35596i 0.735082 + 0.677979i 0.237144π0.237144\pi
−0.735082 + 0.677979i 0.762856π0.762856\pi
3030 0 0
3131 −0.557647 −0.100156 −0.0500782 0.998745i 0.515947π-0.515947\pi
−0.0500782 + 0.998745i 0.515947π0.515947\pi
3232 0 0
3333 3.49824 0.608965
3434 0 0
3535 − 2.15862i − 0.364873i
3636 0 0
3737 − 6.20285i − 1.01974i −0.860251 0.509871i 0.829693π-0.829693\pi
0.860251 0.509871i 0.170307π-0.170307\pi
3838 0 0
3939 0.0840215 0.0134542
4040 0 0
4141 9.27391 1.44834 0.724171 0.689620i 0.242223π-0.242223\pi
0.724171 + 0.689620i 0.242223π0.242223\pi
4242 0 0
4343 − 2.27744i − 0.347307i −0.984807 0.173653i 0.944443π-0.944443\pi
0.984807 0.173653i 0.0555573π-0.0555573\pi
4444 0 0
4545 − 0.473626i − 0.0706040i
4646 0 0
4747 −2.82843 −0.412568 −0.206284 0.978492i 0.566137π-0.566137\pi
−0.206284 + 0.978492i 0.566137π0.566137\pi
4848 0 0
4949 13.7721 1.96745
5050 0 0
5151 − 3.61706i − 0.506490i
5252 0 0
5353 − 0.697947i − 0.0958704i −0.998850 0.0479352i 0.984736π-0.984736\pi
0.998850 0.0479352i 0.0152641π-0.0152641\pi
5454 0 0
5555 1.65685 0.223410
5656 0 0
5757 −3.61706 −0.479091
5858 0 0
5959 − 5.65685i − 0.736460i −0.929735 0.368230i 0.879964π-0.879964\pi
0.929735 0.368230i 0.120036π-0.120036\pi
6060 0 0
6161 − 3.85970i − 0.494184i −0.968992 0.247092i 0.920525π-0.920525\pi
0.968992 0.247092i 0.0794750π-0.0794750\pi
6262 0 0
6363 4.55765 0.574210
6464 0 0
6565 0.0397948 0.00493593
6666 0 0
6767 − 5.33962i − 0.652338i −0.945311 0.326169i 0.894242π-0.894242\pi
0.945311 0.326169i 0.105758π-0.105758\pi
6868 0 0
6969 − 2.82843i − 0.340503i
7070 0 0
7171 9.11529 1.08179 0.540893 0.841091i 0.318086π-0.318086\pi
0.540893 + 0.841091i 0.318086π0.318086\pi
7272 0 0
7373 0.541560 0.0633848 0.0316924 0.999498i 0.489910π-0.489910\pi
0.0316924 + 0.999498i 0.489910π0.489910\pi
7474 0 0
7575 4.77568i 0.551448i
7676 0 0
7777 15.9437i 1.81696i
7878 0 0
7979 10.9937 1.23689 0.618445 0.785828i 0.287763π-0.287763\pi
0.618445 + 0.785828i 0.287763π0.287763\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 − 15.0496i − 1.65191i −0.563738 0.825954i 0.690637π-0.690637\pi
0.563738 0.825954i 0.309363π-0.309363\pi
8484 0 0
8585 − 1.71313i − 0.185815i
8686 0 0
8787 −7.30205 −0.782862
8888 0 0
8989 14.6533 1.55325 0.776625 0.629964i 0.216930π-0.216930\pi
0.776625 + 0.629964i 0.216930π0.216930\pi
9090 0 0
9191 0.382941i 0.0401431i
9292 0 0
9393 − 0.557647i − 0.0578253i
9494 0 0
9595 −1.71313 −0.175764
9696 0 0
9797 4.31724 0.438349 0.219175 0.975686i 0.429664π-0.429664\pi
0.219175 + 0.975686i 0.429664π0.429664\pi
9898 0 0
9999 3.49824i 0.351586i
100100 0 0
101101 0.641669i 0.0638484i 0.999490 + 0.0319242i 0.0101635π0.0101635\pi
−0.999490 + 0.0319242i 0.989836π0.989836\pi
102102 0 0
103103 1.33686 0.131724 0.0658622 0.997829i 0.479020π-0.479020\pi
0.0658622 + 0.997829i 0.479020π0.479020\pi
104104 0 0
105105 2.15862 0.210660
106106 0 0
107107 8.57373i 0.828854i 0.910083 + 0.414427i 0.136018π0.136018\pi
−0.910083 + 0.414427i 0.863982π0.863982\pi
108108 0 0
109109 8.08402i 0.774309i 0.922015 + 0.387154i 0.126542π0.126542\pi
−0.922015 + 0.387154i 0.873458π0.873458\pi
110110 0 0
111111 6.20285 0.588748
112112 0 0
113113 9.55136 0.898516 0.449258 0.893402i 0.351688π-0.351688\pi
0.449258 + 0.893402i 0.351688π0.351688\pi
114114 0 0
115115 − 1.33962i − 0.124920i
116116 0 0
117117 0.0840215i 0.00776779i
118118 0 0
119119 16.4853 1.51120
120120 0 0
121121 −1.23765 −0.112514
122122 0 0
123123 9.27391i 0.836201i
124124 0 0
125125 4.63001i 0.414121i
126126 0 0
127127 5.09921 0.452481 0.226241 0.974071i 0.427356π-0.427356\pi
0.226241 + 0.974071i 0.427356π0.427356\pi
128128 0 0
129129 2.27744 0.200518
130130 0 0
131131 − 2.99647i − 0.261803i −0.991395 0.130901i 0.958213π-0.958213\pi
0.991395 0.130901i 0.0417871π-0.0417871\pi
132132 0 0
133133 − 16.4853i − 1.42946i
134134 0 0
135135 0.473626 0.0407632
136136 0 0
137137 3.37941 0.288723 0.144361 0.989525i 0.453887π-0.453887\pi
0.144361 + 0.989525i 0.453887π0.453887\pi
138138 0 0
139139 8.31724i 0.705459i 0.935725 + 0.352729i 0.114746π0.114746\pi
−0.935725 + 0.352729i 0.885254π0.885254\pi
140140 0 0
141141 − 2.82843i − 0.238197i
142142 0 0
143143 −0.293927 −0.0245794
144144 0 0
145145 −3.45844 −0.287208
146146 0 0
147147 13.7721i 1.13591i
148148 0 0
149149 − 14.1305i − 1.15761i −0.815465 0.578807i 0.803518π-0.803518\pi
0.815465 0.578807i 0.196482π-0.196482\pi
150150 0 0
151151 −9.97685 −0.811905 −0.405952 0.913894i 0.633060π-0.633060\pi
−0.405952 + 0.913894i 0.633060π0.633060\pi
152152 0 0
153153 3.61706 0.292422
154154 0 0
155155 − 0.264116i − 0.0212143i
156156 0 0
157157 22.8562i 1.82412i 0.410056 + 0.912060i 0.365509π0.365509\pi
−0.410056 + 0.912060i 0.634491π0.634491\pi
158158 0 0
159159 0.697947 0.0553508
160160 0 0
161161 12.8910 1.01595
162162 0 0
163163 10.6135i 0.831316i 0.909521 + 0.415658i 0.136449π0.136449\pi
−0.909521 + 0.415658i 0.863551π0.863551\pi
164164 0 0
165165 1.65685i 0.128986i
166166 0 0
167167 −5.83822 −0.451775 −0.225888 0.974153i 0.572528π-0.572528\pi
−0.225888 + 0.974153i 0.572528π0.572528\pi
168168 0 0
169169 12.9929 0.999457
170170 0 0
171171 − 3.61706i − 0.276603i
172172 0 0
173173 − 5.12695i − 0.389795i −0.980824 0.194897i 0.937563π-0.937563\pi
0.980824 0.194897i 0.0624374π-0.0624374\pi
174174 0 0
175175 −21.7659 −1.64534
176176 0 0
177177 5.65685 0.425195
178178 0 0
179179 13.1286i 0.981279i 0.871363 + 0.490640i 0.163237π0.163237\pi
−0.871363 + 0.490640i 0.836763π0.836763\pi
180180 0 0
181181 − 15.3181i − 1.13859i −0.822134 0.569294i 0.807217π-0.807217\pi
0.822134 0.569294i 0.192783π-0.192783\pi
182182 0 0
183183 3.85970 0.285317
184184 0 0
185185 2.93783 0.215993
186186 0 0
187187 12.6533i 0.925303i
188188 0 0
189189 4.55765i 0.331520i
190190 0 0
191191 −8.63001 −0.624446 −0.312223 0.950009i 0.601074π-0.601074\pi
−0.312223 + 0.950009i 0.601074π0.601074\pi
192192 0 0
193193 11.4514 0.824288 0.412144 0.911119i 0.364780π-0.364780\pi
0.412144 + 0.911119i 0.364780π0.364780\pi
194194 0 0
195195 0.0397948i 0.00284976i
196196 0 0
197197 − 10.5925i − 0.754681i −0.926075 0.377340i 0.876839π-0.876839\pi
0.926075 0.377340i 0.123161π-0.123161\pi
198198 0 0
199199 −3.68000 −0.260868 −0.130434 0.991457i 0.541637π-0.541637\pi
−0.130434 + 0.991457i 0.541637π0.541637\pi
200200 0 0
201201 5.33962 0.376627
202202 0 0
203203 − 33.2802i − 2.33581i
204204 0 0
205205 4.39236i 0.306776i
206206 0 0
207207 2.82843 0.196589
208208 0 0
209209 12.6533 0.875249
210210 0 0
211211 14.3102i 0.985153i 0.870269 + 0.492577i 0.163945π0.163945\pi
−0.870269 + 0.492577i 0.836055π0.836055\pi
212212 0 0
213213 9.11529i 0.624570i
214214 0 0
215215 1.07866 0.0735637
216216 0 0
217217 2.54156 0.172532
218218 0 0
219219 0.541560i 0.0365952i
220220 0 0
221221 0.303911i 0.0204433i
222222 0 0
223223 −4.86156 −0.325554 −0.162777 0.986663i 0.552045π-0.552045\pi
−0.162777 + 0.986663i 0.552045π0.552045\pi
224224 0 0
225225 −4.77568 −0.318379
226226 0 0
227227 − 15.0496i − 0.998877i −0.866349 0.499438i 0.833540π-0.833540\pi
0.866349 0.499438i 0.166460π-0.166460\pi
228228 0 0
229229 28.5264i 1.88507i 0.334101 + 0.942537i 0.391567π0.391567\pi
−0.334101 + 0.942537i 0.608433π0.608433\pi
230230 0 0
231231 −15.9437 −1.04902
232232 0 0
233233 −13.5702 −0.889014 −0.444507 0.895775i 0.646621π-0.646621\pi
−0.444507 + 0.895775i 0.646621π0.646621\pi
234234 0 0
235235 − 1.33962i − 0.0873869i
236236 0 0
237237 10.9937i 0.714118i
238238 0 0
239239 −29.3629 −1.89933 −0.949665 0.313267i 0.898576π-0.898576\pi
−0.949665 + 0.313267i 0.898576π0.898576\pi
240240 0 0
241241 −24.0063 −1.54638 −0.773190 0.634175i 0.781340π-0.781340\pi
−0.773190 + 0.634175i 0.781340π0.781340\pi
242242 0 0
243243 1.00000i 0.0641500i
244244 0 0
245245 6.52284i 0.416729i
246246 0 0
247247 0.303911 0.0193374
248248 0 0
249249 15.0496 0.953729
250250 0 0
251251 − 22.2837i − 1.40654i −0.710925 0.703268i 0.751724π-0.751724\pi
0.710925 0.703268i 0.248276π-0.248276\pi
252252 0 0
253253 9.89450i 0.622062i
254254 0 0
255255 1.71313 0.107281
256256 0 0
257257 8.66038 0.540220 0.270110 0.962829i 0.412940π-0.412940\pi
0.270110 + 0.962829i 0.412940π0.412940\pi
258258 0 0
259259 28.2704i 1.75664i
260260 0 0
261261 − 7.30205i − 0.451986i
262262 0 0
263263 13.3208 0.821394 0.410697 0.911772i 0.365285π-0.365285\pi
0.410697 + 0.911772i 0.365285π0.365285\pi
264264 0 0
265265 0.330566 0.0203065
266266 0 0
267267 14.6533i 0.896769i
268268 0 0
269269 − 16.5058i − 1.00638i −0.864177 0.503188i 0.832160π-0.832160\pi
0.864177 0.503188i 0.167840π-0.167840\pi
270270 0 0
271271 21.9769 1.33500 0.667499 0.744610i 0.267365π-0.267365\pi
0.667499 + 0.744610i 0.267365π0.267365\pi
272272 0 0
273273 −0.382941 −0.0231766
274274 0 0
275275 − 16.7064i − 1.00744i
276276 0 0
277277 − 15.4862i − 0.930475i −0.885186 0.465237i 0.845969π-0.845969\pi
0.885186 0.465237i 0.154031π-0.154031\pi
278278 0 0
279279 0.557647 0.0333855
280280 0 0
281281 −22.8910 −1.36556 −0.682780 0.730624i 0.739229π-0.739229\pi
−0.682780 + 0.730624i 0.739229π0.739229\pi
282282 0 0
283283 − 6.34315i − 0.377061i −0.982067 0.188530i 0.939628π-0.939628\pi
0.982067 0.188530i 0.0603724π-0.0603724\pi
284284 0 0
285285 − 1.71313i − 0.101477i
286286 0 0
287287 −42.2672 −2.49496
288288 0 0
289289 −3.91688 −0.230405
290290 0 0
291291 4.31724i 0.253081i
292292 0 0
293293 − 30.5783i − 1.78641i −0.449654 0.893203i 0.648453π-0.648453\pi
0.449654 0.893203i 0.351547π-0.351547\pi
294294 0 0
295295 2.67923 0.155991
296296 0 0
297297 −3.49824 −0.202988
298298 0 0
299299 0.237649i 0.0137436i
300300 0 0
301301 10.3798i 0.598281i
302302 0 0
303303 −0.641669 −0.0368629
304304 0 0
305305 1.82805 0.104674
306306 0 0
307307 − 17.1286i − 0.977582i −0.872401 0.488791i 0.837438π-0.837438\pi
0.872401 0.488791i 0.162562π-0.162562\pi
308308 0 0
309309 1.33686i 0.0760511i
310310 0 0
311311 26.8651 1.52338 0.761689 0.647943i 0.224370π-0.224370\pi
0.761689 + 0.647943i 0.224370π0.224370\pi
312312 0 0
313313 19.6890 1.11289 0.556445 0.830885i 0.312165π-0.312165\pi
0.556445 + 0.830885i 0.312165π0.312165\pi
314314 0 0
315315 2.15862i 0.121624i
316316 0 0
317317 − 30.1860i − 1.69541i −0.530466 0.847706i 0.677983π-0.677983\pi
0.530466 0.847706i 0.322017π-0.322017\pi
318318 0 0
319319 25.5443 1.43021
320320 0 0
321321 −8.57373 −0.478539
322322 0 0
323323 − 13.0831i − 0.727964i
324324 0 0
325325 − 0.401260i − 0.0222579i
326326 0 0
327327 −8.08402 −0.447047
328328 0 0
329329 12.8910 0.710702
330330 0 0
331331 20.7784i 1.14209i 0.820920 + 0.571043i 0.193461π0.193461\pi
−0.820920 + 0.571043i 0.806539π0.806539\pi
332332 0 0
333333 6.20285i 0.339914i
334334 0 0
335335 2.52898 0.138173
336336 0 0
337337 23.0098 1.25342 0.626712 0.779251i 0.284400π-0.284400\pi
0.626712 + 0.779251i 0.284400π0.284400\pi
338338 0 0
339339 9.55136i 0.518759i
340340 0 0
341341 1.95078i 0.105641i
342342 0 0
343343 −30.8651 −1.66656
344344 0 0
345345 1.33962 0.0721225
346346 0 0
347347 15.4186i 0.827716i 0.910341 + 0.413858i 0.135819π0.135819\pi
−0.910341 + 0.413858i 0.864181π0.864181\pi
348348 0 0
349349 − 28.3638i − 1.51828i −0.650927 0.759140i 0.725620π-0.725620\pi
0.650927 0.759140i 0.274380π-0.274380\pi
350350 0 0
351351 −0.0840215 −0.00448474
352352 0 0
353353 −12.2117 −0.649965 −0.324983 0.945720i 0.605358π-0.605358\pi
−0.324983 + 0.945720i 0.605358π0.605358\pi
354354 0 0
355355 4.31724i 0.229135i
356356 0 0
357357 16.4853i 0.872494i
358358 0 0
359359 33.4780 1.76690 0.883452 0.468522i 0.155214π-0.155214\pi
0.883452 + 0.468522i 0.155214π0.155214\pi
360360 0 0
361361 5.91688 0.311415
362362 0 0
363363 − 1.23765i − 0.0649597i
364364 0 0
365365 0.256497i 0.0134256i
366366 0 0
367367 0.702379 0.0366639 0.0183319 0.999832i 0.494164π-0.494164\pi
0.0183319 + 0.999832i 0.494164π0.494164\pi
368368 0 0
369369 −9.27391 −0.482781
370370 0 0
371371 3.18100i 0.165149i
372372 0 0
373373 26.8132i 1.38834i 0.719813 + 0.694168i 0.244227π0.244227\pi
−0.719813 + 0.694168i 0.755773π0.755773\pi
374374 0 0
375375 −4.63001 −0.239093
376376 0 0
377377 0.613530 0.0315984
378378 0 0
379379 2.51509i 0.129192i 0.997912 + 0.0645958i 0.0205758π0.0205758\pi
−0.997912 + 0.0645958i 0.979424π0.979424\pi
380380 0 0
381381 5.09921i 0.261240i
382382 0 0
383383 25.4880 1.30238 0.651188 0.758916i 0.274271π-0.274271\pi
0.651188 + 0.758916i 0.274271π0.274271\pi
384384 0 0
385385 −7.55136 −0.384853
386386 0 0
387387 2.27744i 0.115769i
388388 0 0
389389 16.5532i 0.839281i 0.907690 + 0.419641i 0.137844π0.137844\pi
−0.907690 + 0.419641i 0.862156π0.862156\pi
390390 0 0
391391 10.2306 0.517383
392392 0 0
393393 2.99647 0.151152
394394 0 0
395395 5.20690i 0.261988i
396396 0 0
397397 − 12.7936i − 0.642094i −0.947063 0.321047i 0.895965π-0.895965\pi
0.947063 0.321047i 0.104035π-0.104035\pi
398398 0 0
399399 16.4853 0.825296
400400 0 0
401401 18.0853 0.903137 0.451568 0.892237i 0.350865π-0.350865\pi
0.451568 + 0.892237i 0.350865π0.350865\pi
402402 0 0
403403 0.0468544i 0.00233398i
404404 0 0
405405 0.473626i 0.0235347i
406406 0 0
407407 −21.6990 −1.07558
408408 0 0
409409 −25.2271 −1.24740 −0.623699 0.781665i 0.714371π-0.714371\pi
−0.623699 + 0.781665i 0.714371π0.714371\pi
410410 0 0
411411 3.37941i 0.166694i
412412 0 0
413413 25.7819i 1.26865i
414414 0 0
415415 7.12787 0.349894
416416 0 0
417417 −8.31724 −0.407297
418418 0 0
419419 − 10.2571i − 0.501090i −0.968105 0.250545i 0.919390π-0.919390\pi
0.968105 0.250545i 0.0806098π-0.0806098\pi
420420 0 0
421421 − 3.38775i − 0.165109i −0.996587 0.0825543i 0.973692π-0.973692\pi
0.996587 0.0825543i 0.0263078π-0.0263078\pi
422422 0 0
423423 2.82843 0.137523
424424 0 0
425425 −17.2739 −0.837908
426426 0 0
427427 17.5912i 0.851296i
428428 0 0
429429 − 0.293927i − 0.0141909i
430430 0 0
431431 4.42454 0.213123 0.106561 0.994306i 0.466016π-0.466016\pi
0.106561 + 0.994306i 0.466016π0.466016\pi
432432 0 0
433433 −7.31371 −0.351474 −0.175737 0.984437i 0.556231π-0.556231\pi
−0.175737 + 0.984437i 0.556231π0.556231\pi
434434 0 0
435435 − 3.45844i − 0.165820i
436436 0 0
437437 − 10.2306i − 0.489395i
438438 0 0
439439 29.6533 1.41527 0.707637 0.706576i 0.249761π-0.249761\pi
0.707637 + 0.706576i 0.249761π0.249761\pi
440440 0 0
441441 −13.7721 −0.655817
442442 0 0
443443 − 14.5743i − 0.692446i −0.938152 0.346223i 0.887464π-0.887464\pi
0.938152 0.346223i 0.112536π-0.112536\pi
444444 0 0
445445 6.94019i 0.328997i
446446 0 0
447447 14.1305 0.668349
448448 0 0
449449 −6.48844 −0.306208 −0.153104 0.988210i 0.548927π-0.548927\pi
−0.153104 + 0.988210i 0.548927π0.548927\pi
450450 0 0
451451 − 32.4423i − 1.52765i
452452 0 0
453453 − 9.97685i − 0.468753i
454454 0 0
455455 −0.181370 −0.00850278
456456 0 0
457457 9.00353 0.421167 0.210584 0.977576i 0.432464π-0.432464\pi
0.210584 + 0.977576i 0.432464π0.432464\pi
458458 0 0
459459 3.61706i 0.168830i
460460 0 0
461461 20.6783i 0.963085i 0.876423 + 0.481542i 0.159923π0.159923\pi
−0.876423 + 0.481542i 0.840077π0.840077\pi
462462 0 0
463463 18.6435 0.866437 0.433219 0.901289i 0.357378π-0.357378\pi
0.433219 + 0.901289i 0.357378π0.357378\pi
464464 0 0
465465 0.264116 0.0122481
466466 0 0
467467 − 33.2535i − 1.53879i −0.638773 0.769395i 0.720558π-0.720558\pi
0.638773 0.769395i 0.279442π-0.279442\pi
468468 0 0
469469 24.3361i 1.12374i
470470 0 0
471471 −22.8562 −1.05316
472472 0 0
473473 −7.96703 −0.366325
474474 0 0
475475 17.2739i 0.792582i
476476 0 0
477477 0.697947i 0.0319568i
478478 0 0
479479 −1.08864 −0.0497412 −0.0248706 0.999691i 0.507917π-0.507917\pi
−0.0248706 + 0.999691i 0.507917π0.507917\pi
480480 0 0
481481 −0.521173 −0.0237634
482482 0 0
483483 12.8910i 0.586560i
484484 0 0
485485 2.04476i 0.0928476i
486486 0 0
487487 −35.3298 −1.60095 −0.800473 0.599369i 0.795418π-0.795418\pi
−0.800473 + 0.599369i 0.795418π0.795418\pi
488488 0 0
489489 −10.6135 −0.479960
490490 0 0
491491 − 18.2306i − 0.822735i −0.911470 0.411367i 0.865051π-0.865051\pi
0.911470 0.411367i 0.134949π-0.134949\pi
492492 0 0
493493 − 26.4120i − 1.18953i
494494 0 0
495495 −1.65685 −0.0744701
496496 0 0
497497 −41.5443 −1.86352
498498 0 0
499499 20.3361i 0.910368i 0.890397 + 0.455184i 0.150427π0.150427\pi
−0.890397 + 0.455184i 0.849573π0.849573\pi
500500 0 0
501501 − 5.83822i − 0.260833i
502502 0 0
503503 30.2969 1.35087 0.675435 0.737420i 0.263956π-0.263956\pi
0.675435 + 0.737420i 0.263956π0.263956\pi
504504 0 0
505505 −0.303911 −0.0135239
506506 0 0
507507 12.9929i 0.577037i
508508 0 0
509509 − 14.9660i − 0.663355i −0.943393 0.331677i 0.892385π-0.892385\pi
0.943393 0.331677i 0.107615π-0.107615\pi
510510 0 0
511511 −2.46824 −0.109188
512512 0 0
513513 3.61706 0.159697
514514 0 0
515515 0.633169i 0.0279008i
516516 0 0
517517 9.89450i 0.435160i
518518 0 0
519519 5.12695 0.225048
520520 0 0
521521 −24.9049 −1.09110 −0.545551 0.838078i 0.683680π-0.683680\pi
−0.545551 + 0.838078i 0.683680π0.683680\pi
522522 0 0
523523 − 18.2445i − 0.797775i −0.917000 0.398888i 0.869396π-0.869396\pi
0.917000 0.398888i 0.130604π-0.130604\pi
524524 0 0
525525 − 21.7659i − 0.949940i
526526 0 0
527527 2.01704 0.0878638
528528 0 0
529529 −15.0000 −0.652174
530530 0 0
531531 5.65685i 0.245487i
532532 0 0
533533 − 0.779208i − 0.0337513i
534534 0 0
535535 −4.06074 −0.175561
536536 0 0
537537 −13.1286 −0.566542
538538 0 0
539539 − 48.1782i − 2.07518i
540540 0 0
541541 − 25.8471i − 1.11125i −0.831432 0.555627i 0.812478π-0.812478\pi
0.831432 0.555627i 0.187522π-0.187522\pi
542542 0 0
543543 15.3181 0.657364
544544 0 0
545545 −3.82880 −0.164008
546546 0 0
547547 − 19.4249i − 0.830549i −0.909696 0.415275i 0.863685π-0.863685\pi
0.909696 0.415275i 0.136315π-0.136315\pi
548548 0 0
549549 3.85970i 0.164728i
550550 0 0
551551 −26.4120 −1.12519
552552 0 0
553553 −50.1055 −2.13070
554554 0 0
555555 2.93783i 0.124704i
556556 0 0
557557 − 38.9652i − 1.65101i −0.564397 0.825504i 0.690891π-0.690891\pi
0.564397 0.825504i 0.309109π-0.309109\pi
558558 0 0
559559 −0.191354 −0.00809342
560560 0 0
561561 −12.6533 −0.534224
562562 0 0
563563 − 28.1327i − 1.18565i −0.805330 0.592826i 0.798012π-0.798012\pi
0.805330 0.592826i 0.201988π-0.201988\pi
564564 0 0
565565 4.52377i 0.190316i
566566 0 0
567567 −4.55765 −0.191403
568568 0 0
569569 13.4849 0.565317 0.282658 0.959221i 0.408784π-0.408784\pi
0.282658 + 0.959221i 0.408784π0.408784\pi
570570 0 0
571571 20.9706i 0.877591i 0.898587 + 0.438795i 0.144595π0.144595\pi
−0.898587 + 0.438795i 0.855405π0.855405\pi
572572 0 0
573573 − 8.63001i − 0.360524i
574574 0 0
575575 −13.5077 −0.563308
576576 0 0
577577 −11.6176 −0.483648 −0.241824 0.970320i 0.577746π-0.577746\pi
−0.241824 + 0.970320i 0.577746π0.577746\pi
578578 0 0
579579 11.4514i 0.475903i
580580 0 0
581581 68.5907i 2.84562i
582582 0 0
583583 −2.44158 −0.101120
584584 0 0
585585 −0.0397948 −0.00164531
586586 0 0
587587 − 24.0796i − 0.993871i −0.867787 0.496936i 0.834459π-0.834459\pi
0.867787 0.496936i 0.165541π-0.165541\pi
588588 0 0
589589 − 2.01704i − 0.0831108i
590590 0 0
591591 10.5925 0.435715
592592 0 0
593593 −41.5372 −1.70573 −0.852865 0.522132i 0.825137π-0.825137\pi
−0.852865 + 0.522132i 0.825137π0.825137\pi
594594 0 0
595595 7.80785i 0.320091i
596596 0 0
597597 − 3.68000i − 0.150612i
598598 0 0
599599 6.43160 0.262788 0.131394 0.991330i 0.458055π-0.458055\pi
0.131394 + 0.991330i 0.458055π0.458055\pi
600600 0 0
601601 3.45844 0.141073 0.0705364 0.997509i 0.477529π-0.477529\pi
0.0705364 + 0.997509i 0.477529π0.477529\pi
602602 0 0
603603 5.33962i 0.217446i
604604 0 0
605605 − 0.586182i − 0.0238317i
606606 0 0
607607 −30.1019 −1.22180 −0.610900 0.791708i 0.709192π-0.709192\pi
−0.610900 + 0.791708i 0.709192π0.709192\pi
608608 0 0
609609 33.2802 1.34858
610610 0 0
611611 0.237649i 0.00961424i
612612 0 0
613613 − 3.54246i − 0.143079i −0.997438 0.0715393i 0.977209π-0.977209\pi
0.997438 0.0715393i 0.0227911π-0.0227911\pi
614614 0 0
615615 −4.39236 −0.177117
616616 0 0
617617 22.9098 0.922315 0.461157 0.887318i 0.347434π-0.347434\pi
0.461157 + 0.887318i 0.347434π0.347434\pi
618618 0 0
619619 − 40.4612i − 1.62627i −0.582074 0.813136i 0.697758π-0.697758\pi
0.582074 0.813136i 0.302242π-0.302242\pi
620620 0 0
621621 2.82843i 0.113501i
622622 0 0
623623 −66.7847 −2.67567
624624 0 0
625625 21.6855 0.867420
626626 0 0
627627 12.6533i 0.505325i
628628 0 0
629629 22.4361i 0.894584i
630630 0 0
631631 11.1851 0.445270 0.222635 0.974902i 0.428534π-0.428534\pi
0.222635 + 0.974902i 0.428534π0.428534\pi
632632 0 0
633633 −14.3102 −0.568779
634634 0 0
635635 2.41512i 0.0958409i
636636 0 0
637637 − 1.15716i − 0.0458482i
638638 0 0
639639 −9.11529 −0.360595
640640 0 0
641641 −6.69312 −0.264362 −0.132181 0.991226i 0.542198π-0.542198\pi
−0.132181 + 0.991226i 0.542198π0.542198\pi
642642 0 0
643643 25.3724i 1.00059i 0.865856 + 0.500294i 0.166775π0.166775\pi
−0.865856 + 0.500294i 0.833225π0.833225\pi
644644 0 0
645645 1.07866i 0.0424720i
646646 0 0
647647 −6.72999 −0.264583 −0.132292 0.991211i 0.542234π-0.542234\pi
−0.132292 + 0.991211i 0.542234π0.542234\pi
648648 0 0
649649 −19.7890 −0.776786
650650 0 0
651651 2.54156i 0.0996116i
652652 0 0
653653 37.0144i 1.44849i 0.689545 + 0.724243i 0.257810π0.257810\pi
−0.689545 + 0.724243i 0.742190π0.742190\pi
654654 0 0
655655 1.41921 0.0554529
656656 0 0
657657 −0.541560 −0.0211283
658658 0 0
659659 19.7624i 0.769832i 0.922952 + 0.384916i 0.125770π0.125770\pi
−0.922952 + 0.384916i 0.874230π0.874230\pi
660660 0 0
661661 16.8632i 0.655904i 0.944694 + 0.327952i 0.106358π0.106358\pi
−0.944694 + 0.327952i 0.893642π0.893642\pi
662662 0 0
663663 −0.303911 −0.0118029
664664 0 0
665665 7.80785 0.302776
666666 0 0
667667 − 20.6533i − 0.799700i
668668 0 0
669669 − 4.86156i − 0.187959i
670670 0 0
671671 −13.5021 −0.521244
672672 0 0
673673 −37.3066 −1.43807 −0.719033 0.694976i 0.755415π-0.755415\pi
−0.719033 + 0.694976i 0.755415π0.755415\pi
674674 0 0
675675 − 4.77568i − 0.183816i
676676 0 0
677677 − 0.632805i − 0.0243207i −0.999926 0.0121603i 0.996129π-0.996129\pi
0.999926 0.0121603i 0.00387085π-0.00387085\pi
678678 0 0
679679 −19.6764 −0.755113
680680 0 0
681681 15.0496 0.576702
682682 0 0
683683 − 6.04606i − 0.231346i −0.993287 0.115673i 0.963098π-0.963098\pi
0.993287 0.115673i 0.0369025π-0.0369025\pi
684684 0 0
685685 1.60058i 0.0611549i
686686 0 0
687687 −28.5264 −1.08835
688688 0 0
689689 −0.0586426 −0.00223410
690690 0 0
691691 28.3955i 1.08021i 0.841596 + 0.540107i 0.181616π0.181616\pi
−0.841596 + 0.540107i 0.818384π0.818384\pi
692692 0 0
693693 − 15.9437i − 0.605652i
694694 0 0
695695 −3.93926 −0.149425
696696 0 0
697697 −33.5443 −1.27058
698698 0 0
699699 − 13.5702i − 0.513272i
700700 0 0
701701 14.7738i 0.558000i 0.960291 + 0.279000i 0.0900029π0.0900029\pi
−0.960291 + 0.279000i 0.909997π0.909997\pi
702702 0 0
703703 22.4361 0.846192
704704 0 0
705705 1.33962 0.0504529
706706 0 0
707707 − 2.92450i − 0.109987i
708708 0 0
709709 − 22.7569i − 0.854655i −0.904097 0.427327i 0.859455π-0.859455\pi
0.904097 0.427327i 0.140545π-0.140545\pi
710710 0 0
711711 −10.9937 −0.412296
712712 0 0
713713 1.57726 0.0590690
714714 0 0
715715 − 0.139211i − 0.00520621i
716716 0 0
717717 − 29.3629i − 1.09658i
718718 0 0
719719 30.9957 1.15594 0.577972 0.816057i 0.303844π-0.303844\pi
0.577972 + 0.816057i 0.303844π0.303844\pi
720720 0 0
721721 −6.09292 −0.226912
722722 0 0
723723 − 24.0063i − 0.892803i
724724 0 0
725725 34.8723i 1.29512i
726726 0 0
727727 −41.1117 −1.52475 −0.762375 0.647135i 0.775967π-0.775967\pi
−0.762375 + 0.647135i 0.775967π0.775967\pi
728728 0 0
729729 −1.00000 −0.0370370
730730 0 0
731731 8.23765i 0.304680i
732732 0 0
733733 − 0.206562i − 0.00762954i −0.999993 0.00381477i 0.998786π-0.998786\pi
0.999993 0.00381477i 0.00121428π-0.00121428\pi
734734 0 0
735735 −6.52284 −0.240599
736736 0 0
737737 −18.6792 −0.688058
738738 0 0
739739 2.13215i 0.0784325i 0.999231 + 0.0392162i 0.0124861π0.0124861\pi
−0.999231 + 0.0392162i 0.987514π0.987514\pi
740740 0 0
741741 0.303911i 0.0111644i
742742 0 0
743743 40.5175 1.48644 0.743221 0.669046i 0.233297π-0.233297\pi
0.743221 + 0.669046i 0.233297π0.233297\pi
744744 0 0
745745 6.69256 0.245196
746746 0 0
747747 15.0496i 0.550636i
748748 0 0
749749 − 39.0761i − 1.42781i
750750 0 0
751751 12.5843 0.459208 0.229604 0.973284i 0.426257π-0.426257\pi
0.229604 + 0.973284i 0.426257π0.426257\pi
752752 0 0
753753 22.2837 0.812064
754754 0 0
755755 − 4.72529i − 0.171971i
756756 0 0
757757 − 10.6052i − 0.385452i −0.981253 0.192726i 0.938267π-0.938267\pi
0.981253 0.192726i 0.0617329π-0.0617329\pi
758758 0 0
759759 −9.89450 −0.359148
760760 0 0
761761 −42.8182 −1.55216 −0.776079 0.630635i 0.782794π-0.782794\pi
−0.776079 + 0.630635i 0.782794π0.782794\pi
762762 0 0
763763 − 36.8441i − 1.33385i
764764 0 0
765765 1.71313i 0.0619384i
766766 0 0
767767 −0.475298 −0.0171620
768768 0 0
769769 12.7455 0.459614 0.229807 0.973236i 0.426190π-0.426190\pi
0.229807 + 0.973236i 0.426190π0.426190\pi
770770 0 0
771771 8.66038i 0.311896i
772772 0 0
773773 32.3522i 1.16363i 0.813322 + 0.581814i 0.197657π0.197657\pi
−0.813322 + 0.581814i 0.802343π0.802343\pi
774774 0 0
775775 −2.66314 −0.0956630
776776 0 0
777777 −28.2704 −1.01419
778778 0 0
779779 33.5443i 1.20185i
780780 0 0
781781 − 31.8874i − 1.14102i
782782 0 0
783783 7.30205 0.260954
784784 0 0
785785 −10.8253 −0.386370
786786 0 0
787787 7.36056i 0.262376i 0.991358 + 0.131188i 0.0418791π0.0418791\pi
−0.991358 + 0.131188i 0.958121π0.958121\pi
788788 0 0
789789 13.3208i 0.474232i
790790 0 0
791791 −43.5317 −1.54781
792792 0 0
793793 −0.324298 −0.0115162
794794 0 0
795795 0.330566i 0.0117240i
796796 0 0
797797 − 24.0627i − 0.852344i −0.904642 0.426172i 0.859862π-0.859862\pi
0.904642 0.426172i 0.140138π-0.140138\pi
798798 0 0
799799 10.2306 0.361932
800800 0 0
801801 −14.6533 −0.517750
802802 0 0
803803 − 1.89450i − 0.0668556i
804804 0 0
805805 6.10550i 0.215190i
806806 0 0
807807 16.5058 0.581032
808808 0 0
809809 7.83586 0.275494 0.137747 0.990467i 0.456014π-0.456014\pi
0.137747 + 0.990467i 0.456014π0.456014\pi
810810 0 0
811811 45.7351i 1.60598i 0.595995 + 0.802988i 0.296758π0.296758\pi
−0.595995 + 0.802988i 0.703242π0.703242\pi
812812 0 0
813813 21.9769i 0.770762i
814814 0 0
815815 −5.02684 −0.176083
816816 0 0
817817 8.23765 0.288199
818818 0 0
819819 − 0.382941i − 0.0133810i
820820 0 0
821821 27.3709i 0.955250i 0.878564 + 0.477625i 0.158502π0.158502\pi
−0.878564 + 0.477625i 0.841498π0.841498\pi
822822 0 0
823823 28.8560 1.00586 0.502929 0.864328i 0.332256π-0.332256\pi
0.502929 + 0.864328i 0.332256π0.332256\pi
824824 0 0
825825 16.7064 0.581644
826826 0 0
827827 14.4227i 0.501528i 0.968048 + 0.250764i 0.0806818π0.0806818\pi
−0.968048 + 0.250764i 0.919318π0.919318\pi
828828 0 0
829829 − 21.7497i − 0.755400i −0.925928 0.377700i 0.876715π-0.876715\pi
0.925928 0.377700i 0.123285π-0.123285\pi
830830 0 0
831831 15.4862 0.537210
832832 0 0
833833 −49.8147 −1.72598
834834 0 0
835835 − 2.76513i − 0.0956914i
836836 0 0
837837 0.557647i 0.0192751i
838838 0 0
839839 44.4557 1.53478 0.767390 0.641181i 0.221555π-0.221555\pi
0.767390 + 0.641181i 0.221555π0.221555\pi
840840 0 0
841841 −24.3200 −0.838620
842842 0 0
843843 − 22.8910i − 0.788407i
844844 0 0
845845 6.15379i 0.211697i
846846 0 0
847847 5.64077 0.193819
848848 0 0
849849 6.34315 0.217696
850850 0 0
851851 17.5443i 0.601411i
852852 0 0
853853 − 16.5648i − 0.567169i −0.958947 0.283585i 0.908476π-0.908476\pi
0.958947 0.283585i 0.0915237π-0.0915237\pi
854854 0 0
855855 1.71313 0.0585879
856856 0 0
857857 19.0888 0.652062 0.326031 0.945359i 0.394289π-0.394289\pi
0.326031 + 0.945359i 0.394289π0.394289\pi
858858 0 0
859859 53.9272i 1.83997i 0.391949 + 0.919987i 0.371801π0.371801\pi
−0.391949 + 0.919987i 0.628199π0.628199\pi
860860 0 0
861861 − 42.2672i − 1.44046i
862862 0 0
863863 3.64533 0.124089 0.0620443 0.998073i 0.480238π-0.480238\pi
0.0620443 + 0.998073i 0.480238π0.480238\pi
864864 0 0
865865 2.42826 0.0825632
866866 0 0
867867 − 3.91688i − 0.133024i
868868 0 0
869869 − 38.4586i − 1.30462i
870870 0 0
871871 −0.448643 −0.0152017
872872 0 0
873873 −4.31724 −0.146116
874874 0 0
875875 − 21.1020i − 0.713377i
876876 0 0
877877 56.6481i 1.91287i 0.291945 + 0.956435i 0.405698π0.405698\pi
−0.291945 + 0.956435i 0.594302π0.594302\pi
878878 0 0
879879 30.5783 1.03138
880880 0 0
881881 20.0118 0.674214 0.337107 0.941466i 0.390552π-0.390552\pi
0.337107 + 0.941466i 0.390552π0.390552\pi
882882 0 0
883883 − 15.0292i − 0.505773i −0.967496 0.252887i 0.918620π-0.918620\pi
0.967496 0.252887i 0.0813799π-0.0813799\pi
884884 0 0
885885 2.67923i 0.0900614i
886886 0 0
887887 26.1180 0.876958 0.438479 0.898742i 0.355517π-0.355517\pi
0.438479 + 0.898742i 0.355517π0.355517\pi
888888 0 0
889889 −23.2404 −0.779458
890890 0 0
891891 − 3.49824i − 0.117195i
892892 0 0
893893 − 10.2306i − 0.342354i
894894 0 0
895895 −6.21805 −0.207847
896896 0 0
897897 −0.237649 −0.00793486
898898 0 0
899899 − 4.07197i − 0.135808i
900900 0 0
901901 2.52452i 0.0841038i
902902 0 0
903903 −10.3798 −0.345418
904904 0 0
905905 7.25507 0.241167
906906 0 0
907907 51.2480i 1.70166i 0.525439 + 0.850831i 0.323901π0.323901\pi
−0.525439 + 0.850831i 0.676099π0.676099\pi
908908 0 0
909909 − 0.641669i − 0.0212828i
910910 0 0
911911 21.0535 0.697533 0.348767 0.937210i 0.386601π-0.386601\pi
0.348767 + 0.937210i 0.386601π0.386601\pi
912912 0 0
913913 −52.6470 −1.74236
914914 0 0
915915 1.82805i 0.0604336i
916916 0 0
917917 13.6569i 0.450989i
918918 0 0
919919 −17.8839 −0.589937 −0.294968 0.955507i 0.595309π-0.595309\pi
−0.294968 + 0.955507i 0.595309π0.595309\pi
920920 0 0
921921 17.1286 0.564407
922922 0 0
923923 − 0.765881i − 0.0252093i
924924 0 0
925925 − 29.6228i − 0.973992i
926926 0 0
927927 −1.33686 −0.0439081
928928 0 0
929929 10.2774 0.337192 0.168596 0.985685i 0.446077π-0.446077\pi
0.168596 + 0.985685i 0.446077π0.446077\pi
930930 0 0
931931 49.8147i 1.63261i
932932 0 0
933933 26.8651i 0.879523i
934934 0 0
935935 −5.99294 −0.195990
936936 0 0
937937 13.5780 0.443574 0.221787 0.975095i 0.428811π-0.428811\pi
0.221787 + 0.975095i 0.428811π0.428811\pi
938938 0 0
939939 19.6890i 0.642527i
940940 0 0
941941 − 5.59890i − 0.182519i −0.995827 0.0912595i 0.970911π-0.970911\pi
0.995827 0.0912595i 0.0290893π-0.0290893\pi
942942 0 0
943943 −26.2306 −0.854186
944944 0 0
945945 −2.15862 −0.0702199
946946 0 0
947947 − 46.9106i − 1.52439i −0.647348 0.762194i 0.724122π-0.724122\pi
0.647348 0.762194i 0.275878π-0.275878\pi
948948 0 0
949949 − 0.0455027i − 0.00147708i
950950 0 0
951951 30.1860 0.978847
952952 0 0
953953 −5.59115 −0.181115 −0.0905576 0.995891i 0.528865π-0.528865\pi
−0.0905576 + 0.995891i 0.528865π0.528865\pi
954954 0 0
955955 − 4.08740i − 0.132265i
956956 0 0
957957 25.5443i 0.825730i
958958 0 0
959959 −15.4022 −0.497362
960960 0 0
961961 −30.6890 −0.989969
962962 0 0
963963 − 8.57373i − 0.276285i
964964 0 0
965965 5.42367i 0.174594i
966966 0 0
967967 30.7561 0.989048 0.494524 0.869164i 0.335342π-0.335342\pi
0.494524 + 0.869164i 0.335342π0.335342\pi
968968 0 0
969969 13.0831 0.420290
970970 0 0
971971 11.3668i 0.364779i 0.983226 + 0.182389i 0.0583832π0.0583832\pi
−0.983226 + 0.182389i 0.941617π0.941617\pi
972972 0 0
973973 − 37.9070i − 1.21524i
974974 0 0
975975 0.401260 0.0128506
976976 0 0
977977 −22.8323 −0.730471 −0.365235 0.930915i 0.619012π-0.619012\pi
−0.365235 + 0.930915i 0.619012π0.619012\pi
978978 0 0
979979 − 51.2608i − 1.63830i
980980 0 0
981981 − 8.08402i − 0.258103i
982982 0 0
983983 46.3557 1.47852 0.739258 0.673422i 0.235176π-0.235176\pi
0.739258 + 0.673422i 0.235176π0.235176\pi
984984 0 0
985985 5.01686 0.159850
986986 0 0
987987 12.8910i 0.410324i
988988 0 0
989989 6.44158i 0.204830i
990990 0 0
991991 3.43683 0.109175 0.0545873 0.998509i 0.482616π-0.482616\pi
0.0545873 + 0.998509i 0.482616π0.482616\pi
992992 0 0
993993 −20.7784 −0.659383
994994 0 0
995995 − 1.74294i − 0.0552550i
996996 0 0
997997 31.0320i 0.982794i 0.870936 + 0.491397i 0.163514π0.163514\pi
−0.870936 + 0.491397i 0.836486π0.836486\pi
998998 0 0
999999 −6.20285 −0.196249
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 3072.2.d.f.1537.7 8
4.3 odd 2 3072.2.d.i.1537.3 8
8.3 odd 2 3072.2.d.i.1537.6 8
8.5 even 2 inner 3072.2.d.f.1537.2 8
16.3 odd 4 3072.2.a.o.1.3 4
16.5 even 4 3072.2.a.t.1.2 4
16.11 odd 4 3072.2.a.n.1.2 4
16.13 even 4 3072.2.a.i.1.3 4
32.3 odd 8 192.2.j.a.49.3 8
32.5 even 8 48.2.j.a.13.4 8
32.11 odd 8 384.2.j.a.289.2 8
32.13 even 8 384.2.j.b.97.4 8
32.19 odd 8 384.2.j.a.97.2 8
32.21 even 8 384.2.j.b.289.4 8
32.27 odd 8 192.2.j.a.145.3 8
32.29 even 8 48.2.j.a.37.4 yes 8
48.5 odd 4 9216.2.a.y.1.3 4
48.11 even 4 9216.2.a.x.1.3 4
48.29 odd 4 9216.2.a.bo.1.2 4
48.35 even 4 9216.2.a.bn.1.2 4
96.5 odd 8 144.2.k.b.109.1 8
96.11 even 8 1152.2.k.f.289.2 8
96.29 odd 8 144.2.k.b.37.1 8
96.35 even 8 576.2.k.b.433.3 8
96.53 odd 8 1152.2.k.c.289.2 8
96.59 even 8 576.2.k.b.145.3 8
96.77 odd 8 1152.2.k.c.865.2 8
96.83 even 8 1152.2.k.f.865.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.2.j.a.13.4 8 32.5 even 8
48.2.j.a.37.4 yes 8 32.29 even 8
144.2.k.b.37.1 8 96.29 odd 8
144.2.k.b.109.1 8 96.5 odd 8
192.2.j.a.49.3 8 32.3 odd 8
192.2.j.a.145.3 8 32.27 odd 8
384.2.j.a.97.2 8 32.19 odd 8
384.2.j.a.289.2 8 32.11 odd 8
384.2.j.b.97.4 8 32.13 even 8
384.2.j.b.289.4 8 32.21 even 8
576.2.k.b.145.3 8 96.59 even 8
576.2.k.b.433.3 8 96.35 even 8
1152.2.k.c.289.2 8 96.53 odd 8
1152.2.k.c.865.2 8 96.77 odd 8
1152.2.k.f.289.2 8 96.11 even 8
1152.2.k.f.865.2 8 96.83 even 8
3072.2.a.i.1.3 4 16.13 even 4
3072.2.a.n.1.2 4 16.11 odd 4
3072.2.a.o.1.3 4 16.3 odd 4
3072.2.a.t.1.2 4 16.5 even 4
3072.2.d.f.1537.2 8 8.5 even 2 inner
3072.2.d.f.1537.7 8 1.1 even 1 trivial
3072.2.d.i.1537.3 8 4.3 odd 2
3072.2.d.i.1537.6 8 8.3 odd 2
9216.2.a.x.1.3 4 48.11 even 4
9216.2.a.y.1.3 4 48.5 odd 4
9216.2.a.bn.1.2 4 48.35 even 4
9216.2.a.bo.1.2 4 48.29 odd 4