Properties

Label 1904.2.a.m.1.3
Level 19041904
Weight 22
Character 1904.1
Self dual yes
Analytic conductor 15.20415.204
Analytic rank 11
Dimension 33
CM no
Inner twists 11

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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] = [1904,2,Mod(1,1904)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1904, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 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("1904.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1904=24717 1904 = 2^{4} \cdot 7 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1904.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,0,-1,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 15.203516544915.2035165449
Analytic rank: 11
Dimension: 33
Coefficient field: 3.3.229.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x34x1 x^{3} - 4x - 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 952)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 2.114912.11491 of defining polynomial
Character χ\chi == 1904.1

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+1.47283q31.11491q51.00000q70.830760q9+2.22982q111.64207q151.00000q174.94567q191.47283q219.17548q233.75698q255.64207q27+0.945668q29+1.11491q31+3.28415q33+1.11491q354.94567q37+10.2709q41+11.2166q43+0.926221q459.89134q47+1.00000q491.47283q51+7.83076q532.48604q557.28415q5713.7438q59+0.904539q61+0.830760q639.91302q6713.5140q6914.6894q71+0.756981q735.53341q752.22982q778.00000q795.81756q81+11.9736q83+1.11491q85+1.39281q87+11.1755q89+1.64207q93+5.51396q95+10.0606q971.85244q99+O(q100)q+1.47283 q^{3} -1.11491 q^{5} -1.00000 q^{7} -0.830760 q^{9} +2.22982 q^{11} -1.64207 q^{15} -1.00000 q^{17} -4.94567 q^{19} -1.47283 q^{21} -9.17548 q^{23} -3.75698 q^{25} -5.64207 q^{27} +0.945668 q^{29} +1.11491 q^{31} +3.28415 q^{33} +1.11491 q^{35} -4.94567 q^{37} +10.2709 q^{41} +11.2166 q^{43} +0.926221 q^{45} -9.89134 q^{47} +1.00000 q^{49} -1.47283 q^{51} +7.83076 q^{53} -2.48604 q^{55} -7.28415 q^{57} -13.7438 q^{59} +0.904539 q^{61} +0.830760 q^{63} -9.91302 q^{67} -13.5140 q^{69} -14.6894 q^{71} +0.756981 q^{73} -5.53341 q^{75} -2.22982 q^{77} -8.00000 q^{79} -5.81756 q^{81} +11.9736 q^{83} +1.11491 q^{85} +1.39281 q^{87} +11.1755 q^{89} +1.64207 q^{93} +5.51396 q^{95} +10.0606 q^{97} -1.85244 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3qq3+3q53q7+2q96q114q153q174q19+q214q234q2516q278q293q31+8q333q354q37+9q41+q43++13q97+O(q100) 3 q - q^{3} + 3 q^{5} - 3 q^{7} + 2 q^{9} - 6 q^{11} - 4 q^{15} - 3 q^{17} - 4 q^{19} + q^{21} - 4 q^{23} - 4 q^{25} - 16 q^{27} - 8 q^{29} - 3 q^{31} + 8 q^{33} - 3 q^{35} - 4 q^{37} + 9 q^{41} + q^{43}+ \cdots + 13 q^{97}+O(q^{100}) Copy content Toggle raw display

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 1.47283 0.850341 0.425171 0.905113i 0.360214π-0.360214\pi
0.425171 + 0.905113i 0.360214π0.360214\pi
44 0 0
55 −1.11491 −0.498602 −0.249301 0.968426i 0.580201π-0.580201\pi
−0.249301 + 0.968426i 0.580201π0.580201\pi
66 0 0
77 −1.00000 −0.377964
88 0 0
99 −0.830760 −0.276920
1010 0 0
1111 2.22982 0.672315 0.336157 0.941806i 0.390873π-0.390873\pi
0.336157 + 0.941806i 0.390873π0.390873\pi
1212 0 0
1313 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1414 0 0
1515 −1.64207 −0.423982
1616 0 0
1717 −1.00000 −0.242536
1818 0 0
1919 −4.94567 −1.13461 −0.567307 0.823506i 0.692015π-0.692015\pi
−0.567307 + 0.823506i 0.692015π0.692015\pi
2020 0 0
2121 −1.47283 −0.321399
2222 0 0
2323 −9.17548 −1.91322 −0.956610 0.291371i 0.905889π-0.905889\pi
−0.956610 + 0.291371i 0.905889π0.905889\pi
2424 0 0
2525 −3.75698 −0.751396
2626 0 0
2727 −5.64207 −1.08582
2828 0 0
2929 0.945668 0.175606 0.0878031 0.996138i 0.472015π-0.472015\pi
0.0878031 + 0.996138i 0.472015π0.472015\pi
3030 0 0
3131 1.11491 0.200243 0.100122 0.994975i 0.468077π-0.468077\pi
0.100122 + 0.994975i 0.468077π0.468077\pi
3232 0 0
3333 3.28415 0.571697
3434 0 0
3535 1.11491 0.188454
3636 0 0
3737 −4.94567 −0.813063 −0.406531 0.913637i 0.633262π-0.633262\pi
−0.406531 + 0.913637i 0.633262π0.633262\pi
3838 0 0
3939 0 0
4040 0 0
4141 10.2709 1.60405 0.802026 0.597289i 0.203756π-0.203756\pi
0.802026 + 0.597289i 0.203756π0.203756\pi
4242 0 0
4343 11.2166 1.71052 0.855259 0.518201i 0.173398π-0.173398\pi
0.855259 + 0.518201i 0.173398π0.173398\pi
4444 0 0
4545 0.926221 0.138073
4646 0 0
4747 −9.89134 −1.44280 −0.721400 0.692519i 0.756501π-0.756501\pi
−0.721400 + 0.692519i 0.756501π0.756501\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 −1.47283 −0.206238
5252 0 0
5353 7.83076 1.07564 0.537819 0.843060i 0.319248π-0.319248\pi
0.537819 + 0.843060i 0.319248π0.319248\pi
5454 0 0
5555 −2.48604 −0.335217
5656 0 0
5757 −7.28415 −0.964809
5858 0 0
5959 −13.7438 −1.78929 −0.894644 0.446780i 0.852571π-0.852571\pi
−0.894644 + 0.446780i 0.852571π0.852571\pi
6060 0 0
6161 0.904539 0.115814 0.0579072 0.998322i 0.481557π-0.481557\pi
0.0579072 + 0.998322i 0.481557π0.481557\pi
6262 0 0
6363 0.830760 0.104666
6464 0 0
6565 0 0
6666 0 0
6767 −9.91302 −1.21107 −0.605534 0.795820i 0.707040π-0.707040\pi
−0.605534 + 0.795820i 0.707040π0.707040\pi
6868 0 0
6969 −13.5140 −1.62689
7070 0 0
7171 −14.6894 −1.74332 −0.871658 0.490114i 0.836955π-0.836955\pi
−0.871658 + 0.490114i 0.836955π0.836955\pi
7272 0 0
7373 0.756981 0.0885979 0.0442990 0.999018i 0.485895π-0.485895\pi
0.0442990 + 0.999018i 0.485895π0.485895\pi
7474 0 0
7575 −5.53341 −0.638943
7676 0 0
7777 −2.22982 −0.254111
7878 0 0
7979 −8.00000 −0.900070 −0.450035 0.893011i 0.648589π-0.648589\pi
−0.450035 + 0.893011i 0.648589π0.648589\pi
8080 0 0
8181 −5.81756 −0.646395
8282 0 0
8383 11.9736 1.31427 0.657136 0.753772i 0.271768π-0.271768\pi
0.657136 + 0.753772i 0.271768π0.271768\pi
8484 0 0
8585 1.11491 0.120929
8686 0 0
8787 1.39281 0.149325
8888 0 0
8989 11.1755 1.18460 0.592299 0.805718i 0.298220π-0.298220\pi
0.592299 + 0.805718i 0.298220π0.298220\pi
9090 0 0
9191 0 0
9292 0 0
9393 1.64207 0.170275
9494 0 0
9595 5.51396 0.565721
9696 0 0
9797 10.0606 1.02150 0.510748 0.859730i 0.329368π-0.329368\pi
0.510748 + 0.859730i 0.329368π0.329368\pi
9898 0 0
9999 −1.85244 −0.186177
100100 0 0
101101 −18.6894 −1.85967 −0.929835 0.367978i 0.880050π-0.880050\pi
−0.929835 + 0.367978i 0.880050π0.880050\pi
102102 0 0
103103 −12.1212 −1.19433 −0.597166 0.802118i 0.703707π-0.703707\pi
−0.597166 + 0.802118i 0.703707π0.703707\pi
104104 0 0
105105 1.64207 0.160250
106106 0 0
107107 1.89134 0.182842 0.0914212 0.995812i 0.470859π-0.470859\pi
0.0914212 + 0.995812i 0.470859π0.470859\pi
108108 0 0
109109 −14.0000 −1.34096 −0.670478 0.741929i 0.733911π-0.733911\pi
−0.670478 + 0.741929i 0.733911π0.733911\pi
110110 0 0
111111 −7.28415 −0.691381
112112 0 0
113113 −3.85244 −0.362407 −0.181204 0.983446i 0.557999π-0.557999\pi
−0.181204 + 0.983446i 0.557999π0.557999\pi
114114 0 0
115115 10.2298 0.953935
116116 0 0
117117 0 0
118118 0 0
119119 1.00000 0.0916698
120120 0 0
121121 −6.02792 −0.547993
122122 0 0
123123 15.1274 1.36399
124124 0 0
125125 9.76322 0.873249
126126 0 0
127127 21.2361 1.88440 0.942198 0.335057i 0.108756π-0.108756\pi
0.942198 + 0.335057i 0.108756π0.108756\pi
128128 0 0
129129 16.5202 1.45452
130130 0 0
131131 4.60719 0.402532 0.201266 0.979537i 0.435494π-0.435494\pi
0.201266 + 0.979537i 0.435494π0.435494\pi
132132 0 0
133133 4.94567 0.428844
134134 0 0
135135 6.29039 0.541391
136136 0 0
137137 0.379608 0.0324321 0.0162160 0.999869i 0.494838π-0.494838\pi
0.0162160 + 0.999869i 0.494838π0.494838\pi
138138 0 0
139139 −6.06058 −0.514051 −0.257026 0.966405i 0.582742π-0.582742\pi
−0.257026 + 0.966405i 0.582742π0.582742\pi
140140 0 0
141141 −14.5683 −1.22687
142142 0 0
143143 0 0
144144 0 0
145145 −1.05433 −0.0875575
146146 0 0
147147 1.47283 0.121477
148148 0 0
149149 −10.1887 −0.834690 −0.417345 0.908748i 0.637039π-0.637039\pi
−0.417345 + 0.908748i 0.637039π0.637039\pi
150150 0 0
151151 8.18869 0.666386 0.333193 0.942859i 0.391874π-0.391874\pi
0.333193 + 0.942859i 0.391874π0.391874\pi
152152 0 0
153153 0.830760 0.0671630
154154 0 0
155155 −1.24302 −0.0998417
156156 0 0
157157 −14.2687 −1.13877 −0.569383 0.822072i 0.692818π-0.692818\pi
−0.569383 + 0.822072i 0.692818π0.692818\pi
158158 0 0
159159 11.5334 0.914659
160160 0 0
161161 9.17548 0.723129
162162 0 0
163163 −15.7438 −1.23315 −0.616574 0.787297i 0.711480π-0.711480\pi
−0.616574 + 0.787297i 0.711480π0.711480\pi
164164 0 0
165165 −3.66152 −0.285049
166166 0 0
167167 0.648317 0.0501683 0.0250841 0.999685i 0.492015π-0.492015\pi
0.0250841 + 0.999685i 0.492015π0.492015\pi
168168 0 0
169169 −13.0000 −1.00000
170170 0 0
171171 4.10866 0.314197
172172 0 0
173173 15.9325 1.21132 0.605661 0.795722i 0.292909π-0.292909\pi
0.605661 + 0.795722i 0.292909π0.292909\pi
174174 0 0
175175 3.75698 0.284001
176176 0 0
177177 −20.2423 −1.52150
178178 0 0
179179 17.0257 1.27256 0.636280 0.771458i 0.280472π-0.280472\pi
0.636280 + 0.771458i 0.280472π0.280472\pi
180180 0 0
181181 5.63511 0.418855 0.209427 0.977824i 0.432840π-0.432840\pi
0.209427 + 0.977824i 0.432840π0.432840\pi
182182 0 0
183183 1.33224 0.0984817
184184 0 0
185185 5.51396 0.405395
186186 0 0
187187 −2.22982 −0.163060
188188 0 0
189189 5.64207 0.410400
190190 0 0
191191 −2.88509 −0.208758 −0.104379 0.994538i 0.533285π-0.533285\pi
−0.104379 + 0.994538i 0.533285π0.533285\pi
192192 0 0
193193 17.5264 1.26158 0.630791 0.775953i 0.282731π-0.282731\pi
0.630791 + 0.775953i 0.282731π0.282731\pi
194194 0 0
195195 0 0
196196 0 0
197197 14.9193 1.06295 0.531477 0.847073i 0.321637π-0.321637\pi
0.531477 + 0.847073i 0.321637π0.321637\pi
198198 0 0
199199 16.6483 1.18017 0.590084 0.807342i 0.299095π-0.299095\pi
0.590084 + 0.807342i 0.299095π0.299095\pi
200200 0 0
201201 −14.6002 −1.02982
202202 0 0
203203 −0.945668 −0.0663729
204204 0 0
205205 −11.4512 −0.799783
206206 0 0
207207 7.62263 0.529809
208208 0 0
209209 −11.0279 −0.762818
210210 0 0
211211 −7.40530 −0.509802 −0.254901 0.966967i 0.582043π-0.582043\pi
−0.254901 + 0.966967i 0.582043π0.582043\pi
212212 0 0
213213 −21.6351 −1.48241
214214 0 0
215215 −12.5055 −0.852867
216216 0 0
217217 −1.11491 −0.0756849
218218 0 0
219219 1.11491 0.0753385
220220 0 0
221221 0 0
222222 0 0
223223 −27.1491 −1.81804 −0.909018 0.416756i 0.863167π-0.863167\pi
−0.909018 + 0.416756i 0.863167π0.863167\pi
224224 0 0
225225 3.12115 0.208077
226226 0 0
227227 4.50772 0.299188 0.149594 0.988748i 0.452203π-0.452203\pi
0.149594 + 0.988748i 0.452203π0.452203\pi
228228 0 0
229229 10.2298 0.676005 0.338003 0.941145i 0.390249π-0.390249\pi
0.338003 + 0.941145i 0.390249π0.390249\pi
230230 0 0
231231 −3.28415 −0.216081
232232 0 0
233233 11.5529 0.756853 0.378426 0.925631i 0.376465π-0.376465\pi
0.378426 + 0.925631i 0.376465π0.376465\pi
234234 0 0
235235 11.0279 0.719382
236236 0 0
237237 −11.7827 −0.765367
238238 0 0
239239 30.7570 1.98950 0.994752 0.102317i 0.0326256π-0.0326256\pi
0.994752 + 0.102317i 0.0326256π0.0326256\pi
240240 0 0
241241 −0.967349 −0.0623124 −0.0311562 0.999515i 0.509919π-0.509919\pi
−0.0311562 + 0.999515i 0.509919π0.509919\pi
242242 0 0
243243 8.35793 0.536161
244244 0 0
245245 −1.11491 −0.0712288
246246 0 0
247247 0 0
248248 0 0
249249 17.6351 1.11758
250250 0 0
251251 −0.0264075 −0.00166683 −0.000833413 1.00000i 0.500265π-0.500265\pi
−0.000833413 1.00000i 0.500265π0.500265\pi
252252 0 0
253253 −20.4596 −1.28629
254254 0 0
255255 1.64207 0.102831
256256 0 0
257257 14.7159 0.917950 0.458975 0.888449i 0.348217π-0.348217\pi
0.458975 + 0.888449i 0.348217π0.348217\pi
258258 0 0
259259 4.94567 0.307309
260260 0 0
261261 −0.785623 −0.0486289
262262 0 0
263263 −24.9193 −1.53659 −0.768294 0.640097i 0.778894π-0.778894\pi
−0.768294 + 0.640097i 0.778894π0.778894\pi
264264 0 0
265265 −8.73057 −0.536315
266266 0 0
267267 16.4596 1.00731
268268 0 0
269269 −23.9861 −1.46246 −0.731229 0.682133i 0.761053π-0.761053\pi
−0.731229 + 0.682133i 0.761053π0.761053\pi
270270 0 0
271271 15.0668 0.915244 0.457622 0.889147i 0.348701π-0.348701\pi
0.457622 + 0.889147i 0.348701π0.348701\pi
272272 0 0
273273 0 0
274274 0 0
275275 −8.37737 −0.505175
276276 0 0
277277 0.350966 0.0210875 0.0105437 0.999944i 0.496644π-0.496644\pi
0.0105437 + 0.999944i 0.496644π0.496644\pi
278278 0 0
279279 −0.926221 −0.0554514
280280 0 0
281281 5.30583 0.316519 0.158260 0.987398i 0.449412π-0.449412\pi
0.158260 + 0.987398i 0.449412π0.449412\pi
282282 0 0
283283 −11.6134 −0.690347 −0.345173 0.938539i 0.612180π-0.612180\pi
−0.345173 + 0.938539i 0.612180π0.612180\pi
284284 0 0
285285 8.12115 0.481055
286286 0 0
287287 −10.2709 −0.606275
288288 0 0
289289 1.00000 0.0588235
290290 0 0
291291 14.8176 0.868621
292292 0 0
293293 20.2423 1.18257 0.591284 0.806463i 0.298621π-0.298621\pi
0.591284 + 0.806463i 0.298621π0.298621\pi
294294 0 0
295295 15.3230 0.892142
296296 0 0
297297 −12.5808 −0.730011
298298 0 0
299299 0 0
300300 0 0
301301 −11.2166 −0.646515
302302 0 0
303303 −27.5264 −1.58135
304304 0 0
305305 −1.00848 −0.0577453
306306 0 0
307307 1.20189 0.0685955 0.0342978 0.999412i 0.489081π-0.489081\pi
0.0342978 + 0.999412i 0.489081π0.489081\pi
308308 0 0
309309 −17.8524 −1.01559
310310 0 0
311311 10.2081 0.578850 0.289425 0.957201i 0.406536π-0.406536\pi
0.289425 + 0.957201i 0.406536π0.406536\pi
312312 0 0
313313 18.7375 1.05911 0.529554 0.848276i 0.322359π-0.322359\pi
0.529554 + 0.848276i 0.322359π0.322359\pi
314314 0 0
315315 −0.926221 −0.0521866
316316 0 0
317317 −10.4985 −0.589656 −0.294828 0.955550i 0.595262π-0.595262\pi
−0.294828 + 0.955550i 0.595262π0.595262\pi
318318 0 0
319319 2.10866 0.118063
320320 0 0
321321 2.78562 0.155478
322322 0 0
323323 4.94567 0.275184
324324 0 0
325325 0 0
326326 0 0
327327 −20.6197 −1.14027
328328 0 0
329329 9.89134 0.545327
330330 0 0
331331 −27.0062 −1.48440 −0.742199 0.670180i 0.766217π-0.766217\pi
−0.742199 + 0.670180i 0.766217π0.766217\pi
332332 0 0
333333 4.10866 0.225153
334334 0 0
335335 11.0521 0.603841
336336 0 0
337337 −10.4985 −0.571891 −0.285946 0.958246i 0.592308π-0.592308\pi
−0.285946 + 0.958246i 0.592308π0.592308\pi
338338 0 0
339339 −5.67401 −0.308170
340340 0 0
341341 2.48604 0.134626
342342 0 0
343343 −1.00000 −0.0539949
344344 0 0
345345 15.0668 0.811170
346346 0 0
347347 −15.0668 −0.808829 −0.404415 0.914576i 0.632525π-0.632525\pi
−0.404415 + 0.914576i 0.632525π0.632525\pi
348348 0 0
349349 7.86493 0.421000 0.210500 0.977594i 0.432491π-0.432491\pi
0.210500 + 0.977594i 0.432491π0.432491\pi
350350 0 0
351351 0 0
352352 0 0
353353 29.4053 1.56509 0.782543 0.622596i 0.213922π-0.213922\pi
0.782543 + 0.622596i 0.213922π0.213922\pi
354354 0 0
355355 16.3774 0.869221
356356 0 0
357357 1.47283 0.0779506
358358 0 0
359359 5.91302 0.312077 0.156039 0.987751i 0.450128π-0.450128\pi
0.156039 + 0.987751i 0.450128π0.450128\pi
360360 0 0
361361 5.45963 0.287349
362362 0 0
363363 −8.87813 −0.465981
364364 0 0
365365 −0.843964 −0.0441751
366366 0 0
367367 15.6762 0.818293 0.409147 0.912469i 0.365826π-0.365826\pi
0.409147 + 0.912469i 0.365826π0.365826\pi
368368 0 0
369369 −8.53269 −0.444194
370370 0 0
371371 −7.83076 −0.406553
372372 0 0
373373 −9.81131 −0.508011 −0.254005 0.967203i 0.581748π-0.581748\pi
−0.254005 + 0.967203i 0.581748π0.581748\pi
374374 0 0
375375 14.3796 0.742560
376376 0 0
377377 0 0
378378 0 0
379379 −11.6615 −0.599012 −0.299506 0.954094i 0.596822π-0.596822\pi
−0.299506 + 0.954094i 0.596822π0.596822\pi
380380 0 0
381381 31.2772 1.60238
382382 0 0
383383 27.6087 1.41074 0.705369 0.708840i 0.250781π-0.250781\pi
0.705369 + 0.708840i 0.250781π0.250781\pi
384384 0 0
385385 2.48604 0.126700
386386 0 0
387387 −9.31832 −0.473677
388388 0 0
389389 11.8308 0.599843 0.299922 0.953964i 0.403039π-0.403039\pi
0.299922 + 0.953964i 0.403039π0.403039\pi
390390 0 0
391391 9.17548 0.464024
392392 0 0
393393 6.78562 0.342289
394394 0 0
395395 8.91926 0.448777
396396 0 0
397397 −22.7111 −1.13984 −0.569919 0.821701i 0.693026π-0.693026\pi
−0.569919 + 0.821701i 0.693026π0.693026\pi
398398 0 0
399399 7.28415 0.364663
400400 0 0
401401 37.6087 1.87809 0.939045 0.343795i 0.111713π-0.111713\pi
0.939045 + 0.343795i 0.111713π0.111713\pi
402402 0 0
403403 0 0
404404 0 0
405405 6.48604 0.322294
406406 0 0
407407 −11.0279 −0.546634
408408 0 0
409409 −22.5808 −1.11655 −0.558274 0.829657i 0.688536π-0.688536\pi
−0.558274 + 0.829657i 0.688536π0.688536\pi
410410 0 0
411411 0.559099 0.0275783
412412 0 0
413413 13.7438 0.676287
414414 0 0
415415 −13.3494 −0.655299
416416 0 0
417417 −8.92622 −0.437119
418418 0 0
419419 −24.2904 −1.18666 −0.593332 0.804958i 0.702188π-0.702188\pi
−0.593332 + 0.804958i 0.702188π0.702188\pi
420420 0 0
421421 11.5676 0.563769 0.281885 0.959448i 0.409040π-0.409040\pi
0.281885 + 0.959448i 0.409040π0.409040\pi
422422 0 0
423423 8.21733 0.399540
424424 0 0
425425 3.75698 0.182240
426426 0 0
427427 −0.904539 −0.0437737
428428 0 0
429429 0 0
430430 0 0
431431 22.9457 1.10525 0.552627 0.833429i 0.313625π-0.313625\pi
0.552627 + 0.833429i 0.313625π0.313625\pi
432432 0 0
433433 19.8913 0.955917 0.477958 0.878383i 0.341377π-0.341377\pi
0.477958 + 0.878383i 0.341377π0.341377\pi
434434 0 0
435435 −1.55286 −0.0744538
436436 0 0
437437 45.3789 2.17077
438438 0 0
439439 −19.8936 −0.949468 −0.474734 0.880129i 0.657456π-0.657456\pi
−0.474734 + 0.880129i 0.657456π0.657456\pi
440440 0 0
441441 −0.830760 −0.0395600
442442 0 0
443443 15.7827 0.749857 0.374929 0.927054i 0.377667π-0.377667\pi
0.374929 + 0.927054i 0.377667π0.377667\pi
444444 0 0
445445 −12.4596 −0.590643
446446 0 0
447447 −15.0062 −0.709771
448448 0 0
449449 −41.2702 −1.94766 −0.973831 0.227273i 0.927019π-0.927019\pi
−0.973831 + 0.227273i 0.927019π0.927019\pi
450450 0 0
451451 22.9023 1.07843
452452 0 0
453453 12.0606 0.566655
454454 0 0
455455 0 0
456456 0 0
457457 −36.9923 −1.73043 −0.865214 0.501403i 0.832817π-0.832817\pi
−0.865214 + 0.501403i 0.832817π0.832817\pi
458458 0 0
459459 5.64207 0.263349
460460 0 0
461461 10.3649 0.482741 0.241370 0.970433i 0.422403π-0.422403\pi
0.241370 + 0.970433i 0.422403π0.422403\pi
462462 0 0
463463 −12.2709 −0.570279 −0.285140 0.958486i 0.592040π-0.592040\pi
−0.285140 + 0.958486i 0.592040π0.592040\pi
464464 0 0
465465 −1.83076 −0.0848995
466466 0 0
467467 −8.86341 −0.410150 −0.205075 0.978746i 0.565744π-0.565744\pi
−0.205075 + 0.978746i 0.565744π0.565744\pi
468468 0 0
469469 9.91302 0.457741
470470 0 0
471471 −21.0154 −0.968340
472472 0 0
473473 25.0110 1.15001
474474 0 0
475475 18.5808 0.852545
476476 0 0
477477 −6.50548 −0.297866
478478 0 0
479479 4.56606 0.208629 0.104314 0.994544i 0.466735π-0.466735\pi
0.104314 + 0.994544i 0.466735π0.466735\pi
480480 0 0
481481 0 0
482482 0 0
483483 13.5140 0.614907
484484 0 0
485485 −11.2166 −0.509320
486486 0 0
487487 −23.8649 −1.08142 −0.540712 0.841208i 0.681845π-0.681845\pi
−0.540712 + 0.841208i 0.681845π0.681845\pi
488488 0 0
489489 −23.1880 −1.04860
490490 0 0
491491 7.00624 0.316187 0.158094 0.987424i 0.449465π-0.449465\pi
0.158094 + 0.987424i 0.449465π0.449465\pi
492492 0 0
493493 −0.945668 −0.0425907
494494 0 0
495495 2.06530 0.0928284
496496 0 0
497497 14.6894 0.658912
498498 0 0
499499 −10.2687 −0.459691 −0.229845 0.973227i 0.573822π-0.573822\pi
−0.229845 + 0.973227i 0.573822π0.573822\pi
500500 0 0
501501 0.954863 0.0426601
502502 0 0
503503 −8.53413 −0.380518 −0.190259 0.981734i 0.560933π-0.560933\pi
−0.190259 + 0.981734i 0.560933π0.560933\pi
504504 0 0
505505 20.8370 0.927234
506506 0 0
507507 −19.1468 −0.850341
508508 0 0
509509 −23.8216 −1.05587 −0.527936 0.849284i 0.677034π-0.677034\pi
−0.527936 + 0.849284i 0.677034π0.677034\pi
510510 0 0
511511 −0.756981 −0.0334869
512512 0 0
513513 27.9038 1.23198
514514 0 0
515515 13.5140 0.595496
516516 0 0
517517 −22.0558 −0.970015
518518 0 0
519519 23.4659 1.03004
520520 0 0
521521 −3.48532 −0.152695 −0.0763473 0.997081i 0.524326π-0.524326\pi
−0.0763473 + 0.997081i 0.524326π0.524326\pi
522522 0 0
523523 23.2144 1.01509 0.507547 0.861624i 0.330552π-0.330552\pi
0.507547 + 0.861624i 0.330552π0.330552\pi
524524 0 0
525525 5.53341 0.241498
526526 0 0
527527 −1.11491 −0.0485661
528528 0 0
529529 61.1895 2.66041
530530 0 0
531531 11.4178 0.495490
532532 0 0
533533 0 0
534534 0 0
535535 −2.10866 −0.0911655
536536 0 0
537537 25.0760 1.08211
538538 0 0
539539 2.22982 0.0960449
540540 0 0
541541 −9.08074 −0.390411 −0.195206 0.980762i 0.562537π-0.562537\pi
−0.195206 + 0.980762i 0.562537π0.562537\pi
542542 0 0
543543 8.29959 0.356169
544544 0 0
545545 15.6087 0.668603
546546 0 0
547547 −5.34945 −0.228726 −0.114363 0.993439i 0.536483π-0.536483\pi
−0.114363 + 0.993439i 0.536483π0.536483\pi
548548 0 0
549549 −0.751455 −0.0320713
550550 0 0
551551 −4.67696 −0.199245
552552 0 0
553553 8.00000 0.340195
554554 0 0
555555 8.12115 0.344724
556556 0 0
557557 −13.9472 −0.590961 −0.295481 0.955349i 0.595480π-0.595480\pi
−0.295481 + 0.955349i 0.595480π0.595480\pi
558558 0 0
559559 0 0
560560 0 0
561561 −3.28415 −0.138657
562562 0 0
563563 −8.43322 −0.355418 −0.177709 0.984083i 0.556869π-0.556869\pi
−0.177709 + 0.984083i 0.556869π0.556869\pi
564564 0 0
565565 4.29512 0.180697
566566 0 0
567567 5.81756 0.244314
568568 0 0
569569 −5.89357 −0.247071 −0.123536 0.992340i 0.539423π-0.539423\pi
−0.123536 + 0.992340i 0.539423π0.539423\pi
570570 0 0
571571 −40.2857 −1.68590 −0.842951 0.537990i 0.819184π-0.819184\pi
−0.842951 + 0.537990i 0.819184π0.819184\pi
572572 0 0
573573 −4.24926 −0.177515
574574 0 0
575575 34.4721 1.43759
576576 0 0
577577 27.1616 1.13075 0.565375 0.824834i 0.308731π-0.308731\pi
0.565375 + 0.824834i 0.308731π0.308731\pi
578578 0 0
579579 25.8135 1.07277
580580 0 0
581581 −11.9736 −0.496748
582582 0 0
583583 17.4611 0.723167
584584 0 0
585585 0 0
586586 0 0
587587 −10.2423 −0.422745 −0.211373 0.977406i 0.567793π-0.567793\pi
−0.211373 + 0.977406i 0.567793π0.567793\pi
588588 0 0
589589 −5.51396 −0.227199
590590 0 0
591591 21.9736 0.903873
592592 0 0
593593 27.9736 1.14874 0.574369 0.818597i 0.305248π-0.305248\pi
0.574369 + 0.818597i 0.305248π0.305248\pi
594594 0 0
595595 −1.11491 −0.0457068
596596 0 0
597597 24.5202 1.00355
598598 0 0
599599 −6.00223 −0.245245 −0.122622 0.992453i 0.539130π-0.539130\pi
−0.122622 + 0.992453i 0.539130π0.539130\pi
600600 0 0
601601 −19.8913 −0.811385 −0.405692 0.914010i 0.632970π-0.632970\pi
−0.405692 + 0.914010i 0.632970π0.632970\pi
602602 0 0
603603 8.23534 0.335369
604604 0 0
605605 6.72058 0.273230
606606 0 0
607607 29.4784 1.19649 0.598245 0.801313i 0.295865π-0.295865\pi
0.598245 + 0.801313i 0.295865π0.295865\pi
608608 0 0
609609 −1.39281 −0.0564396
610610 0 0
611611 0 0
612612 0 0
613613 −36.4115 −1.47065 −0.735324 0.677716i 0.762970π-0.762970\pi
−0.735324 + 0.677716i 0.762970π0.762970\pi
614614 0 0
615615 −16.8656 −0.680088
616616 0 0
617617 −7.51396 −0.302501 −0.151250 0.988495i 0.548330π-0.548330\pi
−0.151250 + 0.988495i 0.548330π0.548330\pi
618618 0 0
619619 −21.7438 −0.873956 −0.436978 0.899472i 0.643951π-0.643951\pi
−0.436978 + 0.899472i 0.643951π0.643951\pi
620620 0 0
621621 51.7688 2.07741
622622 0 0
623623 −11.1755 −0.447736
624624 0 0
625625 7.89981 0.315993
626626 0 0
627627 −16.2423 −0.648655
628628 0 0
629629 4.94567 0.197197
630630 0 0
631631 9.57454 0.381156 0.190578 0.981672i 0.438964π-0.438964\pi
0.190578 + 0.981672i 0.438964π0.438964\pi
632632 0 0
633633 −10.9068 −0.433505
634634 0 0
635635 −23.6762 −0.939563
636636 0 0
637637 0 0
638638 0 0
639639 12.2034 0.482759
640640 0 0
641641 22.8759 0.903544 0.451772 0.892134i 0.350792π-0.350792\pi
0.451772 + 0.892134i 0.350792π0.350792\pi
642642 0 0
643643 −28.2834 −1.11539 −0.557695 0.830046i 0.688314π-0.688314\pi
−0.557695 + 0.830046i 0.688314π0.688314\pi
644644 0 0
645645 −18.4185 −0.725228
646646 0 0
647647 10.0125 0.393631 0.196816 0.980440i 0.436940π-0.436940\pi
0.196816 + 0.980440i 0.436940π0.436940\pi
648648 0 0
649649 −30.6461 −1.20296
650650 0 0
651651 −1.64207 −0.0643579
652652 0 0
653653 −2.45963 −0.0962528 −0.0481264 0.998841i 0.515325π-0.515325\pi
−0.0481264 + 0.998841i 0.515325π0.515325\pi
654654 0 0
655655 −5.13659 −0.200703
656656 0 0
657657 −0.628870 −0.0245346
658658 0 0
659659 −33.0187 −1.28623 −0.643114 0.765771i 0.722358π-0.722358\pi
−0.643114 + 0.765771i 0.722358π0.722358\pi
660660 0 0
661661 5.97359 0.232346 0.116173 0.993229i 0.462937π-0.462937\pi
0.116173 + 0.993229i 0.462937π0.462937\pi
662662 0 0
663663 0 0
664664 0 0
665665 −5.51396 −0.213822
666666 0 0
667667 −8.67696 −0.335973
668668 0 0
669669 −39.9861 −1.54595
670670 0 0
671671 2.01696 0.0778637
672672 0 0
673673 6.29512 0.242659 0.121329 0.992612i 0.461284π-0.461284\pi
0.121329 + 0.992612i 0.461284π0.461284\pi
674674 0 0
675675 21.1972 0.815879
676676 0 0
677677 46.5544 1.78923 0.894615 0.446838i 0.147450π-0.147450\pi
0.894615 + 0.446838i 0.147450π0.147450\pi
678678 0 0
679679 −10.0606 −0.386089
680680 0 0
681681 6.63912 0.254412
682682 0 0
683683 −43.9861 −1.68308 −0.841540 0.540194i 0.818351π-0.818351\pi
−0.841540 + 0.540194i 0.818351π0.818351\pi
684684 0 0
685685 −0.423228 −0.0161707
686686 0 0
687687 15.0668 0.574835
688688 0 0
689689 0 0
690690 0 0
691691 9.17772 0.349137 0.174568 0.984645i 0.444147π-0.444147\pi
0.174568 + 0.984645i 0.444147π0.444147\pi
692692 0 0
693693 1.85244 0.0703684
694694 0 0
695695 6.75698 0.256307
696696 0 0
697697 −10.2709 −0.389040
698698 0 0
699699 17.0154 0.643583
700700 0 0
701701 −7.59622 −0.286905 −0.143453 0.989657i 0.545820π-0.545820\pi
−0.143453 + 0.989657i 0.545820π0.545820\pi
702702 0 0
703703 24.4596 0.922512
704704 0 0
705705 16.2423 0.611720
706706 0 0
707707 18.6894 0.702889
708708 0 0
709709 7.63511 0.286743 0.143371 0.989669i 0.454206π-0.454206\pi
0.143371 + 0.989669i 0.454206π0.454206\pi
710710 0 0
711711 6.64608 0.249248
712712 0 0
713713 −10.2298 −0.383110
714714 0 0
715715 0 0
716716 0 0
717717 45.2999 1.69176
718718 0 0
719719 13.6204 0.507955 0.253977 0.967210i 0.418261π-0.418261\pi
0.253977 + 0.967210i 0.418261π0.418261\pi
720720 0 0
721721 12.1212 0.451415
722722 0 0
723723 −1.42474 −0.0529868
724724 0 0
725725 −3.55286 −0.131950
726726 0 0
727727 −10.9457 −0.405952 −0.202976 0.979184i 0.565061π-0.565061\pi
−0.202976 + 0.979184i 0.565061π0.565061\pi
728728 0 0
729729 29.7625 1.10232
730730 0 0
731731 −11.2166 −0.414861
732732 0 0
733733 7.28415 0.269046 0.134523 0.990910i 0.457050π-0.457050\pi
0.134523 + 0.990910i 0.457050π0.457050\pi
734734 0 0
735735 −1.64207 −0.0605688
736736 0 0
737737 −22.1042 −0.814218
738738 0 0
739739 50.3268 1.85130 0.925651 0.378380i 0.123519π-0.123519\pi
0.925651 + 0.378380i 0.123519π0.123519\pi
740740 0 0
741741 0 0
742742 0 0
743743 −14.9317 −0.547793 −0.273896 0.961759i 0.588313π-0.588313\pi
−0.273896 + 0.961759i 0.588313π0.588313\pi
744744 0 0
745745 11.3594 0.416178
746746 0 0
747747 −9.94719 −0.363948
748748 0 0
749749 −1.89134 −0.0691079
750750 0 0
751751 −29.9347 −1.09233 −0.546166 0.837677i 0.683913π-0.683913\pi
−0.546166 + 0.837677i 0.683913π0.683913\pi
752752 0 0
753753 −0.0388938 −0.00141737
754754 0 0
755755 −9.12963 −0.332261
756756 0 0
757757 −6.48827 −0.235820 −0.117910 0.993024i 0.537619π-0.537619\pi
−0.117910 + 0.993024i 0.537619π0.537619\pi
758758 0 0
759759 −30.1336 −1.09378
760760 0 0
761761 −28.2159 −1.02283 −0.511413 0.859335i 0.670878π-0.670878\pi
−0.511413 + 0.859335i 0.670878π0.670878\pi
762762 0 0
763763 14.0000 0.506834
764764 0 0
765765 −0.926221 −0.0334876
766766 0 0
767767 0 0
768768 0 0
769769 −21.8260 −0.787067 −0.393533 0.919310i 0.628747π-0.628747\pi
−0.393533 + 0.919310i 0.628747π0.628747\pi
770770 0 0
771771 21.6740 0.780570
772772 0 0
773773 26.5683 0.955595 0.477798 0.878470i 0.341435π-0.341435\pi
0.477798 + 0.878470i 0.341435π0.341435\pi
774774 0 0
775775 −4.18869 −0.150462
776776 0 0
777777 7.28415 0.261317
778778 0 0
779779 −50.7967 −1.81998
780780 0 0
781781 −32.7547 −1.17206
782782 0 0
783783 −5.33553 −0.190676
784784 0 0
785785 15.9083 0.567791
786786 0 0
787787 −4.98903 −0.177840 −0.0889199 0.996039i 0.528342π-0.528342\pi
−0.0889199 + 0.996039i 0.528342π0.528342\pi
788788 0 0
789789 −36.7019 −1.30662
790790 0 0
791791 3.85244 0.136977
792792 0 0
793793 0 0
794794 0 0
795795 −12.8587 −0.456051
796796 0 0
797797 −47.0963 −1.66824 −0.834118 0.551587i 0.814023π-0.814023\pi
−0.834118 + 0.551587i 0.814023π0.814023\pi
798798 0 0
799799 9.89134 0.349930
800800 0 0
801801 −9.28415 −0.328039
802802 0 0
803803 1.68793 0.0595657
804804 0 0
805805 −10.2298 −0.360554
806806 0 0
807807 −35.3275 −1.24359
808808 0 0
809809 −10.2423 −0.360100 −0.180050 0.983657i 0.557626π-0.557626\pi
−0.180050 + 0.983657i 0.557626π0.557626\pi
810810 0 0
811811 2.98680 0.104881 0.0524403 0.998624i 0.483300π-0.483300\pi
0.0524403 + 0.998624i 0.483300π0.483300\pi
812812 0 0
813813 22.1909 0.778270
814814 0 0
815815 17.5529 0.614850
816816 0 0
817817 −55.4736 −1.94078
818818 0 0
819819 0 0
820820 0 0
821821 −52.7283 −1.84023 −0.920116 0.391646i 0.871906π-0.871906\pi
−0.920116 + 0.391646i 0.871906π0.871906\pi
822822 0 0
823823 6.68945 0.233179 0.116590 0.993180i 0.462804π-0.462804\pi
0.116590 + 0.993180i 0.462804π0.462804\pi
824824 0 0
825825 −12.3385 −0.429571
826826 0 0
827827 −41.5140 −1.44358 −0.721791 0.692111i 0.756681π-0.756681\pi
−0.721791 + 0.692111i 0.756681π0.756681\pi
828828 0 0
829829 −48.4596 −1.68307 −0.841536 0.540201i 0.818348π-0.818348\pi
−0.841536 + 0.540201i 0.818348π0.818348\pi
830830 0 0
831831 0.516914 0.0179316
832832 0 0
833833 −1.00000 −0.0346479
834834 0 0
835835 −0.722813 −0.0250140
836836 0 0
837837 −6.29039 −0.217428
838838 0 0
839839 9.64903 0.333122 0.166561 0.986031i 0.446734π-0.446734\pi
0.166561 + 0.986031i 0.446734π0.446734\pi
840840 0 0
841841 −28.1057 −0.969162
842842 0 0
843843 7.81460 0.269149
844844 0 0
845845 14.4938 0.498602
846846 0 0
847847 6.02792 0.207122
848848 0 0
849849 −17.1047 −0.587030
850850 0 0
851851 45.3789 1.55557
852852 0 0
853853 −35.3619 −1.21077 −0.605385 0.795933i 0.706981π-0.706981\pi
−0.605385 + 0.795933i 0.706981π0.706981\pi
854854 0 0
855855 −4.58078 −0.156659
856856 0 0
857857 29.0451 0.992163 0.496081 0.868276i 0.334772π-0.334772\pi
0.496081 + 0.868276i 0.334772π0.334772\pi
858858 0 0
859859 43.7996 1.49442 0.747212 0.664586i 0.231392π-0.231392\pi
0.747212 + 0.664586i 0.231392π0.231392\pi
860860 0 0
861861 −15.1274 −0.515540
862862 0 0
863863 3.39754 0.115654 0.0578268 0.998327i 0.481583π-0.481583\pi
0.0578268 + 0.998327i 0.481583π0.481583\pi
864864 0 0
865865 −17.7632 −0.603968
866866 0 0
867867 1.47283 0.0500201
868868 0 0
869869 −17.8385 −0.605130
870870 0 0
871871 0 0
872872 0 0
873873 −8.35793 −0.282873
874874 0 0
875875 −9.76322 −0.330057
876876 0 0
877877 −29.0529 −0.981047 −0.490523 0.871428i 0.663194π-0.663194\pi
−0.490523 + 0.871428i 0.663194π0.663194\pi
878878 0 0
879879 29.8135 1.00559
880880 0 0
881881 −11.4923 −0.387185 −0.193592 0.981082i 0.562014π-0.562014\pi
−0.193592 + 0.981082i 0.562014π0.562014\pi
882882 0 0
883883 −25.1927 −0.847802 −0.423901 0.905709i 0.639340π-0.639340\pi
−0.423901 + 0.905709i 0.639340π0.639340\pi
884884 0 0
885885 22.5683 0.758625
886886 0 0
887887 35.1957 1.18176 0.590878 0.806761i 0.298781π-0.298781\pi
0.590878 + 0.806761i 0.298781π0.298781\pi
888888 0 0
889889 −21.2361 −0.712235
890890 0 0
891891 −12.9721 −0.434581
892892 0 0
893893 48.9193 1.63702
894894 0 0
895895 −18.9821 −0.634501
896896 0 0
897897 0 0
898898 0 0
899899 1.05433 0.0351639
900900 0 0
901901 −7.83076 −0.260880
902902 0 0
903903 −16.5202 −0.549758
904904 0 0
905905 −6.28263 −0.208842
906906 0 0
907907 25.1227 0.834184 0.417092 0.908864i 0.363049π-0.363049\pi
0.417092 + 0.908864i 0.363049π0.363049\pi
908908 0 0
909909 15.5264 0.514980
910910 0 0
911911 −22.5110 −0.745823 −0.372912 0.927867i 0.621641π-0.621641\pi
−0.372912 + 0.927867i 0.621641π0.621641\pi
912912 0 0
913913 26.6989 0.883605
914914 0 0
915915 −1.48532 −0.0491032
916916 0 0
917917 −4.60719 −0.152143
918918 0 0
919919 −13.5676 −0.447553 −0.223777 0.974640i 0.571839π-0.571839\pi
−0.223777 + 0.974640i 0.571839π0.571839\pi
920920 0 0
921921 1.77018 0.0583296
922922 0 0
923923 0 0
924924 0 0
925925 18.5808 0.610932
926926 0 0
927927 10.0698 0.330735
928928 0 0
929929 −11.9519 −0.392129 −0.196065 0.980591i 0.562816π-0.562816\pi
−0.196065 + 0.980591i 0.562816π0.562816\pi
930930 0 0
931931 −4.94567 −0.162088
932932 0 0
933933 15.0349 0.492220
934934 0 0
935935 2.48604 0.0813021
936936 0 0
937937 53.0140 1.73189 0.865946 0.500138i 0.166717π-0.166717\pi
0.865946 + 0.500138i 0.166717π0.166717\pi
938938 0 0
939939 27.5973 0.900603
940940 0 0
941941 −27.1204 −0.884101 −0.442050 0.896990i 0.645749π-0.645749\pi
−0.442050 + 0.896990i 0.645749π0.645749\pi
942942 0 0
943943 −94.2409 −3.06890
944944 0 0
945945 −6.29039 −0.204626
946946 0 0
947947 44.5808 1.44868 0.724340 0.689443i 0.242144π-0.242144\pi
0.724340 + 0.689443i 0.242144π0.242144\pi
948948 0 0
949949 0 0
950950 0 0
951951 −15.4626 −0.501409
952952 0 0
953953 −51.8991 −1.68118 −0.840588 0.541675i 0.817791π-0.817791\pi
−0.840588 + 0.541675i 0.817791π0.817791\pi
954954 0 0
955955 3.21661 0.104087
956956 0 0
957957 3.10571 0.100393
958958 0 0
959959 −0.379608 −0.0122582
960960 0 0
961961 −29.7570 −0.959903
962962 0 0
963963 −1.57125 −0.0506327
964964 0 0
965965 −19.5404 −0.629027
966966 0 0
967967 −37.2680 −1.19846 −0.599229 0.800578i 0.704526π-0.704526\pi
−0.599229 + 0.800578i 0.704526π0.704526\pi
968968 0 0
969969 7.28415 0.234001
970970 0 0
971971 3.05433 0.0980182 0.0490091 0.998798i 0.484394π-0.484394\pi
0.0490091 + 0.998798i 0.484394π0.484394\pi
972972 0 0
973973 6.06058 0.194293
974974 0 0
975975 0 0
976976 0 0
977977 −47.3961 −1.51634 −0.758168 0.652059i 0.773905π-0.773905\pi
−0.758168 + 0.652059i 0.773905π0.773905\pi
978978 0 0
979979 24.9193 0.796423
980980 0 0
981981 11.6306 0.371338
982982 0 0
983983 51.1957 1.63289 0.816445 0.577423i 0.195942π-0.195942\pi
0.816445 + 0.577423i 0.195942π0.195942\pi
984984 0 0
985985 −16.6336 −0.529990
986986 0 0
987987 14.5683 0.463714
988988 0 0
989989 −102.918 −3.27260
990990 0 0
991991 −16.9332 −0.537900 −0.268950 0.963154i 0.586677π-0.586677\pi
−0.268950 + 0.963154i 0.586677π0.586677\pi
992992 0 0
993993 −39.7757 −1.26224
994994 0 0
995995 −18.5613 −0.588434
996996 0 0
997997 −53.3069 −1.68825 −0.844123 0.536150i 0.819878π-0.819878\pi
−0.844123 + 0.536150i 0.819878π0.819878\pi
998998 0 0
999999 27.9038 0.882838
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 1904.2.a.m.1.3 3
4.3 odd 2 952.2.a.f.1.1 3
8.3 odd 2 7616.2.a.bc.1.3 3
8.5 even 2 7616.2.a.be.1.1 3
12.11 even 2 8568.2.a.x.1.3 3
28.27 even 2 6664.2.a.j.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
952.2.a.f.1.1 3 4.3 odd 2
1904.2.a.m.1.3 3 1.1 even 1 trivial
6664.2.a.j.1.3 3 28.27 even 2
7616.2.a.bc.1.3 3 8.3 odd 2
7616.2.a.be.1.1 3 8.5 even 2
8568.2.a.x.1.3 3 12.11 even 2