Properties

Label 180.4.a.d.1.1
Level 180180
Weight 44
Character 180.1
Self dual yes
Analytic conductor 10.62010.620
Analytic rank 11
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [180,4,Mod(1,180)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(180, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("180.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 180=22325 180 = 2^{2} \cdot 3^{2} \cdot 5
Weight: k k == 4 4
Character orbit: [χ][\chi] == 180.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 10.620343801010.6203438010
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 60)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 180.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+5.00000q528.0000q7+24.0000q1170.0000q13102.000q17+20.0000q19+72.0000q23+25.0000q25306.000q29136.000q31140.000q35214.000q37+150.000q41292.000q43+72.0000q47+441.000q49+414.000q53+120.000q55+744.000q59418.000q61350.000q65+188.000q67480.000q71+434.000q73672.000q77+1352.00q79+612.000q83510.000q85+30.0000q89+1960.00q91+100.000q95286.000q97+O(q100)q+5.00000 q^{5} -28.0000 q^{7} +24.0000 q^{11} -70.0000 q^{13} -102.000 q^{17} +20.0000 q^{19} +72.0000 q^{23} +25.0000 q^{25} -306.000 q^{29} -136.000 q^{31} -140.000 q^{35} -214.000 q^{37} +150.000 q^{41} -292.000 q^{43} +72.0000 q^{47} +441.000 q^{49} +414.000 q^{53} +120.000 q^{55} +744.000 q^{59} -418.000 q^{61} -350.000 q^{65} +188.000 q^{67} -480.000 q^{71} +434.000 q^{73} -672.000 q^{77} +1352.00 q^{79} +612.000 q^{83} -510.000 q^{85} +30.0000 q^{89} +1960.00 q^{91} +100.000 q^{95} -286.000 q^{97} +O(q^{100})

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 0 0
44 0 0
55 5.00000 0.447214
66 0 0
77 −28.0000 −1.51186 −0.755929 0.654654i 0.772814π-0.772814\pi
−0.755929 + 0.654654i 0.772814π0.772814\pi
88 0 0
99 0 0
1010 0 0
1111 24.0000 0.657843 0.328921 0.944357i 0.393315π-0.393315\pi
0.328921 + 0.944357i 0.393315π0.393315\pi
1212 0 0
1313 −70.0000 −1.49342 −0.746712 0.665148i 0.768369π-0.768369\pi
−0.746712 + 0.665148i 0.768369π0.768369\pi
1414 0 0
1515 0 0
1616 0 0
1717 −102.000 −1.45521 −0.727607 0.685994i 0.759367π-0.759367\pi
−0.727607 + 0.685994i 0.759367π0.759367\pi
1818 0 0
1919 20.0000 0.241490 0.120745 0.992684i 0.461472π-0.461472\pi
0.120745 + 0.992684i 0.461472π0.461472\pi
2020 0 0
2121 0 0
2222 0 0
2323 72.0000 0.652741 0.326370 0.945242i 0.394174π-0.394174\pi
0.326370 + 0.945242i 0.394174π0.394174\pi
2424 0 0
2525 25.0000 0.200000
2626 0 0
2727 0 0
2828 0 0
2929 −306.000 −1.95941 −0.979703 0.200455i 0.935758π-0.935758\pi
−0.979703 + 0.200455i 0.935758π0.935758\pi
3030 0 0
3131 −136.000 −0.787946 −0.393973 0.919122i 0.628900π-0.628900\pi
−0.393973 + 0.919122i 0.628900π0.628900\pi
3232 0 0
3333 0 0
3434 0 0
3535 −140.000 −0.676123
3636 0 0
3737 −214.000 −0.950848 −0.475424 0.879757i 0.657705π-0.657705\pi
−0.475424 + 0.879757i 0.657705π0.657705\pi
3838 0 0
3939 0 0
4040 0 0
4141 150.000 0.571367 0.285684 0.958324i 0.407779π-0.407779\pi
0.285684 + 0.958324i 0.407779π0.407779\pi
4242 0 0
4343 −292.000 −1.03557 −0.517786 0.855510i 0.673244π-0.673244\pi
−0.517786 + 0.855510i 0.673244π0.673244\pi
4444 0 0
4545 0 0
4646 0 0
4747 72.0000 0.223453 0.111726 0.993739i 0.464362π-0.464362\pi
0.111726 + 0.993739i 0.464362π0.464362\pi
4848 0 0
4949 441.000 1.28571
5050 0 0
5151 0 0
5252 0 0
5353 414.000 1.07297 0.536484 0.843911i 0.319752π-0.319752\pi
0.536484 + 0.843911i 0.319752π0.319752\pi
5454 0 0
5555 120.000 0.294196
5656 0 0
5757 0 0
5858 0 0
5959 744.000 1.64170 0.820852 0.571141i 0.193499π-0.193499\pi
0.820852 + 0.571141i 0.193499π0.193499\pi
6060 0 0
6161 −418.000 −0.877367 −0.438684 0.898642i 0.644555π-0.644555\pi
−0.438684 + 0.898642i 0.644555π0.644555\pi
6262 0 0
6363 0 0
6464 0 0
6565 −350.000 −0.667879
6666 0 0
6767 188.000 0.342804 0.171402 0.985201i 0.445170π-0.445170\pi
0.171402 + 0.985201i 0.445170π0.445170\pi
6868 0 0
6969 0 0
7070 0 0
7171 −480.000 −0.802331 −0.401166 0.916006i 0.631395π-0.631395\pi
−0.401166 + 0.916006i 0.631395π0.631395\pi
7272 0 0
7373 434.000 0.695834 0.347917 0.937525i 0.386889π-0.386889\pi
0.347917 + 0.937525i 0.386889π0.386889\pi
7474 0 0
7575 0 0
7676 0 0
7777 −672.000 −0.994565
7878 0 0
7979 1352.00 1.92547 0.962733 0.270452i 0.0871732π-0.0871732\pi
0.962733 + 0.270452i 0.0871732π0.0871732\pi
8080 0 0
8181 0 0
8282 0 0
8383 612.000 0.809346 0.404673 0.914461i 0.367385π-0.367385\pi
0.404673 + 0.914461i 0.367385π0.367385\pi
8484 0 0
8585 −510.000 −0.650791
8686 0 0
8787 0 0
8888 0 0
8989 30.0000 0.0357303 0.0178651 0.999840i 0.494313π-0.494313\pi
0.0178651 + 0.999840i 0.494313π0.494313\pi
9090 0 0
9191 1960.00 2.25784
9292 0 0
9393 0 0
9494 0 0
9595 100.000 0.107998
9696 0 0
9797 −286.000 −0.299370 −0.149685 0.988734i 0.547826π-0.547826\pi
−0.149685 + 0.988734i 0.547826π0.547826\pi
9898 0 0
9999 0 0
100100 0 0
101101 1542.00 1.51916 0.759578 0.650416i 0.225406π-0.225406\pi
0.759578 + 0.650416i 0.225406π0.225406\pi
102102 0 0
103103 1172.00 1.12117 0.560585 0.828097i 0.310576π-0.310576\pi
0.560585 + 0.828097i 0.310576π0.310576\pi
104104 0 0
105105 0 0
106106 0 0
107107 −1956.00 −1.76723 −0.883615 0.468214i 0.844898π-0.844898\pi
−0.883615 + 0.468214i 0.844898π0.844898\pi
108108 0 0
109109 −1858.00 −1.63270 −0.816349 0.577559i 0.804005π-0.804005\pi
−0.816349 + 0.577559i 0.804005π0.804005\pi
110110 0 0
111111 0 0
112112 0 0
113113 −174.000 −0.144854 −0.0724272 0.997374i 0.523074π-0.523074\pi
−0.0724272 + 0.997374i 0.523074π0.523074\pi
114114 0 0
115115 360.000 0.291915
116116 0 0
117117 0 0
118118 0 0
119119 2856.00 2.20008
120120 0 0
121121 −755.000 −0.567243
122122 0 0
123123 0 0
124124 0 0
125125 125.000 0.0894427
126126 0 0
127127 −2068.00 −1.44492 −0.722462 0.691411i 0.756990π-0.756990\pi
−0.722462 + 0.691411i 0.756990π0.756990\pi
128128 0 0
129129 0 0
130130 0 0
131131 −312.000 −0.208088 −0.104044 0.994573i 0.533178π-0.533178\pi
−0.104044 + 0.994573i 0.533178π0.533178\pi
132132 0 0
133133 −560.000 −0.365099
134134 0 0
135135 0 0
136136 0 0
137137 −2646.00 −1.65010 −0.825048 0.565063i 0.808852π-0.808852\pi
−0.825048 + 0.565063i 0.808852π0.808852\pi
138138 0 0
139139 −1276.00 −0.778625 −0.389313 0.921106i 0.627287π-0.627287\pi
−0.389313 + 0.921106i 0.627287π0.627287\pi
140140 0 0
141141 0 0
142142 0 0
143143 −1680.00 −0.982438
144144 0 0
145145 −1530.00 −0.876273
146146 0 0
147147 0 0
148148 0 0
149149 3198.00 1.75832 0.879162 0.476522i 0.158103π-0.158103\pi
0.879162 + 0.476522i 0.158103π0.158103\pi
150150 0 0
151151 −760.000 −0.409589 −0.204794 0.978805i 0.565653π-0.565653\pi
−0.204794 + 0.978805i 0.565653π0.565653\pi
152152 0 0
153153 0 0
154154 0 0
155155 −680.000 −0.352380
156156 0 0
157157 −166.000 −0.0843837 −0.0421919 0.999110i 0.513434π-0.513434\pi
−0.0421919 + 0.999110i 0.513434π0.513434\pi
158158 0 0
159159 0 0
160160 0 0
161161 −2016.00 −0.986851
162162 0 0
163163 3020.00 1.45119 0.725597 0.688120i 0.241564π-0.241564\pi
0.725597 + 0.688120i 0.241564π0.241564\pi
164164 0 0
165165 0 0
166166 0 0
167167 984.000 0.455953 0.227977 0.973667i 0.426789π-0.426789\pi
0.227977 + 0.973667i 0.426789π0.426789\pi
168168 0 0
169169 2703.00 1.23031
170170 0 0
171171 0 0
172172 0 0
173173 −1962.00 −0.862243 −0.431122 0.902294i 0.641882π-0.641882\pi
−0.431122 + 0.902294i 0.641882π0.641882\pi
174174 0 0
175175 −700.000 −0.302372
176176 0 0
177177 0 0
178178 0 0
179179 −576.000 −0.240515 −0.120258 0.992743i 0.538372π-0.538372\pi
−0.120258 + 0.992743i 0.538372π0.538372\pi
180180 0 0
181181 −1210.00 −0.496898 −0.248449 0.968645i 0.579921π-0.579921\pi
−0.248449 + 0.968645i 0.579921π0.579921\pi
182182 0 0
183183 0 0
184184 0 0
185185 −1070.00 −0.425232
186186 0 0
187187 −2448.00 −0.957302
188188 0 0
189189 0 0
190190 0 0
191191 −3384.00 −1.28198 −0.640989 0.767550i 0.721475π-0.721475\pi
−0.640989 + 0.767550i 0.721475π0.721475\pi
192192 0 0
193193 −2038.00 −0.760096 −0.380048 0.924967i 0.624092π-0.624092\pi
−0.380048 + 0.924967i 0.624092π0.624092\pi
194194 0 0
195195 0 0
196196 0 0
197197 −4098.00 −1.48208 −0.741042 0.671459i 0.765668π-0.765668\pi
−0.741042 + 0.671459i 0.765668π0.765668\pi
198198 0 0
199199 −2248.00 −0.800786 −0.400393 0.916343i 0.631126π-0.631126\pi
−0.400393 + 0.916343i 0.631126π0.631126\pi
200200 0 0
201201 0 0
202202 0 0
203203 8568.00 2.96234
204204 0 0
205205 750.000 0.255523
206206 0 0
207207 0 0
208208 0 0
209209 480.000 0.158863
210210 0 0
211211 3260.00 1.06364 0.531819 0.846858i 0.321509π-0.321509\pi
0.531819 + 0.846858i 0.321509π0.321509\pi
212212 0 0
213213 0 0
214214 0 0
215215 −1460.00 −0.463122
216216 0 0
217217 3808.00 1.19126
218218 0 0
219219 0 0
220220 0 0
221221 7140.00 2.17325
222222 0 0
223223 −2980.00 −0.894868 −0.447434 0.894317i 0.647662π-0.647662\pi
−0.447434 + 0.894317i 0.647662π0.647662\pi
224224 0 0
225225 0 0
226226 0 0
227227 3180.00 0.929797 0.464899 0.885364i 0.346091π-0.346091\pi
0.464899 + 0.885364i 0.346091π0.346091\pi
228228 0 0
229229 3374.00 0.973625 0.486813 0.873506i 0.338159π-0.338159\pi
0.486813 + 0.873506i 0.338159π0.338159\pi
230230 0 0
231231 0 0
232232 0 0
233233 −1950.00 −0.548278 −0.274139 0.961690i 0.588393π-0.588393\pi
−0.274139 + 0.961690i 0.588393π0.588393\pi
234234 0 0
235235 360.000 0.0999311
236236 0 0
237237 0 0
238238 0 0
239239 −2232.00 −0.604084 −0.302042 0.953295i 0.597668π-0.597668\pi
−0.302042 + 0.953295i 0.597668π0.597668\pi
240240 0 0
241241 −1822.00 −0.486993 −0.243497 0.969902i 0.578294π-0.578294\pi
−0.243497 + 0.969902i 0.578294π0.578294\pi
242242 0 0
243243 0 0
244244 0 0
245245 2205.00 0.574989
246246 0 0
247247 −1400.00 −0.360647
248248 0 0
249249 0 0
250250 0 0
251251 −1488.00 −0.374190 −0.187095 0.982342i 0.559907π-0.559907\pi
−0.187095 + 0.982342i 0.559907π0.559907\pi
252252 0 0
253253 1728.00 0.429401
254254 0 0
255255 0 0
256256 0 0
257257 2994.00 0.726695 0.363347 0.931654i 0.381634π-0.381634\pi
0.363347 + 0.931654i 0.381634π0.381634\pi
258258 0 0
259259 5992.00 1.43755
260260 0 0
261261 0 0
262262 0 0
263263 2472.00 0.579582 0.289791 0.957090i 0.406414π-0.406414\pi
0.289791 + 0.957090i 0.406414π0.406414\pi
264264 0 0
265265 2070.00 0.479846
266266 0 0
267267 0 0
268268 0 0
269269 −3954.00 −0.896207 −0.448103 0.893982i 0.647900π-0.647900\pi
−0.448103 + 0.893982i 0.647900π0.647900\pi
270270 0 0
271271 −2176.00 −0.487759 −0.243879 0.969806i 0.578420π-0.578420\pi
−0.243879 + 0.969806i 0.578420π0.578420\pi
272272 0 0
273273 0 0
274274 0 0
275275 600.000 0.131569
276276 0 0
277277 1034.00 0.224285 0.112143 0.993692i 0.464229π-0.464229\pi
0.112143 + 0.993692i 0.464229π0.464229\pi
278278 0 0
279279 0 0
280280 0 0
281281 6654.00 1.41261 0.706307 0.707906i 0.250360π-0.250360\pi
0.706307 + 0.707906i 0.250360π0.250360\pi
282282 0 0
283283 −1756.00 −0.368846 −0.184423 0.982847i 0.559042π-0.559042\pi
−0.184423 + 0.982847i 0.559042π0.559042\pi
284284 0 0
285285 0 0
286286 0 0
287287 −4200.00 −0.863826
288288 0 0
289289 5491.00 1.11765
290290 0 0
291291 0 0
292292 0 0
293293 −3234.00 −0.644820 −0.322410 0.946600i 0.604493π-0.604493\pi
−0.322410 + 0.946600i 0.604493π0.604493\pi
294294 0 0
295295 3720.00 0.734192
296296 0 0
297297 0 0
298298 0 0
299299 −5040.00 −0.974818
300300 0 0
301301 8176.00 1.56564
302302 0 0
303303 0 0
304304 0 0
305305 −2090.00 −0.392371
306306 0 0
307307 2036.00 0.378504 0.189252 0.981929i 0.439394π-0.439394\pi
0.189252 + 0.981929i 0.439394π0.439394\pi
308308 0 0
309309 0 0
310310 0 0
311311 96.0000 0.0175037 0.00875187 0.999962i 0.497214π-0.497214\pi
0.00875187 + 0.999962i 0.497214π0.497214\pi
312312 0 0
313313 1202.00 0.217064 0.108532 0.994093i 0.465385π-0.465385\pi
0.108532 + 0.994093i 0.465385π0.465385\pi
314314 0 0
315315 0 0
316316 0 0
317317 3798.00 0.672924 0.336462 0.941697i 0.390770π-0.390770\pi
0.336462 + 0.941697i 0.390770π0.390770\pi
318318 0 0
319319 −7344.00 −1.28898
320320 0 0
321321 0 0
322322 0 0
323323 −2040.00 −0.351420
324324 0 0
325325 −1750.00 −0.298685
326326 0 0
327327 0 0
328328 0 0
329329 −2016.00 −0.337829
330330 0 0
331331 −5668.00 −0.941213 −0.470606 0.882343i 0.655965π-0.655965\pi
−0.470606 + 0.882343i 0.655965π0.655965\pi
332332 0 0
333333 0 0
334334 0 0
335335 940.000 0.153307
336336 0 0
337337 −454.000 −0.0733856 −0.0366928 0.999327i 0.511682π-0.511682\pi
−0.0366928 + 0.999327i 0.511682π0.511682\pi
338338 0 0
339339 0 0
340340 0 0
341341 −3264.00 −0.518345
342342 0 0
343343 −2744.00 −0.431959
344344 0 0
345345 0 0
346346 0 0
347347 5604.00 0.866970 0.433485 0.901161i 0.357284π-0.357284\pi
0.433485 + 0.901161i 0.357284π0.357284\pi
348348 0 0
349349 −11266.0 −1.72795 −0.863976 0.503533i 0.832033π-0.832033\pi
−0.863976 + 0.503533i 0.832033π0.832033\pi
350350 0 0
351351 0 0
352352 0 0
353353 6426.00 0.968899 0.484450 0.874819i 0.339020π-0.339020\pi
0.484450 + 0.874819i 0.339020π0.339020\pi
354354 0 0
355355 −2400.00 −0.358813
356356 0 0
357357 0 0
358358 0 0
359359 −6936.00 −1.01969 −0.509844 0.860267i 0.670297π-0.670297\pi
−0.509844 + 0.860267i 0.670297π0.670297\pi
360360 0 0
361361 −6459.00 −0.941682
362362 0 0
363363 0 0
364364 0 0
365365 2170.00 0.311186
366366 0 0
367367 −388.000 −0.0551865 −0.0275932 0.999619i 0.508784π-0.508784\pi
−0.0275932 + 0.999619i 0.508784π0.508784\pi
368368 0 0
369369 0 0
370370 0 0
371371 −11592.0 −1.62217
372372 0 0
373373 −8062.00 −1.11913 −0.559564 0.828787i 0.689031π-0.689031\pi
−0.559564 + 0.828787i 0.689031π0.689031\pi
374374 0 0
375375 0 0
376376 0 0
377377 21420.0 2.92622
378378 0 0
379379 −3388.00 −0.459182 −0.229591 0.973287i 0.573739π-0.573739\pi
−0.229591 + 0.973287i 0.573739π0.573739\pi
380380 0 0
381381 0 0
382382 0 0
383383 −6984.00 −0.931764 −0.465882 0.884847i 0.654263π-0.654263\pi
−0.465882 + 0.884847i 0.654263π0.654263\pi
384384 0 0
385385 −3360.00 −0.444783
386386 0 0
387387 0 0
388388 0 0
389389 2526.00 0.329237 0.164619 0.986357i 0.447361π-0.447361\pi
0.164619 + 0.986357i 0.447361π0.447361\pi
390390 0 0
391391 −7344.00 −0.949877
392392 0 0
393393 0 0
394394 0 0
395395 6760.00 0.861095
396396 0 0
397397 6146.00 0.776975 0.388487 0.921454i 0.372998π-0.372998\pi
0.388487 + 0.921454i 0.372998π0.372998\pi
398398 0 0
399399 0 0
400400 0 0
401401 −9786.00 −1.21868 −0.609339 0.792910i 0.708565π-0.708565\pi
−0.609339 + 0.792910i 0.708565π0.708565\pi
402402 0 0
403403 9520.00 1.17674
404404 0 0
405405 0 0
406406 0 0
407407 −5136.00 −0.625509
408408 0 0
409409 −886.000 −0.107115 −0.0535573 0.998565i 0.517056π-0.517056\pi
−0.0535573 + 0.998565i 0.517056π0.517056\pi
410410 0 0
411411 0 0
412412 0 0
413413 −20832.0 −2.48202
414414 0 0
415415 3060.00 0.361951
416416 0 0
417417 0 0
418418 0 0
419419 11352.0 1.32358 0.661792 0.749688i 0.269796π-0.269796\pi
0.661792 + 0.749688i 0.269796π0.269796\pi
420420 0 0
421421 10190.0 1.17964 0.589822 0.807533i 0.299198π-0.299198\pi
0.589822 + 0.807533i 0.299198π0.299198\pi
422422 0 0
423423 0 0
424424 0 0
425425 −2550.00 −0.291043
426426 0 0
427427 11704.0 1.32645
428428 0 0
429429 0 0
430430 0 0
431431 −2448.00 −0.273587 −0.136794 0.990600i 0.543680π-0.543680\pi
−0.136794 + 0.990600i 0.543680π0.543680\pi
432432 0 0
433433 −7078.00 −0.785559 −0.392779 0.919633i 0.628486π-0.628486\pi
−0.392779 + 0.919633i 0.628486π0.628486\pi
434434 0 0
435435 0 0
436436 0 0
437437 1440.00 0.157631
438438 0 0
439439 −18088.0 −1.96650 −0.983250 0.182264i 0.941657π-0.941657\pi
−0.983250 + 0.182264i 0.941657π0.941657\pi
440440 0 0
441441 0 0
442442 0 0
443443 −3852.00 −0.413124 −0.206562 0.978433i 0.566228π-0.566228\pi
−0.206562 + 0.978433i 0.566228π0.566228\pi
444444 0 0
445445 150.000 0.0159791
446446 0 0
447447 0 0
448448 0 0
449449 −6522.00 −0.685506 −0.342753 0.939426i 0.611359π-0.611359\pi
−0.342753 + 0.939426i 0.611359π0.611359\pi
450450 0 0
451451 3600.00 0.375870
452452 0 0
453453 0 0
454454 0 0
455455 9800.00 1.00974
456456 0 0
457457 2090.00 0.213930 0.106965 0.994263i 0.465887π-0.465887\pi
0.106965 + 0.994263i 0.465887π0.465887\pi
458458 0 0
459459 0 0
460460 0 0
461461 9894.00 0.999587 0.499793 0.866145i 0.333409π-0.333409\pi
0.499793 + 0.866145i 0.333409π0.333409\pi
462462 0 0
463463 3044.00 0.305544 0.152772 0.988261i 0.451180π-0.451180\pi
0.152772 + 0.988261i 0.451180π0.451180\pi
464464 0 0
465465 0 0
466466 0 0
467467 −10236.0 −1.01427 −0.507137 0.861866i 0.669296π-0.669296\pi
−0.507137 + 0.861866i 0.669296π0.669296\pi
468468 0 0
469469 −5264.00 −0.518271
470470 0 0
471471 0 0
472472 0 0
473473 −7008.00 −0.681244
474474 0 0
475475 500.000 0.0482980
476476 0 0
477477 0 0
478478 0 0
479479 −11496.0 −1.09659 −0.548294 0.836286i 0.684723π-0.684723\pi
−0.548294 + 0.836286i 0.684723π0.684723\pi
480480 0 0
481481 14980.0 1.42002
482482 0 0
483483 0 0
484484 0 0
485485 −1430.00 −0.133882
486486 0 0
487487 −15316.0 −1.42512 −0.712561 0.701610i 0.752465π-0.752465\pi
−0.712561 + 0.701610i 0.752465π0.752465\pi
488488 0 0
489489 0 0
490490 0 0
491491 11616.0 1.06766 0.533832 0.845591i 0.320752π-0.320752\pi
0.533832 + 0.845591i 0.320752π0.320752\pi
492492 0 0
493493 31212.0 2.85135
494494 0 0
495495 0 0
496496 0 0
497497 13440.0 1.21301
498498 0 0
499499 14996.0 1.34532 0.672658 0.739953i 0.265152π-0.265152\pi
0.672658 + 0.739953i 0.265152π0.265152\pi
500500 0 0
501501 0 0
502502 0 0
503503 21648.0 1.91896 0.959480 0.281778i 0.0909240π-0.0909240\pi
0.959480 + 0.281778i 0.0909240π0.0909240\pi
504504 0 0
505505 7710.00 0.679387
506506 0 0
507507 0 0
508508 0 0
509509 −3378.00 −0.294160 −0.147080 0.989125i 0.546987π-0.546987\pi
−0.147080 + 0.989125i 0.546987π0.546987\pi
510510 0 0
511511 −12152.0 −1.05200
512512 0 0
513513 0 0
514514 0 0
515515 5860.00 0.501403
516516 0 0
517517 1728.00 0.146997
518518 0 0
519519 0 0
520520 0 0
521521 16158.0 1.35872 0.679362 0.733804i 0.262257π-0.262257\pi
0.679362 + 0.733804i 0.262257π0.262257\pi
522522 0 0
523523 −76.0000 −0.00635420 −0.00317710 0.999995i 0.501011π-0.501011\pi
−0.00317710 + 0.999995i 0.501011π0.501011\pi
524524 0 0
525525 0 0
526526 0 0
527527 13872.0 1.14663
528528 0 0
529529 −6983.00 −0.573929
530530 0 0
531531 0 0
532532 0 0
533533 −10500.0 −0.853294
534534 0 0
535535 −9780.00 −0.790329
536536 0 0
537537 0 0
538538 0 0
539539 10584.0 0.845798
540540 0 0
541541 9278.00 0.737324 0.368662 0.929563i 0.379816π-0.379816\pi
0.368662 + 0.929563i 0.379816π0.379816\pi
542542 0 0
543543 0 0
544544 0 0
545545 −9290.00 −0.730165
546546 0 0
547547 14564.0 1.13841 0.569206 0.822195i 0.307251π-0.307251\pi
0.569206 + 0.822195i 0.307251π0.307251\pi
548548 0 0
549549 0 0
550550 0 0
551551 −6120.00 −0.473177
552552 0 0
553553 −37856.0 −2.91103
554554 0 0
555555 0 0
556556 0 0
557557 −2154.00 −0.163856 −0.0819281 0.996638i 0.526108π-0.526108\pi
−0.0819281 + 0.996638i 0.526108π0.526108\pi
558558 0 0
559559 20440.0 1.54655
560560 0 0
561561 0 0
562562 0 0
563563 8700.00 0.651263 0.325632 0.945497i 0.394423π-0.394423\pi
0.325632 + 0.945497i 0.394423π0.394423\pi
564564 0 0
565565 −870.000 −0.0647808
566566 0 0
567567 0 0
568568 0 0
569569 −4194.00 −0.309001 −0.154501 0.987993i 0.549377π-0.549377\pi
−0.154501 + 0.987993i 0.549377π0.549377\pi
570570 0 0
571571 −8020.00 −0.587787 −0.293894 0.955838i 0.594951π-0.594951\pi
−0.293894 + 0.955838i 0.594951π0.594951\pi
572572 0 0
573573 0 0
574574 0 0
575575 1800.00 0.130548
576576 0 0
577577 −2686.00 −0.193795 −0.0968974 0.995294i 0.530892π-0.530892\pi
−0.0968974 + 0.995294i 0.530892π0.530892\pi
578578 0 0
579579 0 0
580580 0 0
581581 −17136.0 −1.22362
582582 0 0
583583 9936.00 0.705844
584584 0 0
585585 0 0
586586 0 0
587587 −3012.00 −0.211786 −0.105893 0.994378i 0.533770π-0.533770\pi
−0.105893 + 0.994378i 0.533770π0.533770\pi
588588 0 0
589589 −2720.00 −0.190281
590590 0 0
591591 0 0
592592 0 0
593593 15522.0 1.07489 0.537447 0.843298i 0.319389π-0.319389\pi
0.537447 + 0.843298i 0.319389π0.319389\pi
594594 0 0
595595 14280.0 0.983904
596596 0 0
597597 0 0
598598 0 0
599599 −19224.0 −1.31130 −0.655652 0.755063i 0.727606π-0.727606\pi
−0.655652 + 0.755063i 0.727606π0.727606\pi
600600 0 0
601601 −6502.00 −0.441301 −0.220651 0.975353i 0.570818π-0.570818\pi
−0.220651 + 0.975353i 0.570818π0.570818\pi
602602 0 0
603603 0 0
604604 0 0
605605 −3775.00 −0.253679
606606 0 0
607607 29396.0 1.96565 0.982823 0.184552i 0.0590834π-0.0590834\pi
0.982823 + 0.184552i 0.0590834π0.0590834\pi
608608 0 0
609609 0 0
610610 0 0
611611 −5040.00 −0.333710
612612 0 0
613613 −10006.0 −0.659280 −0.329640 0.944107i 0.606927π-0.606927\pi
−0.329640 + 0.944107i 0.606927π0.606927\pi
614614 0 0
615615 0 0
616616 0 0
617617 −23118.0 −1.50842 −0.754210 0.656633i 0.771980π-0.771980\pi
−0.754210 + 0.656633i 0.771980π0.771980\pi
618618 0 0
619619 14036.0 0.911397 0.455698 0.890134i 0.349390π-0.349390\pi
0.455698 + 0.890134i 0.349390π0.349390\pi
620620 0 0
621621 0 0
622622 0 0
623623 −840.000 −0.0540191
624624 0 0
625625 625.000 0.0400000
626626 0 0
627627 0 0
628628 0 0
629629 21828.0 1.38369
630630 0 0
631631 −4288.00 −0.270527 −0.135264 0.990810i 0.543188π-0.543188\pi
−0.135264 + 0.990810i 0.543188π0.543188\pi
632632 0 0
633633 0 0
634634 0 0
635635 −10340.0 −0.646190
636636 0 0
637637 −30870.0 −1.92012
638638 0 0
639639 0 0
640640 0 0
641641 −1314.00 −0.0809671 −0.0404835 0.999180i 0.512890π-0.512890\pi
−0.0404835 + 0.999180i 0.512890π0.512890\pi
642642 0 0
643643 −628.000 −0.0385162 −0.0192581 0.999815i 0.506130π-0.506130\pi
−0.0192581 + 0.999815i 0.506130π0.506130\pi
644644 0 0
645645 0 0
646646 0 0
647647 10944.0 0.664997 0.332498 0.943104i 0.392108π-0.392108\pi
0.332498 + 0.943104i 0.392108π0.392108\pi
648648 0 0
649649 17856.0 1.07998
650650 0 0
651651 0 0
652652 0 0
653653 −1098.00 −0.0658010 −0.0329005 0.999459i 0.510474π-0.510474\pi
−0.0329005 + 0.999459i 0.510474π0.510474\pi
654654 0 0
655655 −1560.00 −0.0930599
656656 0 0
657657 0 0
658658 0 0
659659 −312.000 −0.0184428 −0.00922139 0.999957i 0.502935π-0.502935\pi
−0.00922139 + 0.999957i 0.502935π0.502935\pi
660660 0 0
661661 8678.00 0.510643 0.255322 0.966856i 0.417819π-0.417819\pi
0.255322 + 0.966856i 0.417819π0.417819\pi
662662 0 0
663663 0 0
664664 0 0
665665 −2800.00 −0.163277
666666 0 0
667667 −22032.0 −1.27898
668668 0 0
669669 0 0
670670 0 0
671671 −10032.0 −0.577170
672672 0 0
673673 −14470.0 −0.828793 −0.414396 0.910097i 0.636007π-0.636007\pi
−0.414396 + 0.910097i 0.636007π0.636007\pi
674674 0 0
675675 0 0
676676 0 0
677677 11838.0 0.672040 0.336020 0.941855i 0.390919π-0.390919\pi
0.336020 + 0.941855i 0.390919π0.390919\pi
678678 0 0
679679 8008.00 0.452605
680680 0 0
681681 0 0
682682 0 0
683683 25548.0 1.43128 0.715642 0.698467i 0.246134π-0.246134\pi
0.715642 + 0.698467i 0.246134π0.246134\pi
684684 0 0
685685 −13230.0 −0.737945
686686 0 0
687687 0 0
688688 0 0
689689 −28980.0 −1.60239
690690 0 0
691691 −18412.0 −1.01364 −0.506820 0.862052i 0.669179π-0.669179\pi
−0.506820 + 0.862052i 0.669179π0.669179\pi
692692 0 0
693693 0 0
694694 0 0
695695 −6380.00 −0.348212
696696 0 0
697697 −15300.0 −0.831462
698698 0 0
699699 0 0
700700 0 0
701701 8814.00 0.474893 0.237447 0.971401i 0.423690π-0.423690\pi
0.237447 + 0.971401i 0.423690π0.423690\pi
702702 0 0
703703 −4280.00 −0.229621
704704 0 0
705705 0 0
706706 0 0
707707 −43176.0 −2.29675
708708 0 0
709709 −17314.0 −0.917124 −0.458562 0.888662i 0.651635π-0.651635\pi
−0.458562 + 0.888662i 0.651635π0.651635\pi
710710 0 0
711711 0 0
712712 0 0
713713 −9792.00 −0.514324
714714 0 0
715715 −8400.00 −0.439360
716716 0 0
717717 0 0
718718 0 0
719719 768.000 0.0398353 0.0199176 0.999802i 0.493660π-0.493660\pi
0.0199176 + 0.999802i 0.493660π0.493660\pi
720720 0 0
721721 −32816.0 −1.69505
722722 0 0
723723 0 0
724724 0 0
725725 −7650.00 −0.391881
726726 0 0
727727 −18196.0 −0.928270 −0.464135 0.885764i 0.653635π-0.653635\pi
−0.464135 + 0.885764i 0.653635π0.653635\pi
728728 0 0
729729 0 0
730730 0 0
731731 29784.0 1.50698
732732 0 0
733733 −18142.0 −0.914175 −0.457087 0.889422i 0.651107π-0.651107\pi
−0.457087 + 0.889422i 0.651107π0.651107\pi
734734 0 0
735735 0 0
736736 0 0
737737 4512.00 0.225511
738738 0 0
739739 −13660.0 −0.679961 −0.339981 0.940432i 0.610420π-0.610420\pi
−0.339981 + 0.940432i 0.610420π0.610420\pi
740740 0 0
741741 0 0
742742 0 0
743743 12768.0 0.630434 0.315217 0.949020i 0.397923π-0.397923\pi
0.315217 + 0.949020i 0.397923π0.397923\pi
744744 0 0
745745 15990.0 0.786347
746746 0 0
747747 0 0
748748 0 0
749749 54768.0 2.67180
750750 0 0
751751 22952.0 1.11522 0.557610 0.830103i 0.311718π-0.311718\pi
0.557610 + 0.830103i 0.311718π0.311718\pi
752752 0 0
753753 0 0
754754 0 0
755755 −3800.00 −0.183174
756756 0 0
757757 15818.0 0.759465 0.379732 0.925096i 0.376016π-0.376016\pi
0.379732 + 0.925096i 0.376016π0.376016\pi
758758 0 0
759759 0 0
760760 0 0
761761 18558.0 0.884004 0.442002 0.897014i 0.354268π-0.354268\pi
0.442002 + 0.897014i 0.354268π0.354268\pi
762762 0 0
763763 52024.0 2.46841
764764 0 0
765765 0 0
766766 0 0
767767 −52080.0 −2.45176
768768 0 0
769769 14978.0 0.702367 0.351184 0.936307i 0.385779π-0.385779\pi
0.351184 + 0.936307i 0.385779π0.385779\pi
770770 0 0
771771 0 0
772772 0 0
773773 −8946.00 −0.416255 −0.208128 0.978102i 0.566737π-0.566737\pi
−0.208128 + 0.978102i 0.566737π0.566737\pi
774774 0 0
775775 −3400.00 −0.157589
776776 0 0
777777 0 0
778778 0 0
779779 3000.00 0.137980
780780 0 0
781781 −11520.0 −0.527808
782782 0 0
783783 0 0
784784 0 0
785785 −830.000 −0.0377375
786786 0 0
787787 −18436.0 −0.835035 −0.417517 0.908669i 0.637100π-0.637100\pi
−0.417517 + 0.908669i 0.637100π0.637100\pi
788788 0 0
789789 0 0
790790 0 0
791791 4872.00 0.218999
792792 0 0
793793 29260.0 1.31028
794794 0 0
795795 0 0
796796 0 0
797797 −16314.0 −0.725058 −0.362529 0.931972i 0.618087π-0.618087\pi
−0.362529 + 0.931972i 0.618087π0.618087\pi
798798 0 0
799799 −7344.00 −0.325172
800800 0 0
801801 0 0
802802 0 0
803803 10416.0 0.457749
804804 0 0
805805 −10080.0 −0.441333
806806 0 0
807807 0 0
808808 0 0
809809 25446.0 1.10585 0.552926 0.833231i 0.313511π-0.313511\pi
0.552926 + 0.833231i 0.313511π0.313511\pi
810810 0 0
811811 42740.0 1.85056 0.925280 0.379284i 0.123830π-0.123830\pi
0.925280 + 0.379284i 0.123830π0.123830\pi
812812 0 0
813813 0 0
814814 0 0
815815 15100.0 0.648994
816816 0 0
817817 −5840.00 −0.250080
818818 0 0
819819 0 0
820820 0 0
821821 −29946.0 −1.27299 −0.636494 0.771282i 0.719616π-0.719616\pi
−0.636494 + 0.771282i 0.719616π0.719616\pi
822822 0 0
823823 −32596.0 −1.38059 −0.690295 0.723528i 0.742519π-0.742519\pi
−0.690295 + 0.723528i 0.742519π0.742519\pi
824824 0 0
825825 0 0
826826 0 0
827827 −3804.00 −0.159949 −0.0799746 0.996797i 0.525484π-0.525484\pi
−0.0799746 + 0.996797i 0.525484π0.525484\pi
828828 0 0
829829 3278.00 0.137334 0.0686669 0.997640i 0.478125π-0.478125\pi
0.0686669 + 0.997640i 0.478125π0.478125\pi
830830 0 0
831831 0 0
832832 0 0
833833 −44982.0 −1.87099
834834 0 0
835835 4920.00 0.203909
836836 0 0
837837 0 0
838838 0 0
839839 5784.00 0.238005 0.119002 0.992894i 0.462030π-0.462030\pi
0.119002 + 0.992894i 0.462030π0.462030\pi
840840 0 0
841841 69247.0 2.83927
842842 0 0
843843 0 0
844844 0 0
845845 13515.0 0.550213
846846 0 0
847847 21140.0 0.857590
848848 0 0
849849 0 0
850850 0 0
851851 −15408.0 −0.620657
852852 0 0
853853 17306.0 0.694661 0.347331 0.937743i 0.387088π-0.387088\pi
0.347331 + 0.937743i 0.387088π0.387088\pi
854854 0 0
855855 0 0
856856 0 0
857857 −31134.0 −1.24098 −0.620488 0.784216i 0.713066π-0.713066\pi
−0.620488 + 0.784216i 0.713066π0.713066\pi
858858 0 0
859859 −10780.0 −0.428183 −0.214091 0.976814i 0.568679π-0.568679\pi
−0.214091 + 0.976814i 0.568679π0.568679\pi
860860 0 0
861861 0 0
862862 0 0
863863 −3456.00 −0.136319 −0.0681597 0.997674i 0.521713π-0.521713\pi
−0.0681597 + 0.997674i 0.521713π0.521713\pi
864864 0 0
865865 −9810.00 −0.385607
866866 0 0
867867 0 0
868868 0 0
869869 32448.0 1.26665
870870 0 0
871871 −13160.0 −0.511951
872872 0 0
873873 0 0
874874 0 0
875875 −3500.00 −0.135225
876876 0 0
877877 2618.00 0.100802 0.0504011 0.998729i 0.483950π-0.483950\pi
0.0504011 + 0.998729i 0.483950π0.483950\pi
878878 0 0
879879 0 0
880880 0 0
881881 26550.0 1.01531 0.507657 0.861559i 0.330512π-0.330512\pi
0.507657 + 0.861559i 0.330512π0.330512\pi
882882 0 0
883883 27596.0 1.05173 0.525866 0.850567i 0.323741π-0.323741\pi
0.525866 + 0.850567i 0.323741π0.323741\pi
884884 0 0
885885 0 0
886886 0 0
887887 37848.0 1.43271 0.716354 0.697737i 0.245810π-0.245810\pi
0.716354 + 0.697737i 0.245810π0.245810\pi
888888 0 0
889889 57904.0 2.18452
890890 0 0
891891 0 0
892892 0 0
893893 1440.00 0.0539617
894894 0 0
895895 −2880.00 −0.107562
896896 0 0
897897 0 0
898898 0 0
899899 41616.0 1.54391
900900 0 0
901901 −42228.0 −1.56140
902902 0 0
903903 0 0
904904 0 0
905905 −6050.00 −0.222220
906906 0 0
907907 −4804.00 −0.175870 −0.0879351 0.996126i 0.528027π-0.528027\pi
−0.0879351 + 0.996126i 0.528027π0.528027\pi
908908 0 0
909909 0 0
910910 0 0
911911 −28608.0 −1.04042 −0.520211 0.854037i 0.674147π-0.674147\pi
−0.520211 + 0.854037i 0.674147π0.674147\pi
912912 0 0
913913 14688.0 0.532423
914914 0 0
915915 0 0
916916 0 0
917917 8736.00 0.314600
918918 0 0
919919 −40768.0 −1.46334 −0.731672 0.681657i 0.761259π-0.761259\pi
−0.731672 + 0.681657i 0.761259π0.761259\pi
920920 0 0
921921 0 0
922922 0 0
923923 33600.0 1.19822
924924 0 0
925925 −5350.00 −0.190170
926926 0 0
927927 0 0
928928 0 0
929929 −27642.0 −0.976216 −0.488108 0.872783i 0.662313π-0.662313\pi
−0.488108 + 0.872783i 0.662313π0.662313\pi
930930 0 0
931931 8820.00 0.310487
932932 0 0
933933 0 0
934934 0 0
935935 −12240.0 −0.428119
936936 0 0
937937 28106.0 0.979918 0.489959 0.871746i 0.337012π-0.337012\pi
0.489959 + 0.871746i 0.337012π0.337012\pi
938938 0 0
939939 0 0
940940 0 0
941941 −14730.0 −0.510291 −0.255146 0.966903i 0.582123π-0.582123\pi
−0.255146 + 0.966903i 0.582123π0.582123\pi
942942 0 0
943943 10800.0 0.372955
944944 0 0
945945 0 0
946946 0 0
947947 9564.00 0.328182 0.164091 0.986445i 0.447531π-0.447531\pi
0.164091 + 0.986445i 0.447531π0.447531\pi
948948 0 0
949949 −30380.0 −1.03917
950950 0 0
951951 0 0
952952 0 0
953953 53898.0 1.83203 0.916017 0.401141i 0.131386π-0.131386\pi
0.916017 + 0.401141i 0.131386π0.131386\pi
954954 0 0
955955 −16920.0 −0.573318
956956 0 0
957957 0 0
958958 0 0
959959 74088.0 2.49471
960960 0 0
961961 −11295.0 −0.379141
962962 0 0
963963 0 0
964964 0 0
965965 −10190.0 −0.339925
966966 0 0
967967 15140.0 0.503485 0.251742 0.967794i 0.418996π-0.418996\pi
0.251742 + 0.967794i 0.418996π0.418996\pi
968968 0 0
969969 0 0
970970 0 0
971971 −23808.0 −0.786854 −0.393427 0.919356i 0.628711π-0.628711\pi
−0.393427 + 0.919356i 0.628711π0.628711\pi
972972 0 0
973973 35728.0 1.17717
974974 0 0
975975 0 0
976976 0 0
977977 −23094.0 −0.756236 −0.378118 0.925757i 0.623429π-0.623429\pi
−0.378118 + 0.925757i 0.623429π0.623429\pi
978978 0 0
979979 720.000 0.0235049
980980 0 0
981981 0 0
982982 0 0
983983 −7584.00 −0.246075 −0.123038 0.992402i 0.539264π-0.539264\pi
−0.123038 + 0.992402i 0.539264π0.539264\pi
984984 0 0
985985 −20490.0 −0.662808
986986 0 0
987987 0 0
988988 0 0
989989 −21024.0 −0.675960
990990 0 0
991991 −26752.0 −0.857523 −0.428761 0.903418i 0.641050π-0.641050\pi
−0.428761 + 0.903418i 0.641050π0.641050\pi
992992 0 0
993993 0 0
994994 0 0
995995 −11240.0 −0.358123
996996 0 0
997997 7778.00 0.247073 0.123536 0.992340i 0.460576π-0.460576\pi
0.123536 + 0.992340i 0.460576π0.460576\pi
998998 0 0
999999 0 0
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 180.4.a.d.1.1 1
3.2 odd 2 60.4.a.a.1.1 1
4.3 odd 2 720.4.a.bb.1.1 1
5.2 odd 4 900.4.d.h.649.1 2
5.3 odd 4 900.4.d.h.649.2 2
5.4 even 2 900.4.a.q.1.1 1
9.2 odd 6 1620.4.i.l.1081.1 2
9.4 even 3 1620.4.i.f.541.1 2
9.5 odd 6 1620.4.i.l.541.1 2
9.7 even 3 1620.4.i.f.1081.1 2
12.11 even 2 240.4.a.i.1.1 1
15.2 even 4 300.4.d.b.49.2 2
15.8 even 4 300.4.d.b.49.1 2
15.14 odd 2 300.4.a.i.1.1 1
24.5 odd 2 960.4.a.bc.1.1 1
24.11 even 2 960.4.a.r.1.1 1
60.23 odd 4 1200.4.f.n.49.2 2
60.47 odd 4 1200.4.f.n.49.1 2
60.59 even 2 1200.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.4.a.a.1.1 1 3.2 odd 2
180.4.a.d.1.1 1 1.1 even 1 trivial
240.4.a.i.1.1 1 12.11 even 2
300.4.a.i.1.1 1 15.14 odd 2
300.4.d.b.49.1 2 15.8 even 4
300.4.d.b.49.2 2 15.2 even 4
720.4.a.bb.1.1 1 4.3 odd 2
900.4.a.q.1.1 1 5.4 even 2
900.4.d.h.649.1 2 5.2 odd 4
900.4.d.h.649.2 2 5.3 odd 4
960.4.a.r.1.1 1 24.11 even 2
960.4.a.bc.1.1 1 24.5 odd 2
1200.4.a.a.1.1 1 60.59 even 2
1200.4.f.n.49.1 2 60.47 odd 4
1200.4.f.n.49.2 2 60.23 odd 4
1620.4.i.f.541.1 2 9.4 even 3
1620.4.i.f.1081.1 2 9.7 even 3
1620.4.i.l.541.1 2 9.5 odd 6
1620.4.i.l.1081.1 2 9.2 odd 6