Properties

Label 2704.2.a.ba.1.3
Level 27042704
Weight 22
Character 2704.1
Self dual yes
Analytic conductor 21.59221.592
Analytic rank 11
Dimension 33
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] = [2704,2,Mod(1,2704)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2704, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2704.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 2704=24132 2704 = 2^{4} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2704.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: 21.591548706621.5915487066
Analytic rank: 11
Dimension: 33
Coefficient field: Q(ζ14)+\Q(\zeta_{14})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x22x+1 x^{3} - x^{2} - 2x + 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 169)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 1.24698-1.24698 of defining polynomial
Character χ\chi == 2704.1

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+2.24698q30.246980q52.35690q7+2.04892q94.24698q110.554958q15+2.15883q170.0881460q195.29590q211.49396q234.93900q252.13706q27+4.63102q296.63102q319.54288q33+0.582105q355.69202q37+11.5918q41+0.295897q430.506041q457.35690q471.44504q49+4.85086q5110.3937q53+1.04892q550.198062q576.78017q59+3.47219q614.82908q63+7.67994q673.35690q698.66487q716.73556q7311.0978q75+10.0097q779.97046q7910.9487q81+1.60925q830.533188q85+10.4058q87+2.88471q8914.8998q93+0.0217703q95+8.05861q978.70171q99+O(q100)q+2.24698 q^{3} -0.246980 q^{5} -2.35690 q^{7} +2.04892 q^{9} -4.24698 q^{11} -0.554958 q^{15} +2.15883 q^{17} -0.0881460 q^{19} -5.29590 q^{21} -1.49396 q^{23} -4.93900 q^{25} -2.13706 q^{27} +4.63102 q^{29} -6.63102 q^{31} -9.54288 q^{33} +0.582105 q^{35} -5.69202 q^{37} +11.5918 q^{41} +0.295897 q^{43} -0.506041 q^{45} -7.35690 q^{47} -1.44504 q^{49} +4.85086 q^{51} -10.3937 q^{53} +1.04892 q^{55} -0.198062 q^{57} -6.78017 q^{59} +3.47219 q^{61} -4.82908 q^{63} +7.67994 q^{67} -3.35690 q^{69} -8.66487 q^{71} -6.73556 q^{73} -11.0978 q^{75} +10.0097 q^{77} -9.97046 q^{79} -10.9487 q^{81} +1.60925 q^{83} -0.533188 q^{85} +10.4058 q^{87} +2.88471 q^{89} -14.8998 q^{93} +0.0217703 q^{95} +8.05861 q^{97} -8.70171 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+2q3+4q53q73q98q112q152q174q192q21+5q235q25q27q295q3110q334q3512q37+7q4113q43++q99+O(q100) 3 q + 2 q^{3} + 4 q^{5} - 3 q^{7} - 3 q^{9} - 8 q^{11} - 2 q^{15} - 2 q^{17} - 4 q^{19} - 2 q^{21} + 5 q^{23} - 5 q^{25} - q^{27} - q^{29} - 5 q^{31} - 10 q^{33} - 4 q^{35} - 12 q^{37} + 7 q^{41} - 13 q^{43}+ \cdots + q^{99}+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 2.24698 1.29729 0.648647 0.761089i 0.275335π-0.275335\pi
0.648647 + 0.761089i 0.275335π0.275335\pi
44 0 0
55 −0.246980 −0.110453 −0.0552263 0.998474i 0.517588π-0.517588\pi
−0.0552263 + 0.998474i 0.517588π0.517588\pi
66 0 0
77 −2.35690 −0.890823 −0.445411 0.895326i 0.646943π-0.646943\pi
−0.445411 + 0.895326i 0.646943π0.646943\pi
88 0 0
99 2.04892 0.682972
1010 0 0
1111 −4.24698 −1.28051 −0.640256 0.768161i 0.721172π-0.721172\pi
−0.640256 + 0.768161i 0.721172π0.721172\pi
1212 0 0
1313 0 0
1414 0 0
1515 −0.554958 −0.143290
1616 0 0
1717 2.15883 0.523594 0.261797 0.965123i 0.415685π-0.415685\pi
0.261797 + 0.965123i 0.415685π0.415685\pi
1818 0 0
1919 −0.0881460 −0.0202221 −0.0101110 0.999949i 0.503218π-0.503218\pi
−0.0101110 + 0.999949i 0.503218π0.503218\pi
2020 0 0
2121 −5.29590 −1.15566
2222 0 0
2323 −1.49396 −0.311512 −0.155756 0.987796i 0.549781π-0.549781\pi
−0.155756 + 0.987796i 0.549781π0.549781\pi
2424 0 0
2525 −4.93900 −0.987800
2626 0 0
2727 −2.13706 −0.411278
2828 0 0
2929 4.63102 0.859959 0.429980 0.902839i 0.358521π-0.358521\pi
0.429980 + 0.902839i 0.358521π0.358521\pi
3030 0 0
3131 −6.63102 −1.19097 −0.595483 0.803368i 0.703039π-0.703039\pi
−0.595483 + 0.803368i 0.703039π0.703039\pi
3232 0 0
3333 −9.54288 −1.66120
3434 0 0
3535 0.582105 0.0983937
3636 0 0
3737 −5.69202 −0.935763 −0.467881 0.883791i 0.654983π-0.654983\pi
−0.467881 + 0.883791i 0.654983π0.654983\pi
3838 0 0
3939 0 0
4040 0 0
4141 11.5918 1.81033 0.905167 0.425056i 0.139746π-0.139746\pi
0.905167 + 0.425056i 0.139746π0.139746\pi
4242 0 0
4343 0.295897 0.0451239 0.0225619 0.999745i 0.492818π-0.492818\pi
0.0225619 + 0.999745i 0.492818π0.492818\pi
4444 0 0
4545 −0.506041 −0.0754361
4646 0 0
4747 −7.35690 −1.07311 −0.536557 0.843864i 0.680275π-0.680275\pi
−0.536557 + 0.843864i 0.680275π0.680275\pi
4848 0 0
4949 −1.44504 −0.206435
5050 0 0
5151 4.85086 0.679256
5252 0 0
5353 −10.3937 −1.42769 −0.713844 0.700304i 0.753048π-0.753048\pi
−0.713844 + 0.700304i 0.753048π0.753048\pi
5454 0 0
5555 1.04892 0.141436
5656 0 0
5757 −0.198062 −0.0262340
5858 0 0
5959 −6.78017 −0.882703 −0.441351 0.897334i 0.645501π-0.645501\pi
−0.441351 + 0.897334i 0.645501π0.645501\pi
6060 0 0
6161 3.47219 0.444568 0.222284 0.974982i 0.428649π-0.428649\pi
0.222284 + 0.974982i 0.428649π0.428649\pi
6262 0 0
6363 −4.82908 −0.608407
6464 0 0
6565 0 0
6666 0 0
6767 7.67994 0.938254 0.469127 0.883131i 0.344569π-0.344569\pi
0.469127 + 0.883131i 0.344569π0.344569\pi
6868 0 0
6969 −3.35690 −0.404123
7070 0 0
7171 −8.66487 −1.02833 −0.514166 0.857691i 0.671898π-0.671898\pi
−0.514166 + 0.857691i 0.671898π0.671898\pi
7272 0 0
7373 −6.73556 −0.788338 −0.394169 0.919038i 0.628968π-0.628968\pi
−0.394169 + 0.919038i 0.628968π0.628968\pi
7474 0 0
7575 −11.0978 −1.28147
7676 0 0
7777 10.0097 1.14071
7878 0 0
7979 −9.97046 −1.12176 −0.560882 0.827896i 0.689538π-0.689538\pi
−0.560882 + 0.827896i 0.689538π0.689538\pi
8080 0 0
8181 −10.9487 −1.21652
8282 0 0
8383 1.60925 0.176638 0.0883192 0.996092i 0.471850π-0.471850\pi
0.0883192 + 0.996092i 0.471850π0.471850\pi
8484 0 0
8585 −0.533188 −0.0578323
8686 0 0
8787 10.4058 1.11562
8888 0 0
8989 2.88471 0.305778 0.152889 0.988243i 0.451142π-0.451142\pi
0.152889 + 0.988243i 0.451142π0.451142\pi
9090 0 0
9191 0 0
9292 0 0
9393 −14.8998 −1.54503
9494 0 0
9595 0.0217703 0.00223358
9696 0 0
9797 8.05861 0.818227 0.409114 0.912483i 0.365838π-0.365838\pi
0.409114 + 0.912483i 0.365838π0.365838\pi
9898 0 0
9999 −8.70171 −0.874555
100100 0 0
101101 −13.3545 −1.32882 −0.664411 0.747367i 0.731318π-0.731318\pi
−0.664411 + 0.747367i 0.731318π0.731318\pi
102102 0 0
103103 −1.36227 −0.134229 −0.0671144 0.997745i 0.521379π-0.521379\pi
−0.0671144 + 0.997745i 0.521379π0.521379\pi
104104 0 0
105105 1.30798 0.127646
106106 0 0
107107 −3.26875 −0.316002 −0.158001 0.987439i 0.550505π-0.550505\pi
−0.158001 + 0.987439i 0.550505π0.550505\pi
108108 0 0
109109 −15.7017 −1.50395 −0.751976 0.659191i 0.770899π-0.770899\pi
−0.751976 + 0.659191i 0.770899π0.770899\pi
110110 0 0
111111 −12.7899 −1.21396
112112 0 0
113113 12.0489 1.13347 0.566733 0.823901i 0.308207π-0.308207\pi
0.566733 + 0.823901i 0.308207π0.308207\pi
114114 0 0
115115 0.368977 0.0344073
116116 0 0
117117 0 0
118118 0 0
119119 −5.08815 −0.466430
120120 0 0
121121 7.03684 0.639712
122122 0 0
123123 26.0465 2.34854
124124 0 0
125125 2.45473 0.219558
126126 0 0
127127 9.80731 0.870258 0.435129 0.900368i 0.356703π-0.356703\pi
0.435129 + 0.900368i 0.356703π0.356703\pi
128128 0 0
129129 0.664874 0.0585389
130130 0 0
131131 6.57673 0.574611 0.287306 0.957839i 0.407240π-0.407240\pi
0.287306 + 0.957839i 0.407240π0.407240\pi
132132 0 0
133133 0.207751 0.0180143
134134 0 0
135135 0.527811 0.0454267
136136 0 0
137137 −6.21983 −0.531396 −0.265698 0.964056i 0.585602π-0.585602\pi
−0.265698 + 0.964056i 0.585602π0.585602\pi
138138 0 0
139139 14.7071 1.24744 0.623719 0.781648i 0.285621π-0.285621\pi
0.623719 + 0.781648i 0.285621π0.285621\pi
140140 0 0
141141 −16.5308 −1.39214
142142 0 0
143143 0 0
144144 0 0
145145 −1.14377 −0.0949848
146146 0 0
147147 −3.24698 −0.267806
148148 0 0
149149 −4.33513 −0.355147 −0.177574 0.984108i 0.556825π-0.556825\pi
−0.177574 + 0.984108i 0.556825π0.556825\pi
150150 0 0
151151 3.94438 0.320989 0.160494 0.987037i 0.448691π-0.448691\pi
0.160494 + 0.987037i 0.448691π0.448691\pi
152152 0 0
153153 4.42327 0.357600
154154 0 0
155155 1.63773 0.131545
156156 0 0
157157 4.45473 0.355526 0.177763 0.984073i 0.443114π-0.443114\pi
0.177763 + 0.984073i 0.443114π0.443114\pi
158158 0 0
159159 −23.3545 −1.85213
160160 0 0
161161 3.52111 0.277502
162162 0 0
163163 16.1588 1.26566 0.632829 0.774292i 0.281894π-0.281894\pi
0.632829 + 0.774292i 0.281894π0.281894\pi
164164 0 0
165165 2.35690 0.183484
166166 0 0
167167 16.1172 1.24719 0.623594 0.781749i 0.285672π-0.285672\pi
0.623594 + 0.781749i 0.285672π0.285672\pi
168168 0 0
169169 0 0
170170 0 0
171171 −0.180604 −0.0138111
172172 0 0
173173 −21.5362 −1.63736 −0.818682 0.574247i 0.805295π-0.805295\pi
−0.818682 + 0.574247i 0.805295π0.805295\pi
174174 0 0
175175 11.6407 0.879955
176176 0 0
177177 −15.2349 −1.14513
178178 0 0
179179 −11.4330 −0.854540 −0.427270 0.904124i 0.640525π-0.640525\pi
−0.427270 + 0.904124i 0.640525π0.640525\pi
180180 0 0
181181 20.9705 1.55872 0.779361 0.626575i 0.215544π-0.215544\pi
0.779361 + 0.626575i 0.215544π0.215544\pi
182182 0 0
183183 7.80194 0.576736
184184 0 0
185185 1.40581 0.103357
186186 0 0
187187 −9.16852 −0.670469
188188 0 0
189189 5.03684 0.366376
190190 0 0
191191 14.4373 1.04464 0.522322 0.852748i 0.325066π-0.325066\pi
0.522322 + 0.852748i 0.325066π0.325066\pi
192192 0 0
193193 13.5797 0.977489 0.488745 0.872427i 0.337455π-0.337455\pi
0.488745 + 0.872427i 0.337455π0.337455\pi
194194 0 0
195195 0 0
196196 0 0
197197 0.560335 0.0399222 0.0199611 0.999801i 0.493646π-0.493646\pi
0.0199611 + 0.999801i 0.493646π0.493646\pi
198198 0 0
199199 −11.4916 −0.814616 −0.407308 0.913291i 0.633532π-0.633532\pi
−0.407308 + 0.913291i 0.633532π0.633532\pi
200200 0 0
201201 17.2567 1.21719
202202 0 0
203203 −10.9148 −0.766071
204204 0 0
205205 −2.86294 −0.199956
206206 0 0
207207 −3.06100 −0.212754
208208 0 0
209209 0.374354 0.0258946
210210 0 0
211211 −8.78448 −0.604748 −0.302374 0.953189i 0.597779π-0.597779\pi
−0.302374 + 0.953189i 0.597779π0.597779\pi
212212 0 0
213213 −19.4698 −1.33405
214214 0 0
215215 −0.0730805 −0.00498405
216216 0 0
217217 15.6286 1.06094
218218 0 0
219219 −15.1347 −1.02271
220220 0 0
221221 0 0
222222 0 0
223223 −2.25906 −0.151278 −0.0756390 0.997135i 0.524100π-0.524100\pi
−0.0756390 + 0.997135i 0.524100π0.524100\pi
224224 0 0
225225 −10.1196 −0.674640
226226 0 0
227227 −6.96615 −0.462359 −0.231180 0.972911i 0.574259π-0.574259\pi
−0.231180 + 0.972911i 0.574259π0.574259\pi
228228 0 0
229229 24.1739 1.59746 0.798728 0.601692i 0.205507π-0.205507\pi
0.798728 + 0.601692i 0.205507π0.205507\pi
230230 0 0
231231 22.4916 1.47984
232232 0 0
233233 −3.06100 −0.200533 −0.100266 0.994961i 0.531969π-0.531969\pi
−0.100266 + 0.994961i 0.531969π0.531969\pi
234234 0 0
235235 1.81700 0.118528
236236 0 0
237237 −22.4034 −1.45526
238238 0 0
239239 −25.1468 −1.62661 −0.813304 0.581839i 0.802333π-0.802333\pi
−0.813304 + 0.581839i 0.802333π0.802333\pi
240240 0 0
241241 20.2664 1.30547 0.652735 0.757586i 0.273621π-0.273621\pi
0.652735 + 0.757586i 0.273621π0.273621\pi
242242 0 0
243243 −18.1903 −1.16691
244244 0 0
245245 0.356896 0.0228012
246246 0 0
247247 0 0
248248 0 0
249249 3.61596 0.229152
250250 0 0
251251 23.7211 1.49726 0.748631 0.662987i 0.230712π-0.230712\pi
0.748631 + 0.662987i 0.230712π0.230712\pi
252252 0 0
253253 6.34481 0.398895
254254 0 0
255255 −1.19806 −0.0750256
256256 0 0
257257 14.2241 0.887278 0.443639 0.896206i 0.353687π-0.353687\pi
0.443639 + 0.896206i 0.353687π0.353687\pi
258258 0 0
259259 13.4155 0.833599
260260 0 0
261261 9.48858 0.587329
262262 0 0
263263 17.0954 1.05415 0.527075 0.849819i 0.323289π-0.323289\pi
0.527075 + 0.849819i 0.323289π0.323289\pi
264264 0 0
265265 2.56704 0.157692
266266 0 0
267267 6.48188 0.396684
268268 0 0
269269 −6.46681 −0.394288 −0.197144 0.980374i 0.563167π-0.563167\pi
−0.197144 + 0.980374i 0.563167π0.563167\pi
270270 0 0
271271 6.44803 0.391690 0.195845 0.980635i 0.437255π-0.437255\pi
0.195845 + 0.980635i 0.437255π0.437255\pi
272272 0 0
273273 0 0
274274 0 0
275275 20.9758 1.26489
276276 0 0
277277 13.4601 0.808739 0.404370 0.914596i 0.367491π-0.367491\pi
0.404370 + 0.914596i 0.367491π0.367491\pi
278278 0 0
279279 −13.5864 −0.813398
280280 0 0
281281 −5.03684 −0.300472 −0.150236 0.988650i 0.548003π-0.548003\pi
−0.150236 + 0.988650i 0.548003π0.548003\pi
282282 0 0
283283 −22.1280 −1.31537 −0.657686 0.753293i 0.728464π-0.728464\pi
−0.657686 + 0.753293i 0.728464π0.728464\pi
284284 0 0
285285 0.0489173 0.00289761
286286 0 0
287287 −27.3207 −1.61269
288288 0 0
289289 −12.3394 −0.725849
290290 0 0
291291 18.1075 1.06148
292292 0 0
293293 −14.9463 −0.873172 −0.436586 0.899663i 0.643813π-0.643813\pi
−0.436586 + 0.899663i 0.643813π0.643813\pi
294294 0 0
295295 1.67456 0.0974968
296296 0 0
297297 9.07606 0.526647
298298 0 0
299299 0 0
300300 0 0
301301 −0.697398 −0.0401974
302302 0 0
303303 −30.0073 −1.72387
304304 0 0
305305 −0.857560 −0.0491037
306306 0 0
307307 19.1293 1.09177 0.545883 0.837861i 0.316194π-0.316194\pi
0.545883 + 0.837861i 0.316194π0.316194\pi
308308 0 0
309309 −3.06100 −0.174134
310310 0 0
311311 0.269815 0.0152998 0.00764990 0.999971i 0.497565π-0.497565\pi
0.00764990 + 0.999971i 0.497565π0.497565\pi
312312 0 0
313313 −23.3937 −1.32229 −0.661146 0.750257i 0.729930π-0.729930\pi
−0.661146 + 0.750257i 0.729930π0.729930\pi
314314 0 0
315315 1.19269 0.0672002
316316 0 0
317317 13.9952 0.786050 0.393025 0.919528i 0.371429π-0.371429\pi
0.393025 + 0.919528i 0.371429π0.371429\pi
318318 0 0
319319 −19.6679 −1.10119
320320 0 0
321321 −7.34481 −0.409948
322322 0 0
323323 −0.190293 −0.0105882
324324 0 0
325325 0 0
326326 0 0
327327 −35.2814 −1.95107
328328 0 0
329329 17.3394 0.955954
330330 0 0
331331 17.8213 0.979548 0.489774 0.871849i 0.337079π-0.337079\pi
0.489774 + 0.871849i 0.337079π0.337079\pi
332332 0 0
333333 −11.6625 −0.639100
334334 0 0
335335 −1.89679 −0.103633
336336 0 0
337337 −27.8485 −1.51700 −0.758501 0.651672i 0.774068π-0.774068\pi
−0.758501 + 0.651672i 0.774068π0.774068\pi
338338 0 0
339339 27.0737 1.47044
340340 0 0
341341 28.1618 1.52505
342342 0 0
343343 19.9041 1.07472
344344 0 0
345345 0.829085 0.0446364
346346 0 0
347347 −1.50365 −0.0807200 −0.0403600 0.999185i 0.512850π-0.512850\pi
−0.0403600 + 0.999185i 0.512850π0.512850\pi
348348 0 0
349349 14.1860 0.759358 0.379679 0.925118i 0.376034π-0.376034\pi
0.379679 + 0.925118i 0.376034π0.376034\pi
350350 0 0
351351 0 0
352352 0 0
353353 7.16852 0.381542 0.190771 0.981635i 0.438901π-0.438901\pi
0.190771 + 0.981635i 0.438901π0.438901\pi
354354 0 0
355355 2.14005 0.113582
356356 0 0
357357 −11.4330 −0.605096
358358 0 0
359359 19.8853 1.04951 0.524753 0.851255i 0.324158π-0.324158\pi
0.524753 + 0.851255i 0.324158π0.324158\pi
360360 0 0
361361 −18.9922 −0.999591
362362 0 0
363363 15.8116 0.829895
364364 0 0
365365 1.66355 0.0870740
366366 0 0
367367 −1.08383 −0.0565757 −0.0282878 0.999600i 0.509006π-0.509006\pi
−0.0282878 + 0.999600i 0.509006π0.509006\pi
368368 0 0
369369 23.7506 1.23641
370370 0 0
371371 24.4969 1.27182
372372 0 0
373373 −6.13036 −0.317418 −0.158709 0.987325i 0.550733π-0.550733\pi
−0.158709 + 0.987325i 0.550733π0.550733\pi
374374 0 0
375375 5.51573 0.284831
376376 0 0
377377 0 0
378378 0 0
379379 −2.40880 −0.123732 −0.0618658 0.998084i 0.519705π-0.519705\pi
−0.0618658 + 0.998084i 0.519705π0.519705\pi
380380 0 0
381381 22.0368 1.12898
382382 0 0
383383 −30.3913 −1.55292 −0.776462 0.630164i 0.782988π-0.782988\pi
−0.776462 + 0.630164i 0.782988π0.782988\pi
384384 0 0
385385 −2.47219 −0.125994
386386 0 0
387387 0.606268 0.0308184
388388 0 0
389389 −15.9409 −0.808237 −0.404118 0.914707i 0.632422π-0.632422\pi
−0.404118 + 0.914707i 0.632422π0.632422\pi
390390 0 0
391391 −3.22521 −0.163106
392392 0 0
393393 14.7778 0.745440
394394 0 0
395395 2.46250 0.123902
396396 0 0
397397 −16.9148 −0.848931 −0.424466 0.905444i 0.639538π-0.639538\pi
−0.424466 + 0.905444i 0.639538π0.639538\pi
398398 0 0
399399 0.466812 0.0233698
400400 0 0
401401 −26.6625 −1.33146 −0.665730 0.746192i 0.731880π-0.731880\pi
−0.665730 + 0.746192i 0.731880π0.731880\pi
402402 0 0
403403 0 0
404404 0 0
405405 2.70410 0.134368
406406 0 0
407407 24.1739 1.19826
408408 0 0
409409 −28.5163 −1.41004 −0.705021 0.709187i 0.749062π-0.749062\pi
−0.705021 + 0.709187i 0.749062π0.749062\pi
410410 0 0
411411 −13.9758 −0.689377
412412 0 0
413413 15.9801 0.786332
414414 0 0
415415 −0.397452 −0.0195102
416416 0 0
417417 33.0465 1.61830
418418 0 0
419419 29.6093 1.44651 0.723253 0.690583i 0.242646π-0.242646\pi
0.723253 + 0.690583i 0.242646π0.242646\pi
420420 0 0
421421 11.6606 0.568301 0.284151 0.958780i 0.408288π-0.408288\pi
0.284151 + 0.958780i 0.408288π0.408288\pi
422422 0 0
423423 −15.0737 −0.732907
424424 0 0
425425 −10.6625 −0.517206
426426 0 0
427427 −8.18359 −0.396032
428428 0 0
429429 0 0
430430 0 0
431431 4.34913 0.209490 0.104745 0.994499i 0.466597π-0.466597\pi
0.104745 + 0.994499i 0.466597π0.466597\pi
432432 0 0
433433 −14.3884 −0.691460 −0.345730 0.938334i 0.612369π-0.612369\pi
−0.345730 + 0.938334i 0.612369π0.612369\pi
434434 0 0
435435 −2.57002 −0.123223
436436 0 0
437437 0.131687 0.00629942
438438 0 0
439439 20.2325 0.965645 0.482822 0.875718i 0.339612π-0.339612\pi
0.482822 + 0.875718i 0.339612π0.339612\pi
440440 0 0
441441 −2.96077 −0.140989
442442 0 0
443443 −8.12200 −0.385888 −0.192944 0.981210i 0.561804π-0.561804\pi
−0.192944 + 0.981210i 0.561804π0.561804\pi
444444 0 0
445445 −0.712464 −0.0337740
446446 0 0
447447 −9.74094 −0.460731
448448 0 0
449449 −12.4916 −0.589513 −0.294757 0.955572i 0.595239π-0.595239\pi
−0.294757 + 0.955572i 0.595239π0.595239\pi
450450 0 0
451451 −49.2301 −2.31816
452452 0 0
453453 8.86294 0.416417
454454 0 0
455455 0 0
456456 0 0
457457 −5.98121 −0.279789 −0.139895 0.990166i 0.544676π-0.544676\pi
−0.139895 + 0.990166i 0.544676π0.544676\pi
458458 0 0
459459 −4.61356 −0.215343
460460 0 0
461461 2.05669 0.0957895 0.0478947 0.998852i 0.484749π-0.484749\pi
0.0478947 + 0.998852i 0.484749π0.484749\pi
462462 0 0
463463 −8.44935 −0.392675 −0.196337 0.980536i 0.562905π-0.562905\pi
−0.196337 + 0.980536i 0.562905π0.562905\pi
464464 0 0
465465 3.67994 0.170653
466466 0 0
467467 −33.5139 −1.55084 −0.775420 0.631446i 0.782462π-0.782462\pi
−0.775420 + 0.631446i 0.782462π0.782462\pi
468468 0 0
469469 −18.1008 −0.835818
470470 0 0
471471 10.0097 0.461222
472472 0 0
473473 −1.25667 −0.0577817
474474 0 0
475475 0.435353 0.0199754
476476 0 0
477477 −21.2959 −0.975072
478478 0 0
479479 −24.7313 −1.13000 −0.565000 0.825091i 0.691124π-0.691124\pi
−0.565000 + 0.825091i 0.691124π0.691124\pi
480480 0 0
481481 0 0
482482 0 0
483483 7.91185 0.360002
484484 0 0
485485 −1.99031 −0.0903754
486486 0 0
487487 −37.7555 −1.71087 −0.855433 0.517913i 0.826709π-0.826709\pi
−0.855433 + 0.517913i 0.826709π0.826709\pi
488488 0 0
489489 36.3086 1.64193
490490 0 0
491491 −31.3110 −1.41304 −0.706522 0.707691i 0.749737π-0.749737\pi
−0.706522 + 0.707691i 0.749737π0.749737\pi
492492 0 0
493493 9.99761 0.450270
494494 0 0
495495 2.14914 0.0965969
496496 0 0
497497 20.4222 0.916061
498498 0 0
499499 21.4873 0.961902 0.480951 0.876748i 0.340292π-0.340292\pi
0.480951 + 0.876748i 0.340292π0.340292\pi
500500 0 0
501501 36.2150 1.61797
502502 0 0
503503 −37.5924 −1.67616 −0.838081 0.545546i 0.816322π-0.816322\pi
−0.838081 + 0.545546i 0.816322π0.816322\pi
504504 0 0
505505 3.29829 0.146772
506506 0 0
507507 0 0
508508 0 0
509509 17.1075 0.758278 0.379139 0.925340i 0.376220π-0.376220\pi
0.379139 + 0.925340i 0.376220π0.376220\pi
510510 0 0
511511 15.8750 0.702269
512512 0 0
513513 0.188374 0.00831690
514514 0 0
515515 0.336454 0.0148259
516516 0 0
517517 31.2446 1.37414
518518 0 0
519519 −48.3913 −2.12414
520520 0 0
521521 −19.8465 −0.869493 −0.434746 0.900553i 0.643162π-0.643162\pi
−0.434746 + 0.900553i 0.643162π0.643162\pi
522522 0 0
523523 11.4300 0.499798 0.249899 0.968272i 0.419603π-0.419603\pi
0.249899 + 0.968272i 0.419603π0.419603\pi
524524 0 0
525525 26.1564 1.14156
526526 0 0
527527 −14.3153 −0.623583
528528 0 0
529529 −20.7681 −0.902960
530530 0 0
531531 −13.8920 −0.602862
532532 0 0
533533 0 0
534534 0 0
535535 0.807315 0.0349033
536536 0 0
537537 −25.6896 −1.10859
538538 0 0
539539 6.13706 0.264342
540540 0 0
541541 −16.1884 −0.695993 −0.347996 0.937496i 0.613138π-0.613138\pi
−0.347996 + 0.937496i 0.613138π0.613138\pi
542542 0 0
543543 47.1202 2.02212
544544 0 0
545545 3.87800 0.166115
546546 0 0
547547 −5.33081 −0.227929 −0.113965 0.993485i 0.536355π-0.536355\pi
−0.113965 + 0.993485i 0.536355π0.536355\pi
548548 0 0
549549 7.11423 0.303628
550550 0 0
551551 −0.408206 −0.0173902
552552 0 0
553553 23.4993 0.999293
554554 0 0
555555 3.15883 0.134085
556556 0 0
557557 −7.39075 −0.313156 −0.156578 0.987666i 0.550046π-0.550046\pi
−0.156578 + 0.987666i 0.550046π0.550046\pi
558558 0 0
559559 0 0
560560 0 0
561561 −20.6015 −0.869795
562562 0 0
563563 9.47889 0.399488 0.199744 0.979848i 0.435989π-0.435989\pi
0.199744 + 0.979848i 0.435989π0.435989\pi
564564 0 0
565565 −2.97584 −0.125194
566566 0 0
567567 25.8049 1.08370
568568 0 0
569569 −10.1438 −0.425249 −0.212624 0.977134i 0.568201π-0.568201\pi
−0.212624 + 0.977134i 0.568201π0.568201\pi
570570 0 0
571571 14.0925 0.589751 0.294876 0.955536i 0.404722π-0.404722\pi
0.294876 + 0.955536i 0.404722π0.404722\pi
572572 0 0
573573 32.4403 1.35521
574574 0 0
575575 7.37867 0.307712
576576 0 0
577577 −25.1545 −1.04720 −0.523598 0.851965i 0.675411π-0.675411\pi
−0.523598 + 0.851965i 0.675411π0.675411\pi
578578 0 0
579579 30.5133 1.26809
580580 0 0
581581 −3.79284 −0.157354
582582 0 0
583583 44.1420 1.82817
584584 0 0
585585 0 0
586586 0 0
587587 43.8353 1.80928 0.904639 0.426180i 0.140141π-0.140141\pi
0.904639 + 0.426180i 0.140141π0.140141\pi
588588 0 0
589589 0.584498 0.0240838
590590 0 0
591591 1.25906 0.0517909
592592 0 0
593593 24.9965 1.02648 0.513242 0.858244i 0.328444π-0.328444\pi
0.513242 + 0.858244i 0.328444π0.328444\pi
594594 0 0
595595 1.25667 0.0515184
596596 0 0
597597 −25.8213 −1.05680
598598 0 0
599599 6.24027 0.254971 0.127485 0.991840i 0.459309π-0.459309\pi
0.127485 + 0.991840i 0.459309π0.459309\pi
600600 0 0
601601 6.32975 0.258196 0.129098 0.991632i 0.458792π-0.458792\pi
0.129098 + 0.991632i 0.458792π0.458792\pi
602602 0 0
603603 15.7356 0.640802
604604 0 0
605605 −1.73795 −0.0706579
606606 0 0
607607 43.6480 1.77162 0.885809 0.464050i 0.153604π-0.153604\pi
0.885809 + 0.464050i 0.153604π0.153604\pi
608608 0 0
609609 −24.5254 −0.993820
610610 0 0
611611 0 0
612612 0 0
613613 25.9541 1.04827 0.524137 0.851634i 0.324388π-0.324388\pi
0.524137 + 0.851634i 0.324388π0.324388\pi
614614 0 0
615615 −6.43296 −0.259402
616616 0 0
617617 −45.9396 −1.84946 −0.924729 0.380626i 0.875709π-0.875709\pi
−0.924729 + 0.380626i 0.875709π0.875709\pi
618618 0 0
619619 6.73556 0.270725 0.135363 0.990796i 0.456780π-0.456780\pi
0.135363 + 0.990796i 0.456780π0.456780\pi
620620 0 0
621621 3.19269 0.128118
622622 0 0
623623 −6.79895 −0.272394
624624 0 0
625625 24.0887 0.963549
626626 0 0
627627 0.841166 0.0335930
628628 0 0
629629 −12.2881 −0.489960
630630 0 0
631631 45.0998 1.79539 0.897696 0.440614i 0.145239π-0.145239\pi
0.897696 + 0.440614i 0.145239π0.145239\pi
632632 0 0
633633 −19.7385 −0.784537
634634 0 0
635635 −2.42221 −0.0961223
636636 0 0
637637 0 0
638638 0 0
639639 −17.7536 −0.702322
640640 0 0
641641 32.5821 1.28692 0.643458 0.765482i 0.277499π-0.277499\pi
0.643458 + 0.765482i 0.277499π0.277499\pi
642642 0 0
643643 25.5754 1.00860 0.504298 0.863530i 0.331751π-0.331751\pi
0.504298 + 0.863530i 0.331751π0.331751\pi
644644 0 0
645645 −0.164210 −0.00646578
646646 0 0
647647 30.1715 1.18616 0.593082 0.805142i 0.297911π-0.297911\pi
0.593082 + 0.805142i 0.297911π0.297911\pi
648648 0 0
649649 28.7952 1.13031
650650 0 0
651651 35.1172 1.37635
652652 0 0
653653 36.9028 1.44412 0.722058 0.691832i 0.243196π-0.243196\pi
0.722058 + 0.691832i 0.243196π0.243196\pi
654654 0 0
655655 −1.62432 −0.0634673
656656 0 0
657657 −13.8006 −0.538413
658658 0 0
659659 −23.6866 −0.922701 −0.461350 0.887218i 0.652635π-0.652635\pi
−0.461350 + 0.887218i 0.652635π0.652635\pi
660660 0 0
661661 31.7590 1.23528 0.617641 0.786460i 0.288089π-0.288089\pi
0.617641 + 0.786460i 0.288089π0.288089\pi
662662 0 0
663663 0 0
664664 0 0
665665 −0.0513102 −0.00198973
666666 0 0
667667 −6.91856 −0.267888
668668 0 0
669669 −5.07606 −0.196252
670670 0 0
671671 −14.7463 −0.569275
672672 0 0
673673 −7.50232 −0.289193 −0.144597 0.989491i 0.546188π-0.546188\pi
−0.144597 + 0.989491i 0.546188π0.546188\pi
674674 0 0
675675 10.5550 0.406261
676676 0 0
677677 −35.0315 −1.34637 −0.673184 0.739475i 0.735074π-0.735074\pi
−0.673184 + 0.739475i 0.735074π0.735074\pi
678678 0 0
679679 −18.9933 −0.728896
680680 0 0
681681 −15.6528 −0.599816
682682 0 0
683683 −24.0834 −0.921524 −0.460762 0.887524i 0.652424π-0.652424\pi
−0.460762 + 0.887524i 0.652424π0.652424\pi
684684 0 0
685685 1.53617 0.0586941
686686 0 0
687687 54.3183 2.07237
688688 0 0
689689 0 0
690690 0 0
691691 2.01447 0.0766342 0.0383171 0.999266i 0.487800π-0.487800\pi
0.0383171 + 0.999266i 0.487800π0.487800\pi
692692 0 0
693693 20.5090 0.779073
694694 0 0
695695 −3.63235 −0.137783
696696 0 0
697697 25.0248 0.947880
698698 0 0
699699 −6.87800 −0.260150
700700 0 0
701701 −48.8189 −1.84387 −0.921933 0.387350i 0.873390π-0.873390\pi
−0.921933 + 0.387350i 0.873390π0.873390\pi
702702 0 0
703703 0.501729 0.0189231
704704 0 0
705705 4.08277 0.153766
706706 0 0
707707 31.4752 1.18375
708708 0 0
709709 20.8060 0.781385 0.390693 0.920521i 0.372236π-0.372236\pi
0.390693 + 0.920521i 0.372236π0.372236\pi
710710 0 0
711711 −20.4286 −0.766134
712712 0 0
713713 9.90648 0.371000
714714 0 0
715715 0 0
716716 0 0
717717 −56.5042 −2.11019
718718 0 0
719719 −21.4306 −0.799225 −0.399613 0.916684i 0.630855π-0.630855\pi
−0.399613 + 0.916684i 0.630855π0.630855\pi
720720 0 0
721721 3.21073 0.119574
722722 0 0
723723 45.5381 1.69358
724724 0 0
725725 −22.8726 −0.849468
726726 0 0
727727 −13.4862 −0.500175 −0.250088 0.968223i 0.580459π-0.580459\pi
−0.250088 + 0.968223i 0.580459π0.580459\pi
728728 0 0
729729 −8.02715 −0.297302
730730 0 0
731731 0.638792 0.0236266
732732 0 0
733733 43.5424 1.60828 0.804138 0.594443i 0.202627π-0.202627\pi
0.804138 + 0.594443i 0.202627π0.202627\pi
734734 0 0
735735 0.801938 0.0295799
736736 0 0
737737 −32.6165 −1.20145
738738 0 0
739739 20.0543 0.737709 0.368855 0.929487i 0.379750π-0.379750\pi
0.368855 + 0.929487i 0.379750π0.379750\pi
740740 0 0
741741 0 0
742742 0 0
743743 −33.1685 −1.21684 −0.608418 0.793617i 0.708195π-0.708195\pi
−0.608418 + 0.793617i 0.708195π0.708195\pi
744744 0 0
745745 1.07069 0.0392270
746746 0 0
747747 3.29722 0.120639
748748 0 0
749749 7.70410 0.281502
750750 0 0
751751 −39.2814 −1.43340 −0.716700 0.697382i 0.754348π-0.754348\pi
−0.716700 + 0.697382i 0.754348π0.754348\pi
752752 0 0
753753 53.3008 1.94239
754754 0 0
755755 −0.974181 −0.0354541
756756 0 0
757757 −46.6426 −1.69526 −0.847628 0.530592i 0.821970π-0.821970\pi
−0.847628 + 0.530592i 0.821970π0.821970\pi
758758 0 0
759759 14.2567 0.517484
760760 0 0
761761 21.8984 0.793818 0.396909 0.917858i 0.370083π-0.370083\pi
0.396909 + 0.917858i 0.370083π0.370083\pi
762762 0 0
763763 37.0073 1.33975
764764 0 0
765765 −1.09246 −0.0394979
766766 0 0
767767 0 0
768768 0 0
769769 −46.7096 −1.68439 −0.842196 0.539172i 0.818737π-0.818737\pi
−0.842196 + 0.539172i 0.818737π0.818737\pi
770770 0 0
771771 31.9614 1.15106
772772 0 0
773773 30.2416 1.08771 0.543857 0.839178i 0.316963π-0.316963\pi
0.543857 + 0.839178i 0.316963π0.316963\pi
774774 0 0
775775 32.7506 1.17644
776776 0 0
777777 30.1444 1.08142
778778 0 0
779779 −1.02177 −0.0366087
780780 0 0
781781 36.7995 1.31679
782782 0 0
783783 −9.89679 −0.353682
784784 0 0
785785 −1.10023 −0.0392688
786786 0 0
787787 28.7023 1.02313 0.511563 0.859246i 0.329067π-0.329067\pi
0.511563 + 0.859246i 0.329067π0.329067\pi
788788 0 0
789789 38.4131 1.36754
790790 0 0
791791 −28.3980 −1.00972
792792 0 0
793793 0 0
794794 0 0
795795 5.76809 0.204573
796796 0 0
797797 −18.5418 −0.656785 −0.328392 0.944541i 0.606507π-0.606507\pi
−0.328392 + 0.944541i 0.606507π0.606507\pi
798798 0 0
799799 −15.8823 −0.561876
800800 0 0
801801 5.91053 0.208838
802802 0 0
803803 28.6058 1.00948
804804 0 0
805805 −0.869641 −0.0306508
806806 0 0
807807 −14.5308 −0.511508
808808 0 0
809809 −10.0677 −0.353962 −0.176981 0.984214i 0.556633π-0.556633\pi
−0.176981 + 0.984214i 0.556633π0.556633\pi
810810 0 0
811811 −10.0285 −0.352147 −0.176074 0.984377i 0.556340π-0.556340\pi
−0.176074 + 0.984377i 0.556340π0.556340\pi
812812 0 0
813813 14.4886 0.508137
814814 0 0
815815 −3.99090 −0.139795
816816 0 0
817817 −0.0260821 −0.000912498 0
818818 0 0
819819 0 0
820820 0 0
821821 26.1704 0.913355 0.456677 0.889632i 0.349039π-0.349039\pi
0.456677 + 0.889632i 0.349039π0.349039\pi
822822 0 0
823823 −1.82238 −0.0635242 −0.0317621 0.999495i 0.510112π-0.510112\pi
−0.0317621 + 0.999495i 0.510112π0.510112\pi
824824 0 0
825825 47.1323 1.64094
826826 0 0
827827 −32.2941 −1.12298 −0.561488 0.827485i 0.689771π-0.689771\pi
−0.561488 + 0.827485i 0.689771π0.689771\pi
828828 0 0
829829 15.1002 0.524453 0.262226 0.965006i 0.415543π-0.415543\pi
0.262226 + 0.965006i 0.415543π0.415543\pi
830830 0 0
831831 30.2446 1.04917
832832 0 0
833833 −3.11960 −0.108088
834834 0 0
835835 −3.98062 −0.137755
836836 0 0
837837 14.1709 0.489818
838838 0 0
839839 −32.9965 −1.13917 −0.569584 0.821933i 0.692896π-0.692896\pi
−0.569584 + 0.821933i 0.692896π0.692896\pi
840840 0 0
841841 −7.55363 −0.260470
842842 0 0
843843 −11.3177 −0.389801
844844 0 0
845845 0 0
846846 0 0
847847 −16.5851 −0.569870
848848 0 0
849849 −49.7211 −1.70642
850850 0 0
851851 8.50365 0.291501
852852 0 0
853853 37.7802 1.29357 0.646784 0.762673i 0.276113π-0.276113\pi
0.646784 + 0.762673i 0.276113π0.276113\pi
854854 0 0
855855 0.0446055 0.00152547
856856 0 0
857857 27.3623 0.934677 0.467339 0.884078i 0.345213π-0.345213\pi
0.467339 + 0.884078i 0.345213π0.345213\pi
858858 0 0
859859 20.0629 0.684538 0.342269 0.939602i 0.388805π-0.388805\pi
0.342269 + 0.939602i 0.388805π0.388805\pi
860860 0 0
861861 −61.3889 −2.09213
862862 0 0
863863 −6.14483 −0.209173 −0.104586 0.994516i 0.533352π-0.533352\pi
−0.104586 + 0.994516i 0.533352π0.533352\pi
864864 0 0
865865 5.31900 0.180851
866866 0 0
867867 −27.7265 −0.941640
868868 0 0
869869 42.3443 1.43643
870870 0 0
871871 0 0
872872 0 0
873873 16.5114 0.558827
874874 0 0
875875 −5.78554 −0.195587
876876 0 0
877877 13.5077 0.456123 0.228061 0.973647i 0.426761π-0.426761\pi
0.228061 + 0.973647i 0.426761π0.426761\pi
878878 0 0
879879 −33.5840 −1.13276
880880 0 0
881881 −5.23431 −0.176348 −0.0881741 0.996105i 0.528103π-0.528103\pi
−0.0881741 + 0.996105i 0.528103π0.528103\pi
882882 0 0
883883 4.57301 0.153894 0.0769470 0.997035i 0.475483π-0.475483\pi
0.0769470 + 0.997035i 0.475483π0.475483\pi
884884 0 0
885885 3.76271 0.126482
886886 0 0
887887 1.64071 0.0550897 0.0275448 0.999621i 0.491231π-0.491231\pi
0.0275448 + 0.999621i 0.491231π0.491231\pi
888888 0 0
889889 −23.1148 −0.775246
890890 0 0
891891 46.4989 1.55777
892892 0 0
893893 0.648481 0.0217006
894894 0 0
895895 2.82371 0.0943861
896896 0 0
897897 0 0
898898 0 0
899899 −30.7084 −1.02418
900900 0 0
901901 −22.4383 −0.747529
902902 0 0
903903 −1.56704 −0.0521478
904904 0 0
905905 −5.17928 −0.172165
906906 0 0
907907 −8.10215 −0.269027 −0.134514 0.990912i 0.542947π-0.542947\pi
−0.134514 + 0.990912i 0.542947π0.542947\pi
908908 0 0
909909 −27.3623 −0.907549
910910 0 0
911911 9.18119 0.304187 0.152093 0.988366i 0.451399π-0.451399\pi
0.152093 + 0.988366i 0.451399π0.451399\pi
912912 0 0
913913 −6.83446 −0.226188
914914 0 0
915915 −1.92692 −0.0637020
916916 0 0
917917 −15.5007 −0.511877
918918 0 0
919919 −27.5036 −0.907262 −0.453631 0.891190i 0.649872π-0.649872\pi
−0.453631 + 0.891190i 0.649872π0.649872\pi
920920 0 0
921921 42.9831 1.41634
922922 0 0
923923 0 0
924924 0 0
925925 28.1129 0.924346
926926 0 0
927927 −2.79118 −0.0916745
928928 0 0
929929 −24.2131 −0.794407 −0.397203 0.917731i 0.630019π-0.630019\pi
−0.397203 + 0.917731i 0.630019π0.630019\pi
930930 0 0
931931 0.127375 0.00417454
932932 0 0
933933 0.606268 0.0198483
934934 0 0
935935 2.26444 0.0740550
936936 0 0
937937 11.1830 0.365333 0.182666 0.983175i 0.441527π-0.441527\pi
0.182666 + 0.983175i 0.441527π0.441527\pi
938938 0 0
939939 −52.5652 −1.71540
940940 0 0
941941 15.9638 0.520404 0.260202 0.965554i 0.416211π-0.416211\pi
0.260202 + 0.965554i 0.416211π0.416211\pi
942942 0 0
943943 −17.3177 −0.563941
944944 0 0
945945 −1.24400 −0.0404672
946946 0 0
947947 6.51466 0.211698 0.105849 0.994382i 0.466244π-0.466244\pi
0.105849 + 0.994382i 0.466244π0.466244\pi
948948 0 0
949949 0 0
950950 0 0
951951 31.4470 1.01974
952952 0 0
953953 47.6469 1.54344 0.771718 0.635965i 0.219398π-0.219398\pi
0.771718 + 0.635965i 0.219398π0.219398\pi
954954 0 0
955955 −3.56571 −0.115384
956956 0 0
957957 −44.1933 −1.42857
958958 0 0
959959 14.6595 0.473380
960960 0 0
961961 12.9705 0.418402
962962 0 0
963963 −6.69740 −0.215821
964964 0 0
965965 −3.35391 −0.107966
966966 0 0
967967 −43.8122 −1.40891 −0.704453 0.709751i 0.748808π-0.748808\pi
−0.704453 + 0.709751i 0.748808π0.748808\pi
968968 0 0
969969 −0.427583 −0.0137360
970970 0 0
971971 −4.29483 −0.137828 −0.0689139 0.997623i 0.521953π-0.521953\pi
−0.0689139 + 0.997623i 0.521953π0.521953\pi
972972 0 0
973973 −34.6631 −1.11125
974974 0 0
975975 0 0
976976 0 0
977977 −26.8019 −0.857470 −0.428735 0.903430i 0.641041π-0.641041\pi
−0.428735 + 0.903430i 0.641041π0.641041\pi
978978 0 0
979979 −12.2513 −0.391553
980980 0 0
981981 −32.1715 −1.02716
982982 0 0
983983 27.2495 0.869124 0.434562 0.900642i 0.356903π-0.356903\pi
0.434562 + 0.900642i 0.356903π0.356903\pi
984984 0 0
985985 −0.138391 −0.00440951
986986 0 0
987987 38.9614 1.24015
988988 0 0
989989 −0.442058 −0.0140566
990990 0 0
991991 −24.3889 −0.774740 −0.387370 0.921924i 0.626616π-0.626616\pi
−0.387370 + 0.921924i 0.626616π0.626616\pi
992992 0 0
993993 40.0441 1.27076
994994 0 0
995995 2.83818 0.0899764
996996 0 0
997997 31.3207 0.991935 0.495967 0.868341i 0.334814π-0.334814\pi
0.495967 + 0.868341i 0.334814π0.334814\pi
998998 0 0
999999 12.1642 0.384859
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 2704.2.a.ba.1.3 3
4.3 odd 2 169.2.a.c.1.1 yes 3
12.11 even 2 1521.2.a.o.1.3 3
13.5 odd 4 2704.2.f.o.337.6 6
13.8 odd 4 2704.2.f.o.337.5 6
13.12 even 2 2704.2.a.z.1.3 3
20.19 odd 2 4225.2.a.bb.1.3 3
28.27 even 2 8281.2.a.bj.1.1 3
52.3 odd 6 169.2.c.b.22.3 6
52.7 even 12 169.2.e.b.23.2 12
52.11 even 12 169.2.e.b.147.5 12
52.15 even 12 169.2.e.b.147.2 12
52.19 even 12 169.2.e.b.23.5 12
52.23 odd 6 169.2.c.c.22.1 6
52.31 even 4 169.2.b.b.168.5 6
52.35 odd 6 169.2.c.b.146.3 6
52.43 odd 6 169.2.c.c.146.1 6
52.47 even 4 169.2.b.b.168.2 6
52.51 odd 2 169.2.a.b.1.3 3
156.47 odd 4 1521.2.b.l.1351.5 6
156.83 odd 4 1521.2.b.l.1351.2 6
156.155 even 2 1521.2.a.r.1.1 3
260.259 odd 2 4225.2.a.bg.1.1 3
364.363 even 2 8281.2.a.bf.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.2.a.b.1.3 3 52.51 odd 2
169.2.a.c.1.1 yes 3 4.3 odd 2
169.2.b.b.168.2 6 52.47 even 4
169.2.b.b.168.5 6 52.31 even 4
169.2.c.b.22.3 6 52.3 odd 6
169.2.c.b.146.3 6 52.35 odd 6
169.2.c.c.22.1 6 52.23 odd 6
169.2.c.c.146.1 6 52.43 odd 6
169.2.e.b.23.2 12 52.7 even 12
169.2.e.b.23.5 12 52.19 even 12
169.2.e.b.147.2 12 52.15 even 12
169.2.e.b.147.5 12 52.11 even 12
1521.2.a.o.1.3 3 12.11 even 2
1521.2.a.r.1.1 3 156.155 even 2
1521.2.b.l.1351.2 6 156.83 odd 4
1521.2.b.l.1351.5 6 156.47 odd 4
2704.2.a.z.1.3 3 13.12 even 2
2704.2.a.ba.1.3 3 1.1 even 1 trivial
2704.2.f.o.337.5 6 13.8 odd 4
2704.2.f.o.337.6 6 13.5 odd 4
4225.2.a.bb.1.3 3 20.19 odd 2
4225.2.a.bg.1.1 3 260.259 odd 2
8281.2.a.bf.1.3 3 364.363 even 2
8281.2.a.bj.1.1 3 28.27 even 2