Properties

Label 1620.2.d.d.649.4
Level 16201620
Weight 22
Character 1620.649
Analytic conductor 12.93612.936
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1620,2,Mod(649,1620)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1620.649");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1620=22345 1620 = 2^{2} \cdot 3^{4} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1620.d (of order 22, degree 11, minimal)

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: no
Analytic conductor: 12.935765127412.9357651274
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.301925376.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6+14x4+43x2+36 x^{6} + 14x^{4} + 43x^{2} + 36 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 180)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 649.4
Root 3.17695i3.17695i of defining polynomial
Character χ\chi == 1620.649
Dual form 1620.2.d.d.649.3

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+(0.123563+2.23265i)q51.28835iq75.09303q113.56951iq130.895796iq17+5.34015q195.06555iq23+(4.96946+0.551747i)q253.00000q296.59877q31+(2.876440.159193i)q357.24970iq37+7.84590q4110.9299iq432.96925iq47+5.34015q49+4.78369iq53+(0.62931111.3710i)q555.75287q59+4.34015q61+(7.969460.441060i)q658.53805iq67+5.34015q71+9.34600iq73+6.56160iq77+0.741379q79+9.21247iq83+(2.000000.110687i)q859.24713q894.59877q91+(0.659846+11.9227i)q953.45882iq97+O(q100)q+(0.123563 + 2.23265i) q^{5} -1.28835i q^{7} -5.09303 q^{11} -3.56951i q^{13} -0.895796i q^{17} +5.34015 q^{19} -5.06555i q^{23} +(-4.96946 + 0.551747i) q^{25} -3.00000 q^{29} -6.59877 q^{31} +(2.87644 - 0.159193i) q^{35} -7.24970i q^{37} +7.84590 q^{41} -10.9299i q^{43} -2.96925i q^{47} +5.34015 q^{49} +4.78369i q^{53} +(-0.629311 - 11.3710i) q^{55} -5.75287 q^{59} +4.34015 q^{61} +(7.96946 - 0.441060i) q^{65} -8.53805i q^{67} +5.34015 q^{71} +9.34600i q^{73} +6.56160i q^{77} +0.741379 q^{79} +9.21247i q^{83} +(2.00000 - 0.110687i) q^{85} -9.24713 q^{89} -4.59877 q^{91} +(0.659846 + 11.9227i) q^{95} -3.45882i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+q5+2q11+3q2518q296q31+17q35+14q413q5534q596q61+15q65+6q79+12q8556q89+6q91+36q95+O(q100) 6 q + q^{5} + 2 q^{11} + 3 q^{25} - 18 q^{29} - 6 q^{31} + 17 q^{35} + 14 q^{41} - 3 q^{55} - 34 q^{59} - 6 q^{61} + 15 q^{65} + 6 q^{79} + 12 q^{85} - 56 q^{89} + 6 q^{91} + 36 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1620Z)×\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times.

nn 811811 12971297 15411541
χ(n)\chi(n) 11 1-1 11

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 0.123563 + 2.23265i 0.0552591 + 0.998472i
66 0 0
77 1.28835i 0.486951i −0.969907 0.243475i 0.921713π-0.921713\pi
0.969907 0.243475i 0.0782875π-0.0782875\pi
88 0 0
99 0 0
1010 0 0
1111 −5.09303 −1.53561 −0.767803 0.640686i 0.778650π-0.778650\pi
−0.767803 + 0.640686i 0.778650π0.778650\pi
1212 0 0
1313 3.56951i 0.990003i −0.868892 0.495002i 0.835167π-0.835167\pi
0.868892 0.495002i 0.164833π-0.164833\pi
1414 0 0
1515 0 0
1616 0 0
1717 0.895796i 0.217262i −0.994082 0.108631i 0.965353π-0.965353\pi
0.994082 0.108631i 0.0346468π-0.0346468\pi
1818 0 0
1919 5.34015 1.22512 0.612558 0.790426i 0.290141π-0.290141\pi
0.612558 + 0.790426i 0.290141π0.290141\pi
2020 0 0
2121 0 0
2222 0 0
2323 5.06555i 1.05624i −0.849169 0.528121i 0.822897π-0.822897\pi
0.849169 0.528121i 0.177103π-0.177103\pi
2424 0 0
2525 −4.96946 + 0.551747i −0.993893 + 0.110349i
2626 0 0
2727 0 0
2828 0 0
2929 −3.00000 −0.557086 −0.278543 0.960424i 0.589851π-0.589851\pi
−0.278543 + 0.960424i 0.589851π0.589851\pi
3030 0 0
3131 −6.59877 −1.18517 −0.592587 0.805506i 0.701894π-0.701894\pi
−0.592587 + 0.805506i 0.701894π0.701894\pi
3232 0 0
3333 0 0
3434 0 0
3535 2.87644 0.159193i 0.486207 0.0269085i
3636 0 0
3737 7.24970i 1.19184i −0.803043 0.595922i 0.796787π-0.796787\pi
0.803043 0.595922i 0.203213π-0.203213\pi
3838 0 0
3939 0 0
4040 0 0
4141 7.84590 1.22532 0.612662 0.790345i 0.290099π-0.290099\pi
0.612662 + 0.790345i 0.290099π0.290099\pi
4242 0 0
4343 10.9299i 1.66679i −0.552675 0.833397i 0.686393π-0.686393\pi
0.552675 0.833397i 0.313607π-0.313607\pi
4444 0 0
4545 0 0
4646 0 0
4747 2.96925i 0.433110i −0.976270 0.216555i 0.930518π-0.930518\pi
0.976270 0.216555i 0.0694821π-0.0694821\pi
4848 0 0
4949 5.34015 0.762879
5050 0 0
5151 0 0
5252 0 0
5353 4.78369i 0.657090i 0.944488 + 0.328545i 0.106558π0.106558\pi
−0.944488 + 0.328545i 0.893442π0.893442\pi
5454 0 0
5555 −0.629311 11.3710i −0.0848562 1.53326i
5656 0 0
5757 0 0
5858 0 0
5959 −5.75287 −0.748960 −0.374480 0.927235i 0.622179π-0.622179\pi
−0.374480 + 0.927235i 0.622179π0.622179\pi
6060 0 0
6161 4.34015 0.555700 0.277850 0.960625i 0.410378π-0.410378\pi
0.277850 + 0.960625i 0.410378π0.410378\pi
6262 0 0
6363 0 0
6464 0 0
6565 7.96946 0.441060i 0.988490 0.0547067i
6666 0 0
6767 8.53805i 1.04309i −0.853224 0.521544i 0.825356π-0.825356\pi
0.853224 0.521544i 0.174644π-0.174644\pi
6868 0 0
6969 0 0
7070 0 0
7171 5.34015 0.633760 0.316880 0.948466i 0.397365π-0.397365\pi
0.316880 + 0.948466i 0.397365π0.397365\pi
7272 0 0
7373 9.34600i 1.09387i 0.837176 + 0.546933i 0.184205π0.184205\pi
−0.837176 + 0.546933i 0.815795π0.815795\pi
7474 0 0
7575 0 0
7676 0 0
7777 6.56160i 0.747764i
7878 0 0
7979 0.741379 0.0834116 0.0417058 0.999130i 0.486721π-0.486721\pi
0.0417058 + 0.999130i 0.486721π0.486721\pi
8080 0 0
8181 0 0
8282 0 0
8383 9.21247i 1.01120i 0.862768 + 0.505600i 0.168729π0.168729\pi
−0.862768 + 0.505600i 0.831271π0.831271\pi
8484 0 0
8585 2.00000 0.110687i 0.216930 0.0120057i
8686 0 0
8787 0 0
8888 0 0
8989 −9.24713 −0.980193 −0.490097 0.871668i 0.663039π-0.663039\pi
−0.490097 + 0.871668i 0.663039π0.663039\pi
9090 0 0
9191 −4.59877 −0.482083
9292 0 0
9393 0 0
9494 0 0
9595 0.659846 + 11.9227i 0.0676988 + 1.22324i
9696 0 0
9797 3.45882i 0.351190i −0.984462 0.175595i 0.943815π-0.943815\pi
0.984462 0.175595i 0.0561849π-0.0561849\pi
9898 0 0
9999 0 0
100100 0 0
101101 16.4332 1.63516 0.817581 0.575813i 0.195314π-0.195314\pi
0.817581 + 0.575813i 0.195314π0.195314\pi
102102 0 0
103103 15.8619i 1.56292i −0.623954 0.781461i 0.714475π-0.714475\pi
0.623954 0.781461i 0.285525π-0.285525\pi
104104 0 0
105105 0 0
106106 0 0
107107 9.53086i 0.921383i −0.887560 0.460691i 0.847601π-0.847601\pi
0.887560 0.460691i 0.152399π-0.152399\pi
108108 0 0
109109 −16.2791 −1.55925 −0.779627 0.626245i 0.784591π-0.784591\pi
−0.779627 + 0.626245i 0.784591π0.784591\pi
110110 0 0
111111 0 0
112112 0 0
113113 18.1796i 1.71019i −0.518469 0.855096i 0.673498π-0.673498\pi
0.518469 0.855096i 0.326502π-0.326502\pi
114114 0 0
115115 11.3096 0.625916i 1.05463 0.0583670i
116116 0 0
117117 0 0
118118 0 0
119119 −1.15410 −0.105796
120120 0 0
121121 14.9389 1.35808
122122 0 0
123123 0 0
124124 0 0
125125 −1.84590 11.0269i −0.165102 0.986276i
126126 0 0
127127 11.9969i 1.06455i −0.846571 0.532275i 0.821337π-0.821337\pi
0.846571 0.532275i 0.178663π-0.178663\pi
128128 0 0
129129 0 0
130130 0 0
131131 −9.93893 −0.868368 −0.434184 0.900824i 0.642963π-0.642963\pi
−0.434184 + 0.900824i 0.642963π0.642963\pi
132132 0 0
133133 6.87999i 0.596571i
134134 0 0
135135 0 0
136136 0 0
137137 5.66581i 0.484063i −0.970268 0.242031i 0.922186π-0.922186\pi
0.970268 0.242031i 0.0778137π-0.0778137\pi
138138 0 0
139139 −7.93893 −0.673371 −0.336686 0.941617i 0.609306π-0.609306\pi
−0.336686 + 0.941617i 0.609306π0.609306\pi
140140 0 0
141141 0 0
142142 0 0
143143 18.1796i 1.52025i
144144 0 0
145145 −0.370689 6.69795i −0.0307841 0.556235i
146146 0 0
147147 0 0
148148 0 0
149149 −14.8344 −1.21528 −0.607641 0.794212i 0.707884π-0.707884\pi
−0.607641 + 0.794212i 0.707884π0.707884\pi
150150 0 0
151151 −0.598775 −0.0487276 −0.0243638 0.999703i 0.507756π-0.507756\pi
−0.0243638 + 0.999703i 0.507756π0.507756\pi
152152 0 0
153153 0 0
154154 0 0
155155 −0.815365 14.7328i −0.0654917 1.18336i
156156 0 0
157157 17.9582i 1.43322i 0.697473 + 0.716611i 0.254308π0.254308\pi
−0.697473 + 0.716611i 0.745692π0.745692\pi
158158 0 0
159159 0 0
160160 0 0
161161 −6.52621 −0.514337
162162 0 0
163163 4.67300i 0.366018i 0.983111 + 0.183009i 0.0585837π0.0585837\pi
−0.983111 + 0.183009i 0.941416π0.941416\pi
164164 0 0
165165 0 0
166166 0 0
167167 5.96135i 0.461303i −0.973036 0.230652i 0.925914π-0.925914\pi
0.973036 0.230652i 0.0740858π-0.0740858\pi
168168 0 0
169169 0.258621 0.0198939
170170 0 0
171171 0 0
172172 0 0
173173 9.81272i 0.746048i 0.927822 + 0.373024i 0.121679π0.121679\pi
−0.927822 + 0.373024i 0.878321π0.878321\pi
174174 0 0
175175 0.710843 + 6.40241i 0.0537347 + 0.483977i
176176 0 0
177177 0 0
178178 0 0
179179 −16.3516 −1.22218 −0.611090 0.791561i 0.709269π-0.709269\pi
−0.611090 + 0.791561i 0.709269π0.709269\pi
180180 0 0
181181 2.93893 0.218449 0.109224 0.994017i 0.465163π-0.465163\pi
0.109224 + 0.994017i 0.465163π0.465163\pi
182182 0 0
183183 0 0
184184 0 0
185185 16.1861 0.895796i 1.19002 0.0658602i
186186 0 0
187187 4.56231i 0.333629i
188188 0 0
189189 0 0
190190 0 0
191191 4.59877 0.332756 0.166378 0.986062i 0.446793π-0.446793\pi
0.166378 + 0.986062i 0.446793π0.446793\pi
192192 0 0
193193 1.58389i 0.114011i 0.998374 + 0.0570056i 0.0181553π0.0181553\pi
−0.998374 + 0.0570056i 0.981845π0.981845\pi
194194 0 0
195195 0 0
196196 0 0
197197 13.0775i 0.931735i 0.884855 + 0.465867i 0.154258π0.154258\pi
−0.884855 + 0.465867i 0.845742π0.845742\pi
198198 0 0
199199 5.34015 0.378553 0.189277 0.981924i 0.439386π-0.439386\pi
0.189277 + 0.981924i 0.439386π0.439386\pi
200200 0 0
201201 0 0
202202 0 0
203203 3.86505i 0.271273i
204204 0 0
205205 0.969464 + 17.5172i 0.0677103 + 1.22345i
206206 0 0
207207 0 0
208208 0 0
209209 −27.1975 −1.88129
210210 0 0
211211 4.59877 0.316593 0.158296 0.987392i 0.449400π-0.449400\pi
0.158296 + 0.987392i 0.449400π0.449400\pi
212212 0 0
213213 0 0
214214 0 0
215215 24.4026 1.35053i 1.66425 0.0921055i
216216 0 0
217217 8.50153i 0.577122i
218218 0 0
219219 0 0
220220 0 0
221221 −3.19755 −0.215090
222222 0 0
223223 8.53805i 0.571750i −0.958267 0.285875i 0.907716π-0.907716\pi
0.958267 0.285875i 0.0922842π-0.0922842\pi
224224 0 0
225225 0 0
226226 0 0
227227 17.2838i 1.14717i 0.819147 + 0.573583i 0.194447π0.194447\pi
−0.819147 + 0.573583i 0.805553π0.805553\pi
228228 0 0
229229 −15.6803 −1.03618 −0.518092 0.855325i 0.673357π-0.673357\pi
−0.518092 + 0.855325i 0.673357π0.673357\pi
230230 0 0
231231 0 0
232232 0 0
233233 15.7649i 1.03279i −0.856349 0.516397i 0.827273π-0.827273\pi
0.856349 0.516397i 0.172727π-0.172727\pi
234234 0 0
235235 6.62931 0.366890i 0.432449 0.0239333i
236236 0 0
237237 0 0
238238 0 0
239239 −1.56682 −0.101349 −0.0506745 0.998715i 0.516137π-0.516137\pi
−0.0506745 + 0.998715i 0.516137π0.516137\pi
240240 0 0
241241 −21.0205 −1.35405 −0.677023 0.735961i 0.736730π-0.736730\pi
−0.677023 + 0.735961i 0.736730π0.736730\pi
242242 0 0
243243 0 0
244244 0 0
245245 0.659846 + 11.9227i 0.0421560 + 0.761713i
246246 0 0
247247 19.0617i 1.21287i
248248 0 0
249249 0 0
250250 0 0
251251 9.85740 0.622193 0.311097 0.950378i 0.399304π-0.399304\pi
0.311097 + 0.950378i 0.399304π0.399304\pi
252252 0 0
253253 25.7990i 1.62197i
254254 0 0
255255 0 0
256256 0 0
257257 25.9097i 1.61620i 0.589044 + 0.808101i 0.299505π0.299505\pi
−0.589044 + 0.808101i 0.700495π0.700495\pi
258258 0 0
259259 −9.34015 −0.580369
260260 0 0
261261 0 0
262262 0 0
263263 19.6391i 1.21100i −0.795845 0.605500i 0.792973π-0.792973\pi
0.795845 0.605500i 0.207027π-0.207027\pi
264264 0 0
265265 −10.6803 + 0.591088i −0.656086 + 0.0363102i
266266 0 0
267267 0 0
268268 0 0
269269 0.279082 0.0170160 0.00850798 0.999964i 0.497292π-0.497292\pi
0.00850798 + 0.999964i 0.497292π0.497292\pi
270270 0 0
271271 9.34015 0.567374 0.283687 0.958917i 0.408442π-0.408442\pi
0.283687 + 0.958917i 0.408442π0.408442\pi
272272 0 0
273273 0 0
274274 0 0
275275 25.3096 2.81006i 1.52623 0.169453i
276276 0 0
277277 18.0689i 1.08566i 0.839844 + 0.542828i 0.182646π0.182646\pi
−0.839844 + 0.542828i 0.817354π0.817354\pi
278278 0 0
279279 0 0
280280 0 0
281281 −7.02046 −0.418806 −0.209403 0.977829i 0.567152π-0.567152\pi
−0.209403 + 0.977829i 0.567152π0.567152\pi
282282 0 0
283283 18.3645i 1.09165i 0.837898 + 0.545827i 0.183784π0.183784\pi
−0.837898 + 0.545827i 0.816216π0.816216\pi
284284 0 0
285285 0 0
286286 0 0
287287 10.1083i 0.596672i
288288 0 0
289289 16.1975 0.952797
290290 0 0
291291 0 0
292292 0 0
293293 10.7085i 0.625598i −0.949819 0.312799i 0.898733π-0.898733\pi
0.949819 0.312799i 0.101267π-0.101267\pi
294294 0 0
295295 −0.710843 12.8442i −0.0413869 0.747816i
296296 0 0
297297 0 0
298298 0 0
299299 −18.0815 −1.04568
300300 0 0
301301 −14.0815 −0.811646
302302 0 0
303303 0 0
304304 0 0
305305 0.536283 + 9.69005i 0.0307075 + 0.554851i
306306 0 0
307307 14.3145i 0.816974i 0.912764 + 0.408487i 0.133944π0.133944\pi
−0.912764 + 0.408487i 0.866056π0.866056\pi
308308 0 0
309309 0 0
310310 0 0
311311 24.4766 1.38794 0.693971 0.720003i 0.255859π-0.255859\pi
0.693971 + 0.720003i 0.255859π0.255859\pi
312312 0 0
313313 31.9772i 1.80746i 0.428103 + 0.903730i 0.359182π0.359182\pi
−0.428103 + 0.903730i 0.640818π0.640818\pi
314314 0 0
315315 0 0
316316 0 0
317317 26.2144i 1.47235i −0.676792 0.736174i 0.736631π-0.736631\pi
0.676792 0.736174i 0.263369π-0.263369\pi
318318 0 0
319319 15.2791 0.855464
320320 0 0
321321 0 0
322322 0 0
323323 4.78369i 0.266172i
324324 0 0
325325 1.96946 + 17.7385i 0.109246 + 0.983957i
326326 0 0
327327 0 0
328328 0 0
329329 −3.82544 −0.210903
330330 0 0
331331 −2.74138 −0.150680 −0.0753399 0.997158i 0.524004π-0.524004\pi
−0.0753399 + 0.997158i 0.524004π0.524004\pi
332332 0 0
333333 0 0
334334 0 0
335335 19.0625 1.05499i 1.04150 0.0576402i
336336 0 0
337337 32.6790i 1.78014i 0.455825 + 0.890069i 0.349344π0.349344\pi
−0.455825 + 0.890069i 0.650656π0.650656\pi
338338 0 0
339339 0 0
340340 0 0
341341 33.6077 1.81996
342342 0 0
343343 15.8984i 0.858435i
344344 0 0
345345 0 0
346346 0 0
347347 13.1369i 0.705225i −0.935769 0.352612i 0.885293π-0.885293\pi
0.935769 0.352612i 0.114707π-0.114707\pi
348348 0 0
349349 14.1975 0.759977 0.379989 0.924991i 0.375928π-0.375928\pi
0.379989 + 0.924991i 0.375928π0.375928\pi
350350 0 0
351351 0 0
352352 0 0
353353 5.10207i 0.271556i 0.990739 + 0.135778i 0.0433534π0.0433534\pi
−0.990739 + 0.135778i 0.956647π0.956647\pi
354354 0 0
355355 0.659846 + 11.9227i 0.0350210 + 0.632791i
356356 0 0
357357 0 0
358358 0 0
359359 −12.8229 −0.676767 −0.338384 0.941008i 0.609880π-0.609880\pi
−0.338384 + 0.941008i 0.609880π0.609880\pi
360360 0 0
361361 9.51724 0.500907
362362 0 0
363363 0 0
364364 0 0
365365 −20.8664 + 1.15482i −1.09220 + 0.0604461i
366366 0 0
367367 5.77649i 0.301531i −0.988570 0.150765i 0.951826π-0.951826\pi
0.988570 0.150765i 0.0481738π-0.0481738\pi
368368 0 0
369369 0 0
370370 0 0
371371 6.16307 0.319970
372372 0 0
373373 12.8048i 0.663008i 0.943454 + 0.331504i 0.107556π0.107556\pi
−0.943454 + 0.331504i 0.892444π0.892444\pi
374374 0 0
375375 0 0
376376 0 0
377377 10.7085i 0.551517i
378378 0 0
379379 7.19755 0.369713 0.184857 0.982765i 0.440818π-0.440818\pi
0.184857 + 0.982765i 0.440818π0.440818\pi
380380 0 0
381381 0 0
382382 0 0
383383 2.41469i 0.123385i 0.998095 + 0.0616923i 0.0196498π0.0196498\pi
−0.998095 + 0.0616923i 0.980350π0.980350\pi
384384 0 0
385385 −14.6498 + 0.810772i −0.746622 + 0.0413208i
386386 0 0
387387 0 0
388388 0 0
389389 −10.6484 −0.539893 −0.269946 0.962875i 0.587006π-0.587006\pi
−0.269946 + 0.962875i 0.587006π0.587006\pi
390390 0 0
391391 −4.53770 −0.229482
392392 0 0
393393 0 0
394394 0 0
395395 0.0916071 + 1.65524i 0.00460925 + 0.0832842i
396396 0 0
397397 10.3068i 0.517284i 0.965973 + 0.258642i 0.0832749π0.0832749\pi
−0.965973 + 0.258642i 0.916725π0.916725\pi
398398 0 0
399399 0 0
400400 0 0
401401 17.7529 0.886536 0.443268 0.896389i 0.353819π-0.353819\pi
0.443268 + 0.896389i 0.353819π0.353819\pi
402402 0 0
403403 23.5544i 1.17333i
404404 0 0
405405 0 0
406406 0 0
407407 36.9229i 1.83020i
408408 0 0
409409 23.1365 1.14403 0.572013 0.820245i 0.306163π-0.306163\pi
0.572013 + 0.820245i 0.306163π0.306163\pi
410410 0 0
411411 0 0
412412 0 0
413413 7.41172i 0.364707i
414414 0 0
415415 −20.5682 + 1.13832i −1.00966 + 0.0558780i
416416 0 0
417417 0 0
418418 0 0
419419 −28.2676 −1.38096 −0.690481 0.723351i 0.742601π-0.742601\pi
−0.690481 + 0.723351i 0.742601π0.742601\pi
420420 0 0
421421 35.1365 1.71245 0.856224 0.516605i 0.172805π-0.172805\pi
0.856224 + 0.516605i 0.172805π0.172805\pi
422422 0 0
423423 0 0
424424 0 0
425425 0.494253 + 4.45163i 0.0239748 + 0.215936i
426426 0 0
427427 5.59164i 0.270598i
428428 0 0
429429 0 0
430430 0 0
431431 −36.8894 −1.77690 −0.888449 0.458976i 0.848216π-0.848216\pi
−0.888449 + 0.458976i 0.848216π0.848216\pi
432432 0 0
433433 11.8120i 0.567649i −0.958876 0.283825i 0.908397π-0.908397\pi
0.958876 0.283825i 0.0916033π-0.0916033\pi
434434 0 0
435435 0 0
436436 0 0
437437 27.0508i 1.29402i
438438 0 0
439439 0.741379 0.0353841 0.0176920 0.999843i 0.494368π-0.494368\pi
0.0176920 + 0.999843i 0.494368π0.494368\pi
440440 0 0
441441 0 0
442442 0 0
443443 5.37026i 0.255149i −0.991829 0.127574i 0.959281π-0.959281\pi
0.991829 0.127574i 0.0407192π-0.0407192\pi
444444 0 0
445445 −1.14260 20.6456i −0.0541646 0.978696i
446446 0 0
447447 0 0
448448 0 0
449449 −21.1975 −1.00037 −0.500187 0.865917i 0.666735π-0.666735\pi
−0.500187 + 0.865917i 0.666735π0.666735\pi
450450 0 0
451451 −39.9594 −1.88161
452452 0 0
453453 0 0
454454 0 0
455455 −0.568239 10.2675i −0.0266395 0.481346i
456456 0 0
457457 0.992806i 0.0464415i −0.999730 0.0232208i 0.992608π-0.992608\pi
0.999730 0.0232208i 0.00739206π-0.00739206\pi
458458 0 0
459459 0 0
460460 0 0
461461 10.3197 0.480636 0.240318 0.970694i 0.422748π-0.422748\pi
0.240318 + 0.970694i 0.422748π0.422748\pi
462462 0 0
463463 13.0638i 0.607128i 0.952811 + 0.303564i 0.0981767π0.0981767\pi
−0.952811 + 0.303564i 0.901823π0.901823\pi
464464 0 0
465465 0 0
466466 0 0
467467 19.3938i 0.897437i 0.893673 + 0.448718i 0.148119π0.148119\pi
−0.893673 + 0.448718i 0.851881π0.851881\pi
468468 0 0
469469 −11.0000 −0.507933
470470 0 0
471471 0 0
472472 0 0
473473 55.6663i 2.55954i
474474 0 0
475475 −26.5377 + 2.94641i −1.21763 + 0.135191i
476476 0 0
477477 0 0
478478 0 0
479479 11.9159 0.544453 0.272227 0.962233i 0.412240π-0.412240\pi
0.272227 + 0.962233i 0.412240π0.412240\pi
480480 0 0
481481 −25.8779 −1.17993
482482 0 0
483483 0 0
484484 0 0
485485 7.72234 0.427383i 0.350653 0.0194064i
486486 0 0
487487 18.8027i 0.852031i 0.904716 + 0.426016i 0.140083π0.140083\pi
−0.904716 + 0.426016i 0.859917π0.859917\pi
488488 0 0
489489 0 0
490490 0 0
491491 −9.93893 −0.448538 −0.224269 0.974527i 0.571999π-0.571999\pi
−0.224269 + 0.974527i 0.571999π0.571999\pi
492492 0 0
493493 2.68739i 0.121034i
494494 0 0
495495 0 0
496496 0 0
497497 6.87999i 0.308610i
498498 0 0
499499 9.93893 0.444928 0.222464 0.974941i 0.428590π-0.428590\pi
0.222464 + 0.974941i 0.428590π0.428590\pi
500500 0 0
501501 0 0
502502 0 0
503503 36.0636i 1.60800i −0.594630 0.803999i 0.702702π-0.702702\pi
0.594630 0.803999i 0.297298π-0.297298\pi
504504 0 0
505505 2.03054 + 36.6896i 0.0903577 + 1.63266i
506506 0 0
507507 0 0
508508 0 0
509509 −40.8779 −1.81188 −0.905940 0.423407i 0.860834π-0.860834\pi
−0.905940 + 0.423407i 0.860834π0.860834\pi
510510 0 0
511511 12.0409 0.532659
512512 0 0
513513 0 0
514514 0 0
515515 35.4141 1.95995i 1.56053 0.0863657i
516516 0 0
517517 15.1225i 0.665087i
518518 0 0
519519 0 0
520520 0 0
521521 17.9504 0.786422 0.393211 0.919448i 0.371364π-0.371364\pi
0.393211 + 0.919448i 0.371364π0.371364\pi
522522 0 0
523523 20.9732i 0.917092i −0.888671 0.458546i 0.848370π-0.848370\pi
0.888671 0.458546i 0.151630π-0.151630\pi
524524 0 0
525525 0 0
526526 0 0
527527 5.91116i 0.257494i
528528 0 0
529529 −2.65985 −0.115645
530530 0 0
531531 0 0
532532 0 0
533533 28.0060i 1.21307i
534534 0 0
535535 21.2791 1.17766i 0.919975 0.0509148i
536536 0 0
537537 0 0
538538 0 0
539539 −27.1975 −1.17148
540540 0 0
541541 −13.6192 −0.585537 −0.292768 0.956183i 0.594576π-0.594576\pi
−0.292768 + 0.956183i 0.594576π0.594576\pi
542542 0 0
543543 0 0
544544 0 0
545545 −2.01149 36.3455i −0.0861630 1.55687i
546546 0 0
547547 8.79708i 0.376136i 0.982156 + 0.188068i 0.0602225π0.0602225\pi
−0.982156 + 0.188068i 0.939777π0.939777\pi
548548 0 0
549549 0 0
550550 0 0
551551 −16.0205 −0.682495
552552 0 0
553553 0.955156i 0.0406174i
554554 0 0
555555 0 0
556556 0 0
557557 33.9308i 1.43770i −0.695168 0.718848i 0.744670π-0.744670\pi
0.695168 0.718848i 0.255330π-0.255330\pi
558558 0 0
559559 −39.0143 −1.65013
560560 0 0
561561 0 0
562562 0 0
563563 33.3626i 1.40607i 0.711158 + 0.703033i 0.248171π0.248171\pi
−0.711158 + 0.703033i 0.751829π0.751829\pi
564564 0 0
565565 40.5887 2.24633i 1.70758 0.0945037i
566566 0 0
567567 0 0
568568 0 0
569569 7.63073 0.319897 0.159948 0.987125i 0.448867π-0.448867\pi
0.159948 + 0.987125i 0.448867π0.448867\pi
570570 0 0
571571 26.4971 1.10887 0.554434 0.832227i 0.312935π-0.312935\pi
0.554434 + 0.832227i 0.312935π0.312935\pi
572572 0 0
573573 0 0
574574 0 0
575575 2.79490 + 25.1731i 0.116556 + 1.04979i
576576 0 0
577577 9.93709i 0.413686i −0.978374 0.206843i 0.933681π-0.933681\pi
0.978374 0.206843i 0.0663190π-0.0663190\pi
578578 0 0
579579 0 0
580580 0 0
581581 11.8689 0.492405
582582 0 0
583583 24.3635i 1.00903i
584584 0 0
585585 0 0
586586 0 0
587587 23.5179i 0.970686i −0.874324 0.485343i 0.838695π-0.838695\pi
0.874324 0.485343i 0.161305π-0.161305\pi
588588 0 0
589589 −35.2385 −1.45198
590590 0 0
591591 0 0
592592 0 0
593593 11.6637i 0.478970i −0.970900 0.239485i 0.923021π-0.923021\pi
0.970900 0.239485i 0.0769786π-0.0769786\pi
594594 0 0
595595 −0.142604 2.57670i −0.00584620 0.105634i
596596 0 0
597597 0 0
598598 0 0
599599 2.06107 0.0842131 0.0421065 0.999113i 0.486593π-0.486593\pi
0.0421065 + 0.999113i 0.486593π0.486593\pi
600600 0 0
601601 −13.9389 −0.568581 −0.284290 0.958738i 0.591758π-0.591758\pi
−0.284290 + 0.958738i 0.591758π0.591758\pi
602602 0 0
603603 0 0
604604 0 0
605605 1.84590 + 33.3534i 0.0750466 + 1.35601i
606606 0 0
607607 47.2526i 1.91792i −0.283537 0.958961i 0.591508π-0.591508\pi
0.283537 0.958961i 0.408492π-0.408492\pi
608608 0 0
609609 0 0
610610 0 0
611611 −10.5988 −0.428781
612612 0 0
613613 31.4648i 1.27085i −0.772162 0.635426i 0.780825π-0.780825\pi
0.772162 0.635426i 0.219175π-0.219175\pi
614614 0 0
615615 0 0
616616 0 0
617617 21.0987i 0.849400i −0.905334 0.424700i 0.860380π-0.860380\pi
0.905334 0.424700i 0.139620π-0.139620\pi
618618 0 0
619619 3.91847 0.157496 0.0787482 0.996895i 0.474908π-0.474908\pi
0.0787482 + 0.996895i 0.474908π0.474908\pi
620620 0 0
621621 0 0
622622 0 0
623623 11.9135i 0.477306i
624624 0 0
625625 24.3912 5.48377i 0.975646 0.219351i
626626 0 0
627627 0 0
628628 0 0
629629 −6.49425 −0.258943
630630 0 0
631631 44.5582 1.77383 0.886916 0.461930i 0.152843π-0.152843\pi
0.886916 + 0.461930i 0.152843π0.152843\pi
632632 0 0
633633 0 0
634634 0 0
635635 26.7848 1.48237i 1.06292 0.0588261i
636636 0 0
637637 19.0617i 0.755253i
638638 0 0
639639 0 0
640640 0 0
641641 15.3287 0.605446 0.302723 0.953079i 0.402104π-0.402104\pi
0.302723 + 0.953079i 0.402104π0.402104\pi
642642 0 0
643643 5.37026i 0.211783i 0.994378 + 0.105891i 0.0337695π0.0337695\pi
−0.994378 + 0.105891i 0.966230π0.966230\pi
644644 0 0
645645 0 0
646646 0 0
647647 2.65087i 0.104216i −0.998641 0.0521082i 0.983406π-0.983406\pi
0.998641 0.0521082i 0.0165941π-0.0165941\pi
648648 0 0
649649 29.2995 1.15011
650650 0 0
651651 0 0
652652 0 0
653653 7.71642i 0.301967i −0.988536 0.150984i 0.951756π-0.951756\pi
0.988536 0.150984i 0.0482440π-0.0482440\pi
654654 0 0
655655 −1.22809 22.1902i −0.0479853 0.867041i
656656 0 0
657657 0 0
658658 0 0
659659 −11.7529 −0.457827 −0.228913 0.973447i 0.573517π-0.573517\pi
−0.228913 + 0.973447i 0.573517π0.573517\pi
660660 0 0
661661 10.0611 0.391330 0.195665 0.980671i 0.437313π-0.437313\pi
0.195665 + 0.980671i 0.437313π0.437313\pi
662662 0 0
663663 0 0
664664 0 0
665665 15.3606 0.850113i 0.595659 0.0329660i
666666 0 0
667667 15.1967i 0.588417i
668668 0 0
669669 0 0
670670 0 0
671671 −22.1045 −0.853336
672672 0 0
673673 32.1986i 1.24116i 0.784141 + 0.620582i 0.213104π0.213104\pi
−0.784141 + 0.620582i 0.786896π0.786896\pi
674674 0 0
675675 0 0
676676 0 0
677677 1.82360i 0.0700866i 0.999386 + 0.0350433i 0.0111569π0.0111569\pi
−0.999386 + 0.0350433i 0.988843π0.988843\pi
678678 0 0
679679 −4.45617 −0.171012
680680 0 0
681681 0 0
682682 0 0
683683 36.5909i 1.40011i 0.714089 + 0.700055i 0.246841π0.246841\pi
−0.714089 + 0.700055i 0.753159π0.753159\pi
684684 0 0
685685 12.6498 0.700085i 0.483323 0.0267489i
686686 0 0
687687 0 0
688688 0 0
689689 17.0754 0.650521
690690 0 0
691691 7.38076 0.280777 0.140389 0.990096i 0.455165π-0.455165\pi
0.140389 + 0.990096i 0.455165π0.455165\pi
692692 0 0
693693 0 0
694694 0 0
695695 −0.980959 17.7249i −0.0372099 0.672342i
696696 0 0
697697 7.02833i 0.266217i
698698 0 0
699699 0 0
700700 0 0
701701 31.1045 1.17480 0.587401 0.809296i 0.300151π-0.300151\pi
0.587401 + 0.809296i 0.300151π0.300151\pi
702702 0 0
703703 38.7145i 1.46015i
704704 0 0
705705 0 0
706706 0 0
707707 21.1717i 0.796243i
708708 0 0
709709 −26.0754 −0.979282 −0.489641 0.871924i 0.662872π-0.662872\pi
−0.489641 + 0.871924i 0.662872π0.662872\pi
710710 0 0
711711 0 0
712712 0 0
713713 33.4265i 1.25183i
714714 0 0
715715 −40.5887 + 2.24633i −1.51793 + 0.0840079i
716716 0 0
717717 0 0
718718 0 0
719719 43.0524 1.60558 0.802792 0.596259i 0.203347π-0.203347\pi
0.802792 + 0.596259i 0.203347π0.203347\pi
720720 0 0
721721 −20.4357 −0.761066
722722 0 0
723723 0 0
724724 0 0
725725 14.9084 1.65524i 0.553684 0.0614741i
726726 0 0
727727 14.2825i 0.529710i −0.964288 0.264855i 0.914676π-0.914676\pi
0.964288 0.264855i 0.0853241π-0.0853241\pi
728728 0 0
729729 0 0
730730 0 0
731731 −9.79096 −0.362132
732732 0 0
733733 3.53186i 0.130452i 0.997871 + 0.0652260i 0.0207768π0.0207768\pi
−0.997871 + 0.0652260i 0.979223π0.979223\pi
734734 0 0
735735 0 0
736736 0 0
737737 43.4845i 1.60177i
738738 0 0
739739 −13.3606 −0.491478 −0.245739 0.969336i 0.579031π-0.579031\pi
−0.245739 + 0.969336i 0.579031π0.579031\pi
740740 0 0
741741 0 0
742742 0 0
743743 21.1625i 0.776378i 0.921580 + 0.388189i 0.126899π0.126899\pi
−0.921580 + 0.388189i 0.873101π0.873101\pi
744744 0 0
745745 −1.83299 33.1201i −0.0671554 1.21343i
746746 0 0
747747 0 0
748748 0 0
749749 −12.2791 −0.448668
750750 0 0
751751 8.08153 0.294899 0.147450 0.989070i 0.452894π-0.452894\pi
0.147450 + 0.989070i 0.452894π0.452894\pi
752752 0 0
753753 0 0
754754 0 0
755755 −0.0739865 1.33686i −0.00269264 0.0486532i
756756 0 0
757757 26.3114i 0.956305i −0.878277 0.478152i 0.841307π-0.841307\pi
0.878277 0.478152i 0.158693π-0.158693\pi
758758 0 0
759759 0 0
760760 0 0
761761 27.1631 0.984660 0.492330 0.870409i 0.336145π-0.336145\pi
0.492330 + 0.870409i 0.336145π0.336145\pi
762762 0 0
763763 20.9732i 0.759279i
764764 0 0
765765 0 0
766766 0 0
767767 20.5349i 0.741473i
768768 0 0
769769 −2.83693 −0.102302 −0.0511512 0.998691i 0.516289π-0.516289\pi
−0.0511512 + 0.998691i 0.516289π0.516289\pi
770770 0 0
771771 0 0
772772 0 0
773773 0 0 1.00000 00
−1.00000 π\pi
774774 0 0
775775 32.7924 3.64085i 1.17794 0.130783i
776776 0 0
777777 0 0
778778 0 0
779779 41.8983 1.50116
780780 0 0
781781 −27.1975 −0.973205
782782 0 0
783783 0 0
784784 0 0
785785 −40.0944 + 2.21897i −1.43103 + 0.0791986i
786786 0 0
787787 3.79088i 0.135130i 0.997715 + 0.0675652i 0.0215231π0.0215231\pi
−0.997715 + 0.0675652i 0.978477π0.978477\pi
788788 0 0
789789 0 0
790790 0 0
791791 −23.4217 −0.832779
792792 0 0
793793 15.4922i 0.550144i
794794 0 0
795795 0 0
796796 0 0
797797 44.0756i 1.56124i 0.625007 + 0.780619i 0.285096π0.285096\pi
−0.625007 + 0.780619i 0.714904π0.714904\pi
798798 0 0
799799 −2.65985 −0.0940986
800800 0 0
801801 0 0
802802 0 0
803803 47.5994i 1.67975i
804804 0 0
805805 −0.806399 14.5707i −0.0284218 0.513551i
806806 0 0
807807 0 0
808808 0 0
809809 −1.48276 −0.0521310 −0.0260655 0.999660i 0.508298π-0.508298\pi
−0.0260655 + 0.999660i 0.508298π0.508298\pi
810810 0 0
811811 51.2385 1.79923 0.899613 0.436688i 0.143849π-0.143849\pi
0.899613 + 0.436688i 0.143849π0.143849\pi
812812 0 0
813813 0 0
814814 0 0
815815 −10.4332 + 0.577411i −0.365458 + 0.0202258i
816816 0 0
817817 58.3673i 2.04201i
818818 0 0
819819 0 0
820820 0 0
821821 22.7123 0.792663 0.396332 0.918107i 0.370283π-0.370283\pi
0.396332 + 0.918107i 0.370283π0.370283\pi
822822 0 0
823823 13.1004i 0.456650i −0.973585 0.228325i 0.926675π-0.926675\pi
0.973585 0.228325i 0.0733249π-0.0733249\pi
824824 0 0
825825 0 0
826826 0 0
827827 34.8631i 1.21231i −0.795346 0.606155i 0.792711π-0.792711\pi
0.795346 0.606155i 0.207289π-0.207289\pi
828828 0 0
829829 25.5988 0.889082 0.444541 0.895758i 0.353367π-0.353367\pi
0.444541 + 0.895758i 0.353367π0.353367\pi
830830 0 0
831831 0 0
832832 0 0
833833 4.78369i 0.165745i
834834 0 0
835835 13.3096 0.736603i 0.460598 0.0254912i
836836 0 0
837837 0 0
838838 0 0
839839 −40.3315 −1.39240 −0.696199 0.717849i 0.745127π-0.745127\pi
−0.696199 + 0.717849i 0.745127π0.745127\pi
840840 0 0
841841 −20.0000 −0.689655
842842 0 0
843843 0 0
844844 0 0
845845 0.0319560 + 0.577411i 0.00109932 + 0.0198635i
846846 0 0
847847 19.2466i 0.661320i
848848 0 0
849849 0 0
850850 0 0
851851 −36.7238 −1.25887
852852 0 0
853853 40.2984i 1.37979i −0.723909 0.689896i 0.757656π-0.757656\pi
0.723909 0.689896i 0.242344π-0.242344\pi
854854 0 0
855855 0 0
856856 0 0
857857 22.0401i 0.752877i −0.926442 0.376438i 0.877149π-0.877149\pi
0.926442 0.376438i 0.122851π-0.122851\pi
858858 0 0
859859 −29.2791 −0.998989 −0.499495 0.866317i 0.666481π-0.666481\pi
−0.499495 + 0.866317i 0.666481π0.666481\pi
860860 0 0
861861 0 0
862862 0 0
863863 46.1491i 1.57093i −0.618904 0.785466i 0.712423π-0.712423\pi
0.618904 0.785466i 0.287577π-0.287577\pi
864864 0 0
865865 −21.9084 + 1.21249i −0.744908 + 0.0412259i
866866 0 0
867867 0 0
868868 0 0
869869 −3.77586 −0.128087
870870 0 0
871871 −30.4766 −1.03266
872872 0 0
873873 0 0
874874 0 0
875875 −14.2065 + 2.37817i −0.480268 + 0.0803967i
876876 0 0
877877 27.6363i 0.933211i −0.884466 0.466606i 0.845477π-0.845477\pi
0.884466 0.466606i 0.154523π-0.154523\pi
878878 0 0
879879 0 0
880880 0 0
881881 −4.79632 −0.161592 −0.0807961 0.996731i 0.525746π-0.525746\pi
−0.0807961 + 0.996731i 0.525746π0.525746\pi
882882 0 0
883883 21.7126i 0.730687i 0.930873 + 0.365343i 0.119048π0.119048\pi
−0.930873 + 0.365343i 0.880952π0.880952\pi
884884 0 0
885885 0 0
886886 0 0
887887 22.0401i 0.740035i −0.929025 0.370018i 0.879352π-0.879352\pi
0.929025 0.370018i 0.120648π-0.120648\pi
888888 0 0
889889 −15.4562 −0.518383
890890 0 0
891891 0 0
892892 0 0
893893 15.8563i 0.530610i
894894 0 0
895895 −2.02046 36.5075i −0.0675366 1.22031i
896896 0 0
897897 0 0
898898 0 0
899899 19.7963 0.660244
900900 0 0
901901 4.28521 0.142761
902902 0 0
903903 0 0
904904 0 0
905905 0.363143 + 6.56160i 0.0120713 + 0.218115i
906906 0 0
907907 39.3011i 1.30497i 0.757801 + 0.652486i 0.226274π0.226274\pi
−0.757801 + 0.652486i 0.773726π0.773726\pi
908908 0 0
909909 0 0
910910 0 0
911911 −15.9389 −0.528080 −0.264040 0.964512i 0.585055π-0.585055\pi
−0.264040 + 0.964512i 0.585055π0.585055\pi
912912 0 0
913913 46.9194i 1.55280i
914914 0 0
915915 0 0
916916 0 0
917917 12.8048i 0.422852i
918918 0 0
919919 6.16307 0.203301 0.101650 0.994820i 0.467588π-0.467588\pi
0.101650 + 0.994820i 0.467588π0.467588\pi
920920 0 0
921921 0 0
922922 0 0
923923 19.0617i 0.627424i
924924 0 0
925925 4.00000 + 36.0271i 0.131519 + 1.18456i
926926 0 0
927927 0 0
928928 0 0
929929 −10.1020 −0.331436 −0.165718 0.986173i 0.552994π-0.552994\pi
−0.165718 + 0.986173i 0.552994π0.552994\pi
930930 0 0
931931 28.5172 0.934615
932932 0 0
933933 0 0
934934 0 0
935935 −10.1861 + 0.563734i −0.333120 + 0.0184361i
936936 0 0
937937 5.00506i 0.163508i −0.996653 0.0817541i 0.973948π-0.973948\pi
0.996653 0.0817541i 0.0260522π-0.0260522\pi
938938 0 0
939939 0 0
940940 0 0
941941 9.98851 0.325616 0.162808 0.986658i 0.447945π-0.447945\pi
0.162808 + 0.986658i 0.447945π0.447945\pi
942942 0 0
943943 39.7438i 1.29424i
944944 0 0
945945 0 0
946946 0 0
947947 47.6223i 1.54752i 0.633481 + 0.773758i 0.281625π0.281625\pi
−0.633481 + 0.773758i 0.718375π0.718375\pi
948948 0 0
949949 33.3606 1.08293
950950 0 0
951951 0 0
952952 0 0
953953 34.2355i 1.10900i −0.832184 0.554499i 0.812910π-0.812910\pi
0.832184 0.554499i 0.187090π-0.187090\pi
954954 0 0
955955 0.568239 + 10.2675i 0.0183878 + 0.332247i
956956 0 0
957957 0 0
958958 0 0
959959 −7.29954 −0.235715
960960 0 0
961961 12.5438 0.404640
962962 0 0
963963 0 0
964964 0 0
965965 −3.53628 + 0.195711i −0.113837 + 0.00630016i
966966 0 0
967967 3.71671i 0.119521i 0.998213 + 0.0597607i 0.0190338π0.0190338\pi
−0.998213 + 0.0597607i 0.980966π0.980966\pi
968968 0 0
969969 0 0
970970 0 0
971971 45.0959 1.44720 0.723598 0.690222i 0.242487π-0.242487\pi
0.723598 + 0.690222i 0.242487π0.242487\pi
972972 0 0
973973 10.2281i 0.327898i
974974 0 0
975975 0 0
976976 0 0
977977 6.58896i 0.210799i −0.994430 0.105400i 0.966388π-0.966388\pi
0.994430 0.105400i 0.0336122π-0.0336122\pi
978978 0 0
979979 47.0959 1.50519
980980 0 0
981981 0 0
982982 0 0
983983 12.2319i 0.390138i −0.980790 0.195069i 0.937507π-0.937507\pi
0.980790 0.195069i 0.0624930π-0.0624930\pi
984984 0 0
985985 −29.1975 + 1.61590i −0.930311 + 0.0514869i
986986 0 0
987987 0 0
988988 0 0
989989 −55.3660 −1.76054
990990 0 0
991991 −32.0000 −1.01651 −0.508257 0.861206i 0.669710π-0.669710\pi
−0.508257 + 0.861206i 0.669710π0.669710\pi
992992 0 0
993993 0 0
994994 0 0
995995 0.659846 + 11.9227i 0.0209185 + 0.377975i
996996 0 0
997997 3.23744i 0.102531i −0.998685 0.0512655i 0.983675π-0.983675\pi
0.998685 0.0512655i 0.0163255π-0.0163255\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 1620.2.d.d.649.4 6
3.2 odd 2 1620.2.d.c.649.3 6
5.2 odd 4 8100.2.a.bd.1.4 6
5.3 odd 4 8100.2.a.bd.1.3 6
5.4 even 2 inner 1620.2.d.d.649.3 6
9.2 odd 6 180.2.r.a.49.4 yes 12
9.4 even 3 540.2.r.a.289.5 12
9.5 odd 6 180.2.r.a.169.3 yes 12
9.7 even 3 540.2.r.a.469.1 12
15.2 even 4 8100.2.a.bc.1.4 6
15.8 even 4 8100.2.a.bc.1.3 6
15.14 odd 2 1620.2.d.c.649.4 6
36.7 odd 6 2160.2.by.e.1009.1 12
36.11 even 6 720.2.by.e.49.3 12
36.23 even 6 720.2.by.e.529.4 12
36.31 odd 6 2160.2.by.e.289.5 12
45.2 even 12 900.2.i.f.301.6 12
45.4 even 6 540.2.r.a.289.1 12
45.7 odd 12 2700.2.i.f.901.3 12
45.13 odd 12 2700.2.i.f.1801.4 12
45.14 odd 6 180.2.r.a.169.4 yes 12
45.22 odd 12 2700.2.i.f.1801.3 12
45.23 even 12 900.2.i.f.601.1 12
45.29 odd 6 180.2.r.a.49.3 12
45.32 even 12 900.2.i.f.601.6 12
45.34 even 6 540.2.r.a.469.5 12
45.38 even 12 900.2.i.f.301.1 12
45.43 odd 12 2700.2.i.f.901.4 12
180.59 even 6 720.2.by.e.529.3 12
180.79 odd 6 2160.2.by.e.1009.5 12
180.119 even 6 720.2.by.e.49.4 12
180.139 odd 6 2160.2.by.e.289.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
180.2.r.a.49.3 12 45.29 odd 6
180.2.r.a.49.4 yes 12 9.2 odd 6
180.2.r.a.169.3 yes 12 9.5 odd 6
180.2.r.a.169.4 yes 12 45.14 odd 6
540.2.r.a.289.1 12 45.4 even 6
540.2.r.a.289.5 12 9.4 even 3
540.2.r.a.469.1 12 9.7 even 3
540.2.r.a.469.5 12 45.34 even 6
720.2.by.e.49.3 12 36.11 even 6
720.2.by.e.49.4 12 180.119 even 6
720.2.by.e.529.3 12 180.59 even 6
720.2.by.e.529.4 12 36.23 even 6
900.2.i.f.301.1 12 45.38 even 12
900.2.i.f.301.6 12 45.2 even 12
900.2.i.f.601.1 12 45.23 even 12
900.2.i.f.601.6 12 45.32 even 12
1620.2.d.c.649.3 6 3.2 odd 2
1620.2.d.c.649.4 6 15.14 odd 2
1620.2.d.d.649.3 6 5.4 even 2 inner
1620.2.d.d.649.4 6 1.1 even 1 trivial
2160.2.by.e.289.1 12 180.139 odd 6
2160.2.by.e.289.5 12 36.31 odd 6
2160.2.by.e.1009.1 12 36.7 odd 6
2160.2.by.e.1009.5 12 180.79 odd 6
2700.2.i.f.901.3 12 45.7 odd 12
2700.2.i.f.901.4 12 45.43 odd 12
2700.2.i.f.1801.3 12 45.22 odd 12
2700.2.i.f.1801.4 12 45.13 odd 12
8100.2.a.bc.1.3 6 15.8 even 4
8100.2.a.bc.1.4 6 15.2 even 4
8100.2.a.bd.1.3 6 5.3 odd 4
8100.2.a.bd.1.4 6 5.2 odd 4