Properties

Label 8512.2.a.bk.1.2
Level 85128512
Weight 22
Character 8512.1
Self dual yes
Analytic conductor 67.96967.969
Analytic rank 00
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] = [8512,2,Mod(1,8512)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8512, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8512.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 8512=26719 8512 = 2^{6} \cdot 7 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 8512.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: 67.968662200567.9686622005
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.1101.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x29x+12 x^{3} - x^{2} - 9x + 12 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 1064)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.431631.43163 of defining polynomial
Character χ\chi == 8512.1

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) == q1.43163q3+2.51882q51.00000q70.950444q91.95044q115.38207q133.60601q153.95044q171.00000q19+1.43163q21+8.51882q23+1.34444q25+5.65556q273.95044q295.95044q31+2.79231q332.51882q357.55645q37+7.70512q39+6.81370q41+5.03763q432.39399q455.65556q47+1.00000q49+5.65556q5111.4316q534.91281q55+1.43163q57+0.617929q595.48118q61+0.950444q6313.5565q650.223935q6712.1958q69+13.5565q71+7.43163q731.92473q75+1.95044q77+5.03763q795.24533q8113.7804q839.95044q85+5.65556q87+10.9385q89+5.38207q91+8.51882q932.51882q95+4.69320q97+1.85379q99+O(q100)q-1.43163 q^{3} +2.51882 q^{5} -1.00000 q^{7} -0.950444 q^{9} -1.95044 q^{11} -5.38207 q^{13} -3.60601 q^{15} -3.95044 q^{17} -1.00000 q^{19} +1.43163 q^{21} +8.51882 q^{23} +1.34444 q^{25} +5.65556 q^{27} -3.95044 q^{29} -5.95044 q^{31} +2.79231 q^{33} -2.51882 q^{35} -7.55645 q^{37} +7.70512 q^{39} +6.81370 q^{41} +5.03763 q^{43} -2.39399 q^{45} -5.65556 q^{47} +1.00000 q^{49} +5.65556 q^{51} -11.4316 q^{53} -4.91281 q^{55} +1.43163 q^{57} +0.617929 q^{59} -5.48118 q^{61} +0.950444 q^{63} -13.5565 q^{65} -0.223935 q^{67} -12.1958 q^{69} +13.5565 q^{71} +7.43163 q^{73} -1.92473 q^{75} +1.95044 q^{77} +5.03763 q^{79} -5.24533 q^{81} -13.7804 q^{83} -9.95044 q^{85} +5.65556 q^{87} +10.9385 q^{89} +5.38207 q^{91} +8.51882 q^{93} -2.51882 q^{95} +4.69320 q^{97} +1.85379 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3qq32q53q7+10q9+7q11+5q15+q173q19+q21+16q23+7q25+14q27+q295q31+12q33+2q35+6q37+33q39+q41++54q99+O(q100) 3 q - q^{3} - 2 q^{5} - 3 q^{7} + 10 q^{9} + 7 q^{11} + 5 q^{15} + q^{17} - 3 q^{19} + q^{21} + 16 q^{23} + 7 q^{25} + 14 q^{27} + q^{29} - 5 q^{31} + 12 q^{33} + 2 q^{35} + 6 q^{37} + 33 q^{39} + q^{41}+ \cdots + 54 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 −1.43163 −0.826550 −0.413275 0.910606i 0.635615π-0.635615\pi
−0.413275 + 0.910606i 0.635615π0.635615\pi
44 0 0
55 2.51882 1.12645 0.563225 0.826304i 0.309561π-0.309561\pi
0.563225 + 0.826304i 0.309561π0.309561\pi
66 0 0
77 −1.00000 −0.377964
88 0 0
99 −0.950444 −0.316815
1010 0 0
1111 −1.95044 −0.588081 −0.294040 0.955793i 0.595000π-0.595000\pi
−0.294040 + 0.955793i 0.595000π0.595000\pi
1212 0 0
1313 −5.38207 −1.49272 −0.746359 0.665544i 0.768200π-0.768200\pi
−0.746359 + 0.665544i 0.768200π0.768200\pi
1414 0 0
1515 −3.60601 −0.931067
1616 0 0
1717 −3.95044 −0.958123 −0.479062 0.877781i 0.659023π-0.659023\pi
−0.479062 + 0.877781i 0.659023π0.659023\pi
1818 0 0
1919 −1.00000 −0.229416
2020 0 0
2121 1.43163 0.312407
2222 0 0
2323 8.51882 1.77630 0.888148 0.459557i 0.151992π-0.151992\pi
0.888148 + 0.459557i 0.151992π0.151992\pi
2424 0 0
2525 1.34444 0.268888
2626 0 0
2727 5.65556 1.08841
2828 0 0
2929 −3.95044 −0.733579 −0.366789 0.930304i 0.619543π-0.619543\pi
−0.366789 + 0.930304i 0.619543π0.619543\pi
3030 0 0
3131 −5.95044 −1.06873 −0.534366 0.845253i 0.679449π-0.679449\pi
−0.534366 + 0.845253i 0.679449π0.679449\pi
3232 0 0
3333 2.79231 0.486078
3434 0 0
3535 −2.51882 −0.425758
3636 0 0
3737 −7.55645 −1.24227 −0.621136 0.783703i 0.713329π-0.713329\pi
−0.621136 + 0.783703i 0.713329π0.713329\pi
3838 0 0
3939 7.70512 1.23381
4040 0 0
4141 6.81370 1.06412 0.532060 0.846706i 0.321418π-0.321418\pi
0.532060 + 0.846706i 0.321418π0.321418\pi
4242 0 0
4343 5.03763 0.768232 0.384116 0.923285i 0.374506π-0.374506\pi
0.384116 + 0.923285i 0.374506π0.374506\pi
4444 0 0
4545 −2.39399 −0.356876
4646 0 0
4747 −5.65556 −0.824949 −0.412474 0.910969i 0.635335π-0.635335\pi
−0.412474 + 0.910969i 0.635335π0.635335\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 5.65556 0.791937
5252 0 0
5353 −11.4316 −1.57025 −0.785127 0.619334i 0.787403π-0.787403\pi
−0.785127 + 0.619334i 0.787403π0.787403\pi
5454 0 0
5555 −4.91281 −0.662443
5656 0 0
5757 1.43163 0.189624
5858 0 0
5959 0.617929 0.0804475 0.0402238 0.999191i 0.487193π-0.487193\pi
0.0402238 + 0.999191i 0.487193π0.487193\pi
6060 0 0
6161 −5.48118 −0.701794 −0.350897 0.936414i 0.614123π-0.614123\pi
−0.350897 + 0.936414i 0.614123π0.614123\pi
6262 0 0
6363 0.950444 0.119745
6464 0 0
6565 −13.5565 −1.68147
6666 0 0
6767 −0.223935 −0.0273581 −0.0136790 0.999906i 0.504354π-0.504354\pi
−0.0136790 + 0.999906i 0.504354π0.504354\pi
6868 0 0
6969 −12.1958 −1.46820
7070 0 0
7171 13.5565 1.60885 0.804427 0.594051i 0.202472π-0.202472\pi
0.804427 + 0.594051i 0.202472π0.202472\pi
7272 0 0
7373 7.43163 0.869806 0.434903 0.900477i 0.356783π-0.356783\pi
0.434903 + 0.900477i 0.356783π0.356783\pi
7474 0 0
7575 −1.92473 −0.222249
7676 0 0
7777 1.95044 0.222274
7878 0 0
7979 5.03763 0.566778 0.283389 0.959005i 0.408541π-0.408541\pi
0.283389 + 0.959005i 0.408541π0.408541\pi
8080 0 0
8181 −5.24533 −0.582814
8282 0 0
8383 −13.7804 −1.51259 −0.756297 0.654229i 0.772993π-0.772993\pi
−0.756297 + 0.654229i 0.772993π0.772993\pi
8484 0 0
8585 −9.95044 −1.07928
8686 0 0
8787 5.65556 0.606340
8888 0 0
8989 10.9385 1.15948 0.579740 0.814801i 0.303154π-0.303154\pi
0.579740 + 0.814801i 0.303154π0.303154\pi
9090 0 0
9191 5.38207 0.564194
9292 0 0
9393 8.51882 0.883360
9494 0 0
9595 −2.51882 −0.258425
9696 0 0
9797 4.69320 0.476522 0.238261 0.971201i 0.423423π-0.423423\pi
0.238261 + 0.971201i 0.423423π0.423423\pi
9898 0 0
9999 1.85379 0.186313
100100 0 0
101101 −17.3821 −1.72958 −0.864790 0.502133i 0.832549π-0.832549\pi
−0.864790 + 0.502133i 0.832549π0.832549\pi
102102 0 0
103103 2.34444 0.231004 0.115502 0.993307i 0.463152π-0.463152\pi
0.115502 + 0.993307i 0.463152π0.463152\pi
104104 0 0
105105 3.60601 0.351910
106106 0 0
107107 15.2830 1.47746 0.738730 0.674002i 0.235426π-0.235426\pi
0.738730 + 0.674002i 0.235426π0.235426\pi
108108 0 0
109109 13.3821 1.28177 0.640885 0.767637i 0.278568π-0.278568\pi
0.640885 + 0.767637i 0.278568π0.278568\pi
110110 0 0
111111 10.8180 1.02680
112112 0 0
113113 14.6436 1.37756 0.688779 0.724971i 0.258147π-0.258147\pi
0.688779 + 0.724971i 0.258147π0.258147\pi
114114 0 0
115115 21.4573 2.00091
116116 0 0
117117 5.11536 0.472915
118118 0 0
119119 3.95044 0.362137
120120 0 0
121121 −7.19577 −0.654161
122122 0 0
123123 −9.75467 −0.879549
124124 0 0
125125 −9.20769 −0.823561
126126 0 0
127127 18.1744 1.61272 0.806358 0.591428i 0.201436π-0.201436\pi
0.806358 + 0.591428i 0.201436π0.201436\pi
128128 0 0
129129 −7.21201 −0.634982
130130 0 0
131131 4.81370 0.420575 0.210287 0.977640i 0.432560π-0.432560\pi
0.210287 + 0.977640i 0.432560π0.432560\pi
132132 0 0
133133 1.00000 0.0867110
134134 0 0
135135 14.2453 1.22604
136136 0 0
137137 −11.7265 −1.00186 −0.500932 0.865487i 0.667009π-0.667009\pi
−0.500932 + 0.865487i 0.667009π0.667009\pi
138138 0 0
139139 9.65556 0.818974 0.409487 0.912316i 0.365708π-0.365708\pi
0.409487 + 0.912316i 0.365708π0.365708\pi
140140 0 0
141141 8.09666 0.681861
142142 0 0
143143 10.4974 0.877839
144144 0 0
145145 −9.95044 −0.826339
146146 0 0
147147 −1.43163 −0.118079
148148 0 0
149149 −4.69320 −0.384482 −0.192241 0.981348i 0.561575π-0.561575\pi
−0.192241 + 0.981348i 0.561575π0.561575\pi
150150 0 0
151151 −4.22394 −0.343739 −0.171869 0.985120i 0.554981π-0.554981\pi
−0.171869 + 0.985120i 0.554981π0.554981\pi
152152 0 0
153153 3.75467 0.303547
154154 0 0
155155 −14.9881 −1.20387
156156 0 0
157157 20.8890 1.66712 0.833560 0.552428i 0.186299π-0.186299\pi
0.833560 + 0.552428i 0.186299π0.186299\pi
158158 0 0
159159 16.3658 1.29789
160160 0 0
161161 −8.51882 −0.671377
162162 0 0
163163 15.1581 1.18728 0.593638 0.804732i 0.297691π-0.297691\pi
0.593638 + 0.804732i 0.297691π0.297691\pi
164164 0 0
165165 7.03331 0.547543
166166 0 0
167167 −6.24533 −0.483278 −0.241639 0.970366i 0.577685π-0.577685\pi
−0.241639 + 0.970366i 0.577685π0.577685\pi
168168 0 0
169169 15.9667 1.22821
170170 0 0
171171 0.950444 0.0726823
172172 0 0
173173 10.9385 0.831640 0.415820 0.909447i 0.363495π-0.363495\pi
0.415820 + 0.909447i 0.363495π0.363495\pi
174174 0 0
175175 −1.34444 −0.101630
176176 0 0
177177 −0.884644 −0.0664939
178178 0 0
179179 −15.4359 −1.15374 −0.576868 0.816837i 0.695725π-0.695725\pi
−0.576868 + 0.816837i 0.695725π0.695725\pi
180180 0 0
181181 2.12482 0.157937 0.0789684 0.996877i 0.474837π-0.474837\pi
0.0789684 + 0.996877i 0.474837π0.474837\pi
182182 0 0
183183 7.84701 0.580068
184184 0 0
185185 −19.0333 −1.39936
186186 0 0
187187 7.70512 0.563454
188188 0 0
189189 −5.65556 −0.411382
190190 0 0
191191 −7.50689 −0.543180 −0.271590 0.962413i 0.587549π-0.587549\pi
−0.271590 + 0.962413i 0.587549π0.587549\pi
192192 0 0
193193 −6.22394 −0.448009 −0.224004 0.974588i 0.571913π-0.571913\pi
−0.224004 + 0.974588i 0.571913π0.571913\pi
194194 0 0
195195 19.4078 1.38982
196196 0 0
197197 10.2949 0.733480 0.366740 0.930323i 0.380474π-0.380474\pi
0.366740 + 0.930323i 0.380474π0.380474\pi
198198 0 0
199199 −19.3821 −1.37396 −0.686979 0.726677i 0.741064π-0.741064\pi
−0.686979 + 0.726677i 0.741064π0.741064\pi
200200 0 0
201201 0.320592 0.0226128
202202 0 0
203203 3.95044 0.277267
204204 0 0
205205 17.1625 1.19868
206206 0 0
207207 −8.09666 −0.562757
208208 0 0
209209 1.95044 0.134915
210210 0 0
211211 −4.39399 −0.302495 −0.151248 0.988496i 0.548329π-0.548329\pi
−0.151248 + 0.988496i 0.548329π0.548329\pi
212212 0 0
213213 −19.4078 −1.32980
214214 0 0
215215 12.6889 0.865374
216216 0 0
217217 5.95044 0.403942
218218 0 0
219219 −10.6393 −0.718939
220220 0 0
221221 21.2616 1.43021
222222 0 0
223223 −11.8299 −0.792191 −0.396096 0.918209i 0.629635π-0.629635\pi
−0.396096 + 0.918209i 0.629635π0.629635\pi
224224 0 0
225225 −1.27781 −0.0851875
226226 0 0
227227 14.2992 0.949071 0.474536 0.880236i 0.342616π-0.342616\pi
0.474536 + 0.880236i 0.342616π0.342616\pi
228228 0 0
229229 14.3488 0.948193 0.474096 0.880473i 0.342775π-0.342775\pi
0.474096 + 0.880473i 0.342775π0.342775\pi
230230 0 0
231231 −2.79231 −0.183720
232232 0 0
233233 −15.8513 −1.03846 −0.519228 0.854636i 0.673780π-0.673780\pi
−0.519228 + 0.854636i 0.673780π0.673780\pi
234234 0 0
235235 −14.2453 −0.929263
236236 0 0
237237 −7.21201 −0.468471
238238 0 0
239239 7.28296 0.471095 0.235548 0.971863i 0.424312π-0.424312\pi
0.235548 + 0.971863i 0.424312π0.424312\pi
240240 0 0
241241 7.82562 0.504093 0.252046 0.967715i 0.418896π-0.418896\pi
0.252046 + 0.967715i 0.418896π0.418896\pi
242242 0 0
243243 −9.45734 −0.606688
244244 0 0
245245 2.51882 0.160921
246246 0 0
247247 5.38207 0.342453
248248 0 0
249249 19.7284 1.25023
250250 0 0
251251 30.1010 1.89996 0.949978 0.312316i 0.101105π-0.101105\pi
0.949978 + 0.312316i 0.101105π0.101105\pi
252252 0 0
253253 −16.6155 −1.04461
254254 0 0
255255 14.2453 0.892077
256256 0 0
257257 3.43163 0.214059 0.107030 0.994256i 0.465866π-0.465866\pi
0.107030 + 0.994256i 0.465866π0.465866\pi
258258 0 0
259259 7.55645 0.469535
260260 0 0
261261 3.75467 0.232409
262262 0 0
263263 7.70512 0.475118 0.237559 0.971373i 0.423653π-0.423653\pi
0.237559 + 0.971373i 0.423653π0.423653\pi
264264 0 0
265265 −28.7942 −1.76881
266266 0 0
267267 −15.6599 −0.958369
268268 0 0
269269 −28.8180 −1.75707 −0.878533 0.477682i 0.841477π-0.841477\pi
−0.878533 + 0.477682i 0.841477π0.841477\pi
270270 0 0
271271 19.3368 1.17463 0.587315 0.809359i 0.300185π-0.300185\pi
0.587315 + 0.809359i 0.300185π0.300185\pi
272272 0 0
273273 −7.70512 −0.466335
274274 0 0
275275 −2.62225 −0.158128
276276 0 0
277277 −19.9762 −1.20025 −0.600125 0.799906i 0.704883π-0.704883\pi
−0.600125 + 0.799906i 0.704883π0.704883\pi
278278 0 0
279279 5.65556 0.338590
280280 0 0
281281 28.1462 1.67906 0.839531 0.543312i 0.182830π-0.182830\pi
0.839531 + 0.543312i 0.182830π0.182830\pi
282282 0 0
283283 −6.56837 −0.390449 −0.195225 0.980759i 0.562544π-0.562544\pi
−0.195225 + 0.980759i 0.562544π0.562544\pi
284284 0 0
285285 3.60601 0.213601
286286 0 0
287287 −6.81370 −0.402200
288288 0 0
289289 −1.39399 −0.0819996
290290 0 0
291291 −6.71891 −0.393869
292292 0 0
293293 13.4812 0.787579 0.393790 0.919201i 0.371164π-0.371164\pi
0.393790 + 0.919201i 0.371164π0.371164\pi
294294 0 0
295295 1.55645 0.0906200
296296 0 0
297297 −11.0309 −0.640075
298298 0 0
299299 −45.8489 −2.65151
300300 0 0
301301 −5.03763 −0.290364
302302 0 0
303303 24.8846 1.42959
304304 0 0
305305 −13.8061 −0.790535
306306 0 0
307307 0.323048 0.0184373 0.00921865 0.999958i 0.497066π-0.497066\pi
0.00921865 + 0.999958i 0.497066π0.497066\pi
308308 0 0
309309 −3.35636 −0.190937
310310 0 0
311311 −17.8513 −1.01226 −0.506128 0.862458i 0.668924π-0.668924\pi
−0.506128 + 0.862458i 0.668924π0.668924\pi
312312 0 0
313313 −12.1744 −0.688137 −0.344068 0.938945i 0.611805π-0.611805\pi
−0.344068 + 0.938945i 0.611805π0.611805\pi
314314 0 0
315315 2.39399 0.134886
316316 0 0
317317 7.72651 0.433964 0.216982 0.976176i 0.430379π-0.430379\pi
0.216982 + 0.976176i 0.430379π0.430379\pi
318318 0 0
319319 7.70512 0.431404
320320 0 0
321321 −21.8795 −1.22119
322322 0 0
323323 3.95044 0.219809
324324 0 0
325325 −7.23586 −0.401373
326326 0 0
327327 −19.1581 −1.05945
328328 0 0
329329 5.65556 0.311801
330330 0 0
331331 10.1205 0.556273 0.278137 0.960542i 0.410283π-0.410283\pi
0.278137 + 0.960542i 0.410283π0.410283\pi
332332 0 0
333333 7.18198 0.393570
334334 0 0
335335 −0.564052 −0.0308175
336336 0 0
337337 33.2377 1.81057 0.905287 0.424800i 0.139656π-0.139656\pi
0.905287 + 0.424800i 0.139656π0.139656\pi
338338 0 0
339339 −20.9642 −1.13862
340340 0 0
341341 11.6060 0.628500
342342 0 0
343343 −1.00000 −0.0539949
344344 0 0
345345 −30.7189 −1.65385
346346 0 0
347347 −3.84701 −0.206518 −0.103259 0.994654i 0.532927π-0.532927\pi
−0.103259 + 0.994654i 0.532927π0.532927\pi
348348 0 0
349349 37.2096 1.99178 0.995891 0.0905605i 0.0288659π-0.0288659\pi
0.995891 + 0.0905605i 0.0288659π0.0288659\pi
350350 0 0
351351 −30.4386 −1.62469
352352 0 0
353353 −15.2616 −0.812291 −0.406146 0.913808i 0.633127π-0.633127\pi
−0.406146 + 0.913808i 0.633127π0.633127\pi
354354 0 0
355355 34.1462 1.81229
356356 0 0
357357 −5.65556 −0.299324
358358 0 0
359359 −30.0019 −1.58344 −0.791719 0.610886i 0.790814π-0.790814\pi
−0.791719 + 0.610886i 0.790814π0.790814\pi
360360 0 0
361361 1.00000 0.0526316
362362 0 0
363363 10.3017 0.540697
364364 0 0
365365 18.7189 0.979792
366366 0 0
367367 0.717041 0.0374293 0.0187146 0.999825i 0.494043π-0.494043\pi
0.0187146 + 0.999825i 0.494043π0.494043\pi
368368 0 0
369369 −6.47604 −0.337129
370370 0 0
371371 11.4316 0.593501
372372 0 0
373373 −32.1719 −1.66580 −0.832900 0.553424i 0.813321π-0.813321\pi
−0.832900 + 0.553424i 0.813321π0.813321\pi
374374 0 0
375375 13.1820 0.680715
376376 0 0
377377 21.2616 1.09503
378378 0 0
379379 −14.8351 −0.762027 −0.381014 0.924569i 0.624425π-0.624425\pi
−0.381014 + 0.924569i 0.624425π0.624425\pi
380380 0 0
381381 −26.0189 −1.33299
382382 0 0
383383 25.1086 1.28299 0.641494 0.767128i 0.278315π-0.278315\pi
0.641494 + 0.767128i 0.278315π0.278315\pi
384384 0 0
385385 4.91281 0.250380
386386 0 0
387387 −4.78799 −0.243387
388388 0 0
389389 1.77606 0.0900501 0.0450250 0.998986i 0.485663π-0.485663\pi
0.0450250 + 0.998986i 0.485663π0.485663\pi
390390 0 0
391391 −33.6531 −1.70191
392392 0 0
393393 −6.89142 −0.347626
394394 0 0
395395 12.6889 0.638447
396396 0 0
397397 10.5898 0.531485 0.265742 0.964044i 0.414383π-0.414383\pi
0.265742 + 0.964044i 0.414383π0.414383\pi
398398 0 0
399399 −1.43163 −0.0716710
400400 0 0
401401 35.8513 1.79033 0.895165 0.445735i 0.147058π-0.147058\pi
0.895165 + 0.445735i 0.147058π0.147058\pi
402402 0 0
403403 32.0257 1.59531
404404 0 0
405405 −13.2120 −0.656510
406406 0 0
407407 14.7384 0.730557
408408 0 0
409409 −9.50689 −0.470086 −0.235043 0.971985i 0.575523π-0.575523\pi
−0.235043 + 0.971985i 0.575523π0.575523\pi
410410 0 0
411411 16.7880 0.828090
412412 0 0
413413 −0.617929 −0.0304063
414414 0 0
415415 −34.7103 −1.70386
416416 0 0
417417 −13.8232 −0.676923
418418 0 0
419419 −23.1838 −1.13261 −0.566303 0.824197i 0.691627π-0.691627\pi
−0.566303 + 0.824197i 0.691627π0.691627\pi
420420 0 0
421421 −27.0095 −1.31636 −0.658180 0.752860i 0.728674π-0.728674\pi
−0.658180 + 0.752860i 0.728674π0.728674\pi
422422 0 0
423423 5.37529 0.261356
424424 0 0
425425 −5.31112 −0.257627
426426 0 0
427427 5.48118 0.265253
428428 0 0
429429 −15.0284 −0.725578
430430 0 0
431431 −10.7641 −0.518490 −0.259245 0.965812i 0.583474π-0.583474\pi
−0.259245 + 0.965812i 0.583474π0.583474\pi
432432 0 0
433433 15.7547 0.757121 0.378561 0.925576i 0.376419π-0.376419\pi
0.378561 + 0.925576i 0.376419π0.376419\pi
434434 0 0
435435 14.2453 0.683011
436436 0 0
437437 −8.51882 −0.407510
438438 0 0
439439 3.45302 0.164804 0.0824018 0.996599i 0.473741π-0.473741\pi
0.0824018 + 0.996599i 0.473741π0.473741\pi
440440 0 0
441441 −0.950444 −0.0452592
442442 0 0
443443 −19.5069 −0.926800 −0.463400 0.886149i 0.653371π-0.653371\pi
−0.463400 + 0.886149i 0.653371π0.653371\pi
444444 0 0
445445 27.5521 1.30610
446446 0 0
447447 6.71891 0.317793
448448 0 0
449449 7.43163 0.350720 0.175360 0.984504i 0.443891π-0.443891\pi
0.175360 + 0.984504i 0.443891π0.443891\pi
450450 0 0
451451 −13.2897 −0.625789
452452 0 0
453453 6.04710 0.284118
454454 0 0
455455 13.5565 0.635536
456456 0 0
457457 1.50689 0.0704895 0.0352448 0.999379i 0.488779π-0.488779\pi
0.0352448 + 0.999379i 0.488779π0.488779\pi
458458 0 0
459459 −22.3420 −1.04283
460460 0 0
461461 −12.9171 −0.601611 −0.300805 0.953686i 0.597255π-0.597255\pi
−0.300805 + 0.953686i 0.597255π0.597255\pi
462462 0 0
463463 9.30680 0.432524 0.216262 0.976335i 0.430613π-0.430613\pi
0.216262 + 0.976335i 0.430613π0.430613\pi
464464 0 0
465465 21.4573 0.995060
466466 0 0
467467 −4.29488 −0.198743 −0.0993717 0.995050i 0.531683π-0.531683\pi
−0.0993717 + 0.995050i 0.531683π0.531683\pi
468468 0 0
469469 0.223935 0.0103404
470470 0 0
471471 −29.9052 −1.37796
472472 0 0
473473 −9.82562 −0.451783
474474 0 0
475475 −1.34444 −0.0616870
476476 0 0
477477 10.8651 0.497480
478478 0 0
479479 −40.8651 −1.86717 −0.933587 0.358350i 0.883340π-0.883340\pi
−0.933587 + 0.358350i 0.883340π0.883340\pi
480480 0 0
481481 40.6694 1.85436
482482 0 0
483483 12.1958 0.554927
484484 0 0
485485 11.8213 0.536778
486486 0 0
487487 37.1600 1.68388 0.841940 0.539571i 0.181414π-0.181414\pi
0.841940 + 0.539571i 0.181414π0.181414\pi
488488 0 0
489489 −21.7008 −0.981344
490490 0 0
491491 37.8770 1.70937 0.854683 0.519149i 0.173751π-0.173751\pi
0.854683 + 0.519149i 0.173751π0.173751\pi
492492 0 0
493493 15.6060 0.702859
494494 0 0
495495 4.66935 0.209872
496496 0 0
497497 −13.5565 −0.608090
498498 0 0
499499 29.3325 1.31310 0.656552 0.754281i 0.272014π-0.272014\pi
0.656552 + 0.754281i 0.272014π0.272014\pi
500500 0 0
501501 8.94098 0.399453
502502 0 0
503503 32.0000 1.42681 0.713405 0.700752i 0.247152π-0.247152\pi
0.713405 + 0.700752i 0.247152π0.247152\pi
504504 0 0
505505 −43.7823 −1.94828
506506 0 0
507507 −22.8583 −1.01517
508508 0 0
509509 6.00000 0.265945 0.132973 0.991120i 0.457548π-0.457548\pi
0.132973 + 0.991120i 0.457548π0.457548\pi
510510 0 0
511511 −7.43163 −0.328756
512512 0 0
513513 −5.65556 −0.249699
514514 0 0
515515 5.90521 0.260215
516516 0 0
517517 11.0309 0.485137
518518 0 0
519519 −15.6599 −0.687393
520520 0 0
521521 11.9052 0.521577 0.260788 0.965396i 0.416018π-0.416018\pi
0.260788 + 0.965396i 0.416018π0.416018\pi
522522 0 0
523523 25.0095 1.09359 0.546794 0.837267i 0.315848π-0.315848\pi
0.546794 + 0.837267i 0.315848π0.315848\pi
524524 0 0
525525 1.92473 0.0840022
526526 0 0
527527 23.5069 1.02398
528528 0 0
529529 49.5702 2.15523
530530 0 0
531531 −0.587307 −0.0254869
532532 0 0
533533 −36.6718 −1.58843
534534 0 0
535535 38.4950 1.66428
536536 0 0
537537 22.0985 0.953622
538538 0 0
539539 −1.95044 −0.0840116
540540 0 0
541541 −8.27349 −0.355705 −0.177853 0.984057i 0.556915π-0.556915\pi
−0.177853 + 0.984057i 0.556915π0.556915\pi
542542 0 0
543543 −3.04195 −0.130543
544544 0 0
545545 33.7070 1.44385
546546 0 0
547547 31.0590 1.32799 0.663994 0.747738i 0.268860π-0.268860\pi
0.663994 + 0.747738i 0.268860π0.268860\pi
548548 0 0
549549 5.20956 0.222338
550550 0 0
551551 3.95044 0.168295
552552 0 0
553553 −5.03763 −0.214222
554554 0 0
555555 27.2486 1.15664
556556 0 0
557557 19.0633 0.807740 0.403870 0.914816i 0.367665π-0.367665\pi
0.403870 + 0.914816i 0.367665π0.367665\pi
558558 0 0
559559 −27.1129 −1.14675
560560 0 0
561561 −11.0309 −0.465723
562562 0 0
563563 33.4573 1.41006 0.705029 0.709178i 0.250934π-0.250934\pi
0.705029 + 0.709178i 0.250934π0.250934\pi
564564 0 0
565565 36.8846 1.55175
566566 0 0
567567 5.24533 0.220283
568568 0 0
569569 18.3206 0.768039 0.384020 0.923325i 0.374540π-0.374540\pi
0.384020 + 0.923325i 0.374540π0.374540\pi
570570 0 0
571571 12.9667 0.542639 0.271319 0.962489i 0.412540π-0.412540\pi
0.271319 + 0.962489i 0.412540π0.412540\pi
572572 0 0
573573 10.7471 0.448965
574574 0 0
575575 11.4530 0.477624
576576 0 0
577577 6.39399 0.266185 0.133093 0.991104i 0.457509π-0.457509\pi
0.133093 + 0.991104i 0.457509π0.457509\pi
578578 0 0
579579 8.91035 0.370302
580580 0 0
581581 13.7804 0.571707
582582 0 0
583583 22.2967 0.923437
584584 0 0
585585 12.8846 0.532714
586586 0 0
587587 −26.5659 −1.09649 −0.548246 0.836317i 0.684704π-0.684704\pi
−0.548246 + 0.836317i 0.684704π0.684704\pi
588588 0 0
589589 5.95044 0.245184
590590 0 0
591591 −14.7384 −0.606258
592592 0 0
593593 −17.3821 −0.713796 −0.356898 0.934143i 0.616166π-0.616166\pi
−0.356898 + 0.934143i 0.616166π0.616166\pi
594594 0 0
595595 9.95044 0.407928
596596 0 0
597597 27.7479 1.13565
598598 0 0
599599 24.8933 1.01711 0.508556 0.861029i 0.330179π-0.330179\pi
0.508556 + 0.861029i 0.330179π0.330179\pi
600600 0 0
601601 20.8608 0.850930 0.425465 0.904975i 0.360111π-0.360111\pi
0.425465 + 0.904975i 0.360111π0.360111\pi
602602 0 0
603603 0.212838 0.00866743
604604 0 0
605605 −18.1248 −0.736879
606606 0 0
607607 −40.7685 −1.65474 −0.827370 0.561657i 0.810164π-0.810164\pi
−0.827370 + 0.561657i 0.810164π0.810164\pi
608608 0 0
609609 −5.65556 −0.229175
610610 0 0
611611 30.4386 1.23142
612612 0 0
613613 43.3839 1.75226 0.876130 0.482074i 0.160116π-0.160116\pi
0.876130 + 0.482074i 0.160116π0.160116\pi
614614 0 0
615615 −24.5702 −0.990768
616616 0 0
617617 −5.43595 −0.218843 −0.109422 0.993995i 0.534900π-0.534900\pi
−0.109422 + 0.993995i 0.534900π0.534900\pi
618618 0 0
619619 −0.393994 −0.0158359 −0.00791797 0.999969i 0.502520π-0.502520\pi
−0.00791797 + 0.999969i 0.502520π0.502520\pi
620620 0 0
621621 48.1787 1.93334
622622 0 0
623623 −10.9385 −0.438243
624624 0 0
625625 −29.9147 −1.19659
626626 0 0
627627 −2.79231 −0.111514
628628 0 0
629629 29.8513 1.19025
630630 0 0
631631 15.5326 0.618343 0.309172 0.951006i 0.399948π-0.399948\pi
0.309172 + 0.951006i 0.399948π0.399948\pi
632632 0 0
633633 6.29056 0.250027
634634 0 0
635635 45.7779 1.81664
636636 0 0
637637 −5.38207 −0.213245
638638 0 0
639639 −12.8846 −0.509709
640640 0 0
641641 −1.92660 −0.0760961 −0.0380480 0.999276i 0.512114π-0.512114\pi
−0.0380480 + 0.999276i 0.512114π0.512114\pi
642642 0 0
643643 1.20769 0.0476267 0.0238134 0.999716i 0.492419π-0.492419\pi
0.0238134 + 0.999716i 0.492419π0.492419\pi
644644 0 0
645645 −18.1657 −0.715275
646646 0 0
647647 26.3444 1.03571 0.517853 0.855469i 0.326731π-0.326731\pi
0.517853 + 0.855469i 0.326731π0.326731\pi
648648 0 0
649649 −1.20524 −0.0473096
650650 0 0
651651 −8.51882 −0.333879
652652 0 0
653653 2.85893 0.111879 0.0559394 0.998434i 0.482185π-0.482185\pi
0.0559394 + 0.998434i 0.482185π0.482185\pi
654654 0 0
655655 12.1248 0.473756
656656 0 0
657657 −7.06334 −0.275567
658658 0 0
659659 −31.3796 −1.22238 −0.611188 0.791485i 0.709308π-0.709308\pi
−0.611188 + 0.791485i 0.709308π0.709308\pi
660660 0 0
661661 −34.6975 −1.34958 −0.674788 0.738011i 0.735765π-0.735765\pi
−0.674788 + 0.738011i 0.735765π0.735765\pi
662662 0 0
663663 −30.4386 −1.18214
664664 0 0
665665 2.51882 0.0976755
666666 0 0
667667 −33.6531 −1.30305
668668 0 0
669669 16.9361 0.654786
670670 0 0
671671 10.6907 0.412711
672672 0 0
673673 −38.8846 −1.49889 −0.749446 0.662065i 0.769680π-0.769680\pi
−0.749446 + 0.662065i 0.769680π0.769680\pi
674674 0 0
675675 7.60355 0.292661
676676 0 0
677677 −7.28974 −0.280167 −0.140084 0.990140i 0.544737π-0.544737\pi
−0.140084 + 0.990140i 0.544737π0.544737\pi
678678 0 0
679679 −4.69320 −0.180108
680680 0 0
681681 −20.4711 −0.784455
682682 0 0
683683 0.320592 0.0122671 0.00613355 0.999981i 0.498048π-0.498048\pi
0.00613355 + 0.999981i 0.498048π0.498048\pi
684684 0 0
685685 −29.5369 −1.12855
686686 0 0
687687 −20.5421 −0.783729
688688 0 0
689689 61.5258 2.34395
690690 0 0
691691 32.9385 1.25304 0.626520 0.779405i 0.284479π-0.284479\pi
0.626520 + 0.779405i 0.284479π0.284479\pi
692692 0 0
693693 −1.85379 −0.0704196
694694 0 0
695695 24.3206 0.922533
696696 0 0
697697 −26.9171 −1.01956
698698 0 0
699699 22.6932 0.858335
700700 0 0
701701 25.6599 0.969160 0.484580 0.874747i 0.338972π-0.338972\pi
0.484580 + 0.874747i 0.338972π0.338972\pi
702702 0 0
703703 7.55645 0.284997
704704 0 0
705705 20.3940 0.768082
706706 0 0
707707 17.3821 0.653720
708708 0 0
709709 3.55645 0.133565 0.0667826 0.997768i 0.478727π-0.478727\pi
0.0667826 + 0.997768i 0.478727π0.478727\pi
710710 0 0
711711 −4.78799 −0.179564
712712 0 0
713713 −50.6907 −1.89838
714714 0 0
715715 26.4411 0.988841
716716 0 0
717717 −10.4265 −0.389384
718718 0 0
719719 5.92473 0.220955 0.110478 0.993879i 0.464762π-0.464762\pi
0.110478 + 0.993879i 0.464762π0.464762\pi
720720 0 0
721721 −2.34444 −0.0873114
722722 0 0
723723 −11.2034 −0.416658
724724 0 0
725725 −5.31112 −0.197250
726726 0 0
727727 −19.8299 −0.735452 −0.367726 0.929934i 0.619864π-0.619864\pi
−0.367726 + 0.929934i 0.619864π0.619864\pi
728728 0 0
729729 29.2754 1.08427
730730 0 0
731731 −19.9009 −0.736061
732732 0 0
733733 −11.3864 −0.420566 −0.210283 0.977641i 0.567439π-0.567439\pi
−0.210283 + 0.977641i 0.567439π0.567439\pi
734734 0 0
735735 −3.60601 −0.133010
736736 0 0
737737 0.436773 0.0160888
738738 0 0
739739 29.2163 1.07474 0.537370 0.843347i 0.319418π-0.319418\pi
0.537370 + 0.843347i 0.319418π0.319418\pi
740740 0 0
741741 −7.70512 −0.283055
742742 0 0
743743 15.8299 0.580744 0.290372 0.956914i 0.406221π-0.406221\pi
0.290372 + 0.956914i 0.406221π0.406221\pi
744744 0 0
745745 −11.8213 −0.433099
746746 0 0
747747 13.0975 0.479212
748748 0 0
749749 −15.2830 −0.558427
750750 0 0
751751 −35.0590 −1.27932 −0.639661 0.768657i 0.720925π-0.720925\pi
−0.639661 + 0.768657i 0.720925π0.720925\pi
752752 0 0
753753 −43.0934 −1.57041
754754 0 0
755755 −10.6393 −0.387204
756756 0 0
757757 −47.8770 −1.74012 −0.870060 0.492945i 0.835920π-0.835920\pi
−0.870060 + 0.492945i 0.835920π0.835920\pi
758758 0 0
759759 23.7872 0.863419
760760 0 0
761761 31.7070 1.14938 0.574689 0.818372i 0.305123π-0.305123\pi
0.574689 + 0.818372i 0.305123π0.305123\pi
762762 0 0
763763 −13.3821 −0.484463
764764 0 0
765765 9.45734 0.341931
766766 0 0
767767 −3.32574 −0.120085
768768 0 0
769769 −36.7641 −1.32575 −0.662874 0.748731i 0.730664π-0.730664\pi
−0.662874 + 0.748731i 0.730664π0.730664\pi
770770 0 0
771771 −4.91281 −0.176931
772772 0 0
773773 33.5044 1.20507 0.602535 0.798092i 0.294157π-0.294157\pi
0.602535 + 0.798092i 0.294157π0.294157\pi
774774 0 0
775775 −8.00000 −0.287368
776776 0 0
777777 −10.8180 −0.388094
778778 0 0
779779 −6.81370 −0.244126
780780 0 0
781781 −26.4411 −0.946137
782782 0 0
783783 −22.3420 −0.798437
784784 0 0
785785 52.6155 1.87793
786786 0 0
787787 2.12296 0.0756753 0.0378376 0.999284i 0.487953π-0.487953\pi
0.0378376 + 0.999284i 0.487953π0.487953\pi
788788 0 0
789789 −11.0309 −0.392709
790790 0 0
791791 −14.6436 −0.520668
792792 0 0
793793 29.5001 1.04758
794794 0 0
795795 41.2225 1.46201
796796 0 0
797797 −34.1676 −1.21028 −0.605139 0.796120i 0.706883π-0.706883\pi
−0.605139 + 0.796120i 0.706883π0.706883\pi
798798 0 0
799799 22.3420 0.790402
800800 0 0
801801 −10.3964 −0.367340
802802 0 0
803803 −14.4950 −0.511516
804804 0 0
805805 −21.4573 −0.756272
806806 0 0
807807 41.2567 1.45230
808808 0 0
809809 −1.63172 −0.0573681 −0.0286841 0.999589i 0.509132π-0.509132\pi
−0.0286841 + 0.999589i 0.509132π0.509132\pi
810810 0 0
811811 19.4617 0.683391 0.341696 0.939811i 0.388999π-0.388999\pi
0.341696 + 0.939811i 0.388999π0.388999\pi
812812 0 0
813813 −27.6831 −0.970890
814814 0 0
815815 38.1806 1.33741
816816 0 0
817817 −5.03763 −0.176244
818818 0 0
819819 −5.11536 −0.178745
820820 0 0
821821 −39.0376 −1.36242 −0.681211 0.732087i 0.738547π-0.738547\pi
−0.681211 + 0.732087i 0.738547π0.738547\pi
822822 0 0
823823 1.48550 0.0517814 0.0258907 0.999665i 0.491758π-0.491758\pi
0.0258907 + 0.999665i 0.491758π0.491758\pi
824824 0 0
825825 3.75408 0.130700
826826 0 0
827827 10.5941 0.368392 0.184196 0.982889i 0.441032π-0.441032\pi
0.184196 + 0.982889i 0.441032π0.441032\pi
828828 0 0
829829 38.8394 1.34895 0.674474 0.738298i 0.264370π-0.264370\pi
0.674474 + 0.738298i 0.264370π0.264370\pi
830830 0 0
831831 28.5984 0.992068
832832 0 0
833833 −3.95044 −0.136875
834834 0 0
835835 −15.7308 −0.544388
836836 0 0
837837 −33.6531 −1.16322
838838 0 0
839839 −40.4993 −1.39819 −0.699095 0.715028i 0.746414π-0.746414\pi
−0.699095 + 0.715028i 0.746414π0.746414\pi
840840 0 0
841841 −13.3940 −0.461862
842842 0 0
843843 −40.2949 −1.38783
844844 0 0
845845 40.2172 1.38351
846846 0 0
847847 7.19577 0.247250
848848 0 0
849849 9.40346 0.322726
850850 0 0
851851 −64.3720 −2.20664
852852 0 0
853853 −8.37015 −0.286588 −0.143294 0.989680i 0.545770π-0.545770\pi
−0.143294 + 0.989680i 0.545770π0.545770\pi
854854 0 0
855855 2.39399 0.0818729
856856 0 0
857857 −14.3230 −0.489266 −0.244633 0.969616i 0.578667π-0.578667\pi
−0.244633 + 0.969616i 0.578667π0.578667\pi
858858 0 0
859859 −0.912810 −0.0311447 −0.0155723 0.999879i 0.504957π-0.504957\pi
−0.0155723 + 0.999879i 0.504957π0.504957\pi
860860 0 0
861861 9.75467 0.332438
862862 0 0
863863 24.1958 0.823634 0.411817 0.911267i 0.364894π-0.364894\pi
0.411817 + 0.911267i 0.364894π0.364894\pi
864864 0 0
865865 27.5521 0.936801
866866 0 0
867867 1.99568 0.0677768
868868 0 0
869869 −9.82562 −0.333311
870870 0 0
871871 1.20524 0.0408379
872872 0 0
873873 −4.46062 −0.150969
874874 0 0
875875 9.20769 0.311277
876876 0 0
877877 4.86325 0.164220 0.0821102 0.996623i 0.473834π-0.473834\pi
0.0821102 + 0.996623i 0.473834π0.473834\pi
878878 0 0
879879 −19.3000 −0.650974
880880 0 0
881881 −36.8608 −1.24187 −0.620936 0.783861i 0.713247π-0.713247\pi
−0.620936 + 0.783861i 0.713247π0.713247\pi
882882 0 0
883883 −17.2077 −0.579085 −0.289542 0.957165i 0.593503π-0.593503\pi
−0.289542 + 0.957165i 0.593503π0.593503\pi
884884 0 0
885885 −2.22826 −0.0749020
886886 0 0
887887 −18.3959 −0.617672 −0.308836 0.951115i 0.599940π-0.599940\pi
−0.308836 + 0.951115i 0.599940π0.599940\pi
888888 0 0
889889 −18.1744 −0.609549
890890 0 0
891891 10.2307 0.342742
892892 0 0
893893 5.65556 0.189256
894894 0 0
895895 −38.8803 −1.29963
896896 0 0
897897 65.6385 2.19161
898898 0 0
899899 23.5069 0.783999
900900 0 0
901901 45.1600 1.50450
902902 0 0
903903 7.21201 0.240001
904904 0 0
905905 5.35204 0.177908
906906 0 0
907907 −31.7308 −1.05360 −0.526802 0.849988i 0.676609π-0.676609\pi
−0.526802 + 0.849988i 0.676609π0.676609\pi
908908 0 0
909909 16.5207 0.547956
910910 0 0
911911 10.9624 0.363199 0.181600 0.983373i 0.441872π-0.441872\pi
0.181600 + 0.983373i 0.441872π0.441872\pi
912912 0 0
913913 26.8779 0.889528
914914 0 0
915915 19.7652 0.653417
916916 0 0
917917 −4.81370 −0.158962
918918 0 0
919919 33.1086 1.09215 0.546076 0.837736i 0.316121π-0.316121\pi
0.546076 + 0.837736i 0.316121π0.316121\pi
920920 0 0
921921 −0.462484 −0.0152394
922922 0 0
923923 −72.9618 −2.40157
924924 0 0
925925 −10.1592 −0.334032
926926 0 0
927927 −2.22826 −0.0731855
928928 0 0
929929 2.74275 0.0899868 0.0449934 0.998987i 0.485673π-0.485673\pi
0.0449934 + 0.998987i 0.485673π0.485673\pi
930930 0 0
931931 −1.00000 −0.0327737
932932 0 0
933933 25.5565 0.836681
934934 0 0
935935 19.4078 0.634702
936936 0 0
937937 21.2291 0.693524 0.346762 0.937953i 0.387281π-0.387281\pi
0.346762 + 0.937953i 0.387281π0.387281\pi
938938 0 0
939939 17.4292 0.568780
940940 0 0
941941 −37.9523 −1.23721 −0.618605 0.785702i 0.712302π-0.712302\pi
−0.618605 + 0.785702i 0.712302π0.712302\pi
942942 0 0
943943 58.0446 1.89019
944944 0 0
945945 −14.2453 −0.463400
946946 0 0
947947 21.7241 0.705937 0.352968 0.935635i 0.385172π-0.385172\pi
0.352968 + 0.935635i 0.385172π0.385172\pi
948948 0 0
949949 −39.9975 −1.29838
950950 0 0
951951 −11.0615 −0.358693
952952 0 0
953953 −4.39831 −0.142475 −0.0712377 0.997459i 0.522695π-0.522695\pi
−0.0712377 + 0.997459i 0.522695π0.522695\pi
954954 0 0
955955 −18.9085 −0.611864
956956 0 0
957957 −11.0309 −0.356577
958958 0 0
959959 11.7265 0.378669
960960 0 0
961961 4.40778 0.142187
962962 0 0
963963 −14.5256 −0.468081
964964 0 0
965965 −15.6770 −0.504659
966966 0 0
967967 59.5865 1.91617 0.958086 0.286481i 0.0924854π-0.0924854\pi
0.958086 + 0.286481i 0.0924854π0.0924854\pi
968968 0 0
969969 −5.65556 −0.181683
970970 0 0
971971 −6.14621 −0.197241 −0.0986207 0.995125i 0.531443π-0.531443\pi
−0.0986207 + 0.995125i 0.531443π0.531443\pi
972972 0 0
973973 −9.65556 −0.309543
974974 0 0
975975 10.3591 0.331755
976976 0 0
977977 −13.3539 −0.427229 −0.213615 0.976918i 0.568524π-0.568524\pi
−0.213615 + 0.976918i 0.568524π0.568524\pi
978978 0 0
979979 −21.3350 −0.681869
980980 0 0
981981 −12.7189 −0.406083
982982 0 0
983983 29.7975 0.950391 0.475196 0.879880i 0.342377π-0.342377\pi
0.475196 + 0.879880i 0.342377π0.342377\pi
984984 0 0
985985 25.9309 0.826228
986986 0 0
987987 −8.09666 −0.257719
988988 0 0
989989 42.9147 1.36461
990990 0 0
991991 43.0138 1.36638 0.683189 0.730242i 0.260593π-0.260593\pi
0.683189 + 0.730242i 0.260593π0.260593\pi
992992 0 0
993993 −14.4888 −0.459788
994994 0 0
995995 −48.8199 −1.54769
996996 0 0
997997 39.0352 1.23626 0.618128 0.786077i 0.287891π-0.287891\pi
0.618128 + 0.786077i 0.287891π0.287891\pi
998998 0 0
999999 −42.7360 −1.35211
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 8512.2.a.bk.1.2 3
4.3 odd 2 8512.2.a.bo.1.2 3
8.3 odd 2 1064.2.a.f.1.2 3
8.5 even 2 2128.2.a.q.1.2 3
24.11 even 2 9576.2.a.ca.1.3 3
56.27 even 2 7448.2.a.bi.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.a.f.1.2 3 8.3 odd 2
2128.2.a.q.1.2 3 8.5 even 2
7448.2.a.bi.1.2 3 56.27 even 2
8512.2.a.bk.1.2 3 1.1 even 1 trivial
8512.2.a.bo.1.2 3 4.3 odd 2
9576.2.a.ca.1.3 3 24.11 even 2