Properties

Label 3724.2.a.m.1.6
Level 37243724
Weight 22
Character 3724.1
Self dual yes
Analytic conductor 29.73629.736
Analytic rank 00
Dimension 77
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [3724,2,Mod(1,3724)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3724, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3724.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 3724=227219 3724 = 2^{2} \cdot 7^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3724.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [7,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 29.736289712729.7362897127
Analytic rank: 00
Dimension: 77
Coefficient field: Q[x]/(x7)\mathbb{Q}[x]/(x^{7} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x718x5+84x34x244x+8 x^{7} - 18x^{5} + 84x^{3} - 4x^{2} - 44x + 8 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 532)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.6
Root 2.77904-2.77904 of defining polynomial
Character χ\chi == 3724.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+2.77904q33.08629q5+4.72304q9+5.16388q11+4.04970q138.57690q15+1.08292q171.00000q19+5.72837q23+4.52516q25+4.78838q273.16724q298.18192q31+14.3506q334.39755q37+11.2543q398.68032q41+7.99159q4314.5766q450.190404q47+3.00948q51+7.44586q5315.9372q552.77904q57+13.2439q59+9.35092q6112.4985q65+8.16585q67+15.9193q694.71652q71+6.50522q73+12.5756q752.31841q790.862030q81+14.7229q833.34221q858.80188q873.67499q8922.7378q93+3.08629q95+16.2607q97+24.3892q99+O(q100)q+2.77904 q^{3} -3.08629 q^{5} +4.72304 q^{9} +5.16388 q^{11} +4.04970 q^{13} -8.57690 q^{15} +1.08292 q^{17} -1.00000 q^{19} +5.72837 q^{23} +4.52516 q^{25} +4.78838 q^{27} -3.16724 q^{29} -8.18192 q^{31} +14.3506 q^{33} -4.39755 q^{37} +11.2543 q^{39} -8.68032 q^{41} +7.99159 q^{43} -14.5766 q^{45} -0.190404 q^{47} +3.00948 q^{51} +7.44586 q^{53} -15.9372 q^{55} -2.77904 q^{57} +13.2439 q^{59} +9.35092 q^{61} -12.4985 q^{65} +8.16585 q^{67} +15.9193 q^{69} -4.71652 q^{71} +6.50522 q^{73} +12.5756 q^{75} -2.31841 q^{79} -0.862030 q^{81} +14.7229 q^{83} -3.34221 q^{85} -8.80188 q^{87} -3.67499 q^{89} -22.7378 q^{93} +3.08629 q^{95} +16.2607 q^{97} +24.3892 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 7q2q5+15q9+14q11+12q1510q177q19+7q23+21q25+2q294q31+24q3312q37+18q394q416q45+16q47+2q516q53++40q99+O(q100) 7 q - 2 q^{5} + 15 q^{9} + 14 q^{11} + 12 q^{15} - 10 q^{17} - 7 q^{19} + 7 q^{23} + 21 q^{25} + 2 q^{29} - 4 q^{31} + 24 q^{33} - 12 q^{37} + 18 q^{39} - 4 q^{41} - 6 q^{45} + 16 q^{47} + 2 q^{51} - 6 q^{53}+ \cdots + 40 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 2.77904 1.60448 0.802238 0.597004i 0.203642π-0.203642\pi
0.802238 + 0.597004i 0.203642π0.203642\pi
44 0 0
55 −3.08629 −1.38023 −0.690115 0.723700i 0.742440π-0.742440\pi
−0.690115 + 0.723700i 0.742440π0.742440\pi
66 0 0
77 0 0
88 0 0
99 4.72304 1.57435
1010 0 0
1111 5.16388 1.55697 0.778484 0.627664i 0.215989π-0.215989\pi
0.778484 + 0.627664i 0.215989π0.215989\pi
1212 0 0
1313 4.04970 1.12318 0.561592 0.827414i 0.310189π-0.310189\pi
0.561592 + 0.827414i 0.310189π0.310189\pi
1414 0 0
1515 −8.57690 −2.21455
1616 0 0
1717 1.08292 0.262647 0.131324 0.991340i 0.458077π-0.458077\pi
0.131324 + 0.991340i 0.458077π0.458077\pi
1818 0 0
1919 −1.00000 −0.229416
2020 0 0
2121 0 0
2222 0 0
2323 5.72837 1.19445 0.597224 0.802075i 0.296271π-0.296271\pi
0.597224 + 0.802075i 0.296271π0.296271\pi
2424 0 0
2525 4.52516 0.905032
2626 0 0
2727 4.78838 0.921525
2828 0 0
2929 −3.16724 −0.588142 −0.294071 0.955784i 0.595010π-0.595010\pi
−0.294071 + 0.955784i 0.595010π0.595010\pi
3030 0 0
3131 −8.18192 −1.46952 −0.734758 0.678329i 0.762704π-0.762704\pi
−0.734758 + 0.678329i 0.762704π0.762704\pi
3232 0 0
3333 14.3506 2.49812
3434 0 0
3535 0 0
3636 0 0
3737 −4.39755 −0.722953 −0.361477 0.932381i 0.617727π-0.617727\pi
−0.361477 + 0.932381i 0.617727π0.617727\pi
3838 0 0
3939 11.2543 1.80212
4040 0 0
4141 −8.68032 −1.35564 −0.677819 0.735229i 0.737075π-0.737075\pi
−0.677819 + 0.735229i 0.737075π0.737075\pi
4242 0 0
4343 7.99159 1.21871 0.609353 0.792899i 0.291429π-0.291429\pi
0.609353 + 0.792899i 0.291429π0.291429\pi
4444 0 0
4545 −14.5766 −2.17296
4646 0 0
4747 −0.190404 −0.0277733 −0.0138866 0.999904i 0.504420π-0.504420\pi
−0.0138866 + 0.999904i 0.504420π0.504420\pi
4848 0 0
4949 0 0
5050 0 0
5151 3.00948 0.421412
5252 0 0
5353 7.44586 1.02277 0.511383 0.859353i 0.329133π-0.329133\pi
0.511383 + 0.859353i 0.329133π0.329133\pi
5454 0 0
5555 −15.9372 −2.14897
5656 0 0
5757 −2.77904 −0.368092
5858 0 0
5959 13.2439 1.72421 0.862107 0.506726i 0.169145π-0.169145\pi
0.862107 + 0.506726i 0.169145π0.169145\pi
6060 0 0
6161 9.35092 1.19726 0.598631 0.801025i 0.295711π-0.295711\pi
0.598631 + 0.801025i 0.295711π0.295711\pi
6262 0 0
6363 0 0
6464 0 0
6565 −12.4985 −1.55025
6666 0 0
6767 8.16585 0.997617 0.498808 0.866712i 0.333771π-0.333771\pi
0.498808 + 0.866712i 0.333771π0.333771\pi
6868 0 0
6969 15.9193 1.91646
7070 0 0
7171 −4.71652 −0.559748 −0.279874 0.960037i 0.590293π-0.590293\pi
−0.279874 + 0.960037i 0.590293π0.590293\pi
7272 0 0
7373 6.50522 0.761378 0.380689 0.924703i 0.375687π-0.375687\pi
0.380689 + 0.924703i 0.375687π0.375687\pi
7474 0 0
7575 12.5756 1.45210
7676 0 0
7777 0 0
7878 0 0
7979 −2.31841 −0.260842 −0.130421 0.991459i 0.541633π-0.541633\pi
−0.130421 + 0.991459i 0.541633π0.541633\pi
8080 0 0
8181 −0.862030 −0.0957811
8282 0 0
8383 14.7229 1.61605 0.808027 0.589146i 0.200536π-0.200536\pi
0.808027 + 0.589146i 0.200536π0.200536\pi
8484 0 0
8585 −3.34221 −0.362514
8686 0 0
8787 −8.80188 −0.943661
8888 0 0
8989 −3.67499 −0.389548 −0.194774 0.980848i 0.562397π-0.562397\pi
−0.194774 + 0.980848i 0.562397π0.562397\pi
9090 0 0
9191 0 0
9292 0 0
9393 −22.7378 −2.35780
9494 0 0
9595 3.08629 0.316646
9696 0 0
9797 16.2607 1.65102 0.825511 0.564386i 0.190887π-0.190887\pi
0.825511 + 0.564386i 0.190887π0.190887\pi
9898 0 0
9999 24.3892 2.45121
100100 0 0
101101 −7.28741 −0.725124 −0.362562 0.931960i 0.618098π-0.618098\pi
−0.362562 + 0.931960i 0.618098π0.618098\pi
102102 0 0
103103 −16.2875 −1.60486 −0.802429 0.596747i 0.796460π-0.796460\pi
−0.802429 + 0.596747i 0.796460π0.796460\pi
104104 0 0
105105 0 0
106106 0 0
107107 −4.56624 −0.441435 −0.220718 0.975338i 0.570840π-0.570840\pi
−0.220718 + 0.975338i 0.570840π0.570840\pi
108108 0 0
109109 13.5687 1.29965 0.649824 0.760084i 0.274842π-0.274842\pi
0.649824 + 0.760084i 0.274842π0.274842\pi
110110 0 0
111111 −12.2210 −1.15996
112112 0 0
113113 −2.16842 −0.203988 −0.101994 0.994785i 0.532522π-0.532522\pi
−0.101994 + 0.994785i 0.532522π0.532522\pi
114114 0 0
115115 −17.6794 −1.64861
116116 0 0
117117 19.1269 1.76828
118118 0 0
119119 0 0
120120 0 0
121121 15.6657 1.42415
122122 0 0
123123 −24.1229 −2.17509
124124 0 0
125125 1.46548 0.131077
126126 0 0
127127 4.27599 0.379433 0.189716 0.981839i 0.439243π-0.439243\pi
0.189716 + 0.981839i 0.439243π0.439243\pi
128128 0 0
129129 22.2089 1.95538
130130 0 0
131131 −10.9881 −0.960039 −0.480019 0.877258i 0.659370π-0.659370\pi
−0.480019 + 0.877258i 0.659370π0.659370\pi
132132 0 0
133133 0 0
134134 0 0
135135 −14.7783 −1.27191
136136 0 0
137137 15.1226 1.29201 0.646004 0.763334i 0.276439π-0.276439\pi
0.646004 + 0.763334i 0.276439π0.276439\pi
138138 0 0
139139 −20.9836 −1.77981 −0.889904 0.456149i 0.849229π-0.849229\pi
−0.889904 + 0.456149i 0.849229π0.849229\pi
140140 0 0
141141 −0.529140 −0.0445616
142142 0 0
143143 20.9122 1.74876
144144 0 0
145145 9.77502 0.811771
146146 0 0
147147 0 0
148148 0 0
149149 −0.419466 −0.0343640 −0.0171820 0.999852i 0.505469π-0.505469\pi
−0.0171820 + 0.999852i 0.505469π0.505469\pi
150150 0 0
151151 3.47957 0.283164 0.141582 0.989927i 0.454781π-0.454781\pi
0.141582 + 0.989927i 0.454781π0.454781\pi
152152 0 0
153153 5.11469 0.413498
154154 0 0
155155 25.2517 2.02827
156156 0 0
157157 6.77536 0.540732 0.270366 0.962758i 0.412855π-0.412855\pi
0.270366 + 0.962758i 0.412855π0.412855\pi
158158 0 0
159159 20.6923 1.64101
160160 0 0
161161 0 0
162162 0 0
163163 11.5176 0.902131 0.451066 0.892491i 0.351044π-0.351044\pi
0.451066 + 0.892491i 0.351044π0.351044\pi
164164 0 0
165165 −44.2901 −3.44798
166166 0 0
167167 14.3708 1.11205 0.556024 0.831166i 0.312326π-0.312326\pi
0.556024 + 0.831166i 0.312326π0.312326\pi
168168 0 0
169169 3.40006 0.261543
170170 0 0
171171 −4.72304 −0.361180
172172 0 0
173173 10.1302 0.770181 0.385091 0.922879i 0.374170π-0.374170\pi
0.385091 + 0.922879i 0.374170π0.374170\pi
174174 0 0
175175 0 0
176176 0 0
177177 36.8054 2.76646
178178 0 0
179179 17.2266 1.28757 0.643786 0.765205i 0.277362π-0.277362\pi
0.643786 + 0.765205i 0.277362π0.277362\pi
180180 0 0
181181 −7.55315 −0.561421 −0.280711 0.959792i 0.590570π-0.590570\pi
−0.280711 + 0.959792i 0.590570π0.590570\pi
182182 0 0
183183 25.9865 1.92098
184184 0 0
185185 13.5721 0.997841
186186 0 0
187187 5.59208 0.408934
188188 0 0
189189 0 0
190190 0 0
191191 −17.4102 −1.25976 −0.629878 0.776694i 0.716895π-0.716895\pi
−0.629878 + 0.776694i 0.716895π0.716895\pi
192192 0 0
193193 −4.31688 −0.310736 −0.155368 0.987857i 0.549656π-0.549656\pi
−0.155368 + 0.987857i 0.549656π0.549656\pi
194194 0 0
195195 −34.7339 −2.48734
196196 0 0
197197 3.63036 0.258652 0.129326 0.991602i 0.458719π-0.458719\pi
0.129326 + 0.991602i 0.458719π0.458719\pi
198198 0 0
199199 −18.4689 −1.30922 −0.654611 0.755966i 0.727168π-0.727168\pi
−0.654611 + 0.755966i 0.727168π0.727168\pi
200200 0 0
201201 22.6932 1.60065
202202 0 0
203203 0 0
204204 0 0
205205 26.7899 1.87109
206206 0 0
207207 27.0553 1.88047
208208 0 0
209209 −5.16388 −0.357193
210210 0 0
211211 −14.4742 −0.996448 −0.498224 0.867048i 0.666014π-0.666014\pi
−0.498224 + 0.867048i 0.666014π0.666014\pi
212212 0 0
213213 −13.1074 −0.898102
214214 0 0
215215 −24.6643 −1.68209
216216 0 0
217217 0 0
218218 0 0
219219 18.0782 1.22161
220220 0 0
221221 4.38551 0.295001
222222 0 0
223223 19.0914 1.27845 0.639226 0.769019i 0.279255π-0.279255\pi
0.639226 + 0.769019i 0.279255π0.279255\pi
224224 0 0
225225 21.3725 1.42483
226226 0 0
227227 −0.119758 −0.00794860 −0.00397430 0.999992i 0.501265π-0.501265\pi
−0.00397430 + 0.999992i 0.501265π0.501265\pi
228228 0 0
229229 −13.8077 −0.912438 −0.456219 0.889868i 0.650797π-0.650797\pi
−0.456219 + 0.889868i 0.650797π0.650797\pi
230230 0 0
231231 0 0
232232 0 0
233233 20.4113 1.33719 0.668593 0.743629i 0.266897π-0.266897\pi
0.668593 + 0.743629i 0.266897π0.266897\pi
234234 0 0
235235 0.587642 0.0383335
236236 0 0
237237 −6.44295 −0.418515
238238 0 0
239239 3.06182 0.198053 0.0990263 0.995085i 0.468427π-0.468427\pi
0.0990263 + 0.995085i 0.468427π0.468427\pi
240240 0 0
241241 −26.1291 −1.68313 −0.841563 0.540159i 0.818364π-0.818364\pi
−0.841563 + 0.540159i 0.818364π0.818364\pi
242242 0 0
243243 −16.7608 −1.07520
244244 0 0
245245 0 0
246246 0 0
247247 −4.04970 −0.257676
248248 0 0
249249 40.9156 2.59292
250250 0 0
251251 −17.5062 −1.10498 −0.552490 0.833520i 0.686322π-0.686322\pi
−0.552490 + 0.833520i 0.686322π0.686322\pi
252252 0 0
253253 29.5806 1.85972
254254 0 0
255255 −9.28812 −0.581645
256256 0 0
257257 6.93487 0.432585 0.216293 0.976329i 0.430603π-0.430603\pi
0.216293 + 0.976329i 0.430603π0.430603\pi
258258 0 0
259259 0 0
260260 0 0
261261 −14.9590 −0.925939
262262 0 0
263263 −10.3126 −0.635902 −0.317951 0.948107i 0.602995π-0.602995\pi
−0.317951 + 0.948107i 0.602995π0.602995\pi
264264 0 0
265265 −22.9800 −1.41165
266266 0 0
267267 −10.2129 −0.625021
268268 0 0
269269 20.0185 1.22055 0.610276 0.792189i 0.291059π-0.291059\pi
0.610276 + 0.792189i 0.291059π0.291059\pi
270270 0 0
271271 −5.60895 −0.340719 −0.170360 0.985382i 0.554493π-0.554493\pi
−0.170360 + 0.985382i 0.554493π0.554493\pi
272272 0 0
273273 0 0
274274 0 0
275275 23.3674 1.40911
276276 0 0
277277 −1.10303 −0.0662747 −0.0331374 0.999451i 0.510550π-0.510550\pi
−0.0331374 + 0.999451i 0.510550π0.510550\pi
278278 0 0
279279 −38.6435 −2.31353
280280 0 0
281281 12.5761 0.750229 0.375115 0.926978i 0.377603π-0.377603\pi
0.375115 + 0.926978i 0.377603π0.377603\pi
282282 0 0
283283 −31.9245 −1.89771 −0.948857 0.315706i 0.897759π-0.897759\pi
−0.948857 + 0.315706i 0.897759π0.897759\pi
284284 0 0
285285 8.57690 0.508052
286286 0 0
287287 0 0
288288 0 0
289289 −15.8273 −0.931016
290290 0 0
291291 45.1890 2.64903
292292 0 0
293293 −0.574159 −0.0335428 −0.0167714 0.999859i 0.505339π-0.505339\pi
−0.0167714 + 0.999859i 0.505339π0.505339\pi
294294 0 0
295295 −40.8746 −2.37981
296296 0 0
297297 24.7266 1.43478
298298 0 0
299299 23.1982 1.34158
300300 0 0
301301 0 0
302302 0 0
303303 −20.2520 −1.16344
304304 0 0
305305 −28.8596 −1.65250
306306 0 0
307307 7.42536 0.423788 0.211894 0.977293i 0.432037π-0.432037\pi
0.211894 + 0.977293i 0.432037π0.432037\pi
308308 0 0
309309 −45.2636 −2.57496
310310 0 0
311311 −32.8935 −1.86522 −0.932610 0.360887i 0.882474π-0.882474\pi
−0.932610 + 0.360887i 0.882474π0.882474\pi
312312 0 0
313313 −19.4604 −1.09997 −0.549985 0.835175i 0.685366π-0.685366\pi
−0.549985 + 0.835175i 0.685366π0.685366\pi
314314 0 0
315315 0 0
316316 0 0
317317 −11.4794 −0.644749 −0.322375 0.946612i 0.604481π-0.604481\pi
−0.322375 + 0.946612i 0.604481π0.604481\pi
318318 0 0
319319 −16.3553 −0.915719
320320 0 0
321321 −12.6897 −0.708272
322322 0 0
323323 −1.08292 −0.0602554
324324 0 0
325325 18.3255 1.01652
326326 0 0
327327 37.7080 2.08526
328328 0 0
329329 0 0
330330 0 0
331331 16.5371 0.908963 0.454481 0.890756i 0.349825π-0.349825\pi
0.454481 + 0.890756i 0.349825π0.349825\pi
332332 0 0
333333 −20.7698 −1.13818
334334 0 0
335335 −25.2021 −1.37694
336336 0 0
337337 −11.7147 −0.638139 −0.319069 0.947731i 0.603370π-0.603370\pi
−0.319069 + 0.947731i 0.603370π0.603370\pi
338338 0 0
339339 −6.02612 −0.327294
340340 0 0
341341 −42.2504 −2.28799
342342 0 0
343343 0 0
344344 0 0
345345 −49.1316 −2.64516
346346 0 0
347347 −32.6556 −1.75304 −0.876522 0.481361i 0.840143π-0.840143\pi
−0.876522 + 0.481361i 0.840143π0.840143\pi
348348 0 0
349349 −12.9112 −0.691123 −0.345561 0.938396i 0.612312π-0.612312\pi
−0.345561 + 0.938396i 0.612312π0.612312\pi
350350 0 0
351351 19.3915 1.03504
352352 0 0
353353 8.76458 0.466492 0.233246 0.972418i 0.425065π-0.425065\pi
0.233246 + 0.972418i 0.425065π0.425065\pi
354354 0 0
355355 14.5565 0.772580
356356 0 0
357357 0 0
358358 0 0
359359 22.0423 1.16335 0.581673 0.813423i 0.302398π-0.302398\pi
0.581673 + 0.813423i 0.302398π0.302398\pi
360360 0 0
361361 1.00000 0.0526316
362362 0 0
363363 43.5354 2.28502
364364 0 0
365365 −20.0770 −1.05088
366366 0 0
367367 −20.4585 −1.06792 −0.533961 0.845509i 0.679297π-0.679297\pi
−0.533961 + 0.845509i 0.679297π0.679297\pi
368368 0 0
369369 −40.9975 −2.13424
370370 0 0
371371 0 0
372372 0 0
373373 −15.9329 −0.824975 −0.412488 0.910963i 0.635340π-0.635340\pi
−0.412488 + 0.910963i 0.635340π0.635340\pi
374374 0 0
375375 4.07263 0.210310
376376 0 0
377377 −12.8264 −0.660592
378378 0 0
379379 −1.32037 −0.0678227 −0.0339113 0.999425i 0.510796π-0.510796\pi
−0.0339113 + 0.999425i 0.510796π0.510796\pi
380380 0 0
381381 11.8831 0.608791
382382 0 0
383383 −25.3496 −1.29530 −0.647651 0.761937i 0.724248π-0.724248\pi
−0.647651 + 0.761937i 0.724248π0.724248\pi
384384 0 0
385385 0 0
386386 0 0
387387 37.7446 1.91866
388388 0 0
389389 −26.9070 −1.36424 −0.682119 0.731241i 0.738941π-0.738941\pi
−0.682119 + 0.731241i 0.738941π0.738941\pi
390390 0 0
391391 6.20338 0.313718
392392 0 0
393393 −30.5364 −1.54036
394394 0 0
395395 7.15529 0.360022
396396 0 0
397397 −5.96986 −0.299619 −0.149809 0.988715i 0.547866π-0.547866\pi
−0.149809 + 0.988715i 0.547866π0.547866\pi
398398 0 0
399399 0 0
400400 0 0
401401 34.9373 1.74469 0.872344 0.488893i 0.162599π-0.162599\pi
0.872344 + 0.488893i 0.162599π0.162599\pi
402402 0 0
403403 −33.1343 −1.65054
404404 0 0
405405 2.66047 0.132200
406406 0 0
407407 −22.7084 −1.12562
408408 0 0
409409 −4.48194 −0.221618 −0.110809 0.993842i 0.535344π-0.535344\pi
−0.110809 + 0.993842i 0.535344π0.535344\pi
410410 0 0
411411 42.0261 2.07300
412412 0 0
413413 0 0
414414 0 0
415415 −45.4392 −2.23052
416416 0 0
417417 −58.3142 −2.85566
418418 0 0
419419 −0.577870 −0.0282308 −0.0141154 0.999900i 0.504493π-0.504493\pi
−0.0141154 + 0.999900i 0.504493π0.504493\pi
420420 0 0
421421 6.21914 0.303103 0.151551 0.988449i 0.451573π-0.451573\pi
0.151551 + 0.988449i 0.451573π0.451573\pi
422422 0 0
423423 −0.899286 −0.0437248
424424 0 0
425425 4.90040 0.237704
426426 0 0
427427 0 0
428428 0 0
429429 58.1156 2.80585
430430 0 0
431431 33.0876 1.59377 0.796887 0.604128i 0.206478π-0.206478\pi
0.796887 + 0.604128i 0.206478π0.206478\pi
432432 0 0
433433 −7.81123 −0.375384 −0.187692 0.982228i 0.560101π-0.560101\pi
−0.187692 + 0.982228i 0.560101π0.560101\pi
434434 0 0
435435 27.1651 1.30247
436436 0 0
437437 −5.72837 −0.274025
438438 0 0
439439 −29.5411 −1.40992 −0.704960 0.709248i 0.749035π-0.749035\pi
−0.704960 + 0.709248i 0.749035π0.749035\pi
440440 0 0
441441 0 0
442442 0 0
443443 −1.89611 −0.0900871 −0.0450436 0.998985i 0.514343π-0.514343\pi
−0.0450436 + 0.998985i 0.514343π0.514343\pi
444444 0 0
445445 11.3421 0.537666
446446 0 0
447447 −1.16571 −0.0551363
448448 0 0
449449 10.1049 0.476881 0.238441 0.971157i 0.423364π-0.423364\pi
0.238441 + 0.971157i 0.423364π0.423364\pi
450450 0 0
451451 −44.8241 −2.11069
452452 0 0
453453 9.66985 0.454329
454454 0 0
455455 0 0
456456 0 0
457457 −12.0503 −0.563688 −0.281844 0.959460i 0.590946π-0.590946\pi
−0.281844 + 0.959460i 0.590946π0.590946\pi
458458 0 0
459459 5.18545 0.242036
460460 0 0
461461 23.7612 1.10667 0.553335 0.832959i 0.313355π-0.313355\pi
0.553335 + 0.832959i 0.313355π0.313355\pi
462462 0 0
463463 −21.2804 −0.988985 −0.494493 0.869182i 0.664646π-0.664646\pi
−0.494493 + 0.869182i 0.664646π0.664646\pi
464464 0 0
465465 70.1755 3.25431
466466 0 0
467467 −11.5986 −0.536719 −0.268360 0.963319i 0.586482π-0.586482\pi
−0.268360 + 0.963319i 0.586482π0.586482\pi
468468 0 0
469469 0 0
470470 0 0
471471 18.8290 0.867592
472472 0 0
473473 41.2676 1.89749
474474 0 0
475475 −4.52516 −0.207629
476476 0 0
477477 35.1671 1.61019
478478 0 0
479479 11.7538 0.537046 0.268523 0.963273i 0.413464π-0.413464\pi
0.268523 + 0.963273i 0.413464π0.413464\pi
480480 0 0
481481 −17.8088 −0.812010
482482 0 0
483483 0 0
484484 0 0
485485 −50.1851 −2.27879
486486 0 0
487487 23.5092 1.06530 0.532651 0.846335i 0.321196π-0.321196\pi
0.532651 + 0.846335i 0.321196π0.321196\pi
488488 0 0
489489 32.0079 1.44745
490490 0 0
491491 29.3052 1.32252 0.661262 0.750155i 0.270021π-0.270021\pi
0.661262 + 0.750155i 0.270021π0.270021\pi
492492 0 0
493493 −3.42988 −0.154474
494494 0 0
495495 −75.2720 −3.38323
496496 0 0
497497 0 0
498498 0 0
499499 −37.1336 −1.66233 −0.831164 0.556027i 0.812325π-0.812325\pi
−0.831164 + 0.556027i 0.812325π0.812325\pi
500500 0 0
501501 39.9370 1.78426
502502 0 0
503503 31.5636 1.40735 0.703675 0.710522i 0.251541π-0.251541\pi
0.703675 + 0.710522i 0.251541π0.251541\pi
504504 0 0
505505 22.4910 1.00084
506506 0 0
507507 9.44888 0.419639
508508 0 0
509509 3.81890 0.169270 0.0846350 0.996412i 0.473028π-0.473028\pi
0.0846350 + 0.996412i 0.473028π0.473028\pi
510510 0 0
511511 0 0
512512 0 0
513513 −4.78838 −0.211412
514514 0 0
515515 50.2680 2.21507
516516 0 0
517517 −0.983224 −0.0432421
518518 0 0
519519 28.1520 1.23574
520520 0 0
521521 −16.3956 −0.718302 −0.359151 0.933279i 0.616934π-0.616934\pi
−0.359151 + 0.933279i 0.616934π0.616934\pi
522522 0 0
523523 28.0981 1.22864 0.614322 0.789055i 0.289429π-0.289429\pi
0.614322 + 0.789055i 0.289429π0.289429\pi
524524 0 0
525525 0 0
526526 0 0
527527 −8.86039 −0.385965
528528 0 0
529529 9.81419 0.426704
530530 0 0
531531 62.5516 2.71451
532532 0 0
533533 −35.1527 −1.52263
534534 0 0
535535 14.0927 0.609282
536536 0 0
537537 47.8732 2.06588
538538 0 0
539539 0 0
540540 0 0
541541 −32.5542 −1.39961 −0.699807 0.714332i 0.746731π-0.746731\pi
−0.699807 + 0.714332i 0.746731π0.746731\pi
542542 0 0
543543 −20.9905 −0.900787
544544 0 0
545545 −41.8770 −1.79381
546546 0 0
547547 −34.6056 −1.47963 −0.739814 0.672812i 0.765086π-0.765086\pi
−0.739814 + 0.672812i 0.765086π0.765086\pi
548548 0 0
549549 44.1647 1.88491
550550 0 0
551551 3.16724 0.134929
552552 0 0
553553 0 0
554554 0 0
555555 37.7174 1.60101
556556 0 0
557557 18.1093 0.767314 0.383657 0.923476i 0.374665π-0.374665\pi
0.383657 + 0.923476i 0.374665π0.374665\pi
558558 0 0
559559 32.3635 1.36883
560560 0 0
561561 15.5406 0.656125
562562 0 0
563563 17.0718 0.719489 0.359745 0.933051i 0.382864π-0.382864\pi
0.359745 + 0.933051i 0.382864π0.382864\pi
564564 0 0
565565 6.69237 0.281550
566566 0 0
567567 0 0
568568 0 0
569569 9.33801 0.391470 0.195735 0.980657i 0.437291π-0.437291\pi
0.195735 + 0.980657i 0.437291π0.437291\pi
570570 0 0
571571 3.93740 0.164775 0.0823876 0.996600i 0.473745π-0.473745\pi
0.0823876 + 0.996600i 0.473745π0.473745\pi
572572 0 0
573573 −48.3835 −2.02125
574574 0 0
575575 25.9218 1.08101
576576 0 0
577577 −16.4363 −0.684254 −0.342127 0.939654i 0.611147π-0.611147\pi
−0.342127 + 0.939654i 0.611147π0.611147\pi
578578 0 0
579579 −11.9968 −0.498569
580580 0 0
581581 0 0
582582 0 0
583583 38.4495 1.59242
584584 0 0
585585 −59.0310 −2.44063
586586 0 0
587587 31.7915 1.31218 0.656089 0.754684i 0.272210π-0.272210\pi
0.656089 + 0.754684i 0.272210π0.272210\pi
588588 0 0
589589 8.18192 0.337130
590590 0 0
591591 10.0889 0.415001
592592 0 0
593593 −28.8411 −1.18436 −0.592182 0.805805i 0.701733π-0.701733\pi
−0.592182 + 0.805805i 0.701733π0.701733\pi
594594 0 0
595595 0 0
596596 0 0
597597 −51.3256 −2.10062
598598 0 0
599599 −44.0348 −1.79921 −0.899606 0.436703i 0.856146π-0.856146\pi
−0.899606 + 0.436703i 0.856146π0.856146\pi
600600 0 0
601601 −2.40658 −0.0981666 −0.0490833 0.998795i 0.515630π-0.515630\pi
−0.0490833 + 0.998795i 0.515630π0.515630\pi
602602 0 0
603603 38.5676 1.57059
604604 0 0
605605 −48.3487 −1.96565
606606 0 0
607607 −3.13678 −0.127318 −0.0636590 0.997972i 0.520277π-0.520277\pi
−0.0636590 + 0.997972i 0.520277π0.520277\pi
608608 0 0
609609 0 0
610610 0 0
611611 −0.771079 −0.0311945
612612 0 0
613613 −9.28527 −0.375028 −0.187514 0.982262i 0.560043π-0.560043\pi
−0.187514 + 0.982262i 0.560043π0.560043\pi
614614 0 0
615615 74.4502 3.00212
616616 0 0
617617 −16.4951 −0.664067 −0.332034 0.943268i 0.607735π-0.607735\pi
−0.332034 + 0.943268i 0.607735π0.607735\pi
618618 0 0
619619 −11.6429 −0.467969 −0.233984 0.972240i 0.575176π-0.575176\pi
−0.233984 + 0.972240i 0.575176π0.575176\pi
620620 0 0
621621 27.4296 1.10071
622622 0 0
623623 0 0
624624 0 0
625625 −27.1487 −1.08595
626626 0 0
627627 −14.3506 −0.573108
628628 0 0
629629 −4.76221 −0.189882
630630 0 0
631631 −28.3865 −1.13005 −0.565024 0.825075i 0.691133π-0.691133\pi
−0.565024 + 0.825075i 0.691133π0.691133\pi
632632 0 0
633633 −40.2244 −1.59878
634634 0 0
635635 −13.1969 −0.523704
636636 0 0
637637 0 0
638638 0 0
639639 −22.2763 −0.881237
640640 0 0
641641 −5.97591 −0.236034 −0.118017 0.993012i 0.537654π-0.537654\pi
−0.118017 + 0.993012i 0.537654π0.537654\pi
642642 0 0
643643 −1.33053 −0.0524711 −0.0262356 0.999656i 0.508352π-0.508352\pi
−0.0262356 + 0.999656i 0.508352π0.508352\pi
644644 0 0
645645 −68.5430 −2.69888
646646 0 0
647647 5.81167 0.228480 0.114240 0.993453i 0.463557π-0.463557\pi
0.114240 + 0.993453i 0.463557π0.463557\pi
648648 0 0
649649 68.3901 2.68455
650650 0 0
651651 0 0
652652 0 0
653653 33.2035 1.29935 0.649676 0.760211i 0.274905π-0.274905\pi
0.649676 + 0.760211i 0.274905π0.274905\pi
654654 0 0
655655 33.9126 1.32507
656656 0 0
657657 30.7244 1.19867
658658 0 0
659659 15.5795 0.606890 0.303445 0.952849i 0.401863π-0.401863\pi
0.303445 + 0.952849i 0.401863π0.401863\pi
660660 0 0
661661 −20.3700 −0.792299 −0.396150 0.918186i 0.629654π-0.629654\pi
−0.396150 + 0.918186i 0.629654π0.629654\pi
662662 0 0
663663 12.1875 0.473323
664664 0 0
665665 0 0
666666 0 0
667667 −18.1431 −0.702505
668668 0 0
669669 53.0556 2.05125
670670 0 0
671671 48.2870 1.86410
672672 0 0
673673 36.1669 1.39413 0.697065 0.717008i 0.254489π-0.254489\pi
0.697065 + 0.717008i 0.254489π0.254489\pi
674674 0 0
675675 21.6682 0.834010
676676 0 0
677677 −18.8558 −0.724686 −0.362343 0.932045i 0.618023π-0.618023\pi
−0.362343 + 0.932045i 0.618023π0.618023\pi
678678 0 0
679679 0 0
680680 0 0
681681 −0.332811 −0.0127534
682682 0 0
683683 −22.2251 −0.850420 −0.425210 0.905095i 0.639800π-0.639800\pi
−0.425210 + 0.905095i 0.639800π0.639800\pi
684684 0 0
685685 −46.6725 −1.78327
686686 0 0
687687 −38.3720 −1.46398
688688 0 0
689689 30.1535 1.14876
690690 0 0
691691 20.1072 0.764912 0.382456 0.923974i 0.375078π-0.375078\pi
0.382456 + 0.923974i 0.375078π0.375078\pi
692692 0 0
693693 0 0
694694 0 0
695695 64.7614 2.45654
696696 0 0
697697 −9.40012 −0.356055
698698 0 0
699699 56.7236 2.14548
700700 0 0
701701 −0.702956 −0.0265503 −0.0132751 0.999912i 0.504226π-0.504226\pi
−0.0132751 + 0.999912i 0.504226π0.504226\pi
702702 0 0
703703 4.39755 0.165857
704704 0 0
705705 1.63308 0.0615052
706706 0 0
707707 0 0
708708 0 0
709709 −13.7387 −0.515969 −0.257985 0.966149i 0.583058π-0.583058\pi
−0.257985 + 0.966149i 0.583058π0.583058\pi
710710 0 0
711711 −10.9500 −0.410655
712712 0 0
713713 −46.8690 −1.75526
714714 0 0
715715 −64.5409 −2.41369
716716 0 0
717717 8.50890 0.317771
718718 0 0
719719 −3.00236 −0.111969 −0.0559845 0.998432i 0.517830π-0.517830\pi
−0.0559845 + 0.998432i 0.517830π0.517830\pi
720720 0 0
721721 0 0
722722 0 0
723723 −72.6138 −2.70054
724724 0 0
725725 −14.3323 −0.532288
726726 0 0
727727 31.2768 1.15999 0.579997 0.814619i 0.303054π-0.303054\pi
0.579997 + 0.814619i 0.303054π0.303054\pi
728728 0 0
729729 −43.9926 −1.62936
730730 0 0
731731 8.65427 0.320090
732732 0 0
733733 −28.4488 −1.05078 −0.525391 0.850861i 0.676081π-0.676081\pi
−0.525391 + 0.850861i 0.676081π0.676081\pi
734734 0 0
735735 0 0
736736 0 0
737737 42.1674 1.55326
738738 0 0
739739 −32.1040 −1.18096 −0.590482 0.807051i 0.701062π-0.701062\pi
−0.590482 + 0.807051i 0.701062π0.701062\pi
740740 0 0
741741 −11.2543 −0.413435
742742 0 0
743743 −17.2263 −0.631972 −0.315986 0.948764i 0.602335π-0.602335\pi
−0.315986 + 0.948764i 0.602335π0.602335\pi
744744 0 0
745745 1.29459 0.0474302
746746 0 0
747747 69.5370 2.54423
748748 0 0
749749 0 0
750750 0 0
751751 −24.1134 −0.879911 −0.439955 0.898020i 0.645006π-0.645006\pi
−0.439955 + 0.898020i 0.645006π0.645006\pi
752752 0 0
753753 −48.6503 −1.77291
754754 0 0
755755 −10.7390 −0.390831
756756 0 0
757757 −15.4641 −0.562054 −0.281027 0.959700i 0.590675π-0.590675\pi
−0.281027 + 0.959700i 0.590675π0.590675\pi
758758 0 0
759759 82.2055 2.98387
760760 0 0
761761 −12.2374 −0.443604 −0.221802 0.975092i 0.571194π-0.571194\pi
−0.221802 + 0.975092i 0.571194π0.571194\pi
762762 0 0
763763 0 0
764764 0 0
765765 −15.7854 −0.570722
766766 0 0
767767 53.6340 1.93661
768768 0 0
769769 28.4514 1.02598 0.512992 0.858393i 0.328537π-0.328537\pi
0.512992 + 0.858393i 0.328537π0.328537\pi
770770 0 0
771771 19.2723 0.694073
772772 0 0
773773 −1.84646 −0.0664125 −0.0332063 0.999449i 0.510572π-0.510572\pi
−0.0332063 + 0.999449i 0.510572π0.510572\pi
774774 0 0
775775 −37.0245 −1.32996
776776 0 0
777777 0 0
778778 0 0
779779 8.68032 0.311005
780780 0 0
781781 −24.3555 −0.871510
782782 0 0
783783 −15.1660 −0.541988
784784 0 0
785785 −20.9107 −0.746334
786786 0 0
787787 37.5576 1.33878 0.669392 0.742909i 0.266555π-0.266555\pi
0.669392 + 0.742909i 0.266555π0.266555\pi
788788 0 0
789789 −28.6591 −1.02029
790790 0 0
791791 0 0
792792 0 0
793793 37.8684 1.34475
794794 0 0
795795 −63.8623 −2.26496
796796 0 0
797797 23.6411 0.837411 0.418706 0.908122i 0.362484π-0.362484\pi
0.418706 + 0.908122i 0.362484π0.362484\pi
798798 0 0
799799 −0.206193 −0.00729458
800800 0 0
801801 −17.3571 −0.613283
802802 0 0
803803 33.5922 1.18544
804804 0 0
805805 0 0
806806 0 0
807807 55.6322 1.95835
808808 0 0
809809 7.98180 0.280625 0.140313 0.990107i 0.455189π-0.455189\pi
0.140313 + 0.990107i 0.455189π0.455189\pi
810810 0 0
811811 21.7435 0.763517 0.381758 0.924262i 0.375319π-0.375319\pi
0.381758 + 0.924262i 0.375319π0.375319\pi
812812 0 0
813813 −15.5875 −0.546676
814814 0 0
815815 −35.5467 −1.24515
816816 0 0
817817 −7.99159 −0.279590
818818 0 0
819819 0 0
820820 0 0
821821 −29.5062 −1.02977 −0.514886 0.857259i 0.672166π-0.672166\pi
−0.514886 + 0.857259i 0.672166π0.672166\pi
822822 0 0
823823 47.1421 1.64327 0.821635 0.570013i 0.193062π-0.193062\pi
0.821635 + 0.570013i 0.193062π0.193062\pi
824824 0 0
825825 64.9388 2.26088
826826 0 0
827827 9.47543 0.329493 0.164747 0.986336i 0.447319π-0.447319\pi
0.164747 + 0.986336i 0.447319π0.447319\pi
828828 0 0
829829 20.1639 0.700322 0.350161 0.936689i 0.386127π-0.386127\pi
0.350161 + 0.936689i 0.386127π0.386127\pi
830830 0 0
831831 −3.06536 −0.106336
832832 0 0
833833 0 0
834834 0 0
835835 −44.3525 −1.53488
836836 0 0
837837 −39.1782 −1.35420
838838 0 0
839839 −12.0088 −0.414591 −0.207296 0.978278i 0.566466π-0.566466\pi
−0.207296 + 0.978278i 0.566466π0.566466\pi
840840 0 0
841841 −18.9686 −0.654089
842842 0 0
843843 34.9495 1.20373
844844 0 0
845845 −10.4935 −0.360989
846846 0 0
847847 0 0
848848 0 0
849849 −88.7193 −3.04484
850850 0 0
851851 −25.1908 −0.863530
852852 0 0
853853 −11.3292 −0.387904 −0.193952 0.981011i 0.562131π-0.562131\pi
−0.193952 + 0.981011i 0.562131π0.562131\pi
854854 0 0
855855 14.5766 0.498511
856856 0 0
857857 43.5287 1.48691 0.743456 0.668785i 0.233185π-0.233185\pi
0.743456 + 0.668785i 0.233185π0.233185\pi
858858 0 0
859859 46.8152 1.59731 0.798657 0.601786i 0.205544π-0.205544\pi
0.798657 + 0.601786i 0.205544π0.205544\pi
860860 0 0
861861 0 0
862862 0 0
863863 27.4038 0.932835 0.466417 0.884565i 0.345544π-0.345544\pi
0.466417 + 0.884565i 0.345544π0.345544\pi
864864 0 0
865865 −31.2645 −1.06303
866866 0 0
867867 −43.9846 −1.49379
868868 0 0
869869 −11.9720 −0.406122
870870 0 0
871871 33.0692 1.12051
872872 0 0
873873 76.7998 2.59928
874874 0 0
875875 0 0
876876 0 0
877877 −30.4575 −1.02848 −0.514238 0.857648i 0.671925π-0.671925\pi
−0.514238 + 0.857648i 0.671925π0.671925\pi
878878 0 0
879879 −1.59561 −0.0538186
880880 0 0
881881 −48.9723 −1.64992 −0.824960 0.565191i 0.808802π-0.808802\pi
−0.824960 + 0.565191i 0.808802π0.808802\pi
882882 0 0
883883 −39.2534 −1.32098 −0.660490 0.750835i 0.729652π-0.729652\pi
−0.660490 + 0.750835i 0.729652π0.729652\pi
884884 0 0
885885 −113.592 −3.81835
886886 0 0
887887 −43.0844 −1.44663 −0.723316 0.690517i 0.757383π-0.757383\pi
−0.723316 + 0.690517i 0.757383π0.757383\pi
888888 0 0
889889 0 0
890890 0 0
891891 −4.45142 −0.149128
892892 0 0
893893 0.190404 0.00637163
894894 0 0
895895 −53.1661 −1.77715
896896 0 0
897897 64.4685 2.15254
898898 0 0
899899 25.9141 0.864284
900900 0 0
901901 8.06329 0.268627
902902 0 0
903903 0 0
904904 0 0
905905 23.3112 0.774890
906906 0 0
907907 22.0151 0.731000 0.365500 0.930811i 0.380898π-0.380898\pi
0.365500 + 0.930811i 0.380898π0.380898\pi
908908 0 0
909909 −34.4187 −1.14160
910910 0 0
911911 27.6824 0.917158 0.458579 0.888654i 0.348359π-0.348359\pi
0.458579 + 0.888654i 0.348359π0.348359\pi
912912 0 0
913913 76.0275 2.51614
914914 0 0
915915 −80.2019 −2.65139
916916 0 0
917917 0 0
918918 0 0
919919 29.0442 0.958079 0.479040 0.877793i 0.340985π-0.340985\pi
0.479040 + 0.877793i 0.340985π0.340985\pi
920920 0 0
921921 20.6353 0.679957
922922 0 0
923923 −19.1005 −0.628700
924924 0 0
925925 −19.8996 −0.654296
926926 0 0
927927 −76.9266 −2.52660
928928 0 0
929929 −6.20578 −0.203605 −0.101803 0.994805i 0.532461π-0.532461\pi
−0.101803 + 0.994805i 0.532461π0.532461\pi
930930 0 0
931931 0 0
932932 0 0
933933 −91.4122 −2.99270
934934 0 0
935935 −17.2588 −0.564422
936936 0 0
937937 23.4286 0.765380 0.382690 0.923877i 0.374998π-0.374998\pi
0.382690 + 0.923877i 0.374998π0.374998\pi
938938 0 0
939939 −54.0813 −1.76487
940940 0 0
941941 −7.80972 −0.254590 −0.127295 0.991865i 0.540629π-0.540629\pi
−0.127295 + 0.991865i 0.540629π0.540629\pi
942942 0 0
943943 −49.7240 −1.61924
944944 0 0
945945 0 0
946946 0 0
947947 34.9744 1.13652 0.568258 0.822850i 0.307618π-0.307618\pi
0.568258 + 0.822850i 0.307618π0.307618\pi
948948 0 0
949949 26.3442 0.855168
950950 0 0
951951 −31.9018 −1.03449
952952 0 0
953953 22.4430 0.727001 0.363501 0.931594i 0.381581π-0.381581\pi
0.363501 + 0.931594i 0.381581π0.381581\pi
954954 0 0
955955 53.7328 1.73875
956956 0 0
957957 −45.4519 −1.46925
958958 0 0
959959 0 0
960960 0 0
961961 35.9438 1.15948
962962 0 0
963963 −21.5665 −0.694971
964964 0 0
965965 13.3231 0.428887
966966 0 0
967967 −15.1114 −0.485949 −0.242975 0.970033i 0.578123π-0.578123\pi
−0.242975 + 0.970033i 0.578123π0.578123\pi
968968 0 0
969969 −3.00948 −0.0966785
970970 0 0
971971 −6.54519 −0.210045 −0.105023 0.994470i 0.533491π-0.533491\pi
−0.105023 + 0.994470i 0.533491π0.533491\pi
972972 0 0
973973 0 0
974974 0 0
975975 50.9273 1.63098
976976 0 0
977977 −6.11997 −0.195795 −0.0978976 0.995196i 0.531212π-0.531212\pi
−0.0978976 + 0.995196i 0.531212π0.531212\pi
978978 0 0
979979 −18.9772 −0.606514
980980 0 0
981981 64.0856 2.04610
982982 0 0
983983 −20.8829 −0.666061 −0.333031 0.942916i 0.608071π-0.608071\pi
−0.333031 + 0.942916i 0.608071π0.608071\pi
984984 0 0
985985 −11.2043 −0.356999
986986 0 0
987987 0 0
988988 0 0
989989 45.7787 1.45568
990990 0 0
991991 32.4748 1.03159 0.515797 0.856711i 0.327496π-0.327496\pi
0.515797 + 0.856711i 0.327496π0.327496\pi
992992 0 0
993993 45.9573 1.45841
994994 0 0
995995 57.0002 1.80703
996996 0 0
997997 −39.9989 −1.26678 −0.633389 0.773833i 0.718337π-0.718337\pi
−0.633389 + 0.773833i 0.718337π0.718337\pi
998998 0 0
999999 −21.0572 −0.666219
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 3724.2.a.m.1.6 7
7.2 even 3 532.2.i.c.305.2 14
7.4 even 3 532.2.i.c.457.2 yes 14
7.6 odd 2 3724.2.a.n.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
532.2.i.c.305.2 14 7.2 even 3
532.2.i.c.457.2 yes 14 7.4 even 3
3724.2.a.m.1.6 7 1.1 even 1 trivial
3724.2.a.n.1.2 7 7.6 odd 2