Properties

Label 3969.2.a.bf.1.2
Level 39693969
Weight 22
Character 3969.1
Self dual yes
Analytic conductor 31.69331.693
Analytic rank 11
Dimension 88
Inner twists 22

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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] = [3969,2,Mod(1,3969)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3969, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("3969.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 3969=3472 3969 = 3^{4} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3969.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,0,6,0,0,0,0,0,-14,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 31.692624562231.6926245622
Analytic rank: 11
Dimension: 88
Coefficient field: 8.8.114612039936.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x811x6+34x436x2+9 x^{8} - 11x^{6} + 34x^{4} - 36x^{2} + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 3 3
Twist minimal: no (minimal twist has level 567)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.52818-1.52818 of defining polynomial
Character χ\chi == 3969.1

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) == q1.52818q2+0.335323q4+2.82528q5+2.54392q84.31752q103.63715q11+5.62908q134.55820q16+3.20220q174.07088q19+0.947380q20+5.55820q224.70318q23+2.98220q258.60223q264.32626q293.58197q31+1.87790q324.89353q344.31156q37+6.22102q38+7.18728q40+3.15192q419.19325q431.21962q44+7.18728q46+4.84643q474.55733q50+1.88756q5214.1341q5310.2760q55+6.61128q58+1.50098q5913.2051q61+5.47388q62+6.24665q64+15.9037q6512.6822q67+1.07377q68+2.91413q712.92912q73+6.58882q741.36506q76+0.893527q7912.8782q804.81668q82+8.04863q83+9.04711q85+14.0489q869.25262q88+5.65727q891.57708q927.40620q9411.5014q955.13578q97+O(q100)q-1.52818 q^{2} +0.335323 q^{4} +2.82528 q^{5} +2.54392 q^{8} -4.31752 q^{10} -3.63715 q^{11} +5.62908 q^{13} -4.55820 q^{16} +3.20220 q^{17} -4.07088 q^{19} +0.947380 q^{20} +5.55820 q^{22} -4.70318 q^{23} +2.98220 q^{25} -8.60223 q^{26} -4.32626 q^{29} -3.58197 q^{31} +1.87790 q^{32} -4.89353 q^{34} -4.31156 q^{37} +6.22102 q^{38} +7.18728 q^{40} +3.15192 q^{41} -9.19325 q^{43} -1.21962 q^{44} +7.18728 q^{46} +4.84643 q^{47} -4.55733 q^{50} +1.88756 q^{52} -14.1341 q^{53} -10.2760 q^{55} +6.61128 q^{58} +1.50098 q^{59} -13.2051 q^{61} +5.47388 q^{62} +6.24665 q^{64} +15.9037 q^{65} -12.6822 q^{67} +1.07377 q^{68} +2.91413 q^{71} -2.92912 q^{73} +6.58882 q^{74} -1.36506 q^{76} +0.893527 q^{79} -12.8782 q^{80} -4.81668 q^{82} +8.04863 q^{83} +9.04711 q^{85} +14.0489 q^{86} -9.25262 q^{88} +5.65727 q^{89} -1.57708 q^{92} -7.40620 q^{94} -11.5014 q^{95} -5.13578 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+6q414q106q13+6q1624q19+2q2220q314q3736q40+10q4336q4634q524q5522q5836q61+38q6418q6732q73+14q97+O(q100) 8 q + 6 q^{4} - 14 q^{10} - 6 q^{13} + 6 q^{16} - 24 q^{19} + 2 q^{22} - 20 q^{31} - 4 q^{37} - 36 q^{40} + 10 q^{43} - 36 q^{46} - 34 q^{52} - 4 q^{55} - 22 q^{58} - 36 q^{61} + 38 q^{64} - 18 q^{67} - 32 q^{73}+ \cdots - 14 q^{97}+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 −1.52818 −1.08058 −0.540292 0.841478i 0.681686π-0.681686\pi
−0.540292 + 0.841478i 0.681686π0.681686\pi
33 0 0
44 0.335323 0.167661
55 2.82528 1.26350 0.631752 0.775171i 0.282336π-0.282336\pi
0.631752 + 0.775171i 0.282336π0.282336\pi
66 0 0
77 0 0
88 2.54392 0.899412
99 0 0
1010 −4.31752 −1.36532
1111 −3.63715 −1.09664 −0.548321 0.836268i 0.684733π-0.684733\pi
−0.548321 + 0.836268i 0.684733π0.684733\pi
1212 0 0
1313 5.62908 1.56123 0.780613 0.625015i 0.214907π-0.214907\pi
0.780613 + 0.625015i 0.214907π0.214907\pi
1414 0 0
1515 0 0
1616 −4.55820 −1.13955
1717 3.20220 0.776648 0.388324 0.921523i 0.373054π-0.373054\pi
0.388324 + 0.921523i 0.373054π0.373054\pi
1818 0 0
1919 −4.07088 −0.933923 −0.466962 0.884278i 0.654651π-0.654651\pi
−0.466962 + 0.884278i 0.654651π0.654651\pi
2020 0.947380 0.211841
2121 0 0
2222 5.55820 1.18501
2323 −4.70318 −0.980680 −0.490340 0.871531i 0.663127π-0.663127\pi
−0.490340 + 0.871531i 0.663127π0.663127\pi
2424 0 0
2525 2.98220 0.596440
2626 −8.60223 −1.68704
2727 0 0
2828 0 0
2929 −4.32626 −0.803366 −0.401683 0.915779i 0.631575π-0.631575\pi
−0.401683 + 0.915779i 0.631575π0.631575\pi
3030 0 0
3131 −3.58197 −0.643341 −0.321670 0.946852i 0.604244π-0.604244\pi
−0.321670 + 0.946852i 0.604244π0.604244\pi
3232 1.87790 0.331969
3333 0 0
3434 −4.89353 −0.839233
3535 0 0
3636 0 0
3737 −4.31156 −0.708815 −0.354408 0.935091i 0.615318π-0.615318\pi
−0.354408 + 0.935091i 0.615318π0.615318\pi
3838 6.22102 1.00918
3939 0 0
4040 7.18728 1.13641
4141 3.15192 0.492246 0.246123 0.969239i 0.420843π-0.420843\pi
0.246123 + 0.969239i 0.420843π0.420843\pi
4242 0 0
4343 −9.19325 −1.40196 −0.700979 0.713182i 0.747253π-0.747253\pi
−0.700979 + 0.713182i 0.747253π0.747253\pi
4444 −1.21962 −0.183864
4545 0 0
4646 7.18728 1.05971
4747 4.84643 0.706924 0.353462 0.935449i 0.385004π-0.385004\pi
0.353462 + 0.935449i 0.385004π0.385004\pi
4848 0 0
4949 0 0
5050 −4.55733 −0.644504
5151 0 0
5252 1.88756 0.261757
5353 −14.1341 −1.94147 −0.970736 0.240147i 0.922804π-0.922804\pi
−0.970736 + 0.240147i 0.922804π0.922804\pi
5454 0 0
5555 −10.2760 −1.38561
5656 0 0
5757 0 0
5858 6.61128 0.868104
5959 1.50098 0.195411 0.0977053 0.995215i 0.468850π-0.468850\pi
0.0977053 + 0.995215i 0.468850π0.468850\pi
6060 0 0
6161 −13.2051 −1.69074 −0.845369 0.534183i 0.820619π-0.820619\pi
−0.845369 + 0.534183i 0.820619π0.820619\pi
6262 5.47388 0.695184
6363 0 0
6464 6.24665 0.780831
6565 15.9037 1.97261
6666 0 0
6767 −12.6822 −1.54937 −0.774686 0.632346i 0.782092π-0.782092\pi
−0.774686 + 0.632346i 0.782092π0.782092\pi
6868 1.07377 0.130214
6969 0 0
7070 0 0
7171 2.91413 0.345844 0.172922 0.984936i 0.444679π-0.444679\pi
0.172922 + 0.984936i 0.444679π0.444679\pi
7272 0 0
7373 −2.92912 −0.342828 −0.171414 0.985199i 0.554834π-0.554834\pi
−0.171414 + 0.985199i 0.554834π0.554834\pi
7474 6.58882 0.765935
7575 0 0
7676 −1.36506 −0.156583
7777 0 0
7878 0 0
7979 0.893527 0.100530 0.0502648 0.998736i 0.483993π-0.483993\pi
0.0502648 + 0.998736i 0.483993π0.483993\pi
8080 −12.8782 −1.43983
8181 0 0
8282 −4.81668 −0.531914
8383 8.04863 0.883452 0.441726 0.897150i 0.354366π-0.354366\pi
0.441726 + 0.897150i 0.354366π0.354366\pi
8484 0 0
8585 9.04711 0.981297
8686 14.0489 1.51493
8787 0 0
8888 −9.25262 −0.986332
8989 5.65727 0.599669 0.299835 0.953991i 0.403069π-0.403069\pi
0.299835 + 0.953991i 0.403069π0.403069\pi
9090 0 0
9191 0 0
9292 −1.57708 −0.164422
9393 0 0
9494 −7.40620 −0.763891
9595 −11.5014 −1.18001
9696 0 0
9797 −5.13578 −0.521460 −0.260730 0.965412i 0.583963π-0.583963\pi
−0.260730 + 0.965412i 0.583963π0.583963\pi
9898 0 0
9999 0 0
100100 1.00000 0.100000
101101 2.52446 0.251193 0.125597 0.992081i 0.459915π-0.459915\pi
0.125597 + 0.992081i 0.459915π0.459915\pi
102102 0 0
103103 −9.84642 −0.970196 −0.485098 0.874460i 0.661216π-0.661216\pi
−0.485098 + 0.874460i 0.661216π0.661216\pi
104104 14.3199 1.40418
105105 0 0
106106 21.5995 2.09792
107107 −2.70252 −0.261262 −0.130631 0.991431i 0.541700π-0.541700\pi
−0.130631 + 0.991431i 0.541700π0.541700\pi
108108 0 0
109109 −9.05747 −0.867548 −0.433774 0.901022i 0.642818π-0.642818\pi
−0.433774 + 0.901022i 0.642818π0.642818\pi
110110 15.7035 1.49727
111111 0 0
112112 0 0
113113 −0.465776 −0.0438165 −0.0219082 0.999760i 0.506974π-0.506974\pi
−0.0219082 + 0.999760i 0.506974π0.506974\pi
114114 0 0
115115 −13.2878 −1.23909
116116 −1.45069 −0.134693
117117 0 0
118118 −2.29376 −0.211158
119119 0 0
120120 0 0
121121 2.22885 0.202623
122122 20.1797 1.82698
123123 0 0
124124 −1.20112 −0.107863
125125 −5.70084 −0.509899
126126 0 0
127127 −15.7574 −1.39825 −0.699123 0.715002i 0.746426π-0.746426\pi
−0.699123 + 0.715002i 0.746426π0.746426\pi
128128 −13.3018 −1.17572
129129 0 0
130130 −24.3037 −2.13157
131131 12.1479 1.06137 0.530685 0.847569i 0.321935π-0.321935\pi
0.530685 + 0.847569i 0.321935π0.321935\pi
132132 0 0
133133 0 0
134134 19.3806 1.67423
135135 0 0
136136 8.14614 0.698526
137137 −2.16337 −0.184829 −0.0924146 0.995721i 0.529459π-0.529459\pi
−0.0924146 + 0.995721i 0.529459π0.529459\pi
138138 0 0
139139 21.4514 1.81949 0.909743 0.415173i 0.136279π-0.136279\pi
0.909743 + 0.415173i 0.136279π0.136279\pi
140140 0 0
141141 0 0
142142 −4.45331 −0.373713
143143 −20.4738 −1.71211
144144 0 0
145145 −12.2229 −1.01506
146146 4.47622 0.370454
147147 0 0
148148 −1.44576 −0.118841
149149 11.0972 0.909121 0.454561 0.890716i 0.349796π-0.349796\pi
0.454561 + 0.890716i 0.349796π0.349796\pi
150150 0 0
151151 2.08710 0.169846 0.0849228 0.996388i 0.472936π-0.472936\pi
0.0849228 + 0.996388i 0.472936π0.472936\pi
152152 −10.3560 −0.839981
153153 0 0
154154 0 0
155155 −10.1201 −0.812863
156156 0 0
157157 21.6154 1.72509 0.862547 0.505978i 0.168868π-0.168868\pi
0.862547 + 0.505978i 0.168868π0.168868\pi
158158 −1.36547 −0.108631
159159 0 0
160160 5.30559 0.419444
161161 0 0
162162 0 0
163163 −9.38243 −0.734889 −0.367444 0.930045i 0.619767π-0.619767\pi
−0.367444 + 0.930045i 0.619767π0.619767\pi
164164 1.05691 0.0825307
165165 0 0
166166 −12.2997 −0.954644
167167 −17.4047 −1.34682 −0.673408 0.739271i 0.735170π-0.735170\pi
−0.673408 + 0.739271i 0.735170π0.735170\pi
168168 0 0
169169 18.6865 1.43743
170170 −13.8256 −1.06037
171171 0 0
172172 −3.08271 −0.235054
173173 21.5476 1.63823 0.819116 0.573628i 0.194465π-0.194465\pi
0.819116 + 0.573628i 0.194465π0.194465\pi
174174 0 0
175175 0 0
176176 16.5789 1.24968
177177 0 0
178178 −8.64530 −0.647993
179179 5.65727 0.422844 0.211422 0.977395i 0.432191π-0.432191\pi
0.211422 + 0.977395i 0.432191π0.432191\pi
180180 0 0
181181 −1.12427 −0.0835664 −0.0417832 0.999127i 0.513304π-0.513304\pi
−0.0417832 + 0.999127i 0.513304π0.513304\pi
182182 0 0
183183 0 0
184184 −11.9645 −0.882035
185185 −12.1813 −0.895591
186186 0 0
187187 −11.6469 −0.851704
188188 1.62512 0.118524
189189 0 0
190190 17.5761 1.27510
191191 3.93900 0.285016 0.142508 0.989794i 0.454483π-0.454483\pi
0.142508 + 0.989794i 0.454483π0.454483\pi
192192 0 0
193193 18.0868 1.30191 0.650957 0.759114i 0.274368π-0.274368\pi
0.650957 + 0.759114i 0.274368π0.274368\pi
194194 7.84838 0.563481
195195 0 0
196196 0 0
197197 25.4842 1.81567 0.907836 0.419326i 0.137734π-0.137734\pi
0.907836 + 0.419326i 0.137734π0.137734\pi
198198 0 0
199199 −12.6291 −0.895252 −0.447626 0.894221i 0.647730π-0.647730\pi
−0.447626 + 0.894221i 0.647730π0.647730\pi
200200 7.58648 0.536445
201201 0 0
202202 −3.85782 −0.271436
203203 0 0
204204 0 0
205205 8.90504 0.621955
206206 15.0471 1.04838
207207 0 0
208208 −25.6585 −1.77910
209209 14.8064 1.02418
210210 0 0
211211 2.31156 0.159134 0.0795670 0.996830i 0.474646π-0.474646\pi
0.0795670 + 0.996830i 0.474646π0.474646\pi
212212 −4.73950 −0.325510
213213 0 0
214214 4.12992 0.282316
215215 −25.9735 −1.77138
216216 0 0
217217 0 0
218218 13.8414 0.937458
219219 0 0
220220 −3.44576 −0.232313
221221 18.0254 1.21252
222222 0 0
223223 −9.29962 −0.622749 −0.311374 0.950287i 0.600789π-0.600789\pi
−0.311374 + 0.950287i 0.600789π0.600789\pi
224224 0 0
225225 0 0
226226 0.711787 0.0473474
227227 1.92818 0.127978 0.0639890 0.997951i 0.479618π-0.479618\pi
0.0639890 + 0.997951i 0.479618π0.479618\pi
228228 0 0
229229 −3.34118 −0.220792 −0.110396 0.993888i 0.535212π-0.535212\pi
−0.110396 + 0.993888i 0.535212π0.535212\pi
230230 20.3061 1.33894
231231 0 0
232232 −11.0057 −0.722556
233233 21.1515 1.38568 0.692842 0.721090i 0.256358π-0.256358\pi
0.692842 + 0.721090i 0.256358π0.256358\pi
234234 0 0
235235 13.6925 0.893201
236236 0.503312 0.0327628
237237 0 0
238238 0 0
239239 −24.1151 −1.55987 −0.779937 0.625858i 0.784749π-0.784749\pi
−0.779937 + 0.625858i 0.784749π0.784749\pi
240240 0 0
241241 −9.23439 −0.594840 −0.297420 0.954747i 0.596126π-0.596126\pi
−0.297420 + 0.954747i 0.596126π0.596126\pi
242242 −3.40608 −0.218951
243243 0 0
244244 −4.42796 −0.283471
245245 0 0
246246 0 0
247247 −22.9153 −1.45807
248248 −9.11225 −0.578628
249249 0 0
250250 8.71189 0.550989
251251 18.5790 1.17270 0.586349 0.810058i 0.300565π-0.300565\pi
0.586349 + 0.810058i 0.300565π0.300565\pi
252252 0 0
253253 17.1062 1.07545
254254 24.0801 1.51092
255255 0 0
256256 7.83416 0.489635
257257 −10.2197 −0.637490 −0.318745 0.947841i 0.603261π-0.603261\pi
−0.318745 + 0.947841i 0.603261π0.603261\pi
258258 0 0
259259 0 0
260260 5.33288 0.330731
261261 0 0
262262 −18.5642 −1.14690
263263 −9.13775 −0.563458 −0.281729 0.959494i 0.590908π-0.590908\pi
−0.281729 + 0.959494i 0.590908π0.590908\pi
264264 0 0
265265 −39.9329 −2.45306
266266 0 0
267267 0 0
268268 −4.25262 −0.259770
269269 −22.9213 −1.39753 −0.698767 0.715349i 0.746268π-0.746268\pi
−0.698767 + 0.715349i 0.746268π0.746268\pi
270270 0 0
271271 9.31563 0.565884 0.282942 0.959137i 0.408690π-0.408690\pi
0.282942 + 0.959137i 0.408690π0.408690\pi
272272 −14.5963 −0.885030
273273 0 0
274274 3.30601 0.199723
275275 −10.8467 −0.654081
276276 0 0
277277 0.183318 0.0110145 0.00550725 0.999985i 0.498247π-0.498247\pi
0.00550725 + 0.999985i 0.498247π0.498247\pi
278278 −32.7815 −1.96611
279279 0 0
280280 0 0
281281 −16.2019 −0.966527 −0.483263 0.875475i 0.660549π-0.660549\pi
−0.483263 + 0.875475i 0.660549π0.660549\pi
282282 0 0
283283 −20.6984 −1.23039 −0.615195 0.788375i 0.710923π-0.710923\pi
−0.615195 + 0.788375i 0.710923π0.710923\pi
284284 0.977175 0.0579847
285285 0 0
286286 31.2876 1.85007
287287 0 0
288288 0 0
289289 −6.74591 −0.396818
290290 18.6787 1.09685
291291 0 0
292292 −0.982202 −0.0574790
293293 −16.0234 −0.936097 −0.468049 0.883703i 0.655043π-0.655043\pi
−0.468049 + 0.883703i 0.655043π0.655043\pi
294294 0 0
295295 4.24068 0.246902
296296 −10.9683 −0.637517
297297 0 0
298298 −16.9585 −0.982382
299299 −26.4746 −1.53106
300300 0 0
301301 0 0
302302 −3.18945 −0.183532
303303 0 0
304304 18.5559 1.06425
305305 −37.3080 −2.13625
306306 0 0
307307 5.32307 0.303804 0.151902 0.988396i 0.451460π-0.451460\pi
0.151902 + 0.988396i 0.451460π0.451460\pi
308308 0 0
309309 0 0
310310 15.4652 0.878367
311311 −18.4259 −1.04484 −0.522420 0.852689i 0.674970π-0.674970\pi
−0.522420 + 0.852689i 0.674970π0.674970\pi
312312 0 0
313313 −4.64688 −0.262657 −0.131329 0.991339i 0.541924π-0.541924\pi
−0.131329 + 0.991339i 0.541924π0.541924\pi
314314 −33.0321 −1.86411
315315 0 0
316316 0.299620 0.0168549
317317 −10.4801 −0.588623 −0.294311 0.955710i 0.595090π-0.595090\pi
−0.294311 + 0.955710i 0.595090π0.595090\pi
318318 0 0
319319 15.7352 0.881004
320320 17.6485 0.986582
321321 0 0
322322 0 0
323323 −13.0358 −0.725329
324324 0 0
325325 16.7871 0.931178
326326 14.3380 0.794109
327327 0 0
328328 8.01822 0.442732
329329 0 0
330330 0 0
331331 12.8535 0.706494 0.353247 0.935530i 0.385077π-0.385077\pi
0.353247 + 0.935530i 0.385077π0.385077\pi
332332 2.69889 0.148121
333333 0 0
334334 26.5975 1.45535
335335 −35.8306 −1.95764
336336 0 0
337337 7.29218 0.397230 0.198615 0.980078i 0.436356π-0.436356\pi
0.198615 + 0.980078i 0.436356π0.436356\pi
338338 −28.5563 −1.55326
339339 0 0
340340 3.03370 0.164526
341341 13.0282 0.705514
342342 0 0
343343 0 0
344344 −23.3869 −1.26094
345345 0 0
346346 −32.9285 −1.77025
347347 17.5388 0.941534 0.470767 0.882258i 0.343977π-0.343977\pi
0.470767 + 0.882258i 0.343977π0.343977\pi
348348 0 0
349349 −21.0160 −1.12496 −0.562481 0.826810i 0.690153π-0.690153\pi
−0.562481 + 0.826810i 0.690153π0.690153\pi
350350 0 0
351351 0 0
352352 −6.83020 −0.364051
353353 −5.05338 −0.268965 −0.134482 0.990916i 0.542937π-0.542937\pi
−0.134482 + 0.990916i 0.542937π0.542937\pi
354354 0 0
355355 8.23324 0.436975
356356 1.89701 0.100541
357357 0 0
358358 −8.64530 −0.456918
359359 −14.4761 −0.764020 −0.382010 0.924158i 0.624768π-0.624768\pi
−0.382010 + 0.924158i 0.624768π0.624768\pi
360360 0 0
361361 −2.42796 −0.127788
362362 1.71808 0.0903005
363363 0 0
364364 0 0
365365 −8.27559 −0.433164
366366 0 0
367367 −14.9228 −0.778966 −0.389483 0.921034i 0.627346π-0.627346\pi
−0.389483 + 0.921034i 0.627346π0.627346\pi
368368 21.4380 1.11754
369369 0 0
370370 18.6152 0.967761
371371 0 0
372372 0 0
373373 7.82107 0.404960 0.202480 0.979286i 0.435100π-0.435100\pi
0.202480 + 0.979286i 0.435100π0.435100\pi
374374 17.7985 0.920338
375375 0 0
376376 12.3289 0.635816
377377 −24.3528 −1.25424
378378 0 0
379379 11.6097 0.596350 0.298175 0.954511i 0.403622π-0.403622\pi
0.298175 + 0.954511i 0.403622π0.403622\pi
380380 −3.85667 −0.197843
381381 0 0
382382 −6.01948 −0.307984
383383 −25.0764 −1.28134 −0.640672 0.767814i 0.721344π-0.721344\pi
−0.640672 + 0.767814i 0.721344π0.721344\pi
384384 0 0
385385 0 0
386386 −27.6398 −1.40683
387387 0 0
388388 −1.72215 −0.0874287
389389 23.4993 1.19146 0.595732 0.803184i 0.296862π-0.296862\pi
0.595732 + 0.803184i 0.296862π0.296862\pi
390390 0 0
391391 −15.0605 −0.761643
392392 0 0
393393 0 0
394394 −38.9443 −1.96198
395395 2.52446 0.127020
396396 0 0
397397 19.7234 0.989889 0.494945 0.868924i 0.335188π-0.335188\pi
0.494945 + 0.868924i 0.335188π0.335188\pi
398398 19.2995 0.967395
399399 0 0
400400 −13.5935 −0.679674
401401 14.3797 0.718086 0.359043 0.933321i 0.383103π-0.383103\pi
0.359043 + 0.933321i 0.383103π0.383103\pi
402402 0 0
403403 −20.1632 −1.00440
404404 0.846510 0.0421154
405405 0 0
406406 0 0
407407 15.6818 0.777317
408408 0 0
409409 11.5759 0.572391 0.286196 0.958171i 0.407609π-0.407609\pi
0.286196 + 0.958171i 0.407609π0.407609\pi
410410 −13.6085 −0.672074
411411 0 0
412412 −3.30173 −0.162664
413413 0 0
414414 0 0
415415 22.7396 1.11624
416416 10.5708 0.518278
417417 0 0
418418 −22.6268 −1.10671
419419 −34.1721 −1.66942 −0.834708 0.550693i 0.814364π-0.814364\pi
−0.834708 + 0.550693i 0.814364π0.814364\pi
420420 0 0
421421 −10.2213 −0.498156 −0.249078 0.968483i 0.580128π-0.580128\pi
−0.249078 + 0.968483i 0.580128π0.580128\pi
422422 −3.53247 −0.171958
423423 0 0
424424 −35.9561 −1.74618
425425 9.54961 0.463224
426426 0 0
427427 0 0
428428 −0.906215 −0.0438036
429429 0 0
430430 39.6921 1.91412
431431 −0.0761051 −0.00366585 −0.00183293 0.999998i 0.500583π-0.500583\pi
−0.00183293 + 0.999998i 0.500583π0.500583\pi
432432 0 0
433433 29.2697 1.40661 0.703305 0.710888i 0.251707π-0.251707\pi
0.703305 + 0.710888i 0.251707π0.251707\pi
434434 0 0
435435 0 0
436436 −3.03717 −0.145454
437437 19.1461 0.915880
438438 0 0
439439 4.34526 0.207388 0.103694 0.994609i 0.466934π-0.466934\pi
0.103694 + 0.994609i 0.466934π0.466934\pi
440440 −26.1412 −1.24623
441441 0 0
442442 −27.5461 −1.31023
443443 −20.5544 −0.976567 −0.488284 0.872685i 0.662377π-0.662377\pi
−0.488284 + 0.872685i 0.662377π0.662377\pi
444444 0 0
445445 15.9834 0.757684
446446 14.2115 0.672932
447447 0 0
448448 0 0
449449 −12.4720 −0.588588 −0.294294 0.955715i 0.595085π-0.595085\pi
−0.294294 + 0.955715i 0.595085π0.595085\pi
450450 0 0
451451 −11.4640 −0.539818
452452 −0.156185 −0.00734633
453453 0 0
454454 −2.94661 −0.138291
455455 0 0
456456 0 0
457457 −30.9348 −1.44707 −0.723534 0.690289i 0.757483π-0.757483\pi
−0.723534 + 0.690289i 0.757483π0.757483\pi
458458 5.10592 0.238584
459459 0 0
460460 −4.45570 −0.207748
461461 −8.02281 −0.373660 −0.186830 0.982392i 0.559821π-0.559821\pi
−0.186830 + 0.982392i 0.559821π0.559821\pi
462462 0 0
463463 −16.8223 −0.781800 −0.390900 0.920433i 0.627836π-0.627836\pi
−0.390900 + 0.920433i 0.627836π0.627836\pi
464464 19.7200 0.915476
465465 0 0
466466 −32.3233 −1.49735
467467 −0.960797 −0.0444604 −0.0222302 0.999753i 0.507077π-0.507077\pi
−0.0222302 + 0.999753i 0.507077π0.507077\pi
468468 0 0
469469 0 0
470470 −20.9246 −0.965179
471471 0 0
472472 3.81837 0.175755
473473 33.4372 1.53745
474474 0 0
475475 −12.1402 −0.557029
476476 0 0
477477 0 0
478478 36.8521 1.68557
479479 −24.1290 −1.10248 −0.551242 0.834346i 0.685846π-0.685846\pi
−0.551242 + 0.834346i 0.685846π0.685846\pi
480480 0 0
481481 −24.2701 −1.10662
482482 14.1118 0.642774
483483 0 0
484484 0.747384 0.0339720
485485 −14.5100 −0.658866
486486 0 0
487487 14.7989 0.670601 0.335301 0.942111i 0.391162π-0.391162\pi
0.335301 + 0.942111i 0.391162π0.391162\pi
488488 −33.5927 −1.52067
489489 0 0
490490 0 0
491491 6.30383 0.284488 0.142244 0.989832i 0.454568π-0.454568\pi
0.142244 + 0.989832i 0.454568π0.454568\pi
492492 0 0
493493 −13.8535 −0.623932
494494 35.0186 1.57556
495495 0 0
496496 16.3274 0.733120
497497 0 0
498498 0 0
499499 −28.5971 −1.28018 −0.640092 0.768298i 0.721104π-0.721104\pi
−0.640092 + 0.768298i 0.721104π0.721104\pi
500500 −1.91162 −0.0854903
501501 0 0
502502 −28.3921 −1.26720
503503 35.4133 1.57900 0.789500 0.613750i 0.210340π-0.210340\pi
0.789500 + 0.613750i 0.210340π0.210340\pi
504504 0 0
505505 7.13231 0.317384
506506 −26.1412 −1.16212
507507 0 0
508508 −5.28382 −0.234432
509509 −32.4883 −1.44002 −0.720010 0.693964i 0.755863π-0.755863\pi
−0.720010 + 0.693964i 0.755863π0.755863\pi
510510 0 0
511511 0 0
512512 14.6316 0.646630
513513 0 0
514514 15.6176 0.688861
515515 −27.8189 −1.22585
516516 0 0
517517 −17.6272 −0.775243
518518 0 0
519519 0 0
520520 40.4578 1.77419
521521 32.9818 1.44496 0.722479 0.691393i 0.243003π-0.243003\pi
0.722479 + 0.691393i 0.243003π0.243003\pi
522522 0 0
523523 −14.2627 −0.623662 −0.311831 0.950138i 0.600942π-0.600942\pi
−0.311831 + 0.950138i 0.600942π0.600942\pi
524524 4.07348 0.177951
525525 0 0
526526 13.9641 0.608863
527527 −11.4702 −0.499649
528528 0 0
529529 −0.880118 −0.0382660
530530 61.0245 2.65073
531531 0 0
532532 0 0
533533 17.7424 0.768508
534534 0 0
535535 −7.63537 −0.330106
536536 −32.2624 −1.39352
537537 0 0
538538 35.0277 1.51015
539539 0 0
540540 0 0
541541 −15.9821 −0.687124 −0.343562 0.939130i 0.611634π-0.611634\pi
−0.343562 + 0.939130i 0.611634π0.611634\pi
542542 −14.2359 −0.611485
543543 0 0
544544 6.01341 0.257823
545545 −25.5899 −1.09615
546546 0 0
547547 −32.0570 −1.37066 −0.685330 0.728233i 0.740342π-0.740342\pi
−0.685330 + 0.728233i 0.740342π0.740342\pi
548548 −0.725427 −0.0309887
549549 0 0
550550 16.5757 0.706790
551551 17.6117 0.750282
552552 0 0
553553 0 0
554554 −0.280142 −0.0119021
555555 0 0
556556 7.19315 0.305057
557557 39.2947 1.66497 0.832486 0.554046i 0.186917π-0.186917\pi
0.832486 + 0.554046i 0.186917π0.186917\pi
558558 0 0
559559 −51.7496 −2.18877
560560 0 0
561561 0 0
562562 24.7594 1.04441
563563 34.5063 1.45427 0.727134 0.686495i 0.240852π-0.240852\pi
0.727134 + 0.686495i 0.240852π0.240852\pi
564564 0 0
565565 −1.31595 −0.0553623
566566 31.6308 1.32954
567567 0 0
568568 7.41332 0.311056
569569 4.28406 0.179597 0.0897985 0.995960i 0.471378π-0.471378\pi
0.0897985 + 0.995960i 0.471378π0.471378\pi
570570 0 0
571571 25.1596 1.05289 0.526447 0.850208i 0.323524π-0.323524\pi
0.526447 + 0.850208i 0.323524π0.323524\pi
572572 −6.86533 −0.287054
573573 0 0
574574 0 0
575575 −14.0258 −0.584917
576576 0 0
577577 44.2563 1.84241 0.921206 0.389075i 0.127205π-0.127205\pi
0.921206 + 0.389075i 0.127205π0.127205\pi
578578 10.3089 0.428795
579579 0 0
580580 −4.09861 −0.170186
581581 0 0
582582 0 0
583583 51.4080 2.12910
584584 −7.45146 −0.308343
585585 0 0
586586 24.4866 1.01153
587587 −13.0046 −0.536757 −0.268378 0.963314i 0.586488π-0.586488\pi
−0.268378 + 0.963314i 0.586488π0.586488\pi
588588 0 0
589589 14.5818 0.600831
590590 −6.48051 −0.266798
591591 0 0
592592 19.6530 0.807731
593593 −28.2328 −1.15938 −0.579691 0.814837i 0.696827π-0.696827\pi
−0.579691 + 0.814837i 0.696827π0.696827\pi
594594 0 0
595595 0 0
596596 3.72116 0.152425
597597 0 0
598598 40.4578 1.65444
599599 −4.99536 −0.204105 −0.102052 0.994779i 0.532541π-0.532541\pi
−0.102052 + 0.994779i 0.532541π0.532541\pi
600600 0 0
601601 −8.15787 −0.332766 −0.166383 0.986061i 0.553209π-0.553209\pi
−0.166383 + 0.986061i 0.553209π0.553209\pi
602602 0 0
603603 0 0
604604 0.699851 0.0284765
605605 6.29712 0.256014
606606 0 0
607607 −16.7277 −0.678956 −0.339478 0.940614i 0.610250π-0.610250\pi
−0.339478 + 0.940614i 0.610250π0.610250\pi
608608 −7.64469 −0.310033
609609 0 0
610610 57.0133 2.30840
611611 27.2809 1.10367
612612 0 0
613613 −16.5876 −0.669968 −0.334984 0.942224i 0.608731π-0.608731\pi
−0.334984 + 0.942224i 0.608731π0.608731\pi
614614 −8.13459 −0.328285
615615 0 0
616616 0 0
617617 −23.7085 −0.954470 −0.477235 0.878776i 0.658361π-0.658361\pi
−0.477235 + 0.878776i 0.658361π0.658361\pi
618618 0 0
619619 7.82412 0.314478 0.157239 0.987561i 0.449741π-0.449741\pi
0.157239 + 0.987561i 0.449741π0.449741\pi
620620 −3.39349 −0.136286
621621 0 0
622622 28.1581 1.12904
623623 0 0
624624 0 0
625625 −31.0175 −1.24070
626626 7.10125 0.283823
627627 0 0
628628 7.24812 0.289231
629629 −13.8065 −0.550500
630630 0 0
631631 −2.54669 −0.101382 −0.0506911 0.998714i 0.516142π-0.516142\pi
−0.0506911 + 0.998714i 0.516142π0.516142\pi
632632 2.27306 0.0904175
633633 0 0
634634 16.0155 0.636056
635635 −44.5191 −1.76669
636636 0 0
637637 0 0
638638 −24.0462 −0.951999
639639 0 0
640640 −37.5812 −1.48553
641641 10.2854 0.406248 0.203124 0.979153i 0.434891π-0.434891\pi
0.203124 + 0.979153i 0.434891π0.434891\pi
642642 0 0
643643 4.92126 0.194076 0.0970378 0.995281i 0.469063π-0.469063\pi
0.0970378 + 0.995281i 0.469063π0.469063\pi
644644 0 0
645645 0 0
646646 19.9209 0.783779
647647 −8.78336 −0.345310 −0.172655 0.984982i 0.555235π-0.555235\pi
−0.172655 + 0.984982i 0.555235π0.555235\pi
648648 0 0
649649 −5.45928 −0.214295
650650 −25.6536 −1.00622
651651 0 0
652652 −3.14614 −0.123212
653653 1.77459 0.0694453 0.0347226 0.999397i 0.488945π-0.488945\pi
0.0347226 + 0.999397i 0.488945π0.488945\pi
654654 0 0
655655 34.3213 1.34104
656656 −14.3671 −0.560940
657657 0 0
658658 0 0
659659 2.34367 0.0912966 0.0456483 0.998958i 0.485465π-0.485465\pi
0.0456483 + 0.998958i 0.485465π0.485465\pi
660660 0 0
661661 22.9094 0.891074 0.445537 0.895264i 0.353013π-0.353013\pi
0.445537 + 0.895264i 0.353013π0.353013\pi
662662 −19.6425 −0.763426
663663 0 0
664664 20.4751 0.794587
665665 0 0
666666 0 0
667667 20.3472 0.787845
668668 −5.83619 −0.225809
669669 0 0
670670 54.7555 2.11539
671671 48.0288 1.85413
672672 0 0
673673 −29.7349 −1.14620 −0.573098 0.819487i 0.694259π-0.694259\pi
−0.573098 + 0.819487i 0.694259π0.694259\pi
674674 −11.1437 −0.429241
675675 0 0
676676 6.26602 0.241001
677677 −25.4960 −0.979891 −0.489946 0.871753i 0.662983π-0.662983\pi
−0.489946 + 0.871753i 0.662983π0.662983\pi
678678 0 0
679679 0 0
680680 23.0151 0.882590
681681 0 0
682682 −19.9093 −0.762367
683683 11.3859 0.435668 0.217834 0.975986i 0.430101π-0.430101\pi
0.217834 + 0.975986i 0.430101π0.430101\pi
684684 0 0
685685 −6.11212 −0.233532
686686 0 0
687687 0 0
688688 41.9047 1.59760
689689 −79.5622 −3.03108
690690 0 0
691691 32.2523 1.22694 0.613468 0.789720i 0.289774π-0.289774\pi
0.613468 + 0.789720i 0.289774π0.289774\pi
692692 7.22539 0.274668
693693 0 0
694694 −26.8024 −1.01741
695695 60.6062 2.29893
696696 0 0
697697 10.0931 0.382302
698698 32.1162 1.21561
699699 0 0
700700 0 0
701701 15.6291 0.590302 0.295151 0.955451i 0.404630π-0.404630\pi
0.295151 + 0.955451i 0.404630π0.404630\pi
702702 0 0
703703 17.5518 0.661979
704704 −22.7200 −0.856292
705705 0 0
706706 7.72246 0.290639
707707 0 0
708708 0 0
709709 −11.8165 −0.443777 −0.221888 0.975072i 0.571222π-0.571222\pi
−0.221888 + 0.975072i 0.571222π0.571222\pi
710710 −12.5818 −0.472188
711711 0 0
712712 14.3916 0.539349
713713 16.8466 0.630912
714714 0 0
715715 −57.8442 −2.16325
716716 1.89701 0.0708946
717717 0 0
718718 22.1221 0.825588
719719 50.7233 1.89166 0.945830 0.324664i 0.105251π-0.105251\pi
0.945830 + 0.324664i 0.105251π0.105251\pi
720720 0 0
721721 0 0
722722 3.71036 0.138085
723723 0 0
724724 −0.376994 −0.0140109
725725 −12.9018 −0.479160
726726 0 0
727727 −2.26602 −0.0840422 −0.0420211 0.999117i 0.513380π-0.513380\pi
−0.0420211 + 0.999117i 0.513380π0.513380\pi
728728 0 0
729729 0 0
730730 12.6466 0.468070
731731 −29.4386 −1.08883
732732 0 0
733733 33.6524 1.24298 0.621490 0.783422i 0.286528π-0.286528\pi
0.621490 + 0.783422i 0.286528π0.286528\pi
734734 22.8047 0.841738
735735 0 0
736736 −8.83209 −0.325555
737737 46.1269 1.69911
738738 0 0
739739 19.6037 0.721135 0.360568 0.932733i 0.382583π-0.382583\pi
0.360568 + 0.932733i 0.382583π0.382583\pi
740740 −4.08468 −0.150156
741741 0 0
742742 0 0
743743 48.8390 1.79173 0.895865 0.444327i 0.146557π-0.146557\pi
0.895865 + 0.444327i 0.146557π0.146557\pi
744744 0 0
745745 31.3528 1.14868
746746 −11.9520 −0.437593
747747 0 0
748748 −3.90546 −0.142798
749749 0 0
750750 0 0
751751 15.8254 0.577476 0.288738 0.957408i 0.406764π-0.406764\pi
0.288738 + 0.957408i 0.406764π0.406764\pi
752752 −22.0910 −0.805576
753753 0 0
754754 37.2154 1.35531
755755 5.89663 0.214600
756756 0 0
757757 −2.18728 −0.0794982 −0.0397491 0.999210i 0.512656π-0.512656\pi
−0.0397491 + 0.999210i 0.512656π0.512656\pi
758758 −17.7417 −0.644407
759759 0 0
760760 −29.2585 −1.06132
761761 27.7562 1.00616 0.503081 0.864240i 0.332200π-0.332200\pi
0.503081 + 0.864240i 0.332200π0.332200\pi
762762 0 0
763763 0 0
764764 1.32084 0.0477861
765765 0 0
766766 38.3212 1.38460
767767 8.44912 0.305080
768768 0 0
769769 −10.0206 −0.361352 −0.180676 0.983543i 0.557829π-0.557829\pi
−0.180676 + 0.983543i 0.557829π0.557829\pi
770770 0 0
771771 0 0
772772 6.06491 0.218281
773773 43.5192 1.56528 0.782639 0.622476i 0.213873π-0.213873\pi
0.782639 + 0.622476i 0.213873π0.213873\pi
774774 0 0
775775 −10.6822 −0.383714
776776 −13.0650 −0.469007
777777 0 0
778778 −35.9111 −1.28748
779779 −12.8311 −0.459720
780780 0 0
781781 −10.5991 −0.379267
782782 23.0151 0.823019
783783 0 0
784784 0 0
785785 61.0694 2.17966
786786 0 0
787787 5.83638 0.208044 0.104022 0.994575i 0.466829π-0.466829\pi
0.104022 + 0.994575i 0.466829π0.466829\pi
788788 8.54542 0.304418
789789 0 0
790790 −3.85782 −0.137255
791791 0 0
792792 0 0
793793 −74.3325 −2.63962
794794 −30.1408 −1.06966
795795 0 0
796796 −4.23482 −0.150099
797797 −36.5800 −1.29573 −0.647865 0.761755i 0.724338π-0.724338\pi
−0.647865 + 0.761755i 0.724338π0.724338\pi
798798 0 0
799799 15.5192 0.549031
800800 5.60027 0.198000
801801 0 0
802802 −21.9747 −0.775952
803803 10.6537 0.375959
804804 0 0
805805 0 0
806806 30.8129 1.08534
807807 0 0
808808 6.42203 0.225926
809809 −22.0499 −0.775232 −0.387616 0.921821i 0.626701π-0.626701\pi
−0.387616 + 0.921821i 0.626701π0.626701\pi
810810 0 0
811811 12.6451 0.444029 0.222015 0.975043i 0.428737π-0.428737\pi
0.222015 + 0.975043i 0.428737π0.428737\pi
812812 0 0
813813 0 0
814814 −23.9645 −0.839956
815815 −26.5080 −0.928534
816816 0 0
817817 37.4246 1.30932
818818 −17.6900 −0.618517
819819 0 0
820820 2.98606 0.104278
821821 −31.0958 −1.08525 −0.542625 0.839975i 0.682570π-0.682570\pi
−0.542625 + 0.839975i 0.682570π0.682570\pi
822822 0 0
823823 −48.9638 −1.70677 −0.853385 0.521281i 0.825454π-0.825454\pi
−0.853385 + 0.521281i 0.825454π0.825454\pi
824824 −25.0485 −0.872606
825825 0 0
826826 0 0
827827 −36.3827 −1.26515 −0.632575 0.774499i 0.718002π-0.718002\pi
−0.632575 + 0.774499i 0.718002π0.718002\pi
828828 0 0
829829 −45.7405 −1.58863 −0.794316 0.607505i 0.792171π-0.792171\pi
−0.794316 + 0.607505i 0.792171π0.792171\pi
830830 −34.7502 −1.20620
831831 0 0
832832 35.1629 1.21905
833833 0 0
834834 0 0
835835 −49.1731 −1.70171
836836 4.96492 0.171715
837837 0 0
838838 52.2210 1.80394
839839 25.5348 0.881559 0.440779 0.897615i 0.354702π-0.354702\pi
0.440779 + 0.897615i 0.354702π0.354702\pi
840840 0 0
841841 −10.2835 −0.354604
842842 15.6200 0.538299
843843 0 0
844844 0.775117 0.0266806
845845 52.7947 1.81619
846846 0 0
847847 0 0
848848 64.4263 2.21241
849849 0 0
850850 −14.5935 −0.500552
851851 20.2780 0.695121
852852 0 0
853853 1.84673 0.0632310 0.0316155 0.999500i 0.489935π-0.489935\pi
0.0316155 + 0.999500i 0.489935π0.489935\pi
854854 0 0
855855 0 0
856856 −6.87499 −0.234982
857857 22.4848 0.768066 0.384033 0.923319i 0.374535π-0.374535\pi
0.384033 + 0.923319i 0.374535π0.374535\pi
858858 0 0
859859 1.14761 0.0391561 0.0195781 0.999808i 0.493768π-0.493768\pi
0.0195781 + 0.999808i 0.493768π0.493768\pi
860860 −8.70951 −0.296992
861861 0 0
862862 0.116302 0.00396126
863863 1.79527 0.0611117 0.0305558 0.999533i 0.490272π-0.490272\pi
0.0305558 + 0.999533i 0.490272π0.490272\pi
864864 0 0
865865 60.8779 2.06991
866866 −44.7292 −1.51996
867867 0 0
868868 0 0
869869 −3.24989 −0.110245
870870 0 0
871871 −71.3889 −2.41892
872872 −23.0415 −0.780283
873873 0 0
874874 −29.2585 −0.989685
875875 0 0
876876 0 0
877877 8.57997 0.289725 0.144862 0.989452i 0.453726π-0.453726\pi
0.144862 + 0.989452i 0.453726π0.453726\pi
878878 −6.64032 −0.224100
879879 0 0
880880 46.8399 1.57897
881881 16.5346 0.557066 0.278533 0.960427i 0.410152π-0.410152\pi
0.278533 + 0.960427i 0.410152π0.410152\pi
882882 0 0
883883 −27.4948 −0.925273 −0.462636 0.886548i 0.653096π-0.653096\pi
−0.462636 + 0.886548i 0.653096π0.653096\pi
884884 6.04434 0.203293
885885 0 0
886886 31.4107 1.05526
887887 43.4419 1.45864 0.729318 0.684175i 0.239837π-0.239837\pi
0.729318 + 0.684175i 0.239837π0.239837\pi
888888 0 0
889889 0 0
890890 −24.4254 −0.818741
891891 0 0
892892 −3.11837 −0.104411
893893 −19.7292 −0.660213
894894 0 0
895895 15.9834 0.534265
896896 0 0
897897 0 0
898898 19.0594 0.636019
899899 15.4965 0.516838
900900 0 0
901901 −45.2603 −1.50784
902902 17.5190 0.583319
903903 0 0
904904 −1.18490 −0.0394091
905905 −3.17638 −0.105586
906906 0 0
907907 11.2952 0.375052 0.187526 0.982260i 0.439953π-0.439953\pi
0.187526 + 0.982260i 0.439953π0.439953\pi
908908 0.646564 0.0214570
909909 0 0
910910 0 0
911911 10.0338 0.332435 0.166217 0.986089i 0.446845π-0.446845\pi
0.166217 + 0.986089i 0.446845π0.446845\pi
912912 0 0
913913 −29.2741 −0.968830
914914 47.2738 1.56368
915915 0 0
916916 −1.12038 −0.0370182
917917 0 0
918918 0 0
919919 −0.357934 −0.0118072 −0.00590358 0.999983i 0.501879π-0.501879\pi
−0.00590358 + 0.999983i 0.501879π0.501879\pi
920920 −33.8031 −1.11445
921921 0 0
922922 12.2603 0.403770
923923 16.4039 0.539941
924924 0 0
925925 −12.8579 −0.422766
926926 25.7075 0.844801
927927 0 0
928928 −8.12427 −0.266692
929929 −33.5264 −1.09997 −0.549983 0.835176i 0.685366π-0.685366\pi
−0.549983 + 0.835176i 0.685366π0.685366\pi
930930 0 0
931931 0 0
932932 7.09259 0.232326
933933 0 0
934934 1.46827 0.0480432
935935 −32.9057 −1.07613
936936 0 0
937937 −12.8772 −0.420680 −0.210340 0.977628i 0.567457π-0.567457\pi
−0.210340 + 0.977628i 0.567457π0.567457\pi
938938 0 0
939939 0 0
940940 4.59141 0.149755
941941 32.0984 1.04638 0.523189 0.852217i 0.324742π-0.324742\pi
0.523189 + 0.852217i 0.324742π0.324742\pi
942942 0 0
943943 −14.8240 −0.482736
944944 −6.84176 −0.222680
945945 0 0
946946 −51.0980 −1.66134
947947 −16.7986 −0.545880 −0.272940 0.962031i 0.587996π-0.587996\pi
−0.272940 + 0.962031i 0.587996π0.587996\pi
948948 0 0
949949 −16.4883 −0.535232
950950 18.5523 0.601917
951951 0 0
952952 0 0
953953 2.69574 0.0873237 0.0436619 0.999046i 0.486098π-0.486098\pi
0.0436619 + 0.999046i 0.486098π0.486098\pi
954954 0 0
955955 11.1288 0.360118
956956 −8.08633 −0.261531
957957 0 0
958958 36.8734 1.19133
959959 0 0
960960 0 0
961961 −18.1695 −0.586112
962962 37.0890 1.19580
963963 0 0
964964 −3.09650 −0.0997316
965965 51.1002 1.64497
966966 0 0
967967 13.6775 0.439837 0.219919 0.975518i 0.429421π-0.429421\pi
0.219919 + 0.975518i 0.429421π0.429421\pi
968968 5.67002 0.182241
969969 0 0
970970 22.1739 0.711960
971971 42.6266 1.36795 0.683977 0.729504i 0.260249π-0.260249\pi
0.683977 + 0.729504i 0.260249π0.260249\pi
972972 0 0
973973 0 0
974974 −22.6153 −0.724641
975975 0 0
976976 60.1915 1.92668
977977 −5.05683 −0.161782 −0.0808911 0.996723i 0.525777π-0.525777\pi
−0.0808911 + 0.996723i 0.525777π0.525777\pi
978978 0 0
979979 −20.5763 −0.657622
980980 0 0
981981 0 0
982982 −9.63336 −0.307413
983983 33.2884 1.06174 0.530868 0.847455i 0.321866π-0.321866\pi
0.530868 + 0.847455i 0.321866π0.321866\pi
984984 0 0
985985 71.9999 2.29411
986986 21.1707 0.674211
987987 0 0
988988 −7.68402 −0.244461
989989 43.2375 1.37487
990990 0 0
991991 32.0879 1.01931 0.509653 0.860380i 0.329774π-0.329774\pi
0.509653 + 0.860380i 0.329774π0.329774\pi
992992 −6.72658 −0.213569
993993 0 0
994994 0 0
995995 −35.6807 −1.13115
996996 0 0
997997 43.2566 1.36995 0.684975 0.728567i 0.259813π-0.259813\pi
0.684975 + 0.728567i 0.259813π0.259813\pi
998998 43.7015 1.38335
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 3969.2.a.bf.1.2 8
3.2 odd 2 inner 3969.2.a.bf.1.7 8
7.3 odd 6 567.2.e.g.163.7 yes 16
7.5 odd 6 567.2.e.g.487.7 yes 16
7.6 odd 2 3969.2.a.bg.1.2 8
21.5 even 6 567.2.e.g.487.2 yes 16
21.17 even 6 567.2.e.g.163.2 16
21.20 even 2 3969.2.a.bg.1.7 8
63.5 even 6 567.2.h.l.298.7 16
63.31 odd 6 567.2.g.l.541.7 16
63.38 even 6 567.2.h.l.352.7 16
63.40 odd 6 567.2.h.l.298.2 16
63.47 even 6 567.2.g.l.109.2 16
63.52 odd 6 567.2.h.l.352.2 16
63.59 even 6 567.2.g.l.541.2 16
63.61 odd 6 567.2.g.l.109.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
567.2.e.g.163.2 16 21.17 even 6
567.2.e.g.163.7 yes 16 7.3 odd 6
567.2.e.g.487.2 yes 16 21.5 even 6
567.2.e.g.487.7 yes 16 7.5 odd 6
567.2.g.l.109.2 16 63.47 even 6
567.2.g.l.109.7 16 63.61 odd 6
567.2.g.l.541.2 16 63.59 even 6
567.2.g.l.541.7 16 63.31 odd 6
567.2.h.l.298.2 16 63.40 odd 6
567.2.h.l.298.7 16 63.5 even 6
567.2.h.l.352.2 16 63.52 odd 6
567.2.h.l.352.7 16 63.38 even 6
3969.2.a.bf.1.2 8 1.1 even 1 trivial
3969.2.a.bf.1.7 8 3.2 odd 2 inner
3969.2.a.bg.1.2 8 7.6 odd 2
3969.2.a.bg.1.7 8 21.20 even 2