Properties

Label 672.3.m.a.127.3
Level 672672
Weight 33
Character 672.127
Analytic conductor 18.31118.311
Analytic rank 00
Dimension 88
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [672,3,Mod(127,672)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(672, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("672.127");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 672=2537 672 = 2^{5} \cdot 3 \cdot 7
Weight: k k == 3 3
Character orbit: [χ][\chi] == 672.m (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 18.310673765018.3106737650
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.49787136.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+3x6+5x4+12x2+16 x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 212 2^{12}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 127.3
Root 1.094450.895644i1.09445 - 0.895644i of defining polynomial
Character χ\chi == 672.127
Dual form 672.3.m.a.127.7

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) == q1.73205iq3+2.91370q5+2.64575iq73.00000q97.40998iq1124.0934q135.04668iq15+17.2598q1712.9926iq19+4.58258q2132.4315iq2316.5103q25+5.19615iq2738.8341q2937.4320iq3112.8345q33+7.70893iq35+70.3892q37+41.7309iq39+24.9436q4128.3154iq438.74110q45+40.8631iq477.00000q4929.8948iq5189.0084q5321.5905iq5522.5038q5780.7391iq5961.6021q617.93725iq6370.2008q6592.1412iq6756.1731q69+61.5975iq7152.4880q73+28.5968iq75+19.6050q77+91.8555iq79+9.00000q8198.3206iq83+50.2898q85+67.2626iq8767.5476q8963.7450iq9164.8341q9337.8564iq95+41.1094q97+22.2299iq99+O(q100)q-1.73205i q^{3} +2.91370 q^{5} +2.64575i q^{7} -3.00000 q^{9} -7.40998i q^{11} -24.0934 q^{13} -5.04668i q^{15} +17.2598 q^{17} -12.9926i q^{19} +4.58258 q^{21} -32.4315i q^{23} -16.5103 q^{25} +5.19615i q^{27} -38.8341 q^{29} -37.4320i q^{31} -12.8345 q^{33} +7.70893i q^{35} +70.3892 q^{37} +41.7309i q^{39} +24.9436 q^{41} -28.3154i q^{43} -8.74110 q^{45} +40.8631i q^{47} -7.00000 q^{49} -29.8948i q^{51} -89.0084 q^{53} -21.5905i q^{55} -22.5038 q^{57} -80.7391i q^{59} -61.6021 q^{61} -7.93725i q^{63} -70.2008 q^{65} -92.1412i q^{67} -56.1731 q^{69} +61.5975i q^{71} -52.4880 q^{73} +28.5968i q^{75} +19.6050 q^{77} +91.8555i q^{79} +9.00000 q^{81} -98.3206i q^{83} +50.2898 q^{85} +67.2626i q^{87} -67.5476 q^{89} -63.7450i q^{91} -64.8341 q^{93} -37.8564i q^{95} +41.1094 q^{97} +22.2299i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+16q524q964q13+64q1788q25+64q29+48q33+128q3748q4556q49160q53+48q57+32q6132q65144q69112q73+112q77+240q97+O(q100) 8 q + 16 q^{5} - 24 q^{9} - 64 q^{13} + 64 q^{17} - 88 q^{25} + 64 q^{29} + 48 q^{33} + 128 q^{37} - 48 q^{45} - 56 q^{49} - 160 q^{53} + 48 q^{57} + 32 q^{61} - 32 q^{65} - 144 q^{69} - 112 q^{73} + 112 q^{77}+ \cdots - 240 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/672Z)×\left(\mathbb{Z}/672\mathbb{Z}\right)^\times.

nn 127127 421421 449449 577577
χ(n)\chi(n) 1-1 11 11 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 − 1.73205i − 0.577350i
44 0 0
55 2.91370 0.582740 0.291370 0.956610i 0.405889π-0.405889\pi
0.291370 + 0.956610i 0.405889π0.405889\pi
66 0 0
77 2.64575i 0.377964i
88 0 0
99 −3.00000 −0.333333
1010 0 0
1111 − 7.40998i − 0.673634i −0.941570 0.336817i 0.890650π-0.890650\pi
0.941570 0.336817i 0.109350π-0.109350\pi
1212 0 0
1313 −24.0934 −1.85333 −0.926667 0.375882i 0.877340π-0.877340\pi
−0.926667 + 0.375882i 0.877340π0.877340\pi
1414 0 0
1515 − 5.04668i − 0.336445i
1616 0 0
1717 17.2598 1.01528 0.507640 0.861569i 0.330518π-0.330518\pi
0.507640 + 0.861569i 0.330518π0.330518\pi
1818 0 0
1919 − 12.9926i − 0.683819i −0.939733 0.341909i 0.888926π-0.888926\pi
0.939733 0.341909i 0.111074π-0.111074\pi
2020 0 0
2121 4.58258 0.218218
2222 0 0
2323 − 32.4315i − 1.41007i −0.709174 0.705033i 0.750932π-0.750932\pi
0.709174 0.705033i 0.249068π-0.249068\pi
2424 0 0
2525 −16.5103 −0.660414
2626 0 0
2727 5.19615i 0.192450i
2828 0 0
2929 −38.8341 −1.33911 −0.669553 0.742764i 0.733514π-0.733514\pi
−0.669553 + 0.742764i 0.733514π0.733514\pi
3030 0 0
3131 − 37.4320i − 1.20748i −0.797180 0.603741i 0.793676π-0.793676\pi
0.797180 0.603741i 0.206324π-0.206324\pi
3232 0 0
3333 −12.8345 −0.388923
3434 0 0
3535 7.70893i 0.220255i
3636 0 0
3737 70.3892 1.90241 0.951205 0.308560i 0.0998469π-0.0998469\pi
0.951205 + 0.308560i 0.0998469π0.0998469\pi
3838 0 0
3939 41.7309i 1.07002i
4040 0 0
4141 24.9436 0.608380 0.304190 0.952611i 0.401614π-0.401614\pi
0.304190 + 0.952611i 0.401614π0.401614\pi
4242 0 0
4343 − 28.3154i − 0.658498i −0.944243 0.329249i 0.893204π-0.893204\pi
0.944243 0.329249i 0.106796π-0.106796\pi
4444 0 0
4545 −8.74110 −0.194247
4646 0 0
4747 40.8631i 0.869427i 0.900569 + 0.434714i 0.143150π0.143150\pi
−0.900569 + 0.434714i 0.856850π0.856850\pi
4848 0 0
4949 −7.00000 −0.142857
5050 0 0
5151 − 29.8948i − 0.586172i
5252 0 0
5353 −89.0084 −1.67940 −0.839702 0.543048i 0.817270π-0.817270\pi
−0.839702 + 0.543048i 0.817270π0.817270\pi
5454 0 0
5555 − 21.5905i − 0.392554i
5656 0 0
5757 −22.5038 −0.394803
5858 0 0
5959 − 80.7391i − 1.36846i −0.729267 0.684229i 0.760139π-0.760139\pi
0.729267 0.684229i 0.239861π-0.239861\pi
6060 0 0
6161 −61.6021 −1.00987 −0.504935 0.863157i 0.668484π-0.668484\pi
−0.504935 + 0.863157i 0.668484π0.668484\pi
6262 0 0
6363 − 7.93725i − 0.125988i
6464 0 0
6565 −70.2008 −1.08001
6666 0 0
6767 − 92.1412i − 1.37524i −0.726070 0.687621i 0.758655π-0.758655\pi
0.726070 0.687621i 0.241345π-0.241345\pi
6868 0 0
6969 −56.1731 −0.814102
7070 0 0
7171 61.5975i 0.867571i 0.901016 + 0.433786i 0.142822π0.142822\pi
−0.901016 + 0.433786i 0.857178π0.857178\pi
7272 0 0
7373 −52.4880 −0.719014 −0.359507 0.933142i 0.617055π-0.617055\pi
−0.359507 + 0.933142i 0.617055π0.617055\pi
7474 0 0
7575 28.5968i 0.381290i
7676 0 0
7777 19.6050 0.254610
7878 0 0
7979 91.8555i 1.16273i 0.813643 + 0.581364i 0.197481π0.197481\pi
−0.813643 + 0.581364i 0.802519π0.802519\pi
8080 0 0
8181 9.00000 0.111111
8282 0 0
8383 − 98.3206i − 1.18459i −0.805723 0.592293i 0.798223π-0.798223\pi
0.805723 0.592293i 0.201777π-0.201777\pi
8484 0 0
8585 50.2898 0.591644
8686 0 0
8787 67.2626i 0.773133i
8888 0 0
8989 −67.5476 −0.758962 −0.379481 0.925200i 0.623897π-0.623897\pi
−0.379481 + 0.925200i 0.623897π0.623897\pi
9090 0 0
9191 − 63.7450i − 0.700495i
9292 0 0
9393 −64.8341 −0.697140
9494 0 0
9595 − 37.8564i − 0.398488i
9696 0 0
9797 41.1094 0.423809 0.211904 0.977290i 0.432033π-0.432033\pi
0.211904 + 0.977290i 0.432033π0.432033\pi
9898 0 0
9999 22.2299i 0.224545i
100100 0 0
101101 −24.8723 −0.246260 −0.123130 0.992391i 0.539293π-0.539293\pi
−0.123130 + 0.992391i 0.539293π0.539293\pi
102102 0 0
103103 − 10.8569i − 0.105407i −0.998610 0.0527036i 0.983216π-0.983216\pi
0.998610 0.0527036i 0.0167839π-0.0167839\pi
104104 0 0
105105 13.3523 0.127164
106106 0 0
107107 29.7875i 0.278388i 0.990265 + 0.139194i 0.0444512π0.0444512\pi
−0.990265 + 0.139194i 0.955549π0.955549\pi
108108 0 0
109109 60.4044 0.554169 0.277085 0.960846i 0.410632π-0.410632\pi
0.277085 + 0.960846i 0.410632π0.410632\pi
110110 0 0
111111 − 121.918i − 1.09836i
112112 0 0
113113 21.5134 0.190384 0.0951922 0.995459i 0.469653π-0.469653\pi
0.0951922 + 0.995459i 0.469653π0.469653\pi
114114 0 0
115115 − 94.4958i − 0.821702i
116116 0 0
117117 72.2801 0.617778
118118 0 0
119119 45.6650i 0.383740i
120120 0 0
121121 66.0922 0.546217
122122 0 0
123123 − 43.2035i − 0.351248i
124124 0 0
125125 −120.949 −0.967590
126126 0 0
127127 − 84.9278i − 0.668723i −0.942445 0.334361i 0.891479π-0.891479\pi
0.942445 0.334361i 0.108521π-0.108521\pi
128128 0 0
129129 −49.0437 −0.380184
130130 0 0
131131 157.348i 1.20113i 0.799576 + 0.600565i 0.205058π0.205058\pi
−0.799576 + 0.600565i 0.794942π0.794942\pi
132132 0 0
133133 34.3751 0.258459
134134 0 0
135135 15.1400i 0.112148i
136136 0 0
137137 −8.23390 −0.0601014 −0.0300507 0.999548i 0.509567π-0.509567\pi
−0.0300507 + 0.999548i 0.509567π0.509567\pi
138138 0 0
139139 − 192.415i − 1.38428i −0.721764 0.692139i 0.756668π-0.756668\pi
0.721764 0.692139i 0.243332π-0.243332\pi
140140 0 0
141141 70.7769 0.501964
142142 0 0
143143 178.531i 1.24847i
144144 0 0
145145 −113.151 −0.780351
146146 0 0
147147 12.1244i 0.0824786i
148148 0 0
149149 59.5926 0.399951 0.199975 0.979801i 0.435914π-0.435914\pi
0.199975 + 0.979801i 0.435914π0.435914\pi
150150 0 0
151151 163.350i 1.08179i 0.841091 + 0.540894i 0.181914π0.181914\pi
−0.841091 + 0.540894i 0.818086π0.818086\pi
152152 0 0
153153 −51.7793 −0.338427
154154 0 0
155155 − 109.066i − 0.703649i
156156 0 0
157157 194.988 1.24196 0.620981 0.783825i 0.286734π-0.286734\pi
0.620981 + 0.783825i 0.286734π0.286734\pi
158158 0 0
159159 154.167i 0.969604i
160160 0 0
161161 85.8058 0.532955
162162 0 0
163163 − 70.8941i − 0.434933i −0.976068 0.217466i 0.930221π-0.930221\pi
0.976068 0.217466i 0.0697793π-0.0697793\pi
164164 0 0
165165 −37.3958 −0.226641
166166 0 0
167167 153.404i 0.918589i 0.888284 + 0.459295i 0.151898π0.151898\pi
−0.888284 + 0.459295i 0.848102π0.848102\pi
168168 0 0
169169 411.490 2.43485
170170 0 0
171171 38.9777i 0.227940i
172172 0 0
173173 70.9393 0.410054 0.205027 0.978756i 0.434272π-0.434272\pi
0.205027 + 0.978756i 0.434272π0.434272\pi
174174 0 0
175175 − 43.6823i − 0.249613i
176176 0 0
177177 −139.844 −0.790080
178178 0 0
179179 288.549i 1.61201i 0.591911 + 0.806003i 0.298374π0.298374\pi
−0.591911 + 0.806003i 0.701626π0.701626\pi
180180 0 0
181181 351.047 1.93949 0.969743 0.244127i 0.0785013π-0.0785013\pi
0.969743 + 0.244127i 0.0785013π0.0785013\pi
182182 0 0
183183 106.698i 0.583049i
184184 0 0
185185 205.093 1.10861
186186 0 0
187187 − 127.894i − 0.683927i
188188 0 0
189189 −13.7477 −0.0727393
190190 0 0
191191 163.611i 0.856601i 0.903636 + 0.428301i 0.140888π0.140888\pi
−0.903636 + 0.428301i 0.859112π0.859112\pi
192192 0 0
193193 −137.688 −0.713408 −0.356704 0.934217i 0.616100π-0.616100\pi
−0.356704 + 0.934217i 0.616100π0.616100\pi
194194 0 0
195195 121.591i 0.623546i
196196 0 0
197197 −170.743 −0.866716 −0.433358 0.901222i 0.642671π-0.642671\pi
−0.433358 + 0.901222i 0.642671π0.642671\pi
198198 0 0
199199 − 202.599i − 1.01809i −0.860741 0.509043i 0.830000π-0.830000\pi
0.860741 0.509043i 0.170000π-0.170000\pi
200200 0 0
201201 −159.593 −0.793996
202202 0 0
203203 − 102.745i − 0.506134i
204204 0 0
205205 72.6781 0.354527
206206 0 0
207207 97.2946i 0.470022i
208208 0 0
209209 −96.2745 −0.460644
210210 0 0
211211 236.951i 1.12299i 0.827480 + 0.561496i 0.189774π0.189774\pi
−0.827480 + 0.561496i 0.810226π0.810226\pi
212212 0 0
213213 106.690 0.500892
214214 0 0
215215 − 82.5026i − 0.383733i
216216 0 0
217217 99.0357 0.456386
218218 0 0
219219 90.9119i 0.415123i
220220 0 0
221221 −415.845 −1.88165
222222 0 0
223223 − 214.219i − 0.960623i −0.877098 0.480311i 0.840524π-0.840524\pi
0.877098 0.480311i 0.159476π-0.159476\pi
224224 0 0
225225 49.5310 0.220138
226226 0 0
227227 − 316.287i − 1.39334i −0.717393 0.696668i 0.754665π-0.754665\pi
0.717393 0.696668i 0.245335π-0.245335\pi
228228 0 0
229229 193.656 0.845660 0.422830 0.906209i 0.361037π-0.361037\pi
0.422830 + 0.906209i 0.361037π0.361037\pi
230230 0 0
231231 − 33.9568i − 0.146999i
232232 0 0
233233 222.042 0.952969 0.476485 0.879183i 0.341911π-0.341911\pi
0.476485 + 0.879183i 0.341911π0.341911\pi
234234 0 0
235235 119.063i 0.506650i
236236 0 0
237237 159.098 0.671302
238238 0 0
239239 − 26.4216i − 0.110551i −0.998471 0.0552754i 0.982396π-0.982396\pi
0.998471 0.0552754i 0.0176037π-0.0176037\pi
240240 0 0
241241 178.900 0.742324 0.371162 0.928568i 0.378959π-0.378959\pi
0.371162 + 0.928568i 0.378959π0.378959\pi
242242 0 0
243243 − 15.5885i − 0.0641500i
244244 0 0
245245 −20.3959 −0.0832486
246246 0 0
247247 313.034i 1.26734i
248248 0 0
249249 −170.296 −0.683921
250250 0 0
251251 24.2905i 0.0967750i 0.998829 + 0.0483875i 0.0154082π0.0154082\pi
−0.998829 + 0.0483875i 0.984592π0.984592\pi
252252 0 0
253253 −240.317 −0.949869
254254 0 0
255255 − 87.1044i − 0.341586i
256256 0 0
257257 308.081 1.19876 0.599380 0.800465i 0.295414π-0.295414\pi
0.599380 + 0.800465i 0.295414π0.295414\pi
258258 0 0
259259 186.232i 0.719043i
260260 0 0
261261 116.502 0.446369
262262 0 0
263263 438.932i 1.66894i 0.551052 + 0.834471i 0.314226π0.314226\pi
−0.551052 + 0.834471i 0.685774π0.685774\pi
264264 0 0
265265 −259.344 −0.978656
266266 0 0
267267 116.996i 0.438187i
268268 0 0
269269 −119.003 −0.442391 −0.221195 0.975229i 0.570996π-0.570996\pi
−0.221195 + 0.975229i 0.570996π0.570996\pi
270270 0 0
271271 − 67.2292i − 0.248078i −0.992277 0.124039i 0.960415π-0.960415\pi
0.992277 0.124039i 0.0395848π-0.0395848\pi
272272 0 0
273273 −110.410 −0.404431
274274 0 0
275275 122.341i 0.444877i
276276 0 0
277277 −182.471 −0.658739 −0.329369 0.944201i 0.606836π-0.606836\pi
−0.329369 + 0.944201i 0.606836π0.606836\pi
278278 0 0
279279 112.296i 0.402494i
280280 0 0
281281 401.986 1.43056 0.715278 0.698840i 0.246300π-0.246300\pi
0.715278 + 0.698840i 0.246300π0.246300\pi
282282 0 0
283283 222.644i 0.786726i 0.919383 + 0.393363i 0.128688π0.128688\pi
−0.919383 + 0.393363i 0.871312π0.871312\pi
284284 0 0
285285 −65.5692 −0.230067
286286 0 0
287287 65.9945i 0.229946i
288288 0 0
289289 8.89923 0.0307932
290290 0 0
291291 − 71.2036i − 0.244686i
292292 0 0
293293 505.760 1.72614 0.863072 0.505081i 0.168537π-0.168537\pi
0.863072 + 0.505081i 0.168537π0.168537\pi
294294 0 0
295295 − 235.249i − 0.797456i
296296 0 0
297297 38.5034 0.129641
298298 0 0
299299 781.384i 2.61333i
300300 0 0
301301 74.9155 0.248889
302302 0 0
303303 43.0801i 0.142179i
304304 0 0
305305 −179.490 −0.588492
306306 0 0
307307 − 156.777i − 0.510675i −0.966852 0.255337i 0.917813π-0.917813\pi
0.966852 0.255337i 0.0821866π-0.0821866\pi
308308 0 0
309309 −18.8048 −0.0608569
310310 0 0
311311 − 525.603i − 1.69004i −0.534734 0.845020i 0.679588π-0.679588\pi
0.534734 0.845020i 0.320412π-0.320412\pi
312312 0 0
313313 −22.7440 −0.0726646 −0.0363323 0.999340i 0.511567π-0.511567\pi
−0.0363323 + 0.999340i 0.511567π0.511567\pi
314314 0 0
315315 − 23.1268i − 0.0734184i
316316 0 0
317317 −323.942 −1.02190 −0.510949 0.859611i 0.670706π-0.670706\pi
−0.510949 + 0.859611i 0.670706π0.670706\pi
318318 0 0
319319 287.760i 0.902067i
320320 0 0
321321 51.5935 0.160728
322322 0 0
323323 − 224.248i − 0.694267i
324324 0 0
325325 397.790 1.22397
326326 0 0
327327 − 104.624i − 0.319950i
328328 0 0
329329 −108.114 −0.328613
330330 0 0
331331 − 454.289i − 1.37247i −0.727378 0.686237i 0.759261π-0.759261\pi
0.727378 0.686237i 0.240739π-0.240739\pi
332332 0 0
333333 −211.168 −0.634137
334334 0 0
335335 − 268.472i − 0.801408i
336336 0 0
337337 −112.431 −0.333622 −0.166811 0.985989i 0.553347π-0.553347\pi
−0.166811 + 0.985989i 0.553347π0.553347\pi
338338 0 0
339339 − 37.2623i − 0.109918i
340340 0 0
341341 −277.370 −0.813402
342342 0 0
343343 − 18.5203i − 0.0539949i
344344 0 0
345345 −163.671 −0.474410
346346 0 0
347347 − 29.7063i − 0.0856088i −0.999083 0.0428044i 0.986371π-0.986371\pi
0.999083 0.0428044i 0.0136292π-0.0136292\pi
348348 0 0
349349 180.808 0.518075 0.259037 0.965867i 0.416595π-0.416595\pi
0.259037 + 0.965867i 0.416595π0.416595\pi
350350 0 0
351351 − 125.193i − 0.356674i
352352 0 0
353353 −309.246 −0.876052 −0.438026 0.898962i 0.644322π-0.644322\pi
−0.438026 + 0.898962i 0.644322π0.644322\pi
354354 0 0
355355 179.477i 0.505568i
356356 0 0
357357 79.0941 0.221552
358358 0 0
359359 21.7887i 0.0606927i 0.999539 + 0.0303464i 0.00966103π0.00966103\pi
−0.999539 + 0.0303464i 0.990339π0.990339\pi
360360 0 0
361361 192.194 0.532392
362362 0 0
363363 − 114.475i − 0.315358i
364364 0 0
365365 −152.934 −0.418998
366366 0 0
367367 331.819i 0.904140i 0.891982 + 0.452070i 0.149314π0.149314\pi
−0.891982 + 0.452070i 0.850686π0.850686\pi
368368 0 0
369369 −74.8307 −0.202793
370370 0 0
371371 − 235.494i − 0.634755i
372372 0 0
373373 −297.079 −0.796458 −0.398229 0.917286i 0.630375π-0.630375\pi
−0.398229 + 0.917286i 0.630375π0.630375\pi
374374 0 0
375375 209.489i 0.558638i
376376 0 0
377377 935.643 2.48181
378378 0 0
379379 − 568.577i − 1.50020i −0.661323 0.750101i 0.730005π-0.730005\pi
0.661323 0.750101i 0.269995π-0.269995\pi
380380 0 0
381381 −147.099 −0.386087
382382 0 0
383383 34.1267i 0.0891036i 0.999007 + 0.0445518i 0.0141860π0.0141860\pi
−0.999007 + 0.0445518i 0.985814π0.985814\pi
384384 0 0
385385 57.1230 0.148371
386386 0 0
387387 84.9462i 0.219499i
388388 0 0
389389 −185.697 −0.477369 −0.238685 0.971097i 0.576716π-0.576716\pi
−0.238685 + 0.971097i 0.576716π0.576716\pi
390390 0 0
391391 − 559.760i − 1.43161i
392392 0 0
393393 272.535 0.693473
394394 0 0
395395 267.640i 0.677568i
396396 0 0
397397 −277.517 −0.699035 −0.349518 0.936930i 0.613654π-0.613654\pi
−0.349518 + 0.936930i 0.613654π0.613654\pi
398398 0 0
399399 − 59.5394i − 0.149221i
400400 0 0
401401 −530.463 −1.32285 −0.661425 0.750012i 0.730048π-0.730048\pi
−0.661425 + 0.750012i 0.730048π0.730048\pi
402402 0 0
403403 901.862i 2.23787i
404404 0 0
405405 26.2233 0.0647489
406406 0 0
407407 − 521.582i − 1.28153i
408408 0 0
409409 681.101 1.66528 0.832642 0.553812i 0.186827π-0.186827\pi
0.832642 + 0.553812i 0.186827π0.186827\pi
410410 0 0
411411 14.2615i 0.0346996i
412412 0 0
413413 213.615 0.517229
414414 0 0
415415 − 286.477i − 0.690306i
416416 0 0
417417 −333.272 −0.799214
418418 0 0
419419 − 208.004i − 0.496430i −0.968705 0.248215i 0.920156π-0.920156\pi
0.968705 0.248215i 0.0798439π-0.0798439\pi
420420 0 0
421421 58.5750 0.139133 0.0695665 0.997577i 0.477838π-0.477838\pi
0.0695665 + 0.997577i 0.477838π0.477838\pi
422422 0 0
423423 − 122.589i − 0.289809i
424424 0 0
425425 −284.965 −0.670505
426426 0 0
427427 − 162.984i − 0.381695i
428428 0 0
429429 309.225 0.720804
430430 0 0
431431 − 376.105i − 0.872634i −0.899793 0.436317i 0.856283π-0.856283\pi
0.899793 0.436317i 0.143717π-0.143717\pi
432432 0 0
433433 −120.961 −0.279355 −0.139677 0.990197i 0.544607π-0.544607\pi
−0.139677 + 0.990197i 0.544607π0.544607\pi
434434 0 0
435435 195.983i 0.450536i
436436 0 0
437437 −421.368 −0.964230
438438 0 0
439439 − 747.561i − 1.70287i −0.524459 0.851436i 0.675732π-0.675732\pi
0.524459 0.851436i 0.324268π-0.324268\pi
440440 0 0
441441 21.0000 0.0476190
442442 0 0
443443 654.425i 1.47726i 0.674112 + 0.738629i 0.264526π0.264526\pi
−0.674112 + 0.738629i 0.735474π0.735474\pi
444444 0 0
445445 −196.813 −0.442277
446446 0 0
447447 − 103.217i − 0.230912i
448448 0 0
449449 412.318 0.918303 0.459152 0.888358i 0.348153π-0.348153\pi
0.459152 + 0.888358i 0.348153π0.348153\pi
450450 0 0
451451 − 184.831i − 0.409825i
452452 0 0
453453 282.930 0.624570
454454 0 0
455455 − 185.734i − 0.408206i
456456 0 0
457457 −860.397 −1.88271 −0.941353 0.337422i 0.890445π-0.890445\pi
−0.941353 + 0.337422i 0.890445π0.890445\pi
458458 0 0
459459 89.6843i 0.195391i
460460 0 0
461461 −406.149 −0.881018 −0.440509 0.897748i 0.645202π-0.645202\pi
−0.440509 + 0.897748i 0.645202π0.645202\pi
462462 0 0
463463 − 492.223i − 1.06312i −0.847022 0.531558i 0.821607π-0.821607\pi
0.847022 0.531558i 0.178393π-0.178393\pi
464464 0 0
465465 −188.907 −0.406252
466466 0 0
467467 − 594.456i − 1.27293i −0.771307 0.636463i 0.780397π-0.780397\pi
0.771307 0.636463i 0.219603π-0.219603\pi
468468 0 0
469469 243.783 0.519792
470470 0 0
471471 − 337.729i − 0.717048i
472472 0 0
473473 −209.817 −0.443587
474474 0 0
475475 214.512i 0.451603i
476476 0 0
477477 267.025 0.559801
478478 0 0
479479 − 201.151i − 0.419940i −0.977708 0.209970i 0.932663π-0.932663\pi
0.977708 0.209970i 0.0673367π-0.0673367\pi
480480 0 0
481481 −1695.91 −3.52580
482482 0 0
483483 − 148.620i − 0.307702i
484484 0 0
485485 119.781 0.246970
486486 0 0
487487 376.266i 0.772619i 0.922369 + 0.386310i 0.126250π0.126250\pi
−0.922369 + 0.386310i 0.873750π0.873750\pi
488488 0 0
489489 −122.792 −0.251109
490490 0 0
491491 186.938i 0.380729i 0.981713 + 0.190365i 0.0609670π0.0609670\pi
−0.981713 + 0.190365i 0.939033π0.939033\pi
492492 0 0
493493 −670.267 −1.35957
494494 0 0
495495 64.7714i 0.130851i
496496 0 0
497497 −162.972 −0.327911
498498 0 0
499499 298.003i 0.597200i 0.954378 + 0.298600i 0.0965196π0.0965196\pi
−0.954378 + 0.298600i 0.903480π0.903480\pi
500500 0 0
501501 265.704 0.530348
502502 0 0
503503 − 474.049i − 0.942444i −0.882015 0.471222i 0.843813π-0.843813\pi
0.882015 0.471222i 0.156187π-0.156187\pi
504504 0 0
505505 −72.4704 −0.143506
506506 0 0
507507 − 712.721i − 1.40576i
508508 0 0
509509 147.496 0.289776 0.144888 0.989448i 0.453718π-0.453718\pi
0.144888 + 0.989448i 0.453718π0.453718\pi
510510 0 0
511511 − 138.870i − 0.271762i
512512 0 0
513513 67.5113 0.131601
514514 0 0
515515 − 31.6339i − 0.0614250i
516516 0 0
517517 302.794 0.585676
518518 0 0
519519 − 122.870i − 0.236745i
520520 0 0
521521 700.270 1.34409 0.672044 0.740511i 0.265417π-0.265417\pi
0.672044 + 0.740511i 0.265417π0.265417\pi
522522 0 0
523523 695.893i 1.33058i 0.746586 + 0.665289i 0.231692π0.231692\pi
−0.746586 + 0.665289i 0.768308π0.768308\pi
524524 0 0
525525 −75.6599 −0.144114
526526 0 0
527527 − 646.067i − 1.22593i
528528 0 0
529529 −522.804 −0.988288
530530 0 0
531531 242.217i 0.456153i
532532 0 0
533533 −600.974 −1.12753
534534 0 0
535535 86.7920i 0.162228i
536536 0 0
537537 499.782 0.930693
538538 0 0
539539 51.8698i 0.0962335i
540540 0 0
541541 596.690 1.10294 0.551470 0.834195i 0.314067π-0.314067\pi
0.551470 + 0.834195i 0.314067π0.314067\pi
542542 0 0
543543 − 608.031i − 1.11976i
544544 0 0
545545 176.000 0.322937
546546 0 0
547547 − 265.842i − 0.486000i −0.970026 0.243000i 0.921868π-0.921868\pi
0.970026 0.243000i 0.0781316π-0.0781316\pi
548548 0 0
549549 184.806 0.336623
550550 0 0
551551 504.554i 0.915705i
552552 0 0
553553 −243.027 −0.439470
554554 0 0
555555 − 355.231i − 0.640057i
556556 0 0
557557 −1021.63 −1.83416 −0.917080 0.398703i 0.869460π-0.869460\pi
−0.917080 + 0.398703i 0.869460π0.869460\pi
558558 0 0
559559 682.213i 1.22042i
560560 0 0
561561 −221.520 −0.394866
562562 0 0
563563 402.546i 0.715002i 0.933913 + 0.357501i 0.116371π0.116371\pi
−0.933913 + 0.357501i 0.883629π0.883629\pi
564564 0 0
565565 62.6837 0.110945
566566 0 0
567567 23.8118i 0.0419961i
568568 0 0
569569 275.167 0.483598 0.241799 0.970326i 0.422263π-0.422263\pi
0.241799 + 0.970326i 0.422263π0.422263\pi
570570 0 0
571571 684.768i 1.19924i 0.800284 + 0.599622i 0.204682π0.204682\pi
−0.800284 + 0.599622i 0.795318π0.795318\pi
572572 0 0
573573 283.382 0.494559
574574 0 0
575575 535.456i 0.931228i
576576 0 0
577577 226.867 0.393183 0.196592 0.980485i 0.437013π-0.437013\pi
0.196592 + 0.980485i 0.437013π0.437013\pi
578578 0 0
579579 238.482i 0.411887i
580580 0 0
581581 260.132 0.447731
582582 0 0
583583 659.550i 1.13130i
584584 0 0
585585 210.602 0.360004
586586 0 0
587587 320.491i 0.545981i 0.962017 + 0.272991i 0.0880128π0.0880128\pi
−0.962017 + 0.272991i 0.911987π0.911987\pi
588588 0 0
589589 −486.337 −0.825699
590590 0 0
591591 295.735i 0.500398i
592592 0 0
593593 −814.649 −1.37378 −0.686888 0.726764i 0.741024π-0.741024\pi
−0.686888 + 0.726764i 0.741024π0.741024\pi
594594 0 0
595595 133.054i 0.223621i
596596 0 0
597597 −350.912 −0.587792
598598 0 0
599599 505.842i 0.844478i 0.906485 + 0.422239i 0.138756π0.138756\pi
−0.906485 + 0.422239i 0.861244π0.861244\pi
600600 0 0
601601 −506.284 −0.842403 −0.421201 0.906967i 0.638391π-0.638391\pi
−0.421201 + 0.906967i 0.638391π0.638391\pi
602602 0 0
603603 276.423i 0.458414i
604604 0 0
605605 192.573 0.318302
606606 0 0
607607 − 286.599i − 0.472156i −0.971734 0.236078i 0.924138π-0.924138\pi
0.971734 0.236078i 0.0758622π-0.0758622\pi
608608 0 0
609609 −177.960 −0.292217
610610 0 0
611611 − 984.528i − 1.61134i
612612 0 0
613613 −300.456 −0.490140 −0.245070 0.969505i 0.578811π-0.578811\pi
−0.245070 + 0.969505i 0.578811π0.578811\pi
614614 0 0
615615 − 125.882i − 0.204686i
616616 0 0
617617 930.734 1.50848 0.754241 0.656597i 0.228005π-0.228005\pi
0.754241 + 0.656597i 0.228005π0.228005\pi
618618 0 0
619619 − 680.636i − 1.09957i −0.835305 0.549787i 0.814709π-0.814709\pi
0.835305 0.549787i 0.185291π-0.185291\pi
620620 0 0
621621 168.519 0.271367
622622 0 0
623623 − 178.714i − 0.286861i
624624 0 0
625625 60.3504 0.0965606
626626 0 0
627627 166.752i 0.265953i
628628 0 0
629629 1214.90 1.93148
630630 0 0
631631 519.319i 0.823009i 0.911408 + 0.411504i 0.134997π0.134997\pi
−0.911408 + 0.411504i 0.865003π0.865003\pi
632632 0 0
633633 410.412 0.648360
634634 0 0
635635 − 247.454i − 0.389692i
636636 0 0
637637 168.653 0.264762
638638 0 0
639639 − 184.793i − 0.289190i
640640 0 0
641641 540.111 0.842607 0.421303 0.906920i 0.361573π-0.361573\pi
0.421303 + 0.906920i 0.361573π0.361573\pi
642642 0 0
643643 − 316.600i − 0.492380i −0.969222 0.246190i 0.920821π-0.920821\pi
0.969222 0.246190i 0.0791786π-0.0791786\pi
644644 0 0
645645 −142.899 −0.221548
646646 0 0
647647 − 745.515i − 1.15226i −0.817356 0.576132i 0.804561π-0.804561\pi
0.817356 0.576132i 0.195439π-0.195439\pi
648648 0 0
649649 −598.275 −0.921841
650650 0 0
651651 − 171.535i − 0.263494i
652652 0 0
653653 −794.499 −1.21669 −0.608345 0.793673i 0.708166π-0.708166\pi
−0.608345 + 0.793673i 0.708166π0.708166\pi
654654 0 0
655655 458.465i 0.699947i
656656 0 0
657657 157.464 0.239671
658658 0 0
659659 − 26.4351i − 0.0401140i −0.999799 0.0200570i 0.993615π-0.993615\pi
0.999799 0.0200570i 0.00638477π-0.00638477\pi
660660 0 0
661661 497.881 0.753223 0.376612 0.926371i 0.377089π-0.377089\pi
0.376612 + 0.926371i 0.377089π0.377089\pi
662662 0 0
663663 720.265i 1.08637i
664664 0 0
665665 100.159 0.150614
666666 0 0
667667 1259.45i 1.88823i
668668 0 0
669669 −371.038 −0.554616
670670 0 0
671671 456.470i 0.680283i
672672 0 0
673673 −94.9961 −0.141153 −0.0705766 0.997506i 0.522484π-0.522484\pi
−0.0705766 + 0.997506i 0.522484π0.522484\pi
674674 0 0
675675 − 85.7903i − 0.127097i
676676 0 0
677677 757.820 1.11938 0.559690 0.828702i 0.310920π-0.310920\pi
0.559690 + 0.828702i 0.310920π0.310920\pi
678678 0 0
679679 108.765i 0.160185i
680680 0 0
681681 −547.826 −0.804443
682682 0 0
683683 − 432.613i − 0.633402i −0.948525 0.316701i 0.897425π-0.897425\pi
0.948525 0.316701i 0.102575π-0.102575\pi
684684 0 0
685685 −23.9911 −0.0350235
686686 0 0
687687 − 335.422i − 0.488242i
688688 0 0
689689 2144.51 3.11250
690690 0 0
691691 − 407.736i − 0.590067i −0.955487 0.295034i 0.904669π-0.904669\pi
0.955487 0.295034i 0.0953308π-0.0953308\pi
692692 0 0
693693 −58.8149 −0.0848699
694694 0 0
695695 − 560.639i − 0.806675i
696696 0 0
697697 430.520 0.617676
698698 0 0
699699 − 384.588i − 0.550197i
700700 0 0
701701 −206.009 −0.293879 −0.146939 0.989145i 0.546942π-0.546942\pi
−0.146939 + 0.989145i 0.546942π0.546942\pi
702702 0 0
703703 − 914.535i − 1.30090i
704704 0 0
705705 206.223 0.292515
706706 0 0
707707 − 65.8059i − 0.0930777i
708708 0 0
709709 511.639 0.721635 0.360817 0.932637i 0.382498π-0.382498\pi
0.360817 + 0.932637i 0.382498π0.382498\pi
710710 0 0
711711 − 275.567i − 0.387576i
712712 0 0
713713 −1213.98 −1.70263
714714 0 0
715715 520.186i 0.727533i
716716 0 0
717717 −45.7636 −0.0638265
718718 0 0
719719 1045.23i 1.45373i 0.686780 + 0.726866i 0.259024π0.259024\pi
−0.686780 + 0.726866i 0.740976π0.740976\pi
720720 0 0
721721 28.7248 0.0398402
722722 0 0
723723 − 309.864i − 0.428581i
724724 0 0
725725 641.164 0.884364
726726 0 0
727727 − 193.079i − 0.265584i −0.991144 0.132792i 0.957606π-0.957606\pi
0.991144 0.132792i 0.0423942π-0.0423942\pi
728728 0 0
729729 −27.0000 −0.0370370
730730 0 0
731731 − 488.717i − 0.668560i
732732 0 0
733733 −851.928 −1.16225 −0.581124 0.813815i 0.697387π-0.697387\pi
−0.581124 + 0.813815i 0.697387π0.697387\pi
734734 0 0
735735 35.3267i 0.0480636i
736736 0 0
737737 −682.764 −0.926410
738738 0 0
739739 189.437i 0.256342i 0.991752 + 0.128171i 0.0409107π0.0409107\pi
−0.991752 + 0.128171i 0.959089π0.959089\pi
740740 0 0
741741 542.191 0.731702
742742 0 0
743743 − 945.745i − 1.27287i −0.771329 0.636436i 0.780408π-0.780408\pi
0.771329 0.636436i 0.219592π-0.219592\pi
744744 0 0
745745 173.635 0.233067
746746 0 0
747747 294.962i 0.394862i
748748 0 0
749749 −78.8104 −0.105221
750750 0 0
751751 902.515i 1.20175i 0.799342 + 0.600876i 0.205181π0.205181\pi
−0.799342 + 0.600876i 0.794819π0.794819\pi
752752 0 0
753753 42.0724 0.0558731
754754 0 0
755755 475.953i 0.630401i
756756 0 0
757757 −1242.26 −1.64103 −0.820513 0.571627i 0.806312π-0.806312\pi
−0.820513 + 0.571627i 0.806312π0.806312\pi
758758 0 0
759759 416.241i 0.548407i
760760 0 0
761761 764.711 1.00488 0.502438 0.864613i 0.332436π-0.332436\pi
0.502438 + 0.864613i 0.332436π0.332436\pi
762762 0 0
763763 159.815i 0.209456i
764764 0 0
765765 −150.869 −0.197215
766766 0 0
767767 1945.27i 2.53621i
768768 0 0
769769 896.436 1.16572 0.582858 0.812574i 0.301934π-0.301934\pi
0.582858 + 0.812574i 0.301934π0.301934\pi
770770 0 0
771771 − 533.612i − 0.692104i
772772 0 0
773773 −483.067 −0.624925 −0.312463 0.949930i 0.601154π-0.601154\pi
−0.312463 + 0.949930i 0.601154π0.601154\pi
774774 0 0
775775 618.015i 0.797438i
776776 0 0
777777 322.564 0.415140
778778 0 0
779779 − 324.081i − 0.416021i
780780 0 0
781781 456.436 0.584426
782782 0 0
783783 − 201.788i − 0.257711i
784784 0 0
785785 568.137 0.723742
786786 0 0
787787 1046.56i 1.32981i 0.746926 + 0.664907i 0.231529π0.231529\pi
−0.746926 + 0.664907i 0.768471π0.768471\pi
788788 0 0
789789 760.252 0.963564
790790 0 0
791791 56.9192i 0.0719585i
792792 0 0
793793 1484.20 1.87163
794794 0 0
795795 449.197i 0.565027i
796796 0 0
797797 820.370 1.02932 0.514661 0.857394i 0.327918π-0.327918\pi
0.514661 + 0.857394i 0.327918π0.327918\pi
798798 0 0
799799 705.287i 0.882712i
800800 0 0
801801 202.643 0.252987
802802 0 0
803803 388.935i 0.484352i
804804 0 0
805805 250.012 0.310574
806806 0 0
807807 206.120i 0.255415i
808808 0 0
809809 −1254.40 −1.55056 −0.775279 0.631619i 0.782391π-0.782391\pi
−0.775279 + 0.631619i 0.782391π0.782391\pi
810810 0 0
811811 − 118.642i − 0.146291i −0.997321 0.0731454i 0.976696π-0.976696\pi
0.997321 0.0731454i 0.0233037π-0.0233037\pi
812812 0 0
813813 −116.444 −0.143228
814814 0 0
815815 − 206.564i − 0.253453i
816816 0 0
817817 −367.889 −0.450293
818818 0 0
819819 191.235i 0.233498i
820820 0 0
821821 1103.74 1.34438 0.672190 0.740378i 0.265354π-0.265354\pi
0.672190 + 0.740378i 0.265354π0.265354\pi
822822 0 0
823823 − 178.011i − 0.216295i −0.994135 0.108147i 0.965508π-0.965508\pi
0.994135 0.108147i 0.0344919π-0.0344919\pi
824824 0 0
825825 211.901 0.256850
826826 0 0
827827 423.395i 0.511964i 0.966682 + 0.255982i 0.0823988π0.0823988\pi
−0.966682 + 0.255982i 0.917601π0.917601\pi
828828 0 0
829829 −1504.17 −1.81444 −0.907222 0.420651i 0.861802π-0.861802\pi
−0.907222 + 0.420651i 0.861802π0.861802\pi
830830 0 0
831831 316.048i 0.380323i
832832 0 0
833833 −120.818 −0.145040
834834 0 0
835835 446.974i 0.535299i
836836 0 0
837837 194.502 0.232380
838838 0 0
839839 − 448.309i − 0.534337i −0.963650 0.267168i 0.913912π-0.913912\pi
0.963650 0.267168i 0.0860880π-0.0860880\pi
840840 0 0
841841 667.084 0.793204
842842 0 0
843843 − 696.261i − 0.825932i
844844 0 0
845845 1198.96 1.41889
846846 0 0
847847 174.864i 0.206451i
848848 0 0
849849 385.630 0.454217
850850 0 0
851851 − 2282.83i − 2.68253i
852852 0 0
853853 120.642 0.141433 0.0707163 0.997496i 0.477471π-0.477471\pi
0.0707163 + 0.997496i 0.477471π0.477471\pi
854854 0 0
855855 113.569i 0.132829i
856856 0 0
857857 −1440.05 −1.68034 −0.840169 0.542325i 0.817544π-0.817544\pi
−0.840169 + 0.542325i 0.817544π0.817544\pi
858858 0 0
859859 − 1531.82i − 1.78326i −0.452765 0.891630i 0.649562π-0.649562\pi
0.452765 0.891630i 0.350438π-0.350438\pi
860860 0 0
861861 114.306 0.132759
862862 0 0
863863 − 78.9293i − 0.0914593i −0.998954 0.0457296i 0.985439π-0.985439\pi
0.998954 0.0457296i 0.0145613π-0.0145613\pi
864864 0 0
865865 206.696 0.238955
866866 0 0
867867 − 15.4139i − 0.0177785i
868868 0 0
869869 680.647 0.783254
870870 0 0
871871 2219.99i 2.54878i
872872 0 0
873873 −123.328 −0.141270
874874 0 0
875875 − 320.000i − 0.365715i
876876 0 0
877877 1050.60 1.19795 0.598975 0.800768i 0.295575π-0.295575\pi
0.598975 + 0.800768i 0.295575π0.295575\pi
878878 0 0
879879 − 876.003i − 0.996590i
880880 0 0
881881 −1135.28 −1.28862 −0.644312 0.764763i 0.722856π-0.722856\pi
−0.644312 + 0.764763i 0.722856π0.722856\pi
882882 0 0
883883 − 1107.98i − 1.25479i −0.778703 0.627393i 0.784122π-0.784122\pi
0.778703 0.627393i 0.215878π-0.215878\pi
884884 0 0
885885 −407.464 −0.460411
886886 0 0
887887 − 396.514i − 0.447028i −0.974701 0.223514i 0.928247π-0.928247\pi
0.974701 0.223514i 0.0717528π-0.0717528\pi
888888 0 0
889889 224.698 0.252753
890890 0 0
891891 − 66.6898i − 0.0748482i
892892 0 0
893893 530.916 0.594530
894894 0 0
895895 840.746i 0.939381i
896896 0 0
897897 1353.40 1.50880
898898 0 0
899899 1453.64i 1.61695i
900900 0 0
901901 −1536.26 −1.70506
902902 0 0
903903 − 129.757i − 0.143696i
904904 0 0
905905 1022.85 1.13022
906906 0 0
907907 815.997i 0.899666i 0.893113 + 0.449833i 0.148516π0.148516\pi
−0.893113 + 0.449833i 0.851484π0.851484\pi
908908 0 0
909909 74.6169 0.0820868
910910 0 0
911911 1799.18i 1.97495i 0.157789 + 0.987473i 0.449563π0.449563\pi
−0.157789 + 0.987473i 0.550437π0.550437\pi
912912 0 0
913913 −728.553 −0.797977
914914 0 0
915915 310.886i 0.339766i
916916 0 0
917917 −416.304 −0.453984
918918 0 0
919919 1694.65i 1.84401i 0.387175 + 0.922006i 0.373451π0.373451\pi
−0.387175 + 0.922006i 0.626549π0.626549\pi
920920 0 0
921921 −271.546 −0.294838
922922 0 0
923923 − 1484.09i − 1.60790i
924924 0 0
925925 −1162.15 −1.25638
926926 0 0
927927 32.5708i 0.0351357i
928928 0 0
929929 365.052 0.392952 0.196476 0.980509i 0.437050π-0.437050\pi
0.196476 + 0.980509i 0.437050π0.437050\pi
930930 0 0
931931 90.9479i 0.0976884i
932932 0 0
933933 −910.370 −0.975745
934934 0 0
935935 − 372.646i − 0.398552i
936936 0 0
937937 −622.594 −0.664455 −0.332228 0.943199i 0.607800π-0.607800\pi
−0.332228 + 0.943199i 0.607800π0.607800\pi
938938 0 0
939939 39.3938i 0.0419529i
940940 0 0
941941 404.487 0.429848 0.214924 0.976631i 0.431050π-0.431050\pi
0.214924 + 0.976631i 0.431050π0.431050\pi
942942 0 0
943943 − 808.958i − 0.857856i
944944 0 0
945945 −40.0568 −0.0423881
946946 0 0
947947 1066.44i 1.12613i 0.826414 + 0.563063i 0.190377π0.190377\pi
−0.826414 + 0.563063i 0.809623π0.809623\pi
948948 0 0
949949 1264.61 1.33257
950950 0 0
951951 561.083i 0.589993i
952952 0 0
953953 1781.50 1.86936 0.934680 0.355491i 0.115686π-0.115686\pi
0.934680 + 0.355491i 0.115686π0.115686\pi
954954 0 0
955955 476.713i 0.499176i
956956 0 0
957957 498.414 0.520809
958958 0 0
959959 − 21.7848i − 0.0227162i
960960 0 0
961961 −440.152 −0.458015
962962 0 0
963963 − 89.3626i − 0.0927961i
964964 0 0
965965 −401.181 −0.415732
966966 0 0
967967 − 1048.75i − 1.08454i −0.840205 0.542269i 0.817565π-0.817565\pi
0.840205 0.542269i 0.182435π-0.182435\pi
968968 0 0
969969 −388.409 −0.400835
970970 0 0
971971 1439.69i 1.48268i 0.671127 + 0.741342i 0.265810π0.265810\pi
−0.671127 + 0.741342i 0.734190π0.734190\pi
972972 0 0
973973 509.082 0.523208
974974 0 0
975975 − 688.992i − 0.706658i
976976 0 0
977977 562.504 0.575746 0.287873 0.957669i 0.407052π-0.407052\pi
0.287873 + 0.957669i 0.407052π0.407052\pi
978978 0 0
979979 500.526i 0.511263i
980980 0 0
981981 −181.213 −0.184723
982982 0 0
983983 − 580.429i − 0.590467i −0.955425 0.295233i 0.904603π-0.904603\pi
0.955425 0.295233i 0.0953974π-0.0953974\pi
984984 0 0
985985 −497.494 −0.505070
986986 0 0
987987 187.258i 0.189725i
988988 0 0
989989 −918.312 −0.928526
990990 0 0
991991 − 1425.05i − 1.43799i −0.695013 0.718997i 0.744602π-0.744602\pi
0.695013 0.718997i 0.255398π-0.255398\pi
992992 0 0
993993 −786.851 −0.792398
994994 0 0
995995 − 590.313i − 0.593279i
996996 0 0
997997 523.575 0.525151 0.262575 0.964912i 0.415428π-0.415428\pi
0.262575 + 0.964912i 0.415428π0.415428\pi
998998 0 0
999999 365.753i 0.366119i
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 672.3.m.a.127.3 8
3.2 odd 2 2016.3.m.b.127.4 8
4.3 odd 2 inner 672.3.m.a.127.7 yes 8
8.3 odd 2 1344.3.m.d.127.2 8
8.5 even 2 1344.3.m.d.127.6 8
12.11 even 2 2016.3.m.b.127.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
672.3.m.a.127.3 8 1.1 even 1 trivial
672.3.m.a.127.7 yes 8 4.3 odd 2 inner
1344.3.m.d.127.2 8 8.3 odd 2
1344.3.m.d.127.6 8 8.5 even 2
2016.3.m.b.127.3 8 12.11 even 2
2016.3.m.b.127.4 8 3.2 odd 2