Properties

Label 672.3.m.a.127.8
Level 672672
Weight 33
Character 672.127
Analytic conductor 18.31118.311
Analytic rank 00
Dimension 88
Inner twists 22

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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 127.8
Root 0.228425+1.39564i0.228425 + 1.39564i of defining polynomial
Character χ\chi == 672.127
Dual form 672.3.m.a.127.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+1.73205iq3+6.37780q5+2.64575iq73.00000q95.17303iq11+8.09335q13+11.0467iq15+25.1978q171.59045iq194.58258q21+15.8485iq23+15.6764q255.19615iq27+23.0850q29+1.68295iq31+8.95995q33+16.8741iq3517.2232q37+14.0181iq39+12.0970q41+31.1494iq4319.1334q4555.6971iq477.00000q49+43.6438iq5156.8217q5332.9926iq55+2.75475q57+47.5731iq59+101.351q617.93725iq63+51.6178q65+58.9752iq6727.4505q69+13.3175iq71+13.9050q73+27.1523iq75+13.6865q77+45.8124iq79+9.00000q81+145.317iq83+160.706q85+39.9845iq87+150.256q89+21.4130iq912.91495q9310.1436iq9590.5264q97+15.5191iq99+O(q100)q+1.73205i q^{3} +6.37780 q^{5} +2.64575i q^{7} -3.00000 q^{9} -5.17303i q^{11} +8.09335 q^{13} +11.0467i q^{15} +25.1978 q^{17} -1.59045i q^{19} -4.58258 q^{21} +15.8485i q^{23} +15.6764 q^{25} -5.19615i q^{27} +23.0850 q^{29} +1.68295i q^{31} +8.95995 q^{33} +16.8741i q^{35} -17.2232 q^{37} +14.0181i q^{39} +12.0970 q^{41} +31.1494i q^{43} -19.1334 q^{45} -55.6971i q^{47} -7.00000 q^{49} +43.6438i q^{51} -56.8217 q^{53} -32.9926i q^{55} +2.75475 q^{57} +47.5731i q^{59} +101.351 q^{61} -7.93725i q^{63} +51.6178 q^{65} +58.9752i q^{67} -27.4505 q^{69} +13.3175i q^{71} +13.9050 q^{73} +27.1523i q^{75} +13.6865 q^{77} +45.8124i q^{79} +9.00000 q^{81} +145.317i q^{83} +160.706 q^{85} +39.9845i q^{87} +150.256 q^{89} +21.4130i q^{91} -2.91495 q^{93} -10.1436i q^{95} -90.5264 q^{97} +15.5191i 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 6.37780 1.27556 0.637780 0.770218i 0.279853π-0.279853\pi
0.637780 + 0.770218i 0.279853π0.279853\pi
66 0 0
77 2.64575i 0.377964i
88 0 0
99 −3.00000 −0.333333
1010 0 0
1111 − 5.17303i − 0.470275i −0.971962 0.235138i 0.924446π-0.924446\pi
0.971962 0.235138i 0.0755541π-0.0755541\pi
1212 0 0
1313 8.09335 0.622566 0.311283 0.950317i 0.399241π-0.399241\pi
0.311283 + 0.950317i 0.399241π0.399241\pi
1414 0 0
1515 11.0467i 0.736445i
1616 0 0
1717 25.1978 1.48222 0.741110 0.671383i 0.234299π-0.234299\pi
0.741110 + 0.671383i 0.234299π0.234299\pi
1818 0 0
1919 − 1.59045i − 0.0837080i −0.999124 0.0418540i 0.986674π-0.986674\pi
0.999124 0.0418540i 0.0133264π-0.0133264\pi
2020 0 0
2121 −4.58258 −0.218218
2222 0 0
2323 15.8485i 0.689066i 0.938774 + 0.344533i 0.111963π0.111963\pi
−0.938774 + 0.344533i 0.888037π0.888037\pi
2424 0 0
2525 15.6764 0.627054
2626 0 0
2727 − 5.19615i − 0.192450i
2828 0 0
2929 23.0850 0.796036 0.398018 0.917378i 0.369698π-0.369698\pi
0.398018 + 0.917378i 0.369698π0.369698\pi
3030 0 0
3131 1.68295i 0.0542887i 0.999632 + 0.0271443i 0.00864137π0.00864137\pi
−0.999632 + 0.0271443i 0.991359π0.991359\pi
3232 0 0
3333 8.95995 0.271514
3434 0 0
3535 16.8741i 0.482117i
3636 0 0
3737 −17.2232 −0.465491 −0.232745 0.972538i 0.574771π-0.574771\pi
−0.232745 + 0.972538i 0.574771π0.574771\pi
3838 0 0
3939 14.0181i 0.359438i
4040 0 0
4141 12.0970 0.295048 0.147524 0.989059i 0.452870π-0.452870\pi
0.147524 + 0.989059i 0.452870π0.452870\pi
4242 0 0
4343 31.1494i 0.724405i 0.932100 + 0.362202i 0.117975π0.117975\pi
−0.932100 + 0.362202i 0.882025π0.882025\pi
4444 0 0
4545 −19.1334 −0.425187
4646 0 0
4747 − 55.6971i − 1.18504i −0.805554 0.592522i 0.798132π-0.798132\pi
0.805554 0.592522i 0.201868π-0.201868\pi
4848 0 0
4949 −7.00000 −0.142857
5050 0 0
5151 43.6438i 0.855761i
5252 0 0
5353 −56.8217 −1.07211 −0.536054 0.844184i 0.680085π-0.680085\pi
−0.536054 + 0.844184i 0.680085π0.680085\pi
5454 0 0
5555 − 32.9926i − 0.599865i
5656 0 0
5757 2.75475 0.0483289
5858 0 0
5959 47.5731i 0.806323i 0.915129 + 0.403161i 0.132089π0.132089\pi
−0.915129 + 0.403161i 0.867911π0.867911\pi
6060 0 0
6161 101.351 1.66149 0.830747 0.556651i 0.187914π-0.187914\pi
0.830747 + 0.556651i 0.187914π0.187914\pi
6262 0 0
6363 − 7.93725i − 0.125988i
6464 0 0
6565 51.6178 0.794120
6666 0 0
6767 58.9752i 0.880226i 0.897942 + 0.440113i 0.145062π0.145062\pi
−0.897942 + 0.440113i 0.854938π0.854938\pi
6868 0 0
6969 −27.4505 −0.397833
7070 0 0
7171 13.3175i 0.187570i 0.995592 + 0.0937851i 0.0298967π0.0298967\pi
−0.995592 + 0.0937851i 0.970103π0.970103\pi
7272 0 0
7373 13.9050 0.190479 0.0952397 0.995454i 0.469638π-0.469638\pi
0.0952397 + 0.995454i 0.469638π0.469638\pi
7474 0 0
7575 27.1523i 0.362030i
7676 0 0
7777 13.6865 0.177747
7878 0 0
7979 45.8124i 0.579904i 0.957041 + 0.289952i 0.0936394π0.0936394\pi
−0.957041 + 0.289952i 0.906361π0.906361\pi
8080 0 0
8181 9.00000 0.111111
8282 0 0
8383 145.317i 1.75080i 0.483396 + 0.875402i 0.339403π0.339403\pi
−0.483396 + 0.875402i 0.660597π0.660597\pi
8484 0 0
8585 160.706 1.89066
8686 0 0
8787 39.9845i 0.459592i
8888 0 0
8989 150.256 1.68827 0.844135 0.536130i 0.180114π-0.180114\pi
0.844135 + 0.536130i 0.180114π0.180114\pi
9090 0 0
9191 21.4130i 0.235308i
9292 0 0
9393 −2.91495 −0.0313436
9494 0 0
9595 − 10.1436i − 0.106775i
9696 0 0
9797 −90.5264 −0.933262 −0.466631 0.884452i 0.654532π-0.654532\pi
−0.466631 + 0.884452i 0.654532π0.654532\pi
9898 0 0
9999 15.5191i 0.156758i
100100 0 0
101101 −157.083 −1.55528 −0.777640 0.628710i 0.783583π-0.783583\pi
−0.777640 + 0.628710i 0.783583π0.783583\pi
102102 0 0
103103 − 142.058i − 1.37920i −0.724188 0.689602i 0.757785π-0.757785\pi
0.724188 0.689602i 0.242215π-0.242215\pi
104104 0 0
105105 −29.2268 −0.278350
106106 0 0
107107 114.293i 1.06816i 0.845433 + 0.534082i 0.179343π0.179343\pi
−0.845433 + 0.534082i 0.820657π0.820657\pi
108108 0 0
109109 171.256 1.57115 0.785577 0.618765i 0.212367π-0.212367\pi
0.785577 + 0.618765i 0.212367π0.212367\pi
110110 0 0
111111 − 29.8314i − 0.268751i
112112 0 0
113113 −113.011 −1.00010 −0.500051 0.865996i 0.666685π-0.666685\pi
−0.500051 + 0.865996i 0.666685π0.666685\pi
114114 0 0
115115 101.079i 0.878946i
116116 0 0
117117 −24.2801 −0.207522
118118 0 0
119119 66.6670i 0.560227i
120120 0 0
121121 94.2398 0.778841
122122 0 0
123123 20.9525i 0.170346i
124124 0 0
125125 −59.4643 −0.475715
126126 0 0
127127 − 189.566i − 1.49265i −0.665583 0.746324i 0.731817π-0.731817\pi
0.665583 0.746324i 0.268183π-0.268183\pi
128128 0 0
129129 −53.9523 −0.418235
130130 0 0
131131 119.818i 0.914641i 0.889302 + 0.457321i 0.151191π0.151191\pi
−0.889302 + 0.457321i 0.848809π0.848809\pi
132132 0 0
133133 4.20794 0.0316387
134134 0 0
135135 − 33.1400i − 0.245482i
136136 0 0
137137 −129.183 −0.942942 −0.471471 0.881881i 0.656277π-0.656277\pi
−0.471471 + 0.881881i 0.656277π0.656277\pi
138138 0 0
139139 − 229.075i − 1.64802i −0.566572 0.824012i 0.691731π-0.691731\pi
0.566572 0.824012i 0.308269π-0.308269\pi
140140 0 0
141141 96.4701 0.684185
142142 0 0
143143 − 41.8672i − 0.292777i
144144 0 0
145145 147.232 1.01539
146146 0 0
147147 − 12.1244i − 0.0824786i
148148 0 0
149149 −72.7587 −0.488313 −0.244157 0.969736i 0.578511π-0.578511\pi
−0.244157 + 0.969736i 0.578511π0.578511\pi
150150 0 0
151151 − 255.512i − 1.69213i −0.533078 0.846066i 0.678965π-0.678965\pi
0.533078 0.846066i 0.321035π-0.321035\pi
152152 0 0
153153 −75.5933 −0.494074
154154 0 0
155155 10.7335i 0.0692485i
156156 0 0
157157 −37.2470 −0.237242 −0.118621 0.992940i 0.537847π-0.537847\pi
−0.118621 + 0.992940i 0.537847π0.537847\pi
158158 0 0
159159 − 98.4180i − 0.618981i
160160 0 0
161161 −41.9313 −0.260443
162162 0 0
163163 − 213.932i − 1.31247i −0.754558 0.656233i 0.772149π-0.772149\pi
0.754558 0.656233i 0.227851π-0.227851\pi
164164 0 0
165165 57.1448 0.346332
166166 0 0
167167 − 75.0723i − 0.449535i −0.974412 0.224767i 0.927838π-0.927838\pi
0.974412 0.224767i 0.0721623π-0.0721623\pi
168168 0 0
169169 −103.498 −0.612412
170170 0 0
171171 4.77136i 0.0279027i
172172 0 0
173173 −33.5589 −0.193982 −0.0969909 0.995285i 0.530922π-0.530922\pi
−0.0969909 + 0.995285i 0.530922π0.530922\pi
174174 0 0
175175 41.4757i 0.237004i
176176 0 0
177177 −82.3989 −0.465531
178178 0 0
179179 − 284.970i − 1.59201i −0.605289 0.796006i 0.706942π-0.706942\pi
0.605289 0.796006i 0.293058π-0.293058\pi
180180 0 0
181181 5.94109 0.0328237 0.0164119 0.999865i 0.494776π-0.494776\pi
0.0164119 + 0.999865i 0.494776π0.494776\pi
182182 0 0
183183 175.545i 0.959263i
184184 0 0
185185 −109.846 −0.593762
186186 0 0
187187 − 130.349i − 0.697052i
188188 0 0
189189 13.7477 0.0727393
190190 0 0
191191 − 22.3638i − 0.117088i −0.998285 0.0585440i 0.981354π-0.981354\pi
0.998285 0.0585440i 0.0186458π-0.0186458\pi
192192 0 0
193193 29.0238 0.150382 0.0751911 0.997169i 0.476043π-0.476043\pi
0.0751911 + 0.997169i 0.476043π0.476043\pi
194194 0 0
195195 89.4047i 0.458486i
196196 0 0
197197 −252.577 −1.28212 −0.641059 0.767492i 0.721505π-0.721505\pi
−0.641059 + 0.767492i 0.721505π0.721505\pi
198198 0 0
199199 − 81.0611i − 0.407342i −0.979039 0.203671i 0.934713π-0.934713\pi
0.979039 0.203671i 0.0652873π-0.0652873\pi
200200 0 0
201201 −102.148 −0.508199
202202 0 0
203203 61.0773i 0.300873i
204204 0 0
205205 77.1520 0.376351
206206 0 0
207207 − 47.5456i − 0.229689i
208208 0 0
209209 −8.22746 −0.0393658
210210 0 0
211211 292.377i 1.38567i 0.721095 + 0.692836i 0.243639π0.243639\pi
−0.721095 + 0.692836i 0.756361π0.756361\pi
212212 0 0
213213 −23.0666 −0.108294
214214 0 0
215215 198.665i 0.924022i
216216 0 0
217217 −4.45266 −0.0205192
218218 0 0
219219 24.0842i 0.109973i
220220 0 0
221221 203.934 0.922780
222222 0 0
223223 49.0529i 0.219968i 0.993933 + 0.109984i 0.0350800π0.0350800\pi
−0.993933 + 0.109984i 0.964920π0.964920\pi
224224 0 0
225225 −47.0291 −0.209018
226226 0 0
227227 − 209.041i − 0.920884i −0.887690 0.460442i 0.847691π-0.847691\pi
0.887690 0.460442i 0.152309π-0.152309\pi
228228 0 0
229229 −439.826 −1.92064 −0.960319 0.278904i 0.910029π-0.910029\pi
−0.960319 + 0.278904i 0.910029π0.910029\pi
230230 0 0
231231 23.7058i 0.102622i
232232 0 0
233233 207.035 0.888563 0.444282 0.895887i 0.353459π-0.353459\pi
0.444282 + 0.895887i 0.353459π0.353459\pi
234234 0 0
235235 − 355.225i − 1.51159i
236236 0 0
237237 −79.3495 −0.334808
238238 0 0
239239 − 189.157i − 0.791454i −0.918368 0.395727i 0.870493π-0.870493\pi
0.918368 0.395727i 0.129507π-0.129507\pi
240240 0 0
241241 179.181 0.743489 0.371745 0.928335i 0.378760π-0.378760\pi
0.371745 + 0.928335i 0.378760π0.378760\pi
242242 0 0
243243 15.5885i 0.0641500i
244244 0 0
245245 −44.6446 −0.182223
246246 0 0
247247 − 12.8721i − 0.0521138i
248248 0 0
249249 −251.696 −1.01083
250250 0 0
251251 191.872i 0.764428i 0.924074 + 0.382214i 0.124838π0.124838\pi
−0.924074 + 0.382214i 0.875162π0.875162\pi
252252 0 0
253253 81.9849 0.324051
254254 0 0
255255 278.351i 1.09157i
256256 0 0
257257 319.778 1.24427 0.622135 0.782910i 0.286265π-0.286265\pi
0.622135 + 0.782910i 0.286265π0.286265\pi
258258 0 0
259259 − 45.5682i − 0.175939i
260260 0 0
261261 −69.2551 −0.265345
262262 0 0
263263 − 113.522i − 0.431644i −0.976433 0.215822i 0.930757π-0.930757\pi
0.976433 0.215822i 0.0692431π-0.0692431\pi
264264 0 0
265265 −362.397 −1.36754
266266 0 0
267267 260.251i 0.974724i
268268 0 0
269269 −406.524 −1.51124 −0.755620 0.655010i 0.772664π-0.772664\pi
−0.755620 + 0.655010i 0.772664π0.772664\pi
270270 0 0
271271 − 508.180i − 1.87520i −0.347712 0.937601i 0.613041π-0.613041\pi
0.347712 0.937601i 0.386959π-0.386959\pi
272272 0 0
273273 −37.0884 −0.135855
274274 0 0
275275 − 81.0943i − 0.294888i
276276 0 0
277277 400.803 1.44694 0.723470 0.690355i 0.242546π-0.242546\pi
0.723470 + 0.690355i 0.242546π0.242546\pi
278278 0 0
279279 − 5.04885i − 0.0180962i
280280 0 0
281281 −544.569 −1.93797 −0.968984 0.247122i 0.920515π-0.920515\pi
−0.968984 + 0.247122i 0.920515π0.920515\pi
282282 0 0
283283 185.268i 0.654656i 0.944911 + 0.327328i 0.106148π0.106148\pi
−0.944911 + 0.327328i 0.893852π0.893852\pi
284284 0 0
285285 17.5692 0.0616464
286286 0 0
287287 32.0055i 0.111518i
288288 0 0
289289 345.927 1.19698
290290 0 0
291291 − 156.796i − 0.538819i
292292 0 0
293293 −465.044 −1.58718 −0.793590 0.608452i 0.791791π-0.791791\pi
−0.793590 + 0.608452i 0.791791π0.791791\pi
294294 0 0
295295 303.412i 1.02851i
296296 0 0
297297 −26.8798 −0.0905045
298298 0 0
299299 128.268i 0.428989i
300300 0 0
301301 −82.4136 −0.273799
302302 0 0
303303 − 272.076i − 0.897941i
304304 0 0
305305 646.397 2.11933
306306 0 0
307307 274.356i 0.893669i 0.894617 + 0.446834i 0.147449π0.147449\pi
−0.894617 + 0.446834i 0.852551π0.852551\pi
308308 0 0
309309 246.052 0.796284
310310 0 0
311311 − 14.2196i − 0.0457223i −0.999739 0.0228612i 0.992722π-0.992722\pi
0.999739 0.0228612i 0.00727757π-0.00727757\pi
312312 0 0
313313 −213.256 −0.681329 −0.340664 0.940185i 0.610652π-0.610652\pi
−0.340664 + 0.940185i 0.610652π0.610652\pi
314314 0 0
315315 − 50.6222i − 0.160706i
316316 0 0
317317 −3.37863 −0.0106582 −0.00532908 0.999986i 0.501696π-0.501696\pi
−0.00532908 + 0.999986i 0.501696π0.501696\pi
318318 0 0
319319 − 119.420i − 0.374356i
320320 0 0
321321 −197.962 −0.616704
322322 0 0
323323 − 40.0758i − 0.124074i
324324 0 0
325325 126.874 0.390383
326326 0 0
327327 296.624i 0.907106i
328328 0 0
329329 147.361 0.447904
330330 0 0
331331 − 456.028i − 1.37773i −0.724891 0.688863i 0.758110π-0.758110\pi
0.724891 0.688863i 0.241890π-0.241890\pi
332332 0 0
333333 51.6695 0.155164
334334 0 0
335335 376.132i 1.12278i
336336 0 0
337337 −149.399 −0.443321 −0.221661 0.975124i 0.571148π-0.571148\pi
−0.221661 + 0.975124i 0.571148π0.571148\pi
338338 0 0
339339 − 195.742i − 0.577409i
340340 0 0
341341 8.70594 0.0255306
342342 0 0
343343 − 18.5203i − 0.0539949i
344344 0 0
345345 −175.074 −0.507460
346346 0 0
347347 − 486.035i − 1.40068i −0.713811 0.700338i 0.753032π-0.753032\pi
0.713811 0.700338i 0.246968π-0.246968\pi
348348 0 0
349349 −349.059 −1.00017 −0.500085 0.865977i 0.666698π-0.666698\pi
−0.500085 + 0.865977i 0.666698π0.666698\pi
350350 0 0
351351 − 42.0543i − 0.119813i
352352 0 0
353353 −47.2923 −0.133973 −0.0669863 0.997754i 0.521338π-0.521338\pi
−0.0669863 + 0.997754i 0.521338π0.521338\pi
354354 0 0
355355 84.9363i 0.239257i
356356 0 0
357357 −115.471 −0.323447
358358 0 0
359359 − 332.202i − 0.925353i −0.886527 0.462677i 0.846889π-0.846889\pi
0.886527 0.462677i 0.153111π-0.153111\pi
360360 0 0
361361 358.470 0.992993
362362 0 0
363363 163.228i 0.449664i
364364 0 0
365365 88.6833 0.242968
366366 0 0
367367 191.517i 0.521843i 0.965360 + 0.260922i 0.0840264π0.0840264\pi
−0.965360 + 0.260922i 0.915974π0.915974\pi
368368 0 0
369369 −36.2909 −0.0983492
370370 0 0
371371 − 150.336i − 0.405218i
372372 0 0
373373 −39.5852 −0.106126 −0.0530632 0.998591i 0.516898π-0.516898\pi
−0.0530632 + 0.998591i 0.516898π0.516898\pi
374374 0 0
375375 − 102.995i − 0.274654i
376376 0 0
377377 186.835 0.495585
378378 0 0
379379 − 390.744i − 1.03099i −0.856894 0.515493i 0.827609π-0.827609\pi
0.856894 0.515493i 0.172391π-0.172391\pi
380380 0 0
381381 328.338 0.861781
382382 0 0
383383 82.0354i 0.214192i 0.994249 + 0.107096i 0.0341552π0.0341552\pi
−0.994249 + 0.107096i 0.965845π0.965845\pi
384384 0 0
385385 87.2901 0.226728
386386 0 0
387387 − 93.4482i − 0.241468i
388388 0 0
389389 192.620 0.495166 0.247583 0.968867i 0.420364π-0.420364\pi
0.247583 + 0.968867i 0.420364π0.420364\pi
390390 0 0
391391 399.347i 1.02135i
392392 0 0
393393 −207.531 −0.528068
394394 0 0
395395 292.183i 0.739703i
396396 0 0
397397 185.930 0.468337 0.234169 0.972196i 0.424763π-0.424763\pi
0.234169 + 0.972196i 0.424763π0.424763\pi
398398 0 0
399399 7.28837i 0.0182666i
400400 0 0
401401 501.532 1.25070 0.625351 0.780343i 0.284956π-0.284956\pi
0.625351 + 0.780343i 0.284956π0.284956\pi
402402 0 0
403403 13.6207i 0.0337983i
404404 0 0
405405 57.4002 0.141729
406406 0 0
407407 89.0959i 0.218909i
408408 0 0
409409 −604.348 −1.47762 −0.738812 0.673912i 0.764613π-0.764613\pi
−0.738812 + 0.673912i 0.764613π0.764613\pi
410410 0 0
411411 − 223.752i − 0.544408i
412412 0 0
413413 −125.866 −0.304761
414414 0 0
415415 926.801i 2.23326i
416416 0 0
417417 396.770 0.951487
418418 0 0
419419 129.024i 0.307932i 0.988076 + 0.153966i 0.0492047π0.0492047\pi
−0.988076 + 0.153966i 0.950795π0.950795\pi
420420 0 0
421421 97.4092 0.231376 0.115688 0.993286i 0.463093π-0.463093\pi
0.115688 + 0.993286i 0.463093π0.463093\pi
422422 0 0
423423 167.091i 0.395015i
424424 0 0
425425 395.009 0.929433
426426 0 0
427427 268.150i 0.627985i
428428 0 0
429429 72.5160 0.169035
430430 0 0
431431 189.028i 0.438580i 0.975660 + 0.219290i 0.0703741π0.0703741\pi
−0.975660 + 0.219290i 0.929626π0.929626\pi
432432 0 0
433433 679.795 1.56996 0.784982 0.619518i 0.212672π-0.212672\pi
0.784982 + 0.619518i 0.212672π0.212672\pi
434434 0 0
435435 255.013i 0.586237i
436436 0 0
437437 25.2063 0.0576804
438438 0 0
439439 − 266.934i − 0.608049i −0.952664 0.304025i 0.901670π-0.901670\pi
0.952664 0.304025i 0.0983305π-0.0983305\pi
440440 0 0
441441 21.0000 0.0476190
442442 0 0
443443 219.470i 0.495418i 0.968835 + 0.247709i 0.0796776π0.0796776\pi
−0.968835 + 0.247709i 0.920322π0.920322\pi
444444 0 0
445445 958.304 2.15349
446446 0 0
447447 − 126.022i − 0.281928i
448448 0 0
449449 −93.1600 −0.207483 −0.103742 0.994604i 0.533082π-0.533082\pi
−0.103742 + 0.994604i 0.533082π0.533082\pi
450450 0 0
451451 − 62.5779i − 0.138754i
452452 0 0
453453 442.560 0.976953
454454 0 0
455455 136.568i 0.300149i
456456 0 0
457457 32.7526 0.0716686 0.0358343 0.999358i 0.488591π-0.488591\pi
0.0358343 + 0.999358i 0.488591π0.488591\pi
458458 0 0
459459 − 130.931i − 0.285254i
460460 0 0
461461 4.03180 0.00874578 0.00437289 0.999990i 0.498608π-0.498608\pi
0.00437289 + 0.999990i 0.498608π0.498608\pi
462462 0 0
463463 789.033i 1.70417i 0.523399 + 0.852087i 0.324664π0.324664\pi
−0.523399 + 0.852087i 0.675336π0.675336\pi
464464 0 0
465465 −18.5910 −0.0399806
466466 0 0
467467 168.642i 0.361118i 0.983564 + 0.180559i 0.0577907π0.0577907\pi
−0.983564 + 0.180559i 0.942209π0.942209\pi
468468 0 0
469469 −156.034 −0.332694
470470 0 0
471471 − 64.5137i − 0.136972i
472472 0 0
473473 161.137 0.340670
474474 0 0
475475 − 24.9325i − 0.0524895i
476476 0 0
477477 170.465 0.357369
478478 0 0
479479 866.788i 1.80958i 0.425860 + 0.904789i 0.359972π0.359972\pi
−0.425860 + 0.904789i 0.640028π0.640028\pi
480480 0 0
481481 −139.393 −0.289799
482482 0 0
483483 − 72.6271i − 0.150367i
484484 0 0
485485 −577.360 −1.19043
486486 0 0
487487 16.5605i 0.0340051i 0.999855 + 0.0170026i 0.00541234π0.00541234\pi
−0.999855 + 0.0170026i 0.994588π0.994588\pi
488488 0 0
489489 370.541 0.757753
490490 0 0
491491 − 17.3669i − 0.0353705i −0.999844 0.0176852i 0.994370π-0.994370\pi
0.999844 0.0176852i 0.00562968π-0.00562968\pi
492492 0 0
493493 581.691 1.17990
494494 0 0
495495 98.9777i 0.199955i
496496 0 0
497497 −35.2347 −0.0708949
498498 0 0
499499 − 194.180i − 0.389139i −0.980889 0.194570i 0.937669π-0.937669\pi
0.980889 0.194570i 0.0623310π-0.0623310\pi
500500 0 0
501501 130.029 0.259539
502502 0 0
503503 839.393i 1.66877i 0.551179 + 0.834387i 0.314178π0.314178\pi
−0.551179 + 0.834387i 0.685822π0.685822\pi
504504 0 0
505505 −1001.85 −1.98385
506506 0 0
507507 − 179.263i − 0.353576i
508508 0 0
509509 217.634 0.427571 0.213785 0.976881i 0.431421π-0.431421\pi
0.213785 + 0.976881i 0.431421π0.431421\pi
510510 0 0
511511 36.7892i 0.0719945i
512512 0 0
513513 −8.26424 −0.0161096
514514 0 0
515515 − 906.018i − 1.75926i
516516 0 0
517517 −288.122 −0.557297
518518 0 0
519519 − 58.1256i − 0.111995i
520520 0 0
521521 −511.156 −0.981106 −0.490553 0.871411i 0.663205π-0.663205\pi
−0.490553 + 0.871411i 0.663205π0.663205\pi
522522 0 0
523523 − 414.920i − 0.793346i −0.917960 0.396673i 0.870165π-0.870165\pi
0.917960 0.396673i 0.129835π-0.129835\pi
524524 0 0
525525 −71.8381 −0.136834
526526 0 0
527527 42.4065i 0.0804678i
528528 0 0
529529 277.824 0.525187
530530 0 0
531531 − 142.719i − 0.268774i
532532 0 0
533533 97.9049 0.183687
534534 0 0
535535 728.941i 1.36251i
536536 0 0
537537 493.583 0.919149
538538 0 0
539539 36.2112i 0.0671822i
540540 0 0
541541 824.298 1.52366 0.761828 0.647780i 0.224302π-0.224302\pi
0.761828 + 0.647780i 0.224302π0.224302\pi
542542 0 0
543543 10.2903i 0.0189508i
544544 0 0
545545 1092.23 2.00410
546546 0 0
547547 − 357.494i − 0.653553i −0.945102 0.326777i 0.894037π-0.894037\pi
0.945102 0.326777i 0.105963π-0.105963\pi
548548 0 0
549549 −304.053 −0.553831
550550 0 0
551551 − 36.7157i − 0.0666346i
552552 0 0
553553 −121.208 −0.219183
554554 0 0
555555 − 190.259i − 0.342808i
556556 0 0
557557 −401.693 −0.721173 −0.360586 0.932726i 0.617423π-0.617423\pi
−0.360586 + 0.932726i 0.617423π0.617423\pi
558558 0 0
559559 252.103i 0.450989i
560560 0 0
561561 225.771 0.402443
562562 0 0
563563 34.6358i 0.0615200i 0.999527 + 0.0307600i 0.00979276π0.00979276\pi
−0.999527 + 0.0307600i 0.990207π0.990207\pi
564564 0 0
565565 −720.765 −1.27569
566566 0 0
567567 23.8118i 0.0419961i
568568 0 0
569569 −650.576 −1.14337 −0.571684 0.820474i 0.693710π-0.693710\pi
−0.571684 + 0.820474i 0.693710π0.693710\pi
570570 0 0
571571 624.560i 1.09380i 0.837198 + 0.546900i 0.184192π0.184192\pi
−0.837198 + 0.546900i 0.815808π0.815808\pi
572572 0 0
573573 38.7353 0.0676008
574574 0 0
575575 248.447i 0.432082i
576576 0 0
577577 −885.685 −1.53498 −0.767491 0.641059i 0.778495π-0.778495\pi
−0.767491 + 0.641059i 0.778495π0.778495\pi
578578 0 0
579579 50.2707i 0.0868232i
580580 0 0
581581 −384.472 −0.661741
582582 0 0
583583 293.940i 0.504185i
584584 0 0
585585 −154.853 −0.264707
586586 0 0
587587 593.145i 1.01047i 0.862982 + 0.505235i 0.168594π0.168594\pi
−0.862982 + 0.505235i 0.831406π0.831406\pi
588588 0 0
589589 2.67665 0.00454440
590590 0 0
591591 − 437.477i − 0.740231i
592592 0 0
593593 812.442 1.37005 0.685027 0.728518i 0.259790π-0.259790\pi
0.685027 + 0.728518i 0.259790π0.259790\pi
594594 0 0
595595 425.189i 0.714603i
596596 0 0
597597 140.402 0.235179
598598 0 0
599599 − 987.235i − 1.64814i −0.566488 0.824070i 0.691698π-0.691698\pi
0.566488 0.824070i 0.308302π-0.308302\pi
600600 0 0
601601 −875.190 −1.45622 −0.728112 0.685458i 0.759602π-0.759602\pi
−0.728112 + 0.685458i 0.759602π0.759602\pi
602602 0 0
603603 − 176.925i − 0.293409i
604604 0 0
605605 601.043 0.993459
606606 0 0
607607 − 1135.57i − 1.87079i −0.353601 0.935396i 0.615043π-0.615043\pi
0.353601 0.935396i 0.384957π-0.384957\pi
608608 0 0
609609 −105.789 −0.173709
610610 0 0
611611 − 450.776i − 0.737768i
612612 0 0
613613 −458.347 −0.747710 −0.373855 0.927487i 0.621964π-0.621964\pi
−0.373855 + 0.927487i 0.621964π0.621964\pi
614614 0 0
615615 133.631i 0.217286i
616616 0 0
617617 712.482 1.15475 0.577376 0.816479i 0.304077π-0.304077\pi
0.577376 + 0.816479i 0.304077π0.304077\pi
618618 0 0
619619 1055.45i 1.70510i 0.522649 + 0.852548i 0.324944π0.324944\pi
−0.522649 + 0.852548i 0.675056π0.675056\pi
620620 0 0
621621 82.3514 0.132611
622622 0 0
623623 397.540i 0.638106i
624624 0 0
625625 −771.161 −1.23386
626626 0 0
627627 − 14.2504i − 0.0227279i
628628 0 0
629629 −433.985 −0.689960
630630 0 0
631631 − 652.825i − 1.03459i −0.855808 0.517294i 0.826940π-0.826940\pi
0.855808 0.517294i 0.173060π-0.173060\pi
632632 0 0
633633 −506.412 −0.800018
634634 0 0
635635 − 1209.02i − 1.90396i
636636 0 0
637637 −56.6535 −0.0889380
638638 0 0
639639 − 39.9524i − 0.0625234i
640640 0 0
641641 −193.690 −0.302168 −0.151084 0.988521i 0.548276π-0.548276\pi
−0.151084 + 0.988521i 0.548276π0.548276\pi
642642 0 0
643643 227.685i 0.354098i 0.984202 + 0.177049i 0.0566551π0.0566551\pi
−0.984202 + 0.177049i 0.943345π0.943345\pi
644644 0 0
645645 −344.097 −0.533484
646646 0 0
647647 − 779.133i − 1.20422i −0.798412 0.602112i 0.794326π-0.794326\pi
0.798412 0.602112i 0.205674π-0.205674\pi
648648 0 0
649649 246.097 0.379194
650650 0 0
651651 − 7.71224i − 0.0118468i
652652 0 0
653653 267.074 0.408995 0.204498 0.978867i 0.434444π-0.434444\pi
0.204498 + 0.978867i 0.434444π0.434444\pi
654654 0 0
655655 764.175i 1.16668i
656656 0 0
657657 −41.7150 −0.0634932
658658 0 0
659659 281.512i 0.427181i 0.976923 + 0.213590i 0.0685158π0.0685158\pi
−0.976923 + 0.213590i 0.931484π0.931484\pi
660660 0 0
661661 671.521 1.01592 0.507958 0.861382i 0.330400π-0.330400\pi
0.507958 + 0.861382i 0.330400π0.330400\pi
662662 0 0
663663 353.225i 0.532767i
664664 0 0
665665 26.8374 0.0403570
666666 0 0
667667 365.864i 0.548522i
668668 0 0
669669 −84.9620 −0.126999
670670 0 0
671671 − 524.292i − 0.781359i
672672 0 0
673673 −1104.65 −1.64138 −0.820690 0.571374i 0.806410π-0.806410\pi
−0.820690 + 0.571374i 0.806410π0.806410\pi
674674 0 0
675675 − 81.4568i − 0.120677i
676676 0 0
677677 −245.606 −0.362785 −0.181393 0.983411i 0.558060π-0.558060\pi
−0.181393 + 0.983411i 0.558060π0.558060\pi
678678 0 0
679679 − 239.510i − 0.352740i
680680 0 0
681681 362.069 0.531673
682682 0 0
683683 502.169i 0.735240i 0.929976 + 0.367620i 0.119827π0.119827\pi
−0.929976 + 0.367620i 0.880173π0.880173\pi
684684 0 0
685685 −823.904 −1.20278
686686 0 0
687687 − 761.801i − 1.10888i
688688 0 0
689689 −459.878 −0.667457
690690 0 0
691691 324.045i 0.468951i 0.972122 + 0.234475i 0.0753372π0.0753372\pi
−0.972122 + 0.234475i 0.924663π0.924663\pi
692692 0 0
693693 −41.0596 −0.0592491
694694 0 0
695695 − 1461.00i − 2.10215i
696696 0 0
697697 304.816 0.437326
698698 0 0
699699 358.596i 0.513012i
700700 0 0
701701 1218.75 1.73858 0.869291 0.494300i 0.164576π-0.164576\pi
0.869291 + 0.494300i 0.164576π0.164576\pi
702702 0 0
703703 27.3926i 0.0389653i
704704 0 0
705705 615.267 0.872720
706706 0 0
707707 − 415.603i − 0.587840i
708708 0 0
709709 −617.631 −0.871130 −0.435565 0.900157i 0.643451π-0.643451\pi
−0.435565 + 0.900157i 0.643451π0.643451\pi
710710 0 0
711711 − 137.437i − 0.193301i
712712 0 0
713713 −26.6723 −0.0374085
714714 0 0
715715 − 267.020i − 0.373455i
716716 0 0
717717 327.630 0.456946
718718 0 0
719719 − 693.411i − 0.964410i −0.876058 0.482205i 0.839836π-0.839836\pi
0.876058 0.482205i 0.160164π-0.160164\pi
720720 0 0
721721 375.850 0.521290
722722 0 0
723723 310.350i 0.429254i
724724 0 0
725725 361.890 0.499158
726726 0 0
727727 407.809i 0.560947i 0.959862 + 0.280474i 0.0904915π0.0904915\pi
−0.959862 + 0.280474i 0.909508π0.909508\pi
728728 0 0
729729 −27.0000 −0.0370370
730730 0 0
731731 784.895i 1.07373i
732732 0 0
733733 −251.068 −0.342521 −0.171260 0.985226i 0.554784π-0.554784\pi
−0.171260 + 0.985226i 0.554784π0.554784\pi
734734 0 0
735735 − 77.3267i − 0.105206i
736736 0 0
737737 305.080 0.413949
738738 0 0
739739 529.073i 0.715931i 0.933735 + 0.357965i 0.116529π0.116529\pi
−0.933735 + 0.357965i 0.883471π0.883471\pi
740740 0 0
741741 22.2951 0.0300879
742742 0 0
743743 563.363i 0.758227i 0.925350 + 0.379114i 0.123771π0.123771\pi
−0.925350 + 0.379114i 0.876229π0.876229\pi
744744 0 0
745745 −464.040 −0.622873
746746 0 0
747747 − 435.950i − 0.583601i
748748 0 0
749749 −302.392 −0.403728
750750 0 0
751751 594.813i 0.792028i 0.918245 + 0.396014i 0.129607π0.129607\pi
−0.918245 + 0.396014i 0.870393π0.870393\pi
752752 0 0
753753 −332.331 −0.441343
754754 0 0
755755 − 1629.61i − 2.15842i
756756 0 0
757757 −239.379 −0.316221 −0.158111 0.987421i 0.550540π-0.550540\pi
−0.158111 + 0.987421i 0.550540π0.550540\pi
758758 0 0
759759 142.002i 0.187091i
760760 0 0
761761 925.966 1.21678 0.608388 0.793640i 0.291817π-0.291817\pi
0.608388 + 0.793640i 0.291817π0.291817\pi
762762 0 0
763763 453.100i 0.593840i
764764 0 0
765765 −482.119 −0.630221
766766 0 0
767767 385.026i 0.501989i
768768 0 0
769769 625.702 0.813657 0.406828 0.913505i 0.366635π-0.366635\pi
0.406828 + 0.913505i 0.366635π0.366635\pi
770770 0 0
771771 553.871i 0.718380i
772772 0 0
773773 497.274 0.643304 0.321652 0.946858i 0.395762π-0.395762\pi
0.321652 + 0.946858i 0.395762π0.395762\pi
774774 0 0
775775 26.3825i 0.0340419i
776776 0 0
777777 78.9264 0.101578
778778 0 0
779779 − 19.2396i − 0.0246979i
780780 0 0
781781 68.8917 0.0882096
782782 0 0
783783 − 119.953i − 0.153197i
784784 0 0
785785 −237.554 −0.302617
786786 0 0
787787 48.9026i 0.0621380i 0.999517 + 0.0310690i 0.00989117π0.00989117\pi
−0.999517 + 0.0310690i 0.990109π0.990109\pi
788788 0 0
789789 196.627 0.249210
790790 0 0
791791 − 299.000i − 0.378003i
792792 0 0
793793 820.270 1.03439
794794 0 0
795795 − 627.691i − 0.789548i
796796 0 0
797797 −547.361 −0.686777 −0.343388 0.939193i 0.611575π-0.611575\pi
−0.343388 + 0.939193i 0.611575π0.611575\pi
798798 0 0
799799 − 1403.44i − 1.75650i
800800 0 0
801801 −450.768 −0.562757
802802 0 0
803803 − 71.9310i − 0.0895778i
804804 0 0
805805 −267.429 −0.332210
806806 0 0
807807 − 704.120i − 0.872515i
808808 0 0
809809 −40.2545 −0.0497583 −0.0248792 0.999690i 0.507920π-0.507920\pi
−0.0248792 + 0.999690i 0.507920π0.507920\pi
810810 0 0
811811 187.630i 0.231356i 0.993287 + 0.115678i 0.0369041π0.0369041\pi
−0.993287 + 0.115678i 0.963096π0.963096\pi
812812 0 0
813813 880.193 1.08265
814814 0 0
815815 − 1364.42i − 1.67413i
816816 0 0
817817 49.5416 0.0606385
818818 0 0
819819 − 64.2390i − 0.0784359i
820820 0 0
821821 −727.736 −0.886402 −0.443201 0.896422i 0.646157π-0.646157\pi
−0.443201 + 0.896422i 0.646157π0.646157\pi
822822 0 0
823823 − 741.649i − 0.901154i −0.892738 0.450577i 0.851218π-0.851218\pi
0.892738 0.450577i 0.148782π-0.148782\pi
824824 0 0
825825 140.459 0.170254
826826 0 0
827827 132.347i 0.160032i 0.996794 + 0.0800161i 0.0254972π0.0254972\pi
−0.996794 + 0.0800161i 0.974503π0.974503\pi
828828 0 0
829829 −1182.43 −1.42634 −0.713169 0.700992i 0.752741π-0.752741\pi
−0.713169 + 0.700992i 0.752741π0.752741\pi
830830 0 0
831831 694.211i 0.835392i
832832 0 0
833833 −176.384 −0.211746
834834 0 0
835835 − 478.797i − 0.573409i
836836 0 0
837837 8.74486 0.0104479
838838 0 0
839839 − 499.514i − 0.595368i −0.954664 0.297684i 0.903786π-0.903786\pi
0.954664 0.297684i 0.0962142π-0.0962142\pi
840840 0 0
841841 −308.081 −0.366326
842842 0 0
843843 − 943.222i − 1.11889i
844844 0 0
845845 −660.087 −0.781168
846846 0 0
847847 249.335i 0.294374i
848848 0 0
849849 −320.893 −0.377966
850850 0 0
851851 − 272.962i − 0.320754i
852852 0 0
853853 −911.533 −1.06862 −0.534310 0.845288i 0.679429π-0.679429\pi
−0.534310 + 0.845288i 0.679429π0.679429\pi
854854 0 0
855855 30.4308i 0.0355916i
856856 0 0
857857 −886.214 −1.03409 −0.517045 0.855958i 0.672968π-0.672968\pi
−0.517045 + 0.855958i 0.672968π0.672968\pi
858858 0 0
859859 − 1636.74i − 1.90540i −0.303911 0.952700i 0.598293π-0.598293\pi
0.303911 0.952700i 0.401707π-0.401707\pi
860860 0 0
861861 −55.4352 −0.0643847
862862 0 0
863863 225.975i 0.261848i 0.991392 + 0.130924i 0.0417944π0.0417944\pi
−0.991392 + 0.130924i 0.958206π0.958206\pi
864864 0 0
865865 −214.032 −0.247436
866866 0 0
867867 599.163i 0.691076i
868868 0 0
869869 236.989 0.272715
870870 0 0
871871 477.307i 0.547999i
872872 0 0
873873 271.579 0.311087
874874 0 0
875875 − 157.328i − 0.179803i
876876 0 0
877877 −388.417 −0.442893 −0.221446 0.975173i 0.571078π-0.571078\pi
−0.221446 + 0.975173i 0.571078π0.571078\pi
878878 0 0
879879 − 805.480i − 0.916359i
880880 0 0
881881 −653.052 −0.741262 −0.370631 0.928780i 0.620859π-0.620859\pi
−0.370631 + 0.928780i 0.620859π0.620859\pi
882882 0 0
883883 386.470i 0.437678i 0.975761 + 0.218839i 0.0702269π0.0702269\pi
−0.975761 + 0.218839i 0.929773π0.929773\pi
884884 0 0
885885 −525.524 −0.593813
886886 0 0
887887 28.5610i 0.0321995i 0.999870 + 0.0160998i 0.00512493π0.00512493\pi
−0.999870 + 0.0160998i 0.994875π0.994875\pi
888888 0 0
889889 501.545 0.564168
890890 0 0
891891 − 46.5573i − 0.0522528i
892892 0 0
893893 −88.5835 −0.0991977
894894 0 0
895895 − 1817.48i − 2.03071i
896896 0 0
897897 −222.166 −0.247677
898898 0 0
899899 38.8509i 0.0432157i
900900 0 0
901901 −1431.78 −1.58910
902902 0 0
903903 − 142.744i − 0.158078i
904904 0 0
905905 37.8911 0.0418686
906906 0 0
907907 541.169i 0.596658i 0.954463 + 0.298329i 0.0964293π0.0964293\pi
−0.954463 + 0.298329i 0.903571π0.903571\pi
908908 0 0
909909 471.250 0.518427
910910 0 0
911911 1175.01i 1.28981i 0.764265 + 0.644903i 0.223102π0.223102\pi
−0.764265 + 0.644903i 0.776898π0.776898\pi
912912 0 0
913913 751.727 0.823360
914914 0 0
915915 1119.59i 1.22360i
916916 0 0
917917 −317.009 −0.345702
918918 0 0
919919 959.135i 1.04367i 0.853046 + 0.521836i 0.174753π0.174753\pi
−0.853046 + 0.521836i 0.825247π0.825247\pi
920920 0 0
921921 −475.199 −0.515960
922922 0 0
923923 107.783i 0.116775i
924924 0 0
925925 −269.996 −0.291888
926926 0 0
927927 426.174i 0.459735i
928928 0 0
929929 −1042.64 −1.12232 −0.561161 0.827707i 0.689645π-0.689645\pi
−0.561161 + 0.827707i 0.689645π0.689645\pi
930930 0 0
931931 11.1332i 0.0119583i
932932 0 0
933933 24.6291 0.0263978
934934 0 0
935935 − 831.338i − 0.889132i
936936 0 0
937937 354.563 0.378402 0.189201 0.981938i 0.439410π-0.439410\pi
0.189201 + 0.981938i 0.439410π0.439410\pi
938938 0 0
939939 − 369.370i − 0.393365i
940940 0 0
941941 1291.59 1.37257 0.686287 0.727331i 0.259240π-0.259240\pi
0.686287 + 0.727331i 0.259240π0.259240\pi
942942 0 0
943943 191.719i 0.203307i
944944 0 0
945945 87.6803 0.0927834
946946 0 0
947947 1678.61i 1.77256i 0.463151 + 0.886279i 0.346719π0.346719\pi
−0.463151 + 0.886279i 0.653281π0.653281\pi
948948 0 0
949949 112.538 0.118586
950950 0 0
951951 − 5.85197i − 0.00615349i
952952 0 0
953953 −1129.47 −1.18517 −0.592586 0.805507i 0.701893π-0.701893\pi
−0.592586 + 0.805507i 0.701893π0.701893\pi
954954 0 0
955955 − 142.632i − 0.149353i
956956 0 0
957957 206.841 0.216135
958958 0 0
959959 − 341.786i − 0.356399i
960960 0 0
961961 958.168 0.997053
962962 0 0
963963 − 342.880i − 0.356054i
964964 0 0
965965 185.108 0.191822
966966 0 0
967967 385.235i 0.398382i 0.979961 + 0.199191i 0.0638314π0.0638314\pi
−0.979961 + 0.199191i 0.936169π0.936169\pi
968968 0 0
969969 69.4134 0.0716341
970970 0 0
971971 1449.76i 1.49306i 0.665354 + 0.746528i 0.268280π0.268280\pi
−0.665354 + 0.746528i 0.731720π0.731720\pi
972972 0 0
973973 606.076 0.622895
974974 0 0
975975 219.753i 0.225387i
976976 0 0
977977 −7.93650 −0.00812333 −0.00406167 0.999992i 0.501293π-0.501293\pi
−0.00406167 + 0.999992i 0.501293π0.501293\pi
978978 0 0
979979 − 777.279i − 0.793952i
980980 0 0
981981 −513.767 −0.523718
982982 0 0
983983 − 149.757i − 0.152347i −0.997095 0.0761735i 0.975730π-0.975730\pi
0.997095 0.0761735i 0.0242703π-0.0242703\pi
984984 0 0
985985 −1610.89 −1.63542
986986 0 0
987987 255.236i 0.258598i
988988 0 0
989989 −493.672 −0.499163
990990 0 0
991991 − 463.743i − 0.467955i −0.972242 0.233977i 0.924826π-0.924826\pi
0.972242 0.233977i 0.0751741π-0.0751741\pi
992992 0 0
993993 789.863 0.795431
994994 0 0
995995 − 516.992i − 0.519590i
996996 0 0
997997 669.502 0.671517 0.335758 0.941948i 0.391007π-0.391007\pi
0.335758 + 0.941948i 0.391007π0.391007\pi
998998 0 0
999999 89.4942i 0.0895838i
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.127.8 yes 8
3.2 odd 2 2016.3.m.b.127.2 8
4.3 odd 2 inner 672.3.m.a.127.4 8
8.3 odd 2 1344.3.m.d.127.5 8
8.5 even 2 1344.3.m.d.127.1 8
12.11 even 2 2016.3.m.b.127.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
672.3.m.a.127.4 8 4.3 odd 2 inner
672.3.m.a.127.8 yes 8 1.1 even 1 trivial
1344.3.m.d.127.1 8 8.5 even 2
1344.3.m.d.127.5 8 8.3 odd 2
2016.3.m.b.127.1 8 12.11 even 2
2016.3.m.b.127.2 8 3.2 odd 2