Properties

Label 153.4.a.f.1.2
Level 153153
Weight 44
Character 153.1
Self dual yes
Analytic conductor 9.0279.027
Analytic rank 11
Dimension 33
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [153,4,Mod(1,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 153=3217 153 = 3^{2} \cdot 17
Weight: k k == 4 4
Character orbit: [χ][\chi] == 153.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-5,0,13,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 9.027292230889.02729223088
Analytic rank: 11
Dimension: 33
Coefficient field: 3.3.5912.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x3x214x10 x^{3} - x^{2} - 14x - 10 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 51)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 0.795427-0.795427 of defining polynomial
Character χ\chi == 153.1

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) == q2.79543q20.185590q47.18559q5+19.9241q7+22.8822q8+20.0868q10+20.2836q1169.3212q1355.6963q1462.4808q1617.0000q172.16352q19+1.33357q2056.7013q22+13.0415q2373.3673q25+193.782q263.69771q28246.831q29166.779q318.39714q32+47.5223q34143.166q35162.065q37+6.04795q38164.422q40253.572q41+556.702q433.76443q4436.4565q46198.218q47+53.9684q49+205.093q50+12.8653q52496.904q53145.750q55+455.907q56+689.997q58+343.050q59+332.776q61+466.218q62+523.320q64+498.114q65169.821q67+3.15503q68+400.211q70+509.616q71621.448q73+453.041q74+0.401527q76+404.132q771122.10q79+448.962q80+708.843q82+485.798q83+122.155q851556.22q86+464.134q881038.49q891381.16q912.42037q92+554.103q94+15.5462q95+1014.67q97150.865q98+O(q100)q-2.79543 q^{2} -0.185590 q^{4} -7.18559 q^{5} +19.9241 q^{7} +22.8822 q^{8} +20.0868 q^{10} +20.2836 q^{11} -69.3212 q^{13} -55.6963 q^{14} -62.4808 q^{16} -17.0000 q^{17} -2.16352 q^{19} +1.33357 q^{20} -56.7013 q^{22} +13.0415 q^{23} -73.3673 q^{25} +193.782 q^{26} -3.69771 q^{28} -246.831 q^{29} -166.779 q^{31} -8.39714 q^{32} +47.5223 q^{34} -143.166 q^{35} -162.065 q^{37} +6.04795 q^{38} -164.422 q^{40} -253.572 q^{41} +556.702 q^{43} -3.76443 q^{44} -36.4565 q^{46} -198.218 q^{47} +53.9684 q^{49} +205.093 q^{50} +12.8653 q^{52} -496.904 q^{53} -145.750 q^{55} +455.907 q^{56} +689.997 q^{58} +343.050 q^{59} +332.776 q^{61} +466.218 q^{62} +523.320 q^{64} +498.114 q^{65} -169.821 q^{67} +3.15503 q^{68} +400.211 q^{70} +509.616 q^{71} -621.448 q^{73} +453.041 q^{74} +0.401527 q^{76} +404.132 q^{77} -1122.10 q^{79} +448.962 q^{80} +708.843 q^{82} +485.798 q^{83} +122.155 q^{85} -1556.22 q^{86} +464.134 q^{88} -1038.49 q^{89} -1381.16 q^{91} -2.42037 q^{92} +554.103 q^{94} +15.5462 q^{95} +1014.67 q^{97} -150.865 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q5q2+13q48q58q733q838q1034q11+36q13+104q1479q1651q17142q19+126q20248q22110q23193q25154q26+4109q98+O(q100) 3 q - 5 q^{2} + 13 q^{4} - 8 q^{5} - 8 q^{7} - 33 q^{8} - 38 q^{10} - 34 q^{11} + 36 q^{13} + 104 q^{14} - 79 q^{16} - 51 q^{17} - 142 q^{19} + 126 q^{20} - 248 q^{22} - 110 q^{23} - 193 q^{25} - 154 q^{26}+ \cdots - 4109 q^{98}+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 −2.79543 −0.988333 −0.494166 0.869367i 0.664527π-0.664527\pi
−0.494166 + 0.869367i 0.664527π0.664527\pi
33 0 0
44 −0.185590 −0.0231987
55 −7.18559 −0.642699 −0.321349 0.946961i 0.604136π-0.604136\pi
−0.321349 + 0.946961i 0.604136π0.604136\pi
66 0 0
77 19.9241 1.07580 0.537899 0.843009i 0.319218π-0.319218\pi
0.537899 + 0.843009i 0.319218π0.319218\pi
88 22.8822 1.01126
99 0 0
1010 20.0868 0.635200
1111 20.2836 0.555976 0.277988 0.960585i 0.410332π-0.410332\pi
0.277988 + 0.960585i 0.410332π0.410332\pi
1212 0 0
1313 −69.3212 −1.47894 −0.739471 0.673189i 0.764924π-0.764924\pi
−0.739471 + 0.673189i 0.764924π0.764924\pi
1414 −55.6963 −1.06325
1515 0 0
1616 −62.4808 −0.976263
1717 −17.0000 −0.242536
1818 0 0
1919 −2.16352 −0.0261234 −0.0130617 0.999915i 0.504158π-0.504158\pi
−0.0130617 + 0.999915i 0.504158π0.504158\pi
2020 1.33357 0.0149098
2121 0 0
2222 −56.7013 −0.549489
2323 13.0415 0.118232 0.0591161 0.998251i 0.481172π-0.481172\pi
0.0591161 + 0.998251i 0.481172π0.481172\pi
2424 0 0
2525 −73.3673 −0.586938
2626 193.782 1.46169
2727 0 0
2828 −3.69771 −0.0249572
2929 −246.831 −1.58053 −0.790264 0.612767i 0.790057π-0.790057\pi
−0.790264 + 0.612767i 0.790057π0.790057\pi
3030 0 0
3131 −166.779 −0.966269 −0.483135 0.875546i 0.660502π-0.660502\pi
−0.483135 + 0.875546i 0.660502π0.660502\pi
3232 −8.39714 −0.0463881
3333 0 0
3434 47.5223 0.239706
3535 −143.166 −0.691414
3636 0 0
3737 −162.065 −0.720090 −0.360045 0.932935i 0.617239π-0.617239\pi
−0.360045 + 0.932935i 0.617239π0.617239\pi
3838 6.04795 0.0258186
3939 0 0
4040 −164.422 −0.649936
4141 −253.572 −0.965886 −0.482943 0.875652i 0.660432π-0.660432\pi
−0.482943 + 0.875652i 0.660432π0.660432\pi
4242 0 0
4343 556.702 1.97433 0.987166 0.159698i 0.0510520π-0.0510520\pi
0.987166 + 0.159698i 0.0510520π0.0510520\pi
4444 −3.76443 −0.0128979
4545 0 0
4646 −36.4565 −0.116853
4747 −198.218 −0.615170 −0.307585 0.951521i 0.599521π-0.599521\pi
−0.307585 + 0.951521i 0.599521π0.599521\pi
4848 0 0
4949 53.9684 0.157342
5050 205.093 0.580090
5151 0 0
5252 12.8653 0.0343096
5353 −496.904 −1.28783 −0.643915 0.765097i 0.722691π-0.722691\pi
−0.643915 + 0.765097i 0.722691π0.722691\pi
5454 0 0
5555 −145.750 −0.357325
5656 455.907 1.08791
5757 0 0
5858 689.997 1.56209
5959 343.050 0.756971 0.378486 0.925607i 0.376445π-0.376445\pi
0.378486 + 0.925607i 0.376445π0.376445\pi
6060 0 0
6161 332.776 0.698484 0.349242 0.937033i 0.386439π-0.386439\pi
0.349242 + 0.937033i 0.386439π0.386439\pi
6262 466.218 0.954995
6363 0 0
6464 523.320 1.02211
6565 498.114 0.950514
6666 0 0
6767 −169.821 −0.309656 −0.154828 0.987941i 0.549482π-0.549482\pi
−0.154828 + 0.987941i 0.549482π0.549482\pi
6868 3.15503 0.00562652
6969 0 0
7070 400.211 0.683347
7171 509.616 0.851835 0.425918 0.904762i 0.359951π-0.359951\pi
0.425918 + 0.904762i 0.359951π0.359951\pi
7272 0 0
7373 −621.448 −0.996370 −0.498185 0.867071i 0.666000π-0.666000\pi
−0.498185 + 0.867071i 0.666000π0.666000\pi
7474 453.041 0.711688
7575 0 0
7676 0.401527 0.000606031 0
7777 404.132 0.598118
7878 0 0
7979 −1122.10 −1.59806 −0.799029 0.601292i 0.794653π-0.794653\pi
−0.799029 + 0.601292i 0.794653π0.794653\pi
8080 448.962 0.627443
8181 0 0
8282 708.843 0.954617
8383 485.798 0.642449 0.321224 0.947003i 0.395906π-0.395906\pi
0.321224 + 0.947003i 0.395906π0.395906\pi
8484 0 0
8585 122.155 0.155877
8686 −1556.22 −1.95130
8787 0 0
8888 464.134 0.562236
8989 −1038.49 −1.23685 −0.618424 0.785844i 0.712229π-0.712229\pi
−0.618424 + 0.785844i 0.712229π0.712229\pi
9090 0 0
9191 −1381.16 −1.59104
9292 −2.42037 −0.00274284
9393 0 0
9494 554.103 0.607993
9595 15.5462 0.0167895
9696 0 0
9797 1014.67 1.06211 0.531054 0.847338i 0.321796π-0.321796\pi
0.531054 + 0.847338i 0.321796π0.321796\pi
9898 −150.865 −0.155507
9999 0 0
100100 13.6162 0.0136162
101101 653.602 0.643919 0.321959 0.946753i 0.395659π-0.395659\pi
0.321959 + 0.946753i 0.395659π0.395659\pi
102102 0 0
103103 489.213 0.467996 0.233998 0.972237i 0.424819π-0.424819\pi
0.233998 + 0.972237i 0.424819π0.424819\pi
104104 −1586.22 −1.49560
105105 0 0
106106 1389.06 1.27281
107107 −486.534 −0.439580 −0.219790 0.975547i 0.570537π-0.570537\pi
−0.219790 + 0.975547i 0.570537π0.570537\pi
108108 0 0
109109 88.6813 0.0779278 0.0389639 0.999241i 0.487594π-0.487594\pi
0.0389639 + 0.999241i 0.487594π0.487594\pi
110110 407.432 0.353156
111111 0 0
112112 −1244.87 −1.05026
113113 −1814.48 −1.51055 −0.755274 0.655409i 0.772496π-0.772496\pi
−0.755274 + 0.655409i 0.772496π0.772496\pi
114114 0 0
115115 −93.7108 −0.0759876
116116 45.8093 0.0366663
117117 0 0
118118 −958.971 −0.748139
119119 −338.709 −0.260919
120120 0 0
121121 −919.576 −0.690891
122122 −930.250 −0.690335
123123 0 0
124124 30.9525 0.0224162
125125 1425.39 1.01992
126126 0 0
127127 −2775.34 −1.93915 −0.969573 0.244803i 0.921277π-0.921277\pi
−0.969573 + 0.244803i 0.921277π0.921277\pi
128128 −1395.73 −0.963796
129129 0 0
130130 −1392.44 −0.939424
131131 1856.34 1.23808 0.619041 0.785359i 0.287521π-0.287521\pi
0.619041 + 0.785359i 0.287521π0.287521\pi
132132 0 0
133133 −43.1061 −0.0281035
134134 474.722 0.306043
135135 0 0
136136 −388.998 −0.245267
137137 1532.70 0.955823 0.477912 0.878408i 0.341394π-0.341394\pi
0.477912 + 0.878408i 0.341394π0.341394\pi
138138 0 0
139139 518.039 0.316111 0.158056 0.987430i 0.449477π-0.449477\pi
0.158056 + 0.987430i 0.449477π0.449477\pi
140140 26.5702 0.0160399
141141 0 0
142142 −1424.59 −0.841897
143143 −1406.08 −0.822256
144144 0 0
145145 1773.62 1.01580
146146 1737.21 0.984745
147147 0 0
148148 30.0776 0.0167052
149149 −3401.05 −1.86997 −0.934983 0.354693i 0.884585π-0.884585\pi
−0.934983 + 0.354693i 0.884585π0.884585\pi
150150 0 0
151151 108.797 0.0586345 0.0293173 0.999570i 0.490667π-0.490667\pi
0.0293173 + 0.999570i 0.490667π0.490667\pi
152152 −49.5061 −0.0264176
153153 0 0
154154 −1129.72 −0.591139
155155 1198.40 0.621020
156156 0 0
157157 3553.34 1.80629 0.903145 0.429335i 0.141252π-0.141252\pi
0.903145 + 0.429335i 0.141252π0.141252\pi
158158 3136.76 1.57941
159159 0 0
160160 60.3384 0.0298135
161161 259.840 0.127194
162162 0 0
163163 −3875.94 −1.86250 −0.931249 0.364384i 0.881280π-0.881280\pi
−0.931249 + 0.364384i 0.881280π0.881280\pi
164164 47.0605 0.0224074
165165 0 0
166166 −1358.01 −0.634953
167167 −730.820 −0.338638 −0.169319 0.985561i 0.554157π-0.554157\pi
−0.169319 + 0.985561i 0.554157π0.554157\pi
168168 0 0
169169 2608.43 1.18727
170170 −341.475 −0.154059
171171 0 0
172172 −103.318 −0.0458020
173173 −2979.89 −1.30958 −0.654789 0.755812i 0.727242π-0.727242\pi
−0.654789 + 0.755812i 0.727242π0.727242\pi
174174 0 0
175175 −1461.77 −0.631427
176176 −1267.34 −0.542779
177177 0 0
178178 2903.02 1.22242
179179 3112.68 1.29974 0.649868 0.760047i 0.274824π-0.274824\pi
0.649868 + 0.760047i 0.274824π0.274824\pi
180180 0 0
181181 2454.92 1.00814 0.504068 0.863664i 0.331836π-0.331836\pi
0.504068 + 0.863664i 0.331836π0.331836\pi
182182 3860.93 1.57248
183183 0 0
184184 298.418 0.119563
185185 1164.53 0.462801
186186 0 0
187187 −344.821 −0.134844
188188 36.7872 0.0142712
189189 0 0
190190 −43.4581 −0.0165936
191191 1806.74 0.684457 0.342228 0.939617i 0.388818π-0.388818\pi
0.342228 + 0.939617i 0.388818π0.388818\pi
192192 0 0
193193 −3252.39 −1.21302 −0.606508 0.795077i 0.707430π-0.707430\pi
−0.606508 + 0.795077i 0.707430π0.707430\pi
194194 −2836.45 −1.04972
195195 0 0
196196 −10.0160 −0.00365015
197197 2227.38 0.805554 0.402777 0.915298i 0.368045π-0.368045\pi
0.402777 + 0.915298i 0.368045π0.368045\pi
198198 0 0
199199 4309.13 1.53500 0.767502 0.641046i 0.221499π-0.221499\pi
0.767502 + 0.641046i 0.221499π0.221499\pi
200200 −1678.81 −0.593548
201201 0 0
202202 −1827.10 −0.636406
203203 −4917.87 −1.70033
204204 0 0
205205 1822.07 0.620774
206206 −1367.56 −0.462536
207207 0 0
208208 4331.25 1.44384
209209 −43.8839 −0.0145240
210210 0 0
211211 4219.39 1.37666 0.688330 0.725398i 0.258344π-0.258344\pi
0.688330 + 0.725398i 0.258344π0.258344\pi
212212 92.2204 0.0298761
213213 0 0
214214 1360.07 0.434451
215215 −4000.23 −1.26890
216216 0 0
217217 −3322.91 −1.03951
218218 −247.902 −0.0770185
219219 0 0
220220 27.0497 0.00828949
221221 1178.46 0.358696
222222 0 0
223223 −4825.85 −1.44916 −0.724580 0.689191i 0.757966π-0.757966\pi
−0.724580 + 0.689191i 0.757966π0.757966\pi
224224 −167.305 −0.0499042
225225 0 0
226226 5072.25 1.49292
227227 1665.18 0.486880 0.243440 0.969916i 0.421724π-0.421724\pi
0.243440 + 0.969916i 0.421724π0.421724\pi
228228 0 0
229229 2726.00 0.786633 0.393317 0.919403i 0.371328π-0.371328\pi
0.393317 + 0.919403i 0.371328π0.371328\pi
230230 261.962 0.0751010
231231 0 0
232232 −5648.03 −1.59833
233233 4836.51 1.35987 0.679937 0.733271i 0.262007π-0.262007\pi
0.679937 + 0.733271i 0.262007π0.262007\pi
234234 0 0
235235 1424.31 0.395369
236236 −63.6666 −0.0175608
237237 0 0
238238 946.837 0.257875
239239 −5200.13 −1.40740 −0.703700 0.710497i 0.748470π-0.748470\pi
−0.703700 + 0.710497i 0.748470π0.748470\pi
240240 0 0
241241 −372.453 −0.0995512 −0.0497756 0.998760i 0.515851π-0.515851\pi
−0.0497756 + 0.998760i 0.515851π0.515851\pi
242242 2570.61 0.682830
243243 0 0
244244 −61.7598 −0.0162040
245245 −387.795 −0.101124
246246 0 0
247247 149.978 0.0386350
248248 −3816.27 −0.977150
249249 0 0
250250 −3984.56 −1.00802
251251 902.694 0.227002 0.113501 0.993538i 0.463793π-0.463793\pi
0.113501 + 0.993538i 0.463793π0.463793\pi
252252 0 0
253253 264.528 0.0657342
254254 7758.26 1.91652
255255 0 0
256256 −284.912 −0.0695585
257257 1361.43 0.330442 0.165221 0.986257i 0.447166π-0.447166\pi
0.165221 + 0.986257i 0.447166π0.447166\pi
258258 0 0
259259 −3228.99 −0.774671
260260 −92.4449 −0.0220507
261261 0 0
262262 −5189.25 −1.22364
263263 1065.57 0.249833 0.124916 0.992167i 0.460134π-0.460134\pi
0.124916 + 0.992167i 0.460134π0.460134\pi
264264 0 0
265265 3570.55 0.827687
266266 120.500 0.0277756
267267 0 0
268268 31.5171 0.00718363
269269 5516.38 1.25033 0.625166 0.780491i 0.285031π-0.285031\pi
0.625166 + 0.780491i 0.285031π0.285031\pi
270270 0 0
271271 6271.52 1.40578 0.702892 0.711296i 0.251892π-0.251892\pi
0.702892 + 0.711296i 0.251892π0.251892\pi
272272 1062.17 0.236779
273273 0 0
274274 −4284.56 −0.944671
275275 −1488.15 −0.326324
276276 0 0
277277 −612.909 −0.132946 −0.0664732 0.997788i 0.521175π-0.521175\pi
−0.0664732 + 0.997788i 0.521175π0.521175\pi
278278 −1448.14 −0.312423
279279 0 0
280280 −3275.96 −0.699200
281281 8957.63 1.90166 0.950831 0.309709i 0.100232π-0.100232\pi
0.950831 + 0.309709i 0.100232π0.100232\pi
282282 0 0
283283 −366.649 −0.0770143 −0.0385072 0.999258i 0.512260π-0.512260\pi
−0.0385072 + 0.999258i 0.512260π0.512260\pi
284284 −94.5797 −0.0197615
285285 0 0
286286 3930.60 0.812662
287287 −5052.19 −1.03910
288288 0 0
289289 289.000 0.0588235
290290 −4958.04 −1.00395
291291 0 0
292292 115.335 0.0231145
293293 −544.260 −0.108519 −0.0542594 0.998527i 0.517280π-0.517280\pi
−0.0542594 + 0.998527i 0.517280π0.517280\pi
294294 0 0
295295 −2465.02 −0.486504
296296 −3708.41 −0.728198
297297 0 0
298298 9507.39 1.84815
299299 −904.052 −0.174858
300300 0 0
301301 11091.8 2.12398
302302 −304.135 −0.0579504
303303 0 0
304304 135.178 0.0255033
305305 −2391.19 −0.448915
306306 0 0
307307 −6140.08 −1.14148 −0.570738 0.821132i 0.693343π-0.693343\pi
−0.570738 + 0.821132i 0.693343π0.693343\pi
308308 −75.0028 −0.0138756
309309 0 0
310310 −3350.05 −0.613774
311311 2449.54 0.446626 0.223313 0.974747i 0.428313π-0.428313\pi
0.223313 + 0.974747i 0.428313π0.428313\pi
312312 0 0
313313 −7062.20 −1.27533 −0.637666 0.770313i 0.720100π-0.720100\pi
−0.637666 + 0.770313i 0.720100π0.720100\pi
314314 −9933.11 −1.78522
315315 0 0
316316 208.251 0.0370730
317317 −4075.00 −0.722002 −0.361001 0.932565i 0.617565π-0.617565\pi
−0.361001 + 0.932565i 0.617565π0.617565\pi
318318 0 0
319319 −5006.61 −0.878735
320320 −3760.36 −0.656909
321321 0 0
322322 −726.362 −0.125710
323323 36.7798 0.00633586
324324 0 0
325325 5085.91 0.868048
326326 10834.9 1.84077
327327 0 0
328328 −5802.30 −0.976763
329329 −3949.30 −0.661799
330330 0 0
331331 3869.63 0.642580 0.321290 0.946981i 0.395883π-0.395883\pi
0.321290 + 0.946981i 0.395883π0.395883\pi
332332 −90.1592 −0.0149040
333333 0 0
334334 2042.95 0.334687
335335 1220.26 0.199015
336336 0 0
337337 −6253.84 −1.01089 −0.505443 0.862860i 0.668671π-0.668671\pi
−0.505443 + 0.862860i 0.668671π0.668671\pi
338338 −7291.67 −1.17342
339339 0 0
340340 −22.6708 −0.00361616
341341 −3382.87 −0.537222
342342 0 0
343343 −5758.68 −0.906530
344344 12738.6 1.99656
345345 0 0
346346 8330.06 1.29430
347347 6632.55 1.02609 0.513046 0.858361i 0.328517π-0.328517\pi
0.513046 + 0.858361i 0.328517π0.328517\pi
348348 0 0
349349 −3485.68 −0.534625 −0.267313 0.963610i 0.586136π-0.586136\pi
−0.267313 + 0.963610i 0.586136π0.586136\pi
350350 4086.28 0.624060
351351 0 0
352352 −170.324 −0.0257906
353353 −6439.69 −0.970963 −0.485481 0.874247i 0.661356π-0.661356\pi
−0.485481 + 0.874247i 0.661356π0.661356\pi
354354 0 0
355355 −3661.89 −0.547473
356356 192.733 0.0286933
357357 0 0
358358 −8701.28 −1.28457
359359 −7104.81 −1.04451 −0.522253 0.852791i 0.674908π-0.674908\pi
−0.522253 + 0.852791i 0.674908π0.674908\pi
360360 0 0
361361 −6854.32 −0.999318
362362 −6862.54 −0.996374
363363 0 0
364364 256.330 0.0369102
365365 4465.47 0.640366
366366 0 0
367367 7921.51 1.12670 0.563350 0.826218i 0.309512π-0.309512\pi
0.563350 + 0.826218i 0.309512π0.309512\pi
368368 −814.843 −0.115426
369369 0 0
370370 −3255.37 −0.457401
371371 −9900.35 −1.38545
372372 0 0
373373 −5560.92 −0.771940 −0.385970 0.922511i 0.626133π-0.626133\pi
−0.385970 + 0.922511i 0.626133π0.626133\pi
374374 963.922 0.133271
375375 0 0
376376 −4535.66 −0.622098
377377 17110.6 2.33751
378378 0 0
379379 3393.45 0.459920 0.229960 0.973200i 0.426140π-0.426140\pi
0.229960 + 0.973200i 0.426140π0.426140\pi
380380 −2.88521 −0.000389495 0
381381 0 0
382382 −5050.61 −0.676471
383383 2057.57 0.274509 0.137255 0.990536i 0.456172π-0.456172\pi
0.137255 + 0.990536i 0.456172π0.456172\pi
384384 0 0
385385 −2903.92 −0.384410
386386 9091.82 1.19886
387387 0 0
388388 −188.313 −0.0246396
389389 −5909.30 −0.770215 −0.385107 0.922872i 0.625836π-0.625836\pi
−0.385107 + 0.922872i 0.625836π0.625836\pi
390390 0 0
391391 −221.705 −0.0286755
392392 1234.92 0.159114
393393 0 0
394394 −6226.47 −0.796155
395395 8062.99 1.02707
396396 0 0
397397 8871.61 1.12154 0.560772 0.827970i 0.310504π-0.310504\pi
0.560772 + 0.827970i 0.310504π0.310504\pi
398398 −12045.8 −1.51710
399399 0 0
400400 4584.05 0.573006
401401 −5958.38 −0.742013 −0.371007 0.928630i 0.620987π-0.620987\pi
−0.371007 + 0.928630i 0.620987π0.620987\pi
402402 0 0
403403 11561.3 1.42906
404404 −121.302 −0.0149381
405405 0 0
406406 13747.5 1.68049
407407 −3287.26 −0.400352
408408 0 0
409409 7517.10 0.908793 0.454397 0.890799i 0.349855π-0.349855\pi
0.454397 + 0.890799i 0.349855π0.349855\pi
410410 −5093.45 −0.613531
411411 0 0
412412 −90.7931 −0.0108569
413413 6834.95 0.814348
414414 0 0
415415 −3490.74 −0.412901
416416 582.100 0.0686052
417417 0 0
418418 122.674 0.0143545
419419 −2102.77 −0.245172 −0.122586 0.992458i 0.539119π-0.539119\pi
−0.122586 + 0.992458i 0.539119π0.539119\pi
420420 0 0
421421 3480.77 0.402951 0.201476 0.979494i 0.435426π-0.435426\pi
0.201476 + 0.979494i 0.435426π0.435426\pi
422422 −11795.0 −1.36060
423423 0 0
424424 −11370.3 −1.30233
425425 1247.24 0.142353
426426 0 0
427427 6630.24 0.751428
428428 90.2958 0.0101977
429429 0 0
430430 11182.4 1.25410
431431 6815.12 0.761654 0.380827 0.924646i 0.375639π-0.375639\pi
0.380827 + 0.924646i 0.375639π0.375639\pi
432432 0 0
433433 2867.85 0.318292 0.159146 0.987255i 0.449126π-0.449126\pi
0.159146 + 0.987255i 0.449126π0.449126\pi
434434 9288.95 1.02738
435435 0 0
436436 −16.4584 −0.00180783
437437 −28.2155 −0.00308863
438438 0 0
439439 −3268.85 −0.355384 −0.177692 0.984086i 0.556863π-0.556863\pi
−0.177692 + 0.984086i 0.556863π0.556863\pi
440440 −3335.07 −0.361349
441441 0 0
442442 −3294.30 −0.354511
443443 −12387.8 −1.32858 −0.664289 0.747476i 0.731265π-0.731265\pi
−0.664289 + 0.747476i 0.731265π0.731265\pi
444444 0 0
445445 7462.15 0.794921
446446 13490.3 1.43225
447447 0 0
448448 10426.7 1.09958
449449 13922.0 1.46329 0.731646 0.681685i 0.238753π-0.238753\pi
0.731646 + 0.681685i 0.238753π0.238753\pi
450450 0 0
451451 −5143.36 −0.537009
452452 336.749 0.0350428
453453 0 0
454454 −4654.88 −0.481199
455455 9924.45 1.02256
456456 0 0
457457 7503.09 0.768008 0.384004 0.923331i 0.374545π-0.374545\pi
0.384004 + 0.923331i 0.374545π0.374545\pi
458458 −7620.32 −0.777455
459459 0 0
460460 17.3918 0.00176282
461461 1804.23 0.182280 0.0911402 0.995838i 0.470949π-0.470949\pi
0.0911402 + 0.995838i 0.470949π0.470949\pi
462462 0 0
463463 1843.06 0.184998 0.0924992 0.995713i 0.470514π-0.470514\pi
0.0924992 + 0.995713i 0.470514π0.470514\pi
464464 15422.2 1.54301
465465 0 0
466466 −13520.1 −1.34401
467467 −11884.3 −1.17760 −0.588799 0.808280i 0.700399π-0.700399\pi
−0.588799 + 0.808280i 0.700399π0.700399\pi
468468 0 0
469469 −3383.52 −0.333127
470470 −3981.55 −0.390756
471471 0 0
472472 7849.74 0.765495
473473 11291.9 1.09768
474474 0 0
475475 158.731 0.0153328
476476 62.8610 0.00605300
477477 0 0
478478 14536.6 1.39098
479479 −4591.44 −0.437971 −0.218986 0.975728i 0.570275π-0.570275\pi
−0.218986 + 0.975728i 0.570275π0.570275\pi
480480 0 0
481481 11234.5 1.06497
482482 1041.17 0.0983897
483483 0 0
484484 170.664 0.0160278
485485 −7291.03 −0.682616
486486 0 0
487487 3075.97 0.286213 0.143106 0.989707i 0.454291π-0.454291\pi
0.143106 + 0.989707i 0.454291π0.454291\pi
488488 7614.64 0.706350
489489 0 0
490490 1084.05 0.0999439
491491 2556.76 0.235000 0.117500 0.993073i 0.462512π-0.462512\pi
0.117500 + 0.993073i 0.462512π0.462512\pi
492492 0 0
493493 4196.12 0.383334
494494 −419.251 −0.0381842
495495 0 0
496496 10420.5 0.943333
497497 10153.6 0.916403
498498 0 0
499499 3551.49 0.318610 0.159305 0.987229i 0.449075π-0.449075\pi
0.159305 + 0.987229i 0.449075π0.449075\pi
500500 −264.537 −0.0236609
501501 0 0
502502 −2523.42 −0.224354
503503 96.3146 0.00853768 0.00426884 0.999991i 0.498641π-0.498641\pi
0.00426884 + 0.999991i 0.498641π0.498641\pi
504504 0 0
505505 −4696.51 −0.413846
506506 −739.469 −0.0649672
507507 0 0
508508 515.075 0.0449858
509509 −19081.4 −1.66163 −0.830815 0.556549i 0.812125π-0.812125\pi
−0.830815 + 0.556549i 0.812125π0.812125\pi
510510 0 0
511511 −12381.8 −1.07189
512512 11962.3 1.03254
513513 0 0
514514 −3805.77 −0.326587
515515 −3515.29 −0.300781
516516 0 0
517517 −4020.57 −0.342020
518518 9026.41 0.765633
519519 0 0
520520 11397.9 0.961217
521521 −9570.95 −0.804820 −0.402410 0.915460i 0.631827π-0.631827\pi
−0.402410 + 0.915460i 0.631827π0.631827\pi
522522 0 0
523523 −16979.2 −1.41959 −0.709797 0.704406i 0.751214π-0.751214\pi
−0.709797 + 0.704406i 0.751214π0.751214\pi
524524 −344.517 −0.0287220
525525 0 0
526526 −2978.73 −0.246918
527527 2835.24 0.234355
528528 0 0
529529 −11996.9 −0.986021
530530 −9981.21 −0.818030
531531 0 0
532532 8.00005 0.000651967 0
533533 17577.9 1.42849
534534 0 0
535535 3496.03 0.282517
536536 −3885.88 −0.313143
537537 0 0
538538 −15420.6 −1.23574
539539 1094.67 0.0874785
540540 0 0
541541 −9339.39 −0.742203 −0.371101 0.928592i 0.621020π-0.621020\pi
−0.371101 + 0.928592i 0.621020π0.621020\pi
542542 −17531.6 −1.38938
543543 0 0
544544 142.751 0.0112508
545545 −637.227 −0.0500841
546546 0 0
547547 3347.48 0.261660 0.130830 0.991405i 0.458236π-0.458236\pi
0.130830 + 0.991405i 0.458236π0.458236\pi
548548 −284.455 −0.0221739
549549 0 0
550550 4160.02 0.322516
551551 534.022 0.0412888
552552 0 0
553553 −22356.9 −1.71919
554554 1713.34 0.131395
555555 0 0
556556 −96.1428 −0.00733339
557557 −20271.9 −1.54209 −0.771047 0.636778i 0.780267π-0.780267\pi
−0.771047 + 0.636778i 0.780267π0.780267\pi
558558 0 0
559559 −38591.3 −2.91992
560560 8945.14 0.675002
561561 0 0
562562 −25040.4 −1.87947
563563 6144.58 0.459970 0.229985 0.973194i 0.426132π-0.426132\pi
0.229985 + 0.973194i 0.426132π0.426132\pi
564564 0 0
565565 13038.1 0.970828
566566 1024.94 0.0761158
567567 0 0
568568 11661.1 0.861428
569569 −19198.3 −1.41447 −0.707237 0.706977i 0.750058π-0.750058\pi
−0.707237 + 0.706977i 0.750058π0.750058\pi
570570 0 0
571571 −2944.07 −0.215772 −0.107886 0.994163i 0.534408π-0.534408\pi
−0.107886 + 0.994163i 0.534408π0.534408\pi
572572 260.955 0.0190753
573573 0 0
574574 14123.0 1.02698
575575 −956.819 −0.0693950
576576 0 0
577577 −1802.77 −0.130070 −0.0650351 0.997883i 0.520716π-0.520716\pi
−0.0650351 + 0.997883i 0.520716π0.520716\pi
578578 −807.878 −0.0581372
579579 0 0
580580 −329.167 −0.0235654
581581 9679.07 0.691145
582582 0 0
583583 −10079.0 −0.716003
584584 −14220.1 −1.00759
585585 0 0
586586 1521.44 0.107253
587587 −24517.6 −1.72394 −0.861969 0.506961i 0.830769π-0.830769\pi
−0.861969 + 0.506961i 0.830769π0.830769\pi
588588 0 0
589589 360.829 0.0252423
590590 6890.77 0.480828
591591 0 0
592592 10126.0 0.702997
593593 14269.5 0.988161 0.494081 0.869416i 0.335505π-0.335505\pi
0.494081 + 0.869416i 0.335505π0.335505\pi
594594 0 0
595595 2433.82 0.167693
596596 631.201 0.0433809
597597 0 0
598598 2527.21 0.172818
599599 −15362.8 −1.04792 −0.523961 0.851742i 0.675546π-0.675546\pi
−0.523961 + 0.851742i 0.675546π0.675546\pi
600600 0 0
601601 19852.3 1.34741 0.673704 0.739001i 0.264702π-0.264702\pi
0.673704 + 0.739001i 0.264702π0.264702\pi
602602 −31006.2 −2.09920
603603 0 0
604604 −20.1917 −0.00136025
605605 6607.69 0.444035
606606 0 0
607607 −19495.1 −1.30359 −0.651796 0.758394i 0.725984π-0.725984\pi
−0.651796 + 0.758394i 0.725984π0.725984\pi
608608 18.1674 0.00121181
609609 0 0
610610 6684.39 0.443677
611611 13740.7 0.909801
612612 0 0
613613 16796.4 1.10669 0.553343 0.832954i 0.313352π-0.313352\pi
0.553343 + 0.832954i 0.313352π0.313352\pi
614614 17164.2 1.12816
615615 0 0
616616 9247.43 0.604853
617617 −1185.68 −0.0773642 −0.0386821 0.999252i 0.512316π-0.512316\pi
−0.0386821 + 0.999252i 0.512316π0.512316\pi
618618 0 0
619619 11747.1 0.762771 0.381385 0.924416i 0.375447π-0.375447\pi
0.381385 + 0.924416i 0.375447π0.375447\pi
620620 −222.412 −0.0144069
621621 0 0
622622 −6847.51 −0.441415
623623 −20690.9 −1.33060
624624 0 0
625625 −1071.33 −0.0685650
626626 19741.9 1.26045
627627 0 0
628628 −659.465 −0.0419037
629629 2755.10 0.174647
630630 0 0
631631 −11744.3 −0.740943 −0.370471 0.928844i 0.620804π-0.620804\pi
−0.370471 + 0.928844i 0.620804π0.620804\pi
632632 −25676.2 −1.61605
633633 0 0
634634 11391.4 0.713578
635635 19942.4 1.24629
636636 0 0
637637 −3741.16 −0.232700
638638 13995.6 0.868483
639639 0 0
640640 10029.1 0.619431
641641 −4318.07 −0.266074 −0.133037 0.991111i 0.542473π-0.542473\pi
−0.133037 + 0.991111i 0.542473π0.542473\pi
642642 0 0
643643 −16920.9 −1.03779 −0.518893 0.854839i 0.673656π-0.673656\pi
−0.518893 + 0.854839i 0.673656π0.673656\pi
644644 −48.2236 −0.00295074
645645 0 0
646646 −102.815 −0.00626194
647647 −12459.5 −0.757084 −0.378542 0.925584i 0.623574π-0.623574\pi
−0.378542 + 0.925584i 0.623574π0.623574\pi
648648 0 0
649649 6958.29 0.420858
650650 −14217.3 −0.857920
651651 0 0
652652 719.336 0.0432076
653653 −12781.8 −0.765990 −0.382995 0.923750i 0.625107π-0.625107\pi
−0.382995 + 0.923750i 0.625107π0.625107\pi
654654 0 0
655655 −13338.9 −0.795714
656656 15843.4 0.942959
657657 0 0
658658 11040.0 0.654078
659659 7400.62 0.437461 0.218731 0.975785i 0.429808π-0.429808\pi
0.218731 + 0.975785i 0.429808π0.429808\pi
660660 0 0
661661 −21906.0 −1.28902 −0.644512 0.764594i 0.722939π-0.722939\pi
−0.644512 + 0.764594i 0.722939π0.722939\pi
662662 −10817.3 −0.635083
663663 0 0
664664 11116.1 0.649683
665665 309.743 0.0180621
666666 0 0
667667 −3219.04 −0.186869
668668 135.633 0.00785598
669669 0 0
670670 −3411.16 −0.196693
671671 6749.89 0.388340
672672 0 0
673673 −440.817 −0.0252485 −0.0126243 0.999920i 0.504019π-0.504019\pi
−0.0126243 + 0.999920i 0.504019π0.504019\pi
674674 17482.2 0.999091
675675 0 0
676676 −484.098 −0.0275431
677677 −17950.8 −1.01906 −0.509532 0.860452i 0.670181π-0.670181\pi
−0.509532 + 0.860452i 0.670181π0.670181\pi
678678 0 0
679679 20216.4 1.14261
680680 2795.18 0.157633
681681 0 0
682682 9456.57 0.530954
683683 32522.6 1.82203 0.911013 0.412377i 0.135301π-0.135301\pi
0.911013 + 0.412377i 0.135301π0.135301\pi
684684 0 0
685685 −11013.4 −0.614306
686686 16098.0 0.895953
687687 0 0
688688 −34783.2 −1.92747
689689 34446.0 1.90463
690690 0 0
691691 29316.7 1.61398 0.806991 0.590564i 0.201095π-0.201095\pi
0.806991 + 0.590564i 0.201095π0.201095\pi
692692 553.038 0.0303805
693693 0 0
694694 −18540.8 −1.01412
695695 −3722.42 −0.203164
696696 0 0
697697 4310.73 0.234262
698698 9743.96 0.528387
699699 0 0
700700 271.291 0.0146483
701701 −25948.5 −1.39809 −0.699045 0.715077i 0.746392π-0.746392\pi
−0.699045 + 0.715077i 0.746392π0.746392\pi
702702 0 0
703703 350.630 0.0188112
704704 10614.8 0.568268
705705 0 0
706706 18001.7 0.959634
707707 13022.4 0.692727
708708 0 0
709709 −22102.6 −1.17077 −0.585387 0.810754i 0.699057π-0.699057\pi
−0.585387 + 0.810754i 0.699057π0.699057\pi
710710 10236.6 0.541086
711711 0 0
712712 −23762.9 −1.25078
713713 −2175.04 −0.114244
714714 0 0
715715 10103.5 0.528463
716716 −577.683 −0.0301523
717717 0 0
718718 19861.0 1.03232
719719 9876.18 0.512266 0.256133 0.966642i 0.417551π-0.417551\pi
0.256133 + 0.966642i 0.417551π0.417551\pi
720720 0 0
721721 9747.12 0.503470
722722 19160.7 0.987658
723723 0 0
724724 −455.608 −0.0233875
725725 18109.3 0.927672
726726 0 0
727727 7187.21 0.366656 0.183328 0.983052i 0.441313π-0.441313\pi
0.183328 + 0.983052i 0.441313π0.441313\pi
728728 −31604.0 −1.60896
729729 0 0
730730 −12482.9 −0.632894
731731 −9463.94 −0.478846
732732 0 0
733733 28840.8 1.45328 0.726642 0.687016i 0.241080π-0.241080\pi
0.726642 + 0.687016i 0.241080π0.241080\pi
734734 −22144.0 −1.11356
735735 0 0
736736 −109.511 −0.00548456
737737 −3444.58 −0.172161
738738 0 0
739739 13008.1 0.647514 0.323757 0.946140i 0.395054π-0.395054\pi
0.323757 + 0.946140i 0.395054π0.395054\pi
740740 −216.126 −0.0107364
741741 0 0
742742 27675.7 1.36928
743743 29485.3 1.45587 0.727934 0.685647i 0.240481π-0.240481\pi
0.727934 + 0.685647i 0.240481π0.240481\pi
744744 0 0
745745 24438.6 1.20182
746746 15545.2 0.762934
747747 0 0
748748 63.9954 0.00312821
749749 −9693.73 −0.472899
750750 0 0
751751 17194.3 0.835458 0.417729 0.908572i 0.362826π-0.362826\pi
0.417729 + 0.908572i 0.362826π0.362826\pi
752752 12384.8 0.600568
753753 0 0
754754 −47831.4 −2.31024
755755 −781.774 −0.0376843
756756 0 0
757757 7578.25 0.363852 0.181926 0.983312i 0.441767π-0.441767\pi
0.181926 + 0.983312i 0.441767π0.441767\pi
758758 −9486.14 −0.454554
759759 0 0
760760 355.730 0.0169785
761761 −12964.9 −0.617577 −0.308789 0.951131i 0.599924π-0.599924\pi
−0.308789 + 0.951131i 0.599924π0.599924\pi
762762 0 0
763763 1766.89 0.0838346
764764 −335.313 −0.0158785
765765 0 0
766766 −5751.79 −0.271306
767767 −23780.6 −1.11952
768768 0 0
769769 −5997.37 −0.281236 −0.140618 0.990064i 0.544909π-0.544909\pi
−0.140618 + 0.990064i 0.544909π0.544909\pi
770770 8117.71 0.379925
771771 0 0
772772 603.611 0.0281405
773773 457.468 0.0212859 0.0106429 0.999943i 0.496612π-0.496612\pi
0.0106429 + 0.999943i 0.496612π0.496612\pi
774774 0 0
775775 12236.1 0.567140
776776 23218.0 1.07407
777777 0 0
778778 16519.0 0.761228
779779 548.608 0.0252323
780780 0 0
781781 10336.8 0.473600
782782 619.761 0.0283409
783783 0 0
784784 −3371.99 −0.153608
785785 −25532.9 −1.16090
786786 0 0
787787 −837.185 −0.0379192 −0.0189596 0.999820i 0.506035π-0.506035\pi
−0.0189596 + 0.999820i 0.506035π0.506035\pi
788788 −413.379 −0.0186878
789789 0 0
790790 −22539.5 −1.01509
791791 −36151.8 −1.62505
792792 0 0
793793 −23068.4 −1.03302
794794 −24799.9 −1.10846
795795 0 0
796796 −799.731 −0.0356102
797797 −21061.7 −0.936063 −0.468032 0.883712i 0.655037π-0.655037\pi
−0.468032 + 0.883712i 0.655037π0.655037\pi
798798 0 0
799799 3369.70 0.149201
800800 616.075 0.0272269
801801 0 0
802802 16656.2 0.733356
803803 −12605.2 −0.553957
804804 0 0
805805 −1867.10 −0.0817474
806806 −32318.8 −1.41238
807807 0 0
808808 14955.9 0.651170
809809 13593.4 0.590752 0.295376 0.955381i 0.404555π-0.404555\pi
0.295376 + 0.955381i 0.404555π0.404555\pi
810810 0 0
811811 21346.1 0.924243 0.462122 0.886817i 0.347088π-0.347088\pi
0.462122 + 0.886817i 0.347088π0.347088\pi
812812 912.707 0.0394455
813813 0 0
814814 9189.30 0.395681
815815 27850.9 1.19702
816816 0 0
817817 −1204.43 −0.0515763
818818 −21013.5 −0.898190
819819 0 0
820820 −338.157 −0.0144012
821821 −10609.9 −0.451019 −0.225510 0.974241i 0.572405π-0.572405\pi
−0.225510 + 0.974241i 0.572405π0.572405\pi
822822 0 0
823823 −16152.8 −0.684145 −0.342072 0.939674i 0.611129π-0.611129\pi
−0.342072 + 0.939674i 0.611129π0.611129\pi
824824 11194.3 0.473266
825825 0 0
826826 −19106.6 −0.804847
827827 17755.3 0.746570 0.373285 0.927717i 0.378231π-0.378231\pi
0.373285 + 0.927717i 0.378231π0.378231\pi
828828 0 0
829829 16425.3 0.688149 0.344075 0.938942i 0.388193π-0.388193\pi
0.344075 + 0.938942i 0.388193π0.388193\pi
830830 9758.12 0.408084
831831 0 0
832832 −36277.2 −1.51164
833833 −917.463 −0.0381611
834834 0 0
835835 5251.37 0.217642
836836 8.14442 0.000336938 0
837837 0 0
838838 5878.15 0.242312
839839 1680.00 0.0691298 0.0345649 0.999402i 0.488995π-0.488995\pi
0.0345649 + 0.999402i 0.488995π0.488995\pi
840840 0 0
841841 36536.4 1.49807
842842 −9730.24 −0.398250
843843 0 0
844844 −783.077 −0.0319368
845845 −18743.1 −0.763056
846846 0 0
847847 −18321.7 −0.743259
848848 31047.0 1.25726
849849 0 0
850850 −3486.58 −0.140693
851851 −2113.57 −0.0851377
852852 0 0
853853 −14637.8 −0.587560 −0.293780 0.955873i 0.594913π-0.594913\pi
−0.293780 + 0.955873i 0.594913π0.594913\pi
854854 −18534.4 −0.742661
855855 0 0
856856 −11133.0 −0.444529
857857 28175.6 1.12306 0.561528 0.827458i 0.310214π-0.310214\pi
0.561528 + 0.827458i 0.310214π0.310214\pi
858858 0 0
859859 −941.593 −0.0374002 −0.0187001 0.999825i 0.505953π-0.505953\pi
−0.0187001 + 0.999825i 0.505953π0.505953\pi
860860 742.403 0.0294369
861861 0 0
862862 −19051.2 −0.752768
863863 17106.4 0.674750 0.337375 0.941370i 0.390461π-0.390461\pi
0.337375 + 0.941370i 0.390461π0.390461\pi
864864 0 0
865865 21412.3 0.841663
866866 −8016.87 −0.314578
867867 0 0
868868 616.699 0.0241154
869869 −22760.3 −0.888482
870870 0 0
871871 11772.2 0.457963
872872 2029.22 0.0788053
873873 0 0
874874 78.8743 0.00305259
875875 28399.5 1.09723
876876 0 0
877877 −16734.4 −0.644332 −0.322166 0.946683i 0.604411π-0.604411\pi
−0.322166 + 0.946683i 0.604411π0.604411\pi
878878 9137.82 0.351237
879879 0 0
880880 9106.56 0.348843
881881 19999.2 0.764802 0.382401 0.923996i 0.375097π-0.375097\pi
0.382401 + 0.923996i 0.375097π0.375097\pi
882882 0 0
883883 10029.6 0.382248 0.191124 0.981566i 0.438787π-0.438787\pi
0.191124 + 0.981566i 0.438787π0.438787\pi
884884 −218.710 −0.00832130
885885 0 0
886886 34629.1 1.31308
887887 40481.7 1.53240 0.766202 0.642600i 0.222144π-0.222144\pi
0.766202 + 0.642600i 0.222144π0.222144\pi
888888 0 0
889889 −55296.0 −2.08613
890890 −20859.9 −0.785646
891891 0 0
892892 895.629 0.0336187
893893 428.847 0.0160704
894894 0 0
895895 −22366.5 −0.835339
896896 −27808.5 −1.03685
897897 0 0
898898 −38917.8 −1.44622
899899 41166.1 1.52722
900900 0 0
901901 8447.37 0.312345
902902 14377.9 0.530744
903903 0 0
904904 −41519.3 −1.52756
905905 −17640.0 −0.647928
906906 0 0
907907 −22918.7 −0.839034 −0.419517 0.907747i 0.637801π-0.637801\pi
−0.419517 + 0.907747i 0.637801π0.637801\pi
908908 −309.040 −0.0112950
909909 0 0
910910 −27743.1 −1.01063
911911 −20326.2 −0.739230 −0.369615 0.929185i 0.620510π-0.620510\pi
−0.369615 + 0.929185i 0.620510π0.620510\pi
912912 0 0
913913 9853.73 0.357186
914914 −20974.3 −0.759048
915915 0 0
916916 −505.918 −0.0182489
917917 36985.7 1.33193
918918 0 0
919919 29975.7 1.07596 0.537980 0.842958i 0.319188π-0.319188\pi
0.537980 + 0.842958i 0.319188π0.319188\pi
920920 −2144.31 −0.0768433
921921 0 0
922922 −5043.59 −0.180154
923923 −35327.2 −1.25981
924924 0 0
925925 11890.3 0.422648
926926 −5152.14 −0.182840
927927 0 0
928928 2072.67 0.0733176
929929 −18708.2 −0.660706 −0.330353 0.943857i 0.607168π-0.607168\pi
−0.330353 + 0.943857i 0.607168π0.607168\pi
930930 0 0
931931 −116.762 −0.00411032
932932 −897.608 −0.0315474
933933 0 0
934934 33221.6 1.16386
935935 2477.74 0.0866640
936936 0 0
937937 −23835.6 −0.831032 −0.415516 0.909586i 0.636399π-0.636399\pi
−0.415516 + 0.909586i 0.636399π0.636399\pi
938938 9458.39 0.329240
939939 0 0
940940 −264.338 −0.00917207
941941 29086.9 1.00766 0.503829 0.863803i 0.331924π-0.331924\pi
0.503829 + 0.863803i 0.331924π0.331924\pi
942942 0 0
943943 −3306.96 −0.114199
944944 −21434.0 −0.739003
945945 0 0
946946 −31565.7 −1.08487
947947 −4232.84 −0.145247 −0.0726234 0.997359i 0.523137π-0.523137\pi
−0.0726234 + 0.997359i 0.523137π0.523137\pi
948948 0 0
949949 43079.5 1.47357
950950 −443.722 −0.0151539
951951 0 0
952952 −7750.42 −0.263858
953953 34662.0 1.17819 0.589093 0.808065i 0.299485π-0.299485\pi
0.589093 + 0.808065i 0.299485π0.299485\pi
954954 0 0
955955 −12982.5 −0.439899
956956 965.093 0.0326499
957957 0 0
958958 12835.0 0.432861
959959 30537.7 1.02827
960960 0 0
961961 −1975.85 −0.0663238
962962 −31405.3 −1.05255
963963 0 0
964964 69.1236 0.00230946
965965 23370.3 0.779604
966966 0 0
967967 21658.2 0.720248 0.360124 0.932904i 0.382734π-0.382734\pi
0.360124 + 0.932904i 0.382734π0.382734\pi
968968 −21041.9 −0.698671
969969 0 0
970970 20381.5 0.674651
971971 −4143.58 −0.136945 −0.0684727 0.997653i 0.521813π-0.521813\pi
−0.0684727 + 0.997653i 0.521813π0.521813\pi
972972 0 0
973973 10321.4 0.340072
974974 −8598.65 −0.282873
975975 0 0
976976 −20792.1 −0.681904
977977 9390.27 0.307494 0.153747 0.988110i 0.450866π-0.450866\pi
0.153747 + 0.988110i 0.450866π0.450866\pi
978978 0 0
979979 −21064.3 −0.687658
980980 71.9709 0.00234594
981981 0 0
982982 −7147.22 −0.232258
983983 42182.9 1.36869 0.684346 0.729157i 0.260088π-0.260088\pi
0.684346 + 0.729157i 0.260088π0.260088\pi
984984 0 0
985985 −16005.0 −0.517728
986986 −11729.9 −0.378862
987987 0 0
988988 −27.8343 −0.000896284 0
989989 7260.22 0.233429
990990 0 0
991991 −9493.78 −0.304319 −0.152159 0.988356i 0.548623π-0.548623\pi
−0.152159 + 0.988356i 0.548623π0.548623\pi
992992 1400.46 0.0448234
993993 0 0
994994 −28383.7 −0.905711
995995 −30963.6 −0.986546
996996 0 0
997997 −53688.9 −1.70546 −0.852731 0.522350i 0.825055π-0.825055\pi
−0.852731 + 0.522350i 0.825055π0.825055\pi
998998 −9927.93 −0.314893
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 153.4.a.f.1.2 3
3.2 odd 2 51.4.a.e.1.2 3
4.3 odd 2 2448.4.a.bd.1.2 3
12.11 even 2 816.4.a.s.1.2 3
15.14 odd 2 1275.4.a.q.1.2 3
21.20 even 2 2499.4.a.n.1.2 3
51.50 odd 2 867.4.a.k.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
51.4.a.e.1.2 3 3.2 odd 2
153.4.a.f.1.2 3 1.1 even 1 trivial
816.4.a.s.1.2 3 12.11 even 2
867.4.a.k.1.2 3 51.50 odd 2
1275.4.a.q.1.2 3 15.14 odd 2
2448.4.a.bd.1.2 3 4.3 odd 2
2499.4.a.n.1.2 3 21.20 even 2