Properties

Label 8001.2.a.x.1.7
Level 80018001
Weight 22
Character 8001.1
Self dual yes
Analytic conductor 63.88863.888
Analytic rank 11
Dimension 2222
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [8001,2,Mod(1,8001)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8001, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8001.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 8001=327127 8001 = 3^{2} \cdot 7 \cdot 127
Weight: k k == 2 2
Character orbit: [χ][\chi] == 8001.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [22,0,0,10,0] 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: 63.888306657263.8883066572
Analytic rank: 11
Dimension: 2222
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.7
Character χ\chi == 8001.1

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) == q0.775659q21.39835q40.833166q5+1.00000q7+2.63596q8+0.646253q100.821214q113.40878q130.775659q14+0.752101q16+2.50310q17+1.40296q19+1.16506q20+0.636982q220.947115q234.30583q25+2.64405q261.39835q281.78577q29+8.51944q315.85530q321.94155q340.833166q352.89168q371.08822q382.19620q402.30169q41+5.58041q43+1.14835q44+0.734638q462.14718q47+1.00000q49+3.33986q50+4.76668q52+0.992903q53+0.684208q55+2.63596q56+1.38515q58+13.0882q597.19849q616.60817q62+3.03751q64+2.84008q655.77977q673.50022q68+0.646253q70+0.675593q7110.0038q73+2.24296q741.96183q760.821214q77+1.57957q790.626625q80+1.78533q823.31531q832.08550q854.32849q862.16469q88+1.39169q893.40878q91+1.32440q92+1.66548q941.16890q954.55016q970.775659q98+O(q100)q-0.775659 q^{2} -1.39835 q^{4} -0.833166 q^{5} +1.00000 q^{7} +2.63596 q^{8} +0.646253 q^{10} -0.821214 q^{11} -3.40878 q^{13} -0.775659 q^{14} +0.752101 q^{16} +2.50310 q^{17} +1.40296 q^{19} +1.16506 q^{20} +0.636982 q^{22} -0.947115 q^{23} -4.30583 q^{25} +2.64405 q^{26} -1.39835 q^{28} -1.78577 q^{29} +8.51944 q^{31} -5.85530 q^{32} -1.94155 q^{34} -0.833166 q^{35} -2.89168 q^{37} -1.08822 q^{38} -2.19620 q^{40} -2.30169 q^{41} +5.58041 q^{43} +1.14835 q^{44} +0.734638 q^{46} -2.14718 q^{47} +1.00000 q^{49} +3.33986 q^{50} +4.76668 q^{52} +0.992903 q^{53} +0.684208 q^{55} +2.63596 q^{56} +1.38515 q^{58} +13.0882 q^{59} -7.19849 q^{61} -6.60817 q^{62} +3.03751 q^{64} +2.84008 q^{65} -5.77977 q^{67} -3.50022 q^{68} +0.646253 q^{70} +0.675593 q^{71} -10.0038 q^{73} +2.24296 q^{74} -1.96183 q^{76} -0.821214 q^{77} +1.57957 q^{79} -0.626625 q^{80} +1.78533 q^{82} -3.31531 q^{83} -2.08550 q^{85} -4.32849 q^{86} -2.16469 q^{88} +1.39169 q^{89} -3.40878 q^{91} +1.32440 q^{92} +1.66548 q^{94} -1.16890 q^{95} -4.55016 q^{97} -0.775659 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 22q+10q4+22q74q1010q136q1618q1934q2226q25+10q2842q3116q3436q3746q4054q4312q46+22q4922q52+56q97+O(q100) 22 q + 10 q^{4} + 22 q^{7} - 4 q^{10} - 10 q^{13} - 6 q^{16} - 18 q^{19} - 34 q^{22} - 26 q^{25} + 10 q^{28} - 42 q^{31} - 16 q^{34} - 36 q^{37} - 46 q^{40} - 54 q^{43} - 12 q^{46} + 22 q^{49} - 22 q^{52}+ \cdots - 56 q^{97}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.775659 −0.548473 −0.274237 0.961662i 0.588425π-0.588425\pi
−0.274237 + 0.961662i 0.588425π0.588425\pi
33 0 0
44 −1.39835 −0.699177
55 −0.833166 −0.372603 −0.186302 0.982493i 0.559650π-0.559650\pi
−0.186302 + 0.982493i 0.559650π0.559650\pi
66 0 0
77 1.00000 0.377964
88 2.63596 0.931953
99 0 0
1010 0.646253 0.204363
1111 −0.821214 −0.247605 −0.123803 0.992307i 0.539509π-0.539509\pi
−0.123803 + 0.992307i 0.539509π0.539509\pi
1212 0 0
1313 −3.40878 −0.945424 −0.472712 0.881217i 0.656725π-0.656725\pi
−0.472712 + 0.881217i 0.656725π0.656725\pi
1414 −0.775659 −0.207303
1515 0 0
1616 0.752101 0.188025
1717 2.50310 0.607091 0.303546 0.952817i 0.401830π-0.401830\pi
0.303546 + 0.952817i 0.401830π0.401830\pi
1818 0 0
1919 1.40296 0.321861 0.160931 0.986966i 0.448550π-0.448550\pi
0.160931 + 0.986966i 0.448550π0.448550\pi
2020 1.16506 0.260516
2121 0 0
2222 0.636982 0.135805
2323 −0.947115 −0.197487 −0.0987436 0.995113i 0.531482π-0.531482\pi
−0.0987436 + 0.995113i 0.531482π0.531482\pi
2424 0 0
2525 −4.30583 −0.861167
2626 2.64405 0.518540
2727 0 0
2828 −1.39835 −0.264264
2929 −1.78577 −0.331610 −0.165805 0.986159i 0.553022π-0.553022\pi
−0.165805 + 0.986159i 0.553022π0.553022\pi
3030 0 0
3131 8.51944 1.53014 0.765068 0.643949i 0.222705π-0.222705\pi
0.765068 + 0.643949i 0.222705π0.222705\pi
3232 −5.85530 −1.03508
3333 0 0
3434 −1.94155 −0.332973
3535 −0.833166 −0.140831
3636 0 0
3737 −2.89168 −0.475390 −0.237695 0.971340i 0.576392π-0.576392\pi
−0.237695 + 0.971340i 0.576392π0.576392\pi
3838 −1.08822 −0.176532
3939 0 0
4040 −2.19620 −0.347249
4141 −2.30169 −0.359464 −0.179732 0.983716i 0.557523π-0.557523\pi
−0.179732 + 0.983716i 0.557523π0.557523\pi
4242 0 0
4343 5.58041 0.851004 0.425502 0.904957i 0.360098π-0.360098\pi
0.425502 + 0.904957i 0.360098π0.360098\pi
4444 1.14835 0.173120
4545 0 0
4646 0.734638 0.108316
4747 −2.14718 −0.313198 −0.156599 0.987662i 0.550053π-0.550053\pi
−0.156599 + 0.987662i 0.550053π0.550053\pi
4848 0 0
4949 1.00000 0.142857
5050 3.33986 0.472327
5151 0 0
5252 4.76668 0.661019
5353 0.992903 0.136386 0.0681929 0.997672i 0.478277π-0.478277\pi
0.0681929 + 0.997672i 0.478277π0.478277\pi
5454 0 0
5555 0.684208 0.0922586
5656 2.63596 0.352245
5757 0 0
5858 1.38515 0.181879
5959 13.0882 1.70394 0.851971 0.523589i 0.175407π-0.175407\pi
0.851971 + 0.523589i 0.175407π0.175407\pi
6060 0 0
6161 −7.19849 −0.921672 −0.460836 0.887485i 0.652450π-0.652450\pi
−0.460836 + 0.887485i 0.652450π0.652450\pi
6262 −6.60817 −0.839239
6363 0 0
6464 3.03751 0.379689
6565 2.84008 0.352268
6666 0 0
6767 −5.77977 −0.706111 −0.353056 0.935602i 0.614857π-0.614857\pi
−0.353056 + 0.935602i 0.614857π0.614857\pi
6868 −3.50022 −0.424464
6969 0 0
7070 0.646253 0.0772420
7171 0.675593 0.0801781 0.0400891 0.999196i 0.487236π-0.487236\pi
0.0400891 + 0.999196i 0.487236π0.487236\pi
7272 0 0
7373 −10.0038 −1.17086 −0.585429 0.810724i 0.699074π-0.699074\pi
−0.585429 + 0.810724i 0.699074π0.699074\pi
7474 2.24296 0.260739
7575 0 0
7676 −1.96183 −0.225038
7777 −0.821214 −0.0935860
7878 0 0
7979 1.57957 0.177716 0.0888578 0.996044i 0.471678π-0.471678\pi
0.0888578 + 0.996044i 0.471678π0.471678\pi
8080 −0.626625 −0.0700589
8181 0 0
8282 1.78533 0.197156
8383 −3.31531 −0.363902 −0.181951 0.983308i 0.558241π-0.558241\pi
−0.181951 + 0.983308i 0.558241π0.558241\pi
8484 0 0
8585 −2.08550 −0.226204
8686 −4.32849 −0.466753
8787 0 0
8888 −2.16469 −0.230757
8989 1.39169 0.147519 0.0737595 0.997276i 0.476500π-0.476500\pi
0.0737595 + 0.997276i 0.476500π0.476500\pi
9090 0 0
9191 −3.40878 −0.357337
9292 1.32440 0.138078
9393 0 0
9494 1.66548 0.171781
9595 −1.16890 −0.119927
9696 0 0
9797 −4.55016 −0.461999 −0.230999 0.972954i 0.574200π-0.574200\pi
−0.230999 + 0.972954i 0.574200π0.574200\pi
9898 −0.775659 −0.0783533
9999 0 0
100100 6.02108 0.602108
101101 −8.82048 −0.877670 −0.438835 0.898568i 0.644609π-0.644609\pi
−0.438835 + 0.898568i 0.644609π0.644609\pi
102102 0 0
103103 5.65003 0.556714 0.278357 0.960478i 0.410210π-0.410210\pi
0.278357 + 0.960478i 0.410210π0.410210\pi
104104 −8.98540 −0.881091
105105 0 0
106106 −0.770154 −0.0748039
107107 20.2463 1.95729 0.978643 0.205567i 0.0659038π-0.0659038\pi
0.978643 + 0.205567i 0.0659038π0.0659038\pi
108108 0 0
109109 −0.369111 −0.0353545 −0.0176772 0.999844i 0.505627π-0.505627\pi
−0.0176772 + 0.999844i 0.505627π0.505627\pi
110110 −0.530712 −0.0506014
111111 0 0
112112 0.752101 0.0710669
113113 10.8983 1.02523 0.512613 0.858620i 0.328677π-0.328677\pi
0.512613 + 0.858620i 0.328677π0.328677\pi
114114 0 0
115115 0.789105 0.0735844
116116 2.49714 0.231854
117117 0 0
118118 −10.1520 −0.934567
119119 2.50310 0.229459
120120 0 0
121121 −10.3256 −0.938692
122122 5.58357 0.505513
123123 0 0
124124 −11.9132 −1.06984
125125 7.75331 0.693477
126126 0 0
127127 1.00000 0.0887357
128128 9.35453 0.826831
129129 0 0
130130 −2.20293 −0.193210
131131 6.34339 0.554224 0.277112 0.960838i 0.410623π-0.410623\pi
0.277112 + 0.960838i 0.410623π0.410623\pi
132132 0 0
133133 1.40296 0.121652
134134 4.48313 0.387283
135135 0 0
136136 6.59808 0.565781
137137 16.5664 1.41536 0.707682 0.706531i 0.249741π-0.249741\pi
0.707682 + 0.706531i 0.249741π0.249741\pi
138138 0 0
139139 −14.6965 −1.24654 −0.623271 0.782006i 0.714197π-0.714197\pi
−0.623271 + 0.782006i 0.714197π0.714197\pi
140140 1.16506 0.0984657
141141 0 0
142142 −0.524029 −0.0439756
143143 2.79933 0.234092
144144 0 0
145145 1.48785 0.123559
146146 7.75955 0.642185
147147 0 0
148148 4.04359 0.332381
149149 −12.6949 −1.04001 −0.520003 0.854164i 0.674069π-0.674069\pi
−0.520003 + 0.854164i 0.674069π0.674069\pi
150150 0 0
151151 −0.318150 −0.0258906 −0.0129453 0.999916i 0.504121π-0.504121\pi
−0.0129453 + 0.999916i 0.504121π0.504121\pi
152152 3.69815 0.299960
153153 0 0
154154 0.636982 0.0513294
155155 −7.09811 −0.570134
156156 0 0
157157 8.24209 0.657790 0.328895 0.944366i 0.393324π-0.393324\pi
0.328895 + 0.944366i 0.393324π0.393324\pi
158158 −1.22521 −0.0974723
159159 0 0
160160 4.87844 0.385674
161161 −0.947115 −0.0746431
162162 0 0
163163 12.7768 1.00076 0.500379 0.865806i 0.333194π-0.333194\pi
0.500379 + 0.865806i 0.333194π0.333194\pi
164164 3.21858 0.251329
165165 0 0
166166 2.57155 0.199591
167167 −19.9015 −1.54002 −0.770010 0.638031i 0.779749π-0.779749\pi
−0.770010 + 0.638031i 0.779749π0.779749\pi
168168 0 0
169169 −1.38025 −0.106173
170170 1.61764 0.124067
171171 0 0
172172 −7.80338 −0.595002
173173 −6.38620 −0.485534 −0.242767 0.970085i 0.578055π-0.578055\pi
−0.242767 + 0.970085i 0.578055π0.578055\pi
174174 0 0
175175 −4.30583 −0.325490
176176 −0.617636 −0.0465561
177177 0 0
178178 −1.07948 −0.0809102
179179 13.5632 1.01376 0.506879 0.862017i 0.330799π-0.330799\pi
0.506879 + 0.862017i 0.330799π0.330799\pi
180180 0 0
181181 −7.27667 −0.540871 −0.270435 0.962738i 0.587168π-0.587168\pi
−0.270435 + 0.962738i 0.587168π0.587168\pi
182182 2.64405 0.195990
183183 0 0
184184 −2.49656 −0.184049
185185 2.40925 0.177132
186186 0 0
187187 −2.05558 −0.150319
188188 3.00251 0.218981
189189 0 0
190190 0.906667 0.0657765
191191 2.22153 0.160744 0.0803721 0.996765i 0.474389π-0.474389\pi
0.0803721 + 0.996765i 0.474389π0.474389\pi
192192 0 0
193193 −15.4286 −1.11057 −0.555287 0.831659i 0.687392π-0.687392\pi
−0.555287 + 0.831659i 0.687392π0.687392\pi
194194 3.52937 0.253394
195195 0 0
196196 −1.39835 −0.0998824
197197 −12.8028 −0.912162 −0.456081 0.889938i 0.650747π-0.650747\pi
−0.456081 + 0.889938i 0.650747π0.650747\pi
198198 0 0
199199 3.89117 0.275838 0.137919 0.990444i 0.455959π-0.455959\pi
0.137919 + 0.990444i 0.455959π0.455959\pi
200200 −11.3500 −0.802567
201201 0 0
202202 6.84168 0.481379
203203 −1.78577 −0.125337
204204 0 0
205205 1.91769 0.133937
206206 −4.38249 −0.305343
207207 0 0
208208 −2.56374 −0.177764
209209 −1.15213 −0.0796945
210210 0 0
211211 23.1279 1.59219 0.796095 0.605172i 0.206896π-0.206896\pi
0.796095 + 0.605172i 0.206896π0.206896\pi
212212 −1.38843 −0.0953577
213213 0 0
214214 −15.7042 −1.07352
215215 −4.64941 −0.317087
216216 0 0
217217 8.51944 0.578337
218218 0.286304 0.0193910
219219 0 0
220220 −0.956765 −0.0645051
221221 −8.53251 −0.573959
222222 0 0
223223 6.28503 0.420877 0.210438 0.977607i 0.432511π-0.432511\pi
0.210438 + 0.977607i 0.432511π0.432511\pi
224224 −5.85530 −0.391224
225225 0 0
226226 −8.45336 −0.562309
227227 −7.52578 −0.499503 −0.249752 0.968310i 0.580349π-0.580349\pi
−0.249752 + 0.968310i 0.580349π0.580349\pi
228228 0 0
229229 −27.0451 −1.78719 −0.893596 0.448872i 0.851826π-0.851826\pi
−0.893596 + 0.448872i 0.851826π0.851826\pi
230230 −0.612076 −0.0403591
231231 0 0
232232 −4.70723 −0.309045
233233 20.8606 1.36663 0.683313 0.730126i 0.260539π-0.260539\pi
0.683313 + 0.730126i 0.260539π0.260539\pi
234234 0 0
235235 1.78896 0.116699
236236 −18.3020 −1.19136
237237 0 0
238238 −1.94155 −0.125852
239239 −20.7716 −1.34360 −0.671800 0.740732i 0.734479π-0.734479\pi
−0.671800 + 0.740732i 0.734479π0.734479\pi
240240 0 0
241241 −26.7249 −1.72150 −0.860750 0.509028i 0.830005π-0.830005\pi
−0.860750 + 0.509028i 0.830005π0.830005\pi
242242 8.00915 0.514847
243243 0 0
244244 10.0660 0.644412
245245 −0.833166 −0.0532291
246246 0 0
247247 −4.78238 −0.304295
248248 22.4569 1.42602
249249 0 0
250250 −6.01392 −0.380354
251251 24.2026 1.52765 0.763827 0.645420i 0.223318π-0.223318\pi
0.763827 + 0.645420i 0.223318π0.223318\pi
252252 0 0
253253 0.777784 0.0488989
254254 −0.775659 −0.0486691
255255 0 0
256256 −13.3309 −0.833184
257257 29.2037 1.82168 0.910838 0.412765i 0.135437π-0.135437\pi
0.910838 + 0.412765i 0.135437π0.135437\pi
258258 0 0
259259 −2.89168 −0.179680
260260 −3.97143 −0.246298
261261 0 0
262262 −4.92030 −0.303977
263263 −8.46412 −0.521920 −0.260960 0.965350i 0.584039π-0.584039\pi
−0.260960 + 0.965350i 0.584039π0.584039\pi
264264 0 0
265265 −0.827253 −0.0508178
266266 −1.08822 −0.0667229
267267 0 0
268268 8.08217 0.493697
269269 25.1306 1.53224 0.766119 0.642699i 0.222185π-0.222185\pi
0.766119 + 0.642699i 0.222185π0.222185\pi
270270 0 0
271271 0.485582 0.0294970 0.0147485 0.999891i 0.495305π-0.495305\pi
0.0147485 + 0.999891i 0.495305π0.495305\pi
272272 1.88259 0.114149
273273 0 0
274274 −12.8499 −0.776290
275275 3.53601 0.213229
276276 0 0
277277 −12.5162 −0.752027 −0.376013 0.926614i 0.622705π-0.622705\pi
−0.376013 + 0.926614i 0.622705π0.622705\pi
278278 11.3995 0.683695
279279 0 0
280280 −2.19620 −0.131248
281281 −4.50129 −0.268524 −0.134262 0.990946i 0.542866π-0.542866\pi
−0.134262 + 0.990946i 0.542866π0.542866\pi
282282 0 0
283283 −4.68047 −0.278225 −0.139112 0.990277i 0.544425π-0.544425\pi
−0.139112 + 0.990277i 0.544425π0.544425\pi
284284 −0.944718 −0.0560587
285285 0 0
286286 −2.17133 −0.128393
287287 −2.30169 −0.135865
288288 0 0
289289 −10.7345 −0.631440
290290 −1.15406 −0.0677688
291291 0 0
292292 13.9889 0.818637
293293 −21.7063 −1.26809 −0.634047 0.773295i 0.718607π-0.718607\pi
−0.634047 + 0.773295i 0.718607π0.718607\pi
294294 0 0
295295 −10.9047 −0.634894
296296 −7.62236 −0.443041
297297 0 0
298298 9.84690 0.570416
299299 3.22850 0.186709
300300 0 0
301301 5.58041 0.321649
302302 0.246775 0.0142003
303303 0 0
304304 1.05517 0.0605180
305305 5.99754 0.343418
306306 0 0
307307 7.76773 0.443328 0.221664 0.975123i 0.428851π-0.428851\pi
0.221664 + 0.975123i 0.428851π0.428851\pi
308308 1.14835 0.0654332
309309 0 0
310310 5.50571 0.312703
311311 −3.35408 −0.190192 −0.0950961 0.995468i 0.530316π-0.530316\pi
−0.0950961 + 0.995468i 0.530316π0.530316\pi
312312 0 0
313313 4.56356 0.257948 0.128974 0.991648i 0.458832π-0.458832\pi
0.128974 + 0.991648i 0.458832π0.458832\pi
314314 −6.39305 −0.360780
315315 0 0
316316 −2.20880 −0.124255
317317 −0.418733 −0.0235184 −0.0117592 0.999931i 0.503743π-0.503743\pi
−0.0117592 + 0.999931i 0.503743π0.503743\pi
318318 0 0
319319 1.46650 0.0821083
320320 −2.53075 −0.141473
321321 0 0
322322 0.734638 0.0409398
323323 3.51175 0.195399
324324 0 0
325325 14.6776 0.814168
326326 −9.91046 −0.548889
327327 0 0
328328 −6.06717 −0.335003
329329 −2.14718 −0.118378
330330 0 0
331331 13.6681 0.751266 0.375633 0.926768i 0.377425π-0.377425\pi
0.375633 + 0.926768i 0.377425π0.377425\pi
332332 4.63597 0.254432
333333 0 0
334334 15.4367 0.844660
335335 4.81551 0.263099
336336 0 0
337337 −13.1006 −0.713637 −0.356819 0.934174i 0.616139π-0.616139\pi
−0.356819 + 0.934174i 0.616139π0.616139\pi
338338 1.07060 0.0582329
339339 0 0
340340 2.91627 0.158157
341341 −6.99628 −0.378870
342342 0 0
343343 1.00000 0.0539949
344344 14.7097 0.793096
345345 0 0
346346 4.95351 0.266302
347347 3.79071 0.203496 0.101748 0.994810i 0.467556π-0.467556\pi
0.101748 + 0.994810i 0.467556π0.467556\pi
348348 0 0
349349 −18.5522 −0.993075 −0.496537 0.868015i 0.665395π-0.665395\pi
−0.496537 + 0.868015i 0.665395π0.665395\pi
350350 3.33986 0.178523
351351 0 0
352352 4.80845 0.256291
353353 −3.95098 −0.210289 −0.105145 0.994457i 0.533531π-0.533531\pi
−0.105145 + 0.994457i 0.533531π0.533531\pi
354354 0 0
355355 −0.562881 −0.0298746
356356 −1.94608 −0.103142
357357 0 0
358358 −10.5204 −0.556019
359359 5.14938 0.271774 0.135887 0.990724i 0.456612π-0.456612\pi
0.135887 + 0.990724i 0.456612π0.456612\pi
360360 0 0
361361 −17.0317 −0.896405
362362 5.64421 0.296653
363363 0 0
364364 4.76668 0.249842
365365 8.33485 0.436266
366366 0 0
367367 −31.8116 −1.66055 −0.830276 0.557353i 0.811817π-0.811817\pi
−0.830276 + 0.557353i 0.811817π0.811817\pi
368368 −0.712326 −0.0371326
369369 0 0
370370 −1.86876 −0.0971521
371371 0.992903 0.0515490
372372 0 0
373373 −17.4919 −0.905695 −0.452848 0.891588i 0.649592π-0.649592\pi
−0.452848 + 0.891588i 0.649592π0.649592\pi
374374 1.59443 0.0824460
375375 0 0
376376 −5.65988 −0.291886
377377 6.08730 0.313512
378378 0 0
379379 −23.3687 −1.20037 −0.600185 0.799861i 0.704906π-0.704906\pi
−0.600185 + 0.799861i 0.704906π0.704906\pi
380380 1.63453 0.0838499
381381 0 0
382382 −1.72315 −0.0881639
383383 −12.7842 −0.653242 −0.326621 0.945155i 0.605910π-0.605910\pi
−0.326621 + 0.945155i 0.605910π0.605910\pi
384384 0 0
385385 0.684208 0.0348705
386386 11.9673 0.609121
387387 0 0
388388 6.36273 0.323019
389389 31.1873 1.58126 0.790630 0.612294i 0.209753π-0.209753\pi
0.790630 + 0.612294i 0.209753π0.209753\pi
390390 0 0
391391 −2.37073 −0.119893
392392 2.63596 0.133136
393393 0 0
394394 9.93060 0.500296
395395 −1.31605 −0.0662174
396396 0 0
397397 36.1511 1.81437 0.907186 0.420729i 0.138226π-0.138226\pi
0.907186 + 0.420729i 0.138226π0.138226\pi
398398 −3.01822 −0.151290
399399 0 0
400400 −3.23842 −0.161921
401401 −22.0119 −1.09922 −0.549611 0.835421i 0.685224π-0.685224\pi
−0.549611 + 0.835421i 0.685224π0.685224\pi
402402 0 0
403403 −29.0409 −1.44663
404404 12.3341 0.613647
405405 0 0
406406 1.38515 0.0687438
407407 2.37469 0.117709
408408 0 0
409409 −23.7967 −1.17667 −0.588335 0.808617i 0.700216π-0.700216\pi
−0.588335 + 0.808617i 0.700216π0.700216\pi
410410 −1.48747 −0.0734611
411411 0 0
412412 −7.90074 −0.389242
413413 13.0882 0.644029
414414 0 0
415415 2.76220 0.135591
416416 19.9594 0.978590
417417 0 0
418418 0.893660 0.0437103
419419 −19.9178 −0.973048 −0.486524 0.873667i 0.661735π-0.661735\pi
−0.486524 + 0.873667i 0.661735π0.661735\pi
420420 0 0
421421 −7.26730 −0.354187 −0.177093 0.984194i 0.556669π-0.556669\pi
−0.177093 + 0.984194i 0.556669π0.556669\pi
422422 −17.9393 −0.873274
423423 0 0
424424 2.61725 0.127105
425425 −10.7779 −0.522807
426426 0 0
427427 −7.19849 −0.348359
428428 −28.3115 −1.36849
429429 0 0
430430 3.60635 0.173914
431431 −11.2632 −0.542529 −0.271264 0.962505i 0.587442π-0.587442\pi
−0.271264 + 0.962505i 0.587442π0.587442\pi
432432 0 0
433433 −37.4552 −1.79998 −0.899992 0.435907i 0.856428π-0.856428\pi
−0.899992 + 0.435907i 0.856428π0.856428\pi
434434 −6.60817 −0.317203
435435 0 0
436436 0.516148 0.0247190
437437 −1.32876 −0.0635634
438438 0 0
439439 −7.93341 −0.378641 −0.189321 0.981915i 0.560629π-0.560629\pi
−0.189321 + 0.981915i 0.560629π0.560629\pi
440440 1.80355 0.0859807
441441 0 0
442442 6.61832 0.314801
443443 −8.55610 −0.406513 −0.203256 0.979126i 0.565152π-0.565152\pi
−0.203256 + 0.979126i 0.565152π0.565152\pi
444444 0 0
445445 −1.15951 −0.0549661
446446 −4.87504 −0.230840
447447 0 0
448448 3.03751 0.143509
449449 −38.8738 −1.83457 −0.917285 0.398232i 0.869624π-0.869624\pi
−0.917285 + 0.398232i 0.869624π0.869624\pi
450450 0 0
451451 1.89018 0.0890051
452452 −15.2397 −0.716815
453453 0 0
454454 5.83743 0.273964
455455 2.84008 0.133145
456456 0 0
457457 −4.65559 −0.217779 −0.108890 0.994054i 0.534730π-0.534730\pi
−0.108890 + 0.994054i 0.534730π0.534730\pi
458458 20.9778 0.980227
459459 0 0
460460 −1.10345 −0.0514485
461461 −0.338860 −0.0157823 −0.00789114 0.999969i 0.502512π-0.502512\pi
−0.00789114 + 0.999969i 0.502512π0.502512\pi
462462 0 0
463463 −34.1206 −1.58572 −0.792858 0.609406i 0.791408π-0.791408\pi
−0.792858 + 0.609406i 0.791408π0.791408\pi
464464 −1.34308 −0.0623510
465465 0 0
466466 −16.1807 −0.749558
467467 −15.2172 −0.704166 −0.352083 0.935969i 0.614527π-0.614527\pi
−0.352083 + 0.935969i 0.614527π0.614527\pi
468468 0 0
469469 −5.77977 −0.266885
470470 −1.38762 −0.0640061
471471 0 0
472472 34.5001 1.58799
473473 −4.58271 −0.210713
474474 0 0
475475 −6.04091 −0.277176
476476 −3.50022 −0.160432
477477 0 0
478478 16.1116 0.736929
479479 41.7641 1.90825 0.954126 0.299405i 0.0967880π-0.0967880\pi
0.954126 + 0.299405i 0.0967880π0.0967880\pi
480480 0 0
481481 9.85710 0.449445
482482 20.7294 0.944197
483483 0 0
484484 14.4389 0.656312
485485 3.79104 0.172142
486486 0 0
487487 12.0202 0.544689 0.272344 0.962200i 0.412201π-0.412201\pi
0.272344 + 0.962200i 0.412201π0.412201\pi
488488 −18.9749 −0.858956
489489 0 0
490490 0.646253 0.0291947
491491 −20.4192 −0.921506 −0.460753 0.887528i 0.652421π-0.652421\pi
−0.460753 + 0.887528i 0.652421π0.652421\pi
492492 0 0
493493 −4.46997 −0.201317
494494 3.70949 0.166898
495495 0 0
496496 6.40748 0.287704
497497 0.675593 0.0303045
498498 0 0
499499 −23.7661 −1.06392 −0.531958 0.846771i 0.678544π-0.678544\pi
−0.531958 + 0.846771i 0.678544π0.678544\pi
500500 −10.8419 −0.484863
501501 0 0
502502 −18.7730 −0.837878
503503 −17.3725 −0.774604 −0.387302 0.921953i 0.626593π-0.626593\pi
−0.387302 + 0.921953i 0.626593π0.626593\pi
504504 0 0
505505 7.34892 0.327023
506506 −0.603295 −0.0268197
507507 0 0
508508 −1.39835 −0.0620419
509509 3.06618 0.135906 0.0679531 0.997689i 0.478353π-0.478353\pi
0.0679531 + 0.997689i 0.478353π0.478353\pi
510510 0 0
511511 −10.0038 −0.442543
512512 −8.36880 −0.369852
513513 0 0
514514 −22.6521 −0.999140
515515 −4.70742 −0.207433
516516 0 0
517517 1.76329 0.0775495
518518 2.24296 0.0985499
519519 0 0
520520 7.48634 0.328298
521521 26.9322 1.17992 0.589961 0.807431i 0.299143π-0.299143\pi
0.589961 + 0.807431i 0.299143π0.299143\pi
522522 0 0
523523 7.30944 0.319619 0.159810 0.987148i 0.448912π-0.448912\pi
0.159810 + 0.987148i 0.448912π0.448912\pi
524524 −8.87030 −0.387501
525525 0 0
526526 6.56527 0.286259
527527 21.3250 0.928932
528528 0 0
529529 −22.1030 −0.960999
530530 0.641666 0.0278722
531531 0 0
532532 −1.96183 −0.0850563
533533 7.84595 0.339846
534534 0 0
535535 −16.8686 −0.729291
536536 −15.2353 −0.658063
537537 0 0
538538 −19.4927 −0.840392
539539 −0.821214 −0.0353722
540540 0 0
541541 −30.5215 −1.31222 −0.656111 0.754664i 0.727800π-0.727800\pi
−0.656111 + 0.754664i 0.727800π0.727800\pi
542542 −0.376646 −0.0161783
543543 0 0
544544 −14.6564 −0.628388
545545 0.307531 0.0131732
546546 0 0
547547 −38.3344 −1.63906 −0.819531 0.573035i 0.805766π-0.805766\pi
−0.819531 + 0.573035i 0.805766π0.805766\pi
548548 −23.1657 −0.989590
549549 0 0
550550 −2.74274 −0.116951
551551 −2.50537 −0.106732
552552 0 0
553553 1.57957 0.0671702
554554 9.70831 0.412467
555555 0 0
556556 20.5509 0.871553
557557 −0.188070 −0.00796880 −0.00398440 0.999992i 0.501268π-0.501268\pi
−0.00398440 + 0.999992i 0.501268π0.501268\pi
558558 0 0
559559 −19.0224 −0.804560
560560 −0.626625 −0.0264798
561561 0 0
562562 3.49146 0.147278
563563 −20.4436 −0.861594 −0.430797 0.902449i 0.641768π-0.641768\pi
−0.430797 + 0.902449i 0.641768π0.641768\pi
564564 0 0
565565 −9.08010 −0.382003
566566 3.63045 0.152599
567567 0 0
568568 1.78084 0.0747223
569569 −27.1530 −1.13831 −0.569157 0.822229i 0.692730π-0.692730\pi
−0.569157 + 0.822229i 0.692730π0.692730\pi
570570 0 0
571571 6.65084 0.278329 0.139165 0.990269i 0.455558π-0.455558\pi
0.139165 + 0.990269i 0.455558π0.455558\pi
572572 −3.91446 −0.163672
573573 0 0
574574 1.78533 0.0745181
575575 4.07812 0.170069
576576 0 0
577577 36.7405 1.52953 0.764764 0.644310i 0.222856π-0.222856\pi
0.764764 + 0.644310i 0.222856π0.222856\pi
578578 8.32629 0.346328
579579 0 0
580580 −2.08054 −0.0863895
581581 −3.31531 −0.137542
582582 0 0
583583 −0.815386 −0.0337698
584584 −26.3697 −1.09119
585585 0 0
586586 16.8366 0.695515
587587 −12.4810 −0.515145 −0.257572 0.966259i 0.582923π-0.582923\pi
−0.257572 + 0.966259i 0.582923π0.582923\pi
588588 0 0
589589 11.9524 0.492491
590590 8.45830 0.348223
591591 0 0
592592 −2.17484 −0.0893853
593593 −44.7690 −1.83844 −0.919221 0.393742i 0.871180π-0.871180\pi
−0.919221 + 0.393742i 0.871180π0.871180\pi
594594 0 0
595595 −2.08550 −0.0854972
596596 17.7519 0.727148
597597 0 0
598598 −2.50422 −0.102405
599599 39.1831 1.60098 0.800490 0.599346i 0.204573π-0.204573\pi
0.800490 + 0.599346i 0.204573π0.204573\pi
600600 0 0
601601 −9.78843 −0.399279 −0.199639 0.979869i 0.563977π-0.563977\pi
−0.199639 + 0.979869i 0.563977π0.563977\pi
602602 −4.32849 −0.176416
603603 0 0
604604 0.444886 0.0181021
605605 8.60295 0.349760
606606 0 0
607607 −11.8224 −0.479857 −0.239929 0.970791i 0.577124π-0.577124\pi
−0.239929 + 0.970791i 0.577124π0.577124\pi
608608 −8.21475 −0.333152
609609 0 0
610610 −4.65204 −0.188356
611611 7.31924 0.296105
612612 0 0
613613 20.7346 0.837461 0.418730 0.908111i 0.362475π-0.362475\pi
0.418730 + 0.908111i 0.362475π0.362475\pi
614614 −6.02511 −0.243154
615615 0 0
616616 −2.16469 −0.0872178
617617 29.3288 1.18073 0.590367 0.807135i 0.298983π-0.298983\pi
0.590367 + 0.807135i 0.298983π0.298983\pi
618618 0 0
619619 15.0032 0.603029 0.301515 0.953462i 0.402508π-0.402508\pi
0.301515 + 0.953462i 0.402508π0.402508\pi
620620 9.92567 0.398624
621621 0 0
622622 2.60162 0.104315
623623 1.39169 0.0557569
624624 0 0
625625 15.0694 0.602775
626626 −3.53977 −0.141477
627627 0 0
628628 −11.5254 −0.459912
629629 −7.23817 −0.288605
630630 0 0
631631 11.3359 0.451273 0.225637 0.974212i 0.427554π-0.427554\pi
0.225637 + 0.974212i 0.427554π0.427554\pi
632632 4.16369 0.165623
633633 0 0
634634 0.324794 0.0128992
635635 −0.833166 −0.0330632
636636 0 0
637637 −3.40878 −0.135061
638638 −1.13750 −0.0450342
639639 0 0
640640 −7.79388 −0.308080
641641 −12.5109 −0.494149 −0.247074 0.968997i 0.579469π-0.579469\pi
−0.247074 + 0.968997i 0.579469π0.579469\pi
642642 0 0
643643 −15.8249 −0.624073 −0.312037 0.950070i 0.601011π-0.601011\pi
−0.312037 + 0.950070i 0.601011π0.601011\pi
644644 1.32440 0.0521888
645645 0 0
646646 −2.72392 −0.107171
647647 −17.2085 −0.676534 −0.338267 0.941050i 0.609841π-0.609841\pi
−0.338267 + 0.941050i 0.609841π0.609841\pi
648648 0 0
649649 −10.7482 −0.421905
650650 −11.3848 −0.446550
651651 0 0
652652 −17.8665 −0.699707
653653 −16.6436 −0.651315 −0.325657 0.945488i 0.605586π-0.605586\pi
−0.325657 + 0.945488i 0.605586π0.605586\pi
654654 0 0
655655 −5.28510 −0.206506
656656 −1.73110 −0.0675883
657657 0 0
658658 1.66548 0.0649270
659659 −35.9180 −1.39917 −0.699583 0.714551i 0.746631π-0.746631\pi
−0.699583 + 0.714551i 0.746631π0.746631\pi
660660 0 0
661661 28.3781 1.10378 0.551890 0.833917i 0.313907π-0.313907\pi
0.551890 + 0.833917i 0.313907π0.313907\pi
662662 −10.6018 −0.412049
663663 0 0
664664 −8.73903 −0.339140
665665 −1.16890 −0.0453280
666666 0 0
667667 1.69133 0.0654887
668668 27.8293 1.07675
669669 0 0
670670 −3.73519 −0.144303
671671 5.91150 0.228211
672672 0 0
673673 −45.0138 −1.73515 −0.867577 0.497303i 0.834324π-0.834324\pi
−0.867577 + 0.497303i 0.834324π0.834324\pi
674674 10.1616 0.391411
675675 0 0
676676 1.93007 0.0742335
677677 24.6030 0.945570 0.472785 0.881178i 0.343249π-0.343249\pi
0.472785 + 0.881178i 0.343249π0.343249\pi
678678 0 0
679679 −4.55016 −0.174619
680680 −5.49730 −0.210812
681681 0 0
682682 5.42673 0.207800
683683 −17.5156 −0.670217 −0.335109 0.942179i 0.608773π-0.608773\pi
−0.335109 + 0.942179i 0.608773π0.608773\pi
684684 0 0
685685 −13.8026 −0.527369
686686 −0.775659 −0.0296148
687687 0 0
688688 4.19703 0.160010
689689 −3.38458 −0.128942
690690 0 0
691691 16.1962 0.616132 0.308066 0.951365i 0.400318π-0.400318\pi
0.308066 + 0.951365i 0.400318π0.400318\pi
692692 8.93017 0.339474
693693 0 0
694694 −2.94029 −0.111612
695695 12.2446 0.464466
696696 0 0
697697 −5.76136 −0.218227
698698 14.3901 0.544675
699699 0 0
700700 6.02108 0.227575
701701 −40.1314 −1.51574 −0.757871 0.652405i 0.773760π-0.773760\pi
−0.757871 + 0.652405i 0.773760π0.773760\pi
702702 0 0
703703 −4.05691 −0.153009
704704 −2.49444 −0.0940129
705705 0 0
706706 3.06461 0.115338
707707 −8.82048 −0.331728
708708 0 0
709709 −30.6274 −1.15024 −0.575118 0.818070i 0.695044π-0.695044\pi
−0.575118 + 0.818070i 0.695044π0.695044\pi
710710 0.436604 0.0163854
711711 0 0
712712 3.66844 0.137481
713713 −8.06889 −0.302182
714714 0 0
715715 −2.33231 −0.0872235
716716 −18.9661 −0.708796
717717 0 0
718718 −3.99416 −0.149061
719719 31.6921 1.18192 0.590958 0.806702i 0.298750π-0.298750\pi
0.590958 + 0.806702i 0.298750π0.298750\pi
720720 0 0
721721 5.65003 0.210418
722722 13.2108 0.491655
723723 0 0
724724 10.1754 0.378164
725725 7.68924 0.285571
726726 0 0
727727 −24.4231 −0.905801 −0.452901 0.891561i 0.649611π-0.649611\pi
−0.452901 + 0.891561i 0.649611π0.649611\pi
728728 −8.98540 −0.333021
729729 0 0
730730 −6.46499 −0.239280
731731 13.9683 0.516637
732732 0 0
733733 11.9558 0.441599 0.220800 0.975319i 0.429133π-0.429133\pi
0.220800 + 0.975319i 0.429133π0.429133\pi
734734 24.6749 0.910769
735735 0 0
736736 5.54564 0.204415
737737 4.74643 0.174837
738738 0 0
739739 −15.0507 −0.553648 −0.276824 0.960921i 0.589282π-0.589282\pi
−0.276824 + 0.960921i 0.589282π0.589282\pi
740740 −3.36899 −0.123846
741741 0 0
742742 −0.770154 −0.0282732
743743 −53.7505 −1.97191 −0.985957 0.166999i 0.946592π-0.946592\pi
−0.985957 + 0.166999i 0.946592π0.946592\pi
744744 0 0
745745 10.5770 0.387510
746746 13.5677 0.496750
747747 0 0
748748 2.87443 0.105100
749749 20.2463 0.739785
750750 0 0
751751 9.76059 0.356169 0.178085 0.984015i 0.443010π-0.443010\pi
0.178085 + 0.984015i 0.443010π0.443010\pi
752752 −1.61489 −0.0588891
753753 0 0
754754 −4.72167 −0.171953
755755 0.265072 0.00964694
756756 0 0
757757 32.3529 1.17589 0.587944 0.808902i 0.299938π-0.299938\pi
0.587944 + 0.808902i 0.299938π0.299938\pi
758758 18.1261 0.658371
759759 0 0
760760 −3.08117 −0.111766
761761 29.5981 1.07293 0.536465 0.843923i 0.319759π-0.319759\pi
0.536465 + 0.843923i 0.319759π0.319759\pi
762762 0 0
763763 −0.369111 −0.0133627
764764 −3.10648 −0.112389
765765 0 0
766766 9.91617 0.358286
767767 −44.6148 −1.61095
768768 0 0
769769 −23.0353 −0.830676 −0.415338 0.909667i 0.636337π-0.636337\pi
−0.415338 + 0.909667i 0.636337π0.636337\pi
770770 −0.530712 −0.0191255
771771 0 0
772772 21.5746 0.776488
773773 −22.4412 −0.807154 −0.403577 0.914946i 0.632233π-0.632233\pi
−0.403577 + 0.914946i 0.632233π0.632233\pi
774774 0 0
775775 −36.6833 −1.31770
776776 −11.9940 −0.430561
777777 0 0
778778 −24.1907 −0.867279
779779 −3.22918 −0.115697
780780 0 0
781781 −0.554806 −0.0198525
782782 1.83887 0.0657580
783783 0 0
784784 0.752101 0.0268608
785785 −6.86703 −0.245095
786786 0 0
787787 34.2193 1.21979 0.609894 0.792483i 0.291212π-0.291212\pi
0.609894 + 0.792483i 0.291212π0.291212\pi
788788 17.9028 0.637762
789789 0 0
790790 1.02080 0.0363185
791791 10.8983 0.387499
792792 0 0
793793 24.5380 0.871371
794794 −28.0409 −0.995135
795795 0 0
796796 −5.44123 −0.192859
797797 −37.5468 −1.32998 −0.664988 0.746854i 0.731563π-0.731563\pi
−0.664988 + 0.746854i 0.731563π0.731563\pi
798798 0 0
799799 −5.37460 −0.190140
800800 25.2119 0.891377
801801 0 0
802802 17.0737 0.602894
803803 8.21527 0.289911
804804 0 0
805805 0.789105 0.0278123
806806 22.5258 0.793437
807807 0 0
808808 −23.2504 −0.817948
809809 −18.2474 −0.641544 −0.320772 0.947156i 0.603942π-0.603942\pi
−0.320772 + 0.947156i 0.603942π0.603942\pi
810810 0 0
811811 −27.7675 −0.975048 −0.487524 0.873110i 0.662100π-0.662100\pi
−0.487524 + 0.873110i 0.662100π0.662100\pi
812812 2.49714 0.0876325
813813 0 0
814814 −1.84195 −0.0645602
815815 −10.6452 −0.372886
816816 0 0
817817 7.82909 0.273905
818818 18.4581 0.645372
819819 0 0
820820 −2.68161 −0.0936459
821821 0.530588 0.0185176 0.00925882 0.999957i 0.497053π-0.497053\pi
0.00925882 + 0.999957i 0.497053π0.497053\pi
822822 0 0
823823 38.3917 1.33825 0.669125 0.743150i 0.266669π-0.266669\pi
0.669125 + 0.743150i 0.266669π0.266669\pi
824824 14.8933 0.518831
825825 0 0
826826 −10.1520 −0.353233
827827 19.9999 0.695464 0.347732 0.937594i 0.386952π-0.386952\pi
0.347732 + 0.937594i 0.386952π0.386952\pi
828828 0 0
829829 8.81614 0.306197 0.153099 0.988211i 0.451075π-0.451075\pi
0.153099 + 0.988211i 0.451075π0.451075\pi
830830 −2.14253 −0.0743682
831831 0 0
832832 −10.3542 −0.358967
833833 2.50310 0.0867273
834834 0 0
835835 16.5812 0.573817
836836 1.61109 0.0557206
837837 0 0
838838 15.4494 0.533691
839839 22.1358 0.764211 0.382106 0.924119i 0.375199π-0.375199\pi
0.382106 + 0.924119i 0.375199π0.375199\pi
840840 0 0
841841 −25.8110 −0.890035
842842 5.63695 0.194262
843843 0 0
844844 −32.3410 −1.11322
845845 1.14997 0.0395603
846846 0 0
847847 −10.3256 −0.354792
848848 0.746763 0.0256440
849849 0 0
850850 8.36000 0.286746
851851 2.73876 0.0938833
852852 0 0
853853 −8.56457 −0.293245 −0.146623 0.989192i 0.546840π-0.546840\pi
−0.146623 + 0.989192i 0.546840π0.546840\pi
854854 5.58357 0.191066
855855 0 0
856856 53.3685 1.82410
857857 6.57137 0.224474 0.112237 0.993681i 0.464198π-0.464198\pi
0.112237 + 0.993681i 0.464198π0.464198\pi
858858 0 0
859859 14.7406 0.502944 0.251472 0.967865i 0.419085π-0.419085\pi
0.251472 + 0.967865i 0.419085π0.419085\pi
860860 6.50152 0.221700
861861 0 0
862862 8.73639 0.297563
863863 −20.0421 −0.682242 −0.341121 0.940019i 0.610807π-0.610807\pi
−0.341121 + 0.940019i 0.610807π0.610807\pi
864864 0 0
865865 5.32077 0.180912
866866 29.0525 0.987243
867867 0 0
868868 −11.9132 −0.404360
869869 −1.29717 −0.0440033
870870 0 0
871871 19.7019 0.667575
872872 −0.972964 −0.0329487
873873 0 0
874874 1.03067 0.0348628
875875 7.75331 0.262110
876876 0 0
877877 −31.0175 −1.04739 −0.523694 0.851907i 0.675446π-0.675446\pi
−0.523694 + 0.851907i 0.675446π0.675446\pi
878878 6.15362 0.207675
879879 0 0
880880 0.514594 0.0173469
881881 4.04652 0.136331 0.0681654 0.997674i 0.478285π-0.478285\pi
0.0681654 + 0.997674i 0.478285π0.478285\pi
882882 0 0
883883 55.7648 1.87663 0.938317 0.345777i 0.112385π-0.112385\pi
0.938317 + 0.345777i 0.112385π0.112385\pi
884884 11.9315 0.401299
885885 0 0
886886 6.63661 0.222961
887887 −56.9316 −1.91158 −0.955788 0.294058i 0.904994π-0.904994\pi
−0.955788 + 0.294058i 0.904994π0.904994\pi
888888 0 0
889889 1.00000 0.0335389
890890 0.899384 0.0301474
891891 0 0
892892 −8.78870 −0.294267
893893 −3.01240 −0.100806
894894 0 0
895895 −11.3004 −0.377730
896896 9.35453 0.312513
897897 0 0
898898 30.1528 1.00621
899899 −15.2138 −0.507408
900900 0 0
901901 2.48534 0.0827986
902902 −1.46613 −0.0488169
903903 0 0
904904 28.7275 0.955463
905905 6.06268 0.201530
906906 0 0
907907 −15.6800 −0.520645 −0.260323 0.965522i 0.583829π-0.583829\pi
−0.260323 + 0.965522i 0.583829π0.583829\pi
908908 10.5237 0.349241
909909 0 0
910910 −2.20293 −0.0730264
911911 23.8935 0.791627 0.395814 0.918331i 0.370463π-0.370463\pi
0.395814 + 0.918331i 0.370463π0.370463\pi
912912 0 0
913913 2.72258 0.0901042
914914 3.61115 0.119446
915915 0 0
916916 37.8186 1.24956
917917 6.34339 0.209477
918918 0 0
919919 −18.0890 −0.596702 −0.298351 0.954456i 0.596437π-0.596437\pi
−0.298351 + 0.954456i 0.596437π0.596437\pi
920920 2.08005 0.0685772
921921 0 0
922922 0.262840 0.00865616
923923 −2.30294 −0.0758024
924924 0 0
925925 12.4511 0.409390
926926 26.4659 0.869723
927927 0 0
928928 10.4562 0.343243
929929 −10.9992 −0.360873 −0.180437 0.983587i 0.557751π-0.557751\pi
−0.180437 + 0.983587i 0.557751π0.557751\pi
930930 0 0
931931 1.40296 0.0459802
932932 −29.1706 −0.955513
933933 0 0
934934 11.8033 0.386216
935935 1.71264 0.0560094
936936 0 0
937937 51.9182 1.69609 0.848046 0.529923i 0.177779π-0.177779\pi
0.848046 + 0.529923i 0.177779π0.177779\pi
938938 4.48313 0.146379
939939 0 0
940940 −2.50159 −0.0815930
941941 13.1964 0.430192 0.215096 0.976593i 0.430994π-0.430994\pi
0.215096 + 0.976593i 0.430994π0.430994\pi
942942 0 0
943943 2.17997 0.0709895
944944 9.84367 0.320384
945945 0 0
946946 3.55462 0.115571
947947 39.0756 1.26979 0.634893 0.772600i 0.281044π-0.281044\pi
0.634893 + 0.772600i 0.281044π0.281044\pi
948948 0 0
949949 34.1008 1.10696
950950 4.68568 0.152024
951951 0 0
952952 6.59808 0.213845
953953 −4.31917 −0.139912 −0.0699559 0.997550i 0.522286π-0.522286\pi
−0.0699559 + 0.997550i 0.522286π0.522286\pi
954954 0 0
955955 −1.85090 −0.0598938
956956 29.0460 0.939415
957957 0 0
958958 −32.3947 −1.04663
959959 16.5664 0.534957
960960 0 0
961961 41.5808 1.34132
962962 −7.64574 −0.246509
963963 0 0
964964 37.3708 1.20363
965965 12.8546 0.413804
966966 0 0
967967 53.6032 1.72376 0.861881 0.507110i 0.169286π-0.169286\pi
0.861881 + 0.507110i 0.169286π0.169286\pi
968968 −27.2179 −0.874817
969969 0 0
970970 −2.94055 −0.0944155
971971 −5.46228 −0.175293 −0.0876465 0.996152i 0.527935π-0.527935\pi
−0.0876465 + 0.996152i 0.527935π0.527935\pi
972972 0 0
973973 −14.6965 −0.471149
974974 −9.32359 −0.298747
975975 0 0
976976 −5.41399 −0.173298
977977 −32.4956 −1.03963 −0.519813 0.854280i 0.673999π-0.673999\pi
−0.519813 + 0.854280i 0.673999π0.673999\pi
978978 0 0
979979 −1.14288 −0.0365265
980980 1.16506 0.0372165
981981 0 0
982982 15.8383 0.505422
983983 −3.17977 −0.101419 −0.0507095 0.998713i 0.516148π-0.516148\pi
−0.0507095 + 0.998713i 0.516148π0.516148\pi
984984 0 0
985985 10.6669 0.339875
986986 3.46717 0.110417
987987 0 0
988988 6.68745 0.212756
989989 −5.28529 −0.168062
990990 0 0
991991 −38.3965 −1.21971 −0.609853 0.792515i 0.708771π-0.708771\pi
−0.609853 + 0.792515i 0.708771π0.708771\pi
992992 −49.8838 −1.58381
993993 0 0
994994 −0.524029 −0.0166212
995995 −3.24199 −0.102778
996996 0 0
997997 24.5944 0.778912 0.389456 0.921045i 0.372663π-0.372663\pi
0.389456 + 0.921045i 0.372663π0.372663\pi
998998 18.4344 0.583530
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 8001.2.a.x.1.7 22
3.2 odd 2 inner 8001.2.a.x.1.16 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8001.2.a.x.1.7 22 1.1 even 1 trivial
8001.2.a.x.1.16 yes 22 3.2 odd 2 inner