Properties

Label 2889.2.a.g.1.23
Level 28892889
Weight 22
Character 2889.1
Self dual yes
Analytic conductor 23.06923.069
Analytic rank 00
Dimension 2323
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] = [2889,2,Mod(1,2889)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2889.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2889, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 2889=33107 2889 = 3^{3} \cdot 107
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2889.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [23,0,0,34,0,0,11,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 23.068781143923.0687811439
Analytic rank: 00
Dimension: 2323
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.23
Character χ\chi == 2889.1

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) == q+2.78337q2+5.74714q4+1.72892q53.54967q7+10.4297q8+4.81223q10+5.67908q113.14186q139.88005q14+17.5353q162.12928q17+2.43961q19+9.93637q20+15.8070q220.396657q232.01082q258.74496q2620.4005q28+6.15089q290.639179q31+27.9480q325.92658q346.13711q355.87803q37+6.79033q38+18.0321q40+11.2696q418.82771q43+32.6385q441.10404q46+4.13563q47+5.60018q495.59686q5018.0567q52+4.05279q53+9.81869q5537.0219q56+17.1202q589.93269q590.241276q611.77907q62+42.7188q645.43204q6513.3559q6712.2373q6817.0818q70+7.26801q7110.0252q7316.3607q74+14.0208q7620.1589q7713.2385q79+30.3173q80+31.3673q82+11.2556q833.68137q8524.5708q86+59.2309q8813.8274q89+11.1526q912.27964q92+11.5110q94+4.21790q950.952876q97+15.5874q98+O(q100)q+2.78337 q^{2} +5.74714 q^{4} +1.72892 q^{5} -3.54967 q^{7} +10.4297 q^{8} +4.81223 q^{10} +5.67908 q^{11} -3.14186 q^{13} -9.88005 q^{14} +17.5353 q^{16} -2.12928 q^{17} +2.43961 q^{19} +9.93637 q^{20} +15.8070 q^{22} -0.396657 q^{23} -2.01082 q^{25} -8.74496 q^{26} -20.4005 q^{28} +6.15089 q^{29} -0.639179 q^{31} +27.9480 q^{32} -5.92658 q^{34} -6.13711 q^{35} -5.87803 q^{37} +6.79033 q^{38} +18.0321 q^{40} +11.2696 q^{41} -8.82771 q^{43} +32.6385 q^{44} -1.10404 q^{46} +4.13563 q^{47} +5.60018 q^{49} -5.59686 q^{50} -18.0567 q^{52} +4.05279 q^{53} +9.81869 q^{55} -37.0219 q^{56} +17.1202 q^{58} -9.93269 q^{59} -0.241276 q^{61} -1.77907 q^{62} +42.7188 q^{64} -5.43204 q^{65} -13.3559 q^{67} -12.2373 q^{68} -17.0818 q^{70} +7.26801 q^{71} -10.0252 q^{73} -16.3607 q^{74} +14.0208 q^{76} -20.1589 q^{77} -13.2385 q^{79} +30.3173 q^{80} +31.3673 q^{82} +11.2556 q^{83} -3.68137 q^{85} -24.5708 q^{86} +59.2309 q^{88} -13.8274 q^{89} +11.1526 q^{91} -2.27964 q^{92} +11.5110 q^{94} +4.21790 q^{95} -0.952876 q^{97} +15.5874 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 23q+34q4+11q73q8+10q10+q11+9q13+q14+60q16+19q19+10q20+13q22+q23+43q2514q26+27q28+7q29+41q316q32++103q98+O(q100) 23 q + 34 q^{4} + 11 q^{7} - 3 q^{8} + 10 q^{10} + q^{11} + 9 q^{13} + q^{14} + 60 q^{16} + 19 q^{19} + 10 q^{20} + 13 q^{22} + q^{23} + 43 q^{25} - 14 q^{26} + 27 q^{28} + 7 q^{29} + 41 q^{31} - 6 q^{32}+ \cdots + 103 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 2.78337 1.96814 0.984069 0.177785i 0.0568932π-0.0568932\pi
0.984069 + 0.177785i 0.0568932π0.0568932\pi
33 0 0
44 5.74714 2.87357
55 1.72892 0.773198 0.386599 0.922248i 0.373650π-0.373650\pi
0.386599 + 0.922248i 0.373650π0.373650\pi
66 0 0
77 −3.54967 −1.34165 −0.670825 0.741615i 0.734060π-0.734060\pi
−0.670825 + 0.741615i 0.734060π0.734060\pi
88 10.4297 3.68745
99 0 0
1010 4.81223 1.52176
1111 5.67908 1.71231 0.856154 0.516722i 0.172848π-0.172848\pi
0.856154 + 0.516722i 0.172848π0.172848\pi
1212 0 0
1313 −3.14186 −0.871396 −0.435698 0.900093i 0.643498π-0.643498\pi
−0.435698 + 0.900093i 0.643498π0.643498\pi
1414 −9.88005 −2.64055
1515 0 0
1616 17.5353 4.38383
1717 −2.12928 −0.516427 −0.258213 0.966088i 0.583134π-0.583134\pi
−0.258213 + 0.966088i 0.583134π0.583134\pi
1818 0 0
1919 2.43961 0.559685 0.279842 0.960046i 0.409718π-0.409718\pi
0.279842 + 0.960046i 0.409718π0.409718\pi
2020 9.93637 2.22184
2121 0 0
2222 15.8070 3.37006
2323 −0.396657 −0.0827086 −0.0413543 0.999145i 0.513167π-0.513167\pi
−0.0413543 + 0.999145i 0.513167π0.513167\pi
2424 0 0
2525 −2.01082 −0.402165
2626 −8.74496 −1.71503
2727 0 0
2828 −20.4005 −3.85533
2929 6.15089 1.14219 0.571095 0.820884i 0.306519π-0.306519\pi
0.571095 + 0.820884i 0.306519π0.306519\pi
3030 0 0
3131 −0.639179 −0.114800 −0.0574000 0.998351i 0.518281π-0.518281\pi
−0.0574000 + 0.998351i 0.518281π0.518281\pi
3232 27.9480 4.94055
3333 0 0
3434 −5.92658 −1.01640
3535 −6.13711 −1.03736
3636 0 0
3737 −5.87803 −0.966343 −0.483171 0.875526i 0.660515π-0.660515\pi
−0.483171 + 0.875526i 0.660515π0.660515\pi
3838 6.79033 1.10154
3939 0 0
4040 18.0321 2.85113
4141 11.2696 1.76001 0.880005 0.474965i 0.157539π-0.157539\pi
0.880005 + 0.474965i 0.157539π0.157539\pi
4242 0 0
4343 −8.82771 −1.34621 −0.673107 0.739545i 0.735041π-0.735041\pi
−0.673107 + 0.739545i 0.735041π0.735041\pi
4444 32.6385 4.92043
4545 0 0
4646 −1.10404 −0.162782
4747 4.13563 0.603244 0.301622 0.953428i 0.402472π-0.402472\pi
0.301622 + 0.953428i 0.402472π0.402472\pi
4848 0 0
4949 5.60018 0.800026
5050 −5.59686 −0.791516
5151 0 0
5252 −18.0567 −2.50402
5353 4.05279 0.556694 0.278347 0.960481i 0.410213π-0.410213\pi
0.278347 + 0.960481i 0.410213π0.410213\pi
5454 0 0
5555 9.81869 1.32395
5656 −37.0219 −4.94726
5757 0 0
5858 17.1202 2.24799
5959 −9.93269 −1.29313 −0.646563 0.762861i 0.723794π-0.723794\pi
−0.646563 + 0.762861i 0.723794π0.723794\pi
6060 0 0
6161 −0.241276 −0.0308922 −0.0154461 0.999881i 0.504917π-0.504917\pi
−0.0154461 + 0.999881i 0.504917π0.504917\pi
6262 −1.77907 −0.225942
6363 0 0
6464 42.7188 5.33985
6565 −5.43204 −0.673762
6666 0 0
6767 −13.3559 −1.63168 −0.815839 0.578279i 0.803725π-0.803725\pi
−0.815839 + 0.578279i 0.803725π0.803725\pi
6868 −12.2373 −1.48399
6969 0 0
7070 −17.0818 −2.04167
7171 7.26801 0.862554 0.431277 0.902220i 0.358063π-0.358063\pi
0.431277 + 0.902220i 0.358063π0.358063\pi
7272 0 0
7373 −10.0252 −1.17336 −0.586680 0.809819i 0.699565π-0.699565\pi
−0.586680 + 0.809819i 0.699565π0.699565\pi
7474 −16.3607 −1.90190
7575 0 0
7676 14.0208 1.60829
7777 −20.1589 −2.29732
7878 0 0
7979 −13.2385 −1.48945 −0.744724 0.667372i 0.767419π-0.767419\pi
−0.744724 + 0.667372i 0.767419π0.767419\pi
8080 30.3173 3.38957
8181 0 0
8282 31.3673 3.46394
8383 11.2556 1.23546 0.617731 0.786389i 0.288052π-0.288052\pi
0.617731 + 0.786389i 0.288052π0.288052\pi
8484 0 0
8585 −3.68137 −0.399300
8686 −24.5708 −2.64954
8787 0 0
8888 59.2309 6.31404
8989 −13.8274 −1.46571 −0.732853 0.680388i 0.761811π-0.761811\pi
−0.732853 + 0.680388i 0.761811π0.761811\pi
9090 0 0
9191 11.1526 1.16911
9292 −2.27964 −0.237669
9393 0 0
9494 11.5110 1.18727
9595 4.21790 0.432747
9696 0 0
9797 −0.952876 −0.0967499 −0.0483749 0.998829i 0.515404π-0.515404\pi
−0.0483749 + 0.998829i 0.515404π0.515404\pi
9898 15.5874 1.57456
9999 0 0
100100 −11.5565 −1.15565
101101 −9.50722 −0.946004 −0.473002 0.881061i 0.656830π-0.656830\pi
−0.473002 + 0.881061i 0.656830π0.656830\pi
102102 0 0
103103 16.4940 1.62520 0.812599 0.582823i 0.198052π-0.198052\pi
0.812599 + 0.582823i 0.198052π0.198052\pi
104104 −32.7686 −3.21323
105105 0 0
106106 11.2804 1.09565
107107 1.00000 0.0966736
108108 0 0
109109 −0.148548 −0.0142283 −0.00711414 0.999975i 0.502265π-0.502265\pi
−0.00711414 + 0.999975i 0.502265π0.502265\pi
110110 27.3290 2.60572
111111 0 0
112112 −62.2447 −5.88157
113113 13.7517 1.29365 0.646827 0.762636i 0.276095π-0.276095\pi
0.646827 + 0.762636i 0.276095π0.276095\pi
114114 0 0
115115 −0.685789 −0.0639502
116116 35.3500 3.28216
117117 0 0
118118 −27.6463 −2.54505
119119 7.55826 0.692864
120120 0 0
121121 21.2519 1.93200
122122 −0.671560 −0.0608002
123123 0 0
124124 −3.67345 −0.329886
125125 −12.1212 −1.08415
126126 0 0
127127 3.20745 0.284615 0.142307 0.989823i 0.454548π-0.454548\pi
0.142307 + 0.989823i 0.454548π0.454548\pi
128128 63.0062 5.56902
129129 0 0
130130 −15.1194 −1.32606
131131 −5.09923 −0.445522 −0.222761 0.974873i 0.571507π-0.571507\pi
−0.222761 + 0.974873i 0.571507π0.571507\pi
132132 0 0
133133 −8.65982 −0.750901
134134 −37.1743 −3.21137
135135 0 0
136136 −22.2077 −1.90430
137137 −11.6481 −0.995164 −0.497582 0.867417i 0.665779π-0.665779\pi
−0.497582 + 0.867417i 0.665779π0.665779\pi
138138 0 0
139139 −16.1938 −1.37354 −0.686770 0.726875i 0.740972π-0.740972\pi
−0.686770 + 0.726875i 0.740972π0.740972\pi
140140 −35.2709 −2.98093
141141 0 0
142142 20.2295 1.69763
143143 −17.8429 −1.49210
144144 0 0
145145 10.6344 0.883140
146146 −27.9038 −2.30933
147147 0 0
148148 −33.7819 −2.77685
149149 14.1284 1.15744 0.578722 0.815525i 0.303551π-0.303551\pi
0.578722 + 0.815525i 0.303551π0.303551\pi
150150 0 0
151151 15.4222 1.25504 0.627519 0.778601i 0.284070π-0.284070\pi
0.627519 + 0.778601i 0.284070π0.284070\pi
152152 25.4443 2.06381
153153 0 0
154154 −56.1096 −4.52144
155155 −1.10509 −0.0887632
156156 0 0
157157 −6.47227 −0.516543 −0.258272 0.966072i 0.583153π-0.583153\pi
−0.258272 + 0.966072i 0.583153π0.583153\pi
158158 −36.8477 −2.93144
159159 0 0
160160 48.3199 3.82002
161161 1.40800 0.110966
162162 0 0
163163 −2.97095 −0.232703 −0.116351 0.993208i 0.537120π-0.537120\pi
−0.116351 + 0.993208i 0.537120π0.537120\pi
164164 64.7677 5.05751
165165 0 0
166166 31.3285 2.43156
167167 −19.5727 −1.51458 −0.757292 0.653076i 0.773478π-0.773478\pi
−0.757292 + 0.653076i 0.773478π0.773478\pi
168168 0 0
169169 −3.12869 −0.240669
170170 −10.2466 −0.785878
171171 0 0
172172 −50.7341 −3.86844
173173 −21.7657 −1.65481 −0.827407 0.561602i 0.810185π-0.810185\pi
−0.827407 + 0.561602i 0.810185π0.810185\pi
174174 0 0
175175 7.13777 0.539564
176176 99.5846 7.50647
177177 0 0
178178 −38.4868 −2.88471
179179 4.34448 0.324722 0.162361 0.986731i 0.448089π-0.448089\pi
0.162361 + 0.986731i 0.448089π0.448089\pi
180180 0 0
181181 −1.97313 −0.146662 −0.0733309 0.997308i 0.523363π-0.523363\pi
−0.0733309 + 0.997308i 0.523363π0.523363\pi
182182 31.0418 2.30097
183183 0 0
184184 −4.13700 −0.304984
185185 −10.1627 −0.747174
186186 0 0
187187 −12.0924 −0.884281
188188 23.7681 1.73346
189189 0 0
190190 11.7400 0.851706
191191 −11.2009 −0.810467 −0.405234 0.914213i 0.632810π-0.632810\pi
−0.405234 + 0.914213i 0.632810π0.632810\pi
192192 0 0
193193 −15.5172 −1.11695 −0.558477 0.829520i 0.688614π-0.688614\pi
−0.558477 + 0.829520i 0.688614π0.688614\pi
194194 −2.65220 −0.190417
195195 0 0
196196 32.1850 2.29893
197197 19.3736 1.38031 0.690155 0.723662i 0.257542π-0.257542\pi
0.690155 + 0.723662i 0.257542π0.257542\pi
198198 0 0
199199 −11.4105 −0.808869 −0.404434 0.914567i 0.632532π-0.632532\pi
−0.404434 + 0.914567i 0.632532π0.632532\pi
200200 −20.9722 −1.48296
201201 0 0
202202 −26.4621 −1.86187
203203 −21.8336 −1.53242
204204 0 0
205205 19.4842 1.36084
206206 45.9088 3.19861
207207 0 0
208208 −55.0936 −3.82006
209209 13.8547 0.958352
210210 0 0
211211 24.3347 1.67527 0.837635 0.546231i 0.183938π-0.183938\pi
0.837635 + 0.546231i 0.183938π0.183938\pi
212212 23.2920 1.59970
213213 0 0
214214 2.78337 0.190267
215215 −15.2624 −1.04089
216216 0 0
217217 2.26888 0.154021
218218 −0.413463 −0.0280032
219219 0 0
220220 56.4294 3.80447
221221 6.68991 0.450012
222222 0 0
223223 12.0252 0.805267 0.402634 0.915361i 0.368095π-0.368095\pi
0.402634 + 0.915361i 0.368095π0.368095\pi
224224 −99.2061 −6.62849
225225 0 0
226226 38.2762 2.54609
227227 0.475204 0.0315404 0.0157702 0.999876i 0.494980π-0.494980\pi
0.0157702 + 0.999876i 0.494980π0.494980\pi
228228 0 0
229229 −1.44231 −0.0953107 −0.0476554 0.998864i 0.515175π-0.515175\pi
−0.0476554 + 0.998864i 0.515175π0.515175\pi
230230 −1.90880 −0.125863
231231 0 0
232232 64.1517 4.21177
233233 24.5324 1.60717 0.803586 0.595189i 0.202923π-0.202923\pi
0.803586 + 0.595189i 0.202923π0.202923\pi
234234 0 0
235235 7.15019 0.466427
236236 −57.0845 −3.71589
237237 0 0
238238 21.0374 1.36365
239239 6.20954 0.401662 0.200831 0.979626i 0.435636π-0.435636\pi
0.200831 + 0.979626i 0.435636π0.435636\pi
240240 0 0
241241 −22.9908 −1.48097 −0.740484 0.672074i 0.765404π-0.765404\pi
−0.740484 + 0.672074i 0.765404π0.765404\pi
242242 59.1520 3.80243
243243 0 0
244244 −1.38665 −0.0887710
245245 9.68229 0.618579
246246 0 0
247247 −7.66492 −0.487707
248248 −6.66643 −0.423319
249249 0 0
250250 −33.7377 −2.13376
251251 −18.1236 −1.14395 −0.571976 0.820270i 0.693823π-0.693823\pi
−0.571976 + 0.820270i 0.693823π0.693823\pi
252252 0 0
253253 −2.25264 −0.141623
254254 8.92750 0.560161
255255 0 0
256256 89.9319 5.62075
257257 9.71144 0.605783 0.302892 0.953025i 0.402048π-0.402048\pi
0.302892 + 0.953025i 0.402048π0.402048\pi
258258 0 0
259259 20.8651 1.29649
260260 −31.2187 −1.93610
261261 0 0
262262 −14.1930 −0.876848
263263 −12.2334 −0.754345 −0.377172 0.926143i 0.623104π-0.623104\pi
−0.377172 + 0.926143i 0.623104π0.623104\pi
264264 0 0
265265 7.00697 0.430435
266266 −24.1035 −1.47788
267267 0 0
268268 −76.7580 −4.68874
269269 −12.2451 −0.746599 −0.373299 0.927711i 0.621774π-0.621774\pi
−0.373299 + 0.927711i 0.621774π0.621774\pi
270270 0 0
271271 20.7511 1.26054 0.630271 0.776375i 0.282944π-0.282944\pi
0.630271 + 0.776375i 0.282944π0.282944\pi
272272 −37.3377 −2.26393
273273 0 0
274274 −32.4209 −1.95862
275275 −11.4196 −0.688629
276276 0 0
277277 7.56500 0.454537 0.227268 0.973832i 0.427021π-0.427021\pi
0.227268 + 0.973832i 0.427021π0.427021\pi
278278 −45.0733 −2.70332
279279 0 0
280280 −64.0081 −3.82521
281281 −8.81794 −0.526034 −0.263017 0.964791i 0.584718π-0.584718\pi
−0.263017 + 0.964791i 0.584718π0.584718\pi
282282 0 0
283283 2.45153 0.145728 0.0728642 0.997342i 0.476786π-0.476786\pi
0.0728642 + 0.997342i 0.476786π0.476786\pi
284284 41.7703 2.47861
285285 0 0
286286 −49.6633 −2.93666
287287 −40.0032 −2.36132
288288 0 0
289289 −12.4662 −0.733303
290290 29.5995 1.73814
291291 0 0
292292 −57.6161 −3.37173
293293 −9.60102 −0.560898 −0.280449 0.959869i 0.590483π-0.590483\pi
−0.280449 + 0.959869i 0.590483π0.590483\pi
294294 0 0
295295 −17.1729 −0.999842
296296 −61.3060 −3.56334
297297 0 0
298298 39.3246 2.27801
299299 1.24624 0.0720720
300300 0 0
301301 31.3355 1.80615
302302 42.9256 2.47009
303303 0 0
304304 42.7794 2.45356
305305 −0.417148 −0.0238858
306306 0 0
307307 −11.4555 −0.653801 −0.326900 0.945059i 0.606004π-0.606004\pi
−0.326900 + 0.945059i 0.606004π0.606004\pi
308308 −115.856 −6.60150
309309 0 0
310310 −3.07588 −0.174698
311311 −11.6364 −0.659838 −0.329919 0.944009i 0.607021π-0.607021\pi
−0.329919 + 0.944009i 0.607021π0.607021\pi
312312 0 0
313313 12.2108 0.690196 0.345098 0.938567i 0.387846π-0.387846\pi
0.345098 + 0.938567i 0.387846π0.387846\pi
314314 −18.0147 −1.01663
315315 0 0
316316 −76.0836 −4.28004
317317 5.21493 0.292900 0.146450 0.989218i 0.453215π-0.453215\pi
0.146450 + 0.989218i 0.453215π0.453215\pi
318318 0 0
319319 34.9314 1.95578
320320 73.8575 4.12876
321321 0 0
322322 3.91899 0.218397
323323 −5.19462 −0.289036
324324 0 0
325325 6.31773 0.350445
326326 −8.26924 −0.457991
327327 0 0
328328 117.538 6.48994
329329 −14.6801 −0.809343
330330 0 0
331331 −1.82861 −0.100509 −0.0502546 0.998736i 0.516003π-0.516003\pi
−0.0502546 + 0.998736i 0.516003π0.516003\pi
332332 64.6875 3.55019
333333 0 0
334334 −54.4782 −2.98091
335335 −23.0913 −1.26161
336336 0 0
337337 16.5836 0.903366 0.451683 0.892178i 0.350824π-0.350824\pi
0.451683 + 0.892178i 0.350824π0.350824\pi
338338 −8.70831 −0.473669
339339 0 0
340340 −21.1573 −1.14742
341341 −3.62995 −0.196573
342342 0 0
343343 4.96890 0.268295
344344 −92.0701 −4.96409
345345 0 0
346346 −60.5819 −3.25690
347347 23.6039 1.26712 0.633561 0.773693i 0.281593π-0.281593\pi
0.633561 + 0.773693i 0.281593π0.281593\pi
348348 0 0
349349 30.2942 1.62161 0.810806 0.585315i 0.199029π-0.199029\pi
0.810806 + 0.585315i 0.199029π0.199029\pi
350350 19.8670 1.06194
351351 0 0
352352 158.719 8.45973
353353 −24.0347 −1.27924 −0.639619 0.768692i 0.720908π-0.720908\pi
−0.639619 + 0.768692i 0.720908π0.720908\pi
354354 0 0
355355 12.5658 0.666925
356356 −79.4682 −4.21181
357357 0 0
358358 12.0923 0.639098
359359 9.27274 0.489396 0.244698 0.969599i 0.421311π-0.421311\pi
0.244698 + 0.969599i 0.421311π0.421311\pi
360360 0 0
361361 −13.0483 −0.686753
362362 −5.49195 −0.288651
363363 0 0
364364 64.0955 3.35952
365365 −17.3328 −0.907239
366366 0 0
367367 −6.49229 −0.338895 −0.169447 0.985539i 0.554198π-0.554198\pi
−0.169447 + 0.985539i 0.554198π0.554198\pi
368368 −6.95551 −0.362581
369369 0 0
370370 −28.2865 −1.47054
371371 −14.3861 −0.746889
372372 0 0
373373 −28.8275 −1.49263 −0.746315 0.665592i 0.768179π-0.768179\pi
−0.746315 + 0.665592i 0.768179π0.768179\pi
374374 −33.6575 −1.74039
375375 0 0
376376 43.1333 2.22443
377377 −19.3252 −0.995301
378378 0 0
379379 33.5296 1.72230 0.861150 0.508352i 0.169745π-0.169745\pi
0.861150 + 0.508352i 0.169745π0.169745\pi
380380 24.2408 1.24353
381381 0 0
382382 −31.1762 −1.59511
383383 36.1553 1.84745 0.923725 0.383057i 0.125129π-0.125129\pi
0.923725 + 0.383057i 0.125129π0.125129\pi
384384 0 0
385385 −34.8532 −1.77628
386386 −43.1902 −2.19832
387387 0 0
388388 −5.47631 −0.278018
389389 22.3865 1.13504 0.567520 0.823359i 0.307903π-0.307903\pi
0.567520 + 0.823359i 0.307903π0.307903\pi
390390 0 0
391391 0.844594 0.0427129
392392 58.4080 2.95005
393393 0 0
394394 53.9238 2.71664
395395 −22.8884 −1.15164
396396 0 0
397397 −22.1309 −1.11072 −0.555359 0.831611i 0.687419π-0.687419\pi
−0.555359 + 0.831611i 0.687419π0.687419\pi
398398 −31.7596 −1.59197
399399 0 0
400400 −35.2605 −1.76302
401401 25.3910 1.26797 0.633983 0.773347i 0.281419π-0.281419\pi
0.633983 + 0.773347i 0.281419π0.281419\pi
402402 0 0
403403 2.00821 0.100036
404404 −54.6393 −2.71841
405405 0 0
406406 −60.7710 −3.01602
407407 −33.3818 −1.65468
408408 0 0
409409 1.93202 0.0955323 0.0477662 0.998859i 0.484790π-0.484790\pi
0.0477662 + 0.998859i 0.484790π0.484790\pi
410410 54.2317 2.67831
411411 0 0
412412 94.7931 4.67012
413413 35.2578 1.73492
414414 0 0
415415 19.4601 0.955258
416416 −87.8087 −4.30517
417417 0 0
418418 38.5628 1.88617
419419 21.6995 1.06009 0.530046 0.847969i 0.322175π-0.322175\pi
0.530046 + 0.847969i 0.322175π0.322175\pi
420420 0 0
421421 3.16184 0.154099 0.0770494 0.997027i 0.475450π-0.475450\pi
0.0770494 + 0.997027i 0.475450π0.475450\pi
422422 67.7324 3.29716
423423 0 0
424424 42.2693 2.05278
425425 4.28161 0.207689
426426 0 0
427427 0.856451 0.0414466
428428 5.74714 0.277798
429429 0 0
430430 −42.4810 −2.04862
431431 6.88142 0.331466 0.165733 0.986171i 0.447001π-0.447001\pi
0.165733 + 0.986171i 0.447001π0.447001\pi
432432 0 0
433433 −26.5310 −1.27500 −0.637500 0.770451i 0.720031π-0.720031\pi
−0.637500 + 0.770451i 0.720031π0.720031\pi
434434 6.31512 0.303136
435435 0 0
436436 −0.853724 −0.0408860
437437 −0.967687 −0.0462908
438438 0 0
439439 3.81140 0.181908 0.0909540 0.995855i 0.471008π-0.471008\pi
0.0909540 + 0.995855i 0.471008π0.471008\pi
440440 102.406 4.88200
441441 0 0
442442 18.6205 0.885687
443443 6.07168 0.288474 0.144237 0.989543i 0.453927π-0.453927\pi
0.144237 + 0.989543i 0.453927π0.453927\pi
444444 0 0
445445 −23.9066 −1.13328
446446 33.4706 1.58488
447447 0 0
448448 −151.638 −7.16421
449449 −13.5395 −0.638970 −0.319485 0.947591i 0.603510π-0.603510\pi
−0.319485 + 0.947591i 0.603510π0.603510\pi
450450 0 0
451451 64.0007 3.01368
452452 79.0332 3.71741
453453 0 0
454454 1.32267 0.0620758
455455 19.2820 0.903953
456456 0 0
457457 −26.3451 −1.23237 −0.616186 0.787600i 0.711323π-0.711323\pi
−0.616186 + 0.787600i 0.711323π0.711323\pi
458458 −4.01449 −0.187585
459459 0 0
460460 −3.94133 −0.183765
461461 −4.90213 −0.228315 −0.114157 0.993463i 0.536417π-0.536417\pi
−0.114157 + 0.993463i 0.536417π0.536417\pi
462462 0 0
463463 23.7951 1.10585 0.552925 0.833231i 0.313512π-0.313512\pi
0.552925 + 0.833231i 0.313512π0.313512\pi
464464 107.858 5.00717
465465 0 0
466466 68.2827 3.16314
467467 22.1075 1.02301 0.511506 0.859280i 0.329088π-0.329088\pi
0.511506 + 0.859280i 0.329088π0.329088\pi
468468 0 0
469469 47.4090 2.18914
470470 19.9016 0.917993
471471 0 0
472472 −103.595 −4.76833
473473 −50.1333 −2.30513
474474 0 0
475475 −4.90562 −0.225085
476476 43.4383 1.99099
477477 0 0
478478 17.2834 0.790527
479479 −11.5334 −0.526974 −0.263487 0.964663i 0.584873π-0.584873\pi
−0.263487 + 0.964663i 0.584873π0.584873\pi
480480 0 0
481481 18.4680 0.842067
482482 −63.9919 −2.91475
483483 0 0
484484 122.138 5.55172
485485 −1.64745 −0.0748068
486486 0 0
487487 −3.23228 −0.146469 −0.0732343 0.997315i 0.523332π-0.523332\pi
−0.0732343 + 0.997315i 0.523332π0.523332\pi
488488 −2.51643 −0.113913
489489 0 0
490490 26.9494 1.21745
491491 39.6591 1.78979 0.894896 0.446275i 0.147250π-0.147250\pi
0.894896 + 0.446275i 0.147250π0.147250\pi
492492 0 0
493493 −13.0970 −0.589858
494494 −21.3343 −0.959875
495495 0 0
496496 −11.2082 −0.503264
497497 −25.7991 −1.15725
498498 0 0
499499 17.1259 0.766663 0.383331 0.923611i 0.374777π-0.374777\pi
0.383331 + 0.923611i 0.374777π0.374777\pi
500500 −69.6621 −3.11538
501501 0 0
502502 −50.4447 −2.25146
503503 2.62311 0.116959 0.0584793 0.998289i 0.481375π-0.481375\pi
0.0584793 + 0.998289i 0.481375π0.481375\pi
504504 0 0
505505 −16.4373 −0.731448
506506 −6.26994 −0.278733
507507 0 0
508508 18.4336 0.817860
509509 11.8631 0.525822 0.262911 0.964820i 0.415317π-0.415317\pi
0.262911 + 0.964820i 0.415317π0.415317\pi
510510 0 0
511511 35.5861 1.57424
512512 124.301 5.49339
513513 0 0
514514 27.0305 1.19227
515515 28.5168 1.25660
516516 0 0
517517 23.4866 1.03294
518518 58.0753 2.55168
519519 0 0
520520 −56.6544 −2.48446
521521 5.88040 0.257625 0.128812 0.991669i 0.458883π-0.458883\pi
0.128812 + 0.991669i 0.458883π0.458883\pi
522522 0 0
523523 −28.4724 −1.24501 −0.622507 0.782615i 0.713886π-0.713886\pi
−0.622507 + 0.782615i 0.713886π0.713886\pi
524524 −29.3060 −1.28024
525525 0 0
526526 −34.0501 −1.48465
527527 1.36099 0.0592858
528528 0 0
529529 −22.8427 −0.993159
530530 19.5030 0.847155
531531 0 0
532532 −49.7692 −2.15777
533533 −35.4074 −1.53367
534534 0 0
535535 1.72892 0.0747479
536536 −139.297 −6.01673
537537 0 0
538538 −34.0827 −1.46941
539539 31.8039 1.36989
540540 0 0
541541 −25.6106 −1.10108 −0.550542 0.834807i 0.685579π-0.685579\pi
−0.550542 + 0.834807i 0.685579π0.685579\pi
542542 57.7580 2.48092
543543 0 0
544544 −59.5091 −2.55143
545545 −0.256828 −0.0110013
546546 0 0
547547 −35.6582 −1.52463 −0.762317 0.647204i 0.775938π-0.775938\pi
−0.762317 + 0.647204i 0.775938π0.775938\pi
548548 −66.9432 −2.85967
549549 0 0
550550 −31.7850 −1.35532
551551 15.0058 0.639267
552552 0 0
553553 46.9924 1.99832
554554 21.0562 0.894592
555555 0 0
556556 −93.0680 −3.94696
557557 −18.3693 −0.778333 −0.389167 0.921167i 0.627237π-0.627237\pi
−0.389167 + 0.921167i 0.627237π0.627237\pi
558558 0 0
559559 27.7355 1.17309
560560 −107.616 −4.54762
561561 0 0
562562 −24.5436 −1.03531
563563 −13.1546 −0.554402 −0.277201 0.960812i 0.589407π-0.589407\pi
−0.277201 + 0.960812i 0.589407π0.589407\pi
564564 0 0
565565 23.7757 1.00025
566566 6.82351 0.286814
567567 0 0
568568 75.8029 3.18062
569569 −32.5854 −1.36605 −0.683026 0.730394i 0.739336π-0.739336\pi
−0.683026 + 0.730394i 0.739336π0.739336\pi
570570 0 0
571571 −6.42384 −0.268829 −0.134415 0.990925i 0.542915π-0.542915\pi
−0.134415 + 0.990925i 0.542915π0.542915\pi
572572 −102.546 −4.28765
573573 0 0
574574 −111.344 −4.64740
575575 0.797606 0.0332625
576576 0 0
577577 36.7758 1.53100 0.765499 0.643437i 0.222492π-0.222492\pi
0.765499 + 0.643437i 0.222492π0.222492\pi
578578 −34.6979 −1.44324
579579 0 0
580580 61.1174 2.53776
581581 −39.9537 −1.65756
582582 0 0
583583 23.0161 0.953231
584584 −104.559 −4.32670
585585 0 0
586586 −26.7232 −1.10392
587587 27.2277 1.12381 0.561903 0.827203i 0.310069π-0.310069\pi
0.561903 + 0.827203i 0.310069π0.310069\pi
588588 0 0
589589 −1.55935 −0.0642518
590590 −47.7984 −1.96783
591591 0 0
592592 −103.073 −4.23629
593593 −5.12388 −0.210413 −0.105206 0.994450i 0.533550π-0.533550\pi
−0.105206 + 0.994450i 0.533550π0.533550\pi
594594 0 0
595595 13.0676 0.535721
596596 81.1980 3.32600
597597 0 0
598598 3.46875 0.141848
599599 44.3742 1.81308 0.906540 0.422120i 0.138714π-0.138714\pi
0.906540 + 0.422120i 0.138714π0.138714\pi
600600 0 0
601601 −16.3358 −0.666349 −0.333175 0.942865i 0.608120π-0.608120\pi
−0.333175 + 0.942865i 0.608120π0.608120\pi
602602 87.2182 3.55475
603603 0 0
604604 88.6334 3.60644
605605 36.7430 1.49382
606606 0 0
607607 46.0730 1.87004 0.935022 0.354589i 0.115379π-0.115379\pi
0.935022 + 0.354589i 0.115379π0.115379\pi
608608 68.1821 2.76515
609609 0 0
610610 −1.16108 −0.0470106
611611 −12.9936 −0.525665
612612 0 0
613613 −10.2974 −0.415907 −0.207954 0.978139i 0.566680π-0.566680\pi
−0.207954 + 0.978139i 0.566680π0.566680\pi
614614 −31.8849 −1.28677
615615 0 0
616616 −210.250 −8.47123
617617 −19.0511 −0.766967 −0.383483 0.923548i 0.625276π-0.625276\pi
−0.383483 + 0.923548i 0.625276π0.625276\pi
618618 0 0
619619 −14.0538 −0.564868 −0.282434 0.959287i 0.591142π-0.591142\pi
−0.282434 + 0.959287i 0.591142π0.591142\pi
620620 −6.35112 −0.255067
621621 0 0
622622 −32.3883 −1.29865
623623 49.0829 1.96646
624624 0 0
625625 −10.9025 −0.436099
626626 33.9872 1.35840
627627 0 0
628628 −37.1970 −1.48432
629629 12.5160 0.499045
630630 0 0
631631 −26.8452 −1.06869 −0.534345 0.845267i 0.679442π-0.679442\pi
−0.534345 + 0.845267i 0.679442π0.679442\pi
632632 −138.073 −5.49226
633633 0 0
634634 14.5151 0.576467
635635 5.54543 0.220064
636636 0 0
637637 −17.5950 −0.697139
638638 97.2269 3.84925
639639 0 0
640640 108.933 4.30595
641641 10.9684 0.433224 0.216612 0.976258i 0.430499π-0.430499\pi
0.216612 + 0.976258i 0.430499π0.430499\pi
642642 0 0
643643 17.7877 0.701479 0.350740 0.936473i 0.385930π-0.385930\pi
0.350740 + 0.936473i 0.385930π0.385930\pi
644644 8.09198 0.318869
645645 0 0
646646 −14.4585 −0.568863
647647 −23.9344 −0.940957 −0.470478 0.882412i 0.655919π-0.655919\pi
−0.470478 + 0.882412i 0.655919π0.655919\pi
648648 0 0
649649 −56.4085 −2.21423
650650 17.5846 0.689724
651651 0 0
652652 −17.0744 −0.668687
653653 37.8092 1.47959 0.739794 0.672834i 0.234923π-0.234923\pi
0.739794 + 0.672834i 0.234923π0.234923\pi
654654 0 0
655655 −8.81617 −0.344476
656656 197.615 7.71559
657657 0 0
658658 −40.8603 −1.59290
659659 23.6412 0.920932 0.460466 0.887677i 0.347682π-0.347682\pi
0.460466 + 0.887677i 0.347682π0.347682\pi
660660 0 0
661661 28.2620 1.09926 0.549632 0.835407i 0.314768π-0.314768\pi
0.549632 + 0.835407i 0.314768π0.314768\pi
662662 −5.08969 −0.197816
663663 0 0
664664 117.392 4.55570
665665 −14.9722 −0.580595
666666 0 0
667667 −2.43979 −0.0944690
668668 −112.487 −4.35226
669669 0 0
670670 −64.2715 −2.48303
671671 −1.37023 −0.0528970
672672 0 0
673673 −9.45589 −0.364498 −0.182249 0.983252i 0.558338π-0.558338\pi
−0.182249 + 0.983252i 0.558338π0.558338\pi
674674 46.1583 1.77795
675675 0 0
676676 −17.9810 −0.691578
677677 43.7700 1.68222 0.841108 0.540867i 0.181904π-0.181904\pi
0.841108 + 0.540867i 0.181904π0.181904\pi
678678 0 0
679679 3.38240 0.129805
680680 −38.3954 −1.47240
681681 0 0
682682 −10.1035 −0.386883
683683 0.922361 0.0352932 0.0176466 0.999844i 0.494383π-0.494383\pi
0.0176466 + 0.999844i 0.494383π0.494383\pi
684684 0 0
685685 −20.1387 −0.769459
686686 13.8303 0.528042
687687 0 0
688688 −154.797 −5.90158
689689 −12.7333 −0.485101
690690 0 0
691691 −17.5370 −0.667139 −0.333570 0.942725i 0.608253π-0.608253\pi
−0.333570 + 0.942725i 0.608253π0.608253\pi
692692 −125.090 −4.75523
693693 0 0
694694 65.6983 2.49387
695695 −27.9978 −1.06202
696696 0 0
697697 −23.9961 −0.908916
698698 84.3200 3.19156
699699 0 0
700700 41.0217 1.55048
701701 6.23367 0.235442 0.117721 0.993047i 0.462441π-0.462441\pi
0.117721 + 0.993047i 0.462441π0.462441\pi
702702 0 0
703703 −14.3401 −0.540847
704704 242.603 9.14346
705705 0 0
706706 −66.8975 −2.51772
707707 33.7475 1.26921
708708 0 0
709709 1.42640 0.0535697 0.0267848 0.999641i 0.491473π-0.491473\pi
0.0267848 + 0.999641i 0.491473π0.491473\pi
710710 34.9753 1.31260
711711 0 0
712712 −144.216 −5.40471
713713 0.253535 0.00949495
714714 0 0
715715 −30.8490 −1.15369
716716 24.9684 0.933111
717717 0 0
718718 25.8095 0.963200
719719 −22.9363 −0.855381 −0.427690 0.903925i 0.640673π-0.640673\pi
−0.427690 + 0.903925i 0.640673π0.640673\pi
720720 0 0
721721 −58.5482 −2.18045
722722 −36.3182 −1.35163
723723 0 0
724724 −11.3399 −0.421443
725725 −12.3683 −0.459349
726726 0 0
727727 24.4810 0.907951 0.453975 0.891014i 0.350005π-0.350005\pi
0.453975 + 0.891014i 0.350005π0.350005\pi
728728 116.318 4.31103
729729 0 0
730730 −48.2435 −1.78557
731731 18.7967 0.695221
732732 0 0
733733 −11.9896 −0.442846 −0.221423 0.975178i 0.571070π-0.571070\pi
−0.221423 + 0.975178i 0.571070π0.571070\pi
734734 −18.0704 −0.666992
735735 0 0
736736 −11.0857 −0.408626
737737 −75.8490 −2.79393
738738 0 0
739739 26.8247 0.986761 0.493381 0.869813i 0.335761π-0.335761\pi
0.493381 + 0.869813i 0.335761π0.335761\pi
740740 −58.4063 −2.14706
741741 0 0
742742 −40.0418 −1.46998
743743 −32.6355 −1.19728 −0.598640 0.801018i 0.704292π-0.704292\pi
−0.598640 + 0.801018i 0.704292π0.704292\pi
744744 0 0
745745 24.4269 0.894934
746746 −80.2375 −2.93770
747747 0 0
748748 −69.4965 −2.54104
749749 −3.54967 −0.129702
750750 0 0
751751 1.29444 0.0472348 0.0236174 0.999721i 0.492482π-0.492482\pi
0.0236174 + 0.999721i 0.492482π0.492482\pi
752752 72.5197 2.64452
753753 0 0
754754 −53.7893 −1.95889
755755 26.6638 0.970394
756756 0 0
757757 46.4735 1.68911 0.844553 0.535472i 0.179866π-0.179866\pi
0.844553 + 0.535472i 0.179866π0.179866\pi
758758 93.3252 3.38972
759759 0 0
760760 43.9913 1.59573
761761 24.3421 0.882399 0.441200 0.897409i 0.354553π-0.354553\pi
0.441200 + 0.897409i 0.354553π0.354553\pi
762762 0 0
763763 0.527296 0.0190894
764764 −64.3730 −2.32893
765765 0 0
766766 100.634 3.63604
767767 31.2072 1.12682
768768 0 0
769769 −0.339803 −0.0122536 −0.00612680 0.999981i 0.501950π-0.501950\pi
−0.00612680 + 0.999981i 0.501950π0.501950\pi
770770 −97.0092 −3.49597
771771 0 0
772772 −89.1797 −3.20965
773773 −4.26285 −0.153324 −0.0766620 0.997057i 0.524426π-0.524426\pi
−0.0766620 + 0.997057i 0.524426π0.524426\pi
774774 0 0
775775 1.28528 0.0461685
776776 −9.93818 −0.356760
777777 0 0
778778 62.3099 2.23392
779779 27.4933 0.985050
780780 0 0
781781 41.2756 1.47696
782782 2.35082 0.0840650
783783 0 0
784784 98.2011 3.50718
785785 −11.1901 −0.399390
786786 0 0
787787 −23.3527 −0.832432 −0.416216 0.909266i 0.636644π-0.636644\pi
−0.416216 + 0.909266i 0.636644π0.636644\pi
788788 111.343 3.96642
789789 0 0
790790 −63.7068 −2.26659
791791 −48.8142 −1.73563
792792 0 0
793793 0.758056 0.0269194
794794 −61.5984 −2.18605
795795 0 0
796796 −65.5777 −2.32434
797797 32.0183 1.13415 0.567073 0.823668i 0.308076π-0.308076\pi
0.567073 + 0.823668i 0.308076π0.308076\pi
798798 0 0
799799 −8.80593 −0.311531
800800 −56.1984 −1.98691
801801 0 0
802802 70.6725 2.49553
803803 −56.9338 −2.00915
804804 0 0
805805 2.43433 0.0857987
806806 5.58960 0.196885
807807 0 0
808808 −99.1572 −3.48834
809809 −14.1222 −0.496512 −0.248256 0.968695i 0.579857π-0.579857\pi
−0.248256 + 0.968695i 0.579857π0.579857\pi
810810 0 0
811811 0.877621 0.0308174 0.0154087 0.999881i 0.495095π-0.495095\pi
0.0154087 + 0.999881i 0.495095π0.495095\pi
812812 −125.481 −4.40352
813813 0 0
814814 −92.9139 −3.25663
815815 −5.13654 −0.179925
816816 0 0
817817 −21.5362 −0.753455
818818 5.37753 0.188021
819819 0 0
820820 111.978 3.91046
821821 20.7361 0.723693 0.361847 0.932238i 0.382146π-0.382146\pi
0.361847 + 0.932238i 0.382146π0.382146\pi
822822 0 0
823823 36.7135 1.27975 0.639876 0.768478i 0.278986π-0.278986\pi
0.639876 + 0.768478i 0.278986π0.278986\pi
824824 172.027 5.99283
825825 0 0
826826 98.1354 3.41457
827827 −35.2998 −1.22750 −0.613748 0.789502i 0.710339π-0.710339\pi
−0.613748 + 0.789502i 0.710339π0.710339\pi
828828 0 0
829829 −42.3140 −1.46963 −0.734813 0.678270i 0.762730π-0.762730\pi
−0.734813 + 0.678270i 0.762730π0.762730\pi
830830 54.1646 1.88008
831831 0 0
832832 −134.217 −4.65312
833833 −11.9244 −0.413155
834834 0 0
835835 −33.8398 −1.17107
836836 79.6251 2.75389
837837 0 0
838838 60.3978 2.08641
839839 44.7290 1.54422 0.772109 0.635490i 0.219202π-0.219202\pi
0.772109 + 0.635490i 0.219202π0.219202\pi
840840 0 0
841841 8.83339 0.304600
842842 8.80058 0.303288
843843 0 0
844844 139.855 4.81400
845845 −5.40927 −0.186085
846846 0 0
847847 −75.4375 −2.59206
848848 71.0671 2.44045
849849 0 0
850850 11.9173 0.408760
851851 2.33156 0.0799249
852852 0 0
853853 12.2848 0.420622 0.210311 0.977635i 0.432552π-0.432552\pi
0.210311 + 0.977635i 0.432552π0.432552\pi
854854 2.38382 0.0815726
855855 0 0
856856 10.4297 0.356479
857857 −27.6446 −0.944321 −0.472161 0.881512i 0.656526π-0.656526\pi
−0.472161 + 0.881512i 0.656526π0.656526\pi
858858 0 0
859859 14.7561 0.503471 0.251735 0.967796i 0.418999π-0.418999\pi
0.251735 + 0.967796i 0.418999π0.418999\pi
860860 −87.7154 −2.99107
861861 0 0
862862 19.1535 0.652372
863863 −38.1926 −1.30009 −0.650045 0.759896i 0.725250π-0.725250\pi
−0.650045 + 0.759896i 0.725250π0.725250\pi
864864 0 0
865865 −37.6312 −1.27950
866866 −73.8456 −2.50938
867867 0 0
868868 13.0396 0.442592
869869 −75.1826 −2.55039
870870 0 0
871871 41.9623 1.42184
872872 −1.54930 −0.0524660
873873 0 0
874874 −2.69343 −0.0911066
875875 43.0262 1.45455
876876 0 0
877877 −27.5717 −0.931029 −0.465514 0.885040i 0.654131π-0.654131\pi
−0.465514 + 0.885040i 0.654131π0.654131\pi
878878 10.6085 0.358020
879879 0 0
880880 172.174 5.80399
881881 10.8507 0.365569 0.182785 0.983153i 0.441489π-0.441489\pi
0.182785 + 0.983153i 0.441489π0.441489\pi
882882 0 0
883883 −15.0379 −0.506067 −0.253033 0.967458i 0.581428π-0.581428\pi
−0.253033 + 0.967458i 0.581428π0.581428\pi
884884 38.4479 1.29314
885885 0 0
886886 16.8997 0.567757
887887 −5.61566 −0.188555 −0.0942776 0.995546i 0.530054π-0.530054\pi
−0.0942776 + 0.995546i 0.530054π0.530054\pi
888888 0 0
889889 −11.3854 −0.381853
890890 −66.5408 −2.23045
891891 0 0
892892 69.1106 2.31399
893893 10.0893 0.337626
894894 0 0
895895 7.51128 0.251074
896896 −223.652 −7.47167
897897 0 0
898898 −37.6855 −1.25758
899899 −3.93152 −0.131124
900900 0 0
901901 −8.62954 −0.287492
902902 178.138 5.93133
903903 0 0
904904 143.426 4.77028
905905 −3.41139 −0.113399
906906 0 0
907907 29.4312 0.977246 0.488623 0.872495i 0.337499π-0.337499\pi
0.488623 + 0.872495i 0.337499π0.337499\pi
908908 2.73106 0.0906335
909909 0 0
910910 53.6688 1.77910
911911 −9.37378 −0.310567 −0.155284 0.987870i 0.549629π-0.549629\pi
−0.155284 + 0.987870i 0.549629π0.549629\pi
912912 0 0
913913 63.9215 2.11549
914914 −73.3282 −2.42548
915915 0 0
916916 −8.28917 −0.273882
917917 18.1006 0.597734
918918 0 0
919919 13.0164 0.429371 0.214685 0.976683i 0.431127π-0.431127\pi
0.214685 + 0.976683i 0.431127π0.431127\pi
920920 −7.15255 −0.235813
921921 0 0
922922 −13.6444 −0.449355
923923 −22.8351 −0.751626
924924 0 0
925925 11.8197 0.388629
926926 66.2304 2.17647
927927 0 0
928928 171.905 5.64305
929929 4.23465 0.138934 0.0694672 0.997584i 0.477870π-0.477870\pi
0.0694672 + 0.997584i 0.477870π0.477870\pi
930930 0 0
931931 13.6623 0.447762
932932 140.991 4.61832
933933 0 0
934934 61.5332 2.01343
935935 −20.9068 −0.683724
936936 0 0
937937 21.3623 0.697876 0.348938 0.937146i 0.386542π-0.386542\pi
0.348938 + 0.937146i 0.386542π0.386542\pi
938938 131.957 4.30854
939939 0 0
940940 41.0932 1.34031
941941 25.7666 0.839968 0.419984 0.907531i 0.362036π-0.362036\pi
0.419984 + 0.907531i 0.362036π0.362036\pi
942942 0 0
943943 −4.47014 −0.145568
944944 −174.173 −5.66885
945945 0 0
946946 −139.539 −4.53682
947947 −38.3680 −1.24679 −0.623396 0.781906i 0.714248π-0.714248\pi
−0.623396 + 0.781906i 0.714248π0.714248\pi
948948 0 0
949949 31.4978 1.02246
950950 −13.6542 −0.442999
951951 0 0
952952 78.8301 2.55490
953953 −29.9836 −0.971264 −0.485632 0.874163i 0.661411π-0.661411\pi
−0.485632 + 0.874163i 0.661411π0.661411\pi
954954 0 0
955955 −19.3655 −0.626652
956956 35.6871 1.15420
957957 0 0
958958 −32.1016 −1.03716
959959 41.3469 1.33516
960960 0 0
961961 −30.5914 −0.986821
962962 51.4032 1.65731
963963 0 0
964964 −132.131 −4.25567
965965 −26.8281 −0.863627
966966 0 0
967967 53.2502 1.71241 0.856205 0.516637i 0.172816π-0.172816\pi
0.856205 + 0.516637i 0.172816π0.172816\pi
968968 221.651 7.12413
969969 0 0
970970 −4.58546 −0.147230
971971 −15.1000 −0.484584 −0.242292 0.970203i 0.577899π-0.577899\pi
−0.242292 + 0.970203i 0.577899π0.577899\pi
972972 0 0
973973 57.4827 1.84281
974974 −8.99662 −0.288270
975975 0 0
976976 −4.23086 −0.135426
977977 45.0898 1.44255 0.721275 0.692648i 0.243556π-0.243556\pi
0.721275 + 0.692648i 0.243556π0.243556\pi
978978 0 0
979979 −78.5271 −2.50974
980980 55.6454 1.77753
981981 0 0
982982 110.386 3.52256
983983 37.7452 1.20389 0.601943 0.798539i 0.294394π-0.294394\pi
0.601943 + 0.798539i 0.294394π0.294394\pi
984984 0 0
985985 33.4954 1.06725
986986 −36.4537 −1.16092
987987 0 0
988988 −44.0514 −1.40146
989989 3.50157 0.111343
990990 0 0
991991 43.3600 1.37738 0.688688 0.725058i 0.258187π-0.258187\pi
0.688688 + 0.725058i 0.258187π0.258187\pi
992992 −17.8638 −0.567175
993993 0 0
994994 −71.8083 −2.27762
995995 −19.7279 −0.625416
996996 0 0
997997 −38.2406 −1.21109 −0.605546 0.795810i 0.707045π-0.707045\pi
−0.605546 + 0.795810i 0.707045π0.707045\pi
998998 47.6678 1.50890
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 2889.2.a.g.1.23 23
3.2 odd 2 2889.2.a.h.1.1 yes 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2889.2.a.g.1.23 23 1.1 even 1 trivial
2889.2.a.h.1.1 yes 23 3.2 odd 2