Properties

Label 4225.2.a.z.1.2
Level 42254225
Weight 22
Character 4225.1
Self dual yes
Analytic conductor 33.73733.737
Analytic rank 00
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4225,2,Mod(1,4225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4225=52132 4225 = 5^{2} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4225.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 33.736794854033.7367948540
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ8)+\Q(\zeta_{8})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x22 x^{2} - 2 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 325)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.414211.41421 of defining polynomial
Character χ\chi == 4225.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+2.41421q2+2.82843q3+3.82843q4+6.82843q6+2.41421q7+4.41421q8+5.00000q96.41421q11+10.8284q12+5.82843q14+3.00000q16+3.82843q17+12.0711q18+3.65685q19+6.82843q2115.4853q22+3.17157q23+12.4853q24+5.65685q27+9.24264q280.171573q291.24264q311.58579q3218.1421q33+9.24264q34+19.1421q366.00000q37+8.82843q38+5.65685q41+16.4853q420.828427q4324.5563q44+7.65685q46+3.58579q47+8.48528q481.17157q49+10.8284q513.00000q53+13.6569q54+10.6569q56+10.3431q570.414214q5813.2426q59+1.00000q613.00000q62+12.0711q639.82843q6443.7990q662.75736q67+14.6569q68+8.97056q69+9.31371q71+22.0711q726.00000q7314.4853q74+14.0000q7615.4853q776.00000q79+1.00000q81+13.6569q82+6.89949q83+26.1421q842.00000q860.485281q8728.3137q88+8.48528q89+12.1421q923.51472q93+8.65685q944.48528q960.828427q972.82843q9832.0711q99+O(q100)q+2.41421 q^{2} +2.82843 q^{3} +3.82843 q^{4} +6.82843 q^{6} +2.41421 q^{7} +4.41421 q^{8} +5.00000 q^{9} -6.41421 q^{11} +10.8284 q^{12} +5.82843 q^{14} +3.00000 q^{16} +3.82843 q^{17} +12.0711 q^{18} +3.65685 q^{19} +6.82843 q^{21} -15.4853 q^{22} +3.17157 q^{23} +12.4853 q^{24} +5.65685 q^{27} +9.24264 q^{28} -0.171573 q^{29} -1.24264 q^{31} -1.58579 q^{32} -18.1421 q^{33} +9.24264 q^{34} +19.1421 q^{36} -6.00000 q^{37} +8.82843 q^{38} +5.65685 q^{41} +16.4853 q^{42} -0.828427 q^{43} -24.5563 q^{44} +7.65685 q^{46} +3.58579 q^{47} +8.48528 q^{48} -1.17157 q^{49} +10.8284 q^{51} -3.00000 q^{53} +13.6569 q^{54} +10.6569 q^{56} +10.3431 q^{57} -0.414214 q^{58} -13.2426 q^{59} +1.00000 q^{61} -3.00000 q^{62} +12.0711 q^{63} -9.82843 q^{64} -43.7990 q^{66} -2.75736 q^{67} +14.6569 q^{68} +8.97056 q^{69} +9.31371 q^{71} +22.0711 q^{72} -6.00000 q^{73} -14.4853 q^{74} +14.0000 q^{76} -15.4853 q^{77} -6.00000 q^{79} +1.00000 q^{81} +13.6569 q^{82} +6.89949 q^{83} +26.1421 q^{84} -2.00000 q^{86} -0.485281 q^{87} -28.3137 q^{88} +8.48528 q^{89} +12.1421 q^{92} -3.51472 q^{93} +8.65685 q^{94} -4.48528 q^{96} -0.828427 q^{97} -2.82843 q^{98} -32.0711 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q2+2q4+8q6+2q7+6q8+10q910q11+16q12+6q14+6q16+2q17+10q184q19+8q2114q22+12q23+8q24+10q28+50q99+O(q100) 2 q + 2 q^{2} + 2 q^{4} + 8 q^{6} + 2 q^{7} + 6 q^{8} + 10 q^{9} - 10 q^{11} + 16 q^{12} + 6 q^{14} + 6 q^{16} + 2 q^{17} + 10 q^{18} - 4 q^{19} + 8 q^{21} - 14 q^{22} + 12 q^{23} + 8 q^{24} + 10 q^{28}+ \cdots - 50 q^{99}+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 2.41421 1.70711 0.853553 0.521005i 0.174443π-0.174443\pi
0.853553 + 0.521005i 0.174443π0.174443\pi
33 2.82843 1.63299 0.816497 0.577350i 0.195913π-0.195913\pi
0.816497 + 0.577350i 0.195913π0.195913\pi
44 3.82843 1.91421
55 0 0
66 6.82843 2.78769
77 2.41421 0.912487 0.456243 0.889855i 0.349195π-0.349195\pi
0.456243 + 0.889855i 0.349195π0.349195\pi
88 4.41421 1.56066
99 5.00000 1.66667
1010 0 0
1111 −6.41421 −1.93396 −0.966979 0.254856i 0.917972π-0.917972\pi
−0.966979 + 0.254856i 0.917972π0.917972\pi
1212 10.8284 3.12590
1313 0 0
1414 5.82843 1.55771
1515 0 0
1616 3.00000 0.750000
1717 3.82843 0.928530 0.464265 0.885696i 0.346319π-0.346319\pi
0.464265 + 0.885696i 0.346319π0.346319\pi
1818 12.0711 2.84518
1919 3.65685 0.838940 0.419470 0.907769i 0.362216π-0.362216\pi
0.419470 + 0.907769i 0.362216π0.362216\pi
2020 0 0
2121 6.82843 1.49008
2222 −15.4853 −3.30147
2323 3.17157 0.661319 0.330659 0.943750i 0.392729π-0.392729\pi
0.330659 + 0.943750i 0.392729π0.392729\pi
2424 12.4853 2.54855
2525 0 0
2626 0 0
2727 5.65685 1.08866
2828 9.24264 1.74669
2929 −0.171573 −0.0318603 −0.0159301 0.999873i 0.505071π-0.505071\pi
−0.0159301 + 0.999873i 0.505071π0.505071\pi
3030 0 0
3131 −1.24264 −0.223185 −0.111592 0.993754i 0.535595π-0.535595\pi
−0.111592 + 0.993754i 0.535595π0.535595\pi
3232 −1.58579 −0.280330
3333 −18.1421 −3.15814
3434 9.24264 1.58510
3535 0 0
3636 19.1421 3.19036
3737 −6.00000 −0.986394 −0.493197 0.869918i 0.664172π-0.664172\pi
−0.493197 + 0.869918i 0.664172π0.664172\pi
3838 8.82843 1.43216
3939 0 0
4040 0 0
4141 5.65685 0.883452 0.441726 0.897150i 0.354366π-0.354366\pi
0.441726 + 0.897150i 0.354366π0.354366\pi
4242 16.4853 2.54373
4343 −0.828427 −0.126334 −0.0631670 0.998003i 0.520120π-0.520120\pi
−0.0631670 + 0.998003i 0.520120π0.520120\pi
4444 −24.5563 −3.70201
4545 0 0
4646 7.65685 1.12894
4747 3.58579 0.523041 0.261520 0.965198i 0.415776π-0.415776\pi
0.261520 + 0.965198i 0.415776π0.415776\pi
4848 8.48528 1.22474
4949 −1.17157 −0.167368
5050 0 0
5151 10.8284 1.51628
5252 0 0
5353 −3.00000 −0.412082 −0.206041 0.978543i 0.566058π-0.566058\pi
−0.206041 + 0.978543i 0.566058π0.566058\pi
5454 13.6569 1.85846
5555 0 0
5656 10.6569 1.42408
5757 10.3431 1.36998
5858 −0.414214 −0.0543889
5959 −13.2426 −1.72404 −0.862022 0.506870i 0.830802π-0.830802\pi
−0.862022 + 0.506870i 0.830802π0.830802\pi
6060 0 0
6161 1.00000 0.128037 0.0640184 0.997949i 0.479608π-0.479608\pi
0.0640184 + 0.997949i 0.479608π0.479608\pi
6262 −3.00000 −0.381000
6363 12.0711 1.52081
6464 −9.82843 −1.22855
6565 0 0
6666 −43.7990 −5.39128
6767 −2.75736 −0.336865 −0.168433 0.985713i 0.553871π-0.553871\pi
−0.168433 + 0.985713i 0.553871π0.553871\pi
6868 14.6569 1.77740
6969 8.97056 1.07993
7070 0 0
7171 9.31371 1.10533 0.552667 0.833402i 0.313610π-0.313610\pi
0.552667 + 0.833402i 0.313610π0.313610\pi
7272 22.0711 2.60110
7373 −6.00000 −0.702247 −0.351123 0.936329i 0.614200π-0.614200\pi
−0.351123 + 0.936329i 0.614200π0.614200\pi
7474 −14.4853 −1.68388
7575 0 0
7676 14.0000 1.60591
7777 −15.4853 −1.76471
7878 0 0
7979 −6.00000 −0.675053 −0.337526 0.941316i 0.609590π-0.609590\pi
−0.337526 + 0.941316i 0.609590π0.609590\pi
8080 0 0
8181 1.00000 0.111111
8282 13.6569 1.50815
8383 6.89949 0.757318 0.378659 0.925536i 0.376385π-0.376385\pi
0.378659 + 0.925536i 0.376385π0.376385\pi
8484 26.1421 2.85234
8585 0 0
8686 −2.00000 −0.215666
8787 −0.485281 −0.0520276
8888 −28.3137 −3.01825
8989 8.48528 0.899438 0.449719 0.893170i 0.351524π-0.351524\pi
0.449719 + 0.893170i 0.351524π0.351524\pi
9090 0 0
9191 0 0
9292 12.1421 1.26591
9393 −3.51472 −0.364459
9494 8.65685 0.892886
9595 0 0
9696 −4.48528 −0.457777
9797 −0.828427 −0.0841140 −0.0420570 0.999115i 0.513391π-0.513391\pi
−0.0420570 + 0.999115i 0.513391π0.513391\pi
9898 −2.82843 −0.285714
9999 −32.0711 −3.22326
100100 0 0
101101 −6.65685 −0.662382 −0.331191 0.943564i 0.607450π-0.607450\pi
−0.331191 + 0.943564i 0.607450π0.607450\pi
102102 26.1421 2.58846
103103 −13.6569 −1.34565 −0.672825 0.739802i 0.734919π-0.734919\pi
−0.672825 + 0.739802i 0.734919π0.734919\pi
104104 0 0
105105 0 0
106106 −7.24264 −0.703467
107107 −16.1421 −1.56052 −0.780260 0.625456i 0.784913π-0.784913\pi
−0.780260 + 0.625456i 0.784913π0.784913\pi
108108 21.6569 2.08393
109109 16.4853 1.57900 0.789502 0.613748i 0.210339π-0.210339\pi
0.789502 + 0.613748i 0.210339π0.210339\pi
110110 0 0
111111 −16.9706 −1.61077
112112 7.24264 0.684365
113113 11.6569 1.09658 0.548292 0.836287i 0.315278π-0.315278\pi
0.548292 + 0.836287i 0.315278π0.315278\pi
114114 24.9706 2.33871
115115 0 0
116116 −0.656854 −0.0609874
117117 0 0
118118 −31.9706 −2.94313
119119 9.24264 0.847271
120120 0 0
121121 30.1421 2.74019
122122 2.41421 0.218573
123123 16.0000 1.44267
124124 −4.75736 −0.427223
125125 0 0
126126 29.1421 2.59619
127127 3.65685 0.324493 0.162247 0.986750i 0.448126π-0.448126\pi
0.162247 + 0.986750i 0.448126π0.448126\pi
128128 −20.5563 −1.81694
129129 −2.34315 −0.206302
130130 0 0
131131 8.48528 0.741362 0.370681 0.928760i 0.379124π-0.379124\pi
0.370681 + 0.928760i 0.379124π0.379124\pi
132132 −69.4558 −6.04536
133133 8.82843 0.765522
134134 −6.65685 −0.575065
135135 0 0
136136 16.8995 1.44912
137137 2.82843 0.241649 0.120824 0.992674i 0.461446π-0.461446\pi
0.120824 + 0.992674i 0.461446π0.461446\pi
138138 21.6569 1.84355
139139 −18.4853 −1.56790 −0.783951 0.620823i 0.786798π-0.786798\pi
−0.783951 + 0.620823i 0.786798π0.786798\pi
140140 0 0
141141 10.1421 0.854122
142142 22.4853 1.88692
143143 0 0
144144 15.0000 1.25000
145145 0 0
146146 −14.4853 −1.19881
147147 −3.31371 −0.273310
148148 −22.9706 −1.88817
149149 −8.82843 −0.723253 −0.361626 0.932323i 0.617778π-0.617778\pi
−0.361626 + 0.932323i 0.617778π0.617778\pi
150150 0 0
151151 8.75736 0.712664 0.356332 0.934359i 0.384027π-0.384027\pi
0.356332 + 0.934359i 0.384027π0.384027\pi
152152 16.1421 1.30930
153153 19.1421 1.54755
154154 −37.3848 −3.01255
155155 0 0
156156 0 0
157157 −23.4853 −1.87433 −0.937165 0.348887i 0.886560π-0.886560\pi
−0.937165 + 0.348887i 0.886560π0.886560\pi
158158 −14.4853 −1.15239
159159 −8.48528 −0.672927
160160 0 0
161161 7.65685 0.603445
162162 2.41421 0.189679
163163 10.0000 0.783260 0.391630 0.920123i 0.371911π-0.371911\pi
0.391630 + 0.920123i 0.371911π0.371911\pi
164164 21.6569 1.69112
165165 0 0
166166 16.6569 1.29282
167167 −5.31371 −0.411187 −0.205594 0.978637i 0.565912π-0.565912\pi
−0.205594 + 0.978637i 0.565912π0.565912\pi
168168 30.1421 2.32552
169169 0 0
170170 0 0
171171 18.2843 1.39823
172172 −3.17157 −0.241830
173173 −18.6569 −1.41845 −0.709227 0.704980i 0.750956π-0.750956\pi
−0.709227 + 0.704980i 0.750956π0.750956\pi
174174 −1.17157 −0.0888167
175175 0 0
176176 −19.2426 −1.45047
177177 −37.4558 −2.81535
178178 20.4853 1.53544
179179 0.686292 0.0512958 0.0256479 0.999671i 0.491835π-0.491835\pi
0.0256479 + 0.999671i 0.491835π0.491835\pi
180180 0 0
181181 −17.4853 −1.29967 −0.649835 0.760075i 0.725162π-0.725162\pi
−0.649835 + 0.760075i 0.725162π0.725162\pi
182182 0 0
183183 2.82843 0.209083
184184 14.0000 1.03209
185185 0 0
186186 −8.48528 −0.622171
187187 −24.5563 −1.79574
188188 13.7279 1.00121
189189 13.6569 0.993390
190190 0 0
191191 25.3137 1.83164 0.915818 0.401594i 0.131544π-0.131544\pi
0.915818 + 0.401594i 0.131544π0.131544\pi
192192 −27.7990 −2.00622
193193 1.65685 0.119263 0.0596315 0.998220i 0.481007π-0.481007\pi
0.0596315 + 0.998220i 0.481007π0.481007\pi
194194 −2.00000 −0.143592
195195 0 0
196196 −4.48528 −0.320377
197197 −12.0000 −0.854965 −0.427482 0.904024i 0.640599π-0.640599\pi
−0.427482 + 0.904024i 0.640599π0.640599\pi
198198 −77.4264 −5.50246
199199 10.0000 0.708881 0.354441 0.935079i 0.384671π-0.384671\pi
0.354441 + 0.935079i 0.384671π0.384671\pi
200200 0 0
201201 −7.79899 −0.550098
202202 −16.0711 −1.13076
203203 −0.414214 −0.0290721
204204 41.4558 2.90249
205205 0 0
206206 −32.9706 −2.29717
207207 15.8579 1.10220
208208 0 0
209209 −23.4558 −1.62247
210210 0 0
211211 17.7990 1.22533 0.612666 0.790342i 0.290097π-0.290097\pi
0.612666 + 0.790342i 0.290097π0.290097\pi
212212 −11.4853 −0.788812
213213 26.3431 1.80500
214214 −38.9706 −2.66397
215215 0 0
216216 24.9706 1.69903
217217 −3.00000 −0.203653
218218 39.7990 2.69553
219219 −16.9706 −1.14676
220220 0 0
221221 0 0
222222 −40.9706 −2.74976
223223 −10.9706 −0.734643 −0.367322 0.930094i 0.619725π-0.619725\pi
−0.367322 + 0.930094i 0.619725π0.619725\pi
224224 −3.82843 −0.255798
225225 0 0
226226 28.1421 1.87199
227227 −8.89949 −0.590680 −0.295340 0.955392i 0.595433π-0.595433\pi
−0.295340 + 0.955392i 0.595433π0.595433\pi
228228 39.5980 2.62244
229229 4.82843 0.319071 0.159536 0.987192i 0.449000π-0.449000\pi
0.159536 + 0.987192i 0.449000π0.449000\pi
230230 0 0
231231 −43.7990 −2.88176
232232 −0.757359 −0.0497231
233233 −20.6274 −1.35135 −0.675674 0.737201i 0.736147π-0.736147\pi
−0.675674 + 0.737201i 0.736147π0.736147\pi
234234 0 0
235235 0 0
236236 −50.6985 −3.30019
237237 −16.9706 −1.10236
238238 22.3137 1.44638
239239 −23.5858 −1.52564 −0.762819 0.646612i 0.776185π-0.776185\pi
−0.762819 + 0.646612i 0.776185π0.776185\pi
240240 0 0
241241 −4.97056 −0.320182 −0.160091 0.987102i 0.551179π-0.551179\pi
−0.160091 + 0.987102i 0.551179π0.551179\pi
242242 72.7696 4.67780
243243 −14.1421 −0.907218
244244 3.82843 0.245090
245245 0 0
246246 38.6274 2.46279
247247 0 0
248248 −5.48528 −0.348316
249249 19.5147 1.23670
250250 0 0
251251 −5.65685 −0.357057 −0.178529 0.983935i 0.557134π-0.557134\pi
−0.178529 + 0.983935i 0.557134π0.557134\pi
252252 46.2132 2.91116
253253 −20.3431 −1.27896
254254 8.82843 0.553945
255255 0 0
256256 −29.9706 −1.87316
257257 6.65685 0.415243 0.207622 0.978209i 0.433428π-0.433428\pi
0.207622 + 0.978209i 0.433428π0.433428\pi
258258 −5.65685 −0.352180
259259 −14.4853 −0.900072
260260 0 0
261261 −0.857864 −0.0531005
262262 20.4853 1.26558
263263 26.1421 1.61199 0.805997 0.591920i 0.201630π-0.201630\pi
0.805997 + 0.591920i 0.201630π0.201630\pi
264264 −80.0833 −4.92878
265265 0 0
266266 21.3137 1.30683
267267 24.0000 1.46878
268268 −10.5563 −0.644832
269269 15.1421 0.923232 0.461616 0.887080i 0.347270π-0.347270\pi
0.461616 + 0.887080i 0.347270π0.347270\pi
270270 0 0
271271 25.7279 1.56286 0.781430 0.623993i 0.214491π-0.214491\pi
0.781430 + 0.623993i 0.214491π0.214491\pi
272272 11.4853 0.696397
273273 0 0
274274 6.82843 0.412520
275275 0 0
276276 34.3431 2.06721
277277 −9.31371 −0.559607 −0.279803 0.960057i 0.590269π-0.590269\pi
−0.279803 + 0.960057i 0.590269π0.590269\pi
278278 −44.6274 −2.67657
279279 −6.21320 −0.371975
280280 0 0
281281 −4.82843 −0.288040 −0.144020 0.989575i 0.546003π-0.546003\pi
−0.144020 + 0.989575i 0.546003π0.546003\pi
282282 24.4853 1.45808
283283 22.4853 1.33661 0.668306 0.743887i 0.267020π-0.267020\pi
0.668306 + 0.743887i 0.267020π0.267020\pi
284284 35.6569 2.11585
285285 0 0
286286 0 0
287287 13.6569 0.806139
288288 −7.92893 −0.467217
289289 −2.34315 −0.137832
290290 0 0
291291 −2.34315 −0.137358
292292 −22.9706 −1.34425
293293 8.82843 0.515762 0.257881 0.966177i 0.416976π-0.416976\pi
0.257881 + 0.966177i 0.416976π0.416976\pi
294294 −8.00000 −0.466569
295295 0 0
296296 −26.4853 −1.53943
297297 −36.2843 −2.10543
298298 −21.3137 −1.23467
299299 0 0
300300 0 0
301301 −2.00000 −0.115278
302302 21.1421 1.21659
303303 −18.8284 −1.08166
304304 10.9706 0.629205
305305 0 0
306306 46.2132 2.64183
307307 −9.31371 −0.531561 −0.265781 0.964034i 0.585630π-0.585630\pi
−0.265781 + 0.964034i 0.585630π0.585630\pi
308308 −59.2843 −3.37803
309309 −38.6274 −2.19744
310310 0 0
311311 9.51472 0.539530 0.269765 0.962926i 0.413054π-0.413054\pi
0.269765 + 0.962926i 0.413054π0.413054\pi
312312 0 0
313313 −2.85786 −0.161536 −0.0807680 0.996733i 0.525737π-0.525737\pi
−0.0807680 + 0.996733i 0.525737π0.525737\pi
314314 −56.6985 −3.19968
315315 0 0
316316 −22.9706 −1.29220
317317 20.1421 1.13130 0.565648 0.824647i 0.308626π-0.308626\pi
0.565648 + 0.824647i 0.308626π0.308626\pi
318318 −20.4853 −1.14876
319319 1.10051 0.0616165
320320 0 0
321321 −45.6569 −2.54832
322322 18.4853 1.03014
323323 14.0000 0.778981
324324 3.82843 0.212690
325325 0 0
326326 24.1421 1.33711
327327 46.6274 2.57850
328328 24.9706 1.37877
329329 8.65685 0.477268
330330 0 0
331331 −27.6569 −1.52016 −0.760079 0.649831i 0.774840π-0.774840\pi
−0.760079 + 0.649831i 0.774840π0.774840\pi
332332 26.4142 1.44967
333333 −30.0000 −1.64399
334334 −12.8284 −0.701940
335335 0 0
336336 20.4853 1.11756
337337 20.7990 1.13299 0.566497 0.824064i 0.308298π-0.308298\pi
0.566497 + 0.824064i 0.308298π0.308298\pi
338338 0 0
339339 32.9706 1.79072
340340 0 0
341341 7.97056 0.431630
342342 44.1421 2.38693
343343 −19.7279 −1.06521
344344 −3.65685 −0.197164
345345 0 0
346346 −45.0416 −2.42145
347347 19.4558 1.04444 0.522222 0.852809i 0.325103π-0.325103\pi
0.522222 + 0.852809i 0.325103π0.325103\pi
348348 −1.85786 −0.0995920
349349 −35.4558 −1.89791 −0.948954 0.315415i 0.897856π-0.897856\pi
−0.948954 + 0.315415i 0.897856π0.897856\pi
350350 0 0
351351 0 0
352352 10.1716 0.542147
353353 26.1421 1.39141 0.695703 0.718330i 0.255093π-0.255093\pi
0.695703 + 0.718330i 0.255093π0.255093\pi
354354 −90.4264 −4.80611
355355 0 0
356356 32.4853 1.72172
357357 26.1421 1.38359
358358 1.65685 0.0875675
359359 −21.3848 −1.12865 −0.564323 0.825554i 0.690863π-0.690863\pi
−0.564323 + 0.825554i 0.690863π0.690863\pi
360360 0 0
361361 −5.62742 −0.296180
362362 −42.2132 −2.21868
363363 85.2548 4.47472
364364 0 0
365365 0 0
366366 6.82843 0.356928
367367 34.8284 1.81803 0.909015 0.416764i 0.136836π-0.136836\pi
0.909015 + 0.416764i 0.136836π0.136836\pi
368368 9.51472 0.495989
369369 28.2843 1.47242
370370 0 0
371371 −7.24264 −0.376019
372372 −13.4558 −0.697653
373373 −1.14214 −0.0591375 −0.0295688 0.999563i 0.509413π-0.509413\pi
−0.0295688 + 0.999563i 0.509413π0.509413\pi
374374 −59.2843 −3.06552
375375 0 0
376376 15.8284 0.816289
377377 0 0
378378 32.9706 1.69582
379379 31.8701 1.63705 0.818527 0.574467i 0.194791π-0.194791\pi
0.818527 + 0.574467i 0.194791π0.194791\pi
380380 0 0
381381 10.3431 0.529895
382382 61.1127 3.12680
383383 27.6569 1.41320 0.706600 0.707614i 0.250228π-0.250228\pi
0.706600 + 0.707614i 0.250228π0.250228\pi
384384 −58.1421 −2.96705
385385 0 0
386386 4.00000 0.203595
387387 −4.14214 −0.210557
388388 −3.17157 −0.161012
389389 28.6274 1.45147 0.725734 0.687976i 0.241500π-0.241500\pi
0.725734 + 0.687976i 0.241500π0.241500\pi
390390 0 0
391391 12.1421 0.614054
392392 −5.17157 −0.261204
393393 24.0000 1.21064
394394 −28.9706 −1.45952
395395 0 0
396396 −122.782 −6.17001
397397 7.65685 0.384286 0.192143 0.981367i 0.438456π-0.438456\pi
0.192143 + 0.981367i 0.438456π0.438456\pi
398398 24.1421 1.21014
399399 24.9706 1.25009
400400 0 0
401401 3.85786 0.192653 0.0963263 0.995350i 0.469291π-0.469291\pi
0.0963263 + 0.995350i 0.469291π0.469291\pi
402402 −18.8284 −0.939077
403403 0 0
404404 −25.4853 −1.26794
405405 0 0
406406 −1.00000 −0.0496292
407407 38.4853 1.90764
408408 47.7990 2.36640
409409 10.8284 0.535431 0.267716 0.963498i 0.413731π-0.413731\pi
0.267716 + 0.963498i 0.413731π0.413731\pi
410410 0 0
411411 8.00000 0.394611
412412 −52.2843 −2.57586
413413 −31.9706 −1.57317
414414 38.2843 1.88157
415415 0 0
416416 0 0
417417 −52.2843 −2.56037
418418 −56.6274 −2.76974
419419 22.8284 1.11524 0.557621 0.830096i 0.311714π-0.311714\pi
0.557621 + 0.830096i 0.311714π0.311714\pi
420420 0 0
421421 16.9706 0.827095 0.413547 0.910483i 0.364290π-0.364290\pi
0.413547 + 0.910483i 0.364290π0.364290\pi
422422 42.9706 2.09177
423423 17.9289 0.871735
424424 −13.2426 −0.643119
425425 0 0
426426 63.5980 3.08133
427427 2.41421 0.116832
428428 −61.7990 −2.98717
429429 0 0
430430 0 0
431431 8.34315 0.401875 0.200938 0.979604i 0.435601π-0.435601\pi
0.200938 + 0.979604i 0.435601π0.435601\pi
432432 16.9706 0.816497
433433 −16.3431 −0.785401 −0.392701 0.919666i 0.628459π-0.628459\pi
−0.392701 + 0.919666i 0.628459π0.628459\pi
434434 −7.24264 −0.347658
435435 0 0
436436 63.1127 3.02255
437437 11.5980 0.554807
438438 −40.9706 −1.95765
439439 14.0000 0.668184 0.334092 0.942541i 0.391570π-0.391570\pi
0.334092 + 0.942541i 0.391570π0.391570\pi
440440 0 0
441441 −5.85786 −0.278946
442442 0 0
443443 29.7990 1.41579 0.707896 0.706316i 0.249644π-0.249644\pi
0.707896 + 0.706316i 0.249644π0.249644\pi
444444 −64.9706 −3.08337
445445 0 0
446446 −26.4853 −1.25411
447447 −24.9706 −1.18107
448448 −23.7279 −1.12104
449449 5.17157 0.244062 0.122031 0.992526i 0.461059π-0.461059\pi
0.122031 + 0.992526i 0.461059π0.461059\pi
450450 0 0
451451 −36.2843 −1.70856
452452 44.6274 2.09910
453453 24.7696 1.16378
454454 −21.4853 −1.00835
455455 0 0
456456 45.6569 2.13808
457457 8.48528 0.396925 0.198462 0.980109i 0.436405π-0.436405\pi
0.198462 + 0.980109i 0.436405π0.436405\pi
458458 11.6569 0.544689
459459 21.6569 1.01086
460460 0 0
461461 19.4558 0.906149 0.453074 0.891473i 0.350327π-0.350327\pi
0.453074 + 0.891473i 0.350327π0.350327\pi
462462 −105.740 −4.91948
463463 28.5563 1.32713 0.663563 0.748120i 0.269043π-0.269043\pi
0.663563 + 0.748120i 0.269043π0.269043\pi
464464 −0.514719 −0.0238952
465465 0 0
466466 −49.7990 −2.30689
467467 −31.1127 −1.43972 −0.719862 0.694117i 0.755795π-0.755795\pi
−0.719862 + 0.694117i 0.755795π0.755795\pi
468468 0 0
469469 −6.65685 −0.307385
470470 0 0
471471 −66.4264 −3.06077
472472 −58.4558 −2.69065
473473 5.31371 0.244325
474474 −40.9706 −1.88184
475475 0 0
476476 35.3848 1.62186
477477 −15.0000 −0.686803
478478 −56.9411 −2.60443
479479 −14.2721 −0.652108 −0.326054 0.945351i 0.605719π-0.605719\pi
−0.326054 + 0.945351i 0.605719π0.605719\pi
480480 0 0
481481 0 0
482482 −12.0000 −0.546585
483483 21.6569 0.985421
484484 115.397 5.24532
485485 0 0
486486 −34.1421 −1.54872
487487 −42.2132 −1.91286 −0.956431 0.291957i 0.905694π-0.905694\pi
−0.956431 + 0.291957i 0.905694π0.905694\pi
488488 4.41421 0.199822
489489 28.2843 1.27906
490490 0 0
491491 11.1716 0.504166 0.252083 0.967706i 0.418884π-0.418884\pi
0.252083 + 0.967706i 0.418884π0.418884\pi
492492 61.2548 2.76158
493493 −0.656854 −0.0295832
494494 0 0
495495 0 0
496496 −3.72792 −0.167389
497497 22.4853 1.00860
498498 47.1127 2.11117
499499 −2.55635 −0.114438 −0.0572190 0.998362i 0.518223π-0.518223\pi
−0.0572190 + 0.998362i 0.518223π0.518223\pi
500500 0 0
501501 −15.0294 −0.671466
502502 −13.6569 −0.609535
503503 14.6274 0.652204 0.326102 0.945335i 0.394265π-0.394265\pi
0.326102 + 0.945335i 0.394265π0.394265\pi
504504 53.2843 2.37347
505505 0 0
506506 −49.1127 −2.18333
507507 0 0
508508 14.0000 0.621150
509509 −14.6274 −0.648349 −0.324174 0.945997i 0.605086π-0.605086\pi
−0.324174 + 0.945997i 0.605086π0.605086\pi
510510 0 0
511511 −14.4853 −0.640791
512512 −31.2426 −1.38074
513513 20.6863 0.913322
514514 16.0711 0.708864
515515 0 0
516516 −8.97056 −0.394907
517517 −23.0000 −1.01154
518518 −34.9706 −1.53652
519519 −52.7696 −2.31633
520520 0 0
521521 0.343146 0.0150335 0.00751674 0.999972i 0.497607π-0.497607\pi
0.00751674 + 0.999972i 0.497607π0.497607\pi
522522 −2.07107 −0.0906482
523523 −6.00000 −0.262362 −0.131181 0.991358i 0.541877π-0.541877\pi
−0.131181 + 0.991358i 0.541877π0.541877\pi
524524 32.4853 1.41913
525525 0 0
526526 63.1127 2.75184
527527 −4.75736 −0.207234
528528 −54.4264 −2.36861
529529 −12.9411 −0.562658
530530 0 0
531531 −66.2132 −2.87341
532532 33.7990 1.46537
533533 0 0
534534 57.9411 2.50736
535535 0 0
536536 −12.1716 −0.525732
537537 1.94113 0.0837657
538538 36.5563 1.57606
539539 7.51472 0.323682
540540 0 0
541541 −33.7990 −1.45313 −0.726566 0.687097i 0.758885π-0.758885\pi
−0.726566 + 0.687097i 0.758885π0.758885\pi
542542 62.1127 2.66797
543543 −49.4558 −2.12235
544544 −6.07107 −0.260295
545545 0 0
546546 0 0
547547 −28.4853 −1.21794 −0.608971 0.793192i 0.708418π-0.708418\pi
−0.608971 + 0.793192i 0.708418π0.708418\pi
548548 10.8284 0.462567
549549 5.00000 0.213395
550550 0 0
551551 −0.627417 −0.0267289
552552 39.5980 1.68540
553553 −14.4853 −0.615977
554554 −22.4853 −0.955308
555555 0 0
556556 −70.7696 −3.00130
557557 27.3137 1.15732 0.578659 0.815569i 0.303576π-0.303576\pi
0.578659 + 0.815569i 0.303576π0.303576\pi
558558 −15.0000 −0.635001
559559 0 0
560560 0 0
561561 −69.4558 −2.93243
562562 −11.6569 −0.491715
563563 18.0000 0.758610 0.379305 0.925272i 0.376163π-0.376163\pi
0.379305 + 0.925272i 0.376163π0.376163\pi
564564 38.8284 1.63497
565565 0 0
566566 54.2843 2.28174
567567 2.41421 0.101387
568568 41.1127 1.72505
569569 −35.2843 −1.47919 −0.739597 0.673050i 0.764984π-0.764984\pi
−0.739597 + 0.673050i 0.764984π0.764984\pi
570570 0 0
571571 −2.00000 −0.0836974 −0.0418487 0.999124i 0.513325π-0.513325\pi
−0.0418487 + 0.999124i 0.513325π0.513325\pi
572572 0 0
573573 71.5980 2.99105
574574 32.9706 1.37616
575575 0 0
576576 −49.1421 −2.04759
577577 −7.17157 −0.298556 −0.149278 0.988795i 0.547695π-0.547695\pi
−0.149278 + 0.988795i 0.547695π0.547695\pi
578578 −5.65685 −0.235294
579579 4.68629 0.194756
580580 0 0
581581 16.6569 0.691043
582582 −5.65685 −0.234484
583583 19.2426 0.796949
584584 −26.4853 −1.09597
585585 0 0
586586 21.3137 0.880461
587587 14.4142 0.594938 0.297469 0.954731i 0.403857π-0.403857\pi
0.297469 + 0.954731i 0.403857π0.403857\pi
588588 −12.6863 −0.523174
589589 −4.54416 −0.187239
590590 0 0
591591 −33.9411 −1.39615
592592 −18.0000 −0.739795
593593 19.6569 0.807210 0.403605 0.914933i 0.367757π-0.367757\pi
0.403605 + 0.914933i 0.367757π0.367757\pi
594594 −87.5980 −3.59419
595595 0 0
596596 −33.7990 −1.38446
597597 28.2843 1.15760
598598 0 0
599599 −3.51472 −0.143608 −0.0718038 0.997419i 0.522876π-0.522876\pi
−0.0718038 + 0.997419i 0.522876π0.522876\pi
600600 0 0
601601 13.8284 0.564073 0.282037 0.959404i 0.408990π-0.408990\pi
0.282037 + 0.959404i 0.408990π0.408990\pi
602602 −4.82843 −0.196792
603603 −13.7868 −0.561442
604604 33.5269 1.36419
605605 0 0
606606 −45.4558 −1.84652
607607 21.5147 0.873255 0.436628 0.899642i 0.356173π-0.356173\pi
0.436628 + 0.899642i 0.356173π0.356173\pi
608608 −5.79899 −0.235180
609609 −1.17157 −0.0474745
610610 0 0
611611 0 0
612612 73.2843 2.96234
613613 −12.8284 −0.518135 −0.259068 0.965859i 0.583415π-0.583415\pi
−0.259068 + 0.965859i 0.583415π0.583415\pi
614614 −22.4853 −0.907432
615615 0 0
616616 −68.3553 −2.75412
617617 6.00000 0.241551 0.120775 0.992680i 0.461462π-0.461462\pi
0.120775 + 0.992680i 0.461462π0.461462\pi
618618 −93.2548 −3.75126
619619 −22.9706 −0.923265 −0.461632 0.887071i 0.652736π-0.652736\pi
−0.461632 + 0.887071i 0.652736π0.652736\pi
620620 0 0
621621 17.9411 0.719953
622622 22.9706 0.921036
623623 20.4853 0.820725
624624 0 0
625625 0 0
626626 −6.89949 −0.275759
627627 −66.3431 −2.64949
628628 −89.9117 −3.58787
629629 −22.9706 −0.915896
630630 0 0
631631 −34.0000 −1.35352 −0.676759 0.736204i 0.736616π-0.736616\pi
−0.676759 + 0.736204i 0.736616π0.736616\pi
632632 −26.4853 −1.05353
633633 50.3431 2.00096
634634 48.6274 1.93124
635635 0 0
636636 −32.4853 −1.28813
637637 0 0
638638 2.65685 0.105186
639639 46.5685 1.84222
640640 0 0
641641 28.1127 1.11038 0.555192 0.831722i 0.312645π-0.312645\pi
0.555192 + 0.831722i 0.312645π0.312645\pi
642642 −110.225 −4.35025
643643 −1.02944 −0.0405970 −0.0202985 0.999794i 0.506462π-0.506462\pi
−0.0202985 + 0.999794i 0.506462π0.506462\pi
644644 29.3137 1.15512
645645 0 0
646646 33.7990 1.32980
647647 −18.8284 −0.740222 −0.370111 0.928988i 0.620680π-0.620680\pi
−0.370111 + 0.928988i 0.620680π0.620680\pi
648648 4.41421 0.173407
649649 84.9411 3.33423
650650 0 0
651651 −8.48528 −0.332564
652652 38.2843 1.49933
653653 22.4558 0.878765 0.439383 0.898300i 0.355197π-0.355197\pi
0.439383 + 0.898300i 0.355197π0.355197\pi
654654 112.569 4.40178
655655 0 0
656656 16.9706 0.662589
657657 −30.0000 −1.17041
658658 20.8995 0.814747
659659 −8.62742 −0.336076 −0.168038 0.985780i 0.553743π-0.553743\pi
−0.168038 + 0.985780i 0.553743π0.553743\pi
660660 0 0
661661 6.82843 0.265595 0.132798 0.991143i 0.457604π-0.457604\pi
0.132798 + 0.991143i 0.457604π0.457604\pi
662662 −66.7696 −2.59507
663663 0 0
664664 30.4558 1.18192
665665 0 0
666666 −72.4264 −2.80647
667667 −0.544156 −0.0210698
668668 −20.3431 −0.787100
669669 −31.0294 −1.19967
670670 0 0
671671 −6.41421 −0.247618
672672 −10.8284 −0.417716
673673 −24.4558 −0.942704 −0.471352 0.881945i 0.656234π-0.656234\pi
−0.471352 + 0.881945i 0.656234π0.656234\pi
674674 50.2132 1.93414
675675 0 0
676676 0 0
677677 41.3137 1.58781 0.793907 0.608039i 0.208043π-0.208043\pi
0.793907 + 0.608039i 0.208043π0.208043\pi
678678 79.5980 3.05694
679679 −2.00000 −0.0767530
680680 0 0
681681 −25.1716 −0.964577
682682 19.2426 0.736839
683683 21.5858 0.825957 0.412979 0.910741i 0.364488π-0.364488\pi
0.412979 + 0.910741i 0.364488π0.364488\pi
684684 70.0000 2.67652
685685 0 0
686686 −47.6274 −1.81842
687687 13.6569 0.521041
688688 −2.48528 −0.0947505
689689 0 0
690690 0 0
691691 −8.89949 −0.338553 −0.169276 0.985569i 0.554143π-0.554143\pi
−0.169276 + 0.985569i 0.554143π0.554143\pi
692692 −71.4264 −2.71522
693693 −77.4264 −2.94119
694694 46.9706 1.78298
695695 0 0
696696 −2.14214 −0.0811974
697697 21.6569 0.820312
698698 −85.5980 −3.23993
699699 −58.3431 −2.20674
700700 0 0
701701 −15.8284 −0.597831 −0.298916 0.954280i 0.596625π-0.596625\pi
−0.298916 + 0.954280i 0.596625π0.596625\pi
702702 0 0
703703 −21.9411 −0.827525
704704 63.0416 2.37597
705705 0 0
706706 63.1127 2.37528
707707 −16.0711 −0.604415
708708 −143.397 −5.38919
709709 49.2548 1.84980 0.924902 0.380205i 0.124147π-0.124147\pi
0.924902 + 0.380205i 0.124147π0.124147\pi
710710 0 0
711711 −30.0000 −1.12509
712712 37.4558 1.40372
713713 −3.94113 −0.147596
714714 63.1127 2.36193
715715 0 0
716716 2.62742 0.0981912
717717 −66.7107 −2.49136
718718 −51.6274 −1.92672
719719 −49.4558 −1.84439 −0.922196 0.386723i 0.873607π-0.873607\pi
−0.922196 + 0.386723i 0.873607π0.873607\pi
720720 0 0
721721 −32.9706 −1.22789
722722 −13.5858 −0.505611
723723 −14.0589 −0.522855
724724 −66.9411 −2.48785
725725 0 0
726726 205.823 7.63882
727727 −16.6863 −0.618860 −0.309430 0.950922i 0.600138π-0.600138\pi
−0.309430 + 0.950922i 0.600138π0.600138\pi
728728 0 0
729729 −43.0000 −1.59259
730730 0 0
731731 −3.17157 −0.117305
732732 10.8284 0.400230
733733 −35.7990 −1.32227 −0.661133 0.750269i 0.729924π-0.729924\pi
−0.661133 + 0.750269i 0.729924π0.729924\pi
734734 84.0833 3.10357
735735 0 0
736736 −5.02944 −0.185388
737737 17.6863 0.651483
738738 68.2843 2.51358
739739 27.7279 1.01999 0.509994 0.860178i 0.329648π-0.329648\pi
0.509994 + 0.860178i 0.329648π0.329648\pi
740740 0 0
741741 0 0
742742 −17.4853 −0.641905
743743 −14.6985 −0.539235 −0.269618 0.962967i 0.586897π-0.586897\pi
−0.269618 + 0.962967i 0.586897π0.586897\pi
744744 −15.5147 −0.568797
745745 0 0
746746 −2.75736 −0.100954
747747 34.4975 1.26220
748748 −94.0122 −3.43743
749749 −38.9706 −1.42395
750750 0 0
751751 31.4558 1.14784 0.573920 0.818911i 0.305422π-0.305422\pi
0.573920 + 0.818911i 0.305422π0.305422\pi
752752 10.7574 0.392281
753753 −16.0000 −0.583072
754754 0 0
755755 0 0
756756 52.2843 1.90156
757757 16.3137 0.592932 0.296466 0.955043i 0.404192π-0.404192\pi
0.296466 + 0.955043i 0.404192π0.404192\pi
758758 76.9411 2.79463
759759 −57.5391 −2.08854
760760 0 0
761761 21.7990 0.790213 0.395106 0.918635i 0.370708π-0.370708\pi
0.395106 + 0.918635i 0.370708π0.370708\pi
762762 24.9706 0.904588
763763 39.7990 1.44082
764764 96.9117 3.50614
765765 0 0
766766 66.7696 2.41248
767767 0 0
768768 −84.7696 −3.05886
769769 −4.97056 −0.179243 −0.0896215 0.995976i 0.528566π-0.528566\pi
−0.0896215 + 0.995976i 0.528566π0.528566\pi
770770 0 0
771771 18.8284 0.678089
772772 6.34315 0.228295
773773 −5.79899 −0.208575 −0.104288 0.994547i 0.533256π-0.533256\pi
−0.104288 + 0.994547i 0.533256π0.533256\pi
774774 −10.0000 −0.359443
775775 0 0
776776 −3.65685 −0.131273
777777 −40.9706 −1.46981
778778 69.1127 2.47781
779779 20.6863 0.741163
780780 0 0
781781 −59.7401 −2.13767
782782 29.3137 1.04826
783783 −0.970563 −0.0346851
784784 −3.51472 −0.125526
785785 0 0
786786 57.9411 2.06669
787787 38.7574 1.38155 0.690775 0.723069i 0.257269π-0.257269\pi
0.690775 + 0.723069i 0.257269π0.257269\pi
788788 −45.9411 −1.63658
789789 73.9411 2.63237
790790 0 0
791791 28.1421 1.00062
792792 −141.569 −5.03042
793793 0 0
794794 18.4853 0.656018
795795 0 0
796796 38.2843 1.35695
797797 11.4853 0.406830 0.203415 0.979093i 0.434796π-0.434796\pi
0.203415 + 0.979093i 0.434796π0.434796\pi
798798 60.2843 2.13404
799799 13.7279 0.485659
800800 0 0
801801 42.4264 1.49906
802802 9.31371 0.328878
803803 38.4853 1.35812
804804 −29.8579 −1.05301
805805 0 0
806806 0 0
807807 42.8284 1.50763
808808 −29.3848 −1.03375
809809 17.3137 0.608718 0.304359 0.952557i 0.401558π-0.401558\pi
0.304359 + 0.952557i 0.401558π0.401558\pi
810810 0 0
811811 −9.58579 −0.336602 −0.168301 0.985736i 0.553828π-0.553828\pi
−0.168301 + 0.985736i 0.553828π0.553828\pi
812812 −1.58579 −0.0556502
813813 72.7696 2.55214
814814 92.9117 3.25655
815815 0 0
816816 32.4853 1.13721
817817 −3.02944 −0.105987
818818 26.1421 0.914038
819819 0 0
820820 0 0
821821 20.8284 0.726917 0.363459 0.931610i 0.381596π-0.381596\pi
0.363459 + 0.931610i 0.381596π0.381596\pi
822822 19.3137 0.673643
823823 20.2843 0.707065 0.353533 0.935422i 0.384980π-0.384980\pi
0.353533 + 0.935422i 0.384980π0.384980\pi
824824 −60.2843 −2.10010
825825 0 0
826826 −77.1838 −2.68557
827827 −32.3553 −1.12511 −0.562553 0.826761i 0.690181π-0.690181\pi
−0.562553 + 0.826761i 0.690181π0.690181\pi
828828 60.7107 2.10984
829829 7.97056 0.276829 0.138415 0.990374i 0.455799π-0.455799\pi
0.138415 + 0.990374i 0.455799π0.455799\pi
830830 0 0
831831 −26.3431 −0.913834
832832 0 0
833833 −4.48528 −0.155406
834834 −126.225 −4.37083
835835 0 0
836836 −89.7990 −3.10576
837837 −7.02944 −0.242973
838838 55.1127 1.90384
839839 1.02944 0.0355401 0.0177701 0.999842i 0.494343π-0.494343\pi
0.0177701 + 0.999842i 0.494343π0.494343\pi
840840 0 0
841841 −28.9706 −0.998985
842842 40.9706 1.41194
843843 −13.6569 −0.470367
844844 68.1421 2.34555
845845 0 0
846846 43.2843 1.48814
847847 72.7696 2.50039
848848 −9.00000 −0.309061
849849 63.5980 2.18268
850850 0 0
851851 −19.0294 −0.652321
852852 100.853 3.45516
853853 −42.4264 −1.45265 −0.726326 0.687350i 0.758774π-0.758774\pi
−0.726326 + 0.687350i 0.758774π0.758774\pi
854854 5.82843 0.199445
855855 0 0
856856 −71.2548 −2.43544
857857 4.62742 0.158070 0.0790348 0.996872i 0.474816π-0.474816\pi
0.0790348 + 0.996872i 0.474816π0.474816\pi
858858 0 0
859859 24.1421 0.823719 0.411860 0.911247i 0.364879π-0.364879\pi
0.411860 + 0.911247i 0.364879π0.364879\pi
860860 0 0
861861 38.6274 1.31642
862862 20.1421 0.686044
863863 29.1838 0.993427 0.496713 0.867915i 0.334540π-0.334540\pi
0.496713 + 0.867915i 0.334540π0.334540\pi
864864 −8.97056 −0.305185
865865 0 0
866866 −39.4558 −1.34076
867867 −6.62742 −0.225079
868868 −11.4853 −0.389836
869869 38.4853 1.30552
870870 0 0
871871 0 0
872872 72.7696 2.46429
873873 −4.14214 −0.140190
874874 28.0000 0.947114
875875 0 0
876876 −64.9706 −2.19515
877877 −15.7990 −0.533494 −0.266747 0.963767i 0.585949π-0.585949\pi
−0.266747 + 0.963767i 0.585949π0.585949\pi
878878 33.7990 1.14066
879879 24.9706 0.842236
880880 0 0
881881 −15.0000 −0.505363 −0.252681 0.967550i 0.581312π-0.581312\pi
−0.252681 + 0.967550i 0.581312π0.581312\pi
882882 −14.1421 −0.476190
883883 −32.9706 −1.10955 −0.554774 0.832001i 0.687195π-0.687195\pi
−0.554774 + 0.832001i 0.687195π0.687195\pi
884884 0 0
885885 0 0
886886 71.9411 2.41691
887887 −8.62742 −0.289680 −0.144840 0.989455i 0.546267π-0.546267\pi
−0.144840 + 0.989455i 0.546267π0.546267\pi
888888 −74.9117 −2.51387
889889 8.82843 0.296096
890890 0 0
891891 −6.41421 −0.214884
892892 −42.0000 −1.40626
893893 13.1127 0.438800
894894 −60.2843 −2.01621
895895 0 0
896896 −49.6274 −1.65794
897897 0 0
898898 12.4853 0.416639
899899 0.213203 0.00711073
900900 0 0
901901 −11.4853 −0.382630
902902 −87.5980 −2.91669
903903 −5.65685 −0.188248
904904 51.4558 1.71140
905905 0 0
906906 59.7990 1.98669
907907 24.0000 0.796907 0.398453 0.917189i 0.369547π-0.369547\pi
0.398453 + 0.917189i 0.369547π0.369547\pi
908908 −34.0711 −1.13069
909909 −33.2843 −1.10397
910910 0 0
911911 6.00000 0.198789 0.0993944 0.995048i 0.468309π-0.468309\pi
0.0993944 + 0.995048i 0.468309π0.468309\pi
912912 31.0294 1.02749
913913 −44.2548 −1.46462
914914 20.4853 0.677593
915915 0 0
916916 18.4853 0.610771
917917 20.4853 0.676484
918918 52.2843 1.72564
919919 −18.9706 −0.625781 −0.312891 0.949789i 0.601297π-0.601297\pi
−0.312891 + 0.949789i 0.601297π0.601297\pi
920920 0 0
921921 −26.3431 −0.868036
922922 46.9706 1.54689
923923 0 0
924924 −167.681 −5.51631
925925 0 0
926926 68.9411 2.26555
927927 −68.2843 −2.24275
928928 0.272078 0.00893140
929929 −30.2843 −0.993595 −0.496797 0.867867i 0.665491π-0.665491\pi
−0.496797 + 0.867867i 0.665491π0.665491\pi
930930 0 0
931931 −4.28427 −0.140411
932932 −78.9706 −2.58677
933933 26.9117 0.881049
934934 −75.1127 −2.45776
935935 0 0
936936 0 0
937937 −1.97056 −0.0643755 −0.0321877 0.999482i 0.510247π-0.510247\pi
−0.0321877 + 0.999482i 0.510247π0.510247\pi
938938 −16.0711 −0.524739
939939 −8.08326 −0.263787
940940 0 0
941941 35.6569 1.16238 0.581190 0.813768i 0.302587π-0.302587\pi
0.581190 + 0.813768i 0.302587π0.302587\pi
942942 −160.368 −5.22506
943943 17.9411 0.584243
944944 −39.7279 −1.29303
945945 0 0
946946 12.8284 0.417088
947947 −26.4142 −0.858347 −0.429173 0.903222i 0.641195π-0.641195\pi
−0.429173 + 0.903222i 0.641195π0.641195\pi
948948 −64.9706 −2.11015
949949 0 0
950950 0 0
951951 56.9706 1.84740
952952 40.7990 1.32230
953953 47.3431 1.53359 0.766797 0.641889i 0.221849π-0.221849\pi
0.766797 + 0.641889i 0.221849π0.221849\pi
954954 −36.2132 −1.17245
955955 0 0
956956 −90.2965 −2.92040
957957 3.11270 0.100619
958958 −34.4558 −1.11322
959959 6.82843 0.220501
960960 0 0
961961 −29.4558 −0.950189
962962 0 0
963963 −80.7107 −2.60087
964964 −19.0294 −0.612897
965965 0 0
966966 52.2843 1.68222
967967 43.7279 1.40620 0.703098 0.711093i 0.251800π-0.251800\pi
0.703098 + 0.711093i 0.251800π0.251800\pi
968968 133.054 4.27651
969969 39.5980 1.27207
970970 0 0
971971 36.8284 1.18188 0.590940 0.806715i 0.298757π-0.298757\pi
0.590940 + 0.806715i 0.298757π0.298757\pi
972972 −54.1421 −1.73661
973973 −44.6274 −1.43069
974974 −101.912 −3.26546
975975 0 0
976976 3.00000 0.0960277
977977 −8.48528 −0.271468 −0.135734 0.990745i 0.543339π-0.543339\pi
−0.135734 + 0.990745i 0.543339π0.543339\pi
978978 68.2843 2.18349
979979 −54.4264 −1.73948
980980 0 0
981981 82.4264 2.63167
982982 26.9706 0.860665
983983 26.6985 0.851549 0.425775 0.904829i 0.360002π-0.360002\pi
0.425775 + 0.904829i 0.360002π0.360002\pi
984984 70.6274 2.25152
985985 0 0
986986 −1.58579 −0.0505017
987987 24.4853 0.779375
988988 0 0
989989 −2.62742 −0.0835470
990990 0 0
991991 −13.5147 −0.429309 −0.214655 0.976690i 0.568863π-0.568863\pi
−0.214655 + 0.976690i 0.568863π0.568863\pi
992992 1.97056 0.0625654
993993 −78.2254 −2.48241
994994 54.2843 1.72179
995995 0 0
996996 74.7107 2.36730
997997 −12.6569 −0.400847 −0.200423 0.979709i 0.564232π-0.564232\pi
−0.200423 + 0.979709i 0.564232π0.564232\pi
998998 −6.17157 −0.195358
999999 −33.9411 −1.07385
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 4225.2.a.z.1.2 2
5.4 even 2 4225.2.a.s.1.1 2
13.12 even 2 325.2.a.f.1.1 2
39.38 odd 2 2925.2.a.bd.1.2 2
52.51 odd 2 5200.2.a.bt.1.1 2
65.12 odd 4 325.2.b.d.274.1 4
65.38 odd 4 325.2.b.d.274.4 4
65.64 even 2 325.2.a.h.1.2 yes 2
195.38 even 4 2925.2.c.q.2224.1 4
195.77 even 4 2925.2.c.q.2224.4 4
195.194 odd 2 2925.2.a.w.1.1 2
260.259 odd 2 5200.2.a.br.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
325.2.a.f.1.1 2 13.12 even 2
325.2.a.h.1.2 yes 2 65.64 even 2
325.2.b.d.274.1 4 65.12 odd 4
325.2.b.d.274.4 4 65.38 odd 4
2925.2.a.w.1.1 2 195.194 odd 2
2925.2.a.bd.1.2 2 39.38 odd 2
2925.2.c.q.2224.1 4 195.38 even 4
2925.2.c.q.2224.4 4 195.77 even 4
4225.2.a.s.1.1 2 5.4 even 2
4225.2.a.z.1.2 2 1.1 even 1 trivial
5200.2.a.br.1.2 2 260.259 odd 2
5200.2.a.bt.1.1 2 52.51 odd 2