Properties

Label 1215.2.a.k.1.1
Level 12151215
Weight 22
Character 1215.1
Self dual yes
Analytic conductor 9.7029.702
Analytic rank 11
Dimension 22
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1215,2,Mod(1,1215)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1215, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("1215.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1215=355 1215 = 3^{5} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1215.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,-1,0,3,2,0,-1,-6,0,-1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 9.701823845599.70182384559
Analytic rank: 11
Dimension: 22
Coefficient field: Q(13)\Q(\sqrt{13})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2x3 x^{2} - x - 3 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 2.302782.30278 of defining polynomial
Character χ\chi == 1215.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q2.30278q2+3.30278q4+1.00000q5+1.30278q73.00000q82.30278q102.30278q11+3.60555q133.00000q14+0.302776q165.30278q176.30278q19+3.30278q20+5.30278q223.00000q23+1.00000q258.30278q26+4.30278q287.60555q29+5.21110q31+5.30278q32+12.2111q34+1.30278q357.90833q37+14.5139q383.00000q406.69722q417.21110q437.60555q44+6.90833q46+6.69722q475.30278q492.30278q50+11.9083q52+8.51388q532.30278q553.90833q56+17.5139q581.39445q59+0.605551q6112.0000q6212.8167q64+3.60555q65+10.3028q6717.5139q683.00000q701.60555q71+12.6056q73+18.2111q7420.8167q763.00000q7712.5139q79+0.302776q80+15.4222q82+14.7250q835.30278q85+16.6056q86+6.90833q88+4.81665q89+4.69722q919.90833q9215.4222q946.30278q9515.7250q97+12.2111q98+O(q100)q-2.30278 q^{2} +3.30278 q^{4} +1.00000 q^{5} +1.30278 q^{7} -3.00000 q^{8} -2.30278 q^{10} -2.30278 q^{11} +3.60555 q^{13} -3.00000 q^{14} +0.302776 q^{16} -5.30278 q^{17} -6.30278 q^{19} +3.30278 q^{20} +5.30278 q^{22} -3.00000 q^{23} +1.00000 q^{25} -8.30278 q^{26} +4.30278 q^{28} -7.60555 q^{29} +5.21110 q^{31} +5.30278 q^{32} +12.2111 q^{34} +1.30278 q^{35} -7.90833 q^{37} +14.5139 q^{38} -3.00000 q^{40} -6.69722 q^{41} -7.21110 q^{43} -7.60555 q^{44} +6.90833 q^{46} +6.69722 q^{47} -5.30278 q^{49} -2.30278 q^{50} +11.9083 q^{52} +8.51388 q^{53} -2.30278 q^{55} -3.90833 q^{56} +17.5139 q^{58} -1.39445 q^{59} +0.605551 q^{61} -12.0000 q^{62} -12.8167 q^{64} +3.60555 q^{65} +10.3028 q^{67} -17.5139 q^{68} -3.00000 q^{70} -1.60555 q^{71} +12.6056 q^{73} +18.2111 q^{74} -20.8167 q^{76} -3.00000 q^{77} -12.5139 q^{79} +0.302776 q^{80} +15.4222 q^{82} +14.7250 q^{83} -5.30278 q^{85} +16.6056 q^{86} +6.90833 q^{88} +4.81665 q^{89} +4.69722 q^{91} -9.90833 q^{92} -15.4222 q^{94} -6.30278 q^{95} -15.7250 q^{97} +12.2111 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2qq2+3q4+2q5q76q8q10q116q143q167q179q19+3q20+7q226q23+2q2513q26+5q288q294q31++10q98+O(q100) 2 q - q^{2} + 3 q^{4} + 2 q^{5} - q^{7} - 6 q^{8} - q^{10} - q^{11} - 6 q^{14} - 3 q^{16} - 7 q^{17} - 9 q^{19} + 3 q^{20} + 7 q^{22} - 6 q^{23} + 2 q^{25} - 13 q^{26} + 5 q^{28} - 8 q^{29} - 4 q^{31}+ \cdots + 10 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 −2.30278 −1.62831 −0.814154 0.580649i 0.802799π-0.802799\pi
−0.814154 + 0.580649i 0.802799π0.802799\pi
33 0 0
44 3.30278 1.65139
55 1.00000 0.447214
66 0 0
77 1.30278 0.492403 0.246201 0.969219i 0.420818π-0.420818\pi
0.246201 + 0.969219i 0.420818π0.420818\pi
88 −3.00000 −1.06066
99 0 0
1010 −2.30278 −0.728202
1111 −2.30278 −0.694313 −0.347156 0.937807i 0.612853π-0.612853\pi
−0.347156 + 0.937807i 0.612853π0.612853\pi
1212 0 0
1313 3.60555 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
1414 −3.00000 −0.801784
1515 0 0
1616 0.302776 0.0756939
1717 −5.30278 −1.28611 −0.643056 0.765819i 0.722334π-0.722334\pi
−0.643056 + 0.765819i 0.722334π0.722334\pi
1818 0 0
1919 −6.30278 −1.44596 −0.722978 0.690871i 0.757227π-0.757227\pi
−0.722978 + 0.690871i 0.757227π0.757227\pi
2020 3.30278 0.738523
2121 0 0
2222 5.30278 1.13056
2323 −3.00000 −0.625543 −0.312772 0.949828i 0.601257π-0.601257\pi
−0.312772 + 0.949828i 0.601257π0.601257\pi
2424 0 0
2525 1.00000 0.200000
2626 −8.30278 −1.62831
2727 0 0
2828 4.30278 0.813148
2929 −7.60555 −1.41232 −0.706158 0.708055i 0.749573π-0.749573\pi
−0.706158 + 0.708055i 0.749573π0.749573\pi
3030 0 0
3131 5.21110 0.935942 0.467971 0.883744i 0.344985π-0.344985\pi
0.467971 + 0.883744i 0.344985π0.344985\pi
3232 5.30278 0.937407
3333 0 0
3434 12.2111 2.09419
3535 1.30278 0.220209
3636 0 0
3737 −7.90833 −1.30012 −0.650060 0.759882i 0.725256π-0.725256\pi
−0.650060 + 0.759882i 0.725256π0.725256\pi
3838 14.5139 2.35446
3939 0 0
4040 −3.00000 −0.474342
4141 −6.69722 −1.04593 −0.522965 0.852354i 0.675174π-0.675174\pi
−0.522965 + 0.852354i 0.675174π0.675174\pi
4242 0 0
4343 −7.21110 −1.09968 −0.549841 0.835269i 0.685312π-0.685312\pi
−0.549841 + 0.835269i 0.685312π0.685312\pi
4444 −7.60555 −1.14658
4545 0 0
4646 6.90833 1.01858
4747 6.69722 0.976891 0.488445 0.872595i 0.337564π-0.337564\pi
0.488445 + 0.872595i 0.337564π0.337564\pi
4848 0 0
4949 −5.30278 −0.757539
5050 −2.30278 −0.325662
5151 0 0
5252 11.9083 1.65139
5353 8.51388 1.16947 0.584736 0.811224i 0.301198π-0.301198\pi
0.584736 + 0.811224i 0.301198π0.301198\pi
5454 0 0
5555 −2.30278 −0.310506
5656 −3.90833 −0.522272
5757 0 0
5858 17.5139 2.29968
5959 −1.39445 −0.181542 −0.0907709 0.995872i 0.528933π-0.528933\pi
−0.0907709 + 0.995872i 0.528933π0.528933\pi
6060 0 0
6161 0.605551 0.0775329 0.0387664 0.999248i 0.487657π-0.487657\pi
0.0387664 + 0.999248i 0.487657π0.487657\pi
6262 −12.0000 −1.52400
6363 0 0
6464 −12.8167 −1.60208
6565 3.60555 0.447214
6666 0 0
6767 10.3028 1.25868 0.629342 0.777128i 0.283324π-0.283324\pi
0.629342 + 0.777128i 0.283324π0.283324\pi
6868 −17.5139 −2.12387
6969 0 0
7070 −3.00000 −0.358569
7171 −1.60555 −0.190544 −0.0952719 0.995451i 0.530372π-0.530372\pi
−0.0952719 + 0.995451i 0.530372π0.530372\pi
7272 0 0
7373 12.6056 1.47537 0.737684 0.675146i 0.235919π-0.235919\pi
0.737684 + 0.675146i 0.235919π0.235919\pi
7474 18.2111 2.11700
7575 0 0
7676 −20.8167 −2.38783
7777 −3.00000 −0.341882
7878 0 0
7979 −12.5139 −1.40792 −0.703961 0.710239i 0.748587π-0.748587\pi
−0.703961 + 0.710239i 0.748587π0.748587\pi
8080 0.302776 0.0338513
8181 0 0
8282 15.4222 1.70310
8383 14.7250 1.61628 0.808138 0.588993i 0.200475π-0.200475\pi
0.808138 + 0.588993i 0.200475π0.200475\pi
8484 0 0
8585 −5.30278 −0.575167
8686 16.6056 1.79062
8787 0 0
8888 6.90833 0.736430
8989 4.81665 0.510564 0.255282 0.966867i 0.417832π-0.417832\pi
0.255282 + 0.966867i 0.417832π0.417832\pi
9090 0 0
9191 4.69722 0.492403
9292 −9.90833 −1.03301
9393 0 0
9494 −15.4222 −1.59068
9595 −6.30278 −0.646651
9696 0 0
9797 −15.7250 −1.59663 −0.798315 0.602240i 0.794275π-0.794275\pi
−0.798315 + 0.602240i 0.794275π0.794275\pi
9898 12.2111 1.23351
9999 0 0
100100 3.30278 0.330278
101101 −17.7250 −1.76370 −0.881851 0.471529i 0.843702π-0.843702\pi
−0.881851 + 0.471529i 0.843702π0.843702\pi
102102 0 0
103103 −8.81665 −0.868731 −0.434365 0.900737i 0.643027π-0.643027\pi
−0.434365 + 0.900737i 0.643027π0.643027\pi
104104 −10.8167 −1.06066
105105 0 0
106106 −19.6056 −1.90426
107107 2.09167 0.202210 0.101105 0.994876i 0.467762π-0.467762\pi
0.101105 + 0.994876i 0.467762π0.467762\pi
108108 0 0
109109 −16.9083 −1.61952 −0.809762 0.586758i 0.800404π-0.800404\pi
−0.809762 + 0.586758i 0.800404π0.800404\pi
110110 5.30278 0.505600
111111 0 0
112112 0.394449 0.0372719
113113 −6.21110 −0.584291 −0.292146 0.956374i 0.594369π-0.594369\pi
−0.292146 + 0.956374i 0.594369π0.594369\pi
114114 0 0
115115 −3.00000 −0.279751
116116 −25.1194 −2.33228
117117 0 0
118118 3.21110 0.295606
119119 −6.90833 −0.633285
120120 0 0
121121 −5.69722 −0.517929
122122 −1.39445 −0.126247
123123 0 0
124124 17.2111 1.54560
125125 1.00000 0.0894427
126126 0 0
127127 0.605551 0.0537340 0.0268670 0.999639i 0.491447π-0.491447\pi
0.0268670 + 0.999639i 0.491447π0.491447\pi
128128 18.9083 1.67128
129129 0 0
130130 −8.30278 −0.728202
131131 10.8167 0.945055 0.472528 0.881316i 0.343342π-0.343342\pi
0.472528 + 0.881316i 0.343342π0.343342\pi
132132 0 0
133133 −8.21110 −0.711993
134134 −23.7250 −2.04953
135135 0 0
136136 15.9083 1.36413
137137 −15.0000 −1.28154 −0.640768 0.767734i 0.721384π-0.721384\pi
−0.640768 + 0.767734i 0.721384π0.721384\pi
138138 0 0
139139 11.0000 0.933008 0.466504 0.884519i 0.345513π-0.345513\pi
0.466504 + 0.884519i 0.345513π0.345513\pi
140140 4.30278 0.363651
141141 0 0
142142 3.69722 0.310264
143143 −8.30278 −0.694313
144144 0 0
145145 −7.60555 −0.631607
146146 −29.0278 −2.40235
147147 0 0
148148 −26.1194 −2.14700
149149 16.1194 1.32056 0.660278 0.751022i 0.270439π-0.270439\pi
0.660278 + 0.751022i 0.270439π0.270439\pi
150150 0 0
151151 −11.1194 −0.904886 −0.452443 0.891793i 0.649447π-0.649447\pi
−0.452443 + 0.891793i 0.649447π0.649447\pi
152152 18.9083 1.53367
153153 0 0
154154 6.90833 0.556689
155155 5.21110 0.418566
156156 0 0
157157 −2.81665 −0.224793 −0.112397 0.993663i 0.535853π-0.535853\pi
−0.112397 + 0.993663i 0.535853π0.535853\pi
158158 28.8167 2.29253
159159 0 0
160160 5.30278 0.419221
161161 −3.90833 −0.308019
162162 0 0
163163 −10.0000 −0.783260 −0.391630 0.920123i 0.628089π-0.628089\pi
−0.391630 + 0.920123i 0.628089π0.628089\pi
164164 −22.1194 −1.72724
165165 0 0
166166 −33.9083 −2.63180
167167 −18.9083 −1.46317 −0.731585 0.681750i 0.761219π-0.761219\pi
−0.731585 + 0.681750i 0.761219π0.761219\pi
168168 0 0
169169 0 0
170170 12.2111 0.936549
171171 0 0
172172 −23.8167 −1.81600
173173 −1.18335 −0.0899681 −0.0449841 0.998988i 0.514324π-0.514324\pi
−0.0449841 + 0.998988i 0.514324π0.514324\pi
174174 0 0
175175 1.30278 0.0984806
176176 −0.697224 −0.0525553
177177 0 0
178178 −11.0917 −0.831356
179179 19.6056 1.46539 0.732694 0.680558i 0.238263π-0.238263\pi
0.732694 + 0.680558i 0.238263π0.238263\pi
180180 0 0
181181 −7.90833 −0.587821 −0.293911 0.955833i 0.594957π-0.594957\pi
−0.293911 + 0.955833i 0.594957π0.594957\pi
182182 −10.8167 −0.801784
183183 0 0
184184 9.00000 0.663489
185185 −7.90833 −0.581432
186186 0 0
187187 12.2111 0.892964
188188 22.1194 1.61323
189189 0 0
190190 14.5139 1.05295
191191 −7.60555 −0.550318 −0.275159 0.961399i 0.588731π-0.588731\pi
−0.275159 + 0.961399i 0.588731π0.588731\pi
192192 0 0
193193 5.00000 0.359908 0.179954 0.983675i 0.442405π-0.442405\pi
0.179954 + 0.983675i 0.442405π0.442405\pi
194194 36.2111 2.59981
195195 0 0
196196 −17.5139 −1.25099
197197 −20.7250 −1.47659 −0.738297 0.674476i 0.764370π-0.764370\pi
−0.738297 + 0.674476i 0.764370π0.764370\pi
198198 0 0
199199 23.4222 1.66036 0.830178 0.557498i 0.188239π-0.188239\pi
0.830178 + 0.557498i 0.188239π0.188239\pi
200200 −3.00000 −0.212132
201201 0 0
202202 40.8167 2.87185
203203 −9.90833 −0.695428
204204 0 0
205205 −6.69722 −0.467754
206206 20.3028 1.41456
207207 0 0
208208 1.09167 0.0756939
209209 14.5139 1.00395
210210 0 0
211211 −2.18335 −0.150308 −0.0751539 0.997172i 0.523945π-0.523945\pi
−0.0751539 + 0.997172i 0.523945π0.523945\pi
212212 28.1194 1.93125
213213 0 0
214214 −4.81665 −0.329260
215215 −7.21110 −0.491793
216216 0 0
217217 6.78890 0.460860
218218 38.9361 2.63708
219219 0 0
220220 −7.60555 −0.512766
221221 −19.1194 −1.28611
222222 0 0
223223 20.9083 1.40013 0.700063 0.714082i 0.253155π-0.253155\pi
0.700063 + 0.714082i 0.253155π0.253155\pi
224224 6.90833 0.461582
225225 0 0
226226 14.3028 0.951406
227227 −7.60555 −0.504798 −0.252399 0.967623i 0.581220π-0.581220\pi
−0.252399 + 0.967623i 0.581220π0.581220\pi
228228 0 0
229229 14.2111 0.939096 0.469548 0.882907i 0.344417π-0.344417\pi
0.469548 + 0.882907i 0.344417π0.344417\pi
230230 6.90833 0.455522
231231 0 0
232232 22.8167 1.49799
233233 22.8167 1.49477 0.747384 0.664392i 0.231309π-0.231309\pi
0.747384 + 0.664392i 0.231309π0.231309\pi
234234 0 0
235235 6.69722 0.436879
236236 −4.60555 −0.299796
237237 0 0
238238 15.9083 1.03118
239239 −20.0278 −1.29549 −0.647744 0.761858i 0.724287π-0.724287\pi
−0.647744 + 0.761858i 0.724287π0.724287\pi
240240 0 0
241241 −2.39445 −0.154240 −0.0771200 0.997022i 0.524572π-0.524572\pi
−0.0771200 + 0.997022i 0.524572π0.524572\pi
242242 13.1194 0.843349
243243 0 0
244244 2.00000 0.128037
245245 −5.30278 −0.338782
246246 0 0
247247 −22.7250 −1.44596
248248 −15.6333 −0.992716
249249 0 0
250250 −2.30278 −0.145640
251251 2.09167 0.132025 0.0660126 0.997819i 0.478972π-0.478972\pi
0.0660126 + 0.997819i 0.478972π0.478972\pi
252252 0 0
253253 6.90833 0.434323
254254 −1.39445 −0.0874955
255255 0 0
256256 −17.9083 −1.11927
257257 −9.90833 −0.618064 −0.309032 0.951052i 0.600005π-0.600005\pi
−0.309032 + 0.951052i 0.600005π0.600005\pi
258258 0 0
259259 −10.3028 −0.640183
260260 11.9083 0.738523
261261 0 0
262262 −24.9083 −1.53884
263263 −5.51388 −0.340000 −0.170000 0.985444i 0.554377π-0.554377\pi
−0.170000 + 0.985444i 0.554377π0.554377\pi
264264 0 0
265265 8.51388 0.523003
266266 18.9083 1.15934
267267 0 0
268268 34.0278 2.07858
269269 21.6972 1.32290 0.661452 0.749988i 0.269941π-0.269941\pi
0.661452 + 0.749988i 0.269941π0.269941\pi
270270 0 0
271271 −15.0278 −0.912871 −0.456436 0.889756i 0.650874π-0.650874\pi
−0.456436 + 0.889756i 0.650874π0.650874\pi
272272 −1.60555 −0.0973508
273273 0 0
274274 34.5416 2.08674
275275 −2.30278 −0.138863
276276 0 0
277277 −3.51388 −0.211128 −0.105564 0.994412i 0.533665π-0.533665\pi
−0.105564 + 0.994412i 0.533665π0.533665\pi
278278 −25.3305 −1.51922
279279 0 0
280280 −3.90833 −0.233567
281281 7.81665 0.466302 0.233151 0.972440i 0.425096π-0.425096\pi
0.233151 + 0.972440i 0.425096π0.425096\pi
282282 0 0
283283 3.11943 0.185431 0.0927154 0.995693i 0.470445π-0.470445\pi
0.0927154 + 0.995693i 0.470445π0.470445\pi
284284 −5.30278 −0.314662
285285 0 0
286286 19.1194 1.13056
287287 −8.72498 −0.515019
288288 0 0
289289 11.1194 0.654084
290290 17.5139 1.02845
291291 0 0
292292 41.6333 2.43641
293293 8.72498 0.509719 0.254859 0.966978i 0.417971π-0.417971\pi
0.254859 + 0.966978i 0.417971π0.417971\pi
294294 0 0
295295 −1.39445 −0.0811879
296296 23.7250 1.37899
297297 0 0
298298 −37.1194 −2.15027
299299 −10.8167 −0.625543
300300 0 0
301301 −9.39445 −0.541487
302302 25.6056 1.47343
303303 0 0
304304 −1.90833 −0.109450
305305 0.605551 0.0346738
306306 0 0
307307 −12.3028 −0.702156 −0.351078 0.936346i 0.614185π-0.614185\pi
−0.351078 + 0.936346i 0.614185π0.614185\pi
308308 −9.90833 −0.564579
309309 0 0
310310 −12.0000 −0.681554
311311 6.00000 0.340229 0.170114 0.985424i 0.445586π-0.445586\pi
0.170114 + 0.985424i 0.445586π0.445586\pi
312312 0 0
313313 16.7250 0.945352 0.472676 0.881236i 0.343288π-0.343288\pi
0.472676 + 0.881236i 0.343288π0.343288\pi
314314 6.48612 0.366033
315315 0 0
316316 −41.3305 −2.32502
317317 6.21110 0.348850 0.174425 0.984670i 0.444193π-0.444193\pi
0.174425 + 0.984670i 0.444193π0.444193\pi
318318 0 0
319319 17.5139 0.980589
320320 −12.8167 −0.716473
321321 0 0
322322 9.00000 0.501550
323323 33.4222 1.85966
324324 0 0
325325 3.60555 0.200000
326326 23.0278 1.27539
327327 0 0
328328 20.0917 1.10938
329329 8.72498 0.481024
330330 0 0
331331 10.9361 0.601102 0.300551 0.953766i 0.402830π-0.402830\pi
0.300551 + 0.953766i 0.402830π0.402830\pi
332332 48.6333 2.66910
333333 0 0
334334 43.5416 2.38249
335335 10.3028 0.562901
336336 0 0
337337 19.5139 1.06299 0.531494 0.847062i 0.321631π-0.321631\pi
0.531494 + 0.847062i 0.321631π0.321631\pi
338338 0 0
339339 0 0
340340 −17.5139 −0.949823
341341 −12.0000 −0.649836
342342 0 0
343343 −16.0278 −0.865417
344344 21.6333 1.16639
345345 0 0
346346 2.72498 0.146496
347347 −13.1194 −0.704288 −0.352144 0.935946i 0.614547π-0.614547\pi
−0.352144 + 0.935946i 0.614547π0.614547\pi
348348 0 0
349349 −4.48612 −0.240137 −0.120068 0.992766i 0.538311π-0.538311\pi
−0.120068 + 0.992766i 0.538311π0.538311\pi
350350 −3.00000 −0.160357
351351 0 0
352352 −12.2111 −0.650854
353353 −24.0000 −1.27739 −0.638696 0.769460i 0.720526π-0.720526\pi
−0.638696 + 0.769460i 0.720526π0.720526\pi
354354 0 0
355355 −1.60555 −0.0852138
356356 15.9083 0.843140
357357 0 0
358358 −45.1472 −2.38610
359359 25.5416 1.34804 0.674018 0.738715i 0.264567π-0.264567\pi
0.674018 + 0.738715i 0.264567π0.264567\pi
360360 0 0
361361 20.7250 1.09079
362362 18.2111 0.957154
363363 0 0
364364 15.5139 0.813148
365365 12.6056 0.659805
366366 0 0
367367 34.0278 1.77623 0.888117 0.459617i 0.152013π-0.152013\pi
0.888117 + 0.459617i 0.152013π0.152013\pi
368368 −0.908327 −0.0473498
369369 0 0
370370 18.2111 0.946750
371371 11.0917 0.575851
372372 0 0
373373 −0.577795 −0.0299171 −0.0149585 0.999888i 0.504762π-0.504762\pi
−0.0149585 + 0.999888i 0.504762π0.504762\pi
374374 −28.1194 −1.45402
375375 0 0
376376 −20.0917 −1.03615
377377 −27.4222 −1.41232
378378 0 0
379379 −11.1194 −0.571167 −0.285583 0.958354i 0.592187π-0.592187\pi
−0.285583 + 0.958354i 0.592187π0.592187\pi
380380 −20.8167 −1.06787
381381 0 0
382382 17.5139 0.896088
383383 −12.0000 −0.613171 −0.306586 0.951843i 0.599187π-0.599187\pi
−0.306586 + 0.951843i 0.599187π0.599187\pi
384384 0 0
385385 −3.00000 −0.152894
386386 −11.5139 −0.586041
387387 0 0
388388 −51.9361 −2.63666
389389 −28.8167 −1.46106 −0.730531 0.682879i 0.760727π-0.760727\pi
−0.730531 + 0.682879i 0.760727π0.760727\pi
390390 0 0
391391 15.9083 0.804519
392392 15.9083 0.803492
393393 0 0
394394 47.7250 2.40435
395395 −12.5139 −0.629642
396396 0 0
397397 7.51388 0.377111 0.188555 0.982063i 0.439620π-0.439620\pi
0.188555 + 0.982063i 0.439620π0.439620\pi
398398 −53.9361 −2.70357
399399 0 0
400400 0.302776 0.0151388
401401 19.8167 0.989596 0.494798 0.869008i 0.335242π-0.335242\pi
0.494798 + 0.869008i 0.335242π0.335242\pi
402402 0 0
403403 18.7889 0.935942
404404 −58.5416 −2.91256
405405 0 0
406406 22.8167 1.13237
407407 18.2111 0.902691
408408 0 0
409409 −7.63331 −0.377443 −0.188721 0.982031i 0.560434π-0.560434\pi
−0.188721 + 0.982031i 0.560434π0.560434\pi
410410 15.4222 0.761648
411411 0 0
412412 −29.1194 −1.43461
413413 −1.81665 −0.0893917
414414 0 0
415415 14.7250 0.722821
416416 19.1194 0.937407
417417 0 0
418418 −33.4222 −1.63473
419419 5.02776 0.245622 0.122811 0.992430i 0.460809π-0.460809\pi
0.122811 + 0.992430i 0.460809π0.460809\pi
420420 0 0
421421 8.69722 0.423877 0.211938 0.977283i 0.432022π-0.432022\pi
0.211938 + 0.977283i 0.432022π0.432022\pi
422422 5.02776 0.244747
423423 0 0
424424 −25.5416 −1.24041
425425 −5.30278 −0.257222
426426 0 0
427427 0.788897 0.0381774
428428 6.90833 0.333927
429429 0 0
430430 16.6056 0.800791
431431 40.8167 1.96607 0.983035 0.183421i 0.0587170π-0.0587170\pi
0.983035 + 0.183421i 0.0587170π0.0587170\pi
432432 0 0
433433 −18.0278 −0.866359 −0.433179 0.901308i 0.642608π-0.642608\pi
−0.433179 + 0.901308i 0.642608π0.642608\pi
434434 −15.6333 −0.750423
435435 0 0
436436 −55.8444 −2.67446
437437 18.9083 0.904508
438438 0 0
439439 −20.1194 −0.960248 −0.480124 0.877201i 0.659408π-0.659408\pi
−0.480124 + 0.877201i 0.659408π0.659408\pi
440440 6.90833 0.329342
441441 0 0
442442 44.0278 2.09419
443443 9.27502 0.440669 0.220335 0.975424i 0.429285π-0.429285\pi
0.220335 + 0.975424i 0.429285π0.429285\pi
444444 0 0
445445 4.81665 0.228331
446446 −48.1472 −2.27984
447447 0 0
448448 −16.6972 −0.788870
449449 −39.2111 −1.85049 −0.925243 0.379375i 0.876139π-0.876139\pi
−0.925243 + 0.379375i 0.876139π0.876139\pi
450450 0 0
451451 15.4222 0.726203
452452 −20.5139 −0.964892
453453 0 0
454454 17.5139 0.821967
455455 4.69722 0.220209
456456 0 0
457457 13.5139 0.632153 0.316076 0.948734i 0.397634π-0.397634\pi
0.316076 + 0.948734i 0.397634π0.397634\pi
458458 −32.7250 −1.52914
459459 0 0
460460 −9.90833 −0.461978
461461 −33.0000 −1.53696 −0.768482 0.639872i 0.778987π-0.778987\pi
−0.768482 + 0.639872i 0.778987π0.778987\pi
462462 0 0
463463 −20.3305 −0.944840 −0.472420 0.881374i 0.656619π-0.656619\pi
−0.472420 + 0.881374i 0.656619π0.656619\pi
464464 −2.30278 −0.106904
465465 0 0
466466 −52.5416 −2.43394
467467 −31.3305 −1.44980 −0.724902 0.688852i 0.758115π-0.758115\pi
−0.724902 + 0.688852i 0.758115π0.758115\pi
468468 0 0
469469 13.4222 0.619780
470470 −15.4222 −0.711373
471471 0 0
472472 4.18335 0.192554
473473 16.6056 0.763524
474474 0 0
475475 −6.30278 −0.289191
476476 −22.8167 −1.04580
477477 0 0
478478 46.1194 2.10945
479479 14.7250 0.672802 0.336401 0.941719i 0.390790π-0.390790\pi
0.336401 + 0.941719i 0.390790π0.390790\pi
480480 0 0
481481 −28.5139 −1.30012
482482 5.51388 0.251150
483483 0 0
484484 −18.8167 −0.855302
485485 −15.7250 −0.714035
486486 0 0
487487 −5.18335 −0.234880 −0.117440 0.993080i 0.537469π-0.537469\pi
−0.117440 + 0.993080i 0.537469π0.537469\pi
488488 −1.81665 −0.0822361
489489 0 0
490490 12.2111 0.551641
491491 −24.6972 −1.11457 −0.557285 0.830321i 0.688157π-0.688157\pi
−0.557285 + 0.830321i 0.688157π0.688157\pi
492492 0 0
493493 40.3305 1.81640
494494 52.3305 2.35446
495495 0 0
496496 1.57779 0.0708451
497497 −2.09167 −0.0938244
498498 0 0
499499 1.78890 0.0800820 0.0400410 0.999198i 0.487251π-0.487251\pi
0.0400410 + 0.999198i 0.487251π0.487251\pi
500500 3.30278 0.147705
501501 0 0
502502 −4.81665 −0.214978
503503 −12.6972 −0.566141 −0.283071 0.959099i 0.591353π-0.591353\pi
−0.283071 + 0.959099i 0.591353π0.591353\pi
504504 0 0
505505 −17.7250 −0.788751
506506 −15.9083 −0.707211
507507 0 0
508508 2.00000 0.0887357
509509 −33.8444 −1.50013 −0.750064 0.661366i 0.769977π-0.769977\pi
−0.750064 + 0.661366i 0.769977π0.769977\pi
510510 0 0
511511 16.4222 0.726476
512512 3.42221 0.151242
513513 0 0
514514 22.8167 1.00640
515515 −8.81665 −0.388508
516516 0 0
517517 −15.4222 −0.678268
518518 23.7250 1.04242
519519 0 0
520520 −10.8167 −0.474342
521521 5.93608 0.260065 0.130032 0.991510i 0.458492π-0.458492\pi
0.130032 + 0.991510i 0.458492π0.458492\pi
522522 0 0
523523 24.3305 1.06390 0.531950 0.846776i 0.321459π-0.321459\pi
0.531950 + 0.846776i 0.321459π0.321459\pi
524524 35.7250 1.56065
525525 0 0
526526 12.6972 0.553625
527527 −27.6333 −1.20373
528528 0 0
529529 −14.0000 −0.608696
530530 −19.6056 −0.851611
531531 0 0
532532 −27.1194 −1.17578
533533 −24.1472 −1.04593
534534 0 0
535535 2.09167 0.0904309
536536 −30.9083 −1.33504
537537 0 0
538538 −49.9638 −2.15409
539539 12.2111 0.525969
540540 0 0
541541 4.30278 0.184991 0.0924954 0.995713i 0.470516π-0.470516\pi
0.0924954 + 0.995713i 0.470516π0.470516\pi
542542 34.6056 1.48644
543543 0 0
544544 −28.1194 −1.20561
545545 −16.9083 −0.724273
546546 0 0
547547 −4.21110 −0.180054 −0.0900269 0.995939i 0.528695π-0.528695\pi
−0.0900269 + 0.995939i 0.528695π0.528695\pi
548548 −49.5416 −2.11631
549549 0 0
550550 5.30278 0.226111
551551 47.9361 2.04215
552552 0 0
553553 −16.3028 −0.693265
554554 8.09167 0.343782
555555 0 0
556556 36.3305 1.54076
557557 −9.00000 −0.381342 −0.190671 0.981654i 0.561066π-0.561066\pi
−0.190671 + 0.981654i 0.561066π0.561066\pi
558558 0 0
559559 −26.0000 −1.09968
560560 0.394449 0.0166685
561561 0 0
562562 −18.0000 −0.759284
563563 24.6333 1.03817 0.519085 0.854723i 0.326273π-0.326273\pi
0.519085 + 0.854723i 0.326273π0.326273\pi
564564 0 0
565565 −6.21110 −0.261303
566566 −7.18335 −0.301939
567567 0 0
568568 4.81665 0.202102
569569 −28.8167 −1.20806 −0.604028 0.796963i 0.706439π-0.706439\pi
−0.604028 + 0.796963i 0.706439π0.706439\pi
570570 0 0
571571 −38.8167 −1.62443 −0.812213 0.583361i 0.801737π-0.801737\pi
−0.812213 + 0.583361i 0.801737π0.801737\pi
572572 −27.4222 −1.14658
573573 0 0
574574 20.0917 0.838610
575575 −3.00000 −0.125109
576576 0 0
577577 20.6333 0.858976 0.429488 0.903073i 0.358694π-0.358694\pi
0.429488 + 0.903073i 0.358694π0.358694\pi
578578 −25.6056 −1.06505
579579 0 0
580580 −25.1194 −1.04303
581581 19.1833 0.795859
582582 0 0
583583 −19.6056 −0.811979
584584 −37.8167 −1.56486
585585 0 0
586586 −20.0917 −0.829979
587587 28.5416 1.17804 0.589020 0.808119i 0.299514π-0.299514\pi
0.589020 + 0.808119i 0.299514π0.299514\pi
588588 0 0
589589 −32.8444 −1.35333
590590 3.21110 0.132199
591591 0 0
592592 −2.39445 −0.0984112
593593 −21.6972 −0.890998 −0.445499 0.895282i 0.646974π-0.646974\pi
−0.445499 + 0.895282i 0.646974π0.646974\pi
594594 0 0
595595 −6.90833 −0.283214
596596 53.2389 2.18075
597597 0 0
598598 24.9083 1.01858
599599 34.7527 1.41996 0.709979 0.704223i 0.248704π-0.248704\pi
0.709979 + 0.704223i 0.248704π0.248704\pi
600600 0 0
601601 18.1833 0.741714 0.370857 0.928690i 0.379064π-0.379064\pi
0.370857 + 0.928690i 0.379064π0.379064\pi
602602 21.6333 0.881708
603603 0 0
604604 −36.7250 −1.49432
605605 −5.69722 −0.231625
606606 0 0
607607 −19.2111 −0.779755 −0.389877 0.920867i 0.627483π-0.627483\pi
−0.389877 + 0.920867i 0.627483π0.627483\pi
608608 −33.4222 −1.35545
609609 0 0
610610 −1.39445 −0.0564596
611611 24.1472 0.976891
612612 0 0
613613 28.5139 1.15166 0.575832 0.817568i 0.304678π-0.304678\pi
0.575832 + 0.817568i 0.304678π0.304678\pi
614614 28.3305 1.14333
615615 0 0
616616 9.00000 0.362620
617617 −34.8167 −1.40167 −0.700833 0.713326i 0.747188π-0.747188\pi
−0.700833 + 0.713326i 0.747188π0.747188\pi
618618 0 0
619619 24.5416 0.986412 0.493206 0.869913i 0.335825π-0.335825\pi
0.493206 + 0.869913i 0.335825π0.335825\pi
620620 17.2111 0.691215
621621 0 0
622622 −13.8167 −0.553997
623623 6.27502 0.251403
624624 0 0
625625 1.00000 0.0400000
626626 −38.5139 −1.53932
627627 0 0
628628 −9.30278 −0.371221
629629 41.9361 1.67210
630630 0 0
631631 13.7889 0.548927 0.274464 0.961597i 0.411500π-0.411500\pi
0.274464 + 0.961597i 0.411500π0.411500\pi
632632 37.5416 1.49333
633633 0 0
634634 −14.3028 −0.568036
635635 0.605551 0.0240306
636636 0 0
637637 −19.1194 −0.757539
638638 −40.3305 −1.59670
639639 0 0
640640 18.9083 0.747417
641641 21.6333 0.854464 0.427232 0.904142i 0.359489π-0.359489\pi
0.427232 + 0.904142i 0.359489π0.359489\pi
642642 0 0
643643 −1.42221 −0.0560863 −0.0280431 0.999607i 0.508928π-0.508928\pi
−0.0280431 + 0.999607i 0.508928π0.508928\pi
644644 −12.9083 −0.508659
645645 0 0
646646 −76.9638 −3.02810
647647 38.2389 1.50332 0.751662 0.659548i 0.229252π-0.229252\pi
0.751662 + 0.659548i 0.229252π0.229252\pi
648648 0 0
649649 3.21110 0.126047
650650 −8.30278 −0.325662
651651 0 0
652652 −33.0278 −1.29347
653653 9.21110 0.360458 0.180229 0.983625i 0.442316π-0.442316\pi
0.180229 + 0.983625i 0.442316π0.442316\pi
654654 0 0
655655 10.8167 0.422642
656656 −2.02776 −0.0791706
657657 0 0
658658 −20.0917 −0.783255
659659 26.7889 1.04355 0.521774 0.853084i 0.325271π-0.325271\pi
0.521774 + 0.853084i 0.325271π0.325271\pi
660660 0 0
661661 −7.84441 −0.305112 −0.152556 0.988295i 0.548750π-0.548750\pi
−0.152556 + 0.988295i 0.548750π0.548750\pi
662662 −25.1833 −0.978779
663663 0 0
664664 −44.1749 −1.71432
665665 −8.21110 −0.318413
666666 0 0
667667 22.8167 0.883464
668668 −62.4500 −2.41626
669669 0 0
670670 −23.7250 −0.916576
671671 −1.39445 −0.0538321
672672 0 0
673673 51.1194 1.97051 0.985255 0.171095i 0.0547304π-0.0547304\pi
0.985255 + 0.171095i 0.0547304π0.0547304\pi
674674 −44.9361 −1.73087
675675 0 0
676676 0 0
677677 28.5416 1.09694 0.548472 0.836169i 0.315210π-0.315210\pi
0.548472 + 0.836169i 0.315210π0.315210\pi
678678 0 0
679679 −20.4861 −0.786185
680680 15.9083 0.610056
681681 0 0
682682 27.6333 1.05813
683683 −4.81665 −0.184304 −0.0921521 0.995745i 0.529375π-0.529375\pi
−0.0921521 + 0.995745i 0.529375π0.529375\pi
684684 0 0
685685 −15.0000 −0.573121
686686 36.9083 1.40917
687687 0 0
688688 −2.18335 −0.0832393
689689 30.6972 1.16947
690690 0 0
691691 15.6056 0.593663 0.296832 0.954930i 0.404070π-0.404070\pi
0.296832 + 0.954930i 0.404070π0.404070\pi
692692 −3.90833 −0.148572
693693 0 0
694694 30.2111 1.14680
695695 11.0000 0.417254
696696 0 0
697697 35.5139 1.34518
698698 10.3305 0.391016
699699 0 0
700700 4.30278 0.162630
701701 −19.6056 −0.740491 −0.370246 0.928934i 0.620727π-0.620727\pi
−0.370246 + 0.928934i 0.620727π0.620727\pi
702702 0 0
703703 49.8444 1.87992
704704 29.5139 1.11235
705705 0 0
706706 55.2666 2.07999
707707 −23.0917 −0.868452
708708 0 0
709709 −1.76114 −0.0661410 −0.0330705 0.999453i 0.510529π-0.510529\pi
−0.0330705 + 0.999453i 0.510529π0.510529\pi
710710 3.69722 0.138754
711711 0 0
712712 −14.4500 −0.541535
713713 −15.6333 −0.585472
714714 0 0
715715 −8.30278 −0.310506
716716 64.7527 2.41992
717717 0 0
718718 −58.8167 −2.19502
719719 20.7250 0.772911 0.386456 0.922308i 0.373699π-0.373699\pi
0.386456 + 0.922308i 0.373699π0.373699\pi
720720 0 0
721721 −11.4861 −0.427766
722722 −47.7250 −1.77614
723723 0 0
724724 −26.1194 −0.970721
725725 −7.60555 −0.282463
726726 0 0
727727 −48.7250 −1.80711 −0.903555 0.428473i 0.859052π-0.859052\pi
−0.903555 + 0.428473i 0.859052π0.859052\pi
728728 −14.0917 −0.522272
729729 0 0
730730 −29.0278 −1.07437
731731 38.2389 1.41432
732732 0 0
733733 29.0000 1.07114 0.535570 0.844491i 0.320097π-0.320097\pi
0.535570 + 0.844491i 0.320097π0.320097\pi
734734 −78.3583 −2.89226
735735 0 0
736736 −15.9083 −0.586389
737737 −23.7250 −0.873921
738738 0 0
739739 −49.8444 −1.83356 −0.916778 0.399397i 0.869220π-0.869220\pi
−0.916778 + 0.399397i 0.869220π0.869220\pi
740740 −26.1194 −0.960169
741741 0 0
742742 −25.5416 −0.937663
743743 16.6056 0.609199 0.304599 0.952481i 0.401477π-0.401477\pi
0.304599 + 0.952481i 0.401477π0.401477\pi
744744 0 0
745745 16.1194 0.590570
746746 1.33053 0.0487142
747747 0 0
748748 40.3305 1.47463
749749 2.72498 0.0995686
750750 0 0
751751 21.6056 0.788398 0.394199 0.919025i 0.371022π-0.371022\pi
0.394199 + 0.919025i 0.371022π0.371022\pi
752752 2.02776 0.0739447
753753 0 0
754754 63.1472 2.29968
755755 −11.1194 −0.404677
756756 0 0
757757 0.880571 0.0320049 0.0160024 0.999872i 0.494906π-0.494906\pi
0.0160024 + 0.999872i 0.494906π0.494906\pi
758758 25.6056 0.930036
759759 0 0
760760 18.9083 0.685877
761761 −42.3583 −1.53549 −0.767743 0.640757i 0.778620π-0.778620\pi
−0.767743 + 0.640757i 0.778620π0.778620\pi
762762 0 0
763763 −22.0278 −0.797458
764764 −25.1194 −0.908789
765765 0 0
766766 27.6333 0.998432
767767 −5.02776 −0.181542
768768 0 0
769769 31.7250 1.14403 0.572016 0.820242i 0.306162π-0.306162\pi
0.572016 + 0.820242i 0.306162π0.306162\pi
770770 6.90833 0.248959
771771 0 0
772772 16.5139 0.594347
773773 −18.0000 −0.647415 −0.323708 0.946157i 0.604929π-0.604929\pi
−0.323708 + 0.946157i 0.604929π0.604929\pi
774774 0 0
775775 5.21110 0.187188
776776 47.1749 1.69348
777777 0 0
778778 66.3583 2.37906
779779 42.2111 1.51237
780780 0 0
781781 3.69722 0.132297
782782 −36.6333 −1.31000
783783 0 0
784784 −1.60555 −0.0573411
785785 −2.81665 −0.100531
786786 0 0
787787 43.8722 1.56387 0.781937 0.623358i 0.214232π-0.214232\pi
0.781937 + 0.623358i 0.214232π0.214232\pi
788788 −68.4500 −2.43843
789789 0 0
790790 28.8167 1.02525
791791 −8.09167 −0.287707
792792 0 0
793793 2.18335 0.0775329
794794 −17.3028 −0.614053
795795 0 0
796796 77.3583 2.74189
797797 17.5778 0.622637 0.311319 0.950306i 0.399229π-0.399229\pi
0.311319 + 0.950306i 0.399229π0.399229\pi
798798 0 0
799799 −35.5139 −1.25639
800800 5.30278 0.187481
801801 0 0
802802 −45.6333 −1.61137
803803 −29.0278 −1.02437
804804 0 0
805805 −3.90833 −0.137750
806806 −43.2666 −1.52400
807807 0 0
808808 53.1749 1.87069
809809 −3.06392 −0.107722 −0.0538608 0.998548i 0.517153π-0.517153\pi
−0.0538608 + 0.998548i 0.517153π0.517153\pi
810810 0 0
811811 47.2111 1.65781 0.828903 0.559392i 0.188965π-0.188965\pi
0.828903 + 0.559392i 0.188965π0.188965\pi
812812 −32.7250 −1.14842
813813 0 0
814814 −41.9361 −1.46986
815815 −10.0000 −0.350285
816816 0 0
817817 45.4500 1.59009
818818 17.5778 0.614593
819819 0 0
820820 −22.1194 −0.772444
821821 −17.0917 −0.596504 −0.298252 0.954487i 0.596403π-0.596403\pi
−0.298252 + 0.954487i 0.596403π0.596403\pi
822822 0 0
823823 −11.1833 −0.389827 −0.194913 0.980820i 0.562443π-0.562443\pi
−0.194913 + 0.980820i 0.562443π0.562443\pi
824824 26.4500 0.921428
825825 0 0
826826 4.18335 0.145557
827827 −16.3944 −0.570091 −0.285045 0.958514i 0.592009π-0.592009\pi
−0.285045 + 0.958514i 0.592009π0.592009\pi
828828 0 0
829829 −30.2389 −1.05024 −0.525119 0.851029i 0.675979π-0.675979\pi
−0.525119 + 0.851029i 0.675979π0.675979\pi
830830 −33.9083 −1.17698
831831 0 0
832832 −46.2111 −1.60208
833833 28.1194 0.974280
834834 0 0
835835 −18.9083 −0.654350
836836 47.9361 1.65790
837837 0 0
838838 −11.5778 −0.399948
839839 14.5778 0.503281 0.251641 0.967821i 0.419030π-0.419030\pi
0.251641 + 0.967821i 0.419030π0.419030\pi
840840 0 0
841841 28.8444 0.994635
842842 −20.0278 −0.690202
843843 0 0
844844 −7.21110 −0.248216
845845 0 0
846846 0 0
847847 −7.42221 −0.255030
848848 2.57779 0.0885218
849849 0 0
850850 12.2111 0.418837
851851 23.7250 0.813282
852852 0 0
853853 −13.6972 −0.468984 −0.234492 0.972118i 0.575343π-0.575343\pi
−0.234492 + 0.972118i 0.575343π0.575343\pi
854854 −1.81665 −0.0621646
855855 0 0
856856 −6.27502 −0.214476
857857 13.6056 0.464757 0.232378 0.972625i 0.425349π-0.425349\pi
0.232378 + 0.972625i 0.425349π0.425349\pi
858858 0 0
859859 −5.39445 −0.184056 −0.0920281 0.995756i 0.529335π-0.529335\pi
−0.0920281 + 0.995756i 0.529335π0.529335\pi
860860 −23.8167 −0.812141
861861 0 0
862862 −93.9916 −3.20137
863863 39.2111 1.33476 0.667381 0.744717i 0.267415π-0.267415\pi
0.667381 + 0.744717i 0.267415π0.267415\pi
864864 0 0
865865 −1.18335 −0.0402350
866866 41.5139 1.41070
867867 0 0
868868 22.4222 0.761059
869869 28.8167 0.977538
870870 0 0
871871 37.1472 1.25868
872872 50.7250 1.71776
873873 0 0
874874 −43.5416 −1.47282
875875 1.30278 0.0440419
876876 0 0
877877 −12.7889 −0.431850 −0.215925 0.976410i 0.569277π-0.569277\pi
−0.215925 + 0.976410i 0.569277π0.569277\pi
878878 46.3305 1.56358
879879 0 0
880880 −0.697224 −0.0235034
881881 10.6056 0.357310 0.178655 0.983912i 0.442825π-0.442825\pi
0.178655 + 0.983912i 0.442825π0.442825\pi
882882 0 0
883883 17.0000 0.572096 0.286048 0.958215i 0.407658π-0.407658\pi
0.286048 + 0.958215i 0.407658π0.407658\pi
884884 −63.1472 −2.12387
885885 0 0
886886 −21.3583 −0.717546
887887 19.1833 0.644114 0.322057 0.946720i 0.395626π-0.395626\pi
0.322057 + 0.946720i 0.395626π0.395626\pi
888888 0 0
889889 0.788897 0.0264588
890890 −11.0917 −0.371794
891891 0 0
892892 69.0555 2.31215
893893 −42.2111 −1.41254
894894 0 0
895895 19.6056 0.655341
896896 24.6333 0.822941
897897 0 0
898898 90.2944 3.01316
899899 −39.6333 −1.32184
900900 0 0
901901 −45.1472 −1.50407
902902 −35.5139 −1.18248
903903 0 0
904904 18.6333 0.619735
905905 −7.90833 −0.262882
906906 0 0
907907 48.3944 1.60691 0.803456 0.595365i 0.202992π-0.202992\pi
0.803456 + 0.595365i 0.202992π0.202992\pi
908908 −25.1194 −0.833618
909909 0 0
910910 −10.8167 −0.358569
911911 −38.9361 −1.29001 −0.645005 0.764178i 0.723145π-0.723145\pi
−0.645005 + 0.764178i 0.723145π0.723145\pi
912912 0 0
913913 −33.9083 −1.12220
914914 −31.1194 −1.02934
915915 0 0
916916 46.9361 1.55081
917917 14.0917 0.465348
918918 0 0
919919 −37.2111 −1.22748 −0.613741 0.789508i 0.710336π-0.710336\pi
−0.613741 + 0.789508i 0.710336π0.710336\pi
920920 9.00000 0.296721
921921 0 0
922922 75.9916 2.50265
923923 −5.78890 −0.190544
924924 0 0
925925 −7.90833 −0.260024
926926 46.8167 1.53849
927927 0 0
928928 −40.3305 −1.32391
929929 −28.3305 −0.929495 −0.464747 0.885443i 0.653855π-0.653855\pi
−0.464747 + 0.885443i 0.653855π0.653855\pi
930930 0 0
931931 33.4222 1.09537
932932 75.3583 2.46844
933933 0 0
934934 72.1472 2.36073
935935 12.2111 0.399346
936936 0 0
937937 11.2111 0.366251 0.183125 0.983090i 0.441379π-0.441379\pi
0.183125 + 0.983090i 0.441379π0.441379\pi
938938 −30.9083 −1.00919
939939 0 0
940940 22.1194 0.721456
941941 25.7527 0.839515 0.419758 0.907636i 0.362115π-0.362115\pi
0.419758 + 0.907636i 0.362115π0.362115\pi
942942 0 0
943943 20.0917 0.654275
944944 −0.422205 −0.0137416
945945 0 0
946946 −38.2389 −1.24325
947947 34.8167 1.13139 0.565695 0.824615i 0.308608π-0.308608\pi
0.565695 + 0.824615i 0.308608π0.308608\pi
948948 0 0
949949 45.4500 1.47537
950950 14.5139 0.470892
951951 0 0
952952 20.7250 0.671700
953953 −35.0278 −1.13466 −0.567330 0.823490i 0.692024π-0.692024\pi
−0.567330 + 0.823490i 0.692024π0.692024\pi
954954 0 0
955955 −7.60555 −0.246110
956956 −66.1472 −2.13935
957957 0 0
958958 −33.9083 −1.09553
959959 −19.5416 −0.631032
960960 0 0
961961 −3.84441 −0.124013
962962 65.6611 2.11700
963963 0 0
964964 −7.90833 −0.254710
965965 5.00000 0.160956
966966 0 0
967967 −26.1833 −0.842000 −0.421000 0.907061i 0.638321π-0.638321\pi
−0.421000 + 0.907061i 0.638321π0.638321\pi
968968 17.0917 0.549347
969969 0 0
970970 36.2111 1.16267
971971 −57.3583 −1.84072 −0.920358 0.391078i 0.872102π-0.872102\pi
−0.920358 + 0.391078i 0.872102π0.872102\pi
972972 0 0
973973 14.3305 0.459416
974974 11.9361 0.382457
975975 0 0
976976 0.183346 0.00586877
977977 7.60555 0.243323 0.121662 0.992572i 0.461178π-0.461178\pi
0.121662 + 0.992572i 0.461178π0.461178\pi
978978 0 0
979979 −11.0917 −0.354491
980980 −17.5139 −0.559460
981981 0 0
982982 56.8722 1.81486
983983 −28.8167 −0.919109 −0.459554 0.888150i 0.651991π-0.651991\pi
−0.459554 + 0.888150i 0.651991π0.651991\pi
984984 0 0
985985 −20.7250 −0.660353
986986 −92.8722 −2.95765
987987 0 0
988988 −75.0555 −2.38783
989989 21.6333 0.687899
990990 0 0
991991 20.0000 0.635321 0.317660 0.948205i 0.397103π-0.397103\pi
0.317660 + 0.948205i 0.397103π0.397103\pi
992992 27.6333 0.877358
993993 0 0
994994 4.81665 0.152775
995995 23.4222 0.742534
996996 0 0
997997 −42.7889 −1.35514 −0.677569 0.735459i 0.736966π-0.736966\pi
−0.677569 + 0.735459i 0.736966π0.736966\pi
998998 −4.11943 −0.130398
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 1215.2.a.k.1.1 2
3.2 odd 2 1215.2.a.m.1.2 yes 2
5.4 even 2 6075.2.a.bo.1.2 2
9.2 odd 6 1215.2.e.l.811.1 4
9.4 even 3 1215.2.e.n.406.2 4
9.5 odd 6 1215.2.e.l.406.1 4
9.7 even 3 1215.2.e.n.811.2 4
15.14 odd 2 6075.2.a.bk.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1215.2.a.k.1.1 2 1.1 even 1 trivial
1215.2.a.m.1.2 yes 2 3.2 odd 2
1215.2.e.l.406.1 4 9.5 odd 6
1215.2.e.l.811.1 4 9.2 odd 6
1215.2.e.n.406.2 4 9.4 even 3
1215.2.e.n.811.2 4 9.7 even 3
6075.2.a.bk.1.1 2 15.14 odd 2
6075.2.a.bo.1.2 2 5.4 even 2