Properties

Label 99.2.d.a.98.3
Level 9999
Weight 22
Character 99.98
Analytic conductor 0.7910.791
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,2,Mod(98,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.98");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 99=3211 99 = 3^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 99.d (of order 22, degree 11, minimal)

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: no
Analytic conductor: 0.7905189800110.790518980011
Analytic rank: 00
Dimension: 44
Coefficient field: Q(2,3)\Q(\sqrt{-2}, \sqrt{3})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+4x2+1 x^{4} + 4x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 98.3
Root 1.93185i-1.93185i of defining polynomial
Character χ\chi == 99.98
Dual form 99.2.d.a.98.4

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+1.73205q2+1.00000q41.41421iq5+2.44949iq71.73205q82.44949iq10+(1.732052.82843i)q11+4.89898iq13+4.24264iq145.00000q167.34847iq191.41421iq20+(3.000004.89898i)q22+2.82843iq23+3.00000q25+8.48528iq26+2.44949iq28+6.92820q294.00000q315.19615q32+3.46410q35+8.00000q3712.7279iq38+2.44949iq406.92820q41+2.44949iq43+(1.732052.82843i)q44+4.89898iq46+2.82843iq47+1.00000q49+5.19615q50+4.89898iq529.89949iq53+(4.00000+2.44949i)q554.24264iq56+12.0000q58+11.3137iq594.89898iq616.92820q62+1.00000q64+6.92820q654.00000q67+6.00000q70+2.82843iq71+13.8564q747.34847iq76+(6.928204.24264i)q7712.2474iq79+7.07107iq8012.0000q8213.8564q83+4.24264iq86+(3.00000+4.89898i)q88+7.07107iq8912.0000q91+2.82843iq92+4.89898iq9410.3923q9510.0000q97+1.73205q98+O(q100)q+1.73205 q^{2} +1.00000 q^{4} -1.41421i q^{5} +2.44949i q^{7} -1.73205 q^{8} -2.44949i q^{10} +(-1.73205 - 2.82843i) q^{11} +4.89898i q^{13} +4.24264i q^{14} -5.00000 q^{16} -7.34847i q^{19} -1.41421i q^{20} +(-3.00000 - 4.89898i) q^{22} +2.82843i q^{23} +3.00000 q^{25} +8.48528i q^{26} +2.44949i q^{28} +6.92820 q^{29} -4.00000 q^{31} -5.19615 q^{32} +3.46410 q^{35} +8.00000 q^{37} -12.7279i q^{38} +2.44949i q^{40} -6.92820 q^{41} +2.44949i q^{43} +(-1.73205 - 2.82843i) q^{44} +4.89898i q^{46} +2.82843i q^{47} +1.00000 q^{49} +5.19615 q^{50} +4.89898i q^{52} -9.89949i q^{53} +(-4.00000 + 2.44949i) q^{55} -4.24264i q^{56} +12.0000 q^{58} +11.3137i q^{59} -4.89898i q^{61} -6.92820 q^{62} +1.00000 q^{64} +6.92820 q^{65} -4.00000 q^{67} +6.00000 q^{70} +2.82843i q^{71} +13.8564 q^{74} -7.34847i q^{76} +(6.92820 - 4.24264i) q^{77} -12.2474i q^{79} +7.07107i q^{80} -12.0000 q^{82} -13.8564 q^{83} +4.24264i q^{86} +(3.00000 + 4.89898i) q^{88} +7.07107i q^{89} -12.0000 q^{91} +2.82843i q^{92} +4.89898i q^{94} -10.3923 q^{95} -10.0000 q^{97} +1.73205 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q420q1612q22+12q2516q31+32q37+4q4916q55+48q58+4q6416q67+24q7048q82+12q8848q9140q97+O(q100) 4 q + 4 q^{4} - 20 q^{16} - 12 q^{22} + 12 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{49} - 16 q^{55} + 48 q^{58} + 4 q^{64} - 16 q^{67} + 24 q^{70} - 48 q^{82} + 12 q^{88} - 48 q^{91} - 40 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/99Z)×\left(\mathbb{Z}/99\mathbb{Z}\right)^\times.

nn 4646 5656
χ(n)\chi(n) 1-1 1-1

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 1.73205 1.22474 0.612372 0.790569i 0.290215π-0.290215\pi
0.612372 + 0.790569i 0.290215π0.290215\pi
33 0 0
44 1.00000 0.500000
55 1.41421i 0.632456i −0.948683 0.316228i 0.897584π-0.897584\pi
0.948683 0.316228i 0.102416π-0.102416\pi
66 0 0
77 2.44949i 0.925820i 0.886405 + 0.462910i 0.153195π0.153195\pi
−0.886405 + 0.462910i 0.846805π0.846805\pi
88 −1.73205 −0.612372
99 0 0
1010 2.44949i 0.774597i
1111 −1.73205 2.82843i −0.522233 0.852803i
1212 0 0
1313 4.89898i 1.35873i 0.733799 + 0.679366i 0.237745π0.237745\pi
−0.733799 + 0.679366i 0.762255π0.762255\pi
1414 4.24264i 1.13389i
1515 0 0
1616 −5.00000 −1.25000
1717 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1818 0 0
1919 7.34847i 1.68585i −0.538028 0.842927i 0.680830π-0.680830\pi
0.538028 0.842927i 0.319170π-0.319170\pi
2020 1.41421i 0.316228i
2121 0 0
2222 −3.00000 4.89898i −0.639602 1.04447i
2323 2.82843i 0.589768i 0.955533 + 0.294884i 0.0952810π0.0952810\pi
−0.955533 + 0.294884i 0.904719π0.904719\pi
2424 0 0
2525 3.00000 0.600000
2626 8.48528i 1.66410i
2727 0 0
2828 2.44949i 0.462910i
2929 6.92820 1.28654 0.643268 0.765641i 0.277578π-0.277578\pi
0.643268 + 0.765641i 0.277578π0.277578\pi
3030 0 0
3131 −4.00000 −0.718421 −0.359211 0.933257i 0.616954π-0.616954\pi
−0.359211 + 0.933257i 0.616954π0.616954\pi
3232 −5.19615 −0.918559
3333 0 0
3434 0 0
3535 3.46410 0.585540
3636 0 0
3737 8.00000 1.31519 0.657596 0.753371i 0.271573π-0.271573\pi
0.657596 + 0.753371i 0.271573π0.271573\pi
3838 12.7279i 2.06474i
3939 0 0
4040 2.44949i 0.387298i
4141 −6.92820 −1.08200 −0.541002 0.841021i 0.681955π-0.681955\pi
−0.541002 + 0.841021i 0.681955π0.681955\pi
4242 0 0
4343 2.44949i 0.373544i 0.982403 + 0.186772i 0.0598025π0.0598025\pi
−0.982403 + 0.186772i 0.940197π0.940197\pi
4444 −1.73205 2.82843i −0.261116 0.426401i
4545 0 0
4646 4.89898i 0.722315i
4747 2.82843i 0.412568i 0.978492 + 0.206284i 0.0661372π0.0661372\pi
−0.978492 + 0.206284i 0.933863π0.933863\pi
4848 0 0
4949 1.00000 0.142857
5050 5.19615 0.734847
5151 0 0
5252 4.89898i 0.679366i
5353 9.89949i 1.35980i −0.733305 0.679900i 0.762023π-0.762023\pi
0.733305 0.679900i 0.237977π-0.237977\pi
5454 0 0
5555 −4.00000 + 2.44949i −0.539360 + 0.330289i
5656 4.24264i 0.566947i
5757 0 0
5858 12.0000 1.57568
5959 11.3137i 1.47292i 0.676481 + 0.736460i 0.263504π0.263504\pi
−0.676481 + 0.736460i 0.736496π0.736496\pi
6060 0 0
6161 4.89898i 0.627250i −0.949547 0.313625i 0.898457π-0.898457\pi
0.949547 0.313625i 0.101543π-0.101543\pi
6262 −6.92820 −0.879883
6363 0 0
6464 1.00000 0.125000
6565 6.92820 0.859338
6666 0 0
6767 −4.00000 −0.488678 −0.244339 0.969690i 0.578571π-0.578571\pi
−0.244339 + 0.969690i 0.578571π0.578571\pi
6868 0 0
6969 0 0
7070 6.00000 0.717137
7171 2.82843i 0.335673i 0.985815 + 0.167836i 0.0536780π0.0536780\pi
−0.985815 + 0.167836i 0.946322π0.946322\pi
7272 0 0
7373 0 0 1.00000 00
−1.00000 π\pi
7474 13.8564 1.61077
7575 0 0
7676 7.34847i 0.842927i
7777 6.92820 4.24264i 0.789542 0.483494i
7878 0 0
7979 12.2474i 1.37795i −0.724787 0.688973i 0.758062π-0.758062\pi
0.724787 0.688973i 0.241938π-0.241938\pi
8080 7.07107i 0.790569i
8181 0 0
8282 −12.0000 −1.32518
8383 −13.8564 −1.52094 −0.760469 0.649374i 0.775031π-0.775031\pi
−0.760469 + 0.649374i 0.775031π0.775031\pi
8484 0 0
8585 0 0
8686 4.24264i 0.457496i
8787 0 0
8888 3.00000 + 4.89898i 0.319801 + 0.522233i
8989 7.07107i 0.749532i 0.927119 + 0.374766i 0.122277π0.122277\pi
−0.927119 + 0.374766i 0.877723π0.877723\pi
9090 0 0
9191 −12.0000 −1.25794
9292 2.82843i 0.294884i
9393 0 0
9494 4.89898i 0.505291i
9595 −10.3923 −1.06623
9696 0 0
9797 −10.0000 −1.01535 −0.507673 0.861550i 0.669494π-0.669494\pi
−0.507673 + 0.861550i 0.669494π0.669494\pi
9898 1.73205 0.174964
9999 0 0
100100 3.00000 0.300000
101101 −13.8564 −1.37876 −0.689382 0.724398i 0.742118π-0.742118\pi
−0.689382 + 0.724398i 0.742118π0.742118\pi
102102 0 0
103103 −4.00000 −0.394132 −0.197066 0.980390i 0.563141π-0.563141\pi
−0.197066 + 0.980390i 0.563141π0.563141\pi
104104 8.48528i 0.832050i
105105 0 0
106106 17.1464i 1.66541i
107107 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
108108 0 0
109109 14.6969i 1.40771i 0.710343 + 0.703856i 0.248540π0.248540\pi
−0.710343 + 0.703856i 0.751460π0.751460\pi
110110 −6.92820 + 4.24264i −0.660578 + 0.404520i
111111 0 0
112112 12.2474i 1.15728i
113113 1.41421i 0.133038i −0.997785 0.0665190i 0.978811π-0.978811\pi
0.997785 0.0665190i 0.0211893π-0.0211893\pi
114114 0 0
115115 4.00000 0.373002
116116 6.92820 0.643268
117117 0 0
118118 19.5959i 1.80395i
119119 0 0
120120 0 0
121121 −5.00000 + 9.79796i −0.454545 + 0.890724i
122122 8.48528i 0.768221i
123123 0 0
124124 −4.00000 −0.359211
125125 11.3137i 1.01193i
126126 0 0
127127 7.34847i 0.652071i −0.945357 0.326036i 0.894287π-0.894287\pi
0.945357 0.326036i 0.105713π-0.105713\pi
128128 12.1244 1.07165
129129 0 0
130130 12.0000 1.05247
131131 3.46410 0.302660 0.151330 0.988483i 0.451644π-0.451644\pi
0.151330 + 0.988483i 0.451644π0.451644\pi
132132 0 0
133133 18.0000 1.56080
134134 −6.92820 −0.598506
135135 0 0
136136 0 0
137137 15.5563i 1.32907i 0.747258 + 0.664534i 0.231370π0.231370\pi
−0.747258 + 0.664534i 0.768630π0.768630\pi
138138 0 0
139139 2.44949i 0.207763i −0.994590 0.103882i 0.966874π-0.966874\pi
0.994590 0.103882i 0.0331263π-0.0331263\pi
140140 3.46410 0.292770
141141 0 0
142142 4.89898i 0.411113i
143143 13.8564 8.48528i 1.15873 0.709575i
144144 0 0
145145 9.79796i 0.813676i
146146 0 0
147147 0 0
148148 8.00000 0.657596
149149 13.8564 1.13516 0.567581 0.823318i 0.307880π-0.307880\pi
0.567581 + 0.823318i 0.307880π0.307880\pi
150150 0 0
151151 2.44949i 0.199337i 0.995021 + 0.0996683i 0.0317782π0.0317782\pi
−0.995021 + 0.0996683i 0.968222π0.968222\pi
152152 12.7279i 1.03237i
153153 0 0
154154 12.0000 7.34847i 0.966988 0.592157i
155155 5.65685i 0.454369i
156156 0 0
157157 14.0000 1.11732 0.558661 0.829396i 0.311315π-0.311315\pi
0.558661 + 0.829396i 0.311315π0.311315\pi
158158 21.2132i 1.68763i
159159 0 0
160160 7.34847i 0.580948i
161161 −6.92820 −0.546019
162162 0 0
163163 8.00000 0.626608 0.313304 0.949653i 0.398564π-0.398564\pi
0.313304 + 0.949653i 0.398564π0.398564\pi
164164 −6.92820 −0.541002
165165 0 0
166166 −24.0000 −1.86276
167167 3.46410 0.268060 0.134030 0.990977i 0.457208π-0.457208\pi
0.134030 + 0.990977i 0.457208π0.457208\pi
168168 0 0
169169 −11.0000 −0.846154
170170 0 0
171171 0 0
172172 2.44949i 0.186772i
173173 6.92820 0.526742 0.263371 0.964695i 0.415166π-0.415166\pi
0.263371 + 0.964695i 0.415166π0.415166\pi
174174 0 0
175175 7.34847i 0.555492i
176176 8.66025 + 14.1421i 0.652791 + 1.06600i
177177 0 0
178178 12.2474i 0.917985i
179179 22.6274i 1.69125i −0.533775 0.845626i 0.679227π-0.679227\pi
0.533775 0.845626i 0.320773π-0.320773\pi
180180 0 0
181181 8.00000 0.594635 0.297318 0.954779i 0.403908π-0.403908\pi
0.297318 + 0.954779i 0.403908π0.403908\pi
182182 −20.7846 −1.54066
183183 0 0
184184 4.89898i 0.361158i
185185 11.3137i 0.831800i
186186 0 0
187187 0 0
188188 2.82843i 0.206284i
189189 0 0
190190 −18.0000 −1.30586
191191 2.82843i 0.204658i 0.994751 + 0.102329i 0.0326294π0.0326294\pi
−0.994751 + 0.102329i 0.967371π0.967371\pi
192192 0 0
193193 9.79796i 0.705273i −0.935760 0.352636i 0.885285π-0.885285\pi
0.935760 0.352636i 0.114715π-0.114715\pi
194194 −17.3205 −1.24354
195195 0 0
196196 1.00000 0.0714286
197197 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
198198 0 0
199199 8.00000 0.567105 0.283552 0.958957i 0.408487π-0.408487\pi
0.283552 + 0.958957i 0.408487π0.408487\pi
200200 −5.19615 −0.367423
201201 0 0
202202 −24.0000 −1.68863
203203 16.9706i 1.19110i
204204 0 0
205205 9.79796i 0.684319i
206206 −6.92820 −0.482711
207207 0 0
208208 24.4949i 1.69842i
209209 −20.7846 + 12.7279i −1.43770 + 0.880409i
210210 0 0
211211 12.2474i 0.843149i 0.906794 + 0.421575i 0.138522π0.138522\pi
−0.906794 + 0.421575i 0.861478π0.861478\pi
212212 9.89949i 0.679900i
213213 0 0
214214 0 0
215215 3.46410 0.236250
216216 0 0
217217 9.79796i 0.665129i
218218 25.4558i 1.72409i
219219 0 0
220220 −4.00000 + 2.44949i −0.269680 + 0.165145i
221221 0 0
222222 0 0
223223 −16.0000 −1.07144 −0.535720 0.844396i 0.679960π-0.679960\pi
−0.535720 + 0.844396i 0.679960π0.679960\pi
224224 12.7279i 0.850420i
225225 0 0
226226 2.44949i 0.162938i
227227 27.7128 1.83936 0.919682 0.392664i 0.128446π-0.128446\pi
0.919682 + 0.392664i 0.128446π0.128446\pi
228228 0 0
229229 −10.0000 −0.660819 −0.330409 0.943838i 0.607187π-0.607187\pi
−0.330409 + 0.943838i 0.607187π0.607187\pi
230230 6.92820 0.456832
231231 0 0
232232 −12.0000 −0.787839
233233 20.7846 1.36165 0.680823 0.732448i 0.261622π-0.261622\pi
0.680823 + 0.732448i 0.261622π0.261622\pi
234234 0 0
235235 4.00000 0.260931
236236 11.3137i 0.736460i
237237 0 0
238238 0 0
239239 −17.3205 −1.12037 −0.560185 0.828367i 0.689270π-0.689270\pi
−0.560185 + 0.828367i 0.689270π0.689270\pi
240240 0 0
241241 19.5959i 1.26228i −0.775667 0.631142i 0.782587π-0.782587\pi
0.775667 0.631142i 0.217413π-0.217413\pi
242242 −8.66025 + 16.9706i −0.556702 + 1.09091i
243243 0 0
244244 4.89898i 0.313625i
245245 1.41421i 0.0903508i
246246 0 0
247247 36.0000 2.29063
248248 6.92820 0.439941
249249 0 0
250250 19.5959i 1.23935i
251251 5.65685i 0.357057i −0.983935 0.178529i 0.942866π-0.942866\pi
0.983935 0.178529i 0.0571337π-0.0571337\pi
252252 0 0
253253 8.00000 4.89898i 0.502956 0.307996i
254254 12.7279i 0.798621i
255255 0 0
256256 19.0000 1.18750
257257 9.89949i 0.617514i −0.951141 0.308757i 0.900087π-0.900087\pi
0.951141 0.308757i 0.0999129π-0.0999129\pi
258258 0 0
259259 19.5959i 1.21763i
260260 6.92820 0.429669
261261 0 0
262262 6.00000 0.370681
263263 −3.46410 −0.213606 −0.106803 0.994280i 0.534061π-0.534061\pi
−0.106803 + 0.994280i 0.534061π0.534061\pi
264264 0 0
265265 −14.0000 −0.860013
266266 31.1769 1.91158
267267 0 0
268268 −4.00000 −0.244339
269269 15.5563i 0.948487i 0.880394 + 0.474244i 0.157278π0.157278\pi
−0.880394 + 0.474244i 0.842722π0.842722\pi
270270 0 0
271271 7.34847i 0.446388i 0.974774 + 0.223194i 0.0716483π0.0716483\pi
−0.974774 + 0.223194i 0.928352π0.928352\pi
272272 0 0
273273 0 0
274274 26.9444i 1.62777i
275275 −5.19615 8.48528i −0.313340 0.511682i
276276 0 0
277277 24.4949i 1.47176i 0.677114 + 0.735878i 0.263230π0.263230\pi
−0.677114 + 0.735878i 0.736770π0.736770\pi
278278 4.24264i 0.254457i
279279 0 0
280280 −6.00000 −0.358569
281281 −13.8564 −0.826604 −0.413302 0.910594i 0.635625π-0.635625\pi
−0.413302 + 0.910594i 0.635625π0.635625\pi
282282 0 0
283283 2.44949i 0.145607i −0.997346 0.0728035i 0.976805π-0.976805\pi
0.997346 0.0728035i 0.0231946π-0.0231946\pi
284284 2.82843i 0.167836i
285285 0 0
286286 24.0000 14.6969i 1.41915 0.869048i
287287 16.9706i 1.00174i
288288 0 0
289289 −17.0000 −1.00000
290290 16.9706i 0.996546i
291291 0 0
292292 0 0
293293 −6.92820 −0.404750 −0.202375 0.979308i 0.564866π-0.564866\pi
−0.202375 + 0.979308i 0.564866π0.564866\pi
294294 0 0
295295 16.0000 0.931556
296296 −13.8564 −0.805387
297297 0 0
298298 24.0000 1.39028
299299 −13.8564 −0.801337
300300 0 0
301301 −6.00000 −0.345834
302302 4.24264i 0.244137i
303303 0 0
304304 36.7423i 2.10732i
305305 −6.92820 −0.396708
306306 0 0
307307 7.34847i 0.419399i −0.977766 0.209700i 0.932751π-0.932751\pi
0.977766 0.209700i 0.0672486π-0.0672486\pi
308308 6.92820 4.24264i 0.394771 0.241747i
309309 0 0
310310 9.79796i 0.556487i
311311 14.1421i 0.801927i −0.916094 0.400963i 0.868675π-0.868675\pi
0.916094 0.400963i 0.131325π-0.131325\pi
312312 0 0
313313 −16.0000 −0.904373 −0.452187 0.891923i 0.649356π-0.649356\pi
−0.452187 + 0.891923i 0.649356π0.649356\pi
314314 24.2487 1.36843
315315 0 0
316316 12.2474i 0.688973i
317317 18.3848i 1.03259i −0.856410 0.516296i 0.827310π-0.827310\pi
0.856410 0.516296i 0.172690π-0.172690\pi
318318 0 0
319319 −12.0000 19.5959i −0.671871 1.09716i
320320 1.41421i 0.0790569i
321321 0 0
322322 −12.0000 −0.668734
323323 0 0
324324 0 0
325325 14.6969i 0.815239i
326326 13.8564 0.767435
327327 0 0
328328 12.0000 0.662589
329329 −6.92820 −0.381964
330330 0 0
331331 8.00000 0.439720 0.219860 0.975531i 0.429440π-0.429440\pi
0.219860 + 0.975531i 0.429440π0.429440\pi
332332 −13.8564 −0.760469
333333 0 0
334334 6.00000 0.328305
335335 5.65685i 0.309067i
336336 0 0
337337 9.79796i 0.533729i −0.963734 0.266864i 0.914012π-0.914012\pi
0.963734 0.266864i 0.0859876π-0.0859876\pi
338338 −19.0526 −1.03632
339339 0 0
340340 0 0
341341 6.92820 + 11.3137i 0.375183 + 0.612672i
342342 0 0
343343 19.5959i 1.05808i
344344 4.24264i 0.228748i
345345 0 0
346346 12.0000 0.645124
347347 13.8564 0.743851 0.371925 0.928263i 0.378698π-0.378698\pi
0.371925 + 0.928263i 0.378698π0.378698\pi
348348 0 0
349349 4.89898i 0.262236i −0.991367 0.131118i 0.958143π-0.958143\pi
0.991367 0.131118i 0.0418567π-0.0418567\pi
350350 12.7279i 0.680336i
351351 0 0
352352 9.00000 + 14.6969i 0.479702 + 0.783349i
353353 32.5269i 1.73123i 0.500708 + 0.865616i 0.333073π0.333073\pi
−0.500708 + 0.865616i 0.666927π0.666927\pi
354354 0 0
355355 4.00000 0.212298
356356 7.07107i 0.374766i
357357 0 0
358358 39.1918i 2.07135i
359359 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
360360 0 0
361361 −35.0000 −1.84211
362362 13.8564 0.728277
363363 0 0
364364 −12.0000 −0.628971
365365 0 0
366366 0 0
367367 8.00000 0.417597 0.208798 0.977959i 0.433045π-0.433045\pi
0.208798 + 0.977959i 0.433045π0.433045\pi
368368 14.1421i 0.737210i
369369 0 0
370370 19.5959i 1.01874i
371371 24.2487 1.25893
372372 0 0
373373 24.4949i 1.26830i −0.773211 0.634149i 0.781351π-0.781351\pi
0.773211 0.634149i 0.218649π-0.218649\pi
374374 0 0
375375 0 0
376376 4.89898i 0.252646i
377377 33.9411i 1.74806i
378378 0 0
379379 −16.0000 −0.821865 −0.410932 0.911666i 0.634797π-0.634797\pi
−0.410932 + 0.911666i 0.634797π0.634797\pi
380380 −10.3923 −0.533114
381381 0 0
382382 4.89898i 0.250654i
383383 36.7696i 1.87884i 0.342773 + 0.939418i 0.388634π0.388634\pi
−0.342773 + 0.939418i 0.611366π0.611366\pi
384384 0 0
385385 −6.00000 9.79796i −0.305788 0.499350i
386386 16.9706i 0.863779i
387387 0 0
388388 −10.0000 −0.507673
389389 9.89949i 0.501924i −0.967997 0.250962i 0.919253π-0.919253\pi
0.967997 0.250962i 0.0807470π-0.0807470\pi
390390 0 0
391391 0 0
392392 −1.73205 −0.0874818
393393 0 0
394394 0 0
395395 −17.3205 −0.871489
396396 0 0
397397 8.00000 0.401508 0.200754 0.979642i 0.435661π-0.435661\pi
0.200754 + 0.979642i 0.435661π0.435661\pi
398398 13.8564 0.694559
399399 0 0
400400 −15.0000 −0.750000
401401 1.41421i 0.0706225i −0.999376 0.0353112i 0.988758π-0.988758\pi
0.999376 0.0353112i 0.0112422π-0.0112422\pi
402402 0 0
403403 19.5959i 0.976142i
404404 −13.8564 −0.689382
405405 0 0
406406 29.3939i 1.45879i
407407 −13.8564 22.6274i −0.686837 1.12160i
408408 0 0
409409 39.1918i 1.93791i −0.247234 0.968956i 0.579522π-0.579522\pi
0.247234 0.968956i 0.420478π-0.420478\pi
410410 16.9706i 0.838116i
411411 0 0
412412 −4.00000 −0.197066
413413 −27.7128 −1.36366
414414 0 0
415415 19.5959i 0.961926i
416416 25.4558i 1.24808i
417417 0 0
418418 −36.0000 + 22.0454i −1.76082 + 1.07828i
419419 11.3137i 0.552711i 0.961056 + 0.276355i 0.0891267π0.0891267\pi
−0.961056 + 0.276355i 0.910873π0.910873\pi
420420 0 0
421421 8.00000 0.389896 0.194948 0.980814i 0.437546π-0.437546\pi
0.194948 + 0.980814i 0.437546π0.437546\pi
422422 21.2132i 1.03264i
423423 0 0
424424 17.1464i 0.832704i
425425 0 0
426426 0 0
427427 12.0000 0.580721
428428 0 0
429429 0 0
430430 6.00000 0.289346
431431 10.3923 0.500580 0.250290 0.968171i 0.419474π-0.419474\pi
0.250290 + 0.968171i 0.419474π0.419474\pi
432432 0 0
433433 −16.0000 −0.768911 −0.384455 0.923144i 0.625611π-0.625611\pi
−0.384455 + 0.923144i 0.625611π0.625611\pi
434434 16.9706i 0.814613i
435435 0 0
436436 14.6969i 0.703856i
437437 20.7846 0.994263
438438 0 0
439439 2.44949i 0.116908i 0.998290 + 0.0584539i 0.0186171π0.0186171\pi
−0.998290 + 0.0584539i 0.981383π0.981383\pi
440440 6.92820 4.24264i 0.330289 0.202260i
441441 0 0
442442 0 0
443443 22.6274i 1.07506i −0.843244 0.537531i 0.819357π-0.819357\pi
0.843244 0.537531i 0.180643π-0.180643\pi
444444 0 0
445445 10.0000 0.474045
446446 −27.7128 −1.31224
447447 0 0
448448 2.44949i 0.115728i
449449 9.89949i 0.467186i −0.972334 0.233593i 0.924952π-0.924952\pi
0.972334 0.233593i 0.0750483π-0.0750483\pi
450450 0 0
451451 12.0000 + 19.5959i 0.565058 + 0.922736i
452452 1.41421i 0.0665190i
453453 0 0
454454 48.0000 2.25275
455455 16.9706i 0.795592i
456456 0 0
457457 9.79796i 0.458329i 0.973388 + 0.229165i 0.0735994π0.0735994\pi
−0.973388 + 0.229165i 0.926401π0.926401\pi
458458 −17.3205 −0.809334
459459 0 0
460460 4.00000 0.186501
461461 6.92820 0.322679 0.161339 0.986899i 0.448419π-0.448419\pi
0.161339 + 0.986899i 0.448419π0.448419\pi
462462 0 0
463463 −28.0000 −1.30127 −0.650635 0.759390i 0.725497π-0.725497\pi
−0.650635 + 0.759390i 0.725497π0.725497\pi
464464 −34.6410 −1.60817
465465 0 0
466466 36.0000 1.66767
467467 22.6274i 1.04707i −0.852004 0.523536i 0.824613π-0.824613\pi
0.852004 0.523536i 0.175387π-0.175387\pi
468468 0 0
469469 9.79796i 0.452428i
470470 6.92820 0.319574
471471 0 0
472472 19.5959i 0.901975i
473473 6.92820 4.24264i 0.318559 0.195077i
474474 0 0
475475 22.0454i 1.01151i
476476 0 0
477477 0 0
478478 −30.0000 −1.37217
479479 38.1051 1.74107 0.870534 0.492109i 0.163774π-0.163774\pi
0.870534 + 0.492109i 0.163774π0.163774\pi
480480 0 0
481481 39.1918i 1.78699i
482482 33.9411i 1.54598i
483483 0 0
484484 −5.00000 + 9.79796i −0.227273 + 0.445362i
485485 14.1421i 0.642161i
486486 0 0
487487 8.00000 0.362515 0.181257 0.983436i 0.441983π-0.441983\pi
0.181257 + 0.983436i 0.441983π0.441983\pi
488488 8.48528i 0.384111i
489489 0 0
490490 2.44949i 0.110657i
491491 −27.7128 −1.25066 −0.625331 0.780360i 0.715036π-0.715036\pi
−0.625331 + 0.780360i 0.715036π0.715036\pi
492492 0 0
493493 0 0
494494 62.3538 2.80543
495495 0 0
496496 20.0000 0.898027
497497 −6.92820 −0.310772
498498 0 0
499499 32.0000 1.43252 0.716258 0.697835i 0.245853π-0.245853\pi
0.716258 + 0.697835i 0.245853π0.245853\pi
500500 11.3137i 0.505964i
501501 0 0
502502 9.79796i 0.437304i
503503 31.1769 1.39011 0.695055 0.718957i 0.255380π-0.255380\pi
0.695055 + 0.718957i 0.255380π0.255380\pi
504504 0 0
505505 19.5959i 0.872007i
506506 13.8564 8.48528i 0.615992 0.377217i
507507 0 0
508508 7.34847i 0.326036i
509509 15.5563i 0.689523i 0.938690 + 0.344762i 0.112040π0.112040\pi
−0.938690 + 0.344762i 0.887960π0.887960\pi
510510 0 0
511511 0 0
512512 8.66025 0.382733
513513 0 0
514514 17.1464i 0.756297i
515515 5.65685i 0.249271i
516516 0 0
517517 8.00000 4.89898i 0.351840 0.215457i
518518 33.9411i 1.49129i
519519 0 0
520520 −12.0000 −0.526235
521521 15.5563i 0.681536i 0.940147 + 0.340768i 0.110687π0.110687\pi
−0.940147 + 0.340768i 0.889313π0.889313\pi
522522 0 0
523523 22.0454i 0.963978i −0.876177 0.481989i 0.839914π-0.839914\pi
0.876177 0.481989i 0.160086π-0.160086\pi
524524 3.46410 0.151330
525525 0 0
526526 −6.00000 −0.261612
527527 0 0
528528 0 0
529529 15.0000 0.652174
530530 −24.2487 −1.05330
531531 0 0
532532 18.0000 0.780399
533533 33.9411i 1.47015i
534534 0 0
535535 0 0
536536 6.92820 0.299253
537537 0 0
538538 26.9444i 1.16166i
539539 −1.73205 2.82843i −0.0746047 0.121829i
540540 0 0
541541 14.6969i 0.631871i −0.948781 0.315935i 0.897682π-0.897682\pi
0.948781 0.315935i 0.102318π-0.102318\pi
542542 12.7279i 0.546711i
543543 0 0
544544 0 0
545545 20.7846 0.890315
546546 0 0
547547 31.8434i 1.36152i 0.732505 + 0.680762i 0.238351π0.238351\pi
−0.732505 + 0.680762i 0.761649π0.761649\pi
548548 15.5563i 0.664534i
549549 0 0
550550 −9.00000 14.6969i −0.383761 0.626680i
551551 50.9117i 2.16891i
552552 0 0
553553 30.0000 1.27573
554554 42.4264i 1.80253i
555555 0 0
556556 2.44949i 0.103882i
557557 −20.7846 −0.880672 −0.440336 0.897833i 0.645141π-0.645141\pi
−0.440336 + 0.897833i 0.645141π0.645141\pi
558558 0 0
559559 −12.0000 −0.507546
560560 −17.3205 −0.731925
561561 0 0
562562 −24.0000 −1.01238
563563 −17.3205 −0.729972 −0.364986 0.931013i 0.618926π-0.618926\pi
−0.364986 + 0.931013i 0.618926π0.618926\pi
564564 0 0
565565 −2.00000 −0.0841406
566566 4.24264i 0.178331i
567567 0 0
568568 4.89898i 0.205557i
569569 −13.8564 −0.580891 −0.290445 0.956892i 0.593803π-0.593803\pi
−0.290445 + 0.956892i 0.593803π0.593803\pi
570570 0 0
571571 2.44949i 0.102508i −0.998686 0.0512540i 0.983678π-0.983678\pi
0.998686 0.0512540i 0.0163218π-0.0163218\pi
572572 13.8564 8.48528i 0.579365 0.354787i
573573 0 0
574574 29.3939i 1.22688i
575575 8.48528i 0.353861i
576576 0 0
577577 −10.0000 −0.416305 −0.208153 0.978096i 0.566745π-0.566745\pi
−0.208153 + 0.978096i 0.566745π0.566745\pi
578578 −29.4449 −1.22474
579579 0 0
580580 9.79796i 0.406838i
581581 33.9411i 1.40812i
582582 0 0
583583 −28.0000 + 17.1464i −1.15964 + 0.710132i
584584 0 0
585585 0 0
586586 −12.0000 −0.495715
587587 28.2843i 1.16742i 0.811963 + 0.583708i 0.198399π0.198399\pi
−0.811963 + 0.583708i 0.801601π0.801601\pi
588588 0 0
589589 29.3939i 1.21115i
590590 27.7128 1.14092
591591 0 0
592592 −40.0000 −1.64399
593593 −41.5692 −1.70704 −0.853522 0.521057i 0.825538π-0.825538\pi
−0.853522 + 0.521057i 0.825538π0.825538\pi
594594 0 0
595595 0 0
596596 13.8564 0.567581
597597 0 0
598598 −24.0000 −0.981433
599599 2.82843i 0.115566i 0.998329 + 0.0577832i 0.0184032π0.0184032\pi
−0.998329 + 0.0577832i 0.981597π0.981597\pi
600600 0 0
601601 19.5959i 0.799334i −0.916660 0.399667i 0.869126π-0.869126\pi
0.916660 0.399667i 0.130874π-0.130874\pi
602602 −10.3923 −0.423559
603603 0 0
604604 2.44949i 0.0996683i
605605 13.8564 + 7.07107i 0.563343 + 0.287480i
606606 0 0
607607 12.2474i 0.497109i 0.968618 + 0.248554i 0.0799554π0.0799554\pi
−0.968618 + 0.248554i 0.920045π0.920045\pi
608608 38.1838i 1.54856i
609609 0 0
610610 −12.0000 −0.485866
611611 −13.8564 −0.560570
612612 0 0
613613 14.6969i 0.593604i 0.954939 + 0.296802i 0.0959201π0.0959201\pi
−0.954939 + 0.296802i 0.904080π0.904080\pi
614614 12.7279i 0.513657i
615615 0 0
616616 −12.0000 + 7.34847i −0.483494 + 0.296078i
617617 26.8701i 1.08175i −0.841104 0.540874i 0.818094π-0.818094\pi
0.841104 0.540874i 0.181906π-0.181906\pi
618618 0 0
619619 −28.0000 −1.12542 −0.562708 0.826656i 0.690240π-0.690240\pi
−0.562708 + 0.826656i 0.690240π0.690240\pi
620620 5.65685i 0.227185i
621621 0 0
622622 24.4949i 0.982156i
623623 −17.3205 −0.693932
624624 0 0
625625 −1.00000 −0.0400000
626626 −27.7128 −1.10763
627627 0 0
628628 14.0000 0.558661
629629 0 0
630630 0 0
631631 44.0000 1.75161 0.875806 0.482663i 0.160330π-0.160330\pi
0.875806 + 0.482663i 0.160330π0.160330\pi
632632 21.2132i 0.843816i
633633 0 0
634634 31.8434i 1.26466i
635635 −10.3923 −0.412406
636636 0 0
637637 4.89898i 0.194105i
638638 −20.7846 33.9411i −0.822871 1.34374i
639639 0 0
640640 17.1464i 0.677772i
641641 32.5269i 1.28474i 0.766396 + 0.642368i 0.222048π0.222048\pi
−0.766396 + 0.642368i 0.777952π0.777952\pi
642642 0 0
643643 −28.0000 −1.10421 −0.552106 0.833774i 0.686176π-0.686176\pi
−0.552106 + 0.833774i 0.686176π0.686176\pi
644644 −6.92820 −0.273009
645645 0 0
646646 0 0
647647 19.7990i 0.778379i 0.921158 + 0.389189i 0.127245π0.127245\pi
−0.921158 + 0.389189i 0.872755π0.872755\pi
648648 0 0
649649 32.0000 19.5959i 1.25611 0.769207i
650650 25.4558i 0.998460i
651651 0 0
652652 8.00000 0.313304
653653 26.8701i 1.05151i −0.850637 0.525753i 0.823784π-0.823784\pi
0.850637 0.525753i 0.176216π-0.176216\pi
654654 0 0
655655 4.89898i 0.191419i
656656 34.6410 1.35250
657657 0 0
658658 −12.0000 −0.467809
659659 38.1051 1.48436 0.742182 0.670198i 0.233791π-0.233791\pi
0.742182 + 0.670198i 0.233791π0.233791\pi
660660 0 0
661661 −22.0000 −0.855701 −0.427850 0.903850i 0.640729π-0.640729\pi
−0.427850 + 0.903850i 0.640729π0.640729\pi
662662 13.8564 0.538545
663663 0 0
664664 24.0000 0.931381
665665 25.4558i 0.987135i
666666 0 0
667667 19.5959i 0.758757i
668668 3.46410 0.134030
669669 0 0
670670 9.79796i 0.378528i
671671 −13.8564 + 8.48528i −0.534921 + 0.327571i
672672 0 0
673673 39.1918i 1.51073i 0.655302 + 0.755367i 0.272541π0.272541\pi
−0.655302 + 0.755367i 0.727459π0.727459\pi
674674 16.9706i 0.653682i
675675 0 0
676676 −11.0000 −0.423077
677677 27.7128 1.06509 0.532545 0.846402i 0.321236π-0.321236\pi
0.532545 + 0.846402i 0.321236π0.321236\pi
678678 0 0
679679 24.4949i 0.940028i
680680 0 0
681681 0 0
682682 12.0000 + 19.5959i 0.459504 + 0.750366i
683683 28.2843i 1.08227i 0.840937 + 0.541134i 0.182005π0.182005\pi
−0.840937 + 0.541134i 0.817995π0.817995\pi
684684 0 0
685685 22.0000 0.840577
686686 33.9411i 1.29588i
687687 0 0
688688 12.2474i 0.466930i
689689 48.4974 1.84760
690690 0 0
691691 44.0000 1.67384 0.836919 0.547326i 0.184354π-0.184354\pi
0.836919 + 0.547326i 0.184354π0.184354\pi
692692 6.92820 0.263371
693693 0 0
694694 24.0000 0.911028
695695 −3.46410 −0.131401
696696 0 0
697697 0 0
698698 8.48528i 0.321173i
699699 0 0
700700 7.34847i 0.277746i
701701 20.7846 0.785024 0.392512 0.919747i 0.371606π-0.371606\pi
0.392512 + 0.919747i 0.371606π0.371606\pi
702702 0 0
703703 58.7878i 2.21722i
704704 −1.73205 2.82843i −0.0652791 0.106600i
705705 0 0
706706 56.3383i 2.12032i
707707 33.9411i 1.27649i
708708 0 0
709709 −10.0000 −0.375558 −0.187779 0.982211i 0.560129π-0.560129\pi
−0.187779 + 0.982211i 0.560129π0.560129\pi
710710 6.92820 0.260011
711711 0 0
712712 12.2474i 0.458993i
713713 11.3137i 0.423702i
714714 0 0
715715 −12.0000 19.5959i −0.448775 0.732846i
716716 22.6274i 0.845626i
717717 0 0
718718 0 0
719719 2.82843i 0.105483i 0.998608 + 0.0527413i 0.0167959π0.0167959\pi
−0.998608 + 0.0527413i 0.983204π0.983204\pi
720720 0 0
721721 9.79796i 0.364895i
722722 −60.6218 −2.25611
723723 0 0
724724 8.00000 0.297318
725725 20.7846 0.771921
726726 0 0
727727 8.00000 0.296704 0.148352 0.988935i 0.452603π-0.452603\pi
0.148352 + 0.988935i 0.452603π0.452603\pi
728728 20.7846 0.770329
729729 0 0
730730 0 0
731731 0 0
732732 0 0
733733 34.2929i 1.26664i 0.773892 + 0.633318i 0.218307π0.218307\pi
−0.773892 + 0.633318i 0.781693π0.781693\pi
734734 13.8564 0.511449
735735 0 0
736736 14.6969i 0.541736i
737737 6.92820 + 11.3137i 0.255204 + 0.416746i
738738 0 0
739739 7.34847i 0.270318i 0.990824 + 0.135159i 0.0431545π0.0431545\pi
−0.990824 + 0.135159i 0.956846π0.956846\pi
740740 11.3137i 0.415900i
741741 0 0
742742 42.0000 1.54187
743743 −27.7128 −1.01668 −0.508342 0.861155i 0.669742π-0.669742\pi
−0.508342 + 0.861155i 0.669742π0.669742\pi
744744 0 0
745745 19.5959i 0.717939i
746746 42.4264i 1.55334i
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −4.00000 −0.145962 −0.0729810 0.997333i 0.523251π-0.523251\pi
−0.0729810 + 0.997333i 0.523251π0.523251\pi
752752 14.1421i 0.515711i
753753 0 0
754754 58.7878i 2.14092i
755755 3.46410 0.126072
756756 0 0
757757 8.00000 0.290765 0.145382 0.989376i 0.453559π-0.453559\pi
0.145382 + 0.989376i 0.453559π0.453559\pi
758758 −27.7128 −1.00657
759759 0 0
760760 18.0000 0.652929
761761 13.8564 0.502294 0.251147 0.967949i 0.419192π-0.419192\pi
0.251147 + 0.967949i 0.419192π0.419192\pi
762762 0 0
763763 −36.0000 −1.30329
764764 2.82843i 0.102329i
765765 0 0
766766 63.6867i 2.30110i
767767 −55.4256 −2.00130
768768 0 0
769769 19.5959i 0.706647i 0.935501 + 0.353323i 0.114948π0.114948\pi
−0.935501 + 0.353323i 0.885052π0.885052\pi
770770 −10.3923 16.9706i −0.374513 0.611577i
771771 0 0
772772 9.79796i 0.352636i
773773 32.5269i 1.16991i 0.811065 + 0.584956i 0.198888π0.198888\pi
−0.811065 + 0.584956i 0.801112π0.801112\pi
774774 0 0
775775 −12.0000 −0.431053
776776 17.3205 0.621770
777777 0 0
778778 17.1464i 0.614729i
779779 50.9117i 1.82410i
780780 0 0
781781 8.00000 4.89898i 0.286263 0.175299i
782782 0 0
783783 0 0
784784 −5.00000 −0.178571
785785 19.7990i 0.706656i
786786 0 0
787787 12.2474i 0.436574i 0.975885 + 0.218287i 0.0700470π0.0700470\pi
−0.975885 + 0.218287i 0.929953π0.929953\pi
788788 0 0
789789 0 0
790790 −30.0000 −1.06735
791791 3.46410 0.123169
792792 0 0
793793 24.0000 0.852265
794794 13.8564 0.491745
795795 0 0
796796 8.00000 0.283552
797797 26.8701i 0.951786i −0.879503 0.475893i 0.842125π-0.842125\pi
0.879503 0.475893i 0.157875π-0.157875\pi
798798 0 0
799799 0 0
800800 −15.5885 −0.551135
801801 0 0
802802 2.44949i 0.0864945i
803803 0 0
804804 0 0
805805 9.79796i 0.345333i
806806 33.9411i 1.19553i
807807 0 0
808808 24.0000 0.844317
809809 −20.7846 −0.730748 −0.365374 0.930861i 0.619059π-0.619059\pi
−0.365374 + 0.930861i 0.619059π0.619059\pi
810810 0 0
811811 22.0454i 0.774119i −0.922055 0.387059i 0.873491π-0.873491\pi
0.922055 0.387059i 0.126509π-0.126509\pi
812812 16.9706i 0.595550i
813813 0 0
814814 −24.0000 39.1918i −0.841200 1.37367i
815815 11.3137i 0.396302i
816816 0 0
817817 18.0000 0.629740
818818 67.8823i 2.37345i
819819 0 0
820820 9.79796i 0.342160i
821821 −13.8564 −0.483592 −0.241796 0.970327i 0.577736π-0.577736\pi
−0.241796 + 0.970327i 0.577736π0.577736\pi
822822 0 0
823823 8.00000 0.278862 0.139431 0.990232i 0.455473π-0.455473\pi
0.139431 + 0.990232i 0.455473π0.455473\pi
824824 6.92820 0.241355
825825 0 0
826826 −48.0000 −1.67013
827827 41.5692 1.44550 0.722752 0.691108i 0.242877π-0.242877\pi
0.722752 + 0.691108i 0.242877π0.242877\pi
828828 0 0
829829 −46.0000 −1.59765 −0.798823 0.601566i 0.794544π-0.794544\pi
−0.798823 + 0.601566i 0.794544π0.794544\pi
830830 33.9411i 1.17811i
831831 0 0
832832 4.89898i 0.169842i
833833 0 0
834834 0 0
835835 4.89898i 0.169536i
836836 −20.7846 + 12.7279i −0.718851 + 0.440204i
837837 0 0
838838 19.5959i 0.676930i
839839 19.7990i 0.683537i 0.939784 + 0.341769i 0.111026π0.111026\pi
−0.939784 + 0.341769i 0.888974π0.888974\pi
840840 0 0
841841 19.0000 0.655172
842842 13.8564 0.477523
843843 0 0
844844 12.2474i 0.421575i
845845 15.5563i 0.535155i
846846 0 0
847847 −24.0000 12.2474i −0.824650 0.420827i
848848 49.4975i 1.69975i
849849 0 0
850850 0 0
851851 22.6274i 0.775658i
852852 0 0
853853 34.2929i 1.17417i −0.809527 0.587083i 0.800276π-0.800276\pi
0.809527 0.587083i 0.199724π-0.199724\pi
854854 20.7846 0.711235
855855 0 0
856856 0 0
857857 −34.6410 −1.18331 −0.591657 0.806190i 0.701526π-0.701526\pi
−0.591657 + 0.806190i 0.701526π0.701526\pi
858858 0 0
859859 −40.0000 −1.36478 −0.682391 0.730987i 0.739060π-0.739060\pi
−0.682391 + 0.730987i 0.739060π0.739060\pi
860860 3.46410 0.118125
861861 0 0
862862 18.0000 0.613082
863863 19.7990i 0.673965i 0.941511 + 0.336983i 0.109406π0.109406\pi
−0.941511 + 0.336983i 0.890594π0.890594\pi
864864 0 0
865865 9.79796i 0.333141i
866866 −27.7128 −0.941720
867867 0 0
868868 9.79796i 0.332564i
869869 −34.6410 + 21.2132i −1.17512 + 0.719609i
870870 0 0
871871 19.5959i 0.663982i
872872 25.4558i 0.862044i
873873 0 0
874874 36.0000 1.21772
875875 27.7128 0.936864
876876 0 0
877877 53.8888i 1.81969i −0.414943 0.909847i 0.636199π-0.636199\pi
0.414943 0.909847i 0.363801π-0.363801\pi
878878 4.24264i 0.143182i
879879 0 0
880880 20.0000 12.2474i 0.674200 0.412861i
881881 9.89949i 0.333522i −0.985997 0.166761i 0.946669π-0.946669\pi
0.985997 0.166761i 0.0533309π-0.0533309\pi
882882 0 0
883883 −28.0000 −0.942275 −0.471138 0.882060i 0.656156π-0.656156\pi
−0.471138 + 0.882060i 0.656156π0.656156\pi
884884 0 0
885885 0 0
886886 39.1918i 1.31668i
887887 55.4256 1.86101 0.930505 0.366279i 0.119368π-0.119368\pi
0.930505 + 0.366279i 0.119368π0.119368\pi
888888 0 0
889889 18.0000 0.603701
890890 17.3205 0.580585
891891 0 0
892892 −16.0000 −0.535720
893893 20.7846 0.695530
894894 0 0
895895 −32.0000 −1.06964
896896 29.6985i 0.992157i
897897 0 0
898898 17.1464i 0.572184i
899899 −27.7128 −0.924274
900900 0 0
901901 0 0
902902 20.7846 + 33.9411i 0.692052 + 1.13012i
903903 0 0
904904 2.44949i 0.0814688i
905905 11.3137i 0.376080i
906906 0 0
907907 −52.0000 −1.72663 −0.863316 0.504664i 0.831616π-0.831616\pi
−0.863316 + 0.504664i 0.831616π0.831616\pi
908908 27.7128 0.919682
909909 0 0
910910 29.3939i 0.974398i
911911 53.7401i 1.78049i 0.455483 + 0.890245i 0.349467π0.349467\pi
−0.455483 + 0.890245i 0.650533π0.650533\pi
912912 0 0
913913 24.0000 + 39.1918i 0.794284 + 1.29706i
914914 16.9706i 0.561336i
915915 0 0
916916 −10.0000 −0.330409
917917 8.48528i 0.280209i
918918 0 0
919919 36.7423i 1.21202i 0.795458 + 0.606009i 0.207230π0.207230\pi
−0.795458 + 0.606009i 0.792770π0.792770\pi
920920 −6.92820 −0.228416
921921 0 0
922922 12.0000 0.395199
923923 −13.8564 −0.456089
924924 0 0
925925 24.0000 0.789115
926926 −48.4974 −1.59372
927927 0 0
928928 −36.0000 −1.18176
929929 9.89949i 0.324792i −0.986726 0.162396i 0.948078π-0.948078\pi
0.986726 0.162396i 0.0519222π-0.0519222\pi
930930 0 0
931931 7.34847i 0.240836i
932932 20.7846 0.680823
933933 0 0
934934 39.1918i 1.28240i
935935 0 0
936936 0 0
937937 29.3939i 0.960256i 0.877198 + 0.480128i 0.159410π0.159410\pi
−0.877198 + 0.480128i 0.840590π0.840590\pi
938938 16.9706i 0.554109i
939939 0 0
940940 4.00000 0.130466
941941 −27.7128 −0.903412 −0.451706 0.892167i 0.649184π-0.649184\pi
−0.451706 + 0.892167i 0.649184π0.649184\pi
942942 0 0
943943 19.5959i 0.638131i
944944 56.5685i 1.84115i
945945 0 0
946946 12.0000 7.34847i 0.390154 0.238919i
947947 22.6274i 0.735292i −0.929966 0.367646i 0.880164π-0.880164\pi
0.929966 0.367646i 0.119836π-0.119836\pi
948948 0 0
949949 0 0
950950 38.1838i 1.23884i
951951 0 0
952952 0 0
953953 20.7846 0.673280 0.336640 0.941634i 0.390710π-0.390710\pi
0.336640 + 0.941634i 0.390710π0.390710\pi
954954 0 0
955955 4.00000 0.129437
956956 −17.3205 −0.560185
957957 0 0
958958 66.0000 2.13236
959959 −38.1051 −1.23048
960960 0 0
961961 −15.0000 −0.483871
962962 67.8823i 2.18861i
963963 0 0
964964 19.5959i 0.631142i
965965 −13.8564 −0.446054
966966 0 0
967967 41.6413i 1.33909i 0.742769 + 0.669547i 0.233512π0.233512\pi
−0.742769 + 0.669547i 0.766488π0.766488\pi
968968 8.66025 16.9706i 0.278351 0.545455i
969969 0 0
970970 24.4949i 0.786484i
971971 56.5685i 1.81537i −0.419651 0.907685i 0.637848π-0.637848\pi
0.419651 0.907685i 0.362152π-0.362152\pi
972972 0 0
973973 6.00000 0.192351
974974 13.8564 0.443988
975975 0 0
976976 24.4949i 0.784063i
977977 35.3553i 1.13112i −0.824708 0.565559i 0.808661π-0.808661\pi
0.824708 0.565559i 0.191339π-0.191339\pi
978978 0 0
979979 20.0000 12.2474i 0.639203 0.391430i
980980 1.41421i 0.0451754i
981981 0 0
982982 −48.0000 −1.53174
983983 48.0833i 1.53362i −0.641875 0.766809i 0.721843π-0.721843\pi
0.641875 0.766809i 0.278157π-0.278157\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 36.0000 1.14531
989989 −6.92820 −0.220304
990990 0 0
991991 −52.0000 −1.65183 −0.825917 0.563791i 0.809342π-0.809342\pi
−0.825917 + 0.563791i 0.809342π0.809342\pi
992992 20.7846 0.659912
993993 0 0
994994 −12.0000 −0.380617
995995 11.3137i 0.358669i
996996 0 0
997997 24.4949i 0.775761i 0.921710 + 0.387881i 0.126793π0.126793\pi
−0.921710 + 0.387881i 0.873207π0.873207\pi
998998 55.4256 1.75447
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 99.2.d.a.98.3 yes 4
3.2 odd 2 inner 99.2.d.a.98.2 yes 4
4.3 odd 2 1584.2.b.e.593.1 4
5.2 odd 4 2475.2.d.a.2474.5 8
5.3 odd 4 2475.2.d.a.2474.3 8
5.4 even 2 2475.2.f.e.2276.1 4
8.3 odd 2 6336.2.b.t.2177.3 4
8.5 even 2 6336.2.b.s.2177.4 4
9.2 odd 6 891.2.g.c.296.3 8
9.4 even 3 891.2.g.c.593.1 8
9.5 odd 6 891.2.g.c.593.4 8
9.7 even 3 891.2.g.c.296.2 8
11.10 odd 2 inner 99.2.d.a.98.1 4
12.11 even 2 1584.2.b.e.593.3 4
15.2 even 4 2475.2.d.a.2474.2 8
15.8 even 4 2475.2.d.a.2474.8 8
15.14 odd 2 2475.2.f.e.2276.3 4
24.5 odd 2 6336.2.b.s.2177.2 4
24.11 even 2 6336.2.b.t.2177.1 4
33.32 even 2 inner 99.2.d.a.98.4 yes 4
44.43 even 2 1584.2.b.e.593.2 4
55.32 even 4 2475.2.d.a.2474.4 8
55.43 even 4 2475.2.d.a.2474.6 8
55.54 odd 2 2475.2.f.e.2276.4 4
88.21 odd 2 6336.2.b.s.2177.3 4
88.43 even 2 6336.2.b.t.2177.4 4
99.32 even 6 891.2.g.c.593.2 8
99.43 odd 6 891.2.g.c.296.4 8
99.65 even 6 891.2.g.c.296.1 8
99.76 odd 6 891.2.g.c.593.3 8
132.131 odd 2 1584.2.b.e.593.4 4
165.32 odd 4 2475.2.d.a.2474.7 8
165.98 odd 4 2475.2.d.a.2474.1 8
165.164 even 2 2475.2.f.e.2276.2 4
264.131 odd 2 6336.2.b.t.2177.2 4
264.197 even 2 6336.2.b.s.2177.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.d.a.98.1 4 11.10 odd 2 inner
99.2.d.a.98.2 yes 4 3.2 odd 2 inner
99.2.d.a.98.3 yes 4 1.1 even 1 trivial
99.2.d.a.98.4 yes 4 33.32 even 2 inner
891.2.g.c.296.1 8 99.65 even 6
891.2.g.c.296.2 8 9.7 even 3
891.2.g.c.296.3 8 9.2 odd 6
891.2.g.c.296.4 8 99.43 odd 6
891.2.g.c.593.1 8 9.4 even 3
891.2.g.c.593.2 8 99.32 even 6
891.2.g.c.593.3 8 99.76 odd 6
891.2.g.c.593.4 8 9.5 odd 6
1584.2.b.e.593.1 4 4.3 odd 2
1584.2.b.e.593.2 4 44.43 even 2
1584.2.b.e.593.3 4 12.11 even 2
1584.2.b.e.593.4 4 132.131 odd 2
2475.2.d.a.2474.1 8 165.98 odd 4
2475.2.d.a.2474.2 8 15.2 even 4
2475.2.d.a.2474.3 8 5.3 odd 4
2475.2.d.a.2474.4 8 55.32 even 4
2475.2.d.a.2474.5 8 5.2 odd 4
2475.2.d.a.2474.6 8 55.43 even 4
2475.2.d.a.2474.7 8 165.32 odd 4
2475.2.d.a.2474.8 8 15.8 even 4
2475.2.f.e.2276.1 4 5.4 even 2
2475.2.f.e.2276.2 4 165.164 even 2
2475.2.f.e.2276.3 4 15.14 odd 2
2475.2.f.e.2276.4 4 55.54 odd 2
6336.2.b.s.2177.1 4 264.197 even 2
6336.2.b.s.2177.2 4 24.5 odd 2
6336.2.b.s.2177.3 4 88.21 odd 2
6336.2.b.s.2177.4 4 8.5 even 2
6336.2.b.t.2177.1 4 24.11 even 2
6336.2.b.t.2177.2 4 264.131 odd 2
6336.2.b.t.2177.3 4 8.3 odd 2
6336.2.b.t.2177.4 4 88.43 even 2