Properties

Label 968.2.k.a.403.1
Level 968968
Weight 22
Character 968.403
Analytic conductor 7.7307.730
Analytic rank 00
Dimension 88
CM discriminant -8
Inner twists 1616

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [968,2,Mod(403,968)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(968, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("968.403");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 968=23112 968 = 2^{3} \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 968.k (of order 1010, degree 44, not 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: 7.729518915667.72951891566
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ10)\Q(\zeta_{10})
Coefficient field: 8.0.64000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x82x6+4x48x2+16 x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 88)
Sato-Tate group: U(1)[D10]\mathrm{U}(1)[D_{10}]

Embedding invariants

Embedding label 403.1
Root 1.345000.437016i-1.34500 - 0.437016i of defining polynomial
Character χ\chi == 968.403
Dual form 968.2.k.a.723.1

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+(0.831254+1.14412i)q2+(0.6180341.90211i)q3+(0.6180341.90211i)q4+(1.66251+2.28825i)q6+(2.68999+0.874032i)q8+(0.8090170.587785i)q94.00000q12+(3.23607+2.35114i)q16+(3.32502+4.57649i)q17+(1.345000.437016i)q18+(8.06998+2.62210i)q19+(3.325024.57649i)q24+(1.545084.75528i)q25+(3.236072.35114i)q275.65685iq328.00000q34+(0.618034+1.90211i)q36+(9.70820+7.05342i)q38+(10.76003.49613i)q418.48528iq43+(2.47214+7.60845i)q48+(5.663124.11450i)q49+(4.15627+5.72061i)q50+(10.76003.49613i)q51+5.65685iq54+(9.9750513.7295i)q57+(1.854105.70634i)q59+(6.47214+4.70228i)q64+14.0000q67+(6.650039.15298i)q68+(1.662512.28825i)q72+(16.1400+5.24419i)q73+(8.090175.87785i)q7516.9706iq76+(3.3991910.4616i)q81+(12.94439.40456i)q82+(1.66251+2.28825i)q83+(9.70820+7.05342i)q86+18.0000q89+(10.76003.49613i)q96+(8.090175.87785i)q97+9.89949iq98+O(q100)q+(-0.831254 + 1.14412i) q^{2} +(0.618034 - 1.90211i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(1.66251 + 2.28825i) q^{6} +(2.68999 + 0.874032i) q^{8} +(-0.809017 - 0.587785i) q^{9} -4.00000 q^{12} +(-3.23607 + 2.35114i) q^{16} +(3.32502 + 4.57649i) q^{17} +(1.34500 - 0.437016i) q^{18} +(8.06998 + 2.62210i) q^{19} +(3.32502 - 4.57649i) q^{24} +(1.54508 - 4.75528i) q^{25} +(3.23607 - 2.35114i) q^{27} -5.65685i q^{32} -8.00000 q^{34} +(-0.618034 + 1.90211i) q^{36} +(-9.70820 + 7.05342i) q^{38} +(-10.7600 - 3.49613i) q^{41} -8.48528i q^{43} +(2.47214 + 7.60845i) q^{48} +(5.66312 - 4.11450i) q^{49} +(4.15627 + 5.72061i) q^{50} +(10.7600 - 3.49613i) q^{51} +5.65685i q^{54} +(9.97505 - 13.7295i) q^{57} +(-1.85410 - 5.70634i) q^{59} +(6.47214 + 4.70228i) q^{64} +14.0000 q^{67} +(6.65003 - 9.15298i) q^{68} +(-1.66251 - 2.28825i) q^{72} +(-16.1400 + 5.24419i) q^{73} +(-8.09017 - 5.87785i) q^{75} -16.9706i q^{76} +(-3.39919 - 10.4616i) q^{81} +(12.9443 - 9.40456i) q^{82} +(1.66251 + 2.28825i) q^{83} +(9.70820 + 7.05342i) q^{86} +18.0000 q^{89} +(-10.7600 - 3.49613i) q^{96} +(-8.09017 - 5.87785i) q^{97} +9.89949i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q4q3+4q42q932q128q1610q25+8q2764q34+4q3624q3816q48+14q49+12q59+16q64+112q6720q75+22q81+32q82+20q97+O(q100) 8 q - 4 q^{3} + 4 q^{4} - 2 q^{9} - 32 q^{12} - 8 q^{16} - 10 q^{25} + 8 q^{27} - 64 q^{34} + 4 q^{36} - 24 q^{38} - 16 q^{48} + 14 q^{49} + 12 q^{59} + 16 q^{64} + 112 q^{67} - 20 q^{75} + 22 q^{81} + 32 q^{82}+ \cdots - 20 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/968Z)×\left(\mathbb{Z}/968\mathbb{Z}\right)^\times.

nn 485485 727727 849849
χ(n)\chi(n) 1-1 1-1 e(710)e\left(\frac{7}{10}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.831254 + 1.14412i −0.587785 + 0.809017i
33 0.618034 1.90211i 0.356822 1.09819i −0.598123 0.801404i 0.704087π-0.704087\pi
0.954945 0.296781i 0.0959133π-0.0959133\pi
44 −0.618034 1.90211i −0.309017 0.951057i
55 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
66 1.66251 + 2.28825i 0.678716 + 0.934172i
77 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
88 2.68999 + 0.874032i 0.951057 + 0.309017i
99 −0.809017 0.587785i −0.269672 0.195928i
1010 0 0
1111 0 0
1212 −4.00000 −1.15470
1313 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
1414 0 0
1515 0 0
1616 −3.23607 + 2.35114i −0.809017 + 0.587785i
1717 3.32502 + 4.57649i 0.806435 + 1.10996i 0.991864 + 0.127304i 0.0406325π0.0406325\pi
−0.185429 + 0.982658i 0.559367π0.559367\pi
1818 1.34500 0.437016i 0.317019 0.103006i
1919 8.06998 + 2.62210i 1.85138 + 0.601550i 0.996584 + 0.0825877i 0.0263185π0.0263185\pi
0.854797 + 0.518962i 0.173682π0.173682\pi
2020 0 0
2121 0 0
2222 0 0
2323 0 0 1.00000 00
−1.00000 π\pi
2424 3.32502 4.57649i 0.678716 0.934172i
2525 1.54508 4.75528i 0.309017 0.951057i
2626 0 0
2727 3.23607 2.35114i 0.622782 0.452477i
2828 0 0
2929 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
3030 0 0
3131 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
3232 5.65685i 1.00000i
3333 0 0
3434 −8.00000 −1.37199
3535 0 0
3636 −0.618034 + 1.90211i −0.103006 + 0.317019i
3737 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
3838 −9.70820 + 7.05342i −1.57488 + 1.14422i
3939 0 0
4040 0 0
4141 −10.7600 3.49613i −1.68043 0.546003i −0.695432 0.718592i 0.744787π-0.744787\pi
−0.984994 + 0.172588i 0.944787π0.944787\pi
4242 0 0
4343 8.48528i 1.29399i −0.762493 0.646997i 0.776025π-0.776025\pi
0.762493 0.646997i 0.223975π-0.223975\pi
4444 0 0
4545 0 0
4646 0 0
4747 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
4848 2.47214 + 7.60845i 0.356822 + 1.09819i
4949 5.66312 4.11450i 0.809017 0.587785i
5050 4.15627 + 5.72061i 0.587785 + 0.809017i
5151 10.7600 3.49613i 1.50670 0.489556i
5252 0 0
5353 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
5454 5.65685i 0.769800i
5555 0 0
5656 0 0
5757 9.97505 13.7295i 1.32123 1.81851i
5858 0 0
5959 −1.85410 5.70634i −0.241384 0.742902i −0.996210 0.0869778i 0.972279π-0.972279\pi
0.754827 0.655924i 0.227721π-0.227721\pi
6060 0 0
6161 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
6262 0 0
6363 0 0
6464 6.47214 + 4.70228i 0.809017 + 0.587785i
6565 0 0
6666 0 0
6767 14.0000 1.71037 0.855186 0.518321i 0.173443π-0.173443\pi
0.855186 + 0.518321i 0.173443π0.173443\pi
6868 6.65003 9.15298i 0.806435 1.10996i
6969 0 0
7070 0 0
7171 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
7272 −1.66251 2.28825i −0.195928 0.269672i
7373 −16.1400 + 5.24419i −1.88904 + 0.613786i −0.908352 + 0.418206i 0.862659π0.862659\pi
−0.980688 + 0.195580i 0.937341π0.937341\pi
7474 0 0
7575 −8.09017 5.87785i −0.934172 0.678716i
7676 16.9706i 1.94666i
7777 0 0
7878 0 0
7979 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
8080 0 0
8181 −3.39919 10.4616i −0.377687 1.16240i
8282 12.9443 9.40456i 1.42946 1.03856i
8383 1.66251 + 2.28825i 0.182484 + 0.251168i 0.890452 0.455077i 0.150388π-0.150388\pi
−0.707968 + 0.706244i 0.750388π0.750388\pi
8484 0 0
8585 0 0
8686 9.70820 + 7.05342i 1.04686 + 0.760590i
8787 0 0
8888 0 0
8989 18.0000 1.90800 0.953998 0.299813i 0.0969242π-0.0969242\pi
0.953998 + 0.299813i 0.0969242π0.0969242\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 −10.7600 3.49613i −1.09819 0.356822i
9797 −8.09017 5.87785i −0.821432 0.596806i 0.0956901 0.995411i 0.469494π-0.469494\pi
−0.917122 + 0.398606i 0.869494π0.869494\pi
9898 9.89949i 1.00000i
9999 0 0
100100 −10.0000 −1.00000
101101 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
102102 −4.94427 + 15.2169i −0.489556 + 1.50670i
103103 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
104104 0 0
105105 0 0
106106 0 0
107107 18.8300 + 6.11822i 1.82036 + 0.591471i 0.999802 + 0.0199092i 0.00633772π0.00633772\pi
0.820559 + 0.571562i 0.193662π0.193662\pi
108108 −6.47214 4.70228i −0.622782 0.452477i
109109 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
110110 0 0
111111 0 0
112112 0 0
113113 −5.56231 + 17.1190i −0.523258 + 1.61042i 0.244478 + 0.969655i 0.421383π0.421383\pi
−0.767736 + 0.640767i 0.778617π0.778617\pi
114114 7.41641 + 22.8254i 0.694610 + 2.13779i
115115 0 0
116116 0 0
117117 0 0
118118 8.06998 + 2.62210i 0.742902 + 0.241384i
119119 0 0
120120 0 0
121121 0 0
122122 0 0
123123 −13.3001 + 18.3060i −1.19923 + 1.65059i
124124 0 0
125125 0 0
126126 0 0
127127 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
128128 −10.7600 + 3.49613i −0.951057 + 0.309017i
129129 −16.1400 5.24419i −1.42104 0.461725i
130130 0 0
131131 14.1421i 1.23560i 0.786334 + 0.617802i 0.211977π0.211977\pi
−0.786334 + 0.617802i 0.788023π0.788023\pi
132132 0 0
133133 0 0
134134 −11.6376 + 16.0177i −1.00533 + 1.38372i
135135 0 0
136136 4.94427 + 15.2169i 0.423968 + 1.30484i
137137 −4.85410 + 3.52671i −0.414714 + 0.301307i −0.775507 0.631338i 0.782506π-0.782506\pi
0.360794 + 0.932646i 0.382506π0.382506\pi
138138 0 0
139139 8.06998 2.62210i 0.684487 0.222403i 0.0539282 0.998545i 0.482826π-0.482826\pi
0.630559 + 0.776142i 0.282826π0.282826\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 4.00000 0.333333
145145 0 0
146146 7.41641 22.8254i 0.613786 1.88904i
147147 −4.32624 13.3148i −0.356822 1.09819i
148148 0 0
149149 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
150150 13.4500 4.37016i 1.09819 0.356822i
151151 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
152152 19.4164 + 14.1068i 1.57488 + 1.14422i
153153 5.65685i 0.457330i
154154 0 0
155155 0 0
156156 0 0
157157 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 14.7950 + 4.80718i 1.16240 + 0.377687i
163163 1.61803 + 1.17557i 0.126734 + 0.0920778i 0.649347 0.760493i 0.275042π-0.275042\pi
−0.522612 + 0.852570i 0.675042π0.675042\pi
164164 22.6274i 1.76690i
165165 0 0
166166 −4.00000 −0.310460
167167 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
168168 0 0
169169 −4.01722 12.3637i −0.309017 0.951057i
170170 0 0
171171 −4.98752 6.86474i −0.381405 0.524960i
172172 −16.1400 + 5.24419i −1.23066 + 0.399866i
173173 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
174174 0 0
175175 0 0
176176 0 0
177177 −12.0000 −0.901975
178178 −14.9626 + 20.5942i −1.12149 + 1.54360i
179179 −5.56231 + 17.1190i −0.415746 + 1.27954i 0.495835 + 0.868416i 0.334862π0.334862\pi
−0.911582 + 0.411119i 0.865138π0.865138\pi
180180 0 0
181181 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
192192 12.9443 9.40456i 0.934172 0.678716i
193193 −9.97505 13.7295i −0.718020 0.988269i −0.999587 0.0287278i 0.990854π-0.990854\pi
0.281568 0.959541i 0.409146π-0.409146\pi
194194 13.4500 4.37016i 0.965652 0.313759i
195195 0 0
196196 −11.3262 8.22899i −0.809017 0.587785i
197197 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
198198 0 0
199199 0 0 1.00000 00
−1.00000 π\pi
200200 8.31254 11.4412i 0.587785 0.809017i
201201 8.65248 26.6296i 0.610299 1.87831i
202202 0 0
203203 0 0
204204 −13.3001 18.3060i −0.931191 1.28167i
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 −14.9626 + 20.5942i −1.03007 + 1.41776i −0.125168 + 0.992136i 0.539947π0.539947\pi
−0.904898 + 0.425628i 0.860053π0.860053\pi
212212 0 0
213213 0 0
214214 −22.6525 + 16.4580i −1.54849 + 1.12504i
215215 0 0
216216 10.7600 3.49613i 0.732124 0.237881i
217217 0 0
218218 0 0
219219 33.9411i 2.29353i
220220 0 0
221221 0 0
222222 0 0
223223 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
224224 0 0
225225 −4.04508 + 2.93893i −0.269672 + 0.195928i
226226 −14.9626 20.5942i −0.995295 1.36991i
227227 −2.68999 + 0.874032i −0.178541 + 0.0580115i −0.396923 0.917852i 0.629922π-0.629922\pi
0.218382 + 0.975863i 0.429922π0.429922\pi
228228 −32.2799 10.4884i −2.13779 0.694610i
229229 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
230230 0 0
231231 0 0
232232 0 0
233233 3.32502 4.57649i 0.217829 0.299816i −0.686092 0.727514i 0.740675π-0.740675\pi
0.903921 + 0.427698i 0.140675π0.140675\pi
234234 0 0
235235 0 0
236236 −9.70820 + 7.05342i −0.631950 + 0.459139i
237237 0 0
238238 0 0
239239 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
240240 0 0
241241 16.9706i 1.09317i −0.837404 0.546585i 0.815928π-0.815928\pi
0.837404 0.546585i 0.184072π-0.184072\pi
242242 0 0
243243 −10.0000 −0.641500
244244 0 0
245245 0 0
246246 −9.88854 30.4338i −0.630471 1.94039i
247247 0 0
248248 0 0
249249 5.37999 1.74806i 0.340943 0.110779i
250250 0 0
251251 −4.85410 3.52671i −0.306388 0.222604i 0.423957 0.905682i 0.360641π-0.360641\pi
−0.730345 + 0.683078i 0.760641π0.760641\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 4.94427 15.2169i 0.309017 0.951057i
257257 9.27051 + 28.5317i 0.578279 + 1.77976i 0.624734 + 0.780838i 0.285208π0.285208\pi
−0.0464552 + 0.998920i 0.514792π0.514792\pi
258258 19.4164 14.1068i 1.20881 0.878254i
259259 0 0
260260 0 0
261261 0 0
262262 −16.1803 11.7557i −0.999625 0.726270i
263263 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
264264 0 0
265265 0 0
266266 0 0
267267 11.1246 34.2380i 0.680815 2.09533i
268268 −8.65248 26.6296i −0.528534 1.62666i
269269 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
270270 0 0
271271 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
272272 −21.5200 6.99226i −1.30484 0.423968i
273273 0 0
274274 8.48528i 0.512615i
275275 0 0
276276 0 0
277277 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
278278 −3.70820 + 11.4127i −0.222403 + 0.684487i
279279 0 0
280280 0 0
281281 −16.6251 22.8825i −0.991769 1.36505i −0.930242 0.366947i 0.880403π-0.880403\pi
−0.0615273 0.998105i 0.519597π-0.519597\pi
282282 0 0
283283 −24.2099 7.86629i −1.43913 0.467602i −0.517505 0.855680i 0.673139π-0.673139\pi
−0.921627 + 0.388078i 0.873139π0.873139\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 −3.32502 + 4.57649i −0.195928 + 0.269672i
289289 −4.63525 + 14.2658i −0.272662 + 0.839168i
290290 0 0
291291 −16.1803 + 11.7557i −0.948508 + 0.689132i
292292 19.9501 + 27.4589i 1.16749 + 1.60691i
293293 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
294294 18.8300 + 6.11822i 1.09819 + 0.356822i
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 −6.18034 + 19.0211i −0.356822 + 1.09819i
301301 0 0
302302 0 0
303303 0 0
304304 −32.2799 + 10.4884i −1.85138 + 0.601550i
305305 0 0
306306 6.47214 + 4.70228i 0.369987 + 0.268812i
307307 8.48528i 0.484281i −0.970241 0.242140i 0.922151π-0.922151\pi
0.970241 0.242140i 0.0778494π-0.0778494\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
312312 0 0
313313 8.09017 5.87785i 0.457283 0.332236i −0.335181 0.942154i 0.608798π-0.608798\pi
0.792465 + 0.609918i 0.208798π0.208798\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
318318 0 0
319319 0 0
320320 0 0
321321 23.2751 32.0354i 1.29909 1.78804i
322322 0 0
323323 14.8328 + 45.6507i 0.825320 + 2.54007i
324324 −17.7984 + 12.9313i −0.988799 + 0.718404i
325325 0 0
326326 −2.68999 + 0.874032i −0.148985 + 0.0484082i
327327 0 0
328328 −25.8885 18.8091i −1.42946 1.03856i
329329 0 0
330330 0 0
331331 −26.0000 −1.42909 −0.714545 0.699590i 0.753366π-0.753366\pi
−0.714545 + 0.699590i 0.753366π0.753366\pi
332332 3.32502 4.57649i 0.182484 0.251168i
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 −32.2799 + 10.4884i −1.75840 + 0.571339i −0.997032 0.0769821i 0.975472π-0.975472\pi
−0.761367 + 0.648321i 0.775472π0.775472\pi
338338 17.4850 + 5.68121i 0.951057 + 0.309017i
339339 29.1246 + 21.1603i 1.58183 + 1.14927i
340340 0 0
341341 0 0
342342 12.0000 0.648886
343343 0 0
344344 7.41641 22.8254i 0.399866 1.23066i
345345 0 0
346346 0 0
347347 21.6126 + 29.7472i 1.16023 + 1.59691i 0.710404 + 0.703795i 0.248512π0.248512\pi
0.449822 + 0.893118i 0.351488π0.351488\pi
348348 0 0
349349 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
350350 0 0
351351 0 0
352352 0 0
353353 −30.0000 −1.59674 −0.798369 0.602168i 0.794304π-0.794304\pi
−0.798369 + 0.602168i 0.794304π0.794304\pi
354354 9.97505 13.7295i 0.530168 0.729713i
355355 0 0
356356 −11.1246 34.2380i −0.589603 1.81461i
357357 0 0
358358 −14.9626 20.5942i −0.790796 1.08844i
359359 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
360360 0 0
361361 42.8779 + 31.1526i 2.25673 + 1.63961i
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
368368 0 0
369369 6.65003 + 9.15298i 0.346187 + 0.476485i
370370 0 0
371371 0 0
372372 0 0
373373 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 30.7426 22.3358i 1.57914 1.14732i 0.661476 0.749966i 0.269930π-0.269930\pi
0.917668 0.397349i 0.130070π-0.130070\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
384384 22.6274i 1.15470i
385385 0 0
386386 24.0000 1.22157
387387 −4.98752 + 6.86474i −0.253530 + 0.348954i
388388 −6.18034 + 19.0211i −0.313759 + 0.965652i
389389 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
390390 0 0
391391 0 0
392392 18.8300 6.11822i 0.951057 0.309017i
393393 26.8999 + 8.74032i 1.35692 + 0.440891i
394394 0 0
395395 0 0
396396 0 0
397397 0 0 1.00000 00
−1.00000 π\pi
398398 0 0
399399 0 0
400400 6.18034 + 19.0211i 0.309017 + 0.951057i
401401 −4.85410 + 3.52671i −0.242402 + 0.176116i −0.702353 0.711829i 0.747867π-0.747867\pi
0.459951 + 0.887945i 0.347867π0.347867\pi
402402 23.2751 + 32.0354i 1.16086 + 1.59778i
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 32.0000 1.58424
409409 −19.9501 + 27.4589i −0.986469 + 1.35776i −0.0531978 + 0.998584i 0.516941π0.516941\pi
−0.933271 + 0.359174i 0.883059π0.883059\pi
410410 0 0
411411 3.70820 + 11.4127i 0.182912 + 0.562946i
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 16.9706i 0.831052i
418418 0 0
419419 18.0000 0.879358 0.439679 0.898155i 0.355092π-0.355092\pi
0.439679 + 0.898155i 0.355092π0.355092\pi
420420 0 0
421421 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
422422 −11.1246 34.2380i −0.541538 1.66668i
423423 0 0
424424 0 0
425425 26.8999 8.74032i 1.30484 0.423968i
426426 0 0
427427 0 0
428428 39.5980i 1.91404i
429429 0 0
430430 0 0
431431 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
432432 −4.94427 + 15.2169i −0.237881 + 0.732124i
433433 11.7426 + 36.1401i 0.564316 + 1.73678i 0.669976 + 0.742382i 0.266304π0.266304\pi
−0.105661 + 0.994402i 0.533696π0.533696\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 −38.8328 28.2137i −1.85550 1.34810i
439439 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
440440 0 0
441441 −7.00000 −0.333333
442442 0 0
443443 −12.9787 + 39.9444i −0.616637 + 1.89781i −0.244416 + 0.969670i 0.578596π0.578596\pi
−0.372221 + 0.928144i 0.621404π0.621404\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 −33.9787 24.6870i −1.60355 1.16505i −0.880236 0.474536i 0.842616π-0.842616\pi
−0.723319 0.690514i 0.757384π-0.757384\pi
450450 7.07107i 0.333333i
451451 0 0
452452 36.0000 1.69330
453453 0 0
454454 1.23607 3.80423i 0.0580115 0.178541i
455455 0 0
456456 38.8328 28.2137i 1.81851 1.32123i
457457 19.9501 + 27.4589i 0.933226 + 1.28448i 0.958588 + 0.284797i 0.0919262π0.0919262\pi
−0.0253618 + 0.999678i 0.508074π0.508074\pi
458458 0 0
459459 21.5200 + 6.99226i 1.00447 + 0.326371i
460460 0 0
461461 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
462462 0 0
463463 0 0 1.00000 00
−1.00000 π\pi
464464 0 0
465465 0 0
466466 2.47214 + 7.60845i 0.114519 + 0.352455i
467467 −24.2705 + 17.6336i −1.12311 + 0.815984i −0.984677 0.174389i 0.944205π-0.944205\pi
−0.138428 + 0.990372i 0.544205π0.544205\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 16.9706i 0.781133i
473473 0 0
474474 0 0
475475 24.9376 34.3237i 1.14422 1.57488i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
480480 0 0
481481 0 0
482482 19.4164 + 14.1068i 0.884393 + 0.642549i
483483 0 0
484484 0 0
485485 0 0
486486 8.31254 11.4412i 0.377064 0.518985i
487487 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
488488 0 0
489489 3.23607 2.35114i 0.146340 0.106322i
490490 0 0
491491 13.4500 4.37016i 0.606989 0.197223i 0.0106338 0.999943i 0.496615π-0.496615\pi
0.596355 + 0.802721i 0.296615π0.296615\pi
492492 43.0399 + 13.9845i 1.94039 + 0.630471i
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 −2.47214 + 7.60845i −0.110779 + 0.340943i
499499 −4.32624 13.3148i −0.193669 0.596052i −0.999990 0.00457310i 0.998544π-0.998544\pi
0.806321 0.591479i 0.201456π-0.201456\pi
500500 0 0
501501 0 0
502502 8.06998 2.62210i 0.360181 0.117030i
503503 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
504504 0 0
505505 0 0
506506 0 0
507507 −26.0000 −1.15470
508508 0 0
509509 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
510510 0 0
511511 0 0
512512 13.3001 + 18.3060i 0.587785 + 0.809017i
513513 32.2799 10.4884i 1.42519 0.463073i
514514 −40.3499 13.1105i −1.77976 0.578279i
515515 0 0
516516 33.9411i 1.49417i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 −1.85410 5.70634i −0.0812297 0.249999i 0.902191 0.431336i 0.141958π-0.141958\pi
−0.983421 + 0.181337i 0.941958π0.941958\pi
522522 0 0
523523 −14.9626 20.5942i −0.654267 0.900522i 0.345007 0.938600i 0.387876π-0.387876\pi
−0.999275 + 0.0380781i 0.987876π0.987876\pi
524524 26.8999 8.74032i 1.17513 0.381823i
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 23.0000 1.00000
530530 0 0
531531 −1.85410 + 5.70634i −0.0804612 + 0.247634i
532532 0 0
533533 0 0
534534 29.9251 + 41.1884i 1.29499 + 1.78240i
535535 0 0
536536 37.6599 + 12.2364i 1.62666 + 0.528534i
537537 29.1246 + 21.1603i 1.25682 + 0.913133i
538538 0 0
539539 0 0
540540 0 0
541541 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
542542 0 0
543543 0 0
544544 25.8885 18.8091i 1.10996 0.806435i
545545 0 0
546546 0 0
547547 8.06998 + 2.62210i 0.345048 + 0.112113i 0.476414 0.879221i 0.341936π-0.341936\pi
−0.131366 + 0.991334i 0.541936π0.541936\pi
548548 9.70820 + 7.05342i 0.414714 + 0.301307i
549549 0 0
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 −9.97505 13.7295i −0.423036 0.582259i
557557 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 40.0000 1.68730
563563 21.6126 29.7472i 0.910863 1.25369i −0.0560088 0.998430i 0.517837π-0.517837\pi
0.966871 0.255264i 0.0821625π-0.0821625\pi
564564 0 0
565565 0 0
566566 29.1246 21.1603i 1.22420 0.889432i
567567 0 0
568568 0 0
569569 −21.5200 6.99226i −0.902163 0.293131i −0.179034 0.983843i 0.557297π-0.557297\pi
−0.723130 + 0.690712i 0.757297π0.757297\pi
570570 0 0
571571 42.4264i 1.77549i −0.460336 0.887745i 0.652271π-0.652271\pi
0.460336 0.887745i 0.347729π-0.347729\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 −2.47214 7.60845i −0.103006 0.317019i
577577 −27.5066 + 19.9847i −1.14511 + 0.831974i −0.987824 0.155579i 0.950276π-0.950276\pi
−0.157290 + 0.987552i 0.550276π0.550276\pi
578578 −12.4688 17.1618i −0.518634 0.713839i
579579 −32.2799 + 10.4884i −1.34151 + 0.435882i
580580 0 0
581581 0 0
582582 28.2843i 1.17242i
583583 0 0
584584 −48.0000 −1.98625
585585 0 0
586586 0 0
587587 −1.85410 5.70634i −0.0765270 0.235526i 0.905474 0.424402i 0.139516π-0.139516\pi
−0.982001 + 0.188876i 0.939516π0.939516\pi
588588 −22.6525 + 16.4580i −0.934172 + 0.678716i
589589 0 0
590590 0 0
591591 0 0
592592 0 0
593593 45.2548i 1.85839i 0.369586 + 0.929197i 0.379500π0.379500\pi
−0.369586 + 0.929197i 0.620500π0.620500\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
600600 −16.6251 22.8825i −0.678716 0.934172i
601601 −16.1400 + 5.24419i −0.658363 + 0.213915i −0.619098 0.785314i 0.712502π-0.712502\pi
−0.0392649 + 0.999229i 0.512502π0.512502\pi
602602 0 0
603603 −11.3262 8.22899i −0.461240 0.335111i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
608608 14.8328 45.6507i 0.601550 1.85138i
609609 0 0
610610 0 0
611611 0 0
612612 −10.7600 + 3.49613i −0.434946 + 0.141323i
613613 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
614614 9.70820 + 7.05342i 0.391791 + 0.284653i
615615 0 0
616616 0 0
617617 −30.0000 −1.20775 −0.603877 0.797077i 0.706378π-0.706378\pi
−0.603877 + 0.797077i 0.706378π0.706378\pi
618618 0 0
619619 8.03444 24.7275i 0.322931 0.993881i −0.649434 0.760418i 0.724994π-0.724994\pi
0.972366 0.233463i 0.0750058π-0.0750058\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −20.2254 14.6946i −0.809017 0.587785i
626626 14.1421i 0.565233i
627627 0 0
628628 0 0
629629 0 0
630630 0 0
631631 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
632632 0 0
633633 29.9251 + 41.1884i 1.18942 + 1.63709i
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 −12.9787 + 39.9444i −0.512628 + 1.57771i 0.274928 + 0.961465i 0.411346π0.411346\pi
−0.787556 + 0.616243i 0.788654π0.788654\pi
642642 17.3050 + 53.2592i 0.682972 + 2.10197i
643643 −40.4508 + 29.3893i −1.59523 + 1.15900i −0.699269 + 0.714859i 0.746491π0.746491\pi
−0.895957 + 0.444140i 0.853509π0.853509\pi
644644 0 0
645645 0 0
646646 −64.5599 20.9768i −2.54007 0.825320i
647647 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
648648 31.1127i 1.22222i
649649 0 0
650650 0 0
651651 0 0
652652 1.23607 3.80423i 0.0484082 0.148985i
653653 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
654654 0 0
655655 0 0
656656 43.0399 13.9845i 1.68043 0.546003i
657657 16.1400 + 5.24419i 0.629680 + 0.204595i
658658 0 0
659659 48.0833i 1.87306i −0.350590 0.936529i 0.614019π-0.614019\pi
0.350590 0.936529i 0.385981π-0.385981\pi
660660 0 0
661661 0 0 1.00000 00
−1.00000 π\pi
662662 21.6126 29.7472i 0.839998 1.15616i
663663 0 0
664664 2.47214 + 7.60845i 0.0959375 + 0.295265i
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 −29.9251 + 41.1884i −1.15353 + 1.58770i −0.420838 + 0.907136i 0.638264π0.638264\pi
−0.732691 + 0.680561i 0.761736π0.761736\pi
674674 14.8328 45.6507i 0.571339 1.75840i
675675 −6.18034 19.0211i −0.237881 0.732124i
676676 −21.0344 + 15.2824i −0.809017 + 0.587785i
677677 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
678678 −48.4199 + 15.7326i −1.85955 + 0.604206i
679679 0 0
680680 0 0
681681 5.65685i 0.216771i
682682 0 0
683683 −42.0000 −1.60709 −0.803543 0.595247i 0.797054π-0.797054\pi
−0.803543 + 0.595247i 0.797054π0.797054\pi
684684 −9.97505 + 13.7295i −0.381405 + 0.524960i
685685 0 0
686686 0 0
687687 0 0
688688 19.9501 + 27.4589i 0.760590 + 1.04686i
689689 0 0
690690 0 0
691691 37.2148 + 27.0381i 1.41572 + 1.02858i 0.992460 + 0.122569i 0.0391133π0.0391133\pi
0.423257 + 0.906010i 0.360887π0.360887\pi
692692 0 0
693693 0 0
694694 −52.0000 −1.97389
695695 0 0
696696 0 0
697697 −19.7771 60.8676i −0.749111 2.30553i
698698 0 0
699699 −6.65003 9.15298i −0.251527 0.346198i
700700 0 0
701701 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 24.9376 34.3237i 0.938540 1.29179i
707707 0 0
708708 7.41641 + 22.8254i 0.278726 + 0.857829i
709709 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
710710 0 0
711711 0 0
712712 48.4199 + 15.7326i 1.81461 + 0.589603i
713713 0 0
714714 0 0
715715 0 0
716716 36.0000 1.34538
717717 0 0
718718 0 0
719719 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
720720 0 0
721721 0 0
722722 −71.2848 + 23.1618i −2.65295 + 0.861995i
723723 −32.2799 10.4884i −1.20050 0.390067i
724724 0 0
725725 0 0
726726 0 0
727727 0 0 1.00000 00
−1.00000 π\pi
728728 0 0
729729 4.01722 12.3637i 0.148786 0.457916i
730730 0 0
731731 38.8328 28.2137i 1.43628 1.04352i
732732 0 0
733733 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 −16.0000 −0.588968
739739 24.9376 34.3237i 0.917345 1.26262i −0.0472504 0.998883i 0.515046π-0.515046\pi
0.964595 0.263734i 0.0849541π-0.0849541\pi
740740 0 0
741741 0 0
742742 0 0
743743 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
744744 0 0
745745 0 0
746746 0 0
747747 2.82843i 0.103487i
748748 0 0
749749 0 0
750750 0 0
751751 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
752752 0 0
753753 −9.70820 + 7.05342i −0.353787 + 0.257041i
754754 0 0
755755 0 0
756756 0 0
757757 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
758758 53.7401i 1.95193i
759759 0 0
760760 0 0
761761 6.65003 9.15298i 0.241063 0.331795i −0.671293 0.741192i 0.734261π-0.734261\pi
0.912356 + 0.409397i 0.134261π0.134261\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 −25.8885 18.8091i −0.934172 0.678716i
769769 50.9117i 1.83592i 0.396670 + 0.917961i 0.370166π0.370166\pi
−0.396670 + 0.917961i 0.629834π0.629834\pi
770770 0 0
771771 60.0000 2.16085
772772 −19.9501 + 27.4589i −0.718020 + 0.988269i
773773 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
774774 −3.70820 11.4127i −0.133289 0.410220i
775775 0 0
776776 −16.6251 22.8825i −0.596806 0.821432i
777777 0 0
778778 0 0
779779 −77.6656 56.4274i −2.78266 2.02172i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −8.65248 + 26.6296i −0.309017 + 0.951057i
785785 0 0
786786 −32.3607 + 23.5114i −1.15427 + 0.838624i
787787 −14.9626 20.5942i −0.533358 0.734104i 0.454280 0.890859i 0.349897π-0.349897\pi
−0.987638 + 0.156755i 0.949897π0.949897\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
798798 0 0
799799 0 0
800800 −26.8999 8.74032i −0.951057 0.309017i
801801 −14.5623 10.5801i −0.514534 0.373831i
802802 8.48528i 0.299626i
803803 0 0
804804 −56.0000 −1.97497
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 −33.2502 45.7649i −1.16901 1.60901i −0.669837 0.742508i 0.733636π-0.733636\pi
−0.499176 0.866501i 0.666364π-0.666364\pi
810810 0 0
811811 −40.3499 13.1105i −1.41688 0.460371i −0.502268 0.864712i 0.667501π-0.667501\pi
−0.914609 + 0.404340i 0.867501π0.867501\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 −26.6001 + 36.6119i −0.931191 + 1.28167i
817817 22.2492 68.4761i 0.778402 2.39567i
818818 −14.8328 45.6507i −0.518617 1.59614i
819819 0 0
820820 0 0
821821 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
822822 −16.1400 5.24419i −0.562946 0.182912i
823823 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
824824 0 0
825825 0 0
826826 0 0
827827 −11.6376 + 16.0177i −0.404677 + 0.556991i −0.961910 0.273366i 0.911863π-0.911863\pi
0.557233 + 0.830356i 0.311863π0.311863\pi
828828 0 0
829829 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
830830 0 0
831831 0 0
832832 0 0
833833 37.6599 + 12.2364i 1.30484 + 0.423968i
834834 19.4164 + 14.1068i 0.672335 + 0.488480i
835835 0 0
836836 0 0
837837 0 0
838838 −14.9626 + 20.5942i −0.516873 + 0.711415i
839839 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
840840 0 0
841841 23.4615 17.0458i 0.809017 0.587785i
842842 0 0
843843 −53.7999 + 17.4806i −1.85297 + 0.602065i
844844 48.4199 + 15.7326i 1.66668 + 0.541538i
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 −29.9251 + 41.1884i −1.02703 + 1.41358i
850850 −12.3607 + 38.0423i −0.423968 + 1.30484i
851851 0 0
852852 0 0
853853 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
854854 0 0
855855 0 0
856856 45.3050 + 32.9160i 1.54849 + 1.12504i
857857 22.6274i 0.772938i 0.922302 + 0.386469i 0.126305π0.126305\pi
−0.922302 + 0.386469i 0.873695π0.873695\pi
858858 0 0
859859 58.0000 1.97893 0.989467 0.144757i 0.0462401π-0.0462401\pi
0.989467 + 0.144757i 0.0462401π0.0462401\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.809017 0.587785i 0.200000π-0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
864864 −13.3001 18.3060i −0.452477 0.622782i
865865 0 0
866866 −51.1099 16.6066i −1.73678 0.564316i
867867 24.2705 + 17.6336i 0.824270 + 0.598867i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 3.09017 + 9.51057i 0.104586 + 0.321884i
874874 0 0
875875 0 0
876876 64.5599 20.9768i 2.18128 0.708739i
877877 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
878878 0 0
879879 0 0
880880 0 0
881881 18.0000 0.606435 0.303218 0.952921i 0.401939π-0.401939\pi
0.303218 + 0.952921i 0.401939π0.401939\pi
882882 5.81878 8.00886i 0.195928 0.269672i
883883 0.618034 1.90211i 0.0207985 0.0640112i −0.940119 0.340848i 0.889286π-0.889286\pi
0.960917 + 0.276836i 0.0892860π0.0892860\pi
884884 0 0
885885 0 0
886886 −34.9127 48.0532i −1.17291 1.61438i
887887 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 56.4899 18.3547i 1.88509 0.612503i
899899 0 0
900900 8.09017 + 5.87785i 0.269672 + 0.195928i
901901 0 0
902902 0 0
903903 0 0
904904 −29.9251 + 41.1884i −0.995295 + 1.36991i
905905 0 0
906906 0 0
907907 8.09017 5.87785i 0.268630 0.195171i −0.445313 0.895375i 0.646908π-0.646908\pi
0.713943 + 0.700204i 0.246908π0.246908\pi
908908 3.32502 + 4.57649i 0.110345 + 0.151876i
909909 0 0
910910 0 0
911911 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
912912 67.8823i 2.24781i
913913 0 0
914914 −48.0000 −1.58770
915915 0 0
916916 0 0
917917 0 0
918918 −25.8885 + 18.8091i −0.854449 + 0.620794i
919919 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
920920 0 0
921921 −16.1400 5.24419i −0.531830 0.172802i
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 43.6869 31.7404i 1.43332 1.04137i 0.443935 0.896059i 0.353582π-0.353582\pi
0.989386 0.145310i 0.0464179π-0.0464179\pi
930930 0 0
931931 56.4899 18.3547i 1.85138 0.601550i
932932 −10.7600 3.49613i −0.352455 0.114519i
933933 0 0
934934 42.4264i 1.38823i
935935 0 0
936936 0 0
937937 −29.9251 + 41.1884i −0.977612 + 1.34557i −0.0395055 + 0.999219i 0.512578π0.512578\pi
−0.938106 + 0.346348i 0.887422π0.887422\pi
938938 0 0
939939 −6.18034 19.0211i −0.201688 0.620731i
940940 0 0
941941 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
942942 0 0
943943 0 0
944944 19.4164 + 14.1068i 0.631950 + 0.459139i
945945 0 0
946946 0 0
947947 −30.0000 −0.974869 −0.487435 0.873160i 0.662067π-0.662067\pi
−0.487435 + 0.873160i 0.662067π0.662067\pi
948948 0 0
949949 0 0
950950 18.5410 + 57.0634i 0.601550 + 1.85138i
951951 0 0
952952 0 0
953953 43.0399 13.9845i 1.39420 0.453003i 0.486889 0.873464i 0.338132π-0.338132\pi
0.907311 + 0.420461i 0.138132π0.138132\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 9.57953 + 29.4828i 0.309017 + 0.951057i
962962 0 0
963963 −11.6376 16.0177i −0.375015 0.516164i
964964 −32.2799 + 10.4884i −1.03967 + 0.337808i
965965 0 0
966966 0 0
967967 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
968968 0 0
969969 96.0000 3.08396
970970 0 0
971971 16.6869 51.3571i 0.535509 1.64813i −0.207039 0.978333i 0.566383π-0.566383\pi
0.742547 0.669793i 0.233617π-0.233617\pi
972972 6.18034 + 19.0211i 0.198234 + 0.610103i
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −4.85410 3.52671i −0.155296 0.112829i 0.507423 0.861697i 0.330598π-0.330598\pi
−0.662720 + 0.748867i 0.730598π0.730598\pi
978978 5.65685i 0.180886i
979979 0 0
980980 0 0
981981 0 0
982982 −6.18034 + 19.0211i −0.197223 + 0.606989i
983983 0 0 −0.309017 0.951057i 0.600000π-0.600000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
984984 −51.7771 + 37.6183i −1.65059 + 1.19923i
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 1.00000 00
−1.00000 π\pi
992992 0 0
993993 −16.0689 + 49.4549i −0.509931 + 1.56941i
994994 0 0
995995 0 0
996996 −6.65003 9.15298i −0.210714 0.290023i
997997 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
998998 18.8300 + 6.11822i 0.596052 + 0.193669i
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 968.2.k.a.403.1 8
8.3 odd 2 CM 968.2.k.a.403.1 8
11.2 odd 10 inner 968.2.k.a.699.1 8
11.3 even 5 inner 968.2.k.a.723.2 8
11.4 even 5 inner 968.2.k.a.475.1 8
11.5 even 5 88.2.g.a.43.1 2
11.6 odd 10 88.2.g.a.43.2 yes 2
11.7 odd 10 inner 968.2.k.a.475.2 8
11.8 odd 10 inner 968.2.k.a.723.1 8
11.9 even 5 inner 968.2.k.a.699.2 8
11.10 odd 2 inner 968.2.k.a.403.2 8
33.5 odd 10 792.2.h.b.307.2 2
33.17 even 10 792.2.h.b.307.1 2
44.27 odd 10 352.2.g.a.175.1 2
44.39 even 10 352.2.g.a.175.2 2
88.3 odd 10 inner 968.2.k.a.723.2 8
88.5 even 10 352.2.g.a.175.1 2
88.19 even 10 inner 968.2.k.a.723.1 8
88.27 odd 10 88.2.g.a.43.1 2
88.35 even 10 inner 968.2.k.a.699.1 8
88.43 even 2 inner 968.2.k.a.403.2 8
88.51 even 10 inner 968.2.k.a.475.2 8
88.59 odd 10 inner 968.2.k.a.475.1 8
88.61 odd 10 352.2.g.a.175.2 2
88.75 odd 10 inner 968.2.k.a.699.2 8
88.83 even 10 88.2.g.a.43.2 yes 2
132.71 even 10 3168.2.h.b.2287.2 2
132.83 odd 10 3168.2.h.b.2287.1 2
176.5 even 20 2816.2.e.d.2815.1 4
176.27 odd 20 2816.2.e.d.2815.4 4
176.61 odd 20 2816.2.e.d.2815.3 4
176.83 even 20 2816.2.e.d.2815.2 4
176.93 even 20 2816.2.e.d.2815.4 4
176.115 odd 20 2816.2.e.d.2815.1 4
176.149 odd 20 2816.2.e.d.2815.2 4
176.171 even 20 2816.2.e.d.2815.3 4
264.5 odd 10 3168.2.h.b.2287.2 2
264.83 odd 10 792.2.h.b.307.1 2
264.149 even 10 3168.2.h.b.2287.1 2
264.203 even 10 792.2.h.b.307.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.2.g.a.43.1 2 11.5 even 5
88.2.g.a.43.1 2 88.27 odd 10
88.2.g.a.43.2 yes 2 11.6 odd 10
88.2.g.a.43.2 yes 2 88.83 even 10
352.2.g.a.175.1 2 44.27 odd 10
352.2.g.a.175.1 2 88.5 even 10
352.2.g.a.175.2 2 44.39 even 10
352.2.g.a.175.2 2 88.61 odd 10
792.2.h.b.307.1 2 33.17 even 10
792.2.h.b.307.1 2 264.83 odd 10
792.2.h.b.307.2 2 33.5 odd 10
792.2.h.b.307.2 2 264.203 even 10
968.2.k.a.403.1 8 1.1 even 1 trivial
968.2.k.a.403.1 8 8.3 odd 2 CM
968.2.k.a.403.2 8 11.10 odd 2 inner
968.2.k.a.403.2 8 88.43 even 2 inner
968.2.k.a.475.1 8 11.4 even 5 inner
968.2.k.a.475.1 8 88.59 odd 10 inner
968.2.k.a.475.2 8 11.7 odd 10 inner
968.2.k.a.475.2 8 88.51 even 10 inner
968.2.k.a.699.1 8 11.2 odd 10 inner
968.2.k.a.699.1 8 88.35 even 10 inner
968.2.k.a.699.2 8 11.9 even 5 inner
968.2.k.a.699.2 8 88.75 odd 10 inner
968.2.k.a.723.1 8 11.8 odd 10 inner
968.2.k.a.723.1 8 88.19 even 10 inner
968.2.k.a.723.2 8 11.3 even 5 inner
968.2.k.a.723.2 8 88.3 odd 10 inner
2816.2.e.d.2815.1 4 176.5 even 20
2816.2.e.d.2815.1 4 176.115 odd 20
2816.2.e.d.2815.2 4 176.83 even 20
2816.2.e.d.2815.2 4 176.149 odd 20
2816.2.e.d.2815.3 4 176.61 odd 20
2816.2.e.d.2815.3 4 176.171 even 20
2816.2.e.d.2815.4 4 176.27 odd 20
2816.2.e.d.2815.4 4 176.93 even 20
3168.2.h.b.2287.1 2 132.83 odd 10
3168.2.h.b.2287.1 2 264.149 even 10
3168.2.h.b.2287.2 2 132.71 even 10
3168.2.h.b.2287.2 2 264.5 odd 10