Properties

Label 1040.2.d.c.209.4
Level 10401040
Weight 22
Character 1040.209
Analytic conductor 8.3048.304
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1040,2,Mod(209,1040)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1040, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1040.209");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1040=24513 1040 = 2^{4} \cdot 5 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1040.d (of order 22, degree 11, 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: 8.304441810218.30444181021
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x62x5+2x4+2x3+4x24x+2 x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 209.4
Root 0.4030320.403032i0.403032 - 0.403032i of defining polynomial
Character χ\chi == 1040.209
Dual form 1040.2.d.c.209.3

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+0.481194iq3+(1.67513+1.48119i)q5+0.806063iq7+2.76845q9+3.67513q111.00000iq13+(0.712742+0.806063i)q15+1.35026iq171.67513q190.387873q216.48119iq23+(0.612127+4.96239i)q25+2.77575iq272.41819q29+5.28726q31+1.76845iq33+(1.19394+1.35026i)q353.76845iq37+0.481194q398.31265q41+6.79384iq43+(4.63752+4.10062i)q45+3.19394iq47+6.35026q490.649738q51+5.73813iq53+(6.15633+5.44358i)q550.806063iq57+5.98778q591.76845q61+2.23155iq63+(1.481191.67513i)q65+9.89446iq67+3.11871q698.56230q7111.7685iq73+(2.38787+0.294552i)q75+2.96239iq772.26187q79+6.96968q813.84367iq83+(2.00000+2.26187i)q851.16362iq872.77575q89+0.806063q91+2.54420iq93+(2.806062.48119i)q95+1.87399iq97+10.1744q99+O(q100)q+0.481194i q^{3} +(1.67513 + 1.48119i) q^{5} +0.806063i q^{7} +2.76845 q^{9} +3.67513 q^{11} -1.00000i q^{13} +(-0.712742 + 0.806063i) q^{15} +1.35026i q^{17} -1.67513 q^{19} -0.387873 q^{21} -6.48119i q^{23} +(0.612127 + 4.96239i) q^{25} +2.77575i q^{27} -2.41819 q^{29} +5.28726 q^{31} +1.76845i q^{33} +(-1.19394 + 1.35026i) q^{35} -3.76845i q^{37} +0.481194 q^{39} -8.31265 q^{41} +6.79384i q^{43} +(4.63752 + 4.10062i) q^{45} +3.19394i q^{47} +6.35026 q^{49} -0.649738 q^{51} +5.73813i q^{53} +(6.15633 + 5.44358i) q^{55} -0.806063i q^{57} +5.98778 q^{59} -1.76845 q^{61} +2.23155i q^{63} +(1.48119 - 1.67513i) q^{65} +9.89446i q^{67} +3.11871 q^{69} -8.56230 q^{71} -11.7685i q^{73} +(-2.38787 + 0.294552i) q^{75} +2.96239i q^{77} -2.26187 q^{79} +6.96968 q^{81} -3.84367i q^{83} +(-2.00000 + 2.26187i) q^{85} -1.16362i q^{87} -2.77575 q^{89} +0.806063 q^{91} +2.54420i q^{93} +(-2.80606 - 2.48119i) q^{95} +1.87399i q^{97} +10.1744 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q6q9+12q1116q154q21+2q2512q29+20q318q358q398q414q45+18q4924q51+16q5516q59+12q612q6524q69+16q99+O(q100) 6 q - 6 q^{9} + 12 q^{11} - 16 q^{15} - 4 q^{21} + 2 q^{25} - 12 q^{29} + 20 q^{31} - 8 q^{35} - 8 q^{39} - 8 q^{41} - 4 q^{45} + 18 q^{49} - 24 q^{51} + 16 q^{55} - 16 q^{59} + 12 q^{61} - 2 q^{65} - 24 q^{69}+ \cdots - 16 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1040Z)×\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times.

nn 261261 417417 561561 911911
χ(n)\chi(n) 11 1-1 11 11

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 0
33 0.481194i 0.277818i 0.990305 + 0.138909i 0.0443595π0.0443595\pi
−0.990305 + 0.138909i 0.955641π0.955641\pi
44 0 0
55 1.67513 + 1.48119i 0.749141 + 0.662410i
66 0 0
77 0.806063i 0.304663i 0.988329 + 0.152332i 0.0486782π0.0486782\pi
−0.988329 + 0.152332i 0.951322π0.951322\pi
88 0 0
99 2.76845 0.922817
1010 0 0
1111 3.67513 1.10809 0.554047 0.832486i 0.313083π-0.313083\pi
0.554047 + 0.832486i 0.313083π0.313083\pi
1212 0 0
1313 1.00000i 0.277350i
1414 0 0
1515 −0.712742 + 0.806063i −0.184029 + 0.208125i
1616 0 0
1717 1.35026i 0.327487i 0.986503 + 0.163743i 0.0523569π0.0523569\pi
−0.986503 + 0.163743i 0.947643π0.947643\pi
1818 0 0
1919 −1.67513 −0.384301 −0.192151 0.981365i 0.561546π-0.561546\pi
−0.192151 + 0.981365i 0.561546π0.561546\pi
2020 0 0
2121 −0.387873 −0.0846409
2222 0 0
2323 6.48119i 1.35142i −0.737166 0.675711i 0.763837π-0.763837\pi
0.737166 0.675711i 0.236163π-0.236163\pi
2424 0 0
2525 0.612127 + 4.96239i 0.122425 + 0.992478i
2626 0 0
2727 2.77575i 0.534193i
2828 0 0
2929 −2.41819 −0.449047 −0.224523 0.974469i 0.572083π-0.572083\pi
−0.224523 + 0.974469i 0.572083π0.572083\pi
3030 0 0
3131 5.28726 0.949620 0.474810 0.880088i 0.342517π-0.342517\pi
0.474810 + 0.880088i 0.342517π0.342517\pi
3232 0 0
3333 1.76845i 0.307848i
3434 0 0
3535 −1.19394 + 1.35026i −0.201812 + 0.228236i
3636 0 0
3737 3.76845i 0.619530i −0.950813 0.309765i 0.899750π-0.899750\pi
0.950813 0.309765i 0.100250π-0.100250\pi
3838 0 0
3939 0.481194 0.0770528
4040 0 0
4141 −8.31265 −1.29822 −0.649109 0.760695i 0.724858π-0.724858\pi
−0.649109 + 0.760695i 0.724858π0.724858\pi
4242 0 0
4343 6.79384i 1.03605i 0.855365 + 0.518026i 0.173333π0.173333\pi
−0.855365 + 0.518026i 0.826667π0.826667\pi
4444 0 0
4545 4.63752 + 4.10062i 0.691321 + 0.611284i
4646 0 0
4747 3.19394i 0.465884i 0.972491 + 0.232942i 0.0748352π0.0748352\pi
−0.972491 + 0.232942i 0.925165π0.925165\pi
4848 0 0
4949 6.35026 0.907180
5050 0 0
5151 −0.649738 −0.0909816
5252 0 0
5353 5.73813i 0.788193i 0.919069 + 0.394097i 0.128943π0.128943\pi
−0.919069 + 0.394097i 0.871057π0.871057\pi
5454 0 0
5555 6.15633 + 5.44358i 0.830119 + 0.734013i
5656 0 0
5757 0.806063i 0.106766i
5858 0 0
5959 5.98778 0.779543 0.389771 0.920912i 0.372554π-0.372554\pi
0.389771 + 0.920912i 0.372554π0.372554\pi
6060 0 0
6161 −1.76845 −0.226427 −0.113214 0.993571i 0.536114π-0.536114\pi
−0.113214 + 0.993571i 0.536114π0.536114\pi
6262 0 0
6363 2.23155i 0.281149i
6464 0 0
6565 1.48119 1.67513i 0.183720 0.207774i
6666 0 0
6767 9.89446i 1.20880i 0.796681 + 0.604400i 0.206587π0.206587\pi
−0.796681 + 0.604400i 0.793413π0.793413\pi
6868 0 0
6969 3.11871 0.375449
7070 0 0
7171 −8.56230 −1.01616 −0.508079 0.861311i 0.669644π-0.669644\pi
−0.508079 + 0.861311i 0.669644π0.669644\pi
7272 0 0
7373 11.7685i 1.37739i −0.725050 0.688697i 0.758183π-0.758183\pi
0.725050 0.688697i 0.241817π-0.241817\pi
7474 0 0
7575 −2.38787 + 0.294552i −0.275728 + 0.0340119i
7676 0 0
7777 2.96239i 0.337596i
7878 0 0
7979 −2.26187 −0.254480 −0.127240 0.991872i 0.540612π-0.540612\pi
−0.127240 + 0.991872i 0.540612π0.540612\pi
8080 0 0
8181 6.96968 0.774409
8282 0 0
8383 3.84367i 0.421898i −0.977497 0.210949i 0.932345π-0.932345\pi
0.977497 0.210949i 0.0676554π-0.0676554\pi
8484 0 0
8585 −2.00000 + 2.26187i −0.216930 + 0.245334i
8686 0 0
8787 1.16362i 0.124753i
8888 0 0
8989 −2.77575 −0.294229 −0.147114 0.989120i 0.546999π-0.546999\pi
−0.147114 + 0.989120i 0.546999π0.546999\pi
9090 0 0
9191 0.806063 0.0844984
9292 0 0
9393 2.54420i 0.263821i
9494 0 0
9595 −2.80606 2.48119i −0.287896 0.254565i
9696 0 0
9797 1.87399i 0.190275i 0.995464 + 0.0951375i 0.0303291π0.0303291\pi
−0.995464 + 0.0951375i 0.969671π0.969671\pi
9898 0 0
9999 10.1744 1.02257
100100 0 0
101101 10.4993 1.04472 0.522359 0.852725i 0.325052π-0.325052\pi
0.522359 + 0.852725i 0.325052π0.325052\pi
102102 0 0
103103 15.3684i 1.51429i −0.653247 0.757145i 0.726594π-0.726594\pi
0.653247 0.757145i 0.273406π-0.273406\pi
104104 0 0
105105 −0.649738 0.574515i −0.0634080 0.0560670i
106106 0 0
107107 11.1309i 1.07607i 0.842923 + 0.538034i 0.180833π0.180833\pi
−0.842923 + 0.538034i 0.819167π0.819167\pi
108108 0 0
109109 −9.58769 −0.918334 −0.459167 0.888350i 0.651852π-0.651852\pi
−0.459167 + 0.888350i 0.651852π0.651852\pi
110110 0 0
111111 1.81336 0.172116
112112 0 0
113113 0.574515i 0.0540459i 0.999635 + 0.0270229i 0.00860271π0.00860271\pi
−0.999635 + 0.0270229i 0.991397π0.991397\pi
114114 0 0
115115 9.59991 10.8568i 0.895196 1.01241i
116116 0 0
117117 2.76845i 0.255943i
118118 0 0
119119 −1.08840 −0.0997732
120120 0 0
121121 2.50659 0.227872
122122 0 0
123123 4.00000i 0.360668i
124124 0 0
125125 −6.32487 + 9.21933i −0.565713 + 0.824602i
126126 0 0
127127 4.29455i 0.381080i −0.981679 0.190540i 0.938976π-0.938976\pi
0.981679 0.190540i 0.0610239π-0.0610239\pi
128128 0 0
129129 −3.26916 −0.287833
130130 0 0
131131 0.836381 0.0730749 0.0365375 0.999332i 0.488367π-0.488367\pi
0.0365375 + 0.999332i 0.488367π0.488367\pi
132132 0 0
133133 1.35026i 0.117083i
134134 0 0
135135 −4.11142 + 4.64974i −0.353855 + 0.400186i
136136 0 0
137137 14.9380i 1.27624i 0.769939 + 0.638118i 0.220287π0.220287\pi
−0.769939 + 0.638118i 0.779713π0.779713\pi
138138 0 0
139139 −8.43866 −0.715758 −0.357879 0.933768i 0.616500π-0.616500\pi
−0.357879 + 0.933768i 0.616500π0.616500\pi
140140 0 0
141141 −1.53690 −0.129431
142142 0 0
143143 3.67513i 0.307330i
144144 0 0
145145 −4.05079 3.58181i −0.336399 0.297453i
146146 0 0
147147 3.05571i 0.252031i
148148 0 0
149149 11.3503 0.929850 0.464925 0.885350i 0.346081π-0.346081\pi
0.464925 + 0.885350i 0.346081π0.346081\pi
150150 0 0
151151 −13.9878 −1.13831 −0.569155 0.822230i 0.692729π-0.692729\pi
−0.569155 + 0.822230i 0.692729π0.692729\pi
152152 0 0
153153 3.73813i 0.302210i
154154 0 0
155155 8.85685 + 7.83146i 0.711399 + 0.629038i
156156 0 0
157157 2.77575i 0.221529i −0.993847 0.110764i 0.964670π-0.964670\pi
0.993847 0.110764i 0.0353299π-0.0353299\pi
158158 0 0
159159 −2.76116 −0.218974
160160 0 0
161161 5.22425 0.411729
162162 0 0
163163 2.23155i 0.174788i −0.996174 0.0873942i 0.972146π-0.972146\pi
0.996174 0.0873942i 0.0278540π-0.0278540\pi
164164 0 0
165165 −2.61942 + 2.96239i −0.203922 + 0.230622i
166166 0 0
167167 15.6932i 1.21438i −0.794557 0.607189i 0.792297π-0.792297\pi
0.794557 0.607189i 0.207703π-0.207703\pi
168168 0 0
169169 −1.00000 −0.0769231
170170 0 0
171171 −4.63752 −0.354640
172172 0 0
173173 25.5877i 1.94540i −0.232075 0.972698i 0.574551π-0.574551\pi
0.232075 0.972698i 0.425449π-0.425449\pi
174174 0 0
175175 −4.00000 + 0.493413i −0.302372 + 0.0372985i
176176 0 0
177177 2.88129i 0.216571i
178178 0 0
179179 12.1260 0.906340 0.453170 0.891424i 0.350293π-0.350293\pi
0.453170 + 0.891424i 0.350293π0.350293\pi
180180 0 0
181181 −2.73084 −0.202982 −0.101491 0.994836i 0.532361π-0.532361\pi
−0.101491 + 0.994836i 0.532361π0.532361\pi
182182 0 0
183183 0.850969i 0.0629054i
184184 0 0
185185 5.58181 6.31265i 0.410383 0.464115i
186186 0 0
187187 4.96239i 0.362886i
188188 0 0
189189 −2.23743 −0.162749
190190 0 0
191191 −20.6253 −1.49239 −0.746197 0.665725i 0.768122π-0.768122\pi
−0.746197 + 0.665725i 0.768122π0.768122\pi
192192 0 0
193193 21.7889i 1.56840i −0.620508 0.784200i 0.713073π-0.713073\pi
0.620508 0.784200i 0.286927π-0.286927\pi
194194 0 0
195195 0.806063 + 0.712742i 0.0577234 + 0.0510405i
196196 0 0
197197 2.00000i 0.142494i −0.997459 0.0712470i 0.977302π-0.977302\pi
0.997459 0.0712470i 0.0226979π-0.0226979\pi
198198 0 0
199199 −16.7513 −1.18747 −0.593734 0.804661i 0.702347π-0.702347\pi
−0.593734 + 0.804661i 0.702347π0.702347\pi
200200 0 0
201201 −4.76116 −0.335826
202202 0 0
203203 1.94921i 0.136808i
204204 0 0
205205 −13.9248 12.3127i −0.972549 0.859953i
206206 0 0
207207 17.9429i 1.24712i
208208 0 0
209209 −6.15633 −0.425842
210210 0 0
211211 4.90175 0.337451 0.168725 0.985663i 0.446035π-0.446035\pi
0.168725 + 0.985663i 0.446035π0.446035\pi
212212 0 0
213213 4.12013i 0.282307i
214214 0 0
215215 −10.0630 + 11.3806i −0.686291 + 0.776149i
216216 0 0
217217 4.26187i 0.289314i
218218 0 0
219219 5.66291 0.382664
220220 0 0
221221 1.35026 0.0908284
222222 0 0
223223 24.9076i 1.66794i −0.551811 0.833969i 0.686063π-0.686063\pi
0.551811 0.833969i 0.313937π-0.313937\pi
224224 0 0
225225 1.69464 + 13.7381i 0.112976 + 0.915876i
226226 0 0
227227 9.95509i 0.660743i 0.943851 + 0.330371i 0.107174π0.107174\pi
−0.943851 + 0.330371i 0.892826π0.892826\pi
228228 0 0
229229 −5.35026 −0.353555 −0.176778 0.984251i 0.556567π-0.556567\pi
−0.176778 + 0.984251i 0.556567π0.556567\pi
230230 0 0
231231 −1.42548 −0.0937900
232232 0 0
233233 10.7612i 0.704987i −0.935814 0.352493i 0.885334π-0.885334\pi
0.935814 0.352493i 0.114666π-0.114666\pi
234234 0 0
235235 −4.73084 + 5.35026i −0.308606 + 0.349013i
236236 0 0
237237 1.08840i 0.0706990i
238238 0 0
239239 −11.8618 −0.767274 −0.383637 0.923484i 0.625329π-0.625329\pi
−0.383637 + 0.923484i 0.625329π0.625329\pi
240240 0 0
241241 −28.6253 −1.84392 −0.921959 0.387288i 0.873412π-0.873412\pi
−0.921959 + 0.387288i 0.873412π0.873412\pi
242242 0 0
243243 11.6810i 0.749337i
244244 0 0
245245 10.6375 + 9.40597i 0.679606 + 0.600925i
246246 0 0
247247 1.67513i 0.106586i
248248 0 0
249249 1.84955 0.117211
250250 0 0
251251 19.3865 1.22366 0.611831 0.790988i 0.290433π-0.290433\pi
0.611831 + 0.790988i 0.290433π0.290433\pi
252252 0 0
253253 23.8192i 1.49750i
254254 0 0
255255 −1.08840 0.962389i −0.0681580 0.0602671i
256256 0 0
257257 22.8627i 1.42614i −0.701094 0.713069i 0.747305π-0.747305\pi
0.701094 0.713069i 0.252695π-0.252695\pi
258258 0 0
259259 3.03761 0.188748
260260 0 0
261261 −6.69464 −0.414388
262262 0 0
263263 21.8822i 1.34932i −0.738130 0.674658i 0.764291π-0.764291\pi
0.738130 0.674658i 0.235709π-0.235709\pi
264264 0 0
265265 −8.49929 + 9.61213i −0.522107 + 0.590468i
266266 0 0
267267 1.33567i 0.0817419i
268268 0 0
269269 −22.7513 −1.38717 −0.693586 0.720374i 0.743970π-0.743970\pi
−0.693586 + 0.720374i 0.743970π0.743970\pi
270270 0 0
271271 −0.123638 −0.00751049 −0.00375525 0.999993i 0.501195π-0.501195\pi
−0.00375525 + 0.999993i 0.501195π0.501195\pi
272272 0 0
273273 0.387873i 0.0234751i
274274 0 0
275275 2.24965 + 18.2374i 0.135659 + 1.09976i
276276 0 0
277277 15.3503i 0.922308i 0.887320 + 0.461154i 0.152564π0.152564\pi
−0.887320 + 0.461154i 0.847436π0.847436\pi
278278 0 0
279279 14.6375 0.876325
280280 0 0
281281 13.9248 0.830683 0.415341 0.909666i 0.363662π-0.363662\pi
0.415341 + 0.909666i 0.363662π0.363662\pi
282282 0 0
283283 20.3815i 1.21156i −0.795634 0.605778i 0.792862π-0.792862\pi
0.795634 0.605778i 0.207138π-0.207138\pi
284284 0 0
285285 1.19394 1.35026i 0.0707227 0.0799826i
286286 0 0
287287 6.70052i 0.395519i
288288 0 0
289289 15.1768 0.892753
290290 0 0
291291 −0.901754 −0.0528618
292292 0 0
293293 5.38058i 0.314337i 0.987572 + 0.157168i 0.0502365π0.0502365\pi
−0.987572 + 0.157168i 0.949763π0.949763\pi
294294 0 0
295295 10.0303 + 8.86907i 0.583988 + 0.516377i
296296 0 0
297297 10.2012i 0.591935i
298298 0 0
299299 −6.48119 −0.374817
300300 0 0
301301 −5.47627 −0.315647
302302 0 0
303303 5.05220i 0.290241i
304304 0 0
305305 −2.96239 2.61942i −0.169626 0.149988i
306306 0 0
307307 19.1695i 1.09406i −0.837113 0.547031i 0.815758π-0.815758\pi
0.837113 0.547031i 0.184242π-0.184242\pi
308308 0 0
309309 7.39517 0.420696
310310 0 0
311311 25.2506 1.43183 0.715915 0.698187i 0.246010π-0.246010\pi
0.715915 + 0.698187i 0.246010π0.246010\pi
312312 0 0
313313 2.81194i 0.158940i 0.996837 + 0.0794702i 0.0253229π0.0253229\pi
−0.996837 + 0.0794702i 0.974677π0.974677\pi
314314 0 0
315315 −3.30536 + 3.73813i −0.186236 + 0.210620i
316316 0 0
317317 23.7685i 1.33497i 0.744624 + 0.667485i 0.232629π0.232629\pi
−0.744624 + 0.667485i 0.767371π0.767371\pi
318318 0 0
319319 −8.88717 −0.497586
320320 0 0
321321 −5.35614 −0.298951
322322 0 0
323323 2.26187i 0.125854i
324324 0 0
325325 4.96239 0.612127i 0.275264 0.0339547i
326326 0 0
327327 4.61354i 0.255129i
328328 0 0
329329 −2.57452 −0.141938
330330 0 0
331331 11.8011 0.648649 0.324325 0.945946i 0.394863π-0.394863\pi
0.324325 + 0.945946i 0.394863π0.394863\pi
332332 0 0
333333 10.4328i 0.571713i
334334 0 0
335335 −14.6556 + 16.5745i −0.800722 + 0.905563i
336336 0 0
337337 16.1114i 0.877645i −0.898574 0.438822i 0.855396π-0.855396\pi
0.898574 0.438822i 0.144604π-0.144604\pi
338338 0 0
339339 −0.276454 −0.0150149
340340 0 0
341341 19.4314 1.05227
342342 0 0
343343 10.7612i 0.581048i
344344 0 0
345345 5.22425 + 4.61942i 0.281264 + 0.248701i
346346 0 0
347347 27.4944i 1.47598i 0.674814 + 0.737988i 0.264224π0.264224\pi
−0.674814 + 0.737988i 0.735776π0.735776\pi
348348 0 0
349349 17.6023 0.942228 0.471114 0.882072i 0.343852π-0.343852\pi
0.471114 + 0.882072i 0.343852π0.343852\pi
350350 0 0
351351 2.77575 0.148158
352352 0 0
353353 15.7685i 0.839270i 0.907693 + 0.419635i 0.137842π0.137842\pi
−0.907693 + 0.419635i 0.862158π0.862158\pi
354354 0 0
355355 −14.3430 12.6824i −0.761246 0.673113i
356356 0 0
357357 0.523730i 0.0277187i
358358 0 0
359359 −14.8242 −0.782389 −0.391195 0.920308i 0.627938π-0.627938\pi
−0.391195 + 0.920308i 0.627938π0.627938\pi
360360 0 0
361361 −16.1939 −0.852312
362362 0 0
363363 1.20616i 0.0633067i
364364 0 0
365365 17.4314 19.7137i 0.912399 1.03186i
366366 0 0
367367 27.0313i 1.41102i −0.708700 0.705510i 0.750718π-0.750718\pi
0.708700 0.705510i 0.249282π-0.249282\pi
368368 0 0
369369 −23.0132 −1.19802
370370 0 0
371371 −4.62530 −0.240134
372372 0 0
373373 12.9525i 0.670657i 0.942101 + 0.335329i 0.108847π0.108847\pi
−0.942101 + 0.335329i 0.891153π0.891153\pi
374374 0 0
375375 −4.43629 3.04349i −0.229089 0.157165i
376376 0 0
377377 2.41819i 0.124543i
378378 0 0
379379 −30.2858 −1.55568 −0.777840 0.628463i 0.783684π-0.783684\pi
−0.777840 + 0.628463i 0.783684π0.783684\pi
380380 0 0
381381 2.06651 0.105871
382382 0 0
383383 21.0943i 1.07787i 0.842348 + 0.538934i 0.181173π0.181173\pi
−0.842348 + 0.538934i 0.818827π0.818827\pi
384384 0 0
385385 −4.38787 + 4.96239i −0.223627 + 0.252907i
386386 0 0
387387 18.8084i 0.956086i
388388 0 0
389389 6.77575 0.343544 0.171772 0.985137i 0.445051π-0.445051\pi
0.171772 + 0.985137i 0.445051π0.445051\pi
390390 0 0
391391 8.75131 0.442573
392392 0 0
393393 0.402462i 0.0203015i
394394 0 0
395395 −3.78892 3.35026i −0.190641 0.168570i
396396 0 0
397397 10.4690i 0.525423i −0.964874 0.262711i 0.915383π-0.915383\pi
0.964874 0.262711i 0.0846167π-0.0846167\pi
398398 0 0
399399 0.649738 0.0325276
400400 0 0
401401 5.01317 0.250346 0.125173 0.992135i 0.460051π-0.460051\pi
0.125173 + 0.992135i 0.460051π0.460051\pi
402402 0 0
403403 5.28726i 0.263377i
404404 0 0
405405 11.6751 + 10.3235i 0.580142 + 0.512977i
406406 0 0
407407 13.8496i 0.686497i
408408 0 0
409409 14.3879 0.711435 0.355717 0.934594i 0.384237π-0.384237\pi
0.355717 + 0.934594i 0.384237π0.384237\pi
410410 0 0
411411 −7.18806 −0.354561
412412 0 0
413413 4.82653i 0.237498i
414414 0 0
415415 5.69323 6.43866i 0.279470 0.316061i
416416 0 0
417417 4.06063i 0.198850i
418418 0 0
419419 17.4617 0.853059 0.426529 0.904474i 0.359736π-0.359736\pi
0.426529 + 0.904474i 0.359736π0.359736\pi
420420 0 0
421421 2.88717 0.140712 0.0703559 0.997522i 0.477586π-0.477586\pi
0.0703559 + 0.997522i 0.477586π0.477586\pi
422422 0 0
423423 8.84226i 0.429925i
424424 0 0
425425 −6.70052 + 0.826531i −0.325023 + 0.0400927i
426426 0 0
427427 1.42548i 0.0689840i
428428 0 0
429429 1.76845 0.0853817
430430 0 0
431431 −0.889535 −0.0428474 −0.0214237 0.999770i 0.506820π-0.506820\pi
−0.0214237 + 0.999770i 0.506820π0.506820\pi
432432 0 0
433433 25.2506i 1.21347i −0.794906 0.606733i 0.792480π-0.792480\pi
0.794906 0.606733i 0.207520π-0.207520\pi
434434 0 0
435435 1.72355 1.94921i 0.0826377 0.0934577i
436436 0 0
437437 10.8568i 0.519354i
438438 0 0
439439 28.8119 1.37512 0.687560 0.726128i 0.258682π-0.258682\pi
0.687560 + 0.726128i 0.258682π0.258682\pi
440440 0 0
441441 17.5804 0.837162
442442 0 0
443443 36.9805i 1.75700i −0.477746 0.878498i 0.658546π-0.658546\pi
0.477746 0.878498i 0.341454π-0.341454\pi
444444 0 0
445445 −4.64974 4.11142i −0.220419 0.194900i
446446 0 0
447447 5.46168i 0.258329i
448448 0 0
449449 12.6859 0.598686 0.299343 0.954146i 0.403232π-0.403232\pi
0.299343 + 0.954146i 0.403232π0.403232\pi
450450 0 0
451451 −30.5501 −1.43855
452452 0 0
453453 6.73084i 0.316242i
454454 0 0
455455 1.35026 + 1.19394i 0.0633012 + 0.0559726i
456456 0 0
457457 25.0494i 1.17176i 0.810398 + 0.585880i 0.199251π0.199251\pi
−0.810398 + 0.585880i 0.800749π0.800749\pi
458458 0 0
459459 −3.74798 −0.174941
460460 0 0
461461 −36.8872 −1.71801 −0.859003 0.511970i 0.828916π-0.828916\pi
−0.859003 + 0.511970i 0.828916π0.828916\pi
462462 0 0
463463 39.0191i 1.81337i 0.421809 + 0.906685i 0.361395π0.361395\pi
−0.421809 + 0.906685i 0.638605π0.638605\pi
464464 0 0
465465 −3.76845 + 4.26187i −0.174758 + 0.197639i
466466 0 0
467467 32.7694i 1.51639i 0.652029 + 0.758194i 0.273918π0.273918\pi
−0.652029 + 0.758194i 0.726082π0.726082\pi
468468 0 0
469469 −7.97556 −0.368277
470470 0 0
471471 1.33567 0.0615446
472472 0 0
473473 24.9683i 1.14804i
474474 0 0
475475 −1.02539 8.31265i −0.0470482 0.381411i
476476 0 0
477477 15.8858i 0.727359i
478478 0 0
479479 16.8749 0.771036 0.385518 0.922700i 0.374023π-0.374023\pi
0.385518 + 0.922700i 0.374023π0.374023\pi
480480 0 0
481481 −3.76845 −0.171827
482482 0 0
483483 2.51388i 0.114386i
484484 0 0
485485 −2.77575 + 3.13918i −0.126040 + 0.142543i
486486 0 0
487487 9.24472i 0.418918i −0.977817 0.209459i 0.932830π-0.932830\pi
0.977817 0.209459i 0.0671703π-0.0671703\pi
488488 0 0
489489 1.07381 0.0485593
490490 0 0
491491 25.7499 1.16208 0.581038 0.813876i 0.302647π-0.302647\pi
0.581038 + 0.813876i 0.302647π0.302647\pi
492492 0 0
493493 3.26519i 0.147057i
494494 0 0
495495 17.0435 + 15.0703i 0.766048 + 0.677360i
496496 0 0
497497 6.90175i 0.309586i
498498 0 0
499499 −27.7015 −1.24009 −0.620044 0.784567i 0.712885π-0.712885\pi
−0.620044 + 0.784567i 0.712885π0.712885\pi
500500 0 0
501501 7.55149 0.337376
502502 0 0
503503 2.35519i 0.105013i −0.998621 0.0525063i 0.983279π-0.983279\pi
0.998621 0.0525063i 0.0167210π-0.0167210\pi
504504 0 0
505505 17.5877 + 15.5515i 0.782642 + 0.692032i
506506 0 0
507507 0.481194i 0.0213706i
508508 0 0
509509 −21.5125 −0.953523 −0.476762 0.879033i 0.658190π-0.658190\pi
−0.476762 + 0.879033i 0.658190π0.658190\pi
510510 0 0
511511 9.48612 0.419641
512512 0 0
513513 4.64974i 0.205291i
514514 0 0
515515 22.7635 25.7440i 1.00308 1.13442i
516516 0 0
517517 11.7381i 0.516243i
518518 0 0
519519 12.3127 0.540465
520520 0 0
521521 37.7440 1.65360 0.826798 0.562499i 0.190160π-0.190160\pi
0.826798 + 0.562499i 0.190160π0.190160\pi
522522 0 0
523523 23.7416i 1.03815i −0.854729 0.519075i 0.826277π-0.826277\pi
0.854729 0.519075i 0.173723π-0.173723\pi
524524 0 0
525525 −0.237428 1.92478i −0.0103622 0.0840042i
526526 0 0
527527 7.13918i 0.310988i
528528 0 0
529529 −19.0059 −0.826343
530530 0 0
531531 16.5769 0.719376
532532 0 0
533533 8.31265i 0.360061i
534534 0 0
535535 −16.4871 + 18.6458i −0.712798 + 0.806127i
536536 0 0
537537 5.83497i 0.251797i
538538 0 0
539539 23.3380 1.00524
540540 0 0
541541 13.0376 0.560531 0.280265 0.959923i 0.409578π-0.409578\pi
0.280265 + 0.959923i 0.409578π0.409578\pi
542542 0 0
543543 1.31406i 0.0563919i
544544 0 0
545545 −16.0606 14.2012i −0.687962 0.608314i
546546 0 0
547547 8.43041i 0.360458i 0.983625 + 0.180229i 0.0576839π0.0576839\pi
−0.983625 + 0.180229i 0.942316π0.942316\pi
548548 0 0
549549 −4.89587 −0.208951
550550 0 0
551551 4.05079 0.172569
552552 0 0
553553 1.82321i 0.0775306i
554554 0 0
555555 3.03761 + 2.68594i 0.128939 + 0.114012i
556556 0 0
557557 13.6932i 0.580201i −0.956996 0.290100i 0.906311π-0.906311\pi
0.956996 0.290100i 0.0936887π-0.0936887\pi
558558 0 0
559559 6.79384 0.287349
560560 0 0
561561 −2.38787 −0.100816
562562 0 0
563563 8.86907i 0.373787i 0.982380 + 0.186893i 0.0598419π0.0598419\pi
−0.982380 + 0.186893i 0.940158π0.940158\pi
564564 0 0
565565 −0.850969 + 0.962389i −0.0358005 + 0.0404880i
566566 0 0
567567 5.61801i 0.235934i
568568 0 0
569569 32.7816 1.37428 0.687139 0.726526i 0.258866π-0.258866\pi
0.687139 + 0.726526i 0.258866π0.258866\pi
570570 0 0
571571 −40.2882 −1.68601 −0.843005 0.537906i 0.819215π-0.819215\pi
−0.843005 + 0.537906i 0.819215π0.819215\pi
572572 0 0
573573 9.92478i 0.414614i
574574 0 0
575575 32.1622 3.96731i 1.34126 0.165448i
576576 0 0
577577 28.8568i 1.20133i −0.799502 0.600663i 0.794903π-0.794903\pi
0.799502 0.600663i 0.205097π-0.205097\pi
578578 0 0
579579 10.4847 0.435729
580580 0 0
581581 3.09825 0.128537
582582 0 0
583583 21.0884i 0.873392i
584584 0 0
585585 4.10062 4.63752i 0.169540 0.191738i
586586 0 0
587587 41.6786i 1.72026i 0.510074 + 0.860131i 0.329618π0.329618\pi
−0.510074 + 0.860131i 0.670382π0.670382\pi
588588 0 0
589589 −8.85685 −0.364940
590590 0 0
591591 0.962389 0.0395874
592592 0 0
593593 22.4993i 0.923935i 0.886897 + 0.461968i 0.152856π0.152856\pi
−0.886897 + 0.461968i 0.847144π0.847144\pi
594594 0 0
595595 −1.82321 1.61213i −0.0747442 0.0660908i
596596 0 0
597597 8.06063i 0.329900i
598598 0 0
599599 4.15045 0.169583 0.0847913 0.996399i 0.472978π-0.472978\pi
0.0847913 + 0.996399i 0.472978π0.472978\pi
600600 0 0
601601 27.9248 1.13908 0.569538 0.821965i 0.307122π-0.307122\pi
0.569538 + 0.821965i 0.307122π0.307122\pi
602602 0 0
603603 27.3923i 1.11550i
604604 0 0
605605 4.19886 + 3.71274i 0.170708 + 0.150944i
606606 0 0
607607 8.19489i 0.332620i 0.986073 + 0.166310i 0.0531853π0.0531853\pi
−0.986073 + 0.166310i 0.946815π0.946815\pi
608608 0 0
609609 0.937951 0.0380077
610610 0 0
611611 3.19394 0.129213
612612 0 0
613613 33.1392i 1.33848i 0.743047 + 0.669239i 0.233380π0.233380\pi
−0.743047 + 0.669239i 0.766620π0.766620\pi
614614 0 0
615615 5.92478 6.70052i 0.238910 0.270191i
616616 0 0
617617 29.0132i 1.16803i 0.811744 + 0.584013i 0.198518π0.198518\pi
−0.811744 + 0.584013i 0.801482π0.801482\pi
618618 0 0
619619 12.2134 0.490900 0.245450 0.969409i 0.421064π-0.421064\pi
0.245450 + 0.969409i 0.421064π0.421064\pi
620620 0 0
621621 17.9902 0.721920
622622 0 0
623623 2.23743i 0.0896406i
624624 0 0
625625 −24.2506 + 6.07522i −0.970024 + 0.243009i
626626 0 0
627627 2.96239i 0.118306i
628628 0 0
629629 5.08840 0.202888
630630 0 0
631631 1.22188 0.0486424 0.0243212 0.999704i 0.492258π-0.492258\pi
0.0243212 + 0.999704i 0.492258π0.492258\pi
632632 0 0
633633 2.35870i 0.0937498i
634634 0 0
635635 6.36107 7.19394i 0.252431 0.285483i
636636 0 0
637637 6.35026i 0.251607i
638638 0 0
639639 −23.7043 −0.937728
640640 0 0
641641 −22.1016 −0.872960 −0.436480 0.899714i 0.643775π-0.643775\pi
−0.436480 + 0.899714i 0.643775π0.643775\pi
642642 0 0
643643 11.6688i 0.460172i −0.973170 0.230086i 0.926099π-0.926099\pi
0.973170 0.230086i 0.0739008π-0.0739008\pi
644644 0 0
645645 −5.47627 4.84226i −0.215628 0.190664i
646646 0 0
647647 11.9575i 0.470096i 0.971984 + 0.235048i 0.0755248π0.0755248\pi
−0.971984 + 0.235048i 0.924475π0.924475\pi
648648 0 0
649649 22.0059 0.863806
650650 0 0
651651 −2.05079 −0.0803766
652652 0 0
653653 10.9986i 0.430408i −0.976569 0.215204i 0.930958π-0.930958\pi
0.976569 0.215204i 0.0690416π-0.0690416\pi
654654 0 0
655655 1.40105 + 1.23884i 0.0547434 + 0.0484056i
656656 0 0
657657 32.5804i 1.27108i
658658 0 0
659659 −2.63989 −0.102835 −0.0514177 0.998677i 0.516374π-0.516374\pi
−0.0514177 + 0.998677i 0.516374π0.516374\pi
660660 0 0
661661 18.3028 0.711896 0.355948 0.934506i 0.384158π-0.384158\pi
0.355948 + 0.934506i 0.384158π0.384158\pi
662662 0 0
663663 0.649738i 0.0252337i
664664 0 0
665665 2.00000 2.26187i 0.0775567 0.0877114i
666666 0 0
667667 15.6728i 0.606852i
668668 0 0
669669 11.9854 0.463383
670670 0 0
671671 −6.49929 −0.250902
672672 0 0
673673 6.71037i 0.258666i 0.991601 + 0.129333i 0.0412836π0.0412836\pi
−0.991601 + 0.129333i 0.958716π0.958716\pi
674674 0 0
675675 −13.7743 + 1.69911i −0.530174 + 0.0653987i
676676 0 0
677677 1.57593i 0.0605679i 0.999541 + 0.0302840i 0.00964116π0.00964116\pi
−0.999541 + 0.0302840i 0.990359π0.990359\pi
678678 0 0
679679 −1.51056 −0.0579698
680680 0 0
681681 −4.79033 −0.183566
682682 0 0
683683 15.1939i 0.581380i −0.956817 0.290690i 0.906115π-0.906115\pi
0.956817 0.290690i 0.0938848π-0.0938848\pi
684684 0 0
685685 −22.1260 + 25.0230i −0.845391 + 0.956081i
686686 0 0
687687 2.57452i 0.0982239i
688688 0 0
689689 5.73813 0.218606
690690 0 0
691691 18.7127 0.711866 0.355933 0.934511i 0.384163π-0.384163\pi
0.355933 + 0.934511i 0.384163π0.384163\pi
692692 0 0
693693 8.20123i 0.311539i
694694 0 0
695695 −14.1359 12.4993i −0.536204 0.474125i
696696 0 0
697697 11.2243i 0.425149i
698698 0 0
699699 5.17821 0.195858
700700 0 0
701701 24.3028 0.917904 0.458952 0.888461i 0.348225π-0.348225\pi
0.458952 + 0.888461i 0.348225π0.348225\pi
702702 0 0
703703 6.31265i 0.238086i
704704 0 0
705705 −2.57452 2.27645i −0.0969619 0.0857362i
706706 0 0
707707 8.46310i 0.318287i
708708 0 0
709709 9.66291 0.362898 0.181449 0.983400i 0.441921π-0.441921\pi
0.181449 + 0.983400i 0.441921π0.441921\pi
710710 0 0
711711 −6.26187 −0.234838
712712 0 0
713713 34.2677i 1.28334i
714714 0 0
715715 5.44358 6.15633i 0.203578 0.230234i
716716 0 0
717717 5.70782i 0.213162i
718718 0 0
719719 28.4142 1.05967 0.529836 0.848100i 0.322254π-0.322254\pi
0.529836 + 0.848100i 0.322254π0.322254\pi
720720 0 0
721721 12.3879 0.461349
722722 0 0
723723 13.7743i 0.512273i
724724 0 0
725725 −1.48024 12.0000i −0.0549747 0.445669i
726726 0 0
727727 34.8545i 1.29268i −0.763049 0.646341i 0.776299π-0.776299\pi
0.763049 0.646341i 0.223701π-0.223701\pi
728728 0 0
729729 15.2882 0.566230
730730 0 0
731731 −9.17347 −0.339293
732732 0 0
733733 6.25202i 0.230923i 0.993312 + 0.115462i 0.0368348π0.0368348\pi
−0.993312 + 0.115462i 0.963165π0.963165\pi
734734 0 0
735735 −4.52610 + 5.11871i −0.166948 + 0.188807i
736736 0 0
737737 36.3634i 1.33946i
738738 0 0
739739 −32.0846 −1.18025 −0.590126 0.807311i 0.700922π-0.700922\pi
−0.590126 + 0.807311i 0.700922π0.700922\pi
740740 0 0
741741 −0.806063 −0.0296115
742742 0 0
743743 30.5442i 1.12056i 0.828304 + 0.560279i 0.189306π0.189306\pi
−0.828304 + 0.560279i 0.810694π0.810694\pi
744744 0 0
745745 19.0132 + 16.8119i 0.696589 + 0.615942i
746746 0 0
747747 10.6410i 0.389335i
748748 0 0
749749 −8.97224 −0.327838
750750 0 0
751751 −28.1622 −1.02765 −0.513827 0.857894i 0.671773π-0.671773\pi
−0.513827 + 0.857894i 0.671773π0.671773\pi
752752 0 0
753753 9.32865i 0.339955i
754754 0 0
755755 −23.4314 20.7186i −0.852755 0.754028i
756756 0 0
757757 35.4109i 1.28703i −0.765433 0.643515i 0.777475π-0.777475\pi
0.765433 0.643515i 0.222525π-0.222525\pi
758758 0 0
759759 11.4617 0.416033
760760 0 0
761761 −19.2388 −0.697407 −0.348704 0.937233i 0.613378π-0.613378\pi
−0.348704 + 0.937233i 0.613378π0.613378\pi
762762 0 0
763763 7.72829i 0.279783i
764764 0 0
765765 −5.53690 + 6.26187i −0.200187 + 0.226398i
766766 0 0
767767 5.98778i 0.216206i
768768 0 0
769769 −48.9643 −1.76570 −0.882849 0.469657i 0.844378π-0.844378\pi
−0.882849 + 0.469657i 0.844378π0.844378\pi
770770 0 0
771771 11.0014 0.396206
772772 0 0
773773 46.1681i 1.66055i 0.557354 + 0.830275i 0.311817π0.311817\pi
−0.557354 + 0.830275i 0.688183π0.688183\pi
774774 0 0
775775 3.23647 + 26.2374i 0.116258 + 0.942476i
776776 0 0
777777 1.46168i 0.0524375i
778778 0 0
779779 13.9248 0.498907
780780 0 0
781781 −31.4676 −1.12600
782782 0 0
783783 6.71228i 0.239877i
784784 0 0
785785 4.11142 4.64974i 0.146743 0.165956i
786786 0 0
787787 22.6458i 0.807234i −0.914928 0.403617i 0.867753π-0.867753\pi
0.914928 0.403617i 0.132247π-0.132247\pi
788788 0 0
789789 10.5296 0.374864
790790 0 0
791791 −0.463096 −0.0164658
792792 0 0
793793 1.76845i 0.0627996i
794794 0 0
795795 −4.62530 4.08981i −0.164043 0.145051i
796796 0 0
797797 8.23743i 0.291785i −0.989300 0.145892i 0.953395π-0.953395\pi
0.989300 0.145892i 0.0466053π-0.0466053\pi
798798 0 0
799799 −4.31265 −0.152571
800800 0 0
801801 −7.68452 −0.271519
802802 0 0
803803 43.2506i 1.52628i
804804 0 0
805805 8.75131 + 7.73813i 0.308443 + 0.272733i
806806 0 0
807807 10.9478i 0.385381i
808808 0 0
809809 −44.1319 −1.55159 −0.775797 0.630982i 0.782652π-0.782652\pi
−0.775797 + 0.630982i 0.782652π0.782652\pi
810810 0 0
811811 −22.6883 −0.796694 −0.398347 0.917235i 0.630416π-0.630416\pi
−0.398347 + 0.917235i 0.630416π0.630416\pi
812812 0 0
813813 0.0594941i 0.00208655i
814814 0 0
815815 3.30536 3.73813i 0.115782 0.130941i
816816 0 0
817817 11.3806i 0.398156i
818818 0 0
819819 2.23155 0.0779766
820820 0 0
821821 −50.2736 −1.75456 −0.877281 0.479978i 0.840645π-0.840645\pi
−0.877281 + 0.479978i 0.840645π0.840645\pi
822822 0 0
823823 5.13093i 0.178853i −0.995993 0.0894265i 0.971497π-0.971497\pi
0.995993 0.0894265i 0.0285034π-0.0285034\pi
824824 0 0
825825 −8.77575 + 1.08252i −0.305532 + 0.0376884i
826826 0 0
827827 18.6946i 0.650076i 0.945701 + 0.325038i 0.105377π0.105377\pi
−0.945701 + 0.325038i 0.894623π0.894623\pi
828828 0 0
829829 3.44121 0.119518 0.0597591 0.998213i 0.480967π-0.480967\pi
0.0597591 + 0.998213i 0.480967π0.480967\pi
830830 0 0
831831 −7.38646 −0.256233
832832 0 0
833833 8.57452i 0.297089i
834834 0 0
835835 23.2447 26.2882i 0.804417 0.909741i
836836 0 0
837837 14.6761i 0.507280i
838838 0 0
839839 −52.6248 −1.81681 −0.908406 0.418090i 0.862700π-0.862700\pi
−0.908406 + 0.418090i 0.862700π0.862700\pi
840840 0 0
841841 −23.1524 −0.798357
842842 0 0
843843 6.70052i 0.230778i
844844 0 0
845845 −1.67513 1.48119i −0.0576263 0.0509546i
846846 0 0
847847 2.02047i 0.0694241i
848848 0 0
849849 9.80748 0.336592
850850 0 0
851851 −24.4241 −0.837246
852852 0 0
853853 6.31853i 0.216342i −0.994132 0.108171i 0.965501π-0.965501\pi
0.994132 0.108171i 0.0344995π-0.0344995\pi
854854 0 0
855855 −7.76845 6.86907i −0.265675 0.234917i
856856 0 0
857857 0.775746i 0.0264990i 0.999912 + 0.0132495i 0.00421757π0.00421757\pi
−0.999912 + 0.0132495i 0.995782π0.995782\pi
858858 0 0
859859 3.24869 0.110844 0.0554220 0.998463i 0.482350π-0.482350\pi
0.0554220 + 0.998463i 0.482350π0.482350\pi
860860 0 0
861861 3.22425 0.109882
862862 0 0
863863 19.9208i 0.678112i 0.940766 + 0.339056i 0.110108π0.110108\pi
−0.940766 + 0.339056i 0.889892π0.889892\pi
864864 0 0
865865 37.9003 42.8627i 1.28865 1.45738i
866866 0 0
867867 7.30299i 0.248022i
868868 0 0
869869 −8.31265 −0.281987
870870 0 0
871871 9.89446 0.335261
872872 0 0
873873 5.18806i 0.175589i
874874 0 0
875875 −7.43136 5.09825i −0.251226 0.172352i
876876 0 0
877877 22.1378i 0.747539i −0.927522 0.373770i 0.878065π-0.878065\pi
0.927522 0.373770i 0.121935π-0.121935\pi
878878 0 0
879879 −2.58910 −0.0873283
880880 0 0
881881 2.23155 0.0751828 0.0375914 0.999293i 0.488031π-0.488031\pi
0.0375914 + 0.999293i 0.488031π0.488031\pi
882882 0 0
883883 4.30440i 0.144855i 0.997374 + 0.0724273i 0.0230745π0.0230745\pi
−0.997374 + 0.0724273i 0.976925π0.976925\pi
884884 0 0
885885 −4.26774 + 4.82653i −0.143459 + 0.162242i
886886 0 0
887887 15.9330i 0.534979i 0.963561 + 0.267489i 0.0861940π0.0861940\pi
−0.963561 + 0.267489i 0.913806π0.913806\pi
888888 0 0
889889 3.46168 0.116101
890890 0 0
891891 25.6145 0.858118
892892 0 0
893893 5.35026i 0.179040i
894894 0 0
895895 20.3127 + 17.9610i 0.678977 + 0.600369i
896896 0 0
897897 3.11871i 0.104131i
898898 0 0
899899 −12.7856 −0.426423
900900 0 0
901901 −7.74798 −0.258123
902902 0 0
903903 2.63515i 0.0876923i
904904 0 0
905905 −4.57452 4.04491i −0.152062 0.134457i
906906 0 0
907907 51.9086i 1.72360i −0.507251 0.861798i 0.669338π-0.669338\pi
0.507251 0.861798i 0.330662π-0.330662\pi
908908 0 0
909909 29.0668 0.964085
910910 0 0
911911 9.67750 0.320630 0.160315 0.987066i 0.448749π-0.448749\pi
0.160315 + 0.987066i 0.448749π0.448749\pi
912912 0 0
913913 14.1260i 0.467503i
914914 0 0
915915 1.26045 1.42548i 0.0416692 0.0471251i
916916 0 0
917917 0.674176i 0.0222632i
918918 0 0
919919 13.5515 0.447022 0.223511 0.974701i 0.428248π-0.428248\pi
0.223511 + 0.974701i 0.428248π0.428248\pi
920920 0 0
921921 9.22425 0.303949
922922 0 0
923923 8.56230i 0.281831i
924924 0 0
925925 18.7005 2.30677i 0.614869 0.0758462i
926926 0 0
927927 42.5466i 1.39741i
928928 0 0
929929 9.44992 0.310042 0.155021 0.987911i 0.450455π-0.450455\pi
0.155021 + 0.987911i 0.450455π0.450455\pi
930930 0 0
931931 −10.6375 −0.348631
932932 0 0
933933 12.1504i 0.397788i
934934 0 0
935935 −7.35026 + 8.31265i −0.240379 + 0.271853i
936936 0 0
937937 16.0409i 0.524035i −0.965063 0.262017i 0.915612π-0.915612\pi
0.965063 0.262017i 0.0843877π-0.0843877\pi
938938 0 0
939939 −1.35309 −0.0441565
940940 0 0
941941 −21.6747 −0.706574 −0.353287 0.935515i 0.614936π-0.614936\pi
−0.353287 + 0.935515i 0.614936π0.614936\pi
942942 0 0
943943 53.8759i 1.75444i
944944 0 0
945945 −3.74798 3.31406i −0.121922 0.107807i
946946 0 0
947947 4.63118i 0.150493i −0.997165 0.0752466i 0.976026π-0.976026\pi
0.997165 0.0752466i 0.0239744π-0.0239744\pi
948948 0 0
949949 −11.7685 −0.382020
950950 0 0
951951 −11.4372 −0.370878
952952 0 0
953953 26.2981i 0.851878i 0.904752 + 0.425939i 0.140056π0.140056\pi
−0.904752 + 0.425939i 0.859944π0.859944\pi
954954 0 0
955955 −34.5501 30.5501i −1.11801 0.988577i
956956 0 0
957957 4.27645i 0.138238i
958958 0 0
959959 −12.0409 −0.388822
960960 0 0
961961 −3.04491 −0.0982228
962962 0 0
963963 30.8155i 0.993014i
964964 0 0
965965 32.2736 36.4993i 1.03892 1.17495i
966966 0 0
967967 11.9405i 0.383981i −0.981397 0.191990i 0.938506π-0.938506\pi
0.981397 0.191990i 0.0614942π-0.0614942\pi
968968 0 0
969969 1.08840 0.0349643
970970 0 0
971971 −30.1524 −0.967635 −0.483818 0.875169i 0.660750π-0.660750\pi
−0.483818 + 0.875169i 0.660750π0.660750\pi
972972 0 0
973973 6.80209i 0.218065i
974974 0 0
975975 0.294552 + 2.38787i 0.00943321 + 0.0764731i
976976 0 0
977977 26.9321i 0.861633i −0.902439 0.430817i 0.858226π-0.858226\pi
0.902439 0.430817i 0.141774π-0.141774\pi
978978 0 0
979979 −10.2012 −0.326033
980980 0 0
981981 −26.5431 −0.847455
982982 0 0
983983 20.5902i 0.656727i 0.944551 + 0.328363i 0.106497π0.106497\pi
−0.944551 + 0.328363i 0.893503π0.893503\pi
984984 0 0
985985 2.96239 3.35026i 0.0943895 0.106748i
986986 0 0
987987 1.23884i 0.0394328i
988988 0 0
989989 44.0322 1.40014
990990 0 0
991991 48.1378 1.52915 0.764573 0.644537i 0.222950π-0.222950\pi
0.764573 + 0.644537i 0.222950π0.222950\pi
992992 0 0
993993 5.67864i 0.180206i
994994 0 0
995995 −28.0606 24.8119i −0.889582 0.786591i
996996 0 0
997997 33.4255i 1.05860i −0.848436 0.529298i 0.822455π-0.822455\pi
0.848436 0.529298i 0.177545π-0.177545\pi
998998 0 0
999999 10.4603 0.330948
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 1040.2.d.c.209.4 6
4.3 odd 2 65.2.b.a.14.1 6
5.2 odd 4 5200.2.a.cb.1.3 3
5.3 odd 4 5200.2.a.cj.1.1 3
5.4 even 2 inner 1040.2.d.c.209.3 6
12.11 even 2 585.2.c.b.469.6 6
20.3 even 4 325.2.a.j.1.1 3
20.7 even 4 325.2.a.k.1.3 3
20.19 odd 2 65.2.b.a.14.6 yes 6
52.3 odd 6 845.2.n.f.529.6 12
52.7 even 12 845.2.l.d.699.1 12
52.11 even 12 845.2.l.d.654.2 12
52.15 even 12 845.2.l.e.654.6 12
52.19 even 12 845.2.l.e.699.5 12
52.23 odd 6 845.2.n.g.529.1 12
52.31 even 4 845.2.d.a.844.1 6
52.35 odd 6 845.2.n.f.484.1 12
52.43 odd 6 845.2.n.g.484.6 12
52.47 even 4 845.2.d.b.844.5 6
52.51 odd 2 845.2.b.c.339.6 6
60.23 odd 4 2925.2.a.bj.1.3 3
60.47 odd 4 2925.2.a.bf.1.1 3
60.59 even 2 585.2.c.b.469.1 6
260.19 even 12 845.2.l.d.699.2 12
260.59 even 12 845.2.l.e.699.6 12
260.99 even 4 845.2.d.a.844.2 6
260.103 even 4 4225.2.a.bh.1.3 3
260.119 even 12 845.2.l.d.654.1 12
260.139 odd 6 845.2.n.f.484.6 12
260.159 odd 6 845.2.n.f.529.1 12
260.179 odd 6 845.2.n.g.529.6 12
260.199 odd 6 845.2.n.g.484.1 12
260.207 even 4 4225.2.a.ba.1.1 3
260.219 even 12 845.2.l.e.654.5 12
260.239 even 4 845.2.d.b.844.6 6
260.259 odd 2 845.2.b.c.339.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.b.a.14.1 6 4.3 odd 2
65.2.b.a.14.6 yes 6 20.19 odd 2
325.2.a.j.1.1 3 20.3 even 4
325.2.a.k.1.3 3 20.7 even 4
585.2.c.b.469.1 6 60.59 even 2
585.2.c.b.469.6 6 12.11 even 2
845.2.b.c.339.1 6 260.259 odd 2
845.2.b.c.339.6 6 52.51 odd 2
845.2.d.a.844.1 6 52.31 even 4
845.2.d.a.844.2 6 260.99 even 4
845.2.d.b.844.5 6 52.47 even 4
845.2.d.b.844.6 6 260.239 even 4
845.2.l.d.654.1 12 260.119 even 12
845.2.l.d.654.2 12 52.11 even 12
845.2.l.d.699.1 12 52.7 even 12
845.2.l.d.699.2 12 260.19 even 12
845.2.l.e.654.5 12 260.219 even 12
845.2.l.e.654.6 12 52.15 even 12
845.2.l.e.699.5 12 52.19 even 12
845.2.l.e.699.6 12 260.59 even 12
845.2.n.f.484.1 12 52.35 odd 6
845.2.n.f.484.6 12 260.139 odd 6
845.2.n.f.529.1 12 260.159 odd 6
845.2.n.f.529.6 12 52.3 odd 6
845.2.n.g.484.1 12 260.199 odd 6
845.2.n.g.484.6 12 52.43 odd 6
845.2.n.g.529.1 12 52.23 odd 6
845.2.n.g.529.6 12 260.179 odd 6
1040.2.d.c.209.3 6 5.4 even 2 inner
1040.2.d.c.209.4 6 1.1 even 1 trivial
2925.2.a.bf.1.1 3 60.47 odd 4
2925.2.a.bj.1.3 3 60.23 odd 4
4225.2.a.ba.1.1 3 260.207 even 4
4225.2.a.bh.1.3 3 260.103 even 4
5200.2.a.cb.1.3 3 5.2 odd 4
5200.2.a.cj.1.1 3 5.3 odd 4