Properties

Label 507.2.x.a.50.1
Level 507507
Weight 22
Character 507.50
Analytic conductor 4.0484.048
Analytic rank 00
Dimension 4848
CM discriminant -3
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(2,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(156))
 
chi = DirichletCharacter(H, H._module([78, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 507=3132 507 = 3 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 507.x (of order 156156, degree 4848, 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: 4.048415382484.04841538248
Analytic rank: 00
Dimension: 4848
Twist minimal: yes
Sato-Tate group: U(1)[D156]\mathrm{U}(1)[D_{156}]

Embedding invariants

Embedding label 50.1
Character χ\chi == 507.50
Dual form 507.2.x.a.71.1

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+(1.642910.548485i)q3+(1.44240+1.38545i)q4+(0.680973+0.0688013i)q7+(2.39833+1.80223i)q9+(1.609853.06731i)q12+(2.59808+2.50000i)q13+(0.161064+3.99676i)q16+(4.019311.07697i)q19+(1.081040.486538i)q21+(4.11492+2.84032i)q25+(2.951754.27635i)q27+(0.886918+1.04269i)q28+(1.98869+10.8519i)q31+(0.962468+5.92230i)q36+(3.49870+9.81714i)q37+(5.639632.68228i)q39+(11.53655.47415i)q43+(1.927556.65466i)q48+(6.399541.30648i)q49+(7.21110+0.00651091i)q52+(7.194070.435161i)q57+(11.3705+1.84789i)q61+(1.50920+1.39228i)q63+(5.30498+5.98809i)q64+(0.26188813.0027i)q67+(13.181810.3273i)q73+(5.202586.92338i)q75+(7.28955+4.01512i)q76+(0.4414060.108797i)q79+(2.50396+8.64466i)q81+(0.8852282.19951i)q84+(1.94122+1.52368i)q91+(9.2193716.7380i)q93+(16.59213.73686i)q97+O(q100)q+(-1.64291 - 0.548485i) q^{3} +(1.44240 + 1.38545i) q^{4} +(0.680973 + 0.0688013i) q^{7} +(2.39833 + 1.80223i) q^{9} +(-1.60985 - 3.06731i) q^{12} +(-2.59808 + 2.50000i) q^{13} +(0.161064 + 3.99676i) q^{16} +(4.01931 - 1.07697i) q^{19} +(-1.08104 - 0.486538i) q^{21} +(4.11492 + 2.84032i) q^{25} +(-2.95175 - 4.27635i) q^{27} +(0.886918 + 1.04269i) q^{28} +(-1.98869 + 10.8519i) q^{31} +(0.962468 + 5.92230i) q^{36} +(3.49870 + 9.81714i) q^{37} +(5.63963 - 2.68228i) q^{39} +(11.5365 - 5.47415i) q^{43} +(1.92755 - 6.65466i) q^{48} +(-6.39954 - 1.30648i) q^{49} +(-7.21110 + 0.00651091i) q^{52} +(-7.19407 - 0.435161i) q^{57} +(11.3705 + 1.84789i) q^{61} +(1.50920 + 1.39228i) q^{63} +(-5.30498 + 5.98809i) q^{64} +(0.261888 - 13.0027i) q^{67} +(-13.1818 - 10.3273i) q^{73} +(-5.20258 - 6.92338i) q^{75} +(7.28955 + 4.01512i) q^{76} +(0.441406 - 0.108797i) q^{79} +(2.50396 + 8.64466i) q^{81} +(-0.885228 - 2.19951i) q^{84} +(-1.94122 + 1.52368i) q^{91} +(9.21937 - 16.7380i) q^{93} +(-16.5921 - 3.73686i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q+10q7+6q98q1614q1918q21+20q28+14q31+2q37+24q39+6q4318q4928q5212q5724q6332q67+34q73+30q75++38q97+O(q100) 48 q + 10 q^{7} + 6 q^{9} - 8 q^{16} - 14 q^{19} - 18 q^{21} + 20 q^{28} + 14 q^{31} + 2 q^{37} + 24 q^{39} + 6 q^{43} - 18 q^{49} - 28 q^{52} - 12 q^{57} - 24 q^{63} - 32 q^{67} + 34 q^{73} + 30 q^{75}+ \cdots + 38 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/507Z)×\left(\mathbb{Z}/507\mathbb{Z}\right)^\times.

nn 170170 340340
χ(n)\chi(n) 1-1 e(19156)e\left(\frac{19}{156}\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 0 −0.927686 0.373361i 0.878205π-0.878205\pi
0.927686 + 0.373361i 0.121795π0.121795\pi
33 −1.64291 0.548485i −0.948536 0.316668i
44 1.44240 + 1.38545i 0.721202 + 0.692724i
55 0 0 −0.954721 0.297503i 0.903846π-0.903846\pi
0.954721 + 0.297503i 0.0961538π0.0961538\pi
66 0 0
77 0.680973 + 0.0688013i 0.257384 + 0.0260044i 0.228369 0.973575i 0.426661π-0.426661\pi
0.0290142 + 0.999579i 0.490763π0.490763\pi
88 0 0
99 2.39833 + 1.80223i 0.799443 + 0.600742i
1010 0 0
1111 0 0 0.140502 0.990080i 0.455128π-0.455128\pi
−0.140502 + 0.990080i 0.544872π0.544872\pi
1212 −1.60985 3.06731i −0.464723 0.885456i
1313 −2.59808 + 2.50000i −0.720577 + 0.693375i
1414 0 0
1515 0 0
1616 0.161064 + 3.99676i 0.0402659 + 0.999189i
1717 0 0 0.774605 0.632445i 0.217949π-0.217949\pi
−0.774605 + 0.632445i 0.782051π0.782051\pi
1818 0 0
1919 4.01931 1.07697i 0.922092 0.247074i 0.233613 0.972330i 0.424945π-0.424945\pi
0.688479 + 0.725256i 0.258279π0.258279\pi
2020 0 0
2121 −1.08104 0.486538i −0.235903 0.106171i
2222 0 0
2323 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
2424 0 0
2525 4.11492 + 2.84032i 0.822984 + 0.568065i
2626 0 0
2727 −2.95175 4.27635i −0.568065 0.822984i
2828 0.886918 + 1.04269i 0.167612 + 0.197050i
2929 0 0 0.919979 0.391967i 0.128205π-0.128205\pi
−0.919979 + 0.391967i 0.871795π0.871795\pi
3030 0 0
3131 −1.98869 + 10.8519i −0.357179 + 1.94906i −0.0451919 + 0.998978i 0.514390π0.514390\pi
−0.311987 + 0.950086i 0.600995π0.600995\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0.962468 + 5.92230i 0.160411 + 0.987050i
3737 3.49870 + 9.81714i 0.575182 + 1.61393i 0.773504 + 0.633791i 0.218502π0.218502\pi
−0.198322 + 0.980137i 0.563549π0.563549\pi
3838 0 0
3939 5.63963 2.68228i 0.903063 0.429508i
4040 0 0
4141 0 0 −0.446798 0.894635i 0.647436π-0.647436\pi
0.446798 + 0.894635i 0.352564π0.352564\pi
4242 0 0
4343 11.5365 5.47415i 1.75930 0.834800i 0.781904 0.623399i 0.214249π-0.214249\pi
0.977399 0.211401i 0.0678026π-0.0678026\pi
4444 0 0
4545 0 0
4646 0 0
4747 0 0 0.517338 0.855781i 0.326923π-0.326923\pi
−0.517338 + 0.855781i 0.673077π0.673077\pi
4848 1.92755 6.65466i 0.278217 0.960518i
4949 −6.39954 1.30648i −0.914221 0.186639i
5050 0 0
5151 0 0
5252 −7.21110 + 0.00651091i −1.00000 + 0.000902901i
5353 0 0 0.354605 0.935016i 0.384615π-0.384615\pi
−0.354605 + 0.935016i 0.615385π0.615385\pi
5454 0 0
5555 0 0
5656 0 0
5757 −7.19407 0.435161i −0.952878 0.0576385i
5858 0 0
5959 0 0 −0.678061 0.735006i 0.737179π-0.737179\pi
0.678061 + 0.735006i 0.262821π0.262821\pi
6060 0 0
6161 11.3705 + 1.84789i 1.45585 + 0.236598i 0.836261 0.548331i 0.184737π-0.184737\pi
0.619586 + 0.784929i 0.287301π0.287301\pi
6262 0 0
6363 1.50920 + 1.39228i 0.190141 + 0.175410i
6464 −5.30498 + 5.98809i −0.663123 + 0.748511i
6565 0 0
6666 0 0
6767 0.261888 13.0027i 0.0319948 1.58853i −0.591242 0.806494i 0.701362π-0.701362\pi
0.623237 0.782033i 0.285817π-0.285817\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 0.551377 0.834256i 0.314103π-0.314103\pi
−0.551377 + 0.834256i 0.685897π0.685897\pi
7272 0 0
7373 −13.1818 10.3273i −1.54281 1.20872i −0.894258 0.447552i 0.852296π-0.852296\pi
−0.648557 0.761166i 0.724627π-0.724627\pi
7474 0 0
7575 −5.20258 6.92338i −0.600742 0.799443i
7676 7.28955 + 4.01512i 0.836169 + 0.460565i
7777 0 0
7878 0 0
7979 0.441406 0.108797i 0.0496620 0.0122406i −0.214406 0.976745i 0.568782π-0.568782\pi
0.264068 + 0.964504i 0.414936π0.414936\pi
8080 0 0
8181 2.50396 + 8.64466i 0.278217 + 0.960518i
8282 0 0
8383 0 0 −0.0603785 0.998176i 0.519231π-0.519231\pi
0.0603785 + 0.998176i 0.480769π0.480769\pi
8484 −0.885228 2.19951i −0.0965863 0.239987i
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
9090 0 0
9191 −1.94122 + 1.52368i −0.203495 + 0.159725i
9292 0 0
9393 9.21937 16.7380i 0.956004 1.73565i
9494 0 0
9595 0 0
9696 0 0
9797 −16.5921 3.73686i −1.68468 0.379420i −0.731501 0.681841i 0.761180π-0.761180\pi
−0.953175 + 0.302420i 0.902205π0.902205\pi
9898 0 0
9999 0 0
100100 2.00026 + 9.79791i 0.200026 + 0.979791i
101101 0 0 0.0804666 0.996757i 0.474359π-0.474359\pi
−0.0804666 + 0.996757i 0.525641π0.525641\pi
102102 0 0
103103 −13.1592 14.8537i −1.29661 1.46358i −0.805645 0.592399i 0.798181π-0.798181\pi
−0.490970 0.871177i 0.663357π-0.663357\pi
104104 0 0
105105 0 0
106106 0 0
107107 0 0 −0.845190 0.534466i 0.820513π-0.820513\pi
0.845190 + 0.534466i 0.179487π0.179487\pi
108108 1.66704 10.2577i 0.160411 0.987050i
109109 −2.57272 + 0.471469i −0.246422 + 0.0451586i −0.302046 0.953293i 0.597670π-0.597670\pi
0.0556241 + 0.998452i 0.482285π0.482285\pi
110110 0 0
111111 −0.363501 18.0477i −0.0345020 1.71301i
112112 −0.165302 + 2.73276i −0.0156195 + 0.258222i
113113 0 0 0.948536 0.316668i 0.102564π-0.102564\pi
−0.948536 + 0.316668i 0.897436π0.897436\pi
114114 0 0
115115 0 0
116116 0 0
117117 −10.7366 + 1.31350i −0.992600 + 0.121433i
118118 0 0
119119 0 0
120120 0 0
121121 −10.5657 3.06039i −0.960518 0.278217i
122122 0 0
123123 0 0
124124 −17.9033 + 12.8977i −1.60776 + 1.15824i
125125 0 0
126126 0 0
127127 8.18527 7.86205i 0.726325 0.697644i −0.235327 0.971916i 0.575616π-0.575616\pi
0.961652 + 0.274272i 0.0884367π0.0884367\pi
128128 0 0
129129 −21.9560 + 2.66594i −1.93312 + 0.234723i
130130 0 0
131131 0 0 0.120537 0.992709i 0.461538π-0.461538\pi
−0.120537 + 0.992709i 0.538462π0.538462\pi
132132 0 0
133133 2.81113 0.456854i 0.243756 0.0396143i
134134 0 0
135135 0 0
136136 0 0
137137 0 0 −0.941967 0.335705i 0.891026π-0.891026\pi
0.941967 + 0.335705i 0.108974π0.108974\pi
138138 0 0
139139 19.0229 12.0294i 1.61351 1.02032i 0.647407 0.762144i 0.275853π-0.275853\pi
0.966098 0.258175i 0.0831210π-0.0831210\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 −6.81678 + 9.87581i −0.568065 + 0.822984i
145145 0 0
146146 0 0
147147 9.79731 + 5.65648i 0.808069 + 0.466539i
148148 −8.55461 + 19.0076i −0.703184 + 1.56241i
149149 0 0 0.875918 0.482459i 0.160256π-0.160256\pi
−0.875918 + 0.482459i 0.839744π0.839744\pi
150150 0 0
151151 19.7946 11.9663i 1.61087 0.973802i 0.630602 0.776107i 0.282808π-0.282808\pi
0.980263 0.197696i 0.0633457π-0.0633457\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 11.8508 + 3.94448i 0.948822 + 0.315811i
157157 4.68563 2.45921i 0.373954 0.196266i −0.267267 0.963623i 0.586121π-0.586121\pi
0.641221 + 0.767356i 0.278428π0.278428\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 0.391770 0.460579i 0.0306858 0.0360754i −0.746156 0.665771i 0.768103π-0.768103\pi
0.776842 + 0.629696i 0.216821π0.216821\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 0.373361 0.927686i 0.378205π-0.378205\pi
−0.373361 + 0.927686i 0.621795π0.621795\pi
168168 0 0
169169 0.500000 12.9904i 0.0384615 0.999260i
170170 0 0
171171 11.5806 + 4.66077i 0.885587 + 0.356418i
172172 24.2245 + 8.08732i 1.84710 + 0.616653i
173173 0 0 −0.721202 0.692724i 0.756410π-0.756410\pi
0.721202 + 0.692724i 0.243590π0.243590\pi
174174 0 0
175175 2.60673 + 2.21730i 0.197050 + 0.167612i
176176 0 0
177177 0 0
178178 0 0
179179 0 0 −0.774605 0.632445i 0.782051π-0.782051\pi
0.774605 + 0.632445i 0.217949π0.217949\pi
180180 0 0
181181 8.11496 + 15.4618i 0.603180 + 1.14926i 0.975260 + 0.221062i 0.0709525π0.0709525\pi
−0.372080 + 0.928201i 0.621355π0.621355\pi
182182 0 0
183183 −17.6673 9.27249i −1.30600 0.685442i
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 −1.71584 3.11516i −0.124809 0.226595i
190190 0 0
191191 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
192192 12.0000 6.92820i 0.866025 0.500000i
193193 1.46521 + 14.5022i 0.105468 + 1.04389i 0.899770 + 0.436365i 0.143734π0.143734\pi
−0.794302 + 0.607524i 0.792163π0.792163\pi
194194 0 0
195195 0 0
196196 −7.42068 10.7507i −0.530048 0.767908i
197197 0 0 −0.647915 0.761712i 0.724359π-0.724359\pi
0.647915 + 0.761712i 0.275641π0.275641\pi
198198 0 0
199199 10.8515 + 17.1602i 0.769239 + 1.21645i 0.971481 + 0.237119i 0.0762031π0.0762031\pi
−0.202241 + 0.979336i 0.564823π0.564823\pi
200200 0 0
201201 −7.56202 + 21.2186i −0.533384 + 1.49664i
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 −10.4103 9.98122i −0.721828 0.692073i
209209 0 0
210210 0 0
211211 −2.81244 2.92806i −0.193616 0.201576i 0.617317 0.786714i 0.288220π-0.288220\pi
−0.810933 + 0.585139i 0.801040π0.801040\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 −2.10087 + 7.25305i −0.142616 + 0.492369i
218218 0 0
219219 15.9922 + 24.1969i 1.08065 + 1.63507i
220220 0 0
221221 0 0
222222 0 0
223223 −2.73557 12.1463i −0.183187 0.813375i −0.978346 0.206974i 0.933638π-0.933638\pi
0.795159 0.606401i 0.207387π-0.207387\pi
224224 0 0
225225 4.75002 + 14.2280i 0.316668 + 0.948536i
226226 0 0
227227 0 0 0.999797 0.0201371i 0.00641026π-0.00641026\pi
−0.999797 + 0.0201371i 0.993590π0.993590\pi
228228 −9.77387 10.5947i −0.647290 0.701651i
229229 −4.75667 25.9563i −0.314330 1.71524i −0.638823 0.769354i 0.720578π-0.720578\pi
0.324493 0.945888i 0.394806π-0.394806\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 0.663123 0.748511i 0.269231π-0.269231\pi
−0.663123 + 0.748511i 0.730769π0.730769\pi
234234 0 0
235235 0 0
236236 0 0
237237 −0.784865 0.0633608i −0.0509824 0.00411573i
238238 0 0
239239 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
240240 0 0
241241 −0.517638 + 2.29838i −0.0333440 + 0.148052i −0.989423 0.145056i 0.953664π-0.953664\pi
0.956079 + 0.293108i 0.0946894π0.0946894\pi
242242 0 0
243243 0.627684 15.5758i 0.0402659 0.999189i
244244 13.8407 + 18.4187i 0.886063 + 1.17914i
245245 0 0
246246 0 0
247247 −7.75004 + 12.8463i −0.493123 + 0.817391i
248248 0 0
249249 0 0
250250 0 0
251251 0 0 −0.0804666 0.996757i 0.525641π-0.525641\pi
0.0804666 + 0.996757i 0.474359π0.474359\pi
252252 0.247953 + 4.09915i 0.0156195 + 0.258222i
253253 0 0
254254 0 0
255255 0 0
256256 −15.9481 + 1.28747i −0.996757 + 0.0804666i
257257 0 0 0.960518 0.278217i 0.0897436π-0.0897436\pi
−0.960518 + 0.278217i 0.910256π0.910256\pi
258258 0 0
259259 1.70709 + 6.92592i 0.106073 + 0.430356i
260260 0 0
261261 0 0
262262 0 0
263263 0 0 0.799443 0.600742i 0.205128π-0.205128\pi
−0.799443 + 0.600742i 0.794872π0.794872\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 18.3923 18.3923i 1.12349 1.12349i
269269 0 0 −0.200026 0.979791i 0.564103π-0.564103\pi
0.200026 + 0.979791i 0.435897π0.435897\pi
270270 0 0
271271 −16.7498 0.337359i −1.01748 0.0204931i −0.491403 0.870933i 0.663516π-0.663516\pi
−0.526073 + 0.850439i 0.676336π0.676336\pi
272272 0 0
273273 4.02498 1.43854i 0.243603 0.0870647i
274274 0 0
275275 0 0
276276 0 0
277277 −5.26128 + 32.3740i −0.316120 + 1.94516i 0.0103260 + 0.999947i 0.496713π0.496713\pi
−0.326446 + 0.945216i 0.605851π0.605851\pi
278278 0 0
279279 −24.3272 + 22.4424i −1.45643 + 1.34359i
280280 0 0
281281 0 0 0.0603785 0.998176i 0.480769π-0.480769\pi
−0.0603785 + 0.998176i 0.519231π0.519231\pi
282282 0 0
283283 10.5454 + 5.00387i 0.626860 + 0.297449i 0.715498 0.698615i 0.246200π-0.246200\pi
−0.0886374 + 0.996064i 0.528251π0.528251\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 3.40044 16.6564i 0.200026 0.979791i
290290 0 0
291291 25.2098 + 15.2399i 1.47783 + 0.893377i
292292 −4.70558 33.1589i −0.275373 1.94048i
293293 0 0 0.811378 0.584522i 0.198718π-0.198718\pi
−0.811378 + 0.584522i 0.801282π0.801282\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 2.08776 17.1942i 0.120537 0.992709i
301301 8.23269 2.93402i 0.474524 0.169114i
302302 0 0
303303 0 0
304304 4.95175 + 15.8907i 0.284002 + 0.911395i
305305 0 0
306306 0 0
307307 −32.0929 5.88124i −1.83164 0.335660i −0.850056 0.526693i 0.823432π-0.823432\pi
−0.981584 + 0.191033i 0.938816π0.938816\pi
308308 0 0
309309 13.4724 + 31.6209i 0.766419 + 1.79885i
310310 0 0
311311 0 0 0.822984 0.568065i 0.192308π-0.192308\pi
−0.822984 + 0.568065i 0.807692π0.807692\pi
312312 0 0
313313 18.8900 27.3669i 1.06773 1.54687i 0.252616 0.967567i 0.418709π-0.418709\pi
0.815111 0.579304i 0.196676π-0.196676\pi
314314 0 0
315315 0 0
316316 0.787418 + 0.454616i 0.0442957 + 0.0255741i
317317 0 0 0.410413 0.911900i 0.365385π-0.365385\pi
−0.410413 + 0.911900i 0.634615π0.634615\pi
318318 0 0
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 0 0
324324 −8.36502 + 15.9382i −0.464723 + 0.885456i
325325 −17.7917 + 2.90792i −0.986905 + 0.161302i
326326 0 0
327327 4.48536 + 0.636518i 0.248041 + 0.0351995i
328328 0 0
329329 0 0
330330 0 0
331331 2.71991 26.9208i 0.149500 1.47970i −0.590468 0.807061i 0.701057π-0.701057\pi
0.739968 0.672642i 0.234841π-0.234841\pi
332332 0 0
333333 −9.30169 + 29.8502i −0.509730 + 1.63578i
334334 0 0
335335 0 0
336336 1.77046 4.39903i 0.0965863 0.239987i
337337 31.3370i 1.70703i 0.521065 + 0.853517i 0.325535π0.325535\pi
−0.521065 + 0.853517i 0.674465π0.674465\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 −8.84217 2.75533i −0.477432 0.148774i
344344 0 0
345345 0 0
346346 0 0
347347 0 0 −0.799443 0.600742i 0.794872π-0.794872\pi
0.799443 + 0.600742i 0.205128π0.205128\pi
348348 0 0
349349 0.640299 4.51200i 0.0342744 0.241522i −0.965551 0.260214i 0.916207π-0.916207\pi
0.999825 + 0.0186925i 0.00595035π0.00595035\pi
350350 0 0
351351 18.3597 + 3.73090i 0.979971 + 0.199141i
352352 0 0
353353 0 0 −0.811378 0.584522i 0.801282π-0.801282\pi
0.811378 + 0.584522i 0.198718π0.198718\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 −0.911900 0.410413i 0.865385π-0.865385\pi
0.911900 + 0.410413i 0.134615π0.134615\pi
360360 0 0
361361 −1.45953 + 0.842661i −0.0768174 + 0.0443506i
362362 0 0
363363 15.6799 + 10.8231i 0.822984 + 0.568065i
364364 −4.91101 0.491699i −0.257407 0.0257720i
365365 0 0
366366 0 0
367367 35.0835 14.9477i 1.83135 0.780264i 0.877792 0.479042i 0.159016π-0.159016\pi
0.953554 0.301222i 0.0973945π-0.0973945\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 36.4877 11.3700i 1.89180 0.589509i
373373 29.6280 + 12.6233i 1.53408 + 0.653609i 0.983456 0.181146i 0.0579805π-0.0579805\pi
0.550622 + 0.834755i 0.314391π0.314391\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 14.4596 + 28.9528i 0.742740 + 1.48720i 0.868790 + 0.495181i 0.164898π0.164898\pi
−0.126050 + 0.992024i 0.540230π0.540230\pi
380380 0 0
381381 −17.7599 + 8.42718i −0.909867 + 0.431737i
382382 0 0
383383 0 0 −0.584522 0.811378i 0.698718π-0.698718\pi
0.584522 + 0.811378i 0.301282π0.301282\pi
384384 0 0
385385 0 0
386386 0 0
387387 37.5340 + 7.66263i 1.90796 + 0.389513i
388388 −18.7553 28.3776i −0.952158 1.44065i
389389 0 0 0.935016 0.354605i 0.115385π-0.115385\pi
−0.935016 + 0.354605i 0.884615π0.884615\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 −14.5546 15.7769i −0.730475 0.791822i 0.254026 0.967197i 0.418245π-0.418245\pi
−0.984502 + 0.175376i 0.943886π0.943886\pi
398398 0 0
399399 −4.86903 0.791294i −0.243756 0.0396143i
400400 −10.6893 + 16.9038i −0.534466 + 0.845190i
401401 0 0 −0.735006 0.678061i 0.762821π-0.762821\pi
0.735006 + 0.678061i 0.237179π0.237179\pi
402402 0 0
403403 −21.9631 33.1659i −1.09406 1.65211i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 −21.8179 + 33.0114i −1.07883 + 1.63231i −0.366574 + 0.930389i 0.619469π0.619469\pi
−0.712254 + 0.701922i 0.752326π0.752326\pi
410410 0 0
411411 0 0
412412 1.59810 39.6564i 0.0787327 1.95373i
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 −37.8510 + 9.32943i −1.85357 + 0.456864i
418418 0 0
419419 0 0 −0.278217 0.960518i 0.589744π-0.589744\pi
0.278217 + 0.960518i 0.410256π0.410256\pi
420420 0 0
421421 −1.74861 28.9080i −0.0852220 1.40889i −0.749798 0.661667i 0.769849π-0.769849\pi
0.664576 0.747221i 0.268612π-0.268612\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 7.61588 + 2.04067i 0.368558 + 0.0987550i
428428 0 0
429429 0 0
430430 0 0
431431 0 0 0.482459 0.875918i 0.339744π-0.339744\pi
−0.482459 + 0.875918i 0.660256π0.660256\pi
432432 16.6161 12.4862i 0.799443 0.600742i
433433 26.5497 + 1.06992i 1.27590 + 0.0514169i 0.668940 0.743317i 0.266748π-0.266748\pi
0.606958 + 0.794734i 0.292389π0.292389\pi
434434 0 0
435435 0 0
436436 −4.36411 2.88433i −0.209003 0.138134i
437437 0 0
438438 0 0
439439 0.652051 8.07710i 0.0311207 0.385499i −0.962383 0.271697i 0.912415π-0.912415\pi
0.993503 0.113802i 0.0363029π-0.0363029\pi
440440 0 0
441441 −12.9936 14.6668i −0.618745 0.698419i
442442 0 0
443443 0 0 −0.748511 0.663123i 0.769231π-0.769231\pi
0.748511 + 0.663123i 0.230769π0.230769\pi
444444 24.4798 26.5357i 1.16176 1.25933i
445445 0 0
446446 0 0
447447 0 0
448448 −4.02454 + 3.71273i −0.190141 + 0.175410i
449449 0 0 −0.0201371 0.999797i 0.506410π-0.506410\pi
0.0201371 + 0.999797i 0.493590π0.493590\pi
450450 0 0
451451 0 0
452452 0 0
453453 −39.0842 + 8.80249i −1.83634 + 0.413577i
454454 0 0
455455 0 0
456456 0 0
457457 −19.8328 + 13.1079i −0.927738 + 0.613161i −0.922154 0.386823i 0.873572π-0.873572\pi
−0.00558406 + 0.999984i 0.501777π0.501777\pi
458458 0 0
459459 0 0
460460 0 0
461461 0 0 −0.140502 0.990080i 0.544872π-0.544872\pi
0.140502 + 0.990080i 0.455128π0.455128\pi
462462 0 0
463463 −15.5139 19.8020i −0.720990 0.920276i 0.278200 0.960523i 0.410262π-0.410262\pi
−0.999190 + 0.0402476i 0.987185π0.987185\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 0.992709 0.120537i 0.0384615π-0.0384615\pi
−0.992709 + 0.120537i 0.961538π0.961538\pi
468468 −17.3063 12.9804i −0.799985 0.600020i
469469 1.07294 8.83644i 0.0495437 0.408029i
470470 0 0
471471 −9.04692 + 1.47027i −0.416860 + 0.0677464i
472472 0 0
473473 0 0
474474 0 0
475475 19.5981 + 6.98449i 0.899221 + 0.320470i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 0.761712 0.647915i 0.224359π-0.224359\pi
−0.761712 + 0.647915i 0.775641π0.775641\pi
480480 0 0
481481 −33.6327 16.7589i −1.53352 0.764142i
482482 0 0
483483 0 0
484484 −11.0000 19.0526i −0.500000 0.866025i
485485 0 0
486486 0 0
487487 −31.4124 + 17.3021i −1.42343 + 0.784032i −0.992946 0.118565i 0.962171π-0.962171\pi
−0.430486 + 0.902597i 0.641658π0.641658\pi
488488 0 0
489489 −0.896266 + 0.541812i −0.0405305 + 0.0245016i
490490 0 0
491491 0 0 0.999189 0.0402659i 0.0128205π-0.0128205\pi
−0.999189 + 0.0402659i 0.987179π0.987179\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 −43.6928 6.20046i −1.96187 0.278409i
497497 0 0
498498 0 0
499499 −19.4014 + 8.73188i −0.868528 + 0.390893i −0.795151 0.606412i 0.792608π-0.792608\pi
−0.0733768 + 0.997304i 0.523378π0.523378\pi
500500 0 0
501501 0 0
502502 0 0
503503 0 0 0.692724 0.721202i 0.256410π-0.256410\pi
−0.692724 + 0.721202i 0.743590π0.743590\pi
504504 0 0
505505 0 0
506506 0 0
507507 −7.94649 + 21.0678i −0.352916 + 0.935655i
508508 22.6989 1.00710
509509 0 0 −0.927686 0.373361i 0.878205π-0.878205\pi
0.927686 + 0.373361i 0.121795π0.121795\pi
510510 0 0
511511 −8.26593 7.93953i −0.365663 0.351224i
512512 0 0
513513 −16.4695 14.0090i −0.727146 0.618513i
514514 0 0
515515 0 0
516516 −35.3630 26.5735i −1.55677 1.16984i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0 0 −0.885456 0.464723i 0.846154π-0.846154\pi
0.885456 + 0.464723i 0.153846π0.153846\pi
522522 0 0
523523 −1.76126 43.7052i −0.0770145 1.91110i −0.330581 0.943778i 0.607245π-0.607245\pi
0.253567 0.967318i 0.418396π-0.418396\pi
524524 0 0
525525 −3.06648 5.07258i −0.133832 0.221385i
526526 0 0
527527 0 0
528528 0 0
529529 11.5000 19.9186i 0.500000 0.866025i
530530 0 0
531531 0 0
532532 4.68774 + 3.23571i 0.203239 + 0.140286i
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 43.5890 13.5829i 1.87404 0.583974i 0.879997 0.474979i 0.157544π-0.157544\pi
0.994042 0.108996i 0.0347635π-0.0347635\pi
542542 0 0
543543 −4.85163 29.8533i −0.208203 1.28113i
544544 0 0
545545 0 0
546546 0 0
547547 −5.44792 44.8677i −0.232936 1.91840i −0.372209 0.928149i 0.621400π-0.621400\pi
0.139273 0.990254i 0.455523π-0.455523\pi
548548 0 0
549549 23.9399 + 24.9241i 1.02173 + 1.06374i
550550 0 0
551551 0 0
552552 0 0
553553 0.308071 0.0437184i 0.0131005 0.00185909i
554554 0 0
555555 0 0
556556 44.1049 + 9.00408i 1.87046 + 0.381858i
557557 0 0 −0.551377 0.834256i 0.685897π-0.685897\pi
0.551377 + 0.834256i 0.314103π0.314103\pi
558558 0 0
559559 −16.2874 + 43.0636i −0.688884 + 1.82139i
560560 0 0
561561 0 0
562562 0 0
563563 0 0 −0.316668 0.948536i 0.602564π-0.602564\pi
0.316668 + 0.948536i 0.397436π0.397436\pi
564564 0 0
565565 0 0
566566 0 0
567567 1.11036 + 6.05906i 0.0466309 + 0.254456i
568568 0 0
569569 0 0 0.534466 0.845190i 0.320513π-0.320513\pi
−0.534466 + 0.845190i 0.679487π0.679487\pi
570570 0 0
571571 −11.8609 + 13.3882i −0.496363 + 0.560279i −0.942293 0.334790i 0.891335π-0.891335\pi
0.445929 + 0.895068i 0.352873π0.352873\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 −23.5150 + 4.80062i −0.979791 + 0.200026i
577577 15.5006 + 15.5006i 0.645299 + 0.645299i 0.951853 0.306554i 0.0991761π-0.0991761\pi
−0.306554 + 0.951853i 0.599176π0.599176\pi
578578 0 0
579579 5.54701 24.6294i 0.230526 1.02356i
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
588588 6.29493 + 21.7326i 0.259598 + 0.896238i
589589 3.69405 + 45.7590i 0.152211 + 1.88547i
590590 0 0
591591 0 0
592592 −38.6732 + 15.5646i −1.58946 + 0.639702i
593593 0 0 0.998176 0.0603785i 0.0192308π-0.0192308\pi
−0.998176 + 0.0603785i 0.980769π0.980769\pi
594594 0 0
595595 0 0
596596 0 0
597597 −8.41588 34.1446i −0.344439 1.39744i
598598 0 0
599599 0 0 −0.970942 0.239316i 0.923077π-0.923077\pi
0.970942 + 0.239316i 0.0769231π0.0769231\pi
600600 0 0
601601 7.65049 5.74897i 0.312070 0.234505i −0.433154 0.901320i 0.642599π-0.642599\pi
0.745223 + 0.666815i 0.232343π0.232343\pi
602602 0 0
603603 24.0618 30.7127i 0.979874 1.25072i
604604 45.1306 + 10.1642i 1.83634 + 0.413577i
605605 0 0
606606 0 0
607607 7.00386 + 34.3072i 0.284278 + 1.39248i 0.831513 + 0.555506i 0.187475π0.187475\pi
−0.547235 + 0.836979i 0.684320π0.684320\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 10.0519 10.8960i 0.405990 0.440086i −0.498300 0.867005i 0.666042π-0.666042\pi
0.904290 + 0.426919i 0.140401π0.140401\pi
614614 0 0
615615 0 0
616616 0 0
617617 0 0 0.735006 0.678061i 0.237179π-0.237179\pi
−0.735006 + 0.678061i 0.762821π0.762821\pi
618618 0 0
619619 −2.15360 + 35.6032i −0.0865605 + 1.43102i 0.652711 + 0.757607i 0.273632π0.273632\pi
−0.739271 + 0.673408i 0.764830π0.764830\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 11.6287 + 22.1082i 0.465522 + 0.885036i
625625 8.86512 + 23.3754i 0.354605 + 0.935016i
626626 0 0
627627 0 0
628628 10.1657 + 2.94453i 0.405655 + 0.117499i
629629 0 0
630630 0 0
631631 −17.4663 + 12.5828i −0.695323 + 0.500915i −0.875806 0.482663i 0.839670π-0.839670\pi
0.180484 + 0.983578i 0.442234π0.442234\pi
632632 0 0
633633 3.01459 + 6.35312i 0.119819 + 0.252514i
634634 0 0
635635 0 0
636636 0 0
637637 19.8927 12.6045i 0.788177 0.499410i
638638 0 0
639639 0 0
640640 0 0
641641 0 0 0.391967 0.919979i 0.371795π-0.371795\pi
−0.391967 + 0.919979i 0.628205π0.628205\pi
642642 0 0
643643 45.3389 + 22.6432i 1.78799 + 0.892959i 0.910871 + 0.412692i 0.135411π0.135411\pi
0.877122 + 0.480268i 0.159461π0.159461\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 −0.391967 0.919979i 0.628205π-0.628205\pi
0.391967 + 0.919979i 0.371795π0.371795\pi
648648 0 0
649649 0 0
650650 0 0
651651 7.42974 10.7638i 0.291194 0.421868i
652652 1.20320 0.121564i 0.0471210 0.00476081i
653653 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
654654 0 0
655655 0 0
656656 0 0
657657 −13.0022 48.5249i −0.507264 1.89314i
658658 0 0
659659 0 0 −0.632445 0.774605i 0.717949π-0.717949\pi
0.632445 + 0.774605i 0.282051π0.282051\pi
660660 0 0
661661 10.4911 14.5628i 0.408058 0.566428i −0.556315 0.830971i 0.687785π-0.687785\pi
0.964374 + 0.264543i 0.0852213π0.0852213\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −2.16775 + 21.4557i −0.0838101 + 0.829525i
670670 0 0
671671 0 0
672672 0 0
673673 −6.00393 + 17.9840i −0.231435 + 0.693231i 0.767220 + 0.641384i 0.221639π0.221639\pi
−0.998655 + 0.0518477i 0.983489π0.983489\pi
674674 0 0
675675 25.9808i 1.00000i
676676 18.7187 18.0447i 0.719950 0.694026i
677677 0 0 1.00000 00
−1.00000 π\pi
678678 0 0
679679 −11.0417 3.68626i −0.423741 0.141466i
680680 0 0
681681 0 0
682682 0 0
683683 0 0 −0.994935 0.100522i 0.967949π-0.967949\pi
0.994935 + 0.100522i 0.0320513π0.0320513\pi
684684 10.2466 + 22.7670i 0.391788 + 0.870518i
685685 0 0
686686 0 0
687687 −6.42185 + 45.2529i −0.245009 + 1.72651i
688688 23.7370 + 45.2270i 0.904963 + 1.72426i
689689 0 0
690690 0 0
691691 5.64072 + 4.06361i 0.214583 + 0.154587i 0.686681 0.726959i 0.259067π-0.259067\pi
−0.472098 + 0.881546i 0.656503π0.656503\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 0.688013 + 6.80973i 0.0260044 + 0.257384i
701701 0 0 −0.822984 0.568065i 0.807692π-0.807692\pi
0.822984 + 0.568065i 0.192308π0.192308\pi
702702 0 0
703703 24.6351 + 35.6901i 0.929130 + 1.34608i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 23.7109 47.4769i 0.890482 1.78303i 0.370610 0.928788i 0.379149π-0.379149\pi
0.519872 0.854244i 0.325980π-0.325980\pi
710710 0 0
711711 1.25471 + 0.534583i 0.0470554 + 0.0200484i
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 0.903450 0.428693i 0.141026π-0.141026\pi
−0.903450 + 0.428693i 0.858974π0.858974\pi
720720 0 0
721721 −7.93911 11.0203i −0.295668 0.410418i
722722 0 0
723723 2.11106 3.49212i 0.0785112 0.129873i
724724 −9.71642 + 33.5450i −0.361108 + 1.24669i
725725 0 0
726726 0 0
727727 3.43881 1.30417i 0.127538 0.0483689i −0.290010 0.957024i 0.593659π-0.593659\pi
0.417548 + 0.908655i 0.362889π0.362889\pi
728728 0 0
729729 −9.57433 + 25.2454i −0.354605 + 0.935016i
730730 0 0
731731 0 0
732732 −12.6368 37.8518i −0.467069 1.39904i
733733 −46.0062 2.78286i −1.69928 0.102787i −0.817949 0.575291i 0.804889π-0.804889\pi
−0.881329 + 0.472504i 0.843350π0.843350\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 29.8222 + 27.5118i 1.09703 + 1.01204i 0.999859 + 0.0167685i 0.00533782π0.00533782\pi
0.0971693 + 0.995268i 0.469021π0.469021\pi
740740 0 0
741741 19.7786 16.8546i 0.726587 0.619169i
742742 0 0
743743 0 0 0.0201371 0.999797i 0.493590π-0.493590\pi
−0.0201371 + 0.999797i 0.506410π0.506410\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −23.7306 31.5797i −0.865942 1.15236i −0.987160 0.159734i 0.948936π-0.948936\pi
0.121218 0.992626i 0.461320π-0.461320\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 1.84096 6.87054i 0.0669549 0.249879i
757757 11.5482 + 39.8690i 0.419727 + 1.44906i 0.840457 + 0.541879i 0.182287π0.182287\pi
−0.420730 + 0.907186i 0.638226π0.638226\pi
758758 0 0
759759 0 0
760760 0 0
761761 0 0 0.927686 0.373361i 0.121795π-0.121795\pi
−0.927686 + 0.373361i 0.878205π0.878205\pi
762762 0 0
763763 −1.78439 + 0.144051i −0.0645994 + 0.00521500i
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 26.9075 + 6.63211i 0.970942 + 0.239316i
769769 −5.76924 + 10.4742i −0.208044 + 0.377710i −0.959339 0.282257i 0.908917π-0.908917\pi
0.751295 + 0.659967i 0.229430π0.229430\pi
770770 0 0
771771 0 0
772772 −17.9786 + 22.9480i −0.647063 + 0.825915i
773773 0 0 −0.975564 0.219715i 0.929487π-0.929487\pi
0.975564 + 0.219715i 0.0705128π0.0705128\pi
774774 0 0
775775 −39.0063 + 39.0063i −1.40115 + 1.40115i
776776 0 0
777777 0.994170 12.3150i 0.0356656 0.441798i
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 4.19093 25.7878i 0.149676 0.920994i
785785 0 0
786786 0 0
787787 1.11545 + 55.3815i 0.0397613 + 1.97414i 0.178912 + 0.983865i 0.442742π0.442742\pi
−0.139151 + 0.990271i 0.544437π0.544437\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 −34.1612 + 23.6254i −1.21310 + 0.838961i
794794 0 0
795795 0 0
796796 −8.12239 + 39.7861i −0.287890 + 1.41018i
797797 0 0 −0.960518 0.278217i 0.910256π-0.910256\pi
0.960518 + 0.278217i 0.0897436π0.0897436\pi
798798 0 0
799799 0 0
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 −40.3048 + 20.1290i −1.42144 + 0.709896i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 0 0 0.987050 0.160411i 0.0512821π-0.0512821\pi
−0.987050 + 0.160411i 0.948718π0.948718\pi
810810 0 0
811811 −16.0605 51.5400i −0.563961 1.80981i −0.586341 0.810064i 0.699432π-0.699432\pi
0.0223803 0.999750i 0.492876π-0.492876\pi
812812 0 0
813813 27.3334 + 9.74125i 0.958623 + 0.341640i
814814 0 0
815815 0 0
816816 0 0
817817 40.4733 34.4268i 1.41598 1.20444i
818818 0 0
819819 −7.40171 + 0.155765i −0.258637 + 0.00544286i
820820 0 0
821821 0 0 0.994935 0.100522i 0.0320513π-0.0320513\pi
−0.994935 + 0.100522i 0.967949π0.967949\pi
822822 0 0
823823 42.1737 + 24.3490i 1.47008 + 0.848753i 0.999436 0.0335690i 0.0106873π-0.0106873\pi
0.470647 + 0.882322i 0.344021π0.344021\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 0.855781 0.517338i 0.173077π-0.173077\pi
−0.855781 + 0.517338i 0.826923π0.826923\pi
828828 0 0
829829 −57.3466 + 2.31099i −1.99173 + 0.0802640i −0.999147 0.0412960i 0.986851π-0.986851\pi
−0.992584 + 0.121560i 0.961210π0.961210\pi
830830 0 0
831831 26.4005 50.3019i 0.915822 1.74495i
832832 −1.18747 28.8200i −0.0411681 0.999152i
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 52.2768 23.5279i 1.80695 0.813242i
838838 0 0
839839 0 0 0.647915 0.761712i 0.275641π-0.275641\pi
−0.647915 + 0.761712i 0.724359π0.724359\pi
840840 0 0
841841 20.0890 20.9149i 0.692724 0.721202i
842842 0 0
843843 0 0
844844 8.11993i 0.279500i
845845 0 0
846846 0 0
847847 −6.98440 2.81098i −0.239987 0.0965863i
848848 0 0
849849 −14.5807 14.0049i −0.500407 0.480648i
850850 0 0
851851 0 0
852852 0 0
853853 −14.0506 31.2191i −0.481083 1.06892i −0.979400 0.201928i 0.935279π-0.935279\pi
0.498317 0.866995i 0.333952π-0.333952\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 −0.464723 0.885456i 0.653846π-0.653846\pi
0.464723 + 0.885456i 0.346154π0.346154\pi
858858 0 0
859859 −30.2494 15.8761i −1.03210 0.541686i −0.138409 0.990375i 0.544199π-0.544199\pi
−0.893688 + 0.448689i 0.851891π0.851891\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.517338 0.855781i 0.673077π-0.673077\pi
0.517338 + 0.855781i 0.326923π0.326923\pi
864864 0 0
865865 0 0
866866 0 0
867867 −14.7224 + 25.5000i −0.500000 + 0.866025i
868868 −13.0790 + 7.55118i −0.443931 + 0.256304i
869869 0 0
870870 0 0
871871 31.8262 + 34.4366i 1.07839 + 1.16684i
872872 0 0
873873 −33.0587 38.8650i −1.11887 1.31538i
874874 0 0
875875 0 0
876876 −10.4563 + 57.0581i −0.353285 + 1.92781i
877877 −3.72653 + 10.4564i −0.125836 + 0.353089i −0.988193 0.153211i 0.951038π-0.951038\pi
0.862357 + 0.506300i 0.168987π0.168987\pi
878878 0 0
879879 0 0
880880 0 0
881881 0 0 −0.160411 0.987050i 0.551282π-0.551282\pi
0.160411 + 0.987050i 0.448718π0.448718\pi
882882 0 0
883883 40.2610 + 4.88857i 1.35489 + 0.164514i 0.765553 0.643373i 0.222466π-0.222466\pi
0.589338 + 0.807887i 0.299389π0.299389\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 −0.692724 0.721202i 0.743590π-0.743590\pi
0.692724 + 0.721202i 0.256410π0.256410\pi
888888 0 0
889889 6.11486 4.79069i 0.205086 0.160675i
890890 0 0
891891 0 0
892892 12.8823 21.3098i 0.431330 0.713506i
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 −12.8608 + 27.1035i −0.428693 + 0.903450i
901901 0 0
902902 0 0
903903 −15.1349 + 0.304833i −0.503657 + 0.0101442i
904904 0 0
905905 0 0
906906 0 0
907907 −31.9527 + 50.5291i −1.06097 + 1.67779i −0.427525 + 0.904004i 0.640614π0.640614\pi
−0.633446 + 0.773787i 0.718360π0.718360\pi
908908 0 0
909909 0 0
910910 0 0
911911 0 0 0.748511 0.663123i 0.230769π-0.230769\pi
−0.748511 + 0.663123i 0.769231π0.769231\pi
912912 0.580529 28.8230i 0.0192232 0.954426i
913913 0 0
914914 0 0
915915 0 0
916916 29.1001 44.0296i 0.961494 1.45478i
917917 0 0
918918 0 0
919919 2.43632 60.4566i 0.0803667 1.99428i −0.0237804 0.999717i 0.507570π-0.507570\pi
0.104147 0.994562i 0.466789π-0.466789\pi
920920 0 0
921921 49.5001 + 27.2649i 1.63108 + 0.898408i
922922 0 0
923923 0 0
924924 0 0
925925 −13.4870 + 50.3342i −0.443450 + 1.65498i
926926 0 0
927927 −4.79041 59.3398i −0.157338 1.94898i
928928 0 0
929929 0 0 −0.373361 0.927686i 0.621795π-0.621795\pi
0.373361 + 0.927686i 0.378205π0.378205\pi
930930 0 0
931931 −27.1288 + 1.64099i −0.889109 + 0.0537812i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 31.5471 + 7.77567i 1.03060 + 0.254020i 0.718131 0.695908i 0.244998π-0.244998\pi
0.312469 + 0.949928i 0.398844π0.398844\pi
938938 0 0
939939 −46.0450 + 34.6006i −1.50262 + 1.12915i
940940 0 0
941941 0 0 0.616719 0.787183i 0.288462π-0.288462\pi
−0.616719 + 0.787183i 0.711538π0.711538\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 −0.999797 0.0201371i 0.993590π-0.993590\pi
0.999797 + 0.0201371i 0.00641026π0.00641026\pi
948948 −1.04431 1.17878i −0.0339176 0.0382850i
949949 60.0656 6.12345i 1.94981 0.198775i
950950 0 0
951951 0 0
952952 0 0
953953 0 0 0.160411 0.987050i 0.448718π-0.448718\pi
−0.160411 + 0.987050i 0.551282π0.551282\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −84.8240 32.1695i −2.73626 1.03773i
962962 0 0
963963 0 0
964964 −3.93093 + 2.59803i −0.126607 + 0.0836770i
965965 0 0
966966 0 0
967967 34.2740 + 20.7194i 1.10218 + 0.666290i 0.946883 0.321578i 0.104213π-0.104213\pi
0.155295 + 0.987868i 0.450367π0.450367\pi
968968 0 0
969969 0 0
970970 0 0
971971 0 0 −0.428693 0.903450i 0.641026π-0.641026\pi
0.428693 + 0.903450i 0.358974π0.358974\pi
972972 22.4849 21.5970i 0.721202 0.692724i
973973 13.7817 6.88288i 0.441823 0.220655i
974974 0 0
975975 30.8251 + 4.98101i 0.987195 + 0.159520i
976976 −5.55419 + 45.7429i −0.177785 + 1.46419i
977977 0 0 0.941967 0.335705i 0.108974π-0.108974\pi
−0.941967 + 0.335705i 0.891026π0.891026\pi
978978 0 0
979979 0 0
980980 0 0
981981 −7.01993 3.50589i −0.224129 0.111935i
982982 0 0
983983 0 0 −0.983620 0.180255i 0.942308π-0.942308\pi
0.983620 + 0.180255i 0.0576923π0.0576923\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 −28.9766 + 7.79230i −0.921868 + 0.247906i
989989 0 0
990990 0 0
991991 −25.0043 43.3087i −0.794288 1.37575i −0.923291 0.384102i 0.874511π-0.874511\pi
0.129003 0.991644i 0.458822π-0.458822\pi
992992 0 0
993993 −19.2343 + 42.7368i −0.610381 + 1.35621i
994994 0 0
995995 0 0
996996 0 0
997997 32.9167 + 40.3156i 1.04248 + 1.27681i 0.959936 + 0.280221i 0.0904077π0.0904077\pi
0.0825460 + 0.996587i 0.473695π0.473695\pi
998998 0 0
999999 31.6542 43.9394i 1.00150 1.39018i
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 507.2.x.a.50.1 48
3.2 odd 2 CM 507.2.x.a.50.1 48
169.71 odd 156 inner 507.2.x.a.71.1 yes 48
507.71 even 156 inner 507.2.x.a.71.1 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.x.a.50.1 48 1.1 even 1 trivial
507.2.x.a.50.1 48 3.2 odd 2 CM
507.2.x.a.71.1 yes 48 169.71 odd 156 inner
507.2.x.a.71.1 yes 48 507.71 even 156 inner