Properties

Label 256.11.c.m.255.15
Level 256256
Weight 1111
Character 256.255
Analytic conductor 162.651162.651
Analytic rank 00
Dimension 1616
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [256,11,Mod(255,256)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(256, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("256.255");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: N N == 256=28 256 = 2^{8}
Weight: k k == 11 11
Character orbit: [χ][\chi] == 256.c (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: 162.651456684162.651456684
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16x14+61429x1223865589x10+9433993075x8796642244899x6++11 ⁣ ⁣56 x^{16} - x^{14} + 61429 x^{12} - 23865589 x^{10} + 9433993075 x^{8} - 796642244899 x^{6} + \cdots + 11\!\cdots\!56 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 217836 2^{178}\cdot 3^{6}
Twist minimal: no (minimal twist has level 8)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 255.15
Root 11.19538.43092i11.1953 - 8.43092i of defining polynomial
Character χ\chi == 256.255
Dual form 256.11.c.m.255.1

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+352.099iq33773.58q515618.2iq764924.4q9+115158.iq11+546374.q131.32867e6iq151.50100e6q17+3.45753e6iq19+5.49914e6q21+3.90931e6iq23+4.47430e6q252.06872e6iq271.57435e7q29+1.36335e7iq314.05471e7q33+5.89365e7iq35+7.96225e7q37+1.92377e8iq39+1.01409e7q414.09302e7iq43+2.44998e8q45+2.36040e8iq47+3.85474e7q495.28499e8iq513.09768e8q534.34559e8iq551.21739e9q57+6.26191e7iq591.02129e9q61+1.01400e9iq632.06179e9q65+6.25414e8iq671.37646e9q69+2.05543e9iq712.44117e9q73+1.57539e9iq75+1.79856e9q773.04489e9iq793.10533e9q81+2.75511e9iq83+5.66413e9q855.54325e9iq872.51922e8q898.53337e9iq914.80035e9q931.30473e10iq951.56384e10q977.47658e9iq99+O(q100)q+352.099i q^{3} -3773.58 q^{5} -15618.2i q^{7} -64924.4 q^{9} +115158. i q^{11} +546374. q^{13} -1.32867e6i q^{15} -1.50100e6 q^{17} +3.45753e6i q^{19} +5.49914e6 q^{21} +3.90931e6i q^{23} +4.47430e6 q^{25} -2.06872e6i q^{27} -1.57435e7 q^{29} +1.36335e7i q^{31} -4.05471e7 q^{33} +5.89365e7i q^{35} +7.96225e7 q^{37} +1.92377e8i q^{39} +1.01409e7 q^{41} -4.09302e7i q^{43} +2.44998e8 q^{45} +2.36040e8i q^{47} +3.85474e7 q^{49} -5.28499e8i q^{51} -3.09768e8 q^{53} -4.34559e8i q^{55} -1.21739e9 q^{57} +6.26191e7i q^{59} -1.02129e9 q^{61} +1.01400e9i q^{63} -2.06179e9 q^{65} +6.25414e8i q^{67} -1.37646e9 q^{69} +2.05543e9i q^{71} -2.44117e9 q^{73} +1.57539e9i q^{75} +1.79856e9 q^{77} -3.04489e9i q^{79} -3.10533e9 q^{81} +2.75511e9i q^{83} +5.66413e9 q^{85} -5.54325e9i q^{87} -2.51922e8 q^{89} -8.53337e9i q^{91} -4.80035e9 q^{93} -1.30473e10i q^{95} -1.56384e10 q^{97} -7.47658e9i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+70992q9741600q17+37585520q25148617408q33185338656q41160864496q492801425728q571678056960q655600145440q7323818130352q8112325192224q89+19395727072q97+O(q100) 16 q + 70992 q^{9} - 741600 q^{17} + 37585520 q^{25} - 148617408 q^{33} - 185338656 q^{41} - 160864496 q^{49} - 2801425728 q^{57} - 1678056960 q^{65} - 5600145440 q^{73} - 23818130352 q^{81} - 12325192224 q^{89}+ \cdots - 19395727072 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/256Z)×\left(\mathbb{Z}/256\mathbb{Z}\right)^\times.

nn 55 255255
χ(n)\chi(n) 11 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 352.099i 1.44897i 0.689293 + 0.724483i 0.257921π0.257921\pi
−0.689293 + 0.724483i 0.742079π0.742079\pi
44 0 0
55 −3773.58 −1.20755 −0.603773 0.797156i 0.706337π-0.706337\pi
−0.603773 + 0.797156i 0.706337π0.706337\pi
66 0 0
77 − 15618.2i − 0.929267i −0.885503 0.464633i 0.846186π-0.846186\pi
0.885503 0.464633i 0.153814π-0.153814\pi
88 0 0
99 −64924.4 −1.09950
1010 0 0
1111 115158.i 0.715042i 0.933905 + 0.357521i 0.116378π0.116378\pi
−0.933905 + 0.357521i 0.883622π0.883622\pi
1212 0 0
1313 546374. 1.47154 0.735772 0.677230i 0.236820π-0.236820\pi
0.735772 + 0.677230i 0.236820π0.236820\pi
1414 0 0
1515 − 1.32867e6i − 1.74969i
1616 0 0
1717 −1.50100e6 −1.05715 −0.528573 0.848888i 0.677273π-0.677273\pi
−0.528573 + 0.848888i 0.677273π0.677273\pi
1818 0 0
1919 3.45753e6i 1.39636i 0.715922 + 0.698180i 0.246007π0.246007\pi
−0.715922 + 0.698180i 0.753993π0.753993\pi
2020 0 0
2121 5.49914e6 1.34648
2222 0 0
2323 3.90931e6i 0.607380i 0.952771 + 0.303690i 0.0982188π0.0982188\pi
−0.952771 + 0.303690i 0.901781π0.901781\pi
2424 0 0
2525 4.47430e6 0.458168
2626 0 0
2727 − 2.06872e6i − 0.144173i
2828 0 0
2929 −1.57435e7 −0.767557 −0.383778 0.923425i 0.625377π-0.625377\pi
−0.383778 + 0.923425i 0.625377π0.625377\pi
3030 0 0
3131 1.36335e7i 0.476212i 0.971239 + 0.238106i 0.0765265π0.0765265\pi
−0.971239 + 0.238106i 0.923473π0.923473\pi
3232 0 0
3333 −4.05471e7 −1.03607
3434 0 0
3535 5.89365e7i 1.12213i
3636 0 0
3737 7.96225e7 1.14823 0.574113 0.818776i 0.305347π-0.305347\pi
0.574113 + 0.818776i 0.305347π0.305347\pi
3838 0 0
3939 1.92377e8i 2.13222i
4040 0 0
4141 1.01409e7 0.0875298 0.0437649 0.999042i 0.486065π-0.486065\pi
0.0437649 + 0.999042i 0.486065π0.486065\pi
4242 0 0
4343 − 4.09302e7i − 0.278421i −0.990263 0.139210i 0.955544π-0.955544\pi
0.990263 0.139210i 0.0444565π-0.0444565\pi
4444 0 0
4545 2.44998e8 1.32770
4646 0 0
4747 2.36040e8i 1.02919i 0.857433 + 0.514595i 0.172058π0.172058\pi
−0.857433 + 0.514595i 0.827942π0.827942\pi
4848 0 0
4949 3.85474e7 0.136463
5050 0 0
5151 − 5.28499e8i − 1.53177i
5252 0 0
5353 −3.09768e8 −0.740725 −0.370362 0.928887i 0.620766π-0.620766\pi
−0.370362 + 0.928887i 0.620766π0.620766\pi
5454 0 0
5555 − 4.34559e8i − 0.863447i
5656 0 0
5757 −1.21739e9 −2.02328
5858 0 0
5959 6.26191e7i 0.0875885i 0.999041 + 0.0437942i 0.0139446π0.0139446\pi
−0.999041 + 0.0437942i 0.986055π0.986055\pi
6060 0 0
6161 −1.02129e9 −1.20921 −0.604603 0.796527i 0.706668π-0.706668\pi
−0.604603 + 0.796527i 0.706668π0.706668\pi
6262 0 0
6363 1.01400e9i 1.02173i
6464 0 0
6565 −2.06179e9 −1.77696
6666 0 0
6767 6.25414e8i 0.463227i 0.972808 + 0.231613i 0.0744004π0.0744004\pi
−0.972808 + 0.231613i 0.925600π0.925600\pi
6868 0 0
6969 −1.37646e9 −0.880073
7070 0 0
7171 2.05543e9i 1.13923i 0.821913 + 0.569614i 0.192907π0.192907\pi
−0.821913 + 0.569614i 0.807093π0.807093\pi
7272 0 0
7373 −2.44117e9 −1.17756 −0.588781 0.808292i 0.700392π-0.700392\pi
−0.588781 + 0.808292i 0.700392π0.700392\pi
7474 0 0
7575 1.57539e9i 0.663870i
7676 0 0
7777 1.79856e9 0.664465
7878 0 0
7979 − 3.04489e9i − 0.989548i −0.869022 0.494774i 0.835251π-0.835251\pi
0.869022 0.494774i 0.164749π-0.164749\pi
8080 0 0
8181 −3.10533e9 −0.890599
8282 0 0
8383 2.75511e9i 0.699438i 0.936855 + 0.349719i 0.113723π0.113723\pi
−0.936855 + 0.349719i 0.886277π0.886277\pi
8484 0 0
8585 5.66413e9 1.27655
8686 0 0
8787 − 5.54325e9i − 1.11216i
8888 0 0
8989 −2.51922e8 −0.0451145 −0.0225573 0.999746i 0.507181π-0.507181\pi
−0.0225573 + 0.999746i 0.507181π0.507181\pi
9090 0 0
9191 − 8.53337e9i − 1.36746i
9292 0 0
9393 −4.80035e9 −0.690014
9494 0 0
9595 − 1.30473e10i − 1.68617i
9696 0 0
9797 −1.56384e10 −1.82110 −0.910549 0.413401i 0.864341π-0.864341\pi
−0.910549 + 0.413401i 0.864341π0.864341\pi
9898 0 0
9999 − 7.47658e9i − 0.786189i
100100 0 0
101101 3.85788e9 0.367064 0.183532 0.983014i 0.441247π-0.441247\pi
0.183532 + 0.983014i 0.441247π0.441247\pi
102102 0 0
103103 − 9.28145e9i − 0.800626i −0.916378 0.400313i 0.868901π-0.868901\pi
0.916378 0.400313i 0.131099π-0.131099\pi
104104 0 0
105105 −2.07515e10 −1.62593
106106 0 0
107107 3.91137e9i 0.278875i 0.990231 + 0.139438i 0.0445294π0.0445294\pi
−0.990231 + 0.139438i 0.955471π0.955471\pi
108108 0 0
109109 1.09799e10 0.713619 0.356809 0.934177i 0.383865π-0.383865\pi
0.356809 + 0.934177i 0.383865π0.383865\pi
110110 0 0
111111 2.80350e10i 1.66374i
112112 0 0
113113 2.02898e10 1.10125 0.550624 0.834753i 0.314390π-0.314390\pi
0.550624 + 0.834753i 0.314390π0.314390\pi
114114 0 0
115115 − 1.47521e10i − 0.733440i
116116 0 0
117117 −3.54730e10 −1.61796
118118 0 0
119119 2.34428e10i 0.982371i
120120 0 0
121121 1.26760e10 0.488714
122122 0 0
123123 3.57058e9i 0.126828i
124124 0 0
125125 1.99672e10 0.654287
126126 0 0
127127 − 6.26328e9i − 0.189576i −0.995497 0.0947880i 0.969783π-0.969783\pi
0.995497 0.0947880i 0.0302173π-0.0302173\pi
128128 0 0
129129 1.44115e10 0.403422
130130 0 0
131131 − 4.99170e9i − 0.129387i −0.997905 0.0646937i 0.979393π-0.979393\pi
0.997905 0.0646937i 0.0206070π-0.0206070\pi
132132 0 0
133133 5.40003e10 1.29759
134134 0 0
135135 7.80649e9i 0.174095i
136136 0 0
137137 5.31439e10 1.10116 0.550580 0.834782i 0.314406π-0.314406\pi
0.550580 + 0.834782i 0.314406π0.314406\pi
138138 0 0
139139 − 3.24537e10i − 0.625446i −0.949844 0.312723i 0.898759π-0.898759\pi
0.949844 0.312723i 0.101241π-0.101241\pi
140140 0 0
141141 −8.31093e10 −1.49126
142142 0 0
143143 6.29195e10i 1.05222i
144144 0 0
145145 5.94093e10 0.926860
146146 0 0
147147 1.35725e10i 0.197730i
148148 0 0
149149 −9.33485e10 −1.27109 −0.635544 0.772064i 0.719224π-0.719224\pi
−0.635544 + 0.772064i 0.719224π0.719224\pi
150150 0 0
151151 − 1.79317e8i − 0.00228422i −0.999999 0.00114211i 0.999636π-0.999636\pi
0.999999 0.00114211i 0.000363545π-0.000363545\pi
152152 0 0
153153 9.74513e10 1.16233
154154 0 0
155155 − 5.14473e10i − 0.575048i
156156 0 0
157157 −4.41399e10 −0.462736 −0.231368 0.972866i 0.574320π-0.574320\pi
−0.231368 + 0.972866i 0.574320π0.574320\pi
158158 0 0
159159 − 1.09069e11i − 1.07328i
160160 0 0
161161 6.10563e10 0.564419
162162 0 0
163163 − 1.06005e11i − 0.921272i −0.887589 0.460636i 0.847621π-0.847621\pi
0.887589 0.460636i 0.152379π-0.152379\pi
164164 0 0
165165 1.53008e11 1.25110
166166 0 0
167167 1.65219e11i 1.27198i 0.771699 + 0.635988i 0.219407π0.219407\pi
−0.771699 + 0.635988i 0.780593π0.780593\pi
168168 0 0
169169 1.60666e11 1.16544
170170 0 0
171171 − 2.24478e11i − 1.53530i
172172 0 0
173173 2.73295e11 1.76361 0.881803 0.471617i 0.156330π-0.156330\pi
0.881803 + 0.471617i 0.156330π0.156330\pi
174174 0 0
175175 − 6.98805e10i − 0.425761i
176176 0 0
177177 −2.20481e10 −0.126913
178178 0 0
179179 − 1.55618e11i − 0.846824i −0.905937 0.423412i 0.860832π-0.860832\pi
0.905937 0.423412i 0.139168π-0.139168\pi
180180 0 0
181181 1.55132e10 0.0798562 0.0399281 0.999203i 0.487287π-0.487287\pi
0.0399281 + 0.999203i 0.487287π0.487287\pi
182182 0 0
183183 − 3.59595e11i − 1.75210i
184184 0 0
185185 −3.00462e11 −1.38654
186186 0 0
187187 − 1.72852e11i − 0.755904i
188188 0 0
189189 −3.23097e10 −0.133975
190190 0 0
191191 2.19148e11i 0.862127i 0.902322 + 0.431063i 0.141861π0.141861\pi
−0.902322 + 0.431063i 0.858139π0.858139\pi
192192 0 0
193193 1.83821e11 0.686451 0.343225 0.939253i 0.388481π-0.388481\pi
0.343225 + 0.939253i 0.388481π0.388481\pi
194194 0 0
195195 − 7.25952e11i − 2.57475i
196196 0 0
197197 −2.89571e10 −0.0975943 −0.0487971 0.998809i 0.515539π-0.515539\pi
−0.0487971 + 0.998809i 0.515539π0.515539\pi
198198 0 0
199199 − 3.25273e11i − 1.04228i −0.853473 0.521138i 0.825508π-0.825508\pi
0.853473 0.521138i 0.174492π-0.174492\pi
200200 0 0
201201 −2.20207e11 −0.671199
202202 0 0
203203 2.45884e11i 0.713265i
204204 0 0
205205 −3.82674e10 −0.105696
206206 0 0
207207 − 2.53810e11i − 0.667815i
208208 0 0
209209 −3.98163e11 −0.998457
210210 0 0
211211 6.20459e11i 1.48354i 0.670652 + 0.741772i 0.266014π0.266014\pi
−0.670652 + 0.741772i 0.733986π0.733986\pi
212212 0 0
213213 −7.23713e11 −1.65070
214214 0 0
215215 1.54454e11i 0.336206i
216216 0 0
217217 2.12931e11 0.442528
218218 0 0
219219 − 8.59533e11i − 1.70625i
220220 0 0
221221 −8.20105e11 −1.55564
222222 0 0
223223 − 5.25673e11i − 0.953217i −0.879116 0.476608i 0.841866π-0.841866\pi
0.879116 0.476608i 0.158134π-0.158134\pi
224224 0 0
225225 −2.90491e11 −0.503756
226226 0 0
227227 − 8.73761e11i − 1.44965i −0.688933 0.724825i 0.741921π-0.741921\pi
0.688933 0.724825i 0.258079π-0.258079\pi
228228 0 0
229229 8.30219e11 1.31830 0.659151 0.752010i 0.270916π-0.270916\pi
0.659151 + 0.752010i 0.270916π0.270916\pi
230230 0 0
231231 6.33272e11i 0.962787i
232232 0 0
233233 −8.33377e11 −1.21356 −0.606781 0.794869i 0.707540π-0.707540\pi
−0.606781 + 0.794869i 0.707540π0.707540\pi
234234 0 0
235235 − 8.90716e11i − 1.24280i
236236 0 0
237237 1.07210e12 1.43382
238238 0 0
239239 9.19325e11i 1.17891i 0.807802 + 0.589454i 0.200657π0.200657\pi
−0.807802 + 0.589454i 0.799343π0.799343\pi
240240 0 0
241241 −1.56744e12 −1.92799 −0.963997 0.265912i 0.914327π-0.914327\pi
−0.963997 + 0.265912i 0.914327π0.914327\pi
242242 0 0
243243 − 1.21554e12i − 1.43462i
244244 0 0
245245 −1.45462e11 −0.164785
246246 0 0
247247 1.88910e12i 2.05481i
248248 0 0
249249 −9.70072e11 −1.01346
250250 0 0
251251 − 1.83947e12i − 1.84639i −0.384331 0.923195i 0.625568π-0.625568\pi
0.384331 0.923195i 0.374432π-0.374432\pi
252252 0 0
253253 −4.50189e11 −0.434303
254254 0 0
255255 1.99433e12i 1.84968i
256256 0 0
257257 −4.69431e11 −0.418703 −0.209352 0.977840i 0.567135π-0.567135\pi
−0.209352 + 0.977840i 0.567135π0.567135\pi
258258 0 0
259259 − 1.24356e12i − 1.06701i
260260 0 0
261261 1.02214e12 0.843929
262262 0 0
263263 − 2.02740e12i − 1.61124i −0.592433 0.805619i 0.701833π-0.701833\pi
0.592433 0.805619i 0.298167π-0.298167\pi
264264 0 0
265265 1.16893e12 0.894459
266266 0 0
267267 − 8.87015e10i − 0.0653694i
268268 0 0
269269 −1.54905e12 −1.09977 −0.549886 0.835239i 0.685329π-0.685329\pi
−0.549886 + 0.835239i 0.685329π0.685329\pi
270270 0 0
271271 − 2.74756e12i − 1.87975i −0.341514 0.939877i 0.610940π-0.610940\pi
0.341514 0.939877i 0.389060π-0.389060\pi
272272 0 0
273273 3.00459e12 1.98140
274274 0 0
275275 5.15253e11i 0.327610i
276276 0 0
277277 −3.44260e11 −0.211100 −0.105550 0.994414i 0.533660π-0.533660\pi
−0.105550 + 0.994414i 0.533660π0.533660\pi
278278 0 0
279279 − 8.85149e11i − 0.523595i
280280 0 0
281281 5.16881e11 0.295025 0.147513 0.989060i 0.452873π-0.452873\pi
0.147513 + 0.989060i 0.452873π0.452873\pi
282282 0 0
283283 − 9.80974e11i − 0.540413i −0.962802 0.270206i 0.912908π-0.912908\pi
0.962802 0.270206i 0.0870919π-0.0870919\pi
284284 0 0
285285 4.59392e12 2.44320
286286 0 0
287287 − 1.58382e11i − 0.0813385i
288288 0 0
289289 2.36996e11 0.117558
290290 0 0
291291 − 5.50625e12i − 2.63871i
292292 0 0
293293 −3.78962e12 −1.75492 −0.877461 0.479648i 0.840764π-0.840764\pi
−0.877461 + 0.479648i 0.840764π0.840764\pi
294294 0 0
295295 − 2.36298e11i − 0.105767i
296296 0 0
297297 2.38230e11 0.103090
298298 0 0
299299 2.13594e12i 0.893787i
300300 0 0
301301 −6.39256e11 −0.258727
302302 0 0
303303 1.35836e12i 0.531864i
304304 0 0
305305 3.85393e12 1.46017
306306 0 0
307307 4.74199e12i 1.73888i 0.494041 + 0.869438i 0.335519π0.335519\pi
−0.494041 + 0.869438i 0.664481π0.664481\pi
308308 0 0
309309 3.26798e12 1.16008
310310 0 0
311311 − 1.77863e12i − 0.611340i −0.952138 0.305670i 0.901120π-0.901120\pi
0.952138 0.305670i 0.0988804π-0.0988804\pi
312312 0 0
313313 2.19482e12 0.730595 0.365297 0.930891i 0.380967π-0.380967\pi
0.365297 + 0.930891i 0.380967π0.380967\pi
314314 0 0
315315 − 3.82642e12i − 1.23379i
316316 0 0
317317 −2.30472e12 −0.719981 −0.359991 0.932956i 0.617220π-0.617220\pi
−0.359991 + 0.932956i 0.617220π0.617220\pi
318318 0 0
319319 − 1.81299e12i − 0.548836i
320320 0 0
321321 −1.37719e12 −0.404080
322322 0 0
323323 − 5.18974e12i − 1.47616i
324324 0 0
325325 2.44464e12 0.674215
326326 0 0
327327 3.86601e12i 1.03401i
328328 0 0
329329 3.68651e12 0.956393
330330 0 0
331331 − 3.59393e12i − 0.904544i −0.891880 0.452272i 0.850614π-0.850614\pi
0.891880 0.452272i 0.149386π-0.149386\pi
332332 0 0
333333 −5.16944e12 −1.26247
334334 0 0
335335 − 2.36005e12i − 0.559368i
336336 0 0
337337 −1.56362e12 −0.359734 −0.179867 0.983691i 0.557567π-0.557567\pi
−0.179867 + 0.983691i 0.557567π0.557567\pi
338338 0 0
339339 7.14401e12i 1.59567i
340340 0 0
341341 −1.57001e12 −0.340512
342342 0 0
343343 − 5.01379e12i − 1.05608i
344344 0 0
345345 5.19419e12 1.06273
346346 0 0
347347 1.77379e10i 0.00352578i 0.999998 + 0.00176289i 0.000561145π0.000561145\pi
−0.999998 + 0.00176289i 0.999439π0.999439\pi
348348 0 0
349349 −1.94015e12 −0.374722 −0.187361 0.982291i 0.559993π-0.559993\pi
−0.187361 + 0.982291i 0.559993π0.559993\pi
350350 0 0
351351 − 1.13030e12i − 0.212157i
352352 0 0
353353 4.41804e12 0.806038 0.403019 0.915192i 0.367961π-0.367961\pi
0.403019 + 0.915192i 0.367961π0.367961\pi
354354 0 0
355355 − 7.75633e12i − 1.37567i
356356 0 0
357357 −8.25419e12 −1.42342
358358 0 0
359359 4.43076e12i 0.743029i 0.928427 + 0.371515i 0.121161π0.121161\pi
−0.928427 + 0.371515i 0.878839π0.878839\pi
360360 0 0
361361 −5.82343e12 −0.949824
362362 0 0
363363 4.46320e12i 0.708130i
364364 0 0
365365 9.21196e12 1.42196
366366 0 0
367367 2.67602e12i 0.401939i 0.979598 + 0.200969i 0.0644092π0.0644092\pi
−0.979598 + 0.200969i 0.935591π0.935591\pi
368368 0 0
369369 −6.58390e11 −0.0962390
370370 0 0
371371 4.83801e12i 0.688331i
372372 0 0
373373 9.92009e12 1.37395 0.686976 0.726680i 0.258938π-0.258938\pi
0.686976 + 0.726680i 0.258938π0.258938\pi
374374 0 0
375375 7.03044e12i 0.948039i
376376 0 0
377377 −8.60182e12 −1.12949
378378 0 0
379379 − 6.20132e11i − 0.0793028i −0.999214 0.0396514i 0.987375π-0.987375\pi
0.999214 0.0396514i 0.0126247π-0.0126247\pi
380380 0 0
381381 2.20529e12 0.274689
382382 0 0
383383 5.18547e12i 0.629207i 0.949223 + 0.314604i 0.101872π0.101872\pi
−0.949223 + 0.314604i 0.898128π0.898128\pi
384384 0 0
385385 −6.78703e12 −0.802373
386386 0 0
387387 2.65737e12i 0.306124i
388388 0 0
389389 −1.84987e12 −0.207679 −0.103840 0.994594i 0.533113π-0.533113\pi
−0.103840 + 0.994594i 0.533113π0.533113\pi
390390 0 0
391391 − 5.86786e12i − 0.642090i
392392 0 0
393393 1.75757e12 0.187478
394394 0 0
395395 1.14902e13i 1.19493i
396396 0 0
397397 6.84533e12 0.694132 0.347066 0.937841i 0.387178π-0.387178\pi
0.347066 + 0.937841i 0.387178π0.387178\pi
398398 0 0
399399 1.90134e13i 1.88017i
400400 0 0
401401 −1.07383e13 −1.03565 −0.517825 0.855486i 0.673258π-0.673258\pi
−0.517825 + 0.855486i 0.673258π0.673258\pi
402402 0 0
403403 7.44901e12i 0.700766i
404404 0 0
405405 1.17182e13 1.07544
406406 0 0
407407 9.16919e12i 0.821030i
408408 0 0
409409 −1.79443e13 −1.56787 −0.783936 0.620841i 0.786791π-0.786791\pi
−0.783936 + 0.620841i 0.786791π0.786791\pi
410410 0 0
411411 1.87119e13i 1.59554i
412412 0 0
413413 9.77997e11 0.0813931
414414 0 0
415415 − 1.03967e13i − 0.844604i
416416 0 0
417417 1.14269e13 0.906250
418418 0 0
419419 1.01675e13i 0.787303i 0.919260 + 0.393652i 0.128788π0.128788\pi
−0.919260 + 0.393652i 0.871212π0.871212\pi
420420 0 0
421421 −1.38694e13 −1.04869 −0.524346 0.851505i 0.675690π-0.675690\pi
−0.524346 + 0.851505i 0.675690π0.675690\pi
422422 0 0
423423 − 1.53247e13i − 1.13160i
424424 0 0
425425 −6.71591e12 −0.484351
426426 0 0
427427 1.59507e13i 1.12368i
428428 0 0
429429 −2.21539e13 −1.52462
430430 0 0
431431 3.51756e11i 0.0236513i 0.999930 + 0.0118257i 0.00376431π0.00376431\pi
−0.999930 + 0.0118257i 0.996236π0.996236\pi
432432 0 0
433433 −1.73769e13 −1.14165 −0.570823 0.821073i 0.693376π-0.693376\pi
−0.570823 + 0.821073i 0.693376π0.693376\pi
434434 0 0
435435 2.09179e13i 1.34299i
436436 0 0
437437 −1.35165e13 −0.848122
438438 0 0
439439 − 1.05808e13i − 0.648928i −0.945898 0.324464i 0.894816π-0.894816\pi
0.945898 0.324464i 0.105184π-0.105184\pi
440440 0 0
441441 −2.50267e12 −0.150041
442442 0 0
443443 − 2.18951e13i − 1.28330i −0.766996 0.641651i 0.778250π-0.778250\pi
0.766996 0.641651i 0.221750π-0.221750\pi
444444 0 0
445445 9.50649e11 0.0544779
446446 0 0
447447 − 3.28679e13i − 1.84176i
448448 0 0
449449 −3.53942e13 −1.93954 −0.969772 0.244011i 0.921537π-0.921537\pi
−0.969772 + 0.244011i 0.921537π0.921537\pi
450450 0 0
451451 1.16780e12i 0.0625875i
452452 0 0
453453 6.31374e10 0.00330975
454454 0 0
455455 3.22014e13i 1.65127i
456456 0 0
457457 1.93883e13 0.972653 0.486326 0.873777i 0.338337π-0.338337\pi
0.486326 + 0.873777i 0.338337π0.338337\pi
458458 0 0
459459 3.10514e12i 0.152412i
460460 0 0
461461 −1.69421e13 −0.813696 −0.406848 0.913496i 0.633372π-0.633372\pi
−0.406848 + 0.913496i 0.633372π0.633372\pi
462462 0 0
463463 − 4.19900e13i − 1.97352i −0.162198 0.986758i 0.551858π-0.551858\pi
0.162198 0.986758i 0.448142π-0.448142\pi
464464 0 0
465465 1.81145e13 0.833224
466466 0 0
467467 9.55773e12i 0.430299i 0.976581 + 0.215150i 0.0690239π0.0690239\pi
−0.976581 + 0.215150i 0.930976π0.930976\pi
468468 0 0
469469 9.76783e12 0.430461
470470 0 0
471471 − 1.55416e13i − 0.670488i
472472 0 0
473473 4.71346e12 0.199083
474474 0 0
475475 1.54700e13i 0.639768i
476476 0 0
477477 2.01115e13 0.814427
478478 0 0
479479 4.05634e13i 1.60863i 0.594201 + 0.804317i 0.297468π0.297468\pi
−0.594201 + 0.804317i 0.702532π0.702532\pi
480480 0 0
481481 4.35036e13 1.68966
482482 0 0
483483 2.14978e13i 0.817823i
484484 0 0
485485 5.90127e13 2.19906
486486 0 0
487487 − 5.27934e13i − 1.92723i −0.267286 0.963617i 0.586127π-0.586127\pi
0.267286 0.963617i 0.413873π-0.413873\pi
488488 0 0
489489 3.73242e13 1.33489
490490 0 0
491491 2.41468e13i 0.846158i 0.906093 + 0.423079i 0.139051π0.139051\pi
−0.906093 + 0.423079i 0.860949π0.860949\pi
492492 0 0
493493 2.36309e13 0.811419
494494 0 0
495495 2.82135e13i 0.949360i
496496 0 0
497497 3.21021e13 1.05865
498498 0 0
499499 2.21286e11i 0.00715238i 0.999994 + 0.00357619i 0.00113834π0.00113834\pi
−0.999994 + 0.00357619i 0.998862π0.998862\pi
500500 0 0
501501 −5.81735e13 −1.84305
502502 0 0
503503 9.04543e12i 0.280924i 0.990086 + 0.140462i 0.0448588π0.0448588\pi
−0.990086 + 0.140462i 0.955141π0.955141\pi
504504 0 0
505505 −1.45580e13 −0.443247
506506 0 0
507507 5.65702e13i 1.68868i
508508 0 0
509509 −2.24139e13 −0.656036 −0.328018 0.944671i 0.606381π-0.606381\pi
−0.328018 + 0.944671i 0.606381π0.606381\pi
510510 0 0
511511 3.81267e13i 1.09427i
512512 0 0
513513 7.15266e12 0.201317
514514 0 0
515515 3.50243e13i 0.966793i
516516 0 0
517517 −2.71819e13 −0.735915
518518 0 0
519519 9.62269e13i 2.55540i
520520 0 0
521521 −2.19502e12 −0.0571807 −0.0285904 0.999591i 0.509102π-0.509102\pi
−0.0285904 + 0.999591i 0.509102π0.509102\pi
522522 0 0
523523 2.91933e13i 0.746062i 0.927819 + 0.373031i 0.121681π0.121681\pi
−0.927819 + 0.373031i 0.878319π0.878319\pi
524524 0 0
525525 2.46048e13 0.616913
526526 0 0
527527 − 2.04639e13i − 0.503425i
528528 0 0
529529 2.61438e13 0.631089
530530 0 0
531531 − 4.06551e12i − 0.0963036i
532532 0 0
533533 5.54070e12 0.128804
534534 0 0
535535 − 1.47599e13i − 0.336755i
536536 0 0
537537 5.47927e13 1.22702
538538 0 0
539539 4.43905e12i 0.0975768i
540540 0 0
541541 4.86387e12 0.104953 0.0524766 0.998622i 0.483288π-0.483288\pi
0.0524766 + 0.998622i 0.483288π0.483288\pi
542542 0 0
543543 5.46218e12i 0.115709i
544544 0 0
545545 −4.14336e13 −0.861728
546546 0 0
547547 3.29297e13i 0.672436i 0.941784 + 0.336218i 0.109148π0.109148\pi
−0.941784 + 0.336218i 0.890852π0.890852\pi
548548 0 0
549549 6.63067e13 1.32952
550550 0 0
551551 − 5.44335e13i − 1.07179i
552552 0 0
553553 −4.75557e13 −0.919554
554554 0 0
555555 − 1.05792e14i − 2.00904i
556556 0 0
557557 4.29354e13 0.800828 0.400414 0.916334i 0.368866π-0.368866\pi
0.400414 + 0.916334i 0.368866π0.368866\pi
558558 0 0
559559 − 2.23632e13i − 0.409709i
560560 0 0
561561 6.08610e13 1.09528
562562 0 0
563563 − 1.01247e14i − 1.78994i −0.446126 0.894970i 0.647197π-0.647197\pi
0.446126 0.894970i 0.352803π-0.352803\pi
564564 0 0
565565 −7.65652e13 −1.32981
566566 0 0
567567 4.84996e13i 0.827604i
568568 0 0
569569 3.75395e12 0.0629401 0.0314701 0.999505i 0.489981π-0.489981\pi
0.0314701 + 0.999505i 0.489981π0.489981\pi
570570 0 0
571571 4.82773e13i 0.795358i 0.917525 + 0.397679i 0.130184π0.130184\pi
−0.917525 + 0.397679i 0.869816π0.869816\pi
572572 0 0
573573 −7.71618e13 −1.24919
574574 0 0
575575 1.74914e13i 0.278283i
576576 0 0
577577 −3.01929e13 −0.472091 −0.236046 0.971742i 0.575851π-0.575851\pi
−0.236046 + 0.971742i 0.575851π0.575851\pi
578578 0 0
579579 6.47232e13i 0.994644i
580580 0 0
581581 4.30299e13 0.649964
582582 0 0
583583 − 3.56723e13i − 0.529649i
584584 0 0
585585 1.33860e14 1.95377
586586 0 0
587587 − 5.82710e13i − 0.836107i −0.908422 0.418053i 0.862712π-0.862712\pi
0.908422 0.418053i 0.137288π-0.137288\pi
588588 0 0
589589 −4.71383e13 −0.664963
590590 0 0
591591 − 1.01958e13i − 0.141411i
592592 0 0
593593 −3.13152e13 −0.427052 −0.213526 0.976937i 0.568495π-0.568495\pi
−0.213526 + 0.976937i 0.568495π0.568495\pi
594594 0 0
595595 − 8.84635e13i − 1.18626i
596596 0 0
597597 1.14528e14 1.51022
598598 0 0
599599 7.34955e13i 0.953074i 0.879154 + 0.476537i 0.158108π0.158108\pi
−0.879154 + 0.476537i 0.841892π0.841892\pi
600600 0 0
601601 −1.07112e14 −1.36605 −0.683024 0.730396i 0.739335π-0.739335\pi
−0.683024 + 0.730396i 0.739335π0.739335\pi
602602 0 0
603603 − 4.06046e13i − 0.509318i
604604 0 0
605605 −4.78339e13 −0.590145
606606 0 0
607607 − 1.36295e13i − 0.165401i −0.996574 0.0827004i 0.973646π-0.973646\pi
0.996574 0.0827004i 0.0263545π-0.0263545\pi
608608 0 0
609609 −8.65756e13 −1.03350
610610 0 0
611611 1.28966e14i 1.51450i
612612 0 0
613613 −1.16805e14 −1.34946 −0.674729 0.738066i 0.735739π-0.735739\pi
−0.674729 + 0.738066i 0.735739π0.735739\pi
614614 0 0
615615 − 1.34739e13i − 0.153150i
616616 0 0
617617 −4.22466e13 −0.472461 −0.236230 0.971697i 0.575912π-0.575912\pi
−0.236230 + 0.971697i 0.575912π0.575912\pi
618618 0 0
619619 − 1.04957e14i − 1.15493i −0.816415 0.577466i 0.804042π-0.804042\pi
0.816415 0.577466i 0.195958π-0.195958\pi
620620 0 0
621621 8.08727e12 0.0875677
622622 0 0
623623 3.93457e12i 0.0419234i
624624 0 0
625625 −1.19042e14 −1.24825
626626 0 0
627627 − 1.40193e14i − 1.44673i
628628 0 0
629629 −1.19513e14 −1.21384
630630 0 0
631631 − 2.87613e12i − 0.0287516i −0.999897 0.0143758i 0.995424π-0.995424\pi
0.999897 0.0143758i 0.00457612π-0.00457612\pi
632632 0 0
633633 −2.18463e14 −2.14960
634634 0 0
635635 2.36350e13i 0.228922i
636636 0 0
637637 2.10613e13 0.200811
638638 0 0
639639 − 1.33447e14i − 1.25258i
640640 0 0
641641 −3.00941e13 −0.278094 −0.139047 0.990286i 0.544404π-0.544404\pi
−0.139047 + 0.990286i 0.544404π0.544404\pi
642642 0 0
643643 − 1.66359e14i − 1.51353i −0.653689 0.756764i 0.726779π-0.726779\pi
0.653689 0.756764i 0.273221π-0.273221\pi
644644 0 0
645645 −5.43829e13 −0.487151
646646 0 0
647647 − 1.73339e14i − 1.52889i −0.644690 0.764444i 0.723013π-0.723013\pi
0.644690 0.764444i 0.276987π-0.276987\pi
648648 0 0
649649 −7.21111e12 −0.0626295
650650 0 0
651651 7.49728e13i 0.641207i
652652 0 0
653653 1.89861e14 1.59908 0.799541 0.600612i 0.205076π-0.205076\pi
0.799541 + 0.600612i 0.205076π0.205076\pi
654654 0 0
655655 1.88366e13i 0.156241i
656656 0 0
657657 1.58492e14 1.29473
658658 0 0
659659 − 9.80342e13i − 0.788771i −0.918945 0.394385i 0.870958π-0.870958\pi
0.918945 0.394385i 0.129042π-0.129042\pi
660660 0 0
661661 1.54197e14 1.22199 0.610996 0.791634i 0.290769π-0.290769\pi
0.610996 + 0.791634i 0.290769π0.290769\pi
662662 0 0
663663 − 2.88758e14i − 2.25406i
664664 0 0
665665 −2.03775e14 −1.56690
666666 0 0
667667 − 6.15461e13i − 0.466199i
668668 0 0
669669 1.85089e14 1.38118
670670 0 0
671671 − 1.17610e14i − 0.864634i
672672 0 0
673673 −6.70067e13 −0.485336 −0.242668 0.970109i 0.578023π-0.578023\pi
−0.242668 + 0.970109i 0.578023π0.578023\pi
674674 0 0
675675 − 9.25608e12i − 0.0660554i
676676 0 0
677677 1.71430e14 1.20543 0.602715 0.797956i 0.294085π-0.294085\pi
0.602715 + 0.797956i 0.294085π0.294085\pi
678678 0 0
679679 2.44243e14i 1.69229i
680680 0 0
681681 3.07650e14 2.10049
682682 0 0
683683 − 5.05521e13i − 0.340123i −0.985433 0.170061i 0.945603π-0.945603\pi
0.985433 0.170061i 0.0543966π-0.0543966\pi
684684 0 0
685685 −2.00543e14 −1.32970
686686 0 0
687687 2.92319e14i 1.91017i
688688 0 0
689689 −1.69249e14 −1.09001
690690 0 0
691691 5.33777e13i 0.338821i 0.985546 + 0.169410i 0.0541863π0.0541863\pi
−0.985546 + 0.169410i 0.945814π0.945814\pi
692692 0 0
693693 −1.16771e14 −0.730580
694694 0 0
695695 1.22467e14i 0.755256i
696696 0 0
697697 −1.52214e13 −0.0925317
698698 0 0
699699 − 2.93431e14i − 1.75841i
700700 0 0
701701 −3.55178e13 −0.209824 −0.104912 0.994481i 0.533456π-0.533456\pi
−0.104912 + 0.994481i 0.533456π0.533456\pi
702702 0 0
703703 2.75297e14i 1.60334i
704704 0 0
705705 3.13620e14 1.80077
706706 0 0
707707 − 6.02531e13i − 0.341101i
708708 0 0
709709 2.13491e14 1.19165 0.595824 0.803115i 0.296826π-0.296826\pi
0.595824 + 0.803115i 0.296826π0.296826\pi
710710 0 0
711711 1.97688e14i 1.08801i
712712 0 0
713713 −5.32977e13 −0.289242
714714 0 0
715715 − 2.37432e14i − 1.27060i
716716 0 0
717717 −3.23693e14 −1.70820
718718 0 0
719719 − 2.65916e14i − 1.38389i −0.721952 0.691943i 0.756755π-0.756755\pi
0.721952 0.691943i 0.243245π-0.243245\pi
720720 0 0
721721 −1.44959e14 −0.743995
722722 0 0
723723 − 5.51893e14i − 2.79360i
724724 0 0
725725 −7.04410e13 −0.351670
726726 0 0
727727 1.56999e14i 0.773082i 0.922272 + 0.386541i 0.126330π0.126330\pi
−0.922272 + 0.386541i 0.873670π0.873670\pi
728728 0 0
729729 2.44622e14 1.18812
730730 0 0
731731 6.14361e13i 0.294332i
732732 0 0
733733 2.64144e14 1.24831 0.624153 0.781302i 0.285444π-0.285444\pi
0.624153 + 0.781302i 0.285444π0.285444\pi
734734 0 0
735735 − 5.12169e13i − 0.238768i
736736 0 0
737737 −7.20216e13 −0.331227
738738 0 0
739739 2.68052e14i 1.21618i 0.793869 + 0.608089i 0.208064π0.208064\pi
−0.793869 + 0.608089i 0.791936π0.791936\pi
740740 0 0
741741 −6.65150e14 −2.97734
742742 0 0
743743 9.68880e13i 0.427884i 0.976846 + 0.213942i 0.0686303π0.0686303\pi
−0.976846 + 0.213942i 0.931370π0.931370\pi
744744 0 0
745745 3.52258e14 1.53490
746746 0 0
747747 − 1.78874e14i − 0.769032i
748748 0 0
749749 6.10885e13 0.259149
750750 0 0
751751 2.13814e13i 0.0895026i 0.998998 + 0.0447513i 0.0142495π0.0142495\pi
−0.998998 + 0.0447513i 0.985750π0.985750\pi
752752 0 0
753753 6.47674e14 2.67536
754754 0 0
755755 6.76669e11i 0.00275830i
756756 0 0
757757 3.45330e14 1.38917 0.694584 0.719412i 0.255589π-0.255589\pi
0.694584 + 0.719412i 0.255589π0.255589\pi
758758 0 0
759759 − 1.58511e14i − 0.629290i
760760 0 0
761761 −1.01279e14 −0.396822 −0.198411 0.980119i 0.563578π-0.563578\pi
−0.198411 + 0.980119i 0.563578π0.563578\pi
762762 0 0
763763 − 1.71486e14i − 0.663142i
764764 0 0
765765 −3.67740e14 −1.40357
766766 0 0
767767 3.42135e13i 0.128890i
768768 0 0
769769 −2.20211e14 −0.818854 −0.409427 0.912343i 0.634271π-0.634271\pi
−0.409427 + 0.912343i 0.634271π0.634271\pi
770770 0 0
771771 − 1.65286e14i − 0.606687i
772772 0 0
773773 −1.15285e14 −0.417709 −0.208855 0.977947i 0.566974π-0.566974\pi
−0.208855 + 0.977947i 0.566974π0.566974\pi
774774 0 0
775775 6.10005e13i 0.218185i
776776 0 0
777777 4.37855e14 1.54606
778778 0 0
779779 3.50623e13i 0.122223i
780780 0 0
781781 −2.36700e14 −0.814596
782782 0 0
783783 3.25689e13i 0.110661i
784784 0 0
785785 1.66566e14 0.558775
786786 0 0
787787 2.91930e14i 0.966953i 0.875357 + 0.483476i 0.160626π0.160626\pi
−0.875357 + 0.483476i 0.839374π0.839374\pi
788788 0 0
789789 7.13843e14 2.33463
790790 0 0
791791 − 3.16890e14i − 1.02335i
792792 0 0
793793 −5.58007e14 −1.77940
794794 0 0
795795 4.11580e14i 1.29604i
796796 0 0
797797 3.56212e14 1.10769 0.553843 0.832621i 0.313161π-0.313161\pi
0.553843 + 0.832621i 0.313161π0.313161\pi
798798 0 0
799799 − 3.54295e14i − 1.08800i
800800 0 0
801801 1.63559e13 0.0496035
802802 0 0
803803 − 2.81121e14i − 0.842007i
804804 0 0
805805 −2.30401e14 −0.681562
806806 0 0
807807 − 5.45417e14i − 1.59353i
808808 0 0
809809 2.42201e14 0.698930 0.349465 0.936949i 0.386363π-0.386363\pi
0.349465 + 0.936949i 0.386363π0.386363\pi
810810 0 0
811811 4.06752e14i 1.15938i 0.814838 + 0.579689i 0.196826π0.196826\pi
−0.814838 + 0.579689i 0.803174π0.803174\pi
812812 0 0
813813 9.67412e14 2.72370
814814 0 0
815815 4.00018e14i 1.11248i
816816 0 0
817817 1.41517e14 0.388776
818818 0 0
819819 5.54024e14i 1.50352i
820820 0 0
821821 −4.04166e14 −1.08354 −0.541768 0.840528i 0.682245π-0.682245\pi
−0.541768 + 0.840528i 0.682245π0.682245\pi
822822 0 0
823823 1.42442e14i 0.377259i 0.982048 + 0.188630i 0.0604045π0.0604045\pi
−0.982048 + 0.188630i 0.939595π0.939595\pi
824824 0 0
825825 −1.81420e14 −0.474695
826826 0 0
827827 3.85554e13i 0.0996684i 0.998758 + 0.0498342i 0.0158693π0.0158693\pi
−0.998758 + 0.0498342i 0.984131π0.984131\pi
828828 0 0
829829 −2.35400e14 −0.601221 −0.300610 0.953747i 0.597190π-0.597190\pi
−0.300610 + 0.953747i 0.597190π0.597190\pi
830830 0 0
831831 − 1.21214e14i − 0.305877i
832832 0 0
833833 −5.78595e13 −0.144261
834834 0 0
835835 − 6.23469e14i − 1.53597i
836836 0 0
837837 2.82040e13 0.0686568
838838 0 0
839839 − 5.54263e14i − 1.33323i −0.745401 0.666616i 0.767742π-0.767742\pi
0.745401 0.666616i 0.232258π-0.232258\pi
840840 0 0
841841 −1.72850e14 −0.410857
842842 0 0
843843 1.81993e14i 0.427481i
844844 0 0
845845 −6.06286e14 −1.40732
846846 0 0
847847 − 1.97976e14i − 0.454146i
848848 0 0
849849 3.45400e14 0.783039
850850 0 0
851851 3.11269e14i 0.697410i
852852 0 0
853853 −2.17078e14 −0.480696 −0.240348 0.970687i 0.577262π-0.577262\pi
−0.240348 + 0.970687i 0.577262π0.577262\pi
854854 0 0
855855 8.47086e14i 1.85395i
856856 0 0
857857 −7.39171e14 −1.59897 −0.799485 0.600685i 0.794894π-0.794894\pi
−0.799485 + 0.600685i 0.794894π0.794894\pi
858858 0 0
859859 − 3.16235e14i − 0.676152i −0.941119 0.338076i 0.890224π-0.890224\pi
0.941119 0.338076i 0.109776π-0.109776\pi
860860 0 0
861861 5.57661e13 0.117857
862862 0 0
863863 3.17121e14i 0.662478i 0.943547 + 0.331239i 0.107467π0.107467\pi
−0.943547 + 0.331239i 0.892533π0.892533\pi
864864 0 0
865865 −1.03130e15 −2.12964
866866 0 0
867867 8.34458e13i 0.170337i
868868 0 0
869869 3.50645e14 0.707569
870870 0 0
871871 3.41710e14i 0.681658i
872872 0 0
873873 1.01531e15 2.00230
874874 0 0
875875 − 3.11852e14i − 0.608007i
876876 0 0
877877 5.34325e14 1.02993 0.514965 0.857211i 0.327805π-0.327805\pi
0.514965 + 0.857211i 0.327805π0.327805\pi
878878 0 0
879879 − 1.33432e15i − 2.54282i
880880 0 0
881881 −1.20104e13 −0.0226297 −0.0113148 0.999936i 0.503602π-0.503602\pi
−0.0113148 + 0.999936i 0.503602π0.503602\pi
882882 0 0
883883 6.89886e14i 1.28521i 0.766198 + 0.642605i 0.222146π0.222146\pi
−0.766198 + 0.642605i 0.777854π0.777854\pi
884884 0 0
885885 8.32003e13 0.153253
886886 0 0
887887 7.40300e13i 0.134831i 0.997725 + 0.0674154i 0.0214753π0.0214753\pi
−0.997725 + 0.0674154i 0.978525π0.978525\pi
888888 0 0
889889 −9.78211e13 −0.176167
890890 0 0
891891 − 3.57604e14i − 0.636816i
892892 0 0
893893 −8.16114e14 −1.43712
894894 0 0
895895 5.87236e14i 1.02258i
896896 0 0
897897 −7.52063e14 −1.29507
898898 0 0
899899 − 2.14639e14i − 0.365519i
900900 0 0
901901 4.64960e14 0.783054
902902 0 0
903903 − 2.25081e14i − 0.374887i
904904 0 0
905905 −5.85404e13 −0.0964301
906906 0 0
907907 1.10129e15i 1.79418i 0.441852 + 0.897088i 0.354322π0.354322\pi
−0.441852 + 0.897088i 0.645678π0.645678\pi
908908 0 0
909909 −2.50471e14 −0.403587
910910 0 0
911911 5.75678e14i 0.917461i 0.888575 + 0.458730i 0.151696π0.151696\pi
−0.888575 + 0.458730i 0.848304π0.848304\pi
912912 0 0
913913 −3.17274e14 −0.500128
914914 0 0
915915 1.35696e15i 2.11574i
916916 0 0
917917 −7.79613e13 −0.120235
918918 0 0
919919 − 2.49831e14i − 0.381126i −0.981675 0.190563i 0.938969π-0.938969\pi
0.981675 0.190563i 0.0610314π-0.0610314\pi
920920 0 0
921921 −1.66965e15 −2.51957
922922 0 0
923923 1.12303e15i 1.67642i
924924 0 0
925925 3.56255e14 0.526081
926926 0 0
927927 6.02593e14i 0.880289i
928928 0 0
929929 −5.75740e14 −0.832046 −0.416023 0.909354i 0.636576π-0.636576\pi
−0.416023 + 0.909354i 0.636576π0.636576\pi
930930 0 0
931931 1.33279e14i 0.190552i
932932 0 0
933933 6.26252e14 0.885811
934934 0 0
935935 6.52272e14i 0.912789i
936936 0 0
937937 −4.19947e14 −0.581428 −0.290714 0.956810i 0.593893π-0.593893\pi
−0.290714 + 0.956810i 0.593893π0.593893\pi
938938 0 0
939939 7.72792e14i 1.05861i
940940 0 0
941941 −4.76423e14 −0.645721 −0.322860 0.946447i 0.604644π-0.604644\pi
−0.322860 + 0.946447i 0.604644π0.604644\pi
942942 0 0
943943 3.96438e13i 0.0531639i
944944 0 0
945945 1.21923e14 0.161781
946946 0 0
947947 7.31112e14i 0.959918i 0.877291 + 0.479959i 0.159348π0.159348\pi
−0.877291 + 0.479959i 0.840652π0.840652\pi
948948 0 0
949949 −1.33379e15 −1.73283
950950 0 0
951951 − 8.11488e14i − 1.04323i
952952 0 0
953953 −4.33318e14 −0.551242 −0.275621 0.961266i 0.588884π-0.588884\pi
−0.275621 + 0.961266i 0.588884π0.588884\pi
954954 0 0
955955 − 8.26974e14i − 1.04106i
956956 0 0
957957 6.38352e14 0.795244
958958 0 0
959959 − 8.30012e14i − 1.02327i
960960 0 0
961961 6.33755e14 0.773222
962962 0 0
963963 − 2.53943e14i − 0.306623i
964964 0 0
965965 −6.93665e14 −0.828921
966966 0 0
967967 1.28203e15i 1.51623i 0.652120 + 0.758115i 0.273880π0.273880\pi
−0.652120 + 0.758115i 0.726120π0.726120\pi
968968 0 0
969969 1.82730e15 2.13890
970970 0 0
971971 1.03910e15i 1.20381i 0.798566 + 0.601907i 0.205592π0.205592\pi
−0.798566 + 0.601907i 0.794408π0.794408\pi
972972 0 0
973973 −5.06868e14 −0.581207
974974 0 0
975975 8.60755e14i 0.976914i
976976 0 0
977977 −8.98564e13 −0.100943 −0.0504715 0.998726i 0.516072π-0.516072\pi
−0.0504715 + 0.998726i 0.516072π0.516072\pi
978978 0 0
979979 − 2.90109e13i − 0.0322588i
980980 0 0
981981 −7.12864e14 −0.784624
982982 0 0
983983 5.65525e14i 0.616147i 0.951363 + 0.308073i 0.0996842π0.0996842\pi
−0.951363 + 0.308073i 0.900316π0.900316\pi
984984 0 0
985985 1.09272e14 0.117850
986986 0 0
987987 1.29802e15i 1.38578i
988988 0 0
989989 1.60009e14 0.169107
990990 0 0
991991 1.22093e15i 1.27739i 0.769461 + 0.638693i 0.220525π0.220525\pi
−0.769461 + 0.638693i 0.779475π0.779475\pi
992992 0 0
993993 1.26542e15 1.31065
994994 0 0
995995 1.22744e15i 1.25860i
996996 0 0
997997 4.49639e14 0.456445 0.228222 0.973609i 0.426709π-0.426709\pi
0.228222 + 0.973609i 0.426709π0.426709\pi
998998 0 0
999999 − 1.64717e14i − 0.165543i
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 256.11.c.m.255.15 16
4.3 odd 2 inner 256.11.c.m.255.1 16
8.3 odd 2 inner 256.11.c.m.255.16 16
8.5 even 2 inner 256.11.c.m.255.2 16
16.3 odd 4 8.11.d.b.3.5 8
16.5 even 4 8.11.d.b.3.6 yes 8
16.11 odd 4 32.11.d.b.15.1 8
16.13 even 4 32.11.d.b.15.2 8
48.5 odd 4 72.11.b.b.19.3 8
48.11 even 4 288.11.b.b.271.7 8
48.29 odd 4 288.11.b.b.271.2 8
48.35 even 4 72.11.b.b.19.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.11.d.b.3.5 8 16.3 odd 4
8.11.d.b.3.6 yes 8 16.5 even 4
32.11.d.b.15.1 8 16.11 odd 4
32.11.d.b.15.2 8 16.13 even 4
72.11.b.b.19.3 8 48.5 odd 4
72.11.b.b.19.4 8 48.35 even 4
256.11.c.m.255.1 16 4.3 odd 2 inner
256.11.c.m.255.2 16 8.5 even 2 inner
256.11.c.m.255.15 16 1.1 even 1 trivial
256.11.c.m.255.16 16 8.3 odd 2 inner
288.11.b.b.271.2 8 48.29 odd 4
288.11.b.b.271.7 8 48.11 even 4