Properties

Label 256.4.b.h.129.4
Level 256256
Weight 44
Character 256.129
Analytic conductor 15.10415.104
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [256,4,Mod(129,256)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(256, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("256.129"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 256=28 256 = 2^{8}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 256.b (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 15.104488961515.1044889615
Analytic rank: 00
Dimension: 44
Coefficient field: Q(ζ12)\Q(\zeta_{12})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 28 2^{8}
Twist minimal: no (minimal twist has level 128)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 129.4
Root 0.866025+0.500000i-0.866025 + 0.500000i of defining polynomial
Character χ\chi == 256.129
Dual form 256.4.b.h.129.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+8.92820iq311.8564iq5+9.85641q752.7128q939.0718iq1191.5692iq13+105.856q1537.1384q1746.4974iq19+88.0000iq21120.708q2315.5744q25229.569iq27+27.2820iq29+81.1487q31+348.841q33116.862iq35+10.9948iq37+817.549q39+205.426q41115.359iq43+624.985iq45+312.841q47245.851q49331.580iq51+90.9948iq53463.251q55+415.138q57+550.631iq59630.974iq61519.559q631085.68q65661.041iq671077.70iq69+494.985q71566.267q73139.051iq75385.108iq7749.4153q79+626.395q81+564.067iq83+440.328iq85243.580q871089.67q89902.543iq91+724.513iq93551.292q95+464.605q97+2059.58iq99+O(q100)q+8.92820i q^{3} -11.8564i q^{5} +9.85641 q^{7} -52.7128 q^{9} -39.0718i q^{11} -91.5692i q^{13} +105.856 q^{15} -37.1384 q^{17} -46.4974i q^{19} +88.0000i q^{21} -120.708 q^{23} -15.5744 q^{25} -229.569i q^{27} +27.2820i q^{29} +81.1487 q^{31} +348.841 q^{33} -116.862i q^{35} +10.9948i q^{37} +817.549 q^{39} +205.426 q^{41} -115.359i q^{43} +624.985i q^{45} +312.841 q^{47} -245.851 q^{49} -331.580i q^{51} +90.9948i q^{53} -463.251 q^{55} +415.138 q^{57} +550.631i q^{59} -630.974i q^{61} -519.559 q^{63} -1085.68 q^{65} -661.041i q^{67} -1077.70i q^{69} +494.985 q^{71} -566.267 q^{73} -139.051i q^{75} -385.108i q^{77} -49.4153 q^{79} +626.395 q^{81} +564.067i q^{83} +440.328i q^{85} -243.580 q^{87} -1089.67 q^{89} -902.543i q^{91} +724.513i q^{93} -551.292 q^{95} +464.605 q^{97} +2059.58i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q16q7100q9+368q15+184q17+16q23284q25+768q31+176q33+1552q39+600q41+32q47540q49+752q55+1328q571136q631904q65++4408q97+O(q100) 4 q - 16 q^{7} - 100 q^{9} + 368 q^{15} + 184 q^{17} + 16 q^{23} - 284 q^{25} + 768 q^{31} + 176 q^{33} + 1552 q^{39} + 600 q^{41} + 32 q^{47} - 540 q^{49} + 752 q^{55} + 1328 q^{57} - 1136 q^{63} - 1904 q^{65}+ \cdots + 4408 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) 1-1 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 8.92820i 1.71823i 0.511780 + 0.859117i 0.328986π0.328986\pi
−0.511780 + 0.859117i 0.671014π0.671014\pi
44 0 0
55 − 11.8564i − 1.06047i −0.847851 0.530235i 0.822104π-0.822104\pi
0.847851 0.530235i 0.177896π-0.177896\pi
66 0 0
77 9.85641 0.532196 0.266098 0.963946i 0.414266π-0.414266\pi
0.266098 + 0.963946i 0.414266π0.414266\pi
88 0 0
99 −52.7128 −1.95233
1010 0 0
1111 − 39.0718i − 1.07096i −0.844547 0.535481i 0.820130π-0.820130\pi
0.844547 0.535481i 0.179870π-0.179870\pi
1212 0 0
1313 − 91.5692i − 1.95359i −0.214166 0.976797i 0.568703π-0.568703\pi
0.214166 0.976797i 0.431297π-0.431297\pi
1414 0 0
1515 105.856 1.82213
1616 0 0
1717 −37.1384 −0.529847 −0.264923 0.964269i 0.585347π-0.585347\pi
−0.264923 + 0.964269i 0.585347π0.585347\pi
1818 0 0
1919 − 46.4974i − 0.561434i −0.959791 0.280717i 0.909428π-0.909428\pi
0.959791 0.280717i 0.0905722π-0.0905722\pi
2020 0 0
2121 88.0000i 0.914437i
2222 0 0
2323 −120.708 −1.09432 −0.547158 0.837029i 0.684290π-0.684290\pi
−0.547158 + 0.837029i 0.684290π0.684290\pi
2424 0 0
2525 −15.5744 −0.124595
2626 0 0
2727 − 229.569i − 1.63632i
2828 0 0
2929 27.2820i 0.174695i 0.996178 + 0.0873473i 0.0278390π0.0278390\pi
−0.996178 + 0.0873473i 0.972161π0.972161\pi
3030 0 0
3131 81.1487 0.470153 0.235077 0.971977i 0.424466π-0.424466\pi
0.235077 + 0.971977i 0.424466π0.424466\pi
3232 0 0
3333 348.841 1.84016
3434 0 0
3535 − 116.862i − 0.564377i
3636 0 0
3737 10.9948i 0.0488525i 0.999702 + 0.0244262i 0.00777589π0.00777589\pi
−0.999702 + 0.0244262i 0.992224π0.992224\pi
3838 0 0
3939 817.549 3.35673
4040 0 0
4141 205.426 0.782490 0.391245 0.920287i 0.372044π-0.372044\pi
0.391245 + 0.920287i 0.372044π0.372044\pi
4242 0 0
4343 − 115.359i − 0.409118i −0.978854 0.204559i 0.934424π-0.934424\pi
0.978854 0.204559i 0.0655760π-0.0655760\pi
4444 0 0
4545 624.985i 2.07038i
4646 0 0
4747 312.841 0.970905 0.485453 0.874263i 0.338655π-0.338655\pi
0.485453 + 0.874263i 0.338655π0.338655\pi
4848 0 0
4949 −245.851 −0.716767
5050 0 0
5151 − 331.580i − 0.910400i
5252 0 0
5353 90.9948i 0.235832i 0.993024 + 0.117916i 0.0376214π0.0376214\pi
−0.993024 + 0.117916i 0.962379π0.962379\pi
5454 0 0
5555 −463.251 −1.13572
5656 0 0
5757 415.138 0.964674
5858 0 0
5959 550.631i 1.21502i 0.794313 + 0.607509i 0.207831π0.207831\pi
−0.794313 + 0.607509i 0.792169π0.792169\pi
6060 0 0
6161 − 630.974i − 1.32439i −0.749330 0.662196i 0.769624π-0.769624\pi
0.749330 0.662196i 0.230376π-0.230376\pi
6262 0 0
6363 −519.559 −1.03902
6464 0 0
6565 −1085.68 −2.07173
6666 0 0
6767 − 661.041i − 1.20536i −0.797984 0.602679i 0.794100π-0.794100\pi
0.797984 0.602679i 0.205900π-0.205900\pi
6868 0 0
6969 − 1077.70i − 1.88029i
7070 0 0
7171 494.985 0.827378 0.413689 0.910418i 0.364240π-0.364240\pi
0.413689 + 0.910418i 0.364240π0.364240\pi
7272 0 0
7373 −566.267 −0.907897 −0.453949 0.891028i 0.649985π-0.649985\pi
−0.453949 + 0.891028i 0.649985π0.649985\pi
7474 0 0
7575 − 139.051i − 0.214083i
7676 0 0
7777 − 385.108i − 0.569962i
7878 0 0
7979 −49.4153 −0.0703754 −0.0351877 0.999381i 0.511203π-0.511203\pi
−0.0351877 + 0.999381i 0.511203π0.511203\pi
8080 0 0
8181 626.395 0.859252
8282 0 0
8383 564.067i 0.745956i 0.927840 + 0.372978i 0.121663π0.121663\pi
−0.927840 + 0.372978i 0.878337π0.878337\pi
8484 0 0
8585 440.328i 0.561886i
8686 0 0
8787 −243.580 −0.300166
8888 0 0
8989 −1089.67 −1.29781 −0.648904 0.760870i 0.724772π-0.724772\pi
−0.648904 + 0.760870i 0.724772π0.724772\pi
9090 0 0
9191 − 902.543i − 1.03970i
9292 0 0
9393 724.513i 0.807833i
9494 0 0
9595 −551.292 −0.595383
9696 0 0
9797 464.605 0.486325 0.243162 0.969986i 0.421815π-0.421815\pi
0.243162 + 0.969986i 0.421815π0.421815\pi
9898 0 0
9999 2059.58i 2.09087i
100100 0 0
101101 − 965.005i − 0.950709i −0.879794 0.475354i 0.842320π-0.842320\pi
0.879794 0.475354i 0.157680π-0.157680\pi
102102 0 0
103103 −1828.99 −1.74967 −0.874836 0.484419i 0.839031π-0.839031\pi
−0.874836 + 0.484419i 0.839031π0.839031\pi
104104 0 0
105105 1043.36 0.969732
106106 0 0
107107 1726.59i 1.55996i 0.625805 + 0.779980i 0.284771π0.284771\pi
−0.625805 + 0.779980i 0.715229π0.715229\pi
108108 0 0
109109 − 423.015i − 0.371720i −0.982576 0.185860i 0.940493π-0.940493\pi
0.982576 0.185860i 0.0595072π-0.0595072\pi
110110 0 0
111111 −98.1642 −0.0839400
112112 0 0
113113 763.108 0.635284 0.317642 0.948211i 0.397109π-0.397109\pi
0.317642 + 0.948211i 0.397109π0.397109\pi
114114 0 0
115115 1431.16i 1.16049i
116116 0 0
117117 4826.87i 3.81405i
118118 0 0
119119 −366.052 −0.281982
120120 0 0
121121 −195.605 −0.146961
122122 0 0
123123 1834.08i 1.34450i
124124 0 0
125125 − 1297.39i − 0.928340i
126126 0 0
127127 2159.38 1.50877 0.754387 0.656430i 0.227934π-0.227934\pi
0.754387 + 0.656430i 0.227934π0.227934\pi
128128 0 0
129129 1029.95 0.702961
130130 0 0
131131 − 710.723i − 0.474016i −0.971508 0.237008i 0.923833π-0.923833\pi
0.971508 0.237008i 0.0761668π-0.0761668\pi
132132 0 0
133133 − 458.297i − 0.298793i
134134 0 0
135135 −2721.87 −1.73527
136136 0 0
137137 987.128 0.615592 0.307796 0.951452i 0.400409π-0.400409\pi
0.307796 + 0.951452i 0.400409π0.400409\pi
138138 0 0
139139 − 2334.15i − 1.42432i −0.702019 0.712158i 0.747718π-0.747718\pi
0.702019 0.712158i 0.252282π-0.252282\pi
140140 0 0
141141 2793.11i 1.66824i
142142 0 0
143143 −3577.77 −2.09223
144144 0 0
145145 323.467 0.185258
146146 0 0
147147 − 2195.01i − 1.23157i
148148 0 0
149149 − 1792.29i − 0.985435i −0.870189 0.492718i 0.836004π-0.836004\pi
0.870189 0.492718i 0.163996π-0.163996\pi
150150 0 0
151151 2864.32 1.54367 0.771837 0.635820i 0.219338π-0.219338\pi
0.771837 + 0.635820i 0.219338π0.219338\pi
152152 0 0
153153 1957.67 1.03443
154154 0 0
155155 − 962.133i − 0.498583i
156156 0 0
157157 − 2123.57i − 1.07949i −0.841830 0.539743i 0.818521π-0.818521\pi
0.841830 0.539743i 0.181479π-0.181479\pi
158158 0 0
159159 −812.420 −0.405215
160160 0 0
161161 −1189.74 −0.582391
162162 0 0
163163 3164.21i 1.52049i 0.649636 + 0.760245i 0.274921π0.274921\pi
−0.649636 + 0.760245i 0.725079π0.725079\pi
164164 0 0
165165 − 4136.00i − 1.95144i
166166 0 0
167167 −1340.34 −0.621069 −0.310534 0.950562i 0.600508π-0.600508\pi
−0.310534 + 0.950562i 0.600508π0.600508\pi
168168 0 0
169169 −6187.92 −2.81653
170170 0 0
171171 2451.01i 1.09610i
172172 0 0
173173 2802.13i 1.23146i 0.787958 + 0.615729i 0.211138π0.211138\pi
−0.787958 + 0.615729i 0.788862π0.788862\pi
174174 0 0
175175 −153.507 −0.0663089
176176 0 0
177177 −4916.14 −2.08768
178178 0 0
179179 1074.84i 0.448810i 0.974496 + 0.224405i 0.0720438π0.0720438\pi
−0.974496 + 0.224405i 0.927956π0.927956\pi
180180 0 0
181181 571.036i 0.234502i 0.993102 + 0.117251i 0.0374081π0.0374081\pi
−0.993102 + 0.117251i 0.962592π0.962592\pi
182182 0 0
183183 5633.47 2.27562
184184 0 0
185185 130.359 0.0518065
186186 0 0
187187 1451.07i 0.567446i
188188 0 0
189189 − 2262.73i − 0.870842i
190190 0 0
191191 −872.657 −0.330593 −0.165296 0.986244i 0.552858π-0.552858\pi
−0.165296 + 0.986244i 0.552858π0.552858\pi
192192 0 0
193193 672.523 0.250825 0.125413 0.992105i 0.459975π-0.459975\pi
0.125413 + 0.992105i 0.459975π0.459975\pi
194194 0 0
195195 − 9693.19i − 3.55971i
196196 0 0
197197 − 3129.56i − 1.13184i −0.824461 0.565918i 0.808522π-0.808522\pi
0.824461 0.565918i 0.191478π-0.191478\pi
198198 0 0
199199 1502.37 0.535176 0.267588 0.963533i 0.413773π-0.413773\pi
0.267588 + 0.963533i 0.413773π0.413773\pi
200200 0 0
201201 5901.91 2.07109
202202 0 0
203203 268.903i 0.0929718i
204204 0 0
205205 − 2435.61i − 0.829807i
206206 0 0
207207 6362.84 2.13646
208208 0 0
209209 −1816.74 −0.601275
210210 0 0
211211 − 1773.70i − 0.578703i −0.957223 0.289352i 0.906560π-0.906560\pi
0.957223 0.289352i 0.0934397π-0.0934397\pi
212212 0 0
213213 4419.32i 1.42163i
214214 0 0
215215 −1367.74 −0.433857
216216 0 0
217217 799.835 0.250214
218218 0 0
219219 − 5055.74i − 1.55998i
220220 0 0
221221 3400.74i 1.03511i
222222 0 0
223223 5413.66 1.62568 0.812838 0.582490i 0.197922π-0.197922\pi
0.812838 + 0.582490i 0.197922π0.197922\pi
224224 0 0
225225 820.969 0.243250
226226 0 0
227227 3744.27i 1.09478i 0.836876 + 0.547392i 0.184379π0.184379\pi
−0.836876 + 0.547392i 0.815621π0.815621\pi
228228 0 0
229229 680.739i 0.196439i 0.995165 + 0.0982194i 0.0313147π0.0313147\pi
−0.995165 + 0.0982194i 0.968685π0.968685\pi
230230 0 0
231231 3438.32 0.979328
232232 0 0
233233 679.271 0.190989 0.0954947 0.995430i 0.469557π-0.469557\pi
0.0954947 + 0.995430i 0.469557π0.469557\pi
234234 0 0
235235 − 3709.17i − 1.02962i
236236 0 0
237237 − 441.190i − 0.120921i
238238 0 0
239239 −3901.27 −1.05587 −0.527934 0.849286i 0.677033π-0.677033\pi
−0.527934 + 0.849286i 0.677033π0.677033\pi
240240 0 0
241241 5859.72 1.56622 0.783108 0.621886i 0.213633π-0.213633\pi
0.783108 + 0.621886i 0.213633π0.213633\pi
242242 0 0
243243 − 605.790i − 0.159924i
244244 0 0
245245 2914.91i 0.760110i
246246 0 0
247247 −4257.73 −1.09681
248248 0 0
249249 −5036.10 −1.28173
250250 0 0
251251 3381.48i 0.850348i 0.905112 + 0.425174i 0.139787π0.139787\pi
−0.905112 + 0.425174i 0.860213π0.860213\pi
252252 0 0
253253 4716.27i 1.17197i
254254 0 0
255255 −3931.34 −0.965452
256256 0 0
257257 3652.22 0.886455 0.443227 0.896409i 0.353833π-0.353833\pi
0.443227 + 0.896409i 0.353833π0.353833\pi
258258 0 0
259259 108.370i 0.0259991i
260260 0 0
261261 − 1438.11i − 0.341061i
262262 0 0
263263 2462.74 0.577410 0.288705 0.957418i 0.406775π-0.406775\pi
0.288705 + 0.957418i 0.406775π0.406775\pi
264264 0 0
265265 1078.87 0.250093
266266 0 0
267267 − 9728.81i − 2.22994i
268268 0 0
269269 − 482.503i − 0.109363i −0.998504 0.0546816i 0.982586π-0.982586\pi
0.998504 0.0546816i 0.0174144π-0.0174144\pi
270270 0 0
271271 3602.48 0.807510 0.403755 0.914867i 0.367705π-0.367705\pi
0.403755 + 0.914867i 0.367705π0.367705\pi
272272 0 0
273273 8058.09 1.78644
274274 0 0
275275 608.519i 0.133437i
276276 0 0
277277 6177.72i 1.34001i 0.742356 + 0.670006i 0.233709π0.233709\pi
−0.742356 + 0.670006i 0.766291π0.766291\pi
278278 0 0
279279 −4277.58 −0.917892
280280 0 0
281281 543.477 0.115378 0.0576888 0.998335i 0.481627π-0.481627\pi
0.0576888 + 0.998335i 0.481627π0.481627\pi
282282 0 0
283283 − 6582.11i − 1.38256i −0.722585 0.691282i 0.757046π-0.757046\pi
0.722585 0.691282i 0.242954π-0.242954\pi
284284 0 0
285285 − 4922.05i − 1.02301i
286286 0 0
287287 2024.76 0.416438
288288 0 0
289289 −3533.74 −0.719262
290290 0 0
291291 4148.09i 0.835620i
292292 0 0
293293 6753.68i 1.34660i 0.739369 + 0.673301i 0.235124π0.235124\pi
−0.739369 + 0.673301i 0.764876π0.764876\pi
294294 0 0
295295 6528.50 1.28849
296296 0 0
297297 −8969.68 −1.75244
298298 0 0
299299 11053.1i 2.13785i
300300 0 0
301301 − 1137.03i − 0.217731i
302302 0 0
303303 8615.76 1.63354
304304 0 0
305305 −7481.09 −1.40448
306306 0 0
307307 − 1821.88i − 0.338698i −0.985556 0.169349i 0.945833π-0.945833\pi
0.985556 0.169349i 0.0541665π-0.0541665\pi
308308 0 0
309309 − 16329.6i − 3.00635i
310310 0 0
311311 −10598.2 −1.93237 −0.966184 0.257852i 0.916985π-0.916985\pi
−0.966184 + 0.257852i 0.916985π0.916985\pi
312312 0 0
313313 7969.69 1.43921 0.719606 0.694382i 0.244322π-0.244322\pi
0.719606 + 0.694382i 0.244322π0.244322\pi
314314 0 0
315315 6160.10i 1.10185i
316316 0 0
317317 − 7773.66i − 1.37733i −0.725082 0.688663i 0.758198π-0.758198\pi
0.725082 0.688663i 0.241802π-0.241802\pi
318318 0 0
319319 1065.96 0.187092
320320 0 0
321321 −15415.3 −2.68038
322322 0 0
323323 1726.84i 0.297474i
324324 0 0
325325 1426.13i 0.243408i
326326 0 0
327327 3776.77 0.638703
328328 0 0
329329 3083.49 0.516712
330330 0 0
331331 8212.87i 1.36381i 0.731442 + 0.681903i 0.238848π0.238848\pi
−0.731442 + 0.681903i 0.761152π0.761152\pi
332332 0 0
333333 − 579.569i − 0.0953760i
334334 0 0
335335 −7837.57 −1.27825
336336 0 0
337337 5260.17 0.850267 0.425133 0.905131i 0.360227π-0.360227\pi
0.425133 + 0.905131i 0.360227π0.360227\pi
338338 0 0
339339 6813.18i 1.09157i
340340 0 0
341341 − 3170.63i − 0.503516i
342342 0 0
343343 −5803.96 −0.913657
344344 0 0
345345 −12777.7 −1.99399
346346 0 0
347347 2162.12i 0.334492i 0.985915 + 0.167246i 0.0534873π0.0534873\pi
−0.985915 + 0.167246i 0.946513π0.946513\pi
348348 0 0
349349 − 2888.90i − 0.443093i −0.975150 0.221546i 0.928890π-0.928890\pi
0.975150 0.221546i 0.0711104π-0.0711104\pi
350350 0 0
351351 −21021.5 −3.19670
352352 0 0
353353 11550.2 1.74152 0.870760 0.491709i 0.163628π-0.163628\pi
0.870760 + 0.491709i 0.163628π0.163628\pi
354354 0 0
355355 − 5868.74i − 0.877409i
356356 0 0
357357 − 3268.18i − 0.484511i
358358 0 0
359359 −6523.97 −0.959114 −0.479557 0.877511i 0.659203π-0.659203\pi
−0.479557 + 0.877511i 0.659203π0.659203\pi
360360 0 0
361361 4696.99 0.684792
362362 0 0
363363 − 1746.40i − 0.252514i
364364 0 0
365365 6713.89i 0.962797i
366366 0 0
367367 −6856.96 −0.975287 −0.487644 0.873043i 0.662143π-0.662143\pi
−0.487644 + 0.873043i 0.662143π0.662143\pi
368368 0 0
369369 −10828.6 −1.52768
370370 0 0
371371 896.882i 0.125509i
372372 0 0
373373 − 5001.68i − 0.694309i −0.937808 0.347155i 0.887148π-0.887148\pi
0.937808 0.347155i 0.112852π-0.112852\pi
374374 0 0
375375 11583.4 1.59511
376376 0 0
377377 2498.19 0.341283
378378 0 0
379379 − 84.9775i − 0.0115172i −0.999983 0.00575858i 0.998167π-0.998167\pi
0.999983 0.00575858i 0.00183302π-0.00183302\pi
380380 0 0
381381 19279.4i 2.59243i
382382 0 0
383383 −2596.76 −0.346444 −0.173222 0.984883i 0.555418π-0.555418\pi
−0.173222 + 0.984883i 0.555418π0.555418\pi
384384 0 0
385385 −4565.99 −0.604427
386386 0 0
387387 6080.90i 0.798732i
388388 0 0
389389 9213.21i 1.20084i 0.799683 + 0.600422i 0.205001π0.205001\pi
−0.799683 + 0.600422i 0.794999π0.794999\pi
390390 0 0
391391 4482.89 0.579820
392392 0 0
393393 6345.48 0.814471
394394 0 0
395395 585.888i 0.0746310i
396396 0 0
397397 6614.19i 0.836163i 0.908409 + 0.418082i 0.137297π0.137297\pi
−0.908409 + 0.418082i 0.862703π0.862703\pi
398398 0 0
399399 4091.77 0.513396
400400 0 0
401401 3434.94 0.427763 0.213881 0.976860i 0.431389π-0.431389\pi
0.213881 + 0.976860i 0.431389π0.431389\pi
402402 0 0
403403 − 7430.73i − 0.918489i
404404 0 0
405405 − 7426.79i − 0.911210i
406406 0 0
407407 429.588 0.0523192
408408 0 0
409409 6435.82 0.778071 0.389035 0.921223i 0.372808π-0.372808\pi
0.389035 + 0.921223i 0.372808π0.372808\pi
410410 0 0
411411 8813.28i 1.05773i
412412 0 0
413413 5427.24i 0.646627i
414414 0 0
415415 6687.80 0.791064
416416 0 0
417417 20839.8 2.44731
418418 0 0
419419 4222.04i 0.492267i 0.969236 + 0.246134i 0.0791602π0.0791602\pi
−0.969236 + 0.246134i 0.920840π0.920840\pi
420420 0 0
421421 5164.92i 0.597917i 0.954266 + 0.298958i 0.0966391π0.0966391\pi
−0.954266 + 0.298958i 0.903361π0.903361\pi
422422 0 0
423423 −16490.7 −1.89552
424424 0 0
425425 578.408 0.0660163
426426 0 0
427427 − 6219.14i − 0.704837i
428428 0 0
429429 − 31943.1i − 3.59493i
430430 0 0
431431 −7476.41 −0.835559 −0.417780 0.908548i 0.637192π-0.637192\pi
−0.417780 + 0.908548i 0.637192π0.637192\pi
432432 0 0
433433 −11289.7 −1.25299 −0.626497 0.779424i 0.715512π-0.715512\pi
−0.626497 + 0.779424i 0.715512π0.715512\pi
434434 0 0
435435 2887.98i 0.318317i
436436 0 0
437437 5612.59i 0.614386i
438438 0 0
439439 −1800.79 −0.195779 −0.0978895 0.995197i 0.531209π-0.531209\pi
−0.0978895 + 0.995197i 0.531209π0.531209\pi
440440 0 0
441441 12959.5 1.39936
442442 0 0
443443 7020.76i 0.752972i 0.926422 + 0.376486i 0.122868π0.122868\pi
−0.926422 + 0.376486i 0.877132π0.877132\pi
444444 0 0
445445 12919.6i 1.37629i
446446 0 0
447447 16001.9 1.69321
448448 0 0
449449 −3318.29 −0.348774 −0.174387 0.984677i 0.555794π-0.555794\pi
−0.174387 + 0.984677i 0.555794π0.555794\pi
450450 0 0
451451 − 8026.35i − 0.838018i
452452 0 0
453453 25573.2i 2.65239i
454454 0 0
455455 −10700.9 −1.10256
456456 0 0
457457 −4468.38 −0.457378 −0.228689 0.973500i 0.573444π-0.573444\pi
−0.228689 + 0.973500i 0.573444π0.573444\pi
458458 0 0
459459 8525.84i 0.866998i
460460 0 0
461461 − 1179.45i − 0.119159i −0.998224 0.0595795i 0.981024π-0.981024\pi
0.998224 0.0595795i 0.0189760π-0.0189760\pi
462462 0 0
463463 −13763.1 −1.38148 −0.690742 0.723101i 0.742716π-0.742716\pi
−0.690742 + 0.723101i 0.742716π0.742716\pi
464464 0 0
465465 8590.11 0.856682
466466 0 0
467467 17014.1i 1.68591i 0.537984 + 0.842955i 0.319186π0.319186\pi
−0.537984 + 0.842955i 0.680814π0.680814\pi
468468 0 0
469469 − 6515.49i − 0.641487i
470470 0 0
471471 18959.7 1.85481
472472 0 0
473473 −4507.28 −0.438150
474474 0 0
475475 724.168i 0.0699518i
476476 0 0
477477 − 4796.59i − 0.460421i
478478 0 0
479479 18976.7 1.81017 0.905083 0.425236i 0.139809π-0.139809\pi
0.905083 + 0.425236i 0.139809π0.139809\pi
480480 0 0
481481 1006.79 0.0954379
482482 0 0
483483 − 10622.3i − 1.00068i
484484 0 0
485485 − 5508.55i − 0.515733i
486486 0 0
487487 10579.6 0.984408 0.492204 0.870480i 0.336191π-0.336191\pi
0.492204 + 0.870480i 0.336191π0.336191\pi
488488 0 0
489489 −28250.7 −2.61256
490490 0 0
491491 − 15200.9i − 1.39716i −0.715533 0.698579i 0.753816π-0.753816\pi
0.715533 0.698579i 0.246184π-0.246184\pi
492492 0 0
493493 − 1013.21i − 0.0925614i
494494 0 0
495495 24419.3 2.21730
496496 0 0
497497 4878.77 0.440327
498498 0 0
499499 − 2553.92i − 0.229117i −0.993417 0.114558i 0.963455π-0.963455\pi
0.993417 0.114558i 0.0365453π-0.0365453\pi
500500 0 0
501501 − 11966.8i − 1.06714i
502502 0 0
503503 4863.70 0.431137 0.215568 0.976489i 0.430840π-0.430840\pi
0.215568 + 0.976489i 0.430840π0.430840\pi
504504 0 0
505505 −11441.5 −1.00820
506506 0 0
507507 − 55247.0i − 4.83946i
508508 0 0
509509 − 17659.5i − 1.53781i −0.639366 0.768903i 0.720803π-0.720803\pi
0.639366 0.768903i 0.279197π-0.279197\pi
510510 0 0
511511 −5581.35 −0.483179
512512 0 0
513513 −10674.4 −0.918685
514514 0 0
515515 21685.3i 1.85547i
516516 0 0
517517 − 12223.3i − 1.03980i
518518 0 0
519519 −25018.0 −2.11593
520520 0 0
521521 3778.19 0.317707 0.158853 0.987302i 0.449220π-0.449220\pi
0.158853 + 0.987302i 0.449220π0.449220\pi
522522 0 0
523523 − 2792.67i − 0.233489i −0.993162 0.116745i 0.962754π-0.962754\pi
0.993162 0.116745i 0.0372459π-0.0372459\pi
524524 0 0
525525 − 1370.54i − 0.113934i
526526 0 0
527527 −3013.74 −0.249109
528528 0 0
529529 2403.34 0.197529
530530 0 0
531531 − 29025.3i − 2.37211i
532532 0 0
533533 − 18810.7i − 1.52867i
534534 0 0
535535 20471.1 1.65429
536536 0 0
537537 −9596.35 −0.771160
538538 0 0
539539 9605.85i 0.767631i
540540 0 0
541541 2062.12i 0.163877i 0.996637 + 0.0819383i 0.0261111π0.0261111\pi
−0.996637 + 0.0819383i 0.973889π0.973889\pi
542542 0 0
543543 −5098.33 −0.402928
544544 0 0
545545 −5015.44 −0.394198
546546 0 0
547547 − 16562.0i − 1.29459i −0.762239 0.647296i 0.775900π-0.775900\pi
0.762239 0.647296i 0.224100π-0.224100\pi
548548 0 0
549549 33260.4i 2.58565i
550550 0 0
551551 1268.54 0.0980795
552552 0 0
553553 −487.057 −0.0374535
554554 0 0
555555 1163.87i 0.0890157i
556556 0 0
557557 9272.94i 0.705399i 0.935737 + 0.352699i 0.114736π0.114736\pi
−0.935737 + 0.352699i 0.885264π0.885264\pi
558558 0 0
559559 −10563.3 −0.799251
560560 0 0
561561 −12955.4 −0.975005
562562 0 0
563563 62.0181i 0.00464254i 0.999997 + 0.00232127i 0.000738884π0.000738884\pi
−0.999997 + 0.00232127i 0.999261π0.999261\pi
564564 0 0
565565 − 9047.71i − 0.673699i
566566 0 0
567567 6174.00 0.457290
568568 0 0
569569 −10015.9 −0.737938 −0.368969 0.929442i 0.620289π-0.620289\pi
−0.368969 + 0.929442i 0.620289π0.620289\pi
570570 0 0
571571 15543.3i 1.13917i 0.821931 + 0.569587i 0.192897π0.192897\pi
−0.821931 + 0.569587i 0.807103π0.807103\pi
572572 0 0
573573 − 7791.26i − 0.568036i
574574 0 0
575575 1879.95 0.136346
576576 0 0
577577 3776.77 0.272494 0.136247 0.990675i 0.456496π-0.456496\pi
0.136247 + 0.990675i 0.456496π0.456496\pi
578578 0 0
579579 6004.42i 0.430976i
580580 0 0
581581 5559.67i 0.396995i
582582 0 0
583583 3555.33 0.252567
584584 0 0
585585 57229.3 4.04469
586586 0 0
587587 − 596.285i − 0.0419273i −0.999780 0.0209637i 0.993327π-0.993327\pi
0.999780 0.0209637i 0.00667343π-0.00667343\pi
588588 0 0
589589 − 3773.21i − 0.263960i
590590 0 0
591591 27941.3 1.94476
592592 0 0
593593 20179.6 1.39743 0.698717 0.715398i 0.253755π-0.253755\pi
0.698717 + 0.715398i 0.253755π0.253755\pi
594594 0 0
595595 4340.06i 0.299034i
596596 0 0
597597 13413.5i 0.919558i
598598 0 0
599599 −13076.3 −0.891960 −0.445980 0.895043i 0.647145π-0.647145\pi
−0.445980 + 0.895043i 0.647145π0.647145\pi
600600 0 0
601601 16866.9 1.14479 0.572393 0.819980i 0.306015π-0.306015\pi
0.572393 + 0.819980i 0.306015π0.306015\pi
602602 0 0
603603 34845.3i 2.35325i
604604 0 0
605605 2319.18i 0.155848i
606606 0 0
607607 19953.0 1.33421 0.667107 0.744962i 0.267532π-0.267532\pi
0.667107 + 0.744962i 0.267532π0.267532\pi
608608 0 0
609609 −2400.82 −0.159747
610610 0 0
611611 − 28646.6i − 1.89676i
612612 0 0
613613 − 7214.32i − 0.475340i −0.971346 0.237670i 0.923616π-0.923616\pi
0.971346 0.237670i 0.0763837π-0.0763837\pi
614614 0 0
615615 21745.6 1.42580
616616 0 0
617617 −22212.9 −1.44936 −0.724681 0.689084i 0.758013π-0.758013\pi
−0.724681 + 0.689084i 0.758013π0.758013\pi
618618 0 0
619619 − 4349.02i − 0.282394i −0.989982 0.141197i 0.954905π-0.954905\pi
0.989982 0.141197i 0.0450951π-0.0450951\pi
620620 0 0
621621 27710.8i 1.79065i
622622 0 0
623623 −10740.2 −0.690688
624624 0 0
625625 −17329.2 −1.10907
626626 0 0
627627 − 16220.2i − 1.03313i
628628 0 0
629629 − 408.331i − 0.0258843i
630630 0 0
631631 10127.9 0.638966 0.319483 0.947592i 0.396491π-0.396491\pi
0.319483 + 0.947592i 0.396491π0.396491\pi
632632 0 0
633633 15835.9 0.994347
634634 0 0
635635 − 25602.5i − 1.60001i
636636 0 0
637637 22512.4i 1.40027i
638638 0 0
639639 −26092.0 −1.61531
640640 0 0
641641 −17624.6 −1.08601 −0.543003 0.839731i 0.682713π-0.682713\pi
−0.543003 + 0.839731i 0.682713π0.682713\pi
642642 0 0
643643 27238.1i 1.67055i 0.549829 + 0.835277i 0.314693π0.314693\pi
−0.549829 + 0.835277i 0.685307π0.685307\pi
644644 0 0
645645 − 12211.5i − 0.745468i
646646 0 0
647647 28702.1 1.74404 0.872021 0.489469i 0.162809π-0.162809\pi
0.872021 + 0.489469i 0.162809π0.162809\pi
648648 0 0
649649 21514.1 1.30124
650650 0 0
651651 7141.09i 0.429925i
652652 0 0
653653 − 7937.84i − 0.475700i −0.971302 0.237850i 0.923557π-0.923557\pi
0.971302 0.237850i 0.0764426π-0.0764426\pi
654654 0 0
655655 −8426.62 −0.502680
656656 0 0
657657 29849.5 1.77251
658658 0 0
659659 3675.29i 0.217252i 0.994083 + 0.108626i 0.0346451π0.0346451\pi
−0.994083 + 0.108626i 0.965355π0.965355\pi
660660 0 0
661661 − 4205.49i − 0.247466i −0.992316 0.123733i 0.960513π-0.960513\pi
0.992316 0.123733i 0.0394866π-0.0394866\pi
662662 0 0
663663 −30362.5 −1.77855
664664 0 0
665665 −5433.76 −0.316860
666666 0 0
667667 − 3293.15i − 0.191171i
668668 0 0
669669 48334.3i 2.79329i
670670 0 0
671671 −24653.3 −1.41838
672672 0 0
673673 −4634.55 −0.265452 −0.132726 0.991153i 0.542373π-0.542373\pi
−0.132726 + 0.991153i 0.542373π0.542373\pi
674674 0 0
675675 3575.40i 0.203877i
676676 0 0
677677 5327.42i 0.302437i 0.988500 + 0.151218i 0.0483196π0.0483196\pi
−0.988500 + 0.151218i 0.951680π0.951680\pi
678678 0 0
679679 4579.34 0.258820
680680 0 0
681681 −33429.6 −1.88109
682682 0 0
683683 2816.05i 0.157764i 0.996884 + 0.0788822i 0.0251351π0.0251351\pi
−0.996884 + 0.0788822i 0.974865π0.974865\pi
684684 0 0
685685 − 11703.8i − 0.652816i
686686 0 0
687687 −6077.77 −0.337528
688688 0 0
689689 8332.33 0.460720
690690 0 0
691691 16910.1i 0.930955i 0.885060 + 0.465477i 0.154117π0.154117\pi
−0.885060 + 0.465477i 0.845883π0.845883\pi
692692 0 0
693693 20300.1i 1.11275i
694694 0 0
695695 −27674.6 −1.51044
696696 0 0
697697 −7629.19 −0.414600
698698 0 0
699699 6064.67i 0.328164i
700700 0 0
701701 − 30588.4i − 1.64808i −0.566528 0.824042i 0.691714π-0.691714\pi
0.566528 0.824042i 0.308286π-0.308286\pi
702702 0 0
703703 511.232 0.0274274
704704 0 0
705705 33116.2 1.76912
706706 0 0
707707 − 9511.48i − 0.505963i
708708 0 0
709709 − 21242.9i − 1.12524i −0.826716 0.562619i 0.809794π-0.809794\pi
0.826716 0.562619i 0.190206π-0.190206\pi
710710 0 0
711711 2604.82 0.137396
712712 0 0
713713 −9795.28 −0.514496
714714 0 0
715715 42419.5i 2.21874i
716716 0 0
717717 − 34831.3i − 1.81423i
718718 0 0
719719 −12452.7 −0.645907 −0.322954 0.946415i 0.604676π-0.604676\pi
−0.322954 + 0.946415i 0.604676π0.604676\pi
720720 0 0
721721 −18027.3 −0.931168
722722 0 0
723723 52316.8i 2.69112i
724724 0 0
725725 − 424.901i − 0.0217661i
726726 0 0
727727 −27178.3 −1.38650 −0.693251 0.720696i 0.743822π-0.743822\pi
−0.693251 + 0.720696i 0.743822π0.743822\pi
728728 0 0
729729 22321.3 1.13404
730730 0 0
731731 4284.25i 0.216770i
732732 0 0
733733 − 21999.7i − 1.10856i −0.832329 0.554282i 0.812993π-0.812993\pi
0.832329 0.554282i 0.187007π-0.187007\pi
734734 0 0
735735 −26024.9 −1.30605
736736 0 0
737737 −25828.1 −1.29089
738738 0 0
739739 − 13644.0i − 0.679166i −0.940576 0.339583i 0.889714π-0.889714\pi
0.940576 0.339583i 0.110286π-0.110286\pi
740740 0 0
741741 − 38013.9i − 1.88458i
742742 0 0
743743 −13980.2 −0.690286 −0.345143 0.938550i 0.612170π-0.612170\pi
−0.345143 + 0.938550i 0.612170π0.612170\pi
744744 0 0
745745 −21250.1 −1.04502
746746 0 0
747747 − 29733.5i − 1.45635i
748748 0 0
749749 17018.0i 0.830204i
750750 0 0
751751 21138.7 1.02711 0.513557 0.858055i 0.328327π-0.328327\pi
0.513557 + 0.858055i 0.328327π0.328327\pi
752752 0 0
753753 −30190.6 −1.46110
754754 0 0
755755 − 33960.5i − 1.63702i
756756 0 0
757757 28328.1i 1.36011i 0.733162 + 0.680054i 0.238044π0.238044\pi
−0.733162 + 0.680054i 0.761956π0.761956\pi
758758 0 0
759759 −42107.8 −2.01372
760760 0 0
761761 1093.79 0.0521023 0.0260512 0.999661i 0.491707π-0.491707\pi
0.0260512 + 0.999661i 0.491707π0.491707\pi
762762 0 0
763763 − 4169.41i − 0.197828i
764764 0 0
765765 − 23210.9i − 1.09699i
766766 0 0
767767 50420.8 2.37365
768768 0 0
769769 −1659.21 −0.0778059 −0.0389029 0.999243i 0.512386π-0.512386\pi
−0.0389029 + 0.999243i 0.512386π0.512386\pi
770770 0 0
771771 32607.7i 1.52314i
772772 0 0
773773 7537.89i 0.350736i 0.984503 + 0.175368i 0.0561115π0.0561115\pi
−0.984503 + 0.175368i 0.943888π0.943888\pi
774774 0 0
775775 −1263.84 −0.0585787
776776 0 0
777777 −967.546 −0.0446725
778778 0 0
779779 − 9551.76i − 0.439316i
780780 0 0
781781 − 19339.9i − 0.886091i
782782 0 0
783783 6263.11 0.285856
784784 0 0
785785 −25177.9 −1.14476
786786 0 0
787787 − 9304.20i − 0.421422i −0.977548 0.210711i 0.932422π-0.932422\pi
0.977548 0.210711i 0.0675778π-0.0675778\pi
788788 0 0
789789 21987.8i 0.992126i
790790 0 0
791791 7521.50 0.338096
792792 0 0
793793 −57777.8 −2.58733
794794 0 0
795795 9632.39i 0.429718i
796796 0 0
797797 − 38619.5i − 1.71640i −0.513314 0.858201i 0.671582π-0.671582\pi
0.513314 0.858201i 0.328418π-0.328418\pi
798798 0 0
799799 −11618.4 −0.514431
800800 0 0
801801 57439.7 2.53375
802802 0 0
803803 22125.1i 0.972324i
804804 0 0
805805 14106.1i 0.617608i
806806 0 0
807807 4307.88 0.187912
808808 0 0
809809 18550.5 0.806179 0.403090 0.915160i 0.367936π-0.367936\pi
0.403090 + 0.915160i 0.367936π0.367936\pi
810810 0 0
811811 3704.80i 0.160411i 0.996778 + 0.0802054i 0.0255576π0.0255576\pi
−0.996778 + 0.0802054i 0.974442π0.974442\pi
812812 0 0
813813 32163.7i 1.38749i
814814 0 0
815815 37516.2 1.61243
816816 0 0
817817 −5363.90 −0.229693
818818 0 0
819819 47575.6i 2.02982i
820820 0 0
821821 − 5544.86i − 0.235709i −0.993031 0.117854i 0.962398π-0.962398\pi
0.993031 0.117854i 0.0376016π-0.0376016\pi
822822 0 0
823823 3915.39 0.165835 0.0829174 0.996556i 0.473576π-0.473576\pi
0.0829174 + 0.996556i 0.473576π0.473576\pi
824824 0 0
825825 −5432.98 −0.229275
826826 0 0
827827 35091.2i 1.47550i 0.675073 + 0.737751i 0.264112π0.264112\pi
−0.675073 + 0.737751i 0.735888π0.735888\pi
828828 0 0
829829 3532.71i 0.148005i 0.997258 + 0.0740025i 0.0235773π0.0235773\pi
−0.997258 + 0.0740025i 0.976423π0.976423\pi
830830 0 0
831831 −55156.0 −2.30245
832832 0 0
833833 9130.53 0.379777
834834 0 0
835835 15891.6i 0.658624i
836836 0 0
837837 − 18629.3i − 0.769320i
838838 0 0
839839 30081.1 1.23780 0.618900 0.785470i 0.287579π-0.287579\pi
0.618900 + 0.785470i 0.287579π0.287579\pi
840840 0 0
841841 23644.7 0.969482
842842 0 0
843843 4852.27i 0.198246i
844844 0 0
845845 73366.5i 2.98685i
846846 0 0
847847 −1927.97 −0.0782121
848848 0 0
849849 58766.4 2.37557
850850 0 0
851851 − 1327.16i − 0.0534601i
852852 0 0
853853 − 11222.1i − 0.450453i −0.974306 0.225226i 0.927688π-0.927688\pi
0.974306 0.225226i 0.0723122π-0.0723122\pi
854854 0 0
855855 29060.2 1.16238
856856 0 0
857857 27486.0 1.09557 0.547785 0.836619i 0.315471π-0.315471\pi
0.547785 + 0.836619i 0.315471π0.315471\pi
858858 0 0
859859 − 14976.2i − 0.594855i −0.954744 0.297427i 0.903871π-0.903871\pi
0.954744 0.297427i 0.0961287π-0.0961287\pi
860860 0 0
861861 18077.5i 0.715538i
862862 0 0
863863 −9419.49 −0.371545 −0.185772 0.982593i 0.559479π-0.559479\pi
−0.185772 + 0.982593i 0.559479π0.559479\pi
864864 0 0
865865 33223.2 1.30592
866866 0 0
867867 − 31549.9i − 1.23586i
868868 0 0
869869 1930.75i 0.0753694i
870870 0 0
871871 −60531.0 −2.35478
872872 0 0
873873 −24490.7 −0.949465
874874 0 0
875875 − 12787.6i − 0.494059i
876876 0 0
877877 − 21069.8i − 0.811263i −0.914037 0.405631i 0.867052π-0.867052\pi
0.914037 0.405631i 0.132948π-0.132948\pi
878878 0 0
879879 −60298.2 −2.31378
880880 0 0
881881 −14511.7 −0.554952 −0.277476 0.960733i 0.589498π-0.589498\pi
−0.277476 + 0.960733i 0.589498π0.589498\pi
882882 0 0
883883 − 26515.9i − 1.01057i −0.862953 0.505284i 0.831388π-0.831388\pi
0.862953 0.505284i 0.168612π-0.168612\pi
884884 0 0
885885 58287.8i 2.21392i
886886 0 0
887887 29223.6 1.10624 0.553119 0.833102i 0.313437π-0.313437\pi
0.553119 + 0.833102i 0.313437π0.313437\pi
888888 0 0
889889 21283.8 0.802964
890890 0 0
891891 − 24474.4i − 0.920227i
892892 0 0
893893 − 14546.3i − 0.545099i
894894 0 0
895895 12743.7 0.475949
896896 0 0
897897 −98684.4 −3.67333
898898 0 0
899899 2213.90i 0.0821332i
900900 0 0
901901 − 3379.41i − 0.124955i
902902 0 0
903903 10151.6 0.374113
904904 0 0
905905 6770.44 0.248682
906906 0 0
907907 − 32139.3i − 1.17659i −0.808646 0.588296i 0.799799π-0.799799\pi
0.808646 0.588296i 0.200201π-0.200201\pi
908908 0 0
909909 50868.1i 1.85609i
910910 0 0
911911 21430.7 0.779396 0.389698 0.920943i 0.372579π-0.372579\pi
0.389698 + 0.920943i 0.372579π0.372579\pi
912912 0 0
913913 22039.1 0.798891
914914 0 0
915915 − 66792.7i − 2.41322i
916916 0 0
917917 − 7005.17i − 0.252270i
918918 0 0
919919 −11676.1 −0.419106 −0.209553 0.977797i 0.567201π-0.567201\pi
−0.209553 + 0.977797i 0.567201π0.567201\pi
920920 0 0
921921 16266.1 0.581962
922922 0 0
923923 − 45325.3i − 1.61636i
924924 0 0
925925 − 171.238i − 0.00608677i
926926 0 0
927927 96411.5 3.41593
928928 0 0
929929 41969.7 1.48222 0.741110 0.671383i 0.234300π-0.234300\pi
0.741110 + 0.671383i 0.234300π0.234300\pi
930930 0 0
931931 11431.4i 0.402417i
932932 0 0
933933 − 94622.6i − 3.32026i
934934 0 0
935935 17204.4 0.601759
936936 0 0
937937 45948.6 1.60200 0.801001 0.598663i 0.204301π-0.204301\pi
0.801001 + 0.598663i 0.204301π0.204301\pi
938938 0 0
939939 71155.0i 2.47290i
940940 0 0
941941 − 15000.1i − 0.519648i −0.965656 0.259824i 0.916335π-0.916335\pi
0.965656 0.259824i 0.0836645π-0.0836645\pi
942942 0 0
943943 −24796.4 −0.856292
944944 0 0
945945 −26827.8 −0.923502
946946 0 0
947947 − 37423.2i − 1.28415i −0.766642 0.642075i 0.778074π-0.778074\pi
0.766642 0.642075i 0.221926π-0.221926\pi
948948 0 0
949949 51852.6i 1.77366i
950950 0 0
951951 69404.8 2.36657
952952 0 0
953953 55403.0 1.88319 0.941594 0.336750i 0.109328π-0.109328\pi
0.941594 + 0.336750i 0.109328π0.109328\pi
954954 0 0
955955 10346.6i 0.350584i
956956 0 0
957957 9517.09i 0.321467i
958958 0 0
959959 9729.54 0.327615
960960 0 0
961961 −23205.9 −0.778956
962962 0 0
963963 − 91013.4i − 3.04555i
964964 0 0
965965 − 7973.70i − 0.265992i
966966 0 0
967967 −31440.5 −1.04556 −0.522780 0.852467i 0.675105π-0.675105\pi
−0.522780 + 0.852467i 0.675105π0.675105\pi
968968 0 0
969969 −15417.6 −0.511129
970970 0 0
971971 19010.3i 0.628290i 0.949375 + 0.314145i 0.101718π0.101718\pi
−0.949375 + 0.314145i 0.898282π0.898282\pi
972972 0 0
973973 − 23006.3i − 0.758015i
974974 0 0
975975 −12732.8 −0.418232
976976 0 0
977977 −8504.01 −0.278472 −0.139236 0.990259i 0.544465π-0.544465\pi
−0.139236 + 0.990259i 0.544465π0.544465\pi
978978 0 0
979979 42575.4i 1.38990i
980980 0 0
981981 22298.3i 0.725720i
982982 0 0
983983 52828.3 1.71410 0.857051 0.515232i 0.172294π-0.172294\pi
0.857051 + 0.515232i 0.172294π0.172294\pi
984984 0 0
985985 −37105.3 −1.20028
986986 0 0
987987 27530.0i 0.887831i
988988 0 0
989989 13924.7i 0.447705i
990990 0 0
991991 −13275.5 −0.425541 −0.212770 0.977102i 0.568249π-0.568249\pi
−0.212770 + 0.977102i 0.568249π0.568249\pi
992992 0 0
993993 −73326.1 −2.34334
994994 0 0
995995 − 17812.7i − 0.567538i
996996 0 0
997997 20858.1i 0.662570i 0.943531 + 0.331285i 0.107482π0.107482\pi
−0.943531 + 0.331285i 0.892518π0.892518\pi
998998 0 0
999999 2524.08 0.0799382
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 256.4.b.h.129.4 4
4.3 odd 2 256.4.b.i.129.1 4
8.3 odd 2 256.4.b.i.129.4 4
8.5 even 2 inner 256.4.b.h.129.1 4
16.3 odd 4 128.4.a.h.1.2 yes 2
16.5 even 4 128.4.a.g.1.2 yes 2
16.11 odd 4 128.4.a.e.1.1 2
16.13 even 4 128.4.a.f.1.1 yes 2
48.5 odd 4 1152.4.a.t.1.1 2
48.11 even 4 1152.4.a.s.1.1 2
48.29 odd 4 1152.4.a.r.1.2 2
48.35 even 4 1152.4.a.q.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
128.4.a.e.1.1 2 16.11 odd 4
128.4.a.f.1.1 yes 2 16.13 even 4
128.4.a.g.1.2 yes 2 16.5 even 4
128.4.a.h.1.2 yes 2 16.3 odd 4
256.4.b.h.129.1 4 8.5 even 2 inner
256.4.b.h.129.4 4 1.1 even 1 trivial
256.4.b.i.129.1 4 4.3 odd 2
256.4.b.i.129.4 4 8.3 odd 2
1152.4.a.q.1.2 2 48.35 even 4
1152.4.a.r.1.2 2 48.29 odd 4
1152.4.a.s.1.1 2 48.11 even 4
1152.4.a.t.1.1 2 48.5 odd 4