Properties

Label 1152.4.c.b.1151.12
Level 11521152
Weight 44
Character 1152.1151
Analytic conductor 67.97067.970
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1152,4,Mod(1151,1152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1152.1151");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 1152=2732 1152 = 2^{7} \cdot 3^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1152.c (of order 22, degree 11, 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: 67.970200326667.9702003266
Analytic rank: 00
Dimension: 1212
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x124x114x10+12x9+88x8+356x7+1278x6+3320x5+8177x4++98 x^{12} - 4 x^{11} - 4 x^{10} + 12 x^{9} + 88 x^{8} + 356 x^{7} + 1278 x^{6} + 3320 x^{5} + 8177 x^{4} + \cdots + 98 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 23334 2^{33}\cdot 3^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1151.12
Root 0.8431602.03557i-0.843160 - 2.03557i of defining polynomial
Character χ\chi == 1152.1151
Dual form 1152.4.c.b.1151.1

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+19.4649iq522.2014iq7+31.9589q1112.7921q13+1.79939iq1755.3042iq19152.218q23253.882q25+292.254iq29271.560iq31+432.148q35114.334q37+300.192iq41+371.823iq43+35.2663q47149.902q49391.098iq53+622.077iq5522.8408q59662.958q61248.997iq65926.894iq671071.12q71+9.27078q73709.534iq77+565.805iq79566.393q8335.0248q85911.883iq89+284.003iq91+1076.49q95+466.815q97+O(q100)q+19.4649i q^{5} -22.2014i q^{7} +31.9589 q^{11} -12.7921 q^{13} +1.79939i q^{17} -55.3042i q^{19} -152.218 q^{23} -253.882 q^{25} +292.254i q^{29} -271.560i q^{31} +432.148 q^{35} -114.334 q^{37} +300.192i q^{41} +371.823i q^{43} +35.2663 q^{47} -149.902 q^{49} -391.098i q^{53} +622.077i q^{55} -22.8408 q^{59} -662.958 q^{61} -248.997i q^{65} -926.894i q^{67} -1071.12 q^{71} +9.27078 q^{73} -709.534i q^{77} +565.805i q^{79} -566.393 q^{83} -35.0248 q^{85} -911.883i q^{89} +284.003i q^{91} +1076.49 q^{95} +466.815 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q240q23300q25+864q35264q37624q47+132q49+1632q59312q614080q71+432q73+3744q83+1704q855856q95+96q97+O(q100) 12 q - 240 q^{23} - 300 q^{25} + 864 q^{35} - 264 q^{37} - 624 q^{47} + 132 q^{49} + 1632 q^{59} - 312 q^{61} - 4080 q^{71} + 432 q^{73} + 3744 q^{83} + 1704 q^{85} - 5856 q^{95} + 96 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1152Z)×\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times.

nn 127127 641641 901901
χ(n)\chi(n) 1-1 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 0 0
44 0 0
55 19.4649i 1.74099i 0.492176 + 0.870496i 0.336202π0.336202\pi
−0.492176 + 0.870496i 0.663798π0.663798\pi
66 0 0
77 − 22.2014i − 1.19876i −0.800463 0.599382i 0.795413π-0.795413\pi
0.800463 0.599382i 0.204587π-0.204587\pi
88 0 0
99 0 0
1010 0 0
1111 31.9589 0.875999 0.437999 0.898975i 0.355687π-0.355687\pi
0.437999 + 0.898975i 0.355687π0.355687\pi
1212 0 0
1313 −12.7921 −0.272915 −0.136457 0.990646i 0.543572π-0.543572\pi
−0.136457 + 0.990646i 0.543572π0.543572\pi
1414 0 0
1515 0 0
1616 0 0
1717 1.79939i 0.0256715i 0.999918 + 0.0128357i 0.00408585π0.00408585\pi
−0.999918 + 0.0128357i 0.995914π0.995914\pi
1818 0 0
1919 − 55.3042i − 0.667772i −0.942614 0.333886i 0.891640π-0.891640\pi
0.942614 0.333886i 0.108360π-0.108360\pi
2020 0 0
2121 0 0
2222 0 0
2323 −152.218 −1.37999 −0.689994 0.723815i 0.742387π-0.742387\pi
−0.689994 + 0.723815i 0.742387π0.742387\pi
2424 0 0
2525 −253.882 −2.03105
2626 0 0
2727 0 0
2828 0 0
2929 292.254i 1.87139i 0.352811 + 0.935695i 0.385226π0.385226\pi
−0.352811 + 0.935695i 0.614774π0.614774\pi
3030 0 0
3131 − 271.560i − 1.57334i −0.617372 0.786672i 0.711803π-0.711803\pi
0.617372 0.786672i 0.288197π-0.288197\pi
3232 0 0
3333 0 0
3434 0 0
3535 432.148 2.08704
3636 0 0
3737 −114.334 −0.508013 −0.254006 0.967203i 0.581748π-0.581748\pi
−0.254006 + 0.967203i 0.581748π0.581748\pi
3838 0 0
3939 0 0
4040 0 0
4141 300.192i 1.14347i 0.820439 + 0.571734i 0.193729π0.193729\pi
−0.820439 + 0.571734i 0.806271π0.806271\pi
4242 0 0
4343 371.823i 1.31866i 0.751853 + 0.659331i 0.229160π0.229160\pi
−0.751853 + 0.659331i 0.770840π0.770840\pi
4444 0 0
4545 0 0
4646 0 0
4747 35.2663 0.109449 0.0547246 0.998501i 0.482572π-0.482572\pi
0.0547246 + 0.998501i 0.482572π0.482572\pi
4848 0 0
4949 −149.902 −0.437033
5050 0 0
5151 0 0
5252 0 0
5353 − 391.098i − 1.01361i −0.862060 0.506806i 0.830826π-0.830826\pi
0.862060 0.506806i 0.169174π-0.169174\pi
5454 0 0
5555 622.077i 1.52511i
5656 0 0
5757 0 0
5858 0 0
5959 −22.8408 −0.0504003 −0.0252001 0.999682i 0.508022π-0.508022\pi
−0.0252001 + 0.999682i 0.508022π0.508022\pi
6060 0 0
6161 −662.958 −1.39153 −0.695763 0.718272i 0.744933π-0.744933\pi
−0.695763 + 0.718272i 0.744933π0.744933\pi
6262 0 0
6363 0 0
6464 0 0
6565 − 248.997i − 0.475142i
6666 0 0
6767 − 926.894i − 1.69012i −0.534671 0.845060i 0.679564π-0.679564\pi
0.534671 0.845060i 0.320436π-0.320436\pi
6868 0 0
6969 0 0
7070 0 0
7171 −1071.12 −1.79040 −0.895198 0.445669i 0.852966π-0.852966\pi
−0.895198 + 0.445669i 0.852966π0.852966\pi
7272 0 0
7373 9.27078 0.0148639 0.00743193 0.999972i 0.497634π-0.497634\pi
0.00743193 + 0.999972i 0.497634π0.497634\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 709.534i − 1.05011i
7878 0 0
7979 565.805i 0.805798i 0.915245 + 0.402899i 0.131997π0.131997\pi
−0.915245 + 0.402899i 0.868003π0.868003\pi
8080 0 0
8181 0 0
8282 0 0
8383 −566.393 −0.749032 −0.374516 0.927220i 0.622191π-0.622191\pi
−0.374516 + 0.927220i 0.622191π0.622191\pi
8484 0 0
8585 −35.0248 −0.0446938
8686 0 0
8787 0 0
8888 0 0
8989 − 911.883i − 1.08606i −0.839713 0.543031i 0.817277π-0.817277\pi
0.839713 0.543031i 0.182723π-0.182723\pi
9090 0 0
9191 284.003i 0.327160i
9292 0 0
9393 0 0
9494 0 0
9595 1076.49 1.16259
9696 0 0
9797 466.815 0.488638 0.244319 0.969695i 0.421436π-0.421436\pi
0.244319 + 0.969695i 0.421436π0.421436\pi
9898 0 0
9999 0 0
100100 0 0
101101 − 615.098i − 0.605986i −0.952993 0.302993i 0.902014π-0.902014\pi
0.952993 0.302993i 0.0979858π-0.0979858\pi
102102 0 0
103103 1834.29i 1.75474i 0.479818 + 0.877368i 0.340703π0.340703\pi
−0.479818 + 0.877368i 0.659297π0.659297\pi
104104 0 0
105105 0 0
106106 0 0
107107 −565.082 −0.510547 −0.255273 0.966869i 0.582166π-0.582166\pi
−0.255273 + 0.966869i 0.582166π0.582166\pi
108108 0 0
109109 −314.783 −0.276612 −0.138306 0.990390i 0.544166π-0.544166\pi
−0.138306 + 0.990390i 0.544166π0.544166\pi
110110 0 0
111111 0 0
112112 0 0
113113 − 2245.29i − 1.86920i −0.355703 0.934599i 0.615759π-0.615759\pi
0.355703 0.934599i 0.384241π-0.384241\pi
114114 0 0
115115 − 2962.91i − 2.40255i
116116 0 0
117117 0 0
118118 0 0
119119 39.9489 0.0307740
120120 0 0
121121 −309.626 −0.232626
122122 0 0
123123 0 0
124124 0 0
125125 − 2508.66i − 1.79505i
126126 0 0
127127 1020.85i 0.713273i 0.934243 + 0.356637i 0.116077π0.116077\pi
−0.934243 + 0.356637i 0.883923π0.883923\pi
128128 0 0
129129 0 0
130130 0 0
131131 1164.80 0.776864 0.388432 0.921477i 0.373017π-0.373017\pi
0.388432 + 0.921477i 0.373017π0.373017\pi
132132 0 0
133133 −1227.83 −0.800500
134134 0 0
135135 0 0
136136 0 0
137137 − 1915.28i − 1.19440i −0.802091 0.597202i 0.796279π-0.796279\pi
0.802091 0.597202i 0.203721π-0.203721\pi
138138 0 0
139139 − 3016.58i − 1.84074i −0.391051 0.920369i 0.627888π-0.627888\pi
0.391051 0.920369i 0.372112π-0.372112\pi
140140 0 0
141141 0 0
142142 0 0
143143 −408.822 −0.239073
144144 0 0
145145 −5688.70 −3.25807
146146 0 0
147147 0 0
148148 0 0
149149 39.8288i 0.0218987i 0.999940 + 0.0109493i 0.00348535π0.00348535\pi
−0.999940 + 0.0109493i 0.996515π0.996515\pi
150150 0 0
151151 − 2021.62i − 1.08952i −0.838592 0.544760i 0.816621π-0.816621\pi
0.838592 0.544760i 0.183379π-0.183379\pi
152152 0 0
153153 0 0
154154 0 0
155155 5285.89 2.73918
156156 0 0
157157 1260.53 0.640772 0.320386 0.947287i 0.396187π-0.396187\pi
0.320386 + 0.947287i 0.396187π0.396187\pi
158158 0 0
159159 0 0
160160 0 0
161161 3379.46i 1.65428i
162162 0 0
163163 1803.46i 0.866611i 0.901247 + 0.433305i 0.142653π0.142653\pi
−0.901247 + 0.433305i 0.857347π0.857347\pi
164164 0 0
165165 0 0
166166 0 0
167167 −2030.46 −0.940847 −0.470424 0.882441i 0.655899π-0.655899\pi
−0.470424 + 0.882441i 0.655899π0.655899\pi
168168 0 0
169169 −2033.36 −0.925518
170170 0 0
171171 0 0
172172 0 0
173173 1541.47i 0.677432i 0.940889 + 0.338716i 0.109993π0.109993\pi
−0.940889 + 0.338716i 0.890007π0.890007\pi
174174 0 0
175175 5636.53i 2.43475i
176176 0 0
177177 0 0
178178 0 0
179179 −2660.38 −1.11087 −0.555436 0.831560i 0.687448π-0.687448\pi
−0.555436 + 0.831560i 0.687448π0.687448\pi
180180 0 0
181181 −3890.04 −1.59748 −0.798741 0.601675i 0.794500π-0.794500\pi
−0.798741 + 0.601675i 0.794500π0.794500\pi
182182 0 0
183183 0 0
184184 0 0
185185 − 2225.51i − 0.884446i
186186 0 0
187187 57.5065i 0.0224882i
188188 0 0
189189 0 0
190190 0 0
191191 −1980.04 −0.750107 −0.375053 0.927003i 0.622376π-0.622376\pi
−0.375053 + 0.927003i 0.622376π0.622376\pi
192192 0 0
193193 3510.71 1.30936 0.654679 0.755907i 0.272804π-0.272804\pi
0.654679 + 0.755907i 0.272804π0.272804\pi
194194 0 0
195195 0 0
196196 0 0
197197 582.273i 0.210585i 0.994441 + 0.105292i 0.0335779π0.0335779\pi
−0.994441 + 0.105292i 0.966422π0.966422\pi
198198 0 0
199199 − 3859.19i − 1.37473i −0.726313 0.687364i 0.758768π-0.758768\pi
0.726313 0.687364i 0.241232π-0.241232\pi
200200 0 0
201201 0 0
202202 0 0
203203 6488.46 2.24335
204204 0 0
205205 −5843.21 −1.99077
206206 0 0
207207 0 0
208208 0 0
209209 − 1767.47i − 0.584967i
210210 0 0
211211 − 3152.87i − 1.02868i −0.857585 0.514342i 0.828036π-0.828036\pi
0.857585 0.514342i 0.171964π-0.171964\pi
212212 0 0
213213 0 0
214214 0 0
215215 −7237.49 −2.29578
216216 0 0
217217 −6029.02 −1.88607
218218 0 0
219219 0 0
220220 0 0
221221 − 23.0179i − 0.00700612i
222222 0 0
223223 3930.70i 1.18035i 0.807274 + 0.590177i 0.200942π0.200942\pi
−0.807274 + 0.590177i 0.799058π0.799058\pi
224224 0 0
225225 0 0
226226 0 0
227227 −604.951 −0.176881 −0.0884406 0.996081i 0.528188π-0.528188\pi
−0.0884406 + 0.996081i 0.528188π0.528188\pi
228228 0 0
229229 −3047.32 −0.879355 −0.439678 0.898156i 0.644907π-0.644907\pi
−0.439678 + 0.898156i 0.644907π0.644907\pi
230230 0 0
231231 0 0
232232 0 0
233233 5242.57i 1.47404i 0.675869 + 0.737022i 0.263768π0.263768\pi
−0.675869 + 0.737022i 0.736232π0.736232\pi
234234 0 0
235235 686.454i 0.190550i
236236 0 0
237237 0 0
238238 0 0
239239 −3218.81 −0.871162 −0.435581 0.900150i 0.643457π-0.643457\pi
−0.435581 + 0.900150i 0.643457π0.643457\pi
240240 0 0
241241 −4991.45 −1.33414 −0.667069 0.744996i 0.732452π-0.732452\pi
−0.667069 + 0.744996i 0.732452π0.732452\pi
242242 0 0
243243 0 0
244244 0 0
245245 − 2917.83i − 0.760872i
246246 0 0
247247 707.458i 0.182245i
248248 0 0
249249 0 0
250250 0 0
251251 1930.14 0.485376 0.242688 0.970104i 0.421971π-0.421971\pi
0.242688 + 0.970104i 0.421971π0.421971\pi
252252 0 0
253253 −4864.74 −1.20887
254254 0 0
255255 0 0
256256 0 0
257257 − 136.590i − 0.0331526i −0.999863 0.0165763i 0.994723π-0.994723\pi
0.999863 0.0165763i 0.00527665π-0.00527665\pi
258258 0 0
259259 2538.39i 0.608987i
260260 0 0
261261 0 0
262262 0 0
263263 1726.50 0.404793 0.202397 0.979304i 0.435127π-0.435127\pi
0.202397 + 0.979304i 0.435127π0.435127\pi
264264 0 0
265265 7612.67 1.76469
266266 0 0
267267 0 0
268268 0 0
269269 − 3174.73i − 0.719579i −0.933033 0.359790i 0.882848π-0.882848\pi
0.933033 0.359790i 0.117152π-0.117152\pi
270270 0 0
271271 2453.18i 0.549889i 0.961460 + 0.274945i 0.0886596π0.0886596\pi
−0.961460 + 0.274945i 0.911340π0.911340\pi
272272 0 0
273273 0 0
274274 0 0
275275 −8113.79 −1.77920
276276 0 0
277277 4665.27 1.01195 0.505973 0.862549i 0.331134π-0.331134\pi
0.505973 + 0.862549i 0.331134π0.331134\pi
278278 0 0
279279 0 0
280280 0 0
281281 − 1304.96i − 0.277038i −0.990360 0.138519i 0.955766π-0.955766\pi
0.990360 0.138519i 0.0442342π-0.0442342\pi
282282 0 0
283283 − 1487.84i − 0.312518i −0.987716 0.156259i 0.950057π-0.950057\pi
0.987716 0.156259i 0.0499435π-0.0499435\pi
284284 0 0
285285 0 0
286286 0 0
287287 6664.69 1.37075
288288 0 0
289289 4909.76 0.999341
290290 0 0
291291 0 0
292292 0 0
293293 − 1936.50i − 0.386114i −0.981188 0.193057i 0.938160π-0.938160\pi
0.981188 0.193057i 0.0618402π-0.0618402\pi
294294 0 0
295295 − 444.593i − 0.0877465i
296296 0 0
297297 0 0
298298 0 0
299299 1947.19 0.376619
300300 0 0
301301 8254.99 1.58076
302302 0 0
303303 0 0
304304 0 0
305305 − 12904.4i − 2.42263i
306306 0 0
307307 − 5884.32i − 1.09393i −0.837156 0.546964i 0.815783π-0.815783\pi
0.837156 0.546964i 0.184217π-0.184217\pi
308308 0 0
309309 0 0
310310 0 0
311311 1160.58 0.211610 0.105805 0.994387i 0.466258π-0.466258\pi
0.105805 + 0.994387i 0.466258π0.466258\pi
312312 0 0
313313 −6605.01 −1.19277 −0.596385 0.802698i 0.703397π-0.703397\pi
−0.596385 + 0.802698i 0.703397π0.703397\pi
314314 0 0
315315 0 0
316316 0 0
317317 2661.31i 0.471526i 0.971811 + 0.235763i 0.0757590π0.0757590\pi
−0.971811 + 0.235763i 0.924241π0.924241\pi
318318 0 0
319319 9340.14i 1.63933i
320320 0 0
321321 0 0
322322 0 0
323323 99.5137 0.0171427
324324 0 0
325325 3247.68 0.554304
326326 0 0
327327 0 0
328328 0 0
329329 − 782.961i − 0.131204i
330330 0 0
331331 4233.72i 0.703040i 0.936180 + 0.351520i 0.114335π0.114335\pi
−0.936180 + 0.351520i 0.885665π0.885665\pi
332332 0 0
333333 0 0
334334 0 0
335335 18041.9 2.94249
336336 0 0
337337 −4641.65 −0.750286 −0.375143 0.926967i 0.622406π-0.622406\pi
−0.375143 + 0.926967i 0.622406π0.622406\pi
338338 0 0
339339 0 0
340340 0 0
341341 − 8678.77i − 1.37825i
342342 0 0
343343 − 4287.04i − 0.674864i
344344 0 0
345345 0 0
346346 0 0
347347 4554.37 0.704587 0.352293 0.935890i 0.385402π-0.385402\pi
0.352293 + 0.935890i 0.385402π0.385402\pi
348348 0 0
349349 −747.324 −0.114623 −0.0573113 0.998356i 0.518253π-0.518253\pi
−0.0573113 + 0.998356i 0.518253π0.518253\pi
350350 0 0
351351 0 0
352352 0 0
353353 6594.80i 0.994351i 0.867650 + 0.497175i 0.165629π0.165629\pi
−0.867650 + 0.497175i 0.834371π0.834371\pi
354354 0 0
355355 − 20849.2i − 3.11706i
356356 0 0
357357 0 0
358358 0 0
359359 −13093.3 −1.92489 −0.962447 0.271471i 0.912490π-0.912490\pi
−0.962447 + 0.271471i 0.912490π0.912490\pi
360360 0 0
361361 3800.44 0.554081
362362 0 0
363363 0 0
364364 0 0
365365 180.455i 0.0258779i
366366 0 0
367367 − 12114.5i − 1.72309i −0.507682 0.861544i 0.669498π-0.669498\pi
0.507682 0.861544i 0.330502π-0.330502\pi
368368 0 0
369369 0 0
370370 0 0
371371 −8682.92 −1.21508
372372 0 0
373373 12969.7 1.80039 0.900196 0.435486i 0.143423π-0.143423\pi
0.900196 + 0.435486i 0.143423π0.143423\pi
374374 0 0
375375 0 0
376376 0 0
377377 − 3738.55i − 0.510730i
378378 0 0
379379 12527.1i 1.69783i 0.528532 + 0.848913i 0.322743π0.322743\pi
−0.528532 + 0.848913i 0.677257π0.677257\pi
380380 0 0
381381 0 0
382382 0 0
383383 6966.21 0.929391 0.464695 0.885471i 0.346164π-0.346164\pi
0.464695 + 0.885471i 0.346164π0.346164\pi
384384 0 0
385385 13811.0 1.82824
386386 0 0
387387 0 0
388388 0 0
389389 13156.5i 1.71481i 0.514645 + 0.857403i 0.327924π0.327924\pi
−0.514645 + 0.857403i 0.672076π0.672076\pi
390390 0 0
391391 − 273.899i − 0.0354263i
392392 0 0
393393 0 0
394394 0 0
395395 −11013.3 −1.40289
396396 0 0
397397 −1737.94 −0.219709 −0.109855 0.993948i 0.535039π-0.535039\pi
−0.109855 + 0.993948i 0.535039π0.535039\pi
398398 0 0
399399 0 0
400400 0 0
401401 506.378i 0.0630606i 0.999503 + 0.0315303i 0.0100381π0.0100381\pi
−0.999503 + 0.0315303i 0.989962π0.989962\pi
402402 0 0
403403 3473.83i 0.429389i
404404 0 0
405405 0 0
406406 0 0
407407 −3654.01 −0.445019
408408 0 0
409409 9910.80 1.19818 0.599092 0.800680i 0.295528π-0.295528\pi
0.599092 + 0.800680i 0.295528π0.295528\pi
410410 0 0
411411 0 0
412412 0 0
413413 507.098i 0.0604180i
414414 0 0
415415 − 11024.8i − 1.30406i
416416 0 0
417417 0 0
418418 0 0
419419 −4058.63 −0.473215 −0.236607 0.971605i 0.576036π-0.576036\pi
−0.236607 + 0.971605i 0.576036π0.576036\pi
420420 0 0
421421 −7852.53 −0.909048 −0.454524 0.890735i 0.650191π-0.650191\pi
−0.454524 + 0.890735i 0.650191π0.650191\pi
422422 0 0
423423 0 0
424424 0 0
425425 − 456.831i − 0.0521401i
426426 0 0
427427 14718.6i 1.66811i
428428 0 0
429429 0 0
430430 0 0
431431 10717.2 1.19775 0.598873 0.800844i 0.295615π-0.295615\pi
0.598873 + 0.800844i 0.295615π0.295615\pi
432432 0 0
433433 −5190.51 −0.576074 −0.288037 0.957619i 0.593003π-0.593003\pi
−0.288037 + 0.957619i 0.593003π0.593003\pi
434434 0 0
435435 0 0
436436 0 0
437437 8418.32i 0.921516i
438438 0 0
439439 2101.72i 0.228495i 0.993452 + 0.114248i 0.0364457π0.0364457\pi
−0.993452 + 0.114248i 0.963554π0.963554\pi
440440 0 0
441441 0 0
442442 0 0
443443 −586.526 −0.0629045 −0.0314523 0.999505i 0.510013π-0.510013\pi
−0.0314523 + 0.999505i 0.510013π0.510013\pi
444444 0 0
445445 17749.7 1.89082
446446 0 0
447447 0 0
448448 0 0
449449 16423.7i 1.72624i 0.504995 + 0.863122i 0.331494π0.331494\pi
−0.504995 + 0.863122i 0.668506π0.668506\pi
450450 0 0
451451 9593.83i 1.00168i
452452 0 0
453453 0 0
454454 0 0
455455 −5528.08 −0.569583
456456 0 0
457457 −5904.11 −0.604338 −0.302169 0.953254i 0.597711π-0.597711\pi
−0.302169 + 0.953254i 0.597711π0.597711\pi
458458 0 0
459459 0 0
460460 0 0
461461 9501.12i 0.959894i 0.877298 + 0.479947i 0.159344π0.159344\pi
−0.877298 + 0.479947i 0.840656π0.840656\pi
462462 0 0
463463 1341.81i 0.134685i 0.997730 + 0.0673424i 0.0214520π0.0214520\pi
−0.997730 + 0.0673424i 0.978548π0.978548\pi
464464 0 0
465465 0 0
466466 0 0
467467 19268.8 1.90933 0.954663 0.297689i 0.0962159π-0.0962159\pi
0.954663 + 0.297689i 0.0962159π0.0962159\pi
468468 0 0
469469 −20578.3 −2.02605
470470 0 0
471471 0 0
472472 0 0
473473 11883.1i 1.15515i
474474 0 0
475475 14040.7i 1.35628i
476476 0 0
477477 0 0
478478 0 0
479479 −12832.2 −1.22404 −0.612021 0.790841i 0.709643π-0.709643\pi
−0.612021 + 0.790841i 0.709643π0.709643\pi
480480 0 0
481481 1462.58 0.138644
482482 0 0
483483 0 0
484484 0 0
485485 9086.49i 0.850714i
486486 0 0
487487 − 15784.6i − 1.46872i −0.678758 0.734362i 0.737481π-0.737481\pi
0.678758 0.734362i 0.262519π-0.262519\pi
488488 0 0
489489 0 0
490490 0 0
491491 15306.9 1.40691 0.703453 0.710742i 0.251640π-0.251640\pi
0.703453 + 0.710742i 0.251640π0.251640\pi
492492 0 0
493493 −525.878 −0.0480413
494494 0 0
495495 0 0
496496 0 0
497497 23780.3i 2.14626i
498498 0 0
499499 10479.3i 0.940117i 0.882635 + 0.470058i 0.155767π0.155767\pi
−0.882635 + 0.470058i 0.844233π0.844233\pi
500500 0 0
501501 0 0
502502 0 0
503503 −9919.58 −0.879308 −0.439654 0.898167i 0.644899π-0.644899\pi
−0.439654 + 0.898167i 0.644899π0.644899\pi
504504 0 0
505505 11972.8 1.05502
506506 0 0
507507 0 0
508508 0 0
509509 − 10028.1i − 0.873254i −0.899643 0.436627i 0.856173π-0.856173\pi
0.899643 0.436627i 0.143827π-0.143827\pi
510510 0 0
511511 − 205.824i − 0.0178183i
512512 0 0
513513 0 0
514514 0 0
515515 −35704.2 −3.05498
516516 0 0
517517 1127.07 0.0958774
518518 0 0
519519 0 0
520520 0 0
521521 10216.7i 0.859122i 0.903038 + 0.429561i 0.141332π0.141332\pi
−0.903038 + 0.429561i 0.858668π0.858668\pi
522522 0 0
523523 12295.9i 1.02803i 0.857780 + 0.514017i 0.171843π0.171843\pi
−0.857780 + 0.514017i 0.828157π0.828157\pi
524524 0 0
525525 0 0
526526 0 0
527527 488.641 0.0403900
528528 0 0
529529 11003.4 0.904365
530530 0 0
531531 0 0
532532 0 0
533533 − 3840.09i − 0.312069i
534534 0 0
535535 − 10999.3i − 0.888858i
536536 0 0
537537 0 0
538538 0 0
539539 −4790.72 −0.382841
540540 0 0
541541 9786.98 0.777773 0.388887 0.921286i 0.372860π-0.372860\pi
0.388887 + 0.921286i 0.372860π0.372860\pi
542542 0 0
543543 0 0
544544 0 0
545545 − 6127.22i − 0.481580i
546546 0 0
547547 351.890i 0.0275059i 0.999905 + 0.0137530i 0.00437784π0.00437784\pi
−0.999905 + 0.0137530i 0.995622π0.995622\pi
548548 0 0
549549 0 0
550550 0 0
551551 16162.9 1.24966
552552 0 0
553553 12561.7 0.965960
554554 0 0
555555 0 0
556556 0 0
557557 22996.2i 1.74933i 0.484724 + 0.874667i 0.338920π0.338920\pi
−0.484724 + 0.874667i 0.661080π0.661080\pi
558558 0 0
559559 − 4756.40i − 0.359882i
560560 0 0
561561 0 0
562562 0 0
563563 590.483 0.0442023 0.0221011 0.999756i 0.492964π-0.492964\pi
0.0221011 + 0.999756i 0.492964π0.492964\pi
564564 0 0
565565 43704.4 3.25426
566566 0 0
567567 0 0
568568 0 0
569569 8863.10i 0.653006i 0.945196 + 0.326503i 0.105870π0.105870\pi
−0.945196 + 0.326503i 0.894130π0.894130\pi
570570 0 0
571571 − 86.0835i − 0.00630907i −0.999995 0.00315454i 0.998996π-0.998996\pi
0.999995 0.00315454i 0.00100412π-0.00100412\pi
572572 0 0
573573 0 0
574574 0 0
575575 38645.4 2.80283
576576 0 0
577577 −10676.7 −0.770320 −0.385160 0.922850i 0.625854π-0.625854\pi
−0.385160 + 0.922850i 0.625854π0.625854\pi
578578 0 0
579579 0 0
580580 0 0
581581 12574.7i 0.897912i
582582 0 0
583583 − 12499.1i − 0.887922i
584584 0 0
585585 0 0
586586 0 0
587587 14828.7 1.04267 0.521335 0.853352i 0.325434π-0.325434\pi
0.521335 + 0.853352i 0.325434π0.325434\pi
588588 0 0
589589 −15018.4 −1.05063
590590 0 0
591591 0 0
592592 0 0
593593 − 7625.52i − 0.528065i −0.964514 0.264033i 0.914947π-0.914947\pi
0.964514 0.264033i 0.0850526π-0.0850526\pi
594594 0 0
595595 777.600i 0.0535773i
596596 0 0
597597 0 0
598598 0 0
599599 2515.53 0.171589 0.0857945 0.996313i 0.472657π-0.472657\pi
0.0857945 + 0.996313i 0.472657π0.472657\pi
600600 0 0
601601 −884.652 −0.0600428 −0.0300214 0.999549i 0.509558π-0.509558\pi
−0.0300214 + 0.999549i 0.509558π0.509558\pi
602602 0 0
603603 0 0
604604 0 0
605605 − 6026.83i − 0.405001i
606606 0 0
607607 − 3262.44i − 0.218152i −0.994033 0.109076i 0.965211π-0.965211\pi
0.994033 0.109076i 0.0347892π-0.0347892\pi
608608 0 0
609609 0 0
610610 0 0
611611 −451.130 −0.0298703
612612 0 0
613613 7103.23 0.468021 0.234010 0.972234i 0.424815π-0.424815\pi
0.234010 + 0.972234i 0.424815π0.424815\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 17015.2i − 1.11022i −0.831776 0.555111i 0.812676π-0.812676\pi
0.831776 0.555111i 0.187324π-0.187324\pi
618618 0 0
619619 − 14796.3i − 0.960763i −0.877060 0.480381i 0.840498π-0.840498\pi
0.877060 0.480381i 0.159502π-0.159502\pi
620620 0 0
621621 0 0
622622 0 0
623623 −20245.1 −1.30193
624624 0 0
625625 17095.7 1.09412
626626 0 0
627627 0 0
628628 0 0
629629 − 205.732i − 0.0130414i
630630 0 0
631631 − 6518.78i − 0.411265i −0.978629 0.205633i 0.934075π-0.934075\pi
0.978629 0.205633i 0.0659252π-0.0659252\pi
632632 0 0
633633 0 0
634634 0 0
635635 −19870.7 −1.24180
636636 0 0
637637 1917.57 0.119273
638638 0 0
639639 0 0
640640 0 0
641641 − 23065.6i − 1.42127i −0.703559 0.710637i 0.748407π-0.748407\pi
0.703559 0.710637i 0.251593π-0.251593\pi
642642 0 0
643643 11825.3i 0.725264i 0.931932 + 0.362632i 0.118122π0.118122\pi
−0.931932 + 0.362632i 0.881878π0.881878\pi
644644 0 0
645645 0 0
646646 0 0
647647 14019.2 0.851857 0.425929 0.904757i 0.359947π-0.359947\pi
0.425929 + 0.904757i 0.359947π0.359947\pi
648648 0 0
649649 −729.968 −0.0441506
650650 0 0
651651 0 0
652652 0 0
653653 − 7701.14i − 0.461514i −0.973011 0.230757i 0.925880π-0.925880\pi
0.973011 0.230757i 0.0741203π-0.0741203\pi
654654 0 0
655655 22672.7i 1.35251i
656656 0 0
657657 0 0
658658 0 0
659659 −24026.7 −1.42026 −0.710128 0.704073i 0.751363π-0.751363\pi
−0.710128 + 0.704073i 0.751363π0.751363\pi
660660 0 0
661661 1278.87 0.0752530 0.0376265 0.999292i 0.488020π-0.488020\pi
0.0376265 + 0.999292i 0.488020π0.488020\pi
662662 0 0
663663 0 0
664664 0 0
665665 − 23899.6i − 1.39366i
666666 0 0
667667 − 44486.5i − 2.58249i
668668 0 0
669669 0 0
670670 0 0
671671 −21187.4 −1.21897
672672 0 0
673673 −2951.17 −0.169033 −0.0845164 0.996422i 0.526935π-0.526935\pi
−0.0845164 + 0.996422i 0.526935π0.526935\pi
674674 0 0
675675 0 0
676676 0 0
677677 5263.47i 0.298806i 0.988776 + 0.149403i 0.0477351π0.0477351\pi
−0.988776 + 0.149403i 0.952265π0.952265\pi
678678 0 0
679679 − 10363.9i − 0.585761i
680680 0 0
681681 0 0
682682 0 0
683683 −14057.0 −0.787517 −0.393759 0.919214i 0.628825π-0.628825\pi
−0.393759 + 0.919214i 0.628825π0.628825\pi
684684 0 0
685685 37280.7 2.07945
686686 0 0
687687 0 0
688688 0 0
689689 5002.96i 0.276629i
690690 0 0
691691 16916.0i 0.931282i 0.884974 + 0.465641i 0.154176π0.154176\pi
−0.884974 + 0.465641i 0.845824π0.845824\pi
692692 0 0
693693 0 0
694694 0 0
695695 58717.3 3.20471
696696 0 0
697697 −540.162 −0.0293545
698698 0 0
699699 0 0
700700 0 0
701701 3743.98i 0.201723i 0.994900 + 0.100862i 0.0321600π0.0321600\pi
−0.994900 + 0.100862i 0.967840π0.967840\pi
702702 0 0
703703 6323.18i 0.339237i
704704 0 0
705705 0 0
706706 0 0
707707 −13656.0 −0.726433
708708 0 0
709709 −5993.31 −0.317466 −0.158733 0.987322i 0.550741π-0.550741\pi
−0.158733 + 0.987322i 0.550741π0.550741\pi
710710 0 0
711711 0 0
712712 0 0
713713 41336.4i 2.17119i
714714 0 0
715715 − 7957.68i − 0.416224i
716716 0 0
717717 0 0
718718 0 0
719719 9158.35 0.475033 0.237517 0.971383i 0.423667π-0.423667\pi
0.237517 + 0.971383i 0.423667π0.423667\pi
720720 0 0
721721 40723.8 2.10351
722722 0 0
723723 0 0
724724 0 0
725725 − 74198.0i − 3.80089i
726726 0 0
727727 − 20102.5i − 1.02553i −0.858529 0.512765i 0.828621π-0.828621\pi
0.858529 0.512765i 0.171379π-0.171379\pi
728728 0 0
729729 0 0
730730 0 0
731731 −669.053 −0.0338520
732732 0 0
733733 −8493.27 −0.427975 −0.213988 0.976836i 0.568645π-0.568645\pi
−0.213988 + 0.976836i 0.568645π0.568645\pi
734734 0 0
735735 0 0
736736 0 0
737737 − 29622.5i − 1.48054i
738738 0 0
739739 3413.95i 0.169938i 0.996384 + 0.0849689i 0.0270791π0.0270791\pi
−0.996384 + 0.0849689i 0.972921π0.972921\pi
740740 0 0
741741 0 0
742742 0 0
743743 −199.861 −0.00986836 −0.00493418 0.999988i 0.501571π-0.501571\pi
−0.00493418 + 0.999988i 0.501571π0.501571\pi
744744 0 0
745745 −775.263 −0.0381254
746746 0 0
747747 0 0
748748 0 0
749749 12545.6i 0.612025i
750750 0 0
751751 − 1351.41i − 0.0656641i −0.999461 0.0328321i 0.989547π-0.989547\pi
0.999461 0.0328321i 0.0104526π-0.0104526\pi
752752 0 0
753753 0 0
754754 0 0
755755 39350.7 1.89684
756756 0 0
757757 33084.3 1.58847 0.794233 0.607613i 0.207873π-0.207873\pi
0.794233 + 0.607613i 0.207873π0.207873\pi
758758 0 0
759759 0 0
760760 0 0
761761 15677.9i 0.746811i 0.927668 + 0.373406i 0.121810π0.121810\pi
−0.927668 + 0.373406i 0.878190π0.878190\pi
762762 0 0
763763 6988.63i 0.331593i
764764 0 0
765765 0 0
766766 0 0
767767 292.182 0.0137550
768768 0 0
769769 −39525.9 −1.85350 −0.926750 0.375679i 0.877410π-0.877410\pi
−0.926750 + 0.375679i 0.877410π0.877410\pi
770770 0 0
771771 0 0
772772 0 0
773773 29192.3i 1.35831i 0.733994 + 0.679156i 0.237654π0.237654\pi
−0.733994 + 0.679156i 0.762346π0.762346\pi
774774 0 0
775775 68944.1i 3.19554i
776776 0 0
777777 0 0
778778 0 0
779779 16601.9 0.763575
780780 0 0
781781 −34231.7 −1.56838
782782 0 0
783783 0 0
784784 0 0
785785 24536.1i 1.11558i
786786 0 0
787787 24107.0i 1.09190i 0.837819 + 0.545949i 0.183831π0.183831\pi
−0.837819 + 0.545949i 0.816169π0.816169\pi
788788 0 0
789789 0 0
790790 0 0
791791 −49848.7 −2.24073
792792 0 0
793793 8480.62 0.379768
794794 0 0
795795 0 0
796796 0 0
797797 8464.67i 0.376203i 0.982150 + 0.188102i 0.0602334π0.0602334\pi
−0.982150 + 0.188102i 0.939767π0.939767\pi
798798 0 0
799799 63.4576i 0.00280972i
800800 0 0
801801 0 0
802802 0 0
803803 296.284 0.0130207
804804 0 0
805805 −65780.8 −2.88008
806806 0 0
807807 0 0
808808 0 0
809809 − 29597.4i − 1.28626i −0.765755 0.643132i 0.777635π-0.777635\pi
0.765755 0.643132i 0.222365π-0.222365\pi
810810 0 0
811811 14572.2i 0.630949i 0.948934 + 0.315474i 0.102164π0.102164\pi
−0.948934 + 0.315474i 0.897836π0.897836\pi
812812 0 0
813813 0 0
814814 0 0
815815 −35104.0 −1.50876
816816 0 0
817817 20563.4 0.880565
818818 0 0
819819 0 0
820820 0 0
821821 7894.06i 0.335572i 0.985823 + 0.167786i 0.0536618π0.0536618\pi
−0.985823 + 0.167786i 0.946338π0.946338\pi
822822 0 0
823823 2643.21i 0.111952i 0.998432 + 0.0559760i 0.0178270π0.0178270\pi
−0.998432 + 0.0559760i 0.982173π0.982173\pi
824824 0 0
825825 0 0
826826 0 0
827827 11809.6 0.496567 0.248284 0.968687i 0.420133π-0.420133\pi
0.248284 + 0.968687i 0.420133π0.420133\pi
828828 0 0
829829 −13461.7 −0.563987 −0.281993 0.959416i 0.590996π-0.590996\pi
−0.281993 + 0.959416i 0.590996π0.590996\pi
830830 0 0
831831 0 0
832832 0 0
833833 − 269.732i − 0.0112193i
834834 0 0
835835 − 39522.6i − 1.63801i
836836 0 0
837837 0 0
838838 0 0
839839 −12513.7 −0.514922 −0.257461 0.966289i 0.582886π-0.582886\pi
−0.257461 + 0.966289i 0.582886π0.582886\pi
840840 0 0
841841 −61023.7 −2.50210
842842 0 0
843843 0 0
844844 0 0
845845 − 39579.1i − 1.61132i
846846 0 0
847847 6874.13i 0.278864i
848848 0 0
849849 0 0
850850 0 0
851851 17403.8 0.701051
852852 0 0
853853 −25549.9 −1.02557 −0.512786 0.858517i 0.671386π-0.671386\pi
−0.512786 + 0.858517i 0.671386π0.671386\pi
854854 0 0
855855 0 0
856856 0 0
857857 32706.4i 1.30365i 0.758370 + 0.651825i 0.225996π0.225996\pi
−0.758370 + 0.651825i 0.774004π0.774004\pi
858858 0 0
859859 27072.8i 1.07534i 0.843157 + 0.537668i 0.180695π0.180695\pi
−0.843157 + 0.537668i 0.819305π0.819305\pi
860860 0 0
861861 0 0
862862 0 0
863863 −28641.5 −1.12974 −0.564870 0.825180i 0.691074π-0.691074\pi
−0.564870 + 0.825180i 0.691074π0.691074\pi
864864 0 0
865865 −30004.5 −1.17940
866866 0 0
867867 0 0
868868 0 0
869869 18082.5i 0.705877i
870870 0 0
871871 11856.9i 0.461259i
872872 0 0
873873 0 0
874874 0 0
875875 −55695.9 −2.15185
876876 0 0
877877 −7094.49 −0.273163 −0.136581 0.990629i 0.543612π-0.543612\pi
−0.136581 + 0.990629i 0.543612π0.543612\pi
878878 0 0
879879 0 0
880880 0 0
881881 43494.2i 1.66329i 0.555310 + 0.831643i 0.312600π0.312600\pi
−0.555310 + 0.831643i 0.687400π0.687400\pi
882882 0 0
883883 1247.80i 0.0475560i 0.999717 + 0.0237780i 0.00756948π0.00756948\pi
−0.999717 + 0.0237780i 0.992431π0.992431\pi
884884 0 0
885885 0 0
886886 0 0
887887 7320.80 0.277123 0.138562 0.990354i 0.455752π-0.455752\pi
0.138562 + 0.990354i 0.455752π0.455752\pi
888888 0 0
889889 22664.3 0.855046
890890 0 0
891891 0 0
892892 0 0
893893 − 1950.38i − 0.0730871i
894894 0 0
895895 − 51783.9i − 1.93402i
896896 0 0
897897 0 0
898898 0 0
899899 79364.7 2.94434
900900 0 0
901901 703.736 0.0260209
902902 0 0
903903 0 0
904904 0 0
905905 − 75719.1i − 2.78120i
906906 0 0
907907 − 40054.6i − 1.46636i −0.680034 0.733181i 0.738035π-0.738035\pi
0.680034 0.733181i 0.261965π-0.261965\pi
908908 0 0
909909 0 0
910910 0 0
911911 −11863.6 −0.431458 −0.215729 0.976453i 0.569213π-0.569213\pi
−0.215729 + 0.976453i 0.569213π0.569213\pi
912912 0 0
913913 −18101.3 −0.656151
914914 0 0
915915 0 0
916916 0 0
917917 − 25860.2i − 0.931277i
918918 0 0
919919 41184.9i 1.47831i 0.673537 + 0.739153i 0.264774π0.264774\pi
−0.673537 + 0.739153i 0.735226π0.735226\pi
920920 0 0
921921 0 0
922922 0 0
923923 13701.8 0.488625
924924 0 0
925925 29027.4 1.03180
926926 0 0
927927 0 0
928928 0 0
929929 15430.9i 0.544962i 0.962161 + 0.272481i 0.0878442π0.0878442\pi
−0.962161 + 0.272481i 0.912156π0.912156\pi
930930 0 0
931931 8290.24i 0.291839i
932932 0 0
933933 0 0
934934 0 0
935935 −1119.36 −0.0391517
936936 0 0
937937 −19757.6 −0.688852 −0.344426 0.938813i 0.611926π-0.611926\pi
−0.344426 + 0.938813i 0.611926π0.611926\pi
938938 0 0
939939 0 0
940940 0 0
941941 47029.5i 1.62924i 0.579993 + 0.814622i 0.303055π0.303055\pi
−0.579993 + 0.814622i 0.696945π0.696945\pi
942942 0 0
943943 − 45694.7i − 1.57797i
944944 0 0
945945 0 0
946946 0 0
947947 13487.8 0.462825 0.231412 0.972856i 0.425665π-0.425665\pi
0.231412 + 0.972856i 0.425665π0.425665\pi
948948 0 0
949949 −118.593 −0.00405657
950950 0 0
951951 0 0
952952 0 0
953953 − 8080.06i − 0.274647i −0.990526 0.137324i 0.956150π-0.956150\pi
0.990526 0.137324i 0.0438500π-0.0438500\pi
954954 0 0
955955 − 38541.2i − 1.30593i
956956 0 0
957957 0 0
958958 0 0
959959 −42521.9 −1.43181
960960 0 0
961961 −43953.9 −1.47541
962962 0 0
963963 0 0
964964 0 0
965965 68335.5i 2.27958i
966966 0 0
967967 − 28145.7i − 0.935994i −0.883730 0.467997i 0.844976π-0.844976\pi
0.883730 0.467997i 0.155024π-0.155024\pi
968968 0 0
969969 0 0
970970 0 0
971971 −17202.4 −0.568539 −0.284269 0.958744i 0.591751π-0.591751\pi
−0.284269 + 0.958744i 0.591751π0.591751\pi
972972 0 0
973973 −66972.2 −2.20661
974974 0 0
975975 0 0
976976 0 0
977977 − 24457.7i − 0.800893i −0.916320 0.400446i 0.868855π-0.868855\pi
0.916320 0.400446i 0.131145π-0.131145\pi
978978 0 0
979979 − 29142.8i − 0.951388i
980980 0 0
981981 0 0
982982 0 0
983983 15491.0 0.502632 0.251316 0.967905i 0.419137π-0.419137\pi
0.251316 + 0.967905i 0.419137π0.419137\pi
984984 0 0
985985 −11333.9 −0.366627
986986 0 0
987987 0 0
988988 0 0
989989 − 56598.2i − 1.81974i
990990 0 0
991991 − 7771.50i − 0.249112i −0.992213 0.124556i 0.960249π-0.960249\pi
0.992213 0.124556i 0.0397506π-0.0397506\pi
992992 0 0
993993 0 0
994994 0 0
995995 75118.7 2.39339
996996 0 0
997997 −53099.2 −1.68673 −0.843364 0.537343i 0.819428π-0.819428\pi
−0.843364 + 0.537343i 0.819428π0.819428\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1152.4.c.b.1151.12 yes 12
3.2 odd 2 1152.4.c.c.1151.1 yes 12
4.3 odd 2 1152.4.c.c.1151.12 yes 12
8.3 odd 2 1152.4.c.d.1151.1 yes 12
8.5 even 2 1152.4.c.a.1151.1 12
12.11 even 2 inner 1152.4.c.b.1151.1 yes 12
16.3 odd 4 2304.4.f.k.1151.11 12
16.5 even 4 2304.4.f.j.1151.2 12
16.11 odd 4 2304.4.f.i.1151.1 12
16.13 even 4 2304.4.f.l.1151.12 12
24.5 odd 2 1152.4.c.d.1151.12 yes 12
24.11 even 2 1152.4.c.a.1151.12 yes 12
48.5 odd 4 2304.4.f.k.1151.12 12
48.11 even 4 2304.4.f.l.1151.11 12
48.29 odd 4 2304.4.f.i.1151.2 12
48.35 even 4 2304.4.f.j.1151.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1152.4.c.a.1151.1 12 8.5 even 2
1152.4.c.a.1151.12 yes 12 24.11 even 2
1152.4.c.b.1151.1 yes 12 12.11 even 2 inner
1152.4.c.b.1151.12 yes 12 1.1 even 1 trivial
1152.4.c.c.1151.1 yes 12 3.2 odd 2
1152.4.c.c.1151.12 yes 12 4.3 odd 2
1152.4.c.d.1151.1 yes 12 8.3 odd 2
1152.4.c.d.1151.12 yes 12 24.5 odd 2
2304.4.f.i.1151.1 12 16.11 odd 4
2304.4.f.i.1151.2 12 48.29 odd 4
2304.4.f.j.1151.1 12 48.35 even 4
2304.4.f.j.1151.2 12 16.5 even 4
2304.4.f.k.1151.11 12 16.3 odd 4
2304.4.f.k.1151.12 12 48.5 odd 4
2304.4.f.l.1151.11 12 48.11 even 4
2304.4.f.l.1151.12 12 16.13 even 4