Properties

Label 2205.4.a.c.1.1
Level 22052205
Weight 44
Character 2205.1
Self dual yes
Analytic conductor 130.099130.099
Analytic rank 00
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2205,4,Mod(1,2205)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2205.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 2205=32572 2205 = 3^{2} \cdot 5 \cdot 7^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 2205.a (trivial)

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: yes
Analytic conductor: 130.099211563130.099211563
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 15)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 2205.1

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) == q3.00000q2+1.00000q45.00000q5+21.0000q8+15.0000q10+24.0000q1174.0000q1371.0000q16+54.0000q17+124.000q195.00000q2072.0000q22+120.000q23+25.0000q25+222.000q26+78.0000q29200.000q31+45.0000q32162.000q3470.0000q37372.000q38105.000q40+330.000q41+92.0000q43+24.0000q44360.000q4624.0000q4775.0000q5074.0000q52450.000q53120.000q55234.000q58+24.0000q59+322.000q61+600.000q62+433.000q64+370.000q65196.000q67+54.0000q68+288.000q71+430.000q73+210.000q74+124.000q76520.000q79+355.000q80990.000q82+156.000q83270.000q85276.000q86+504.000q88+1026.00q89+120.000q92+72.0000q94620.000q95+286.000q97+O(q100)q-3.00000 q^{2} +1.00000 q^{4} -5.00000 q^{5} +21.0000 q^{8} +15.0000 q^{10} +24.0000 q^{11} -74.0000 q^{13} -71.0000 q^{16} +54.0000 q^{17} +124.000 q^{19} -5.00000 q^{20} -72.0000 q^{22} +120.000 q^{23} +25.0000 q^{25} +222.000 q^{26} +78.0000 q^{29} -200.000 q^{31} +45.0000 q^{32} -162.000 q^{34} -70.0000 q^{37} -372.000 q^{38} -105.000 q^{40} +330.000 q^{41} +92.0000 q^{43} +24.0000 q^{44} -360.000 q^{46} -24.0000 q^{47} -75.0000 q^{50} -74.0000 q^{52} -450.000 q^{53} -120.000 q^{55} -234.000 q^{58} +24.0000 q^{59} +322.000 q^{61} +600.000 q^{62} +433.000 q^{64} +370.000 q^{65} -196.000 q^{67} +54.0000 q^{68} +288.000 q^{71} +430.000 q^{73} +210.000 q^{74} +124.000 q^{76} -520.000 q^{79} +355.000 q^{80} -990.000 q^{82} +156.000 q^{83} -270.000 q^{85} -276.000 q^{86} +504.000 q^{88} +1026.00 q^{89} +120.000 q^{92} +72.0000 q^{94} -620.000 q^{95} +286.000 q^{97} +O(q^{100})

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 −3.00000 −1.06066 −0.530330 0.847791i 0.677932π-0.677932\pi
−0.530330 + 0.847791i 0.677932π0.677932\pi
33 0 0
44 1.00000 0.125000
55 −5.00000 −0.447214
66 0 0
77 0 0
88 21.0000 0.928078
99 0 0
1010 15.0000 0.474342
1111 24.0000 0.657843 0.328921 0.944357i 0.393315π-0.393315\pi
0.328921 + 0.944357i 0.393315π0.393315\pi
1212 0 0
1313 −74.0000 −1.57876 −0.789381 0.613904i 0.789598π-0.789598\pi
−0.789381 + 0.613904i 0.789598π0.789598\pi
1414 0 0
1515 0 0
1616 −71.0000 −1.10938
1717 54.0000 0.770407 0.385204 0.922832i 0.374131π-0.374131\pi
0.385204 + 0.922832i 0.374131π0.374131\pi
1818 0 0
1919 124.000 1.49724 0.748620 0.663000i 0.230717π-0.230717\pi
0.748620 + 0.663000i 0.230717π0.230717\pi
2020 −5.00000 −0.0559017
2121 0 0
2222 −72.0000 −0.697748
2323 120.000 1.08790 0.543951 0.839117i 0.316928π-0.316928\pi
0.543951 + 0.839117i 0.316928π0.316928\pi
2424 0 0
2525 25.0000 0.200000
2626 222.000 1.67453
2727 0 0
2828 0 0
2929 78.0000 0.499456 0.249728 0.968316i 0.419659π-0.419659\pi
0.249728 + 0.968316i 0.419659π0.419659\pi
3030 0 0
3131 −200.000 −1.15874 −0.579372 0.815063i 0.696702π-0.696702\pi
−0.579372 + 0.815063i 0.696702π0.696702\pi
3232 45.0000 0.248592
3333 0 0
3434 −162.000 −0.817140
3535 0 0
3636 0 0
3737 −70.0000 −0.311025 −0.155513 0.987834i 0.549703π-0.549703\pi
−0.155513 + 0.987834i 0.549703π0.549703\pi
3838 −372.000 −1.58806
3939 0 0
4040 −105.000 −0.415049
4141 330.000 1.25701 0.628504 0.777806i 0.283668π-0.283668\pi
0.628504 + 0.777806i 0.283668π0.283668\pi
4242 0 0
4343 92.0000 0.326276 0.163138 0.986603i 0.447838π-0.447838\pi
0.163138 + 0.986603i 0.447838π0.447838\pi
4444 24.0000 0.0822304
4545 0 0
4646 −360.000 −1.15389
4747 −24.0000 −0.0744843 −0.0372421 0.999306i 0.511857π-0.511857\pi
−0.0372421 + 0.999306i 0.511857π0.511857\pi
4848 0 0
4949 0 0
5050 −75.0000 −0.212132
5151 0 0
5252 −74.0000 −0.197345
5353 −450.000 −1.16627 −0.583134 0.812376i 0.698174π-0.698174\pi
−0.583134 + 0.812376i 0.698174π0.698174\pi
5454 0 0
5555 −120.000 −0.294196
5656 0 0
5757 0 0
5858 −234.000 −0.529754
5959 24.0000 0.0529582 0.0264791 0.999649i 0.491570π-0.491570\pi
0.0264791 + 0.999649i 0.491570π0.491570\pi
6060 0 0
6161 322.000 0.675867 0.337933 0.941170i 0.390272π-0.390272\pi
0.337933 + 0.941170i 0.390272π0.390272\pi
6262 600.000 1.22903
6363 0 0
6464 433.000 0.845703
6565 370.000 0.706044
6666 0 0
6767 −196.000 −0.357391 −0.178696 0.983904i 0.557188π-0.557188\pi
−0.178696 + 0.983904i 0.557188π0.557188\pi
6868 54.0000 0.0963009
6969 0 0
7070 0 0
7171 288.000 0.481399 0.240699 0.970600i 0.422623π-0.422623\pi
0.240699 + 0.970600i 0.422623π0.422623\pi
7272 0 0
7373 430.000 0.689420 0.344710 0.938709i 0.387977π-0.387977\pi
0.344710 + 0.938709i 0.387977π0.387977\pi
7474 210.000 0.329892
7575 0 0
7676 124.000 0.187155
7777 0 0
7878 0 0
7979 −520.000 −0.740564 −0.370282 0.928919i 0.620739π-0.620739\pi
−0.370282 + 0.928919i 0.620739π0.620739\pi
8080 355.000 0.496128
8181 0 0
8282 −990.000 −1.33326
8383 156.000 0.206304 0.103152 0.994666i 0.467107π-0.467107\pi
0.103152 + 0.994666i 0.467107π0.467107\pi
8484 0 0
8585 −270.000 −0.344537
8686 −276.000 −0.346068
8787 0 0
8888 504.000 0.610529
8989 1026.00 1.22198 0.610988 0.791640i 0.290773π-0.290773\pi
0.610988 + 0.791640i 0.290773π0.290773\pi
9090 0 0
9191 0 0
9292 120.000 0.135988
9393 0 0
9494 72.0000 0.0790025
9595 −620.000 −0.669586
9696 0 0
9797 286.000 0.299370 0.149685 0.988734i 0.452174π-0.452174\pi
0.149685 + 0.988734i 0.452174π0.452174\pi
9898 0 0
9999 0 0
100100 25.0000 0.0250000
101101 −1734.00 −1.70831 −0.854156 0.520017i 0.825925π-0.825925\pi
−0.854156 + 0.520017i 0.825925π0.825925\pi
102102 0 0
103103 −452.000 −0.432397 −0.216198 0.976349i 0.569366π-0.569366\pi
−0.216198 + 0.976349i 0.569366π0.569366\pi
104104 −1554.00 −1.46521
105105 0 0
106106 1350.00 1.23702
107107 1404.00 1.26850 0.634251 0.773127i 0.281308π-0.281308\pi
0.634251 + 0.773127i 0.281308π0.281308\pi
108108 0 0
109109 −1474.00 −1.29526 −0.647631 0.761954i 0.724240π-0.724240\pi
−0.647631 + 0.761954i 0.724240π0.724240\pi
110110 360.000 0.312042
111111 0 0
112112 0 0
113113 −1086.00 −0.904091 −0.452046 0.891995i 0.649306π-0.649306\pi
−0.452046 + 0.891995i 0.649306π0.649306\pi
114114 0 0
115115 −600.000 −0.486524
116116 78.0000 0.0624321
117117 0 0
118118 −72.0000 −0.0561707
119119 0 0
120120 0 0
121121 −755.000 −0.567243
122122 −966.000 −0.716865
123123 0 0
124124 −200.000 −0.144843
125125 −125.000 −0.0894427
126126 0 0
127127 1244.00 0.869190 0.434595 0.900626i 0.356891π-0.356891\pi
0.434595 + 0.900626i 0.356891π0.356891\pi
128128 −1659.00 −1.14560
129129 0 0
130130 −1110.00 −0.748873
131131 2328.00 1.55266 0.776329 0.630327i 0.217079π-0.217079\pi
0.776329 + 0.630327i 0.217079π0.217079\pi
132132 0 0
133133 0 0
134134 588.000 0.379071
135135 0 0
136136 1134.00 0.714998
137137 −2118.00 −1.32082 −0.660412 0.750903i 0.729618π-0.729618\pi
−0.660412 + 0.750903i 0.729618π0.729618\pi
138138 0 0
139139 −2324.00 −1.41812 −0.709062 0.705147i 0.750881π-0.750881\pi
−0.709062 + 0.705147i 0.750881π0.750881\pi
140140 0 0
141141 0 0
142142 −864.000 −0.510600
143143 −1776.00 −1.03858
144144 0 0
145145 −390.000 −0.223364
146146 −1290.00 −0.731241
147147 0 0
148148 −70.0000 −0.0388781
149149 −258.000 −0.141854 −0.0709268 0.997482i 0.522596π-0.522596\pi
−0.0709268 + 0.997482i 0.522596π0.522596\pi
150150 0 0
151151 −808.000 −0.435458 −0.217729 0.976009i 0.569865π-0.569865\pi
−0.217729 + 0.976009i 0.569865π0.569865\pi
152152 2604.00 1.38955
153153 0 0
154154 0 0
155155 1000.00 0.518206
156156 0 0
157157 −2378.00 −1.20882 −0.604411 0.796673i 0.706592π-0.706592\pi
−0.604411 + 0.796673i 0.706592π0.706592\pi
158158 1560.00 0.785487
159159 0 0
160160 −225.000 −0.111174
161161 0 0
162162 0 0
163163 −52.0000 −0.0249874 −0.0124937 0.999922i 0.503977π-0.503977\pi
−0.0124937 + 0.999922i 0.503977π0.503977\pi
164164 330.000 0.157126
165165 0 0
166166 −468.000 −0.218818
167167 −3720.00 −1.72373 −0.861863 0.507141i 0.830702π-0.830702\pi
−0.861863 + 0.507141i 0.830702π0.830702\pi
168168 0 0
169169 3279.00 1.49249
170170 810.000 0.365436
171171 0 0
172172 92.0000 0.0407845
173173 426.000 0.187215 0.0936075 0.995609i 0.470160π-0.470160\pi
0.0936075 + 0.995609i 0.470160π0.470160\pi
174174 0 0
175175 0 0
176176 −1704.00 −0.729795
177177 0 0
178178 −3078.00 −1.29610
179179 1440.00 0.601289 0.300644 0.953736i 0.402798π-0.402798\pi
0.300644 + 0.953736i 0.402798π0.402798\pi
180180 0 0
181181 3130.00 1.28537 0.642683 0.766133i 0.277821π-0.277821\pi
0.642683 + 0.766133i 0.277821π0.277821\pi
182182 0 0
183183 0 0
184184 2520.00 1.00966
185185 350.000 0.139095
186186 0 0
187187 1296.00 0.506807
188188 −24.0000 −0.00931053
189189 0 0
190190 1860.00 0.710203
191191 −3576.00 −1.35471 −0.677357 0.735655i 0.736875π-0.736875\pi
−0.677357 + 0.735655i 0.736875π0.736875\pi
192192 0 0
193193 2666.00 0.994315 0.497158 0.867660i 0.334377π-0.334377\pi
0.497158 + 0.867660i 0.334377π0.334377\pi
194194 −858.000 −0.317530
195195 0 0
196196 0 0
197197 2718.00 0.982992 0.491496 0.870880i 0.336450π-0.336450\pi
0.491496 + 0.870880i 0.336450π0.336450\pi
198198 0 0
199199 3832.00 1.36504 0.682521 0.730866i 0.260884π-0.260884\pi
0.682521 + 0.730866i 0.260884π0.260884\pi
200200 525.000 0.185616
201201 0 0
202202 5202.00 1.81194
203203 0 0
204204 0 0
205205 −1650.00 −0.562151
206206 1356.00 0.458626
207207 0 0
208208 5254.00 1.75144
209209 2976.00 0.984948
210210 0 0
211211 1100.00 0.358896 0.179448 0.983767i 0.442569π-0.442569\pi
0.179448 + 0.983767i 0.442569π0.442569\pi
212212 −450.000 −0.145784
213213 0 0
214214 −4212.00 −1.34545
215215 −460.000 −0.145915
216216 0 0
217217 0 0
218218 4422.00 1.37383
219219 0 0
220220 −120.000 −0.0367745
221221 −3996.00 −1.21629
222222 0 0
223223 −1964.00 −0.589772 −0.294886 0.955532i 0.595282π-0.595282\pi
−0.294886 + 0.955532i 0.595282π0.595282\pi
224224 0 0
225225 0 0
226226 3258.00 0.958933
227227 660.000 0.192977 0.0964884 0.995334i 0.469239π-0.469239\pi
0.0964884 + 0.995334i 0.469239π0.469239\pi
228228 0 0
229229 1906.00 0.550009 0.275004 0.961443i 0.411321π-0.411321\pi
0.275004 + 0.961443i 0.411321π0.411321\pi
230230 1800.00 0.516037
231231 0 0
232232 1638.00 0.463534
233233 1458.00 0.409943 0.204972 0.978768i 0.434290π-0.434290\pi
0.204972 + 0.978768i 0.434290π0.434290\pi
234234 0 0
235235 120.000 0.0333104
236236 24.0000 0.00661978
237237 0 0
238238 0 0
239239 −1176.00 −0.318281 −0.159140 0.987256i 0.550872π-0.550872\pi
−0.159140 + 0.987256i 0.550872π0.550872\pi
240240 0 0
241241 −866.000 −0.231469 −0.115734 0.993280i 0.536922π-0.536922\pi
−0.115734 + 0.993280i 0.536922π0.536922\pi
242242 2265.00 0.601652
243243 0 0
244244 322.000 0.0844834
245245 0 0
246246 0 0
247247 −9176.00 −2.36379
248248 −4200.00 −1.07540
249249 0 0
250250 375.000 0.0948683
251251 432.000 0.108636 0.0543179 0.998524i 0.482702π-0.482702\pi
0.0543179 + 0.998524i 0.482702π0.482702\pi
252252 0 0
253253 2880.00 0.715668
254254 −3732.00 −0.921915
255255 0 0
256256 1513.00 0.369385
257257 2526.00 0.613103 0.306552 0.951854i 0.400825π-0.400825\pi
0.306552 + 0.951854i 0.400825π0.400825\pi
258258 0 0
259259 0 0
260260 370.000 0.0882555
261261 0 0
262262 −6984.00 −1.64684
263263 −5448.00 −1.27733 −0.638666 0.769484i 0.720513π-0.720513\pi
−0.638666 + 0.769484i 0.720513π0.720513\pi
264264 0 0
265265 2250.00 0.521571
266266 0 0
267267 0 0
268268 −196.000 −0.0446739
269269 −2574.00 −0.583418 −0.291709 0.956507i 0.594224π-0.594224\pi
−0.291709 + 0.956507i 0.594224π0.594224\pi
270270 0 0
271271 3184.00 0.713706 0.356853 0.934161i 0.383850π-0.383850\pi
0.356853 + 0.934161i 0.383850π0.383850\pi
272272 −3834.00 −0.854671
273273 0 0
274274 6354.00 1.40095
275275 600.000 0.131569
276276 0 0
277277 3962.00 0.859399 0.429699 0.902972i 0.358620π-0.358620\pi
0.429699 + 0.902972i 0.358620π0.358620\pi
278278 6972.00 1.50415
279279 0 0
280280 0 0
281281 8286.00 1.75908 0.879540 0.475825i 0.157851π-0.157851\pi
0.879540 + 0.475825i 0.157851π0.157851\pi
282282 0 0
283283 2716.00 0.570493 0.285246 0.958454i 0.407925π-0.407925\pi
0.285246 + 0.958454i 0.407925π0.407925\pi
284284 288.000 0.0601748
285285 0 0
286286 5328.00 1.10158
287287 0 0
288288 0 0
289289 −1997.00 −0.406473
290290 1170.00 0.236913
291291 0 0
292292 430.000 0.0861776
293293 6018.00 1.19992 0.599958 0.800032i 0.295184π-0.295184\pi
0.599958 + 0.800032i 0.295184π0.295184\pi
294294 0 0
295295 −120.000 −0.0236836
296296 −1470.00 −0.288655
297297 0 0
298298 774.000 0.150458
299299 −8880.00 −1.71754
300300 0 0
301301 0 0
302302 2424.00 0.461873
303303 0 0
304304 −8804.00 −1.66100
305305 −1610.00 −0.302257
306306 0 0
307307 −9236.00 −1.71702 −0.858512 0.512793i 0.828611π-0.828611\pi
−0.858512 + 0.512793i 0.828611π0.828611\pi
308308 0 0
309309 0 0
310310 −3000.00 −0.549640
311311 1536.00 0.280060 0.140030 0.990147i 0.455280π-0.455280\pi
0.140030 + 0.990147i 0.455280π0.455280\pi
312312 0 0
313313 7342.00 1.32586 0.662930 0.748681i 0.269313π-0.269313\pi
0.662930 + 0.748681i 0.269313π0.269313\pi
314314 7134.00 1.28215
315315 0 0
316316 −520.000 −0.0925705
317317 3894.00 0.689933 0.344967 0.938615i 0.387890π-0.387890\pi
0.344967 + 0.938615i 0.387890π0.387890\pi
318318 0 0
319319 1872.00 0.328564
320320 −2165.00 −0.378210
321321 0 0
322322 0 0
323323 6696.00 1.15348
324324 0 0
325325 −1850.00 −0.315752
326326 156.000 0.0265032
327327 0 0
328328 6930.00 1.16660
329329 0 0
330330 0 0
331331 3692.00 0.613084 0.306542 0.951857i 0.400828π-0.400828\pi
0.306542 + 0.951857i 0.400828π0.400828\pi
332332 156.000 0.0257880
333333 0 0
334334 11160.0 1.82829
335335 980.000 0.159830
336336 0 0
337337 −8998.00 −1.45446 −0.727229 0.686395i 0.759192π-0.759192\pi
−0.727229 + 0.686395i 0.759192π0.759192\pi
338338 −9837.00 −1.58302
339339 0 0
340340 −270.000 −0.0430671
341341 −4800.00 −0.762271
342342 0 0
343343 0 0
344344 1932.00 0.302809
345345 0 0
346346 −1278.00 −0.198571
347347 −5244.00 −0.811276 −0.405638 0.914034i 0.632951π-0.632951\pi
−0.405638 + 0.914034i 0.632951π0.632951\pi
348348 0 0
349349 −6302.00 −0.966585 −0.483293 0.875459i 0.660559π-0.660559\pi
−0.483293 + 0.875459i 0.660559π0.660559\pi
350350 0 0
351351 0 0
352352 1080.00 0.163535
353353 3414.00 0.514756 0.257378 0.966311i 0.417141π-0.417141\pi
0.257378 + 0.966311i 0.417141π0.417141\pi
354354 0 0
355355 −1440.00 −0.215288
356356 1026.00 0.152747
357357 0 0
358358 −4320.00 −0.637763
359359 −4824.00 −0.709195 −0.354597 0.935019i 0.615382π-0.615382\pi
−0.354597 + 0.935019i 0.615382π0.615382\pi
360360 0 0
361361 8517.00 1.24173
362362 −9390.00 −1.36334
363363 0 0
364364 0 0
365365 −2150.00 −0.308318
366366 0 0
367367 3508.00 0.498954 0.249477 0.968381i 0.419741π-0.419741\pi
0.249477 + 0.968381i 0.419741π0.419741\pi
368368 −8520.00 −1.20689
369369 0 0
370370 −1050.00 −0.147532
371371 0 0
372372 0 0
373373 10802.0 1.49948 0.749740 0.661732i 0.230178π-0.230178\pi
0.749740 + 0.661732i 0.230178π0.230178\pi
374374 −3888.00 −0.537550
375375 0 0
376376 −504.000 −0.0691272
377377 −5772.00 −0.788523
378378 0 0
379379 1460.00 0.197876 0.0989382 0.995094i 0.468455π-0.468455\pi
0.0989382 + 0.995094i 0.468455π0.468455\pi
380380 −620.000 −0.0836982
381381 0 0
382382 10728.0 1.43689
383383 −4872.00 −0.649994 −0.324997 0.945715i 0.605363π-0.605363\pi
−0.324997 + 0.945715i 0.605363π0.605363\pi
384384 0 0
385385 0 0
386386 −7998.00 −1.05463
387387 0 0
388388 286.000 0.0374213
389389 14046.0 1.83075 0.915373 0.402606i 0.131896π-0.131896\pi
0.915373 + 0.402606i 0.131896π0.131896\pi
390390 0 0
391391 6480.00 0.838127
392392 0 0
393393 0 0
394394 −8154.00 −1.04262
395395 2600.00 0.331190
396396 0 0
397397 2734.00 0.345631 0.172816 0.984954i 0.444714π-0.444714\pi
0.172816 + 0.984954i 0.444714π0.444714\pi
398398 −11496.0 −1.44785
399399 0 0
400400 −1775.00 −0.221875
401401 15942.0 1.98530 0.992650 0.121019i 0.0386161π-0.0386161\pi
0.992650 + 0.121019i 0.0386161π0.0386161\pi
402402 0 0
403403 14800.0 1.82938
404404 −1734.00 −0.213539
405405 0 0
406406 0 0
407407 −1680.00 −0.204606
408408 0 0
409409 −8714.00 −1.05350 −0.526748 0.850022i 0.676589π-0.676589\pi
−0.526748 + 0.850022i 0.676589π0.676589\pi
410410 4950.00 0.596251
411411 0 0
412412 −452.000 −0.0540496
413413 0 0
414414 0 0
415415 −780.000 −0.0922619
416416 −3330.00 −0.392468
417417 0 0
418418 −8928.00 −1.04470
419419 11976.0 1.39634 0.698169 0.715933i 0.253998π-0.253998\pi
0.698169 + 0.715933i 0.253998π0.253998\pi
420420 0 0
421421 11054.0 1.27967 0.639833 0.768514i 0.279004π-0.279004\pi
0.639833 + 0.768514i 0.279004π0.279004\pi
422422 −3300.00 −0.380667
423423 0 0
424424 −9450.00 −1.08239
425425 1350.00 0.154081
426426 0 0
427427 0 0
428428 1404.00 0.158563
429429 0 0
430430 1380.00 0.154766
431431 −720.000 −0.0804668 −0.0402334 0.999190i 0.512810π-0.512810\pi
−0.0402334 + 0.999190i 0.512810π0.512810\pi
432432 0 0
433433 15622.0 1.73382 0.866912 0.498462i 0.166102π-0.166102\pi
0.866912 + 0.498462i 0.166102π0.166102\pi
434434 0 0
435435 0 0
436436 −1474.00 −0.161908
437437 14880.0 1.62885
438438 0 0
439439 9880.00 1.07414 0.537069 0.843538i 0.319531π-0.319531\pi
0.537069 + 0.843538i 0.319531π0.319531\pi
440440 −2520.00 −0.273037
441441 0 0
442442 11988.0 1.29007
443443 16116.0 1.72843 0.864215 0.503123i 0.167816π-0.167816\pi
0.864215 + 0.503123i 0.167816π0.167816\pi
444444 0 0
445445 −5130.00 −0.546484
446446 5892.00 0.625548
447447 0 0
448448 0 0
449449 −9018.00 −0.947852 −0.473926 0.880565i 0.657164π-0.657164\pi
−0.473926 + 0.880565i 0.657164π0.657164\pi
450450 0 0
451451 7920.00 0.826914
452452 −1086.00 −0.113011
453453 0 0
454454 −1980.00 −0.204683
455455 0 0
456456 0 0
457457 −3670.00 −0.375657 −0.187829 0.982202i 0.560145π-0.560145\pi
−0.187829 + 0.982202i 0.560145π0.560145\pi
458458 −5718.00 −0.583372
459459 0 0
460460 −600.000 −0.0608155
461461 17562.0 1.77428 0.887141 0.461499i 0.152688π-0.152688\pi
0.887141 + 0.461499i 0.152688π0.152688\pi
462462 0 0
463463 1172.00 0.117640 0.0588202 0.998269i 0.481266π-0.481266\pi
0.0588202 + 0.998269i 0.481266π0.481266\pi
464464 −5538.00 −0.554084
465465 0 0
466466 −4374.00 −0.434810
467467 6876.00 0.681335 0.340667 0.940184i 0.389347π-0.389347\pi
0.340667 + 0.940184i 0.389347π0.389347\pi
468468 0 0
469469 0 0
470470 −360.000 −0.0353310
471471 0 0
472472 504.000 0.0491493
473473 2208.00 0.214638
474474 0 0
475475 3100.00 0.299448
476476 0 0
477477 0 0
478478 3528.00 0.337588
479479 2280.00 0.217486 0.108743 0.994070i 0.465317π-0.465317\pi
0.108743 + 0.994070i 0.465317π0.465317\pi
480480 0 0
481481 5180.00 0.491035
482482 2598.00 0.245510
483483 0 0
484484 −755.000 −0.0709053
485485 −1430.00 −0.133882
486486 0 0
487487 −3076.00 −0.286215 −0.143108 0.989707i 0.545710π-0.545710\pi
−0.143108 + 0.989707i 0.545710π0.545710\pi
488488 6762.00 0.627257
489489 0 0
490490 0 0
491491 18912.0 1.73826 0.869131 0.494582i 0.164679π-0.164679\pi
0.869131 + 0.494582i 0.164679π0.164679\pi
492492 0 0
493493 4212.00 0.384785
494494 27528.0 2.50717
495495 0 0
496496 14200.0 1.28548
497497 0 0
498498 0 0
499499 9956.00 0.893170 0.446585 0.894741i 0.352640π-0.352640\pi
0.446585 + 0.894741i 0.352640π0.352640\pi
500500 −125.000 −0.0111803
501501 0 0
502502 −1296.00 −0.115226
503503 −10656.0 −0.944588 −0.472294 0.881441i 0.656574π-0.656574\pi
−0.472294 + 0.881441i 0.656574π0.656574\pi
504504 0 0
505505 8670.00 0.763980
506506 −8640.00 −0.759081
507507 0 0
508508 1244.00 0.108649
509509 −2766.00 −0.240866 −0.120433 0.992721i 0.538428π-0.538428\pi
−0.120433 + 0.992721i 0.538428π0.538428\pi
510510 0 0
511511 0 0
512512 8733.00 0.753804
513513 0 0
514514 −7578.00 −0.650294
515515 2260.00 0.193374
516516 0 0
517517 −576.000 −0.0489989
518518 0 0
519519 0 0
520520 7770.00 0.655264
521521 10530.0 0.885466 0.442733 0.896654i 0.354009π-0.354009\pi
0.442733 + 0.896654i 0.354009π0.354009\pi
522522 0 0
523523 −12692.0 −1.06115 −0.530576 0.847637i 0.678024π-0.678024\pi
−0.530576 + 0.847637i 0.678024π0.678024\pi
524524 2328.00 0.194082
525525 0 0
526526 16344.0 1.35481
527527 −10800.0 −0.892705
528528 0 0
529529 2233.00 0.183529
530530 −6750.00 −0.553210
531531 0 0
532532 0 0
533533 −24420.0 −1.98452
534534 0 0
535535 −7020.00 −0.567292
536536 −4116.00 −0.331687
537537 0 0
538538 7722.00 0.618809
539539 0 0
540540 0 0
541541 18110.0 1.43920 0.719602 0.694386i 0.244324π-0.244324\pi
0.719602 + 0.694386i 0.244324π0.244324\pi
542542 −9552.00 −0.756999
543543 0 0
544544 2430.00 0.191517
545545 7370.00 0.579259
546546 0 0
547547 3620.00 0.282962 0.141481 0.989941i 0.454814π-0.454814\pi
0.141481 + 0.989941i 0.454814π0.454814\pi
548548 −2118.00 −0.165103
549549 0 0
550550 −1800.00 −0.139550
551551 9672.00 0.747806
552552 0 0
553553 0 0
554554 −11886.0 −0.911530
555555 0 0
556556 −2324.00 −0.177265
557557 14166.0 1.07762 0.538809 0.842428i 0.318875π-0.318875\pi
0.538809 + 0.842428i 0.318875π0.318875\pi
558558 0 0
559559 −6808.00 −0.515112
560560 0 0
561561 0 0
562562 −24858.0 −1.86579
563563 −13404.0 −1.00339 −0.501697 0.865043i 0.667291π-0.667291\pi
−0.501697 + 0.865043i 0.667291π0.667291\pi
564564 0 0
565565 5430.00 0.404322
566566 −8148.00 −0.605099
567567 0 0
568568 6048.00 0.446775
569569 18654.0 1.37437 0.687185 0.726483i 0.258846π-0.258846\pi
0.687185 + 0.726483i 0.258846π0.258846\pi
570570 0 0
571571 −7684.00 −0.563162 −0.281581 0.959537i 0.590859π-0.590859\pi
−0.281581 + 0.959537i 0.590859π0.590859\pi
572572 −1776.00 −0.129822
573573 0 0
574574 0 0
575575 3000.00 0.217580
576576 0 0
577577 1726.00 0.124531 0.0622654 0.998060i 0.480167π-0.480167\pi
0.0622654 + 0.998060i 0.480167π0.480167\pi
578578 5991.00 0.431129
579579 0 0
580580 −390.000 −0.0279205
581581 0 0
582582 0 0
583583 −10800.0 −0.767222
584584 9030.00 0.639836
585585 0 0
586586 −18054.0 −1.27270
587587 10596.0 0.745049 0.372524 0.928022i 0.378492π-0.378492\pi
0.372524 + 0.928022i 0.378492π0.378492\pi
588588 0 0
589589 −24800.0 −1.73492
590590 360.000 0.0251203
591591 0 0
592592 4970.00 0.345043
593593 2862.00 0.198193 0.0990963 0.995078i 0.468405π-0.468405\pi
0.0990963 + 0.995078i 0.468405π0.468405\pi
594594 0 0
595595 0 0
596596 −258.000 −0.0177317
597597 0 0
598598 26640.0 1.82172
599599 23592.0 1.60925 0.804627 0.593781i 0.202365π-0.202365\pi
0.804627 + 0.593781i 0.202365π0.202365\pi
600600 0 0
601601 9574.00 0.649803 0.324902 0.945748i 0.394669π-0.394669\pi
0.324902 + 0.945748i 0.394669π0.394669\pi
602602 0 0
603603 0 0
604604 −808.000 −0.0544322
605605 3775.00 0.253679
606606 0 0
607607 −17444.0 −1.16644 −0.583221 0.812314i 0.698208π-0.698208\pi
−0.583221 + 0.812314i 0.698208π0.698208\pi
608608 5580.00 0.372202
609609 0 0
610610 4830.00 0.320592
611611 1776.00 0.117593
612612 0 0
613613 −2374.00 −0.156419 −0.0782096 0.996937i 0.524920π-0.524920\pi
−0.0782096 + 0.996937i 0.524920π0.524920\pi
614614 27708.0 1.82118
615615 0 0
616616 0 0
617617 12162.0 0.793555 0.396778 0.917915i 0.370128π-0.370128\pi
0.396778 + 0.917915i 0.370128π0.370128\pi
618618 0 0
619619 −8804.00 −0.571668 −0.285834 0.958279i 0.592271π-0.592271\pi
−0.285834 + 0.958279i 0.592271π0.592271\pi
620620 1000.00 0.0647758
621621 0 0
622622 −4608.00 −0.297048
623623 0 0
624624 0 0
625625 625.000 0.0400000
626626 −22026.0 −1.40629
627627 0 0
628628 −2378.00 −0.151103
629629 −3780.00 −0.239616
630630 0 0
631631 −12688.0 −0.800478 −0.400239 0.916411i 0.631073π-0.631073\pi
−0.400239 + 0.916411i 0.631073π0.631073\pi
632632 −10920.0 −0.687301
633633 0 0
634634 −11682.0 −0.731785
635635 −6220.00 −0.388714
636636 0 0
637637 0 0
638638 −5616.00 −0.348495
639639 0 0
640640 8295.00 0.512326
641641 9150.00 0.563812 0.281906 0.959442i 0.409033π-0.409033\pi
0.281906 + 0.959442i 0.409033π0.409033\pi
642642 0 0
643643 −25292.0 −1.55120 −0.775598 0.631227i 0.782552π-0.782552\pi
−0.775598 + 0.631227i 0.782552π0.782552\pi
644644 0 0
645645 0 0
646646 −20088.0 −1.22345
647647 −2736.00 −0.166249 −0.0831246 0.996539i 0.526490π-0.526490\pi
−0.0831246 + 0.996539i 0.526490π0.526490\pi
648648 0 0
649649 576.000 0.0348382
650650 5550.00 0.334906
651651 0 0
652652 −52.0000 −0.00312343
653653 −22218.0 −1.33148 −0.665741 0.746183i 0.731884π-0.731884\pi
−0.665741 + 0.746183i 0.731884π0.731884\pi
654654 0 0
655655 −11640.0 −0.694370
656656 −23430.0 −1.39449
657657 0 0
658658 0 0
659659 −14520.0 −0.858299 −0.429149 0.903234i 0.641187π-0.641187\pi
−0.429149 + 0.903234i 0.641187π0.641187\pi
660660 0 0
661661 10618.0 0.624799 0.312400 0.949951i 0.398867π-0.398867\pi
0.312400 + 0.949951i 0.398867π0.398867\pi
662662 −11076.0 −0.650273
663663 0 0
664664 3276.00 0.191466
665665 0 0
666666 0 0
667667 9360.00 0.543359
668668 −3720.00 −0.215466
669669 0 0
670670 −2940.00 −0.169526
671671 7728.00 0.444614
672672 0 0
673673 1370.00 0.0784690 0.0392345 0.999230i 0.487508π-0.487508\pi
0.0392345 + 0.999230i 0.487508π0.487508\pi
674674 26994.0 1.54269
675675 0 0
676676 3279.00 0.186561
677677 −13758.0 −0.781038 −0.390519 0.920595i 0.627704π-0.627704\pi
−0.390519 + 0.920595i 0.627704π0.627704\pi
678678 0 0
679679 0 0
680680 −5670.00 −0.319757
681681 0 0
682682 14400.0 0.808511
683683 −11988.0 −0.671608 −0.335804 0.941932i 0.609008π-0.609008\pi
−0.335804 + 0.941932i 0.609008π0.609008\pi
684684 0 0
685685 10590.0 0.590691
686686 0 0
687687 0 0
688688 −6532.00 −0.361962
689689 33300.0 1.84126
690690 0 0
691691 −32996.0 −1.81654 −0.908268 0.418388i 0.862595π-0.862595\pi
−0.908268 + 0.418388i 0.862595π0.862595\pi
692692 426.000 0.0234019
693693 0 0
694694 15732.0 0.860488
695695 11620.0 0.634204
696696 0 0
697697 17820.0 0.968408
698698 18906.0 1.02522
699699 0 0
700700 0 0
701701 25902.0 1.39558 0.697792 0.716300i 0.254166π-0.254166\pi
0.697792 + 0.716300i 0.254166π0.254166\pi
702702 0 0
703703 −8680.00 −0.465679
704704 10392.0 0.556340
705705 0 0
706706 −10242.0 −0.545981
707707 0 0
708708 0 0
709709 −27394.0 −1.45106 −0.725531 0.688189i 0.758406π-0.758406\pi
−0.725531 + 0.688189i 0.758406π0.758406\pi
710710 4320.00 0.228347
711711 0 0
712712 21546.0 1.13409
713713 −24000.0 −1.26060
714714 0 0
715715 8880.00 0.464466
716716 1440.00 0.0751611
717717 0 0
718718 14472.0 0.752215
719719 34848.0 1.80753 0.903763 0.428033i 0.140793π-0.140793\pi
0.903763 + 0.428033i 0.140793π0.140793\pi
720720 0 0
721721 0 0
722722 −25551.0 −1.31705
723723 0 0
724724 3130.00 0.160671
725725 1950.00 0.0998913
726726 0 0
727727 −28028.0 −1.42985 −0.714925 0.699201i 0.753539π-0.753539\pi
−0.714925 + 0.699201i 0.753539π0.753539\pi
728728 0 0
729729 0 0
730730 6450.00 0.327021
731731 4968.00 0.251365
732732 0 0
733733 −18002.0 −0.907120 −0.453560 0.891226i 0.649846π-0.649846\pi
−0.453560 + 0.891226i 0.649846π0.649846\pi
734734 −10524.0 −0.529221
735735 0 0
736736 5400.00 0.270444
737737 −4704.00 −0.235107
738738 0 0
739739 15284.0 0.760800 0.380400 0.924822i 0.375786π-0.375786\pi
0.380400 + 0.924822i 0.375786π0.375786\pi
740740 350.000 0.0173868
741741 0 0
742742 0 0
743743 18768.0 0.926691 0.463345 0.886178i 0.346649π-0.346649\pi
0.463345 + 0.886178i 0.346649π0.346649\pi
744744 0 0
745745 1290.00 0.0634388
746746 −32406.0 −1.59044
747747 0 0
748748 1296.00 0.0633509
749749 0 0
750750 0 0
751751 8696.00 0.422532 0.211266 0.977429i 0.432241π-0.432241\pi
0.211266 + 0.977429i 0.432241π0.432241\pi
752752 1704.00 0.0826310
753753 0 0
754754 17316.0 0.836355
755755 4040.00 0.194743
756756 0 0
757757 −38662.0 −1.85627 −0.928134 0.372247i 0.878587π-0.878587\pi
−0.928134 + 0.372247i 0.878587π0.878587\pi
758758 −4380.00 −0.209880
759759 0 0
760760 −13020.0 −0.621428
761761 23874.0 1.13723 0.568615 0.822604i 0.307479π-0.307479\pi
0.568615 + 0.822604i 0.307479π0.307479\pi
762762 0 0
763763 0 0
764764 −3576.00 −0.169339
765765 0 0
766766 14616.0 0.689422
767767 −1776.00 −0.0836084
768768 0 0
769769 −23618.0 −1.10753 −0.553763 0.832675i 0.686808π-0.686808\pi
−0.553763 + 0.832675i 0.686808π0.686808\pi
770770 0 0
771771 0 0
772772 2666.00 0.124289
773773 11538.0 0.536860 0.268430 0.963299i 0.413495π-0.413495\pi
0.268430 + 0.963299i 0.413495π0.413495\pi
774774 0 0
775775 −5000.00 −0.231749
776776 6006.00 0.277839
777777 0 0
778778 −42138.0 −1.94180
779779 40920.0 1.88204
780780 0 0
781781 6912.00 0.316685
782782 −19440.0 −0.888968
783783 0 0
784784 0 0
785785 11890.0 0.540602
786786 0 0
787787 14884.0 0.674152 0.337076 0.941478i 0.390562π-0.390562\pi
0.337076 + 0.941478i 0.390562π0.390562\pi
788788 2718.00 0.122874
789789 0 0
790790 −7800.00 −0.351280
791791 0 0
792792 0 0
793793 −23828.0 −1.06703
794794 −8202.00 −0.366597
795795 0 0
796796 3832.00 0.170630
797797 −11334.0 −0.503728 −0.251864 0.967763i 0.581043π-0.581043\pi
−0.251864 + 0.967763i 0.581043π0.581043\pi
798798 0 0
799799 −1296.00 −0.0573832
800800 1125.00 0.0497184
801801 0 0
802802 −47826.0 −2.10573
803803 10320.0 0.453530
804804 0 0
805805 0 0
806806 −44400.0 −1.94035
807807 0 0
808808 −36414.0 −1.58545
809809 −44730.0 −1.94391 −0.971955 0.235167i 0.924436π-0.924436\pi
−0.971955 + 0.235167i 0.924436π0.924436\pi
810810 0 0
811811 42748.0 1.85091 0.925453 0.378862i 0.123684π-0.123684\pi
0.925453 + 0.378862i 0.123684π0.123684\pi
812812 0 0
813813 0 0
814814 5040.00 0.217017
815815 260.000 0.0111747
816816 0 0
817817 11408.0 0.488513
818818 26142.0 1.11740
819819 0 0
820820 −1650.00 −0.0702689
821821 31686.0 1.34695 0.673477 0.739208i 0.264800π-0.264800\pi
0.673477 + 0.739208i 0.264800π0.264800\pi
822822 0 0
823823 11036.0 0.467425 0.233713 0.972306i 0.424913π-0.424913\pi
0.233713 + 0.972306i 0.424913π0.424913\pi
824824 −9492.00 −0.401298
825825 0 0
826826 0 0
827827 −25884.0 −1.08836 −0.544181 0.838968i 0.683159π-0.683159\pi
−0.544181 + 0.838968i 0.683159π0.683159\pi
828828 0 0
829829 −15950.0 −0.668234 −0.334117 0.942532i 0.608438π-0.608438\pi
−0.334117 + 0.942532i 0.608438π0.608438\pi
830830 2340.00 0.0978585
831831 0 0
832832 −32042.0 −1.33516
833833 0 0
834834 0 0
835835 18600.0 0.770874
836836 2976.00 0.123119
837837 0 0
838838 −35928.0 −1.48104
839839 13800.0 0.567853 0.283927 0.958846i 0.408363π-0.408363\pi
0.283927 + 0.958846i 0.408363π0.408363\pi
840840 0 0
841841 −18305.0 −0.750543
842842 −33162.0 −1.35729
843843 0 0
844844 1100.00 0.0448620
845845 −16395.0 −0.667462
846846 0 0
847847 0 0
848848 31950.0 1.29383
849849 0 0
850850 −4050.00 −0.163428
851851 −8400.00 −0.338365
852852 0 0
853853 27862.0 1.11838 0.559189 0.829040i 0.311113π-0.311113\pi
0.559189 + 0.829040i 0.311113π0.311113\pi
854854 0 0
855855 0 0
856856 29484.0 1.17727
857857 −7314.00 −0.291530 −0.145765 0.989319i 0.546564π-0.546564\pi
−0.145765 + 0.989319i 0.546564π0.546564\pi
858858 0 0
859859 28780.0 1.14314 0.571572 0.820552i 0.306334π-0.306334\pi
0.571572 + 0.820552i 0.306334π0.306334\pi
860860 −460.000 −0.0182394
861861 0 0
862862 2160.00 0.0853479
863863 32688.0 1.28935 0.644677 0.764455i 0.276992π-0.276992\pi
0.644677 + 0.764455i 0.276992π0.276992\pi
864864 0 0
865865 −2130.00 −0.0837251
866866 −46866.0 −1.83900
867867 0 0
868868 0 0
869869 −12480.0 −0.487175
870870 0 0
871871 14504.0 0.564236
872872 −30954.0 −1.20210
873873 0 0
874874 −44640.0 −1.72766
875875 0 0
876876 0 0
877877 36650.0 1.41115 0.705577 0.708633i 0.250688π-0.250688\pi
0.705577 + 0.708633i 0.250688π0.250688\pi
878878 −29640.0 −1.13930
879879 0 0
880880 8520.00 0.326374
881881 −2646.00 −0.101187 −0.0505936 0.998719i 0.516111π-0.516111\pi
−0.0505936 + 0.998719i 0.516111π0.516111\pi
882882 0 0
883883 10892.0 0.415113 0.207557 0.978223i 0.433449π-0.433449\pi
0.207557 + 0.978223i 0.433449π0.433449\pi
884884 −3996.00 −0.152036
885885 0 0
886886 −48348.0 −1.83328
887887 −43464.0 −1.64530 −0.822648 0.568550i 0.807504π-0.807504\pi
−0.822648 + 0.568550i 0.807504π0.807504\pi
888888 0 0
889889 0 0
890890 15390.0 0.579634
891891 0 0
892892 −1964.00 −0.0737215
893893 −2976.00 −0.111521
894894 0 0
895895 −7200.00 −0.268904
896896 0 0
897897 0 0
898898 27054.0 1.00535
899899 −15600.0 −0.578742
900900 0 0
901901 −24300.0 −0.898502
902902 −23760.0 −0.877075
903903 0 0
904904 −22806.0 −0.839067
905905 −15650.0 −0.574833
906906 0 0
907907 −14884.0 −0.544890 −0.272445 0.962171i 0.587832π-0.587832\pi
−0.272445 + 0.962171i 0.587832π0.587832\pi
908908 660.000 0.0241221
909909 0 0
910910 0 0
911911 1248.00 0.0453876 0.0226938 0.999742i 0.492776π-0.492776\pi
0.0226938 + 0.999742i 0.492776π0.492776\pi
912912 0 0
913913 3744.00 0.135716
914914 11010.0 0.398445
915915 0 0
916916 1906.00 0.0687511
917917 0 0
918918 0 0
919919 −6640.00 −0.238339 −0.119169 0.992874i 0.538023π-0.538023\pi
−0.119169 + 0.992874i 0.538023π0.538023\pi
920920 −12600.0 −0.451532
921921 0 0
922922 −52686.0 −1.88191
923923 −21312.0 −0.760014
924924 0 0
925925 −1750.00 −0.0622050
926926 −3516.00 −0.124776
927927 0 0
928928 3510.00 0.124161
929929 29946.0 1.05758 0.528792 0.848751i 0.322645π-0.322645\pi
0.528792 + 0.848751i 0.322645π0.322645\pi
930930 0 0
931931 0 0
932932 1458.00 0.0512429
933933 0 0
934934 −20628.0 −0.722665
935935 −6480.00 −0.226651
936936 0 0
937937 −45002.0 −1.56900 −0.784499 0.620130i 0.787080π-0.787080\pi
−0.784499 + 0.620130i 0.787080π0.787080\pi
938938 0 0
939939 0 0
940940 120.000 0.00416380
941941 6090.00 0.210976 0.105488 0.994421i 0.466360π-0.466360\pi
0.105488 + 0.994421i 0.466360π0.466360\pi
942942 0 0
943943 39600.0 1.36750
944944 −1704.00 −0.0587505
945945 0 0
946946 −6624.00 −0.227658
947947 −56388.0 −1.93491 −0.967457 0.253035i 0.918571π-0.918571\pi
−0.967457 + 0.253035i 0.918571π0.918571\pi
948948 0 0
949949 −31820.0 −1.08843
950950 −9300.00 −0.317612
951951 0 0
952952 0 0
953953 −10854.0 −0.368936 −0.184468 0.982839i 0.559056π-0.559056\pi
−0.184468 + 0.982839i 0.559056π0.559056\pi
954954 0 0
955955 17880.0 0.605846
956956 −1176.00 −0.0397851
957957 0 0
958958 −6840.00 −0.230679
959959 0 0
960960 0 0
961961 10209.0 0.342687
962962 −15540.0 −0.520821
963963 0 0
964964 −866.000 −0.0289336
965965 −13330.0 −0.444671
966966 0 0
967967 −42316.0 −1.40723 −0.703615 0.710582i 0.748432π-0.748432\pi
−0.703615 + 0.710582i 0.748432π0.748432\pi
968968 −15855.0 −0.526445
969969 0 0
970970 4290.00 0.142004
971971 24480.0 0.809063 0.404532 0.914524i 0.367435π-0.367435\pi
0.404532 + 0.914524i 0.367435π0.367435\pi
972972 0 0
973973 0 0
974974 9228.00 0.303577
975975 0 0
976976 −22862.0 −0.749790
977977 6906.00 0.226144 0.113072 0.993587i 0.463931π-0.463931\pi
0.113072 + 0.993587i 0.463931π0.463931\pi
978978 0 0
979979 24624.0 0.803868
980980 0 0
981981 0 0
982982 −56736.0 −1.84371
983983 6960.00 0.225829 0.112914 0.993605i 0.463981π-0.463981\pi
0.112914 + 0.993605i 0.463981π0.463981\pi
984984 0 0
985985 −13590.0 −0.439608
986986 −12636.0 −0.408126
987987 0 0
988988 −9176.00 −0.295473
989989 11040.0 0.354956
990990 0 0
991991 47792.0 1.53195 0.765975 0.642870i 0.222256π-0.222256\pi
0.765975 + 0.642870i 0.222256π0.222256\pi
992992 −9000.00 −0.288055
993993 0 0
994994 0 0
995995 −19160.0 −0.610465
996996 0 0
997997 −9938.00 −0.315687 −0.157843 0.987464i 0.550454π-0.550454\pi
−0.157843 + 0.987464i 0.550454π0.550454\pi
998998 −29868.0 −0.947350
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 2205.4.a.c.1.1 1
3.2 odd 2 735.4.a.i.1.1 1
7.6 odd 2 45.4.a.b.1.1 1
21.20 even 2 15.4.a.b.1.1 1
28.27 even 2 720.4.a.r.1.1 1
35.13 even 4 225.4.b.d.199.2 2
35.27 even 4 225.4.b.d.199.1 2
35.34 odd 2 225.4.a.g.1.1 1
63.13 odd 6 405.4.e.k.136.1 2
63.20 even 6 405.4.e.d.271.1 2
63.34 odd 6 405.4.e.k.271.1 2
63.41 even 6 405.4.e.d.136.1 2
84.83 odd 2 240.4.a.f.1.1 1
105.62 odd 4 75.4.b.a.49.2 2
105.83 odd 4 75.4.b.a.49.1 2
105.104 even 2 75.4.a.a.1.1 1
168.83 odd 2 960.4.a.l.1.1 1
168.125 even 2 960.4.a.bi.1.1 1
231.230 odd 2 1815.4.a.a.1.1 1
420.83 even 4 1200.4.f.m.49.2 2
420.167 even 4 1200.4.f.m.49.1 2
420.419 odd 2 1200.4.a.o.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.4.a.b.1.1 1 21.20 even 2
45.4.a.b.1.1 1 7.6 odd 2
75.4.a.a.1.1 1 105.104 even 2
75.4.b.a.49.1 2 105.83 odd 4
75.4.b.a.49.2 2 105.62 odd 4
225.4.a.g.1.1 1 35.34 odd 2
225.4.b.d.199.1 2 35.27 even 4
225.4.b.d.199.2 2 35.13 even 4
240.4.a.f.1.1 1 84.83 odd 2
405.4.e.d.136.1 2 63.41 even 6
405.4.e.d.271.1 2 63.20 even 6
405.4.e.k.136.1 2 63.13 odd 6
405.4.e.k.271.1 2 63.34 odd 6
720.4.a.r.1.1 1 28.27 even 2
735.4.a.i.1.1 1 3.2 odd 2
960.4.a.l.1.1 1 168.83 odd 2
960.4.a.bi.1.1 1 168.125 even 2
1200.4.a.o.1.1 1 420.419 odd 2
1200.4.f.m.49.1 2 420.167 even 4
1200.4.f.m.49.2 2 420.83 even 4
1815.4.a.a.1.1 1 231.230 odd 2
2205.4.a.c.1.1 1 1.1 even 1 trivial