Properties

Label 9801.2.a.bp.1.2
Level 98019801
Weight 22
Character 9801.1
Self dual yes
Analytic conductor 78.26178.261
Analytic rank 00
Dimension 55
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] = [9801,2,Mod(1,9801)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9801, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9801.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 9801=34112 9801 = 3^{4} \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9801.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: 78.261379021178.2613790211
Analytic rank: 00
Dimension: 55
Coefficient field: 5.5.5144904.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x5x49x3+4x2+20x+3 x^{5} - x^{4} - 9x^{3} + 4x^{2} + 20x + 3 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.52027-1.52027 of defining polynomial
Character χ\chi == 9801.1

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) == q1.52027q2+0.311228q4+1.08767q52.25617q7+2.56739q81.65355q106.66038q13+3.42999q144.52559q165.92449q172.94494q19+0.338512q201.36367q233.81698q25+10.1256q260.702181q28+4.90971q29+1.12796q31+1.74535q32+9.00683q342.45396q35+0.220942q37+4.47711q38+2.79247q404.79628q417.34915q43+2.07315q469.42999q471.90971q49+5.80285q502.07289q52+2.06189q535.79247q567.46410q58+8.60794q5912.5676q611.71480q62+6.39779q647.24427q652.90971q671.84386q68+3.73068q708.76192q71+1.17644q730.335892q740.916546q7613.9650q794.92233q80+7.29164q8215.8901q836.44386q85+11.1727q86+0.635716q89+15.0269q910.424412q92+14.3361q943.20311q95+4.77493q97+2.90329q98+O(q100)q-1.52027 q^{2} +0.311228 q^{4} +1.08767 q^{5} -2.25617 q^{7} +2.56739 q^{8} -1.65355 q^{10} -6.66038 q^{13} +3.42999 q^{14} -4.52559 q^{16} -5.92449 q^{17} -2.94494 q^{19} +0.338512 q^{20} -1.36367 q^{23} -3.81698 q^{25} +10.1256 q^{26} -0.702181 q^{28} +4.90971 q^{29} +1.12796 q^{31} +1.74535 q^{32} +9.00683 q^{34} -2.45396 q^{35} +0.220942 q^{37} +4.47711 q^{38} +2.79247 q^{40} -4.79628 q^{41} -7.34915 q^{43} +2.07315 q^{46} -9.42999 q^{47} -1.90971 q^{49} +5.80285 q^{50} -2.07289 q^{52} +2.06189 q^{53} -5.79247 q^{56} -7.46410 q^{58} +8.60794 q^{59} -12.5676 q^{61} -1.71480 q^{62} +6.39779 q^{64} -7.24427 q^{65} -2.90971 q^{67} -1.84386 q^{68} +3.73068 q^{70} -8.76192 q^{71} +1.17644 q^{73} -0.335892 q^{74} -0.916546 q^{76} -13.9650 q^{79} -4.92233 q^{80} +7.29164 q^{82} -15.8901 q^{83} -6.44386 q^{85} +11.1727 q^{86} +0.635716 q^{89} +15.0269 q^{91} -0.424412 q^{92} +14.3361 q^{94} -3.20311 q^{95} +4.77493 q^{97} +2.90329 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 5q+q2+9q44q53q7+12q8+5q1013q14+9q16+4q17+q19+7q20+q23+15q257q26q28+3q29+24q31+20q32+25q34+12q98+O(q100) 5 q + q^{2} + 9 q^{4} - 4 q^{5} - 3 q^{7} + 12 q^{8} + 5 q^{10} - 13 q^{14} + 9 q^{16} + 4 q^{17} + q^{19} + 7 q^{20} + q^{23} + 15 q^{25} - 7 q^{26} - q^{28} + 3 q^{29} + 24 q^{31} + 20 q^{32} + 25 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) Copy content Toggle raw display

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 −1.52027 −1.07499 −0.537497 0.843265i 0.680630π-0.680630\pi
−0.537497 + 0.843265i 0.680630π0.680630\pi
33 0 0
44 0.311228 0.155614
55 1.08767 0.486419 0.243210 0.969974i 0.421800π-0.421800\pi
0.243210 + 0.969974i 0.421800π0.421800\pi
66 0 0
77 −2.25617 −0.852751 −0.426375 0.904546i 0.640210π-0.640210\pi
−0.426375 + 0.904546i 0.640210π0.640210\pi
88 2.56739 0.907711
99 0 0
1010 −1.65355 −0.522898
1111 0 0
1212 0 0
1313 −6.66038 −1.84726 −0.923629 0.383289i 0.874791π-0.874791\pi
−0.923629 + 0.383289i 0.874791π0.874791\pi
1414 3.42999 0.916702
1515 0 0
1616 −4.52559 −1.13140
1717 −5.92449 −1.43690 −0.718449 0.695579i 0.755148π-0.755148\pi
−0.718449 + 0.695579i 0.755148π0.755148\pi
1818 0 0
1919 −2.94494 −0.675615 −0.337808 0.941215i 0.609685π-0.609685\pi
−0.337808 + 0.941215i 0.609685π0.609685\pi
2020 0.338512 0.0756935
2121 0 0
2222 0 0
2323 −1.36367 −0.284345 −0.142172 0.989842i 0.545409π-0.545409\pi
−0.142172 + 0.989842i 0.545409π0.545409\pi
2424 0 0
2525 −3.81698 −0.763397
2626 10.1256 1.98579
2727 0 0
2828 −0.702181 −0.132700
2929 4.90971 0.911711 0.455856 0.890054i 0.349333π-0.349333\pi
0.455856 + 0.890054i 0.349333π0.349333\pi
3030 0 0
3131 1.12796 0.202587 0.101293 0.994857i 0.467702π-0.467702\pi
0.101293 + 0.994857i 0.467702π0.467702\pi
3232 1.74535 0.308536
3333 0 0
3434 9.00683 1.54466
3535 −2.45396 −0.414794
3636 0 0
3737 0.220942 0.0363227 0.0181613 0.999835i 0.494219π-0.494219\pi
0.0181613 + 0.999835i 0.494219π0.494219\pi
3838 4.47711 0.726283
3939 0 0
4040 2.79247 0.441528
4141 −4.79628 −0.749052 −0.374526 0.927216i 0.622195π-0.622195\pi
−0.374526 + 0.927216i 0.622195π0.622195\pi
4242 0 0
4343 −7.34915 −1.12074 −0.560368 0.828244i 0.689340π-0.689340\pi
−0.560368 + 0.828244i 0.689340π0.689340\pi
4444 0 0
4545 0 0
4646 2.07315 0.305669
4747 −9.42999 −1.37550 −0.687752 0.725945i 0.741403π-0.741403\pi
−0.687752 + 0.725945i 0.741403π0.741403\pi
4848 0 0
4949 −1.90971 −0.272816
5050 5.80285 0.820647
5151 0 0
5252 −2.07289 −0.287459
5353 2.06189 0.283223 0.141611 0.989922i 0.454772π-0.454772\pi
0.141611 + 0.989922i 0.454772π0.454772\pi
5454 0 0
5555 0 0
5656 −5.79247 −0.774051
5757 0 0
5858 −7.46410 −0.980085
5959 8.60794 1.12066 0.560329 0.828270i 0.310675π-0.310675\pi
0.560329 + 0.828270i 0.310675π0.310675\pi
6060 0 0
6161 −12.5676 −1.60912 −0.804561 0.593870i 0.797599π-0.797599\pi
−0.804561 + 0.593870i 0.797599π0.797599\pi
6262 −1.71480 −0.217780
6363 0 0
6464 6.39779 0.799723
6565 −7.24427 −0.898541
6666 0 0
6767 −2.90971 −0.355478 −0.177739 0.984078i 0.556878π-0.556878\pi
−0.177739 + 0.984078i 0.556878π0.556878\pi
6868 −1.84386 −0.223601
6969 0 0
7070 3.73068 0.445902
7171 −8.76192 −1.03985 −0.519924 0.854212i 0.674040π-0.674040\pi
−0.519924 + 0.854212i 0.674040π0.674040\pi
7272 0 0
7373 1.17644 0.137692 0.0688460 0.997627i 0.478068π-0.478068\pi
0.0688460 + 0.997627i 0.478068π0.478068\pi
7474 −0.335892 −0.0390467
7575 0 0
7676 −0.916546 −0.105135
7777 0 0
7878 0 0
7979 −13.9650 −1.57119 −0.785594 0.618742i 0.787643π-0.787643\pi
−0.785594 + 0.618742i 0.787643π0.787643\pi
8080 −4.92233 −0.550334
8181 0 0
8282 7.29164 0.805227
8383 −15.8901 −1.74417 −0.872084 0.489356i 0.837232π-0.837232\pi
−0.872084 + 0.489356i 0.837232π0.837232\pi
8484 0 0
8585 −6.44386 −0.698935
8686 11.1727 1.20478
8787 0 0
8888 0 0
8989 0.635716 0.0673857 0.0336929 0.999432i 0.489273π-0.489273\pi
0.0336929 + 0.999432i 0.489273π0.489273\pi
9090 0 0
9191 15.0269 1.57525
9292 −0.424412 −0.0442480
9393 0 0
9494 14.3361 1.47866
9595 −3.20311 −0.328632
9696 0 0
9797 4.77493 0.484820 0.242410 0.970174i 0.422062π-0.422062\pi
0.242410 + 0.970174i 0.422062π0.422062\pi
9898 2.90329 0.293276
9999 0 0
100100 −1.18795 −0.118795
101101 8.92449 0.888020 0.444010 0.896022i 0.353556π-0.353556\pi
0.444010 + 0.896022i 0.353556π0.353556\pi
102102 0 0
103103 2.93811 0.289500 0.144750 0.989468i 0.453762π-0.453762\pi
0.144750 + 0.989468i 0.453762π0.453762\pi
104104 −17.0998 −1.67678
105105 0 0
106106 −3.13464 −0.304463
107107 11.0619 1.06939 0.534697 0.845044i 0.320426π-0.320426\pi
0.534697 + 0.845044i 0.320426π0.320426\pi
108108 0 0
109109 15.3142 1.46683 0.733416 0.679780i 0.237925π-0.237925\pi
0.733416 + 0.679780i 0.237925π0.237925\pi
110110 0 0
111111 0 0
112112 10.2105 0.964800
113113 −12.8987 −1.21341 −0.606704 0.794927i 0.707509π-0.707509\pi
−0.606704 + 0.794927i 0.707509π0.707509\pi
114114 0 0
115115 −1.48322 −0.138311
116116 1.52804 0.141875
117117 0 0
118118 −13.0864 −1.20470
119119 13.3666 1.22532
120120 0 0
121121 0 0
122122 19.1062 1.72980
123123 0 0
124124 0.351051 0.0315253
125125 −9.58993 −0.857750
126126 0 0
127127 20.7553 1.84174 0.920869 0.389871i 0.127480π-0.127480\pi
0.920869 + 0.389871i 0.127480π0.127480\pi
128128 −13.2171 −1.16823
129129 0 0
130130 11.0133 0.965927
131131 10.5500 0.921758 0.460879 0.887463i 0.347534π-0.347534\pi
0.460879 + 0.887463i 0.347534π0.347534\pi
132132 0 0
133133 6.64427 0.576131
134134 4.42356 0.382137
135135 0 0
136136 −15.2105 −1.30429
137137 −11.9624 −1.02202 −0.511009 0.859575i 0.670728π-0.670728\pi
−0.511009 + 0.859575i 0.670728π0.670728\pi
138138 0 0
139139 12.6631 1.07407 0.537034 0.843560i 0.319545π-0.319545\pi
0.537034 + 0.843560i 0.319545π0.319545\pi
140140 −0.763739 −0.0645477
141141 0 0
142142 13.3205 1.11783
143143 0 0
144144 0 0
145145 5.34013 0.443474
146146 −1.78851 −0.148018
147147 0 0
148148 0.0687633 0.00565231
149149 −13.3131 −1.09065 −0.545325 0.838225i 0.683594π-0.683594\pi
−0.545325 + 0.838225i 0.683594π0.683594\pi
150150 0 0
151151 −8.26300 −0.672433 −0.336217 0.941785i 0.609147π-0.609147\pi
−0.336217 + 0.941785i 0.609147π0.609147\pi
152152 −7.56082 −0.613263
153153 0 0
154154 0 0
155155 1.22684 0.0985421
156156 0 0
157157 22.3628 1.78475 0.892374 0.451298i 0.149039π-0.149039\pi
0.892374 + 0.451298i 0.149039π0.149039\pi
158158 21.2306 1.68902
159159 0 0
160160 1.89835 0.150078
161161 3.07666 0.242475
162162 0 0
163163 9.15930 0.717412 0.358706 0.933451i 0.383218π-0.383218\pi
0.358706 + 0.933451i 0.383218π0.383218\pi
164164 −1.49273 −0.116563
165165 0 0
166166 24.1573 1.87497
167167 −19.9346 −1.54259 −0.771294 0.636479i 0.780390π-0.780390\pi
−0.771294 + 0.636479i 0.780390π0.780390\pi
168168 0 0
169169 31.3607 2.41236
170170 9.79642 0.751351
171171 0 0
172172 −2.28726 −0.174402
173173 23.3672 1.77658 0.888289 0.459285i 0.151894π-0.151894\pi
0.888289 + 0.459285i 0.151894π0.151894\pi
174174 0 0
175175 8.61175 0.650987
176176 0 0
177177 0 0
178178 −0.966461 −0.0724393
179179 10.8595 0.811678 0.405839 0.913945i 0.366979π-0.366979\pi
0.405839 + 0.913945i 0.366979π0.366979\pi
180180 0 0
181181 12.4309 0.923980 0.461990 0.886885i 0.347136π-0.347136\pi
0.461990 + 0.886885i 0.347136π0.347136\pi
182182 −22.8450 −1.69339
183183 0 0
184184 −3.50108 −0.258103
185185 0.240311 0.0176680
186186 0 0
187187 0 0
188188 −2.93487 −0.214048
189189 0 0
190190 4.86960 0.353278
191191 2.34494 0.169674 0.0848370 0.996395i 0.472963π-0.472963\pi
0.0848370 + 0.996395i 0.472963π0.472963\pi
192192 0 0
193193 4.17644 0.300627 0.150313 0.988638i 0.451972π-0.451972\pi
0.150313 + 0.988638i 0.451972π0.451972\pi
194194 −7.25919 −0.521179
195195 0 0
196196 −0.594356 −0.0424540
197197 −15.4170 −1.09841 −0.549207 0.835686i 0.685070π-0.685070\pi
−0.549207 + 0.835686i 0.685070π0.685070\pi
198198 0 0
199199 −5.76678 −0.408796 −0.204398 0.978888i 0.565524π-0.565524\pi
−0.204398 + 0.978888i 0.565524π0.565524\pi
200200 −9.79970 −0.692943
201201 0 0
202202 −13.5676 −0.954616
203203 −11.0771 −0.777462
204204 0 0
205205 −5.21675 −0.364353
206206 −4.46672 −0.311211
207207 0 0
208208 30.1422 2.08998
209209 0 0
210210 0 0
211211 −10.6959 −0.736333 −0.368167 0.929760i 0.620014π-0.620014\pi
−0.368167 + 0.929760i 0.620014π0.620014\pi
212212 0.641718 0.0440734
213213 0 0
214214 −16.8171 −1.14959
215215 −7.99342 −0.545147
216216 0 0
217217 −2.54486 −0.172756
218218 −23.2817 −1.57684
219219 0 0
220220 0 0
221221 39.4593 2.65432
222222 0 0
223223 −21.5772 −1.44491 −0.722457 0.691415i 0.756987π-0.756987\pi
−0.722457 + 0.691415i 0.756987π0.756987\pi
224224 −3.93779 −0.263105
225225 0 0
226226 19.6096 1.30441
227227 4.17914 0.277379 0.138690 0.990336i 0.455711π-0.455711\pi
0.138690 + 0.990336i 0.455711π0.455711\pi
228228 0 0
229229 −19.5701 −1.29323 −0.646614 0.762817i 0.723816π-0.723816\pi
−0.646614 + 0.762817i 0.723816π0.723816\pi
230230 2.25489 0.148683
231231 0 0
232232 12.6052 0.827570
233233 −10.4641 −0.685526 −0.342763 0.939422i 0.611363π-0.611363\pi
−0.342763 + 0.939422i 0.611363π0.611363\pi
234234 0 0
235235 −10.2567 −0.669072
236236 2.67903 0.174390
237237 0 0
238238 −20.3209 −1.31721
239239 −13.8412 −0.895316 −0.447658 0.894205i 0.647742π-0.647742\pi
−0.447658 + 0.894205i 0.647742π0.647742\pi
240240 0 0
241241 −2.13234 −0.137356 −0.0686781 0.997639i 0.521878π-0.521878\pi
−0.0686781 + 0.997639i 0.521878π0.521878\pi
242242 0 0
243243 0 0
244244 −3.91140 −0.250402
245245 −2.07713 −0.132703
246246 0 0
247247 19.6144 1.24804
248248 2.89591 0.183890
249249 0 0
250250 14.5793 0.922076
251251 15.5736 0.982996 0.491498 0.870879i 0.336450π-0.336450\pi
0.491498 + 0.870879i 0.336450π0.336450\pi
252252 0 0
253253 0 0
254254 −31.5538 −1.97986
255255 0 0
256256 7.29797 0.456123
257257 6.94630 0.433298 0.216649 0.976250i 0.430487π-0.430487\pi
0.216649 + 0.976250i 0.430487π0.430487\pi
258258 0 0
259259 −0.498482 −0.0309742
260260 −2.25462 −0.139825
261261 0 0
262262 −16.0389 −0.990885
263263 −28.7587 −1.77334 −0.886668 0.462406i 0.846986π-0.846986\pi
−0.886668 + 0.462406i 0.846986π0.846986\pi
264264 0 0
265265 2.24265 0.137765
266266 −10.1011 −0.619338
267267 0 0
268268 −0.905583 −0.0553173
269269 −7.91233 −0.482424 −0.241212 0.970473i 0.577545π-0.577545\pi
−0.241212 + 0.970473i 0.577545π0.577545\pi
270270 0 0
271271 14.4421 0.877297 0.438649 0.898659i 0.355457π-0.355457\pi
0.438649 + 0.898659i 0.355457π0.355457\pi
272272 26.8118 1.62570
273273 0 0
274274 18.1861 1.09866
275275 0 0
276276 0 0
277277 −13.5300 −0.812940 −0.406470 0.913664i 0.633240π-0.633240\pi
−0.406470 + 0.913664i 0.633240π0.633240\pi
278278 −19.2513 −1.15462
279279 0 0
280280 −6.30027 −0.376513
281281 −5.25347 −0.313395 −0.156698 0.987647i 0.550085π-0.550085\pi
−0.156698 + 0.987647i 0.550085π0.550085\pi
282282 0 0
283283 −17.8919 −1.06356 −0.531781 0.846882i 0.678477π-0.678477\pi
−0.531781 + 0.846882i 0.678477π0.678477\pi
284284 −2.72695 −0.161815
285285 0 0
286286 0 0
287287 10.8212 0.638755
288288 0 0
289289 18.0995 1.06468
290290 −8.11845 −0.476732
291291 0 0
292292 0.366141 0.0214268
293293 −9.22950 −0.539193 −0.269596 0.962973i 0.586890π-0.586890\pi
−0.269596 + 0.962973i 0.586890π0.586890\pi
294294 0 0
295295 9.36256 0.545109
296296 0.567245 0.0329705
297297 0 0
298298 20.2395 1.17244
299299 9.08256 0.525258
300300 0 0
301301 16.5809 0.955708
302302 12.5620 0.722862
303303 0 0
304304 13.3276 0.764390
305305 −13.6694 −0.782708
306306 0 0
307307 −30.2755 −1.72791 −0.863957 0.503566i 0.832021π-0.832021\pi
−0.863957 + 0.503566i 0.832021π0.832021\pi
308308 0 0
309309 0 0
310310 −1.86513 −0.105932
311311 7.17472 0.406841 0.203420 0.979091i 0.434794π-0.434794\pi
0.203420 + 0.979091i 0.434794π0.434794\pi
312312 0 0
313313 −29.7516 −1.68166 −0.840831 0.541297i 0.817933π-0.817933\pi
−0.840831 + 0.541297i 0.817933π0.817933\pi
314314 −33.9976 −1.91859
315315 0 0
316316 −4.34630 −0.244499
317317 −29.2162 −1.64095 −0.820473 0.571685i 0.806290π-0.806290\pi
−0.820473 + 0.571685i 0.806290π0.806290\pi
318318 0 0
319319 0 0
320320 6.95865 0.389001
321321 0 0
322322 −4.67737 −0.260660
323323 17.4472 0.970791
324324 0 0
325325 25.4226 1.41019
326326 −13.9246 −0.771214
327327 0 0
328328 −12.3139 −0.679923
329329 21.2756 1.17296
330330 0 0
331331 30.5439 1.67885 0.839423 0.543478i 0.182893π-0.182893\pi
0.839423 + 0.543478i 0.182893π0.182893\pi
332332 −4.94545 −0.271417
333333 0 0
334334 30.3061 1.65827
335335 −3.16480 −0.172911
336336 0 0
337337 −23.1138 −1.25909 −0.629544 0.776965i 0.716758π-0.716758\pi
−0.629544 + 0.776965i 0.716758π0.716758\pi
338338 −47.6767 −2.59327
339339 0 0
340340 −2.00551 −0.108764
341341 0 0
342342 0 0
343343 20.1018 1.08539
344344 −18.8682 −1.01730
345345 0 0
346346 −35.5246 −1.90981
347347 25.5935 1.37393 0.686966 0.726690i 0.258942π-0.258942\pi
0.686966 + 0.726690i 0.258942π0.258942\pi
348348 0 0
349349 2.43088 0.130122 0.0650611 0.997881i 0.479276π-0.479276\pi
0.0650611 + 0.997881i 0.479276π0.479276\pi
350350 −13.0922 −0.699808
351351 0 0
352352 0 0
353353 0.825819 0.0439539 0.0219770 0.999758i 0.493004π-0.493004\pi
0.0219770 + 0.999758i 0.493004π0.493004\pi
354354 0 0
355355 −9.53004 −0.505802
356356 0.197852 0.0104861
357357 0 0
358358 −16.5094 −0.872549
359359 −29.7329 −1.56924 −0.784622 0.619975i 0.787143π-0.787143\pi
−0.784622 + 0.619975i 0.787143π0.787143\pi
360360 0 0
361361 −10.3273 −0.543544
362362 −18.8983 −0.993274
363363 0 0
364364 4.67679 0.245131
365365 1.27957 0.0669760
366366 0 0
367367 36.3364 1.89674 0.948372 0.317159i 0.102729π-0.102729\pi
0.948372 + 0.317159i 0.102729π0.102729\pi
368368 6.17141 0.321707
369369 0 0
370370 −0.365338 −0.0189930
371371 −4.65197 −0.241518
372372 0 0
373373 −0.309250 −0.0160123 −0.00800617 0.999968i 0.502548π-0.502548\pi
−0.00800617 + 0.999968i 0.502548π0.502548\pi
374374 0 0
375375 0 0
376376 −24.2105 −1.24856
377377 −32.7006 −1.68416
378378 0 0
379379 −16.7314 −0.859434 −0.429717 0.902964i 0.641387π-0.641387\pi
−0.429717 + 0.902964i 0.641387π0.641387\pi
380380 −0.996896 −0.0511397
381381 0 0
382382 −3.56495 −0.182399
383383 12.3894 0.633071 0.316535 0.948581i 0.397480π-0.397480\pi
0.316535 + 0.948581i 0.397480π0.397480\pi
384384 0 0
385385 0 0
386386 −6.34933 −0.323172
387387 0 0
388388 1.48609 0.0754447
389389 21.8529 1.10799 0.553994 0.832521i 0.313103π-0.313103\pi
0.553994 + 0.832521i 0.313103π0.313103\pi
390390 0 0
391391 8.07904 0.408575
392392 −4.90299 −0.247638
393393 0 0
394394 23.4380 1.18079
395395 −15.1893 −0.764256
396396 0 0
397397 21.9721 1.10275 0.551374 0.834258i 0.314104π-0.314104\pi
0.551374 + 0.834258i 0.314104π0.314104\pi
398398 8.76707 0.439453
399399 0 0
400400 17.2741 0.863705
401401 −16.2137 −0.809675 −0.404837 0.914389i 0.632672π-0.632672\pi
−0.404837 + 0.914389i 0.632672π0.632672\pi
402402 0 0
403403 −7.51261 −0.374230
404404 2.77755 0.138188
405405 0 0
406406 16.8403 0.835768
407407 0 0
408408 0 0
409409 −9.02007 −0.446014 −0.223007 0.974817i 0.571587π-0.571587\pi
−0.223007 + 0.974817i 0.571587π0.571587\pi
410410 7.93087 0.391678
411411 0 0
412412 0.914420 0.0450502
413413 −19.4209 −0.955642
414414 0 0
415415 −17.2832 −0.848397
416416 −11.6247 −0.569946
417417 0 0
418418 0 0
419419 22.7915 1.11344 0.556718 0.830702i 0.312060π-0.312060\pi
0.556718 + 0.830702i 0.312060π0.312060\pi
420420 0 0
421421 20.5745 1.00274 0.501370 0.865233i 0.332829π-0.332829\pi
0.501370 + 0.865233i 0.332829π0.332829\pi
422422 16.2606 0.791554
423423 0 0
424424 5.29369 0.257084
425425 22.6137 1.09692
426426 0 0
427427 28.3547 1.37218
428428 3.44277 0.166412
429429 0 0
430430 12.1522 0.586030
431431 5.19653 0.250308 0.125154 0.992137i 0.460057π-0.460057\pi
0.125154 + 0.992137i 0.460057π0.460057\pi
432432 0 0
433433 3.76824 0.181090 0.0905451 0.995892i 0.471139π-0.471139\pi
0.0905451 + 0.995892i 0.471139π0.471139\pi
434434 3.86887 0.185712
435435 0 0
436436 4.76620 0.228259
437437 4.01592 0.192108
438438 0 0
439439 11.1730 0.533257 0.266628 0.963799i 0.414090π-0.414090\pi
0.266628 + 0.963799i 0.414090π0.414090\pi
440440 0 0
441441 0 0
442442 −59.9889 −2.85338
443443 16.1963 0.769509 0.384755 0.923019i 0.374286π-0.374286\pi
0.384755 + 0.923019i 0.374286π0.374286\pi
444444 0 0
445445 0.691446 0.0327777
446446 32.8032 1.55328
447447 0 0
448448 −14.4345 −0.681964
449449 3.27004 0.154323 0.0771614 0.997019i 0.475414π-0.475414\pi
0.0771614 + 0.997019i 0.475414π0.475414\pi
450450 0 0
451451 0 0
452452 −4.01444 −0.188823
453453 0 0
454454 −6.35343 −0.298181
455455 16.3443 0.766231
456456 0 0
457457 15.2626 0.713954 0.356977 0.934113i 0.383807π-0.383807\pi
0.356977 + 0.934113i 0.383807π0.383807\pi
458458 29.7519 1.39021
459459 0 0
460460 −0.461618 −0.0215231
461461 7.82454 0.364425 0.182213 0.983259i 0.441674π-0.441674\pi
0.182213 + 0.983259i 0.441674π0.441674\pi
462462 0 0
463463 16.8395 0.782599 0.391299 0.920263i 0.372026π-0.372026\pi
0.391299 + 0.920263i 0.372026π0.372026\pi
464464 −22.2194 −1.03151
465465 0 0
466466 15.9083 0.736937
467467 −38.0169 −1.75921 −0.879606 0.475704i 0.842193π-0.842193\pi
−0.879606 + 0.475704i 0.842193π0.842193\pi
468468 0 0
469469 6.56480 0.303134
470470 15.5929 0.719249
471471 0 0
472472 22.1000 1.01723
473473 0 0
474474 0 0
475475 11.2408 0.515762
476476 4.16006 0.190676
477477 0 0
478478 21.0425 0.962460
479479 −15.5460 −0.710317 −0.355158 0.934806i 0.615573π-0.615573\pi
−0.355158 + 0.934806i 0.615573π0.615573\pi
480480 0 0
481481 −1.47156 −0.0670973
482482 3.24174 0.147657
483483 0 0
484484 0 0
485485 5.19353 0.235826
486486 0 0
487487 −21.1203 −0.957053 −0.478526 0.878073i 0.658829π-0.658829\pi
−0.478526 + 0.878073i 0.658829π0.658829\pi
488488 −32.2661 −1.46062
489489 0 0
490490 3.15781 0.142655
491491 41.3904 1.86792 0.933960 0.357377i 0.116329π-0.116329\pi
0.933960 + 0.357377i 0.116329π0.116329\pi
492492 0 0
493493 −29.0875 −1.31004
494494 −29.8192 −1.34163
495495 0 0
496496 −5.10467 −0.229206
497497 19.7683 0.886732
498498 0 0
499499 7.07932 0.316914 0.158457 0.987366i 0.449348π-0.449348\pi
0.158457 + 0.987366i 0.449348π0.449348\pi
500500 −2.98465 −0.133478
501501 0 0
502502 −23.6761 −1.05672
503503 44.1749 1.96966 0.984830 0.173524i 0.0555154π-0.0555154\pi
0.984830 + 0.173524i 0.0555154π0.0555154\pi
504504 0 0
505505 9.70686 0.431950
506506 0 0
507507 0 0
508508 6.45964 0.286600
509509 25.8703 1.14668 0.573341 0.819317i 0.305647π-0.305647\pi
0.573341 + 0.819317i 0.305647π0.305647\pi
510510 0 0
511511 −2.65424 −0.117417
512512 15.3392 0.677905
513513 0 0
514514 −10.5603 −0.465793
515515 3.19568 0.140818
516516 0 0
517517 0 0
518518 0.757828 0.0332971
519519 0 0
520520 −18.5989 −0.815615
521521 −25.5813 −1.12074 −0.560369 0.828243i 0.689341π-0.689341\pi
−0.560369 + 0.828243i 0.689341π0.689341\pi
522522 0 0
523523 7.58921 0.331853 0.165926 0.986138i 0.446939π-0.446939\pi
0.165926 + 0.986138i 0.446939π0.446939\pi
524524 3.28345 0.143438
525525 0 0
526526 43.7210 1.90633
527527 −6.68256 −0.291097
528528 0 0
529529 −21.1404 −0.919148
530530 −3.40944 −0.148097
531531 0 0
532532 2.06788 0.0896540
533533 31.9450 1.38369
534534 0 0
535535 12.0316 0.520173
536536 −7.47038 −0.322671
537537 0 0
538538 12.0289 0.518603
539539 0 0
540540 0 0
541541 31.6585 1.36111 0.680553 0.732699i 0.261740π-0.261740\pi
0.680553 + 0.732699i 0.261740π0.261740\pi
542542 −21.9560 −0.943090
543543 0 0
544544 −10.3403 −0.443336
545545 16.6567 0.713495
546546 0 0
547547 −30.8160 −1.31760 −0.658798 0.752320i 0.728935π-0.728935\pi
−0.658798 + 0.752320i 0.728935π0.728935\pi
548548 −3.72303 −0.159040
549549 0 0
550550 0 0
551551 −14.4588 −0.615966
552552 0 0
553553 31.5074 1.33983
554554 20.5693 0.873906
555555 0 0
556556 3.94110 0.167140
557557 4.98818 0.211356 0.105678 0.994400i 0.466299π-0.466299\pi
0.105678 + 0.994400i 0.466299π0.466299\pi
558558 0 0
559559 48.9481 2.07029
560560 11.1056 0.469297
561561 0 0
562562 7.98670 0.336898
563563 −3.03235 −0.127798 −0.0638992 0.997956i 0.520354π-0.520354\pi
−0.0638992 + 0.997956i 0.520354π0.520354\pi
564564 0 0
565565 −14.0295 −0.590225
566566 27.2005 1.14332
567567 0 0
568568 −22.4953 −0.943882
569569 47.5101 1.99173 0.995863 0.0908639i 0.0289628π-0.0289628\pi
0.995863 + 0.0908639i 0.0289628π0.0289628\pi
570570 0 0
571571 −8.47272 −0.354572 −0.177286 0.984159i 0.556732π-0.556732\pi
−0.177286 + 0.984159i 0.556732π0.556732\pi
572572 0 0
573573 0 0
574574 −16.4512 −0.686658
575575 5.20510 0.217068
576576 0 0
577577 −35.2635 −1.46804 −0.734020 0.679128i 0.762358π-0.762358\pi
−0.734020 + 0.679128i 0.762358π0.762358\pi
578578 −27.5162 −1.14452
579579 0 0
580580 1.66200 0.0690106
581581 35.8508 1.48734
582582 0 0
583583 0 0
584584 3.02039 0.124984
585585 0 0
586586 14.0313 0.579630
587587 −25.3219 −1.04515 −0.522574 0.852594i 0.675028π-0.675028\pi
−0.522574 + 0.852594i 0.675028π0.675028\pi
588588 0 0
589589 −3.32176 −0.136871
590590 −14.2336 −0.585990
591591 0 0
592592 −0.999894 −0.0410954
593593 39.8626 1.63696 0.818480 0.574535i 0.194817π-0.194817\pi
0.818480 + 0.574535i 0.194817π0.194817\pi
594594 0 0
595595 14.5384 0.596017
596596 −4.14340 −0.169720
597597 0 0
598598 −13.8080 −0.564649
599599 −31.9030 −1.30352 −0.651761 0.758425i 0.725969π-0.725969\pi
−0.651761 + 0.758425i 0.725969π0.725969\pi
600600 0 0
601601 −18.0780 −0.737417 −0.368709 0.929545i 0.620200π-0.620200\pi
−0.368709 + 0.929545i 0.620200π0.620200\pi
602602 −25.2075 −1.02738
603603 0 0
604604 −2.57167 −0.104640
605605 0 0
606606 0 0
607607 1.54758 0.0628145 0.0314072 0.999507i 0.490001π-0.490001\pi
0.0314072 + 0.999507i 0.490001π0.490001\pi
608608 −5.13993 −0.208452
609609 0 0
610610 20.7812 0.841407
611611 62.8073 2.54091
612612 0 0
613613 −10.7046 −0.432355 −0.216177 0.976354i 0.569359π-0.569359\pi
−0.216177 + 0.976354i 0.569359π0.569359\pi
614614 46.0270 1.85750
615615 0 0
616616 0 0
617617 32.0693 1.29106 0.645530 0.763735i 0.276636π-0.276636\pi
0.645530 + 0.763735i 0.276636π0.276636\pi
618618 0 0
619619 14.2834 0.574098 0.287049 0.957916i 0.407326π-0.407326\pi
0.287049 + 0.957916i 0.407326π0.407326\pi
620620 0.381826 0.0153345
621621 0 0
622622 −10.9075 −0.437352
623623 −1.43428 −0.0574632
624624 0 0
625625 8.65427 0.346171
626626 45.2306 1.80778
627627 0 0
628628 6.95993 0.277731
629629 −1.30897 −0.0521920
630630 0 0
631631 −20.6442 −0.821833 −0.410917 0.911673i 0.634791π-0.634791\pi
−0.410917 + 0.911673i 0.634791π0.634791\pi
632632 −35.8537 −1.42618
633633 0 0
634634 44.4166 1.76401
635635 22.5749 0.895857
636636 0 0
637637 12.7194 0.503962
638638 0 0
639639 0 0
640640 −14.3758 −0.568252
641641 −11.7046 −0.462304 −0.231152 0.972918i 0.574249π-0.574249\pi
−0.231152 + 0.972918i 0.574249π0.574249\pi
642642 0 0
643643 18.4574 0.727888 0.363944 0.931421i 0.381430π-0.381430\pi
0.363944 + 0.931421i 0.381430π0.381430\pi
644644 0.957543 0.0377325
645645 0 0
646646 −26.5246 −1.04360
647647 −26.2873 −1.03346 −0.516730 0.856148i 0.672851π-0.672851\pi
−0.516730 + 0.856148i 0.672851π0.672851\pi
648648 0 0
649649 0 0
650650 −38.6492 −1.51595
651651 0 0
652652 2.85063 0.111639
653653 −27.9054 −1.09202 −0.546011 0.837778i 0.683854π-0.683854\pi
−0.546011 + 0.837778i 0.683854π0.683854\pi
654654 0 0
655655 11.4749 0.448361
656656 21.7060 0.847477
657657 0 0
658658 −32.3447 −1.26093
659659 −45.9712 −1.79078 −0.895392 0.445278i 0.853105π-0.853105\pi
−0.895392 + 0.445278i 0.853105π0.853105\pi
660660 0 0
661661 −12.1654 −0.473181 −0.236590 0.971609i 0.576030π-0.576030\pi
−0.236590 + 0.971609i 0.576030π0.576030\pi
662662 −46.4351 −1.80475
663663 0 0
664664 −40.7962 −1.58320
665665 7.22675 0.280241
666666 0 0
667667 −6.69523 −0.259240
668668 −6.20421 −0.240048
669669 0 0
670670 4.81135 0.185879
671671 0 0
672672 0 0
673673 38.4548 1.48232 0.741161 0.671327i 0.234275π-0.234275\pi
0.741161 + 0.671327i 0.234275π0.234275\pi
674674 35.1392 1.35351
675675 0 0
676676 9.76030 0.375396
677677 −2.09086 −0.0803583 −0.0401791 0.999192i 0.512793π-0.512793\pi
−0.0401791 + 0.999192i 0.512793π0.512793\pi
678678 0 0
679679 −10.7730 −0.413431
680680 −16.5439 −0.634431
681681 0 0
682682 0 0
683683 −41.6302 −1.59294 −0.796468 0.604681i 0.793301π-0.793301\pi
−0.796468 + 0.604681i 0.793301π0.793301\pi
684684 0 0
685685 −13.0111 −0.497129
686686 −30.5602 −1.16679
687687 0 0
688688 33.2593 1.26800
689689 −13.7330 −0.523185
690690 0 0
691691 20.5196 0.780603 0.390301 0.920687i 0.372371π-0.372371\pi
0.390301 + 0.920687i 0.372371π0.372371\pi
692692 7.27253 0.276460
693693 0 0
694694 −38.9091 −1.47697
695695 13.7732 0.522447
696696 0 0
697697 28.4155 1.07631
698698 −3.69560 −0.139881
699699 0 0
700700 2.68021 0.101303
701701 12.6814 0.478972 0.239486 0.970900i 0.423021π-0.423021\pi
0.239486 + 0.970900i 0.423021π0.423021\pi
702702 0 0
703703 −0.650661 −0.0245401
704704 0 0
705705 0 0
706706 −1.25547 −0.0472502
707707 −20.1351 −0.757259
708708 0 0
709709 19.5544 0.734380 0.367190 0.930146i 0.380320π-0.380320\pi
0.367190 + 0.930146i 0.380320π0.380320\pi
710710 14.4883 0.543735
711711 0 0
712712 1.63213 0.0611667
713713 −1.53816 −0.0576045
714714 0 0
715715 0 0
716716 3.37978 0.126308
717717 0 0
718718 45.2021 1.68693
719719 −32.9171 −1.22760 −0.613800 0.789462i 0.710360π-0.710360\pi
−0.613800 + 0.789462i 0.710360π0.710360\pi
720720 0 0
721721 −6.62886 −0.246872
722722 15.7004 0.584307
723723 0 0
724724 3.86883 0.143784
725725 −18.7403 −0.695997
726726 0 0
727727 5.34049 0.198068 0.0990339 0.995084i 0.468425π-0.468425\pi
0.0990339 + 0.995084i 0.468425π0.468425\pi
728728 38.5800 1.42987
729729 0 0
730730 −1.94530 −0.0719988
731731 43.5400 1.61038
732732 0 0
733733 −1.98487 −0.0733128 −0.0366564 0.999328i 0.511671π-0.511671\pi
−0.0366564 + 0.999328i 0.511671π0.511671\pi
734734 −55.2412 −2.03899
735735 0 0
736736 −2.38007 −0.0877307
737737 0 0
738738 0 0
739739 −6.52951 −0.240192 −0.120096 0.992762i 0.538320π-0.538320\pi
−0.120096 + 0.992762i 0.538320π0.538320\pi
740740 0.0747915 0.00274939
741741 0 0
742742 7.07227 0.259631
743743 7.07132 0.259421 0.129711 0.991552i 0.458595π-0.458595\pi
0.129711 + 0.991552i 0.458595π0.458595\pi
744744 0 0
745745 −14.4802 −0.530513
746746 0.470144 0.0172132
747747 0 0
748748 0 0
749749 −24.9575 −0.911926
750750 0 0
751751 −24.6750 −0.900403 −0.450202 0.892927i 0.648648π-0.648648\pi
−0.450202 + 0.892927i 0.648648π0.648648\pi
752752 42.6763 1.55624
753753 0 0
754754 49.7138 1.81047
755755 −8.98738 −0.327084
756756 0 0
757757 4.53023 0.164654 0.0823271 0.996605i 0.473765π-0.473765\pi
0.0823271 + 0.996605i 0.473765π0.473765\pi
758758 25.4363 0.923888
759759 0 0
760760 −8.22364 −0.298303
761761 33.9151 1.22942 0.614710 0.788753i 0.289273π-0.289273\pi
0.614710 + 0.788753i 0.289273π0.289273\pi
762762 0 0
763763 −34.5513 −1.25084
764764 0.729810 0.0264036
765765 0 0
766766 −18.8353 −0.680548
767767 −57.3321 −2.07014
768768 0 0
769769 2.78366 0.100381 0.0501906 0.998740i 0.484017π-0.484017\pi
0.0501906 + 0.998740i 0.484017π0.484017\pi
770770 0 0
771771 0 0
772772 1.29982 0.0467817
773773 −7.15532 −0.257359 −0.128680 0.991686i 0.541074π-0.541074\pi
−0.128680 + 0.991686i 0.541074π0.541074\pi
774774 0 0
775775 −4.30539 −0.154654
776776 12.2591 0.440077
777777 0 0
778778 −33.2224 −1.19108
779779 14.1247 0.506071
780780 0 0
781781 0 0
782782 −12.2823 −0.439216
783783 0 0
784784 8.64259 0.308664
785785 24.3233 0.868135
786786 0 0
787787 20.0978 0.716411 0.358205 0.933643i 0.383389π-0.383389\pi
0.358205 + 0.933643i 0.383389π0.383389\pi
788788 −4.79819 −0.170928
789789 0 0
790790 23.0919 0.821571
791791 29.1016 1.03474
792792 0 0
793793 83.7053 2.97246
794794 −33.4036 −1.18545
795795 0 0
796796 −1.79478 −0.0636143
797797 21.8979 0.775663 0.387832 0.921730i 0.373224π-0.373224\pi
0.387832 + 0.921730i 0.373224π0.373224\pi
798798 0 0
799799 55.8678 1.97646
800800 −6.66195 −0.235536
801801 0 0
802802 24.6493 0.870396
803803 0 0
804804 0 0
805805 3.34638 0.117945
806806 11.4212 0.402295
807807 0 0
808808 22.9127 0.806065
809809 −5.33571 −0.187593 −0.0937967 0.995591i 0.529900π-0.529900\pi
−0.0937967 + 0.995591i 0.529900π0.529900\pi
810810 0 0
811811 7.04918 0.247530 0.123765 0.992312i 0.460503π-0.460503\pi
0.123765 + 0.992312i 0.460503π0.460503\pi
812812 −3.44751 −0.120984
813813 0 0
814814 0 0
815815 9.96226 0.348963
816816 0 0
817817 21.6428 0.757186
818818 13.7130 0.479462
819819 0 0
820820 −1.62360 −0.0566984
821821 2.35318 0.0821264 0.0410632 0.999157i 0.486926π-0.486926\pi
0.0410632 + 0.999157i 0.486926π0.486926\pi
822822 0 0
823823 −48.7811 −1.70040 −0.850201 0.526457i 0.823520π-0.823520\pi
−0.850201 + 0.526457i 0.823520π0.823520\pi
824824 7.54328 0.262783
825825 0 0
826826 29.5251 1.02731
827827 21.2670 0.739527 0.369764 0.929126i 0.379439π-0.379439\pi
0.369764 + 0.929126i 0.379439π0.379439\pi
828828 0 0
829829 24.7732 0.860408 0.430204 0.902732i 0.358442π-0.358442\pi
0.430204 + 0.902732i 0.358442π0.358442\pi
830830 26.2751 0.912022
831831 0 0
832832 −42.6117 −1.47729
833833 11.3141 0.392010
834834 0 0
835835 −21.6822 −0.750344
836836 0 0
837837 0 0
838838 −34.6492 −1.19694
839839 −3.50888 −0.121140 −0.0605701 0.998164i 0.519292π-0.519292\pi
−0.0605701 + 0.998164i 0.519292π0.519292\pi
840840 0 0
841841 −4.89470 −0.168783
842842 −31.2789 −1.07794
843843 0 0
844844 −3.32885 −0.114584
845845 34.1099 1.17342
846846 0 0
847847 0 0
848848 −9.33129 −0.320438
849849 0 0
850850 −34.3789 −1.17919
851851 −0.301292 −0.0103282
852852 0 0
853853 2.29563 0.0786008 0.0393004 0.999227i 0.487487π-0.487487\pi
0.0393004 + 0.999227i 0.487487π0.487487\pi
854854 −43.1069 −1.47509
855855 0 0
856856 28.4002 0.970700
857857 −15.8536 −0.541548 −0.270774 0.962643i 0.587280π-0.587280\pi
−0.270774 + 0.962643i 0.587280π0.587280\pi
858858 0 0
859859 4.97552 0.169763 0.0848813 0.996391i 0.472949π-0.472949\pi
0.0848813 + 0.996391i 0.472949π0.472949\pi
860860 −2.48777 −0.0848324
861861 0 0
862862 −7.90014 −0.269080
863863 40.3432 1.37330 0.686650 0.726988i 0.259081π-0.259081\pi
0.686650 + 0.726988i 0.259081π0.259081\pi
864864 0 0
865865 25.4158 0.864161
866866 −5.72876 −0.194671
867867 0 0
868868 −0.792029 −0.0268832
869869 0 0
870870 0 0
871871 19.3798 0.656660
872872 39.3175 1.33146
873873 0 0
874874 −6.10530 −0.206515
875875 21.6365 0.731447
876876 0 0
877877 −44.3405 −1.49727 −0.748637 0.662980i 0.769291π-0.769291\pi
−0.748637 + 0.662980i 0.769291π0.769291\pi
878878 −16.9860 −0.573248
879879 0 0
880880 0 0
881881 −48.6174 −1.63796 −0.818981 0.573820i 0.805461π-0.805461\pi
−0.818981 + 0.573820i 0.805461π0.805461\pi
882882 0 0
883883 −11.8277 −0.398033 −0.199017 0.979996i 0.563775π-0.563775\pi
−0.199017 + 0.979996i 0.563775π0.563775\pi
884884 12.2808 0.413049
885885 0 0
886886 −24.6228 −0.827218
887887 −17.6043 −0.591094 −0.295547 0.955328i 0.595502π-0.595502\pi
−0.295547 + 0.955328i 0.595502π0.595502\pi
888888 0 0
889889 −46.8275 −1.57054
890890 −1.05119 −0.0352359
891891 0 0
892892 −6.71541 −0.224849
893893 27.7707 0.929312
894894 0 0
895895 11.8115 0.394815
896896 29.8199 0.996213
897897 0 0
898898 −4.97135 −0.165896
899899 5.53794 0.184701
900900 0 0
901901 −12.2157 −0.406963
902902 0 0
903903 0 0
904904 −33.1161 −1.10142
905905 13.5206 0.449442
906906 0 0
907907 31.4287 1.04357 0.521786 0.853076i 0.325266π-0.325266\pi
0.521786 + 0.853076i 0.325266π0.325266\pi
908908 1.30066 0.0431641
909909 0 0
910910 −24.8477 −0.823695
911911 −25.4380 −0.842798 −0.421399 0.906875i 0.638461π-0.638461\pi
−0.421399 + 0.906875i 0.638461π0.638461\pi
912912 0 0
913913 0 0
914914 −23.2033 −0.767497
915915 0 0
916916 −6.09075 −0.201244
917917 −23.8026 −0.786030
918918 0 0
919919 −33.3699 −1.10077 −0.550386 0.834910i 0.685519π-0.685519\pi
−0.550386 + 0.834910i 0.685519π0.685519\pi
920920 −3.80800 −0.125546
921921 0 0
922922 −11.8954 −0.391755
923923 58.3577 1.92087
924924 0 0
925925 −0.843332 −0.0277286
926926 −25.6007 −0.841290
927927 0 0
928928 8.56915 0.281296
929929 −14.4401 −0.473765 −0.236883 0.971538i 0.576126π-0.576126\pi
−0.236883 + 0.971538i 0.576126π0.576126\pi
930930 0 0
931931 5.62399 0.184319
932932 −3.25672 −0.106677
933933 0 0
934934 57.7960 1.89114
935935 0 0
936936 0 0
937937 29.6541 0.968757 0.484379 0.874859i 0.339046π-0.339046\pi
0.484379 + 0.874859i 0.339046π0.339046\pi
938938 −9.98028 −0.325868
939939 0 0
940940 −3.19216 −0.104117
941941 43.1420 1.40639 0.703194 0.710998i 0.251756π-0.251756\pi
0.703194 + 0.710998i 0.251756π0.251756\pi
942942 0 0
943943 6.54054 0.212989
944944 −38.9560 −1.26791
945945 0 0
946946 0 0
947947 37.0608 1.20432 0.602158 0.798377i 0.294308π-0.294308\pi
0.602158 + 0.798377i 0.294308π0.294308\pi
948948 0 0
949949 −7.83554 −0.254352
950950 −17.0890 −0.554442
951951 0 0
952952 34.3174 1.11223
953953 25.1122 0.813463 0.406731 0.913548i 0.366669π-0.366669\pi
0.406731 + 0.913548i 0.366669π0.366669\pi
954954 0 0
955955 2.55051 0.0825326
956956 −4.30778 −0.139323
957957 0 0
958958 23.6342 0.763587
959959 26.9892 0.871526
960960 0 0
961961 −29.7277 −0.958959
962962 2.23717 0.0721292
963963 0 0
964964 −0.663644 −0.0213745
965965 4.54257 0.146231
966966 0 0
967967 7.41108 0.238324 0.119162 0.992875i 0.461979π-0.461979\pi
0.119162 + 0.992875i 0.461979π0.461979\pi
968968 0 0
969969 0 0
970970 −7.89557 −0.253512
971971 2.88466 0.0925733 0.0462866 0.998928i 0.485261π-0.485261\pi
0.0462866 + 0.998928i 0.485261π0.485261\pi
972972 0 0
973973 −28.5700 −0.915913
974974 32.1086 1.02883
975975 0 0
976976 56.8761 1.82056
977977 −17.9632 −0.574693 −0.287346 0.957827i 0.592773π-0.592773\pi
−0.287346 + 0.957827i 0.592773π0.592773\pi
978978 0 0
979979 0 0
980980 −0.646461 −0.0206504
981981 0 0
982982 −62.9246 −2.00800
983983 −31.5601 −1.00661 −0.503305 0.864109i 0.667883π-0.667883\pi
−0.503305 + 0.864109i 0.667883π0.667883\pi
984984 0 0
985985 −16.7685 −0.534290
986986 44.2210 1.40828
987987 0 0
988988 6.10455 0.194211
989989 10.0218 0.318675
990990 0 0
991991 28.4307 0.903132 0.451566 0.892238i 0.350866π-0.350866\pi
0.451566 + 0.892238i 0.350866π0.350866\pi
992992 1.96867 0.0625054
993993 0 0
994994 −30.0533 −0.953232
995995 −6.27233 −0.198846
996996 0 0
997997 41.4489 1.31270 0.656350 0.754457i 0.272099π-0.272099\pi
0.656350 + 0.754457i 0.272099π0.272099\pi
998998 −10.7625 −0.340681
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 9801.2.a.bp.1.2 yes 5
3.2 odd 2 9801.2.a.bo.1.4 yes 5
11.10 odd 2 9801.2.a.bn.1.4 5
33.32 even 2 9801.2.a.bq.1.2 yes 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9801.2.a.bn.1.4 5 11.10 odd 2
9801.2.a.bo.1.4 yes 5 3.2 odd 2
9801.2.a.bp.1.2 yes 5 1.1 even 1 trivial
9801.2.a.bq.1.2 yes 5 33.32 even 2