Properties

Label 1323.2.c.d.1322.2
Level 13231323
Weight 22
Character 1323.1322
Analytic conductor 10.56410.564
Analytic rank 00
Dimension 1212
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(1322,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.1322");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1323=3372 1323 = 3^{3} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1323.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: 10.564208187410.5642081874
Analytic rank: 00
Dimension: 1212
Coefficient field: 12.0.13026266817859584.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x129x10+59x8180x6+403x4198x2+81 x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 2634 2^{6}\cdot 3^{4}
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1322.2
Root 0.6179420.356769i-0.617942 - 0.356769i of defining polynomial
Character χ\chi == 1323.1322
Dual form 1323.2.c.d.1322.12

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) == q2.49086iq24.20440q4+1.23588q5+5.49086iq83.07842iq105.49086iq11+2.96793iq13+5.26819q16+4.31430q175.55019iq195.19615q2013.6770q221.63148iq233.47259q25+7.39272q26+0.509136iq298.13244iq312.14061iq3210.7463iq343.06379q3713.8248q38+6.78607iq40+0.354034q410.0637877q43+23.0858iq444.06379q469.86449q47+8.64975iq5012.4784iq52+4.12234iq536.78607iq55+1.26819q583.07842q596.89655iq6120.2568q62+5.20440q64+3.66802iq6512.3320q6718.1391q684.63148iq71+7.03869iq73+7.63148iq74+23.3352iq760.331977q79+6.51087q800.881850iq82+7.39272q83+5.33198q85+0.158887iq86+30.1496q88+3.43245q89+6.85939iq92+24.5711iq946.85939iq954.45644iq97+O(q100)q-2.49086i q^{2} -4.20440 q^{4} +1.23588 q^{5} +5.49086i q^{8} -3.07842i q^{10} -5.49086i q^{11} +2.96793i q^{13} +5.26819 q^{16} +4.31430 q^{17} -5.55019i q^{19} -5.19615 q^{20} -13.6770 q^{22} -1.63148i q^{23} -3.47259 q^{25} +7.39272 q^{26} +0.509136i q^{29} -8.13244i q^{31} -2.14061i q^{32} -10.7463i q^{34} -3.06379 q^{37} -13.8248 q^{38} +6.78607i q^{40} +0.354034 q^{41} -0.0637877 q^{43} +23.0858i q^{44} -4.06379 q^{46} -9.86449 q^{47} +8.64975i q^{50} -12.4784i q^{52} +4.12234i q^{53} -6.78607i q^{55} +1.26819 q^{58} -3.07842 q^{59} -6.89655i q^{61} -20.2568 q^{62} +5.20440 q^{64} +3.66802i q^{65} -12.3320 q^{67} -18.1391 q^{68} -4.63148i q^{71} +7.03869i q^{73} +7.63148i q^{74} +23.3352i q^{76} -0.331977 q^{79} +6.51087 q^{80} -0.881850i q^{82} +7.39272 q^{83} +5.33198 q^{85} +0.158887i q^{86} +30.1496 q^{88} +3.43245 q^{89} +6.85939i q^{92} +24.5711i q^{94} -6.85939i q^{95} -4.45644i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q16q4+8q1640q22+48q2516q37+20q4328q4640q58+28q6472q67+72q7912q85+148q88+O(q100) 12 q - 16 q^{4} + 8 q^{16} - 40 q^{22} + 48 q^{25} - 16 q^{37} + 20 q^{43} - 28 q^{46} - 40 q^{58} + 28 q^{64} - 72 q^{67} + 72 q^{79} - 12 q^{85} + 148 q^{88}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1323Z)×\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times.

nn 785785 10811081
χ(n)\chi(n) 1-1 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 − 2.49086i − 1.76131i −0.473761 0.880653i 0.657104π-0.657104\pi
0.473761 0.880653i 0.342896π-0.342896\pi
33 0 0
44 −4.20440 −2.10220
55 1.23588 0.552704 0.276352 0.961056i 0.410874π-0.410874\pi
0.276352 + 0.961056i 0.410874π0.410874\pi
66 0 0
77 0 0
88 5.49086i 1.94131i
99 0 0
1010 − 3.07842i − 0.973481i
1111 − 5.49086i − 1.65556i −0.561055 0.827779i 0.689604π-0.689604\pi
0.561055 0.827779i 0.310396π-0.310396\pi
1212 0 0
1313 2.96793i 0.823157i 0.911374 + 0.411578i 0.135022π0.135022\pi
−0.911374 + 0.411578i 0.864978π0.864978\pi
1414 0 0
1515 0 0
1616 5.26819 1.31705
1717 4.31430 1.04637 0.523186 0.852219i 0.324743π-0.324743\pi
0.523186 + 0.852219i 0.324743π0.324743\pi
1818 0 0
1919 − 5.55019i − 1.27330i −0.771153 0.636650i 0.780320π-0.780320\pi
0.771153 0.636650i 0.219680π-0.219680\pi
2020 −5.19615 −1.16190
2121 0 0
2222 −13.6770 −2.91594
2323 − 1.63148i − 0.340187i −0.985428 0.170093i 0.945593π-0.945593\pi
0.985428 0.170093i 0.0544069π-0.0544069\pi
2424 0 0
2525 −3.47259 −0.694518
2626 7.39272 1.44983
2727 0 0
2828 0 0
2929 0.509136i 0.0945443i 0.998882 + 0.0472721i 0.0150528π0.0150528\pi
−0.998882 + 0.0472721i 0.984947π0.984947\pi
3030 0 0
3131 − 8.13244i − 1.46063i −0.683111 0.730314i 0.739374π-0.739374\pi
0.683111 0.730314i 0.260626π-0.260626\pi
3232 − 2.14061i − 0.378411i
3333 0 0
3434 − 10.7463i − 1.84298i
3535 0 0
3636 0 0
3737 −3.06379 −0.503684 −0.251842 0.967768i 0.581036π-0.581036\pi
−0.251842 + 0.967768i 0.581036π0.581036\pi
3838 −13.8248 −2.24267
3939 0 0
4040 6.78607i 1.07297i
4141 0.354034 0.0552908 0.0276454 0.999618i 0.491199π-0.491199\pi
0.0276454 + 0.999618i 0.491199π0.491199\pi
4242 0 0
4343 −0.0637877 −0.00972754 −0.00486377 0.999988i 0.501548π-0.501548\pi
−0.00486377 + 0.999988i 0.501548π0.501548\pi
4444 23.0858i 3.48031i
4545 0 0
4646 −4.06379 −0.599173
4747 −9.86449 −1.43888 −0.719442 0.694553i 0.755602π-0.755602\pi
−0.719442 + 0.694553i 0.755602π0.755602\pi
4848 0 0
4949 0 0
5050 8.64975i 1.22326i
5151 0 0
5252 − 12.4784i − 1.73044i
5353 4.12234i 0.566247i 0.959083 + 0.283124i 0.0913706π0.0913706\pi
−0.959083 + 0.283124i 0.908629π0.908629\pi
5454 0 0
5555 − 6.78607i − 0.915034i
5656 0 0
5757 0 0
5858 1.26819 0.166521
5959 −3.07842 −0.400776 −0.200388 0.979717i 0.564220π-0.564220\pi
−0.200388 + 0.979717i 0.564220π0.564220\pi
6060 0 0
6161 − 6.89655i − 0.883013i −0.897258 0.441507i 0.854444π-0.854444\pi
0.897258 0.441507i 0.145556π-0.145556\pi
6262 −20.2568 −2.57262
6363 0 0
6464 5.20440 0.650550
6565 3.66802i 0.454962i
6666 0 0
6767 −12.3320 −1.50659 −0.753295 0.657682i 0.771537π-0.771537\pi
−0.753295 + 0.657682i 0.771537π0.771537\pi
6868 −18.1391 −2.19968
6969 0 0
7070 0 0
7171 − 4.63148i − 0.549655i −0.961494 0.274828i 0.911379π-0.911379\pi
0.961494 0.274828i 0.0886208π-0.0886208\pi
7272 0 0
7373 7.03869i 0.823816i 0.911225 + 0.411908i 0.135137π0.135137\pi
−0.911225 + 0.411908i 0.864863π0.864863\pi
7474 7.63148i 0.887141i
7575 0 0
7676 23.3352i 2.67673i
7777 0 0
7878 0 0
7979 −0.331977 −0.0373503 −0.0186752 0.999826i 0.505945π-0.505945\pi
−0.0186752 + 0.999826i 0.505945π0.505945\pi
8080 6.51087 0.727937
8181 0 0
8282 − 0.881850i − 0.0973841i
8383 7.39272 0.811457 0.405728 0.913994i 0.367018π-0.367018\pi
0.405728 + 0.913994i 0.367018π0.367018\pi
8484 0 0
8585 5.33198 0.578334
8686 0.158887i 0.0171332i
8787 0 0
8888 30.1496 3.21396
8989 3.43245 0.363839 0.181920 0.983313i 0.441769π-0.441769\pi
0.181920 + 0.983313i 0.441769π0.441769\pi
9090 0 0
9191 0 0
9292 6.85939i 0.715140i
9393 0 0
9494 24.5711i 2.53432i
9595 − 6.85939i − 0.703758i
9696 0 0
9797 − 4.45644i − 0.452482i −0.974071 0.226241i 0.927356π-0.927356\pi
0.974071 0.226241i 0.0726438π-0.0726438\pi
9898 0 0
9999 0 0
100100 14.6002 1.46002
101101 9.15642 0.911098 0.455549 0.890211i 0.349443π-0.349443\pi
0.455549 + 0.890211i 0.349443π0.349443\pi
102102 0 0
103103 − 4.20382i − 0.414215i −0.978318 0.207107i 0.933595π-0.933595\pi
0.978318 0.207107i 0.0664049π-0.0664049\pi
104104 −16.2965 −1.59801
105105 0 0
106106 10.2682 0.997335
107107 10.3137i 0.997063i 0.866871 + 0.498532i 0.166127π0.166127\pi
−0.866871 + 0.498532i 0.833873π0.833873\pi
108108 0 0
109109 0.127575 0.0122195 0.00610976 0.999981i 0.498055π-0.498055\pi
0.00610976 + 0.999981i 0.498055π0.498055\pi
110110 −16.9032 −1.61165
111111 0 0
112112 0 0
113113 − 2.29950i − 0.216319i −0.994134 0.108159i 0.965504π-0.965504\pi
0.994134 0.108159i 0.0344957π-0.0344957\pi
114114 0 0
115115 − 2.01632i − 0.188023i
116116 − 2.14061i − 0.198751i
117117 0 0
118118 7.66792i 0.705889i
119119 0 0
120120 0 0
121121 −19.1496 −1.74087
122122 −17.1784 −1.55526
123123 0 0
124124 34.1920i 3.07054i
125125 −10.4711 −0.936567
126126 0 0
127127 −0.386795 −0.0343225 −0.0171613 0.999853i 0.505463π-0.505463\pi
−0.0171613 + 0.999853i 0.505463π0.505463\pi
128128 − 17.2447i − 1.52423i
129129 0 0
130130 9.13654 0.801328
131131 20.8634 1.82285 0.911424 0.411469i 0.134984π-0.134984\pi
0.911424 + 0.411469i 0.134984π0.134984\pi
132132 0 0
133133 0 0
134134 30.7173i 2.65357i
135135 0 0
136136 23.6892i 2.03134i
137137 0.700500i 0.0598477i 0.999552 + 0.0299239i 0.00952648π0.00952648\pi
−0.999552 + 0.0299239i 0.990474π0.990474\pi
138138 0 0
139139 − 11.5965i − 0.983606i −0.870707 0.491803i 0.836338π-0.836338\pi
0.870707 0.491803i 0.163662π-0.163662\pi
140140 0 0
141141 0 0
142142 −11.5364 −0.968111
143143 16.2965 1.36278
144144 0 0
145145 0.629233i 0.0522550i
146146 17.5324 1.45099
147147 0 0
148148 12.8814 1.05884
149149 − 0.350250i − 0.0286936i −0.999897 0.0143468i 0.995433π-0.995433\pi
0.999897 0.0143468i 0.00456688π-0.00456688\pi
150150 0 0
151151 4.65498 0.378817 0.189409 0.981898i 0.439343π-0.439343\pi
0.189409 + 0.981898i 0.439343π0.439343\pi
152152 30.4753 2.47187
153153 0 0
154154 0 0
155155 − 10.0507i − 0.807296i
156156 0 0
157157 1.23588i 0.0986343i 0.998783 + 0.0493171i 0.0157045π0.0157045\pi
−0.998783 + 0.0493171i 0.984295π0.984295\pi
158158 0.826910i 0.0657854i
159159 0 0
160160 − 2.64555i − 0.209149i
161161 0 0
162162 0 0
163163 −19.6132 −1.53622 −0.768112 0.640315i 0.778804π-0.778804\pi
−0.768112 + 0.640315i 0.778804π0.778804\pi
164164 −1.48850 −0.116232
165165 0 0
166166 − 18.4143i − 1.42922i
167167 23.6892 1.83313 0.916564 0.399887i 0.130951π-0.130951\pi
0.916564 + 0.399887i 0.130951π0.130951\pi
168168 0 0
169169 4.19136 0.322413
170170 − 13.2812i − 1.01862i
171171 0 0
172172 0.268189 0.0204492
173173 11.9822 0.910992 0.455496 0.890238i 0.349462π-0.349462\pi
0.455496 + 0.890238i 0.349462π0.349462\pi
174174 0 0
175175 0 0
176176 − 28.9269i − 2.18045i
177177 0 0
178178 − 8.54977i − 0.640832i
179179 − 22.3853i − 1.67316i −0.547848 0.836578i 0.684553π-0.684553\pi
0.547848 0.836578i 0.315447π-0.315447\pi
180180 0 0
181181 8.90380i 0.661815i 0.943663 + 0.330907i 0.107355π0.107355\pi
−0.943663 + 0.330907i 0.892645π0.892645\pi
182182 0 0
183183 0 0
184184 8.95822 0.660409
185185 −3.78649 −0.278388
186186 0 0
187187 − 23.6892i − 1.73233i
188188 41.4743 3.02482
189189 0 0
190190 −17.0858 −1.23953
191191 − 11.4909i − 0.831450i −0.909490 0.415725i 0.863528π-0.863528\pi
0.909490 0.415725i 0.136472π-0.136472\pi
192192 0 0
193193 11.0220 0.793381 0.396691 0.917952i 0.370159π-0.370159\pi
0.396691 + 0.917952i 0.370159π0.370159\pi
194194 −11.1004 −0.796960
195195 0 0
196196 0 0
197197 − 19.8228i − 1.41232i −0.708053 0.706159i 0.750426π-0.750426\pi
0.708053 0.706159i 0.249574π-0.249574\pi
198198 0 0
199199 8.66025i 0.613909i 0.951724 + 0.306955i 0.0993100π0.0993100\pi
−0.951724 + 0.306955i 0.900690π0.900690\pi
200200 − 19.0675i − 1.34828i
201201 0 0
202202 − 22.8074i − 1.60472i
203203 0 0
204204 0 0
205205 0.437545 0.0305595
206206 −10.4711 −0.729559
207207 0 0
208208 15.6356i 1.08414i
209209 −30.4753 −2.10802
210210 0 0
211211 22.1626 1.52574 0.762869 0.646553i 0.223790π-0.223790\pi
0.762869 + 0.646553i 0.223790π0.223790\pi
212212 − 17.3320i − 1.19037i
213213 0 0
214214 25.6900 1.75613
215215 −0.0788343 −0.00537645
216216 0 0
217217 0 0
218218 − 0.317773i − 0.0215223i
219219 0 0
220220 28.5314i 1.92358i
221221 12.8046i 0.861328i
222222 0 0
223223 18.7457i 1.25531i 0.778493 + 0.627653i 0.215984π0.215984\pi
−0.778493 + 0.627653i 0.784016π0.784016\pi
224224 0 0
225225 0 0
226226 −5.72774 −0.381004
227227 −14.1788 −0.941079 −0.470540 0.882379i 0.655941π-0.655941\pi
−0.470540 + 0.882379i 0.655941π0.655941\pi
228228 0 0
229229 − 4.07075i − 0.269003i −0.990913 0.134501i 0.957057π-0.957057\pi
0.990913 0.134501i 0.0429433π-0.0429433\pi
230230 −5.02237 −0.331165
231231 0 0
232232 −2.79560 −0.183540
233233 − 6.96345i − 0.456191i −0.973639 0.228096i 0.926750π-0.926750\pi
0.973639 0.228096i 0.0732499π-0.0732499\pi
234234 0 0
235235 −12.1914 −0.795277
236236 12.9429 0.842511
237237 0 0
238238 0 0
239239 26.5401i 1.71674i 0.513033 + 0.858369i 0.328522π0.328522\pi
−0.513033 + 0.858369i 0.671478π0.671478\pi
240240 0 0
241241 − 13.6038i − 0.876297i −0.898903 0.438149i 0.855634π-0.855634\pi
0.898903 0.438149i 0.144366π-0.144366\pi
242242 47.6990i 3.06621i
243243 0 0
244244 28.9959i 1.85627i
245245 0 0
246246 0 0
247247 16.4726 1.04813
248248 44.6541 2.83554
249249 0 0
250250 26.0822i 1.64958i
251251 −2.55060 −0.160993 −0.0804963 0.996755i 0.525651π-0.525651\pi
−0.0804963 + 0.996755i 0.525651π0.525651\pi
252252 0 0
253253 −8.95822 −0.563198
254254 0.963454i 0.0604525i
255255 0 0
256256 −32.5453 −2.03408
257257 −18.0602 −1.12657 −0.563283 0.826264i 0.690462π-0.690462\pi
−0.563283 + 0.826264i 0.690462π0.690462\pi
258258 0 0
259259 0 0
260260 − 15.4218i − 0.956422i
261261 0 0
262262 − 51.9680i − 3.21059i
263263 − 8.06902i − 0.497557i −0.968560 0.248779i 0.919971π-0.919971\pi
0.968560 0.248779i 0.0800292π-0.0800292\pi
264264 0 0
265265 5.09474i 0.312967i
266266 0 0
267267 0 0
268268 51.8486 3.16716
269269 2.09515 0.127744 0.0638718 0.997958i 0.479655π-0.479655\pi
0.0638718 + 0.997958i 0.479655π0.479655\pi
270270 0 0
271271 24.6027i 1.49451i 0.664537 + 0.747255i 0.268629π0.268629\pi
−0.664537 + 0.747255i 0.731371π0.731371\pi
272272 22.7286 1.37812
273273 0 0
274274 1.74485 0.105410
275275 19.0675i 1.14981i
276276 0 0
277277 −21.6990 −1.30377 −0.651883 0.758319i 0.726021π-0.726021\pi
−0.651883 + 0.758319i 0.726021π0.726021\pi
278278 −28.8854 −1.73243
279279 0 0
280280 0 0
281281 − 22.6315i − 1.35008i −0.737781 0.675040i 0.764126π-0.764126\pi
0.737781 0.675040i 0.235874π-0.235874\pi
282282 0 0
283283 9.54210i 0.567219i 0.958940 + 0.283610i 0.0915320π0.0915320\pi
−0.958940 + 0.283610i 0.908468π0.908468\pi
284284 19.4726i 1.15549i
285285 0 0
286286 − 40.5924i − 2.40028i
287287 0 0
288288 0 0
289289 1.61320 0.0948944
290290 1.56733 0.0920371
291291 0 0
292292 − 29.5935i − 1.73183i
293293 26.3348 1.53850 0.769248 0.638951i 0.220631π-0.220631\pi
0.769248 + 0.638951i 0.220631π0.220631\pi
294294 0 0
295295 −3.80457 −0.221511
296296 − 16.8228i − 0.977808i
297297 0 0
298298 −0.872425 −0.0505382
299299 4.84212 0.280027
300300 0 0
301301 0 0
302302 − 11.5949i − 0.667213i
303303 0 0
304304 − 29.2394i − 1.67700i
305305 − 8.52334i − 0.488045i
306306 0 0
307307 − 6.81772i − 0.389108i −0.980892 0.194554i 0.937674π-0.937674\pi
0.980892 0.194554i 0.0623259π-0.0623259\pi
308308 0 0
309309 0 0
310310 −25.0350 −1.42190
311311 26.9414 1.52771 0.763855 0.645388i 0.223304π-0.223304\pi
0.763855 + 0.645388i 0.223304π0.223304\pi
312312 0 0
313313 23.1614i 1.30916i 0.755992 + 0.654581i 0.227155π0.227155\pi
−0.755992 + 0.654581i 0.772845π0.772845\pi
314314 3.07842 0.173725
315315 0 0
316316 1.39576 0.0785179
317317 25.0675i 1.40793i 0.710234 + 0.703966i 0.248589π0.248589\pi
−0.710234 + 0.703966i 0.751411π0.751411\pi
318318 0 0
319319 2.79560 0.156523
320320 6.43204 0.359562
321321 0 0
322322 0 0
323323 − 23.9452i − 1.33235i
324324 0 0
325325 − 10.3064i − 0.571697i
326326 48.8538i 2.70576i
327327 0 0
328328 1.94395i 0.107337i
329329 0 0
330330 0 0
331331 −8.39576 −0.461473 −0.230736 0.973016i 0.574114π-0.574114\pi
−0.230736 + 0.973016i 0.574114π0.574114\pi
332332 −31.0820 −1.70584
333333 0 0
334334 − 59.0067i − 3.22870i
335335 −15.2409 −0.832699
336336 0 0
337337 −28.2902 −1.54107 −0.770533 0.637401i 0.780010π-0.780010\pi
−0.770533 + 0.637401i 0.780010π0.780010\pi
338338 − 10.4401i − 0.567867i
339339 0 0
340340 −22.4178 −1.21577
341341 −44.6541 −2.41816
342342 0 0
343343 0 0
344344 − 0.350250i − 0.0188842i
345345 0 0
346346 − 29.8461i − 1.60454i
347347 − 9.96345i − 0.534866i −0.963576 0.267433i 0.913825π-0.913825\pi
0.963576 0.267433i 0.0861754π-0.0861754\pi
348348 0 0
349349 − 22.4624i − 1.20239i −0.799104 0.601193i 0.794692π-0.794692\pi
0.799104 0.601193i 0.205308π-0.205308\pi
350350 0 0
351351 0 0
352352 −11.7538 −0.626481
353353 32.0652 1.70666 0.853330 0.521371i 0.174579π-0.174579\pi
0.853330 + 0.521371i 0.174579π0.174579\pi
354354 0 0
355355 − 5.72397i − 0.303797i
356356 −14.4314 −0.764863
357357 0 0
358358 −55.7587 −2.94694
359359 − 11.8736i − 0.626664i −0.949644 0.313332i 0.898555π-0.898555\pi
0.949644 0.313332i 0.101445π-0.101445\pi
360360 0 0
361361 −11.8046 −0.621293
362362 22.1782 1.16566
363363 0 0
364364 0 0
365365 8.69900i 0.455326i
366366 0 0
367367 13.5721i 0.708460i 0.935158 + 0.354230i 0.115257π0.115257\pi
−0.935158 + 0.354230i 0.884743π0.884743\pi
368368 − 8.59493i − 0.448042i
369369 0 0
370370 9.43162i 0.490327i
371371 0 0
372372 0 0
373373 30.1716 1.56223 0.781113 0.624390i 0.214652π-0.214652\pi
0.781113 + 0.624390i 0.214652π0.214652\pi
374374 −59.0067 −3.05116
375375 0 0
376376 − 54.1646i − 2.79332i
377377 −1.51108 −0.0778248
378378 0 0
379379 −12.6770 −0.651173 −0.325587 0.945512i 0.605562π-0.605562\pi
−0.325587 + 0.945512i 0.605562π0.605562\pi
380380 28.8396i 1.47944i
381381 0 0
382382 −28.6222 −1.46444
383383 31.9864 1.63443 0.817214 0.576334i 0.195517π-0.195517\pi
0.817214 + 0.576334i 0.195517π0.195517\pi
384384 0 0
385385 0 0
386386 − 27.4543i − 1.39739i
387387 0 0
388388 18.7366i 0.951209i
389389 − 7.57666i − 0.384152i −0.981380 0.192076i 0.938478π-0.938478\pi
0.981380 0.192076i 0.0615220π-0.0615220\pi
390390 0 0
391391 − 7.03869i − 0.355962i
392392 0 0
393393 0 0
394394 −49.3760 −2.48753
395395 −0.410285 −0.0206437
396396 0 0
397397 − 0.951618i − 0.0477603i −0.999715 0.0238802i 0.992398π-0.992398\pi
0.999715 0.0238802i 0.00760202π-0.00760202\pi
398398 21.5715 1.08128
399399 0 0
400400 −18.2943 −0.914713
401401 21.0325i 1.05031i 0.851006 + 0.525156i 0.175993π0.175993\pi
−0.851006 + 0.525156i 0.824007π0.824007\pi
402402 0 0
403403 24.1365 1.20233
404404 −38.4973 −1.91531
405405 0 0
406406 0 0
407407 16.8228i 0.833877i
408408 0 0
409409 − 20.1463i − 0.996171i −0.867128 0.498085i 0.834037π-0.834037\pi
0.867128 0.498085i 0.165963π-0.165963\pi
410410 − 1.08986i − 0.0538246i
411411 0 0
412412 17.6745i 0.870762i
413413 0 0
414414 0 0
415415 9.13654 0.448495
416416 6.35320 0.311491
417417 0 0
418418 75.9099i 3.71287i
419419 9.58929 0.468467 0.234234 0.972180i 0.424742π-0.424742\pi
0.234234 + 0.972180i 0.424742π0.424742\pi
420420 0 0
421421 8.61320 0.419782 0.209891 0.977725i 0.432689π-0.432689\pi
0.209891 + 0.977725i 0.432689π0.432689\pi
422422 − 55.2041i − 2.68729i
423423 0 0
424424 −22.6352 −1.09926
425425 −14.9818 −0.726724
426426 0 0
427427 0 0
428428 − 43.3630i − 2.09603i
429429 0 0
430430 0.196365i 0.00946958i
431431 − 11.5457i − 0.556136i −0.960561 0.278068i 0.910306π-0.910306\pi
0.960561 0.278068i 0.0896940π-0.0896940\pi
432432 0 0
433433 − 22.8707i − 1.09910i −0.835462 0.549548i 0.814800π-0.814800\pi
0.835462 0.549548i 0.185200π-0.185200\pi
434434 0 0
435435 0 0
436436 −0.536379 −0.0256879
437437 −9.05500 −0.433160
438438 0 0
439439 0.252617i 0.0120567i 0.999982 + 0.00602837i 0.00191890π0.00191890\pi
−0.999982 + 0.00602837i 0.998081π0.998081\pi
440440 37.2614 1.77637
441441 0 0
442442 31.8944 1.51706
443443 − 21.7721i − 1.03442i −0.855858 0.517212i 0.826970π-0.826970\pi
0.855858 0.517212i 0.173030π-0.173030\pi
444444 0 0
445445 4.24211 0.201095
446446 46.6930 2.21098
447447 0 0
448448 0 0
449449 10.7904i 0.509229i 0.967043 + 0.254614i 0.0819485π0.0819485\pi
−0.967043 + 0.254614i 0.918051π0.918051\pi
450450 0 0
451451 − 1.94395i − 0.0915371i
452452 9.66802i 0.454746i
453453 0 0
454454 35.3174i 1.65753i
455455 0 0
456456 0 0
457457 35.0220 1.63826 0.819130 0.573608i 0.194457π-0.194457\pi
0.819130 + 0.573608i 0.194457π0.194457\pi
458458 −10.1397 −0.473797
459459 0 0
460460 8.47741i 0.395261i
461461 32.9471 1.53450 0.767249 0.641349i 0.221625π-0.221625\pi
0.767249 + 0.641349i 0.221625π0.221625\pi
462462 0 0
463463 −5.22641 −0.242892 −0.121446 0.992598i 0.538753π-0.538753\pi
−0.121446 + 0.992598i 0.538753π0.538753\pi
464464 2.68223i 0.124519i
465465 0 0
466466 −17.3450 −0.803492
467467 21.6665 1.00260 0.501302 0.865272i 0.332855π-0.332855\pi
0.501302 + 0.865272i 0.332855π0.332855\pi
468468 0 0
469469 0 0
470470 30.3670i 1.40073i
471471 0 0
472472 − 16.9032i − 0.778032i
473473 0.350250i 0.0161045i
474474 0 0
475475 19.2735i 0.884330i
476476 0 0
477477 0 0
478478 66.1078 3.02370
479479 22.4308 1.02489 0.512444 0.858721i 0.328740π-0.328740\pi
0.512444 + 0.858721i 0.328740π0.328740\pi
480480 0 0
481481 − 9.09312i − 0.414611i
482482 −33.8852 −1.54343
483483 0 0
484484 80.5125 3.65966
485485 − 5.50764i − 0.250089i
486486 0 0
487487 22.1626 1.00428 0.502142 0.864785i 0.332545π-0.332545\pi
0.502142 + 0.864785i 0.332545π0.332545\pi
488488 37.8680 1.71421
489489 0 0
490490 0 0
491491 15.4543i 0.697444i 0.937226 + 0.348722i 0.113384π0.113384\pi
−0.937226 + 0.348722i 0.886616π0.886616\pi
492492 0 0
493493 2.19657i 0.0989285i
494494 − 41.0310i − 1.84607i
495495 0 0
496496 − 42.8432i − 1.92372i
497497 0 0
498498 0 0
499499 −1.34502 −0.0602112 −0.0301056 0.999547i 0.509584π-0.509584\pi
−0.0301056 + 0.999547i 0.509584π0.509584\pi
500500 44.0249 1.96885
501501 0 0
502502 6.35320i 0.283557i
503503 −18.1391 −0.808781 −0.404390 0.914586i 0.632516π-0.632516\pi
−0.404390 + 0.914586i 0.632516π0.632516\pi
504504 0 0
505505 11.3163 0.503568
506506 22.3137i 0.991965i
507507 0 0
508508 1.62624 0.0721529
509509 28.1838 1.24922 0.624612 0.780935i 0.285257π-0.285257\pi
0.624612 + 0.780935i 0.285257π0.285257\pi
510510 0 0
511511 0 0
512512 46.5767i 2.05842i
513513 0 0
514514 44.9856i 1.98423i
515515 − 5.19543i − 0.228938i
516516 0 0
517517 54.1646i 2.38215i
518518 0 0
519519 0 0
520520 −20.1406 −0.883224
521521 −34.1830 −1.49758 −0.748792 0.662806i 0.769366π-0.769366\pi
−0.748792 + 0.662806i 0.769366π0.769366\pi
522522 0 0
523523 36.8531i 1.61147i 0.592273 + 0.805737i 0.298231π0.298231\pi
−0.592273 + 0.805737i 0.701769π0.701769\pi
524524 −87.7183 −3.83199
525525 0 0
526526 −20.0988 −0.876351
527527 − 35.0858i − 1.52836i
528528 0 0
529529 20.3383 0.884273
530530 12.6903 0.551231
531531 0 0
532532 0 0
533533 1.05075i 0.0455130i
534534 0 0
535535 12.7465i 0.551081i
536536 − 67.7132i − 2.92476i
537537 0 0
538538 − 5.21874i − 0.224996i
539539 0 0
540540 0 0
541541 −38.4178 −1.65171 −0.825855 0.563883i 0.809307π-0.809307\pi
−0.825855 + 0.563883i 0.809307π0.809307\pi
542542 61.2821 2.63229
543543 0 0
544544 − 9.23526i − 0.395958i
545545 0.157669 0.00675378
546546 0 0
547547 11.9959 0.512909 0.256454 0.966556i 0.417446π-0.417446\pi
0.256454 + 0.966556i 0.417446π0.417446\pi
548548 − 2.94518i − 0.125812i
549549 0 0
550550 47.4946 2.02518
551551 2.82580 0.120383
552552 0 0
553553 0 0
554554 54.0492i 2.29633i
555555 0 0
556556 48.7565i 2.06774i
557557 8.70457i 0.368824i 0.982849 + 0.184412i 0.0590381π0.0590381\pi
−0.982849 + 0.184412i 0.940962π0.940962\pi
558558 0 0
559559 − 0.189318i − 0.00800729i
560560 0 0
561561 0 0
562562 −56.3719 −2.37791
563563 −23.4366 −0.987736 −0.493868 0.869537i 0.664417π-0.664417\pi
−0.493868 + 0.869537i 0.664417π0.664417\pi
564564 0 0
565565 − 2.84192i − 0.119560i
566566 23.7681 0.999047
567567 0 0
568568 25.4308 1.06705
569569 34.3137i 1.43851i 0.694749 + 0.719253i 0.255516π0.255516\pi
−0.694749 + 0.719253i 0.744484π0.744484\pi
570570 0 0
571571 21.4726 0.898600 0.449300 0.893381i 0.351673π-0.351673\pi
0.449300 + 0.893381i 0.351673π0.351673\pi
572572 −68.5171 −2.86485
573573 0 0
574574 0 0
575575 5.66545i 0.236266i
576576 0 0
577577 28.6193i 1.19144i 0.803194 + 0.595718i 0.203132π0.203132\pi
−0.803194 + 0.595718i 0.796868π0.796868\pi
578578 − 4.01827i − 0.167138i
579579 0 0
580580 − 2.64555i − 0.109850i
581581 0 0
582582 0 0
583583 22.6352 0.937455
584584 −38.6485 −1.59929
585585 0 0
586586 − 65.5964i − 2.70976i
587587 18.5157 0.764224 0.382112 0.924116i 0.375197π-0.375197\pi
0.382112 + 0.924116i 0.375197π0.375197\pi
588588 0 0
589589 −45.1365 −1.85982
590590 9.47666i 0.390148i
591591 0 0
592592 −16.1406 −0.663375
593593 −18.7457 −0.769794 −0.384897 0.922960i 0.625763π-0.625763\pi
−0.384897 + 0.922960i 0.625763π0.625763\pi
594594 0 0
595595 0 0
596596 1.47259i 0.0603197i
597597 0 0
598598 − 12.0611i − 0.493213i
599599 25.8721i 1.05710i 0.848901 + 0.528552i 0.177265π0.177265\pi
−0.848901 + 0.528552i 0.822735π0.822735\pi
600600 0 0
601601 14.5735i 0.594467i 0.954805 + 0.297234i 0.0960640π0.0960640\pi
−0.954805 + 0.297234i 0.903936π0.903936\pi
602602 0 0
603603 0 0
604604 −19.5714 −0.796350
605605 −23.6667 −0.962187
606606 0 0
607607 22.2796i 0.904300i 0.891942 + 0.452150i 0.149343π0.149343\pi
−0.891942 + 0.452150i 0.850657π0.850657\pi
608608 −11.8808 −0.481830
609609 0 0
610610 −21.2305 −0.859597
611611 − 29.2772i − 1.18443i
612612 0 0
613613 25.2223 1.01872 0.509360 0.860553i 0.329882π-0.329882\pi
0.509360 + 0.860553i 0.329882π0.329882\pi
614614 −16.9820 −0.685338
615615 0 0
616616 0 0
617617 2.03655i 0.0819882i 0.999159 + 0.0409941i 0.0130525π0.0130525\pi
−0.999159 + 0.0409941i 0.986948π0.986948\pi
618618 0 0
619619 − 38.0011i − 1.52739i −0.645575 0.763697i 0.723382π-0.723382\pi
0.645575 0.763697i 0.276618π-0.276618\pi
620620 42.2574i 1.69710i
621621 0 0
622622 − 67.1075i − 2.69076i
623623 0 0
624624 0 0
625625 4.42184 0.176874
626626 57.6920 2.30583
627627 0 0
628628 − 5.19615i − 0.207349i
629629 −13.2181 −0.527040
630630 0 0
631631 2.80457 0.111648 0.0558240 0.998441i 0.482221π-0.482221\pi
0.0558240 + 0.998441i 0.482221π0.482221\pi
632632 − 1.82284i − 0.0725087i
633633 0 0
634634 62.4398 2.47980
635635 −0.478034 −0.0189702
636636 0 0
637637 0 0
638638 − 6.96345i − 0.275686i
639639 0 0
640640 − 21.3124i − 0.842448i
641641 − 1.87766i − 0.0741631i −0.999312 0.0370815i 0.988194π-0.988194\pi
0.999312 0.0370815i 0.0118061π-0.0118061\pi
642642 0 0
643643 − 14.5735i − 0.574724i −0.957822 0.287362i 0.907222π-0.907222\pi
0.957822 0.287362i 0.0927783π-0.0927783\pi
644644 0 0
645645 0 0
646646 −59.6442 −2.34667
647647 36.4584 1.43333 0.716663 0.697419i 0.245668π-0.245668\pi
0.716663 + 0.697419i 0.245668π0.245668\pi
648648 0 0
649649 16.9032i 0.663508i
650650 −25.6719 −1.00693
651651 0 0
652652 82.4618 3.22945
653653 15.0716i 0.589797i 0.955529 + 0.294898i 0.0952858π0.0952858\pi
−0.955529 + 0.294898i 0.904714π0.904714\pi
654654 0 0
655655 25.7848 1.00750
656656 1.86512 0.0728206
657657 0 0
658658 0 0
659659 − 31.4670i − 1.22578i −0.790168 0.612891i 0.790007π-0.790007\pi
0.790168 0.612891i 0.209993π-0.209993\pi
660660 0 0
661661 13.7524i 0.534906i 0.963571 + 0.267453i 0.0861820π0.0861820\pi
−0.963571 + 0.267453i 0.913818π0.913818\pi
662662 20.9127i 0.812795i
663663 0 0
664664 40.5924i 1.57529i
665665 0 0
666666 0 0
667667 0.830645 0.0321627
668668 −99.5991 −3.85360
669669 0 0
670670 37.9630i 1.46664i
671671 −37.8680 −1.46188
672672 0 0
673673 11.7448 0.452731 0.226365 0.974042i 0.427316π-0.427316\pi
0.226365 + 0.974042i 0.427316π0.427316\pi
674674 70.4670i 2.71429i
675675 0 0
676676 −17.6222 −0.677776
677677 −21.7453 −0.835740 −0.417870 0.908507i 0.637223π-0.637223\pi
−0.417870 + 0.908507i 0.637223π0.637223\pi
678678 0 0
679679 0 0
680680 29.2772i 1.12273i
681681 0 0
682682 111.227i 4.25911i
683683 12.8919i 0.493293i 0.969105 + 0.246647i 0.0793287π0.0793287\pi
−0.969105 + 0.246647i 0.920671π0.920671\pi
684684 0 0
685685 0.865736i 0.0330781i
686686 0 0
687687 0 0
688688 −0.336046 −0.0128116
689689 −12.2348 −0.466110
690690 0 0
691691 − 10.3381i − 0.393279i −0.980476 0.196639i 0.936997π-0.936997\pi
0.980476 0.196639i 0.0630028π-0.0630028\pi
692692 −50.3781 −1.91509
693693 0 0
694694 −24.8176 −0.942063
695695 − 14.3320i − 0.543643i
696696 0 0
697697 1.52741 0.0578547
698698 −55.9508 −2.11777
699699 0 0
700700 0 0
701701 − 41.2056i − 1.55631i −0.628071 0.778156i 0.716155π-0.716155\pi
0.628071 0.778156i 0.283845π-0.283845\pi
702702 0 0
703703 17.0046i 0.641340i
704704 − 28.5767i − 1.07702i
705705 0 0
706706 − 79.8701i − 3.00595i
707707 0 0
708708 0 0
709709 28.6002 1.07410 0.537051 0.843550i 0.319538π-0.319538\pi
0.537051 + 0.843550i 0.319538π0.319538\pi
710710 −14.2576 −0.535079
711711 0 0
712712 18.8471i 0.706326i
713713 −13.2679 −0.496886
714714 0 0
715715 20.1406 0.753216
716716 94.1168i 3.51731i
717717 0 0
718718 −29.5755 −1.10375
719719 −1.76370 −0.0657749 −0.0328875 0.999459i 0.510470π-0.510470\pi
−0.0328875 + 0.999459i 0.510470π0.510470\pi
720720 0 0
721721 0 0
722722 29.4036i 1.09429i
723723 0 0
724724 − 37.4352i − 1.39127i
725725 − 1.76802i − 0.0656627i
726726 0 0
727727 20.0358i 0.743088i 0.928415 + 0.371544i 0.121171π0.121171\pi
−0.928415 + 0.371544i 0.878829π0.878829\pi
728728 0 0
729729 0 0
730730 21.6680 0.801970
731731 −0.275200 −0.0101786
732732 0 0
733733 15.4237i 0.569689i 0.958574 + 0.284844i 0.0919419π0.0919419\pi
−0.958574 + 0.284844i 0.908058π0.908058\pi
734734 33.8064 1.24782
735735 0 0
736736 −3.49236 −0.128730
737737 67.7132i 2.49425i
738738 0 0
739739 −32.4569 −1.19395 −0.596973 0.802261i 0.703630π-0.703630\pi
−0.596973 + 0.802261i 0.703630π0.703630\pi
740740 15.9199 0.585227
741741 0 0
742742 0 0
743743 − 7.52184i − 0.275950i −0.990436 0.137975i 0.955941π-0.955941\pi
0.990436 0.137975i 0.0440593π-0.0440593\pi
744744 0 0
745745 − 0.432868i − 0.0158591i
746746 − 75.1533i − 2.75156i
747747 0 0
748748 99.5991i 3.64170i
749749 0 0
750750 0 0
751751 25.8463 0.943147 0.471573 0.881827i 0.343686π-0.343686\pi
0.471573 + 0.881827i 0.343686π0.343686\pi
752752 −51.9680 −1.89508
753753 0 0
754754 3.76390i 0.137073i
755755 5.75302 0.209374
756756 0 0
757757 33.5103 1.21795 0.608976 0.793188i 0.291580π-0.291580\pi
0.608976 + 0.793188i 0.291580π0.291580\pi
758758 31.5767i 1.14692i
759759 0 0
760760 37.6640 1.36622
761761 −8.73002 −0.316463 −0.158232 0.987402i 0.550579π-0.550579\pi
−0.158232 + 0.987402i 0.550579π0.550579\pi
762762 0 0
763763 0 0
764764 48.3122i 1.74787i
765765 0 0
766766 − 79.6738i − 2.87873i
767767 − 9.13654i − 0.329902i
768768 0 0
769769 − 5.04495i − 0.181926i −0.995854 0.0909628i 0.971006π-0.971006\pi
0.995854 0.0909628i 0.0289944π-0.0289944\pi
770770 0 0
771771 0 0
772772 −46.3409 −1.66785
773773 5.80280 0.208712 0.104356 0.994540i 0.466722π-0.466722\pi
0.104356 + 0.994540i 0.466722π0.466722\pi
774774 0 0
775775 28.2406i 1.01443i
776776 24.4697 0.878410
777777 0 0
778778 −18.8724 −0.676609
779779 − 1.96495i − 0.0704018i
780780 0 0
781781 −25.4308 −0.909986
782782 −17.5324 −0.626958
783783 0 0
784784 0 0
785785 1.52741i 0.0545156i
786786 0 0
787787 24.7042i 0.880608i 0.897849 + 0.440304i 0.145129π0.145129\pi
−0.897849 + 0.440304i 0.854871π0.854871\pi
788788 83.3432i 2.96898i
789789 0 0
790790 1.02196i 0.0363599i
791791 0 0
792792 0 0
793793 20.4685 0.726859
794794 −2.37035 −0.0841206
795795 0 0
796796 − 36.4112i − 1.29056i
797797 4.39314 0.155613 0.0778064 0.996968i 0.475208π-0.475208\pi
0.0778064 + 0.996968i 0.475208π0.475208\pi
798798 0 0
799799 −42.5584 −1.50561
800800 7.43348i 0.262813i
801801 0 0
802802 52.3890 1.84992
803803 38.6485 1.36387
804804 0 0
805805 0 0
806806 − 60.1208i − 2.11767i
807807 0 0
808808 50.2767i 1.76873i
809809 50.7315i 1.78362i 0.452406 + 0.891812i 0.350566π0.350566\pi
−0.452406 + 0.891812i 0.649434π0.649434\pi
810810 0 0
811811 31.8126i 1.11709i 0.829474 + 0.558546i 0.188641π0.188641\pi
−0.829474 + 0.558546i 0.811359π0.811359\pi
812812 0 0
813813 0 0
814814 41.9034 1.46871
815815 −24.2396 −0.849078
816816 0 0
817817 0.354034i 0.0123861i
818818 −50.1817 −1.75456
819819 0 0
820820 −1.83961 −0.0642421
821821 − 25.9437i − 0.905441i −0.891653 0.452720i 0.850454π-0.850454\pi
0.891653 0.452720i 0.149546π-0.149546\pi
822822 0 0
823823 −0.140614 −0.00490149 −0.00245074 0.999997i 0.500780π-0.500780\pi
−0.00245074 + 0.999997i 0.500780π0.500780\pi
824824 23.0826 0.804120
825825 0 0
826826 0 0
827827 16.1772i 0.562535i 0.959629 + 0.281267i 0.0907548π0.0907548\pi
−0.959629 + 0.281267i 0.909245π0.909245\pi
828828 0 0
829829 33.3237i 1.15738i 0.815548 + 0.578690i 0.196436π0.196436\pi
−0.815548 + 0.578690i 0.803564π0.803564\pi
830830 − 22.7579i − 0.789938i
831831 0 0
832832 15.4463i 0.535505i
833833 0 0
834834 0 0
835835 29.2772 1.01318
836836 128.130 4.43148
837837 0 0
838838 − 23.8856i − 0.825115i
839839 −21.4701 −0.741230 −0.370615 0.928787i 0.620853π-0.620853\pi
−0.370615 + 0.928787i 0.620853π0.620853\pi
840840 0 0
841841 28.7408 0.991061
842842 − 21.4543i − 0.739365i
843843 0 0
844844 −93.1806 −3.20741
845845 5.18004 0.178199
846846 0 0
847847 0 0
848848 21.7173i 0.745774i
849849 0 0
850850 37.3176i 1.27998i
851851 4.99850i 0.171346i
852852 0 0
853853 − 25.1842i − 0.862291i −0.902282 0.431146i 0.858110π-0.858110\pi
0.902282 0.431146i 0.141890π-0.141890\pi
854854 0 0
855855 0 0
856856 −56.6311 −1.93561
857857 −29.0366 −0.991871 −0.495936 0.868359i 0.665175π-0.665175\pi
−0.495936 + 0.868359i 0.665175π0.665175\pi
858858 0 0
859859 − 23.8314i − 0.813116i −0.913625 0.406558i 0.866729π-0.866729\pi
0.913625 0.406558i 0.133271π-0.133271\pi
860860 0.331451 0.0113024
861861 0 0
862862 −28.7587 −0.979526
863863 − 31.8777i − 1.08513i −0.840014 0.542564i 0.817454π-0.817454\pi
0.840014 0.542564i 0.182546π-0.182546\pi
864864 0 0
865865 14.8086 0.503509
866866 −56.9678 −1.93584
867867 0 0
868868 0 0
869869 1.82284i 0.0618356i
870870 0 0
871871 − 36.6005i − 1.24016i
872872 0.700500i 0.0237219i
873873 0 0
874874 22.5548i 0.762927i
875875 0 0
876876 0 0
877877 −2.28123 −0.0770316 −0.0385158 0.999258i 0.512263π-0.512263\pi
−0.0385158 + 0.999258i 0.512263π0.512263\pi
878878 0.629233 0.0212356
879879 0 0
880880 − 35.7503i − 1.20514i
881881 11.8808 0.400275 0.200137 0.979768i 0.435861π-0.435861\pi
0.200137 + 0.979768i 0.435861π0.435861\pi
882882 0 0
883883 −49.7120 −1.67294 −0.836472 0.548010i 0.815385π-0.815385\pi
−0.836472 + 0.548010i 0.815385π0.815385\pi
884884 − 53.8355i − 1.81069i
885885 0 0
886886 −54.2313 −1.82194
887887 12.3588 0.414969 0.207485 0.978238i 0.433472π-0.433472\pi
0.207485 + 0.978238i 0.433472π0.433472\pi
888888 0 0
889889 0 0
890890 − 10.5665i − 0.354191i
891891 0 0
892892 − 78.8145i − 2.63890i
893893 54.7497i 1.83213i
894894 0 0
895895 − 27.6656i − 0.924760i
896896 0 0
897897 0 0
898898 26.8773 0.896908
899899 4.14052 0.138094
900900 0 0
901901 17.7850i 0.592505i
902902 −4.84212 −0.161225
903903 0 0
904904 12.6262 0.419943
905905 11.0041i 0.365788i
906906 0 0
907907 −35.7628 −1.18748 −0.593742 0.804656i 0.702350π-0.702350\pi
−0.593742 + 0.804656i 0.702350π0.702350\pi
908908 59.6133 1.97834
909909 0 0
910910 0 0
911911 47.9228i 1.58775i 0.608078 + 0.793877i 0.291941π0.291941\pi
−0.608078 + 0.793877i 0.708059π0.708059\pi
912912 0 0
913913 − 40.5924i − 1.34341i
914914 − 87.2350i − 2.88548i
915915 0 0
916916 17.1151i 0.565498i
917917 0 0
918918 0 0
919919 −34.4816 −1.13744 −0.568721 0.822531i 0.692562π-0.692562\pi
−0.568721 + 0.822531i 0.692562π0.692562\pi
920920 11.0713 0.365011
921921 0 0
922922 − 82.0667i − 2.70272i
923923 13.7459 0.452453
924924 0 0
925925 10.6393 0.349817
926926 13.0183i 0.427807i
927927 0 0
928928 1.08986 0.0357766
929929 −58.3549 −1.91456 −0.957280 0.289161i 0.906624π-0.906624\pi
−0.957280 + 0.289161i 0.906624π0.906624\pi
930930 0 0
931931 0 0
932932 29.2772i 0.959005i
933933 0 0
934934 − 53.9682i − 1.76589i
935935 − 29.2772i − 0.957465i
936936 0 0
937937 − 29.8596i − 0.975471i −0.872992 0.487735i 0.837823π-0.837823\pi
0.872992 0.487735i 0.162177π-0.162177\pi
938938 0 0
939939 0 0
940940 51.2574 1.67183
941941 16.2177 0.528682 0.264341 0.964429i 0.414846π-0.414846\pi
0.264341 + 0.964429i 0.414846π0.414846\pi
942942 0 0
943943 − 0.577598i − 0.0188092i
944944 −16.2177 −0.527841
945945 0 0
946946 0.872425 0.0283650
947947 − 28.1939i − 0.916180i −0.888906 0.458090i 0.848534π-0.848534\pi
0.888906 0.458090i 0.151466π-0.151466\pi
948948 0 0
949949 −20.8904 −0.678130
950950 48.0077 1.55758
951951 0 0
952952 0 0
953953 56.3488i 1.82532i 0.408725 + 0.912658i 0.365973π0.365973\pi
−0.408725 + 0.912658i 0.634027π0.634027\pi
954954 0 0
955955 − 14.2014i − 0.459546i
956956 − 111.585i − 3.60893i
957957 0 0
958958 − 55.8720i − 1.80514i
959959 0 0
960960 0 0
961961 −35.1365 −1.13344
962962 −22.6497 −0.730257
963963 0 0
964964 57.1958i 1.84215i
965965 13.6219 0.438505
966966 0 0
967967 34.0310 1.09436 0.547181 0.837014i 0.315701π-0.315701\pi
0.547181 + 0.837014i 0.315701π0.315701\pi
968968 − 105.148i − 3.37958i
969969 0 0
970970 −13.7188 −0.440483
971971 32.6945 1.04922 0.524608 0.851344i 0.324212π-0.324212\pi
0.524608 + 0.851344i 0.324212π0.324212\pi
972972 0 0
973973 0 0
974974 − 55.2041i − 1.76885i
975975 0 0
976976 − 36.3324i − 1.16297i
977977 − 24.6625i − 0.789022i −0.918891 0.394511i 0.870914π-0.870914\pi
0.918891 0.394511i 0.129086π-0.129086\pi
978978 0 0
979979 − 18.8471i − 0.602357i
980980 0 0
981981 0 0
982982 38.4946 1.22841
983983 −17.7915 −0.567461 −0.283730 0.958904i 0.591572π-0.591572\pi
−0.283730 + 0.958904i 0.591572π0.591572\pi
984984 0 0
985985 − 24.4987i − 0.780594i
986986 5.47135 0.174243
987987 0 0
988988 −69.2574 −2.20337
989989 0.104068i 0.00330918i
990990 0 0
991991 −31.9034 −1.01344 −0.506722 0.862109i 0.669143π-0.669143\pi
−0.506722 + 0.862109i 0.669143π0.669143\pi
992992 −17.4084 −0.552718
993993 0 0
994994 0 0
995995 10.7031i 0.339310i
996996 0 0
997997 38.9553i 1.23373i 0.787070 + 0.616864i 0.211597π0.211597\pi
−0.787070 + 0.616864i 0.788403π0.788403\pi
998998 3.35025i 0.106050i
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 1323.2.c.d.1322.2 12
3.2 odd 2 inner 1323.2.c.d.1322.11 12
7.2 even 3 189.2.p.d.80.1 yes 12
7.3 odd 6 189.2.p.d.26.6 yes 12
7.6 odd 2 inner 1323.2.c.d.1322.1 12
21.2 odd 6 189.2.p.d.80.6 yes 12
21.17 even 6 189.2.p.d.26.1 12
21.20 even 2 inner 1323.2.c.d.1322.12 12
63.2 odd 6 567.2.s.f.458.1 12
63.16 even 3 567.2.s.f.458.6 12
63.23 odd 6 567.2.i.f.269.6 12
63.31 odd 6 567.2.s.f.26.1 12
63.38 even 6 567.2.i.f.215.6 12
63.52 odd 6 567.2.i.f.215.1 12
63.58 even 3 567.2.i.f.269.1 12
63.59 even 6 567.2.s.f.26.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.p.d.26.1 12 21.17 even 6
189.2.p.d.26.6 yes 12 7.3 odd 6
189.2.p.d.80.1 yes 12 7.2 even 3
189.2.p.d.80.6 yes 12 21.2 odd 6
567.2.i.f.215.1 12 63.52 odd 6
567.2.i.f.215.6 12 63.38 even 6
567.2.i.f.269.1 12 63.58 even 3
567.2.i.f.269.6 12 63.23 odd 6
567.2.s.f.26.1 12 63.31 odd 6
567.2.s.f.26.6 12 63.59 even 6
567.2.s.f.458.1 12 63.2 odd 6
567.2.s.f.458.6 12 63.16 even 3
1323.2.c.d.1322.1 12 7.6 odd 2 inner
1323.2.c.d.1322.2 12 1.1 even 1 trivial
1323.2.c.d.1322.11 12 3.2 odd 2 inner
1323.2.c.d.1322.12 12 21.20 even 2 inner