Properties

Label 1323.2.c.d.1322.5
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 1322.5
Root 1.656040.956115i1.65604 - 0.956115i of defining polynomial
Character χ\chi == 1323.1322
Dual form 1323.2.c.d.1322.7

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) == q0.656620iq2+1.56885q43.31208q52.34338iq8+2.17478iq10+2.34338iq11+1.58003iq13+1.59899q161.13730q174.44938iq195.19615q20+1.53871q229.39331iq23+5.96986q25+1.03748q263.65662iq297.31873iq315.73669iq32+0.746774iq345.16784q372.92155q38+7.76146iq409.64553q412.16784q43+3.67641iq446.16784q46+5.58668q473.91993iq50+2.47883iq52+10.0499iq537.76146iq552.40101q582.17478q594.00665iq614.80563q620.568850q645.23317iq6510.7668q671.78425q686.39331iq7110.6830iq73+3.39331iq746.98041iq76+1.23317q795.29597q80+6.33345iq82+1.03748q83+3.76683q85+1.42345iq86+5.49143q887.47075q8914.7367iq923.66833iq94+14.7367iq95+13.5524iq97+O(q100)q-0.656620i q^{2} +1.56885 q^{4} -3.31208 q^{5} -2.34338i q^{8} +2.17478i q^{10} +2.34338i q^{11} +1.58003i q^{13} +1.59899 q^{16} -1.13730 q^{17} -4.44938i q^{19} -5.19615 q^{20} +1.53871 q^{22} -9.39331i q^{23} +5.96986 q^{25} +1.03748 q^{26} -3.65662i q^{29} -7.31873i q^{31} -5.73669i q^{32} +0.746774i q^{34} -5.16784 q^{37} -2.92155 q^{38} +7.76146i q^{40} -9.64553 q^{41} -2.16784 q^{43} +3.67641i q^{44} -6.16784 q^{46} +5.58668 q^{47} -3.91993i q^{50} +2.47883i q^{52} +10.0499i q^{53} -7.76146i q^{55} -2.40101 q^{58} -2.17478 q^{59} -4.00665i q^{61} -4.80563 q^{62} -0.568850 q^{64} -5.23317i q^{65} -10.7668 q^{67} -1.78425 q^{68} -6.39331i q^{71} -10.6830i q^{73} +3.39331i q^{74} -6.98041i q^{76} +1.23317 q^{79} -5.29597 q^{80} +6.33345i q^{82} +1.03748 q^{83} +3.76683 q^{85} +1.42345i q^{86} +5.49143 q^{88} -7.47075 q^{89} -14.7367i q^{92} -3.66833i q^{94} +14.7367i q^{95} +13.5524i 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 − 0.656620i − 0.464301i −0.972680 0.232150i 0.925424π-0.925424\pi
0.972680 0.232150i 0.0745761π-0.0745761\pi
33 0 0
44 1.56885 0.784425
55 −3.31208 −1.48121 −0.740603 0.671943i 0.765460π-0.765460\pi
−0.740603 + 0.671943i 0.765460π0.765460\pi
66 0 0
77 0 0
88 − 2.34338i − 0.828510i
99 0 0
1010 2.17478i 0.687725i
1111 2.34338i 0.706556i 0.935518 + 0.353278i 0.114933π0.114933\pi
−0.935518 + 0.353278i 0.885067π0.885067\pi
1212 0 0
1313 1.58003i 0.438221i 0.975700 + 0.219110i 0.0703155π0.0703155\pi
−0.975700 + 0.219110i 0.929685π0.929685\pi
1414 0 0
1515 0 0
1616 1.59899 0.399747
1717 −1.13730 −0.275836 −0.137918 0.990444i 0.544041π-0.544041\pi
−0.137918 + 0.990444i 0.544041π0.544041\pi
1818 0 0
1919 − 4.44938i − 1.02076i −0.859950 0.510379i 0.829505π-0.829505\pi
0.859950 0.510379i 0.170495π-0.170495\pi
2020 −5.19615 −1.16190
2121 0 0
2222 1.53871 0.328054
2323 − 9.39331i − 1.95864i −0.202317 0.979320i 0.564847π-0.564847\pi
0.202317 0.979320i 0.435153π-0.435153\pi
2424 0 0
2525 5.96986 1.19397
2626 1.03748 0.203466
2727 0 0
2828 0 0
2929 − 3.65662i − 0.679017i −0.940603 0.339509i 0.889739π-0.889739\pi
0.940603 0.339509i 0.110261π-0.110261\pi
3030 0 0
3131 − 7.31873i − 1.31448i −0.753680 0.657241i 0.771723π-0.771723\pi
0.753680 0.657241i 0.228277π-0.228277\pi
3232 − 5.73669i − 1.01411i
3333 0 0
3434 0.746774i 0.128071i
3535 0 0
3636 0 0
3737 −5.16784 −0.849587 −0.424794 0.905290i 0.639653π-0.639653\pi
−0.424794 + 0.905290i 0.639653π0.639653\pi
3838 −2.92155 −0.473938
3939 0 0
4040 7.76146i 1.22719i
4141 −9.64553 −1.50638 −0.753189 0.657804i 0.771486π-0.771486\pi
−0.753189 + 0.657804i 0.771486π0.771486\pi
4242 0 0
4343 −2.16784 −0.330592 −0.165296 0.986244i 0.552858π-0.552858\pi
−0.165296 + 0.986244i 0.552858π0.552858\pi
4444 3.67641i 0.554240i
4545 0 0
4646 −6.16784 −0.909398
4747 5.58668 0.814901 0.407450 0.913227i 0.366418π-0.366418\pi
0.407450 + 0.913227i 0.366418π0.366418\pi
4848 0 0
4949 0 0
5050 − 3.91993i − 0.554362i
5151 0 0
5252 2.47883i 0.343751i
5353 10.0499i 1.38046i 0.723588 + 0.690232i 0.242491π0.242491\pi
−0.723588 + 0.690232i 0.757509π0.757509\pi
5454 0 0
5555 − 7.76146i − 1.04655i
5656 0 0
5757 0 0
5858 −2.40101 −0.315268
5959 −2.17478 −0.283132 −0.141566 0.989929i 0.545214π-0.545214\pi
−0.141566 + 0.989929i 0.545214π0.545214\pi
6060 0 0
6161 − 4.00665i − 0.512999i −0.966544 0.256500i 0.917431π-0.917431\pi
0.966544 0.256500i 0.0825692π-0.0825692\pi
6262 −4.80563 −0.610315
6363 0 0
6464 −0.568850 −0.0711062
6565 − 5.23317i − 0.649095i
6666 0 0
6767 −10.7668 −1.31538 −0.657689 0.753290i 0.728466π-0.728466\pi
−0.657689 + 0.753290i 0.728466π0.728466\pi
6868 −1.78425 −0.216372
6969 0 0
7070 0 0
7171 − 6.39331i − 0.758746i −0.925244 0.379373i 0.876140π-0.876140\pi
0.925244 0.379373i 0.123860π-0.123860\pi
7272 0 0
7373 − 10.6830i − 1.25035i −0.780484 0.625176i 0.785027π-0.785027\pi
0.780484 0.625176i 0.214973π-0.214973\pi
7474 3.39331i 0.394464i
7575 0 0
7676 − 6.98041i − 0.800707i
7777 0 0
7878 0 0
7979 1.23317 0.138743 0.0693714 0.997591i 0.477901π-0.477901\pi
0.0693714 + 0.997591i 0.477901π0.477901\pi
8080 −5.29597 −0.592108
8181 0 0
8282 6.33345i 0.699413i
8383 1.03748 0.113878 0.0569390 0.998378i 0.481866π-0.481866\pi
0.0569390 + 0.998378i 0.481866π0.481866\pi
8484 0 0
8585 3.76683 0.408570
8686 1.42345i 0.153494i
8787 0 0
8888 5.49143 0.585388
8989 −7.47075 −0.791898 −0.395949 0.918272i 0.629584π-0.629584\pi
−0.395949 + 0.918272i 0.629584π0.629584\pi
9090 0 0
9191 0 0
9292 − 14.7367i − 1.53641i
9393 0 0
9494 − 3.66833i − 0.378359i
9595 14.7367i 1.51195i
9696 0 0
9797 13.5524i 1.37603i 0.725695 + 0.688017i 0.241518π0.241518\pi
−0.725695 + 0.688017i 0.758482π0.758482\pi
9898 0 0
9999 0 0
100100 9.36581 0.936581
101101 13.7044 1.36364 0.681819 0.731521i 0.261189π-0.261189\pi
0.681819 + 0.731521i 0.261189π0.261189\pi
102102 0 0
103103 − 4.89211i − 0.482033i −0.970521 0.241017i 0.922519π-0.922519\pi
0.970521 0.241017i 0.0774809π-0.0774809\pi
104104 3.70260 0.363070
105105 0 0
106106 6.59899 0.640950
107107 − 2.45359i − 0.237197i −0.992942 0.118599i 0.962160π-0.962160\pi
0.992942 0.118599i 0.0378401π-0.0378401\pi
108108 0 0
109109 4.33568 0.415282 0.207641 0.978205i 0.433421π-0.433421\pi
0.207641 + 0.978205i 0.433421π0.433421\pi
110110 −5.09633 −0.485916
111111 0 0
112112 0 0
113113 − 7.16013i − 0.673569i −0.941582 0.336784i 0.890661π-0.890661\pi
0.941582 0.336784i 0.109339π-0.109339\pi
114114 0 0
115115 31.1114i 2.90115i
116116 − 5.73669i − 0.532638i
117117 0 0
118118 1.42800i 0.131458i
119119 0 0
120120 0 0
121121 5.50857 0.500779
122122 −2.63085 −0.238186
123123 0 0
124124 − 11.4820i − 1.03111i
125125 −3.21226 −0.287313
126126 0 0
127127 −17.7065 −1.57120 −0.785601 0.618733i 0.787646π-0.787646\pi
−0.785601 + 0.618733i 0.787646π0.787646\pi
128128 − 11.0999i − 0.981098i
129129 0 0
130130 −3.43621 −0.301375
131131 13.6046 1.18864 0.594318 0.804230i 0.297422π-0.297422\pi
0.594318 + 0.804230i 0.297422π0.297422\pi
132132 0 0
133133 0 0
134134 7.06972i 0.610731i
135135 0 0
136136 2.66513i 0.228533i
137137 − 10.1601i − 0.868039i −0.900904 0.434019i 0.857095π-0.857095\pi
0.900904 0.434019i 0.142905π-0.142905\pi
138138 0 0
139139 − 3.85463i − 0.326945i −0.986548 0.163473i 0.947730π-0.947730\pi
0.986548 0.163473i 0.0522695π-0.0522695\pi
140140 0 0
141141 0 0
142142 −4.19798 −0.352286
143143 −3.70260 −0.309627
144144 0 0
145145 12.1110i 1.00576i
146146 −7.01468 −0.580539
147147 0 0
148148 −8.10756 −0.666437
149149 5.08007i 0.416175i 0.978110 + 0.208088i 0.0667239π0.0667239\pi
−0.978110 + 0.208088i 0.933276π0.933276\pi
150150 0 0
151151 18.3055 1.48968 0.744842 0.667241i 0.232525π-0.232525\pi
0.744842 + 0.667241i 0.232525π0.232525\pi
152152 −10.4266 −0.845707
153153 0 0
154154 0 0
155155 24.2402i 1.94702i
156156 0 0
157157 3.31208i 0.264333i 0.991228 + 0.132166i 0.0421933π0.0421933\pi
−0.991228 + 0.132166i 0.957807π0.957807\pi
158158 − 0.809727i − 0.0644184i
159159 0 0
160160 19.0004i 1.50211i
161161 0 0
162162 0 0
163163 −2.29345 −0.179637 −0.0898185 0.995958i 0.528629π-0.528629\pi
−0.0898185 + 0.995958i 0.528629π0.528629\pi
164164 −15.1324 −1.18164
165165 0 0
166166 − 0.681229i − 0.0528737i
167167 −2.66513 −0.206234 −0.103117 0.994669i 0.532882π-0.532882\pi
−0.103117 + 0.994669i 0.532882π0.532882\pi
168168 0 0
169169 10.5035 0.807963
170170 − 2.47338i − 0.189699i
171171 0 0
172172 −3.40101 −0.259325
173173 −2.56530 −0.195036 −0.0975182 0.995234i 0.531090π-0.531090\pi
−0.0975182 + 0.995234i 0.531090π0.531090\pi
174174 0 0
175175 0 0
176176 3.74704i 0.282444i
177177 0 0
178178 4.90545i 0.367679i
179179 − 13.8365i − 1.03419i −0.855927 0.517096i 0.827013π-0.827013\pi
0.855927 0.517096i 0.172987π-0.172987\pi
180180 0 0
181181 4.74008i 0.352328i 0.984361 + 0.176164i 0.0563688π0.0563688\pi
−0.984361 + 0.176164i 0.943631π0.943631\pi
182182 0 0
183183 0 0
184184 −22.0121 −1.62275
185185 17.1163 1.25841
186186 0 0
187187 − 2.66513i − 0.194893i
188188 8.76466 0.639228
189189 0 0
190190 9.67641 0.702001
191191 8.34338i 0.603706i 0.953355 + 0.301853i 0.0976051π0.0976051\pi
−0.953355 + 0.301853i 0.902395π0.902395\pi
192192 0 0
193193 −17.8442 −1.28446 −0.642229 0.766513i 0.721990π-0.721990\pi
−0.642229 + 0.766513i 0.721990π0.721990\pi
194194 8.89876 0.638893
195195 0 0
196196 0 0
197197 15.1102i 1.07656i 0.842767 + 0.538279i 0.180925π0.180925\pi
−0.842767 + 0.538279i 0.819075π0.819075\pi
198198 0 0
199199 − 8.66025i − 0.613909i −0.951724 0.306955i 0.900690π-0.900690\pi
0.951724 0.306955i 0.0993100π-0.0993100\pi
200200 − 13.9897i − 0.989218i
201201 0 0
202202 − 8.99858i − 0.633138i
203203 0 0
204204 0 0
205205 31.9468 2.23126
206206 −3.21226 −0.223809
207207 0 0
208208 2.52645i 0.175177i
209209 10.4266 0.721222
210210 0 0
211211 −14.5809 −1.00379 −0.501897 0.864928i 0.667364π-0.667364\pi
−0.501897 + 0.864928i 0.667364π0.667364\pi
212212 15.7668i 1.08287i
213213 0 0
214214 −1.61107 −0.110131
215215 7.18005 0.489675
216216 0 0
217217 0 0
218218 − 2.84689i − 0.192816i
219219 0 0
220220 − 12.1766i − 0.820943i
221221 − 1.79696i − 0.120877i
222222 0 0
223223 − 10.5832i − 0.708703i −0.935112 0.354351i 0.884702π-0.884702\pi
0.935112 0.354351i 0.115298π-0.115298\pi
224224 0 0
225225 0 0
226226 −4.70149 −0.312738
227227 6.72398 0.446286 0.223143 0.974786i 0.428368π-0.428368\pi
0.223143 + 0.974786i 0.428368π0.428368\pi
228228 0 0
229229 12.2630i 0.810364i 0.914236 + 0.405182i 0.132792π0.132792\pi
−0.914236 + 0.405182i 0.867208π0.867208\pi
230230 20.4284 1.34701
231231 0 0
232232 −8.56885 −0.562573
233233 − 5.62648i − 0.368603i −0.982870 0.184302i 0.940998π-0.940998\pi
0.982870 0.184302i 0.0590023π-0.0590023\pi
234234 0 0
235235 −18.5035 −1.20704
236236 −3.41190 −0.222096
237237 0 0
238238 0 0
239239 15.9595i 1.03234i 0.856488 + 0.516168i 0.172642π0.172642\pi
−0.856488 + 0.516168i 0.827358π0.827358\pi
240240 0 0
241241 − 4.58806i − 0.295543i −0.989022 0.147771i 0.952790π-0.952790\pi
0.989022 0.147771i 0.0472100π-0.0472100\pi
242242 − 3.61704i − 0.232512i
243243 0 0
244244 − 6.28583i − 0.402409i
245245 0 0
246246 0 0
247247 7.03014 0.447317
248248 −17.1506 −1.08906
249249 0 0
250250 2.10923i 0.133400i
251251 13.8042 0.871314 0.435657 0.900113i 0.356516π-0.356516\pi
0.435657 + 0.900113i 0.356516π0.356516\pi
252252 0 0
253253 22.0121 1.38389
254254 11.6265i 0.729510i
255255 0 0
256256 −8.42609 −0.526631
257257 −8.96430 −0.559178 −0.279589 0.960120i 0.590198π-0.590198\pi
−0.279589 + 0.960120i 0.590198π0.590198\pi
258258 0 0
259259 0 0
260260 − 8.21006i − 0.509166i
261261 0 0
262262 − 8.93303i − 0.551885i
263263 28.5534i 1.76068i 0.474343 + 0.880340i 0.342686π0.342686\pi
−0.474343 + 0.880340i 0.657314π0.657314\pi
264264 0 0
265265 − 33.2861i − 2.04475i
266266 0 0
267267 0 0
268268 −16.8915 −1.03181
269269 23.9313 1.45912 0.729559 0.683918i 0.239725π-0.239725\pi
0.729559 + 0.683918i 0.239725π0.239725\pi
270270 0 0
271271 − 14.6032i − 0.887080i −0.896255 0.443540i 0.853722π-0.853722\pi
0.896255 0.443540i 0.146278π-0.146278\pi
272272 −1.81853 −0.110265
273273 0 0
274274 −6.67135 −0.403031
275275 13.9897i 0.843608i
276276 0 0
277277 22.3830 1.34486 0.672431 0.740160i 0.265250π-0.265250\pi
0.672431 + 0.740160i 0.265250π0.265250\pi
278278 −2.53103 −0.151801
279279 0 0
280280 0 0
281281 11.6067i 0.692397i 0.938161 + 0.346199i 0.112528π0.112528\pi
−0.938161 + 0.346199i 0.887472π0.887472\pi
282282 0 0
283283 − 14.9937i − 0.891283i −0.895211 0.445642i 0.852976π-0.852976\pi
0.895211 0.445642i 0.147024π-0.147024\pi
284284 − 10.0301i − 0.595179i
285285 0 0
286286 2.43121i 0.143760i
287287 0 0
288288 0 0
289289 −15.7065 −0.923915
290290 7.95234 0.466977
291291 0 0
292292 − 16.7600i − 0.980807i
293293 16.3352 0.954314 0.477157 0.878818i 0.341667π-0.341667\pi
0.477157 + 0.878818i 0.341667π0.341667\pi
294294 0 0
295295 7.20304 0.419377
296296 12.1102i 0.703891i
297297 0 0
298298 3.33568 0.193231
299299 14.8417 0.858317
300300 0 0
301301 0 0
302302 − 12.0198i − 0.691661i
303303 0 0
304304 − 7.11450i − 0.408045i
305305 13.2703i 0.759857i
306306 0 0
307307 3.17340i 0.181115i 0.995891 + 0.0905577i 0.0288650π0.0288650\pi
−0.995891 + 0.0905577i 0.971135π0.971135\pi
308308 0 0
309309 0 0
310310 15.9166 0.904003
311311 25.1342 1.42523 0.712614 0.701556i 0.247511π-0.247511\pi
0.712614 + 0.701556i 0.247511π0.247511\pi
312312 0 0
313313 18.6441i 1.05383i 0.849919 + 0.526914i 0.176651π0.176651\pi
−0.849919 + 0.526914i 0.823349π0.823349\pi
314314 2.17478 0.122730
315315 0 0
316316 1.93466 0.108833
317317 7.98965i 0.448744i 0.974504 + 0.224372i 0.0720330π0.0720330\pi
−0.974504 + 0.224372i 0.927967π0.927967\pi
318318 0 0
319319 8.56885 0.479763
320320 1.88407 0.105323
321321 0 0
322322 0 0
323323 5.06028i 0.281561i
324324 0 0
325325 9.43254i 0.523223i
326326 1.50593i 0.0834056i
327327 0 0
328328 22.6031i 1.24805i
329329 0 0
330330 0 0
331331 −8.93466 −0.491094 −0.245547 0.969385i 0.578967π-0.578967\pi
−0.245547 + 0.969385i 0.578967π0.578967\pi
332332 1.62765 0.0893287
333333 0 0
334334 1.74998i 0.0957544i
335335 35.6606 1.94835
336336 0 0
337337 4.24526 0.231254 0.115627 0.993293i 0.463112π-0.463112\pi
0.115627 + 0.993293i 0.463112π0.463112\pi
338338 − 6.89682i − 0.375138i
339339 0 0
340340 5.90958 0.320492
341341 17.1506 0.928755
342342 0 0
343343 0 0
344344 5.08007i 0.273899i
345345 0 0
346346 1.68443i 0.0905556i
347347 − 2.62648i − 0.140997i −0.997512 0.0704985i 0.977541π-0.977541\pi
0.997512 0.0704985i 0.0224590π-0.0224590\pi
348348 0 0
349349 32.4918i 1.73924i 0.493718 + 0.869622i 0.335637π0.335637\pi
−0.493718 + 0.869622i 0.664363π0.664363\pi
350350 0 0
351351 0 0
352352 13.4432 0.716527
353353 −23.3842 −1.24461 −0.622307 0.782773i 0.713805π-0.713805\pi
−0.622307 + 0.782773i 0.713805π0.713805\pi
354354 0 0
355355 21.1751i 1.12386i
356356 −11.7205 −0.621185
357357 0 0
358358 −9.08536 −0.480176
359359 21.3504i 1.12683i 0.826174 + 0.563416i 0.190513π0.190513\pi
−0.826174 + 0.563416i 0.809487π0.809487\pi
360360 0 0
361361 −0.796965 −0.0419455
362362 3.11243 0.163586
363363 0 0
364364 0 0
365365 35.3830i 1.85203i
366366 0 0
367367 15.5229i 0.810289i 0.914253 + 0.405145i 0.132779π0.132779\pi
−0.914253 + 0.405145i 0.867221π0.867221\pi
368368 − 15.0198i − 0.782961i
369369 0 0
370370 − 11.2389i − 0.584283i
371371 0 0
372372 0 0
373373 −23.3528 −1.20916 −0.604582 0.796543i 0.706660π-0.706660\pi
−0.604582 + 0.796543i 0.706660π0.706660\pi
374374 −1.74998 −0.0904891
375375 0 0
376376 − 13.0917i − 0.675153i
377377 5.77756 0.297559
378378 0 0
379379 2.53871 0.130405 0.0652024 0.997872i 0.479231π-0.479231\pi
0.0652024 + 0.997872i 0.479231π0.479231\pi
380380 23.1196i 1.18601i
381381 0 0
382382 5.47843 0.280301
383383 −16.2041 −0.827993 −0.413996 0.910278i 0.635867π-0.635867\pi
−0.413996 + 0.910278i 0.635867π0.635867\pi
384384 0 0
385385 0 0
386386 11.7169i 0.596374i
387387 0 0
388388 21.2616i 1.07939i
389389 − 22.3330i − 1.13233i −0.824292 0.566165i 0.808427π-0.808427\pi
0.824292 0.566165i 0.191573π-0.191573\pi
390390 0 0
391391 10.6830i 0.540263i
392392 0 0
393393 0 0
394394 9.92167 0.499847
395395 −4.08437 −0.205507
396396 0 0
397397 − 32.6914i − 1.64073i −0.571837 0.820367i 0.693769π-0.693769\pi
0.571837 0.820367i 0.306231π-0.306231\pi
398398 −5.68650 −0.285038
399399 0 0
400400 9.54574 0.477287
401401 − 28.9270i − 1.44454i −0.691609 0.722272i 0.743098π-0.743098\pi
0.691609 0.722272i 0.256902π-0.256902\pi
402402 0 0
403403 11.5638 0.576033
404404 21.5001 1.06967
405405 0 0
406406 0 0
407407 − 12.1102i − 0.600281i
408408 0 0
409409 1.05082i 0.0519598i 0.999662 + 0.0259799i 0.00827059π0.00827059\pi
−0.999662 + 0.0259799i 0.991729π0.991729\pi
410410 − 20.9769i − 1.03597i
411411 0 0
412412 − 7.67498i − 0.378119i
413413 0 0
414414 0 0
415415 −3.43621 −0.168677
416416 9.06412 0.444405
417417 0 0
418418 − 6.84631i − 0.334864i
419419 −3.12120 −0.152480 −0.0762402 0.997089i 0.524292π-0.524292\pi
−0.0762402 + 0.997089i 0.524292π0.524292\pi
420420 0 0
421421 −8.70655 −0.424331 −0.212166 0.977234i 0.568052π-0.568052\pi
−0.212166 + 0.977234i 0.568052π0.568052\pi
422422 9.57414i 0.466062i
423423 0 0
424424 23.5508 1.14373
425425 −6.78952 −0.329340
426426 0 0
427427 0 0
428428 − 3.84931i − 0.186063i
429429 0 0
430430 − 4.71457i − 0.227357i
431431 27.2831i 1.31418i 0.753812 + 0.657090i 0.228213π0.228213\pi
−0.753812 + 0.657090i 0.771787π0.771787\pi
432432 0 0
433433 12.8711i 0.618547i 0.950973 + 0.309274i 0.100086π0.100086\pi
−0.950973 + 0.309274i 0.899914π0.899914\pi
434434 0 0
435435 0 0
436436 6.80202 0.325758
437437 −41.7944 −1.99930
438438 0 0
439439 − 18.4445i − 0.880306i −0.897923 0.440153i 0.854924π-0.854924\pi
0.897923 0.440153i 0.145076π-0.145076\pi
440440 −18.1880 −0.867081
441441 0 0
442442 −1.17992 −0.0561233
443443 2.87000i 0.136358i 0.997673 + 0.0681790i 0.0217189π0.0217189\pi
−0.997673 + 0.0681790i 0.978281π0.978281\pi
444444 0 0
445445 24.7437 1.17296
446446 −6.94914 −0.329051
447447 0 0
448448 0 0
449449 1.81675i 0.0857380i 0.999081 + 0.0428690i 0.0136498π0.0136498\pi
−0.999081 + 0.0428690i 0.986350π0.986350\pi
450450 0 0
451451 − 22.6031i − 1.06434i
452452 − 11.2332i − 0.528364i
453453 0 0
454454 − 4.41510i − 0.207211i
455455 0 0
456456 0 0
457457 6.15575 0.287954 0.143977 0.989581i 0.454011π-0.454011\pi
0.143977 + 0.989581i 0.454011π0.454011\pi
458458 8.05216 0.376253
459459 0 0
460460 48.8091i 2.27573i
461461 −17.0507 −0.794132 −0.397066 0.917790i 0.629972π-0.629972\pi
−0.397066 + 0.917790i 0.629972π0.629972\pi
462462 0 0
463463 29.4131 1.36694 0.683471 0.729977i 0.260469π-0.260469\pi
0.683471 + 0.729977i 0.260469π0.260469\pi
464464 − 5.84689i − 0.271435i
465465 0 0
466466 −3.69446 −0.171143
467467 27.1181 1.25487 0.627437 0.778667i 0.284104π-0.284104\pi
0.627437 + 0.778667i 0.284104π0.284104\pi
468468 0 0
469469 0 0
470470 12.1498i 0.560428i
471471 0 0
472472 5.09633i 0.234578i
473473 − 5.08007i − 0.233582i
474474 0 0
475475 − 26.5622i − 1.21876i
476476 0 0
477477 0 0
478478 10.4793 0.479314
479479 21.5569 0.984960 0.492480 0.870324i 0.336090π-0.336090\pi
0.492480 + 0.870324i 0.336090π0.336090\pi
480480 0 0
481481 − 8.16532i − 0.372307i
482482 −3.01261 −0.137221
483483 0 0
484484 8.64212 0.392824
485485 − 44.8865i − 2.03819i
486486 0 0
487487 −14.5809 −0.660725 −0.330363 0.943854i 0.607171π-0.607171\pi
−0.330363 + 0.943854i 0.607171π0.607171\pi
488488 −9.38910 −0.425025
489489 0 0
490490 0 0
491491 0.283102i 0.0127762i 0.999980 + 0.00638811i 0.00203341π0.00203341\pi
−0.999980 + 0.00638811i 0.997967π0.997967\pi
492492 0 0
493493 4.15867i 0.187297i
494494 − 4.61613i − 0.207690i
495495 0 0
496496 − 11.7026i − 0.525461i
497497 0 0
498498 0 0
499499 12.3055 0.550871 0.275436 0.961319i 0.411178π-0.411178\pi
0.275436 + 0.961319i 0.411178π0.411178\pi
500500 −5.03955 −0.225375
501501 0 0
502502 − 9.06412i − 0.404552i
503503 −1.78425 −0.0795559 −0.0397779 0.999209i 0.512665π-0.512665\pi
−0.0397779 + 0.999209i 0.512665π0.512665\pi
504504 0 0
505505 −45.3900 −2.01983
506506 − 14.4536i − 0.642540i
507507 0 0
508508 −27.7789 −1.23249
509509 −39.0725 −1.73186 −0.865928 0.500168i 0.833272π-0.833272\pi
−0.865928 + 0.500168i 0.833272π0.833272\pi
510510 0 0
511511 0 0
512512 − 16.6670i − 0.736583i
513513 0 0
514514 5.88614i 0.259627i
515515 16.2030i 0.713991i
516516 0 0
517517 13.0917i 0.575773i
518518 0 0
519519 0 0
520520 −12.2633 −0.537782
521521 20.3628 0.892111 0.446056 0.895005i 0.352828π-0.352828\pi
0.446056 + 0.895005i 0.352828π0.352828\pi
522522 0 0
523523 − 1.43259i − 0.0626426i −0.999509 0.0313213i 0.990028π-0.990028\pi
0.999509 0.0313213i 0.00997151π-0.00997151\pi
524524 21.3435 0.932396
525525 0 0
526526 18.7488 0.817485
527527 8.32359i 0.362581i
528528 0 0
529529 −65.2342 −2.83627
530530 −21.8564 −0.949380
531531 0 0
532532 0 0
533533 − 15.2402i − 0.660126i
534534 0 0
535535 8.12647i 0.351338i
536536 25.2308i 1.08980i
537537 0 0
538538 − 15.7138i − 0.677470i
539539 0 0
540540 0 0
541541 −10.0904 −0.433821 −0.216910 0.976192i 0.569598π-0.569598\pi
−0.216910 + 0.976192i 0.569598π0.569598\pi
542542 −9.58875 −0.411872
543543 0 0
544544 6.52433i 0.279729i
545545 −14.3601 −0.615119
546546 0 0
547547 7.30048 0.312146 0.156073 0.987746i 0.450117π-0.450117\pi
0.156073 + 0.987746i 0.450117π0.450117\pi
548548 − 15.9397i − 0.680911i
549549 0 0
550550 9.18589 0.391688
551551 −16.2697 −0.693112
552552 0 0
553553 0 0
554554 − 14.6971i − 0.624420i
555555 0 0
556556 − 6.04733i − 0.256464i
557557 − 22.8597i − 0.968595i −0.874903 0.484297i 0.839075π-0.839075\pi
0.874903 0.484297i 0.160925π-0.160925\pi
558558 0 0
559559 − 3.42524i − 0.144872i
560560 0 0
561561 0 0
562562 7.62119 0.321481
563563 21.1096 0.889663 0.444832 0.895614i 0.353264π-0.353264\pi
0.444832 + 0.895614i 0.353264π0.353264\pi
564564 0 0
565565 23.7149i 0.997694i
566566 −9.84517 −0.413824
567567 0 0
568568 −14.9819 −0.628629
569569 − 26.4536i − 1.10899i −0.832186 0.554496i 0.812911π-0.812911\pi
0.832186 0.554496i 0.187089π-0.187089\pi
570570 0 0
571571 12.0301 0.503446 0.251723 0.967799i 0.419003π-0.419003\pi
0.251723 + 0.967799i 0.419003π0.419003\pi
572572 −5.80883 −0.242879
573573 0 0
574574 0 0
575575 − 56.0767i − 2.33856i
576576 0 0
577577 − 36.8413i − 1.53372i −0.641812 0.766862i 0.721817π-0.721817\pi
0.641812 0.766862i 0.278183π-0.278183\pi
578578 10.3132i 0.428974i
579579 0 0
580580 19.0004i 0.788947i
581581 0 0
582582 0 0
583583 −23.5508 −0.975374
584584 −25.0343 −1.03593
585585 0 0
586586 − 10.7260i − 0.443089i
587587 −28.7712 −1.18752 −0.593758 0.804644i 0.702356π-0.702356\pi
−0.593758 + 0.804644i 0.702356π0.702356\pi
588588 0 0
589589 −32.5638 −1.34177
590590 − 4.72966i − 0.194717i
591591 0 0
592592 −8.26331 −0.339620
593593 −10.5832 −0.434599 −0.217300 0.976105i 0.569725π-0.569725\pi
−0.217300 + 0.976105i 0.569725π0.569725\pi
594594 0 0
595595 0 0
596596 7.96986i 0.326458i
597597 0 0
598598 − 9.74535i − 0.398517i
599599 18.1927i 0.743333i 0.928366 + 0.371666i 0.121214π0.121214\pi
−0.928366 + 0.371666i 0.878786π0.878786\pi
600600 0 0
601601 − 26.4101i − 1.07729i −0.842532 0.538646i 0.818936π-0.818936\pi
0.842532 0.538646i 0.181064π-0.181064\pi
602602 0 0
603603 0 0
604604 28.7186 1.16854
605605 −18.2448 −0.741757
606606 0 0
607607 24.9776i 1.01381i 0.862003 + 0.506904i 0.169210π0.169210\pi
−0.862003 + 0.506904i 0.830790π0.830790\pi
608608 −25.5247 −1.03516
609609 0 0
610610 8.71358 0.352802
611611 8.82710i 0.357106i
612612 0 0
613613 −14.1126 −0.570003 −0.285002 0.958527i 0.591994π-0.591994\pi
−0.285002 + 0.958527i 0.591994π0.591994\pi
614614 2.08372 0.0840920
615615 0 0
616616 0 0
617617 − 14.6265i − 0.588840i −0.955676 0.294420i 0.904874π-0.904874\pi
0.955676 0.294420i 0.0951264π-0.0951264\pi
618618 0 0
619619 − 26.5442i − 1.06690i −0.845831 0.533452i 0.820895π-0.820895\pi
0.845831 0.533452i 0.179105π-0.179105\pi
620620 38.0292i 1.52729i
621621 0 0
622622 − 16.5036i − 0.661734i
623623 0 0
624624 0 0
625625 −19.2101 −0.768403
626626 12.2421 0.489293
627627 0 0
628628 5.19615i 0.207349i
629629 5.87738 0.234347
630630 0 0
631631 −8.20304 −0.326558 −0.163279 0.986580i 0.552207π-0.552207\pi
−0.163279 + 0.986580i 0.552207π0.552207\pi
632632 − 2.88979i − 0.114950i
633633 0 0
634634 5.24617 0.208352
635635 58.6455 2.32727
636636 0 0
637637 0 0
638638 − 5.62648i − 0.222755i
639639 0 0
640640 36.7636i 1.45321i
641641 16.0499i 0.633934i 0.948437 + 0.316967i 0.102664π0.102664\pi
−0.948437 + 0.316967i 0.897336π0.897336\pi
642642 0 0
643643 26.4101i 1.04151i 0.853705 + 0.520757i 0.174350π0.174350\pi
−0.853705 + 0.520757i 0.825650π0.825650\pi
644644 0 0
645645 0 0
646646 3.32268 0.130729
647647 −31.7015 −1.24632 −0.623158 0.782096i 0.714151π-0.714151\pi
−0.623158 + 0.782096i 0.714151π0.714151\pi
648648 0 0
649649 − 5.09633i − 0.200048i
650650 6.19360 0.242933
651651 0 0
652652 −3.59808 −0.140912
653653 13.2901i 0.520083i 0.965597 + 0.260041i 0.0837362π0.0837362\pi
−0.965597 + 0.260041i 0.916264π0.916264\pi
654654 0 0
655655 −45.0594 −1.76062
656656 −15.4231 −0.602171
657657 0 0
658658 0 0
659659 − 36.2125i − 1.41064i −0.708890 0.705319i 0.750804π-0.750804\pi
0.708890 0.705319i 0.249196π-0.249196\pi
660660 0 0
661661 50.7930i 1.97562i 0.155674 + 0.987809i 0.450245π0.450245\pi
−0.155674 + 0.987809i 0.549755π0.549755\pi
662662 5.86668i 0.228015i
663663 0 0
664664 − 2.43121i − 0.0943491i
665665 0 0
666666 0 0
667667 −34.3478 −1.32995
668668 −4.18118 −0.161775
669669 0 0
670670 − 23.4155i − 0.904618i
671671 9.38910 0.362462
672672 0 0
673673 3.32865 0.128310 0.0641550 0.997940i 0.479565π-0.479565\pi
0.0641550 + 0.997940i 0.479565π0.479565\pi
674674 − 2.78752i − 0.107371i
675675 0 0
676676 16.4784 0.633786
677677 −19.9380 −0.766280 −0.383140 0.923690i 0.625157π-0.625157\pi
−0.383140 + 0.923690i 0.625157π0.625157\pi
678678 0 0
679679 0 0
680680 − 8.82710i − 0.338504i
681681 0 0
682682 − 11.2614i − 0.431222i
683683 − 28.6636i − 1.09678i −0.836221 0.548392i 0.815240π-0.815240\pi
0.836221 0.548392i 0.184760π-0.184760\pi
684684 0 0
685685 33.6512i 1.28574i
686686 0 0
687687 0 0
688688 −3.46635 −0.132153
689689 −15.8792 −0.604948
690690 0 0
691691 20.3674i 0.774812i 0.921909 + 0.387406i 0.126629π0.126629\pi
−0.921909 + 0.387406i 0.873371π0.873371\pi
692692 −4.02458 −0.152991
693693 0 0
694694 −1.72460 −0.0654650
695695 12.7668i 0.484273i
696696 0 0
697697 10.9699 0.415513
698698 21.3347 0.807532
699699 0 0
700700 0 0
701701 49.1172i 1.85513i 0.373659 + 0.927566i 0.378103π0.378103\pi
−0.373659 + 0.927566i 0.621897π0.621897\pi
702702 0 0
703703 22.9937i 0.867222i
704704 − 1.33303i − 0.0502405i
705705 0 0
706706 15.3545i 0.577876i
707707 0 0
708708 0 0
709709 23.3658 0.877522 0.438761 0.898604i 0.355418π-0.355418\pi
0.438761 + 0.898604i 0.355418π0.355418\pi
710710 13.9040 0.521809
711711 0 0
712712 17.5068i 0.656095i
713713 −68.7471 −2.57460
714714 0 0
715715 12.2633 0.458622
716716 − 21.7075i − 0.811246i
717717 0 0
718718 14.0191 0.523189
719719 −12.6669 −0.472396 −0.236198 0.971705i 0.575901π-0.575901\pi
−0.236198 + 0.971705i 0.575901π0.575901\pi
720720 0 0
721721 0 0
722722 0.523303i 0.0194753i
723723 0 0
724724 7.43648i 0.276374i
725725 − 21.8295i − 0.810728i
726726 0 0
727727 2.70398i 0.100285i 0.998742 + 0.0501426i 0.0159676π0.0159676\pi
−0.998742 + 0.0501426i 0.984032π0.984032\pi
728728 0 0
729729 0 0
730730 23.2332 0.859898
731731 2.46548 0.0911891
732732 0 0
733733 − 21.8087i − 0.805524i −0.915305 0.402762i 0.868050π-0.868050\pi
0.915305 0.402762i 0.131950π-0.131950\pi
734734 10.1927 0.376218
735735 0 0
736736 −53.8865 −1.98628
737737 − 25.2308i − 0.929387i
738738 0 0
739739 32.1267 1.18180 0.590899 0.806745i 0.298773π-0.298773\pi
0.590899 + 0.806745i 0.298773π0.298773\pi
740740 26.8529 0.987131
741741 0 0
742742 0 0
743743 − 41.2728i − 1.51415i −0.653328 0.757075i 0.726628π-0.726628\pi
0.653328 0.757075i 0.273372π-0.273372\pi
744744 0 0
745745 − 16.8256i − 0.616442i
746746 15.3339i 0.561415i
747747 0 0
748748 − 4.18118i − 0.152879i
749749 0 0
750750 0 0
751751 45.8091 1.67160 0.835798 0.549037i 0.185005π-0.185005\pi
0.835798 + 0.549037i 0.185005π0.185005\pi
752752 8.93303 0.325754
753753 0 0
754754 − 3.79366i − 0.138157i
755755 −60.6294 −2.20653
756756 0 0
757757 50.3427 1.82974 0.914868 0.403752i 0.132294π-0.132294\pi
0.914868 + 0.403752i 0.132294π0.132294\pi
758758 − 1.66697i − 0.0605471i
759759 0 0
760760 34.5337 1.25267
761761 30.3646 1.10072 0.550358 0.834929i 0.314491π-0.314491\pi
0.550358 + 0.834929i 0.314491π0.314491\pi
762762 0 0
763763 0 0
764764 13.0895i 0.473562i
765765 0 0
766766 10.6400i 0.384438i
767767 − 3.43621i − 0.124074i
768768 0 0
769769 − 41.3383i − 1.49070i −0.666675 0.745349i 0.732283π-0.732283\pi
0.666675 0.745349i 0.267717π-0.267717\pi
770770 0 0
771771 0 0
772772 −27.9949 −1.00756
773773 13.9951 0.503368 0.251684 0.967809i 0.419016π-0.419016\pi
0.251684 + 0.967809i 0.419016π0.419016\pi
774774 0 0
775775 − 43.6918i − 1.56946i
776776 31.7583 1.14006
777777 0 0
778778 −14.6643 −0.525741
779779 42.9166i 1.53765i
780780 0 0
781781 14.9819 0.536096
782782 7.01468 0.250845
783783 0 0
784784 0 0
785785 − 10.9699i − 0.391531i
786786 0 0
787787 13.4868i 0.480753i 0.970680 + 0.240377i 0.0772709π0.0772709\pi
−0.970680 + 0.240377i 0.922729π0.922729\pi
788788 23.7056i 0.844478i
789789 0 0
790790 2.68188i 0.0954170i
791791 0 0
792792 0 0
793793 6.33062 0.224807
794794 −21.4658 −0.761794
795795 0 0
796796 − 13.5866i − 0.481566i
797797 −8.31735 −0.294616 −0.147308 0.989091i 0.547061π-0.547061\pi
−0.147308 + 0.989091i 0.547061π0.547061\pi
798798 0 0
799799 −6.35373 −0.224779
800800 − 34.2472i − 1.21082i
801801 0 0
802802 −18.9940 −0.670703
803803 25.0343 0.883443
804804 0 0
805805 0 0
806806 − 7.59302i − 0.267453i
807807 0 0
808808 − 32.1146i − 1.12979i
809809 − 14.5440i − 0.511340i −0.966764 0.255670i 0.917704π-0.917704\pi
0.966764 0.255670i 0.0822960π-0.0822960\pi
810810 0 0
811811 41.8287i 1.46880i 0.678715 + 0.734401i 0.262537π0.262537\pi
−0.678715 + 0.734401i 0.737463π0.737463\pi
812812 0 0
813813 0 0
814814 −7.95181 −0.278711
815815 7.59609 0.266079
816816 0 0
817817 9.64553i 0.337454i
818818 0.689991 0.0241250
819819 0 0
820820 50.1196 1.75025
821821 − 46.4828i − 1.62226i −0.584865 0.811131i 0.698852π-0.698852\pi
0.584865 0.811131i 0.301148π-0.301148\pi
822822 0 0
823823 7.73669 0.269684 0.134842 0.990867i 0.456947π-0.456947\pi
0.134842 + 0.990867i 0.456947π0.456947\pi
824824 −11.4641 −0.399369
825825 0 0
826826 0 0
827827 − 20.8898i − 0.726409i −0.931709 0.363205i 0.881683π-0.881683\pi
0.931709 0.363205i 0.118317π-0.118317\pi
828828 0 0
829829 47.6062i 1.65343i 0.562619 + 0.826716i 0.309794π0.309794\pi
−0.562619 + 0.826716i 0.690206π0.690206\pi
830830 2.25628i 0.0783168i
831831 0 0
832832 − 0.898798i − 0.0311602i
833833 0 0
834834 0 0
835835 8.82710 0.305475
836836 16.3577 0.565744
837837 0 0
838838 2.04944i 0.0707968i
839839 −22.4035 −0.773455 −0.386727 0.922194i 0.626395π-0.626395\pi
−0.386727 + 0.922194i 0.626395π0.626395\pi
840840 0 0
841841 15.6291 0.538935
842842 5.71690i 0.197017i
843843 0 0
844844 −22.8753 −0.787400
845845 −34.7885 −1.19676
846846 0 0
847847 0 0
848848 16.0697i 0.551836i
849849 0 0
850850 4.45814i 0.152913i
851851 48.5431i 1.66404i
852852 0 0
853853 − 48.4273i − 1.65812i −0.559160 0.829060i 0.688876π-0.688876\pi
0.559160 0.829060i 0.311124π-0.311124\pi
854854 0 0
855855 0 0
856856 −5.74968 −0.196520
857857 −49.0655 −1.67605 −0.838023 0.545636i 0.816288π-0.816288\pi
−0.838023 + 0.545636i 0.816288π0.816288\pi
858858 0 0
859859 12.0245i 0.410272i 0.978733 + 0.205136i 0.0657636π0.0657636\pi
−0.978733 + 0.205136i 0.934236π0.934236\pi
860860 11.2644 0.384113
861861 0 0
862862 17.9146 0.610175
863863 46.0499i 1.56756i 0.621040 + 0.783779i 0.286710π0.286710\pi
−0.621040 + 0.783779i 0.713290π0.713290\pi
864864 0 0
865865 8.49649 0.288889
866866 8.45145 0.287192
867867 0 0
868868 0 0
869869 2.88979i 0.0980296i
870870 0 0
871871 − 17.0119i − 0.576426i
872872 − 10.1601i − 0.344066i
873873 0 0
874874 27.4430i 0.928275i
875875 0 0
876876 0 0
877877 13.4734 0.454964 0.227482 0.973782i 0.426951π-0.426951\pi
0.227482 + 0.973782i 0.426951π0.426951\pi
878878 −12.1110 −0.408727
879879 0 0
880880 − 12.4105i − 0.418357i
881881 25.5247 0.859949 0.429974 0.902841i 0.358523π-0.358523\pi
0.429974 + 0.902841i 0.358523π0.358523\pi
882882 0 0
883883 6.45532 0.217239 0.108619 0.994083i 0.465357π-0.465357\pi
0.108619 + 0.994083i 0.465357π0.465357\pi
884884 − 2.81917i − 0.0948189i
885885 0 0
886886 1.88450 0.0633111
887887 −33.1208 −1.11209 −0.556043 0.831153i 0.687681π-0.687681\pi
−0.556043 + 0.831153i 0.687681π0.687681\pi
888888 0 0
889889 0 0
890890 − 16.2472i − 0.544608i
891891 0 0
892892 − 16.6034i − 0.555924i
893893 − 24.8572i − 0.831816i
894894 0 0
895895 45.8277i 1.53185i
896896 0 0
897897 0 0
898898 1.19292 0.0398082
899899 −26.7618 −0.892556
900900 0 0
901901 − 11.4298i − 0.380781i
902902 −14.8417 −0.494174
903903 0 0
904904 −16.7789 −0.558058
905905 − 15.6995i − 0.521870i
906906 0 0
907907 6.21512 0.206370 0.103185 0.994662i 0.467097π-0.467097\pi
0.103185 + 0.994662i 0.467097π0.467097\pi
908908 10.5489 0.350078
909909 0 0
910910 0 0
911911 − 18.0475i − 0.597941i −0.954262 0.298970i 0.903357π-0.903357\pi
0.954262 0.298970i 0.0966432π-0.0966432\pi
912912 0 0
913913 2.43121i 0.0804611i
914914 − 4.04199i − 0.133697i
915915 0 0
916916 19.2389i 0.635670i
917917 0 0
918918 0 0
919919 −8.25825 −0.272415 −0.136207 0.990680i 0.543491π-0.543491\pi
−0.136207 + 0.990680i 0.543491π0.543491\pi
920920 72.9057 2.40363
921921 0 0
922922 11.1959i 0.368716i
923923 10.1016 0.332498
924924 0 0
925925 −30.8513 −1.01438
926926 − 19.3132i − 0.634672i
927927 0 0
928928 −20.9769 −0.688600
929929 −34.7709 −1.14080 −0.570399 0.821368i 0.693211π-0.693211\pi
−0.570399 + 0.821368i 0.693211π0.693211\pi
930930 0 0
931931 0 0
932932 − 8.82710i − 0.289141i
933933 0 0
934934 − 17.8063i − 0.582639i
935935 8.82710i 0.288677i
936936 0 0
937937 − 51.0703i − 1.66839i −0.551466 0.834197i 0.685931π-0.685931\pi
0.551466 0.834197i 0.314069π-0.314069\pi
938938 0 0
939939 0 0
940940 −29.0292 −0.946829
941941 3.47744 0.113361 0.0566807 0.998392i 0.481948π-0.481948\pi
0.0566807 + 0.998392i 0.481948π0.481948\pi
942942 0 0
943943 90.6034i 2.95045i
944944 −3.47744 −0.113181
945945 0 0
946946 −3.33568 −0.108452
947947 − 14.3401i − 0.465989i −0.972478 0.232995i 0.925148π-0.925148\pi
0.972478 0.232995i 0.0748525π-0.0748525\pi
948948 0 0
949949 16.8794 0.547930
950950 −17.4413 −0.565869
951951 0 0
952952 0 0
953953 − 7.53697i − 0.244147i −0.992521 0.122073i 0.961046π-0.961046\pi
0.992521 0.122073i 0.0389543π-0.0389543\pi
954954 0 0
955955 − 27.6339i − 0.894213i
956956 25.0381i 0.809789i
957957 0 0
958958 − 14.1547i − 0.457318i
959959 0 0
960960 0 0
961961 −22.5638 −0.727864
962962 −5.36152 −0.172862
963963 0 0
964964 − 7.19797i − 0.231831i
965965 59.1015 1.90255
966966 0 0
967967 −11.6161 −0.373550 −0.186775 0.982403i 0.559803π-0.559803\pi
−0.186775 + 0.982403i 0.559803π0.559803\pi
968968 − 12.9087i − 0.414901i
969969 0 0
970970 −29.4734 −0.946333
971971 −35.4952 −1.13910 −0.569548 0.821958i 0.692882π-0.692882\pi
−0.569548 + 0.821958i 0.692882π0.692882\pi
972972 0 0
973973 0 0
974974 9.57414i 0.306775i
975975 0 0
976976 − 6.40659i − 0.205070i
977977 − 32.0094i − 1.02407i −0.858964 0.512036i 0.828891π-0.828891\pi
0.858964 0.512036i 0.171109π-0.171109\pi
978978 0 0
979979 − 17.5068i − 0.559520i
980980 0 0
981981 0 0
982982 0.185891 0.00593201
983983 49.4648 1.57768 0.788841 0.614598i 0.210682π-0.210682\pi
0.788841 + 0.614598i 0.210682π0.210682\pi
984984 0 0
985985 − 50.0462i − 1.59460i
986986 2.73067 0.0869623
987987 0 0
988988 11.0292 0.350887
989989 20.3632i 0.647511i
990990 0 0
991991 17.9518 0.570258 0.285129 0.958489i 0.407964π-0.407964\pi
0.285129 + 0.958489i 0.407964π0.407964\pi
992992 −41.9853 −1.33303
993993 0 0
994994 0 0
995995 28.6834i 0.909326i
996996 0 0
997997 − 33.5037i − 1.06107i −0.847662 0.530537i 0.821990π-0.821990\pi
0.847662 0.530537i 0.178010π-0.178010\pi
998998 − 8.08007i − 0.255770i
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.1322.5 12
3.2 odd 2 inner 1323.2.c.d.1322.8 12
7.4 even 3 189.2.p.d.26.4 yes 12
7.5 odd 6 189.2.p.d.80.3 yes 12
7.6 odd 2 inner 1323.2.c.d.1322.6 12
21.5 even 6 189.2.p.d.80.4 yes 12
21.11 odd 6 189.2.p.d.26.3 12
21.20 even 2 inner 1323.2.c.d.1322.7 12
63.4 even 3 567.2.s.f.26.3 12
63.5 even 6 567.2.i.f.269.4 12
63.11 odd 6 567.2.i.f.215.4 12
63.25 even 3 567.2.i.f.215.3 12
63.32 odd 6 567.2.s.f.26.4 12
63.40 odd 6 567.2.i.f.269.3 12
63.47 even 6 567.2.s.f.458.3 12
63.61 odd 6 567.2.s.f.458.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.p.d.26.3 12 21.11 odd 6
189.2.p.d.26.4 yes 12 7.4 even 3
189.2.p.d.80.3 yes 12 7.5 odd 6
189.2.p.d.80.4 yes 12 21.5 even 6
567.2.i.f.215.3 12 63.25 even 3
567.2.i.f.215.4 12 63.11 odd 6
567.2.i.f.269.3 12 63.40 odd 6
567.2.i.f.269.4 12 63.5 even 6
567.2.s.f.26.3 12 63.4 even 3
567.2.s.f.26.4 12 63.32 odd 6
567.2.s.f.458.3 12 63.47 even 6
567.2.s.f.458.4 12 63.61 odd 6
1323.2.c.d.1322.5 12 1.1 even 1 trivial
1323.2.c.d.1322.6 12 7.6 odd 2 inner
1323.2.c.d.1322.7 12 21.20 even 2 inner
1323.2.c.d.1322.8 12 3.2 odd 2 inner