Properties

Label 3364.2.a.q.1.7
Level 33643364
Weight 22
Character 3364.1
Self dual yes
Analytic conductor 26.86226.862
Analytic rank 11
Dimension 88
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3364,2,Mod(1,3364)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3364, 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("3364.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3364=22292 3364 = 2^{2} \cdot 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3364.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: 26.861675240026.8616752400
Analytic rank: 11
Dimension: 88
Coefficient field: 8.8.3266578125.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8x710x6+6x5+29x49x325x2x+1 x^{8} - x^{7} - 10x^{6} + 6x^{5} + 29x^{4} - 9x^{3} - 25x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.7
Root 1.580011.58001 of defining polynomial
Character χ\chi == 3364.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+0.729419q3+0.767443q52.02171q72.46795q9+3.70678q111.24494q13+0.559788q15+3.58130q173.29207q191.47467q212.34621q234.41103q253.98843q275.93955q31+2.70380q331.55155q350.856538q370.908085q397.92138q41+8.30193q431.89401q452.40165q472.91270q49+2.61227q51+11.7655q53+2.84474q552.40130q57+1.61067q5914.4889q61+4.98947q630.955422q654.41071q671.71137q69+15.2115q710.840227q733.21749q757.49402q779.84833q79+4.49461q8112.8266q83+2.74844q85+2.46866q89+2.51691q914.33242q932.52648q9516.1133q979.14813q99+O(q100)q+0.729419 q^{3} +0.767443 q^{5} -2.02171 q^{7} -2.46795 q^{9} +3.70678 q^{11} -1.24494 q^{13} +0.559788 q^{15} +3.58130 q^{17} -3.29207 q^{19} -1.47467 q^{21} -2.34621 q^{23} -4.41103 q^{25} -3.98843 q^{27} -5.93955 q^{31} +2.70380 q^{33} -1.55155 q^{35} -0.856538 q^{37} -0.908085 q^{39} -7.92138 q^{41} +8.30193 q^{43} -1.89401 q^{45} -2.40165 q^{47} -2.91270 q^{49} +2.61227 q^{51} +11.7655 q^{53} +2.84474 q^{55} -2.40130 q^{57} +1.61067 q^{59} -14.4889 q^{61} +4.98947 q^{63} -0.955422 q^{65} -4.41071 q^{67} -1.71137 q^{69} +15.2115 q^{71} -0.840227 q^{73} -3.21749 q^{75} -7.49402 q^{77} -9.84833 q^{79} +4.49461 q^{81} -12.8266 q^{83} +2.74844 q^{85} +2.46866 q^{89} +2.51691 q^{91} -4.33242 q^{93} -2.52648 q^{95} -16.1133 q^{97} -9.14813 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q4q3q52q7+4q95q11+4q13+17q1515q1711q1919q213q23+3q2516q27+9q3116q33+9q35+2q379q39++11q99+O(q100) 8 q - 4 q^{3} - q^{5} - 2 q^{7} + 4 q^{9} - 5 q^{11} + 4 q^{13} + 17 q^{15} - 15 q^{17} - 11 q^{19} - 19 q^{21} - 3 q^{23} + 3 q^{25} - 16 q^{27} + 9 q^{31} - 16 q^{33} + 9 q^{35} + 2 q^{37} - 9 q^{39}+ \cdots + 11 q^{99}+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 0 0
33 0.729419 0.421130 0.210565 0.977580i 0.432470π-0.432470\pi
0.210565 + 0.977580i 0.432470π0.432470\pi
44 0 0
55 0.767443 0.343211 0.171606 0.985166i 0.445105π-0.445105\pi
0.171606 + 0.985166i 0.445105π0.445105\pi
66 0 0
77 −2.02171 −0.764134 −0.382067 0.924135i 0.624788π-0.624788\pi
−0.382067 + 0.924135i 0.624788π0.624788\pi
88 0 0
99 −2.46795 −0.822649
1010 0 0
1111 3.70678 1.11764 0.558818 0.829290i 0.311255π-0.311255\pi
0.558818 + 0.829290i 0.311255π0.311255\pi
1212 0 0
1313 −1.24494 −0.345285 −0.172642 0.984985i 0.555231π-0.555231\pi
−0.172642 + 0.984985i 0.555231π0.555231\pi
1414 0 0
1515 0.559788 0.144537
1616 0 0
1717 3.58130 0.868593 0.434296 0.900770i 0.356997π-0.356997\pi
0.434296 + 0.900770i 0.356997π0.356997\pi
1818 0 0
1919 −3.29207 −0.755254 −0.377627 0.925958i 0.623260π-0.623260\pi
−0.377627 + 0.925958i 0.623260π0.623260\pi
2020 0 0
2121 −1.47467 −0.321800
2222 0 0
2323 −2.34621 −0.489219 −0.244609 0.969622i 0.578660π-0.578660\pi
−0.244609 + 0.969622i 0.578660π0.578660\pi
2424 0 0
2525 −4.41103 −0.882206
2626 0 0
2727 −3.98843 −0.767573
2828 0 0
2929 0 0
3030 0 0
3131 −5.93955 −1.06677 −0.533387 0.845871i 0.679081π-0.679081\pi
−0.533387 + 0.845871i 0.679081π0.679081\pi
3232 0 0
3333 2.70380 0.470670
3434 0 0
3535 −1.55155 −0.262259
3636 0 0
3737 −0.856538 −0.140814 −0.0704070 0.997518i 0.522430π-0.522430\pi
−0.0704070 + 0.997518i 0.522430π0.522430\pi
3838 0 0
3939 −0.908085 −0.145410
4040 0 0
4141 −7.92138 −1.23711 −0.618556 0.785741i 0.712282π-0.712282\pi
−0.618556 + 0.785741i 0.712282π0.712282\pi
4242 0 0
4343 8.30193 1.26603 0.633016 0.774139i 0.281817π-0.281817\pi
0.633016 + 0.774139i 0.281817π0.281817\pi
4444 0 0
4545 −1.89401 −0.282342
4646 0 0
4747 −2.40165 −0.350316 −0.175158 0.984540i 0.556044π-0.556044\pi
−0.175158 + 0.984540i 0.556044π0.556044\pi
4848 0 0
4949 −2.91270 −0.416100
5050 0 0
5151 2.61227 0.365791
5252 0 0
5353 11.7655 1.61611 0.808055 0.589107i 0.200520π-0.200520\pi
0.808055 + 0.589107i 0.200520π0.200520\pi
5454 0 0
5555 2.84474 0.383585
5656 0 0
5757 −2.40130 −0.318060
5858 0 0
5959 1.61067 0.209692 0.104846 0.994488i 0.466565π-0.466565\pi
0.104846 + 0.994488i 0.466565π0.466565\pi
6060 0 0
6161 −14.4889 −1.85511 −0.927556 0.373684i 0.878095π-0.878095\pi
−0.927556 + 0.373684i 0.878095π0.878095\pi
6262 0 0
6363 4.98947 0.628614
6464 0 0
6565 −0.955422 −0.118506
6666 0 0
6767 −4.41071 −0.538854 −0.269427 0.963021i 0.586834π-0.586834\pi
−0.269427 + 0.963021i 0.586834π0.586834\pi
6868 0 0
6969 −1.71137 −0.206025
7070 0 0
7171 15.2115 1.80527 0.902636 0.430404i 0.141629π-0.141629\pi
0.902636 + 0.430404i 0.141629π0.141629\pi
7272 0 0
7373 −0.840227 −0.0983412 −0.0491706 0.998790i 0.515658π-0.515658\pi
−0.0491706 + 0.998790i 0.515658π0.515658\pi
7474 0 0
7575 −3.21749 −0.371524
7676 0 0
7777 −7.49402 −0.854023
7878 0 0
7979 −9.84833 −1.10802 −0.554012 0.832509i 0.686904π-0.686904\pi
−0.554012 + 0.832509i 0.686904π0.686904\pi
8080 0 0
8181 4.49461 0.499401
8282 0 0
8383 −12.8266 −1.40790 −0.703949 0.710250i 0.748582π-0.748582\pi
−0.703949 + 0.710250i 0.748582π0.748582\pi
8484 0 0
8585 2.74844 0.298111
8686 0 0
8787 0 0
8888 0 0
8989 2.46866 0.261677 0.130839 0.991404i 0.458233π-0.458233\pi
0.130839 + 0.991404i 0.458233π0.458233\pi
9090 0 0
9191 2.51691 0.263844
9292 0 0
9393 −4.33242 −0.449251
9494 0 0
9595 −2.52648 −0.259211
9696 0 0
9797 −16.1133 −1.63606 −0.818030 0.575175i 0.804934π-0.804934\pi
−0.818030 + 0.575175i 0.804934π0.804934\pi
9898 0 0
9999 −9.14813 −0.919422
100100 0 0
101101 12.7240 1.26608 0.633042 0.774117i 0.281806π-0.281806\pi
0.633042 + 0.774117i 0.281806π0.281806\pi
102102 0 0
103103 −17.3194 −1.70653 −0.853264 0.521480i 0.825380π-0.825380\pi
−0.853264 + 0.521480i 0.825380π0.825380\pi
104104 0 0
105105 −1.13173 −0.110445
106106 0 0
107107 −6.79254 −0.656660 −0.328330 0.944563i 0.606486π-0.606486\pi
−0.328330 + 0.944563i 0.606486π0.606486\pi
108108 0 0
109109 9.13608 0.875078 0.437539 0.899199i 0.355850π-0.355850\pi
0.437539 + 0.899199i 0.355850π0.355850\pi
110110 0 0
111111 −0.624776 −0.0593011
112112 0 0
113113 −12.0253 −1.13125 −0.565623 0.824664i 0.691364π-0.691364\pi
−0.565623 + 0.824664i 0.691364π0.691364\pi
114114 0 0
115115 −1.80058 −0.167905
116116 0 0
117117 3.07245 0.284048
118118 0 0
119119 −7.24034 −0.663721
120120 0 0
121121 2.74021 0.249110
122122 0 0
123123 −5.77801 −0.520986
124124 0 0
125125 −7.22243 −0.645994
126126 0 0
127127 8.30315 0.736786 0.368393 0.929670i 0.379908π-0.379908\pi
0.368393 + 0.929670i 0.379908π0.379908\pi
128128 0 0
129129 6.05559 0.533165
130130 0 0
131131 2.12640 0.185784 0.0928920 0.995676i 0.470389π-0.470389\pi
0.0928920 + 0.995676i 0.470389π0.470389\pi
132132 0 0
133133 6.65561 0.577115
134134 0 0
135135 −3.06089 −0.263440
136136 0 0
137137 −18.2911 −1.56272 −0.781359 0.624082i 0.785473π-0.785473\pi
−0.781359 + 0.624082i 0.785473π0.785473\pi
138138 0 0
139139 −18.6779 −1.58424 −0.792119 0.610367i 0.791022π-0.791022\pi
−0.792119 + 0.610367i 0.791022π0.791022\pi
140140 0 0
141141 −1.75181 −0.147529
142142 0 0
143143 −4.61472 −0.385903
144144 0 0
145145 0 0
146146 0 0
147147 −2.12458 −0.175232
148148 0 0
149149 22.3871 1.83403 0.917013 0.398858i 0.130593π-0.130593\pi
0.917013 + 0.398858i 0.130593π0.130593\pi
150150 0 0
151151 0.319407 0.0259930 0.0129965 0.999916i 0.495863π-0.495863\pi
0.0129965 + 0.999916i 0.495863π0.495863\pi
152152 0 0
153153 −8.83846 −0.714547
154154 0 0
155155 −4.55827 −0.366129
156156 0 0
157157 −17.1206 −1.36637 −0.683187 0.730243i 0.739407π-0.739407\pi
−0.683187 + 0.730243i 0.739407π0.739407\pi
158158 0 0
159159 8.58195 0.680593
160160 0 0
161161 4.74335 0.373828
162162 0 0
163163 15.9530 1.24954 0.624769 0.780810i 0.285193π-0.285193\pi
0.624769 + 0.780810i 0.285193π0.285193\pi
164164 0 0
165165 2.07501 0.161539
166166 0 0
167167 −6.06511 −0.469332 −0.234666 0.972076i 0.575400π-0.575400\pi
−0.234666 + 0.972076i 0.575400π0.575400\pi
168168 0 0
169169 −11.4501 −0.880778
170170 0 0
171171 8.12467 0.621309
172172 0 0
173173 0.821089 0.0624263 0.0312131 0.999513i 0.490063π-0.490063\pi
0.0312131 + 0.999513i 0.490063π0.490063\pi
174174 0 0
175175 8.91782 0.674124
176176 0 0
177177 1.17486 0.0883076
178178 0 0
179179 20.0466 1.49835 0.749177 0.662370i 0.230449π-0.230449\pi
0.749177 + 0.662370i 0.230449π0.230449\pi
180180 0 0
181181 −6.89043 −0.512162 −0.256081 0.966655i 0.582431π-0.582431\pi
−0.256081 + 0.966655i 0.582431π0.582431\pi
182182 0 0
183183 −10.5685 −0.781244
184184 0 0
185185 −0.657344 −0.0483289
186186 0 0
187187 13.2751 0.970770
188188 0 0
189189 8.06343 0.586529
190190 0 0
191191 15.4002 1.11432 0.557159 0.830406i 0.311891π-0.311891\pi
0.557159 + 0.830406i 0.311891π0.311891\pi
192192 0 0
193193 −18.0067 −1.29615 −0.648077 0.761575i 0.724427π-0.724427\pi
−0.648077 + 0.761575i 0.724427π0.724427\pi
194194 0 0
195195 −0.696904 −0.0499063
196196 0 0
197197 −7.34986 −0.523656 −0.261828 0.965115i 0.584325π-0.584325\pi
−0.261828 + 0.965115i 0.584325π0.584325\pi
198198 0 0
199199 −10.5618 −0.748709 −0.374355 0.927286i 0.622136π-0.622136\pi
−0.374355 + 0.927286i 0.622136π0.622136\pi
200200 0 0
201201 −3.21726 −0.226928
202202 0 0
203203 0 0
204204 0 0
205205 −6.07921 −0.424590
206206 0 0
207207 5.79032 0.402455
208208 0 0
209209 −12.2030 −0.844098
210210 0 0
211211 −7.13512 −0.491202 −0.245601 0.969371i 0.578985π-0.578985\pi
−0.245601 + 0.969371i 0.578985π0.578985\pi
212212 0 0
213213 11.0956 0.760255
214214 0 0
215215 6.37126 0.434516
216216 0 0
217217 12.0080 0.815159
218218 0 0
219219 −0.612878 −0.0414145
220220 0 0
221221 −4.45851 −0.299912
222222 0 0
223223 0.144735 0.00969217 0.00484608 0.999988i 0.498457π-0.498457\pi
0.00484608 + 0.999988i 0.498457π0.498457\pi
224224 0 0
225225 10.8862 0.725746
226226 0 0
227227 14.0201 0.930545 0.465272 0.885168i 0.345956π-0.345956\pi
0.465272 + 0.885168i 0.345956π0.345956\pi
228228 0 0
229229 −4.15050 −0.274273 −0.137136 0.990552i 0.543790π-0.543790\pi
−0.137136 + 0.990552i 0.543790π0.543790\pi
230230 0 0
231231 −5.46629 −0.359655
232232 0 0
233233 21.6954 1.42131 0.710656 0.703540i 0.248398π-0.248398\pi
0.710656 + 0.703540i 0.248398π0.248398\pi
234234 0 0
235235 −1.84313 −0.120232
236236 0 0
237237 −7.18357 −0.466623
238238 0 0
239239 24.5869 1.59039 0.795197 0.606351i 0.207367π-0.207367\pi
0.795197 + 0.606351i 0.207367π0.207367\pi
240240 0 0
241241 2.48439 0.160034 0.0800168 0.996794i 0.474503π-0.474503\pi
0.0800168 + 0.996794i 0.474503π0.474503\pi
242242 0 0
243243 15.2437 0.977886
244244 0 0
245245 −2.23533 −0.142810
246246 0 0
247247 4.09844 0.260778
248248 0 0
249249 −9.35595 −0.592909
250250 0 0
251251 7.75412 0.489435 0.244718 0.969594i 0.421305π-0.421305\pi
0.244718 + 0.969594i 0.421305π0.421305\pi
252252 0 0
253253 −8.69688 −0.546768
254254 0 0
255255 2.00477 0.125543
256256 0 0
257257 −31.2147 −1.94712 −0.973559 0.228434i 0.926639π-0.926639\pi
−0.973559 + 0.228434i 0.926639π0.926639\pi
258258 0 0
259259 1.73167 0.107601
260260 0 0
261261 0 0
262262 0 0
263263 −10.4590 −0.644929 −0.322464 0.946582i 0.604511π-0.604511\pi
−0.322464 + 0.946582i 0.604511π0.604511\pi
264264 0 0
265265 9.02932 0.554667
266266 0 0
267267 1.80069 0.110200
268268 0 0
269269 −0.685928 −0.0418218 −0.0209109 0.999781i 0.506657π-0.506657\pi
−0.0209109 + 0.999781i 0.506657π0.506657\pi
270270 0 0
271271 −16.1931 −0.983660 −0.491830 0.870691i 0.663672π-0.663672\pi
−0.491830 + 0.870691i 0.663672π0.663672\pi
272272 0 0
273273 1.83588 0.111113
274274 0 0
275275 −16.3507 −0.985985
276276 0 0
277277 14.8322 0.891183 0.445591 0.895236i 0.352993π-0.352993\pi
0.445591 + 0.895236i 0.352993π0.352993\pi
278278 0 0
279279 14.6585 0.877581
280280 0 0
281281 −7.37493 −0.439951 −0.219976 0.975505i 0.570598π-0.570598\pi
−0.219976 + 0.975505i 0.570598π0.570598\pi
282282 0 0
283283 23.9057 1.42105 0.710524 0.703673i 0.248458π-0.248458\pi
0.710524 + 0.703673i 0.248458π0.248458\pi
284284 0 0
285285 −1.84286 −0.109162
286286 0 0
287287 16.0147 0.945319
288288 0 0
289289 −4.17430 −0.245547
290290 0 0
291291 −11.7534 −0.688995
292292 0 0
293293 −3.37749 −0.197315 −0.0986576 0.995121i 0.531455π-0.531455\pi
−0.0986576 + 0.995121i 0.531455π0.531455\pi
294294 0 0
295295 1.23610 0.0719685
296296 0 0
297297 −14.7842 −0.857867
298298 0 0
299299 2.92090 0.168920
300300 0 0
301301 −16.7841 −0.967418
302302 0 0
303303 9.28113 0.533187
304304 0 0
305305 −11.1194 −0.636695
306306 0 0
307307 −10.1287 −0.578075 −0.289038 0.957318i 0.593335π-0.593335\pi
−0.289038 + 0.957318i 0.593335π0.593335\pi
308308 0 0
309309 −12.6331 −0.718671
310310 0 0
311311 −14.3866 −0.815786 −0.407893 0.913030i 0.633736π-0.633736\pi
−0.407893 + 0.913030i 0.633736π0.633736\pi
312312 0 0
313313 29.7699 1.68269 0.841346 0.540497i 0.181764π-0.181764\pi
0.841346 + 0.540497i 0.181764π0.181764\pi
314314 0 0
315315 3.82913 0.215747
316316 0 0
317317 3.38943 0.190369 0.0951846 0.995460i 0.469656π-0.469656\pi
0.0951846 + 0.995460i 0.469656π0.469656\pi
318318 0 0
319319 0 0
320320 0 0
321321 −4.95461 −0.276540
322322 0 0
323323 −11.7899 −0.656008
324324 0 0
325325 5.49148 0.304612
326326 0 0
327327 6.66404 0.368522
328328 0 0
329329 4.85543 0.267688
330330 0 0
331331 −14.6345 −0.804385 −0.402192 0.915555i 0.631752π-0.631752\pi
−0.402192 + 0.915555i 0.631752π0.631752\pi
332332 0 0
333333 2.11389 0.115841
334334 0 0
335335 −3.38497 −0.184941
336336 0 0
337337 −11.2957 −0.615315 −0.307657 0.951497i 0.599545π-0.599545\pi
−0.307657 + 0.951497i 0.599545π0.599545\pi
338338 0 0
339339 −8.77149 −0.476402
340340 0 0
341341 −22.0166 −1.19227
342342 0 0
343343 20.0406 1.08209
344344 0 0
345345 −1.31338 −0.0707100
346346 0 0
347347 1.57899 0.0847648 0.0423824 0.999101i 0.486505π-0.486505\pi
0.0423824 + 0.999101i 0.486505π0.486505\pi
348348 0 0
349349 −4.99875 −0.267577 −0.133788 0.991010i 0.542714π-0.542714\pi
−0.133788 + 0.991010i 0.542714π0.542714\pi
350350 0 0
351351 4.96536 0.265031
352352 0 0
353353 −8.23964 −0.438552 −0.219276 0.975663i 0.570370π-0.570370\pi
−0.219276 + 0.975663i 0.570370π0.570370\pi
354354 0 0
355355 11.6740 0.619589
356356 0 0
357357 −5.28124 −0.279513
358358 0 0
359359 −6.20747 −0.327617 −0.163809 0.986492i 0.552378π-0.552378\pi
−0.163809 + 0.986492i 0.552378π0.552378\pi
360360 0 0
361361 −8.16225 −0.429592
362362 0 0
363363 1.99876 0.104908
364364 0 0
365365 −0.644827 −0.0337518
366366 0 0
367367 26.1215 1.36353 0.681765 0.731571i 0.261212π-0.261212\pi
0.681765 + 0.731571i 0.261212π0.261212\pi
368368 0 0
369369 19.5496 1.01771
370370 0 0
371371 −23.7863 −1.23492
372372 0 0
373373 14.2786 0.739316 0.369658 0.929168i 0.379475π-0.379475\pi
0.369658 + 0.929168i 0.379475π0.379475\pi
374374 0 0
375375 −5.26818 −0.272048
376376 0 0
377377 0 0
378378 0 0
379379 19.6128 1.00744 0.503720 0.863867i 0.331964π-0.331964\pi
0.503720 + 0.863867i 0.331964π0.331964\pi
380380 0 0
381381 6.05648 0.310283
382382 0 0
383383 −15.9953 −0.817322 −0.408661 0.912686i 0.634004π-0.634004\pi
−0.408661 + 0.912686i 0.634004π0.634004\pi
384384 0 0
385385 −5.75124 −0.293110
386386 0 0
387387 −20.4887 −1.04150
388388 0 0
389389 −4.89046 −0.247956 −0.123978 0.992285i 0.539565π-0.539565\pi
−0.123978 + 0.992285i 0.539565π0.539565\pi
390390 0 0
391391 −8.40248 −0.424932
392392 0 0
393393 1.55103 0.0782393
394394 0 0
395395 −7.55804 −0.380286
396396 0 0
397397 27.4917 1.37977 0.689884 0.723920i 0.257661π-0.257661\pi
0.689884 + 0.723920i 0.257661π0.257661\pi
398398 0 0
399399 4.85473 0.243041
400400 0 0
401401 −18.2792 −0.912821 −0.456410 0.889769i 0.650865π-0.650865\pi
−0.456410 + 0.889769i 0.650865π0.650865\pi
402402 0 0
403403 7.39440 0.368341
404404 0 0
405405 3.44935 0.171400
406406 0 0
407407 −3.17500 −0.157379
408408 0 0
409409 1.66374 0.0822665 0.0411332 0.999154i 0.486903π-0.486903\pi
0.0411332 + 0.999154i 0.486903π0.486903\pi
410410 0 0
411411 −13.3419 −0.658108
412412 0 0
413413 −3.25631 −0.160233
414414 0 0
415415 −9.84366 −0.483206
416416 0 0
417417 −13.6240 −0.667171
418418 0 0
419419 8.97520 0.438467 0.219234 0.975672i 0.429644π-0.429644\pi
0.219234 + 0.975672i 0.429644π0.429644\pi
420420 0 0
421421 19.7189 0.961041 0.480521 0.876983i 0.340448π-0.340448\pi
0.480521 + 0.876983i 0.340448π0.340448\pi
422422 0 0
423423 5.92714 0.288187
424424 0 0
425425 −15.7972 −0.766278
426426 0 0
427427 29.2923 1.41755
428428 0 0
429429 −3.36607 −0.162515
430430 0 0
431431 30.2008 1.45472 0.727362 0.686254i 0.240746π-0.240746\pi
0.727362 + 0.686254i 0.240746π0.240746\pi
432432 0 0
433433 9.82867 0.472336 0.236168 0.971712i 0.424108π-0.424108\pi
0.236168 + 0.971712i 0.424108π0.424108\pi
434434 0 0
435435 0 0
436436 0 0
437437 7.72390 0.369484
438438 0 0
439439 −12.4301 −0.593257 −0.296628 0.954993i 0.595862π-0.595862\pi
−0.296628 + 0.954993i 0.595862π0.595862\pi
440440 0 0
441441 7.18838 0.342304
442442 0 0
443443 28.9783 1.37680 0.688399 0.725332i 0.258314π-0.258314\pi
0.688399 + 0.725332i 0.258314π0.258314\pi
444444 0 0
445445 1.89456 0.0898106
446446 0 0
447447 16.3296 0.772364
448448 0 0
449449 −5.23266 −0.246945 −0.123472 0.992348i 0.539403π-0.539403\pi
−0.123472 + 0.992348i 0.539403π0.539403\pi
450450 0 0
451451 −29.3628 −1.38264
452452 0 0
453453 0.232982 0.0109464
454454 0 0
455455 1.93158 0.0905541
456456 0 0
457457 −28.4744 −1.33198 −0.665989 0.745962i 0.731990π-0.731990\pi
−0.665989 + 0.745962i 0.731990π0.731990\pi
458458 0 0
459459 −14.2838 −0.666708
460460 0 0
461461 −34.7454 −1.61825 −0.809127 0.587634i 0.800059π-0.800059\pi
−0.809127 + 0.587634i 0.800059π0.800059\pi
462462 0 0
463463 20.2963 0.943247 0.471624 0.881800i 0.343668π-0.343668\pi
0.471624 + 0.881800i 0.343668π0.343668\pi
464464 0 0
465465 −3.32489 −0.154188
466466 0 0
467467 −3.44474 −0.159404 −0.0797018 0.996819i 0.525397π-0.525397\pi
−0.0797018 + 0.996819i 0.525397π0.525397\pi
468468 0 0
469469 8.91716 0.411756
470470 0 0
471471 −12.4881 −0.575422
472472 0 0
473473 30.7734 1.41496
474474 0 0
475475 14.5214 0.666289
476476 0 0
477477 −29.0365 −1.32949
478478 0 0
479479 −36.4072 −1.66349 −0.831745 0.555158i 0.812658π-0.812658\pi
−0.831745 + 0.555158i 0.812658π0.812658\pi
480480 0 0
481481 1.06634 0.0486209
482482 0 0
483483 3.45989 0.157431
484484 0 0
485485 −12.3661 −0.561514
486486 0 0
487487 −0.113357 −0.00513670 −0.00256835 0.999997i 0.500818π-0.500818\pi
−0.00256835 + 0.999997i 0.500818π0.500818\pi
488488 0 0
489489 11.6365 0.526218
490490 0 0
491491 −20.9051 −0.943436 −0.471718 0.881749i 0.656366π-0.656366\pi
−0.471718 + 0.881749i 0.656366π0.656366\pi
492492 0 0
493493 0 0
494494 0 0
495495 −7.02067 −0.315556
496496 0 0
497497 −30.7532 −1.37947
498498 0 0
499499 36.9570 1.65442 0.827211 0.561891i 0.189926π-0.189926\pi
0.827211 + 0.561891i 0.189926π0.189926\pi
500500 0 0
501501 −4.42401 −0.197650
502502 0 0
503503 34.8086 1.55204 0.776019 0.630709i 0.217236π-0.217236\pi
0.776019 + 0.630709i 0.217236π0.217236\pi
504504 0 0
505505 9.76494 0.434534
506506 0 0
507507 −8.35194 −0.370923
508508 0 0
509509 21.1709 0.938382 0.469191 0.883097i 0.344546π-0.344546\pi
0.469191 + 0.883097i 0.344546π0.344546\pi
510510 0 0
511511 1.69869 0.0751458
512512 0 0
513513 13.1302 0.579712
514514 0 0
515515 −13.2916 −0.585699
516516 0 0
517517 −8.90237 −0.391526
518518 0 0
519519 0.598919 0.0262896
520520 0 0
521521 0.988926 0.0433257 0.0216628 0.999765i 0.493104π-0.493104\pi
0.0216628 + 0.999765i 0.493104π0.493104\pi
522522 0 0
523523 −24.5416 −1.07313 −0.536564 0.843859i 0.680278π-0.680278\pi
−0.536564 + 0.843859i 0.680278π0.680278\pi
524524 0 0
525525 6.50483 0.283894
526526 0 0
527527 −21.2713 −0.926593
528528 0 0
529529 −17.4953 −0.760665
530530 0 0
531531 −3.97506 −0.172503
532532 0 0
533533 9.86166 0.427156
534534 0 0
535535 −5.21289 −0.225373
536536 0 0
537537 14.6224 0.631002
538538 0 0
539539 −10.7967 −0.465048
540540 0 0
541541 19.6472 0.844698 0.422349 0.906433i 0.361206π-0.361206\pi
0.422349 + 0.906433i 0.361206π0.361206\pi
542542 0 0
543543 −5.02601 −0.215687
544544 0 0
545545 7.01142 0.300336
546546 0 0
547547 19.9629 0.853551 0.426775 0.904358i 0.359650π-0.359650\pi
0.426775 + 0.904358i 0.359650π0.359650\pi
548548 0 0
549549 35.7578 1.52611
550550 0 0
551551 0 0
552552 0 0
553553 19.9105 0.846679
554554 0 0
555555 −0.479480 −0.0203528
556556 0 0
557557 11.4997 0.487257 0.243629 0.969869i 0.421662π-0.421662\pi
0.243629 + 0.969869i 0.421662π0.421662\pi
558558 0 0
559559 −10.3354 −0.437142
560560 0 0
561561 9.68310 0.408821
562562 0 0
563563 44.7407 1.88560 0.942798 0.333365i 0.108184π-0.108184\pi
0.942798 + 0.333365i 0.108184π0.108184\pi
564564 0 0
565565 −9.22874 −0.388256
566566 0 0
567567 −9.08678 −0.381609
568568 0 0
569569 −25.6562 −1.07556 −0.537781 0.843084i 0.680737π-0.680737\pi
−0.537781 + 0.843084i 0.680737π0.680737\pi
570570 0 0
571571 −22.1209 −0.925730 −0.462865 0.886429i 0.653178π-0.653178\pi
−0.462865 + 0.886429i 0.653178π0.653178\pi
572572 0 0
573573 11.2332 0.469273
574574 0 0
575575 10.3492 0.431592
576576 0 0
577577 6.41863 0.267211 0.133606 0.991035i 0.457344π-0.457344\pi
0.133606 + 0.991035i 0.457344π0.457344\pi
578578 0 0
579579 −13.1345 −0.545850
580580 0 0
581581 25.9316 1.07582
582582 0 0
583583 43.6119 1.80622
584584 0 0
585585 2.35793 0.0974885
586586 0 0
587587 18.3752 0.758427 0.379213 0.925309i 0.376195π-0.376195\pi
0.379213 + 0.925309i 0.376195π0.376195\pi
588588 0 0
589589 19.5534 0.805686
590590 0 0
591591 −5.36113 −0.220528
592592 0 0
593593 −42.9405 −1.76336 −0.881678 0.471851i 0.843586π-0.843586\pi
−0.881678 + 0.471851i 0.843586π0.843586\pi
594594 0 0
595595 −5.55655 −0.227796
596596 0 0
597597 −7.70402 −0.315304
598598 0 0
599599 36.0434 1.47269 0.736346 0.676605i 0.236550π-0.236550\pi
0.736346 + 0.676605i 0.236550π0.236550\pi
600600 0 0
601601 36.9395 1.50679 0.753396 0.657567i 0.228414π-0.228414\pi
0.753396 + 0.657567i 0.228414π0.228414\pi
602602 0 0
603603 10.8854 0.443288
604604 0 0
605605 2.10295 0.0854972
606606 0 0
607607 −22.4913 −0.912893 −0.456446 0.889751i 0.650878π-0.650878\pi
−0.456446 + 0.889751i 0.650878π0.650878\pi
608608 0 0
609609 0 0
610610 0 0
611611 2.98991 0.120959
612612 0 0
613613 −4.90637 −0.198167 −0.0990833 0.995079i 0.531591π-0.531591\pi
−0.0990833 + 0.995079i 0.531591π0.531591\pi
614614 0 0
615615 −4.43429 −0.178808
616616 0 0
617617 −3.17098 −0.127659 −0.0638295 0.997961i 0.520331π-0.520331\pi
−0.0638295 + 0.997961i 0.520331π0.520331\pi
618618 0 0
619619 20.7571 0.834299 0.417149 0.908838i 0.363029π-0.363029\pi
0.417149 + 0.908838i 0.363029π0.363029\pi
620620 0 0
621621 9.35769 0.375511
622622 0 0
623623 −4.99091 −0.199957
624624 0 0
625625 16.5124 0.660494
626626 0 0
627627 −8.90110 −0.355476
628628 0 0
629629 −3.06752 −0.122310
630630 0 0
631631 −14.0960 −0.561151 −0.280576 0.959832i 0.590525π-0.590525\pi
−0.280576 + 0.959832i 0.590525π0.590525\pi
632632 0 0
633633 −5.20449 −0.206860
634634 0 0
635635 6.37220 0.252873
636636 0 0
637637 3.62614 0.143673
638638 0 0
639639 −37.5412 −1.48511
640640 0 0
641641 −26.1964 −1.03470 −0.517349 0.855775i 0.673081π-0.673081\pi
−0.517349 + 0.855775i 0.673081π0.673081\pi
642642 0 0
643643 22.3949 0.883170 0.441585 0.897219i 0.354416π-0.354416\pi
0.441585 + 0.897219i 0.354416π0.354416\pi
644644 0 0
645645 4.64732 0.182988
646646 0 0
647647 32.6252 1.28263 0.641314 0.767278i 0.278389π-0.278389\pi
0.641314 + 0.767278i 0.278389π0.278389\pi
648648 0 0
649649 5.97041 0.234359
650650 0 0
651651 8.75890 0.343288
652652 0 0
653653 −22.2236 −0.869678 −0.434839 0.900508i 0.643195π-0.643195\pi
−0.434839 + 0.900508i 0.643195π0.643195\pi
654654 0 0
655655 1.63189 0.0637631
656656 0 0
657657 2.07364 0.0809003
658658 0 0
659659 35.3819 1.37828 0.689142 0.724627i 0.257988π-0.257988\pi
0.689142 + 0.724627i 0.257988π0.257988\pi
660660 0 0
661661 41.8752 1.62876 0.814378 0.580334i 0.197078π-0.197078\pi
0.814378 + 0.580334i 0.197078π0.197078\pi
662662 0 0
663663 −3.25212 −0.126302
664664 0 0
665665 5.10780 0.198072
666666 0 0
667667 0 0
668668 0 0
669669 0.105572 0.00408167
670670 0 0
671671 −53.7071 −2.07334
672672 0 0
673673 −32.3743 −1.24794 −0.623970 0.781449i 0.714481π-0.714481\pi
−0.623970 + 0.781449i 0.714481π0.714481\pi
674674 0 0
675675 17.5931 0.677158
676676 0 0
677677 38.9484 1.49691 0.748454 0.663186i 0.230796π-0.230796\pi
0.748454 + 0.663186i 0.230796π0.230796\pi
678678 0 0
679679 32.5764 1.25017
680680 0 0
681681 10.2265 0.391881
682682 0 0
683683 39.9899 1.53017 0.765086 0.643928i 0.222696π-0.222696\pi
0.765086 + 0.643928i 0.222696π0.222696\pi
684684 0 0
685685 −14.0374 −0.536342
686686 0 0
687687 −3.02745 −0.115505
688688 0 0
689689 −14.6473 −0.558018
690690 0 0
691691 −19.7880 −0.752770 −0.376385 0.926463i 0.622833π-0.622833\pi
−0.376385 + 0.926463i 0.622833π0.622833\pi
692692 0 0
693693 18.4949 0.702561
694694 0 0
695695 −14.3342 −0.543728
696696 0 0
697697 −28.3688 −1.07455
698698 0 0
699699 15.8250 0.598557
700700 0 0
701701 −29.4121 −1.11088 −0.555440 0.831557i 0.687450π-0.687450\pi
−0.555440 + 0.831557i 0.687450π0.687450\pi
702702 0 0
703703 2.81979 0.106350
704704 0 0
705705 −1.34441 −0.0506335
706706 0 0
707707 −25.7242 −0.967458
708708 0 0
709709 −40.5367 −1.52239 −0.761193 0.648525i 0.775386π-0.775386\pi
−0.761193 + 0.648525i 0.775386π0.775386\pi
710710 0 0
711711 24.3052 0.911515
712712 0 0
713713 13.9354 0.521886
714714 0 0
715715 −3.54154 −0.132446
716716 0 0
717717 17.9342 0.669763
718718 0 0
719719 5.08472 0.189628 0.0948141 0.995495i 0.469774π-0.469774\pi
0.0948141 + 0.995495i 0.469774π0.469774\pi
720720 0 0
721721 35.0147 1.30402
722722 0 0
723723 1.81216 0.0673951
724724 0 0
725725 0 0
726726 0 0
727727 −5.33242 −0.197768 −0.0988842 0.995099i 0.531527π-0.531527\pi
−0.0988842 + 0.995099i 0.531527π0.531527\pi
728728 0 0
729729 −2.36474 −0.0875830
730730 0 0
731731 29.7317 1.09967
732732 0 0
733733 8.74448 0.322985 0.161492 0.986874i 0.448369π-0.448369\pi
0.161492 + 0.986874i 0.448369π0.448369\pi
734734 0 0
735735 −1.63049 −0.0601416
736736 0 0
737737 −16.3495 −0.602242
738738 0 0
739739 −25.1780 −0.926186 −0.463093 0.886310i 0.653260π-0.653260\pi
−0.463093 + 0.886310i 0.653260π0.653260\pi
740740 0 0
741741 2.98948 0.109821
742742 0 0
743743 50.9579 1.86946 0.934731 0.355355i 0.115640π-0.115640\pi
0.934731 + 0.355355i 0.115640π0.115640\pi
744744 0 0
745745 17.1808 0.629458
746746 0 0
747747 31.6553 1.15821
748748 0 0
749749 13.7325 0.501776
750750 0 0
751751 22.5333 0.822253 0.411126 0.911578i 0.365135π-0.365135\pi
0.411126 + 0.911578i 0.365135π0.365135\pi
752752 0 0
753753 5.65600 0.206116
754754 0 0
755755 0.245127 0.00892108
756756 0 0
757757 20.2369 0.735522 0.367761 0.929920i 0.380124π-0.380124\pi
0.367761 + 0.929920i 0.380124π0.380124\pi
758758 0 0
759759 −6.34367 −0.230261
760760 0 0
761761 41.6120 1.50844 0.754218 0.656625i 0.228016π-0.228016\pi
0.754218 + 0.656625i 0.228016π0.228016\pi
762762 0 0
763763 −18.4705 −0.668677
764764 0 0
765765 −6.78301 −0.245240
766766 0 0
767767 −2.00519 −0.0724034
768768 0 0
769769 3.47614 0.125353 0.0626764 0.998034i 0.480036π-0.480036\pi
0.0626764 + 0.998034i 0.480036π0.480036\pi
770770 0 0
771771 −22.7686 −0.819991
772772 0 0
773773 21.1005 0.758932 0.379466 0.925206i 0.376108π-0.376108\pi
0.379466 + 0.925206i 0.376108π0.376108\pi
774774 0 0
775775 26.1995 0.941115
776776 0 0
777777 1.26311 0.0453140
778778 0 0
779779 26.0778 0.934333
780780 0 0
781781 56.3857 2.01764
782782 0 0
783783 0 0
784784 0 0
785785 −13.1391 −0.468955
786786 0 0
787787 14.2337 0.507378 0.253689 0.967286i 0.418356π-0.418356\pi
0.253689 + 0.967286i 0.418356π0.418356\pi
788788 0 0
789789 −7.62899 −0.271599
790790 0 0
791791 24.3117 0.864423
792792 0 0
793793 18.0378 0.640542
794794 0 0
795795 6.58616 0.233587
796796 0 0
797797 −50.5995 −1.79233 −0.896163 0.443724i 0.853657π-0.853657\pi
−0.896163 + 0.443724i 0.853657π0.853657\pi
798798 0 0
799799 −8.60101 −0.304282
800800 0 0
801801 −6.09252 −0.215269
802802 0 0
803803 −3.11454 −0.109910
804804 0 0
805805 3.64025 0.128302
806806 0 0
807807 −0.500329 −0.0176124
808808 0 0
809809 −53.0220 −1.86415 −0.932077 0.362261i 0.882005π-0.882005\pi
−0.932077 + 0.362261i 0.882005π0.882005\pi
810810 0 0
811811 36.6813 1.28805 0.644027 0.765003i 0.277262π-0.277262\pi
0.644027 + 0.765003i 0.277262π0.277262\pi
812812 0 0
813813 −11.8116 −0.414249
814814 0 0
815815 12.2430 0.428855
816816 0 0
817817 −27.3306 −0.956175
818818 0 0
819819 −6.21160 −0.217051
820820 0 0
821821 26.0472 0.909054 0.454527 0.890733i 0.349808π-0.349808\pi
0.454527 + 0.890733i 0.349808π0.349808\pi
822822 0 0
823823 −0.553811 −0.0193046 −0.00965231 0.999953i 0.503072π-0.503072\pi
−0.00965231 + 0.999953i 0.503072π0.503072\pi
824824 0 0
825825 −11.9265 −0.415228
826826 0 0
827827 −46.5323 −1.61809 −0.809043 0.587750i 0.800014π-0.800014\pi
−0.809043 + 0.587750i 0.800014π0.800014\pi
828828 0 0
829829 −15.5265 −0.539258 −0.269629 0.962964i 0.586901π-0.586901\pi
−0.269629 + 0.962964i 0.586901π0.586901\pi
830830 0 0
831831 10.8189 0.375304
832832 0 0
833833 −10.4312 −0.361421
834834 0 0
835835 −4.65463 −0.161080
836836 0 0
837837 23.6895 0.818828
838838 0 0
839839 −44.4093 −1.53318 −0.766590 0.642137i 0.778048π-0.778048\pi
−0.766590 + 0.642137i 0.778048π0.778048\pi
840840 0 0
841841 0 0
842842 0 0
843843 −5.37942 −0.185277
844844 0 0
845845 −8.78732 −0.302293
846846 0 0
847847 −5.53989 −0.190353
848848 0 0
849849 17.4373 0.598446
850850 0 0
851851 2.00962 0.0688888
852852 0 0
853853 −3.03167 −0.103803 −0.0519013 0.998652i 0.516528π-0.516528\pi
−0.0519013 + 0.998652i 0.516528π0.516528\pi
854854 0 0
855855 6.23522 0.213240
856856 0 0
857857 −3.80022 −0.129813 −0.0649064 0.997891i 0.520675π-0.520675\pi
−0.0649064 + 0.997891i 0.520675π0.520675\pi
858858 0 0
859859 −11.1993 −0.382115 −0.191057 0.981579i 0.561192π-0.561192\pi
−0.191057 + 0.981579i 0.561192π0.561192\pi
860860 0 0
861861 11.6814 0.398103
862862 0 0
863863 −36.4426 −1.24052 −0.620260 0.784396i 0.712973π-0.712973\pi
−0.620260 + 0.784396i 0.712973π0.712973\pi
864864 0 0
865865 0.630139 0.0214254
866866 0 0
867867 −3.04481 −0.103407
868868 0 0
869869 −36.5056 −1.23837
870870 0 0
871871 5.49108 0.186058
872872 0 0
873873 39.7669 1.34590
874874 0 0
875875 14.6016 0.493626
876876 0 0
877877 −27.6875 −0.934940 −0.467470 0.884009i 0.654834π-0.654834\pi
−0.467470 + 0.884009i 0.654834π0.654834\pi
878878 0 0
879879 −2.46361 −0.0830954
880880 0 0
881881 −22.6489 −0.763062 −0.381531 0.924356i 0.624603π-0.624603\pi
−0.381531 + 0.924356i 0.624603π0.624603\pi
882882 0 0
883883 −28.0182 −0.942887 −0.471443 0.881896i 0.656267π-0.656267\pi
−0.471443 + 0.881896i 0.656267π0.656267\pi
884884 0 0
885885 0.901635 0.0303081
886886 0 0
887887 6.85335 0.230113 0.115057 0.993359i 0.463295π-0.463295\pi
0.115057 + 0.993359i 0.463295π0.463295\pi
888888 0 0
889889 −16.7866 −0.563003
890890 0 0
891891 16.6605 0.558148
892892 0 0
893893 7.90640 0.264578
894894 0 0
895895 15.3846 0.514252
896896 0 0
897897 2.13056 0.0711373
898898 0 0
899899 0 0
900900 0 0
901901 42.1356 1.40374
902902 0 0
903903 −12.2426 −0.407409
904904 0 0
905905 −5.28801 −0.175780
906906 0 0
907907 −2.49857 −0.0829636 −0.0414818 0.999139i 0.513208π-0.513208\pi
−0.0414818 + 0.999139i 0.513208π0.513208\pi
908908 0 0
909909 −31.4021 −1.04154
910910 0 0
911911 39.7230 1.31608 0.658041 0.752982i 0.271385π-0.271385\pi
0.658041 + 0.752982i 0.271385π0.271385\pi
912912 0 0
913913 −47.5452 −1.57352
914914 0 0
915915 −8.11071 −0.268132
916916 0 0
917917 −4.29895 −0.141964
918918 0 0
919919 0.936263 0.0308845 0.0154422 0.999881i 0.495084π-0.495084\pi
0.0154422 + 0.999881i 0.495084π0.495084\pi
920920 0 0
921921 −7.38807 −0.243445
922922 0 0
923923 −18.9374 −0.623333
924924 0 0
925925 3.77822 0.124227
926926 0 0
927927 42.7433 1.40387
928928 0 0
929929 12.6079 0.413653 0.206827 0.978378i 0.433686π-0.433686\pi
0.206827 + 0.978378i 0.433686π0.433686\pi
930930 0 0
931931 9.58882 0.314261
932932 0 0
933933 −10.4938 −0.343553
934934 0 0
935935 10.1879 0.333179
936936 0 0
937937 2.55653 0.0835183 0.0417592 0.999128i 0.486704π-0.486704\pi
0.0417592 + 0.999128i 0.486704π0.486704\pi
938938 0 0
939939 21.7147 0.708633
940940 0 0
941941 35.4450 1.15547 0.577736 0.816223i 0.303936π-0.303936\pi
0.577736 + 0.816223i 0.303936π0.303936\pi
942942 0 0
943943 18.5852 0.605218
944944 0 0
945945 6.18823 0.201303
946946 0 0
947947 13.9515 0.453362 0.226681 0.973969i 0.427213π-0.427213\pi
0.226681 + 0.973969i 0.427213π0.427213\pi
948948 0 0
949949 1.04603 0.0339557
950950 0 0
951951 2.47232 0.0801703
952952 0 0
953953 −2.34460 −0.0759490 −0.0379745 0.999279i 0.512091π-0.512091\pi
−0.0379745 + 0.999279i 0.512091π0.512091\pi
954954 0 0
955955 11.8188 0.382446
956956 0 0
957957 0 0
958958 0 0
959959 36.9793 1.19413
960960 0 0
961961 4.27827 0.138009
962962 0 0
963963 16.7636 0.540201
964964 0 0
965965 −13.8192 −0.444854
966966 0 0
967967 −36.0689 −1.15990 −0.579949 0.814653i 0.696928π-0.696928\pi
−0.579949 + 0.814653i 0.696928π0.696928\pi
968968 0 0
969969 −8.59978 −0.276265
970970 0 0
971971 −33.0640 −1.06108 −0.530538 0.847661i 0.678010π-0.678010\pi
−0.530538 + 0.847661i 0.678010π0.678010\pi
972972 0 0
973973 37.7612 1.21057
974974 0 0
975975 4.00559 0.128282
976976 0 0
977977 40.2148 1.28659 0.643293 0.765620i 0.277568π-0.277568\pi
0.643293 + 0.765620i 0.277568π0.277568\pi
978978 0 0
979979 9.15077 0.292460
980980 0 0
981981 −22.5474 −0.719882
982982 0 0
983983 5.32325 0.169785 0.0848927 0.996390i 0.472945π-0.472945\pi
0.0848927 + 0.996390i 0.472945π0.472945\pi
984984 0 0
985985 −5.64060 −0.179725
986986 0 0
987987 3.54164 0.112732
988988 0 0
989989 −19.4781 −0.619367
990990 0 0
991991 −27.9955 −0.889307 −0.444654 0.895703i 0.646673π-0.646673\pi
−0.444654 + 0.895703i 0.646673π0.646673\pi
992992 0 0
993993 −10.6747 −0.338751
994994 0 0
995995 −8.10562 −0.256965
996996 0 0
997997 −19.4084 −0.614671 −0.307336 0.951601i 0.599437π-0.599437\pi
−0.307336 + 0.951601i 0.599437π0.599437\pi
998998 0 0
999999 3.41624 0.108085
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 3364.2.a.q.1.7 8
29.12 odd 4 3364.2.c.k.1681.12 16
29.17 odd 4 3364.2.c.k.1681.5 16
29.28 even 2 3364.2.a.r.1.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3364.2.a.q.1.7 8 1.1 even 1 trivial
3364.2.a.r.1.2 yes 8 29.28 even 2
3364.2.c.k.1681.5 16 29.17 odd 4
3364.2.c.k.1681.12 16 29.12 odd 4