Properties

Label 3364.2.a.p.1.4
Level 33643364
Weight 22
Character 3364.1
Self dual yes
Analytic conductor 26.86226.862
Analytic rank 00
Dimension 66
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: 00
Dimension: 66
Coefficient field: 6.6.6456289.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x512x4+3x3+40x2+6x29 x^{6} - x^{5} - 12x^{4} + 3x^{3} + 40x^{2} + 6x - 29 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 116)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 1.46835-1.46835 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+2.46835q3+3.45542q50.468352q7+3.09276q9+6.44782q112.67149q13+8.52918q15+3.05467q17+5.65536q191.15606q212.65625q23+6.93990q25+0.228972q27+0.162294q31+15.9155q331.61835q358.00432q376.59417q397.71247q416.04030q43+10.6868q4510.2021q476.78065q49+7.54001q51+2.66487q53+22.2799q55+13.9594q57+3.41835q596.43590q611.44850q639.23110q65+2.23003q676.55657q697.96768q713.69941q73+17.1301q753.01985q774.67133q798.71311q81+8.87003q83+10.5552q85+1.02703q89+1.25120q91+0.400599q93+19.5416q95+18.5120q97+19.9416q99+O(q100)q+2.46835 q^{3} +3.45542 q^{5} -0.468352 q^{7} +3.09276 q^{9} +6.44782 q^{11} -2.67149 q^{13} +8.52918 q^{15} +3.05467 q^{17} +5.65536 q^{19} -1.15606 q^{21} -2.65625 q^{23} +6.93990 q^{25} +0.228972 q^{27} +0.162294 q^{31} +15.9155 q^{33} -1.61835 q^{35} -8.00432 q^{37} -6.59417 q^{39} -7.71247 q^{41} -6.04030 q^{43} +10.6868 q^{45} -10.2021 q^{47} -6.78065 q^{49} +7.54001 q^{51} +2.66487 q^{53} +22.2799 q^{55} +13.9594 q^{57} +3.41835 q^{59} -6.43590 q^{61} -1.44850 q^{63} -9.23110 q^{65} +2.23003 q^{67} -6.55657 q^{69} -7.96768 q^{71} -3.69941 q^{73} +17.1301 q^{75} -3.01985 q^{77} -4.67133 q^{79} -8.71311 q^{81} +8.87003 q^{83} +10.5552 q^{85} +1.02703 q^{89} +1.25120 q^{91} +0.400599 q^{93} +19.5416 q^{95} +18.5120 q^{97} +19.9416 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+5q3+10q5+7q7+11q9+9q11+14q13+10q15+5q17+9q1919q21+15q23+16q25+20q2711q31+22q33+10q3516q37+22q39++8q99+O(q100) 6 q + 5 q^{3} + 10 q^{5} + 7 q^{7} + 11 q^{9} + 9 q^{11} + 14 q^{13} + 10 q^{15} + 5 q^{17} + 9 q^{19} - 19 q^{21} + 15 q^{23} + 16 q^{25} + 20 q^{27} - 11 q^{31} + 22 q^{33} + 10 q^{35} - 16 q^{37} + 22 q^{39}+ \cdots + 8 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 2.46835 1.42510 0.712552 0.701619i 0.247539π-0.247539\pi
0.712552 + 0.701619i 0.247539π0.247539\pi
44 0 0
55 3.45542 1.54531 0.772655 0.634827i 0.218929π-0.218929\pi
0.772655 + 0.634827i 0.218929π0.218929\pi
66 0 0
77 −0.468352 −0.177021 −0.0885103 0.996075i 0.528211π-0.528211\pi
−0.0885103 + 0.996075i 0.528211π0.528211\pi
88 0 0
99 3.09276 1.03092
1010 0 0
1111 6.44782 1.94409 0.972045 0.234795i 0.0754418π-0.0754418\pi
0.972045 + 0.234795i 0.0754418π0.0754418\pi
1212 0 0
1313 −2.67149 −0.740937 −0.370468 0.928845i 0.620803π-0.620803\pi
−0.370468 + 0.928845i 0.620803π0.620803\pi
1414 0 0
1515 8.52918 2.20223
1616 0 0
1717 3.05467 0.740867 0.370434 0.928859i 0.379209π-0.379209\pi
0.370434 + 0.928859i 0.379209π0.379209\pi
1818 0 0
1919 5.65536 1.29743 0.648714 0.761033i 0.275307π-0.275307\pi
0.648714 + 0.761033i 0.275307π0.275307\pi
2020 0 0
2121 −1.15606 −0.252273
2222 0 0
2323 −2.65625 −0.553867 −0.276934 0.960889i 0.589318π-0.589318\pi
−0.276934 + 0.960889i 0.589318π0.589318\pi
2424 0 0
2525 6.93990 1.38798
2626 0 0
2727 0.228972 0.0440656
2828 0 0
2929 0 0
3030 0 0
3131 0.162294 0.0291489 0.0145745 0.999894i 0.495361π-0.495361\pi
0.0145745 + 0.999894i 0.495361π0.495361\pi
3232 0 0
3333 15.9155 2.77053
3434 0 0
3535 −1.61835 −0.273551
3636 0 0
3737 −8.00432 −1.31590 −0.657951 0.753061i 0.728576π-0.728576\pi
−0.657951 + 0.753061i 0.728576π0.728576\pi
3838 0 0
3939 −6.59417 −1.05591
4040 0 0
4141 −7.71247 −1.20449 −0.602243 0.798313i 0.705726π-0.705726\pi
−0.602243 + 0.798313i 0.705726π0.705726\pi
4242 0 0
4343 −6.04030 −0.921137 −0.460568 0.887624i 0.652354π-0.652354\pi
−0.460568 + 0.887624i 0.652354π0.652354\pi
4444 0 0
4545 10.6868 1.59309
4646 0 0
4747 −10.2021 −1.48813 −0.744065 0.668107i 0.767105π-0.767105\pi
−0.744065 + 0.668107i 0.767105π0.767105\pi
4848 0 0
4949 −6.78065 −0.968664
5050 0 0
5151 7.54001 1.05581
5252 0 0
5353 2.66487 0.366049 0.183024 0.983108i 0.441411π-0.441411\pi
0.183024 + 0.983108i 0.441411π0.441411\pi
5454 0 0
5555 22.2799 3.00422
5656 0 0
5757 13.9594 1.84897
5858 0 0
5959 3.41835 0.445031 0.222516 0.974929i 0.428573π-0.428573\pi
0.222516 + 0.974929i 0.428573π0.428573\pi
6060 0 0
6161 −6.43590 −0.824033 −0.412016 0.911176i 0.635175π-0.635175\pi
−0.412016 + 0.911176i 0.635175π0.635175\pi
6262 0 0
6363 −1.44850 −0.182494
6464 0 0
6565 −9.23110 −1.14498
6666 0 0
6767 2.23003 0.272441 0.136221 0.990679i 0.456504π-0.456504\pi
0.136221 + 0.990679i 0.456504π0.456504\pi
6868 0 0
6969 −6.55657 −0.789318
7070 0 0
7171 −7.96768 −0.945590 −0.472795 0.881172i 0.656755π-0.656755\pi
−0.472795 + 0.881172i 0.656755π0.656755\pi
7272 0 0
7373 −3.69941 −0.432984 −0.216492 0.976284i 0.569461π-0.569461\pi
−0.216492 + 0.976284i 0.569461π0.569461\pi
7474 0 0
7575 17.1301 1.97802
7676 0 0
7777 −3.01985 −0.344144
7878 0 0
7979 −4.67133 −0.525566 −0.262783 0.964855i 0.584640π-0.584640\pi
−0.262783 + 0.964855i 0.584640π0.584640\pi
8080 0 0
8181 −8.71311 −0.968123
8282 0 0
8383 8.87003 0.973612 0.486806 0.873510i 0.338162π-0.338162\pi
0.486806 + 0.873510i 0.338162π0.338162\pi
8484 0 0
8585 10.5552 1.14487
8686 0 0
8787 0 0
8888 0 0
8989 1.02703 0.108865 0.0544324 0.998517i 0.482665π-0.482665\pi
0.0544324 + 0.998517i 0.482665π0.482665\pi
9090 0 0
9191 1.25120 0.131161
9292 0 0
9393 0.400599 0.0415402
9494 0 0
9595 19.5416 2.00493
9696 0 0
9797 18.5120 1.87961 0.939807 0.341706i 0.111005π-0.111005\pi
0.939807 + 0.341706i 0.111005π0.111005\pi
9898 0 0
9999 19.9416 2.00420
100100 0 0
101101 −10.9463 −1.08919 −0.544597 0.838698i 0.683317π-0.683317\pi
−0.544597 + 0.838698i 0.683317π0.683317\pi
102102 0 0
103103 2.04246 0.201249 0.100625 0.994924i 0.467916π-0.467916\pi
0.100625 + 0.994924i 0.467916π0.467916\pi
104104 0 0
105105 −3.99466 −0.389839
106106 0 0
107107 11.5539 1.11696 0.558478 0.829519i 0.311385π-0.311385\pi
0.558478 + 0.829519i 0.311385π0.311385\pi
108108 0 0
109109 3.58211 0.343103 0.171552 0.985175i 0.445122π-0.445122\pi
0.171552 + 0.985175i 0.445122π0.445122\pi
110110 0 0
111111 −19.7575 −1.87530
112112 0 0
113113 −5.62812 −0.529449 −0.264724 0.964324i 0.585281π-0.585281\pi
−0.264724 + 0.964324i 0.585281π0.585281\pi
114114 0 0
115115 −9.17846 −0.855896
116116 0 0
117117 −8.26227 −0.763847
118118 0 0
119119 −1.43066 −0.131149
120120 0 0
121121 30.5743 2.77949
122122 0 0
123123 −19.0371 −1.71652
124124 0 0
125125 6.70316 0.599549
126126 0 0
127127 −9.38911 −0.833149 −0.416575 0.909102i 0.636770π-0.636770\pi
−0.416575 + 0.909102i 0.636770π0.636770\pi
128128 0 0
129129 −14.9096 −1.31272
130130 0 0
131131 −2.20199 −0.192389 −0.0961945 0.995363i 0.530667π-0.530667\pi
−0.0961945 + 0.995363i 0.530667π0.530667\pi
132132 0 0
133133 −2.64870 −0.229671
134134 0 0
135135 0.791192 0.0680950
136136 0 0
137137 2.00184 0.171029 0.0855144 0.996337i 0.472747π-0.472747\pi
0.0855144 + 0.996337i 0.472747π0.472747\pi
138138 0 0
139139 9.98524 0.846937 0.423469 0.905911i 0.360812π-0.360812\pi
0.423469 + 0.905911i 0.360812π0.360812\pi
140140 0 0
141141 −25.1824 −2.12074
142142 0 0
143143 −17.2253 −1.44045
144144 0 0
145145 0 0
146146 0 0
147147 −16.7370 −1.38045
148148 0 0
149149 8.25714 0.676451 0.338226 0.941065i 0.390173π-0.390173\pi
0.338226 + 0.941065i 0.390173π0.390173\pi
150150 0 0
151151 8.70287 0.708230 0.354115 0.935202i 0.384782π-0.384782\pi
0.354115 + 0.935202i 0.384782π0.384782\pi
152152 0 0
153153 9.44738 0.763776
154154 0 0
155155 0.560794 0.0450441
156156 0 0
157157 21.5884 1.72294 0.861472 0.507805i 0.169543π-0.169543\pi
0.861472 + 0.507805i 0.169543π0.169543\pi
158158 0 0
159159 6.57785 0.521657
160160 0 0
161161 1.24406 0.0980458
162162 0 0
163163 −6.74986 −0.528690 −0.264345 0.964428i 0.585156π-0.585156\pi
−0.264345 + 0.964428i 0.585156π0.585156\pi
164164 0 0
165165 54.9946 4.28133
166166 0 0
167167 −18.9056 −1.46296 −0.731481 0.681862i 0.761171π-0.761171\pi
−0.731481 + 0.681862i 0.761171π0.761171\pi
168168 0 0
169169 −5.86316 −0.451012
170170 0 0
171171 17.4907 1.33755
172172 0 0
173173 4.33780 0.329797 0.164899 0.986311i 0.447270π-0.447270\pi
0.164899 + 0.986311i 0.447270π0.447270\pi
174174 0 0
175175 −3.25032 −0.245701
176176 0 0
177177 8.43769 0.634216
178178 0 0
179179 −2.40824 −0.180000 −0.0900000 0.995942i 0.528687π-0.528687\pi
−0.0900000 + 0.995942i 0.528687π0.528687\pi
180180 0 0
181181 22.8390 1.69761 0.848803 0.528709i 0.177324π-0.177324\pi
0.848803 + 0.528709i 0.177324π0.177324\pi
182182 0 0
183183 −15.8861 −1.17433
184184 0 0
185185 −27.6582 −2.03347
186186 0 0
187187 19.6960 1.44031
188188 0 0
189189 −0.107239 −0.00780051
190190 0 0
191191 4.17124 0.301820 0.150910 0.988547i 0.451780π-0.451780\pi
0.150910 + 0.988547i 0.451780π0.451780\pi
192192 0 0
193193 19.4221 1.39803 0.699017 0.715105i 0.253621π-0.253621\pi
0.699017 + 0.715105i 0.253621π0.253621\pi
194194 0 0
195195 −22.7856 −1.63171
196196 0 0
197197 −7.09440 −0.505455 −0.252727 0.967538i 0.581328π-0.581328\pi
−0.252727 + 0.967538i 0.581328π0.581328\pi
198198 0 0
199199 2.33313 0.165391 0.0826956 0.996575i 0.473647π-0.473647\pi
0.0826956 + 0.996575i 0.473647π0.473647\pi
200200 0 0
201201 5.50450 0.388257
202202 0 0
203203 0 0
204204 0 0
205205 −26.6498 −1.86130
206206 0 0
207207 −8.21516 −0.570993
208208 0 0
209209 36.4647 2.52232
210210 0 0
211211 7.19592 0.495387 0.247694 0.968838i 0.420327π-0.420327\pi
0.247694 + 0.968838i 0.420327π0.420327\pi
212212 0 0
213213 −19.6671 −1.34756
214214 0 0
215215 −20.8717 −1.42344
216216 0 0
217217 −0.0760109 −0.00515995
218218 0 0
219219 −9.13146 −0.617047
220220 0 0
221221 −8.16052 −0.548936
222222 0 0
223223 −7.01578 −0.469812 −0.234906 0.972018i 0.575478π-0.575478\pi
−0.234906 + 0.972018i 0.575478π0.575478\pi
224224 0 0
225225 21.4635 1.43090
226226 0 0
227227 −21.3154 −1.41475 −0.707377 0.706837i 0.750122π-0.750122\pi
−0.707377 + 0.706837i 0.750122π0.750122\pi
228228 0 0
229229 −20.5594 −1.35860 −0.679300 0.733860i 0.737717π-0.737717\pi
−0.679300 + 0.733860i 0.737717π0.737717\pi
230230 0 0
231231 −7.45405 −0.490441
232232 0 0
233233 −1.22159 −0.0800287 −0.0400144 0.999199i 0.512740π-0.512740\pi
−0.0400144 + 0.999199i 0.512740π0.512740\pi
234234 0 0
235235 −35.2525 −2.29962
236236 0 0
237237 −11.5305 −0.748986
238238 0 0
239239 19.4380 1.25734 0.628670 0.777673i 0.283600π-0.283600\pi
0.628670 + 0.777673i 0.283600π0.283600\pi
240240 0 0
241241 8.35978 0.538501 0.269250 0.963070i 0.413224π-0.413224\pi
0.269250 + 0.963070i 0.413224π0.413224\pi
242242 0 0
243243 −22.1939 −1.42374
244244 0 0
245245 −23.4300 −1.49688
246246 0 0
247247 −15.1082 −0.961312
248248 0 0
249249 21.8944 1.38750
250250 0 0
251251 −22.3163 −1.40859 −0.704297 0.709906i 0.748737π-0.748737\pi
−0.704297 + 0.709906i 0.748737π0.748737\pi
252252 0 0
253253 −17.1270 −1.07677
254254 0 0
255255 26.0539 1.63156
256256 0 0
257257 −16.5994 −1.03544 −0.517721 0.855549i 0.673220π-0.673220\pi
−0.517721 + 0.855549i 0.673220π0.673220\pi
258258 0 0
259259 3.74884 0.232942
260260 0 0
261261 0 0
262262 0 0
263263 −2.46065 −0.151730 −0.0758652 0.997118i 0.524172π-0.524172\pi
−0.0758652 + 0.997118i 0.524172π0.524172\pi
264264 0 0
265265 9.20825 0.565658
266266 0 0
267267 2.53507 0.155144
268268 0 0
269269 −5.30716 −0.323583 −0.161792 0.986825i 0.551727π-0.551727\pi
−0.161792 + 0.986825i 0.551727π0.551727\pi
270270 0 0
271271 2.63276 0.159929 0.0799643 0.996798i 0.474519π-0.474519\pi
0.0799643 + 0.996798i 0.474519π0.474519\pi
272272 0 0
273273 3.08839 0.186918
274274 0 0
275275 44.7472 2.69836
276276 0 0
277277 17.3377 1.04172 0.520861 0.853641i 0.325611π-0.325611\pi
0.520861 + 0.853641i 0.325611π0.325611\pi
278278 0 0
279279 0.501938 0.0300502
280280 0 0
281281 −13.7434 −0.819863 −0.409932 0.912116i 0.634447π-0.634447\pi
−0.409932 + 0.912116i 0.634447π0.634447\pi
282282 0 0
283283 −25.3515 −1.50699 −0.753495 0.657454i 0.771634π-0.771634\pi
−0.753495 + 0.657454i 0.771634π0.771634\pi
284284 0 0
285285 48.2356 2.85723
286286 0 0
287287 3.61215 0.213219
288288 0 0
289289 −7.66896 −0.451116
290290 0 0
291291 45.6943 2.67864
292292 0 0
293293 7.55111 0.441140 0.220570 0.975371i 0.429208π-0.429208\pi
0.220570 + 0.975371i 0.429208π0.429208\pi
294294 0 0
295295 11.8118 0.687711
296296 0 0
297297 1.47637 0.0856675
298298 0 0
299299 7.09614 0.410381
300300 0 0
301301 2.82899 0.163060
302302 0 0
303303 −27.0192 −1.55221
304304 0 0
305305 −22.2387 −1.27339
306306 0 0
307307 4.89496 0.279370 0.139685 0.990196i 0.455391π-0.455391\pi
0.139685 + 0.990196i 0.455391π0.455391\pi
308308 0 0
309309 5.04151 0.286801
310310 0 0
311311 −9.19809 −0.521576 −0.260788 0.965396i 0.583982π-0.583982\pi
−0.260788 + 0.965396i 0.583982π0.583982\pi
312312 0 0
313313 15.2320 0.860963 0.430481 0.902599i 0.358344π-0.358344\pi
0.430481 + 0.902599i 0.358344π0.358344\pi
314314 0 0
315315 −5.00518 −0.282010
316316 0 0
317317 14.3572 0.806379 0.403190 0.915116i 0.367902π-0.367902\pi
0.403190 + 0.915116i 0.367902π0.367902\pi
318318 0 0
319319 0 0
320320 0 0
321321 28.5191 1.59178
322322 0 0
323323 17.2753 0.961222
324324 0 0
325325 −18.5398 −1.02841
326326 0 0
327327 8.84190 0.488958
328328 0 0
329329 4.77818 0.263430
330330 0 0
331331 15.3588 0.844198 0.422099 0.906550i 0.361293π-0.361293\pi
0.422099 + 0.906550i 0.361293π0.361293\pi
332332 0 0
333333 −24.7554 −1.35659
334334 0 0
335335 7.70568 0.421006
336336 0 0
337337 −0.850248 −0.0463160 −0.0231580 0.999732i 0.507372π-0.507372\pi
−0.0231580 + 0.999732i 0.507372π0.507372\pi
338338 0 0
339339 −13.8922 −0.754520
340340 0 0
341341 1.04644 0.0566681
342342 0 0
343343 6.45420 0.348494
344344 0 0
345345 −22.6557 −1.21974
346346 0 0
347347 −7.35642 −0.394913 −0.197457 0.980312i 0.563268π-0.563268\pi
−0.197457 + 0.980312i 0.563268π0.563268\pi
348348 0 0
349349 18.9497 1.01436 0.507178 0.861841i 0.330689π-0.330689\pi
0.507178 + 0.861841i 0.330689π0.330689\pi
350350 0 0
351351 −0.611694 −0.0326498
352352 0 0
353353 −14.4116 −0.767051 −0.383525 0.923530i 0.625290π-0.625290\pi
−0.383525 + 0.923530i 0.625290π0.625290\pi
354354 0 0
355355 −27.5317 −1.46123
356356 0 0
357357 −3.53138 −0.186901
358358 0 0
359359 12.8159 0.676400 0.338200 0.941074i 0.390182π-0.390182\pi
0.338200 + 0.941074i 0.390182π0.390182\pi
360360 0 0
361361 12.9830 0.683318
362362 0 0
363363 75.4683 3.96106
364364 0 0
365365 −12.7830 −0.669093
366366 0 0
367367 −5.89514 −0.307724 −0.153862 0.988092i 0.549171π-0.549171\pi
−0.153862 + 0.988092i 0.549171π0.549171\pi
368368 0 0
369369 −23.8528 −1.24173
370370 0 0
371371 −1.24810 −0.0647981
372372 0 0
373373 12.7655 0.660975 0.330487 0.943810i 0.392787π-0.392787\pi
0.330487 + 0.943810i 0.392787π0.392787\pi
374374 0 0
375375 16.5458 0.854419
376376 0 0
377377 0 0
378378 0 0
379379 −19.5994 −1.00675 −0.503377 0.864067i 0.667909π-0.667909\pi
−0.503377 + 0.864067i 0.667909π0.667909\pi
380380 0 0
381381 −23.1756 −1.18732
382382 0 0
383383 22.1758 1.13313 0.566565 0.824017i 0.308272π-0.308272\pi
0.566565 + 0.824017i 0.308272π0.308272\pi
384384 0 0
385385 −10.4348 −0.531809
386386 0 0
387387 −18.6812 −0.949619
388388 0 0
389389 −24.1533 −1.22462 −0.612312 0.790617i 0.709760π-0.709760\pi
−0.612312 + 0.790617i 0.709760π0.709760\pi
390390 0 0
391391 −8.11399 −0.410342
392392 0 0
393393 −5.43530 −0.274174
394394 0 0
395395 −16.1414 −0.812162
396396 0 0
397397 −15.8597 −0.795976 −0.397988 0.917391i 0.630291π-0.630291\pi
−0.397988 + 0.917391i 0.630291π0.630291\pi
398398 0 0
399399 −6.53792 −0.327305
400400 0 0
401401 23.9221 1.19461 0.597307 0.802013i 0.296237π-0.296237\pi
0.597307 + 0.802013i 0.296237π0.296237\pi
402402 0 0
403403 −0.433567 −0.0215975
404404 0 0
405405 −30.1074 −1.49605
406406 0 0
407407 −51.6104 −2.55823
408408 0 0
409409 25.4293 1.25740 0.628699 0.777649i 0.283588π-0.283588\pi
0.628699 + 0.777649i 0.283588π0.283588\pi
410410 0 0
411411 4.94125 0.243734
412412 0 0
413413 −1.60099 −0.0787797
414414 0 0
415415 30.6496 1.50453
416416 0 0
417417 24.6471 1.20697
418418 0 0
419419 20.2925 0.991352 0.495676 0.868508i 0.334920π-0.334920\pi
0.495676 + 0.868508i 0.334920π0.334920\pi
420420 0 0
421421 −25.7015 −1.25261 −0.626306 0.779577i 0.715434π-0.715434\pi
−0.626306 + 0.779577i 0.715434π0.715434\pi
422422 0 0
423423 −31.5527 −1.53415
424424 0 0
425425 21.1991 1.02831
426426 0 0
427427 3.01427 0.145871
428428 0 0
429429 −42.5180 −2.05279
430430 0 0
431431 29.5645 1.42407 0.712037 0.702142i 0.247773π-0.247773\pi
0.712037 + 0.702142i 0.247773π0.247773\pi
432432 0 0
433433 −19.6937 −0.946421 −0.473211 0.880949i 0.656905π-0.656905\pi
−0.473211 + 0.880949i 0.656905π0.656905\pi
434434 0 0
435435 0 0
436436 0 0
437437 −15.0221 −0.718602
438438 0 0
439439 32.3494 1.54395 0.771977 0.635650i 0.219268π-0.219268\pi
0.771977 + 0.635650i 0.219268π0.219268\pi
440440 0 0
441441 −20.9709 −0.998616
442442 0 0
443443 −16.8125 −0.798787 −0.399394 0.916779i 0.630779π-0.630779\pi
−0.399394 + 0.916779i 0.630779π0.630779\pi
444444 0 0
445445 3.54881 0.168230
446446 0 0
447447 20.3815 0.964013
448448 0 0
449449 18.4958 0.872873 0.436436 0.899735i 0.356240π-0.356240\pi
0.436436 + 0.899735i 0.356240π0.356240\pi
450450 0 0
451451 −49.7286 −2.34163
452452 0 0
453453 21.4818 1.00930
454454 0 0
455455 4.32340 0.202684
456456 0 0
457457 28.0543 1.31232 0.656162 0.754620i 0.272179π-0.272179\pi
0.656162 + 0.754620i 0.272179π0.272179\pi
458458 0 0
459459 0.699434 0.0326468
460460 0 0
461461 28.0684 1.30727 0.653637 0.756808i 0.273242π-0.273242\pi
0.653637 + 0.756808i 0.273242π0.273242\pi
462462 0 0
463463 21.0969 0.980454 0.490227 0.871595i 0.336914π-0.336914\pi
0.490227 + 0.871595i 0.336914π0.336914\pi
464464 0 0
465465 1.38424 0.0641925
466466 0 0
467467 9.71569 0.449589 0.224794 0.974406i 0.427829π-0.427829\pi
0.224794 + 0.974406i 0.427829π0.427829\pi
468468 0 0
469469 −1.04444 −0.0482277
470470 0 0
471471 53.2878 2.45537
472472 0 0
473473 −38.9467 −1.79077
474474 0 0
475475 39.2476 1.80080
476476 0 0
477477 8.24182 0.377367
478478 0 0
479479 11.5269 0.526677 0.263339 0.964703i 0.415176π-0.415176\pi
0.263339 + 0.964703i 0.415176π0.415176\pi
480480 0 0
481481 21.3834 0.975000
482482 0 0
483483 3.07078 0.139726
484484 0 0
485485 63.9668 2.90458
486486 0 0
487487 −18.4196 −0.834671 −0.417336 0.908752i 0.637036π-0.637036\pi
−0.417336 + 0.908752i 0.637036π0.637036\pi
488488 0 0
489489 −16.6610 −0.753438
490490 0 0
491491 −15.3585 −0.693121 −0.346560 0.938028i 0.612650π-0.612650\pi
−0.346560 + 0.938028i 0.612650π0.612650\pi
492492 0 0
493493 0 0
494494 0 0
495495 68.9064 3.09711
496496 0 0
497497 3.73168 0.167389
498498 0 0
499499 −35.0821 −1.57049 −0.785246 0.619184i 0.787464π-0.787464\pi
−0.785246 + 0.619184i 0.787464π0.787464\pi
500500 0 0
501501 −46.6658 −2.08487
502502 0 0
503503 −22.4221 −0.999751 −0.499875 0.866097i 0.666621π-0.666621\pi
−0.499875 + 0.866097i 0.666621π0.666621\pi
504504 0 0
505505 −37.8239 −1.68314
506506 0 0
507507 −14.4723 −0.642739
508508 0 0
509509 27.3980 1.21440 0.607198 0.794551i 0.292294π-0.292294\pi
0.607198 + 0.794551i 0.292294π0.292294\pi
510510 0 0
511511 1.73263 0.0766470
512512 0 0
513513 1.29492 0.0571719
514514 0 0
515515 7.05754 0.310993
516516 0 0
517517 −65.7814 −2.89306
518518 0 0
519519 10.7072 0.469995
520520 0 0
521521 17.6915 0.775078 0.387539 0.921853i 0.373325π-0.373325\pi
0.387539 + 0.921853i 0.373325π0.373325\pi
522522 0 0
523523 −11.8131 −0.516552 −0.258276 0.966071i 0.583154π-0.583154\pi
−0.258276 + 0.966071i 0.583154π0.583154\pi
524524 0 0
525525 −8.02293 −0.350149
526526 0 0
527527 0.495756 0.0215955
528528 0 0
529529 −15.9443 −0.693231
530530 0 0
531531 10.5721 0.458792
532532 0 0
533533 20.6038 0.892448
534534 0 0
535535 39.9235 1.72604
536536 0 0
537537 −5.94437 −0.256519
538538 0 0
539539 −43.7204 −1.88317
540540 0 0
541541 −5.21901 −0.224383 −0.112191 0.993687i 0.535787π-0.535787\pi
−0.112191 + 0.993687i 0.535787π0.535787\pi
542542 0 0
543543 56.3746 2.41926
544544 0 0
545545 12.3777 0.530201
546546 0 0
547547 −27.1921 −1.16265 −0.581324 0.813672i 0.697465π-0.697465\pi
−0.581324 + 0.813672i 0.697465π0.697465\pi
548548 0 0
549549 −19.9047 −0.849513
550550 0 0
551551 0 0
552552 0 0
553553 2.18783 0.0930360
554554 0 0
555555 −68.2703 −2.89791
556556 0 0
557557 11.1087 0.470691 0.235346 0.971912i 0.424378π-0.424378\pi
0.235346 + 0.971912i 0.424378π0.424378\pi
558558 0 0
559559 16.1366 0.682504
560560 0 0
561561 48.6166 2.05260
562562 0 0
563563 −15.3337 −0.646237 −0.323118 0.946359i 0.604731π-0.604731\pi
−0.323118 + 0.946359i 0.604731π0.604731\pi
564564 0 0
565565 −19.4475 −0.818162
566566 0 0
567567 4.08080 0.171378
568568 0 0
569569 8.08646 0.339002 0.169501 0.985530i 0.445784π-0.445784\pi
0.169501 + 0.985530i 0.445784π0.445784\pi
570570 0 0
571571 −22.8857 −0.957737 −0.478869 0.877887i 0.658953π-0.658953\pi
−0.478869 + 0.877887i 0.658953π0.658953\pi
572572 0 0
573573 10.2961 0.430125
574574 0 0
575575 −18.4341 −0.768756
576576 0 0
577577 −9.49247 −0.395177 −0.197588 0.980285i 0.563311π-0.563311\pi
−0.197588 + 0.980285i 0.563311π0.563311\pi
578578 0 0
579579 47.9406 1.99234
580580 0 0
581581 −4.15430 −0.172349
582582 0 0
583583 17.1826 0.711632
584584 0 0
585585 −28.5496 −1.18038
586586 0 0
587587 −20.0335 −0.826870 −0.413435 0.910534i 0.635671π-0.635671\pi
−0.413435 + 0.910534i 0.635671π0.635671\pi
588588 0 0
589589 0.917832 0.0378186
590590 0 0
591591 −17.5115 −0.720326
592592 0 0
593593 1.35116 0.0554856 0.0277428 0.999615i 0.491168π-0.491168\pi
0.0277428 + 0.999615i 0.491168π0.491168\pi
594594 0 0
595595 −4.94354 −0.202665
596596 0 0
597597 5.75899 0.235700
598598 0 0
599599 −6.74712 −0.275680 −0.137840 0.990455i 0.544016π-0.544016\pi
−0.137840 + 0.990455i 0.544016π0.544016\pi
600600 0 0
601601 1.52795 0.0623264 0.0311632 0.999514i 0.490079π-0.490079\pi
0.0311632 + 0.999514i 0.490079π0.490079\pi
602602 0 0
603603 6.89695 0.280866
604604 0 0
605605 105.647 4.29516
606606 0 0
607607 8.34258 0.338615 0.169307 0.985563i 0.445847π-0.445847\pi
0.169307 + 0.985563i 0.445847π0.445847\pi
608608 0 0
609609 0 0
610610 0 0
611611 27.2548 1.10261
612612 0 0
613613 −12.5594 −0.507270 −0.253635 0.967300i 0.581626π-0.581626\pi
−0.253635 + 0.967300i 0.581626π0.581626\pi
614614 0 0
615615 −65.7811 −2.65255
616616 0 0
617617 33.9771 1.36787 0.683933 0.729545i 0.260268π-0.260268\pi
0.683933 + 0.729545i 0.260268π0.260268\pi
618618 0 0
619619 14.9084 0.599221 0.299610 0.954062i 0.403143π-0.403143\pi
0.299610 + 0.954062i 0.403143π0.403143\pi
620620 0 0
621621 −0.608206 −0.0244065
622622 0 0
623623 −0.481011 −0.0192713
624624 0 0
625625 −11.5373 −0.461492
626626 0 0
627627 90.0077 3.59456
628628 0 0
629629 −24.4506 −0.974908
630630 0 0
631631 −31.8662 −1.26857 −0.634286 0.773098i 0.718706π-0.718706\pi
−0.634286 + 0.773098i 0.718706π0.718706\pi
632632 0 0
633633 17.7621 0.705978
634634 0 0
635635 −32.4433 −1.28747
636636 0 0
637637 18.1144 0.717719
638638 0 0
639639 −24.6422 −0.974829
640640 0 0
641641 −2.12216 −0.0838202 −0.0419101 0.999121i 0.513344π-0.513344\pi
−0.0419101 + 0.999121i 0.513344π0.513344\pi
642642 0 0
643643 −25.5435 −1.00734 −0.503669 0.863897i 0.668017π-0.668017\pi
−0.503669 + 0.863897i 0.668017π0.668017\pi
644644 0 0
645645 −51.5188 −2.02855
646646 0 0
647647 2.30704 0.0906993 0.0453496 0.998971i 0.485560π-0.485560\pi
0.0453496 + 0.998971i 0.485560π0.485560\pi
648648 0 0
649649 22.0409 0.865181
650650 0 0
651651 −0.187622 −0.00735347
652652 0 0
653653 −45.3683 −1.77540 −0.887699 0.460425i 0.847697π-0.847697\pi
−0.887699 + 0.460425i 0.847697π0.847697\pi
654654 0 0
655655 −7.60880 −0.297301
656656 0 0
657657 −11.4414 −0.446372
658658 0 0
659659 30.2677 1.17906 0.589531 0.807746i 0.299313π-0.299313\pi
0.589531 + 0.807746i 0.299313π0.299313\pi
660660 0 0
661661 −17.9479 −0.698093 −0.349047 0.937105i 0.613494π-0.613494\pi
−0.349047 + 0.937105i 0.613494π0.613494\pi
662662 0 0
663663 −20.1430 −0.782291
664664 0 0
665665 −9.15235 −0.354913
666666 0 0
667667 0 0
668668 0 0
669669 −17.3174 −0.669530
670670 0 0
671671 −41.4975 −1.60199
672672 0 0
673673 −13.9718 −0.538572 −0.269286 0.963060i 0.586788π-0.586788\pi
−0.269286 + 0.963060i 0.586788π0.586788\pi
674674 0 0
675675 1.58904 0.0611622
676676 0 0
677677 39.6603 1.52427 0.762135 0.647418i 0.224151π-0.224151\pi
0.762135 + 0.647418i 0.224151π0.224151\pi
678678 0 0
679679 −8.67016 −0.332730
680680 0 0
681681 −52.6140 −2.01617
682682 0 0
683683 33.0054 1.26291 0.631457 0.775411i 0.282457π-0.282457\pi
0.631457 + 0.775411i 0.282457π0.282457\pi
684684 0 0
685685 6.91720 0.264292
686686 0 0
687687 −50.7478 −1.93615
688688 0 0
689689 −7.11918 −0.271219
690690 0 0
691691 45.9365 1.74751 0.873753 0.486370i 0.161679π-0.161679\pi
0.873753 + 0.486370i 0.161679π0.161679\pi
692692 0 0
693693 −9.33968 −0.354785
694694 0 0
695695 34.5032 1.30878
696696 0 0
697697 −23.5591 −0.892364
698698 0 0
699699 −3.01530 −0.114049
700700 0 0
701701 26.2314 0.990748 0.495374 0.868680i 0.335031π-0.335031\pi
0.495374 + 0.868680i 0.335031π0.335031\pi
702702 0 0
703703 −45.2672 −1.70729
704704 0 0
705705 −87.0157 −3.27720
706706 0 0
707707 5.12671 0.192810
708708 0 0
709709 1.09356 0.0410695 0.0205347 0.999789i 0.493463π-0.493463\pi
0.0205347 + 0.999789i 0.493463π0.493463\pi
710710 0 0
711711 −14.4473 −0.541817
712712 0 0
713713 −0.431095 −0.0161446
714714 0 0
715715 −59.5204 −2.22594
716716 0 0
717717 47.9798 1.79184
718718 0 0
719719 39.4380 1.47079 0.735394 0.677639i 0.236997π-0.236997\pi
0.735394 + 0.677639i 0.236997π0.236997\pi
720720 0 0
721721 −0.956590 −0.0356253
722722 0 0
723723 20.6349 0.767420
724724 0 0
725725 0 0
726726 0 0
727727 −0.447183 −0.0165851 −0.00829255 0.999966i 0.502640π-0.502640\pi
−0.00829255 + 0.999966i 0.502640π0.502640\pi
728728 0 0
729729 −28.6431 −1.06086
730730 0 0
731731 −18.4511 −0.682440
732732 0 0
733733 −28.4633 −1.05132 −0.525658 0.850696i 0.676181π-0.676181\pi
−0.525658 + 0.850696i 0.676181π0.676181\pi
734734 0 0
735735 −57.8334 −2.13322
736736 0 0
737737 14.3788 0.529651
738738 0 0
739739 −22.0518 −0.811190 −0.405595 0.914053i 0.632936π-0.632936\pi
−0.405595 + 0.914053i 0.632936π0.632936\pi
740740 0 0
741741 −37.2924 −1.36997
742742 0 0
743743 −25.1379 −0.922220 −0.461110 0.887343i 0.652549π-0.652549\pi
−0.461110 + 0.887343i 0.652549π0.652549\pi
744744 0 0
745745 28.5319 1.04533
746746 0 0
747747 27.4329 1.00372
748748 0 0
749749 −5.41129 −0.197724
750750 0 0
751751 −2.28503 −0.0833819 −0.0416909 0.999131i 0.513274π-0.513274\pi
−0.0416909 + 0.999131i 0.513274π0.513274\pi
752752 0 0
753753 −55.0845 −2.00739
754754 0 0
755755 30.0721 1.09443
756756 0 0
757757 8.95161 0.325352 0.162676 0.986680i 0.447988π-0.447988\pi
0.162676 + 0.986680i 0.447988π0.447988\pi
758758 0 0
759759 −42.2756 −1.53451
760760 0 0
761761 47.7847 1.73220 0.866098 0.499875i 0.166621π-0.166621\pi
0.866098 + 0.499875i 0.166621π0.166621\pi
762762 0 0
763763 −1.67769 −0.0607364
764764 0 0
765765 32.6446 1.18027
766766 0 0
767767 −9.13207 −0.329740
768768 0 0
769769 41.2072 1.48597 0.742985 0.669308i 0.233409π-0.233409\pi
0.742985 + 0.669308i 0.233409π0.233409\pi
770770 0 0
771771 −40.9732 −1.47561
772772 0 0
773773 −24.4331 −0.878796 −0.439398 0.898292i 0.644808π-0.644808\pi
−0.439398 + 0.898292i 0.644808π0.644808\pi
774774 0 0
775775 1.12631 0.0404581
776776 0 0
777777 9.25346 0.331966
778778 0 0
779779 −43.6167 −1.56273
780780 0 0
781781 −51.3742 −1.83831
782782 0 0
783783 0 0
784784 0 0
785785 74.5970 2.66248
786786 0 0
787787 35.0439 1.24918 0.624591 0.780952i 0.285266π-0.285266\pi
0.624591 + 0.780952i 0.285266π0.285266\pi
788788 0 0
789789 −6.07376 −0.216232
790790 0 0
791791 2.63594 0.0937233
792792 0 0
793793 17.1934 0.610556
794794 0 0
795795 22.7292 0.806122
796796 0 0
797797 43.6491 1.54613 0.773066 0.634326i 0.218722π-0.218722\pi
0.773066 + 0.634326i 0.218722π0.218722\pi
798798 0 0
799799 −31.1641 −1.10251
800800 0 0
801801 3.17636 0.112231
802802 0 0
803803 −23.8531 −0.841759
804804 0 0
805805 4.29875 0.151511
806806 0 0
807807 −13.0999 −0.461140
808808 0 0
809809 23.0748 0.811266 0.405633 0.914036i 0.367051π-0.367051\pi
0.405633 + 0.914036i 0.367051π0.367051\pi
810810 0 0
811811 −48.5305 −1.70414 −0.852068 0.523431i 0.824652π-0.824652\pi
−0.852068 + 0.523431i 0.824652π0.824652\pi
812812 0 0
813813 6.49857 0.227915
814814 0 0
815815 −23.3236 −0.816989
816816 0 0
817817 −34.1600 −1.19511
818818 0 0
819819 3.86965 0.135217
820820 0 0
821821 46.7925 1.63307 0.816534 0.577297i 0.195893π-0.195893\pi
0.816534 + 0.577297i 0.195893π0.195893\pi
822822 0 0
823823 −46.0330 −1.60461 −0.802305 0.596914i 0.796393π-0.796393\pi
−0.802305 + 0.596914i 0.796393π0.796393\pi
824824 0 0
825825 110.452 3.84544
826826 0 0
827827 −34.5022 −1.19976 −0.599879 0.800091i 0.704785π-0.704785\pi
−0.599879 + 0.800091i 0.704785π0.704785\pi
828828 0 0
829829 −10.1549 −0.352694 −0.176347 0.984328i 0.556428π-0.556428\pi
−0.176347 + 0.984328i 0.556428π0.556428\pi
830830 0 0
831831 42.7956 1.48456
832832 0 0
833833 −20.7127 −0.717651
834834 0 0
835835 −65.3268 −2.26073
836836 0 0
837837 0.0371608 0.00128446
838838 0 0
839839 40.1921 1.38758 0.693792 0.720176i 0.255939π-0.255939\pi
0.693792 + 0.720176i 0.255939π0.255939\pi
840840 0 0
841841 0 0
842842 0 0
843843 −33.9236 −1.16839
844844 0 0
845845 −20.2597 −0.696953
846846 0 0
847847 −14.3196 −0.492026
848848 0 0
849849 −62.5764 −2.14762
850850 0 0
851851 21.2615 0.728835
852852 0 0
853853 −31.5341 −1.07971 −0.539854 0.841759i 0.681521π-0.681521\pi
−0.539854 + 0.841759i 0.681521π0.681521\pi
854854 0 0
855855 60.4375 2.06692
856856 0 0
857857 4.79855 0.163915 0.0819576 0.996636i 0.473883π-0.473883\pi
0.0819576 + 0.996636i 0.473883π0.473883\pi
858858 0 0
859859 0.576452 0.0196683 0.00983415 0.999952i 0.496870π-0.496870\pi
0.00983415 + 0.999952i 0.496870π0.496870\pi
860860 0 0
861861 8.91606 0.303859
862862 0 0
863863 −31.9164 −1.08645 −0.543223 0.839588i 0.682796π-0.682796\pi
−0.543223 + 0.839588i 0.682796π0.682796\pi
864864 0 0
865865 14.9889 0.509638
866866 0 0
867867 −18.9297 −0.642886
868868 0 0
869869 −30.1199 −1.02175
870870 0 0
871871 −5.95749 −0.201862
872872 0 0
873873 57.2534 1.93773
874874 0 0
875875 −3.13944 −0.106132
876876 0 0
877877 42.0117 1.41863 0.709317 0.704890i 0.249003π-0.249003\pi
0.709317 + 0.704890i 0.249003π0.249003\pi
878878 0 0
879879 18.6388 0.628671
880880 0 0
881881 21.9247 0.738661 0.369331 0.929298i 0.379587π-0.379587\pi
0.369331 + 0.929298i 0.379587π0.379587\pi
882882 0 0
883883 −33.7438 −1.13557 −0.567784 0.823178i 0.692199π-0.692199\pi
−0.567784 + 0.823178i 0.692199π0.692199\pi
884884 0 0
885885 29.1557 0.980059
886886 0 0
887887 −39.5840 −1.32910 −0.664550 0.747244i 0.731377π-0.731377\pi
−0.664550 + 0.747244i 0.731377π0.731377\pi
888888 0 0
889889 4.39741 0.147485
890890 0 0
891891 −56.1805 −1.88212
892892 0 0
893893 −57.6966 −1.93074
894894 0 0
895895 −8.32146 −0.278156
896896 0 0
897897 17.5158 0.584835
898898 0 0
899899 0 0
900900 0 0
901901 8.14032 0.271194
902902 0 0
903903 6.98294 0.232378
904904 0 0
905905 78.9181 2.62333
906906 0 0
907907 −32.1363 −1.06707 −0.533534 0.845778i 0.679136π-0.679136\pi
−0.533534 + 0.845778i 0.679136π0.679136\pi
908908 0 0
909909 −33.8542 −1.12287
910910 0 0
911911 −55.7892 −1.84838 −0.924189 0.381936i 0.875257π-0.875257\pi
−0.924189 + 0.381936i 0.875257π0.875257\pi
912912 0 0
913913 57.1923 1.89279
914914 0 0
915915 −54.8930 −1.81471
916916 0 0
917917 1.03131 0.0340568
918918 0 0
919919 −12.0026 −0.395929 −0.197965 0.980209i 0.563433π-0.563433\pi
−0.197965 + 0.980209i 0.563433π0.563433\pi
920920 0 0
921921 12.0825 0.398132
922922 0 0
923923 21.2856 0.700623
924924 0 0
925925 −55.5491 −1.82644
926926 0 0
927927 6.31684 0.207472
928928 0 0
929929 −44.1037 −1.44700 −0.723498 0.690326i 0.757467π-0.757467\pi
−0.723498 + 0.690326i 0.757467π0.757467\pi
930930 0 0
931931 −38.3470 −1.25677
932932 0 0
933933 −22.7041 −0.743299
934934 0 0
935935 68.0578 2.22573
936936 0 0
937937 −1.83132 −0.0598265 −0.0299132 0.999552i 0.509523π-0.509523\pi
−0.0299132 + 0.999552i 0.509523π0.509523\pi
938938 0 0
939939 37.5979 1.22696
940940 0 0
941941 −14.3133 −0.466599 −0.233300 0.972405i 0.574952π-0.574952\pi
−0.233300 + 0.972405i 0.574952π0.574952\pi
942942 0 0
943943 20.4863 0.667125
944944 0 0
945945 −0.370557 −0.0120542
946946 0 0
947947 34.1252 1.10892 0.554460 0.832210i 0.312925π-0.312925\pi
0.554460 + 0.832210i 0.312925π0.312925\pi
948948 0 0
949949 9.88293 0.320814
950950 0 0
951951 35.4386 1.14917
952952 0 0
953953 −29.6491 −0.960429 −0.480214 0.877151i 0.659441π-0.659441\pi
−0.480214 + 0.877151i 0.659441π0.659441\pi
954954 0 0
955955 14.4134 0.466405
956956 0 0
957957 0 0
958958 0 0
959959 −0.937567 −0.0302756
960960 0 0
961961 −30.9737 −0.999150
962962 0 0
963963 35.7334 1.15149
964964 0 0
965965 67.1115 2.16040
966966 0 0
967967 −45.7185 −1.47021 −0.735104 0.677954i 0.762867π-0.762867\pi
−0.735104 + 0.677954i 0.762867π0.762867\pi
968968 0 0
969969 42.6414 1.36984
970970 0 0
971971 −26.0642 −0.836441 −0.418221 0.908345i 0.637346π-0.637346\pi
−0.418221 + 0.908345i 0.637346π0.637346\pi
972972 0 0
973973 −4.67661 −0.149925
974974 0 0
975975 −45.7629 −1.46558
976976 0 0
977977 10.0813 0.322528 0.161264 0.986911i 0.448443π-0.448443\pi
0.161264 + 0.986911i 0.448443π0.448443\pi
978978 0 0
979979 6.62209 0.211643
980980 0 0
981981 11.0786 0.353713
982982 0 0
983983 −32.0567 −1.02245 −0.511225 0.859447i 0.670808π-0.670808\pi
−0.511225 + 0.859447i 0.670808π0.670808\pi
984984 0 0
985985 −24.5141 −0.781084
986986 0 0
987987 11.7942 0.375415
988988 0 0
989989 16.0446 0.510187
990990 0 0
991991 52.2812 1.66077 0.830383 0.557193i 0.188122π-0.188122\pi
0.830383 + 0.557193i 0.188122π0.188122\pi
992992 0 0
993993 37.9110 1.20307
994994 0 0
995995 8.06194 0.255581
996996 0 0
997997 −40.0799 −1.26934 −0.634672 0.772782i 0.718865π-0.718865\pi
−0.634672 + 0.772782i 0.718865π0.718865\pi
998998 0 0
999999 −1.83276 −0.0579860
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.p.1.4 6
29.5 even 14 116.2.g.b.25.2 12
29.6 even 14 116.2.g.b.65.2 yes 12
29.12 odd 4 3364.2.c.j.1681.10 12
29.17 odd 4 3364.2.c.j.1681.3 12
29.28 even 2 3364.2.a.m.1.3 6
87.5 odd 14 1044.2.u.c.721.2 12
87.35 odd 14 1044.2.u.c.181.2 12
116.35 odd 14 464.2.u.g.65.1 12
116.63 odd 14 464.2.u.g.257.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
116.2.g.b.25.2 12 29.5 even 14
116.2.g.b.65.2 yes 12 29.6 even 14
464.2.u.g.65.1 12 116.35 odd 14
464.2.u.g.257.1 12 116.63 odd 14
1044.2.u.c.181.2 12 87.35 odd 14
1044.2.u.c.721.2 12 87.5 odd 14
3364.2.a.m.1.3 6 29.28 even 2
3364.2.a.p.1.4 6 1.1 even 1 trivial
3364.2.c.j.1681.3 12 29.17 odd 4
3364.2.c.j.1681.10 12 29.12 odd 4