Properties

Label 676.2.d.e.337.4
Level 676676
Weight 22
Character 676.337
Analytic conductor 5.3985.398
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [676,2,Mod(337,676)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(676, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("676.337"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 676=22132 676 = 2^{2} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 676.d (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.397887176645.39788717664
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.153664.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x6+5x4+6x2+1 x^{6} + 5x^{4} + 6x^{2} + 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
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 337.4
Root 1.24698i-1.24698i of defining polynomial
Character χ\chi == 676.337
Dual form 676.2.d.e.337.3

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.35690q3+4.24698iq5+2.13706iq71.15883q93.35690iq11+5.76271iq15+0.0609989q17+6.18598iq19+2.89977iq21+5.09783q2313.0368q255.64310q272.13706q292.85086iq314.55496iq339.07606q353.47219iq37+5.39612iq41+8.61356q434.92154iq45+6.96077iq47+2.43296q49+0.0827692q51+0.0217703q53+14.2567q55+8.39373iq57+5.81163iq59+10.6799q612.47650iq637.40581iq67+6.91723q69+0.0489173iq714.51573iq7317.6896q75+7.17390q77+12.8170q794.18060q81+3.55496iq83+0.259061iq852.89977q872.34721iq893.86831iq9326.2717q953.42327iq97+3.89008iq99+O(q100)q+1.35690 q^{3} +4.24698i q^{5} +2.13706i q^{7} -1.15883 q^{9} -3.35690i q^{11} +5.76271i q^{15} +0.0609989 q^{17} +6.18598i q^{19} +2.89977i q^{21} +5.09783 q^{23} -13.0368 q^{25} -5.64310 q^{27} -2.13706 q^{29} -2.85086i q^{31} -4.55496i q^{33} -9.07606 q^{35} -3.47219i q^{37} +5.39612i q^{41} +8.61356 q^{43} -4.92154i q^{45} +6.96077i q^{47} +2.43296 q^{49} +0.0827692 q^{51} +0.0217703 q^{53} +14.2567 q^{55} +8.39373i q^{57} +5.81163i q^{59} +10.6799 q^{61} -2.47650i q^{63} -7.40581i q^{67} +6.91723 q^{69} +0.0489173i q^{71} -4.51573i q^{73} -17.6896 q^{75} +7.17390 q^{77} +12.8170 q^{79} -4.18060 q^{81} +3.55496i q^{83} +0.259061i q^{85} -2.89977 q^{87} -2.34721i q^{89} -3.86831i q^{93} -26.2717 q^{95} -3.42327i q^{97} +3.89008i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+10q9+20q176q2322q2542q272q2924q3510q4324q49+14q516q53+32q55+16q61+28q6914q7524q77+18q79+54q95+O(q100) 6 q + 10 q^{9} + 20 q^{17} - 6 q^{23} - 22 q^{25} - 42 q^{27} - 2 q^{29} - 24 q^{35} - 10 q^{43} - 24 q^{49} + 14 q^{51} - 6 q^{53} + 32 q^{55} + 16 q^{61} + 28 q^{69} - 14 q^{75} - 24 q^{77} + 18 q^{79}+ \cdots - 54 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/676Z)×\left(\mathbb{Z}/676\mathbb{Z}\right)^\times.

nn 339339 509509
χ(n)\chi(n) 11 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 0
33 1.35690 0.783404 0.391702 0.920092i 0.371886π-0.371886\pi
0.391702 + 0.920092i 0.371886π0.371886\pi
44 0 0
55 4.24698i 1.89931i 0.313302 + 0.949654i 0.398565π0.398565\pi
−0.313302 + 0.949654i 0.601435π0.601435\pi
66 0 0
77 2.13706i 0.807734i 0.914818 + 0.403867i 0.132334π0.132334\pi
−0.914818 + 0.403867i 0.867666π0.867666\pi
88 0 0
99 −1.15883 −0.386278
1010 0 0
1111 − 3.35690i − 1.01214i −0.862492 0.506071i 0.831097π-0.831097\pi
0.862492 0.506071i 0.168903π-0.168903\pi
1212 0 0
1313 0 0
1414 0 0
1515 5.76271i 1.48793i
1616 0 0
1717 0.0609989 0.0147944 0.00739721 0.999973i 0.497645π-0.497645\pi
0.00739721 + 0.999973i 0.497645π0.497645\pi
1818 0 0
1919 6.18598i 1.41916i 0.704624 + 0.709581i 0.251116π0.251116\pi
−0.704624 + 0.709581i 0.748884π0.748884\pi
2020 0 0
2121 2.89977i 0.632782i
2222 0 0
2323 5.09783 1.06297 0.531486 0.847067i 0.321634π-0.321634\pi
0.531486 + 0.847067i 0.321634π0.321634\pi
2424 0 0
2525 −13.0368 −2.60737
2626 0 0
2727 −5.64310 −1.08602
2828 0 0
2929 −2.13706 −0.396843 −0.198421 0.980117i 0.563581π-0.563581\pi
−0.198421 + 0.980117i 0.563581π0.563581\pi
3030 0 0
3131 − 2.85086i − 0.512029i −0.966673 0.256014i 0.917591π-0.917591\pi
0.966673 0.256014i 0.0824094π-0.0824094\pi
3232 0 0
3333 − 4.55496i − 0.792916i
3434 0 0
3535 −9.07606 −1.53413
3636 0 0
3737 − 3.47219i − 0.570824i −0.958405 0.285412i 0.907870π-0.907870\pi
0.958405 0.285412i 0.0921305π-0.0921305\pi
3838 0 0
3939 0 0
4040 0 0
4141 5.39612i 0.842733i 0.906890 + 0.421367i 0.138449π0.138449\pi
−0.906890 + 0.421367i 0.861551π0.861551\pi
4242 0 0
4343 8.61356 1.31356 0.656778 0.754084i 0.271919π-0.271919\pi
0.656778 + 0.754084i 0.271919π0.271919\pi
4444 0 0
4545 − 4.92154i − 0.733660i
4646 0 0
4747 6.96077i 1.01533i 0.861554 + 0.507666i 0.169492π0.169492\pi
−0.861554 + 0.507666i 0.830508π0.830508\pi
4848 0 0
4949 2.43296 0.347566
5050 0 0
5151 0.0827692 0.0115900
5252 0 0
5353 0.0217703 0.00299038 0.00149519 0.999999i 0.499524π-0.499524\pi
0.00149519 + 0.999999i 0.499524π0.499524\pi
5454 0 0
5555 14.2567 1.92237
5656 0 0
5757 8.39373i 1.11178i
5858 0 0
5959 5.81163i 0.756609i 0.925681 + 0.378305i 0.123493π0.123493\pi
−0.925681 + 0.378305i 0.876507π0.876507\pi
6060 0 0
6161 10.6799 1.36743 0.683713 0.729751i 0.260364π-0.260364\pi
0.683713 + 0.729751i 0.260364π0.260364\pi
6262 0 0
6363 − 2.47650i − 0.312010i
6464 0 0
6565 0 0
6666 0 0
6767 − 7.40581i − 0.904764i −0.891824 0.452382i 0.850574π-0.850574\pi
0.891824 0.452382i 0.149426π-0.149426\pi
6868 0 0
6969 6.91723 0.832737
7070 0 0
7171 0.0489173i 0.00580542i 0.999996 + 0.00290271i 0.000923963π0.000923963\pi
−0.999996 + 0.00290271i 0.999076π0.999076\pi
7272 0 0
7373 − 4.51573i − 0.528526i −0.964451 0.264263i 0.914871π-0.914871\pi
0.964451 0.264263i 0.0851287π-0.0851287\pi
7474 0 0
7575 −17.6896 −2.04262
7676 0 0
7777 7.17390 0.817542
7878 0 0
7979 12.8170 1.44203 0.721013 0.692922i 0.243677π-0.243677\pi
0.721013 + 0.692922i 0.243677π0.243677\pi
8080 0 0
8181 −4.18060 −0.464512
8282 0 0
8383 3.55496i 0.390207i 0.980783 + 0.195104i 0.0625043π0.0625043\pi
−0.980783 + 0.195104i 0.937496π0.937496\pi
8484 0 0
8585 0.259061i 0.0280991i
8686 0 0
8787 −2.89977 −0.310888
8888 0 0
8989 − 2.34721i − 0.248803i −0.992232 0.124402i 0.960299π-0.960299\pi
0.992232 0.124402i 0.0397012π-0.0397012\pi
9090 0 0
9191 0 0
9292 0 0
9393 − 3.86831i − 0.401125i
9494 0 0
9595 −26.2717 −2.69542
9696 0 0
9797 − 3.42327i − 0.347581i −0.984783 0.173790i 0.944399π-0.944399\pi
0.984783 0.173790i 0.0556015π-0.0556015\pi
9898 0 0
9999 3.89008i 0.390968i
100100 0 0
101101 11.3787 1.13222 0.566110 0.824330i 0.308448π-0.308448\pi
0.566110 + 0.824330i 0.308448π0.308448\pi
102102 0 0
103103 6.07606 0.598692 0.299346 0.954145i 0.403231π-0.403231\pi
0.299346 + 0.954145i 0.403231π0.403231\pi
104104 0 0
105105 −12.3153 −1.20185
106106 0 0
107107 −16.0368 −1.55034 −0.775170 0.631753i 0.782336π-0.782336\pi
−0.775170 + 0.631753i 0.782336π0.782336\pi
108108 0 0
109109 − 14.9095i − 1.42807i −0.700111 0.714034i 0.746866π-0.746866\pi
0.700111 0.714034i 0.253134π-0.253134\pi
110110 0 0
111111 − 4.71140i − 0.447186i
112112 0 0
113113 8.24459 0.775585 0.387793 0.921747i 0.373238π-0.373238\pi
0.387793 + 0.921747i 0.373238π0.373238\pi
114114 0 0
115115 21.6504i 2.01891i
116116 0 0
117117 0 0
118118 0 0
119119 0.130359i 0.0119500i
120120 0 0
121121 −0.268750 −0.0244318
122122 0 0
123123 7.32198i 0.660201i
124124 0 0
125125 − 34.1323i − 3.05288i
126126 0 0
127127 6.64310 0.589480 0.294740 0.955577i 0.404767π-0.404767\pi
0.294740 + 0.955577i 0.404767π0.404767\pi
128128 0 0
129129 11.6877 1.02905
130130 0 0
131131 7.86294 0.686988 0.343494 0.939155i 0.388390π-0.388390\pi
0.343494 + 0.939155i 0.388390π0.388390\pi
132132 0 0
133133 −13.2198 −1.14630
134134 0 0
135135 − 23.9661i − 2.06268i
136136 0 0
137137 0.987918i 0.0844036i 0.999109 + 0.0422018i 0.0134372π0.0134372\pi
−0.999109 + 0.0422018i 0.986563π0.986563\pi
138138 0 0
139139 −12.0368 −1.02095 −0.510476 0.859892i 0.670531π-0.670531\pi
−0.510476 + 0.859892i 0.670531π0.670531\pi
140140 0 0
141141 9.44504i 0.795416i
142142 0 0
143143 0 0
144144 0 0
145145 − 9.07606i − 0.753726i
146146 0 0
147147 3.30127 0.272284
148148 0 0
149149 2.35929i 0.193280i 0.995319 + 0.0966402i 0.0308096π0.0308096\pi
−0.995319 + 0.0966402i 0.969190π0.969190\pi
150150 0 0
151151 7.43967i 0.605431i 0.953081 + 0.302716i 0.0978933π0.0978933\pi
−0.953081 + 0.302716i 0.902107π0.902107\pi
152152 0 0
153153 −0.0706876 −0.00571475
154154 0 0
155155 12.1075 0.972500
156156 0 0
157157 −10.9487 −0.873801 −0.436900 0.899510i 0.643924π-0.643924\pi
−0.436900 + 0.899510i 0.643924π0.643924\pi
158158 0 0
159159 0.0295400 0.00234267
160160 0 0
161161 10.8944i 0.858599i
162162 0 0
163163 − 7.02475i − 0.550221i −0.961413 0.275111i 0.911286π-0.911286\pi
0.961413 0.275111i 0.0887145π-0.0887145\pi
164164 0 0
165165 19.3448 1.50599
166166 0 0
167167 15.4819i 1.19802i 0.800740 + 0.599012i 0.204440π0.204440\pi
−0.800740 + 0.599012i 0.795560π0.795560\pi
168168 0 0
169169 0 0
170170 0 0
171171 − 7.16852i − 0.548191i
172172 0 0
173173 −13.7802 −1.04769 −0.523843 0.851815i 0.675502π-0.675502\pi
−0.523843 + 0.851815i 0.675502π0.675502\pi
174174 0 0
175175 − 27.8605i − 2.10606i
176176 0 0
177177 7.88577i 0.592731i
178178 0 0
179179 −22.1226 −1.65352 −0.826760 0.562555i 0.809819π-0.809819\pi
−0.826760 + 0.562555i 0.809819π0.809819\pi
180180 0 0
181181 13.6407 1.01391 0.506953 0.861974i 0.330772π-0.330772\pi
0.506953 + 0.861974i 0.330772π0.330772\pi
182182 0 0
183183 14.4916 1.07125
184184 0 0
185185 14.7463 1.08417
186186 0 0
187187 − 0.204767i − 0.0149740i
188188 0 0
189189 − 12.0597i − 0.877212i
190190 0 0
191191 4.49157 0.324998 0.162499 0.986709i 0.448045π-0.448045\pi
0.162499 + 0.986709i 0.448045π0.448045\pi
192192 0 0
193193 − 25.7754i − 1.85535i −0.373385 0.927676i 0.621803π-0.621803\pi
0.373385 0.927676i 0.378197π-0.378197\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 18.6233i − 1.32685i −0.748242 0.663426i 0.769102π-0.769102\pi
0.748242 0.663426i 0.230898π-0.230898\pi
198198 0 0
199199 11.9661 0.848258 0.424129 0.905602i 0.360580π-0.360580\pi
0.424129 + 0.905602i 0.360580π0.360580\pi
200200 0 0
201201 − 10.0489i − 0.708796i
202202 0 0
203203 − 4.56704i − 0.320543i
204204 0 0
205205 −22.9172 −1.60061
206206 0 0
207207 −5.90754 −0.410603
208208 0 0
209209 20.7657 1.43639
210210 0 0
211211 2.96077 0.203828 0.101914 0.994793i 0.467503π-0.467503\pi
0.101914 + 0.994793i 0.467503π0.467503\pi
212212 0 0
213213 0.0663757i 0.00454799i
214214 0 0
215215 36.5816i 2.49485i
216216 0 0
217217 6.09246 0.413583
218218 0 0
219219 − 6.12737i − 0.414050i
220220 0 0
221221 0 0
222222 0 0
223223 − 5.44265i − 0.364467i −0.983255 0.182233i 0.941667π-0.941667\pi
0.983255 0.182233i 0.0583326π-0.0583326\pi
224224 0 0
225225 15.1075 1.00717
226226 0 0
227227 22.4480i 1.48993i 0.667105 + 0.744964i 0.267533π0.267533\pi
−0.667105 + 0.744964i 0.732467π0.732467\pi
228228 0 0
229229 16.6136i 1.09786i 0.835870 + 0.548928i 0.184964π0.184964\pi
−0.835870 + 0.548928i 0.815036π0.815036\pi
230230 0 0
231231 9.73423 0.640466
232232 0 0
233233 −9.73125 −0.637515 −0.318758 0.947836i 0.603266π-0.603266\pi
−0.318758 + 0.947836i 0.603266π0.603266\pi
234234 0 0
235235 −29.5623 −1.92843
236236 0 0
237237 17.3913 1.12969
238238 0 0
239239 − 2.82908i − 0.182998i −0.995805 0.0914991i 0.970834π-0.970834\pi
0.995805 0.0914991i 0.0291659π-0.0291659\pi
240240 0 0
241241 − 18.3448i − 1.18169i −0.806784 0.590847i 0.798794π-0.798794\pi
0.806784 0.590847i 0.201206π-0.201206\pi
242242 0 0
243243 11.2567 0.722116
244244 0 0
245245 10.3327i 0.660134i
246246 0 0
247247 0 0
248248 0 0
249249 4.82371i 0.305690i
250250 0 0
251251 2.53750 0.160166 0.0800828 0.996788i 0.474482π-0.474482\pi
0.0800828 + 0.996788i 0.474482π0.474482\pi
252252 0 0
253253 − 17.1129i − 1.07588i
254254 0 0
255255 0.351519i 0.0220130i
256256 0 0
257257 23.4862 1.46503 0.732514 0.680752i 0.238347π-0.238347\pi
0.732514 + 0.680752i 0.238347π0.238347\pi
258258 0 0
259259 7.42029 0.461074
260260 0 0
261261 2.47650 0.153292
262262 0 0
263263 −15.8092 −0.974839 −0.487420 0.873168i 0.662062π-0.662062\pi
−0.487420 + 0.873168i 0.662062π0.662062\pi
264264 0 0
265265 0.0924579i 0.00567964i
266266 0 0
267267 − 3.18492i − 0.194914i
268268 0 0
269269 −30.8582 −1.88145 −0.940727 0.339164i 0.889856π-0.889856\pi
−0.940727 + 0.339164i 0.889856π0.889856\pi
270270 0 0
271271 − 16.1933i − 0.983671i −0.870688 0.491836i 0.836326π-0.836326\pi
0.870688 0.491836i 0.163674π-0.163674\pi
272272 0 0
273273 0 0
274274 0 0
275275 43.7633i 2.63903i
276276 0 0
277277 −13.1075 −0.787555 −0.393777 0.919206i 0.628832π-0.628832\pi
−0.393777 + 0.919206i 0.628832π0.628832\pi
278278 0 0
279279 3.30367i 0.197785i
280280 0 0
281281 − 14.2687i − 0.851202i −0.904911 0.425601i 0.860063π-0.860063\pi
0.904911 0.425601i 0.139937π-0.139937\pi
282282 0 0
283283 7.95646 0.472962 0.236481 0.971636i 0.424006π-0.424006\pi
0.236481 + 0.971636i 0.424006π0.424006\pi
284284 0 0
285285 −35.6480 −2.11161
286286 0 0
287287 −11.5319 −0.680704
288288 0 0
289289 −16.9963 −0.999781
290290 0 0
291291 − 4.64502i − 0.272296i
292292 0 0
293293 − 19.6300i − 1.14679i −0.819278 0.573397i 0.805625π-0.805625\pi
0.819278 0.573397i 0.194375π-0.194375\pi
294294 0 0
295295 −24.6819 −1.43703
296296 0 0
297297 18.9433i 1.09920i
298298 0 0
299299 0 0
300300 0 0
301301 18.4077i 1.06100i
302302 0 0
303303 15.4397 0.886986
304304 0 0
305305 45.3575i 2.59716i
306306 0 0
307307 15.6775i 0.894765i 0.894343 + 0.447382i 0.147644π0.147644\pi
−0.894343 + 0.447382i 0.852356π0.852356\pi
308308 0 0
309309 8.24459 0.469018
310310 0 0
311311 −16.4983 −0.935531 −0.467766 0.883853i 0.654941π-0.654941\pi
−0.467766 + 0.883853i 0.654941π0.654941\pi
312312 0 0
313313 −11.3937 −0.644012 −0.322006 0.946738i 0.604357π-0.604357\pi
−0.322006 + 0.946738i 0.604357π0.604357\pi
314314 0 0
315315 10.5176 0.592602
316316 0 0
317317 25.4470i 1.42924i 0.699511 + 0.714622i 0.253401π0.253401\pi
−0.699511 + 0.714622i 0.746599π0.746599\pi
318318 0 0
319319 7.17390i 0.401661i
320320 0 0
321321 −21.7603 −1.21454
322322 0 0
323323 0.377338i 0.0209957i
324324 0 0
325325 0 0
326326 0 0
327327 − 20.2306i − 1.11875i
328328 0 0
329329 −14.8756 −0.820119
330330 0 0
331331 8.95539i 0.492233i 0.969240 + 0.246117i 0.0791546π0.0791546\pi
−0.969240 + 0.246117i 0.920845π0.920845\pi
332332 0 0
333333 4.02369i 0.220497i
334334 0 0
335335 31.4523 1.71842
336336 0 0
337337 −19.3110 −1.05194 −0.525968 0.850505i 0.676297π-0.676297\pi
−0.525968 + 0.850505i 0.676297π0.676297\pi
338338 0 0
339339 11.1870 0.607597
340340 0 0
341341 −9.57002 −0.518246
342342 0 0
343343 20.1588i 1.08847i
344344 0 0
345345 29.3773i 1.58162i
346346 0 0
347347 36.0411 1.93479 0.967395 0.253272i 0.0815068π-0.0815068\pi
0.967395 + 0.253272i 0.0815068π0.0815068\pi
348348 0 0
349349 − 23.2416i − 1.24409i −0.782980 0.622047i 0.786301π-0.786301\pi
0.782980 0.622047i 0.213699π-0.213699\pi
350350 0 0
351351 0 0
352352 0 0
353353 24.2349i 1.28989i 0.764228 + 0.644947i 0.223120π0.223120\pi
−0.764228 + 0.644947i 0.776880π0.776880\pi
354354 0 0
355355 −0.207751 −0.0110263
356356 0 0
357357 0.176883i 0.00936164i
358358 0 0
359359 − 17.7332i − 0.935921i −0.883749 0.467960i 0.844989π-0.844989\pi
0.883749 0.467960i 0.155011π-0.155011\pi
360360 0 0
361361 −19.2664 −1.01402
362362 0 0
363363 −0.364666 −0.0191400
364364 0 0
365365 19.1782 1.00383
366366 0 0
367367 30.2083 1.57686 0.788431 0.615123i 0.210894π-0.210894\pi
0.788431 + 0.615123i 0.210894π0.210894\pi
368368 0 0
369369 − 6.25321i − 0.325529i
370370 0 0
371371 0.0465244i 0.00241543i
372372 0 0
373373 −0.681268 −0.0352747 −0.0176374 0.999844i 0.505614π-0.505614\pi
−0.0176374 + 0.999844i 0.505614π0.505614\pi
374374 0 0
375375 − 46.3139i − 2.39164i
376376 0 0
377377 0 0
378378 0 0
379379 36.4959i 1.87467i 0.348433 + 0.937334i 0.386714π0.386714\pi
−0.348433 + 0.937334i 0.613286π0.613286\pi
380380 0 0
381381 9.01400 0.461801
382382 0 0
383383 − 5.20775i − 0.266104i −0.991109 0.133052i 0.957522π-0.957522\pi
0.991109 0.133052i 0.0424777π-0.0424777\pi
384384 0 0
385385 30.4674i 1.55276i
386386 0 0
387387 −9.98169 −0.507398
388388 0 0
389389 17.5254 0.888574 0.444287 0.895885i 0.353457π-0.353457\pi
0.444287 + 0.895885i 0.353457π0.353457\pi
390390 0 0
391391 0.310962 0.0157260
392392 0 0
393393 10.6692 0.538189
394394 0 0
395395 54.4336i 2.73885i
396396 0 0
397397 29.8049i 1.49587i 0.663774 + 0.747933i 0.268954π0.268954\pi
−0.663774 + 0.747933i 0.731046π0.731046\pi
398398 0 0
399399 −17.9379 −0.898020
400400 0 0
401401 − 16.3341i − 0.815684i −0.913053 0.407842i 0.866281π-0.866281\pi
0.913053 0.407842i 0.133719π-0.133719\pi
402402 0 0
403403 0 0
404404 0 0
405405 − 17.7549i − 0.882250i
406406 0 0
407407 −11.6558 −0.577755
408408 0 0
409409 − 9.49827i − 0.469659i −0.972037 0.234830i 0.924547π-0.924547\pi
0.972037 0.234830i 0.0754532π-0.0754532\pi
410410 0 0
411411 1.34050i 0.0661221i
412412 0 0
413413 −12.4198 −0.611139
414414 0 0
415415 −15.0978 −0.741124
416416 0 0
417417 −16.3327 −0.799817
418418 0 0
419419 12.4450 0.607980 0.303990 0.952675i 0.401681π-0.401681\pi
0.303990 + 0.952675i 0.401681π0.401681\pi
420420 0 0
421421 3.65578i 0.178172i 0.996024 + 0.0890858i 0.0283945π0.0283945\pi
−0.996024 + 0.0890858i 0.971605π0.971605\pi
422422 0 0
423423 − 8.06638i − 0.392201i
424424 0 0
425425 −0.795233 −0.0385745
426426 0 0
427427 22.8237i 1.10452i
428428 0 0
429429 0 0
430430 0 0
431431 − 35.6219i − 1.71585i −0.513777 0.857924i 0.671754π-0.671754\pi
0.513777 0.857924i 0.328246π-0.328246\pi
432432 0 0
433433 34.6926 1.66722 0.833610 0.552353i 0.186270π-0.186270\pi
0.833610 + 0.552353i 0.186270π0.186270\pi
434434 0 0
435435 − 12.3153i − 0.590472i
436436 0 0
437437 31.5351i 1.50853i
438438 0 0
439439 −9.48858 −0.452865 −0.226433 0.974027i 0.572706π-0.572706\pi
−0.226433 + 0.974027i 0.572706π0.572706\pi
440440 0 0
441441 −2.81940 −0.134257
442442 0 0
443443 14.1849 0.673946 0.336973 0.941514i 0.390597π-0.390597\pi
0.336973 + 0.941514i 0.390597π0.390597\pi
444444 0 0
445445 9.96854 0.472554
446446 0 0
447447 3.20131i 0.151417i
448448 0 0
449449 6.99894i 0.330300i 0.986268 + 0.165150i 0.0528109π0.0528109\pi
−0.986268 + 0.165150i 0.947189π0.947189\pi
450450 0 0
451451 18.1142 0.852966
452452 0 0
453453 10.0949i 0.474297i
454454 0 0
455455 0 0
456456 0 0
457457 3.21313i 0.150304i 0.997172 + 0.0751519i 0.0239442π0.0239442\pi
−0.997172 + 0.0751519i 0.976056π0.976056\pi
458458 0 0
459459 −0.344223 −0.0160670
460460 0 0
461461 15.5278i 0.723202i 0.932333 + 0.361601i 0.117770π0.117770\pi
−0.932333 + 0.361601i 0.882230π0.882230\pi
462462 0 0
463463 − 32.0834i − 1.49104i −0.666483 0.745520i 0.732201π-0.732201\pi
0.666483 0.745520i 0.267799π-0.267799\pi
464464 0 0
465465 16.4286 0.761860
466466 0 0
467467 −7.24459 −0.335239 −0.167620 0.985852i 0.553608π-0.553608\pi
−0.167620 + 0.985852i 0.553608π0.553608\pi
468468 0 0
469469 15.8267 0.730809
470470 0 0
471471 −14.8562 −0.684539
472472 0 0
473473 − 28.9148i − 1.32951i
474474 0 0
475475 − 80.6456i − 3.70027i
476476 0 0
477477 −0.0252281 −0.00115512
478478 0 0
479479 − 5.78209i − 0.264190i −0.991237 0.132095i 0.957830π-0.957830\pi
0.991237 0.132095i 0.0421704π-0.0421704\pi
480480 0 0
481481 0 0
482482 0 0
483483 14.7826i 0.672630i
484484 0 0
485485 14.5386 0.660162
486486 0 0
487487 4.14782i 0.187956i 0.995574 + 0.0939778i 0.0299583π0.0299583\pi
−0.995574 + 0.0939778i 0.970042π0.970042\pi
488488 0 0
489489 − 9.53186i − 0.431046i
490490 0 0
491491 −7.19375 −0.324649 −0.162325 0.986737i 0.551899π-0.551899\pi
−0.162325 + 0.986737i 0.551899π0.551899\pi
492492 0 0
493493 −0.130359 −0.00587105
494494 0 0
495495 −16.5211 −0.742569
496496 0 0
497497 −0.104539 −0.00468924
498498 0 0
499499 − 41.5066i − 1.85809i −0.369964 0.929046i 0.620630π-0.620630\pi
0.369964 0.929046i 0.379370π-0.379370\pi
500500 0 0
501501 21.0073i 0.938537i
502502 0 0
503503 −25.8605 −1.15306 −0.576532 0.817074i 0.695595π-0.695595\pi
−0.576532 + 0.817074i 0.695595π0.695595\pi
504504 0 0
505505 48.3250i 2.15043i
506506 0 0
507507 0 0
508508 0 0
509509 35.3924i 1.56874i 0.620293 + 0.784370i 0.287014π0.287014\pi
−0.620293 + 0.784370i 0.712986π0.712986\pi
510510 0 0
511511 9.65040 0.426909
512512 0 0
513513 − 34.9081i − 1.54123i
514514 0 0
515515 25.8049i 1.13710i
516516 0 0
517517 23.3666 1.02766
518518 0 0
519519 −18.6983 −0.820762
520520 0 0
521521 −34.2620 −1.50105 −0.750524 0.660844i 0.770199π-0.770199\pi
−0.750524 + 0.660844i 0.770199π0.770199\pi
522522 0 0
523523 −14.6028 −0.638536 −0.319268 0.947664i 0.603437π-0.603437\pi
−0.319268 + 0.947664i 0.603437π0.603437\pi
524524 0 0
525525 − 37.8039i − 1.64990i
526526 0 0
527527 − 0.173899i − 0.00757516i
528528 0 0
529529 2.98792 0.129909
530530 0 0
531531 − 6.73471i − 0.292261i
532532 0 0
533533 0 0
534534 0 0
535535 − 68.1081i − 2.94457i
536536 0 0
537537 −30.0180 −1.29537
538538 0 0
539539 − 8.16719i − 0.351786i
540540 0 0
541541 − 18.8866i − 0.811999i −0.913873 0.406000i 0.866923π-0.866923\pi
0.913873 0.406000i 0.133077π-0.133077\pi
542542 0 0
543543 18.5090 0.794298
544544 0 0
545545 63.3202 2.71234
546546 0 0
547547 −34.6752 −1.48260 −0.741301 0.671172i 0.765791π-0.765791\pi
−0.741301 + 0.671172i 0.765791π0.765791\pi
548548 0 0
549549 −12.3763 −0.528206
550550 0 0
551551 − 13.2198i − 0.563184i
552552 0 0
553553 27.3907i 1.16477i
554554 0 0
555555 20.0092 0.849344
556556 0 0
557557 4.25667i 0.180361i 0.995925 + 0.0901804i 0.0287444π0.0287444\pi
−0.995925 + 0.0901804i 0.971256π0.971256\pi
558558 0 0
559559 0 0
560560 0 0
561561 − 0.277848i − 0.0117307i
562562 0 0
563563 −21.1371 −0.890821 −0.445411 0.895326i 0.646942π-0.646942\pi
−0.445411 + 0.895326i 0.646942π0.646942\pi
564564 0 0
565565 35.0146i 1.47307i
566566 0 0
567567 − 8.93422i − 0.375202i
568568 0 0
569569 −35.4795 −1.48738 −0.743689 0.668526i 0.766926π-0.766926\pi
−0.743689 + 0.668526i 0.766926π0.766926\pi
570570 0 0
571571 −3.94033 −0.164898 −0.0824488 0.996595i 0.526274π-0.526274\pi
−0.0824488 + 0.996595i 0.526274π0.526274\pi
572572 0 0
573573 6.09459 0.254605
574574 0 0
575575 −66.4596 −2.77156
576576 0 0
577577 − 16.6256i − 0.692135i −0.938210 0.346067i 0.887517π-0.887517\pi
0.938210 0.346067i 0.112483π-0.112483\pi
578578 0 0
579579 − 34.9745i − 1.45349i
580580 0 0
581581 −7.59717 −0.315184
582582 0 0
583583 − 0.0730805i − 0.00302669i
584584 0 0
585585 0 0
586586 0 0
587587 − 8.00298i − 0.330318i −0.986267 0.165159i 0.947186π-0.947186\pi
0.986267 0.165159i 0.0528138π-0.0528138\pi
588588 0 0
589589 17.6353 0.726651
590590 0 0
591591 − 25.2698i − 1.03946i
592592 0 0
593593 − 15.8345i − 0.650243i −0.945672 0.325122i 0.894595π-0.894595\pi
0.945672 0.325122i 0.105405π-0.105405\pi
594594 0 0
595595 −0.553630 −0.0226966
596596 0 0
597597 16.2368 0.664529
598598 0 0
599599 25.9226 1.05917 0.529585 0.848257i 0.322348π-0.322348\pi
0.529585 + 0.848257i 0.322348π0.322348\pi
600600 0 0
601601 20.0616 0.818329 0.409165 0.912461i 0.365820π-0.365820\pi
0.409165 + 0.912461i 0.365820π0.365820\pi
602602 0 0
603603 8.58211i 0.349490i
604604 0 0
605605 − 1.14138i − 0.0464035i
606606 0 0
607607 41.7614 1.69504 0.847521 0.530762i 0.178094π-0.178094\pi
0.847521 + 0.530762i 0.178094π0.178094\pi
608608 0 0
609609 − 6.19700i − 0.251115i
610610 0 0
611611 0 0
612612 0 0
613613 − 12.4179i − 0.501554i −0.968045 0.250777i 0.919314π-0.919314\pi
0.968045 0.250777i 0.0806861π-0.0806861\pi
614614 0 0
615615 −31.0963 −1.25392
616616 0 0
617617 − 17.2198i − 0.693244i −0.938005 0.346622i 0.887329π-0.887329\pi
0.938005 0.346622i 0.112671π-0.112671\pi
618618 0 0
619619 − 42.6136i − 1.71278i −0.516326 0.856392i 0.672701π-0.672701\pi
0.516326 0.856392i 0.327299π-0.327299\pi
620620 0 0
621621 −28.7676 −1.15440
622622 0 0
623623 5.01613 0.200967
624624 0 0
625625 79.7749 3.19100
626626 0 0
627627 28.1769 1.12528
628628 0 0
629629 − 0.211800i − 0.00844501i
630630 0 0
631631 26.8605i 1.06930i 0.845073 + 0.534651i 0.179557π0.179557\pi
−0.845073 + 0.534651i 0.820443π0.820443\pi
632632 0 0
633633 4.01746 0.159680
634634 0 0
635635 28.2131i 1.11960i
636636 0 0
637637 0 0
638638 0 0
639639 − 0.0566871i − 0.00224251i
640640 0 0
641641 −33.3045 −1.31545 −0.657725 0.753258i 0.728481π-0.728481\pi
−0.657725 + 0.753258i 0.728481π0.728481\pi
642642 0 0
643643 30.6746i 1.20969i 0.796344 + 0.604843i 0.206764π0.206764\pi
−0.796344 + 0.604843i 0.793236π0.793236\pi
644644 0 0
645645 49.6375i 1.95447i
646646 0 0
647647 3.25608 0.128010 0.0640048 0.997950i 0.479613π-0.479613\pi
0.0640048 + 0.997950i 0.479613π0.479613\pi
648648 0 0
649649 19.5090 0.765796
650650 0 0
651651 8.26683 0.324003
652652 0 0
653653 14.8183 0.579886 0.289943 0.957044i 0.406364π-0.406364\pi
0.289943 + 0.957044i 0.406364π0.406364\pi
654654 0 0
655655 33.3937i 1.30480i
656656 0 0
657657 5.23298i 0.204158i
658658 0 0
659659 30.5392 1.18964 0.594818 0.803860i 0.297224π-0.297224\pi
0.594818 + 0.803860i 0.297224π0.297224\pi
660660 0 0
661661 19.3676i 0.753314i 0.926353 + 0.376657i 0.122927π0.122927\pi
−0.926353 + 0.376657i 0.877073π0.877073\pi
662662 0 0
663663 0 0
664664 0 0
665665 − 56.1444i − 2.17718i
666666 0 0
667667 −10.8944 −0.421833
668668 0 0
669669 − 7.38511i − 0.285525i
670670 0 0
671671 − 35.8514i − 1.38403i
672672 0 0
673673 −41.5459 −1.60148 −0.800738 0.599015i 0.795559π-0.795559\pi
−0.800738 + 0.599015i 0.795559π0.795559\pi
674674 0 0
675675 73.5682 2.83164
676676 0 0
677677 −40.6064 −1.56063 −0.780315 0.625387i 0.784941π-0.784941\pi
−0.780315 + 0.625387i 0.784941π0.784941\pi
678678 0 0
679679 7.31575 0.280753
680680 0 0
681681 30.4596i 1.16722i
682682 0 0
683683 2.40581i 0.0920559i 0.998940 + 0.0460279i 0.0146563π0.0146563\pi
−0.998940 + 0.0460279i 0.985344π0.985344\pi
684684 0 0
685685 −4.19567 −0.160308
686686 0 0
687687 22.5429i 0.860064i
688688 0 0
689689 0 0
690690 0 0
691691 6.81269i 0.259167i 0.991569 + 0.129583i 0.0413640π0.0413640\pi
−0.991569 + 0.129583i 0.958636π0.958636\pi
692692 0 0
693693 −8.31336 −0.315798
694694 0 0
695695 − 51.1202i − 1.93910i
696696 0 0
697697 0.329158i 0.0124677i
698698 0 0
699699 −13.2043 −0.499432
700700 0 0
701701 12.7802 0.482700 0.241350 0.970438i 0.422410π-0.422410\pi
0.241350 + 0.970438i 0.422410π0.422410\pi
702702 0 0
703703 21.4789 0.810092
704704 0 0
705705 −40.1129 −1.51074
706706 0 0
707707 24.3169i 0.914532i
708708 0 0
709709 4.94139i 0.185578i 0.995686 + 0.0927890i 0.0295782π0.0295782\pi
−0.995686 + 0.0927890i 0.970422π0.970422\pi
710710 0 0
711711 −14.8528 −0.557023
712712 0 0
713713 − 14.5332i − 0.544272i
714714 0 0
715715 0 0
716716 0 0
717717 − 3.83877i − 0.143362i
718718 0 0
719719 37.6155 1.40282 0.701410 0.712758i 0.252554π-0.252554\pi
0.701410 + 0.712758i 0.252554π0.252554\pi
720720 0 0
721721 12.9849i 0.483584i
722722 0 0
723723 − 24.8920i − 0.925744i
724724 0 0
725725 27.8605 1.03471
726726 0 0
727727 17.1879 0.637464 0.318732 0.947845i 0.396743π-0.396743\pi
0.318732 + 0.947845i 0.396743π0.396743\pi
728728 0 0
729729 27.8159 1.03022
730730 0 0
731731 0.525418 0.0194333
732732 0 0
733733 − 19.2597i − 0.711371i −0.934606 0.355686i 0.884247π-0.884247\pi
0.934606 0.355686i 0.115753π-0.115753\pi
734734 0 0
735735 14.0204i 0.517152i
736736 0 0
737737 −24.8605 −0.915750
738738 0 0
739739 − 18.0785i − 0.665027i −0.943099 0.332513i 0.892103π-0.892103\pi
0.943099 0.332513i 0.107897π-0.107897\pi
740740 0 0
741741 0 0
742742 0 0
743743 32.8219i 1.20412i 0.798451 + 0.602059i 0.205653π0.205653\pi
−0.798451 + 0.602059i 0.794347π0.794347\pi
744744 0 0
745745 −10.0199 −0.367099
746746 0 0
747747 − 4.11960i − 0.150728i
748748 0 0
749749 − 34.2717i − 1.25226i
750750 0 0
751751 33.1702 1.21040 0.605198 0.796075i 0.293094π-0.293094\pi
0.605198 + 0.796075i 0.293094π0.293094\pi
752752 0 0
753753 3.44312 0.125474
754754 0 0
755755 −31.5961 −1.14990
756756 0 0
757757 −0.736627 −0.0267732 −0.0133866 0.999910i 0.504261π-0.504261\pi
−0.0133866 + 0.999910i 0.504261π0.504261\pi
758758 0 0
759759 − 23.2204i − 0.842848i
760760 0 0
761761 − 36.3817i − 1.31883i −0.751777 0.659417i 0.770803π-0.770803\pi
0.751777 0.659417i 0.229197π-0.229197\pi
762762 0 0
763763 31.8625 1.15350
764764 0 0
765765 − 0.300209i − 0.0108541i
766766 0 0
767767 0 0
768768 0 0
769769 − 11.4523i − 0.412982i −0.978449 0.206491i 0.933796π-0.933796\pi
0.978449 0.206491i 0.0662044π-0.0662044\pi
770770 0 0
771771 31.8683 1.14771
772772 0 0
773773 7.57732i 0.272537i 0.990672 + 0.136269i 0.0435110π0.0435110\pi
−0.990672 + 0.136269i 0.956489π0.956489\pi
774774 0 0
775775 37.1661i 1.33505i
776776 0 0
777777 10.0686 0.361207
778778 0 0
779779 −33.3803 −1.19597
780780 0 0
781781 0.164210 0.00587591
782782 0 0
783783 12.0597 0.430977
784784 0 0
785785 − 46.4989i − 1.65962i
786786 0 0
787787 30.5066i 1.08744i 0.839265 + 0.543722i 0.182985π0.182985\pi
−0.839265 + 0.543722i 0.817015π0.817015\pi
788788 0 0
789789 −21.4515 −0.763693
790790 0 0
791791 17.6192i 0.626467i
792792 0 0
793793 0 0
794794 0 0
795795 0.125456i 0.00444946i
796796 0 0
797797 −36.2435 −1.28381 −0.641906 0.766784i 0.721856π-0.721856\pi
−0.641906 + 0.766784i 0.721856π0.721856\pi
798798 0 0
799799 0.424600i 0.0150213i
800800 0 0
801801 2.72002i 0.0961073i
802802 0 0
803803 −15.1588 −0.534944
804804 0 0
805805 −46.2683 −1.63074
806806 0 0
807807 −41.8713 −1.47394
808808 0 0
809809 22.3236 0.784857 0.392429 0.919782i 0.371635π-0.371635\pi
0.392429 + 0.919782i 0.371635π0.371635\pi
810810 0 0
811811 − 39.4922i − 1.38676i −0.720573 0.693379i 0.756121π-0.756121\pi
0.720573 0.693379i 0.243879π-0.243879\pi
812812 0 0
813813 − 21.9726i − 0.770612i
814814 0 0
815815 29.8340 1.04504
816816 0 0
817817 53.2833i 1.86415i
818818 0 0
819819 0 0
820820 0 0
821821 11.3830i 0.397269i 0.980074 + 0.198634i 0.0636506π0.0636506\pi
−0.980074 + 0.198634i 0.936349π0.936349\pi
822822 0 0
823823 −25.6848 −0.895317 −0.447659 0.894205i 0.647742π-0.647742\pi
−0.447659 + 0.894205i 0.647742π0.647742\pi
824824 0 0
825825 59.3822i 2.06742i
826826 0 0
827827 36.7251i 1.27706i 0.769598 + 0.638529i 0.220457π0.220457\pi
−0.769598 + 0.638529i 0.779543π0.779543\pi
828828 0 0
829829 11.5808 0.402217 0.201109 0.979569i 0.435546π-0.435546\pi
0.201109 + 0.979569i 0.435546π0.435546\pi
830830 0 0
831831 −17.7855 −0.616974
832832 0 0
833833 0.148408 0.00514203
834834 0 0
835835 −65.7512 −2.27541
836836 0 0
837837 16.0877i 0.556071i
838838 0 0
839839 − 13.4577i − 0.464612i −0.972643 0.232306i 0.925373π-0.925373\pi
0.972643 0.232306i 0.0746271π-0.0746271\pi
840840 0 0
841841 −24.4330 −0.842516
842842 0 0
843843 − 19.3612i − 0.666835i
844844 0 0
845845 0 0
846846 0 0
847847 − 0.574335i − 0.0197344i
848848 0 0
849849 10.7961 0.370521
850850 0 0
851851 − 17.7006i − 0.606770i
852852 0 0
853853 5.34050i 0.182855i 0.995812 + 0.0914277i 0.0291430π0.0291430\pi
−0.995812 + 0.0914277i 0.970857π0.970857\pi
854854 0 0
855855 30.4446 1.04118
856856 0 0
857857 −49.3381 −1.68536 −0.842679 0.538417i 0.819023π-0.819023\pi
−0.842679 + 0.538417i 0.819023π0.819023\pi
858858 0 0
859859 −4.92500 −0.168039 −0.0840194 0.996464i 0.526776π-0.526776\pi
−0.0840194 + 0.996464i 0.526776π0.526776\pi
860860 0 0
861861 −15.6475 −0.533266
862862 0 0
863863 − 40.0315i − 1.36269i −0.731964 0.681343i 0.761396π-0.761396\pi
0.731964 0.681343i 0.238604π-0.238604\pi
864864 0 0
865865 − 58.5241i − 1.98988i
866866 0 0
867867 −23.0622 −0.783233
868868 0 0
869869 − 43.0253i − 1.45953i
870870 0 0
871871 0 0
872872 0 0
873873 3.96700i 0.134263i
874874 0 0
875875 72.9428 2.46592
876876 0 0
877877 − 28.9379i − 0.977165i −0.872518 0.488582i 0.837514π-0.837514\pi
0.872518 0.488582i 0.162486π-0.162486\pi
878878 0 0
879879 − 26.6358i − 0.898404i
880880 0 0
881881 −21.6692 −0.730053 −0.365027 0.930997i 0.618940π-0.618940\pi
−0.365027 + 0.930997i 0.618940π0.618940\pi
882882 0 0
883883 −11.7614 −0.395802 −0.197901 0.980222i 0.563412π-0.563412\pi
−0.197901 + 0.980222i 0.563412π0.563412\pi
884884 0 0
885885 −33.4907 −1.12578
886886 0 0
887887 26.8485 0.901483 0.450742 0.892654i 0.351160π-0.351160\pi
0.450742 + 0.892654i 0.351160π0.351160\pi
888888 0 0
889889 14.1967i 0.476143i
890890 0 0
891891 14.0339i 0.470152i
892892 0 0
893893 −43.0592 −1.44092
894894 0 0
895895 − 93.9542i − 3.14054i
896896 0 0
897897 0 0
898898 0 0
899899 6.09246i 0.203195i
900900 0 0
901901 0.00132796 4.42409e−5 0
902902 0 0
903903 24.9774i 0.831195i
904904 0 0
905905 57.9318i 1.92572i
906906 0 0
907907 −16.4306 −0.545568 −0.272784 0.962075i 0.587944π-0.587944\pi
−0.272784 + 0.962075i 0.587944π0.587944\pi
908908 0 0
909909 −13.1860 −0.437351
910910 0 0
911911 26.0519 0.863138 0.431569 0.902080i 0.357960π-0.357960\pi
0.431569 + 0.902080i 0.357960π0.357960\pi
912912 0 0
913913 11.9336 0.394945
914914 0 0
915915 61.5454i 2.03463i
916916 0 0
917917 16.8036i 0.554904i
918918 0 0
919919 4.36957 0.144139 0.0720694 0.997400i 0.477040π-0.477040\pi
0.0720694 + 0.997400i 0.477040π0.477040\pi
920920 0 0
921921 21.2728i 0.700963i
922922 0 0
923923 0 0
924924 0 0
925925 45.2664i 1.48835i
926926 0 0
927927 −7.04115 −0.231262
928928 0 0
929929 − 32.2868i − 1.05930i −0.848218 0.529648i 0.822324π-0.822324\pi
0.848218 0.529648i 0.177676π-0.177676\pi
930930 0 0
931931 15.0502i 0.493252i
932932 0 0
933933 −22.3864 −0.732899
934934 0 0
935935 0.869641 0.0284403
936936 0 0
937937 −48.5730 −1.58681 −0.793405 0.608693i 0.791694π-0.791694\pi
−0.793405 + 0.608693i 0.791694π0.791694\pi
938938 0 0
939939 −15.4601 −0.504522
940940 0 0
941941 4.82849i 0.157404i 0.996898 + 0.0787022i 0.0250776π0.0250776\pi
−0.996898 + 0.0787022i 0.974922π0.974922\pi
942942 0 0
943943 27.5086i 0.895802i
944944 0 0
945945 51.2172 1.66609
946946 0 0
947947 35.1065i 1.14081i 0.821365 + 0.570403i 0.193213π0.193213\pi
−0.821365 + 0.570403i 0.806787π0.806787\pi
948948 0 0
949949 0 0
950950 0 0
951951 34.5289i 1.11968i
952952 0 0
953953 28.1866 0.913053 0.456526 0.889710i 0.349093π-0.349093\pi
0.456526 + 0.889710i 0.349093π0.349093\pi
954954 0 0
955955 19.0756i 0.617272i
956956 0 0
957957 9.73423i 0.314663i
958958 0 0
959959 −2.11124 −0.0681756
960960 0 0
961961 22.8726 0.737827
962962 0 0
963963 18.5840 0.598862
964964 0 0
965965 109.468 3.52388
966966 0 0
967967 44.6674i 1.43641i 0.695834 + 0.718203i 0.255035π0.255035\pi
−0.695834 + 0.718203i 0.744965π0.744965\pi
968968 0 0
969969 0.512009i 0.0164481i
970970 0 0
971971 −14.9108 −0.478510 −0.239255 0.970957i 0.576903π-0.576903\pi
−0.239255 + 0.970957i 0.576903π0.576903\pi
972972 0 0
973973 − 25.7235i − 0.824657i
974974 0 0
975975 0 0
976976 0 0
977977 − 35.2127i − 1.12655i −0.826269 0.563276i 0.809541π-0.809541\pi
0.826269 0.563276i 0.190459π-0.190459\pi
978978 0 0
979979 −7.87933 −0.251824
980980 0 0
981981 17.2776i 0.551631i
982982 0 0
983983 30.5646i 0.974861i 0.873162 + 0.487430i 0.162066π0.162066\pi
−0.873162 + 0.487430i 0.837934π0.837934\pi
984984 0 0
985985 79.0926 2.52010
986986 0 0
987987 −20.1847 −0.642485
988988 0 0
989989 43.9105 1.39627
990990 0 0
991991 62.5739 1.98772 0.993862 0.110626i 0.0352856π-0.0352856\pi
0.993862 + 0.110626i 0.0352856π0.0352856\pi
992992 0 0
993993 12.1515i 0.385617i
994994 0 0
995995 50.8200i 1.61110i
996996 0 0
997997 −1.88444 −0.0596809 −0.0298405 0.999555i 0.509500π-0.509500\pi
−0.0298405 + 0.999555i 0.509500π0.509500\pi
998998 0 0
999999 19.5939i 0.619924i
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 676.2.d.e.337.4 6
3.2 odd 2 6084.2.b.p.4393.1 6
4.3 odd 2 2704.2.f.n.337.4 6
13.2 odd 12 676.2.e.g.529.2 6
13.3 even 3 676.2.h.e.485.4 12
13.4 even 6 676.2.h.e.361.3 12
13.5 odd 4 676.2.a.h.1.2 yes 3
13.6 odd 12 676.2.e.g.653.2 6
13.7 odd 12 676.2.e.f.653.2 6
13.8 odd 4 676.2.a.g.1.2 3
13.9 even 3 676.2.h.e.361.4 12
13.10 even 6 676.2.h.e.485.3 12
13.11 odd 12 676.2.e.f.529.2 6
13.12 even 2 inner 676.2.d.e.337.3 6
39.5 even 4 6084.2.a.x.1.1 3
39.8 even 4 6084.2.a.bc.1.3 3
39.38 odd 2 6084.2.b.p.4393.6 6
52.31 even 4 2704.2.a.y.1.2 3
52.47 even 4 2704.2.a.x.1.2 3
52.51 odd 2 2704.2.f.n.337.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
676.2.a.g.1.2 3 13.8 odd 4
676.2.a.h.1.2 yes 3 13.5 odd 4
676.2.d.e.337.3 6 13.12 even 2 inner
676.2.d.e.337.4 6 1.1 even 1 trivial
676.2.e.f.529.2 6 13.11 odd 12
676.2.e.f.653.2 6 13.7 odd 12
676.2.e.g.529.2 6 13.2 odd 12
676.2.e.g.653.2 6 13.6 odd 12
676.2.h.e.361.3 12 13.4 even 6
676.2.h.e.361.4 12 13.9 even 3
676.2.h.e.485.3 12 13.10 even 6
676.2.h.e.485.4 12 13.3 even 3
2704.2.a.x.1.2 3 52.47 even 4
2704.2.a.y.1.2 3 52.31 even 4
2704.2.f.n.337.3 6 52.51 odd 2
2704.2.f.n.337.4 6 4.3 odd 2
6084.2.a.x.1.1 3 39.5 even 4
6084.2.a.bc.1.3 3 39.8 even 4
6084.2.b.p.4393.1 6 3.2 odd 2
6084.2.b.p.4393.6 6 39.38 odd 2