Properties

Label 616.4.a.i.1.5
Level 616616
Weight 44
Character 616.1
Self dual yes
Analytic conductor 36.34536.345
Analytic rank 00
Dimension 66
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] = [616,4,Mod(1,616)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(616, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("616.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 616=23711 616 = 2^{3} \cdot 7 \cdot 11
Weight: k k == 4 4
Character orbit: [χ][\chi] == 616.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: 36.345176563536.3451765635
Analytic rank: 00
Dimension: 66
Coefficient field: Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x547x4+10x3+612x2+240x1440 x^{6} - x^{5} - 47x^{4} + 10x^{3} + 612x^{2} + 240x - 1440 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 265 2^{6}\cdot 5
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 3.68968-3.68968 of defining polynomial
Character χ\chi == 616.1

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+3.73933q3+19.7791q5+7.00000q713.0174q911.0000q1119.4047q13+73.9605q15+70.8148q17+18.1735q19+26.1753q21+150.203q23+266.213q25149.638q27+36.1152q29+312.071q3141.1326q33+138.454q35341.208q3772.5606q39+181.399q41+334.357q43257.473q45255.999q47+49.0000q49+264.800q51674.234q53217.570q55+67.9566q57+396.486q59+495.662q6191.1220q63383.808q65820.499q67+561.660q69259.971q71+362.323q73+995.456q7577.0000q7739.4291q79208.076q81+649.668q83+1400.65q85+135.047q87386.836q89135.833q91+1166.94q93+359.455q95+336.297q97+143.192q99+O(q100)q+3.73933 q^{3} +19.7791 q^{5} +7.00000 q^{7} -13.0174 q^{9} -11.0000 q^{11} -19.4047 q^{13} +73.9605 q^{15} +70.8148 q^{17} +18.1735 q^{19} +26.1753 q^{21} +150.203 q^{23} +266.213 q^{25} -149.638 q^{27} +36.1152 q^{29} +312.071 q^{31} -41.1326 q^{33} +138.454 q^{35} -341.208 q^{37} -72.5606 q^{39} +181.399 q^{41} +334.357 q^{43} -257.473 q^{45} -255.999 q^{47} +49.0000 q^{49} +264.800 q^{51} -674.234 q^{53} -217.570 q^{55} +67.9566 q^{57} +396.486 q^{59} +495.662 q^{61} -91.1220 q^{63} -383.808 q^{65} -820.499 q^{67} +561.660 q^{69} -259.971 q^{71} +362.323 q^{73} +995.456 q^{75} -77.0000 q^{77} -39.4291 q^{79} -208.076 q^{81} +649.668 q^{83} +1400.65 q^{85} +135.047 q^{87} -386.836 q^{89} -135.833 q^{91} +1166.94 q^{93} +359.455 q^{95} +336.297 q^{97} +143.192 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+2q5+42q7+60q966q116q13+126q1514q17+80q19+254q23+220q25+90q27+132q2952q31+14q35518q37+332q39+486q41+660q99+O(q100) 6 q + 2 q^{5} + 42 q^{7} + 60 q^{9} - 66 q^{11} - 6 q^{13} + 126 q^{15} - 14 q^{17} + 80 q^{19} + 254 q^{23} + 220 q^{25} + 90 q^{27} + 132 q^{29} - 52 q^{31} + 14 q^{35} - 518 q^{37} + 332 q^{39} + 486 q^{41}+ \cdots - 660 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 3.73933 0.719634 0.359817 0.933023i 0.382839π-0.382839\pi
0.359817 + 0.933023i 0.382839π0.382839\pi
44 0 0
55 19.7791 1.76910 0.884548 0.466449i 0.154467π-0.154467\pi
0.884548 + 0.466449i 0.154467π0.154467\pi
66 0 0
77 7.00000 0.377964
88 0 0
99 −13.0174 −0.482127
1010 0 0
1111 −11.0000 −0.301511
1212 0 0
1313 −19.4047 −0.413992 −0.206996 0.978342i 0.566369π-0.566369\pi
−0.206996 + 0.978342i 0.566369π0.566369\pi
1414 0 0
1515 73.9605 1.27310
1616 0 0
1717 70.8148 1.01030 0.505151 0.863031i 0.331437π-0.331437\pi
0.505151 + 0.863031i 0.331437π0.331437\pi
1818 0 0
1919 18.1735 0.219436 0.109718 0.993963i 0.465005π-0.465005\pi
0.109718 + 0.993963i 0.465005π0.465005\pi
2020 0 0
2121 26.1753 0.271996
2222 0 0
2323 150.203 1.36172 0.680860 0.732413i 0.261606π-0.261606\pi
0.680860 + 0.732413i 0.261606π0.261606\pi
2424 0 0
2525 266.213 2.12970
2626 0 0
2727 −149.638 −1.06659
2828 0 0
2929 36.1152 0.231256 0.115628 0.993293i 0.463112π-0.463112\pi
0.115628 + 0.993293i 0.463112π0.463112\pi
3030 0 0
3131 312.071 1.80805 0.904026 0.427477i 0.140598π-0.140598\pi
0.904026 + 0.427477i 0.140598π0.140598\pi
3232 0 0
3333 −41.1326 −0.216978
3434 0 0
3535 138.454 0.668656
3636 0 0
3737 −341.208 −1.51606 −0.758031 0.652219i 0.773838π-0.773838\pi
−0.758031 + 0.652219i 0.773838π0.773838\pi
3838 0 0
3939 −72.5606 −0.297923
4040 0 0
4141 181.399 0.690968 0.345484 0.938425i 0.387715π-0.387715\pi
0.345484 + 0.938425i 0.387715π0.387715\pi
4242 0 0
4343 334.357 1.18579 0.592894 0.805280i 0.297985π-0.297985\pi
0.592894 + 0.805280i 0.297985π0.297985\pi
4444 0 0
4545 −257.473 −0.852930
4646 0 0
4747 −255.999 −0.794497 −0.397248 0.917711i 0.630035π-0.630035\pi
−0.397248 + 0.917711i 0.630035π0.630035\pi
4848 0 0
4949 49.0000 0.142857
5050 0 0
5151 264.800 0.727047
5252 0 0
5353 −674.234 −1.74742 −0.873710 0.486448i 0.838292π-0.838292\pi
−0.873710 + 0.486448i 0.838292π0.838292\pi
5454 0 0
5555 −217.570 −0.533403
5656 0 0
5757 67.9566 0.157913
5858 0 0
5959 396.486 0.874883 0.437442 0.899247i 0.355885π-0.355885\pi
0.437442 + 0.899247i 0.355885π0.355885\pi
6060 0 0
6161 495.662 1.04038 0.520189 0.854051i 0.325862π-0.325862\pi
0.520189 + 0.854051i 0.325862π0.325862\pi
6262 0 0
6363 −91.1220 −0.182227
6464 0 0
6565 −383.808 −0.732392
6666 0 0
6767 −820.499 −1.49612 −0.748059 0.663632i 0.769014π-0.769014\pi
−0.748059 + 0.663632i 0.769014π0.769014\pi
6868 0 0
6969 561.660 0.979940
7070 0 0
7171 −259.971 −0.434547 −0.217274 0.976111i 0.569716π-0.569716\pi
−0.217274 + 0.976111i 0.569716π0.569716\pi
7272 0 0
7373 362.323 0.580914 0.290457 0.956888i 0.406193π-0.406193\pi
0.290457 + 0.956888i 0.406193π0.406193\pi
7474 0 0
7575 995.456 1.53261
7676 0 0
7777 −77.0000 −0.113961
7878 0 0
7979 −39.4291 −0.0561535 −0.0280767 0.999606i 0.508938π-0.508938\pi
−0.0280767 + 0.999606i 0.508938π0.508938\pi
8080 0 0
8181 −208.076 −0.285426
8282 0 0
8383 649.668 0.859160 0.429580 0.903029i 0.358662π-0.358662\pi
0.429580 + 0.903029i 0.358662π0.358662\pi
8484 0 0
8585 1400.65 1.78732
8686 0 0
8787 135.047 0.166420
8888 0 0
8989 −386.836 −0.460725 −0.230363 0.973105i 0.573991π-0.573991\pi
−0.230363 + 0.973105i 0.573991π0.573991\pi
9090 0 0
9191 −135.833 −0.156474
9292 0 0
9393 1166.94 1.30114
9494 0 0
9595 359.455 0.388203
9696 0 0
9797 336.297 0.352019 0.176009 0.984389i 0.443681π-0.443681\pi
0.176009 + 0.984389i 0.443681π0.443681\pi
9898 0 0
9999 143.192 0.145367
100100 0 0
101101 590.589 0.581840 0.290920 0.956747i 0.406039π-0.406039\pi
0.290920 + 0.956747i 0.406039π0.406039\pi
102102 0 0
103103 698.936 0.668623 0.334312 0.942463i 0.391496π-0.391496\pi
0.334312 + 0.942463i 0.391496π0.391496\pi
104104 0 0
105105 517.724 0.481187
106106 0 0
107107 489.378 0.442149 0.221075 0.975257i 0.429044π-0.429044\pi
0.221075 + 0.975257i 0.429044π0.429044\pi
108108 0 0
109109 −2146.51 −1.88623 −0.943113 0.332474i 0.892117π-0.892117\pi
−0.943113 + 0.332474i 0.892117π0.892117\pi
110110 0 0
111111 −1275.89 −1.09101
112112 0 0
113113 −1657.61 −1.37996 −0.689978 0.723830i 0.742380π-0.742380\pi
−0.689978 + 0.723830i 0.742380π0.742380\pi
114114 0 0
115115 2970.89 2.40901
116116 0 0
117117 252.600 0.199597
118118 0 0
119119 495.704 0.381858
120120 0 0
121121 121.000 0.0909091
122122 0 0
123123 678.308 0.497244
124124 0 0
125125 2793.06 1.99855
126126 0 0
127127 110.623 0.0772929 0.0386464 0.999253i 0.487695π-0.487695\pi
0.0386464 + 0.999253i 0.487695π0.487695\pi
128128 0 0
129129 1250.27 0.853333
130130 0 0
131131 −2789.56 −1.86050 −0.930249 0.366930i 0.880409π-0.880409\pi
−0.930249 + 0.366930i 0.880409π0.880409\pi
132132 0 0
133133 127.214 0.0829390
134134 0 0
135135 −2959.71 −1.88690
136136 0 0
137137 253.276 0.157948 0.0789739 0.996877i 0.474836π-0.474836\pi
0.0789739 + 0.996877i 0.474836π0.474836\pi
138138 0 0
139139 1417.34 0.864873 0.432437 0.901664i 0.357654π-0.357654\pi
0.432437 + 0.901664i 0.357654π0.357654\pi
140140 0 0
141141 −957.265 −0.571747
142142 0 0
143143 213.452 0.124823
144144 0 0
145145 714.326 0.409114
146146 0 0
147147 183.227 0.102805
148148 0 0
149149 −2943.98 −1.61866 −0.809329 0.587355i 0.800169π-0.800169\pi
−0.809329 + 0.587355i 0.800169π0.800169\pi
150150 0 0
151151 1090.43 0.587668 0.293834 0.955856i 0.405069π-0.405069\pi
0.293834 + 0.955856i 0.405069π0.405069\pi
152152 0 0
153153 −921.827 −0.487094
154154 0 0
155155 6172.48 3.19862
156156 0 0
157157 1219.91 0.620126 0.310063 0.950716i 0.399650π-0.399650\pi
0.310063 + 0.950716i 0.399650π0.399650\pi
158158 0 0
159159 −2521.18 −1.25750
160160 0 0
161161 1051.42 0.514682
162162 0 0
163163 −57.0393 −0.0274090 −0.0137045 0.999906i 0.504362π-0.504362\pi
−0.0137045 + 0.999906i 0.504362π0.504362\pi
164164 0 0
165165 −813.566 −0.383855
166166 0 0
167167 2091.75 0.969249 0.484625 0.874722i 0.338956π-0.338956\pi
0.484625 + 0.874722i 0.338956π0.338956\pi
168168 0 0
169169 −1820.46 −0.828610
170170 0 0
171171 −236.572 −0.105796
172172 0 0
173173 −333.342 −0.146495 −0.0732473 0.997314i 0.523336π-0.523336\pi
−0.0732473 + 0.997314i 0.523336π0.523336\pi
174174 0 0
175175 1863.49 0.804952
176176 0 0
177177 1482.59 0.629596
178178 0 0
179179 648.025 0.270590 0.135295 0.990805i 0.456802π-0.456802\pi
0.135295 + 0.990805i 0.456802π0.456802\pi
180180 0 0
181181 −3579.98 −1.47015 −0.735077 0.677984i 0.762854π-0.762854\pi
−0.735077 + 0.677984i 0.762854π0.762854\pi
182182 0 0
183183 1853.44 0.748691
184184 0 0
185185 −6748.79 −2.68206
186186 0 0
187187 −778.963 −0.304617
188188 0 0
189189 −1047.47 −0.403133
190190 0 0
191191 −1058.90 −0.401148 −0.200574 0.979679i 0.564281π-0.564281\pi
−0.200574 + 0.979679i 0.564281π0.564281\pi
192192 0 0
193193 −1106.19 −0.412566 −0.206283 0.978492i 0.566137π-0.566137\pi
−0.206283 + 0.978492i 0.566137π0.566137\pi
194194 0 0
195195 −1435.18 −0.527054
196196 0 0
197197 −2183.49 −0.789681 −0.394841 0.918750i 0.629200π-0.629200\pi
−0.394841 + 0.918750i 0.629200π0.629200\pi
198198 0 0
199199 −275.244 −0.0980479 −0.0490239 0.998798i 0.515611π-0.515611\pi
−0.0490239 + 0.998798i 0.515611π0.515611\pi
200200 0 0
201201 −3068.11 −1.07666
202202 0 0
203203 252.807 0.0874066
204204 0 0
205205 3587.90 1.22239
206206 0 0
207207 −1955.26 −0.656523
208208 0 0
209209 −199.908 −0.0661624
210210 0 0
211211 −184.206 −0.0601006 −0.0300503 0.999548i 0.509567π-0.509567\pi
−0.0300503 + 0.999548i 0.509567π0.509567\pi
212212 0 0
213213 −972.116 −0.312715
214214 0 0
215215 6613.27 2.09777
216216 0 0
217217 2184.50 0.683380
218218 0 0
219219 1354.85 0.418046
220220 0 0
221221 −1374.14 −0.418257
222222 0 0
223223 −762.855 −0.229079 −0.114539 0.993419i 0.536539π-0.536539\pi
−0.114539 + 0.993419i 0.536539π0.536539\pi
224224 0 0
225225 −3465.41 −1.02679
226226 0 0
227227 5280.62 1.54399 0.771997 0.635626i 0.219258π-0.219258\pi
0.771997 + 0.635626i 0.219258π0.219258\pi
228228 0 0
229229 5266.64 1.51978 0.759890 0.650052i 0.225253π-0.225253\pi
0.759890 + 0.650052i 0.225253π0.225253\pi
230230 0 0
231231 −287.928 −0.0820099
232232 0 0
233233 −6792.89 −1.90994 −0.954972 0.296695i 0.904116π-0.904116\pi
−0.954972 + 0.296695i 0.904116π0.904116\pi
234234 0 0
235235 −5063.44 −1.40554
236236 0 0
237237 −147.438 −0.0404099
238238 0 0
239239 6317.30 1.70976 0.854879 0.518828i 0.173631π-0.173631\pi
0.854879 + 0.518828i 0.173631π0.173631\pi
240240 0 0
241241 1271.42 0.339831 0.169915 0.985459i 0.445651π-0.445651\pi
0.169915 + 0.985459i 0.445651π0.445651\pi
242242 0 0
243243 3262.17 0.861187
244244 0 0
245245 969.176 0.252728
246246 0 0
247247 −352.651 −0.0908448
248248 0 0
249249 2429.32 0.618281
250250 0 0
251251 −760.172 −0.191162 −0.0955810 0.995422i 0.530471π-0.530471\pi
−0.0955810 + 0.995422i 0.530471π0.530471\pi
252252 0 0
253253 −1652.24 −0.410574
254254 0 0
255255 5237.50 1.28622
256256 0 0
257257 −1133.67 −0.275160 −0.137580 0.990491i 0.543932π-0.543932\pi
−0.137580 + 0.990491i 0.543932π0.543932\pi
258258 0 0
259259 −2388.46 −0.573018
260260 0 0
261261 −470.127 −0.111495
262262 0 0
263263 −7535.49 −1.76676 −0.883381 0.468656i 0.844739π-0.844739\pi
−0.883381 + 0.468656i 0.844739π0.844739\pi
264264 0 0
265265 −13335.7 −3.09135
266266 0 0
267267 −1446.51 −0.331554
268268 0 0
269269 −6111.16 −1.38514 −0.692572 0.721349i 0.743523π-0.743523\pi
−0.692572 + 0.721349i 0.743523π0.743523\pi
270270 0 0
271271 3162.44 0.708872 0.354436 0.935080i 0.384673π-0.384673\pi
0.354436 + 0.935080i 0.384673π0.384673\pi
272272 0 0
273273 −507.924 −0.112604
274274 0 0
275275 −2928.34 −0.642129
276276 0 0
277277 2078.80 0.450914 0.225457 0.974253i 0.427612π-0.427612\pi
0.225457 + 0.974253i 0.427612π0.427612\pi
278278 0 0
279279 −4062.36 −0.871711
280280 0 0
281281 −8558.16 −1.81686 −0.908429 0.418040i 0.862717π-0.862717\pi
−0.908429 + 0.418040i 0.862717π0.862717\pi
282282 0 0
283283 383.249 0.0805011 0.0402505 0.999190i 0.487184π-0.487184\pi
0.0402505 + 0.999190i 0.487184π0.487184\pi
284284 0 0
285285 1344.12 0.279364
286286 0 0
287287 1269.79 0.261161
288288 0 0
289289 101.739 0.0207082
290290 0 0
291291 1257.52 0.253324
292292 0 0
293293 −3728.36 −0.743389 −0.371695 0.928355i 0.621223π-0.621223\pi
−0.371695 + 0.928355i 0.621223π0.621223\pi
294294 0 0
295295 7842.14 1.54775
296296 0 0
297297 1646.02 0.321589
298298 0 0
299299 −2914.65 −0.563742
300300 0 0
301301 2340.50 0.448186
302302 0 0
303303 2208.41 0.418712
304304 0 0
305305 9803.75 1.84053
306306 0 0
307307 −7148.19 −1.32889 −0.664444 0.747338i 0.731332π-0.731332\pi
−0.664444 + 0.747338i 0.731332π0.731332\pi
308308 0 0
309309 2613.55 0.481164
310310 0 0
311311 −5641.46 −1.02861 −0.514305 0.857607i 0.671950π-0.671950\pi
−0.514305 + 0.857607i 0.671950π0.671950\pi
312312 0 0
313313 9533.22 1.72156 0.860781 0.508975i 0.169975π-0.169975\pi
0.860781 + 0.508975i 0.169975π0.169975\pi
314314 0 0
315315 −1802.31 −0.322377
316316 0 0
317317 −3133.29 −0.555153 −0.277576 0.960704i 0.589531π-0.589531\pi
−0.277576 + 0.960704i 0.589531π0.589531\pi
318318 0 0
319319 −397.267 −0.0697263
320320 0 0
321321 1829.95 0.318186
322322 0 0
323323 1286.95 0.221696
324324 0 0
325325 −5165.78 −0.881680
326326 0 0
327327 −8026.51 −1.35739
328328 0 0
329329 −1792.00 −0.300292
330330 0 0
331331 −11538.6 −1.91608 −0.958038 0.286640i 0.907462π-0.907462\pi
−0.958038 + 0.286640i 0.907462π0.907462\pi
332332 0 0
333333 4441.66 0.730935
334334 0 0
335335 −16228.7 −2.64678
336336 0 0
337337 −2167.24 −0.350318 −0.175159 0.984540i 0.556044π-0.556044\pi
−0.175159 + 0.984540i 0.556044π0.556044\pi
338338 0 0
339339 −6198.35 −0.993063
340340 0 0
341341 −3432.78 −0.545148
342342 0 0
343343 343.000 0.0539949
344344 0 0
345345 11109.1 1.73361
346346 0 0
347347 −620.740 −0.0960318 −0.0480159 0.998847i 0.515290π-0.515290\pi
−0.0480159 + 0.998847i 0.515290π0.515290\pi
348348 0 0
349349 −156.193 −0.0239564 −0.0119782 0.999928i 0.503813π-0.503813\pi
−0.0119782 + 0.999928i 0.503813π0.503813\pi
350350 0 0
351351 2903.69 0.441560
352352 0 0
353353 2174.30 0.327836 0.163918 0.986474i 0.447587π-0.447587\pi
0.163918 + 0.986474i 0.447587π0.447587\pi
354354 0 0
355355 −5141.99 −0.768756
356356 0 0
357357 1853.60 0.274798
358358 0 0
359359 5993.02 0.881058 0.440529 0.897738i 0.354791π-0.354791\pi
0.440529 + 0.897738i 0.354791π0.354791\pi
360360 0 0
361361 −6528.72 −0.951848
362362 0 0
363363 452.459 0.0654213
364364 0 0
365365 7166.43 1.02769
366366 0 0
367367 −10822.6 −1.53934 −0.769669 0.638443i 0.779579π-0.779579\pi
−0.769669 + 0.638443i 0.779579π0.779579\pi
368368 0 0
369369 −2361.34 −0.333134
370370 0 0
371371 −4719.64 −0.660462
372372 0 0
373373 11115.4 1.54298 0.771491 0.636240i 0.219511π-0.219511\pi
0.771491 + 0.636240i 0.219511π0.219511\pi
374374 0 0
375375 10444.2 1.43823
376376 0 0
377377 −700.805 −0.0957382
378378 0 0
379379 −11919.0 −1.61540 −0.807702 0.589591i 0.799289π-0.799289\pi
−0.807702 + 0.589591i 0.799289π0.799289\pi
380380 0 0
381381 413.655 0.0556226
382382 0 0
383383 3655.90 0.487749 0.243875 0.969807i 0.421581π-0.421581\pi
0.243875 + 0.969807i 0.421581π0.421581\pi
384384 0 0
385385 −1522.99 −0.201607
386386 0 0
387387 −4352.47 −0.571701
388388 0 0
389389 4389.79 0.572162 0.286081 0.958205i 0.407647π-0.407647\pi
0.286081 + 0.958205i 0.407647π0.407647\pi
390390 0 0
391391 10636.6 1.37575
392392 0 0
393393 −10431.1 −1.33888
394394 0 0
395395 −779.873 −0.0993409
396396 0 0
397397 −7234.62 −0.914598 −0.457299 0.889313i 0.651183π-0.651183\pi
−0.457299 + 0.889313i 0.651183π0.651183\pi
398398 0 0
399399 475.696 0.0596857
400400 0 0
401401 14345.9 1.78653 0.893266 0.449528i 0.148408π-0.148408\pi
0.893266 + 0.449528i 0.148408π0.148408\pi
402402 0 0
403403 −6055.65 −0.748520
404404 0 0
405405 −4115.55 −0.504946
406406 0 0
407407 3753.29 0.457110
408408 0 0
409409 −15651.9 −1.89227 −0.946135 0.323773i 0.895048π-0.895048\pi
−0.946135 + 0.323773i 0.895048π0.895048\pi
410410 0 0
411411 947.082 0.113665
412412 0 0
413413 2775.40 0.330675
414414 0 0
415415 12849.8 1.51994
416416 0 0
417417 5299.91 0.622392
418418 0 0
419419 −7162.22 −0.835077 −0.417538 0.908659i 0.637107π-0.637107\pi
−0.417538 + 0.908659i 0.637107π0.637107\pi
420420 0 0
421421 −5125.05 −0.593301 −0.296651 0.954986i 0.595870π-0.595870\pi
−0.296651 + 0.954986i 0.595870π0.595870\pi
422422 0 0
423423 3332.45 0.383048
424424 0 0
425425 18851.8 2.15164
426426 0 0
427427 3469.64 0.393226
428428 0 0
429429 798.166 0.0898271
430430 0 0
431431 15125.2 1.69038 0.845192 0.534463i 0.179486π-0.179486\pi
0.845192 + 0.534463i 0.179486π0.179486\pi
432432 0 0
433433 −9009.60 −0.999940 −0.499970 0.866043i 0.666656π-0.666656\pi
−0.499970 + 0.866043i 0.666656π0.666656\pi
434434 0 0
435435 2671.10 0.294413
436436 0 0
437437 2729.72 0.298810
438438 0 0
439439 8544.58 0.928954 0.464477 0.885585i 0.346242π-0.346242\pi
0.464477 + 0.885585i 0.346242π0.346242\pi
440440 0 0
441441 −637.854 −0.0688753
442442 0 0
443443 6815.43 0.730950 0.365475 0.930821i 0.380907π-0.380907\pi
0.365475 + 0.930821i 0.380907π0.380907\pi
444444 0 0
445445 −7651.27 −0.815068
446446 0 0
447447 −11008.5 −1.16484
448448 0 0
449449 10587.3 1.11279 0.556397 0.830917i 0.312184π-0.312184\pi
0.556397 + 0.830917i 0.312184π0.312184\pi
450450 0 0
451451 −1995.38 −0.208335
452452 0 0
453453 4077.47 0.422906
454454 0 0
455455 −2686.65 −0.276818
456456 0 0
457457 −7189.63 −0.735923 −0.367962 0.929841i 0.619944π-0.619944\pi
−0.367962 + 0.929841i 0.619944π0.619944\pi
458458 0 0
459459 −10596.6 −1.07758
460460 0 0
461461 12715.2 1.28461 0.642304 0.766450i 0.277979π-0.277979\pi
0.642304 + 0.766450i 0.277979π0.277979\pi
462462 0 0
463463 −2900.83 −0.291173 −0.145586 0.989346i 0.546507π-0.546507\pi
−0.145586 + 0.989346i 0.546507π0.546507\pi
464464 0 0
465465 23080.9 2.30183
466466 0 0
467467 5640.30 0.558891 0.279445 0.960162i 0.409849π-0.409849\pi
0.279445 + 0.960162i 0.409849π0.409849\pi
468468 0 0
469469 −5743.49 −0.565480
470470 0 0
471471 4561.66 0.446263
472472 0 0
473473 −3677.92 −0.357529
474474 0 0
475475 4838.01 0.467333
476476 0 0
477477 8776.80 0.842478
478478 0 0
479479 7611.96 0.726095 0.363047 0.931771i 0.381736π-0.381736\pi
0.363047 + 0.931771i 0.381736π0.381736\pi
480480 0 0
481481 6621.05 0.627638
482482 0 0
483483 3931.62 0.370383
484484 0 0
485485 6651.65 0.622755
486486 0 0
487487 −1984.97 −0.184698 −0.0923488 0.995727i 0.529437π-0.529437\pi
−0.0923488 + 0.995727i 0.529437π0.529437\pi
488488 0 0
489489 −213.288 −0.0197244
490490 0 0
491491 7934.81 0.729313 0.364657 0.931142i 0.381186π-0.381186\pi
0.364657 + 0.931142i 0.381186π0.381186\pi
492492 0 0
493493 2557.49 0.233638
494494 0 0
495495 2832.20 0.257168
496496 0 0
497497 −1819.80 −0.164243
498498 0 0
499499 −13405.5 −1.20263 −0.601313 0.799013i 0.705356π-0.705356\pi
−0.601313 + 0.799013i 0.705356π0.705356\pi
500500 0 0
501501 7821.74 0.697505
502502 0 0
503503 9355.38 0.829296 0.414648 0.909982i 0.363905π-0.363905\pi
0.414648 + 0.909982i 0.363905π0.363905\pi
504504 0 0
505505 11681.3 1.02933
506506 0 0
507507 −6807.28 −0.596296
508508 0 0
509509 22230.5 1.93585 0.967927 0.251233i 0.0808361π-0.0808361\pi
0.967927 + 0.251233i 0.0808361π0.0808361\pi
510510 0 0
511511 2536.26 0.219565
512512 0 0
513513 −2719.45 −0.234048
514514 0 0
515515 13824.3 1.18286
516516 0 0
517517 2815.99 0.239550
518518 0 0
519519 −1246.48 −0.105422
520520 0 0
521521 −15130.6 −1.27233 −0.636165 0.771553i 0.719480π-0.719480\pi
−0.636165 + 0.771553i 0.719480π0.719480\pi
522522 0 0
523523 20491.1 1.71322 0.856610 0.515964i 0.172566π-0.172566\pi
0.856610 + 0.515964i 0.172566π0.172566\pi
524524 0 0
525525 6968.20 0.579270
526526 0 0
527527 22099.3 1.82668
528528 0 0
529529 10394.1 0.854283
530530 0 0
531531 −5161.23 −0.421805
532532 0 0
533533 −3519.99 −0.286055
534534 0 0
535535 9679.46 0.782205
536536 0 0
537537 2423.18 0.194726
538538 0 0
539539 −539.000 −0.0430730
540540 0 0
541541 16251.4 1.29150 0.645752 0.763547i 0.276544π-0.276544\pi
0.645752 + 0.763547i 0.276544π0.276544\pi
542542 0 0
543543 −13386.7 −1.05797
544544 0 0
545545 −42456.1 −3.33691
546546 0 0
547547 −17652.3 −1.37981 −0.689906 0.723899i 0.742348π-0.742348\pi
−0.689906 + 0.723899i 0.742348π0.742348\pi
548548 0 0
549549 −6452.25 −0.501594
550550 0 0
551551 656.339 0.0507459
552552 0 0
553553 −276.004 −0.0212240
554554 0 0
555555 −25235.9 −1.93010
556556 0 0
557557 −14086.4 −1.07156 −0.535782 0.844356i 0.679983π-0.679983\pi
−0.535782 + 0.844356i 0.679983π0.679983\pi
558558 0 0
559559 −6488.09 −0.490907
560560 0 0
561561 −2912.80 −0.219213
562562 0 0
563563 −9787.92 −0.732702 −0.366351 0.930477i 0.619393π-0.619393\pi
−0.366351 + 0.930477i 0.619393π0.619393\pi
564564 0 0
565565 −32786.1 −2.44127
566566 0 0
567567 −1456.53 −0.107881
568568 0 0
569569 24992.9 1.84140 0.920700 0.390270i 0.127618π-0.127618\pi
0.920700 + 0.390270i 0.127618π0.127618\pi
570570 0 0
571571 −14480.8 −1.06130 −0.530649 0.847592i 0.678052π-0.678052\pi
−0.530649 + 0.847592i 0.678052π0.678052\pi
572572 0 0
573573 −3959.57 −0.288679
574574 0 0
575575 39986.1 2.90006
576576 0 0
577577 2348.23 0.169425 0.0847125 0.996405i 0.473003π-0.473003\pi
0.0847125 + 0.996405i 0.473003π0.473003\pi
578578 0 0
579579 −4136.40 −0.296896
580580 0 0
581581 4547.67 0.324732
582582 0 0
583583 7416.58 0.526867
584584 0 0
585585 4996.19 0.353106
586586 0 0
587587 −9755.88 −0.685977 −0.342988 0.939340i 0.611439π-0.611439\pi
−0.342988 + 0.939340i 0.611439π0.611439\pi
588588 0 0
589589 5671.42 0.396752
590590 0 0
591591 −8164.78 −0.568281
592592 0 0
593593 12901.1 0.893396 0.446698 0.894685i 0.352600π-0.352600\pi
0.446698 + 0.894685i 0.352600π0.352600\pi
594594 0 0
595595 9804.57 0.675543
596596 0 0
597597 −1029.23 −0.0705586
598598 0 0
599599 −13063.4 −0.891082 −0.445541 0.895262i 0.646989π-0.646989\pi
−0.445541 + 0.895262i 0.646989π0.646989\pi
600600 0 0
601601 −18806.4 −1.27642 −0.638212 0.769861i 0.720326π-0.720326\pi
−0.638212 + 0.769861i 0.720326π0.720326\pi
602602 0 0
603603 10680.8 0.721319
604604 0 0
605605 2393.27 0.160827
606606 0 0
607607 −10192.9 −0.681573 −0.340787 0.940141i 0.610693π-0.610693\pi
−0.340787 + 0.940141i 0.610693π0.610693\pi
608608 0 0
609609 945.326 0.0629007
610610 0 0
611611 4967.59 0.328915
612612 0 0
613613 −8546.34 −0.563105 −0.281553 0.959546i 0.590849π-0.590849\pi
−0.281553 + 0.959546i 0.590849π0.590849\pi
614614 0 0
615615 13416.3 0.879672
616616 0 0
617617 −83.9771 −0.00547940 −0.00273970 0.999996i 0.500872π-0.500872\pi
−0.00273970 + 0.999996i 0.500872π0.500872\pi
618618 0 0
619619 1254.82 0.0814786 0.0407393 0.999170i 0.487029π-0.487029\pi
0.0407393 + 0.999170i 0.487029π0.487029\pi
620620 0 0
621621 −22476.2 −1.45240
622622 0 0
623623 −2707.85 −0.174138
624624 0 0
625625 21967.6 1.40593
626626 0 0
627627 −747.522 −0.0476127
628628 0 0
629629 −24162.6 −1.53168
630630 0 0
631631 −10941.6 −0.690300 −0.345150 0.938547i 0.612172π-0.612172\pi
−0.345150 + 0.938547i 0.612172π0.612172\pi
632632 0 0
633633 −688.805 −0.0432504
634634 0 0
635635 2188.02 0.136739
636636 0 0
637637 −950.831 −0.0591418
638638 0 0
639639 3384.15 0.209507
640640 0 0
641641 10785.4 0.664585 0.332293 0.943176i 0.392178π-0.392178\pi
0.332293 + 0.943176i 0.392178π0.392178\pi
642642 0 0
643643 9787.54 0.600285 0.300142 0.953894i 0.402966π-0.402966\pi
0.300142 + 0.953894i 0.402966π0.402966\pi
644644 0 0
645645 24729.2 1.50963
646646 0 0
647647 11154.8 0.677808 0.338904 0.940821i 0.389944π-0.389944\pi
0.338904 + 0.940821i 0.389944π0.389944\pi
648648 0 0
649649 −4361.35 −0.263787
650650 0 0
651651 8168.55 0.491783
652652 0 0
653653 11300.3 0.677202 0.338601 0.940930i 0.390046π-0.390046\pi
0.338601 + 0.940930i 0.390046π0.390046\pi
654654 0 0
655655 −55175.0 −3.29140
656656 0 0
657657 −4716.52 −0.280075
658658 0 0
659659 −9671.17 −0.571677 −0.285839 0.958278i 0.592272π-0.592272\pi
−0.285839 + 0.958278i 0.592272π0.592272\pi
660660 0 0
661661 1455.20 0.0856290 0.0428145 0.999083i 0.486368π-0.486368\pi
0.0428145 + 0.999083i 0.486368π0.486368\pi
662662 0 0
663663 −5138.36 −0.300992
664664 0 0
665665 2516.19 0.146727
666666 0 0
667667 5424.63 0.314906
668668 0 0
669669 −2852.56 −0.164853
670670 0 0
671671 −5452.28 −0.313686
672672 0 0
673673 13180.6 0.754943 0.377472 0.926021i 0.376794π-0.376794\pi
0.377472 + 0.926021i 0.376794π0.376794\pi
674674 0 0
675675 −39835.6 −2.27152
676676 0 0
677677 −22201.2 −1.26036 −0.630180 0.776449i 0.717019π-0.717019\pi
−0.630180 + 0.776449i 0.717019π0.717019\pi
678678 0 0
679679 2354.08 0.133051
680680 0 0
681681 19745.9 1.11111
682682 0 0
683683 −17792.8 −0.996813 −0.498406 0.866944i 0.666081π-0.666081\pi
−0.498406 + 0.866944i 0.666081π0.666081\pi
684684 0 0
685685 5009.57 0.279425
686686 0 0
687687 19693.7 1.09368
688688 0 0
689689 13083.3 0.723418
690690 0 0
691691 −4729.48 −0.260373 −0.130187 0.991490i 0.541558π-0.541558\pi
−0.130187 + 0.991490i 0.541558π0.541558\pi
692692 0 0
693693 1002.34 0.0549435
694694 0 0
695695 28033.8 1.53004
696696 0 0
697697 12845.7 0.698086
698698 0 0
699699 −25400.8 −1.37446
700700 0 0
701701 21835.4 1.17648 0.588241 0.808686i 0.299821π-0.299821\pi
0.588241 + 0.808686i 0.299821π0.299821\pi
702702 0 0
703703 −6200.94 −0.332678
704704 0 0
705705 −18933.8 −1.01147
706706 0 0
707707 4134.13 0.219915
708708 0 0
709709 −26123.5 −1.38376 −0.691881 0.722011i 0.743218π-0.743218\pi
−0.691881 + 0.722011i 0.743218π0.743218\pi
710710 0 0
711711 513.266 0.0270731
712712 0 0
713713 46874.1 2.46206
714714 0 0
715715 4221.89 0.220825
716716 0 0
717717 23622.4 1.23040
718718 0 0
719719 −6644.44 −0.344640 −0.172320 0.985041i 0.555126π-0.555126\pi
−0.172320 + 0.985041i 0.555126π0.555126\pi
720720 0 0
721721 4892.55 0.252716
722722 0 0
723723 4754.25 0.244554
724724 0 0
725725 9614.33 0.492507
726726 0 0
727727 36976.7 1.88637 0.943185 0.332268i 0.107814π-0.107814\pi
0.943185 + 0.332268i 0.107814π0.107814\pi
728728 0 0
729729 17816.4 0.905165
730730 0 0
731731 23677.4 1.19800
732732 0 0
733733 2768.13 0.139486 0.0697430 0.997565i 0.477782π-0.477782\pi
0.0697430 + 0.997565i 0.477782π0.477782\pi
734734 0 0
735735 3624.07 0.181872
736736 0 0
737737 9025.49 0.451097
738738 0 0
739739 −16615.1 −0.827059 −0.413529 0.910491i 0.635704π-0.635704\pi
−0.413529 + 0.910491i 0.635704π0.635704\pi
740740 0 0
741741 −1318.68 −0.0653750
742742 0 0
743743 −9526.59 −0.470386 −0.235193 0.971949i 0.575572π-0.575572\pi
−0.235193 + 0.971949i 0.575572π0.575572\pi
744744 0 0
745745 −58229.2 −2.86356
746746 0 0
747747 −8457.01 −0.414225
748748 0 0
749749 3425.65 0.167117
750750 0 0
751751 −108.237 −0.00525914 −0.00262957 0.999997i 0.500837π-0.500837\pi
−0.00262957 + 0.999997i 0.500837π0.500837\pi
752752 0 0
753753 −2842.53 −0.137567
754754 0 0
755755 21567.7 1.03964
756756 0 0
757757 6511.07 0.312614 0.156307 0.987709i 0.450041π-0.450041\pi
0.156307 + 0.987709i 0.450041π0.450041\pi
758758 0 0
759759 −6178.26 −0.295463
760760 0 0
761761 7693.24 0.366465 0.183232 0.983070i 0.441344π-0.441344\pi
0.183232 + 0.983070i 0.441344π0.441344\pi
762762 0 0
763763 −15025.6 −0.712926
764764 0 0
765765 −18232.9 −0.861716
766766 0 0
767767 −7693.70 −0.362195
768768 0 0
769769 15859.2 0.743690 0.371845 0.928295i 0.378725π-0.378725\pi
0.371845 + 0.928295i 0.378725π0.378725\pi
770770 0 0
771771 −4239.14 −0.198014
772772 0 0
773773 15798.8 0.735115 0.367558 0.930001i 0.380194π-0.380194\pi
0.367558 + 0.930001i 0.380194π0.380194\pi
774774 0 0
775775 83077.3 3.85061
776776 0 0
777777 −8931.22 −0.412363
778778 0 0
779779 3296.64 0.151623
780780 0 0
781781 2859.68 0.131021
782782 0 0
783783 −5404.22 −0.246655
784784 0 0
785785 24128.8 1.09706
786786 0 0
787787 −14535.5 −0.658365 −0.329182 0.944266i 0.606773π-0.606773\pi
−0.329182 + 0.944266i 0.606773π0.606773\pi
788788 0 0
789789 −28177.7 −1.27142
790790 0 0
791791 −11603.3 −0.521574
792792 0 0
793793 −9618.18 −0.430708
794794 0 0
795795 −49866.7 −2.22464
796796 0 0
797797 −5259.27 −0.233743 −0.116871 0.993147i 0.537287π-0.537287\pi
−0.116871 + 0.993147i 0.537287π0.537287\pi
798798 0 0
799799 −18128.5 −0.802681
800800 0 0
801801 5035.62 0.222128
802802 0 0
803803 −3985.56 −0.175152
804804 0 0
805805 20796.2 0.910522
806806 0 0
807807 −22851.6 −0.996796
808808 0 0
809809 24785.4 1.07714 0.538570 0.842581i 0.318965π-0.318965\pi
0.538570 + 0.842581i 0.318965π0.318965\pi
810810 0 0
811811 −33695.3 −1.45894 −0.729471 0.684012i 0.760234π-0.760234\pi
−0.729471 + 0.684012i 0.760234π0.760234\pi
812812 0 0
813813 11825.4 0.510128
814814 0 0
815815 −1128.19 −0.0484891
816816 0 0
817817 6076.42 0.260205
818818 0 0
819819 1768.20 0.0754406
820820 0 0
821821 25640.1 1.08994 0.544972 0.838454i 0.316540π-0.316540\pi
0.544972 + 0.838454i 0.316540π0.316540\pi
822822 0 0
823823 8504.28 0.360195 0.180097 0.983649i 0.442359π-0.442359\pi
0.180097 + 0.983649i 0.442359π0.442359\pi
824824 0 0
825825 −10950.0 −0.462098
826826 0 0
827827 18345.0 0.771365 0.385682 0.922632i 0.373966π-0.373966\pi
0.385682 + 0.922632i 0.373966π0.373966\pi
828828 0 0
829829 2469.13 0.103446 0.0517228 0.998661i 0.483529π-0.483529\pi
0.0517228 + 0.998661i 0.483529π0.483529\pi
830830 0 0
831831 7773.33 0.324493
832832 0 0
833833 3469.93 0.144329
834834 0 0
835835 41373.0 1.71470
836836 0 0
837837 −46697.8 −1.92845
838838 0 0
839839 −16861.3 −0.693824 −0.346912 0.937898i 0.612770π-0.612770\pi
−0.346912 + 0.937898i 0.612770π0.612770\pi
840840 0 0
841841 −23084.7 −0.946521
842842 0 0
843843 −32001.7 −1.30747
844844 0 0
845845 −36007.0 −1.46589
846846 0 0
847847 847.000 0.0343604
848848 0 0
849849 1433.09 0.0579313
850850 0 0
851851 −51250.6 −2.06445
852852 0 0
853853 7865.78 0.315732 0.157866 0.987461i 0.449539π-0.449539\pi
0.157866 + 0.987461i 0.449539π0.449539\pi
854854 0 0
855855 −4679.18 −0.187163
856856 0 0
857857 6288.35 0.250649 0.125324 0.992116i 0.460003π-0.460003\pi
0.125324 + 0.992116i 0.460003π0.460003\pi
858858 0 0
859859 34023.0 1.35140 0.675698 0.737179i 0.263842π-0.263842\pi
0.675698 + 0.737179i 0.263842π0.263842\pi
860860 0 0
861861 4748.16 0.187941
862862 0 0
863863 −19584.8 −0.772509 −0.386255 0.922392i 0.626231π-0.626231\pi
−0.386255 + 0.922392i 0.626231π0.626231\pi
864864 0 0
865865 −6593.21 −0.259163
866866 0 0
867867 380.437 0.0149023
868868 0 0
869869 433.721 0.0169309
870870 0 0
871871 15921.6 0.619381
872872 0 0
873873 −4377.73 −0.169718
874874 0 0
875875 19551.4 0.755382
876876 0 0
877877 −20098.0 −0.773844 −0.386922 0.922113i 0.626462π-0.626462\pi
−0.386922 + 0.922113i 0.626462π0.626462\pi
878878 0 0
879879 −13941.5 −0.534968
880880 0 0
881881 −10876.4 −0.415930 −0.207965 0.978136i 0.566684π-0.566684\pi
−0.207965 + 0.978136i 0.566684π0.566684\pi
882882 0 0
883883 19724.9 0.751751 0.375875 0.926670i 0.377342π-0.377342\pi
0.375875 + 0.926670i 0.377342π0.377342\pi
884884 0 0
885885 29324.3 1.11382
886886 0 0
887887 −39575.2 −1.49809 −0.749045 0.662519i 0.769488π-0.769488\pi
−0.749045 + 0.662519i 0.769488π0.769488\pi
888888 0 0
889889 774.360 0.0292140
890890 0 0
891891 2288.83 0.0860592
892892 0 0
893893 −4652.40 −0.174341
894894 0 0
895895 12817.4 0.478701
896896 0 0
897897 −10898.8 −0.405688
898898 0 0
899899 11270.5 0.418123
900900 0 0
901901 −47745.8 −1.76542
902902 0 0
903903 8751.88 0.322530
904904 0 0
905905 −70808.8 −2.60084
906906 0 0
907907 14301.8 0.523578 0.261789 0.965125i 0.415688π-0.415688\pi
0.261789 + 0.965125i 0.415688π0.415688\pi
908908 0 0
909909 −7687.96 −0.280521
910910 0 0
911911 −16663.3 −0.606016 −0.303008 0.952988i 0.597991π-0.597991\pi
−0.303008 + 0.952988i 0.597991π0.597991\pi
912912 0 0
913913 −7146.35 −0.259047
914914 0 0
915915 36659.4 1.32451
916916 0 0
917917 −19526.9 −0.703202
918918 0 0
919919 −32690.6 −1.17341 −0.586705 0.809800i 0.699575π-0.699575\pi
−0.586705 + 0.809800i 0.699575π0.699575\pi
920920 0 0
921921 −26729.4 −0.956313
922922 0 0
923923 5044.66 0.179899
924924 0 0
925925 −90834.0 −3.22876
926926 0 0
927927 −9098.36 −0.322362
928928 0 0
929929 −22269.0 −0.786463 −0.393231 0.919440i 0.628643π-0.628643\pi
−0.393231 + 0.919440i 0.628643π0.628643\pi
930930 0 0
931931 890.500 0.0313480
932932 0 0
933933 −21095.3 −0.740222
934934 0 0
935935 −15407.2 −0.538897
936936 0 0
937937 −56186.9 −1.95896 −0.979480 0.201543i 0.935404π-0.935404\pi
−0.979480 + 0.201543i 0.935404π0.935404\pi
938938 0 0
939939 35647.8 1.23889
940940 0 0
941941 27795.0 0.962901 0.481451 0.876473i 0.340110π-0.340110\pi
0.481451 + 0.876473i 0.340110π0.340110\pi
942942 0 0
943943 27246.7 0.940905
944944 0 0
945945 −20718.0 −0.713181
946946 0 0
947947 −39834.1 −1.36688 −0.683440 0.730007i 0.739517π-0.739517\pi
−0.683440 + 0.730007i 0.739517π0.739517\pi
948948 0 0
949949 −7030.78 −0.240494
950950 0 0
951951 −11716.4 −0.399506
952952 0 0
953953 6560.61 0.223000 0.111500 0.993764i 0.464434π-0.464434\pi
0.111500 + 0.993764i 0.464434π0.464434\pi
954954 0 0
955955 −20944.1 −0.709669
956956 0 0
957957 −1485.51 −0.0501774
958958 0 0
959959 1772.93 0.0596986
960960 0 0
961961 67597.4 2.26905
962962 0 0
963963 −6370.45 −0.213172
964964 0 0
965965 −21879.4 −0.729868
966966 0 0
967967 4283.37 0.142444 0.0712222 0.997460i 0.477310π-0.477310\pi
0.0712222 + 0.997460i 0.477310π0.477310\pi
968968 0 0
969969 4812.33 0.159540
970970 0 0
971971 50140.4 1.65714 0.828569 0.559887i 0.189155π-0.189155\pi
0.828569 + 0.559887i 0.189155π0.189155\pi
972972 0 0
973973 9921.40 0.326891
974974 0 0
975975 −19316.5 −0.634487
976976 0 0
977977 16287.5 0.533352 0.266676 0.963786i 0.414075π-0.414075\pi
0.266676 + 0.963786i 0.414075π0.414075\pi
978978 0 0
979979 4255.20 0.138914
980980 0 0
981981 27942.1 0.909400
982982 0 0
983983 −50147.5 −1.62712 −0.813560 0.581482i 0.802473π-0.802473\pi
−0.813560 + 0.581482i 0.802473π0.802473\pi
984984 0 0
985985 −43187.5 −1.39702
986986 0 0
987987 −6700.86 −0.216100
988988 0 0
989989 50221.5 1.61471
990990 0 0
991991 14908.0 0.477870 0.238935 0.971036i 0.423202π-0.423202\pi
0.238935 + 0.971036i 0.423202π0.423202\pi
992992 0 0
993993 −43146.8 −1.37887
994994 0 0
995995 −5444.08 −0.173456
996996 0 0
997997 20565.1 0.653263 0.326631 0.945152i 0.394086π-0.394086\pi
0.326631 + 0.945152i 0.394086π0.394086\pi
998998 0 0
999999 51057.8 1.61701
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 616.4.a.i.1.5 6
4.3 odd 2 1232.4.a.bb.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
616.4.a.i.1.5 6 1.1 even 1 trivial
1232.4.a.bb.1.2 6 4.3 odd 2