Properties

Label 2320.4.a.o.1.6
Level 23202320
Weight 44
Character 2320.1
Self dual yes
Analytic conductor 136.884136.884
Analytic rank 11
Dimension 66
CM no
Inner twists 11

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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] = [2320,4,Mod(1,2320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2320, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2320.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 2320=24529 2320 = 2^{4} \cdot 5 \cdot 29
Weight: k k == 4 4
Character orbit: [χ][\chi] == 2320.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,5,0,-30,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 136.884431213136.884431213
Analytic rank: 11
Dimension: 66
Coefficient field: Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x6x591x4+90x3+1784x21456x3720 x^{6} - x^{5} - 91x^{4} + 90x^{3} + 1784x^{2} - 1456x - 3720 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 25 2^{5}
Twist minimal: no (minimal twist has level 580)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.6
Root 4.88726-4.88726 of defining polynomial
Character χ\chi == 2320.1

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+8.48308q35.00000q57.07143q7+44.9627q9+49.6170q11+11.3703q1342.4154q1543.7733q17140.693q1959.9876q21171.311q23+25.0000q25+152.379q2729.0000q2924.3789q31+420.905q33+35.3572q35+62.2739q37+96.4552q39161.107q41350.585q43224.813q45211.265q47292.995q49371.332q51581.165q53248.085q551193.51q57+609.450q59169.936q61317.951q6356.8515q65+322.156q671453.25q69+419.068q71138.501q73+212.077q75350.863q7715.7298q79+78.6508q81+1051.81q83+218.866q85246.009q87+606.725q8980.4044q91206.808q93+703.464q95+1506.62q97+2230.91q99+O(q100)q+8.48308 q^{3} -5.00000 q^{5} -7.07143 q^{7} +44.9627 q^{9} +49.6170 q^{11} +11.3703 q^{13} -42.4154 q^{15} -43.7733 q^{17} -140.693 q^{19} -59.9876 q^{21} -171.311 q^{23} +25.0000 q^{25} +152.379 q^{27} -29.0000 q^{29} -24.3789 q^{31} +420.905 q^{33} +35.3572 q^{35} +62.2739 q^{37} +96.4552 q^{39} -161.107 q^{41} -350.585 q^{43} -224.813 q^{45} -211.265 q^{47} -292.995 q^{49} -371.332 q^{51} -581.165 q^{53} -248.085 q^{55} -1193.51 q^{57} +609.450 q^{59} -169.936 q^{61} -317.951 q^{63} -56.8515 q^{65} +322.156 q^{67} -1453.25 q^{69} +419.068 q^{71} -138.501 q^{73} +212.077 q^{75} -350.863 q^{77} -15.7298 q^{79} +78.6508 q^{81} +1051.81 q^{83} +218.866 q^{85} -246.009 q^{87} +606.725 q^{89} -80.4044 q^{91} -206.808 q^{93} +703.464 q^{95} +1506.62 q^{97} +2230.91 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+5q330q59q7+45q9+10q11+13q1325q1523q1710q1952q2175q23+150q25+116q27174q29+127q3172q33+45q35++2976q99+O(q100) 6 q + 5 q^{3} - 30 q^{5} - 9 q^{7} + 45 q^{9} + 10 q^{11} + 13 q^{13} - 25 q^{15} - 23 q^{17} - 10 q^{19} - 52 q^{21} - 75 q^{23} + 150 q^{25} + 116 q^{27} - 174 q^{29} + 127 q^{31} - 72 q^{33} + 45 q^{35}+ \cdots + 2976 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 8.48308 1.63257 0.816285 0.577649i 0.196030π-0.196030\pi
0.816285 + 0.577649i 0.196030π0.196030\pi
44 0 0
55 −5.00000 −0.447214
66 0 0
77 −7.07143 −0.381822 −0.190911 0.981607i 0.561144π-0.561144\pi
−0.190911 + 0.981607i 0.561144π0.561144\pi
88 0 0
99 44.9627 1.66528
1010 0 0
1111 49.6170 1.36001 0.680004 0.733209i 0.261978π-0.261978\pi
0.680004 + 0.733209i 0.261978π0.261978\pi
1212 0 0
1313 11.3703 0.242581 0.121291 0.992617i 0.461297π-0.461297\pi
0.121291 + 0.992617i 0.461297π0.461297\pi
1414 0 0
1515 −42.4154 −0.730107
1616 0 0
1717 −43.7733 −0.624505 −0.312252 0.949999i 0.601083π-0.601083\pi
−0.312252 + 0.949999i 0.601083π0.601083\pi
1818 0 0
1919 −140.693 −1.69880 −0.849398 0.527753i 0.823035π-0.823035\pi
−0.849398 + 0.527753i 0.823035π0.823035\pi
2020 0 0
2121 −59.9876 −0.623350
2222 0 0
2323 −171.311 −1.55308 −0.776539 0.630069i 0.783027π-0.783027\pi
−0.776539 + 0.630069i 0.783027π0.783027\pi
2424 0 0
2525 25.0000 0.200000
2626 0 0
2727 152.379 1.08612
2828 0 0
2929 −29.0000 −0.185695
3030 0 0
3131 −24.3789 −0.141245 −0.0706223 0.997503i 0.522499π-0.522499\pi
−0.0706223 + 0.997503i 0.522499π0.522499\pi
3232 0 0
3333 420.905 2.22031
3434 0 0
3535 35.3572 0.170756
3636 0 0
3737 62.2739 0.276696 0.138348 0.990384i 0.455821π-0.455821\pi
0.138348 + 0.990384i 0.455821π0.455821\pi
3838 0 0
3939 96.4552 0.396031
4040 0 0
4141 −161.107 −0.613675 −0.306838 0.951762i 0.599271π-0.599271\pi
−0.306838 + 0.951762i 0.599271π0.599271\pi
4242 0 0
4343 −350.585 −1.24334 −0.621671 0.783279i 0.713546π-0.713546\pi
−0.621671 + 0.783279i 0.713546π0.713546\pi
4444 0 0
4545 −224.813 −0.744738
4646 0 0
4747 −211.265 −0.655664 −0.327832 0.944736i 0.606318π-0.606318\pi
−0.327832 + 0.944736i 0.606318π0.606318\pi
4848 0 0
4949 −292.995 −0.854212
5050 0 0
5151 −371.332 −1.01955
5252 0 0
5353 −581.165 −1.50621 −0.753106 0.657900i 0.771445π-0.771445\pi
−0.753106 + 0.657900i 0.771445π0.771445\pi
5454 0 0
5555 −248.085 −0.608214
5656 0 0
5757 −1193.51 −2.77340
5858 0 0
5959 609.450 1.34481 0.672404 0.740184i 0.265262π-0.265262\pi
0.672404 + 0.740184i 0.265262π0.265262\pi
6060 0 0
6161 −169.936 −0.356690 −0.178345 0.983968i 0.557074π-0.557074\pi
−0.178345 + 0.983968i 0.557074π0.557074\pi
6262 0 0
6363 −317.951 −0.635842
6464 0 0
6565 −56.8515 −0.108486
6666 0 0
6767 322.156 0.587428 0.293714 0.955893i 0.405109π-0.405109\pi
0.293714 + 0.955893i 0.405109π0.405109\pi
6868 0 0
6969 −1453.25 −2.53551
7070 0 0
7171 419.068 0.700483 0.350241 0.936660i 0.386100π-0.386100\pi
0.350241 + 0.936660i 0.386100π0.386100\pi
7272 0 0
7373 −138.501 −0.222059 −0.111030 0.993817i 0.535415π-0.535415\pi
−0.111030 + 0.993817i 0.535415π0.535415\pi
7474 0 0
7575 212.077 0.326514
7676 0 0
7777 −350.863 −0.519280
7878 0 0
7979 −15.7298 −0.0224017 −0.0112009 0.999937i 0.503565π-0.503565\pi
−0.0112009 + 0.999937i 0.503565π0.503565\pi
8080 0 0
8181 78.6508 0.107889
8282 0 0
8383 1051.81 1.39097 0.695487 0.718538i 0.255189π-0.255189\pi
0.695487 + 0.718538i 0.255189π0.255189\pi
8484 0 0
8585 218.866 0.279287
8686 0 0
8787 −246.009 −0.303161
8888 0 0
8989 606.725 0.722615 0.361307 0.932447i 0.382331π-0.382331\pi
0.361307 + 0.932447i 0.382331π0.382331\pi
9090 0 0
9191 −80.4044 −0.0926227
9292 0 0
9393 −206.808 −0.230592
9494 0 0
9595 703.464 0.759725
9696 0 0
9797 1506.62 1.57705 0.788525 0.615002i 0.210845π-0.210845\pi
0.788525 + 0.615002i 0.210845π0.210845\pi
9898 0 0
9999 2230.91 2.26480
100100 0 0
101101 −788.748 −0.777063 −0.388531 0.921436i 0.627017π-0.627017\pi
−0.388531 + 0.921436i 0.627017π0.627017\pi
102102 0 0
103103 342.031 0.327198 0.163599 0.986527i 0.447690π-0.447690\pi
0.163599 + 0.986527i 0.447690π0.447690\pi
104104 0 0
105105 299.938 0.278771
106106 0 0
107107 −29.0515 −0.0262478 −0.0131239 0.999914i 0.504178π-0.504178\pi
−0.0131239 + 0.999914i 0.504178π0.504178\pi
108108 0 0
109109 −1294.70 −1.13771 −0.568853 0.822439i 0.692613π-0.692613\pi
−0.568853 + 0.822439i 0.692613π0.692613\pi
110110 0 0
111111 528.275 0.451726
112112 0 0
113113 1072.95 0.893228 0.446614 0.894727i 0.352630π-0.352630\pi
0.446614 + 0.894727i 0.352630π0.352630\pi
114114 0 0
115115 856.555 0.694558
116116 0 0
117117 511.240 0.403967
118118 0 0
119119 309.540 0.238449
120120 0 0
121121 1130.84 0.849621
122122 0 0
123123 −1366.68 −1.00187
124124 0 0
125125 −125.000 −0.0894427
126126 0 0
127127 −1534.40 −1.07210 −0.536048 0.844188i 0.680083π-0.680083\pi
−0.536048 + 0.844188i 0.680083π0.680083\pi
128128 0 0
129129 −2974.04 −2.02984
130130 0 0
131131 −2216.05 −1.47800 −0.738998 0.673707i 0.764701π-0.764701\pi
−0.738998 + 0.673707i 0.764701π0.764701\pi
132132 0 0
133133 994.899 0.648637
134134 0 0
135135 −761.895 −0.485729
136136 0 0
137137 −1791.50 −1.11721 −0.558606 0.829433i 0.688663π-0.688663\pi
−0.558606 + 0.829433i 0.688663π0.688663\pi
138138 0 0
139139 1597.56 0.974844 0.487422 0.873167i 0.337937π-0.337937\pi
0.487422 + 0.873167i 0.337937π0.337937\pi
140140 0 0
141141 −1792.18 −1.07042
142142 0 0
143143 564.160 0.329912
144144 0 0
145145 145.000 0.0830455
146146 0 0
147147 −2485.50 −1.39456
148148 0 0
149149 −3028.56 −1.66516 −0.832581 0.553903i 0.813138π-0.813138\pi
−0.832581 + 0.553903i 0.813138π0.813138\pi
150150 0 0
151151 1004.38 0.541293 0.270646 0.962679i 0.412763π-0.412763\pi
0.270646 + 0.962679i 0.412763π0.412763\pi
152152 0 0
153153 −1968.16 −1.03998
154154 0 0
155155 121.895 0.0631665
156156 0 0
157157 −1590.05 −0.808281 −0.404141 0.914697i 0.632429π-0.632429\pi
−0.404141 + 0.914697i 0.632429π0.632429\pi
158158 0 0
159159 −4930.07 −2.45900
160160 0 0
161161 1211.41 0.592999
162162 0 0
163163 670.551 0.322219 0.161109 0.986937i 0.448493π-0.448493\pi
0.161109 + 0.986937i 0.448493π0.448493\pi
164164 0 0
165165 −2104.52 −0.992952
166166 0 0
167167 397.647 0.184257 0.0921283 0.995747i 0.470633π-0.470633\pi
0.0921283 + 0.995747i 0.470633π0.470633\pi
168168 0 0
169169 −2067.72 −0.941154
170170 0 0
171171 −6325.92 −2.82898
172172 0 0
173173 2673.82 1.17507 0.587534 0.809199i 0.300099π-0.300099\pi
0.587534 + 0.809199i 0.300099π0.300099\pi
174174 0 0
175175 −176.786 −0.0763643
176176 0 0
177177 5170.02 2.19549
178178 0 0
179179 −375.124 −0.156637 −0.0783186 0.996928i 0.524955π-0.524955\pi
−0.0783186 + 0.996928i 0.524955π0.524955\pi
180180 0 0
181181 −2962.43 −1.21655 −0.608276 0.793726i 0.708139π-0.708139\pi
−0.608276 + 0.793726i 0.708139π0.708139\pi
182182 0 0
183183 −1441.58 −0.582322
184184 0 0
185185 −311.369 −0.123742
186186 0 0
187187 −2171.90 −0.849331
188188 0 0
189189 −1077.54 −0.414706
190190 0 0
191191 −3178.65 −1.20418 −0.602092 0.798427i 0.705666π-0.705666\pi
−0.602092 + 0.798427i 0.705666π0.705666\pi
192192 0 0
193193 271.618 0.101303 0.0506515 0.998716i 0.483870π-0.483870\pi
0.0506515 + 0.998716i 0.483870π0.483870\pi
194194 0 0
195195 −482.276 −0.177110
196196 0 0
197197 2936.50 1.06202 0.531008 0.847367i 0.321813π-0.321813\pi
0.531008 + 0.847367i 0.321813π0.321813\pi
198198 0 0
199199 −4011.65 −1.42904 −0.714519 0.699616i 0.753354π-0.753354\pi
−0.714519 + 0.699616i 0.753354π0.753354\pi
200200 0 0
201201 2732.88 0.959017
202202 0 0
203203 205.072 0.0709025
204204 0 0
205205 805.535 0.274444
206206 0 0
207207 −7702.60 −2.58632
208208 0 0
209209 −6980.75 −2.31038
210210 0 0
211211 5321.80 1.73634 0.868171 0.496266i 0.165296π-0.165296\pi
0.868171 + 0.496266i 0.165296π0.165296\pi
212212 0 0
213213 3554.99 1.14359
214214 0 0
215215 1752.92 0.556039
216216 0 0
217217 172.394 0.0539302
218218 0 0
219219 −1174.92 −0.362527
220220 0 0
221221 −497.716 −0.151493
222222 0 0
223223 −4132.12 −1.24084 −0.620420 0.784270i 0.713038π-0.713038\pi
−0.620420 + 0.784270i 0.713038π0.713038\pi
224224 0 0
225225 1124.07 0.333057
226226 0 0
227227 6160.58 1.80129 0.900643 0.434559i 0.143096π-0.143096\pi
0.900643 + 0.434559i 0.143096π0.143096\pi
228228 0 0
229229 −5702.79 −1.64564 −0.822819 0.568304i 0.807600π-0.807600\pi
−0.822819 + 0.568304i 0.807600π0.807600\pi
230230 0 0
231231 −2976.40 −0.847761
232232 0 0
233233 −2533.81 −0.712427 −0.356214 0.934405i 0.615932π-0.615932\pi
−0.356214 + 0.934405i 0.615932π0.615932\pi
234234 0 0
235235 1056.33 0.293222
236236 0 0
237237 −133.437 −0.0365724
238238 0 0
239239 −339.594 −0.0919101 −0.0459550 0.998944i 0.514633π-0.514633\pi
−0.0459550 + 0.998944i 0.514633π0.514633\pi
240240 0 0
241241 2490.58 0.665693 0.332847 0.942981i 0.391991π-0.391991\pi
0.332847 + 0.942981i 0.391991π0.391991\pi
242242 0 0
243243 −3447.03 −0.909988
244244 0 0
245245 1464.97 0.382015
246246 0 0
247247 −1599.72 −0.412096
248248 0 0
249249 8922.57 2.27086
250250 0 0
251251 −1934.93 −0.486581 −0.243291 0.969953i 0.578227π-0.578227\pi
−0.243291 + 0.969953i 0.578227π0.578227\pi
252252 0 0
253253 −8499.93 −2.11220
254254 0 0
255255 1856.66 0.455956
256256 0 0
257257 −741.416 −0.179954 −0.0899772 0.995944i 0.528679π-0.528679\pi
−0.0899772 + 0.995944i 0.528679π0.528679\pi
258258 0 0
259259 −440.366 −0.105649
260260 0 0
261261 −1303.92 −0.309236
262262 0 0
263263 4691.78 1.10003 0.550014 0.835155i 0.314622π-0.314622\pi
0.550014 + 0.835155i 0.314622π0.314622\pi
264264 0 0
265265 2905.83 0.673598
266266 0 0
267267 5146.90 1.17972
268268 0 0
269269 −6449.25 −1.46178 −0.730888 0.682498i 0.760894π-0.760894\pi
−0.730888 + 0.682498i 0.760894π0.760894\pi
270270 0 0
271271 5486.65 1.22985 0.614926 0.788585i 0.289186π-0.289186\pi
0.614926 + 0.788585i 0.289186π0.289186\pi
272272 0 0
273273 −682.077 −0.151213
274274 0 0
275275 1240.42 0.272002
276276 0 0
277277 −4441.54 −0.963417 −0.481708 0.876332i 0.659984π-0.659984\pi
−0.481708 + 0.876332i 0.659984π0.659984\pi
278278 0 0
279279 −1096.14 −0.235212
280280 0 0
281281 492.309 0.104515 0.0522575 0.998634i 0.483358π-0.483358\pi
0.0522575 + 0.998634i 0.483358π0.483358\pi
282282 0 0
283283 −4850.65 −1.01887 −0.509437 0.860508i 0.670146π-0.670146\pi
−0.509437 + 0.860508i 0.670146π0.670146\pi
284284 0 0
285285 5967.54 1.24030
286286 0 0
287287 1139.26 0.234314
288288 0 0
289289 −2996.90 −0.609994
290290 0 0
291291 12780.8 2.57465
292292 0 0
293293 6560.79 1.30814 0.654071 0.756433i 0.273060π-0.273060\pi
0.654071 + 0.756433i 0.273060π0.273060\pi
294294 0 0
295295 −3047.25 −0.601416
296296 0 0
297297 7560.58 1.47714
298298 0 0
299299 −1947.86 −0.376748
300300 0 0
301301 2479.14 0.474734
302302 0 0
303303 −6691.01 −1.26861
304304 0 0
305305 849.681 0.159517
306306 0 0
307307 −7308.77 −1.35874 −0.679370 0.733796i 0.737747π-0.737747\pi
−0.679370 + 0.733796i 0.737747π0.737747\pi
308308 0 0
309309 2901.48 0.534173
310310 0 0
311311 761.424 0.138831 0.0694154 0.997588i 0.477887π-0.477887\pi
0.0694154 + 0.997588i 0.477887π0.477887\pi
312312 0 0
313313 5238.58 0.946014 0.473007 0.881059i 0.343169π-0.343169\pi
0.473007 + 0.881059i 0.343169π0.343169\pi
314314 0 0
315315 1589.75 0.284357
316316 0 0
317317 −8054.16 −1.42702 −0.713512 0.700643i 0.752897π-0.752897\pi
−0.713512 + 0.700643i 0.752897π0.752897\pi
318318 0 0
319319 −1438.89 −0.252547
320320 0 0
321321 −246.446 −0.0428513
322322 0 0
323323 6158.58 1.06091
324324 0 0
325325 284.258 0.0485162
326326 0 0
327327 −10983.1 −1.85738
328328 0 0
329329 1493.95 0.250347
330330 0 0
331331 115.772 0.0192249 0.00961243 0.999954i 0.496940π-0.496940\pi
0.00961243 + 0.999954i 0.496940π0.496940\pi
332332 0 0
333333 2800.00 0.460778
334334 0 0
335335 −1610.78 −0.262706
336336 0 0
337337 5101.77 0.824662 0.412331 0.911034i 0.364715π-0.364715\pi
0.412331 + 0.911034i 0.364715π0.364715\pi
338338 0 0
339339 9101.94 1.45826
340340 0 0
341341 −1209.61 −0.192094
342342 0 0
343343 4497.40 0.707978
344344 0 0
345345 7266.23 1.13391
346346 0 0
347347 −7932.92 −1.22727 −0.613633 0.789591i 0.710293π-0.710293\pi
−0.613633 + 0.789591i 0.710293π0.710293\pi
348348 0 0
349349 −3840.43 −0.589035 −0.294518 0.955646i 0.595159π-0.595159\pi
−0.294518 + 0.955646i 0.595159π0.595159\pi
350350 0 0
351351 1732.60 0.263473
352352 0 0
353353 −5282.31 −0.796456 −0.398228 0.917287i 0.630375π-0.630375\pi
−0.398228 + 0.917287i 0.630375π0.630375\pi
354354 0 0
355355 −2095.34 −0.313265
356356 0 0
357357 2625.85 0.389285
358358 0 0
359359 5124.61 0.753389 0.376694 0.926338i 0.377061π-0.377061\pi
0.376694 + 0.926338i 0.377061π0.377061\pi
360360 0 0
361361 12935.4 1.88591
362362 0 0
363363 9593.05 1.38706
364364 0 0
365365 692.505 0.0993078
366366 0 0
367367 5397.49 0.767702 0.383851 0.923395i 0.374598π-0.374598\pi
0.383851 + 0.923395i 0.374598π0.374598\pi
368368 0 0
369369 −7243.81 −1.02194
370370 0 0
371371 4109.67 0.575104
372372 0 0
373373 −2075.12 −0.288058 −0.144029 0.989573i 0.546006π-0.546006\pi
−0.144029 + 0.989573i 0.546006π0.546006\pi
374374 0 0
375375 −1060.39 −0.146021
376376 0 0
377377 −329.739 −0.0450462
378378 0 0
379379 −1471.60 −0.199448 −0.0997242 0.995015i 0.531796π-0.531796\pi
−0.0997242 + 0.995015i 0.531796π0.531796\pi
380380 0 0
381381 −13016.5 −1.75027
382382 0 0
383383 2887.39 0.385219 0.192609 0.981276i 0.438305π-0.438305\pi
0.192609 + 0.981276i 0.438305π0.438305\pi
384384 0 0
385385 1754.32 0.232229
386386 0 0
387387 −15763.2 −2.07052
388388 0 0
389389 8032.30 1.04692 0.523462 0.852049i 0.324640π-0.324640\pi
0.523462 + 0.852049i 0.324640π0.324640\pi
390390 0 0
391391 7498.84 0.969905
392392 0 0
393393 −18799.0 −2.41293
394394 0 0
395395 78.6488 0.0100184
396396 0 0
397397 −2958.09 −0.373961 −0.186980 0.982364i 0.559870π-0.559870\pi
−0.186980 + 0.982364i 0.559870π0.559870\pi
398398 0 0
399399 8439.81 1.05895
400400 0 0
401401 11859.8 1.47694 0.738470 0.674287i 0.235549π-0.235549\pi
0.738470 + 0.674287i 0.235549π0.235549\pi
402402 0 0
403403 −277.196 −0.0342633
404404 0 0
405405 −393.254 −0.0482492
406406 0 0
407407 3089.84 0.376309
408408 0 0
409409 9048.69 1.09396 0.546979 0.837146i 0.315778π-0.315778\pi
0.546979 + 0.837146i 0.315778π0.315778\pi
410410 0 0
411411 −15197.4 −1.82393
412412 0 0
413413 −4309.69 −0.513477
414414 0 0
415415 −5259.04 −0.622063
416416 0 0
417417 13552.2 1.59150
418418 0 0
419419 −12491.8 −1.45648 −0.728239 0.685323i 0.759661π-0.759661\pi
−0.728239 + 0.685323i 0.759661π0.759661\pi
420420 0 0
421421 2674.89 0.309658 0.154829 0.987941i 0.450517π-0.450517\pi
0.154829 + 0.987941i 0.450517π0.450517\pi
422422 0 0
423423 −9499.05 −1.09187
424424 0 0
425425 −1094.33 −0.124901
426426 0 0
427427 1201.69 0.136192
428428 0 0
429429 4785.82 0.538605
430430 0 0
431431 14304.3 1.59864 0.799321 0.600905i 0.205193π-0.205193\pi
0.799321 + 0.600905i 0.205193π0.205193\pi
432432 0 0
433433 −13331.8 −1.47965 −0.739824 0.672800i 0.765091π-0.765091\pi
−0.739824 + 0.672800i 0.765091π0.765091\pi
434434 0 0
435435 1230.05 0.135578
436436 0 0
437437 24102.2 2.63836
438438 0 0
439439 2642.00 0.287234 0.143617 0.989633i 0.454127π-0.454127\pi
0.143617 + 0.989633i 0.454127π0.454127\pi
440440 0 0
441441 −13173.8 −1.42251
442442 0 0
443443 13499.5 1.44781 0.723906 0.689899i 0.242345π-0.242345\pi
0.723906 + 0.689899i 0.242345π0.242345\pi
444444 0 0
445445 −3033.62 −0.323163
446446 0 0
447447 −25691.5 −2.71849
448448 0 0
449449 −7584.76 −0.797209 −0.398605 0.917123i 0.630505π-0.630505\pi
−0.398605 + 0.917123i 0.630505π0.630505\pi
450450 0 0
451451 −7993.65 −0.834603
452452 0 0
453453 8520.23 0.883698
454454 0 0
455455 402.022 0.0414221
456456 0 0
457457 −2116.33 −0.216625 −0.108313 0.994117i 0.534545π-0.534545\pi
−0.108313 + 0.994117i 0.534545π0.534545\pi
458458 0 0
459459 −6670.13 −0.678289
460460 0 0
461461 10534.8 1.06432 0.532162 0.846643i 0.321380π-0.321380\pi
0.532162 + 0.846643i 0.321380π0.321380\pi
462462 0 0
463463 11067.4 1.11089 0.555447 0.831552i 0.312547π-0.312547\pi
0.555447 + 0.831552i 0.312547π0.312547\pi
464464 0 0
465465 1034.04 0.103124
466466 0 0
467467 3678.32 0.364480 0.182240 0.983254i 0.441665π-0.441665\pi
0.182240 + 0.983254i 0.441665π0.441665\pi
468468 0 0
469469 −2278.11 −0.224293
470470 0 0
471471 −13488.6 −1.31958
472472 0 0
473473 −17395.0 −1.69095
474474 0 0
475475 −3517.32 −0.339759
476476 0 0
477477 −26130.8 −2.50827
478478 0 0
479479 −4779.57 −0.455917 −0.227959 0.973671i 0.573205π-0.573205\pi
−0.227959 + 0.973671i 0.573205π0.573205\pi
480480 0 0
481481 708.073 0.0671213
482482 0 0
483483 10276.5 0.968112
484484 0 0
485485 −7533.09 −0.705278
486486 0 0
487487 12663.6 1.17833 0.589163 0.808015i 0.299458π-0.299458\pi
0.589163 + 0.808015i 0.299458π0.299458\pi
488488 0 0
489489 5688.34 0.526045
490490 0 0
491491 7219.24 0.663543 0.331772 0.943360i 0.392354π-0.392354\pi
0.331772 + 0.943360i 0.392354π0.392354\pi
492492 0 0
493493 1269.43 0.115968
494494 0 0
495495 −11154.6 −1.01285
496496 0 0
497497 −2963.41 −0.267459
498498 0 0
499499 −5718.31 −0.512999 −0.256500 0.966544i 0.582569π-0.582569\pi
−0.256500 + 0.966544i 0.582569π0.582569\pi
500500 0 0
501501 3373.27 0.300812
502502 0 0
503503 17206.0 1.52520 0.762602 0.646868i 0.223921π-0.223921\pi
0.762602 + 0.646868i 0.223921π0.223921\pi
504504 0 0
505505 3943.74 0.347513
506506 0 0
507507 −17540.6 −1.53650
508508 0 0
509509 −18691.0 −1.62763 −0.813817 0.581121i 0.802614π-0.802614\pi
−0.813817 + 0.581121i 0.802614π0.802614\pi
510510 0 0
511511 979.400 0.0847869
512512 0 0
513513 −21438.6 −1.84510
514514 0 0
515515 −1710.16 −0.146327
516516 0 0
517517 −10482.3 −0.891708
518518 0 0
519519 22682.2 1.91838
520520 0 0
521521 −7074.55 −0.594898 −0.297449 0.954738i 0.596136π-0.596136\pi
−0.297449 + 0.954738i 0.596136π0.596136\pi
522522 0 0
523523 12647.5 1.05743 0.528716 0.848799i 0.322674π-0.322674\pi
0.528716 + 0.848799i 0.322674π0.322674\pi
524524 0 0
525525 −1499.69 −0.124670
526526 0 0
527527 1067.14 0.0882079
528528 0 0
529529 17180.5 1.41205
530530 0 0
531531 27402.5 2.23949
532532 0 0
533533 −1831.84 −0.148866
534534 0 0
535535 145.257 0.0117384
536536 0 0
537537 −3182.21 −0.255721
538538 0 0
539539 −14537.5 −1.16174
540540 0 0
541541 2430.45 0.193148 0.0965742 0.995326i 0.469211π-0.469211\pi
0.0965742 + 0.995326i 0.469211π0.469211\pi
542542 0 0
543543 −25130.6 −1.98611
544544 0 0
545545 6473.51 0.508797
546546 0 0
547547 13829.9 1.08103 0.540515 0.841334i 0.318229π-0.318229\pi
0.540515 + 0.841334i 0.318229π0.318229\pi
548548 0 0
549549 −7640.79 −0.593991
550550 0 0
551551 4080.09 0.315459
552552 0 0
553553 111.232 0.00855346
554554 0 0
555555 −2641.37 −0.202018
556556 0 0
557557 −19656.7 −1.49530 −0.747649 0.664094i 0.768817π-0.768817\pi
−0.747649 + 0.664094i 0.768817π0.768817\pi
558558 0 0
559559 −3986.26 −0.301611
560560 0 0
561561 −18424.4 −1.38659
562562 0 0
563563 18649.4 1.39605 0.698026 0.716073i 0.254062π-0.254062\pi
0.698026 + 0.716073i 0.254062π0.254062\pi
564564 0 0
565565 −5364.76 −0.399464
566566 0 0
567567 −556.174 −0.0411942
568568 0 0
569569 −13392.7 −0.986734 −0.493367 0.869821i 0.664234π-0.664234\pi
−0.493367 + 0.869821i 0.664234π0.664234\pi
570570 0 0
571571 −7573.58 −0.555069 −0.277535 0.960716i 0.589517π-0.589517\pi
−0.277535 + 0.960716i 0.589517π0.589517\pi
572572 0 0
573573 −26964.8 −1.96591
574574 0 0
575575 −4282.77 −0.310616
576576 0 0
577577 −12135.1 −0.875549 −0.437775 0.899085i 0.644233π-0.644233\pi
−0.437775 + 0.899085i 0.644233π0.644233\pi
578578 0 0
579579 2304.16 0.165384
580580 0 0
581581 −7437.79 −0.531104
582582 0 0
583583 −28835.7 −2.04846
584584 0 0
585585 −2556.20 −0.180659
586586 0 0
587587 −11035.3 −0.775940 −0.387970 0.921672i 0.626824π-0.626824\pi
−0.387970 + 0.921672i 0.626824π0.626824\pi
588588 0 0
589589 3429.94 0.239946
590590 0 0
591591 24910.6 1.73382
592592 0 0
593593 2023.70 0.140140 0.0700702 0.997542i 0.477678π-0.477678\pi
0.0700702 + 0.997542i 0.477678π0.477678\pi
594594 0 0
595595 −1547.70 −0.106638
596596 0 0
597597 −34031.2 −2.33300
598598 0 0
599599 14464.5 0.986651 0.493326 0.869845i 0.335781π-0.335781\pi
0.493326 + 0.869845i 0.335781π0.335781\pi
600600 0 0
601601 3879.55 0.263312 0.131656 0.991295i 0.457971π-0.457971\pi
0.131656 + 0.991295i 0.457971π0.457971\pi
602602 0 0
603603 14485.0 0.978235
604604 0 0
605605 −5654.22 −0.379962
606606 0 0
607607 −13794.8 −0.922430 −0.461215 0.887289i 0.652586π-0.652586\pi
−0.461215 + 0.887289i 0.652586π0.652586\pi
608608 0 0
609609 1739.64 0.115753
610610 0 0
611611 −2402.15 −0.159052
612612 0 0
613613 16546.1 1.09020 0.545100 0.838371i 0.316492π-0.316492\pi
0.545100 + 0.838371i 0.316492π0.316492\pi
614614 0 0
615615 6833.42 0.448049
616616 0 0
617617 −5014.18 −0.327169 −0.163585 0.986529i 0.552306π-0.552306\pi
−0.163585 + 0.986529i 0.552306π0.552306\pi
618618 0 0
619619 20464.2 1.32880 0.664398 0.747379i 0.268688π-0.268688\pi
0.664398 + 0.747379i 0.268688π0.268688\pi
620620 0 0
621621 −26104.2 −1.68684
622622 0 0
623623 −4290.41 −0.275910
624624 0 0
625625 625.000 0.0400000
626626 0 0
627627 −59218.3 −3.77185
628628 0 0
629629 −2725.93 −0.172798
630630 0 0
631631 28218.5 1.78029 0.890144 0.455678i 0.150603π-0.150603\pi
0.890144 + 0.455678i 0.150603π0.150603\pi
632632 0 0
633633 45145.3 2.83470
634634 0 0
635635 7672.01 0.479456
636636 0 0
637637 −3331.44 −0.207216
638638 0 0
639639 18842.4 1.16650
640640 0 0
641641 −8127.40 −0.500800 −0.250400 0.968142i 0.580562π-0.580562\pi
−0.250400 + 0.968142i 0.580562π0.580562\pi
642642 0 0
643643 −11416.6 −0.700195 −0.350097 0.936713i 0.613852π-0.613852\pi
−0.350097 + 0.936713i 0.613852π0.613852\pi
644644 0 0
645645 14870.2 0.907773
646646 0 0
647647 −21087.5 −1.28135 −0.640675 0.767812i 0.721345π-0.721345\pi
−0.640675 + 0.767812i 0.721345π0.721345\pi
648648 0 0
649649 30239.1 1.82895
650650 0 0
651651 1462.43 0.0880449
652652 0 0
653653 25908.5 1.55265 0.776324 0.630334i 0.217082π-0.217082\pi
0.776324 + 0.630334i 0.217082π0.217082\pi
654654 0 0
655655 11080.3 0.660980
656656 0 0
657657 −6227.38 −0.369792
658658 0 0
659659 9718.64 0.574483 0.287242 0.957858i 0.407262π-0.407262\pi
0.287242 + 0.957858i 0.407262π0.407262\pi
660660 0 0
661661 20789.9 1.22335 0.611675 0.791109i 0.290496π-0.290496\pi
0.611675 + 0.791109i 0.290496π0.290496\pi
662662 0 0
663663 −4222.16 −0.247323
664664 0 0
665665 −4974.50 −0.290079
666666 0 0
667667 4968.02 0.288399
668668 0 0
669669 −35053.1 −2.02576
670670 0 0
671671 −8431.72 −0.485102
672672 0 0
673673 31415.5 1.79938 0.899688 0.436533i 0.143794π-0.143794\pi
0.899688 + 0.436533i 0.143794π0.143794\pi
674674 0 0
675675 3809.47 0.217225
676676 0 0
677677 18356.1 1.04207 0.521037 0.853534i 0.325546π-0.325546\pi
0.521037 + 0.853534i 0.325546π0.325546\pi
678678 0 0
679679 −10653.9 −0.602152
680680 0 0
681681 52260.7 2.94073
682682 0 0
683683 −4497.91 −0.251988 −0.125994 0.992031i 0.540212π-0.540212\pi
−0.125994 + 0.992031i 0.540212π0.540212\pi
684684 0 0
685685 8957.48 0.499632
686686 0 0
687687 −48377.2 −2.68662
688688 0 0
689689 −6608.03 −0.365379
690690 0 0
691691 −32246.3 −1.77526 −0.887632 0.460553i 0.847651π-0.847651\pi
−0.887632 + 0.460553i 0.847651π0.847651\pi
692692 0 0
693693 −15775.8 −0.864749
694694 0 0
695695 −7987.80 −0.435963
696696 0 0
697697 7052.18 0.383243
698698 0 0
699699 −21494.5 −1.16309
700700 0 0
701701 12062.9 0.649944 0.324972 0.945724i 0.394645π-0.394645\pi
0.324972 + 0.945724i 0.394645π0.394645\pi
702702 0 0
703703 −8761.48 −0.470051
704704 0 0
705705 8960.90 0.478705
706706 0 0
707707 5577.58 0.296699
708708 0 0
709709 −29560.0 −1.56579 −0.782897 0.622151i 0.786259π-0.786259\pi
−0.782897 + 0.622151i 0.786259π0.786259\pi
710710 0 0
711711 −707.252 −0.0373052
712712 0 0
713713 4176.38 0.219364
714714 0 0
715715 −2820.80 −0.147541
716716 0 0
717717 −2880.80 −0.150050
718718 0 0
719719 10289.1 0.533683 0.266841 0.963740i 0.414020π-0.414020\pi
0.266841 + 0.963740i 0.414020π0.414020\pi
720720 0 0
721721 −2418.65 −0.124931
722722 0 0
723723 21127.8 1.08679
724724 0 0
725725 −725.000 −0.0371391
726726 0 0
727727 −11916.5 −0.607923 −0.303961 0.952684i 0.598309π-0.598309\pi
−0.303961 + 0.952684i 0.598309π0.598309\pi
728728 0 0
729729 −31365.0 −1.59351
730730 0 0
731731 15346.2 0.776472
732732 0 0
733733 −13690.9 −0.689883 −0.344941 0.938624i 0.612101π-0.612101\pi
−0.344941 + 0.938624i 0.612101π0.612101\pi
734734 0 0
735735 12427.5 0.623667
736736 0 0
737737 15984.4 0.798907
738738 0 0
739739 −2562.38 −0.127549 −0.0637744 0.997964i 0.520314π-0.520314\pi
−0.0637744 + 0.997964i 0.520314π0.520314\pi
740740 0 0
741741 −13570.6 −0.672776
742742 0 0
743743 −28880.9 −1.42603 −0.713014 0.701150i 0.752670π-0.752670\pi
−0.713014 + 0.701150i 0.752670π0.752670\pi
744744 0 0
745745 15142.8 0.744683
746746 0 0
747747 47292.1 2.31637
748748 0 0
749749 205.436 0.0100220
750750 0 0
751751 38418.9 1.86675 0.933373 0.358909i 0.116851π-0.116851\pi
0.933373 + 0.358909i 0.116851π0.116851\pi
752752 0 0
753753 −16414.2 −0.794378
754754 0 0
755755 −5021.89 −0.242073
756756 0 0
757757 3302.67 0.158570 0.0792850 0.996852i 0.474736π-0.474736\pi
0.0792850 + 0.996852i 0.474736π0.474736\pi
758758 0 0
759759 −72105.6 −3.44831
760760 0 0
761761 8833.40 0.420776 0.210388 0.977618i 0.432527π-0.432527\pi
0.210388 + 0.977618i 0.432527π0.432527\pi
762762 0 0
763763 9155.39 0.434400
764764 0 0
765765 9840.82 0.465092
766766 0 0
767767 6929.64 0.326225
768768 0 0
769769 −6910.59 −0.324060 −0.162030 0.986786i 0.551804π-0.551804\pi
−0.162030 + 0.986786i 0.551804π0.551804\pi
770770 0 0
771771 −6289.49 −0.293788
772772 0 0
773773 −25699.3 −1.19578 −0.597892 0.801577i 0.703995π-0.703995\pi
−0.597892 + 0.801577i 0.703995π0.703995\pi
774774 0 0
775775 −609.473 −0.0282489
776776 0 0
777777 −3735.66 −0.172479
778778 0 0
779779 22666.6 1.04251
780780 0 0
781781 20792.9 0.952662
782782 0 0
783783 −4418.99 −0.201688
784784 0 0
785785 7950.27 0.361474
786786 0 0
787787 −21967.0 −0.994966 −0.497483 0.867474i 0.665742π-0.665742\pi
−0.497483 + 0.867474i 0.665742π0.665742\pi
788788 0 0
789789 39800.7 1.79587
790790 0 0
791791 −7587.31 −0.341054
792792 0 0
793793 −1932.23 −0.0865264
794794 0 0
795795 24650.4 1.09970
796796 0 0
797797 −33264.7 −1.47842 −0.739208 0.673477i 0.764800π-0.764800\pi
−0.739208 + 0.673477i 0.764800π0.764800\pi
798798 0 0
799799 9247.77 0.409465
800800 0 0
801801 27280.0 1.20336
802802 0 0
803803 −6872.00 −0.302002
804804 0 0
805805 −6057.07 −0.265197
806806 0 0
807807 −54709.5 −2.38645
808808 0 0
809809 −23154.0 −1.00624 −0.503121 0.864216i 0.667815π-0.667815\pi
−0.503121 + 0.864216i 0.667815π0.667815\pi
810810 0 0
811811 −27819.4 −1.20453 −0.602263 0.798298i 0.705734π-0.705734\pi
−0.602263 + 0.798298i 0.705734π0.705734\pi
812812 0 0
813813 46543.7 2.00782
814814 0 0
815815 −3352.76 −0.144101
816816 0 0
817817 49324.7 2.11218
818818 0 0
819819 −3615.20 −0.154243
820820 0 0
821821 −11310.9 −0.480818 −0.240409 0.970672i 0.577282π-0.577282\pi
−0.240409 + 0.970672i 0.577282π0.577282\pi
822822 0 0
823823 −12873.4 −0.545249 −0.272625 0.962121i 0.587892π-0.587892\pi
−0.272625 + 0.962121i 0.587892π0.587892\pi
824824 0 0
825825 10522.6 0.444062
826826 0 0
827827 12564.4 0.528305 0.264153 0.964481i 0.414908π-0.414908\pi
0.264153 + 0.964481i 0.414908π0.414908\pi
828828 0 0
829829 20023.0 0.838877 0.419439 0.907784i 0.362227π-0.362227\pi
0.419439 + 0.907784i 0.362227π0.362227\pi
830830 0 0
831831 −37678.0 −1.57285
832832 0 0
833833 12825.3 0.533460
834834 0 0
835835 −1988.24 −0.0824021
836836 0 0
837837 −3714.83 −0.153409
838838 0 0
839839 −38199.5 −1.57186 −0.785932 0.618313i 0.787816π-0.787816\pi
−0.785932 + 0.618313i 0.787816π0.787816\pi
840840 0 0
841841 841.000 0.0344828
842842 0 0
843843 4176.30 0.170628
844844 0 0
845845 10338.6 0.420897
846846 0 0
847847 −7996.69 −0.324403
848848 0 0
849849 −41148.5 −1.66338
850850 0 0
851851 −10668.2 −0.429731
852852 0 0
853853 7748.13 0.311009 0.155505 0.987835i 0.450300π-0.450300\pi
0.155505 + 0.987835i 0.450300π0.450300\pi
854854 0 0
855855 31629.6 1.26516
856856 0 0
857857 −41669.4 −1.66091 −0.830455 0.557085i 0.811920π-0.811920\pi
−0.830455 + 0.557085i 0.811920π0.811920\pi
858858 0 0
859859 31271.5 1.24211 0.621053 0.783769i 0.286705π-0.286705\pi
0.621053 + 0.783769i 0.286705π0.286705\pi
860860 0 0
861861 9664.42 0.382535
862862 0 0
863863 22150.9 0.873727 0.436863 0.899528i 0.356089π-0.356089\pi
0.436863 + 0.899528i 0.356089π0.356089\pi
864864 0 0
865865 −13369.1 −0.525507
866866 0 0
867867 −25423.0 −0.995858
868868 0 0
869869 −780.463 −0.0304665
870870 0 0
871871 3663.02 0.142499
872872 0 0
873873 67741.6 2.62624
874874 0 0
875875 883.929 0.0341512
876876 0 0
877877 1057.91 0.0407332 0.0203666 0.999793i 0.493517π-0.493517\pi
0.0203666 + 0.999793i 0.493517π0.493517\pi
878878 0 0
879879 55655.8 2.13563
880880 0 0
881881 43948.4 1.68066 0.840328 0.542078i 0.182362π-0.182362\pi
0.840328 + 0.542078i 0.182362π0.182362\pi
882882 0 0
883883 1203.63 0.0458724 0.0229362 0.999737i 0.492699π-0.492699\pi
0.0229362 + 0.999737i 0.492699π0.492699\pi
884884 0 0
885885 −25850.1 −0.981854
886886 0 0
887887 25700.6 0.972875 0.486438 0.873715i 0.338296π-0.338296\pi
0.486438 + 0.873715i 0.338296π0.338296\pi
888888 0 0
889889 10850.4 0.409349
890890 0 0
891891 3902.41 0.146729
892892 0 0
893893 29723.5 1.11384
894894 0 0
895895 1875.62 0.0700503
896896 0 0
897897 −16523.8 −0.615067
898898 0 0
899899 706.988 0.0262285
900900 0 0
901901 25439.5 0.940636
902902 0 0
903903 21030.7 0.775037
904904 0 0
905905 14812.2 0.544058
906906 0 0
907907 26715.7 0.978037 0.489018 0.872273i 0.337355π-0.337355\pi
0.489018 + 0.872273i 0.337355π0.337355\pi
908908 0 0
909909 −35464.2 −1.29403
910910 0 0
911911 −41003.4 −1.49122 −0.745611 0.666381i 0.767842π-0.767842\pi
−0.745611 + 0.666381i 0.767842π0.767842\pi
912912 0 0
913913 52187.5 1.89174
914914 0 0
915915 7207.92 0.260422
916916 0 0
917917 15670.7 0.564331
918918 0 0
919919 −18318.5 −0.657533 −0.328766 0.944411i 0.606633π-0.606633\pi
−0.328766 + 0.944411i 0.606633π0.606633\pi
920920 0 0
921921 −62000.9 −2.21824
922922 0 0
923923 4764.94 0.169924
924924 0 0
925925 1556.85 0.0553393
926926 0 0
927927 15378.7 0.544877
928928 0 0
929929 −45848.5 −1.61920 −0.809602 0.586980i 0.800317π-0.800317\pi
−0.809602 + 0.586980i 0.800317π0.800317\pi
930930 0 0
931931 41222.2 1.45113
932932 0 0
933933 6459.22 0.226651
934934 0 0
935935 10859.5 0.379832
936936 0 0
937937 5905.46 0.205894 0.102947 0.994687i 0.467173π-0.467173\pi
0.102947 + 0.994687i 0.467173π0.467173\pi
938938 0 0
939939 44439.3 1.54443
940940 0 0
941941 2680.04 0.0928446 0.0464223 0.998922i 0.485218π-0.485218\pi
0.0464223 + 0.998922i 0.485218π0.485218\pi
942942 0 0
943943 27599.4 0.953086
944944 0 0
945945 5387.69 0.185462
946946 0 0
947947 −5804.87 −0.199190 −0.0995950 0.995028i 0.531755π-0.531755\pi
−0.0995950 + 0.995028i 0.531755π0.531755\pi
948948 0 0
949949 −1574.80 −0.0538674
950950 0 0
951951 −68324.1 −2.32972
952952 0 0
953953 −43474.4 −1.47773 −0.738864 0.673854i 0.764638π-0.764638\pi
−0.738864 + 0.673854i 0.764638π0.764638\pi
954954 0 0
955955 15893.3 0.538527
956956 0 0
957957 −12206.2 −0.412301
958958 0 0
959959 12668.5 0.426575
960960 0 0
961961 −29196.7 −0.980050
962962 0 0
963963 −1306.23 −0.0437100
964964 0 0
965965 −1358.09 −0.0453041
966966 0 0
967967 36054.7 1.19901 0.599504 0.800371i 0.295364π-0.295364\pi
0.599504 + 0.800371i 0.295364π0.295364\pi
968968 0 0
969969 52243.8 1.73200
970970 0 0
971971 −16675.6 −0.551130 −0.275565 0.961282i 0.588865π-0.588865\pi
−0.275565 + 0.961282i 0.588865π0.588865\pi
972972 0 0
973973 −11297.0 −0.372216
974974 0 0
975975 2411.38 0.0792062
976976 0 0
977977 −24732.7 −0.809896 −0.404948 0.914340i 0.632710π-0.632710\pi
−0.404948 + 0.914340i 0.632710π0.632710\pi
978978 0 0
979979 30103.9 0.982761
980980 0 0
981981 −58213.3 −1.89460
982982 0 0
983983 −23711.9 −0.769370 −0.384685 0.923048i 0.625690π-0.625690\pi
−0.384685 + 0.923048i 0.625690π0.625690\pi
984984 0 0
985985 −14682.5 −0.474948
986986 0 0
987987 12673.3 0.408708
988988 0 0
989989 60059.0 1.93101
990990 0 0
991991 −29289.2 −0.938852 −0.469426 0.882972i 0.655539π-0.655539\pi
−0.469426 + 0.882972i 0.655539π0.655539\pi
992992 0 0
993993 982.107 0.0313859
994994 0 0
995995 20058.3 0.639085
996996 0 0
997997 28945.4 0.919470 0.459735 0.888056i 0.347944π-0.347944\pi
0.459735 + 0.888056i 0.347944π0.347944\pi
998998 0 0
999999 9489.23 0.300527
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 2320.4.a.o.1.6 6
4.3 odd 2 580.4.a.a.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.4.a.a.1.1 6 4.3 odd 2
2320.4.a.o.1.6 6 1.1 even 1 trivial