Properties

Label 1305.4.a.n.1.6
Level 13051305
Weight 44
Character 1305.1
Self dual yes
Analytic conductor 76.99776.997
Analytic rank 11
Dimension 77
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1305,4,Mod(1,1305)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1305, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("1305.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 1305=32529 1305 = 3^{2} \cdot 5 \cdot 29
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1305.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [7,2,0,22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 76.997492557576.9974925575
Analytic rank: 11
Dimension: 77
Coefficient field: Q[x]/(x7)\mathbb{Q}[x]/(x^{7} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x72x637x5+55x4+336x3227x2824x166 x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 23 2^{3}
Twist minimal: no (minimal twist has level 435)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.6
Root 3.577203.57720 of defining polynomial
Character χ\chi == 1305.1

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+3.57720q2+4.79637q45.00000q5+15.0281q711.4600q817.8860q1070.8260q11+62.2117q13+53.7587q1479.3658q16+67.1848q17+118.988q1923.9818q20253.359q2272.5383q23+25.0000q25+222.544q26+72.0804q2829.0000q29180.227q31192.227q32+240.334q3475.1407q3547.8439q37+425.646q38+57.3002q40371.956q41409.069q43339.707q44259.484q46125.891q47117.155q49+89.4300q50+298.390q52+215.764q53+354.130q55172.223q56103.739q58356.919q59466.115q61644.707q6252.7086q64311.059q65578.359q67+322.243q68268.793q70870.924q71+411.904q73171.147q74+570.712q761064.38q77+1120.23q79+396.829q801330.56q821079.28q83335.924q851463.32q86+811.668q88388.993q89+934.926q91347.920q92450.339q94594.942q951528.82q97419.088q98+O(q100)q+3.57720 q^{2} +4.79637 q^{4} -5.00000 q^{5} +15.0281 q^{7} -11.4600 q^{8} -17.8860 q^{10} -70.8260 q^{11} +62.2117 q^{13} +53.7587 q^{14} -79.3658 q^{16} +67.1848 q^{17} +118.988 q^{19} -23.9818 q^{20} -253.359 q^{22} -72.5383 q^{23} +25.0000 q^{25} +222.544 q^{26} +72.0804 q^{28} -29.0000 q^{29} -180.227 q^{31} -192.227 q^{32} +240.334 q^{34} -75.1407 q^{35} -47.8439 q^{37} +425.646 q^{38} +57.3002 q^{40} -371.956 q^{41} -409.069 q^{43} -339.707 q^{44} -259.484 q^{46} -125.891 q^{47} -117.155 q^{49} +89.4300 q^{50} +298.390 q^{52} +215.764 q^{53} +354.130 q^{55} -172.223 q^{56} -103.739 q^{58} -356.919 q^{59} -466.115 q^{61} -644.707 q^{62} -52.7086 q^{64} -311.059 q^{65} -578.359 q^{67} +322.243 q^{68} -268.793 q^{70} -870.924 q^{71} +411.904 q^{73} -171.147 q^{74} +570.712 q^{76} -1064.38 q^{77} +1120.23 q^{79} +396.829 q^{80} -1330.56 q^{82} -1079.28 q^{83} -335.924 q^{85} -1463.32 q^{86} +811.668 q^{88} -388.993 q^{89} +934.926 q^{91} -347.920 q^{92} -450.339 q^{94} -594.942 q^{95} -1528.82 q^{97} -419.088 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 7q+2q2+22q435q550q7+33q810q1076q11+30q1389q14+138q16+140q17+90q19110q20+61q2234q23+175q25+241q26++761q98+O(q100) 7 q + 2 q^{2} + 22 q^{4} - 35 q^{5} - 50 q^{7} + 33 q^{8} - 10 q^{10} - 76 q^{11} + 30 q^{13} - 89 q^{14} + 138 q^{16} + 140 q^{17} + 90 q^{19} - 110 q^{20} + 61 q^{22} - 34 q^{23} + 175 q^{25} + 241 q^{26}+ \cdots + 761 q^{98}+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 3.57720 1.26473 0.632366 0.774670i 0.282084π-0.282084\pi
0.632366 + 0.774670i 0.282084π0.282084\pi
33 0 0
44 4.79637 0.599546
55 −5.00000 −0.447214
66 0 0
77 15.0281 0.811443 0.405721 0.913997i 0.367020π-0.367020\pi
0.405721 + 0.913997i 0.367020π0.367020\pi
88 −11.4600 −0.506467
99 0 0
1010 −17.8860 −0.565605
1111 −70.8260 −1.94135 −0.970674 0.240399i 0.922722π-0.922722\pi
−0.970674 + 0.240399i 0.922722π0.922722\pi
1212 0 0
1313 62.2117 1.32726 0.663632 0.748059i 0.269014π-0.269014\pi
0.663632 + 0.748059i 0.269014π0.269014\pi
1414 53.7587 1.02626
1515 0 0
1616 −79.3658 −1.24009
1717 67.1848 0.958513 0.479256 0.877675i 0.340906π-0.340906\pi
0.479256 + 0.877675i 0.340906π0.340906\pi
1818 0 0
1919 118.988 1.43673 0.718364 0.695667i 0.244891π-0.244891\pi
0.718364 + 0.695667i 0.244891π0.244891\pi
2020 −23.9818 −0.268125
2121 0 0
2222 −253.359 −2.45528
2323 −72.5383 −0.657621 −0.328810 0.944396i 0.606648π-0.606648\pi
−0.328810 + 0.944396i 0.606648π0.606648\pi
2424 0 0
2525 25.0000 0.200000
2626 222.544 1.67863
2727 0 0
2828 72.0804 0.486497
2929 −29.0000 −0.185695
3030 0 0
3131 −180.227 −1.04418 −0.522092 0.852889i 0.674848π-0.674848\pi
−0.522092 + 0.852889i 0.674848π0.674848\pi
3232 −192.227 −1.06191
3333 0 0
3434 240.334 1.21226
3535 −75.1407 −0.362888
3636 0 0
3737 −47.8439 −0.212581 −0.106290 0.994335i 0.533897π-0.533897\pi
−0.106290 + 0.994335i 0.533897π0.533897\pi
3838 425.646 1.81708
3939 0 0
4040 57.3002 0.226499
4141 −371.956 −1.41682 −0.708411 0.705800i 0.750588π-0.750588\pi
−0.708411 + 0.705800i 0.750588π0.750588\pi
4242 0 0
4343 −409.069 −1.45075 −0.725377 0.688352i 0.758334π-0.758334\pi
−0.725377 + 0.688352i 0.758334π0.758334\pi
4444 −339.707 −1.16393
4545 0 0
4646 −259.484 −0.831714
4747 −125.891 −0.390705 −0.195353 0.980733i 0.562585π-0.562585\pi
−0.195353 + 0.980733i 0.562585π0.562585\pi
4848 0 0
4949 −117.155 −0.341560
5050 89.4300 0.252946
5151 0 0
5252 298.390 0.795755
5353 215.764 0.559198 0.279599 0.960117i 0.409798π-0.409798\pi
0.279599 + 0.960117i 0.409798π0.409798\pi
5454 0 0
5555 354.130 0.868197
5656 −172.223 −0.410969
5757 0 0
5858 −103.739 −0.234855
5959 −356.919 −0.787575 −0.393788 0.919201i 0.628835π-0.628835\pi
−0.393788 + 0.919201i 0.628835π0.628835\pi
6060 0 0
6161 −466.115 −0.978358 −0.489179 0.872183i 0.662704π-0.662704\pi
−0.489179 + 0.872183i 0.662704π0.662704\pi
6262 −644.707 −1.32061
6363 0 0
6464 −52.7086 −0.102946
6565 −311.059 −0.593570
6666 0 0
6767 −578.359 −1.05459 −0.527297 0.849681i 0.676794π-0.676794\pi
−0.527297 + 0.849681i 0.676794π0.676794\pi
6868 322.243 0.574672
6969 0 0
7070 −268.793 −0.458956
7171 −870.924 −1.45577 −0.727885 0.685699i 0.759497π-0.759497\pi
−0.727885 + 0.685699i 0.759497π0.759497\pi
7272 0 0
7373 411.904 0.660407 0.330204 0.943910i 0.392883π-0.392883\pi
0.330204 + 0.943910i 0.392883π0.392883\pi
7474 −171.147 −0.268857
7575 0 0
7676 570.712 0.861384
7777 −1064.38 −1.57529
7878 0 0
7979 1120.23 1.59538 0.797692 0.603065i 0.206054π-0.206054\pi
0.797692 + 0.603065i 0.206054π0.206054\pi
8080 396.829 0.554585
8181 0 0
8282 −1330.56 −1.79190
8383 −1079.28 −1.42730 −0.713652 0.700501i 0.752960π-0.752960\pi
−0.713652 + 0.700501i 0.752960π0.752960\pi
8484 0 0
8585 −335.924 −0.428660
8686 −1463.32 −1.83481
8787 0 0
8888 811.668 0.983229
8989 −388.993 −0.463294 −0.231647 0.972800i 0.574411π-0.574411\pi
−0.231647 + 0.972800i 0.574411π0.574411\pi
9090 0 0
9191 934.926 1.07700
9292 −347.920 −0.394274
9393 0 0
9494 −450.339 −0.494137
9595 −594.942 −0.642524
9696 0 0
9797 −1528.82 −1.60029 −0.800147 0.599803i 0.795245π-0.795245\pi
−0.800147 + 0.599803i 0.795245π0.795245\pi
9898 −419.088 −0.431982
9999 0 0
100100 119.909 0.119909
101101 1425.50 1.40439 0.702193 0.711987i 0.252204π-0.252204\pi
0.702193 + 0.711987i 0.252204π0.252204\pi
102102 0 0
103103 −1595.68 −1.52648 −0.763240 0.646116i 0.776392π-0.776392\pi
−0.763240 + 0.646116i 0.776392π0.776392\pi
104104 −712.949 −0.672215
105105 0 0
106106 771.832 0.707236
107107 155.104 0.140135 0.0700675 0.997542i 0.477679π-0.477679\pi
0.0700675 + 0.997542i 0.477679π0.477679\pi
108108 0 0
109109 1212.23 1.06524 0.532618 0.846356i 0.321208π-0.321208\pi
0.532618 + 0.846356i 0.321208π0.321208\pi
110110 1266.79 1.09804
111111 0 0
112112 −1192.72 −1.00626
113113 1152.01 0.959043 0.479521 0.877530i 0.340810π-0.340810\pi
0.479521 + 0.877530i 0.340810π0.340810\pi
114114 0 0
115115 362.691 0.294097
116116 −139.095 −0.111333
117117 0 0
118118 −1276.77 −0.996072
119119 1009.66 0.777778
120120 0 0
121121 3685.32 2.76883
122122 −1667.39 −1.23736
123123 0 0
124124 −864.434 −0.626036
125125 −125.000 −0.0894427
126126 0 0
127127 398.743 0.278604 0.139302 0.990250i 0.455514π-0.455514\pi
0.139302 + 0.990250i 0.455514π0.455514\pi
128128 1349.27 0.931715
129129 0 0
130130 −1112.72 −0.750707
131131 385.241 0.256937 0.128468 0.991714i 0.458994π-0.458994\pi
0.128468 + 0.991714i 0.458994π0.458994\pi
132132 0 0
133133 1788.17 1.16582
134134 −2068.90 −1.33378
135135 0 0
136136 −769.941 −0.485455
137137 351.877 0.219437 0.109719 0.993963i 0.465005π-0.465005\pi
0.109719 + 0.993963i 0.465005π0.465005\pi
138138 0 0
139139 1138.48 0.694711 0.347355 0.937734i 0.387080π-0.387080\pi
0.347355 + 0.937734i 0.387080π0.387080\pi
140140 −360.402 −0.217568
141141 0 0
142142 −3115.47 −1.84116
143143 −4406.21 −2.57668
144144 0 0
145145 145.000 0.0830455
146146 1473.46 0.835238
147147 0 0
148148 −229.477 −0.127452
149149 −1200.59 −0.660107 −0.330053 0.943962i 0.607067π-0.607067\pi
−0.330053 + 0.943962i 0.607067π0.607067\pi
150150 0 0
151151 −1539.35 −0.829605 −0.414802 0.909911i 0.636149π-0.636149\pi
−0.414802 + 0.909911i 0.636149π0.636149\pi
152152 −1363.61 −0.727655
153153 0 0
154154 −3807.51 −1.99232
155155 901.134 0.466973
156156 0 0
157157 223.134 0.113427 0.0567136 0.998390i 0.481938π-0.481938\pi
0.0567136 + 0.998390i 0.481938π0.481938\pi
158158 4007.28 2.01773
159159 0 0
160160 961.136 0.474903
161161 −1090.11 −0.533622
162162 0 0
163163 −3114.71 −1.49671 −0.748353 0.663301i 0.769155π-0.769155\pi
−0.748353 + 0.663301i 0.769155π0.769155\pi
164164 −1784.04 −0.849450
165165 0 0
166166 −3860.79 −1.80516
167167 1720.78 0.797351 0.398676 0.917092i 0.369470π-0.369470\pi
0.398676 + 0.917092i 0.369470π0.369470\pi
168168 0 0
169169 1673.30 0.761629
170170 −1201.67 −0.542140
171171 0 0
172172 −1962.04 −0.869793
173173 −2438.70 −1.07174 −0.535870 0.844301i 0.680016π-0.680016\pi
−0.535870 + 0.844301i 0.680016π0.680016\pi
174174 0 0
175175 375.703 0.162289
176176 5621.16 2.40745
177177 0 0
178178 −1391.50 −0.585942
179179 2248.00 0.938676 0.469338 0.883018i 0.344493π-0.344493\pi
0.469338 + 0.883018i 0.344493π0.344493\pi
180180 0 0
181181 −2357.13 −0.967977 −0.483989 0.875074i 0.660812π-0.660812\pi
−0.483989 + 0.875074i 0.660812π0.660812\pi
182182 3344.42 1.36211
183183 0 0
184184 831.292 0.333063
185185 239.219 0.0950689
186186 0 0
187187 −4758.43 −1.86081
188188 −603.821 −0.234246
189189 0 0
190190 −2128.23 −0.812621
191191 −1922.56 −0.728331 −0.364166 0.931334i 0.618646π-0.618646\pi
−0.364166 + 0.931334i 0.618646π0.618646\pi
192192 0 0
193193 1840.68 0.686504 0.343252 0.939243i 0.388472π-0.388472\pi
0.343252 + 0.939243i 0.388472π0.388472\pi
194194 −5468.91 −2.02394
195195 0 0
196196 −561.919 −0.204781
197197 2712.79 0.981109 0.490555 0.871410i 0.336794π-0.336794\pi
0.490555 + 0.871410i 0.336794π0.336794\pi
198198 0 0
199199 224.631 0.0800185 0.0400093 0.999199i 0.487261π-0.487261\pi
0.0400093 + 0.999199i 0.487261π0.487261\pi
200200 −286.501 −0.101293
201201 0 0
202202 5099.31 1.77617
203203 −435.816 −0.150681
204204 0 0
205205 1859.78 0.633622
206206 −5708.08 −1.93059
207207 0 0
208208 −4937.48 −1.64593
209209 −8427.48 −2.78919
210210 0 0
211211 −4160.10 −1.35731 −0.678656 0.734456i 0.737437π-0.737437\pi
−0.678656 + 0.734456i 0.737437π0.737437\pi
212212 1034.88 0.335265
213213 0 0
214214 554.837 0.177233
215215 2045.34 0.648797
216216 0 0
217217 −2708.47 −0.847295
218218 4336.40 1.34724
219219 0 0
220220 1698.54 0.520524
221221 4179.68 1.27220
222222 0 0
223223 −1746.41 −0.524432 −0.262216 0.965009i 0.584453π-0.584453\pi
−0.262216 + 0.965009i 0.584453π0.584453\pi
224224 −2888.81 −0.861683
225225 0 0
226226 4120.97 1.21293
227227 −129.508 −0.0378666 −0.0189333 0.999821i 0.506027π-0.506027\pi
−0.0189333 + 0.999821i 0.506027π0.506027\pi
228228 0 0
229229 −682.166 −0.196851 −0.0984253 0.995144i 0.531381π-0.531381\pi
−0.0984253 + 0.995144i 0.531381π0.531381\pi
230230 1297.42 0.371954
231231 0 0
232232 332.341 0.0940486
233233 −1731.11 −0.486732 −0.243366 0.969935i 0.578252π-0.578252\pi
−0.243366 + 0.969935i 0.578252π0.578252\pi
234234 0 0
235235 629.457 0.174729
236236 −1711.92 −0.472188
237237 0 0
238238 3611.77 0.983681
239239 −3308.38 −0.895402 −0.447701 0.894183i 0.647757π-0.647757\pi
−0.447701 + 0.894183i 0.647757π0.647757\pi
240240 0 0
241241 3586.39 0.958588 0.479294 0.877654i 0.340893π-0.340893\pi
0.479294 + 0.877654i 0.340893π0.340893\pi
242242 13183.1 3.50183
243243 0 0
244244 −2235.66 −0.586571
245245 585.776 0.152750
246246 0 0
247247 7402.48 1.90692
248248 2065.41 0.528844
249249 0 0
250250 −447.150 −0.113121
251251 2956.22 0.743406 0.371703 0.928352i 0.378774π-0.378774\pi
0.371703 + 0.928352i 0.378774π0.378774\pi
252252 0 0
253253 5137.59 1.27667
254254 1426.39 0.352360
255255 0 0
256256 5248.27 1.28132
257257 −2258.12 −0.548084 −0.274042 0.961718i 0.588361π-0.588361\pi
−0.274042 + 0.961718i 0.588361π0.588361\pi
258258 0 0
259259 −719.004 −0.172497
260260 −1491.95 −0.355873
261261 0 0
262262 1378.09 0.324956
263263 −2908.67 −0.681963 −0.340981 0.940070i 0.610759π-0.610759\pi
−0.340981 + 0.940070i 0.610759π0.610759\pi
264264 0 0
265265 −1078.82 −0.250081
266266 6396.66 1.47445
267267 0 0
268268 −2774.02 −0.632277
269269 297.910 0.0675238 0.0337619 0.999430i 0.489251π-0.489251\pi
0.0337619 + 0.999430i 0.489251π0.489251\pi
270270 0 0
271271 6993.04 1.56752 0.783758 0.621067i 0.213300π-0.213300\pi
0.783758 + 0.621067i 0.213300π0.213300\pi
272272 −5332.18 −1.18864
273273 0 0
274274 1258.73 0.277529
275275 −1770.65 −0.388270
276276 0 0
277277 5701.84 1.23679 0.618394 0.785868i 0.287784π-0.287784\pi
0.618394 + 0.785868i 0.287784π0.287784\pi
278278 4072.58 0.878622
279279 0 0
280280 861.115 0.183791
281281 1216.34 0.258223 0.129112 0.991630i 0.458787π-0.458787\pi
0.129112 + 0.991630i 0.458787π0.458787\pi
282282 0 0
283283 4096.17 0.860396 0.430198 0.902735i 0.358444π-0.358444\pi
0.430198 + 0.902735i 0.358444π0.358444\pi
284284 −4177.27 −0.872801
285285 0 0
286286 −15761.9 −3.25881
287287 −5589.80 −1.14967
288288 0 0
289289 −399.197 −0.0812532
290290 518.694 0.105030
291291 0 0
292292 1975.64 0.395944
293293 −5854.29 −1.16727 −0.583637 0.812015i 0.698371π-0.698371\pi
−0.583637 + 0.812015i 0.698371π0.698371\pi
294294 0 0
295295 1784.60 0.352214
296296 548.292 0.107665
297297 0 0
298298 −4294.74 −0.834858
299299 −4512.73 −0.872836
300300 0 0
301301 −6147.54 −1.17720
302302 −5506.56 −1.04923
303303 0 0
304304 −9443.62 −1.78167
305305 2330.57 0.437535
306306 0 0
307307 −2748.38 −0.510940 −0.255470 0.966817i 0.582230π-0.582230\pi
−0.255470 + 0.966817i 0.582230π0.582230\pi
308308 −5105.17 −0.944461
309309 0 0
310310 3223.54 0.590595
311311 10289.0 1.87600 0.938000 0.346634i 0.112675π-0.112675\pi
0.938000 + 0.346634i 0.112675π0.112675\pi
312312 0 0
313313 8540.93 1.54237 0.771185 0.636611i 0.219664π-0.219664\pi
0.771185 + 0.636611i 0.219664π0.219664\pi
314314 798.196 0.143455
315315 0 0
316316 5373.02 0.956506
317317 131.153 0.0232375 0.0116187 0.999933i 0.496302π-0.496302\pi
0.0116187 + 0.999933i 0.496302π0.496302\pi
318318 0 0
319319 2053.95 0.360499
320320 263.543 0.0460391
321321 0 0
322322 −3899.56 −0.674888
323323 7994.22 1.37712
324324 0 0
325325 1555.29 0.265453
326326 −11142.0 −1.89293
327327 0 0
328328 4262.63 0.717574
329329 −1891.91 −0.317035
330330 0 0
331331 −7274.79 −1.20803 −0.604016 0.796972i 0.706434π-0.706434\pi
−0.604016 + 0.796972i 0.706434π0.706434\pi
332332 −5176.61 −0.855734
333333 0 0
334334 6155.56 1.00844
335335 2891.79 0.471628
336336 0 0
337337 4663.56 0.753830 0.376915 0.926248i 0.376985π-0.376985\pi
0.376915 + 0.926248i 0.376985π0.376985\pi
338338 5985.72 0.963256
339339 0 0
340340 −1611.22 −0.257001
341341 12764.7 2.02712
342342 0 0
343343 −6915.27 −1.08860
344344 4687.94 0.734759
345345 0 0
346346 −8723.72 −1.35546
347347 −6050.81 −0.936093 −0.468046 0.883704i 0.655042π-0.655042\pi
−0.468046 + 0.883704i 0.655042π0.655042\pi
348348 0 0
349349 12824.0 1.96691 0.983455 0.181152i 0.0579825π-0.0579825\pi
0.983455 + 0.181152i 0.0579825π0.0579825\pi
350350 1343.97 0.205251
351351 0 0
352352 13614.7 2.06155
353353 −12514.5 −1.88691 −0.943457 0.331494i 0.892447π-0.892447\pi
−0.943457 + 0.331494i 0.892447π0.892447\pi
354354 0 0
355355 4354.62 0.651040
356356 −1865.75 −0.277766
357357 0 0
358358 8041.53 1.18717
359359 −3394.70 −0.499068 −0.249534 0.968366i 0.580277π-0.580277\pi
−0.249534 + 0.968366i 0.580277π0.580277\pi
360360 0 0
361361 7299.26 1.06419
362362 −8431.92 −1.22423
363363 0 0
364364 4484.25 0.645710
365365 −2059.52 −0.295343
366366 0 0
367367 −9991.93 −1.42118 −0.710592 0.703604i 0.751573π-0.751573\pi
−0.710592 + 0.703604i 0.751573π0.751573\pi
368368 5757.06 0.815509
369369 0 0
370370 855.735 0.120237
371371 3242.54 0.453758
372372 0 0
373373 7219.40 1.00216 0.501081 0.865400i 0.332936π-0.332936\pi
0.501081 + 0.865400i 0.332936π0.332936\pi
374374 −17021.9 −2.35342
375375 0 0
376376 1442.72 0.197879
377377 −1804.14 −0.246467
378378 0 0
379379 10797.8 1.46345 0.731724 0.681601i 0.238716π-0.238716\pi
0.731724 + 0.681601i 0.238716π0.238716\pi
380380 −2853.56 −0.385223
381381 0 0
382382 −6877.37 −0.921144
383383 3396.75 0.453174 0.226587 0.973991i 0.427243π-0.427243\pi
0.226587 + 0.973991i 0.427243π0.427243\pi
384384 0 0
385385 5321.91 0.704493
386386 6584.49 0.868243
387387 0 0
388388 −7332.80 −0.959450
389389 4927.07 0.642192 0.321096 0.947047i 0.395949π-0.395949\pi
0.321096 + 0.947047i 0.395949π0.395949\pi
390390 0 0
391391 −4873.47 −0.630338
392392 1342.60 0.172989
393393 0 0
394394 9704.21 1.24084
395395 −5601.13 −0.713477
396396 0 0
397397 −7777.55 −0.983234 −0.491617 0.870812i 0.663594π-0.663594\pi
−0.491617 + 0.870812i 0.663594π0.663594\pi
398398 803.551 0.101202
399399 0 0
400400 −1984.14 −0.248018
401401 −6058.22 −0.754446 −0.377223 0.926122i 0.623121π-0.623121\pi
−0.377223 + 0.926122i 0.623121π0.623121\pi
402402 0 0
403403 −11212.2 −1.38591
404404 6837.24 0.841994
405405 0 0
406406 −1559.00 −0.190571
407407 3388.59 0.412693
408408 0 0
409409 −15078.2 −1.82291 −0.911454 0.411403i 0.865039π-0.865039\pi
−0.911454 + 0.411403i 0.865039π0.865039\pi
410410 6652.80 0.801362
411411 0 0
412412 −7653.48 −0.915194
413413 −5363.83 −0.639073
414414 0 0
415415 5396.39 0.638309
416416 −11958.8 −1.40944
417417 0 0
418418 −30146.8 −3.52758
419419 −5698.22 −0.664383 −0.332192 0.943212i 0.607788π-0.607788\pi
−0.332192 + 0.943212i 0.607788π0.607788\pi
420420 0 0
421421 846.838 0.0980341 0.0490171 0.998798i 0.484391π-0.484391\pi
0.0490171 + 0.998798i 0.484391π0.484391\pi
422422 −14881.5 −1.71664
423423 0 0
424424 −2472.67 −0.283215
425425 1679.62 0.191703
426426 0 0
427427 −7004.83 −0.793882
428428 743.934 0.0840173
429429 0 0
430430 7316.61 0.820554
431431 7518.27 0.840237 0.420119 0.907469i 0.361988π-0.361988\pi
0.420119 + 0.907469i 0.361988π0.361988\pi
432432 0 0
433433 12686.0 1.40797 0.703987 0.710213i 0.251401π-0.251401\pi
0.703987 + 0.710213i 0.251401π0.251401\pi
434434 −9688.75 −1.07160
435435 0 0
436436 5814.31 0.638658
437437 −8631.22 −0.944822
438438 0 0
439439 10530.4 1.14485 0.572424 0.819958i 0.306003π-0.306003\pi
0.572424 + 0.819958i 0.306003π0.306003\pi
440440 −4058.34 −0.439713
441441 0 0
442442 14951.6 1.60899
443443 5199.17 0.557608 0.278804 0.960348i 0.410062π-0.410062\pi
0.278804 + 0.960348i 0.410062π0.410062\pi
444444 0 0
445445 1944.96 0.207191
446446 −6247.27 −0.663266
447447 0 0
448448 −792.112 −0.0835352
449449 11836.7 1.24412 0.622058 0.782971i 0.286297π-0.286297\pi
0.622058 + 0.782971i 0.286297π0.286297\pi
450450 0 0
451451 26344.1 2.75055
452452 5525.46 0.574990
453453 0 0
454454 −463.274 −0.0478911
455455 −4674.63 −0.481648
456456 0 0
457457 404.451 0.0413992 0.0206996 0.999786i 0.493411π-0.493411\pi
0.0206996 + 0.999786i 0.493411π0.493411\pi
458458 −2440.24 −0.248963
459459 0 0
460460 1739.60 0.176325
461461 −7072.59 −0.714541 −0.357270 0.934001i 0.616293π-0.616293\pi
−0.357270 + 0.934001i 0.616293π0.616293\pi
462462 0 0
463463 −6500.22 −0.652464 −0.326232 0.945290i 0.605779π-0.605779\pi
−0.326232 + 0.945290i 0.605779π0.605779\pi
464464 2301.61 0.230279
465465 0 0
466466 −6192.51 −0.615585
467467 8850.61 0.876997 0.438498 0.898732i 0.355511π-0.355511\pi
0.438498 + 0.898732i 0.355511π0.355511\pi
468468 0 0
469469 −8691.65 −0.855742
470470 2251.69 0.220985
471471 0 0
472472 4090.31 0.398881
473473 28972.7 2.81642
474474 0 0
475475 2974.71 0.287346
476476 4842.71 0.466314
477477 0 0
478478 −11834.7 −1.13244
479479 8582.91 0.818712 0.409356 0.912375i 0.365753π-0.365753\pi
0.409356 + 0.912375i 0.365753π0.365753\pi
480480 0 0
481481 −2976.45 −0.282150
482482 12829.2 1.21236
483483 0 0
484484 17676.1 1.66004
485485 7644.12 0.715674
486486 0 0
487487 −2823.62 −0.262732 −0.131366 0.991334i 0.541936π-0.541936\pi
−0.131366 + 0.991334i 0.541936π0.541936\pi
488488 5341.69 0.495506
489489 0 0
490490 2095.44 0.193188
491491 13116.2 1.20555 0.602776 0.797911i 0.294061π-0.294061\pi
0.602776 + 0.797911i 0.294061π0.294061\pi
492492 0 0
493493 −1948.36 −0.177991
494494 26480.2 2.41174
495495 0 0
496496 14303.8 1.29488
497497 −13088.4 −1.18127
498498 0 0
499499 −16495.4 −1.47983 −0.739916 0.672699i 0.765135π-0.765135\pi
−0.739916 + 0.672699i 0.765135π0.765135\pi
500500 −599.546 −0.0536250
501501 0 0
502502 10575.0 0.940209
503503 16677.3 1.47834 0.739169 0.673520i 0.235219π-0.235219\pi
0.739169 + 0.673520i 0.235219π0.235219\pi
504504 0 0
505505 −7127.52 −0.628060
506506 18378.2 1.61465
507507 0 0
508508 1912.52 0.167036
509509 −9386.35 −0.817373 −0.408686 0.912675i 0.634013π-0.634013\pi
−0.408686 + 0.912675i 0.634013π0.634013\pi
510510 0 0
511511 6190.15 0.535883
512512 7979.98 0.688806
513513 0 0
514514 −8077.75 −0.693180
515515 7978.42 0.682662
516516 0 0
517517 8916.37 0.758495
518518 −2572.02 −0.218162
519519 0 0
520520 3564.74 0.300624
521521 16530.2 1.39002 0.695009 0.719001i 0.255400π-0.255400\pi
0.695009 + 0.719001i 0.255400π0.255400\pi
522522 0 0
523523 −18295.9 −1.52968 −0.764842 0.644217i 0.777183π-0.777183\pi
−0.764842 + 0.644217i 0.777183π0.777183\pi
524524 1847.76 0.154045
525525 0 0
526526 −10404.9 −0.862500
527527 −12108.5 −1.00086
528528 0 0
529529 −6905.20 −0.567535
530530 −3859.16 −0.316285
531531 0 0
532532 8576.74 0.698964
533533 −23140.0 −1.88050
534534 0 0
535535 −775.518 −0.0626703
536536 6628.01 0.534117
537537 0 0
538538 1065.68 0.0853994
539539 8297.63 0.663088
540540 0 0
541541 −949.695 −0.0754724 −0.0377362 0.999288i 0.512015π-0.512015\pi
−0.0377362 + 0.999288i 0.512015π0.512015\pi
542542 25015.5 1.98249
543543 0 0
544544 −12914.7 −1.01786
545545 −6061.16 −0.476388
546546 0 0
547547 18017.4 1.40835 0.704177 0.710024i 0.251316π-0.251316\pi
0.704177 + 0.710024i 0.251316π0.251316\pi
548548 1687.73 0.131563
549549 0 0
550550 −6333.97 −0.491057
551551 −3450.67 −0.266794
552552 0 0
553553 16834.9 1.29456
554554 20396.6 1.56420
555555 0 0
556556 5460.58 0.416511
557557 11387.6 0.866263 0.433131 0.901331i 0.357409π-0.357409\pi
0.433131 + 0.901331i 0.357409π0.357409\pi
558558 0 0
559559 −25448.9 −1.92553
560560 5963.60 0.450014
561561 0 0
562562 4351.09 0.326583
563563 277.822 0.0207971 0.0103986 0.999946i 0.496690π-0.496690\pi
0.0103986 + 0.999946i 0.496690π0.496690\pi
564564 0 0
565565 −5760.04 −0.428897
566566 14652.8 1.08817
567567 0 0
568568 9980.82 0.737299
569569 −15475.5 −1.14019 −0.570093 0.821580i 0.693093π-0.693093\pi
−0.570093 + 0.821580i 0.693093π0.693093\pi
570570 0 0
571571 −3245.82 −0.237887 −0.118944 0.992901i 0.537951π-0.537951\pi
−0.118944 + 0.992901i 0.537951π0.537951\pi
572572 −21133.8 −1.54484
573573 0 0
574574 −19995.8 −1.45402
575575 −1813.46 −0.131524
576576 0 0
577577 −23087.9 −1.66579 −0.832895 0.553430i 0.813318π-0.813318\pi
−0.832895 + 0.553430i 0.813318π0.813318\pi
578578 −1428.01 −0.102764
579579 0 0
580580 695.473 0.0497896
581581 −16219.5 −1.15818
582582 0 0
583583 −15281.7 −1.08560
584584 −4720.44 −0.334474
585585 0 0
586586 −20942.0 −1.47629
587587 −13526.1 −0.951075 −0.475537 0.879696i 0.657746π-0.657746\pi
−0.475537 + 0.879696i 0.657746π0.657746\pi
588588 0 0
589589 −21444.9 −1.50021
590590 6383.86 0.445457
591591 0 0
592592 3797.17 0.263619
593593 −15964.6 −1.10554 −0.552770 0.833334i 0.686429π-0.686429\pi
−0.552770 + 0.833334i 0.686429π0.686429\pi
594594 0 0
595595 −5048.31 −0.347833
596596 −5758.46 −0.395764
597597 0 0
598598 −16142.9 −1.10390
599599 −22.9584 −0.00156603 −0.000783017 1.00000i 0.500249π-0.500249\pi
−0.000783017 1.00000i 0.500249π0.500249\pi
600600 0 0
601601 −7471.32 −0.507090 −0.253545 0.967324i 0.581597π-0.581597\pi
−0.253545 + 0.967324i 0.581597π0.581597\pi
602602 −21991.0 −1.48885
603603 0 0
604604 −7383.28 −0.497386
605605 −18426.6 −1.23826
606606 0 0
607607 23036.9 1.54042 0.770212 0.637788i 0.220151π-0.220151\pi
0.770212 + 0.637788i 0.220151π0.220151\pi
608608 −22872.8 −1.52568
609609 0 0
610610 8336.93 0.553365
611611 −7831.91 −0.518569
612612 0 0
613613 −20040.0 −1.32040 −0.660202 0.751088i 0.729530π-0.729530\pi
−0.660202 + 0.751088i 0.729530π0.729530\pi
614614 −9831.52 −0.646202
615615 0 0
616616 12197.9 0.797834
617617 27464.4 1.79202 0.896010 0.444035i 0.146453π-0.146453\pi
0.896010 + 0.444035i 0.146453π0.146453\pi
618618 0 0
619619 3585.29 0.232803 0.116402 0.993202i 0.462864π-0.462864\pi
0.116402 + 0.993202i 0.462864π0.462864\pi
620620 4322.17 0.279972
621621 0 0
622622 36805.9 2.37264
623623 −5845.83 −0.375936
624624 0 0
625625 625.000 0.0400000
626626 30552.6 1.95069
627627 0 0
628628 1070.23 0.0680048
629629 −3214.38 −0.203761
630630 0 0
631631 −27135.3 −1.71195 −0.855973 0.517020i 0.827041π-0.827041\pi
−0.855973 + 0.517020i 0.827041π0.827041\pi
632632 −12837.8 −0.808009
633633 0 0
634634 469.160 0.0293892
635635 −1993.72 −0.124596
636636 0 0
637637 −7288.43 −0.453341
638638 7347.40 0.455935
639639 0 0
640640 −6746.34 −0.416676
641641 −23443.5 −1.44456 −0.722278 0.691603i 0.756905π-0.756905\pi
−0.722278 + 0.691603i 0.756905π0.756905\pi
642642 0 0
643643 −9339.29 −0.572792 −0.286396 0.958111i 0.592457π-0.592457\pi
−0.286396 + 0.958111i 0.592457π0.592457\pi
644644 −5228.59 −0.319931
645645 0 0
646646 28596.9 1.74169
647647 −1103.56 −0.0670562 −0.0335281 0.999438i 0.510674π-0.510674\pi
−0.0335281 + 0.999438i 0.510674π0.510674\pi
648648 0 0
649649 25279.2 1.52896
650650 5563.60 0.335726
651651 0 0
652652 −14939.3 −0.897344
653653 3127.51 0.187425 0.0937127 0.995599i 0.470126π-0.470126\pi
0.0937127 + 0.995599i 0.470126π0.470126\pi
654654 0 0
655655 −1926.21 −0.114906
656656 29520.6 1.75699
657657 0 0
658658 −6767.75 −0.400964
659659 −16004.5 −0.946050 −0.473025 0.881049i 0.656838π-0.656838\pi
−0.473025 + 0.881049i 0.656838π0.656838\pi
660660 0 0
661661 10807.3 0.635939 0.317970 0.948101i 0.396999π-0.396999\pi
0.317970 + 0.948101i 0.396999π0.396999\pi
662662 −26023.4 −1.52784
663663 0 0
664664 12368.6 0.722882
665665 −8940.87 −0.521372
666666 0 0
667667 2103.61 0.122117
668668 8253.47 0.478049
669669 0 0
670670 10344.5 0.596483
671671 33013.0 1.89933
672672 0 0
673673 23835.6 1.36522 0.682612 0.730781i 0.260844π-0.260844\pi
0.682612 + 0.730781i 0.260844π0.260844\pi
674674 16682.5 0.953392
675675 0 0
676676 8025.75 0.456631
677677 −5081.10 −0.288453 −0.144227 0.989545i 0.546069π-0.546069\pi
−0.144227 + 0.989545i 0.546069π0.546069\pi
678678 0 0
679679 −22975.4 −1.29855
680680 3849.70 0.217102
681681 0 0
682682 45662.0 2.56377
683683 −7815.19 −0.437833 −0.218917 0.975744i 0.570252π-0.570252\pi
−0.218917 + 0.975744i 0.570252π0.570252\pi
684684 0 0
685685 −1759.38 −0.0981352
686686 −24737.3 −1.37679
687687 0 0
688688 32466.1 1.79907
689689 13423.1 0.742204
690690 0 0
691691 8815.96 0.485347 0.242674 0.970108i 0.421976π-0.421976\pi
0.242674 + 0.970108i 0.421976π0.421976\pi
692692 −11696.9 −0.642557
693693 0 0
694694 −21644.9 −1.18391
695695 −5692.41 −0.310684
696696 0 0
697697 −24989.8 −1.35804
698698 45873.9 2.48761
699699 0 0
700700 1802.01 0.0972994
701701 4100.40 0.220927 0.110464 0.993880i 0.464766π-0.464766\pi
0.110464 + 0.993880i 0.464766π0.464766\pi
702702 0 0
703703 −5692.87 −0.305420
704704 3733.14 0.199855
705705 0 0
706706 −44767.0 −2.38644
707707 21422.7 1.13958
708708 0 0
709709 −17803.3 −0.943042 −0.471521 0.881855i 0.656295π-0.656295\pi
−0.471521 + 0.881855i 0.656295π0.656295\pi
710710 15577.4 0.823391
711711 0 0
712712 4457.87 0.234643
713713 13073.3 0.686677
714714 0 0
715715 22031.0 1.15233
716716 10782.2 0.562780
717717 0 0
718718 −12143.5 −0.631187
719719 4213.37 0.218543 0.109271 0.994012i 0.465148π-0.465148\pi
0.109271 + 0.994012i 0.465148π0.465148\pi
720720 0 0
721721 −23980.1 −1.23865
722722 26110.9 1.34591
723723 0 0
724724 −11305.6 −0.580347
725725 −725.000 −0.0371391
726726 0 0
727727 29559.3 1.50797 0.753984 0.656893i 0.228130π-0.228130\pi
0.753984 + 0.656893i 0.228130π0.228130\pi
728728 −10714.3 −0.545464
729729 0 0
730730 −7367.32 −0.373530
731731 −27483.2 −1.39057
732732 0 0
733733 23312.9 1.17474 0.587369 0.809319i 0.300164π-0.300164\pi
0.587369 + 0.809319i 0.300164π0.300164\pi
734734 −35743.1 −1.79742
735735 0 0
736736 13943.8 0.698337
737737 40962.8 2.04733
738738 0 0
739739 27985.2 1.39303 0.696517 0.717540i 0.254732π-0.254732\pi
0.696517 + 0.717540i 0.254732π0.254732\pi
740740 1147.38 0.0569982
741741 0 0
742742 11599.2 0.573881
743743 2542.48 0.125538 0.0627690 0.998028i 0.480007π-0.480007\pi
0.0627690 + 0.998028i 0.480007π0.480007\pi
744744 0 0
745745 6002.94 0.295209
746746 25825.3 1.26747
747747 0 0
748748 −22823.2 −1.11564
749749 2330.92 0.113712
750750 0 0
751751 33600.2 1.63261 0.816305 0.577622i 0.196019π-0.196019\pi
0.816305 + 0.577622i 0.196019π0.196019\pi
752752 9991.46 0.484510
753753 0 0
754754 −6453.77 −0.311714
755755 7696.74 0.371011
756756 0 0
757757 −34022.4 −1.63351 −0.816754 0.576986i 0.804229π-0.804229\pi
−0.816754 + 0.576986i 0.804229π0.804229\pi
758758 38626.0 1.85087
759759 0 0
760760 6818.06 0.325417
761761 −15032.8 −0.716084 −0.358042 0.933705i 0.616556π-0.616556\pi
−0.358042 + 0.933705i 0.616556π0.616556\pi
762762 0 0
763763 18217.6 0.864378
764764 −9221.28 −0.436668
765765 0 0
766766 12150.8 0.573144
767767 −22204.6 −1.04532
768768 0 0
769769 −24042.9 −1.12745 −0.563725 0.825963i 0.690632π-0.690632\pi
−0.563725 + 0.825963i 0.690632π0.690632\pi
770770 19037.5 0.890994
771771 0 0
772772 8828.59 0.411590
773773 −17441.1 −0.811530 −0.405765 0.913977i 0.632995π-0.632995\pi
−0.405765 + 0.913977i 0.632995π0.632995\pi
774774 0 0
775775 −4505.67 −0.208837
776776 17520.4 0.810496
777777 0 0
778778 17625.1 0.812200
779779 −44258.5 −2.03559
780780 0 0
781781 61684.0 2.82616
782782 −17433.4 −0.797208
783783 0 0
784784 9298.12 0.423566
785785 −1115.67 −0.0507262
786786 0 0
787787 −38211.9 −1.73076 −0.865379 0.501119i 0.832922π-0.832922\pi
−0.865379 + 0.501119i 0.832922π0.832922\pi
788788 13011.6 0.588220
789789 0 0
790790 −20036.4 −0.902357
791791 17312.5 0.778208
792792 0 0
793793 −28997.8 −1.29854
794794 −27821.8 −1.24353
795795 0 0
796796 1077.41 0.0479748
797797 −18149.9 −0.806655 −0.403327 0.915056i 0.632146π-0.632146\pi
−0.403327 + 0.915056i 0.632146π0.632146\pi
798798 0 0
799799 −8457.99 −0.374496
800800 −4805.68 −0.212383
801801 0 0
802802 −21671.5 −0.954172
803803 −29173.5 −1.28208
804804 0 0
805805 5450.57 0.238643
806806 −40108.3 −1.75280
807807 0 0
808808 −16336.3 −0.711275
809809 339.522 0.0147552 0.00737759 0.999973i 0.497652π-0.497652\pi
0.00737759 + 0.999973i 0.497652π0.497652\pi
810810 0 0
811811 26295.4 1.13854 0.569270 0.822151i 0.307226π-0.307226\pi
0.569270 + 0.822151i 0.307226π0.307226\pi
812812 −2090.33 −0.0903403
813813 0 0
814814 12121.7 0.521946
815815 15573.6 0.669347
816816 0 0
817817 −48674.5 −2.08434
818818 −53937.8 −2.30549
819819 0 0
820820 8920.18 0.379886
821821 46289.6 1.96775 0.983873 0.178867i 0.0572433π-0.0572433\pi
0.983873 + 0.178867i 0.0572433π0.0572433\pi
822822 0 0
823823 −28099.3 −1.19013 −0.595067 0.803676i 0.702874π-0.702874\pi
−0.595067 + 0.803676i 0.702874π0.702874\pi
824824 18286.6 0.773111
825825 0 0
826826 −19187.5 −0.808255
827827 38732.3 1.62860 0.814301 0.580443i 0.197121π-0.197121\pi
0.814301 + 0.580443i 0.197121π0.197121\pi
828828 0 0
829829 −9334.33 −0.391067 −0.195534 0.980697i 0.562644π-0.562644\pi
−0.195534 + 0.980697i 0.562644π0.562644\pi
830830 19304.0 0.807290
831831 0 0
832832 −3279.09 −0.136637
833833 −7871.06 −0.327390
834834 0 0
835835 −8603.88 −0.356586
836836 −40421.3 −1.67225
837837 0 0
838838 −20383.7 −0.840266
839839 40742.1 1.67649 0.838245 0.545294i 0.183582π-0.183582\pi
0.838245 + 0.545294i 0.183582π0.183582\pi
840840 0 0
841841 841.000 0.0344828
842842 3029.31 0.123987
843843 0 0
844844 −19953.4 −0.813771
845845 −8366.49 −0.340611
846846 0 0
847847 55383.5 2.24675
848848 −17124.3 −0.693457
849849 0 0
850850 6008.34 0.242452
851851 3470.51 0.139797
852852 0 0
853853 −29088.9 −1.16762 −0.583812 0.811889i 0.698440π-0.698440\pi
−0.583812 + 0.811889i 0.698440π0.698440\pi
854854 −25057.7 −1.00405
855855 0 0
856856 −1777.49 −0.0709737
857857 −31564.0 −1.25812 −0.629059 0.777357i 0.716560π-0.716560\pi
−0.629059 + 0.777357i 0.716560π0.716560\pi
858858 0 0
859859 21654.5 0.860120 0.430060 0.902800i 0.358492π-0.358492\pi
0.430060 + 0.902800i 0.358492π0.358492\pi
860860 9810.22 0.388983
861861 0 0
862862 26894.4 1.06267
863863 −2304.51 −0.0908996 −0.0454498 0.998967i 0.514472π-0.514472\pi
−0.0454498 + 0.998967i 0.514472π0.514472\pi
864864 0 0
865865 12193.5 0.479297
866866 45380.5 1.78071
867867 0 0
868868 −12990.8 −0.507992
869869 −79341.1 −3.09720
870870 0 0
871871 −35980.7 −1.39972
872872 −13892.2 −0.539507
873873 0 0
874874 −30875.6 −1.19495
875875 −1878.52 −0.0725777
876876 0 0
877877 42141.0 1.62258 0.811289 0.584645i 0.198766π-0.198766\pi
0.811289 + 0.584645i 0.198766π0.198766\pi
878878 37669.4 1.44793
879879 0 0
880880 −28105.8 −1.07664
881881 −3482.39 −0.133172 −0.0665861 0.997781i 0.521211π-0.521211\pi
−0.0665861 + 0.997781i 0.521211π0.521211\pi
882882 0 0
883883 28559.6 1.08846 0.544229 0.838937i 0.316822π-0.316822\pi
0.544229 + 0.838937i 0.316822π0.316822\pi
884884 20047.3 0.762742
885885 0 0
886886 18598.5 0.705224
887887 42485.5 1.60826 0.804128 0.594456i 0.202633π-0.202633\pi
0.804128 + 0.594456i 0.202633π0.202633\pi
888888 0 0
889889 5992.37 0.226072
890890 6957.52 0.262041
891891 0 0
892892 −8376.43 −0.314421
893893 −14979.6 −0.561337
894894 0 0
895895 −11240.0 −0.419789
896896 20277.0 0.756034
897897 0 0
898898 42342.3 1.57347
899899 5226.58 0.193900
900900 0 0
901901 14496.1 0.535999
902902 94238.2 3.47870
903903 0 0
904904 −13202.1 −0.485724
905905 11785.6 0.432893
906906 0 0
907907 −22359.4 −0.818559 −0.409280 0.912409i 0.634220π-0.634220\pi
−0.409280 + 0.912409i 0.634220π0.634220\pi
908908 −621.166 −0.0227028
909909 0 0
910910 −16722.1 −0.609156
911911 14833.6 0.539471 0.269735 0.962934i 0.413064π-0.413064\pi
0.269735 + 0.962934i 0.413064π0.413064\pi
912912 0 0
913913 76440.9 2.77089
914914 1446.80 0.0523588
915915 0 0
916916 −3271.92 −0.118021
917917 5789.46 0.208489
918918 0 0
919919 −41161.8 −1.47748 −0.738740 0.673991i 0.764579π-0.764579\pi
−0.738740 + 0.673991i 0.764579π0.764579\pi
920920 −4156.46 −0.148950
921921 0 0
922922 −25300.1 −0.903702
923923 −54181.7 −1.93219
924924 0 0
925925 −1196.10 −0.0425161
926926 −23252.6 −0.825192
927927 0 0
928928 5574.59 0.197193
929929 −29321.8 −1.03554 −0.517771 0.855519i 0.673238π-0.673238\pi
−0.517771 + 0.855519i 0.673238π0.673238\pi
930930 0 0
931931 −13940.1 −0.490729
932932 −8303.02 −0.291818
933933 0 0
934934 31660.4 1.10917
935935 23792.2 0.832178
936936 0 0
937937 −42922.5 −1.49650 −0.748249 0.663418i 0.769105π-0.769105\pi
−0.748249 + 0.663418i 0.769105π0.769105\pi
938938 −31091.8 −1.08228
939939 0 0
940940 3019.10 0.104758
941941 13239.3 0.458650 0.229325 0.973350i 0.426348π-0.426348\pi
0.229325 + 0.973350i 0.426348π0.426348\pi
942942 0 0
943943 26981.0 0.931732
944944 28327.2 0.976665
945945 0 0
946946 103641. 3.56201
947947 19266.8 0.661126 0.330563 0.943784i 0.392761π-0.392761\pi
0.330563 + 0.943784i 0.392761π0.392761\pi
948948 0 0
949949 25625.3 0.876534
950950 10641.1 0.363415
951951 0 0
952952 −11570.8 −0.393919
953953 14816.2 0.503615 0.251807 0.967777i 0.418975π-0.418975\pi
0.251807 + 0.967777i 0.418975π0.418975\pi
954954 0 0
955955 9612.78 0.325720
956956 −15868.2 −0.536835
957957 0 0
958958 30702.8 1.03545
959959 5288.05 0.178061
960960 0 0
961961 2690.68 0.0903185
962962 −10647.4 −0.356845
963963 0 0
964964 17201.6 0.574717
965965 −9203.41 −0.307014
966966 0 0
967967 1342.65 0.0446502 0.0223251 0.999751i 0.492893π-0.492893\pi
0.0223251 + 0.999751i 0.492893π0.492893\pi
968968 −42233.9 −1.40232
969969 0 0
970970 27344.6 0.905135
971971 11211.1 0.370526 0.185263 0.982689i 0.440686π-0.440686\pi
0.185263 + 0.982689i 0.440686π0.440686\pi
972972 0 0
973973 17109.3 0.563718
974974 −10100.7 −0.332285
975975 0 0
976976 36993.6 1.21325
977977 −30870.2 −1.01088 −0.505438 0.862863i 0.668669π-0.668669\pi
−0.505438 + 0.862863i 0.668669π0.668669\pi
978978 0 0
979979 27550.8 0.899414
980980 2809.60 0.0915809
981981 0 0
982982 46919.3 1.52470
983983 −28549.4 −0.926332 −0.463166 0.886272i 0.653287π-0.653287\pi
−0.463166 + 0.886272i 0.653287π0.653287\pi
984984 0 0
985985 −13564.0 −0.438765
986986 −6969.68 −0.225111
987987 0 0
988988 35505.0 1.14328
989989 29673.1 0.954046
990990 0 0
991991 −20806.0 −0.666927 −0.333464 0.942763i 0.608217π-0.608217\pi
−0.333464 + 0.942763i 0.608217π0.608217\pi
992992 34644.5 1.10883
993993 0 0
994994 −46819.7 −1.49399
995995 −1123.16 −0.0357854
996996 0 0
997997 57999.9 1.84240 0.921201 0.389088i 0.127210π-0.127210\pi
0.921201 + 0.389088i 0.127210π0.127210\pi
998998 −59007.4 −1.87159
999999 0 0
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 1305.4.a.n.1.6 7
3.2 odd 2 435.4.a.i.1.2 7
15.14 odd 2 2175.4.a.n.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
435.4.a.i.1.2 7 3.2 odd 2
1305.4.a.n.1.6 7 1.1 even 1 trivial
2175.4.a.n.1.6 7 15.14 odd 2