Properties

Label 1859.4.a.j.1.14
Level 18591859
Weight 44
Character 1859.1
Self dual yes
Analytic conductor 109.685109.685
Analytic rank 11
Dimension 1818
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] = [1859,4,Mod(1,1859)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1859, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("1859.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 1859=11132 1859 = 11 \cdot 13^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1859.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [18,-2,0,76,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 109.684550701109.684550701
Analytic rank: 11
Dimension: 1818
Coefficient field: Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x182x17108x16+212x15+4721x148963x13107626x12+194656x11++9847296 x^{18} - 2 x^{17} - 108 x^{16} + 212 x^{15} + 4721 x^{14} - 8963 x^{13} - 107626 x^{12} + 194656 x^{11} + \cdots + 9847296 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 2532 2^{5}\cdot 3^{2}
Twist minimal: no (minimal twist has level 143)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.14
Root 2.40428-2.40428 of defining polynomial
Character χ\chi == 1859.1

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+2.40428q2+7.21858q32.21943q4+9.84845q5+17.3555q6+8.26104q724.5704q8+25.1078q9+23.6784q1011.0000q1116.0212q12+19.8618q14+71.0918q1541.3186q16113.178q17+60.3663q18121.759q1921.8580q20+59.6329q2126.4471q2269.3004q23177.363q2428.0079q2513.6587q2718.3348q28209.888q29+170.925q30+18.1919q31+97.2215q3279.4043q33272.112q34+81.3584q3555.7252q36228.240q37292.742q38241.980q40460.524q41+143.374q42+386.056q43+24.4138q44+247.273q45166.618q46+322.380q47298.262q48274.755q4967.3390q50816.984q51+249.880q5332.8393q54108.333q55202.977q56878.923q57504.629q5856.7513q59157.784q60+775.933q61+43.7384q62+207.417q63+564.297q64190.910q66387.156q67+251.191q68500.250q69+195.609q70+116.894q71616.909q72+1016.35q73548.754q74202.177q75+270.235q7690.8714q77429.294q79406.925q80776.508q811107.23q82+950.500q83132.351q841114.63q85+928.187q861515.09q87+270.274q88+671.495q89+594.515q90+153.808q92+131.320q93+775.093q941199.13q95+701.801q96+968.442q97660.589q98276.186q99+O(q100)q+2.40428 q^{2} +7.21858 q^{3} -2.21943 q^{4} +9.84845 q^{5} +17.3555 q^{6} +8.26104 q^{7} -24.5704 q^{8} +25.1078 q^{9} +23.6784 q^{10} -11.0000 q^{11} -16.0212 q^{12} +19.8618 q^{14} +71.0918 q^{15} -41.3186 q^{16} -113.178 q^{17} +60.3663 q^{18} -121.759 q^{19} -21.8580 q^{20} +59.6329 q^{21} -26.4471 q^{22} -69.3004 q^{23} -177.363 q^{24} -28.0079 q^{25} -13.6587 q^{27} -18.3348 q^{28} -209.888 q^{29} +170.925 q^{30} +18.1919 q^{31} +97.2215 q^{32} -79.4043 q^{33} -272.112 q^{34} +81.3584 q^{35} -55.7252 q^{36} -228.240 q^{37} -292.742 q^{38} -241.980 q^{40} -460.524 q^{41} +143.374 q^{42} +386.056 q^{43} +24.4138 q^{44} +247.273 q^{45} -166.618 q^{46} +322.380 q^{47} -298.262 q^{48} -274.755 q^{49} -67.3390 q^{50} -816.984 q^{51} +249.880 q^{53} -32.8393 q^{54} -108.333 q^{55} -202.977 q^{56} -878.923 q^{57} -504.629 q^{58} -56.7513 q^{59} -157.784 q^{60} +775.933 q^{61} +43.7384 q^{62} +207.417 q^{63} +564.297 q^{64} -190.910 q^{66} -387.156 q^{67} +251.191 q^{68} -500.250 q^{69} +195.609 q^{70} +116.894 q^{71} -616.909 q^{72} +1016.35 q^{73} -548.754 q^{74} -202.177 q^{75} +270.235 q^{76} -90.8714 q^{77} -429.294 q^{79} -406.925 q^{80} -776.508 q^{81} -1107.23 q^{82} +950.500 q^{83} -132.351 q^{84} -1114.63 q^{85} +928.187 q^{86} -1515.09 q^{87} +270.274 q^{88} +671.495 q^{89} +594.515 q^{90} +153.808 q^{92} +131.320 q^{93} +775.093 q^{94} -1199.13 q^{95} +701.801 q^{96} +968.442 q^{97} -660.589 q^{98} -276.186 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 18q2q2+76q420q549q628q7+12q8+180q9+56q10198q11+54q12+4q1460q15+364q16138q17298q1824q19160q20+1980q99+O(q100) 18 q - 2 q^{2} + 76 q^{4} - 20 q^{5} - 49 q^{6} - 28 q^{7} + 12 q^{8} + 180 q^{9} + 56 q^{10} - 198 q^{11} + 54 q^{12} + 4 q^{14} - 60 q^{15} + 364 q^{16} - 138 q^{17} - 298 q^{18} - 24 q^{19} - 160 q^{20}+ \cdots - 1980 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 2.40428 0.850042 0.425021 0.905184i 0.360267π-0.360267\pi
0.425021 + 0.905184i 0.360267π0.360267\pi
33 7.21858 1.38922 0.694608 0.719389i 0.255578π-0.255578\pi
0.694608 + 0.719389i 0.255578π0.255578\pi
44 −2.21943 −0.277429
55 9.84845 0.880873 0.440436 0.897784i 0.354824π-0.354824\pi
0.440436 + 0.897784i 0.354824π0.354824\pi
66 17.3555 1.18089
77 8.26104 0.446054 0.223027 0.974812i 0.428406π-0.428406\pi
0.223027 + 0.974812i 0.428406π0.428406\pi
88 −24.5704 −1.08587
99 25.1078 0.929920
1010 23.6784 0.748778
1111 −11.0000 −0.301511
1212 −16.0212 −0.385409
1313 0 0
1414 19.8618 0.379164
1515 71.0918 1.22372
1616 −41.3186 −0.645604
1717 −113.178 −1.61469 −0.807344 0.590082i 0.799096π-0.799096\pi
−0.807344 + 0.590082i 0.799096π0.799096\pi
1818 60.3663 0.790471
1919 −121.759 −1.47017 −0.735087 0.677972i 0.762859π-0.762859\pi
−0.735087 + 0.677972i 0.762859π0.762859\pi
2020 −21.8580 −0.244380
2121 59.6329 0.619665
2222 −26.4471 −0.256297
2323 −69.3004 −0.628266 −0.314133 0.949379i 0.601714π-0.601714\pi
−0.314133 + 0.949379i 0.601714π0.601714\pi
2424 −177.363 −1.50850
2525 −28.0079 −0.224064
2626 0 0
2727 −13.6587 −0.0973561
2828 −18.3348 −0.123748
2929 −209.888 −1.34397 −0.671985 0.740564i 0.734558π-0.734558\pi
−0.671985 + 0.740564i 0.734558π0.734558\pi
3030 170.925 1.04021
3131 18.1919 0.105399 0.0526994 0.998610i 0.483217π-0.483217\pi
0.0526994 + 0.998610i 0.483217π0.483217\pi
3232 97.2215 0.537078
3333 −79.4043 −0.418864
3434 −272.112 −1.37255
3535 81.3584 0.392917
3636 −55.7252 −0.257987
3737 −228.240 −1.01412 −0.507060 0.861911i 0.669268π-0.669268\pi
−0.507060 + 0.861911i 0.669268π0.669268\pi
3838 −292.742 −1.24971
3939 0 0
4040 −241.980 −0.956511
4141 −460.524 −1.75419 −0.877095 0.480317i 0.840522π-0.840522\pi
−0.877095 + 0.480317i 0.840522π0.840522\pi
4242 143.374 0.526741
4343 386.056 1.36914 0.684570 0.728947i 0.259990π-0.259990\pi
0.684570 + 0.728947i 0.259990π0.259990\pi
4444 24.4138 0.0836481
4545 247.273 0.819141
4646 −166.618 −0.534053
4747 322.380 1.00051 0.500255 0.865878i 0.333239π-0.333239\pi
0.500255 + 0.865878i 0.333239π0.333239\pi
4848 −298.262 −0.896883
4949 −274.755 −0.801036
5050 −67.3390 −0.190463
5151 −816.984 −2.24315
5252 0 0
5353 249.880 0.647617 0.323809 0.946123i 0.395037π-0.395037\pi
0.323809 + 0.946123i 0.395037π0.395037\pi
5454 −32.8393 −0.0827568
5555 −108.333 −0.265593
5656 −202.977 −0.484356
5757 −878.923 −2.04239
5858 −504.629 −1.14243
5959 −56.7513 −0.125227 −0.0626135 0.998038i 0.519944π-0.519944\pi
−0.0626135 + 0.998038i 0.519944π0.519944\pi
6060 −157.784 −0.339496
6161 775.933 1.62866 0.814328 0.580405i 0.197106π-0.197106\pi
0.814328 + 0.580405i 0.197106π0.197106\pi
6262 43.7384 0.0895933
6363 207.417 0.414795
6464 564.297 1.10214
6565 0 0
6666 −190.910 −0.356052
6767 −387.156 −0.705949 −0.352975 0.935633i 0.614830π-0.614830\pi
−0.352975 + 0.935633i 0.614830π0.614830\pi
6868 251.191 0.447962
6969 −500.250 −0.872797
7070 195.609 0.333996
7171 116.894 0.195391 0.0976957 0.995216i 0.468853π-0.468853\pi
0.0976957 + 0.995216i 0.468853π0.468853\pi
7272 −616.909 −1.00977
7373 1016.35 1.62952 0.814759 0.579800i 0.196869π-0.196869\pi
0.814759 + 0.579800i 0.196869π0.196869\pi
7474 −548.754 −0.862045
7575 −202.177 −0.311273
7676 270.235 0.407870
7777 −90.8714 −0.134490
7878 0 0
7979 −429.294 −0.611384 −0.305692 0.952131i 0.598888π-0.598888\pi
−0.305692 + 0.952131i 0.598888π0.598888\pi
8080 −406.925 −0.568695
8181 −776.508 −1.06517
8282 −1107.23 −1.49113
8383 950.500 1.25700 0.628500 0.777810i 0.283669π-0.283669\pi
0.628500 + 0.777810i 0.283669π0.283669\pi
8484 −132.351 −0.171913
8585 −1114.63 −1.42233
8686 928.187 1.16383
8787 −1515.09 −1.86706
8888 270.274 0.327402
8989 671.495 0.799757 0.399878 0.916568i 0.369052π-0.369052\pi
0.399878 + 0.916568i 0.369052π0.369052\pi
9090 594.515 0.696304
9191 0 0
9292 153.808 0.174300
9393 131.320 0.146422
9494 775.093 0.850476
9595 −1199.13 −1.29504
9696 701.801 0.746117
9797 968.442 1.01371 0.506857 0.862030i 0.330807π-0.330807\pi
0.506857 + 0.862030i 0.330807π0.330807\pi
9898 −660.589 −0.680914
9999 −276.186 −0.280381
100100 62.1618 0.0621618
101101 498.778 0.491388 0.245694 0.969347i 0.420984π-0.420984\pi
0.245694 + 0.969347i 0.420984π0.420984\pi
102102 −1964.26 −1.90677
103103 774.677 0.741079 0.370540 0.928817i 0.379173π-0.379173\pi
0.370540 + 0.928817i 0.379173π0.379173\pi
104104 0 0
105105 587.292 0.545846
106106 600.782 0.550501
107107 −1370.11 −1.23788 −0.618940 0.785438i 0.712438π-0.712438\pi
−0.618940 + 0.785438i 0.712438π0.712438\pi
108108 30.3146 0.0270094
109109 −845.710 −0.743159 −0.371579 0.928401i 0.621184π-0.621184\pi
−0.371579 + 0.928401i 0.621184π0.621184\pi
110110 −260.463 −0.225765
111111 −1647.57 −1.40883
112112 −341.335 −0.287974
113113 1313.27 1.09330 0.546648 0.837362i 0.315904π-0.315904\pi
0.546648 + 0.837362i 0.315904π0.315904\pi
114114 −2113.18 −1.73612
115115 −682.502 −0.553423
116116 465.832 0.372857
117117 0 0
118118 −136.446 −0.106448
119119 −934.967 −0.720238
120120 −1746.75 −1.32880
121121 121.000 0.0909091
122122 1865.56 1.38442
123123 −3324.33 −2.43695
124124 −40.3757 −0.0292407
125125 −1506.89 −1.07824
126126 498.688 0.352593
127127 43.6232 0.0304798 0.0152399 0.999884i 0.495149π-0.495149\pi
0.0152399 + 0.999884i 0.495149π0.495149\pi
128128 578.956 0.399789
129129 2786.78 1.90203
130130 0 0
131131 728.367 0.485784 0.242892 0.970053i 0.421904π-0.421904\pi
0.242892 + 0.970053i 0.421904π0.421904\pi
132132 176.233 0.116205
133133 −1005.85 −0.655777
134134 −930.831 −0.600086
135135 −134.517 −0.0857583
136136 2780.83 1.75334
137137 34.8683 0.0217445 0.0108723 0.999941i 0.496539π-0.496539\pi
0.0108723 + 0.999941i 0.496539π0.496539\pi
138138 −1202.74 −0.741914
139139 −298.899 −0.182391 −0.0911954 0.995833i 0.529069π-0.529069\pi
−0.0911954 + 0.995833i 0.529069π0.529069\pi
140140 −180.570 −0.109007
141141 2327.13 1.38992
142142 281.046 0.166091
143143 0 0
144144 −1037.42 −0.600360
145145 −2067.07 −1.18387
146146 2443.59 1.38516
147147 −1983.34 −1.11281
148148 506.564 0.281347
149149 58.7860 0.0323217 0.0161609 0.999869i 0.494856π-0.494856\pi
0.0161609 + 0.999869i 0.494856π0.494856\pi
150150 −486.091 −0.264595
151151 −2550.58 −1.37459 −0.687296 0.726378i 0.741202π-0.741202\pi
−0.687296 + 0.726378i 0.741202π0.741202\pi
152152 2991.65 1.59642
153153 −2841.65 −1.50153
154154 −218.480 −0.114322
155155 179.162 0.0928429
156156 0 0
157157 −373.767 −0.189999 −0.0949995 0.995477i 0.530285π-0.530285\pi
−0.0949995 + 0.995477i 0.530285π0.530285\pi
158158 −1032.14 −0.519701
159159 1803.78 0.899680
160160 957.482 0.473097
161161 −572.493 −0.280241
162162 −1866.94 −0.905438
163163 −3013.03 −1.44784 −0.723922 0.689882i 0.757662π-0.757662\pi
−0.723922 + 0.689882i 0.757662π0.757662\pi
164164 1022.10 0.486664
165165 −782.010 −0.368966
166166 2285.27 1.06850
167167 −2373.33 −1.09972 −0.549861 0.835256i 0.685319π-0.685319\pi
−0.549861 + 0.835256i 0.685319π0.685319\pi
168168 −1465.20 −0.672875
169169 0 0
170170 −2679.88 −1.20904
171171 −3057.09 −1.36714
172172 −856.826 −0.379839
173173 913.000 0.401237 0.200619 0.979669i 0.435705π-0.435705\pi
0.200619 + 0.979669i 0.435705π0.435705\pi
174174 −3642.70 −1.58708
175175 −231.375 −0.0999444
176176 454.505 0.194657
177177 −409.664 −0.173967
178178 1614.46 0.679826
179179 1911.51 0.798173 0.399086 0.916913i 0.369327π-0.369327\pi
0.399086 + 0.916913i 0.369327π0.369327\pi
180180 −548.807 −0.227254
181181 3241.61 1.33120 0.665600 0.746308i 0.268176π-0.268176\pi
0.665600 + 0.746308i 0.268176π0.268176\pi
182182 0 0
183183 5601.13 2.26255
184184 1702.74 0.682214
185185 −2247.81 −0.893311
186186 315.729 0.124464
187187 1244.96 0.486846
188188 −715.502 −0.277571
189189 −112.835 −0.0434261
190190 −2883.05 −1.10083
191191 1252.48 0.474483 0.237242 0.971451i 0.423757π-0.423757\pi
0.237242 + 0.971451i 0.423757π0.423757\pi
192192 4073.42 1.53111
193193 −617.618 −0.230348 −0.115174 0.993345i 0.536743π-0.536743\pi
−0.115174 + 0.993345i 0.536743π0.536743\pi
194194 2328.41 0.861700
195195 0 0
196196 609.801 0.222231
197197 2712.30 0.980930 0.490465 0.871461i 0.336827π-0.336827\pi
0.490465 + 0.871461i 0.336827π0.336827\pi
198198 −664.029 −0.238336
199199 2309.96 0.822856 0.411428 0.911442i 0.365030π-0.365030\pi
0.411428 + 0.911442i 0.365030π0.365030\pi
200200 688.166 0.243303
201201 −2794.71 −0.980716
202202 1199.20 0.417701
203203 −1733.89 −0.599483
204204 1813.24 0.622315
205205 −4535.45 −1.54522
206206 1862.54 0.629948
207207 −1739.98 −0.584238
208208 0 0
209209 1339.34 0.443274
210210 1412.01 0.463992
211211 −4349.05 −1.41896 −0.709481 0.704724i 0.751071π-0.751071\pi
−0.709481 + 0.704724i 0.751071π0.751071\pi
212212 −554.593 −0.179668
213213 843.810 0.271441
214214 −3294.12 −1.05225
215215 3802.06 1.20604
216216 335.599 0.105716
217217 150.284 0.0470135
218218 −2033.32 −0.631716
219219 7336.60 2.26375
220220 240.438 0.0736833
221221 0 0
222222 −3961.22 −1.19757
223223 −1591.00 −0.477762 −0.238881 0.971049i 0.576781π-0.576781\pi
−0.238881 + 0.971049i 0.576781π0.576781\pi
224224 803.150 0.239566
225225 −703.219 −0.208361
226226 3157.48 0.929347
227227 −4976.41 −1.45505 −0.727524 0.686083i 0.759329π-0.759329\pi
−0.727524 + 0.686083i 0.759329π0.759329\pi
228228 1950.71 0.566619
229229 −2216.11 −0.639495 −0.319748 0.947503i 0.603598π-0.603598\pi
−0.319748 + 0.947503i 0.603598π0.603598\pi
230230 −1640.93 −0.470432
231231 −655.962 −0.186836
232232 5157.02 1.45937
233233 −64.8342 −0.0182293 −0.00911465 0.999958i 0.502901π-0.502901\pi
−0.00911465 + 0.999958i 0.502901π0.502901\pi
234234 0 0
235235 3174.95 0.881322
236236 125.956 0.0347416
237237 −3098.89 −0.849344
238238 −2247.92 −0.612232
239239 −3858.71 −1.04435 −0.522174 0.852839i 0.674879π-0.674879\pi
−0.522174 + 0.852839i 0.674879π0.674879\pi
240240 −2937.42 −0.790039
241241 −6737.07 −1.80072 −0.900359 0.435148i 0.856696π-0.856696\pi
−0.900359 + 0.435148i 0.856696π0.856696\pi
242242 290.918 0.0772765
243243 −5236.50 −1.38239
244244 −1722.13 −0.451837
245245 −2705.91 −0.705610
246246 −7992.62 −2.07151
247247 0 0
248248 −446.982 −0.114449
249249 6861.26 1.74624
250250 −3622.99 −0.916552
251251 2556.90 0.642989 0.321495 0.946911i 0.395815π-0.395815\pi
0.321495 + 0.946911i 0.395815π0.395815\pi
252252 −460.348 −0.115076
253253 762.304 0.189429
254254 104.882 0.0259091
255255 −8046.03 −1.97593
256256 −3122.40 −0.762305
257257 −5227.70 −1.26885 −0.634426 0.772983i 0.718764π-0.718764\pi
−0.634426 + 0.772983i 0.718764π0.718764\pi
258258 6700.19 1.61680
259259 −1885.50 −0.452353
260260 0 0
261261 −5269.82 −1.24979
262262 1751.20 0.412937
263263 6104.51 1.43125 0.715627 0.698482i 0.246141π-0.246141\pi
0.715627 + 0.698482i 0.246141π0.246141\pi
264264 1951.00 0.454831
265265 2460.93 0.570468
266266 −2418.35 −0.557438
267267 4847.24 1.11103
268268 859.267 0.195851
269269 6147.70 1.39343 0.696713 0.717350i 0.254645π-0.254645\pi
0.696713 + 0.717350i 0.254645π0.254645\pi
270270 −323.416 −0.0728982
271271 3285.68 0.736498 0.368249 0.929727i 0.379957π-0.379957\pi
0.368249 + 0.929727i 0.379957π0.379957\pi
272272 4676.36 1.04245
273273 0 0
274274 83.8332 0.0184838
275275 308.087 0.0675577
276276 1110.27 0.242140
277277 −750.813 −0.162859 −0.0814296 0.996679i 0.525949π-0.525949\pi
−0.0814296 + 0.996679i 0.525949π0.525949\pi
278278 −718.638 −0.155040
279279 456.759 0.0980124
280280 −1999.01 −0.426656
281281 −7388.62 −1.56857 −0.784285 0.620400i 0.786970π-0.786970\pi
−0.784285 + 0.620400i 0.786970π0.786970\pi
282282 5595.07 1.18149
283283 −2895.26 −0.608145 −0.304073 0.952649i 0.598347π-0.598347\pi
−0.304073 + 0.952649i 0.598347π0.598347\pi
284284 −259.439 −0.0542073
285285 −8656.03 −1.79908
286286 0 0
287287 −3804.41 −0.782463
288288 2441.02 0.499440
289289 7896.25 1.60721
290290 −4969.81 −1.00634
291291 6990.77 1.40827
292292 −2255.72 −0.452076
293293 −2565.06 −0.511441 −0.255720 0.966751i 0.582313π-0.582313\pi
−0.255720 + 0.966751i 0.582313π0.582313\pi
294294 −4768.51 −0.945936
295295 −558.913 −0.110309
296296 5607.95 1.10120
297297 150.246 0.0293540
298298 141.338 0.0274748
299299 0 0
300300 448.720 0.0863561
301301 3189.22 0.610710
302302 −6132.31 −1.16846
303303 3600.46 0.682644
304304 5030.90 0.949150
305305 7641.74 1.43464
306306 −6832.13 −1.27636
307307 −5707.87 −1.06113 −0.530563 0.847646i 0.678019π-0.678019\pi
−0.530563 + 0.847646i 0.678019π0.678019\pi
308308 201.683 0.0373116
309309 5592.06 1.02952
310310 430.756 0.0789203
311311 1750.47 0.319165 0.159582 0.987185i 0.448985π-0.448985\pi
0.159582 + 0.987185i 0.448985π0.448985\pi
312312 0 0
313313 −6425.08 −1.16028 −0.580139 0.814518i 0.697002π-0.697002\pi
−0.580139 + 0.814518i 0.697002π0.697002\pi
314314 −898.641 −0.161507
315315 2042.73 0.365381
316316 952.789 0.169616
317317 9721.92 1.72252 0.861258 0.508168i 0.169677π-0.169677\pi
0.861258 + 0.508168i 0.169677π0.169677\pi
318318 4336.79 0.764765
319319 2308.76 0.405222
320320 5557.45 0.970847
321321 −9890.22 −1.71968
322322 −1376.43 −0.238216
323323 13780.4 2.37387
324324 1723.41 0.295509
325325 0 0
326326 −7244.16 −1.23073
327327 −6104.82 −1.03241
328328 11315.3 1.90482
329329 2663.20 0.446282
330330 −1880.17 −0.313636
331331 −4560.44 −0.757294 −0.378647 0.925541i 0.623611π-0.623611\pi
−0.378647 + 0.925541i 0.623611π0.623611\pi
332332 −2109.57 −0.348728
333333 −5730.62 −0.943051
334334 −5706.14 −0.934809
335335 −3812.89 −0.621851
336336 −2463.95 −0.400058
337337 −3870.54 −0.625643 −0.312822 0.949812i 0.601274π-0.601274\pi
−0.312822 + 0.949812i 0.601274π0.601274\pi
338338 0 0
339339 9479.97 1.51882
340340 2473.84 0.394597
341341 −200.111 −0.0317789
342342 −7350.11 −1.16213
343343 −5103.30 −0.803359
344344 −9485.55 −1.48670
345345 −4926.69 −0.768823
346346 2195.11 0.341068
347347 −2536.47 −0.392406 −0.196203 0.980563i 0.562861π-0.562861\pi
−0.196203 + 0.980563i 0.562861π0.562861\pi
348348 3362.64 0.517979
349349 450.127 0.0690394 0.0345197 0.999404i 0.489010π-0.489010\pi
0.0345197 + 0.999404i 0.489010π0.489010\pi
350350 −556.290 −0.0849569
351351 0 0
352352 −1069.44 −0.161935
353353 −7860.81 −1.18524 −0.592619 0.805483i 0.701906π-0.701906\pi
−0.592619 + 0.805483i 0.701906π0.701906\pi
354354 −984.946 −0.147879
355355 1151.23 0.172115
356356 −1490.34 −0.221876
357357 −6749.13 −1.00057
358358 4595.81 0.678480
359359 −7509.91 −1.10406 −0.552030 0.833824i 0.686147π-0.686147\pi
−0.552030 + 0.833824i 0.686147π0.686147\pi
360360 −6075.60 −0.889479
361361 7966.13 1.16141
362362 7793.75 1.13158
363363 873.448 0.126292
364364 0 0
365365 10009.5 1.43540
366366 13466.7 1.92326
367367 2168.03 0.308366 0.154183 0.988042i 0.450726π-0.450726\pi
0.154183 + 0.988042i 0.450726π0.450726\pi
368368 2863.40 0.405611
369369 −11562.8 −1.63126
370370 −5404.38 −0.759352
371371 2064.27 0.288872
372372 −291.455 −0.0406217
373373 −2525.90 −0.350633 −0.175317 0.984512i 0.556095π-0.556095\pi
−0.175317 + 0.984512i 0.556095π0.556095\pi
374374 2993.23 0.413840
375375 −10877.6 −1.49791
376376 −7921.01 −1.08642
377377 0 0
378378 −271.287 −0.0369140
379379 −12858.2 −1.74270 −0.871349 0.490663i 0.836755π-0.836755\pi
−0.871349 + 0.490663i 0.836755π0.836755\pi
380380 2661.40 0.359281
381381 314.897 0.0423430
382382 3011.32 0.403331
383383 −6495.09 −0.866536 −0.433268 0.901265i 0.642640π-0.642640\pi
−0.433268 + 0.901265i 0.642640π0.642640\pi
384384 4179.24 0.555393
385385 −894.943 −0.118469
386386 −1484.93 −0.195805
387387 9693.03 1.27319
388388 −2149.39 −0.281234
389389 10018.2 1.30577 0.652886 0.757456i 0.273558π-0.273558\pi
0.652886 + 0.757456i 0.273558π0.273558\pi
390390 0 0
391391 7843.27 1.01445
392392 6750.84 0.869819
393393 5257.77 0.674859
394394 6521.12 0.833831
395395 −4227.88 −0.538551
396396 612.977 0.0777860
397397 5201.52 0.657574 0.328787 0.944404i 0.393360π-0.393360\pi
0.328787 + 0.944404i 0.393360π0.393360\pi
398398 5553.78 0.699462
399399 −7260.82 −0.911016
400400 1157.25 0.144656
401401 −3116.36 −0.388088 −0.194044 0.980993i 0.562161π-0.562161\pi
−0.194044 + 0.980993i 0.562161π0.562161\pi
402402 −6719.28 −0.833649
403403 0 0
404404 −1107.00 −0.136326
405405 −7647.40 −0.938278
406406 −4168.76 −0.509586
407407 2510.64 0.305769
408408 20073.6 2.43576
409409 7577.28 0.916070 0.458035 0.888934i 0.348553π-0.348553\pi
0.458035 + 0.888934i 0.348553π0.348553\pi
410410 −10904.5 −1.31350
411411 251.700 0.0302078
412412 −1719.34 −0.205597
413413 −468.825 −0.0558580
414414 −4183.41 −0.496626
415415 9360.96 1.10726
416416 0 0
417417 −2157.63 −0.253380
418418 3220.16 0.376802
419419 1434.43 0.167247 0.0836234 0.996497i 0.473351π-0.473351\pi
0.0836234 + 0.996497i 0.473351π0.473351\pi
420420 −1303.46 −0.151434
421421 −84.9736 −0.00983696 −0.00491848 0.999988i 0.501566π-0.501566\pi
−0.00491848 + 0.999988i 0.501566π0.501566\pi
422422 −10456.3 −1.20618
423423 8094.27 0.930395
424424 −6139.66 −0.703227
425425 3169.88 0.361793
426426 2028.76 0.230736
427427 6410.01 0.726468
428428 3040.86 0.343424
429429 0 0
430430 9141.21 1.02518
431431 10844.3 1.21195 0.605974 0.795484i 0.292783π-0.292783\pi
0.605974 + 0.795484i 0.292783π0.292783\pi
432432 564.358 0.0628535
433433 −4075.42 −0.452315 −0.226157 0.974091i 0.572616π-0.572616\pi
−0.226157 + 0.974091i 0.572616π0.572616\pi
434434 361.325 0.0399635
435435 −14921.3 −1.64465
436436 1877.00 0.206174
437437 8437.91 0.923661
438438 17639.3 1.92428
439439 15183.4 1.65071 0.825356 0.564613i 0.190975π-0.190975\pi
0.825356 + 0.564613i 0.190975π0.190975\pi
440440 2661.78 0.288399
441441 −6898.51 −0.744899
442442 0 0
443443 −2203.06 −0.236276 −0.118138 0.992997i 0.537693π-0.537693\pi
−0.118138 + 0.992997i 0.537693π0.537693\pi
444444 3656.67 0.390851
445445 6613.19 0.704484
446446 −3825.20 −0.406118
447447 424.351 0.0449018
448448 4661.68 0.491615
449449 −2387.96 −0.250990 −0.125495 0.992094i 0.540052π-0.540052\pi
−0.125495 + 0.992094i 0.540052π0.540052\pi
450450 −1690.74 −0.177116
451451 5065.77 0.528908
452452 −2914.73 −0.303312
453453 −18411.6 −1.90960
454454 −11964.7 −1.23685
455455 0 0
456456 21595.5 2.21777
457457 −13211.2 −1.35228 −0.676141 0.736772i 0.736349π-0.736349\pi
−0.676141 + 0.736772i 0.736349π0.736349\pi
458458 −5328.14 −0.543598
459459 1545.86 0.157200
460460 1514.77 0.153536
461461 15369.8 1.55280 0.776400 0.630240i 0.217044π-0.217044\pi
0.776400 + 0.630240i 0.217044π0.217044\pi
462462 −1577.12 −0.158818
463463 15981.6 1.60416 0.802081 0.597215i 0.203726π-0.203726\pi
0.802081 + 0.597215i 0.203726π0.203726\pi
464464 8672.27 0.867672
465465 1293.30 0.128979
466466 −155.880 −0.0154957
467467 −6285.94 −0.622867 −0.311433 0.950268i 0.600809π-0.600809\pi
−0.311433 + 0.950268i 0.600809π0.600809\pi
468468 0 0
469469 −3198.31 −0.314892
470470 7633.46 0.749161
471471 −2698.06 −0.263950
472472 1394.40 0.135980
473473 −4246.62 −0.412811
474474 −7450.60 −0.721977
475475 3410.21 0.329413
476476 2075.10 0.199815
477477 6273.96 0.602232
478478 −9277.41 −0.887739
479479 −2421.85 −0.231017 −0.115509 0.993306i 0.536850π-0.536850\pi
−0.115509 + 0.993306i 0.536850π0.536850\pi
480480 6911.65 0.657234
481481 0 0
482482 −16197.8 −1.53069
483483 −4132.58 −0.389315
484484 −268.552 −0.0252208
485485 9537.65 0.892954
486486 −12590.0 −1.17509
487487 −2565.70 −0.238733 −0.119367 0.992850i 0.538086π-0.538086\pi
−0.119367 + 0.992850i 0.538086π0.538086\pi
488488 −19065.0 −1.76850
489489 −21749.8 −2.01137
490490 −6505.78 −0.599798
491491 −12252.8 −1.12619 −0.563097 0.826391i 0.690390π-0.690390\pi
−0.563097 + 0.826391i 0.690390π0.690390\pi
492492 7378.13 0.676081
493493 23754.6 2.17009
494494 0 0
495495 −2720.01 −0.246980
496496 −751.665 −0.0680458
497497 965.667 0.0871551
498498 16496.4 1.48438
499499 −13403.0 −1.20241 −0.601203 0.799096i 0.705312π-0.705312\pi
−0.601203 + 0.799096i 0.705312π0.705312\pi
500500 3344.45 0.299136
501501 −17132.0 −1.52775
502502 6147.51 0.546567
503503 12682.2 1.12420 0.562098 0.827070i 0.309994π-0.309994\pi
0.562098 + 0.827070i 0.309994π0.309994\pi
504504 −5096.31 −0.450412
505505 4912.19 0.432851
506506 1832.79 0.161023
507507 0 0
508508 −96.8188 −0.00845599
509509 −12218.3 −1.06399 −0.531993 0.846749i 0.678557π-0.678557\pi
−0.531993 + 0.846749i 0.678557π0.678557\pi
510510 −19344.9 −1.67962
511511 8396.11 0.726853
512512 −12138.8 −1.04778
513513 1663.06 0.143131
514514 −12568.9 −1.07858
515515 7629.37 0.652796
516516 −6185.06 −0.527679
517517 −3546.18 −0.301665
518518 −4533.27 −0.384519
519519 6590.56 0.557405
520520 0 0
521521 −2805.00 −0.235872 −0.117936 0.993021i 0.537628π-0.537628\pi
−0.117936 + 0.993021i 0.537628π0.537628\pi
522522 −12670.1 −1.06237
523523 749.381 0.0626542 0.0313271 0.999509i 0.490027π-0.490027\pi
0.0313271 + 0.999509i 0.490027π0.490027\pi
524524 −1616.56 −0.134771
525525 −1670.20 −0.138844
526526 14676.9 1.21663
527527 −2058.92 −0.170186
528528 3280.88 0.270420
529529 −7364.46 −0.605281
530530 5916.78 0.484922
531531 −1424.90 −0.116451
532532 2232.42 0.181932
533533 0 0
534534 11654.1 0.944425
535535 −13493.4 −1.09042
536536 9512.57 0.766568
537537 13798.4 1.10883
538538 14780.8 1.18447
539539 3022.31 0.241521
540540 298.552 0.0237919
541541 −8234.62 −0.654407 −0.327203 0.944954i 0.606106π-0.606106\pi
−0.327203 + 0.944954i 0.606106π0.606106\pi
542542 7899.70 0.626054
543543 23399.8 1.84932
544544 −11003.3 −0.867213
545545 −8328.94 −0.654628
546546 0 0
547547 −9637.00 −0.753288 −0.376644 0.926358i 0.622922π-0.622922\pi
−0.376644 + 0.926358i 0.622922π0.622922\pi
548548 −77.3879 −0.00603257
549549 19482.0 1.51452
550550 740.729 0.0574269
551551 25555.6 1.97587
552552 12291.3 0.947743
553553 −3546.41 −0.272710
554554 −1805.16 −0.138437
555555 −16226.0 −1.24100
556556 663.388 0.0506005
557557 11704.8 0.890388 0.445194 0.895434i 0.353135π-0.353135\pi
0.445194 + 0.895434i 0.353135π0.353135\pi
558558 1098.18 0.0833147
559559 0 0
560560 −3361.62 −0.253668
561561 8986.82 0.676335
562562 −17764.3 −1.33335
563563 −14175.9 −1.06118 −0.530590 0.847628i 0.678030π-0.678030\pi
−0.530590 + 0.847628i 0.678030π0.678030\pi
564564 −5164.91 −0.385606
565565 12933.7 0.963055
566566 −6961.01 −0.516949
567567 −6414.76 −0.475123
568568 −2872.14 −0.212169
569569 −19427.1 −1.43133 −0.715665 0.698443i 0.753876π-0.753876\pi
−0.715665 + 0.698443i 0.753876π0.753876\pi
570570 −20811.5 −1.52930
571571 −18855.7 −1.38194 −0.690968 0.722886i 0.742815π-0.742815\pi
−0.690968 + 0.722886i 0.742815π0.742815\pi
572572 0 0
573573 9041.13 0.659160
574574 −9146.86 −0.665126
575575 1940.96 0.140772
576576 14168.3 1.02490
577577 2869.39 0.207026 0.103513 0.994628i 0.466992π-0.466992\pi
0.103513 + 0.994628i 0.466992π0.466992\pi
578578 18984.8 1.36620
579579 −4458.32 −0.320003
580580 4587.72 0.328439
581581 7852.11 0.560689
582582 16807.8 1.19709
583583 −2748.68 −0.195264
584584 −24972.1 −1.76944
585585 0 0
586586 −6167.11 −0.434746
587587 15021.8 1.05625 0.528123 0.849168i 0.322896π-0.322896\pi
0.528123 + 0.849168i 0.322896π0.322896\pi
588588 4401.90 0.308727
589589 −2215.02 −0.154955
590590 −1343.78 −0.0937672
591591 19578.9 1.36272
592592 9430.58 0.654720
593593 8072.54 0.559021 0.279511 0.960143i 0.409828π-0.409828\pi
0.279511 + 0.960143i 0.409828π0.409828\pi
594594 361.232 0.0249521
595595 −9207.98 −0.634438
596596 −130.472 −0.00896699
597597 16674.6 1.14313
598598 0 0
599599 −5732.54 −0.391027 −0.195514 0.980701i 0.562637π-0.562637\pi
−0.195514 + 0.980701i 0.562637π0.562637\pi
600600 4967.58 0.338001
601601 2207.06 0.149796 0.0748982 0.997191i 0.476137π-0.476137\pi
0.0748982 + 0.997191i 0.476137π0.476137\pi
602602 7667.79 0.519129
603603 −9720.65 −0.656476
604604 5660.85 0.381352
605605 1191.66 0.0800793
606606 8656.53 0.580276
607607 12291.7 0.821919 0.410959 0.911654i 0.365194π-0.365194\pi
0.410959 + 0.911654i 0.365194π0.365194\pi
608608 −11837.5 −0.789599
609609 −12516.2 −0.832812
610610 18372.9 1.21950
611611 0 0
612612 6306.86 0.416568
613613 −22390.4 −1.47527 −0.737634 0.675201i 0.764057π-0.764057\pi
−0.737634 + 0.675201i 0.764057π0.764057\pi
614614 −13723.3 −0.902001
615615 −32739.5 −2.14664
616616 2232.75 0.146039
617617 −28056.9 −1.83068 −0.915340 0.402683i 0.868078π-0.868078\pi
−0.915340 + 0.402683i 0.868078π0.868078\pi
618618 13444.9 0.875134
619619 17407.7 1.13033 0.565166 0.824977i 0.308812π-0.308812\pi
0.565166 + 0.824977i 0.308812π0.308812\pi
620620 −397.639 −0.0257573
621621 946.552 0.0611656
622622 4208.63 0.271303
623623 5547.25 0.356735
624624 0 0
625625 −11339.6 −0.725732
626626 −15447.7 −0.986284
627627 9668.15 0.615804
628628 829.551 0.0527113
629629 25831.8 1.63749
630630 4911.31 0.310589
631631 −23766.3 −1.49940 −0.749699 0.661779i 0.769802π-0.769802\pi
−0.749699 + 0.661779i 0.769802π0.769802\pi
632632 10547.9 0.663882
633633 −31394.0 −1.97124
634634 23374.2 1.46421
635635 429.621 0.0268488
636636 −4003.37 −0.249598
637637 0 0
638638 5550.92 0.344456
639639 2934.96 0.181698
640640 5701.82 0.352163
641641 −6864.68 −0.422993 −0.211497 0.977379i 0.567834π-0.567834\pi
−0.211497 + 0.977379i 0.567834π0.567834\pi
642642 −23778.9 −1.46180
643643 −25251.4 −1.54871 −0.774354 0.632752i 0.781925π-0.781925\pi
−0.774354 + 0.632752i 0.781925π0.781925\pi
644644 1270.61 0.0777470
645645 27445.4 1.67545
646646 33131.9 2.01789
647647 −28831.7 −1.75192 −0.875960 0.482384i 0.839771π-0.839771\pi
−0.875960 + 0.482384i 0.839771π0.839771\pi
648648 19079.1 1.15663
649649 624.264 0.0377574
650650 0 0
651651 1084.84 0.0653120
652652 6687.22 0.401674
653653 21931.3 1.31430 0.657150 0.753760i 0.271762π-0.271762\pi
0.657150 + 0.753760i 0.271762π0.271762\pi
654654 −14677.7 −0.877590
655655 7173.29 0.427914
656656 19028.2 1.13251
657657 25518.4 1.51532
658658 6403.07 0.379358
659659 −9007.44 −0.532443 −0.266222 0.963912i 0.585775π-0.585775\pi
−0.266222 + 0.963912i 0.585775π0.585775\pi
660660 1735.62 0.102362
661661 −15820.6 −0.930937 −0.465469 0.885064i 0.654114π-0.654114\pi
−0.465469 + 0.885064i 0.654114π0.654114\pi
662662 −10964.6 −0.643731
663663 0 0
664664 −23354.2 −1.36494
665665 −9906.08 −0.577656
666666 −13778.0 −0.801633
667667 14545.3 0.844372
668668 5267.44 0.305095
669669 −11484.7 −0.663715
670670 −9167.25 −0.528600
671671 −8535.26 −0.491058
672672 5797.60 0.332809
673673 −4378.50 −0.250786 −0.125393 0.992107i 0.540019π-0.540019\pi
−0.125393 + 0.992107i 0.540019π0.540019\pi
674674 −9305.86 −0.531823
675675 382.552 0.0218140
676676 0 0
677677 −20157.2 −1.14432 −0.572159 0.820142i 0.693894π-0.693894\pi
−0.572159 + 0.820142i 0.693894π0.693894\pi
678678 22792.5 1.29106
679679 8000.33 0.452172
680680 27386.8 1.54447
681681 −35922.6 −2.02137
682682 −481.123 −0.0270134
683683 −5932.96 −0.332384 −0.166192 0.986093i 0.553147π-0.553147\pi
−0.166192 + 0.986093i 0.553147π0.553147\pi
684684 6785.02 0.379286
685685 343.399 0.0191542
686686 −12269.8 −0.682889
687687 −15997.1 −0.888397
688688 −15951.3 −0.883921
689689 0 0
690690 −11845.1 −0.653532
691691 −1087.33 −0.0598613 −0.0299307 0.999552i 0.509529π-0.509529\pi
−0.0299307 + 0.999552i 0.509529π0.509529\pi
692692 −2026.34 −0.111315
693693 −2281.58 −0.125065
694694 −6098.39 −0.333562
695695 −2943.70 −0.160663
696696 37226.3 2.02739
697697 52121.2 2.83247
698698 1082.23 0.0586864
699699 −468.010 −0.0253244
700700 513.521 0.0277275
701701 −22965.0 −1.23734 −0.618671 0.785650i 0.712329π-0.712329\pi
−0.618671 + 0.785650i 0.712329π0.712329\pi
702702 0 0
703703 27790.2 1.49093
704704 −6207.27 −0.332308
705705 22918.6 1.22435
706706 −18899.6 −1.00750
707707 4120.42 0.219186
708708 909.222 0.0482636
709709 17234.7 0.912923 0.456461 0.889743i 0.349117π-0.349117\pi
0.456461 + 0.889743i 0.349117π0.349117\pi
710710 2767.87 0.146305
711711 −10778.6 −0.568538
712712 −16498.9 −0.868430
713713 −1260.71 −0.0662185
714714 −16226.8 −0.850522
715715 0 0
716716 −4242.47 −0.221437
717717 −27854.4 −1.45082
718718 −18055.9 −0.938497
719719 −8404.20 −0.435916 −0.217958 0.975958i 0.569940π-0.569940\pi
−0.217958 + 0.975958i 0.569940π0.569940\pi
720720 −10217.0 −0.528840
721721 6399.63 0.330561
722722 19152.8 0.987250
723723 −48632.1 −2.50159
724724 −7194.55 −0.369314
725725 5878.52 0.301135
726726 2100.01 0.107354
727727 31053.6 1.58420 0.792101 0.610390i 0.208987π-0.208987\pi
0.792101 + 0.610390i 0.208987π0.208987\pi
728728 0 0
729729 −16834.3 −0.855273
730730 24065.6 1.22015
731731 −43693.0 −2.21073
732732 −12431.3 −0.627699
733733 4116.72 0.207441 0.103721 0.994606i 0.466925π-0.466925\pi
0.103721 + 0.994606i 0.466925π0.466925\pi
734734 5212.55 0.262124
735735 −19532.9 −0.980245
736736 −6737.49 −0.337428
737737 4258.71 0.212852
738738 −27800.1 −1.38664
739739 32205.9 1.60313 0.801565 0.597908i 0.204001π-0.204001\pi
0.801565 + 0.597908i 0.204001π0.204001\pi
740740 4988.88 0.247831
741741 0 0
742742 4963.09 0.245553
743743 −7624.80 −0.376483 −0.188241 0.982123i 0.560279π-0.560279\pi
−0.188241 + 0.982123i 0.560279π0.560279\pi
744744 −3226.57 −0.158995
745745 578.951 0.0284713
746746 −6072.98 −0.298053
747747 23865.0 1.16891
748748 −2763.10 −0.135065
749749 −11318.5 −0.552162
750750 −26152.8 −1.27329
751751 16416.1 0.797644 0.398822 0.917028i 0.369419π-0.369419\pi
0.398822 + 0.917028i 0.369419π0.369419\pi
752752 −13320.3 −0.645933
753753 18457.2 0.893250
754754 0 0
755755 −25119.3 −1.21084
756756 250.430 0.0120477
757757 18466.2 0.886610 0.443305 0.896371i 0.353806π-0.353806\pi
0.443305 + 0.896371i 0.353806π0.353806\pi
758758 −30914.8 −1.48137
759759 5502.75 0.263158
760760 29463.2 1.40624
761761 35699.7 1.70054 0.850270 0.526346i 0.176438π-0.176438\pi
0.850270 + 0.526346i 0.176438π0.176438\pi
762762 757.102 0.0359933
763763 −6986.44 −0.331489
764764 −2779.80 −0.131636
765765 −27985.9 −1.32266
766766 −15616.0 −0.736592
767767 0 0
768768 −22539.3 −1.05901
769769 17150.4 0.804237 0.402119 0.915588i 0.368274π-0.368274\pi
0.402119 + 0.915588i 0.368274π0.368274\pi
770770 −2151.69 −0.100703
771771 −37736.6 −1.76271
772772 1370.76 0.0639052
773773 −12687.9 −0.590365 −0.295182 0.955441i 0.595380π-0.595380\pi
−0.295182 + 0.955441i 0.595380π0.595380\pi
774774 23304.8 1.08226
775775 −509.518 −0.0236160
776776 −23795.0 −1.10076
777777 −13610.6 −0.628415
778778 24086.7 1.10996
779779 56072.7 2.57897
780780 0 0
781781 −1285.84 −0.0589127
782782 18857.4 0.862328
783783 2866.79 0.130844
784784 11352.5 0.517152
785785 −3681.03 −0.167365
786786 12641.2 0.573658
787787 8986.98 0.407053 0.203527 0.979069i 0.434760π-0.434760\pi
0.203527 + 0.979069i 0.434760π0.434760\pi
788788 −6019.76 −0.272139
789789 44065.8 1.98832
790790 −10165.0 −0.457791
791791 10849.0 0.487669
792792 6786.00 0.304457
793793 0 0
794794 12505.9 0.558965
795795 17764.4 0.792503
796796 −5126.80 −0.228285
797797 13773.0 0.612127 0.306064 0.952011i 0.400988π-0.400988\pi
0.306064 + 0.952011i 0.400988π0.400988\pi
798798 −17457.0 −0.774402
799799 −36486.3 −1.61551
800800 −2722.97 −0.120340
801801 16859.8 0.743710
802802 −7492.60 −0.329891
803803 −11179.9 −0.491318
804804 6202.68 0.272079
805805 −5638.17 −0.246856
806806 0 0
807807 44377.6 1.93577
808808 −12255.2 −0.533583
809809 −32953.4 −1.43211 −0.716057 0.698041i 0.754055π-0.754055\pi
−0.716057 + 0.698041i 0.754055π0.754055\pi
810810 −18386.5 −0.797575
811811 −2030.80 −0.0879299 −0.0439649 0.999033i 0.513999π-0.513999\pi
−0.0439649 + 0.999033i 0.513999π0.513999\pi
812812 3848.25 0.166314
813813 23717.9 1.02315
814814 6036.29 0.259916
815815 −29673.7 −1.27537
816816 33756.6 1.44818
817817 −47005.6 −2.01287
818818 18217.9 0.778698
819819 0 0
820820 10066.1 0.428689
821821 29724.1 1.26355 0.631777 0.775150i 0.282326π-0.282326\pi
0.631777 + 0.775150i 0.282326π0.282326\pi
822822 605.156 0.0256779
823823 −8511.11 −0.360485 −0.180242 0.983622i 0.557688π-0.557688\pi
−0.180242 + 0.983622i 0.557688π0.557688\pi
824824 −19034.1 −0.804714
825825 2223.95 0.0938522
826826 −1127.19 −0.0474816
827827 −8120.27 −0.341438 −0.170719 0.985320i 0.554609π-0.554609\pi
−0.170719 + 0.985320i 0.554609π0.554609\pi
828828 3861.78 0.162085
829829 1460.74 0.0611986 0.0305993 0.999532i 0.490258π-0.490258\pi
0.0305993 + 0.999532i 0.490258π0.490258\pi
830830 22506.4 0.941214
831831 −5419.80 −0.226246
832832 0 0
833833 31096.2 1.29342
834834 −5187.54 −0.215384
835835 −23373.6 −0.968715
836836 −2972.59 −0.122977
837837 −248.477 −0.0102612
838838 3448.77 0.142167
839839 −8636.35 −0.355376 −0.177688 0.984087i 0.556862π-0.556862\pi
−0.177688 + 0.984087i 0.556862π0.556862\pi
840840 −14430.0 −0.592717
841841 19663.8 0.806257
842842 −204.300 −0.00836182
843843 −53335.3 −2.17908
844844 9652.43 0.393662
845845 0 0
846846 19460.9 0.790874
847847 999.585 0.0405504
848848 −10324.7 −0.418104
849849 −20899.6 −0.844845
850850 7621.28 0.307539
851851 15817.1 0.637138
852852 −1872.78 −0.0753056
853853 13608.2 0.546232 0.273116 0.961981i 0.411946π-0.411946\pi
0.273116 + 0.961981i 0.411946π0.411946\pi
854854 15411.5 0.617528
855855 −30107.6 −1.20428
856856 33664.1 1.34418
857857 −42926.8 −1.71103 −0.855514 0.517780i 0.826759π-0.826759\pi
−0.855514 + 0.517780i 0.826759π0.826759\pi
858858 0 0
859859 46779.1 1.85807 0.929035 0.369993i 0.120640π-0.120640\pi
0.929035 + 0.369993i 0.120640π0.120640\pi
860860 −8438.41 −0.334590
861861 −27462.4 −1.08701
862862 26072.7 1.03021
863863 −14603.1 −0.576008 −0.288004 0.957629i 0.592992π-0.592992\pi
−0.288004 + 0.957629i 0.592992π0.592992\pi
864864 −1327.92 −0.0522878
865865 8991.63 0.353439
866866 −9798.46 −0.384486
867867 56999.6 2.23277
868868 −333.545 −0.0130429
869869 4722.23 0.184339
870870 −35875.0 −1.39802
871871 0 0
872872 20779.4 0.806973
873873 24315.5 0.942674
874874 20287.1 0.785150
875875 −12448.5 −0.480955
876876 −16283.1 −0.628031
877877 11327.6 0.436152 0.218076 0.975932i 0.430022π-0.430022\pi
0.218076 + 0.975932i 0.430022π0.430022\pi
878878 36505.1 1.40317
879879 −18516.1 −0.710502
880880 4476.17 0.171468
881881 49324.6 1.88625 0.943126 0.332435i 0.107870π-0.107870\pi
0.943126 + 0.332435i 0.107870π0.107870\pi
882882 −16586.0 −0.633195
883883 −471.552 −0.0179717 −0.00898584 0.999960i 0.502860π-0.502860\pi
−0.00898584 + 0.999960i 0.502860π0.502860\pi
884884 0 0
885885 −4034.55 −0.153243
886886 −5296.77 −0.200845
887887 6113.72 0.231430 0.115715 0.993282i 0.463084π-0.463084\pi
0.115715 + 0.993282i 0.463084π0.463084\pi
888888 40481.4 1.52981
889889 360.373 0.0135956
890890 15900.0 0.598840
891891 8541.59 0.321160
892892 3531.11 0.132545
893893 −39252.5 −1.47093
894894 1020.26 0.0381684
895895 18825.4 0.703089
896896 4782.78 0.178327
897897 0 0
898898 −5741.32 −0.213352
899899 −3818.25 −0.141653
900900 1560.75 0.0578055
901901 −28280.9 −1.04570
902902 12179.5 0.449594
903903 23021.6 0.848408
904904 −32267.7 −1.18718
905905 31924.9 1.17262
906906 −44266.6 −1.62324
907907 40444.5 1.48064 0.740319 0.672256i 0.234674π-0.234674\pi
0.740319 + 0.672256i 0.234674π0.234674\pi
908908 11044.8 0.403673
909909 12523.2 0.456952
910910 0 0
911911 −11594.1 −0.421657 −0.210829 0.977523i 0.567616π-0.567616\pi
−0.210829 + 0.977523i 0.567616π0.567616\pi
912912 36315.9 1.31857
913913 −10455.5 −0.378999
914914 −31763.4 −1.14950
915915 55162.5 1.99302
916916 4918.50 0.177415
917917 6017.07 0.216686
918918 3716.69 0.133626
919919 29311.0 1.05210 0.526050 0.850454i 0.323673π-0.323673\pi
0.526050 + 0.850454i 0.323673π0.323673\pi
920920 16769.3 0.600944
921921 −41202.7 −1.47413
922922 36953.2 1.31995
923923 0 0
924924 1455.86 0.0518338
925925 6392.54 0.227228
926926 38424.2 1.36360
927927 19450.5 0.689145
928928 −20405.6 −0.721817
929929 49127.2 1.73500 0.867498 0.497441i 0.165727π-0.165727\pi
0.867498 + 0.497441i 0.165727π0.165727\pi
930930 3109.45 0.109637
931931 33453.8 1.17766
932932 143.895 0.00505734
933933 12635.9 0.443389
934934 −15113.2 −0.529463
935935 12260.9 0.428850
936936 0 0
937937 39342.0 1.37166 0.685831 0.727761i 0.259439π-0.259439\pi
0.685831 + 0.727761i 0.259439π0.259439\pi
938938 −7689.63 −0.267671
939939 −46379.9 −1.61188
940940 −7046.59 −0.244505
941941 13059.3 0.452413 0.226207 0.974079i 0.427368π-0.427368\pi
0.226207 + 0.974079i 0.427368π0.427368\pi
942942 −6486.90 −0.224368
943943 31914.5 1.10210
944944 2344.89 0.0808470
945945 −1111.25 −0.0382529
946946 −10210.1 −0.350907
947947 7521.97 0.258111 0.129055 0.991637i 0.458805π-0.458805\pi
0.129055 + 0.991637i 0.458805π0.458805\pi
948948 6877.78 0.235633
949949 0 0
950950 8199.09 0.280014
951951 70178.4 2.39295
952952 22972.5 0.782083
953953 50289.9 1.70939 0.854696 0.519129i 0.173744π-0.173744\pi
0.854696 + 0.519129i 0.173744π0.173744\pi
954954 15084.4 0.511922
955955 12335.0 0.417959
956956 8564.15 0.289733
957957 16666.0 0.562941
958958 −5822.82 −0.196374
959959 288.048 0.00969924
960960 40116.9 1.34872
961961 −29460.1 −0.988891
962962 0 0
963963 −34400.4 −1.15113
964964 14952.5 0.499572
965965 −6082.58 −0.202907
966966 −9935.89 −0.330934
967967 41353.9 1.37524 0.687618 0.726073i 0.258657π-0.258657\pi
0.687618 + 0.726073i 0.258657π0.258657\pi
968968 −2973.02 −0.0987153
969969 99474.7 3.29782
970970 22931.2 0.759048
971971 22813.7 0.753992 0.376996 0.926215i 0.376957π-0.376957\pi
0.376996 + 0.926215i 0.376957π0.376957\pi
972972 11622.1 0.383516
973973 −2469.22 −0.0813561
974974 −6168.66 −0.202933
975975 0 0
976976 −32060.5 −1.05147
977977 40607.9 1.32975 0.664873 0.746956i 0.268486π-0.268486\pi
0.664873 + 0.746956i 0.268486π0.268486\pi
978978 −52292.6 −1.70975
979979 −7386.45 −0.241136
980980 6005.60 0.195757
981981 −21234.0 −0.691078
982982 −29459.2 −0.957311
983983 3870.30 0.125578 0.0627891 0.998027i 0.480000π-0.480000\pi
0.0627891 + 0.998027i 0.480000π0.480000\pi
984984 81680.0 2.64620
985985 26711.9 0.864074
986986 57112.8 1.84467
987987 19224.5 0.619982
988988 0 0
989989 −26753.8 −0.860184
990990 −6539.66 −0.209944
991991 16961.5 0.543692 0.271846 0.962341i 0.412366π-0.412366\pi
0.271846 + 0.962341i 0.412366π0.412366\pi
992992 1768.64 0.0566074
993993 −32919.9 −1.05204
994994 2321.74 0.0740855
995995 22749.5 0.724832
996996 −15228.1 −0.484459
997997 −19436.4 −0.617409 −0.308704 0.951158i 0.599895π-0.599895\pi
−0.308704 + 0.951158i 0.599895π0.599895\pi
998998 −32224.6 −1.02210
999999 3117.46 0.0987309
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 1859.4.a.j.1.14 18
13.5 odd 4 143.4.b.a.12.10 36
13.8 odd 4 143.4.b.a.12.27 yes 36
13.12 even 2 1859.4.a.k.1.5 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.b.a.12.10 36 13.5 odd 4
143.4.b.a.12.27 yes 36 13.8 odd 4
1859.4.a.j.1.14 18 1.1 even 1 trivial
1859.4.a.k.1.5 18 13.12 even 2