Properties

Label 483.4.a.i.1.9
Level 483483
Weight 44
Character 483.1
Self dual yes
Analytic conductor 28.49828.498
Analytic rank 00
Dimension 99
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] = [483,4,Mod(1,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, 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("483.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 483=3723 483 = 3 \cdot 7 \cdot 23
Weight: k k == 4 4
Character orbit: [χ][\chi] == 483.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [9,8,27] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 28.497922532828.4979225328
Analytic rank: 00
Dimension: 99
Coefficient field: Q[x]/(x9)\mathbb{Q}[x]/(x^{9} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x9x851x7+34x6+861x5401x45403x3+1772x2+8716x192 x^{9} - x^{8} - 51x^{7} + 34x^{6} + 861x^{5} - 401x^{4} - 5403x^{3} + 1772x^{2} + 8716x - 192 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.9
Root 4.47249-4.47249 of defining polynomial
Character χ\chi == 483.1

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+5.47249q2+3.00000q3+21.9481q4+8.93744q5+16.4175q6+7.00000q7+76.3311q8+9.00000q9+48.9100q1064.9462q11+65.8444q12+34.6747q13+38.3074q14+26.8123q15+242.136q1630.9018q17+49.2524q18138.470q19+196.160q20+21.0000q21355.417q2223.0000q23+228.993q2445.1222q25+189.757q26+27.0000q27+153.637q28+16.0755q29+146.730q30142.943q31+714.437q32194.839q33169.110q34+62.5621q35+197.533q36+368.798q37757.774q38+104.024q39+682.204q4079.8823q41+114.922q42441.379q431425.45q44+80.4369q45125.867q46+197.161q47+726.408q48+49.0000q49246.931q5092.7055q51+761.046q52+38.9761q53+147.757q54580.453q55+534.317q56415.409q57+87.9728q58+854.084q59+588.480q60+435.416q61782.257q62+63.0000q63+1972.66q64+309.903q651066.25q66796.063q67678.238q6869.0000q69+342.370q70236.179q71+686.980q72+646.398q73+2018.25q74135.367q753039.15q76454.623q77+569.271q78859.016q79+2164.07q80+81.0000q81437.155q82+821.976q83+460.911q84276.183q852415.44q86+48.2264q874957.41q88+576.608q89+440.190q90+242.723q91504.807q92428.830q93+1078.96q941237.56q95+2143.31q96+1651.08q97+268.152q98584.516q99+O(q100)q+5.47249 q^{2} +3.00000 q^{3} +21.9481 q^{4} +8.93744 q^{5} +16.4175 q^{6} +7.00000 q^{7} +76.3311 q^{8} +9.00000 q^{9} +48.9100 q^{10} -64.9462 q^{11} +65.8444 q^{12} +34.6747 q^{13} +38.3074 q^{14} +26.8123 q^{15} +242.136 q^{16} -30.9018 q^{17} +49.2524 q^{18} -138.470 q^{19} +196.160 q^{20} +21.0000 q^{21} -355.417 q^{22} -23.0000 q^{23} +228.993 q^{24} -45.1222 q^{25} +189.757 q^{26} +27.0000 q^{27} +153.637 q^{28} +16.0755 q^{29} +146.730 q^{30} -142.943 q^{31} +714.437 q^{32} -194.839 q^{33} -169.110 q^{34} +62.5621 q^{35} +197.533 q^{36} +368.798 q^{37} -757.774 q^{38} +104.024 q^{39} +682.204 q^{40} -79.8823 q^{41} +114.922 q^{42} -441.379 q^{43} -1425.45 q^{44} +80.4369 q^{45} -125.867 q^{46} +197.161 q^{47} +726.408 q^{48} +49.0000 q^{49} -246.931 q^{50} -92.7055 q^{51} +761.046 q^{52} +38.9761 q^{53} +147.757 q^{54} -580.453 q^{55} +534.317 q^{56} -415.409 q^{57} +87.9728 q^{58} +854.084 q^{59} +588.480 q^{60} +435.416 q^{61} -782.257 q^{62} +63.0000 q^{63} +1972.66 q^{64} +309.903 q^{65} -1066.25 q^{66} -796.063 q^{67} -678.238 q^{68} -69.0000 q^{69} +342.370 q^{70} -236.179 q^{71} +686.980 q^{72} +646.398 q^{73} +2018.25 q^{74} -135.367 q^{75} -3039.15 q^{76} -454.623 q^{77} +569.271 q^{78} -859.016 q^{79} +2164.07 q^{80} +81.0000 q^{81} -437.155 q^{82} +821.976 q^{83} +460.911 q^{84} -276.183 q^{85} -2415.44 q^{86} +48.2264 q^{87} -4957.41 q^{88} +576.608 q^{89} +440.190 q^{90} +242.723 q^{91} -504.807 q^{92} -428.830 q^{93} +1078.96 q^{94} -1237.56 q^{95} +2143.31 q^{96} +1651.08 q^{97} +268.152 q^{98} -584.516 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 9q+8q2+27q3+38q4+39q5+24q6+63q7+135q8+81q9+81q10+38q11+114q12+107q13+56q14+117q15+178q16+170q17+72q18++342q99+O(q100) 9 q + 8 q^{2} + 27 q^{3} + 38 q^{4} + 39 q^{5} + 24 q^{6} + 63 q^{7} + 135 q^{8} + 81 q^{9} + 81 q^{10} + 38 q^{11} + 114 q^{12} + 107 q^{13} + 56 q^{14} + 117 q^{15} + 178 q^{16} + 170 q^{17} + 72 q^{18}+ \cdots + 342 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 5.47249 1.93482 0.967409 0.253220i 0.0814898π-0.0814898\pi
0.967409 + 0.253220i 0.0814898π0.0814898\pi
33 3.00000 0.577350
44 21.9481 2.74352
55 8.93744 0.799389 0.399694 0.916648i 0.369116π-0.369116\pi
0.399694 + 0.916648i 0.369116π0.369116\pi
66 16.4175 1.11707
77 7.00000 0.377964
88 76.3311 3.37339
99 9.00000 0.333333
1010 48.9100 1.54667
1111 −64.9462 −1.78018 −0.890092 0.455782i 0.849360π-0.849360\pi
−0.890092 + 0.455782i 0.849360π0.849360\pi
1212 65.8444 1.58397
1313 34.6747 0.739772 0.369886 0.929077i 0.379397π-0.379397\pi
0.369886 + 0.929077i 0.379397π0.379397\pi
1414 38.3074 0.731292
1515 26.8123 0.461527
1616 242.136 3.78337
1717 −30.9018 −0.440870 −0.220435 0.975402i 0.570748π-0.570748\pi
−0.220435 + 0.975402i 0.570748π0.570748\pi
1818 49.2524 0.644939
1919 −138.470 −1.67195 −0.835977 0.548765i 0.815098π-0.815098\pi
−0.835977 + 0.548765i 0.815098π0.815098\pi
2020 196.160 2.19314
2121 21.0000 0.218218
2222 −355.417 −3.44433
2323 −23.0000 −0.208514
2424 228.993 1.94763
2525 −45.1222 −0.360978
2626 189.757 1.43132
2727 27.0000 0.192450
2828 153.637 1.03695
2929 16.0755 0.102936 0.0514679 0.998675i 0.483610π-0.483610\pi
0.0514679 + 0.998675i 0.483610π0.483610\pi
3030 146.730 0.892971
3131 −142.943 −0.828174 −0.414087 0.910237i 0.635899π-0.635899\pi
−0.414087 + 0.910237i 0.635899π0.635899\pi
3232 714.437 3.94675
3333 −194.839 −1.02779
3434 −169.110 −0.853003
3535 62.5621 0.302141
3636 197.533 0.914506
3737 368.798 1.63865 0.819325 0.573329i 0.194348π-0.194348\pi
0.819325 + 0.573329i 0.194348π0.194348\pi
3838 −757.774 −3.23493
3939 104.024 0.427108
4040 682.204 2.69665
4141 −79.8823 −0.304281 −0.152140 0.988359i 0.548617π-0.548617\pi
−0.152140 + 0.988359i 0.548617π0.548617\pi
4242 114.922 0.422212
4343 −441.379 −1.56534 −0.782670 0.622437i 0.786143π-0.786143\pi
−0.782670 + 0.622437i 0.786143π0.786143\pi
4444 −1425.45 −4.88396
4545 80.4369 0.266463
4646 −125.867 −0.403437
4747 197.161 0.611893 0.305946 0.952049i 0.401027π-0.401027\pi
0.305946 + 0.952049i 0.401027π0.401027\pi
4848 726.408 2.18433
4949 49.0000 0.142857
5050 −246.931 −0.698426
5151 −92.7055 −0.254537
5252 761.046 2.02958
5353 38.9761 0.101015 0.0505073 0.998724i 0.483916π-0.483916\pi
0.0505073 + 0.998724i 0.483916π0.483916\pi
5454 147.757 0.372356
5555 −580.453 −1.42306
5656 534.317 1.27502
5757 −415.409 −0.965303
5858 87.9728 0.199162
5959 854.084 1.88461 0.942307 0.334750i 0.108652π-0.108652\pi
0.942307 + 0.334750i 0.108652π0.108652\pi
6060 588.480 1.26621
6161 435.416 0.913923 0.456962 0.889486i 0.348938π-0.348938\pi
0.456962 + 0.889486i 0.348938π0.348938\pi
6262 −782.257 −1.60237
6363 63.0000 0.125988
6464 1972.66 3.85286
6565 309.903 0.591366
6666 −1066.25 −1.98858
6767 −796.063 −1.45156 −0.725781 0.687926i 0.758521π-0.758521\pi
−0.725781 + 0.687926i 0.758521π0.758521\pi
6868 −678.238 −1.20954
6969 −69.0000 −0.120386
7070 342.370 0.584587
7171 −236.179 −0.394779 −0.197389 0.980325i 0.563246π-0.563246\pi
−0.197389 + 0.980325i 0.563246π0.563246\pi
7272 686.980 1.12446
7373 646.398 1.03637 0.518186 0.855268i 0.326608π-0.326608\pi
0.518186 + 0.855268i 0.326608π0.326608\pi
7474 2018.25 3.17049
7575 −135.367 −0.208411
7676 −3039.15 −4.58704
7777 −454.623 −0.672846
7878 569.271 0.826375
7979 −859.016 −1.22338 −0.611689 0.791098i 0.709510π-0.709510\pi
−0.611689 + 0.791098i 0.709510π0.709510\pi
8080 2164.07 3.02439
8181 81.0000 0.111111
8282 −437.155 −0.588728
8383 821.976 1.08703 0.543516 0.839399i 0.317093π-0.317093\pi
0.543516 + 0.839399i 0.317093π0.317093\pi
8484 460.911 0.598685
8585 −276.183 −0.352427
8686 −2415.44 −3.02865
8787 48.2264 0.0594300
8888 −4957.41 −6.00525
8989 576.608 0.686745 0.343373 0.939199i 0.388431π-0.388431\pi
0.343373 + 0.939199i 0.388431π0.388431\pi
9090 440.190 0.515557
9191 242.723 0.279608
9292 −504.807 −0.572063
9393 −428.830 −0.478147
9494 1078.96 1.18390
9595 −1237.56 −1.33654
9696 2143.31 2.27865
9797 1651.08 1.72826 0.864131 0.503268i 0.167869π-0.167869\pi
0.864131 + 0.503268i 0.167869π0.167869\pi
9898 268.152 0.276402
9999 −584.516 −0.593394
100100 −990.349 −0.990349
101101 −1177.39 −1.15995 −0.579974 0.814635i 0.696937π-0.696937\pi
−0.579974 + 0.814635i 0.696937π0.696937\pi
102102 −507.330 −0.492482
103103 1358.79 1.29986 0.649930 0.759994i 0.274798π-0.274798\pi
0.649930 + 0.759994i 0.274798π0.274798\pi
104104 2646.76 2.49554
105105 187.686 0.174441
106106 213.296 0.195445
107107 −550.175 −0.497079 −0.248539 0.968622i 0.579951π-0.579951\pi
−0.248539 + 0.968622i 0.579951π0.579951\pi
108108 592.600 0.527990
109109 −996.931 −0.876042 −0.438021 0.898965i 0.644321π-0.644321\pi
−0.438021 + 0.898965i 0.644321π0.644321\pi
110110 −3176.52 −2.75336
111111 1106.40 0.946075
112112 1694.95 1.42998
113113 1890.29 1.57366 0.786828 0.617172i 0.211722π-0.211722\pi
0.786828 + 0.617172i 0.211722π0.211722\pi
114114 −2273.32 −1.86768
115115 −205.561 −0.166684
116116 352.827 0.282406
117117 312.073 0.246591
118118 4673.96 3.64638
119119 −216.313 −0.166633
120120 2046.61 1.55691
121121 2887.01 2.16905
122122 2382.81 1.76827
123123 −239.647 −0.175677
124124 −3137.34 −2.27211
125125 −1520.46 −1.08795
126126 344.767 0.243764
127127 −2062.71 −1.44123 −0.720613 0.693337i 0.756140π-0.756140\pi
−0.720613 + 0.693337i 0.756140π0.756140\pi
128128 5079.89 3.50783
129129 −1324.14 −0.903750
130130 1695.94 1.14418
131131 −1112.85 −0.742218 −0.371109 0.928589i 0.621022π-0.621022\pi
−0.371109 + 0.928589i 0.621022π0.621022\pi
132132 −4276.35 −2.81976
133133 −969.288 −0.631939
134134 −4356.45 −2.80851
135135 241.311 0.153842
136136 −2358.77 −1.48723
137137 −456.121 −0.284446 −0.142223 0.989835i 0.545425π-0.545425\pi
−0.142223 + 0.989835i 0.545425π0.545425\pi
138138 −377.602 −0.232925
139139 618.754 0.377569 0.188784 0.982019i 0.439545π-0.439545\pi
0.188784 + 0.982019i 0.439545π0.439545\pi
140140 1373.12 0.828928
141141 591.484 0.353276
142142 −1292.49 −0.763824
143143 −2251.99 −1.31693
144144 2179.22 1.26112
145145 143.674 0.0822858
146146 3537.40 2.00519
147147 147.000 0.0824786
148148 8094.44 4.49567
149149 191.696 0.105398 0.0526992 0.998610i 0.483218π-0.483218\pi
0.0526992 + 0.998610i 0.483218π0.483218\pi
150150 −740.792 −0.403236
151151 −1503.50 −0.810288 −0.405144 0.914253i 0.632779π-0.632779\pi
−0.405144 + 0.914253i 0.632779π0.632779\pi
152152 −10569.5 −5.64015
153153 −278.116 −0.146957
154154 −2487.92 −1.30183
155155 −1277.55 −0.662033
156156 2283.14 1.17178
157157 −1360.53 −0.691605 −0.345803 0.938307i 0.612393π-0.612393\pi
−0.345803 + 0.938307i 0.612393π0.612393\pi
158158 −4700.96 −2.36701
159159 116.928 0.0583209
160160 6385.24 3.15498
161161 −161.000 −0.0788110
162162 443.272 0.214980
163163 2283.61 1.09734 0.548670 0.836039i 0.315134π-0.315134\pi
0.548670 + 0.836039i 0.315134π0.315134\pi
164164 −1753.27 −0.834800
165165 −1741.36 −0.821603
166166 4498.26 2.10321
167167 −970.287 −0.449599 −0.224800 0.974405i 0.572173π-0.572173\pi
−0.224800 + 0.974405i 0.572173π0.572173\pi
168168 1602.95 0.736134
169169 −994.664 −0.452737
170170 −1511.41 −0.681881
171171 −1246.23 −0.557318
172172 −9687.45 −4.29454
173173 −2175.48 −0.956062 −0.478031 0.878343i 0.658649π-0.658649\pi
−0.478031 + 0.878343i 0.658649π0.658649\pi
174174 263.919 0.114986
175175 −315.855 −0.136437
176176 −15725.8 −6.73510
177177 2562.25 1.08808
178178 3155.48 1.32873
179179 3254.30 1.35887 0.679435 0.733736i 0.262225π-0.262225\pi
0.679435 + 0.733736i 0.262225π0.262225\pi
180180 1765.44 0.731046
181181 1147.73 0.471325 0.235663 0.971835i 0.424274π-0.424274\pi
0.235663 + 0.971835i 0.424274π0.424274\pi
182182 1328.30 0.540990
183183 1306.25 0.527654
184184 −1755.61 −0.703400
185185 3296.11 1.30992
186186 −2346.77 −0.925126
187187 2006.96 0.784830
188188 4327.33 1.67874
189189 189.000 0.0727393
190190 −6772.56 −2.58596
191191 −865.071 −0.327719 −0.163859 0.986484i 0.552394π-0.552394\pi
−0.163859 + 0.986484i 0.552394π0.552394\pi
192192 5917.99 2.22445
193193 −2005.48 −0.747969 −0.373984 0.927435i 0.622009π-0.622009\pi
−0.373984 + 0.927435i 0.622009π0.622009\pi
194194 9035.49 3.34387
195195 929.710 0.341425
196196 1075.46 0.391931
197197 −218.707 −0.0790975 −0.0395488 0.999218i 0.512592π-0.512592\pi
−0.0395488 + 0.999218i 0.512592π0.512592\pi
198198 −3198.76 −1.14811
199199 −273.538 −0.0974401 −0.0487201 0.998812i 0.515514π-0.515514\pi
−0.0487201 + 0.998812i 0.515514π0.515514\pi
200200 −3444.23 −1.21772
201201 −2388.19 −0.838059
202202 −6443.26 −2.24429
203203 112.528 0.0389061
204204 −2034.71 −0.698326
205205 −713.943 −0.243239
206206 7435.96 2.51499
207207 −207.000 −0.0695048
208208 8395.99 2.79883
209209 8993.08 2.97638
210210 1027.11 0.337511
211211 899.743 0.293559 0.146779 0.989169i 0.453109π-0.453109\pi
0.146779 + 0.989169i 0.453109π0.453109\pi
212212 855.453 0.277136
213213 −708.537 −0.227926
214214 −3010.83 −0.961756
215215 −3944.80 −1.25132
216216 2060.94 0.649209
217217 −1000.60 −0.313020
218218 −5455.69 −1.69498
219219 1939.19 0.598349
220220 −12739.9 −3.90419
221221 −1071.51 −0.326144
222222 6054.74 1.83048
223223 −827.023 −0.248348 −0.124174 0.992260i 0.539628π-0.539628\pi
−0.124174 + 0.992260i 0.539628π0.539628\pi
224224 5001.06 1.49173
225225 −406.100 −0.120326
226226 10344.6 3.04474
227227 −3323.67 −0.971806 −0.485903 0.874013i 0.661509π-0.661509\pi
−0.485903 + 0.874013i 0.661509π0.661509\pi
228228 −9117.46 −2.64833
229229 4620.63 1.33336 0.666681 0.745343i 0.267714π-0.267714\pi
0.666681 + 0.745343i 0.267714π0.267714\pi
230230 −1124.93 −0.322503
231231 −1363.87 −0.388468
232232 1227.06 0.347243
233233 −2523.32 −0.709478 −0.354739 0.934965i 0.615430π-0.615430\pi
−0.354739 + 0.934965i 0.615430π0.615430\pi
234234 1707.81 0.477108
235235 1762.12 0.489140
236236 18745.5 5.17047
237237 −2577.05 −0.706318
238238 −1183.77 −0.322405
239239 4250.48 1.15038 0.575190 0.818020i 0.304928π-0.304928\pi
0.575190 + 0.818020i 0.304928π0.304928\pi
240240 6492.22 1.74613
241241 −7054.93 −1.88568 −0.942838 0.333250i 0.891855π-0.891855\pi
−0.942838 + 0.333250i 0.891855π0.891855\pi
242242 15799.1 4.19672
243243 243.000 0.0641500
244244 9556.58 2.50736
245245 437.934 0.114198
246246 −1311.46 −0.339902
247247 −4801.40 −1.23686
248248 −10911.0 −2.79375
249249 2465.93 0.627598
250250 −8320.68 −2.10498
251251 5829.72 1.46601 0.733005 0.680223i 0.238117π-0.238117\pi
0.733005 + 0.680223i 0.238117π0.238117\pi
252252 1382.73 0.345651
253253 1493.76 0.371194
254254 −11288.2 −2.78851
255255 −828.550 −0.203474
256256 12018.3 2.93416
257257 −1639.22 −0.397866 −0.198933 0.980013i 0.563748π-0.563748\pi
−0.198933 + 0.980013i 0.563748π0.563748\pi
258258 −7246.32 −1.74859
259259 2581.59 0.619352
260260 6801.80 1.62242
261261 144.679 0.0343120
262262 −6090.09 −1.43606
263263 −273.365 −0.0640927 −0.0320464 0.999486i 0.510202π-0.510202\pi
−0.0320464 + 0.999486i 0.510202π0.510202\pi
264264 −14872.2 −3.46713
265265 348.346 0.0807500
266266 −5304.42 −1.22269
267267 1729.82 0.396492
268268 −17472.1 −3.98238
269269 7443.39 1.68711 0.843553 0.537046i 0.180460π-0.180460\pi
0.843553 + 0.537046i 0.180460π0.180460\pi
270270 1320.57 0.297657
271271 3102.28 0.695388 0.347694 0.937608i 0.386965π-0.386965\pi
0.347694 + 0.937608i 0.386965π0.386965\pi
272272 −7482.44 −1.66798
273273 728.169 0.161432
274274 −2496.12 −0.550350
275275 2930.52 0.642606
276276 −1514.42 −0.330281
277277 2151.15 0.466608 0.233304 0.972404i 0.425046π-0.425046\pi
0.233304 + 0.972404i 0.425046π0.425046\pi
278278 3386.13 0.730527
279279 −1286.49 −0.276058
280280 4775.43 1.01924
281281 664.784 0.141131 0.0705653 0.997507i 0.477520π-0.477520\pi
0.0705653 + 0.997507i 0.477520π0.477520\pi
282282 3236.89 0.683525
283283 2923.45 0.614067 0.307033 0.951699i 0.400664π-0.400664\pi
0.307033 + 0.951699i 0.400664π0.400664\pi
284284 −5183.69 −1.08308
285285 −3712.69 −0.771652
286286 −12324.0 −2.54802
287287 −559.176 −0.115007
288288 6429.94 1.31558
289289 −3958.08 −0.805633
290290 786.252 0.159208
291291 4953.23 0.997812
292292 14187.2 2.84330
293293 −1765.02 −0.351924 −0.175962 0.984397i 0.556304π-0.556304\pi
−0.175962 + 0.984397i 0.556304π0.556304\pi
294294 804.456 0.159581
295295 7633.32 1.50654
296296 28150.8 5.52781
297297 −1753.55 −0.342596
298298 1049.06 0.203927
299299 −797.519 −0.154253
300300 −2971.05 −0.571778
301301 −3089.65 −0.591643
302302 −8227.91 −1.56776
303303 −3532.17 −0.669696
304304 −33528.5 −6.32562
305305 3891.50 0.730580
306306 −1521.99 −0.284334
307307 −4091.63 −0.760657 −0.380328 0.924852i 0.624189π-0.624189\pi
−0.380328 + 0.924852i 0.624189π0.624189\pi
308308 −9978.14 −1.84596
309309 4076.37 0.750474
310310 −6991.37 −1.28091
311311 2508.33 0.457346 0.228673 0.973503i 0.426561π-0.426561\pi
0.228673 + 0.973503i 0.426561π0.426561\pi
312312 7940.28 1.44080
313313 −2276.71 −0.411142 −0.205571 0.978642i 0.565905π-0.565905\pi
−0.205571 + 0.978642i 0.565905π0.565905\pi
314314 −7445.48 −1.33813
315315 563.059 0.100714
316316 −18853.8 −3.35636
317317 2282.31 0.404377 0.202188 0.979347i 0.435195π-0.435195\pi
0.202188 + 0.979347i 0.435195π0.435195\pi
318318 639.889 0.112840
319319 −1044.04 −0.183245
320320 17630.6 3.07993
321321 −1650.52 −0.286988
322322 −881.071 −0.152485
323323 4278.97 0.737115
324324 1777.80 0.304835
325325 −1564.60 −0.267041
326326 12497.0 2.12315
327327 −2990.79 −0.505783
328328 −6097.50 −1.02646
329329 1380.13 0.231274
330330 −9529.56 −1.58965
331331 −6834.36 −1.13490 −0.567448 0.823409i 0.692069π-0.692069\pi
−0.567448 + 0.823409i 0.692069π0.692069\pi
332332 18040.9 2.98229
333333 3319.19 0.546217
334334 −5309.89 −0.869892
335335 −7114.76 −1.16036
336336 5084.85 0.825600
337337 −2946.37 −0.476258 −0.238129 0.971234i 0.576534π-0.576534\pi
−0.238129 + 0.971234i 0.576534π0.576534\pi
338338 −5443.29 −0.875964
339339 5670.86 0.908551
340340 −6061.71 −0.966889
341341 9283.63 1.47430
342342 −6819.96 −1.07831
343343 343.000 0.0539949
344344 −33690.9 −5.28050
345345 −616.683 −0.0962351
346346 −11905.3 −1.84981
347347 10980.7 1.69878 0.849391 0.527764i 0.176970π-0.176970\pi
0.849391 + 0.527764i 0.176970π0.176970\pi
348348 1058.48 0.163047
349349 −1299.92 −0.199379 −0.0996894 0.995019i 0.531785π-0.531785\pi
−0.0996894 + 0.995019i 0.531785π0.531785\pi
350350 −1728.52 −0.263980
351351 936.218 0.142369
352352 −46400.0 −7.02593
353353 −5177.82 −0.780702 −0.390351 0.920666i 0.627646π-0.627646\pi
−0.390351 + 0.920666i 0.627646π0.627646\pi
354354 14021.9 2.10524
355355 −2110.83 −0.315582
356356 12655.5 1.88410
357357 −648.938 −0.0962058
358358 17809.1 2.62916
359359 11913.7 1.75148 0.875740 0.482784i 0.160374π-0.160374\pi
0.875740 + 0.482784i 0.160374π0.160374\pi
360360 6139.84 0.898883
361361 12314.9 1.79543
362362 6280.93 0.911929
363363 8661.02 1.25230
364364 5327.32 0.767108
365365 5777.14 0.828464
366366 7148.43 1.02091
367367 2003.44 0.284956 0.142478 0.989798i 0.454493π-0.454493\pi
0.142478 + 0.989798i 0.454493π0.454493\pi
368368 −5569.12 −0.788888
369369 −718.940 −0.101427
370370 18037.9 2.53445
371371 272.833 0.0381800
372372 −9412.03 −1.31180
373373 5882.77 0.816618 0.408309 0.912844i 0.366119π-0.366119\pi
0.408309 + 0.912844i 0.366119π0.366119\pi
374374 10983.0 1.51850
375375 −4561.37 −0.628128
376376 15049.5 2.06415
377377 557.412 0.0761491
378378 1034.30 0.140737
379379 −11601.1 −1.57232 −0.786162 0.618020i 0.787935π-0.787935\pi
−0.786162 + 0.618020i 0.787935π0.787935\pi
380380 −27162.2 −3.66682
381381 −6188.13 −0.832093
382382 −4734.09 −0.634076
383383 −1653.63 −0.220618 −0.110309 0.993897i 0.535184π-0.535184\pi
−0.110309 + 0.993897i 0.535184π0.535184\pi
384384 15239.7 2.02525
385385 −4063.17 −0.537865
386386 −10975.0 −1.44718
387387 −3972.41 −0.521780
388388 36238.0 4.74152
389389 −11585.3 −1.51002 −0.755008 0.655716i 0.772367π-0.772367\pi
−0.755008 + 0.655716i 0.772367π0.772367\pi
390390 5087.83 0.660595
391391 710.742 0.0919278
392392 3740.22 0.481913
393393 −3338.56 −0.428520
394394 −1196.87 −0.153039
395395 −7677.41 −0.977955
396396 −12829.0 −1.62799
397397 −2639.48 −0.333682 −0.166841 0.985984i 0.553357π-0.553357\pi
−0.166841 + 0.985984i 0.553357π0.553357\pi
398398 −1496.93 −0.188529
399399 −2907.86 −0.364850
400400 −10925.7 −1.36571
401401 2043.37 0.254466 0.127233 0.991873i 0.459390π-0.459390\pi
0.127233 + 0.991873i 0.459390π0.459390\pi
402402 −13069.3 −1.62149
403403 −4956.52 −0.612660
404404 −25841.5 −3.18234
405405 723.932 0.0888210
406406 615.810 0.0752762
407407 −23952.0 −2.91710
408408 −7076.31 −0.858651
409409 2054.04 0.248327 0.124163 0.992262i 0.460375π-0.460375\pi
0.124163 + 0.992262i 0.460375π0.460375\pi
410410 −3907.04 −0.470622
411411 −1368.36 −0.164225
412412 29822.9 3.56619
413413 5978.59 0.712317
414414 −1132.81 −0.134479
415415 7346.36 0.868961
416416 24772.9 2.91969
417417 1856.26 0.217989
418418 49214.5 5.75876
419419 −3741.09 −0.436191 −0.218095 0.975927i 0.569984π-0.569984\pi
−0.218095 + 0.975927i 0.569984π0.569984\pi
420420 4119.36 0.478582
421421 −7830.25 −0.906468 −0.453234 0.891392i 0.649730π-0.649730\pi
−0.453234 + 0.891392i 0.649730π0.649730\pi
422422 4923.83 0.567982
423423 1774.45 0.203964
424424 2975.09 0.340762
425425 1394.36 0.159144
426426 −3877.46 −0.440994
427427 3047.91 0.345431
428428 −12075.3 −1.36374
429429 −6755.97 −0.760330
430430 −21587.9 −2.42107
431431 14614.5 1.63331 0.816654 0.577128i 0.195827π-0.195827\pi
0.816654 + 0.577128i 0.195827π0.195827\pi
432432 6537.67 0.728110
433433 −1920.46 −0.213144 −0.106572 0.994305i 0.533987π-0.533987\pi
−0.106572 + 0.994305i 0.533987π0.533987\pi
434434 −5475.80 −0.605637
435435 431.021 0.0475077
436436 −21880.8 −2.40344
437437 3184.80 0.348626
438438 10612.2 1.15770
439439 4703.07 0.511310 0.255655 0.966768i 0.417709π-0.417709\pi
0.255655 + 0.966768i 0.417709π0.417709\pi
440440 −44306.6 −4.80053
441441 441.000 0.0476190
442442 −5863.84 −0.631028
443443 5855.09 0.627954 0.313977 0.949431i 0.398338π-0.398338\pi
0.313977 + 0.949431i 0.398338π0.398338\pi
444444 24283.3 2.59557
445445 5153.40 0.548976
446446 −4525.87 −0.480507
447447 575.088 0.0608518
448448 13808.6 1.45624
449449 14581.6 1.53262 0.766312 0.642469i 0.222090π-0.222090\pi
0.766312 + 0.642469i 0.222090π0.222090\pi
450450 −2222.38 −0.232809
451451 5188.05 0.541676
452452 41488.3 4.31735
453453 −4510.51 −0.467820
454454 −18188.8 −1.88027
455455 2169.32 0.223515
456456 −31708.6 −3.25634
457457 −1552.87 −0.158950 −0.0794752 0.996837i 0.525324π-0.525324\pi
−0.0794752 + 0.996837i 0.525324π0.525324\pi
458458 25286.4 2.57981
459459 −834.349 −0.0848455
460460 −4511.68 −0.457301
461461 11609.2 1.17287 0.586436 0.809996i 0.300531π-0.300531\pi
0.586436 + 0.809996i 0.300531π0.300531\pi
462462 −7463.76 −0.751614
463463 −15818.5 −1.58779 −0.793897 0.608053i 0.791951π-0.791951\pi
−0.793897 + 0.608053i 0.791951π0.791951\pi
464464 3892.45 0.389445
465465 −3832.64 −0.382225
466466 −13808.9 −1.37271
467467 11797.8 1.16903 0.584516 0.811382i 0.301285π-0.301285\pi
0.584516 + 0.811382i 0.301285π0.301285\pi
468468 6849.41 0.676526
469469 −5572.44 −0.548639
470470 9643.17 0.946397
471471 −4081.59 −0.399298
472472 65193.1 6.35753
473473 28665.9 2.78659
474474 −14102.9 −1.36660
475475 6248.06 0.603538
476476 −4747.66 −0.457161
477477 350.785 0.0336716
478478 23260.7 2.22578
479479 −9158.14 −0.873582 −0.436791 0.899563i 0.643885π-0.643885\pi
−0.436791 + 0.899563i 0.643885π0.643885\pi
480480 19155.7 1.82153
481481 12788.0 1.21223
482482 −38608.0 −3.64844
483483 −483.000 −0.0455016
484484 63364.5 5.95083
485485 14756.4 1.38155
486486 1329.81 0.124119
487487 16332.9 1.51974 0.759871 0.650074i 0.225262π-0.225262\pi
0.759871 + 0.650074i 0.225262π0.225262\pi
488488 33235.8 3.08302
489489 6850.84 0.633549
490490 2396.59 0.220953
491491 17333.9 1.59321 0.796607 0.604498i 0.206626π-0.206626\pi
0.796607 + 0.604498i 0.206626π0.206626\pi
492492 −5259.80 −0.481972
493493 −496.761 −0.0453814
494494 −26275.6 −2.39311
495495 −5224.07 −0.474353
496496 −34611.7 −3.13329
497497 −1653.25 −0.149212
498498 13494.8 1.21429
499499 9399.30 0.843227 0.421614 0.906776i 0.361464π-0.361464\pi
0.421614 + 0.906776i 0.361464π0.361464\pi
500500 −33371.2 −2.98481
501501 −2910.86 −0.259576
502502 31903.1 2.83646
503503 16313.9 1.44612 0.723062 0.690783i 0.242734π-0.242734\pi
0.723062 + 0.690783i 0.242734π0.242734\pi
504504 4808.86 0.425007
505505 −10522.9 −0.927249
506506 8174.60 0.718192
507507 −2983.99 −0.261388
508508 −45272.6 −3.95403
509509 14553.0 1.26729 0.633643 0.773626i 0.281559π-0.281559\pi
0.633643 + 0.773626i 0.281559π0.281559\pi
510510 −4534.23 −0.393684
511511 4524.78 0.391712
512512 25131.0 2.16922
513513 −3738.68 −0.321768
514514 −8970.59 −0.769797
515515 12144.1 1.03909
516516 −29062.3 −2.47945
517517 −12804.9 −1.08928
518518 14127.7 1.19833
519519 −6526.44 −0.551983
520520 23655.2 1.99491
521521 3658.55 0.307647 0.153823 0.988098i 0.450841π-0.450841\pi
0.153823 + 0.988098i 0.450841π0.450841\pi
522522 791.756 0.0663874
523523 9660.17 0.807667 0.403834 0.914832i 0.367677π-0.367677\pi
0.403834 + 0.914832i 0.367677π0.367677\pi
524524 −24425.1 −2.03629
525525 −947.566 −0.0787718
526526 −1495.99 −0.124008
527527 4417.21 0.365117
528528 −47177.4 −3.88851
529529 529.000 0.0434783
530530 1906.32 0.156236
531531 7686.75 0.628205
532532 −21274.1 −1.73374
533533 −2769.90 −0.225098
534534 9466.44 0.767140
535535 −4917.15 −0.397359
536536 −60764.4 −4.89668
537537 9762.89 0.784544
538538 40733.9 3.26424
539539 −3182.36 −0.254312
540540 5296.32 0.422069
541541 −11525.7 −0.915950 −0.457975 0.888965i 0.651425π-0.651425\pi
−0.457975 + 0.888965i 0.651425π0.651425\pi
542542 16977.2 1.34545
543543 3443.18 0.272120
544544 −22077.4 −1.74000
545545 −8910.00 −0.700298
546546 3984.90 0.312340
547547 −18887.0 −1.47633 −0.738163 0.674623i 0.764306π-0.764306\pi
−0.738163 + 0.674623i 0.764306π0.764306\pi
548548 −10011.0 −0.780381
549549 3918.75 0.304641
550550 16037.2 1.24333
551551 −2225.97 −0.172104
552552 −5266.84 −0.406108
553553 −6013.11 −0.462394
554554 11772.2 0.902801
555555 9888.34 0.756282
556556 13580.5 1.03587
557557 −13486.0 −1.02589 −0.512943 0.858423i 0.671445π-0.671445\pi
−0.512943 + 0.858423i 0.671445π0.671445\pi
558558 −7040.31 −0.534122
559559 −15304.7 −1.15800
560560 15148.5 1.14311
561561 6020.87 0.453122
562562 3638.02 0.273062
563563 −16192.7 −1.21215 −0.606075 0.795408i 0.707257π-0.707257\pi
−0.606075 + 0.795408i 0.707257π0.707257\pi
564564 12982.0 0.969220
565565 16894.3 1.25796
566566 15998.5 1.18811
567567 567.000 0.0419961
568568 −18027.8 −1.33174
569569 9293.58 0.684722 0.342361 0.939568i 0.388773π-0.388773\pi
0.342361 + 0.939568i 0.388773π0.388773\pi
570570 −20317.7 −1.49301
571571 15286.5 1.12035 0.560175 0.828374i 0.310734π-0.310734\pi
0.560175 + 0.828374i 0.310734π0.310734\pi
572572 −49427.0 −3.61302
573573 −2595.21 −0.189209
574574 −3060.08 −0.222518
575575 1037.81 0.0752690
576576 17754.0 1.28429
577577 −10993.2 −0.793161 −0.396581 0.918000i 0.629803π-0.629803\pi
−0.396581 + 0.918000i 0.629803π0.629803\pi
578578 −21660.5 −1.55875
579579 −6016.45 −0.431840
580580 3153.37 0.225752
581581 5753.83 0.410859
582582 27106.5 1.93058
583583 −2531.35 −0.179825
584584 49340.2 3.49608
585585 2789.13 0.197122
586586 −9659.06 −0.680908
587587 −5939.95 −0.417663 −0.208831 0.977952i 0.566966π-0.566966\pi
−0.208831 + 0.977952i 0.566966π0.566966\pi
588588 3226.38 0.226282
589589 19793.3 1.38467
590590 41773.3 2.91488
591591 −656.120 −0.0456670
592592 89299.3 6.19963
593593 −11704.3 −0.810518 −0.405259 0.914202i 0.632819π-0.632819\pi
−0.405259 + 0.914202i 0.632819π0.632819\pi
594594 −9596.27 −0.662861
595595 −1933.28 −0.133205
596596 4207.37 0.289162
597597 −820.614 −0.0562571
598598 −4364.41 −0.298452
599599 −3212.92 −0.219159 −0.109580 0.993978i 0.534950π-0.534950\pi
−0.109580 + 0.993978i 0.534950π0.534950\pi
600600 −10332.7 −0.703050
601601 24141.0 1.63849 0.819246 0.573442i 0.194392π-0.194392\pi
0.819246 + 0.573442i 0.194392π0.194392\pi
602602 −16908.1 −1.14472
603603 −7164.57 −0.483854
604604 −32999.1 −2.22304
605605 25802.5 1.73392
606606 −19329.8 −1.29574
607607 −8240.03 −0.550993 −0.275496 0.961302i 0.588842π-0.588842\pi
−0.275496 + 0.961302i 0.588842π0.588842\pi
608608 −98927.9 −6.59878
609609 337.585 0.0224624
610610 21296.2 1.41354
611611 6836.52 0.452661
612612 −6104.14 −0.403178
613613 −24760.8 −1.63145 −0.815726 0.578438i 0.803662π-0.803662\pi
−0.815726 + 0.578438i 0.803662π0.803662\pi
614614 −22391.4 −1.47173
615615 −2141.83 −0.140434
616616 −34701.9 −2.26977
617617 −4624.30 −0.301730 −0.150865 0.988554i 0.548206π-0.548206\pi
−0.150865 + 0.988554i 0.548206π0.548206\pi
618618 22307.9 1.45203
619619 −1330.77 −0.0864103 −0.0432051 0.999066i 0.513757π-0.513757\pi
−0.0432051 + 0.999066i 0.513757π0.513757\pi
620620 −28039.8 −1.81630
621621 −621.000 −0.0401286
622622 13726.8 0.884880
623623 4036.25 0.259565
624624 25188.0 1.61591
625625 −7948.71 −0.508717
626626 −12459.3 −0.795484
627627 26979.2 1.71842
628628 −29861.1 −1.89743
629629 −11396.5 −0.722432
630630 3081.33 0.194862
631631 −29390.6 −1.85423 −0.927117 0.374773i 0.877721π-0.877721\pi
−0.927117 + 0.374773i 0.877721π0.877721\pi
632632 −65569.6 −4.12693
633633 2699.23 0.169486
634634 12489.9 0.782396
635635 −18435.3 −1.15210
636636 2566.36 0.160004
637637 1699.06 0.105682
638638 −5713.50 −0.354545
639639 −2125.61 −0.131593
640640 45401.2 2.80412
641641 −8899.76 −0.548392 −0.274196 0.961674i 0.588412π-0.588412\pi
−0.274196 + 0.961674i 0.588412π0.588412\pi
642642 −9032.48 −0.555270
643643 24093.0 1.47766 0.738830 0.673892i 0.235379π-0.235379\pi
0.738830 + 0.673892i 0.235379π0.235379\pi
644644 −3533.65 −0.216219
645645 −11834.4 −0.722447
646646 23416.6 1.42618
647647 −15696.8 −0.953796 −0.476898 0.878959i 0.658239π-0.658239\pi
−0.476898 + 0.878959i 0.658239π0.658239\pi
648648 6182.82 0.374821
649649 −55469.5 −3.35496
650650 −8562.26 −0.516676
651651 −3001.81 −0.180722
652652 50121.1 3.01057
653653 8664.84 0.519267 0.259634 0.965707i 0.416398π-0.416398\pi
0.259634 + 0.965707i 0.416398π0.416398\pi
654654 −16367.1 −0.978598
655655 −9946.07 −0.593321
656656 −19342.4 −1.15121
657657 5817.58 0.345457
658658 7552.75 0.447472
659659 −18667.0 −1.10343 −0.551716 0.834032i 0.686027π-0.686027\pi
−0.551716 + 0.834032i 0.686027π0.686027\pi
660660 −38219.6 −2.25408
661661 14121.6 0.830964 0.415482 0.909601i 0.363613π-0.363613\pi
0.415482 + 0.909601i 0.363613π0.363613\pi
662662 −37401.0 −2.19582
663663 −3214.54 −0.188299
664664 62742.3 3.66698
665665 −8662.95 −0.505165
666666 18164.2 1.05683
667667 −369.736 −0.0214636
668668 −21296.0 −1.23348
669669 −2481.07 −0.143384
670670 −38935.5 −2.24509
671671 −28278.6 −1.62695
672672 15003.2 0.861251
673673 31238.5 1.78923 0.894617 0.446833i 0.147448π-0.147448\pi
0.894617 + 0.446833i 0.147448π0.147448\pi
674674 −16124.0 −0.921473
675675 −1218.30 −0.0694702
676676 −21831.0 −1.24209
677677 23202.3 1.31719 0.658596 0.752497i 0.271151π-0.271151\pi
0.658596 + 0.752497i 0.271151π0.271151\pi
678678 31033.7 1.75788
679679 11557.5 0.653221
680680 −21081.4 −1.18887
681681 −9971.02 −0.561073
682682 50804.6 2.85250
683683 −11108.7 −0.622348 −0.311174 0.950353i 0.600722π-0.600722\pi
−0.311174 + 0.950353i 0.600722π0.600722\pi
684684 −27352.4 −1.52901
685685 −4076.55 −0.227383
686686 1877.06 0.104470
687687 13861.9 0.769817
688688 −106874. −5.92227
689689 1351.49 0.0747278
690690 −3374.79 −0.186197
691691 −32784.6 −1.80490 −0.902449 0.430797i 0.858233π-0.858233\pi
−0.902449 + 0.430797i 0.858233π0.858233\pi
692692 −47747.8 −2.62297
693693 −4091.61 −0.224282
694694 60092.0 3.28683
695695 5530.08 0.301824
696696 3681.17 0.200481
697697 2468.51 0.134148
698698 −7113.80 −0.385761
699699 −7569.97 −0.409618
700700 −6932.44 −0.374317
701701 −2027.49 −0.109240 −0.0546200 0.998507i 0.517395π-0.517395\pi
−0.0546200 + 0.998507i 0.517395π0.517395\pi
702702 5123.44 0.275458
703703 −51067.4 −2.73975
704704 −128117. −6.85880
705705 5286.35 0.282405
706706 −28335.6 −1.51052
707707 −8241.73 −0.438419
708708 56236.6 2.98517
709709 −31315.4 −1.65878 −0.829389 0.558671i 0.811311π-0.811311\pi
−0.829389 + 0.558671i 0.811311π0.811311\pi
710710 −11551.5 −0.610593
711711 −7731.15 −0.407793
712712 44013.1 2.31666
713713 3287.70 0.172686
714714 −3551.31 −0.186141
715715 −20127.0 −1.05274
716716 71425.8 3.72808
717717 12751.5 0.664173
718718 65197.6 3.38879
719719 13785.9 0.715060 0.357530 0.933902i 0.383619π-0.383619\pi
0.357530 + 0.933902i 0.383619π0.383619\pi
720720 19476.7 1.00813
721721 9511.53 0.491301
722722 67392.9 3.47383
723723 −21164.8 −1.08870
724724 25190.5 1.29309
725725 −725.361 −0.0371575
726726 47397.4 2.42298
727727 11853.4 0.604700 0.302350 0.953197i 0.402229π-0.402229\pi
0.302350 + 0.953197i 0.402229π0.402229\pi
728728 18527.3 0.943225
729729 729.000 0.0370370
730730 31615.3 1.60293
731731 13639.4 0.690112
732732 28669.7 1.44763
733733 −6857.02 −0.345525 −0.172762 0.984964i 0.555269π-0.555269\pi
−0.172762 + 0.984964i 0.555269π0.555269\pi
734734 10963.8 0.551338
735735 1313.80 0.0659325
736736 −16432.1 −0.822953
737737 51701.3 2.58404
738738 −3934.39 −0.196243
739739 7095.95 0.353219 0.176609 0.984281i 0.443487π-0.443487\pi
0.176609 + 0.984281i 0.443487π0.443487\pi
740740 72343.5 3.59379
741741 −14404.2 −0.714104
742742 1493.07 0.0738712
743743 −26319.1 −1.29953 −0.649767 0.760133i 0.725134π-0.725134\pi
−0.649767 + 0.760133i 0.725134π0.725134\pi
744744 −32733.1 −1.61297
745745 1713.27 0.0842543
746746 32193.4 1.58001
747747 7397.79 0.362344
748748 44049.0 2.15319
749749 −3851.22 −0.187878
750750 −24962.0 −1.21531
751751 27498.1 1.33611 0.668055 0.744112i 0.267127π-0.267127\pi
0.668055 + 0.744112i 0.267127π0.267127\pi
752752 47739.9 2.31502
753753 17489.1 0.846401
754754 3050.43 0.147335
755755 −13437.5 −0.647735
756756 4148.20 0.199562
757757 28018.2 1.34523 0.672614 0.739994i 0.265172π-0.265172\pi
0.672614 + 0.739994i 0.265172π0.265172\pi
758758 −63487.2 −3.04216
759759 4481.29 0.214309
760760 −94464.6 −4.50867
761761 −30614.8 −1.45833 −0.729163 0.684340i 0.760091π-0.760091\pi
−0.729163 + 0.684340i 0.760091π0.760091\pi
762762 −33864.5 −1.60995
763763 −6978.51 −0.331113
764764 −18986.7 −0.899103
765765 −2485.65 −0.117476
766766 −9049.48 −0.426855
767767 29615.1 1.39418
768768 36054.9 1.69404
769769 −36535.2 −1.71326 −0.856628 0.515935i 0.827445π-0.827445\pi
−0.856628 + 0.515935i 0.827445π0.827445\pi
770770 −22235.6 −1.04067
771771 −4917.65 −0.229708
772772 −44016.7 −2.05207
773773 −2926.76 −0.136181 −0.0680907 0.997679i 0.521691π-0.521691\pi
−0.0680907 + 0.997679i 0.521691π0.521691\pi
774774 −21739.0 −1.00955
775775 6449.92 0.298952
776776 126028. 5.83010
777777 7744.77 0.357583
778778 −63400.2 −2.92160
779779 11061.3 0.508743
780780 20405.4 0.936706
781781 15338.9 0.702778
782782 3889.53 0.177864
783783 434.038 0.0198100
784784 11864.7 0.540482
785785 −12159.6 −0.552861
786786 −18270.3 −0.829108
787787 −15882.5 −0.719376 −0.359688 0.933073i 0.617117π-0.617117\pi
−0.359688 + 0.933073i 0.617117π0.617117\pi
788788 −4800.21 −0.217005
789789 −820.094 −0.0370040
790790 −42014.5 −1.89216
791791 13232.0 0.594786
792792 −44616.7 −2.00175
793793 15097.9 0.676095
794794 −14444.5 −0.645614
795795 1045.04 0.0466210
796796 −6003.65 −0.267329
797797 −16842.7 −0.748556 −0.374278 0.927316i 0.622109π-0.622109\pi
−0.374278 + 0.927316i 0.622109π0.622109\pi
798798 −15913.3 −0.705919
799799 −6092.65 −0.269765
800800 −32237.0 −1.42469
801801 5189.47 0.228915
802802 11182.3 0.492345
803803 −41981.1 −1.84493
804804 −52416.3 −2.29923
805805 −1438.93 −0.0630007
806806 −27124.5 −1.18539
807807 22330.2 0.974051
808808 −89871.4 −3.91295
809809 18173.9 0.789815 0.394907 0.918721i 0.370777π-0.370777\pi
0.394907 + 0.918721i 0.370777π0.370777\pi
810810 3961.71 0.171852
811811 −13426.0 −0.581321 −0.290661 0.956826i 0.593875π-0.593875\pi
−0.290661 + 0.956826i 0.593875π0.593875\pi
812812 2469.79 0.106740
813813 9306.84 0.401482
814814 −131077. −5.64405
815815 20409.7 0.877201
816816 −22447.3 −0.963007
817817 61117.6 2.61718
818818 11240.7 0.480467
819819 2184.51 0.0932025
820820 −15669.7 −0.667330
821821 −21961.4 −0.933569 −0.466784 0.884371i 0.654588π-0.654588\pi
−0.466784 + 0.884371i 0.654588π0.654588\pi
822822 −7488.35 −0.317745
823823 −5614.14 −0.237784 −0.118892 0.992907i 0.537934π-0.537934\pi
−0.118892 + 0.992907i 0.537934π0.537934\pi
824824 103718. 4.38493
825825 8791.55 0.371009
826826 32717.7 1.37820
827827 10174.5 0.427815 0.213907 0.976854i 0.431381π-0.431381\pi
0.213907 + 0.976854i 0.431381π0.431381\pi
828828 −4543.27 −0.190688
829829 −27711.0 −1.16097 −0.580485 0.814271i 0.697137π-0.697137\pi
−0.580485 + 0.814271i 0.697137π0.697137\pi
830830 40202.9 1.68128
831831 6453.46 0.269396
832832 68401.6 2.85024
833833 −1514.19 −0.0629815
834834 10158.4 0.421770
835835 −8671.88 −0.359404
836836 197381. 8.16576
837837 −3859.47 −0.159382
838838 −20473.1 −0.843950
839839 −1474.25 −0.0606637 −0.0303319 0.999540i 0.509656π-0.509656\pi
−0.0303319 + 0.999540i 0.509656π0.509656\pi
840840 14326.3 0.588457
841841 −24130.6 −0.989404
842842 −42850.9 −1.75385
843843 1994.35 0.0814818
844844 19747.7 0.805383
845845 −8889.74 −0.361913
846846 9710.68 0.394633
847847 20209.1 0.819825
848848 9437.51 0.382176
849849 8770.34 0.354532
850850 7630.61 0.307915
851851 −8482.36 −0.341682
852852 −15551.1 −0.625318
853853 −31045.8 −1.24617 −0.623087 0.782152i 0.714122π-0.714122\pi
−0.623087 + 0.782152i 0.714122π0.714122\pi
854854 16679.7 0.668345
855855 −11138.1 −0.445514
856856 −41995.4 −1.67684
857857 −41409.9 −1.65057 −0.825283 0.564720i 0.808984π-0.808984\pi
−0.825283 + 0.564720i 0.808984π0.808984\pi
858858 −36972.0 −1.47110
859859 4188.80 0.166380 0.0831898 0.996534i 0.473489π-0.473489\pi
0.0831898 + 0.996534i 0.473489π0.473489\pi
860860 −86580.9 −3.43301
861861 −1677.53 −0.0663995
862862 79977.7 3.16015
863863 −14097.9 −0.556082 −0.278041 0.960569i 0.589685π-0.589685\pi
−0.278041 + 0.960569i 0.589685π0.589685\pi
864864 19289.8 0.759552
865865 −19443.2 −0.764265
866866 −10509.7 −0.412395
867867 −11874.2 −0.465133
868868 −21961.4 −0.858777
869869 55789.8 2.17784
870870 2358.76 0.0919187
871871 −27603.3 −1.07382
872872 −76096.8 −2.95523
873873 14859.7 0.576087
874874 17428.8 0.674528
875875 −10643.2 −0.411207
876876 42561.7 1.64158
877877 −26701.7 −1.02811 −0.514055 0.857757i 0.671857π-0.671857\pi
−0.514055 + 0.857757i 0.671857π0.671857\pi
878878 25737.5 0.989291
879879 −5295.06 −0.203183
880880 −140548. −5.38396
881881 −12186.4 −0.466029 −0.233014 0.972473i 0.574859π-0.574859\pi
−0.233014 + 0.972473i 0.574859π0.574859\pi
882882 2413.37 0.0921342
883883 −43820.5 −1.67008 −0.835039 0.550191i 0.814555π-0.814555\pi
−0.835039 + 0.550191i 0.814555π0.814555\pi
884884 −23517.7 −0.894781
885885 22900.0 0.869801
886886 32041.9 1.21498
887887 −12779.0 −0.483741 −0.241871 0.970309i 0.577761π-0.577761\pi
−0.241871 + 0.970309i 0.577761π0.577761\pi
888888 84452.3 3.19148
889889 −14439.0 −0.544732
890890 28201.9 1.06217
891891 −5260.64 −0.197798
892892 −18151.6 −0.681346
893893 −27300.9 −1.02306
894894 3147.17 0.117737
895895 29085.1 1.08626
896896 35559.2 1.32584
897897 −2392.56 −0.0890581
898898 79797.6 2.96535
899899 −2297.88 −0.0852488
900900 −8913.14 −0.330116
901901 −1204.43 −0.0445344
902902 28391.5 1.04804
903903 −9268.96 −0.341585
904904 144288. 5.30855
905905 10257.7 0.376772
906906 −24683.7 −0.905146
907907 −7244.34 −0.265209 −0.132604 0.991169i 0.542334π-0.542334\pi
−0.132604 + 0.991169i 0.542334π0.542334\pi
908908 −72948.5 −2.66617
909909 −10596.5 −0.386649
910910 11871.6 0.432461
911911 −19922.1 −0.724531 −0.362266 0.932075i 0.617997π-0.617997\pi
−0.362266 + 0.932075i 0.617997π0.617997\pi
912912 −100585. −3.65210
913913 −53384.2 −1.93512
914914 −8498.09 −0.307540
915915 11674.5 0.421801
916916 101414. 3.65810
917917 −7789.98 −0.280532
918918 −4565.97 −0.164161
919919 −12768.2 −0.458306 −0.229153 0.973390i 0.573596π-0.573596\pi
−0.229153 + 0.973390i 0.573596π0.573596\pi
920920 −15690.7 −0.562290
921921 −12274.9 −0.439165
922922 63531.2 2.26929
923923 −8189.44 −0.292046
924924 −29934.4 −1.06577
925925 −16641.0 −0.591516
926926 −86566.6 −3.07209
927927 12229.1 0.433287
928928 11484.9 0.406262
929929 27889.7 0.984964 0.492482 0.870323i 0.336090π-0.336090\pi
0.492482 + 0.870323i 0.336090π0.336090\pi
930930 −20974.1 −0.739536
931931 −6785.01 −0.238851
932932 −55382.3 −1.94647
933933 7525.00 0.264049
934934 64563.4 2.26186
935935 17937.0 0.627384
936936 23820.8 0.831846
937937 −33958.2 −1.18395 −0.591977 0.805955i 0.701652π-0.701652\pi
−0.591977 + 0.805955i 0.701652π0.701652\pi
938938 −30495.1 −1.06152
939939 −6830.14 −0.237373
940940 38675.2 1.34196
941941 39002.5 1.35116 0.675582 0.737285i 0.263892π-0.263892\pi
0.675582 + 0.737285i 0.263892π0.263892\pi
942942 −22336.4 −0.772570
943943 1837.29 0.0634469
944944 206804. 7.13020
945945 1689.18 0.0581470
946946 156874. 5.39155
947947 −6375.90 −0.218784 −0.109392 0.993999i 0.534890π-0.534890\pi
−0.109392 + 0.993999i 0.534890π0.534890\pi
948948 −56561.4 −1.93780
949949 22413.7 0.766679
950950 34192.4 1.16774
951951 6846.94 0.233467
952952 −16511.4 −0.562119
953953 11469.9 0.389871 0.194935 0.980816i 0.437550π-0.437550\pi
0.194935 + 0.980816i 0.437550π0.437550\pi
954954 1919.67 0.0651483
955955 −7731.52 −0.261975
956956 93290.2 3.15609
957957 −3132.12 −0.105796
958958 −50117.8 −1.69022
959959 −3192.85 −0.107510
960960 52891.7 1.77820
961961 −9358.17 −0.314127
962962 69982.1 2.34544
963963 −4951.57 −0.165693
964964 −154843. −5.17339
965965 −17923.9 −0.597918
966966 −2643.21 −0.0880372
967967 −11097.4 −0.369045 −0.184523 0.982828i 0.559074π-0.559074\pi
−0.184523 + 0.982828i 0.559074π0.559074\pi
968968 220368. 7.31705
969969 12836.9 0.425573
970970 80754.2 2.67305
971971 19350.8 0.639545 0.319773 0.947494i 0.396394π-0.396394\pi
0.319773 + 0.947494i 0.396394π0.396394\pi
972972 5333.40 0.175997
973973 4331.28 0.142708
974974 89381.7 2.94042
975975 −4693.80 −0.154176
976976 105430. 3.45771
977977 19020.2 0.622834 0.311417 0.950273i 0.399196π-0.399196\pi
0.311417 + 0.950273i 0.399196π0.399196\pi
978978 37491.1 1.22580
979979 −37448.5 −1.22253
980980 9611.85 0.313305
981981 −8972.37 −0.292014
982982 94859.6 3.08258
983983 48405.2 1.57059 0.785293 0.619125i 0.212512π-0.212512\pi
0.785293 + 0.619125i 0.212512π0.212512\pi
984984 −18292.5 −0.592626
985985 −1954.68 −0.0632297
986986 −2718.52 −0.0878046
987987 4140.39 0.133526
988988 −105382. −3.39336
989989 10151.7 0.326396
990990 −28588.7 −0.917786
991991 31822.7 1.02006 0.510031 0.860156i 0.329634π-0.329634\pi
0.510031 + 0.860156i 0.329634π0.329634\pi
992992 −102124. −3.26859
993993 −20503.1 −0.655233
994994 −9047.41 −0.288699
995995 −2444.73 −0.0778926
996996 54122.6 1.72183
997997 −7520.08 −0.238880 −0.119440 0.992841i 0.538110π-0.538110\pi
−0.119440 + 0.992841i 0.538110π0.538110\pi
998998 51437.6 1.63149
999999 9957.56 0.315358
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 483.4.a.i.1.9 9
3.2 odd 2 1449.4.a.j.1.1 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.4.a.i.1.9 9 1.1 even 1 trivial
1449.4.a.j.1.1 9 3.2 odd 2