Properties

Label 507.4.a.i.1.1
Level 507507
Weight 44
Character 507.1
Self dual yes
Analytic conductor 29.91429.914
Analytic rank 00
Dimension 44
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,4,Mod(1,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 507=3132 507 = 3 \cdot 13^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 507.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 29.913968372929.9139683729
Analytic rank: 00
Dimension: 44
Coefficient field: Q[x]/(x4)\mathbb{Q}[x]/(x^{4} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x42x325x2+24x+78 x^{4} - 2x^{3} - 25x^{2} + 24x + 78 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 39)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 5.330395.33039 of defining polynomial
Character χ\chi == 507.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q5.33039q23.00000q3+20.4131q4+16.4131q5+15.9912q69.67968q766.1667q8+9.00000q987.4882q1027.5882q1161.2393q12+51.5965q1449.2393q15+189.390q16+107.928q1747.9735q18+2.24723q19+335.042q20+29.0391q21+147.056q22+41.8090q23+198.500q24+144.390q2527.0000q27197.592q28+61.6213q29+262.465q30191.932q31480.187q32+82.7645q33575.300q34158.874q35+183.718q3698.4236q3711.9786q381086.00q40+30.7452q41154.790q42+238.325q43563.160q44+147.718q45222.858q46+511.482q47568.169q48249.304q49769.653q50323.785q51+492.825q53+143.921q54452.807q55+640.472q566.74170q57328.466q58484.179q591005.13q60444.021q61+1023.07q6287.1172q63+1044.47q64441.167q66190.114q67+2203.15q68125.427q69+846.858q70484.785q71595.500q72+957.780q73+524.636q74433.169q75+45.8729q76+267.045q77375.216q79+3108.47q80+81.0000q81163.884q82+715.765q83+592.777q84+1771.43q851270.37q86184.864q87+1825.42q88+1038.15q89787.394q90+853.451q92+575.796q932726.40q94+36.8840q95+1440.56q9665.5636q97+1328.89q98248.293q99+O(q100)q-5.33039 q^{2} -3.00000 q^{3} +20.4131 q^{4} +16.4131 q^{5} +15.9912 q^{6} -9.67968 q^{7} -66.1667 q^{8} +9.00000 q^{9} -87.4882 q^{10} -27.5882 q^{11} -61.2393 q^{12} +51.5965 q^{14} -49.2393 q^{15} +189.390 q^{16} +107.928 q^{17} -47.9735 q^{18} +2.24723 q^{19} +335.042 q^{20} +29.0391 q^{21} +147.056 q^{22} +41.8090 q^{23} +198.500 q^{24} +144.390 q^{25} -27.0000 q^{27} -197.592 q^{28} +61.6213 q^{29} +262.465 q^{30} -191.932 q^{31} -480.187 q^{32} +82.7645 q^{33} -575.300 q^{34} -158.874 q^{35} +183.718 q^{36} -98.4236 q^{37} -11.9786 q^{38} -1086.00 q^{40} +30.7452 q^{41} -154.790 q^{42} +238.325 q^{43} -563.160 q^{44} +147.718 q^{45} -222.858 q^{46} +511.482 q^{47} -568.169 q^{48} -249.304 q^{49} -769.653 q^{50} -323.785 q^{51} +492.825 q^{53} +143.921 q^{54} -452.807 q^{55} +640.472 q^{56} -6.74170 q^{57} -328.466 q^{58} -484.179 q^{59} -1005.13 q^{60} -444.021 q^{61} +1023.07 q^{62} -87.1172 q^{63} +1044.47 q^{64} -441.167 q^{66} -190.114 q^{67} +2203.15 q^{68} -125.427 q^{69} +846.858 q^{70} -484.785 q^{71} -595.500 q^{72} +957.780 q^{73} +524.636 q^{74} -433.169 q^{75} +45.8729 q^{76} +267.045 q^{77} -375.216 q^{79} +3108.47 q^{80} +81.0000 q^{81} -163.884 q^{82} +715.765 q^{83} +592.777 q^{84} +1771.43 q^{85} -1270.37 q^{86} -184.864 q^{87} +1825.42 q^{88} +1038.15 q^{89} -787.394 q^{90} +853.451 q^{92} +575.796 q^{93} -2726.40 q^{94} +36.8840 q^{95} +1440.56 q^{96} -65.5636 q^{97} +1328.89 q^{98} -248.293 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q2q212q3+22q4+6q5+6q6+14q754q8+36q962q1040q1166q12+40q1418q15+122q16+98q1718q18124q19+466q20+360q99+O(q100) 4 q - 2 q^{2} - 12 q^{3} + 22 q^{4} + 6 q^{5} + 6 q^{6} + 14 q^{7} - 54 q^{8} + 36 q^{9} - 62 q^{10} - 40 q^{11} - 66 q^{12} + 40 q^{14} - 18 q^{15} + 122 q^{16} + 98 q^{17} - 18 q^{18} - 124 q^{19} + 466 q^{20}+ \cdots - 360 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 −5.33039 −1.88458 −0.942289 0.334800i 0.891331π-0.891331\pi
−0.942289 + 0.334800i 0.891331π0.891331\pi
33 −3.00000 −0.577350
44 20.4131 2.55164
55 16.4131 1.46803 0.734016 0.679132i 0.237644π-0.237644\pi
0.734016 + 0.679132i 0.237644π0.237644\pi
66 15.9912 1.08806
77 −9.67968 −0.522654 −0.261327 0.965250i 0.584160π-0.584160\pi
−0.261327 + 0.965250i 0.584160π0.584160\pi
88 −66.1667 −2.92418
99 9.00000 0.333333
1010 −87.4882 −2.76662
1111 −27.5882 −0.756195 −0.378098 0.925766i 0.623422π-0.623422\pi
−0.378098 + 0.925766i 0.623422π0.623422\pi
1212 −61.2393 −1.47319
1313 0 0
1414 51.5965 0.984982
1515 −49.2393 −0.847568
1616 189.390 2.95921
1717 107.928 1.53979 0.769895 0.638171i 0.220309π-0.220309\pi
0.769895 + 0.638171i 0.220309π0.220309\pi
1818 −47.9735 −0.628193
1919 2.24723 0.0271342 0.0135671 0.999908i 0.495681π-0.495681\pi
0.0135671 + 0.999908i 0.495681π0.495681\pi
2020 335.042 3.74588
2121 29.0391 0.301754
2222 147.056 1.42511
2323 41.8090 0.379034 0.189517 0.981877i 0.439308π-0.439308\pi
0.189517 + 0.981877i 0.439308π0.439308\pi
2424 198.500 1.68828
2525 144.390 1.15512
2626 0 0
2727 −27.0000 −0.192450
2828 −197.592 −1.33362
2929 61.6213 0.394579 0.197289 0.980345i 0.436786π-0.436786\pi
0.197289 + 0.980345i 0.436786π0.436786\pi
3030 262.465 1.59731
3131 −191.932 −1.11200 −0.556000 0.831182i 0.687665π-0.687665\pi
−0.556000 + 0.831182i 0.687665π0.687665\pi
3232 −480.187 −2.65269
3333 82.7645 0.436589
3434 −575.300 −2.90185
3535 −158.874 −0.767272
3636 183.718 0.850545
3737 −98.4236 −0.437317 −0.218659 0.975801i 0.570168π-0.570168\pi
−0.218659 + 0.975801i 0.570168π0.570168\pi
3838 −11.9786 −0.0511366
3939 0 0
4040 −1086.00 −4.29279
4141 30.7452 0.117112 0.0585561 0.998284i 0.481350π-0.481350\pi
0.0585561 + 0.998284i 0.481350π0.481350\pi
4242 −154.790 −0.568680
4343 238.325 0.845216 0.422608 0.906313i 0.361115π-0.361115\pi
0.422608 + 0.906313i 0.361115π0.361115\pi
4444 −563.160 −1.92953
4545 147.718 0.489344
4646 −222.858 −0.714319
4747 511.482 1.58739 0.793695 0.608316i 0.208155π-0.208155\pi
0.793695 + 0.608316i 0.208155π0.208155\pi
4848 −568.169 −1.70850
4949 −249.304 −0.726833
5050 −769.653 −2.17691
5151 −323.785 −0.888998
5252 0 0
5353 492.825 1.27726 0.638630 0.769514i 0.279502π-0.279502\pi
0.638630 + 0.769514i 0.279502π0.279502\pi
5454 143.921 0.362687
5555 −452.807 −1.11012
5656 640.472 1.52833
5757 −6.74170 −0.0156660
5858 −328.466 −0.743615
5959 −484.179 −1.06838 −0.534192 0.845363i 0.679384π-0.679384\pi
−0.534192 + 0.845363i 0.679384π0.679384\pi
6060 −1005.13 −2.16269
6161 −444.021 −0.931985 −0.465993 0.884789i 0.654303π-0.654303\pi
−0.465993 + 0.884789i 0.654303π0.654303\pi
6262 1023.07 2.09565
6363 −87.1172 −0.174218
6464 1044.47 2.03998
6565 0 0
6666 −441.167 −0.822787
6767 −190.114 −0.346658 −0.173329 0.984864i 0.555452π-0.555452\pi
−0.173329 + 0.984864i 0.555452π0.555452\pi
6868 2203.15 3.92898
6969 −125.427 −0.218835
7070 846.858 1.44598
7171 −484.785 −0.810329 −0.405164 0.914244i 0.632786π-0.632786\pi
−0.405164 + 0.914244i 0.632786π0.632786\pi
7272 −595.500 −0.974727
7373 957.780 1.53561 0.767806 0.640683i 0.221349π-0.221349\pi
0.767806 + 0.640683i 0.221349π0.221349\pi
7474 524.636 0.824159
7575 −433.169 −0.666907
7676 45.8729 0.0692367
7777 267.045 0.395228
7878 0 0
7979 −375.216 −0.534368 −0.267184 0.963646i 0.586093π-0.586093\pi
−0.267184 + 0.963646i 0.586093π0.586093\pi
8080 3108.47 4.34422
8181 81.0000 0.111111
8282 −163.884 −0.220707
8383 715.765 0.946571 0.473286 0.880909i 0.343068π-0.343068\pi
0.473286 + 0.880909i 0.343068π0.343068\pi
8484 592.777 0.769967
8585 1771.43 2.26046
8686 −1270.37 −1.59288
8787 −184.864 −0.227810
8888 1825.42 2.21125
8989 1038.15 1.23645 0.618224 0.786002i 0.287852π-0.287852\pi
0.618224 + 0.786002i 0.287852π0.287852\pi
9090 −787.394 −0.922207
9191 0 0
9292 853.451 0.967157
9393 575.796 0.642013
9494 −2726.40 −2.99156
9595 36.8840 0.0398339
9696 1440.56 1.53153
9797 −65.5636 −0.0686286 −0.0343143 0.999411i 0.510925π-0.510925\pi
−0.0343143 + 0.999411i 0.510925π0.510925\pi
9898 1328.89 1.36977
9999 −248.293 −0.252065
100100 2947.44 2.94744
101101 531.798 0.523920 0.261960 0.965079i 0.415631π-0.415631\pi
0.261960 + 0.965079i 0.415631π0.415631\pi
102102 1725.90 1.67539
103103 −735.984 −0.704064 −0.352032 0.935988i 0.614509π-0.614509\pi
−0.352032 + 0.935988i 0.614509π0.614509\pi
104104 0 0
105105 476.621 0.442985
106106 −2626.95 −2.40710
107107 −783.265 −0.707673 −0.353837 0.935307i 0.615123π-0.615123\pi
−0.353837 + 0.935307i 0.615123π0.615123\pi
108108 −551.153 −0.491063
109109 532.339 0.467788 0.233894 0.972262i 0.424853π-0.424853\pi
0.233894 + 0.972262i 0.424853π0.424853\pi
110110 2413.64 2.09210
111111 295.271 0.252485
112112 −1833.23 −1.54664
113113 −180.589 −0.150340 −0.0751699 0.997171i 0.523950π-0.523950\pi
−0.0751699 + 0.997171i 0.523950π0.523950\pi
114114 35.9359 0.0295237
115115 686.215 0.556434
116116 1257.88 1.00682
117117 0 0
118118 2580.86 2.01346
119119 −1044.71 −0.804777
120120 3258.00 2.47844
121121 −569.893 −0.428169
122122 2366.81 1.75640
123123 −92.2357 −0.0676147
124124 −3917.92 −2.83742
125125 318.242 0.227716
126126 464.369 0.328327
127127 1431.63 1.00029 0.500146 0.865941i 0.333280π-0.333280\pi
0.500146 + 0.865941i 0.333280π0.333280\pi
128128 −1725.94 −1.19182
129129 −714.976 −0.487986
130130 0 0
131131 2067.32 1.37880 0.689400 0.724381i 0.257874π-0.257874\pi
0.689400 + 0.724381i 0.257874π0.257874\pi
132132 1689.48 1.11402
133133 −21.7525 −0.0141818
134134 1013.38 0.653304
135135 −443.153 −0.282523
136136 −7141.25 −4.50262
137137 387.512 0.241660 0.120830 0.992673i 0.461444π-0.461444\pi
0.120830 + 0.992673i 0.461444π0.461444\pi
138138 668.575 0.412412
139139 752.568 0.459223 0.229611 0.973282i 0.426254π-0.426254\pi
0.229611 + 0.973282i 0.426254π0.426254\pi
140140 −3243.10 −1.95780
141141 −1534.45 −0.916480
142142 2584.09 1.52713
143143 0 0
144144 1704.51 0.986404
145145 1011.40 0.579254
146146 −5105.34 −2.89398
147147 747.911 0.419637
148148 −2009.13 −1.11587
149149 2636.72 1.44972 0.724862 0.688895i 0.241904π-0.241904\pi
0.724862 + 0.688895i 0.241904π0.241904\pi
150150 2308.96 1.25684
151151 3332.42 1.79595 0.897975 0.440046i 0.145038π-0.145038\pi
0.897975 + 0.440046i 0.145038π0.145038\pi
152152 −148.692 −0.0793454
153153 971.354 0.513263
154154 −1423.45 −0.744839
155155 −3150.20 −1.63245
156156 0 0
157157 −1625.26 −0.826179 −0.413089 0.910690i 0.635550π-0.635550\pi
−0.413089 + 0.910690i 0.635550π0.635550\pi
158158 2000.05 1.00706
159159 −1478.48 −0.737426
160160 −7881.36 −3.89423
161161 −404.698 −0.198104
162162 −431.762 −0.209398
163163 1835.37 0.881944 0.440972 0.897521i 0.354634π-0.354634\pi
0.440972 + 0.897521i 0.354634π0.354634\pi
164164 627.605 0.298828
165165 1358.42 0.640927
166166 −3815.31 −1.78389
167167 −1945.00 −0.901248 −0.450624 0.892714i 0.648798π-0.648798\pi
−0.450624 + 0.892714i 0.648798π0.648798\pi
168168 −1921.42 −0.882384
169169 0 0
170170 −9442.44 −4.26001
171171 20.2251 0.00904474
172172 4864.96 2.15668
173173 2531.63 1.11258 0.556289 0.830989i 0.312225π-0.312225\pi
0.556289 + 0.830989i 0.312225π0.312225\pi
174174 985.397 0.429326
175175 −1397.65 −0.603726
176176 −5224.91 −2.23774
177177 1452.54 0.616832
178178 −5533.76 −2.33018
179179 4263.01 1.78007 0.890035 0.455892i 0.150680π-0.150680\pi
0.890035 + 0.455892i 0.150680π0.150680\pi
180180 3015.38 1.24863
181181 3944.61 1.61989 0.809946 0.586504i 0.199496π-0.199496\pi
0.809946 + 0.586504i 0.199496π0.199496\pi
182182 0 0
183183 1332.06 0.538082
184184 −2766.36 −1.10836
185185 −1615.43 −0.641995
186186 −3069.22 −1.20992
187187 −2977.54 −1.16438
188188 10440.9 4.05044
189189 261.351 0.100585
190190 −196.606 −0.0750701
191191 −214.109 −0.0811119 −0.0405559 0.999177i 0.512913π-0.512913\pi
−0.0405559 + 0.999177i 0.512913π0.512913\pi
192192 −3133.42 −1.17779
193193 1207.19 0.450234 0.225117 0.974332i 0.427724π-0.427724\pi
0.225117 + 0.974332i 0.427724π0.427724\pi
194194 349.480 0.129336
195195 0 0
196196 −5089.06 −1.85461
197197 927.631 0.335487 0.167744 0.985831i 0.446352π-0.446352\pi
0.167744 + 0.985831i 0.446352π0.446352\pi
198198 1323.50 0.475036
199199 478.951 0.170613 0.0853064 0.996355i 0.472813π-0.472813\pi
0.0853064 + 0.996355i 0.472813π0.472813\pi
200200 −9553.77 −3.37777
201201 570.341 0.200143
202202 −2834.69 −0.987368
203203 −596.474 −0.206228
204204 −6609.44 −2.26840
205205 504.624 0.171924
206206 3923.08 1.32686
207207 376.281 0.126345
208208 0 0
209209 −61.9970 −0.0205188
210210 −2540.58 −0.834840
211211 −1450.95 −0.473402 −0.236701 0.971583i 0.576066π-0.576066\pi
−0.236701 + 0.971583i 0.576066π0.576066\pi
212212 10060.1 3.25910
213213 1454.35 0.467843
214214 4175.11 1.33367
215215 3911.66 1.24080
216216 1786.50 0.562759
217217 1857.84 0.581191
218218 −2837.58 −0.881583
219219 −2873.34 −0.886586
220220 −9243.19 −2.83262
221221 0 0
222222 −1573.91 −0.475828
223223 2059.79 0.618536 0.309268 0.950975i 0.399916π-0.399916\pi
0.309268 + 0.950975i 0.399916π0.399916\pi
224224 4648.06 1.38644
225225 1299.51 0.385039
226226 962.612 0.283327
227227 −4482.46 −1.31062 −0.655311 0.755359i 0.727463π-0.727463\pi
−0.655311 + 0.755359i 0.727463π0.727463\pi
228228 −137.619 −0.0399738
229229 1630.39 0.470477 0.235239 0.971938i 0.424413π-0.424413\pi
0.235239 + 0.971938i 0.424413π0.424413\pi
230230 −3657.80 −1.04864
231231 −801.134 −0.228185
232232 −4077.27 −1.15382
233233 −1903.69 −0.535258 −0.267629 0.963522i 0.586240π-0.586240\pi
−0.267629 + 0.963522i 0.586240π0.586240\pi
234234 0 0
235235 8395.00 2.33034
236236 −9883.58 −2.72613
237237 1125.65 0.308517
238238 5568.72 1.51667
239239 −3763.79 −1.01866 −0.509328 0.860572i 0.670106π-0.670106\pi
−0.509328 + 0.860572i 0.670106π0.670106\pi
240240 −9325.40 −2.50813
241241 3614.74 0.966166 0.483083 0.875575i 0.339517π-0.339517\pi
0.483083 + 0.875575i 0.339517π0.339517\pi
242242 3037.75 0.806918
243243 −243.000 −0.0641500
244244 −9063.85 −2.37809
245245 −4091.84 −1.06701
246246 491.652 0.127425
247247 0 0
248248 12699.5 3.25169
249249 −2147.30 −0.546503
250250 −1696.36 −0.429148
251251 −5729.77 −1.44088 −0.720438 0.693520i 0.756059π-0.756059\pi
−0.720438 + 0.693520i 0.756059π0.756059\pi
252252 −1778.33 −0.444541
253253 −1153.43 −0.286624
254254 −7631.18 −1.88513
255255 −5314.30 −1.30508
256256 844.191 0.206101
257257 −5525.79 −1.34120 −0.670602 0.741818i 0.733964π-0.733964\pi
−0.670602 + 0.741818i 0.733964π0.733964\pi
258258 3811.10 0.919647
259259 952.709 0.228565
260260 0 0
261261 554.591 0.131526
262262 −11019.6 −2.59846
263263 5223.21 1.22463 0.612313 0.790615i 0.290239π-0.290239\pi
0.612313 + 0.790615i 0.290239π0.290239\pi
264264 −5476.25 −1.27667
265265 8088.78 1.87506
266266 115.949 0.0267267
267267 −3114.46 −0.713864
268268 −3880.81 −0.884545
269269 7203.88 1.63282 0.816410 0.577473i 0.195961π-0.195961\pi
0.816410 + 0.577473i 0.195961π0.195961\pi
270270 2362.18 0.532436
271271 8577.69 1.92272 0.961360 0.275293i 0.0887750π-0.0887750\pi
0.961360 + 0.275293i 0.0887750π0.0887750\pi
272272 20440.5 4.55656
273273 0 0
274274 −2065.59 −0.455427
275275 −3983.44 −0.873493
276276 −2560.35 −0.558388
277277 7169.19 1.55507 0.777536 0.628838i 0.216469π-0.216469\pi
0.777536 + 0.628838i 0.216469π0.216469\pi
278278 −4011.48 −0.865442
279279 −1727.39 −0.370667
280280 10512.1 2.24364
281281 −849.157 −0.180272 −0.0901360 0.995929i 0.528730π-0.528730\pi
−0.0901360 + 0.995929i 0.528730π0.528730\pi
282282 8179.20 1.72718
283283 1115.37 0.234283 0.117141 0.993115i 0.462627π-0.462627\pi
0.117141 + 0.993115i 0.462627π0.462627\pi
284284 −9895.95 −2.06766
285285 −110.652 −0.0229981
286286 0 0
287287 −297.604 −0.0612091
288288 −4321.69 −0.884229
289289 6735.49 1.37095
290290 −5391.14 −1.09165
291291 196.691 0.0396227
292292 19551.2 3.91832
293293 1863.53 0.371565 0.185782 0.982591i 0.440518π-0.440518\pi
0.185782 + 0.982591i 0.440518π0.440518\pi
294294 −3986.66 −0.790839
295295 −7946.87 −1.56842
296296 6512.36 1.27879
297297 744.880 0.145530
298298 −14054.8 −2.73212
299299 0 0
300300 −8842.31 −1.70170
301301 −2306.91 −0.441755
302302 −17763.1 −3.38461
303303 −1595.39 −0.302485
304304 425.602 0.0802959
305305 −7287.76 −1.36818
306306 −5177.70 −0.967285
307307 6387.50 1.18747 0.593736 0.804660i 0.297652π-0.297652\pi
0.593736 + 0.804660i 0.297652π0.297652\pi
308308 5451.21 1.00848
309309 2207.95 0.406492
310310 16791.8 3.07648
311311 −3492.59 −0.636806 −0.318403 0.947955i 0.603147π-0.603147\pi
−0.318403 + 0.947955i 0.603147π0.603147\pi
312312 0 0
313313 −5912.01 −1.06762 −0.533812 0.845603i 0.679241π-0.679241\pi
−0.533812 + 0.845603i 0.679241π0.679241\pi
314314 8663.29 1.55700
315315 −1429.86 −0.255757
316316 −7659.31 −1.36351
317317 1677.54 0.297224 0.148612 0.988896i 0.452519π-0.452519\pi
0.148612 + 0.988896i 0.452519π0.452519\pi
318318 7880.86 1.38974
319319 −1700.02 −0.298378
320320 17143.0 2.99476
321321 2349.79 0.408575
322322 2157.20 0.373342
323323 242.540 0.0417810
324324 1653.46 0.283515
325325 0 0
326326 −9783.22 −1.66209
327327 −1597.02 −0.270077
328328 −2034.31 −0.342457
329329 −4950.98 −0.829655
330330 −7240.92 −1.20788
331331 −2010.31 −0.333827 −0.166913 0.985972i 0.553380π-0.553380\pi
−0.166913 + 0.985972i 0.553380π0.553380\pi
332332 14611.0 2.41531
333333 −885.812 −0.145772
334334 10367.6 1.69847
335335 −3120.35 −0.508905
336336 5499.69 0.892955
337337 7139.24 1.15400 0.577002 0.816743i 0.304222π-0.304222\pi
0.577002 + 0.816743i 0.304222π0.304222\pi
338338 0 0
339339 541.768 0.0867988
340340 36160.5 5.76787
341341 5295.05 0.840889
342342 −107.808 −0.0170455
343343 5733.31 0.902536
344344 −15769.2 −2.47156
345345 −2058.64 −0.321257
346346 −13494.6 −2.09674
347347 1.13990 0.000176349 0 8.81743e−5 1.00000i 0.499972π-0.499972\pi
8.81743e−5 1.00000i 0.499972π0.499972\pi
348348 −3773.64 −0.581289
349349 −12199.1 −1.87107 −0.935535 0.353235i 0.885082π-0.885082\pi
−0.935535 + 0.353235i 0.885082π0.885082\pi
350350 7450.00 1.13777
351351 0 0
352352 13247.5 2.00595
353353 10892.3 1.64232 0.821160 0.570698i 0.193327π-0.193327\pi
0.821160 + 0.570698i 0.193327π0.193327\pi
354354 −7742.59 −1.16247
355355 −7956.81 −1.18959
356356 21191.9 3.15497
357357 3134.13 0.464638
358358 −22723.5 −3.35468
359359 3525.78 0.518339 0.259169 0.965832i 0.416551π-0.416551\pi
0.259169 + 0.965832i 0.416551π0.416551\pi
360360 −9773.99 −1.43093
361361 −6853.95 −0.999264
362362 −21026.3 −3.05281
363363 1709.68 0.247204
364364 0 0
365365 15720.1 2.25433
366366 −7100.42 −1.01406
367367 2383.75 0.339049 0.169525 0.985526i 0.445777π-0.445777\pi
0.169525 + 0.985526i 0.445777π0.445777\pi
368368 7918.19 1.12164
369369 276.707 0.0390374
370370 8610.90 1.20989
371371 −4770.39 −0.667564
372372 11753.8 1.63818
373373 −13282.2 −1.84377 −0.921885 0.387463i 0.873352π-0.873352\pi
−0.921885 + 0.387463i 0.873352π0.873352\pi
374374 15871.5 2.19437
375375 −954.727 −0.131472
376376 −33843.1 −4.64181
377377 0 0
378378 −1393.11 −0.189560
379379 4436.73 0.601318 0.300659 0.953732i 0.402793π-0.402793\pi
0.300659 + 0.953732i 0.402793π0.402793\pi
380380 752.917 0.101642
381381 −4294.90 −0.577519
382382 1141.28 0.152862
383383 810.412 0.108120 0.0540602 0.998538i 0.482784π-0.482784\pi
0.0540602 + 0.998538i 0.482784π0.482784\pi
384384 5177.83 0.688100
385385 4383.03 0.580207
386386 −6434.78 −0.848501
387387 2144.93 0.281739
388388 −1338.35 −0.175115
389389 3463.79 0.451469 0.225734 0.974189i 0.427522π-0.427522\pi
0.225734 + 0.974189i 0.427522π0.427522\pi
390390 0 0
391391 4512.37 0.583633
392392 16495.6 2.12539
393393 −6201.96 −0.796050
394394 −4944.64 −0.632252
395395 −6158.45 −0.784469
396396 −5068.44 −0.643178
397397 −425.405 −0.0537796 −0.0268898 0.999638i 0.508560π-0.508560\pi
−0.0268898 + 0.999638i 0.508560π0.508560\pi
398398 −2553.00 −0.321533
399399 65.2575 0.00818787
400400 27345.9 3.41823
401401 1186.85 0.147801 0.0739007 0.997266i 0.476455π-0.476455\pi
0.0739007 + 0.997266i 0.476455π0.476455\pi
402402 −3040.14 −0.377185
403403 0 0
404404 10855.6 1.33685
405405 1329.46 0.163115
406406 3179.44 0.388653
407407 2715.33 0.330697
408408 21423.7 2.59959
409409 −8007.42 −0.968071 −0.484036 0.875048i 0.660830π-0.660830\pi
−0.484036 + 0.875048i 0.660830π0.660830\pi
410410 −2689.84 −0.324005
411411 −1162.54 −0.139522
412412 −15023.7 −1.79652
413413 4686.70 0.558395
414414 −2005.73 −0.238106
415415 11747.9 1.38960
416416 0 0
417417 −2257.70 −0.265132
418418 330.468 0.0386692
419419 6832.46 0.796629 0.398314 0.917249i 0.369595π-0.369595\pi
0.398314 + 0.917249i 0.369595π0.369595\pi
420420 9729.30 1.13034
421421 −10739.6 −1.24326 −0.621632 0.783309i 0.713530π-0.713530\pi
−0.621632 + 0.783309i 0.713530π0.713530\pi
422422 7734.16 0.892163
423423 4603.34 0.529130
424424 −32608.6 −3.73494
425425 15583.7 1.77864
426426 −7752.28 −0.881688
427427 4297.99 0.487106
428428 −15988.9 −1.80573
429429 0 0
430430 −20850.7 −2.33839
431431 −5214.45 −0.582763 −0.291382 0.956607i 0.594115π-0.594115\pi
−0.291382 + 0.956607i 0.594115π0.594115\pi
432432 −5113.52 −0.569501
433433 8642.24 0.959168 0.479584 0.877496i 0.340788π-0.340788\pi
0.479584 + 0.877496i 0.340788π0.340788\pi
434434 −9903.02 −1.09530
435435 −3034.19 −0.334432
436436 10866.7 1.19362
437437 93.9545 0.0102848
438438 15316.0 1.67084
439439 −13026.2 −1.41619 −0.708097 0.706116i 0.750446π-0.750446\pi
−0.708097 + 0.706116i 0.750446π0.750446\pi
440440 29960.7 3.24619
441441 −2243.73 −0.242278
442442 0 0
443443 −11533.0 −1.23690 −0.618450 0.785824i 0.712239π-0.712239\pi
−0.618450 + 0.785824i 0.712239π0.712239\pi
444444 6027.39 0.644250
445445 17039.3 1.81515
446446 −10979.5 −1.16568
447447 −7910.17 −0.836998
448448 −10110.2 −1.06621
449449 −9882.75 −1.03874 −0.519372 0.854548i 0.673834π-0.673834\pi
−0.519372 + 0.854548i 0.673834π0.673834\pi
450450 −6926.88 −0.725636
451451 −848.204 −0.0885596
452452 −3686.38 −0.383613
453453 −9997.26 −1.03689
454454 23893.3 2.46997
455455 0 0
456456 446.075 0.0458101
457457 15628.1 1.59967 0.799836 0.600218i 0.204920π-0.204920\pi
0.799836 + 0.600218i 0.204920π0.204920\pi
458458 −8690.63 −0.886652
459459 −2914.06 −0.296333
460460 14007.8 1.41982
461461 7747.46 0.782723 0.391361 0.920237i 0.372004π-0.372004\pi
0.391361 + 0.920237i 0.372004π0.372004\pi
462462 4270.36 0.430033
463463 333.422 0.0334675 0.0167337 0.999860i 0.494673π-0.494673\pi
0.0167337 + 0.999860i 0.494673π0.494673\pi
464464 11670.4 1.16764
465465 9450.59 0.942496
466466 10147.4 1.00874
467467 8198.33 0.812363 0.406182 0.913792i 0.366860π-0.366860\pi
0.406182 + 0.913792i 0.366860π0.366860\pi
468468 0 0
469469 1840.24 0.181182
470470 −44748.7 −4.39171
471471 4875.79 0.476995
472472 32036.5 3.12415
473473 −6574.96 −0.639148
474474 −6000.14 −0.581425
475475 324.477 0.0313432
476476 −21325.8 −2.05350
477477 4435.43 0.425753
478478 20062.5 1.91974
479479 6435.88 0.613910 0.306955 0.951724i 0.400690π-0.400690\pi
0.306955 + 0.951724i 0.400690π0.400690\pi
480480 23644.1 2.24833
481481 0 0
482482 −19268.0 −1.82082
483483 1214.09 0.114375
484484 −11633.3 −1.09253
485485 −1076.10 −0.100749
486486 1295.29 0.120896
487487 −8095.37 −0.753257 −0.376629 0.926364i 0.622917π-0.622917\pi
−0.376629 + 0.926364i 0.622917π0.622917\pi
488488 29379.4 2.72529
489489 −5506.10 −0.509191
490490 21811.1 2.01087
491491 5116.46 0.470270 0.235135 0.971963i 0.424447π-0.424447\pi
0.235135 + 0.971963i 0.424447π0.424447\pi
492492 −1882.82 −0.172528
493493 6650.67 0.607568
494494 0 0
495495 −4075.26 −0.370039
496496 −36349.9 −3.29064
497497 4692.56 0.423521
498498 11445.9 1.02993
499499 18050.7 1.61936 0.809682 0.586870i 0.199640π-0.199640\pi
0.809682 + 0.586870i 0.199640π0.199640\pi
500500 6496.31 0.581047
501501 5834.99 0.520336
502502 30541.9 2.71544
503503 10531.1 0.933512 0.466756 0.884386i 0.345423π-0.345423\pi
0.466756 + 0.884386i 0.345423π0.345423\pi
504504 5764.25 0.509445
505505 8728.45 0.769131
506506 6148.25 0.540165
507507 0 0
508508 29224.1 2.55238
509509 1963.31 0.170967 0.0854834 0.996340i 0.472757π-0.472757\pi
0.0854834 + 0.996340i 0.472757π0.472757\pi
510510 28327.3 2.45952
511511 −9271.00 −0.802593
512512 9307.69 0.803409
513513 −60.6753 −0.00522198
514514 29454.6 2.52760
515515 −12079.8 −1.03359
516516 −14594.9 −1.24516
517517 −14110.9 −1.20038
518518 −5078.31 −0.430750
519519 −7594.89 −0.642348
520520 0 0
521521 −7044.93 −0.592407 −0.296203 0.955125i 0.595721π-0.595721\pi
−0.296203 + 0.955125i 0.595721π0.595721\pi
522522 −2956.19 −0.247872
523523 −3213.29 −0.268657 −0.134328 0.990937i 0.542888π-0.542888\pi
−0.134328 + 0.990937i 0.542888π0.542888\pi
524524 42200.4 3.51819
525525 4192.94 0.348561
526526 −27841.7 −2.30790
527527 −20714.9 −1.71225
528528 15674.7 1.29196
529529 −10419.0 −0.856333
530530 −43116.4 −3.53369
531531 −4357.61 −0.356128
532532 −444.036 −0.0361868
533533 0 0
534534 16601.3 1.34533
535535 −12855.8 −1.03889
536536 12579.2 1.01369
537537 −12789.0 −1.02772
538538 −38399.5 −3.07718
539539 6877.83 0.549627
540540 −9046.13 −0.720895
541541 −11251.4 −0.894150 −0.447075 0.894497i 0.647534π-0.647534\pi
−0.447075 + 0.894497i 0.647534π0.647534\pi
542542 −45722.4 −3.62352
543543 −11833.8 −0.935245
544544 −51825.8 −4.08458
545545 8737.33 0.686727
546546 0 0
547547 1533.54 0.119871 0.0599353 0.998202i 0.480911π-0.480911\pi
0.0599353 + 0.998202i 0.480911π0.480911\pi
548548 7910.31 0.616628
549549 −3996.19 −0.310662
550550 21233.3 1.64617
551551 138.477 0.0107066
552552 8299.08 0.639914
553553 3631.97 0.279289
554554 −38214.6 −2.93066
555555 4846.30 0.370656
556556 15362.2 1.17177
557557 −16845.7 −1.28146 −0.640731 0.767766i 0.721369π-0.721369\pi
−0.640731 + 0.767766i 0.721369π0.721369\pi
558558 9207.65 0.698550
559559 0 0
560560 −30089.0 −2.27052
561561 8932.62 0.672256
562562 4526.34 0.339737
563563 −20820.1 −1.55855 −0.779273 0.626685i 0.784411π-0.784411\pi
−0.779273 + 0.626685i 0.784411π0.784411\pi
564564 −31322.8 −2.33852
565565 −2964.03 −0.220704
566566 −5945.37 −0.441524
567567 −784.054 −0.0580726
568568 32076.6 2.36955
569569 23636.6 1.74147 0.870735 0.491752i 0.163643π-0.163643\pi
0.870735 + 0.491752i 0.163643π0.163643\pi
570570 589.819 0.0433417
571571 −26955.1 −1.97554 −0.987771 0.155913i 0.950168π-0.950168\pi
−0.987771 + 0.155913i 0.950168π0.950168\pi
572572 0 0
573573 642.326 0.0468300
574574 1586.35 0.115353
575575 6036.78 0.437828
576576 9400.25 0.679995
577577 −23499.8 −1.69551 −0.847755 0.530388i 0.822046π-0.822046\pi
−0.847755 + 0.530388i 0.822046π0.822046\pi
578578 −35902.8 −2.58367
579579 −3621.56 −0.259943
580580 20645.7 1.47805
581581 −6928.38 −0.494729
582582 −1048.44 −0.0746721
583583 −13596.1 −0.965857
584584 −63373.1 −4.49040
585585 0 0
586586 −9933.33 −0.700243
587587 −4637.50 −0.326082 −0.163041 0.986619i 0.552130π-0.552130\pi
−0.163041 + 0.986619i 0.552130π0.552130\pi
588588 15267.2 1.07076
589589 −431.316 −0.0301733
590590 42359.9 2.95582
591591 −2782.89 −0.193694
592592 −18640.4 −1.29411
593593 −12633.5 −0.874869 −0.437434 0.899250i 0.644113π-0.644113\pi
−0.437434 + 0.899250i 0.644113π0.644113\pi
594594 −3970.51 −0.274262
595595 −17146.9 −1.18144
596596 53823.7 3.69917
597597 −1436.85 −0.0985033
598598 0 0
599599 −18757.1 −1.27946 −0.639730 0.768600i 0.720954π-0.720954\pi
−0.639730 + 0.768600i 0.720954π0.720954\pi
600600 28661.3 1.95016
601601 −3632.98 −0.246576 −0.123288 0.992371i 0.539344π-0.539344\pi
−0.123288 + 0.992371i 0.539344π0.539344\pi
602602 12296.8 0.832522
603603 −1711.02 −0.115553
604604 68025.0 4.58261
605605 −9353.71 −0.628566
606606 8504.08 0.570057
607607 −12700.0 −0.849219 −0.424610 0.905377i 0.639589π-0.639589\pi
−0.424610 + 0.905377i 0.639589π0.639589\pi
608608 −1079.09 −0.0719786
609609 1789.42 0.119066
610610 38846.6 2.57845
611611 0 0
612612 19828.3 1.30966
613613 −21640.1 −1.42584 −0.712918 0.701248i 0.752627π-0.752627\pi
−0.712918 + 0.701248i 0.752627π0.752627\pi
614614 −34047.9 −2.23788
615615 −1513.87 −0.0992605
616616 −17669.5 −1.15572
617617 16541.7 1.07933 0.539663 0.841881i 0.318552π-0.318552\pi
0.539663 + 0.841881i 0.318552π0.318552\pi
618618 −11769.2 −0.766066
619619 21138.9 1.37261 0.686303 0.727316i 0.259233π-0.259233\pi
0.686303 + 0.727316i 0.259233π0.259233\pi
620620 −64305.2 −4.16542
621621 −1128.84 −0.0729451
622622 18616.9 1.20011
623623 −10049.0 −0.646235
624624 0 0
625625 −12825.4 −0.820823
626626 31513.3 2.01202
627627 185.991 0.0118465
628628 −33176.6 −2.10811
629629 −10622.7 −0.673377
630630 7621.73 0.481995
631631 −5489.80 −0.346348 −0.173174 0.984891i 0.555402π-0.555402\pi
−0.173174 + 0.984891i 0.555402π0.555402\pi
632632 24826.8 1.56259
633633 4352.86 0.273319
634634 −8941.94 −0.560141
635635 23497.5 1.46846
636636 −30180.3 −1.88164
637637 0 0
638638 9061.76 0.562318
639639 −4363.06 −0.270110
640640 −28328.1 −1.74963
641641 4297.04 0.264778 0.132389 0.991198i 0.457735π-0.457735\pi
0.132389 + 0.991198i 0.457735π0.457735\pi
642642 −12525.3 −0.769993
643643 −25696.9 −1.57603 −0.788016 0.615655i 0.788892π-0.788892\pi
−0.788016 + 0.615655i 0.788892π0.788892\pi
644644 −8261.14 −0.505488
645645 −11735.0 −0.716378
646646 −1292.83 −0.0787396
647647 2174.98 0.132160 0.0660798 0.997814i 0.478951π-0.478951\pi
0.0660798 + 0.997814i 0.478951π0.478951\pi
648648 −5359.50 −0.324909
649649 13357.6 0.807907
650650 0 0
651651 −5573.52 −0.335551
652652 37465.5 2.25040
653653 −15454.5 −0.926160 −0.463080 0.886316i 0.653256π-0.653256\pi
−0.463080 + 0.886316i 0.653256π0.653256\pi
654654 8512.73 0.508982
655655 33931.1 2.02412
656656 5822.82 0.346560
657657 8620.02 0.511870
658658 26390.7 1.56355
659659 −3148.77 −0.186129 −0.0930643 0.995660i 0.529666π-0.529666\pi
−0.0930643 + 0.995660i 0.529666π0.529666\pi
660660 27729.6 1.63541
661661 2099.70 0.123553 0.0617767 0.998090i 0.480323π-0.480323\pi
0.0617767 + 0.998090i 0.480323π0.480323\pi
662662 10715.7 0.629122
663663 0 0
664664 −47359.8 −2.76795
665665 −357.026 −0.0208193
666666 4721.73 0.274720
667667 2576.32 0.149559
668668 −39703.4 −2.29966
669669 −6179.36 −0.357112
670670 16632.7 0.959071
671671 12249.7 0.704763
672672 −13944.2 −0.800460
673673 30970.8 1.77390 0.886950 0.461865i 0.152819π-0.152819\pi
0.886950 + 0.461865i 0.152819π0.152819\pi
674674 −38055.0 −2.17481
675675 −3898.52 −0.222302
676676 0 0
677677 14640.6 0.831141 0.415570 0.909561i 0.363582π-0.363582\pi
0.415570 + 0.909561i 0.363582π0.363582\pi
678678 −2887.83 −0.163579
679679 634.635 0.0358690
680680 −117210. −6.60999
681681 13447.4 0.756688
682682 −28224.7 −1.58472
683683 6685.83 0.374563 0.187281 0.982306i 0.440032π-0.440032\pi
0.187281 + 0.982306i 0.440032π0.440032\pi
684684 412.856 0.0230789
685685 6360.27 0.354764
686686 −30560.8 −1.70090
687687 −4891.18 −0.271630
688688 45136.3 2.50117
689689 0 0
690690 10973.4 0.605434
691691 30194.1 1.66228 0.831141 0.556062i 0.187688π-0.187688\pi
0.831141 + 0.556062i 0.187688π0.187688\pi
692692 51678.4 2.83890
693693 2403.40 0.131743
694694 −6.07611 −0.000332343 0
695695 12352.0 0.674154
696696 12231.8 0.666158
697697 3318.28 0.180328
698698 65026.0 3.52618
699699 5711.08 0.309031
700700 −28530.3 −1.54049
701701 −30300.9 −1.63260 −0.816298 0.577631i 0.803977π-0.803977\pi
−0.816298 + 0.577631i 0.803977π0.803977\pi
702702 0 0
703703 −221.181 −0.0118663
704704 −28815.1 −1.54263
705705 −25185.0 −1.34542
706706 −58060.3 −3.09508
707707 −5147.64 −0.273829
708708 29650.8 1.57393
709709 −26123.2 −1.38375 −0.691875 0.722017i 0.743215π-0.743215\pi
−0.691875 + 0.722017i 0.743215π0.743215\pi
710710 42412.9 2.24187
711711 −3376.94 −0.178123
712712 −68691.1 −3.61560
713713 −8024.48 −0.421486
714714 −16706.2 −0.875647
715715 0 0
716716 87021.3 4.54209
717717 11291.4 0.588122
718718 −18793.8 −0.976850
719719 19325.7 1.00240 0.501200 0.865331i 0.332892π-0.332892\pi
0.501200 + 0.865331i 0.332892π0.332892\pi
720720 27976.2 1.44807
721721 7124.09 0.367982
722722 36534.2 1.88319
723723 −10844.2 −0.557816
724724 80521.7 4.13338
725725 8897.47 0.455784
726726 −9113.26 −0.465875
727727 26065.8 1.32975 0.664875 0.746954i 0.268485π-0.268485\pi
0.664875 + 0.746954i 0.268485π0.268485\pi
728728 0 0
729729 729.000 0.0370370
730730 −83794.4 −4.24845
731731 25722.0 1.30145
732732 27191.5 1.37299
733733 −1055.45 −0.0531843 −0.0265921 0.999646i 0.508466π-0.508466\pi
−0.0265921 + 0.999646i 0.508466π0.508466\pi
734734 −12706.4 −0.638965
735735 12275.5 0.616041
736736 −20076.2 −1.00546
737737 5244.89 0.262141
738738 −1474.96 −0.0735690
739739 −9410.40 −0.468426 −0.234213 0.972185i 0.575251π-0.575251\pi
−0.234213 + 0.972185i 0.575251π0.575251\pi
740740 −32976.0 −1.63814
741741 0 0
742742 25428.1 1.25808
743743 7523.70 0.371491 0.185746 0.982598i 0.440530π-0.440530\pi
0.185746 + 0.982598i 0.440530π0.440530\pi
744744 −38098.5 −1.87736
745745 43276.8 2.12824
746746 70799.4 3.47473
747747 6441.89 0.315524
748748 −60780.8 −2.97108
749749 7581.76 0.369868
750750 5089.07 0.247769
751751 −12984.1 −0.630886 −0.315443 0.948945i 0.602153π-0.602153\pi
−0.315443 + 0.948945i 0.602153π0.602153\pi
752752 96869.3 4.69742
753753 17189.3 0.831890
754754 0 0
755755 54695.3 2.63651
756756 5334.99 0.256656
757757 −27934.6 −1.34122 −0.670609 0.741811i 0.733967π-0.733967\pi
−0.670609 + 0.741811i 0.733967π0.733967\pi
758758 −23649.5 −1.13323
759759 3460.30 0.165482
760760 −2440.49 −0.116482
761761 15519.3 0.739255 0.369627 0.929180i 0.379485π-0.379485\pi
0.369627 + 0.929180i 0.379485π0.379485\pi
762762 22893.5 1.08838
763763 −5152.88 −0.244491
764764 −4370.62 −0.206968
765765 15942.9 0.753487
766766 −4319.82 −0.203761
767767 0 0
768768 −2532.57 −0.118993
769769 −12885.2 −0.604228 −0.302114 0.953272i 0.597692π-0.597692\pi
−0.302114 + 0.953272i 0.597692π0.597692\pi
770770 −23363.3 −1.09345
771771 16577.4 0.774344
772772 24642.4 1.14883
773773 −5892.04 −0.274155 −0.137078 0.990560i 0.543771π-0.543771\pi
−0.137078 + 0.990560i 0.543771π0.543771\pi
774774 −11433.3 −0.530958
775775 −27713.0 −1.28449
776776 4338.12 0.200682
777777 −2858.13 −0.131962
778778 −18463.4 −0.850828
779779 69.0916 0.00317775
780780 0 0
781781 13374.3 0.612766
782782 −24052.7 −1.09990
783783 −1663.77 −0.0759367
784784 −47215.5 −2.15085
785785 −26675.6 −1.21286
786786 33058.9 1.50022
787787 21020.4 0.952091 0.476045 0.879421i 0.342070π-0.342070\pi
0.476045 + 0.879421i 0.342070π0.342070\pi
788788 18935.8 0.856042
789789 −15669.6 −0.707038
790790 32827.0 1.47839
791791 1748.05 0.0785757
792792 16428.7 0.737084
793793 0 0
794794 2267.58 0.101352
795795 −24266.4 −1.08256
796796 9776.87 0.435342
797797 31355.6 1.39356 0.696782 0.717283i 0.254614π-0.254614\pi
0.696782 + 0.717283i 0.254614π0.254614\pi
798798 −347.848 −0.0154307
799799 55203.3 2.44425
800800 −69334.0 −3.06416
801801 9343.37 0.412150
802802 −6326.37 −0.278543
803803 −26423.4 −1.16122
804804 11642.4 0.510692
805805 −6642.34 −0.290822
806806 0 0
807807 −21611.7 −0.942709
808808 −35187.3 −1.53204
809809 −18132.5 −0.788017 −0.394009 0.919107i 0.628912π-0.628912\pi
−0.394009 + 0.919107i 0.628912π0.628912\pi
810810 −7086.55 −0.307402
811811 24755.3 1.07186 0.535928 0.844263i 0.319962π-0.319962\pi
0.535928 + 0.844263i 0.319962π0.319962\pi
812812 −12175.9 −0.526219
813813 −25733.1 −1.11008
814814 −14473.8 −0.623225
815815 30124.0 1.29472
816816 −61321.4 −2.63073
817817 535.572 0.0229343
818818 42682.7 1.82441
819819 0 0
820820 10300.9 0.438688
821821 −4082.65 −0.173551 −0.0867755 0.996228i 0.527656π-0.527656\pi
−0.0867755 + 0.996228i 0.527656π0.527656\pi
822822 6196.77 0.262941
823823 −34327.0 −1.45391 −0.726954 0.686687i 0.759065π-0.759065\pi
−0.726954 + 0.686687i 0.759065π0.759065\pi
824824 48697.6 2.05881
825825 11950.3 0.504312
826826 −24981.9 −1.05234
827827 −3228.87 −0.135767 −0.0678833 0.997693i 0.521625π-0.521625\pi
−0.0678833 + 0.997693i 0.521625π0.521625\pi
828828 7681.06 0.322386
829829 −10452.4 −0.437908 −0.218954 0.975735i 0.570265π-0.570265\pi
−0.218954 + 0.975735i 0.570265π0.570265\pi
830830 −62621.0 −2.61880
831831 −21507.6 −0.897821
832832 0 0
833833 −26906.9 −1.11917
834834 12034.5 0.499663
835835 −31923.4 −1.32306
836836 −1265.55 −0.0523564
837837 5182.16 0.214004
838838 −36419.7 −1.50131
839839 28289.0 1.16406 0.582028 0.813169i 0.302259π-0.302259\pi
0.582028 + 0.813169i 0.302259π0.302259\pi
840840 −31536.4 −1.29537
841841 −20591.8 −0.844308
842842 57246.1 2.34303
843843 2547.47 0.104080
844844 −29618.5 −1.20795
845845 0 0
846846 −24537.6 −0.997187
847847 5516.39 0.223784
848848 93335.9 3.77968
849849 −3346.12 −0.135263
850850 −83067.2 −3.35198
851851 −4114.99 −0.165758
852852 29687.8 1.19377
853853 26631.8 1.06900 0.534498 0.845170i 0.320501π-0.320501\pi
0.534498 + 0.845170i 0.320501π0.320501\pi
854854 −22910.0 −0.917989
855855 331.956 0.0132780
856856 51826.0 2.06936
857857 11796.7 0.470209 0.235104 0.971970i 0.424457π-0.424457\pi
0.235104 + 0.971970i 0.424457π0.424457\pi
858858 0 0
859859 −22672.8 −0.900567 −0.450283 0.892886i 0.648677π-0.648677\pi
−0.450283 + 0.892886i 0.648677π0.648677\pi
860860 79849.0 3.16608
861861 892.812 0.0353391
862862 27795.0 1.09826
863863 −21421.1 −0.844940 −0.422470 0.906377i 0.638837π-0.638837\pi
−0.422470 + 0.906377i 0.638837π0.638837\pi
864864 12965.1 0.510510
865865 41551.9 1.63330
866866 −46066.6 −1.80763
867867 −20206.5 −0.791520
868868 37924.3 1.48299
869869 10351.5 0.404086
870870 16173.4 0.630264
871871 0 0
872872 −35223.1 −1.36790
873873 −590.072 −0.0228762
874874 −500.814 −0.0193825
875875 −3080.48 −0.119016
876876 −58653.7 −2.26224
877877 5155.20 0.198493 0.0992466 0.995063i 0.468357π-0.468357\pi
0.0992466 + 0.995063i 0.468357π0.468357\pi
878878 69435.0 2.66893
879879 −5590.58 −0.214523
880880 −85756.9 −3.28507
881881 23692.2 0.906027 0.453013 0.891504i 0.350349π-0.350349\pi
0.453013 + 0.891504i 0.350349π0.350349\pi
882882 11960.0 0.456591
883883 −14591.5 −0.556108 −0.278054 0.960565i 0.589689π-0.589689\pi
−0.278054 + 0.960565i 0.589689π0.589689\pi
884884 0 0
885885 23840.6 0.905529
886886 61475.2 2.33104
887887 −9722.26 −0.368029 −0.184014 0.982924i 0.558909π-0.558909\pi
−0.184014 + 0.982924i 0.558909π0.558909\pi
888888 −19537.1 −0.738312
889889 −13857.8 −0.522806
890890 −90826.1 −3.42078
891891 −2234.64 −0.0840217
892892 42046.6 1.57828
893893 1149.42 0.0430726
894894 42164.3 1.57739
895895 69969.2 2.61320
896896 16706.6 0.622911
897897 0 0
898898 52678.9 1.95759
899899 −11827.1 −0.438771
900900 26526.9 0.982479
901901 53189.7 1.96671
902902 4521.26 0.166898
903903 6920.74 0.255048
904904 11949.0 0.439621
905905 64743.2 2.37805
906906 53289.3 1.95411
907907 11799.0 0.431951 0.215975 0.976399i 0.430707π-0.430707\pi
0.215975 + 0.976399i 0.430707π0.430707\pi
908908 −91500.9 −3.34423
909909 4786.18 0.174640
910910 0 0
911911 −43012.4 −1.56429 −0.782143 0.623099i 0.785873π-0.785873\pi
−0.782143 + 0.623099i 0.785873π0.785873\pi
912912 −1276.81 −0.0463589
913913 −19746.6 −0.715793
914914 −83303.8 −3.01471
915915 21863.3 0.789921
916916 33281.3 1.20049
917917 −20011.0 −0.720635
918918 15533.1 0.558462
919919 −4951.41 −0.177728 −0.0888639 0.996044i 0.528324π-0.528324\pi
−0.0888639 + 0.996044i 0.528324π0.528324\pi
920920 −45404.5 −1.62711
921921 −19162.5 −0.685587
922922 −41297.0 −1.47510
923923 0 0
924924 −16353.6 −0.582245
925925 −14211.3 −0.505152
926926 −1777.27 −0.0630721
927927 −6623.85 −0.234688
928928 −29589.8 −1.04669
929929 8934.86 0.315547 0.157774 0.987475i 0.449568π-0.449568\pi
0.157774 + 0.987475i 0.449568π0.449568\pi
930930 −50375.4 −1.77621
931931 −560.243 −0.0197221
932932 −38860.2 −1.36578
933933 10477.8 0.367660
934934 −43700.3 −1.53096
935935 −48870.6 −1.70935
936936 0 0
937937 −13182.8 −0.459620 −0.229810 0.973235i 0.573811π-0.573811\pi
−0.229810 + 0.973235i 0.573811π0.573811\pi
938938 −9809.20 −0.341452
939939 17736.0 0.616393
940940 171368. 5.94618
941941 21693.7 0.751536 0.375768 0.926714i 0.377379π-0.377379\pi
0.375768 + 0.926714i 0.377379π0.377379\pi
942942 −25989.9 −0.898934
943943 1285.43 0.0443895
944944 −91698.4 −3.16158
945945 4289.59 0.147662
946946 35047.1 1.20452
947947 49790.0 1.70851 0.854254 0.519856i 0.174014π-0.174014\pi
0.854254 + 0.519856i 0.174014π0.174014\pi
948948 22977.9 0.787224
949949 0 0
950950 −1729.59 −0.0590687
951951 −5032.61 −0.171602
952952 69125.0 2.35331
953953 4217.93 0.143371 0.0716853 0.997427i 0.477162π-0.477162\pi
0.0716853 + 0.997427i 0.477162π0.477162\pi
954954 −23642.6 −0.802365
955955 −3514.19 −0.119075
956956 −76830.5 −2.59924
957957 5100.05 0.172269
958958 −34305.8 −1.15696
959959 −3750.99 −0.126304
960960 −51429.0 −1.72903
961961 7046.87 0.236544
962962 0 0
963963 −7049.38 −0.235891
964964 73788.1 2.46530
965965 19813.7 0.660958
966966 −6471.60 −0.215549
967967 40927.9 1.36107 0.680534 0.732717i 0.261748π-0.261748\pi
0.680534 + 0.732717i 0.261748π0.261748\pi
968968 37707.9 1.25204
969969 −727.619 −0.0241223
970970 5736.04 0.189869
971971 −17114.8 −0.565645 −0.282822 0.959172i 0.591271π-0.591271\pi
−0.282822 + 0.959172i 0.591271π0.591271\pi
972972 −4960.38 −0.163688
973973 −7284.62 −0.240015
974974 43151.5 1.41957
975975 0 0
976976 −84093.0 −2.75794
977977 118.470 0.00387940 0.00193970 0.999998i 0.499383π-0.499383\pi
0.00193970 + 0.999998i 0.499383π0.499383\pi
978978 29349.7 0.959610
979979 −28640.7 −0.934996
980980 −83527.2 −2.72263
981981 4791.05 0.155929
982982 −27272.8 −0.886261
983983 −26002.8 −0.843705 −0.421852 0.906665i 0.638620π-0.638620\pi
−0.421852 + 0.906665i 0.638620π0.638620\pi
984984 6102.93 0.197718
985985 15225.3 0.492506
986986 −35450.7 −1.14501
987987 14853.0 0.479002
988988 0 0
989989 9964.14 0.320365
990990 21722.8 0.697368
991991 −16062.0 −0.514860 −0.257430 0.966297i 0.582876π-0.582876\pi
−0.257430 + 0.966297i 0.582876π0.582876\pi
992992 92163.3 2.94979
993993 6030.93 0.192735
994994 −25013.2 −0.798159
995995 7861.07 0.250465
996996 −43832.9 −1.39448
997997 1361.54 0.0432503 0.0216251 0.999766i 0.493116π-0.493116\pi
0.0216251 + 0.999766i 0.493116π0.493116\pi
998998 −96217.5 −3.05182
999999 2657.44 0.0841617
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 507.4.a.i.1.1 4
3.2 odd 2 1521.4.a.bb.1.4 4
13.4 even 6 39.4.e.c.16.1 8
13.5 odd 4 507.4.b.h.337.8 8
13.8 odd 4 507.4.b.h.337.1 8
13.10 even 6 39.4.e.c.22.1 yes 8
13.12 even 2 507.4.a.m.1.4 4
39.17 odd 6 117.4.g.e.55.4 8
39.23 odd 6 117.4.g.e.100.4 8
39.38 odd 2 1521.4.a.v.1.1 4
52.23 odd 6 624.4.q.i.529.1 8
52.43 odd 6 624.4.q.i.289.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.e.c.16.1 8 13.4 even 6
39.4.e.c.22.1 yes 8 13.10 even 6
117.4.g.e.55.4 8 39.17 odd 6
117.4.g.e.100.4 8 39.23 odd 6
507.4.a.i.1.1 4 1.1 even 1 trivial
507.4.a.m.1.4 4 13.12 even 2
507.4.b.h.337.1 8 13.8 odd 4
507.4.b.h.337.8 8 13.5 odd 4
624.4.q.i.289.1 8 52.43 odd 6
624.4.q.i.529.1 8 52.23 odd 6
1521.4.a.v.1.1 4 39.38 odd 2
1521.4.a.bb.1.4 4 3.2 odd 2