Properties

Label 1250.4.a.c.1.3
Level 12501250
Weight 44
Character 1250.1
Self dual yes
Analytic conductor 73.75273.752
Analytic rank 00
Dimension 66
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1250,4,Mod(1,1250)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1250, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("1250.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 1250=254 1250 = 2 \cdot 5^{4}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1250.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,-12,8,24,0,-16,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 73.752387507273.7523875072
Analytic rank: 00
Dimension: 66
Coefficient field: Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x6x5145x4+120x3+5125x22431x1069 x^{6} - x^{5} - 145x^{4} + 120x^{3} + 5125x^{2} - 2431x - 1069 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 5 5
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 0.278104-0.278104 of defining polynomial
Character χ\chi == 1250.1

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) == q2.00000q2+0.660070q3+4.00000q41.32014q615.8349q78.00000q826.5643q95.50104q11+2.64028q12+63.8038q13+31.6697q14+16.0000q1681.0213q17+53.1286q18+20.0588q1910.4521q21+11.0021q2284.1633q235.28056q24127.608q2635.3562q2763.3395q2898.1075q29+197.566q3132.0000q323.63107q33+162.043q34106.257q3696.5325q3740.1175q38+42.1149q3929.9555q41+20.9042q42247.303q4322.0041q44+168.327q46339.902q47+10.5611q4892.2570q4953.4797q51+255.215q52106.039q53+70.7124q54+126.679q56+13.2402q57+196.215q58+417.834q59+780.727q61395.131q62+420.642q63+64.0000q64+7.26213q66645.674q67324.085q6855.5537q6934.6744q71+212.514q72+1142.77q73+193.065q74+80.2350q76+87.1082q7784.2299q78+1038.37q79+693.899q81+59.9110q82+457.171q8341.8085q84+494.606q8664.7578q87+44.0083q88+331.800q891010.32q91336.653q92+130.407q93+679.803q9421.1222q96+630.243q97+184.514q98+146.131q99+O(q100)q-2.00000 q^{2} +0.660070 q^{3} +4.00000 q^{4} -1.32014 q^{6} -15.8349 q^{7} -8.00000 q^{8} -26.5643 q^{9} -5.50104 q^{11} +2.64028 q^{12} +63.8038 q^{13} +31.6697 q^{14} +16.0000 q^{16} -81.0213 q^{17} +53.1286 q^{18} +20.0588 q^{19} -10.4521 q^{21} +11.0021 q^{22} -84.1633 q^{23} -5.28056 q^{24} -127.608 q^{26} -35.3562 q^{27} -63.3395 q^{28} -98.1075 q^{29} +197.566 q^{31} -32.0000 q^{32} -3.63107 q^{33} +162.043 q^{34} -106.257 q^{36} -96.5325 q^{37} -40.1175 q^{38} +42.1149 q^{39} -29.9555 q^{41} +20.9042 q^{42} -247.303 q^{43} -22.0041 q^{44} +168.327 q^{46} -339.902 q^{47} +10.5611 q^{48} -92.2570 q^{49} -53.4797 q^{51} +255.215 q^{52} -106.039 q^{53} +70.7124 q^{54} +126.679 q^{56} +13.2402 q^{57} +196.215 q^{58} +417.834 q^{59} +780.727 q^{61} -395.131 q^{62} +420.642 q^{63} +64.0000 q^{64} +7.26213 q^{66} -645.674 q^{67} -324.085 q^{68} -55.5537 q^{69} -34.6744 q^{71} +212.514 q^{72} +1142.77 q^{73} +193.065 q^{74} +80.2350 q^{76} +87.1082 q^{77} -84.2299 q^{78} +1038.37 q^{79} +693.899 q^{81} +59.9110 q^{82} +457.171 q^{83} -41.8085 q^{84} +494.606 q^{86} -64.7578 q^{87} +44.0083 q^{88} +331.800 q^{89} -1010.32 q^{91} -336.653 q^{92} +130.407 q^{93} +679.803 q^{94} -21.1222 q^{96} +630.243 q^{97} +184.514 q^{98} +146.131 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q12q2+8q3+24q416q66q748q8+142q9+107q11+32q1242q13+12q14+96q16156q17284q18+50q19+122q21214q22++2389q99+O(q100) 6 q - 12 q^{2} + 8 q^{3} + 24 q^{4} - 16 q^{6} - 6 q^{7} - 48 q^{8} + 142 q^{9} + 107 q^{11} + 32 q^{12} - 42 q^{13} + 12 q^{14} + 96 q^{16} - 156 q^{17} - 284 q^{18} + 50 q^{19} + 122 q^{21} - 214 q^{22}+ \cdots + 2389 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 −2.00000 −0.707107
33 0.660070 0.127030 0.0635152 0.997981i 0.479769π-0.479769\pi
0.0635152 + 0.997981i 0.479769π0.479769\pi
44 4.00000 0.500000
55 0 0
66 −1.32014 −0.0898241
77 −15.8349 −0.855002 −0.427501 0.904015i 0.640606π-0.640606\pi
−0.427501 + 0.904015i 0.640606π0.640606\pi
88 −8.00000 −0.353553
99 −26.5643 −0.983863
1010 0 0
1111 −5.50104 −0.150784 −0.0753920 0.997154i 0.524021π-0.524021\pi
−0.0753920 + 0.997154i 0.524021π0.524021\pi
1212 2.64028 0.0635152
1313 63.8038 1.36123 0.680615 0.732641i 0.261713π-0.261713\pi
0.680615 + 0.732641i 0.261713π0.261713\pi
1414 31.6697 0.604578
1515 0 0
1616 16.0000 0.250000
1717 −81.0213 −1.15591 −0.577957 0.816067i 0.696150π-0.696150\pi
−0.577957 + 0.816067i 0.696150π0.696150\pi
1818 53.1286 0.695696
1919 20.0588 0.242200 0.121100 0.992640i 0.461358π-0.461358\pi
0.121100 + 0.992640i 0.461358π0.461358\pi
2020 0 0
2121 −10.4521 −0.108611
2222 11.0021 0.106620
2323 −84.1633 −0.763012 −0.381506 0.924366i 0.624594π-0.624594\pi
−0.381506 + 0.924366i 0.624594π0.624594\pi
2424 −5.28056 −0.0449121
2525 0 0
2626 −127.608 −0.962535
2727 −35.3562 −0.252011
2828 −63.3395 −0.427501
2929 −98.1075 −0.628211 −0.314105 0.949388i 0.601704π-0.601704\pi
−0.314105 + 0.949388i 0.601704π0.601704\pi
3030 0 0
3131 197.566 1.14464 0.572320 0.820031i 0.306044π-0.306044\pi
0.572320 + 0.820031i 0.306044π0.306044\pi
3232 −32.0000 −0.176777
3333 −3.63107 −0.0191542
3434 162.043 0.817355
3535 0 0
3636 −106.257 −0.491932
3737 −96.5325 −0.428915 −0.214457 0.976733i 0.568798π-0.568798\pi
−0.214457 + 0.976733i 0.568798π0.568798\pi
3838 −40.1175 −0.171261
3939 42.1149 0.172918
4040 0 0
4141 −29.9555 −0.114104 −0.0570520 0.998371i 0.518170π-0.518170\pi
−0.0570520 + 0.998371i 0.518170π0.518170\pi
4242 20.9042 0.0767998
4343 −247.303 −0.877055 −0.438527 0.898718i 0.644500π-0.644500\pi
−0.438527 + 0.898718i 0.644500π0.644500\pi
4444 −22.0041 −0.0753920
4545 0 0
4646 168.327 0.539531
4747 −339.902 −1.05489 −0.527444 0.849590i 0.676850π-0.676850\pi
−0.527444 + 0.849590i 0.676850π0.676850\pi
4848 10.5611 0.0317576
4949 −92.2570 −0.268971
5050 0 0
5151 −53.4797 −0.146836
5252 255.215 0.680615
5353 −106.039 −0.274821 −0.137411 0.990514i 0.543878π-0.543878\pi
−0.137411 + 0.990514i 0.543878π0.543878\pi
5454 70.7124 0.178199
5555 0 0
5656 126.679 0.302289
5757 13.2402 0.0307667
5858 196.215 0.444212
5959 417.834 0.921989 0.460994 0.887403i 0.347493π-0.347493\pi
0.460994 + 0.887403i 0.347493π0.347493\pi
6060 0 0
6161 780.727 1.63872 0.819359 0.573280i 0.194329π-0.194329\pi
0.819359 + 0.573280i 0.194329π0.194329\pi
6262 −395.131 −0.809382
6363 420.642 0.841206
6464 64.0000 0.125000
6565 0 0
6666 7.26213 0.0135440
6767 −645.674 −1.17734 −0.588669 0.808374i 0.700348π-0.700348\pi
−0.588669 + 0.808374i 0.700348π0.700348\pi
6868 −324.085 −0.577957
6969 −55.5537 −0.0969257
7070 0 0
7171 −34.6744 −0.0579590 −0.0289795 0.999580i 0.509226π-0.509226\pi
−0.0289795 + 0.999580i 0.509226π0.509226\pi
7272 212.514 0.347848
7373 1142.77 1.83221 0.916107 0.400934i 0.131314π-0.131314\pi
0.916107 + 0.400934i 0.131314π0.131314\pi
7474 193.065 0.303288
7575 0 0
7676 80.2350 0.121100
7777 87.1082 0.128921
7878 −84.2299 −0.122271
7979 1038.37 1.47881 0.739403 0.673263i 0.235108π-0.235108\pi
0.739403 + 0.673263i 0.235108π0.235108\pi
8080 0 0
8181 693.899 0.951850
8282 59.9110 0.0806837
8383 457.171 0.604591 0.302296 0.953214i 0.402247π-0.402247\pi
0.302296 + 0.953214i 0.402247π0.402247\pi
8484 −41.8085 −0.0543057
8585 0 0
8686 494.606 0.620171
8787 −64.7578 −0.0798019
8888 44.0083 0.0533102
8989 331.800 0.395177 0.197588 0.980285i 0.436689π-0.436689\pi
0.197588 + 0.980285i 0.436689π0.436689\pi
9090 0 0
9191 −1010.32 −1.16385
9292 −336.653 −0.381506
9393 130.407 0.145404
9494 679.803 0.745919
9595 0 0
9696 −21.1222 −0.0224560
9797 630.243 0.659706 0.329853 0.944032i 0.393001π-0.393001\pi
0.329853 + 0.944032i 0.393001π0.393001\pi
9898 184.514 0.190191
9999 146.131 0.148351
100100 0 0
101101 −1840.58 −1.81331 −0.906655 0.421872i 0.861373π-0.861373\pi
−0.906655 + 0.421872i 0.861373π0.861373\pi
102102 106.959 0.103829
103103 −1279.88 −1.22437 −0.612185 0.790714i 0.709709π-0.709709\pi
−0.612185 + 0.790714i 0.709709π0.709709\pi
104104 −510.430 −0.481267
105105 0 0
106106 212.077 0.194328
107107 446.971 0.403835 0.201917 0.979403i 0.435283π-0.435283\pi
0.201917 + 0.979403i 0.435283π0.435283\pi
108108 −141.425 −0.126006
109109 −295.021 −0.259247 −0.129623 0.991563i 0.541377π-0.541377\pi
−0.129623 + 0.991563i 0.541377π0.541377\pi
110110 0 0
111111 −63.7182 −0.0544852
112112 −253.358 −0.213751
113113 −194.457 −0.161885 −0.0809425 0.996719i 0.525793π-0.525793\pi
−0.0809425 + 0.996719i 0.525793π0.525793\pi
114114 −26.4804 −0.0217554
115115 0 0
116116 −392.430 −0.314105
117117 −1694.90 −1.33926
118118 −835.668 −0.651944
119119 1282.96 0.988310
120120 0 0
121121 −1300.74 −0.977264
122122 −1561.45 −1.15875
123123 −19.7727 −0.0144947
124124 790.262 0.572320
125125 0 0
126126 −841.285 −0.594822
127127 2355.03 1.64547 0.822737 0.568422i 0.192446π-0.192446\pi
0.822737 + 0.568422i 0.192446π0.192446\pi
128128 −128.000 −0.0883883
129129 −163.237 −0.111413
130130 0 0
131131 1828.59 1.21958 0.609790 0.792563i 0.291254π-0.291254\pi
0.609790 + 0.792563i 0.291254π0.291254\pi
132132 −14.5243 −0.00957709
133133 −317.628 −0.207081
134134 1291.35 0.832503
135135 0 0
136136 648.170 0.408678
137137 −2666.23 −1.66271 −0.831355 0.555742i 0.812434π-0.812434\pi
−0.831355 + 0.555742i 0.812434π0.812434\pi
138138 111.107 0.0685368
139139 1661.15 1.01365 0.506823 0.862050i 0.330820π-0.330820\pi
0.506823 + 0.862050i 0.330820π0.330820\pi
140140 0 0
141141 −224.359 −0.134003
142142 69.3487 0.0409832
143143 −350.987 −0.205252
144144 −425.029 −0.245966
145145 0 0
146146 −2285.55 −1.29557
147147 −60.8960 −0.0341675
148148 −386.130 −0.214457
149149 3305.09 1.81721 0.908603 0.417660i 0.137150π-0.137150\pi
0.908603 + 0.417660i 0.137150π0.137150\pi
150150 0 0
151151 −998.295 −0.538014 −0.269007 0.963138i 0.586695π-0.586695\pi
−0.269007 + 0.963138i 0.586695π0.586695\pi
152152 −160.470 −0.0856305
153153 2152.27 1.13726
154154 −174.216 −0.0911607
155155 0 0
156156 168.460 0.0864588
157157 62.1627 0.0315995 0.0157998 0.999875i 0.494971π-0.494971\pi
0.0157998 + 0.999875i 0.494971π0.494971\pi
158158 −2076.74 −1.04567
159159 −69.9929 −0.0349107
160160 0 0
161161 1332.71 0.652377
162162 −1387.80 −0.673060
163163 97.1898 0.0467024 0.0233512 0.999727i 0.492566π-0.492566\pi
0.0233512 + 0.999727i 0.492566π0.492566\pi
164164 −119.822 −0.0570520
165165 0 0
166166 −914.343 −0.427511
167167 −4112.06 −1.90539 −0.952696 0.303924i 0.901703π-0.901703\pi
−0.952696 + 0.303924i 0.901703π0.901703\pi
168168 83.6169 0.0383999
169169 1873.92 0.852946
170170 0 0
171171 −532.847 −0.238291
172172 −989.212 −0.438527
173173 794.694 0.349245 0.174623 0.984635i 0.444129π-0.444129\pi
0.174623 + 0.984635i 0.444129π0.444129\pi
174174 129.516 0.0564285
175175 0 0
176176 −88.0166 −0.0376960
177177 275.799 0.117121
178178 −663.600 −0.279432
179179 4716.85 1.96957 0.984787 0.173763i 0.0555927π-0.0555927\pi
0.984787 + 0.173763i 0.0555927π0.0555927\pi
180180 0 0
181181 1678.68 0.689364 0.344682 0.938719i 0.387987π-0.387987\pi
0.344682 + 0.938719i 0.387987π0.387987\pi
182182 2020.65 0.822970
183183 515.334 0.208167
184184 673.307 0.269765
185185 0 0
186186 −260.814 −0.102816
187187 445.701 0.174293
188188 −1359.61 −0.527444
189189 559.860 0.215470
190190 0 0
191191 2621.45 0.993098 0.496549 0.868009i 0.334600π-0.334600\pi
0.496549 + 0.868009i 0.334600π0.334600\pi
192192 42.2445 0.0158788
193193 1271.64 0.474274 0.237137 0.971476i 0.423791π-0.423791\pi
0.237137 + 0.971476i 0.423791π0.423791\pi
194194 −1260.49 −0.466482
195195 0 0
196196 −369.028 −0.134485
197197 3664.05 1.32514 0.662570 0.749000i 0.269466π-0.269466\pi
0.662570 + 0.749000i 0.269466π0.269466\pi
198198 −292.262 −0.104900
199199 −2278.43 −0.811626 −0.405813 0.913956i 0.633012π-0.633012\pi
−0.405813 + 0.913956i 0.633012π0.633012\pi
200200 0 0
201201 −426.190 −0.149558
202202 3681.16 1.28220
203203 1553.52 0.537122
204204 −213.919 −0.0734182
205205 0 0
206206 2559.76 0.865761
207207 2235.74 0.750699
208208 1020.86 0.340307
209209 −110.344 −0.0365199
210210 0 0
211211 5210.61 1.70006 0.850032 0.526731i 0.176583π-0.176583\pi
0.850032 + 0.526731i 0.176583π0.176583\pi
212212 −424.154 −0.137411
213213 −22.8875 −0.00736256
214214 −893.942 −0.285554
215215 0 0
216216 282.849 0.0890994
217217 −3128.42 −0.978669
218218 590.042 0.183315
219219 754.311 0.232747
220220 0 0
221221 −5169.46 −1.57347
222222 127.436 0.0385269
223223 −801.962 −0.240822 −0.120411 0.992724i 0.538421π-0.538421\pi
−0.120411 + 0.992724i 0.538421π0.538421\pi
224224 506.716 0.151145
225225 0 0
226226 388.915 0.114470
227227 2943.54 0.860660 0.430330 0.902672i 0.358397π-0.358397\pi
0.430330 + 0.902672i 0.358397π0.358397\pi
228228 52.9607 0.0153834
229229 5430.56 1.56708 0.783541 0.621340i 0.213412π-0.213412\pi
0.783541 + 0.621340i 0.213412π0.213412\pi
230230 0 0
231231 57.4975 0.0163769
232232 784.860 0.222106
233233 2356.15 0.662474 0.331237 0.943548i 0.392534π-0.392534\pi
0.331237 + 0.943548i 0.392534π0.392534\pi
234234 3389.81 0.947003
235235 0 0
236236 1671.34 0.460994
237237 685.396 0.187853
238238 −2565.92 −0.698841
239239 5153.04 1.39465 0.697327 0.716753i 0.254373π-0.254373\pi
0.697327 + 0.716753i 0.254373π0.254373\pi
240240 0 0
241241 −3074.54 −0.821778 −0.410889 0.911685i 0.634782π-0.634782\pi
−0.410889 + 0.911685i 0.634782π0.634782\pi
242242 2601.48 0.691030
243243 1412.64 0.372925
244244 3122.91 0.819359
245245 0 0
246246 39.5454 0.0102493
247247 1279.82 0.329689
248248 −1580.52 −0.404691
249249 301.765 0.0768015
250250 0 0
251251 3095.48 0.778426 0.389213 0.921148i 0.372747π-0.372747\pi
0.389213 + 0.921148i 0.372747π0.372747\pi
252252 1682.57 0.420603
253253 462.985 0.115050
254254 −4710.06 −1.16353
255255 0 0
256256 256.000 0.0625000
257257 4559.39 1.10664 0.553321 0.832968i 0.313360π-0.313360\pi
0.553321 + 0.832968i 0.313360π0.313360\pi
258258 326.475 0.0787807
259259 1528.58 0.366723
260260 0 0
261261 2606.16 0.618073
262262 −3657.19 −0.862374
263263 4239.53 0.993994 0.496997 0.867752i 0.334436π-0.334436\pi
0.496997 + 0.867752i 0.334436π0.334436\pi
264264 29.0485 0.00677202
265265 0 0
266266 635.255 0.146429
267267 219.011 0.0501995
268268 −2582.70 −0.588669
269269 −612.740 −0.138883 −0.0694413 0.997586i 0.522122π-0.522122\pi
−0.0694413 + 0.997586i 0.522122π0.522122\pi
270270 0 0
271271 −7582.91 −1.69974 −0.849869 0.526994i 0.823319π-0.823319\pi
−0.849869 + 0.526994i 0.823319π0.823319\pi
272272 −1296.34 −0.288979
273273 −666.885 −0.147845
274274 5332.46 1.17571
275275 0 0
276276 −222.215 −0.0484629
277277 2701.65 0.586015 0.293008 0.956110i 0.405344π-0.405344\pi
0.293008 + 0.956110i 0.405344π0.405344\pi
278278 −3322.30 −0.716757
279279 −5248.19 −1.12617
280280 0 0
281281 −5892.76 −1.25101 −0.625503 0.780222i 0.715106π-0.715106\pi
−0.625503 + 0.780222i 0.715106π0.715106\pi
282282 448.717 0.0947544
283283 −2995.93 −0.629293 −0.314646 0.949209i 0.601886π-0.601886\pi
−0.314646 + 0.949209i 0.601886π0.601886\pi
284284 −138.697 −0.0289795
285285 0 0
286286 701.974 0.145135
287287 474.341 0.0975591
288288 850.058 0.173924
289289 1651.45 0.336139
290290 0 0
291291 416.004 0.0838027
292292 4571.10 0.916107
293293 4031.15 0.803763 0.401881 0.915692i 0.368356π-0.368356\pi
0.401881 + 0.915692i 0.368356π0.368356\pi
294294 121.792 0.0241601
295295 0 0
296296 772.260 0.151644
297297 194.496 0.0379993
298298 −6610.19 −1.28496
299299 −5369.94 −1.03863
300300 0 0
301301 3916.01 0.749884
302302 1996.59 0.380433
303303 −1214.91 −0.230346
304304 320.940 0.0605499
305305 0 0
306306 −4304.55 −0.804166
307307 −3707.11 −0.689173 −0.344587 0.938755i 0.611981π-0.611981\pi
−0.344587 + 0.938755i 0.611981π0.611981\pi
308308 348.433 0.0644604
309309 −844.809 −0.155532
310310 0 0
311311 −14.0723 −0.00256581 −0.00128291 0.999999i 0.500408π-0.500408\pi
−0.00128291 + 0.999999i 0.500408π0.500408\pi
312312 −336.920 −0.0611356
313313 865.165 0.156236 0.0781182 0.996944i 0.475109π-0.475109\pi
0.0781182 + 0.996944i 0.475109π0.475109\pi
314314 −124.325 −0.0223442
315315 0 0
316316 4153.48 0.739403
317317 −7354.40 −1.30304 −0.651521 0.758631i 0.725869π-0.725869\pi
−0.651521 + 0.758631i 0.725869π0.725869\pi
318318 139.986 0.0246856
319319 539.693 0.0947241
320320 0 0
321321 295.032 0.0512993
322322 −2665.43 −0.461300
323323 −1625.19 −0.279962
324324 2775.60 0.475925
325325 0 0
326326 −194.380 −0.0330236
327327 −194.734 −0.0329322
328328 239.644 0.0403418
329329 5382.30 0.901932
330330 0 0
331331 10052.2 1.66924 0.834620 0.550827i 0.185687π-0.185687\pi
0.834620 + 0.550827i 0.185687π0.185687\pi
332332 1828.69 0.302296
333333 2564.32 0.421993
334334 8224.11 1.34732
335335 0 0
336336 −167.234 −0.0271528
337337 8909.55 1.44016 0.720080 0.693891i 0.244105π-0.244105\pi
0.720080 + 0.693891i 0.244105π0.244105\pi
338338 −3747.85 −0.603124
339339 −128.355 −0.0205643
340340 0 0
341341 −1086.82 −0.172593
342342 1065.69 0.168497
343343 6892.24 1.08497
344344 1978.42 0.310086
345345 0 0
346346 −1589.39 −0.246954
347347 10035.8 1.55260 0.776298 0.630366i 0.217095π-0.217095\pi
0.776298 + 0.630366i 0.217095π0.217095\pi
348348 −259.031 −0.0399009
349349 −999.782 −0.153344 −0.0766721 0.997056i 0.524429π-0.524429\pi
−0.0766721 + 0.997056i 0.524429π0.524429\pi
350350 0 0
351351 −2255.86 −0.343045
352352 176.033 0.0266551
353353 6654.40 1.00334 0.501669 0.865060i 0.332720π-0.332720\pi
0.501669 + 0.865060i 0.332720π0.332720\pi
354354 −551.599 −0.0828168
355355 0 0
356356 1327.20 0.197588
357357 846.844 0.125545
358358 −9433.70 −1.39270
359359 −10416.8 −1.53142 −0.765709 0.643187i 0.777612π-0.777612\pi
−0.765709 + 0.643187i 0.777612π0.777612\pi
360360 0 0
361361 −6456.65 −0.941339
362362 −3357.35 −0.487454
363363 −858.578 −0.124142
364364 −4041.30 −0.581927
365365 0 0
366366 −1030.67 −0.147196
367367 −1614.50 −0.229636 −0.114818 0.993387i 0.536628π-0.536628\pi
−0.114818 + 0.993387i 0.536628π0.536628\pi
368368 −1346.61 −0.190753
369369 795.747 0.112263
370370 0 0
371371 1679.11 0.234973
372372 521.628 0.0727020
373373 −1308.52 −0.181642 −0.0908209 0.995867i 0.528949π-0.528949\pi
−0.0908209 + 0.995867i 0.528949π0.528949\pi
374374 −891.402 −0.123244
375375 0 0
376376 2719.21 0.372959
377377 −6259.63 −0.855139
378378 −1119.72 −0.152360
379379 5971.07 0.809270 0.404635 0.914478i 0.367399π-0.367399\pi
0.404635 + 0.914478i 0.367399π0.367399\pi
380380 0 0
381381 1554.48 0.209025
382382 −5242.91 −0.702226
383383 8021.89 1.07023 0.535117 0.844778i 0.320268π-0.320268\pi
0.535117 + 0.844778i 0.320268π0.320268\pi
384384 −84.4889 −0.0112280
385385 0 0
386386 −2543.29 −0.335362
387387 6569.43 0.862902
388388 2520.97 0.329853
389389 2599.92 0.338872 0.169436 0.985541i 0.445805π-0.445805\pi
0.169436 + 0.985541i 0.445805π0.445805\pi
390390 0 0
391391 6819.02 0.881976
392392 738.056 0.0950955
393393 1207.00 0.154924
394394 −7328.09 −0.937015
395395 0 0
396396 584.525 0.0741754
397397 −3934.06 −0.497343 −0.248671 0.968588i 0.579994π-0.579994\pi
−0.248671 + 0.968588i 0.579994π0.579994\pi
398398 4556.86 0.573906
399399 −209.656 −0.0263056
400400 0 0
401401 −2617.21 −0.325929 −0.162964 0.986632i 0.552106π-0.552106\pi
−0.162964 + 0.986632i 0.552106π0.552106\pi
402402 852.380 0.105753
403403 12605.4 1.55812
404404 −7362.31 −0.906655
405405 0 0
406406 −3107.04 −0.379802
407407 531.029 0.0646735
408408 427.838 0.0519145
409409 −7160.34 −0.865663 −0.432832 0.901475i 0.642486π-0.642486\pi
−0.432832 + 0.901475i 0.642486π0.642486\pi
410410 0 0
411411 −1759.90 −0.211215
412412 −5119.51 −0.612185
413413 −6616.34 −0.788303
414414 −4471.48 −0.530824
415415 0 0
416416 −2041.72 −0.240634
417417 1096.48 0.128764
418418 220.688 0.0258234
419419 −8203.43 −0.956476 −0.478238 0.878230i 0.658724π-0.658724\pi
−0.478238 + 0.878230i 0.658724π0.658724\pi
420420 0 0
421421 13503.1 1.56318 0.781590 0.623793i 0.214409π-0.214409\pi
0.781590 + 0.623793i 0.214409π0.214409\pi
422422 −10421.2 −1.20213
423423 9029.25 1.03787
424424 848.309 0.0971640
425425 0 0
426426 45.7750 0.00520612
427427 −12362.7 −1.40111
428428 1787.88 0.201917
429429 −231.676 −0.0260732
430430 0 0
431431 −11298.0 −1.26265 −0.631327 0.775517i 0.717489π-0.717489\pi
−0.631327 + 0.775517i 0.717489π0.717489\pi
432432 −565.699 −0.0630028
433433 494.980 0.0549359 0.0274679 0.999623i 0.491256π-0.491256\pi
0.0274679 + 0.999623i 0.491256π0.491256\pi
434434 6256.85 0.692024
435435 0 0
436436 −1180.08 −0.129623
437437 −1688.21 −0.184801
438438 −1508.62 −0.164577
439439 −9269.10 −1.00772 −0.503861 0.863785i 0.668088π-0.668088\pi
−0.503861 + 0.863785i 0.668088π0.668088\pi
440440 0 0
441441 2450.74 0.264630
442442 10338.9 1.11261
443443 −14313.6 −1.53512 −0.767561 0.640976i 0.778530π-0.778530\pi
−0.767561 + 0.640976i 0.778530π0.778530\pi
444444 −254.873 −0.0272426
445445 0 0
446446 1603.92 0.170287
447447 2181.59 0.230841
448448 −1013.43 −0.106875
449449 −8501.11 −0.893524 −0.446762 0.894653i 0.647423π-0.647423\pi
−0.446762 + 0.894653i 0.647423π0.647423\pi
450450 0 0
451451 164.786 0.0172051
452452 −777.829 −0.0809425
453453 −658.944 −0.0683442
454454 −5887.09 −0.608579
455455 0 0
456456 −105.921 −0.0108777
457457 −16042.6 −1.64211 −0.821053 0.570852i 0.806613π-0.806613\pi
−0.821053 + 0.570852i 0.806613π0.806613\pi
458458 −10861.1 −1.10809
459459 2864.60 0.291303
460460 0 0
461461 −2936.38 −0.296662 −0.148331 0.988938i 0.547390π-0.547390\pi
−0.148331 + 0.988938i 0.547390π0.547390\pi
462462 −114.995 −0.0115802
463463 8714.07 0.874681 0.437340 0.899296i 0.355921π-0.355921\pi
0.437340 + 0.899296i 0.355921π0.355921\pi
464464 −1569.72 −0.157053
465465 0 0
466466 −4712.30 −0.468440
467467 10347.5 1.02532 0.512662 0.858591i 0.328660π-0.328660\pi
0.512662 + 0.858591i 0.328660π0.328660\pi
468468 −6779.61 −0.669632
469469 10224.2 1.00663
470470 0 0
471471 41.0317 0.00401410
472472 −3342.67 −0.325972
473473 1360.42 0.132246
474474 −1370.79 −0.132832
475475 0 0
476476 5131.85 0.494155
477477 2816.84 0.270386
478478 −10306.1 −0.986169
479479 −2017.43 −0.192440 −0.0962200 0.995360i 0.530675π-0.530675\pi
−0.0962200 + 0.995360i 0.530675π0.530675\pi
480480 0 0
481481 −6159.14 −0.583851
482482 6149.08 0.581085
483483 879.685 0.0828717
484484 −5202.95 −0.488632
485485 0 0
486486 −2825.28 −0.263698
487487 5149.95 0.479192 0.239596 0.970873i 0.422985π-0.422985\pi
0.239596 + 0.970873i 0.422985π0.422985\pi
488488 −6245.82 −0.579375
489489 64.1520 0.00593263
490490 0 0
491491 −9008.67 −0.828015 −0.414008 0.910273i 0.635871π-0.635871\pi
−0.414008 + 0.910273i 0.635871π0.635871\pi
492492 −79.0908 −0.00724734
493493 7948.80 0.726158
494494 −2559.65 −0.233126
495495 0 0
496496 3161.05 0.286160
497497 549.064 0.0495551
498498 −603.530 −0.0543069
499499 6847.91 0.614337 0.307169 0.951655i 0.400618π-0.400618\pi
0.307169 + 0.951655i 0.400618π0.400618\pi
500500 0 0
501501 −2714.24 −0.242043
502502 −6190.96 −0.550430
503503 −17526.3 −1.55360 −0.776798 0.629750i 0.783157π-0.783157\pi
−0.776798 + 0.629750i 0.783157π0.783157\pi
504504 −3365.14 −0.297411
505505 0 0
506506 −925.971 −0.0813526
507507 1236.92 0.108350
508508 9420.12 0.822737
509509 −10921.0 −0.951015 −0.475508 0.879712i 0.657736π-0.657736\pi
−0.475508 + 0.879712i 0.657736π0.657736\pi
510510 0 0
511511 −18095.7 −1.56655
512512 −512.000 −0.0441942
513513 −709.201 −0.0610370
514514 −9118.78 −0.782514
515515 0 0
516516 −652.949 −0.0557064
517517 1869.81 0.159060
518518 −3057.16 −0.259312
519519 524.553 0.0443648
520520 0 0
521521 21731.3 1.82738 0.913689 0.406415i 0.133221π-0.133221\pi
0.913689 + 0.406415i 0.133221π0.133221\pi
522522 −5212.32 −0.437044
523523 21974.2 1.83722 0.918610 0.395166i 0.129313π-0.129313\pi
0.918610 + 0.395166i 0.129313π0.129313\pi
524524 7314.38 0.609790
525525 0 0
526526 −8479.05 −0.702860
527527 −16007.0 −1.32311
528528 −58.0971 −0.00478854
529529 −5083.54 −0.417813
530530 0 0
531531 −11099.5 −0.907111
532532 −1270.51 −0.103541
533533 −1911.27 −0.155322
534534 −438.022 −0.0354964
535535 0 0
536536 5165.39 0.416252
537537 3113.45 0.250196
538538 1225.48 0.0982048
539539 507.509 0.0405565
540540 0 0
541541 −5318.63 −0.422672 −0.211336 0.977413i 0.567781π-0.567781\pi
−0.211336 + 0.977413i 0.567781π0.567781\pi
542542 15165.8 1.20190
543543 1108.04 0.0875703
544544 2592.68 0.204339
545545 0 0
546546 1333.77 0.104542
547547 13549.1 1.05908 0.529542 0.848284i 0.322364π-0.322364\pi
0.529542 + 0.848284i 0.322364π0.322364\pi
548548 −10664.9 −0.831355
549549 −20739.5 −1.61228
550550 0 0
551551 −1967.91 −0.152152
552552 444.429 0.0342684
553553 −16442.4 −1.26438
554554 −5403.29 −0.414375
555555 0 0
556556 6644.60 0.506823
557557 −10078.9 −0.766707 −0.383354 0.923602i 0.625231π-0.625231\pi
−0.383354 + 0.923602i 0.625231π0.625231\pi
558558 10496.4 0.796321
559559 −15778.9 −1.19387
560560 0 0
561561 294.194 0.0221406
562562 11785.5 0.884594
563563 12267.1 0.918287 0.459143 0.888362i 0.348156π-0.348156\pi
0.459143 + 0.888362i 0.348156π0.348156\pi
564564 −897.435 −0.0670015
565565 0 0
566566 5991.87 0.444977
567567 −10987.8 −0.813834
568568 277.395 0.0204916
569569 −20017.6 −1.47484 −0.737419 0.675436i 0.763956π-0.763956\pi
−0.737419 + 0.675436i 0.763956π0.763956\pi
570570 0 0
571571 19167.6 1.40479 0.702397 0.711785i 0.252113π-0.252113\pi
0.702397 + 0.711785i 0.252113π0.252113\pi
572572 −1403.95 −0.102626
573573 1730.34 0.126154
574574 −948.682 −0.0689847
575575 0 0
576576 −1700.12 −0.122983
577577 −22491.1 −1.62273 −0.811365 0.584540i 0.801275π-0.801275\pi
−0.811365 + 0.584540i 0.801275π0.801275\pi
578578 −3302.90 −0.237686
579579 839.373 0.0602473
580580 0 0
581581 −7239.25 −0.516927
582582 −832.008 −0.0592575
583583 583.322 0.0414387
584584 −9142.19 −0.647785
585585 0 0
586586 −8062.31 −0.568346
587587 9659.60 0.679207 0.339604 0.940569i 0.389707π-0.389707\pi
0.339604 + 0.940569i 0.389707π0.389707\pi
588588 −243.584 −0.0170837
589589 3962.92 0.277231
590590 0 0
591591 2418.53 0.168333
592592 −1544.52 −0.107229
593593 −5572.36 −0.385884 −0.192942 0.981210i 0.561803π-0.561803\pi
−0.192942 + 0.981210i 0.561803π0.561803\pi
594594 −388.991 −0.0268695
595595 0 0
596596 13220.4 0.908603
597597 −1503.92 −0.103101
598598 10739.9 0.734425
599599 −7911.99 −0.539692 −0.269846 0.962904i 0.586973π-0.586973\pi
−0.269846 + 0.962904i 0.586973π0.586973\pi
600600 0 0
601601 19247.9 1.30638 0.653192 0.757192i 0.273429π-0.273429\pi
0.653192 + 0.757192i 0.273429π0.273429\pi
602602 −7832.02 −0.530248
603603 17151.9 1.15834
604604 −3993.18 −0.269007
605605 0 0
606606 2429.82 0.162879
607607 −5839.82 −0.390496 −0.195248 0.980754i 0.562551π-0.562551\pi
−0.195248 + 0.980754i 0.562551π0.562551\pi
608608 −641.880 −0.0428153
609609 1025.43 0.0682308
610610 0 0
611611 −21687.0 −1.43595
612612 8609.10 0.568631
613613 12124.1 0.798835 0.399418 0.916769i 0.369212π-0.369212\pi
0.399418 + 0.916769i 0.369212π0.369212\pi
614614 7414.23 0.487319
615615 0 0
616616 −696.865 −0.0455804
617617 11825.0 0.771565 0.385783 0.922590i 0.373932π-0.373932\pi
0.385783 + 0.922590i 0.373932π0.373932\pi
618618 1689.62 0.109978
619619 −14009.0 −0.909645 −0.454822 0.890582i 0.650297π-0.650297\pi
−0.454822 + 0.890582i 0.650297π0.650297\pi
620620 0 0
621621 2975.69 0.192287
622622 28.1446 0.00181430
623623 −5254.01 −0.337877
624624 673.839 0.0432294
625625 0 0
626626 −1730.33 −0.110476
627627 −72.8347 −0.00463913
628628 248.651 0.0157998
629629 7821.19 0.495789
630630 0 0
631631 2071.70 0.130702 0.0653510 0.997862i 0.479183π-0.479183\pi
0.0653510 + 0.997862i 0.479183π0.479183\pi
632632 −8306.96 −0.522837
633633 3439.37 0.215960
634634 14708.8 0.921390
635635 0 0
636636 −279.971 −0.0174553
637637 −5886.34 −0.366131
638638 −1079.39 −0.0669801
639639 921.101 0.0570237
640640 0 0
641641 −875.590 −0.0539528 −0.0269764 0.999636i 0.508588π-0.508588\pi
−0.0269764 + 0.999636i 0.508588π0.508588\pi
642642 −590.064 −0.0362741
643643 −7757.55 −0.475782 −0.237891 0.971292i 0.576456π-0.576456\pi
−0.237891 + 0.971292i 0.576456π0.576456\pi
644644 5330.86 0.326188
645645 0 0
646646 3250.37 0.197963
647647 −22628.2 −1.37497 −0.687485 0.726198i 0.741285π-0.741285\pi
−0.687485 + 0.726198i 0.741285π0.741285\pi
648648 −5551.19 −0.336530
649649 −2298.52 −0.139021
650650 0 0
651651 −2064.98 −0.124321
652652 388.759 0.0233512
653653 6584.08 0.394571 0.197286 0.980346i 0.436787π-0.436787\pi
0.197286 + 0.980346i 0.436787π0.436787\pi
654654 389.469 0.0232866
655655 0 0
656656 −479.288 −0.0285260
657657 −30357.0 −1.80265
658658 −10764.6 −0.637762
659659 215.219 0.0127219 0.00636094 0.999980i 0.497975π-0.497975\pi
0.00636094 + 0.999980i 0.497975π0.497975\pi
660660 0 0
661661 26476.8 1.55799 0.778994 0.627032i 0.215730π-0.215730\pi
0.778994 + 0.627032i 0.215730π0.215730\pi
662662 −20104.4 −1.18033
663663 −3412.21 −0.199878
664664 −3657.37 −0.213755
665665 0 0
666666 −5128.64 −0.298394
667667 8257.05 0.479332
668668 −16448.2 −0.952696
669669 −529.351 −0.0305918
670670 0 0
671671 −4294.81 −0.247093
672672 334.468 0.0192000
673673 −13606.4 −0.779327 −0.389663 0.920957i 0.627409π-0.627409\pi
−0.389663 + 0.920957i 0.627409π0.627409\pi
674674 −17819.1 −1.01835
675675 0 0
676676 7495.69 0.426473
677677 −17729.5 −1.00650 −0.503251 0.864140i 0.667863π-0.667863\pi
−0.503251 + 0.864140i 0.667863π0.667863\pi
678678 256.711 0.0145412
679679 −9979.81 −0.564050
680680 0 0
681681 1942.94 0.109330
682682 2173.63 0.122042
683683 −17693.6 −0.991256 −0.495628 0.868535i 0.665062π-0.665062\pi
−0.495628 + 0.868535i 0.665062π0.665062\pi
684684 −2131.39 −0.119146
685685 0 0
686686 −13784.5 −0.767192
687687 3584.55 0.199067
688688 −3956.85 −0.219264
689689 −6765.66 −0.374095
690690 0 0
691691 21596.3 1.18895 0.594473 0.804116i 0.297361π-0.297361\pi
0.594473 + 0.804116i 0.297361π0.297361\pi
692692 3178.78 0.174623
693693 −2313.97 −0.126840
694694 −20071.6 −1.09785
695695 0 0
696696 518.062 0.0282142
697697 2427.03 0.131894
698698 1999.56 0.108431
699699 1555.22 0.0841544
700700 0 0
701701 −13380.6 −0.720939 −0.360469 0.932771i 0.617384π-0.617384\pi
−0.360469 + 0.932771i 0.617384π0.617384\pi
702702 4511.72 0.242569
703703 −1936.32 −0.103883
704704 −352.066 −0.0188480
705705 0 0
706706 −13308.8 −0.709467
707707 29145.3 1.55039
708708 1103.20 0.0585603
709709 17755.9 0.940530 0.470265 0.882525i 0.344158π-0.344158\pi
0.470265 + 0.882525i 0.344158π0.344158\pi
710710 0 0
711711 −27583.6 −1.45494
712712 −2654.40 −0.139716
713713 −16627.8 −0.873373
714714 −1693.69 −0.0887741
715715 0 0
716716 18867.4 0.984787
717717 3401.36 0.177164
718718 20833.7 1.08288
719719 5858.00 0.303848 0.151924 0.988392i 0.451453π-0.451453\pi
0.151924 + 0.988392i 0.451453π0.451453\pi
720720 0 0
721721 20266.7 1.04684
722722 12913.3 0.665627
723723 −2029.41 −0.104391
724724 6714.70 0.344682
725725 0 0
726726 1717.16 0.0877819
727727 2258.37 0.115211 0.0576056 0.998339i 0.481653π-0.481653\pi
0.0576056 + 0.998339i 0.481653π0.481653\pi
728728 8082.60 0.411485
729729 −17802.8 −0.904477
730730 0 0
731731 20036.8 1.01380
732732 2061.34 0.104084
733733 21005.7 1.05847 0.529237 0.848474i 0.322478π-0.322478\pi
0.529237 + 0.848474i 0.322478π0.322478\pi
734734 3229.01 0.162377
735735 0 0
736736 2693.23 0.134883
737737 3551.87 0.177524
738738 −1591.49 −0.0793817
739739 −30135.7 −1.50008 −0.750040 0.661393i 0.769966π-0.769966\pi
−0.750040 + 0.661393i 0.769966π0.769966\pi
740740 0 0
741741 844.773 0.0418806
742742 −3358.21 −0.166151
743743 −11814.8 −0.583367 −0.291683 0.956515i 0.594215π-0.594215\pi
−0.291683 + 0.956515i 0.594215π0.594215\pi
744744 −1043.26 −0.0514081
745745 0 0
746746 2617.03 0.128440
747747 −12144.4 −0.594835
748748 1782.80 0.0871467
749749 −7077.73 −0.345280
750750 0 0
751751 22130.5 1.07530 0.537651 0.843168i 0.319312π-0.319312\pi
0.537651 + 0.843168i 0.319312π0.319312\pi
752752 −5438.43 −0.263722
753753 2043.23 0.0988839
754754 12519.3 0.604674
755755 0 0
756756 2239.44 0.107735
757757 8303.35 0.398666 0.199333 0.979932i 0.436122π-0.436122\pi
0.199333 + 0.979932i 0.436122π0.436122\pi
758758 −11942.1 −0.572241
759759 305.603 0.0146149
760760 0 0
761761 8025.03 0.382270 0.191135 0.981564i 0.438783π-0.438783\pi
0.191135 + 0.981564i 0.438783π0.438783\pi
762762 −3108.97 −0.147803
763763 4671.62 0.221657
764764 10485.8 0.496549
765765 0 0
766766 −16043.8 −0.756769
767767 26659.4 1.25504
768768 168.978 0.00793941
769769 −5180.39 −0.242925 −0.121463 0.992596i 0.538758π-0.538758\pi
−0.121463 + 0.992596i 0.538758π0.538758\pi
770770 0 0
771771 3009.52 0.140577
772772 5086.57 0.237137
773773 −26023.3 −1.21086 −0.605430 0.795899i 0.706999π-0.706999\pi
−0.605430 + 0.795899i 0.706999π0.706999\pi
774774 −13138.9 −0.610164
775775 0 0
776776 −5041.94 −0.233241
777777 1008.97 0.0465850
778778 −5199.84 −0.239619
779779 −600.870 −0.0276359
780780 0 0
781781 190.745 0.00873930
782782 −13638.0 −0.623651
783783 3468.71 0.158316
784784 −1476.11 −0.0672427
785785 0 0
786786 −2414.00 −0.109548
787787 20158.3 0.913044 0.456522 0.889712i 0.349095π-0.349095\pi
0.456522 + 0.889712i 0.349095π0.349095\pi
788788 14656.2 0.662570
789789 2798.38 0.126268
790790 0 0
791791 3079.21 0.138412
792792 −1169.05 −0.0524500
793793 49813.3 2.23067
794794 7868.13 0.351674
795795 0 0
796796 −9113.72 −0.405813
797797 1492.92 0.0663511 0.0331755 0.999450i 0.489438π-0.489438\pi
0.0331755 + 0.999450i 0.489438π0.489438\pi
798798 419.313 0.0186009
799799 27539.3 1.21936
800800 0 0
801801 −8814.04 −0.388800
802802 5234.43 0.230466
803803 −6286.44 −0.276269
804804 −1704.76 −0.0747789
805805 0 0
806806 −25210.9 −1.10176
807807 −404.451 −0.0176423
808808 14724.6 0.641102
809809 −32899.3 −1.42976 −0.714881 0.699246i 0.753519π-0.753519\pi
−0.714881 + 0.699246i 0.753519π0.753519\pi
810810 0 0
811811 13832.3 0.598914 0.299457 0.954110i 0.403194π-0.403194\pi
0.299457 + 0.954110i 0.403194π0.403194\pi
812812 6214.08 0.268561
813813 −5005.25 −0.215918
814814 −1062.06 −0.0457311
815815 0 0
816816 −855.675 −0.0367091
817817 −4960.59 −0.212422
818818 14320.7 0.612116
819819 26838.6 1.14507
820820 0 0
821821 −34809.0 −1.47971 −0.739855 0.672766i 0.765106π-0.765106\pi
−0.739855 + 0.672766i 0.765106π0.765106\pi
822822 3519.79 0.149351
823823 28468.8 1.20579 0.602893 0.797822i 0.294015π-0.294015\pi
0.602893 + 0.797822i 0.294015π0.294015\pi
824824 10239.0 0.432880
825825 0 0
826826 13232.7 0.557414
827827 26950.0 1.13319 0.566593 0.823998i 0.308261π-0.308261\pi
0.566593 + 0.823998i 0.308261π0.308261\pi
828828 8942.96 0.375349
829829 775.483 0.0324893 0.0162446 0.999868i 0.494829π-0.494829\pi
0.0162446 + 0.999868i 0.494829π0.494829\pi
830830 0 0
831831 1783.28 0.0744418
832832 4083.44 0.170154
833833 7474.78 0.310907
834834 −2192.95 −0.0910499
835835 0 0
836836 −441.376 −0.0182599
837837 −6985.16 −0.288462
838838 16406.9 0.676331
839839 37781.8 1.55468 0.777338 0.629084i 0.216570π-0.216570\pi
0.777338 + 0.629084i 0.216570π0.216570\pi
840840 0 0
841841 −14763.9 −0.605352
842842 −27006.1 −1.10533
843843 −3889.63 −0.158916
844844 20842.5 0.850032
845845 0 0
846846 −18058.5 −0.733882
847847 20597.0 0.835563
848848 −1696.62 −0.0687053
849849 −1977.53 −0.0799393
850850 0 0
851851 8124.49 0.327267
852852 −91.5500 −0.00368128
853853 −10089.8 −0.405005 −0.202503 0.979282i 0.564907π-0.564907\pi
−0.202503 + 0.979282i 0.564907π0.564907\pi
854854 24725.4 0.990733
855855 0 0
856856 −3575.77 −0.142777
857857 29927.3 1.19288 0.596440 0.802658i 0.296581π-0.296581\pi
0.596440 + 0.802658i 0.296581π0.296581\pi
858858 463.352 0.0184366
859859 −8506.89 −0.337894 −0.168947 0.985625i 0.554037π-0.554037\pi
−0.168947 + 0.985625i 0.554037π0.554037\pi
860860 0 0
861861 313.098 0.0123930
862862 22595.9 0.892831
863863 −16995.9 −0.670392 −0.335196 0.942148i 0.608803π-0.608803\pi
−0.335196 + 0.942148i 0.608803π0.608803\pi
864864 1131.40 0.0445497
865865 0 0
866866 −989.960 −0.0388455
867867 1090.07 0.0426998
868868 −12513.7 −0.489335
869869 −5712.11 −0.222980
870870 0 0
871871 −41196.4 −1.60263
872872 2360.17 0.0916575
873873 −16742.0 −0.649060
874874 3376.42 0.130674
875875 0 0
876876 3017.24 0.116373
877877 30356.9 1.16885 0.584424 0.811448i 0.301320π-0.301320\pi
0.584424 + 0.811448i 0.301320π0.301320\pi
878878 18538.2 0.712567
879879 2660.84 0.102102
880880 0 0
881881 −42101.5 −1.61003 −0.805015 0.593255i 0.797843π-0.797843\pi
−0.805015 + 0.593255i 0.797843π0.797843\pi
882882 −4901.49 −0.187122
883883 −39597.1 −1.50912 −0.754558 0.656234i 0.772148π-0.772148\pi
−0.754558 + 0.656234i 0.772148π0.772148\pi
884884 −20677.9 −0.786733
885885 0 0
886886 28627.2 1.08550
887887 −4172.22 −0.157936 −0.0789680 0.996877i 0.525163π-0.525163\pi
−0.0789680 + 0.996877i 0.525163π0.525163\pi
888888 509.745 0.0192634
889889 −37291.6 −1.40688
890890 0 0
891891 −3817.16 −0.143524
892892 −3207.85 −0.120411
893893 −6818.00 −0.255494
894894 −4363.18 −0.163229
895895 0 0
896896 2026.86 0.0755723
897897 −3544.53 −0.131938
898898 17002.2 0.631817
899899 −19382.7 −0.719074
900900 0 0
901901 8591.38 0.317670
902902 −329.572 −0.0121658
903903 2584.84 0.0952581
904904 1555.66 0.0572350
905905 0 0
906906 1317.89 0.0483266
907907 6248.25 0.228743 0.114371 0.993438i 0.463515π-0.463515\pi
0.114371 + 0.993438i 0.463515π0.463515\pi
908908 11774.2 0.430330
909909 48893.7 1.78405
910910 0 0
911911 5191.71 0.188813 0.0944066 0.995534i 0.469905π-0.469905\pi
0.0944066 + 0.995534i 0.469905π0.469905\pi
912912 211.843 0.00769169
913913 −2514.92 −0.0911627
914914 32085.2 1.16114
915915 0 0
916916 21722.3 0.783541
917917 −28955.6 −1.04274
918918 −5729.21 −0.205983
919919 2826.18 0.101444 0.0507221 0.998713i 0.483848π-0.483848\pi
0.0507221 + 0.998713i 0.483848π0.483848\pi
920920 0 0
921921 −2446.95 −0.0875460
922922 5872.77 0.209771
923923 −2212.36 −0.0788955
924924 229.990 0.00818843
925925 0 0
926926 −17428.1 −0.618493
927927 33999.1 1.20461
928928 3139.44 0.111053
929929 −12961.0 −0.457735 −0.228868 0.973458i 0.573502π-0.573502\pi
−0.228868 + 0.973458i 0.573502π0.573502\pi
930930 0 0
931931 −1850.56 −0.0651446
932932 9424.60 0.331237
933933 −9.28871 −0.000325937 0
934934 −20695.0 −0.725013
935935 0 0
936936 13559.2 0.473501
937937 −34128.2 −1.18988 −0.594941 0.803769i 0.702825π-0.702825\pi
−0.594941 + 0.803769i 0.702825π0.702825\pi
938938 −20448.3 −0.711792
939939 571.069 0.0198468
940940 0 0
941941 −41298.5 −1.43071 −0.715353 0.698763i 0.753734π-0.753734\pi
−0.715353 + 0.698763i 0.753734π0.753734\pi
942942 −82.0635 −0.00283840
943943 2521.15 0.0870626
944944 6685.34 0.230497
945945 0 0
946946 −2720.85 −0.0935120
947947 21393.9 0.734116 0.367058 0.930198i 0.380365π-0.380365\pi
0.367058 + 0.930198i 0.380365π0.380365\pi
948948 2741.59 0.0939267
949949 72913.3 2.49406
950950 0 0
951951 −4854.42 −0.165526
952952 −10263.7 −0.349420
953953 24381.0 0.828728 0.414364 0.910111i 0.364004π-0.364004\pi
0.414364 + 0.910111i 0.364004π0.364004\pi
954954 −5633.68 −0.191192
955955 0 0
956956 20612.1 0.697327
957957 356.235 0.0120329
958958 4034.86 0.136076
959959 42219.4 1.42162
960960 0 0
961961 9241.14 0.310199
962962 12318.3 0.412845
963963 −11873.5 −0.397318
964964 −12298.2 −0.410889
965965 0 0
966966 −1759.37 −0.0585992
967967 25361.5 0.843402 0.421701 0.906735i 0.361433π-0.361433\pi
0.421701 + 0.906735i 0.361433π0.361433\pi
968968 10405.9 0.345515
969969 −1072.74 −0.0355637
970970 0 0
971971 −40071.3 −1.32436 −0.662178 0.749347i 0.730368π-0.730368\pi
−0.662178 + 0.749347i 0.730368π0.730368\pi
972972 5650.55 0.186463
973973 −26304.1 −0.866671
974974 −10299.9 −0.338840
975975 0 0
976976 12491.6 0.409680
977977 −4847.90 −0.158749 −0.0793746 0.996845i 0.525292π-0.525292\pi
−0.0793746 + 0.996845i 0.525292π0.525292\pi
978978 −128.304 −0.00419500
979979 −1825.24 −0.0595864
980980 0 0
981981 7837.03 0.255063
982982 18017.3 0.585495
983983 −575.902 −0.0186861 −0.00934304 0.999956i 0.502974π-0.502974\pi
−0.00934304 + 0.999956i 0.502974π0.502974\pi
984984 158.182 0.00512464
985985 0 0
986986 −15897.6 −0.513471
987987 3552.69 0.114573
988988 5119.30 0.164845
989989 20813.8 0.669203
990990 0 0
991991 49749.5 1.59470 0.797348 0.603520i 0.206235π-0.206235\pi
0.797348 + 0.603520i 0.206235π0.206235\pi
992992 −6322.10 −0.202346
993993 6635.15 0.212044
994994 −1098.13 −0.0350408
995995 0 0
996996 1207.06 0.0384008
997997 −42066.3 −1.33626 −0.668130 0.744044i 0.732905π-0.732905\pi
−0.668130 + 0.744044i 0.732905π0.732905\pi
998998 −13695.8 −0.434402
999999 3413.02 0.108091
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 1250.4.a.c.1.3 6
5.4 even 2 1250.4.a.f.1.4 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1250.4.a.c.1.3 6 1.1 even 1 trivial
1250.4.a.f.1.4 yes 6 5.4 even 2