Properties

Label 99.4.a.d.1.1
Level 9999
Weight 44
Character 99.1
Self dual yes
Analytic conductor 5.8415.841
Analytic rank 11
Dimension 22
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] = [99,4,Mod(1,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, 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("99.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 99=3211 99 = 3^{2} \cdot 11
Weight: k k == 4 4
Character orbit: [χ][\chi] == 99.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: 5.841189090575.84118909057
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ12)+\Q(\zeta_{12})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x23 x^{2} - 3 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.73205-1.73205 of defining polynomial
Character χ\chi == 99.1

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) == q4.46410q2+11.9282q46.53590q5+9.32051q717.5359q8+29.1769q10+11.0000q11+1.89488q1341.6077q1417.1436q1661.2154q17121.923q1977.9615q2049.1051q22117.177q2382.2820q258.45895q26+111.177q28+139.990q29314.067q31+216.818q32+273.272q3460.9179q35+88.6410q37+544.277q38+114.613q4092.1436q41+396.697q43+131.210q44+523.090q46+82.7461q47256.128q49+367.315q50+22.6025q52581.787q5371.8949q55163.443q56624.928q58697.338q59+184.095q61+1402.03q62830.749q6412.3848q65219.405q67730.190q68+271.944q70+886.628q71+338.708q73395.703q741454.32q76+102.526q77+208.536q79+112.049q80+411.338q82463.923q83+400.098q851770.90q86192.895q881137.68q89+17.6613q911397.71q92369.387q94+796.877q95+1522.49q97+1143.38q98+O(q100)q-4.46410 q^{2} +11.9282 q^{4} -6.53590 q^{5} +9.32051 q^{7} -17.5359 q^{8} +29.1769 q^{10} +11.0000 q^{11} +1.89488 q^{13} -41.6077 q^{14} -17.1436 q^{16} -61.2154 q^{17} -121.923 q^{19} -77.9615 q^{20} -49.1051 q^{22} -117.177 q^{23} -82.2820 q^{25} -8.45895 q^{26} +111.177 q^{28} +139.990 q^{29} -314.067 q^{31} +216.818 q^{32} +273.272 q^{34} -60.9179 q^{35} +88.6410 q^{37} +544.277 q^{38} +114.613 q^{40} -92.1436 q^{41} +396.697 q^{43} +131.210 q^{44} +523.090 q^{46} +82.7461 q^{47} -256.128 q^{49} +367.315 q^{50} +22.6025 q^{52} -581.787 q^{53} -71.8949 q^{55} -163.443 q^{56} -624.928 q^{58} -697.338 q^{59} +184.095 q^{61} +1402.03 q^{62} -830.749 q^{64} -12.3848 q^{65} -219.405 q^{67} -730.190 q^{68} +271.944 q^{70} +886.628 q^{71} +338.708 q^{73} -395.703 q^{74} -1454.32 q^{76} +102.526 q^{77} +208.536 q^{79} +112.049 q^{80} +411.338 q^{82} -463.923 q^{83} +400.098 q^{85} -1770.90 q^{86} -192.895 q^{88} -1137.68 q^{89} +17.6613 q^{91} -1397.71 q^{92} -369.387 q^{94} +796.877 q^{95} +1522.49 q^{97} +1143.38 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q2+10q420q516q742q84q10+22q11+80q13104q1462q16164q1736q1952q2022q22172q2326q25+184q26++1878q98+O(q100) 2 q - 2 q^{2} + 10 q^{4} - 20 q^{5} - 16 q^{7} - 42 q^{8} - 4 q^{10} + 22 q^{11} + 80 q^{13} - 104 q^{14} - 62 q^{16} - 164 q^{17} - 36 q^{19} - 52 q^{20} - 22 q^{22} - 172 q^{23} - 26 q^{25} + 184 q^{26}+ \cdots + 1878 q^{98}+O(q^{100}) Copy content Toggle raw display

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −4.46410 −1.57830 −0.789149 0.614202i 0.789478π-0.789478\pi
−0.789149 + 0.614202i 0.789478π0.789478\pi
33 0 0
44 11.9282 1.49103
55 −6.53590 −0.584589 −0.292294 0.956328i 0.594419π-0.594419\pi
−0.292294 + 0.956328i 0.594419π0.594419\pi
66 0 0
77 9.32051 0.503260 0.251630 0.967823i 0.419033π-0.419033\pi
0.251630 + 0.967823i 0.419033π0.419033\pi
88 −17.5359 −0.774985
99 0 0
1010 29.1769 0.922655
1111 11.0000 0.301511
1212 0 0
1313 1.89488 0.0404266 0.0202133 0.999796i 0.493565π-0.493565\pi
0.0202133 + 0.999796i 0.493565π0.493565\pi
1414 −41.6077 −0.794295
1515 0 0
1616 −17.1436 −0.267869
1717 −61.2154 −0.873348 −0.436674 0.899620i 0.643844π-0.643844\pi
−0.436674 + 0.899620i 0.643844π0.643844\pi
1818 0 0
1919 −121.923 −1.47216 −0.736081 0.676894i 0.763326π-0.763326\pi
−0.736081 + 0.676894i 0.763326π0.763326\pi
2020 −77.9615 −0.871636
2121 0 0
2222 −49.1051 −0.475875
2323 −117.177 −1.06231 −0.531154 0.847275i 0.678241π-0.678241\pi
−0.531154 + 0.847275i 0.678241π0.678241\pi
2424 0 0
2525 −82.2820 −0.658256
2626 −8.45895 −0.0638052
2727 0 0
2828 111.177 0.750374
2929 139.990 0.896394 0.448197 0.893935i 0.352066π-0.352066\pi
0.448197 + 0.893935i 0.352066π0.352066\pi
3030 0 0
3131 −314.067 −1.81961 −0.909807 0.415032i 0.863771π-0.863771\pi
−0.909807 + 0.415032i 0.863771π0.863771\pi
3232 216.818 1.19776
3333 0 0
3434 273.272 1.37840
3535 −60.9179 −0.294200
3636 0 0
3737 88.6410 0.393851 0.196926 0.980418i 0.436904π-0.436904\pi
0.196926 + 0.980418i 0.436904π0.436904\pi
3838 544.277 2.32351
3939 0 0
4040 114.613 0.453047
4141 −92.1436 −0.350986 −0.175493 0.984481i 0.556152π-0.556152\pi
−0.175493 + 0.984481i 0.556152π0.556152\pi
4242 0 0
4343 396.697 1.40688 0.703439 0.710755i 0.251647π-0.251647\pi
0.703439 + 0.710755i 0.251647π0.251647\pi
4444 131.210 0.449561
4545 0 0
4646 523.090 1.67664
4747 82.7461 0.256803 0.128402 0.991722i 0.459015π-0.459015\pi
0.128402 + 0.991722i 0.459015π0.459015\pi
4848 0 0
4949 −256.128 −0.746729
5050 367.315 1.03892
5151 0 0
5252 22.6025 0.0602771
5353 −581.787 −1.50782 −0.753911 0.656976i 0.771835π-0.771835\pi
−0.753911 + 0.656976i 0.771835π0.771835\pi
5454 0 0
5555 −71.8949 −0.176260
5656 −163.443 −0.390019
5757 0 0
5858 −624.928 −1.41478
5959 −697.338 −1.53874 −0.769371 0.638803i 0.779430π-0.779430\pi
−0.769371 + 0.638803i 0.779430π0.779430\pi
6060 0 0
6161 184.095 0.386409 0.193204 0.981159i 0.438112π-0.438112\pi
0.193204 + 0.981159i 0.438112π0.438112\pi
6262 1402.03 2.87189
6363 0 0
6464 −830.749 −1.62256
6565 −12.3848 −0.0236329
6666 0 0
6767 −219.405 −0.400068 −0.200034 0.979789i 0.564105π-0.564105\pi
−0.200034 + 0.979789i 0.564105π0.564105\pi
6868 −730.190 −1.30218
6969 0 0
7070 271.944 0.464336
7171 886.628 1.48202 0.741010 0.671494i 0.234347π-0.234347\pi
0.741010 + 0.671494i 0.234347π0.234347\pi
7272 0 0
7373 338.708 0.543051 0.271526 0.962431i 0.412472π-0.412472\pi
0.271526 + 0.962431i 0.412472π0.412472\pi
7474 −395.703 −0.621615
7575 0 0
7676 −1454.32 −2.19503
7777 102.526 0.151739
7878 0 0
7979 208.536 0.296989 0.148494 0.988913i 0.452557π-0.452557\pi
0.148494 + 0.988913i 0.452557π0.452557\pi
8080 112.049 0.156593
8181 0 0
8282 411.338 0.553960
8383 −463.923 −0.613520 −0.306760 0.951787i 0.599245π-0.599245\pi
−0.306760 + 0.951787i 0.599245π0.599245\pi
8484 0 0
8585 400.098 0.510549
8686 −1770.90 −2.22047
8787 0 0
8888 −192.895 −0.233667
8989 −1137.68 −1.35499 −0.677495 0.735528i 0.736934π-0.736934\pi
−0.677495 + 0.735528i 0.736934π0.736934\pi
9090 0 0
9191 17.6613 0.0203451
9292 −1397.71 −1.58393
9393 0 0
9494 −369.387 −0.405313
9595 796.877 0.860609
9696 0 0
9797 1522.49 1.59367 0.796833 0.604199i 0.206507π-0.206507\pi
0.796833 + 0.604199i 0.206507π0.206507\pi
9898 1143.38 1.17856
9999 0 0
100100 −981.477 −0.981477
101101 −1819.34 −1.79239 −0.896193 0.443665i 0.853678π-0.853678\pi
−0.896193 + 0.443665i 0.853678π0.853678\pi
102102 0 0
103103 1142.24 1.09270 0.546349 0.837558i 0.316017π-0.316017\pi
0.546349 + 0.837558i 0.316017π0.316017\pi
104104 −33.2285 −0.0313300
105105 0 0
106106 2597.16 2.37979
107107 1056.59 0.954625 0.477313 0.878734i 0.341611π-0.341611\pi
0.477313 + 0.878734i 0.341611π0.341611\pi
108108 0 0
109109 −1382.68 −1.21502 −0.607508 0.794314i 0.707831π-0.707831\pi
−0.607508 + 0.794314i 0.707831π0.707831\pi
110110 320.946 0.278191
111111 0 0
112112 −159.787 −0.134808
113113 263.405 0.219284 0.109642 0.993971i 0.465030π-0.465030\pi
0.109642 + 0.993971i 0.465030π0.465030\pi
114114 0 0
115115 765.856 0.621013
116116 1669.83 1.33655
117117 0 0
118118 3112.99 2.42859
119119 −570.559 −0.439521
120120 0 0
121121 121.000 0.0909091
122122 −821.818 −0.609868
123123 0 0
124124 −3746.25 −2.71309
125125 1354.77 0.969398
126126 0 0
127127 −1217.68 −0.850800 −0.425400 0.905006i 0.639867π-0.639867\pi
−0.425400 + 0.905006i 0.639867π0.639867\pi
128128 1974.00 1.36312
129129 0 0
130130 55.2868 0.0372998
131131 925.626 0.617346 0.308673 0.951168i 0.400115π-0.400115\pi
0.308673 + 0.951168i 0.400115π0.400115\pi
132132 0 0
133133 −1136.38 −0.740880
134134 979.446 0.631427
135135 0 0
136136 1073.47 0.676831
137137 1116.32 0.696160 0.348080 0.937465i 0.386834π-0.386834\pi
0.348080 + 0.937465i 0.386834π0.386834\pi
138138 0 0
139139 −576.846 −0.351996 −0.175998 0.984391i 0.556315π-0.556315\pi
−0.175998 + 0.984391i 0.556315π0.556315\pi
140140 −726.641 −0.438660
141141 0 0
142142 −3958.00 −2.33907
143143 20.8437 0.0121891
144144 0 0
145145 −914.958 −0.524022
146146 −1512.03 −0.857097
147147 0 0
148148 1057.33 0.587242
149149 −1630.36 −0.896404 −0.448202 0.893932i 0.647935π-0.647935\pi
−0.448202 + 0.893932i 0.647935π0.647935\pi
150150 0 0
151151 1348.67 0.726842 0.363421 0.931625i 0.381609π-0.381609\pi
0.363421 + 0.931625i 0.381609π0.381609\pi
152152 2138.03 1.14090
153153 0 0
154154 −457.685 −0.239489
155155 2052.71 1.06373
156156 0 0
157157 −1357.54 −0.690088 −0.345044 0.938587i 0.612136π-0.612136\pi
−0.345044 + 0.938587i 0.612136π0.612136\pi
158158 −930.925 −0.468737
159159 0 0
160160 −1417.10 −0.700197
161161 −1092.15 −0.534617
162162 0 0
163163 −817.507 −0.392835 −0.196418 0.980520i 0.562931π-0.562931\pi
−0.196418 + 0.980520i 0.562931π0.562931\pi
164164 −1099.11 −0.523329
165165 0 0
166166 2071.00 0.968318
167167 1665.68 0.771822 0.385911 0.922536i 0.373887π-0.373887\pi
0.385911 + 0.922536i 0.373887π0.373887\pi
168168 0 0
169169 −2193.41 −0.998366
170170 −1786.08 −0.805799
171171 0 0
172172 4731.89 2.09769
173173 731.907 0.321652 0.160826 0.986983i 0.448584π-0.448584\pi
0.160826 + 0.986983i 0.448584π0.448584\pi
174174 0 0
175175 −766.910 −0.331274
176176 −188.580 −0.0807654
177177 0 0
178178 5078.73 2.13858
179179 4272.97 1.78423 0.892114 0.451811i 0.149222π-0.149222\pi
0.892114 + 0.451811i 0.149222π0.149222\pi
180180 0 0
181181 1049.04 0.430797 0.215398 0.976526i 0.430895π-0.430895\pi
0.215398 + 0.976526i 0.430895π0.430895\pi
182182 −78.8417 −0.0321106
183183 0 0
184184 2054.80 0.823272
185185 −579.349 −0.230241
186186 0 0
187187 −673.369 −0.263324
188188 987.013 0.382901
189189 0 0
190190 −3557.34 −1.35830
191191 2369.05 0.897480 0.448740 0.893662i 0.351873π-0.351873\pi
0.448740 + 0.893662i 0.351873π0.351873\pi
192192 0 0
193193 4519.52 1.68561 0.842804 0.538221i 0.180903π-0.180903\pi
0.842804 + 0.538221i 0.180903π0.180903\pi
194194 −6796.56 −2.51528
195195 0 0
196196 −3055.15 −1.11339
197197 −3624.62 −1.31088 −0.655440 0.755247i 0.727517π-0.727517\pi
−0.655440 + 0.755247i 0.727517π0.727517\pi
198198 0 0
199199 −1015.00 −0.361565 −0.180782 0.983523i 0.557863π-0.557863\pi
−0.180782 + 0.983523i 0.557863π0.557863\pi
200200 1442.89 0.510138
201201 0 0
202202 8121.71 2.82892
203203 1304.78 0.451119
204204 0 0
205205 602.241 0.205182
206206 −5099.06 −1.72460
207207 0 0
208208 −32.4851 −0.0108290
209209 −1341.15 −0.443873
210210 0 0
211211 610.912 0.199322 0.0996610 0.995021i 0.468224π-0.468224\pi
0.0996610 + 0.995021i 0.468224π0.468224\pi
212212 −6939.67 −2.24820
213213 0 0
214214 −4716.75 −1.50668
215215 −2592.77 −0.822445
216216 0 0
217217 −2927.26 −0.915739
218218 6172.42 1.91766
219219 0 0
220220 −857.577 −0.262808
221221 −115.996 −0.0353065
222222 0 0
223223 −444.565 −0.133499 −0.0667495 0.997770i 0.521263π-0.521263\pi
−0.0667495 + 0.997770i 0.521263π0.521263\pi
224224 2020.85 0.602785
225225 0 0
226226 −1175.87 −0.346095
227227 −5816.84 −1.70078 −0.850390 0.526152i 0.823634π-0.823634\pi
−0.850390 + 0.526152i 0.823634π0.823634\pi
228228 0 0
229229 −5815.83 −1.67826 −0.839129 0.543933i 0.816935π-0.816935\pi
−0.839129 + 0.543933i 0.816935π0.816935\pi
230230 −3418.86 −0.980144
231231 0 0
232232 −2454.84 −0.694692
233233 2408.26 0.677125 0.338562 0.940944i 0.390059π-0.390059\pi
0.338562 + 0.940944i 0.390059π0.390059\pi
234234 0 0
235235 −540.820 −0.150124
236236 −8317.99 −2.29430
237237 0 0
238238 2547.03 0.693695
239239 6298.09 1.70456 0.852280 0.523086i 0.175220π-0.175220\pi
0.852280 + 0.523086i 0.175220π0.175220\pi
240240 0 0
241241 4040.05 1.07984 0.539922 0.841715i 0.318454π-0.318454\pi
0.539922 + 0.841715i 0.318454π0.318454\pi
242242 −540.156 −0.143482
243243 0 0
244244 2195.92 0.576145
245245 1674.03 0.436529
246246 0 0
247247 −231.030 −0.0595145
248248 5507.44 1.41017
249249 0 0
250250 −6047.85 −1.53000
251251 2394.38 0.602120 0.301060 0.953605i 0.402660π-0.402660\pi
0.301060 + 0.953605i 0.402660π0.402660\pi
252252 0 0
253253 −1288.95 −0.320298
254254 5435.84 1.34282
255255 0 0
256256 −2166.16 −0.528847
257257 2181.73 0.529544 0.264772 0.964311i 0.414703π-0.414703\pi
0.264772 + 0.964311i 0.414703π0.414703\pi
258258 0 0
259259 826.179 0.198210
260260 −147.728 −0.0352373
261261 0 0
262262 −4132.09 −0.974356
263263 3883.01 0.910406 0.455203 0.890388i 0.349567π-0.349567\pi
0.455203 + 0.890388i 0.349567π0.349567\pi
264264 0 0
265265 3802.50 0.881456
266266 5072.94 1.16933
267267 0 0
268268 −2617.11 −0.596512
269269 −3612.57 −0.818818 −0.409409 0.912351i 0.634265π-0.634265\pi
−0.409409 + 0.912351i 0.634265π0.634265\pi
270270 0 0
271271 −716.290 −0.160559 −0.0802795 0.996772i 0.525581π-0.525581\pi
−0.0802795 + 0.996772i 0.525581π0.525581\pi
272272 1049.45 0.233943
273273 0 0
274274 −4983.38 −1.09875
275275 −905.102 −0.198472
276276 0 0
277277 6995.36 1.51737 0.758683 0.651460i 0.225843π-0.225843\pi
0.758683 + 0.651460i 0.225843π0.225843\pi
278278 2575.10 0.555554
279279 0 0
280280 1068.25 0.228001
281281 −8787.00 −1.86544 −0.932720 0.360603i 0.882571π-0.882571\pi
−0.932720 + 0.360603i 0.882571π0.882571\pi
282282 0 0
283283 3572.22 0.750342 0.375171 0.926956i 0.377584π-0.377584\pi
0.375171 + 0.926956i 0.377584π0.377584\pi
284284 10575.9 2.20973
285285 0 0
286286 −93.0484 −0.0192380
287287 −858.825 −0.176637
288288 0 0
289289 −1165.68 −0.237264
290290 4084.47 0.827063
291291 0 0
292292 4040.17 0.809703
293293 −4840.00 −0.965038 −0.482519 0.875886i 0.660278π-0.660278\pi
−0.482519 + 0.875886i 0.660278π0.660278\pi
294294 0 0
295295 4557.73 0.899530
296296 −1554.40 −0.305229
297297 0 0
298298 7278.09 1.41479
299299 −222.036 −0.0429455
300300 0 0
301301 3697.42 0.708026
302302 −6020.60 −1.14717
303303 0 0
304304 2090.20 0.394346
305305 −1203.22 −0.225890
306306 0 0
307307 4917.94 0.914273 0.457136 0.889397i 0.348875π-0.348875\pi
0.457136 + 0.889397i 0.348875π0.348875\pi
308308 1222.95 0.226246
309309 0 0
310310 −9163.50 −1.67888
311311 4875.93 0.889031 0.444516 0.895771i 0.353376π-0.353376\pi
0.444516 + 0.895771i 0.353376π0.353376\pi
312312 0 0
313313 4283.96 0.773622 0.386811 0.922159i 0.373577π-0.373577\pi
0.386811 + 0.922159i 0.373577π0.373577\pi
314314 6060.21 1.08916
315315 0 0
316316 2487.46 0.442818
317317 −8879.08 −1.57318 −0.786592 0.617474i 0.788156π-0.788156\pi
−0.786592 + 0.617474i 0.788156π0.788156\pi
318318 0 0
319319 1539.89 0.270273
320320 5429.69 0.948527
321321 0 0
322322 4875.46 0.843785
323323 7463.57 1.28571
324324 0 0
325325 −155.915 −0.0266111
326326 3649.44 0.620011
327327 0 0
328328 1615.82 0.272008
329329 771.236 0.129239
330330 0 0
331331 −7084.95 −1.17651 −0.588254 0.808676i 0.700185π-0.700185\pi
−0.588254 + 0.808676i 0.700185π0.700185\pi
332332 −5533.77 −0.914774
333333 0 0
334334 −7435.77 −1.21817
335335 1434.01 0.233875
336336 0 0
337337 −11557.2 −1.86813 −0.934066 0.357099i 0.883766π-0.883766\pi
−0.934066 + 0.357099i 0.883766π0.883766\pi
338338 9791.60 1.57572
339339 0 0
340340 4772.45 0.761242
341341 −3454.73 −0.548634
342342 0 0
343343 −5584.18 −0.879059
344344 −6956.44 −1.09031
345345 0 0
346346 −3267.31 −0.507664
347347 −3384.55 −0.523608 −0.261804 0.965121i 0.584317π-0.584317\pi
−0.261804 + 0.965121i 0.584317π0.584317\pi
348348 0 0
349349 8069.34 1.23766 0.618828 0.785527i 0.287608π-0.287608\pi
0.618828 + 0.785527i 0.287608π0.287608\pi
350350 3423.57 0.522849
351351 0 0
352352 2385.00 0.361139
353353 498.421 0.0751509 0.0375755 0.999294i 0.488037π-0.488037\pi
0.0375755 + 0.999294i 0.488037π0.488037\pi
354354 0 0
355355 −5794.91 −0.866372
356356 −13570.5 −2.02032
357357 0 0
358358 −19075.0 −2.81604
359359 −488.919 −0.0718779 −0.0359390 0.999354i 0.511442π-0.511442\pi
−0.0359390 + 0.999354i 0.511442π0.511442\pi
360360 0 0
361361 8006.23 1.16726
362362 −4683.00 −0.679926
363363 0 0
364364 210.667 0.0303351
365365 −2213.76 −0.317461
366366 0 0
367367 −4204.61 −0.598034 −0.299017 0.954248i 0.596659π-0.596659\pi
−0.299017 + 0.954248i 0.596659π0.596659\pi
368368 2008.83 0.284559
369369 0 0
370370 2586.27 0.363389
371371 −5422.55 −0.758827
372372 0 0
373373 −8499.45 −1.17985 −0.589926 0.807457i 0.700843π-0.700843\pi
−0.589926 + 0.807457i 0.700843π0.700843\pi
374374 3005.99 0.415604
375375 0 0
376376 −1451.03 −0.199019
377377 265.264 0.0362382
378378 0 0
379379 −3902.19 −0.528871 −0.264436 0.964403i 0.585186π-0.585186\pi
−0.264436 + 0.964403i 0.585186π0.585186\pi
380380 9505.31 1.28319
381381 0 0
382382 −10575.7 −1.41649
383383 −11681.3 −1.55845 −0.779226 0.626743i 0.784387π-0.784387\pi
−0.779226 + 0.626743i 0.784387π0.784387\pi
384384 0 0
385385 −670.097 −0.0887047
386386 −20175.6 −2.66039
387387 0 0
388388 18160.6 2.37620
389389 −8914.04 −1.16185 −0.580925 0.813957i 0.697309π-0.697309\pi
−0.580925 + 0.813957i 0.697309π0.697309\pi
390390 0 0
391391 7173.03 0.927764
392392 4491.44 0.578704
393393 0 0
394394 16180.7 2.06896
395395 −1362.97 −0.173616
396396 0 0
397397 −13445.5 −1.69977 −0.849885 0.526967i 0.823329π-0.823329\pi
−0.849885 + 0.526967i 0.823329π0.823329\pi
398398 4531.06 0.570657
399399 0 0
400400 1410.61 0.176326
401401 11815.1 1.47137 0.735683 0.677326i 0.236861π-0.236861\pi
0.735683 + 0.677326i 0.236861π0.236861\pi
402402 0 0
403403 −595.119 −0.0735608
404404 −21701.4 −2.67249
405405 0 0
406406 −5824.65 −0.712001
407407 975.051 0.118751
408408 0 0
409409 −14699.5 −1.77713 −0.888564 0.458752i 0.848297π-0.848297\pi
−0.888564 + 0.458752i 0.848297π0.848297\pi
410410 −2688.47 −0.323839
411411 0 0
412412 13624.8 1.62924
413413 −6499.55 −0.774387
414414 0 0
415415 3032.15 0.358657
416416 410.844 0.0484214
417417 0 0
418418 5987.05 0.700565
419419 6376.77 0.743498 0.371749 0.928333i 0.378758π-0.378758\pi
0.371749 + 0.928333i 0.378758π0.378758\pi
420420 0 0
421421 6745.79 0.780925 0.390463 0.920619i 0.372315π-0.372315\pi
0.390463 + 0.920619i 0.372315π0.372315\pi
422422 −2727.17 −0.314590
423423 0 0
424424 10202.2 1.16854
425425 5036.93 0.574887
426426 0 0
427427 1715.86 0.194464
428428 12603.3 1.42337
429429 0 0
430430 11574.4 1.29806
431431 −13592.8 −1.51913 −0.759563 0.650434i 0.774587π-0.774587\pi
−0.759563 + 0.650434i 0.774587π0.774587\pi
432432 0 0
433433 −2511.11 −0.278698 −0.139349 0.990243i 0.544501π-0.544501\pi
−0.139349 + 0.990243i 0.544501π0.544501\pi
434434 13067.6 1.44531
435435 0 0
436436 −16492.9 −1.81162
437437 14286.6 1.56389
438438 0 0
439439 9721.66 1.05692 0.528462 0.848957i 0.322769π-0.322769\pi
0.528462 + 0.848957i 0.322769π0.322769\pi
440440 1260.74 0.136599
441441 0 0
442442 517.818 0.0557242
443443 11323.6 1.21445 0.607226 0.794529i 0.292282π-0.292282\pi
0.607226 + 0.794529i 0.292282π0.292282\pi
444444 0 0
445445 7435.77 0.792111
446446 1984.58 0.210701
447447 0 0
448448 −7743.00 −0.816568
449449 −10422.4 −1.09546 −0.547732 0.836654i 0.684509π-0.684509\pi
−0.547732 + 0.836654i 0.684509π0.684509\pi
450450 0 0
451451 −1013.58 −0.105826
452452 3141.95 0.326958
453453 0 0
454454 25967.0 2.68434
455455 −115.432 −0.0118935
456456 0 0
457457 −6168.96 −0.631448 −0.315724 0.948851i 0.602247π-0.602247\pi
−0.315724 + 0.948851i 0.602247π0.602247\pi
458458 25962.5 2.64879
459459 0 0
460460 9135.29 0.925946
461461 2860.00 0.288945 0.144472 0.989509i 0.453851π-0.453851\pi
0.144472 + 0.989509i 0.453851π0.453851\pi
462462 0 0
463463 −10508.4 −1.05478 −0.527392 0.849622i 0.676830π-0.676830\pi
−0.527392 + 0.849622i 0.676830π0.676830\pi
464464 −2399.93 −0.240116
465465 0 0
466466 −10750.7 −1.06871
467467 9373.42 0.928802 0.464401 0.885625i 0.346270π-0.346270\pi
0.464401 + 0.885625i 0.346270π0.346270\pi
468468 0 0
469469 −2044.97 −0.201339
470470 2414.28 0.236941
471471 0 0
472472 12228.5 1.19250
473473 4363.67 0.424190
474474 0 0
475475 10032.1 0.969059
476476 −6805.74 −0.655337
477477 0 0
478478 −28115.3 −2.69030
479479 −556.775 −0.0531100 −0.0265550 0.999647i 0.508454π-0.508454\pi
−0.0265550 + 0.999647i 0.508454π0.508454\pi
480480 0 0
481481 167.964 0.0159221
482482 −18035.2 −1.70431
483483 0 0
484484 1443.31 0.135548
485485 −9950.85 −0.931639
486486 0 0
487487 −6462.85 −0.601355 −0.300677 0.953726i 0.597213π-0.597213\pi
−0.300677 + 0.953726i 0.597213π0.597213\pi
488488 −3228.27 −0.299461
489489 0 0
490490 −7473.03 −0.688974
491491 3106.60 0.285538 0.142769 0.989756i 0.454399π-0.454399\pi
0.142769 + 0.989756i 0.454399π0.454399\pi
492492 0 0
493493 −8569.52 −0.782864
494494 1031.34 0.0939316
495495 0 0
496496 5384.23 0.487418
497497 8263.82 0.745841
498498 0 0
499499 223.024 0.0200079 0.0100039 0.999950i 0.496816π-0.496816\pi
0.0100039 + 0.999950i 0.496816π0.496816\pi
500500 16160.0 1.44540
501501 0 0
502502 −10688.8 −0.950325
503503 −12042.2 −1.06747 −0.533734 0.845653i 0.679212π-0.679212\pi
−0.533734 + 0.845653i 0.679212π0.679212\pi
504504 0 0
505505 11891.0 1.04781
506506 5753.99 0.505525
507507 0 0
508508 −14524.7 −1.26856
509509 −5229.03 −0.455349 −0.227674 0.973737i 0.573112π-0.573112\pi
−0.227674 + 0.973737i 0.573112π0.573112\pi
510510 0 0
511511 3156.93 0.273296
512512 −6122.06 −0.528437
513513 0 0
514514 −9739.48 −0.835778
515515 −7465.54 −0.638778
516516 0 0
517517 910.207 0.0774292
518518 −3688.15 −0.312834
519519 0 0
520520 217.178 0.0183152
521521 21307.2 1.79171 0.895857 0.444342i 0.146562π-0.146562\pi
0.895857 + 0.444342i 0.146562π0.146562\pi
522522 0 0
523523 12533.6 1.04791 0.523956 0.851746i 0.324456π-0.324456\pi
0.523956 + 0.851746i 0.324456π0.324456\pi
524524 11041.0 0.920478
525525 0 0
526526 −17334.2 −1.43689
527527 19225.7 1.58916
528528 0 0
529529 1563.43 0.128498
530530 −16974.7 −1.39120
531531 0 0
532532 −13555.0 −1.10467
533533 −174.601 −0.0141892
534534 0 0
535535 −6905.80 −0.558063
536536 3847.46 0.310047
537537 0 0
538538 16126.9 1.29234
539539 −2817.41 −0.225147
540540 0 0
541541 1194.10 0.0948952 0.0474476 0.998874i 0.484891π-0.484891\pi
0.0474476 + 0.998874i 0.484891π0.484891\pi
542542 3197.59 0.253410
543543 0 0
544544 −13272.6 −1.04606
545545 9037.05 0.710284
546546 0 0
547547 −17077.5 −1.33488 −0.667441 0.744662i 0.732611π-0.732611\pi
−0.667441 + 0.744662i 0.732611π0.732611\pi
548548 13315.7 1.03799
549549 0 0
550550 4040.47 0.313248
551551 −17068.0 −1.31964
552552 0 0
553553 1943.66 0.149463
554554 −31228.0 −2.39485
555555 0 0
556556 −6880.73 −0.524835
557557 14523.5 1.10481 0.552407 0.833574i 0.313709π-0.313709\pi
0.552407 + 0.833574i 0.313709π0.313709\pi
558558 0 0
559559 751.695 0.0568753
560560 1044.35 0.0788070
561561 0 0
562562 39226.1 2.94422
563563 5179.82 0.387751 0.193875 0.981026i 0.437894π-0.437894\pi
0.193875 + 0.981026i 0.437894π0.437894\pi
564564 0 0
565565 −1721.59 −0.128191
566566 −15946.8 −1.18426
567567 0 0
568568 −15547.8 −1.14854
569569 10532.1 0.775971 0.387985 0.921666i 0.373171π-0.373171\pi
0.387985 + 0.921666i 0.373171π0.373171\pi
570570 0 0
571571 16946.5 1.24201 0.621007 0.783805i 0.286724π-0.286724\pi
0.621007 + 0.783805i 0.286724π0.286724\pi
572572 248.628 0.0181742
573573 0 0
574574 3833.88 0.278786
575575 9641.55 0.699271
576576 0 0
577577 13375.8 0.965060 0.482530 0.875879i 0.339718π-0.339718\pi
0.482530 + 0.875879i 0.339718π0.339718\pi
578578 5203.70 0.374473
579579 0 0
580580 −10913.8 −0.781330
581581 −4324.00 −0.308760
582582 0 0
583583 −6399.66 −0.454626
584584 −5939.54 −0.420856
585585 0 0
586586 21606.3 1.52312
587587 −22817.6 −1.60440 −0.802201 0.597054i 0.796338π-0.796338\pi
−0.802201 + 0.597054i 0.796338π0.796338\pi
588588 0 0
589589 38292.0 2.67877
590590 −20346.2 −1.41973
591591 0 0
592592 −1519.63 −0.105500
593593 1325.54 0.0917934 0.0458967 0.998946i 0.485385π-0.485385\pi
0.0458967 + 0.998946i 0.485385π0.485385\pi
594594 0 0
595595 3729.11 0.256939
596596 −19447.2 −1.33656
597597 0 0
598598 991.193 0.0677808
599599 −1757.35 −0.119872 −0.0599361 0.998202i 0.519090π-0.519090\pi
−0.0599361 + 0.998202i 0.519090π0.519090\pi
600600 0 0
601601 −12632.4 −0.857382 −0.428691 0.903451i 0.641025π-0.641025\pi
−0.428691 + 0.903451i 0.641025π0.641025\pi
602602 −16505.7 −1.11748
603603 0 0
604604 16087.2 1.08374
605605 −790.844 −0.0531444
606606 0 0
607607 13468.3 0.900598 0.450299 0.892878i 0.351317π-0.351317\pi
0.450299 + 0.892878i 0.351317π0.351317\pi
608608 −26435.1 −1.76330
609609 0 0
610610 5371.32 0.356522
611611 156.794 0.0103817
612612 0 0
613613 2901.94 0.191205 0.0956023 0.995420i 0.469522π-0.469522\pi
0.0956023 + 0.995420i 0.469522π0.469522\pi
614614 −21954.2 −1.44300
615615 0 0
616616 −1797.88 −0.117595
617617 22969.7 1.49874 0.749372 0.662149i 0.230355π-0.230355\pi
0.749372 + 0.662149i 0.230355π0.230355\pi
618618 0 0
619619 2859.62 0.185683 0.0928416 0.995681i 0.470405π-0.470405\pi
0.0928416 + 0.995681i 0.470405π0.470405\pi
620620 24485.1 1.58604
621621 0 0
622622 −21766.6 −1.40316
623623 −10603.8 −0.681912
624624 0 0
625625 1430.59 0.0915576
626626 −19124.0 −1.22101
627627 0 0
628628 −16193.1 −1.02894
629629 −5426.19 −0.343969
630630 0 0
631631 −990.450 −0.0624869 −0.0312434 0.999512i 0.509947π-0.509947\pi
−0.0312434 + 0.999512i 0.509947π0.509947\pi
632632 −3656.86 −0.230162
633633 0 0
634634 39637.1 2.48295
635635 7958.63 0.497368
636636 0 0
637637 −485.333 −0.0301877
638638 −6874.21 −0.426571
639639 0 0
640640 −12901.9 −0.796862
641641 2721.01 0.167665 0.0838327 0.996480i 0.473284π-0.473284\pi
0.0838327 + 0.996480i 0.473284π0.473284\pi
642642 0 0
643643 1014.22 0.0622033 0.0311017 0.999516i 0.490098π-0.490098\pi
0.0311017 + 0.999516i 0.490098π0.490098\pi
644644 −13027.4 −0.797128
645645 0 0
646646 −33318.1 −2.02923
647647 25988.5 1.57916 0.789578 0.613650i 0.210299π-0.210299\pi
0.789578 + 0.613650i 0.210299π0.210299\pi
648648 0 0
649649 −7670.72 −0.463948
650650 696.019 0.0420002
651651 0 0
652652 −9751.39 −0.585727
653653 −1127.80 −0.0675870 −0.0337935 0.999429i 0.510759π-0.510759\pi
−0.0337935 + 0.999429i 0.510759π0.510759\pi
654654 0 0
655655 −6049.79 −0.360893
656656 1579.67 0.0940181
657657 0 0
658658 −3442.88 −0.203978
659659 −28673.0 −1.69490 −0.847452 0.530873i 0.821864π-0.821864\pi
−0.847452 + 0.530873i 0.821864π0.821864\pi
660660 0 0
661661 −14066.2 −0.827705 −0.413852 0.910344i 0.635817π-0.635817\pi
−0.413852 + 0.910344i 0.635817π0.635817\pi
662662 31628.0 1.85688
663663 0 0
664664 8135.31 0.475469
665665 7427.30 0.433110
666666 0 0
667667 −16403.6 −0.952246
668668 19868.6 1.15081
669669 0 0
670670 −6401.56 −0.369125
671671 2025.04 0.116507
672672 0 0
673673 −11713.0 −0.670879 −0.335439 0.942062i 0.608885π-0.608885\pi
−0.335439 + 0.942062i 0.608885π0.608885\pi
674674 51592.5 2.94847
675675 0 0
676676 −26163.4 −1.48859
677677 3194.15 0.181331 0.0906655 0.995881i 0.471101π-0.471101\pi
0.0906655 + 0.995881i 0.471101π0.471101\pi
678678 0 0
679679 14190.4 0.802029
680680 −7016.07 −0.395668
681681 0 0
682682 15422.3 0.865909
683683 −1138.53 −0.0637845 −0.0318923 0.999491i 0.510153π-0.510153\pi
−0.0318923 + 0.999491i 0.510153π0.510153\pi
684684 0 0
685685 −7296.17 −0.406967
686686 24928.3 1.38742
687687 0 0
688688 −6800.82 −0.376859
689689 −1102.42 −0.0609561
690690 0 0
691691 4538.68 0.249869 0.124934 0.992165i 0.460128π-0.460128\pi
0.124934 + 0.992165i 0.460128π0.460128\pi
692692 8730.34 0.479592
693693 0 0
694694 15109.0 0.826410
695695 3770.21 0.205773
696696 0 0
697697 5640.61 0.306533
698698 −36022.4 −1.95339
699699 0 0
700700 −9147.86 −0.493938
701701 −18226.5 −0.982036 −0.491018 0.871150i 0.663375π-0.663375\pi
−0.491018 + 0.871150i 0.663375π0.663375\pi
702702 0 0
703703 −10807.4 −0.579812
704704 −9138.23 −0.489219
705705 0 0
706706 −2225.00 −0.118611
707707 −16957.2 −0.902036
708708 0 0
709709 −9626.62 −0.509923 −0.254962 0.966951i 0.582063π-0.582063\pi
−0.254962 + 0.966951i 0.582063π0.582063\pi
710710 25869.1 1.36739
711711 0 0
712712 19950.3 1.05010
713713 36801.4 1.93299
714714 0 0
715715 −136.232 −0.00712560
716716 50968.8 2.66033
717717 0 0
718718 2182.59 0.113445
719719 217.065 0.0112589 0.00562947 0.999984i 0.498208π-0.498208\pi
0.00562947 + 0.999984i 0.498208π0.498208\pi
720720 0 0
721721 10646.2 0.549911
722722 −35740.6 −1.84228
723723 0 0
724724 12513.1 0.642329
725725 −11518.6 −0.590057
726726 0 0
727727 −28648.2 −1.46149 −0.730746 0.682650i 0.760828π-0.760828\pi
−0.730746 + 0.682650i 0.760828π0.760828\pi
728728 −309.706 −0.0157671
729729 0 0
730730 9882.44 0.501049
731731 −24284.0 −1.22869
732732 0 0
733733 −5760.02 −0.290247 −0.145123 0.989414i 0.546358π-0.546358\pi
−0.145123 + 0.989414i 0.546358π0.546358\pi
734734 18769.8 0.943877
735735 0 0
736736 −25406.1 −1.27239
737737 −2413.46 −0.120625
738738 0 0
739739 −17937.2 −0.892870 −0.446435 0.894816i 0.647307π-0.647307\pi
−0.446435 + 0.894816i 0.647307π0.647307\pi
740740 −6910.59 −0.343295
741741 0 0
742742 24206.8 1.19766
743743 −20217.9 −0.998279 −0.499140 0.866522i 0.666351π-0.666351\pi
−0.499140 + 0.866522i 0.666351π0.666351\pi
744744 0 0
745745 10655.9 0.524027
746746 37942.4 1.86216
747747 0 0
748748 −8032.09 −0.392623
749749 9848.00 0.480425
750750 0 0
751751 6649.29 0.323084 0.161542 0.986866i 0.448353π-0.448353\pi
0.161542 + 0.986866i 0.448353π0.448353\pi
752752 −1418.57 −0.0687896
753753 0 0
754754 −1184.17 −0.0571946
755755 −8814.76 −0.424903
756756 0 0
757757 9493.38 0.455803 0.227901 0.973684i 0.426814π-0.426814\pi
0.227901 + 0.973684i 0.426814π0.426814\pi
758758 17419.8 0.834717
759759 0 0
760760 −13973.9 −0.666958
761761 18781.3 0.894642 0.447321 0.894374i 0.352378π-0.352378\pi
0.447321 + 0.894374i 0.352378π0.352378\pi
762762 0 0
763763 −12887.3 −0.611469
764764 28258.5 1.33817
765765 0 0
766766 52146.5 2.45970
767767 −1321.37 −0.0622061
768768 0 0
769769 −11023.8 −0.516942 −0.258471 0.966019i 0.583219π-0.583219\pi
−0.258471 + 0.966019i 0.583219π0.583219\pi
770770 2991.38 0.140002
771771 0 0
772772 53909.8 2.51328
773773 −14027.8 −0.652710 −0.326355 0.945247i 0.605820π-0.605820\pi
−0.326355 + 0.945247i 0.605820π0.605820\pi
774774 0 0
775775 25842.0 1.19777
776776 −26698.3 −1.23507
777777 0 0
778778 39793.2 1.83375
779779 11234.4 0.516708
780780 0 0
781781 9752.91 0.446846
782782 −32021.1 −1.46429
783783 0 0
784784 4390.96 0.200025
785785 8872.77 0.403417
786786 0 0
787787 −30940.0 −1.40139 −0.700693 0.713463i 0.747126π-0.747126\pi
−0.700693 + 0.713463i 0.747126π0.747126\pi
788788 −43235.2 −1.95456
789789 0 0
790790 6084.43 0.274018
791791 2455.07 0.110357
792792 0 0
793793 348.838 0.0156212
794794 60022.0 2.68275
795795 0 0
796796 −12107.1 −0.539102
797797 −33897.3 −1.50653 −0.753265 0.657717i 0.771522π-0.771522\pi
−0.753265 + 0.657717i 0.771522π0.771522\pi
798798 0 0
799799 −5065.34 −0.224279
800800 −17840.2 −0.788434
801801 0 0
802802 −52743.8 −2.32226
803803 3725.78 0.163736
804804 0 0
805805 7138.17 0.312531
806806 2656.67 0.116101
807807 0 0
808808 31903.7 1.38907
809809 34155.0 1.48433 0.742166 0.670216i 0.233798π-0.233798\pi
0.742166 + 0.670216i 0.233798π0.233798\pi
810810 0 0
811811 42765.4 1.85166 0.925830 0.377941i 0.123368π-0.123368\pi
0.925830 + 0.377941i 0.123368π0.123368\pi
812812 15563.6 0.672631
813813 0 0
814814 −4352.73 −0.187424
815815 5343.15 0.229647
816816 0 0
817817 −48366.6 −2.07115
818818 65620.3 2.80484
819819 0 0
820820 7183.66 0.305932
821821 −15670.6 −0.666148 −0.333074 0.942901i 0.608086π-0.608086\pi
−0.333074 + 0.942901i 0.608086π0.608086\pi
822822 0 0
823823 16111.0 0.682373 0.341186 0.939996i 0.389171π-0.389171\pi
0.341186 + 0.939996i 0.389171π0.389171\pi
824824 −20030.1 −0.846824
825825 0 0
826826 29014.6 1.22221
827827 −12505.1 −0.525810 −0.262905 0.964822i 0.584681π-0.584681\pi
−0.262905 + 0.964822i 0.584681π0.584681\pi
828828 0 0
829829 −5981.63 −0.250604 −0.125302 0.992119i 0.539990π-0.539990\pi
−0.125302 + 0.992119i 0.539990π0.539990\pi
830830 −13535.8 −0.566067
831831 0 0
832832 −1574.17 −0.0655944
833833 15679.0 0.652154
834834 0 0
835835 −10886.7 −0.451198
836836 −15997.6 −0.661826
837837 0 0
838838 −28466.6 −1.17346
839839 −42174.9 −1.73545 −0.867724 0.497047i 0.834418π-0.834418\pi
−0.867724 + 0.497047i 0.834418π0.834418\pi
840840 0 0
841841 −4791.89 −0.196477
842842 −30113.9 −1.23253
843843 0 0
844844 7287.09 0.297194
845845 14335.9 0.583633
846846 0 0
847847 1127.78 0.0457509
848848 9973.92 0.403898
849849 0 0
850850 −22485.4 −0.907343
851851 −10386.7 −0.418391
852852 0 0
853853 20426.0 0.819898 0.409949 0.912108i 0.365546π-0.365546\pi
0.409949 + 0.912108i 0.365546π0.365546\pi
854854 −7659.76 −0.306922
855855 0 0
856856 −18528.3 −0.739820
857857 −4325.90 −0.172427 −0.0862136 0.996277i 0.527477π-0.527477\pi
−0.0862136 + 0.996277i 0.527477π0.527477\pi
858858 0 0
859859 −37355.7 −1.48377 −0.741887 0.670525i 0.766069π-0.766069\pi
−0.741887 + 0.670525i 0.766069π0.766069\pi
860860 −30927.1 −1.22629
861861 0 0
862862 60679.7 2.39763
863863 −38444.8 −1.51643 −0.758214 0.652006i 0.773928π-0.773928\pi
−0.758214 + 0.652006i 0.773928π0.773928\pi
864864 0 0
865865 −4783.67 −0.188034
866866 11209.8 0.439868
867867 0 0
868868 −34917.0 −1.36539
869869 2293.89 0.0895455
870870 0 0
871871 −415.747 −0.0161734
872872 24246.5 0.941618
873873 0 0
874874 −63776.7 −2.46828
875875 12627.2 0.487859
876876 0 0
877877 −21521.3 −0.828645 −0.414323 0.910130i 0.635982π-0.635982\pi
−0.414323 + 0.910130i 0.635982π0.635982\pi
878878 −43398.5 −1.66814
879879 0 0
880880 1232.54 0.0472145
881881 −24114.4 −0.922173 −0.461086 0.887355i 0.652540π-0.652540\pi
−0.461086 + 0.887355i 0.652540π0.652540\pi
882882 0 0
883883 5203.36 0.198309 0.0991546 0.995072i 0.468386π-0.468386\pi
0.0991546 + 0.995072i 0.468386π0.468386\pi
884884 −1383.62 −0.0526429
885885 0 0
886886 −50549.9 −1.91677
887887 −25749.8 −0.974738 −0.487369 0.873196i 0.662043π-0.662043\pi
−0.487369 + 0.873196i 0.662043π0.662043\pi
888888 0 0
889889 −11349.4 −0.428174
890890 −33194.0 −1.25019
891891 0 0
892892 −5302.86 −0.199050
893893 −10088.7 −0.378056
894894 0 0
895895 −27927.7 −1.04304
896896 18398.7 0.686002
897897 0 0
898898 46526.6 1.72897
899899 −43966.1 −1.63109
900900 0 0
901901 35614.3 1.31685
902902 4524.72 0.167025
903903 0 0
904904 −4619.04 −0.169941
905905 −6856.39 −0.251839
906906 0 0
907907 41969.7 1.53647 0.768237 0.640166i 0.221134π-0.221134\pi
0.768237 + 0.640166i 0.221134π0.221134\pi
908908 −69384.4 −2.53591
909909 0 0
910910 515.301 0.0187715
911911 5980.10 0.217486 0.108743 0.994070i 0.465317π-0.465317\pi
0.108743 + 0.994070i 0.465317π0.465317\pi
912912 0 0
913913 −5103.15 −0.184983
914914 27538.9 0.996613
915915 0 0
916916 −69372.4 −2.50232
917917 8627.30 0.310685
918918 0 0
919919 8614.03 0.309195 0.154598 0.987978i 0.450592π-0.450592\pi
0.154598 + 0.987978i 0.450592π0.450592\pi
920920 −13430.0 −0.481275
921921 0 0
922922 −12767.3 −0.456041
923923 1680.06 0.0599130
924924 0 0
925925 −7293.56 −0.259255
926926 46910.4 1.66476
927927 0 0
928928 30352.3 1.07367
929929 29940.6 1.05740 0.528698 0.848810i 0.322681π-0.322681\pi
0.528698 + 0.848810i 0.322681π0.322681\pi
930930 0 0
931931 31227.9 1.09931
932932 28726.2 1.00961
933933 0 0
934934 −41843.9 −1.46593
935935 4401.07 0.153936
936936 0 0
937937 7361.97 0.256676 0.128338 0.991731i 0.459036π-0.459036\pi
0.128338 + 0.991731i 0.459036π0.459036\pi
938938 9128.94 0.317772
939939 0 0
940940 −6451.01 −0.223839
941941 13364.9 0.463001 0.231501 0.972835i 0.425636π-0.425636\pi
0.231501 + 0.972835i 0.425636π0.425636\pi
942942 0 0
943943 10797.1 0.372855
944944 11954.9 0.412180
945945 0 0
946946 −19479.9 −0.669498
947947 11892.5 0.408081 0.204041 0.978962i 0.434593π-0.434593\pi
0.204041 + 0.978962i 0.434593π0.434593\pi
948948 0 0
949949 641.811 0.0219537
950950 −44784.2 −1.52946
951951 0 0
952952 10005.3 0.340622
953953 39943.0 1.35769 0.678846 0.734280i 0.262480π-0.262480\pi
0.678846 + 0.734280i 0.262480π0.262480\pi
954954 0 0
955955 −15483.9 −0.524656
956956 75124.9 2.54154
957957 0 0
958958 2485.50 0.0838235
959959 10404.7 0.350350
960960 0 0
961961 68846.9 2.31100
962962 −749.810 −0.0251298
963963 0 0
964964 48190.5 1.61007
965965 −29539.1 −0.985387
966966 0 0
967967 51655.2 1.71781 0.858903 0.512138i 0.171146π-0.171146\pi
0.858903 + 0.512138i 0.171146π0.171146\pi
968968 −2121.84 −0.0704531
969969 0 0
970970 44421.6 1.47040
971971 11420.4 0.377445 0.188722 0.982030i 0.439565π-0.439565\pi
0.188722 + 0.982030i 0.439565π0.439565\pi
972972 0 0
973973 −5376.50 −0.177145
974974 28850.8 0.949117
975975 0 0
976976 −3156.05 −0.103507
977977 31161.4 1.02041 0.510205 0.860053i 0.329570π-0.329570\pi
0.510205 + 0.860053i 0.329570π0.329570\pi
978978 0 0
979979 −12514.5 −0.408545
980980 19968.1 0.650876
981981 0 0
982982 −13868.2 −0.450664
983983 −23732.3 −0.770032 −0.385016 0.922910i 0.625804π-0.625804\pi
−0.385016 + 0.922910i 0.625804π0.625804\pi
984984 0 0
985985 23690.2 0.766326
986986 38255.2 1.23559
987987 0 0
988988 −2755.77 −0.0887376
989989 −46483.8 −1.49454
990990 0 0
991991 25272.0 0.810081 0.405041 0.914299i 0.367257π-0.367257\pi
0.405041 + 0.914299i 0.367257π0.367257\pi
992992 −68095.3 −2.17946
993993 0 0
994994 −36890.5 −1.17716
995995 6633.93 0.211367
996996 0 0
997997 −31125.7 −0.988726 −0.494363 0.869256i 0.664599π-0.664599\pi
−0.494363 + 0.869256i 0.664599π0.664599\pi
998998 −995.603 −0.0315784
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 99.4.a.d.1.1 2
3.2 odd 2 99.4.a.g.1.2 yes 2
4.3 odd 2 1584.4.a.w.1.2 2
5.4 even 2 2475.4.a.r.1.2 2
11.10 odd 2 1089.4.a.w.1.2 2
12.11 even 2 1584.4.a.bk.1.1 2
15.14 odd 2 2475.4.a.m.1.1 2
33.32 even 2 1089.4.a.l.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.4.a.d.1.1 2 1.1 even 1 trivial
99.4.a.g.1.2 yes 2 3.2 odd 2
1089.4.a.l.1.1 2 33.32 even 2
1089.4.a.w.1.2 2 11.10 odd 2
1584.4.a.w.1.2 2 4.3 odd 2
1584.4.a.bk.1.1 2 12.11 even 2
2475.4.a.m.1.1 2 15.14 odd 2
2475.4.a.r.1.2 2 5.4 even 2