Properties

Label 538.4.a.d.1.10
Level 538538
Weight 44
Character 538.1
Self dual yes
Analytic conductor 31.74331.743
Analytic rank 00
Dimension 2121
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] = [538,4,Mod(1,538)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(538, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("538.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 538=2269 538 = 2 \cdot 269
Weight: k k == 4 4
Character orbit: [χ][\chi] == 538.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: 31.743027583131.7430275831
Analytic rank: 00
Dimension: 2121
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.10
Character χ\chi == 538.1

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) == q+2.00000q21.07079q3+4.00000q4+3.57975q52.14158q6+21.8456q7+8.00000q825.8534q9+7.15950q108.22614q114.28316q12+58.2254q13+43.6912q143.83316q15+16.0000q16+96.3094q1751.7068q1860.2758q19+14.3190q2023.3921q2116.4523q226.40795q238.56633q24112.185q25+116.451q26+56.5949q27+87.3825q284.93073q297.66633q30+233.572q31+32.0000q32+8.80847q33+192.619q34+78.2019q35103.414q36+412.339q37120.552q3862.3472q39+28.6380q40+164.282q4146.7842q42370.699q4332.9045q4492.5487q4512.8159q46+280.972q4717.1327q48+134.231q49224.371q50103.127q51+232.901q52538.290q53+113.190q5429.4475q55+174.765q56+64.5428q579.86146q58+109.523q5915.3327q60+94.6721q61+467.143q62564.784q63+64.0000q64+208.432q65+17.6169q66+886.190q67+385.238q68+6.86157q69+156.404q70+785.631q71206.827q72+397.954q73+824.679q74+120.127q75241.103q76179.705q77124.694q78860.750q79+57.2760q80+637.441q81+328.564q82+546.057q8393.5684q84+344.764q85741.399q86+5.27978q8765.8091q88+774.506q89185.097q90+1271.97q9125.6318q92250.106q93+561.944q94215.772q9534.2653q96815.667q97+268.463q98+212.674q99+O(q100)q+2.00000 q^{2} -1.07079 q^{3} +4.00000 q^{4} +3.57975 q^{5} -2.14158 q^{6} +21.8456 q^{7} +8.00000 q^{8} -25.8534 q^{9} +7.15950 q^{10} -8.22614 q^{11} -4.28316 q^{12} +58.2254 q^{13} +43.6912 q^{14} -3.83316 q^{15} +16.0000 q^{16} +96.3094 q^{17} -51.7068 q^{18} -60.2758 q^{19} +14.3190 q^{20} -23.3921 q^{21} -16.4523 q^{22} -6.40795 q^{23} -8.56633 q^{24} -112.185 q^{25} +116.451 q^{26} +56.5949 q^{27} +87.3825 q^{28} -4.93073 q^{29} -7.66633 q^{30} +233.572 q^{31} +32.0000 q^{32} +8.80847 q^{33} +192.619 q^{34} +78.2019 q^{35} -103.414 q^{36} +412.339 q^{37} -120.552 q^{38} -62.3472 q^{39} +28.6380 q^{40} +164.282 q^{41} -46.7842 q^{42} -370.699 q^{43} -32.9045 q^{44} -92.5487 q^{45} -12.8159 q^{46} +280.972 q^{47} -17.1327 q^{48} +134.231 q^{49} -224.371 q^{50} -103.127 q^{51} +232.901 q^{52} -538.290 q^{53} +113.190 q^{54} -29.4475 q^{55} +174.765 q^{56} +64.5428 q^{57} -9.86146 q^{58} +109.523 q^{59} -15.3327 q^{60} +94.6721 q^{61} +467.143 q^{62} -564.784 q^{63} +64.0000 q^{64} +208.432 q^{65} +17.6169 q^{66} +886.190 q^{67} +385.238 q^{68} +6.86157 q^{69} +156.404 q^{70} +785.631 q^{71} -206.827 q^{72} +397.954 q^{73} +824.679 q^{74} +120.127 q^{75} -241.103 q^{76} -179.705 q^{77} -124.694 q^{78} -860.750 q^{79} +57.2760 q^{80} +637.441 q^{81} +328.564 q^{82} +546.057 q^{83} -93.5684 q^{84} +344.764 q^{85} -741.399 q^{86} +5.27978 q^{87} -65.8091 q^{88} +774.506 q^{89} -185.097 q^{90} +1271.97 q^{91} -25.6318 q^{92} -250.106 q^{93} +561.944 q^{94} -215.772 q^{95} -34.2653 q^{96} -815.667 q^{97} +268.463 q^{98} +212.674 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 21q+42q2+6q3+84q4+54q5+12q6+52q7+168q8+309q9+108q10+99q11+24q12+81q13+104q14+277q15+336q16+228q17+618q18+4470q99+O(q100) 21 q + 42 q^{2} + 6 q^{3} + 84 q^{4} + 54 q^{5} + 12 q^{6} + 52 q^{7} + 168 q^{8} + 309 q^{9} + 108 q^{10} + 99 q^{11} + 24 q^{12} + 81 q^{13} + 104 q^{14} + 277 q^{15} + 336 q^{16} + 228 q^{17} + 618 q^{18}+ \cdots - 4470 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 −1.07079 −0.206074 −0.103037 0.994678i 0.532856π-0.532856\pi
−0.103037 + 0.994678i 0.532856π0.532856\pi
44 4.00000 0.500000
55 3.57975 0.320183 0.160091 0.987102i 0.448821π-0.448821\pi
0.160091 + 0.987102i 0.448821π0.448821\pi
66 −2.14158 −0.145716
77 21.8456 1.17955 0.589776 0.807567i 0.299216π-0.299216\pi
0.589776 + 0.807567i 0.299216π0.299216\pi
88 8.00000 0.353553
99 −25.8534 −0.957534
1010 7.15950 0.226403
1111 −8.22614 −0.225479 −0.112740 0.993625i 0.535963π-0.535963\pi
−0.112740 + 0.993625i 0.535963π0.535963\pi
1212 −4.28316 −0.103037
1313 58.2254 1.24222 0.621108 0.783725i 0.286683π-0.286683\pi
0.621108 + 0.783725i 0.286683π0.286683\pi
1414 43.6912 0.834070
1515 −3.83316 −0.0659812
1616 16.0000 0.250000
1717 96.3094 1.37403 0.687014 0.726644i 0.258921π-0.258921\pi
0.687014 + 0.726644i 0.258921π0.258921\pi
1818 −51.7068 −0.677078
1919 −60.2758 −0.727801 −0.363901 0.931438i 0.618555π-0.618555\pi
−0.363901 + 0.931438i 0.618555π0.618555\pi
2020 14.3190 0.160091
2121 −23.3921 −0.243075
2222 −16.4523 −0.159438
2323 −6.40795 −0.0580935 −0.0290467 0.999578i 0.509247π-0.509247\pi
−0.0290467 + 0.999578i 0.509247π0.509247\pi
2424 −8.56633 −0.0728581
2525 −112.185 −0.897483
2626 116.451 0.878379
2727 56.5949 0.403396
2828 87.3825 0.589776
2929 −4.93073 −0.0315729 −0.0157864 0.999875i 0.505025π-0.505025\pi
−0.0157864 + 0.999875i 0.505025π0.505025\pi
3030 −7.66633 −0.0466558
3131 233.572 1.35325 0.676625 0.736328i 0.263442π-0.263442\pi
0.676625 + 0.736328i 0.263442π0.263442\pi
3232 32.0000 0.176777
3333 8.80847 0.0464654
3434 192.619 0.971584
3535 78.2019 0.377672
3636 −103.414 −0.478767
3737 412.339 1.83211 0.916056 0.401049i 0.131354π-0.131354\pi
0.916056 + 0.401049i 0.131354π0.131354\pi
3838 −120.552 −0.514633
3939 −62.3472 −0.255988
4040 28.6380 0.113202
4141 164.282 0.625769 0.312885 0.949791i 0.398705π-0.398705\pi
0.312885 + 0.949791i 0.398705π0.398705\pi
4242 −46.7842 −0.171880
4343 −370.699 −1.31468 −0.657339 0.753595i 0.728318π-0.728318\pi
−0.657339 + 0.753595i 0.728318π0.728318\pi
4444 −32.9045 −0.112740
4545 −92.5487 −0.306586
4646 −12.8159 −0.0410783
4747 280.972 0.871999 0.436000 0.899947i 0.356395π-0.356395\pi
0.436000 + 0.899947i 0.356395π0.356395\pi
4848 −17.1327 −0.0515184
4949 134.231 0.391345
5050 −224.371 −0.634616
5151 −103.127 −0.283151
5252 232.901 0.621108
5353 −538.290 −1.39509 −0.697545 0.716541i 0.745724π-0.745724\pi
−0.697545 + 0.716541i 0.745724π0.745724\pi
5454 113.190 0.285244
5555 −29.4475 −0.0721946
5656 174.765 0.417035
5757 64.5428 0.149981
5858 −9.86146 −0.0223254
5959 109.523 0.241673 0.120837 0.992672i 0.461442π-0.461442\pi
0.120837 + 0.992672i 0.461442π0.461442\pi
6060 −15.3327 −0.0329906
6161 94.6721 0.198713 0.0993567 0.995052i 0.468322π-0.468322\pi
0.0993567 + 0.995052i 0.468322π0.468322\pi
6262 467.143 0.956892
6363 −564.784 −1.12946
6464 64.0000 0.125000
6565 208.432 0.397736
6666 17.6169 0.0328560
6767 886.190 1.61590 0.807950 0.589251i 0.200577π-0.200577\pi
0.807950 + 0.589251i 0.200577π0.200577\pi
6868 385.238 0.687014
6969 6.86157 0.0119715
7070 156.404 0.267055
7171 785.631 1.31320 0.656600 0.754239i 0.271994π-0.271994\pi
0.656600 + 0.754239i 0.271994π0.271994\pi
7272 −206.827 −0.338539
7373 397.954 0.638041 0.319020 0.947748i 0.396646π-0.396646\pi
0.319020 + 0.947748i 0.396646π0.396646\pi
7474 824.679 1.29550
7575 120.127 0.184948
7676 −241.103 −0.363901
7777 −179.705 −0.265965
7878 −124.694 −0.181011
7979 −860.750 −1.22585 −0.612924 0.790142i 0.710007π-0.710007\pi
−0.612924 + 0.790142i 0.710007π0.710007\pi
8080 57.2760 0.0800456
8181 637.441 0.874404
8282 328.564 0.442486
8383 546.057 0.722140 0.361070 0.932539i 0.382412π-0.382412\pi
0.361070 + 0.932539i 0.382412π0.382412\pi
8484 −93.5684 −0.121537
8585 344.764 0.439940
8686 −741.399 −0.929617
8787 5.27978 0.00650634
8888 −65.8091 −0.0797190
8989 774.506 0.922443 0.461222 0.887285i 0.347411π-0.347411\pi
0.461222 + 0.887285i 0.347411π0.347411\pi
9090 −185.097 −0.216789
9191 1271.97 1.46526
9292 −25.6318 −0.0290467
9393 −250.106 −0.278869
9494 561.944 0.616597
9595 −215.772 −0.233029
9696 −34.2653 −0.0364290
9797 −815.667 −0.853798 −0.426899 0.904299i 0.640394π-0.640394\pi
−0.426899 + 0.904299i 0.640394π0.640394\pi
9898 268.463 0.276723
9999 212.674 0.215904
100100 −448.742 −0.448742
101101 502.110 0.494671 0.247336 0.968930i 0.420445π-0.420445\pi
0.247336 + 0.968930i 0.420445π0.420445\pi
102102 −206.254 −0.200218
103103 −185.721 −0.177666 −0.0888331 0.996047i 0.528314π-0.528314\pi
−0.0888331 + 0.996047i 0.528314π0.528314\pi
104104 465.803 0.439190
105105 −83.7379 −0.0778284
106106 −1076.58 −0.986477
107107 −1365.90 −1.23408 −0.617042 0.786930i 0.711669π-0.711669\pi
−0.617042 + 0.786930i 0.711669π0.711669\pi
108108 226.380 0.201698
109109 −2096.35 −1.84215 −0.921074 0.389388i 0.872686π-0.872686\pi
−0.921074 + 0.389388i 0.872686π0.872686\pi
110110 −58.8950 −0.0510493
111111 −441.529 −0.377550
112112 349.530 0.294888
113113 2208.72 1.83875 0.919374 0.393385i 0.128696π-0.128696\pi
0.919374 + 0.393385i 0.128696π0.128696\pi
114114 129.086 0.106052
115115 −22.9389 −0.0186005
116116 −19.7229 −0.0157864
117117 −1505.32 −1.18946
118118 219.046 0.170889
119119 2103.94 1.62074
120120 −30.6653 −0.0233279
121121 −1263.33 −0.949159
122122 189.344 0.140512
123123 −175.912 −0.128955
124124 934.287 0.676625
125125 −849.064 −0.607541
126126 −1129.57 −0.798650
127127 −1467.93 −1.02565 −0.512826 0.858493i 0.671401π-0.671401\pi
−0.512826 + 0.858493i 0.671401π0.671401\pi
128128 128.000 0.0883883
129129 396.942 0.270921
130130 416.864 0.281242
131131 1897.13 1.26529 0.632645 0.774442i 0.281969π-0.281969\pi
0.632645 + 0.774442i 0.281969π0.281969\pi
132132 35.2339 0.0232327
133133 −1316.76 −0.858480
134134 1772.38 1.14261
135135 202.596 0.129160
136136 770.475 0.485792
137137 −2858.81 −1.78281 −0.891404 0.453210i 0.850279π-0.850279\pi
−0.891404 + 0.453210i 0.850279π0.850279\pi
138138 13.7231 0.00846516
139139 617.009 0.376504 0.188252 0.982121i 0.439718π-0.439718\pi
0.188252 + 0.982121i 0.439718π0.439718\pi
140140 312.807 0.188836
141141 −300.862 −0.179696
142142 1571.26 0.928573
143143 −478.970 −0.280094
144144 −413.655 −0.239383
145145 −17.6508 −0.0101091
146146 795.908 0.451163
147147 −143.734 −0.0806459
148148 1649.36 0.916056
149149 −62.6156 −0.0344273 −0.0172137 0.999852i 0.505480π-0.505480\pi
−0.0172137 + 0.999852i 0.505480π0.505480\pi
150150 240.254 0.130778
151151 −1001.39 −0.539683 −0.269841 0.962905i 0.586971π-0.586971\pi
−0.269841 + 0.962905i 0.586971π0.586971\pi
152152 −482.207 −0.257317
153153 −2489.93 −1.31568
154154 −359.410 −0.188066
155155 836.128 0.433287
156156 −249.389 −0.127994
157157 2783.04 1.41472 0.707358 0.706855i 0.249887π-0.249887\pi
0.707358 + 0.706855i 0.249887π0.249887\pi
158158 −1721.50 −0.866805
159159 576.396 0.287491
160160 114.552 0.0566008
161161 −139.986 −0.0685243
162162 1274.88 0.618297
163163 −2128.83 −1.02296 −0.511480 0.859295i 0.670903π-0.670903\pi
−0.511480 + 0.859295i 0.670903π0.670903\pi
164164 657.128 0.312885
165165 31.5321 0.0148774
166166 1092.11 0.510630
167167 −325.804 −0.150967 −0.0754834 0.997147i 0.524050π-0.524050\pi
−0.0754834 + 0.997147i 0.524050π0.524050\pi
168168 −187.137 −0.0859400
169169 1193.19 0.543101
170170 689.527 0.311084
171171 1558.34 0.696894
172172 −1482.80 −0.657339
173173 −3267.42 −1.43594 −0.717969 0.696075i 0.754928π-0.754928\pi
−0.717969 + 0.696075i 0.754928π0.754928\pi
174174 10.5596 0.00460068
175175 −2450.76 −1.05863
176176 −131.618 −0.0563698
177177 −117.276 −0.0498025
178178 1549.01 0.652266
179179 −3804.63 −1.58867 −0.794335 0.607481i 0.792180π-0.792180\pi
−0.794335 + 0.607481i 0.792180π0.792180\pi
180180 −370.195 −0.153293
181181 1711.08 0.702674 0.351337 0.936249i 0.385727π-0.385727\pi
0.351337 + 0.936249i 0.385727π0.385727\pi
182182 2543.94 1.03609
183183 −101.374 −0.0409496
184184 −51.2636 −0.0205391
185185 1476.07 0.586611
186186 −500.213 −0.197190
187187 −792.254 −0.309815
188188 1123.89 0.436000
189189 1236.35 0.475827
190190 −431.545 −0.164777
191191 152.979 0.0579536 0.0289768 0.999580i 0.490775π-0.490775\pi
0.0289768 + 0.999580i 0.490775π0.490775\pi
192192 −68.5306 −0.0257592
193193 −1941.96 −0.724275 −0.362138 0.932125i 0.617953π-0.617953\pi
−0.362138 + 0.932125i 0.617953π0.617953\pi
194194 −1631.33 −0.603727
195195 −223.187 −0.0819630
196196 536.925 0.195672
197197 −3797.57 −1.37343 −0.686715 0.726927i 0.740948π-0.740948\pi
−0.686715 + 0.726927i 0.740948π0.740948\pi
198198 425.347 0.152667
199199 −3201.64 −1.14049 −0.570246 0.821474i 0.693152π-0.693152\pi
−0.570246 + 0.821474i 0.693152π0.693152\pi
200200 −897.483 −0.317308
201201 −948.924 −0.332995
202202 1004.22 0.349785
203203 −107.715 −0.0372419
204204 −412.509 −0.141576
205205 588.088 0.200360
206206 −371.442 −0.125629
207207 165.667 0.0556264
208208 931.606 0.310554
209209 495.837 0.164104
210210 −167.476 −0.0550330
211211 −3485.21 −1.13712 −0.568559 0.822642i 0.692499π-0.692499\pi
−0.568559 + 0.822642i 0.692499π0.692499\pi
212212 −2153.16 −0.697545
213213 −841.246 −0.270616
214214 −2731.81 −0.872629
215215 −1327.01 −0.420937
216216 452.760 0.142622
217217 5102.52 1.59623
218218 −4192.70 −1.30259
219219 −426.125 −0.131483
220220 −117.790 −0.0360973
221221 5607.65 1.70684
222222 −883.059 −0.266968
223223 −4524.34 −1.35862 −0.679309 0.733852i 0.737721π-0.737721\pi
−0.679309 + 0.733852i 0.737721π0.737721\pi
224224 699.060 0.208517
225225 2900.37 0.859370
226226 4417.43 1.30019
227227 −5620.04 −1.64324 −0.821620 0.570036i 0.806929π-0.806929\pi
−0.821620 + 0.570036i 0.806929π0.806929\pi
228228 258.171 0.0749904
229229 6124.22 1.76725 0.883624 0.468198i 0.155097π-0.155097\pi
0.883624 + 0.468198i 0.155097π0.155097\pi
230230 −45.8777 −0.0131526
231231 192.427 0.0548084
232232 −39.4458 −0.0111627
233233 2786.25 0.783404 0.391702 0.920092i 0.371886π-0.371886\pi
0.391702 + 0.920092i 0.371886π0.371886\pi
234234 −3010.65 −0.841078
235235 1005.81 0.279199
236236 438.093 0.120837
237237 921.684 0.252615
238238 4207.88 1.14603
239239 −4121.43 −1.11545 −0.557727 0.830025i 0.688326π-0.688326\pi
−0.557727 + 0.830025i 0.688326π0.688326\pi
240240 −61.3306 −0.0164953
241241 −3587.84 −0.958976 −0.479488 0.877548i 0.659178π-0.659178\pi
−0.479488 + 0.877548i 0.659178π0.659178\pi
242242 −2526.66 −0.671157
243243 −2210.63 −0.583588
244244 378.688 0.0993567
245245 480.515 0.125302
246246 −351.823 −0.0911847
247247 −3509.58 −0.904086
248248 1868.57 0.478446
249249 −584.713 −0.148814
250250 −1698.13 −0.429596
251251 −741.237 −0.186400 −0.0932001 0.995647i 0.529710π-0.529710\pi
−0.0932001 + 0.995647i 0.529710π0.529710\pi
252252 −2259.14 −0.564731
253253 52.7127 0.0130989
254254 −2935.86 −0.725245
255255 −369.170 −0.0906600
256256 256.000 0.0625000
257257 4479.55 1.08726 0.543632 0.839324i 0.317049π-0.317049\pi
0.543632 + 0.839324i 0.317049π0.317049\pi
258258 793.883 0.191570
259259 9007.81 2.16107
260260 833.729 0.198868
261261 127.476 0.0302321
262262 3794.26 0.894695
263263 −4976.09 −1.16669 −0.583343 0.812226i 0.698256π-0.698256\pi
−0.583343 + 0.812226i 0.698256π0.698256\pi
264264 70.4678 0.0164280
265265 −1926.94 −0.446683
266266 −2633.53 −0.607037
267267 −829.334 −0.190091
268268 3544.76 0.807950
269269 269.000 0.0609711
270270 405.192 0.0913303
271271 7800.47 1.74850 0.874252 0.485472i 0.161352π-0.161352\pi
0.874252 + 0.485472i 0.161352π0.161352\pi
272272 1540.95 0.343507
273273 −1362.01 −0.301952
274274 −5717.62 −1.26064
275275 922.852 0.202364
276276 27.4463 0.00598577
277277 −613.914 −0.133164 −0.0665821 0.997781i 0.521209π-0.521209\pi
−0.0665821 + 0.997781i 0.521209π0.521209\pi
278278 1234.02 0.266228
279279 −6038.62 −1.29578
280280 625.615 0.133527
281281 6835.54 1.45115 0.725576 0.688142i 0.241573π-0.241573\pi
0.725576 + 0.688142i 0.241573π0.241573\pi
282282 −601.724 −0.127064
283283 −4487.09 −0.942508 −0.471254 0.881998i 0.656198π-0.656198\pi
−0.471254 + 0.881998i 0.656198π0.656198\pi
284284 3142.52 0.656600
285285 231.047 0.0480212
286286 −957.939 −0.198056
287287 3588.84 0.738128
288288 −827.309 −0.169270
289289 4362.50 0.887951
290290 −35.3016 −0.00714820
291291 873.409 0.175945
292292 1591.82 0.319020
293293 2822.15 0.562703 0.281351 0.959605i 0.409217π-0.409217\pi
0.281351 + 0.959605i 0.409217π0.409217\pi
294294 −287.467 −0.0570253
295295 392.066 0.0773795
296296 3298.72 0.647750
297297 −465.558 −0.0909576
298298 −125.231 −0.0243438
299299 −373.105 −0.0721646
300300 480.508 0.0924739
301301 −8098.16 −1.55073
302302 −2002.78 −0.381613
303303 −537.654 −0.101939
304304 −964.413 −0.181950
305305 338.902 0.0636246
306306 −4979.85 −0.930324
307307 −4371.54 −0.812694 −0.406347 0.913719i 0.633198π-0.633198\pi
−0.406347 + 0.913719i 0.633198π0.633198\pi
308308 −718.820 −0.132982
309309 198.868 0.0366124
310310 1672.26 0.306380
311311 2304.21 0.420127 0.210064 0.977688i 0.432633π-0.432633\pi
0.210064 + 0.977688i 0.432633π0.432633\pi
312312 −498.777 −0.0905055
313313 −1436.95 −0.259493 −0.129747 0.991547i 0.541416π-0.541416\pi
−0.129747 + 0.991547i 0.541416π0.541416\pi
314314 5566.07 1.00036
315315 −2021.78 −0.361634
316316 −3443.00 −0.612924
317317 1132.55 0.200664 0.100332 0.994954i 0.468010π-0.468010\pi
0.100332 + 0.994954i 0.468010π0.468010\pi
318318 1152.79 0.203287
319319 40.5609 0.00711903
320320 229.104 0.0400228
321321 1462.60 0.254312
322322 −279.971 −0.0484540
323323 −5805.13 −1.00002
324324 2549.76 0.437202
325325 −6532.03 −1.11487
326326 −4257.65 −0.723343
327327 2244.75 0.379618
328328 1314.26 0.221243
329329 6138.01 1.02857
330330 63.0642 0.0105199
331331 7127.43 1.18356 0.591781 0.806099i 0.298425π-0.298425\pi
0.591781 + 0.806099i 0.298425π0.298425\pi
332332 2184.23 0.361070
333333 −10660.4 −1.75431
334334 −651.607 −0.106750
335335 3172.34 0.517383
336336 −374.274 −0.0607687
337337 823.690 0.133143 0.0665716 0.997782i 0.478794π-0.478794\pi
0.0665716 + 0.997782i 0.478794π0.478794\pi
338338 2386.38 0.384030
339339 −2365.07 −0.378918
340340 1379.05 0.219970
341341 −1921.39 −0.305130
342342 3116.67 0.492778
343343 −4560.68 −0.717941
344344 −2965.60 −0.464809
345345 24.5627 0.00383308
346346 −6534.84 −1.01536
347347 690.577 0.106836 0.0534180 0.998572i 0.482988π-0.482988\pi
0.0534180 + 0.998572i 0.482988π0.482988\pi
348348 21.1191 0.00325317
349349 −12611.4 −1.93430 −0.967151 0.254204i 0.918186π-0.918186\pi
−0.967151 + 0.254204i 0.918186π0.918186\pi
350350 −4901.52 −0.748564
351351 3295.26 0.501105
352352 −263.236 −0.0398595
353353 6730.47 1.01481 0.507403 0.861709i 0.330606π-0.330606\pi
0.507403 + 0.861709i 0.330606π0.330606\pi
354354 −234.553 −0.0352157
355355 2812.36 0.420464
356356 3098.02 0.461222
357357 −2252.88 −0.333992
358358 −7609.27 −1.12336
359359 −9445.25 −1.38858 −0.694292 0.719694i 0.744282π-0.744282\pi
−0.694292 + 0.719694i 0.744282π0.744282\pi
360360 −740.390 −0.108394
361361 −3225.83 −0.470306
362362 3422.17 0.496865
363363 1352.76 0.195597
364364 5087.88 0.732630
365365 1424.58 0.204290
366366 −202.748 −0.0289558
367367 −4695.88 −0.667910 −0.333955 0.942589i 0.608383π-0.608383\pi
−0.333955 + 0.942589i 0.608383π0.608383\pi
368368 −102.527 −0.0145234
369369 −4247.25 −0.599195
370370 2952.14 0.414796
371371 −11759.3 −1.64558
372372 −1000.43 −0.139435
373373 9084.77 1.26110 0.630552 0.776147i 0.282829π-0.282829\pi
0.630552 + 0.776147i 0.282829π0.282829\pi
374374 −1584.51 −0.219072
375375 909.170 0.125198
376376 2247.78 0.308298
377377 −287.094 −0.0392203
378378 2472.70 0.336461
379379 5892.69 0.798647 0.399324 0.916810i 0.369245π-0.369245\pi
0.399324 + 0.916810i 0.369245π0.369245\pi
380380 −863.089 −0.116515
381381 1571.85 0.211360
382382 305.957 0.0409794
383383 −933.493 −0.124541 −0.0622706 0.998059i 0.519834π-0.519834\pi
−0.0622706 + 0.998059i 0.519834π0.519834\pi
384384 −137.061 −0.0182145
385385 −643.299 −0.0851573
386386 −3883.91 −0.512140
387387 9583.84 1.25885
388388 −3262.67 −0.426899
389389 2777.53 0.362022 0.181011 0.983481i 0.442063π-0.442063\pi
0.181011 + 0.983481i 0.442063π0.442063\pi
390390 −446.375 −0.0579566
391391 −617.146 −0.0798220
392392 1073.85 0.138361
393393 −2031.43 −0.260743
394394 −7595.14 −0.971161
395395 −3081.27 −0.392495
396396 850.695 0.107952
397397 −7805.98 −0.986828 −0.493414 0.869794i 0.664251π-0.664251\pi
−0.493414 + 0.869794i 0.664251π0.664251\pi
398398 −6403.28 −0.806450
399399 1409.98 0.176910
400400 −1794.97 −0.224371
401401 8022.81 0.999103 0.499551 0.866284i 0.333498π-0.333498\pi
0.499551 + 0.866284i 0.333498π0.333498\pi
402402 −1897.85 −0.235463
403403 13599.8 1.68103
404404 2008.44 0.247336
405405 2281.88 0.279969
406406 −215.430 −0.0263340
407407 −3391.96 −0.413104
408408 −825.018 −0.100109
409409 9213.29 1.11386 0.556929 0.830560i 0.311980π-0.311980\pi
0.556929 + 0.830560i 0.311980π0.311980\pi
410410 1176.18 0.141676
411411 3061.19 0.367390
412412 −742.884 −0.0888331
413413 2392.60 0.285066
414414 331.335 0.0393338
415415 1954.75 0.231217
416416 1863.21 0.219595
417417 −660.687 −0.0775875
418418 991.674 0.116039
419419 11521.7 1.34337 0.671684 0.740838i 0.265571π-0.265571\pi
0.671684 + 0.740838i 0.265571π0.265571\pi
420420 −334.951 −0.0389142
421421 8085.69 0.936038 0.468019 0.883718i 0.344968π-0.344968\pi
0.468019 + 0.883718i 0.344968π0.344968\pi
422422 −6970.42 −0.804064
423423 −7264.08 −0.834969
424424 −4306.32 −0.493239
425425 −10804.5 −1.23317
426426 −1682.49 −0.191354
427427 2068.17 0.234393
428428 −5463.62 −0.617042
429429 512.876 0.0577201
430430 −2654.02 −0.297647
431431 −4853.07 −0.542376 −0.271188 0.962526i 0.587417π-0.587417\pi
−0.271188 + 0.962526i 0.587417π0.587417\pi
432432 905.519 0.100849
433433 13920.7 1.54500 0.772500 0.635015i 0.219006π-0.219006\pi
0.772500 + 0.635015i 0.219006π0.219006\pi
434434 10205.0 1.12870
435435 18.9003 0.00208322
436436 −8385.41 −0.921074
437437 386.244 0.0422805
438438 −852.251 −0.0929729
439439 −3973.50 −0.431993 −0.215996 0.976394i 0.569300π-0.569300\pi
−0.215996 + 0.976394i 0.569300π0.569300\pi
440440 −235.580 −0.0255246
441441 −3470.34 −0.374726
442442 11215.3 1.20692
443443 −6421.16 −0.688665 −0.344332 0.938848i 0.611895π-0.611895\pi
−0.344332 + 0.938848i 0.611895π0.611895\pi
444444 −1766.12 −0.188775
445445 2772.54 0.295350
446446 −9048.67 −0.960688
447447 67.0482 0.00709456
448448 1398.12 0.147444
449449 2952.10 0.310285 0.155143 0.987892i 0.450416π-0.450416\pi
0.155143 + 0.987892i 0.450416π0.450416\pi
450450 5800.75 0.607667
451451 −1351.41 −0.141098
452452 8834.86 0.919374
453453 1072.28 0.111214
454454 −11240.1 −1.16195
455455 4553.33 0.469151
456456 516.342 0.0530262
457457 −8150.75 −0.834302 −0.417151 0.908837i 0.636971π-0.636971\pi
−0.417151 + 0.908837i 0.636971π0.636971\pi
458458 12248.4 1.24963
459459 5450.63 0.554278
460460 −91.7554 −0.00930026
461461 7658.84 0.773769 0.386885 0.922128i 0.373551π-0.373551\pi
0.386885 + 0.922128i 0.373551π0.373551\pi
462462 384.853 0.0387554
463463 −4448.60 −0.446532 −0.223266 0.974758i 0.571672π-0.571672\pi
−0.223266 + 0.974758i 0.571672π0.571672\pi
464464 −78.8917 −0.00789322
465465 −895.319 −0.0892890
466466 5572.49 0.553950
467467 12558.2 1.24437 0.622187 0.782869i 0.286244π-0.286244\pi
0.622187 + 0.782869i 0.286244π0.286244\pi
468468 −6021.30 −0.594732
469469 19359.4 1.90604
470470 2011.62 0.197423
471471 −2980.05 −0.291536
472472 876.186 0.0854443
473473 3049.42 0.296433
474474 1843.37 0.178626
475475 6762.07 0.653189
476476 8415.76 0.810369
477477 13916.6 1.33585
478478 −8242.87 −0.788745
479479 3513.52 0.335150 0.167575 0.985859i 0.446406π-0.446406\pi
0.167575 + 0.985859i 0.446406π0.446406\pi
480480 −122.661 −0.0116639
481481 24008.6 2.27588
482482 −7175.68 −0.678098
483483 149.895 0.0141211
484484 −5053.32 −0.474580
485485 −2919.88 −0.273371
486486 −4421.26 −0.412659
487487 3237.81 0.301271 0.150636 0.988589i 0.451868π-0.451868\pi
0.150636 + 0.988589i 0.451868π0.451868\pi
488488 757.377 0.0702558
489489 2279.53 0.210805
490490 961.029 0.0886018
491491 10817.6 0.994283 0.497141 0.867670i 0.334383π-0.334383\pi
0.497141 + 0.867670i 0.334383π0.334383\pi
492492 −703.647 −0.0644773
493493 −474.876 −0.0433820
494494 −7019.16 −0.639285
495495 761.318 0.0691287
496496 3737.15 0.338312
497497 17162.6 1.54899
498498 −1169.43 −0.105227
499499 1503.59 0.134890 0.0674448 0.997723i 0.478515π-0.478515\pi
0.0674448 + 0.997723i 0.478515π0.478515\pi
500500 −3396.26 −0.303771
501501 348.868 0.0311103
502502 −1482.47 −0.131805
503503 6539.69 0.579702 0.289851 0.957072i 0.406394π-0.406394\pi
0.289851 + 0.957072i 0.406394π0.406394\pi
504504 −4518.27 −0.399325
505505 1797.43 0.158385
506506 105.425 0.00926231
507507 −1277.66 −0.111919
508508 −5871.72 −0.512826
509509 −20298.1 −1.76758 −0.883791 0.467882i 0.845017π-0.845017\pi
−0.883791 + 0.467882i 0.845017π0.845017\pi
510510 −738.340 −0.0641063
511511 8693.55 0.752603
512512 512.000 0.0441942
513513 −3411.31 −0.293592
514514 8959.10 0.768811
515515 −664.834 −0.0568856
516516 1587.77 0.135460
517517 −2311.31 −0.196618
518518 18015.6 1.52811
519519 3498.72 0.295909
520520 1667.46 0.140621
521521 −11072.1 −0.931048 −0.465524 0.885035i 0.654134π-0.654134\pi
−0.465524 + 0.885035i 0.654134π0.654134\pi
522522 254.952 0.0213773
523523 17025.7 1.42348 0.711741 0.702442i 0.247907π-0.247907\pi
0.711741 + 0.702442i 0.247907π0.247907\pi
524524 7588.52 0.632645
525525 2624.25 0.218156
526526 −9952.17 −0.824972
527527 22495.2 1.85940
528528 140.936 0.0116163
529529 −12125.9 −0.996625
530530 −3853.88 −0.315853
531531 −2831.55 −0.231410
532532 −5267.05 −0.429240
533533 9565.38 0.777340
534534 −1658.67 −0.134415
535535 −4889.60 −0.395132
536536 7089.52 0.571307
537537 4073.97 0.327383
538538 538.000 0.0431131
539539 −1104.20 −0.0882402
540540 810.383 0.0645802
541541 −18983.3 −1.50861 −0.754304 0.656525i 0.772026π-0.772026\pi
−0.754304 + 0.656525i 0.772026π0.772026\pi
542542 15600.9 1.23638
543543 −1832.21 −0.144803
544544 3081.90 0.242896
545545 −7504.41 −0.589823
546546 −2724.03 −0.213512
547547 −15459.3 −1.20839 −0.604197 0.796835i 0.706506π-0.706506\pi
−0.604197 + 0.796835i 0.706506π0.706506\pi
548548 −11435.2 −0.891404
549549 −2447.60 −0.190275
550550 1845.70 0.143093
551551 297.204 0.0229788
552552 54.8926 0.00423258
553553 −18803.6 −1.44595
554554 −1227.83 −0.0941613
555555 −1580.56 −0.120885
556556 2468.03 0.188252
557557 1001.16 0.0761588 0.0380794 0.999275i 0.487876π-0.487876\pi
0.0380794 + 0.999275i 0.487876π0.487876\pi
558558 −12077.2 −0.916256
559559 −21584.1 −1.63311
560560 1251.23 0.0944181
561561 848.339 0.0638447
562562 13671.1 1.02612
563563 −17512.2 −1.31093 −0.655463 0.755227i 0.727527π-0.727527\pi
−0.655463 + 0.755227i 0.727527π0.727527\pi
564564 −1203.45 −0.0898481
565565 7906.65 0.588735
566566 −8974.18 −0.666454
567567 13925.3 1.03141
568568 6285.04 0.464286
569569 −2267.59 −0.167069 −0.0835346 0.996505i 0.526621π-0.526621\pi
−0.0835346 + 0.996505i 0.526621π0.526621\pi
570570 462.094 0.0339561
571571 −18349.0 −1.34481 −0.672403 0.740186i 0.734738π-0.734738\pi
−0.672403 + 0.740186i 0.734738π0.734738\pi
572572 −1915.88 −0.140047
573573 −163.808 −0.0119427
574574 7177.68 0.521935
575575 718.878 0.0521379
576576 −1654.62 −0.119692
577577 19403.1 1.39993 0.699966 0.714176i 0.253198π-0.253198\pi
0.699966 + 0.714176i 0.253198π0.253198\pi
578578 8725.01 0.627876
579579 2079.43 0.149254
580580 −70.6031 −0.00505454
581581 11929.0 0.851802
582582 1746.82 0.124412
583583 4428.04 0.314564
584584 3183.63 0.225581
585585 −5388.68 −0.380846
586586 5644.30 0.397891
587587 323.054 0.0227153 0.0113576 0.999935i 0.496385π-0.496385\pi
0.0113576 + 0.999935i 0.496385π0.496385\pi
588588 −574.935 −0.0403230
589589 −14078.7 −0.984896
590590 784.132 0.0547156
591591 4066.40 0.283028
592592 6597.43 0.458028
593593 −8308.92 −0.575390 −0.287695 0.957722i 0.592889π-0.592889\pi
−0.287695 + 0.957722i 0.592889π0.592889\pi
594594 −931.115 −0.0643167
595595 7531.58 0.518932
596596 −250.462 −0.0172137
597597 3428.28 0.235026
598598 −746.210 −0.0510281
599599 11217.2 0.765145 0.382572 0.923925i 0.375038π-0.375038\pi
0.382572 + 0.923925i 0.375038π0.375038\pi
600600 961.017 0.0653889
601601 20658.0 1.40209 0.701046 0.713116i 0.252717π-0.252717\pi
0.701046 + 0.713116i 0.252717π0.252717\pi
602602 −16196.3 −1.09653
603603 −22911.0 −1.54728
604604 −4005.57 −0.269841
605605 −4522.41 −0.303904
606606 −1075.31 −0.0720816
607607 −18832.4 −1.25928 −0.629642 0.776885i 0.716798π-0.716798\pi
−0.629642 + 0.776885i 0.716798π0.716798\pi
608608 −1928.83 −0.128658
609609 115.340 0.00767458
610610 677.805 0.0449894
611611 16359.7 1.08321
612612 −9959.71 −0.657839
613613 526.582 0.0346956 0.0173478 0.999850i 0.494478π-0.494478\pi
0.0173478 + 0.999850i 0.494478π0.494478\pi
614614 −8743.08 −0.574661
615615 −629.720 −0.0412890
616616 −1437.64 −0.0940328
617617 24329.0 1.58744 0.793718 0.608286i 0.208143π-0.208143\pi
0.793718 + 0.608286i 0.208143π0.208143\pi
618618 397.736 0.0258888
619619 −2155.18 −0.139942 −0.0699709 0.997549i 0.522291π-0.522291\pi
−0.0699709 + 0.997549i 0.522291π0.522291\pi
620620 3344.51 0.216643
621621 −362.658 −0.0234347
622622 4608.42 0.297075
623623 16919.6 1.08807
624624 −997.555 −0.0639970
625625 10983.7 0.702959
626626 −2873.91 −0.183489
627627 −530.938 −0.0338176
628628 11132.1 0.707358
629629 39712.2 2.51737
630630 −4043.57 −0.255714
631631 6719.25 0.423913 0.211957 0.977279i 0.432016π-0.432016\pi
0.211957 + 0.977279i 0.432016π0.432016\pi
632632 −6886.00 −0.433403
633633 3731.93 0.234330
634634 2265.10 0.141891
635635 −5254.83 −0.328396
636636 2305.58 0.143746
637637 7815.67 0.486135
638638 81.1217 0.00503392
639639 −20311.2 −1.25743
640640 458.208 0.0283004
641641 22238.9 1.37033 0.685167 0.728386i 0.259729π-0.259729\pi
0.685167 + 0.728386i 0.259729π0.259729\pi
642642 2925.20 0.179826
643643 11950.4 0.732934 0.366467 0.930431i 0.380567π-0.380567\pi
0.366467 + 0.930431i 0.380567π0.380567\pi
644644 −559.943 −0.0342622
645645 1420.95 0.0867440
646646 −11610.3 −0.707120
647647 13860.5 0.842213 0.421107 0.907011i 0.361642π-0.361642\pi
0.421107 + 0.907011i 0.361642π0.361642\pi
648648 5099.53 0.309149
649649 −900.953 −0.0544923
650650 −13064.1 −0.788331
651651 −5463.73 −0.328941
652652 −8515.31 −0.511480
653653 19213.2 1.15141 0.575706 0.817657i 0.304727π-0.304727\pi
0.575706 + 0.817657i 0.304727π0.304727\pi
654654 4489.51 0.268431
655655 6791.25 0.405124
656656 2628.51 0.156442
657657 −10288.5 −0.610945
658658 12276.0 0.727308
659659 −27657.4 −1.63487 −0.817436 0.576019i 0.804605π-0.804605\pi
−0.817436 + 0.576019i 0.804605π0.804605\pi
660660 126.128 0.00743870
661661 −26363.2 −1.55130 −0.775651 0.631162i 0.782578π-0.782578\pi
−0.775651 + 0.631162i 0.782578π0.782578\pi
662662 14254.9 0.836904
663663 −6004.62 −0.351735
664664 4368.46 0.255315
665665 −4713.68 −0.274870
666666 −21320.8 −1.24048
667667 31.5959 0.00183418
668668 −1303.21 −0.0754834
669669 4844.62 0.279976
670670 6344.68 0.365845
671671 −778.786 −0.0448058
672672 −748.547 −0.0429700
673673 19235.4 1.10174 0.550870 0.834591i 0.314296π-0.314296\pi
0.550870 + 0.834591i 0.314296π0.314296\pi
674674 1647.38 0.0941464
675675 −6349.13 −0.362041
676676 4772.77 0.271550
677677 −10104.2 −0.573614 −0.286807 0.957988i 0.592594π-0.592594\pi
−0.286807 + 0.957988i 0.592594π0.592594\pi
678678 −4730.15 −0.267935
679679 −17818.8 −1.00710
680680 2758.11 0.155542
681681 6017.89 0.338629
682682 −3842.79 −0.215759
683683 −28965.6 −1.62275 −0.811376 0.584524i 0.801281π-0.801281\pi
−0.811376 + 0.584524i 0.801281π0.801281\pi
684684 6233.34 0.348447
685685 −10233.8 −0.570824
686686 −9121.36 −0.507661
687687 −6557.75 −0.364183
688688 −5931.19 −0.328669
689689 −31342.1 −1.73300
690690 49.1254 0.00271040
691691 −9945.49 −0.547532 −0.273766 0.961796i 0.588269π-0.588269\pi
−0.273766 + 0.961796i 0.588269π0.588269\pi
692692 −13069.7 −0.717969
693693 4645.99 0.254670
694694 1381.15 0.0755445
695695 2208.74 0.120550
696696 42.2382 0.00230034
697697 15821.9 0.859824
698698 −25222.7 −1.36776
699699 −2983.49 −0.161439
700700 −9803.04 −0.529314
701701 19180.8 1.03345 0.516726 0.856151i 0.327151π-0.327151\pi
0.516726 + 0.856151i 0.327151π0.327151\pi
702702 6590.52 0.354335
703703 −24854.1 −1.33341
704704 −526.473 −0.0281849
705705 −1077.01 −0.0575356
706706 13460.9 0.717576
707707 10968.9 0.583491
708708 −469.106 −0.0249012
709709 −24843.9 −1.31598 −0.657992 0.753025i 0.728594π-0.728594\pi
−0.657992 + 0.753025i 0.728594π0.728594\pi
710710 5624.72 0.297313
711711 22253.3 1.17379
712712 6196.05 0.326133
713713 −1496.72 −0.0786149
714714 −4505.76 −0.236168
715715 −1714.59 −0.0896813
716716 −15218.5 −0.794335
717717 4413.19 0.229866
718718 −18890.5 −0.981877
719719 15118.5 0.784180 0.392090 0.919927i 0.371752π-0.371752\pi
0.392090 + 0.919927i 0.371752π0.371752\pi
720720 −1480.78 −0.0766464
721721 −4057.19 −0.209567
722722 −6451.65 −0.332556
723723 3841.83 0.197620
724724 6844.34 0.351337
725725 553.156 0.0283361
726726 2705.53 0.138308
727727 −25394.6 −1.29551 −0.647753 0.761850i 0.724291π-0.724291\pi
−0.647753 + 0.761850i 0.724291π0.724291\pi
728728 10175.8 0.518047
729729 −14843.8 −0.754142
730730 2849.15 0.144455
731731 −35701.8 −1.80640
732732 −405.496 −0.0204748
733733 −5116.13 −0.257802 −0.128901 0.991657i 0.541145π-0.541145\pi
−0.128901 + 0.991657i 0.541145π0.541145\pi
734734 −9391.77 −0.472284
735735 −514.531 −0.0258214
736736 −205.054 −0.0102696
737737 −7289.92 −0.364352
738738 −8494.50 −0.423695
739739 31608.5 1.57339 0.786696 0.617340i 0.211790π-0.211790\pi
0.786696 + 0.617340i 0.211790π0.211790\pi
740740 5904.29 0.293305
741741 3758.03 0.186308
742742 −23518.5 −1.16360
743743 −15791.3 −0.779712 −0.389856 0.920876i 0.627475π-0.627475\pi
−0.389856 + 0.920876i 0.627475π0.627475\pi
744744 −2000.85 −0.0985951
745745 −224.148 −0.0110230
746746 18169.5 0.891735
747747 −14117.4 −0.691473
748748 −3169.02 −0.154907
749749 −29839.0 −1.45567
750750 1818.34 0.0885286
751751 957.250 0.0465120 0.0232560 0.999730i 0.492597π-0.492597\pi
0.0232560 + 0.999730i 0.492597π0.492597\pi
752752 4495.55 0.218000
753753 793.710 0.0384122
754754 −574.187 −0.0277330
755755 −3584.73 −0.172797
756756 4945.41 0.237914
757757 2875.44 0.138058 0.0690288 0.997615i 0.478010π-0.478010\pi
0.0690288 + 0.997615i 0.478010π0.478010\pi
758758 11785.4 0.564729
759759 −56.4442 −0.00269934
760760 −1726.18 −0.0823883
761761 −23338.6 −1.11173 −0.555863 0.831274i 0.687612π-0.687612\pi
−0.555863 + 0.831274i 0.687612π0.687612\pi
762762 3143.69 0.149454
763763 −45796.1 −2.17291
764764 611.914 0.0289768
765765 −8913.31 −0.421257
766766 −1866.99 −0.0880639
767767 6377.03 0.300210
768768 −274.122 −0.0128796
769769 −23060.7 −1.08139 −0.540695 0.841219i 0.681839π-0.681839\pi
−0.540695 + 0.841219i 0.681839π0.681839\pi
770770 −1286.60 −0.0602153
771771 −4796.66 −0.224056
772772 −7767.83 −0.362138
773773 265.574 0.0123571 0.00617855 0.999981i 0.498033π-0.498033\pi
0.00617855 + 0.999981i 0.498033π0.498033\pi
774774 19167.7 0.890140
775775 −26203.3 −1.21452
776776 −6525.34 −0.301863
777777 −9645.48 −0.445341
778778 5555.07 0.255988
779779 −9902.23 −0.455435
780780 −892.749 −0.0409815
781781 −6462.70 −0.296100
782782 −1234.29 −0.0564427
783783 −279.054 −0.0127364
784784 2147.70 0.0978362
785785 9962.57 0.452967
786786 −4062.86 −0.184373
787787 6091.06 0.275887 0.137943 0.990440i 0.455951π-0.455951\pi
0.137943 + 0.990440i 0.455951π0.455951\pi
788788 −15190.3 −0.686715
789789 5328.35 0.240424
790790 −6162.54 −0.277536
791791 48250.8 2.16890
792792 1701.39 0.0763336
793793 5512.32 0.246845
794794 −15612.0 −0.697793
795795 2063.35 0.0920497
796796 −12806.6 −0.570246
797797 41859.8 1.86041 0.930206 0.367038i 0.119628π-0.119628\pi
0.930206 + 0.367038i 0.119628π0.119628\pi
798798 2819.96 0.125094
799799 27060.2 1.19815
800800 −3589.93 −0.158654
801801 −20023.6 −0.883270
802802 16045.6 0.706472
803803 −3273.62 −0.143865
804804 −3795.70 −0.166497
805805 −501.114 −0.0219403
806806 27199.6 1.18867
807807 −288.043 −0.0125645
808808 4016.88 0.174893
809809 43545.0 1.89241 0.946205 0.323569i 0.104883π-0.104883\pi
0.946205 + 0.323569i 0.104883π0.104883\pi
810810 4563.76 0.197968
811811 −39925.7 −1.72871 −0.864354 0.502884i 0.832272π-0.832272\pi
−0.864354 + 0.502884i 0.832272π0.832272\pi
812812 −430.860 −0.0186209
813813 −8352.67 −0.360321
814814 −6783.92 −0.292108
815815 −7620.67 −0.327534
816816 −1650.04 −0.0707878
817817 22344.2 0.956824
818818 18426.6 0.787616
819819 −32884.7 −1.40304
820820 2352.35 0.100180
821821 17214.7 0.731789 0.365894 0.930656i 0.380763π-0.380763\pi
0.365894 + 0.930656i 0.380763π0.380763\pi
822822 6122.38 0.259784
823823 −29224.4 −1.23779 −0.618893 0.785476i 0.712418π-0.712418\pi
−0.618893 + 0.785476i 0.712418π0.712418\pi
824824 −1485.77 −0.0628145
825825 −988.182 −0.0417019
826826 4785.21 0.201572
827827 −16267.4 −0.684008 −0.342004 0.939699i 0.611106π-0.611106\pi
−0.342004 + 0.939699i 0.611106π0.611106\pi
828828 662.669 0.0278132
829829 −26702.5 −1.11872 −0.559358 0.828926i 0.688952π-0.688952\pi
−0.559358 + 0.828926i 0.688952π0.688952\pi
830830 3909.50 0.163495
831831 657.373 0.0274417
832832 3726.42 0.155277
833833 12927.7 0.537719
834834 −1321.37 −0.0548627
835835 −1166.30 −0.0483369
836836 1983.35 0.0820521
837837 13219.0 0.545896
838838 23043.4 0.949905
839839 6917.49 0.284646 0.142323 0.989820i 0.454543π-0.454543\pi
0.142323 + 0.989820i 0.454543π0.454543\pi
840840 −669.903 −0.0275165
841841 −24364.7 −0.999003
842842 16171.4 0.661879
843843 −7319.43 −0.299045
844844 −13940.8 −0.568559
845845 4271.33 0.173891
846846 −14528.2 −0.590412
847847 −27598.2 −1.11958
848848 −8612.63 −0.348772
849849 4804.73 0.194226
850850 −21609.0 −0.871980
851851 −2642.25 −0.106434
852852 −3364.98 −0.135308
853853 34464.8 1.38341 0.691707 0.722178i 0.256859π-0.256859\pi
0.691707 + 0.722178i 0.256859π0.256859\pi
854854 4136.34 0.165741
855855 5578.45 0.223133
856856 −10927.2 −0.436314
857857 35655.3 1.42119 0.710595 0.703601i 0.248426π-0.248426\pi
0.710595 + 0.703601i 0.248426π0.248426\pi
858858 1025.75 0.0408142
859859 −32614.7 −1.29546 −0.647729 0.761871i 0.724281π-0.724281\pi
−0.647729 + 0.761871i 0.724281π0.724281\pi
860860 −5308.04 −0.210468
861861 −3842.90 −0.152109
862862 −9706.14 −0.383518
863863 47219.5 1.86254 0.931268 0.364334i 0.118703π-0.118703\pi
0.931268 + 0.364334i 0.118703π0.118703\pi
864864 1811.04 0.0713111
865865 −11696.5 −0.459762
866866 27841.4 1.09248
867867 −4671.33 −0.182983
868868 20410.1 0.798114
869869 7080.65 0.276403
870870 37.8006 0.00147306
871871 51598.7 2.00730
872872 −16770.8 −0.651297
873873 21087.8 0.817541
874874 772.489 0.0298968
875875 −18548.3 −0.716627
876876 −1704.50 −0.0657417
877877 −17600.9 −0.677698 −0.338849 0.940841i 0.610038π-0.610038\pi
−0.338849 + 0.940841i 0.610038π0.610038\pi
878878 −7947.00 −0.305465
879879 −3021.93 −0.115958
880880 −471.160 −0.0180486
881881 −16179.3 −0.618723 −0.309362 0.950944i 0.600115π-0.600115\pi
−0.309362 + 0.950944i 0.600115π0.600115\pi
882882 −6940.67 −0.264971
883883 −17880.9 −0.681472 −0.340736 0.940159i 0.610676π-0.610676\pi
−0.340736 + 0.940159i 0.610676π0.610676\pi
884884 22430.6 0.853419
885885 −419.820 −0.0159459
886886 −12842.3 −0.486960
887887 −45387.9 −1.71812 −0.859062 0.511872i 0.828952π-0.828952\pi
−0.859062 + 0.511872i 0.828952π0.828952\pi
888888 −3532.23 −0.133484
889889 −32067.9 −1.20981
890890 5545.07 0.208844
891891 −5243.67 −0.197160
892892 −18097.3 −0.679309
893893 −16935.8 −0.634642
894894 134.096 0.00501661
895895 −13619.6 −0.508664
896896 2796.24 0.104259
897897 399.518 0.0148712
898898 5904.19 0.219405
899899 −1151.68 −0.0427260
900900 11601.5 0.429685
901901 −51842.4 −1.91689
902902 −2702.81 −0.0997714
903903 8671.44 0.319565
904904 17669.7 0.650095
905905 6125.25 0.224984
906906 2144.56 0.0786405
907907 −6376.42 −0.233435 −0.116717 0.993165i 0.537237π-0.537237\pi
−0.116717 + 0.993165i 0.537237π0.537237\pi
908908 −22480.2 −0.821620
909909 −12981.2 −0.473664
910910 9106.66 0.331740
911911 −18032.0 −0.655793 −0.327896 0.944714i 0.606340π-0.606340\pi
−0.327896 + 0.944714i 0.606340π0.606340\pi
912912 1032.68 0.0374952
913913 −4491.94 −0.162828
914914 −16301.5 −0.589941
915915 −362.894 −0.0131114
916916 24496.9 0.883624
917917 41444.0 1.49248
918918 10901.3 0.391934
919919 17176.0 0.616522 0.308261 0.951302i 0.400253π-0.400253\pi
0.308261 + 0.951302i 0.400253π0.400253\pi
920920 −183.511 −0.00657628
921921 4681.01 0.167475
922922 15317.7 0.547138
923923 45743.6 1.63128
924924 769.706 0.0274042
925925 −46258.5 −1.64429
926926 −8897.21 −0.315745
927927 4801.52 0.170121
928928 −157.783 −0.00558135
929929 11842.9 0.418249 0.209124 0.977889i 0.432939π-0.432939\pi
0.209124 + 0.977889i 0.432939π0.432939\pi
930930 −1790.64 −0.0631369
931931 −8090.90 −0.284821
932932 11145.0 0.391702
933933 −2467.32 −0.0865773
934934 25116.3 0.879905
935935 −2836.07 −0.0991973
936936 −12042.6 −0.420539
937937 45534.5 1.58756 0.793782 0.608202i 0.208109π-0.208109\pi
0.793782 + 0.608202i 0.208109π0.208109\pi
938938 38718.7 1.34777
939939 1538.68 0.0534747
940940 4023.24 0.139599
941941 −16808.3 −0.582291 −0.291146 0.956679i 0.594036π-0.594036\pi
−0.291146 + 0.956679i 0.594036π0.594036\pi
942942 −5960.10 −0.206147
943943 −1052.71 −0.0363531
944944 1752.37 0.0604183
945945 4425.83 0.152352
946946 6098.85 0.209610
947947 −10403.1 −0.356974 −0.178487 0.983942i 0.557120π-0.557120\pi
−0.178487 + 0.983942i 0.557120π0.557120\pi
948948 3686.73 0.126308
949949 23171.0 0.792584
950950 13524.1 0.461874
951951 −1212.72 −0.0413515
952952 16831.5 0.573017
953953 −9475.84 −0.322091 −0.161045 0.986947i 0.551487π-0.551487\pi
−0.161045 + 0.986947i 0.551487π0.551487\pi
954954 27833.2 0.944585
955955 547.625 0.0185557
956956 −16485.7 −0.557727
957957 −43.4322 −0.00146705
958958 7027.03 0.236987
959959 −62452.5 −2.10292
960960 −245.322 −0.00824765
961961 24764.8 0.831283
962962 48017.2 1.60929
963963 35313.3 1.18168
964964 −14351.4 −0.479488
965965 −6951.72 −0.231900
966966 299.791 0.00998510
967967 39930.0 1.32788 0.663942 0.747784i 0.268882π-0.268882\pi
0.663942 + 0.747784i 0.268882π0.268882\pi
968968 −10106.6 −0.335578
969969 6216.08 0.206078
970970 −5839.77 −0.193303
971971 −27957.2 −0.923984 −0.461992 0.886884i 0.652865π-0.652865\pi
−0.461992 + 0.886884i 0.652865π0.652865\pi
972972 −8842.52 −0.291794
973973 13478.9 0.444106
974974 6475.62 0.213031
975975 6994.44 0.229745
976976 1514.75 0.0496784
977977 −30853.6 −1.01033 −0.505166 0.863022i 0.668569π-0.668569\pi
−0.505166 + 0.863022i 0.668569π0.668569\pi
978978 4559.06 0.149062
979979 −6371.19 −0.207992
980980 1922.06 0.0626509
981981 54197.8 1.76392
982982 21635.3 0.703064
983983 −46.9863 −0.00152455 −0.000762274 1.00000i 0.500243π-0.500243\pi
−0.000762274 1.00000i 0.500243π0.500243\pi
984984 −1407.29 −0.0455923
985985 −13594.3 −0.439748
986986 −949.752 −0.0306757
987987 −6572.52 −0.211961
988988 −14038.3 −0.452043
989989 2375.42 0.0763742
990990 1522.64 0.0488814
991991 −42948.4 −1.37669 −0.688346 0.725383i 0.741663π-0.741663\pi
−0.688346 + 0.725383i 0.741663π0.741663\pi
992992 7474.30 0.239223
993993 −7631.98 −0.243901
994994 34325.2 1.09530
995995 −11461.1 −0.365166
996996 −2338.85 −0.0744070
997997 14125.8 0.448714 0.224357 0.974507i 0.427972π-0.427972\pi
0.224357 + 0.974507i 0.427972π0.427972\pi
998998 3007.18 0.0953814
999999 23336.3 0.739068
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 538.4.a.d.1.10 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
538.4.a.d.1.10 21 1.1 even 1 trivial