Properties

Label 538.4.a.c.1.16
Level 538538
Weight 44
Character 538.1
Self dual yes
Analytic conductor 31.74331.743
Analytic rank 11
Dimension 1818
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: 11
Dimension: 1818
Coefficient field: Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x188x17299x16+2191x15+37840x14247598x132647415x12+88752454191 x^{18} - 8 x^{17} - 299 x^{16} + 2191 x^{15} + 37840 x^{14} - 247598 x^{13} - 2647415 x^{12} + \cdots - 88752454191 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 32 3^{2}
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.16
Root 7.359517.35951 of defining polynomial
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) == q2.00000q2+6.35951q3+4.00000q4+6.17843q512.7190q627.3928q78.00000q8+13.4434q912.3569q1040.4875q11+25.4381q12+70.4369q13+54.7855q14+39.2918q15+16.0000q16109.655q1726.8868q18+124.330q19+24.7137q20174.205q21+80.9751q22+47.2294q2350.8761q2486.8270q25140.874q2686.2134q27109.571q28275.186q2978.5836q30+78.4699q3132.0000q32257.481q33+219.309q34169.244q35+53.7736q36411.965q37248.660q38+447.945q3949.4275q40+367.077q41+348.409q42323.524q43161.950q44+83.0592q4594.4588q46345.631q47+101.752q48+407.364q49+173.654q50697.350q51+281.748q52183.659q53+172.427q54250.150q55+219.142q56+790.678q57+550.373q58+4.65834q59+157.167q60178.061q61156.940q62368.252q63+64.0000q64+435.190q65+514.962q66184.917q67438.619q68+300.356q69+338.489q70429.952q71107.547q72+608.426q73+823.930q74552.177q75+497.320q76+1109.07q77895.889q78+535.072q79+98.8549q80911.247q81734.155q82601.154q83696.819q84677.494q85+647.048q861750.05q87+323.900q88479.696q89166.118q901929.46q91+188.918q92+499.030q93+691.261q94+768.164q95203.504q96+903.154q97814.728q98544.290q99+O(q100)q-2.00000 q^{2} +6.35951 q^{3} +4.00000 q^{4} +6.17843 q^{5} -12.7190 q^{6} -27.3928 q^{7} -8.00000 q^{8} +13.4434 q^{9} -12.3569 q^{10} -40.4875 q^{11} +25.4381 q^{12} +70.4369 q^{13} +54.7855 q^{14} +39.2918 q^{15} +16.0000 q^{16} -109.655 q^{17} -26.8868 q^{18} +124.330 q^{19} +24.7137 q^{20} -174.205 q^{21} +80.9751 q^{22} +47.2294 q^{23} -50.8761 q^{24} -86.8270 q^{25} -140.874 q^{26} -86.2134 q^{27} -109.571 q^{28} -275.186 q^{29} -78.5836 q^{30} +78.4699 q^{31} -32.0000 q^{32} -257.481 q^{33} +219.309 q^{34} -169.244 q^{35} +53.7736 q^{36} -411.965 q^{37} -248.660 q^{38} +447.945 q^{39} -49.4275 q^{40} +367.077 q^{41} +348.409 q^{42} -323.524 q^{43} -161.950 q^{44} +83.0592 q^{45} -94.4588 q^{46} -345.631 q^{47} +101.752 q^{48} +407.364 q^{49} +173.654 q^{50} -697.350 q^{51} +281.748 q^{52} -183.659 q^{53} +172.427 q^{54} -250.150 q^{55} +219.142 q^{56} +790.678 q^{57} +550.373 q^{58} +4.65834 q^{59} +157.167 q^{60} -178.061 q^{61} -156.940 q^{62} -368.252 q^{63} +64.0000 q^{64} +435.190 q^{65} +514.962 q^{66} -184.917 q^{67} -438.619 q^{68} +300.356 q^{69} +338.489 q^{70} -429.952 q^{71} -107.547 q^{72} +608.426 q^{73} +823.930 q^{74} -552.177 q^{75} +497.320 q^{76} +1109.07 q^{77} -895.889 q^{78} +535.072 q^{79} +98.8549 q^{80} -911.247 q^{81} -734.155 q^{82} -601.154 q^{83} -696.819 q^{84} -677.494 q^{85} +647.048 q^{86} -1750.05 q^{87} +323.900 q^{88} -479.696 q^{89} -166.118 q^{90} -1929.46 q^{91} +188.918 q^{92} +499.030 q^{93} +691.261 q^{94} +768.164 q^{95} -203.504 q^{96} +903.154 q^{97} -814.728 q^{98} -544.290 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 18q36q210q3+72q426q5+20q69q7144q8+178q9+52q10130q1140q1227q13+18q14143q15+288q16110q17356q18+9455q99+O(q100) 18 q - 36 q^{2} - 10 q^{3} + 72 q^{4} - 26 q^{5} + 20 q^{6} - 9 q^{7} - 144 q^{8} + 178 q^{9} + 52 q^{10} - 130 q^{11} - 40 q^{12} - 27 q^{13} + 18 q^{14} - 143 q^{15} + 288 q^{16} - 110 q^{17} - 356 q^{18}+ \cdots - 9455 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 6.35951 1.22389 0.611944 0.790901i 0.290388π-0.290388\pi
0.611944 + 0.790901i 0.290388π0.290388\pi
44 4.00000 0.500000
55 6.17843 0.552616 0.276308 0.961069i 0.410889π-0.410889\pi
0.276308 + 0.961069i 0.410889π0.410889\pi
66 −12.7190 −0.865420
77 −27.3928 −1.47907 −0.739535 0.673118i 0.764955π-0.764955\pi
−0.739535 + 0.673118i 0.764955π0.764955\pi
88 −8.00000 −0.353553
99 13.4434 0.497904
1010 −12.3569 −0.390758
1111 −40.4875 −1.10977 −0.554884 0.831928i 0.687237π-0.687237\pi
−0.554884 + 0.831928i 0.687237π0.687237\pi
1212 25.4381 0.611944
1313 70.4369 1.50275 0.751373 0.659878i 0.229392π-0.229392\pi
0.751373 + 0.659878i 0.229392π0.229392\pi
1414 54.7855 1.04586
1515 39.2918 0.676340
1616 16.0000 0.250000
1717 −109.655 −1.56442 −0.782211 0.623014i 0.785908π-0.785908\pi
−0.782211 + 0.623014i 0.785908π0.785908\pi
1818 −26.8868 −0.352071
1919 124.330 1.50122 0.750612 0.660743i 0.229759π-0.229759\pi
0.750612 + 0.660743i 0.229759π0.229759\pi
2020 24.7137 0.276308
2121 −174.205 −1.81022
2222 80.9751 0.784725
2323 47.2294 0.428175 0.214087 0.976815i 0.431322π-0.431322\pi
0.214087 + 0.976815i 0.431322π0.431322\pi
2424 −50.8761 −0.432710
2525 −86.8270 −0.694616
2626 −140.874 −1.06260
2727 −86.2134 −0.614510
2828 −109.571 −0.739535
2929 −275.186 −1.76210 −0.881049 0.473026i 0.843162π-0.843162\pi
−0.881049 + 0.473026i 0.843162π0.843162\pi
3030 −78.5836 −0.478245
3131 78.4699 0.454633 0.227316 0.973821i 0.427005π-0.427005\pi
0.227316 + 0.973821i 0.427005π0.427005\pi
3232 −32.0000 −0.176777
3333 −257.481 −1.35823
3434 219.309 1.10621
3535 −169.244 −0.817358
3636 53.7736 0.248952
3737 −411.965 −1.83045 −0.915225 0.402943i 0.867987π-0.867987\pi
−0.915225 + 0.402943i 0.867987π0.867987\pi
3838 −248.660 −1.06153
3939 447.945 1.83919
4040 −49.4275 −0.195379
4141 367.077 1.39824 0.699120 0.715004i 0.253575π-0.253575\pi
0.699120 + 0.715004i 0.253575π0.253575\pi
4242 348.409 1.28002
4343 −323.524 −1.14737 −0.573686 0.819075i 0.694487π-0.694487\pi
−0.573686 + 0.819075i 0.694487π0.694487\pi
4444 −161.950 −0.554884
4545 83.0592 0.275150
4646 −94.4588 −0.302765
4747 −345.631 −1.07267 −0.536334 0.844006i 0.680191π-0.680191\pi
−0.536334 + 0.844006i 0.680191π0.680191\pi
4848 101.752 0.305972
4949 407.364 1.18765
5050 173.654 0.491167
5151 −697.350 −1.91468
5252 281.748 0.751373
5353 −183.659 −0.475991 −0.237995 0.971266i 0.576490π-0.576490\pi
−0.237995 + 0.971266i 0.576490π0.576490\pi
5454 172.427 0.434524
5555 −250.150 −0.613276
5656 219.142 0.522930
5757 790.678 1.83733
5858 550.373 1.24599
5959 4.65834 0.0102790 0.00513952 0.999987i 0.498364π-0.498364\pi
0.00513952 + 0.999987i 0.498364π0.498364\pi
6060 157.167 0.338170
6161 −178.061 −0.373744 −0.186872 0.982384i 0.559835π-0.559835\pi
−0.186872 + 0.982384i 0.559835π0.559835\pi
6262 −156.940 −0.321474
6363 −368.252 −0.736435
6464 64.0000 0.125000
6565 435.190 0.830441
6666 514.962 0.960416
6767 −184.917 −0.337183 −0.168591 0.985686i 0.553922π-0.553922\pi
−0.168591 + 0.985686i 0.553922π0.553922\pi
6868 −438.619 −0.782211
6969 300.356 0.524038
7070 338.489 0.577959
7171 −429.952 −0.718675 −0.359337 0.933208i 0.616997π-0.616997\pi
−0.359337 + 0.933208i 0.616997π0.616997\pi
7272 −107.547 −0.176036
7373 608.426 0.975492 0.487746 0.872986i 0.337819π-0.337819\pi
0.487746 + 0.872986i 0.337819π0.337819\pi
7474 823.930 1.29432
7575 −552.177 −0.850132
7676 497.320 0.750612
7777 1109.07 1.64143
7878 −895.889 −1.30051
7979 535.072 0.762029 0.381015 0.924569i 0.375575π-0.375575\pi
0.381015 + 0.924569i 0.375575π0.375575\pi
8080 98.8549 0.138154
8181 −911.247 −1.25000
8282 −734.155 −0.988705
8383 −601.154 −0.795003 −0.397502 0.917601i 0.630123π-0.630123\pi
−0.397502 + 0.917601i 0.630123π0.630123\pi
8484 −696.819 −0.905109
8585 −677.494 −0.864524
8686 647.048 0.811314
8787 −1750.05 −2.15661
8888 323.900 0.392362
8989 −479.696 −0.571322 −0.285661 0.958331i 0.592213π-0.592213\pi
−0.285661 + 0.958331i 0.592213π0.592213\pi
9090 −166.118 −0.194560
9191 −1929.46 −2.22267
9292 188.918 0.214087
9393 499.030 0.556420
9494 691.261 0.758491
9595 768.164 0.829600
9696 −203.504 −0.216355
9797 903.154 0.945376 0.472688 0.881230i 0.343284π-0.343284\pi
0.472688 + 0.881230i 0.343284π0.343284\pi
9898 −814.728 −0.839796
9999 −544.290 −0.552558
100100 −347.308 −0.347308
101101 1647.75 1.62334 0.811669 0.584118i 0.198559π-0.198559\pi
0.811669 + 0.584118i 0.198559π0.198559\pi
102102 1394.70 1.35388
103103 −893.871 −0.855104 −0.427552 0.903991i 0.640624π-0.640624\pi
−0.427552 + 0.903991i 0.640624π0.640624\pi
104104 −563.495 −0.531301
105105 −1076.31 −1.00036
106106 367.318 0.336576
107107 −328.384 −0.296693 −0.148346 0.988935i 0.547395π-0.547395\pi
−0.148346 + 0.988935i 0.547395π0.547395\pi
108108 −344.853 −0.307255
109109 −1566.74 −1.37675 −0.688376 0.725354i 0.741676π-0.741676\pi
−0.688376 + 0.725354i 0.741676π0.741676\pi
110110 500.299 0.433651
111111 −2619.90 −2.24027
112112 −438.284 −0.369768
113113 −572.155 −0.476317 −0.238158 0.971226i 0.576544π-0.576544\pi
−0.238158 + 0.971226i 0.576544π0.576544\pi
114114 −1581.36 −1.29919
115115 291.804 0.236616
116116 −1100.75 −0.881049
117117 946.912 0.748222
118118 −9.31667 −0.00726838
119119 3003.75 2.31389
120120 −314.335 −0.239122
121121 308.241 0.231586
122122 356.122 0.264277
123123 2334.43 1.71129
124124 313.880 0.227316
125125 −1308.76 −0.936472
126126 736.504 0.520738
127127 1310.29 0.915506 0.457753 0.889079i 0.348654π-0.348654\pi
0.457753 + 0.889079i 0.348654π0.348654\pi
128128 −128.000 −0.0883883
129129 −2057.46 −1.40426
130130 −870.380 −0.587210
131131 −553.665 −0.369267 −0.184633 0.982807i 0.559110π-0.559110\pi
−0.184633 + 0.982807i 0.559110π0.559110\pi
132132 −1029.92 −0.679117
133133 −3405.74 −2.22042
134134 369.835 0.238424
135135 −532.664 −0.339588
136136 877.237 0.553107
137137 2665.66 1.66235 0.831177 0.556009i 0.187668π-0.187668\pi
0.831177 + 0.556009i 0.187668π0.187668\pi
138138 −600.712 −0.370551
139139 131.133 0.0800185 0.0400093 0.999199i 0.487261π-0.487261\pi
0.0400093 + 0.999199i 0.487261π0.487261\pi
140140 −676.978 −0.408679
141141 −2198.04 −1.31283
142142 859.904 0.508180
143143 −2851.82 −1.66770
144144 215.094 0.124476
145145 −1700.22 −0.973763
146146 −1216.85 −0.689777
147147 2590.64 1.45355
148148 −1647.86 −0.915225
149149 −439.481 −0.241635 −0.120818 0.992675i 0.538552π-0.538552\pi
−0.120818 + 0.992675i 0.538552π0.538552\pi
150150 1104.35 0.601134
151151 −1887.85 −1.01742 −0.508711 0.860937i 0.669878π-0.669878\pi
−0.508711 + 0.860937i 0.669878π0.669878\pi
152152 −994.640 −0.530763
153153 −1474.13 −0.778931
154154 −2218.13 −1.16066
155155 484.821 0.251237
156156 1791.78 0.919597
157157 3238.51 1.64625 0.823126 0.567859i 0.192228π-0.192228\pi
0.823126 + 0.567859i 0.192228π0.192228\pi
158158 −1070.14 −0.538836
159159 −1167.98 −0.582560
160160 −197.710 −0.0976896
161161 −1293.74 −0.633300
162162 1822.49 0.883880
163163 −663.913 −0.319029 −0.159514 0.987196i 0.550993π-0.550993\pi
−0.159514 + 0.987196i 0.550993π0.550993\pi
164164 1468.31 0.699120
165165 −1590.83 −0.750581
166166 1202.31 0.562152
167167 −3567.76 −1.65318 −0.826591 0.562803i 0.809723π-0.809723\pi
−0.826591 + 0.562803i 0.809723π0.809723\pi
168168 1393.64 0.640009
169169 2764.36 1.25824
170170 1354.99 0.611311
171171 1671.42 0.747465
172172 −1294.10 −0.573686
173173 1103.31 0.484874 0.242437 0.970167i 0.422053π-0.422053\pi
0.242437 + 0.970167i 0.422053π0.422053\pi
174174 3500.10 1.52495
175175 2378.43 1.02739
176176 −647.801 −0.277442
177177 29.6247 0.0125804
178178 959.392 0.403986
179179 3368.29 1.40647 0.703233 0.710959i 0.251739π-0.251739\pi
0.703233 + 0.710959i 0.251739π0.251739\pi
180180 332.237 0.137575
181181 1780.04 0.730992 0.365496 0.930813i 0.380899π-0.380899\pi
0.365496 + 0.930813i 0.380899π0.380899\pi
182182 3858.93 1.57166
183183 −1132.38 −0.457421
184184 −377.835 −0.151383
185185 −2545.30 −1.01154
186186 −998.061 −0.393448
187187 4439.65 1.73615
188188 −1382.52 −0.536334
189189 2361.62 0.908904
190190 −1536.33 −0.586616
191191 −330.785 −0.125313 −0.0626564 0.998035i 0.519957π-0.519957\pi
−0.0626564 + 0.998035i 0.519957π0.519957\pi
192192 407.009 0.152986
193193 −1215.48 −0.453328 −0.226664 0.973973i 0.572782π-0.572782\pi
−0.226664 + 0.973973i 0.572782π0.572782\pi
194194 −1806.31 −0.668481
195195 2767.60 1.01637
196196 1629.46 0.593825
197197 1866.53 0.675051 0.337526 0.941316i 0.390410π-0.390410\pi
0.337526 + 0.941316i 0.390410π0.390410\pi
198198 1088.58 0.390717
199199 3625.79 1.29158 0.645792 0.763513i 0.276527π-0.276527\pi
0.645792 + 0.763513i 0.276527π0.276527\pi
200200 694.616 0.245584
201201 −1175.98 −0.412674
202202 −3295.50 −1.14787
203203 7538.12 2.60627
204204 −2789.40 −0.957339
205205 2267.96 0.772690
206206 1787.74 0.604650
207207 634.924 0.213190
208208 1126.99 0.375686
209209 −5033.81 −1.66601
210210 2152.62 0.707358
211211 −3798.32 −1.23928 −0.619638 0.784887i 0.712721π-0.712721\pi
−0.619638 + 0.784887i 0.712721π0.712721\pi
212212 −734.636 −0.237995
213213 −2734.28 −0.879578
214214 656.769 0.209793
215215 −1998.87 −0.634056
216216 689.707 0.217262
217217 −2149.51 −0.672434
218218 3133.47 0.973511
219219 3869.30 1.19389
220220 −1000.60 −0.306638
221221 −7723.74 −2.35093
222222 5239.79 1.58411
223223 −3788.32 −1.13760 −0.568800 0.822476i 0.692592π-0.692592\pi
−0.568800 + 0.822476i 0.692592π0.692592\pi
224224 876.569 0.261465
225225 −1167.25 −0.345852
226226 1144.31 0.336807
227227 −1698.92 −0.496745 −0.248373 0.968665i 0.579896π-0.579896\pi
−0.248373 + 0.968665i 0.579896π0.579896\pi
228228 3162.71 0.918665
229229 4577.02 1.32078 0.660388 0.750925i 0.270392π-0.270392\pi
0.660388 + 0.750925i 0.270392π0.270392\pi
230230 −583.608 −0.167313
231231 7053.12 2.00892
232232 2201.49 0.622995
233233 780.610 0.219483 0.109741 0.993960i 0.464998π-0.464998\pi
0.109741 + 0.993960i 0.464998π0.464998\pi
234234 −1893.82 −0.529073
235235 −2135.46 −0.592773
236236 18.6333 0.00513952
237237 3402.80 0.932639
238238 −6007.49 −1.63617
239239 −1222.46 −0.330854 −0.165427 0.986222i 0.552900π-0.552900\pi
−0.165427 + 0.986222i 0.552900π0.552900\pi
240240 628.669 0.169085
241241 1200.72 0.320934 0.160467 0.987041i 0.448700π-0.448700\pi
0.160467 + 0.987041i 0.448700π0.448700\pi
242242 −616.482 −0.163756
243243 −3467.32 −0.915346
244244 −712.245 −0.186872
245245 2516.87 0.656314
246246 −4668.87 −1.21007
247247 8757.42 2.25596
248248 −627.759 −0.160737
249249 −3823.05 −0.972996
250250 2617.52 0.662185
251251 −5592.27 −1.40630 −0.703150 0.711042i 0.748224π-0.748224\pi
−0.703150 + 0.711042i 0.748224π0.748224\pi
252252 −1473.01 −0.368217
253253 −1912.20 −0.475175
254254 −2620.58 −0.647361
255255 −4308.53 −1.05808
256256 256.000 0.0625000
257257 −1159.99 −0.281550 −0.140775 0.990042i 0.544959π-0.544959\pi
−0.140775 + 0.990042i 0.544959π0.544959\pi
258258 4114.91 0.992958
259259 11284.9 2.70737
260260 1740.76 0.415220
261261 −3699.44 −0.877355
262262 1107.33 0.261111
263263 2853.19 0.668954 0.334477 0.942404i 0.391440π-0.391440\pi
0.334477 + 0.942404i 0.391440π0.391440\pi
264264 2059.85 0.480208
265265 −1134.73 −0.263040
266266 6811.49 1.57007
267267 −3050.63 −0.699235
268268 −739.669 −0.168591
269269 269.000 0.0609711
270270 1065.33 0.240125
271271 5693.80 1.27629 0.638143 0.769918i 0.279703π-0.279703\pi
0.638143 + 0.769918i 0.279703π0.279703\pi
272272 −1754.47 −0.391105
273273 −12270.4 −2.72030
274274 −5331.31 −1.17546
275275 3515.41 0.770863
276276 1201.42 0.262019
277277 7862.07 1.70537 0.852683 0.522429i 0.174974π-0.174974\pi
0.852683 + 0.522429i 0.174974π0.174974\pi
278278 −262.267 −0.0565817
279279 1054.90 0.226363
280280 1353.96 0.288980
281281 6976.11 1.48099 0.740497 0.672059i 0.234590π-0.234590\pi
0.740497 + 0.672059i 0.234590π0.234590\pi
282282 4396.08 0.928309
283283 −3720.29 −0.781443 −0.390722 0.920509i 0.627774π-0.627774\pi
−0.390722 + 0.920509i 0.627774π0.627774\pi
284284 −1719.81 −0.359337
285285 4885.15 1.01534
286286 5703.64 1.17924
287287 −10055.3 −2.06810
288288 −430.189 −0.0880178
289289 7111.15 1.44741
290290 3400.44 0.688554
291291 5743.62 1.15703
292292 2433.71 0.487746
293293 4601.52 0.917487 0.458743 0.888569i 0.348300π-0.348300\pi
0.458743 + 0.888569i 0.348300π0.348300\pi
294294 −5181.27 −1.02782
295295 28.7812 0.00568036
296296 3295.72 0.647162
297297 3490.57 0.681964
298298 878.962 0.170862
299299 3326.70 0.643437
300300 −2208.71 −0.425066
301301 8862.23 1.69704
302302 3775.69 0.719426
303303 10478.9 1.98678
304304 1989.28 0.375306
305305 −1100.14 −0.206537
306306 2948.26 0.550788
307307 2573.22 0.478376 0.239188 0.970973i 0.423119π-0.423119\pi
0.239188 + 0.970973i 0.423119π0.423119\pi
308308 4436.26 0.820713
309309 −5684.58 −1.04655
310310 −969.642 −0.177652
311311 −2998.14 −0.546653 −0.273327 0.961921i 0.588124π-0.588124\pi
−0.273327 + 0.961921i 0.588124π0.588124\pi
312312 −3583.56 −0.650253
313313 7468.20 1.34865 0.674325 0.738435i 0.264435π-0.264435\pi
0.674325 + 0.738435i 0.264435π0.264435\pi
314314 −6477.03 −1.16408
315315 −2275.22 −0.406966
316316 2140.29 0.381015
317317 −8629.09 −1.52889 −0.764445 0.644689i 0.776987π-0.776987\pi
−0.764445 + 0.644689i 0.776987π0.776987\pi
318318 2335.96 0.411932
319319 11141.6 1.95552
320320 395.420 0.0690770
321321 −2088.37 −0.363119
322322 2587.49 0.447811
323323 −13633.4 −2.34855
324324 −3644.99 −0.624998
325325 −6115.82 −1.04383
326326 1327.83 0.225587
327327 −9963.67 −1.68499
328328 −2936.62 −0.494353
329329 9467.78 1.58655
330330 3181.66 0.530741
331331 −8905.99 −1.47891 −0.739453 0.673209i 0.764916π-0.764916\pi
−0.739453 + 0.673209i 0.764916π0.764916\pi
332332 −2404.62 −0.397502
333333 −5538.21 −0.911388
334334 7135.52 1.16898
335335 −1142.50 −0.186332
336336 −2787.28 −0.452555
337337 −3263.04 −0.527446 −0.263723 0.964598i 0.584950π-0.584950\pi
−0.263723 + 0.964598i 0.584950π0.584950\pi
338338 −5528.72 −0.889712
339339 −3638.62 −0.582959
340340 −2709.98 −0.432262
341341 −3177.05 −0.504537
342342 −3342.84 −0.528537
343343 −1763.11 −0.277548
344344 2588.19 0.405657
345345 1855.73 0.289592
346346 −2206.62 −0.342858
347347 −4533.53 −0.701362 −0.350681 0.936495i 0.614050π-0.614050\pi
−0.350681 + 0.936495i 0.614050π0.614050\pi
348348 −7000.20 −1.07831
349349 6669.32 1.02292 0.511462 0.859306i 0.329104π-0.329104\pi
0.511462 + 0.859306i 0.329104π0.329104\pi
350350 −4756.86 −0.726471
351351 −6072.60 −0.923452
352352 1295.60 0.196181
353353 −7899.51 −1.19107 −0.595536 0.803329i 0.703060π-0.703060\pi
−0.595536 + 0.803329i 0.703060π0.703060\pi
354354 −59.2495 −0.00889569
355355 −2656.43 −0.397151
356356 −1918.78 −0.285661
357357 19102.4 2.83194
358358 −6736.57 −0.994522
359359 −2084.92 −0.306513 −0.153256 0.988186i 0.548976π-0.548976\pi
−0.153256 + 0.988186i 0.548976π0.548976\pi
360360 −664.473 −0.0972800
361361 8598.94 1.25367
362362 −3560.08 −0.516889
363363 1960.26 0.283435
364364 −7717.85 −1.11133
365365 3759.12 0.539073
366366 2264.77 0.323446
367367 −8620.84 −1.22617 −0.613085 0.790017i 0.710072π-0.710072\pi
−0.613085 + 0.790017i 0.710072π0.710072\pi
368368 755.671 0.107044
369369 4934.77 0.696189
370370 5090.60 0.715264
371371 5030.93 0.704024
372372 1996.12 0.278210
373373 8148.00 1.13107 0.565533 0.824726i 0.308671π-0.308671\pi
0.565533 + 0.824726i 0.308671π0.308671\pi
374374 −8879.30 −1.22764
375375 −8323.07 −1.14614
376376 2765.04 0.379245
377377 −19383.3 −2.64798
378378 −4723.25 −0.642692
379379 −6970.22 −0.944686 −0.472343 0.881415i 0.656592π-0.656592\pi
−0.472343 + 0.881415i 0.656592π0.656592\pi
380380 3072.66 0.414800
381381 8332.79 1.12048
382382 661.569 0.0886095
383383 −1444.60 −0.192730 −0.0963649 0.995346i 0.530722π-0.530722\pi
−0.0963649 + 0.995346i 0.530722π0.530722\pi
384384 −814.018 −0.108178
385385 6852.29 0.907078
386386 2430.96 0.320551
387387 −4349.27 −0.571281
388388 3612.62 0.472688
389389 −12982.9 −1.69219 −0.846094 0.533033i 0.821052π-0.821052\pi
−0.846094 + 0.533033i 0.821052π0.821052\pi
390390 −5535.19 −0.718680
391391 −5178.93 −0.669845
392392 −3258.91 −0.419898
393393 −3521.04 −0.451942
394394 −3733.07 −0.477333
395395 3305.91 0.421109
396396 −2177.16 −0.276279
397397 −2000.41 −0.252890 −0.126445 0.991974i 0.540357π-0.540357\pi
−0.126445 + 0.991974i 0.540357π0.540357\pi
398398 −7251.57 −0.913288
399399 −21658.9 −2.71754
400400 −1389.23 −0.173654
401401 −10956.7 −1.36447 −0.682236 0.731132i 0.738992π-0.738992\pi
−0.682236 + 0.731132i 0.738992π0.738992\pi
402402 2351.97 0.291805
403403 5527.18 0.683197
404404 6590.99 0.811669
405405 −5630.08 −0.690767
406406 −15076.2 −1.84291
407407 16679.5 2.03138
408408 5578.80 0.676941
409409 7376.63 0.891812 0.445906 0.895080i 0.352882π-0.352882\pi
0.445906 + 0.895080i 0.352882π0.352882\pi
410410 −4535.93 −0.546374
411411 16952.3 2.03454
412412 −3575.48 −0.427552
413413 −127.605 −0.0152034
414414 −1269.85 −0.150748
415415 −3714.19 −0.439331
416416 −2253.98 −0.265650
417417 833.944 0.0979338
418418 10067.6 1.17805
419419 678.679 0.0791304 0.0395652 0.999217i 0.487403π-0.487403\pi
0.0395652 + 0.999217i 0.487403π0.487403\pi
420420 −4305.25 −0.500178
421421 −30.7798 −0.00356322 −0.00178161 0.999998i 0.500567π-0.500567\pi
−0.00178161 + 0.999998i 0.500567π0.500567\pi
422422 7596.65 0.876301
423423 −4646.45 −0.534085
424424 1469.27 0.168288
425425 9520.98 1.08667
426426 5468.57 0.621956
427427 4877.59 0.552794
428428 −1313.54 −0.148346
429429 −18136.2 −2.04108
430430 3997.75 0.448345
431431 10181.0 1.13783 0.568914 0.822397i 0.307364π-0.307364\pi
0.568914 + 0.822397i 0.307364π0.307364\pi
432432 −1379.41 −0.153628
433433 −3149.27 −0.349525 −0.174762 0.984611i 0.555916π-0.555916\pi
−0.174762 + 0.984611i 0.555916π0.555916\pi
434434 4299.02 0.475483
435435 −10812.6 −1.19178
436436 −6266.94 −0.688376
437437 5872.03 0.642786
438438 −7738.59 −0.844211
439439 9021.45 0.980798 0.490399 0.871498i 0.336851π-0.336851\pi
0.490399 + 0.871498i 0.336851π0.336851\pi
440440 2001.20 0.216826
441441 5476.36 0.591336
442442 15447.5 1.66236
443443 −6946.79 −0.745038 −0.372519 0.928025i 0.621506π-0.621506\pi
−0.372519 + 0.928025i 0.621506π0.621506\pi
444444 −10479.6 −1.12013
445445 −2963.77 −0.315722
446446 7576.64 0.804405
447447 −2794.88 −0.295735
448448 −1753.14 −0.184884
449449 −1814.13 −0.190677 −0.0953384 0.995445i 0.530393π-0.530393\pi
−0.0953384 + 0.995445i 0.530393π0.530393\pi
450450 2334.50 0.244554
451451 −14862.1 −1.55172
452452 −2288.62 −0.238158
453453 −12005.8 −1.24521
454454 3397.84 0.351252
455455 −11921.1 −1.22828
456456 −6325.42 −0.649595
457457 −7242.82 −0.741368 −0.370684 0.928759i 0.620877π-0.620877\pi
−0.370684 + 0.928759i 0.620877π0.620877\pi
458458 −9154.03 −0.933930
459459 9453.70 0.961353
460460 1167.22 0.118308
461461 −10017.5 −1.01207 −0.506033 0.862514i 0.668888π-0.668888\pi
−0.506033 + 0.862514i 0.668888π0.668888\pi
462462 −14106.2 −1.42052
463463 9661.74 0.969804 0.484902 0.874568i 0.338855π-0.338855\pi
0.484902 + 0.874568i 0.338855π0.338855\pi
464464 −4402.98 −0.440524
465465 3083.23 0.307486
466466 −1561.22 −0.155198
467467 −13821.0 −1.36950 −0.684751 0.728777i 0.740089π-0.740089\pi
−0.684751 + 0.728777i 0.740089π0.740089\pi
468468 3787.65 0.374111
469469 5065.40 0.498717
470470 4270.91 0.419154
471471 20595.4 2.01483
472472 −37.2667 −0.00363419
473473 13098.7 1.27332
474474 −6805.59 −0.659475
475475 −10795.2 −1.04277
476476 12015.0 1.15695
477477 −2469.00 −0.236998
478478 2444.91 0.233949
479479 7605.97 0.725523 0.362762 0.931882i 0.381834π-0.381834\pi
0.362762 + 0.931882i 0.381834π0.381834\pi
480480 −1257.34 −0.119561
481481 −29017.6 −2.75070
482482 −2401.44 −0.226935
483483 −8227.59 −0.775089
484484 1232.96 0.115793
485485 5580.08 0.522430
486486 6934.65 0.647247
487487 14839.7 1.38081 0.690403 0.723425i 0.257433π-0.257433\pi
0.690403 + 0.723425i 0.257433π0.257433\pi
488488 1424.49 0.132139
489489 −4222.16 −0.390456
490490 −5033.74 −0.464084
491491 19099.2 1.75547 0.877734 0.479148i 0.159054π-0.159054\pi
0.877734 + 0.479148i 0.159054π0.159054\pi
492492 9337.73 0.855645
493493 30175.5 2.75666
494494 −17514.8 −1.59520
495495 −3362.86 −0.305352
496496 1255.52 0.113658
497497 11777.6 1.06297
498498 7646.10 0.688012
499499 −14020.5 −1.25780 −0.628900 0.777486i 0.716494π-0.716494\pi
−0.628900 + 0.777486i 0.716494π0.716494\pi
500500 −5235.04 −0.468236
501501 −22689.2 −2.02331
502502 11184.5 0.994404
503503 4852.50 0.430144 0.215072 0.976598i 0.431001π-0.431001\pi
0.215072 + 0.976598i 0.431001π0.431001\pi
504504 2946.02 0.260369
505505 10180.5 0.897082
506506 3824.41 0.335999
507507 17580.0 1.53995
508508 5241.15 0.457753
509509 19208.0 1.67266 0.836328 0.548230i 0.184698π-0.184698\pi
0.836328 + 0.548230i 0.184698π0.184698\pi
510510 8617.06 0.748177
511511 −16666.5 −1.44282
512512 −512.000 −0.0441942
513513 −10718.9 −0.922517
514514 2319.99 0.199086
515515 −5522.72 −0.472544
516516 −8229.82 −0.702128
517517 13993.7 1.19041
518518 −22569.7 −1.91440
519519 7016.52 0.593432
520520 −3481.52 −0.293605
521521 −17217.0 −1.44778 −0.723888 0.689917i 0.757647π-0.757647\pi
−0.723888 + 0.689917i 0.757647π0.757647\pi
522522 7398.88 0.620383
523523 −2732.00 −0.228417 −0.114209 0.993457i 0.536433π-0.536433\pi
−0.114209 + 0.993457i 0.536433π0.536433\pi
524524 −2214.66 −0.184633
525525 15125.7 1.25741
526526 −5706.37 −0.473022
527527 −8604.59 −0.711237
528528 −4119.70 −0.339558
529529 −9936.38 −0.816667
530530 2269.45 0.185997
531531 62.6239 0.00511797
532532 −13623.0 −1.11021
533533 25855.8 2.10120
534534 6101.26 0.494434
535535 −2028.90 −0.163957
536536 1479.34 0.119212
537537 21420.7 1.72136
538538 −538.000 −0.0431131
539539 −16493.2 −1.31802
540540 −2130.65 −0.169794
541541 14736.7 1.17113 0.585565 0.810626i 0.300873π-0.300873\pi
0.585565 + 0.810626i 0.300873π0.300873\pi
542542 −11387.6 −0.902471
543543 11320.2 0.894653
544544 3508.95 0.276553
545545 −9679.97 −0.760815
546546 24540.9 1.92354
547547 19894.1 1.55505 0.777525 0.628852i 0.216475π-0.216475\pi
0.777525 + 0.628852i 0.216475π0.216475\pi
548548 10662.6 0.831177
549549 −2393.75 −0.186089
550550 −7030.82 −0.545082
551551 −34213.9 −2.64530
552552 −2402.85 −0.185275
553553 −14657.1 −1.12710
554554 −15724.1 −1.20588
555555 −16186.9 −1.23801
556556 524.533 0.0400093
557557 9446.18 0.718577 0.359288 0.933227i 0.383019π-0.383019\pi
0.359288 + 0.933227i 0.383019π0.383019\pi
558558 −2109.80 −0.160063
559559 −22788.1 −1.72421
560560 −2707.91 −0.204339
561561 28234.0 2.12485
562562 −13952.2 −1.04722
563563 −3008.57 −0.225215 −0.112608 0.993640i 0.535920π-0.535920\pi
−0.112608 + 0.993640i 0.535920π0.535920\pi
564564 −8792.17 −0.656413
565565 −3535.02 −0.263220
566566 7440.58 0.552564
567567 24961.6 1.84883
568568 3439.62 0.254090
569569 −12918.2 −0.951776 −0.475888 0.879506i 0.657873π-0.657873\pi
−0.475888 + 0.879506i 0.657873π0.657873\pi
570570 −9770.30 −0.717953
571571 14536.3 1.06537 0.532684 0.846314i 0.321183π-0.321183\pi
0.532684 + 0.846314i 0.321183π0.321183\pi
572572 −11407.3 −0.833850
573573 −2103.63 −0.153369
574574 20110.5 1.46236
575575 −4100.79 −0.297417
576576 860.378 0.0622380
577577 7050.72 0.508709 0.254355 0.967111i 0.418137π-0.418137\pi
0.254355 + 0.967111i 0.418137π0.418137\pi
578578 −14222.3 −1.02348
579579 −7729.87 −0.554823
580580 −6800.88 −0.486881
581581 16467.3 1.17587
582582 −11487.2 −0.818147
583583 7435.90 0.528240
584584 −4867.41 −0.344889
585585 5850.43 0.413480
586586 −9203.04 −0.648761
587587 11549.5 0.812092 0.406046 0.913853i 0.366907π-0.366907\pi
0.406046 + 0.913853i 0.366907π0.366907\pi
588588 10362.5 0.726776
589589 9756.16 0.682505
590590 −57.5624 −0.00401662
591591 11870.3 0.826188
592592 −6591.44 −0.457613
593593 −27141.0 −1.87950 −0.939752 0.341858i 0.888944π-0.888944\pi
−0.939752 + 0.341858i 0.888944π0.888944\pi
594594 −6981.13 −0.482221
595595 18558.4 1.27869
596596 −1757.92 −0.120818
597597 23058.2 1.58076
598598 −6653.39 −0.454979
599599 24871.7 1.69655 0.848274 0.529558i 0.177642π-0.177642\pi
0.848274 + 0.529558i 0.177642π0.177642\pi
600600 4417.42 0.300567
601601 17802.6 1.20829 0.604145 0.796875i 0.293515π-0.293515\pi
0.604145 + 0.796875i 0.293515π0.293515\pi
602602 −17724.5 −1.19999
603603 −2485.92 −0.167884
604604 −7551.39 −0.508711
605605 1904.45 0.127978
606606 −20957.8 −1.40487
607607 −13047.0 −0.872427 −0.436214 0.899843i 0.643681π-0.643681\pi
−0.436214 + 0.899843i 0.643681π0.643681\pi
608608 −3978.56 −0.265381
609609 47938.7 3.18978
610610 2200.28 0.146044
611611 −24345.2 −1.61195
612612 −5896.53 −0.389466
613613 15441.5 1.01742 0.508708 0.860939i 0.330123π-0.330123\pi
0.508708 + 0.860939i 0.330123π0.330123\pi
614614 −5146.45 −0.338263
615615 14423.1 0.945686
616616 −8872.53 −0.580332
617617 7104.35 0.463550 0.231775 0.972769i 0.425547π-0.425547\pi
0.231775 + 0.972769i 0.425547π0.425547\pi
618618 11369.2 0.740024
619619 −2739.51 −0.177884 −0.0889420 0.996037i 0.528349π-0.528349\pi
−0.0889420 + 0.996037i 0.528349π0.528349\pi
620620 1939.28 0.125619
621621 −4071.81 −0.263118
622622 5996.29 0.386542
623623 13140.2 0.845026
624624 7167.11 0.459798
625625 2767.29 0.177107
626626 −14936.4 −0.953640
627627 −32012.6 −2.03901
628628 12954.1 0.823126
629629 45173.9 2.86360
630630 4550.44 0.287768
631631 −11035.2 −0.696205 −0.348103 0.937456i 0.613174π-0.613174\pi
−0.348103 + 0.937456i 0.613174π0.613174\pi
632632 −4280.58 −0.269418
633633 −24155.5 −1.51674
634634 17258.2 1.08109
635635 8095.53 0.505923
636636 −4671.93 −0.291280
637637 28693.5 1.78474
638638 −22283.2 −1.38276
639639 −5780.02 −0.357831
640640 −790.839 −0.0488448
641641 9542.16 0.587976 0.293988 0.955809i 0.405017π-0.405017\pi
0.293988 + 0.955809i 0.405017π0.405017\pi
642642 4176.73 0.256764
643643 −11642.5 −0.714053 −0.357026 0.934094i 0.616209π-0.616209\pi
−0.357026 + 0.934094i 0.616209π0.616209\pi
644644 −5174.98 −0.316650
645645 −12711.9 −0.776014
646646 27266.7 1.66067
647647 25181.2 1.53010 0.765051 0.643969i 0.222714π-0.222714\pi
0.765051 + 0.643969i 0.222714π0.222714\pi
648648 7289.97 0.441940
649649 −188.605 −0.0114074
650650 12231.6 0.738100
651651 −13669.8 −0.822984
652652 −2655.65 −0.159514
653653 1039.40 0.0622890 0.0311445 0.999515i 0.490085π-0.490085\pi
0.0311445 + 0.999515i 0.490085π0.490085\pi
654654 19927.3 1.19147
655655 −3420.78 −0.204063
656656 5873.24 0.349560
657657 8179.32 0.485701
658658 −18935.6 −1.12186
659659 −12230.6 −0.722967 −0.361483 0.932379i 0.617730π-0.617730\pi
−0.361483 + 0.932379i 0.617730π0.617730\pi
660660 −6363.32 −0.375291
661661 −10681.1 −0.628514 −0.314257 0.949338i 0.601755π-0.601755\pi
−0.314257 + 0.949338i 0.601755π0.601755\pi
662662 17812.0 1.04574
663663 −49119.2 −2.87727
664664 4809.24 0.281076
665665 −21042.2 −1.22704
666666 11076.4 0.644449
667667 −12996.9 −0.754485
668668 −14271.0 −0.826591
669669 −24091.9 −1.39230
670670 2285.00 0.131757
671671 7209.26 0.414770
672672 5574.55 0.320004
673673 −20703.6 −1.18583 −0.592916 0.805264i 0.702023π-0.702023\pi
−0.592916 + 0.805264i 0.702023π0.702023\pi
674674 6526.08 0.372960
675675 7485.64 0.426848
676676 11057.4 0.629122
677677 −667.158 −0.0378744 −0.0189372 0.999821i 0.506028π-0.506028\pi
−0.0189372 + 0.999821i 0.506028π0.506028\pi
678678 7277.25 0.412214
679679 −24739.9 −1.39828
680680 5419.95 0.305655
681681 −10804.3 −0.607961
682682 6354.11 0.356761
683683 −9663.02 −0.541354 −0.270677 0.962670i 0.587248π-0.587248\pi
−0.270677 + 0.962670i 0.587248π0.587248\pi
684684 6685.67 0.373732
685685 16469.6 0.918643
686686 3526.22 0.196256
687687 29107.6 1.61648
688688 −5176.39 −0.286843
689689 −12936.4 −0.715293
690690 −3711.46 −0.204772
691691 −20862.9 −1.14857 −0.574286 0.818655i 0.694720π-0.694720\pi
−0.574286 + 0.818655i 0.694720π0.694720\pi
692692 4413.24 0.242437
693693 14909.6 0.817272
694694 9067.05 0.495937
695695 810.198 0.0442195
696696 14000.4 0.762477
697697 −40251.7 −2.18744
698698 −13338.6 −0.723316
699699 4964.30 0.268622
700700 9513.73 0.513693
701701 25666.5 1.38290 0.691448 0.722426i 0.256973π-0.256973\pi
0.691448 + 0.722426i 0.256973π0.256973\pi
702702 12145.2 0.652979
703703 −51219.6 −2.74792
704704 −2591.20 −0.138721
705705 −13580.5 −0.725489
706706 15799.0 0.842215
707707 −45136.4 −2.40103
708708 118.499 0.00629020
709709 −18647.3 −0.987750 −0.493875 0.869533i 0.664420π-0.664420\pi
−0.493875 + 0.869533i 0.664420π0.664420\pi
710710 5312.86 0.280828
711711 7193.19 0.379417
712712 3837.57 0.201993
713713 3706.09 0.194662
714714 −38204.7 −2.00249
715715 −17619.8 −0.921597
716716 13473.1 0.703233
717717 −7774.23 −0.404929
718718 4169.85 0.216737
719719 10863.7 0.563486 0.281743 0.959490i 0.409087π-0.409087\pi
0.281743 + 0.959490i 0.409087π0.409087\pi
720720 1328.95 0.0687874
721721 24485.6 1.26476
722722 −17197.9 −0.886481
723723 7636.00 0.392788
724724 7120.17 0.365496
725725 23893.6 1.22398
726726 −3920.52 −0.200419
727727 −25838.8 −1.31817 −0.659085 0.752068i 0.729056π-0.729056\pi
−0.659085 + 0.752068i 0.729056π0.729056\pi
728728 15435.7 0.785831
729729 2553.17 0.129714
730730 −7518.24 −0.381182
731731 35475.9 1.79497
732732 −4529.53 −0.228711
733733 −13280.0 −0.669179 −0.334589 0.942364i 0.608598π-0.608598\pi
−0.334589 + 0.942364i 0.608598π0.608598\pi
734734 17241.7 0.867033
735735 16006.1 0.803256
736736 −1511.34 −0.0756913
737737 7486.84 0.374195
738738 −9869.53 −0.492280
739739 −25232.1 −1.25599 −0.627995 0.778217i 0.716124π-0.716124\pi
−0.627995 + 0.778217i 0.716124π0.716124\pi
740740 −10181.2 −0.505768
741741 55692.9 2.76104
742742 −10061.9 −0.497820
743743 −29048.3 −1.43429 −0.717146 0.696923i 0.754552π-0.754552\pi
−0.717146 + 0.696923i 0.754552π0.754552\pi
744744 −3992.24 −0.196724
745745 −2715.30 −0.133532
746746 −16296.0 −0.799784
747747 −8081.56 −0.395835
748748 17758.6 0.868073
749749 8995.36 0.438830
750750 16646.1 0.810441
751751 −33303.9 −1.61821 −0.809106 0.587662i 0.800048π-0.800048\pi
−0.809106 + 0.587662i 0.800048π0.800048\pi
752752 −5530.09 −0.268167
753753 −35564.1 −1.72115
754754 38766.6 1.87241
755755 −11663.9 −0.562244
756756 9446.49 0.454452
757757 22528.3 1.08164 0.540821 0.841137i 0.318113π-0.318113\pi
0.540821 + 0.841137i 0.318113π0.318113\pi
758758 13940.4 0.667994
759759 −12160.7 −0.581561
760760 −6145.32 −0.293308
761761 18284.3 0.870967 0.435484 0.900197i 0.356577π-0.356577\pi
0.435484 + 0.900197i 0.356577π0.356577\pi
762762 −16665.6 −0.792297
763763 42917.2 2.03631
764764 −1323.14 −0.0626564
765765 −9107.82 −0.430450
766766 2889.20 0.136281
767767 328.119 0.0154468
768768 1628.04 0.0764930
769769 −3298.29 −0.154667 −0.0773337 0.997005i 0.524641π-0.524641\pi
−0.0773337 + 0.997005i 0.524641π0.524641\pi
770770 −13704.6 −0.641401
771771 −7377.00 −0.344586
772772 −4861.93 −0.226664
773773 −21641.1 −1.00695 −0.503477 0.864009i 0.667946π-0.667946\pi
−0.503477 + 0.864009i 0.667946π0.667946\pi
774774 8698.53 0.403956
775775 −6813.30 −0.315795
776776 −7225.23 −0.334241
777777 71766.3 3.31351
778778 25965.9 1.19656
779779 45638.7 2.09907
780780 11070.4 0.508184
781781 17407.7 0.797563
782782 10357.9 0.473652
783783 23724.7 1.08283
784784 6517.82 0.296913
785785 20008.9 0.909745
786786 7042.08 0.319571
787787 −20051.8 −0.908220 −0.454110 0.890946i 0.650043π-0.650043\pi
−0.454110 + 0.890946i 0.650043π0.650043\pi
788788 7466.14 0.337526
789789 18144.9 0.818726
790790 −6611.81 −0.297769
791791 15672.9 0.704506
792792 4354.32 0.195359
793793 −12542.1 −0.561643
794794 4000.81 0.178821
795795 −7216.30 −0.321932
796796 14503.1 0.645792
797797 −21663.1 −0.962794 −0.481397 0.876503i 0.659871π-0.659871\pi
−0.481397 + 0.876503i 0.659871π0.659871\pi
798798 43317.7 1.92159
799799 37900.0 1.67811
800800 2778.46 0.122792
801801 −6448.74 −0.284463
802802 21913.5 0.964827
803803 −24633.7 −1.08257
804804 −4703.93 −0.206337
805805 −7993.32 −0.349972
806806 −11054.4 −0.483093
807807 1710.71 0.0746218
808808 −13182.0 −0.573937
809809 −11734.5 −0.509968 −0.254984 0.966945i 0.582070π-0.582070\pi
−0.254984 + 0.966945i 0.582070π0.582070\pi
810810 11260.2 0.488446
811811 19350.0 0.837818 0.418909 0.908028i 0.362413π-0.362413\pi
0.418909 + 0.908028i 0.362413π0.362413\pi
812812 30152.5 1.30313
813813 36209.8 1.56203
814814 −33358.9 −1.43640
815815 −4101.94 −0.176300
816816 −11157.6 −0.478669
817817 −40223.8 −1.72246
818818 −14753.3 −0.630606
819819 −25938.5 −1.10667
820820 9071.85 0.386345
821821 −27906.0 −1.18627 −0.593134 0.805104i 0.702110π-0.702110\pi
−0.593134 + 0.805104i 0.702110π0.702110\pi
822822 −33904.5 −1.43863
823823 −22165.0 −0.938788 −0.469394 0.882989i 0.655528π-0.655528\pi
−0.469394 + 0.882989i 0.655528π0.655528\pi
824824 7150.97 0.302325
825825 22356.3 0.943450
826826 255.209 0.0107505
827827 −41485.3 −1.74436 −0.872179 0.489186i 0.837294π-0.837294\pi
−0.872179 + 0.489186i 0.837294π0.837294\pi
828828 2539.70 0.106595
829829 −37169.9 −1.55725 −0.778626 0.627488i 0.784083π-0.784083\pi
−0.778626 + 0.627488i 0.784083π0.784083\pi
830830 7428.39 0.310654
831831 49998.9 2.08718
832832 4507.96 0.187843
833833 −44669.4 −1.85799
834834 −1667.89 −0.0692497
835835 −22043.2 −0.913575
836836 −20135.3 −0.833005
837837 −6765.15 −0.279376
838838 −1357.36 −0.0559536
839839 −30671.4 −1.26209 −0.631046 0.775746i 0.717374π-0.717374\pi
−0.631046 + 0.775746i 0.717374π0.717374\pi
840840 8610.50 0.353679
841841 51338.5 2.10499
842842 61.5596 0.00251958
843843 44364.6 1.81257
844844 −15193.3 −0.619638
845845 17079.4 0.695325
846846 9292.90 0.377655
847847 −8443.57 −0.342532
848848 −2938.55 −0.118998
849849 −23659.2 −0.956400
850850 −19042.0 −0.768393
851851 −19456.9 −0.783752
852852 −10937.1 −0.439789
853853 30642.8 1.23000 0.614999 0.788528i 0.289156π-0.289156\pi
0.614999 + 0.788528i 0.289156π0.289156\pi
854854 −9755.18 −0.390885
855855 10326.7 0.413061
856856 2627.08 0.104897
857857 27495.8 1.09596 0.547980 0.836491i 0.315397π-0.315397\pi
0.547980 + 0.836491i 0.315397π0.315397\pi
858858 36272.3 1.44326
859859 17570.5 0.697902 0.348951 0.937141i 0.386538π-0.386538\pi
0.348951 + 0.937141i 0.386538π0.386538\pi
860860 −7995.49 −0.317028
861861 −63946.6 −2.53112
862862 −20362.1 −0.804566
863863 −36296.2 −1.43168 −0.715839 0.698265i 0.753956π-0.753956\pi
−0.715839 + 0.698265i 0.753956π0.753956\pi
864864 2758.83 0.108631
865865 6816.73 0.267949
866866 6298.53 0.247151
867867 45223.4 1.77147
868868 −8598.03 −0.336217
869869 −21663.7 −0.845676
870870 21625.1 0.842714
871871 −13025.0 −0.506700
872872 12533.9 0.486756
873873 12141.5 0.470706
874874 −11744.1 −0.454518
875875 35850.5 1.38511
876876 15477.2 0.596947
877877 21916.4 0.843858 0.421929 0.906629i 0.361353π-0.361353\pi
0.421929 + 0.906629i 0.361353π0.361353\pi
878878 −18042.9 −0.693529
879879 29263.4 1.12290
880880 −4002.39 −0.153319
881881 −21877.8 −0.836644 −0.418322 0.908299i 0.637382π-0.637382\pi
−0.418322 + 0.908299i 0.637382π0.637382\pi
882882 −10952.7 −0.418137
883883 −39950.2 −1.52257 −0.761285 0.648417i 0.775431π-0.775431\pi
−0.761285 + 0.648417i 0.775431π0.775431\pi
884884 −30895.0 −1.17546
885885 183.035 0.00695213
886886 13893.6 0.526822
887887 −47496.9 −1.79796 −0.898980 0.437990i 0.855691π-0.855691\pi
−0.898980 + 0.437990i 0.855691π0.855691\pi
888888 20959.2 0.792054
889889 −35892.4 −1.35410
890890 5927.54 0.223249
891891 36894.1 1.38721
892892 −15153.3 −0.568800
893893 −42972.2 −1.61031
894894 5589.77 0.209116
895895 20810.7 0.777236
896896 3506.28 0.130733
897897 21156.2 0.787496
898898 3628.25 0.134829
899899 −21593.8 −0.801107
900900 −4669.00 −0.172926
901901 20139.1 0.744650
902902 29724.1 1.09723
903903 56359.4 2.07699
904904 4577.24 0.168403
905905 10997.9 0.403958
906906 24011.6 0.880498
907907 15797.8 0.578345 0.289173 0.957277i 0.406620π-0.406620\pi
0.289173 + 0.957277i 0.406620π0.406620\pi
908908 −6795.68 −0.248373
909909 22151.3 0.808266
910910 23842.1 0.868526
911911 48925.8 1.77935 0.889673 0.456598i 0.150932π-0.150932\pi
0.889673 + 0.456598i 0.150932π0.150932\pi
912912 12650.8 0.459333
913913 24339.3 0.882270
914914 14485.6 0.524226
915915 −6996.35 −0.252778
916916 18308.1 0.660388
917917 15166.4 0.546172
918918 −18907.4 −0.679779
919919 −55381.3 −1.98788 −0.993940 0.109927i 0.964938π-0.964938\pi
−0.993940 + 0.109927i 0.964938π0.964938\pi
920920 −2334.43 −0.0836564
921921 16364.4 0.585480
922922 20035.0 0.715638
923923 −30284.5 −1.07999
924924 28212.5 1.00446
925925 35769.7 1.27146
926926 −19323.5 −0.685755
927927 −12016.7 −0.425760
928928 8805.96 0.311498
929929 2585.64 0.0913154 0.0456577 0.998957i 0.485462π-0.485462\pi
0.0456577 + 0.998957i 0.485462π0.485462\pi
930930 −6166.45 −0.217426
931931 50647.6 1.78293
932932 3122.44 0.109741
933933 −19066.7 −0.669043
934934 27641.9 0.968384
935935 27430.1 0.959422
936936 −7575.29 −0.264537
937937 −23216.3 −0.809439 −0.404720 0.914441i 0.632631π-0.632631\pi
−0.404720 + 0.914441i 0.632631π0.632631\pi
938938 −10130.8 −0.352646
939939 47494.1 1.65060
940940 −8541.82 −0.296387
941941 −20316.7 −0.703830 −0.351915 0.936032i 0.614469π-0.614469\pi
−0.351915 + 0.936032i 0.614469π0.614469\pi
942942 −41190.7 −1.42470
943943 17336.8 0.598691
944944 74.5334 0.00256976
945945 14591.1 0.502275
946946 −26197.4 −0.900371
947947 −35872.2 −1.23093 −0.615464 0.788165i 0.711031π-0.711031\pi
−0.615464 + 0.788165i 0.711031π0.711031\pi
948948 13611.2 0.466319
949949 42855.7 1.46592
950950 21590.4 0.737352
951951 −54876.8 −1.87119
952952 −24030.0 −0.818084
953953 31515.4 1.07123 0.535616 0.844462i 0.320079π-0.320079\pi
0.535616 + 0.844462i 0.320079π0.320079\pi
954954 4938.00 0.167583
955955 −2043.73 −0.0692498
956956 −4889.83 −0.165427
957957 70855.3 2.39334
958958 −15211.9 −0.513022
959959 −73019.7 −2.45874
960960 2514.68 0.0845425
961961 −23633.5 −0.793309
962962 58035.1 1.94504
963963 −4414.60 −0.147724
964964 4802.88 0.160467
965965 −7509.78 −0.250516
966966 16455.2 0.548071
967967 36425.5 1.21134 0.605670 0.795716i 0.292905π-0.292905\pi
0.605670 + 0.795716i 0.292905π0.292905\pi
968968 −2465.93 −0.0818780
969969 −86701.5 −2.87436
970970 −11160.2 −0.369413
971971 4958.17 0.163867 0.0819337 0.996638i 0.473890π-0.473890\pi
0.0819337 + 0.996638i 0.473890π0.473890\pi
972972 −13869.3 −0.457673
973973 −3592.10 −0.118353
974974 −29679.5 −0.976377
975975 −38893.7 −1.27753
976976 −2848.98 −0.0934361
977977 −28872.8 −0.945469 −0.472734 0.881205i 0.656733π-0.656733\pi
−0.472734 + 0.881205i 0.656733π0.656733\pi
978978 8444.32 0.276094
979979 19421.7 0.634035
980980 10067.5 0.328157
981981 −21062.3 −0.685490
982982 −38198.4 −1.24130
983983 −20864.5 −0.676982 −0.338491 0.940970i 0.609916π-0.609916\pi
−0.338491 + 0.940970i 0.609916π0.609916\pi
984984 −18675.5 −0.605033
985985 11532.3 0.373044
986986 −60350.9 −1.94925
987987 60210.5 1.94176
988988 35029.7 1.12798
989989 −15279.9 −0.491275
990990 6725.72 0.215917
991991 −14583.2 −0.467457 −0.233729 0.972302i 0.575093π-0.575093\pi
−0.233729 + 0.972302i 0.575093π0.575093\pi
992992 −2511.04 −0.0803685
993993 −56637.8 −1.81002
994994 −23555.2 −0.751634
995995 22401.7 0.713750
996996 −15292.2 −0.486498
997997 −28556.6 −0.907117 −0.453559 0.891226i 0.649846π-0.649846\pi
−0.453559 + 0.891226i 0.649846π0.649846\pi
998998 28040.9 0.889399
999999 35516.9 1.12483
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.c.1.16 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
538.4.a.c.1.16 18 1.1 even 1 trivial