Properties

Label 275.4.a.k.1.6
Level 275275
Weight 44
Character 275.1
Self dual yes
Analytic conductor 16.22616.226
Analytic rank 00
Dimension 1010
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [275,4,Mod(1,275)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(275, 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("275.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 275=5211 275 = 5^{2} \cdot 11
Weight: k k == 4 4
Character orbit: [χ][\chi] == 275.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: 16.225525251616.2255252516
Analytic rank: 00
Dimension: 1010
Coefficient field: Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x1072x8+1771x617056x4+52892x23136 x^{10} - 72x^{8} + 1771x^{6} - 17056x^{4} + 52892x^{2} - 3136 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 2452 2^{4}\cdot 5^{2}
Twist minimal: no (minimal twist has level 55)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.6
Root 0.2458900.245890 of defining polynomial
Character χ\chi == 275.1

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+0.245890q2+2.52576q37.93954q4+0.621060q610.5016q73.91938q820.6205q9+11.0000q1120.0534q12+63.0258q132.58224q14+62.5526q16+133.900q175.07039q18+76.1851q1926.5245q21+2.70479q22169.684q239.89940q24+15.4974q26120.278q27+83.3777q28+202.349q29+191.639q31+46.7361q32+27.7833q33+32.9246q34+163.718q3621.5915q37+18.7332q38+159.188q39+305.966q416.52211q42285.731q4387.3349q4441.7236q46123.908q47+157.993q48232.717q49+338.198q51500.396q52+480.068q5329.5752q54+41.1597q56+192.425q57+49.7556q58+364.714q59+9.11965q61+47.1222q62+216.548q63488.929q64+6.83166q66+568.827q671063.10q68428.580q69157.805q71+80.8197q72+212.831q735.30915q74604.874q76115.517q77+39.1428q78+792.027q79+252.962q81+75.2340q82587.824q83+210.592q8470.2586q86+511.084q8743.1132q88+698.243q89661.871q91+1347.21q92+484.033q9330.4677q94+118.044q961837.23q9757.2228q98226.826q99+O(q100)q+0.245890 q^{2} +2.52576 q^{3} -7.93954 q^{4} +0.621060 q^{6} -10.5016 q^{7} -3.91938 q^{8} -20.6205 q^{9} +11.0000 q^{11} -20.0534 q^{12} +63.0258 q^{13} -2.58224 q^{14} +62.5526 q^{16} +133.900 q^{17} -5.07039 q^{18} +76.1851 q^{19} -26.5245 q^{21} +2.70479 q^{22} -169.684 q^{23} -9.89940 q^{24} +15.4974 q^{26} -120.278 q^{27} +83.3777 q^{28} +202.349 q^{29} +191.639 q^{31} +46.7361 q^{32} +27.7833 q^{33} +32.9246 q^{34} +163.718 q^{36} -21.5915 q^{37} +18.7332 q^{38} +159.188 q^{39} +305.966 q^{41} -6.52211 q^{42} -285.731 q^{43} -87.3349 q^{44} -41.7236 q^{46} -123.908 q^{47} +157.993 q^{48} -232.717 q^{49} +338.198 q^{51} -500.396 q^{52} +480.068 q^{53} -29.5752 q^{54} +41.1597 q^{56} +192.425 q^{57} +49.7556 q^{58} +364.714 q^{59} +9.11965 q^{61} +47.1222 q^{62} +216.548 q^{63} -488.929 q^{64} +6.83166 q^{66} +568.827 q^{67} -1063.10 q^{68} -428.580 q^{69} -157.805 q^{71} +80.8197 q^{72} +212.831 q^{73} -5.30915 q^{74} -604.874 q^{76} -115.517 q^{77} +39.1428 q^{78} +792.027 q^{79} +252.962 q^{81} +75.2340 q^{82} -587.824 q^{83} +210.592 q^{84} -70.2586 q^{86} +511.084 q^{87} -43.1132 q^{88} +698.243 q^{89} -661.871 q^{91} +1347.21 q^{92} +484.033 q^{93} -30.4677 q^{94} +118.044 q^{96} -1837.23 q^{97} -57.2228 q^{98} -226.826 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+64q4+26q6+152q9+110q11+34q14+468q16+90q19+302q21+206q24+392q2658q29+1242q3166q34+1786q36384q39+416q41++1672q99+O(q100) 10 q + 64 q^{4} + 26 q^{6} + 152 q^{9} + 110 q^{11} + 34 q^{14} + 468 q^{16} + 90 q^{19} + 302 q^{21} + 206 q^{24} + 392 q^{26} - 58 q^{29} + 1242 q^{31} - 66 q^{34} + 1786 q^{36} - 384 q^{39} + 416 q^{41}+ \cdots + 1672 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 0.245890 0.0869354 0.0434677 0.999055i 0.486159π-0.486159\pi
0.0434677 + 0.999055i 0.486159π0.486159\pi
33 2.52576 0.486082 0.243041 0.970016i 0.421855π-0.421855\pi
0.243041 + 0.970016i 0.421855π0.421855\pi
44 −7.93954 −0.992442
55 0 0
66 0.621060 0.0422578
77 −10.5016 −0.567032 −0.283516 0.958967i 0.591501π-0.591501\pi
−0.283516 + 0.958967i 0.591501π0.591501\pi
88 −3.91938 −0.173214
99 −20.6205 −0.763724
1010 0 0
1111 11.0000 0.301511
1212 −20.0534 −0.482409
1313 63.0258 1.34463 0.672316 0.740265i 0.265300π-0.265300\pi
0.672316 + 0.740265i 0.265300π0.265300\pi
1414 −2.58224 −0.0492952
1515 0 0
1616 62.5526 0.977384
1717 133.900 1.91032 0.955160 0.296091i 0.0956832π-0.0956832\pi
0.955160 + 0.296091i 0.0956832π0.0956832\pi
1818 −5.07039 −0.0663946
1919 76.1851 0.919898 0.459949 0.887945i 0.347868π-0.347868\pi
0.459949 + 0.887945i 0.347868π0.347868\pi
2020 0 0
2121 −26.5245 −0.275624
2222 2.70479 0.0262120
2323 −169.684 −1.53833 −0.769163 0.639053i 0.779326π-0.779326\pi
−0.769163 + 0.639053i 0.779326π0.779326\pi
2424 −9.89940 −0.0841961
2525 0 0
2626 15.4974 0.116896
2727 −120.278 −0.857315
2828 83.3777 0.562747
2929 202.349 1.29570 0.647849 0.761769i 0.275669π-0.275669\pi
0.647849 + 0.761769i 0.275669π0.275669\pi
3030 0 0
3131 191.639 1.11030 0.555151 0.831750i 0.312660π-0.312660\pi
0.555151 + 0.831750i 0.312660π0.312660\pi
3232 46.7361 0.258183
3333 27.7833 0.146559
3434 32.9246 0.166074
3535 0 0
3636 163.718 0.757952
3737 −21.5915 −0.0959359 −0.0479679 0.998849i 0.515275π-0.515275\pi
−0.0479679 + 0.998849i 0.515275π0.515275\pi
3838 18.7332 0.0799717
3939 159.188 0.653602
4040 0 0
4141 305.966 1.16546 0.582729 0.812666i 0.301985π-0.301985\pi
0.582729 + 0.812666i 0.301985π0.301985\pi
4242 −6.52211 −0.0239615
4343 −285.731 −1.01334 −0.506670 0.862140i 0.669124π-0.669124\pi
−0.506670 + 0.862140i 0.669124π0.669124\pi
4444 −87.3349 −0.299233
4545 0 0
4646 −41.7236 −0.133735
4747 −123.908 −0.384548 −0.192274 0.981341i 0.561586π-0.561586\pi
−0.192274 + 0.981341i 0.561586π0.561586\pi
4848 157.993 0.475089
4949 −232.717 −0.678474
5050 0 0
5151 338.198 0.928573
5252 −500.396 −1.33447
5353 480.068 1.24420 0.622098 0.782939i 0.286280π-0.286280\pi
0.622098 + 0.782939i 0.286280π0.286280\pi
5454 −29.5752 −0.0745310
5555 0 0
5656 41.1597 0.0982178
5757 192.425 0.447146
5858 49.7556 0.112642
5959 364.714 0.804776 0.402388 0.915469i 0.368180π-0.368180\pi
0.402388 + 0.915469i 0.368180π0.368180\pi
6060 0 0
6161 9.11965 0.0191418 0.00957091 0.999954i 0.496953π-0.496953\pi
0.00957091 + 0.999954i 0.496953π0.496953\pi
6262 47.1222 0.0965245
6363 216.548 0.433056
6464 −488.929 −0.954939
6565 0 0
6666 6.83166 0.0127412
6767 568.827 1.03721 0.518607 0.855013i 0.326451π-0.326451\pi
0.518607 + 0.855013i 0.326451π0.326451\pi
6868 −1063.10 −1.89588
6969 −428.580 −0.747753
7070 0 0
7171 −157.805 −0.263775 −0.131887 0.991265i 0.542104π-0.542104\pi
−0.131887 + 0.991265i 0.542104π0.542104\pi
7272 80.8197 0.132287
7373 212.831 0.341232 0.170616 0.985338i 0.445424π-0.445424\pi
0.170616 + 0.985338i 0.445424π0.445424\pi
7474 −5.30915 −0.00834022
7575 0 0
7676 −604.874 −0.912945
7777 −115.517 −0.170967
7878 39.1428 0.0568211
7979 792.027 1.12798 0.563988 0.825783i 0.309267π-0.309267\pi
0.563988 + 0.825783i 0.309267π0.309267\pi
8080 0 0
8181 252.962 0.346998
8282 75.2340 0.101320
8383 −587.824 −0.777375 −0.388687 0.921370i 0.627071π-0.627071\pi
−0.388687 + 0.921370i 0.627071π0.627071\pi
8484 210.592 0.273541
8585 0 0
8686 −70.2586 −0.0880951
8787 511.084 0.629816
8888 −43.1132 −0.0522259
8989 698.243 0.831613 0.415807 0.909453i 0.363499π-0.363499\pi
0.415807 + 0.909453i 0.363499π0.363499\pi
9090 0 0
9191 −661.871 −0.762449
9292 1347.21 1.52670
9393 484.033 0.539698
9494 −30.4677 −0.0334309
9595 0 0
9696 118.044 0.125498
9797 −1837.23 −1.92312 −0.961558 0.274601i 0.911454π-0.911454\pi
−0.961558 + 0.274601i 0.911454π0.911454\pi
9898 −57.2228 −0.0589834
9999 −226.826 −0.230271
100100 0 0
101101 81.1351 0.0799331 0.0399666 0.999201i 0.487275π-0.487275\pi
0.0399666 + 0.999201i 0.487275π0.487275\pi
102102 83.1597 0.0807258
103103 17.0321 0.0162935 0.00814673 0.999967i 0.497407π-0.497407\pi
0.00814673 + 0.999967i 0.497407π0.497407\pi
104104 −247.022 −0.232909
105105 0 0
106106 118.044 0.108165
107107 128.189 0.115817 0.0579087 0.998322i 0.481557π-0.481557\pi
0.0579087 + 0.998322i 0.481557π0.481557\pi
108108 954.952 0.850836
109109 −206.739 −0.181670 −0.0908351 0.995866i 0.528954π-0.528954\pi
−0.0908351 + 0.995866i 0.528954π0.528954\pi
110110 0 0
111111 −54.5350 −0.0466327
112112 −656.901 −0.554208
113113 291.669 0.242814 0.121407 0.992603i 0.461259π-0.461259\pi
0.121407 + 0.992603i 0.461259π0.461259\pi
114114 47.3155 0.0388728
115115 0 0
116116 −1606.56 −1.28590
117117 −1299.63 −1.02693
118118 89.6797 0.0699635
119119 −1406.16 −1.08321
120120 0 0
121121 121.000 0.0909091
122122 2.24243 0.00166410
123123 772.795 0.566509
124124 −1521.52 −1.10191
125125 0 0
126126 53.2472 0.0376479
127127 1241.35 0.867336 0.433668 0.901073i 0.357219π-0.357219\pi
0.433668 + 0.901073i 0.357219π0.357219\pi
128128 −494.112 −0.341201
129129 −721.689 −0.492567
130130 0 0
131131 −2013.62 −1.34298 −0.671491 0.741013i 0.734346π-0.734346\pi
−0.671491 + 0.741013i 0.734346π0.734346\pi
132132 −220.587 −0.145452
133133 −800.064 −0.521612
134134 139.869 0.0901706
135135 0 0
136136 −524.803 −0.330894
137137 −214.973 −0.134061 −0.0670307 0.997751i 0.521353π-0.521353\pi
−0.0670307 + 0.997751i 0.521353π0.521353\pi
138138 −105.384 −0.0650062
139139 2073.76 1.26543 0.632714 0.774386i 0.281941π-0.281941\pi
0.632714 + 0.774386i 0.281941π0.281941\pi
140140 0 0
141141 −312.960 −0.186922
142142 −38.8028 −0.0229314
143143 693.284 0.405422
144144 −1289.87 −0.746451
145145 0 0
146146 52.3330 0.0296652
147147 −587.786 −0.329794
148148 171.427 0.0952108
149149 −357.210 −0.196401 −0.0982007 0.995167i 0.531309π-0.531309\pi
−0.0982007 + 0.995167i 0.531309π0.531309\pi
150150 0 0
151151 −1097.04 −0.591229 −0.295615 0.955307i 0.595524π-0.595524\pi
−0.295615 + 0.955307i 0.595524π0.595524\pi
152152 −298.598 −0.159339
153153 −2761.08 −1.45896
154154 −28.4046 −0.0148631
155155 0 0
156156 −1263.88 −0.648662
157157 804.745 0.409081 0.204540 0.978858i 0.434430π-0.434430\pi
0.204540 + 0.978858i 0.434430π0.434430\pi
158158 194.752 0.0980610
159159 1212.54 0.604782
160160 0 0
161161 1781.95 0.872280
162162 62.2008 0.0301664
163163 −2112.00 −1.01487 −0.507437 0.861689i 0.669407π-0.669407\pi
−0.507437 + 0.861689i 0.669407π0.669407\pi
164164 −2429.23 −1.15665
165165 0 0
166166 −144.540 −0.0675814
167167 −45.0510 −0.0208752 −0.0104376 0.999946i 0.503322π-0.503322\pi
−0.0104376 + 0.999946i 0.503322π0.503322\pi
168168 103.959 0.0477419
169169 1775.25 0.808034
170170 0 0
171171 −1570.98 −0.702548
172172 2268.58 1.00568
173173 1381.34 0.607058 0.303529 0.952822i 0.401835π-0.401835\pi
0.303529 + 0.952822i 0.401835π0.401835\pi
174174 125.671 0.0547533
175175 0 0
176176 688.078 0.294692
177177 921.180 0.391187
178178 171.691 0.0722966
179179 −92.1182 −0.0384650 −0.0192325 0.999815i 0.506122π-0.506122\pi
−0.0192325 + 0.999815i 0.506122π0.506122\pi
180180 0 0
181181 −759.559 −0.311920 −0.155960 0.987763i 0.549847π-0.549847\pi
−0.155960 + 0.987763i 0.549847π0.549847\pi
182182 −162.748 −0.0662838
183183 23.0340 0.00930450
184184 665.054 0.266459
185185 0 0
186186 119.019 0.0469189
187187 1472.90 0.575983
188188 983.769 0.381642
189189 1263.11 0.486125
190190 0 0
191191 1496.04 0.566752 0.283376 0.959009i 0.408546π-0.408546\pi
0.283376 + 0.959009i 0.408546π0.408546\pi
192192 −1234.92 −0.464179
193193 3483.32 1.29914 0.649572 0.760300i 0.274948π-0.274948\pi
0.649572 + 0.760300i 0.274948π0.274948\pi
194194 −451.757 −0.167187
195195 0 0
196196 1847.66 0.673347
197197 −1648.00 −0.596017 −0.298009 0.954563i 0.596322π-0.596322\pi
−0.298009 + 0.954563i 0.596322π0.596322\pi
198198 −55.7743 −0.0200187
199199 2761.91 0.983851 0.491925 0.870637i 0.336293π-0.336293\pi
0.491925 + 0.870637i 0.336293π0.336293\pi
200200 0 0
201201 1436.72 0.504171
202202 19.9503 0.00694902
203203 −2124.98 −0.734702
204204 −2685.14 −0.921555
205205 0 0
206206 4.18804 0.00141648
207207 3498.97 1.17486
208208 3942.42 1.31422
209209 838.036 0.277360
210210 0 0
211211 3345.09 1.09140 0.545701 0.837980i 0.316264π-0.316264\pi
0.545701 + 0.837980i 0.316264π0.316264\pi
212212 −3811.52 −1.23479
213213 −398.578 −0.128216
214214 31.5204 0.0100686
215215 0 0
216216 471.415 0.148499
217217 −2012.51 −0.629577
218218 −50.8352 −0.0157936
219219 537.559 0.165867
220220 0 0
221221 8439.13 2.56868
222222 −13.4096 −0.00405403
223223 −3935.15 −1.18169 −0.590846 0.806784i 0.701206π-0.701206\pi
−0.590846 + 0.806784i 0.701206π0.701206\pi
224224 −490.803 −0.146398
225225 0 0
226226 71.7187 0.0211091
227227 −3157.35 −0.923175 −0.461588 0.887095i 0.652720π-0.652720\pi
−0.461588 + 0.887095i 0.652720π0.652720\pi
228228 −1527.77 −0.443767
229229 3945.40 1.13851 0.569257 0.822160i 0.307231π-0.307231\pi
0.569257 + 0.822160i 0.307231π0.307231\pi
230230 0 0
231231 −291.769 −0.0831039
232232 −793.082 −0.224433
233233 144.268 0.0405636 0.0202818 0.999794i 0.493544π-0.493544\pi
0.0202818 + 0.999794i 0.493544π0.493544\pi
234234 −319.566 −0.0892763
235235 0 0
236236 −2895.66 −0.798693
237237 2000.47 0.548289
238238 −345.761 −0.0941695
239239 655.848 0.177503 0.0887517 0.996054i 0.471712π-0.471712\pi
0.0887517 + 0.996054i 0.471712π0.471712\pi
240240 0 0
241241 1949.94 0.521191 0.260595 0.965448i 0.416081π-0.416081\pi
0.260595 + 0.965448i 0.416081π0.416081\pi
242242 29.7527 0.00790322
243243 3886.43 1.02598
244244 −72.4058 −0.0189972
245245 0 0
246246 190.023 0.0492497
247247 4801.62 1.23692
248248 −751.105 −0.192320
249249 −1484.70 −0.377868
250250 0 0
251251 −6016.61 −1.51301 −0.756504 0.653989i 0.773094π-0.773094\pi
−0.756504 + 0.653989i 0.773094π0.773094\pi
252252 −1719.29 −0.429783
253253 −1866.52 −0.463823
254254 305.235 0.0754022
255255 0 0
256256 3789.93 0.925276
257257 649.498 0.157644 0.0788221 0.996889i 0.474884π-0.474884\pi
0.0788221 + 0.996889i 0.474884π0.474884\pi
258258 −177.456 −0.0428215
259259 226.745 0.0543987
260260 0 0
261261 −4172.54 −0.989555
262262 −495.130 −0.116753
263263 4534.73 1.06321 0.531604 0.846993i 0.321589π-0.321589\pi
0.531604 + 0.846993i 0.321589π0.321589\pi
264264 −108.893 −0.0253861
265265 0 0
266266 −196.728 −0.0453465
267267 1763.59 0.404233
268268 −4516.23 −1.02937
269269 −3873.76 −0.878019 −0.439009 0.898482i 0.644671π-0.644671\pi
−0.439009 + 0.898482i 0.644671π0.644671\pi
270270 0 0
271271 8052.53 1.80501 0.902503 0.430684i 0.141728π-0.141728\pi
0.902503 + 0.430684i 0.141728π0.141728\pi
272272 8375.77 1.86712
273273 −1671.73 −0.370613
274274 −52.8599 −0.0116547
275275 0 0
276276 3402.73 0.742101
277277 −6923.67 −1.50182 −0.750908 0.660407i 0.770384π-0.770384\pi
−0.750908 + 0.660407i 0.770384π0.770384\pi
278278 509.919 0.110010
279279 −3951.70 −0.847964
280280 0 0
281281 −1994.96 −0.423520 −0.211760 0.977322i 0.567920π-0.567920\pi
−0.211760 + 0.977322i 0.567920π0.567920\pi
282282 −76.9540 −0.0162501
283283 −4636.33 −0.973855 −0.486928 0.873442i 0.661882π-0.661882\pi
−0.486928 + 0.873442i 0.661882π0.661882\pi
284284 1252.90 0.261781
285285 0 0
286286 170.472 0.0352455
287287 −3213.12 −0.660853
288288 −963.724 −0.197181
289289 13016.1 2.64932
290290 0 0
291291 −4640.40 −0.934793
292292 −1689.78 −0.338653
293293 326.024 0.0650052 0.0325026 0.999472i 0.489652π-0.489652\pi
0.0325026 + 0.999472i 0.489652π0.489652\pi
294294 −144.531 −0.0286708
295295 0 0
296296 84.6254 0.0166174
297297 −1323.06 −0.258490
298298 −87.8346 −0.0170742
299299 −10694.4 −2.06848
300300 0 0
301301 3000.63 0.574597
302302 −269.751 −0.0513987
303303 204.928 0.0388541
304304 4765.57 0.899093
305305 0 0
306306 −678.924 −0.126835
307307 −2137.32 −0.397339 −0.198669 0.980067i 0.563662π-0.563662\pi
−0.198669 + 0.980067i 0.563662π0.563662\pi
308308 917.155 0.169675
309309 43.0191 0.00791996
310310 0 0
311311 2422.78 0.441747 0.220874 0.975302i 0.429109π-0.429109\pi
0.220874 + 0.975302i 0.429109π0.429109\pi
312312 −623.918 −0.113213
313313 4607.87 0.832115 0.416058 0.909338i 0.363411π-0.363411\pi
0.416058 + 0.909338i 0.363411π0.363411\pi
314314 197.879 0.0355636
315315 0 0
316316 −6288.33 −1.11945
317317 5773.18 1.02288 0.511442 0.859318i 0.329111π-0.329111\pi
0.511442 + 0.859318i 0.329111π0.329111\pi
318318 298.151 0.0525770
319319 2225.84 0.390668
320320 0 0
321321 323.774 0.0562968
322322 438.164 0.0758320
323323 10201.2 1.75730
324324 −2008.40 −0.344376
325325 0 0
326326 −519.320 −0.0882285
327327 −522.174 −0.0883066
328328 −1199.20 −0.201873
329329 1301.23 0.218051
330330 0 0
331331 8976.09 1.49054 0.745272 0.666760i 0.232319π-0.232319\pi
0.745272 + 0.666760i 0.232319π0.232319\pi
332332 4667.05 0.771499
333333 445.229 0.0732685
334334 −11.0776 −0.00181479
335335 0 0
336336 −1659.17 −0.269391
337337 3868.16 0.625258 0.312629 0.949875i 0.398790π-0.398790\pi
0.312629 + 0.949875i 0.398790π0.398790\pi
338338 436.517 0.0702467
339339 736.686 0.118027
340340 0 0
341341 2108.03 0.334769
342342 −386.288 −0.0610763
343343 6045.94 0.951749
344344 1119.89 0.175524
345345 0 0
346346 339.657 0.0527749
347347 −11307.6 −1.74935 −0.874677 0.484706i 0.838926π-0.838926\pi
−0.874677 + 0.484706i 0.838926π0.838926\pi
348348 −4057.77 −0.625056
349349 −3296.03 −0.505537 −0.252768 0.967527i 0.581341π-0.581341\pi
−0.252768 + 0.967527i 0.581341π0.581341\pi
350350 0 0
351351 −7580.61 −1.15277
352352 514.097 0.0778451
353353 −3675.46 −0.554179 −0.277089 0.960844i 0.589370π-0.589370\pi
−0.277089 + 0.960844i 0.589370π0.589370\pi
354354 226.509 0.0340080
355355 0 0
356356 −5543.72 −0.825328
357357 −3551.62 −0.526531
358358 −22.6510 −0.00334397
359359 −5319.46 −0.782034 −0.391017 0.920383i 0.627877π-0.627877\pi
−0.391017 + 0.920383i 0.627877π0.627877\pi
360360 0 0
361361 −1054.83 −0.153788
362362 −186.768 −0.0271169
363363 305.617 0.0441893
364364 5254.95 0.756687
365365 0 0
366366 5.66385 0.000808891 0
367367 −1408.85 −0.200386 −0.100193 0.994968i 0.531946π-0.531946\pi
−0.100193 + 0.994968i 0.531946π0.531946\pi
368368 −10614.1 −1.50353
369369 −6309.18 −0.890089
370370 0 0
371371 −5041.47 −0.705500
372372 −3843.00 −0.535619
373373 −7785.80 −1.08079 −0.540393 0.841413i 0.681725π-0.681725\pi
−0.540393 + 0.841413i 0.681725π0.681725\pi
374374 362.171 0.0500733
375375 0 0
376376 485.641 0.0666091
377377 12753.2 1.74224
378378 310.586 0.0422615
379379 355.192 0.0481398 0.0240699 0.999710i 0.492338π-0.492338\pi
0.0240699 + 0.999710i 0.492338π0.492338\pi
380380 0 0
381381 3135.34 0.421597
382382 367.861 0.0492708
383383 −2611.83 −0.348454 −0.174227 0.984705i 0.555743π-0.555743\pi
−0.174227 + 0.984705i 0.555743π0.555743\pi
384384 −1248.01 −0.165852
385385 0 0
386386 856.515 0.112942
387387 5891.94 0.773912
388388 14586.7 1.90858
389389 −5258.80 −0.685428 −0.342714 0.939440i 0.611346π-0.611346\pi
−0.342714 + 0.939440i 0.611346π0.611346\pi
390390 0 0
391391 −22720.6 −2.93869
392392 912.105 0.117521
393393 −5085.91 −0.652800
394394 −405.228 −0.0518150
395395 0 0
396396 1800.89 0.228531
397397 967.463 0.122306 0.0611531 0.998128i 0.480522π-0.480522\pi
0.0611531 + 0.998128i 0.480522π0.480522\pi
398398 679.126 0.0855315
399399 −2020.77 −0.253546
400400 0 0
401401 −12713.0 −1.58318 −0.791592 0.611050i 0.790747π-0.790747\pi
−0.791592 + 0.611050i 0.790747π0.790747\pi
402402 353.276 0.0438303
403403 12078.2 1.49295
404404 −644.175 −0.0793290
405405 0 0
406406 −522.513 −0.0638716
407407 −237.507 −0.0289258
408408 −1325.53 −0.160842
409409 874.540 0.105729 0.0528646 0.998602i 0.483165π-0.483165\pi
0.0528646 + 0.998602i 0.483165π0.483165\pi
410410 0 0
411411 −542.971 −0.0651649
412412 −135.227 −0.0161703
413413 −3830.08 −0.456334
414414 860.363 0.102137
415415 0 0
416416 2945.58 0.347161
417417 5237.83 0.615102
418418 206.065 0.0241124
419419 2682.23 0.312734 0.156367 0.987699i 0.450022π-0.450022\pi
0.156367 + 0.987699i 0.450022π0.450022\pi
420420 0 0
421421 6853.07 0.793345 0.396672 0.917960i 0.370165π-0.370165\pi
0.396672 + 0.917960i 0.370165π0.370165\pi
422422 822.526 0.0948814
423423 2555.04 0.293689
424424 −1881.57 −0.215512
425425 0 0
426426 −98.0064 −0.0111465
427427 −95.7708 −0.0108540
428428 −1017.76 −0.114942
429429 1751.07 0.197068
430430 0 0
431431 −12404.3 −1.38630 −0.693151 0.720793i 0.743778π-0.743778\pi
−0.693151 + 0.720793i 0.743778π0.743778\pi
432432 −7523.70 −0.837926
433433 −10034.7 −1.11372 −0.556858 0.830608i 0.687993π-0.687993\pi
−0.556858 + 0.830608i 0.687993π0.687993\pi
434434 −494.857 −0.0547325
435435 0 0
436436 1641.42 0.180297
437437 −12927.4 −1.41510
438438 132.181 0.0144197
439439 −1016.19 −0.110479 −0.0552393 0.998473i 0.517592π-0.517592\pi
−0.0552393 + 0.998473i 0.517592π0.517592\pi
440440 0 0
441441 4798.75 0.518167
442442 2075.10 0.223309
443443 −13425.8 −1.43991 −0.719955 0.694020i 0.755838π-0.755838\pi
−0.719955 + 0.694020i 0.755838π0.755838\pi
444444 432.983 0.0462803
445445 0 0
446446 −967.616 −0.102731
447447 −902.227 −0.0954672
448448 5134.52 0.541481
449449 −1006.56 −0.105796 −0.0528982 0.998600i 0.516846π-0.516846\pi
−0.0528982 + 0.998600i 0.516846π0.516846\pi
450450 0 0
451451 3365.62 0.351399
452452 −2315.72 −0.240979
453453 −2770.85 −0.287386
454454 −776.363 −0.0802566
455455 0 0
456456 −754.187 −0.0774518
457457 11568.6 1.18415 0.592077 0.805882i 0.298308π-0.298308\pi
0.592077 + 0.805882i 0.298308π0.298308\pi
458458 970.137 0.0989771
459459 −16105.2 −1.63775
460460 0 0
461461 −17359.4 −1.75381 −0.876906 0.480663i 0.840396π-0.840396\pi
−0.876906 + 0.480663i 0.840396π0.840396\pi
462462 −71.7432 −0.00722467
463463 −4837.20 −0.485537 −0.242768 0.970084i 0.578056π-0.578056\pi
−0.242768 + 0.970084i 0.578056π0.578056\pi
464464 12657.4 1.26639
465465 0 0
466466 35.4742 0.00352641
467467 −666.327 −0.0660256 −0.0330128 0.999455i 0.510510π-0.510510\pi
−0.0330128 + 0.999455i 0.510510π0.510510\pi
468468 10318.4 1.01917
469469 −5973.59 −0.588134
470470 0 0
471471 2032.59 0.198847
472472 −1429.45 −0.139398
473473 −3143.05 −0.305534
474474 491.896 0.0476657
475475 0 0
476476 11164.2 1.07503
477477 −9899.26 −0.950223
478478 161.267 0.0154313
479479 −6115.67 −0.583366 −0.291683 0.956515i 0.594215π-0.594215\pi
−0.291683 + 0.956515i 0.594215π0.594215\pi
480480 0 0
481481 −1360.82 −0.128998
482482 479.473 0.0453099
483483 4500.77 0.424000
484484 −960.684 −0.0902220
485485 0 0
486486 955.635 0.0891944
487487 −17161.4 −1.59683 −0.798417 0.602105i 0.794329π-0.794329\pi
−0.798417 + 0.602105i 0.794329π0.794329\pi
488488 −35.7434 −0.00331563
489489 −5334.40 −0.493313
490490 0 0
491491 16482.4 1.51495 0.757477 0.652862i 0.226432π-0.226432\pi
0.757477 + 0.652862i 0.226432π0.226432\pi
492492 −6135.64 −0.562227
493493 27094.4 2.47520
494494 1180.67 0.107532
495495 0 0
496496 11987.5 1.08519
497497 1657.20 0.149569
498498 −365.074 −0.0328501
499499 17008.9 1.52590 0.762951 0.646456i 0.223750π-0.223750\pi
0.762951 + 0.646456i 0.223750π0.223750\pi
500500 0 0
501501 −113.788 −0.0101470
502502 −1479.43 −0.131534
503503 12515.0 1.10938 0.554689 0.832058i 0.312837π-0.312837\pi
0.554689 + 0.832058i 0.312837π0.312837\pi
504504 −848.735 −0.0750113
505505 0 0
506506 −458.959 −0.0403226
507507 4483.85 0.392771
508508 −9855.71 −0.860781
509509 1833.43 0.159657 0.0798284 0.996809i 0.474563π-0.474563\pi
0.0798284 + 0.996809i 0.474563π0.474563\pi
510510 0 0
511511 −2235.06 −0.193490
512512 4884.80 0.421640
513513 −9163.39 −0.788642
514514 159.705 0.0137049
515515 0 0
516516 5729.87 0.488844
517517 −1362.98 −0.115946
518518 55.7545 0.00472917
519519 3488.92 0.295080
520520 0 0
521521 9607.94 0.807930 0.403965 0.914774i 0.367632π-0.367632\pi
0.403965 + 0.914774i 0.367632π0.367632\pi
522522 −1025.99 −0.0860274
523523 −22737.4 −1.90103 −0.950515 0.310680i 0.899443π-0.899443\pi
−0.950515 + 0.310680i 0.899443π0.899443\pi
524524 15987.2 1.33283
525525 0 0
526526 1115.05 0.0924304
527527 25660.4 2.12103
528528 1737.92 0.143245
529529 16625.5 1.36644
530530 0 0
531531 −7520.61 −0.614626
532532 6352.14 0.517669
533533 19283.7 1.56711
534534 433.650 0.0351421
535535 0 0
536536 −2229.45 −0.179660
537537 −232.668 −0.0186972
538538 −952.519 −0.0763309
539539 −2559.88 −0.204568
540540 0 0
541541 17169.2 1.36444 0.682218 0.731149i 0.261015π-0.261015\pi
0.682218 + 0.731149i 0.261015π0.261015\pi
542542 1980.04 0.156919
543543 −1918.46 −0.151619
544544 6257.95 0.493212
545545 0 0
546546 −411.061 −0.0322194
547547 8825.65 0.689868 0.344934 0.938627i 0.387901π-0.387901\pi
0.344934 + 0.938627i 0.387901π0.387901\pi
548548 1706.79 0.133048
549549 −188.052 −0.0146191
550550 0 0
551551 15416.0 1.19191
552552 1679.77 0.129521
553553 −8317.54 −0.639598
554554 −1702.46 −0.130561
555555 0 0
556556 −16464.7 −1.25586
557557 5127.25 0.390034 0.195017 0.980800i 0.437524π-0.437524\pi
0.195017 + 0.980800i 0.437524π0.437524\pi
558558 −971.685 −0.0737181
559559 −18008.5 −1.36257
560560 0 0
561561 3720.18 0.279975
562562 −490.541 −0.0368189
563563 −7376.40 −0.552182 −0.276091 0.961132i 0.589039π-0.589039\pi
−0.276091 + 0.961132i 0.589039π0.589039\pi
564564 2484.76 0.185509
565565 0 0
566566 −1140.03 −0.0846625
567567 −2656.50 −0.196759
568568 618.498 0.0456894
569569 −4994.96 −0.368013 −0.184007 0.982925i 0.558907π-0.558907\pi
−0.184007 + 0.982925i 0.558907π0.558907\pi
570570 0 0
571571 −17437.0 −1.27796 −0.638981 0.769223i 0.720644π-0.720644\pi
−0.638981 + 0.769223i 0.720644π0.720644\pi
572572 −5504.35 −0.402358
573573 3778.63 0.275488
574574 −790.076 −0.0574515
575575 0 0
576576 10082.0 0.729309
577577 −6214.31 −0.448362 −0.224181 0.974548i 0.571971π-0.571971\pi
−0.224181 + 0.974548i 0.571971π0.571971\pi
578578 3200.54 0.230320
579579 8798.02 0.631491
580580 0 0
581581 6173.09 0.440796
582582 −1141.03 −0.0812666
583583 5280.75 0.375139
584584 −834.165 −0.0591061
585585 0 0
586586 80.1661 0.00565125
587587 −17894.4 −1.25823 −0.629115 0.777312i 0.716583π-0.716583\pi
−0.629115 + 0.777312i 0.716583π0.716583\pi
588588 4666.75 0.327302
589589 14600.0 1.02136
590590 0 0
591591 −4162.46 −0.289714
592592 −1350.61 −0.0937662
593593 −9135.21 −0.632611 −0.316305 0.948657i 0.602442π-0.602442\pi
−0.316305 + 0.948657i 0.602442π0.602442\pi
594594 −325.327 −0.0224719
595595 0 0
596596 2836.08 0.194917
597597 6975.91 0.478233
598598 −2629.66 −0.179824
599599 −10733.3 −0.732138 −0.366069 0.930588i 0.619297π-0.619297\pi
−0.366069 + 0.930588i 0.619297π0.619297\pi
600600 0 0
601601 22991.7 1.56048 0.780241 0.625479i 0.215096π-0.215096\pi
0.780241 + 0.625479i 0.215096π0.215096\pi
602602 737.827 0.0499528
603603 −11729.5 −0.792145
604604 8709.97 0.586761
605605 0 0
606606 50.3897 0.00337779
607607 7737.80 0.517410 0.258705 0.965956i 0.416704π-0.416704\pi
0.258705 + 0.965956i 0.416704π0.416704\pi
608608 3560.59 0.237502
609609 −5367.19 −0.357126
610610 0 0
611611 −7809.37 −0.517076
612612 21921.7 1.44793
613613 7184.13 0.473351 0.236676 0.971589i 0.423942π-0.423942\pi
0.236676 + 0.971589i 0.423942π0.423942\pi
614614 −525.545 −0.0345428
615615 0 0
616616 452.757 0.0296138
617617 8472.83 0.552842 0.276421 0.961037i 0.410852π-0.410852\pi
0.276421 + 0.961037i 0.410852π0.410852\pi
618618 10.5780 0.000688525 0
619619 −19905.0 −1.29249 −0.646243 0.763132i 0.723661π-0.723661\pi
−0.646243 + 0.763132i 0.723661π0.723661\pi
620620 0 0
621621 20409.2 1.31883
622622 595.739 0.0384035
623623 −7332.66 −0.471552
624624 9957.61 0.638820
625625 0 0
626626 1133.03 0.0723403
627627 2116.68 0.134820
628628 −6389.30 −0.405989
629629 −2891.10 −0.183268
630630 0 0
631631 −10106.1 −0.637585 −0.318792 0.947825i 0.603277π-0.603277\pi
−0.318792 + 0.947825i 0.603277π0.603277\pi
632632 −3104.26 −0.195381
633633 8448.90 0.530511
634634 1419.57 0.0889248
635635 0 0
636636 −9626.97 −0.600211
637637 −14667.2 −0.912298
638638 547.312 0.0339628
639639 3254.03 0.201451
640640 0 0
641641 9871.80 0.608288 0.304144 0.952626i 0.401630π-0.401630\pi
0.304144 + 0.952626i 0.401630π0.401630\pi
642642 79.6128 0.00489419
643643 −17121.0 −1.05006 −0.525029 0.851085i 0.675945π-0.675945\pi
−0.525029 + 0.851085i 0.675945π0.675945\pi
644644 −14147.8 −0.865688
645645 0 0
646646 2508.37 0.152771
647647 −31134.9 −1.89187 −0.945934 0.324360i 0.894851π-0.894851\pi
−0.945934 + 0.324360i 0.894851π0.894851\pi
648648 −991.453 −0.0601048
649649 4011.86 0.242649
650650 0 0
651651 −5083.12 −0.306026
652652 16768.3 1.00720
653653 6956.15 0.416868 0.208434 0.978036i 0.433163π-0.433163\pi
0.208434 + 0.978036i 0.433163π0.433163\pi
654654 −128.397 −0.00767697
655655 0 0
656656 19138.9 1.13910
657657 −4388.69 −0.260607
658658 319.959 0.0189564
659659 −24539.2 −1.45055 −0.725273 0.688461i 0.758287π-0.758287\pi
−0.725273 + 0.688461i 0.758287π0.758287\pi
660660 0 0
661661 8010.03 0.471338 0.235669 0.971833i 0.424272π-0.424272\pi
0.235669 + 0.971833i 0.424272π0.424272\pi
662662 2207.13 0.129581
663663 21315.2 1.24859
664664 2303.91 0.134652
665665 0 0
666666 109.478 0.00636963
667667 −34335.3 −1.99320
668668 357.684 0.0207174
669669 −9939.24 −0.574400
670670 0 0
671671 100.316 0.00577148
672672 −1239.65 −0.0711615
673673 32455.9 1.85896 0.929481 0.368870i 0.120255π-0.120255\pi
0.929481 + 0.368870i 0.120255π0.120255\pi
674674 951.143 0.0543571
675675 0 0
676676 −14094.7 −0.801927
677677 −29149.4 −1.65480 −0.827402 0.561610i 0.810182π-0.810182\pi
−0.827402 + 0.561610i 0.810182π0.810182\pi
678678 181.144 0.0102608
679679 19293.8 1.09047
680680 0 0
681681 −7974.71 −0.448739
682682 518.344 0.0291032
683683 4649.07 0.260457 0.130228 0.991484i 0.458429π-0.458429\pi
0.130228 + 0.991484i 0.458429π0.458429\pi
684684 12472.8 0.697238
685685 0 0
686686 1486.64 0.0827407
687687 9965.14 0.553411
688688 −17873.2 −0.990423
689689 30256.7 1.67299
690690 0 0
691691 4286.03 0.235960 0.117980 0.993016i 0.462358π-0.462358\pi
0.117980 + 0.993016i 0.462358π0.462358\pi
692692 −10967.2 −0.602470
693693 2382.03 0.130571
694694 −2780.44 −0.152081
695695 0 0
696696 −2003.13 −0.109093
697697 40968.7 2.22640
698698 −810.462 −0.0439490
699699 364.387 0.0197173
700700 0 0
701701 22751.0 1.22581 0.612905 0.790157i 0.290001π-0.290001\pi
0.612905 + 0.790157i 0.290001π0.290001\pi
702702 −1864.00 −0.100217
703703 −1644.95 −0.0882512
704704 −5378.21 −0.287925
705705 0 0
706706 −903.761 −0.0481777
707707 −852.047 −0.0453247
708708 −7313.74 −0.388231
709709 −541.209 −0.0286679 −0.0143339 0.999897i 0.504563π-0.504563\pi
−0.0143339 + 0.999897i 0.504563π0.504563\pi
710710 0 0
711711 −16332.0 −0.861462
712712 −2736.68 −0.144047
713713 −32518.0 −1.70801
714714 −873.308 −0.0457741
715715 0 0
716716 731.376 0.0381743
717717 1656.51 0.0862813
718718 −1308.00 −0.0679865
719719 11819.9 0.613085 0.306543 0.951857i 0.400828π-0.400828\pi
0.306543 + 0.951857i 0.400828π0.400828\pi
720720 0 0
721721 −178.864 −0.00923892
722722 −259.374 −0.0133696
723723 4925.09 0.253342
724724 6030.55 0.309563
725725 0 0
726726 75.1482 0.00384161
727727 28.3305 0.00144528 0.000722642 1.00000i 0.499770π-0.499770\pi
0.000722642 1.00000i 0.499770π0.499770\pi
728728 2594.12 0.132067
729729 2986.21 0.151715
730730 0 0
731731 −38259.3 −1.93580
732732 −182.880 −0.00923418
733733 3239.61 0.163244 0.0816220 0.996663i 0.473990π-0.473990\pi
0.0816220 + 0.996663i 0.473990π0.473990\pi
734734 −346.423 −0.0174206
735735 0 0
736736 −7930.35 −0.397169
737737 6257.10 0.312732
738738 −1551.37 −0.0773802
739739 −10380.6 −0.516720 −0.258360 0.966049i 0.583182π-0.583182\pi
−0.258360 + 0.966049i 0.583182π0.583182\pi
740740 0 0
741741 12127.7 0.601247
742742 −1239.65 −0.0613329
743743 12344.3 0.609515 0.304758 0.952430i 0.401425π-0.401425\pi
0.304758 + 0.952430i 0.401425π0.401425\pi
744744 −1897.11 −0.0934831
745745 0 0
746746 −1914.45 −0.0939586
747747 12121.3 0.593700
748748 −11694.1 −0.571630
749749 −1346.18 −0.0656722
750750 0 0
751751 −5340.50 −0.259491 −0.129745 0.991547i 0.541416π-0.541416\pi
−0.129745 + 0.991547i 0.541416π0.541416\pi
752752 −7750.73 −0.375851
753753 −15196.5 −0.735447
754754 3135.89 0.151462
755755 0 0
756756 −10028.5 −0.482451
757757 22616.5 1.08588 0.542939 0.839772i 0.317312π-0.317312\pi
0.542939 + 0.839772i 0.317312π0.317312\pi
758758 87.3383 0.00418505
759759 −4714.38 −0.225456
760760 0 0
761761 −36847.6 −1.75522 −0.877611 0.479373i 0.840864π-0.840864\pi
−0.877611 + 0.479373i 0.840864π0.840864\pi
762762 770.950 0.0366517
763763 2171.09 0.103013
764764 −11877.9 −0.562468
765765 0 0
766766 −642.223 −0.0302930
767767 22986.4 1.08213
768768 9572.45 0.449760
769769 −30448.8 −1.42785 −0.713923 0.700225i 0.753083π-0.753083\pi
−0.713923 + 0.700225i 0.753083π0.753083\pi
770770 0 0
771771 1640.47 0.0766281
772772 −27656.0 −1.28933
773773 8119.13 0.377781 0.188890 0.981998i 0.439511π-0.439511\pi
0.188890 + 0.981998i 0.439511π0.439511\pi
774774 1448.77 0.0672804
775775 0 0
776776 7200.80 0.333110
777777 572.704 0.0264423
778778 −1293.09 −0.0595880
779779 23310.0 1.07210
780780 0 0
781781 −1735.86 −0.0795311
782782 −5586.77 −0.255476
783783 −24338.1 −1.11082
784784 −14557.0 −0.663130
785785 0 0
786786 −1250.58 −0.0567514
787787 39807.6 1.80303 0.901517 0.432744i 0.142455π-0.142455\pi
0.901517 + 0.432744i 0.142455π0.142455\pi
788788 13084.4 0.591513
789789 11453.6 0.516807
790790 0 0
791791 −3062.99 −0.137683
792792 889.017 0.0398862
793793 574.773 0.0257387
794794 237.890 0.0106327
795795 0 0
796796 −21928.3 −0.976415
797797 26083.3 1.15924 0.579621 0.814886i 0.303201π-0.303201\pi
0.579621 + 0.814886i 0.303201π0.303201\pi
798798 −496.887 −0.0220421
799799 −16591.2 −0.734610
800800 0 0
801801 −14398.1 −0.635123
802802 −3126.00 −0.137635
803803 2341.14 0.102885
804804 −11406.9 −0.500361
805805 0 0
806806 2969.91 0.129790
807807 −9784.17 −0.426789
808808 −317.999 −0.0138455
809809 −24719.7 −1.07429 −0.537143 0.843491i 0.680496π-0.680496\pi
−0.537143 + 0.843491i 0.680496π0.680496\pi
810810 0 0
811811 −39107.6 −1.69328 −0.846642 0.532163i 0.821379π-0.821379\pi
−0.846642 + 0.532163i 0.821379π0.821379\pi
812812 16871.4 0.729150
813813 20338.7 0.877381
814814 −58.4007 −0.00251467
815815 0 0
816816 21155.2 0.907572
817817 −21768.5 −0.932170
818818 215.041 0.00919161
819819 13648.1 0.582301
820820 0 0
821821 −8149.66 −0.346438 −0.173219 0.984883i 0.555417π-0.555417\pi
−0.173219 + 0.984883i 0.555417π0.555417\pi
822822 −133.511 −0.00566514
823823 1052.83 0.0445923 0.0222962 0.999751i 0.492902π-0.492902\pi
0.0222962 + 0.999751i 0.492902π0.492902\pi
824824 −66.7554 −0.00282225
825825 0 0
826826 −941.779 −0.0396715
827827 −14414.1 −0.606078 −0.303039 0.952978i 0.598001π-0.598001\pi
−0.303039 + 0.952978i 0.598001π0.598001\pi
828828 −27780.2 −1.16598
829829 25958.2 1.08753 0.543767 0.839236i 0.316997π-0.316997\pi
0.543767 + 0.839236i 0.316997π0.316997\pi
830830 0 0
831831 −17487.5 −0.730006
832832 −30815.1 −1.28404
833833 −31160.7 −1.29610
834834 1287.93 0.0534741
835835 0 0
836836 −6653.62 −0.275263
837837 −23049.9 −0.951879
838838 659.535 0.0271877
839839 −39.9909 −0.00164558 −0.000822789 1.00000i 0.500262π-0.500262\pi
−0.000822789 1.00000i 0.500262π0.500262\pi
840840 0 0
841841 16556.0 0.678832
842842 1685.10 0.0689697
843843 −5038.78 −0.205866
844844 −26558.5 −1.08315
845845 0 0
846846 628.260 0.0255319
847847 −1270.69 −0.0515484
848848 30029.5 1.21606
849849 −11710.2 −0.473374
850850 0 0
851851 3663.73 0.147581
852852 3164.52 0.127247
853853 10756.0 0.431743 0.215871 0.976422i 0.430741π-0.430741\pi
0.215871 + 0.976422i 0.430741π0.430741\pi
854854 −23.5491 −0.000943599 0
855855 0 0
856856 −502.420 −0.0200612
857857 −37977.4 −1.51375 −0.756875 0.653560i 0.773275π-0.773275\pi
−0.756875 + 0.653560i 0.773275π0.773275\pi
858858 430.570 0.0171322
859859 −12471.3 −0.495361 −0.247681 0.968842i 0.579668π-0.579668\pi
−0.247681 + 0.968842i 0.579668π0.579668\pi
860860 0 0
861861 −8115.57 −0.321229
862862 −3050.11 −0.120519
863863 30920.2 1.21963 0.609813 0.792545i 0.291245π-0.291245\pi
0.609813 + 0.792545i 0.291245π0.291245\pi
864864 −5621.32 −0.221344
865865 0 0
866866 −2467.45 −0.0968212
867867 32875.5 1.28779
868868 15978.4 0.624819
869869 8712.30 0.340097
870870 0 0
871871 35850.8 1.39467
872872 810.290 0.0314678
873873 37884.7 1.46873
874874 −3178.71 −0.123022
875875 0 0
876876 −4267.97 −0.164613
877877 1896.09 0.0730061 0.0365030 0.999334i 0.488378π-0.488378\pi
0.0365030 + 0.999334i 0.488378π0.488378\pi
878878 −249.871 −0.00960450
879879 823.457 0.0315979
880880 0 0
881881 −9451.40 −0.361437 −0.180718 0.983535i 0.557842π-0.557842\pi
−0.180718 + 0.983535i 0.557842π0.557842\pi
882882 1179.97 0.0450471
883883 −17623.7 −0.671669 −0.335834 0.941921i 0.609018π-0.609018\pi
−0.335834 + 0.941921i 0.609018π0.609018\pi
884884 −67002.8 −2.54926
885885 0 0
886886 −3301.28 −0.125179
887887 43411.7 1.64332 0.821658 0.569980i 0.193049π-0.193049\pi
0.821658 + 0.569980i 0.193049π0.193049\pi
888888 213.743 0.00807743
889889 −13036.1 −0.491807
890890 0 0
891891 2782.58 0.104624
892892 31243.3 1.17276
893893 −9439.91 −0.353745
894894 −221.849 −0.00829948
895895 0 0
896896 5188.96 0.193472
897897 −27011.6 −1.00545
898898 −247.504 −0.00919745
899899 38777.9 1.43862
900900 0 0
901901 64280.9 2.37681
902902 827.574 0.0305490
903903 7578.87 0.279301
904904 −1143.16 −0.0420587
905905 0 0
906906 −681.325 −0.0249840
907907 −37888.6 −1.38707 −0.693534 0.720423i 0.743947π-0.743947\pi
−0.693534 + 0.720423i 0.743947π0.743947\pi
908908 25067.9 0.916198
909909 −1673.05 −0.0610468
910910 0 0
911911 −42276.8 −1.53753 −0.768766 0.639530i 0.779129π-0.779129\pi
−0.768766 + 0.639530i 0.779129π0.779129\pi
912912 12036.7 0.437033
913913 −6466.07 −0.234387
914914 2844.62 0.102945
915915 0 0
916916 −31324.7 −1.12991
917917 21146.2 0.761514
918918 −3960.11 −0.142378
919919 32790.8 1.17701 0.588504 0.808494i 0.299717π-0.299717\pi
0.588504 + 0.808494i 0.299717π0.299717\pi
920920 0 0
921921 −5398.34 −0.193139
922922 −4268.51 −0.152468
923923 −9945.79 −0.354680
924924 2316.51 0.0824758
925925 0 0
926926 −1189.42 −0.0422103
927927 −351.212 −0.0124437
928928 9457.00 0.334527
929929 25997.1 0.918122 0.459061 0.888405i 0.348186π-0.348186\pi
0.459061 + 0.888405i 0.348186π0.348186\pi
930930 0 0
931931 −17729.5 −0.624127
932932 −1145.42 −0.0402571
933933 6119.36 0.214726
934934 −163.843 −0.00573996
935935 0 0
936936 5093.73 0.177878
937937 −23318.7 −0.813008 −0.406504 0.913649i 0.633252π-0.633252\pi
−0.406504 + 0.913649i 0.633252π0.633252\pi
938938 −1468.85 −0.0511296
939939 11638.4 0.404477
940940 0 0
941941 47178.4 1.63440 0.817201 0.576353i 0.195525π-0.195525\pi
0.817201 + 0.576353i 0.195525π0.195525\pi
942942 499.795 0.0172868
943943 −51917.4 −1.79285
944944 22813.8 0.786575
945945 0 0
946946 −772.845 −0.0265617
947947 −18988.7 −0.651584 −0.325792 0.945441i 0.605631π-0.605631\pi
−0.325792 + 0.945441i 0.605631π0.605631\pi
948948 −15882.8 −0.544145
949949 13413.8 0.458832
950950 0 0
951951 14581.7 0.497206
952952 5511.27 0.187627
953953 −33650.1 −1.14379 −0.571896 0.820326i 0.693792π-0.693792\pi
−0.571896 + 0.820326i 0.693792π0.693792\pi
954954 −2434.13 −0.0826080
955955 0 0
956956 −5207.13 −0.176162
957957 5621.93 0.189897
958958 −1503.79 −0.0507151
959959 2257.56 0.0760172
960960 0 0
961961 6934.46 0.232770
962962 −334.613 −0.0112145
963963 −2643.32 −0.0884526
964964 −15481.7 −0.517252
965965 0 0
966966 1106.70 0.0368606
967967 −25555.9 −0.849869 −0.424934 0.905224i 0.639703π-0.639703\pi
−0.424934 + 0.905224i 0.639703π0.639703\pi
968968 −474.245 −0.0157467
969969 25765.6 0.854192
970970 0 0
971971 23379.4 0.772690 0.386345 0.922354i 0.373737π-0.373737\pi
0.386345 + 0.922354i 0.373737π0.373737\pi
972972 −30856.4 −1.01823
973973 −21777.8 −0.717538
974974 −4219.83 −0.138821
975975 0 0
976976 570.457 0.0187089
977977 −5631.85 −0.184421 −0.0922103 0.995740i 0.529393π-0.529393\pi
−0.0922103 + 0.995740i 0.529393π0.529393\pi
978978 −1311.68 −0.0428863
979979 7680.67 0.250741
980980 0 0
981981 4263.08 0.138746
982982 4052.88 0.131703
983983 −24438.5 −0.792946 −0.396473 0.918046i 0.629766π-0.629766\pi
−0.396473 + 0.918046i 0.629766π0.629766\pi
984984 −3028.88 −0.0981271
985985 0 0
986986 6662.26 0.215182
987987 3286.58 0.105991
988988 −38122.7 −1.22757
989989 48484.0 1.55885
990990 0 0
991991 −13590.4 −0.435635 −0.217817 0.975990i 0.569894π-0.569894\pi
−0.217817 + 0.975990i 0.569894π0.569894\pi
992992 8956.46 0.286661
993993 22671.4 0.724528
994994 407.491 0.0130028
995995 0 0
996996 11787.8 0.375012
997997 24783.1 0.787249 0.393624 0.919271i 0.371221π-0.371221\pi
0.393624 + 0.919271i 0.371221π0.371221\pi
998998 4182.34 0.132655
999999 2596.99 0.0822473
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 275.4.a.k.1.6 10
3.2 odd 2 2475.4.a.bw.1.5 10
5.2 odd 4 55.4.b.b.34.6 yes 10
5.3 odd 4 55.4.b.b.34.5 10
5.4 even 2 inner 275.4.a.k.1.5 10
15.2 even 4 495.4.c.b.199.5 10
15.8 even 4 495.4.c.b.199.6 10
15.14 odd 2 2475.4.a.bw.1.6 10
20.3 even 4 880.4.b.i.529.5 10
20.7 even 4 880.4.b.i.529.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.4.b.b.34.5 10 5.3 odd 4
55.4.b.b.34.6 yes 10 5.2 odd 4
275.4.a.k.1.5 10 5.4 even 2 inner
275.4.a.k.1.6 10 1.1 even 1 trivial
495.4.c.b.199.5 10 15.2 even 4
495.4.c.b.199.6 10 15.8 even 4
880.4.b.i.529.5 10 20.3 even 4
880.4.b.i.529.6 10 20.7 even 4
2475.4.a.bw.1.5 10 3.2 odd 2
2475.4.a.bw.1.6 10 15.14 odd 2