Properties

Label 966.2.a.n.1.2
Level 966966
Weight 22
Character 966.1
Self dual yes
Analytic conductor 7.7147.714
Analytic rank 00
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(1,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 966=23723 966 = 2 \cdot 3 \cdot 7 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 966.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: 7.713548835267.71354883526
Analytic rank: 00
Dimension: 22
Coefficient field: Q(41)\Q(\sqrt{41})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x10 x^{2} - x - 10 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 3.701563.70156 of defining polynomial
Character χ\chi == 966.1

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) == q1.00000q2+1.00000q3+1.00000q4+3.70156q51.00000q6+1.00000q71.00000q8+1.00000q93.70156q104.00000q11+1.00000q12+5.70156q131.00000q14+3.70156q15+1.00000q16+4.00000q171.00000q185.40312q19+3.70156q20+1.00000q21+4.00000q22+1.00000q231.00000q24+8.70156q255.70156q26+1.00000q27+1.00000q28+0.298438q293.70156q302.00000q311.00000q324.00000q334.00000q34+3.70156q35+1.00000q36+4.29844q37+5.40312q38+5.70156q393.70156q400.298438q411.00000q421.70156q434.00000q44+3.70156q451.00000q4611.1047q47+1.00000q48+1.00000q498.70156q50+4.00000q51+5.70156q529.40312q531.00000q5414.8062q551.00000q565.40312q570.298438q587.40312q59+3.70156q602.00000q61+2.00000q62+1.00000q63+1.00000q64+21.1047q65+4.00000q66+14.8062q67+4.00000q68+1.00000q693.70156q707.40312q711.00000q72+1.40312q734.29844q74+8.70156q755.40312q764.00000q775.70156q78+8.00000q79+3.70156q80+1.00000q81+0.298438q82+13.4031q83+1.00000q84+14.8062q85+1.70156q86+0.298438q87+4.00000q8811.4031q893.70156q90+5.70156q91+1.00000q922.00000q93+11.1047q9420.0000q951.00000q96+6.29844q971.00000q984.00000q99+O(q100)q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.70156 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.70156 q^{10} -4.00000 q^{11} +1.00000 q^{12} +5.70156 q^{13} -1.00000 q^{14} +3.70156 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -5.40312 q^{19} +3.70156 q^{20} +1.00000 q^{21} +4.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +8.70156 q^{25} -5.70156 q^{26} +1.00000 q^{27} +1.00000 q^{28} +0.298438 q^{29} -3.70156 q^{30} -2.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -4.00000 q^{34} +3.70156 q^{35} +1.00000 q^{36} +4.29844 q^{37} +5.40312 q^{38} +5.70156 q^{39} -3.70156 q^{40} -0.298438 q^{41} -1.00000 q^{42} -1.70156 q^{43} -4.00000 q^{44} +3.70156 q^{45} -1.00000 q^{46} -11.1047 q^{47} +1.00000 q^{48} +1.00000 q^{49} -8.70156 q^{50} +4.00000 q^{51} +5.70156 q^{52} -9.40312 q^{53} -1.00000 q^{54} -14.8062 q^{55} -1.00000 q^{56} -5.40312 q^{57} -0.298438 q^{58} -7.40312 q^{59} +3.70156 q^{60} -2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +21.1047 q^{65} +4.00000 q^{66} +14.8062 q^{67} +4.00000 q^{68} +1.00000 q^{69} -3.70156 q^{70} -7.40312 q^{71} -1.00000 q^{72} +1.40312 q^{73} -4.29844 q^{74} +8.70156 q^{75} -5.40312 q^{76} -4.00000 q^{77} -5.70156 q^{78} +8.00000 q^{79} +3.70156 q^{80} +1.00000 q^{81} +0.298438 q^{82} +13.4031 q^{83} +1.00000 q^{84} +14.8062 q^{85} +1.70156 q^{86} +0.298438 q^{87} +4.00000 q^{88} -11.4031 q^{89} -3.70156 q^{90} +5.70156 q^{91} +1.00000 q^{92} -2.00000 q^{93} +11.1047 q^{94} -20.0000 q^{95} -1.00000 q^{96} +6.29844 q^{97} -1.00000 q^{98} -4.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q2+2q3+2q4+q52q6+2q72q8+2q9q108q11+2q12+5q132q14+q15+2q16+8q172q18+2q19+q20+2q21+8q99+O(q100) 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} - 8 q^{11} + 2 q^{12} + 5 q^{13} - 2 q^{14} + q^{15} + 2 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{19} + q^{20} + 2 q^{21}+ \cdots - 8 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 −1.00000 −0.707107
33 1.00000 0.577350
44 1.00000 0.500000
55 3.70156 1.65539 0.827694 0.561179i 0.189652π-0.189652\pi
0.827694 + 0.561179i 0.189652π0.189652\pi
66 −1.00000 −0.408248
77 1.00000 0.377964
88 −1.00000 −0.353553
99 1.00000 0.333333
1010 −3.70156 −1.17054
1111 −4.00000 −1.20605 −0.603023 0.797724i 0.706037π-0.706037\pi
−0.603023 + 0.797724i 0.706037π0.706037\pi
1212 1.00000 0.288675
1313 5.70156 1.58133 0.790664 0.612250i 0.209735π-0.209735\pi
0.790664 + 0.612250i 0.209735π0.209735\pi
1414 −1.00000 −0.267261
1515 3.70156 0.955739
1616 1.00000 0.250000
1717 4.00000 0.970143 0.485071 0.874475i 0.338794π-0.338794\pi
0.485071 + 0.874475i 0.338794π0.338794\pi
1818 −1.00000 −0.235702
1919 −5.40312 −1.23956 −0.619781 0.784775i 0.712779π-0.712779\pi
−0.619781 + 0.784775i 0.712779π0.712779\pi
2020 3.70156 0.827694
2121 1.00000 0.218218
2222 4.00000 0.852803
2323 1.00000 0.208514
2424 −1.00000 −0.204124
2525 8.70156 1.74031
2626 −5.70156 −1.11817
2727 1.00000 0.192450
2828 1.00000 0.188982
2929 0.298438 0.0554185 0.0277093 0.999616i 0.491179π-0.491179\pi
0.0277093 + 0.999616i 0.491179π0.491179\pi
3030 −3.70156 −0.675810
3131 −2.00000 −0.359211 −0.179605 0.983739i 0.557482π-0.557482\pi
−0.179605 + 0.983739i 0.557482π0.557482\pi
3232 −1.00000 −0.176777
3333 −4.00000 −0.696311
3434 −4.00000 −0.685994
3535 3.70156 0.625678
3636 1.00000 0.166667
3737 4.29844 0.706659 0.353329 0.935499i 0.385049π-0.385049\pi
0.353329 + 0.935499i 0.385049π0.385049\pi
3838 5.40312 0.876502
3939 5.70156 0.912981
4040 −3.70156 −0.585268
4141 −0.298438 −0.0466082 −0.0233041 0.999728i 0.507419π-0.507419\pi
−0.0233041 + 0.999728i 0.507419π0.507419\pi
4242 −1.00000 −0.154303
4343 −1.70156 −0.259486 −0.129743 0.991548i 0.541415π-0.541415\pi
−0.129743 + 0.991548i 0.541415π0.541415\pi
4444 −4.00000 −0.603023
4545 3.70156 0.551796
4646 −1.00000 −0.147442
4747 −11.1047 −1.61978 −0.809892 0.586578i 0.800475π-0.800475\pi
−0.809892 + 0.586578i 0.800475π0.800475\pi
4848 1.00000 0.144338
4949 1.00000 0.142857
5050 −8.70156 −1.23059
5151 4.00000 0.560112
5252 5.70156 0.790664
5353 −9.40312 −1.29162 −0.645809 0.763499i 0.723480π-0.723480\pi
−0.645809 + 0.763499i 0.723480π0.723480\pi
5454 −1.00000 −0.136083
5555 −14.8062 −1.99647
5656 −1.00000 −0.133631
5757 −5.40312 −0.715661
5858 −0.298438 −0.0391868
5959 −7.40312 −0.963805 −0.481902 0.876225i 0.660054π-0.660054\pi
−0.481902 + 0.876225i 0.660054π0.660054\pi
6060 3.70156 0.477870
6161 −2.00000 −0.256074 −0.128037 0.991769i 0.540868π-0.540868\pi
−0.128037 + 0.991769i 0.540868π0.540868\pi
6262 2.00000 0.254000
6363 1.00000 0.125988
6464 1.00000 0.125000
6565 21.1047 2.61771
6666 4.00000 0.492366
6767 14.8062 1.80887 0.904436 0.426610i 0.140292π-0.140292\pi
0.904436 + 0.426610i 0.140292π0.140292\pi
6868 4.00000 0.485071
6969 1.00000 0.120386
7070 −3.70156 −0.442421
7171 −7.40312 −0.878589 −0.439295 0.898343i 0.644772π-0.644772\pi
−0.439295 + 0.898343i 0.644772π0.644772\pi
7272 −1.00000 −0.117851
7373 1.40312 0.164223 0.0821116 0.996623i 0.473834π-0.473834\pi
0.0821116 + 0.996623i 0.473834π0.473834\pi
7474 −4.29844 −0.499683
7575 8.70156 1.00477
7676 −5.40312 −0.619781
7777 −4.00000 −0.455842
7878 −5.70156 −0.645575
7979 8.00000 0.900070 0.450035 0.893011i 0.351411π-0.351411\pi
0.450035 + 0.893011i 0.351411π0.351411\pi
8080 3.70156 0.413847
8181 1.00000 0.111111
8282 0.298438 0.0329570
8383 13.4031 1.47118 0.735592 0.677425i 0.236904π-0.236904\pi
0.735592 + 0.677425i 0.236904π0.236904\pi
8484 1.00000 0.109109
8585 14.8062 1.60596
8686 1.70156 0.183484
8787 0.298438 0.0319959
8888 4.00000 0.426401
8989 −11.4031 −1.20873 −0.604364 0.796708i 0.706573π-0.706573\pi
−0.604364 + 0.796708i 0.706573π0.706573\pi
9090 −3.70156 −0.390179
9191 5.70156 0.597686
9292 1.00000 0.104257
9393 −2.00000 −0.207390
9494 11.1047 1.14536
9595 −20.0000 −2.05196
9696 −1.00000 −0.102062
9797 6.29844 0.639509 0.319755 0.947500i 0.396399π-0.396399\pi
0.319755 + 0.947500i 0.396399π0.396399\pi
9898 −1.00000 −0.101015
9999 −4.00000 −0.402015
100100 8.70156 0.870156
101101 −3.40312 −0.338624 −0.169312 0.985563i 0.554154π-0.554154\pi
−0.169312 + 0.985563i 0.554154π0.554154\pi
102102 −4.00000 −0.396059
103103 2.29844 0.226472 0.113236 0.993568i 0.463878π-0.463878\pi
0.113236 + 0.993568i 0.463878π0.463878\pi
104104 −5.70156 −0.559084
105105 3.70156 0.361235
106106 9.40312 0.913312
107107 18.8062 1.81807 0.909034 0.416721i 0.136821π-0.136821\pi
0.909034 + 0.416721i 0.136821π0.136821\pi
108108 1.00000 0.0962250
109109 −7.70156 −0.737676 −0.368838 0.929494i 0.620244π-0.620244\pi
−0.368838 + 0.929494i 0.620244π0.620244\pi
110110 14.8062 1.41172
111111 4.29844 0.407990
112112 1.00000 0.0944911
113113 7.10469 0.668353 0.334176 0.942511i 0.391542π-0.391542\pi
0.334176 + 0.942511i 0.391542π0.391542\pi
114114 5.40312 0.506049
115115 3.70156 0.345172
116116 0.298438 0.0277093
117117 5.70156 0.527110
118118 7.40312 0.681513
119119 4.00000 0.366679
120120 −3.70156 −0.337905
121121 5.00000 0.454545
122122 2.00000 0.181071
123123 −0.298438 −0.0269092
124124 −2.00000 −0.179605
125125 13.7016 1.22550
126126 −1.00000 −0.0890871
127127 −5.70156 −0.505932 −0.252966 0.967475i 0.581406π-0.581406\pi
−0.252966 + 0.967475i 0.581406π0.581406\pi
128128 −1.00000 −0.0883883
129129 −1.70156 −0.149814
130130 −21.1047 −1.85100
131131 −7.40312 −0.646814 −0.323407 0.946260i 0.604828π-0.604828\pi
−0.323407 + 0.946260i 0.604828π0.604828\pi
132132 −4.00000 −0.348155
133133 −5.40312 −0.468510
134134 −14.8062 −1.27907
135135 3.70156 0.318580
136136 −4.00000 −0.342997
137137 −19.7016 −1.68322 −0.841609 0.540087i 0.818391π-0.818391\pi
−0.841609 + 0.540087i 0.818391π0.818391\pi
138138 −1.00000 −0.0851257
139139 17.7016 1.50143 0.750713 0.660628i 0.229710π-0.229710\pi
0.750713 + 0.660628i 0.229710π0.229710\pi
140140 3.70156 0.312839
141141 −11.1047 −0.935183
142142 7.40312 0.621256
143143 −22.8062 −1.90715
144144 1.00000 0.0833333
145145 1.10469 0.0917392
146146 −1.40312 −0.116123
147147 1.00000 0.0824786
148148 4.29844 0.353329
149149 −20.2094 −1.65562 −0.827808 0.561011i 0.810412π-0.810412\pi
−0.827808 + 0.561011i 0.810412π0.810412\pi
150150 −8.70156 −0.710480
151151 23.9109 1.94584 0.972922 0.231133i 0.0742433π-0.0742433\pi
0.972922 + 0.231133i 0.0742433π0.0742433\pi
152152 5.40312 0.438251
153153 4.00000 0.323381
154154 4.00000 0.322329
155155 −7.40312 −0.594633
156156 5.70156 0.456490
157157 −1.40312 −0.111982 −0.0559908 0.998431i 0.517832π-0.517832\pi
−0.0559908 + 0.998431i 0.517832π0.517832\pi
158158 −8.00000 −0.636446
159159 −9.40312 −0.745716
160160 −3.70156 −0.292634
161161 1.00000 0.0788110
162162 −1.00000 −0.0785674
163163 −10.8062 −0.846411 −0.423205 0.906034i 0.639095π-0.639095\pi
−0.423205 + 0.906034i 0.639095π0.639095\pi
164164 −0.298438 −0.0233041
165165 −14.8062 −1.15266
166166 −13.4031 −1.04028
167167 −13.4031 −1.03716 −0.518582 0.855028i 0.673540π-0.673540\pi
−0.518582 + 0.855028i 0.673540π0.673540\pi
168168 −1.00000 −0.0771517
169169 19.5078 1.50060
170170 −14.8062 −1.13559
171171 −5.40312 −0.413187
172172 −1.70156 −0.129743
173173 19.4031 1.47519 0.737596 0.675242i 0.235961π-0.235961\pi
0.737596 + 0.675242i 0.235961π0.235961\pi
174174 −0.298438 −0.0226245
175175 8.70156 0.657776
176176 −4.00000 −0.301511
177177 −7.40312 −0.556453
178178 11.4031 0.854700
179179 −25.1047 −1.87641 −0.938206 0.346077i 0.887514π-0.887514\pi
−0.938206 + 0.346077i 0.887514π0.887514\pi
180180 3.70156 0.275898
181181 −16.8062 −1.24920 −0.624599 0.780945i 0.714738π-0.714738\pi
−0.624599 + 0.780945i 0.714738π0.714738\pi
182182 −5.70156 −0.422628
183183 −2.00000 −0.147844
184184 −1.00000 −0.0737210
185185 15.9109 1.16980
186186 2.00000 0.146647
187187 −16.0000 −1.17004
188188 −11.1047 −0.809892
189189 1.00000 0.0727393
190190 20.0000 1.45095
191191 22.8062 1.65020 0.825101 0.564985i 0.191118π-0.191118\pi
0.825101 + 0.564985i 0.191118π0.191118\pi
192192 1.00000 0.0721688
193193 −23.1047 −1.66311 −0.831556 0.555441i 0.812549π-0.812549\pi
−0.831556 + 0.555441i 0.812549π0.812549\pi
194194 −6.29844 −0.452201
195195 21.1047 1.51134
196196 1.00000 0.0714286
197197 22.5078 1.60362 0.801808 0.597582i 0.203872π-0.203872\pi
0.801808 + 0.597582i 0.203872π0.203872\pi
198198 4.00000 0.284268
199199 −2.29844 −0.162932 −0.0814660 0.996676i 0.525960π-0.525960\pi
−0.0814660 + 0.996676i 0.525960π0.525960\pi
200200 −8.70156 −0.615293
201201 14.8062 1.04435
202202 3.40312 0.239443
203203 0.298438 0.0209462
204204 4.00000 0.280056
205205 −1.10469 −0.0771546
206206 −2.29844 −0.160140
207207 1.00000 0.0695048
208208 5.70156 0.395332
209209 21.6125 1.49497
210210 −3.70156 −0.255432
211211 10.8062 0.743933 0.371966 0.928246i 0.378684π-0.378684\pi
0.371966 + 0.928246i 0.378684π0.378684\pi
212212 −9.40312 −0.645809
213213 −7.40312 −0.507254
214214 −18.8062 −1.28557
215215 −6.29844 −0.429550
216216 −1.00000 −0.0680414
217217 −2.00000 −0.135769
218218 7.70156 0.521616
219219 1.40312 0.0948143
220220 −14.8062 −0.998237
221221 22.8062 1.53411
222222 −4.29844 −0.288492
223223 −22.0000 −1.47323 −0.736614 0.676313i 0.763577π-0.763577\pi
−0.736614 + 0.676313i 0.763577π0.763577\pi
224224 −1.00000 −0.0668153
225225 8.70156 0.580104
226226 −7.10469 −0.472597
227227 −23.1047 −1.53351 −0.766756 0.641939i 0.778130π-0.778130\pi
−0.766756 + 0.641939i 0.778130π0.778130\pi
228228 −5.40312 −0.357831
229229 −14.5969 −0.964589 −0.482294 0.876009i 0.660196π-0.660196\pi
−0.482294 + 0.876009i 0.660196π0.660196\pi
230230 −3.70156 −0.244074
231231 −4.00000 −0.263181
232232 −0.298438 −0.0195934
233233 −26.0000 −1.70332 −0.851658 0.524097i 0.824403π-0.824403\pi
−0.851658 + 0.524097i 0.824403π0.824403\pi
234234 −5.70156 −0.372723
235235 −41.1047 −2.68137
236236 −7.40312 −0.481902
237237 8.00000 0.519656
238238 −4.00000 −0.259281
239239 10.8062 0.698998 0.349499 0.936937i 0.386352π-0.386352\pi
0.349499 + 0.936937i 0.386352π0.386352\pi
240240 3.70156 0.238935
241241 −15.9109 −1.02491 −0.512457 0.858713i 0.671264π-0.671264\pi
−0.512457 + 0.858713i 0.671264π0.671264\pi
242242 −5.00000 −0.321412
243243 1.00000 0.0641500
244244 −2.00000 −0.128037
245245 3.70156 0.236484
246246 0.298438 0.0190277
247247 −30.8062 −1.96015
248248 2.00000 0.127000
249249 13.4031 0.849388
250250 −13.7016 −0.866563
251251 19.7016 1.24355 0.621776 0.783195i 0.286412π-0.286412\pi
0.621776 + 0.783195i 0.286412π0.286412\pi
252252 1.00000 0.0629941
253253 −4.00000 −0.251478
254254 5.70156 0.357748
255255 14.8062 0.927203
256256 1.00000 0.0625000
257257 2.00000 0.124757 0.0623783 0.998053i 0.480131π-0.480131\pi
0.0623783 + 0.998053i 0.480131π0.480131\pi
258258 1.70156 0.105935
259259 4.29844 0.267092
260260 21.1047 1.30886
261261 0.298438 0.0184728
262262 7.40312 0.457367
263263 9.70156 0.598224 0.299112 0.954218i 0.403310π-0.403310\pi
0.299112 + 0.954218i 0.403310π0.403310\pi
264264 4.00000 0.246183
265265 −34.8062 −2.13813
266266 5.40312 0.331287
267267 −11.4031 −0.697860
268268 14.8062 0.904436
269269 −10.2094 −0.622476 −0.311238 0.950332i 0.600744π-0.600744\pi
−0.311238 + 0.950332i 0.600744π0.600744\pi
270270 −3.70156 −0.225270
271271 1.40312 0.0852337 0.0426169 0.999091i 0.486431π-0.486431\pi
0.0426169 + 0.999091i 0.486431π0.486431\pi
272272 4.00000 0.242536
273273 5.70156 0.345074
274274 19.7016 1.19021
275275 −34.8062 −2.09890
276276 1.00000 0.0601929
277277 −21.4031 −1.28599 −0.642995 0.765871i 0.722308π-0.722308\pi
−0.642995 + 0.765871i 0.722308π0.722308\pi
278278 −17.7016 −1.06167
279279 −2.00000 −0.119737
280280 −3.70156 −0.221211
281281 14.5078 0.865463 0.432732 0.901523i 0.357550π-0.357550\pi
0.432732 + 0.901523i 0.357550π0.357550\pi
282282 11.1047 0.661274
283283 4.80625 0.285702 0.142851 0.989744i 0.454373π-0.454373\pi
0.142851 + 0.989744i 0.454373π0.454373\pi
284284 −7.40312 −0.439295
285285 −20.0000 −1.18470
286286 22.8062 1.34856
287287 −0.298438 −0.0176162
288288 −1.00000 −0.0589256
289289 −1.00000 −0.0588235
290290 −1.10469 −0.0648694
291291 6.29844 0.369221
292292 1.40312 0.0821116
293293 −20.8062 −1.21551 −0.607757 0.794123i 0.707931π-0.707931\pi
−0.607757 + 0.794123i 0.707931π0.707931\pi
294294 −1.00000 −0.0583212
295295 −27.4031 −1.59547
296296 −4.29844 −0.249842
297297 −4.00000 −0.232104
298298 20.2094 1.17070
299299 5.70156 0.329730
300300 8.70156 0.502385
301301 −1.70156 −0.0980764
302302 −23.9109 −1.37592
303303 −3.40312 −0.195504
304304 −5.40312 −0.309890
305305 −7.40312 −0.423902
306306 −4.00000 −0.228665
307307 11.9109 0.679793 0.339896 0.940463i 0.389608π-0.389608\pi
0.339896 + 0.940463i 0.389608π0.389608\pi
308308 −4.00000 −0.227921
309309 2.29844 0.130754
310310 7.40312 0.420469
311311 13.4031 0.760021 0.380011 0.924982i 0.375920π-0.375920\pi
0.380011 + 0.924982i 0.375920π0.375920\pi
312312 −5.70156 −0.322787
313313 −6.20937 −0.350974 −0.175487 0.984482i 0.556150π-0.556150\pi
−0.175487 + 0.984482i 0.556150π0.556150\pi
314314 1.40312 0.0791829
315315 3.70156 0.208559
316316 8.00000 0.450035
317317 −8.29844 −0.466087 −0.233043 0.972466i 0.574868π-0.574868\pi
−0.233043 + 0.972466i 0.574868π0.574868\pi
318318 9.40312 0.527301
319319 −1.19375 −0.0668373
320320 3.70156 0.206924
321321 18.8062 1.04966
322322 −1.00000 −0.0557278
323323 −21.6125 −1.20255
324324 1.00000 0.0555556
325325 49.6125 2.75201
326326 10.8062 0.598503
327327 −7.70156 −0.425897
328328 0.298438 0.0164785
329329 −11.1047 −0.612221
330330 14.8062 0.815057
331331 −20.0000 −1.09930 −0.549650 0.835395i 0.685239π-0.685239\pi
−0.549650 + 0.835395i 0.685239π0.685239\pi
332332 13.4031 0.735592
333333 4.29844 0.235553
334334 13.4031 0.733386
335335 54.8062 2.99439
336336 1.00000 0.0545545
337337 −4.20937 −0.229299 −0.114650 0.993406i 0.536575π-0.536575\pi
−0.114650 + 0.993406i 0.536575π0.536575\pi
338338 −19.5078 −1.06109
339339 7.10469 0.385874
340340 14.8062 0.802982
341341 8.00000 0.433224
342342 5.40312 0.292167
343343 1.00000 0.0539949
344344 1.70156 0.0917421
345345 3.70156 0.199285
346346 −19.4031 −1.04312
347347 −10.2984 −0.552849 −0.276425 0.961036i 0.589150π-0.589150\pi
−0.276425 + 0.961036i 0.589150π0.589150\pi
348348 0.298438 0.0159979
349349 12.5969 0.674295 0.337148 0.941452i 0.390538π-0.390538\pi
0.337148 + 0.941452i 0.390538π0.390538\pi
350350 −8.70156 −0.465118
351351 5.70156 0.304327
352352 4.00000 0.213201
353353 4.29844 0.228783 0.114391 0.993436i 0.463508π-0.463508\pi
0.114391 + 0.993436i 0.463508π0.463508\pi
354354 7.40312 0.393472
355355 −27.4031 −1.45441
356356 −11.4031 −0.604364
357357 4.00000 0.211702
358358 25.1047 1.32682
359359 −2.89531 −0.152809 −0.0764044 0.997077i 0.524344π-0.524344\pi
−0.0764044 + 0.997077i 0.524344π0.524344\pi
360360 −3.70156 −0.195089
361361 10.1938 0.536513
362362 16.8062 0.883317
363363 5.00000 0.262432
364364 5.70156 0.298843
365365 5.19375 0.271853
366366 2.00000 0.104542
367367 −17.1047 −0.892857 −0.446429 0.894819i 0.647304π-0.647304\pi
−0.446429 + 0.894819i 0.647304π0.647304\pi
368368 1.00000 0.0521286
369369 −0.298438 −0.0155361
370370 −15.9109 −0.827170
371371 −9.40312 −0.488186
372372 −2.00000 −0.103695
373373 −0.806248 −0.0417460 −0.0208730 0.999782i 0.506645π-0.506645\pi
−0.0208730 + 0.999782i 0.506645π0.506645\pi
374374 16.0000 0.827340
375375 13.7016 0.707546
376376 11.1047 0.572680
377377 1.70156 0.0876349
378378 −1.00000 −0.0514344
379379 13.7016 0.703802 0.351901 0.936037i 0.385535π-0.385535\pi
0.351901 + 0.936037i 0.385535π0.385535\pi
380380 −20.0000 −1.02598
381381 −5.70156 −0.292100
382382 −22.8062 −1.16687
383383 29.6125 1.51313 0.756564 0.653920i 0.226877π-0.226877\pi
0.756564 + 0.653920i 0.226877π0.226877\pi
384384 −1.00000 −0.0510310
385385 −14.8062 −0.754596
386386 23.1047 1.17600
387387 −1.70156 −0.0864953
388388 6.29844 0.319755
389389 −6.00000 −0.304212 −0.152106 0.988364i 0.548606π-0.548606\pi
−0.152106 + 0.988364i 0.548606π0.548606\pi
390390 −21.1047 −1.06868
391391 4.00000 0.202289
392392 −1.00000 −0.0505076
393393 −7.40312 −0.373438
394394 −22.5078 −1.13393
395395 29.6125 1.48997
396396 −4.00000 −0.201008
397397 8.59688 0.431465 0.215732 0.976453i 0.430786π-0.430786\pi
0.215732 + 0.976453i 0.430786π0.430786\pi
398398 2.29844 0.115210
399399 −5.40312 −0.270495
400400 8.70156 0.435078
401401 30.0000 1.49813 0.749064 0.662497i 0.230503π-0.230503\pi
0.749064 + 0.662497i 0.230503π0.230503\pi
402402 −14.8062 −0.738469
403403 −11.4031 −0.568030
404404 −3.40312 −0.169312
405405 3.70156 0.183932
406406 −0.298438 −0.0148112
407407 −17.1938 −0.852263
408408 −4.00000 −0.198030
409409 5.40312 0.267167 0.133584 0.991038i 0.457352π-0.457352\pi
0.133584 + 0.991038i 0.457352π0.457352\pi
410410 1.10469 0.0545566
411411 −19.7016 −0.971806
412412 2.29844 0.113236
413413 −7.40312 −0.364284
414414 −1.00000 −0.0491473
415415 49.6125 2.43538
416416 −5.70156 −0.279542
417417 17.7016 0.866849
418418 −21.6125 −1.05710
419419 −0.209373 −0.0102285 −0.00511426 0.999987i 0.501628π-0.501628\pi
−0.00511426 + 0.999987i 0.501628π0.501628\pi
420420 3.70156 0.180618
421421 −15.7016 −0.765247 −0.382624 0.923904i 0.624979π-0.624979\pi
−0.382624 + 0.923904i 0.624979π0.624979\pi
422422 −10.8062 −0.526040
423423 −11.1047 −0.539928
424424 9.40312 0.456656
425425 34.8062 1.68835
426426 7.40312 0.358683
427427 −2.00000 −0.0967868
428428 18.8062 0.909034
429429 −22.8062 −1.10110
430430 6.29844 0.303738
431431 −3.91093 −0.188383 −0.0941916 0.995554i 0.530027π-0.530027\pi
−0.0941916 + 0.995554i 0.530027π0.530027\pi
432432 1.00000 0.0481125
433433 31.3141 1.50486 0.752429 0.658674i 0.228882π-0.228882\pi
0.752429 + 0.658674i 0.228882π0.228882\pi
434434 2.00000 0.0960031
435435 1.10469 0.0529657
436436 −7.70156 −0.368838
437437 −5.40312 −0.258466
438438 −1.40312 −0.0670439
439439 −22.0000 −1.05000 −0.525001 0.851101i 0.675935π-0.675935\pi
−0.525001 + 0.851101i 0.675935π0.675935\pi
440440 14.8062 0.705860
441441 1.00000 0.0476190
442442 −22.8062 −1.08478
443443 −13.7016 −0.650981 −0.325490 0.945545i 0.605529π-0.605529\pi
−0.325490 + 0.945545i 0.605529π0.605529\pi
444444 4.29844 0.203995
445445 −42.2094 −2.00092
446446 22.0000 1.04173
447447 −20.2094 −0.955871
448448 1.00000 0.0472456
449449 −38.4187 −1.81309 −0.906546 0.422106i 0.861291π-0.861291\pi
−0.906546 + 0.422106i 0.861291π0.861291\pi
450450 −8.70156 −0.410196
451451 1.19375 0.0562116
452452 7.10469 0.334176
453453 23.9109 1.12343
454454 23.1047 1.08436
455455 21.1047 0.989403
456456 5.40312 0.253024
457457 28.2094 1.31958 0.659789 0.751451i 0.270645π-0.270645\pi
0.659789 + 0.751451i 0.270645π0.270645\pi
458458 14.5969 0.682067
459459 4.00000 0.186704
460460 3.70156 0.172586
461461 −2.20937 −0.102901 −0.0514504 0.998676i 0.516384π-0.516384\pi
−0.0514504 + 0.998676i 0.516384π0.516384\pi
462462 4.00000 0.186097
463463 −22.2984 −1.03630 −0.518148 0.855291i 0.673378π-0.673378\pi
−0.518148 + 0.855291i 0.673378π0.673378\pi
464464 0.298438 0.0138546
465465 −7.40312 −0.343312
466466 26.0000 1.20443
467467 −3.70156 −0.171288 −0.0856439 0.996326i 0.527295π-0.527295\pi
−0.0856439 + 0.996326i 0.527295π0.527295\pi
468468 5.70156 0.263555
469469 14.8062 0.683689
470470 41.1047 1.89602
471471 −1.40312 −0.0646526
472472 7.40312 0.340756
473473 6.80625 0.312952
474474 −8.00000 −0.367452
475475 −47.0156 −2.15722
476476 4.00000 0.183340
477477 −9.40312 −0.430539
478478 −10.8062 −0.494266
479479 16.5969 0.758331 0.379165 0.925329i 0.376211π-0.376211\pi
0.379165 + 0.925329i 0.376211π0.376211\pi
480480 −3.70156 −0.168952
481481 24.5078 1.11746
482482 15.9109 0.724723
483483 1.00000 0.0455016
484484 5.00000 0.227273
485485 23.3141 1.05864
486486 −1.00000 −0.0453609
487487 −6.29844 −0.285409 −0.142705 0.989765i 0.545580π-0.545580\pi
−0.142705 + 0.989765i 0.545580π0.545580\pi
488488 2.00000 0.0905357
489489 −10.8062 −0.488675
490490 −3.70156 −0.167220
491491 −9.61250 −0.433806 −0.216903 0.976193i 0.569596π-0.569596\pi
−0.216903 + 0.976193i 0.569596π0.569596\pi
492492 −0.298438 −0.0134546
493493 1.19375 0.0537639
494494 30.8062 1.38604
495495 −14.8062 −0.665491
496496 −2.00000 −0.0898027
497497 −7.40312 −0.332076
498498 −13.4031 −0.600608
499499 −23.4031 −1.04767 −0.523834 0.851820i 0.675499π-0.675499\pi
−0.523834 + 0.851820i 0.675499π0.675499\pi
500500 13.7016 0.612752
501501 −13.4031 −0.598807
502502 −19.7016 −0.879324
503503 4.59688 0.204965 0.102482 0.994735i 0.467322π-0.467322\pi
0.102482 + 0.994735i 0.467322π0.467322\pi
504504 −1.00000 −0.0445435
505505 −12.5969 −0.560554
506506 4.00000 0.177822
507507 19.5078 0.866372
508508 −5.70156 −0.252966
509509 37.6125 1.66714 0.833572 0.552410i 0.186292π-0.186292\pi
0.833572 + 0.552410i 0.186292π0.186292\pi
510510 −14.8062 −0.655632
511511 1.40312 0.0620706
512512 −1.00000 −0.0441942
513513 −5.40312 −0.238554
514514 −2.00000 −0.0882162
515515 8.50781 0.374899
516516 −1.70156 −0.0749071
517517 44.4187 1.95353
518518 −4.29844 −0.188863
519519 19.4031 0.851703
520520 −21.1047 −0.925502
521521 −20.5969 −0.902366 −0.451183 0.892432i 0.648998π-0.648998\pi
−0.451183 + 0.892432i 0.648998π0.648998\pi
522522 −0.298438 −0.0130623
523523 20.8062 0.909794 0.454897 0.890544i 0.349676π-0.349676\pi
0.454897 + 0.890544i 0.349676π0.349676\pi
524524 −7.40312 −0.323407
525525 8.70156 0.379767
526526 −9.70156 −0.423008
527527 −8.00000 −0.348485
528528 −4.00000 −0.174078
529529 1.00000 0.0434783
530530 34.8062 1.51189
531531 −7.40312 −0.321268
532532 −5.40312 −0.234255
533533 −1.70156 −0.0737028
534534 11.4031 0.493461
535535 69.6125 3.00961
536536 −14.8062 −0.639533
537537 −25.1047 −1.08335
538538 10.2094 0.440157
539539 −4.00000 −0.172292
540540 3.70156 0.159290
541541 33.4031 1.43611 0.718056 0.695985i 0.245032π-0.245032\pi
0.718056 + 0.695985i 0.245032π0.245032\pi
542542 −1.40312 −0.0602693
543543 −16.8062 −0.721225
544544 −4.00000 −0.171499
545545 −28.5078 −1.22114
546546 −5.70156 −0.244004
547547 29.0156 1.24062 0.620309 0.784357i 0.287007π-0.287007\pi
0.620309 + 0.784357i 0.287007π0.287007\pi
548548 −19.7016 −0.841609
549549 −2.00000 −0.0853579
550550 34.8062 1.48414
551551 −1.61250 −0.0686947
552552 −1.00000 −0.0425628
553553 8.00000 0.340195
554554 21.4031 0.909332
555555 15.9109 0.675382
556556 17.7016 0.750713
557557 −37.4031 −1.58482 −0.792411 0.609988i 0.791174π-0.791174\pi
−0.792411 + 0.609988i 0.791174π0.791174\pi
558558 2.00000 0.0846668
559559 −9.70156 −0.410332
560560 3.70156 0.156420
561561 −16.0000 −0.675521
562562 −14.5078 −0.611975
563563 −3.10469 −0.130847 −0.0654235 0.997858i 0.520840π-0.520840\pi
−0.0654235 + 0.997858i 0.520840π0.520840\pi
564564 −11.1047 −0.467592
565565 26.2984 1.10638
566566 −4.80625 −0.202022
567567 1.00000 0.0419961
568568 7.40312 0.310628
569569 31.7016 1.32900 0.664499 0.747289i 0.268645π-0.268645\pi
0.664499 + 0.747289i 0.268645π0.268645\pi
570570 20.0000 0.837708
571571 −14.8062 −0.619622 −0.309811 0.950798i 0.600266π-0.600266\pi
−0.309811 + 0.950798i 0.600266π0.600266\pi
572572 −22.8062 −0.953577
573573 22.8062 0.952745
574574 0.298438 0.0124566
575575 8.70156 0.362880
576576 1.00000 0.0416667
577577 −10.0000 −0.416305 −0.208153 0.978096i 0.566745π-0.566745\pi
−0.208153 + 0.978096i 0.566745π0.566745\pi
578578 1.00000 0.0415945
579579 −23.1047 −0.960198
580580 1.10469 0.0458696
581581 13.4031 0.556055
582582 −6.29844 −0.261079
583583 37.6125 1.55775
584584 −1.40312 −0.0580617
585585 21.1047 0.872571
586586 20.8062 0.859498
587587 14.8062 0.611119 0.305560 0.952173i 0.401156π-0.401156\pi
0.305560 + 0.952173i 0.401156π0.401156\pi
588588 1.00000 0.0412393
589589 10.8062 0.445264
590590 27.4031 1.12817
591591 22.5078 0.925848
592592 4.29844 0.176665
593593 43.7016 1.79461 0.897304 0.441413i 0.145523π-0.145523\pi
0.897304 + 0.441413i 0.145523π0.145523\pi
594594 4.00000 0.164122
595595 14.8062 0.606997
596596 −20.2094 −0.827808
597597 −2.29844 −0.0940688
598598 −5.70156 −0.233154
599599 13.6125 0.556192 0.278096 0.960553i 0.410297π-0.410297\pi
0.278096 + 0.960553i 0.410297π0.410297\pi
600600 −8.70156 −0.355240
601601 −13.4031 −0.546725 −0.273362 0.961911i 0.588136π-0.588136\pi
−0.273362 + 0.961911i 0.588136π0.588136\pi
602602 1.70156 0.0693505
603603 14.8062 0.602957
604604 23.9109 0.972922
605605 18.5078 0.752450
606606 3.40312 0.138242
607607 −39.6125 −1.60782 −0.803911 0.594750i 0.797251π-0.797251\pi
−0.803911 + 0.594750i 0.797251π0.797251\pi
608608 5.40312 0.219126
609609 0.298438 0.0120933
610610 7.40312 0.299744
611611 −63.3141 −2.56141
612612 4.00000 0.161690
613613 3.70156 0.149505 0.0747523 0.997202i 0.476183π-0.476183\pi
0.0747523 + 0.997202i 0.476183π0.476183\pi
614614 −11.9109 −0.480686
615615 −1.10469 −0.0445453
616616 4.00000 0.161165
617617 −19.1938 −0.772711 −0.386356 0.922350i 0.626266π-0.626266\pi
−0.386356 + 0.922350i 0.626266π0.626266\pi
618618 −2.29844 −0.0924567
619619 −7.19375 −0.289141 −0.144571 0.989494i 0.546180π-0.546180\pi
−0.144571 + 0.989494i 0.546180π0.546180\pi
620620 −7.40312 −0.297317
621621 1.00000 0.0401286
622622 −13.4031 −0.537416
623623 −11.4031 −0.456857
624624 5.70156 0.228245
625625 7.20937 0.288375
626626 6.20937 0.248176
627627 21.6125 0.863120
628628 −1.40312 −0.0559908
629629 17.1938 0.685560
630630 −3.70156 −0.147474
631631 −29.6125 −1.17885 −0.589427 0.807821i 0.700647π-0.700647\pi
−0.589427 + 0.807821i 0.700647π0.700647\pi
632632 −8.00000 −0.318223
633633 10.8062 0.429510
634634 8.29844 0.329573
635635 −21.1047 −0.837514
636636 −9.40312 −0.372858
637637 5.70156 0.225904
638638 1.19375 0.0472611
639639 −7.40312 −0.292863
640640 −3.70156 −0.146317
641641 −20.7172 −0.818280 −0.409140 0.912472i 0.634171π-0.634171\pi
−0.409140 + 0.912472i 0.634171π0.634171\pi
642642 −18.8062 −0.742223
643643 0.806248 0.0317953 0.0158977 0.999874i 0.494939π-0.494939\pi
0.0158977 + 0.999874i 0.494939π0.494939\pi
644644 1.00000 0.0394055
645645 −6.29844 −0.248001
646646 21.6125 0.850332
647647 −6.59688 −0.259350 −0.129675 0.991557i 0.541393π-0.541393\pi
−0.129675 + 0.991557i 0.541393π0.541393\pi
648648 −1.00000 −0.0392837
649649 29.6125 1.16239
650650 −49.6125 −1.94596
651651 −2.00000 −0.0783862
652652 −10.8062 −0.423205
653653 7.10469 0.278028 0.139014 0.990290i 0.455607π-0.455607\pi
0.139014 + 0.990290i 0.455607π0.455607\pi
654654 7.70156 0.301155
655655 −27.4031 −1.07073
656656 −0.298438 −0.0116520
657657 1.40312 0.0547411
658658 11.1047 0.432906
659659 8.00000 0.311636 0.155818 0.987786i 0.450199π-0.450199\pi
0.155818 + 0.987786i 0.450199π0.450199\pi
660660 −14.8062 −0.576332
661661 42.4187 1.64990 0.824949 0.565207i 0.191204π-0.191204\pi
0.824949 + 0.565207i 0.191204π0.191204\pi
662662 20.0000 0.777322
663663 22.8062 0.885721
664664 −13.4031 −0.520142
665665 −20.0000 −0.775567
666666 −4.29844 −0.166561
667667 0.298438 0.0115556
668668 −13.4031 −0.518582
669669 −22.0000 −0.850569
670670 −54.8062 −2.11735
671671 8.00000 0.308837
672672 −1.00000 −0.0385758
673673 7.70156 0.296873 0.148437 0.988922i 0.452576π-0.452576\pi
0.148437 + 0.988922i 0.452576π0.452576\pi
674674 4.20937 0.162139
675675 8.70156 0.334923
676676 19.5078 0.750300
677677 −50.4187 −1.93775 −0.968875 0.247551i 0.920374π-0.920374\pi
−0.968875 + 0.247551i 0.920374π0.920374\pi
678678 −7.10469 −0.272854
679679 6.29844 0.241712
680680 −14.8062 −0.567794
681681 −23.1047 −0.885374
682682 −8.00000 −0.306336
683683 33.6125 1.28615 0.643073 0.765805i 0.277659π-0.277659\pi
0.643073 + 0.765805i 0.277659π0.277659\pi
684684 −5.40312 −0.206594
685685 −72.9266 −2.78638
686686 −1.00000 −0.0381802
687687 −14.5969 −0.556906
688688 −1.70156 −0.0648714
689689 −53.6125 −2.04247
690690 −3.70156 −0.140916
691691 −0.507811 −0.0193180 −0.00965901 0.999953i 0.503075π-0.503075\pi
−0.00965901 + 0.999953i 0.503075π0.503075\pi
692692 19.4031 0.737596
693693 −4.00000 −0.151947
694694 10.2984 0.390923
695695 65.5234 2.48545
696696 −0.298438 −0.0113123
697697 −1.19375 −0.0452166
698698 −12.5969 −0.476799
699699 −26.0000 −0.983410
700700 8.70156 0.328888
701701 47.0156 1.77576 0.887878 0.460079i 0.152179π-0.152179\pi
0.887878 + 0.460079i 0.152179π0.152179\pi
702702 −5.70156 −0.215192
703703 −23.2250 −0.875947
704704 −4.00000 −0.150756
705705 −41.1047 −1.54809
706706 −4.29844 −0.161774
707707 −3.40312 −0.127988
708708 −7.40312 −0.278226
709709 23.1938 0.871060 0.435530 0.900174i 0.356561π-0.356561\pi
0.435530 + 0.900174i 0.356561π0.356561\pi
710710 27.4031 1.02842
711711 8.00000 0.300023
712712 11.4031 0.427350
713713 −2.00000 −0.0749006
714714 −4.00000 −0.149696
715715 −84.4187 −3.15708
716716 −25.1047 −0.938206
717717 10.8062 0.403567
718718 2.89531 0.108052
719719 −5.91093 −0.220441 −0.110220 0.993907i 0.535156π-0.535156\pi
−0.110220 + 0.993907i 0.535156π0.535156\pi
720720 3.70156 0.137949
721721 2.29844 0.0855983
722722 −10.1938 −0.379372
723723 −15.9109 −0.591734
724724 −16.8062 −0.624599
725725 2.59688 0.0964455
726726 −5.00000 −0.185567
727727 −12.0000 −0.445055 −0.222528 0.974926i 0.571431π-0.571431\pi
−0.222528 + 0.974926i 0.571431π0.571431\pi
728728 −5.70156 −0.211314
729729 1.00000 0.0370370
730730 −5.19375 −0.192229
731731 −6.80625 −0.251738
732732 −2.00000 −0.0739221
733733 52.2094 1.92840 0.964199 0.265181i 0.0854318π-0.0854318\pi
0.964199 + 0.265181i 0.0854318π0.0854318\pi
734734 17.1047 0.631345
735735 3.70156 0.136534
736736 −1.00000 −0.0368605
737737 −59.2250 −2.18158
738738 0.298438 0.0109857
739739 −29.0156 −1.06736 −0.533678 0.845687i 0.679191π-0.679191\pi
−0.533678 + 0.845687i 0.679191π0.679191\pi
740740 15.9109 0.584898
741741 −30.8062 −1.13170
742742 9.40312 0.345200
743743 32.0000 1.17397 0.586983 0.809599i 0.300316π-0.300316\pi
0.586983 + 0.809599i 0.300316π0.300316\pi
744744 2.00000 0.0733236
745745 −74.8062 −2.74069
746746 0.806248 0.0295189
747747 13.4031 0.490395
748748 −16.0000 −0.585018
749749 18.8062 0.687165
750750 −13.7016 −0.500310
751751 29.6125 1.08058 0.540288 0.841480i 0.318315π-0.318315\pi
0.540288 + 0.841480i 0.318315π0.318315\pi
752752 −11.1047 −0.404946
753753 19.7016 0.717965
754754 −1.70156 −0.0619672
755755 88.5078 3.22113
756756 1.00000 0.0363696
757757 −26.4187 −0.960206 −0.480103 0.877212i 0.659401π-0.659401\pi
−0.480103 + 0.877212i 0.659401π0.659401\pi
758758 −13.7016 −0.497663
759759 −4.00000 −0.145191
760760 20.0000 0.725476
761761 −35.6125 −1.29095 −0.645476 0.763781i 0.723341π-0.723341\pi
−0.645476 + 0.763781i 0.723341π0.723341\pi
762762 5.70156 0.206546
763763 −7.70156 −0.278815
764764 22.8062 0.825101
765765 14.8062 0.535321
766766 −29.6125 −1.06994
767767 −42.2094 −1.52409
768768 1.00000 0.0360844
769769 15.9109 0.573763 0.286881 0.957966i 0.407381π-0.407381\pi
0.286881 + 0.957966i 0.407381π0.407381\pi
770770 14.8062 0.533580
771771 2.00000 0.0720282
772772 −23.1047 −0.831556
773773 −7.10469 −0.255538 −0.127769 0.991804i 0.540782π-0.540782\pi
−0.127769 + 0.991804i 0.540782π0.540782\pi
774774 1.70156 0.0611614
775775 −17.4031 −0.625139
776776 −6.29844 −0.226101
777777 4.29844 0.154206
778778 6.00000 0.215110
779779 1.61250 0.0577737
780780 21.1047 0.755669
781781 29.6125 1.05962
782782 −4.00000 −0.143040
783783 0.298438 0.0106653
784784 1.00000 0.0357143
785785 −5.19375 −0.185373
786786 7.40312 0.264061
787787 −18.5969 −0.662907 −0.331454 0.943472i 0.607539π-0.607539\pi
−0.331454 + 0.943472i 0.607539π0.607539\pi
788788 22.5078 0.801808
789789 9.70156 0.345385
790790 −29.6125 −1.05357
791791 7.10469 0.252614
792792 4.00000 0.142134
793793 −11.4031 −0.404937
794794 −8.59688 −0.305092
795795 −34.8062 −1.23445
796796 −2.29844 −0.0814660
797797 15.7016 0.556178 0.278089 0.960555i 0.410299π-0.410299\pi
0.278089 + 0.960555i 0.410299π0.410299\pi
798798 5.40312 0.191269
799799 −44.4187 −1.57142
800800 −8.70156 −0.307647
801801 −11.4031 −0.402910
802802 −30.0000 −1.05934
803803 −5.61250 −0.198061
804804 14.8062 0.522176
805805 3.70156 0.130463
806806 11.4031 0.401658
807807 −10.2094 −0.359387
808808 3.40312 0.119721
809809 31.0156 1.09045 0.545226 0.838289i 0.316444π-0.316444\pi
0.545226 + 0.838289i 0.316444π0.316444\pi
810810 −3.70156 −0.130060
811811 52.5078 1.84380 0.921899 0.387430i 0.126637π-0.126637\pi
0.921899 + 0.387430i 0.126637π0.126637\pi
812812 0.298438 0.0104731
813813 1.40312 0.0492097
814814 17.1938 0.602641
815815 −40.0000 −1.40114
816816 4.00000 0.140028
817817 9.19375 0.321649
818818 −5.40312 −0.188916
819819 5.70156 0.199229
820820 −1.10469 −0.0385773
821821 27.6125 0.963683 0.481841 0.876258i 0.339968π-0.339968\pi
0.481841 + 0.876258i 0.339968π0.339968\pi
822822 19.7016 0.687171
823823 −13.7016 −0.477606 −0.238803 0.971068i 0.576755π-0.576755\pi
−0.238803 + 0.971068i 0.576755π0.576755\pi
824824 −2.29844 −0.0800699
825825 −34.8062 −1.21180
826826 7.40312 0.257588
827827 −47.4031 −1.64837 −0.824184 0.566322i 0.808366π-0.808366\pi
−0.824184 + 0.566322i 0.808366π0.808366\pi
828828 1.00000 0.0347524
829829 55.4031 1.92423 0.962115 0.272644i 0.0878981π-0.0878981\pi
0.962115 + 0.272644i 0.0878981π0.0878981\pi
830830 −49.6125 −1.72207
831831 −21.4031 −0.742466
832832 5.70156 0.197666
833833 4.00000 0.138592
834834 −17.7016 −0.612955
835835 −49.6125 −1.71691
836836 21.6125 0.747484
837837 −2.00000 −0.0691301
838838 0.209373 0.00723266
839839 42.2094 1.45723 0.728615 0.684924i 0.240165π-0.240165\pi
0.728615 + 0.684924i 0.240165π0.240165\pi
840840 −3.70156 −0.127716
841841 −28.9109 −0.996929
842842 15.7016 0.541112
843843 14.5078 0.499676
844844 10.8062 0.371966
845845 72.2094 2.48408
846846 11.1047 0.381787
847847 5.00000 0.171802
848848 −9.40312 −0.322905
849849 4.80625 0.164950
850850 −34.8062 −1.19384
851851 4.29844 0.147349
852852 −7.40312 −0.253627
853853 9.10469 0.311739 0.155869 0.987778i 0.450182π-0.450182\pi
0.155869 + 0.987778i 0.450182π0.450182\pi
854854 2.00000 0.0684386
855855 −20.0000 −0.683986
856856 −18.8062 −0.642784
857857 −0.298438 −0.0101944 −0.00509722 0.999987i 0.501623π-0.501623\pi
−0.00509722 + 0.999987i 0.501623π0.501623\pi
858858 22.8062 0.778592
859859 −15.4922 −0.528587 −0.264293 0.964442i 0.585139π-0.585139\pi
−0.264293 + 0.964442i 0.585139π0.585139\pi
860860 −6.29844 −0.214775
861861 −0.298438 −0.0101707
862862 3.91093 0.133207
863863 −6.38750 −0.217433 −0.108717 0.994073i 0.534674π-0.534674\pi
−0.108717 + 0.994073i 0.534674π0.534674\pi
864864 −1.00000 −0.0340207
865865 71.8219 2.44202
866866 −31.3141 −1.06410
867867 −1.00000 −0.0339618
868868 −2.00000 −0.0678844
869869 −32.0000 −1.08553
870870 −1.10469 −0.0374524
871871 84.4187 2.86042
872872 7.70156 0.260808
873873 6.29844 0.213170
874874 5.40312 0.182763
875875 13.7016 0.463197
876876 1.40312 0.0474072
877877 −17.4031 −0.587662 −0.293831 0.955857i 0.594930π-0.594930\pi
−0.293831 + 0.955857i 0.594930π0.594930\pi
878878 22.0000 0.742464
879879 −20.8062 −0.701777
880880 −14.8062 −0.499119
881881 6.20937 0.209199 0.104600 0.994514i 0.466644π-0.466644\pi
0.104600 + 0.994514i 0.466644π0.466644\pi
882882 −1.00000 −0.0336718
883883 −24.5969 −0.827751 −0.413875 0.910334i 0.635825π-0.635825\pi
−0.413875 + 0.910334i 0.635825π0.635825\pi
884884 22.8062 0.767057
885885 −27.4031 −0.921146
886886 13.7016 0.460313
887887 −28.2094 −0.947178 −0.473589 0.880746i 0.657042π-0.657042\pi
−0.473589 + 0.880746i 0.657042π0.657042\pi
888888 −4.29844 −0.144246
889889 −5.70156 −0.191224
890890 42.2094 1.41486
891891 −4.00000 −0.134005
892892 −22.0000 −0.736614
893893 60.0000 2.00782
894894 20.2094 0.675903
895895 −92.9266 −3.10619
896896 −1.00000 −0.0334077
897897 5.70156 0.190370
898898 38.4187 1.28205
899899 −0.596876 −0.0199069
900900 8.70156 0.290052
901901 −37.6125 −1.25305
902902 −1.19375 −0.0397476
903903 −1.70156 −0.0566244
904904 −7.10469 −0.236298
905905 −62.2094 −2.06791
906906 −23.9109 −0.794388
907907 20.5078 0.680951 0.340475 0.940253i 0.389412π-0.389412\pi
0.340475 + 0.940253i 0.389412π0.389412\pi
908908 −23.1047 −0.766756
909909 −3.40312 −0.112875
910910 −21.1047 −0.699614
911911 53.1047 1.75944 0.879718 0.475495i 0.157731π-0.157731\pi
0.879718 + 0.475495i 0.157731π0.157731\pi
912912 −5.40312 −0.178915
913913 −53.6125 −1.77431
914914 −28.2094 −0.933083
915915 −7.40312 −0.244740
916916 −14.5969 −0.482294
917917 −7.40312 −0.244473
918918 −4.00000 −0.132020
919919 −52.4187 −1.72913 −0.864567 0.502517i 0.832407π-0.832407\pi
−0.864567 + 0.502517i 0.832407π0.832407\pi
920920 −3.70156 −0.122037
921921 11.9109 0.392479
922922 2.20937 0.0727618
923923 −42.2094 −1.38934
924924 −4.00000 −0.131590
925925 37.4031 1.22981
926926 22.2984 0.732772
927927 2.29844 0.0754906
928928 −0.298438 −0.00979670
929929 −45.9109 −1.50629 −0.753144 0.657855i 0.771464π-0.771464\pi
−0.753144 + 0.657855i 0.771464π0.771464\pi
930930 7.40312 0.242758
931931 −5.40312 −0.177080
932932 −26.0000 −0.851658
933933 13.4031 0.438799
934934 3.70156 0.121119
935935 −59.2250 −1.93686
936936 −5.70156 −0.186361
937937 25.1047 0.820134 0.410067 0.912055i 0.365505π-0.365505\pi
0.410067 + 0.912055i 0.365505π0.365505\pi
938938 −14.8062 −0.483441
939939 −6.20937 −0.202635
940940 −41.1047 −1.34069
941941 25.3141 0.825215 0.412607 0.910909i 0.364618π-0.364618\pi
0.412607 + 0.910909i 0.364618π0.364618\pi
942942 1.40312 0.0457163
943943 −0.298438 −0.00971847
944944 −7.40312 −0.240951
945945 3.70156 0.120412
946946 −6.80625 −0.221290
947947 15.9109 0.517036 0.258518 0.966006i 0.416766π-0.416766\pi
0.258518 + 0.966006i 0.416766π0.416766\pi
948948 8.00000 0.259828
949949 8.00000 0.259691
950950 47.0156 1.52539
951951 −8.29844 −0.269095
952952 −4.00000 −0.129641
953953 61.2250 1.98327 0.991636 0.129066i 0.0411978π-0.0411978\pi
0.991636 + 0.129066i 0.0411978π0.0411978\pi
954954 9.40312 0.304437
955955 84.4187 2.73173
956956 10.8062 0.349499
957957 −1.19375 −0.0385885
958958 −16.5969 −0.536221
959959 −19.7016 −0.636197
960960 3.70156 0.119467
961961 −27.0000 −0.870968
962962 −24.5078 −0.790164
963963 18.8062 0.606023
964964 −15.9109 −0.512457
965965 −85.5234 −2.75310
966966 −1.00000 −0.0321745
967967 −14.8062 −0.476137 −0.238068 0.971248i 0.576514π-0.576514\pi
−0.238068 + 0.971248i 0.576514π0.576514\pi
968968 −5.00000 −0.160706
969969 −21.6125 −0.694293
970970 −23.3141 −0.748569
971971 49.8219 1.59886 0.799430 0.600759i 0.205135π-0.205135\pi
0.799430 + 0.600759i 0.205135π0.205135\pi
972972 1.00000 0.0320750
973973 17.7016 0.567486
974974 6.29844 0.201815
975975 49.6125 1.58887
976976 −2.00000 −0.0640184
977977 16.7172 0.534830 0.267415 0.963581i 0.413831π-0.413831\pi
0.267415 + 0.963581i 0.413831π0.413831\pi
978978 10.8062 0.345546
979979 45.6125 1.45778
980980 3.70156 0.118242
981981 −7.70156 −0.245892
982982 9.61250 0.306747
983983 42.2094 1.34627 0.673135 0.739520i 0.264947π-0.264947\pi
0.673135 + 0.739520i 0.264947π0.264947\pi
984984 0.298438 0.00951385
985985 83.3141 2.65461
986986 −1.19375 −0.0380168
987987 −11.1047 −0.353466
988988 −30.8062 −0.980077
989989 −1.70156 −0.0541065
990990 14.8062 0.470573
991991 28.0000 0.889449 0.444725 0.895667i 0.353302π-0.353302\pi
0.444725 + 0.895667i 0.353302π0.353302\pi
992992 2.00000 0.0635001
993993 −20.0000 −0.634681
994994 7.40312 0.234813
995995 −8.50781 −0.269716
996996 13.4031 0.424694
997997 −23.4031 −0.741184 −0.370592 0.928796i 0.620845π-0.620845\pi
−0.370592 + 0.928796i 0.620845π0.620845\pi
998998 23.4031 0.740813
999999 4.29844 0.135997
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 966.2.a.n.1.2 2
3.2 odd 2 2898.2.a.bb.1.1 2
4.3 odd 2 7728.2.a.bc.1.2 2
7.6 odd 2 6762.2.a.bo.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.a.n.1.2 2 1.1 even 1 trivial
2898.2.a.bb.1.1 2 3.2 odd 2
6762.2.a.bo.1.1 2 7.6 odd 2
7728.2.a.bc.1.2 2 4.3 odd 2