Properties

Label 165.2.a.c.1.2
Level 165165
Weight 22
Character 165.1
Self dual yes
Analytic conductor 1.3181.318
Analytic rank 00
Dimension 33
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] = [165,2,Mod(1,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, 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("165.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 165=3511 165 = 3 \cdot 5 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 165.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: 1.317531633351.31753163335
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x23x+1 x^{3} - x^{2} - 3x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.48119-1.48119 of defining polynomial
Character χ\chi == 165.1

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) == q0.193937q2+1.00000q31.96239q4+1.00000q50.193937q6+3.35026q7+0.768452q8+1.00000q90.193937q10+1.00000q111.96239q12+2.96239q130.649738q14+1.00000q15+3.77575q164.57452q170.193937q184.31265q191.96239q20+3.35026q210.193937q226.70052q23+0.768452q24+1.00000q250.574515q26+1.00000q276.57452q283.61213q290.193937q30+9.92478q312.26916q32+1.00000q33+0.887166q34+3.35026q351.96239q362.00000q37+0.836381q38+2.96239q39+0.768452q404.38787q410.649738q429.27504q431.96239q44+1.00000q45+1.29948q469.92478q47+3.77575q48+4.22425q490.193937q504.57452q515.81336q52+4.70052q530.193937q54+1.00000q55+2.57452q564.31265q57+0.700523q58+10.7005q591.96239q608.70052q611.92478q62+3.35026q637.11142q64+2.96239q650.193937q66+5.92478q67+8.97698q686.70052q690.649738q70+9.92478q71+0.768452q727.73813q73+0.387873q74+1.00000q75+8.46310q76+3.35026q770.574515q78+11.5369q79+3.77575q80+1.00000q81+0.850969q82+10.8872q836.57452q844.57452q85+1.79877q863.61213q87+0.768452q882.77575q890.193937q90+9.92478q91+13.1490q92+9.92478q93+1.92478q944.31265q952.26916q96+0.0752228q970.819237q98+1.00000q99+O(q100)q-0.193937 q^{2} +1.00000 q^{3} -1.96239 q^{4} +1.00000 q^{5} -0.193937 q^{6} +3.35026 q^{7} +0.768452 q^{8} +1.00000 q^{9} -0.193937 q^{10} +1.00000 q^{11} -1.96239 q^{12} +2.96239 q^{13} -0.649738 q^{14} +1.00000 q^{15} +3.77575 q^{16} -4.57452 q^{17} -0.193937 q^{18} -4.31265 q^{19} -1.96239 q^{20} +3.35026 q^{21} -0.193937 q^{22} -6.70052 q^{23} +0.768452 q^{24} +1.00000 q^{25} -0.574515 q^{26} +1.00000 q^{27} -6.57452 q^{28} -3.61213 q^{29} -0.193937 q^{30} +9.92478 q^{31} -2.26916 q^{32} +1.00000 q^{33} +0.887166 q^{34} +3.35026 q^{35} -1.96239 q^{36} -2.00000 q^{37} +0.836381 q^{38} +2.96239 q^{39} +0.768452 q^{40} -4.38787 q^{41} -0.649738 q^{42} -9.27504 q^{43} -1.96239 q^{44} +1.00000 q^{45} +1.29948 q^{46} -9.92478 q^{47} +3.77575 q^{48} +4.22425 q^{49} -0.193937 q^{50} -4.57452 q^{51} -5.81336 q^{52} +4.70052 q^{53} -0.193937 q^{54} +1.00000 q^{55} +2.57452 q^{56} -4.31265 q^{57} +0.700523 q^{58} +10.7005 q^{59} -1.96239 q^{60} -8.70052 q^{61} -1.92478 q^{62} +3.35026 q^{63} -7.11142 q^{64} +2.96239 q^{65} -0.193937 q^{66} +5.92478 q^{67} +8.97698 q^{68} -6.70052 q^{69} -0.649738 q^{70} +9.92478 q^{71} +0.768452 q^{72} -7.73813 q^{73} +0.387873 q^{74} +1.00000 q^{75} +8.46310 q^{76} +3.35026 q^{77} -0.574515 q^{78} +11.5369 q^{79} +3.77575 q^{80} +1.00000 q^{81} +0.850969 q^{82} +10.8872 q^{83} -6.57452 q^{84} -4.57452 q^{85} +1.79877 q^{86} -3.61213 q^{87} +0.768452 q^{88} -2.77575 q^{89} -0.193937 q^{90} +9.92478 q^{91} +13.1490 q^{92} +9.92478 q^{93} +1.92478 q^{94} -4.31265 q^{95} -2.26916 q^{96} +0.0752228 q^{97} -0.819237 q^{98} +1.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3qq2+3q3+5q4+3q5q69q8+3q9q10+3q11+5q122q1312q14+3q15+13q162q17q18+8q19+5q20q22++3q99+O(q100) 3 q - q^{2} + 3 q^{3} + 5 q^{4} + 3 q^{5} - q^{6} - 9 q^{8} + 3 q^{9} - q^{10} + 3 q^{11} + 5 q^{12} - 2 q^{13} - 12 q^{14} + 3 q^{15} + 13 q^{16} - 2 q^{17} - q^{18} + 8 q^{19} + 5 q^{20} - q^{22}+ \cdots + 3 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 −0.193937 −0.137134 −0.0685669 0.997647i 0.521843π-0.521843\pi
−0.0685669 + 0.997647i 0.521843π0.521843\pi
33 1.00000 0.577350
44 −1.96239 −0.981194
55 1.00000 0.447214
66 −0.193937 −0.0791743
77 3.35026 1.26628 0.633140 0.774037i 0.281766π-0.281766\pi
0.633140 + 0.774037i 0.281766π0.281766\pi
88 0.768452 0.271689
99 1.00000 0.333333
1010 −0.193937 −0.0613281
1111 1.00000 0.301511
1212 −1.96239 −0.566493
1313 2.96239 0.821619 0.410809 0.911721i 0.365246π-0.365246\pi
0.410809 + 0.911721i 0.365246π0.365246\pi
1414 −0.649738 −0.173650
1515 1.00000 0.258199
1616 3.77575 0.943937
1717 −4.57452 −1.10948 −0.554741 0.832023i 0.687183π-0.687183\pi
−0.554741 + 0.832023i 0.687183π0.687183\pi
1818 −0.193937 −0.0457113
1919 −4.31265 −0.989390 −0.494695 0.869067i 0.664720π-0.664720\pi
−0.494695 + 0.869067i 0.664720π0.664720\pi
2020 −1.96239 −0.438803
2121 3.35026 0.731087
2222 −0.193937 −0.0413474
2323 −6.70052 −1.39716 −0.698578 0.715534i 0.746183π-0.746183\pi
−0.698578 + 0.715534i 0.746183π0.746183\pi
2424 0.768452 0.156860
2525 1.00000 0.200000
2626 −0.574515 −0.112672
2727 1.00000 0.192450
2828 −6.57452 −1.24247
2929 −3.61213 −0.670755 −0.335378 0.942084i 0.608864π-0.608864\pi
−0.335378 + 0.942084i 0.608864π0.608864\pi
3030 −0.193937 −0.0354078
3131 9.92478 1.78254 0.891271 0.453470i 0.149814π-0.149814\pi
0.891271 + 0.453470i 0.149814π0.149814\pi
3232 −2.26916 −0.401134
3333 1.00000 0.174078
3434 0.887166 0.152148
3535 3.35026 0.566298
3636 −1.96239 −0.327065
3737 −2.00000 −0.328798 −0.164399 0.986394i 0.552568π-0.552568\pi
−0.164399 + 0.986394i 0.552568π0.552568\pi
3838 0.836381 0.135679
3939 2.96239 0.474362
4040 0.768452 0.121503
4141 −4.38787 −0.685271 −0.342635 0.939468i 0.611320π-0.611320\pi
−0.342635 + 0.939468i 0.611320π0.611320\pi
4242 −0.649738 −0.100257
4343 −9.27504 −1.41443 −0.707215 0.706998i 0.750049π-0.750049\pi
−0.707215 + 0.706998i 0.750049π0.750049\pi
4444 −1.96239 −0.295841
4545 1.00000 0.149071
4646 1.29948 0.191597
4747 −9.92478 −1.44768 −0.723839 0.689969i 0.757624π-0.757624\pi
−0.723839 + 0.689969i 0.757624π0.757624\pi
4848 3.77575 0.544982
4949 4.22425 0.603465
5050 −0.193937 −0.0274268
5151 −4.57452 −0.640560
5252 −5.81336 −0.806168
5353 4.70052 0.645667 0.322833 0.946456i 0.395365π-0.395365\pi
0.322833 + 0.946456i 0.395365π0.395365\pi
5454 −0.193937 −0.0263914
5555 1.00000 0.134840
5656 2.57452 0.344034
5757 −4.31265 −0.571224
5858 0.700523 0.0919832
5959 10.7005 1.39309 0.696545 0.717513i 0.254720π-0.254720\pi
0.696545 + 0.717513i 0.254720π0.254720\pi
6060 −1.96239 −0.253343
6161 −8.70052 −1.11399 −0.556994 0.830517i 0.688045π-0.688045\pi
−0.556994 + 0.830517i 0.688045π0.688045\pi
6262 −1.92478 −0.244447
6363 3.35026 0.422093
6464 −7.11142 −0.888927
6565 2.96239 0.367439
6666 −0.193937 −0.0238719
6767 5.92478 0.723827 0.361913 0.932212i 0.382124π-0.382124\pi
0.361913 + 0.932212i 0.382124π0.382124\pi
6868 8.97698 1.08862
6969 −6.70052 −0.806648
7070 −0.649738 −0.0776586
7171 9.92478 1.17785 0.588927 0.808186i 0.299550π-0.299550\pi
0.588927 + 0.808186i 0.299550π0.299550\pi
7272 0.768452 0.0905629
7373 −7.73813 −0.905680 −0.452840 0.891592i 0.649589π-0.649589\pi
−0.452840 + 0.891592i 0.649589π0.649589\pi
7474 0.387873 0.0450893
7575 1.00000 0.115470
7676 8.46310 0.970784
7777 3.35026 0.381798
7878 −0.574515 −0.0650511
7979 11.5369 1.29800 0.649002 0.760787i 0.275187π-0.275187\pi
0.649002 + 0.760787i 0.275187π0.275187\pi
8080 3.77575 0.422141
8181 1.00000 0.111111
8282 0.850969 0.0939738
8383 10.8872 1.19502 0.597511 0.801861i 0.296156π-0.296156\pi
0.597511 + 0.801861i 0.296156π0.296156\pi
8484 −6.57452 −0.717338
8585 −4.57452 −0.496176
8686 1.79877 0.193966
8787 −3.61213 −0.387261
8888 0.768452 0.0819173
8989 −2.77575 −0.294229 −0.147114 0.989120i 0.546999π-0.546999\pi
−0.147114 + 0.989120i 0.546999π0.546999\pi
9090 −0.193937 −0.0204427
9191 9.92478 1.04040
9292 13.1490 1.37088
9393 9.92478 1.02915
9494 1.92478 0.198526
9595 −4.31265 −0.442469
9696 −2.26916 −0.231595
9797 0.0752228 0.00763772 0.00381886 0.999993i 0.498784π-0.498784\pi
0.00381886 + 0.999993i 0.498784π0.498784\pi
9898 −0.819237 −0.0827555
9999 1.00000 0.100504
100100 −1.96239 −0.196239
101101 −15.0884 −1.50135 −0.750676 0.660671i 0.770272π-0.770272\pi
−0.750676 + 0.660671i 0.770272π0.770272\pi
102102 0.887166 0.0878425
103103 −3.22425 −0.317695 −0.158848 0.987303i 0.550778π-0.550778\pi
−0.158848 + 0.987303i 0.550778π0.550778\pi
104104 2.27645 0.223225
105105 3.35026 0.326952
106106 −0.911603 −0.0885427
107107 −0.962389 −0.0930376 −0.0465188 0.998917i 0.514813π-0.514813\pi
−0.0465188 + 0.998917i 0.514813π0.514813\pi
108108 −1.96239 −0.188831
109109 11.4010 1.09202 0.546011 0.837778i 0.316146π-0.316146\pi
0.546011 + 0.837778i 0.316146π0.316146\pi
110110 −0.193937 −0.0184911
111111 −2.00000 −0.189832
112112 12.6497 1.19529
113113 −6.00000 −0.564433 −0.282216 0.959351i 0.591070π-0.591070\pi
−0.282216 + 0.959351i 0.591070π0.591070\pi
114114 0.836381 0.0783342
115115 −6.70052 −0.624827
116116 7.08840 0.658141
117117 2.96239 0.273873
118118 −2.07522 −0.191040
119119 −15.3258 −1.40492
120120 0.768452 0.0701498
121121 1.00000 0.0909091
122122 1.68735 0.152765
123123 −4.38787 −0.395641
124124 −19.4763 −1.74902
125125 1.00000 0.0894427
126126 −0.649738 −0.0578833
127127 −14.5745 −1.29328 −0.646640 0.762796i 0.723826π-0.723826\pi
−0.646640 + 0.762796i 0.723826π0.723826\pi
128128 5.91748 0.523037
129129 −9.27504 −0.816622
130130 −0.574515 −0.0503883
131131 −5.92478 −0.517650 −0.258825 0.965924i 0.583335π-0.583335\pi
−0.258825 + 0.965924i 0.583335π0.583335\pi
132132 −1.96239 −0.170804
133133 −14.4485 −1.25284
134134 −1.14903 −0.0992612
135135 1.00000 0.0860663
136136 −3.51530 −0.301434
137137 13.8496 1.18325 0.591624 0.806214i 0.298487π-0.298487\pi
0.591624 + 0.806214i 0.298487π0.298487\pi
138138 1.29948 0.110619
139139 13.6121 1.15457 0.577283 0.816544i 0.304113π-0.304113\pi
0.577283 + 0.816544i 0.304113π0.304113\pi
140140 −6.57452 −0.555648
141141 −9.92478 −0.835817
142142 −1.92478 −0.161524
143143 2.96239 0.247727
144144 3.77575 0.314646
145145 −3.61213 −0.299971
146146 1.50071 0.124199
147147 4.22425 0.348411
148148 3.92478 0.322615
149149 1.53690 0.125908 0.0629540 0.998016i 0.479948π-0.479948\pi
0.0629540 + 0.998016i 0.479948π0.479948\pi
150150 −0.193937 −0.0158349
151151 −6.76116 −0.550215 −0.275108 0.961413i 0.588713π-0.588713\pi
−0.275108 + 0.961413i 0.588713π0.588713\pi
152152 −3.31406 −0.268806
153153 −4.57452 −0.369828
154154 −0.649738 −0.0523574
155155 9.92478 0.797177
156156 −5.81336 −0.465441
157157 −5.47627 −0.437054 −0.218527 0.975831i 0.570125π-0.570125\pi
−0.218527 + 0.975831i 0.570125π0.570125\pi
158158 −2.23743 −0.178000
159159 4.70052 0.372776
160160 −2.26916 −0.179393
161161 −22.4485 −1.76919
162162 −0.193937 −0.0152371
163163 12.6253 0.988890 0.494445 0.869209i 0.335371π-0.335371\pi
0.494445 + 0.869209i 0.335371π0.335371\pi
164164 8.61071 0.672384
165165 1.00000 0.0778499
166166 −2.11142 −0.163878
167167 18.3634 1.42101 0.710503 0.703695i 0.248468π-0.248468\pi
0.710503 + 0.703695i 0.248468π0.248468\pi
168168 2.57452 0.198628
169169 −4.22425 −0.324943
170170 0.887166 0.0680425
171171 −4.31265 −0.329797
172172 18.2012 1.38783
173173 −8.57452 −0.651908 −0.325954 0.945386i 0.605686π-0.605686\pi
−0.325954 + 0.945386i 0.605686π0.605686\pi
174174 0.700523 0.0531065
175175 3.35026 0.253256
176176 3.77575 0.284608
177177 10.7005 0.804301
178178 0.538319 0.0403487
179179 14.1768 1.05962 0.529812 0.848115i 0.322263π-0.322263\pi
0.529812 + 0.848115i 0.322263π0.322263\pi
180180 −1.96239 −0.146268
181181 −5.22425 −0.388316 −0.194158 0.980970i 0.562197π-0.562197\pi
−0.194158 + 0.980970i 0.562197π0.562197\pi
182182 −1.92478 −0.142674
183183 −8.70052 −0.643161
184184 −5.14903 −0.379592
185185 −2.00000 −0.147043
186186 −1.92478 −0.141132
187187 −4.57452 −0.334522
188188 19.4763 1.42045
189189 3.35026 0.243696
190190 0.836381 0.0606774
191191 −16.6253 −1.20296 −0.601482 0.798886i 0.705423π-0.705423\pi
−0.601482 + 0.798886i 0.705423π0.705423\pi
192192 −7.11142 −0.513222
193193 −16.3634 −1.17787 −0.588933 0.808182i 0.700452π-0.700452\pi
−0.588933 + 0.808182i 0.700452π0.700452\pi
194194 −0.0145884 −0.00104739
195195 2.96239 0.212141
196196 −8.28963 −0.592116
197197 −20.4241 −1.45515 −0.727577 0.686026i 0.759354π-0.759354\pi
−0.727577 + 0.686026i 0.759354π0.759354\pi
198198 −0.193937 −0.0137825
199199 −8.62530 −0.611431 −0.305716 0.952123i 0.598896π-0.598896\pi
−0.305716 + 0.952123i 0.598896π0.598896\pi
200200 0.768452 0.0543378
201201 5.92478 0.417902
202202 2.92619 0.205886
203203 −12.1016 −0.849364
204204 8.97698 0.628514
205205 −4.38787 −0.306462
206206 0.625301 0.0435668
207207 −6.70052 −0.465719
208208 11.1852 0.775556
209209 −4.31265 −0.298312
210210 −0.649738 −0.0448362
211211 9.08840 0.625671 0.312836 0.949807i 0.398721π-0.398721\pi
0.312836 + 0.949807i 0.398721π0.398721\pi
212212 −9.22425 −0.633524
213213 9.92478 0.680035
214214 0.186642 0.0127586
215215 −9.27504 −0.632552
216216 0.768452 0.0522865
217217 33.2506 2.25720
218218 −2.21108 −0.149753
219219 −7.73813 −0.522895
220220 −1.96239 −0.132304
221221 −13.5515 −0.911572
222222 0.387873 0.0260323
223223 −6.70052 −0.448700 −0.224350 0.974509i 0.572026π-0.572026\pi
−0.224350 + 0.974509i 0.572026π0.572026\pi
224224 −7.60228 −0.507949
225225 1.00000 0.0666667
226226 1.16362 0.0774028
227227 16.9624 1.12583 0.562917 0.826514i 0.309679π-0.309679\pi
0.562917 + 0.826514i 0.309679π0.309679\pi
228228 8.46310 0.560482
229229 25.8496 1.70819 0.854093 0.520120i 0.174113π-0.174113\pi
0.854093 + 0.520120i 0.174113π0.174113\pi
230230 1.29948 0.0856849
231231 3.35026 0.220431
232232 −2.77575 −0.182237
233233 −19.2750 −1.26275 −0.631375 0.775478i 0.717509π-0.717509\pi
−0.631375 + 0.775478i 0.717509π0.717509\pi
234234 −0.574515 −0.0375573
235235 −9.92478 −0.647421
236236 −20.9986 −1.36689
237237 11.5369 0.749402
238238 2.97224 0.192662
239239 26.5501 1.71738 0.858691 0.512494i 0.171278π-0.171278\pi
0.858691 + 0.512494i 0.171278π0.171278\pi
240240 3.77575 0.243723
241241 28.5501 1.83907 0.919536 0.393006i 0.128565π-0.128565\pi
0.919536 + 0.393006i 0.128565π0.128565\pi
242242 −0.193937 −0.0124667
243243 1.00000 0.0641500
244244 17.0738 1.09304
245245 4.22425 0.269878
246246 0.850969 0.0542558
247247 −12.7757 −0.812901
248248 7.62672 0.484297
249249 10.8872 0.689946
250250 −0.193937 −0.0122656
251251 29.9248 1.88884 0.944418 0.328748i 0.106627π-0.106627\pi
0.944418 + 0.328748i 0.106627π0.106627\pi
252252 −6.57452 −0.414156
253253 −6.70052 −0.421258
254254 2.82653 0.177352
255255 −4.57452 −0.286467
256256 13.0752 0.817201
257257 8.70052 0.542724 0.271362 0.962477i 0.412526π-0.412526\pi
0.271362 + 0.962477i 0.412526π0.412526\pi
258258 1.79877 0.111986
259259 −6.70052 −0.416350
260260 −5.81336 −0.360529
261261 −3.61213 −0.223585
262262 1.14903 0.0709874
263263 12.2882 0.757724 0.378862 0.925453i 0.376316π-0.376316\pi
0.378862 + 0.925453i 0.376316π0.376316\pi
264264 0.768452 0.0472950
265265 4.70052 0.288751
266266 2.80209 0.171807
267267 −2.77575 −0.169873
268268 −11.6267 −0.710215
269269 −5.84955 −0.356654 −0.178327 0.983971i 0.557068π-0.557068\pi
−0.178327 + 0.983971i 0.557068π0.557068\pi
270270 −0.193937 −0.0118026
271271 −5.08840 −0.309098 −0.154549 0.987985i 0.549392π-0.549392\pi
−0.154549 + 0.987985i 0.549392π0.549392\pi
272272 −17.2722 −1.04728
273273 9.92478 0.600675
274274 −2.68594 −0.162263
275275 1.00000 0.0603023
276276 13.1490 0.791479
277277 1.41090 0.0847725 0.0423863 0.999101i 0.486504π-0.486504\pi
0.0423863 + 0.999101i 0.486504π0.486504\pi
278278 −2.63989 −0.158330
279279 9.92478 0.594181
280280 2.57452 0.153857
281281 −4.38787 −0.261759 −0.130879 0.991398i 0.541780π-0.541780\pi
−0.130879 + 0.991398i 0.541780π0.541780\pi
282282 1.92478 0.114619
283283 26.5745 1.57969 0.789845 0.613306i 0.210161π-0.210161\pi
0.789845 + 0.613306i 0.210161π0.210161\pi
284284 −19.4763 −1.15570
285285 −4.31265 −0.255459
286286 −0.574515 −0.0339718
287287 −14.7005 −0.867744
288288 −2.26916 −0.133711
289289 3.92619 0.230952
290290 0.700523 0.0411362
291291 0.0752228 0.00440964
292292 15.1852 0.888648
293293 −3.42548 −0.200119 −0.100059 0.994981i 0.531903π-0.531903\pi
−0.100059 + 0.994981i 0.531903π0.531903\pi
294294 −0.819237 −0.0477789
295295 10.7005 0.623009
296296 −1.53690 −0.0893307
297297 1.00000 0.0580259
298298 −0.298062 −0.0172663
299299 −19.8496 −1.14793
300300 −1.96239 −0.113299
301301 −31.0738 −1.79106
302302 1.31124 0.0754531
303303 −15.0884 −0.866806
304304 −16.2835 −0.933921
305305 −8.70052 −0.498191
306306 0.887166 0.0507159
307307 −16.6497 −0.950251 −0.475125 0.879918i 0.657597π-0.657597\pi
−0.475125 + 0.879918i 0.657597π0.657597\pi
308308 −6.57452 −0.374618
309309 −3.22425 −0.183421
310310 −1.92478 −0.109320
311311 32.9986 1.87118 0.935589 0.353091i 0.114869π-0.114869\pi
0.935589 + 0.353091i 0.114869π0.114869\pi
312312 2.27645 0.128879
313313 15.4010 0.870519 0.435259 0.900305i 0.356657π-0.356657\pi
0.435259 + 0.900305i 0.356657π0.356657\pi
314314 1.06205 0.0599349
315315 3.35026 0.188766
316316 −22.6399 −1.27359
317317 2.15045 0.120781 0.0603905 0.998175i 0.480765π-0.480765\pi
0.0603905 + 0.998175i 0.480765π0.480765\pi
318318 −0.911603 −0.0511202
319319 −3.61213 −0.202240
320320 −7.11142 −0.397540
321321 −0.962389 −0.0537153
322322 4.35359 0.242616
323323 19.7283 1.09771
324324 −1.96239 −0.109022
325325 2.96239 0.164324
326326 −2.44851 −0.135610
327327 11.4010 0.630479
328328 −3.37187 −0.186180
329329 −33.2506 −1.83316
330330 −0.193937 −0.0106759
331331 −14.5501 −0.799745 −0.399872 0.916571i 0.630946π-0.630946\pi
−0.399872 + 0.916571i 0.630946π0.630946\pi
332332 −21.3649 −1.17255
333333 −2.00000 −0.109599
334334 −3.56134 −0.194868
335335 5.92478 0.323705
336336 12.6497 0.690100
337337 16.2619 0.885840 0.442920 0.896561i 0.353943π-0.353943\pi
0.442920 + 0.896561i 0.353943π0.353943\pi
338338 0.819237 0.0445606
339339 −6.00000 −0.325875
340340 8.97698 0.486845
341341 9.92478 0.537457
342342 0.836381 0.0452263
343343 −9.29948 −0.502125
344344 −7.12742 −0.384285
345345 −6.70052 −0.360744
346346 1.66291 0.0893987
347347 −0.962389 −0.0516637 −0.0258319 0.999666i 0.508223π-0.508223\pi
−0.0258319 + 0.999666i 0.508223π0.508223\pi
348348 7.08840 0.379978
349349 20.7005 1.10807 0.554037 0.832492i 0.313087π-0.313087\pi
0.554037 + 0.832492i 0.313087π0.313087\pi
350350 −0.649738 −0.0347300
351351 2.96239 0.158121
352352 −2.26916 −0.120947
353353 20.5501 1.09377 0.546885 0.837208i 0.315813π-0.315813\pi
0.546885 + 0.837208i 0.315813π0.315813\pi
354354 −2.07522 −0.110297
355355 9.92478 0.526752
356356 5.44709 0.288695
357357 −15.3258 −0.811129
358358 −2.74940 −0.145310
359359 17.9248 0.946034 0.473017 0.881053i 0.343165π-0.343165\pi
0.473017 + 0.881053i 0.343165π0.343165\pi
360360 0.768452 0.0405010
361361 −0.401047 −0.0211077
362362 1.01317 0.0532512
363363 1.00000 0.0524864
364364 −19.4763 −1.02083
365365 −7.73813 −0.405032
366366 1.68735 0.0881992
367367 −29.6531 −1.54788 −0.773939 0.633261i 0.781716π-0.781716\pi
−0.773939 + 0.633261i 0.781716π0.781716\pi
368368 −25.2995 −1.31883
369369 −4.38787 −0.228424
370370 0.387873 0.0201646
371371 15.7480 0.817595
372372 −19.4763 −1.00980
373373 −9.13918 −0.473209 −0.236604 0.971606i 0.576035π-0.576035\pi
−0.236604 + 0.971606i 0.576035π0.576035\pi
374374 0.887166 0.0458743
375375 1.00000 0.0516398
376376 −7.62672 −0.393318
377377 −10.7005 −0.551105
378378 −0.649738 −0.0334189
379379 −20.0000 −1.02733 −0.513665 0.857991i 0.671713π-0.671713\pi
−0.513665 + 0.857991i 0.671713π0.671713\pi
380380 8.46310 0.434148
381381 −14.5745 −0.746675
382382 3.22425 0.164967
383383 −34.9234 −1.78450 −0.892250 0.451541i 0.850874π-0.850874\pi
−0.892250 + 0.451541i 0.850874π0.850874\pi
384384 5.91748 0.301975
385385 3.35026 0.170745
386386 3.17347 0.161525
387387 −9.27504 −0.471477
388388 −0.147616 −0.00749408
389389 2.77575 0.140736 0.0703680 0.997521i 0.477583π-0.477583\pi
0.0703680 + 0.997521i 0.477583π0.477583\pi
390390 −0.574515 −0.0290917
391391 30.6516 1.55012
392392 3.24614 0.163955
393393 −5.92478 −0.298865
394394 3.96097 0.199551
395395 11.5369 0.580485
396396 −1.96239 −0.0986137
397397 −19.9248 −0.999996 −0.499998 0.866027i 0.666666π-0.666666\pi
−0.499998 + 0.866027i 0.666666π0.666666\pi
398398 1.67276 0.0838479
399399 −14.4485 −0.723330
400400 3.77575 0.188787
401401 2.00000 0.0998752 0.0499376 0.998752i 0.484098π-0.484098\pi
0.0499376 + 0.998752i 0.484098π0.484098\pi
402402 −1.14903 −0.0573085
403403 29.4010 1.46457
404404 29.6093 1.47312
405405 1.00000 0.0496904
406406 2.34694 0.116477
407407 −2.00000 −0.0991363
408408 −3.51530 −0.174033
409409 −13.0738 −0.646458 −0.323229 0.946321i 0.604768π-0.604768\pi
−0.323229 + 0.946321i 0.604768π0.604768\pi
410410 0.850969 0.0420264
411411 13.8496 0.683148
412412 6.32724 0.311721
413413 35.8496 1.76404
414414 1.29948 0.0638658
415415 10.8872 0.534430
416416 −6.72213 −0.329580
417417 13.6121 0.666589
418418 0.836381 0.0409087
419419 7.22425 0.352928 0.176464 0.984307i 0.443534π-0.443534\pi
0.176464 + 0.984307i 0.443534π0.443534\pi
420420 −6.57452 −0.320804
421421 30.6253 1.49259 0.746293 0.665618i 0.231832π-0.231832\pi
0.746293 + 0.665618i 0.231832π0.231832\pi
422422 −1.76257 −0.0858007
423423 −9.92478 −0.482559
424424 3.61213 0.175420
425425 −4.57452 −0.221897
426426 −1.92478 −0.0932558
427427 −29.1490 −1.41062
428428 1.88858 0.0912880
429429 2.96239 0.143025
430430 1.79877 0.0867444
431431 −33.8759 −1.63174 −0.815872 0.578232i 0.803743π-0.803743\pi
−0.815872 + 0.578232i 0.803743π0.803743\pi
432432 3.77575 0.181661
433433 −9.47627 −0.455400 −0.227700 0.973731i 0.573121π-0.573121\pi
−0.227700 + 0.973731i 0.573121π0.573121\pi
434434 −6.44851 −0.309538
435435 −3.61213 −0.173188
436436 −22.3733 −1.07149
437437 28.8970 1.38233
438438 1.50071 0.0717066
439439 −29.4617 −1.40613 −0.703065 0.711126i 0.748186π-0.748186\pi
−0.703065 + 0.711126i 0.748186π0.748186\pi
440440 0.768452 0.0366345
441441 4.22425 0.201155
442442 2.62813 0.125007
443443 −19.0738 −0.906224 −0.453112 0.891454i 0.649686π-0.649686\pi
−0.453112 + 0.891454i 0.649686π0.649686\pi
444444 3.92478 0.186262
445445 −2.77575 −0.131583
446446 1.29948 0.0615320
447447 1.53690 0.0726931
448448 −23.8251 −1.12563
449449 35.8759 1.69309 0.846544 0.532318i 0.178679π-0.178679\pi
0.846544 + 0.532318i 0.178679π0.178679\pi
450450 −0.193937 −0.00914226
451451 −4.38787 −0.206617
452452 11.7743 0.553818
453453 −6.76116 −0.317667
454454 −3.28963 −0.154390
455455 9.92478 0.465281
456456 −3.31406 −0.155195
457457 5.28963 0.247438 0.123719 0.992317i 0.460518π-0.460518\pi
0.123719 + 0.992317i 0.460518π0.460518\pi
458458 −5.01317 −0.234250
459459 −4.57452 −0.213520
460460 13.1490 0.613077
461461 36.3390 1.69248 0.846238 0.532805i 0.178862π-0.178862\pi
0.846238 + 0.532805i 0.178862π0.178862\pi
462462 −0.649738 −0.0302286
463463 10.5501 0.490304 0.245152 0.969485i 0.421162π-0.421162\pi
0.245152 + 0.969485i 0.421162π0.421162\pi
464464 −13.6385 −0.633150
465465 9.92478 0.460251
466466 3.73813 0.173166
467467 18.7005 0.865357 0.432679 0.901548i 0.357569π-0.357569\pi
0.432679 + 0.901548i 0.357569π0.357569\pi
468468 −5.81336 −0.268723
469469 19.8496 0.916567
470470 1.92478 0.0887834
471471 −5.47627 −0.252333
472472 8.22284 0.378487
473473 −9.27504 −0.426467
474474 −2.23743 −0.102768
475475 −4.31265 −0.197878
476476 30.0752 1.37850
477477 4.70052 0.215222
478478 −5.14903 −0.235511
479479 −9.29948 −0.424904 −0.212452 0.977172i 0.568145π-0.568145\pi
−0.212452 + 0.977172i 0.568145π0.568145\pi
480480 −2.26916 −0.103572
481481 −5.92478 −0.270147
482482 −5.53690 −0.252199
483483 −22.4485 −1.02144
484484 −1.96239 −0.0891995
485485 0.0752228 0.00341569
486486 −0.193937 −0.00879714
487487 −35.4763 −1.60758 −0.803792 0.594911i 0.797187π-0.797187\pi
−0.803792 + 0.594911i 0.797187π0.797187\pi
488488 −6.68594 −0.302658
489489 12.6253 0.570936
490490 −0.819237 −0.0370094
491491 24.7757 1.11811 0.559057 0.829129i 0.311163π-0.311163\pi
0.559057 + 0.829129i 0.311163π0.311163\pi
492492 8.61071 0.388201
493493 16.5237 0.744191
494494 2.47768 0.111476
495495 1.00000 0.0449467
496496 37.4734 1.68261
497497 33.2506 1.49149
498498 −2.11142 −0.0946150
499499 14.1768 0.634640 0.317320 0.948318i 0.397217π-0.397217\pi
0.317320 + 0.948318i 0.397217π0.397217\pi
500500 −1.96239 −0.0877607
501501 18.3634 0.820418
502502 −5.80351 −0.259023
503503 −8.43866 −0.376261 −0.188131 0.982144i 0.560243π-0.560243\pi
−0.188131 + 0.982144i 0.560243π0.560243\pi
504504 2.57452 0.114678
505505 −15.0884 −0.671425
506506 1.29948 0.0577688
507507 −4.22425 −0.187606
508508 28.6009 1.26896
509509 1.10299 0.0488890 0.0244445 0.999701i 0.492218π-0.492218\pi
0.0244445 + 0.999701i 0.492218π0.492218\pi
510510 0.887166 0.0392844
511511 −25.9248 −1.14684
512512 −14.3707 −0.635103
513513 −4.31265 −0.190408
514514 −1.68735 −0.0744258
515515 −3.22425 −0.142078
516516 18.2012 0.801265
517517 −9.92478 −0.436491
518518 1.29948 0.0570957
519519 −8.57452 −0.376379
520520 2.27645 0.0998291
521521 −12.4485 −0.545379 −0.272690 0.962102i 0.587913π-0.587913\pi
−0.272690 + 0.962102i 0.587913π0.587913\pi
522522 0.700523 0.0306611
523523 30.0508 1.31403 0.657015 0.753878i 0.271819π-0.271819\pi
0.657015 + 0.753878i 0.271819π0.271819\pi
524524 11.6267 0.507915
525525 3.35026 0.146217
526526 −2.38313 −0.103910
527527 −45.4010 −1.97770
528528 3.77575 0.164318
529529 21.8970 0.952044
530530 −0.911603 −0.0395975
531531 10.7005 0.464363
532532 28.3536 1.22928
533533 −12.9986 −0.563031
534534 0.538319 0.0232953
535535 −0.962389 −0.0416077
536536 4.55291 0.196656
537537 14.1768 0.611774
538538 1.13444 0.0489093
539539 4.22425 0.181951
540540 −1.96239 −0.0844478
541541 −18.0000 −0.773880 −0.386940 0.922105i 0.626468π-0.626468\pi
−0.386940 + 0.922105i 0.626468π0.626468\pi
542542 0.986826 0.0423878
543543 −5.22425 −0.224194
544544 10.3803 0.445052
545545 11.4010 0.488367
546546 −1.92478 −0.0823729
547547 −14.3028 −0.611544 −0.305772 0.952105i 0.598914π-0.598914\pi
−0.305772 + 0.952105i 0.598914π0.598914\pi
548548 −27.1782 −1.16100
549549 −8.70052 −0.371329
550550 −0.193937 −0.00826948
551551 15.5778 0.663638
552552 −5.14903 −0.219157
553553 38.6516 1.64364
554554 −0.273624 −0.0116252
555555 −2.00000 −0.0848953
556556 −26.7123 −1.13285
557557 −11.7988 −0.499930 −0.249965 0.968255i 0.580419π-0.580419\pi
−0.249965 + 0.968255i 0.580419π0.580419\pi
558558 −1.92478 −0.0814823
559559 −27.4763 −1.16212
560560 12.6497 0.534549
561561 −4.57452 −0.193136
562562 0.850969 0.0358960
563563 30.4847 1.28478 0.642389 0.766379i 0.277944π-0.277944\pi
0.642389 + 0.766379i 0.277944π0.277944\pi
564564 19.4763 0.820099
565565 −6.00000 −0.252422
566566 −5.15377 −0.216629
567567 3.35026 0.140698
568568 7.62672 0.320010
569569 −27.0884 −1.13560 −0.567802 0.823165i 0.692206π-0.692206\pi
−0.567802 + 0.823165i 0.692206π0.692206\pi
570570 0.836381 0.0350321
571571 7.28489 0.304863 0.152432 0.988314i 0.451290π-0.451290\pi
0.152432 + 0.988314i 0.451290π0.451290\pi
572572 −5.81336 −0.243069
573573 −16.6253 −0.694532
574574 2.85097 0.118997
575575 −6.70052 −0.279431
576576 −7.11142 −0.296309
577577 −31.6239 −1.31652 −0.658260 0.752791i 0.728707π-0.728707\pi
−0.658260 + 0.752791i 0.728707π0.728707\pi
578578 −0.761432 −0.0316714
579579 −16.3634 −0.680041
580580 7.08840 0.294330
581581 36.4749 1.51323
582582 −0.0145884 −0.000604711 0
583583 4.70052 0.194676
584584 −5.94639 −0.246063
585585 2.96239 0.122480
586586 0.664327 0.0274431
587587 33.1490 1.36821 0.684103 0.729385i 0.260194π-0.260194\pi
0.684103 + 0.729385i 0.260194π0.260194\pi
588588 −8.28963 −0.341858
589589 −42.8021 −1.76363
590590 −2.07522 −0.0854356
591591 −20.4241 −0.840134
592592 −7.55149 −0.310364
593593 34.4993 1.41672 0.708358 0.705853i 0.249436π-0.249436\pi
0.708358 + 0.705853i 0.249436π0.249436\pi
594594 −0.193937 −0.00795731
595595 −15.3258 −0.628298
596596 −3.01600 −0.123540
597597 −8.62530 −0.353010
598598 3.84955 0.157420
599599 −14.4485 −0.590350 −0.295175 0.955443i 0.595378π-0.595378\pi
−0.295175 + 0.955443i 0.595378π0.595378\pi
600600 0.768452 0.0313719
601601 −15.9248 −0.649585 −0.324793 0.945785i 0.605295π-0.605295\pi
−0.324793 + 0.945785i 0.605295π0.605295\pi
602602 6.02635 0.245616
603603 5.92478 0.241276
604604 13.2680 0.539868
605605 1.00000 0.0406558
606606 2.92619 0.118868
607607 −14.5745 −0.591561 −0.295781 0.955256i 0.595580π-0.595580\pi
−0.295781 + 0.955256i 0.595580π0.595580\pi
608608 9.78609 0.396878
609609 −12.1016 −0.490380
610610 1.68735 0.0683188
611611 −29.4010 −1.18944
612612 8.97698 0.362873
613613 16.4123 0.662887 0.331443 0.943475i 0.392464π-0.392464\pi
0.331443 + 0.943475i 0.392464π0.392464\pi
614614 3.22899 0.130312
615615 −4.38787 −0.176936
616616 2.57452 0.103730
617617 −17.8496 −0.718596 −0.359298 0.933223i 0.616984π-0.616984\pi
−0.359298 + 0.933223i 0.616984π0.616984\pi
618618 0.625301 0.0251533
619619 −0.402462 −0.0161763 −0.00808815 0.999967i 0.502575π-0.502575\pi
−0.00808815 + 0.999967i 0.502575π0.502575\pi
620620 −19.4763 −0.782186
621621 −6.70052 −0.268883
622622 −6.39963 −0.256602
623623 −9.29948 −0.372576
624624 11.1852 0.447767
625625 1.00000 0.0400000
626626 −2.98683 −0.119378
627627 −4.31265 −0.172231
628628 10.7466 0.428835
629629 9.14903 0.364796
630630 −0.649738 −0.0258862
631631 −38.0263 −1.51380 −0.756902 0.653528i 0.773288π-0.773288\pi
−0.756902 + 0.653528i 0.773288π0.773288\pi
632632 8.86556 0.352653
633633 9.08840 0.361231
634634 −0.417050 −0.0165632
635635 −14.5745 −0.578372
636636 −9.22425 −0.365765
637637 12.5139 0.495818
638638 0.700523 0.0277340
639639 9.92478 0.392618
640640 5.91748 0.233909
641641 −28.0263 −1.10697 −0.553487 0.832858i 0.686703π-0.686703\pi
−0.553487 + 0.832858i 0.686703π0.686703\pi
642642 0.186642 0.00736619
643643 −4.62530 −0.182404 −0.0912020 0.995832i 0.529071π-0.529071\pi
−0.0912020 + 0.995832i 0.529071π0.529071\pi
644644 44.0527 1.73592
645645 −9.27504 −0.365204
646646 −3.82604 −0.150533
647647 23.5778 0.926941 0.463470 0.886112i 0.346604π-0.346604\pi
0.463470 + 0.886112i 0.346604π0.346604\pi
648648 0.768452 0.0301876
649649 10.7005 0.420032
650650 −0.574515 −0.0225344
651651 33.2506 1.30319
652652 −24.7757 −0.970293
653653 −2.25202 −0.0881282 −0.0440641 0.999029i 0.514031π-0.514031\pi
−0.0440641 + 0.999029i 0.514031π0.514031\pi
654654 −2.21108 −0.0864601
655655 −5.92478 −0.231500
656656 −16.5675 −0.646852
657657 −7.73813 −0.301893
658658 6.44851 0.251389
659659 −41.4010 −1.61276 −0.806378 0.591401i 0.798575π-0.798575\pi
−0.806378 + 0.591401i 0.798575π0.798575\pi
660660 −1.96239 −0.0763859
661661 3.40105 0.132285 0.0661427 0.997810i 0.478931π-0.478931\pi
0.0661427 + 0.997810i 0.478931π0.478931\pi
662662 2.82179 0.109672
663663 −13.5515 −0.526296
664664 8.36626 0.324674
665665 −14.4485 −0.560289
666666 0.387873 0.0150298
667667 24.2031 0.937149
668668 −36.0362 −1.39428
669669 −6.70052 −0.259057
670670 −1.14903 −0.0443909
671671 −8.70052 −0.335880
672672 −7.60228 −0.293264
673673 0.887166 0.0341977 0.0170989 0.999854i 0.494557π-0.494557\pi
0.0170989 + 0.999854i 0.494557π0.494557\pi
674674 −3.15377 −0.121479
675675 1.00000 0.0384900
676676 8.28963 0.318832
677677 18.9018 0.726453 0.363227 0.931701i 0.381675π-0.381675\pi
0.363227 + 0.931701i 0.381675π0.381675\pi
678678 1.16362 0.0446885
679679 0.252016 0.00967149
680680 −3.51530 −0.134805
681681 16.9624 0.650000
682682 −1.92478 −0.0737035
683683 −20.8773 −0.798848 −0.399424 0.916766i 0.630790π-0.630790\pi
−0.399424 + 0.916766i 0.630790π0.630790\pi
684684 8.46310 0.323595
685685 13.8496 0.529164
686686 1.80351 0.0688583
687687 25.8496 0.986222
688688 −35.0202 −1.33513
689689 13.9248 0.530492
690690 1.29948 0.0494702
691691 −2.44851 −0.0931456 −0.0465728 0.998915i 0.514830π-0.514830\pi
−0.0465728 + 0.998915i 0.514830π0.514830\pi
692692 16.8265 0.639649
693693 3.35026 0.127266
694694 0.186642 0.00708485
695695 13.6121 0.516337
696696 −2.77575 −0.105214
697697 20.0724 0.760296
698698 −4.01459 −0.151954
699699 −19.2750 −0.729049
700700 −6.57452 −0.248493
701701 −2.98683 −0.112811 −0.0564054 0.998408i 0.517964π-0.517964\pi
−0.0564054 + 0.998408i 0.517964π0.517964\pi
702702 −0.574515 −0.0216837
703703 8.62530 0.325309
704704 −7.11142 −0.268022
705705 −9.92478 −0.373789
706706 −3.98541 −0.149993
707707 −50.5501 −1.90113
708708 −20.9986 −0.789175
709709 24.1768 0.907979 0.453989 0.891007i 0.350000π-0.350000\pi
0.453989 + 0.891007i 0.350000π0.350000\pi
710710 −1.92478 −0.0722356
711711 11.5369 0.432668
712712 −2.13303 −0.0799386
713713 −66.5012 −2.49049
714714 2.97224 0.111233
715715 2.96239 0.110787
716716 −27.8204 −1.03970
717717 26.5501 0.991531
718718 −3.47627 −0.129733
719719 −30.0263 −1.11979 −0.559897 0.828562i 0.689159π-0.689159\pi
−0.559897 + 0.828562i 0.689159π0.689159\pi
720720 3.77575 0.140714
721721 −10.8021 −0.402291
722722 0.0777777 0.00289459
723723 28.5501 1.06179
724724 10.2520 0.381013
725725 −3.61213 −0.134151
726726 −0.193937 −0.00719766
727727 14.9525 0.554559 0.277279 0.960789i 0.410567π-0.410567\pi
0.277279 + 0.960789i 0.410567π0.410567\pi
728728 7.62672 0.282665
729729 1.00000 0.0370370
730730 1.50071 0.0555437
731731 42.4288 1.56929
732732 17.0738 0.631066
733733 −19.1128 −0.705949 −0.352974 0.935633i 0.614830π-0.614830\pi
−0.352974 + 0.935633i 0.614830π0.614830\pi
734734 5.75081 0.212266
735735 4.22425 0.155814
736736 15.2046 0.560447
737737 5.92478 0.218242
738738 0.850969 0.0313246
739739 −3.31406 −0.121910 −0.0609549 0.998141i 0.519415π-0.519415\pi
−0.0609549 + 0.998141i 0.519415π0.519415\pi
740740 3.92478 0.144278
741741 −12.7757 −0.469329
742742 −3.05411 −0.112120
743743 −34.9887 −1.28361 −0.641806 0.766867i 0.721815π-0.721815\pi
−0.641806 + 0.766867i 0.721815π0.721815\pi
744744 7.62672 0.279609
745745 1.53690 0.0563078
746746 1.77242 0.0648930
747747 10.8872 0.398341
748748 8.97698 0.328231
749749 −3.22425 −0.117812
750750 −0.193937 −0.00708156
751751 −26.9234 −0.982447 −0.491224 0.871033i 0.663450π-0.663450\pi
−0.491224 + 0.871033i 0.663450π0.663450\pi
752752 −37.4734 −1.36652
753753 29.9248 1.09052
754754 2.07522 0.0755752
755755 −6.76116 −0.246064
756756 −6.57452 −0.239113
757757 15.9248 0.578796 0.289398 0.957209i 0.406545π-0.406545\pi
0.289398 + 0.957209i 0.406545π0.406545\pi
758758 3.87873 0.140882
759759 −6.70052 −0.243214
760760 −3.31406 −0.120214
761761 −30.9380 −1.12150 −0.560750 0.827985i 0.689487π-0.689487\pi
−0.560750 + 0.827985i 0.689487π0.689487\pi
762762 2.82653 0.102394
763763 38.1965 1.38281
764764 32.6253 1.18034
765765 −4.57452 −0.165392
766766 6.77292 0.244715
767767 31.6991 1.14459
768768 13.0752 0.471811
769769 9.32582 0.336298 0.168149 0.985762i 0.446221π-0.446221\pi
0.168149 + 0.985762i 0.446221π0.446221\pi
770770 −0.649738 −0.0234149
771771 8.70052 0.313342
772772 32.1114 1.15572
773773 44.7005 1.60777 0.803883 0.594787i 0.202764π-0.202764\pi
0.803883 + 0.594787i 0.202764π0.202764\pi
774774 1.79877 0.0646554
775775 9.92478 0.356509
776776 0.0578051 0.00207508
777777 −6.70052 −0.240380
778778 −0.538319 −0.0192997
779779 18.9234 0.678000
780780 −5.81336 −0.208152
781781 9.92478 0.355136
782782 −5.94448 −0.212574
783783 −3.61213 −0.129087
784784 15.9497 0.569633
785785 −5.47627 −0.195456
786786 1.14903 0.0409846
787787 21.6775 0.772719 0.386360 0.922348i 0.373732π-0.373732\pi
0.386360 + 0.922348i 0.373732π0.373732\pi
788788 40.0800 1.42779
789789 12.2882 0.437472
790790 −2.23743 −0.0796041
791791 −20.1016 −0.714730
792792 0.768452 0.0273058
793793 −25.7743 −0.915273
794794 3.86414 0.137133
795795 4.70052 0.166710
796796 16.9262 0.599933
797797 22.7466 0.805725 0.402862 0.915261i 0.368015π-0.368015\pi
0.402862 + 0.915261i 0.368015π0.368015\pi
798798 2.80209 0.0991930
799799 45.4010 1.60617
800800 −2.26916 −0.0802269
801801 −2.77575 −0.0980762
802802 −0.387873 −0.0136963
803803 −7.73813 −0.273073
804804 −11.6267 −0.410043
805805 −22.4485 −0.791206
806806 −5.70194 −0.200842
807807 −5.84955 −0.205914
808808 −11.5947 −0.407900
809809 −23.6121 −0.830158 −0.415079 0.909785i 0.636246π-0.636246\pi
−0.415079 + 0.909785i 0.636246π0.636246\pi
810810 −0.193937 −0.00681424
811811 −26.0870 −0.916038 −0.458019 0.888942i 0.651441π-0.651441\pi
−0.458019 + 0.888942i 0.651441π0.651441\pi
812812 23.7480 0.833391
813813 −5.08840 −0.178458
814814 0.387873 0.0135949
815815 12.6253 0.442245
816816 −17.2722 −0.604648
817817 40.0000 1.39942
818818 2.53549 0.0886513
819819 9.92478 0.346800
820820 8.61071 0.300699
821821 −54.4142 −1.89907 −0.949535 0.313662i 0.898444π-0.898444\pi
−0.949535 + 0.313662i 0.898444π0.898444\pi
822822 −2.68594 −0.0936827
823823 0.121269 0.00422716 0.00211358 0.999998i 0.499327π-0.499327\pi
0.00211358 + 0.999998i 0.499327π0.499327\pi
824824 −2.47768 −0.0863142
825825 1.00000 0.0348155
826826 −6.95254 −0.241910
827827 −18.2130 −0.633328 −0.316664 0.948538i 0.602563π-0.602563\pi
−0.316664 + 0.948538i 0.602563π0.602563\pi
828828 13.1490 0.456960
829829 13.0738 0.454072 0.227036 0.973886i 0.427096π-0.427096\pi
0.227036 + 0.973886i 0.427096π0.427096\pi
830830 −2.11142 −0.0732884
831831 1.41090 0.0489434
832832 −21.0668 −0.730359
833833 −19.3239 −0.669534
834834 −2.63989 −0.0914119
835835 18.3634 0.635493
836836 8.46310 0.292702
837837 9.92478 0.343050
838838 −1.40105 −0.0483984
839839 −26.5501 −0.916610 −0.458305 0.888795i 0.651543π-0.651543\pi
−0.458305 + 0.888795i 0.651543π0.651543\pi
840840 2.57452 0.0888292
841841 −15.9525 −0.550088
842842 −5.93937 −0.204684
843843 −4.38787 −0.151126
844844 −17.8350 −0.613905
845845 −4.22425 −0.145319
846846 1.92478 0.0661752
847847 3.35026 0.115116
848848 17.7480 0.609468
849849 26.5745 0.912035
850850 0.887166 0.0304295
851851 13.4010 0.459382
852852 −19.4763 −0.667246
853853 40.6155 1.39065 0.695323 0.718697i 0.255261π-0.255261\pi
0.695323 + 0.718697i 0.255261π0.255261\pi
854854 5.65306 0.193444
855855 −4.31265 −0.147490
856856 −0.739549 −0.0252773
857857 20.1721 0.689064 0.344532 0.938775i 0.388038π-0.388038\pi
0.344532 + 0.938775i 0.388038π0.388038\pi
858858 −0.574515 −0.0196136
859859 21.8035 0.743926 0.371963 0.928248i 0.378685π-0.378685\pi
0.371963 + 0.928248i 0.378685π0.378685\pi
860860 18.2012 0.620657
861861 −14.7005 −0.500993
862862 6.56978 0.223767
863863 35.4274 1.20596 0.602981 0.797755i 0.293979π-0.293979\pi
0.602981 + 0.797755i 0.293979π0.293979\pi
864864 −2.26916 −0.0771984
865865 −8.57452 −0.291542
866866 1.83780 0.0624508
867867 3.92619 0.133340
868868 −65.2506 −2.21475
869869 11.5369 0.391363
870870 0.700523 0.0237500
871871 17.5515 0.594710
872872 8.76116 0.296690
873873 0.0752228 0.00254591
874874 −5.60419 −0.189564
875875 3.35026 0.113260
876876 15.1852 0.513061
877877 −14.0362 −0.473969 −0.236984 0.971513i 0.576159π-0.576159\pi
−0.236984 + 0.971513i 0.576159π0.576159\pi
878878 5.71370 0.192828
879879 −3.42548 −0.115539
880880 3.77575 0.127280
881881 −21.0738 −0.709995 −0.354997 0.934867i 0.615518π-0.615518\pi
−0.354997 + 0.934867i 0.615518π0.615518\pi
882882 −0.819237 −0.0275852
883883 −42.1476 −1.41838 −0.709190 0.705017i 0.750939π-0.750939\pi
−0.709190 + 0.705017i 0.750939π0.750939\pi
884884 26.5933 0.894429
885885 10.7005 0.359694
886886 3.69911 0.124274
887887 6.93604 0.232889 0.116445 0.993197i 0.462850π-0.462850\pi
0.116445 + 0.993197i 0.462850π0.462850\pi
888888 −1.53690 −0.0515751
889889 −48.8284 −1.63765
890890 0.538319 0.0180445
891891 1.00000 0.0335013
892892 13.1490 0.440262
893893 42.8021 1.43232
894894 −0.298062 −0.00996868
895895 14.1768 0.473878
896896 19.8251 0.662311
897897 −19.8496 −0.662757
898898 −6.95765 −0.232180
899899 −35.8496 −1.19565
900900 −1.96239 −0.0654130
901901 −21.5026 −0.716356
902902 0.850969 0.0283342
903903 −31.0738 −1.03407
904904 −4.61071 −0.153350
905905 −5.22425 −0.173660
906906 1.31124 0.0435629
907907 53.2017 1.76653 0.883267 0.468870i 0.155339π-0.155339\pi
0.883267 + 0.468870i 0.155339π0.155339\pi
908908 −33.2868 −1.10466
909909 −15.0884 −0.500451
910910 −1.92478 −0.0638057
911911 36.4749 1.20847 0.604233 0.796808i 0.293480π-0.293480\pi
0.604233 + 0.796808i 0.293480π0.293480\pi
912912 −16.2835 −0.539200
913913 10.8872 0.360313
914914 −1.02585 −0.0339322
915915 −8.70052 −0.287630
916916 −50.7269 −1.67606
917917 −19.8496 −0.655490
918918 0.887166 0.0292808
919919 9.73340 0.321075 0.160538 0.987030i 0.448677π-0.448677\pi
0.160538 + 0.987030i 0.448677π0.448677\pi
920920 −5.14903 −0.169759
921921 −16.6497 −0.548628
922922 −7.04746 −0.232096
923923 29.4010 0.967747
924924 −6.57452 −0.216286
925925 −2.00000 −0.0657596
926926 −2.04605 −0.0672372
927927 −3.22425 −0.105898
928928 8.19649 0.269063
929929 −24.1768 −0.793215 −0.396607 0.917988i 0.629813π-0.629813\pi
−0.396607 + 0.917988i 0.629813π0.629813\pi
930930 −1.92478 −0.0631159
931931 −18.2177 −0.597062
932932 37.8251 1.23900
933933 32.9986 1.08033
934934 −3.62672 −0.118670
935935 −4.57452 −0.149603
936936 2.27645 0.0744082
937937 −7.48612 −0.244561 −0.122280 0.992496i 0.539021π-0.539021\pi
−0.122280 + 0.992496i 0.539021π0.539021\pi
938938 −3.84955 −0.125692
939939 15.4010 0.502594
940940 19.4763 0.635246
941941 −21.2360 −0.692274 −0.346137 0.938184i 0.612507π-0.612507\pi
−0.346137 + 0.938184i 0.612507π0.612507\pi
942942 1.06205 0.0346034
943943 29.4010 0.957430
944944 40.4025 1.31499
945945 3.35026 0.108984
946946 1.79877 0.0584830
947947 −15.4763 −0.502911 −0.251456 0.967869i 0.580909π-0.580909\pi
−0.251456 + 0.967869i 0.580909π0.580909\pi
948948 −22.6399 −0.735309
949949 −22.9234 −0.744124
950950 0.836381 0.0271358
951951 2.15045 0.0697330
952952 −11.7772 −0.381700
953953 −32.0508 −1.03823 −0.519113 0.854705i 0.673738π-0.673738\pi
−0.519113 + 0.854705i 0.673738π0.673738\pi
954954 −0.911603 −0.0295142
955955 −16.6253 −0.537982
956956 −52.1016 −1.68509
957957 −3.61213 −0.116763
958958 1.80351 0.0582687
959959 46.3996 1.49832
960960 −7.11142 −0.229520
961961 67.5012 2.17746
962962 1.14903 0.0370462
963963 −0.962389 −0.0310125
964964 −56.0263 −1.80449
965965 −16.3634 −0.526758
966966 4.35359 0.140074
967967 −17.3766 −0.558794 −0.279397 0.960176i 0.590135π-0.590135\pi
−0.279397 + 0.960176i 0.590135π0.590135\pi
968968 0.768452 0.0246990
969969 19.7283 0.633764
970970 −0.0145884 −0.000468407 0
971971 36.2031 1.16181 0.580907 0.813970i 0.302698π-0.302698\pi
0.580907 + 0.813970i 0.302698π0.302698\pi
972972 −1.96239 −0.0629436
973973 45.6042 1.46200
974974 6.88015 0.220454
975975 2.96239 0.0948724
976976 −32.8510 −1.05153
977977 −28.1476 −0.900522 −0.450261 0.892897i 0.648669π-0.648669\pi
−0.450261 + 0.892897i 0.648669π0.648669\pi
978978 −2.44851 −0.0782946
979979 −2.77575 −0.0887132
980980 −8.28963 −0.264802
981981 11.4010 0.364007
982982 −4.80492 −0.153331
983983 7.07381 0.225619 0.112810 0.993617i 0.464015π-0.464015\pi
0.112810 + 0.993617i 0.464015π0.464015\pi
984984 −3.37187 −0.107491
985985 −20.4241 −0.650765
986986 −3.20456 −0.102054
987987 −33.2506 −1.05838
988988 25.0710 0.797614
989989 62.1476 1.97618
990990 −0.193937 −0.00616371
991991 44.4260 1.41124 0.705619 0.708592i 0.250669π-0.250669\pi
0.705619 + 0.708592i 0.250669π0.250669\pi
992992 −22.5209 −0.715039
993993 −14.5501 −0.461733
994994 −6.44851 −0.204534
995995 −8.62530 −0.273440
996996 −21.3649 −0.676971
997997 −28.4847 −0.902120 −0.451060 0.892494i 0.648954π-0.648954\pi
−0.451060 + 0.892494i 0.648954π0.648954\pi
998998 −2.74940 −0.0870307
999999 −2.00000 −0.0632772
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 165.2.a.c.1.2 3
3.2 odd 2 495.2.a.e.1.2 3
4.3 odd 2 2640.2.a.be.1.1 3
5.2 odd 4 825.2.c.g.199.3 6
5.3 odd 4 825.2.c.g.199.4 6
5.4 even 2 825.2.a.k.1.2 3
7.6 odd 2 8085.2.a.bk.1.2 3
11.10 odd 2 1815.2.a.m.1.2 3
12.11 even 2 7920.2.a.cj.1.1 3
15.2 even 4 2475.2.c.r.199.4 6
15.8 even 4 2475.2.c.r.199.3 6
15.14 odd 2 2475.2.a.bb.1.2 3
33.32 even 2 5445.2.a.z.1.2 3
55.54 odd 2 9075.2.a.cf.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.a.c.1.2 3 1.1 even 1 trivial
495.2.a.e.1.2 3 3.2 odd 2
825.2.a.k.1.2 3 5.4 even 2
825.2.c.g.199.3 6 5.2 odd 4
825.2.c.g.199.4 6 5.3 odd 4
1815.2.a.m.1.2 3 11.10 odd 2
2475.2.a.bb.1.2 3 15.14 odd 2
2475.2.c.r.199.3 6 15.8 even 4
2475.2.c.r.199.4 6 15.2 even 4
2640.2.a.be.1.1 3 4.3 odd 2
5445.2.a.z.1.2 3 33.32 even 2
7920.2.a.cj.1.1 3 12.11 even 2
8085.2.a.bk.1.2 3 7.6 odd 2
9075.2.a.cf.1.2 3 55.54 odd 2