Properties

Label 275.2.a.g.1.1
Level 275275
Weight 22
Character 275.1
Self dual yes
Analytic conductor 2.1962.196
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] = [275,2,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, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("275.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 275=5211 275 = 5^{2} \cdot 11
Weight: k k == 2 2
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: 2.195886055592.19588605559
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ10)+\Q(\zeta_{10})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x1 x^{2} - x - 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 0.618034-0.618034 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) == q0.618034q2+0.381966q31.61803q40.236068q6+3.85410q7+2.23607q82.85410q9+1.00000q110.618034q12+1.76393q132.38197q14+1.85410q16+1.61803q17+1.76393q18+6.70820q19+1.47214q210.618034q22+7.09017q23+0.854102q241.09017q262.23607q276.23607q283.61803q293.00000q315.61803q32+0.381966q331.00000q34+4.61803q36+5.76393q374.14590q38+0.673762q393.00000q410.909830q426.00000q431.61803q444.38197q465.94427q47+0.708204q48+7.85410q49+0.618034q512.85410q526.32624q53+1.38197q54+8.61803q56+2.56231q57+2.23607q58+9.47214q5911.0902q61+1.85410q6211.0000q630.236068q640.236068q66+8.00000q672.61803q68+2.70820q6914.1803q716.38197q72+12.6180q733.56231q7410.8541q76+3.85410q770.416408q780.854102q79+7.70820q81+1.85410q8216.8541q832.38197q84+3.70820q861.38197q87+2.23607q8818.0902q89+6.79837q9111.4721q921.14590q93+3.67376q942.14590q960.618034q974.85410q982.85410q99+O(q100)q-0.618034 q^{2} +0.381966 q^{3} -1.61803 q^{4} -0.236068 q^{6} +3.85410 q^{7} +2.23607 q^{8} -2.85410 q^{9} +1.00000 q^{11} -0.618034 q^{12} +1.76393 q^{13} -2.38197 q^{14} +1.85410 q^{16} +1.61803 q^{17} +1.76393 q^{18} +6.70820 q^{19} +1.47214 q^{21} -0.618034 q^{22} +7.09017 q^{23} +0.854102 q^{24} -1.09017 q^{26} -2.23607 q^{27} -6.23607 q^{28} -3.61803 q^{29} -3.00000 q^{31} -5.61803 q^{32} +0.381966 q^{33} -1.00000 q^{34} +4.61803 q^{36} +5.76393 q^{37} -4.14590 q^{38} +0.673762 q^{39} -3.00000 q^{41} -0.909830 q^{42} -6.00000 q^{43} -1.61803 q^{44} -4.38197 q^{46} -5.94427 q^{47} +0.708204 q^{48} +7.85410 q^{49} +0.618034 q^{51} -2.85410 q^{52} -6.32624 q^{53} +1.38197 q^{54} +8.61803 q^{56} +2.56231 q^{57} +2.23607 q^{58} +9.47214 q^{59} -11.0902 q^{61} +1.85410 q^{62} -11.0000 q^{63} -0.236068 q^{64} -0.236068 q^{66} +8.00000 q^{67} -2.61803 q^{68} +2.70820 q^{69} -14.1803 q^{71} -6.38197 q^{72} +12.6180 q^{73} -3.56231 q^{74} -10.8541 q^{76} +3.85410 q^{77} -0.416408 q^{78} -0.854102 q^{79} +7.70820 q^{81} +1.85410 q^{82} -16.8541 q^{83} -2.38197 q^{84} +3.70820 q^{86} -1.38197 q^{87} +2.23607 q^{88} -18.0902 q^{89} +6.79837 q^{91} -11.4721 q^{92} -1.14590 q^{93} +3.67376 q^{94} -2.14590 q^{96} -0.618034 q^{97} -4.85410 q^{98} -2.85410 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q2+3q3q4+4q6+q7+q9+2q11+q12+8q137q143q16+q17+8q186q21+q22+3q235q24+9q268q285q29++q99+O(q100) 2 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{6} + q^{7} + q^{9} + 2 q^{11} + q^{12} + 8 q^{13} - 7 q^{14} - 3 q^{16} + q^{17} + 8 q^{18} - 6 q^{21} + q^{22} + 3 q^{23} - 5 q^{24} + 9 q^{26} - 8 q^{28} - 5 q^{29}+ \cdots + 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 −0.618034 −0.437016 −0.218508 0.975835i 0.570119π-0.570119\pi
−0.218508 + 0.975835i 0.570119π0.570119\pi
33 0.381966 0.220528 0.110264 0.993902i 0.464830π-0.464830\pi
0.110264 + 0.993902i 0.464830π0.464830\pi
44 −1.61803 −0.809017
55 0 0
66 −0.236068 −0.0963743
77 3.85410 1.45671 0.728357 0.685198i 0.240284π-0.240284\pi
0.728357 + 0.685198i 0.240284π0.240284\pi
88 2.23607 0.790569
99 −2.85410 −0.951367
1010 0 0
1111 1.00000 0.301511
1212 −0.618034 −0.178411
1313 1.76393 0.489227 0.244613 0.969621i 0.421339π-0.421339\pi
0.244613 + 0.969621i 0.421339π0.421339\pi
1414 −2.38197 −0.636607
1515 0 0
1616 1.85410 0.463525
1717 1.61803 0.392431 0.196215 0.980561i 0.437135π-0.437135\pi
0.196215 + 0.980561i 0.437135π0.437135\pi
1818 1.76393 0.415763
1919 6.70820 1.53897 0.769484 0.638666i 0.220514π-0.220514\pi
0.769484 + 0.638666i 0.220514π0.220514\pi
2020 0 0
2121 1.47214 0.321246
2222 −0.618034 −0.131765
2323 7.09017 1.47840 0.739201 0.673485i 0.235203π-0.235203\pi
0.739201 + 0.673485i 0.235203π0.235203\pi
2424 0.854102 0.174343
2525 0 0
2626 −1.09017 −0.213800
2727 −2.23607 −0.430331
2828 −6.23607 −1.17851
2929 −3.61803 −0.671852 −0.335926 0.941888i 0.609049π-0.609049\pi
−0.335926 + 0.941888i 0.609049π0.609049\pi
3030 0 0
3131 −3.00000 −0.538816 −0.269408 0.963026i 0.586828π-0.586828\pi
−0.269408 + 0.963026i 0.586828π0.586828\pi
3232 −5.61803 −0.993137
3333 0.381966 0.0664917
3434 −1.00000 −0.171499
3535 0 0
3636 4.61803 0.769672
3737 5.76393 0.947585 0.473792 0.880637i 0.342885π-0.342885\pi
0.473792 + 0.880637i 0.342885π0.342885\pi
3838 −4.14590 −0.672553
3939 0.673762 0.107888
4040 0 0
4141 −3.00000 −0.468521 −0.234261 0.972174i 0.575267π-0.575267\pi
−0.234261 + 0.972174i 0.575267π0.575267\pi
4242 −0.909830 −0.140390
4343 −6.00000 −0.914991 −0.457496 0.889212i 0.651253π-0.651253\pi
−0.457496 + 0.889212i 0.651253π0.651253\pi
4444 −1.61803 −0.243928
4545 0 0
4646 −4.38197 −0.646086
4747 −5.94427 −0.867061 −0.433531 0.901139i 0.642732π-0.642732\pi
−0.433531 + 0.901139i 0.642732π0.642732\pi
4848 0.708204 0.102220
4949 7.85410 1.12201
5050 0 0
5151 0.618034 0.0865421
5252 −2.85410 −0.395793
5353 −6.32624 −0.868976 −0.434488 0.900678i 0.643071π-0.643071\pi
−0.434488 + 0.900678i 0.643071π0.643071\pi
5454 1.38197 0.188062
5555 0 0
5656 8.61803 1.15163
5757 2.56231 0.339386
5858 2.23607 0.293610
5959 9.47214 1.23317 0.616584 0.787289i 0.288516π-0.288516\pi
0.616584 + 0.787289i 0.288516π0.288516\pi
6060 0 0
6161 −11.0902 −1.41995 −0.709975 0.704226i 0.751294π-0.751294\pi
−0.709975 + 0.704226i 0.751294π0.751294\pi
6262 1.85410 0.235471
6363 −11.0000 −1.38587
6464 −0.236068 −0.0295085
6565 0 0
6666 −0.236068 −0.0290580
6767 8.00000 0.977356 0.488678 0.872464i 0.337479π-0.337479\pi
0.488678 + 0.872464i 0.337479π0.337479\pi
6868 −2.61803 −0.317483
6969 2.70820 0.326029
7070 0 0
7171 −14.1803 −1.68290 −0.841448 0.540338i 0.818297π-0.818297\pi
−0.841448 + 0.540338i 0.818297π0.818297\pi
7272 −6.38197 −0.752122
7373 12.6180 1.47683 0.738415 0.674347i 0.235575π-0.235575\pi
0.738415 + 0.674347i 0.235575π0.235575\pi
7474 −3.56231 −0.414110
7575 0 0
7676 −10.8541 −1.24505
7777 3.85410 0.439216
7878 −0.416408 −0.0471489
7979 −0.854102 −0.0960940 −0.0480470 0.998845i 0.515300π-0.515300\pi
−0.0480470 + 0.998845i 0.515300π0.515300\pi
8080 0 0
8181 7.70820 0.856467
8282 1.85410 0.204751
8383 −16.8541 −1.84998 −0.924989 0.379994i 0.875926π-0.875926\pi
−0.924989 + 0.379994i 0.875926π0.875926\pi
8484 −2.38197 −0.259894
8585 0 0
8686 3.70820 0.399866
8787 −1.38197 −0.148162
8888 2.23607 0.238366
8989 −18.0902 −1.91755 −0.958777 0.284159i 0.908286π-0.908286\pi
−0.958777 + 0.284159i 0.908286π0.908286\pi
9090 0 0
9191 6.79837 0.712663
9292 −11.4721 −1.19605
9393 −1.14590 −0.118824
9494 3.67376 0.378920
9595 0 0
9696 −2.14590 −0.219015
9797 −0.618034 −0.0627518 −0.0313759 0.999508i 0.509989π-0.509989\pi
−0.0313759 + 0.999508i 0.509989π0.509989\pi
9898 −4.85410 −0.490338
9999 −2.85410 −0.286848
100100 0 0
101101 5.09017 0.506491 0.253245 0.967402i 0.418502π-0.418502\pi
0.253245 + 0.967402i 0.418502π0.418502\pi
102102 −0.381966 −0.0378203
103103 7.61803 0.750627 0.375314 0.926898i 0.377535π-0.377535\pi
0.375314 + 0.926898i 0.377535π0.377535\pi
104104 3.94427 0.386768
105105 0 0
106106 3.90983 0.379756
107107 0.236068 0.0228216 0.0114108 0.999935i 0.496368π-0.496368\pi
0.0114108 + 0.999935i 0.496368π0.496368\pi
108108 3.61803 0.348145
109109 8.09017 0.774898 0.387449 0.921891i 0.373356π-0.373356\pi
0.387449 + 0.921891i 0.373356π0.373356\pi
110110 0 0
111111 2.20163 0.208969
112112 7.14590 0.675224
113113 19.6525 1.84875 0.924375 0.381486i 0.124587π-0.124587\pi
0.924375 + 0.381486i 0.124587π0.124587\pi
114114 −1.58359 −0.148317
115115 0 0
116116 5.85410 0.543540
117117 −5.03444 −0.465434
118118 −5.85410 −0.538914
119119 6.23607 0.571659
120120 0 0
121121 1.00000 0.0909091
122122 6.85410 0.620541
123123 −1.14590 −0.103322
124124 4.85410 0.435911
125125 0 0
126126 6.79837 0.605647
127127 1.61803 0.143577 0.0717886 0.997420i 0.477129π-0.477129\pi
0.0717886 + 0.997420i 0.477129π0.477129\pi
128128 11.3820 1.00603
129129 −2.29180 −0.201781
130130 0 0
131131 −1.09017 −0.0952486 −0.0476243 0.998865i 0.515165π-0.515165\pi
−0.0476243 + 0.998865i 0.515165π0.515165\pi
132132 −0.618034 −0.0537930
133133 25.8541 2.24183
134134 −4.94427 −0.427120
135135 0 0
136136 3.61803 0.310244
137137 −14.5623 −1.24414 −0.622071 0.782961i 0.713708π-0.713708\pi
−0.622071 + 0.782961i 0.713708π0.713708\pi
138138 −1.67376 −0.142480
139139 −16.7082 −1.41717 −0.708586 0.705625i 0.750666π-0.750666\pi
−0.708586 + 0.705625i 0.750666π0.750666\pi
140140 0 0
141141 −2.27051 −0.191211
142142 8.76393 0.735453
143143 1.76393 0.147507
144144 −5.29180 −0.440983
145145 0 0
146146 −7.79837 −0.645398
147147 3.00000 0.247436
148148 −9.32624 −0.766612
149149 8.94427 0.732743 0.366372 0.930469i 0.380600π-0.380600\pi
0.366372 + 0.930469i 0.380600π0.380600\pi
150150 0 0
151151 −3.00000 −0.244137 −0.122068 0.992522i 0.538953π-0.538953\pi
−0.122068 + 0.992522i 0.538953π0.538953\pi
152152 15.0000 1.21666
153153 −4.61803 −0.373346
154154 −2.38197 −0.191944
155155 0 0
156156 −1.09017 −0.0872835
157157 21.4164 1.70922 0.854608 0.519274i 0.173798π-0.173798\pi
0.854608 + 0.519274i 0.173798π0.173798\pi
158158 0.527864 0.0419946
159159 −2.41641 −0.191634
160160 0 0
161161 27.3262 2.15361
162162 −4.76393 −0.374290
163163 −0.145898 −0.0114276 −0.00571381 0.999984i 0.501819π-0.501819\pi
−0.00571381 + 0.999984i 0.501819π0.501819\pi
164164 4.85410 0.379042
165165 0 0
166166 10.4164 0.808470
167167 −18.7082 −1.44768 −0.723842 0.689966i 0.757626π-0.757626\pi
−0.723842 + 0.689966i 0.757626π0.757626\pi
168168 3.29180 0.253968
169169 −9.88854 −0.760657
170170 0 0
171171 −19.1459 −1.46412
172172 9.70820 0.740244
173173 3.47214 0.263982 0.131991 0.991251i 0.457863π-0.457863\pi
0.131991 + 0.991251i 0.457863π0.457863\pi
174174 0.854102 0.0647493
175175 0 0
176176 1.85410 0.139758
177177 3.61803 0.271948
178178 11.1803 0.838002
179179 −11.3820 −0.850728 −0.425364 0.905022i 0.639854π-0.639854\pi
−0.425364 + 0.905022i 0.639854π0.639854\pi
180180 0 0
181181 5.09017 0.378349 0.189175 0.981943i 0.439419π-0.439419\pi
0.189175 + 0.981943i 0.439419π0.439419\pi
182182 −4.20163 −0.311445
183183 −4.23607 −0.313139
184184 15.8541 1.16878
185185 0 0
186186 0.708204 0.0519280
187187 1.61803 0.118322
188188 9.61803 0.701467
189189 −8.61803 −0.626870
190190 0 0
191191 −9.90983 −0.717050 −0.358525 0.933520i 0.616720π-0.616720\pi
−0.358525 + 0.933520i 0.616720π0.616720\pi
192192 −0.0901699 −0.00650746
193193 −4.94427 −0.355896 −0.177948 0.984040i 0.556946π-0.556946\pi
−0.177948 + 0.984040i 0.556946π0.556946\pi
194194 0.381966 0.0274236
195195 0 0
196196 −12.7082 −0.907729
197197 −8.90983 −0.634799 −0.317400 0.948292i 0.602810π-0.602810\pi
−0.317400 + 0.948292i 0.602810π0.602810\pi
198198 1.76393 0.125357
199199 8.09017 0.573497 0.286748 0.958006i 0.407426π-0.407426\pi
0.286748 + 0.958006i 0.407426π0.407426\pi
200200 0 0
201201 3.05573 0.215534
202202 −3.14590 −0.221345
203203 −13.9443 −0.978696
204204 −1.00000 −0.0700140
205205 0 0
206206 −4.70820 −0.328036
207207 −20.2361 −1.40650
208208 3.27051 0.226769
209209 6.70820 0.464016
210210 0 0
211211 17.0000 1.17033 0.585164 0.810915i 0.301030π-0.301030\pi
0.585164 + 0.810915i 0.301030π0.301030\pi
212212 10.2361 0.703016
213213 −5.41641 −0.371126
214214 −0.145898 −0.00997338
215215 0 0
216216 −5.00000 −0.340207
217217 −11.5623 −0.784900
218218 −5.00000 −0.338643
219219 4.81966 0.325682
220220 0 0
221221 2.85410 0.191988
222222 −1.36068 −0.0913228
223223 −18.8885 −1.26487 −0.632435 0.774613i 0.717945π-0.717945\pi
−0.632435 + 0.774613i 0.717945π0.717945\pi
224224 −21.6525 −1.44672
225225 0 0
226226 −12.1459 −0.807933
227227 5.03444 0.334148 0.167074 0.985944i 0.446568π-0.446568\pi
0.167074 + 0.985944i 0.446568π0.446568\pi
228228 −4.14590 −0.274569
229229 −17.0344 −1.12567 −0.562834 0.826570i 0.690289π-0.690289\pi
−0.562834 + 0.826570i 0.690289π0.690289\pi
230230 0 0
231231 1.47214 0.0968594
232232 −8.09017 −0.531146
233233 −22.5066 −1.47445 −0.737227 0.675645i 0.763865π-0.763865\pi
−0.737227 + 0.675645i 0.763865π0.763865\pi
234234 3.11146 0.203402
235235 0 0
236236 −15.3262 −0.997653
237237 −0.326238 −0.0211914
238238 −3.85410 −0.249824
239239 8.61803 0.557454 0.278727 0.960370i 0.410087π-0.410087\pi
0.278727 + 0.960370i 0.410087π0.410087\pi
240240 0 0
241241 −12.2705 −0.790413 −0.395207 0.918592i 0.629327π-0.629327\pi
−0.395207 + 0.918592i 0.629327π0.629327\pi
242242 −0.618034 −0.0397287
243243 9.65248 0.619207
244244 17.9443 1.14876
245245 0 0
246246 0.708204 0.0451534
247247 11.8328 0.752904
248248 −6.70820 −0.425971
249249 −6.43769 −0.407972
250250 0 0
251251 6.27051 0.395791 0.197896 0.980223i 0.436589π-0.436589\pi
0.197896 + 0.980223i 0.436589π0.436589\pi
252252 17.7984 1.12119
253253 7.09017 0.445755
254254 −1.00000 −0.0627456
255255 0 0
256256 −6.56231 −0.410144
257257 6.94427 0.433172 0.216586 0.976264i 0.430508π-0.430508\pi
0.216586 + 0.976264i 0.430508π0.430508\pi
258258 1.41641 0.0881817
259259 22.2148 1.38036
260260 0 0
261261 10.3262 0.639178
262262 0.673762 0.0416252
263263 −21.0000 −1.29492 −0.647458 0.762101i 0.724168π-0.724168\pi
−0.647458 + 0.762101i 0.724168π0.724168\pi
264264 0.854102 0.0525663
265265 0 0
266266 −15.9787 −0.979718
267267 −6.90983 −0.422875
268268 −12.9443 −0.790697
269269 14.6738 0.894675 0.447338 0.894365i 0.352372π-0.352372\pi
0.447338 + 0.894365i 0.352372π0.352372\pi
270270 0 0
271271 −9.18034 −0.557666 −0.278833 0.960340i 0.589948π-0.589948\pi
−0.278833 + 0.960340i 0.589948π0.589948\pi
272272 3.00000 0.181902
273273 2.59675 0.157162
274274 9.00000 0.543710
275275 0 0
276276 −4.38197 −0.263763
277277 −2.52786 −0.151885 −0.0759423 0.997112i 0.524196π-0.524196\pi
−0.0759423 + 0.997112i 0.524196π0.524196\pi
278278 10.3262 0.619327
279279 8.56231 0.512612
280280 0 0
281281 19.3607 1.15496 0.577481 0.816404i 0.304036π-0.304036\pi
0.577481 + 0.816404i 0.304036π0.304036\pi
282282 1.40325 0.0835625
283283 −9.61803 −0.571733 −0.285866 0.958269i 0.592281π-0.592281\pi
−0.285866 + 0.958269i 0.592281π0.592281\pi
284284 22.9443 1.36149
285285 0 0
286286 −1.09017 −0.0644631
287287 −11.5623 −0.682501
288288 16.0344 0.944839
289289 −14.3820 −0.845998
290290 0 0
291291 −0.236068 −0.0138385
292292 −20.4164 −1.19478
293293 11.8885 0.694536 0.347268 0.937766i 0.387109π-0.387109\pi
0.347268 + 0.937766i 0.387109π0.387109\pi
294294 −1.85410 −0.108133
295295 0 0
296296 12.8885 0.749131
297297 −2.23607 −0.129750
298298 −5.52786 −0.320221
299299 12.5066 0.723274
300300 0 0
301301 −23.1246 −1.33288
302302 1.85410 0.106692
303303 1.94427 0.111696
304304 12.4377 0.713351
305305 0 0
306306 2.85410 0.163158
307307 −22.4508 −1.28134 −0.640669 0.767817i 0.721343π-0.721343\pi
−0.640669 + 0.767817i 0.721343π0.721343\pi
308308 −6.23607 −0.355333
309309 2.90983 0.165534
310310 0 0
311311 3.18034 0.180341 0.0901703 0.995926i 0.471259π-0.471259\pi
0.0901703 + 0.995926i 0.471259π0.471259\pi
312312 1.50658 0.0852932
313313 1.23607 0.0698667 0.0349333 0.999390i 0.488878π-0.488878\pi
0.0349333 + 0.999390i 0.488878π0.488878\pi
314314 −13.2361 −0.746955
315315 0 0
316316 1.38197 0.0777417
317317 14.3820 0.807772 0.403886 0.914809i 0.367659π-0.367659\pi
0.403886 + 0.914809i 0.367659π0.367659\pi
318318 1.49342 0.0837470
319319 −3.61803 −0.202571
320320 0 0
321321 0.0901699 0.00503280
322322 −16.8885 −0.941162
323323 10.8541 0.603938
324324 −12.4721 −0.692896
325325 0 0
326326 0.0901699 0.00499405
327327 3.09017 0.170887
328328 −6.70820 −0.370399
329329 −22.9098 −1.26306
330330 0 0
331331 3.18034 0.174807 0.0874036 0.996173i 0.472143π-0.472143\pi
0.0874036 + 0.996173i 0.472143π0.472143\pi
332332 27.2705 1.49666
333333 −16.4508 −0.901501
334334 11.5623 0.632661
335335 0 0
336336 2.72949 0.148906
337337 −25.4164 −1.38452 −0.692260 0.721648i 0.743385π-0.743385\pi
−0.692260 + 0.721648i 0.743385π0.743385\pi
338338 6.11146 0.332419
339339 7.50658 0.407701
340340 0 0
341341 −3.00000 −0.162459
342342 11.8328 0.639845
343343 3.29180 0.177740
344344 −13.4164 −0.723364
345345 0 0
346346 −2.14590 −0.115364
347347 0.437694 0.0234967 0.0117483 0.999931i 0.496260π-0.496260\pi
0.0117483 + 0.999931i 0.496260π0.496260\pi
348348 2.23607 0.119866
349349 −31.8328 −1.70397 −0.851986 0.523565i 0.824602π-0.824602\pi
−0.851986 + 0.523565i 0.824602π0.824602\pi
350350 0 0
351351 −3.94427 −0.210530
352352 −5.61803 −0.299442
353353 −23.3607 −1.24336 −0.621682 0.783270i 0.713550π-0.713550\pi
−0.621682 + 0.783270i 0.713550π0.713550\pi
354354 −2.23607 −0.118846
355355 0 0
356356 29.2705 1.55133
357357 2.38197 0.126067
358358 7.03444 0.371782
359359 4.47214 0.236030 0.118015 0.993012i 0.462347π-0.462347\pi
0.118015 + 0.993012i 0.462347π0.462347\pi
360360 0 0
361361 26.0000 1.36842
362362 −3.14590 −0.165345
363363 0.381966 0.0200480
364364 −11.0000 −0.576557
365365 0 0
366366 2.61803 0.136847
367367 13.8541 0.723178 0.361589 0.932338i 0.382234π-0.382234\pi
0.361589 + 0.932338i 0.382234π0.382234\pi
368368 13.1459 0.685277
369369 8.56231 0.445736
370370 0 0
371371 −24.3820 −1.26585
372372 1.85410 0.0961307
373373 25.1803 1.30379 0.651894 0.758310i 0.273975π-0.273975\pi
0.651894 + 0.758310i 0.273975π0.273975\pi
374374 −1.00000 −0.0517088
375375 0 0
376376 −13.2918 −0.685472
377377 −6.38197 −0.328688
378378 5.32624 0.273952
379379 −22.2361 −1.14219 −0.571095 0.820884i 0.693481π-0.693481\pi
−0.571095 + 0.820884i 0.693481π0.693481\pi
380380 0 0
381381 0.618034 0.0316628
382382 6.12461 0.313362
383383 22.9443 1.17240 0.586199 0.810167i 0.300624π-0.300624\pi
0.586199 + 0.810167i 0.300624π0.300624\pi
384384 4.34752 0.221859
385385 0 0
386386 3.05573 0.155532
387387 17.1246 0.870493
388388 1.00000 0.0507673
389389 14.4721 0.733766 0.366883 0.930267i 0.380425π-0.380425\pi
0.366883 + 0.930267i 0.380425π0.380425\pi
390390 0 0
391391 11.4721 0.580171
392392 17.5623 0.887030
393393 −0.416408 −0.0210050
394394 5.50658 0.277417
395395 0 0
396396 4.61803 0.232065
397397 26.0902 1.30943 0.654714 0.755877i 0.272789π-0.272789\pi
0.654714 + 0.755877i 0.272789π0.272789\pi
398398 −5.00000 −0.250627
399399 9.87539 0.494388
400400 0 0
401401 −10.3607 −0.517388 −0.258694 0.965959i 0.583292π-0.583292\pi
−0.258694 + 0.965959i 0.583292π0.583292\pi
402402 −1.88854 −0.0941920
403403 −5.29180 −0.263603
404404 −8.23607 −0.409760
405405 0 0
406406 8.61803 0.427706
407407 5.76393 0.285708
408408 1.38197 0.0684175
409409 −20.1246 −0.995098 −0.497549 0.867436i 0.665767π-0.665767\pi
−0.497549 + 0.867436i 0.665767π0.665767\pi
410410 0 0
411411 −5.56231 −0.274368
412412 −12.3262 −0.607270
413413 36.5066 1.79637
414414 12.5066 0.614665
415415 0 0
416416 −9.90983 −0.485869
417417 −6.38197 −0.312526
418418 −4.14590 −0.202783
419419 −1.18034 −0.0576634 −0.0288317 0.999584i 0.509179π-0.509179\pi
−0.0288317 + 0.999584i 0.509179π0.509179\pi
420420 0 0
421421 21.2705 1.03666 0.518331 0.855180i 0.326554π-0.326554\pi
0.518331 + 0.855180i 0.326554π0.326554\pi
422422 −10.5066 −0.511452
423423 16.9656 0.824894
424424 −14.1459 −0.686986
425425 0 0
426426 3.34752 0.162188
427427 −42.7426 −2.06846
428428 −0.381966 −0.0184630
429429 0.673762 0.0325295
430430 0 0
431431 23.1803 1.11656 0.558279 0.829653i 0.311462π-0.311462\pi
0.558279 + 0.829653i 0.311462π0.311462\pi
432432 −4.14590 −0.199470
433433 16.8885 0.811612 0.405806 0.913959i 0.366991π-0.366991\pi
0.405806 + 0.913959i 0.366991π0.366991\pi
434434 7.14590 0.343014
435435 0 0
436436 −13.0902 −0.626905
437437 47.5623 2.27521
438438 −2.97871 −0.142328
439439 −34.2705 −1.63564 −0.817821 0.575473i 0.804818π-0.804818\pi
−0.817821 + 0.575473i 0.804818π0.804818\pi
440440 0 0
441441 −22.4164 −1.06745
442442 −1.76393 −0.0839017
443443 −5.34752 −0.254069 −0.127034 0.991898i 0.540546π-0.540546\pi
−0.127034 + 0.991898i 0.540546π0.540546\pi
444444 −3.56231 −0.169060
445445 0 0
446446 11.6738 0.552769
447447 3.41641 0.161591
448448 −0.909830 −0.0429854
449449 0.326238 0.0153961 0.00769806 0.999970i 0.497550π-0.497550\pi
0.00769806 + 0.999970i 0.497550π0.497550\pi
450450 0 0
451451 −3.00000 −0.141264
452452 −31.7984 −1.49567
453453 −1.14590 −0.0538390
454454 −3.11146 −0.146028
455455 0 0
456456 5.72949 0.268308
457457 38.9787 1.82335 0.911674 0.410915i 0.134791π-0.134791\pi
0.911674 + 0.410915i 0.134791π0.134791\pi
458458 10.5279 0.491935
459459 −3.61803 −0.168875
460460 0 0
461461 13.1803 0.613870 0.306935 0.951731i 0.400697π-0.400697\pi
0.306935 + 0.951731i 0.400697π0.400697\pi
462462 −0.909830 −0.0423291
463463 −33.3607 −1.55040 −0.775201 0.631714i 0.782352π-0.782352\pi
−0.775201 + 0.631714i 0.782352π0.782352\pi
464464 −6.70820 −0.311421
465465 0 0
466466 13.9098 0.644360
467467 28.5279 1.32011 0.660056 0.751216i 0.270533π-0.270533\pi
0.660056 + 0.751216i 0.270533π0.270533\pi
468468 8.14590 0.376544
469469 30.8328 1.42373
470470 0 0
471471 8.18034 0.376930
472472 21.1803 0.974904
473473 −6.00000 −0.275880
474474 0.201626 0.00926099
475475 0 0
476476 −10.0902 −0.462482
477477 18.0557 0.826715
478478 −5.32624 −0.243616
479479 1.58359 0.0723562 0.0361781 0.999345i 0.488482π-0.488482\pi
0.0361781 + 0.999345i 0.488482π0.488482\pi
480480 0 0
481481 10.1672 0.463584
482482 7.58359 0.345423
483483 10.4377 0.474932
484484 −1.61803 −0.0735470
485485 0 0
486486 −5.96556 −0.270603
487487 −3.58359 −0.162388 −0.0811940 0.996698i 0.525873π-0.525873\pi
−0.0811940 + 0.996698i 0.525873π0.525873\pi
488488 −24.7984 −1.12257
489489 −0.0557281 −0.00252011
490490 0 0
491491 −29.1803 −1.31689 −0.658445 0.752629i 0.728786π-0.728786\pi
−0.658445 + 0.752629i 0.728786π0.728786\pi
492492 1.85410 0.0835894
493493 −5.85410 −0.263655
494494 −7.31308 −0.329031
495495 0 0
496496 −5.56231 −0.249755
497497 −54.6525 −2.45150
498498 3.97871 0.178290
499499 5.20163 0.232857 0.116428 0.993199i 0.462855π-0.462855\pi
0.116428 + 0.993199i 0.462855π0.462855\pi
500500 0 0
501501 −7.14590 −0.319255
502502 −3.87539 −0.172967
503503 24.6525 1.09920 0.549600 0.835428i 0.314780π-0.314780\pi
0.549600 + 0.835428i 0.314780π0.314780\pi
504504 −24.5967 −1.09563
505505 0 0
506506 −4.38197 −0.194802
507507 −3.77709 −0.167746
508508 −2.61803 −0.116156
509509 18.6180 0.825230 0.412615 0.910906i 0.364616π-0.364616\pi
0.412615 + 0.910906i 0.364616π0.364616\pi
510510 0 0
511511 48.6312 2.15132
512512 −18.7082 −0.826794
513513 −15.0000 −0.662266
514514 −4.29180 −0.189303
515515 0 0
516516 3.70820 0.163245
517517 −5.94427 −0.261429
518518 −13.7295 −0.603239
519519 1.32624 0.0582154
520520 0 0
521521 −24.1803 −1.05936 −0.529680 0.848198i 0.677688π-0.677688\pi
−0.529680 + 0.848198i 0.677688π0.677688\pi
522522 −6.38197 −0.279331
523523 5.05573 0.221072 0.110536 0.993872i 0.464743π-0.464743\pi
0.110536 + 0.993872i 0.464743π0.464743\pi
524524 1.76393 0.0770577
525525 0 0
526526 12.9787 0.565899
527527 −4.85410 −0.211448
528528 0.708204 0.0308206
529529 27.2705 1.18567
530530 0 0
531531 −27.0344 −1.17319
532532 −41.8328 −1.81368
533533 −5.29180 −0.229213
534534 4.27051 0.184803
535535 0 0
536536 17.8885 0.772667
537537 −4.34752 −0.187610
538538 −9.06888 −0.390987
539539 7.85410 0.338300
540540 0 0
541541 −8.72949 −0.375310 −0.187655 0.982235i 0.560089π-0.560089\pi
−0.187655 + 0.982235i 0.560089π0.560089\pi
542542 5.67376 0.243709
543543 1.94427 0.0834367
544544 −9.09017 −0.389738
545545 0 0
546546 −1.60488 −0.0686825
547547 −27.8541 −1.19096 −0.595478 0.803372i 0.703037π-0.703037\pi
−0.595478 + 0.803372i 0.703037π0.703037\pi
548548 23.5623 1.00653
549549 31.6525 1.35089
550550 0 0
551551 −24.2705 −1.03396
552552 6.05573 0.257749
553553 −3.29180 −0.139981
554554 1.56231 0.0663760
555555 0 0
556556 27.0344 1.14652
557557 −14.2361 −0.603202 −0.301601 0.953434i 0.597521π-0.597521\pi
−0.301601 + 0.953434i 0.597521π0.597521\pi
558558 −5.29180 −0.224020
559559 −10.5836 −0.447638
560560 0 0
561561 0.618034 0.0260934
562562 −11.9656 −0.504737
563563 16.0344 0.675771 0.337886 0.941187i 0.390288π-0.390288\pi
0.337886 + 0.941187i 0.390288π0.390288\pi
564564 3.67376 0.154693
565565 0 0
566566 5.94427 0.249856
567567 29.7082 1.24763
568568 −31.7082 −1.33045
569569 28.6180 1.19973 0.599865 0.800101i 0.295221π-0.295221\pi
0.599865 + 0.800101i 0.295221π0.295221\pi
570570 0 0
571571 2.72949 0.114226 0.0571128 0.998368i 0.481811π-0.481811\pi
0.0571128 + 0.998368i 0.481811π0.481811\pi
572572 −2.85410 −0.119336
573573 −3.78522 −0.158130
574574 7.14590 0.298264
575575 0 0
576576 0.673762 0.0280734
577577 −4.56231 −0.189931 −0.0949656 0.995481i 0.530274π-0.530274\pi
−0.0949656 + 0.995481i 0.530274π0.530274\pi
578578 8.88854 0.369715
579579 −1.88854 −0.0784852
580580 0 0
581581 −64.9574 −2.69489
582582 0.145898 0.00604767
583583 −6.32624 −0.262006
584584 28.2148 1.16754
585585 0 0
586586 −7.34752 −0.303523
587587 25.0344 1.03328 0.516641 0.856202i 0.327182π-0.327182\pi
0.516641 + 0.856202i 0.327182π0.327182\pi
588588 −4.85410 −0.200180
589589 −20.1246 −0.829220
590590 0 0
591591 −3.40325 −0.139991
592592 10.6869 0.439230
593593 9.00000 0.369586 0.184793 0.982777i 0.440839π-0.440839\pi
0.184793 + 0.982777i 0.440839π0.440839\pi
594594 1.38197 0.0567028
595595 0 0
596596 −14.4721 −0.592802
597597 3.09017 0.126472
598598 −7.72949 −0.316082
599599 −15.3262 −0.626213 −0.313107 0.949718i 0.601370π-0.601370\pi
−0.313107 + 0.949718i 0.601370π0.601370\pi
600600 0 0
601601 11.2705 0.459734 0.229867 0.973222i 0.426171π-0.426171\pi
0.229867 + 0.973222i 0.426171π0.426171\pi
602602 14.2918 0.582490
603603 −22.8328 −0.929824
604604 4.85410 0.197511
605605 0 0
606606 −1.20163 −0.0488127
607607 12.4721 0.506228 0.253114 0.967436i 0.418545π-0.418545\pi
0.253114 + 0.967436i 0.418545π0.418545\pi
608608 −37.6869 −1.52841
609609 −5.32624 −0.215830
610610 0 0
611611 −10.4853 −0.424189
612612 7.47214 0.302043
613613 26.5623 1.07284 0.536421 0.843951i 0.319776π-0.319776\pi
0.536421 + 0.843951i 0.319776π0.319776\pi
614614 13.8754 0.559965
615615 0 0
616616 8.61803 0.347230
617617 −15.8197 −0.636876 −0.318438 0.947944i 0.603158π-0.603158\pi
−0.318438 + 0.947944i 0.603158π0.603158\pi
618618 −1.79837 −0.0723412
619619 12.8885 0.518034 0.259017 0.965873i 0.416601π-0.416601\pi
0.259017 + 0.965873i 0.416601π0.416601\pi
620620 0 0
621621 −15.8541 −0.636203
622622 −1.96556 −0.0788117
623623 −69.7214 −2.79333
624624 1.24922 0.0500090
625625 0 0
626626 −0.763932 −0.0305329
627627 2.56231 0.102329
628628 −34.6525 −1.38278
629629 9.32624 0.371861
630630 0 0
631631 2.72949 0.108659 0.0543296 0.998523i 0.482698π-0.482698\pi
0.0543296 + 0.998523i 0.482698π0.482698\pi
632632 −1.90983 −0.0759690
633633 6.49342 0.258090
634634 −8.88854 −0.353009
635635 0 0
636636 3.90983 0.155035
637637 13.8541 0.548920
638638 2.23607 0.0885268
639639 40.4721 1.60105
640640 0 0
641641 −3.00000 −0.118493 −0.0592464 0.998243i 0.518870π-0.518870\pi
−0.0592464 + 0.998243i 0.518870π0.518870\pi
642642 −0.0557281 −0.00219941
643643 37.4164 1.47556 0.737780 0.675042i 0.235874π-0.235874\pi
0.737780 + 0.675042i 0.235874π0.235874\pi
644644 −44.2148 −1.74231
645645 0 0
646646 −6.70820 −0.263931
647647 43.6525 1.71616 0.858078 0.513519i 0.171659π-0.171659\pi
0.858078 + 0.513519i 0.171659π0.171659\pi
648648 17.2361 0.677097
649649 9.47214 0.371814
650650 0 0
651651 −4.41641 −0.173093
652652 0.236068 0.00924514
653653 −34.7426 −1.35958 −0.679792 0.733405i 0.737930π-0.737930\pi
−0.679792 + 0.733405i 0.737930π0.737930\pi
654654 −1.90983 −0.0746803
655655 0 0
656656 −5.56231 −0.217172
657657 −36.0132 −1.40501
658658 14.1591 0.551977
659659 −24.2705 −0.945445 −0.472722 0.881211i 0.656729π-0.656729\pi
−0.472722 + 0.881211i 0.656729π0.656729\pi
660660 0 0
661661 −26.8197 −1.04316 −0.521582 0.853201i 0.674658π-0.674658\pi
−0.521582 + 0.853201i 0.674658π0.674658\pi
662662 −1.96556 −0.0763936
663663 1.09017 0.0423387
664664 −37.6869 −1.46254
665665 0 0
666666 10.1672 0.393970
667667 −25.6525 −0.993268
668668 30.2705 1.17120
669669 −7.21478 −0.278940
670670 0 0
671671 −11.0902 −0.428131
672672 −8.27051 −0.319042
673673 −24.4164 −0.941183 −0.470592 0.882351i 0.655960π-0.655960\pi
−0.470592 + 0.882351i 0.655960π0.655960\pi
674674 15.7082 0.605057
675675 0 0
676676 16.0000 0.615385
677677 −2.65248 −0.101943 −0.0509715 0.998700i 0.516232π-0.516232\pi
−0.0509715 + 0.998700i 0.516232π0.516232\pi
678678 −4.63932 −0.178172
679679 −2.38197 −0.0914115
680680 0 0
681681 1.92299 0.0736890
682682 1.85410 0.0709972
683683 1.36068 0.0520650 0.0260325 0.999661i 0.491713π-0.491713\pi
0.0260325 + 0.999661i 0.491713π0.491713\pi
684684 30.9787 1.18450
685685 0 0
686686 −2.03444 −0.0776754
687687 −6.50658 −0.248241
688688 −11.1246 −0.424122
689689 −11.1591 −0.425126
690690 0 0
691691 18.9098 0.719364 0.359682 0.933075i 0.382885π-0.382885\pi
0.359682 + 0.933075i 0.382885π0.382885\pi
692692 −5.61803 −0.213566
693693 −11.0000 −0.417855
694694 −0.270510 −0.0102684
695695 0 0
696696 −3.09017 −0.117133
697697 −4.85410 −0.183862
698698 19.6738 0.744663
699699 −8.59675 −0.325159
700700 0 0
701701 44.3607 1.67548 0.837740 0.546070i 0.183877π-0.183877\pi
0.837740 + 0.546070i 0.183877π0.183877\pi
702702 2.43769 0.0920048
703703 38.6656 1.45830
704704 −0.236068 −0.00889715
705705 0 0
706706 14.4377 0.543370
707707 19.6180 0.737812
708708 −5.85410 −0.220011
709709 21.3050 0.800124 0.400062 0.916488i 0.368989π-0.368989\pi
0.400062 + 0.916488i 0.368989π0.368989\pi
710710 0 0
711711 2.43769 0.0914207
712712 −40.4508 −1.51596
713713 −21.2705 −0.796587
714714 −1.47214 −0.0550933
715715 0 0
716716 18.4164 0.688253
717717 3.29180 0.122934
718718 −2.76393 −0.103149
719719 15.6525 0.583739 0.291869 0.956458i 0.405723π-0.405723\pi
0.291869 + 0.956458i 0.405723π0.405723\pi
720720 0 0
721721 29.3607 1.09345
722722 −16.0689 −0.598022
723723 −4.68692 −0.174308
724724 −8.23607 −0.306091
725725 0 0
726726 −0.236068 −0.00876130
727727 −7.72949 −0.286671 −0.143335 0.989674i 0.545783π-0.545783\pi
−0.143335 + 0.989674i 0.545783π0.545783\pi
728728 15.2016 0.563410
729729 −19.4377 −0.719915
730730 0 0
731731 −9.70820 −0.359071
732732 6.85410 0.253335
733733 −7.83282 −0.289312 −0.144656 0.989482i 0.546207π-0.546207\pi
−0.144656 + 0.989482i 0.546207π0.546207\pi
734734 −8.56231 −0.316040
735735 0 0
736736 −39.8328 −1.46826
737737 8.00000 0.294684
738738 −5.29180 −0.194794
739739 −35.8541 −1.31891 −0.659457 0.751742i 0.729214π-0.729214\pi
−0.659457 + 0.751742i 0.729214π0.729214\pi
740740 0 0
741741 4.51973 0.166037
742742 15.0689 0.553196
743743 34.3262 1.25931 0.629654 0.776876i 0.283197π-0.283197\pi
0.629654 + 0.776876i 0.283197π0.283197\pi
744744 −2.56231 −0.0939387
745745 0 0
746746 −15.5623 −0.569777
747747 48.1033 1.76001
748748 −2.61803 −0.0957248
749749 0.909830 0.0332445
750750 0 0
751751 −22.2705 −0.812662 −0.406331 0.913726i 0.633192π-0.633192\pi
−0.406331 + 0.913726i 0.633192π0.633192\pi
752752 −11.0213 −0.401905
753753 2.39512 0.0872831
754754 3.94427 0.143642
755755 0 0
756756 13.9443 0.507148
757757 −12.5279 −0.455333 −0.227666 0.973739i 0.573110π-0.573110\pi
−0.227666 + 0.973739i 0.573110π0.573110\pi
758758 13.7426 0.499155
759759 2.70820 0.0983016
760760 0 0
761761 12.0000 0.435000 0.217500 0.976060i 0.430210π-0.430210\pi
0.217500 + 0.976060i 0.430210π0.430210\pi
762762 −0.381966 −0.0138372
763763 31.1803 1.12880
764764 16.0344 0.580106
765765 0 0
766766 −14.1803 −0.512357
767767 16.7082 0.603298
768768 −2.50658 −0.0904483
769769 −5.00000 −0.180305 −0.0901523 0.995928i 0.528735π-0.528735\pi
−0.0901523 + 0.995928i 0.528735π0.528735\pi
770770 0 0
771771 2.65248 0.0955266
772772 8.00000 0.287926
773773 9.20163 0.330959 0.165480 0.986213i 0.447083π-0.447083\pi
0.165480 + 0.986213i 0.447083π0.447083\pi
774774 −10.5836 −0.380419
775775 0 0
776776 −1.38197 −0.0496097
777777 8.48529 0.304408
778778 −8.94427 −0.320668
779779 −20.1246 −0.721039
780780 0 0
781781 −14.1803 −0.507412
782782 −7.09017 −0.253544
783783 8.09017 0.289119
784784 14.5623 0.520082
785785 0 0
786786 0.257354 0.00917952
787787 34.7082 1.23721 0.618607 0.785701i 0.287697π-0.287697\pi
0.618607 + 0.785701i 0.287697π0.287697\pi
788788 14.4164 0.513563
789789 −8.02129 −0.285565
790790 0 0
791791 75.7426 2.69310
792792 −6.38197 −0.226773
793793 −19.5623 −0.694678
794794 −16.1246 −0.572241
795795 0 0
796796 −13.0902 −0.463969
797797 27.7984 0.984669 0.492334 0.870406i 0.336144π-0.336144\pi
0.492334 + 0.870406i 0.336144π0.336144\pi
798798 −6.10333 −0.216055
799799 −9.61803 −0.340262
800800 0 0
801801 51.6312 1.82430
802802 6.40325 0.226107
803803 12.6180 0.445281
804804 −4.94427 −0.174371
805805 0 0
806806 3.27051 0.115199
807807 5.60488 0.197301
808808 11.3820 0.400416
809809 −43.4164 −1.52644 −0.763220 0.646139i 0.776383π-0.776383\pi
−0.763220 + 0.646139i 0.776383π0.776383\pi
810810 0 0
811811 17.0000 0.596951 0.298475 0.954417i 0.403522π-0.403522\pi
0.298475 + 0.954417i 0.403522π0.403522\pi
812812 22.5623 0.791782
813813 −3.50658 −0.122981
814814 −3.56231 −0.124859
815815 0 0
816816 1.14590 0.0401145
817817 −40.2492 −1.40814
818818 12.4377 0.434874
819819 −19.4033 −0.678005
820820 0 0
821821 −40.3607 −1.40860 −0.704299 0.709904i 0.748738π-0.748738\pi
−0.704299 + 0.709904i 0.748738π0.748738\pi
822822 3.43769 0.119903
823823 0.583592 0.0203427 0.0101714 0.999948i 0.496762π-0.496762\pi
0.0101714 + 0.999948i 0.496762π0.496762\pi
824824 17.0344 0.593423
825825 0 0
826826 −22.5623 −0.785043
827827 −26.0689 −0.906504 −0.453252 0.891382i 0.649736π-0.649736\pi
−0.453252 + 0.891382i 0.649736π0.649736\pi
828828 32.7426 1.13789
829829 51.1033 1.77489 0.887446 0.460912i 0.152478π-0.152478\pi
0.887446 + 0.460912i 0.152478π0.152478\pi
830830 0 0
831831 −0.965558 −0.0334948
832832 −0.416408 −0.0144363
833833 12.7082 0.440313
834834 3.94427 0.136579
835835 0 0
836836 −10.8541 −0.375397
837837 6.70820 0.231869
838838 0.729490 0.0251998
839839 43.3394 1.49624 0.748121 0.663562i 0.230956π-0.230956\pi
0.748121 + 0.663562i 0.230956π0.230956\pi
840840 0 0
841841 −15.9098 −0.548615
842842 −13.1459 −0.453038
843843 7.39512 0.254702
844844 −27.5066 −0.946815
845845 0 0
846846 −10.4853 −0.360492
847847 3.85410 0.132429
848848 −11.7295 −0.402792
849849 −3.67376 −0.126083
850850 0 0
851851 40.8673 1.40091
852852 8.76393 0.300247
853853 43.1459 1.47729 0.738644 0.674096i 0.235467π-0.235467\pi
0.738644 + 0.674096i 0.235467π0.235467\pi
854854 26.4164 0.903951
855855 0 0
856856 0.527864 0.0180420
857857 −30.8197 −1.05278 −0.526390 0.850243i 0.676455π-0.676455\pi
−0.526390 + 0.850243i 0.676455π0.676455\pi
858858 −0.416408 −0.0142159
859859 −6.18034 −0.210870 −0.105435 0.994426i 0.533624π-0.533624\pi
−0.105435 + 0.994426i 0.533624π0.533624\pi
860860 0 0
861861 −4.41641 −0.150511
862862 −14.3262 −0.487954
863863 48.5967 1.65425 0.827126 0.562016i 0.189974π-0.189974\pi
0.827126 + 0.562016i 0.189974π0.189974\pi
864864 12.5623 0.427378
865865 0 0
866866 −10.4377 −0.354687
867867 −5.49342 −0.186566
868868 18.7082 0.634998
869869 −0.854102 −0.0289734
870870 0 0
871871 14.1115 0.478148
872872 18.0902 0.612610
873873 1.76393 0.0597001
874874 −29.3951 −0.994305
875875 0 0
876876 −7.79837 −0.263483
877877 31.4164 1.06086 0.530428 0.847730i 0.322031π-0.322031\pi
0.530428 + 0.847730i 0.322031π0.322031\pi
878878 21.1803 0.714802
879879 4.54102 0.153165
880880 0 0
881881 −1.09017 −0.0367288 −0.0183644 0.999831i 0.505846π-0.505846\pi
−0.0183644 + 0.999831i 0.505846π0.505846\pi
882882 13.8541 0.466492
883883 −0.347524 −0.0116951 −0.00584756 0.999983i 0.501861π-0.501861\pi
−0.00584756 + 0.999983i 0.501861π0.501861\pi
884884 −4.61803 −0.155321
885885 0 0
886886 3.30495 0.111032
887887 −42.7771 −1.43631 −0.718157 0.695881i 0.755014π-0.755014\pi
−0.718157 + 0.695881i 0.755014π0.755014\pi
888888 4.92299 0.165205
889889 6.23607 0.209151
890890 0 0
891891 7.70820 0.258235
892892 30.5623 1.02330
893893 −39.8754 −1.33438
894894 −2.11146 −0.0706177
895895 0 0
896896 43.8673 1.46550
897897 4.77709 0.159502
898898 −0.201626 −0.00672835
899899 10.8541 0.362005
900900 0 0
901901 −10.2361 −0.341013
902902 1.85410 0.0617348
903903 −8.83282 −0.293938
904904 43.9443 1.46156
905905 0 0
906906 0.708204 0.0235285
907907 −38.8328 −1.28942 −0.644711 0.764426i 0.723022π-0.723022\pi
−0.644711 + 0.764426i 0.723022π0.723022\pi
908908 −8.14590 −0.270331
909909 −14.5279 −0.481859
910910 0 0
911911 −18.0000 −0.596367 −0.298183 0.954509i 0.596381π-0.596381\pi
−0.298183 + 0.954509i 0.596381π0.596381\pi
912912 4.75078 0.157314
913913 −16.8541 −0.557789
914914 −24.0902 −0.796832
915915 0 0
916916 27.5623 0.910684
917917 −4.20163 −0.138750
918918 2.23607 0.0738012
919919 −3.41641 −0.112697 −0.0563484 0.998411i 0.517946π-0.517946\pi
−0.0563484 + 0.998411i 0.517946π0.517946\pi
920920 0 0
921921 −8.57546 −0.282571
922922 −8.14590 −0.268271
923923 −25.0132 −0.823318
924924 −2.38197 −0.0783609
925925 0 0
926926 20.6180 0.677551
927927 −21.7426 −0.714122
928928 20.3262 0.667241
929929 5.40325 0.177275 0.0886375 0.996064i 0.471749π-0.471749\pi
0.0886375 + 0.996064i 0.471749π0.471749\pi
930930 0 0
931931 52.6869 1.72674
932932 36.4164 1.19286
933933 1.21478 0.0397702
934934 −17.6312 −0.576910
935935 0 0
936936 −11.2574 −0.367958
937937 14.8328 0.484567 0.242283 0.970206i 0.422104π-0.422104\pi
0.242283 + 0.970206i 0.422104π0.422104\pi
938938 −19.0557 −0.622192
939939 0.472136 0.0154076
940940 0 0
941941 −47.7214 −1.55567 −0.777836 0.628467i 0.783683π-0.783683\pi
−0.777836 + 0.628467i 0.783683π0.783683\pi
942942 −5.05573 −0.164725
943943 −21.2705 −0.692663
944944 17.5623 0.571604
945945 0 0
946946 3.70820 0.120564
947947 5.36068 0.174199 0.0870993 0.996200i 0.472240π-0.472240\pi
0.0870993 + 0.996200i 0.472240π0.472240\pi
948948 0.527864 0.0171442
949949 22.2574 0.722504
950950 0 0
951951 5.49342 0.178136
952952 13.9443 0.451936
953953 −0.472136 −0.0152940 −0.00764699 0.999971i 0.502434π-0.502434\pi
−0.00764699 + 0.999971i 0.502434π0.502434\pi
954954 −11.1591 −0.361288
955955 0 0
956956 −13.9443 −0.450990
957957 −1.38197 −0.0446726
958958 −0.978714 −0.0316208
959959 −56.1246 −1.81236
960960 0 0
961961 −22.0000 −0.709677
962962 −6.28367 −0.202594
963963 −0.673762 −0.0217117
964964 19.8541 0.639458
965965 0 0
966966 −6.45085 −0.207553
967967 3.72949 0.119932 0.0599662 0.998200i 0.480901π-0.480901\pi
0.0599662 + 0.998200i 0.480901π0.480901\pi
968968 2.23607 0.0718699
969969 4.14590 0.133185
970970 0 0
971971 35.0902 1.12610 0.563049 0.826424i 0.309628π-0.309628\pi
0.563049 + 0.826424i 0.309628π0.309628\pi
972972 −15.6180 −0.500949
973973 −64.3951 −2.06441
974974 2.21478 0.0709662
975975 0 0
976976 −20.5623 −0.658183
977977 −1.06888 −0.0341966 −0.0170983 0.999854i 0.505443π-0.505443\pi
−0.0170983 + 0.999854i 0.505443π0.505443\pi
978978 0.0344419 0.00110133
979979 −18.0902 −0.578164
980980 0 0
981981 −23.0902 −0.737212
982982 18.0344 0.575502
983983 −10.4721 −0.334009 −0.167005 0.985956i 0.553409π-0.553409\pi
−0.167005 + 0.985956i 0.553409π0.553409\pi
984984 −2.56231 −0.0816833
985985 0 0
986986 3.61803 0.115222
987987 −8.75078 −0.278540
988988 −19.1459 −0.609112
989989 −42.5410 −1.35273
990990 0 0
991991 −12.2705 −0.389786 −0.194893 0.980825i 0.562436π-0.562436\pi
−0.194893 + 0.980825i 0.562436π0.562436\pi
992992 16.8541 0.535118
993993 1.21478 0.0385499
994994 33.7771 1.07134
995995 0 0
996996 10.4164 0.330057
997997 38.8541 1.23052 0.615261 0.788324i 0.289051π-0.289051\pi
0.615261 + 0.788324i 0.289051π0.289051\pi
998998 −3.21478 −0.101762
999999 −12.8885 −0.407775
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 275.2.a.g.1.1 yes 2
3.2 odd 2 2475.2.a.n.1.2 2
4.3 odd 2 4400.2.a.bg.1.2 2
5.2 odd 4 275.2.b.e.199.2 4
5.3 odd 4 275.2.b.e.199.3 4
5.4 even 2 275.2.a.d.1.2 2
11.10 odd 2 3025.2.a.i.1.2 2
15.2 even 4 2475.2.c.p.199.3 4
15.8 even 4 2475.2.c.p.199.2 4
15.14 odd 2 2475.2.a.s.1.1 2
20.3 even 4 4400.2.b.x.4049.2 4
20.7 even 4 4400.2.b.x.4049.3 4
20.19 odd 2 4400.2.a.bv.1.1 2
55.54 odd 2 3025.2.a.m.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
275.2.a.d.1.2 2 5.4 even 2
275.2.a.g.1.1 yes 2 1.1 even 1 trivial
275.2.b.e.199.2 4 5.2 odd 4
275.2.b.e.199.3 4 5.3 odd 4
2475.2.a.n.1.2 2 3.2 odd 2
2475.2.a.s.1.1 2 15.14 odd 2
2475.2.c.p.199.2 4 15.8 even 4
2475.2.c.p.199.3 4 15.2 even 4
3025.2.a.i.1.2 2 11.10 odd 2
3025.2.a.m.1.1 2 55.54 odd 2
4400.2.a.bg.1.2 2 4.3 odd 2
4400.2.a.bv.1.1 2 20.19 odd 2
4400.2.b.x.4049.2 4 20.3 even 4
4400.2.b.x.4049.3 4 20.7 even 4