Properties

Label 1275.2.a.m.1.1
Level 12751275
Weight 22
Character 1275.1
Self dual yes
Analytic conductor 10.18110.181
Analytic rank 11
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] = [1275,2,Mod(1,1275)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1275, 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("1275.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1275=35217 1275 = 3 \cdot 5^{2} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1275.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: 10.180926257710.1809262577
Analytic rank: 11
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: no (minimal twist has level 255)
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 == 1275.1

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) == q0.618034q21.00000q31.61803q4+0.618034q6+1.00000q7+2.23607q8+1.00000q93.00000q11+1.61803q122.00000q130.618034q14+1.85410q16+1.00000q170.618034q18+0.236068q191.00000q21+1.85410q22+8.47214q232.23607q24+1.23607q261.00000q271.61803q281.76393q296.47214q315.61803q32+3.00000q330.618034q341.61803q36+8.70820q370.145898q38+2.00000q398.23607q41+0.618034q42+0.472136q43+4.85410q445.23607q460.708204q471.85410q486.00000q491.00000q51+3.23607q52+3.00000q53+0.618034q54+2.23607q560.236068q57+1.09017q58+8.94427q5910.0000q61+4.00000q62+1.00000q630.236068q641.85410q6614.4721q671.61803q688.47214q694.94427q71+2.23607q726.23607q735.38197q740.381966q763.00000q771.23607q78+2.00000q79+1.00000q81+5.09017q8212.9443q83+1.61803q840.291796q86+1.76393q876.70820q8812.0000q892.00000q9113.7082q92+6.47214q93+0.437694q94+5.61803q9613.4164q97+3.70820q983.00000q99+O(q100)q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} +0.618034 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} -3.00000 q^{11} +1.61803 q^{12} -2.00000 q^{13} -0.618034 q^{14} +1.85410 q^{16} +1.00000 q^{17} -0.618034 q^{18} +0.236068 q^{19} -1.00000 q^{21} +1.85410 q^{22} +8.47214 q^{23} -2.23607 q^{24} +1.23607 q^{26} -1.00000 q^{27} -1.61803 q^{28} -1.76393 q^{29} -6.47214 q^{31} -5.61803 q^{32} +3.00000 q^{33} -0.618034 q^{34} -1.61803 q^{36} +8.70820 q^{37} -0.145898 q^{38} +2.00000 q^{39} -8.23607 q^{41} +0.618034 q^{42} +0.472136 q^{43} +4.85410 q^{44} -5.23607 q^{46} -0.708204 q^{47} -1.85410 q^{48} -6.00000 q^{49} -1.00000 q^{51} +3.23607 q^{52} +3.00000 q^{53} +0.618034 q^{54} +2.23607 q^{56} -0.236068 q^{57} +1.09017 q^{58} +8.94427 q^{59} -10.0000 q^{61} +4.00000 q^{62} +1.00000 q^{63} -0.236068 q^{64} -1.85410 q^{66} -14.4721 q^{67} -1.61803 q^{68} -8.47214 q^{69} -4.94427 q^{71} +2.23607 q^{72} -6.23607 q^{73} -5.38197 q^{74} -0.381966 q^{76} -3.00000 q^{77} -1.23607 q^{78} +2.00000 q^{79} +1.00000 q^{81} +5.09017 q^{82} -12.9443 q^{83} +1.61803 q^{84} -0.291796 q^{86} +1.76393 q^{87} -6.70820 q^{88} -12.0000 q^{89} -2.00000 q^{91} -13.7082 q^{92} +6.47214 q^{93} +0.437694 q^{94} +5.61803 q^{96} -13.4164 q^{97} +3.70820 q^{98} -3.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q22q3q4q6+2q7+2q96q11+q124q13+q143q16+2q17+q184q192q213q22+8q232q262q27q28+6q99+O(q100) 2 q + q^{2} - 2 q^{3} - q^{4} - q^{6} + 2 q^{7} + 2 q^{9} - 6 q^{11} + q^{12} - 4 q^{13} + q^{14} - 3 q^{16} + 2 q^{17} + q^{18} - 4 q^{19} - 2 q^{21} - 3 q^{22} + 8 q^{23} - 2 q^{26} - 2 q^{27} - q^{28}+ \cdots - 6 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 −1.00000 −0.577350
44 −1.61803 −0.809017
55 0 0
66 0.618034 0.252311
77 1.00000 0.377964 0.188982 0.981981i 0.439481π-0.439481\pi
0.188982 + 0.981981i 0.439481π0.439481\pi
88 2.23607 0.790569
99 1.00000 0.333333
1010 0 0
1111 −3.00000 −0.904534 −0.452267 0.891883i 0.649385π-0.649385\pi
−0.452267 + 0.891883i 0.649385π0.649385\pi
1212 1.61803 0.467086
1313 −2.00000 −0.554700 −0.277350 0.960769i 0.589456π-0.589456\pi
−0.277350 + 0.960769i 0.589456π0.589456\pi
1414 −0.618034 −0.165177
1515 0 0
1616 1.85410 0.463525
1717 1.00000 0.242536
1818 −0.618034 −0.145672
1919 0.236068 0.0541577 0.0270789 0.999633i 0.491379π-0.491379\pi
0.0270789 + 0.999633i 0.491379π0.491379\pi
2020 0 0
2121 −1.00000 −0.218218
2222 1.85410 0.395296
2323 8.47214 1.76656 0.883281 0.468844i 0.155329π-0.155329\pi
0.883281 + 0.468844i 0.155329π0.155329\pi
2424 −2.23607 −0.456435
2525 0 0
2626 1.23607 0.242413
2727 −1.00000 −0.192450
2828 −1.61803 −0.305780
2929 −1.76393 −0.327554 −0.163777 0.986497i 0.552368π-0.552368\pi
−0.163777 + 0.986497i 0.552368π0.552368\pi
3030 0 0
3131 −6.47214 −1.16243 −0.581215 0.813750i 0.697422π-0.697422\pi
−0.581215 + 0.813750i 0.697422π0.697422\pi
3232 −5.61803 −0.993137
3333 3.00000 0.522233
3434 −0.618034 −0.105992
3535 0 0
3636 −1.61803 −0.269672
3737 8.70820 1.43162 0.715810 0.698295i 0.246058π-0.246058\pi
0.715810 + 0.698295i 0.246058π0.246058\pi
3838 −0.145898 −0.0236678
3939 2.00000 0.320256
4040 0 0
4141 −8.23607 −1.28626 −0.643129 0.765758i 0.722364π-0.722364\pi
−0.643129 + 0.765758i 0.722364π0.722364\pi
4242 0.618034 0.0953647
4343 0.472136 0.0720001 0.0360000 0.999352i 0.488538π-0.488538\pi
0.0360000 + 0.999352i 0.488538π0.488538\pi
4444 4.85410 0.731783
4545 0 0
4646 −5.23607 −0.772016
4747 −0.708204 −0.103302 −0.0516511 0.998665i 0.516448π-0.516448\pi
−0.0516511 + 0.998665i 0.516448π0.516448\pi
4848 −1.85410 −0.267617
4949 −6.00000 −0.857143
5050 0 0
5151 −1.00000 −0.140028
5252 3.23607 0.448762
5353 3.00000 0.412082 0.206041 0.978543i 0.433942π-0.433942\pi
0.206041 + 0.978543i 0.433942π0.433942\pi
5454 0.618034 0.0841038
5555 0 0
5656 2.23607 0.298807
5757 −0.236068 −0.0312680
5858 1.09017 0.143146
5959 8.94427 1.16445 0.582223 0.813029i 0.302183π-0.302183\pi
0.582223 + 0.813029i 0.302183π0.302183\pi
6060 0 0
6161 −10.0000 −1.28037 −0.640184 0.768221i 0.721142π-0.721142\pi
−0.640184 + 0.768221i 0.721142π0.721142\pi
6262 4.00000 0.508001
6363 1.00000 0.125988
6464 −0.236068 −0.0295085
6565 0 0
6666 −1.85410 −0.228224
6767 −14.4721 −1.76805 −0.884026 0.467437i 0.845177π-0.845177\pi
−0.884026 + 0.467437i 0.845177π0.845177\pi
6868 −1.61803 −0.196215
6969 −8.47214 −1.01993
7070 0 0
7171 −4.94427 −0.586777 −0.293389 0.955993i 0.594783π-0.594783\pi
−0.293389 + 0.955993i 0.594783π0.594783\pi
7272 2.23607 0.263523
7373 −6.23607 −0.729877 −0.364938 0.931032i 0.618910π-0.618910\pi
−0.364938 + 0.931032i 0.618910π0.618910\pi
7474 −5.38197 −0.625641
7575 0 0
7676 −0.381966 −0.0438145
7777 −3.00000 −0.341882
7878 −1.23607 −0.139957
7979 2.00000 0.225018 0.112509 0.993651i 0.464111π-0.464111\pi
0.112509 + 0.993651i 0.464111π0.464111\pi
8080 0 0
8181 1.00000 0.111111
8282 5.09017 0.562115
8383 −12.9443 −1.42082 −0.710409 0.703789i 0.751490π-0.751490\pi
−0.710409 + 0.703789i 0.751490π0.751490\pi
8484 1.61803 0.176542
8585 0 0
8686 −0.291796 −0.0314652
8787 1.76393 0.189113
8888 −6.70820 −0.715097
8989 −12.0000 −1.27200 −0.635999 0.771690i 0.719412π-0.719412\pi
−0.635999 + 0.771690i 0.719412π0.719412\pi
9090 0 0
9191 −2.00000 −0.209657
9292 −13.7082 −1.42918
9393 6.47214 0.671129
9494 0.437694 0.0451447
9595 0 0
9696 5.61803 0.573388
9797 −13.4164 −1.36223 −0.681115 0.732177i 0.738505π-0.738505\pi
−0.681115 + 0.732177i 0.738505π0.738505\pi
9898 3.70820 0.374585
9999 −3.00000 −0.301511
100100 0 0
101101 −5.52786 −0.550043 −0.275022 0.961438i 0.588685π-0.588685\pi
−0.275022 + 0.961438i 0.588685π0.588685\pi
102102 0.618034 0.0611945
103103 −6.94427 −0.684239 −0.342120 0.939656i 0.611145π-0.611145\pi
−0.342120 + 0.939656i 0.611145π0.611145\pi
104104 −4.47214 −0.438529
105105 0 0
106106 −1.85410 −0.180086
107107 2.47214 0.238990 0.119495 0.992835i 0.461872π-0.461872\pi
0.119495 + 0.992835i 0.461872π0.461872\pi
108108 1.61803 0.155695
109109 −6.47214 −0.619918 −0.309959 0.950750i 0.600315π-0.600315\pi
−0.309959 + 0.950750i 0.600315π0.600315\pi
110110 0 0
111111 −8.70820 −0.826546
112112 1.85410 0.175196
113113 1.05573 0.0993145 0.0496573 0.998766i 0.484187π-0.484187\pi
0.0496573 + 0.998766i 0.484187π0.484187\pi
114114 0.145898 0.0136646
115115 0 0
116116 2.85410 0.264997
117117 −2.00000 −0.184900
118118 −5.52786 −0.508881
119119 1.00000 0.0916698
120120 0 0
121121 −2.00000 −0.181818
122122 6.18034 0.559542
123123 8.23607 0.742621
124124 10.4721 0.940426
125125 0 0
126126 −0.618034 −0.0550588
127127 −6.00000 −0.532414 −0.266207 0.963916i 0.585770π-0.585770\pi
−0.266207 + 0.963916i 0.585770π0.585770\pi
128128 11.3820 1.00603
129129 −0.472136 −0.0415693
130130 0 0
131131 16.9443 1.48043 0.740214 0.672371i 0.234724π-0.234724\pi
0.740214 + 0.672371i 0.234724π0.234724\pi
132132 −4.85410 −0.422495
133133 0.236068 0.0204697
134134 8.94427 0.772667
135135 0 0
136136 2.23607 0.191741
137137 16.4164 1.40255 0.701274 0.712892i 0.252615π-0.252615\pi
0.701274 + 0.712892i 0.252615π0.252615\pi
138138 5.23607 0.445724
139139 −12.9443 −1.09792 −0.548959 0.835849i 0.684976π-0.684976\pi
−0.548959 + 0.835849i 0.684976π0.684976\pi
140140 0 0
141141 0.708204 0.0596415
142142 3.05573 0.256431
143143 6.00000 0.501745
144144 1.85410 0.154508
145145 0 0
146146 3.85410 0.318968
147147 6.00000 0.494872
148148 −14.0902 −1.15820
149149 1.52786 0.125167 0.0625837 0.998040i 0.480066π-0.480066\pi
0.0625837 + 0.998040i 0.480066π0.480066\pi
150150 0 0
151151 13.7639 1.12009 0.560046 0.828461i 0.310783π-0.310783\pi
0.560046 + 0.828461i 0.310783π0.310783\pi
152152 0.527864 0.0428154
153153 1.00000 0.0808452
154154 1.85410 0.149408
155155 0 0
156156 −3.23607 −0.259093
157157 −19.4164 −1.54960 −0.774799 0.632208i 0.782149π-0.782149\pi
−0.774799 + 0.632208i 0.782149π0.782149\pi
158158 −1.23607 −0.0983363
159159 −3.00000 −0.237915
160160 0 0
161161 8.47214 0.667698
162162 −0.618034 −0.0485573
163163 −16.4164 −1.28583 −0.642916 0.765937i 0.722276π-0.722276\pi
−0.642916 + 0.765937i 0.722276π0.722276\pi
164164 13.3262 1.04060
165165 0 0
166166 8.00000 0.620920
167167 18.4721 1.42942 0.714708 0.699423i 0.246559π-0.246559\pi
0.714708 + 0.699423i 0.246559π0.246559\pi
168168 −2.23607 −0.172516
169169 −9.00000 −0.692308
170170 0 0
171171 0.236068 0.0180526
172172 −0.763932 −0.0582493
173173 −20.3607 −1.54799 −0.773997 0.633189i 0.781745π-0.781745\pi
−0.773997 + 0.633189i 0.781745π0.781745\pi
174174 −1.09017 −0.0826456
175175 0 0
176176 −5.56231 −0.419275
177177 −8.94427 −0.672293
178178 7.41641 0.555883
179179 −1.52786 −0.114198 −0.0570990 0.998369i 0.518185π-0.518185\pi
−0.0570990 + 0.998369i 0.518185π0.518185\pi
180180 0 0
181181 13.8885 1.03233 0.516164 0.856490i 0.327360π-0.327360\pi
0.516164 + 0.856490i 0.327360π0.327360\pi
182182 1.23607 0.0916235
183183 10.0000 0.739221
184184 18.9443 1.39659
185185 0 0
186186 −4.00000 −0.293294
187187 −3.00000 −0.219382
188188 1.14590 0.0835732
189189 −1.00000 −0.0727393
190190 0 0
191191 4.47214 0.323592 0.161796 0.986824i 0.448271π-0.448271\pi
0.161796 + 0.986824i 0.448271π0.448271\pi
192192 0.236068 0.0170367
193193 9.41641 0.677808 0.338904 0.940821i 0.389944π-0.389944\pi
0.338904 + 0.940821i 0.389944π0.389944\pi
194194 8.29180 0.595316
195195 0 0
196196 9.70820 0.693443
197197 22.4721 1.60107 0.800537 0.599284i 0.204548π-0.204548\pi
0.800537 + 0.599284i 0.204548π0.204548\pi
198198 1.85410 0.131765
199199 13.4164 0.951064 0.475532 0.879698i 0.342256π-0.342256\pi
0.475532 + 0.879698i 0.342256π0.342256\pi
200200 0 0
201201 14.4721 1.02079
202202 3.41641 0.240378
203203 −1.76393 −0.123804
204204 1.61803 0.113285
205205 0 0
206206 4.29180 0.299024
207207 8.47214 0.588854
208208 −3.70820 −0.257118
209209 −0.708204 −0.0489875
210210 0 0
211211 −18.3607 −1.26400 −0.632001 0.774968i 0.717766π-0.717766\pi
−0.632001 + 0.774968i 0.717766π0.717766\pi
212212 −4.85410 −0.333381
213213 4.94427 0.338776
214214 −1.52786 −0.104443
215215 0 0
216216 −2.23607 −0.152145
217217 −6.47214 −0.439357
218218 4.00000 0.270914
219219 6.23607 0.421394
220220 0 0
221221 −2.00000 −0.134535
222222 5.38197 0.361214
223223 1.41641 0.0948497 0.0474248 0.998875i 0.484899π-0.484899\pi
0.0474248 + 0.998875i 0.484899π0.484899\pi
224224 −5.61803 −0.375371
225225 0 0
226226 −0.652476 −0.0434020
227227 3.05573 0.202816 0.101408 0.994845i 0.467665π-0.467665\pi
0.101408 + 0.994845i 0.467665π0.467665\pi
228228 0.381966 0.0252963
229229 −16.4164 −1.08483 −0.542413 0.840112i 0.682489π-0.682489\pi
−0.542413 + 0.840112i 0.682489π0.682489\pi
230230 0 0
231231 3.00000 0.197386
232232 −3.94427 −0.258954
233233 12.0000 0.786146 0.393073 0.919507i 0.371412π-0.371412\pi
0.393073 + 0.919507i 0.371412π0.371412\pi
234234 1.23607 0.0808043
235235 0 0
236236 −14.4721 −0.942056
237237 −2.00000 −0.129914
238238 −0.618034 −0.0400612
239239 0.472136 0.0305399 0.0152700 0.999883i 0.495139π-0.495139\pi
0.0152700 + 0.999883i 0.495139π0.495139\pi
240240 0 0
241241 4.94427 0.318489 0.159244 0.987239i 0.449094π-0.449094\pi
0.159244 + 0.987239i 0.449094π0.449094\pi
242242 1.23607 0.0794575
243243 −1.00000 −0.0641500
244244 16.1803 1.03584
245245 0 0
246246 −5.09017 −0.324537
247247 −0.472136 −0.0300413
248248 −14.4721 −0.918982
249249 12.9443 0.820310
250250 0 0
251251 −11.8885 −0.750398 −0.375199 0.926944i 0.622426π-0.622426\pi
−0.375199 + 0.926944i 0.622426π0.622426\pi
252252 −1.61803 −0.101927
253253 −25.4164 −1.59792
254254 3.70820 0.232673
255255 0 0
256256 −6.56231 −0.410144
257257 −13.0557 −0.814394 −0.407197 0.913340i 0.633494π-0.633494\pi
−0.407197 + 0.913340i 0.633494π0.633494\pi
258258 0.291796 0.0181664
259259 8.70820 0.541101
260260 0 0
261261 −1.76393 −0.109185
262262 −10.4721 −0.646971
263263 21.6525 1.33515 0.667574 0.744543i 0.267333π-0.267333\pi
0.667574 + 0.744543i 0.267333π0.267333\pi
264264 6.70820 0.412861
265265 0 0
266266 −0.145898 −0.00894558
267267 12.0000 0.734388
268268 23.4164 1.43038
269269 −7.18034 −0.437793 −0.218897 0.975748i 0.570246π-0.570246\pi
−0.218897 + 0.975748i 0.570246π0.570246\pi
270270 0 0
271271 21.8885 1.32963 0.664817 0.747006i 0.268509π-0.268509\pi
0.664817 + 0.747006i 0.268509π0.268509\pi
272272 1.85410 0.112421
273273 2.00000 0.121046
274274 −10.1459 −0.612936
275275 0 0
276276 13.7082 0.825137
277277 −29.4164 −1.76746 −0.883730 0.467996i 0.844976π-0.844976\pi
−0.883730 + 0.467996i 0.844976π0.844976\pi
278278 8.00000 0.479808
279279 −6.47214 −0.387477
280280 0 0
281281 −14.3607 −0.856686 −0.428343 0.903616i 0.640903π-0.640903\pi
−0.428343 + 0.903616i 0.640903π0.640903\pi
282282 −0.437694 −0.0260643
283283 −17.4721 −1.03861 −0.519305 0.854589i 0.673809π-0.673809\pi
−0.519305 + 0.854589i 0.673809π0.673809\pi
284284 8.00000 0.474713
285285 0 0
286286 −3.70820 −0.219271
287287 −8.23607 −0.486160
288288 −5.61803 −0.331046
289289 1.00000 0.0588235
290290 0 0
291291 13.4164 0.786484
292292 10.0902 0.590483
293293 8.88854 0.519274 0.259637 0.965706i 0.416397π-0.416397\pi
0.259637 + 0.965706i 0.416397π0.416397\pi
294294 −3.70820 −0.216267
295295 0 0
296296 19.4721 1.13179
297297 3.00000 0.174078
298298 −0.944272 −0.0547002
299299 −16.9443 −0.979913
300300 0 0
301301 0.472136 0.0272135
302302 −8.50658 −0.489499
303303 5.52786 0.317567
304304 0.437694 0.0251035
305305 0 0
306306 −0.618034 −0.0353307
307307 34.8328 1.98801 0.994007 0.109317i 0.0348665π-0.0348665\pi
0.994007 + 0.109317i 0.0348665π0.0348665\pi
308308 4.85410 0.276588
309309 6.94427 0.395046
310310 0 0
311311 10.5279 0.596980 0.298490 0.954413i 0.403517π-0.403517\pi
0.298490 + 0.954413i 0.403517π0.403517\pi
312312 4.47214 0.253185
313313 6.70820 0.379170 0.189585 0.981864i 0.439286π-0.439286\pi
0.189585 + 0.981864i 0.439286π0.439286\pi
314314 12.0000 0.677199
315315 0 0
316316 −3.23607 −0.182043
317317 −11.5279 −0.647469 −0.323735 0.946148i 0.604939π-0.604939\pi
−0.323735 + 0.946148i 0.604939π0.604939\pi
318318 1.85410 0.103973
319319 5.29180 0.296284
320320 0 0
321321 −2.47214 −0.137981
322322 −5.23607 −0.291795
323323 0.236068 0.0131352
324324 −1.61803 −0.0898908
325325 0 0
326326 10.1459 0.561929
327327 6.47214 0.357910
328328 −18.4164 −1.01688
329329 −0.708204 −0.0390445
330330 0 0
331331 10.1246 0.556499 0.278249 0.960509i 0.410246π-0.410246\pi
0.278249 + 0.960509i 0.410246π0.410246\pi
332332 20.9443 1.14947
333333 8.70820 0.477207
334334 −11.4164 −0.624678
335335 0 0
336336 −1.85410 −0.101150
337337 31.6525 1.72422 0.862110 0.506721i 0.169143π-0.169143\pi
0.862110 + 0.506721i 0.169143π0.169143\pi
338338 5.56231 0.302550
339339 −1.05573 −0.0573393
340340 0 0
341341 19.4164 1.05146
342342 −0.145898 −0.00788926
343343 −13.0000 −0.701934
344344 1.05573 0.0569210
345345 0 0
346346 12.5836 0.676498
347347 −10.4721 −0.562174 −0.281087 0.959682i 0.590695π-0.590695\pi
−0.281087 + 0.959682i 0.590695π0.590695\pi
348348 −2.85410 −0.152996
349349 −32.4164 −1.73521 −0.867605 0.497254i 0.834342π-0.834342\pi
−0.867605 + 0.497254i 0.834342π0.834342\pi
350350 0 0
351351 2.00000 0.106752
352352 16.8541 0.898327
353353 −16.5279 −0.879689 −0.439845 0.898074i 0.644967π-0.644967\pi
−0.439845 + 0.898074i 0.644967π0.644967\pi
354354 5.52786 0.293803
355355 0 0
356356 19.4164 1.02907
357357 −1.00000 −0.0529256
358358 0.944272 0.0499063
359359 −11.8885 −0.627453 −0.313727 0.949513i 0.601578π-0.601578\pi
−0.313727 + 0.949513i 0.601578π0.601578\pi
360360 0 0
361361 −18.9443 −0.997067
362362 −8.58359 −0.451144
363363 2.00000 0.104973
364364 3.23607 0.169616
365365 0 0
366366 −6.18034 −0.323052
367367 −12.0000 −0.626395 −0.313197 0.949688i 0.601400π-0.601400\pi
−0.313197 + 0.949688i 0.601400π0.601400\pi
368368 15.7082 0.818847
369369 −8.23607 −0.428753
370370 0 0
371371 3.00000 0.155752
372372 −10.4721 −0.542955
373373 0.472136 0.0244463 0.0122231 0.999925i 0.496109π-0.496109\pi
0.0122231 + 0.999925i 0.496109π0.496109\pi
374374 1.85410 0.0958733
375375 0 0
376376 −1.58359 −0.0816675
377377 3.52786 0.181694
378378 0.618034 0.0317882
379379 36.3607 1.86772 0.933861 0.357635i 0.116417π-0.116417\pi
0.933861 + 0.357635i 0.116417π0.116417\pi
380380 0 0
381381 6.00000 0.307389
382382 −2.76393 −0.141415
383383 5.65248 0.288828 0.144414 0.989517i 0.453870π-0.453870\pi
0.144414 + 0.989517i 0.453870π0.453870\pi
384384 −11.3820 −0.580834
385385 0 0
386386 −5.81966 −0.296213
387387 0.472136 0.0240000
388388 21.7082 1.10207
389389 −28.3607 −1.43794 −0.718972 0.695039i 0.755387π-0.755387\pi
−0.718972 + 0.695039i 0.755387π0.755387\pi
390390 0 0
391391 8.47214 0.428454
392392 −13.4164 −0.677631
393393 −16.9443 −0.854725
394394 −13.8885 −0.699695
395395 0 0
396396 4.85410 0.243928
397397 −16.2361 −0.814865 −0.407432 0.913235i 0.633576π-0.633576\pi
−0.407432 + 0.913235i 0.633576π0.633576\pi
398398 −8.29180 −0.415630
399399 −0.236068 −0.0118182
400400 0 0
401401 11.2918 0.563885 0.281943 0.959431i 0.409021π-0.409021\pi
0.281943 + 0.959431i 0.409021π0.409021\pi
402402 −8.94427 −0.446100
403403 12.9443 0.644800
404404 8.94427 0.444994
405405 0 0
406406 1.09017 0.0541042
407407 −26.1246 −1.29495
408408 −2.23607 −0.110702
409409 35.8328 1.77182 0.885909 0.463858i 0.153535π-0.153535\pi
0.885909 + 0.463858i 0.153535π0.153535\pi
410410 0 0
411411 −16.4164 −0.809762
412412 11.2361 0.553561
413413 8.94427 0.440119
414414 −5.23607 −0.257339
415415 0 0
416416 11.2361 0.550894
417417 12.9443 0.633884
418418 0.437694 0.0214083
419419 −21.0000 −1.02592 −0.512959 0.858413i 0.671451π-0.671451\pi
−0.512959 + 0.858413i 0.671451π0.671451\pi
420420 0 0
421421 4.41641 0.215243 0.107621 0.994192i 0.465677π-0.465677\pi
0.107621 + 0.994192i 0.465677π0.465677\pi
422422 11.3475 0.552389
423423 −0.708204 −0.0344341
424424 6.70820 0.325779
425425 0 0
426426 −3.05573 −0.148051
427427 −10.0000 −0.483934
428428 −4.00000 −0.193347
429429 −6.00000 −0.289683
430430 0 0
431431 −27.4721 −1.32329 −0.661643 0.749819i 0.730141π-0.730141\pi
−0.661643 + 0.749819i 0.730141π0.730141\pi
432432 −1.85410 −0.0892055
433433 6.00000 0.288342 0.144171 0.989553i 0.453949π-0.453949\pi
0.144171 + 0.989553i 0.453949π0.453949\pi
434434 4.00000 0.192006
435435 0 0
436436 10.4721 0.501524
437437 2.00000 0.0956730
438438 −3.85410 −0.184156
439439 1.41641 0.0676015 0.0338007 0.999429i 0.489239π-0.489239\pi
0.0338007 + 0.999429i 0.489239π0.489239\pi
440440 0 0
441441 −6.00000 −0.285714
442442 1.23607 0.0587938
443443 −4.94427 −0.234909 −0.117455 0.993078i 0.537474π-0.537474\pi
−0.117455 + 0.993078i 0.537474π0.537474\pi
444444 14.0902 0.668690
445445 0 0
446446 −0.875388 −0.0414508
447447 −1.52786 −0.0722655
448448 −0.236068 −0.0111532
449449 1.41641 0.0668444 0.0334222 0.999441i 0.489359π-0.489359\pi
0.0334222 + 0.999441i 0.489359π0.489359\pi
450450 0 0
451451 24.7082 1.16346
452452 −1.70820 −0.0803472
453453 −13.7639 −0.646686
454454 −1.88854 −0.0886338
455455 0 0
456456 −0.527864 −0.0247195
457457 −34.0000 −1.59045 −0.795226 0.606313i 0.792648π-0.792648\pi
−0.795226 + 0.606313i 0.792648π0.792648\pi
458458 10.1459 0.474087
459459 −1.00000 −0.0466760
460460 0 0
461461 2.94427 0.137128 0.0685642 0.997647i 0.478158π-0.478158\pi
0.0685642 + 0.997647i 0.478158π0.478158\pi
462462 −1.85410 −0.0862606
463463 −3.41641 −0.158774 −0.0793870 0.996844i 0.525296π-0.525296\pi
−0.0793870 + 0.996844i 0.525296π0.525296\pi
464464 −3.27051 −0.151830
465465 0 0
466466 −7.41641 −0.343558
467467 −5.76393 −0.266723 −0.133361 0.991067i 0.542577π-0.542577\pi
−0.133361 + 0.991067i 0.542577π0.542577\pi
468468 3.23607 0.149587
469469 −14.4721 −0.668261
470470 0 0
471471 19.4164 0.894661
472472 20.0000 0.920575
473473 −1.41641 −0.0651265
474474 1.23607 0.0567745
475475 0 0
476476 −1.61803 −0.0741625
477477 3.00000 0.137361
478478 −0.291796 −0.0133464
479479 41.8885 1.91394 0.956968 0.290193i 0.0937194π-0.0937194\pi
0.956968 + 0.290193i 0.0937194π0.0937194\pi
480480 0 0
481481 −17.4164 −0.794120
482482 −3.05573 −0.139185
483483 −8.47214 −0.385496
484484 3.23607 0.147094
485485 0 0
486486 0.618034 0.0280346
487487 38.8328 1.75968 0.879841 0.475267i 0.157649π-0.157649\pi
0.879841 + 0.475267i 0.157649π0.157649\pi
488488 −22.3607 −1.01222
489489 16.4164 0.742376
490490 0 0
491491 −32.8328 −1.48172 −0.740862 0.671657i 0.765583π-0.765583\pi
−0.740862 + 0.671657i 0.765583π0.765583\pi
492492 −13.3262 −0.600793
493493 −1.76393 −0.0794435
494494 0.291796 0.0131285
495495 0 0
496496 −12.0000 −0.538816
497497 −4.94427 −0.221781
498498 −8.00000 −0.358489
499499 −38.3607 −1.71726 −0.858630 0.512596i 0.828684π-0.828684\pi
−0.858630 + 0.512596i 0.828684π0.828684\pi
500500 0 0
501501 −18.4721 −0.825274
502502 7.34752 0.327936
503503 33.8885 1.51102 0.755508 0.655140i 0.227390π-0.227390\pi
0.755508 + 0.655140i 0.227390π0.227390\pi
504504 2.23607 0.0996024
505505 0 0
506506 15.7082 0.698315
507507 9.00000 0.399704
508508 9.70820 0.430732
509509 −19.0557 −0.844630 −0.422315 0.906449i 0.638782π-0.638782\pi
−0.422315 + 0.906449i 0.638782π0.638782\pi
510510 0 0
511511 −6.23607 −0.275867
512512 −18.7082 −0.826794
513513 −0.236068 −0.0104227
514514 8.06888 0.355903
515515 0 0
516516 0.763932 0.0336302
517517 2.12461 0.0934403
518518 −5.38197 −0.236470
519519 20.3607 0.893735
520520 0 0
521521 −15.7639 −0.690630 −0.345315 0.938487i 0.612228π-0.612228\pi
−0.345315 + 0.938487i 0.612228π0.612228\pi
522522 1.09017 0.0477154
523523 −12.8328 −0.561140 −0.280570 0.959834i 0.590523π-0.590523\pi
−0.280570 + 0.959834i 0.590523π0.590523\pi
524524 −27.4164 −1.19769
525525 0 0
526526 −13.3820 −0.583481
527527 −6.47214 −0.281931
528528 5.56231 0.242068
529529 48.7771 2.12074
530530 0 0
531531 8.94427 0.388148
532532 −0.381966 −0.0165603
533533 16.4721 0.713487
534534 −7.41641 −0.320939
535535 0 0
536536 −32.3607 −1.39777
537537 1.52786 0.0659322
538538 4.43769 0.191323
539539 18.0000 0.775315
540540 0 0
541541 −3.41641 −0.146883 −0.0734414 0.997300i 0.523398π-0.523398\pi
−0.0734414 + 0.997300i 0.523398π0.523398\pi
542542 −13.5279 −0.581072
543543 −13.8885 −0.596014
544544 −5.61803 −0.240871
545545 0 0
546546 −1.23607 −0.0528988
547547 −26.4164 −1.12948 −0.564742 0.825268i 0.691024π-0.691024\pi
−0.564742 + 0.825268i 0.691024π0.691024\pi
548548 −26.5623 −1.13469
549549 −10.0000 −0.426790
550550 0 0
551551 −0.416408 −0.0177396
552552 −18.9443 −0.806322
553553 2.00000 0.0850487
554554 18.1803 0.772409
555555 0 0
556556 20.9443 0.888235
557557 43.8885 1.85962 0.929809 0.368043i 0.119972π-0.119972\pi
0.929809 + 0.368043i 0.119972π0.119972\pi
558558 4.00000 0.169334
559559 −0.944272 −0.0399384
560560 0 0
561561 3.00000 0.126660
562562 8.87539 0.374386
563563 −20.1246 −0.848151 −0.424076 0.905627i 0.639401π-0.639401\pi
−0.424076 + 0.905627i 0.639401π0.639401\pi
564564 −1.14590 −0.0482510
565565 0 0
566566 10.7984 0.453890
567567 1.00000 0.0419961
568568 −11.0557 −0.463888
569569 43.8885 1.83990 0.919952 0.392032i 0.128228π-0.128228\pi
0.919952 + 0.392032i 0.128228π0.128228\pi
570570 0 0
571571 −12.8328 −0.537037 −0.268518 0.963275i 0.586534π-0.586534\pi
−0.268518 + 0.963275i 0.586534π0.586534\pi
572572 −9.70820 −0.405920
573573 −4.47214 −0.186826
574574 5.09017 0.212460
575575 0 0
576576 −0.236068 −0.00983617
577577 29.3050 1.21998 0.609991 0.792409i 0.291173π-0.291173\pi
0.609991 + 0.792409i 0.291173π0.291173\pi
578578 −0.618034 −0.0257068
579579 −9.41641 −0.391333
580580 0 0
581581 −12.9443 −0.537019
582582 −8.29180 −0.343706
583583 −9.00000 −0.372742
584584 −13.9443 −0.577018
585585 0 0
586586 −5.49342 −0.226931
587587 2.23607 0.0922924 0.0461462 0.998935i 0.485306π-0.485306\pi
0.0461462 + 0.998935i 0.485306π0.485306\pi
588588 −9.70820 −0.400360
589589 −1.52786 −0.0629545
590590 0 0
591591 −22.4721 −0.924380
592592 16.1459 0.663592
593593 −8.52786 −0.350197 −0.175099 0.984551i 0.556024π-0.556024\pi
−0.175099 + 0.984551i 0.556024π0.556024\pi
594594 −1.85410 −0.0760747
595595 0 0
596596 −2.47214 −0.101263
597597 −13.4164 −0.549097
598598 10.4721 0.428237
599599 −4.47214 −0.182727 −0.0913633 0.995818i 0.529122π-0.529122\pi
−0.0913633 + 0.995818i 0.529122π0.529122\pi
600600 0 0
601601 −27.4164 −1.11834 −0.559169 0.829053i 0.688880π-0.688880\pi
−0.559169 + 0.829053i 0.688880π0.688880\pi
602602 −0.291796 −0.0118927
603603 −14.4721 −0.589351
604604 −22.2705 −0.906174
605605 0 0
606606 −3.41641 −0.138782
607607 11.1115 0.451000 0.225500 0.974243i 0.427598π-0.427598\pi
0.225500 + 0.974243i 0.427598π0.427598\pi
608608 −1.32624 −0.0537861
609609 1.76393 0.0714781
610610 0 0
611611 1.41641 0.0573017
612612 −1.61803 −0.0654051
613613 25.0557 1.01199 0.505996 0.862536i 0.331125π-0.331125\pi
0.505996 + 0.862536i 0.331125π0.331125\pi
614614 −21.5279 −0.868794
615615 0 0
616616 −6.70820 −0.270281
617617 −23.8885 −0.961717 −0.480858 0.876798i 0.659675π-0.659675\pi
−0.480858 + 0.876798i 0.659675π0.659675\pi
618618 −4.29180 −0.172641
619619 27.8885 1.12094 0.560468 0.828176i 0.310621π-0.310621\pi
0.560468 + 0.828176i 0.310621π0.310621\pi
620620 0 0
621621 −8.47214 −0.339975
622622 −6.50658 −0.260890
623623 −12.0000 −0.480770
624624 3.70820 0.148447
625625 0 0
626626 −4.14590 −0.165703
627627 0.708204 0.0282829
628628 31.4164 1.25365
629629 8.70820 0.347219
630630 0 0
631631 −32.1246 −1.27886 −0.639430 0.768849i 0.720830π-0.720830\pi
−0.639430 + 0.768849i 0.720830π0.720830\pi
632632 4.47214 0.177892
633633 18.3607 0.729772
634634 7.12461 0.282954
635635 0 0
636636 4.85410 0.192478
637637 12.0000 0.475457
638638 −3.27051 −0.129481
639639 −4.94427 −0.195592
640640 0 0
641641 −36.7082 −1.44989 −0.724943 0.688808i 0.758134π-0.758134\pi
−0.724943 + 0.688808i 0.758134π0.758134\pi
642642 1.52786 0.0603000
643643 31.2492 1.23235 0.616175 0.787610i 0.288682π-0.288682\pi
0.616175 + 0.787610i 0.288682π0.288682\pi
644644 −13.7082 −0.540179
645645 0 0
646646 −0.145898 −0.00574028
647647 19.0557 0.749158 0.374579 0.927195i 0.377787π-0.377787\pi
0.374579 + 0.927195i 0.377787π0.377787\pi
648648 2.23607 0.0878410
649649 −26.8328 −1.05328
650650 0 0
651651 6.47214 0.253663
652652 26.5623 1.04026
653653 −29.3050 −1.14679 −0.573396 0.819279i 0.694374π-0.694374\pi
−0.573396 + 0.819279i 0.694374π0.694374\pi
654654 −4.00000 −0.156412
655655 0 0
656656 −15.2705 −0.596213
657657 −6.23607 −0.243292
658658 0.437694 0.0170631
659659 −26.8328 −1.04526 −0.522629 0.852560i 0.675049π-0.675049\pi
−0.522629 + 0.852560i 0.675049π0.675049\pi
660660 0 0
661661 −28.4164 −1.10527 −0.552635 0.833423i 0.686378π-0.686378\pi
−0.552635 + 0.833423i 0.686378π0.686378\pi
662662 −6.25735 −0.243199
663663 2.00000 0.0776736
664664 −28.9443 −1.12326
665665 0 0
666666 −5.38197 −0.208547
667667 −14.9443 −0.578645
668668 −29.8885 −1.15642
669669 −1.41641 −0.0547615
670670 0 0
671671 30.0000 1.15814
672672 5.61803 0.216720
673673 12.4721 0.480766 0.240383 0.970678i 0.422727π-0.422727\pi
0.240383 + 0.970678i 0.422727π0.422727\pi
674674 −19.5623 −0.753512
675675 0 0
676676 14.5623 0.560089
677677 30.9443 1.18928 0.594642 0.803990i 0.297294π-0.297294\pi
0.594642 + 0.803990i 0.297294π0.297294\pi
678678 0.652476 0.0250582
679679 −13.4164 −0.514874
680680 0 0
681681 −3.05573 −0.117096
682682 −12.0000 −0.459504
683683 41.7771 1.59856 0.799278 0.600962i 0.205216π-0.205216\pi
0.799278 + 0.600962i 0.205216π0.205216\pi
684684 −0.381966 −0.0146048
685685 0 0
686686 8.03444 0.306756
687687 16.4164 0.626325
688688 0.875388 0.0333739
689689 −6.00000 −0.228582
690690 0 0
691691 34.2492 1.30290 0.651451 0.758691i 0.274161π-0.274161\pi
0.651451 + 0.758691i 0.274161π0.274161\pi
692692 32.9443 1.25235
693693 −3.00000 −0.113961
694694 6.47214 0.245679
695695 0 0
696696 3.94427 0.149507
697697 −8.23607 −0.311963
698698 20.0344 0.758315
699699 −12.0000 −0.453882
700700 0 0
701701 −18.0000 −0.679851 −0.339925 0.940452i 0.610402π-0.610402\pi
−0.339925 + 0.940452i 0.610402π0.610402\pi
702702 −1.23607 −0.0466524
703703 2.05573 0.0775333
704704 0.708204 0.0266914
705705 0 0
706706 10.2148 0.384438
707707 −5.52786 −0.207897
708708 14.4721 0.543896
709709 −10.5836 −0.397475 −0.198738 0.980053i 0.563684π-0.563684\pi
−0.198738 + 0.980053i 0.563684π0.563684\pi
710710 0 0
711711 2.00000 0.0750059
712712 −26.8328 −1.00560
713713 −54.8328 −2.05351
714714 0.618034 0.0231293
715715 0 0
716716 2.47214 0.0923881
717717 −0.472136 −0.0176322
718718 7.34752 0.274207
719719 −34.3050 −1.27936 −0.639679 0.768642i 0.720933π-0.720933\pi
−0.639679 + 0.768642i 0.720933π0.720933\pi
720720 0 0
721721 −6.94427 −0.258618
722722 11.7082 0.435734
723723 −4.94427 −0.183879
724724 −22.4721 −0.835170
725725 0 0
726726 −1.23607 −0.0458748
727727 35.3050 1.30939 0.654694 0.755894i 0.272797π-0.272797\pi
0.654694 + 0.755894i 0.272797π0.272797\pi
728728 −4.47214 −0.165748
729729 1.00000 0.0370370
730730 0 0
731731 0.472136 0.0174626
732732 −16.1803 −0.598043
733733 5.52786 0.204176 0.102088 0.994775i 0.467448π-0.467448\pi
0.102088 + 0.994775i 0.467448π0.467448\pi
734734 7.41641 0.273745
735735 0 0
736736 −47.5967 −1.75444
737737 43.4164 1.59926
738738 5.09017 0.187372
739739 −38.8328 −1.42849 −0.714244 0.699897i 0.753229π-0.753229\pi
−0.714244 + 0.699897i 0.753229π0.753229\pi
740740 0 0
741741 0.472136 0.0173443
742742 −1.85410 −0.0680662
743743 15.8885 0.582894 0.291447 0.956587i 0.405863π-0.405863\pi
0.291447 + 0.956587i 0.405863π0.405863\pi
744744 14.4721 0.530574
745745 0 0
746746 −0.291796 −0.0106834
747747 −12.9443 −0.473606
748748 4.85410 0.177484
749749 2.47214 0.0903299
750750 0 0
751751 39.8885 1.45555 0.727777 0.685814i 0.240554π-0.240554\pi
0.727777 + 0.685814i 0.240554π0.240554\pi
752752 −1.31308 −0.0478832
753753 11.8885 0.433243
754754 −2.18034 −0.0794033
755755 0 0
756756 1.61803 0.0588473
757757 −31.4164 −1.14185 −0.570924 0.821003i 0.693415π-0.693415\pi
−0.570924 + 0.821003i 0.693415π0.693415\pi
758758 −22.4721 −0.816225
759759 25.4164 0.922557
760760 0 0
761761 −22.9443 −0.831729 −0.415865 0.909427i 0.636521π-0.636521\pi
−0.415865 + 0.909427i 0.636521π0.636521\pi
762762 −3.70820 −0.134334
763763 −6.47214 −0.234307
764764 −7.23607 −0.261792
765765 0 0
766766 −3.49342 −0.126222
767767 −17.8885 −0.645918
768768 6.56231 0.236797
769769 31.9443 1.15194 0.575970 0.817471i 0.304625π-0.304625\pi
0.575970 + 0.817471i 0.304625π0.304625\pi
770770 0 0
771771 13.0557 0.470191
772772 −15.2361 −0.548358
773773 −50.7771 −1.82632 −0.913162 0.407596i 0.866367π-0.866367\pi
−0.913162 + 0.407596i 0.866367π0.866367\pi
774774 −0.291796 −0.0104884
775775 0 0
776776 −30.0000 −1.07694
777777 −8.70820 −0.312405
778778 17.5279 0.628404
779779 −1.94427 −0.0696608
780780 0 0
781781 14.8328 0.530760
782782 −5.23607 −0.187241
783783 1.76393 0.0630378
784784 −11.1246 −0.397308
785785 0 0
786786 10.4721 0.373529
787787 −46.4164 −1.65457 −0.827283 0.561785i 0.810115π-0.810115\pi
−0.827283 + 0.561785i 0.810115π0.810115\pi
788788 −36.3607 −1.29530
789789 −21.6525 −0.770849
790790 0 0
791791 1.05573 0.0375374
792792 −6.70820 −0.238366
793793 20.0000 0.710221
794794 10.0344 0.356109
795795 0 0
796796 −21.7082 −0.769427
797797 −39.0000 −1.38145 −0.690725 0.723117i 0.742709π-0.742709\pi
−0.690725 + 0.723117i 0.742709π0.742709\pi
798798 0.145898 0.00516473
799799 −0.708204 −0.0250545
800800 0 0
801801 −12.0000 −0.423999
802802 −6.97871 −0.246427
803803 18.7082 0.660198
804804 −23.4164 −0.825833
805805 0 0
806806 −8.00000 −0.281788
807807 7.18034 0.252760
808808 −12.3607 −0.434847
809809 16.4721 0.579129 0.289565 0.957158i 0.406489π-0.406489\pi
0.289565 + 0.957158i 0.406489π0.406489\pi
810810 0 0
811811 2.00000 0.0702295 0.0351147 0.999383i 0.488820π-0.488820\pi
0.0351147 + 0.999383i 0.488820π0.488820\pi
812812 2.85410 0.100159
813813 −21.8885 −0.767665
814814 16.1459 0.565913
815815 0 0
816816 −1.85410 −0.0649066
817817 0.111456 0.00389936
818818 −22.1459 −0.774313
819819 −2.00000 −0.0698857
820820 0 0
821821 16.4721 0.574882 0.287441 0.957798i 0.407196π-0.407196\pi
0.287441 + 0.957798i 0.407196π0.407196\pi
822822 10.1459 0.353879
823823 7.00000 0.244005 0.122002 0.992530i 0.461068π-0.461068\pi
0.122002 + 0.992530i 0.461068π0.461068\pi
824824 −15.5279 −0.540939
825825 0 0
826826 −5.52786 −0.192339
827827 35.8885 1.24797 0.623983 0.781438i 0.285513π-0.285513\pi
0.623983 + 0.781438i 0.285513π0.285513\pi
828828 −13.7082 −0.476393
829829 −23.3607 −0.811350 −0.405675 0.914017i 0.632964π-0.632964\pi
−0.405675 + 0.914017i 0.632964π0.632964\pi
830830 0 0
831831 29.4164 1.02044
832832 0.472136 0.0163684
833833 −6.00000 −0.207888
834834 −8.00000 −0.277017
835835 0 0
836836 1.14590 0.0396317
837837 6.47214 0.223710
838838 12.9787 0.448342
839839 10.4164 0.359614 0.179807 0.983702i 0.442453π-0.442453\pi
0.179807 + 0.983702i 0.442453π0.442453\pi
840840 0 0
841841 −25.8885 −0.892708
842842 −2.72949 −0.0940644
843843 14.3607 0.494608
844844 29.7082 1.02260
845845 0 0
846846 0.437694 0.0150482
847847 −2.00000 −0.0687208
848848 5.56231 0.191010
849849 17.4721 0.599642
850850 0 0
851851 73.7771 2.52905
852852 −8.00000 −0.274075
853853 56.2492 1.92594 0.962968 0.269614i 0.0868962π-0.0868962\pi
0.962968 + 0.269614i 0.0868962π0.0868962\pi
854854 6.18034 0.211487
855855 0 0
856856 5.52786 0.188939
857857 −9.63932 −0.329273 −0.164636 0.986354i 0.552645π-0.552645\pi
−0.164636 + 0.986354i 0.552645π0.552645\pi
858858 3.70820 0.126596
859859 14.8197 0.505640 0.252820 0.967513i 0.418642π-0.418642\pi
0.252820 + 0.967513i 0.418642π0.418642\pi
860860 0 0
861861 8.23607 0.280684
862862 16.9787 0.578297
863863 27.7639 0.945095 0.472548 0.881305i 0.343334π-0.343334\pi
0.472548 + 0.881305i 0.343334π0.343334\pi
864864 5.61803 0.191129
865865 0 0
866866 −3.70820 −0.126010
867867 −1.00000 −0.0339618
868868 10.4721 0.355447
869869 −6.00000 −0.203536
870870 0 0
871871 28.9443 0.980739
872872 −14.4721 −0.490088
873873 −13.4164 −0.454077
874874 −1.23607 −0.0418106
875875 0 0
876876 −10.0902 −0.340915
877877 13.8754 0.468539 0.234269 0.972172i 0.424730π-0.424730\pi
0.234269 + 0.972172i 0.424730π0.424730\pi
878878 −0.875388 −0.0295429
879879 −8.88854 −0.299803
880880 0 0
881881 −51.0689 −1.72055 −0.860277 0.509827i 0.829710π-0.829710\pi
−0.860277 + 0.509827i 0.829710π0.829710\pi
882882 3.70820 0.124862
883883 −3.16718 −0.106584 −0.0532921 0.998579i 0.516971π-0.516971\pi
−0.0532921 + 0.998579i 0.516971π0.516971\pi
884884 3.23607 0.108841
885885 0 0
886886 3.05573 0.102659
887887 −31.3050 −1.05112 −0.525559 0.850757i 0.676144π-0.676144\pi
−0.525559 + 0.850757i 0.676144π0.676144\pi
888888 −19.4721 −0.653442
889889 −6.00000 −0.201234
890890 0 0
891891 −3.00000 −0.100504
892892 −2.29180 −0.0767350
893893 −0.167184 −0.00559461
894894 0.944272 0.0315812
895895 0 0
896896 11.3820 0.380245
897897 16.9443 0.565753
898898 −0.875388 −0.0292121
899899 11.4164 0.380759
900900 0 0
901901 3.00000 0.0999445
902902 −15.2705 −0.508452
903903 −0.472136 −0.0157117
904904 2.36068 0.0785150
905905 0 0
906906 8.50658 0.282612
907907 40.4164 1.34200 0.671002 0.741455i 0.265864π-0.265864\pi
0.671002 + 0.741455i 0.265864π0.265864\pi
908908 −4.94427 −0.164081
909909 −5.52786 −0.183348
910910 0 0
911911 31.2492 1.03533 0.517666 0.855582i 0.326801π-0.326801\pi
0.517666 + 0.855582i 0.326801π0.326801\pi
912912 −0.437694 −0.0144935
913913 38.8328 1.28518
914914 21.0132 0.695053
915915 0 0
916916 26.5623 0.877643
917917 16.9443 0.559549
918918 0.618034 0.0203982
919919 −5.29180 −0.174560 −0.0872801 0.996184i 0.527818π-0.527818\pi
−0.0872801 + 0.996184i 0.527818π0.527818\pi
920920 0 0
921921 −34.8328 −1.14778
922922 −1.81966 −0.0599273
923923 9.88854 0.325485
924924 −4.85410 −0.159688
925925 0 0
926926 2.11146 0.0693868
927927 −6.94427 −0.228080
928928 9.90983 0.325306
929929 52.4853 1.72199 0.860993 0.508616i 0.169843π-0.169843\pi
0.860993 + 0.508616i 0.169843π0.169843\pi
930930 0 0
931931 −1.41641 −0.0464209
932932 −19.4164 −0.636006
933933 −10.5279 −0.344667
934934 3.56231 0.116562
935935 0 0
936936 −4.47214 −0.146176
937937 9.88854 0.323045 0.161522 0.986869i 0.448360π-0.448360\pi
0.161522 + 0.986869i 0.448360π0.448360\pi
938938 8.94427 0.292041
939939 −6.70820 −0.218914
940940 0 0
941941 −3.52786 −0.115005 −0.0575025 0.998345i 0.518314π-0.518314\pi
−0.0575025 + 0.998345i 0.518314π0.518314\pi
942942 −12.0000 −0.390981
943943 −69.7771 −2.27225
944944 16.5836 0.539750
945945 0 0
946946 0.875388 0.0284613
947947 19.5279 0.634570 0.317285 0.948330i 0.397229π-0.397229\pi
0.317285 + 0.948330i 0.397229π0.397229\pi
948948 3.23607 0.105103
949949 12.4721 0.404863
950950 0 0
951951 11.5279 0.373817
952952 2.23607 0.0724714
953953 5.36068 0.173649 0.0868247 0.996224i 0.472328π-0.472328\pi
0.0868247 + 0.996224i 0.472328π0.472328\pi
954954 −1.85410 −0.0600288
955955 0 0
956956 −0.763932 −0.0247073
957957 −5.29180 −0.171059
958958 −25.8885 −0.836421
959959 16.4164 0.530113
960960 0 0
961961 10.8885 0.351243
962962 10.7639 0.347043
963963 2.47214 0.0796635
964964 −8.00000 −0.257663
965965 0 0
966966 5.23607 0.168468
967967 −46.0000 −1.47926 −0.739630 0.673014i 0.765000π-0.765000\pi
−0.739630 + 0.673014i 0.765000π0.765000\pi
968968 −4.47214 −0.143740
969969 −0.236068 −0.00758360
970970 0 0
971971 41.3050 1.32554 0.662769 0.748823i 0.269381π-0.269381\pi
0.662769 + 0.748823i 0.269381π0.269381\pi
972972 1.61803 0.0518985
973973 −12.9443 −0.414974
974974 −24.0000 −0.769010
975975 0 0
976976 −18.5410 −0.593484
977977 −30.9443 −0.989995 −0.494997 0.868894i 0.664831π-0.664831\pi
−0.494997 + 0.868894i 0.664831π0.664831\pi
978978 −10.1459 −0.324430
979979 36.0000 1.15056
980980 0 0
981981 −6.47214 −0.206639
982982 20.2918 0.647537
983983 42.4721 1.35465 0.677325 0.735684i 0.263139π-0.263139\pi
0.677325 + 0.735684i 0.263139π0.263139\pi
984984 18.4164 0.587094
985985 0 0
986986 1.09017 0.0347181
987987 0.708204 0.0225424
988988 0.763932 0.0243039
989989 4.00000 0.127193
990990 0 0
991991 −24.0000 −0.762385 −0.381193 0.924496i 0.624487π-0.624487\pi
−0.381193 + 0.924496i 0.624487π0.624487\pi
992992 36.3607 1.15445
993993 −10.1246 −0.321295
994994 3.05573 0.0969218
995995 0 0
996996 −20.9443 −0.663645
997997 −14.5967 −0.462284 −0.231142 0.972920i 0.574246π-0.574246\pi
−0.231142 + 0.972920i 0.574246π0.574246\pi
998998 23.7082 0.750470
999999 −8.70820 −0.275515
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 1275.2.a.m.1.1 2
3.2 odd 2 3825.2.a.q.1.2 2
5.2 odd 4 255.2.b.b.154.2 4
5.3 odd 4 255.2.b.b.154.3 yes 4
5.4 even 2 1275.2.a.i.1.2 2
15.2 even 4 765.2.b.b.154.3 4
15.8 even 4 765.2.b.b.154.2 4
15.14 odd 2 3825.2.a.w.1.1 2
20.3 even 4 4080.2.m.n.2449.4 4
20.7 even 4 4080.2.m.n.2449.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
255.2.b.b.154.2 4 5.2 odd 4
255.2.b.b.154.3 yes 4 5.3 odd 4
765.2.b.b.154.2 4 15.8 even 4
765.2.b.b.154.3 4 15.2 even 4
1275.2.a.i.1.2 2 5.4 even 2
1275.2.a.m.1.1 2 1.1 even 1 trivial
3825.2.a.q.1.2 2 3.2 odd 2
3825.2.a.w.1.1 2 15.14 odd 2
4080.2.m.n.2449.2 4 20.7 even 4
4080.2.m.n.2449.4 4 20.3 even 4