Properties

Label 8925.2.a.cu.1.2
Level 89258925
Weight 22
Character 8925.1
Self dual yes
Analytic conductor 71.26671.266
Analytic rank 11
Dimension 1414
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] = [8925,2,Mod(1,8925)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8925, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8925.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 8925=352717 8925 = 3 \cdot 5^{2} \cdot 7 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 8925.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: 71.266483804071.2664838040
Analytic rank: 11
Dimension: 1414
Coefficient field: Q[x]/(x14)\mathbb{Q}[x]/(x^{14} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x143x1318x12+54x11+124x10366x9416x8+1164x7+727x6+40 x^{14} - 3 x^{13} - 18 x^{12} + 54 x^{11} + 124 x^{10} - 366 x^{9} - 416 x^{8} + 1164 x^{7} + 727 x^{6} + \cdots - 40 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 26 2^{6}
Twist minimal: no (minimal twist has level 1785)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 2.534682.53468 of defining polynomial
Character χ\chi == 8925.1

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) == q2.53468q21.00000q3+4.42458q4+2.53468q61.00000q76.14554q8+1.00000q9+2.67562q114.42458q122.82990q13+2.53468q14+6.72778q16+1.00000q172.53468q18+6.17364q19+1.00000q216.78182q22+2.83634q23+6.14554q24+7.17288q261.00000q274.42458q283.59961q29+0.268975q314.76167q322.67562q332.53468q34+4.42458q360.972382q3715.6482q38+2.82990q399.16460q412.53468q424.71924q43+11.8385q447.18921q46+13.4273q476.72778q48+1.00000q491.00000q5112.5211q5210.3318q53+2.53468q54+6.14554q566.17364q57+9.12383q58+7.82368q5912.2096q610.681766q621.00000q631.38627q64+6.78182q66+0.100710q67+4.42458q682.83634q69+13.9605q716.14554q7212.9290q73+2.46467q74+27.3158q762.67562q777.17288q7813.0779q79+1.00000q81+23.2293q828.22428q83+4.42458q84+11.9617q86+3.59961q8716.4431q88+9.68583q89+2.82990q91+12.5496q920.268975q9334.0339q94+4.76167q96+5.84462q972.53468q98+2.67562q99+O(q100)q-2.53468 q^{2} -1.00000 q^{3} +4.42458 q^{4} +2.53468 q^{6} -1.00000 q^{7} -6.14554 q^{8} +1.00000 q^{9} +2.67562 q^{11} -4.42458 q^{12} -2.82990 q^{13} +2.53468 q^{14} +6.72778 q^{16} +1.00000 q^{17} -2.53468 q^{18} +6.17364 q^{19} +1.00000 q^{21} -6.78182 q^{22} +2.83634 q^{23} +6.14554 q^{24} +7.17288 q^{26} -1.00000 q^{27} -4.42458 q^{28} -3.59961 q^{29} +0.268975 q^{31} -4.76167 q^{32} -2.67562 q^{33} -2.53468 q^{34} +4.42458 q^{36} -0.972382 q^{37} -15.6482 q^{38} +2.82990 q^{39} -9.16460 q^{41} -2.53468 q^{42} -4.71924 q^{43} +11.8385 q^{44} -7.18921 q^{46} +13.4273 q^{47} -6.72778 q^{48} +1.00000 q^{49} -1.00000 q^{51} -12.5211 q^{52} -10.3318 q^{53} +2.53468 q^{54} +6.14554 q^{56} -6.17364 q^{57} +9.12383 q^{58} +7.82368 q^{59} -12.2096 q^{61} -0.681766 q^{62} -1.00000 q^{63} -1.38627 q^{64} +6.78182 q^{66} +0.100710 q^{67} +4.42458 q^{68} -2.83634 q^{69} +13.9605 q^{71} -6.14554 q^{72} -12.9290 q^{73} +2.46467 q^{74} +27.3158 q^{76} -2.67562 q^{77} -7.17288 q^{78} -13.0779 q^{79} +1.00000 q^{81} +23.2293 q^{82} -8.22428 q^{83} +4.42458 q^{84} +11.9617 q^{86} +3.59961 q^{87} -16.4431 q^{88} +9.68583 q^{89} +2.82990 q^{91} +12.5496 q^{92} -0.268975 q^{93} -34.0339 q^{94} +4.76167 q^{96} +5.84462 q^{97} -2.53468 q^{98} +2.67562 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 14q3q214q3+17q4+3q614q715q8+14q9+4q1117q12+q13+3q14+19q16+14q173q186q19+14q2112q227q23++4q99+O(q100) 14 q - 3 q^{2} - 14 q^{3} + 17 q^{4} + 3 q^{6} - 14 q^{7} - 15 q^{8} + 14 q^{9} + 4 q^{11} - 17 q^{12} + q^{13} + 3 q^{14} + 19 q^{16} + 14 q^{17} - 3 q^{18} - 6 q^{19} + 14 q^{21} - 12 q^{22} - 7 q^{23}+ \cdots + 4 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 −2.53468 −1.79229 −0.896143 0.443765i 0.853643π-0.853643\pi
−0.896143 + 0.443765i 0.853643π0.853643\pi
33 −1.00000 −0.577350
44 4.42458 2.21229
55 0 0
66 2.53468 1.03478
77 −1.00000 −0.377964
88 −6.14554 −2.17278
99 1.00000 0.333333
1010 0 0
1111 2.67562 0.806729 0.403364 0.915039i 0.367841π-0.367841\pi
0.403364 + 0.915039i 0.367841π0.367841\pi
1212 −4.42458 −1.27727
1313 −2.82990 −0.784873 −0.392436 0.919779i 0.628368π-0.628368\pi
−0.392436 + 0.919779i 0.628368π0.628368\pi
1414 2.53468 0.677421
1515 0 0
1616 6.72778 1.68194
1717 1.00000 0.242536
1818 −2.53468 −0.597429
1919 6.17364 1.41633 0.708165 0.706047i 0.249523π-0.249523\pi
0.708165 + 0.706047i 0.249523π0.249523\pi
2020 0 0
2121 1.00000 0.218218
2222 −6.78182 −1.44589
2323 2.83634 0.591418 0.295709 0.955278i 0.404444π-0.404444\pi
0.295709 + 0.955278i 0.404444π0.404444\pi
2424 6.14554 1.25445
2525 0 0
2626 7.17288 1.40672
2727 −1.00000 −0.192450
2828 −4.42458 −0.836168
2929 −3.59961 −0.668430 −0.334215 0.942497i 0.608471π-0.608471\pi
−0.334215 + 0.942497i 0.608471π0.608471\pi
3030 0 0
3131 0.268975 0.0483094 0.0241547 0.999708i 0.492311π-0.492311\pi
0.0241547 + 0.999708i 0.492311π0.492311\pi
3232 −4.76167 −0.841751
3333 −2.67562 −0.465765
3434 −2.53468 −0.434693
3535 0 0
3636 4.42458 0.737431
3737 −0.972382 −0.159859 −0.0799293 0.996801i 0.525469π-0.525469\pi
−0.0799293 + 0.996801i 0.525469π0.525469\pi
3838 −15.6482 −2.53847
3939 2.82990 0.453146
4040 0 0
4141 −9.16460 −1.43127 −0.715635 0.698475i 0.753862π-0.753862\pi
−0.715635 + 0.698475i 0.753862π0.753862\pi
4242 −2.53468 −0.391109
4343 −4.71924 −0.719677 −0.359839 0.933015i 0.617168π-0.617168\pi
−0.359839 + 0.933015i 0.617168π0.617168\pi
4444 11.8385 1.78472
4545 0 0
4646 −7.18921 −1.05999
4747 13.4273 1.95857 0.979287 0.202479i 0.0648998π-0.0648998\pi
0.979287 + 0.202479i 0.0648998π0.0648998\pi
4848 −6.72778 −0.971071
4949 1.00000 0.142857
5050 0 0
5151 −1.00000 −0.140028
5252 −12.5211 −1.73637
5353 −10.3318 −1.41919 −0.709593 0.704612i 0.751121π-0.751121\pi
−0.709593 + 0.704612i 0.751121π0.751121\pi
5454 2.53468 0.344926
5555 0 0
5656 6.14554 0.821232
5757 −6.17364 −0.817718
5858 9.12383 1.19802
5959 7.82368 1.01856 0.509278 0.860602i 0.329912π-0.329912\pi
0.509278 + 0.860602i 0.329912π0.329912\pi
6060 0 0
6161 −12.2096 −1.56328 −0.781642 0.623727i 0.785618π-0.785618\pi
−0.781642 + 0.623727i 0.785618π0.785618\pi
6262 −0.681766 −0.0865843
6363 −1.00000 −0.125988
6464 −1.38627 −0.173284
6565 0 0
6666 6.78182 0.834785
6767 0.100710 0.0123036 0.00615182 0.999981i 0.498042π-0.498042\pi
0.00615182 + 0.999981i 0.498042π0.498042\pi
6868 4.42458 0.536560
6969 −2.83634 −0.341455
7070 0 0
7171 13.9605 1.65680 0.828401 0.560136i 0.189251π-0.189251\pi
0.828401 + 0.560136i 0.189251π0.189251\pi
7272 −6.14554 −0.724258
7373 −12.9290 −1.51323 −0.756614 0.653861i 0.773148π-0.773148\pi
−0.756614 + 0.653861i 0.773148π0.773148\pi
7474 2.46467 0.286513
7575 0 0
7676 27.3158 3.13334
7777 −2.67562 −0.304915
7878 −7.17288 −0.812168
7979 −13.0779 −1.47138 −0.735691 0.677317i 0.763142π-0.763142\pi
−0.735691 + 0.677317i 0.763142π0.763142\pi
8080 0 0
8181 1.00000 0.111111
8282 23.2293 2.56525
8383 −8.22428 −0.902732 −0.451366 0.892339i 0.649063π-0.649063\pi
−0.451366 + 0.892339i 0.649063π0.649063\pi
8484 4.42458 0.482762
8585 0 0
8686 11.9617 1.28987
8787 3.59961 0.385918
8888 −16.4431 −1.75284
8989 9.68583 1.02670 0.513348 0.858181i 0.328405π-0.328405\pi
0.513348 + 0.858181i 0.328405π0.328405\pi
9090 0 0
9191 2.82990 0.296654
9292 12.5496 1.30839
9393 −0.268975 −0.0278914
9494 −34.0339 −3.51032
9595 0 0
9696 4.76167 0.485985
9797 5.84462 0.593431 0.296715 0.954966i 0.404109π-0.404109\pi
0.296715 + 0.954966i 0.404109π0.404109\pi
9898 −2.53468 −0.256041
9999 2.67562 0.268910
100100 0 0
101101 3.76952 0.375081 0.187541 0.982257i 0.439948π-0.439948\pi
0.187541 + 0.982257i 0.439948π0.439948\pi
102102 2.53468 0.250970
103103 15.3905 1.51648 0.758238 0.651978i 0.226061π-0.226061\pi
0.758238 + 0.651978i 0.226061π0.226061\pi
104104 17.3912 1.70535
105105 0 0
106106 26.1878 2.54359
107107 −10.4289 −1.00820 −0.504098 0.863647i 0.668175π-0.668175\pi
−0.504098 + 0.863647i 0.668175π0.668175\pi
108108 −4.42458 −0.425756
109109 −12.1216 −1.16104 −0.580519 0.814247i 0.697150π-0.697150\pi
−0.580519 + 0.814247i 0.697150π0.697150\pi
110110 0 0
111111 0.972382 0.0922944
112112 −6.72778 −0.635715
113113 6.13424 0.577061 0.288531 0.957471i 0.406833π-0.406833\pi
0.288531 + 0.957471i 0.406833π0.406833\pi
114114 15.6482 1.46559
115115 0 0
116116 −15.9268 −1.47876
117117 −2.82990 −0.261624
118118 −19.8305 −1.82555
119119 −1.00000 −0.0916698
120120 0 0
121121 −3.84107 −0.349189
122122 30.9475 2.80185
123123 9.16460 0.826344
124124 1.19010 0.106875
125125 0 0
126126 2.53468 0.225807
127127 18.9227 1.67912 0.839560 0.543267i 0.182813π-0.182813\pi
0.839560 + 0.543267i 0.182813π0.182813\pi
128128 13.0371 1.15233
129129 4.71924 0.415506
130130 0 0
131131 −8.60741 −0.752033 −0.376017 0.926613i 0.622706π-0.622706\pi
−0.376017 + 0.926613i 0.622706π0.622706\pi
132132 −11.8385 −1.03041
133133 −6.17364 −0.535322
134134 −0.255266 −0.0220517
135135 0 0
136136 −6.14554 −0.526975
137137 −9.20549 −0.786478 −0.393239 0.919436i 0.628646π-0.628646\pi
−0.393239 + 0.919436i 0.628646π0.628646\pi
138138 7.18921 0.611986
139139 −16.3493 −1.38673 −0.693363 0.720589i 0.743872π-0.743872\pi
−0.693363 + 0.720589i 0.743872π0.743872\pi
140140 0 0
141141 −13.4273 −1.13078
142142 −35.3852 −2.96946
143143 −7.57172 −0.633179
144144 6.72778 0.560648
145145 0 0
146146 32.7709 2.71214
147147 −1.00000 −0.0824786
148148 −4.30239 −0.353654
149149 5.64922 0.462802 0.231401 0.972858i 0.425669π-0.425669\pi
0.231401 + 0.972858i 0.425669π0.425669\pi
150150 0 0
151151 −0.979344 −0.0796979 −0.0398489 0.999206i 0.512688π-0.512688\pi
−0.0398489 + 0.999206i 0.512688π0.512688\pi
152152 −37.9403 −3.07737
153153 1.00000 0.0808452
154154 6.78182 0.546495
155155 0 0
156156 12.5211 1.00249
157157 13.5350 1.08021 0.540104 0.841598i 0.318385π-0.318385\pi
0.540104 + 0.841598i 0.318385π0.318385\pi
158158 33.1483 2.63714
159159 10.3318 0.819367
160160 0 0
161161 −2.83634 −0.223535
162162 −2.53468 −0.199143
163163 −1.69805 −0.133001 −0.0665007 0.997786i 0.521183π-0.521183\pi
−0.0665007 + 0.997786i 0.521183π0.521183\pi
164164 −40.5495 −3.16639
165165 0 0
166166 20.8459 1.61795
167167 −5.93222 −0.459049 −0.229525 0.973303i 0.573717π-0.573717\pi
−0.229525 + 0.973303i 0.573717π0.573717\pi
168168 −6.14554 −0.474138
169169 −4.99167 −0.383975
170170 0 0
171171 6.17364 0.472110
172172 −20.8807 −1.59214
173173 −11.0062 −0.836786 −0.418393 0.908266i 0.637407π-0.637407\pi
−0.418393 + 0.908266i 0.637407π0.637407\pi
174174 −9.12383 −0.691676
175175 0 0
176176 18.0010 1.35687
177177 −7.82368 −0.588064
178178 −24.5504 −1.84013
179179 18.2252 1.36221 0.681106 0.732185i 0.261499π-0.261499\pi
0.681106 + 0.732185i 0.261499π0.261499\pi
180180 0 0
181181 −4.89359 −0.363738 −0.181869 0.983323i 0.558215π-0.558215\pi
−0.181869 + 0.983323i 0.558215π0.558215\pi
182182 −7.17288 −0.531689
183183 12.2096 0.902563
184184 −17.4308 −1.28502
185185 0 0
186186 0.681766 0.0499895
187187 2.67562 0.195660
188188 59.4102 4.33294
189189 1.00000 0.0727393
190190 0 0
191191 3.22202 0.233137 0.116569 0.993183i 0.462811π-0.462811\pi
0.116569 + 0.993183i 0.462811π0.462811\pi
192192 1.38627 0.100046
193193 −7.47523 −0.538079 −0.269040 0.963129i 0.586706π-0.586706\pi
−0.269040 + 0.963129i 0.586706π0.586706\pi
194194 −14.8142 −1.06360
195195 0 0
196196 4.42458 0.316042
197197 −1.31764 −0.0938780 −0.0469390 0.998898i 0.514947π-0.514947\pi
−0.0469390 + 0.998898i 0.514947π0.514947\pi
198198 −6.78182 −0.481963
199199 −3.75784 −0.266386 −0.133193 0.991090i 0.542523π-0.542523\pi
−0.133193 + 0.991090i 0.542523π0.542523\pi
200200 0 0
201201 −0.100710 −0.00710351
202202 −9.55451 −0.672253
203203 3.59961 0.252643
204204 −4.42458 −0.309783
205205 0 0
206206 −39.0101 −2.71796
207207 2.83634 0.197139
208208 −19.0389 −1.32011
209209 16.5183 1.14259
210210 0 0
211211 3.94059 0.271281 0.135641 0.990758i 0.456691π-0.456691\pi
0.135641 + 0.990758i 0.456691π0.456691\pi
212212 −45.7140 −3.13965
213213 −13.9605 −0.956555
214214 26.4338 1.80698
215215 0 0
216216 6.14554 0.418151
217217 −0.268975 −0.0182592
218218 30.7243 2.08091
219219 12.9290 0.873663
220220 0 0
221221 −2.82990 −0.190360
222222 −2.46467 −0.165418
223223 −12.3046 −0.823976 −0.411988 0.911189i 0.635165π-0.635165\pi
−0.411988 + 0.911189i 0.635165π0.635165\pi
224224 4.76167 0.318152
225225 0 0
226226 −15.5483 −1.03426
227227 10.7792 0.715441 0.357720 0.933829i 0.383554π-0.383554\pi
0.357720 + 0.933829i 0.383554π0.383554\pi
228228 −27.3158 −1.80903
229229 −16.8801 −1.11547 −0.557734 0.830020i 0.688329π-0.688329\pi
−0.557734 + 0.830020i 0.688329π0.688329\pi
230230 0 0
231231 2.67562 0.176043
232232 22.1215 1.45235
233233 −14.4278 −0.945194 −0.472597 0.881279i 0.656683π-0.656683\pi
−0.472597 + 0.881279i 0.656683π0.656683\pi
234234 7.17288 0.468906
235235 0 0
236236 34.6165 2.25334
237237 13.0779 0.849503
238238 2.53468 0.164299
239239 6.81210 0.440638 0.220319 0.975428i 0.429290π-0.429290\pi
0.220319 + 0.975428i 0.429290π0.429290\pi
240240 0 0
241241 0.719989 0.0463786 0.0231893 0.999731i 0.492618π-0.492618\pi
0.0231893 + 0.999731i 0.492618π0.492618\pi
242242 9.73588 0.625846
243243 −1.00000 −0.0641500
244244 −54.0226 −3.45844
245245 0 0
246246 −23.2293 −1.48105
247247 −17.4708 −1.11164
248248 −1.65300 −0.104965
249249 8.22428 0.521192
250250 0 0
251251 −24.1847 −1.52653 −0.763263 0.646088i 0.776404π-0.776404\pi
−0.763263 + 0.646088i 0.776404π0.776404\pi
252252 −4.42458 −0.278723
253253 7.58896 0.477114
254254 −47.9630 −3.00946
255255 0 0
256256 −30.2722 −1.89202
257257 −21.4316 −1.33687 −0.668433 0.743773i 0.733035π-0.733035\pi
−0.668433 + 0.743773i 0.733035π0.733035\pi
258258 −11.9617 −0.744706
259259 0.972382 0.0604209
260260 0 0
261261 −3.59961 −0.222810
262262 21.8170 1.34786
263263 −8.00460 −0.493585 −0.246793 0.969068i 0.579377π-0.579377\pi
−0.246793 + 0.969068i 0.579377π0.579377\pi
264264 16.4431 1.01200
265265 0 0
266266 15.6482 0.959451
267267 −9.68583 −0.592763
268268 0.445598 0.0272193
269269 15.2324 0.928735 0.464367 0.885643i 0.346282π-0.346282\pi
0.464367 + 0.885643i 0.346282π0.346282\pi
270270 0 0
271271 12.3967 0.753048 0.376524 0.926407i 0.377119π-0.377119\pi
0.376524 + 0.926407i 0.377119π0.377119\pi
272272 6.72778 0.407931
273273 −2.82990 −0.171273
274274 23.3329 1.40959
275275 0 0
276276 −12.5496 −0.755399
277277 −22.2410 −1.33633 −0.668166 0.744013i 0.732920π-0.732920\pi
−0.668166 + 0.744013i 0.732920π0.732920\pi
278278 41.4401 2.48541
279279 0.268975 0.0161031
280280 0 0
281281 30.3105 1.80817 0.904086 0.427350i 0.140553π-0.140553\pi
0.904086 + 0.427350i 0.140553π0.140553\pi
282282 34.0339 2.02669
283283 7.53626 0.447984 0.223992 0.974591i 0.428091π-0.428091\pi
0.223992 + 0.974591i 0.428091π0.428091\pi
284284 61.7692 3.66533
285285 0 0
286286 19.1919 1.13484
287287 9.16460 0.540969
288288 −4.76167 −0.280584
289289 1.00000 0.0588235
290290 0 0
291291 −5.84462 −0.342618
292292 −57.2056 −3.34770
293293 27.8572 1.62743 0.813717 0.581261i 0.197441π-0.197441\pi
0.813717 + 0.581261i 0.197441π0.197441\pi
294294 2.53468 0.147825
295295 0 0
296296 5.97581 0.347337
297297 −2.67562 −0.155255
298298 −14.3190 −0.829475
299299 −8.02656 −0.464188
300300 0 0
301301 4.71924 0.272012
302302 2.48232 0.142841
303303 −3.76952 −0.216553
304304 41.5349 2.38219
305305 0 0
306306 −2.53468 −0.144898
307307 −14.2241 −0.811814 −0.405907 0.913914i 0.633044π-0.633044\pi
−0.405907 + 0.913914i 0.633044π0.633044\pi
308308 −11.8385 −0.674561
309309 −15.3905 −0.875538
310310 0 0
311311 −18.4183 −1.04440 −0.522202 0.852822i 0.674889π-0.674889\pi
−0.522202 + 0.852822i 0.674889π0.674889\pi
312312 −17.3912 −0.984585
313313 9.24130 0.522349 0.261175 0.965292i 0.415890π-0.415890\pi
0.261175 + 0.965292i 0.415890π0.415890\pi
314314 −34.3068 −1.93604
315315 0 0
316316 −57.8644 −3.25513
317317 10.1457 0.569839 0.284920 0.958551i 0.408033π-0.408033\pi
0.284920 + 0.958551i 0.408033π0.408033\pi
318318 −26.1878 −1.46854
319319 −9.63116 −0.539242
320320 0 0
321321 10.4289 0.582082
322322 7.18921 0.400639
323323 6.17364 0.343510
324324 4.42458 0.245810
325325 0 0
326326 4.30400 0.238377
327327 12.1216 0.670326
328328 56.3214 3.10983
329329 −13.4273 −0.740271
330330 0 0
331331 8.09315 0.444840 0.222420 0.974951i 0.428604π-0.428604\pi
0.222420 + 0.974951i 0.428604π0.428604\pi
332332 −36.3890 −1.99711
333333 −0.972382 −0.0532862
334334 15.0363 0.822748
335335 0 0
336336 6.72778 0.367030
337337 6.19090 0.337240 0.168620 0.985681i 0.446069π-0.446069\pi
0.168620 + 0.985681i 0.446069π0.446069\pi
338338 12.6523 0.688193
339339 −6.13424 −0.333166
340340 0 0
341341 0.719675 0.0389726
342342 −15.6482 −0.846156
343343 −1.00000 −0.0539949
344344 29.0023 1.56370
345345 0 0
346346 27.8972 1.49976
347347 25.4722 1.36742 0.683710 0.729754i 0.260365π-0.260365\pi
0.683710 + 0.729754i 0.260365π0.260365\pi
348348 15.9268 0.853764
349349 11.6109 0.621519 0.310759 0.950489i 0.399417π-0.399417\pi
0.310759 + 0.950489i 0.399417π0.399417\pi
350350 0 0
351351 2.82990 0.151049
352352 −12.7404 −0.679065
353353 27.4324 1.46008 0.730040 0.683404i 0.239501π-0.239501\pi
0.730040 + 0.683404i 0.239501π0.239501\pi
354354 19.8305 1.05398
355355 0 0
356356 42.8558 2.27135
357357 1.00000 0.0529256
358358 −46.1949 −2.44148
359359 −9.01857 −0.475982 −0.237991 0.971267i 0.576489π-0.576489\pi
−0.237991 + 0.971267i 0.576489π0.576489\pi
360360 0 0
361361 19.1138 1.00599
362362 12.4037 0.651923
363363 3.84107 0.201604
364364 12.5211 0.656285
365365 0 0
366366 −30.9475 −1.61765
367367 0.540557 0.0282168 0.0141084 0.999900i 0.495509π-0.495509\pi
0.0141084 + 0.999900i 0.495509π0.495509\pi
368368 19.0823 0.994732
369369 −9.16460 −0.477090
370370 0 0
371371 10.3318 0.536402
372372 −1.19010 −0.0617040
373373 −6.14299 −0.318072 −0.159036 0.987273i 0.550839π-0.550839\pi
−0.159036 + 0.987273i 0.550839π0.550839\pi
374374 −6.78182 −0.350680
375375 0 0
376376 −82.5180 −4.25554
377377 10.1865 0.524632
378378 −2.53468 −0.130370
379379 −5.98190 −0.307269 −0.153635 0.988128i 0.549098π-0.549098\pi
−0.153635 + 0.988128i 0.549098π0.549098\pi
380380 0 0
381381 −18.9227 −0.969440
382382 −8.16678 −0.417849
383383 16.7998 0.858427 0.429214 0.903203i 0.358791π-0.358791\pi
0.429214 + 0.903203i 0.358791π0.358791\pi
384384 −13.0371 −0.665296
385385 0 0
386386 18.9473 0.964392
387387 −4.71924 −0.239892
388388 25.8600 1.31284
389389 6.62924 0.336116 0.168058 0.985777i 0.446250π-0.446250\pi
0.168058 + 0.985777i 0.446250π0.446250\pi
390390 0 0
391391 2.83634 0.143440
392392 −6.14554 −0.310396
393393 8.60741 0.434187
394394 3.33979 0.168256
395395 0 0
396396 11.8385 0.594907
397397 −11.0069 −0.552421 −0.276211 0.961097i 0.589079π-0.589079\pi
−0.276211 + 0.961097i 0.589079π0.589079\pi
398398 9.52490 0.477440
399399 6.17364 0.309068
400400 0 0
401401 11.8228 0.590405 0.295202 0.955435i 0.404613π-0.404613\pi
0.295202 + 0.955435i 0.404613π0.404613\pi
402402 0.255266 0.0127315
403403 −0.761173 −0.0379167
404404 16.6786 0.829789
405405 0 0
406406 −9.12383 −0.452808
407407 −2.60172 −0.128963
408408 6.14554 0.304249
409409 −16.2239 −0.802222 −0.401111 0.916029i 0.631376π-0.631376\pi
−0.401111 + 0.916029i 0.631376π0.631376\pi
410410 0 0
411411 9.20549 0.454074
412412 68.0968 3.35489
413413 −7.82368 −0.384978
414414 −7.18921 −0.353330
415415 0 0
416416 13.4750 0.660668
417417 16.3493 0.800627
418418 −41.8685 −2.04786
419419 10.0431 0.490637 0.245318 0.969443i 0.421108π-0.421108\pi
0.245318 + 0.969443i 0.421108π0.421108\pi
420420 0 0
421421 −0.327910 −0.0159814 −0.00799069 0.999968i 0.502544π-0.502544\pi
−0.00799069 + 0.999968i 0.502544π0.502544\pi
422422 −9.98812 −0.486214
423423 13.4273 0.652858
424424 63.4946 3.08357
425425 0 0
426426 35.3852 1.71442
427427 12.2096 0.590866
428428 −46.1434 −2.23042
429429 7.57172 0.365566
430430 0 0
431431 30.6790 1.47775 0.738877 0.673840i 0.235356π-0.235356\pi
0.738877 + 0.673840i 0.235356π0.235356\pi
432432 −6.72778 −0.323690
433433 −22.8410 −1.09767 −0.548834 0.835931i 0.684928π-0.684928\pi
−0.548834 + 0.835931i 0.684928π0.684928\pi
434434 0.681766 0.0327258
435435 0 0
436436 −53.6330 −2.56856
437437 17.5105 0.837643
438438 −32.7709 −1.56585
439439 −3.59112 −0.171395 −0.0856975 0.996321i 0.527312π-0.527312\pi
−0.0856975 + 0.996321i 0.527312π0.527312\pi
440440 0 0
441441 1.00000 0.0476190
442442 7.17288 0.341179
443443 −11.0622 −0.525583 −0.262792 0.964853i 0.584643π-0.584643\pi
−0.262792 + 0.964853i 0.584643π0.584643\pi
444444 4.30239 0.204182
445445 0 0
446446 31.1881 1.47680
447447 −5.64922 −0.267199
448448 1.38627 0.0654953
449449 31.5468 1.48878 0.744392 0.667742i 0.232739π-0.232739\pi
0.744392 + 0.667742i 0.232739π0.232739\pi
450450 0 0
451451 −24.5209 −1.15465
452452 27.1415 1.27663
453453 0.979344 0.0460136
454454 −27.3218 −1.28228
455455 0 0
456456 37.9403 1.77672
457457 −17.7329 −0.829512 −0.414756 0.909933i 0.636133π-0.636133\pi
−0.414756 + 0.909933i 0.636133π0.636133\pi
458458 42.7856 1.99924
459459 −1.00000 −0.0466760
460460 0 0
461461 −42.3347 −1.97173 −0.985863 0.167556i 0.946413π-0.946413\pi
−0.985863 + 0.167556i 0.946413π0.946413\pi
462462 −6.78182 −0.315519
463463 13.1494 0.611105 0.305553 0.952175i 0.401159π-0.401159\pi
0.305553 + 0.952175i 0.401159π0.401159\pi
464464 −24.2173 −1.12426
465465 0 0
466466 36.5697 1.69406
467467 23.4306 1.08424 0.542119 0.840302i 0.317622π-0.317622\pi
0.542119 + 0.840302i 0.317622π0.317622\pi
468468 −12.5211 −0.578789
469469 −0.100710 −0.00465034
470470 0 0
471471 −13.5350 −0.623659
472472 −48.0807 −2.21309
473473 −12.6269 −0.580584
474474 −33.1483 −1.52255
475475 0 0
476476 −4.42458 −0.202800
477477 −10.3318 −0.473062
478478 −17.2665 −0.789750
479479 −34.2130 −1.56323 −0.781617 0.623759i 0.785605π-0.785605\pi
−0.781617 + 0.623759i 0.785605π0.785605\pi
480480 0 0
481481 2.75174 0.125469
482482 −1.82494 −0.0831237
483483 2.83634 0.129058
484484 −16.9952 −0.772507
485485 0 0
486486 2.53468 0.114975
487487 23.0901 1.04631 0.523157 0.852236i 0.324754π-0.324754\pi
0.523157 + 0.852236i 0.324754π0.324754\pi
488488 75.0348 3.39667
489489 1.69805 0.0767884
490490 0 0
491491 −13.7848 −0.622099 −0.311049 0.950394i 0.600680π-0.600680\pi
−0.311049 + 0.950394i 0.600680π0.600680\pi
492492 40.5495 1.82811
493493 −3.59961 −0.162118
494494 44.2828 1.99238
495495 0 0
496496 1.80961 0.0812537
497497 −13.9605 −0.626212
498498 −20.8459 −0.934126
499499 −35.6592 −1.59632 −0.798162 0.602443i 0.794194π-0.794194\pi
−0.798162 + 0.602443i 0.794194π0.794194\pi
500500 0 0
501501 5.93222 0.265032
502502 61.3005 2.73597
503503 19.4662 0.867955 0.433978 0.900924i 0.357110π-0.357110\pi
0.433978 + 0.900924i 0.357110π0.357110\pi
504504 6.14554 0.273744
505505 0 0
506506 −19.2356 −0.855125
507507 4.99167 0.221688
508508 83.7251 3.71470
509509 −37.2678 −1.65187 −0.825934 0.563767i 0.809351π-0.809351\pi
−0.825934 + 0.563767i 0.809351π0.809351\pi
510510 0 0
511511 12.9290 0.571947
512512 50.6562 2.23871
513513 −6.17364 −0.272573
514514 54.3221 2.39605
515515 0 0
516516 20.8807 0.919220
517517 35.9263 1.58004
518518 −2.46467 −0.108292
519519 11.0062 0.483119
520520 0 0
521521 20.1590 0.883182 0.441591 0.897216i 0.354414π-0.354414\pi
0.441591 + 0.897216i 0.354414π0.354414\pi
522522 9.12383 0.399339
523523 1.53917 0.0673031 0.0336516 0.999434i 0.489286π-0.489286\pi
0.0336516 + 0.999434i 0.489286π0.489286\pi
524524 −38.0842 −1.66372
525525 0 0
526526 20.2891 0.884646
527527 0.268975 0.0117168
528528 −18.0010 −0.783391
529529 −14.9552 −0.650225
530530 0 0
531531 7.82368 0.339519
532532 −27.3158 −1.18429
533533 25.9349 1.12336
534534 24.5504 1.06240
535535 0 0
536536 −0.618915 −0.0267331
537537 −18.2252 −0.786474
538538 −38.6092 −1.66456
539539 2.67562 0.115247
540540 0 0
541541 −40.9976 −1.76262 −0.881311 0.472536i 0.843339π-0.843339\pi
−0.881311 + 0.472536i 0.843339π0.843339\pi
542542 −31.4217 −1.34968
543543 4.89359 0.210004
544544 −4.76167 −0.204155
545545 0 0
546546 7.17288 0.306971
547547 −20.3683 −0.870885 −0.435442 0.900217i 0.643408π-0.643408\pi
−0.435442 + 0.900217i 0.643408π0.643408\pi
548548 −40.7305 −1.73992
549549 −12.2096 −0.521095
550550 0 0
551551 −22.2227 −0.946717
552552 17.4308 0.741906
553553 13.0779 0.556130
554554 56.3737 2.39509
555555 0 0
556556 −72.3387 −3.06784
557557 17.9048 0.758650 0.379325 0.925263i 0.376156π-0.376156\pi
0.379325 + 0.925263i 0.376156π0.376156\pi
558558 −0.681766 −0.0288614
559559 13.3550 0.564855
560560 0 0
561561 −2.67562 −0.112965
562562 −76.8273 −3.24076
563563 −43.4886 −1.83283 −0.916413 0.400233i 0.868929π-0.868929\pi
−0.916413 + 0.400233i 0.868929π0.868929\pi
564564 −59.4102 −2.50162
565565 0 0
566566 −19.1020 −0.802916
567567 −1.00000 −0.0419961
568568 −85.7945 −3.59986
569569 36.2315 1.51890 0.759452 0.650564i 0.225467π-0.225467\pi
0.759452 + 0.650564i 0.225467π0.225467\pi
570570 0 0
571571 26.4307 1.10609 0.553045 0.833152i 0.313466π-0.313466\pi
0.553045 + 0.833152i 0.313466π0.313466\pi
572572 −33.5017 −1.40078
573573 −3.22202 −0.134602
574574 −23.2293 −0.969572
575575 0 0
576576 −1.38627 −0.0577614
577577 7.24749 0.301717 0.150859 0.988555i 0.451796π-0.451796\pi
0.150859 + 0.988555i 0.451796π0.451796\pi
578578 −2.53468 −0.105429
579579 7.47523 0.310660
580580 0 0
581581 8.22428 0.341200
582582 14.8142 0.614069
583583 −27.6440 −1.14490
584584 79.4558 3.28791
585585 0 0
586586 −70.6090 −2.91683
587587 −44.9985 −1.85729 −0.928644 0.370972i 0.879025π-0.879025\pi
−0.928644 + 0.370972i 0.879025π0.879025\pi
588588 −4.42458 −0.182467
589589 1.66056 0.0684220
590590 0 0
591591 1.31764 0.0542005
592592 −6.54197 −0.268873
593593 38.0682 1.56328 0.781638 0.623733i 0.214385π-0.214385\pi
0.781638 + 0.623733i 0.214385π0.214385\pi
594594 6.78182 0.278262
595595 0 0
596596 24.9955 1.02385
597597 3.75784 0.153798
598598 20.3447 0.831958
599599 −11.6339 −0.475350 −0.237675 0.971345i 0.576385π-0.576385\pi
−0.237675 + 0.971345i 0.576385π0.576385\pi
600600 0 0
601601 7.59027 0.309614 0.154807 0.987945i 0.450524π-0.450524\pi
0.154807 + 0.987945i 0.450524π0.450524\pi
602602 −11.9617 −0.487524
603603 0.100710 0.00410121
604604 −4.33319 −0.176315
605605 0 0
606606 9.55451 0.388125
607607 −28.0706 −1.13935 −0.569675 0.821870i 0.692931π-0.692931\pi
−0.569675 + 0.821870i 0.692931π0.692931\pi
608608 −29.3968 −1.19220
609609 −3.59961 −0.145863
610610 0 0
611611 −37.9979 −1.53723
612612 4.42458 0.178853
613613 35.9949 1.45382 0.726911 0.686732i 0.240955π-0.240955\pi
0.726911 + 0.686732i 0.240955π0.240955\pi
614614 36.0536 1.45500
615615 0 0
616616 16.4431 0.662511
617617 −11.5231 −0.463903 −0.231951 0.972727i 0.574511π-0.574511\pi
−0.231951 + 0.972727i 0.574511π0.574511\pi
618618 39.0101 1.56921
619619 −43.6477 −1.75435 −0.877176 0.480170i 0.840575π-0.840575\pi
−0.877176 + 0.480170i 0.840575π0.840575\pi
620620 0 0
621621 −2.83634 −0.113818
622622 46.6844 1.87187
623623 −9.68583 −0.388055
624624 19.0389 0.762167
625625 0 0
626626 −23.4237 −0.936200
627627 −16.5183 −0.659677
628628 59.8866 2.38974
629629 −0.972382 −0.0387714
630630 0 0
631631 28.5906 1.13817 0.569086 0.822278i 0.307297π-0.307297\pi
0.569086 + 0.822278i 0.307297π0.307297\pi
632632 80.3709 3.19698
633633 −3.94059 −0.156624
634634 −25.7161 −1.02132
635635 0 0
636636 45.7140 1.81268
637637 −2.82990 −0.112125
638638 24.4119 0.966476
639639 13.9605 0.552267
640640 0 0
641641 23.7289 0.937236 0.468618 0.883401i 0.344752π-0.344752\pi
0.468618 + 0.883401i 0.344752π0.344752\pi
642642 −26.4338 −1.04326
643643 42.9662 1.69442 0.847211 0.531257i 0.178280π-0.178280\pi
0.847211 + 0.531257i 0.178280π0.178280\pi
644644 −12.5496 −0.494525
645645 0 0
646646 −15.6482 −0.615669
647647 −42.7951 −1.68245 −0.841225 0.540686i 0.818165π-0.818165\pi
−0.841225 + 0.540686i 0.818165π0.818165\pi
648648 −6.14554 −0.241419
649649 20.9332 0.821699
650650 0 0
651651 0.268975 0.0105420
652652 −7.51316 −0.294238
653653 7.30739 0.285960 0.142980 0.989726i 0.454332π-0.454332\pi
0.142980 + 0.989726i 0.454332π0.454332\pi
654654 −30.7243 −1.20142
655655 0 0
656656 −61.6574 −2.40732
657657 −12.9290 −0.504410
658658 34.0339 1.32678
659659 8.24440 0.321156 0.160578 0.987023i 0.448664π-0.448664\pi
0.160578 + 0.987023i 0.448664π0.448664\pi
660660 0 0
661661 −8.85399 −0.344380 −0.172190 0.985064i 0.555084π-0.555084\pi
−0.172190 + 0.985064i 0.555084π0.555084\pi
662662 −20.5135 −0.797280
663663 2.82990 0.109904
664664 50.5426 1.96143
665665 0 0
666666 2.46467 0.0955042
667667 −10.2097 −0.395322
668668 −26.2476 −1.01555
669669 12.3046 0.475723
670670 0 0
671671 −32.6683 −1.26115
672672 −4.76167 −0.183685
673673 40.6122 1.56549 0.782743 0.622345i 0.213820π-0.213820\pi
0.782743 + 0.622345i 0.213820π0.213820\pi
674674 −15.6919 −0.604431
675675 0 0
676676 −22.0861 −0.849464
677677 −10.6023 −0.407478 −0.203739 0.979025i 0.565309π-0.565309\pi
−0.203739 + 0.979025i 0.565309π0.565309\pi
678678 15.5483 0.597130
679679 −5.84462 −0.224296
680680 0 0
681681 −10.7792 −0.413060
682682 −1.82414 −0.0698501
683683 −16.1464 −0.617827 −0.308913 0.951090i 0.599965π-0.599965\pi
−0.308913 + 0.951090i 0.599965π0.599965\pi
684684 27.3158 1.04445
685685 0 0
686686 2.53468 0.0967744
687687 16.8801 0.644016
688688 −31.7500 −1.21046
689689 29.2380 1.11388
690690 0 0
691691 −31.5928 −1.20185 −0.600923 0.799307i 0.705200π-0.705200\pi
−0.600923 + 0.799307i 0.705200π0.705200\pi
692692 −48.6979 −1.85122
693693 −2.67562 −0.101638
694694 −64.5638 −2.45081
695695 0 0
696696 −22.1215 −0.838514
697697 −9.16460 −0.347134
698698 −29.4299 −1.11394
699699 14.4278 0.545708
700700 0 0
701701 −15.0683 −0.569122 −0.284561 0.958658i 0.591848π-0.591848\pi
−0.284561 + 0.958658i 0.591848π0.591848\pi
702702 −7.17288 −0.270723
703703 −6.00314 −0.226413
704704 −3.70914 −0.139793
705705 0 0
706706 −69.5323 −2.61688
707707 −3.76952 −0.141767
708708 −34.6165 −1.30097
709709 32.9168 1.23622 0.618108 0.786093i 0.287899π-0.287899\pi
0.618108 + 0.786093i 0.287899π0.287899\pi
710710 0 0
711711 −13.0779 −0.490461
712712 −59.5246 −2.23078
713713 0.762906 0.0285711
714714 −2.53468 −0.0948579
715715 0 0
716716 80.6387 3.01361
717717 −6.81210 −0.254402
718718 22.8592 0.853097
719719 −50.5233 −1.88420 −0.942101 0.335330i 0.891152π-0.891152\pi
−0.942101 + 0.335330i 0.891152π0.891152\pi
720720 0 0
721721 −15.3905 −0.573174
722722 −48.4473 −1.80302
723723 −0.719989 −0.0267767
724724 −21.6521 −0.804694
725725 0 0
726726 −9.73588 −0.361332
727727 39.0916 1.44983 0.724914 0.688839i 0.241879π-0.241879\pi
0.724914 + 0.688839i 0.241879π0.241879\pi
728728 −17.3912 −0.644562
729729 1.00000 0.0370370
730730 0 0
731731 −4.71924 −0.174547
732732 54.0226 1.99673
733733 15.1802 0.560695 0.280347 0.959899i 0.409550π-0.409550\pi
0.280347 + 0.959899i 0.409550π0.409550\pi
734734 −1.37014 −0.0505727
735735 0 0
736736 −13.5057 −0.497827
737737 0.269460 0.00992570
738738 23.2293 0.855082
739739 −33.2452 −1.22294 −0.611472 0.791266i 0.709422π-0.709422\pi
−0.611472 + 0.791266i 0.709422π0.709422\pi
740740 0 0
741741 17.4708 0.641805
742742 −26.1878 −0.961386
743743 13.0619 0.479194 0.239597 0.970872i 0.422985π-0.422985\pi
0.239597 + 0.970872i 0.422985π0.422985\pi
744744 1.65300 0.0606018
745745 0 0
746746 15.5705 0.570077
747747 −8.22428 −0.300911
748748 11.8385 0.432858
749749 10.4289 0.381062
750750 0 0
751751 0.708627 0.0258582 0.0129291 0.999916i 0.495884π-0.495884\pi
0.0129291 + 0.999916i 0.495884π0.495884\pi
752752 90.3359 3.29421
753753 24.1847 0.881340
754754 −25.8195 −0.940292
755755 0 0
756756 4.42458 0.160921
757757 22.8545 0.830663 0.415331 0.909670i 0.363666π-0.363666\pi
0.415331 + 0.909670i 0.363666π0.363666\pi
758758 15.1622 0.550715
759759 −7.58896 −0.275462
760760 0 0
761761 −19.0731 −0.691399 −0.345700 0.938345i 0.612358π-0.612358\pi
−0.345700 + 0.938345i 0.612358π0.612358\pi
762762 47.9630 1.73751
763763 12.1216 0.438831
764764 14.2561 0.515767
765765 0 0
766766 −42.5819 −1.53855
767767 −22.1402 −0.799437
768768 30.2722 1.09236
769769 24.5762 0.886239 0.443120 0.896463i 0.353872π-0.353872\pi
0.443120 + 0.896463i 0.353872π0.353872\pi
770770 0 0
771771 21.4316 0.771840
772772 −33.0748 −1.19039
773773 −38.3443 −1.37915 −0.689575 0.724214i 0.742203π-0.742203\pi
−0.689575 + 0.724214i 0.742203π0.742203\pi
774774 11.9617 0.429956
775775 0 0
776776 −35.9183 −1.28939
777777 −0.972382 −0.0348840
778778 −16.8030 −0.602416
779779 −56.5789 −2.02715
780780 0 0
781781 37.3528 1.33659
782782 −7.18921 −0.257086
783783 3.59961 0.128639
784784 6.72778 0.240278
785785 0 0
786786 −21.8170 −0.778187
787787 45.5389 1.62329 0.811643 0.584154i 0.198574π-0.198574\pi
0.811643 + 0.584154i 0.198574π0.198574\pi
788788 −5.83001 −0.207686
789789 8.00460 0.284971
790790 0 0
791791 −6.13424 −0.218109
792792 −16.4431 −0.584280
793793 34.5520 1.22698
794794 27.8990 0.990097
795795 0 0
796796 −16.6269 −0.589324
797797 19.1640 0.678825 0.339412 0.940638i 0.389772π-0.389772\pi
0.339412 + 0.940638i 0.389772π0.389772\pi
798798 −15.6482 −0.553939
799799 13.4273 0.475024
800800 0 0
801801 9.68583 0.342232
802802 −29.9671 −1.05817
803803 −34.5931 −1.22077
804804 −0.445598 −0.0157150
805805 0 0
806806 1.92933 0.0679577
807807 −15.2324 −0.536205
808808 −23.1657 −0.814967
809809 −22.3419 −0.785500 −0.392750 0.919645i 0.628476π-0.628476\pi
−0.392750 + 0.919645i 0.628476π0.628476\pi
810810 0 0
811811 21.2903 0.747604 0.373802 0.927509i 0.378054π-0.378054\pi
0.373802 + 0.927509i 0.378054π0.378054\pi
812812 15.9268 0.558920
813813 −12.3967 −0.434772
814814 6.59452 0.231138
815815 0 0
816816 −6.72778 −0.235519
817817 −29.1349 −1.01930
818818 41.1224 1.43781
819819 2.82990 0.0988847
820820 0 0
821821 −9.71416 −0.339027 −0.169513 0.985528i 0.554220π-0.554220\pi
−0.169513 + 0.985528i 0.554220π0.554220\pi
822822 −23.3329 −0.813830
823823 10.8097 0.376803 0.188401 0.982092i 0.439669π-0.439669\pi
0.188401 + 0.982092i 0.439669π0.439669\pi
824824 −94.5832 −3.29496
825825 0 0
826826 19.8305 0.689991
827827 1.59735 0.0555454 0.0277727 0.999614i 0.491159π-0.491159\pi
0.0277727 + 0.999614i 0.491159π0.491159\pi
828828 12.5496 0.436130
829829 −13.4929 −0.468629 −0.234315 0.972161i 0.575285π-0.575285\pi
−0.234315 + 0.972161i 0.575285π0.575285\pi
830830 0 0
831831 22.2410 0.771531
832832 3.92301 0.136006
833833 1.00000 0.0346479
834834 −41.4401 −1.43495
835835 0 0
836836 73.0866 2.52775
837837 −0.268975 −0.00929715
838838 −25.4560 −0.879362
839839 2.17356 0.0750397 0.0375198 0.999296i 0.488054π-0.488054\pi
0.0375198 + 0.999296i 0.488054π0.488054\pi
840840 0 0
841841 −16.0428 −0.553201
842842 0.831147 0.0286432
843843 −30.3105 −1.04395
844844 17.4355 0.600154
845845 0 0
846846 −34.0339 −1.17011
847847 3.84107 0.131981
848848 −69.5102 −2.38699
849849 −7.53626 −0.258644
850850 0 0
851851 −2.75801 −0.0945433
852852 −61.7692 −2.11618
853853 −40.4215 −1.38400 −0.692002 0.721895i 0.743271π-0.743271\pi
−0.692002 + 0.721895i 0.743271π0.743271\pi
854854 −30.9475 −1.05900
855855 0 0
856856 64.0909 2.19058
857857 −31.2983 −1.06913 −0.534564 0.845128i 0.679524π-0.679524\pi
−0.534564 + 0.845128i 0.679524π0.679524\pi
858858 −19.1919 −0.655200
859859 −35.0656 −1.19642 −0.598211 0.801339i 0.704122π-0.704122\pi
−0.598211 + 0.801339i 0.704122π0.704122\pi
860860 0 0
861861 −9.16460 −0.312329
862862 −77.7613 −2.64856
863863 −42.9879 −1.46333 −0.731663 0.681666i 0.761256π-0.761256\pi
−0.731663 + 0.681666i 0.761256π0.761256\pi
864864 4.76167 0.161995
865865 0 0
866866 57.8945 1.96734
867867 −1.00000 −0.0339618
868868 −1.19010 −0.0403948
869869 −34.9915 −1.18701
870870 0 0
871871 −0.284998 −0.00965679
872872 74.4937 2.52267
873873 5.84462 0.197810
874874 −44.3836 −1.50130
875875 0 0
876876 57.2056 1.93280
877877 3.94069 0.133068 0.0665338 0.997784i 0.478806π-0.478806\pi
0.0665338 + 0.997784i 0.478806π0.478806\pi
878878 9.10233 0.307189
879879 −27.8572 −0.939600
880880 0 0
881881 −25.2993 −0.852355 −0.426177 0.904640i 0.640140π-0.640140\pi
−0.426177 + 0.904640i 0.640140π0.640140\pi
882882 −2.53468 −0.0853470
883883 −50.1801 −1.68869 −0.844347 0.535797i 0.820011π-0.820011\pi
−0.844347 + 0.535797i 0.820011π0.820011\pi
884884 −12.5211 −0.421131
885885 0 0
886886 28.0392 0.941996
887887 −46.5689 −1.56363 −0.781815 0.623510i 0.785706π-0.785706\pi
−0.781815 + 0.623510i 0.785706π0.785706\pi
888888 −5.97581 −0.200535
889889 −18.9227 −0.634648
890890 0 0
891891 2.67562 0.0896365
892892 −54.4427 −1.82288
893893 82.8953 2.77399
894894 14.3190 0.478897
895895 0 0
896896 −13.0371 −0.435538
897897 8.02656 0.267999
898898 −79.9609 −2.66833
899899 −0.968205 −0.0322915
900900 0 0
901901 −10.3318 −0.344203
902902 62.1527 2.06946
903903 −4.71924 −0.157046
904904 −37.6982 −1.25382
905905 0 0
906906 −2.48232 −0.0824695
907907 5.67017 0.188275 0.0941375 0.995559i 0.469991π-0.469991\pi
0.0941375 + 0.995559i 0.469991π0.469991\pi
908908 47.6935 1.58276
909909 3.76952 0.125027
910910 0 0
911911 14.3073 0.474022 0.237011 0.971507i 0.423832π-0.423832\pi
0.237011 + 0.971507i 0.423832π0.423832\pi
912912 −41.5349 −1.37536
913913 −22.0050 −0.728260
914914 44.9473 1.48672
915915 0 0
916916 −74.6874 −2.46774
917917 8.60741 0.284242
918918 2.53468 0.0836568
919919 7.39494 0.243936 0.121968 0.992534i 0.461079π-0.461079\pi
0.121968 + 0.992534i 0.461079π0.461079\pi
920920 0 0
921921 14.2241 0.468701
922922 107.305 3.53390
923923 −39.5067 −1.30038
924924 11.8385 0.389458
925925 0 0
926926 −33.3295 −1.09528
927927 15.3905 0.505492
928928 17.1401 0.562652
929929 −53.4925 −1.75503 −0.877516 0.479547i 0.840801π-0.840801\pi
−0.877516 + 0.479547i 0.840801π0.840801\pi
930930 0 0
931931 6.17364 0.202333
932932 −63.8369 −2.09105
933933 18.4183 0.602987
934934 −59.3890 −1.94327
935935 0 0
936936 17.3912 0.568451
937937 −15.9601 −0.521394 −0.260697 0.965421i 0.583952π-0.583952\pi
−0.260697 + 0.965421i 0.583952π0.583952\pi
938938 0.255266 0.00833474
939939 −9.24130 −0.301579
940940 0 0
941941 −29.6449 −0.966396 −0.483198 0.875511i 0.660525π-0.660525\pi
−0.483198 + 0.875511i 0.660525π0.660525\pi
942942 34.3068 1.11778
943943 −25.9939 −0.846479
944944 52.6360 1.71316
945945 0 0
946946 32.0050 1.04057
947947 34.8186 1.13145 0.565727 0.824593i 0.308596π-0.308596\pi
0.565727 + 0.824593i 0.308596π0.308596\pi
948948 57.8644 1.87935
949949 36.5879 1.18769
950950 0 0
951951 −10.1457 −0.328997
952952 6.14554 0.199178
953953 −44.3859 −1.43780 −0.718901 0.695113i 0.755354π-0.755354\pi
−0.718901 + 0.695113i 0.755354π0.755354\pi
954954 26.1878 0.847863
955955 0 0
956956 30.1407 0.974820
957957 9.63116 0.311331
958958 86.7189 2.80176
959959 9.20549 0.297261
960960 0 0
961961 −30.9277 −0.997666
962962 −6.97478 −0.224876
963963 −10.4289 −0.336065
964964 3.18565 0.102603
965965 0 0
966966 −7.18921 −0.231309
967967 13.5056 0.434312 0.217156 0.976137i 0.430322π-0.430322\pi
0.217156 + 0.976137i 0.430322π0.430322\pi
968968 23.6055 0.758708
969969 −6.17364 −0.198326
970970 0 0
971971 51.2881 1.64591 0.822956 0.568105i 0.192323π-0.192323\pi
0.822956 + 0.568105i 0.192323π0.192323\pi
972972 −4.42458 −0.141919
973973 16.3493 0.524133
974974 −58.5260 −1.87530
975975 0 0
976976 −82.1437 −2.62936
977977 −54.6359 −1.74796 −0.873979 0.485964i 0.838469π-0.838469\pi
−0.873979 + 0.485964i 0.838469π0.838469\pi
978978 −4.30400 −0.137627
979979 25.9156 0.828265
980980 0 0
981981 −12.1216 −0.387013
982982 34.9400 1.11498
983983 21.4549 0.684305 0.342152 0.939645i 0.388844π-0.388844\pi
0.342152 + 0.939645i 0.388844π0.388844\pi
984984 −56.3214 −1.79546
985985 0 0
986986 9.12383 0.290562
987987 13.4273 0.427396
988988 −77.3009 −2.45927
989989 −13.3854 −0.425630
990990 0 0
991991 −44.8117 −1.42349 −0.711745 0.702438i 0.752095π-0.752095\pi
−0.711745 + 0.702438i 0.752095π0.752095\pi
992992 −1.28077 −0.0406645
993993 −8.09315 −0.256828
994994 35.3852 1.12235
995995 0 0
996996 36.3890 1.15303
997997 −45.3790 −1.43717 −0.718584 0.695440i 0.755209π-0.755209\pi
−0.718584 + 0.695440i 0.755209π0.755209\pi
998998 90.3845 2.86107
999999 0.972382 0.0307648
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 8925.2.a.cu.1.2 14
5.2 odd 4 1785.2.g.g.1429.2 28
5.3 odd 4 1785.2.g.g.1429.27 yes 28
5.4 even 2 8925.2.a.cx.1.13 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1785.2.g.g.1429.2 28 5.2 odd 4
1785.2.g.g.1429.27 yes 28 5.3 odd 4
8925.2.a.cu.1.2 14 1.1 even 1 trivial
8925.2.a.cx.1.13 14 5.4 even 2