Properties

Label 1305.2.a.s.1.5
Level 13051305
Weight 22
Character 1305.1
Self dual yes
Analytic conductor 10.42010.420
Analytic rank 00
Dimension 77
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] = [1305,2,Mod(1,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, 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("1305.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1305=32529 1305 = 3^{2} \cdot 5 \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1305.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: 10.420477463810.4204774638
Analytic rank: 00
Dimension: 77
Coefficient field: Q[x]/(x7)\mathbb{Q}[x]/(x^{7} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x7x613x5+12x4+47x337x235x+18 x^{7} - x^{6} - 13x^{5} + 12x^{4} + 47x^{3} - 37x^{2} - 35x + 18 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 2 2
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 0.897436-0.897436 of defining polynomial
Character χ\chi == 1305.1

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) == q+0.897436q21.19461q41.00000q5+3.83036q72.86696q80.897436q102.82632q11+0.989088q13+3.43750q140.183696q161.01091q17+5.13268q19+1.19461q202.53645q22+7.78936q23+1.00000q25+0.887643q264.57577q28+1.00000q291.13268q31+5.56906q320.907229q343.83036q35+10.7648q37+4.60625q38+2.86696q40+2.58070q414.24141q43+3.37635q44+6.99045q46+0.252519q47+7.67162q49+0.897436q501.18157q52+5.70648q53+2.82632q5510.9815q56+0.897436q583.66071q5910.3820q611.01651q62+5.36527q640.989088q65+3.75939q67+1.20764q683.43750q706.26536q71+10.7545q73+9.66071q746.13154q7610.8258q77+10.7853q79+0.183696q80+2.31601q82+1.06004q83+1.01091q853.80639q86+8.10295q88+14.3024q89+3.78856q919.30523q92+0.226620q945.13268q95+13.8941q97+6.88479q98+O(q100)q+0.897436 q^{2} -1.19461 q^{4} -1.00000 q^{5} +3.83036 q^{7} -2.86696 q^{8} -0.897436 q^{10} -2.82632 q^{11} +0.989088 q^{13} +3.43750 q^{14} -0.183696 q^{16} -1.01091 q^{17} +5.13268 q^{19} +1.19461 q^{20} -2.53645 q^{22} +7.78936 q^{23} +1.00000 q^{25} +0.887643 q^{26} -4.57577 q^{28} +1.00000 q^{29} -1.13268 q^{31} +5.56906 q^{32} -0.907229 q^{34} -3.83036 q^{35} +10.7648 q^{37} +4.60625 q^{38} +2.86696 q^{40} +2.58070 q^{41} -4.24141 q^{43} +3.37635 q^{44} +6.99045 q^{46} +0.252519 q^{47} +7.67162 q^{49} +0.897436 q^{50} -1.18157 q^{52} +5.70648 q^{53} +2.82632 q^{55} -10.9815 q^{56} +0.897436 q^{58} -3.66071 q^{59} -10.3820 q^{61} -1.01651 q^{62} +5.36527 q^{64} -0.989088 q^{65} +3.75939 q^{67} +1.20764 q^{68} -3.43750 q^{70} -6.26536 q^{71} +10.7545 q^{73} +9.66071 q^{74} -6.13154 q^{76} -10.8258 q^{77} +10.7853 q^{79} +0.183696 q^{80} +2.31601 q^{82} +1.06004 q^{83} +1.01091 q^{85} -3.80639 q^{86} +8.10295 q^{88} +14.3024 q^{89} +3.78856 q^{91} -9.30523 q^{92} +0.226620 q^{94} -5.13268 q^{95} +13.8941 q^{97} +6.88479 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 7qq2+13q47q5+10q7+q10+3q11+6q13+9q14+21q168q17+10q1913q20+9q2211q23+7q253q26+25q28+7q29++20q98+O(q100) 7 q - q^{2} + 13 q^{4} - 7 q^{5} + 10 q^{7} + q^{10} + 3 q^{11} + 6 q^{13} + 9 q^{14} + 21 q^{16} - 8 q^{17} + 10 q^{19} - 13 q^{20} + 9 q^{22} - 11 q^{23} + 7 q^{25} - 3 q^{26} + 25 q^{28} + 7 q^{29}+ \cdots + 20 q^{98}+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 0.897436 0.634583 0.317292 0.948328i 0.397227π-0.397227\pi
0.317292 + 0.948328i 0.397227π0.397227\pi
33 0 0
44 −1.19461 −0.597304
55 −1.00000 −0.447214
66 0 0
77 3.83036 1.44774 0.723869 0.689937i 0.242362π-0.242362\pi
0.723869 + 0.689937i 0.242362π0.242362\pi
88 −2.86696 −1.01362
99 0 0
1010 −0.897436 −0.283794
1111 −2.82632 −0.852169 −0.426084 0.904683i 0.640107π-0.640107\pi
−0.426084 + 0.904683i 0.640107π0.640107\pi
1212 0 0
1313 0.989088 0.274324 0.137162 0.990549i 0.456202π-0.456202\pi
0.137162 + 0.990549i 0.456202π0.456202\pi
1414 3.43750 0.918711
1515 0 0
1616 −0.183696 −0.0459240
1717 −1.01091 −0.245182 −0.122591 0.992457i 0.539120π-0.539120\pi
−0.122591 + 0.992457i 0.539120π0.539120\pi
1818 0 0
1919 5.13268 1.17752 0.588759 0.808309i 0.299617π-0.299617\pi
0.588759 + 0.808309i 0.299617π0.299617\pi
2020 1.19461 0.267122
2121 0 0
2222 −2.53645 −0.540772
2323 7.78936 1.62419 0.812097 0.583523i 0.198326π-0.198326\pi
0.812097 + 0.583523i 0.198326π0.198326\pi
2424 0 0
2525 1.00000 0.200000
2626 0.887643 0.174081
2727 0 0
2828 −4.57577 −0.864740
2929 1.00000 0.185695
3030 0 0
3131 −1.13268 −0.203435 −0.101718 0.994813i 0.532434π-0.532434\pi
−0.101718 + 0.994813i 0.532434π0.532434\pi
3232 5.56906 0.984480
3333 0 0
3434 −0.907229 −0.155589
3535 −3.83036 −0.647448
3636 0 0
3737 10.7648 1.76972 0.884860 0.465857i 0.154254π-0.154254\pi
0.884860 + 0.465857i 0.154254π0.154254\pi
3838 4.60625 0.747233
3939 0 0
4040 2.86696 0.453306
4141 2.58070 0.403037 0.201519 0.979485i 0.435412π-0.435412\pi
0.201519 + 0.979485i 0.435412π0.435412\pi
4242 0 0
4343 −4.24141 −0.646809 −0.323404 0.946261i 0.604827π-0.604827\pi
−0.323404 + 0.946261i 0.604827π0.604827\pi
4444 3.37635 0.509004
4545 0 0
4646 6.99045 1.03069
4747 0.252519 0.0368337 0.0184168 0.999830i 0.494137π-0.494137\pi
0.0184168 + 0.999830i 0.494137π0.494137\pi
4848 0 0
4949 7.67162 1.09595
5050 0.897436 0.126917
5151 0 0
5252 −1.18157 −0.163855
5353 5.70648 0.783846 0.391923 0.919998i 0.371810π-0.371810\pi
0.391923 + 0.919998i 0.371810π0.371810\pi
5454 0 0
5555 2.82632 0.381101
5656 −10.9815 −1.46746
5757 0 0
5858 0.897436 0.117839
5959 −3.66071 −0.476584 −0.238292 0.971194i 0.576588π-0.576588\pi
−0.238292 + 0.971194i 0.576588π0.576588\pi
6060 0 0
6161 −10.3820 −1.32927 −0.664637 0.747166i 0.731414π-0.731414\pi
−0.664637 + 0.747166i 0.731414π0.731414\pi
6262 −1.01651 −0.129096
6363 0 0
6464 5.36527 0.670659
6565 −0.989088 −0.122681
6666 0 0
6767 3.75939 0.459283 0.229641 0.973275i 0.426245π-0.426245\pi
0.229641 + 0.973275i 0.426245π0.426245\pi
6868 1.20764 0.146448
6969 0 0
7070 −3.43750 −0.410860
7171 −6.26536 −0.743561 −0.371781 0.928321i 0.621253π-0.621253\pi
−0.371781 + 0.928321i 0.621253π0.621253\pi
7272 0 0
7373 10.7545 1.25872 0.629359 0.777115i 0.283318π-0.283318\pi
0.629359 + 0.777115i 0.283318π0.283318\pi
7474 9.66071 1.12303
7575 0 0
7676 −6.13154 −0.703336
7777 −10.8258 −1.23372
7878 0 0
7979 10.7853 1.21344 0.606722 0.794914i 0.292484π-0.292484\pi
0.606722 + 0.794914i 0.292484π0.292484\pi
8080 0.183696 0.0205378
8181 0 0
8282 2.31601 0.255761
8383 1.06004 0.116355 0.0581773 0.998306i 0.481471π-0.481471\pi
0.0581773 + 0.998306i 0.481471π0.481471\pi
8484 0 0
8585 1.01091 0.109649
8686 −3.80639 −0.410454
8787 0 0
8888 8.10295 0.863777
8989 14.3024 1.51606 0.758028 0.652222i 0.226163π-0.226163\pi
0.758028 + 0.652222i 0.226163π0.226163\pi
9090 0 0
9191 3.78856 0.397149
9292 −9.30523 −0.970137
9393 0 0
9494 0.226620 0.0233740
9595 −5.13268 −0.526602
9696 0 0
9797 13.8941 1.41073 0.705364 0.708845i 0.250784π-0.250784\pi
0.705364 + 0.708845i 0.250784π0.250784\pi
9898 6.88479 0.695469
9999 0 0
100100 −1.19461 −0.119461
101101 −14.4729 −1.44011 −0.720053 0.693919i 0.755883π-0.755883\pi
−0.720053 + 0.693919i 0.755883π0.755883\pi
102102 0 0
103103 8.70934 0.858157 0.429079 0.903267i 0.358838π-0.358838\pi
0.429079 + 0.903267i 0.358838π0.358838\pi
104104 −2.83567 −0.278061
105105 0 0
106106 5.12121 0.497415
107107 −1.89530 −0.183226 −0.0916129 0.995795i 0.529202π-0.529202\pi
−0.0916129 + 0.995795i 0.529202π0.529202\pi
108108 0 0
109109 6.62461 0.634522 0.317261 0.948338i 0.397237π-0.397237\pi
0.317261 + 0.948338i 0.397237π0.397237\pi
110110 2.53645 0.241841
111111 0 0
112112 −0.703621 −0.0664859
113113 1.00061 0.0941294 0.0470647 0.998892i 0.485013π-0.485013\pi
0.0470647 + 0.998892i 0.485013π0.485013\pi
114114 0 0
115115 −7.78936 −0.726361
116116 −1.19461 −0.110917
117117 0 0
118118 −3.28526 −0.302432
119119 −3.87215 −0.354960
120120 0 0
121121 −3.01190 −0.273809
122122 −9.31715 −0.843535
123123 0 0
124124 1.35311 0.121513
125125 −1.00000 −0.0894427
126126 0 0
127127 −9.89406 −0.877955 −0.438978 0.898498i 0.644659π-0.644659\pi
−0.438978 + 0.898498i 0.644659π0.644659\pi
128128 −6.32313 −0.558891
129129 0 0
130130 −0.887643 −0.0778515
131131 13.1169 1.14603 0.573013 0.819546i 0.305774π-0.305774\pi
0.573013 + 0.819546i 0.305774π0.305774\pi
132132 0 0
133133 19.6600 1.70474
134134 3.37381 0.291453
135135 0 0
136136 2.89824 0.248522
137137 0.0709655 0.00606299 0.00303149 0.999995i 0.499035π-0.499035\pi
0.00303149 + 0.999995i 0.499035π0.499035\pi
138138 0 0
139139 −12.2462 −1.03871 −0.519354 0.854559i 0.673827π-0.673827\pi
−0.519354 + 0.854559i 0.673827π0.673827\pi
140140 4.57577 0.386723
141141 0 0
142142 −5.62276 −0.471851
143143 −2.79548 −0.233770
144144 0 0
145145 −1.00000 −0.0830455
146146 9.65147 0.798761
147147 0 0
148148 −12.8597 −1.05706
149149 −7.32142 −0.599794 −0.299897 0.953972i 0.596952π-0.596952\pi
−0.299897 + 0.953972i 0.596952π0.596952\pi
150150 0 0
151151 −23.3800 −1.90264 −0.951318 0.308211i 0.900270π-0.900270\pi
−0.951318 + 0.308211i 0.900270π0.900270\pi
152152 −14.7152 −1.19356
153153 0 0
154154 −9.71549 −0.782896
155155 1.13268 0.0909789
156156 0 0
157157 −0.931394 −0.0743333 −0.0371667 0.999309i 0.511833π-0.511833\pi
−0.0371667 + 0.999309i 0.511833π0.511833\pi
158158 9.67914 0.770031
159159 0 0
160160 −5.56906 −0.440273
161161 29.8360 2.35141
162162 0 0
163163 −1.03087 −0.0807441 −0.0403721 0.999185i 0.512854π-0.512854\pi
−0.0403721 + 0.999185i 0.512854π0.512854\pi
164164 −3.08292 −0.240736
165165 0 0
166166 0.951319 0.0738366
167167 −22.4729 −1.73900 −0.869502 0.493930i 0.835560π-0.835560\pi
−0.869502 + 0.493930i 0.835560π0.835560\pi
168168 0 0
169169 −12.0217 −0.924747
170170 0.907229 0.0695813
171171 0 0
172172 5.06682 0.386341
173173 −21.2142 −1.61289 −0.806444 0.591310i 0.798611π-0.798611\pi
−0.806444 + 0.591310i 0.798611π0.798611\pi
174174 0 0
175175 3.83036 0.289548
176176 0.519184 0.0391350
177177 0 0
178178 12.8355 0.962064
179179 10.8003 0.807249 0.403625 0.914925i 0.367750π-0.367750\pi
0.403625 + 0.914925i 0.367750π0.367750\pi
180180 0 0
181181 −0.438278 −0.0325770 −0.0162885 0.999867i 0.505185π-0.505185\pi
−0.0162885 + 0.999867i 0.505185π0.505185\pi
182182 3.39999 0.252024
183183 0 0
184184 −22.3318 −1.64632
185185 −10.7648 −0.791443
186186 0 0
187187 2.85716 0.208937
188188 −0.301661 −0.0220009
189189 0 0
190190 −4.60625 −0.334173
191191 2.64477 0.191369 0.0956844 0.995412i 0.469496π-0.469496\pi
0.0956844 + 0.995412i 0.469496π0.469496\pi
192192 0 0
193193 −16.4494 −1.18406 −0.592028 0.805917i 0.701673π-0.701673\pi
−0.592028 + 0.805917i 0.701673π0.701673\pi
194194 12.4690 0.895224
195195 0 0
196196 −9.16458 −0.654613
197197 −22.1732 −1.57977 −0.789887 0.613253i 0.789861π-0.789861\pi
−0.789887 + 0.613253i 0.789861π0.789861\pi
198198 0 0
199199 11.4778 0.813638 0.406819 0.913509i 0.366638π-0.366638\pi
0.406819 + 0.913509i 0.366638π0.366638\pi
200200 −2.86696 −0.202724
201201 0 0
202202 −12.9885 −0.913867
203203 3.83036 0.268838
204204 0 0
205205 −2.58070 −0.180244
206206 7.81608 0.544572
207207 0 0
208208 −0.181691 −0.0125980
209209 −14.5066 −1.00344
210210 0 0
211211 10.2941 0.708673 0.354337 0.935118i 0.384707π-0.384707\pi
0.354337 + 0.935118i 0.384707π0.384707\pi
212212 −6.81701 −0.468194
213213 0 0
214214 −1.70091 −0.116272
215215 4.24141 0.289262
216216 0 0
217217 −4.33856 −0.294521
218218 5.94516 0.402657
219219 0 0
220220 −3.37635 −0.227633
221221 −0.999881 −0.0672593
222222 0 0
223223 −13.3163 −0.891724 −0.445862 0.895102i 0.647103π-0.647103\pi
−0.445862 + 0.895102i 0.647103π0.647103\pi
224224 21.3315 1.42527
225225 0 0
226226 0.897984 0.0597330
227227 −24.5678 −1.63062 −0.815312 0.579022i 0.803434π-0.803434\pi
−0.815312 + 0.579022i 0.803434π0.803434\pi
228228 0 0
229229 −25.5488 −1.68831 −0.844157 0.536096i 0.819898π-0.819898\pi
−0.844157 + 0.536096i 0.819898π0.819898\pi
230230 −6.99045 −0.460937
231231 0 0
232232 −2.86696 −0.188225
233233 −5.77745 −0.378493 −0.189247 0.981930i 0.560605π-0.560605\pi
−0.189247 + 0.981930i 0.560605π0.560605\pi
234234 0 0
235235 −0.252519 −0.0164725
236236 4.37311 0.284666
237237 0 0
238238 −3.47501 −0.225251
239239 −4.16575 −0.269460 −0.134730 0.990882i 0.543017π-0.543017\pi
−0.134730 + 0.990882i 0.543017π0.543017\pi
240240 0 0
241241 11.3115 0.728637 0.364319 0.931274i 0.381302π-0.381302\pi
0.364319 + 0.931274i 0.381302π0.381302\pi
242242 −2.70298 −0.173754
243243 0 0
244244 12.4024 0.793981
245245 −7.67162 −0.490122
246246 0 0
247247 5.07667 0.323021
248248 3.24734 0.206206
249249 0 0
250250 −0.897436 −0.0567589
251251 6.70959 0.423505 0.211753 0.977323i 0.432083π-0.432083\pi
0.211753 + 0.977323i 0.432083π0.432083\pi
252252 0 0
253253 −22.0152 −1.38409
254254 −8.87929 −0.557136
255255 0 0
256256 −16.4051 −1.02532
257257 20.0804 1.25258 0.626290 0.779590i 0.284573π-0.284573\pi
0.626290 + 0.779590i 0.284573π0.284573\pi
258258 0 0
259259 41.2330 2.56209
260260 1.18157 0.0732780
261261 0 0
262262 11.7716 0.727249
263263 25.4859 1.57153 0.785765 0.618526i 0.212270π-0.212270\pi
0.785765 + 0.618526i 0.212270π0.212270\pi
264264 0 0
265265 −5.70648 −0.350546
266266 17.6436 1.08180
267267 0 0
268268 −4.49100 −0.274331
269269 26.1794 1.59618 0.798092 0.602535i 0.205843π-0.205843\pi
0.798092 + 0.602535i 0.205843π0.205843\pi
270270 0 0
271271 3.60583 0.219039 0.109519 0.993985i 0.465069π-0.465069\pi
0.109519 + 0.993985i 0.465069π0.465069\pi
272272 0.185700 0.0112597
273273 0 0
274274 0.0636870 0.00384747
275275 −2.82632 −0.170434
276276 0 0
277277 15.4340 0.927336 0.463668 0.886009i 0.346533π-0.346533\pi
0.463668 + 0.886009i 0.346533π0.346533\pi
278278 −10.9902 −0.659147
279279 0 0
280280 10.9815 0.656268
281281 −9.13957 −0.545221 −0.272611 0.962124i 0.587887π-0.587887\pi
−0.272611 + 0.962124i 0.587887π0.587887\pi
282282 0 0
283283 13.9174 0.827302 0.413651 0.910436i 0.364253π-0.364253\pi
0.413651 + 0.910436i 0.364253π0.364253\pi
284284 7.48464 0.444132
285285 0 0
286286 −2.50877 −0.148347
287287 9.88499 0.583493
288288 0 0
289289 −15.9781 −0.939886
290290 −0.897436 −0.0526993
291291 0 0
292292 −12.8474 −0.751837
293293 20.2400 1.18244 0.591218 0.806512i 0.298647π-0.298647\pi
0.591218 + 0.806512i 0.298647π0.298647\pi
294294 0 0
295295 3.66071 0.213135
296296 −30.8622 −1.79383
297297 0 0
298298 −6.57051 −0.380619
299299 7.70436 0.445555
300300 0 0
301301 −16.2461 −0.936410
302302 −20.9820 −1.20738
303303 0 0
304304 −0.942852 −0.0540763
305305 10.3820 0.594470
306306 0 0
307307 −2.57263 −0.146828 −0.0734140 0.997302i 0.523389π-0.523389\pi
−0.0734140 + 0.997302i 0.523389π0.523389\pi
308308 12.9326 0.736904
309309 0 0
310310 1.01651 0.0577337
311311 19.0082 1.07785 0.538927 0.842352i 0.318830π-0.318830\pi
0.538927 + 0.842352i 0.318830π0.318830\pi
312312 0 0
313313 0.555016 0.0313713 0.0156857 0.999877i 0.495007π-0.495007\pi
0.0156857 + 0.999877i 0.495007π0.495007\pi
314314 −0.835867 −0.0471707
315315 0 0
316316 −12.8842 −0.724795
317317 28.5513 1.60360 0.801801 0.597592i 0.203876π-0.203876\pi
0.801801 + 0.597592i 0.203876π0.203876\pi
318318 0 0
319319 −2.82632 −0.158244
320320 −5.36527 −0.299928
321321 0 0
322322 26.7759 1.49216
323323 −5.18869 −0.288706
324324 0 0
325325 0.989088 0.0548647
326326 −0.925142 −0.0512389
327327 0 0
328328 −7.39875 −0.408528
329329 0.967237 0.0533255
330330 0 0
331331 3.88679 0.213637 0.106819 0.994279i 0.465934π-0.465934\pi
0.106819 + 0.994279i 0.465934π0.465934\pi
332332 −1.26633 −0.0694990
333333 0 0
334334 −20.1680 −1.10354
335335 −3.75939 −0.205397
336336 0 0
337337 7.48393 0.407676 0.203838 0.979005i 0.434658π-0.434658\pi
0.203838 + 0.979005i 0.434658π0.434658\pi
338338 −10.7887 −0.586829
339339 0 0
340340 −1.20764 −0.0654937
341341 3.20132 0.173361
342342 0 0
343343 2.57255 0.138905
344344 12.1599 0.655620
345345 0 0
346346 −19.0384 −1.02351
347347 −34.8424 −1.87044 −0.935220 0.354068i 0.884798π-0.884798\pi
−0.935220 + 0.354068i 0.884798π0.884798\pi
348348 0 0
349349 16.1457 0.864257 0.432128 0.901812i 0.357763π-0.357763\pi
0.432128 + 0.901812i 0.357763π0.357763\pi
350350 3.43750 0.183742
351351 0 0
352352 −15.7400 −0.838943
353353 −2.02732 −0.107903 −0.0539516 0.998544i 0.517182π-0.517182\pi
−0.0539516 + 0.998544i 0.517182π0.517182\pi
354354 0 0
355355 6.26536 0.332531
356356 −17.0858 −0.905546
357357 0 0
358358 9.69254 0.512267
359359 9.77827 0.516077 0.258039 0.966135i 0.416924π-0.416924\pi
0.258039 + 0.966135i 0.416924π0.416924\pi
360360 0 0
361361 7.34439 0.386547
362362 −0.393327 −0.0206728
363363 0 0
364364 −4.52584 −0.237219
365365 −10.7545 −0.562915
366366 0 0
367367 9.26435 0.483595 0.241797 0.970327i 0.422263π-0.422263\pi
0.241797 + 0.970327i 0.422263π0.422263\pi
368368 −1.43087 −0.0745894
369369 0 0
370370 −9.66071 −0.502236
371371 21.8579 1.13480
372372 0 0
373373 −19.3544 −1.00213 −0.501067 0.865408i 0.667059π-0.667059\pi
−0.501067 + 0.865408i 0.667059π0.667059\pi
374374 2.56412 0.132588
375375 0 0
376376 −0.723961 −0.0373354
377377 0.989088 0.0509406
378378 0 0
379379 15.8048 0.811838 0.405919 0.913909i 0.366952π-0.366952\pi
0.405919 + 0.913909i 0.366952π0.366952\pi
380380 6.13154 0.314541
381381 0 0
382382 2.37351 0.121439
383383 2.60067 0.132888 0.0664440 0.997790i 0.478835π-0.478835\pi
0.0664440 + 0.997790i 0.478835π0.478835\pi
384384 0 0
385385 10.8258 0.551735
386386 −14.7623 −0.751383
387387 0 0
388388 −16.5979 −0.842633
389389 −13.4068 −0.679750 −0.339875 0.940471i 0.610385π-0.610385\pi
−0.339875 + 0.940471i 0.610385π0.610385\pi
390390 0 0
391391 −7.87436 −0.398223
392392 −21.9942 −1.11088
393393 0 0
394394 −19.8990 −1.00250
395395 −10.7853 −0.542669
396396 0 0
397397 −33.8760 −1.70019 −0.850093 0.526633i 0.823454π-0.823454\pi
−0.850093 + 0.526633i 0.823454π0.823454\pi
398398 10.3006 0.516321
399399 0 0
400400 −0.183696 −0.00918479
401401 25.8578 1.29128 0.645639 0.763643i 0.276591π-0.276591\pi
0.645639 + 0.763643i 0.276591π0.276591\pi
402402 0 0
403403 −1.12032 −0.0558070
404404 17.2894 0.860181
405405 0 0
406406 3.43750 0.170600
407407 −30.4248 −1.50810
408408 0 0
409409 −12.3900 −0.612646 −0.306323 0.951928i 0.599099π-0.599099\pi
−0.306323 + 0.951928i 0.599099π0.599099\pi
410410 −2.31601 −0.114380
411411 0 0
412412 −10.4043 −0.512581
413413 −14.0218 −0.689969
414414 0 0
415415 −1.06004 −0.0520353
416416 5.50829 0.270066
417417 0 0
418418 −13.0188 −0.636768
419419 32.4545 1.58551 0.792753 0.609543i 0.208647π-0.208647\pi
0.792753 + 0.609543i 0.208647π0.208647\pi
420420 0 0
421421 13.2642 0.646458 0.323229 0.946321i 0.395232π-0.395232\pi
0.323229 + 0.946321i 0.395232π0.395232\pi
422422 9.23828 0.449712
423423 0 0
424424 −16.3602 −0.794524
425425 −1.01091 −0.0490364
426426 0 0
427427 −39.7666 −1.92444
428428 2.26414 0.109441
429429 0 0
430430 3.80639 0.183561
431431 15.5050 0.746849 0.373425 0.927661i 0.378183π-0.378183\pi
0.373425 + 0.927661i 0.378183π0.378183\pi
432432 0 0
433433 1.39425 0.0670034 0.0335017 0.999439i 0.489334π-0.489334\pi
0.0335017 + 0.999439i 0.489334π0.489334\pi
434434 −3.89358 −0.186898
435435 0 0
436436 −7.91381 −0.379003
437437 39.9803 1.91252
438438 0 0
439439 20.2277 0.965416 0.482708 0.875781i 0.339653π-0.339653\pi
0.482708 + 0.875781i 0.339653π0.339653\pi
440440 −8.10295 −0.386293
441441 0 0
442442 −0.897330 −0.0426816
443443 −15.1065 −0.717731 −0.358865 0.933389i 0.616836π-0.616836\pi
−0.358865 + 0.933389i 0.616836π0.616836\pi
444444 0 0
445445 −14.3024 −0.678001
446446 −11.9505 −0.565873
447447 0 0
448448 20.5509 0.970938
449449 38.3771 1.81113 0.905564 0.424210i 0.139448π-0.139448\pi
0.905564 + 0.424210i 0.139448π0.139448\pi
450450 0 0
451451 −7.29389 −0.343456
452452 −1.19534 −0.0562239
453453 0 0
454454 −22.0481 −1.03477
455455 −3.78856 −0.177610
456456 0 0
457457 −22.2230 −1.03955 −0.519775 0.854303i 0.673984π-0.673984\pi
−0.519775 + 0.854303i 0.673984π0.673984\pi
458458 −22.9284 −1.07138
459459 0 0
460460 9.30523 0.433858
461461 −5.81739 −0.270943 −0.135472 0.990781i 0.543255π-0.543255\pi
−0.135472 + 0.990781i 0.543255π0.543255\pi
462462 0 0
463463 26.7453 1.24296 0.621479 0.783431i 0.286532π-0.286532\pi
0.621479 + 0.783431i 0.286532π0.286532\pi
464464 −0.183696 −0.00852787
465465 0 0
466466 −5.18489 −0.240185
467467 13.7869 0.637980 0.318990 0.947758i 0.396656π-0.396656\pi
0.318990 + 0.947758i 0.396656π0.396656\pi
468468 0 0
469469 14.3998 0.664921
470470 −0.226620 −0.0104532
471471 0 0
472472 10.4951 0.483076
473473 11.9876 0.551190
474474 0 0
475475 5.13268 0.235503
476476 4.62570 0.212019
477477 0 0
478478 −3.73849 −0.170995
479479 −15.6990 −0.717304 −0.358652 0.933471i 0.616764π-0.616764\pi
−0.358652 + 0.933471i 0.616764π0.616764\pi
480480 0 0
481481 10.6473 0.485476
482482 10.1513 0.462381
483483 0 0
484484 3.59803 0.163547
485485 −13.8941 −0.630897
486486 0 0
487487 30.0638 1.36232 0.681160 0.732135i 0.261476π-0.261476\pi
0.681160 + 0.732135i 0.261476π0.261476\pi
488488 29.7646 1.34738
489489 0 0
490490 −6.88479 −0.311023
491491 −35.3955 −1.59738 −0.798689 0.601744i 0.794473π-0.794473\pi
−0.798689 + 0.601744i 0.794473π0.794473\pi
492492 0 0
493493 −1.01091 −0.0455292
494494 4.55599 0.204984
495495 0 0
496496 0.208068 0.00934254
497497 −23.9985 −1.07648
498498 0 0
499499 8.84462 0.395940 0.197970 0.980208i 0.436565π-0.436565\pi
0.197970 + 0.980208i 0.436565π0.436565\pi
500500 1.19461 0.0534245
501501 0 0
502502 6.02143 0.268749
503503 −24.2714 −1.08221 −0.541104 0.840956i 0.681993π-0.681993\pi
−0.541104 + 0.840956i 0.681993π0.681993\pi
504504 0 0
505505 14.4729 0.644035
506506 −19.7573 −0.878318
507507 0 0
508508 11.8195 0.524406
509509 −7.45863 −0.330598 −0.165299 0.986243i 0.552859π-0.552859\pi
−0.165299 + 0.986243i 0.552859π0.552859\pi
510510 0 0
511511 41.1935 1.82229
512512 −2.07631 −0.0917608
513513 0 0
514514 18.0209 0.794866
515515 −8.70934 −0.383780
516516 0 0
517517 −0.713700 −0.0313885
518518 37.0040 1.62586
519519 0 0
520520 2.83567 0.124352
521521 −30.8783 −1.35280 −0.676401 0.736533i 0.736461π-0.736461\pi
−0.676401 + 0.736533i 0.736461π0.736461\pi
522522 0 0
523523 −39.1262 −1.71087 −0.855435 0.517910i 0.826710π-0.826710\pi
−0.855435 + 0.517910i 0.826710π0.826710\pi
524524 −15.6695 −0.684526
525525 0 0
526526 22.8720 0.997266
527527 1.14504 0.0498786
528528 0 0
529529 37.6741 1.63800
530530 −5.12121 −0.222451
531531 0 0
532532 −23.4860 −1.01825
533533 2.55254 0.110563
534534 0 0
535535 1.89530 0.0819410
536536 −10.7780 −0.465539
537537 0 0
538538 23.4943 1.01291
539539 −21.6825 −0.933931
540540 0 0
541541 −27.9986 −1.20375 −0.601877 0.798589i 0.705580π-0.705580\pi
−0.601877 + 0.798589i 0.705580π0.705580\pi
542542 3.23601 0.138998
543543 0 0
544544 −5.62983 −0.241377
545545 −6.62461 −0.283767
546546 0 0
547547 7.05192 0.301518 0.150759 0.988571i 0.451828π-0.451828\pi
0.150759 + 0.988571i 0.451828π0.451828\pi
548548 −0.0847759 −0.00362145
549549 0 0
550550 −2.53645 −0.108154
551551 5.13268 0.218659
552552 0 0
553553 41.3116 1.75675
554554 13.8510 0.588472
555555 0 0
556556 14.6294 0.620424
557557 38.4865 1.63073 0.815363 0.578949i 0.196537π-0.196537\pi
0.815363 + 0.578949i 0.196537π0.196537\pi
558558 0 0
559559 −4.19513 −0.177435
560560 0.703621 0.0297334
561561 0 0
562562 −8.20218 −0.345988
563563 −45.6728 −1.92488 −0.962439 0.271498i 0.912481π-0.912481\pi
−0.962439 + 0.271498i 0.912481π0.912481\pi
564564 0 0
565565 −1.00061 −0.0420960
566566 12.4900 0.524992
567567 0 0
568568 17.9625 0.753690
569569 44.9498 1.88439 0.942196 0.335062i 0.108757π-0.108757\pi
0.942196 + 0.335062i 0.108757π0.108757\pi
570570 0 0
571571 −1.65737 −0.0693587 −0.0346793 0.999398i 0.511041π-0.511041\pi
−0.0346793 + 0.999398i 0.511041π0.511041\pi
572572 3.33951 0.139632
573573 0 0
574574 8.87115 0.370275
575575 7.78936 0.324839
576576 0 0
577577 −9.23893 −0.384622 −0.192311 0.981334i 0.561598π-0.561598\pi
−0.192311 + 0.981334i 0.561598π0.561598\pi
578578 −14.3393 −0.596436
579579 0 0
580580 1.19461 0.0496034
581581 4.06033 0.168451
582582 0 0
583583 −16.1284 −0.667969
584584 −30.8326 −1.27586
585585 0 0
586586 18.1641 0.750354
587587 10.6148 0.438120 0.219060 0.975711i 0.429701π-0.429701\pi
0.219060 + 0.975711i 0.429701π0.429701\pi
588588 0 0
589589 −5.81367 −0.239548
590590 3.28526 0.135252
591591 0 0
592592 −1.97745 −0.0812726
593593 −39.7432 −1.63206 −0.816029 0.578011i 0.803829π-0.803829\pi
−0.816029 + 0.578011i 0.803829π0.803829\pi
594594 0 0
595595 3.87215 0.158743
596596 8.74623 0.358259
597597 0 0
598598 6.91417 0.282742
599599 7.31224 0.298770 0.149385 0.988779i 0.452271π-0.452271\pi
0.149385 + 0.988779i 0.452271π0.452271\pi
600600 0 0
601601 −21.4162 −0.873585 −0.436793 0.899562i 0.643886π-0.643886\pi
−0.436793 + 0.899562i 0.643886π0.643886\pi
602602 −14.5798 −0.594230
603603 0 0
604604 27.9299 1.13645
605605 3.01190 0.122451
606606 0 0
607607 19.3315 0.784639 0.392320 0.919829i 0.371673π-0.371673\pi
0.392320 + 0.919829i 0.371673π0.371673\pi
608608 28.5842 1.15924
609609 0 0
610610 9.31715 0.377240
611611 0.249763 0.0101043
612612 0 0
613613 −27.5848 −1.11414 −0.557069 0.830466i 0.688074π-0.688074\pi
−0.557069 + 0.830466i 0.688074π0.688074\pi
614614 −2.30878 −0.0931746
615615 0 0
616616 31.0372 1.25052
617617 9.03573 0.363765 0.181882 0.983320i 0.441781π-0.441781\pi
0.181882 + 0.983320i 0.441781π0.441781\pi
618618 0 0
619619 −41.7871 −1.67956 −0.839782 0.542923i 0.817318π-0.817318\pi
−0.839782 + 0.542923i 0.817318π0.817318\pi
620620 −1.35311 −0.0543421
621621 0 0
622622 17.0586 0.683989
623623 54.7835 2.19485
624624 0 0
625625 1.00000 0.0400000
626626 0.498091 0.0199077
627627 0 0
628628 1.11265 0.0443996
629629 −10.8823 −0.433904
630630 0 0
631631 44.6303 1.77670 0.888351 0.459164i 0.151851π-0.151851\pi
0.888351 + 0.459164i 0.151851π0.151851\pi
632632 −30.9211 −1.22997
633633 0 0
634634 25.6230 1.01762
635635 9.89406 0.392634
636636 0 0
637637 7.58791 0.300644
638638 −2.53645 −0.100419
639639 0 0
640640 6.32313 0.249944
641641 −38.4320 −1.51797 −0.758986 0.651107i 0.774305π-0.774305\pi
−0.758986 + 0.651107i 0.774305π0.774305\pi
642642 0 0
643643 −3.33226 −0.131411 −0.0657057 0.997839i 0.520930π-0.520930\pi
−0.0657057 + 0.997839i 0.520930π0.520930\pi
644644 −35.6423 −1.40450
645645 0 0
646646 −4.65652 −0.183208
647647 −25.0180 −0.983559 −0.491779 0.870720i 0.663653π-0.663653\pi
−0.491779 + 0.870720i 0.663653π0.663653\pi
648648 0 0
649649 10.3464 0.406130
650650 0.887643 0.0348162
651651 0 0
652652 1.23149 0.0482288
653653 −24.9697 −0.977142 −0.488571 0.872524i 0.662482π-0.662482\pi
−0.488571 + 0.872524i 0.662482π0.662482\pi
654654 0 0
655655 −13.1169 −0.512519
656656 −0.474064 −0.0185091
657657 0 0
658658 0.868034 0.0338395
659659 37.4164 1.45754 0.728769 0.684760i 0.240093π-0.240093\pi
0.728769 + 0.684760i 0.240093π0.240093\pi
660660 0 0
661661 −39.5042 −1.53653 −0.768267 0.640130i 0.778881π-0.778881\pi
−0.768267 + 0.640130i 0.778881π0.778881\pi
662662 3.48814 0.135571
663663 0 0
664664 −3.03909 −0.117940
665665 −19.6600 −0.762381
666666 0 0
667667 7.78936 0.301605
668668 26.8463 1.03871
669669 0 0
670670 −3.37381 −0.130342
671671 29.3428 1.13277
672672 0 0
673673 −49.7546 −1.91790 −0.958950 0.283576i 0.908479π-0.908479\pi
−0.958950 + 0.283576i 0.908479π0.908479\pi
674674 6.71635 0.258704
675675 0 0
676676 14.3612 0.552355
677677 −2.62339 −0.100825 −0.0504126 0.998728i 0.516054π-0.516054\pi
−0.0504126 + 0.998728i 0.516054π0.516054\pi
678678 0 0
679679 53.2192 2.04236
680680 −2.89824 −0.111142
681681 0 0
682682 2.87298 0.110012
683683 18.9784 0.726188 0.363094 0.931752i 0.381720π-0.381720\pi
0.363094 + 0.931752i 0.381720π0.381720\pi
684684 0 0
685685 −0.0709655 −0.00271145
686686 2.30870 0.0881467
687687 0 0
688688 0.779129 0.0297040
689689 5.64421 0.215027
690690 0 0
691691 33.6342 1.27951 0.639753 0.768580i 0.279037π-0.279037\pi
0.639753 + 0.768580i 0.279037π0.279037\pi
692692 25.3427 0.963385
693693 0 0
694694 −31.2689 −1.18695
695695 12.2462 0.464524
696696 0 0
697697 −2.60886 −0.0988176
698698 14.4897 0.548443
699699 0 0
700700 −4.57577 −0.172948
701701 29.6166 1.11861 0.559303 0.828964i 0.311069π-0.311069\pi
0.559303 + 0.828964i 0.311069π0.311069\pi
702702 0 0
703703 55.2522 2.08388
704704 −15.1640 −0.571514
705705 0 0
706706 −1.81939 −0.0684736
707707 −55.4363 −2.08490
708708 0 0
709709 −35.4031 −1.32959 −0.664795 0.747026i 0.731481π-0.731481\pi
−0.664795 + 0.747026i 0.731481π0.731481\pi
710710 5.62276 0.211018
711711 0 0
712712 −41.0045 −1.53671
713713 −8.82284 −0.330418
714714 0 0
715715 2.79548 0.104545
716716 −12.9021 −0.482173
717717 0 0
718718 8.77538 0.327494
719719 −7.78651 −0.290388 −0.145194 0.989403i 0.546381π-0.546381\pi
−0.145194 + 0.989403i 0.546381π0.546381\pi
720720 0 0
721721 33.3599 1.24239
722722 6.59112 0.245296
723723 0 0
724724 0.523571 0.0194584
725725 1.00000 0.0371391
726726 0 0
727727 −7.78963 −0.288901 −0.144451 0.989512i 0.546142π-0.546142\pi
−0.144451 + 0.989512i 0.546142π0.546142\pi
728728 −10.8616 −0.402559
729729 0 0
730730 −9.65147 −0.357217
731731 4.28769 0.158586
732732 0 0
733733 −0.518655 −0.0191570 −0.00957848 0.999954i 0.503049π-0.503049\pi
−0.00957848 + 0.999954i 0.503049π0.503049\pi
734734 8.31416 0.306881
735735 0 0
736736 43.3794 1.59899
737737 −10.6253 −0.391386
738738 0 0
739739 30.7195 1.13003 0.565017 0.825079i 0.308870π-0.308870\pi
0.565017 + 0.825079i 0.308870π0.308870\pi
740740 12.8597 0.472732
741741 0 0
742742 19.6160 0.720127
743743 −21.7734 −0.798790 −0.399395 0.916779i 0.630780π-0.630780\pi
−0.399395 + 0.916779i 0.630780π0.630780\pi
744744 0 0
745745 7.32142 0.268236
746746 −17.3694 −0.635938
747747 0 0
748748 −3.41319 −0.124799
749749 −7.25968 −0.265263
750750 0 0
751751 24.9369 0.909961 0.454981 0.890501i 0.349646π-0.349646\pi
0.454981 + 0.890501i 0.349646π0.349646\pi
752752 −0.0463867 −0.00169155
753753 0 0
754754 0.887643 0.0323261
755755 23.3800 0.850885
756756 0 0
757757 1.27972 0.0465123 0.0232561 0.999730i 0.492597π-0.492597\pi
0.0232561 + 0.999730i 0.492597π0.492597\pi
758758 14.1838 0.515179
759759 0 0
760760 14.7152 0.533775
761761 1.95635 0.0709177 0.0354588 0.999371i 0.488711π-0.488711\pi
0.0354588 + 0.999371i 0.488711π0.488711\pi
762762 0 0
763763 25.3746 0.918622
764764 −3.15946 −0.114305
765765 0 0
766766 2.33394 0.0843286
767767 −3.62077 −0.130738
768768 0 0
769769 −22.1931 −0.800302 −0.400151 0.916449i 0.631042π-0.631042\pi
−0.400151 + 0.916449i 0.631042π0.631042\pi
770770 9.71549 0.350122
771771 0 0
772772 19.6506 0.707242
773773 15.6896 0.564317 0.282158 0.959368i 0.408950π-0.408950\pi
0.282158 + 0.959368i 0.408950π0.408950\pi
774774 0 0
775775 −1.13268 −0.0406870
776776 −39.8337 −1.42995
777777 0 0
778778 −12.0317 −0.431358
779779 13.2459 0.474583
780780 0 0
781781 17.7079 0.633639
782782 −7.06673 −0.252706
783783 0 0
784784 −1.40925 −0.0503302
785785 0.931394 0.0332429
786786 0 0
787787 −8.82023 −0.314407 −0.157204 0.987566i 0.550248π-0.550248\pi
−0.157204 + 0.987566i 0.550248π0.550248\pi
788788 26.4882 0.943605
789789 0 0
790790 −9.67914 −0.344368
791791 3.83269 0.136275
792792 0 0
793793 −10.2687 −0.364651
794794 −30.4015 −1.07891
795795 0 0
796796 −13.7114 −0.485989
797797 14.5755 0.516290 0.258145 0.966106i 0.416889π-0.416889\pi
0.258145 + 0.966106i 0.416889π0.416889\pi
798798 0 0
799799 −0.255274 −0.00903096
800800 5.56906 0.196896
801801 0 0
802802 23.2058 0.819424
803803 −30.3957 −1.07264
804804 0 0
805805 −29.8360 −1.05158
806806 −1.00541 −0.0354142
807807 0 0
808808 41.4932 1.45972
809809 10.4702 0.368111 0.184056 0.982916i 0.441077π-0.441077\pi
0.184056 + 0.982916i 0.441077π0.441077\pi
810810 0 0
811811 −9.74921 −0.342341 −0.171171 0.985241i 0.554755π-0.554755\pi
−0.171171 + 0.985241i 0.554755π0.554755\pi
812812 −4.57577 −0.160578
813813 0 0
814814 −27.3043 −0.957015
815815 1.03087 0.0361099
816816 0 0
817817 −21.7698 −0.761628
818818 −11.1192 −0.388775
819819 0 0
820820 3.08292 0.107660
821821 −40.9219 −1.42819 −0.714093 0.700051i 0.753160π-0.753160\pi
−0.714093 + 0.700051i 0.753160π0.753160\pi
822822 0 0
823823 −4.87322 −0.169870 −0.0849348 0.996387i 0.527068π-0.527068\pi
−0.0849348 + 0.996387i 0.527068π0.527068\pi
824824 −24.9693 −0.869847
825825 0 0
826826 −12.5837 −0.437843
827827 −15.6198 −0.543153 −0.271577 0.962417i 0.587545π-0.587545\pi
−0.271577 + 0.962417i 0.587545π0.587545\pi
828828 0 0
829829 −51.5007 −1.78869 −0.894346 0.447375i 0.852359π-0.852359\pi
−0.894346 + 0.447375i 0.852359π0.852359\pi
830830 −0.951319 −0.0330207
831831 0 0
832832 5.30672 0.183977
833833 −7.75534 −0.268706
834834 0 0
835835 22.4729 0.777706
836836 17.3297 0.599361
837837 0 0
838838 29.1258 1.00614
839839 −38.1841 −1.31826 −0.659130 0.752029i 0.729075π-0.729075\pi
−0.659130 + 0.752029i 0.729075π0.729075\pi
840840 0 0
841841 1.00000 0.0344828
842842 11.9038 0.410232
843843 0 0
844844 −12.2974 −0.423293
845845 12.0217 0.413559
846846 0 0
847847 −11.5366 −0.396403
848848 −1.04826 −0.0359973
849849 0 0
850850 −0.907229 −0.0311177
851851 83.8508 2.87437
852852 0 0
853853 −38.0575 −1.30306 −0.651531 0.758622i 0.725873π-0.725873\pi
−0.651531 + 0.758622i 0.725873π0.725873\pi
854854 −35.6880 −1.22122
855855 0 0
856856 5.43375 0.185722
857857 −21.8229 −0.745455 −0.372728 0.927941i 0.621577π-0.621577\pi
−0.372728 + 0.927941i 0.621577π0.621577\pi
858858 0 0
859859 −55.1041 −1.88013 −0.940065 0.340996i 0.889236π-0.889236\pi
−0.940065 + 0.340996i 0.889236π0.889236\pi
860860 −5.06682 −0.172777
861861 0 0
862862 13.9147 0.473938
863863 10.5055 0.357612 0.178806 0.983884i 0.442777π-0.442777\pi
0.178806 + 0.983884i 0.442777π0.442777\pi
864864 0 0
865865 21.2142 0.721306
866866 1.25125 0.0425192
867867 0 0
868868 5.18288 0.175918
869869 −30.4828 −1.03406
870870 0 0
871871 3.71837 0.125992
872872 −18.9925 −0.643166
873873 0 0
874874 35.8797 1.21365
875875 −3.83036 −0.129490
876876 0 0
877877 −12.0379 −0.406492 −0.203246 0.979128i 0.565149π-0.565149\pi
−0.203246 + 0.979128i 0.565149π0.565149\pi
878878 18.1531 0.612637
879879 0 0
880880 −0.519184 −0.0175017
881881 −40.8416 −1.37599 −0.687994 0.725716i 0.741509π-0.741509\pi
−0.687994 + 0.725716i 0.741509π0.741509\pi
882882 0 0
883883 41.6187 1.40058 0.700290 0.713858i 0.253054π-0.253054\pi
0.700290 + 0.713858i 0.253054π0.253054\pi
884884 1.19447 0.0401742
885885 0 0
886886 −13.5571 −0.455460
887887 17.0891 0.573797 0.286898 0.957961i 0.407376π-0.407376\pi
0.286898 + 0.957961i 0.407376π0.407376\pi
888888 0 0
889889 −37.8978 −1.27105
890890 −12.8355 −0.430248
891891 0 0
892892 15.9077 0.532630
893893 1.29610 0.0433723
894894 0 0
895895 −10.8003 −0.361013
896896 −24.2198 −0.809128
897897 0 0
898898 34.4410 1.14931
899899 −1.13268 −0.0377769
900900 0 0
901901 −5.76875 −0.192185
902902 −6.54580 −0.217951
903903 0 0
904904 −2.86871 −0.0954117
905905 0.438278 0.0145689
906906 0 0
907907 22.8887 0.760006 0.380003 0.924985i 0.375923π-0.375923\pi
0.380003 + 0.924985i 0.375923π0.375923\pi
908908 29.3489 0.973978
909909 0 0
910910 −3.39999 −0.112709
911911 36.0929 1.19581 0.597906 0.801566i 0.296000π-0.296000\pi
0.597906 + 0.801566i 0.296000π0.296000\pi
912912 0 0
913913 −2.99602 −0.0991537
914914 −19.9437 −0.659681
915915 0 0
916916 30.5208 1.00844
917917 50.2423 1.65915
918918 0 0
919919 9.94627 0.328097 0.164049 0.986452i 0.447545π-0.447545\pi
0.164049 + 0.986452i 0.447545π0.447545\pi
920920 22.3318 0.736256
921921 0 0
922922 −5.22074 −0.171936
923923 −6.19699 −0.203976
924924 0 0
925925 10.7648 0.353944
926926 24.0022 0.788760
927927 0 0
928928 5.56906 0.182813
929929 30.2310 0.991846 0.495923 0.868366i 0.334830π-0.334830\pi
0.495923 + 0.868366i 0.334830π0.334830\pi
930930 0 0
931931 39.3760 1.29050
932932 6.90179 0.226076
933933 0 0
934934 12.3728 0.404852
935935 −2.85716 −0.0934393
936936 0 0
937937 28.4312 0.928808 0.464404 0.885624i 0.346269π-0.346269\pi
0.464404 + 0.885624i 0.346269π0.346269\pi
938938 12.9229 0.421948
939939 0 0
940940 0.301661 0.00983910
941941 7.18322 0.234166 0.117083 0.993122i 0.462646π-0.462646\pi
0.117083 + 0.993122i 0.462646π0.462646\pi
942942 0 0
943943 20.1020 0.654610
944944 0.672458 0.0218866
945945 0 0
946946 10.7581 0.349776
947947 44.1518 1.43474 0.717370 0.696692i 0.245346π-0.245346\pi
0.717370 + 0.696692i 0.245346π0.245346\pi
948948 0 0
949949 10.6371 0.345296
950950 4.60625 0.149447
951951 0 0
952952 11.1013 0.359795
953953 −21.5308 −0.697452 −0.348726 0.937225i 0.613386π-0.613386\pi
−0.348726 + 0.937225i 0.613386π0.613386\pi
954954 0 0
955955 −2.64477 −0.0855827
956956 4.97644 0.160949
957957 0 0
958958 −14.0888 −0.455189
959959 0.271823 0.00877762
960960 0 0
961961 −29.7170 −0.958614
962962 9.55529 0.308075
963963 0 0
964964 −13.5128 −0.435218
965965 16.4494 0.529526
966966 0 0
967967 −25.0483 −0.805498 −0.402749 0.915310i 0.631945π-0.631945\pi
−0.402749 + 0.915310i 0.631945π0.631945\pi
968968 8.63498 0.277539
969969 0 0
970970 −12.4690 −0.400356
971971 52.1718 1.67427 0.837136 0.546995i 0.184228π-0.184228\pi
0.837136 + 0.546995i 0.184228π0.184228\pi
972972 0 0
973973 −46.9072 −1.50378
974974 26.9803 0.864506
975975 0 0
976976 1.90712 0.0610456
977977 −21.1021 −0.675115 −0.337557 0.941305i 0.609601π-0.609601\pi
−0.337557 + 0.941305i 0.609601π0.609601\pi
978978 0 0
979979 −40.4233 −1.29194
980980 9.16458 0.292752
981981 0 0
982982 −31.7652 −1.01367
983983 19.1395 0.610457 0.305228 0.952279i 0.401267π-0.401267\pi
0.305228 + 0.952279i 0.401267π0.401267\pi
984984 0 0
985985 22.1732 0.706496
986986 −0.907229 −0.0288921
987987 0 0
988988 −6.06463 −0.192942
989989 −33.0378 −1.05054
990990 0 0
991991 −19.2995 −0.613069 −0.306535 0.951860i 0.599170π-0.599170\pi
−0.306535 + 0.951860i 0.599170π0.599170\pi
992992 −6.30795 −0.200278
993993 0 0
994994 −21.5372 −0.683117
995995 −11.4778 −0.363870
996996 0 0
997997 27.8422 0.881771 0.440886 0.897563i 0.354664π-0.354664\pi
0.440886 + 0.897563i 0.354664π0.354664\pi
998998 7.93749 0.251257
999999 0 0
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 1305.2.a.s.1.5 7
3.2 odd 2 1305.2.a.t.1.3 yes 7
5.4 even 2 6525.2.a.bw.1.3 7
15.14 odd 2 6525.2.a.bv.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1305.2.a.s.1.5 7 1.1 even 1 trivial
1305.2.a.t.1.3 yes 7 3.2 odd 2
6525.2.a.bv.1.5 7 15.14 odd 2
6525.2.a.bw.1.3 7 5.4 even 2