Properties

Label 2535.2.a.bj.1.4
Level 25352535
Weight 22
Character 2535.1
Self dual yes
Analytic conductor 20.24220.242
Analytic rank 00
Dimension 44
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] = [2535,2,Mod(1,2535)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2535, 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("2535.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 2535=35132 2535 = 3 \cdot 5 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2535.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: 20.242076912420.2420769124
Analytic rank: 00
Dimension: 44
Coefficient field: 4.4.13824.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x46x2+6 x^{4} - 6x^{2} + 6 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 195)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 2.175332.17533 of defining polynomial
Character χ\chi == 2535.1

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+2.17533q21.00000q3+2.73205q41.00000q52.17533q60.443277q7+1.59245q8+1.00000q92.17533q10+1.59245q112.73205q120.964273q14+1.00000q152.00000q16+3.76778q17+2.17533q18+1.54715q192.73205q20+0.443277q21+3.46410q22+0.705897q231.59245q24+1.00000q251.00000q271.21106q28+2.49983q29+2.17533q30+6.18490q317.53556q321.59245q33+8.19615q34+0.443277q35+2.73205q36+10.3507q37+3.36556q381.59245q40+6.02082q41+0.964273q42+4.72248q43+4.35066q441.00000q45+1.53556q46+5.41712q47+2.00000q486.80351q49+2.17533q503.76778q51+5.51641q532.17533q541.59245q550.705897q561.54715q57+5.43795q58+8.72214q59+2.73205q609.73205q61+13.4542q620.443277q6312.3923q643.46410q6613.6960q67+10.2938q680.705897q69+0.964273q7015.1488q71+1.59245q72+10.7939q73+22.5161q741.00000q75+4.22689q760.705897q77+10.7317q79+2.00000q80+1.00000q81+13.0973q829.12801q83+1.21106q843.76778q85+10.2729q862.49983q87+2.53590q88+4.75653q892.17533q90+1.92855q926.18490q93+11.7840q941.54715q95+7.53556q96+8.41712q9714.7999q98+1.59245q99+O(q100)q+2.17533 q^{2} -1.00000 q^{3} +2.73205 q^{4} -1.00000 q^{5} -2.17533 q^{6} -0.443277 q^{7} +1.59245 q^{8} +1.00000 q^{9} -2.17533 q^{10} +1.59245 q^{11} -2.73205 q^{12} -0.964273 q^{14} +1.00000 q^{15} -2.00000 q^{16} +3.76778 q^{17} +2.17533 q^{18} +1.54715 q^{19} -2.73205 q^{20} +0.443277 q^{21} +3.46410 q^{22} +0.705897 q^{23} -1.59245 q^{24} +1.00000 q^{25} -1.00000 q^{27} -1.21106 q^{28} +2.49983 q^{29} +2.17533 q^{30} +6.18490 q^{31} -7.53556 q^{32} -1.59245 q^{33} +8.19615 q^{34} +0.443277 q^{35} +2.73205 q^{36} +10.3507 q^{37} +3.36556 q^{38} -1.59245 q^{40} +6.02082 q^{41} +0.964273 q^{42} +4.72248 q^{43} +4.35066 q^{44} -1.00000 q^{45} +1.53556 q^{46} +5.41712 q^{47} +2.00000 q^{48} -6.80351 q^{49} +2.17533 q^{50} -3.76778 q^{51} +5.51641 q^{53} -2.17533 q^{54} -1.59245 q^{55} -0.705897 q^{56} -1.54715 q^{57} +5.43795 q^{58} +8.72214 q^{59} +2.73205 q^{60} -9.73205 q^{61} +13.4542 q^{62} -0.443277 q^{63} -12.3923 q^{64} -3.46410 q^{66} -13.6960 q^{67} +10.2938 q^{68} -0.705897 q^{69} +0.964273 q^{70} -15.1488 q^{71} +1.59245 q^{72} +10.7939 q^{73} +22.5161 q^{74} -1.00000 q^{75} +4.22689 q^{76} -0.705897 q^{77} +10.7317 q^{79} +2.00000 q^{80} +1.00000 q^{81} +13.0973 q^{82} -9.12801 q^{83} +1.21106 q^{84} -3.76778 q^{85} +10.2729 q^{86} -2.49983 q^{87} +2.53590 q^{88} +4.75653 q^{89} -2.17533 q^{90} +1.92855 q^{92} -6.18490 q^{93} +11.7840 q^{94} -1.54715 q^{95} +7.53556 q^{96} +8.41712 q^{97} -14.7999 q^{98} +1.59245 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q3+4q44q5+4q94q1212q14+4q158q16+12q194q20+4q254q27+12q2812q29+12q31+12q34+4q36+24q37+24q98+O(q100) 4 q - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{9} - 4 q^{12} - 12 q^{14} + 4 q^{15} - 8 q^{16} + 12 q^{19} - 4 q^{20} + 4 q^{25} - 4 q^{27} + 12 q^{28} - 12 q^{29} + 12 q^{31} + 12 q^{34} + 4 q^{36} + 24 q^{37}+ \cdots - 24 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 2.17533 1.53819 0.769095 0.639135i 0.220708π-0.220708\pi
0.769095 + 0.639135i 0.220708π0.220708\pi
33 −1.00000 −0.577350
44 2.73205 1.36603
55 −1.00000 −0.447214
66 −2.17533 −0.888074
77 −0.443277 −0.167543 −0.0837715 0.996485i 0.526697π-0.526697\pi
−0.0837715 + 0.996485i 0.526697π0.526697\pi
88 1.59245 0.563016
99 1.00000 0.333333
1010 −2.17533 −0.687899
1111 1.59245 0.480142 0.240071 0.970755i 0.422829π-0.422829\pi
0.240071 + 0.970755i 0.422829π0.422829\pi
1212 −2.73205 −0.788675
1313 0 0
1414 −0.964273 −0.257713
1515 1.00000 0.258199
1616 −2.00000 −0.500000
1717 3.76778 0.913820 0.456910 0.889513i 0.348956π-0.348956\pi
0.456910 + 0.889513i 0.348956π0.348956\pi
1818 2.17533 0.512730
1919 1.54715 0.354941 0.177470 0.984126i 0.443209π-0.443209\pi
0.177470 + 0.984126i 0.443209π0.443209\pi
2020 −2.73205 −0.610905
2121 0.443277 0.0967310
2222 3.46410 0.738549
2323 0.705897 0.147190 0.0735948 0.997288i 0.476553π-0.476553\pi
0.0735948 + 0.997288i 0.476553π0.476553\pi
2424 −1.59245 −0.325058
2525 1.00000 0.200000
2626 0 0
2727 −1.00000 −0.192450
2828 −1.21106 −0.228868
2929 2.49983 0.464207 0.232103 0.972691i 0.425439π-0.425439\pi
0.232103 + 0.972691i 0.425439π0.425439\pi
3030 2.17533 0.397159
3131 6.18490 1.11084 0.555420 0.831570i 0.312557π-0.312557\pi
0.555420 + 0.831570i 0.312557π0.312557\pi
3232 −7.53556 −1.33211
3333 −1.59245 −0.277210
3434 8.19615 1.40563
3535 0.443277 0.0749275
3636 2.73205 0.455342
3737 10.3507 1.70164 0.850819 0.525459i 0.176107π-0.176107\pi
0.850819 + 0.525459i 0.176107π0.176107\pi
3838 3.36556 0.545966
3939 0 0
4040 −1.59245 −0.251789
4141 6.02082 0.940295 0.470147 0.882588i 0.344201π-0.344201\pi
0.470147 + 0.882588i 0.344201π0.344201\pi
4242 0.964273 0.148790
4343 4.72248 0.720171 0.360086 0.932919i 0.382748π-0.382748\pi
0.360086 + 0.932919i 0.382748π0.382748\pi
4444 4.35066 0.655886
4545 −1.00000 −0.149071
4646 1.53556 0.226405
4747 5.41712 0.790169 0.395084 0.918645i 0.370715π-0.370715\pi
0.395084 + 0.918645i 0.370715π0.370715\pi
4848 2.00000 0.288675
4949 −6.80351 −0.971929
5050 2.17533 0.307638
5151 −3.76778 −0.527594
5252 0 0
5353 5.51641 0.757737 0.378869 0.925450i 0.376313π-0.376313\pi
0.378869 + 0.925450i 0.376313π0.376313\pi
5454 −2.17533 −0.296025
5555 −1.59245 −0.214726
5656 −0.705897 −0.0943294
5757 −1.54715 −0.204925
5858 5.43795 0.714037
5959 8.72214 1.13553 0.567763 0.823192i 0.307809π-0.307809\pi
0.567763 + 0.823192i 0.307809π0.307809\pi
6060 2.73205 0.352706
6161 −9.73205 −1.24606 −0.623031 0.782197i 0.714099π-0.714099\pi
−0.623031 + 0.782197i 0.714099π0.714099\pi
6262 13.4542 1.70868
6363 −0.443277 −0.0558476
6464 −12.3923 −1.54904
6565 0 0
6666 −3.46410 −0.426401
6767 −13.6960 −1.67323 −0.836615 0.547791i 0.815469π-0.815469\pi
−0.836615 + 0.547791i 0.815469π0.815469\pi
6868 10.2938 1.24830
6969 −0.705897 −0.0849800
7070 0.964273 0.115253
7171 −15.1488 −1.79784 −0.898918 0.438117i 0.855645π-0.855645\pi
−0.898918 + 0.438117i 0.855645π0.855645\pi
7272 1.59245 0.187672
7373 10.7939 1.26333 0.631667 0.775240i 0.282371π-0.282371\pi
0.631667 + 0.775240i 0.282371π0.282371\pi
7474 22.5161 2.61744
7575 −1.00000 −0.115470
7676 4.22689 0.484858
7777 −0.705897 −0.0804444
7878 0 0
7979 10.7317 1.20741 0.603706 0.797207i 0.293690π-0.293690\pi
0.603706 + 0.797207i 0.293690π0.293690\pi
8080 2.00000 0.223607
8181 1.00000 0.111111
8282 13.0973 1.44635
8383 −9.12801 −1.00193 −0.500964 0.865468i 0.667021π-0.667021\pi
−0.500964 + 0.865468i 0.667021π0.667021\pi
8484 1.21106 0.132137
8585 −3.76778 −0.408673
8686 10.2729 1.10776
8787 −2.49983 −0.268010
8888 2.53590 0.270328
8989 4.75653 0.504191 0.252095 0.967702i 0.418880π-0.418880\pi
0.252095 + 0.967702i 0.418880π0.418880\pi
9090 −2.17533 −0.229300
9191 0 0
9292 1.92855 0.201065
9393 −6.18490 −0.641344
9494 11.7840 1.21543
9595 −1.54715 −0.158734
9696 7.53556 0.769095
9797 8.41712 0.854629 0.427315 0.904103i 0.359460π-0.359460\pi
0.427315 + 0.904103i 0.359460π0.359460\pi
9898 −14.7999 −1.49501
9999 1.59245 0.160047
100100 2.73205 0.273205
101101 −6.70590 −0.667262 −0.333631 0.942704i 0.608274π-0.608274\pi
−0.333631 + 0.942704i 0.608274π0.608274\pi
102102 −8.19615 −0.811540
103103 1.74197 0.171641 0.0858205 0.996311i 0.472649π-0.472649\pi
0.0858205 + 0.996311i 0.472649π0.472649\pi
104104 0 0
105105 −0.443277 −0.0432594
106106 12.0000 1.16554
107107 11.9186 1.15222 0.576109 0.817373i 0.304570π-0.304570\pi
0.576109 + 0.817373i 0.304570π0.304570\pi
108108 −2.73205 −0.262892
109109 17.0407 1.63220 0.816102 0.577908i 0.196131π-0.196131\pi
0.816102 + 0.577908i 0.196131π0.196131\pi
110110 −3.46410 −0.330289
111111 −10.3507 −0.982441
112112 0.886554 0.0837715
113113 −3.46410 −0.325875 −0.162938 0.986636i 0.552097π-0.552097\pi
−0.162938 + 0.986636i 0.552097π0.552097\pi
114114 −3.36556 −0.315213
115115 −0.705897 −0.0658252
116116 6.82966 0.634118
117117 0 0
118118 18.9735 1.74665
119119 −1.67017 −0.153104
120120 1.59245 0.145370
121121 −8.46410 −0.769464
122122 −21.1704 −1.91668
123123 −6.02082 −0.542879
124124 16.8975 1.51744
125125 −1.00000 −0.0894427
126126 −0.964273 −0.0859042
127127 14.2510 1.26457 0.632287 0.774734i 0.282116π-0.282116\pi
0.632287 + 0.774734i 0.282116π0.282116\pi
128128 −11.8862 −1.05060
129129 −4.72248 −0.415791
130130 0 0
131131 10.0354 0.876796 0.438398 0.898781i 0.355546π-0.355546\pi
0.438398 + 0.898781i 0.355546π0.355546\pi
132132 −4.35066 −0.378676
133133 −0.685816 −0.0594678
134134 −29.7932 −2.57374
135135 1.00000 0.0860663
136136 6.00000 0.514496
137137 −9.28419 −0.793202 −0.396601 0.917991i 0.629810π-0.629810\pi
−0.396601 + 0.917991i 0.629810π0.629810\pi
138138 −1.53556 −0.130715
139139 −6.51641 −0.552715 −0.276357 0.961055i 0.589127π-0.589127\pi
−0.276357 + 0.961055i 0.589127π0.589127\pi
140140 1.21106 0.102353
141141 −5.41712 −0.456204
142142 −32.9537 −2.76541
143143 0 0
144144 −2.00000 −0.166667
145145 −2.49983 −0.207599
146146 23.4803 1.94325
147147 6.80351 0.561144
148148 28.2785 2.32448
149149 0.0568941 0.00466094 0.00233047 0.999997i 0.499258π-0.499258\pi
0.00233047 + 0.999997i 0.499258π0.499258\pi
150150 −2.17533 −0.177615
151151 −17.3004 −1.40789 −0.703944 0.710255i 0.748580π-0.748580\pi
−0.703944 + 0.710255i 0.748580π0.748580\pi
152152 2.46376 0.199837
153153 3.76778 0.304607
154154 −1.53556 −0.123739
155155 −6.18490 −0.496783
156156 0 0
157157 −1.34898 −0.107660 −0.0538300 0.998550i 0.517143π-0.517143\pi
−0.0538300 + 0.998550i 0.517143π0.517143\pi
158158 23.3450 1.85723
159159 −5.51641 −0.437480
160160 7.53556 0.595738
161161 −0.312908 −0.0246606
162162 2.17533 0.170910
163163 2.97918 0.233347 0.116674 0.993170i 0.462777π-0.462777\pi
0.116674 + 0.993170i 0.462777π0.462777\pi
164164 16.4492 1.28447
165165 1.59245 0.123972
166166 −19.8564 −1.54116
167167 23.8141 1.84279 0.921394 0.388629i 0.127051π-0.127051\pi
0.921394 + 0.388629i 0.127051π0.127051\pi
168168 0.705897 0.0544611
169169 0 0
170170 −8.19615 −0.628616
171171 1.54715 0.118314
172172 12.9020 0.983772
173173 −24.6762 −1.87609 −0.938047 0.346509i 0.887367π-0.887367\pi
−0.938047 + 0.346509i 0.887367π0.887367\pi
174174 −5.43795 −0.412250
175175 −0.443277 −0.0335086
176176 −3.18490 −0.240071
177177 −8.72214 −0.655596
178178 10.3470 0.775541
179179 −2.88488 −0.215626 −0.107813 0.994171i 0.534385π-0.534385\pi
−0.107813 + 0.994171i 0.534385π0.534385\pi
180180 −2.73205 −0.203635
181181 7.41086 0.550845 0.275422 0.961323i 0.411182π-0.411182\pi
0.275422 + 0.961323i 0.411182π0.411182\pi
182182 0 0
183183 9.73205 0.719414
184184 1.12411 0.0828701
185185 −10.3507 −0.760995
186186 −13.4542 −0.986509
187187 6.00000 0.438763
188188 14.7999 1.07939
189189 0.443277 0.0322437
190190 −3.36556 −0.244163
191191 −16.2577 −1.17637 −0.588183 0.808728i 0.700156π-0.700156\pi
−0.588183 + 0.808728i 0.700156π0.700156\pi
192192 12.3923 0.894338
193193 11.2775 0.811774 0.405887 0.913923i 0.366963π-0.366963\pi
0.405887 + 0.913923i 0.366963π0.366963\pi
194194 18.3100 1.31458
195195 0 0
196196 −18.5875 −1.32768
197197 −24.6669 −1.75745 −0.878723 0.477333i 0.841604π-0.841604\pi
−0.878723 + 0.477333i 0.841604π0.841604\pi
198198 3.46410 0.246183
199199 −22.0711 −1.56458 −0.782290 0.622915i 0.785948π-0.785948\pi
−0.782290 + 0.622915i 0.785948π0.785948\pi
200200 1.59245 0.112603
201201 13.6960 0.966040
202202 −14.5875 −1.02637
203203 −1.10812 −0.0777745
204204 −10.2938 −0.720707
205205 −6.02082 −0.420513
206206 3.78935 0.264016
207207 0.705897 0.0490632
208208 0 0
209209 2.46376 0.170422
210210 −0.964273 −0.0665411
211211 −21.5161 −1.48123 −0.740614 0.671931i 0.765465π-0.765465\pi
−0.740614 + 0.671931i 0.765465π0.765465\pi
212212 15.0711 1.03509
213213 15.1488 1.03798
214214 25.9269 1.77233
215215 −4.72248 −0.322070
216216 −1.59245 −0.108353
217217 −2.74162 −0.186114
218218 37.0691 2.51064
219219 −10.7939 −0.729386
220220 −4.35066 −0.293321
221221 0 0
222222 −22.5161 −1.51118
223223 21.2365 1.42210 0.711051 0.703140i 0.248219π-0.248219\pi
0.711051 + 0.703140i 0.248219π0.248219\pi
224224 3.34034 0.223186
225225 1.00000 0.0666667
226226 −7.53556 −0.501258
227227 −10.4499 −0.693587 −0.346794 0.937941i 0.612730π-0.612730\pi
−0.346794 + 0.937941i 0.612730π0.612730\pi
228228 −4.22689 −0.279933
229229 21.4135 1.41505 0.707523 0.706690i 0.249813π-0.249813\pi
0.707523 + 0.706690i 0.249813π0.249813\pi
230230 −1.53556 −0.101252
231231 0.705897 0.0464446
232232 3.98085 0.261356
233233 3.24179 0.212377 0.106189 0.994346i 0.466135π-0.466135\pi
0.106189 + 0.994346i 0.466135π0.466135\pi
234234 0 0
235235 −5.41712 −0.353374
236236 23.8293 1.55116
237237 −10.7317 −0.697099
238238 −3.63317 −0.235503
239239 −18.3129 −1.18456 −0.592282 0.805731i 0.701773π-0.701773\pi
−0.592282 + 0.805731i 0.701773π0.701773\pi
240240 −2.00000 −0.129099
241241 −6.63741 −0.427553 −0.213777 0.976883i 0.568576π-0.568576\pi
−0.213777 + 0.976883i 0.568576π0.568576\pi
242242 −18.4122 −1.18358
243243 −1.00000 −0.0641500
244244 −26.5885 −1.70215
245245 6.80351 0.434660
246246 −13.0973 −0.835051
247247 0 0
248248 9.84915 0.625422
249249 9.12801 0.578464
250250 −2.17533 −0.137580
251251 −19.8816 −1.25492 −0.627459 0.778650i 0.715905π-0.715905\pi
−0.627459 + 0.778650i 0.715905π0.715905\pi
252252 −1.21106 −0.0762893
253253 1.12411 0.0706719
254254 31.0007 1.94515
255255 3.76778 0.235947
256256 −1.07180 −0.0669873
257257 1.00957 0.0629754 0.0314877 0.999504i 0.489975π-0.489975\pi
0.0314877 + 0.999504i 0.489975π0.489975\pi
258258 −10.2729 −0.639565
259259 −4.58821 −0.285097
260260 0 0
261261 2.49983 0.154736
262262 21.8303 1.34868
263263 −21.5719 −1.33018 −0.665089 0.746764i 0.731607π-0.731607\pi
−0.665089 + 0.746764i 0.731607π0.731607\pi
264264 −2.53590 −0.156074
265265 −5.51641 −0.338870
266266 −1.49187 −0.0914727
267267 −4.75653 −0.291095
268268 −37.4181 −2.28568
269269 −4.65068 −0.283557 −0.141779 0.989898i 0.545282π-0.545282\pi
−0.141779 + 0.989898i 0.545282π0.545282\pi
270270 2.17533 0.132386
271271 −5.31992 −0.323162 −0.161581 0.986859i 0.551659π-0.551659\pi
−0.161581 + 0.986859i 0.551659π0.551659\pi
272272 −7.53556 −0.456910
273273 0 0
274274 −20.1962 −1.22009
275275 1.59245 0.0960284
276276 −1.92855 −0.116085
277277 9.35948 0.562357 0.281178 0.959655i 0.409275π-0.409275\pi
0.281178 + 0.959655i 0.409275π0.409275\pi
278278 −14.1753 −0.850180
279279 6.18490 0.370280
280280 0.705897 0.0421854
281281 13.1449 0.784161 0.392080 0.919931i 0.371756π-0.371756\pi
0.392080 + 0.919931i 0.371756π0.371756\pi
282282 −11.7840 −0.701728
283283 −3.64367 −0.216594 −0.108297 0.994119i 0.534540π-0.534540\pi
−0.108297 + 0.994119i 0.534540π0.534540\pi
284284 −41.3874 −2.45589
285285 1.54715 0.0916453
286286 0 0
287287 −2.66889 −0.157540
288288 −7.53556 −0.444037
289289 −2.80385 −0.164932
290290 −5.43795 −0.319327
291291 −8.41712 −0.493420
292292 29.4896 1.72575
293293 19.6348 1.14708 0.573540 0.819178i 0.305570π-0.305570\pi
0.573540 + 0.819178i 0.305570π0.305570\pi
294294 14.7999 0.863145
295295 −8.72214 −0.507822
296296 16.4829 0.958049
297297 −1.59245 −0.0924033
298298 0.123763 0.00716941
299299 0 0
300300 −2.73205 −0.157735
301301 −2.09337 −0.120660
302302 −37.6341 −2.16560
303303 6.70590 0.385244
304304 −3.09430 −0.177470
305305 9.73205 0.557256
306306 8.19615 0.468543
307307 4.74863 0.271019 0.135509 0.990776i 0.456733π-0.456733\pi
0.135509 + 0.990776i 0.456733π0.456733\pi
308308 −1.92855 −0.109889
309309 −1.74197 −0.0990970
310310 −13.4542 −0.764146
311311 5.45512 0.309332 0.154666 0.987967i 0.450570π-0.450570\pi
0.154666 + 0.987967i 0.450570π0.450570\pi
312312 0 0
313313 −7.23855 −0.409147 −0.204573 0.978851i 0.565581π-0.565581\pi
−0.204573 + 0.978851i 0.565581π0.565581\pi
314314 −2.93447 −0.165602
315315 0.443277 0.0249758
316316 29.3196 1.64935
317317 −21.0142 −1.18028 −0.590138 0.807302i 0.700927π-0.700927\pi
−0.590138 + 0.807302i 0.700927π0.700927\pi
318318 −12.0000 −0.672927
319319 3.98085 0.222885
320320 12.3923 0.692751
321321 −11.9186 −0.665233
322322 −0.680677 −0.0379326
323323 5.82932 0.324352
324324 2.73205 0.151781
325325 0 0
326326 6.48068 0.358932
327327 −17.0407 −0.942354
328328 9.58786 0.529401
329329 −2.40129 −0.132387
330330 3.46410 0.190693
331331 15.5136 0.852707 0.426354 0.904557i 0.359798π-0.359798\pi
0.426354 + 0.904557i 0.359798π0.359798\pi
332332 −24.9382 −1.36866
333333 10.3507 0.567212
334334 51.8034 2.83456
335335 13.6960 0.748291
336336 −0.886554 −0.0483655
337337 −32.8124 −1.78741 −0.893703 0.448660i 0.851901π-0.851901\pi
−0.893703 + 0.448660i 0.851901π0.851901\pi
338338 0 0
339339 3.46410 0.188144
340340 −10.2938 −0.558258
341341 9.84915 0.533361
342342 3.36556 0.181989
343343 6.11878 0.330383
344344 7.52031 0.405468
345345 0.705897 0.0380042
346346 −53.6787 −2.88579
347347 −19.4634 −1.04485 −0.522426 0.852685i 0.674973π-0.674973\pi
−0.522426 + 0.852685i 0.674973π0.674973\pi
348348 −6.82966 −0.366108
349349 9.72114 0.520361 0.260180 0.965560i 0.416218π-0.416218\pi
0.260180 + 0.965560i 0.416218π0.416218\pi
350350 −0.964273 −0.0515425
351351 0 0
352352 −12.0000 −0.639602
353353 23.0176 1.22510 0.612551 0.790431i 0.290143π-0.290143\pi
0.612551 + 0.790431i 0.290143π0.290143\pi
354354 −18.9735 −1.00843
355355 15.1488 0.804016
356356 12.9951 0.688737
357357 1.67017 0.0883947
358358 −6.27555 −0.331673
359359 10.4131 0.549584 0.274792 0.961504i 0.411391π-0.411391\pi
0.274792 + 0.961504i 0.411391π0.411391\pi
360360 −1.59245 −0.0839295
361361 −16.6063 −0.874017
362362 16.1210 0.847303
363363 8.46410 0.444250
364364 0 0
365365 −10.7939 −0.564980
366366 21.1704 1.10659
367367 −3.63153 −0.189565 −0.0947823 0.995498i 0.530215π-0.530215\pi
−0.0947823 + 0.995498i 0.530215π0.530215\pi
368368 −1.41179 −0.0735948
369369 6.02082 0.313432
370370 −22.5161 −1.17055
371371 −2.44530 −0.126954
372372 −16.8975 −0.876093
373373 19.8389 1.02722 0.513609 0.858024i 0.328308π-0.328308\pi
0.513609 + 0.858024i 0.328308π0.328308\pi
374374 13.0520 0.674901
375375 1.00000 0.0516398
376376 8.62650 0.444878
377377 0 0
378378 0.964273 0.0495968
379379 −6.83390 −0.351034 −0.175517 0.984476i 0.556160π-0.556160\pi
−0.175517 + 0.984476i 0.556160π0.556160\pi
380380 −4.22689 −0.216835
381381 −14.2510 −0.730102
382382 −35.3658 −1.80947
383383 38.8839 1.98687 0.993437 0.114379i 0.0364879π-0.0364879\pi
0.993437 + 0.114379i 0.0364879π0.0364879\pi
384384 11.8862 0.606566
385385 0.705897 0.0359758
386386 24.5323 1.24866
387387 4.72248 0.240057
388388 22.9960 1.16745
389389 8.84881 0.448652 0.224326 0.974514i 0.427982π-0.427982\pi
0.224326 + 0.974514i 0.427982π0.427982\pi
390390 0 0
391391 2.65966 0.134505
392392 −10.8342 −0.547212
393393 −10.0354 −0.506218
394394 −53.6586 −2.70328
395395 −10.7317 −0.539971
396396 4.35066 0.218629
397397 −17.0378 −0.855103 −0.427552 0.903991i 0.640624π-0.640624\pi
−0.427552 + 0.903991i 0.640624π0.640624\pi
398398 −48.0119 −2.40662
399399 0.685816 0.0343337
400400 −2.00000 −0.100000
401401 7.69099 0.384070 0.192035 0.981388i 0.438491π-0.438491\pi
0.192035 + 0.981388i 0.438491π0.438491\pi
402402 29.7932 1.48595
403403 0 0
404404 −18.3209 −0.911496
405405 −1.00000 −0.0496904
406406 −2.41052 −0.119632
407407 16.4829 0.817027
408408 −6.00000 −0.297044
409409 −9.08330 −0.449140 −0.224570 0.974458i 0.572098π-0.572098\pi
−0.224570 + 0.974458i 0.572098π0.572098\pi
410410 −13.0973 −0.646828
411411 9.28419 0.457955
412412 4.75914 0.234466
413413 −3.86632 −0.190249
414414 1.53556 0.0754685
415415 9.12801 0.448076
416416 0 0
417417 6.51641 0.319110
418418 5.35948 0.262141
419419 −12.9907 −0.634636 −0.317318 0.948319i 0.602782π-0.602782\pi
−0.317318 + 0.948319i 0.602782π0.602782\pi
420420 −1.21106 −0.0590934
421421 −19.8859 −0.969178 −0.484589 0.874742i 0.661031π-0.661031\pi
−0.484589 + 0.874742i 0.661031π0.661031\pi
422422 −46.8045 −2.27841
423423 5.41712 0.263390
424424 8.78461 0.426618
425425 3.76778 0.182764
426426 32.9537 1.59661
427427 4.31399 0.208769
428428 32.5623 1.57396
429429 0 0
430430 −10.2729 −0.495405
431431 −39.1280 −1.88473 −0.942365 0.334587i 0.891403π-0.891403\pi
−0.942365 + 0.334587i 0.891403π0.891403\pi
432432 2.00000 0.0962250
433433 38.1399 1.83289 0.916444 0.400164i 0.131047π-0.131047\pi
0.916444 + 0.400164i 0.131047π0.131047\pi
434434 −5.96393 −0.286278
435435 2.49983 0.119858
436436 46.5561 2.22963
437437 1.09213 0.0522436
438438 −23.4803 −1.12193
439439 6.75086 0.322201 0.161100 0.986938i 0.448496π-0.448496\pi
0.161100 + 0.986938i 0.448496π0.448496\pi
440440 −2.53590 −0.120894
441441 −6.80351 −0.323976
442442 0 0
443443 −12.2647 −0.582713 −0.291357 0.956614i 0.594107π-0.594107\pi
−0.291357 + 0.956614i 0.594107π0.594107\pi
444444 −28.2785 −1.34204
445445 −4.75653 −0.225481
446446 46.1964 2.18746
447447 −0.0568941 −0.00269100
448448 5.49322 0.259530
449449 23.4026 1.10444 0.552219 0.833699i 0.313781π-0.313781\pi
0.552219 + 0.833699i 0.313781π0.313781\pi
450450 2.17533 0.102546
451451 9.58786 0.451475
452452 −9.46410 −0.445154
453453 17.3004 0.812845
454454 −22.7321 −1.06687
455455 0 0
456456 −2.46376 −0.115376
457457 29.5630 1.38290 0.691451 0.722424i 0.256972π-0.256972\pi
0.691451 + 0.722424i 0.256972π0.256972\pi
458458 46.5814 2.17661
459459 −3.76778 −0.175865
460460 −1.92855 −0.0899189
461461 9.57498 0.445951 0.222976 0.974824i 0.428423π-0.428423\pi
0.222976 + 0.974824i 0.428423π0.428423\pi
462462 1.53556 0.0714405
463463 20.0241 0.930600 0.465300 0.885153i 0.345946π-0.345946\pi
0.465300 + 0.885153i 0.345946π0.345946\pi
464464 −4.99966 −0.232103
465465 6.18490 0.286818
466466 7.05197 0.326676
467467 15.7942 0.730868 0.365434 0.930837i 0.380921π-0.380921\pi
0.365434 + 0.930837i 0.380921π0.380921\pi
468468 0 0
469469 6.07111 0.280338
470470 −11.7840 −0.543556
471471 1.34898 0.0621576
472472 13.8896 0.639319
473473 7.52031 0.345784
474474 −23.3450 −1.07227
475475 1.54715 0.0709881
476476 −4.56299 −0.209144
477477 5.51641 0.252579
478478 −39.8366 −1.82208
479479 −26.7485 −1.22217 −0.611086 0.791564i 0.709267π-0.709267\pi
−0.611086 + 0.791564i 0.709267π0.709267\pi
480480 −7.53556 −0.343950
481481 0 0
482482 −14.4385 −0.657657
483483 0.312908 0.0142378
484484 −23.1244 −1.05111
485485 −8.41712 −0.382202
486486 −2.17533 −0.0986749
487487 −28.3238 −1.28347 −0.641737 0.766925i 0.721786π-0.721786\pi
−0.641737 + 0.766925i 0.721786π0.721786\pi
488488 −15.4978 −0.701553
489489 −2.97918 −0.134723
490490 14.7999 0.668589
491491 9.50017 0.428737 0.214368 0.976753i 0.431231π-0.431231\pi
0.214368 + 0.976753i 0.431231π0.431231\pi
492492 −16.4492 −0.741587
493493 9.41880 0.424201
494494 0 0
495495 −1.59245 −0.0715753
496496 −12.3698 −0.555420
497497 6.71513 0.301215
498498 19.8564 0.889787
499499 23.1767 1.03753 0.518765 0.854917i 0.326392π-0.326392\pi
0.518765 + 0.854917i 0.326392π0.326392\pi
500500 −2.73205 −0.122181
501501 −23.8141 −1.06393
502502 −43.2491 −1.93030
503503 −40.3533 −1.79927 −0.899633 0.436647i 0.856166π-0.856166\pi
−0.899633 + 0.436647i 0.856166π0.856166\pi
504504 −0.705897 −0.0314431
505505 6.70590 0.298408
506506 2.44530 0.108707
507507 0 0
508508 38.9345 1.72744
509509 −10.2938 −0.456263 −0.228131 0.973630i 0.573262π-0.573262\pi
−0.228131 + 0.973630i 0.573262π0.573262\pi
510510 8.19615 0.362932
511511 −4.78470 −0.211663
512512 21.4409 0.947564
513513 −1.54715 −0.0683083
514514 2.19615 0.0968681
515515 −1.74197 −0.0767602
516516 −12.9020 −0.567981
517517 8.62650 0.379393
518518 −9.98085 −0.438534
519519 24.6762 1.08316
520520 0 0
521521 43.7218 1.91549 0.957743 0.287624i 0.0928655π-0.0928655\pi
0.957743 + 0.287624i 0.0928655π0.0928655\pi
522522 5.43795 0.238012
523523 7.19556 0.314640 0.157320 0.987548i 0.449715π-0.449715\pi
0.157320 + 0.987548i 0.449715π0.449715\pi
524524 27.4172 1.19773
525525 0.443277 0.0193462
526526 −46.9259 −2.04607
527527 23.3033 1.01511
528528 3.18490 0.138605
529529 −22.5017 −0.978335
530530 −12.0000 −0.521247
531531 8.72214 0.378508
532532 −1.87368 −0.0812345
533533 0 0
534534 −10.3470 −0.447759
535535 −11.9186 −0.515287
536536 −21.8102 −0.942056
537537 2.88488 0.124492
538538 −10.1168 −0.436164
539539 −10.8342 −0.466664
540540 2.73205 0.117569
541541 −24.7159 −1.06262 −0.531310 0.847177i 0.678300π-0.678300\pi
−0.531310 + 0.847177i 0.678300π0.678300\pi
542542 −11.5726 −0.497084
543543 −7.41086 −0.318030
544544 −28.3923 −1.21731
545545 −17.0407 −0.729944
546546 0 0
547547 −6.97187 −0.298096 −0.149048 0.988830i 0.547621π-0.547621\pi
−0.149048 + 0.988830i 0.547621π0.547621\pi
548548 −25.3649 −1.08353
549549 −9.73205 −0.415354
550550 3.46410 0.147710
551551 3.86761 0.164766
552552 −1.12411 −0.0478451
553553 −4.75712 −0.202293
554554 20.3599 0.865011
555555 10.3507 0.439361
556556 −17.8032 −0.755022
557557 1.67575 0.0710038 0.0355019 0.999370i 0.488697π-0.488697\pi
0.0355019 + 0.999370i 0.488697π0.488697\pi
558558 13.4542 0.569561
559559 0 0
560560 −0.886554 −0.0374637
561561 −6.00000 −0.253320
562562 28.5945 1.20619
563563 2.05231 0.0864945 0.0432472 0.999064i 0.486230π-0.486230\pi
0.0432472 + 0.999064i 0.486230π0.486230\pi
564564 −14.7999 −0.623186
565565 3.46410 0.145736
566566 −7.92618 −0.333162
567567 −0.443277 −0.0186159
568568 −24.1238 −1.01221
569569 −41.2191 −1.72799 −0.863996 0.503498i 0.832046π-0.832046\pi
−0.863996 + 0.503498i 0.832046π0.832046\pi
570570 3.36556 0.140968
571571 30.7115 1.28524 0.642619 0.766186i 0.277848π-0.277848\pi
0.642619 + 0.766186i 0.277848π0.277848\pi
572572 0 0
573573 16.2577 0.679175
574574 −5.80572 −0.242326
575575 0.705897 0.0294379
576576 −12.3923 −0.516346
577577 44.8752 1.86818 0.934090 0.357038i 0.116213π-0.116213\pi
0.934090 + 0.357038i 0.116213π0.116213\pi
578578 −6.09929 −0.253697
579579 −11.2775 −0.468678
580580 −6.82966 −0.283586
581581 4.04623 0.167866
582582 −18.3100 −0.758974
583583 8.78461 0.363821
584584 17.1888 0.711278
585585 0 0
586586 42.7122 1.76443
587587 −23.8717 −0.985291 −0.492645 0.870230i 0.663970π-0.663970\pi
−0.492645 + 0.870230i 0.663970π0.663970\pi
588588 18.5875 0.766537
589589 9.56897 0.394282
590590 −18.9735 −0.781127
591591 24.6669 1.01466
592592 −20.7013 −0.850819
593593 −26.8263 −1.10162 −0.550811 0.834630i 0.685682π-0.685682\pi
−0.550811 + 0.834630i 0.685682π0.685682\pi
594594 −3.46410 −0.142134
595595 1.67017 0.0684703
596596 0.155437 0.00636697
597597 22.0711 0.903311
598598 0 0
599599 −26.4919 −1.08243 −0.541215 0.840885i 0.682035π-0.682035\pi
−0.541215 + 0.840885i 0.682035π0.682035\pi
600600 −1.59245 −0.0650115
601601 23.2290 0.947530 0.473765 0.880651i 0.342895π-0.342895\pi
0.473765 + 0.880651i 0.342895π0.342895\pi
602602 −4.55376 −0.185597
603603 −13.6960 −0.557743
604604 −47.2656 −1.92321
605605 8.46410 0.344115
606606 14.5875 0.592578
607607 10.5812 0.429478 0.214739 0.976672i 0.431110π-0.431110\pi
0.214739 + 0.976672i 0.431110π0.431110\pi
608608 −11.6586 −0.472820
609609 1.10812 0.0449031
610610 21.1704 0.857164
611611 0 0
612612 10.2938 0.416101
613613 6.31735 0.255155 0.127578 0.991829i 0.459280π-0.459280\pi
0.127578 + 0.991829i 0.459280π0.459280\pi
614614 10.3298 0.416878
615615 6.02082 0.242783
616616 −1.12411 −0.0452915
617617 −32.7277 −1.31757 −0.658784 0.752332i 0.728929π-0.728929\pi
−0.658784 + 0.752332i 0.728929π0.728929\pi
618618 −3.78935 −0.152430
619619 21.0143 0.844635 0.422317 0.906448i 0.361217π-0.361217\pi
0.422317 + 0.906448i 0.361217π0.361217\pi
620620 −16.8975 −0.678618
621621 −0.705897 −0.0283267
622622 11.8667 0.475810
623623 −2.10846 −0.0844736
624624 0 0
625625 1.00000 0.0400000
626626 −15.7462 −0.629345
627627 −2.46376 −0.0983931
628628 −3.68547 −0.147066
629629 38.9990 1.55499
630630 0.964273 0.0384175
631631 15.5657 0.619661 0.309830 0.950792i 0.399728π-0.399728\pi
0.309830 + 0.950792i 0.399728π0.399728\pi
632632 17.0897 0.679792
633633 21.5161 0.855187
634634 −45.7128 −1.81549
635635 −14.2510 −0.565535
636636 −15.0711 −0.597608
637637 0 0
638638 8.65966 0.342839
639639 −15.1488 −0.599279
640640 11.8862 0.469844
641641 13.7910 0.544713 0.272356 0.962196i 0.412197π-0.412197\pi
0.272356 + 0.962196i 0.412197π0.412197\pi
642642 −25.9269 −1.02325
643643 −27.6698 −1.09119 −0.545596 0.838049i 0.683697π-0.683697\pi
−0.545596 + 0.838049i 0.683697π0.683697\pi
644644 −0.854880 −0.0336870
645645 4.72248 0.185947
646646 12.6807 0.498915
647647 −35.8293 −1.40860 −0.704298 0.709905i 0.748738π-0.748738\pi
−0.704298 + 0.709905i 0.748738π0.748738\pi
648648 1.59245 0.0625574
649649 13.8896 0.545213
650650 0 0
651651 2.74162 0.107453
652652 8.13926 0.318758
653653 −45.2305 −1.77001 −0.885003 0.465585i 0.845844π-0.845844\pi
−0.885003 + 0.465585i 0.845844π0.845844\pi
654654 −37.0691 −1.44952
655655 −10.0354 −0.392115
656656 −12.0416 −0.470147
657657 10.7939 0.421111
658658 −5.22358 −0.203636
659659 −2.37316 −0.0924451 −0.0462226 0.998931i 0.514718π-0.514718\pi
−0.0462226 + 0.998931i 0.514718π0.514718\pi
660660 4.35066 0.169349
661661 −13.1763 −0.512500 −0.256250 0.966611i 0.582487π-0.582487\pi
−0.256250 + 0.966611i 0.582487π0.582487\pi
662662 33.7473 1.31162
663663 0 0
664664 −14.5359 −0.564102
665665 0.685816 0.0265948
666666 22.5161 0.872480
667667 1.76462 0.0683264
668668 65.0613 2.51730
669669 −21.2365 −0.821052
670670 29.7932 1.15101
671671 −15.4978 −0.598286
672672 −3.34034 −0.128856
673673 12.7869 0.492900 0.246450 0.969156i 0.420736π-0.420736\pi
0.246450 + 0.969156i 0.420736π0.420736\pi
674674 −71.3777 −2.74937
675675 −1.00000 −0.0384900
676676 0 0
677677 16.0794 0.617981 0.308991 0.951065i 0.400009π-0.400009\pi
0.308991 + 0.951065i 0.400009π0.400009\pi
678678 7.53556 0.289401
679679 −3.73112 −0.143187
680680 −6.00000 −0.230089
681681 10.4499 0.400443
682682 21.4251 0.820410
683683 −6.31162 −0.241507 −0.120754 0.992682i 0.538531π-0.538531\pi
−0.120754 + 0.992682i 0.538531π0.538531\pi
684684 4.22689 0.161619
685685 9.28419 0.354731
686686 13.3103 0.508191
687687 −21.4135 −0.816977
688688 −9.44496 −0.360086
689689 0 0
690690 1.53556 0.0584576
691691 −36.7143 −1.39668 −0.698339 0.715767i 0.746077π-0.746077\pi
−0.698339 + 0.715767i 0.746077π0.746077\pi
692692 −67.4165 −2.56279
693693 −0.705897 −0.0268148
694694 −42.3393 −1.60718
695695 6.51641 0.247182
696696 −3.98085 −0.150894
697697 22.6851 0.859261
698698 21.1467 0.800413
699699 −3.24179 −0.122616
700700 −1.21106 −0.0457736
701701 −52.0509 −1.96594 −0.982968 0.183774i 0.941168π-0.941168\pi
−0.982968 + 0.183774i 0.941168π0.941168\pi
702702 0 0
703703 16.0140 0.603980
704704 −19.7341 −0.743758
705705 5.41712 0.204021
706706 50.0708 1.88444
707707 2.97257 0.111795
708708 −23.8293 −0.895561
709709 0.936098 0.0351559 0.0175779 0.999845i 0.494404π-0.494404\pi
0.0175779 + 0.999845i 0.494404π0.494404\pi
710710 32.9537 1.23673
711711 10.7317 0.402471
712712 7.57453 0.283868
713713 4.36590 0.163504
714714 3.63317 0.135968
715715 0 0
716716 −7.88163 −0.294550
717717 18.3129 0.683908
718718 22.6520 0.845364
719719 0.997435 0.0371980 0.0185990 0.999827i 0.494079π-0.494079\pi
0.0185990 + 0.999827i 0.494079π0.494079\pi
720720 2.00000 0.0745356
721721 −0.772173 −0.0287572
722722 −36.1242 −1.34440
723723 6.63741 0.246848
724724 20.2468 0.752468
725725 2.49983 0.0928413
726726 18.4122 0.683341
727727 15.4879 0.574416 0.287208 0.957868i 0.407273π-0.407273\pi
0.287208 + 0.957868i 0.407273π0.407273\pi
728728 0 0
729729 1.00000 0.0370370
730730 −23.4803 −0.869046
731731 17.7932 0.658107
732732 26.5885 0.982738
733733 −3.34533 −0.123562 −0.0617812 0.998090i 0.519678π-0.519678\pi
−0.0617812 + 0.998090i 0.519678π0.519678\pi
734734 −7.89978 −0.291586
735735 −6.80351 −0.250951
736736 −5.31932 −0.196073
737737 −21.8102 −0.803388
738738 13.0973 0.482117
739739 13.0936 0.481656 0.240828 0.970568i 0.422581π-0.422581\pi
0.240828 + 0.970568i 0.422581π0.422581\pi
740740 −28.2785 −1.03954
741741 0 0
742742 −5.31932 −0.195279
743743 5.07373 0.186137 0.0930685 0.995660i 0.470332π-0.470332\pi
0.0930685 + 0.995660i 0.470332π0.470332\pi
744744 −9.84915 −0.361087
745745 −0.0568941 −0.00208444
746746 43.1561 1.58006
747747 −9.12801 −0.333976
748748 16.3923 0.599362
749749 −5.28325 −0.193046
750750 2.17533 0.0794317
751751 19.0338 0.694552 0.347276 0.937763i 0.387107π-0.387107\pi
0.347276 + 0.937763i 0.387107π0.387107\pi
752752 −10.8342 −0.395084
753753 19.8816 0.724527
754754 0 0
755755 17.3004 0.629627
756756 1.21106 0.0440456
757757 44.8089 1.62861 0.814303 0.580439i 0.197119π-0.197119\pi
0.814303 + 0.580439i 0.197119π0.197119\pi
758758 −14.8660 −0.539957
759759 −1.12411 −0.0408024
760760 −2.46376 −0.0893700
761761 37.9623 1.37613 0.688065 0.725649i 0.258460π-0.258460\pi
0.688065 + 0.725649i 0.258460π0.258460\pi
762762 −31.0007 −1.12304
763763 −7.55376 −0.273464
764764 −44.4168 −1.60694
765765 −3.76778 −0.136224
766766 84.5852 3.05619
767767 0 0
768768 1.07180 0.0386751
769769 24.8650 0.896654 0.448327 0.893870i 0.352020π-0.352020\pi
0.448327 + 0.893870i 0.352020π0.352020\pi
770770 1.53556 0.0553376
771771 −1.00957 −0.0363589
772772 30.8108 1.10890
773773 29.3026 1.05394 0.526970 0.849884i 0.323328π-0.323328\pi
0.526970 + 0.849884i 0.323328π0.323328\pi
774774 10.2729 0.369253
775775 6.18490 0.222168
776776 13.4039 0.481170
777777 4.58821 0.164601
778778 19.2491 0.690112
779779 9.31512 0.333749
780780 0 0
781781 −24.1238 −0.863216
782782 5.78564 0.206894
783783 −2.49983 −0.0893366
784784 13.6070 0.485965
785785 1.34898 0.0481471
786786 −21.8303 −0.778659
787787 10.6702 0.380350 0.190175 0.981750i 0.439094π-0.439094\pi
0.190175 + 0.981750i 0.439094π0.439094\pi
788788 −67.3913 −2.40071
789789 21.5719 0.767979
790790 −23.3450 −0.830577
791791 1.53556 0.0545981
792792 2.53590 0.0901092
793793 0 0
794794 −37.0628 −1.31531
795795 5.51641 0.195647
796796 −60.2994 −2.13726
797797 18.8800 0.668764 0.334382 0.942438i 0.391472π-0.391472\pi
0.334382 + 0.942438i 0.391472π0.391472\pi
798798 1.49187 0.0528118
799799 20.4105 0.722072
800800 −7.53556 −0.266422
801801 4.75653 0.168064
802802 16.7304 0.590772
803803 17.1888 0.606580
804804 37.4181 1.31964
805805 0.312908 0.0110285
806806 0 0
807807 4.65068 0.163712
808808 −10.6788 −0.375679
809809 43.6203 1.53361 0.766805 0.641880i 0.221845π-0.221845\pi
0.766805 + 0.641880i 0.221845π0.221845\pi
810810 −2.17533 −0.0764332
811811 3.31656 0.116460 0.0582301 0.998303i 0.481454π-0.481454\pi
0.0582301 + 0.998303i 0.481454π0.481454\pi
812812 −3.02743 −0.106242
813813 5.31992 0.186578
814814 35.8557 1.25674
815815 −2.97918 −0.104356
816816 7.53556 0.263797
817817 7.30638 0.255618
818818 −19.7592 −0.690863
819819 0 0
820820 −16.4492 −0.574431
821821 7.20740 0.251540 0.125770 0.992059i 0.459860π-0.459860\pi
0.125770 + 0.992059i 0.459860π0.459860\pi
822822 20.1962 0.704422
823823 9.80291 0.341708 0.170854 0.985296i 0.445347π-0.445347\pi
0.170854 + 0.985296i 0.445347π0.445347\pi
824824 2.77399 0.0966367
825825 −1.59245 −0.0554420
826826 −8.41052 −0.292639
827827 −3.92322 −0.136424 −0.0682118 0.997671i 0.521729π-0.521729\pi
−0.0682118 + 0.997671i 0.521729π0.521729\pi
828828 1.92855 0.0670216
829829 10.4242 0.362047 0.181024 0.983479i 0.442059π-0.442059\pi
0.181024 + 0.983479i 0.442059π0.442059\pi
830830 19.8564 0.689226
831831 −9.35948 −0.324677
832832 0 0
833833 −25.6341 −0.888169
834834 14.1753 0.490851
835835 −23.8141 −0.824120
836836 6.73112 0.232801
837837 −6.18490 −0.213781
838838 −28.2590 −0.976190
839839 −10.2521 −0.353942 −0.176971 0.984216i 0.556630π-0.556630\pi
−0.176971 + 0.984216i 0.556630π0.556630\pi
840840 −0.705897 −0.0243557
841841 −22.7509 −0.784512
842842 −43.2583 −1.49078
843843 −13.1449 −0.452735
844844 −58.7830 −2.02339
845845 0 0
846846 11.7840 0.405143
847847 3.75194 0.128918
848848 −11.0328 −0.378869
849849 3.64367 0.125051
850850 8.19615 0.281126
851851 7.30649 0.250463
852852 41.3874 1.41791
853853 −26.3671 −0.902792 −0.451396 0.892324i 0.649074π-0.649074\pi
−0.451396 + 0.892324i 0.649074π0.649074\pi
854854 9.38435 0.321126
855855 −1.54715 −0.0529114
856856 18.9798 0.648717
857857 1.04855 0.0358178 0.0179089 0.999840i 0.494299π-0.494299\pi
0.0179089 + 0.999840i 0.494299π0.494299\pi
858858 0 0
859859 −19.6076 −0.669003 −0.334501 0.942395i 0.608568π-0.608568\pi
−0.334501 + 0.942395i 0.608568π0.608568\pi
860860 −12.9020 −0.439956
861861 2.66889 0.0909556
862862 −85.1162 −2.89907
863863 −25.6925 −0.874582 −0.437291 0.899320i 0.644062π-0.644062\pi
−0.437291 + 0.899320i 0.644062π0.644062\pi
864864 7.53556 0.256365
865865 24.6762 0.839014
866866 82.9668 2.81933
867867 2.80385 0.0952237
868868 −7.49026 −0.254236
869869 17.0897 0.579729
870870 5.43795 0.184364
871871 0 0
872872 27.1365 0.918958
873873 8.41712 0.284876
874874 2.37574 0.0803605
875875 0.443277 0.0149855
876876 −29.4896 −0.996360
877877 36.4141 1.22962 0.614809 0.788676i 0.289233π-0.289233\pi
0.614809 + 0.788676i 0.289233π0.289233\pi
878878 14.6853 0.495606
879879 −19.6348 −0.662267
880880 3.18490 0.107363
881881 16.0383 0.540344 0.270172 0.962812i 0.412919π-0.412919\pi
0.270172 + 0.962812i 0.412919π0.412919\pi
882882 −14.7999 −0.498337
883883 27.4548 0.923927 0.461963 0.886899i 0.347145π-0.347145\pi
0.461963 + 0.886899i 0.347145π0.347145\pi
884884 0 0
885885 8.72214 0.293191
886886 −26.6797 −0.896323
887887 −31.9642 −1.07325 −0.536626 0.843820i 0.680301π-0.680301\pi
−0.536626 + 0.843820i 0.680301π0.680301\pi
888888 −16.4829 −0.553130
889889 −6.31715 −0.211870
890890 −10.3470 −0.346832
891891 1.59245 0.0533491
892892 58.0193 1.94263
893893 8.38110 0.280463
894894 −0.123763 −0.00413926
895895 2.88488 0.0964308
896896 5.26888 0.176021
897897 0 0
898898 50.9084 1.69883
899899 15.4612 0.515660
900900 2.73205 0.0910684
901901 20.7846 0.692436
902902 20.8567 0.694454
903903 2.09337 0.0696628
904904 −5.51641 −0.183473
905905 −7.41086 −0.246345
906906 37.6341 1.25031
907907 31.6797 1.05191 0.525953 0.850514i 0.323709π-0.323709\pi
0.525953 + 0.850514i 0.323709π0.323709\pi
908908 −28.5498 −0.947458
909909 −6.70590 −0.222421
910910 0 0
911911 −25.9227 −0.858858 −0.429429 0.903101i 0.641285π-0.641285\pi
−0.429429 + 0.903101i 0.641285π0.641285\pi
912912 3.09430 0.102463
913913 −14.5359 −0.481068
914914 64.3093 2.12716
915915 −9.73205 −0.321732
916916 58.5029 1.93299
917917 −4.44845 −0.146901
918918 −8.19615 −0.270513
919919 −12.0194 −0.396483 −0.198242 0.980153i 0.563523π-0.563523\pi
−0.198242 + 0.980153i 0.563523π0.563523\pi
920920 −1.12411 −0.0370607
921921 −4.74863 −0.156473
922922 20.8287 0.685958
923923 0 0
924924 1.92855 0.0634445
925925 10.3507 0.340327
926926 43.5591 1.43144
927927 1.74197 0.0572137
928928 −18.8376 −0.618375
929929 21.3576 0.700721 0.350360 0.936615i 0.386059π-0.386059\pi
0.350360 + 0.936615i 0.386059π0.386059\pi
930930 13.4542 0.441180
931931 −10.5260 −0.344977
932932 8.85675 0.290112
933933 −5.45512 −0.178593
934934 34.3575 1.12421
935935 −6.00000 −0.196221
936936 0 0
937937 15.8029 0.516259 0.258129 0.966110i 0.416894π-0.416894\pi
0.258129 + 0.966110i 0.416894π0.416894\pi
938938 13.2067 0.431213
939939 7.23855 0.236221
940940 −14.7999 −0.482718
941941 6.50590 0.212086 0.106043 0.994362i 0.466182π-0.466182\pi
0.106043 + 0.994362i 0.466182π0.466182\pi
942942 2.93447 0.0956101
943943 4.25008 0.138402
944944 −17.4443 −0.567763
945945 −0.443277 −0.0144198
946946 16.3591 0.531882
947947 −27.8836 −0.906095 −0.453048 0.891486i 0.649663π-0.649663\pi
−0.453048 + 0.891486i 0.649663π0.649663\pi
948948 −29.3196 −0.952255
949949 0 0
950950 3.36556 0.109193
951951 21.0142 0.681433
952952 −2.65966 −0.0862001
953953 51.8861 1.68075 0.840377 0.542002i 0.182333π-0.182333\pi
0.840377 + 0.542002i 0.182333π0.182333\pi
954954 12.0000 0.388514
955955 16.2577 0.526087
956956 −50.0318 −1.61814
957957 −3.98085 −0.128683
958958 −58.1868 −1.87993
959959 4.11547 0.132895
960960 −12.3923 −0.399960
961961 7.25300 0.233968
962962 0 0
963963 11.9186 0.384072
964964 −18.1337 −0.584048
965965 −11.2775 −0.363036
966966 0.680677 0.0219004
967967 21.4251 0.688986 0.344493 0.938789i 0.388051π-0.388051\pi
0.344493 + 0.938789i 0.388051π0.388051\pi
968968 −13.4787 −0.433221
969969 −5.82932 −0.187265
970970 −18.3100 −0.587899
971971 −6.67273 −0.214138 −0.107069 0.994252i 0.534147π-0.534147\pi
−0.107069 + 0.994252i 0.534147π0.534147\pi
972972 −2.73205 −0.0876306
973973 2.88857 0.0926034
974974 −61.6136 −1.97423
975975 0 0
976976 19.4641 0.623031
977977 9.82542 0.314343 0.157171 0.987571i 0.449762π-0.449762\pi
0.157171 + 0.987571i 0.449762π0.449762\pi
978978 −6.48068 −0.207229
979979 7.57453 0.242083
980980 18.5875 0.593757
981981 17.0407 0.544068
982982 20.6660 0.659478
983983 8.83034 0.281644 0.140822 0.990035i 0.455025π-0.455025\pi
0.140822 + 0.990035i 0.455025π0.455025\pi
984984 −9.58786 −0.305650
985985 24.6669 0.785953
986986 20.4890 0.652502
987987 2.40129 0.0764338
988988 0 0
989989 3.33358 0.106002
990990 −3.46410 −0.110096
991991 12.3332 0.391779 0.195889 0.980626i 0.437241π-0.437241\pi
0.195889 + 0.980626i 0.437241π0.437241\pi
992992 −46.6067 −1.47976
993993 −15.5136 −0.492311
994994 14.6076 0.463325
995995 22.0711 0.699701
996996 24.9382 0.790196
997997 −13.0503 −0.413308 −0.206654 0.978414i 0.566257π-0.566257\pi
−0.206654 + 0.978414i 0.566257π0.566257\pi
998998 50.4168 1.59592
999999 −10.3507 −0.327480
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 2535.2.a.bj.1.4 4
3.2 odd 2 7605.2.a.ci.1.1 4
13.2 odd 12 195.2.bb.b.121.4 8
13.7 odd 12 195.2.bb.b.166.4 yes 8
13.12 even 2 2535.2.a.bk.1.1 4
39.2 even 12 585.2.bu.d.316.1 8
39.20 even 12 585.2.bu.d.361.1 8
39.38 odd 2 7605.2.a.ch.1.4 4
65.2 even 12 975.2.w.h.199.1 8
65.7 even 12 975.2.w.i.49.4 8
65.28 even 12 975.2.w.i.199.4 8
65.33 even 12 975.2.w.h.49.1 8
65.54 odd 12 975.2.bc.j.901.1 8
65.59 odd 12 975.2.bc.j.751.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.bb.b.121.4 8 13.2 odd 12
195.2.bb.b.166.4 yes 8 13.7 odd 12
585.2.bu.d.316.1 8 39.2 even 12
585.2.bu.d.361.1 8 39.20 even 12
975.2.w.h.49.1 8 65.33 even 12
975.2.w.h.199.1 8 65.2 even 12
975.2.w.i.49.4 8 65.7 even 12
975.2.w.i.199.4 8 65.28 even 12
975.2.bc.j.751.1 8 65.59 odd 12
975.2.bc.j.901.1 8 65.54 odd 12
2535.2.a.bj.1.4 4 1.1 even 1 trivial
2535.2.a.bk.1.1 4 13.12 even 2
7605.2.a.ch.1.4 4 39.38 odd 2
7605.2.a.ci.1.1 4 3.2 odd 2