Properties

Label 1881.2.a.r.1.7
Level 18811881
Weight 22
Character 1881.1
Self dual yes
Analytic conductor 15.02015.020
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] = [1881,2,Mod(1,1881)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1881, 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("1881.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1881=321119 1881 = 3^{2} \cdot 11 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1881.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: 15.019860620215.0198606202
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: x7x69x5+7x4+22x312x29x1 x^{7} - x^{6} - 9x^{5} + 7x^{4} + 22x^{3} - 12x^{2} - 9x - 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.7
Root 0.327599-0.327599 of defining polynomial
Character χ\chi == 1881.1

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+2.44300q2+3.96824q4+0.800323q5+0.588123q7+4.80840q8+1.95519q101.00000q11+2.31077q13+1.43678q14+3.81044q16+6.57145q17+1.00000q19+3.17587q202.44300q224.10043q234.35948q25+5.64521q26+2.33381q28+4.73715q29+4.02301q310.307914q32+16.0540q34+0.470688q355.91366q37+2.44300q38+3.84827q40+11.1741q41+7.80457q433.96824q4410.0174q462.56595q476.65411q4910.6502q50+9.16969q5211.4718q530.800323q55+2.82793q56+11.5728q58+2.46799q598.36670q61+9.82821q628.37311q64+1.84936q652.82416q67+26.0771q68+1.14989q70+4.05247q718.44391q7314.4470q74+3.96824q760.588123q77+12.6320q79+3.04958q80+27.2983q820.0137315q83+5.25928q85+19.0666q864.80840q8810.7746q89+1.35902q9116.2715q926.26860q94+0.800323q957.37915q9716.2560q98+O(q100)q+2.44300 q^{2} +3.96824 q^{4} +0.800323 q^{5} +0.588123 q^{7} +4.80840 q^{8} +1.95519 q^{10} -1.00000 q^{11} +2.31077 q^{13} +1.43678 q^{14} +3.81044 q^{16} +6.57145 q^{17} +1.00000 q^{19} +3.17587 q^{20} -2.44300 q^{22} -4.10043 q^{23} -4.35948 q^{25} +5.64521 q^{26} +2.33381 q^{28} +4.73715 q^{29} +4.02301 q^{31} -0.307914 q^{32} +16.0540 q^{34} +0.470688 q^{35} -5.91366 q^{37} +2.44300 q^{38} +3.84827 q^{40} +11.1741 q^{41} +7.80457 q^{43} -3.96824 q^{44} -10.0174 q^{46} -2.56595 q^{47} -6.65411 q^{49} -10.6502 q^{50} +9.16969 q^{52} -11.4718 q^{53} -0.800323 q^{55} +2.82793 q^{56} +11.5728 q^{58} +2.46799 q^{59} -8.36670 q^{61} +9.82821 q^{62} -8.37311 q^{64} +1.84936 q^{65} -2.82416 q^{67} +26.0771 q^{68} +1.14989 q^{70} +4.05247 q^{71} -8.44391 q^{73} -14.4470 q^{74} +3.96824 q^{76} -0.588123 q^{77} +12.6320 q^{79} +3.04958 q^{80} +27.2983 q^{82} -0.0137315 q^{83} +5.25928 q^{85} +19.0666 q^{86} -4.80840 q^{88} -10.7746 q^{89} +1.35902 q^{91} -16.2715 q^{92} -6.26860 q^{94} +0.800323 q^{95} -7.37915 q^{97} -16.2560 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 7q+2q2+6q4+8q52q7+6q8+6q107q117q13+6q14+5q17+7q19+20q202q22+22q23+3q25+10q26+2q28+18q29+14q32+62q98+O(q100) 7 q + 2 q^{2} + 6 q^{4} + 8 q^{5} - 2 q^{7} + 6 q^{8} + 6 q^{10} - 7 q^{11} - 7 q^{13} + 6 q^{14} + 5 q^{17} + 7 q^{19} + 20 q^{20} - 2 q^{22} + 22 q^{23} + 3 q^{25} + 10 q^{26} + 2 q^{28} + 18 q^{29} + 14 q^{32}+ \cdots - 62 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 2.44300 1.72746 0.863730 0.503955i 0.168122π-0.168122\pi
0.863730 + 0.503955i 0.168122π0.168122\pi
33 0 0
44 3.96824 1.98412
55 0.800323 0.357915 0.178958 0.983857i 0.442728π-0.442728\pi
0.178958 + 0.983857i 0.442728π0.442728\pi
66 0 0
77 0.588123 0.222290 0.111145 0.993804i 0.464548π-0.464548\pi
0.111145 + 0.993804i 0.464548π0.464548\pi
88 4.80840 1.70003
99 0 0
1010 1.95519 0.618284
1111 −1.00000 −0.301511
1212 0 0
1313 2.31077 0.640892 0.320446 0.947267i 0.396167π-0.396167\pi
0.320446 + 0.947267i 0.396167π0.396167\pi
1414 1.43678 0.383997
1515 0 0
1616 3.81044 0.952609
1717 6.57145 1.59381 0.796905 0.604104i 0.206469π-0.206469\pi
0.796905 + 0.604104i 0.206469π0.206469\pi
1818 0 0
1919 1.00000 0.229416
2020 3.17587 0.710146
2121 0 0
2222 −2.44300 −0.520849
2323 −4.10043 −0.855000 −0.427500 0.904015i 0.640606π-0.640606\pi
−0.427500 + 0.904015i 0.640606π0.640606\pi
2424 0 0
2525 −4.35948 −0.871897
2626 5.64521 1.10712
2727 0 0
2828 2.33381 0.441049
2929 4.73715 0.879666 0.439833 0.898079i 0.355038π-0.355038\pi
0.439833 + 0.898079i 0.355038π0.355038\pi
3030 0 0
3131 4.02301 0.722554 0.361277 0.932458i 0.382341π-0.382341\pi
0.361277 + 0.932458i 0.382341π0.382341\pi
3232 −0.307914 −0.0544320
3333 0 0
3434 16.0540 2.75324
3535 0.470688 0.0795608
3636 0 0
3737 −5.91366 −0.972199 −0.486099 0.873903i 0.661581π-0.661581\pi
−0.486099 + 0.873903i 0.661581π0.661581\pi
3838 2.44300 0.396307
3939 0 0
4040 3.84827 0.608465
4141 11.1741 1.74510 0.872551 0.488524i 0.162464π-0.162464\pi
0.872551 + 0.488524i 0.162464π0.162464\pi
4242 0 0
4343 7.80457 1.19019 0.595093 0.803657i 0.297115π-0.297115\pi
0.595093 + 0.803657i 0.297115π0.297115\pi
4444 −3.96824 −0.598234
4545 0 0
4646 −10.0174 −1.47698
4747 −2.56595 −0.374282 −0.187141 0.982333i 0.559922π-0.559922\pi
−0.187141 + 0.982333i 0.559922π0.559922\pi
4848 0 0
4949 −6.65411 −0.950587
5050 −10.6502 −1.50617
5151 0 0
5252 9.16969 1.27161
5353 −11.4718 −1.57578 −0.787889 0.615818i 0.788826π-0.788826\pi
−0.787889 + 0.615818i 0.788826π0.788826\pi
5454 0 0
5555 −0.800323 −0.107915
5656 2.82793 0.377898
5757 0 0
5858 11.5728 1.51959
5959 2.46799 0.321304 0.160652 0.987011i 0.448640π-0.448640\pi
0.160652 + 0.987011i 0.448640π0.448640\pi
6060 0 0
6161 −8.36670 −1.07125 −0.535623 0.844457i 0.679923π-0.679923\pi
−0.535623 + 0.844457i 0.679923π0.679923\pi
6262 9.82821 1.24818
6363 0 0
6464 −8.37311 −1.04664
6565 1.84936 0.229385
6666 0 0
6767 −2.82416 −0.345025 −0.172513 0.985007i 0.555189π-0.555189\pi
−0.172513 + 0.985007i 0.555189π0.555189\pi
6868 26.0771 3.16231
6969 0 0
7070 1.14989 0.137438
7171 4.05247 0.480939 0.240470 0.970657i 0.422699π-0.422699\pi
0.240470 + 0.970657i 0.422699π0.422699\pi
7272 0 0
7373 −8.44391 −0.988285 −0.494143 0.869381i 0.664518π-0.664518\pi
−0.494143 + 0.869381i 0.664518π0.664518\pi
7474 −14.4470 −1.67944
7575 0 0
7676 3.96824 0.455188
7777 −0.588123 −0.0670229
7878 0 0
7979 12.6320 1.42121 0.710603 0.703593i 0.248422π-0.248422\pi
0.710603 + 0.703593i 0.248422π0.248422\pi
8080 3.04958 0.340953
8181 0 0
8282 27.2983 3.01459
8383 −0.0137315 −0.00150723 −0.000753615 1.00000i 0.500240π-0.500240\pi
−0.000753615 1.00000i 0.500240π0.500240\pi
8484 0 0
8585 5.25928 0.570449
8686 19.0666 2.05600
8787 0 0
8888 −4.80840 −0.512577
8989 −10.7746 −1.14211 −0.571054 0.820912i 0.693465π-0.693465\pi
−0.571054 + 0.820912i 0.693465π0.693465\pi
9090 0 0
9191 1.35902 0.142464
9292 −16.2715 −1.69642
9393 0 0
9494 −6.26860 −0.646557
9595 0.800323 0.0821114
9696 0 0
9797 −7.37915 −0.749239 −0.374619 0.927179i 0.622227π-0.622227\pi
−0.374619 + 0.927179i 0.622227π0.622227\pi
9898 −16.2560 −1.64210
9999 0 0
100100 −17.2995 −1.72995
101101 −0.938512 −0.0933854 −0.0466927 0.998909i 0.514868π-0.514868\pi
−0.0466927 + 0.998909i 0.514868π0.514868\pi
102102 0 0
103103 10.0710 0.992323 0.496161 0.868230i 0.334742π-0.334742\pi
0.496161 + 0.868230i 0.334742π0.334742\pi
104104 11.1111 1.08953
105105 0 0
106106 −28.0257 −2.72209
107107 15.6571 1.51363 0.756817 0.653627i 0.226754π-0.226754\pi
0.756817 + 0.653627i 0.226754π0.226754\pi
108108 0 0
109109 −7.55580 −0.723714 −0.361857 0.932234i 0.617857π-0.617857\pi
−0.361857 + 0.932234i 0.617857π0.617857\pi
110110 −1.95519 −0.186420
111111 0 0
112112 2.24101 0.211755
113113 −16.3998 −1.54276 −0.771379 0.636375i 0.780433π-0.780433\pi
−0.771379 + 0.636375i 0.780433π0.780433\pi
114114 0 0
115115 −3.28167 −0.306017
116116 18.7981 1.74536
117117 0 0
118118 6.02928 0.555040
119119 3.86482 0.354288
120120 0 0
121121 1.00000 0.0909091
122122 −20.4398 −1.85054
123123 0 0
124124 15.9643 1.43363
125125 −7.49061 −0.669980
126126 0 0
127127 −12.5780 −1.11611 −0.558057 0.829802i 0.688453π-0.688453\pi
−0.558057 + 0.829802i 0.688453π0.688453\pi
128128 −19.8397 −1.75359
129129 0 0
130130 4.51799 0.396254
131131 −4.21358 −0.368142 −0.184071 0.982913i 0.558928π-0.558928\pi
−0.184071 + 0.982913i 0.558928π0.558928\pi
132132 0 0
133133 0.588123 0.0509967
134134 −6.89940 −0.596018
135135 0 0
136136 31.5982 2.70952
137137 −6.74711 −0.576444 −0.288222 0.957564i 0.593064π-0.593064\pi
−0.288222 + 0.957564i 0.593064π0.593064\pi
138138 0 0
139139 −18.3905 −1.55986 −0.779930 0.625867i 0.784745π-0.784745\pi
−0.779930 + 0.625867i 0.784745π0.784745\pi
140140 1.86780 0.157858
141141 0 0
142142 9.90016 0.830803
143143 −2.31077 −0.193236
144144 0 0
145145 3.79125 0.314846
146146 −20.6285 −1.70722
147147 0 0
148148 −23.4668 −1.92896
149149 22.6306 1.85397 0.926984 0.375101i 0.122392π-0.122392\pi
0.926984 + 0.375101i 0.122392π0.122392\pi
150150 0 0
151151 11.3444 0.923197 0.461599 0.887089i 0.347276π-0.347276\pi
0.461599 + 0.887089i 0.347276π0.347276\pi
152152 4.80840 0.390013
153153 0 0
154154 −1.43678 −0.115779
155155 3.21971 0.258613
156156 0 0
157157 3.14378 0.250901 0.125451 0.992100i 0.459962π-0.459962\pi
0.125451 + 0.992100i 0.459962π0.459962\pi
158158 30.8599 2.45508
159159 0 0
160160 −0.246430 −0.0194820
161161 −2.41156 −0.190058
162162 0 0
163163 −17.9653 −1.40715 −0.703576 0.710620i 0.748415π-0.748415\pi
−0.703576 + 0.710620i 0.748415π0.748415\pi
164164 44.3415 3.46249
165165 0 0
166166 −0.0335461 −0.00260368
167167 −7.19830 −0.557021 −0.278511 0.960433i 0.589841π-0.589841\pi
−0.278511 + 0.960433i 0.589841π0.589841\pi
168168 0 0
169169 −7.66034 −0.589257
170170 12.8484 0.985428
171171 0 0
172172 30.9704 2.36147
173173 −4.80689 −0.365461 −0.182731 0.983163i 0.558494π-0.558494\pi
−0.182731 + 0.983163i 0.558494π0.558494\pi
174174 0 0
175175 −2.56391 −0.193814
176176 −3.81044 −0.287222
177177 0 0
178178 −26.3224 −1.97295
179179 15.4138 1.15208 0.576040 0.817422i 0.304597π-0.304597\pi
0.576040 + 0.817422i 0.304597π0.304597\pi
180180 0 0
181181 1.03075 0.0766149 0.0383074 0.999266i 0.487803π-0.487803\pi
0.0383074 + 0.999266i 0.487803π0.487803\pi
182182 3.32008 0.246100
183183 0 0
184184 −19.7165 −1.45352
185185 −4.73283 −0.347965
186186 0 0
187187 −6.57145 −0.480552
188188 −10.1823 −0.742619
189189 0 0
190190 1.95519 0.141844
191191 21.9471 1.58803 0.794017 0.607895i 0.207986π-0.207986\pi
0.794017 + 0.607895i 0.207986π0.207986\pi
192192 0 0
193193 −14.3468 −1.03271 −0.516354 0.856375i 0.672711π-0.672711\pi
−0.516354 + 0.856375i 0.672711π0.672711\pi
194194 −18.0272 −1.29428
195195 0 0
196196 −26.4051 −1.88608
197197 7.47661 0.532687 0.266343 0.963878i 0.414185π-0.414185\pi
0.266343 + 0.963878i 0.414185π0.414185\pi
198198 0 0
199199 −12.9940 −0.921119 −0.460559 0.887629i 0.652351π-0.652351\pi
−0.460559 + 0.887629i 0.652351π0.652351\pi
200200 −20.9621 −1.48225
201201 0 0
202202 −2.29278 −0.161320
203203 2.78603 0.195541
204204 0 0
205205 8.94288 0.624598
206206 24.6034 1.71420
207207 0 0
208208 8.80504 0.610520
209209 −1.00000 −0.0691714
210210 0 0
211211 −27.9511 −1.92423 −0.962117 0.272636i 0.912105π-0.912105\pi
−0.962117 + 0.272636i 0.912105π0.912105\pi
212212 −45.5230 −3.12653
213213 0 0
214214 38.2504 2.61474
215215 6.24618 0.425986
216216 0 0
217217 2.36603 0.160616
218218 −18.4588 −1.25019
219219 0 0
220220 −3.17587 −0.214117
221221 15.1851 1.02146
222222 0 0
223223 11.3216 0.758150 0.379075 0.925366i 0.376242π-0.376242\pi
0.379075 + 0.925366i 0.376242π0.376242\pi
224224 −0.181091 −0.0120997
225225 0 0
226226 −40.0646 −2.66505
227227 −1.50898 −0.100154 −0.0500772 0.998745i 0.515947π-0.515947\pi
−0.0500772 + 0.998745i 0.515947π0.515947\pi
228228 0 0
229229 −21.2793 −1.40618 −0.703089 0.711102i 0.748196π-0.748196\pi
−0.703089 + 0.711102i 0.748196π0.748196\pi
230230 −8.01711 −0.528633
231231 0 0
232232 22.7781 1.49546
233233 25.8325 1.69234 0.846172 0.532910i 0.178902π-0.178902\pi
0.846172 + 0.532910i 0.178902π0.178902\pi
234234 0 0
235235 −2.05358 −0.133961
236236 9.79355 0.637506
237237 0 0
238238 9.44175 0.612018
239239 22.5612 1.45936 0.729682 0.683787i 0.239668π-0.239668\pi
0.729682 + 0.683787i 0.239668π0.239668\pi
240240 0 0
241241 1.23059 0.0792691 0.0396346 0.999214i 0.487381π-0.487381\pi
0.0396346 + 0.999214i 0.487381π0.487381\pi
242242 2.44300 0.157042
243243 0 0
244244 −33.2011 −2.12548
245245 −5.32544 −0.340230
246246 0 0
247247 2.31077 0.147031
248248 19.3443 1.22836
249249 0 0
250250 −18.2995 −1.15736
251251 3.67960 0.232254 0.116127 0.993234i 0.462952π-0.462952\pi
0.116127 + 0.993234i 0.462952π0.462952\pi
252252 0 0
253253 4.10043 0.257792
254254 −30.7280 −1.92804
255255 0 0
256256 −31.7220 −1.98263
257257 9.00012 0.561412 0.280706 0.959794i 0.409431π-0.409431\pi
0.280706 + 0.959794i 0.409431π0.409431\pi
258258 0 0
259259 −3.47796 −0.216110
260260 7.33871 0.455127
261261 0 0
262262 −10.2938 −0.635950
263263 −0.317206 −0.0195598 −0.00977989 0.999952i 0.503113π-0.503113\pi
−0.00977989 + 0.999952i 0.503113π0.503113\pi
264264 0 0
265265 −9.18117 −0.563994
266266 1.43678 0.0880949
267267 0 0
268268 −11.2069 −0.684572
269269 −17.9973 −1.09731 −0.548656 0.836048i 0.684860π-0.684860\pi
−0.548656 + 0.836048i 0.684860π0.684860\pi
270270 0 0
271271 −0.262808 −0.0159644 −0.00798222 0.999968i 0.502541π-0.502541\pi
−0.00798222 + 0.999968i 0.502541π0.502541\pi
272272 25.0401 1.51828
273273 0 0
274274 −16.4832 −0.995785
275275 4.35948 0.262887
276276 0 0
277277 −6.20953 −0.373094 −0.186547 0.982446i 0.559730π-0.559730\pi
−0.186547 + 0.982446i 0.559730π0.559730\pi
278278 −44.9279 −2.69460
279279 0 0
280280 2.26326 0.135256
281281 −7.29039 −0.434908 −0.217454 0.976071i 0.569775π-0.569775\pi
−0.217454 + 0.976071i 0.569775π0.569775\pi
282282 0 0
283283 −15.9557 −0.948468 −0.474234 0.880399i 0.657275π-0.657275\pi
−0.474234 + 0.880399i 0.657275π0.657275\pi
284284 16.0811 0.954241
285285 0 0
286286 −5.64521 −0.333808
287287 6.57175 0.387918
288288 0 0
289289 26.1839 1.54023
290290 9.26201 0.543884
291291 0 0
292292 −33.5075 −1.96088
293293 2.82613 0.165105 0.0825523 0.996587i 0.473693π-0.473693\pi
0.0825523 + 0.996587i 0.473693π0.473693\pi
294294 0 0
295295 1.97518 0.115000
296296 −28.4352 −1.65276
297297 0 0
298298 55.2864 3.20266
299299 −9.47516 −0.547963
300300 0 0
301301 4.59005 0.264566
302302 27.7144 1.59479
303303 0 0
304304 3.81044 0.218544
305305 −6.69606 −0.383415
306306 0 0
307307 16.7858 0.958016 0.479008 0.877811i 0.340997π-0.340997\pi
0.479008 + 0.877811i 0.340997π0.340997\pi
308308 −2.33381 −0.132981
309309 0 0
310310 7.86574 0.446744
311311 14.6719 0.831970 0.415985 0.909372i 0.363437π-0.363437\pi
0.415985 + 0.909372i 0.363437π0.363437\pi
312312 0 0
313313 27.4425 1.55114 0.775572 0.631259i 0.217462π-0.217462\pi
0.775572 + 0.631259i 0.217462π0.217462\pi
314314 7.68026 0.433422
315315 0 0
316316 50.1266 2.81984
317317 3.15940 0.177450 0.0887249 0.996056i 0.471721π-0.471721\pi
0.0887249 + 0.996056i 0.471721π0.471721\pi
318318 0 0
319319 −4.73715 −0.265229
320320 −6.70119 −0.374608
321321 0 0
322322 −5.89144 −0.328317
323323 6.57145 0.365645
324324 0 0
325325 −10.0738 −0.558792
326326 −43.8892 −2.43080
327327 0 0
328328 53.7295 2.96672
329329 −1.50909 −0.0831989
330330 0 0
331331 9.26332 0.509158 0.254579 0.967052i 0.418063π-0.418063\pi
0.254579 + 0.967052i 0.418063π0.418063\pi
332332 −0.0544899 −0.00299052
333333 0 0
334334 −17.5854 −0.962232
335335 −2.26024 −0.123490
336336 0 0
337337 −13.9986 −0.762555 −0.381277 0.924461i 0.624516π-0.624516\pi
−0.381277 + 0.924461i 0.624516π0.624516\pi
338338 −18.7142 −1.01792
339339 0 0
340340 20.8701 1.13184
341341 −4.02301 −0.217858
342342 0 0
343343 −8.03030 −0.433595
344344 37.5275 2.02335
345345 0 0
346346 −11.7432 −0.631320
347347 30.9325 1.66054 0.830272 0.557358i 0.188185π-0.188185\pi
0.830272 + 0.557358i 0.188185π0.188185\pi
348348 0 0
349349 −17.3337 −0.927852 −0.463926 0.885874i 0.653560π-0.653560\pi
−0.463926 + 0.885874i 0.653560π0.653560\pi
350350 −6.26363 −0.334805
351351 0 0
352352 0.307914 0.0164119
353353 −7.09753 −0.377763 −0.188882 0.982000i 0.560486π-0.560486\pi
−0.188882 + 0.982000i 0.560486π0.560486\pi
354354 0 0
355355 3.24328 0.172135
356356 −42.7563 −2.26608
357357 0 0
358358 37.6558 1.99017
359359 −25.6409 −1.35328 −0.676638 0.736316i 0.736564π-0.736564\pi
−0.676638 + 0.736316i 0.736564π0.736564\pi
360360 0 0
361361 1.00000 0.0526316
362362 2.51811 0.132349
363363 0 0
364364 5.39290 0.282665
365365 −6.75785 −0.353722
366366 0 0
367367 8.81606 0.460195 0.230097 0.973168i 0.426096π-0.426096\pi
0.230097 + 0.973168i 0.426096π0.426096\pi
368368 −15.6244 −0.814481
369369 0 0
370370 −11.5623 −0.601095
371371 −6.74685 −0.350279
372372 0 0
373373 14.5020 0.750887 0.375443 0.926845i 0.377490π-0.377490\pi
0.375443 + 0.926845i 0.377490π0.377490\pi
374374 −16.0540 −0.830134
375375 0 0
376376 −12.3381 −0.636289
377377 10.9465 0.563771
378378 0 0
379379 10.5223 0.540495 0.270248 0.962791i 0.412894π-0.412894\pi
0.270248 + 0.962791i 0.412894π0.412894\pi
380380 3.17587 0.162919
381381 0 0
382382 53.6166 2.74327
383383 −27.5133 −1.40586 −0.702932 0.711257i 0.748126π-0.748126\pi
−0.702932 + 0.711257i 0.748126π0.748126\pi
384384 0 0
385385 −0.470688 −0.0239885
386386 −35.0493 −1.78396
387387 0 0
388388 −29.2822 −1.48658
389389 −6.36132 −0.322532 −0.161266 0.986911i 0.551558π-0.551558\pi
−0.161266 + 0.986911i 0.551558π0.551558\pi
390390 0 0
391391 −26.9458 −1.36271
392392 −31.9956 −1.61602
393393 0 0
394394 18.2653 0.920195
395395 10.1096 0.508671
396396 0 0
397397 18.5939 0.933203 0.466601 0.884468i 0.345478π-0.345478\pi
0.466601 + 0.884468i 0.345478π0.345478\pi
398398 −31.7443 −1.59120
399399 0 0
400400 −16.6115 −0.830577
401401 17.7160 0.884695 0.442348 0.896844i 0.354146π-0.354146\pi
0.442348 + 0.896844i 0.354146π0.354146\pi
402402 0 0
403403 9.29626 0.463079
404404 −3.72424 −0.185288
405405 0 0
406406 6.80626 0.337789
407407 5.91366 0.293129
408408 0 0
409409 −22.6211 −1.11854 −0.559271 0.828985i 0.688919π-0.688919\pi
−0.559271 + 0.828985i 0.688919π0.688919\pi
410410 21.8474 1.07897
411411 0 0
412412 39.9640 1.96889
413413 1.45148 0.0714226
414414 0 0
415415 −0.0109896 −0.000539460 0
416416 −0.711518 −0.0348850
417417 0 0
418418 −2.44300 −0.119491
419419 −19.1301 −0.934569 −0.467284 0.884107i 0.654768π-0.654768\pi
−0.467284 + 0.884107i 0.654768π0.654768\pi
420420 0 0
421421 16.6696 0.812428 0.406214 0.913778i 0.366849π-0.366849\pi
0.406214 + 0.913778i 0.366849π0.366849\pi
422422 −68.2845 −3.32404
423423 0 0
424424 −55.1612 −2.67886
425425 −28.6481 −1.38964
426426 0 0
427427 −4.92065 −0.238127
428428 62.1313 3.00323
429429 0 0
430430 15.2594 0.735873
431431 −19.6828 −0.948087 −0.474044 0.880501i 0.657206π-0.657206\pi
−0.474044 + 0.880501i 0.657206π0.657206\pi
432432 0 0
433433 −19.6530 −0.944462 −0.472231 0.881475i 0.656551π-0.656551\pi
−0.472231 + 0.881475i 0.656551π0.656551\pi
434434 5.78020 0.277458
435435 0 0
436436 −29.9832 −1.43593
437437 −4.10043 −0.196150
438438 0 0
439439 −6.05821 −0.289143 −0.144571 0.989494i 0.546180π-0.546180\pi
−0.144571 + 0.989494i 0.546180π0.546180\pi
440440 −3.84827 −0.183459
441441 0 0
442442 37.0972 1.76453
443443 −7.01333 −0.333214 −0.166607 0.986023i 0.553281π-0.553281\pi
−0.166607 + 0.986023i 0.553281π0.553281\pi
444444 0 0
445445 −8.62318 −0.408778
446446 27.6586 1.30967
447447 0 0
448448 −4.92442 −0.232657
449449 16.7703 0.791439 0.395719 0.918372i 0.370495π-0.370495\pi
0.395719 + 0.918372i 0.370495π0.370495\pi
450450 0 0
451451 −11.1741 −0.526168
452452 −65.0781 −3.06102
453453 0 0
454454 −3.68643 −0.173013
455455 1.08765 0.0509899
456456 0 0
457457 31.9584 1.49495 0.747476 0.664289i 0.231265π-0.231265\pi
0.747476 + 0.664289i 0.231265π0.231265\pi
458458 −51.9854 −2.42912
459459 0 0
460460 −13.0225 −0.607175
461461 13.3466 0.621612 0.310806 0.950473i 0.399401π-0.399401\pi
0.310806 + 0.950473i 0.399401π0.399401\pi
462462 0 0
463463 −27.6018 −1.28277 −0.641383 0.767221i 0.721639π-0.721639\pi
−0.641383 + 0.767221i 0.721639π0.721639\pi
464464 18.0506 0.837978
465465 0 0
466466 63.1087 2.92346
467467 23.2142 1.07422 0.537112 0.843511i 0.319515π-0.319515\pi
0.537112 + 0.843511i 0.319515π0.319515\pi
468468 0 0
469469 −1.66095 −0.0766956
470470 −5.01690 −0.231412
471471 0 0
472472 11.8671 0.546226
473473 −7.80457 −0.358855
474474 0 0
475475 −4.35948 −0.200027
476476 15.3365 0.702949
477477 0 0
478478 55.1170 2.52099
479479 −4.07012 −0.185969 −0.0929843 0.995668i 0.529641π-0.529641\pi
−0.0929843 + 0.995668i 0.529641π0.529641\pi
480480 0 0
481481 −13.6651 −0.623075
482482 3.00632 0.136934
483483 0 0
484484 3.96824 0.180374
485485 −5.90570 −0.268164
486486 0 0
487487 −7.50704 −0.340177 −0.170088 0.985429i 0.554405π-0.554405\pi
−0.170088 + 0.985429i 0.554405π0.554405\pi
488488 −40.2305 −1.82115
489489 0 0
490490 −13.0100 −0.587733
491491 −16.2778 −0.734606 −0.367303 0.930101i 0.619719π-0.619719\pi
−0.367303 + 0.930101i 0.619719π0.619719\pi
492492 0 0
493493 31.1299 1.40202
494494 5.64521 0.253990
495495 0 0
496496 15.3294 0.688312
497497 2.38335 0.106908
498498 0 0
499499 41.0613 1.83816 0.919079 0.394073i 0.128934π-0.128934\pi
0.919079 + 0.394073i 0.128934π0.128934\pi
500500 −29.7245 −1.32932
501501 0 0
502502 8.98926 0.401210
503503 29.1287 1.29878 0.649392 0.760454i 0.275024π-0.275024\pi
0.649392 + 0.760454i 0.275024π0.275024\pi
504504 0 0
505505 −0.751112 −0.0334241
506506 10.0174 0.445326
507507 0 0
508508 −49.9124 −2.21450
509509 −14.3959 −0.638087 −0.319044 0.947740i 0.603362π-0.603362\pi
−0.319044 + 0.947740i 0.603362π0.603362\pi
510510 0 0
511511 −4.96606 −0.219686
512512 −37.8175 −1.67131
513513 0 0
514514 21.9873 0.969817
515515 8.06003 0.355167
516516 0 0
517517 2.56595 0.112850
518518 −8.49664 −0.373321
519519 0 0
520520 8.89247 0.389961
521521 20.3390 0.891067 0.445534 0.895265i 0.353014π-0.353014\pi
0.445534 + 0.895265i 0.353014π0.353014\pi
522522 0 0
523523 45.0421 1.96955 0.984776 0.173829i 0.0556140π-0.0556140\pi
0.984776 + 0.173829i 0.0556140π0.0556140\pi
524524 −16.7205 −0.730437
525525 0 0
526526 −0.774934 −0.0337887
527527 26.4370 1.15161
528528 0 0
529529 −6.18643 −0.268975
530530 −22.4296 −0.974278
531531 0 0
532532 2.33381 0.101184
533533 25.8208 1.11842
534534 0 0
535535 12.5308 0.541752
536536 −13.5797 −0.586552
537537 0 0
538538 −43.9673 −1.89556
539539 6.65411 0.286613
540540 0 0
541541 10.4800 0.450569 0.225284 0.974293i 0.427669π-0.427669\pi
0.225284 + 0.974293i 0.427669π0.427669\pi
542542 −0.642039 −0.0275779
543543 0 0
544544 −2.02344 −0.0867542
545545 −6.04708 −0.259028
546546 0 0
547547 −9.59366 −0.410195 −0.205098 0.978742i 0.565751π-0.565751\pi
−0.205098 + 0.978742i 0.565751π0.565751\pi
548548 −26.7741 −1.14373
549549 0 0
550550 10.6502 0.454126
551551 4.73715 0.201809
552552 0 0
553553 7.42915 0.315920
554554 −15.1699 −0.644506
555555 0 0
556556 −72.9778 −3.09495
557557 10.5593 0.447413 0.223706 0.974657i 0.428184π-0.428184\pi
0.223706 + 0.974657i 0.428184π0.428184\pi
558558 0 0
559559 18.0346 0.762781
560560 1.79353 0.0757904
561561 0 0
562562 −17.8104 −0.751287
563563 −36.1211 −1.52232 −0.761162 0.648562i 0.775371π-0.775371\pi
−0.761162 + 0.648562i 0.775371π0.775371\pi
564564 0 0
565565 −13.1251 −0.552177
566566 −38.9797 −1.63844
567567 0 0
568568 19.4859 0.817609
569569 2.74039 0.114883 0.0574416 0.998349i 0.481706π-0.481706\pi
0.0574416 + 0.998349i 0.481706π0.481706\pi
570570 0 0
571571 4.82157 0.201776 0.100888 0.994898i 0.467832π-0.467832\pi
0.100888 + 0.994898i 0.467832π0.467832\pi
572572 −9.16969 −0.383404
573573 0 0
574574 16.0548 0.670113
575575 17.8758 0.745472
576576 0 0
577577 −27.2712 −1.13531 −0.567657 0.823265i 0.692150π-0.692150\pi
−0.567657 + 0.823265i 0.692150π0.692150\pi
578578 63.9673 2.66069
579579 0 0
580580 15.0446 0.624692
581581 −0.00807582 −0.000335041 0
582582 0 0
583583 11.4718 0.475115
584584 −40.6017 −1.68011
585585 0 0
586586 6.90424 0.285212
587587 21.7232 0.896613 0.448307 0.893880i 0.352027π-0.352027\pi
0.448307 + 0.893880i 0.352027π0.352027\pi
588588 0 0
589589 4.02301 0.165765
590590 4.82537 0.198657
591591 0 0
592592 −22.5336 −0.926126
593593 −19.5478 −0.802730 −0.401365 0.915918i 0.631464π-0.631464\pi
−0.401365 + 0.915918i 0.631464π0.631464\pi
594594 0 0
595595 3.09310 0.126805
596596 89.8034 3.67849
597597 0 0
598598 −23.1478 −0.946584
599599 5.21220 0.212965 0.106482 0.994315i 0.466041π-0.466041\pi
0.106482 + 0.994315i 0.466041π0.466041\pi
600600 0 0
601601 41.4095 1.68913 0.844564 0.535454i 0.179860π-0.179860\pi
0.844564 + 0.535454i 0.179860π0.179860\pi
602602 11.2135 0.457027
603603 0 0
604604 45.0174 1.83173
605605 0.800323 0.0325377
606606 0 0
607607 26.5388 1.07718 0.538589 0.842568i 0.318957π-0.318957\pi
0.538589 + 0.842568i 0.318957π0.318957\pi
608608 −0.307914 −0.0124875
609609 0 0
610610 −16.3585 −0.662335
611611 −5.92931 −0.239874
612612 0 0
613613 −17.4161 −0.703428 −0.351714 0.936107i 0.614401π-0.614401\pi
−0.351714 + 0.936107i 0.614401π0.614401\pi
614614 41.0076 1.65493
615615 0 0
616616 −2.82793 −0.113941
617617 20.2862 0.816694 0.408347 0.912827i 0.366105π-0.366105\pi
0.408347 + 0.912827i 0.366105π0.366105\pi
618618 0 0
619619 14.6703 0.589648 0.294824 0.955551i 0.404739π-0.404739\pi
0.294824 + 0.955551i 0.404739π0.404739\pi
620620 12.7766 0.513119
621621 0 0
622622 35.8435 1.43719
623623 −6.33681 −0.253879
624624 0 0
625625 15.8025 0.632101
626626 67.0420 2.67954
627627 0 0
628628 12.4753 0.497818
629629 −38.8613 −1.54950
630630 0 0
631631 −6.86206 −0.273174 −0.136587 0.990628i 0.543613π-0.543613\pi
−0.136587 + 0.990628i 0.543613π0.543613\pi
632632 60.7395 2.41609
633633 0 0
634634 7.71842 0.306538
635635 −10.0664 −0.399474
636636 0 0
637637 −15.3761 −0.609224
638638 −11.5728 −0.458173
639639 0 0
640640 −15.8781 −0.627638
641641 14.2086 0.561206 0.280603 0.959824i 0.409466π-0.409466\pi
0.280603 + 0.959824i 0.409466π0.409466\pi
642642 0 0
643643 28.5456 1.12573 0.562864 0.826549i 0.309699π-0.309699\pi
0.562864 + 0.826549i 0.309699π0.309699\pi
644644 −9.56965 −0.377097
645645 0 0
646646 16.0540 0.631638
647647 16.0786 0.632116 0.316058 0.948740i 0.397641π-0.397641\pi
0.316058 + 0.948740i 0.397641π0.397641\pi
648648 0 0
649649 −2.46799 −0.0968769
650650 −24.6102 −0.965291
651651 0 0
652652 −71.2907 −2.79196
653653 −31.3855 −1.22821 −0.614106 0.789224i 0.710483π-0.710483\pi
−0.614106 + 0.789224i 0.710483π0.710483\pi
654654 0 0
655655 −3.37222 −0.131764
656656 42.5782 1.66240
657657 0 0
658658 −3.68671 −0.143723
659659 1.37686 0.0536349 0.0268174 0.999640i 0.491463π-0.491463\pi
0.0268174 + 0.999640i 0.491463π0.491463\pi
660660 0 0
661661 −20.2558 −0.787860 −0.393930 0.919141i 0.628885π-0.628885\pi
−0.393930 + 0.919141i 0.628885π0.628885\pi
662662 22.6303 0.879551
663663 0 0
664664 −0.0660266 −0.00256233
665665 0.470688 0.0182525
666666 0 0
667667 −19.4244 −0.752115
668668 −28.5646 −1.10520
669669 0 0
670670 −5.52175 −0.213324
671671 8.36670 0.322993
672672 0 0
673673 −10.4733 −0.403715 −0.201858 0.979415i 0.564698π-0.564698\pi
−0.201858 + 0.979415i 0.564698π0.564698\pi
674674 −34.1987 −1.31728
675675 0 0
676676 −30.3981 −1.16916
677677 10.1457 0.389933 0.194966 0.980810i 0.437540π-0.437540\pi
0.194966 + 0.980810i 0.437540π0.437540\pi
678678 0 0
679679 −4.33985 −0.166548
680680 25.2887 0.969778
681681 0 0
682682 −9.82821 −0.376342
683683 12.9495 0.495499 0.247750 0.968824i 0.420309π-0.420309\pi
0.247750 + 0.968824i 0.420309π0.420309\pi
684684 0 0
685685 −5.39986 −0.206318
686686 −19.6180 −0.749019
687687 0 0
688688 29.7388 1.13378
689689 −26.5088 −1.00990
690690 0 0
691691 32.7663 1.24649 0.623245 0.782027i 0.285814π-0.285814\pi
0.623245 + 0.782027i 0.285814π0.285814\pi
692692 −19.0749 −0.725119
693693 0 0
694694 75.5681 2.86852
695695 −14.7183 −0.558298
696696 0 0
697697 73.4300 2.78136
698698 −42.3462 −1.60283
699699 0 0
700700 −10.1742 −0.384549
701701 −0.0542369 −0.00204850 −0.00102425 0.999999i 0.500326π-0.500326\pi
−0.00102425 + 0.999999i 0.500326π0.500326\pi
702702 0 0
703703 −5.91366 −0.223038
704704 8.37311 0.315573
705705 0 0
706706 −17.3392 −0.652571
707707 −0.551960 −0.0207586
708708 0 0
709709 9.61093 0.360946 0.180473 0.983580i 0.442237π-0.442237\pi
0.180473 + 0.983580i 0.442237π0.442237\pi
710710 7.92333 0.297357
711711 0 0
712712 −51.8087 −1.94161
713713 −16.4961 −0.617784
714714 0 0
715715 −1.84936 −0.0691622
716716 61.1655 2.28586
717717 0 0
718718 −62.6407 −2.33773
719719 22.3065 0.831892 0.415946 0.909389i 0.363450π-0.363450\pi
0.415946 + 0.909389i 0.363450π0.363450\pi
720720 0 0
721721 5.92298 0.220583
722722 2.44300 0.0909190
723723 0 0
724724 4.09025 0.152013
725725 −20.6515 −0.766978
726726 0 0
727727 36.6445 1.35907 0.679534 0.733644i 0.262182π-0.262182\pi
0.679534 + 0.733644i 0.262182π0.262182\pi
728728 6.53470 0.242192
729729 0 0
730730 −16.5094 −0.611041
731731 51.2874 1.89693
732732 0 0
733733 31.2843 1.15551 0.577755 0.816210i 0.303929π-0.303929\pi
0.577755 + 0.816210i 0.303929π0.303929\pi
734734 21.5376 0.794968
735735 0 0
736736 1.26258 0.0465393
737737 2.82416 0.104029
738738 0 0
739739 41.0054 1.50841 0.754205 0.656639i 0.228023π-0.228023\pi
0.754205 + 0.656639i 0.228023π0.228023\pi
740740 −18.7810 −0.690403
741741 0 0
742742 −16.4825 −0.605093
743743 39.7923 1.45984 0.729918 0.683535i 0.239558π-0.239558\pi
0.729918 + 0.683535i 0.239558π0.239558\pi
744744 0 0
745745 18.1117 0.663563
746746 35.4284 1.29713
747747 0 0
748748 −26.0771 −0.953472
749749 9.20833 0.336465
750750 0 0
751751 3.25214 0.118672 0.0593361 0.998238i 0.481102π-0.481102\pi
0.0593361 + 0.998238i 0.481102π0.481102\pi
752752 −9.77737 −0.356544
753753 0 0
754754 26.7422 0.973893
755755 9.07921 0.330426
756756 0 0
757757 26.5536 0.965108 0.482554 0.875866i 0.339709π-0.339709\pi
0.482554 + 0.875866i 0.339709π0.339709\pi
758758 25.7060 0.933684
759759 0 0
760760 3.84827 0.139591
761761 3.21425 0.116516 0.0582582 0.998302i 0.481445π-0.481445\pi
0.0582582 + 0.998302i 0.481445π0.481445\pi
762762 0 0
763763 −4.44374 −0.160874
764764 87.0912 3.15085
765765 0 0
766766 −67.2149 −2.42857
767767 5.70295 0.205921
768768 0 0
769769 31.9235 1.15119 0.575596 0.817734i 0.304770π-0.304770\pi
0.575596 + 0.817734i 0.304770π0.304770\pi
770770 −1.14989 −0.0414392
771771 0 0
772772 −56.9317 −2.04902
773773 2.02574 0.0728609 0.0364305 0.999336i 0.488401π-0.488401\pi
0.0364305 + 0.999336i 0.488401π0.488401\pi
774774 0 0
775775 −17.5383 −0.629993
776776 −35.4819 −1.27373
777777 0 0
778778 −15.5407 −0.557161
779779 11.1741 0.400354
780780 0 0
781781 −4.05247 −0.145009
782782 −65.8285 −2.35402
783783 0 0
784784 −25.3551 −0.905538
785785 2.51604 0.0898013
786786 0 0
787787 −48.7384 −1.73734 −0.868668 0.495395i 0.835023π-0.835023\pi
−0.868668 + 0.495395i 0.835023π0.835023\pi
788788 29.6690 1.05691
789789 0 0
790790 24.6978 0.878710
791791 −9.64507 −0.342939
792792 0 0
793793 −19.3335 −0.686554
794794 45.4249 1.61207
795795 0 0
796796 −51.5632 −1.82761
797797 −8.62944 −0.305670 −0.152835 0.988252i 0.548840π-0.548840\pi
−0.152835 + 0.988252i 0.548840π0.548840\pi
798798 0 0
799799 −16.8620 −0.596534
800800 1.34234 0.0474590
801801 0 0
802802 43.2802 1.52828
803803 8.44391 0.297979
804804 0 0
805805 −1.93003 −0.0680245
806806 22.7107 0.799951
807807 0 0
808808 −4.51274 −0.158758
809809 46.5536 1.63674 0.818369 0.574693i 0.194879π-0.194879\pi
0.818369 + 0.574693i 0.194879π0.194879\pi
810810 0 0
811811 −16.4402 −0.577292 −0.288646 0.957436i 0.593205π-0.593205\pi
−0.288646 + 0.957436i 0.593205π0.593205\pi
812812 11.0556 0.387976
813813 0 0
814814 14.4470 0.506369
815815 −14.3781 −0.503641
816816 0 0
817817 7.80457 0.273047
818818 −55.2633 −1.93224
819819 0 0
820820 35.4875 1.23928
821821 7.61708 0.265838 0.132919 0.991127i 0.457565π-0.457565\pi
0.132919 + 0.991127i 0.457565π0.457565\pi
822822 0 0
823823 6.33183 0.220714 0.110357 0.993892i 0.464801π-0.464801\pi
0.110357 + 0.993892i 0.464801π0.464801\pi
824824 48.4253 1.68698
825825 0 0
826826 3.54596 0.123380
827827 −1.70709 −0.0593615 −0.0296807 0.999559i 0.509449π-0.509449\pi
−0.0296807 + 0.999559i 0.509449π0.509449\pi
828828 0 0
829829 −53.8836 −1.87145 −0.935727 0.352724i 0.885255π-0.885255\pi
−0.935727 + 0.352724i 0.885255π0.885255\pi
830830 −0.0268477 −0.000931896 0
831831 0 0
832832 −19.3483 −0.670782
833833 −43.7271 −1.51506
834834 0 0
835835 −5.76096 −0.199366
836836 −3.96824 −0.137244
837837 0 0
838838 −46.7349 −1.61443
839839 40.6382 1.40299 0.701494 0.712676i 0.252517π-0.252517\pi
0.701494 + 0.712676i 0.252517π0.252517\pi
840840 0 0
841841 −6.55942 −0.226187
842842 40.7238 1.40344
843843 0 0
844844 −110.917 −3.81791
845845 −6.13074 −0.210904
846846 0 0
847847 0.588123 0.0202082
848848 −43.7127 −1.50110
849849 0 0
850850 −69.9873 −2.40054
851851 24.2486 0.831230
852852 0 0
853853 44.3438 1.51830 0.759151 0.650915i 0.225614π-0.225614\pi
0.759151 + 0.650915i 0.225614π0.225614\pi
854854 −12.0211 −0.411355
855855 0 0
856856 75.2858 2.57322
857857 32.4832 1.10961 0.554803 0.831982i 0.312794π-0.312794\pi
0.554803 + 0.831982i 0.312794π0.312794\pi
858858 0 0
859859 −4.04454 −0.137998 −0.0689990 0.997617i 0.521981π-0.521981\pi
−0.0689990 + 0.997617i 0.521981π0.521981\pi
860860 24.7863 0.845206
861861 0 0
862862 −48.0850 −1.63778
863863 −29.4268 −1.00170 −0.500850 0.865534i 0.666979π-0.666979\pi
−0.500850 + 0.865534i 0.666979π0.666979\pi
864864 0 0
865865 −3.84707 −0.130804
866866 −48.0122 −1.63152
867867 0 0
868868 9.38896 0.318682
869869 −12.6320 −0.428510
870870 0 0
871871 −6.52597 −0.221124
872872 −36.3313 −1.23033
873873 0 0
874874 −10.0174 −0.338842
875875 −4.40540 −0.148930
876876 0 0
877877 31.1047 1.05033 0.525166 0.851000i 0.324003π-0.324003\pi
0.525166 + 0.851000i 0.324003π0.324003\pi
878878 −14.8002 −0.499483
879879 0 0
880880 −3.04958 −0.102801
881881 −25.1336 −0.846774 −0.423387 0.905949i 0.639159π-0.639159\pi
−0.423387 + 0.905949i 0.639159π0.639159\pi
882882 0 0
883883 −38.8941 −1.30889 −0.654446 0.756109i 0.727098π-0.727098\pi
−0.654446 + 0.756109i 0.727098π0.727098\pi
884884 60.2581 2.02670
885885 0 0
886886 −17.1336 −0.575613
887887 −38.1500 −1.28095 −0.640476 0.767978i 0.721263π-0.721263\pi
−0.640476 + 0.767978i 0.721263π0.721263\pi
888888 0 0
889889 −7.39740 −0.248101
890890 −21.0664 −0.706147
891891 0 0
892892 44.9268 1.50426
893893 −2.56595 −0.0858661
894894 0 0
895895 12.3360 0.412347
896896 −11.6682 −0.389806
897897 0 0
898898 40.9698 1.36718
899899 19.0576 0.635607
900900 0 0
901901 −75.3865 −2.51149
902902 −27.2983 −0.908934
903903 0 0
904904 −78.8566 −2.62273
905905 0.824931 0.0274216
906906 0 0
907907 −2.68659 −0.0892067 −0.0446034 0.999005i 0.514202π-0.514202\pi
−0.0446034 + 0.999005i 0.514202π0.514202\pi
908908 −5.98798 −0.198718
909909 0 0
910910 2.65713 0.0880831
911911 38.5099 1.27589 0.637945 0.770082i 0.279785π-0.279785\pi
0.637945 + 0.770082i 0.279785π0.279785\pi
912912 0 0
913913 0.0137315 0.000454447 0
914914 78.0744 2.58247
915915 0 0
916916 −84.4414 −2.79002
917917 −2.47810 −0.0818341
918918 0 0
919919 3.56656 0.117650 0.0588250 0.998268i 0.481265π-0.481265\pi
0.0588250 + 0.998268i 0.481265π0.481265\pi
920920 −15.7796 −0.520238
921921 0 0
922922 32.6056 1.07381
923923 9.36432 0.308230
924924 0 0
925925 25.7805 0.847657
926926 −67.4312 −2.21593
927927 0 0
928928 −1.45863 −0.0478820
929929 27.3654 0.897829 0.448914 0.893575i 0.351811π-0.351811\pi
0.448914 + 0.893575i 0.351811π0.351811\pi
930930 0 0
931931 −6.65411 −0.218080
932932 102.510 3.35781
933933 0 0
934934 56.7122 1.85568
935935 −5.25928 −0.171997
936936 0 0
937937 −47.8748 −1.56400 −0.782001 0.623277i 0.785801π-0.785801\pi
−0.782001 + 0.623277i 0.785801π0.785801\pi
938938 −4.05770 −0.132489
939939 0 0
940940 −8.14911 −0.265795
941941 7.37140 0.240301 0.120150 0.992756i 0.461662π-0.461662\pi
0.120150 + 0.992756i 0.461662π0.461662\pi
942942 0 0
943943 −45.8187 −1.49206
944944 9.40410 0.306077
945945 0 0
946946 −19.0666 −0.619907
947947 −56.4061 −1.83295 −0.916475 0.400091i 0.868978π-0.868978\pi
−0.916475 + 0.400091i 0.868978π0.868978\pi
948948 0 0
949949 −19.5119 −0.633384
950950 −10.6502 −0.345538
951951 0 0
952952 18.5836 0.602298
953953 −37.0454 −1.20002 −0.600009 0.799993i 0.704836π-0.704836\pi
−0.600009 + 0.799993i 0.704836π0.704836\pi
954954 0 0
955955 17.5647 0.568382
956956 89.5283 2.89555
957957 0 0
958958 −9.94330 −0.321253
959959 −3.96813 −0.128138
960960 0 0
961961 −14.8154 −0.477915
962962 −33.3838 −1.07634
963963 0 0
964964 4.88327 0.157279
965965 −11.4821 −0.369622
966966 0 0
967967 54.7029 1.75913 0.879563 0.475783i 0.157835π-0.157835\pi
0.879563 + 0.475783i 0.157835π0.157835\pi
968968 4.80840 0.154548
969969 0 0
970970 −14.4276 −0.463243
971971 −50.3142 −1.61466 −0.807330 0.590101i 0.799088π-0.799088\pi
−0.807330 + 0.590101i 0.799088π0.799088\pi
972972 0 0
973973 −10.8159 −0.346741
974974 −18.3397 −0.587641
975975 0 0
976976 −31.8808 −1.02048
977977 −51.7607 −1.65597 −0.827985 0.560750i 0.810513π-0.810513\pi
−0.827985 + 0.560750i 0.810513π0.810513\pi
978978 0 0
979979 10.7746 0.344359
980980 −21.1326 −0.675056
981981 0 0
982982 −39.7666 −1.26900
983983 25.8291 0.823821 0.411910 0.911224i 0.364862π-0.364862\pi
0.411910 + 0.911224i 0.364862π0.364862\pi
984984 0 0
985985 5.98370 0.190657
986986 76.0503 2.42194
987987 0 0
988988 9.16969 0.291727
989989 −32.0021 −1.01761
990990 0 0
991991 −54.6641 −1.73646 −0.868232 0.496159i 0.834743π-0.834743\pi
−0.868232 + 0.496159i 0.834743π0.834743\pi
992992 −1.23874 −0.0393300
993993 0 0
994994 5.82252 0.184679
995995 −10.3994 −0.329682
996996 0 0
997997 −4.18723 −0.132611 −0.0663055 0.997799i 0.521121π-0.521121\pi
−0.0663055 + 0.997799i 0.521121π0.521121\pi
998998 100.313 3.17534
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 1881.2.a.r.1.7 yes 7
3.2 odd 2 1881.2.a.n.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1881.2.a.n.1.1 7 3.2 odd 2
1881.2.a.r.1.7 yes 7 1.1 even 1 trivial