Properties

Label 140.2.c.a.139.4
Level 140140
Weight 22
Character 140.139
Analytic conductor 1.1181.118
Analytic rank 00
Dimension 44
CM discriminant -20
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [140,2,Mod(139,140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(140, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("140.139");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 140=2257 140 = 2^{2} \cdot 5 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 140.c (of order 22, degree 11, minimal)

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: no
Analytic conductor: 1.117905628301.11790562830
Analytic rank: 00
Dimension: 44
Coefficient field: Q(2,5)\Q(\sqrt{2}, \sqrt{-5})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+4x2+9 x^{4} + 4x^{2} + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: U(1)[D2]\mathrm{U}(1)[D_{2}]

Embedding invariants

Embedding label 139.4
Root 0.7071071.58114i-0.707107 - 1.58114i of defining polynomial
Character χ\chi == 140.139
Dual form 140.2.c.a.139.3

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+1.41421q2+3.16228iq3+2.00000q42.23607iq5+4.47214iq6+(2.121321.58114i)q7+2.82843q87.00000q93.16228iq10+6.32456iq12+(3.000002.23607i)q14+7.07107q15+4.00000q169.89949q184.47214iq20+(5.000006.70820i)q211.41421q23+8.94427iq245.00000q2512.6491iq27+(4.242643.16228i)q28+6.00000q29+10.0000q30+5.65685q32+(3.53553+4.74342i)q3514.0000q366.32456iq40+4.47214iq41+(7.071079.48683i)q4212.7279q43+15.6525iq452.00000q46+9.48683iq47+12.6491iq48+(2.00000+6.70820i)q497.07107q5017.8885iq54+(6.000004.47214i)q56+8.48528q58+14.1421q6013.4164iq61+(14.8492+11.0680i)q63+8.00000q64+4.24264q674.47214iq69+(5.00000+6.70820i)q7019.7990q7215.8114iq758.94427iq80+19.0000q81+6.32456iq829.48683iq83+(10.000013.4164i)q8418.0000q86+18.9737iq87+17.8885iq89+22.1359iq902.82843q92+13.4164iq94+17.8885iq96+(2.82843+9.48683i)q98+O(q100)q+1.41421 q^{2} +3.16228i q^{3} +2.00000 q^{4} -2.23607i q^{5} +4.47214i q^{6} +(-2.12132 - 1.58114i) q^{7} +2.82843 q^{8} -7.00000 q^{9} -3.16228i q^{10} +6.32456i q^{12} +(-3.00000 - 2.23607i) q^{14} +7.07107 q^{15} +4.00000 q^{16} -9.89949 q^{18} -4.47214i q^{20} +(5.00000 - 6.70820i) q^{21} -1.41421 q^{23} +8.94427i q^{24} -5.00000 q^{25} -12.6491i q^{27} +(-4.24264 - 3.16228i) q^{28} +6.00000 q^{29} +10.0000 q^{30} +5.65685 q^{32} +(-3.53553 + 4.74342i) q^{35} -14.0000 q^{36} -6.32456i q^{40} +4.47214i q^{41} +(7.07107 - 9.48683i) q^{42} -12.7279 q^{43} +15.6525i q^{45} -2.00000 q^{46} +9.48683i q^{47} +12.6491i q^{48} +(2.00000 + 6.70820i) q^{49} -7.07107 q^{50} -17.8885i q^{54} +(-6.00000 - 4.47214i) q^{56} +8.48528 q^{58} +14.1421 q^{60} -13.4164i q^{61} +(14.8492 + 11.0680i) q^{63} +8.00000 q^{64} +4.24264 q^{67} -4.47214i q^{69} +(-5.00000 + 6.70820i) q^{70} -19.7990 q^{72} -15.8114i q^{75} -8.94427i q^{80} +19.0000 q^{81} +6.32456i q^{82} -9.48683i q^{83} +(10.0000 - 13.4164i) q^{84} -18.0000 q^{86} +18.9737i q^{87} +17.8885i q^{89} +22.1359i q^{90} -2.82843 q^{92} +13.4164i q^{94} +17.8885i q^{96} +(2.82843 + 9.48683i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+8q428q912q14+16q16+20q2120q25+24q29+40q3056q368q46+8q4924q56+32q6420q70+76q81+40q8472q86+O(q100) 4 q + 8 q^{4} - 28 q^{9} - 12 q^{14} + 16 q^{16} + 20 q^{21} - 20 q^{25} + 24 q^{29} + 40 q^{30} - 56 q^{36} - 8 q^{46} + 8 q^{49} - 24 q^{56} + 32 q^{64} - 20 q^{70} + 76 q^{81} + 40 q^{84} - 72 q^{86}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/140Z)×\left(\mathbb{Z}/140\mathbb{Z}\right)^\times.

nn 5757 7171 101101
χ(n)\chi(n) 1-1 1-1 1-1

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 1.41421 1.00000
33 3.16228i 1.82574i 0.408248 + 0.912871i 0.366140π0.366140\pi
−0.408248 + 0.912871i 0.633860π0.633860\pi
44 2.00000 1.00000
55 2.23607i 1.00000i
66 4.47214i 1.82574i
77 −2.12132 1.58114i −0.801784 0.597614i
88 2.82843 1.00000
99 −7.00000 −2.33333
1010 3.16228i 1.00000i
1111 0 0 1.00000 00
−1.00000 π\pi
1212 6.32456i 1.82574i
1313 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1414 −3.00000 2.23607i −0.801784 0.597614i
1515 7.07107 1.82574
1616 4.00000 1.00000
1717 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1818 −9.89949 −2.33333
1919 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2020 4.47214i 1.00000i
2121 5.00000 6.70820i 1.09109 1.46385i
2222 0 0
2323 −1.41421 −0.294884 −0.147442 0.989071i 0.547104π-0.547104\pi
−0.147442 + 0.989071i 0.547104π0.547104\pi
2424 8.94427i 1.82574i
2525 −5.00000 −1.00000
2626 0 0
2727 12.6491i 2.43432i
2828 −4.24264 3.16228i −0.801784 0.597614i
2929 6.00000 1.11417 0.557086 0.830455i 0.311919π-0.311919\pi
0.557086 + 0.830455i 0.311919π0.311919\pi
3030 10.0000 1.82574
3131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3232 5.65685 1.00000
3333 0 0
3434 0 0
3535 −3.53553 + 4.74342i −0.597614 + 0.801784i
3636 −14.0000 −2.33333
3737 0 0 1.00000 00
−1.00000 π\pi
3838 0 0
3939 0 0
4040 6.32456i 1.00000i
4141 4.47214i 0.698430i 0.937043 + 0.349215i 0.113552π0.113552\pi
−0.937043 + 0.349215i 0.886448π0.886448\pi
4242 7.07107 9.48683i 1.09109 1.46385i
4343 −12.7279 −1.94099 −0.970495 0.241121i 0.922485π-0.922485\pi
−0.970495 + 0.241121i 0.922485π0.922485\pi
4444 0 0
4545 15.6525i 2.33333i
4646 −2.00000 −0.294884
4747 9.48683i 1.38380i 0.721995 + 0.691898i 0.243225π0.243225\pi
−0.721995 + 0.691898i 0.756775π0.756775\pi
4848 12.6491i 1.82574i
4949 2.00000 + 6.70820i 0.285714 + 0.958315i
5050 −7.07107 −1.00000
5151 0 0
5252 0 0
5353 0 0 1.00000 00
−1.00000 π\pi
5454 17.8885i 2.43432i
5555 0 0
5656 −6.00000 4.47214i −0.801784 0.597614i
5757 0 0
5858 8.48528 1.11417
5959 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6060 14.1421 1.82574
6161 13.4164i 1.71780i −0.512148 0.858898i 0.671150π-0.671150\pi
0.512148 0.858898i 0.328850π-0.328850\pi
6262 0 0
6363 14.8492 + 11.0680i 1.87083 + 1.39443i
6464 8.00000 1.00000
6565 0 0
6666 0 0
6767 4.24264 0.518321 0.259161 0.965834i 0.416554π-0.416554\pi
0.259161 + 0.965834i 0.416554π0.416554\pi
6868 0 0
6969 4.47214i 0.538382i
7070 −5.00000 + 6.70820i −0.597614 + 0.801784i
7171 0 0 1.00000 00
−1.00000 π\pi
7272 −19.7990 −2.33333
7373 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7474 0 0
7575 15.8114i 1.82574i
7676 0 0
7777 0 0
7878 0 0
7979 0 0 1.00000 00
−1.00000 π\pi
8080 8.94427i 1.00000i
8181 19.0000 2.11111
8282 6.32456i 0.698430i
8383 9.48683i 1.04132i −0.853766 0.520658i 0.825687π-0.825687\pi
0.853766 0.520658i 0.174313π-0.174313\pi
8484 10.0000 13.4164i 1.09109 1.46385i
8585 0 0
8686 −18.0000 −1.94099
8787 18.9737i 2.03419i
8888 0 0
8989 17.8885i 1.89618i 0.317999 + 0.948091i 0.396989π0.396989\pi
−0.317999 + 0.948091i 0.603011π0.603011\pi
9090 22.1359i 2.33333i
9191 0 0
9292 −2.82843 −0.294884
9393 0 0
9494 13.4164i 1.38380i
9595 0 0
9696 17.8885i 1.82574i
9797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
9898 2.82843 + 9.48683i 0.285714 + 0.958315i
9999 0 0
100100 −10.0000 −1.00000
101101 8.94427i 0.889988i 0.895533 + 0.444994i 0.146794π0.146794\pi
−0.895533 + 0.444994i 0.853206π0.853206\pi
102102 0 0
103103 15.8114i 1.55794i −0.627060 0.778971i 0.715742π-0.715742\pi
0.627060 0.778971i 0.284258π-0.284258\pi
104104 0 0
105105 −15.0000 11.1803i −1.46385 1.09109i
106106 0 0
107107 18.3848 1.77732 0.888662 0.458563i 0.151636π-0.151636\pi
0.888662 + 0.458563i 0.151636π0.151636\pi
108108 25.2982i 2.43432i
109109 −16.0000 −1.53252 −0.766261 0.642529i 0.777885π-0.777885\pi
−0.766261 + 0.642529i 0.777885π0.777885\pi
110110 0 0
111111 0 0
112112 −8.48528 6.32456i −0.801784 0.597614i
113113 0 0 1.00000 00
−1.00000 π\pi
114114 0 0
115115 3.16228i 0.294884i
116116 12.0000 1.11417
117117 0 0
118118 0 0
119119 0 0
120120 20.0000 1.82574
121121 11.0000 1.00000
122122 18.9737i 1.71780i
123123 −14.1421 −1.27515
124124 0 0
125125 11.1803i 1.00000i
126126 21.0000 + 15.6525i 1.87083 + 1.39443i
127127 −4.24264 −0.376473 −0.188237 0.982124i 0.560277π-0.560277\pi
−0.188237 + 0.982124i 0.560277π0.560277\pi
128128 11.3137 1.00000
129129 40.2492i 3.54375i
130130 0 0
131131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
132132 0 0
133133 0 0
134134 6.00000 0.518321
135135 −28.2843 −2.43432
136136 0 0
137137 0 0 1.00000 00
−1.00000 π\pi
138138 6.32456i 0.538382i
139139 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
140140 −7.07107 + 9.48683i −0.597614 + 0.801784i
141141 −30.0000 −2.52646
142142 0 0
143143 0 0
144144 −28.0000 −2.33333
145145 13.4164i 1.11417i
146146 0 0
147147 −21.2132 + 6.32456i −1.74964 + 0.521641i
148148 0 0
149149 24.0000 1.96616 0.983078 0.183186i 0.0586410π-0.0586410\pi
0.983078 + 0.183186i 0.0586410π0.0586410\pi
150150 22.3607i 1.82574i
151151 0 0 1.00000 00
−1.00000 π\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
158158 0 0
159159 0 0
160160 12.6491i 1.00000i
161161 3.00000 + 2.23607i 0.236433 + 0.176227i
162162 26.8701 2.11111
163163 12.7279 0.996928 0.498464 0.866910i 0.333898π-0.333898\pi
0.498464 + 0.866910i 0.333898π0.333898\pi
164164 8.94427i 0.698430i
165165 0 0
166166 13.4164i 1.04132i
167167 9.48683i 0.734113i −0.930199 0.367057i 0.880366π-0.880366\pi
0.930199 0.367057i 0.119634π-0.119634\pi
168168 14.1421 18.9737i 1.09109 1.46385i
169169 −13.0000 −1.00000
170170 0 0
171171 0 0
172172 −25.4558 −1.94099
173173 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
174174 26.8328i 2.03419i
175175 10.6066 + 7.90569i 0.801784 + 0.597614i
176176 0 0
177177 0 0
178178 25.2982i 1.89618i
179179 0 0 1.00000 00
−1.00000 π\pi
180180 31.3050i 2.33333i
181181 26.8328i 1.99447i −0.0743294 0.997234i 0.523682π-0.523682\pi
0.0743294 0.997234i 0.476318π-0.476318\pi
182182 0 0
183183 42.4264 3.13625
184184 −4.00000 −0.294884
185185 0 0
186186 0 0
187187 0 0
188188 18.9737i 1.38380i
189189 −20.0000 + 26.8328i −1.45479 + 1.95180i
190190 0 0
191191 0 0 1.00000 00
−1.00000 π\pi
192192 25.2982i 1.82574i
193193 0 0 1.00000 00
−1.00000 π\pi
194194 0 0
195195 0 0
196196 4.00000 + 13.4164i 0.285714 + 0.958315i
197197 0 0 1.00000 00
−1.00000 π\pi
198198 0 0
199199 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
200200 −14.1421 −1.00000
201201 13.4164i 0.946320i
202202 12.6491i 0.889988i
203203 −12.7279 9.48683i −0.893325 0.665845i
204204 0 0
205205 10.0000 0.698430
206206 22.3607i 1.55794i
207207 9.89949 0.688062
208208 0 0
209209 0 0
210210 −21.2132 15.8114i −1.46385 1.09109i
211211 0 0 1.00000 00
−1.00000 π\pi
212212 0 0
213213 0 0
214214 26.0000 1.77732
215215 28.4605i 1.94099i
216216 35.7771i 2.43432i
217217 0 0
218218 −22.6274 −1.53252
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 3.16228i 0.211762i −0.994379 0.105881i 0.966234π-0.966234\pi
0.994379 0.105881i 0.0337662π-0.0337662\pi
224224 −12.0000 8.94427i −0.801784 0.597614i
225225 35.0000 2.33333
226226 0 0
227227 28.4605i 1.88899i −0.328526 0.944495i 0.606552π-0.606552\pi
0.328526 0.944495i 0.393448π-0.393448\pi
228228 0 0
229229 26.8328i 1.77316i 0.462573 + 0.886581i 0.346926π0.346926\pi
−0.462573 + 0.886581i 0.653074π0.653074\pi
230230 4.47214i 0.294884i
231231 0 0
232232 16.9706 1.11417
233233 0 0 1.00000 00
−1.00000 π\pi
234234 0 0
235235 21.2132 1.38380
236236 0 0
237237 0 0
238238 0 0
239239 0 0 1.00000 00
−1.00000 π\pi
240240 28.2843 1.82574
241241 13.4164i 0.864227i 0.901819 + 0.432113i 0.142232π0.142232\pi
−0.901819 + 0.432113i 0.857768π0.857768\pi
242242 15.5563 1.00000
243243 22.1359i 1.42002i
244244 26.8328i 1.71780i
245245 15.0000 4.47214i 0.958315 0.285714i
246246 −20.0000 −1.27515
247247 0 0
248248 0 0
249249 30.0000 1.90117
250250 15.8114i 1.00000i
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 29.6985 + 22.1359i 1.87083 + 1.39443i
253253 0 0
254254 −6.00000 −0.376473
255255 0 0
256256 16.0000 1.00000
257257 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
258258 56.9210i 3.54375i
259259 0 0
260260 0 0
261261 −42.0000 −2.59973
262262 0 0
263263 −15.5563 −0.959246 −0.479623 0.877475i 0.659226π-0.659226\pi
−0.479623 + 0.877475i 0.659226π0.659226\pi
264264 0 0
265265 0 0
266266 0 0
267267 −56.5685 −3.46194
268268 8.48528 0.518321
269269 22.3607i 1.36335i −0.731653 0.681677i 0.761251π-0.761251\pi
0.731653 0.681677i 0.238749π-0.238749\pi
270270 −40.0000 −2.43432
271271 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 8.94427i 0.538382i
277277 0 0 1.00000 00
−1.00000 π\pi
278278 0 0
279279 0 0
280280 −10.0000 + 13.4164i −0.597614 + 0.801784i
281281 −12.0000 −0.715860 −0.357930 0.933748i 0.616517π-0.616517\pi
−0.357930 + 0.933748i 0.616517π0.616517\pi
282282 −42.4264 −2.52646
283283 15.8114i 0.939889i 0.882696 + 0.469945i 0.155726π0.155726\pi
−0.882696 + 0.469945i 0.844274π0.844274\pi
284284 0 0
285285 0 0
286286 0 0
287287 7.07107 9.48683i 0.417392 0.559990i
288288 −39.5980 −2.33333
289289 −17.0000 −1.00000
290290 18.9737i 1.11417i
291291 0 0
292292 0 0
293293 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
294294 −30.0000 + 8.94427i −1.74964 + 0.521641i
295295 0 0
296296 0 0
297297 0 0
298298 33.9411 1.96616
299299 0 0
300300 31.6228i 1.82574i
301301 27.0000 + 20.1246i 1.55625 + 1.15996i
302302 0 0
303303 −28.2843 −1.62489
304304 0 0
305305 −30.0000 −1.71780
306306 0 0
307307 34.7851i 1.98529i 0.121070 + 0.992644i 0.461367π0.461367\pi
−0.121070 + 0.992644i 0.538633π0.538633\pi
308308 0 0
309309 50.0000 2.84440
310310 0 0
311311 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
312312 0 0
313313 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
314314 0 0
315315 24.7487 33.2039i 1.39443 1.87083i
316316 0 0
317317 0 0 1.00000 00
−1.00000 π\pi
318318 0 0
319319 0 0
320320 17.8885i 1.00000i
321321 58.1378i 3.24493i
322322 4.24264 + 3.16228i 0.236433 + 0.176227i
323323 0 0
324324 38.0000 2.11111
325325 0 0
326326 18.0000 0.996928
327327 50.5964i 2.79799i
328328 12.6491i 0.698430i
329329 15.0000 20.1246i 0.826977 1.10951i
330330 0 0
331331 0 0 1.00000 00
−1.00000 π\pi
332332 18.9737i 1.04132i
333333 0 0
334334 13.4164i 0.734113i
335335 9.48683i 0.518321i
336336 20.0000 26.8328i 1.09109 1.46385i
337337 0 0 1.00000 00
−1.00000 π\pi
338338 −18.3848 −1.00000
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 6.36396 17.3925i 0.343622 0.939108i
344344 −36.0000 −1.94099
345345 −10.0000 −0.538382
346346 0 0
347347 24.0416 1.29062 0.645311 0.763920i 0.276728π-0.276728\pi
0.645311 + 0.763920i 0.276728π0.276728\pi
348348 37.9473i 2.03419i
349349 26.8328i 1.43633i −0.695874 0.718164i 0.744983π-0.744983\pi
0.695874 0.718164i 0.255017π-0.255017\pi
350350 15.0000 + 11.1803i 0.801784 + 0.597614i
351351 0 0
352352 0 0
353353 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
354354 0 0
355355 0 0
356356 35.7771i 1.89618i
357357 0 0
358358 0 0
359359 0 0 1.00000 00
−1.00000 π\pi
360360 44.2719i 2.33333i
361361 −19.0000 −1.00000
362362 37.9473i 1.99447i
363363 34.7851i 1.82574i
364364 0 0
365365 0 0
366366 60.0000 3.13625
367367 3.16228i 0.165070i 0.996588 + 0.0825348i 0.0263016π0.0263016\pi
−0.996588 + 0.0825348i 0.973698π0.973698\pi
368368 −5.65685 −0.294884
369369 31.3050i 1.62967i
370370 0 0
371371 0 0
372372 0 0
373373 0 0 1.00000 00
−1.00000 π\pi
374374 0 0
375375 −35.3553 −1.82574
376376 26.8328i 1.38380i
377377 0 0
378378 −28.2843 + 37.9473i −1.45479 + 1.95180i
379379 0 0 1.00000 00
−1.00000 π\pi
380380 0 0
381381 13.4164i 0.687343i
382382 0 0
383383 28.4605i 1.45426i 0.686498 + 0.727132i 0.259147π0.259147\pi
−0.686498 + 0.727132i 0.740853π0.740853\pi
384384 35.7771i 1.82574i
385385 0 0
386386 0 0
387387 89.0955 4.52898
388388 0 0
389389 −24.0000 −1.21685 −0.608424 0.793612i 0.708198π-0.708198\pi
−0.608424 + 0.793612i 0.708198π0.708198\pi
390390 0 0
391391 0 0
392392 5.65685 + 18.9737i 0.285714 + 0.958315i
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
398398 0 0
399399 0 0
400400 −20.0000 −1.00000
401401 −18.0000 −0.898877 −0.449439 0.893311i 0.648376π-0.648376\pi
−0.449439 + 0.893311i 0.648376π0.648376\pi
402402 18.9737i 0.946320i
403403 0 0
404404 17.8885i 0.889988i
405405 42.4853i 2.11111i
406406 −18.0000 13.4164i −0.893325 0.665845i
407407 0 0
408408 0 0
409409 40.2492i 1.99020i 0.0988936 + 0.995098i 0.468470π0.468470\pi
−0.0988936 + 0.995098i 0.531530π0.531530\pi
410410 14.1421 0.698430
411411 0 0
412412 31.6228i 1.55794i
413413 0 0
414414 14.0000 0.688062
415415 −21.2132 −1.04132
416416 0 0
417417 0 0
418418 0 0
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 −30.0000 22.3607i −1.46385 1.09109i
421421 −8.00000 −0.389896 −0.194948 0.980814i 0.562454π-0.562454\pi
−0.194948 + 0.980814i 0.562454π0.562454\pi
422422 0 0
423423 66.4078i 3.22886i
424424 0 0
425425 0 0
426426 0 0
427427 −21.2132 + 28.4605i −1.02658 + 1.37730i
428428 36.7696 1.77732
429429 0 0
430430 40.2492i 1.94099i
431431 0 0 1.00000 00
−1.00000 π\pi
432432 50.5964i 2.43432i
433433 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
434434 0 0
435435 42.4264 2.03419
436436 −32.0000 −1.53252
437437 0 0
438438 0 0
439439 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
440440 0 0
441441 −14.0000 46.9574i −0.666667 2.23607i
442442 0 0
443443 −41.0122 −1.94855 −0.974274 0.225367i 0.927642π-0.927642\pi
−0.974274 + 0.225367i 0.927642π0.927642\pi
444444 0 0
445445 40.0000 1.89618
446446 4.47214i 0.211762i
447447 75.8947i 3.58969i
448448 −16.9706 12.6491i −0.801784 0.597614i
449449 −36.0000 −1.69895 −0.849473 0.527633i 0.823080π-0.823080\pi
−0.849473 + 0.527633i 0.823080π0.823080\pi
450450 49.4975 2.33333
451451 0 0
452452 0 0
453453 0 0
454454 40.2492i 1.88899i
455455 0 0
456456 0 0
457457 0 0 1.00000 00
−1.00000 π\pi
458458 37.9473i 1.77316i
459459 0 0
460460 6.32456i 0.294884i
461461 8.94427i 0.416576i −0.978068 0.208288i 0.933211π-0.933211\pi
0.978068 0.208288i 0.0667892π-0.0667892\pi
462462 0 0
463463 −12.7279 −0.591517 −0.295758 0.955263i 0.595572π-0.595572\pi
−0.295758 + 0.955263i 0.595572π0.595572\pi
464464 24.0000 1.11417
465465 0 0
466466 0 0
467467 28.4605i 1.31699i 0.752583 + 0.658497i 0.228808π0.228808\pi
−0.752583 + 0.658497i 0.771192π0.771192\pi
468468 0 0
469469 −9.00000 6.70820i −0.415581 0.309756i
470470 30.0000 1.38380
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
480480 40.0000 1.82574
481481 0 0
482482 18.9737i 0.864227i
483483 −7.07107 + 9.48683i −0.321745 + 0.431666i
484484 22.0000 1.00000
485485 0 0
486486 31.3050i 1.42002i
487487 −38.1838 −1.73027 −0.865136 0.501538i 0.832768π-0.832768\pi
−0.865136 + 0.501538i 0.832768π0.832768\pi
488488 37.9473i 1.71780i
489489 40.2492i 1.82013i
490490 21.2132 6.32456i 0.958315 0.285714i
491491 0 0 1.00000 00
−1.00000 π\pi
492492 −28.2843 −1.27515
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 42.4264 1.90117
499499 0 0 1.00000 00
−1.00000 π\pi
500500 22.3607i 1.00000i
501501 30.0000 1.34030
502502 0 0
503503 9.48683i 0.422997i −0.977378 0.211498i 0.932166π-0.932166\pi
0.977378 0.211498i 0.0678343π-0.0678343\pi
504504 42.0000 + 31.3050i 1.87083 + 1.39443i
505505 20.0000 0.889988
506506 0 0
507507 41.1096i 1.82574i
508508 −8.48528 −0.376473
509509 44.7214i 1.98224i −0.132973 0.991120i 0.542452π-0.542452\pi
0.132973 0.991120i 0.457548π-0.457548\pi
510510 0 0
511511 0 0
512512 22.6274 1.00000
513513 0 0
514514 0 0
515515 −35.3553 −1.55794
516516 80.4984i 3.54375i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 17.8885i 0.783711i −0.920027 0.391856i 0.871833π-0.871833\pi
0.920027 0.391856i 0.128167π-0.128167\pi
522522 −59.3970 −2.59973
523523 34.7851i 1.52104i −0.649312 0.760522i 0.724943π-0.724943\pi
0.649312 0.760522i 0.275057π-0.275057\pi
524524 0 0
525525 −25.0000 + 33.5410i −1.09109 + 1.46385i
526526 −22.0000 −0.959246
527527 0 0
528528 0 0
529529 −21.0000 −0.913043
530530 0 0
531531 0 0
532532 0 0
533533 0 0
534534 −80.0000 −3.46194
535535 41.1096i 1.77732i
536536 12.0000 0.518321
537537 0 0
538538 31.6228i 1.36335i
539539 0 0
540540 −56.5685 −2.43432
541541 38.0000 1.63375 0.816874 0.576816i 0.195705π-0.195705\pi
0.816874 + 0.576816i 0.195705π0.195705\pi
542542 0 0
543543 84.8528 3.64138
544544 0 0
545545 35.7771i 1.53252i
546546 0 0
547547 46.6690 1.99542 0.997712 0.0676046i 0.0215356π-0.0215356\pi
0.997712 + 0.0676046i 0.0215356π0.0215356\pi
548548 0 0
549549 93.9149i 4.00819i
550550 0 0
551551 0 0
552552 12.6491i 0.538382i
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 0 0 1.00000 00
−1.00000 π\pi
558558 0 0
559559 0 0
560560 −14.1421 + 18.9737i −0.597614 + 0.801784i
561561 0 0
562562 −16.9706 −0.715860
563563 47.4342i 1.99911i 0.0298010 + 0.999556i 0.490513π0.490513\pi
−0.0298010 + 0.999556i 0.509487π0.509487\pi
564564 −60.0000 −2.52646
565565 0 0
566566 22.3607i 0.939889i
567567 −40.3051 30.0416i −1.69265 1.26163i
568568 0 0
569569 36.0000 1.50920 0.754599 0.656186i 0.227831π-0.227831\pi
0.754599 + 0.656186i 0.227831π0.227831\pi
570570 0 0
571571 0 0 1.00000 00
−1.00000 π\pi
572572 0 0
573573 0 0
574574 10.0000 13.4164i 0.417392 0.559990i
575575 7.07107 0.294884
576576 −56.0000 −2.33333
577577 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
578578 −24.0416 −1.00000
579579 0 0
580580 26.8328i 1.11417i
581581 −15.0000 + 20.1246i −0.622305 + 0.834910i
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 47.4342i 1.95782i −0.204298 0.978909i 0.565491π-0.565491\pi
0.204298 0.978909i 0.434509π-0.434509\pi
588588 −42.4264 + 12.6491i −1.74964 + 0.521641i
589589 0 0
590590 0 0
591591 0 0
592592 0 0
593593 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
594594 0 0
595595 0 0
596596 48.0000 1.96616
597597 0 0
598598 0 0
599599 0 0 1.00000 00
−1.00000 π\pi
600600 44.7214i 1.82574i
601601 40.2492i 1.64180i −0.571072 0.820900i 0.693472π-0.693472\pi
0.571072 0.820900i 0.306528π-0.306528\pi
602602 38.1838 + 28.4605i 1.55625 + 1.15996i
603603 −29.6985 −1.20942
604604 0 0
605605 24.5967i 1.00000i
606606 −40.0000 −1.62489
607607 15.8114i 0.641764i −0.947119 0.320882i 0.896021π-0.896021\pi
0.947119 0.320882i 0.103979π-0.103979\pi
608608 0 0
609609 30.0000 40.2492i 1.21566 1.63098i
610610 −42.4264 −1.71780
611611 0 0
612612 0 0
613613 0 0 1.00000 00
−1.00000 π\pi
614614 49.1935i 1.98529i
615615 31.6228i 1.27515i
616616 0 0
617617 0 0 1.00000 00
−1.00000 π\pi
618618 70.7107 2.84440
619619 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
620620 0 0
621621 17.8885i 0.717843i
622622 0 0
623623 28.2843 37.9473i 1.13319 1.52033i
624624 0 0
625625 25.0000 1.00000
626626 0 0
627627 0 0
628628 0 0
629629 0 0
630630 35.0000 46.9574i 1.39443 1.87083i
631631 0 0 1.00000 00
−1.00000 π\pi
632632 0 0
633633 0 0
634634 0 0
635635 9.48683i 0.376473i
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 25.2982i 1.00000i
641641 12.0000 0.473972 0.236986 0.971513i 0.423841π-0.423841\pi
0.236986 + 0.971513i 0.423841π0.423841\pi
642642 82.2192i 3.24493i
643643 41.1096i 1.62120i 0.585597 + 0.810602i 0.300860π0.300860\pi
−0.585597 + 0.810602i 0.699140π0.699140\pi
644644 6.00000 + 4.47214i 0.236433 + 0.176227i
645645 −90.0000 −3.54375
646646 0 0
647647 47.4342i 1.86483i 0.361390 + 0.932415i 0.382302π0.382302\pi
−0.361390 + 0.932415i 0.617698π0.617698\pi
648648 53.7401 2.11111
649649 0 0
650650 0 0
651651 0 0
652652 25.4558 0.996928
653653 0 0 1.00000 00
−1.00000 π\pi
654654 71.5542i 2.79799i
655655 0 0
656656 17.8885i 0.698430i
657657 0 0
658658 21.2132 28.4605i 0.826977 1.10951i
659659 0 0 1.00000 00
−1.00000 π\pi
660660 0 0
661661 40.2492i 1.56551i 0.622328 + 0.782757i 0.286187π0.286187\pi
−0.622328 + 0.782757i 0.713813π0.713813\pi
662662 0 0
663663 0 0
664664 26.8328i 1.04132i
665665 0 0
666666 0 0
667667 −8.48528 −0.328551
668668 18.9737i 0.734113i
669669 10.0000 0.386622
670670 13.4164i 0.518321i
671671 0 0
672672 28.2843 37.9473i 1.09109 1.46385i
673673 0 0 1.00000 00
−1.00000 π\pi
674674 0 0
675675 63.2456i 2.43432i
676676 −26.0000 −1.00000
677677 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
678678 0 0
679679 0 0
680680 0 0
681681 90.0000 3.44881
682682 0 0
683683 43.8406 1.67751 0.838757 0.544505i 0.183283π-0.183283\pi
0.838757 + 0.544505i 0.183283π0.183283\pi
684684 0 0
685685 0 0
686686 9.00000 24.5967i 0.343622 0.939108i
687687 −84.8528 −3.23734
688688 −50.9117 −1.94099
689689 0 0
690690 −14.1421 −0.538382
691691 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
692692 0 0
693693 0 0
694694 34.0000 1.29062
695695 0 0
696696 53.6656i 2.03419i
697697 0 0
698698 37.9473i 1.43633i
699699 0 0
700700 21.2132 + 15.8114i 0.801784 + 0.597614i
701701 48.0000 1.81293 0.906467 0.422276i 0.138769π-0.138769\pi
0.906467 + 0.422276i 0.138769π0.138769\pi
702702 0 0
703703 0 0
704704 0 0
705705 67.0820i 2.52646i
706706 0 0
707707 14.1421 18.9737i 0.531870 0.713578i
708708 0 0
709709 −46.0000 −1.72757 −0.863783 0.503864i 0.831911π-0.831911\pi
−0.863783 + 0.503864i 0.831911π0.831911\pi
710710 0 0
711711 0 0
712712 50.5964i 1.89618i
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
720720 62.6099i 2.33333i
721721 −25.0000 + 33.5410i −0.931049 + 1.24913i
722722 −26.8701 −1.00000
723723 −42.4264 −1.57786
724724 53.6656i 1.99447i
725725 −30.0000 −1.11417
726726 49.1935i 1.82574i
727727 53.7587i 1.99380i −0.0786754 0.996900i 0.525069π-0.525069\pi
0.0786754 0.996900i 0.474931π-0.474931\pi
728728 0 0
729729 −13.0000 −0.481481
730730 0 0
731731 0 0
732732 84.8528 3.13625
733733 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
734734 4.47214i 0.165070i
735735 14.1421 + 47.4342i 0.521641 + 1.74964i
736736 −8.00000 −0.294884
737737 0 0
738738 44.2719i 1.62967i
739739 0 0 1.00000 00
−1.00000 π\pi
740740 0 0
741741 0 0
742742 0 0
743743 26.8701 0.985767 0.492883 0.870095i 0.335943π-0.335943\pi
0.492883 + 0.870095i 0.335943π0.335943\pi
744744 0 0
745745 53.6656i 1.96616i
746746 0 0
747747 66.4078i 2.42974i
748748 0 0
749749 −39.0000 29.0689i −1.42503 1.06215i
750750 −50.0000 −1.82574
751751 0 0 1.00000 00
−1.00000 π\pi
752752 37.9473i 1.38380i
753753 0 0
754754 0 0
755755 0 0
756756 −40.0000 + 53.6656i −1.45479 + 1.95180i
757757 0 0 1.00000 00
−1.00000 π\pi
758758 0 0
759759 0 0
760760 0 0
761761 35.7771i 1.29692i −0.761249 0.648459i 0.775414π-0.775414\pi
0.761249 0.648459i 0.224586π-0.224586\pi
762762 18.9737i 0.687343i
763763 33.9411 + 25.2982i 1.22875 + 0.915857i
764764 0 0
765765 0 0
766766 40.2492i 1.45426i
767767 0 0
768768 50.5964i 1.82574i
769769 53.6656i 1.93523i 0.252426 + 0.967616i 0.418771π0.418771\pi
−0.252426 + 0.967616i 0.581229π0.581229\pi
770770 0 0
771771 0 0
772772 0 0
773773 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
774774 126.000 4.52898
775775 0 0
776776 0 0
777777 0 0
778778 −33.9411 −1.21685
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 75.8947i 2.71225i
784784 8.00000 + 26.8328i 0.285714 + 0.958315i
785785 0 0
786786 0 0
787787 41.1096i 1.46540i −0.680552 0.732700i 0.738260π-0.738260\pi
0.680552 0.732700i 0.261740π-0.261740\pi
788788 0 0
789789 49.1935i 1.75133i
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
798798 0 0
799799 0 0
800800 −28.2843 −1.00000
801801 125.220i 4.42442i
802802 −25.4558 −0.898877
803803 0 0
804804 26.8328i 0.946320i
805805 5.00000 6.70820i 0.176227 0.236433i
806806 0 0
807807 70.7107 2.48913
808808 25.2982i 0.889988i
809809 54.0000 1.89854 0.949269 0.314464i 0.101825π-0.101825\pi
0.949269 + 0.314464i 0.101825π0.101825\pi
810810 60.0833i 2.11111i
811811 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
812812 −25.4558 18.9737i −0.893325 0.665845i
813813 0 0
814814 0 0
815815 28.4605i 0.996928i
816816 0 0
817817 0 0
818818 56.9210i 1.99020i
819819 0 0
820820 20.0000 0.698430
821821 −48.0000 −1.67521 −0.837606 0.546275i 0.816045π-0.816045\pi
−0.837606 + 0.546275i 0.816045π0.816045\pi
822822 0 0
823823 −55.1543 −1.92256 −0.961280 0.275575i 0.911132π-0.911132\pi
−0.961280 + 0.275575i 0.911132π0.911132\pi
824824 44.7214i 1.55794i
825825 0 0
826826 0 0
827827 −32.5269 −1.13107 −0.565536 0.824724i 0.691331π-0.691331\pi
−0.565536 + 0.824724i 0.691331π0.691331\pi
828828 19.7990 0.688062
829829 13.4164i 0.465971i 0.972480 + 0.232986i 0.0748495π0.0748495\pi
−0.972480 + 0.232986i 0.925151π0.925151\pi
830830 −30.0000 −1.04132
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 −21.2132 −0.734113
836836 0 0
837837 0 0
838838 0 0
839839 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
840840 −42.4264 31.6228i −1.46385 1.09109i
841841 7.00000 0.241379
842842 −11.3137 −0.389896
843843 37.9473i 1.30698i
844844 0 0
845845 29.0689i 1.00000i
846846 93.9149i 3.22886i
847847 −23.3345 17.3925i −0.801784 0.597614i
848848 0 0
849849 −50.0000 −1.71600
850850 0 0
851851 0 0
852852 0 0
853853 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
854854 −30.0000 + 40.2492i −1.02658 + 1.37730i
855855 0 0
856856 52.0000 1.77732
857857 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
858858 0 0
859859 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
860860 56.9210i 1.94099i
861861 30.0000 + 22.3607i 1.02240 + 0.762050i
862862 0 0
863863 57.9828 1.97376 0.986878 0.161468i 0.0516228π-0.0516228\pi
0.986878 + 0.161468i 0.0516228π0.0516228\pi
864864 71.5542i 2.43432i
865865 0 0
866866 0 0
867867 53.7587i 1.82574i
868868 0 0
869869 0 0
870870 60.0000 2.03419
871871 0 0
872872 −45.2548 −1.53252
873873 0 0
874874 0 0
875875 17.6777 23.7171i 0.597614 0.801784i
876876 0 0
877877 0 0 1.00000 00
−1.00000 π\pi
878878 0 0
879879 0 0
880880 0 0
881881 58.1378i 1.95871i −0.202145 0.979356i 0.564791π-0.564791\pi
0.202145 0.979356i 0.435209π-0.435209\pi
882882 −19.7990 66.4078i −0.666667 2.23607i
883883 55.1543 1.85609 0.928045 0.372467i 0.121488π-0.121488\pi
0.928045 + 0.372467i 0.121488π0.121488\pi
884884 0 0
885885 0 0
886886 −58.0000 −1.94855
887887 28.4605i 0.955610i 0.878466 + 0.477805i 0.158567π0.158567\pi
−0.878466 + 0.477805i 0.841433π0.841433\pi
888888 0 0
889889 9.00000 + 6.70820i 0.301850 + 0.224986i
890890 56.5685 1.89618
891891 0 0
892892 6.32456i 0.211762i
893893 0 0
894894 107.331i 3.58969i
895895 0 0
896896 −24.0000 17.8885i −0.801784 0.597614i
897897 0 0
898898 −50.9117 −1.69895
899899 0 0
900900 70.0000 2.33333
901901 0 0
902902 0 0
903903 −63.6396 + 85.3815i −2.11779 + 2.84132i
904904 0 0
905905 −60.0000 −1.99447
906906 0 0
907907 4.24264 0.140875 0.0704373 0.997516i 0.477561π-0.477561\pi
0.0704373 + 0.997516i 0.477561π0.477561\pi
908908 56.9210i 1.88899i
909909 62.6099i 2.07664i
910910 0 0
911911 0 0 1.00000 00
−1.00000 π\pi
912912 0 0
913913 0 0
914914 0 0
915915 94.8683i 3.13625i
916916 53.6656i 1.77316i
917917 0 0
918918 0 0
919919 0 0 1.00000 00
−1.00000 π\pi
920920 8.94427i 0.294884i
921921 −110.000 −3.62462
922922 12.6491i 0.416576i
923923 0 0
924924 0 0
925925 0 0
926926 −18.0000 −0.591517
927927 110.680i 3.63520i
928928 33.9411 1.11417
929929 49.1935i 1.61399i 0.590561 + 0.806993i 0.298907π0.298907\pi
−0.590561 + 0.806993i 0.701093π0.701093\pi
930930 0 0
931931 0 0
932932 0 0
933933 0 0
934934 40.2492i 1.31699i
935935 0 0
936936 0 0
937937 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
938938 −12.7279 9.48683i −0.415581 0.309756i
939939 0 0
940940 42.4264 1.38380
941941 44.7214i 1.45787i 0.684580 + 0.728937i 0.259985π0.259985\pi
−0.684580 + 0.728937i 0.740015π0.740015\pi
942942 0 0
943943 6.32456i 0.205956i
944944 0 0
945945 60.0000 + 44.7214i 1.95180 + 1.45479i
946946 0 0
947947 −60.8112 −1.97610 −0.988049 0.154140i 0.950739π-0.950739\pi
−0.988049 + 0.154140i 0.950739π0.950739\pi
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 0 0 1.00000 00
−1.00000 π\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 56.5685 1.82574
961961 −31.0000 −1.00000
962962 0 0
963963 −128.693 −4.14709
964964 26.8328i 0.864227i
965965 0 0
966966 −10.0000 + 13.4164i −0.321745 + 0.431666i
967967 46.6690 1.50078 0.750388 0.660998i 0.229867π-0.229867\pi
0.750388 + 0.660998i 0.229867π0.229867\pi
968968 31.1127 1.00000
969969 0 0
970970 0 0
971971 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
972972 44.2719i 1.42002i
973973 0 0
974974 −54.0000 −1.73027
975975 0 0
976976 53.6656i 1.71780i
977977 0 0 1.00000 00
−1.00000 π\pi
978978 56.9210i 1.82013i
979979 0 0
980980 30.0000 8.94427i 0.958315 0.285714i
981981 112.000 3.57588
982982 0 0
983983 47.4342i 1.51291i 0.654043 + 0.756457i 0.273072π0.273072\pi
−0.654043 + 0.756457i 0.726928π0.726928\pi
984984 −40.0000 −1.27515
985985 0 0
986986 0 0
987987 63.6396 + 47.4342i 2.02567 + 1.50985i
988988 0 0
989989 18.0000 0.572367
990990 0 0
991991 0 0 1.00000 00
−1.00000 π\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 60.0000 1.90117
997997 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
998998 0 0
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 140.2.c.a.139.4 yes 4
4.3 odd 2 inner 140.2.c.a.139.1 4
5.2 odd 4 700.2.g.d.251.4 4
5.3 odd 4 700.2.g.d.251.1 4
5.4 even 2 inner 140.2.c.a.139.1 4
7.2 even 3 980.2.s.b.619.1 8
7.3 odd 6 980.2.s.b.19.1 8
7.4 even 3 980.2.s.b.19.2 8
7.5 odd 6 980.2.s.b.619.2 8
7.6 odd 2 inner 140.2.c.a.139.3 yes 4
8.3 odd 2 2240.2.e.a.2239.4 4
8.5 even 2 2240.2.e.a.2239.2 4
20.3 even 4 700.2.g.d.251.4 4
20.7 even 4 700.2.g.d.251.1 4
20.19 odd 2 CM 140.2.c.a.139.4 yes 4
28.3 even 6 980.2.s.b.19.4 8
28.11 odd 6 980.2.s.b.19.3 8
28.19 even 6 980.2.s.b.619.3 8
28.23 odd 6 980.2.s.b.619.4 8
28.27 even 2 inner 140.2.c.a.139.2 yes 4
35.4 even 6 980.2.s.b.19.3 8
35.9 even 6 980.2.s.b.619.4 8
35.13 even 4 700.2.g.d.251.2 4
35.19 odd 6 980.2.s.b.619.3 8
35.24 odd 6 980.2.s.b.19.4 8
35.27 even 4 700.2.g.d.251.3 4
35.34 odd 2 inner 140.2.c.a.139.2 yes 4
40.19 odd 2 2240.2.e.a.2239.2 4
40.29 even 2 2240.2.e.a.2239.4 4
56.13 odd 2 2240.2.e.a.2239.3 4
56.27 even 2 2240.2.e.a.2239.1 4
140.19 even 6 980.2.s.b.619.2 8
140.27 odd 4 700.2.g.d.251.2 4
140.39 odd 6 980.2.s.b.19.2 8
140.59 even 6 980.2.s.b.19.1 8
140.79 odd 6 980.2.s.b.619.1 8
140.83 odd 4 700.2.g.d.251.3 4
140.139 even 2 inner 140.2.c.a.139.3 yes 4
280.69 odd 2 2240.2.e.a.2239.1 4
280.139 even 2 2240.2.e.a.2239.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.c.a.139.1 4 4.3 odd 2 inner
140.2.c.a.139.1 4 5.4 even 2 inner
140.2.c.a.139.2 yes 4 28.27 even 2 inner
140.2.c.a.139.2 yes 4 35.34 odd 2 inner
140.2.c.a.139.3 yes 4 7.6 odd 2 inner
140.2.c.a.139.3 yes 4 140.139 even 2 inner
140.2.c.a.139.4 yes 4 1.1 even 1 trivial
140.2.c.a.139.4 yes 4 20.19 odd 2 CM
700.2.g.d.251.1 4 5.3 odd 4
700.2.g.d.251.1 4 20.7 even 4
700.2.g.d.251.2 4 35.13 even 4
700.2.g.d.251.2 4 140.27 odd 4
700.2.g.d.251.3 4 35.27 even 4
700.2.g.d.251.3 4 140.83 odd 4
700.2.g.d.251.4 4 5.2 odd 4
700.2.g.d.251.4 4 20.3 even 4
980.2.s.b.19.1 8 7.3 odd 6
980.2.s.b.19.1 8 140.59 even 6
980.2.s.b.19.2 8 7.4 even 3
980.2.s.b.19.2 8 140.39 odd 6
980.2.s.b.19.3 8 28.11 odd 6
980.2.s.b.19.3 8 35.4 even 6
980.2.s.b.19.4 8 28.3 even 6
980.2.s.b.19.4 8 35.24 odd 6
980.2.s.b.619.1 8 7.2 even 3
980.2.s.b.619.1 8 140.79 odd 6
980.2.s.b.619.2 8 7.5 odd 6
980.2.s.b.619.2 8 140.19 even 6
980.2.s.b.619.3 8 28.19 even 6
980.2.s.b.619.3 8 35.19 odd 6
980.2.s.b.619.4 8 28.23 odd 6
980.2.s.b.619.4 8 35.9 even 6
2240.2.e.a.2239.1 4 56.27 even 2
2240.2.e.a.2239.1 4 280.69 odd 2
2240.2.e.a.2239.2 4 8.5 even 2
2240.2.e.a.2239.2 4 40.19 odd 2
2240.2.e.a.2239.3 4 56.13 odd 2
2240.2.e.a.2239.3 4 280.139 even 2
2240.2.e.a.2239.4 4 8.3 odd 2
2240.2.e.a.2239.4 4 40.29 even 2