Properties

Label 1521.2.b.l.1351.6
Level 15211521
Weight 22
Character 1521.1351
Analytic conductor 12.14512.145
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1521,2,Mod(1351,1521)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1521.1351");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1521=32132 1521 = 3^{2} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1521.b (of order 22, degree 11, not 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: 12.145246147412.1452461474
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.153664.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6+5x4+6x2+1 x^{6} + 5x^{4} + 6x^{2} + 1 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 169)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1351.6
Root 0.445042i0.445042i of defining polynomial
Character χ\chi == 1521.1351
Dual form 1521.2.b.l.1351.1

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+2.24698iq23.04892q4+1.44504iq52.04892iq72.35690iq83.24698q102.55496iq11+4.60388q140.801938q165.29590q175.85086iq194.40581iq20+5.74094q221.89008q23+2.91185q25+6.24698iq282.26875q294.26875iq316.51573iq3211.8998iq34+2.96077q355.35690iq37+13.1468q38+3.40581q401.27413iq416.13706q43+7.78986iq444.24698iq462.95108iq47+2.80194q49+6.54288iq505.52111q53+3.69202q554.82908q565.09783iq5812.2078iq59+8.56465q61+9.59179q62+13.0368q64+0.576728iq67+16.1468q68+6.65279iq70+4.59419iq71+10.5526iq73+12.0368q74+17.8388iq765.23490q7715.7778q791.15883iq80+2.86294q827.72348iq837.65279iq8513.7899iq866.02177q88+6.61356iq89+5.76271q92+6.63102q94+8.45473q95+11.9269iq97+6.29590iq98+O(q100)q+2.24698i q^{2} -3.04892 q^{4} +1.44504i q^{5} -2.04892i q^{7} -2.35690i q^{8} -3.24698 q^{10} -2.55496i q^{11} +4.60388 q^{14} -0.801938 q^{16} -5.29590 q^{17} -5.85086i q^{19} -4.40581i q^{20} +5.74094 q^{22} -1.89008 q^{23} +2.91185 q^{25} +6.24698i q^{28} -2.26875 q^{29} -4.26875i q^{31} -6.51573i q^{32} -11.8998i q^{34} +2.96077 q^{35} -5.35690i q^{37} +13.1468 q^{38} +3.40581 q^{40} -1.27413i q^{41} -6.13706 q^{43} +7.78986i q^{44} -4.24698i q^{46} -2.95108i q^{47} +2.80194 q^{49} +6.54288i q^{50} -5.52111 q^{53} +3.69202 q^{55} -4.82908 q^{56} -5.09783i q^{58} -12.2078i q^{59} +8.56465 q^{61} +9.59179 q^{62} +13.0368 q^{64} +0.576728i q^{67} +16.1468 q^{68} +6.65279i q^{70} +4.59419i q^{71} +10.5526i q^{73} +12.0368 q^{74} +17.8388i q^{76} -5.23490 q^{77} -15.7778 q^{79} -1.15883i q^{80} +2.86294 q^{82} -7.72348i q^{83} -7.65279i q^{85} -13.7899i q^{86} -6.02177 q^{88} +6.61356i q^{89} +5.76271 q^{92} +6.63102 q^{94} +8.45473 q^{95} +11.9269i q^{97} +6.29590i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q10q10+10q14+4q164q17+6q2210q23+10q25+2q298q35+24q386q4026q43+8q492q53+12q558q56+8q61+2q62++6q95+O(q100) 6 q - 10 q^{10} + 10 q^{14} + 4 q^{16} - 4 q^{17} + 6 q^{22} - 10 q^{23} + 10 q^{25} + 2 q^{29} - 8 q^{35} + 24 q^{38} - 6 q^{40} - 26 q^{43} + 8 q^{49} - 2 q^{53} + 12 q^{55} - 8 q^{56} + 8 q^{61} + 2 q^{62}+ \cdots + 6 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1521Z)×\left(\mathbb{Z}/1521\mathbb{Z}\right)^\times.

nn 677677 847847
χ(n)\chi(n) 11 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 2.24698i 1.58885i 0.607359 + 0.794427i 0.292229π0.292229\pi
−0.607359 + 0.794427i 0.707771π0.707771\pi
33 0 0
44 −3.04892 −1.52446
55 1.44504i 0.646242i 0.946358 + 0.323121i 0.104732π0.104732\pi
−0.946358 + 0.323121i 0.895268π0.895268\pi
66 0 0
77 − 2.04892i − 0.774418i −0.921992 0.387209i 0.873439π-0.873439\pi
0.921992 0.387209i 0.126561π-0.126561\pi
88 − 2.35690i − 0.833289i
99 0 0
1010 −3.24698 −1.02679
1111 − 2.55496i − 0.770349i −0.922844 0.385174i 0.874141π-0.874141\pi
0.922844 0.385174i 0.125859π-0.125859\pi
1212 0 0
1313 0 0
1414 4.60388 1.23044
1515 0 0
1616 −0.801938 −0.200484
1717 −5.29590 −1.28444 −0.642222 0.766519i 0.721987π-0.721987\pi
−0.642222 + 0.766519i 0.721987π0.721987\pi
1818 0 0
1919 − 5.85086i − 1.34228i −0.741331 0.671139i 0.765805π-0.765805\pi
0.741331 0.671139i 0.234195π-0.234195\pi
2020 − 4.40581i − 0.985170i
2121 0 0
2222 5.74094 1.22397
2323 −1.89008 −0.394110 −0.197055 0.980392i 0.563138π-0.563138\pi
−0.197055 + 0.980392i 0.563138π0.563138\pi
2424 0 0
2525 2.91185 0.582371
2626 0 0
2727 0 0
2828 6.24698i 1.18057i
2929 −2.26875 −0.421296 −0.210648 0.977562i 0.567557π-0.567557\pi
−0.210648 + 0.977562i 0.567557π0.567557\pi
3030 0 0
3131 − 4.26875i − 0.766690i −0.923605 0.383345i 0.874772π-0.874772\pi
0.923605 0.383345i 0.125228π-0.125228\pi
3232 − 6.51573i − 1.15183i
3333 0 0
3434 − 11.8998i − 2.04079i
3535 2.96077 0.500462
3636 0 0
3737 − 5.35690i − 0.880668i −0.897834 0.440334i 0.854860π-0.854860\pi
0.897834 0.440334i 0.145140π-0.145140\pi
3838 13.1468 2.13268
3939 0 0
4040 3.40581 0.538506
4141 − 1.27413i − 0.198985i −0.995038 0.0994926i 0.968278π-0.968278\pi
0.995038 0.0994926i 0.0317220π-0.0317220\pi
4242 0 0
4343 −6.13706 −0.935893 −0.467947 0.883757i 0.655006π-0.655006\pi
−0.467947 + 0.883757i 0.655006π0.655006\pi
4444 7.78986i 1.17437i
4545 0 0
4646 − 4.24698i − 0.626183i
4747 − 2.95108i − 0.430460i −0.976563 0.215230i 0.930950π-0.930950\pi
0.976563 0.215230i 0.0690501π-0.0690501\pi
4848 0 0
4949 2.80194 0.400277
5050 6.54288i 0.925302i
5151 0 0
5252 0 0
5353 −5.52111 −0.758382 −0.379191 0.925318i 0.623798π-0.623798\pi
−0.379191 + 0.925318i 0.623798π0.623798\pi
5454 0 0
5555 3.69202 0.497832
5656 −4.82908 −0.645314
5757 0 0
5858 − 5.09783i − 0.669378i
5959 − 12.2078i − 1.58931i −0.607059 0.794657i 0.707651π-0.707651\pi
0.607059 0.794657i 0.292349π-0.292349\pi
6060 0 0
6161 8.56465 1.09659 0.548295 0.836285i 0.315277π-0.315277\pi
0.548295 + 0.836285i 0.315277π0.315277\pi
6262 9.59179 1.21816
6363 0 0
6464 13.0368 1.62960
6565 0 0
6666 0 0
6767 0.576728i 0.0704586i 0.999379 + 0.0352293i 0.0112162π0.0112162\pi
−0.999379 + 0.0352293i 0.988784π0.988784\pi
6868 16.1468 1.95808
6969 0 0
7070 6.65279i 0.795161i
7171 4.59419i 0.545230i 0.962123 + 0.272615i 0.0878885π0.0878885\pi
−0.962123 + 0.272615i 0.912112π0.912112\pi
7272 0 0
7373 10.5526i 1.23508i 0.786538 + 0.617542i 0.211872π0.211872\pi
−0.786538 + 0.617542i 0.788128π0.788128\pi
7474 12.0368 1.39925
7575 0 0
7676 17.8388i 2.04625i
7777 −5.23490 −0.596572
7878 0 0
7979 −15.7778 −1.77514 −0.887569 0.460674i 0.847608π-0.847608\pi
−0.887569 + 0.460674i 0.847608π0.847608\pi
8080 − 1.15883i − 0.129562i
8181 0 0
8282 2.86294 0.316158
8383 − 7.72348i − 0.847762i −0.905718 0.423881i 0.860667π-0.860667\pi
0.905718 0.423881i 0.139333π-0.139333\pi
8484 0 0
8585 − 7.65279i − 0.830062i
8686 − 13.7899i − 1.48700i
8787 0 0
8888 −6.02177 −0.641923
8989 6.61356i 0.701036i 0.936556 + 0.350518i 0.113995π0.113995\pi
−0.936556 + 0.350518i 0.886005π0.886005\pi
9090 0 0
9191 0 0
9292 5.76271 0.600804
9393 0 0
9494 6.63102 0.683938
9595 8.45473 0.867437
9696 0 0
9797 11.9269i 1.21100i 0.795847 + 0.605498i 0.207026π0.207026\pi
−0.795847 + 0.605498i 0.792974π0.792974\pi
9898 6.29590i 0.635982i
9999 0 0
100100 −8.87800 −0.887800
101101 13.0640 1.29991 0.649957 0.759971i 0.274787π-0.274787\pi
0.649957 + 0.759971i 0.274787π0.274787\pi
102102 0 0
103103 −9.16852 −0.903401 −0.451701 0.892170i 0.649182π-0.649182\pi
−0.451701 + 0.892170i 0.649182π0.649182\pi
104104 0 0
105105 0 0
106106 − 12.4058i − 1.20496i
107107 6.89977 0.667026 0.333513 0.942745i 0.391766π-0.391766\pi
0.333513 + 0.942745i 0.391766π0.391766\pi
108108 0 0
109109 0.121998i 0.0116853i 0.999983 + 0.00584264i 0.00185978π0.00185978\pi
−0.999983 + 0.00584264i 0.998140π0.998140\pi
110110 8.29590i 0.790983i
111111 0 0
112112 1.64310i 0.155259i
113113 −7.30798 −0.687477 −0.343738 0.939065i 0.611693π-0.611693\pi
−0.343738 + 0.939065i 0.611693π0.611693\pi
114114 0 0
115115 − 2.73125i − 0.254690i
116116 6.91723 0.642249
117117 0 0
118118 27.4306 2.52519
119119 10.8509i 0.994696i
120120 0 0
121121 4.47219 0.406563
122122 19.2446i 1.74232i
123123 0 0
124124 13.0151i 1.16879i
125125 11.4330i 1.02260i
126126 0 0
127127 18.9705 1.68336 0.841678 0.539980i 0.181568π-0.181568\pi
0.841678 + 0.539980i 0.181568π0.181568\pi
128128 16.2620i 1.43738i
129129 0 0
130130 0 0
131131 −3.25667 −0.284536 −0.142268 0.989828i 0.545440π-0.545440\pi
−0.142268 + 0.989828i 0.545440π0.545440\pi
132132 0 0
133133 −11.9879 −1.03948
134134 −1.29590 −0.111948
135135 0 0
136136 12.4819i 1.07031i
137137 0.792249i 0.0676864i 0.999427 + 0.0338432i 0.0107747π0.0107747\pi
−0.999427 + 0.0338432i 0.989225π0.989225\pi
138138 0 0
139139 −11.3394 −0.961799 −0.480899 0.876776i 0.659690π-0.659690\pi
−0.480899 + 0.876776i 0.659690π0.659690\pi
140140 −9.02715 −0.762933
141141 0 0
142142 −10.3230 −0.866291
143143 0 0
144144 0 0
145145 − 3.27844i − 0.272260i
146146 −23.7114 −1.96237
147147 0 0
148148 16.3327i 1.34254i
149149 − 8.40581i − 0.688631i −0.938854 0.344316i 0.888111π-0.888111\pi
0.938854 0.344316i 0.111889π-0.111889\pi
150150 0 0
151151 − 14.1293i − 1.14983i −0.818215 0.574913i 0.805036π-0.805036\pi
0.818215 0.574913i 0.194964π-0.194964\pi
152152 −13.7899 −1.11851
153153 0 0
154154 − 11.7627i − 0.947866i
155155 6.16852 0.495468
156156 0 0
157157 −9.43296 −0.752832 −0.376416 0.926451i 0.622844π-0.622844\pi
−0.376416 + 0.926451i 0.622844π0.622844\pi
158158 − 35.4523i − 2.82044i
159159 0 0
160160 9.41550 0.744361
161161 3.87263i 0.305206i
162162 0 0
163163 − 8.70410i − 0.681758i −0.940107 0.340879i 0.889275π-0.889275\pi
0.940107 0.340879i 0.110725π-0.110725\pi
164164 3.88471i 0.303345i
165165 0 0
166166 17.3545 1.34697
167167 − 23.8538i − 1.84587i −0.384961 0.922933i 0.625785π-0.625785\pi
0.384961 0.922933i 0.374215π-0.374215\pi
168168 0 0
169169 0 0
170170 17.1957 1.31885
171171 0 0
172172 18.7114 1.42673
173173 −18.8552 −1.43353 −0.716766 0.697314i 0.754378π-0.754378\pi
−0.716766 + 0.697314i 0.754378π0.754378\pi
174174 0 0
175175 − 5.96615i − 0.450998i
176176 2.04892i 0.154443i
177177 0 0
178178 −14.8605 −1.11384
179179 6.02177 0.450088 0.225044 0.974349i 0.427747π-0.427747\pi
0.225044 + 0.974349i 0.427747π0.427747\pi
180180 0 0
181181 4.77777 0.355129 0.177565 0.984109i 0.443178π-0.443178\pi
0.177565 + 0.984109i 0.443178π0.443178\pi
182182 0 0
183183 0 0
184184 4.45473i 0.328407i
185185 7.74094 0.569125
186186 0 0
187187 13.5308i 0.989470i
188188 8.99761i 0.656218i
189189 0 0
190190 18.9976i 1.37823i
191191 −18.4306 −1.33359 −0.666795 0.745242i 0.732334π-0.732334\pi
−0.666795 + 0.745242i 0.732334π0.732334\pi
192192 0 0
193193 − 6.05429i − 0.435798i −0.975971 0.217899i 0.930080π-0.930080\pi
0.975971 0.217899i 0.0699203π-0.0699203\pi
194194 −26.7995 −1.92410
195195 0 0
196196 −8.54288 −0.610205
197197 11.4155i 0.813321i 0.913579 + 0.406660i 0.133307π0.133307\pi
−0.913579 + 0.406660i 0.866693π0.866693\pi
198198 0 0
199199 13.9051 0.985710 0.492855 0.870111i 0.335953π-0.335953\pi
0.492855 + 0.870111i 0.335953π0.335953\pi
200200 − 6.86294i − 0.485283i
201201 0 0
202202 29.3545i 2.06538i
203203 4.64848i 0.326259i
204204 0 0
205205 1.84117 0.128593
206206 − 20.6015i − 1.43537i
207207 0 0
208208 0 0
209209 −14.9487 −1.03402
210210 0 0
211211 −13.2446 −0.911795 −0.455897 0.890032i 0.650682π-0.650682\pi
−0.455897 + 0.890032i 0.650682π0.650682\pi
212212 16.8334 1.15612
213213 0 0
214214 15.5036i 1.05981i
215215 − 8.86831i − 0.604814i
216216 0 0
217217 −8.74632 −0.593739
218218 −0.274127 −0.0185662
219219 0 0
220220 −11.2567 −0.758924
221221 0 0
222222 0 0
223223 − 7.33513i − 0.491196i −0.969372 0.245598i 0.921016π-0.921016\pi
0.969372 0.245598i 0.0789844π-0.0789844\pi
224224 −13.3502 −0.891997
225225 0 0
226226 − 16.4209i − 1.09230i
227227 8.67456i 0.575751i 0.957668 + 0.287875i 0.0929489π0.0929489\pi
−0.957668 + 0.287875i 0.907051π0.907051\pi
228228 0 0
229229 13.6866i 0.904439i 0.891907 + 0.452219i 0.149368π0.149368\pi
−0.891907 + 0.452219i 0.850632π0.850632\pi
230230 6.13706 0.404666
231231 0 0
232232 5.34721i 0.351061i
233233 −5.08815 −0.333336 −0.166668 0.986013i 0.553301π-0.553301\pi
−0.166668 + 0.986013i 0.553301π0.553301\pi
234234 0 0
235235 4.26444 0.278181
236236 37.2204i 2.42284i
237237 0 0
238238 −24.3817 −1.58043
239239 10.9239i 0.706611i 0.935508 + 0.353305i 0.114942π0.114942\pi
−0.935508 + 0.353305i 0.885058π0.885058\pi
240240 0 0
241241 − 11.9148i − 0.767502i −0.923437 0.383751i 0.874632π-0.874632\pi
0.923437 0.383751i 0.125368π-0.125368\pi
242242 10.0489i 0.645969i
243243 0 0
244244 −26.1129 −1.67171
245245 4.04892i 0.258676i
246246 0 0
247247 0 0
248248 −10.0610 −0.638874
249249 0 0
250250 −25.6896 −1.62475
251251 22.3478 1.41058 0.705290 0.708919i 0.250817π-0.250817\pi
0.705290 + 0.708919i 0.250817π0.250817\pi
252252 0 0
253253 4.82908i 0.303602i
254254 42.6262i 2.67461i
255255 0 0
256256 −10.4668 −0.654176
257257 −18.6601 −1.16398 −0.581992 0.813194i 0.697727π-0.697727\pi
−0.581992 + 0.813194i 0.697727π0.697727\pi
258258 0 0
259259 −10.9758 −0.682005
260260 0 0
261261 0 0
262262 − 7.31767i − 0.452087i
263263 −14.3991 −0.887887 −0.443944 0.896055i 0.646421π-0.646421\pi
−0.443944 + 0.896055i 0.646421π0.646421\pi
264264 0 0
265265 − 7.97823i − 0.490099i
266266 − 26.9366i − 1.65159i
267267 0 0
268268 − 1.75840i − 0.107411i
269269 −0.652793 −0.0398015 −0.0199007 0.999802i 0.506335π-0.506335\pi
−0.0199007 + 0.999802i 0.506335π0.506335\pi
270270 0 0
271271 1.99569i 0.121229i 0.998161 + 0.0606147i 0.0193061π0.0193061\pi
−0.998161 + 0.0606147i 0.980694π0.980694\pi
272272 4.24698 0.257511
273273 0 0
274274 −1.78017 −0.107544
275275 − 7.43967i − 0.448629i
276276 0 0
277277 −11.7845 −0.708061 −0.354030 0.935234i 0.615189π-0.615189\pi
−0.354030 + 0.935234i 0.615189π0.615189\pi
278278 − 25.4795i − 1.52816i
279279 0 0
280280 − 6.97823i − 0.417029i
281281 − 6.47219i − 0.386098i −0.981189 0.193049i 0.938162π-0.938162\pi
0.981189 0.193049i 0.0618377π-0.0618377\pi
282282 0 0
283283 −6.58104 −0.391202 −0.195601 0.980684i 0.562666π-0.562666\pi
−0.195601 + 0.980684i 0.562666π0.562666\pi
284284 − 14.0073i − 0.831180i
285285 0 0
286286 0 0
287287 −2.61058 −0.154098
288288 0 0
289289 11.0465 0.649796
290290 7.36658 0.432581
291291 0 0
292292 − 32.1739i − 1.88284i
293293 − 24.3381i − 1.42185i −0.703269 0.710924i 0.748277π-0.748277\pi
0.703269 0.710924i 0.251723π-0.251723\pi
294294 0 0
295295 17.6407 1.02708
296296 −12.6256 −0.733851
297297 0 0
298298 18.8877 1.09413
299299 0 0
300300 0 0
301301 12.5743i 0.724773i
302302 31.7482 1.82691
303303 0 0
304304 4.69202i 0.269106i
305305 12.3763i 0.708663i
306306 0 0
307307 14.0737i 0.803227i 0.915809 + 0.401613i 0.131550π0.131550\pi
−0.915809 + 0.401613i 0.868450π0.868450\pi
308308 15.9608 0.909449
309309 0 0
310310 13.8605i 0.787226i
311311 −29.7700 −1.68810 −0.844051 0.536263i 0.819836π-0.819836\pi
−0.844051 + 0.536263i 0.819836π0.819836\pi
312312 0 0
313313 −7.47889 −0.422732 −0.211366 0.977407i 0.567791π-0.567791\pi
−0.211366 + 0.977407i 0.567791π0.567791\pi
314314 − 21.1957i − 1.19614i
315315 0 0
316316 48.1051 2.70613
317317 − 30.0301i − 1.68666i −0.537396 0.843330i 0.680592π-0.680592\pi
0.537396 0.843330i 0.319408π-0.319408\pi
318318 0 0
319319 5.79656i 0.324545i
320320 18.8388i 1.05312i
321321 0 0
322322 −8.70171 −0.484927
323323 30.9855i 1.72408i
324324 0 0
325325 0 0
326326 19.5579 1.08321
327327 0 0
328328 −3.00298 −0.165812
329329 −6.04652 −0.333356
330330 0 0
331331 − 15.7168i − 0.863872i −0.901904 0.431936i 0.857831π-0.857831\pi
0.901904 0.431936i 0.142169π-0.142169\pi
332332 23.5483i 1.29238i
333333 0 0
334334 53.5991 2.93281
335335 −0.833397 −0.0455333
336336 0 0
337337 −1.95407 −0.106445 −0.0532224 0.998583i 0.516949π-0.516949\pi
−0.0532224 + 0.998583i 0.516949π0.516949\pi
338338 0 0
339339 0 0
340340 23.3327i 1.26540i
341341 −10.9065 −0.590619
342342 0 0
343343 − 20.0834i − 1.08440i
344344 14.4644i 0.779869i
345345 0 0
346346 − 42.3672i − 2.27767i
347347 17.1250 0.919317 0.459659 0.888096i 0.347972π-0.347972\pi
0.459659 + 0.888096i 0.347972π0.347972\pi
348348 0 0
349349 10.4668i 0.560276i 0.959960 + 0.280138i 0.0903802π0.0903802\pi
−0.959960 + 0.280138i 0.909620π0.909620\pi
350350 13.4058 0.716571
351351 0 0
352352 −16.6474 −0.887310
353353 − 15.5308i − 0.826621i −0.910590 0.413310i 0.864372π-0.864372\pi
0.910590 0.413310i 0.135628π-0.135628\pi
354354 0 0
355355 −6.63879 −0.352351
356356 − 20.1642i − 1.06870i
357357 0 0
358358 13.5308i 0.715125i
359359 − 21.4263i − 1.13083i −0.824805 0.565417i 0.808715π-0.808715\pi
0.824805 0.565417i 0.191285π-0.191285\pi
360360 0 0
361361 −15.2325 −0.801711
362362 10.7356i 0.564249i
363363 0 0
364364 0 0
365365 −15.2489 −0.798164
366366 0 0
367367 34.3032 1.79061 0.895306 0.445452i 0.146957π-0.146957\pi
0.895306 + 0.445452i 0.146957π0.146957\pi
368368 1.51573 0.0790129
369369 0 0
370370 17.3937i 0.904257i
371371 11.3123i 0.587305i
372372 0 0
373373 −12.5961 −0.652202 −0.326101 0.945335i 0.605735π-0.605735\pi
−0.326101 + 0.945335i 0.605735π0.605735\pi
374374 −30.4034 −1.57212
375375 0 0
376376 −6.95539 −0.358697
377377 0 0
378378 0 0
379379 16.5386i 0.849529i 0.905304 + 0.424765i 0.139643π0.139643\pi
−0.905304 + 0.424765i 0.860357π0.860357\pi
380380 −25.7778 −1.32237
381381 0 0
382382 − 41.4131i − 2.11888i
383383 − 7.53617i − 0.385080i −0.981289 0.192540i 0.938327π-0.938327\pi
0.981289 0.192540i 0.0616726π-0.0616726\pi
384384 0 0
385385 − 7.56465i − 0.385530i
386386 13.6039 0.692419
387387 0 0
388388 − 36.3642i − 1.84611i
389389 35.5555 1.80274 0.901369 0.433052i 0.142563π-0.142563\pi
0.901369 + 0.433052i 0.142563π0.142563\pi
390390 0 0
391391 10.0097 0.506212
392392 − 6.60388i − 0.333546i
393393 0 0
394394 −25.6504 −1.29225
395395 − 22.7995i − 1.14717i
396396 0 0
397397 − 1.35152i − 0.0678308i −0.999425 0.0339154i 0.989202π-0.989202\pi
0.999425 0.0339154i 0.0107977π-0.0107977\pi
398398 31.2446i 1.56615i
399399 0 0
400400 −2.33513 −0.116756
401401 0.579121i 0.0289199i 0.999895 + 0.0144600i 0.00460291π0.00460291\pi
−0.999895 + 0.0144600i 0.995397π0.995397\pi
402402 0 0
403403 0 0
404404 −39.8310 −1.98167
405405 0 0
406406 −10.4450 −0.518379
407407 −13.6866 −0.678422
408408 0 0
409409 − 15.1575i − 0.749490i −0.927128 0.374745i 0.877730π-0.877730\pi
0.927128 0.374745i 0.122270π-0.122270\pi
410410 4.13706i 0.204315i
411411 0 0
412412 27.9541 1.37720
413413 −25.0127 −1.23079
414414 0 0
415415 11.1608 0.547860
416416 0 0
417417 0 0
418418 − 33.5894i − 1.64291i
419419 35.7235 1.74521 0.872603 0.488430i 0.162430π-0.162430\pi
0.872603 + 0.488430i 0.162430π0.162430\pi
420420 0 0
421421 − 35.0465i − 1.70806i −0.520221 0.854032i 0.674151π-0.674151\pi
0.520221 0.854032i 0.325849π-0.325849\pi
422422 − 29.7603i − 1.44871i
423423 0 0
424424 13.0127i 0.631951i
425425 −15.4209 −0.748022
426426 0 0
427427 − 17.5483i − 0.849220i
428428 −21.0368 −1.01685
429429 0 0
430430 19.9269 0.960961
431431 34.2814i 1.65128i 0.564199 + 0.825639i 0.309185π0.309185\pi
−0.564199 + 0.825639i 0.690815π0.690815\pi
432432 0 0
433433 −13.7385 −0.660232 −0.330116 0.943940i 0.607088π-0.607088\pi
−0.330116 + 0.943940i 0.607088π0.607088\pi
434434 − 19.6528i − 0.943364i
435435 0 0
436436 − 0.371961i − 0.0178137i
437437 11.0586i 0.529005i
438438 0 0
439439 −10.2403 −0.488742 −0.244371 0.969682i 0.578581π-0.578581\pi
−0.244371 + 0.969682i 0.578581π0.578581\pi
440440 − 8.70171i − 0.414838i
441441 0 0
442442 0 0
443443 −12.1763 −0.578513 −0.289257 0.957252i 0.593408π-0.593408\pi
−0.289257 + 0.957252i 0.593408π0.593408\pi
444444 0 0
445445 −9.55688 −0.453039
446446 16.4819 0.780440
447447 0 0
448448 − 26.7114i − 1.26199i
449449 − 12.9051i − 0.609032i −0.952507 0.304516i 0.901505π-0.901505\pi
0.952507 0.304516i 0.0984947π-0.0984947\pi
450450 0 0
451451 −3.25534 −0.153288
452452 22.2814 1.04803
453453 0 0
454454 −19.4916 −0.914785
455455 0 0
456456 0 0
457457 4.65710i 0.217850i 0.994050 + 0.108925i 0.0347409π0.0347409\pi
−0.994050 + 0.108925i 0.965259π0.965259\pi
458458 −30.7536 −1.43702
459459 0 0
460460 8.32736i 0.388265i
461461 31.5405i 1.46899i 0.678616 + 0.734493i 0.262580π0.262580\pi
−0.678616 + 0.734493i 0.737420π0.737420\pi
462462 0 0
463463 − 17.6504i − 0.820284i −0.912022 0.410142i 0.865479π-0.865479\pi
0.912022 0.410142i 0.134521π-0.134521\pi
464464 1.81940 0.0844633
465465 0 0
466466 − 11.4330i − 0.529622i
467467 −32.1726 −1.48877 −0.744385 0.667751i 0.767257π-0.767257\pi
−0.744385 + 0.667751i 0.767257π0.767257\pi
468468 0 0
469469 1.18167 0.0545644
470470 9.58211i 0.441990i
471471 0 0
472472 −28.7724 −1.32436
473473 15.6799i 0.720964i
474474 0 0
475475 − 17.0368i − 0.781704i
476476 − 33.0834i − 1.51637i
477477 0 0
478478 −24.5459 −1.12270
479479 − 34.8998i − 1.59461i −0.603576 0.797306i 0.706258π-0.706258\pi
0.603576 0.797306i 0.293742π-0.293742\pi
480480 0 0
481481 0 0
482482 26.7724 1.21945
483483 0 0
484484 −13.6353 −0.619788
485485 −17.2349 −0.782596
486486 0 0
487487 41.8351i 1.89573i 0.318676 + 0.947864i 0.396762π0.396762\pi
−0.318676 + 0.947864i 0.603238π0.603238\pi
488488 − 20.1860i − 0.913776i
489489 0 0
490490 −9.09783 −0.410998
491491 21.8455 0.985873 0.492936 0.870065i 0.335924π-0.335924\pi
0.492936 + 0.870065i 0.335924π0.335924\pi
492492 0 0
493493 12.0151 0.541131
494494 0 0
495495 0 0
496496 3.42327i 0.153709i
497497 9.41311 0.422236
498498 0 0
499499 23.5472i 1.05412i 0.849829 + 0.527058i 0.176705π0.176705\pi
−0.849829 + 0.527058i 0.823295π0.823295\pi
500500 − 34.8582i − 1.55890i
501501 0 0
502502 50.2150i 2.24121i
503503 7.08682 0.315986 0.157993 0.987440i 0.449498π-0.449498\pi
0.157993 + 0.987440i 0.449498π0.449498\pi
504504 0 0
505505 18.8780i 0.840060i
506506 −10.8509 −0.482379
507507 0 0
508508 −57.8394 −2.56621
509509 − 7.61894i − 0.337704i −0.985641 0.168852i 0.945994π-0.945994\pi
0.985641 0.168852i 0.0540059π-0.0540059\pi
510510 0 0
511511 21.6213 0.956471
512512 9.00538i 0.397985i
513513 0 0
514514 − 41.9288i − 1.84940i
515515 − 13.2489i − 0.583816i
516516 0 0
517517 −7.53989 −0.331604
518518 − 24.6625i − 1.08361i
519519 0 0
520520 0 0
521521 39.5133 1.73111 0.865555 0.500813i 0.166966π-0.166966\pi
0.865555 + 0.500813i 0.166966π0.166966\pi
522522 0 0
523523 −15.8194 −0.691734 −0.345867 0.938284i 0.612415π-0.612415\pi
−0.345867 + 0.938284i 0.612415π0.612415\pi
524524 9.92931 0.433764
525525 0 0
526526 − 32.3545i − 1.41072i
527527 22.6069i 0.984770i
528528 0 0
529529 −19.4276 −0.844678
530530 17.9269 0.778696
531531 0 0
532532 36.5502 1.58465
533533 0 0
534534 0 0
535535 9.97046i 0.431061i
536536 1.35929 0.0587123
537537 0 0
538538 − 1.46681i − 0.0632388i
539539 − 7.15883i − 0.308353i
540540 0 0
541541 − 34.4819i − 1.48249i −0.671234 0.741246i 0.734235π-0.734235\pi
0.671234 0.741246i 0.265765π-0.265765\pi
542542 −4.48427 −0.192616
543543 0 0
544544 34.5066i 1.47946i
545545 −0.176292 −0.00755152
546546 0 0
547547 36.8582 1.57594 0.787970 0.615713i 0.211132π-0.211132\pi
0.787970 + 0.615713i 0.211132π0.211132\pi
548548 − 2.41550i − 0.103185i
549549 0 0
550550 16.7168 0.712806
551551 13.2741i 0.565497i
552552 0 0
553553 32.3274i 1.37470i
554554 − 26.4795i − 1.12501i
555555 0 0
556556 34.5730 1.46622
557557 1.27652i 0.0540879i 0.999634 + 0.0270439i 0.00860940π0.00860940\pi
−0.999634 + 0.0270439i 0.991391π0.991391\pi
558558 0 0
559559 0 0
560560 −2.37435 −0.100335
561561 0 0
562562 14.5429 0.613454
563563 −9.12737 −0.384673 −0.192336 0.981329i 0.561607π-0.561607\pi
−0.192336 + 0.981329i 0.561607π0.561607\pi
564564 0 0
565565 − 10.5603i − 0.444277i
566566 − 14.7875i − 0.621563i
567567 0 0
568568 10.8280 0.454334
569569 −5.72156 −0.239860 −0.119930 0.992782i 0.538267π-0.538267\pi
−0.119930 + 0.992782i 0.538267π0.538267\pi
570570 0 0
571571 −7.60148 −0.318112 −0.159056 0.987270i 0.550845π-0.550845\pi
−0.159056 + 0.987270i 0.550845π0.550845\pi
572572 0 0
573573 0 0
574574 − 5.86592i − 0.244839i
575575 −5.50365 −0.229518
576576 0 0
577577 45.1564i 1.87989i 0.341330 + 0.939944i 0.389123π0.389123\pi
−0.341330 + 0.939944i 0.610877π0.610877\pi
578578 24.8213i 1.03243i
579579 0 0
580580 9.99569i 0.415048i
581581 −15.8248 −0.656522
582582 0 0
583583 14.1062i 0.584219i
584584 24.8713 1.02918
585585 0 0
586586 54.6872 2.25911
587587 32.4040i 1.33746i 0.743507 + 0.668728i 0.233161π0.233161\pi
−0.743507 + 0.668728i 0.766839π0.766839\pi
588588 0 0
589589 −24.9758 −1.02911
590590 39.6383i 1.63188i
591591 0 0
592592 4.29590i 0.176560i
593593 36.6848i 1.50647i 0.657754 + 0.753233i 0.271507π0.271507\pi
−0.657754 + 0.753233i 0.728493π0.728493\pi
594594 0 0
595595 −15.6799 −0.642815
596596 25.6286i 1.04979i
597597 0 0
598598 0 0
599599 9.99223 0.408271 0.204136 0.978943i 0.434562π-0.434562\pi
0.204136 + 0.978943i 0.434562π0.434562\pi
600600 0 0
601601 −1.81163 −0.0738978 −0.0369489 0.999317i 0.511764π-0.511764\pi
−0.0369489 + 0.999317i 0.511764π0.511764\pi
602602 −28.2543 −1.15156
603603 0 0
604604 43.0790i 1.75286i
605605 6.46250i 0.262738i
606606 0 0
607607 11.2161 0.455248 0.227624 0.973749i 0.426904π-0.426904\pi
0.227624 + 0.973749i 0.426904π0.426904\pi
608608 −38.1226 −1.54608
609609 0 0
610610 −27.8092 −1.12596
611611 0 0
612612 0 0
613613 − 20.8944i − 0.843917i −0.906615 0.421958i 0.861343π-0.861343\pi
0.906615 0.421958i 0.138657π-0.138657\pi
614614 −31.6233 −1.27621
615615 0 0
616616 12.3381i 0.497117i
617617 − 12.0992i − 0.487094i −0.969889 0.243547i 0.921689π-0.921689\pi
0.969889 0.243547i 0.0783110π-0.0783110\pi
618618 0 0
619619 10.5526i 0.424143i 0.977254 + 0.212072i 0.0680210π0.0680210\pi
−0.977254 + 0.212072i 0.931979π0.931979\pi
620620 −18.8073 −0.755320
621621 0 0
622622 − 66.8926i − 2.68215i
623623 13.5506 0.542895
624624 0 0
625625 −1.96184 −0.0784735
626626 − 16.8049i − 0.671660i
627627 0 0
628628 28.7603 1.14766
629629 28.3696i 1.13117i
630630 0 0
631631 13.8514i 0.551417i 0.961241 + 0.275709i 0.0889125π0.0889125\pi
−0.961241 + 0.275709i 0.911087π0.911087\pi
632632 37.1866i 1.47920i
633633 0 0
634634 67.4771 2.67986
635635 27.4131i 1.08786i
636636 0 0
637637 0 0
638638 −13.0248 −0.515655
639639 0 0
640640 −23.4993 −0.928893
641641 34.9608 1.38087 0.690434 0.723396i 0.257420π-0.257420\pi
0.690434 + 0.723396i 0.257420π0.257420\pi
642642 0 0
643643 33.3980i 1.31709i 0.752541 + 0.658545i 0.228828π0.228828\pi
−0.752541 + 0.658545i 0.771172π0.771172\pi
644644 − 11.8073i − 0.465273i
645645 0 0
646646 −69.6238 −2.73931
647647 2.32842 0.0915397 0.0457698 0.998952i 0.485426π-0.485426\pi
0.0457698 + 0.998952i 0.485426π0.485426\pi
648648 0 0
649649 −31.1903 −1.22433
650650 0 0
651651 0 0
652652 26.5381i 1.03931i
653653 −14.5714 −0.570221 −0.285111 0.958495i 0.592030π-0.592030\pi
−0.285111 + 0.958495i 0.592030π0.592030\pi
654654 0 0
655655 − 4.70602i − 0.183879i
656656 1.02177i 0.0398934i
657657 0 0
658658 − 13.5864i − 0.529654i
659659 −11.1395 −0.433932 −0.216966 0.976179i 0.569616π-0.569616\pi
−0.216966 + 0.976179i 0.569616π0.569616\pi
660660 0 0
661661 13.8498i 0.538694i 0.963043 + 0.269347i 0.0868079π0.0868079\pi
−0.963043 + 0.269347i 0.913192π0.913192\pi
662662 35.3153 1.37257
663663 0 0
664664 −18.2034 −0.706430
665665 − 17.3230i − 0.671759i
666666 0 0
667667 4.28813 0.166037
668668 72.7284i 2.81395i
669669 0 0
670670 − 1.87263i − 0.0723458i
671671 − 21.8823i − 0.844757i
672672 0 0
673673 6.52973 0.251703 0.125851 0.992049i 0.459834π-0.459834\pi
0.125851 + 0.992049i 0.459834π0.459834\pi
674674 − 4.39075i − 0.169125i
675675 0 0
676676 0 0
677677 11.3104 0.434693 0.217346 0.976095i 0.430260π-0.430260\pi
0.217346 + 0.976095i 0.430260π0.430260\pi
678678 0 0
679679 24.4373 0.937816
680680 −18.0368 −0.691681
681681 0 0
682682 − 24.5066i − 0.938407i
683683 14.1793i 0.542555i 0.962501 + 0.271277i 0.0874461π0.0874461\pi
−0.962501 + 0.271277i 0.912554π0.912554\pi
684684 0 0
685685 −1.14483 −0.0437418
686686 45.1269 1.72295
687687 0 0
688688 4.92154 0.187632
689689 0 0
690690 0 0
691691 30.7952i 1.17151i 0.810490 + 0.585753i 0.199201π0.199201\pi
−0.810490 + 0.585753i 0.800799π0.800799\pi
692692 57.4878 2.18536
693693 0 0
694694 38.4795i 1.46066i
695695 − 16.3860i − 0.621555i
696696 0 0
697697 6.74764i 0.255585i
698698 −23.5187 −0.890196
699699 0 0
700700 18.1903i 0.687528i
701701 6.73184 0.254258 0.127129 0.991886i 0.459424π-0.459424\pi
0.127129 + 0.991886i 0.459424π0.459424\pi
702702 0 0
703703 −31.3424 −1.18210
704704 − 33.3086i − 1.25536i
705705 0 0
706706 34.8974 1.31338
707707 − 26.7670i − 1.00668i
708708 0 0
709709 47.6252i 1.78860i 0.447467 + 0.894300i 0.352326π0.352326\pi
−0.447467 + 0.894300i 0.647674π0.647674\pi
710710 − 14.9172i − 0.559834i
711711 0 0
712712 15.5875 0.584166
713713 8.06829i 0.302160i
714714 0 0
715715 0 0
716716 −18.3599 −0.686141
717717 0 0
718718 48.1444 1.79673
719719 −5.99330 −0.223512 −0.111756 0.993736i 0.535648π-0.535648\pi
−0.111756 + 0.993736i 0.535648π0.535648\pi
720720 0 0
721721 18.7855i 0.699610i
722722 − 34.2271i − 1.27380i
723723 0 0
724724 −14.5670 −0.541380
725725 −6.60627 −0.245351
726726 0 0
727727 24.1226 0.894657 0.447329 0.894370i 0.352375π-0.352375\pi
0.447329 + 0.894370i 0.352375π0.352375\pi
728728 0 0
729729 0 0
730730 − 34.2640i − 1.26817i
731731 32.5013 1.20210
732732 0 0
733733 36.0646i 1.33208i 0.745918 + 0.666038i 0.232011π0.232011\pi
−0.745918 + 0.666038i 0.767989π0.767989\pi
734734 77.0786i 2.84502i
735735 0 0
736736 12.3153i 0.453947i
737737 1.47352 0.0542777
738738 0 0
739739 − 27.5254i − 1.01254i −0.862375 0.506269i 0.831024π-0.831024\pi
0.862375 0.506269i 0.168976π-0.168976\pi
740740 −23.6015 −0.867608
741741 0 0
742742 −25.4185 −0.933142
743743 10.4692i 0.384078i 0.981387 + 0.192039i 0.0615100π0.0615100\pi
−0.981387 + 0.192039i 0.938490π0.938490\pi
744744 0 0
745745 12.1468 0.445023
746746 − 28.3032i − 1.03625i
747747 0 0
748748 − 41.2543i − 1.50841i
749749 − 14.1371i − 0.516557i
750750 0 0
751751 −4.06770 −0.148433 −0.0742163 0.997242i 0.523646π-0.523646\pi
−0.0742163 + 0.997242i 0.523646π0.523646\pi
752752 2.36658i 0.0863005i
753753 0 0
754754 0 0
755755 20.4174 0.743066
756756 0 0
757757 20.4336 0.742670 0.371335 0.928499i 0.378900π-0.378900\pi
0.371335 + 0.928499i 0.378900π0.378900\pi
758758 −37.1618 −1.34978
759759 0 0
760760 − 19.9269i − 0.722825i
761761 − 27.0237i − 0.979608i −0.871833 0.489804i 0.837068π-0.837068\pi
0.871833 0.489804i 0.162932π-0.162932\pi
762762 0 0
763763 0.249964 0.00904929
764764 56.1933 2.03300
765765 0 0
766766 16.9336 0.611837
767767 0 0
768768 0 0
769769 − 37.9407i − 1.36818i −0.729400 0.684088i 0.760201π-0.760201\pi
0.729400 0.684088i 0.239799π-0.239799\pi
770770 16.9976 0.612551
771771 0 0
772772 18.4590i 0.664355i
773773 16.3375i 0.587620i 0.955864 + 0.293810i 0.0949232π0.0949232\pi
−0.955864 + 0.293810i 0.905077π0.905077\pi
774774 0 0
775775 − 12.4300i − 0.446498i
776776 28.1105 1.00911
777777 0 0
778778 79.8926i 2.86429i
779779 −7.45473 −0.267093
780780 0 0
781781 11.7380 0.420017
782782 22.4916i 0.804297i
783783 0 0
784784 −2.24698 −0.0802493
785785 − 13.6310i − 0.486512i
786786 0 0
787787 18.6907i 0.666251i 0.942882 + 0.333126i 0.108103π0.108103\pi
−0.942882 + 0.333126i 0.891897π0.891897\pi
788788 − 34.8049i − 1.23987i
789789 0 0
790790 51.2301 1.82269
791791 14.9734i 0.532394i
792792 0 0
793793 0 0
794794 3.03684 0.107773
795795 0 0
796796 −42.3957 −1.50267
797797 29.2519 1.03615 0.518077 0.855334i 0.326648π-0.326648\pi
0.518077 + 0.855334i 0.326648π0.326648\pi
798798 0 0
799799 15.6286i 0.552901i
800800 − 18.9729i − 0.670792i
801801 0 0
802802 −1.30127 −0.0459496
803803 26.9614 0.951446
804804 0 0
805805 −5.59611 −0.197237
806806 0 0
807807 0 0
808808 − 30.7904i − 1.08320i
809809 6.65087 0.233832 0.116916 0.993142i 0.462699π-0.462699\pi
0.116916 + 0.993142i 0.462699π0.462699\pi
810810 0 0
811811 3.89200i 0.136667i 0.997663 + 0.0683333i 0.0217681π0.0217681\pi
−0.997663 + 0.0683333i 0.978232π0.978232\pi
812812 − 14.1728i − 0.497369i
813813 0 0
814814 − 30.7536i − 1.07791i
815815 12.5778 0.440581
816816 0 0
817817 35.9071i 1.25623i
818818 34.0586 1.19083
819819 0 0
820820 −5.61356 −0.196034
821821 − 45.9982i − 1.60535i −0.596418 0.802674i 0.703410π-0.703410\pi
0.596418 0.802674i 0.296590π-0.296590\pi
822822 0 0
823823 −7.95300 −0.277224 −0.138612 0.990347i 0.544264π-0.544264\pi
−0.138612 + 0.990347i 0.544264π0.544264\pi
824824 21.6093i 0.752794i
825825 0 0
826826 − 56.2030i − 1.95555i
827827 27.9648i 0.972432i 0.873839 + 0.486216i 0.161623π0.161623\pi
−0.873839 + 0.486216i 0.838377π0.838377\pi
828828 0 0
829829 −27.6310 −0.959665 −0.479833 0.877360i 0.659303π-0.659303\pi
−0.479833 + 0.877360i 0.659303π0.659303\pi
830830 25.0780i 0.870470i
831831 0 0
832832 0 0
833833 −14.8388 −0.514133
834834 0 0
835835 34.4698 1.19288
836836 45.5773 1.57632
837837 0 0
838838 80.2699i 2.77288i
839839 28.6848i 0.990311i 0.868804 + 0.495155i 0.164889π0.164889\pi
−0.868804 + 0.495155i 0.835111π0.835111\pi
840840 0 0
841841 −23.8528 −0.822509
842842 78.7488 2.71386
843843 0 0
844844 40.3817 1.38999
845845 0 0
846846 0 0
847847 − 9.16315i − 0.314849i
848848 4.42758 0.152044
849849 0 0
850850 − 34.6504i − 1.18850i
851851 10.1250i 0.347080i
852852 0 0
853853 43.2078i 1.47941i 0.672934 + 0.739703i 0.265034π0.265034\pi
−0.672934 + 0.739703i 0.734966π0.734966\pi
854854 39.4306 1.34929
855855 0 0
856856 − 16.2620i − 0.555825i
857857 35.1685 1.20133 0.600667 0.799499i 0.294902π-0.294902\pi
0.600667 + 0.799499i 0.294902π0.294902\pi
858858 0 0
859859 27.3793 0.934168 0.467084 0.884213i 0.345305π-0.345305\pi
0.467084 + 0.884213i 0.345305π0.345305\pi
860860 27.0388i 0.922014i
861861 0 0
862862 −77.0297 −2.62364
863863 41.3913i 1.40898i 0.709715 + 0.704489i 0.248824π0.248824\pi
−0.709715 + 0.704489i 0.751176π0.751176\pi
864864 0 0
865865 − 27.2465i − 0.926409i
866866 − 30.8702i − 1.04901i
867867 0 0
868868 26.6668 0.905130
869869 40.3116i 1.36748i
870870 0 0
871871 0 0
872872 0.287536 0.00973721
873873 0 0
874874 −24.8485 −0.840512
875875 23.4252 0.791916
876876 0 0
877877 − 24.7472i − 0.835653i −0.908527 0.417826i 0.862792π-0.862792\pi
0.908527 0.417826i 0.137208π-0.137208\pi
878878 − 23.0097i − 0.776539i
879879 0 0
880880 −2.96077 −0.0998076
881881 −28.5875 −0.963137 −0.481568 0.876409i 0.659933π-0.659933\pi
−0.481568 + 0.876409i 0.659933π0.659933\pi
882882 0 0
883883 −9.61702 −0.323639 −0.161819 0.986820i 0.551736π-0.551736\pi
−0.161819 + 0.986820i 0.551736π0.551736\pi
884884 0 0
885885 0 0
886886 − 27.3599i − 0.919173i
887887 −15.9661 −0.536091 −0.268045 0.963406i 0.586378π-0.586378\pi
−0.268045 + 0.963406i 0.586378π0.586378\pi
888888 0 0
889889 − 38.8689i − 1.30362i
890890 − 21.4741i − 0.719814i
891891 0 0
892892 22.3642i 0.748809i
893893 −17.2664 −0.577797
894894 0 0
895895 8.70171i 0.290866i
896896 33.3196 1.11313
897897 0 0
898898 28.9976 0.967663
899899 9.68473i 0.323004i
900900 0 0
901901 29.2392 0.974099
902902 − 7.31468i − 0.243552i
903903 0 0
904904 17.2241i 0.572867i
905905 6.90408i 0.229500i
906906 0 0
907907 28.8364 0.957496 0.478748 0.877952i 0.341091π-0.341091\pi
0.478748 + 0.877952i 0.341091π0.341091\pi
908908 − 26.4480i − 0.877709i
909909 0 0
910910 0 0
911911 −38.5633 −1.27766 −0.638830 0.769348i 0.720581π-0.720581\pi
−0.638830 + 0.769348i 0.720581π0.720581\pi
912912 0 0
913913 −19.7332 −0.653073
914914 −10.4644 −0.346132
915915 0 0
916916 − 41.7294i − 1.37878i
917917 6.67264i 0.220350i
918918 0 0
919919 8.87502 0.292760 0.146380 0.989228i 0.453238π-0.453238\pi
0.146380 + 0.989228i 0.453238π0.453238\pi
920920 −6.43727 −0.212231
921921 0 0
922922 −70.8708 −2.33401
923923 0 0
924924 0 0
925925 − 15.5985i − 0.512875i
926926 39.6601 1.30331
927927 0 0
928928 14.7826i 0.485261i
929929 − 24.2295i − 0.794945i −0.917614 0.397472i 0.869887π-0.869887\pi
0.917614 0.397472i 0.130113π-0.130113\pi
930930 0 0
931931 − 16.3937i − 0.537283i
932932 15.5133 0.508156
933933 0 0
934934 − 72.2911i − 2.36544i
935935 −19.5526 −0.639437
936936 0 0
937937 17.2644 0.564005 0.282002 0.959414i 0.409001π-0.409001\pi
0.282002 + 0.959414i 0.409001π0.409001\pi
938938 2.65519i 0.0866949i
939939 0 0
940940 −13.0019 −0.424076
941941 − 4.34050i − 0.141496i −0.997494 0.0707482i 0.977461π-0.977461\pi
0.997494 0.0707482i 0.0225387π-0.0225387\pi
942942 0 0
943943 2.40821i 0.0784220i
944944 9.78986i 0.318633i
945945 0 0
946946 −35.2325 −1.14551
947947 − 45.0146i − 1.46278i −0.681961 0.731389i 0.738872π-0.738872\pi
0.681961 0.731389i 0.261128π-0.261128\pi
948948 0 0
949949 0 0
950950 38.2814 1.24201
951951 0 0
952952 25.5743 0.828869
953953 −46.8859 −1.51878 −0.759391 0.650634i 0.774503π-0.774503\pi
−0.759391 + 0.650634i 0.774503π0.774503\pi
954954 0 0
955955 − 26.6329i − 0.861822i
956956 − 33.3062i − 1.07720i
957957 0 0
958958 78.4191 2.53361
959959 1.62325 0.0524176
960960 0 0
961961 12.7778 0.412186
962962 0 0
963963 0 0
964964 36.3274i 1.17003i
965965 8.74871 0.281631
966966 0 0
967967 6.29457i 0.202420i 0.994865 + 0.101210i 0.0322714π0.0322714\pi
−0.994865 + 0.101210i 0.967729π0.967729\pi
968968 − 10.5405i − 0.338784i
969969 0 0
970970 − 38.7265i − 1.24343i
971971 41.8068 1.34165 0.670823 0.741618i 0.265941π-0.265941\pi
0.670823 + 0.741618i 0.265941π0.265941\pi
972972 0 0
973973 23.2336i 0.744834i
974974 −94.0025 −3.01203
975975 0 0
976976 −6.86831 −0.219849
977977 − 23.7530i − 0.759926i −0.925002 0.379963i 0.875937π-0.875937\pi
0.925002 0.379963i 0.124063π-0.124063\pi
978978 0 0
979979 16.8974 0.540043
980980 − 12.3448i − 0.394341i
981981 0 0
982982 49.0863i 1.56641i
983983 − 55.7251i − 1.77736i −0.458532 0.888678i 0.651625π-0.651625\pi
0.458532 0.888678i 0.348375π-0.348375\pi
984984 0 0
985985 −16.4959 −0.525602
986986 26.9976i 0.859779i
987987 0 0
988988 0 0
989989 11.5996 0.368845
990990 0 0
991991 −35.5512 −1.12932 −0.564661 0.825323i 0.690993π-0.690993\pi
−0.564661 + 0.825323i 0.690993π0.690993\pi
992992 −27.8140 −0.883096
993993 0 0
994994 21.1511i 0.670871i
995995 20.0935i 0.637007i
996996 0 0
997997 6.61058 0.209359 0.104680 0.994506i 0.466618π-0.466618\pi
0.104680 + 0.994506i 0.466618π0.466618\pi
998998 −52.9101 −1.67484
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 1521.2.b.l.1351.6 6
3.2 odd 2 169.2.b.b.168.1 6
12.11 even 2 2704.2.f.o.337.3 6
13.5 odd 4 1521.2.a.r.1.3 3
13.8 odd 4 1521.2.a.o.1.1 3
13.12 even 2 inner 1521.2.b.l.1351.1 6
39.2 even 12 169.2.c.c.22.3 6
39.5 even 4 169.2.a.b.1.1 3
39.8 even 4 169.2.a.c.1.3 yes 3
39.11 even 12 169.2.c.b.22.1 6
39.17 odd 6 169.2.e.b.23.6 12
39.20 even 12 169.2.c.b.146.1 6
39.23 odd 6 169.2.e.b.147.1 12
39.29 odd 6 169.2.e.b.147.6 12
39.32 even 12 169.2.c.c.146.3 6
39.35 odd 6 169.2.e.b.23.1 12
39.38 odd 2 169.2.b.b.168.6 6
156.47 odd 4 2704.2.a.ba.1.2 3
156.83 odd 4 2704.2.a.z.1.2 3
156.155 even 2 2704.2.f.o.337.4 6
195.44 even 4 4225.2.a.bg.1.3 3
195.164 even 4 4225.2.a.bb.1.1 3
273.83 odd 4 8281.2.a.bf.1.1 3
273.125 odd 4 8281.2.a.bj.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.2.a.b.1.1 3 39.5 even 4
169.2.a.c.1.3 yes 3 39.8 even 4
169.2.b.b.168.1 6 3.2 odd 2
169.2.b.b.168.6 6 39.38 odd 2
169.2.c.b.22.1 6 39.11 even 12
169.2.c.b.146.1 6 39.20 even 12
169.2.c.c.22.3 6 39.2 even 12
169.2.c.c.146.3 6 39.32 even 12
169.2.e.b.23.1 12 39.35 odd 6
169.2.e.b.23.6 12 39.17 odd 6
169.2.e.b.147.1 12 39.23 odd 6
169.2.e.b.147.6 12 39.29 odd 6
1521.2.a.o.1.1 3 13.8 odd 4
1521.2.a.r.1.3 3 13.5 odd 4
1521.2.b.l.1351.1 6 13.12 even 2 inner
1521.2.b.l.1351.6 6 1.1 even 1 trivial
2704.2.a.z.1.2 3 156.83 odd 4
2704.2.a.ba.1.2 3 156.47 odd 4
2704.2.f.o.337.3 6 12.11 even 2
2704.2.f.o.337.4 6 156.155 even 2
4225.2.a.bb.1.1 3 195.164 even 4
4225.2.a.bg.1.3 3 195.44 even 4
8281.2.a.bf.1.1 3 273.83 odd 4
8281.2.a.bj.1.3 3 273.125 odd 4