Properties

Label 1521.2.a.n.1.1
Level 15211521
Weight 22
Character 1521.1
Self dual yes
Analytic conductor 12.14512.145
Analytic rank 11
Dimension 33
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] = [1521,2,Mod(1,1521)]
 
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, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1521.1");
 
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.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: 12.145246147412.1452461474
Analytic rank: 11
Dimension: 33
Coefficient field: Q(ζ14)+\Q(\zeta_{14})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x22x+1 x^{3} - x^{2} - 2x + 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 507)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.24698-1.24698 of defining polynomial
Character χ\chi == 1521.1

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) == q2.69202q2+5.24698q4+1.04892q5+0.554958q78.74094q82.82371q102.91185q111.49396q14+13.0368q16+4.85086q170.753020q19+5.50365q20+7.83877q225.76271q233.89977q25+2.91185q28+1.91185q299.51573q3117.6136q3213.0586q34+0.582105q35+5.75302q37+2.02715q389.16852q404.91185q4111.0978q4315.2784q44+15.5133q460.753020q476.69202q49+10.4983q50+7.58211q533.05429q554.85086q565.14675q584.09783q593.42327q61+25.6165q62+21.3424q641.87263q67+25.4523q681.56704q70+10.5036q71+10.4765q7315.4873q743.95108q761.61596q77+1.33513q79+13.6746q80+13.2228q822.64310q83+5.08815q85+29.8756q86+25.4523q889.92692q8930.2368q92+2.02715q940.789856q95+17.0737q97+18.0151q98+O(q100)q-2.69202 q^{2} +5.24698 q^{4} +1.04892 q^{5} +0.554958 q^{7} -8.74094 q^{8} -2.82371 q^{10} -2.91185 q^{11} -1.49396 q^{14} +13.0368 q^{16} +4.85086 q^{17} -0.753020 q^{19} +5.50365 q^{20} +7.83877 q^{22} -5.76271 q^{23} -3.89977 q^{25} +2.91185 q^{28} +1.91185 q^{29} -9.51573 q^{31} -17.6136 q^{32} -13.0586 q^{34} +0.582105 q^{35} +5.75302 q^{37} +2.02715 q^{38} -9.16852 q^{40} -4.91185 q^{41} -11.0978 q^{43} -15.2784 q^{44} +15.5133 q^{46} -0.753020 q^{47} -6.69202 q^{49} +10.4983 q^{50} +7.58211 q^{53} -3.05429 q^{55} -4.85086 q^{56} -5.14675 q^{58} -4.09783 q^{59} -3.42327 q^{61} +25.6165 q^{62} +21.3424 q^{64} -1.87263 q^{67} +25.4523 q^{68} -1.56704 q^{70} +10.5036 q^{71} +10.4765 q^{73} -15.4873 q^{74} -3.95108 q^{76} -1.61596 q^{77} +1.33513 q^{79} +13.6746 q^{80} +13.2228 q^{82} -2.64310 q^{83} +5.08815 q^{85} +29.8756 q^{86} +25.4523 q^{88} -9.92692 q^{89} -30.2368 q^{92} +2.02715 q^{94} -0.789856 q^{95} +17.0737 q^{97} +18.0151 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q3q2+11q46q5+2q712q8q105q11+5q14+11q16+q177q1915q209q22+11q25+5q28+2q2916q3122q32++29q98+O(q100) 3 q - 3 q^{2} + 11 q^{4} - 6 q^{5} + 2 q^{7} - 12 q^{8} - q^{10} - 5 q^{11} + 5 q^{14} + 11 q^{16} + q^{17} - 7 q^{19} - 15 q^{20} - 9 q^{22} + 11 q^{25} + 5 q^{28} + 2 q^{29} - 16 q^{31} - 22 q^{32}+ \cdots + 29 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 −2.69202 −1.90355 −0.951773 0.306802i 0.900741π-0.900741\pi
−0.951773 + 0.306802i 0.900741π0.900741\pi
33 0 0
44 5.24698 2.62349
55 1.04892 0.469090 0.234545 0.972105i 0.424640π-0.424640\pi
0.234545 + 0.972105i 0.424640π0.424640\pi
66 0 0
77 0.554958 0.209754 0.104877 0.994485i 0.466555π-0.466555\pi
0.104877 + 0.994485i 0.466555π0.466555\pi
88 −8.74094 −3.09039
99 0 0
1010 −2.82371 −0.892935
1111 −2.91185 −0.877957 −0.438979 0.898498i 0.644660π-0.644660\pi
−0.438979 + 0.898498i 0.644660π0.644660\pi
1212 0 0
1313 0 0
1414 −1.49396 −0.399277
1515 0 0
1616 13.0368 3.25921
1717 4.85086 1.17651 0.588253 0.808677i 0.299816π-0.299816\pi
0.588253 + 0.808677i 0.299816π0.299816\pi
1818 0 0
1919 −0.753020 −0.172755 −0.0863774 0.996262i 0.527529π-0.527529\pi
−0.0863774 + 0.996262i 0.527529π0.527529\pi
2020 5.50365 1.23065
2121 0 0
2222 7.83877 1.67123
2323 −5.76271 −1.20161 −0.600804 0.799396i 0.705153π-0.705153\pi
−0.600804 + 0.799396i 0.705153π0.705153\pi
2424 0 0
2525 −3.89977 −0.779954
2626 0 0
2727 0 0
2828 2.91185 0.550289
2929 1.91185 0.355022 0.177511 0.984119i 0.443195π-0.443195\pi
0.177511 + 0.984119i 0.443195π0.443195\pi
3030 0 0
3131 −9.51573 −1.70908 −0.854538 0.519389i 0.826159π-0.826159\pi
−0.854538 + 0.519389i 0.826159π0.826159\pi
3232 −17.6136 −3.11367
3333 0 0
3434 −13.0586 −2.23953
3535 0.582105 0.0983937
3636 0 0
3737 5.75302 0.945791 0.472895 0.881119i 0.343209π-0.343209\pi
0.472895 + 0.881119i 0.343209π0.343209\pi
3838 2.02715 0.328847
3939 0 0
4040 −9.16852 −1.44967
4141 −4.91185 −0.767103 −0.383551 0.923520i 0.625299π-0.625299\pi
−0.383551 + 0.923520i 0.625299π0.625299\pi
4242 0 0
4343 −11.0978 −1.69240 −0.846202 0.532862i 0.821116π-0.821116\pi
−0.846202 + 0.532862i 0.821116π0.821116\pi
4444 −15.2784 −2.30331
4545 0 0
4646 15.5133 2.28732
4747 −0.753020 −0.109839 −0.0549197 0.998491i 0.517490π-0.517490\pi
−0.0549197 + 0.998491i 0.517490π0.517490\pi
4848 0 0
4949 −6.69202 −0.956003
5050 10.4983 1.48468
5151 0 0
5252 0 0
5353 7.58211 1.04148 0.520741 0.853715i 0.325656π-0.325656\pi
0.520741 + 0.853715i 0.325656π0.325656\pi
5454 0 0
5555 −3.05429 −0.411841
5656 −4.85086 −0.648223
5757 0 0
5858 −5.14675 −0.675802
5959 −4.09783 −0.533493 −0.266746 0.963767i 0.585949π-0.585949\pi
−0.266746 + 0.963767i 0.585949π0.585949\pi
6060 0 0
6161 −3.42327 −0.438305 −0.219153 0.975691i 0.570329π-0.570329\pi
−0.219153 + 0.975691i 0.570329π0.570329\pi
6262 25.6165 3.25330
6363 0 0
6464 21.3424 2.66780
6565 0 0
6666 0 0
6767 −1.87263 −0.228778 −0.114389 0.993436i 0.536491π-0.536491\pi
−0.114389 + 0.993436i 0.536491π0.536491\pi
6868 25.4523 3.08655
6969 0 0
7070 −1.56704 −0.187297
7171 10.5036 1.24655 0.623277 0.782001i 0.285801π-0.285801\pi
0.623277 + 0.782001i 0.285801π0.285801\pi
7272 0 0
7373 10.4765 1.22618 0.613091 0.790012i 0.289926π-0.289926\pi
0.613091 + 0.790012i 0.289926π0.289926\pi
7474 −15.4873 −1.80036
7575 0 0
7676 −3.95108 −0.453220
7777 −1.61596 −0.184155
7878 0 0
7979 1.33513 0.150213 0.0751067 0.997176i 0.476070π-0.476070\pi
0.0751067 + 0.997176i 0.476070π0.476070\pi
8080 13.6746 1.52886
8181 0 0
8282 13.2228 1.46022
8383 −2.64310 −0.290118 −0.145059 0.989423i 0.546337π-0.546337\pi
−0.145059 + 0.989423i 0.546337π0.546337\pi
8484 0 0
8585 5.08815 0.551887
8686 29.8756 3.22157
8787 0 0
8888 25.4523 2.71323
8989 −9.92692 −1.05225 −0.526126 0.850407i 0.676356π-0.676356\pi
−0.526126 + 0.850407i 0.676356π0.676356\pi
9090 0 0
9191 0 0
9292 −30.2368 −3.15241
9393 0 0
9494 2.02715 0.209084
9595 −0.789856 −0.0810375
9696 0 0
9797 17.0737 1.73357 0.866784 0.498683i 0.166183π-0.166183\pi
0.866784 + 0.498683i 0.166183π0.166183\pi
9898 18.0151 1.81980
9999 0 0
100100 −20.4620 −2.04620
101101 −7.32304 −0.728670 −0.364335 0.931268i 0.618704π-0.618704\pi
−0.364335 + 0.931268i 0.618704π0.618704\pi
102102 0 0
103103 −4.21983 −0.415792 −0.207896 0.978151i 0.566662π-0.566662\pi
−0.207896 + 0.978151i 0.566662π0.566662\pi
104104 0 0
105105 0 0
106106 −20.4112 −1.98251
107107 −6.39373 −0.618105 −0.309053 0.951045i 0.600012π-0.600012\pi
−0.309053 + 0.951045i 0.600012π0.600012\pi
108108 0 0
109109 −3.46011 −0.331418 −0.165709 0.986175i 0.552991π-0.552991\pi
−0.165709 + 0.986175i 0.552991π0.552991\pi
110110 8.22223 0.783958
111111 0 0
112112 7.23490 0.683634
113113 −9.35690 −0.880223 −0.440111 0.897943i 0.645061π-0.645061\pi
−0.440111 + 0.897943i 0.645061π0.645061\pi
114114 0 0
115115 −6.04461 −0.563662
116116 10.0315 0.931398
117117 0 0
118118 11.0315 1.01553
119119 2.69202 0.246777
120120 0 0
121121 −2.52111 −0.229191
122122 9.21552 0.834334
123123 0 0
124124 −49.9288 −4.48374
125125 −9.33513 −0.834959
126126 0 0
127127 −4.48188 −0.397702 −0.198851 0.980030i 0.563721π-0.563721\pi
−0.198851 + 0.980030i 0.563721π0.563721\pi
128128 −22.2271 −1.96462
129129 0 0
130130 0 0
131131 9.21744 0.805331 0.402666 0.915347i 0.368084π-0.368084\pi
0.402666 + 0.915347i 0.368084π0.368084\pi
132132 0 0
133133 −0.417895 −0.0362361
134134 5.04115 0.435489
135135 0 0
136136 −42.4010 −3.63586
137137 7.46980 0.638188 0.319094 0.947723i 0.396621π-0.396621\pi
0.319094 + 0.947723i 0.396621π0.396621\pi
138138 0 0
139139 −17.9976 −1.52654 −0.763269 0.646081i 0.776407π-0.776407\pi
−0.763269 + 0.646081i 0.776407π0.776407\pi
140140 3.05429 0.258135
141141 0 0
142142 −28.2760 −2.37287
143143 0 0
144144 0 0
145145 2.00538 0.166537
146146 −28.2030 −2.33409
147147 0 0
148148 30.1860 2.48127
149149 −15.3351 −1.25630 −0.628151 0.778091i 0.716188π-0.716188\pi
−0.628151 + 0.778091i 0.716188π0.716188\pi
150150 0 0
151151 2.53079 0.205953 0.102977 0.994684i 0.467163π-0.467163\pi
0.102977 + 0.994684i 0.467163π0.467163\pi
152152 6.58211 0.533879
153153 0 0
154154 4.35019 0.350548
155155 −9.98121 −0.801710
156156 0 0
157157 17.2392 1.37584 0.687919 0.725787i 0.258524π-0.258524\pi
0.687919 + 0.725787i 0.258524π0.258524\pi
158158 −3.59419 −0.285938
159159 0 0
160160 −18.4752 −1.46059
161161 −3.19806 −0.252043
162162 0 0
163163 15.7071 1.23027 0.615137 0.788420i 0.289101π-0.289101\pi
0.615137 + 0.788420i 0.289101π0.289101\pi
164164 −25.7724 −2.01249
165165 0 0
166166 7.11529 0.552254
167167 −5.39612 −0.417565 −0.208782 0.977962i 0.566950π-0.566950\pi
−0.208782 + 0.977962i 0.566950π0.566950\pi
168168 0 0
169169 0 0
170170 −13.6974 −1.05054
171171 0 0
172172 −58.2301 −4.44000
173173 −23.9420 −1.82028 −0.910138 0.414306i 0.864024π-0.864024\pi
−0.910138 + 0.414306i 0.864024π0.864024\pi
174174 0 0
175175 −2.16421 −0.163599
176176 −37.9614 −2.86145
177177 0 0
178178 26.7235 2.00301
179179 −18.4088 −1.37594 −0.687969 0.725740i 0.741498π-0.741498\pi
−0.687969 + 0.725740i 0.741498π0.741498\pi
180180 0 0
181181 −3.63342 −0.270070 −0.135035 0.990841i 0.543115π-0.543115\pi
−0.135035 + 0.990841i 0.543115π0.543115\pi
182182 0 0
183183 0 0
184184 50.3715 3.71344
185185 6.03444 0.443661
186186 0 0
187187 −14.1250 −1.03292
188188 −3.95108 −0.288162
189189 0 0
190190 2.12631 0.154259
191191 21.1782 1.53240 0.766201 0.642601i 0.222145π-0.222145\pi
0.766201 + 0.642601i 0.222145π0.222145\pi
192192 0 0
193193 −17.6112 −1.26768 −0.633840 0.773464i 0.718522π-0.718522\pi
−0.633840 + 0.773464i 0.718522π0.718522\pi
194194 −45.9627 −3.29993
195195 0 0
196196 −35.1129 −2.50806
197197 4.66248 0.332188 0.166094 0.986110i 0.446884π-0.446884\pi
0.166094 + 0.986110i 0.446884π0.446884\pi
198198 0 0
199199 15.0368 1.06593 0.532967 0.846136i 0.321077π-0.321077\pi
0.532967 + 0.846136i 0.321077π0.321077\pi
200200 34.0877 2.41036
201201 0 0
202202 19.7138 1.38706
203203 1.06100 0.0744675
204204 0 0
205205 −5.15213 −0.359840
206206 11.3599 0.791480
207207 0 0
208208 0 0
209209 2.19269 0.151671
210210 0 0
211211 −0.460107 −0.0316751 −0.0158375 0.999875i 0.505041π-0.505041\pi
−0.0158375 + 0.999875i 0.505041π0.505041\pi
212212 39.7832 2.73232
213213 0 0
214214 17.2121 1.17659
215215 −11.6407 −0.793890
216216 0 0
217217 −5.28083 −0.358486
218218 9.31468 0.630870
219219 0 0
220220 −16.0258 −1.08046
221221 0 0
222222 0 0
223223 −16.3502 −1.09489 −0.547445 0.836842i 0.684399π-0.684399\pi
−0.547445 + 0.836842i 0.684399π0.684399\pi
224224 −9.77479 −0.653106
225225 0 0
226226 25.1890 1.67555
227227 −6.56033 −0.435425 −0.217712 0.976013i 0.569859π-0.569859\pi
−0.217712 + 0.976013i 0.569859π0.569859\pi
228228 0 0
229229 −3.95539 −0.261380 −0.130690 0.991423i 0.541719π-0.541719\pi
−0.130690 + 0.991423i 0.541719π0.541719\pi
230230 16.2722 1.07296
231231 0 0
232232 −16.7114 −1.09716
233233 −8.35690 −0.547478 −0.273739 0.961804i 0.588261π-0.588261\pi
−0.273739 + 0.961804i 0.588261π0.588261\pi
234234 0 0
235235 −0.789856 −0.0515245
236236 −21.5013 −1.39961
237237 0 0
238238 −7.24698 −0.469752
239239 −20.1008 −1.30021 −0.650107 0.759843i 0.725276π-0.725276\pi
−0.650107 + 0.759843i 0.725276π0.725276\pi
240240 0 0
241241 −19.0127 −1.22471 −0.612357 0.790581i 0.709778π-0.709778\pi
−0.612357 + 0.790581i 0.709778π0.709778\pi
242242 6.78687 0.436277
243243 0 0
244244 −17.9618 −1.14989
245245 −7.01938 −0.448452
246246 0 0
247247 0 0
248248 83.1764 5.28171
249249 0 0
250250 25.1304 1.58938
251251 0.763774 0.0482090 0.0241045 0.999709i 0.492327π-0.492327\pi
0.0241045 + 0.999709i 0.492327π0.492327\pi
252252 0 0
253253 16.7802 1.05496
254254 12.0653 0.757045
255255 0 0
256256 17.1511 1.07194
257257 13.0911 0.816602 0.408301 0.912847i 0.366121π-0.366121\pi
0.408301 + 0.912847i 0.366121π0.366121\pi
258258 0 0
259259 3.19269 0.198384
260260 0 0
261261 0 0
262262 −24.8135 −1.53299
263263 −18.3773 −1.13320 −0.566598 0.823995i 0.691741π-0.691741\pi
−0.566598 + 0.823995i 0.691741π0.691741\pi
264264 0 0
265265 7.95300 0.488549
266266 1.12498 0.0689771
267267 0 0
268268 −9.82563 −0.600196
269269 −23.6625 −1.44273 −0.721363 0.692557i 0.756484π-0.756484\pi
−0.721363 + 0.692557i 0.756484π0.756484\pi
270270 0 0
271271 −19.7530 −1.19991 −0.599955 0.800034i 0.704815π-0.704815\pi
−0.599955 + 0.800034i 0.704815π0.704815\pi
272272 63.2398 3.83448
273273 0 0
274274 −20.1089 −1.21482
275275 11.3556 0.684767
276276 0 0
277277 1.77777 0.106816 0.0534081 0.998573i 0.482992π-0.482992\pi
0.0534081 + 0.998573i 0.482992π0.482992\pi
278278 48.4499 2.90583
279279 0 0
280280 −5.08815 −0.304075
281281 −1.62133 −0.0967207 −0.0483603 0.998830i 0.515400π-0.515400\pi
−0.0483603 + 0.998830i 0.515400π0.515400\pi
282282 0 0
283283 4.98361 0.296245 0.148122 0.988969i 0.452677π-0.452677\pi
0.148122 + 0.988969i 0.452677π0.452677\pi
284284 55.1124 3.27032
285285 0 0
286286 0 0
287287 −2.72587 −0.160903
288288 0 0
289289 6.53079 0.384164
290290 −5.39852 −0.317012
291291 0 0
292292 54.9700 3.21688
293293 0.0717525 0.00419183 0.00209591 0.999998i 0.499333π-0.499333\pi
0.00209591 + 0.999998i 0.499333π0.499333\pi
294294 0 0
295295 −4.29829 −0.250256
296296 −50.2868 −2.92286
297297 0 0
298298 41.2825 2.39143
299299 0 0
300300 0 0
301301 −6.15883 −0.354989
302302 −6.81295 −0.392041
303303 0 0
304304 −9.81700 −0.563044
305305 −3.59073 −0.205605
306306 0 0
307307 −5.19806 −0.296669 −0.148335 0.988937i 0.547391π-0.547391\pi
−0.148335 + 0.988937i 0.547391π0.547391\pi
308308 −8.47889 −0.483130
309309 0 0
310310 26.8696 1.52609
311311 22.5429 1.27829 0.639145 0.769087i 0.279289π-0.279289\pi
0.639145 + 0.769087i 0.279289π0.279289\pi
312312 0 0
313313 22.6612 1.28088 0.640442 0.768006i 0.278751π-0.278751\pi
0.640442 + 0.768006i 0.278751π0.278751\pi
314314 −46.4083 −2.61897
315315 0 0
316316 7.00538 0.394083
317317 −26.3424 −1.47954 −0.739769 0.672861i 0.765065π-0.765065\pi
−0.739769 + 0.672861i 0.765065π0.765065\pi
318318 0 0
319319 −5.56704 −0.311694
320320 22.3864 1.25144
321321 0 0
322322 8.60925 0.479775
323323 −3.65279 −0.203247
324324 0 0
325325 0 0
326326 −42.2838 −2.34188
327327 0 0
328328 42.9342 2.37065
329329 −0.417895 −0.0230393
330330 0 0
331331 −11.2295 −0.617230 −0.308615 0.951187i 0.599866π-0.599866\pi
−0.308615 + 0.951187i 0.599866π0.599866\pi
332332 −13.8683 −0.761123
333333 0 0
334334 14.5265 0.794854
335335 −1.96423 −0.107317
336336 0 0
337337 2.30798 0.125724 0.0628618 0.998022i 0.479977π-0.479977\pi
0.0628618 + 0.998022i 0.479977π0.479977\pi
338338 0 0
339339 0 0
340340 26.6974 1.44787
341341 27.7084 1.50049
342342 0 0
343343 −7.59850 −0.410280
344344 97.0055 5.23019
345345 0 0
346346 64.4523 3.46498
347347 9.13706 0.490503 0.245252 0.969459i 0.421129π-0.421129\pi
0.245252 + 0.969459i 0.421129π0.421129\pi
348348 0 0
349349 23.9758 1.28340 0.641699 0.766957i 0.278230π-0.278230\pi
0.641699 + 0.766957i 0.278230π0.278230\pi
350350 5.82610 0.311418
351351 0 0
352352 51.2881 2.73367
353353 27.1239 1.44366 0.721830 0.692070i 0.243301π-0.243301\pi
0.721830 + 0.692070i 0.243301π0.243301\pi
354354 0 0
355355 11.0175 0.584746
356356 −52.0863 −2.76057
357357 0 0
358358 49.5569 2.61916
359359 26.0790 1.37640 0.688200 0.725521i 0.258401π-0.258401\pi
0.688200 + 0.725521i 0.258401π0.258401\pi
360360 0 0
361361 −18.4330 −0.970156
362362 9.78123 0.514090
363363 0 0
364364 0 0
365365 10.9890 0.575190
366366 0 0
367367 9.57434 0.499776 0.249888 0.968275i 0.419606π-0.419606\pi
0.249888 + 0.968275i 0.419606π0.419606\pi
368368 −75.1275 −3.91629
369369 0 0
370370 −16.2448 −0.844530
371371 4.20775 0.218456
372372 0 0
373373 28.1497 1.45754 0.728769 0.684760i 0.240093π-0.240093\pi
0.728769 + 0.684760i 0.240093π0.240093\pi
374374 38.0248 1.96621
375375 0 0
376376 6.58211 0.339446
377377 0 0
378378 0 0
379379 16.0465 0.824255 0.412127 0.911126i 0.364786π-0.364786\pi
0.412127 + 0.911126i 0.364786π0.364786\pi
380380 −4.14436 −0.212601
381381 0 0
382382 −57.0122 −2.91700
383383 24.6165 1.25785 0.628923 0.777467i 0.283496π-0.283496\pi
0.628923 + 0.777467i 0.283496π0.283496\pi
384384 0 0
385385 −1.69501 −0.0863855
386386 47.4097 2.41309
387387 0 0
388388 89.5852 4.54800
389389 17.2198 0.873080 0.436540 0.899685i 0.356204π-0.356204\pi
0.436540 + 0.899685i 0.356204π0.356204\pi
390390 0 0
391391 −27.9541 −1.41370
392392 58.4946 2.95442
393393 0 0
394394 −12.5515 −0.632335
395395 1.40044 0.0704636
396396 0 0
397397 −2.03923 −0.102346 −0.0511730 0.998690i 0.516296π-0.516296\pi
−0.0511730 + 0.998690i 0.516296π0.516296\pi
398398 −40.4795 −2.02905
399399 0 0
400400 −50.8407 −2.54203
401401 1.46144 0.0729806 0.0364903 0.999334i 0.488382π-0.488382\pi
0.0364903 + 0.999334i 0.488382π0.488382\pi
402402 0 0
403403 0 0
404404 −38.4239 −1.91166
405405 0 0
406406 −2.85623 −0.141752
407407 −16.7520 −0.830364
408408 0 0
409409 −29.9390 −1.48039 −0.740194 0.672393i 0.765266π-0.765266\pi
−0.740194 + 0.672393i 0.765266π0.765266\pi
410410 13.8696 0.684973
411411 0 0
412412 −22.1414 −1.09083
413413 −2.27413 −0.111902
414414 0 0
415415 −2.77240 −0.136092
416416 0 0
417417 0 0
418418 −5.90276 −0.288713
419419 −6.64742 −0.324748 −0.162374 0.986729i 0.551915π-0.551915\pi
−0.162374 + 0.986729i 0.551915π0.551915\pi
420420 0 0
421421 13.5646 0.661100 0.330550 0.943788i 0.392766π-0.392766\pi
0.330550 + 0.943788i 0.392766π0.392766\pi
422422 1.23862 0.0602950
423423 0 0
424424 −66.2747 −3.21858
425425 −18.9172 −0.917620
426426 0 0
427427 −1.89977 −0.0919364
428428 −33.5478 −1.62159
429429 0 0
430430 31.3370 1.51121
431431 −35.9463 −1.73147 −0.865736 0.500501i 0.833149π-0.833149\pi
−0.865736 + 0.500501i 0.833149π0.833149\pi
432432 0 0
433433 −32.4741 −1.56061 −0.780303 0.625402i 0.784935π-0.784935\pi
−0.780303 + 0.625402i 0.784935π0.784935\pi
434434 14.2161 0.682395
435435 0 0
436436 −18.1551 −0.869472
437437 4.33944 0.207583
438438 0 0
439439 12.8321 0.612441 0.306221 0.951961i 0.400935π-0.400935\pi
0.306221 + 0.951961i 0.400935π0.400935\pi
440440 26.6974 1.27275
441441 0 0
442442 0 0
443443 −11.9608 −0.568273 −0.284137 0.958784i 0.591707π-0.591707\pi
−0.284137 + 0.958784i 0.591707π0.591707\pi
444444 0 0
445445 −10.4125 −0.493601
446446 44.0151 2.08417
447447 0 0
448448 11.8442 0.559584
449449 12.4789 0.588915 0.294458 0.955665i 0.404861π-0.404861\pi
0.294458 + 0.955665i 0.404861π0.404861\pi
450450 0 0
451451 14.3026 0.673483
452452 −49.0954 −2.30926
453453 0 0
454454 17.6606 0.828851
455455 0 0
456456 0 0
457457 32.4523 1.51806 0.759028 0.651058i 0.225674π-0.225674\pi
0.759028 + 0.651058i 0.225674π0.225674\pi
458458 10.6480 0.497549
459459 0 0
460460 −31.7159 −1.47876
461461 −24.4034 −1.13658 −0.568290 0.822828i 0.692395π-0.692395\pi
−0.568290 + 0.822828i 0.692395π0.692395\pi
462462 0 0
463463 −33.1836 −1.54217 −0.771086 0.636731i 0.780286π-0.780286\pi
−0.771086 + 0.636731i 0.780286π0.780286\pi
464464 24.9245 1.15709
465465 0 0
466466 22.4969 1.04215
467467 38.5206 1.78252 0.891261 0.453490i 0.149821π-0.149821\pi
0.891261 + 0.453490i 0.149821π0.149821\pi
468468 0 0
469469 −1.03923 −0.0479871
470470 2.12631 0.0980794
471471 0 0
472472 35.8189 1.64870
473473 32.3153 1.48586
474474 0 0
475475 2.93661 0.134741
476476 14.1250 0.647417
477477 0 0
478478 54.1118 2.47502
479479 8.34481 0.381284 0.190642 0.981660i 0.438943π-0.438943\pi
0.190642 + 0.981660i 0.438943π0.438943\pi
480480 0 0
481481 0 0
482482 51.1825 2.33130
483483 0 0
484484 −13.2282 −0.601282
485485 17.9089 0.813200
486486 0 0
487487 −14.8586 −0.673309 −0.336654 0.941628i 0.609295π-0.609295\pi
−0.336654 + 0.941628i 0.609295π0.609295\pi
488488 29.9226 1.35453
489489 0 0
490490 18.8963 0.853648
491491 −4.99894 −0.225599 −0.112799 0.993618i 0.535982π-0.535982\pi
−0.112799 + 0.993618i 0.535982π0.535982\pi
492492 0 0
493493 9.27413 0.417686
494494 0 0
495495 0 0
496496 −124.055 −5.57023
497497 5.82908 0.261470
498498 0 0
499499 −0.385371 −0.0172516 −0.00862579 0.999963i 0.502746π-0.502746\pi
−0.00862579 + 0.999963i 0.502746π0.502746\pi
500500 −48.9812 −2.19051
501501 0 0
502502 −2.05610 −0.0917681
503503 −22.6179 −1.00848 −0.504241 0.863563i 0.668228π-0.668228\pi
−0.504241 + 0.863563i 0.668228π0.668228\pi
504504 0 0
505505 −7.68127 −0.341812
506506 −45.1726 −2.00817
507507 0 0
508508 −23.5163 −1.04337
509509 11.6039 0.514333 0.257166 0.966367i 0.417211π-0.417211\pi
0.257166 + 0.966367i 0.417211π0.417211\pi
510510 0 0
511511 5.81402 0.257197
512512 −1.71678 −0.0758715
513513 0 0
514514 −35.2416 −1.55444
515515 −4.42626 −0.195044
516516 0 0
517517 2.19269 0.0964342
518518 −8.59478 −0.377633
519519 0 0
520520 0 0
521521 1.62671 0.0712675 0.0356337 0.999365i 0.488655π-0.488655\pi
0.0356337 + 0.999365i 0.488655π0.488655\pi
522522 0 0
523523 10.0718 0.440407 0.220203 0.975454i 0.429328π-0.429328\pi
0.220203 + 0.975454i 0.429328π0.429328\pi
524524 48.3637 2.11278
525525 0 0
526526 49.4722 2.15709
527527 −46.1594 −2.01074
528528 0 0
529529 10.2088 0.443862
530530 −21.4097 −0.929976
531531 0 0
532532 −2.19269 −0.0950650
533533 0 0
534534 0 0
535535 −6.70650 −0.289947
536536 16.3685 0.707012
537537 0 0
538538 63.6999 2.74630
539539 19.4862 0.839330
540540 0 0
541541 −20.4674 −0.879962 −0.439981 0.898007i 0.645015π-0.645015\pi
−0.439981 + 0.898007i 0.645015π0.645015\pi
542542 53.1756 2.28409
543543 0 0
544544 −85.4408 −3.66325
545545 −3.62937 −0.155465
546546 0 0
547547 −27.5478 −1.17786 −0.588929 0.808185i 0.700450π-0.700450\pi
−0.588929 + 0.808185i 0.700450π0.700450\pi
548548 39.1939 1.67428
549549 0 0
550550 −30.5694 −1.30348
551551 −1.43967 −0.0613318
552552 0 0
553553 0.740939 0.0315079
554554 −4.78581 −0.203329
555555 0 0
556556 −94.4331 −4.00485
557557 −37.9855 −1.60950 −0.804749 0.593615i 0.797700π-0.797700\pi
−0.804749 + 0.593615i 0.797700π0.797700\pi
558558 0 0
559559 0 0
560560 7.58881 0.320686
561561 0 0
562562 4.36467 0.184112
563563 29.7724 1.25476 0.627378 0.778714i 0.284128π-0.284128\pi
0.627378 + 0.778714i 0.284128π0.284128\pi
564564 0 0
565565 −9.81461 −0.412904
566566 −13.4160 −0.563916
567567 0 0
568568 −91.8117 −3.85234
569569 21.9541 0.920362 0.460181 0.887825i 0.347784π-0.347784\pi
0.460181 + 0.887825i 0.347784π0.347784\pi
570570 0 0
571571 2.46575 0.103188 0.0515942 0.998668i 0.483570π-0.483570\pi
0.0515942 + 0.998668i 0.483570π0.483570\pi
572572 0 0
573573 0 0
574574 7.33811 0.306287
575575 22.4733 0.937199
576576 0 0
577577 17.4547 0.726650 0.363325 0.931662i 0.381641π-0.381641\pi
0.363325 + 0.931662i 0.381641π0.381641\pi
578578 −17.5810 −0.731275
579579 0 0
580580 10.5222 0.436909
581581 −1.46681 −0.0608536
582582 0 0
583583 −22.0780 −0.914377
584584 −91.5745 −3.78938
585585 0 0
586586 −0.193159 −0.00797934
587587 −6.26337 −0.258517 −0.129259 0.991611i 0.541260π-0.541260\pi
−0.129259 + 0.991611i 0.541260π0.541260\pi
588588 0 0
589589 7.16554 0.295251
590590 11.5711 0.476374
591591 0 0
592592 75.0012 3.08253
593593 −22.8745 −0.939345 −0.469672 0.882841i 0.655628π-0.655628\pi
−0.469672 + 0.882841i 0.655628π0.655628\pi
594594 0 0
595595 2.82371 0.115761
596596 −80.4631 −3.29590
597597 0 0
598598 0 0
599599 1.05621 0.0431557 0.0215778 0.999767i 0.493131π-0.493131\pi
0.0215778 + 0.999767i 0.493131π0.493131\pi
600600 0 0
601601 −33.3236 −1.35930 −0.679650 0.733537i 0.737868π-0.737868\pi
−0.679650 + 0.733537i 0.737868π0.737868\pi
602602 16.5797 0.675739
603603 0 0
604604 13.2790 0.540316
605605 −2.64443 −0.107511
606606 0 0
607607 16.2403 0.659172 0.329586 0.944125i 0.393091π-0.393091\pi
0.329586 + 0.944125i 0.393091π0.393091\pi
608608 13.2634 0.537901
609609 0 0
610610 9.66632 0.391378
611611 0 0
612612 0 0
613613 11.0479 0.446219 0.223109 0.974793i 0.428379π-0.428379\pi
0.223109 + 0.974793i 0.428379π0.428379\pi
614614 13.9933 0.564723
615615 0 0
616616 14.1250 0.569112
617617 4.65950 0.187584 0.0937922 0.995592i 0.470101π-0.470101\pi
0.0937922 + 0.995592i 0.470101π0.470101\pi
618618 0 0
619619 31.9259 1.28321 0.641604 0.767036i 0.278269π-0.278269\pi
0.641604 + 0.767036i 0.278269π0.278269\pi
620620 −52.3712 −2.10328
621621 0 0
622622 −60.6859 −2.43328
623623 −5.50902 −0.220714
624624 0 0
625625 9.70709 0.388283
626626 −61.0043 −2.43822
627627 0 0
628628 90.4538 3.60950
629629 27.9071 1.11273
630630 0 0
631631 −39.4413 −1.57013 −0.785067 0.619411i 0.787372π-0.787372\pi
−0.785067 + 0.619411i 0.787372π0.787372\pi
632632 −11.6703 −0.464218
633633 0 0
634634 70.9144 2.81637
635635 −4.70112 −0.186558
636636 0 0
637637 0 0
638638 14.9866 0.593325
639639 0 0
640640 −23.3144 −0.921583
641641 −45.4510 −1.79521 −0.897603 0.440804i 0.854693π-0.854693\pi
−0.897603 + 0.440804i 0.854693π0.854693\pi
642642 0 0
643643 −29.7469 −1.17310 −0.586552 0.809912i 0.699515π-0.699515\pi
−0.586552 + 0.809912i 0.699515π0.699515\pi
644644 −16.7802 −0.661231
645645 0 0
646646 9.83340 0.386890
647647 16.9312 0.665635 0.332818 0.942991i 0.392001π-0.392001\pi
0.332818 + 0.942991i 0.392001π0.392001\pi
648648 0 0
649649 11.9323 0.468384
650650 0 0
651651 0 0
652652 82.4148 3.22761
653653 33.1976 1.29912 0.649561 0.760309i 0.274953π-0.274953\pi
0.649561 + 0.760309i 0.274953π0.274953\pi
654654 0 0
655655 9.66833 0.377773
656656 −64.0350 −2.50015
657657 0 0
658658 1.12498 0.0438564
659659 42.6571 1.66168 0.830842 0.556508i 0.187859π-0.187859\pi
0.830842 + 0.556508i 0.187859π0.187859\pi
660660 0 0
661661 38.6902 1.50488 0.752438 0.658664i 0.228878π-0.228878\pi
0.752438 + 0.658664i 0.228878π0.228878\pi
662662 30.2301 1.17493
663663 0 0
664664 23.1032 0.896578
665665 −0.438337 −0.0169980
666666 0 0
667667 −11.0175 −0.426598
668668 −28.3134 −1.09548
669669 0 0
670670 5.28775 0.204283
671671 9.96807 0.384813
672672 0 0
673673 −2.59419 −0.0999986 −0.0499993 0.998749i 0.515922π-0.515922\pi
−0.0499993 + 0.998749i 0.515922π0.515922\pi
674674 −6.21313 −0.239321
675675 0 0
676676 0 0
677677 −1.75302 −0.0673740 −0.0336870 0.999432i 0.510725π-0.510725\pi
−0.0336870 + 0.999432i 0.510725π0.510725\pi
678678 0 0
679679 9.47517 0.363624
680680 −44.4752 −1.70555
681681 0 0
682682 −74.5916 −2.85626
683683 −16.3351 −0.625046 −0.312523 0.949910i 0.601174π-0.601174\pi
−0.312523 + 0.949910i 0.601174π0.601174\pi
684684 0 0
685685 7.83520 0.299368
686686 20.4553 0.780988
687687 0 0
688688 −144.681 −5.51590
689689 0 0
690690 0 0
691691 15.9105 0.605265 0.302632 0.953107i 0.402135π-0.402135\pi
0.302632 + 0.953107i 0.402135π0.402135\pi
692692 −125.623 −4.77547
693693 0 0
694694 −24.5972 −0.933696
695695 −18.8780 −0.716083
696696 0 0
697697 −23.8267 −0.902500
698698 −64.5435 −2.44301
699699 0 0
700700 −11.3556 −0.429200
701701 20.8635 0.788005 0.394002 0.919109i 0.371090π-0.371090\pi
0.394002 + 0.919109i 0.371090π0.371090\pi
702702 0 0
703703 −4.33214 −0.163390
704704 −62.1460 −2.34222
705705 0 0
706706 −73.0182 −2.74807
707707 −4.06398 −0.152842
708708 0 0
709709 15.6485 0.587691 0.293846 0.955853i 0.405065π-0.405065\pi
0.293846 + 0.955853i 0.405065π0.405065\pi
710710 −29.6592 −1.11309
711711 0 0
712712 86.7706 3.25187
713713 54.8364 2.05364
714714 0 0
715715 0 0
716716 −96.5906 −3.60976
717717 0 0
718718 −70.2054 −2.62004
719719 27.1594 1.01288 0.506438 0.862276i 0.330962π-0.330962\pi
0.506438 + 0.862276i 0.330962π0.330962\pi
720720 0 0
721721 −2.34183 −0.0872143
722722 49.6219 1.84674
723723 0 0
724724 −19.0645 −0.708525
725725 −7.45580 −0.276901
726726 0 0
727727 31.7784 1.17859 0.589297 0.807916i 0.299405π-0.299405\pi
0.589297 + 0.807916i 0.299405π0.299405\pi
728728 0 0
729729 0 0
730730 −29.5826 −1.09490
731731 −53.8340 −1.99112
732732 0 0
733733 46.8907 1.73195 0.865973 0.500090i 0.166700π-0.166700\pi
0.865973 + 0.500090i 0.166700π0.166700\pi
734734 −25.7743 −0.951347
735735 0 0
736736 101.502 3.74141
737737 5.45281 0.200857
738738 0 0
739739 17.0479 0.627115 0.313558 0.949569i 0.398479π-0.398479\pi
0.313558 + 0.949569i 0.398479π0.398479\pi
740740 31.6626 1.16394
741741 0 0
742742 −11.3274 −0.415840
743743 11.6324 0.426750 0.213375 0.976970i 0.431554π-0.431554\pi
0.213375 + 0.976970i 0.431554π0.431554\pi
744744 0 0
745745 −16.0853 −0.589319
746746 −75.7797 −2.77449
747747 0 0
748748 −74.1135 −2.70986
749749 −3.54825 −0.129650
750750 0 0
751751 −13.0295 −0.475455 −0.237727 0.971332i 0.576402π-0.576402\pi
−0.237727 + 0.971332i 0.576402π0.576402\pi
752752 −9.81700 −0.357989
753753 0 0
754754 0 0
755755 2.65459 0.0966106
756756 0 0
757757 22.7899 0.828311 0.414156 0.910206i 0.364077π-0.364077\pi
0.414156 + 0.910206i 0.364077π0.364077\pi
758758 −43.1976 −1.56901
759759 0 0
760760 6.90408 0.250437
761761 38.3424 1.38991 0.694956 0.719052i 0.255424π-0.255424\pi
0.694956 + 0.719052i 0.255424π0.255424\pi
762762 0 0
763763 −1.92021 −0.0695164
764764 111.122 4.02024
765765 0 0
766766 −66.2683 −2.39437
767767 0 0
768768 0 0
769769 −3.63879 −0.131218 −0.0656091 0.997845i 0.520899π-0.520899\pi
−0.0656091 + 0.997845i 0.520899π0.520899\pi
770770 4.56299 0.164439
771771 0 0
772772 −92.4055 −3.32575
773773 39.3424 1.41505 0.707524 0.706689i 0.249812π-0.249812\pi
0.707524 + 0.706689i 0.249812π0.249812\pi
774774 0 0
775775 37.1092 1.33300
776776 −149.240 −5.35740
777777 0 0
778778 −46.3562 −1.66195
779779 3.69873 0.132521
780780 0 0
781781 −30.5851 −1.09442
782782 75.2529 2.69104
783783 0 0
784784 −87.2428 −3.11581
785785 18.0825 0.645392
786786 0 0
787787 −25.4252 −0.906310 −0.453155 0.891432i 0.649702π-0.649702\pi
−0.453155 + 0.891432i 0.649702π0.649702\pi
788788 24.4639 0.871492
789789 0 0
790790 −3.77000 −0.134131
791791 −5.19269 −0.184631
792792 0 0
793793 0 0
794794 5.48965 0.194820
795795 0 0
796796 78.8980 2.79646
797797 −20.7138 −0.733720 −0.366860 0.930276i 0.619567π-0.619567\pi
−0.366860 + 0.930276i 0.619567π0.619567\pi
798798 0 0
799799 −3.65279 −0.129227
800800 68.6889 2.42852
801801 0 0
802802 −3.93422 −0.138922
803803 −30.5060 −1.07653
804804 0 0
805805 −3.35450 −0.118231
806806 0 0
807807 0 0
808808 64.0103 2.25187
809809 −11.0978 −0.390179 −0.195090 0.980785i 0.562500π-0.562500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
810810 0 0
811811 −4.84223 −0.170034 −0.0850169 0.996380i 0.527094π-0.527094\pi
−0.0850169 + 0.996380i 0.527094π0.527094\pi
812812 5.56704 0.195365
813813 0 0
814814 45.0966 1.58064
815815 16.4754 0.577109
816816 0 0
817817 8.35690 0.292371
818818 80.5964 2.81799
819819 0 0
820820 −27.0331 −0.944037
821821 43.7381 1.52647 0.763235 0.646121i 0.223610π-0.223610\pi
0.763235 + 0.646121i 0.223610π0.223610\pi
822822 0 0
823823 12.0998 0.421771 0.210885 0.977511i 0.432365π-0.432365\pi
0.210885 + 0.977511i 0.432365π0.432365\pi
824824 36.8853 1.28496
825825 0 0
826826 6.12200 0.213012
827827 35.3212 1.22824 0.614120 0.789213i 0.289511π-0.289511\pi
0.614120 + 0.789213i 0.289511π0.289511\pi
828828 0 0
829829 53.4946 1.85794 0.928971 0.370152i 0.120694π-0.120694\pi
0.928971 + 0.370152i 0.120694π0.120694\pi
830830 7.46335 0.259057
831831 0 0
832832 0 0
833833 −32.4620 −1.12474
834834 0 0
835835 −5.66009 −0.195875
836836 11.5050 0.397908
837837 0 0
838838 17.8950 0.618172
839839 −23.1521 −0.799300 −0.399650 0.916668i 0.630868π-0.630868\pi
−0.399650 + 0.916668i 0.630868π0.630868\pi
840840 0 0
841841 −25.3448 −0.873959
842842 −36.5163 −1.25844
843843 0 0
844844 −2.41417 −0.0830993
845845 0 0
846846 0 0
847847 −1.39911 −0.0480739
848848 98.8467 3.39441
849849 0 0
850850 50.9256 1.74673
851851 −33.1530 −1.13647
852852 0 0
853853 26.7265 0.915097 0.457548 0.889185i 0.348728π-0.348728\pi
0.457548 + 0.889185i 0.348728π0.348728\pi
854854 5.11423 0.175005
855855 0 0
856856 55.8872 1.91019
857857 −42.6064 −1.45541 −0.727703 0.685892i 0.759412π-0.759412\pi
−0.727703 + 0.685892i 0.759412π0.759412\pi
858858 0 0
859859 33.6079 1.14669 0.573344 0.819315i 0.305646π-0.305646\pi
0.573344 + 0.819315i 0.305646π0.305646\pi
860860 −61.0786 −2.08276
861861 0 0
862862 96.7682 3.29594
863863 −18.7047 −0.636715 −0.318358 0.947971i 0.603131π-0.603131\pi
−0.318358 + 0.947971i 0.603131π0.603131\pi
864864 0 0
865865 −25.1132 −0.853873
866866 87.4210 2.97069
867867 0 0
868868 −27.7084 −0.940485
869869 −3.88769 −0.131881
870870 0 0
871871 0 0
872872 30.2446 1.02421
873873 0 0
874874 −11.6819 −0.395145
875875 −5.18060 −0.175136
876876 0 0
877877 36.8237 1.24345 0.621724 0.783236i 0.286433π-0.286433\pi
0.621724 + 0.783236i 0.286433π0.286433\pi
878878 −34.5442 −1.16581
879879 0 0
880880 −39.8183 −1.34228
881881 41.1250 1.38554 0.692768 0.721161i 0.256391π-0.256391\pi
0.692768 + 0.721161i 0.256391π0.256391\pi
882882 0 0
883883 30.7482 1.03476 0.517380 0.855756i 0.326907π-0.326907\pi
0.517380 + 0.855756i 0.326907π0.326907\pi
884884 0 0
885885 0 0
886886 32.1987 1.08173
887887 −7.58940 −0.254827 −0.127414 0.991850i 0.540668π-0.540668\pi
−0.127414 + 0.991850i 0.540668π0.540668\pi
888888 0 0
889889 −2.48725 −0.0834198
890890 28.0307 0.939592
891891 0 0
892892 −85.7891 −2.87243
893893 0.567040 0.0189753
894894 0 0
895895 −19.3093 −0.645439
896896 −12.3351 −0.412088
897897 0 0
898898 −33.5934 −1.12103
899899 −18.1927 −0.606760
900900 0 0
901901 36.7797 1.22531
902902 −38.5029 −1.28201
903903 0 0
904904 81.7881 2.72023
905905 −3.81115 −0.126687
906906 0 0
907907 19.3333 0.641952 0.320976 0.947087i 0.395989π-0.395989\pi
0.320976 + 0.947087i 0.395989π0.395989\pi
908908 −34.4219 −1.14233
909909 0 0
910910 0 0
911911 −22.7149 −0.752577 −0.376288 0.926503i 0.622800π-0.622800\pi
−0.376288 + 0.926503i 0.622800π0.622800\pi
912912 0 0
913913 7.69633 0.254711
914914 −87.3624 −2.88969
915915 0 0
916916 −20.7539 −0.685727
917917 5.11529 0.168922
918918 0 0
919919 14.2911 0.471420 0.235710 0.971823i 0.424258π-0.424258\pi
0.235710 + 0.971823i 0.424258π0.424258\pi
920920 52.8355 1.74194
921921 0 0
922922 65.6945 2.16353
923923 0 0
924924 0 0
925925 −22.4355 −0.737674
926926 89.3309 2.93560
927927 0 0
928928 −33.6746 −1.10542
929929 −32.7211 −1.07354 −0.536772 0.843727i 0.680356π-0.680356\pi
−0.536772 + 0.843727i 0.680356π0.680356\pi
930930 0 0
931931 5.03923 0.165154
932932 −43.8485 −1.43630
933933 0 0
934934 −103.698 −3.39311
935935 −14.8159 −0.484533
936936 0 0
937937 −4.01400 −0.131132 −0.0655658 0.997848i 0.520885π-0.520885\pi
−0.0655658 + 0.997848i 0.520885π0.520885\pi
938938 2.79763 0.0913457
939939 0 0
940940 −4.14436 −0.135174
941941 28.2669 0.921476 0.460738 0.887536i 0.347585π-0.347585\pi
0.460738 + 0.887536i 0.347585π0.347585\pi
942942 0 0
943943 28.3056 0.921757
944944 −53.4228 −1.73876
945945 0 0
946946 −86.9934 −2.82840
947947 37.8455 1.22981 0.614906 0.788600i 0.289194π-0.289194\pi
0.614906 + 0.788600i 0.289194π0.289194\pi
948948 0 0
949949 0 0
950950 −7.90541 −0.256485
951951 0 0
952952 −23.5308 −0.762637
953953 40.8256 1.32247 0.661236 0.750178i 0.270032π-0.270032\pi
0.661236 + 0.750178i 0.270032π0.270032\pi
954954 0 0
955955 22.2142 0.718834
956956 −105.469 −3.41110
957957 0 0
958958 −22.4644 −0.725792
959959 4.14542 0.133863
960960 0 0
961961 59.5491 1.92094
962962 0 0
963963 0 0
964964 −99.7591 −3.21302
965965 −18.4727 −0.594656
966966 0 0
967967 10.2798 0.330575 0.165288 0.986245i 0.447145π-0.447145\pi
0.165288 + 0.986245i 0.447145π0.447145\pi
968968 22.0368 0.708291
969969 0 0
970970 −48.2111 −1.54796
971971 19.4805 0.625161 0.312580 0.949891i 0.398807π-0.398807\pi
0.312580 + 0.949891i 0.398807π0.398807\pi
972972 0 0
973973 −9.98792 −0.320198
974974 39.9997 1.28167
975975 0 0
976976 −44.6286 −1.42853
977977 −47.0538 −1.50539 −0.752693 0.658372i 0.771245π-0.771245\pi
−0.752693 + 0.658372i 0.771245π0.771245\pi
978978 0 0
979979 28.9057 0.923831
980980 −36.8305 −1.17651
981981 0 0
982982 13.4572 0.429438
983983 −34.4295 −1.09813 −0.549065 0.835779i 0.685016π-0.685016\pi
−0.549065 + 0.835779i 0.685016π0.685016\pi
984984 0 0
985985 4.89056 0.155826
986986 −24.9661 −0.795084
987987 0 0
988988 0 0
989989 63.9536 2.03361
990990 0 0
991991 7.30798 0.232146 0.116073 0.993241i 0.462969π-0.462969\pi
0.116073 + 0.993241i 0.462969π0.462969\pi
992992 167.606 5.32149
993993 0 0
994994 −15.6920 −0.497721
995995 15.7724 0.500019
996996 0 0
997997 −35.6915 −1.13036 −0.565181 0.824967i 0.691194π-0.691194\pi
−0.565181 + 0.824967i 0.691194π0.691194\pi
998998 1.03743 0.0328392
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.a.n.1.1 3
3.2 odd 2 507.2.a.l.1.3 yes 3
12.11 even 2 8112.2.a.cp.1.1 3
13.5 odd 4 1521.2.b.k.1351.6 6
13.8 odd 4 1521.2.b.k.1351.1 6
13.12 even 2 1521.2.a.s.1.3 3
39.2 even 12 507.2.j.i.316.6 12
39.5 even 4 507.2.b.f.337.1 6
39.8 even 4 507.2.b.f.337.6 6
39.11 even 12 507.2.j.i.316.1 12
39.17 odd 6 507.2.e.l.484.3 6
39.20 even 12 507.2.j.i.361.6 12
39.23 odd 6 507.2.e.l.22.3 6
39.29 odd 6 507.2.e.i.22.1 6
39.32 even 12 507.2.j.i.361.1 12
39.35 odd 6 507.2.e.i.484.1 6
39.38 odd 2 507.2.a.i.1.1 3
156.155 even 2 8112.2.a.cg.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.a.i.1.1 3 39.38 odd 2
507.2.a.l.1.3 yes 3 3.2 odd 2
507.2.b.f.337.1 6 39.5 even 4
507.2.b.f.337.6 6 39.8 even 4
507.2.e.i.22.1 6 39.29 odd 6
507.2.e.i.484.1 6 39.35 odd 6
507.2.e.l.22.3 6 39.23 odd 6
507.2.e.l.484.3 6 39.17 odd 6
507.2.j.i.316.1 12 39.11 even 12
507.2.j.i.316.6 12 39.2 even 12
507.2.j.i.361.1 12 39.32 even 12
507.2.j.i.361.6 12 39.20 even 12
1521.2.a.n.1.1 3 1.1 even 1 trivial
1521.2.a.s.1.3 3 13.12 even 2
1521.2.b.k.1351.1 6 13.8 odd 4
1521.2.b.k.1351.6 6 13.5 odd 4
8112.2.a.cg.1.3 3 156.155 even 2
8112.2.a.cp.1.1 3 12.11 even 2