Properties

Label 9025.2.a.cv.1.1
Level 90259025
Weight 22
Character 9025.1
Self dual yes
Analytic conductor 72.06572.065
Analytic rank 00
Dimension 4040
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9025,2,Mod(1,9025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9025, 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("9025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 9025=52192 9025 = 5^{2} \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9025.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: 72.064987824272.0649878242
Analytic rank: 00
Dimension: 4040
Twist minimal: no (minimal twist has level 1805)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 9025.1

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) == q2.66900q21.76244q3+5.12357q4+4.70394q62.20993q78.33681q8+0.106178q9+2.86854q119.02996q124.83675q13+5.89830q14+12.0038q16+2.06280q170.283389q18+3.89485q217.65613q224.40865q23+14.6931q24+12.9093q26+5.10017q2711.3227q288.08729q293.97776q3115.3646q325.05561q335.50563q34+0.544010q36+9.05780q37+8.52446q391.21984q4110.3954q42+5.13320q43+14.6972q44+11.7667q462.50131q4721.1559q482.11623q493.63556q5124.7814q52+1.22600q5313.6124q54+18.4237q56+21.5850q580.244718q59+0.498155q61+10.6166q620.234645q63+17.0004q64+13.4934q667.09797q67+10.5689q68+7.76996q69+9.59683q710.885185q720.287288q7324.1753q746.33926q7722.7518q7815.8865q799.30726q81+3.25576q825.70094q83+19.9555q8413.7005q86+14.2533q8723.9144q8816.6834q89+10.6889q9122.5880q92+7.01055q93+6.67600q94+27.0791q960.202690q97+5.64821q98+0.304575q99+O(q100)q-2.66900 q^{2} -1.76244 q^{3} +5.12357 q^{4} +4.70394 q^{6} -2.20993 q^{7} -8.33681 q^{8} +0.106178 q^{9} +2.86854 q^{11} -9.02996 q^{12} -4.83675 q^{13} +5.89830 q^{14} +12.0038 q^{16} +2.06280 q^{17} -0.283389 q^{18} +3.89485 q^{21} -7.65613 q^{22} -4.40865 q^{23} +14.6931 q^{24} +12.9093 q^{26} +5.10017 q^{27} -11.3227 q^{28} -8.08729 q^{29} -3.97776 q^{31} -15.3646 q^{32} -5.05561 q^{33} -5.50563 q^{34} +0.544010 q^{36} +9.05780 q^{37} +8.52446 q^{39} -1.21984 q^{41} -10.3954 q^{42} +5.13320 q^{43} +14.6972 q^{44} +11.7667 q^{46} -2.50131 q^{47} -21.1559 q^{48} -2.11623 q^{49} -3.63556 q^{51} -24.7814 q^{52} +1.22600 q^{53} -13.6124 q^{54} +18.4237 q^{56} +21.5850 q^{58} -0.244718 q^{59} +0.498155 q^{61} +10.6166 q^{62} -0.234645 q^{63} +17.0004 q^{64} +13.4934 q^{66} -7.09797 q^{67} +10.5689 q^{68} +7.76996 q^{69} +9.59683 q^{71} -0.885185 q^{72} -0.287288 q^{73} -24.1753 q^{74} -6.33926 q^{77} -22.7518 q^{78} -15.8865 q^{79} -9.30726 q^{81} +3.25576 q^{82} -5.70094 q^{83} +19.9555 q^{84} -13.7005 q^{86} +14.2533 q^{87} -23.9144 q^{88} -16.6834 q^{89} +10.6889 q^{91} -22.5880 q^{92} +7.01055 q^{93} +6.67600 q^{94} +27.0791 q^{96} -0.202690 q^{97} +5.64821 q^{98} +0.304575 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q+48q4+20q6+52q9+20q11+40q16+92q24+76q26+156q36+80q39+48q44+72q49+32q54+80q61+72q64+16q66+100q74+40q81++128q99+O(q100) 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9} + 20 q^{11} + 40 q^{16} + 92 q^{24} + 76 q^{26} + 156 q^{36} + 80 q^{39} + 48 q^{44} + 72 q^{49} + 32 q^{54} + 80 q^{61} + 72 q^{64} + 16 q^{66} + 100 q^{74} + 40 q^{81}+ \cdots + 128 q^{99}+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 −2.66900 −1.88727 −0.943634 0.330989i 0.892618π-0.892618\pi
−0.943634 + 0.330989i 0.892618π0.892618\pi
33 −1.76244 −1.01754 −0.508771 0.860902i 0.669900π-0.669900\pi
−0.508771 + 0.860902i 0.669900π0.669900\pi
44 5.12357 2.56178
55 0 0
66 4.70394 1.92038
77 −2.20993 −0.835274 −0.417637 0.908614i 0.637142π-0.637142\pi
−0.417637 + 0.908614i 0.637142π0.637142\pi
88 −8.33681 −2.94751
99 0.106178 0.0353926
1010 0 0
1111 2.86854 0.864897 0.432448 0.901659i 0.357650π-0.357650\pi
0.432448 + 0.901659i 0.357650π0.357650\pi
1212 −9.02996 −2.60672
1313 −4.83675 −1.34147 −0.670736 0.741696i 0.734022π-0.734022\pi
−0.670736 + 0.741696i 0.734022π0.734022\pi
1414 5.89830 1.57639
1515 0 0
1616 12.0038 3.00095
1717 2.06280 0.500304 0.250152 0.968207i 0.419519π-0.419519\pi
0.250152 + 0.968207i 0.419519π0.419519\pi
1818 −0.283389 −0.0667954
1919 0 0
2020 0 0
2121 3.89485 0.849926
2222 −7.65613 −1.63229
2323 −4.40865 −0.919267 −0.459634 0.888109i 0.652019π-0.652019\pi
−0.459634 + 0.888109i 0.652019π0.652019\pi
2424 14.6931 2.99921
2525 0 0
2626 12.9093 2.53172
2727 5.10017 0.981529
2828 −11.3227 −2.13979
2929 −8.08729 −1.50177 −0.750886 0.660432i 0.770373π-0.770373\pi
−0.750886 + 0.660432i 0.770373π0.770373\pi
3030 0 0
3131 −3.97776 −0.714427 −0.357213 0.934023i 0.616273π-0.616273\pi
−0.357213 + 0.934023i 0.616273π0.616273\pi
3232 −15.3646 −2.71610
3333 −5.05561 −0.880069
3434 −5.50563 −0.944207
3535 0 0
3636 0.544010 0.0906683
3737 9.05780 1.48909 0.744546 0.667571i 0.232666π-0.232666\pi
0.744546 + 0.667571i 0.232666π0.232666\pi
3838 0 0
3939 8.52446 1.36501
4040 0 0
4141 −1.21984 −0.190507 −0.0952537 0.995453i 0.530366π-0.530366\pi
−0.0952537 + 0.995453i 0.530366π0.530366\pi
4242 −10.3954 −1.60404
4343 5.13320 0.782806 0.391403 0.920219i 0.371990π-0.371990\pi
0.391403 + 0.920219i 0.371990π0.371990\pi
4444 14.6972 2.21568
4545 0 0
4646 11.7667 1.73490
4747 −2.50131 −0.364854 −0.182427 0.983219i 0.558395π-0.558395\pi
−0.182427 + 0.983219i 0.558395π0.558395\pi
4848 −21.1559 −3.05360
4949 −2.11623 −0.302318
5050 0 0
5151 −3.63556 −0.509080
5252 −24.7814 −3.43656
5353 1.22600 0.168404 0.0842018 0.996449i 0.473166π-0.473166\pi
0.0842018 + 0.996449i 0.473166π0.473166\pi
5454 −13.6124 −1.85241
5555 0 0
5656 18.4237 2.46197
5757 0 0
5858 21.5850 2.83425
5959 −0.244718 −0.0318596 −0.0159298 0.999873i 0.505071π-0.505071\pi
−0.0159298 + 0.999873i 0.505071π0.505071\pi
6060 0 0
6161 0.498155 0.0637823 0.0318911 0.999491i 0.489847π-0.489847\pi
0.0318911 + 0.999491i 0.489847π0.489847\pi
6262 10.6166 1.34832
6363 −0.234645 −0.0295625
6464 17.0004 2.12506
6565 0 0
6666 13.4934 1.66093
6767 −7.09797 −0.867155 −0.433578 0.901116i 0.642749π-0.642749\pi
−0.433578 + 0.901116i 0.642749π0.642749\pi
6868 10.5689 1.28167
6969 7.76996 0.935393
7070 0 0
7171 9.59683 1.13893 0.569467 0.822014i 0.307150π-0.307150\pi
0.569467 + 0.822014i 0.307150π0.307150\pi
7272 −0.885185 −0.104320
7373 −0.287288 −0.0336245 −0.0168122 0.999859i 0.505352π-0.505352\pi
−0.0168122 + 0.999859i 0.505352π0.505352\pi
7474 −24.1753 −2.81032
7575 0 0
7676 0 0
7777 −6.33926 −0.722425
7878 −22.7518 −2.57613
7979 −15.8865 −1.78737 −0.893687 0.448691i 0.851890π-0.851890\pi
−0.893687 + 0.448691i 0.851890π0.851890\pi
8080 0 0
8181 −9.30726 −1.03414
8282 3.25576 0.359539
8383 −5.70094 −0.625759 −0.312879 0.949793i 0.601294π-0.601294\pi
−0.312879 + 0.949793i 0.601294π0.601294\pi
8484 19.9555 2.17733
8585 0 0
8686 −13.7005 −1.47737
8787 14.2533 1.52812
8888 −23.9144 −2.54929
8989 −16.6834 −1.76844 −0.884220 0.467072i 0.845309π-0.845309\pi
−0.884220 + 0.467072i 0.845309π0.845309\pi
9090 0 0
9191 10.6889 1.12050
9292 −22.5880 −2.35496
9393 7.01055 0.726960
9494 6.67600 0.688577
9595 0 0
9696 27.0791 2.76375
9797 −0.202690 −0.0205801 −0.0102900 0.999947i 0.503275π-0.503275\pi
−0.0102900 + 0.999947i 0.503275π0.503275\pi
9898 5.64821 0.570556
9999 0.304575 0.0306110
100100 0 0
101101 2.36522 0.235349 0.117674 0.993052i 0.462456π-0.462456\pi
0.117674 + 0.993052i 0.462456π0.462456\pi
102102 9.70331 0.960771
103103 −1.07422 −0.105846 −0.0529231 0.998599i 0.516854π-0.516854\pi
−0.0529231 + 0.998599i 0.516854π0.516854\pi
104104 40.3230 3.95400
105105 0 0
106106 −3.27219 −0.317823
107107 0.186188 0.0179994 0.00899972 0.999960i 0.497135π-0.497135\pi
0.00899972 + 0.999960i 0.497135π0.497135\pi
108108 26.1311 2.51446
109109 13.1387 1.25846 0.629229 0.777220i 0.283371π-0.283371\pi
0.629229 + 0.777220i 0.283371π0.283371\pi
110110 0 0
111111 −15.9638 −1.51522
112112 −26.5275 −2.50662
113113 −4.36458 −0.410586 −0.205293 0.978701i 0.565815π-0.565815\pi
−0.205293 + 0.978701i 0.565815π0.565815\pi
114114 0 0
115115 0 0
116116 −41.4358 −3.84721
117117 −0.513556 −0.0474783
118118 0.653154 0.0601277
119119 −4.55864 −0.417890
120120 0 0
121121 −2.77149 −0.251953
122122 −1.32958 −0.120374
123123 2.14989 0.193849
124124 −20.3803 −1.83021
125125 0 0
126126 0.626269 0.0557925
127127 −3.40581 −0.302217 −0.151108 0.988517i 0.548284π-0.548284\pi
−0.151108 + 0.988517i 0.548284π0.548284\pi
128128 −14.6451 −1.29445
129129 −9.04694 −0.796538
130130 0 0
131131 0.573140 0.0500755 0.0250378 0.999687i 0.492029π-0.492029\pi
0.0250378 + 0.999687i 0.492029π0.492029\pi
132132 −25.9028 −2.25455
133133 0 0
134134 18.9445 1.63655
135135 0 0
136136 −17.1972 −1.47465
137137 −4.82207 −0.411977 −0.205988 0.978554i 0.566041π-0.566041\pi
−0.205988 + 0.978554i 0.566041π0.566041\pi
138138 −20.7380 −1.76534
139139 −14.9925 −1.27164 −0.635822 0.771836i 0.719339π-0.719339\pi
−0.635822 + 0.771836i 0.719339π0.719339\pi
140140 0 0
141141 4.40840 0.371254
142142 −25.6139 −2.14947
143143 −13.8744 −1.16024
144144 1.27454 0.106212
145145 0 0
146146 0.766771 0.0634584
147147 3.72971 0.307622
148148 46.4082 3.81473
149149 12.6439 1.03583 0.517914 0.855433i 0.326709π-0.326709\pi
0.517914 + 0.855433i 0.326709π0.326709\pi
150150 0 0
151151 −11.0266 −0.897328 −0.448664 0.893701i 0.648100π-0.648100\pi
−0.448664 + 0.893701i 0.648100π0.648100\pi
152152 0 0
153153 0.219024 0.0177071
154154 16.9195 1.36341
155155 0 0
156156 43.6756 3.49685
157157 −22.4216 −1.78944 −0.894718 0.446632i 0.852623π-0.852623\pi
−0.894718 + 0.446632i 0.852623π0.852623\pi
158158 42.4011 3.37325
159159 −2.16074 −0.171358
160160 0 0
161161 9.74279 0.767840
162162 24.8411 1.95170
163163 −1.74791 −0.136907 −0.0684535 0.997654i 0.521806π-0.521806\pi
−0.0684535 + 0.997654i 0.521806π0.521806\pi
164164 −6.24994 −0.488039
165165 0 0
166166 15.2158 1.18098
167167 21.0484 1.62877 0.814386 0.580324i 0.197074π-0.197074\pi
0.814386 + 0.580324i 0.197074π0.197074\pi
168168 −32.4706 −2.50516
169169 10.3941 0.799549
170170 0 0
171171 0 0
172172 26.3003 2.00538
173173 11.6088 0.882602 0.441301 0.897359i 0.354517π-0.354517\pi
0.441301 + 0.897359i 0.354517π0.354517\pi
174174 −38.0421 −2.88397
175175 0 0
176176 34.4334 2.59551
177177 0.431300 0.0324185
178178 44.5281 3.33752
179179 3.98091 0.297547 0.148774 0.988871i 0.452467π-0.452467\pi
0.148774 + 0.988871i 0.452467π0.452467\pi
180180 0 0
181181 −2.81859 −0.209504 −0.104752 0.994498i 0.533405π-0.533405\pi
−0.104752 + 0.994498i 0.533405π0.533405\pi
182182 −28.5286 −2.11468
183183 −0.877967 −0.0649012
184184 36.7541 2.70955
185185 0 0
186186 −18.7112 −1.37197
187187 5.91723 0.432711
188188 −12.8156 −0.934676
189189 −11.2710 −0.819845
190190 0 0
191191 −19.8105 −1.43344 −0.716719 0.697362i 0.754357π-0.754357\pi
−0.716719 + 0.697362i 0.754357π0.754357\pi
192192 −29.9622 −2.16233
193193 −5.52399 −0.397626 −0.198813 0.980037i 0.563709π-0.563709\pi
−0.198813 + 0.980037i 0.563709π0.563709\pi
194194 0.540981 0.0388402
195195 0 0
196196 −10.8426 −0.774474
197197 20.4993 1.46051 0.730257 0.683173i 0.239400π-0.239400\pi
0.730257 + 0.683173i 0.239400π0.239400\pi
198198 −0.812912 −0.0577712
199199 −17.2575 −1.22335 −0.611677 0.791107i 0.709505π-0.709505\pi
−0.611677 + 0.791107i 0.709505π0.709505\pi
200200 0 0
201201 12.5097 0.882367
202202 −6.31279 −0.444166
203203 17.8723 1.25439
204204 −18.6270 −1.30415
205205 0 0
206206 2.86710 0.199760
207207 −0.468101 −0.0325353
208208 −58.0594 −4.02570
209209 0 0
210210 0 0
211211 21.2379 1.46207 0.731037 0.682337i 0.239036π-0.239036\pi
0.731037 + 0.682337i 0.239036π0.239036\pi
212212 6.28148 0.431414
213213 −16.9138 −1.15891
214214 −0.496935 −0.0339698
215215 0 0
216216 −42.5192 −2.89306
217217 8.79056 0.596742
218218 −35.0672 −2.37505
219219 0.506326 0.0342143
220220 0 0
221221 −9.97726 −0.671143
222222 42.6074 2.85962
223223 −28.8555 −1.93231 −0.966154 0.257967i 0.916947π-0.916947\pi
−0.966154 + 0.257967i 0.916947π0.916947\pi
224224 33.9546 2.26869
225225 0 0
226226 11.6491 0.774885
227227 −8.42533 −0.559209 −0.279604 0.960115i 0.590203π-0.590203\pi
−0.279604 + 0.960115i 0.590203π0.590203\pi
228228 0 0
229229 24.6658 1.62996 0.814981 0.579487i 0.196747π-0.196747\pi
0.814981 + 0.579487i 0.196747π0.196747\pi
230230 0 0
231231 11.1725 0.735099
232232 67.4221 4.42648
233233 −20.7240 −1.35768 −0.678839 0.734287i 0.737516π-0.737516\pi
−0.678839 + 0.734287i 0.737516π0.737516\pi
234234 1.37068 0.0896042
235235 0 0
236236 −1.25383 −0.0816175
237237 27.9990 1.81873
238238 12.1670 0.788671
239239 10.4341 0.674924 0.337462 0.941339i 0.390431π-0.390431\pi
0.337462 + 0.941339i 0.390431π0.390431\pi
240240 0 0
241241 20.0493 1.29149 0.645744 0.763554i 0.276548π-0.276548\pi
0.645744 + 0.763554i 0.276548π0.276548\pi
242242 7.39710 0.475504
243243 1.10292 0.0707524
244244 2.55233 0.163396
245245 0 0
246246 −5.73807 −0.365846
247247 0 0
248248 33.1618 2.10578
249249 10.0475 0.636736
250250 0 0
251251 −0.614289 −0.0387736 −0.0193868 0.999812i 0.506171π-0.506171\pi
−0.0193868 + 0.999812i 0.506171π0.506171\pi
252252 −1.20222 −0.0757328
253253 −12.6464 −0.795071
254254 9.09012 0.570365
255255 0 0
256256 5.08679 0.317924
257257 10.1007 0.630064 0.315032 0.949081i 0.397985π-0.397985\pi
0.315032 + 0.949081i 0.397985π0.397985\pi
258258 24.1463 1.50328
259259 −20.0171 −1.24380
260260 0 0
261261 −0.858691 −0.0531517
262262 −1.52971 −0.0945060
263263 6.14445 0.378883 0.189441 0.981892i 0.439332π-0.439332\pi
0.189441 + 0.981892i 0.439332π0.439332\pi
264264 42.1477 2.59401
265265 0 0
266266 0 0
267267 29.4034 1.79946
268268 −36.3669 −2.22146
269269 23.0791 1.40716 0.703579 0.710617i 0.251584π-0.251584\pi
0.703579 + 0.710617i 0.251584π0.251584\pi
270270 0 0
271271 13.7769 0.836885 0.418443 0.908243i 0.362576π-0.362576\pi
0.418443 + 0.908243i 0.362576π0.362576\pi
272272 24.7615 1.50139
273273 −18.8384 −1.14015
274274 12.8701 0.777511
275275 0 0
276276 39.8099 2.39628
277277 −18.2471 −1.09636 −0.548181 0.836360i 0.684679π-0.684679\pi
−0.548181 + 0.836360i 0.684679π0.684679\pi
278278 40.0149 2.39993
279279 −0.422350 −0.0252855
280280 0 0
281281 −20.3990 −1.21690 −0.608451 0.793591i 0.708209π-0.708209\pi
−0.608451 + 0.793591i 0.708209π0.708209\pi
282282 −11.7660 −0.700656
283283 −19.5454 −1.16186 −0.580928 0.813955i 0.697310π-0.697310\pi
−0.580928 + 0.813955i 0.697310π0.697310\pi
284284 49.1700 2.91770
285285 0 0
286286 37.0308 2.18968
287287 2.69576 0.159126
288288 −1.63138 −0.0961299
289289 −12.7448 −0.749696
290290 0 0
291291 0.357229 0.0209411
292292 −1.47194 −0.0861386
293293 9.22402 0.538873 0.269436 0.963018i 0.413163π-0.413163\pi
0.269436 + 0.963018i 0.413163π0.413163\pi
294294 −9.95461 −0.580565
295295 0 0
296296 −75.5131 −4.38911
297297 14.6300 0.848921
298298 −33.7466 −1.95489
299299 21.3235 1.23317
300300 0 0
301301 −11.3440 −0.653857
302302 29.4299 1.69350
303303 −4.16855 −0.239477
304304 0 0
305305 0 0
306306 −0.584576 −0.0334180
307307 7.75219 0.442441 0.221220 0.975224i 0.428996π-0.428996\pi
0.221220 + 0.975224i 0.428996π0.428996\pi
308308 −32.4796 −1.85070
309309 1.89325 0.107703
310310 0 0
311311 24.8427 1.40870 0.704350 0.709853i 0.251239π-0.251239\pi
0.704350 + 0.709853i 0.251239π0.251239\pi
312312 −71.0667 −4.02336
313313 −5.79256 −0.327415 −0.163707 0.986509i 0.552345π-0.552345\pi
−0.163707 + 0.986509i 0.552345π0.552345\pi
314314 59.8432 3.37715
315315 0 0
316316 −81.3957 −4.57886
317317 −4.59924 −0.258319 −0.129159 0.991624i 0.541228π-0.541228\pi
−0.129159 + 0.991624i 0.541228π0.541228\pi
318318 5.76702 0.323398
319319 −23.1987 −1.29888
320320 0 0
321321 −0.328144 −0.0183152
322322 −26.0035 −1.44912
323323 0 0
324324 −47.6864 −2.64924
325325 0 0
326326 4.66518 0.258380
327327 −23.1561 −1.28053
328328 10.1696 0.561522
329329 5.52771 0.304753
330330 0 0
331331 7.39548 0.406493 0.203246 0.979128i 0.434851π-0.434851\pi
0.203246 + 0.979128i 0.434851π0.434851\pi
332332 −29.2091 −1.60306
333333 0.961738 0.0527029
334334 −56.1781 −3.07393
335335 0 0
336336 46.7531 2.55059
337337 −16.6765 −0.908425 −0.454212 0.890893i 0.650079π-0.650079\pi
−0.454212 + 0.890893i 0.650079π0.650079\pi
338338 −27.7420 −1.50896
339339 7.69230 0.417788
340340 0 0
341341 −11.4104 −0.617906
342342 0 0
343343 20.1462 1.08779
344344 −42.7945 −2.30733
345345 0 0
346346 −30.9840 −1.66571
347347 −36.0300 −1.93419 −0.967095 0.254417i 0.918116π-0.918116\pi
−0.967095 + 0.254417i 0.918116π0.918116\pi
348348 73.0278 3.91470
349349 −23.6370 −1.26526 −0.632629 0.774455i 0.718024π-0.718024\pi
−0.632629 + 0.774455i 0.718024π0.718024\pi
350350 0 0
351351 −24.6683 −1.31669
352352 −44.0739 −2.34914
353353 −33.9305 −1.80594 −0.902968 0.429708i 0.858617π-0.858617\pi
−0.902968 + 0.429708i 0.858617π0.858617\pi
354354 −1.15114 −0.0611825
355355 0 0
356356 −85.4786 −4.53036
357357 8.03432 0.425221
358358 −10.6251 −0.561551
359359 −9.28731 −0.490165 −0.245083 0.969502i 0.578815π-0.578815\pi
−0.245083 + 0.969502i 0.578815π0.578815\pi
360360 0 0
361361 0 0
362362 7.52282 0.395391
363363 4.88457 0.256373
364364 54.7651 2.87047
365365 0 0
366366 2.34329 0.122486
367367 11.4283 0.596555 0.298277 0.954479i 0.403588π-0.403588\pi
0.298277 + 0.954479i 0.403588π0.403588\pi
368368 −52.9206 −2.75868
369369 −0.129520 −0.00674256
370370 0 0
371371 −2.70936 −0.140663
372372 35.9190 1.86231
373373 −25.7467 −1.33312 −0.666558 0.745454i 0.732233π-0.732233\pi
−0.666558 + 0.745454i 0.732233π0.732233\pi
374374 −15.7931 −0.816642
375375 0 0
376376 20.8529 1.07541
377377 39.1162 2.01459
378378 30.0823 1.54727
379379 −20.3628 −1.04597 −0.522984 0.852343i 0.675181π-0.675181\pi
−0.522984 + 0.852343i 0.675181π0.675181\pi
380380 0 0
381381 6.00252 0.307519
382382 52.8742 2.70528
383383 −18.1004 −0.924886 −0.462443 0.886649i 0.653027π-0.653027\pi
−0.462443 + 0.886649i 0.653027π0.653027\pi
384384 25.8110 1.31716
385385 0 0
386386 14.7435 0.750426
387387 0.545033 0.0277056
388388 −1.03850 −0.0527217
389389 −30.3016 −1.53635 −0.768175 0.640239i 0.778835π-0.778835\pi
−0.768175 + 0.640239i 0.778835π0.778835\pi
390390 0 0
391391 −9.09418 −0.459913
392392 17.6426 0.891084
393393 −1.01012 −0.0509540
394394 −54.7126 −2.75638
395395 0 0
396396 1.56051 0.0784187
397397 3.57059 0.179203 0.0896015 0.995978i 0.471441π-0.471441\pi
0.0896015 + 0.995978i 0.471441π0.471441\pi
398398 46.0604 2.30880
399399 0 0
400400 0 0
401401 −0.553079 −0.0276194 −0.0138097 0.999905i 0.504396π-0.504396\pi
−0.0138097 + 0.999905i 0.504396π0.504396\pi
402402 −33.3884 −1.66526
403403 19.2394 0.958384
404404 12.1184 0.602912
405405 0 0
406406 −47.7012 −2.36737
407407 25.9826 1.28791
408408 30.3089 1.50052
409409 −2.56270 −0.126718 −0.0633588 0.997991i 0.520181π-0.520181\pi
−0.0633588 + 0.997991i 0.520181π0.520181\pi
410410 0 0
411411 8.49858 0.419204
412412 −5.50385 −0.271155
413413 0.540810 0.0266115
414414 1.24936 0.0614028
415415 0 0
416416 74.3146 3.64357
417417 26.4232 1.29395
418418 0 0
419419 −9.01138 −0.440235 −0.220117 0.975473i 0.570644π-0.570644\pi
−0.220117 + 0.975473i 0.570644π0.570644\pi
420420 0 0
421421 −8.61610 −0.419923 −0.209962 0.977710i 0.567334π-0.567334\pi
−0.209962 + 0.977710i 0.567334π0.567334\pi
422422 −56.6839 −2.75933
423423 −0.265584 −0.0129131
424424 −10.2209 −0.496371
425425 0 0
426426 45.1429 2.18718
427427 −1.10089 −0.0532756
428428 0.953945 0.0461107
429429 24.4527 1.18059
430430 0 0
431431 5.21526 0.251210 0.125605 0.992080i 0.459913π-0.459913\pi
0.125605 + 0.992080i 0.459913π0.459913\pi
432432 61.2215 2.94552
433433 5.17272 0.248585 0.124293 0.992246i 0.460334π-0.460334\pi
0.124293 + 0.992246i 0.460334π0.460334\pi
434434 −23.4620 −1.12621
435435 0 0
436436 67.3170 3.22390
437437 0 0
438438 −1.35138 −0.0645716
439439 −16.1031 −0.768560 −0.384280 0.923217i 0.625550π-0.625550\pi
−0.384280 + 0.923217i 0.625550π0.625550\pi
440440 0 0
441441 −0.224697 −0.0106998
442442 26.6293 1.26663
443443 12.1169 0.575693 0.287846 0.957677i 0.407061π-0.407061\pi
0.287846 + 0.957677i 0.407061π0.407061\pi
444444 −81.7915 −3.88165
445445 0 0
446446 77.0154 3.64678
447447 −22.2841 −1.05400
448448 −37.5697 −1.77500
449449 −7.07384 −0.333835 −0.166918 0.985971i 0.553381π-0.553381\pi
−0.166918 + 0.985971i 0.553381π0.553381\pi
450450 0 0
451451 −3.49916 −0.164769
452452 −22.3622 −1.05183
453453 19.4336 0.913069
454454 22.4872 1.05538
455455 0 0
456456 0 0
457457 −26.3810 −1.23405 −0.617027 0.786942i 0.711663π-0.711663\pi
−0.617027 + 0.786942i 0.711663π0.711663\pi
458458 −65.8331 −3.07618
459459 10.5207 0.491062
460460 0 0
461461 −9.59005 −0.446653 −0.223327 0.974744i 0.571692π-0.571692\pi
−0.223327 + 0.974744i 0.571692π0.571692\pi
462462 −29.8195 −1.38733
463463 6.50235 0.302190 0.151095 0.988519i 0.451720π-0.451720\pi
0.151095 + 0.988519i 0.451720π0.451720\pi
464464 −97.0783 −4.50674
465465 0 0
466466 55.3125 2.56230
467467 8.71364 0.403219 0.201610 0.979466i 0.435383π-0.435383\pi
0.201610 + 0.979466i 0.435383π0.435383\pi
468468 −2.63124 −0.121629
469469 15.6860 0.724312
470470 0 0
471471 39.5165 1.82083
472472 2.04017 0.0939064
473473 14.7248 0.677047
474474 −74.7293 −3.43243
475475 0 0
476476 −23.3565 −1.07054
477477 0.130174 0.00596025
478478 −27.8486 −1.27376
479479 27.3003 1.24738 0.623692 0.781670i 0.285632π-0.285632\pi
0.623692 + 0.781670i 0.285632π0.285632\pi
480480 0 0
481481 −43.8103 −1.99758
482482 −53.5115 −2.43738
483483 −17.1710 −0.781309
484484 −14.1999 −0.645450
485485 0 0
486486 −2.94370 −0.133529
487487 −35.5582 −1.61129 −0.805647 0.592395i 0.798182π-0.798182\pi
−0.805647 + 0.592395i 0.798182π0.798182\pi
488488 −4.15302 −0.187999
489489 3.08058 0.139309
490490 0 0
491491 41.5813 1.87654 0.938269 0.345906i 0.112428π-0.112428\pi
0.938269 + 0.345906i 0.112428π0.112428\pi
492492 11.0151 0.496600
493493 −16.6825 −0.751342
494494 0 0
495495 0 0
496496 −47.7483 −2.14396
497497 −21.2083 −0.951321
498498 −26.8169 −1.20169
499499 −27.1248 −1.21427 −0.607136 0.794598i 0.707682π-0.707682\pi
−0.607136 + 0.794598i 0.707682π0.707682\pi
500500 0 0
501501 −37.0964 −1.65734
502502 1.63954 0.0731762
503503 34.8198 1.55254 0.776269 0.630401i 0.217110π-0.217110\pi
0.776269 + 0.630401i 0.217110π0.217110\pi
504504 1.95619 0.0871358
505505 0 0
506506 33.7532 1.50051
507507 −18.3190 −0.813575
508508 −17.4499 −0.774215
509509 41.2656 1.82907 0.914533 0.404512i 0.132559π-0.132559\pi
0.914533 + 0.404512i 0.132559π0.132559\pi
510510 0 0
511511 0.634884 0.0280856
512512 15.7135 0.694443
513513 0 0
514514 −26.9588 −1.18910
515515 0 0
516516 −46.3526 −2.04056
517517 −7.17511 −0.315561
518518 53.4256 2.34738
519519 −20.4598 −0.898085
520520 0 0
521521 −33.5554 −1.47009 −0.735045 0.678018i 0.762839π-0.762839\pi
−0.735045 + 0.678018i 0.762839π0.762839\pi
522522 2.29185 0.100311
523523 −2.43983 −0.106687 −0.0533433 0.998576i 0.516988π-0.516988\pi
−0.0533433 + 0.998576i 0.516988π0.516988\pi
524524 2.93652 0.128283
525525 0 0
526526 −16.3995 −0.715054
527527 −8.20534 −0.357430
528528 −60.6866 −2.64105
529529 −3.56380 −0.154948
530530 0 0
531531 −0.0259837 −0.00112760
532532 0 0
533533 5.90007 0.255560
534534 −78.4778 −3.39607
535535 0 0
536536 59.1744 2.55594
537537 −7.01609 −0.302767
538538 −61.5981 −2.65568
539539 −6.07048 −0.261474
540540 0 0
541541 −27.7635 −1.19365 −0.596823 0.802373i 0.703571π-0.703571\pi
−0.596823 + 0.802373i 0.703571π0.703571\pi
542542 −36.7705 −1.57943
543543 4.96758 0.213179
544544 −31.6941 −1.35887
545545 0 0
546546 50.2798 2.15177
547547 25.2149 1.07811 0.539056 0.842270i 0.318781π-0.318781\pi
0.539056 + 0.842270i 0.318781π0.318781\pi
548548 −24.7062 −1.05540
549549 0.0528931 0.00225742
550550 0 0
551551 0 0
552552 −64.7767 −2.75708
553553 35.1080 1.49295
554554 48.7015 2.06913
555555 0 0
556556 −76.8148 −3.25767
557557 −18.0110 −0.763151 −0.381576 0.924338i 0.624618π-0.624618\pi
−0.381576 + 0.924338i 0.624618π0.624618\pi
558558 1.12725 0.0477205
559559 −24.8280 −1.05011
560560 0 0
561561 −10.4287 −0.440302
562562 54.4450 2.29662
563563 8.99696 0.379177 0.189588 0.981864i 0.439285π-0.439285\pi
0.189588 + 0.981864i 0.439285π0.439285\pi
564564 22.5867 0.951073
565565 0 0
566566 52.1668 2.19273
567567 20.5684 0.863790
568568 −80.0069 −3.35701
569569 25.4166 1.06552 0.532759 0.846267i 0.321155π-0.321155\pi
0.532759 + 0.846267i 0.321155π0.321155\pi
570570 0 0
571571 16.9476 0.709233 0.354617 0.935012i 0.384611π-0.384611\pi
0.354617 + 0.935012i 0.384611π0.384611\pi
572572 −71.0864 −2.97227
573573 34.9147 1.45858
574574 −7.19499 −0.300313
575575 0 0
576576 1.80507 0.0752113
577577 25.1670 1.04772 0.523859 0.851805i 0.324492π-0.324492\pi
0.523859 + 0.851805i 0.324492π0.324492\pi
578578 34.0160 1.41488
579579 9.73568 0.404601
580580 0 0
581581 12.5986 0.522680
582582 −0.953444 −0.0395215
583583 3.51682 0.145652
584584 2.39506 0.0991083
585585 0 0
586586 −24.6189 −1.01700
587587 −1.13849 −0.0469903 −0.0234952 0.999724i 0.507479π-0.507479\pi
−0.0234952 + 0.999724i 0.507479π0.507479\pi
588588 19.1094 0.788060
589589 0 0
590590 0 0
591591 −36.1287 −1.48613
592592 108.728 4.46870
593593 −5.56477 −0.228518 −0.114259 0.993451i 0.536449π-0.536449\pi
−0.114259 + 0.993451i 0.536449π0.536449\pi
594594 −39.0476 −1.60214
595595 0 0
596596 64.7819 2.65357
597597 30.4153 1.24482
598598 −56.9125 −2.32733
599599 −10.5181 −0.429758 −0.214879 0.976641i 0.568936π-0.568936\pi
−0.214879 + 0.976641i 0.568936π0.568936\pi
600600 0 0
601601 36.9336 1.50655 0.753277 0.657703i 0.228472π-0.228472\pi
0.753277 + 0.657703i 0.228472π0.228472\pi
602602 30.2771 1.23400
603603 −0.753648 −0.0306909
604604 −56.4953 −2.29876
605605 0 0
606606 11.1259 0.451958
607607 31.6955 1.28648 0.643240 0.765665i 0.277590π-0.277590\pi
0.643240 + 0.765665i 0.277590π0.277590\pi
608608 0 0
609609 −31.4988 −1.27640
610610 0 0
611611 12.0982 0.489441
612612 1.12219 0.0453617
613613 −24.7004 −0.997641 −0.498820 0.866705i 0.666233π-0.666233\pi
−0.498820 + 0.866705i 0.666233π0.666233\pi
614614 −20.6906 −0.835004
615615 0 0
616616 52.8492 2.12935
617617 −17.9984 −0.724589 −0.362294 0.932064i 0.618006π-0.618006\pi
−0.362294 + 0.932064i 0.618006π0.618006\pi
618618 −5.05308 −0.203265
619619 32.0927 1.28991 0.644957 0.764219i 0.276875π-0.276875\pi
0.644957 + 0.764219i 0.276875π0.276875\pi
620620 0 0
621621 −22.4849 −0.902287
622622 −66.3052 −2.65860
623623 36.8691 1.47713
624624 102.326 4.09632
625625 0 0
626626 15.4603 0.617920
627627 0 0
628628 −114.878 −4.58415
629629 18.6845 0.744998
630630 0 0
631631 −6.97644 −0.277728 −0.138864 0.990311i 0.544345π-0.544345\pi
−0.138864 + 0.990311i 0.544345π0.544345\pi
632632 132.443 5.26829
633633 −37.4304 −1.48772
634634 12.2754 0.487517
635635 0 0
636636 −11.0707 −0.438982
637637 10.2357 0.405551
638638 61.9173 2.45133
639639 1.01897 0.0403099
640640 0 0
641641 −27.8888 −1.10154 −0.550770 0.834657i 0.685666π-0.685666\pi
−0.550770 + 0.834657i 0.685666π0.685666\pi
642642 0.875816 0.0345657
643643 6.24974 0.246466 0.123233 0.992378i 0.460674π-0.460674\pi
0.123233 + 0.992378i 0.460674π0.460674\pi
644644 49.9179 1.96704
645645 0 0
646646 0 0
647647 22.1840 0.872142 0.436071 0.899912i 0.356370π-0.356370\pi
0.436071 + 0.899912i 0.356370π0.356370\pi
648648 77.5928 3.04813
649649 −0.701984 −0.0275553
650650 0 0
651651 −15.4928 −0.607210
652652 −8.95554 −0.350726
653653 11.3373 0.443664 0.221832 0.975085i 0.428796π-0.428796\pi
0.221832 + 0.975085i 0.428796π0.428796\pi
654654 61.8036 2.41671
655655 0 0
656656 −14.6428 −0.571704
657657 −0.0305036 −0.00119006
658658 −14.7535 −0.575150
659659 26.6149 1.03677 0.518385 0.855147i 0.326533π-0.326533\pi
0.518385 + 0.855147i 0.326533π0.326533\pi
660660 0 0
661661 −45.7240 −1.77846 −0.889228 0.457465i 0.848758π-0.848758\pi
−0.889228 + 0.457465i 0.848758π0.848758\pi
662662 −19.7386 −0.767161
663663 17.5843 0.682917
664664 47.5276 1.84443
665665 0 0
666666 −2.56688 −0.0994646
667667 35.6540 1.38053
668668 107.843 4.17256
669669 50.8560 1.96620
670670 0 0
671671 1.42898 0.0551651
672672 −59.8427 −2.30848
673673 25.6435 0.988484 0.494242 0.869324i 0.335446π-0.335446\pi
0.494242 + 0.869324i 0.335446π0.335446\pi
674674 44.5095 1.71444
675675 0 0
676676 53.2550 2.04827
677677 7.17287 0.275676 0.137838 0.990455i 0.455985π-0.455985\pi
0.137838 + 0.990455i 0.455985π0.455985\pi
678678 −20.5307 −0.788479
679679 0.447931 0.0171900
680680 0 0
681681 14.8491 0.569019
682682 30.4543 1.16615
683683 −6.25807 −0.239458 −0.119729 0.992807i 0.538203π-0.538203\pi
−0.119729 + 0.992807i 0.538203π0.538203\pi
684684 0 0
685685 0 0
686686 −53.7702 −2.05296
687687 −43.4719 −1.65856
688688 61.6180 2.34916
689689 −5.92984 −0.225909
690690 0 0
691691 −19.4240 −0.738925 −0.369463 0.929246i 0.620458π-0.620458\pi
−0.369463 + 0.929246i 0.620458π0.620458\pi
692692 59.4786 2.26104
693693 −0.673089 −0.0255685
694694 96.1640 3.65034
695695 0 0
696696 −118.827 −4.50413
697697 −2.51630 −0.0953115
698698 63.0872 2.38788
699699 36.5248 1.38149
700700 0 0
701701 9.49134 0.358483 0.179241 0.983805i 0.442636π-0.442636\pi
0.179241 + 0.983805i 0.442636π0.442636\pi
702702 65.8396 2.48496
703703 0 0
704704 48.7664 1.83795
705705 0 0
706706 90.5604 3.40829
707707 −5.22697 −0.196580
708708 2.20980 0.0830492
709709 −21.9473 −0.824246 −0.412123 0.911128i 0.635213π-0.635213\pi
−0.412123 + 0.911128i 0.635213π0.635213\pi
710710 0 0
711711 −1.68680 −0.0632599
712712 139.086 5.21248
713713 17.5366 0.656749
714714 −21.4436 −0.802507
715715 0 0
716716 20.3965 0.762251
717717 −18.3894 −0.686764
718718 24.7878 0.925074
719719 −3.61331 −0.134754 −0.0673768 0.997728i 0.521463π-0.521463\pi
−0.0673768 + 0.997728i 0.521463π0.521463\pi
720720 0 0
721721 2.37395 0.0884105
722722 0 0
723723 −35.3355 −1.31414
724724 −14.4412 −0.536704
725725 0 0
726726 −13.0369 −0.483845
727727 −41.1295 −1.52541 −0.762705 0.646747i 0.776129π-0.776129\pi
−0.762705 + 0.646747i 0.776129π0.776129\pi
728728 −89.1109 −3.30267
729729 25.9780 0.962146
730730 0 0
731731 10.5888 0.391641
732732 −4.49832 −0.166263
733733 26.4052 0.975297 0.487648 0.873040i 0.337855π-0.337855\pi
0.487648 + 0.873040i 0.337855π0.337855\pi
734734 −30.5023 −1.12586
735735 0 0
736736 67.7370 2.49682
737737 −20.3608 −0.750000
738738 0.345690 0.0127250
739739 −16.0961 −0.592106 −0.296053 0.955172i 0.595670π-0.595670\pi
−0.296053 + 0.955172i 0.595670π0.595670\pi
740740 0 0
741741 0 0
742742 7.23129 0.265469
743743 51.0206 1.87176 0.935882 0.352315i 0.114605π-0.114605\pi
0.935882 + 0.352315i 0.114605π0.114605\pi
744744 −58.4456 −2.14272
745745 0 0
746746 68.7181 2.51595
747747 −0.605314 −0.0221473
748748 30.3173 1.10851
749749 −0.411461 −0.0150345
750750 0 0
751751 −7.88161 −0.287604 −0.143802 0.989606i 0.545933π-0.545933\pi
−0.143802 + 0.989606i 0.545933π0.545933\pi
752752 −30.0253 −1.09491
753753 1.08264 0.0394538
754754 −104.401 −3.80206
755755 0 0
756756 −57.7478 −2.10027
757757 31.9261 1.16037 0.580186 0.814484i 0.302980π-0.302980\pi
0.580186 + 0.814484i 0.302980π0.302980\pi
758758 54.3484 1.97402
759759 22.2884 0.809019
760760 0 0
761761 21.6563 0.785039 0.392519 0.919744i 0.371604π-0.371604\pi
0.392519 + 0.919744i 0.371604π0.371604\pi
762762 −16.0207 −0.580370
763763 −29.0355 −1.05116
764764 −101.500 −3.67216
765765 0 0
766766 48.3099 1.74551
767767 1.18364 0.0427388
768768 −8.96514 −0.323502
769769 14.8767 0.536467 0.268233 0.963354i 0.413560π-0.413560\pi
0.268233 + 0.963354i 0.413560π0.413560\pi
770770 0 0
771771 −17.8018 −0.641117
772772 −28.3025 −1.01863
773773 1.66685 0.0599524 0.0299762 0.999551i 0.490457π-0.490457\pi
0.0299762 + 0.999551i 0.490457π0.490457\pi
774774 −1.45469 −0.0522879
775775 0 0
776776 1.68979 0.0606599
777777 35.2788 1.26562
778778 80.8749 2.89951
779779 0 0
780780 0 0
781781 27.5289 0.985060
782782 24.2724 0.867979
783783 −41.2466 −1.47403
784784 −25.4028 −0.907242
785785 0 0
786786 2.69602 0.0961638
787787 4.38273 0.156228 0.0781138 0.996944i 0.475110π-0.475110\pi
0.0781138 + 0.996944i 0.475110π0.475110\pi
788788 105.029 3.74152
789789 −10.8292 −0.385530
790790 0 0
791791 9.64541 0.342951
792792 −2.53919 −0.0902261
793793 −2.40945 −0.0855621
794794 −9.52992 −0.338204
795795 0 0
796796 −88.4202 −3.13397
797797 9.86857 0.349563 0.174781 0.984607i 0.444078π-0.444078\pi
0.174781 + 0.984607i 0.444078π0.444078\pi
798798 0 0
799799 −5.15972 −0.182538
800800 0 0
801801 −1.77141 −0.0625897
802802 1.47617 0.0521253
803803 −0.824096 −0.0290817
804804 64.0944 2.26043
805805 0 0
806806 −51.3501 −1.80873
807807 −40.6754 −1.43184
808808 −19.7184 −0.693691
809809 −40.4522 −1.42222 −0.711112 0.703079i 0.751808π-0.751808\pi
−0.711112 + 0.703079i 0.751808π0.751808\pi
810810 0 0
811811 −28.9125 −1.01526 −0.507628 0.861576i 0.669478π-0.669478\pi
−0.507628 + 0.861576i 0.669478π0.669478\pi
812812 91.5700 3.21348
813813 −24.2808 −0.851566
814814 −69.3477 −2.43064
815815 0 0
816816 −43.6406 −1.52773
817817 0 0
818818 6.83986 0.239150
819819 1.13492 0.0396573
820820 0 0
821821 −13.2912 −0.463866 −0.231933 0.972732i 0.574505π-0.574505\pi
−0.231933 + 0.972732i 0.574505π0.574505\pi
822822 −22.6827 −0.791151
823823 47.8247 1.66706 0.833532 0.552471i 0.186315π-0.186315\pi
0.833532 + 0.552471i 0.186315π0.186315\pi
824824 8.95558 0.311982
825825 0 0
826826 −1.44342 −0.0502230
827827 51.7917 1.80098 0.900488 0.434882i 0.143210π-0.143210\pi
0.900488 + 0.434882i 0.143210π0.143210\pi
828828 −2.39835 −0.0833484
829829 8.42434 0.292589 0.146295 0.989241i 0.453265π-0.453265\pi
0.146295 + 0.989241i 0.453265π0.453265\pi
830830 0 0
831831 32.1593 1.11559
832832 −82.2269 −2.85070
833833 −4.36536 −0.151251
834834 −70.5236 −2.44203
835835 0 0
836836 0 0
837837 −20.2873 −0.701231
838838 24.0514 0.830841
839839 23.7821 0.821051 0.410525 0.911849i 0.365345π-0.365345\pi
0.410525 + 0.911849i 0.365345π0.365345\pi
840840 0 0
841841 36.4042 1.25532
842842 22.9964 0.792508
843843 35.9519 1.23825
844844 108.814 3.74552
845845 0 0
846846 0.708844 0.0243706
847847 6.12478 0.210450
848848 14.7166 0.505371
849849 34.4476 1.18224
850850 0 0
851851 −39.9327 −1.36887
852852 −86.6589 −2.96889
853853 −27.3430 −0.936205 −0.468102 0.883674i 0.655062π-0.655062\pi
−0.468102 + 0.883674i 0.655062π0.655062\pi
854854 2.93827 0.100545
855855 0 0
856856 −1.55221 −0.0530534
857857 30.7007 1.04872 0.524358 0.851498i 0.324305π-0.324305\pi
0.524358 + 0.851498i 0.324305π0.324305\pi
858858 −65.2644 −2.22809
859859 −36.8449 −1.25713 −0.628567 0.777756i 0.716358π-0.716358\pi
−0.628567 + 0.777756i 0.716358π0.716358\pi
860860 0 0
861861 −4.75110 −0.161917
862862 −13.9195 −0.474102
863863 −4.42788 −0.150727 −0.0753634 0.997156i 0.524012π-0.524012\pi
−0.0753634 + 0.997156i 0.524012π0.524012\pi
864864 −78.3620 −2.66593
865865 0 0
866866 −13.8060 −0.469147
867867 22.4620 0.762848
868868 45.0390 1.52872
869869 −45.5711 −1.54589
870870 0 0
871871 34.3311 1.16326
872872 −109.535 −3.70931
873873 −0.0215212 −0.000728384 0
874874 0 0
875875 0 0
876876 2.59419 0.0876497
877877 0.177859 0.00600587 0.00300294 0.999995i 0.499044π-0.499044\pi
0.00300294 + 0.999995i 0.499044π0.499044\pi
878878 42.9792 1.45048
879879 −16.2567 −0.548326
880880 0 0
881881 35.4916 1.19574 0.597871 0.801593i 0.296014π-0.296014\pi
0.597871 + 0.801593i 0.296014π0.296014\pi
882882 0.599715 0.0201935
883883 44.6775 1.50352 0.751759 0.659438i 0.229206π-0.229206\pi
0.751759 + 0.659438i 0.229206π0.229206\pi
884884 −51.1192 −1.71932
885885 0 0
886886 −32.3401 −1.08649
887887 34.5396 1.15973 0.579863 0.814714i 0.303106π-0.303106\pi
0.579863 + 0.814714i 0.303106π0.303106\pi
888888 133.087 4.46611
889889 7.52659 0.252434
890890 0 0
891891 −26.6982 −0.894424
892892 −147.843 −4.95015
893893 0 0
894894 59.4762 1.98918
895895 0 0
896896 32.3645 1.08122
897897 −37.5813 −1.25480
898898 18.8801 0.630037
899899 32.1693 1.07291
900900 0 0
901901 2.52899 0.0842529
902902 9.33927 0.310964
903903 19.9931 0.665327
904904 36.3867 1.21020
905905 0 0
906906 −51.8683 −1.72321
907907 30.4093 1.00972 0.504862 0.863200i 0.331543π-0.331543\pi
0.504862 + 0.863200i 0.331543π0.331543\pi
908908 −43.1677 −1.43257
909909 0.251135 0.00832961
910910 0 0
911911 48.5898 1.60985 0.804926 0.593375i 0.202205π-0.202205\pi
0.804926 + 0.593375i 0.202205π0.202205\pi
912912 0 0
913913 −16.3534 −0.541217
914914 70.4110 2.32899
915915 0 0
916916 126.377 4.17561
917917 −1.26660 −0.0418268
918918 −28.0797 −0.926767
919919 46.0057 1.51759 0.758794 0.651331i 0.225789π-0.225789\pi
0.758794 + 0.651331i 0.225789π0.225789\pi
920920 0 0
921921 −13.6627 −0.450202
922922 25.5958 0.842954
923923 −46.4174 −1.52785
924924 57.2432 1.88316
925925 0 0
926926 −17.3548 −0.570313
927927 −0.114059 −0.00374618
928928 124.258 4.07896
929929 47.6797 1.56432 0.782161 0.623077i 0.214118π-0.214118\pi
0.782161 + 0.623077i 0.214118π0.214118\pi
930930 0 0
931931 0 0
932932 −106.181 −3.47808
933933 −43.7836 −1.43341
934934 −23.2567 −0.760983
935935 0 0
936936 4.28142 0.139942
937937 −32.4440 −1.05990 −0.529950 0.848029i 0.677789π-0.677789\pi
−0.529950 + 0.848029i 0.677789π0.677789\pi
938938 −41.8659 −1.36697
939939 10.2090 0.333158
940940 0 0
941941 22.9865 0.749339 0.374669 0.927159i 0.377756π-0.377756\pi
0.374669 + 0.927159i 0.377756π0.377756\pi
942942 −105.470 −3.43639
943943 5.37786 0.175127
944944 −2.93755 −0.0956092
945945 0 0
946946 −39.3005 −1.27777
947947 −19.5969 −0.636814 −0.318407 0.947954i 0.603148π-0.603148\pi
−0.318407 + 0.947954i 0.603148π0.603148\pi
948948 143.455 4.65919
949949 1.38954 0.0451063
950950 0 0
951951 8.10586 0.262850
952952 38.0045 1.23173
953953 21.8067 0.706387 0.353194 0.935550i 0.385096π-0.385096\pi
0.353194 + 0.935550i 0.385096π0.385096\pi
954954 −0.347434 −0.0112486
955955 0 0
956956 53.4597 1.72901
957957 40.8862 1.32166
958958 −72.8646 −2.35415
959959 10.6564 0.344113
960960 0 0
961961 −15.1774 −0.489594
962962 116.930 3.76997
963963 0.0197690 0.000637048 0
964964 102.724 3.30851
965965 0 0
966966 45.8295 1.47454
967967 −30.6010 −0.984063 −0.492031 0.870577i 0.663745π-0.663745\pi
−0.492031 + 0.870577i 0.663745π0.663745\pi
968968 23.1054 0.742634
969969 0 0
970970 0 0
971971 −24.6525 −0.791136 −0.395568 0.918437i 0.629452π-0.629452\pi
−0.395568 + 0.918437i 0.629452π0.629452\pi
972972 5.65089 0.181252
973973 33.1322 1.06217
974974 94.9048 3.04095
975975 0 0
976976 5.97976 0.191408
977977 −40.0301 −1.28067 −0.640337 0.768094i 0.721205π-0.721205\pi
−0.640337 + 0.768094i 0.721205π0.721205\pi
978978 −8.22207 −0.262913
979979 −47.8570 −1.52952
980980 0 0
981981 1.39504 0.0445402
982982 −110.981 −3.54153
983983 −18.0067 −0.574323 −0.287162 0.957882i 0.592712π-0.592712\pi
−0.287162 + 0.957882i 0.592712π0.592712\pi
984984 −17.9232 −0.571372
985985 0 0
986986 44.5256 1.41798
987987 −9.74224 −0.310099
988988 0 0
989989 −22.6305 −0.719608
990990 0 0
991991 −47.2626 −1.50135 −0.750674 0.660673i 0.770271π-0.770271\pi
−0.750674 + 0.660673i 0.770271π0.770271\pi
992992 61.1166 1.94045
993993 −13.0341 −0.413623
994994 56.6049 1.79540
995995 0 0
996996 51.4792 1.63118
997997 30.7551 0.974024 0.487012 0.873395i 0.338087π-0.338087\pi
0.487012 + 0.873395i 0.338087π0.338087\pi
998998 72.3961 2.29166
999999 46.1964 1.46159
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 9025.2.a.cv.1.1 40
5.2 odd 4 1805.2.b.m.1084.1 40
5.3 odd 4 1805.2.b.m.1084.40 yes 40
5.4 even 2 inner 9025.2.a.cv.1.40 40
19.18 odd 2 inner 9025.2.a.cv.1.39 40
95.18 even 4 1805.2.b.m.1084.2 yes 40
95.37 even 4 1805.2.b.m.1084.39 yes 40
95.94 odd 2 inner 9025.2.a.cv.1.2 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.b.m.1084.1 40 5.2 odd 4
1805.2.b.m.1084.2 yes 40 95.18 even 4
1805.2.b.m.1084.39 yes 40 95.37 even 4
1805.2.b.m.1084.40 yes 40 5.3 odd 4
9025.2.a.cv.1.1 40 1.1 even 1 trivial
9025.2.a.cv.1.2 40 95.94 odd 2 inner
9025.2.a.cv.1.39 40 19.18 odd 2 inner
9025.2.a.cv.1.40 40 5.4 even 2 inner