Properties

Label 1521.2.a.r.1.1
Level 15211521
Weight 22
Character 1521.1
Self dual yes
Analytic conductor 12.14512.145
Analytic rank 00
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: 00
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 169)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.801941.80194 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) == q0.801938q21.35690q40.246980q52.35690q7+2.69202q8+0.198062q10+4.24698q11+1.89008q14+0.554958q162.15883q170.0881460q19+0.335126q203.40581q221.49396q234.93900q25+3.19806q284.63102q296.63102q315.82908q32+1.73125q34+0.582105q35+5.69202q37+0.0706876q380.664874q40+11.5918q410.295897q435.76271q44+1.19806q46+7.35690q471.44504q49+3.96077q50+10.3937q531.04892q556.34481q56+3.71379q58+6.78017q59+3.47219q61+5.31767q62+3.56465q64+7.67994q67+2.92931q680.466812q70+8.66487q71+6.73556q734.56465q74+0.119605q7610.0097q77+9.97046q790.137063q809.29590q821.60925q83+0.533188q85+0.237291q86+11.4330q88+2.88471q89+2.02715q925.89977q94+0.0217703q958.05861q97+1.15883q98+O(q100)q-0.801938 q^{2} -1.35690 q^{4} -0.246980 q^{5} -2.35690 q^{7} +2.69202 q^{8} +0.198062 q^{10} +4.24698 q^{11} +1.89008 q^{14} +0.554958 q^{16} -2.15883 q^{17} -0.0881460 q^{19} +0.335126 q^{20} -3.40581 q^{22} -1.49396 q^{23} -4.93900 q^{25} +3.19806 q^{28} -4.63102 q^{29} -6.63102 q^{31} -5.82908 q^{32} +1.73125 q^{34} +0.582105 q^{35} +5.69202 q^{37} +0.0706876 q^{38} -0.664874 q^{40} +11.5918 q^{41} -0.295897 q^{43} -5.76271 q^{44} +1.19806 q^{46} +7.35690 q^{47} -1.44504 q^{49} +3.96077 q^{50} +10.3937 q^{53} -1.04892 q^{55} -6.34481 q^{56} +3.71379 q^{58} +6.78017 q^{59} +3.47219 q^{61} +5.31767 q^{62} +3.56465 q^{64} +7.67994 q^{67} +2.92931 q^{68} -0.466812 q^{70} +8.66487 q^{71} +6.73556 q^{73} -4.56465 q^{74} +0.119605 q^{76} -10.0097 q^{77} +9.97046 q^{79} -0.137063 q^{80} -9.29590 q^{82} -1.60925 q^{83} +0.533188 q^{85} +0.237291 q^{86} +11.4330 q^{88} +2.88471 q^{89} +2.02715 q^{92} -5.89977 q^{94} +0.0217703 q^{95} -8.05861 q^{97} +1.15883 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+2q2+4q53q7+3q8+5q10+8q11+5q14+2q16+2q174q19+3q22+5q235q25+14q28+q295q317q32+13q344q35+5q98+O(q100) 3 q + 2 q^{2} + 4 q^{5} - 3 q^{7} + 3 q^{8} + 5 q^{10} + 8 q^{11} + 5 q^{14} + 2 q^{16} + 2 q^{17} - 4 q^{19} + 3 q^{22} + 5 q^{23} - 5 q^{25} + 14 q^{28} + q^{29} - 5 q^{31} - 7 q^{32} + 13 q^{34} - 4 q^{35}+ \cdots - 5 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 −0.801938 −0.567056 −0.283528 0.958964i 0.591505π-0.591505\pi
−0.283528 + 0.958964i 0.591505π0.591505\pi
33 0 0
44 −1.35690 −0.678448
55 −0.246980 −0.110453 −0.0552263 0.998474i 0.517588π-0.517588\pi
−0.0552263 + 0.998474i 0.517588π0.517588\pi
66 0 0
77 −2.35690 −0.890823 −0.445411 0.895326i 0.646943π-0.646943\pi
−0.445411 + 0.895326i 0.646943π0.646943\pi
88 2.69202 0.951773
99 0 0
1010 0.198062 0.0626328
1111 4.24698 1.28051 0.640256 0.768161i 0.278828π-0.278828\pi
0.640256 + 0.768161i 0.278828π0.278828\pi
1212 0 0
1313 0 0
1414 1.89008 0.505146
1515 0 0
1616 0.554958 0.138740
1717 −2.15883 −0.523594 −0.261797 0.965123i 0.584315π-0.584315\pi
−0.261797 + 0.965123i 0.584315π0.584315\pi
1818 0 0
1919 −0.0881460 −0.0202221 −0.0101110 0.999949i 0.503218π-0.503218\pi
−0.0101110 + 0.999949i 0.503218π0.503218\pi
2020 0.335126 0.0749364
2121 0 0
2222 −3.40581 −0.726122
2323 −1.49396 −0.311512 −0.155756 0.987796i 0.549781π-0.549781\pi
−0.155756 + 0.987796i 0.549781π0.549781\pi
2424 0 0
2525 −4.93900 −0.987800
2626 0 0
2727 0 0
2828 3.19806 0.604377
2929 −4.63102 −0.859959 −0.429980 0.902839i 0.641479π-0.641479\pi
−0.429980 + 0.902839i 0.641479π0.641479\pi
3030 0 0
3131 −6.63102 −1.19097 −0.595483 0.803368i 0.703039π-0.703039\pi
−0.595483 + 0.803368i 0.703039π0.703039\pi
3232 −5.82908 −1.03045
3333 0 0
3434 1.73125 0.296907
3535 0.582105 0.0983937
3636 0 0
3737 5.69202 0.935763 0.467881 0.883791i 0.345017π-0.345017\pi
0.467881 + 0.883791i 0.345017π0.345017\pi
3838 0.0706876 0.0114670
3939 0 0
4040 −0.664874 −0.105126
4141 11.5918 1.81033 0.905167 0.425056i 0.139746π-0.139746\pi
0.905167 + 0.425056i 0.139746π0.139746\pi
4242 0 0
4343 −0.295897 −0.0451239 −0.0225619 0.999745i 0.507182π-0.507182\pi
−0.0225619 + 0.999745i 0.507182π0.507182\pi
4444 −5.76271 −0.868761
4545 0 0
4646 1.19806 0.176645
4747 7.35690 1.07311 0.536557 0.843864i 0.319725π-0.319725\pi
0.536557 + 0.843864i 0.319725π0.319725\pi
4848 0 0
4949 −1.44504 −0.206435
5050 3.96077 0.560138
5151 0 0
5252 0 0
5353 10.3937 1.42769 0.713844 0.700304i 0.246952π-0.246952\pi
0.713844 + 0.700304i 0.246952π0.246952\pi
5454 0 0
5555 −1.04892 −0.141436
5656 −6.34481 −0.847861
5757 0 0
5858 3.71379 0.487645
5959 6.78017 0.882703 0.441351 0.897334i 0.354499π-0.354499\pi
0.441351 + 0.897334i 0.354499π0.354499\pi
6060 0 0
6161 3.47219 0.444568 0.222284 0.974982i 0.428649π-0.428649\pi
0.222284 + 0.974982i 0.428649π0.428649\pi
6262 5.31767 0.675344
6363 0 0
6464 3.56465 0.445581
6565 0 0
6666 0 0
6767 7.67994 0.938254 0.469127 0.883131i 0.344569π-0.344569\pi
0.469127 + 0.883131i 0.344569π0.344569\pi
6868 2.92931 0.355231
6969 0 0
7070 −0.466812 −0.0557947
7171 8.66487 1.02833 0.514166 0.857691i 0.328102π-0.328102\pi
0.514166 + 0.857691i 0.328102π0.328102\pi
7272 0 0
7373 6.73556 0.788338 0.394169 0.919038i 0.371032π-0.371032\pi
0.394169 + 0.919038i 0.371032π0.371032\pi
7474 −4.56465 −0.530629
7575 0 0
7676 0.119605 0.0137196
7777 −10.0097 −1.14071
7878 0 0
7979 9.97046 1.12176 0.560882 0.827896i 0.310462π-0.310462\pi
0.560882 + 0.827896i 0.310462π0.310462\pi
8080 −0.137063 −0.0153241
8181 0 0
8282 −9.29590 −1.02656
8383 −1.60925 −0.176638 −0.0883192 0.996092i 0.528150π-0.528150\pi
−0.0883192 + 0.996092i 0.528150π0.528150\pi
8484 0 0
8585 0.533188 0.0578323
8686 0.237291 0.0255877
8787 0 0
8888 11.4330 1.21876
8989 2.88471 0.305778 0.152889 0.988243i 0.451142π-0.451142\pi
0.152889 + 0.988243i 0.451142π0.451142\pi
9090 0 0
9191 0 0
9292 2.02715 0.211345
9393 0 0
9494 −5.89977 −0.608515
9595 0.0217703 0.00223358
9696 0 0
9797 −8.05861 −0.818227 −0.409114 0.912483i 0.634162π-0.634162\pi
−0.409114 + 0.912483i 0.634162π0.634162\pi
9898 1.15883 0.117060
9999 0 0
100100 6.70171 0.670171
101101 13.3545 1.32882 0.664411 0.747367i 0.268682π-0.268682\pi
0.664411 + 0.747367i 0.268682π0.268682\pi
102102 0 0
103103 1.36227 0.134229 0.0671144 0.997745i 0.478621π-0.478621\pi
0.0671144 + 0.997745i 0.478621π0.478621\pi
104104 0 0
105105 0 0
106106 −8.33513 −0.809579
107107 −3.26875 −0.316002 −0.158001 0.987439i 0.550505π-0.550505\pi
−0.158001 + 0.987439i 0.550505π0.550505\pi
108108 0 0
109109 15.7017 1.50395 0.751976 0.659191i 0.229101π-0.229101\pi
0.751976 + 0.659191i 0.229101π0.229101\pi
110110 0.841166 0.0802021
111111 0 0
112112 −1.30798 −0.123592
113113 −12.0489 −1.13347 −0.566733 0.823901i 0.691793π-0.691793\pi
−0.566733 + 0.823901i 0.691793π0.691793\pi
114114 0 0
115115 0.368977 0.0344073
116116 6.28382 0.583438
117117 0 0
118118 −5.43727 −0.500541
119119 5.08815 0.466430
120120 0 0
121121 7.03684 0.639712
122122 −2.78448 −0.252095
123123 0 0
124124 8.99761 0.808009
125125 2.45473 0.219558
126126 0 0
127127 −9.80731 −0.870258 −0.435129 0.900368i 0.643297π-0.643297\pi
−0.435129 + 0.900368i 0.643297π0.643297\pi
128128 8.79954 0.777777
129129 0 0
130130 0 0
131131 6.57673 0.574611 0.287306 0.957839i 0.407240π-0.407240\pi
0.287306 + 0.957839i 0.407240π0.407240\pi
132132 0 0
133133 0.207751 0.0180143
134134 −6.15883 −0.532042
135135 0 0
136136 −5.81163 −0.498343
137137 −6.21983 −0.531396 −0.265698 0.964056i 0.585602π-0.585602\pi
−0.265698 + 0.964056i 0.585602π0.585602\pi
138138 0 0
139139 −14.7071 −1.24744 −0.623719 0.781648i 0.714379π-0.714379\pi
−0.623719 + 0.781648i 0.714379π0.714379\pi
140140 −0.789856 −0.0667550
141141 0 0
142142 −6.94869 −0.583121
143143 0 0
144144 0 0
145145 1.14377 0.0949848
146146 −5.40150 −0.447031
147147 0 0
148148 −7.72348 −0.634866
149149 −4.33513 −0.355147 −0.177574 0.984108i 0.556825π-0.556825\pi
−0.177574 + 0.984108i 0.556825π0.556825\pi
150150 0 0
151151 3.94438 0.320989 0.160494 0.987037i 0.448691π-0.448691\pi
0.160494 + 0.987037i 0.448691π0.448691\pi
152152 −0.237291 −0.0192468
153153 0 0
154154 8.02715 0.646846
155155 1.63773 0.131545
156156 0 0
157157 4.45473 0.355526 0.177763 0.984073i 0.443114π-0.443114\pi
0.177763 + 0.984073i 0.443114π0.443114\pi
158158 −7.99569 −0.636103
159159 0 0
160160 1.43967 0.113816
161161 3.52111 0.277502
162162 0 0
163163 16.1588 1.26566 0.632829 0.774292i 0.281894π-0.281894\pi
0.632829 + 0.774292i 0.281894π0.281894\pi
164164 −15.7289 −1.22822
165165 0 0
166166 1.29052 0.100164
167167 −16.1172 −1.24719 −0.623594 0.781749i 0.714328π-0.714328\pi
−0.623594 + 0.781749i 0.714328π0.714328\pi
168168 0 0
169169 0 0
170170 −0.427583 −0.0327942
171171 0 0
172172 0.401501 0.0306142
173173 21.5362 1.63736 0.818682 0.574247i 0.194705π-0.194705\pi
0.818682 + 0.574247i 0.194705π0.194705\pi
174174 0 0
175175 11.6407 0.879955
176176 2.35690 0.177658
177177 0 0
178178 −2.31336 −0.173393
179179 −11.4330 −0.854540 −0.427270 0.904124i 0.640525π-0.640525\pi
−0.427270 + 0.904124i 0.640525π0.640525\pi
180180 0 0
181181 20.9705 1.55872 0.779361 0.626575i 0.215544π-0.215544\pi
0.779361 + 0.626575i 0.215544π0.215544\pi
182182 0 0
183183 0 0
184184 −4.02177 −0.296489
185185 −1.40581 −0.103357
186186 0 0
187187 −9.16852 −0.670469
188188 −9.98254 −0.728052
189189 0 0
190190 −0.0174584 −0.00126657
191191 14.4373 1.04464 0.522322 0.852748i 0.325066π-0.325066\pi
0.522322 + 0.852748i 0.325066π0.325066\pi
192192 0 0
193193 −13.5797 −0.977489 −0.488745 0.872427i 0.662545π-0.662545\pi
−0.488745 + 0.872427i 0.662545π0.662545\pi
194194 6.46250 0.463980
195195 0 0
196196 1.96077 0.140055
197197 0.560335 0.0399222 0.0199611 0.999801i 0.493646π-0.493646\pi
0.0199611 + 0.999801i 0.493646π0.493646\pi
198198 0 0
199199 11.4916 0.814616 0.407308 0.913291i 0.366468π-0.366468\pi
0.407308 + 0.913291i 0.366468π0.366468\pi
200200 −13.2959 −0.940162
201201 0 0
202202 −10.7095 −0.753516
203203 10.9148 0.766071
204204 0 0
205205 −2.86294 −0.199956
206206 −1.09246 −0.0761151
207207 0 0
208208 0 0
209209 −0.374354 −0.0258946
210210 0 0
211211 8.78448 0.604748 0.302374 0.953189i 0.402221π-0.402221\pi
0.302374 + 0.953189i 0.402221π0.402221\pi
212212 −14.1032 −0.968613
213213 0 0
214214 2.62133 0.179191
215215 0.0730805 0.00498405
216216 0 0
217217 15.6286 1.06094
218218 −12.5918 −0.852824
219219 0 0
220220 1.42327 0.0959570
221221 0 0
222222 0 0
223223 −2.25906 −0.151278 −0.0756390 0.997135i 0.524100π-0.524100\pi
−0.0756390 + 0.997135i 0.524100π0.524100\pi
224224 13.7385 0.917945
225225 0 0
226226 9.66248 0.642739
227227 6.96615 0.462359 0.231180 0.972911i 0.425741π-0.425741\pi
0.231180 + 0.972911i 0.425741π0.425741\pi
228228 0 0
229229 −24.1739 −1.59746 −0.798728 0.601692i 0.794493π-0.794493\pi
−0.798728 + 0.601692i 0.794493π0.794493\pi
230230 −0.295897 −0.0195109
231231 0 0
232232 −12.4668 −0.818486
233233 3.06100 0.200533 0.100266 0.994961i 0.468031π-0.468031\pi
0.100266 + 0.994961i 0.468031π0.468031\pi
234234 0 0
235235 −1.81700 −0.118528
236236 −9.19998 −0.598868
237237 0 0
238238 −4.08038 −0.264492
239239 25.1468 1.62661 0.813304 0.581839i 0.197667π-0.197667\pi
0.813304 + 0.581839i 0.197667π0.197667\pi
240240 0 0
241241 −20.2664 −1.30547 −0.652735 0.757586i 0.726379π-0.726379\pi
−0.652735 + 0.757586i 0.726379π0.726379\pi
242242 −5.64310 −0.362752
243243 0 0
244244 −4.71140 −0.301616
245245 0.356896 0.0228012
246246 0 0
247247 0 0
248248 −17.8509 −1.13353
249249 0 0
250250 −1.96854 −0.124501
251251 23.7211 1.49726 0.748631 0.662987i 0.230712π-0.230712\pi
0.748631 + 0.662987i 0.230712π0.230712\pi
252252 0 0
253253 −6.34481 −0.398895
254254 7.86486 0.493485
255255 0 0
256256 −14.1860 −0.886624
257257 −14.2241 −0.887278 −0.443639 0.896206i 0.646313π-0.646313\pi
−0.443639 + 0.896206i 0.646313π0.646313\pi
258258 0 0
259259 −13.4155 −0.833599
260260 0 0
261261 0 0
262262 −5.27413 −0.325837
263263 17.0954 1.05415 0.527075 0.849819i 0.323289π-0.323289\pi
0.527075 + 0.849819i 0.323289π0.323289\pi
264264 0 0
265265 −2.56704 −0.157692
266266 −0.166603 −0.0102151
267267 0 0
268268 −10.4209 −0.636556
269269 6.46681 0.394288 0.197144 0.980374i 0.436833π-0.436833\pi
0.197144 + 0.980374i 0.436833π0.436833\pi
270270 0 0
271271 6.44803 0.391690 0.195845 0.980635i 0.437255π-0.437255\pi
0.195845 + 0.980635i 0.437255π0.437255\pi
272272 −1.19806 −0.0726432
273273 0 0
274274 4.98792 0.301331
275275 −20.9758 −1.26489
276276 0 0
277277 13.4601 0.808739 0.404370 0.914596i 0.367491π-0.367491\pi
0.404370 + 0.914596i 0.367491π0.367491\pi
278278 11.7942 0.707367
279279 0 0
280280 1.56704 0.0936485
281281 −5.03684 −0.300472 −0.150236 0.988650i 0.548003π-0.548003\pi
−0.150236 + 0.988650i 0.548003π0.548003\pi
282282 0 0
283283 22.1280 1.31537 0.657686 0.753293i 0.271536π-0.271536\pi
0.657686 + 0.753293i 0.271536π0.271536\pi
284284 −11.7573 −0.697669
285285 0 0
286286 0 0
287287 −27.3207 −1.61269
288288 0 0
289289 −12.3394 −0.725849
290290 −0.917231 −0.0538616
291291 0 0
292292 −9.13946 −0.534846
293293 −14.9463 −0.873172 −0.436586 0.899663i 0.643813π-0.643813\pi
−0.436586 + 0.899663i 0.643813π0.643813\pi
294294 0 0
295295 −1.67456 −0.0974968
296296 15.3230 0.890634
297297 0 0
298298 3.47650 0.201388
299299 0 0
300300 0 0
301301 0.697398 0.0401974
302302 −3.16315 −0.182019
303303 0 0
304304 −0.0489173 −0.00280560
305305 −0.857560 −0.0491037
306306 0 0
307307 19.1293 1.09177 0.545883 0.837861i 0.316194π-0.316194\pi
0.545883 + 0.837861i 0.316194π0.316194\pi
308308 13.5821 0.773912
309309 0 0
310310 −1.31336 −0.0745936
311311 0.269815 0.0152998 0.00764990 0.999971i 0.497565π-0.497565\pi
0.00764990 + 0.999971i 0.497565π0.497565\pi
312312 0 0
313313 −23.3937 −1.32229 −0.661146 0.750257i 0.729930π-0.729930\pi
−0.661146 + 0.750257i 0.729930π0.729930\pi
314314 −3.57242 −0.201603
315315 0 0
316316 −13.5289 −0.761059
317317 13.9952 0.786050 0.393025 0.919528i 0.371429π-0.371429\pi
0.393025 + 0.919528i 0.371429π0.371429\pi
318318 0 0
319319 −19.6679 −1.10119
320320 −0.880395 −0.0492156
321321 0 0
322322 −2.82371 −0.157359
323323 0.190293 0.0105882
324324 0 0
325325 0 0
326326 −12.9584 −0.717698
327327 0 0
328328 31.2054 1.72303
329329 −17.3394 −0.955954
330330 0 0
331331 17.8213 0.979548 0.489774 0.871849i 0.337079π-0.337079\pi
0.489774 + 0.871849i 0.337079π0.337079\pi
332332 2.18359 0.119840
333333 0 0
334334 12.9250 0.707225
335335 −1.89679 −0.103633
336336 0 0
337337 −27.8485 −1.51700 −0.758501 0.651672i 0.774068π-0.774068\pi
−0.758501 + 0.651672i 0.774068π0.774068\pi
338338 0 0
339339 0 0
340340 −0.723480 −0.0392362
341341 −28.1618 −1.52505
342342 0 0
343343 19.9041 1.07472
344344 −0.796561 −0.0429477
345345 0 0
346346 −17.2707 −0.928477
347347 −1.50365 −0.0807200 −0.0403600 0.999185i 0.512850π-0.512850\pi
−0.0403600 + 0.999185i 0.512850π0.512850\pi
348348 0 0
349349 −14.1860 −0.759358 −0.379679 0.925118i 0.623966π-0.623966\pi
−0.379679 + 0.925118i 0.623966π0.623966\pi
350350 −9.33513 −0.498983
351351 0 0
352352 −24.7560 −1.31950
353353 7.16852 0.381542 0.190771 0.981635i 0.438901π-0.438901\pi
0.190771 + 0.981635i 0.438901π0.438901\pi
354354 0 0
355355 −2.14005 −0.113582
356356 −3.91425 −0.207455
357357 0 0
358358 9.16852 0.484571
359359 −19.8853 −1.04951 −0.524753 0.851255i 0.675842π-0.675842\pi
−0.524753 + 0.851255i 0.675842π0.675842\pi
360360 0 0
361361 −18.9922 −0.999591
362362 −16.8170 −0.883882
363363 0 0
364364 0 0
365365 −1.66355 −0.0870740
366366 0 0
367367 1.08383 0.0565757 0.0282878 0.999600i 0.490994π-0.490994\pi
0.0282878 + 0.999600i 0.490994π0.490994\pi
368368 −0.829085 −0.0432190
369369 0 0
370370 1.12737 0.0586094
371371 −24.4969 −1.27182
372372 0 0
373373 −6.13036 −0.317418 −0.158709 0.987325i 0.550733π-0.550733\pi
−0.158709 + 0.987325i 0.550733π0.550733\pi
374374 7.35258 0.380193
375375 0 0
376376 19.8049 1.02136
377377 0 0
378378 0 0
379379 −2.40880 −0.123732 −0.0618658 0.998084i 0.519705π-0.519705\pi
−0.0618658 + 0.998084i 0.519705π0.519705\pi
380380 −0.0295400 −0.00151537
381381 0 0
382382 −11.5778 −0.592371
383383 30.3913 1.55292 0.776462 0.630164i 0.217012π-0.217012\pi
0.776462 + 0.630164i 0.217012π0.217012\pi
384384 0 0
385385 2.47219 0.125994
386386 10.8901 0.554291
387387 0 0
388388 10.9347 0.555125
389389 15.9409 0.808237 0.404118 0.914707i 0.367578π-0.367578\pi
0.404118 + 0.914707i 0.367578π0.367578\pi
390390 0 0
391391 3.22521 0.163106
392392 −3.89008 −0.196479
393393 0 0
394394 −0.449354 −0.0226381
395395 −2.46250 −0.123902
396396 0 0
397397 16.9148 0.848931 0.424466 0.905444i 0.360462π-0.360462\pi
0.424466 + 0.905444i 0.360462π0.360462\pi
398398 −9.21552 −0.461932
399399 0 0
400400 −2.74094 −0.137047
401401 −26.6625 −1.33146 −0.665730 0.746192i 0.731880π-0.731880\pi
−0.665730 + 0.746192i 0.731880π0.731880\pi
402402 0 0
403403 0 0
404404 −18.1207 −0.901537
405405 0 0
406406 −8.75302 −0.434405
407407 24.1739 1.19826
408408 0 0
409409 28.5163 1.41004 0.705021 0.709187i 0.250938π-0.250938\pi
0.705021 + 0.709187i 0.250938π0.250938\pi
410410 2.29590 0.113386
411411 0 0
412412 −1.84846 −0.0910672
413413 −15.9801 −0.786332
414414 0 0
415415 0.397452 0.0195102
416416 0 0
417417 0 0
418418 0.300209 0.0146837
419419 29.6093 1.44651 0.723253 0.690583i 0.242646π-0.242646\pi
0.723253 + 0.690583i 0.242646π0.242646\pi
420420 0 0
421421 −11.6606 −0.568301 −0.284151 0.958780i 0.591712π-0.591712\pi
−0.284151 + 0.958780i 0.591712π0.591712\pi
422422 −7.04461 −0.342926
423423 0 0
424424 27.9801 1.35884
425425 10.6625 0.517206
426426 0 0
427427 −8.18359 −0.396032
428428 4.43535 0.214391
429429 0 0
430430 −0.0586060 −0.00282623
431431 −4.34913 −0.209490 −0.104745 0.994499i 0.533403π-0.533403\pi
−0.104745 + 0.994499i 0.533403π0.533403\pi
432432 0 0
433433 −14.3884 −0.691460 −0.345730 0.938334i 0.612369π-0.612369\pi
−0.345730 + 0.938334i 0.612369π0.612369\pi
434434 −12.5332 −0.601612
435435 0 0
436436 −21.3056 −1.02035
437437 0.131687 0.00629942
438438 0 0
439439 −20.2325 −0.965645 −0.482822 0.875718i 0.660388π-0.660388\pi
−0.482822 + 0.875718i 0.660388π0.660388\pi
440440 −2.82371 −0.134615
441441 0 0
442442 0 0
443443 −8.12200 −0.385888 −0.192944 0.981210i 0.561804π-0.561804\pi
−0.192944 + 0.981210i 0.561804π0.561804\pi
444444 0 0
445445 −0.712464 −0.0337740
446446 1.81163 0.0857830
447447 0 0
448448 −8.40150 −0.396934
449449 −12.4916 −0.589513 −0.294757 0.955572i 0.595239π-0.595239\pi
−0.294757 + 0.955572i 0.595239π0.595239\pi
450450 0 0
451451 49.2301 2.31816
452452 16.3491 0.768998
453453 0 0
454454 −5.58642 −0.262184
455455 0 0
456456 0 0
457457 5.98121 0.279789 0.139895 0.990166i 0.455324π-0.455324\pi
0.139895 + 0.990166i 0.455324π0.455324\pi
458458 19.3860 0.905847
459459 0 0
460460 −0.500664 −0.0233436
461461 2.05669 0.0957895 0.0478947 0.998852i 0.484749π-0.484749\pi
0.0478947 + 0.998852i 0.484749π0.484749\pi
462462 0 0
463463 −8.44935 −0.392675 −0.196337 0.980536i 0.562905π-0.562905\pi
−0.196337 + 0.980536i 0.562905π0.562905\pi
464464 −2.57002 −0.119310
465465 0 0
466466 −2.45473 −0.113713
467467 −33.5139 −1.55084 −0.775420 0.631446i 0.782462π-0.782462\pi
−0.775420 + 0.631446i 0.782462π0.782462\pi
468468 0 0
469469 −18.1008 −0.835818
470470 1.45712 0.0672121
471471 0 0
472472 18.2524 0.840133
473473 −1.25667 −0.0577817
474474 0 0
475475 0.435353 0.0199754
476476 −6.90408 −0.316448
477477 0 0
478478 −20.1661 −0.922377
479479 24.7313 1.13000 0.565000 0.825091i 0.308876π-0.308876\pi
0.565000 + 0.825091i 0.308876π0.308876\pi
480480 0 0
481481 0 0
482482 16.2524 0.740275
483483 0 0
484484 −9.54825 −0.434012
485485 1.99031 0.0903754
486486 0 0
487487 −37.7555 −1.71087 −0.855433 0.517913i 0.826709π-0.826709\pi
−0.855433 + 0.517913i 0.826709π0.826709\pi
488488 9.34721 0.423128
489489 0 0
490490 −0.286208 −0.0129296
491491 −31.3110 −1.41304 −0.706522 0.707691i 0.749737π-0.749737\pi
−0.706522 + 0.707691i 0.749737π0.749737\pi
492492 0 0
493493 9.99761 0.450270
494494 0 0
495495 0 0
496496 −3.67994 −0.165234
497497 −20.4222 −0.916061
498498 0 0
499499 21.4873 0.961902 0.480951 0.876748i 0.340292π-0.340292\pi
0.480951 + 0.876748i 0.340292π0.340292\pi
500500 −3.33081 −0.148959
501501 0 0
502502 −19.0228 −0.849031
503503 −37.5924 −1.67616 −0.838081 0.545546i 0.816322π-0.816322\pi
−0.838081 + 0.545546i 0.816322π0.816322\pi
504504 0 0
505505 −3.29829 −0.146772
506506 5.08815 0.226196
507507 0 0
508508 13.3075 0.590425
509509 17.1075 0.758278 0.379139 0.925340i 0.376220π-0.376220\pi
0.379139 + 0.925340i 0.376220π0.376220\pi
510510 0 0
511511 −15.8750 −0.702269
512512 −6.22282 −0.275012
513513 0 0
514514 11.4069 0.503136
515515 −0.336454 −0.0148259
516516 0 0
517517 31.2446 1.37414
518518 10.7584 0.472697
519519 0 0
520520 0 0
521521 19.8465 0.869493 0.434746 0.900553i 0.356838π-0.356838\pi
0.434746 + 0.900553i 0.356838π0.356838\pi
522522 0 0
523523 −11.4300 −0.499798 −0.249899 0.968272i 0.580397π-0.580397\pi
−0.249899 + 0.968272i 0.580397π0.580397\pi
524524 −8.92394 −0.389844
525525 0 0
526526 −13.7095 −0.597762
527527 14.3153 0.623583
528528 0 0
529529 −20.7681 −0.902960
530530 2.05861 0.0894201
531531 0 0
532532 −0.281896 −0.0122218
533533 0 0
534534 0 0
535535 0.807315 0.0349033
536536 20.6746 0.893005
537537 0 0
538538 −5.18598 −0.223584
539539 −6.13706 −0.264342
540540 0 0
541541 16.1884 0.695993 0.347996 0.937496i 0.386862π-0.386862\pi
0.347996 + 0.937496i 0.386862π0.386862\pi
542542 −5.17092 −0.222110
543543 0 0
544544 12.5840 0.539536
545545 −3.87800 −0.166115
546546 0 0
547547 5.33081 0.227929 0.113965 0.993485i 0.463645π-0.463645\pi
0.113965 + 0.993485i 0.463645π0.463645\pi
548548 8.43967 0.360525
549549 0 0
550550 16.8213 0.717263
551551 0.408206 0.0173902
552552 0 0
553553 −23.4993 −0.999293
554554 −10.7942 −0.458600
555555 0 0
556556 19.9560 0.846322
557557 −7.39075 −0.313156 −0.156578 0.987666i 0.550046π-0.550046\pi
−0.156578 + 0.987666i 0.550046π0.550046\pi
558558 0 0
559559 0 0
560560 0.323044 0.0136511
561561 0 0
562562 4.03923 0.170385
563563 9.47889 0.399488 0.199744 0.979848i 0.435989π-0.435989\pi
0.199744 + 0.979848i 0.435989π0.435989\pi
564564 0 0
565565 2.97584 0.125194
566566 −17.7453 −0.745889
567567 0 0
568568 23.3260 0.978738
569569 10.1438 0.425249 0.212624 0.977134i 0.431799π-0.431799\pi
0.212624 + 0.977134i 0.431799π0.431799\pi
570570 0 0
571571 −14.0925 −0.589751 −0.294876 0.955536i 0.595278π-0.595278\pi
−0.294876 + 0.955536i 0.595278π0.595278\pi
572572 0 0
573573 0 0
574574 21.9095 0.914483
575575 7.37867 0.307712
576576 0 0
577577 25.1545 1.04720 0.523598 0.851965i 0.324589π-0.324589\pi
0.523598 + 0.851965i 0.324589π0.324589\pi
578578 9.89546 0.411597
579579 0 0
580580 −1.55197 −0.0644422
581581 3.79284 0.157354
582582 0 0
583583 44.1420 1.82817
584584 18.1323 0.750319
585585 0 0
586586 11.9860 0.495137
587587 −43.8353 −1.80928 −0.904639 0.426180i 0.859859π-0.859859\pi
−0.904639 + 0.426180i 0.859859π0.859859\pi
588588 0 0
589589 0.584498 0.0240838
590590 1.34290 0.0552861
591591 0 0
592592 3.15883 0.129827
593593 24.9965 1.02648 0.513242 0.858244i 0.328444π-0.328444\pi
0.513242 + 0.858244i 0.328444π0.328444\pi
594594 0 0
595595 −1.25667 −0.0515184
596596 5.88231 0.240949
597597 0 0
598598 0 0
599599 6.24027 0.254971 0.127485 0.991840i 0.459309π-0.459309\pi
0.127485 + 0.991840i 0.459309π0.459309\pi
600600 0 0
601601 6.32975 0.258196 0.129098 0.991632i 0.458792π-0.458792\pi
0.129098 + 0.991632i 0.458792π0.458792\pi
602602 −0.559270 −0.0227941
603603 0 0
604604 −5.35211 −0.217774
605605 −1.73795 −0.0706579
606606 0 0
607607 −43.6480 −1.77162 −0.885809 0.464050i 0.846396π-0.846396\pi
−0.885809 + 0.464050i 0.846396π0.846396\pi
608608 0.513811 0.0208378
609609 0 0
610610 0.687710 0.0278445
611611 0 0
612612 0 0
613613 −25.9541 −1.04827 −0.524137 0.851634i 0.675612π-0.675612\pi
−0.524137 + 0.851634i 0.675612π0.675612\pi
614614 −15.3405 −0.619092
615615 0 0
616616 −26.9463 −1.08570
617617 −45.9396 −1.84946 −0.924729 0.380626i 0.875709π-0.875709\pi
−0.924729 + 0.380626i 0.875709π0.875709\pi
618618 0 0
619619 6.73556 0.270725 0.135363 0.990796i 0.456780π-0.456780\pi
0.135363 + 0.990796i 0.456780π0.456780\pi
620620 −2.22223 −0.0892467
621621 0 0
622622 −0.216375 −0.00867583
623623 −6.79895 −0.272394
624624 0 0
625625 24.0887 0.963549
626626 18.7603 0.749813
627627 0 0
628628 −6.04461 −0.241206
629629 −12.2881 −0.489960
630630 0 0
631631 45.0998 1.79539 0.897696 0.440614i 0.145239π-0.145239\pi
0.897696 + 0.440614i 0.145239π0.145239\pi
632632 26.8407 1.06767
633633 0 0
634634 −11.2233 −0.445734
635635 2.42221 0.0961223
636636 0 0
637637 0 0
638638 15.7724 0.624435
639639 0 0
640640 −2.17331 −0.0859075
641641 −32.5821 −1.28692 −0.643458 0.765482i 0.722501π-0.722501\pi
−0.643458 + 0.765482i 0.722501π0.722501\pi
642642 0 0
643643 25.5754 1.00860 0.504298 0.863530i 0.331751π-0.331751\pi
0.504298 + 0.863530i 0.331751π0.331751\pi
644644 −4.77777 −0.188271
645645 0 0
646646 −0.152603 −0.00600408
647647 30.1715 1.18616 0.593082 0.805142i 0.297911π-0.297911\pi
0.593082 + 0.805142i 0.297911π0.297911\pi
648648 0 0
649649 28.7952 1.13031
650650 0 0
651651 0 0
652652 −21.9259 −0.858683
653653 −36.9028 −1.44412 −0.722058 0.691832i 0.756804π-0.756804\pi
−0.722058 + 0.691832i 0.756804π0.756804\pi
654654 0 0
655655 −1.62432 −0.0634673
656656 6.43296 0.251165
657657 0 0
658658 13.9051 0.542079
659659 −23.6866 −0.922701 −0.461350 0.887218i 0.652635π-0.652635\pi
−0.461350 + 0.887218i 0.652635π0.652635\pi
660660 0 0
661661 −31.7590 −1.23528 −0.617641 0.786460i 0.711911π-0.711911\pi
−0.617641 + 0.786460i 0.711911π0.711911\pi
662662 −14.2916 −0.555458
663663 0 0
664664 −4.33214 −0.168120
665665 −0.0513102 −0.00198973
666666 0 0
667667 6.91856 0.267888
668668 21.8694 0.846152
669669 0 0
670670 1.52111 0.0587655
671671 14.7463 0.569275
672672 0 0
673673 −7.50232 −0.289193 −0.144597 0.989491i 0.546188π-0.546188\pi
−0.144597 + 0.989491i 0.546188π0.546188\pi
674674 22.3327 0.860225
675675 0 0
676676 0 0
677677 35.0315 1.34637 0.673184 0.739475i 0.264926π-0.264926\pi
0.673184 + 0.739475i 0.264926π0.264926\pi
678678 0 0
679679 18.9933 0.728896
680680 1.43535 0.0550433
681681 0 0
682682 22.5840 0.864787
683683 24.0834 0.921524 0.460762 0.887524i 0.347576π-0.347576\pi
0.460762 + 0.887524i 0.347576π0.347576\pi
684684 0 0
685685 1.53617 0.0586941
686686 −15.9618 −0.609426
687687 0 0
688688 −0.164210 −0.00626046
689689 0 0
690690 0 0
691691 2.01447 0.0766342 0.0383171 0.999266i 0.487800π-0.487800\pi
0.0383171 + 0.999266i 0.487800π0.487800\pi
692692 −29.2223 −1.11087
693693 0 0
694694 1.20583 0.0457728
695695 3.63235 0.137783
696696 0 0
697697 −25.0248 −0.947880
698698 11.3763 0.430598
699699 0 0
700700 −15.7952 −0.597004
701701 48.8189 1.84387 0.921933 0.387350i 0.126610π-0.126610\pi
0.921933 + 0.387350i 0.126610π0.126610\pi
702702 0 0
703703 −0.501729 −0.0189231
704704 15.1390 0.570572
705705 0 0
706706 −5.74871 −0.216355
707707 −31.4752 −1.18375
708708 0 0
709709 −20.8060 −0.781385 −0.390693 0.920521i 0.627764π-0.627764\pi
−0.390693 + 0.920521i 0.627764π0.627764\pi
710710 1.71618 0.0644073
711711 0 0
712712 7.76569 0.291032
713713 9.90648 0.371000
714714 0 0
715715 0 0
716716 15.5133 0.579761
717717 0 0
718718 15.9468 0.595128
719719 −21.4306 −0.799225 −0.399613 0.916684i 0.630855π-0.630855\pi
−0.399613 + 0.916684i 0.630855π0.630855\pi
720720 0 0
721721 −3.21073 −0.119574
722722 15.2306 0.566824
723723 0 0
724724 −28.4547 −1.05751
725725 22.8726 0.849468
726726 0 0
727727 13.4862 0.500175 0.250088 0.968223i 0.419541π-0.419541\pi
0.250088 + 0.968223i 0.419541π0.419541\pi
728728 0 0
729729 0 0
730730 1.33406 0.0493758
731731 0.638792 0.0236266
732732 0 0
733733 −43.5424 −1.60828 −0.804138 0.594443i 0.797373π-0.797373\pi
−0.804138 + 0.594443i 0.797373π0.797373\pi
734734 −0.869167 −0.0320816
735735 0 0
736736 8.70841 0.320996
737737 32.6165 1.20145
738738 0 0
739739 20.0543 0.737709 0.368855 0.929487i 0.379750π-0.379750\pi
0.368855 + 0.929487i 0.379750π0.379750\pi
740740 1.90754 0.0701226
741741 0 0
742742 19.6450 0.721191
743743 33.1685 1.21684 0.608418 0.793617i 0.291805π-0.291805\pi
0.608418 + 0.793617i 0.291805π0.291805\pi
744744 0 0
745745 1.07069 0.0392270
746746 4.91617 0.179994
747747 0 0
748748 12.4407 0.454878
749749 7.70410 0.281502
750750 0 0
751751 39.2814 1.43340 0.716700 0.697382i 0.245652π-0.245652\pi
0.716700 + 0.697382i 0.245652π0.245652\pi
752752 4.08277 0.148883
753753 0 0
754754 0 0
755755 −0.974181 −0.0354541
756756 0 0
757757 −46.6426 −1.69526 −0.847628 0.530592i 0.821970π-0.821970\pi
−0.847628 + 0.530592i 0.821970π0.821970\pi
758758 1.93171 0.0701627
759759 0 0
760760 0.0586060 0.00212586
761761 21.8984 0.793818 0.396909 0.917858i 0.370083π-0.370083\pi
0.396909 + 0.917858i 0.370083π0.370083\pi
762762 0 0
763763 −37.0073 −1.33975
764764 −19.5899 −0.708737
765765 0 0
766766 −24.3720 −0.880595
767767 0 0
768768 0 0
769769 46.7096 1.68439 0.842196 0.539172i 0.181263π-0.181263\pi
0.842196 + 0.539172i 0.181263π0.181263\pi
770770 −1.98254 −0.0714458
771771 0 0
772772 18.4263 0.663175
773773 30.2416 1.08771 0.543857 0.839178i 0.316963π-0.316963\pi
0.543857 + 0.839178i 0.316963π0.316963\pi
774774 0 0
775775 32.7506 1.17644
776776 −21.6939 −0.778767
777777 0 0
778778 −12.7836 −0.458315
779779 −1.02177 −0.0366087
780780 0 0
781781 36.7995 1.31679
782782 −2.58642 −0.0924901
783783 0 0
784784 −0.801938 −0.0286406
785785 −1.10023 −0.0392688
786786 0 0
787787 28.7023 1.02313 0.511563 0.859246i 0.329067π-0.329067\pi
0.511563 + 0.859246i 0.329067π0.329067\pi
788788 −0.760316 −0.0270851
789789 0 0
790790 1.97477 0.0702592
791791 28.3980 1.00972
792792 0 0
793793 0 0
794794 −13.5646 −0.481391
795795 0 0
796796 −15.5929 −0.552674
797797 18.5418 0.656785 0.328392 0.944541i 0.393493π-0.393493\pi
0.328392 + 0.944541i 0.393493π0.393493\pi
798798 0 0
799799 −15.8823 −0.561876
800800 28.7899 1.01788
801801 0 0
802802 21.3817 0.755012
803803 28.6058 1.00948
804804 0 0
805805 −0.869641 −0.0306508
806806 0 0
807807 0 0
808808 35.9506 1.26474
809809 10.0677 0.353962 0.176981 0.984214i 0.443367π-0.443367\pi
0.176981 + 0.984214i 0.443367π0.443367\pi
810810 0 0
811811 −10.0285 −0.352147 −0.176074 0.984377i 0.556340π-0.556340\pi
−0.176074 + 0.984377i 0.556340π0.556340\pi
812812 −14.8103 −0.519740
813813 0 0
814814 −19.3860 −0.679478
815815 −3.99090 −0.139795
816816 0 0
817817 0.0260821 0.000912498 0
818818 −22.8683 −0.799572
819819 0 0
820820 3.88471 0.135660
821821 26.1704 0.913355 0.456677 0.889632i 0.349039π-0.349039\pi
0.456677 + 0.889632i 0.349039π0.349039\pi
822822 0 0
823823 1.82238 0.0635242 0.0317621 0.999495i 0.489888π-0.489888\pi
0.0317621 + 0.999495i 0.489888π0.489888\pi
824824 3.66727 0.127755
825825 0 0
826826 12.8151 0.445894
827827 32.2941 1.12298 0.561488 0.827485i 0.310229π-0.310229\pi
0.561488 + 0.827485i 0.310229π0.310229\pi
828828 0 0
829829 15.1002 0.524453 0.262226 0.965006i 0.415543π-0.415543\pi
0.262226 + 0.965006i 0.415543π0.415543\pi
830830 −0.318732 −0.0110634
831831 0 0
832832 0 0
833833 3.11960 0.108088
834834 0 0
835835 3.98062 0.137755
836836 0.507960 0.0175682
837837 0 0
838838 −23.7448 −0.820250
839839 32.9965 1.13917 0.569584 0.821933i 0.307104π-0.307104\pi
0.569584 + 0.821933i 0.307104π0.307104\pi
840840 0 0
841841 −7.55363 −0.260470
842842 9.35105 0.322258
843843 0 0
844844 −11.9196 −0.410290
845845 0 0
846846 0 0
847847 −16.5851 −0.569870
848848 5.76809 0.198077
849849 0 0
850850 −8.55065 −0.293285
851851 −8.50365 −0.291501
852852 0 0
853853 −37.7802 −1.29357 −0.646784 0.762673i 0.723887π-0.723887\pi
−0.646784 + 0.762673i 0.723887π0.723887\pi
854854 6.56273 0.224572
855855 0 0
856856 −8.79954 −0.300762
857857 −27.3623 −0.934677 −0.467339 0.884078i 0.654787π-0.654787\pi
−0.467339 + 0.884078i 0.654787π0.654787\pi
858858 0 0
859859 −20.0629 −0.684538 −0.342269 0.939602i 0.611195π-0.611195\pi
−0.342269 + 0.939602i 0.611195π0.611195\pi
860860 −0.0991626 −0.00338142
861861 0 0
862862 3.48773 0.118792
863863 6.14483 0.209173 0.104586 0.994516i 0.466648π-0.466648\pi
0.104586 + 0.994516i 0.466648π0.466648\pi
864864 0 0
865865 −5.31900 −0.180851
866866 11.5386 0.392096
867867 0 0
868868 −21.2064 −0.719793
869869 42.3443 1.43643
870870 0 0
871871 0 0
872872 42.2693 1.43142
873873 0 0
874874 −0.105604 −0.00357212
875875 −5.78554 −0.195587
876876 0 0
877877 −13.5077 −0.456123 −0.228061 0.973647i 0.573239π-0.573239\pi
−0.228061 + 0.973647i 0.573239π0.573239\pi
878878 16.2252 0.547574
879879 0 0
880880 −0.582105 −0.0196228
881881 5.23431 0.176348 0.0881741 0.996105i 0.471897π-0.471897\pi
0.0881741 + 0.996105i 0.471897π0.471897\pi
882882 0 0
883883 −4.57301 −0.153894 −0.0769470 0.997035i 0.524517π-0.524517\pi
−0.0769470 + 0.997035i 0.524517π0.524517\pi
884884 0 0
885885 0 0
886886 6.51334 0.218820
887887 1.64071 0.0550897 0.0275448 0.999621i 0.491231π-0.491231\pi
0.0275448 + 0.999621i 0.491231π0.491231\pi
888888 0 0
889889 23.1148 0.775246
890890 0.571352 0.0191517
891891 0 0
892892 3.06531 0.102634
893893 −0.648481 −0.0217006
894894 0 0
895895 2.82371 0.0943861
896896 −20.7396 −0.692862
897897 0 0
898898 10.0175 0.334287
899899 30.7084 1.02418
900900 0 0
901901 −22.4383 −0.747529
902902 −39.4795 −1.31452
903903 0 0
904904 −32.4359 −1.07880
905905 −5.17928 −0.172165
906906 0 0
907907 8.10215 0.269027 0.134514 0.990912i 0.457053π-0.457053\pi
0.134514 + 0.990912i 0.457053π0.457053\pi
908908 −9.45234 −0.313687
909909 0 0
910910 0 0
911911 9.18119 0.304187 0.152093 0.988366i 0.451399π-0.451399\pi
0.152093 + 0.988366i 0.451399π0.451399\pi
912912 0 0
913913 −6.83446 −0.226188
914914 −4.79656 −0.158656
915915 0 0
916916 32.8015 1.08379
917917 −15.5007 −0.511877
918918 0 0
919919 27.5036 0.907262 0.453631 0.891190i 0.350128π-0.350128\pi
0.453631 + 0.891190i 0.350128π0.350128\pi
920920 0.993295 0.0327480
921921 0 0
922922 −1.64933 −0.0543180
923923 0 0
924924 0 0
925925 −28.1129 −0.924346
926926 6.77586 0.222668
927927 0 0
928928 26.9946 0.886142
929929 −24.2131 −0.794407 −0.397203 0.917731i 0.630019π-0.630019\pi
−0.397203 + 0.917731i 0.630019π0.630019\pi
930930 0 0
931931 0.127375 0.00417454
932932 −4.15346 −0.136051
933933 0 0
934934 26.8761 0.879412
935935 2.26444 0.0740550
936936 0 0
937937 11.1830 0.365333 0.182666 0.983175i 0.441527π-0.441527\pi
0.182666 + 0.983175i 0.441527π0.441527\pi
938938 14.5157 0.473955
939939 0 0
940940 2.46548 0.0804152
941941 15.9638 0.520404 0.260202 0.965554i 0.416211π-0.416211\pi
0.260202 + 0.965554i 0.416211π0.416211\pi
942942 0 0
943943 −17.3177 −0.563941
944944 3.76271 0.122466
945945 0 0
946946 1.00777 0.0327654
947947 −6.51466 −0.211698 −0.105849 0.994382i 0.533756π-0.533756\pi
−0.105849 + 0.994382i 0.533756π0.533756\pi
948948 0 0
949949 0 0
950950 −0.349126 −0.0113271
951951 0 0
952952 13.6974 0.443935
953953 −47.6469 −1.54344 −0.771718 0.635965i 0.780602π-0.780602\pi
−0.771718 + 0.635965i 0.780602π0.780602\pi
954954 0 0
955955 −3.56571 −0.115384
956956 −34.1215 −1.10357
957957 0 0
958958 −19.8329 −0.640773
959959 14.6595 0.473380
960960 0 0
961961 12.9705 0.418402
962962 0 0
963963 0 0
964964 27.4993 0.885694
965965 3.35391 0.107966
966966 0 0
967967 −43.8122 −1.40891 −0.704453 0.709751i 0.748808π-0.748808\pi
−0.704453 + 0.709751i 0.748808π0.748808\pi
968968 18.9433 0.608861
969969 0 0
970970 −1.59611 −0.0512479
971971 −4.29483 −0.137828 −0.0689139 0.997623i 0.521953π-0.521953\pi
−0.0689139 + 0.997623i 0.521953π0.521953\pi
972972 0 0
973973 34.6631 1.11125
974974 30.2776 0.970156
975975 0 0
976976 1.92692 0.0616792
977977 −26.8019 −0.857470 −0.428735 0.903430i 0.641041π-0.641041\pi
−0.428735 + 0.903430i 0.641041π0.641041\pi
978978 0 0
979979 12.2513 0.391553
980980 −0.484271 −0.0154695
981981 0 0
982982 25.1094 0.801275
983983 −27.2495 −0.869124 −0.434562 0.900642i 0.643097π-0.643097\pi
−0.434562 + 0.900642i 0.643097π0.643097\pi
984984 0 0
985985 −0.138391 −0.00440951
986986 −8.01746 −0.255328
987987 0 0
988988 0 0
989989 0.442058 0.0140566
990990 0 0
991991 24.3889 0.774740 0.387370 0.921924i 0.373384π-0.373384\pi
0.387370 + 0.921924i 0.373384π0.373384\pi
992992 38.6528 1.22723
993993 0 0
994994 16.3773 0.519458
995995 −2.83818 −0.0899764
996996 0 0
997997 31.3207 0.991935 0.495967 0.868341i 0.334814π-0.334814\pi
0.495967 + 0.868341i 0.334814π0.334814\pi
998998 −17.2314 −0.545452
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.r.1.1 3
3.2 odd 2 169.2.a.b.1.3 3
12.11 even 2 2704.2.a.z.1.3 3
13.5 odd 4 1521.2.b.l.1351.5 6
13.8 odd 4 1521.2.b.l.1351.2 6
13.12 even 2 1521.2.a.o.1.3 3
15.14 odd 2 4225.2.a.bg.1.1 3
21.20 even 2 8281.2.a.bf.1.3 3
39.2 even 12 169.2.e.b.147.5 12
39.5 even 4 169.2.b.b.168.2 6
39.8 even 4 169.2.b.b.168.5 6
39.11 even 12 169.2.e.b.147.2 12
39.17 odd 6 169.2.c.b.146.3 6
39.20 even 12 169.2.e.b.23.5 12
39.23 odd 6 169.2.c.b.22.3 6
39.29 odd 6 169.2.c.c.22.1 6
39.32 even 12 169.2.e.b.23.2 12
39.35 odd 6 169.2.c.c.146.1 6
39.38 odd 2 169.2.a.c.1.1 yes 3
156.47 odd 4 2704.2.f.o.337.6 6
156.83 odd 4 2704.2.f.o.337.5 6
156.155 even 2 2704.2.a.ba.1.3 3
195.194 odd 2 4225.2.a.bb.1.3 3
273.272 even 2 8281.2.a.bj.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.2.a.b.1.3 3 3.2 odd 2
169.2.a.c.1.1 yes 3 39.38 odd 2
169.2.b.b.168.2 6 39.5 even 4
169.2.b.b.168.5 6 39.8 even 4
169.2.c.b.22.3 6 39.23 odd 6
169.2.c.b.146.3 6 39.17 odd 6
169.2.c.c.22.1 6 39.29 odd 6
169.2.c.c.146.1 6 39.35 odd 6
169.2.e.b.23.2 12 39.32 even 12
169.2.e.b.23.5 12 39.20 even 12
169.2.e.b.147.2 12 39.11 even 12
169.2.e.b.147.5 12 39.2 even 12
1521.2.a.o.1.3 3 13.12 even 2
1521.2.a.r.1.1 3 1.1 even 1 trivial
1521.2.b.l.1351.2 6 13.8 odd 4
1521.2.b.l.1351.5 6 13.5 odd 4
2704.2.a.z.1.3 3 12.11 even 2
2704.2.a.ba.1.3 3 156.155 even 2
2704.2.f.o.337.5 6 156.83 odd 4
2704.2.f.o.337.6 6 156.47 odd 4
4225.2.a.bb.1.3 3 195.194 odd 2
4225.2.a.bg.1.1 3 15.14 odd 2
8281.2.a.bf.1.3 3 21.20 even 2
8281.2.a.bj.1.1 3 273.272 even 2