Properties

Label 1386.2.g.a.881.7
Level 13861386
Weight 22
Character 1386.881
Analytic conductor 11.06711.067
Analytic rank 00
Dimension 1616
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1386,2,Mod(881,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1386.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1386=232711 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1386.g (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 11.067265720111.0672657201
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x164x14+8x12+80x10+1189x82028x6+1800x4+1080x2+324 x^{16} - 4x^{14} + 8x^{12} + 80x^{10} + 1189x^{8} - 2028x^{6} + 1800x^{4} + 1080x^{2} + 324 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 2934 2^{9}\cdot 3^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 881.7
Root 2.43348+1.00798i-2.43348 + 1.00798i of defining polynomial
Character χ\chi == 1386.881
Dual form 1386.2.g.a.881.15

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) == q1.00000iq21.00000q4+2.01596q5+(1.784501.95335i)q7+1.00000iq82.01596iq10+1.00000iq11+(1.953351.78450i)q14+1.00000q16+5.92266q17+0.657927iq192.01596q20+1.00000q227.87575iq230.935886q25+(1.78450+1.95335i)q281.32636iq29+10.6942iq311.00000iq325.92266iq34+(3.597493.93788i)q35+5.87575q37+0.657927q38+2.01596iq40+4.56462q411.56900q431.00000iq447.87575q46+0.532690q47+(0.6311226.97149i)q49+0.935886iq507.44475iq53+2.01596iq55+(1.95335+1.78450i)q561.32636q58+4.03193q59+0.250475iq61+10.6942q621.00000q647.81164q675.92266q68+(3.937883.59749i)q70+0.609527iq71+0.532690iq735.87575iq740.657927iq76+(1.95335+1.78450i)q7712.7711q79+2.01596q804.56462iq82+13.3681q83+11.9399q85+1.56900iq861.00000q88+5.22255q89+7.87575iq920.532690iq94+1.32636iq952.71607iq97+(6.97149+0.631122i)q98+O(q100)q-1.00000i q^{2} -1.00000 q^{4} +2.01596 q^{5} +(1.78450 - 1.95335i) q^{7} +1.00000i q^{8} -2.01596i q^{10} +1.00000i q^{11} +(-1.95335 - 1.78450i) q^{14} +1.00000 q^{16} +5.92266 q^{17} +0.657927i q^{19} -2.01596 q^{20} +1.00000 q^{22} -7.87575i q^{23} -0.935886 q^{25} +(-1.78450 + 1.95335i) q^{28} -1.32636i q^{29} +10.6942i q^{31} -1.00000i q^{32} -5.92266i q^{34} +(3.59749 - 3.93788i) q^{35} +5.87575 q^{37} +0.657927 q^{38} +2.01596i q^{40} +4.56462 q^{41} -1.56900 q^{43} -1.00000i q^{44} -7.87575 q^{46} +0.532690 q^{47} +(-0.631122 - 6.97149i) q^{49} +0.935886i q^{50} -7.44475i q^{53} +2.01596i q^{55} +(1.95335 + 1.78450i) q^{56} -1.32636 q^{58} +4.03193 q^{59} +0.250475i q^{61} +10.6942 q^{62} -1.00000 q^{64} -7.81164 q^{67} -5.92266 q^{68} +(-3.93788 - 3.59749i) q^{70} +0.609527i q^{71} +0.532690i q^{73} -5.87575i q^{74} -0.657927i q^{76} +(1.95335 + 1.78450i) q^{77} -12.7711 q^{79} +2.01596 q^{80} -4.56462i q^{82} +13.3681 q^{83} +11.9399 q^{85} +1.56900i q^{86} -1.00000 q^{88} +5.22255 q^{89} +7.87575i q^{92} -0.532690i q^{94} +1.32636i q^{95} -2.71607i q^{97} +(-6.97149 + 0.631122i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q16q48q7+16q16+16q22+16q25+8q2816q37+48q4316q46+8q4916q5816q64+16q678q7016q79+112q8516q88+O(q100) 16 q - 16 q^{4} - 8 q^{7} + 16 q^{16} + 16 q^{22} + 16 q^{25} + 8 q^{28} - 16 q^{37} + 48 q^{43} - 16 q^{46} + 8 q^{49} - 16 q^{58} - 16 q^{64} + 16 q^{67} - 8 q^{70} - 16 q^{79} + 112 q^{85} - 16 q^{88}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1386Z)×\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times.

nn 155155 199199 11351135
χ(n)\chi(n) 1-1 1-1 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.00000i 0.707107i
33 0 0
44 −1.00000 −0.500000
55 2.01596 0.901567 0.450783 0.892633i 0.351145π-0.351145\pi
0.450783 + 0.892633i 0.351145π0.351145\pi
66 0 0
77 1.78450 1.95335i 0.674477 0.738295i
88 1.00000i 0.353553i
99 0 0
1010 2.01596i 0.637504i
1111 1.00000i 0.301511i
1212 0 0
1313 0 0 1.00000 00
−1.00000 π\pi
1414 −1.95335 1.78450i −0.522054 0.476928i
1515 0 0
1616 1.00000 0.250000
1717 5.92266 1.43646 0.718228 0.695808i 0.244954π-0.244954\pi
0.718228 + 0.695808i 0.244954π0.244954\pi
1818 0 0
1919 0.657927i 0.150939i 0.997148 + 0.0754695i 0.0240455π0.0240455\pi
−0.997148 + 0.0754695i 0.975954π0.975954\pi
2020 −2.01596 −0.450783
2121 0 0
2222 1.00000 0.213201
2323 7.87575i 1.64221i −0.570778 0.821104i 0.693358π-0.693358\pi
0.570778 0.821104i 0.306642π-0.306642\pi
2424 0 0
2525 −0.935886 −0.187177
2626 0 0
2727 0 0
2828 −1.78450 + 1.95335i −0.337239 + 0.369148i
2929 1.32636i 0.246299i −0.992388 0.123149i 0.960701π-0.960701\pi
0.992388 0.123149i 0.0392994π-0.0392994\pi
3030 0 0
3131 10.6942i 1.92074i 0.278732 + 0.960369i 0.410086π0.410086\pi
−0.278732 + 0.960369i 0.589914π0.589914\pi
3232 1.00000i 0.176777i
3333 0 0
3434 5.92266i 1.01573i
3535 3.59749 3.93788i 0.608087 0.665623i
3636 0 0
3737 5.87575 0.965968 0.482984 0.875629i 0.339553π-0.339553\pi
0.482984 + 0.875629i 0.339553π0.339553\pi
3838 0.657927 0.106730
3939 0 0
4040 2.01596i 0.318752i
4141 4.56462 0.712874 0.356437 0.934319i 0.383991π-0.383991\pi
0.356437 + 0.934319i 0.383991π0.383991\pi
4242 0 0
4343 −1.56900 −0.239270 −0.119635 0.992818i 0.538172π-0.538172\pi
−0.119635 + 0.992818i 0.538172π0.538172\pi
4444 1.00000i 0.150756i
4545 0 0
4646 −7.87575 −1.16122
4747 0.532690 0.0777008 0.0388504 0.999245i 0.487630π-0.487630\pi
0.0388504 + 0.999245i 0.487630π0.487630\pi
4848 0 0
4949 −0.631122 6.97149i −0.0901603 0.995927i
5050 0.935886i 0.132354i
5151 0 0
5252 0 0
5353 7.44475i 1.02262i −0.859398 0.511308i 0.829161π-0.829161\pi
0.859398 0.511308i 0.170839π-0.170839\pi
5454 0 0
5555 2.01596i 0.271833i
5656 1.95335 + 1.78450i 0.261027 + 0.238464i
5757 0 0
5858 −1.32636 −0.174159
5959 4.03193 0.524913 0.262456 0.964944i 0.415467π-0.415467\pi
0.262456 + 0.964944i 0.415467π0.415467\pi
6060 0 0
6161 0.250475i 0.0320700i 0.999871 + 0.0160350i 0.00510432π0.00510432\pi
−0.999871 + 0.0160350i 0.994896π0.994896\pi
6262 10.6942 1.35817
6363 0 0
6464 −1.00000 −0.125000
6565 0 0
6666 0 0
6767 −7.81164 −0.954344 −0.477172 0.878810i 0.658338π-0.658338\pi
−0.477172 + 0.878810i 0.658338π0.658338\pi
6868 −5.92266 −0.718228
6969 0 0
7070 −3.93788 3.59749i −0.470666 0.429982i
7171 0.609527i 0.0723376i 0.999346 + 0.0361688i 0.0115154π0.0115154\pi
−0.999346 + 0.0361688i 0.988485π0.988485\pi
7272 0 0
7373 0.532690i 0.0623466i 0.999514 + 0.0311733i 0.00992438π0.00992438\pi
−0.999514 + 0.0311733i 0.990076π0.990076\pi
7474 5.87575i 0.683043i
7575 0 0
7676 0.657927i 0.0754695i
7777 1.95335 + 1.78450i 0.222604 + 0.203363i
7878 0 0
7979 −12.7711 −1.43686 −0.718431 0.695598i 0.755139π-0.755139\pi
−0.718431 + 0.695598i 0.755139π0.755139\pi
8080 2.01596 0.225392
8181 0 0
8282 4.56462i 0.504078i
8383 13.3681 1.46734 0.733670 0.679506i 0.237806π-0.237806\pi
0.733670 + 0.679506i 0.237806π0.237806\pi
8484 0 0
8585 11.9399 1.29506
8686 1.56900i 0.169190i
8787 0 0
8888 −1.00000 −0.106600
8989 5.22255 0.553589 0.276794 0.960929i 0.410728π-0.410728\pi
0.276794 + 0.960929i 0.410728π0.410728\pi
9090 0 0
9191 0 0
9292 7.87575i 0.821104i
9393 0 0
9494 0.532690i 0.0549428i
9595 1.32636i 0.136082i
9696 0 0
9797 2.71607i 0.275776i −0.990448 0.137888i 0.955969π-0.955969\pi
0.990448 0.137888i 0.0440313π-0.0440313\pi
9898 −6.97149 + 0.631122i −0.704227 + 0.0637530i
9999 0 0
100100 0.935886 0.0935886
101101 3.41352 0.339658 0.169829 0.985474i 0.445678π-0.445678\pi
0.169829 + 0.985474i 0.445678π0.445678\pi
102102 0 0
103103 13.3681i 1.31720i −0.752494 0.658599i 0.771149π-0.771149\pi
0.752494 0.658599i 0.228851π-0.228851\pi
104104 0 0
105105 0 0
106106 −7.44475 −0.723098
107107 14.4002i 1.39212i −0.717982 0.696062i 0.754934π-0.754934\pi
0.717982 0.696062i 0.245066π-0.245066\pi
108108 0 0
109109 −3.41140 −0.326753 −0.163376 0.986564i 0.552238π-0.552238\pi
−0.163376 + 0.986564i 0.552238π0.552238\pi
110110 2.01596 0.192215
111111 0 0
112112 1.78450 1.95335i 0.168619 0.184574i
113113 4.95947i 0.466548i −0.972411 0.233274i 0.925056π-0.925056\pi
0.972411 0.233274i 0.0749439π-0.0749439\pi
114114 0 0
115115 15.8772i 1.48056i
116116 1.32636i 0.123149i
117117 0 0
118118 4.03193i 0.371169i
119119 10.5690 11.5690i 0.968857 1.06053i
120120 0 0
121121 −1.00000 −0.0909091
122122 0.250475 0.0226769
123123 0 0
124124 10.6942i 0.960369i
125125 −11.9665 −1.07032
126126 0 0
127127 9.50488 0.843422 0.421711 0.906730i 0.361430π-0.361430\pi
0.421711 + 0.906730i 0.361430π0.361430\pi
128128 1.00000i 0.0883883i
129129 0 0
130130 0 0
131131 −19.0838 −1.66736 −0.833681 0.552247i 0.813771π-0.813771\pi
−0.833681 + 0.552247i 0.813771π0.813771\pi
132132 0 0
133133 1.28516 + 1.17407i 0.111438 + 0.101805i
134134 7.81164i 0.674823i
135135 0 0
136136 5.92266i 0.507864i
137137 8.05428i 0.688124i −0.938947 0.344062i 0.888197π-0.888197\pi
0.938947 0.344062i 0.111803π-0.111803\pi
138138 0 0
139139 19.3725i 1.64315i 0.570099 + 0.821576i 0.306905π0.306905\pi
−0.570099 + 0.821576i 0.693095π0.693095\pi
140140 −3.59749 + 3.93788i −0.304043 + 0.332811i
141141 0 0
142142 0.609527 0.0511504
143143 0 0
144144 0 0
145145 2.67389i 0.222055i
146146 0.532690 0.0440857
147147 0 0
148148 −5.87575 −0.482984
149149 3.26224i 0.267253i 0.991032 + 0.133627i 0.0426623π0.0426623\pi
−0.991032 + 0.133627i 0.957338π0.957338\pi
150150 0 0
151151 −14.1785 −1.15383 −0.576916 0.816803i 0.695744π-0.695744\pi
−0.576916 + 0.816803i 0.695744π0.695744\pi
152152 −0.657927 −0.0533650
153153 0 0
154154 1.78450 1.95335i 0.143799 0.157405i
155155 21.5592i 1.73167i
156156 0 0
157157 11.7596i 0.938518i 0.883061 + 0.469259i 0.155479π0.155479\pi
−0.883061 + 0.469259i 0.844521π0.844521\pi
158158 12.7711i 1.01602i
159159 0 0
160160 2.01596i 0.159376i
161161 −15.3841 14.0543i −1.21243 1.10763i
162162 0 0
163163 12.5285 0.981306 0.490653 0.871355i 0.336758π-0.336758\pi
0.490653 + 0.871355i 0.336758π0.336758\pi
164164 −4.56462 −0.356437
165165 0 0
166166 13.3681i 1.03757i
167167 −23.0722 −1.78538 −0.892691 0.450669i 0.851185π-0.851185\pi
−0.892691 + 0.450669i 0.851185π0.851185\pi
168168 0 0
169169 13.0000 1.00000
170170 11.9399i 0.915746i
171171 0 0
172172 1.56900 0.119635
173173 17.7244 1.34756 0.673782 0.738930i 0.264669π-0.264669\pi
0.673782 + 0.738930i 0.264669π0.264669\pi
174174 0 0
175175 −1.67009 + 1.82811i −0.126247 + 0.138192i
176176 1.00000i 0.0753778i
177177 0 0
178178 5.22255i 0.391446i
179179 3.81164i 0.284895i −0.989802 0.142448i 0.954503π-0.954503\pi
0.989802 0.142448i 0.0454973π-0.0454973\pi
180180 0 0
181181 19.1260i 1.42163i 0.703382 + 0.710813i 0.251673π0.251673\pi
−0.703382 + 0.710813i 0.748327π0.748327\pi
182182 0 0
183183 0 0
184184 7.87575 0.580608
185185 11.8453 0.870885
186186 0 0
187187 5.92266i 0.433108i
188188 −0.532690 −0.0388504
189189 0 0
190190 1.32636 0.0962242
191191 21.6665i 1.56773i 0.620931 + 0.783865i 0.286755π0.286755\pi
−0.620931 + 0.783865i 0.713245π0.713245\pi
192192 0 0
193193 −21.6233 −1.55648 −0.778239 0.627968i 0.783887π-0.783887\pi
−0.778239 + 0.627968i 0.783887π0.783887\pi
194194 −2.71607 −0.195003
195195 0 0
196196 0.631122 + 6.97149i 0.0450802 + 0.497964i
197197 21.6914i 1.54545i 0.634743 + 0.772723i 0.281106π0.281106\pi
−0.634743 + 0.772723i 0.718894π0.718894\pi
198198 0 0
199199 3.94621i 0.279740i −0.990170 0.139870i 0.955332π-0.955332\pi
0.990170 0.139870i 0.0446684π-0.0446684\pi
200200 0.935886i 0.0661771i
201201 0 0
202202 3.41352i 0.240175i
203203 −2.59084 2.36689i −0.181841 0.166123i
204204 0 0
205205 9.20211 0.642703
206206 −13.3681 −0.931400
207207 0 0
208208 0 0
209209 −0.657927 −0.0455098
210210 0 0
211211 2.30277 0.158529 0.0792647 0.996854i 0.474743π-0.474743\pi
0.0792647 + 0.996854i 0.474743π0.474743\pi
212212 7.44475i 0.511308i
213213 0 0
214214 −14.4002 −0.984380
215215 −3.16305 −0.215718
216216 0 0
217217 20.8895 + 19.0838i 1.41807 + 1.29549i
218218 3.41140i 0.231049i
219219 0 0
220220 2.01596i 0.135916i
221221 0 0
222222 0 0
223223 18.2571i 1.22259i −0.791404 0.611294i 0.790649π-0.790649\pi
0.791404 0.611294i 0.209351π-0.209351\pi
224224 −1.95335 1.78450i −0.130513 0.119232i
225225 0 0
226226 −4.95947 −0.329899
227227 −20.0739 −1.33235 −0.666177 0.745794i 0.732070π-0.732070\pi
−0.666177 + 0.745794i 0.732070π0.732070\pi
228228 0 0
229229 14.6840i 0.970344i 0.874419 + 0.485172i 0.161243π0.161243\pi
−0.874419 + 0.485172i 0.838757π0.838757\pi
230230 −15.8772 −1.04691
231231 0 0
232232 1.32636 0.0870797
233233 2.48528i 0.162816i 0.996681 + 0.0814081i 0.0259417π0.0259417\pi
−0.996681 + 0.0814081i 0.974058π0.974058\pi
234234 0 0
235235 1.07388 0.0700525
236236 −4.03193 −0.262456
237237 0 0
238238 −11.5690 10.5690i −0.749907 0.685085i
239239 22.3610i 1.44642i 0.690631 + 0.723208i 0.257333π0.257333\pi
−0.690631 + 0.723208i 0.742667π0.742667\pi
240240 0 0
241241 3.45706i 0.222689i −0.993782 0.111344i 0.964484π-0.964484\pi
0.993782 0.111344i 0.0355156π-0.0355156\pi
242242 1.00000i 0.0642824i
243243 0 0
244244 0.250475i 0.0160350i
245245 −1.27232 14.0543i −0.0812855 0.897895i
246246 0 0
247247 0 0
248248 −10.6942 −0.679083
249249 0 0
250250 11.9665i 0.756830i
251251 3.78145 0.238683 0.119342 0.992853i 0.461922π-0.461922\pi
0.119342 + 0.992853i 0.461922π0.461922\pi
252252 0 0
253253 7.87575 0.495144
254254 9.50488i 0.596390i
255255 0 0
256256 1.00000 0.0625000
257257 −5.22255 −0.325774 −0.162887 0.986645i 0.552081π-0.552081\pi
−0.162887 + 0.986645i 0.552081π0.552081\pi
258258 0 0
259259 10.4853 11.4774i 0.651524 0.713170i
260260 0 0
261261 0 0
262262 19.0838i 1.17900i
263263 13.7306i 0.846664i 0.905975 + 0.423332i 0.139140π0.139140\pi
−0.905975 + 0.423332i 0.860860π0.860860\pi
264264 0 0
265265 15.0084i 0.921956i
266266 1.17407 1.28516i 0.0719869 0.0787982i
267267 0 0
268268 7.81164 0.477172
269269 29.6093 1.80531 0.902655 0.430366i 0.141615π-0.141615\pi
0.902655 + 0.430366i 0.141615π0.141615\pi
270270 0 0
271271 15.5015i 0.941651i 0.882226 + 0.470825i 0.156044π0.156044\pi
−0.882226 + 0.470825i 0.843956π0.843956\pi
272272 5.92266 0.359114
273273 0 0
274274 −8.05428 −0.486577
275275 0.935886i 0.0564360i
276276 0 0
277277 −19.0347 −1.14368 −0.571841 0.820364i 0.693771π-0.693771\pi
−0.571841 + 0.820364i 0.693771π0.693771\pi
278278 19.3725 1.16188
279279 0 0
280280 3.93788 + 3.59749i 0.235333 + 0.214991i
281281 10.9706i 0.654449i 0.944947 + 0.327224i 0.106113π0.106113\pi
−0.944947 + 0.327224i 0.893887π0.893887\pi
282282 0 0
283283 19.2091i 1.14186i 0.820999 + 0.570930i 0.193417π0.193417\pi
−0.820999 + 0.570930i 0.806583π0.806583\pi
284284 0.609527i 0.0361688i
285285 0 0
286286 0 0
287287 8.14556 8.91628i 0.480817 0.526311i
288288 0 0
289289 18.0779 1.06340
290290 −2.67389 −0.157016
291291 0 0
292292 0.532690i 0.0311733i
293293 9.91105 0.579010 0.289505 0.957177i 0.406509π-0.406509\pi
0.289505 + 0.957177i 0.406509π0.406509\pi
294294 0 0
295295 8.12823 0.473244
296296 5.87575i 0.341521i
297297 0 0
298298 3.26224 0.188977
299299 0 0
300300 0 0
301301 −2.79988 + 3.06480i −0.161382 + 0.176652i
302302 14.1785i 0.815883i
303303 0 0
304304 0.657927i 0.0377347i
305305 0.504949i 0.0289133i
306306 0 0
307307 1.64427i 0.0938433i 0.998899 + 0.0469216i 0.0149411π0.0149411\pi
−0.998899 + 0.0469216i 0.985059π0.985059\pi
308308 −1.95335 1.78450i −0.111302 0.101681i
309309 0 0
310310 21.5592 1.22448
311311 2.14120 0.121416 0.0607082 0.998156i 0.480664π-0.480664\pi
0.0607082 + 0.998156i 0.480664π0.480664\pi
312312 0 0
313313 12.7932i 0.723116i 0.932350 + 0.361558i 0.117755π0.117755\pi
−0.932350 + 0.361558i 0.882245π0.882245\pi
314314 11.7596 0.663632
315315 0 0
316316 12.7711 0.718431
317317 6.51604i 0.365977i 0.983115 + 0.182989i 0.0585771π0.0585771\pi
−0.983115 + 0.182989i 0.941423π0.941423\pi
318318 0 0
319319 1.32636 0.0742618
320320 −2.01596 −0.112696
321321 0 0
322322 −14.0543 + 15.3841i −0.783214 + 0.857321i
323323 3.89668i 0.216817i
324324 0 0
325325 0 0
326326 12.5285i 0.693888i
327327 0 0
328328 4.56462i 0.252039i
329329 0.950585 1.04053i 0.0524074 0.0573662i
330330 0 0
331331 −30.2159 −1.66081 −0.830407 0.557157i 0.811892π-0.811892\pi
−0.830407 + 0.557157i 0.811892π0.811892\pi
332332 −13.3681 −0.733670
333333 0 0
334334 23.0722i 1.26246i
335335 −15.7480 −0.860405
336336 0 0
337337 24.8895 1.35582 0.677909 0.735146i 0.262886π-0.262886\pi
0.677909 + 0.735146i 0.262886π0.262886\pi
338338 13.0000i 0.707107i
339339 0 0
340340 −11.9399 −0.647530
341341 −10.6942 −0.579124
342342 0 0
343343 −14.7440 11.2078i −0.796100 0.605166i
344344 1.56900i 0.0845948i
345345 0 0
346346 17.7244i 0.952872i
347347 9.09481i 0.488235i −0.969746 0.244117i 0.921502π-0.921502\pi
0.969746 0.244117i 0.0784982π-0.0784982\pi
348348 0 0
349349 31.8335i 1.70401i 0.523534 + 0.852005i 0.324613π0.324613\pi
−0.523534 + 0.852005i 0.675387π0.675387\pi
350350 1.82811 + 1.67009i 0.0977165 + 0.0892699i
351351 0 0
352352 1.00000 0.0533002
353353 −10.9052 −0.580424 −0.290212 0.956962i 0.593726π-0.593726\pi
−0.290212 + 0.956962i 0.593726π0.593726\pi
354354 0 0
355355 1.22879i 0.0652171i
356356 −5.22255 −0.276794
357357 0 0
358358 −3.81164 −0.201451
359359 23.6874i 1.25017i 0.780556 + 0.625086i 0.214936π0.214936\pi
−0.780556 + 0.625086i 0.785064π0.785064\pi
360360 0 0
361361 18.5671 0.977217
362362 19.1260 1.00524
363363 0 0
364364 0 0
365365 1.07388i 0.0562097i
366366 0 0
367367 13.1176i 0.684735i −0.939566 0.342367i 0.888771π-0.888771\pi
0.939566 0.342367i 0.111229π-0.111229\pi
368368 7.87575i 0.410552i
369369 0 0
370370 11.8453i 0.615809i
371371 −14.5422 13.2852i −0.754992 0.689731i
372372 0 0
373373 3.38649 0.175346 0.0876729 0.996149i 0.472057π-0.472057\pi
0.0876729 + 0.996149i 0.472057π0.472057\pi
374374 5.92266 0.306253
375375 0 0
376376 0.532690i 0.0274714i
377377 0 0
378378 0 0
379379 8.52847 0.438078 0.219039 0.975716i 0.429708π-0.429708\pi
0.219039 + 0.975716i 0.429708π0.429708\pi
380380 1.32636i 0.0680408i
381381 0 0
382382 21.6665 1.10855
383383 −10.1180 −0.517005 −0.258503 0.966011i 0.583229π-0.583229\pi
−0.258503 + 0.966011i 0.583229π0.583229\pi
384384 0 0
385385 3.93788 + 3.59749i 0.200693 + 0.183345i
386386 21.6233i 1.10060i
387387 0 0
388388 2.71607i 0.137888i
389389 16.7920i 0.851390i −0.904867 0.425695i 0.860030π-0.860030\pi
0.904867 0.425695i 0.139970π-0.139970\pi
390390 0 0
391391 46.6454i 2.35896i
392392 6.97149 0.631122i 0.352113 0.0318765i
393393 0 0
394394 21.6914 1.09280
395395 −25.7461 −1.29543
396396 0 0
397397 13.4856i 0.676821i 0.940999 + 0.338411i 0.109889π0.109889\pi
−0.940999 + 0.338411i 0.890111π0.890111\pi
398398 −3.94621 −0.197806
399399 0 0
400400 −0.935886 −0.0467943
401401 13.5298i 0.675646i 0.941210 + 0.337823i 0.109690π0.109690\pi
−0.941210 + 0.337823i 0.890310π0.890310\pi
402402 0 0
403403 0 0
404404 −3.41352 −0.169829
405405 0 0
406406 −2.36689 + 2.59084i −0.117467 + 0.128581i
407407 5.87575i 0.291250i
408408 0 0
409409 27.0606i 1.33806i −0.743235 0.669031i 0.766709π-0.766709\pi
0.743235 0.669031i 0.233291π-0.233291\pi
410410 9.20211i 0.454460i
411411 0 0
412412 13.3681i 0.658599i
413413 7.19498 7.87575i 0.354042 0.387541i
414414 0 0
415415 26.9496 1.32291
416416 0 0
417417 0 0
418418 0.657927i 0.0321803i
419419 −10.7799 −0.526634 −0.263317 0.964709i 0.584817π-0.584817\pi
−0.263317 + 0.964709i 0.584817π0.584817\pi
420420 0 0
421421 23.0948 1.12557 0.562786 0.826603i 0.309729π-0.309729\pi
0.562786 + 0.826603i 0.309729π0.309729\pi
422422 2.30277i 0.112097i
423423 0 0
424424 7.44475 0.361549
425425 −5.54293 −0.268872
426426 0 0
427427 0.489264 + 0.446973i 0.0236772 + 0.0216305i
428428 14.4002i 0.696062i
429429 0 0
430430 3.16305i 0.152536i
431431 13.8508i 0.667172i 0.942720 + 0.333586i 0.108259π0.108259\pi
−0.942720 + 0.333586i 0.891741π0.891741\pi
432432 0 0
433433 36.3968i 1.74912i 0.484919 + 0.874559i 0.338849π0.338849\pi
−0.484919 + 0.874559i 0.661151π0.661151\pi
434434 19.0838 20.8895i 0.916053 1.00273i
435435 0 0
436436 3.41140 0.163376
437437 5.18167 0.247873
438438 0 0
439439 24.9603i 1.19129i −0.803248 0.595645i 0.796897π-0.796897\pi
0.803248 0.595645i 0.203103π-0.203103\pi
440440 −2.01596 −0.0961074
441441 0 0
442442 0 0
443443 7.20610i 0.342372i −0.985239 0.171186i 0.945240π-0.945240\pi
0.985239 0.171186i 0.0547599π-0.0547599\pi
444444 0 0
445445 10.5285 0.499097
446446 −18.2571 −0.864500
447447 0 0
448448 −1.78450 + 1.95335i −0.0843097 + 0.0922869i
449449 31.8490i 1.50305i −0.659707 0.751523i 0.729320π-0.729320\pi
0.659707 0.751523i 0.270680π-0.270680\pi
450450 0 0
451451 4.56462i 0.214940i
452452 4.95947i 0.233274i
453453 0 0
454454 20.0739i 0.942116i
455455 0 0
456456 0 0
457457 −10.4853 −0.490481 −0.245240 0.969462i 0.578867π-0.578867\pi
−0.245240 + 0.969462i 0.578867π0.578867\pi
458458 14.6840 0.686137
459459 0 0
460460 15.8772i 0.740280i
461461 −24.3881 −1.13587 −0.567933 0.823075i 0.692257π-0.692257\pi
−0.567933 + 0.823075i 0.692257π0.692257\pi
462462 0 0
463463 −22.6410 −1.05222 −0.526109 0.850417i 0.676349π-0.676349\pi
−0.526109 + 0.850417i 0.676349π0.676349\pi
464464 1.32636i 0.0615747i
465465 0 0
466466 2.48528 0.115128
467467 27.6355 1.27882 0.639409 0.768867i 0.279179π-0.279179\pi
0.639409 + 0.768867i 0.279179π0.279179\pi
468468 0 0
469469 −13.9399 + 15.2588i −0.643683 + 0.704588i
470470 1.07388i 0.0495346i
471471 0 0
472472 4.03193i 0.185585i
473473 1.56900i 0.0721427i
474474 0 0
475475 0.615745i 0.0282523i
476476 −10.5690 + 11.5690i −0.484428 + 0.530264i
477477 0 0
478478 22.3610 1.02277
479479 −34.4166 −1.57253 −0.786267 0.617887i 0.787989π-0.787989\pi
−0.786267 + 0.617887i 0.787989π0.787989\pi
480480 0 0
481481 0 0
482482 −3.45706 −0.157465
483483 0 0
484484 1.00000 0.0454545
485485 5.47551i 0.248630i
486486 0 0
487487 −15.2662 −0.691779 −0.345889 0.938275i 0.612423π-0.612423\pi
−0.345889 + 0.938275i 0.612423π0.612423\pi
488488 −0.250475 −0.0113385
489489 0 0
490490 −14.0543 + 1.27232i −0.634908 + 0.0574776i
491491 23.6273i 1.06628i 0.846026 + 0.533142i 0.178989π0.178989\pi
−0.846026 + 0.533142i 0.821011π0.821011\pi
492492 0 0
493493 7.85557i 0.353797i
494494 0 0
495495 0 0
496496 10.6942i 0.480185i
497497 1.19062 + 1.08770i 0.0534065 + 0.0487901i
498498 0 0
499499 −36.0484 −1.61375 −0.806875 0.590723i 0.798843π-0.798843\pi
−0.806875 + 0.590723i 0.798843π0.798843\pi
500500 11.9665 0.535160
501501 0 0
502502 3.78145i 0.168775i
503503 31.1361 1.38829 0.694145 0.719836i 0.255783π-0.255783\pi
0.694145 + 0.719836i 0.255783π0.255783\pi
504504 0 0
505505 6.88154 0.306225
506506 7.87575i 0.350120i
507507 0 0
508508 −9.50488 −0.421711
509509 21.5454 0.954984 0.477492 0.878636i 0.341546π-0.341546\pi
0.477492 + 0.878636i 0.341546π0.341546\pi
510510 0 0
511511 1.04053 + 0.950585i 0.0460302 + 0.0420514i
512512 1.00000i 0.0441942i
513513 0 0
514514 5.22255i 0.230357i
515515 26.9496i 1.18754i
516516 0 0
517517 0.532690i 0.0234277i
518518 −11.4774 10.4853i −0.504287 0.460697i
519519 0 0
520520 0 0
521521 −24.0663 −1.05437 −0.527183 0.849752i 0.676752π-0.676752\pi
−0.527183 + 0.849752i 0.676752π0.676752\pi
522522 0 0
523523 7.11327i 0.311042i −0.987833 0.155521i 0.950294π-0.950294\pi
0.987833 0.155521i 0.0497056π-0.0497056\pi
524524 19.0838 0.833681
525525 0 0
526526 13.7306 0.598682
527527 63.3382i 2.75905i
528528 0 0
529529 −39.0275 −1.69685
530530 −15.0084 −0.651922
531531 0 0
532532 −1.28516 1.17407i −0.0557188 0.0509024i
533533 0 0
534534 0 0
535535 29.0304i 1.25509i
536536 7.81164i 0.337411i
537537 0 0
538538 29.6093i 1.27655i
539539 6.97149 0.631122i 0.300283 0.0271844i
540540 0 0
541541 4.24849 0.182657 0.0913285 0.995821i 0.470889π-0.470889\pi
0.0913285 + 0.995821i 0.470889π0.470889\pi
542542 15.5015 0.665848
543543 0 0
544544 5.92266i 0.253932i
545545 −6.87726 −0.294589
546546 0 0
547547 9.69723 0.414624 0.207312 0.978275i 0.433529π-0.433529\pi
0.207312 + 0.978275i 0.433529π0.433529\pi
548548 8.05428i 0.344062i
549549 0 0
550550 −0.935886 −0.0399063
551551 0.872648 0.0371760
552552 0 0
553553 −22.7900 + 24.9464i −0.969131 + 1.06083i
554554 19.0347i 0.808706i
555555 0 0
556556 19.3725i 0.821576i
557557 21.6914i 0.919093i 0.888154 + 0.459547i 0.151988π0.151988\pi
−0.888154 + 0.459547i 0.848012π0.848012\pi
558558 0 0
559559 0 0
560560 3.59749 3.93788i 0.152022 0.166406i
561561 0 0
562562 10.9706 0.462765
563563 −1.68243 −0.0709062 −0.0354531 0.999371i 0.511287π-0.511287\pi
−0.0354531 + 0.999371i 0.511287π0.511287\pi
564564 0 0
565565 9.99812i 0.420624i
566566 19.2091 0.807417
567567 0 0
568568 −0.609527 −0.0255752
569569 14.4853i 0.607255i 0.952791 + 0.303627i 0.0981978π0.0981978\pi
−0.952791 + 0.303627i 0.901802π0.901802\pi
570570 0 0
571571 −26.7542 −1.11963 −0.559814 0.828619i 0.689127π-0.689127\pi
−0.559814 + 0.828619i 0.689127π0.689127\pi
572572 0 0
573573 0 0
574574 −8.91628 8.14556i −0.372158 0.339989i
575575 7.37081i 0.307384i
576576 0 0
577577 42.3630i 1.76359i 0.471629 + 0.881797i 0.343666π0.343666\pi
−0.471629 + 0.881797i 0.656334π0.656334\pi
578578 18.0779i 0.751940i
579579 0 0
580580 2.67389i 0.111027i
581581 23.8554 26.1125i 0.989688 1.08333i
582582 0 0
583583 7.44475 0.308330
584584 −0.532690 −0.0220429
585585 0 0
586586 9.91105i 0.409422i
587587 −2.05172 −0.0846835 −0.0423418 0.999103i 0.513482π-0.513482\pi
−0.0423418 + 0.999103i 0.513482π0.513482\pi
588588 0 0
589589 −7.03602 −0.289914
590590 8.12823i 0.334634i
591591 0 0
592592 5.87575 0.241492
593593 −40.2640 −1.65344 −0.826721 0.562611i 0.809797π-0.809797\pi
−0.826721 + 0.562611i 0.809797π0.809797\pi
594594 0 0
595595 21.3067 23.3227i 0.873489 0.956137i
596596 3.26224i 0.133627i
597597 0 0
598598 0 0
599599 35.6273i 1.45569i −0.685741 0.727845i 0.740522π-0.740522\pi
0.685741 0.727845i 0.259478π-0.259478\pi
600600 0 0
601601 39.6574i 1.61766i −0.588044 0.808829i 0.700102π-0.700102\pi
0.588044 0.808829i 0.299898π-0.299898\pi
602602 3.06480 + 2.79988i 0.124912 + 0.114115i
603603 0 0
604604 14.1785 0.576916
605605 −2.01596 −0.0819606
606606 0 0
607607 23.6444i 0.959698i −0.877351 0.479849i 0.840691π-0.840691\pi
0.877351 0.479849i 0.159309π-0.159309\pi
608608 0.657927 0.0266825
609609 0 0
610610 0.504949 0.0204448
611611 0 0
612612 0 0
613613 −36.0654 −1.45667 −0.728333 0.685223i 0.759705π-0.759705\pi
−0.728333 + 0.685223i 0.759705π0.759705\pi
614614 1.64427 0.0663572
615615 0 0
616616 −1.78450 + 1.95335i −0.0718995 + 0.0787026i
617617 2.45192i 0.0987108i 0.998781 + 0.0493554i 0.0157167π0.0157167\pi
−0.998781 + 0.0493554i 0.984283π0.984283\pi
618618 0 0
619619 12.9107i 0.518925i −0.965753 0.259462i 0.916455π-0.916455\pi
0.965753 0.259462i 0.0835453π-0.0835453\pi
620620 21.5592i 0.865837i
621621 0 0
622622 2.14120i 0.0858544i
623623 9.31963 10.2014i 0.373383 0.408712i
624624 0 0
625625 −19.4447 −0.777788
626626 12.7932 0.511321
627627 0 0
628628 11.7596i 0.469259i
629629 34.8001 1.38757
630630 0 0
631631 −6.53245 −0.260053 −0.130026 0.991511i 0.541506π-0.541506\pi
−0.130026 + 0.991511i 0.541506π0.541506\pi
632632 12.7711i 0.508008i
633633 0 0
634634 6.51604 0.258785
635635 19.1615 0.760401
636636 0 0
637637 0 0
638638 1.32636i 0.0525110i
639639 0 0
640640 2.01596i 0.0796880i
641641 6.03336i 0.238303i 0.992876 + 0.119152i 0.0380175π0.0380175\pi
−0.992876 + 0.119152i 0.961983π0.961983\pi
642642 0 0
643643 9.21360i 0.363349i −0.983359 0.181675i 0.941848π-0.941848\pi
0.983359 0.181675i 0.0581517π-0.0581517\pi
644644 15.3841 + 14.0543i 0.606217 + 0.553816i
645645 0 0
646646 3.89668 0.153313
647647 1.72732 0.0679080 0.0339540 0.999423i 0.489190π-0.489190\pi
0.0339540 + 0.999423i 0.489190π0.489190\pi
648648 0 0
649649 4.03193i 0.158267i
650650 0 0
651651 0 0
652652 −12.5285 −0.490653
653653 41.9575i 1.64193i −0.570982 0.820963i 0.693437π-0.693437\pi
0.570982 0.820963i 0.306563π-0.306563\pi
654654 0 0
655655 −38.4723 −1.50324
656656 4.56462 0.178218
657657 0 0
658658 −1.04053 0.950585i −0.0405640 0.0370577i
659659 10.3963i 0.404981i 0.979284 + 0.202490i 0.0649035π0.0649035\pi
−0.979284 + 0.202490i 0.935097π0.935097\pi
660660 0 0
661661 34.0922i 1.32603i −0.748605 0.663016i 0.769276π-0.769276\pi
0.748605 0.663016i 0.230724π-0.230724\pi
662662 30.2159i 1.17437i
663663 0 0
664664 13.3681i 0.518783i
665665 2.59084 + 2.36689i 0.100468 + 0.0917839i
666666 0 0
667667 −10.4461 −0.404474
668668 23.0722 0.892691
669669 0 0
670670 15.7480i 0.608398i
671671 −0.250475 −0.00966948
672672 0 0
673673 9.66513 0.372563 0.186282 0.982496i 0.440356π-0.440356\pi
0.186282 + 0.982496i 0.440356π0.440356\pi
674674 24.8895i 0.958708i
675675 0 0
676676 −13.0000 −0.500000
677677 −45.8609 −1.76258 −0.881288 0.472579i 0.843323π-0.843323\pi
−0.881288 + 0.472579i 0.843323π0.843323\pi
678678 0 0
679679 −5.30543 4.84683i −0.203604 0.186004i
680680 11.9399i 0.457873i
681681 0 0
682682 10.6942i 0.409503i
683683 3.93190i 0.150450i 0.997167 + 0.0752250i 0.0239675π0.0239675\pi
−0.997167 + 0.0752250i 0.976032π0.976032\pi
684684 0 0
685685 16.2371i 0.620389i
686686 −11.2078 + 14.7440i −0.427917 + 0.562927i
687687 0 0
688688 −1.56900 −0.0598175
689689 0 0
690690 0 0
691691 17.6940i 0.673113i 0.941663 + 0.336557i 0.109262π0.109262\pi
−0.941663 + 0.336557i 0.890738π0.890738\pi
692692 −17.7244 −0.673782
693693 0 0
694694 −9.09481 −0.345234
695695 39.0542i 1.48141i
696696 0 0
697697 27.0347 1.02401
698698 31.8335 1.20492
699699 0 0
700700 1.67009 1.82811i 0.0631234 0.0690960i
701701 27.9189i 1.05448i −0.849715 0.527242i 0.823226π-0.823226\pi
0.849715 0.527242i 0.176774π-0.176774\pi
702702 0 0
703703 3.86582i 0.145802i
704704 1.00000i 0.0376889i
705705 0 0
706706 10.9052i 0.410422i
707707 6.09143 6.66779i 0.229092 0.250768i
708708 0 0
709709 −25.4951 −0.957487 −0.478743 0.877955i 0.658908π-0.658908\pi
−0.478743 + 0.877955i 0.658908π0.658908\pi
710710 1.22879 0.0461155
711711 0 0
712712 5.22255i 0.195723i
713713 84.2250 3.15425
714714 0 0
715715 0 0
716716 3.81164i 0.142448i
717717 0 0
718718 23.6874 0.884006
719719 43.0169 1.60426 0.802130 0.597150i 0.203700π-0.203700\pi
0.802130 + 0.597150i 0.203700π0.203700\pi
720720 0 0
721721 −26.1125 23.8554i −0.972482 0.888421i
722722 18.5671i 0.690997i
723723 0 0
724724 19.1260i 0.710813i
725725 1.24132i 0.0461015i
726726 0 0
727727 30.2686i 1.12260i −0.827613 0.561299i 0.810302π-0.810302\pi
0.827613 0.561299i 0.189698π-0.189698\pi
728728 0 0
729729 0 0
730730 1.07388 0.0397462
731731 −9.29264 −0.343701
732732 0 0
733733 7.56291i 0.279342i −0.990198 0.139671i 0.955395π-0.955395\pi
0.990198 0.139671i 0.0446046π-0.0446046\pi
734734 −13.1176 −0.484181
735735 0 0
736736 −7.87575 −0.290304
737737 7.81164i 0.287745i
738738 0 0
739739 −17.1923 −0.632428 −0.316214 0.948688i 0.602412π-0.602412\pi
−0.316214 + 0.948688i 0.602412π0.602412\pi
740740 −11.8453 −0.435442
741741 0 0
742742 −13.2852 + 14.5422i −0.487714 + 0.533860i
743743 23.9843i 0.879899i 0.898022 + 0.439950i 0.145004π0.145004\pi
−0.898022 + 0.439950i 0.854996π0.854996\pi
744744 0 0
745745 6.57657i 0.240947i
746746 3.38649i 0.123988i
747747 0 0
748748 5.92266i 0.216554i
749749 −28.1287 25.6972i −1.02780 0.938956i
750750 0 0
751751 −32.4736 −1.18498 −0.592489 0.805579i 0.701855π-0.701855\pi
−0.592489 + 0.805579i 0.701855π0.701855\pi
752752 0.532690 0.0194252
753753 0 0
754754 0 0
755755 −28.5834 −1.04026
756756 0 0
757757 40.0315 1.45497 0.727485 0.686124i 0.240689π-0.240689\pi
0.727485 + 0.686124i 0.240689π0.240689\pi
758758 8.52847i 0.309768i
759759 0 0
760760 −1.32636 −0.0481121
761761 20.6923 0.750097 0.375048 0.927005i 0.377626π-0.377626\pi
0.375048 + 0.927005i 0.377626π0.377626\pi
762762 0 0
763763 −6.08764 + 6.66364i −0.220387 + 0.241240i
764764 21.6665i 0.783865i
765765 0 0
766766 10.1180i 0.365578i
767767 0 0
768768 0 0
769769 33.6030i 1.21176i −0.795557 0.605878i 0.792822π-0.792822\pi
0.795557 0.605878i 0.207178π-0.207178\pi
770770 3.59749 3.93788i 0.129644 0.141911i
771771 0 0
772772 21.6233 0.778239
773773 13.9825 0.502916 0.251458 0.967868i 0.419090π-0.419090\pi
0.251458 + 0.967868i 0.419090π0.419090\pi
774774 0 0
775775 10.0086i 0.359518i
776776 2.71607 0.0975014
777777 0 0
778778 −16.7920 −0.602024
779779 3.00319i 0.107600i
780780 0 0
781781 −0.609527 −0.0218106
782782 −46.6454 −1.66804
783783 0 0
784784 −0.631122 6.97149i −0.0225401 0.248982i
785785 23.7069i 0.846137i
786786 0 0
787787 20.4800i 0.730034i 0.931001 + 0.365017i 0.118937π0.118937\pi
−0.931001 + 0.365017i 0.881063π0.881063\pi
788788 21.6914i 0.772723i
789789 0 0
790790 25.7461i 0.916006i
791791 −9.68757 8.85018i −0.344450 0.314676i
792792 0 0
793793 0 0
794794 13.4856 0.478585
795795 0 0
796796 3.94621i 0.139870i
797797 −38.1741 −1.35220 −0.676098 0.736812i 0.736330π-0.736330\pi
−0.676098 + 0.736812i 0.736330π0.736330\pi
798798 0 0
799799 3.15494 0.111614
800800 0.935886i 0.0330886i
801801 0 0
802802 13.5298 0.477754
803803 −0.532690 −0.0187982
804804 0 0
805805 −31.0138 28.3329i −1.09309 0.998605i
806806 0 0
807807 0 0
808808 3.41352i 0.120087i
809809 22.8503i 0.803374i −0.915777 0.401687i 0.868424π-0.868424\pi
0.915777 0.401687i 0.131576π-0.131576\pi
810810 0 0
811811 27.1859i 0.954624i 0.878734 + 0.477312i 0.158389π0.158389\pi
−0.878734 + 0.477312i 0.841611π0.841611\pi
812812 2.59084 + 2.36689i 0.0909206 + 0.0830614i
813813 0 0
814814 5.87575 0.205945
815815 25.2570 0.884713
816816 0 0
817817 1.03229i 0.0361152i
818818 −27.0606 −0.946152
819819 0 0
820820 −9.20211 −0.321352
821821 22.6135i 0.789217i 0.918849 + 0.394608i 0.129120π0.129120\pi
−0.918849 + 0.394608i 0.870880π0.870880\pi
822822 0 0
823823 36.9706 1.28871 0.644356 0.764725i 0.277125π-0.277125\pi
0.644356 + 0.764725i 0.277125π0.277125\pi
824824 13.3681 0.465700
825825 0 0
826826 −7.87575 7.19498i −0.274033 0.250345i
827827 36.8463i 1.28127i −0.767845 0.640636i 0.778671π-0.778671\pi
0.767845 0.640636i 0.221329π-0.221329\pi
828828 0 0
829829 34.8858i 1.21163i −0.795604 0.605817i 0.792846π-0.792846\pi
0.795604 0.605817i 0.207154π-0.207154\pi
830830 26.9496i 0.935436i
831831 0 0
832832 0 0
833833 −3.73792 41.2897i −0.129511 1.43061i
834834 0 0
835835 −46.5128 −1.60964
836836 0.657927 0.0227549
837837 0 0
838838 10.7799i 0.372387i
839839 −41.3715 −1.42830 −0.714152 0.699991i 0.753187π-0.753187\pi
−0.714152 + 0.699991i 0.753187π0.753187\pi
840840 0 0
841841 27.2408 0.939337
842842 23.0948i 0.795900i
843843 0 0
844844 −2.30277 −0.0792647
845845 26.2075 0.901567
846846 0 0
847847 −1.78450 + 1.95335i −0.0613161 + 0.0671178i
848848 7.44475i 0.255654i
849849 0 0
850850 5.54293i 0.190121i
851851 46.2760i 1.58632i
852852 0 0
853853 6.66093i 0.228066i 0.993477 + 0.114033i 0.0363770π0.0363770\pi
−0.993477 + 0.114033i 0.963623π0.963623\pi
854854 0.446973 0.489264i 0.0152951 0.0167423i
855855 0 0
856856 14.4002 0.492190
857857 19.6691 0.671885 0.335943 0.941882i 0.390945π-0.390945\pi
0.335943 + 0.941882i 0.390945π0.390945\pi
858858 0 0
859859 33.8062i 1.15345i −0.816937 0.576726i 0.804330π-0.804330\pi
0.816937 0.576726i 0.195670π-0.195670\pi
860860 3.16305 0.107859
861861 0 0
862862 13.8508 0.471762
863863 0.846317i 0.0288090i −0.999896 0.0144045i 0.995415π-0.995415\pi
0.999896 0.0144045i 0.00458525π-0.00458525\pi
864864 0 0
865865 35.7318 1.21492
866866 36.3968 1.23681
867867 0 0
868868 −20.8895 19.0838i −0.709036 0.647747i
869869 12.7711i 0.433230i
870870 0 0
871871 0 0
872872 3.41140i 0.115524i
873873 0 0
874874 5.18167i 0.175273i
875875 −21.3543 + 23.3748i −0.721906 + 0.790212i
876876 0 0
877877 49.8039 1.68176 0.840879 0.541222i 0.182038π-0.182038\pi
0.840879 + 0.541222i 0.182038π0.182038\pi
878878 −24.9603 −0.842369
879879 0 0
880880 2.01596i 0.0679582i
881881 39.1207 1.31801 0.659004 0.752139i 0.270978π-0.270978\pi
0.659004 + 0.752139i 0.270978π0.270978\pi
882882 0 0
883883 24.4501 0.822810 0.411405 0.911453i 0.365038π-0.365038\pi
0.411405 + 0.911453i 0.365038π0.365038\pi
884884 0 0
885885 0 0
886886 −7.20610 −0.242094
887887 −28.3025 −0.950307 −0.475153 0.879903i 0.657607π-0.657607\pi
−0.475153 + 0.879903i 0.657607π0.657607\pi
888888 0 0
889889 16.9615 18.5663i 0.568869 0.622695i
890890 10.5285i 0.352915i
891891 0 0
892892 18.2571i 0.611294i
893893 0.350471i 0.0117281i
894894 0 0
895895 7.68413i 0.256852i
896896 1.95335 + 1.78450i 0.0652567 + 0.0596159i
897897 0 0
898898 −31.8490 −1.06281
899899 14.1844 0.473075
900900 0 0
901901 44.0927i 1.46894i
902902 4.56462 0.151985
903903 0 0
904904 4.95947 0.164950
905905 38.5574i 1.28169i
906906 0 0
907907 42.3244 1.40536 0.702680 0.711506i 0.251987π-0.251987\pi
0.702680 + 0.711506i 0.251987π0.251987\pi
908908 20.0739 0.666177
909909 0 0
910910 0 0
911911 15.2622i 0.505661i 0.967511 + 0.252830i 0.0813615π0.0813615\pi
−0.967511 + 0.252830i 0.918639π0.918639\pi
912912 0 0
913913 13.3681i 0.442420i
914914 10.4853i 0.346822i
915915 0 0
916916 14.6840i 0.485172i
917917 −34.0551 + 37.2773i −1.12460 + 1.23101i
918918 0 0
919919 −50.2951 −1.65908 −0.829540 0.558447i 0.811398π-0.811398\pi
−0.829540 + 0.558447i 0.811398π0.811398\pi
920920 15.8772 0.523457
921921 0 0
922922 24.3881i 0.803179i
923923 0 0
924924 0 0
925925 −5.49903 −0.180807
926926 22.6410i 0.744030i
927927 0 0
928928 −1.32636 −0.0435399
929929 −8.43957 −0.276893 −0.138447 0.990370i 0.544211π-0.544211\pi
−0.138447 + 0.990370i 0.544211π0.544211\pi
930930 0 0
931931 4.58674 0.415233i 0.150324 0.0136087i
932932 2.48528i 0.0814081i
933933 0 0
934934 27.6355i 0.904261i
935935 11.9399i 0.390475i
936936 0 0
937937 13.7782i 0.450115i −0.974345 0.225057i 0.927743π-0.927743\pi
0.974345 0.225057i 0.0722570π-0.0722570\pi
938938 15.2588 + 13.9399i 0.498219 + 0.455153i
939939 0 0
940940 −1.07388 −0.0350262
941941 28.6705 0.934631 0.467315 0.884091i 0.345221π-0.345221\pi
0.467315 + 0.884091i 0.345221π0.345221\pi
942942 0 0
943943 35.9498i 1.17069i
944944 4.03193 0.131228
945945 0 0
946946 −1.56900 −0.0510126
947947 19.0609i 0.619397i 0.950835 + 0.309698i 0.100228π0.100228\pi
−0.950835 + 0.309698i 0.899772π0.899772\pi
948948 0 0
949949 0 0
950950 −0.615745 −0.0199774
951951 0 0
952952 11.5690 + 10.5690i 0.374953 + 0.342543i
953953 7.72400i 0.250205i −0.992144 0.125102i 0.960074π-0.960074\pi
0.992144 0.125102i 0.0399260π-0.0399260\pi
954954 0 0
955955 43.6788i 1.41341i
956956 22.3610i 0.723208i
957957 0 0
958958 34.4166i 1.11195i
959959 −15.7328 14.3729i −0.508039 0.464124i
960960 0 0
961961 −83.3663 −2.68923
962962 0 0
963963 0 0
964964 3.45706i 0.111344i
965965 −43.5918 −1.40327
966966 0 0
967967 −41.7666 −1.34312 −0.671561 0.740949i 0.734376π-0.734376\pi
−0.671561 + 0.740949i 0.734376π0.734376\pi
968968 1.00000i 0.0321412i
969969 0 0
970970 −5.47551 −0.175808
971971 52.8054 1.69461 0.847303 0.531110i 0.178225π-0.178225\pi
0.847303 + 0.531110i 0.178225π0.178225\pi
972972 0 0
973973 37.8411 + 34.5702i 1.21313 + 1.10827i
974974 15.2662i 0.489161i
975975 0 0
976976 0.250475i 0.00801751i
977977 33.5481i 1.07330i −0.843806 0.536649i 0.819690π-0.819690\pi
0.843806 0.536649i 0.180310π-0.180310\pi
978978 0 0
979979 5.22255i 0.166913i
980980 1.27232 + 14.0543i 0.0406428 + 0.448948i
981981 0 0
982982 23.6273 0.753976
983983 14.1077 0.449967 0.224984 0.974363i 0.427767π-0.427767\pi
0.224984 + 0.974363i 0.427767π0.427767\pi
984984 0 0
985985 43.7291i 1.39332i
986986 −7.85557 −0.250172
987987 0 0
988988 0 0
989989 12.3571i 0.392931i
990990 0 0
991991 2.39626 0.0761197 0.0380599 0.999275i 0.487882π-0.487882\pi
0.0380599 + 0.999275i 0.487882π0.487882\pi
992992 10.6942 0.339542
993993 0 0
994994 1.08770 1.19062i 0.0344998 0.0377641i
995995 7.95543i 0.252204i
996996 0 0
997997 50.6773i 1.60497i 0.596674 + 0.802483i 0.296488π0.296488\pi
−0.596674 + 0.802483i 0.703512π0.703512\pi
998998 36.0484i 1.14109i
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 1386.2.g.a.881.7 yes 16
3.2 odd 2 inner 1386.2.g.a.881.10 yes 16
7.6 odd 2 inner 1386.2.g.a.881.2 16
21.20 even 2 inner 1386.2.g.a.881.15 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.g.a.881.2 16 7.6 odd 2 inner
1386.2.g.a.881.7 yes 16 1.1 even 1 trivial
1386.2.g.a.881.10 yes 16 3.2 odd 2 inner
1386.2.g.a.881.15 yes 16 21.20 even 2 inner