Properties

Label 1360.2.e.d.1089.8
Level 13601360
Weight 22
Character 1360.1089
Analytic conductor 10.86010.860
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1360,2,Mod(1089,1360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1360, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("1360.1089");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1360=24517 1360 = 2^{4} \cdot 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1360.e (of order 22, degree 11, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 10.859654674910.8596546749
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.619810816.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x82x5+14x48x3+2x2+2x+1 x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 85)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1089.8
Root 0.252709+0.252709i-0.252709 + 0.252709i of defining polynomial
Character χ\chi == 1360.1089
Dual form 1360.2.e.d.1089.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+2.87228iq3+(0.1464262.23127i)q51.42058iq75.24997q90.0740063q11+5.70167iq13+(6.40882+0.420575i)q151.00000iq174.90340q19+4.08029q21+3.88311iq23+(4.957120.653431i)q256.46254iq275.91424q290.388531q310.212567iq33+(3.169690.208009i)q35+9.91424iq3716.3768q396.61055q41+6.94628iq43+(0.768731+11.7141i)q45+5.70167iq47+4.98197q49+2.87228q51+0.0216729iq53+(0.0108364+0.165128i)q5514.0839iq572.00000q593.47337q61+7.45798iq63+(12.7220+0.834872i)q65+6.71251iq6711.1534q693.84023q7113.5356iq73+(1.8768314.2382i)q75+0.105132iq771.06000q79+2.81228q8111.8497iq83+(2.231270.146426i)q8516.9873iq87+1.99452q89+8.09965q911.11597iq93+(0.717985+10.9408i)q95+5.34109iq97+0.388531q99+O(q100)q+2.87228i q^{3} +(0.146426 - 2.23127i) q^{5} -1.42058i q^{7} -5.24997 q^{9} -0.0740063 q^{11} +5.70167i q^{13} +(6.40882 + 0.420575i) q^{15} -1.00000i q^{17} -4.90340 q^{19} +4.08029 q^{21} +3.88311i q^{23} +(-4.95712 - 0.653431i) q^{25} -6.46254i q^{27} -5.91424 q^{29} -0.388531 q^{31} -0.212567i q^{33} +(-3.16969 - 0.208009i) q^{35} +9.91424i q^{37} -16.3768 q^{39} -6.61055 q^{41} +6.94628i q^{43} +(-0.768731 + 11.7141i) q^{45} +5.70167i q^{47} +4.98197 q^{49} +2.87228 q^{51} +0.0216729i q^{53} +(-0.0108364 + 0.165128i) q^{55} -14.0839i q^{57} -2.00000 q^{59} -3.47337 q^{61} +7.45798i q^{63} +(12.7220 + 0.834872i) q^{65} +6.71251i q^{67} -11.1534 q^{69} -3.84023 q^{71} -13.5356i q^{73} +(1.87683 - 14.2382i) q^{75} +0.105132i q^{77} -1.06000 q^{79} +2.81228 q^{81} -11.8497i q^{83} +(-2.23127 - 0.146426i) q^{85} -16.9873i q^{87} +1.99452 q^{89} +8.09965 q^{91} -1.11597i q^{93} +(-0.717985 + 10.9408i) q^{95} +5.34109i q^{97} +0.388531 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q2q58q9+4q11+8q19+24q2112q25+8q29+24q3144q3912q4122q4516q49+8q51+8q5516q59+12q61+20q658q69+24q99+O(q100) 8 q - 2 q^{5} - 8 q^{9} + 4 q^{11} + 8 q^{19} + 24 q^{21} - 12 q^{25} + 8 q^{29} + 24 q^{31} - 44 q^{39} - 12 q^{41} - 22 q^{45} - 16 q^{49} + 8 q^{51} + 8 q^{55} - 16 q^{59} + 12 q^{61} + 20 q^{65} - 8 q^{69}+ \cdots - 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1360Z)×\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times.

nn 241241 341341 511511 817817
χ(n)\chi(n) 11 11 11 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 2.87228i 1.65831i 0.559019 + 0.829155i 0.311178π0.311178\pi
−0.559019 + 0.829155i 0.688822π0.688822\pi
44 0 0
55 0.146426 2.23127i 0.0654836 0.997854i
66 0 0
77 1.42058i 0.536927i −0.963290 0.268464i 0.913484π-0.913484\pi
0.963290 0.268464i 0.0865159π-0.0865159\pi
88 0 0
99 −5.24997 −1.74999
1010 0 0
1111 −0.0740063 −0.0223137 −0.0111569 0.999938i 0.503551π-0.503551\pi
−0.0111569 + 0.999938i 0.503551π0.503551\pi
1212 0 0
1313 5.70167i 1.58136i 0.612230 + 0.790680i 0.290273π0.290273\pi
−0.612230 + 0.790680i 0.709727π0.709727\pi
1414 0 0
1515 6.40882 + 0.420575i 1.65475 + 0.108592i
1616 0 0
1717 1.00000i 0.242536i
1818 0 0
1919 −4.90340 −1.12492 −0.562459 0.826825i 0.690144π-0.690144\pi
−0.562459 + 0.826825i 0.690144π0.690144\pi
2020 0 0
2121 4.08029 0.890391
2222 0 0
2323 3.88311i 0.809685i 0.914386 + 0.404842i 0.132674π0.132674\pi
−0.914386 + 0.404842i 0.867326π0.867326\pi
2424 0 0
2525 −4.95712 0.653431i −0.991424 0.130686i
2626 0 0
2727 6.46254i 1.24372i
2828 0 0
2929 −5.91424 −1.09825 −0.549123 0.835741i 0.685038π-0.685038\pi
−0.549123 + 0.835741i 0.685038π0.685038\pi
3030 0 0
3131 −0.388531 −0.0697822 −0.0348911 0.999391i 0.511108π-0.511108\pi
−0.0348911 + 0.999391i 0.511108π0.511108\pi
3232 0 0
3333 0.212567i 0.0370031i
3434 0 0
3535 −3.16969 0.208009i −0.535775 0.0351599i
3636 0 0
3737 9.91424i 1.62989i 0.579538 + 0.814945i 0.303233π0.303233\pi
−0.579538 + 0.814945i 0.696767π0.696767\pi
3838 0 0
3939 −16.3768 −2.62238
4040 0 0
4141 −6.61055 −1.03239 −0.516197 0.856470i 0.672653π-0.672653\pi
−0.516197 + 0.856470i 0.672653π0.672653\pi
4242 0 0
4343 6.94628i 1.05930i 0.848217 + 0.529649i 0.177676π0.177676\pi
−0.848217 + 0.529649i 0.822324π0.822324\pi
4444 0 0
4545 −0.768731 + 11.7141i −0.114596 + 1.74623i
4646 0 0
4747 5.70167i 0.831674i 0.909439 + 0.415837i 0.136511π0.136511\pi
−0.909439 + 0.415837i 0.863489π0.863489\pi
4848 0 0
4949 4.98197 0.711709
5050 0 0
5151 2.87228 0.402199
5252 0 0
5353 0.0216729i 0.00297700i 0.999999 + 0.00148850i 0.000473804π0.000473804\pi
−0.999999 + 0.00148850i 0.999526π0.999526\pi
5454 0 0
5555 −0.0108364 + 0.165128i −0.00146118 + 0.0222658i
5656 0 0
5757 14.0839i 1.86546i
5858 0 0
5959 −2.00000 −0.260378 −0.130189 0.991489i 0.541558π-0.541558\pi
−0.130189 + 0.991489i 0.541558π0.541558\pi
6060 0 0
6161 −3.47337 −0.444720 −0.222360 0.974965i 0.571376π-0.571376\pi
−0.222360 + 0.974965i 0.571376π0.571376\pi
6262 0 0
6363 7.45798i 0.939617i
6464 0 0
6565 12.7220 + 0.834872i 1.57796 + 0.103553i
6666 0 0
6767 6.71251i 0.820063i 0.912071 + 0.410032i 0.134482π0.134482\pi
−0.912071 + 0.410032i 0.865518π0.865518\pi
6868 0 0
6969 −11.1534 −1.34271
7070 0 0
7171 −3.84023 −0.455752 −0.227876 0.973690i 0.573178π-0.573178\pi
−0.227876 + 0.973690i 0.573178π0.573178\pi
7272 0 0
7373 13.5356i 1.58422i −0.610375 0.792112i 0.708981π-0.708981\pi
0.610375 0.792112i 0.291019π-0.291019\pi
7474 0 0
7575 1.87683 14.2382i 0.216718 1.64409i
7676 0 0
7777 0.105132i 0.0119808i
7878 0 0
7979 −1.06000 −0.119259 −0.0596295 0.998221i 0.518992π-0.518992\pi
−0.0596295 + 0.998221i 0.518992π0.518992\pi
8080 0 0
8181 2.81228 0.312476
8282 0 0
8383 11.8497i 1.30067i −0.759647 0.650336i 0.774628π-0.774628\pi
0.759647 0.650336i 0.225372π-0.225372\pi
8484 0 0
8585 −2.23127 0.146426i −0.242015 0.0158821i
8686 0 0
8787 16.9873i 1.82123i
8888 0 0
8989 1.99452 0.211419 0.105710 0.994397i 0.466289π-0.466289\pi
0.105710 + 0.994397i 0.466289π0.466289\pi
9090 0 0
9191 8.09965 0.849075
9292 0 0
9393 1.11597i 0.115720i
9494 0 0
9595 −0.717985 + 10.9408i −0.0736637 + 1.12250i
9696 0 0
9797 5.34109i 0.542306i 0.962536 + 0.271153i 0.0874049π0.0874049\pi
−0.962536 + 0.271153i 0.912595π0.912595\pi
9898 0 0
9999 0.388531 0.0390488
100100 0 0
101101 11.4305 1.13738 0.568688 0.822553i 0.307451π-0.307451\pi
0.568688 + 0.822553i 0.307451π0.307451\pi
102102 0 0
103103 8.21257i 0.809208i 0.914492 + 0.404604i 0.132591π0.132591\pi
−0.914492 + 0.404604i 0.867409π0.867409\pi
104104 0 0
105105 0.597459 9.10421i 0.0583061 0.888480i
106106 0 0
107107 6.34882i 0.613764i −0.951748 0.306882i 0.900714π-0.900714\pi
0.951748 0.306882i 0.0992857π-0.0992857\pi
108108 0 0
109109 −0.292852 −0.0280501 −0.0140251 0.999902i 0.504464π-0.504464\pi
−0.0140251 + 0.999902i 0.504464π0.504464\pi
110110 0 0
111111 −28.4764 −2.70286
112112 0 0
113113 8.62311i 0.811194i −0.914052 0.405597i 0.867064π-0.867064\pi
0.914052 0.405597i 0.132936π-0.132936\pi
114114 0 0
115115 8.66427 + 0.568588i 0.807947 + 0.0530211i
116116 0 0
117117 29.9336i 2.76736i
118118 0 0
119119 −1.42058 −0.130224
120120 0 0
121121 −10.9945 −0.999502
122122 0 0
123123 18.9873i 1.71203i
124124 0 0
125125 −2.18383 + 10.9650i −0.195328 + 0.980738i
126126 0 0
127127 17.2640i 1.53193i −0.642882 0.765965i 0.722261π-0.722261\pi
0.642882 0.765965i 0.277739π-0.277739\pi
128128 0 0
129129 −19.9516 −1.75664
130130 0 0
131131 14.7188 1.28599 0.642993 0.765872i 0.277692π-0.277692\pi
0.642993 + 0.765872i 0.277692π0.277692\pi
132132 0 0
133133 6.96565i 0.603999i
134134 0 0
135135 −14.4197 0.946283i −1.24105 0.0814430i
136136 0 0
137137 1.36230i 0.116389i −0.998305 0.0581946i 0.981466π-0.981466\pi
0.998305 0.0581946i 0.0185344π-0.0185344\pi
138138 0 0
139139 −13.7454 −1.16587 −0.582933 0.812520i 0.698095π-0.698095\pi
−0.582933 + 0.812520i 0.698095π0.698095\pi
140140 0 0
141141 −16.3768 −1.37917
142142 0 0
143143 0.421960i 0.0352860i
144144 0 0
145145 −0.865997 + 13.1963i −0.0719172 + 1.09589i
146146 0 0
147147 14.3096i 1.18023i
148148 0 0
149149 17.3628 1.42241 0.711207 0.702983i 0.248149π-0.248149\pi
0.711207 + 0.702983i 0.248149π0.248149\pi
150150 0 0
151151 3.59654 0.292682 0.146341 0.989234i 0.453250π-0.453250\pi
0.146341 + 0.989234i 0.453250π0.453250\pi
152152 0 0
153153 5.24997i 0.424435i
154154 0 0
155155 −0.0568910 + 0.866917i −0.00456959 + 0.0696324i
156156 0 0
157157 5.19308i 0.414453i 0.978293 + 0.207226i 0.0664437π0.0664437\pi
−0.978293 + 0.207226i 0.933556π0.933556\pi
158158 0 0
159159 −0.0622505 −0.00493678
160160 0 0
161161 5.51625 0.434742
162162 0 0
163163 6.56687i 0.514357i 0.966364 + 0.257178i 0.0827928π0.0827928\pi
−0.966364 + 0.257178i 0.917207π0.917207\pi
164164 0 0
165165 −0.474293 0.0311252i −0.0369237 0.00242310i
166166 0 0
167167 0.897123i 0.0694214i 0.999397 + 0.0347107i 0.0110510π0.0110510\pi
−0.999397 + 0.0347107i 0.988949π0.988949\pi
168168 0 0
169169 −19.5091 −1.50070
170170 0 0
171171 25.7427 1.96859
172172 0 0
173173 3.83031i 0.291213i 0.989343 + 0.145607i 0.0465134π0.0465134\pi
−0.989343 + 0.145607i 0.953487π0.953487\pi
174174 0 0
175175 −0.928248 + 7.04196i −0.0701689 + 0.532322i
176176 0 0
177177 5.74455i 0.431787i
178178 0 0
179179 9.74455 0.728342 0.364171 0.931332i 0.381352π-0.381352\pi
0.364171 + 0.931332i 0.381352π0.381352\pi
180180 0 0
181181 22.4764 1.67066 0.835330 0.549749i 0.185277π-0.185277\pi
0.835330 + 0.549749i 0.185277π0.185277\pi
182182 0 0
183183 9.97649i 0.737483i
184184 0 0
185185 22.1213 + 1.45170i 1.62639 + 0.106731i
186186 0 0
187187 0.0740063i 0.00541188i
188188 0 0
189189 −9.18052 −0.667785
190190 0 0
191191 5.47655 0.396269 0.198135 0.980175i 0.436512π-0.436512\pi
0.198135 + 0.980175i 0.436512π0.436512\pi
192192 0 0
193193 2.14484i 0.154389i −0.997016 0.0771944i 0.975404π-0.975404\pi
0.997016 0.0771944i 0.0245962π-0.0245962\pi
194194 0 0
195195 −2.39798 + 36.5410i −0.171723 + 2.61675i
196196 0 0
197197 9.78513i 0.697162i 0.937279 + 0.348581i 0.113336π0.113336\pi
−0.937279 + 0.348581i 0.886664π0.886664\pi
198198 0 0
199199 −1.47257 −0.104388 −0.0521939 0.998637i 0.516621π-0.516621\pi
−0.0521939 + 0.998637i 0.516621π0.516621\pi
200200 0 0
201201 −19.2802 −1.35992
202202 0 0
203203 8.40162i 0.589678i
204204 0 0
205205 −0.967955 + 14.7499i −0.0676049 + 1.03018i
206206 0 0
207207 20.3862i 1.41694i
208208 0 0
209209 0.362883 0.0251011
210210 0 0
211211 4.87591 0.335672 0.167836 0.985815i 0.446322π-0.446322\pi
0.167836 + 0.985815i 0.446322π0.446322\pi
212212 0 0
213213 11.0302i 0.755777i
214214 0 0
215215 15.4990 + 1.01712i 1.05702 + 0.0693667i
216216 0 0
217217 0.551937i 0.0374680i
218218 0 0
219219 38.8781 2.62714
220220 0 0
221221 5.70167 0.383536
222222 0 0
223223 20.0536i 1.34289i 0.741055 + 0.671444i 0.234326π0.234326\pi
−0.741055 + 0.671444i 0.765674π0.765674\pi
224224 0 0
225225 26.0247 + 3.43049i 1.73498 + 0.228700i
226226 0 0
227227 14.1308i 0.937893i 0.883227 + 0.468946i 0.155366π0.155366\pi
−0.883227 + 0.468946i 0.844634π0.844634\pi
228228 0 0
229229 −11.2156 −0.741149 −0.370575 0.928803i 0.620839π-0.620839\pi
−0.370575 + 0.928803i 0.620839π0.620839\pi
230230 0 0
231231 −0.301967 −0.0198680
232232 0 0
233233 13.8285i 0.905934i 0.891527 + 0.452967i 0.149634π0.149634\pi
−0.891527 + 0.452967i 0.850366π0.850366\pi
234234 0 0
235235 12.7220 + 0.834872i 0.829889 + 0.0544610i
236236 0 0
237237 3.04460i 0.197768i
238238 0 0
239239 −16.2851 −1.05339 −0.526697 0.850053i 0.676570π-0.676570\pi
−0.526697 + 0.850053i 0.676570π0.676570\pi
240240 0 0
241241 4.94081 0.318265 0.159133 0.987257i 0.449130π-0.449130\pi
0.159133 + 0.987257i 0.449130π0.449130\pi
242242 0 0
243243 11.3100i 0.725535i
244244 0 0
245245 0.729489 11.1161i 0.0466053 0.710182i
246246 0 0
247247 27.9576i 1.77890i
248248 0 0
249249 34.0356 2.15692
250250 0 0
251251 −12.9160 −0.815248 −0.407624 0.913150i 0.633643π-0.633643\pi
−0.407624 + 0.913150i 0.633643π0.633643\pi
252252 0 0
253253 0.287375i 0.0180671i
254254 0 0
255255 0.420575 6.40882i 0.0263375 0.401336i
256256 0 0
257257 13.6159i 0.849337i 0.905349 + 0.424669i 0.139609π0.139609\pi
−0.905349 + 0.424669i 0.860391π0.860391\pi
258258 0 0
259259 14.0839 0.875132
260260 0 0
261261 31.0496 1.92192
262262 0 0
263263 12.6719i 0.781385i 0.920521 + 0.390692i 0.127764π0.127764\pi
−0.920521 + 0.390692i 0.872236π0.872236\pi
264264 0 0
265265 0.0483580 + 0.00317347i 0.00297061 + 0.000194945i
266266 0 0
267267 5.72882i 0.350598i
268268 0 0
269269 25.8967 1.57895 0.789474 0.613784i 0.210354π-0.210354\pi
0.789474 + 0.613784i 0.210354π0.210354\pi
270270 0 0
271271 −21.2211 −1.28909 −0.644545 0.764566i 0.722953π-0.722953\pi
−0.644545 + 0.764566i 0.722953π0.722953\pi
272272 0 0
273273 23.2644i 1.40803i
274274 0 0
275275 0.366858 + 0.0483580i 0.0221224 + 0.00291610i
276276 0 0
277277 2.05908i 0.123718i −0.998085 0.0618590i 0.980297π-0.980297\pi
0.998085 0.0618590i 0.0197029π-0.0197029\pi
278278 0 0
279279 2.03978 0.122118
280280 0 0
281281 −21.7336 −1.29652 −0.648259 0.761420i 0.724503π-0.724503\pi
−0.648259 + 0.761420i 0.724503π0.724503\pi
282282 0 0
283283 5.32226i 0.316375i 0.987409 + 0.158188i 0.0505651π0.0505651\pi
−0.987409 + 0.158188i 0.949435π0.949435\pi
284284 0 0
285285 −31.4250 2.06225i −1.86146 0.122157i
286286 0 0
287287 9.39078i 0.554321i
288288 0 0
289289 −1.00000 −0.0588235
290290 0 0
291291 −15.3411 −0.899311
292292 0 0
293293 23.3285i 1.36287i 0.731880 + 0.681434i 0.238643π0.238643\pi
−0.731880 + 0.681434i 0.761357π0.761357\pi
294294 0 0
295295 −0.292852 + 4.46254i −0.0170505 + 0.259819i
296296 0 0
297297 0.478268i 0.0277519i
298298 0 0
299299 −22.1402 −1.28040
300300 0 0
301301 9.86772 0.568766
302302 0 0
303303 32.8315i 1.88612i
304304 0 0
305305 −0.508592 + 7.75003i −0.0291219 + 0.443765i
306306 0 0
307307 17.4588i 0.996425i 0.867055 + 0.498213i 0.166010π0.166010\pi
−0.867055 + 0.498213i 0.833990π0.833990\pi
308308 0 0
309309 −23.5888 −1.34192
310310 0 0
311311 −2.98997 −0.169545 −0.0847727 0.996400i 0.527016π-0.527016\pi
−0.0847727 + 0.996400i 0.527016π0.527016\pi
312312 0 0
313313 7.76028i 0.438637i 0.975653 + 0.219319i 0.0703834π0.0703834\pi
−0.975653 + 0.219319i 0.929617π0.929617\pi
314314 0 0
315315 16.6408 + 1.09204i 0.937600 + 0.0615295i
316316 0 0
317317 6.88951i 0.386953i −0.981105 0.193477i 0.938024π-0.938024\pi
0.981105 0.193477i 0.0619764π-0.0619764\pi
318318 0 0
319319 0.437691 0.0245060
320320 0 0
321321 18.2356 1.01781
322322 0 0
323323 4.90340i 0.272833i
324324 0 0
325325 3.72565 28.2639i 0.206662 1.56780i
326326 0 0
327327 0.841151i 0.0465158i
328328 0 0
329329 8.09965 0.446548
330330 0 0
331331 −15.8565 −0.871552 −0.435776 0.900055i 0.643526π-0.643526\pi
−0.435776 + 0.900055i 0.643526π0.643526\pi
332332 0 0
333333 52.0495i 2.85229i
334334 0 0
335335 14.9774 + 0.982885i 0.818303 + 0.0537007i
336336 0 0
337337 19.1787i 1.04473i −0.852722 0.522365i 0.825050π-0.825050\pi
0.852722 0.522365i 0.174950π-0.174950\pi
338338 0 0
339339 24.7679 1.34521
340340 0 0
341341 0.0287537 0.00155710
342342 0 0
343343 17.0213i 0.919063i
344344 0 0
345345 −1.63314 + 24.8862i −0.0879254 + 1.33983i
346346 0 0
347347 33.5775i 1.80253i −0.433265 0.901266i 0.642639π-0.642639\pi
0.433265 0.901266i 0.357361π-0.357361\pi
348348 0 0
349349 −8.61649 −0.461230 −0.230615 0.973045i 0.574074π-0.574074\pi
−0.230615 + 0.973045i 0.574074π0.574074\pi
350350 0 0
351351 36.8473 1.96676
352352 0 0
353353 0.596657i 0.0317569i 0.999874 + 0.0158784i 0.00505447π0.00505447\pi
−0.999874 + 0.0158784i 0.994946π0.994946\pi
354354 0 0
355355 −0.562309 + 8.56859i −0.0298443 + 0.454773i
356356 0 0
357357 4.08029i 0.215952i
358358 0 0
359359 31.5514 1.66522 0.832608 0.553862i 0.186847π-0.186847\pi
0.832608 + 0.553862i 0.186847π0.186847\pi
360360 0 0
361361 5.04335 0.265439
362362 0 0
363363 31.5793i 1.65748i
364364 0 0
365365 −30.2016 1.98197i −1.58082 0.103741i
366366 0 0
367367 1.37723i 0.0718908i −0.999354 0.0359454i 0.988556π-0.988556\pi
0.999354 0.0359454i 0.0114442π-0.0114442\pi
368368 0 0
369369 34.7052 1.80668
370370 0 0
371371 0.0307879 0.00159843
372372 0 0
373373 28.5627i 1.47892i 0.673201 + 0.739459i 0.264919π0.264919\pi
−0.673201 + 0.739459i 0.735081π0.735081\pi
374374 0 0
375375 −31.4945 6.27256i −1.62637 0.323914i
376376 0 0
377377 33.7210i 1.73672i
378378 0 0
379379 −24.2405 −1.24515 −0.622576 0.782559i 0.713914π-0.713914\pi
−0.622576 + 0.782559i 0.713914π0.713914\pi
380380 0 0
381381 49.5869 2.54041
382382 0 0
383383 24.4678i 1.25025i −0.780527 0.625123i 0.785049π-0.785049\pi
0.780527 0.625123i 0.214951π-0.214951\pi
384384 0 0
385385 0.234577 + 0.0153940i 0.0119551 + 0.000784550i
386386 0 0
387387 36.4678i 1.85376i
388388 0 0
389389 10.9711 0.556258 0.278129 0.960544i 0.410286π-0.410286\pi
0.278129 + 0.960544i 0.410286π0.410286\pi
390390 0 0
391391 3.88311 0.196377
392392 0 0
393393 42.2764i 2.13256i
394394 0 0
395395 −0.155211 + 2.36514i −0.00780951 + 0.119003i
396396 0 0
397397 26.8550i 1.34782i −0.738815 0.673908i 0.764614π-0.764614\pi
0.738815 0.673908i 0.235386π-0.235386\pi
398398 0 0
399399 −20.0073 −1.00162
400400 0 0
401401 −17.5080 −0.874308 −0.437154 0.899387i 0.644014π-0.644014\pi
−0.437154 + 0.899387i 0.644014π0.644014\pi
402402 0 0
403403 2.21528i 0.110351i
404404 0 0
405405 0.411790 6.27495i 0.0204620 0.311805i
406406 0 0
407407 0.733716i 0.0363690i
408408 0 0
409409 17.8285 0.881561 0.440781 0.897615i 0.354702π-0.354702\pi
0.440781 + 0.897615i 0.354702π0.354702\pi
410410 0 0
411411 3.91290 0.193009
412412 0 0
413413 2.84115i 0.139804i
414414 0 0
415415 −26.4398 1.73510i −1.29788 0.0851727i
416416 0 0
417417 39.4805i 1.93337i
418418 0 0
419419 34.7826 1.69924 0.849622 0.527393i 0.176830π-0.176830\pi
0.849622 + 0.527393i 0.176830π0.176830\pi
420420 0 0
421421 −17.0676 −0.831824 −0.415912 0.909405i 0.636538π-0.636538\pi
−0.415912 + 0.909405i 0.636538π0.636538\pi
422422 0 0
423423 29.9336i 1.45542i
424424 0 0
425425 −0.653431 + 4.95712i −0.0316960 + 0.240456i
426426 0 0
427427 4.93419i 0.238782i
428428 0 0
429429 1.21198 0.0585152
430430 0 0
431431 22.5970 1.08846 0.544229 0.838937i 0.316822π-0.316822\pi
0.544229 + 0.838937i 0.316822π0.316822\pi
432432 0 0
433433 13.3513i 0.641625i −0.947143 0.320812i 0.896044π-0.896044\pi
0.947143 0.320812i 0.103956π-0.103956\pi
434434 0 0
435435 −37.9033 2.48738i −1.81732 0.119261i
436436 0 0
437437 19.0405i 0.910829i
438438 0 0
439439 5.73280 0.273611 0.136806 0.990598i 0.456316π-0.456316\pi
0.136806 + 0.990598i 0.456316π0.456316\pi
440440 0 0
441441 −26.1552 −1.24548
442442 0 0
443443 38.8153i 1.84417i −0.386985 0.922086i 0.626483π-0.626483\pi
0.386985 0.922086i 0.373517π-0.373517\pi
444444 0 0
445445 0.292050 4.45032i 0.0138445 0.210965i
446446 0 0
447447 49.8707i 2.35880i
448448 0 0
449449 25.3848 1.19798 0.598992 0.800755i 0.295568π-0.295568\pi
0.598992 + 0.800755i 0.295568π0.295568\pi
450450 0 0
451451 0.489222 0.0230366
452452 0 0
453453 10.3303i 0.485358i
454454 0 0
455455 1.18600 18.0725i 0.0556005 0.847252i
456456 0 0
457457 8.90110i 0.416376i 0.978089 + 0.208188i 0.0667566π0.0667566\pi
−0.978089 + 0.208188i 0.933243π0.933243\pi
458458 0 0
459459 −6.46254 −0.301645
460460 0 0
461461 −13.9124 −0.647965 −0.323983 0.946063i 0.605022π-0.605022\pi
−0.323983 + 0.946063i 0.605022π0.605022\pi
462462 0 0
463463 37.5085i 1.74317i 0.490247 + 0.871583i 0.336906π0.336906\pi
−0.490247 + 0.871583i 0.663094π0.663094\pi
464464 0 0
465465 −2.49002 0.163407i −0.115472 0.00757780i
466466 0 0
467467 11.2108i 0.518776i 0.965773 + 0.259388i 0.0835208π0.0835208\pi
−0.965773 + 0.259388i 0.916479π0.916479\pi
468468 0 0
469469 9.53562 0.440314
470470 0 0
471471 −14.9160 −0.687291
472472 0 0
473473 0.514069i 0.0236369i
474474 0 0
475475 24.3067 + 3.20403i 1.11527 + 0.147011i
476476 0 0
477477 0.113782i 0.00520972i
478478 0 0
479479 5.16559 0.236022 0.118011 0.993012i 0.462348π-0.462348\pi
0.118011 + 0.993012i 0.462348π0.462348\pi
480480 0 0
481481 −56.5277 −2.57744
482482 0 0
483483 15.8442i 0.720936i
484484 0 0
485485 11.9174 + 0.782074i 0.541142 + 0.0355122i
486486 0 0
487487 34.0560i 1.54322i −0.636094 0.771612i 0.719451π-0.719451\pi
0.636094 0.771612i 0.280549π-0.280549\pi
488488 0 0
489489 −18.8619 −0.852963
490490 0 0
491491 18.3051 0.826099 0.413050 0.910708i 0.364464π-0.364464\pi
0.413050 + 0.910708i 0.364464π0.364464\pi
492492 0 0
493493 5.91424i 0.266364i
494494 0 0
495495 0.0568910 0.866917i 0.00255706 0.0389650i
496496 0 0
497497 5.45534i 0.244705i
498498 0 0
499499 40.7792 1.82553 0.912764 0.408488i 0.133944π-0.133944\pi
0.912764 + 0.408488i 0.133944π0.133944\pi
500500 0 0
501501 −2.57678 −0.115122
502502 0 0
503503 10.7274i 0.478313i 0.970981 + 0.239156i 0.0768709π0.0768709\pi
−0.970981 + 0.239156i 0.923129π0.923129\pi
504504 0 0
505505 1.67372 25.5045i 0.0744795 1.13494i
506506 0 0
507507 56.0354i 2.48862i
508508 0 0
509509 21.5278 0.954205 0.477102 0.878848i 0.341687π-0.341687\pi
0.477102 + 0.878848i 0.341687π0.341687\pi
510510 0 0
511511 −19.2284 −0.850613
512512 0 0
513513 31.6884i 1.39908i
514514 0 0
515515 18.3244 + 1.20253i 0.807471 + 0.0529899i
516516 0 0
517517 0.421960i 0.0185578i
518518 0 0
519519 −11.0017 −0.482922
520520 0 0
521521 −20.5451 −0.900098 −0.450049 0.893004i 0.648594π-0.648594\pi
−0.450049 + 0.893004i 0.648594π0.648594\pi
522522 0 0
523523 20.0508i 0.876762i 0.898789 + 0.438381i 0.144448π0.144448\pi
−0.898789 + 0.438381i 0.855552π0.855552\pi
524524 0 0
525525 −20.2265 2.66618i −0.882755 0.116362i
526526 0 0
527527 0.388531i 0.0169247i
528528 0 0
529529 7.92144 0.344410
530530 0 0
531531 10.4999 0.455659
532532 0 0
533533 37.6912i 1.63259i
534534 0 0
535535 −14.1659 0.929632i −0.612447 0.0401915i
536536 0 0
537537 27.9890i 1.20782i
538538 0 0
539539 −0.368697 −0.0158809
540540 0 0
541541 −8.55768 −0.367924 −0.183962 0.982933i 0.558892π-0.558892\pi
−0.183962 + 0.982933i 0.558892π0.558892\pi
542542 0 0
543543 64.5585i 2.77047i
544544 0 0
545545 −0.0428811 + 0.653431i −0.00183682 + 0.0279899i
546546 0 0
547547 11.2911i 0.482771i −0.970429 0.241385i 0.922398π-0.922398\pi
0.970429 0.241385i 0.0776018π-0.0776018\pi
548548 0 0
549549 18.2351 0.778256
550550 0 0
551551 28.9999 1.23544
552552 0 0
553553 1.50580i 0.0640333i
554554 0 0
555555 −4.16969 + 63.5386i −0.176993 + 2.69706i
556556 0 0
557557 22.4662i 0.951922i −0.879466 0.475961i 0.842100π-0.842100\pi
0.879466 0.475961i 0.157900π-0.157900\pi
558558 0 0
559559 −39.6054 −1.67513
560560 0 0
561561 −0.212567 −0.00897457
562562 0 0
563563 6.32795i 0.266691i 0.991070 + 0.133346i 0.0425721π0.0425721\pi
−0.991070 + 0.133346i 0.957428π0.957428\pi
564564 0 0
565565 −19.2405 1.26265i −0.809453 0.0531199i
566566 0 0
567567 3.99506i 0.167777i
568568 0 0
569569 16.6885 0.699620 0.349810 0.936821i 0.386246π-0.386246\pi
0.349810 + 0.936821i 0.386246π0.386246\pi
570570 0 0
571571 6.20629 0.259725 0.129863 0.991532i 0.458546π-0.458546\pi
0.129863 + 0.991532i 0.458546π0.458546\pi
572572 0 0
573573 15.7302i 0.657137i
574574 0 0
575575 2.53735 19.2491i 0.105815 0.802741i
576576 0 0
577577 23.9273i 0.996105i 0.867147 + 0.498052i 0.165951π0.165951\pi
−0.867147 + 0.498052i 0.834049π0.834049\pi
578578 0 0
579579 6.16057 0.256025
580580 0 0
581581 −16.8334 −0.698366
582582 0 0
583583 0.00160393i 6.64279e-5i
584584 0 0
585585 −66.7899 4.38305i −2.76142 0.181217i
586586 0 0
587587 26.1140i 1.07784i 0.842357 + 0.538920i 0.181168π0.181168\pi
−0.842357 + 0.538920i 0.818832π0.818832\pi
588588 0 0
589589 1.90512 0.0784992
590590 0 0
591591 −28.1056 −1.15611
592592 0 0
593593 29.8969i 1.22772i −0.789415 0.613860i 0.789616π-0.789616\pi
0.789415 0.613860i 0.210384π-0.210384\pi
594594 0 0
595595 −0.208009 + 3.16969i −0.00852754 + 0.129944i
596596 0 0
597597 4.22963i 0.173107i
598598 0 0
599599 15.8194 0.646362 0.323181 0.946337i 0.395248π-0.395248\pi
0.323181 + 0.946337i 0.395248π0.395248\pi
600600 0 0
601601 32.4048 1.32182 0.660910 0.750466i 0.270171π-0.270171\pi
0.660910 + 0.750466i 0.270171π0.270171\pi
602602 0 0
603603 35.2405i 1.43510i
604604 0 0
605605 −1.60988 + 24.5317i −0.0654510 + 0.997357i
606606 0 0
607607 20.4218i 0.828895i 0.910073 + 0.414447i 0.136025π0.136025\pi
−0.910073 + 0.414447i 0.863975π0.863975\pi
608608 0 0
609609 −24.1318 −0.977869
610610 0 0
611611 −32.5091 −1.31518
612612 0 0
613613 12.0930i 0.488433i −0.969721 0.244217i 0.921469π-0.921469\pi
0.969721 0.244217i 0.0785308π-0.0785308\pi
614614 0 0
615615 −42.3658 2.78024i −1.70835 0.112110i
616616 0 0
617617 3.79742i 0.152878i −0.997074 0.0764392i 0.975645π-0.975645\pi
0.997074 0.0764392i 0.0243551π-0.0243551\pi
618618 0 0
619619 −0.765306 −0.0307602 −0.0153801 0.999882i 0.504896π-0.504896\pi
−0.0153801 + 0.999882i 0.504896π0.504896\pi
620620 0 0
621621 25.0948 1.00702
622622 0 0
623623 2.83337i 0.113517i
624624 0 0
625625 24.1461 + 6.47827i 0.965842 + 0.259131i
626626 0 0
627627 1.04230i 0.0416254i
628628 0 0
629629 9.91424 0.395307
630630 0 0
631631 −41.7318 −1.66132 −0.830658 0.556784i 0.812035π-0.812035\pi
−0.830658 + 0.556784i 0.812035π0.812035\pi
632632 0 0
633633 14.0050i 0.556648i
634634 0 0
635635 −38.5206 2.52789i −1.52864 0.100316i
636636 0 0
637637 28.4055i 1.12547i
638638 0 0
639639 20.1611 0.797561
640640 0 0
641641 22.6429 0.894342 0.447171 0.894448i 0.352431π-0.352431\pi
0.447171 + 0.894448i 0.352431π0.352431\pi
642642 0 0
643643 24.8814i 0.981226i −0.871377 0.490613i 0.836773π-0.836773\pi
0.871377 0.490613i 0.163227π-0.163227\pi
644644 0 0
645645 −2.92144 + 44.5175i −0.115031 + 1.75287i
646646 0 0
647647 35.6376i 1.40106i 0.713624 + 0.700529i 0.247053π0.247053\pi
−0.713624 + 0.700529i 0.752947π0.752947\pi
648648 0 0
649649 0.148013 0.00581000
650650 0 0
651651 −1.58532 −0.0621335
652652 0 0
653653 8.31930i 0.325559i 0.986662 + 0.162780i 0.0520460π0.0520460\pi
−0.986662 + 0.162780i 0.947954π0.947954\pi
654654 0 0
655655 2.15521 32.8416i 0.0842111 1.28323i
656656 0 0
657657 71.0616i 2.77238i
658658 0 0
659659 −3.44669 −0.134264 −0.0671320 0.997744i 0.521385π-0.521385\pi
−0.0671320 + 0.997744i 0.521385π0.521385\pi
660660 0 0
661661 −36.6867 −1.42695 −0.713473 0.700682i 0.752879π-0.752879\pi
−0.713473 + 0.700682i 0.752879π0.752879\pi
662662 0 0
663663 16.3768i 0.636021i
664664 0 0
665665 15.5422 + 1.01995i 0.602702 + 0.0395520i
666666 0 0
667667 22.9657i 0.889234i
668668 0 0
669669 −57.5995 −2.22692
670670 0 0
671671 0.257052 0.00992336
672672 0 0
673673 41.5075i 1.60000i −0.600002 0.799998i 0.704834π-0.704834\pi
0.600002 0.799998i 0.295166π-0.295166\pi
674674 0 0
675675 −4.22282 + 32.0356i −0.162536 + 1.23305i
676676 0 0
677677 26.7378i 1.02762i 0.857905 + 0.513809i 0.171766π0.171766\pi
−0.857905 + 0.513809i 0.828234π0.828234\pi
678678 0 0
679679 7.58742 0.291179
680680 0 0
681681 −40.5875 −1.55532
682682 0 0
683683 37.8270i 1.44741i 0.690110 + 0.723704i 0.257562π0.257562\pi
−0.690110 + 0.723704i 0.742438π0.742438\pi
684684 0 0
685685 −3.03966 0.199476i −0.116139 0.00762159i
686686 0 0
687687 32.2144i 1.22905i
688688 0 0
689689 −0.123572 −0.00470770
690690 0 0
691691 −33.0739 −1.25819 −0.629095 0.777328i 0.716574π-0.716574\pi
−0.629095 + 0.777328i 0.716574π0.716574\pi
692692 0 0
693693 0.551937i 0.0209664i
694694 0 0
695695 −2.01268 + 30.6696i −0.0763451 + 1.16336i
696696 0 0
697697 6.61055i 0.250392i
698698 0 0
699699 −39.7192 −1.50232
700700 0 0
701701 −24.7292 −0.934008 −0.467004 0.884255i 0.654667π-0.654667\pi
−0.467004 + 0.884255i 0.654667π0.654667\pi
702702 0 0
703703 48.6135i 1.83349i
704704 0 0
705705 −2.39798 + 36.5410i −0.0903133 + 1.37621i
706706 0 0
707707 16.2379i 0.610688i
708708 0 0
709709 −40.5902 −1.52440 −0.762199 0.647343i 0.775880π-0.775880\pi
−0.762199 + 0.647343i 0.775880π0.775880\pi
710710 0 0
711711 5.56495 0.208702
712712 0 0
713713 1.50871i 0.0565016i
714714 0 0
715715 −0.941505 0.0617858i −0.0352103 0.00231066i
716716 0 0
717717 46.7752i 1.74685i
718718 0 0
719719 32.1253 1.19807 0.599036 0.800722i 0.295551π-0.295551\pi
0.599036 + 0.800722i 0.295551π0.295551\pi
720720 0 0
721721 11.6666 0.434486
722722 0 0
723723 14.1914i 0.527782i
724724 0 0
725725 29.3176 + 3.86455i 1.08883 + 0.143526i
726726 0 0
727727 11.3089i 0.419425i 0.977763 + 0.209713i 0.0672528π0.0672528\pi
−0.977763 + 0.209713i 0.932747π0.932747\pi
728728 0 0
729729 40.9222 1.51564
730730 0 0
731731 6.94628 0.256918
732732 0 0
733733 32.5450i 1.20208i 0.799220 + 0.601039i 0.205246π0.205246\pi
−0.799220 + 0.601039i 0.794754π0.794754\pi
734734 0 0
735735 31.9285 + 2.09529i 1.17770 + 0.0772860i
736736 0 0
737737 0.496768i 0.0182987i
738738 0 0
739739 −29.6821 −1.09187 −0.545936 0.837827i 0.683826π-0.683826\pi
−0.545936 + 0.837827i 0.683826π0.683826\pi
740740 0 0
741741 80.3019 2.94996
742742 0 0
743743 27.9705i 1.02614i −0.858348 0.513069i 0.828509π-0.828509\pi
0.858348 0.513069i 0.171491π-0.171491\pi
744744 0 0
745745 2.54236 38.7410i 0.0931448 1.41936i
746746 0 0
747747 62.2105i 2.27616i
748748 0 0
749749 −9.01898 −0.329546
750750 0 0
751751 52.7167 1.92366 0.961829 0.273650i 0.0882309π-0.0882309\pi
0.961829 + 0.273650i 0.0882309π0.0882309\pi
752752 0 0
753753 37.0982i 1.35193i
754754 0 0
755755 0.526626 8.02485i 0.0191659 0.292054i
756756 0 0
757757 7.80911i 0.283827i −0.989879 0.141913i 0.954675π-0.954675\pi
0.989879 0.141913i 0.0453255π-0.0453255\pi
758758 0 0
759759 0.825420 0.0299608
760760 0 0
761761 19.2266 0.696963 0.348481 0.937316i 0.386697π-0.386697\pi
0.348481 + 0.937316i 0.386697π0.386697\pi
762762 0 0
763763 0.416018i 0.0150609i
764764 0 0
765765 11.7141 + 0.768731i 0.423524 + 0.0277935i
766766 0 0
767767 11.4033i 0.411751i
768768 0 0
769769 1.45851 0.0525953 0.0262977 0.999654i 0.491628π-0.491628\pi
0.0262977 + 0.999654i 0.491628π0.491628\pi
770770 0 0
771771 −39.1087 −1.40846
772772 0 0
773773 18.8055i 0.676388i 0.941076 + 0.338194i 0.109816π0.109816\pi
−0.941076 + 0.338194i 0.890184π0.890184\pi
774774 0 0
775775 1.92599 + 0.253878i 0.0691837 + 0.00911957i
776776 0 0
777777 40.4529i 1.45124i
778778 0 0
779779 32.4142 1.16136
780780 0 0
781781 0.284201 0.0101695
782782 0 0
783783 38.2210i 1.36591i
784784 0 0
785785 11.5872 + 0.760401i 0.413563 + 0.0271399i
786786 0 0
787787 19.0449i 0.678877i −0.940628 0.339439i 0.889763π-0.889763\pi
0.940628 0.339439i 0.110237π-0.110237\pi
788788 0 0
789789 −36.3973 −1.29578
790790 0 0
791791 −12.2498 −0.435552
792792 0 0
793793 19.8040i 0.703262i
794794 0 0
795795 −0.00911508 + 0.138898i −0.000323278 + 0.00492619i
796796 0 0
797797 49.6667i 1.75929i 0.475634 + 0.879643i 0.342219π0.342219\pi
−0.475634 + 0.879643i 0.657781π0.657781\pi
798798 0 0
799799 5.70167 0.201711
800800 0 0
801801 −10.4712 −0.369981
802802 0 0
803803 1.00172i 0.0353500i
804804 0 0
805805 0.807722 12.3082i 0.0284685 0.433809i
806806 0 0
807807 74.3824i 2.61838i
808808 0 0
809809 −38.2625 −1.34524 −0.672619 0.739989i 0.734831π-0.734831\pi
−0.672619 + 0.739989i 0.734831π0.734831\pi
810810 0 0
811811 31.4356 1.10385 0.551927 0.833893i 0.313893π-0.313893\pi
0.551927 + 0.833893i 0.313893π0.313893\pi
812812 0 0
813813 60.9529i 2.13771i
814814 0 0
815815 14.6524 + 0.961559i 0.513253 + 0.0336819i
816816 0 0
817817 34.0604i 1.19162i
818818 0 0
819819 −42.5229 −1.48587
820820 0 0
821821 42.9887 1.50031 0.750157 0.661259i 0.229978π-0.229978\pi
0.750157 + 0.661259i 0.229978π0.229978\pi
822822 0 0
823823 12.7450i 0.444263i 0.975017 + 0.222132i 0.0713014π0.0713014\pi
−0.975017 + 0.222132i 0.928699π0.928699\pi
824824 0 0
825825 −0.138898 + 1.05372i −0.00483579 + 0.0366857i
826826 0 0
827827 12.8443i 0.446639i 0.974745 + 0.223319i 0.0716893π0.0716893\pi
−0.974745 + 0.223319i 0.928311π0.928311\pi
828828 0 0
829829 17.2491 0.599087 0.299543 0.954083i 0.403166π-0.403166\pi
0.299543 + 0.954083i 0.403166π0.403166\pi
830830 0 0
831831 5.91424 0.205163
832832 0 0
833833 4.98197i 0.172615i
834834 0 0
835835 2.00172 + 0.131362i 0.0692724 + 0.00454597i
836836 0 0
837837 2.51090i 0.0867892i
838838 0 0
839839 −17.7454 −0.612638 −0.306319 0.951929i 0.599097π-0.599097\pi
−0.306319 + 0.951929i 0.599097π0.599097\pi
840840 0 0
841841 5.97821 0.206145
842842 0 0
843843 62.4249i 2.15003i
844844 0 0
845845 −2.85663 + 43.5299i −0.0982711 + 1.49748i
846846 0 0
847847 15.6185i 0.536660i
848848 0 0
849849 −15.2870 −0.524648
850850 0 0
851851 −38.4981 −1.31970
852852 0 0
853853 45.1570i 1.54615i 0.634317 + 0.773073i 0.281282π0.281282\pi
−0.634317 + 0.773073i 0.718718π0.718718\pi
854854 0 0
855855 3.76940 57.4389i 0.128911 1.96437i
856856 0 0
857857 40.5102i 1.38380i −0.721993 0.691900i 0.756774π-0.756774\pi
0.721993 0.691900i 0.243226π-0.243226\pi
858858 0 0
859859 −25.4439 −0.868135 −0.434068 0.900880i 0.642922π-0.642922\pi
−0.434068 + 0.900880i 0.642922π0.642922\pi
860860 0 0
861861 −26.9729 −0.919235
862862 0 0
863863 21.6953i 0.738517i 0.929327 + 0.369259i 0.120388π0.120388\pi
−0.929327 + 0.369259i 0.879612π0.879612\pi
864864 0 0
865865 8.54646 + 0.560857i 0.290588 + 0.0190697i
866866 0 0
867867 2.87228i 0.0975476i
868868 0 0
869869 0.0784464 0.00266111
870870 0 0
871871 −38.2725 −1.29681
872872 0 0
873873 28.0406i 0.949030i
874874 0 0
875875 15.5766 + 3.10230i 0.526585 + 0.104877i
876876 0 0
877877 15.4643i 0.522191i 0.965313 + 0.261095i 0.0840837π0.0840837\pi
−0.965313 + 0.261095i 0.915916π0.915916\pi
878878 0 0
879879 −67.0060 −2.26006
880880 0 0
881881 −13.2839 −0.447544 −0.223772 0.974641i 0.571837π-0.571837\pi
−0.223772 + 0.974641i 0.571837π0.571837\pi
882882 0 0
883883 30.1936i 1.01609i −0.861329 0.508047i 0.830368π-0.830368\pi
0.861329 0.508047i 0.169632π-0.169632\pi
884884 0 0
885885 −12.8176 0.841151i −0.430860 0.0282750i
886886 0 0
887887 39.7258i 1.33386i −0.745120 0.666930i 0.767608π-0.767608\pi
0.745120 0.666930i 0.232392π-0.232392\pi
888888 0 0
889889 −24.5248 −0.822535
890890 0 0
891891 −0.208126 −0.00697250
892892 0 0
893893 27.9576i 0.935565i
894894 0 0
895895 1.42685 21.7427i 0.0476945 0.726779i
896896 0 0
897897 63.5929i 2.12330i
898898 0 0
899899 2.29786 0.0766381
900900 0 0
901901 0.0216729 0.000722028
902902 0 0
903903 28.3428i 0.943190i
904904 0 0
905905 3.29113 50.1510i 0.109401 1.66707i
906906 0 0
907907 20.4051i 0.677541i 0.940869 + 0.338771i 0.110011π0.110011\pi
−0.940869 + 0.338771i 0.889989π0.889989\pi
908908 0 0
909909 −60.0098 −1.99040
910910 0 0
911911 44.1137 1.46155 0.730776 0.682618i 0.239159π-0.239159\pi
0.730776 + 0.682618i 0.239159π0.239159\pi
912912 0 0
913913 0.876951i 0.0290228i
914914 0 0
915915 −22.2602 1.46082i −0.735900 0.0482931i
916916 0 0
917917 20.9091i 0.690481i
918918 0 0
919919 38.1261 1.25766 0.628832 0.777541i 0.283533π-0.283533\pi
0.628832 + 0.777541i 0.283533π0.283533\pi
920920 0 0
921921 −50.1464 −1.65238
922922 0 0
923923 21.8957i 0.720707i
924924 0 0
925925 6.47827 49.1461i 0.213004 1.61591i
926926 0 0
927927 43.1157i 1.41611i
928928 0 0
929929 −11.6168 −0.381134 −0.190567 0.981674i 0.561033π-0.561033\pi
−0.190567 + 0.981674i 0.561033π0.561033\pi
930930 0 0
931931 −24.4286 −0.800614
932932 0 0
933933 8.58801i 0.281159i
934934 0 0
935935 0.165128 + 0.0108364i 0.00540026 + 0.000354389i
936936 0 0
937937 39.8889i 1.30311i −0.758600 0.651557i 0.774116π-0.774116\pi
0.758600 0.651557i 0.225884π-0.225884\pi
938938 0 0
939939 −22.2897 −0.727396
940940 0 0
941941 −21.8113 −0.711028 −0.355514 0.934671i 0.615694π-0.615694\pi
−0.355514 + 0.934671i 0.615694π0.615694\pi
942942 0 0
943943 25.6695i 0.835914i
944944 0 0
945945 −1.34427 + 20.4842i −0.0437290 + 0.666351i
946946 0 0
947947 18.2678i 0.593625i −0.954936 0.296812i 0.904076π-0.904076\pi
0.954936 0.296812i 0.0959236π-0.0959236\pi
948948 0 0
949949 77.1757 2.50523
950950 0 0
951951 19.7886 0.641688
952952 0 0
953953 27.5942i 0.893865i 0.894568 + 0.446932i 0.147484π0.147484\pi
−0.894568 + 0.446932i 0.852516π0.852516\pi
954954 0 0
955955 0.801908 12.2196i 0.0259491 0.395419i
956956 0 0
957957 1.25717i 0.0406385i
958958 0 0
959959 −1.93525 −0.0624925
960960 0 0
961961 −30.8490 −0.995130
962962 0 0
963963 33.3311i 1.07408i
964964 0 0
965965 −4.78571 0.314060i −0.154058 0.0101099i
966966 0 0
967967 36.3289i 1.16826i −0.811661 0.584129i 0.801436π-0.801436\pi
0.811661 0.584129i 0.198564π-0.198564\pi
968968 0 0
969969 −14.0839 −0.452441
970970 0 0
971971 −45.2409 −1.45185 −0.725925 0.687774i 0.758588π-0.758588\pi
−0.725925 + 0.687774i 0.758588π0.758588\pi
972972 0 0
973973 19.5263i 0.625985i
974974 0 0
975975 81.1816 + 10.7011i 2.59989 + 0.342709i
976976 0 0
977977 10.8393i 0.346780i 0.984853 + 0.173390i 0.0554722π0.0554722\pi
−0.984853 + 0.173390i 0.944528π0.944528\pi
978978 0 0
979979 −0.147607 −0.00471755
980980 0 0
981981 1.53746 0.0490874
982982 0 0
983983 3.69018i 0.117699i −0.998267 0.0588493i 0.981257π-0.981257\pi
0.998267 0.0588493i 0.0187431π-0.0187431\pi
984984 0 0
985985 21.8333 + 1.43280i 0.695665 + 0.0456527i
986986 0 0
987987 23.2644i 0.740515i
988988 0 0
989989 −26.9732 −0.857698
990990 0 0
991991 −36.6378 −1.16384 −0.581919 0.813247i 0.697698π-0.697698\pi
−0.581919 + 0.813247i 0.697698π0.697698\pi
992992 0 0
993993 45.5442i 1.44530i
994994 0 0
995995 −0.215623 + 3.28570i −0.00683569 + 0.104164i
996996 0 0
997997 32.6021i 1.03252i 0.856432 + 0.516259i 0.172676π0.172676\pi
−0.856432 + 0.516259i 0.827324π0.827324\pi
998998 0 0
999999 64.0711 2.02712
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 1360.2.e.d.1089.8 8
4.3 odd 2 85.2.b.a.69.6 yes 8
5.2 odd 4 6800.2.a.bw.1.4 4
5.3 odd 4 6800.2.a.bt.1.1 4
5.4 even 2 inner 1360.2.e.d.1089.1 8
12.11 even 2 765.2.b.c.154.3 8
20.3 even 4 425.2.a.h.1.3 4
20.7 even 4 425.2.a.g.1.2 4
20.19 odd 2 85.2.b.a.69.3 8
60.23 odd 4 3825.2.a.bh.1.2 4
60.47 odd 4 3825.2.a.bj.1.3 4
60.59 even 2 765.2.b.c.154.6 8
68.67 odd 2 1445.2.b.e.579.6 8
340.67 even 4 7225.2.a.v.1.2 4
340.203 even 4 7225.2.a.w.1.3 4
340.339 odd 2 1445.2.b.e.579.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
85.2.b.a.69.3 8 20.19 odd 2
85.2.b.a.69.6 yes 8 4.3 odd 2
425.2.a.g.1.2 4 20.7 even 4
425.2.a.h.1.3 4 20.3 even 4
765.2.b.c.154.3 8 12.11 even 2
765.2.b.c.154.6 8 60.59 even 2
1360.2.e.d.1089.1 8 5.4 even 2 inner
1360.2.e.d.1089.8 8 1.1 even 1 trivial
1445.2.b.e.579.3 8 340.339 odd 2
1445.2.b.e.579.6 8 68.67 odd 2
3825.2.a.bh.1.2 4 60.23 odd 4
3825.2.a.bj.1.3 4 60.47 odd 4
6800.2.a.bt.1.1 4 5.3 odd 4
6800.2.a.bw.1.4 4 5.2 odd 4
7225.2.a.v.1.2 4 340.67 even 4
7225.2.a.w.1.3 4 340.203 even 4