Properties

Label 1008.2.q.k.529.4
Level 10081008
Weight 22
Character 1008.529
Analytic conductor 8.0498.049
Analytic rank 00
Dimension 2222
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1008,2,Mod(529,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 4])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.529"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1008=24327 1008 = 2^{4} \cdot 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1008.q (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [22,0,-2,0,3,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 8.048920523758.04892052375
Analytic rank: 00
Dimension: 2222
Relative dimension: 1111 over Q(ζ3)\Q(\zeta_{3})
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 529.4
Character χ\chi == 1008.529
Dual form 1008.2.q.k.625.4

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.22753+1.22195i)q3+(1.764793.05671i)q5+(2.639860.176417i)q7+(0.01368312.99997i)q9+(1.160362.00981i)q11+(2.358844.08563i)q13+(1.56880+5.90871i)q15+(0.636946+1.10322i)q17+(2.783864.82178i)q19+(3.02495+3.44233i)q21+(1.64855+2.85537i)q23+(3.728996.45880i)q25+(3.64901+3.69929i)q27+(4.32116+7.48447i)q298.51642q31+(3.88027+1.04921i)q33+(4.119568.38064i)q35+(2.840244.91943i)q37+(7.88798+2.13287i)q39+(1.66553+2.88478i)q41+(0.0444165+0.0769317i)q43+(9.145895.33615i)q457.05213q47+(6.937750.931432i)q49+(0.5662082.13256i)q51+(3.418165.92042i)q538.19121q55+(9.30925+2.51717i)q57+7.99490q59+13.3553q61+(0.4931237.92192i)q6316.6514q656.12804q67+(1.465465.51951i)q691.30202q71+(6.6452911.5100i)q73+(12.4698+3.37177i)q75+(3.417775.10092i)q77+10.0281q79+(8.999630.0820978i)q81+(5.9024310.2233i)q83+(2.24815+3.89392i)q85+(3.8412614.4677i)q87+(0.561496+0.972540i)q89+(6.9477810.3694i)q91+(10.454210.4066i)q9319.6517q95+(3.50818+6.07635i)q97+(6.04525+3.45356i)q99+O(q100)q+(-1.22753 + 1.22195i) q^{3} +(1.76479 - 3.05671i) q^{5} +(2.63986 - 0.176417i) q^{7} +(0.0136831 - 2.99997i) q^{9} +(-1.16036 - 2.00981i) q^{11} +(-2.35884 - 4.08563i) q^{13} +(1.56880 + 5.90871i) q^{15} +(-0.636946 + 1.10322i) q^{17} +(-2.78386 - 4.82178i) q^{19} +(-3.02495 + 3.44233i) q^{21} +(-1.64855 + 2.85537i) q^{23} +(-3.72899 - 6.45880i) q^{25} +(3.64901 + 3.69929i) q^{27} +(-4.32116 + 7.48447i) q^{29} -8.51642 q^{31} +(3.88027 + 1.04921i) q^{33} +(4.11956 - 8.38064i) q^{35} +(-2.84024 - 4.91943i) q^{37} +(7.88798 + 2.13287i) q^{39} +(1.66553 + 2.88478i) q^{41} +(-0.0444165 + 0.0769317i) q^{43} +(-9.14589 - 5.33615i) q^{45} -7.05213 q^{47} +(6.93775 - 0.931432i) q^{49} +(-0.566208 - 2.13256i) q^{51} +(3.41816 - 5.92042i) q^{53} -8.19121 q^{55} +(9.30925 + 2.51717i) q^{57} +7.99490 q^{59} +13.3553 q^{61} +(-0.493123 - 7.92192i) q^{63} -16.6514 q^{65} -6.12804 q^{67} +(-1.46546 - 5.51951i) q^{69} -1.30202 q^{71} +(6.64529 - 11.5100i) q^{73} +(12.4698 + 3.37177i) q^{75} +(-3.41777 - 5.10092i) q^{77} +10.0281 q^{79} +(-8.99963 - 0.0820978i) q^{81} +(5.90243 - 10.2233i) q^{83} +(2.24815 + 3.89392i) q^{85} +(-3.84126 - 14.4677i) q^{87} +(0.561496 + 0.972540i) q^{89} +(-6.94778 - 10.3694i) q^{91} +(10.4542 - 10.4066i) q^{93} -19.6517 q^{95} +(-3.50818 + 6.07635i) q^{97} +(-6.04525 + 3.45356i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 22q2q3+3q5+5q7+10q9+3q113q13+q15+7q17+q192q2310q25+4q27+9q298q31+29q3314q35+2q37+16q39++56q99+O(q100) 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9} + 3 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 2 q^{23} - 10 q^{25} + 4 q^{27} + 9 q^{29} - 8 q^{31} + 29 q^{33} - 14 q^{35} + 2 q^{37} + 16 q^{39}+ \cdots + 56 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1008Z)×\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times.

nn 127127 577577 757757 785785
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right) 11 e(23)e\left(\frac{2}{3}\right)

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 −1.22753 + 1.22195i −0.708718 + 0.705492i
44 0 0
55 1.76479 3.05671i 0.789239 1.36700i −0.137194 0.990544i 0.543808π-0.543808\pi
0.926433 0.376459i 0.122858π-0.122858\pi
66 0 0
77 2.63986 0.176417i 0.997774 0.0666792i
88 0 0
99 0.0136831 2.99997i 0.00456103 0.999990i
1010 0 0
1111 −1.16036 2.00981i −0.349863 0.605981i 0.636362 0.771391i 0.280439π-0.280439\pi
−0.986225 + 0.165410i 0.947105π0.947105\pi
1212 0 0
1313 −2.35884 4.08563i −0.654224 1.13315i −0.982088 0.188424i 0.939662π-0.939662\pi
0.327864 0.944725i 0.393671π-0.393671\pi
1414 0 0
1515 1.56880 + 5.90871i 0.405062 + 1.52562i
1616 0 0
1717 −0.636946 + 1.10322i −0.154482 + 0.267571i −0.932870 0.360212i 0.882704π-0.882704\pi
0.778388 + 0.627783i 0.216038π0.216038\pi
1818 0 0
1919 −2.78386 4.82178i −0.638661 1.10619i −0.985727 0.168352i 0.946155π-0.946155\pi
0.347066 0.937841i 0.387178π-0.387178\pi
2020 0 0
2121 −3.02495 + 3.44233i −0.660099 + 0.751179i
2222 0 0
2323 −1.64855 + 2.85537i −0.343746 + 0.595386i −0.985125 0.171838i 0.945029π-0.945029\pi
0.641379 + 0.767224i 0.278363π0.278363\pi
2424 0 0
2525 −3.72899 6.45880i −0.745798 1.29176i
2626 0 0
2727 3.64901 + 3.69929i 0.702253 + 0.711928i
2828 0 0
2929 −4.32116 + 7.48447i −0.802419 + 1.38983i 0.115601 + 0.993296i 0.463121π0.463121\pi
−0.918020 + 0.396535i 0.870213π0.870213\pi
3030 0 0
3131 −8.51642 −1.52959 −0.764797 0.644272i 0.777161π-0.777161\pi
−0.764797 + 0.644272i 0.777161π0.777161\pi
3232 0 0
3333 3.88027 + 1.04921i 0.675469 + 0.182643i
3434 0 0
3535 4.11956 8.38064i 0.696332 1.41659i
3636 0 0
3737 −2.84024 4.91943i −0.466932 0.808750i 0.532354 0.846522i 0.321307π-0.321307\pi
−0.999286 + 0.0377716i 0.987974π0.987974\pi
3838 0 0
3939 7.88798 + 2.13287i 1.26309 + 0.341533i
4040 0 0
4141 1.66553 + 2.88478i 0.260112 + 0.450528i 0.966272 0.257525i 0.0829071π-0.0829071\pi
−0.706159 + 0.708053i 0.749574π0.749574\pi
4242 0 0
4343 −0.0444165 + 0.0769317i −0.00677346 + 0.0117320i −0.869392 0.494123i 0.835489π-0.835489\pi
0.862619 + 0.505855i 0.168823π0.168823\pi
4444 0 0
4545 −9.14589 5.33615i −1.36339 0.795466i
4646 0 0
4747 −7.05213 −1.02866 −0.514330 0.857593i 0.671959π-0.671959\pi
−0.514330 + 0.857593i 0.671959π0.671959\pi
4848 0 0
4949 6.93775 0.931432i 0.991108 0.133062i
5050 0 0
5151 −0.566208 2.13256i −0.0792850 0.298618i
5252 0 0
5353 3.41816 5.92042i 0.469520 0.813233i −0.529873 0.848077i 0.677760π-0.677760\pi
0.999393 + 0.0348444i 0.0110936π0.0110936\pi
5454 0 0
5555 −8.19121 −1.10450
5656 0 0
5757 9.30925 + 2.51717i 1.23304 + 0.333408i
5858 0 0
5959 7.99490 1.04085 0.520423 0.853908i 0.325774π-0.325774\pi
0.520423 + 0.853908i 0.325774π0.325774\pi
6060 0 0
6161 13.3553 1.70997 0.854985 0.518653i 0.173566π-0.173566\pi
0.854985 + 0.518653i 0.173566π0.173566\pi
6262 0 0
6363 −0.493123 7.92192i −0.0621277 0.998068i
6464 0 0
6565 −16.6514 −2.06536
6666 0 0
6767 −6.12804 −0.748660 −0.374330 0.927296i 0.622127π-0.622127\pi
−0.374330 + 0.927296i 0.622127π0.622127\pi
6868 0 0
6969 −1.46546 5.51951i −0.176421 0.664471i
7070 0 0
7171 −1.30202 −0.154522 −0.0772609 0.997011i 0.524617π-0.524617\pi
−0.0772609 + 0.997011i 0.524617π0.524617\pi
7272 0 0
7373 6.64529 11.5100i 0.777772 1.34714i −0.155451 0.987844i 0.549683π-0.549683\pi
0.933223 0.359297i 0.116984π-0.116984\pi
7474 0 0
7575 12.4698 + 3.37177i 1.43989 + 0.389338i
7676 0 0
7777 −3.41777 5.10092i −0.389491 0.581303i
7878 0 0
7979 10.0281 1.12824 0.564122 0.825691i 0.309215π-0.309215\pi
0.564122 + 0.825691i 0.309215π0.309215\pi
8080 0 0
8181 −8.99963 0.0820978i −0.999958 0.00912197i
8282 0 0
8383 5.90243 10.2233i 0.647876 1.12215i −0.335753 0.941950i 0.608991π-0.608991\pi
0.983629 0.180204i 0.0576758π-0.0576758\pi
8484 0 0
8585 2.24815 + 3.89392i 0.243847 + 0.422355i
8686 0 0
8787 −3.84126 14.4677i −0.411826 1.55110i
8888 0 0
8989 0.561496 + 0.972540i 0.0595185 + 0.103089i 0.894249 0.447569i 0.147710π-0.147710\pi
−0.834731 + 0.550658i 0.814377π0.814377\pi
9090 0 0
9191 −6.94778 10.3694i −0.728325 1.08700i
9292 0 0
9393 10.4542 10.4066i 1.08405 1.07912i
9494 0 0
9595 −19.6517 −2.01622
9696 0 0
9797 −3.50818 + 6.07635i −0.356202 + 0.616960i −0.987323 0.158724i 0.949262π-0.949262\pi
0.631121 + 0.775685i 0.282595π0.282595\pi
9898 0 0
9999 −6.04525 + 3.45356i −0.607570 + 0.347096i
100100 0 0
101101 4.87055 + 8.43605i 0.484638 + 0.839418i 0.999844 0.0176482i 0.00561789π-0.00561789\pi
−0.515206 + 0.857066i 0.672285π0.672285\pi
102102 0 0
103103 5.14279 8.90757i 0.506734 0.877689i −0.493236 0.869896i 0.664186π-0.664186\pi
0.999970 0.00779301i 0.00248062π-0.00248062\pi
104104 0 0
105105 5.18381 + 15.3214i 0.505888 + 1.49522i
106106 0 0
107107 −2.72201 4.71465i −0.263146 0.455783i 0.703930 0.710269i 0.251427π-0.251427\pi
−0.967076 + 0.254487i 0.918094π0.918094\pi
108108 0 0
109109 0.417404 0.722965i 0.0399800 0.0692475i −0.845343 0.534224i 0.820604π-0.820604\pi
0.885323 + 0.464977i 0.153937π0.153937\pi
110110 0 0
111111 9.49778 + 2.56815i 0.901490 + 0.243758i
112112 0 0
113113 5.44881 + 9.43761i 0.512581 + 0.887815i 0.999894 + 0.0145882i 0.00464372π0.00464372\pi
−0.487313 + 0.873227i 0.662023π0.662023\pi
114114 0 0
115115 5.81870 + 10.0783i 0.542596 + 0.939804i
116116 0 0
117117 −12.2890 + 7.02054i −1.13612 + 0.649049i
118118 0 0
119119 −1.48682 + 3.02472i −0.136297 + 0.277276i
120120 0 0
121121 2.80711 4.86205i 0.255192 0.442005i
122122 0 0
123123 −5.56956 1.50598i −0.502190 0.135790i
124124 0 0
125125 −8.67565 −0.775974
126126 0 0
127127 9.90354 0.878797 0.439399 0.898292i 0.355192π-0.355192\pi
0.439399 + 0.898292i 0.355192π0.355192\pi
128128 0 0
129129 −0.0394837 0.148711i −0.00347635 0.0130933i
130130 0 0
131131 8.59220 14.8821i 0.750704 1.30026i −0.196778 0.980448i 0.563048π-0.563048\pi
0.947482 0.319809i 0.103619π-0.103619\pi
132132 0 0
133133 −8.19964 12.2377i −0.710999 1.06115i
134134 0 0
135135 17.7474 4.62550i 1.52745 0.398100i
136136 0 0
137137 8.04696 + 13.9377i 0.687498 + 1.19078i 0.972645 + 0.232298i 0.0746243π0.0746243\pi
−0.285147 + 0.958484i 0.592042π0.592042\pi
138138 0 0
139139 −1.11151 1.92519i −0.0942768 0.163292i 0.815030 0.579419i 0.196721π-0.196721\pi
−0.909307 + 0.416127i 0.863387π0.863387\pi
140140 0 0
141141 8.65674 8.61735i 0.729029 0.725711i
142142 0 0
143143 −5.47422 + 9.48163i −0.457778 + 0.792894i
144144 0 0
145145 15.2519 + 26.4171i 1.26660 + 2.19382i
146146 0 0
147147 −7.37817 + 9.62094i −0.608541 + 0.793522i
148148 0 0
149149 −3.46846 + 6.00755i −0.284147 + 0.492158i −0.972402 0.233312i 0.925044π-0.925044\pi
0.688255 + 0.725469i 0.258377π0.258377\pi
150150 0 0
151151 7.75834 + 13.4378i 0.631365 + 1.09356i 0.987273 + 0.159035i 0.0508383π0.0508383\pi
−0.355908 + 0.934521i 0.615828π0.615828\pi
152152 0 0
153153 3.30092 + 1.92591i 0.266863 + 0.155701i
154154 0 0
155155 −15.0297 + 26.0322i −1.20722 + 2.09096i
156156 0 0
157157 0.802110 0.0640154 0.0320077 0.999488i 0.489810π-0.489810\pi
0.0320077 + 0.999488i 0.489810π0.489810\pi
158158 0 0
159159 3.03855 + 11.4443i 0.240972 + 0.907595i
160160 0 0
161161 −3.84821 + 7.82862i −0.303281 + 0.616982i
162162 0 0
163163 −1.77500 3.07438i −0.139028 0.240804i 0.788101 0.615546i 0.211065π-0.211065\pi
−0.927129 + 0.374742i 0.877731π0.877731\pi
164164 0 0
165165 10.0550 10.0092i 0.782781 0.779219i
166166 0 0
167167 −0.865131 1.49845i −0.0669459 0.115954i 0.830610 0.556855i 0.187992π-0.187992\pi
−0.897556 + 0.440901i 0.854659π0.854659\pi
168168 0 0
169169 −4.62823 + 8.01633i −0.356018 + 0.616641i
170170 0 0
171171 −14.5033 + 8.28551i −1.10909 + 0.633609i
172172 0 0
173173 2.23458 0.169892 0.0849462 0.996386i 0.472928π-0.472928\pi
0.0849462 + 0.996386i 0.472928π0.472928\pi
174174 0 0
175175 −10.9835 16.3925i −0.830272 1.23916i
176176 0 0
177177 −9.81401 + 9.76935i −0.737666 + 0.734309i
178178 0 0
179179 0.350412 0.606931i 0.0261910 0.0453641i −0.852633 0.522511i 0.824996π-0.824996\pi
0.878824 + 0.477146i 0.158329π0.158329\pi
180180 0 0
181181 −19.6339 −1.45938 −0.729688 0.683780i 0.760335π-0.760335\pi
−0.729688 + 0.683780i 0.760335π0.760335\pi
182182 0 0
183183 −16.3941 + 16.3195i −1.21189 + 1.20637i
184184 0 0
185185 −20.0497 −1.47408
186186 0 0
187187 2.95636 0.216190
188188 0 0
189189 10.2855 + 9.12186i 0.748160 + 0.663518i
190190 0 0
191191 −16.0858 −1.16393 −0.581963 0.813215i 0.697715π-0.697715\pi
−0.581963 + 0.813215i 0.697715π0.697715\pi
192192 0 0
193193 −0.585463 −0.0421426 −0.0210713 0.999778i 0.506708π-0.506708\pi
−0.0210713 + 0.999778i 0.506708π0.506708\pi
194194 0 0
195195 20.4402 20.3472i 1.46375 1.45709i
196196 0 0
197197 −17.2923 −1.23203 −0.616014 0.787735i 0.711254π-0.711254\pi
−0.616014 + 0.787735i 0.711254π0.711254\pi
198198 0 0
199199 12.2119 21.1517i 0.865681 1.49940i −0.000687656 1.00000i 0.500219π-0.500219\pi
0.866369 0.499404i 0.166448π-0.166448\pi
200200 0 0
201201 7.52239 7.48815i 0.530588 0.528174i
202202 0 0
203203 −10.0869 + 20.5203i −0.707960 + 1.44024i
204204 0 0
205205 11.7573 0.821164
206206 0 0
207207 8.54347 + 4.98467i 0.593812 + 0.346458i
208208 0 0
209209 −6.46058 + 11.1900i −0.446888 + 0.774032i
210210 0 0
211211 5.58733 + 9.67754i 0.384648 + 0.666230i 0.991720 0.128417i 0.0409895π-0.0409895\pi
−0.607072 + 0.794647i 0.707656π0.707656\pi
212212 0 0
213213 1.59828 1.59101i 0.109512 0.109014i
214214 0 0
215215 0.156772 + 0.271537i 0.0106918 + 0.0185187i
216216 0 0
217217 −22.4822 + 1.50244i −1.52619 + 0.101992i
218218 0 0
219219 5.90728 + 22.2491i 0.399177 + 1.50345i
220220 0 0
221221 6.00981 0.404263
222222 0 0
223223 1.32951 2.30277i 0.0890303 0.154205i −0.818071 0.575117i 0.804957π-0.804957\pi
0.907101 + 0.420912i 0.138290π0.138290\pi
224224 0 0
225225 −19.4272 + 11.0985i −1.29515 + 0.739898i
226226 0 0
227227 5.95786 + 10.3193i 0.395437 + 0.684917i 0.993157 0.116788i 0.0372598π-0.0372598\pi
−0.597720 + 0.801705i 0.703927π0.703927\pi
228228 0 0
229229 14.8064 25.6454i 0.978434 1.69470i 0.310330 0.950629i 0.399561π-0.399561\pi
0.668104 0.744068i 0.267106π-0.267106\pi
230230 0 0
231231 10.4285 + 2.08522i 0.686144 + 0.137197i
232232 0 0
233233 1.84417 + 3.19420i 0.120816 + 0.209259i 0.920090 0.391708i 0.128116π-0.128116\pi
−0.799274 + 0.600967i 0.794782π0.794782\pi
234234 0 0
235235 −12.4456 + 21.5563i −0.811859 + 1.40618i
236236 0 0
237237 −12.3098 + 12.2538i −0.799607 + 0.795968i
238238 0 0
239239 −8.03590 13.9186i −0.519799 0.900319i −0.999735 0.0230153i 0.992673π-0.992673\pi
0.479936 0.877304i 0.340660π-0.340660\pi
240240 0 0
241241 −2.24933 3.89596i −0.144892 0.250961i 0.784440 0.620204i 0.212950π-0.212950\pi
−0.929333 + 0.369243i 0.879617π0.879617\pi
242242 0 0
243243 11.1477 10.8963i 0.715124 0.698998i
244244 0 0
245245 9.39658 22.8505i 0.600326 1.45986i
246246 0 0
247247 −13.1333 + 22.7476i −0.835654 + 1.44740i
248248 0 0
249249 5.24692 + 19.7619i 0.332510 + 1.25236i
250250 0 0
251251 17.2696 1.09005 0.545023 0.838421i 0.316521π-0.316521\pi
0.545023 + 0.838421i 0.316521π0.316521\pi
252252 0 0
253253 7.65167 0.481057
254254 0 0
255255 −7.51786 2.03279i −0.470786 0.127298i
256256 0 0
257257 −2.41087 + 4.17574i −0.150386 + 0.260476i −0.931369 0.364076i 0.881385π-0.881385\pi
0.780984 + 0.624552i 0.214718π0.214718\pi
258258 0 0
259259 −8.36571 12.4856i −0.519820 0.775815i
260260 0 0
261261 22.3940 + 13.0658i 1.38616 + 0.808750i
262262 0 0
263263 14.0452 + 24.3270i 0.866062 + 1.50006i 0.865988 + 0.500064i 0.166690π0.166690\pi
7.41948e−5 1.00000i 0.499976π0.499976\pi
264264 0 0
265265 −12.0647 20.8966i −0.741128 1.28367i
266266 0 0
267267 −1.87765 0.507707i −0.114910 0.0310712i
268268 0 0
269269 12.4126 21.4993i 0.756810 1.31083i −0.187659 0.982234i 0.560090π-0.560090\pi
0.944469 0.328599i 0.106577π-0.106577\pi
270270 0 0
271271 4.79671 + 8.30815i 0.291379 + 0.504684i 0.974136 0.225962i 0.0725524π-0.0725524\pi
−0.682757 + 0.730646i 0.739219π0.739219\pi
272272 0 0
273273 21.1995 + 4.23891i 1.28305 + 0.256551i
274274 0 0
275275 −8.65398 + 14.9891i −0.521854 + 0.903878i
276276 0 0
277277 −8.46914 14.6690i −0.508862 0.881374i −0.999947 0.0102629i 0.996733π-0.996733\pi
0.491086 0.871111i 0.336600π-0.336600\pi
278278 0 0
279279 −0.116531 + 25.5490i −0.00697653 + 1.52958i
280280 0 0
281281 11.4291 19.7958i 0.681805 1.18092i −0.292625 0.956227i 0.594529π-0.594529\pi
0.974430 0.224693i 0.0721379π-0.0721379\pi
282282 0 0
283283 −8.35621 −0.496725 −0.248363 0.968667i 0.579892π-0.579892\pi
−0.248363 + 0.968667i 0.579892π0.579892\pi
284284 0 0
285285 24.1232 24.0134i 1.42893 1.42243i
286286 0 0
287287 4.90570 + 7.32161i 0.289574 + 0.432181i
288288 0 0
289289 7.68860 + 13.3170i 0.452271 + 0.783356i
290290 0 0
291291 −3.11857 11.7458i −0.182814 0.688549i
292292 0 0
293293 −2.16141 3.74368i −0.126271 0.218708i 0.795958 0.605352i 0.206968π-0.206968\pi
−0.922229 + 0.386644i 0.873634π0.873634\pi
294294 0 0
295295 14.1093 24.4381i 0.821477 1.42284i
296296 0 0
297297 3.20068 11.6263i 0.185722 0.674629i
298298 0 0
299299 15.5546 0.899548
300300 0 0
301301 −0.103682 + 0.210925i −0.00597610 + 0.0121575i
302302 0 0
303303 −16.2872 4.40397i −0.935675 0.253002i
304304 0 0
305305 23.5693 40.8233i 1.34958 2.33753i
306306 0 0
307307 9.22888 0.526720 0.263360 0.964698i 0.415169π-0.415169\pi
0.263360 + 0.964698i 0.415169π0.415169\pi
308308 0 0
309309 4.57164 + 17.2186i 0.260072 + 0.979530i
310310 0 0
311311 19.1073 1.08348 0.541738 0.840548i 0.317767π-0.317767\pi
0.541738 + 0.840548i 0.317767π0.317767\pi
312312 0 0
313313 5.67903 0.320997 0.160499 0.987036i 0.448690π-0.448690\pi
0.160499 + 0.987036i 0.448690π0.448690\pi
314314 0 0
315315 −25.0853 12.4732i −1.41340 0.702786i
316316 0 0
317317 −28.2681 −1.58770 −0.793848 0.608116i 0.791925π-0.791925\pi
−0.793848 + 0.608116i 0.791925π0.791925\pi
318318 0 0
319319 20.0565 1.12295
320320 0 0
321321 9.10242 + 2.46125i 0.508048 + 0.137373i
322322 0 0
323323 7.09266 0.394646
324324 0 0
325325 −17.5922 + 30.4705i −0.975838 + 1.69020i
326326 0 0
327327 0.371048 + 1.39751i 0.0205190 + 0.0772825i
328328 0 0
329329 −18.6167 + 1.24411i −1.02637 + 0.0685902i
330330 0 0
331331 6.68091 0.367216 0.183608 0.983000i 0.441222π-0.441222\pi
0.183608 + 0.983000i 0.441222π0.441222\pi
332332 0 0
333333 −14.7970 + 8.45331i −0.810871 + 0.463238i
334334 0 0
335335 −10.8147 + 18.7317i −0.590872 + 1.02342i
336336 0 0
337337 −3.49421 6.05215i −0.190342 0.329681i 0.755022 0.655700i 0.227626π-0.227626\pi
−0.945363 + 0.326018i 0.894293π0.894293\pi
338338 0 0
339339 −18.2209 4.92683i −0.989622 0.267589i
340340 0 0
341341 9.88215 + 17.1164i 0.535148 + 0.926904i
342342 0 0
343343 18.1504 3.68279i 0.980030 0.198852i
344344 0 0
345345 −19.4578 5.26129i −1.04757 0.283258i
346346 0 0
347347 −8.28821 −0.444934 −0.222467 0.974940i 0.571411π-0.571411\pi
−0.222467 + 0.974940i 0.571411π0.571411\pi
348348 0 0
349349 3.05373 5.28921i 0.163462 0.283125i −0.772646 0.634837i 0.781067π-0.781067\pi
0.936108 + 0.351712i 0.114400π0.114400\pi
350350 0 0
351351 6.50648 23.6345i 0.347290 1.26152i
352352 0 0
353353 13.3604 + 23.1409i 0.711104 + 1.23167i 0.964443 + 0.264290i 0.0851377π0.0851377\pi
−0.253340 + 0.967377i 0.581529π0.581529\pi
354354 0 0
355355 −2.29780 + 3.97991i −0.121955 + 0.211232i
356356 0 0
357357 −1.87093 5.52977i −0.0990201 0.292667i
358358 0 0
359359 −2.45603 4.25397i −0.129624 0.224516i 0.793907 0.608040i 0.208044π-0.208044\pi
−0.923531 + 0.383523i 0.874711π0.874711\pi
360360 0 0
361361 −5.99972 + 10.3918i −0.315775 + 0.546938i
362362 0 0
363363 2.49536 + 9.39848i 0.130972 + 0.493292i
364364 0 0
365365 −23.4551 40.6255i −1.22770 2.12643i
366366 0 0
367367 −15.3532 26.5925i −0.801430 1.38812i −0.918675 0.395015i 0.870740π-0.870740\pi
0.117245 0.993103i 0.462594π-0.462594\pi
368368 0 0
369369 8.67705 4.95707i 0.451709 0.258055i
370370 0 0
371371 7.97901 16.2321i 0.414250 0.842730i
372372 0 0
373373 −8.29190 + 14.3620i −0.429338 + 0.743635i −0.996815 0.0797543i 0.974586π-0.974586\pi
0.567477 + 0.823390i 0.307920π0.307920\pi
374374 0 0
375375 10.6497 10.6012i 0.549946 0.547443i
376376 0 0
377377 40.7716 2.09985
378378 0 0
379379 −4.08857 −0.210016 −0.105008 0.994471i 0.533487π-0.533487\pi
−0.105008 + 0.994471i 0.533487π0.533487\pi
380380 0 0
381381 −12.1569 + 12.1016i −0.622819 + 0.619985i
382382 0 0
383383 15.1769 26.2871i 0.775503 1.34321i −0.159009 0.987277i 0.550830π-0.550830\pi
0.934511 0.355933i 0.115837π-0.115837\pi
384384 0 0
385385 −21.6237 + 1.44507i −1.10205 + 0.0736474i
386386 0 0
387387 0.230185 + 0.134301i 0.0117010 + 0.00682690i
388388 0 0
389389 1.73382 + 3.00307i 0.0879082 + 0.152261i 0.906627 0.421934i 0.138648π-0.138648\pi
−0.818719 + 0.574195i 0.805315π0.805315\pi
390390 0 0
391391 −2.10007 3.63743i −0.106205 0.183953i
392392 0 0
393393 7.63797 + 28.7675i 0.385285 + 1.45113i
394394 0 0
395395 17.6974 30.6529i 0.890455 1.54231i
396396 0 0
397397 −7.04243 12.1979i −0.353450 0.612193i 0.633402 0.773823i 0.281658π-0.281658\pi
−0.986851 + 0.161630i 0.948325π0.948325\pi
398398 0 0
399399 25.0192 + 5.00269i 1.25253 + 0.250448i
400400 0 0
401401 5.46593 9.46726i 0.272955 0.472772i −0.696662 0.717400i 0.745332π-0.745332\pi
0.969617 + 0.244627i 0.0786656π0.0786656\pi
402402 0 0
403403 20.0888 + 34.7949i 1.00070 + 1.73326i
404404 0 0
405405 −16.1334 + 27.3644i −0.801676 + 1.35975i
406406 0 0
407407 −6.59142 + 11.4167i −0.326725 + 0.565904i
408408 0 0
409409 15.9879 0.790553 0.395276 0.918562i 0.370649π-0.370649\pi
0.395276 + 0.918562i 0.370649π0.370649\pi
410410 0 0
411411 −26.9091 7.27609i −1.32733 0.358903i
412412 0 0
413413 21.1054 1.41043i 1.03853 0.0694029i
414414 0 0
415415 −20.8331 36.0841i −1.02266 1.77130i
416416 0 0
417417 3.71689 + 1.00503i 0.182017 + 0.0492165i
418418 0 0
419419 3.56197 + 6.16951i 0.174014 + 0.301400i 0.939819 0.341671i 0.110993π-0.110993\pi
−0.765806 + 0.643072i 0.777660π0.777660\pi
420420 0 0
421421 −16.6326 + 28.8086i −0.810625 + 1.40404i 0.101802 + 0.994805i 0.467539π0.467539\pi
−0.912427 + 0.409239i 0.865794π0.865794\pi
422422 0 0
423423 −0.0964951 + 21.1562i −0.00469175 + 1.02865i
424424 0 0
425425 9.50066 0.460849
426426 0 0
427427 35.2561 2.35610i 1.70616 0.114019i
428428 0 0
429429 −4.86627 18.3283i −0.234946 0.884897i
430430 0 0
431431 2.62382 4.54459i 0.126385 0.218905i −0.795889 0.605443i 0.792996π-0.792996\pi
0.922273 + 0.386538i 0.126329π0.126329\pi
432432 0 0
433433 22.1053 1.06231 0.531156 0.847274i 0.321758π-0.321758\pi
0.531156 + 0.847274i 0.321758π0.321758\pi
434434 0 0
435435 −51.0025 13.7908i −2.44538 0.661220i
436436 0 0
437437 18.3573 0.878149
438438 0 0
439439 −34.6165 −1.65216 −0.826079 0.563555i 0.809433π-0.809433\pi
−0.826079 + 0.563555i 0.809433π0.809433\pi
440440 0 0
441441 −2.69934 20.8258i −0.128540 0.991704i
442442 0 0
443443 4.40923 0.209489 0.104744 0.994499i 0.466598π-0.466598\pi
0.104744 + 0.994499i 0.466598π0.466598\pi
444444 0 0
445445 3.96370 0.187897
446446 0 0
447447 −3.08326 11.6128i −0.145833 0.549265i
448448 0 0
449449 −19.6336 −0.926568 −0.463284 0.886210i 0.653329π-0.653329\pi
−0.463284 + 0.886210i 0.653329π0.653329\pi
450450 0 0
451451 3.86525 6.69481i 0.182007 0.315246i
452452 0 0
453453 −25.9440 7.01512i −1.21895 0.329599i
454454 0 0
455455 −43.9575 + 2.93759i −2.06076 + 0.137716i
456456 0 0
457457 −30.8392 −1.44259 −0.721297 0.692626i 0.756454π-0.756454\pi
−0.721297 + 0.692626i 0.756454π0.756454\pi
458458 0 0
459459 −6.40536 + 1.66943i −0.298976 + 0.0779221i
460460 0 0
461461 −13.6297 + 23.6074i −0.634800 + 1.09951i 0.351757 + 0.936091i 0.385584π0.385584\pi
−0.986557 + 0.163415i 0.947749π0.947749\pi
462462 0 0
463463 0.959750 + 1.66234i 0.0446034 + 0.0772553i 0.887465 0.460875i 0.152464π-0.152464\pi
−0.842862 + 0.538130i 0.819131π0.819131\pi
464464 0 0
465465 −13.3605 50.3210i −0.619581 2.33358i
466466 0 0
467467 −4.88655 8.46376i −0.226123 0.391656i 0.730533 0.682877i 0.239272π-0.239272\pi
−0.956656 + 0.291221i 0.905938π0.905938\pi
468468 0 0
469469 −16.1772 + 1.08109i −0.746994 + 0.0499201i
470470 0 0
471471 −0.984618 + 0.980138i −0.0453688 + 0.0451624i
472472 0 0
473473 0.206158 0.00947913
474474 0 0
475475 −20.7619 + 35.9607i −0.952623 + 1.64999i
476476 0 0
477477 −17.7143 10.3354i −0.811083 0.473225i
478478 0 0
479479 7.68809 + 13.3162i 0.351278 + 0.608431i 0.986474 0.163920i 0.0524139π-0.0524139\pi
−0.635196 + 0.772351i 0.719081π0.719081\pi
480480 0 0
481481 −13.3993 + 23.2083i −0.610956 + 1.05821i
482482 0 0
483483 −4.84236 14.3122i −0.220335 0.651228i
484484 0 0
485485 12.3824 + 21.4470i 0.562258 + 0.973859i
486486 0 0
487487 −5.18342 + 8.97794i −0.234883 + 0.406829i −0.959239 0.282597i 0.908804π-0.908804\pi
0.724356 + 0.689427i 0.242137π0.242137\pi
488488 0 0
489489 5.93561 + 1.60496i 0.268418 + 0.0725788i
490490 0 0
491491 6.94718 + 12.0329i 0.313522 + 0.543035i 0.979122 0.203273i 0.0651578π-0.0651578\pi
−0.665600 + 0.746308i 0.731825π0.731825\pi
492492 0 0
493493 −5.50469 9.53440i −0.247919 0.429408i
494494 0 0
495495 −0.112081 + 24.5734i −0.00503768 + 1.10449i
496496 0 0
497497 −3.43717 + 0.229699i −0.154178 + 0.0103034i
498498 0 0
499499 −1.70488 + 2.95294i −0.0763210 + 0.132192i −0.901660 0.432446i 0.857651π-0.857651\pi
0.825339 + 0.564638i 0.190984π0.190984\pi
500500 0 0
501501 2.89301 + 0.782255i 0.129250 + 0.0349486i
502502 0 0
503503 −43.8911 −1.95701 −0.978504 0.206227i 0.933881π-0.933881\pi
−0.978504 + 0.206227i 0.933881π0.933881\pi
504504 0 0
505505 34.3821 1.52998
506506 0 0
507507 −4.11423 15.4958i −0.182719 0.688192i
508508 0 0
509509 −19.6674 + 34.0649i −0.871742 + 1.50990i −0.0115483 + 0.999933i 0.503676π0.503676\pi
−0.860193 + 0.509968i 0.829657π0.829657\pi
510510 0 0
511511 15.5121 31.5571i 0.686215 1.39600i
512512 0 0
513513 7.67882 27.8930i 0.339028 1.23151i
514514 0 0
515515 −18.1519 31.4400i −0.799869 1.38541i
516516 0 0
517517 8.18305 + 14.1735i 0.359890 + 0.623348i
518518 0 0
519519 −2.74303 + 2.73055i −0.120406 + 0.119858i
520520 0 0
521521 12.4779 21.6124i 0.546669 0.946858i −0.451831 0.892104i 0.649229π-0.649229\pi
0.998500 0.0547547i 0.0174377π-0.0174377\pi
522522 0 0
523523 15.1575 + 26.2536i 0.662792 + 1.14799i 0.979879 + 0.199594i 0.0639622π0.0639622\pi
−0.317086 + 0.948397i 0.602704π0.602704\pi
524524 0 0
525525 33.5134 + 6.70112i 1.46264 + 0.292461i
526526 0 0
527527 5.42449 9.39550i 0.236295 0.409274i
528528 0 0
529529 6.06457 + 10.5041i 0.263677 + 0.456702i
530530 0 0
531531 0.109395 23.9844i 0.00474734 1.04084i
532532 0 0
533533 7.85744 13.6095i 0.340343 0.589492i
534534 0 0
535535 −19.2151 −0.830742
536536 0 0
537537 0.311496 + 1.17321i 0.0134420 + 0.0506279i
538538 0 0
539539 −9.92233 12.8628i −0.427385 0.554039i
540540 0 0
541541 −14.2812 24.7357i −0.613996 1.06347i −0.990560 0.137082i 0.956228π-0.956228\pi
0.376563 0.926391i 0.377106π-0.377106\pi
542542 0 0
543543 24.1013 23.9916i 1.03429 1.02958i
544544 0 0
545545 −1.47326 2.55177i −0.0631077 0.109306i
546546 0 0
547547 −3.89233 + 6.74171i −0.166424 + 0.288255i −0.937160 0.348900i 0.886555π-0.886555\pi
0.770736 + 0.637154i 0.219889π0.219889\pi
548548 0 0
549549 0.182742 40.0654i 0.00779923 1.70995i
550550 0 0
551551 48.1179 2.04989
552552 0 0
553553 26.4727 1.76912i 1.12573 0.0752305i
554554 0 0
555555 24.6117 24.4997i 1.04471 1.03996i
556556 0 0
557557 −23.2470 + 40.2650i −0.985008 + 1.70608i −0.343108 + 0.939296i 0.611480π0.611480\pi
−0.641900 + 0.766788i 0.721854π0.721854\pi
558558 0 0
559559 0.419086 0.0177254
560560 0 0
561561 −3.62903 + 3.61252i −0.153218 + 0.152521i
562562 0 0
563563 −27.9826 −1.17933 −0.589663 0.807650i 0.700739π-0.700739\pi
−0.589663 + 0.807650i 0.700739π0.700739\pi
564564 0 0
565565 38.4641 1.61820
566566 0 0
567567 −23.7723 + 1.37096i −0.998341 + 0.0575748i
568568 0 0
569569 8.89957 0.373090 0.186545 0.982446i 0.440271π-0.440271\pi
0.186545 + 0.982446i 0.440271π0.440271\pi
570570 0 0
571571 32.3304 1.35298 0.676492 0.736450i 0.263500π-0.263500\pi
0.676492 + 0.736450i 0.263500π0.263500\pi
572572 0 0
573573 19.7459 19.6560i 0.824895 0.821141i
574574 0 0
575575 24.5897 1.02546
576576 0 0
577577 −16.8414 + 29.1701i −0.701115 + 1.21437i 0.266960 + 0.963707i 0.413981π0.413981\pi
−0.968075 + 0.250659i 0.919353π0.919353\pi
578578 0 0
579579 0.718676 0.715406i 0.0298672 0.0297313i
580580 0 0
581581 13.7780 28.0294i 0.571610 1.16286i
582582 0 0
583583 −15.8652 −0.657071
584584 0 0
585585 −0.227843 + 49.9538i −0.00942016 + 2.06534i
586586 0 0
587587 1.24076 2.14907i 0.0512118 0.0887015i −0.839283 0.543695i 0.817025π-0.817025\pi
0.890495 + 0.454993i 0.150358π0.150358\pi
588588 0 0
589589 23.7085 + 41.0643i 0.976891 + 1.69202i
590590 0 0
591591 21.2270 21.1304i 0.873160 0.869187i
592592 0 0
593593 −15.0903 26.1371i −0.619684 1.07332i −0.989543 0.144236i 0.953928π-0.953928\pi
0.369859 0.929088i 0.379406π-0.379406\pi
594594 0 0
595595 6.62177 + 9.88280i 0.271466 + 0.405155i
596596 0 0
597597 10.8557 + 40.8868i 0.444295 + 1.67339i
598598 0 0
599599 16.4083 0.670424 0.335212 0.942143i 0.391192π-0.391192\pi
0.335212 + 0.942143i 0.391192π0.391192\pi
600600 0 0
601601 −2.96998 + 5.14416i −0.121148 + 0.209835i −0.920221 0.391400i 0.871991π-0.871991\pi
0.799073 + 0.601235i 0.205324π0.205324\pi
602602 0 0
603603 −0.0838506 + 18.3839i −0.00341466 + 0.748652i
604604 0 0
605605 −9.90793 17.1610i −0.402815 0.697695i
606606 0 0
607607 −2.97573 + 5.15412i −0.120781 + 0.209199i −0.920076 0.391740i 0.871873π-0.871873\pi
0.799295 + 0.600939i 0.205207π0.205207\pi
608608 0 0
609609 −12.6927 37.5150i −0.514336 1.52019i
610610 0 0
611611 16.6348 + 28.8124i 0.672974 + 1.16562i
612612 0 0
613613 15.5920 27.0062i 0.629756 1.09077i −0.357845 0.933781i 0.616488π-0.616488\pi
0.987601 0.156988i 0.0501783π-0.0501783\pi
614614 0 0
615615 −14.4325 + 14.3668i −0.581973 + 0.579325i
616616 0 0
617617 −11.1437 19.3014i −0.448627 0.777045i 0.549670 0.835382i 0.314754π-0.314754\pi
−0.998297 + 0.0583367i 0.981420π0.981420\pi
618618 0 0
619619 17.2943 + 29.9547i 0.695118 + 1.20398i 0.970141 + 0.242543i 0.0779814π0.0779814\pi
−0.275022 + 0.961438i 0.588685π0.588685\pi
620620 0 0
621621 −16.5784 + 4.32083i −0.665269 + 0.173389i
622622 0 0
623623 1.65384 + 2.46831i 0.0662599 + 0.0988909i
624624 0 0
625625 3.33422 5.77504i 0.133369 0.231002i
626626 0 0
627627 −5.74308 21.6307i −0.229357 0.863846i
628628 0 0
629629 7.23631 0.288530
630630 0 0
631631 26.2933 1.04672 0.523360 0.852112i 0.324678π-0.324678\pi
0.523360 + 0.852112i 0.324678π0.324678\pi
632632 0 0
633633 −18.6841 5.05209i −0.742627 0.200802i
634634 0 0
635635 17.4777 30.2723i 0.693582 1.20132i
636636 0 0
637637 −20.1705 26.1480i −0.799185 1.03602i
638638 0 0
639639 −0.0178157 + 3.90603i −0.000704779 + 0.154520i
640640 0 0
641641 16.2673 + 28.1758i 0.642519 + 1.11288i 0.984869 + 0.173303i 0.0554441π0.0554441\pi
−0.342349 + 0.939573i 0.611223π0.611223\pi
642642 0 0
643643 −5.21987 9.04107i −0.205851 0.356545i 0.744552 0.667564i 0.232663π-0.232663\pi
−0.950404 + 0.311019i 0.899330π0.899330\pi
644644 0 0
645645 −0.524247 0.141754i −0.0206422 0.00558155i
646646 0 0
647647 −0.685824 + 1.18788i −0.0269625 + 0.0467005i −0.879192 0.476468i 0.841917π-0.841917\pi
0.852229 + 0.523168i 0.175250π0.175250\pi
648648 0 0
649649 −9.27699 16.0682i −0.364154 0.630733i
650650 0 0
651651 25.7617 29.3164i 1.00968 1.14900i
652652 0 0
653653 3.62567 6.27985i 0.141883 0.245749i −0.786322 0.617816i 0.788018π-0.788018\pi
0.928206 + 0.372067i 0.121351π0.121351\pi
654654 0 0
655655 −30.3269 52.5277i −1.18497 2.05243i
656656 0 0
657657 −34.4386 20.0931i −1.34358 0.783908i
658658 0 0
659659 13.3187 23.0686i 0.518822 0.898626i −0.480939 0.876754i 0.659704π-0.659704\pi
0.999761 0.0218722i 0.00696268π-0.00696268\pi
660660 0 0
661661 −34.8199 −1.35434 −0.677168 0.735828i 0.736793π-0.736793\pi
−0.677168 + 0.735828i 0.736793π0.736793\pi
662662 0 0
663663 −7.37725 + 7.34367i −0.286508 + 0.285205i
664664 0 0
665665 −51.8779 + 3.46689i −2.01174 + 0.134440i
666666 0 0
667667 −14.2473 24.6770i −0.551657 0.955498i
668668 0 0
669669 1.18185 + 4.45132i 0.0456931 + 0.172098i
670670 0 0
671671 −15.4970 26.8416i −0.598255 1.03621i
672672 0 0
673673 8.23841 14.2693i 0.317567 0.550043i −0.662412 0.749139i 0.730467π-0.730467\pi
0.979980 + 0.199096i 0.0638007π0.0638007\pi
674674 0 0
675675 10.2858 37.3628i 0.395901 1.43810i
676676 0 0
677677 −21.1654 −0.813450 −0.406725 0.913551i 0.633329π-0.633329\pi
−0.406725 + 0.913551i 0.633329π0.633329\pi
678678 0 0
679679 −8.18916 + 16.6596i −0.314271 + 0.639339i
680680 0 0
681681 −19.9231 5.38712i −0.763457 0.206435i
682682 0 0
683683 −14.0756 + 24.3796i −0.538587 + 0.932859i 0.460394 + 0.887715i 0.347708π0.347708\pi
−0.998980 + 0.0451447i 0.985625π0.985625\pi
684684 0 0
685685 56.8049 2.17040
686686 0 0
687687 13.1620 + 49.5733i 0.502163 + 1.89134i
688688 0 0
689689 −32.2515 −1.22869
690690 0 0
691691 −19.0796 −0.725822 −0.362911 0.931824i 0.618217π-0.618217\pi
−0.362911 + 0.931824i 0.618217π0.618217\pi
692692 0 0
693693 −15.3494 + 10.1834i −0.583074 + 0.386835i
694694 0 0
695695 −7.84632 −0.297628
696696 0 0
697697 −4.24341 −0.160731
698698 0 0
699699 −6.16694 1.66751i −0.233255 0.0630710i
700700 0 0
701701 23.8508 0.900834 0.450417 0.892818i 0.351275π-0.351275\pi
0.450417 + 0.892818i 0.351275π0.351275\pi
702702 0 0
703703 −15.8136 + 27.3900i −0.596422 + 1.03303i
704704 0 0
705705 −11.0634 41.6690i −0.416671 1.56934i
706706 0 0
707707 14.3459 + 21.4108i 0.539532 + 0.805235i
708708 0 0
709709 20.0986 0.754817 0.377409 0.926047i 0.376815π-0.376815\pi
0.377409 + 0.926047i 0.376815π0.376815\pi
710710 0 0
711711 0.137215 30.0839i 0.00514596 1.12823i
712712 0 0
713713 14.0397 24.3175i 0.525792 0.910698i
714714 0 0
715715 19.3217 + 33.4662i 0.722592 + 1.25157i
716716 0 0
717717 26.8722 + 7.26610i 1.00356 + 0.271357i
718718 0 0
719719 3.29246 + 5.70270i 0.122788 + 0.212675i 0.920866 0.389879i 0.127483π-0.127483\pi
−0.798078 + 0.602554i 0.794150π0.794150\pi
720720 0 0
721721 12.0048 24.4220i 0.447082 0.909524i
722722 0 0
723723 7.52180 + 2.03386i 0.279739 + 0.0756399i
724724 0 0
725725 64.4542 2.39377
726726 0 0
727727 −18.2342 + 31.5826i −0.676269 + 1.17133i 0.299827 + 0.953994i 0.403071π0.403071\pi
−0.976096 + 0.217339i 0.930262π0.930262\pi
728728 0 0
729729 −0.369433 + 26.9975i −0.0136827 + 0.999906i
730730 0 0
731731 −0.0565818 0.0980026i −0.00209276 0.00362476i
732732 0 0
733733 −11.6824 + 20.2345i −0.431498 + 0.747377i −0.997003 0.0773684i 0.975348π-0.975348\pi
0.565504 + 0.824745i 0.308682π0.308682\pi
734734 0 0
735735 16.3875 + 39.5319i 0.604462 + 1.45816i
736736 0 0
737737 7.11077 + 12.3162i 0.261928 + 0.453673i
738738 0 0
739739 −14.4596 + 25.0448i −0.531906 + 0.921288i 0.467400 + 0.884046i 0.345191π0.345191\pi
−0.999306 + 0.0372422i 0.988143π0.988143\pi
740740 0 0
741741 −11.6748 43.9717i −0.428884 1.61534i
742742 0 0
743743 −11.6794 20.2292i −0.428474 0.742139i 0.568264 0.822847i 0.307615π-0.307615\pi
−0.996738 + 0.0807074i 0.974282π0.974282\pi
744744 0 0
745745 12.2422 + 21.2042i 0.448521 + 0.776860i
746746 0 0
747747 −30.5888 17.8470i −1.11919 0.652987i
748748 0 0
749749 −8.01747 11.9658i −0.292952 0.437222i
750750 0 0
751751 −0.856616 + 1.48370i −0.0312584 + 0.0541411i −0.881231 0.472685i 0.843285π-0.843285\pi
0.849973 + 0.526826i 0.176618π0.176618\pi
752752 0 0
753753 −21.1990 + 21.1025i −0.772535 + 0.769019i
754754 0 0
755755 54.7675 1.99319
756756 0 0
757757 28.4587 1.03435 0.517175 0.855880i 0.326984π-0.326984\pi
0.517175 + 0.855880i 0.326984π0.326984\pi
758758 0 0
759759 −9.39269 + 9.34995i −0.340933 + 0.339382i
760760 0 0
761761 17.0525 29.5358i 0.618154 1.07067i −0.371669 0.928365i 0.621214π-0.621214\pi
0.989822 0.142308i 0.0454524π-0.0454524\pi
762762 0 0
763763 0.974346 1.98216i 0.0352737 0.0717592i
764764 0 0
765765 11.7124 6.69111i 0.423463 0.241918i
766766 0 0
767767 −18.8587 32.6642i −0.680947 1.17943i
768768 0 0
769769 2.48467 + 4.30357i 0.0895995 + 0.155191i 0.907342 0.420394i 0.138108π-0.138108\pi
−0.817742 + 0.575584i 0.804775π0.804775\pi
770770 0 0
771771 −2.14312 8.07183i −0.0771826 0.290700i
772772 0 0
773773 −5.74814 + 9.95607i −0.206746 + 0.358095i −0.950688 0.310150i 0.899621π-0.899621\pi
0.743941 + 0.668245i 0.232954π0.232954\pi
774774 0 0
775775 31.7576 + 55.0058i 1.14077 + 1.97587i
776776 0 0
777777 25.5259 + 5.10400i 0.915737 + 0.183105i
778778 0 0
779779 9.27320 16.0617i 0.332247 0.575469i
780780 0 0
781781 1.51082 + 2.61682i 0.0540615 + 0.0936373i
782782 0 0
783783 −43.4551 + 11.3257i −1.55296 + 0.404748i
784784 0 0
785785 1.41556 2.45182i 0.0505235 0.0875092i
786786 0 0
787787 −48.6011 −1.73244 −0.866221 0.499661i 0.833458π-0.833458\pi
−0.866221 + 0.499661i 0.833458π0.833458\pi
788788 0 0
789789 −46.9672 12.6997i −1.67208 0.452121i
790790 0 0
791791 16.0491 + 23.9527i 0.570639 + 0.851661i
792792 0 0
793793 −31.5030 54.5647i −1.11870 1.93765i
794794 0 0
795795 40.3445 + 10.9089i 1.43087 + 0.386900i
796796 0 0
797797 16.8556 + 29.1947i 0.597056 + 1.03413i 0.993253 + 0.115965i 0.0369962π0.0369962\pi
−0.396198 + 0.918165i 0.629670π0.629670\pi
798798 0 0
799799 4.49183 7.78007i 0.158909 0.275239i
800800 0 0
801801 2.92527 1.67116i 0.103359 0.0590476i
802802 0 0
803803 −30.8438 −1.08846
804804 0 0
805805 17.1385 + 25.5788i 0.604054 + 0.901533i
806806 0 0
807807 11.0341 + 41.5587i 0.388418 + 1.46293i
808808 0 0
809809 −7.93617 + 13.7459i −0.279021 + 0.483278i −0.971142 0.238503i 0.923343π-0.923343\pi
0.692121 + 0.721782i 0.256677π0.256677\pi
810810 0 0
811811 −27.2524 −0.956963 −0.478481 0.878098i 0.658813π-0.658813\pi
−0.478481 + 0.878098i 0.658813π0.658813\pi
812812 0 0
813813 −16.0403 4.33720i −0.562556 0.152112i
814814 0 0
815815 −12.5300 −0.438907
816816 0 0
817817 0.494597 0.0173038
818818 0 0
819819 −31.2028 + 20.7012i −1.09031 + 0.723360i
820820 0 0
821821 24.3389 0.849433 0.424717 0.905326i 0.360374π-0.360374\pi
0.424717 + 0.905326i 0.360374π0.360374\pi
822822 0 0
823823 11.5380 0.402188 0.201094 0.979572i 0.435550π-0.435550\pi
0.201094 + 0.979572i 0.435550π0.435550\pi
824824 0 0
825825 −7.69289 28.9744i −0.267832 1.00876i
826826 0 0
827827 34.8582 1.21214 0.606069 0.795412i 0.292745π-0.292745\pi
0.606069 + 0.795412i 0.292745π0.292745\pi
828828 0 0
829829 −7.64018 + 13.2332i −0.265354 + 0.459607i −0.967656 0.252272i 0.918822π-0.918822\pi
0.702302 + 0.711879i 0.252156π0.252156\pi
830830 0 0
831831 28.3209 + 7.65783i 0.982442 + 0.265647i
832832 0 0
833833 −3.39140 + 8.24716i −0.117505 + 0.285747i
834834 0 0
835835 −6.10711 −0.211345
836836 0 0
837837 −31.0765 31.5047i −1.07416 1.08896i
838838 0 0
839839 8.39990 14.5490i 0.289997 0.502289i −0.683812 0.729658i 0.739679π-0.739679\pi
0.973809 + 0.227369i 0.0730125π0.0730125\pi
840840 0 0
841841 −22.8448 39.5684i −0.787753 1.36443i
842842 0 0
843843 10.1598 + 38.2659i 0.349923 + 1.31795i
844844 0 0
845845 16.3357 + 28.2943i 0.561967 + 0.973355i
846846 0 0
847847 6.55263 13.3304i 0.225151 0.458037i
848848 0 0
849849 10.2575 10.2109i 0.352038 0.350436i
850850 0 0
851851 18.7291 0.642024
852852 0 0
853853 −11.4270 + 19.7921i −0.391253 + 0.677670i −0.992615 0.121306i 0.961292π-0.961292\pi
0.601362 + 0.798977i 0.294625π0.294625\pi
854854 0 0
855855 −0.268897 + 58.9546i −0.00919607 + 2.01620i
856856 0 0
857857 17.5871 + 30.4618i 0.600765 + 1.04056i 0.992705 + 0.120565i 0.0384706π0.0384706\pi
−0.391940 + 0.919991i 0.628196π0.628196\pi
858858 0 0
859859 5.28520 9.15424i 0.180329 0.312339i −0.761664 0.647973i 0.775617π-0.775617\pi
0.941993 + 0.335634i 0.108950π0.108950\pi
860860 0 0
861861 −14.9685 2.99302i −0.510127 0.102002i
862862 0 0
863863 7.29326 + 12.6323i 0.248265 + 0.430008i 0.963045 0.269342i 0.0868061π-0.0868061\pi
−0.714779 + 0.699350i 0.753473π0.753473\pi
864864 0 0
865865 3.94358 6.83048i 0.134086 0.232243i
866866 0 0
867867 −25.7108 6.95206i −0.873184 0.236104i
868868 0 0
869869 −11.6362 20.1545i −0.394731 0.683694i
870870 0 0
871871 14.4551 + 25.0369i 0.489791 + 0.848343i
872872 0 0
873873 18.1809 + 10.6076i 0.615329 + 0.359012i
874874 0 0
875875 −22.9025 + 1.53053i −0.774247 + 0.0517413i
876876 0 0
877877 −5.65914 + 9.80192i −0.191096 + 0.330987i −0.945614 0.325292i 0.894537π-0.894537\pi
0.754518 + 0.656279i 0.227871π0.227871\pi
878878 0 0
879879 7.22779 + 1.95436i 0.243787 + 0.0659188i
880880 0 0
881881 −0.733220 −0.0247028 −0.0123514 0.999924i 0.503932π-0.503932\pi
−0.0123514 + 0.999924i 0.503932π0.503932\pi
882882 0 0
883883 14.1726 0.476944 0.238472 0.971149i 0.423353π-0.423353\pi
0.238472 + 0.971149i 0.423353π0.423353\pi
884884 0 0
885885 12.5424 + 47.2395i 0.421608 + 1.58794i
886886 0 0
887887 −16.8162 + 29.1266i −0.564634 + 0.977975i 0.432449 + 0.901658i 0.357649π0.357649\pi
−0.997084 + 0.0763170i 0.975684π0.975684\pi
888888 0 0
889889 26.1440 1.74715i 0.876842 0.0585975i
890890 0 0
891891 10.2778 + 18.1828i 0.344321 + 0.609147i
892892 0 0
893893 19.6321 + 34.0038i 0.656964 + 1.13790i
894894 0 0
895895 −1.23681 2.14221i −0.0413419 0.0716063i
896896 0 0
897897 −19.0939 + 19.0070i −0.637525 + 0.634624i
898898 0 0
899899 36.8008 63.7408i 1.22737 2.12588i
900900 0 0
901901 4.35436 + 7.54198i 0.145065 + 0.251260i
902902 0 0
903903 −0.130467 0.385611i −0.00434166 0.0128323i
904904 0 0
905905 −34.6498 + 60.0152i −1.15180 + 1.99497i
906906 0 0
907907 4.79255 + 8.30094i 0.159134 + 0.275628i 0.934557 0.355814i 0.115796π-0.115796\pi
−0.775423 + 0.631443i 0.782463π0.782463\pi
908908 0 0
909909 25.3745 14.4961i 0.841620 0.480805i
910910 0 0
911911 9.37499 16.2380i 0.310607 0.537988i −0.667887 0.744263i 0.732801π-0.732801\pi
0.978494 + 0.206275i 0.0661342π0.0661342\pi
912912 0 0
913913 −27.3959 −0.906672
914914 0 0
915915 20.9518 + 78.9125i 0.692644 + 2.60877i
916916 0 0
917917 20.0568 40.8026i 0.662333 1.34742i
918918 0 0
919919 −21.2895 36.8745i −0.702276 1.21638i −0.967666 0.252236i 0.918834π-0.918834\pi
0.265390 0.964141i 0.414499π-0.414499\pi
920920 0 0
921921 −11.3288 + 11.2772i −0.373296 + 0.371597i
922922 0 0
923923 3.07126 + 5.31958i 0.101092 + 0.175096i
924924 0 0
925925 −21.1824 + 36.6890i −0.696474 + 1.20633i
926926 0 0
927927 −26.6521 15.5501i −0.875368 0.510732i
928928 0 0
929929 38.1524 1.25174 0.625869 0.779928i 0.284744π-0.284744\pi
0.625869 + 0.779928i 0.284744π0.284744\pi
930930 0 0
931931 −23.8049 30.8594i −0.780173 1.01137i
932932 0 0
933933 −23.4549 + 23.3481i −0.767878 + 0.764383i
934934 0 0
935935 5.21736 9.03673i 0.170626 0.295533i
936936 0 0
937937 6.48960 0.212006 0.106003 0.994366i 0.466195π-0.466195\pi
0.106003 + 0.994366i 0.466195π0.466195\pi
938938 0 0
939939 −6.97120 + 6.93948i −0.227497 + 0.226461i
940940 0 0
941941 −0.466471 −0.0152065 −0.00760326 0.999971i 0.502420π-0.502420\pi
−0.00760326 + 0.999971i 0.502420π0.502420\pi
942942 0 0
943943 −10.9828 −0.357650
944944 0 0
945945 46.0347 15.3416i 1.49751 0.499063i
946946 0 0
947947 15.1115 0.491058 0.245529 0.969389i 0.421038π-0.421038\pi
0.245529 + 0.969389i 0.421038π0.421038\pi
948948 0 0
949949 −62.7006 −2.03535
950950 0 0
951951 34.7001 34.5422i 1.12523 1.12011i
952952 0 0
953953 19.6802 0.637503 0.318751 0.947838i 0.396736π-0.396736\pi
0.318751 + 0.947838i 0.396736π0.396736\pi
954954 0 0
955955 −28.3881 + 49.1696i −0.918616 + 1.59109i
956956 0 0
957957 −24.6200 + 24.5080i −0.795852 + 0.792231i
958958 0 0
959959 23.7017 + 35.3741i 0.765368 + 1.14229i
960960 0 0
961961 41.5293 1.33966
962962 0 0
963963 −14.1811 + 8.10142i −0.456978 + 0.261065i
964964 0 0
965965 −1.03322 + 1.78959i −0.0332606 + 0.0576090i
966966 0 0
967967 −8.83228 15.2980i −0.284027 0.491949i 0.688346 0.725383i 0.258337π-0.258337\pi
−0.972373 + 0.233433i 0.925004π0.925004\pi
968968 0 0
969969 −8.70649 + 8.66687i −0.279693 + 0.278420i
970970 0 0
971971 11.7523 + 20.3555i 0.377148 + 0.653240i 0.990646 0.136456i 0.0435713π-0.0435713\pi
−0.613498 + 0.789697i 0.710238π0.710238\pi
972972 0 0
973973 −3.27386 4.88614i −0.104955 0.156642i
974974 0 0
975975 −15.6384 58.9003i −0.500830 1.88632i
976976 0 0
977977 −5.43379 −0.173842 −0.0869211 0.996215i 0.527703π-0.527703\pi
−0.0869211 + 0.996215i 0.527703π0.527703\pi
978978 0 0
979979 1.30308 2.25700i 0.0416466 0.0721341i
980980 0 0
981981 −2.16316 1.26209i −0.0690644 0.0402955i
982982 0 0
983983 −1.05345 1.82463i −0.0335998 0.0581966i 0.848736 0.528816i 0.177364π-0.177364\pi
−0.882336 + 0.470619i 0.844031π0.844031\pi
984984 0 0
985985 −30.5174 + 52.8577i −0.972366 + 1.68419i
986986 0 0
987987 21.3324 24.2758i 0.679017 0.772707i
988988 0 0
989989 −0.146446 0.253651i −0.00465670 0.00806564i
990990 0 0
991991 −8.91172 + 15.4356i −0.283090 + 0.490327i −0.972144 0.234383i 0.924693π-0.924693\pi
0.689054 + 0.724710i 0.258026π0.258026\pi
992992 0 0
993993 −8.20105 + 8.16373i −0.260252 + 0.259068i
994994 0 0
995995 −43.1031 74.6567i −1.36646 2.36678i
996996 0 0
997997 18.2477 + 31.6060i 0.577911 + 1.00097i 0.995719 + 0.0924360i 0.0294653π0.0294653\pi
−0.417807 + 0.908536i 0.637201π0.637201\pi
998998 0 0
999999 7.83434 28.4579i 0.247867 0.900369i
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 1008.2.q.k.529.4 22
3.2 odd 2 3024.2.q.k.2881.1 22
4.3 odd 2 504.2.q.d.25.8 22
7.2 even 3 1008.2.t.k.961.5 22
9.4 even 3 1008.2.t.k.193.5 22
9.5 odd 6 3024.2.t.l.1873.11 22
12.11 even 2 1512.2.q.c.1369.1 22
21.2 odd 6 3024.2.t.l.289.11 22
28.23 odd 6 504.2.t.d.457.7 yes 22
36.23 even 6 1512.2.t.d.361.11 22
36.31 odd 6 504.2.t.d.193.7 yes 22
63.23 odd 6 3024.2.q.k.2305.1 22
63.58 even 3 inner 1008.2.q.k.625.4 22
84.23 even 6 1512.2.t.d.289.11 22
252.23 even 6 1512.2.q.c.793.1 22
252.247 odd 6 504.2.q.d.121.8 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.q.d.25.8 22 4.3 odd 2
504.2.q.d.121.8 yes 22 252.247 odd 6
504.2.t.d.193.7 yes 22 36.31 odd 6
504.2.t.d.457.7 yes 22 28.23 odd 6
1008.2.q.k.529.4 22 1.1 even 1 trivial
1008.2.q.k.625.4 22 63.58 even 3 inner
1008.2.t.k.193.5 22 9.4 even 3
1008.2.t.k.961.5 22 7.2 even 3
1512.2.q.c.793.1 22 252.23 even 6
1512.2.q.c.1369.1 22 12.11 even 2
1512.2.t.d.289.11 22 84.23 even 6
1512.2.t.d.361.11 22 36.23 even 6
3024.2.q.k.2305.1 22 63.23 odd 6
3024.2.q.k.2881.1 22 3.2 odd 2
3024.2.t.l.289.11 22 21.2 odd 6
3024.2.t.l.1873.11 22 9.5 odd 6