Properties

Label 1008.2.q.k.625.3
Level 10081008
Weight 22
Character 1008.625
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 625.3
Character χ\chi == 1008.625
Dual form 1008.2.q.k.529.3

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+(1.34477+1.09160i)q3+(0.918286+1.59052i)q5+(0.3616562.62092i)q7+(0.6168382.93590i)q9+(1.54860+2.68225i)q11+(2.402254.16081i)q13+(2.971091.13649i)q15+(1.87185+3.24214i)q17+(2.714084.70093i)q19+(2.37464+3.91932i)q21+(3.979146.89208i)q23+(0.8135031.40903i)q25+(2.37531+4.62146i)q27+(0.3252670.563379i)q291.03668q31+(0.8454165.29746i)q33+(4.500721.83153i)q35+(0.8737121.51331i)q37+(1.31144+8.21764i)q39+(2.522604.36927i)q41+(6.09645+10.5594i)q43+(5.236031.71490i)q45+4.61383q47+(6.738411.89574i)q49+(6.056322.31664i)q51+(4.55082+7.88226i)q535.68821q55+(1.48168+9.28438i)q57+5.79727q594.81245q61+(7.471672.67847i)q63+8.82379q65+14.4774q67+(12.8744+4.92468i)q69+5.00714q71+(1.813643.14131i)q73+(0.444111+2.78284i)q75+(6.46989+5.02879i)q77+14.3581q79+(8.239023.62195i)q81+(3.831396.63616i)q83+(3.43778+5.95441i)q85+(1.05239+0.402558i)q87+(5.76798+9.99043i)q89+(10.03647.80087i)q91+(1.394111.13164i)q93+9.96922q95+(1.044801.80964i)q97+(6.91957+6.20103i)q99+O(q100)q+(-1.34477 + 1.09160i) q^{3} +(0.918286 + 1.59052i) q^{5} +(0.361656 - 2.62092i) q^{7} +(0.616838 - 2.93590i) q^{9} +(-1.54860 + 2.68225i) q^{11} +(2.40225 - 4.16081i) q^{13} +(-2.97109 - 1.13649i) q^{15} +(1.87185 + 3.24214i) q^{17} +(2.71408 - 4.70093i) q^{19} +(2.37464 + 3.91932i) q^{21} +(-3.97914 - 6.89208i) q^{23} +(0.813503 - 1.40903i) q^{25} +(2.37531 + 4.62146i) q^{27} +(-0.325267 - 0.563379i) q^{29} -1.03668 q^{31} +(-0.845416 - 5.29746i) q^{33} +(4.50072 - 1.83153i) q^{35} +(0.873712 - 1.51331i) q^{37} +(1.31144 + 8.21764i) q^{39} +(2.52260 - 4.36927i) q^{41} +(6.09645 + 10.5594i) q^{43} +(5.23603 - 1.71490i) q^{45} +4.61383 q^{47} +(-6.73841 - 1.89574i) q^{49} +(-6.05632 - 2.31664i) q^{51} +(4.55082 + 7.88226i) q^{53} -5.68821 q^{55} +(1.48168 + 9.28438i) q^{57} +5.79727 q^{59} -4.81245 q^{61} +(-7.47167 - 2.67847i) q^{63} +8.82379 q^{65} +14.4774 q^{67} +(12.8744 + 4.92468i) q^{69} +5.00714 q^{71} +(-1.81364 - 3.14131i) q^{73} +(0.444111 + 2.78284i) q^{75} +(6.46989 + 5.02879i) q^{77} +14.3581 q^{79} +(-8.23902 - 3.62195i) q^{81} +(-3.83139 - 6.63616i) q^{83} +(-3.43778 + 5.95441i) q^{85} +(1.05239 + 0.402558i) q^{87} +(-5.76798 + 9.99043i) q^{89} +(-10.0364 - 7.80087i) q^{91} +(1.39411 - 1.13164i) q^{93} +9.96922 q^{95} +(-1.04480 - 1.80964i) q^{97} +(6.91957 + 6.20103i) 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(13)e\left(\frac{1}{3}\right) 11 e(13)e\left(\frac{1}{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 −1.34477 + 1.09160i −0.776406 + 0.630233i
44 0 0
55 0.918286 + 1.59052i 0.410670 + 0.711301i 0.994963 0.100242i 0.0319616π-0.0319616\pi
−0.584293 + 0.811543i 0.698628π0.698628\pi
66 0 0
77 0.361656 2.62092i 0.136693 0.990613i
88 0 0
99 0.616838 2.93590i 0.205613 0.978633i
1010 0 0
1111 −1.54860 + 2.68225i −0.466919 + 0.808728i −0.999286 0.0377862i 0.987969π-0.987969\pi
0.532367 + 0.846514i 0.321303π0.321303\pi
1212 0 0
1313 2.40225 4.16081i 0.666263 1.15400i −0.312678 0.949859i 0.601226π-0.601226\pi
0.978941 0.204143i 0.0654406π-0.0654406\pi
1414 0 0
1515 −2.97109 1.13649i −0.767132 0.293441i
1616 0 0
1717 1.87185 + 3.24214i 0.453990 + 0.786333i 0.998629 0.0523367i 0.0166669π-0.0166669\pi
−0.544640 + 0.838670i 0.683334π0.683334\pi
1818 0 0
1919 2.71408 4.70093i 0.622654 1.07847i −0.366336 0.930483i 0.619388π-0.619388\pi
0.988990 0.147985i 0.0472788π-0.0472788\pi
2020 0 0
2121 2.37464 + 3.91932i 0.518188 + 0.855267i
2222 0 0
2323 −3.97914 6.89208i −0.829709 1.43710i −0.898267 0.439450i 0.855173π-0.855173\pi
0.0685581 0.997647i 0.478160π-0.478160\pi
2424 0 0
2525 0.813503 1.40903i 0.162701 0.281806i
2626 0 0
2727 2.37531 + 4.62146i 0.457128 + 0.889401i
2828 0 0
2929 −0.325267 0.563379i −0.0604006 0.104617i 0.834244 0.551396i 0.185904π-0.185904\pi
−0.894645 + 0.446779i 0.852571π0.852571\pi
3030 0 0
3131 −1.03668 −0.186194 −0.0930970 0.995657i 0.529677π-0.529677\pi
−0.0930970 + 0.995657i 0.529677π0.529677\pi
3232 0 0
3333 −0.845416 5.29746i −0.147168 0.922169i
3434 0 0
3535 4.50072 1.83153i 0.760760 0.309585i
3636 0 0
3737 0.873712 1.51331i 0.143637 0.248787i −0.785226 0.619209i 0.787453π-0.787453\pi
0.928864 + 0.370422i 0.120787π0.120787\pi
3838 0 0
3939 1.31144 + 8.21764i 0.209999 + 1.31588i
4040 0 0
4141 2.52260 4.36927i 0.393964 0.682365i −0.599005 0.800745i 0.704437π-0.704437\pi
0.992968 + 0.118381i 0.0377703π0.0377703\pi
4242 0 0
4343 6.09645 + 10.5594i 0.929699 + 1.61029i 0.783824 + 0.620984i 0.213267π0.213267\pi
0.145876 + 0.989303i 0.453400π0.453400\pi
4444 0 0
4545 5.23603 1.71490i 0.780542 0.255643i
4646 0 0
4747 4.61383 0.672996 0.336498 0.941684i 0.390757π-0.390757\pi
0.336498 + 0.941684i 0.390757π0.390757\pi
4848 0 0
4949 −6.73841 1.89574i −0.962630 0.270820i
5050 0 0
5151 −6.05632 2.31664i −0.848054 0.324395i
5252 0 0
5353 4.55082 + 7.88226i 0.625104 + 1.08271i 0.988521 + 0.151085i 0.0482766π0.0482766\pi
−0.363417 + 0.931626i 0.618390π0.618390\pi
5454 0 0
5555 −5.68821 −0.766998
5656 0 0
5757 1.48168 + 9.28438i 0.196254 + 1.22975i
5858 0 0
5959 5.79727 0.754740 0.377370 0.926063i 0.376828π-0.376828\pi
0.377370 + 0.926063i 0.376828π0.376828\pi
6060 0 0
6161 −4.81245 −0.616172 −0.308086 0.951359i 0.599688π-0.599688\pi
−0.308086 + 0.951359i 0.599688π0.599688\pi
6262 0 0
6363 −7.47167 2.67847i −0.941342 0.337455i
6464 0 0
6565 8.82379 1.09446
6666 0 0
6767 14.4774 1.76870 0.884348 0.466828i 0.154603π-0.154603\pi
0.884348 + 0.466828i 0.154603π0.154603\pi
6868 0 0
6969 12.8744 + 4.92468i 1.54990 + 0.592861i
7070 0 0
7171 5.00714 0.594238 0.297119 0.954840i 0.403974π-0.403974\pi
0.297119 + 0.954840i 0.403974π0.403974\pi
7272 0 0
7373 −1.81364 3.14131i −0.212270 0.367662i 0.740155 0.672437i 0.234752π-0.234752\pi
−0.952425 + 0.304774i 0.901419π0.901419\pi
7474 0 0
7575 0.444111 + 2.78284i 0.0512816 + 0.321335i
7676 0 0
7777 6.46989 + 5.02879i 0.737312 + 0.573084i
7878 0 0
7979 14.3581 1.61541 0.807705 0.589587i 0.200710π-0.200710\pi
0.807705 + 0.589587i 0.200710π0.200710\pi
8080 0 0
8181 −8.23902 3.62195i −0.915447 0.402439i
8282 0 0
8383 −3.83139 6.63616i −0.420550 0.728414i 0.575443 0.817842i 0.304829π-0.304829\pi
−0.995993 + 0.0894279i 0.971496π0.971496\pi
8484 0 0
8585 −3.43778 + 5.95441i −0.372880 + 0.645847i
8686 0 0
8787 1.05239 + 0.402558i 0.112828 + 0.0431587i
8888 0 0
8989 −5.76798 + 9.99043i −0.611405 + 1.05898i 0.379599 + 0.925151i 0.376062π0.376062\pi
−0.991004 + 0.133833i 0.957271π0.957271\pi
9090 0 0
9191 −10.0364 7.80087i −1.05210 0.817753i
9292 0 0
9393 1.39411 1.13164i 0.144562 0.117346i
9494 0 0
9595 9.96922 1.02282
9696 0 0
9797 −1.04480 1.80964i −0.106083 0.183741i 0.808097 0.589049i 0.200498π-0.200498\pi
−0.914180 + 0.405308i 0.867164π0.867164\pi
9898 0 0
9999 6.91957 + 6.20103i 0.695443 + 0.623227i
100100 0 0
101101 8.22661 14.2489i 0.818578 1.41782i −0.0881520 0.996107i 0.528096π-0.528096\pi
0.906730 0.421712i 0.138571π-0.138571\pi
102102 0 0
103103 −3.87346 6.70903i −0.381663 0.661060i 0.609637 0.792681i 0.291315π-0.291315\pi
−0.991300 + 0.131621i 0.957982π0.957982\pi
104104 0 0
105105 −4.05316 + 7.37596i −0.395548 + 0.719820i
106106 0 0
107107 −3.74746 + 6.49080i −0.362281 + 0.627489i −0.988336 0.152290i 0.951335π-0.951335\pi
0.626055 + 0.779779i 0.284669π0.284669\pi
108108 0 0
109109 −4.30644 7.45897i −0.412482 0.714440i 0.582678 0.812703i 0.302005π-0.302005\pi
−0.995160 + 0.0982628i 0.968671π0.968671\pi
110110 0 0
111111 0.476981 + 2.98881i 0.0452730 + 0.283685i
112112 0 0
113113 −1.55747 + 2.69762i −0.146514 + 0.253771i −0.929937 0.367719i 0.880139π-0.880139\pi
0.783422 + 0.621490i 0.213472π0.213472\pi
114114 0 0
115115 7.30798 12.6578i 0.681473 1.18035i
116116 0 0
117117 −10.7339 9.61930i −0.992353 0.889305i
118118 0 0
119119 9.17433 3.73342i 0.841010 0.342242i
120120 0 0
121121 0.703704 + 1.21885i 0.0639731 + 0.110805i
122122 0 0
123123 1.37715 + 8.62934i 0.124173 + 0.778081i
124124 0 0
125125 12.1710 1.08860
126126 0 0
127127 −10.8866 −0.966033 −0.483017 0.875611i 0.660459π-0.660459\pi
−0.483017 + 0.875611i 0.660459π0.660459\pi
128128 0 0
129129 −19.7249 7.54510i −1.73668 0.664309i
130130 0 0
131131 −8.02790 13.9047i −0.701401 1.21486i −0.967975 0.251048i 0.919225π-0.919225\pi
0.266574 0.963815i 0.414108π-0.414108\pi
132132 0 0
133133 −11.3392 8.81351i −0.983232 0.764228i
134134 0 0
135135 −5.16930 + 8.02179i −0.444903 + 0.690406i
136136 0 0
137137 −6.72031 + 11.6399i −0.574155 + 0.994465i 0.421978 + 0.906606i 0.361336π0.361336\pi
−0.996133 + 0.0878590i 0.971998π0.971998\pi
138138 0 0
139139 4.06953 7.04863i 0.345173 0.597857i −0.640212 0.768198i 0.721154π-0.721154\pi
0.985385 + 0.170341i 0.0544869π0.0544869\pi
140140 0 0
141141 −6.20456 + 5.03644i −0.522518 + 0.424144i
142142 0 0
143143 7.44022 + 12.8868i 0.622182 + 1.07765i
144144 0 0
145145 0.597376 1.03469i 0.0496094 0.0859260i
146146 0 0
147147 11.1310 4.80628i 0.918071 0.396415i
148148 0 0
149149 −3.76479 6.52081i −0.308424 0.534205i 0.669594 0.742727i 0.266468π-0.266468\pi
−0.978018 + 0.208522i 0.933135π0.933135\pi
150150 0 0
151151 −2.83616 + 4.91237i −0.230803 + 0.399763i −0.958045 0.286619i 0.907469π-0.907469\pi
0.727241 + 0.686382i 0.240802π0.240802\pi
152152 0 0
153153 10.6732 3.49569i 0.862878 0.282610i
154154 0 0
155155 −0.951973 1.64886i −0.0764643 0.132440i
156156 0 0
157157 0.436763 0.0348575 0.0174287 0.999848i 0.494452π-0.494452\pi
0.0174287 + 0.999848i 0.494452π0.494452\pi
158158 0 0
159159 −14.7241 5.63220i −1.16769 0.446663i
160160 0 0
161161 −19.5026 + 7.93644i −1.53702 + 0.625479i
162162 0 0
163163 −9.12649 + 15.8076i −0.714842 + 1.23814i 0.248178 + 0.968714i 0.420168π0.420168\pi
−0.963020 + 0.269429i 0.913165π0.913165\pi
164164 0 0
165165 7.64936 6.20923i 0.595502 0.483388i
166166 0 0
167167 −0.765108 + 1.32521i −0.0592058 + 0.102548i −0.894109 0.447849i 0.852190π-0.852190\pi
0.834903 + 0.550397i 0.185523π0.185523\pi
168168 0 0
169169 −5.04157 8.73226i −0.387813 0.671713i
170170 0 0
171171 −12.1273 10.8680i −0.927399 0.831096i
172172 0 0
173173 2.16949 0.164943 0.0824716 0.996593i 0.473719π-0.473719\pi
0.0824716 + 0.996593i 0.473719π0.473719\pi
174174 0 0
175175 −3.39874 2.64171i −0.256921 0.199694i
176176 0 0
177177 −7.79602 + 6.32827i −0.585985 + 0.475662i
178178 0 0
179179 1.08263 + 1.87517i 0.0809195 + 0.140157i 0.903645 0.428282i 0.140881π-0.140881\pi
−0.822726 + 0.568439i 0.807548π0.807548\pi
180180 0 0
181181 0.557838 0.0414638 0.0207319 0.999785i 0.493400π-0.493400\pi
0.0207319 + 0.999785i 0.493400π0.493400\pi
182182 0 0
183183 6.47167 5.25325i 0.478399 0.388332i
184184 0 0
185185 3.20927 0.235950
186186 0 0
187187 −11.5949 −0.847906
188188 0 0
189189 12.9715 4.55411i 0.943539 0.331262i
190190 0 0
191191 23.9997 1.73655 0.868277 0.496079i 0.165227π-0.165227\pi
0.868277 + 0.496079i 0.165227π0.165227\pi
192192 0 0
193193 −21.2794 −1.53172 −0.765862 0.643005i 0.777687π-0.777687\pi
−0.765862 + 0.643005i 0.777687π0.777687\pi
194194 0 0
195195 −11.8660 + 9.63201i −0.849743 + 0.689763i
196196 0 0
197197 −14.8768 −1.05993 −0.529964 0.848020i 0.677795π-0.677795\pi
−0.529964 + 0.848020i 0.677795π0.677795\pi
198198 0 0
199199 −6.17884 10.7021i −0.438006 0.758649i 0.559530 0.828810i 0.310982π-0.310982\pi
−0.997536 + 0.0701616i 0.977649π0.977649\pi
200200 0 0
201201 −19.4688 + 15.8035i −1.37323 + 1.11469i
202202 0 0
203203 −1.59420 + 0.648749i −0.111891 + 0.0455332i
204204 0 0
205205 9.26586 0.647156
206206 0 0
207207 −22.6889 + 7.43107i −1.57699 + 0.516495i
208208 0 0
209209 8.40604 + 14.5597i 0.581458 + 1.00711i
210210 0 0
211211 −8.65802 + 14.9961i −0.596043 + 1.03238i 0.397356 + 0.917664i 0.369928π0.369928\pi
−0.993399 + 0.114712i 0.963406π0.963406\pi
212212 0 0
213213 −6.73347 + 5.46577i −0.461370 + 0.374508i
214214 0 0
215215 −11.1966 + 19.3930i −0.763599 + 1.32259i
216216 0 0
217217 −0.374923 + 2.71706i −0.0254514 + 0.184446i
218218 0 0
219219 5.86797 + 2.24460i 0.396521 + 0.151676i
220220 0 0
221221 17.9866 1.20991
222222 0 0
223223 −1.14489 1.98301i −0.0766677 0.132792i 0.825143 0.564925i 0.191095π-0.191095\pi
−0.901810 + 0.432132i 0.857761π0.857761\pi
224224 0 0
225225 −3.63497 3.25751i −0.242331 0.217167i
226226 0 0
227227 −1.78013 + 3.08328i −0.118152 + 0.204644i −0.919035 0.394176i 0.871030π-0.871030\pi
0.800884 + 0.598820i 0.204364π0.204364\pi
228228 0 0
229229 13.4799 + 23.3478i 0.890775 + 1.54287i 0.838949 + 0.544211i 0.183171π0.183171\pi
0.0518260 + 0.998656i 0.483496π0.483496\pi
230230 0 0
231231 −14.1899 + 0.299909i −0.933630 + 0.0197325i
232232 0 0
233233 10.7321 18.5885i 0.703081 1.21777i −0.264298 0.964441i 0.585140π-0.585140\pi
0.967380 0.253332i 0.0815264π-0.0815264\pi
234234 0 0
235235 4.23681 + 7.33837i 0.276379 + 0.478703i
236236 0 0
237237 −19.3084 + 15.6732i −1.25421 + 1.01808i
238238 0 0
239239 −4.65970 + 8.07083i −0.301411 + 0.522059i −0.976456 0.215718i 0.930791π-0.930791\pi
0.675045 + 0.737777i 0.264124π0.264124\pi
240240 0 0
241241 10.1003 17.4943i 0.650620 1.12691i −0.332353 0.943155i 0.607842π-0.607842\pi
0.982973 0.183752i 0.0588242π-0.0588242\pi
242242 0 0
243243 15.0333 4.12297i 0.964389 0.264489i
244244 0 0
245245 −3.17258 12.4584i −0.202689 0.795937i
246246 0 0
247247 −13.0398 22.5856i −0.829702 1.43709i
248248 0 0
249249 12.3964 + 4.74182i 0.785588 + 0.300500i
250250 0 0
251251 −27.1837 −1.71582 −0.857910 0.513800i 0.828238π-0.828238\pi
−0.857910 + 0.513800i 0.828238π0.828238\pi
252252 0 0
253253 24.6483 1.54963
254254 0 0
255255 −1.87677 11.7600i −0.117528 0.736441i
256256 0 0
257257 −14.2411 24.6662i −0.888333 1.53864i −0.841845 0.539719i 0.818531π-0.818531\pi
−0.0464876 0.998919i 0.514803π-0.514803\pi
258258 0 0
259259 −3.65028 2.83722i −0.226818 0.176297i
260260 0 0
261261 −1.85466 + 0.607438i −0.114801 + 0.0375995i
262262 0 0
263263 1.79907 3.11608i 0.110935 0.192146i −0.805212 0.592987i 0.797949π-0.797949\pi
0.916148 + 0.400841i 0.131282π0.131282\pi
264264 0 0
265265 −8.35791 + 14.4763i −0.513422 + 0.889274i
266266 0 0
267267 −3.14888 19.7312i −0.192708 1.20753i
268268 0 0
269269 11.2261 + 19.4443i 0.684470 + 1.18554i 0.973603 + 0.228248i 0.0732997π0.0732997\pi
−0.289133 + 0.957289i 0.593367π0.593367\pi
270270 0 0
271271 14.7935 25.6231i 0.898642 1.55649i 0.0694115 0.997588i 0.477888π-0.477888\pi
0.829231 0.558906i 0.188779π-0.188779\pi
272272 0 0
273273 22.0120 0.465231i 1.33223 0.0281570i
274274 0 0
275275 2.51958 + 4.36403i 0.151936 + 0.263161i
276276 0 0
277277 10.1933 17.6554i 0.612459 1.06081i −0.378366 0.925656i 0.623514π-0.623514\pi
0.990825 0.135153i 0.0431527π-0.0431527\pi
278278 0 0
279279 −0.639467 + 3.04360i −0.0382839 + 0.182216i
280280 0 0
281281 −2.23968 3.87924i −0.133608 0.231416i 0.791457 0.611225i 0.209323π-0.209323\pi
−0.925065 + 0.379809i 0.875990π0.875990\pi
282282 0 0
283283 −2.07680 −0.123453 −0.0617264 0.998093i 0.519661π-0.519661\pi
−0.0617264 + 0.998093i 0.519661π0.519661\pi
284284 0 0
285285 −13.4064 + 10.8824i −0.794124 + 0.644615i
286286 0 0
287287 −10.5392 8.19169i −0.622108 0.483540i
288288 0 0
289289 1.49237 2.58486i 0.0877865 0.152051i
290290 0 0
291291 3.38041 + 1.29306i 0.198163 + 0.0758007i
292292 0 0
293293 −0.887340 + 1.53692i −0.0518389 + 0.0897877i −0.890780 0.454434i 0.849842π-0.849842\pi
0.838942 + 0.544222i 0.183175π0.183175\pi
294294 0 0
295295 5.32355 + 9.22066i 0.309949 + 0.536847i
296296 0 0
297297 −16.0743 0.785616i −0.932725 0.0455860i
298298 0 0
299299 −38.2355 −2.21122
300300 0 0
301301 29.8800 12.1594i 1.72225 0.700858i
302302 0 0
303303 4.49111 + 28.1417i 0.258007 + 1.61670i
304304 0 0
305305 −4.41921 7.65429i −0.253043 0.438283i
306306 0 0
307307 −19.6315 −1.12043 −0.560215 0.828347i 0.689282π-0.689282\pi
−0.560215 + 0.828347i 0.689282π0.689282\pi
308308 0 0
309309 12.5325 + 4.79388i 0.712948 + 0.272714i
310310 0 0
311311 13.3159 0.755076 0.377538 0.925994i 0.376771π-0.376771\pi
0.377538 + 0.925994i 0.376771π0.376771\pi
312312 0 0
313313 4.65281 0.262992 0.131496 0.991317i 0.458022π-0.458022\pi
0.131496 + 0.991317i 0.458022π0.458022\pi
314314 0 0
315315 −2.60098 14.3434i −0.146548 0.808160i
316316 0 0
317317 −4.12552 −0.231713 −0.115856 0.993266i 0.536961π-0.536961\pi
−0.115856 + 0.993266i 0.536961π0.536961\pi
318318 0 0
319319 2.01483 0.112809
320320 0 0
321321 −2.04583 12.8194i −0.114187 0.715508i
322322 0 0
323323 20.3214 1.13071
324324 0 0
325325 −3.90847 6.76967i −0.216803 0.375514i
326326 0 0
327327 13.9334 + 5.32975i 0.770517 + 0.294736i
328328 0 0
329329 1.66862 12.0925i 0.0919939 0.666679i
330330 0 0
331331 −0.0440594 −0.00242172 −0.00121086 0.999999i 0.500385π-0.500385\pi
−0.00121086 + 0.999999i 0.500385π0.500385\pi
332332 0 0
333333 −3.90400 3.49860i −0.213938 0.191722i
334334 0 0
335335 13.2944 + 23.0266i 0.726350 + 1.25808i
336336 0 0
337337 −13.3351 + 23.0970i −0.726407 + 1.25817i 0.231986 + 0.972719i 0.425478π0.425478\pi
−0.958392 + 0.285454i 0.907856π0.907856\pi
338338 0 0
339339 −0.850261 5.32782i −0.0461798 0.289367i
340340 0 0
341341 1.60541 2.78064i 0.0869376 0.150580i
342342 0 0
343343 −7.40556 + 16.9752i −0.399863 + 0.916575i
344344 0 0
345345 3.98960 + 24.9992i 0.214793 + 1.34591i
346346 0 0
347347 −10.8252 −0.581126 −0.290563 0.956856i 0.593843π-0.593843\pi
−0.290563 + 0.956856i 0.593843π0.593843\pi
348348 0 0
349349 −2.69555 4.66884i −0.144290 0.249917i 0.784818 0.619726i 0.212756π-0.212756\pi
−0.929108 + 0.369809i 0.879423π0.879423\pi
350350 0 0
351351 24.9351 + 1.21868i 1.33094 + 0.0650483i
352352 0 0
353353 4.47307 7.74759i 0.238078 0.412362i −0.722085 0.691804i 0.756816π-0.756816\pi
0.960163 + 0.279442i 0.0901494π0.0901494\pi
354354 0 0
355355 4.59798 + 7.96394i 0.244036 + 0.422682i
356356 0 0
357357 −8.26203 + 15.0353i −0.437273 + 0.795751i
358358 0 0
359359 −1.84157 + 3.18969i −0.0971942 + 0.168345i −0.910522 0.413460i 0.864320π-0.864320\pi
0.813328 + 0.581805i 0.197653π0.197653\pi
360360 0 0
361361 −5.23251 9.06297i −0.275395 0.476998i
362362 0 0
363363 −2.27682 0.870920i −0.119502 0.0457114i
364364 0 0
365365 3.33087 5.76924i 0.174346 0.301976i
366366 0 0
367367 −3.74988 + 6.49498i −0.195742 + 0.339035i −0.947144 0.320810i 0.896045π-0.896045\pi
0.751401 + 0.659845i 0.229378π0.229378\pi
368368 0 0
369369 −11.2717 10.1012i −0.586781 0.525849i
370370 0 0
371371 22.3046 9.07666i 1.15800 0.471237i
372372 0 0
373373 −4.11917 7.13461i −0.213282 0.369416i 0.739458 0.673203i 0.235082π-0.235082\pi
−0.952740 + 0.303787i 0.901749π0.901749\pi
374374 0 0
375375 −16.3672 + 13.2858i −0.845199 + 0.686075i
376376 0 0
377377 −3.12549 −0.160971
378378 0 0
379379 3.92853 0.201795 0.100897 0.994897i 0.467829π-0.467829\pi
0.100897 + 0.994897i 0.467829π0.467829\pi
380380 0 0
381381 14.6401 11.8838i 0.750034 0.608826i
382382 0 0
383383 11.9632 + 20.7210i 0.611293 + 1.05879i 0.991023 + 0.133694i 0.0426838π0.0426838\pi
−0.379729 + 0.925098i 0.623983π0.623983\pi
384384 0 0
385385 −2.05718 + 14.9083i −0.104843 + 0.759799i
386386 0 0
387387 34.7617 11.3851i 1.76704 0.578740i
388388 0 0
389389 −6.32875 + 10.9617i −0.320881 + 0.555781i −0.980670 0.195669i 0.937312π-0.937312\pi
0.659789 + 0.751451i 0.270645π0.270645\pi
390390 0 0
391391 14.8967 25.8018i 0.753359 1.30486i
392392 0 0
393393 25.9741 + 9.93551i 1.31022 + 0.501180i
394394 0 0
395395 13.1848 + 22.8368i 0.663400 + 1.14904i
396396 0 0
397397 −17.7703 + 30.7791i −0.891866 + 1.54476i −0.0542297 + 0.998528i 0.517270π0.517270\pi
−0.837636 + 0.546229i 0.816063π0.816063\pi
398398 0 0
399399 24.8694 0.525623i 1.24503 0.0263141i
400400 0 0
401401 1.66166 + 2.87808i 0.0829794 + 0.143724i 0.904528 0.426413i 0.140223π-0.140223\pi
−0.821549 + 0.570138i 0.806890π0.806890\pi
402402 0 0
403403 −2.49037 + 4.31345i −0.124054 + 0.214868i
404404 0 0
405405 −1.80500 16.4303i −0.0896912 0.816428i
406406 0 0
407407 2.70605 + 4.68702i 0.134134 + 0.232327i
408408 0 0
409409 22.5129 1.11319 0.556595 0.830784i 0.312107π-0.312107\pi
0.556595 + 0.830784i 0.312107π0.312107\pi
410410 0 0
411411 −3.66878 22.9889i −0.180968 1.13396i
412412 0 0
413413 2.09662 15.1942i 0.103168 0.747656i
414414 0 0
415415 7.03662 12.1878i 0.345414 0.598275i
416416 0 0
417417 2.22165 + 13.9211i 0.108795 + 0.681719i
418418 0 0
419419 3.59772 6.23144i 0.175760 0.304426i −0.764664 0.644429i 0.777095π-0.777095\pi
0.940424 + 0.340004i 0.110428π0.110428\pi
420420 0 0
421421 16.8121 + 29.1193i 0.819370 + 1.41919i 0.906147 + 0.422962i 0.139010π0.139010\pi
−0.0867773 + 0.996228i 0.527657π0.527657\pi
422422 0 0
423423 2.84599 13.5457i 0.138377 0.658616i
424424 0 0
425425 6.09102 0.295458
426426 0 0
427427 −1.74045 + 12.6130i −0.0842264 + 0.610388i
428428 0 0
429429 −24.0726 9.20818i −1.16224 0.444575i
430430 0 0
431431 −16.4871 28.5565i −0.794156 1.37552i −0.923373 0.383903i 0.874580π-0.874580\pi
0.129217 0.991616i 0.458754π-0.458754\pi
432432 0 0
433433 19.8977 0.956221 0.478110 0.878300i 0.341322π-0.341322\pi
0.478110 + 0.878300i 0.341322π0.341322\pi
434434 0 0
435435 0.326122 + 2.04351i 0.0156364 + 0.0979789i
436436 0 0
437437 −43.1989 −2.06648
438438 0 0
439439 −29.1268 −1.39015 −0.695074 0.718938i 0.744628π-0.744628\pi
−0.695074 + 0.718938i 0.744628π0.744628\pi
440440 0 0
441441 −9.72221 + 18.6139i −0.462962 + 0.886378i
442442 0 0
443443 −13.7663 −0.654058 −0.327029 0.945014i 0.606048π-0.606048\pi
−0.327029 + 0.945014i 0.606048π0.606048\pi
444444 0 0
445445 −21.1866 −1.00434
446446 0 0
447447 12.1809 + 4.65939i 0.576136 + 0.220382i
448448 0 0
449449 −12.0958 −0.570838 −0.285419 0.958403i 0.592133π-0.592133\pi
−0.285419 + 0.958403i 0.592133π0.592133\pi
450450 0 0
451451 7.81297 + 13.5325i 0.367898 + 0.637218i
452452 0 0
453453 −1.54833 9.70197i −0.0727468 0.455838i
454454 0 0
455455 3.19118 23.1264i 0.149605 1.08418i
456456 0 0
457457 −8.35476 −0.390819 −0.195410 0.980722i 0.562604π-0.562604\pi
−0.195410 + 0.980722i 0.562604π0.562604\pi
458458 0 0
459459 −10.5372 + 16.3517i −0.491834 + 0.763234i
460460 0 0
461461 11.1673 + 19.3423i 0.520112 + 0.900860i 0.999727 + 0.0233807i 0.00744299π0.00744299\pi
−0.479615 + 0.877479i 0.659224π0.659224\pi
462462 0 0
463463 0.0370790 0.0642228i 0.00172321 0.00298469i −0.865163 0.501492i 0.832785π-0.832785\pi
0.866886 + 0.498507i 0.166118π0.166118\pi
464464 0 0
465465 3.08008 + 1.17818i 0.142835 + 0.0546369i
466466 0 0
467467 −14.5828 + 25.2581i −0.674810 + 1.16880i 0.301715 + 0.953398i 0.402441π0.402441\pi
−0.976524 + 0.215407i 0.930892π0.930892\pi
468468 0 0
469469 5.23584 37.9441i 0.241769 1.75209i
470470 0 0
471471 −0.587348 + 0.476768i −0.0270635 + 0.0219683i
472472 0 0
473473 −37.7637 −1.73638
474474 0 0
475475 −4.41583 7.64845i −0.202612 0.350935i
476476 0 0
477477 25.9486 8.49869i 1.18811 0.389128i
478478 0 0
479479 13.9551 24.1710i 0.637626 1.10440i −0.348326 0.937373i 0.613250π-0.613250\pi
0.985952 0.167027i 0.0534168π-0.0534168\pi
480480 0 0
481481 −4.19774 7.27070i −0.191401 0.331515i
482482 0 0
483483 17.5633 31.9617i 0.799157 1.45431i
484484 0 0
485485 1.91884 3.32353i 0.0871301 0.150914i
486486 0 0
487487 2.14409 + 3.71367i 0.0971580 + 0.168283i 0.910507 0.413493i 0.135691π-0.135691\pi
−0.813349 + 0.581776i 0.802358π0.802358\pi
488488 0 0
489489 −4.98238 31.2200i −0.225311 1.41182i
490490 0 0
491491 5.22215 9.04503i 0.235672 0.408196i −0.723796 0.690015i 0.757604π-0.757604\pi
0.959468 + 0.281818i 0.0909375π0.0909375\pi
492492 0 0
493493 1.21770 2.10912i 0.0548425 0.0949900i
494494 0 0
495495 −3.50871 + 16.7000i −0.157705 + 0.750610i
496496 0 0
497497 1.81086 13.1233i 0.0812282 0.588660i
498498 0 0
499499 −3.06312 5.30548i −0.137124 0.237506i 0.789283 0.614030i 0.210453π-0.210453\pi
−0.926407 + 0.376524i 0.877119π0.877119\pi
500500 0 0
501501 −0.417691 2.61729i −0.0186611 0.116932i
502502 0 0
503503 12.4469 0.554982 0.277491 0.960728i 0.410497π-0.410497\pi
0.277491 + 0.960728i 0.410497π0.410497\pi
504504 0 0
505505 30.2175 1.34466
506506 0 0
507507 16.3119 + 6.23957i 0.724436 + 0.277109i
508508 0 0
509509 −5.90450 10.2269i −0.261712 0.453299i 0.704985 0.709222i 0.250954π-0.250954\pi
−0.966697 + 0.255923i 0.917620π0.917620\pi
510510 0 0
511511 −8.88902 + 3.61731i −0.393227 + 0.160021i
512512 0 0
513513 28.1720 + 1.37688i 1.24382 + 0.0607906i
514514 0 0
515515 7.11388 12.3216i 0.313475 0.542955i
516516 0 0
517517 −7.14495 + 12.3754i −0.314235 + 0.544271i
518518 0 0
519519 −2.91748 + 2.36821i −0.128063 + 0.103953i
520520 0 0
521521 5.54828 + 9.60991i 0.243075 + 0.421018i 0.961589 0.274495i 0.0885107π-0.0885107\pi
−0.718514 + 0.695513i 0.755177π0.755177\pi
522522 0 0
523523 −10.6209 + 18.3960i −0.464421 + 0.804401i −0.999175 0.0406065i 0.987071π-0.987071\pi
0.534754 + 0.845008i 0.320404π0.320404\pi
524524 0 0
525525 7.45422 0.157547i 0.325329 0.00687592i
526526 0 0
527527 −1.94052 3.36107i −0.0845302 0.146411i
528528 0 0
529529 −20.1672 + 34.9305i −0.876833 + 1.51872i
530530 0 0
531531 3.57598 17.0202i 0.155184 0.738614i
532532 0 0
533533 −12.1198 20.9921i −0.524967 0.909269i
534534 0 0
535535 −13.7650 −0.595111
536536 0 0
537537 −3.50282 1.33989i −0.151158 0.0578204i
538538 0 0
539539 15.5199 15.1383i 0.668490 0.652054i
540540 0 0
541541 −6.33567 + 10.9737i −0.272392 + 0.471796i −0.969474 0.245195i 0.921148π-0.921148\pi
0.697082 + 0.716991i 0.254481π0.254481\pi
542542 0 0
543543 −0.750167 + 0.608934i −0.0321928 + 0.0261319i
544544 0 0
545545 7.90908 13.6989i 0.338788 0.586798i
546546 0 0
547547 21.4805 + 37.2053i 0.918438 + 1.59078i 0.801788 + 0.597609i 0.203883π0.203883\pi
0.116651 + 0.993173i 0.462784π0.462784\pi
548548 0 0
549549 −2.96850 + 14.1289i −0.126693 + 0.603006i
550550 0 0
551551 −3.53121 −0.150435
552552 0 0
553553 5.19268 37.6313i 0.220815 1.60025i
554554 0 0
555555 −4.31574 + 3.50322i −0.183193 + 0.148704i
556556 0 0
557557 16.5129 + 28.6012i 0.699673 + 1.21187i 0.968580 + 0.248703i 0.0800044π0.0800044\pi
−0.268906 + 0.963166i 0.586662π0.586662\pi
558558 0 0
559559 58.5807 2.47770
560560 0 0
561561 15.5926 12.6570i 0.658319 0.534378i
562562 0 0
563563 −36.8132 −1.55149 −0.775746 0.631046i 0.782626π-0.782626\pi
−0.775746 + 0.631046i 0.782626π0.782626\pi
564564 0 0
565565 −5.72081 −0.240676
566566 0 0
567567 −12.4725 + 20.2839i −0.523797 + 0.851843i
568568 0 0
569569 44.3571 1.85955 0.929774 0.368132i 0.120002π-0.120002\pi
0.929774 + 0.368132i 0.120002π0.120002\pi
570570 0 0
571571 42.5872 1.78222 0.891110 0.453787i 0.149927π-0.149927\pi
0.891110 + 0.453787i 0.149927π0.149927\pi
572572 0 0
573573 −32.2741 + 26.1979i −1.34827 + 1.09443i
574574 0 0
575575 −12.9482 −0.539977
576576 0 0
577577 16.3209 + 28.2687i 0.679450 + 1.17684i 0.975147 + 0.221559i 0.0711147π0.0711147\pi
−0.295697 + 0.955282i 0.595552π0.595552\pi
578578 0 0
579579 28.6160 23.2285i 1.18924 0.965343i
580580 0 0
581581 −18.7785 + 7.64175i −0.779063 + 0.317033i
582582 0 0
583583 −28.1895 −1.16749
584584 0 0
585585 5.44285 25.9058i 0.225034 1.07107i
586586 0 0
587587 13.1270 + 22.7366i 0.541809 + 0.938441i 0.998800 + 0.0489701i 0.0155939π0.0155939\pi
−0.456991 + 0.889471i 0.651073π0.651073\pi
588588 0 0
589589 −2.81365 + 4.87338i −0.115934 + 0.200804i
590590 0 0
591591 20.0059 16.2394i 0.822934 0.668002i
592592 0 0
593593 −2.59998 + 4.50330i −0.106768 + 0.184928i −0.914459 0.404678i 0.867384π-0.867384\pi
0.807691 + 0.589606i 0.200717π0.200717\pi
594594 0 0
595595 14.3627 + 11.1636i 0.588814 + 0.457663i
596596 0 0
597597 19.9915 + 7.64707i 0.818196 + 0.312974i
598598 0 0
599599 −26.3675 −1.07735 −0.538673 0.842515i 0.681074π-0.681074\pi
−0.538673 + 0.842515i 0.681074π0.681074\pi
600600 0 0
601601 −15.4505 26.7611i −0.630239 1.09161i −0.987503 0.157603i 0.949623π-0.949623\pi
0.357263 0.934004i 0.383710π-0.383710\pi
602602 0 0
603603 8.93021 42.5042i 0.363666 1.73091i
604604 0 0
605605 −1.29240 + 2.23851i −0.0525436 + 0.0910082i
606606 0 0
607607 3.83661 + 6.64519i 0.155723 + 0.269720i 0.933322 0.359040i 0.116896π-0.116896\pi
−0.777599 + 0.628760i 0.783563π0.783563\pi
608608 0 0
609609 1.43568 2.61265i 0.0581765 0.105870i
610610 0 0
611611 11.0836 19.1973i 0.448393 0.776639i
612612 0 0
613613 7.97498 + 13.8131i 0.322106 + 0.557905i 0.980922 0.194399i 0.0622758π-0.0622758\pi
−0.658816 + 0.752304i 0.728942π0.728942\pi
614614 0 0
615615 −12.4605 + 10.1146i −0.502456 + 0.407859i
616616 0 0
617617 −3.67011 + 6.35682i −0.147753 + 0.255916i −0.930397 0.366554i 0.880537π-0.880537\pi
0.782644 + 0.622470i 0.213871π0.213871\pi
618618 0 0
619619 10.2842 17.8127i 0.413357 0.715955i −0.581898 0.813262i 0.697690π-0.697690\pi
0.995254 + 0.0973072i 0.0310229π0.0310229\pi
620620 0 0
621621 22.3998 34.7603i 0.898873 1.39488i
622622 0 0
623623 24.0981 + 18.7305i 0.965469 + 0.750421i
624624 0 0
625625 7.10891 + 12.3130i 0.284356 + 0.492520i
626626 0 0
627627 −27.1975 10.4035i −1.08616 0.415476i
628628 0 0
629629 6.54182 0.260840
630630 0 0
631631 5.09394 0.202787 0.101393 0.994846i 0.467670π-0.467670\pi
0.101393 + 0.994846i 0.467670π0.467670\pi
632632 0 0
633633 −4.72662 29.6175i −0.187866 1.17719i
634634 0 0
635635 −9.99705 17.3154i −0.396721 0.687141i
636636 0 0
637637 −24.0751 + 23.4832i −0.953892 + 0.930439i
638638 0 0
639639 3.08859 14.7005i 0.122183 0.581541i
640640 0 0
641641 −6.31861 + 10.9442i −0.249570 + 0.432268i −0.963407 0.268044i 0.913623π-0.913623\pi
0.713836 + 0.700312i 0.246956π0.246956\pi
642642 0 0
643643 −12.4329 + 21.5344i −0.490306 + 0.849235i −0.999938 0.0111579i 0.996448π-0.996448\pi
0.509632 + 0.860393i 0.329782π0.329782\pi
644644 0 0
645645 −6.11247 38.3013i −0.240678 1.50811i
646646 0 0
647647 −1.12339 1.94577i −0.0441650 0.0764960i 0.843098 0.537760i 0.180729π-0.180729\pi
−0.887263 + 0.461264i 0.847396π0.847396\pi
648648 0 0
649649 −8.97762 + 15.5497i −0.352403 + 0.610379i
650650 0 0
651651 −2.46175 4.06310i −0.0964835 0.159246i
652652 0 0
653653 −1.02881 1.78195i −0.0402604 0.0697330i 0.845193 0.534461i 0.179485π-0.179485\pi
−0.885453 + 0.464728i 0.846152π0.846152\pi
654654 0 0
655655 14.7438 25.5370i 0.576088 0.997815i
656656 0 0
657657 −10.3413 + 3.38697i −0.403452 + 0.132138i
658658 0 0
659659 4.16599 + 7.21571i 0.162284 + 0.281084i 0.935687 0.352830i 0.114781π-0.114781\pi
−0.773403 + 0.633914i 0.781447π0.781447\pi
660660 0 0
661661 34.0926 1.32605 0.663024 0.748598i 0.269273π-0.269273\pi
0.663024 + 0.748598i 0.269273π0.269273\pi
662662 0 0
663663 −24.1879 + 19.6341i −0.939379 + 0.762523i
664664 0 0
665665 3.60543 26.1285i 0.139812 1.01322i
666666 0 0
667667 −2.58857 + 4.48353i −0.100230 + 0.173603i
668668 0 0
669669 3.70427 + 1.41694i 0.143215 + 0.0547823i
670670 0 0
671671 7.45255 12.9082i 0.287702 0.498315i
672672 0 0
673673 0.571008 + 0.989016i 0.0220108 + 0.0381237i 0.876821 0.480817i 0.159660π-0.159660\pi
−0.854810 + 0.518941i 0.826327π0.826327\pi
674674 0 0
675675 8.44410 + 0.412697i 0.325013 + 0.0158847i
676676 0 0
677677 36.3812 1.39824 0.699121 0.715004i 0.253575π-0.253575\pi
0.699121 + 0.715004i 0.253575π0.253575\pi
678678 0 0
679679 −5.12077 + 2.08386i −0.196517 + 0.0799711i
680680 0 0
681681 −0.971817 6.08950i −0.0372401 0.233350i
682682 0 0
683683 −3.11274 5.39142i −0.119106 0.206297i 0.800308 0.599589i 0.204669π-0.204669\pi
−0.919414 + 0.393292i 0.871336π0.871336\pi
684684 0 0
685685 −24.6846 −0.943152
686686 0 0
687687 −43.6138 16.6830i −1.66397 0.636496i
688688 0 0
689689 43.7288 1.66593
690690 0 0
691691 39.8259 1.51505 0.757525 0.652806i 0.226408π-0.226408\pi
0.757525 + 0.652806i 0.226408π0.226408\pi
692692 0 0
693693 18.7549 15.8930i 0.712440 0.603725i
694694 0 0
695695 14.9480 0.567008
696696 0 0
697697 18.8877 0.715422
698698 0 0
699699 5.85890 + 36.7124i 0.221604 + 1.38859i
700700 0 0
701701 −48.3337 −1.82554 −0.912769 0.408477i 0.866060π-0.866060\pi
−0.912769 + 0.408477i 0.866060π0.866060\pi
702702 0 0
703703 −4.74265 8.21452i −0.178873 0.309816i
704704 0 0
705705 −13.7081 5.24357i −0.516277 0.197484i
706706 0 0
707707 −34.3700 26.7145i −1.29262 1.00470i
708708 0 0
709709 −16.0840 −0.604046 −0.302023 0.953301i 0.597662π-0.597662\pi
−0.302023 + 0.953301i 0.597662π0.597662\pi
710710 0 0
711711 8.85660 42.1539i 0.332149 1.58089i
712712 0 0
713713 4.12512 + 7.14491i 0.154487 + 0.267579i
714714 0 0
715715 −13.6645 + 23.6676i −0.511023 + 0.885117i
716716 0 0
717717 −2.54384 15.9400i −0.0950015 0.595288i
718718 0 0
719719 −21.0734 + 36.5002i −0.785906 + 1.36123i 0.142550 + 0.989788i 0.454470π0.454470\pi
−0.928456 + 0.371442i 0.878864π0.878864\pi
720720 0 0
721721 −18.9847 + 7.72566i −0.707026 + 0.287718i
722722 0 0
723723 5.51402 + 34.5514i 0.205069 + 1.28498i
724724 0 0
725725 −1.05842 −0.0393089
726726 0 0
727727 12.9548 + 22.4384i 0.480467 + 0.832192i 0.999749 0.0224103i 0.00713401π-0.00713401\pi
−0.519282 + 0.854603i 0.673801π0.673801\pi
728728 0 0
729729 −15.7158 + 21.9548i −0.582068 + 0.813140i
730730 0 0
731731 −22.8232 + 39.5310i −0.844148 + 1.46211i
732732 0 0
733733 −10.2027 17.6716i −0.376846 0.652716i 0.613756 0.789496i 0.289658π-0.289658\pi
−0.990601 + 0.136780i 0.956325π0.956325\pi
734734 0 0
735735 17.8659 + 13.2906i 0.658994 + 0.490229i
736736 0 0
737737 −22.4196 + 38.8320i −0.825838 + 1.43039i
738738 0 0
739739 11.8953 + 20.6033i 0.437576 + 0.757903i 0.997502 0.0706392i 0.0225039π-0.0225039\pi
−0.559926 + 0.828542i 0.689171π0.689171\pi
740740 0 0
741741 42.1899 + 16.1383i 1.54989 + 0.592857i
742742 0 0
743743 −21.6320 + 37.4678i −0.793603 + 1.37456i 0.130120 + 0.991498i 0.458464π0.458464\pi
−0.923723 + 0.383062i 0.874870π0.874870\pi
744744 0 0
745745 6.91430 11.9759i 0.253321 0.438764i
746746 0 0
747747 −21.8465 + 7.15515i −0.799320 + 0.261793i
748748 0 0
749749 15.6565 + 12.1692i 0.572078 + 0.444654i
750750 0 0
751751 −7.18465 12.4442i −0.262172 0.454095i 0.704647 0.709558i 0.251105π-0.251105\pi
−0.966819 + 0.255463i 0.917772π0.917772\pi
752752 0 0
753753 36.5560 29.6736i 1.33217 1.08137i
754754 0 0
755755 −10.4176 −0.379136
756756 0 0
757757 39.7854 1.44603 0.723013 0.690835i 0.242757π-0.242757\pi
0.723013 + 0.690835i 0.242757π0.242757\pi
758758 0 0
759759 −33.1465 + 26.9060i −1.20314 + 0.976626i
760760 0 0
761761 11.1966 + 19.3932i 0.405878 + 0.703002i 0.994423 0.105463i 0.0336324π-0.0336324\pi
−0.588545 + 0.808464i 0.700299π0.700299\pi
762762 0 0
763763 −21.1068 + 8.58924i −0.764117 + 0.310951i
764764 0 0
765765 15.3610 + 13.7659i 0.555378 + 0.497707i
766766 0 0
767767 13.9265 24.1213i 0.502856 0.870971i
768768 0 0
769769 −1.45546 + 2.52093i −0.0524853 + 0.0909071i −0.891074 0.453857i 0.850048π-0.850048\pi
0.838589 + 0.544764i 0.183381π0.183381\pi
770770 0 0
771771 46.0766 + 17.6251i 1.65941 + 0.634751i
772772 0 0
773773 −6.68612 11.5807i −0.240483 0.416529i 0.720369 0.693591i 0.243972π-0.243972\pi
−0.960852 + 0.277062i 0.910639π0.910639\pi
774774 0 0
775775 −0.843347 + 1.46072i −0.0302939 + 0.0524706i
776776 0 0
777777 8.00591 0.169207i 0.287211 0.00607028i
778778 0 0
779779 −13.6931 23.7171i −0.490606 0.849754i
780780 0 0
781781 −7.75403 + 13.4304i −0.277461 + 0.480577i
782782 0 0
783783 1.83103 2.84141i 0.0654355 0.101544i
784784 0 0
785785 0.401073 + 0.694679i 0.0143149 + 0.0247941i
786786 0 0
787787 23.8528 0.850260 0.425130 0.905132i 0.360228π-0.360228\pi
0.425130 + 0.905132i 0.360228π0.360228\pi
788788 0 0
789789 0.982156 + 6.15428i 0.0349657 + 0.219098i
790790 0 0
791791 6.50696 + 5.05761i 0.231361 + 0.179828i
792792 0 0
793793 −11.5607 + 20.0237i −0.410533 + 0.711063i
794794 0 0
795795 −4.56279 28.5909i −0.161825 1.01401i
796796 0 0
797797 −6.10559 + 10.5752i −0.216271 + 0.374593i −0.953665 0.300870i 0.902723π-0.902723\pi
0.737394 + 0.675463i 0.236056π0.236056\pi
798798 0 0
799799 8.63639 + 14.9587i 0.305533 + 0.529199i
800800 0 0
801801 25.7730 + 23.0967i 0.910645 + 0.816082i
802802 0 0
803803 11.2344 0.396452
804804 0 0
805805 −30.5320 23.7314i −1.07611 0.836421i
806806 0 0
807807 −36.3219 13.8937i −1.27859 0.489082i
808808 0 0
809809 26.7838 + 46.3910i 0.941669 + 1.63102i 0.762287 + 0.647240i 0.224077π0.224077\pi
0.179383 + 0.983779i 0.442590π0.442590\pi
810810 0 0
811811 −1.81310 −0.0636667 −0.0318334 0.999493i 0.510135π-0.510135\pi
−0.0318334 + 0.999493i 0.510135π0.510135\pi
812812 0 0
813813 8.07614 + 50.6059i 0.283243 + 1.77483i
814814 0 0
815815 −33.5229 −1.17426
816816 0 0
817817 66.1851 2.31552
818818 0 0
819819 −29.0934 + 24.6539i −1.01661 + 0.861476i
820820 0 0
821821 −39.6743 −1.38464 −0.692321 0.721590i 0.743412π-0.743412\pi
−0.692321 + 0.721590i 0.743412π0.743412\pi
822822 0 0
823823 −16.8131 −0.586069 −0.293034 0.956102i 0.594665π-0.594665\pi
−0.293034 + 0.956102i 0.594665π0.594665\pi
824824 0 0
825825 −8.15202 3.11828i −0.283817 0.108565i
826826 0 0
827827 −37.2198 −1.29426 −0.647130 0.762379i 0.724031π-0.724031\pi
−0.647130 + 0.762379i 0.724031π0.724031\pi
828828 0 0
829829 −11.4365 19.8086i −0.397206 0.687981i 0.596174 0.802855i 0.296687π-0.296687\pi
−0.993380 + 0.114874i 0.963354π0.963354\pi
830830 0 0
831831 5.56479 + 34.8695i 0.193041 + 1.20961i
832832 0 0
833833 −6.46703 25.3954i −0.224069 0.879898i
834834 0 0
835835 −2.81035 −0.0972562
836836 0 0
837837 −2.46245 4.79100i −0.0851146 0.165601i
838838 0 0
839839 −18.4071 31.8820i −0.635484 1.10069i −0.986412 0.164288i 0.947467π-0.947467\pi
0.350929 0.936402i 0.385866π-0.385866\pi
840840 0 0
841841 14.2884 24.7482i 0.492704 0.853388i
842842 0 0
843843 7.24643 + 2.77188i 0.249580 + 0.0954686i
844844 0 0
845845 9.25921 16.0374i 0.318527 0.551704i
846846 0 0
847847 3.44901 1.40354i 0.118509 0.0482264i
848848 0 0
849849 2.79282 2.26702i 0.0958495 0.0778040i
850850 0 0
851851 −13.9065 −0.476709
852852 0 0
853853 6.98355 + 12.0959i 0.239112 + 0.414155i 0.960460 0.278419i 0.0898102π-0.0898102\pi
−0.721347 + 0.692573i 0.756477π0.756477\pi
854854 0 0
855855 6.14939 29.2686i 0.210305 1.00097i
856856 0 0
857857 −8.78386 + 15.2141i −0.300051 + 0.519703i −0.976147 0.217110i 0.930337π-0.930337\pi
0.676096 + 0.736813i 0.263670π0.263670\pi
858858 0 0
859859 1.42288 + 2.46451i 0.0485482 + 0.0840879i 0.889278 0.457366i 0.151207π-0.151207\pi
−0.840730 + 0.541454i 0.817874π0.817874\pi
860860 0 0
861861 23.1148 0.488539i 0.787751 0.0166493i
862862 0 0
863863 27.7115 47.9977i 0.943310 1.63386i 0.184210 0.982887i 0.441027π-0.441027\pi
0.759100 0.650974i 0.225639π-0.225639\pi
864864 0 0
865865 1.99221 + 3.45061i 0.0677372 + 0.117324i
866866 0 0
867867 0.814721 + 5.10512i 0.0276694 + 0.173379i
868868 0 0
869869 −22.2348 + 38.5119i −0.754265 + 1.30643i
870870 0 0
871871 34.7783 60.2378i 1.17842 2.04108i
872872 0 0
873873 −5.95739 + 1.95116i −0.201627 + 0.0660368i
874874 0 0
875875 4.40170 31.8991i 0.148805 1.07839i
876876 0 0
877877 −27.4345 47.5179i −0.926396 1.60456i −0.789301 0.614006i 0.789557π-0.789557\pi
−0.137095 0.990558i 0.543776π-0.543776\pi
878878 0 0
879879 −0.484420 3.03542i −0.0163391 0.102382i
880880 0 0
881881 −51.1572 −1.72353 −0.861765 0.507307i 0.830641π-0.830641\pi
−0.861765 + 0.507307i 0.830641π0.830641\pi
882882 0 0
883883 −38.6438 −1.30047 −0.650234 0.759734i 0.725329π-0.725329\pi
−0.650234 + 0.759734i 0.725329π0.725329\pi
884884 0 0
885885 −17.2242 6.58854i −0.578985 0.221471i
886886 0 0
887887 −8.92626 15.4607i −0.299714 0.519121i 0.676356 0.736575i 0.263558π-0.263558\pi
−0.976071 + 0.217454i 0.930225π0.930225\pi
888888 0 0
889889 −3.93722 + 28.5330i −0.132050 + 0.956966i
890890 0 0
891891 22.4739 16.4901i 0.752903 0.552441i
892892 0 0
893893 12.5223 21.6893i 0.419043 0.725805i
894894 0 0
895895 −1.98833 + 3.44388i −0.0664624 + 0.115116i
896896 0 0
897897 51.4182 41.7377i 1.71680 1.39358i
898898 0 0
899899 0.337199 + 0.584047i 0.0112462 + 0.0194790i
900900 0 0
901901 −17.0369 + 29.5088i −0.567581 + 0.983080i
902902 0 0
903903 −26.9087 + 48.9686i −0.895465 + 1.62957i
904904 0 0
905905 0.512255 + 0.887252i 0.0170279 + 0.0294932i
906906 0 0
907907 −18.2332 + 31.5807i −0.605422 + 1.04862i 0.386563 + 0.922263i 0.373662π0.373662\pi
−0.991985 + 0.126358i 0.959671π0.959671\pi
908908 0 0
909909 −36.7589 32.9418i −1.21921 1.09261i
910910 0 0
911911 −18.9847 32.8825i −0.628993 1.08945i −0.987754 0.156018i 0.950134π-0.950134\pi
0.358762 0.933429i 0.383199π-0.383199\pi
912912 0 0
913913 23.7331 0.785451
914914 0 0
915915 14.2982 + 5.46931i 0.472685 + 0.180810i
916916 0 0
917917 −39.3465 + 16.0117i −1.29934 + 0.528754i
918918 0 0
919919 1.21770 2.10911i 0.0401681 0.0695732i −0.845242 0.534383i 0.820544π-0.820544\pi
0.885411 + 0.464810i 0.153877π0.153877\pi
920920 0 0
921921 26.4000 21.4297i 0.869909 0.706132i
922922 0 0
923923 12.0284 20.8338i 0.395919 0.685752i
924924 0 0
925925 −1.42153 2.46217i −0.0467398 0.0809557i
926926 0 0
927927 −22.0863 + 7.23371i −0.725410 + 0.237586i
928928 0 0
929929 −35.4808 −1.16409 −0.582044 0.813157i 0.697747π-0.697747\pi
−0.582044 + 0.813157i 0.697747π0.697747\pi
930930 0 0
931931 −27.2004 + 26.5316i −0.891456 + 0.869538i
932932 0 0
933933 −17.9069 + 14.5356i −0.586245 + 0.475874i
934934 0 0
935935 −10.6475 18.4420i −0.348209 0.603116i
936936 0 0
937937 −30.0427 −0.981452 −0.490726 0.871314i 0.663268π-0.663268\pi
−0.490726 + 0.871314i 0.663268π0.663268\pi
938938 0 0
939939 −6.25698 + 5.07899i −0.204189 + 0.165746i
940940 0 0
941941 −30.2499 −0.986119 −0.493060 0.869996i 0.664122π-0.664122\pi
−0.493060 + 0.869996i 0.664122π0.664122\pi
942942 0 0
943943 −40.1511 −1.30750
944944 0 0
945945 19.1549 + 16.4494i 0.623110 + 0.535100i
946946 0 0
947947 −33.9889 −1.10449 −0.552245 0.833682i 0.686229π-0.686229\pi
−0.552245 + 0.833682i 0.686229π0.686229\pi
948948 0 0
949949 −17.4272 −0.565711
950950 0 0
951951 5.54790 4.50340i 0.179903 0.146033i
952952 0 0
953953 −21.4324 −0.694265 −0.347132 0.937816i 0.612845π-0.612845\pi
−0.347132 + 0.937816i 0.612845π0.612845\pi
954954 0 0
955955 22.0385 + 38.1719i 0.713151 + 1.23521i
956956 0 0
957957 −2.70949 + 2.19938i −0.0875854 + 0.0710958i
958958 0 0
959959 28.0768 + 21.8230i 0.906647 + 0.704702i
960960 0 0
961961 −29.9253 −0.965332
962962 0 0
963963 16.7448 + 15.0060i 0.539592 + 0.483560i
964964 0 0
965965 −19.5406 33.8452i −0.629033 1.08952i
966966 0 0
967967 −12.4095 + 21.4938i −0.399061 + 0.691194i −0.993610 0.112865i 0.963997π-0.963997\pi
0.594549 + 0.804059i 0.297331π0.297331\pi
968968 0 0
969969 −27.3277 + 22.1828i −0.877893 + 0.712613i
970970 0 0
971971 13.9437 24.1512i 0.447475 0.775050i −0.550746 0.834673i 0.685657π-0.685657\pi
0.998221 + 0.0596234i 0.0189900π0.0189900\pi
972972 0 0
973973 −17.0021 13.2151i −0.545062 0.423656i
974974 0 0
975975 12.6458 + 4.83721i 0.404988 + 0.154915i
976976 0 0
977977 27.2473 0.871719 0.435859 0.900015i 0.356445π-0.356445\pi
0.435859 + 0.900015i 0.356445π0.356445\pi
978978 0 0
979979 −17.8645 30.9423i −0.570953 0.988920i
980980 0 0
981981 −24.5552 + 8.04230i −0.783986 + 0.256771i
982982 0 0
983983 −6.94539 + 12.0298i −0.221523 + 0.383690i −0.955271 0.295733i 0.904436π-0.904436\pi
0.733747 + 0.679422i 0.237770π0.237770\pi
984984 0 0
985985 −13.6611 23.6618i −0.435280 0.753928i
986986 0 0
987987 10.9562 + 18.0831i 0.348738 + 0.575591i
988988 0 0
989989 48.5173 84.0344i 1.54276 2.67214i
990990 0 0
991991 −21.3271 36.9397i −0.677479 1.17343i −0.975738 0.218942i 0.929739π-0.929739\pi
0.298259 0.954485i 0.403594π-0.403594\pi
992992 0 0
993993 0.0592500 0.0480950i 0.00188024 0.00152625i
994994 0 0
995995 11.3479 19.6551i 0.359752 0.623108i
996996 0 0
997997 −21.5905 + 37.3959i −0.683779 + 1.18434i 0.290040 + 0.957014i 0.406331π0.406331\pi
−0.973819 + 0.227325i 0.927002π0.927002\pi
998998 0 0
999999 9.06905 + 0.443241i 0.286932 + 0.0140235i
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.625.3 22
3.2 odd 2 3024.2.q.k.2305.4 22
4.3 odd 2 504.2.q.d.121.9 yes 22
7.4 even 3 1008.2.t.k.193.11 22
9.2 odd 6 3024.2.t.l.289.8 22
9.7 even 3 1008.2.t.k.961.11 22
12.11 even 2 1512.2.q.c.793.4 22
21.11 odd 6 3024.2.t.l.1873.8 22
28.11 odd 6 504.2.t.d.193.1 yes 22
36.7 odd 6 504.2.t.d.457.1 yes 22
36.11 even 6 1512.2.t.d.289.8 22
63.11 odd 6 3024.2.q.k.2881.4 22
63.25 even 3 inner 1008.2.q.k.529.3 22
84.11 even 6 1512.2.t.d.361.8 22
252.11 even 6 1512.2.q.c.1369.4 22
252.151 odd 6 504.2.q.d.25.9 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.q.d.25.9 22 252.151 odd 6
504.2.q.d.121.9 yes 22 4.3 odd 2
504.2.t.d.193.1 yes 22 28.11 odd 6
504.2.t.d.457.1 yes 22 36.7 odd 6
1008.2.q.k.529.3 22 63.25 even 3 inner
1008.2.q.k.625.3 22 1.1 even 1 trivial
1008.2.t.k.193.11 22 7.4 even 3
1008.2.t.k.961.11 22 9.7 even 3
1512.2.q.c.793.4 22 12.11 even 2
1512.2.q.c.1369.4 22 252.11 even 6
1512.2.t.d.289.8 22 36.11 even 6
1512.2.t.d.361.8 22 84.11 even 6
3024.2.q.k.2305.4 22 3.2 odd 2
3024.2.q.k.2881.4 22 63.11 odd 6
3024.2.t.l.289.8 22 9.2 odd 6
3024.2.t.l.1873.8 22 21.11 odd 6