Properties

Label 2646.2.f.l.883.1
Level 26462646
Weight 22
Character 2646.883
Analytic conductor 21.12821.128
Analytic rank 00
Dimension 66
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] = [2646,2,Mod(883,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) 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("2646.883"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2646=23372 2646 = 2 \cdot 3^{3} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2646.f (of order 33, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,-3,0,-3,-1,0,0,6,0,2,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 21.128416374821.1284163748
Analytic rank: 00
Dimension: 66
Relative dimension: 33 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 6.0.309123.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x63x5+10x415x3+19x212x+3 x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 3 3
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 883.1
Root 0.5000001.41036i0.500000 - 1.41036i of defining polynomial
Character χ\chi == 2646.883
Dual form 2646.2.f.l.1765.1

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+(0.500000+0.866025i)q2+(0.5000000.866025i)q4+(1.590972.75564i)q5+1.00000q8+3.18194q10+(1.590972.75564i)q11+(2.85185+4.93955i)q13+(0.500000+0.866025i)q161.52175q17+1.28263q19+(1.59097+2.75564i)q20+(1.59097+2.75564i)q22+(1.11956+1.93914i)q23+(2.56238+4.43818i)q255.70370q26+(3.540636.13255i)q29+(4.71053+8.15888i)q31+(0.5000000.866025i)q32+(0.7608771.31788i)q341.00000q37+(0.641315+1.11079i)q38+(1.590972.75564i)q40+(2.80150+4.85235i)q41+(3.414235.91362i)q433.18194q442.23912q46+(2.91423+5.04759i)q47+(2.562384.43818i)q50+(2.851854.93955i)q52+2.05718q5310.1248q55+(3.54063+6.13255i)q58+(0.5623820.974074i)q59+(1.56238+2.70612i)q619.42107q62+1.00000q64+(9.0744215.7174i)q65+(5.483459.49761i)q67+(0.760877+1.31788i)q688.69002q71+4.96690q73+(0.5000000.866025i)q74+(0.6413151.11079i)q76+(2.069223.58399i)q79+3.18194q805.60301q82+(4.033796.98673i)q83+(2.42107+4.19341i)q85+(3.41423+5.91362i)q86+(1.590972.75564i)q88+0.225450q89+(1.119561.93914i)q92+(2.914235.04759i)q94+(2.040633.53447i)q95+(7.4210712.8537i)q97+O(q100)q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.59097 - 2.75564i) q^{5} +1.00000 q^{8} +3.18194 q^{10} +(1.59097 - 2.75564i) q^{11} +(2.85185 + 4.93955i) q^{13} +(-0.500000 + 0.866025i) q^{16} -1.52175 q^{17} +1.28263 q^{19} +(-1.59097 + 2.75564i) q^{20} +(1.59097 + 2.75564i) q^{22} +(1.11956 + 1.93914i) q^{23} +(-2.56238 + 4.43818i) q^{25} -5.70370 q^{26} +(3.54063 - 6.13255i) q^{29} +(4.71053 + 8.15888i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.760877 - 1.31788i) q^{34} -1.00000 q^{37} +(-0.641315 + 1.11079i) q^{38} +(-1.59097 - 2.75564i) q^{40} +(2.80150 + 4.85235i) q^{41} +(3.41423 - 5.91362i) q^{43} -3.18194 q^{44} -2.23912 q^{46} +(-2.91423 + 5.04759i) q^{47} +(-2.56238 - 4.43818i) q^{50} +(2.85185 - 4.93955i) q^{52} +2.05718 q^{53} -10.1248 q^{55} +(3.54063 + 6.13255i) q^{58} +(-0.562382 - 0.974074i) q^{59} +(-1.56238 + 2.70612i) q^{61} -9.42107 q^{62} +1.00000 q^{64} +(9.07442 - 15.7174i) q^{65} +(-5.48345 - 9.49761i) q^{67} +(0.760877 + 1.31788i) q^{68} -8.69002 q^{71} +4.96690 q^{73} +(0.500000 - 0.866025i) q^{74} +(-0.641315 - 1.11079i) q^{76} +(2.06922 - 3.58399i) q^{79} +3.18194 q^{80} -5.60301 q^{82} +(4.03379 - 6.98673i) q^{83} +(2.42107 + 4.19341i) q^{85} +(3.41423 + 5.91362i) q^{86} +(1.59097 - 2.75564i) q^{88} +0.225450 q^{89} +(1.11956 - 1.93914i) q^{92} +(-2.91423 - 5.04759i) q^{94} +(-2.04063 - 3.53447i) q^{95} +(7.42107 - 12.8537i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q3q23q4q5+6q8+2q10+q11+8q133q168q17+6q19q20+q22+7q23+2q2516q26+5q29+20q313q32+4q34++28q97+O(q100) 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} + 2 q^{10} + q^{11} + 8 q^{13} - 3 q^{16} - 8 q^{17} + 6 q^{19} - q^{20} + q^{22} + 7 q^{23} + 2 q^{25} - 16 q^{26} + 5 q^{29} + 20 q^{31} - 3 q^{32} + 4 q^{34}+ \cdots + 28 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2646Z)×\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times.

nn 785785 10811081
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.500000 + 0.866025i −0.353553 + 0.612372i
33 0 0
44 −0.500000 0.866025i −0.250000 0.433013i
55 −1.59097 2.75564i −0.711504 1.23236i −0.964292 0.264840i 0.914681π-0.914681\pi
0.252788 0.967522i 0.418652π-0.418652\pi
66 0 0
77 0 0
88 1.00000 0.353553
99 0 0
1010 3.18194 1.00622
1111 1.59097 2.75564i 0.479696 0.830858i −0.520033 0.854146i 0.674080π-0.674080\pi
0.999729 + 0.0232884i 0.00741361π0.00741361\pi
1212 0 0
1313 2.85185 + 4.93955i 0.790960 + 1.36998i 0.925373 + 0.379058i 0.123752π0.123752\pi
−0.134412 + 0.990925i 0.542915π0.542915\pi
1414 0 0
1515 0 0
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 −1.52175 −0.369079 −0.184540 0.982825i 0.559079π-0.559079\pi
−0.184540 + 0.982825i 0.559079π0.559079\pi
1818 0 0
1919 1.28263 0.294256 0.147128 0.989117i 0.452997π-0.452997\pi
0.147128 + 0.989117i 0.452997π0.452997\pi
2020 −1.59097 + 2.75564i −0.355752 + 0.616181i
2121 0 0
2222 1.59097 + 2.75564i 0.339196 + 0.587505i
2323 1.11956 + 1.93914i 0.233445 + 0.404338i 0.958820 0.284016i 0.0916669π-0.0916669\pi
−0.725375 + 0.688354i 0.758334π0.758334\pi
2424 0 0
2525 −2.56238 + 4.43818i −0.512476 + 0.887635i
2626 −5.70370 −1.11859
2727 0 0
2828 0 0
2929 3.54063 6.13255i 0.657478 1.13879i −0.323788 0.946130i 0.604957π-0.604957\pi
0.981266 0.192656i 0.0617101π-0.0617101\pi
3030 0 0
3131 4.71053 + 8.15888i 0.846037 + 1.46538i 0.884718 + 0.466127i 0.154351π0.154351\pi
−0.0386810 + 0.999252i 0.512316π0.512316\pi
3232 −0.500000 0.866025i −0.0883883 0.153093i
3333 0 0
3434 0.760877 1.31788i 0.130489 0.226014i
3535 0 0
3636 0 0
3737 −1.00000 −0.164399 −0.0821995 0.996616i 0.526194π-0.526194\pi
−0.0821995 + 0.996616i 0.526194π0.526194\pi
3838 −0.641315 + 1.11079i −0.104035 + 0.180194i
3939 0 0
4040 −1.59097 2.75564i −0.251555 0.435706i
4141 2.80150 + 4.85235i 0.437522 + 0.757810i 0.997498 0.0706992i 0.0225230π-0.0225230\pi
−0.559976 + 0.828509i 0.689190π0.689190\pi
4242 0 0
4343 3.41423 5.91362i 0.520665 0.901819i −0.479046 0.877790i 0.659017π-0.659017\pi
0.999711 0.0240288i 0.00764935π-0.00764935\pi
4444 −3.18194 −0.479696
4545 0 0
4646 −2.23912 −0.330141
4747 −2.91423 + 5.04759i −0.425084 + 0.736267i −0.996428 0.0844432i 0.973089π-0.973089\pi
0.571344 + 0.820711i 0.306422π0.306422\pi
4848 0 0
4949 0 0
5050 −2.56238 4.43818i −0.362375 0.627653i
5151 0 0
5252 2.85185 4.93955i 0.395480 0.684992i
5353 2.05718 0.282575 0.141288 0.989969i 0.454876π-0.454876\pi
0.141288 + 0.989969i 0.454876π0.454876\pi
5454 0 0
5555 −10.1248 −1.36522
5656 0 0
5757 0 0
5858 3.54063 + 6.13255i 0.464907 + 0.805243i
5959 −0.562382 0.974074i −0.0732159 0.126814i 0.827093 0.562065i 0.189993π-0.189993\pi
−0.900309 + 0.435251i 0.856660π0.856660\pi
6060 0 0
6161 −1.56238 + 2.70612i −0.200042 + 0.346484i −0.948542 0.316652i 0.897441π-0.897441\pi
0.748499 + 0.663135i 0.230775π0.230775\pi
6262 −9.42107 −1.19648
6363 0 0
6464 1.00000 0.125000
6565 9.07442 15.7174i 1.12554 1.94950i
6666 0 0
6767 −5.48345 9.49761i −0.669910 1.16032i −0.977929 0.208938i 0.932999π-0.932999\pi
0.308019 0.951380i 0.400334π-0.400334\pi
6868 0.760877 + 1.31788i 0.0922699 + 0.159816i
6969 0 0
7070 0 0
7171 −8.69002 −1.03132 −0.515658 0.856794i 0.672452π-0.672452\pi
−0.515658 + 0.856794i 0.672452π0.672452\pi
7272 0 0
7373 4.96690 0.581331 0.290666 0.956825i 0.406123π-0.406123\pi
0.290666 + 0.956825i 0.406123π0.406123\pi
7474 0.500000 0.866025i 0.0581238 0.100673i
7575 0 0
7676 −0.641315 1.11079i −0.0735639 0.127416i
7777 0 0
7878 0 0
7979 2.06922 3.58399i 0.232805 0.403231i −0.725827 0.687877i 0.758543π-0.758543\pi
0.958633 + 0.284646i 0.0918762π0.0918762\pi
8080 3.18194 0.355752
8181 0 0
8282 −5.60301 −0.618749
8383 4.03379 6.98673i 0.442766 0.766893i −0.555127 0.831765i 0.687331π-0.687331\pi
0.997894 + 0.0648718i 0.0206639π0.0206639\pi
8484 0 0
8585 2.42107 + 4.19341i 0.262602 + 0.454839i
8686 3.41423 + 5.91362i 0.368166 + 0.637682i
8787 0 0
8888 1.59097 2.75564i 0.169598 0.293753i
8989 0.225450 0.0238977 0.0119488 0.999929i 0.496196π-0.496196\pi
0.0119488 + 0.999929i 0.496196π0.496196\pi
9090 0 0
9191 0 0
9292 1.11956 1.93914i 0.116722 0.202169i
9393 0 0
9494 −2.91423 5.04759i −0.300580 0.520620i
9595 −2.04063 3.53447i −0.209364 0.362629i
9696 0 0
9797 7.42107 12.8537i 0.753495 1.30509i −0.192624 0.981273i 0.561700π-0.561700\pi
0.946119 0.323819i 0.104967π-0.104967\pi
9898 0 0
9999 0 0
100100 5.12476 0.512476
101101 9.29467 16.0988i 0.924854 1.60189i 0.133058 0.991108i 0.457520π-0.457520\pi
0.791796 0.610786i 0.209146π-0.209146\pi
102102 0 0
103103 0.141315 + 0.244765i 0.0139242 + 0.0241174i 0.872904 0.487893i 0.162234π-0.162234\pi
−0.858979 + 0.512010i 0.828901π0.828901\pi
104104 2.85185 + 4.93955i 0.279647 + 0.484362i
105105 0 0
106106 −1.02859 + 1.78157i −0.0999055 + 0.173041i
107107 11.3776 1.09991 0.549955 0.835194i 0.314645π-0.314645\pi
0.549955 + 0.835194i 0.314645π0.314645\pi
108108 0 0
109109 4.42107 0.423461 0.211731 0.977328i 0.432090π-0.432090\pi
0.211731 + 0.977328i 0.432090π0.432090\pi
110110 5.06238 8.76830i 0.482679 0.836025i
111111 0 0
112112 0 0
113113 1.60752 + 2.78431i 0.151223 + 0.261926i 0.931677 0.363287i 0.118345π-0.118345\pi
−0.780454 + 0.625213i 0.785012π0.785012\pi
114114 0 0
115115 3.56238 6.17023i 0.332194 0.575377i
116116 −7.08126 −0.657478
117117 0 0
118118 1.12476 0.103543
119119 0 0
120120 0 0
121121 0.437618 + 0.757977i 0.0397835 + 0.0689070i
122122 −1.56238 2.70612i −0.141451 0.245001i
123123 0 0
124124 4.71053 8.15888i 0.423018 0.732689i
125125 0.396990 0.0355079
126126 0 0
127127 20.1053 1.78406 0.892030 0.451976i 0.149281π-0.149281\pi
0.892030 + 0.451976i 0.149281π0.149281\pi
128128 −0.500000 + 0.866025i −0.0441942 + 0.0765466i
129129 0 0
130130 9.07442 + 15.7174i 0.795879 + 1.37850i
131131 3.18194 + 5.51129i 0.278008 + 0.481523i 0.970890 0.239528i 0.0769926π-0.0769926\pi
−0.692882 + 0.721051i 0.743659π0.743659\pi
132132 0 0
133133 0 0
134134 10.9669 0.947396
135135 0 0
136136 −1.52175 −0.130489
137137 1.37072 2.37416i 0.117109 0.202838i −0.801512 0.597979i 0.795971π-0.795971\pi
0.918621 + 0.395140i 0.129304π0.129304\pi
138138 0 0
139139 −3.98345 6.89953i −0.337872 0.585211i 0.646161 0.763202i 0.276374π-0.276374\pi
−0.984032 + 0.177991i 0.943040π0.943040\pi
140140 0 0
141141 0 0
142142 4.34501 7.52578i 0.364625 0.631550i
143143 18.1488 1.51768
144144 0 0
145145 −22.5322 −1.87119
146146 −2.48345 + 4.30146i −0.205532 + 0.355991i
147147 0 0
148148 0.500000 + 0.866025i 0.0410997 + 0.0711868i
149149 −11.6300 20.1437i −0.952764 1.65024i −0.739404 0.673262i 0.764893π-0.764893\pi
−0.213360 0.976974i 0.568441π-0.568441\pi
150150 0 0
151151 4.06238 7.03625i 0.330592 0.572602i −0.652036 0.758188i 0.726085π-0.726085\pi
0.982628 + 0.185586i 0.0594183π0.0594183\pi
152152 1.28263 0.104035
153153 0 0
154154 0 0
155155 14.9887 25.9611i 1.20392 2.08525i
156156 0 0
157157 5.63160 + 9.75422i 0.449451 + 0.778471i 0.998350 0.0574170i 0.0182864π-0.0182864\pi
−0.548900 + 0.835888i 0.684953π0.684953\pi
158158 2.06922 + 3.58399i 0.164618 + 0.285127i
159159 0 0
160160 −1.59097 + 2.75564i −0.125777 + 0.217853i
161161 0 0
162162 0 0
163163 3.98057 0.311782 0.155891 0.987774i 0.450175π-0.450175\pi
0.155891 + 0.987774i 0.450175π0.450175\pi
164164 2.80150 4.85235i 0.218761 0.378905i
165165 0 0
166166 4.03379 + 6.98673i 0.313083 + 0.542276i
167167 −2.61956 4.53721i −0.202708 0.351100i 0.746692 0.665170i 0.231641π-0.231641\pi
−0.949400 + 0.314070i 0.898307π0.898307\pi
168168 0 0
169169 −9.76608 + 16.9153i −0.751237 + 1.30118i
170170 −4.84213 −0.371375
171171 0 0
172172 −6.82846 −0.520665
173173 1.27579 2.20974i 0.0969968 0.168003i −0.813443 0.581644i 0.802410π-0.802410\pi
0.910440 + 0.413641i 0.135743π0.135743\pi
174174 0 0
175175 0 0
176176 1.59097 + 2.75564i 0.119924 + 0.207714i
177177 0 0
178178 −0.112725 + 0.195246i −0.00844910 + 0.0146343i
179179 7.03775 0.526026 0.263013 0.964792i 0.415284π-0.415284\pi
0.263013 + 0.964792i 0.415284π0.415284\pi
180180 0 0
181181 −12.9669 −0.963822 −0.481911 0.876220i 0.660057π-0.660057\pi
−0.481911 + 0.876220i 0.660057π0.660057\pi
182182 0 0
183183 0 0
184184 1.11956 + 1.93914i 0.0825352 + 0.142955i
185185 1.59097 + 2.75564i 0.116971 + 0.202599i
186186 0 0
187187 −2.42107 + 4.19341i −0.177046 + 0.306653i
188188 5.82846 0.425084
189189 0 0
190190 4.08126 0.296085
191191 0.990285 1.71522i 0.0716545 0.124109i −0.827972 0.560769i 0.810505π-0.810505\pi
0.899627 + 0.436660i 0.143839π0.143839\pi
192192 0 0
193193 2.27292 + 3.93680i 0.163608 + 0.283377i 0.936160 0.351574i 0.114353π-0.114353\pi
−0.772552 + 0.634951i 0.781020π0.781020\pi
194194 7.42107 + 12.8537i 0.532802 + 0.922839i
195195 0 0
196196 0 0
197197 21.8148 1.55424 0.777120 0.629353i 0.216680π-0.216680\pi
0.777120 + 0.629353i 0.216680π0.216680\pi
198198 0 0
199199 −12.2826 −0.870693 −0.435346 0.900263i 0.643374π-0.643374\pi
−0.435346 + 0.900263i 0.643374π0.643374\pi
200200 −2.56238 + 4.43818i −0.181188 + 0.313826i
201201 0 0
202202 9.29467 + 16.0988i 0.653971 + 1.13271i
203203 0 0
204204 0 0
205205 8.91423 15.4399i 0.622597 1.07837i
206206 −0.282630 −0.0196918
207207 0 0
208208 −5.70370 −0.395480
209209 2.04063 3.53447i 0.141153 0.244485i
210210 0 0
211211 −8.32846 14.4253i −0.573355 0.993080i −0.996218 0.0868863i 0.972308π-0.972308\pi
0.422863 0.906193i 0.361025π-0.361025\pi
212212 −1.02859 1.78157i −0.0706438 0.122359i
213213 0 0
214214 −5.68878 + 9.85326i −0.388877 + 0.673555i
215215 −21.7278 −1.48182
216216 0 0
217217 0 0
218218 −2.21053 + 3.82876i −0.149716 + 0.259316i
219219 0 0
220220 5.06238 + 8.76830i 0.341306 + 0.591159i
221221 −4.33981 7.51677i −0.291927 0.505633i
222222 0 0
223223 −5.32846 + 9.22916i −0.356820 + 0.618031i −0.987428 0.158071i 0.949472π-0.949472\pi
0.630608 + 0.776102i 0.282806π0.282806\pi
224224 0 0
225225 0 0
226226 −3.21505 −0.213862
227227 −7.25404 + 12.5644i −0.481468 + 0.833926i −0.999774 0.0212688i 0.993229π-0.993229\pi
0.518306 + 0.855195i 0.326563π0.326563\pi
228228 0 0
229229 −5.12476 8.87635i −0.338654 0.586566i 0.645526 0.763738i 0.276638π-0.276638\pi
−0.984180 + 0.177173i 0.943305π0.943305\pi
230230 3.56238 + 6.17023i 0.234896 + 0.406853i
231231 0 0
232232 3.54063 6.13255i 0.232454 0.402622i
233233 1.08126 0.0708355 0.0354177 0.999373i 0.488724π-0.488724\pi
0.0354177 + 0.999373i 0.488724π0.488724\pi
234234 0 0
235235 18.5458 1.20980
236236 −0.562382 + 0.974074i −0.0366079 + 0.0634068i
237237 0 0
238238 0 0
239239 6.16019 + 10.6698i 0.398470 + 0.690170i 0.993537 0.113506i 0.0362081π-0.0362081\pi
−0.595068 + 0.803676i 0.702875π0.702875\pi
240240 0 0
241241 6.50000 11.2583i 0.418702 0.725213i −0.577107 0.816668i 0.695819π-0.695819\pi
0.995809 + 0.0914555i 0.0291519π0.0291519\pi
242242 −0.875237 −0.0562623
243243 0 0
244244 3.12476 0.200042
245245 0 0
246246 0 0
247247 3.65787 + 6.33561i 0.232744 + 0.403125i
248248 4.71053 + 8.15888i 0.299119 + 0.518090i
249249 0 0
250250 −0.198495 + 0.343803i −0.0125539 + 0.0217440i
251251 −5.11109 −0.322609 −0.161305 0.986905i 0.551570π-0.551570\pi
−0.161305 + 0.986905i 0.551570π0.551570\pi
252252 0 0
253253 7.12476 0.447930
254254 −10.0527 + 17.4117i −0.630760 + 1.09251i
255255 0 0
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 3.83009 + 6.63392i 0.238915 + 0.413813i 0.960403 0.278614i 0.0898750π-0.0898750\pi
−0.721488 + 0.692427i 0.756542π0.756542\pi
258258 0 0
259259 0 0
260260 −18.1488 −1.12554
261261 0 0
262262 −6.36389 −0.393162
263263 −1.54746 + 2.68029i −0.0954208 + 0.165274i −0.909784 0.415082i 0.863753π-0.863753\pi
0.814363 + 0.580355i 0.197086π0.197086\pi
264264 0 0
265265 −3.27292 5.66886i −0.201054 0.348235i
266266 0 0
267267 0 0
268268 −5.48345 + 9.49761i −0.334955 + 0.580159i
269269 −26.8903 −1.63953 −0.819765 0.572700i 0.805896π-0.805896\pi
−0.819765 + 0.572700i 0.805896π0.805896\pi
270270 0 0
271271 22.2164 1.34955 0.674776 0.738023i 0.264240π-0.264240\pi
0.674776 + 0.738023i 0.264240π0.264240\pi
272272 0.760877 1.31788i 0.0461349 0.0799080i
273273 0 0
274274 1.37072 + 2.37416i 0.0828084 + 0.143428i
275275 8.15335 + 14.1220i 0.491666 + 0.851590i
276276 0 0
277277 7.31875 12.6764i 0.439741 0.761653i −0.557928 0.829889i 0.688404π-0.688404\pi
0.997669 + 0.0682357i 0.0217370π0.0217370\pi
278278 7.96690 0.477823
279279 0 0
280280 0 0
281281 −11.6992 + 20.2636i −0.697915 + 1.20882i 0.271273 + 0.962502i 0.412555π0.412555\pi
−0.969188 + 0.246322i 0.920778π0.920778\pi
282282 0 0
283283 13.0624 + 22.6247i 0.776478 + 1.34490i 0.933960 + 0.357377i 0.116329π0.116329\pi
−0.157482 + 0.987522i 0.550338π0.550338\pi
284284 4.34501 + 7.52578i 0.257829 + 0.446573i
285285 0 0
286286 −9.07442 + 15.7174i −0.536582 + 0.929387i
287287 0 0
288288 0 0
289289 −14.6843 −0.863780
290290 11.2661 19.5134i 0.661567 1.14587i
291291 0 0
292292 −2.48345 4.30146i −0.145333 0.251724i
293293 −12.9315 22.3980i −0.755465 1.30850i −0.945143 0.326657i 0.894078π-0.894078\pi
0.189678 0.981846i 0.439255π-0.439255\pi
294294 0 0
295295 −1.78947 + 3.09945i −0.104187 + 0.180457i
296296 −1.00000 −0.0581238
297297 0 0
298298 23.2599 1.34741
299299 −6.38564 + 11.0603i −0.369291 + 0.639631i
300300 0 0
301301 0 0
302302 4.06238 + 7.03625i 0.233764 + 0.404891i
303303 0 0
304304 −0.641315 + 1.11079i −0.0367819 + 0.0637082i
305305 9.94282 0.569324
306306 0 0
307307 3.53216 0.201591 0.100795 0.994907i 0.467861π-0.467861\pi
0.100795 + 0.994907i 0.467861π0.467861\pi
308308 0 0
309309 0 0
310310 14.9887 + 25.9611i 0.851298 + 1.47449i
311311 0.851848 + 1.47544i 0.0483039 + 0.0836648i 0.889166 0.457584i 0.151285π-0.151285\pi
−0.840863 + 0.541249i 0.817952π0.817952\pi
312312 0 0
313313 1.42107 2.46136i 0.0803234 0.139124i −0.823065 0.567947i 0.807738π-0.807738\pi
0.903389 + 0.428822i 0.141071π0.141071\pi
314314 −11.2632 −0.635619
315315 0 0
316316 −4.13844 −0.232805
317317 −12.4601 + 21.5815i −0.699827 + 1.21214i 0.268700 + 0.963224i 0.413406π0.413406\pi
−0.968526 + 0.248911i 0.919927π0.919927\pi
318318 0 0
319319 −11.2661 19.5134i −0.630779 1.09254i
320320 −1.59097 2.75564i −0.0889380 0.154045i
321321 0 0
322322 0 0
323323 −1.95185 −0.108604
324324 0 0
325325 −29.2301 −1.62139
326326 −1.99028 + 3.44727i −0.110232 + 0.190927i
327327 0 0
328328 2.80150 + 4.85235i 0.154687 + 0.267926i
329329 0 0
330330 0 0
331331 3.58577 6.21074i 0.197092 0.341373i −0.750492 0.660879i 0.770184π-0.770184\pi
0.947584 + 0.319506i 0.103517π0.103517\pi
332332 −8.06758 −0.442766
333333 0 0
334334 5.23912 0.286672
335335 −17.4480 + 30.2209i −0.953287 + 1.65114i
336336 0 0
337337 −10.9211 18.9158i −0.594908 1.03041i −0.993560 0.113309i 0.963855π-0.963855\pi
0.398651 0.917103i 0.369478π-0.369478\pi
338338 −9.76608 16.9153i −0.531205 0.920073i
339339 0 0
340340 2.42107 4.19341i 0.131301 0.227420i
341341 29.9773 1.62336
342342 0 0
343343 0 0
344344 3.41423 5.91362i 0.184083 0.318841i
345345 0 0
346346 1.27579 + 2.20974i 0.0685871 + 0.118796i
347347 −1.05555 1.82826i −0.0566646 0.0981460i 0.836302 0.548270i 0.184713π-0.184713\pi
−0.892966 + 0.450124i 0.851380π0.851380\pi
348348 0 0
349349 18.1082 31.3643i 0.969310 1.67889i 0.271751 0.962368i 0.412397π-0.412397\pi
0.697559 0.716527i 0.254269π-0.254269\pi
350350 0 0
351351 0 0
352352 −3.18194 −0.169598
353353 −5.24433 + 9.08344i −0.279127 + 0.483463i −0.971168 0.238396i 0.923378π-0.923378\pi
0.692041 + 0.721858i 0.256712π0.256712\pi
354354 0 0
355355 13.8256 + 23.9466i 0.733786 + 1.27095i
356356 −0.112725 0.195246i −0.00597442 0.0103480i
357357 0 0
358358 −3.51887 + 6.09487i −0.185978 + 0.322124i
359359 32.4419 1.71222 0.856108 0.516796i 0.172876π-0.172876\pi
0.856108 + 0.516796i 0.172876π0.172876\pi
360360 0 0
361361 −17.3549 −0.913414
362362 6.48345 11.2297i 0.340762 0.590218i
363363 0 0
364364 0 0
365365 −7.90219 13.6870i −0.413620 0.716410i
366366 0 0
367367 9.05555 15.6847i 0.472696 0.818733i −0.526816 0.849979i 0.676614π-0.676614\pi
0.999512 + 0.0312465i 0.00994768π0.00994768\pi
368368 −2.23912 −0.116722
369369 0 0
370370 −3.18194 −0.165421
371371 0 0
372372 0 0
373373 5.83530 + 10.1070i 0.302140 + 0.523322i 0.976621 0.214971i 0.0689656π-0.0689656\pi
−0.674480 + 0.738293i 0.735632π0.735632\pi
374374 −2.42107 4.19341i −0.125190 0.216836i
375375 0 0
376376 −2.91423 + 5.04759i −0.150290 + 0.260310i
377377 40.3893 2.08016
378378 0 0
379379 14.2690 0.732947 0.366474 0.930428i 0.380565π-0.380565\pi
0.366474 + 0.930428i 0.380565π0.380565\pi
380380 −2.04063 + 3.53447i −0.104682 + 0.181315i
381381 0 0
382382 0.990285 + 1.71522i 0.0506674 + 0.0877585i
383383 −0.824893 1.42876i −0.0421501 0.0730061i 0.844181 0.536059i 0.180087π-0.180087\pi
−0.886331 + 0.463053i 0.846754π0.846754\pi
384384 0 0
385385 0 0
386386 −4.54583 −0.231377
387387 0 0
388388 −14.8421 −0.753495
389389 −16.0338 + 27.7713i −0.812946 + 1.40806i 0.0978483 + 0.995201i 0.468804π0.468804\pi
−0.910794 + 0.412862i 0.864529π0.864529\pi
390390 0 0
391391 −1.70370 2.95089i −0.0861596 0.149233i
392392 0 0
393393 0 0
394394 −10.9074 + 18.8922i −0.549507 + 0.951773i
395395 −13.1683 −0.662568
396396 0 0
397397 37.9338 1.90384 0.951921 0.306343i 0.0991054π-0.0991054\pi
0.951921 + 0.306343i 0.0991054π0.0991054\pi
398398 6.14132 10.6371i 0.307836 0.533188i
399399 0 0
400400 −2.56238 4.43818i −0.128119 0.221909i
401401 5.30959 + 9.19647i 0.265148 + 0.459250i 0.967602 0.252479i 0.0812458π-0.0812458\pi
−0.702454 + 0.711729i 0.747913π0.747913\pi
402402 0 0
403403 −26.8675 + 46.5358i −1.33836 + 2.31811i
404404 −18.5893 −0.924854
405405 0 0
406406 0 0
407407 −1.59097 + 2.75564i −0.0788615 + 0.136592i
408408 0 0
409409 −2.77292 4.80283i −0.137112 0.237485i 0.789290 0.614020i 0.210449π-0.210449\pi
−0.926402 + 0.376535i 0.877115π0.877115\pi
410410 8.91423 + 15.4399i 0.440242 + 0.762522i
411411 0 0
412412 0.141315 0.244765i 0.00696209 0.0120587i
413413 0 0
414414 0 0
415415 −25.6706 −1.26012
416416 2.85185 4.93955i 0.139823 0.242181i
417417 0 0
418418 2.04063 + 3.53447i 0.0998104 + 0.172877i
419419 −2.77455 4.80566i −0.135546 0.234772i 0.790260 0.612772i 0.209945π-0.209945\pi
−0.925806 + 0.378000i 0.876612π0.876612\pi
420420 0 0
421421 −3.42107 + 5.92546i −0.166733 + 0.288789i −0.937269 0.348606i 0.886655π-0.886655\pi
0.770537 + 0.637396i 0.219988π0.219988\pi
422422 16.6569 0.810846
423423 0 0
424424 2.05718 0.0999055
425425 3.89931 6.75381i 0.189144 0.327608i
426426 0 0
427427 0 0
428428 −5.68878 9.85326i −0.274978 0.476275i
429429 0 0
430430 10.8639 18.8168i 0.523903 0.907427i
431431 33.1078 1.59475 0.797374 0.603486i 0.206222π-0.206222\pi
0.797374 + 0.603486i 0.206222π0.206222\pi
432432 0 0
433433 −12.1111 −0.582022 −0.291011 0.956720i 0.593992π-0.593992\pi
−0.291011 + 0.956720i 0.593992π0.593992\pi
434434 0 0
435435 0 0
436436 −2.21053 3.82876i −0.105865 0.183364i
437437 1.43598 + 2.48720i 0.0686924 + 0.118979i
438438 0 0
439439 4.41711 7.65066i 0.210817 0.365146i −0.741153 0.671336i 0.765721π-0.765721\pi
0.951970 + 0.306190i 0.0990542π0.0990542\pi
440440 −10.1248 −0.482679
441441 0 0
442442 8.67962 0.412847
443443 8.75924 15.1715i 0.416164 0.720817i −0.579386 0.815053i 0.696708π-0.696708\pi
0.995550 + 0.0942360i 0.0300408π0.0300408\pi
444444 0 0
445445 −0.358685 0.621261i −0.0170033 0.0294506i
446446 −5.32846 9.22916i −0.252310 0.437014i
447447 0 0
448448 0 0
449449 −31.2301 −1.47384 −0.736920 0.675980i 0.763720π-0.763720\pi
−0.736920 + 0.675980i 0.763720π0.763720\pi
450450 0 0
451451 17.8285 0.839509
452452 1.60752 2.78431i 0.0756115 0.130963i
453453 0 0
454454 −7.25404 12.5644i −0.340449 0.589675i
455455 0 0
456456 0 0
457457 16.0624 27.8209i 0.751367 1.30140i −0.195794 0.980645i 0.562728π-0.562728\pi
0.947161 0.320760i 0.103938π-0.103938\pi
458458 10.2495 0.478929
459459 0 0
460460 −7.12476 −0.332194
461461 −1.23229 + 2.13438i −0.0573933 + 0.0994081i −0.893295 0.449472i 0.851612π-0.851612\pi
0.835901 + 0.548880i 0.184946π0.184946\pi
462462 0 0
463463 15.1735 + 26.2812i 0.705171 + 1.22139i 0.966630 + 0.256177i 0.0824631π0.0824631\pi
−0.261459 + 0.965215i 0.584204π0.584204\pi
464464 3.54063 + 6.13255i 0.164370 + 0.284696i
465465 0 0
466466 −0.540628 + 0.936396i −0.0250441 + 0.0433777i
467467 −15.9636 −0.738709 −0.369354 0.929289i 0.620421π-0.620421\pi
−0.369354 + 0.929289i 0.620421π0.620421\pi
468468 0 0
469469 0 0
470470 −9.27292 + 16.0612i −0.427728 + 0.740846i
471471 0 0
472472 −0.562382 0.974074i −0.0258857 0.0448354i
473473 −10.8639 18.8168i −0.499522 0.865198i
474474 0 0
475475 −3.28659 + 5.69254i −0.150799 + 0.261192i
476476 0 0
477477 0 0
478478 −12.3204 −0.563521
479479 −11.5865 + 20.0683i −0.529399 + 0.916946i 0.470013 + 0.882659i 0.344249π0.344249\pi
−0.999412 + 0.0342863i 0.989084π0.989084\pi
480480 0 0
481481 −2.85185 4.93955i −0.130033 0.225224i
482482 6.50000 + 11.2583i 0.296067 + 0.512803i
483483 0 0
484484 0.437618 0.757977i 0.0198917 0.0344535i
485485 −47.2268 −2.14446
486486 0 0
487487 −3.41315 −0.154665 −0.0773323 0.997005i 0.524640π-0.524640\pi
−0.0773323 + 0.997005i 0.524640π0.524640\pi
488488 −1.56238 + 2.70612i −0.0707257 + 0.122500i
489489 0 0
490490 0 0
491491 9.58414 + 16.6002i 0.432526 + 0.749157i 0.997090 0.0762323i 0.0242890π-0.0242890\pi
−0.564564 + 0.825389i 0.690956π0.690956\pi
492492 0 0
493493 −5.38796 + 9.33223i −0.242662 + 0.420302i
494494 −7.31573 −0.329150
495495 0 0
496496 −9.42107 −0.423018
497497 0 0
498498 0 0
499499 −20.5848 35.6540i −0.921503 1.59609i −0.797090 0.603860i 0.793629π-0.793629\pi
−0.124413 0.992231i 0.539705π-0.539705\pi
500500 −0.198495 0.343803i −0.00887697 0.0153754i
501501 0 0
502502 2.55555 4.42633i 0.114060 0.197557i
503503 26.4542 1.17953 0.589767 0.807574i 0.299220π-0.299220\pi
0.589767 + 0.807574i 0.299220π0.299220\pi
504504 0 0
505505 −59.1502 −2.63215
506506 −3.56238 + 6.17023i −0.158367 + 0.274300i
507507 0 0
508508 −10.0527 17.4117i −0.446015 0.772521i
509509 6.38564 + 11.0603i 0.283039 + 0.490237i 0.972132 0.234436i 0.0753242π-0.0753242\pi
−0.689093 + 0.724673i 0.741991π0.741991\pi
510510 0 0
511511 0 0
512512 1.00000 0.0441942
513513 0 0
514514 −7.66019 −0.337876
515515 0.449657 0.778828i 0.0198142 0.0343193i
516516 0 0
517517 9.27292 + 16.0612i 0.407822 + 0.706369i
518518 0 0
519519 0 0
520520 9.07442 15.7174i 0.397940 0.689252i
521521 −6.81230 −0.298452 −0.149226 0.988803i 0.547678π-0.547678\pi
−0.149226 + 0.988803i 0.547678π0.547678\pi
522522 0 0
523523 −29.5070 −1.29025 −0.645125 0.764077i 0.723195π-0.723195\pi
−0.645125 + 0.764077i 0.723195π0.723195\pi
524524 3.18194 5.51129i 0.139004 0.240762i
525525 0 0
526526 −1.54746 2.68029i −0.0674727 0.116866i
527527 −7.16827 12.4158i −0.312255 0.540841i
528528 0 0
529529 8.99316 15.5766i 0.391007 0.677244i
530530 6.54583 0.284333
531531 0 0
532532 0 0
533533 −15.9789 + 27.6763i −0.692125 + 1.19879i
534534 0 0
535535 −18.1014 31.3525i −0.782591 1.35549i
536536 −5.48345 9.49761i −0.236849 0.410234i
537537 0 0
538538 13.4451 23.2877i 0.579661 1.00400i
539539 0 0
540540 0 0
541541 −29.4016 −1.26408 −0.632038 0.774938i 0.717781π-0.717781\pi
−0.632038 + 0.774938i 0.717781π0.717781\pi
542542 −11.1082 + 19.2400i −0.477139 + 0.826428i
543543 0 0
544544 0.760877 + 1.31788i 0.0326223 + 0.0565035i
545545 −7.03379 12.1829i −0.301295 0.521857i
546546 0 0
547547 17.6150 30.5102i 0.753165 1.30452i −0.193116 0.981176i 0.561859π-0.561859\pi
0.946281 0.323344i 0.104807π-0.104807\pi
548548 −2.74145 −0.117109
549549 0 0
550550 −16.3067 −0.695320
551551 4.54132 7.86579i 0.193467 0.335094i
552552 0 0
553553 0 0
554554 7.31875 + 12.6764i 0.310944 + 0.538570i
555555 0 0
556556 −3.98345 + 6.89953i −0.168936 + 0.292605i
557557 −6.73818 −0.285506 −0.142753 0.989758i 0.545595π-0.545595\pi
−0.142753 + 0.989758i 0.545595π0.545595\pi
558558 0 0
559559 38.9475 1.64730
560560 0 0
561561 0 0
562562 −11.6992 20.2636i −0.493500 0.854768i
563563 −0.729964 1.26433i −0.0307643 0.0532853i 0.850233 0.526406i 0.176461π-0.176461\pi
−0.880998 + 0.473121i 0.843127π0.843127\pi
564564 0 0
565565 5.11505 8.85952i 0.215192 0.372723i
566566 −26.1248 −1.09811
567567 0 0
568568 −8.69002 −0.364625
569569 9.78263 16.9440i 0.410109 0.710330i −0.584792 0.811183i 0.698824π-0.698824\pi
0.994901 + 0.100853i 0.0321573π0.0321573\pi
570570 0 0
571571 10.9629 + 18.9884i 0.458785 + 0.794638i 0.998897 0.0469545i 0.0149516π-0.0149516\pi
−0.540112 + 0.841593i 0.681618π0.681618\pi
572572 −9.07442 15.7174i −0.379421 0.657176i
573573 0 0
574574 0 0
575575 −11.4750 −0.478540
576576 0 0
577577 −24.7310 −1.02957 −0.514783 0.857320i 0.672128π-0.672128\pi
−0.514783 + 0.857320i 0.672128π0.672128\pi
578578 7.34213 12.7169i 0.305392 0.528955i
579579 0 0
580580 11.2661 + 19.5134i 0.467798 + 0.810251i
581581 0 0
582582 0 0
583583 3.27292 5.66886i 0.135550 0.234780i
584584 4.96690 0.205532
585585 0 0
586586 25.8629 1.06839
587587 18.0796 31.3148i 0.746226 1.29250i −0.203394 0.979097i 0.565197π-0.565197\pi
0.949620 0.313404i 0.101469π-0.101469\pi
588588 0 0
589589 6.04187 + 10.4648i 0.248951 + 0.431196i
590590 −1.78947 3.09945i −0.0736712 0.127602i
591591 0 0
592592 0.500000 0.866025i 0.0205499 0.0355934i
593593 −15.1078 −0.620404 −0.310202 0.950671i 0.600397π-0.600397\pi
−0.310202 + 0.950671i 0.600397π0.600397\pi
594594 0 0
595595 0 0
596596 −11.6300 + 20.1437i −0.476382 + 0.825118i
597597 0 0
598598 −6.38564 11.0603i −0.261128 0.452287i
599599 −2.72708 4.72345i −0.111426 0.192995i 0.804920 0.593384i 0.202208π-0.202208\pi
−0.916345 + 0.400389i 0.868875π0.868875\pi
600600 0 0
601601 −3.36840 + 5.83424i −0.137400 + 0.237984i −0.926512 0.376266i 0.877208π-0.877208\pi
0.789112 + 0.614250i 0.210541π0.210541\pi
602602 0 0
603603 0 0
604604 −8.12476 −0.330592
605605 1.39248 2.41184i 0.0566122 0.0980553i
606606 0 0
607607 −3.33530 5.77690i −0.135376 0.234477i 0.790365 0.612636i 0.209891π-0.209891\pi
−0.925741 + 0.378159i 0.876557π0.876557\pi
608608 −0.641315 1.11079i −0.0260088 0.0450485i
609609 0 0
610610 −4.97141 + 8.61073i −0.201287 + 0.348638i
611611 −33.2438 −1.34490
612612 0 0
613613 −1.30998 −0.0529094 −0.0264547 0.999650i 0.508422π-0.508422\pi
−0.0264547 + 0.999650i 0.508422π0.508422\pi
614614 −1.76608 + 3.05894i −0.0712731 + 0.123449i
615615 0 0
616616 0 0
617617 −17.2483 29.8749i −0.694390 1.20272i −0.970386 0.241560i 0.922341π-0.922341\pi
0.275996 0.961159i 0.410992π-0.410992\pi
618618 0 0
619619 8.22421 14.2447i 0.330559 0.572545i −0.652063 0.758165i 0.726096π-0.726096\pi
0.982622 + 0.185620i 0.0594295π0.0594295\pi
620620 −29.9773 −1.20392
621621 0 0
622622 −1.70370 −0.0683120
623623 0 0
624624 0 0
625625 12.1803 + 21.0969i 0.487212 + 0.843877i
626626 1.42107 + 2.46136i 0.0567972 + 0.0983757i
627627 0 0
628628 5.63160 9.75422i 0.224725 0.389236i
629629 1.52175 0.0606763
630630 0 0
631631 −30.0118 −1.19475 −0.597375 0.801962i 0.703790π-0.703790\pi
−0.597375 + 0.801962i 0.703790π0.703790\pi
632632 2.06922 3.58399i 0.0823091 0.142564i
633633 0 0
634634 −12.4601 21.5815i −0.494852 0.857109i
635635 −31.9870 55.4031i −1.26937 2.19861i
636636 0 0
637637 0 0
638638 22.5322 0.892057
639639 0 0
640640 3.18194 0.125777
641641 13.9497 24.1615i 0.550978 0.954322i −0.447226 0.894421i 0.647588π-0.647588\pi
0.998204 0.0599014i 0.0190786π-0.0190786\pi
642642 0 0
643643 14.2524 + 24.6859i 0.562060 + 0.973516i 0.997317 + 0.0732100i 0.0233243π0.0233243\pi
−0.435257 + 0.900306i 0.643342π0.643342\pi
644644 0 0
645645 0 0
646646 0.975923 1.69035i 0.0383972 0.0665059i
647647 16.7141 0.657099 0.328550 0.944487i 0.393440π-0.393440\pi
0.328550 + 0.944487i 0.393440π0.393440\pi
648648 0 0
649649 −3.57893 −0.140485
650650 14.6150 25.3140i 0.573249 0.992897i
651651 0 0
652652 −1.99028 3.44727i −0.0779456 0.135006i
653653 19.0825 + 33.0519i 0.746756 + 1.29342i 0.949370 + 0.314161i 0.101723π0.101723\pi
−0.202614 + 0.979259i 0.564944π0.564944\pi
654654 0 0
655655 10.1248 17.5366i 0.395607 0.685212i
656656 −5.60301 −0.218761
657657 0 0
658658 0 0
659659 −4.37072 + 7.57031i −0.170259 + 0.294898i −0.938510 0.345251i 0.887794π-0.887794\pi
0.768251 + 0.640148i 0.221127π0.221127\pi
660660 0 0
661661 10.0419 + 17.3930i 0.390584 + 0.676511i 0.992527 0.122028i 0.0389399π-0.0389399\pi
−0.601943 + 0.798539i 0.705607π0.705607\pi
662662 3.58577 + 6.21074i 0.139365 + 0.241387i
663663 0 0
664664 4.03379 6.98673i 0.156541 0.271138i
665665 0 0
666666 0 0
667667 15.8558 0.613939
668668 −2.61956 + 4.53721i −0.101354 + 0.175550i
669669 0 0
670670 −17.4480 30.2209i −0.674076 1.16753i
671671 4.97141 + 8.61073i 0.191919 + 0.332414i
672672 0 0
673673 −17.0264 + 29.4906i −0.656319 + 1.13678i 0.325242 + 0.945631i 0.394554π0.394554\pi
−0.981561 + 0.191148i 0.938779π0.938779\pi
674674 21.8421 0.841328
675675 0 0
676676 19.5322 0.751237
677677 −0.358685 + 0.621261i −0.0137854 + 0.0238770i −0.872836 0.488014i 0.837721π-0.837721\pi
0.859050 + 0.511891i 0.171055π0.171055\pi
678678 0 0
679679 0 0
680680 2.42107 + 4.19341i 0.0928437 + 0.160810i
681681 0 0
682682 −14.9887 + 25.9611i −0.573945 + 0.994102i
683683 −21.0539 −0.805605 −0.402803 0.915287i 0.631964π-0.631964\pi
−0.402803 + 0.915287i 0.631964π0.631964\pi
684684 0 0
685685 −8.72313 −0.333294
686686 0 0
687687 0 0
688688 3.41423 + 5.91362i 0.130166 + 0.225455i
689689 5.86677 + 10.1615i 0.223506 + 0.387124i
690690 0 0
691691 −2.92395 + 5.06442i −0.111232 + 0.192660i −0.916267 0.400567i 0.868813π-0.868813\pi
0.805035 + 0.593227i 0.202146π0.202146\pi
692692 −2.55159 −0.0969968
693693 0 0
694694 2.11109 0.0801359
695695 −12.6751 + 21.9539i −0.480794 + 0.832760i
696696 0 0
697697 −4.26320 7.38408i −0.161480 0.279692i
698698 18.1082 + 31.3643i 0.685406 + 1.18716i
699699 0 0
700700 0 0
701701 −10.2711 −0.387935 −0.193967 0.981008i 0.562136π-0.562136\pi
−0.193967 + 0.981008i 0.562136π0.562136\pi
702702 0 0
703703 −1.28263 −0.0483753
704704 1.59097 2.75564i 0.0599620 0.103857i
705705 0 0
706706 −5.24433 9.08344i −0.197373 0.341860i
707707 0 0
708708 0 0
709709 −21.7427 + 37.6594i −0.816564 + 1.41433i 0.0916356 + 0.995793i 0.470790π0.470790\pi
−0.908200 + 0.418538i 0.862543π0.862543\pi
710710 −27.6512 −1.03773
711711 0 0
712712 0.225450 0.00844910
713713 −10.5475 + 18.2687i −0.395006 + 0.684170i
714714 0 0
715715 −28.8743 50.0117i −1.07984 1.87033i
716716 −3.51887 6.09487i −0.131507 0.227776i
717717 0 0
718718 −16.2209 + 28.0955i −0.605360 + 1.04851i
719719 50.8824 1.89759 0.948796 0.315889i 0.102303π-0.102303\pi
0.948796 + 0.315889i 0.102303π0.102303\pi
720720 0 0
721721 0 0
722722 8.67743 15.0297i 0.322941 0.559349i
723723 0 0
724724 6.48345 + 11.2297i 0.240955 + 0.417347i
725725 18.1449 + 31.4279i 0.673884 + 1.16720i
726726 0 0
727727 6.07210 10.5172i 0.225202 0.390061i −0.731178 0.682186i 0.761029π-0.761029\pi
0.956380 + 0.292126i 0.0943626π0.0943626\pi
728728 0 0
729729 0 0
730730 15.8044 0.584946
731731 −5.19562 + 8.99907i −0.192167 + 0.332843i
732732 0 0
733733 23.0848 + 39.9841i 0.852657 + 1.47685i 0.878801 + 0.477188i 0.158344π0.158344\pi
−0.0261440 + 0.999658i 0.508323π0.508323\pi
734734 9.05555 + 15.6847i 0.334246 + 0.578932i
735735 0 0
736736 1.11956 1.93914i 0.0412676 0.0714776i
737737 −34.8960 −1.28541
738738 0 0
739739 4.99208 0.183637 0.0918184 0.995776i 0.470732π-0.470732\pi
0.0918184 + 0.995776i 0.470732π0.470732\pi
740740 1.59097 2.75564i 0.0584853 0.101299i
741741 0 0
742742 0 0
743743 15.7060 + 27.2036i 0.576198 + 0.998004i 0.995910 + 0.0903470i 0.0287976π0.0287976\pi
−0.419712 + 0.907657i 0.637869π0.637869\pi
744744 0 0
745745 −37.0059 + 64.0961i −1.35579 + 2.34830i
746746 −11.6706 −0.427291
747747 0 0
748748 4.84213 0.177046
749749 0 0
750750 0 0
751751 −1.64815 2.85468i −0.0601419 0.104169i 0.834387 0.551179i 0.185822π-0.185822\pi
−0.894529 + 0.447010i 0.852489π0.852489\pi
752752 −2.91423 5.04759i −0.106271 0.184067i
753753 0 0
754754 −20.1947 + 34.9782i −0.735447 + 1.27383i
755755 −25.8525 −0.940870
756756 0 0
757757 −10.1384 −0.368488 −0.184244 0.982881i 0.558984π-0.558984\pi
−0.184244 + 0.982881i 0.558984π0.558984\pi
758758 −7.13448 + 12.3573i −0.259136 + 0.448837i
759759 0 0
760760 −2.04063 3.53447i −0.0740214 0.128209i
761761 7.03379 + 12.1829i 0.254975 + 0.441629i 0.964889 0.262659i 0.0845995π-0.0845995\pi
−0.709914 + 0.704288i 0.751266π0.751266\pi
762762 0 0
763763 0 0
764764 −1.98057 −0.0716545
765765 0 0
766766 1.64979 0.0596092
767767 3.20765 5.55582i 0.115822 0.200609i
768768 0 0
769769 11.3461 + 19.6520i 0.409151 + 0.708669i 0.994795 0.101899i 0.0324918π-0.0324918\pi
−0.585644 + 0.810568i 0.699158π0.699158\pi
770770 0 0
771771 0 0
772772 2.27292 3.93680i 0.0818040 0.141689i
773773 0.655544 0.0235783 0.0117891 0.999931i 0.496247π-0.496247\pi
0.0117891 + 0.999931i 0.496247π0.496247\pi
774774 0 0
775775 −48.2807 −1.73430
776776 7.42107 12.8537i 0.266401 0.461420i
777777 0 0
778778 −16.0338 27.7713i −0.574839 0.995651i
779779 3.59329 + 6.22377i 0.128743 + 0.222990i
780780 0 0
781781 −13.8256 + 23.9466i −0.494718 + 0.856877i
782782 3.40739 0.121848
783783 0 0
784784 0 0
785785 17.9194 31.0374i 0.639572 1.10777i
786786 0 0
787787 −0.270036 0.467717i −0.00962576 0.0166723i 0.861172 0.508313i 0.169731π-0.169731\pi
−0.870798 + 0.491641i 0.836397π0.836397\pi
788788 −10.9074 18.8922i −0.388560 0.673005i
789789 0 0
790790 6.58414 11.4041i 0.234253 0.405738i
791791 0 0
792792 0 0
793793 −17.8227 −0.632903
794794 −18.9669 + 32.8516i −0.673110 + 1.16586i
795795 0 0
796796 6.14132 + 10.6371i 0.217673 + 0.377021i
797797 12.5550 + 21.7459i 0.444721 + 0.770279i 0.998033 0.0626954i 0.0199697π-0.0199697\pi
−0.553312 + 0.832974i 0.686636π0.686636\pi
798798 0 0
799799 4.43474 7.68119i 0.156890 0.271741i
800800 5.12476 0.181188
801801 0 0
802802 −10.6192 −0.374976
803803 7.90219 13.6870i 0.278862 0.483004i
804804 0 0
805805 0 0
806806 −26.8675 46.5358i −0.946366 1.63915i
807807 0 0
808808 9.29467 16.0988i 0.326985 0.566355i
809809 −29.1729 −1.02567 −0.512833 0.858489i 0.671404π-0.671404\pi
−0.512833 + 0.858489i 0.671404π0.671404\pi
810810 0 0
811811 −15.4290 −0.541785 −0.270892 0.962610i 0.587319π-0.587319\pi
−0.270892 + 0.962610i 0.587319π0.587319\pi
812812 0 0
813813 0 0
814814 −1.59097 2.75564i −0.0557635 0.0965853i
815815 −6.33297 10.9690i −0.221834 0.384228i
816816 0 0
817817 4.37919 7.58499i 0.153209 0.265365i
818818 5.54583 0.193905
819819 0 0
820820 −17.8285 −0.622597
821821 4.24364 7.35019i 0.148104 0.256524i −0.782423 0.622748i 0.786016π-0.786016\pi
0.930527 + 0.366224i 0.119350π0.119350\pi
822822 0 0
823823 −14.5487 25.1991i −0.507136 0.878385i −0.999966 0.00825976i 0.997371π-0.997371\pi
0.492830 0.870126i 0.335963π-0.335963\pi
824824 0.141315 + 0.244765i 0.00492294 + 0.00852679i
825825 0 0
826826 0 0
827827 25.9396 0.902007 0.451003 0.892522i 0.351066π-0.351066\pi
0.451003 + 0.892522i 0.351066π0.351066\pi
828828 0 0
829829 −6.21642 −0.215905 −0.107953 0.994156i 0.534429π-0.534429\pi
−0.107953 + 0.994156i 0.534429π0.534429\pi
830830 12.8353 22.2314i 0.445520 0.771663i
831831 0 0
832832 2.85185 + 4.93955i 0.0988701 + 0.171248i
833833 0 0
834834 0 0
835835 −8.33530 + 14.4372i −0.288455 + 0.499618i
836836 −4.08126 −0.141153
837837 0 0
838838 5.54910 0.191690
839839 −21.2947 + 36.8834i −0.735174 + 1.27336i 0.219474 + 0.975618i 0.429566π0.429566\pi
−0.954647 + 0.297740i 0.903767π0.903767\pi
840840 0 0
841841 −10.5721 18.3114i −0.364555 0.631428i
842842 −3.42107 5.92546i −0.117898 0.204205i
843843 0 0
844844 −8.32846 + 14.4253i −0.286677 + 0.496540i
845845 62.1502 2.13803
846846 0 0
847847 0 0
848848 −1.02859 + 1.78157i −0.0353219 + 0.0611794i
849849 0 0
850850 3.89931 + 6.75381i 0.133745 + 0.231654i
851851 −1.11956 1.93914i −0.0383781 0.0664728i
852852 0 0
853853 −10.6969 + 18.5275i −0.366254 + 0.634370i −0.988976 0.148073i 0.952693π-0.952693\pi
0.622723 + 0.782442i 0.286026π0.286026\pi
854854 0 0
855855 0 0
856856 11.3776 0.388877
857857 −18.4218 + 31.9074i −0.629275 + 1.08994i 0.358422 + 0.933560i 0.383315π0.383315\pi
−0.987697 + 0.156377i 0.950019π0.950019\pi
858858 0 0
859859 8.81875 + 15.2745i 0.300892 + 0.521160i 0.976338 0.216249i 0.0693824π-0.0693824\pi
−0.675446 + 0.737409i 0.736049π0.736049\pi
860860 10.8639 + 18.8168i 0.370455 + 0.641648i
861861 0 0
862862 −16.5539 + 28.6722i −0.563828 + 0.976579i
863863 −0.760877 −0.0259005 −0.0129503 0.999916i 0.504122π-0.504122\pi
−0.0129503 + 0.999916i 0.504122π0.504122\pi
864864 0 0
865865 −8.11901 −0.276054
866866 6.05555 10.4885i 0.205776 0.356414i
867867 0 0
868868 0 0
869869 −6.58414 11.4041i −0.223351 0.386856i
870870 0 0
871871 31.2759 54.1715i 1.05974 1.83553i
872872 4.42107 0.149716
873873 0 0
874874 −2.87197 −0.0971457
875875 0 0
876876 0 0
877877 20.7495 + 35.9392i 0.700662 + 1.21358i 0.968234 + 0.250044i 0.0804451π0.0804451\pi
−0.267573 + 0.963538i 0.586222π0.586222\pi
878878 4.41711 + 7.65066i 0.149070 + 0.258197i
879879 0 0
880880 5.06238 8.76830i 0.170653 0.295579i
881881 −8.35486 −0.281482 −0.140741 0.990046i 0.544949π-0.544949\pi
−0.140741 + 0.990046i 0.544949π0.544949\pi
882882 0 0
883883 35.6181 1.19864 0.599322 0.800508i 0.295437π-0.295437\pi
0.599322 + 0.800508i 0.295437π0.295437\pi
884884 −4.33981 + 7.51677i −0.145964 + 0.252816i
885885 0 0
886886 8.75924 + 15.1715i 0.294272 + 0.509695i
887887 −18.5550 32.1382i −0.623016 1.07909i −0.988921 0.148443i 0.952574π-0.952574\pi
0.365905 0.930652i 0.380759π-0.380759\pi
888888 0 0
889889 0 0
890890 0.717370 0.0240463
891891 0 0
892892 10.6569 0.356820
893893 −3.73788 + 6.47420i −0.125083 + 0.216651i
894894 0 0
895895 −11.1969 19.3935i −0.374270 0.648254i
896896 0 0
897897 0 0
898898 15.6150 27.0461i 0.521081 0.902539i
899899 66.7130 2.22500
900900 0 0
901901 −3.13052 −0.104293
902902 −8.91423 + 15.4399i −0.296811 + 0.514092i
903903 0 0
904904 1.60752 + 2.78431i 0.0534654 + 0.0926048i
905905 20.6300 + 35.7321i 0.685763 + 1.18778i
906906 0 0
907907 24.0751 41.6993i 0.799401 1.38460i −0.120606 0.992700i 0.538484π-0.538484\pi
0.920007 0.391902i 0.128183π-0.128183\pi
908908 14.5081 0.481468
909909 0 0
910910 0 0
911911 −17.4428 + 30.2119i −0.577906 + 1.00096i 0.417813 + 0.908533i 0.362797π0.362797\pi
−0.995719 + 0.0924301i 0.970537π0.970537\pi
912912 0 0
913913 −12.8353 22.2314i −0.424786 0.735751i
914914 16.0624 + 27.8209i 0.531296 + 0.920232i
915915 0 0
916916 −5.12476 + 8.87635i −0.169327 + 0.293283i
917917 0 0
918918 0 0
919919 51.7349 1.70658 0.853289 0.521439i 0.174605π-0.174605\pi
0.853289 + 0.521439i 0.174605π0.174605\pi
920920 3.56238 6.17023i 0.117448 0.203426i
921921 0 0
922922 −1.23229 2.13438i −0.0405832 0.0702922i
923923 −24.7826 42.9248i −0.815730 1.41289i
924924 0 0
925925 2.56238 4.43818i 0.0842506 0.145926i
926926 −30.3469 −0.997262
927927 0 0
928928 −7.08126 −0.232454
929929 −25.4142 + 44.0187i −0.833814 + 1.44421i 0.0611787 + 0.998127i 0.480514π0.480514\pi
−0.894993 + 0.446081i 0.852819π0.852819\pi
930930 0 0
931931 0 0
932932 −0.540628 0.936396i −0.0177089 0.0306727i
933933 0 0
934934 7.98181 13.8249i 0.261173 0.452365i
935935 15.4074 0.503876
936936 0 0
937937 2.54583 0.0831686 0.0415843 0.999135i 0.486759π-0.486759\pi
0.0415843 + 0.999135i 0.486759π0.486759\pi
938938 0 0
939939 0 0
940940 −9.27292 16.0612i −0.302449 0.523857i
941941 0.578933 + 1.00274i 0.0188727 + 0.0326885i 0.875308 0.483567i 0.160659π-0.160659\pi
−0.856435 + 0.516255i 0.827326π0.827326\pi
942942 0 0
943943 −6.27292 + 10.8650i −0.204274 + 0.353813i
944944 1.12476 0.0366079
945945 0 0
946946 21.7278 0.706431
947947 4.90739 8.49985i 0.159469 0.276208i −0.775208 0.631706i 0.782355π-0.782355\pi
0.934677 + 0.355497i 0.115689π0.115689\pi
948948 0 0
949949 14.1648 + 24.5342i 0.459810 + 0.796414i
950950 −3.28659 5.69254i −0.106631 0.184690i
951951 0 0
952952 0 0
953953 −6.53791 −0.211784 −0.105892 0.994378i 0.533770π-0.533770\pi
−0.105892 + 0.994378i 0.533770π0.533770\pi
954954 0 0
955955 −6.30206 −0.203930
956956 6.16019 10.6698i 0.199235 0.345085i
957957 0 0
958958 −11.5865 20.0683i −0.374341 0.648378i
959959 0 0
960960 0 0
961961 −28.8782 + 50.0186i −0.931556 + 1.61350i
962962 5.70370 0.183895
963963 0 0
964964 −13.0000 −0.418702
965965 7.23229 12.5267i 0.232816 0.403248i
966966 0 0
967967 14.4445 + 25.0185i 0.464502 + 0.804542i 0.999179 0.0405151i 0.0128999π-0.0128999\pi
−0.534677 + 0.845057i 0.679567π0.679567\pi
968968 0.437618 + 0.757977i 0.0140656 + 0.0243623i
969969 0 0
970970 23.6134 40.8996i 0.758181 1.31321i
971971 5.33654 0.171258 0.0856289 0.996327i 0.472710π-0.472710\pi
0.0856289 + 0.996327i 0.472710π0.472710\pi
972972 0 0
973973 0 0
974974 1.70658 2.95588i 0.0546822 0.0947124i
975975 0 0
976976 −1.56238 2.70612i −0.0500106 0.0866209i
977977 −24.0361 41.6318i −0.768983 1.33192i −0.938115 0.346325i 0.887429π-0.887429\pi
0.169131 0.985594i 0.445904π-0.445904\pi
978978 0 0
979979 0.358685 0.621261i 0.0114636 0.0198556i
980980 0 0
981981 0 0
982982 −19.1683 −0.611684
983983 14.7313 25.5154i 0.469857 0.813816i −0.529549 0.848279i 0.677639π-0.677639\pi
0.999406 + 0.0344634i 0.0109722π0.0109722\pi
984984 0 0
985985 −34.7067 60.1138i −1.10585 1.91538i
986986 −5.38796 9.33223i −0.171588 0.297199i
987987 0 0
988988 3.65787 6.33561i 0.116372 0.201563i
989989 15.2898 0.486186
990990 0 0
991991 −30.8285 −0.979298 −0.489649 0.871920i 0.662875π-0.662875\pi
−0.489649 + 0.871920i 0.662875π0.662875\pi
992992 4.71053 8.15888i 0.149560 0.259045i
993993 0 0
994994 0 0
995995 19.5413 + 33.8466i 0.619501 + 1.07301i
996996 0 0
997997 −2.77292 + 4.80283i −0.0878191 + 0.152107i −0.906589 0.422015i 0.861323π-0.861323\pi
0.818770 + 0.574122i 0.194656π0.194656\pi
998998 41.1696 1.30320
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2646.2.f.l.883.1 6
3.2 odd 2 882.2.f.n.295.2 6
7.2 even 3 378.2.e.d.235.1 6
7.3 odd 6 2646.2.h.o.667.1 6
7.4 even 3 378.2.h.c.289.3 6
7.5 odd 6 2646.2.e.p.2125.3 6
7.6 odd 2 2646.2.f.m.883.3 6
9.2 odd 6 7938.2.a.bv.1.1 3
9.4 even 3 inner 2646.2.f.l.1765.1 6
9.5 odd 6 882.2.f.n.589.2 6
9.7 even 3 7938.2.a.ca.1.3 3
21.2 odd 6 126.2.e.c.25.3 6
21.5 even 6 882.2.e.o.655.1 6
21.11 odd 6 126.2.h.d.79.1 yes 6
21.17 even 6 882.2.h.p.79.3 6
21.20 even 2 882.2.f.o.295.2 6
28.11 odd 6 3024.2.t.h.289.3 6
28.23 odd 6 3024.2.q.g.2881.1 6
63.2 odd 6 1134.2.g.m.487.3 6
63.4 even 3 378.2.e.d.37.1 6
63.5 even 6 882.2.h.p.67.3 6
63.11 odd 6 1134.2.g.m.163.3 6
63.13 odd 6 2646.2.f.m.1765.3 6
63.16 even 3 1134.2.g.l.487.1 6
63.20 even 6 7938.2.a.bw.1.3 3
63.23 odd 6 126.2.h.d.67.1 yes 6
63.25 even 3 1134.2.g.l.163.1 6
63.31 odd 6 2646.2.e.p.1549.3 6
63.32 odd 6 126.2.e.c.121.3 yes 6
63.34 odd 6 7938.2.a.bz.1.1 3
63.40 odd 6 2646.2.h.o.361.1 6
63.41 even 6 882.2.f.o.589.2 6
63.58 even 3 378.2.h.c.361.3 6
63.59 even 6 882.2.e.o.373.1 6
84.11 even 6 1008.2.t.h.961.3 6
84.23 even 6 1008.2.q.g.529.1 6
252.23 even 6 1008.2.t.h.193.3 6
252.67 odd 6 3024.2.q.g.2305.1 6
252.95 even 6 1008.2.q.g.625.1 6
252.247 odd 6 3024.2.t.h.1873.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.c.25.3 6 21.2 odd 6
126.2.e.c.121.3 yes 6 63.32 odd 6
126.2.h.d.67.1 yes 6 63.23 odd 6
126.2.h.d.79.1 yes 6 21.11 odd 6
378.2.e.d.37.1 6 63.4 even 3
378.2.e.d.235.1 6 7.2 even 3
378.2.h.c.289.3 6 7.4 even 3
378.2.h.c.361.3 6 63.58 even 3
882.2.e.o.373.1 6 63.59 even 6
882.2.e.o.655.1 6 21.5 even 6
882.2.f.n.295.2 6 3.2 odd 2
882.2.f.n.589.2 6 9.5 odd 6
882.2.f.o.295.2 6 21.20 even 2
882.2.f.o.589.2 6 63.41 even 6
882.2.h.p.67.3 6 63.5 even 6
882.2.h.p.79.3 6 21.17 even 6
1008.2.q.g.529.1 6 84.23 even 6
1008.2.q.g.625.1 6 252.95 even 6
1008.2.t.h.193.3 6 252.23 even 6
1008.2.t.h.961.3 6 84.11 even 6
1134.2.g.l.163.1 6 63.25 even 3
1134.2.g.l.487.1 6 63.16 even 3
1134.2.g.m.163.3 6 63.11 odd 6
1134.2.g.m.487.3 6 63.2 odd 6
2646.2.e.p.1549.3 6 63.31 odd 6
2646.2.e.p.2125.3 6 7.5 odd 6
2646.2.f.l.883.1 6 1.1 even 1 trivial
2646.2.f.l.1765.1 6 9.4 even 3 inner
2646.2.f.m.883.3 6 7.6 odd 2
2646.2.f.m.1765.3 6 63.13 odd 6
2646.2.h.o.361.1 6 63.40 odd 6
2646.2.h.o.667.1 6 7.3 odd 6
3024.2.q.g.2305.1 6 252.67 odd 6
3024.2.q.g.2881.1 6 28.23 odd 6
3024.2.t.h.289.3 6 28.11 odd 6
3024.2.t.h.1873.3 6 252.247 odd 6
7938.2.a.bv.1.1 3 9.2 odd 6
7938.2.a.bw.1.3 3 63.20 even 6
7938.2.a.bz.1.1 3 63.34 odd 6
7938.2.a.ca.1.3 3 9.7 even 3