Properties

Label 1350.2.j.g.1099.2
Level 13501350
Weight 22
Character 1350.1099
Analytic conductor 10.78010.780
Analytic rank 00
Dimension 88
Inner twists 44

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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] = [1350,2,Mod(199,1350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) 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("1350.199"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1350=23352 1350 = 2 \cdot 3^{3} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1350.j (of order 66, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,0,4,0,0,0,0,0,0,0,0,0,8,0,-4,0,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 10.779804272910.7798042729
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(ζ24)\Q(\zeta_{24})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x8x4+1 x^{8} - x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 2232 2^{2}\cdot 3^{2}
Twist minimal: no (minimal twist has level 450)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 1099.2
Root 0.965926+0.258819i-0.965926 + 0.258819i of defining polynomial
Character χ\chi == 1350.1099
Dual form 1350.2.j.g.199.2

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+(0.8660250.500000i)q2+(0.500000+0.866025i)q4+(0.389270+0.224745i)q71.00000iq8+(2.44949+4.24264i)q11+(0.3892700.224745i)q13+(0.2247450.389270i)q14+(0.500000+0.866025i)q164.89898iq177.44949q19+(4.242642.44949i)q22+(2.12132+1.22474i)q230.449490q26+0.449490iq28+(1.224742.12132i)q29+(2.224743.85337i)q31+(0.8660250.500000i)q32+(2.44949+4.24264i)q3411.3485iq37+(6.45145+3.72474i)q38+(4.50000+7.79423i)q41+(2.20881+1.27526i)q434.89898q44+2.44949q46+(9.438795.44949i)q47+(3.398985.88721i)q49+(0.389270+0.224745i)q523.55051iq53+(0.2247450.389270i)q56+(2.12132+1.22474i)q58+(2.72474+4.71940i)q59+(4.00000+6.92820i)q61+4.44949iq621.00000q64+(0.3017830.174235i)q67+(4.242642.44949i)q6813.3485q71+1.00000iq73+(5.67423+9.82806i)q74+(3.724746.45145i)q76+(1.90702+1.10102i)q77+(8.3484714.4600i)q799.00000iq82+(4.71940+2.72474i)q83+(1.275262.20881i)q86+(4.24264+2.44949i)q889.00000q89+0.202041q91+(2.121321.22474i)q92+(5.44949+9.43879i)q94+(7.619264.39898i)q97+6.79796iq98+O(q100)q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.389270 + 0.224745i) q^{7} -1.00000i q^{8} +(-2.44949 + 4.24264i) q^{11} +(0.389270 - 0.224745i) q^{13} +(-0.224745 - 0.389270i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.89898i q^{17} -7.44949 q^{19} +(4.24264 - 2.44949i) q^{22} +(-2.12132 + 1.22474i) q^{23} -0.449490 q^{26} +0.449490i q^{28} +(1.22474 - 2.12132i) q^{29} +(-2.22474 - 3.85337i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.44949 + 4.24264i) q^{34} -11.3485i q^{37} +(6.45145 + 3.72474i) q^{38} +(4.50000 + 7.79423i) q^{41} +(2.20881 + 1.27526i) q^{43} -4.89898 q^{44} +2.44949 q^{46} +(-9.43879 - 5.44949i) q^{47} +(-3.39898 - 5.88721i) q^{49} +(0.389270 + 0.224745i) q^{52} -3.55051i q^{53} +(0.224745 - 0.389270i) q^{56} +(-2.12132 + 1.22474i) q^{58} +(2.72474 + 4.71940i) q^{59} +(-4.00000 + 6.92820i) q^{61} +4.44949i q^{62} -1.00000 q^{64} +(0.301783 - 0.174235i) q^{67} +(4.24264 - 2.44949i) q^{68} -13.3485 q^{71} +1.00000i q^{73} +(-5.67423 + 9.82806i) q^{74} +(-3.72474 - 6.45145i) q^{76} +(-1.90702 + 1.10102i) q^{77} +(8.34847 - 14.4600i) q^{79} -9.00000i q^{82} +(4.71940 + 2.72474i) q^{83} +(-1.27526 - 2.20881i) q^{86} +(4.24264 + 2.44949i) q^{88} -9.00000 q^{89} +0.202041 q^{91} +(-2.12132 - 1.22474i) q^{92} +(5.44949 + 9.43879i) q^{94} +(-7.61926 - 4.39898i) q^{97} +6.79796i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+4q4+8q144q1640q19+16q268q31+36q41+12q498q56+12q5932q618q6448q7116q7420q76+8q7920q8672q89++24q94+O(q100) 8 q + 4 q^{4} + 8 q^{14} - 4 q^{16} - 40 q^{19} + 16 q^{26} - 8 q^{31} + 36 q^{41} + 12 q^{49} - 8 q^{56} + 12 q^{59} - 32 q^{61} - 8 q^{64} - 48 q^{71} - 16 q^{74} - 20 q^{76} + 8 q^{79} - 20 q^{86} - 72 q^{89}+ \cdots + 24 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1350Z)×\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times.

nn 10011001 10271027
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.866025 0.500000i −0.612372 0.353553i
33 0 0
44 0.500000 + 0.866025i 0.250000 + 0.433013i
55 0 0
66 0 0
77 0.389270 + 0.224745i 0.147130 + 0.0849456i 0.571758 0.820422i 0.306262π-0.306262\pi
−0.424628 + 0.905368i 0.639595π0.639595\pi
88 1.00000i 0.353553i
99 0 0
1010 0 0
1111 −2.44949 + 4.24264i −0.738549 + 1.27920i 0.214600 + 0.976702i 0.431155π0.431155\pi
−0.953149 + 0.302502i 0.902178π0.902178\pi
1212 0 0
1313 0.389270 0.224745i 0.107964 0.0623330i −0.445046 0.895508i 0.646813π-0.646813\pi
0.553010 + 0.833175i 0.313479π0.313479\pi
1414 −0.224745 0.389270i −0.0600656 0.104037i
1515 0 0
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 4.89898i 1.18818i −0.804400 0.594089i 0.797513π-0.797513\pi
0.804400 0.594089i 0.202487π-0.202487\pi
1818 0 0
1919 −7.44949 −1.70903 −0.854515 0.519427i 0.826146π-0.826146\pi
−0.854515 + 0.519427i 0.826146π0.826146\pi
2020 0 0
2121 0 0
2222 4.24264 2.44949i 0.904534 0.522233i
2323 −2.12132 + 1.22474i −0.442326 + 0.255377i −0.704584 0.709621i 0.748866π-0.748866\pi
0.262258 + 0.964998i 0.415533π0.415533\pi
2424 0 0
2525 0 0
2626 −0.449490 −0.0881522
2727 0 0
2828 0.449490i 0.0849456i
2929 1.22474 2.12132i 0.227429 0.393919i −0.729616 0.683857i 0.760301π-0.760301\pi
0.957046 + 0.289938i 0.0936346π0.0936346\pi
3030 0 0
3131 −2.22474 3.85337i −0.399576 0.692086i 0.594098 0.804393i 0.297509π-0.297509\pi
−0.993674 + 0.112307i 0.964176π0.964176\pi
3232 0.866025 0.500000i 0.153093 0.0883883i
3333 0 0
3434 −2.44949 + 4.24264i −0.420084 + 0.727607i
3535 0 0
3636 0 0
3737 11.3485i 1.86568i −0.360295 0.932838i 0.617324π-0.617324\pi
0.360295 0.932838i 0.382676π-0.382676\pi
3838 6.45145 + 3.72474i 1.04656 + 0.604233i
3939 0 0
4040 0 0
4141 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i 0.0813924π0.0813924\pi
−0.264704 + 0.964330i 0.585274π0.585274\pi
4242 0 0
4343 2.20881 + 1.27526i 0.336840 + 0.194475i 0.658874 0.752254i 0.271033π-0.271033\pi
−0.322034 + 0.946728i 0.604366π0.604366\pi
4444 −4.89898 −0.738549
4545 0 0
4646 2.44949 0.361158
4747 −9.43879 5.44949i −1.37679 0.794890i −0.385018 0.922909i 0.625805π-0.625805\pi
−0.991772 + 0.128019i 0.959138π0.959138\pi
4848 0 0
4949 −3.39898 5.88721i −0.485568 0.841029i
5050 0 0
5151 0 0
5252 0.389270 + 0.224745i 0.0539820 + 0.0311665i
5353 3.55051i 0.487700i −0.969813 0.243850i 0.921590π-0.921590\pi
0.969813 0.243850i 0.0784105π-0.0784105\pi
5454 0 0
5555 0 0
5656 0.224745 0.389270i 0.0300328 0.0520183i
5757 0 0
5858 −2.12132 + 1.22474i −0.278543 + 0.160817i
5959 2.72474 + 4.71940i 0.354732 + 0.614413i 0.987072 0.160278i 0.0512389π-0.0512389\pi
−0.632340 + 0.774691i 0.717906π0.717906\pi
6060 0 0
6161 −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i 0.337817π0.337817\pi
−0.999901 + 0.0140840i 0.995517π0.995517\pi
6262 4.44949i 0.565086i
6363 0 0
6464 −1.00000 −0.125000
6565 0 0
6666 0 0
6767 0.301783 0.174235i 0.0368687 0.0212861i −0.481452 0.876472i 0.659891π-0.659891\pi
0.518321 + 0.855186i 0.326557π0.326557\pi
6868 4.24264 2.44949i 0.514496 0.297044i
6969 0 0
7070 0 0
7171 −13.3485 −1.58417 −0.792086 0.610410i 0.791005π-0.791005\pi
−0.792086 + 0.610410i 0.791005π0.791005\pi
7272 0 0
7373 1.00000i 0.117041i 0.998286 + 0.0585206i 0.0186383π0.0186383\pi
−0.998286 + 0.0585206i 0.981362π0.981362\pi
7474 −5.67423 + 9.82806i −0.659616 + 1.14249i
7575 0 0
7676 −3.72474 6.45145i −0.427258 0.740032i
7777 −1.90702 + 1.10102i −0.217325 + 0.125473i
7878 0 0
7979 8.34847 14.4600i 0.939276 1.62687i 0.172451 0.985018i 0.444831π-0.444831\pi
0.766825 0.641856i 0.221835π-0.221835\pi
8080 0 0
8181 0 0
8282 9.00000i 0.993884i
8383 4.71940 + 2.72474i 0.518021 + 0.299080i 0.736125 0.676846i 0.236654π-0.236654\pi
−0.218104 + 0.975926i 0.569987π0.569987\pi
8484 0 0
8585 0 0
8686 −1.27526 2.20881i −0.137514 0.238182i
8787 0 0
8888 4.24264 + 2.44949i 0.452267 + 0.261116i
8989 −9.00000 −0.953998 −0.476999 0.878904i 0.658275π-0.658275\pi
−0.476999 + 0.878904i 0.658275π0.658275\pi
9090 0 0
9191 0.202041 0.0211797
9292 −2.12132 1.22474i −0.221163 0.127688i
9393 0 0
9494 5.44949 + 9.43879i 0.562072 + 0.973537i
9595 0 0
9696 0 0
9797 −7.61926 4.39898i −0.773618 0.446649i 0.0605456 0.998165i 0.480716π-0.480716\pi
−0.834164 + 0.551517i 0.814049π0.814049\pi
9898 6.79796i 0.686698i
9999 0 0
100100 0 0
101101 4.22474 7.31747i 0.420378 0.728116i −0.575599 0.817732i 0.695231π-0.695231\pi
0.995976 + 0.0896167i 0.0285642π0.0285642\pi
102102 0 0
103103 −14.4600 + 8.34847i −1.42478 + 0.822599i −0.996703 0.0811413i 0.974143π-0.974143\pi
−0.428081 + 0.903740i 0.640810π0.640810\pi
104104 −0.224745 0.389270i −0.0220380 0.0381710i
105105 0 0
106106 −1.77526 + 3.07483i −0.172428 + 0.298654i
107107 9.24745i 0.893985i −0.894538 0.446992i 0.852495π-0.852495\pi
0.894538 0.446992i 0.147505π-0.147505\pi
108108 0 0
109109 −5.55051 −0.531642 −0.265821 0.964022i 0.585643π-0.585643\pi
−0.265821 + 0.964022i 0.585643π0.585643\pi
110110 0 0
111111 0 0
112112 −0.389270 + 0.224745i −0.0367825 + 0.0212364i
113113 −3.55159 + 2.05051i −0.334105 + 0.192896i −0.657662 0.753313i 0.728455π-0.728455\pi
0.323557 + 0.946209i 0.395121π0.395121\pi
114114 0 0
115115 0 0
116116 2.44949 0.227429
117117 0 0
118118 5.44949i 0.501666i
119119 1.10102 1.90702i 0.100930 0.174817i
120120 0 0
121121 −6.50000 11.2583i −0.590909 1.02348i
122122 6.92820 4.00000i 0.627250 0.362143i
123123 0 0
124124 2.22474 3.85337i 0.199788 0.346043i
125125 0 0
126126 0 0
127127 3.34847i 0.297129i 0.988903 + 0.148564i 0.0474652π0.0474652\pi
−0.988903 + 0.148564i 0.952535π0.952535\pi
128128 0.866025 + 0.500000i 0.0765466 + 0.0441942i
129129 0 0
130130 0 0
131131 −1.89898 3.28913i −0.165915 0.287373i 0.771065 0.636756i 0.219724π-0.219724\pi
−0.936980 + 0.349384i 0.886391π0.886391\pi
132132 0 0
133133 −2.89986 1.67423i −0.251450 0.145175i
134134 −0.348469 −0.0301032
135135 0 0
136136 −4.89898 −0.420084
137137 2.59808 + 1.50000i 0.221969 + 0.128154i 0.606861 0.794808i 0.292428π-0.292428\pi
−0.384893 + 0.922961i 0.625762π0.625762\pi
138138 0 0
139139 −2.00000 3.46410i −0.169638 0.293821i 0.768655 0.639664i 0.220926π-0.220926\pi
−0.938293 + 0.345843i 0.887593π0.887593\pi
140140 0 0
141141 0 0
142142 11.5601 + 6.67423i 0.970103 + 0.560089i
143143 2.20204i 0.184144i
144144 0 0
145145 0 0
146146 0.500000 0.866025i 0.0413803 0.0716728i
147147 0 0
148148 9.82806 5.67423i 0.807862 0.466419i
149149 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i 0.0876260π-0.0876260\pi
−0.716578 + 0.697507i 0.754293π0.754293\pi
150150 0 0
151151 −10.0000 + 17.3205i −0.813788 + 1.40952i 0.0964061 + 0.995342i 0.469265π0.469265\pi
−0.910195 + 0.414181i 0.864068π0.864068\pi
152152 7.44949i 0.604233i
153153 0 0
154154 2.20204 0.177446
155155 0 0
156156 0 0
157157 −17.1455 + 9.89898i −1.36836 + 0.790025i −0.990719 0.135926i 0.956599π-0.956599\pi
−0.377644 + 0.925951i 0.623266π0.623266\pi
158158 −14.4600 + 8.34847i −1.15037 + 0.664169i
159159 0 0
160160 0 0
161161 −1.10102 −0.0867726
162162 0 0
163163 7.44949i 0.583489i −0.956496 0.291745i 0.905764π-0.905764\pi
0.956496 0.291745i 0.0942357π-0.0942357\pi
164164 −4.50000 + 7.79423i −0.351391 + 0.608627i
165165 0 0
166166 −2.72474 4.71940i −0.211481 0.366296i
167167 −16.9706 + 9.79796i −1.31322 + 0.758189i −0.982628 0.185584i 0.940582π-0.940582\pi
−0.330593 + 0.943773i 0.607249π0.607249\pi
168168 0 0
169169 −6.39898 + 11.0834i −0.492229 + 0.852566i
170170 0 0
171171 0 0
172172 2.55051i 0.194475i
173173 −8.48528 4.89898i −0.645124 0.372463i 0.141462 0.989944i 0.454820π-0.454820\pi
−0.786586 + 0.617481i 0.788153π0.788153\pi
174174 0 0
175175 0 0
176176 −2.44949 4.24264i −0.184637 0.319801i
177177 0 0
178178 7.79423 + 4.50000i 0.584202 + 0.337289i
179179 9.24745 0.691187 0.345593 0.938384i 0.387678π-0.387678\pi
0.345593 + 0.938384i 0.387678π0.387678\pi
180180 0 0
181181 17.7980 1.32291 0.661456 0.749984i 0.269939π-0.269939\pi
0.661456 + 0.749984i 0.269939π0.269939\pi
182182 −0.174973 0.101021i −0.0129698 0.00748814i
183183 0 0
184184 1.22474 + 2.12132i 0.0902894 + 0.156386i
185185 0 0
186186 0 0
187187 20.7846 + 12.0000i 1.51992 + 0.877527i
188188 10.8990i 0.794890i
189189 0 0
190190 0 0
191191 −0.550510 + 0.953512i −0.0398335 + 0.0689937i −0.885255 0.465106i 0.846016π-0.846016\pi
0.845421 + 0.534100i 0.179349π0.179349\pi
192192 0 0
193193 −17.3205 + 10.0000i −1.24676 + 0.719816i −0.970461 0.241257i 0.922440π-0.922440\pi
−0.276296 + 0.961073i 0.589107π0.589107\pi
194194 4.39898 + 7.61926i 0.315828 + 0.547031i
195195 0 0
196196 3.39898 5.88721i 0.242784 0.420515i
197197 0.247449i 0.0176300i 0.999961 + 0.00881500i 0.00280594π0.00280594\pi
−0.999961 + 0.00881500i 0.997194π0.997194\pi
198198 0 0
199199 13.7980 0.978111 0.489056 0.872253i 0.337341π-0.337341\pi
0.489056 + 0.872253i 0.337341π0.337341\pi
200200 0 0
201201 0 0
202202 −7.31747 + 4.22474i −0.514856 + 0.297252i
203203 0.953512 0.550510i 0.0669234 0.0386382i
204204 0 0
205205 0 0
206206 16.6969 1.16333
207207 0 0
208208 0.449490i 0.0311665i
209209 18.2474 31.6055i 1.26220 2.18620i
210210 0 0
211211 1.72474 + 2.98735i 0.118736 + 0.205657i 0.919267 0.393634i 0.128782π-0.128782\pi
−0.800531 + 0.599292i 0.795449π0.795449\pi
212212 3.07483 1.77526i 0.211180 0.121925i
213213 0 0
214214 −4.62372 + 8.00853i −0.316071 + 0.547452i
215215 0 0
216216 0 0
217217 2.00000i 0.135769i
218218 4.80688 + 2.77526i 0.325563 + 0.187964i
219219 0 0
220220 0 0
221221 −1.10102 1.90702i −0.0740627 0.128280i
222222 0 0
223223 15.4135 + 8.89898i 1.03216 + 0.595920i 0.917604 0.397497i 0.130121π-0.130121\pi
0.114560 + 0.993416i 0.463454π0.463454\pi
224224 0.449490 0.0300328
225225 0 0
226226 4.10102 0.272796
227227 11.8226 + 6.82577i 0.784692 + 0.453042i 0.838090 0.545531i 0.183672π-0.183672\pi
−0.0533987 + 0.998573i 0.517005π0.517005\pi
228228 0 0
229229 6.57321 + 11.3851i 0.434370 + 0.752351i 0.997244 0.0741916i 0.0236376π-0.0236376\pi
−0.562874 + 0.826543i 0.690304π0.690304\pi
230230 0 0
231231 0 0
232232 −2.12132 1.22474i −0.139272 0.0804084i
233233 23.6969i 1.55244i −0.630463 0.776219i 0.717135π-0.717135\pi
0.630463 0.776219i 0.282865π-0.282865\pi
234234 0 0
235235 0 0
236236 −2.72474 + 4.71940i −0.177366 + 0.307207i
237237 0 0
238238 −1.90702 + 1.10102i −0.123614 + 0.0713686i
239239 −7.22474 12.5136i −0.467330 0.809439i 0.531973 0.846761i 0.321451π-0.321451\pi
−0.999303 + 0.0373219i 0.988117π0.988117\pi
240240 0 0
241241 1.60102 2.77305i 0.103131 0.178628i −0.809842 0.586648i 0.800447π-0.800447\pi
0.912973 + 0.408020i 0.133781π0.133781\pi
242242 13.0000i 0.835672i
243243 0 0
244244 −8.00000 −0.512148
245245 0 0
246246 0 0
247247 −2.89986 + 1.67423i −0.184514 + 0.106529i
248248 −3.85337 + 2.22474i −0.244689 + 0.141271i
249249 0 0
250250 0 0
251251 0.550510 0.0347479 0.0173739 0.999849i 0.494469π-0.494469\pi
0.0173739 + 0.999849i 0.494469π0.494469\pi
252252 0 0
253253 12.0000i 0.754434i
254254 1.67423 2.89986i 0.105051 0.181953i
255255 0 0
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 11.0834 6.39898i 0.691361 0.399157i −0.112761 0.993622i 0.535969π-0.535969\pi
0.804122 + 0.594465i 0.202636π0.202636\pi
258258 0 0
259259 2.55051 4.41761i 0.158481 0.274497i
260260 0 0
261261 0 0
262262 3.79796i 0.234639i
263263 −17.7098 10.2247i −1.09203 0.630485i −0.157915 0.987453i 0.550477π-0.550477\pi
−0.934117 + 0.356968i 0.883811π0.883811\pi
264264 0 0
265265 0 0
266266 1.67423 + 2.89986i 0.102654 + 0.177802i
267267 0 0
268268 0.301783 + 0.174235i 0.0184343 + 0.0106431i
269269 14.4495 0.881001 0.440500 0.897752i 0.354801π-0.354801\pi
0.440500 + 0.897752i 0.354801π0.354801\pi
270270 0 0
271271 15.3485 0.932353 0.466177 0.884692i 0.345631π-0.345631\pi
0.466177 + 0.884692i 0.345631π0.345631\pi
272272 4.24264 + 2.44949i 0.257248 + 0.148522i
273273 0 0
274274 −1.50000 2.59808i −0.0906183 0.156956i
275275 0 0
276276 0 0
277277 1.34278 + 0.775255i 0.0806799 + 0.0465806i 0.539797 0.841795i 0.318501π-0.318501\pi
−0.459117 + 0.888376i 0.651834π0.651834\pi
278278 4.00000i 0.239904i
279279 0 0
280280 0 0
281281 9.55051 16.5420i 0.569736 0.986811i −0.426856 0.904320i 0.640379π-0.640379\pi
0.996592 0.0824916i 0.0262878π-0.0262878\pi
282282 0 0
283283 11.4726 6.62372i 0.681977 0.393740i −0.118623 0.992939i 0.537848π-0.537848\pi
0.800599 + 0.599200i 0.204515π0.204515\pi
284284 −6.67423 11.5601i −0.396043 0.685967i
285285 0 0
286286 1.10102 1.90702i 0.0651047 0.112765i
287287 4.04541i 0.238793i
288288 0 0
289289 −7.00000 −0.411765
290290 0 0
291291 0 0
292292 −0.866025 + 0.500000i −0.0506803 + 0.0292603i
293293 13.8957 8.02270i 0.811797 0.468691i −0.0357824 0.999360i 0.511392π-0.511392\pi
0.847580 + 0.530668i 0.178059π0.178059\pi
294294 0 0
295295 0 0
296296 −11.3485 −0.659616
297297 0 0
298298 6.00000i 0.347571i
299299 −0.550510 + 0.953512i −0.0318368 + 0.0551430i
300300 0 0
301301 0.573214 + 0.992836i 0.0330395 + 0.0572261i
302302 17.3205 10.0000i 0.996683 0.575435i
303303 0 0
304304 3.72474 6.45145i 0.213629 0.370016i
305305 0 0
306306 0 0
307307 22.6969i 1.29538i 0.761903 + 0.647691i 0.224265π0.224265\pi
−0.761903 + 0.647691i 0.775735π0.775735\pi
308308 −1.90702 1.10102i −0.108663 0.0627365i
309309 0 0
310310 0 0
311311 −0.550510 0.953512i −0.0312166 0.0540687i 0.849995 0.526791i 0.176605π-0.176605\pi
−0.881212 + 0.472722i 0.843271π0.843271\pi
312312 0 0
313313 −5.10867 2.94949i −0.288759 0.166715i 0.348623 0.937263i 0.386649π-0.386649\pi
−0.637382 + 0.770548i 0.719983π0.719983\pi
314314 19.7980 1.11726
315315 0 0
316316 16.6969 0.939276
317317 14.8492 + 8.57321i 0.834017 + 0.481520i 0.855226 0.518255i 0.173418π-0.173418\pi
−0.0212094 + 0.999775i 0.506752π0.506752\pi
318318 0 0
319319 6.00000 + 10.3923i 0.335936 + 0.581857i
320320 0 0
321321 0 0
322322 0.953512 + 0.550510i 0.0531371 + 0.0306787i
323323 36.4949i 2.03063i
324324 0 0
325325 0 0
326326 −3.72474 + 6.45145i −0.206295 + 0.357313i
327327 0 0
328328 7.79423 4.50000i 0.430364 0.248471i
329329 −2.44949 4.24264i −0.135045 0.233904i
330330 0 0
331331 −3.17423 + 5.49794i −0.174472 + 0.302194i −0.939978 0.341234i 0.889155π-0.889155\pi
0.765507 + 0.643428i 0.222488π0.222488\pi
332332 5.44949i 0.299080i
333333 0 0
334334 19.5959 1.07224
335335 0 0
336336 0 0
337337 −18.0990 + 10.4495i −0.985918 + 0.569220i −0.904052 0.427423i 0.859421π-0.859421\pi
−0.0818663 + 0.996643i 0.526088π0.526088\pi
338338 11.0834 6.39898i 0.602855 0.348059i
339339 0 0
340340 0 0
341341 21.7980 1.18043
342342 0 0
343343 6.20204i 0.334879i
344344 1.27526 2.20881i 0.0687571 0.119091i
345345 0 0
346346 4.89898 + 8.48528i 0.263371 + 0.456172i
347347 −10.3923 + 6.00000i −0.557888 + 0.322097i −0.752297 0.658824i 0.771054π-0.771054\pi
0.194409 + 0.980921i 0.437721π0.437721\pi
348348 0 0
349349 7.00000 12.1244i 0.374701 0.649002i −0.615581 0.788074i 0.711079π-0.711079\pi
0.990282 + 0.139072i 0.0444119π0.0444119\pi
350350 0 0
351351 0 0
352352 4.89898i 0.261116i
353353 7.79423 + 4.50000i 0.414845 + 0.239511i 0.692869 0.721063i 0.256346π-0.256346\pi
−0.278024 + 0.960574i 0.589680π0.589680\pi
354354 0 0
355355 0 0
356356 −4.50000 7.79423i −0.238500 0.413093i
357357 0 0
358358 −8.00853 4.62372i −0.423264 0.244371i
359359 −14.2020 −0.749555 −0.374778 0.927115i 0.622281π-0.622281\pi
−0.374778 + 0.927115i 0.622281π0.622281\pi
360360 0 0
361361 36.4949 1.92078
362362 −15.4135 8.89898i −0.810115 0.467720i
363363 0 0
364364 0.101021 + 0.174973i 0.00529491 + 0.00917106i
365365 0 0
366366 0 0
367367 10.9959 + 6.34847i 0.573980 + 0.331387i 0.758737 0.651397i 0.225817π-0.225817\pi
−0.184757 + 0.982784i 0.559150π0.559150\pi
368368 2.44949i 0.127688i
369369 0 0
370370 0 0
371371 0.797959 1.38211i 0.0414280 0.0717553i
372372 0 0
373373 20.4347 11.7980i 1.05807 0.610875i 0.133170 0.991093i 0.457484π-0.457484\pi
0.924897 + 0.380218i 0.124151π0.124151\pi
374374 −12.0000 20.7846i −0.620505 1.07475i
375375 0 0
376376 −5.44949 + 9.43879i −0.281036 + 0.486769i
377377 1.10102i 0.0567054i
378378 0 0
379379 8.89898 0.457110 0.228555 0.973531i 0.426600π-0.426600\pi
0.228555 + 0.973531i 0.426600π0.426600\pi
380380 0 0
381381 0 0
382382 0.953512 0.550510i 0.0487859 0.0281666i
383383 18.6633 10.7753i 0.953650 0.550590i 0.0594368 0.998232i 0.481070π-0.481070\pi
0.894213 + 0.447642i 0.147736π0.147736\pi
384384 0 0
385385 0 0
386386 20.0000 1.01797
387387 0 0
388388 8.79796i 0.446649i
389389 −12.7980 + 22.1667i −0.648882 + 1.12390i 0.334508 + 0.942393i 0.391430π0.391430\pi
−0.983390 + 0.181504i 0.941903π0.941903\pi
390390 0 0
391391 6.00000 + 10.3923i 0.303433 + 0.525561i
392392 −5.88721 + 3.39898i −0.297349 + 0.171674i
393393 0 0
394394 0.123724 0.214297i 0.00623314 0.0107961i
395395 0 0
396396 0 0
397397 17.5959i 0.883114i −0.897233 0.441557i 0.854426π-0.854426\pi
0.897233 0.441557i 0.145574π-0.145574\pi
398398 −11.9494 6.89898i −0.598968 0.345815i
399399 0 0
400400 0 0
401401 19.3485 + 33.5125i 0.966216 + 1.67354i 0.706311 + 0.707902i 0.250358π0.250358\pi
0.259906 + 0.965634i 0.416308π0.416308\pi
402402 0 0
403403 −1.73205 1.00000i −0.0862796 0.0498135i
404404 8.44949 0.420378
405405 0 0
406406 −1.10102 −0.0546427
407407 48.1475 + 27.7980i 2.38658 + 1.37789i
408408 0 0
409409 0.0505103 + 0.0874863i 0.00249757 + 0.00432592i 0.867271 0.497835i 0.165872π-0.165872\pi
−0.864774 + 0.502161i 0.832538π0.832538\pi
410410 0 0
411411 0 0
412412 −14.4600 8.34847i −0.712392 0.411300i
413413 2.44949i 0.120532i
414414 0 0
415415 0 0
416416 0.224745 0.389270i 0.0110190 0.0190855i
417417 0 0
418418 −31.6055 + 18.2474i −1.54588 + 0.892512i
419419 13.0732 + 22.6435i 0.638668 + 1.10621i 0.985725 + 0.168362i 0.0538477π0.0538477\pi
−0.347057 + 0.937844i 0.612819π0.612819\pi
420420 0 0
421421 13.0227 22.5560i 0.634688 1.09931i −0.351893 0.936040i 0.614462π-0.614462\pi
0.986581 0.163271i 0.0522046π-0.0522046\pi
422422 3.44949i 0.167919i
423423 0 0
424424 −3.55051 −0.172428
425425 0 0
426426 0 0
427427 −3.11416 + 1.79796i −0.150705 + 0.0870093i
428428 8.00853 4.62372i 0.387107 0.223496i
429429 0 0
430430 0 0
431431 −25.3485 −1.22099 −0.610496 0.792019i 0.709030π-0.709030\pi
−0.610496 + 0.792019i 0.709030π0.709030\pi
432432 0 0
433433 9.59592i 0.461150i −0.973055 0.230575i 0.925939π-0.925939\pi
0.973055 0.230575i 0.0740608π-0.0740608\pi
434434 −1.00000 + 1.73205i −0.0480015 + 0.0831411i
435435 0 0
436436 −2.77526 4.80688i −0.132911 0.230208i
437437 15.8028 9.12372i 0.755948 0.436447i
438438 0 0
439439 1.67423 2.89986i 0.0799069 0.138403i −0.823303 0.567603i 0.807871π-0.807871\pi
0.903210 + 0.429200i 0.141204π0.141204\pi
440440 0 0
441441 0 0
442442 2.20204i 0.104740i
443443 −7.10318 4.10102i −0.337482 0.194845i 0.321676 0.946850i 0.395754π-0.395754\pi
−0.659158 + 0.752004i 0.729087π0.729087\pi
444444 0 0
445445 0 0
446446 −8.89898 15.4135i −0.421379 0.729850i
447447 0 0
448448 −0.389270 0.224745i −0.0183913 0.0106182i
449449 −28.5959 −1.34952 −0.674762 0.738035i 0.735754π-0.735754\pi
−0.674762 + 0.738035i 0.735754π0.735754\pi
450450 0 0
451451 −44.0908 −2.07616
452452 −3.55159 2.05051i −0.167053 0.0964479i
453453 0 0
454454 −6.82577 11.8226i −0.320349 0.554861i
455455 0 0
456456 0 0
457457 −11.8619 6.84847i −0.554876 0.320358i 0.196210 0.980562i 0.437136π-0.437136\pi
−0.751086 + 0.660204i 0.770470π0.770470\pi
458458 13.1464i 0.614292i
459459 0 0
460460 0 0
461461 2.32577 4.02834i 0.108322 0.187619i −0.806769 0.590867i 0.798786π-0.798786\pi
0.915090 + 0.403249i 0.132119π0.132119\pi
462462 0 0
463463 4.63191 2.67423i 0.215263 0.124282i −0.388492 0.921452i 0.627004π-0.627004\pi
0.603755 + 0.797170i 0.293671π0.293671\pi
464464 1.22474 + 2.12132i 0.0568574 + 0.0984798i
465465 0 0
466466 −11.8485 + 20.5222i −0.548870 + 0.950670i
467467 10.3485i 0.478870i 0.970912 + 0.239435i 0.0769622π0.0769622\pi
−0.970912 + 0.239435i 0.923038π0.923038\pi
468468 0 0
469469 0.156633 0.00723266
470470 0 0
471471 0 0
472472 4.71940 2.72474i 0.217228 0.125417i
473473 −10.8209 + 6.24745i −0.497545 + 0.287258i
474474 0 0
475475 0 0
476476 2.20204 0.100930
477477 0 0
478478 14.4495i 0.660904i
479479 −0.123724 + 0.214297i −0.00565311 + 0.00979147i −0.868838 0.495096i 0.835133π-0.835133\pi
0.863185 + 0.504888i 0.168466π0.168466\pi
480480 0 0
481481 −2.55051 4.41761i −0.116293 0.201426i
482482 −2.77305 + 1.60102i −0.126309 + 0.0729245i
483483 0 0
484484 6.50000 11.2583i 0.295455 0.511742i
485485 0 0
486486 0 0
487487 24.4495i 1.10791i −0.832546 0.553956i 0.813118π-0.813118\pi
0.832546 0.553956i 0.186882π-0.186882\pi
488488 6.92820 + 4.00000i 0.313625 + 0.181071i
489489 0 0
490490 0 0
491491 −13.6237 23.5970i −0.614830 1.06492i −0.990414 0.138129i 0.955891π-0.955891\pi
0.375584 0.926788i 0.377442π-0.377442\pi
492492 0 0
493493 −10.3923 6.00000i −0.468046 0.270226i
494494 3.34847 0.150655
495495 0 0
496496 4.44949 0.199788
497497 −5.19615 3.00000i −0.233079 0.134568i
498498 0 0
499499 −4.17423 7.22999i −0.186864 0.323659i 0.757339 0.653022i 0.226499π-0.226499\pi
−0.944203 + 0.329364i 0.893166π0.893166\pi
500500 0 0
501501 0 0
502502 −0.476756 0.275255i −0.0212787 0.0122852i
503503 21.5505i 0.960890i 0.877025 + 0.480445i 0.159525π0.159525\pi
−0.877025 + 0.480445i 0.840475π0.840475\pi
504504 0 0
505505 0 0
506506 −6.00000 + 10.3923i −0.266733 + 0.461994i
507507 0 0
508508 −2.89986 + 1.67423i −0.128660 + 0.0742821i
509509 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
510510 0 0
511511 −0.224745 + 0.389270i −0.00994213 + 0.0172203i
512512 1.00000i 0.0441942i
513513 0 0
514514 −12.7980 −0.564494
515515 0 0
516516 0 0
517517 46.2405 26.6969i 2.03365 1.17413i
518518 −4.41761 + 2.55051i −0.194099 + 0.112063i
519519 0 0
520520 0 0
521521 29.3939 1.28777 0.643885 0.765123i 0.277322π-0.277322\pi
0.643885 + 0.765123i 0.277322π0.277322\pi
522522 0 0
523523 20.3485i 0.889776i 0.895586 + 0.444888i 0.146757π0.146757\pi
−0.895586 + 0.444888i 0.853243π0.853243\pi
524524 1.89898 3.28913i 0.0829573 0.143686i
525525 0 0
526526 10.2247 + 17.7098i 0.445820 + 0.772183i
527527 −18.8776 + 10.8990i −0.822321 + 0.474767i
528528 0 0
529529 −8.50000 + 14.7224i −0.369565 + 0.640106i
530530 0 0
531531 0 0
532532 3.34847i 0.145175i
533533 3.50343 + 2.02270i 0.151750 + 0.0876130i
534534 0 0
535535 0 0
536536 −0.174235 0.301783i −0.00752579 0.0130350i
537537 0 0
538538 −12.5136 7.22474i −0.539501 0.311481i
539539 33.3031 1.43446
540540 0 0
541541 −37.7980 −1.62506 −0.812531 0.582919i 0.801911π-0.801911\pi
−0.812531 + 0.582919i 0.801911π0.801911\pi
542542 −13.2922 7.67423i −0.570947 0.329637i
543543 0 0
544544 −2.44949 4.24264i −0.105021 0.181902i
545545 0 0
546546 0 0
547547 −13.5546 7.82577i −0.579554 0.334606i 0.181402 0.983409i 0.441936π-0.441936\pi
−0.760956 + 0.648803i 0.775270π0.775270\pi
548548 3.00000i 0.128154i
549549 0 0
550550 0 0
551551 −9.12372 + 15.8028i −0.388684 + 0.673220i
552552 0 0
553553 6.49961 3.75255i 0.276392 0.159575i
554554 −0.775255 1.34278i −0.0329374 0.0570493i
555555 0 0
556556 2.00000 3.46410i 0.0848189 0.146911i
557557 41.3939i 1.75391i −0.480568 0.876957i 0.659570π-0.659570\pi
0.480568 0.876957i 0.340430π-0.340430\pi
558558 0 0
559559 1.14643 0.0484887
560560 0 0
561561 0 0
562562 −16.5420 + 9.55051i −0.697781 + 0.402864i
563563 −20.7364 + 11.9722i −0.873937 + 0.504568i −0.868655 0.495418i 0.835015π-0.835015\pi
−0.00528250 + 0.999986i 0.501681π0.501681\pi
564564 0 0
565565 0 0
566566 −13.2474 −0.556832
567567 0 0
568568 13.3485i 0.560089i
569569 −16.8990 + 29.2699i −0.708442 + 1.22706i 0.256993 + 0.966413i 0.417268π0.417268\pi
−0.965435 + 0.260644i 0.916065π0.916065\pi
570570 0 0
571571 −12.9722 22.4685i −0.542869 0.940277i −0.998738 0.0502301i 0.984005π-0.984005\pi
0.455868 0.890047i 0.349329π-0.349329\pi
572572 −1.90702 + 1.10102i −0.0797367 + 0.0460360i
573573 0 0
574574 2.02270 3.50343i 0.0844260 0.146230i
575575 0 0
576576 0 0
577577 40.3939i 1.68162i 0.541331 + 0.840810i 0.317921π0.317921\pi
−0.541331 + 0.840810i 0.682079π0.682079\pi
578578 6.06218 + 3.50000i 0.252153 + 0.145581i
579579 0 0
580580 0 0
581581 1.22474 + 2.12132i 0.0508110 + 0.0880072i
582582 0 0
583583 15.0635 + 8.69694i 0.623868 + 0.360190i
584584 1.00000 0.0413803
585585 0 0
586586 −16.0454 −0.662830
587587 −23.1202 13.3485i −0.954274 0.550950i −0.0598679 0.998206i 0.519068π-0.519068\pi
−0.894406 + 0.447256i 0.852401π0.852401\pi
588588 0 0
589589 16.5732 + 28.7056i 0.682887 + 1.18280i
590590 0 0
591591 0 0
592592 9.82806 + 5.67423i 0.403931 + 0.233210i
593593 7.89898i 0.324372i −0.986760 0.162186i 0.948146π-0.948146\pi
0.986760 0.162186i 0.0518545π-0.0518545\pi
594594 0 0
595595 0 0
596596 −3.00000 + 5.19615i −0.122885 + 0.212843i
597597 0 0
598598 0.953512 0.550510i 0.0389920 0.0225120i
599599 11.3258 + 19.6168i 0.462758 + 0.801521i 0.999097 0.0424819i 0.0135265π-0.0135265\pi
−0.536339 + 0.844003i 0.680193π0.680193\pi
600600 0 0
601601 8.24745 14.2850i 0.336420 0.582697i −0.647336 0.762205i 0.724117π-0.724117\pi
0.983757 + 0.179507i 0.0574503π0.0574503\pi
602602 1.14643i 0.0467249i
603603 0 0
604604 −20.0000 −0.813788
605605 0 0
606606 0 0
607607 2.89986 1.67423i 0.117702 0.0679551i −0.439993 0.898001i 0.645019π-0.645019\pi
0.557695 + 0.830046i 0.311686π0.311686\pi
608608 −6.45145 + 3.72474i −0.261641 + 0.151058i
609609 0 0
610610 0 0
611611 −4.89898 −0.198191
612612 0 0
613613 12.0454i 0.486509i −0.969962 0.243255i 0.921785π-0.921785\pi
0.969962 0.243255i 0.0782151π-0.0782151\pi
614614 11.3485 19.6561i 0.457987 0.793257i
615615 0 0
616616 1.10102 + 1.90702i 0.0443614 + 0.0768362i
617617 −38.4462 + 22.1969i −1.54779 + 0.893615i −0.549476 + 0.835509i 0.685173π0.685173\pi
−0.998310 + 0.0581058i 0.981494π0.981494\pi
618618 0 0
619619 −15.8712 + 27.4897i −0.637916 + 1.10490i 0.347973 + 0.937505i 0.386870π0.386870\pi
−0.985889 + 0.167399i 0.946463π0.946463\pi
620620 0 0
621621 0 0
622622 1.10102i 0.0441469i
623623 −3.50343 2.02270i −0.140362 0.0810379i
624624 0 0
625625 0 0
626626 2.94949 + 5.10867i 0.117885 + 0.204183i
627627 0 0
628628 −17.1455 9.89898i −0.684181 0.395012i
629629 −55.5959 −2.21675
630630 0 0
631631 −6.20204 −0.246899 −0.123450 0.992351i 0.539396π-0.539396\pi
−0.123450 + 0.992351i 0.539396π0.539396\pi
632632 −14.4600 8.34847i −0.575187 0.332084i
633633 0 0
634634 −8.57321 14.8492i −0.340486 0.589739i
635635 0 0
636636 0 0
637637 −2.64624 1.52781i −0.104848 0.0605339i
638638 12.0000i 0.475085i
639639 0 0
640640 0 0
641641 −7.19694 + 12.4655i −0.284262 + 0.492356i −0.972430 0.233195i 0.925082π-0.925082\pi
0.688168 + 0.725551i 0.258415π0.258415\pi
642642 0 0
643643 15.2867 8.82577i 0.602848 0.348054i −0.167313 0.985904i 0.553509π-0.553509\pi
0.770161 + 0.637850i 0.220176π0.220176\pi
644644 −0.550510 0.953512i −0.0216931 0.0375736i
645645 0 0
646646 18.2474 31.6055i 0.717936 1.24350i
647647 24.2474i 0.953266i −0.879102 0.476633i 0.841857π-0.841857\pi
0.879102 0.476633i 0.158143π-0.158143\pi
648648 0 0
649649 −26.6969 −1.04795
650650 0 0
651651 0 0
652652 6.45145 3.72474i 0.252658 0.145872i
653653 15.8028 9.12372i 0.618410 0.357039i −0.157840 0.987465i 0.550453π-0.550453\pi
0.776250 + 0.630426i 0.217120π0.217120\pi
654654 0 0
655655 0 0
656656 −9.00000 −0.351391
657657 0 0
658658 4.89898i 0.190982i
659659 −4.92679 + 8.53344i −0.191920 + 0.332416i −0.945887 0.324497i 0.894805π-0.894805\pi
0.753966 + 0.656913i 0.228138π0.228138\pi
660660 0 0
661661 −3.69694 6.40329i −0.143794 0.249059i 0.785128 0.619333i 0.212597π-0.212597\pi
−0.928922 + 0.370274i 0.879264π0.879264\pi
662662 5.49794 3.17423i 0.213683 0.123370i
663663 0 0
664664 2.72474 4.71940i 0.105741 0.183148i
665665 0 0
666666 0 0
667667 6.00000i 0.232321i
668668 −16.9706 9.79796i −0.656611 0.379094i
669669 0 0
670670 0 0
671671 −19.5959 33.9411i −0.756492 1.31028i
672672 0 0
673673 19.6561 + 11.3485i 0.757688 + 0.437451i 0.828465 0.560041i 0.189215π-0.189215\pi
−0.0707771 + 0.997492i 0.522548π0.522548\pi
674674 20.8990 0.804999
675675 0 0
676676 −12.7980 −0.492229
677677 −22.3810 12.9217i −0.860172 0.496621i 0.00389777 0.999992i 0.498759π-0.498759\pi
−0.864070 + 0.503372i 0.832093π0.832093\pi
678678 0 0
679679 −1.97730 3.42478i −0.0758817 0.131431i
680680 0 0
681681 0 0
682682 −18.8776 10.8990i −0.722860 0.417343i
683683 41.9444i 1.60496i 0.596681 + 0.802479i 0.296486π0.296486\pi
−0.596681 + 0.802479i 0.703514π0.703514\pi
684684 0 0
685685 0 0
686686 −3.10102 + 5.37113i −0.118398 + 0.205071i
687687 0 0
688688 −2.20881 + 1.27526i −0.0842100 + 0.0486186i
689689 −0.797959 1.38211i −0.0303998 0.0526540i
690690 0 0
691691 −19.5227 + 33.8143i −0.742679 + 1.28636i 0.208593 + 0.978003i 0.433112π0.433112\pi
−0.951271 + 0.308355i 0.900222π0.900222\pi
692692 9.79796i 0.372463i
693693 0 0
694694 12.0000 0.455514
695695 0 0
696696 0 0
697697 38.1838 22.0454i 1.44631 0.835029i
698698 −12.1244 + 7.00000i −0.458914 + 0.264954i
699699 0 0
700700 0 0
701701 −33.7980 −1.27653 −0.638266 0.769816i 0.720348π-0.720348\pi
−0.638266 + 0.769816i 0.720348π0.720348\pi
702702 0 0
703703 84.5403i 3.18850i
704704 2.44949 4.24264i 0.0923186 0.159901i
705705 0 0
706706 −4.50000 7.79423i −0.169360 0.293340i
707707 3.28913 1.89898i 0.123700 0.0714185i
708708 0 0
709709 2.22474 3.85337i 0.0835520 0.144716i −0.821221 0.570610i 0.806707π-0.806707\pi
0.904773 + 0.425894i 0.140040π0.140040\pi
710710 0 0
711711 0 0
712712 9.00000i 0.337289i
713713 9.43879 + 5.44949i 0.353486 + 0.204085i
714714 0 0
715715 0 0
716716 4.62372 + 8.00853i 0.172797 + 0.299293i
717717 0 0
718718 12.2993 + 7.10102i 0.459007 + 0.265008i
719719 7.95459 0.296656 0.148328 0.988938i 0.452611π-0.452611\pi
0.148328 + 0.988938i 0.452611π0.452611\pi
720720 0 0
721721 −7.50510 −0.279505
722722 −31.6055 18.2474i −1.17624 0.679100i
723723 0 0
724724 8.89898 + 15.4135i 0.330728 + 0.572838i
725725 0 0
726726 0 0
727727 13.8564 + 8.00000i 0.513906 + 0.296704i 0.734438 0.678676i 0.237446π-0.237446\pi
−0.220532 + 0.975380i 0.570779π0.570779\pi
728728 0.202041i 0.00748814i
729729 0 0
730730 0 0
731731 6.24745 10.8209i 0.231070 0.400225i
732732 0 0
733733 −22.5167 + 13.0000i −0.831672 + 0.480166i −0.854425 0.519575i 0.826090π-0.826090\pi
0.0227529 + 0.999741i 0.492757π0.492757\pi
734734 −6.34847 10.9959i −0.234326 0.405865i
735735 0 0
736736 −1.22474 + 2.12132i −0.0451447 + 0.0781929i
737737 1.70714i 0.0628834i
738738 0 0
739739 −3.04541 −0.112027 −0.0560136 0.998430i 0.517839π-0.517839\pi
−0.0560136 + 0.998430i 0.517839π0.517839\pi
740740 0 0
741741 0 0
742742 −1.38211 + 0.797959i −0.0507387 + 0.0292940i
743743 42.7370 24.6742i 1.56787 0.905210i 0.571452 0.820635i 0.306380π-0.306380\pi
0.996417 0.0845746i 0.0269531π-0.0269531\pi
744744 0 0
745745 0 0
746746 −23.5959 −0.863908
747747 0 0
748748 24.0000i 0.877527i
749749 2.07832 3.59975i 0.0759400 0.131532i
750750 0 0
751751 2.97730 + 5.15683i 0.108643 + 0.188175i 0.915221 0.402953i 0.132016π-0.132016\pi
−0.806578 + 0.591128i 0.798683π0.798683\pi
752752 9.43879 5.44949i 0.344197 0.198722i
753753 0 0
754754 −0.550510 + 0.953512i −0.0200484 + 0.0347248i
755755 0 0
756756 0 0
757757 38.0454i 1.38278i −0.722480 0.691392i 0.756998π-0.756998\pi
0.722480 0.691392i 0.243002π-0.243002\pi
758758 −7.70674 4.44949i −0.279921 0.161613i
759759 0 0
760760 0 0
761761 6.94949 + 12.0369i 0.251919 + 0.436336i 0.964054 0.265706i 0.0856051π-0.0856051\pi
−0.712135 + 0.702042i 0.752272π0.752272\pi
762762 0 0
763763 −2.16064 1.24745i −0.0782206 0.0451607i
764764 −1.10102 −0.0398335
765765 0 0
766766 −21.5505 −0.778652
767767 2.12132 + 1.22474i 0.0765964 + 0.0442230i
768768 0 0
769769 −14.0959 24.4148i −0.508312 0.880422i −0.999954 0.00962438i 0.996936π-0.996936\pi
0.491642 0.870797i 0.336397π-0.336397\pi
770770 0 0
771771 0 0
772772 −17.3205 10.0000i −0.623379 0.359908i
773773 10.4041i 0.374209i −0.982340 0.187104i 0.940090π-0.940090\pi
0.982340 0.187104i 0.0599103π-0.0599103\pi
774774 0 0
775775 0 0
776776 −4.39898 + 7.61926i −0.157914 + 0.273515i
777777 0 0
778778 22.1667 12.7980i 0.794715 0.458829i
779779 −33.5227 58.0630i −1.20108 2.08032i
780780 0 0
781781 32.6969 56.6328i 1.16999 2.02648i
782782 12.0000i 0.429119i
783783 0 0
784784 6.79796 0.242784
785785 0 0
786786 0 0
787787 30.0484 17.3485i 1.07111 0.618406i 0.142626 0.989777i 0.454445π-0.454445\pi
0.928485 + 0.371370i 0.121112π0.121112\pi
788788 −0.214297 + 0.123724i −0.00763401 + 0.00440750i
789789 0 0
790790 0 0
791791 −1.84337 −0.0655426
792792 0 0
793793 3.59592i 0.127695i
794794 −8.79796 + 15.2385i −0.312228 + 0.540795i
795795 0 0
796796 6.89898 + 11.9494i 0.244528 + 0.423535i
797797 26.1951 15.1237i 0.927877 0.535710i 0.0417372 0.999129i 0.486711π-0.486711\pi
0.886139 + 0.463419i 0.153377π0.153377\pi
798798 0 0
799799 −26.6969 + 46.2405i −0.944470 + 1.63587i
800800 0 0
801801 0 0
802802 38.6969i 1.36644i
803803 −4.24264 2.44949i −0.149720 0.0864406i
804804 0 0
805805 0 0
806806 1.00000 + 1.73205i 0.0352235 + 0.0610089i
807807 0 0
808808 −7.31747 4.22474i −0.257428 0.148626i
809809 −6.30306 −0.221604 −0.110802 0.993843i 0.535342π-0.535342\pi
−0.110802 + 0.993843i 0.535342π0.535342\pi
810810 0 0
811811 −28.5505 −1.00254 −0.501272 0.865290i 0.667134π-0.667134\pi
−0.501272 + 0.865290i 0.667134π0.667134\pi
812812 0.953512 + 0.550510i 0.0334617 + 0.0193191i
813813 0 0
814814 −27.7980 48.1475i −0.974318 1.68757i
815815 0 0
816816 0 0
817817 −16.4545 9.50000i −0.575669 0.332363i
818818 0.101021i 0.00353210i
819819 0 0
820820 0 0
821821 13.5959 23.5488i 0.474501 0.821860i −0.525073 0.851057i 0.675962π-0.675962\pi
0.999574 + 0.0291978i 0.00929526π0.00929526\pi
822822 0 0
823823 14.8099 8.55051i 0.516241 0.298052i −0.219154 0.975690i 0.570330π-0.570330\pi
0.735395 + 0.677638i 0.236996π0.236996\pi
824824 8.34847 + 14.4600i 0.290833 + 0.503737i
825825 0 0
826826 1.22474 2.12132i 0.0426143 0.0738102i
827827 35.9444i 1.24991i 0.780661 + 0.624954i 0.214882π0.214882\pi
−0.780661 + 0.624954i 0.785118π0.785118\pi
828828 0 0
829829 46.7423 1.62343 0.811714 0.584055i 0.198535π-0.198535\pi
0.811714 + 0.584055i 0.198535π0.198535\pi
830830 0 0
831831 0 0
832832 −0.389270 + 0.224745i −0.0134955 + 0.00779163i
833833 −28.8413 + 16.6515i −0.999292 + 0.576941i
834834 0 0
835835 0 0
836836 36.4949 1.26220
837837 0 0
838838 26.1464i 0.903213i
839839 −18.6742 + 32.3447i −0.644706 + 1.11666i 0.339663 + 0.940547i 0.389687π0.389687\pi
−0.984369 + 0.176117i 0.943646π0.943646\pi
840840 0 0
841841 11.5000 + 19.9186i 0.396552 + 0.686848i
842842 −22.5560 + 13.0227i −0.777331 + 0.448792i
843843 0 0
844844 −1.72474 + 2.98735i −0.0593682 + 0.102829i
845845 0 0
846846 0 0
847847 5.84337i 0.200780i
848848 3.07483 + 1.77526i 0.105590 + 0.0609625i
849849 0 0
850850 0 0
851851 13.8990 + 24.0737i 0.476451 + 0.825237i
852852 0 0
853853 −39.8372 23.0000i −1.36400 0.787505i −0.373845 0.927491i 0.621961π-0.621961\pi
−0.990153 + 0.139986i 0.955294π0.955294\pi
854854 3.59592 0.123050
855855 0 0
856856 −9.24745 −0.316071
857857 −43.2138 24.9495i −1.47615 0.852258i −0.476517 0.879165i 0.658101π-0.658101\pi
−0.999638 + 0.0269070i 0.991434π0.991434\pi
858858 0 0
859859 −10.1742 17.6223i −0.347140 0.601265i 0.638600 0.769539i 0.279514π-0.279514\pi
−0.985740 + 0.168274i 0.946181π0.946181\pi
860860 0 0
861861 0 0
862862 21.9524 + 12.6742i 0.747702 + 0.431686i
863863 43.8434i 1.49245i −0.665696 0.746223i 0.731865π-0.731865\pi
0.665696 0.746223i 0.268135π-0.268135\pi
864864 0 0
865865 0 0
866866 −4.79796 + 8.31031i −0.163041 + 0.282396i
867867 0 0
868868 1.73205 1.00000i 0.0587896 0.0339422i
869869 40.8990 + 70.8391i 1.38740 + 2.40305i
870870 0 0
871871 0.0783167 0.135648i 0.00265366 0.00459627i
872872 5.55051i 0.187964i
873873 0 0
874874 −18.2474 −0.617229
875875 0 0
876876 0 0
877877 −27.5378 + 15.8990i −0.929887 + 0.536870i −0.886776 0.462200i 0.847060π-0.847060\pi
−0.0431110 + 0.999070i 0.513727π0.513727\pi
878878 −2.89986 + 1.67423i −0.0978655 + 0.0565027i
879879 0 0
880880 0 0
881881 −38.6969 −1.30373 −0.651866 0.758334i 0.726014π-0.726014\pi
−0.651866 + 0.758334i 0.726014π0.726014\pi
882882 0 0
883883 47.7980i 1.60853i −0.594271 0.804265i 0.702559π-0.702559\pi
0.594271 0.804265i 0.297441π-0.297441\pi
884884 1.10102 1.90702i 0.0370313 0.0641401i
885885 0 0
886886 4.10102 + 7.10318i 0.137776 + 0.238636i
887887 −4.76756 + 2.75255i −0.160079 + 0.0924216i −0.577899 0.816108i 0.696127π-0.696127\pi
0.417821 + 0.908530i 0.362794π0.362794\pi
888888 0 0
889889 −0.752551 + 1.30346i −0.0252398 + 0.0437165i
890890 0 0
891891 0 0
892892 17.7980i 0.595920i
893893 70.3142 + 40.5959i 2.35297 + 1.35849i
894894 0 0
895895 0 0
896896 0.224745 + 0.389270i 0.00750820 + 0.0130046i
897897 0 0
898898 24.7648 + 14.2980i 0.826412 + 0.477129i
899899 −10.8990 −0.363501
900900 0 0
901901 −17.3939 −0.579474
902902 38.1838 + 22.0454i 1.27138 + 0.734032i
903903 0 0
904904 2.05051 + 3.55159i 0.0681990 + 0.118124i
905905 0 0
906906 0 0
907907 −31.4787 18.1742i −1.04523 0.603466i −0.123922 0.992292i 0.539547π-0.539547\pi
−0.921311 + 0.388826i 0.872881π0.872881\pi
908908 13.6515i 0.453042i
909909 0 0
910910 0 0
911911 −3.67423 + 6.36396i −0.121733 + 0.210847i −0.920451 0.390858i 0.872178π-0.872178\pi
0.798718 + 0.601705i 0.205512π0.205512\pi
912912 0 0
913913 −23.1202 + 13.3485i −0.765168 + 0.441770i
914914 6.84847 + 11.8619i 0.226527 + 0.392357i
915915 0 0
916916 −6.57321 + 11.3851i −0.217185 + 0.376176i
917917 1.70714i 0.0563748i
918918 0 0
919919 −3.34847 −0.110456 −0.0552279 0.998474i 0.517589π-0.517589\pi
−0.0552279 + 0.998474i 0.517589π0.517589\pi
920920 0 0
921921 0 0
922922 −4.02834 + 2.32577i −0.132666 + 0.0765950i
923923 −5.19615 + 3.00000i −0.171033 + 0.0987462i
924924 0 0
925925 0 0
926926 −5.34847 −0.175762
927927 0 0
928928 2.44949i 0.0804084i
929929 25.5959 44.3334i 0.839775 1.45453i −0.0503079 0.998734i 0.516020π-0.516020\pi
0.890083 0.455799i 0.150646π-0.150646\pi
930930 0 0
931931 25.3207 + 43.8567i 0.829851 + 1.43734i
932932 20.5222 11.8485i 0.672225 0.388110i
933933 0 0
934934 5.17423 8.96204i 0.169306 0.293247i
935935 0 0
936936 0 0
937937 7.20204i 0.235280i 0.993056 + 0.117640i 0.0375330π0.0375330\pi
−0.993056 + 0.117640i 0.962467π0.962467\pi
938938 −0.135648 0.0783167i −0.00442908 0.00255713i
939939 0 0
940940 0 0
941941 26.8207 + 46.4548i 0.874329 + 1.51438i 0.857476 + 0.514524i 0.172031π0.172031\pi
0.0168524 + 0.999858i 0.494635π0.494635\pi
942942 0 0
943943 −19.0919 11.0227i −0.621717 0.358949i
944944 −5.44949 −0.177366
945945 0 0
946946 12.4949 0.406244
947947 22.6435 + 13.0732i 0.735814 + 0.424822i 0.820545 0.571581i 0.193670π-0.193670\pi
−0.0847314 + 0.996404i 0.527003π0.527003\pi
948948 0 0
949949 0.224745 + 0.389270i 0.00729553 + 0.0126362i
950950 0 0
951951 0 0
952952 −1.90702 1.10102i −0.0618070 0.0356843i
953953 2.20204i 0.0713311i 0.999364 + 0.0356656i 0.0113551π0.0113551\pi
−0.999364 + 0.0356656i 0.988645π0.988645\pi
954954 0 0
955955 0 0
956956 7.22474 12.5136i 0.233665 0.404720i
957957 0 0
958958 0.214297 0.123724i 0.00692362 0.00399735i
959959 0.674235 + 1.16781i 0.0217722 + 0.0377105i
960960 0 0
961961 5.60102 9.70125i 0.180678 0.312944i
962962 5.10102i 0.164464i
963963 0 0
964964 3.20204 0.103131
965965 0 0
966966 0 0
967967 27.7128 16.0000i 0.891184 0.514525i 0.0168544 0.999858i 0.494635π-0.494635\pi
0.874330 + 0.485333i 0.161301π0.161301\pi
968968 −11.2583 + 6.50000i −0.361856 + 0.208918i
969969 0 0
970970 0 0
971971 40.8434 1.31073 0.655363 0.755314i 0.272516π-0.272516\pi
0.655363 + 0.755314i 0.272516π0.272516\pi
972972 0 0
973973 1.79796i 0.0576399i
974974 −12.2247 + 21.1739i −0.391706 + 0.678455i
975975 0 0
976976 −4.00000 6.92820i −0.128037 0.221766i
977977 7.79423 4.50000i 0.249359 0.143968i −0.370111 0.928987i 0.620681π-0.620681\pi
0.619471 + 0.785020i 0.287347π0.287347\pi
978978 0 0
979979 22.0454 38.1838i 0.704574 1.22036i
980980 0 0
981981 0 0
982982 27.2474i 0.869501i
983983 11.3458 + 6.55051i 0.361875 + 0.208929i 0.669903 0.742449i 0.266336π-0.266336\pi
−0.308028 + 0.951377i 0.599669π0.599669\pi
984984 0 0
985985 0 0
986986 6.00000 + 10.3923i 0.191079 + 0.330958i
987987 0 0
988988 −2.89986 1.67423i −0.0922568 0.0532645i
989989 −6.24745 −0.198657
990990 0 0
991991 −16.0000 −0.508257 −0.254128 0.967170i 0.581789π-0.581789\pi
−0.254128 + 0.967170i 0.581789π0.581789\pi
992992 −3.85337 2.22474i −0.122345 0.0706357i
993993 0 0
994994 3.00000 + 5.19615i 0.0951542 + 0.164812i
995995 0 0
996996 0 0
997997 6.96753 + 4.02270i 0.220664 + 0.127400i 0.606258 0.795268i 0.292670π-0.292670\pi
−0.385594 + 0.922669i 0.626003π0.626003\pi
998998 8.34847i 0.264266i
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 1350.2.j.g.1099.2 8
3.2 odd 2 450.2.j.f.349.4 8
5.2 odd 4 1350.2.e.n.451.1 4
5.3 odd 4 1350.2.e.k.451.2 4
5.4 even 2 inner 1350.2.j.g.1099.3 8
9.2 odd 6 4050.2.c.y.649.1 4
9.4 even 3 inner 1350.2.j.g.199.3 8
9.5 odd 6 450.2.j.f.49.1 8
9.7 even 3 4050.2.c.w.649.3 4
15.2 even 4 450.2.e.l.151.1 4
15.8 even 4 450.2.e.m.151.2 yes 4
15.14 odd 2 450.2.j.f.349.1 8
45.2 even 12 4050.2.a.bu.1.2 2
45.4 even 6 inner 1350.2.j.g.199.2 8
45.7 odd 12 4050.2.a.bl.1.2 2
45.13 odd 12 1350.2.e.k.901.2 4
45.14 odd 6 450.2.j.f.49.4 8
45.22 odd 12 1350.2.e.n.901.1 4
45.23 even 12 450.2.e.m.301.1 yes 4
45.29 odd 6 4050.2.c.y.649.4 4
45.32 even 12 450.2.e.l.301.2 yes 4
45.34 even 6 4050.2.c.w.649.2 4
45.38 even 12 4050.2.a.br.1.1 2
45.43 odd 12 4050.2.a.by.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.e.l.151.1 4 15.2 even 4
450.2.e.l.301.2 yes 4 45.32 even 12
450.2.e.m.151.2 yes 4 15.8 even 4
450.2.e.m.301.1 yes 4 45.23 even 12
450.2.j.f.49.1 8 9.5 odd 6
450.2.j.f.49.4 8 45.14 odd 6
450.2.j.f.349.1 8 15.14 odd 2
450.2.j.f.349.4 8 3.2 odd 2
1350.2.e.k.451.2 4 5.3 odd 4
1350.2.e.k.901.2 4 45.13 odd 12
1350.2.e.n.451.1 4 5.2 odd 4
1350.2.e.n.901.1 4 45.22 odd 12
1350.2.j.g.199.2 8 45.4 even 6 inner
1350.2.j.g.199.3 8 9.4 even 3 inner
1350.2.j.g.1099.2 8 1.1 even 1 trivial
1350.2.j.g.1099.3 8 5.4 even 2 inner
4050.2.a.bl.1.2 2 45.7 odd 12
4050.2.a.br.1.1 2 45.38 even 12
4050.2.a.bu.1.2 2 45.2 even 12
4050.2.a.by.1.1 2 45.43 odd 12
4050.2.c.w.649.2 4 45.34 even 6
4050.2.c.w.649.3 4 9.7 even 3
4050.2.c.y.649.1 4 9.2 odd 6
4050.2.c.y.649.4 4 45.29 odd 6