Properties

Label 484.2.c.d.483.14
Level 484484
Weight 22
Character 484.483
Analytic conductor 3.8653.865
Analytic rank 00
Dimension 1616
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [484,2,Mod(483,484)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(484, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("484.483");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 484=22112 484 = 2^{2} \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 484.c (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.864759457833.86475945783
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x165x15+13x1425x13+35x1230x112x10+60x9116x8++256 x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 28 2^{8}
Twist minimal: no (minimal twist has level 44)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 483.14
Root 0.5443891.30524i-0.544389 - 1.30524i of defining polynomial
Character χ\chi == 484.483
Dual form 484.2.c.d.483.13

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.20762+0.735975i)q20.740676iq3+(0.916683+1.77755i)q41.34841q5+(0.5451180.894453i)q6+1.62837q7+(0.201231+2.82126i)q8+2.45140q9+(1.628370.992398i)q10+(1.316590.678965i)q12+3.55723iq13+(1.96645+1.19844i)q14+0.998737iq15+(2.31939+3.25890i)q160.0699655iq17+(2.96035+1.80417i)q18+7.95154q19+(1.236072.39688i)q201.20609iq215.30988iq23+(2.08964+0.149047i)q243.18178q25+(2.61803+4.29578i)q264.03772iq27+(1.49270+2.89451i)q28+3.93630iq29+(0.735045+1.20609i)q30+3.69389iq31+(5.19940+2.22850i)q32+(0.05149280.0844916i)q342.19572q35+(2.24716+4.35749i)q366.87861q37+(9.60242+5.85213i)q38+2.63476q39+(0.2713423.80423i)q405.78625iq41+(0.8876541.45650i)q42+1.89516q433.30550q45+(3.907936.41230i)q469.80536iq47+(2.41379+1.71791i)q484.34841q49+(3.842372.34171i)q500.0518217q51+(6.32317+3.26086i)q523.88765q53+(2.971664.87602i)q54+(0.327678+4.59405i)q565.88951iq57+(2.89701+4.75354i)q584.86161iq59+(1.77531+0.915525i)q60+1.34602iq61+(2.71861+4.46080i)q62+3.99178q63+(7.919011.13545i)q644.79662iq65+4.91303iq67+(0.1243670.0641362i)q683.93290q69+(2.651591.61599i)q706.97557iq71+(0.493297+6.91604i)q7210.1222iq73+(8.306735.06248i)q74+2.35667iq75+(7.28904+14.1343i)q76+(3.18178+1.93911i)q786.00456q79+(3.127494.39435i)q80+4.36356q81+(4.258536.98758i)q823.61193q83+(2.143891.10560i)q84+0.0943425iq85+(2.28863+1.39479i)q86+2.91552q875.39711q89+(3.991782.43277i)q90+5.79249iq91+(9.438584.86747i)q92+2.73597q93+(7.2164911.8411i)q9410.7220q95+(1.65060+3.85107i)q96+7.32624q97+(5.251223.20032i)q98+O(q100)q+(1.20762 + 0.735975i) q^{2} -0.740676i q^{3} +(0.916683 + 1.77755i) q^{4} -1.34841 q^{5} +(0.545118 - 0.894453i) q^{6} +1.62837 q^{7} +(-0.201231 + 2.82126i) q^{8} +2.45140 q^{9} +(-1.62837 - 0.992398i) q^{10} +(1.31659 - 0.678965i) q^{12} +3.55723i q^{13} +(1.96645 + 1.19844i) q^{14} +0.998737i q^{15} +(-2.31939 + 3.25890i) q^{16} -0.0699655i q^{17} +(2.96035 + 1.80417i) q^{18} +7.95154 q^{19} +(-1.23607 - 2.39688i) q^{20} -1.20609i q^{21} -5.30988i q^{23} +(2.08964 + 0.149047i) q^{24} -3.18178 q^{25} +(-2.61803 + 4.29578i) q^{26} -4.03772i q^{27} +(1.49270 + 2.89451i) q^{28} +3.93630i q^{29} +(-0.735045 + 1.20609i) q^{30} +3.69389i q^{31} +(-5.19940 + 2.22850i) q^{32} +(0.0514928 - 0.0844916i) q^{34} -2.19572 q^{35} +(2.24716 + 4.35749i) q^{36} -6.87861 q^{37} +(9.60242 + 5.85213i) q^{38} +2.63476 q^{39} +(0.271342 - 3.80423i) q^{40} -5.78625i q^{41} +(0.887654 - 1.45650i) q^{42} +1.89516 q^{43} -3.30550 q^{45} +(3.90793 - 6.41230i) q^{46} -9.80536i q^{47} +(2.41379 + 1.71791i) q^{48} -4.34841 q^{49} +(-3.84237 - 2.34171i) q^{50} -0.0518217 q^{51} +(-6.32317 + 3.26086i) q^{52} -3.88765 q^{53} +(2.97166 - 4.87602i) q^{54} +(-0.327678 + 4.59405i) q^{56} -5.88951i q^{57} +(-2.89701 + 4.75354i) q^{58} -4.86161i q^{59} +(-1.77531 + 0.915525i) q^{60} +1.34602i q^{61} +(-2.71861 + 4.46080i) q^{62} +3.99178 q^{63} +(-7.91901 - 1.13545i) q^{64} -4.79662i q^{65} +4.91303i q^{67} +(0.124367 - 0.0641362i) q^{68} -3.93290 q^{69} +(-2.65159 - 1.61599i) q^{70} -6.97557i q^{71} +(-0.493297 + 6.91604i) q^{72} -10.1222i q^{73} +(-8.30673 - 5.06248i) q^{74} +2.35667i q^{75} +(7.28904 + 14.1343i) q^{76} +(3.18178 + 1.93911i) q^{78} -6.00456 q^{79} +(3.12749 - 4.39435i) q^{80} +4.36356 q^{81} +(4.25853 - 6.98758i) q^{82} -3.61193 q^{83} +(2.14389 - 1.10560i) q^{84} +0.0943425i q^{85} +(2.28863 + 1.39479i) q^{86} +2.91552 q^{87} -5.39711 q^{89} +(-3.99178 - 2.43277i) q^{90} +5.79249i q^{91} +(9.43858 - 4.86747i) q^{92} +2.73597 q^{93} +(7.21649 - 11.8411i) q^{94} -10.7220 q^{95} +(1.65060 + 3.85107i) q^{96} +7.32624 q^{97} +(-5.25122 - 3.20032i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+4q4+4q522q1212q1412q16+16q204q2524q266q34+50q3612q37+42q38+4q42+40q45+74q4844q4952q53+8q97+O(q100) 16 q + 4 q^{4} + 4 q^{5} - 22 q^{12} - 12 q^{14} - 12 q^{16} + 16 q^{20} - 4 q^{25} - 24 q^{26} - 6 q^{34} + 50 q^{36} - 12 q^{37} + 42 q^{38} + 4 q^{42} + 40 q^{45} + 74 q^{48} - 44 q^{49} - 52 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/484Z)×\left(\mathbb{Z}/484\mathbb{Z}\right)^\times.

nn 243243 365365
χ(n)\chi(n) 1-1 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 1.20762 + 0.735975i 0.853915 + 0.520413i
33 0.740676i 0.427629i −0.976874 0.213815i 0.931411π-0.931411\pi
0.976874 0.213815i 0.0685889π-0.0685889\pi
44 0.916683 + 1.77755i 0.458341 + 0.888776i
55 −1.34841 −0.603029 −0.301515 0.953462i 0.597492π-0.597492\pi
−0.301515 + 0.953462i 0.597492π0.597492\pi
66 0.545118 0.894453i 0.222544 0.365159i
77 1.62837 0.615466 0.307733 0.951473i 0.400430π-0.400430\pi
0.307733 + 0.951473i 0.400430π0.400430\pi
88 −0.201231 + 2.82126i −0.0711458 + 0.997466i
99 2.45140 0.817133
1010 −1.62837 0.992398i −0.514936 0.313824i
1111 0 0
1212 1.31659 0.678965i 0.380067 0.196000i
1313 3.55723i 0.986599i 0.869859 + 0.493300i 0.164209π0.164209\pi
−0.869859 + 0.493300i 0.835791π0.835791\pi
1414 1.96645 + 1.19844i 0.525555 + 0.320296i
1515 0.998737i 0.257873i
1616 −2.31939 + 3.25890i −0.579846 + 0.814726i
1717 0.0699655i 0.0169691i −0.999964 0.00848456i 0.997299π-0.997299\pi
0.999964 0.00848456i 0.00270075π-0.00270075\pi
1818 2.96035 + 1.80417i 0.697762 + 0.425246i
1919 7.95154 1.82421 0.912104 0.409959i 0.134457π-0.134457\pi
0.912104 + 0.409959i 0.134457π0.134457\pi
2020 −1.23607 2.39688i −0.276393 0.535958i
2121 1.20609i 0.263191i
2222 0 0
2323 5.30988i 1.10719i −0.832787 0.553593i 0.813256π-0.813256\pi
0.832787 0.553593i 0.186744π-0.186744\pi
2424 2.08964 + 0.149047i 0.426546 + 0.0304240i
2525 −3.18178 −0.636356
2626 −2.61803 + 4.29578i −0.513439 + 0.842472i
2727 4.03772i 0.777059i
2828 1.49270 + 2.89451i 0.282093 + 0.547011i
2929 3.93630i 0.730952i 0.930821 + 0.365476i 0.119094π0.119094\pi
−0.930821 + 0.365476i 0.880906π0.880906\pi
3030 −0.735045 + 1.20609i −0.134200 + 0.220201i
3131 3.69389i 0.663441i 0.943378 + 0.331721i 0.107629π0.107629\pi
−0.943378 + 0.331721i 0.892371π0.892371\pi
3232 −5.19940 + 2.22850i −0.919133 + 0.393947i
3333 0 0
3434 0.0514928 0.0844916i 0.00883095 0.0144902i
3535 −2.19572 −0.371144
3636 2.24716 + 4.35749i 0.374526 + 0.726249i
3737 −6.87861 −1.13084 −0.565418 0.824804i 0.691285π-0.691285\pi
−0.565418 + 0.824804i 0.691285π0.691285\pi
3838 9.60242 + 5.85213i 1.55772 + 0.949341i
3939 2.63476 0.421899
4040 0.271342 3.80423i 0.0429030 0.601501i
4141 5.78625i 0.903660i −0.892104 0.451830i 0.850771π-0.850771\pi
0.892104 0.451830i 0.149229π-0.149229\pi
4242 0.887654 1.45650i 0.136968 0.224743i
4343 1.89516 0.289009 0.144505 0.989504i 0.453841π-0.453841\pi
0.144505 + 0.989504i 0.453841π0.453841\pi
4444 0 0
4545 −3.30550 −0.492755
4646 3.90793 6.41230i 0.576193 0.945442i
4747 9.80536i 1.43026i −0.698992 0.715129i 0.746368π-0.746368\pi
0.698992 0.715129i 0.253632π-0.253632\pi
4848 2.41379 + 1.71791i 0.348401 + 0.247959i
4949 −4.34841 −0.621202
5050 −3.84237 2.34171i −0.543394 0.331168i
5151 −0.0518217 −0.00725650
5252 −6.32317 + 3.26086i −0.876866 + 0.452199i
5353 −3.88765 −0.534010 −0.267005 0.963695i 0.586034π-0.586034\pi
−0.267005 + 0.963695i 0.586034π0.586034\pi
5454 2.97166 4.87602i 0.404391 0.663543i
5555 0 0
5656 −0.327678 + 4.59405i −0.0437878 + 0.613906i
5757 5.88951i 0.780085i
5858 −2.89701 + 4.75354i −0.380397 + 0.624171i
5959 4.86161i 0.632927i −0.948605 0.316464i 0.897504π-0.897504\pi
0.948605 0.316464i 0.102496π-0.102496\pi
6060 −1.77531 + 0.915525i −0.229191 + 0.118194i
6161 1.34602i 0.172341i 0.996280 + 0.0861704i 0.0274629π0.0274629\pi
−0.996280 + 0.0861704i 0.972537π0.972537\pi
6262 −2.71861 + 4.46080i −0.345263 + 0.566523i
6363 3.99178 0.502917
6464 −7.91901 1.13545i −0.989877 0.141931i
6565 4.79662i 0.594948i
6666 0 0
6767 4.91303i 0.600223i 0.953904 + 0.300111i 0.0970238π0.0970238\pi
−0.953904 + 0.300111i 0.902976π0.902976\pi
6868 0.124367 0.0641362i 0.0150818 0.00777765i
6969 −3.93290 −0.473465
7070 −2.65159 1.61599i −0.316925 0.193148i
7171 6.97557i 0.827848i −0.910311 0.413924i 0.864158π-0.864158\pi
0.910311 0.413924i 0.135842π-0.135842\pi
7272 −0.493297 + 6.91604i −0.0581356 + 0.815063i
7373 10.1222i 1.18471i −0.805676 0.592356i 0.798198π-0.798198\pi
0.805676 0.592356i 0.201802π-0.201802\pi
7474 −8.30673 5.06248i −0.965638 0.588501i
7575 2.35667i 0.272124i
7676 7.28904 + 14.1343i 0.836110 + 1.62131i
7777 0 0
7878 3.18178 + 1.93911i 0.360266 + 0.219561i
7979 −6.00456 −0.675566 −0.337783 0.941224i 0.609677π-0.609677\pi
−0.337783 + 0.941224i 0.609677π0.609677\pi
8080 3.12749 4.39435i 0.349664 0.491303i
8181 4.36356 0.484840
8282 4.25853 6.98758i 0.470276 0.771649i
8383 −3.61193 −0.396461 −0.198230 0.980155i 0.563519π-0.563519\pi
−0.198230 + 0.980155i 0.563519π0.563519\pi
8484 2.14389 1.10560i 0.233918 0.120631i
8585 0.0943425i 0.0102329i
8686 2.28863 + 1.39479i 0.246789 + 0.150404i
8787 2.91552 0.312576
8888 0 0
8989 −5.39711 −0.572093 −0.286046 0.958216i 0.592341π-0.592341\pi
−0.286046 + 0.958216i 0.592341π0.592341\pi
9090 −3.99178 2.43277i −0.420771 0.256436i
9191 5.79249i 0.607218i
9292 9.43858 4.86747i 0.984040 0.507469i
9393 2.73597 0.283707
9494 7.21649 11.8411i 0.744325 1.22132i
9595 −10.7220 −1.10005
9696 1.65060 + 3.85107i 0.168463 + 0.393048i
9797 7.32624 0.743867 0.371933 0.928259i 0.378695π-0.378695\pi
0.371933 + 0.928259i 0.378695π0.378695\pi
9898 −5.25122 3.20032i −0.530454 0.323281i
9999 0 0
100100 −2.91668 5.65578i −0.291668 0.565578i
101101 9.57267i 0.952516i 0.879306 + 0.476258i 0.158007π0.158007\pi
−0.879306 + 0.476258i 0.841993π0.841993\pi
102102 −0.0625809 0.0381395i −0.00619643 0.00377637i
103103 10.3215i 1.01701i −0.861060 0.508503i 0.830199π-0.830199\pi
0.861060 0.508503i 0.169801π-0.169801\pi
104104 −10.0359 0.715824i −0.984099 0.0701924i
105105 1.62631i 0.158712i
106106 −4.69480 2.86121i −0.455999 0.277906i
107107 −11.0772 −1.07087 −0.535435 0.844577i 0.679852π-0.679852\pi
−0.535435 + 0.844577i 0.679852π0.679852\pi
108108 7.17726 3.70131i 0.690632 0.356158i
109109 8.95933i 0.858149i 0.903269 + 0.429074i 0.141160π0.141160\pi
−0.903269 + 0.429074i 0.858840π0.858840\pi
110110 0 0
111111 5.09482i 0.483579i
112112 −3.77682 + 5.30670i −0.356875 + 0.501436i
113113 11.0231 1.03696 0.518481 0.855089i 0.326498π-0.326498\pi
0.518481 + 0.855089i 0.326498π0.326498\pi
114114 4.33453 7.11228i 0.405966 0.666126i
115115 7.15991i 0.667665i
116116 −6.99697 + 3.60834i −0.649653 + 0.335026i
117117 8.72020i 0.806183i
118118 3.57802 5.87096i 0.329383 0.540466i
119119 0.113930i 0.0104439i
120120 −2.81770 0.200977i −0.257219 0.0183466i
121121 0 0
122122 −0.990640 + 1.62548i −0.0896883 + 0.147164i
123123 −4.28573 −0.386432
124124 −6.56608 + 3.38612i −0.589651 + 0.304083i
125125 11.0324 0.986770
126126 4.82055 + 2.93785i 0.429449 + 0.261725i
127127 −10.2923 −0.913298 −0.456649 0.889647i 0.650950π-0.650950\pi
−0.456649 + 0.889647i 0.650950π0.650950\pi
128128 −8.72748 7.19938i −0.771408 0.636341i
129129 1.40370i 0.123589i
130130 3.53019 5.79249i 0.309618 0.508035i
131131 1.86768 0.163180 0.0815901 0.996666i 0.474000π-0.474000\pi
0.0815901 + 0.996666i 0.474000π0.474000\pi
132132 0 0
133133 12.9480 1.12274
134134 −3.61587 + 5.93307i −0.312363 + 0.512539i
135135 5.44452i 0.468589i
136136 0.197391 + 0.0140792i 0.0169261 + 0.00120728i
137137 −1.25447 −0.107177 −0.0535885 0.998563i 0.517066π-0.517066\pi
−0.0535885 + 0.998563i 0.517066π0.517066\pi
138138 −4.74944 2.89451i −0.404299 0.246397i
139139 6.29114 0.533608 0.266804 0.963751i 0.414032π-0.414032\pi
0.266804 + 0.963751i 0.414032π0.414032\pi
140140 −2.01277 3.90300i −0.170111 0.329864i
141141 −7.26259 −0.611620
142142 5.13384 8.42382i 0.430822 0.706912i
143143 0 0
144144 −5.68574 + 7.98888i −0.473812 + 0.665740i
145145 5.30776i 0.440785i
146146 7.44967 12.2237i 0.616539 1.01164i
147147 3.22076i 0.265644i
148148 −6.30550 12.2271i −0.518309 1.00506i
149149 17.1557i 1.40545i −0.711462 0.702724i 0.751967π-0.751967\pi
0.711462 0.702724i 0.248033π-0.248033\pi
150150 −1.73445 + 2.84595i −0.141617 + 0.232371i
151151 −12.1583 −0.989428 −0.494714 0.869056i 0.664727π-0.664727\pi
−0.494714 + 0.869056i 0.664727π0.664727\pi
152152 −1.60009 + 22.4334i −0.129785 + 1.81959i
153153 0.171513i 0.0138660i
154154 0 0
155155 4.98089i 0.400074i
156156 2.41524 + 4.68342i 0.193374 + 0.374974i
157157 −5.30173 −0.423124 −0.211562 0.977365i 0.567855π-0.567855\pi
−0.211562 + 0.977365i 0.567855π0.567855\pi
158158 −7.25121 4.41920i −0.576876 0.351573i
159159 2.87949i 0.228358i
160160 7.01095 3.00494i 0.554264 0.237562i
161161 8.64644i 0.681435i
162162 5.26951 + 3.21147i 0.414012 + 0.252317i
163163 10.0576i 0.787768i −0.919160 0.393884i 0.871131π-0.871131\pi
0.919160 0.393884i 0.128869π-0.128869\pi
164164 10.2854 5.30415i 0.803152 0.414185i
165165 0 0
166166 −4.36183 2.65829i −0.338544 0.206323i
167167 21.9076 1.69526 0.847632 0.530585i 0.178028π-0.178028\pi
0.847632 + 0.530585i 0.178028π0.178028\pi
168168 3.40270 + 0.242703i 0.262524 + 0.0187249i
169169 0.346084 0.0266219
170170 −0.0694337 + 0.113930i −0.00532532 + 0.00873801i
171171 19.4924 1.49062
172172 1.73726 + 3.36874i 0.132465 + 0.256864i
173173 11.8322i 0.899586i 0.893133 + 0.449793i 0.148502π0.148502\pi
−0.893133 + 0.449793i 0.851498π0.851498\pi
174174 3.52083 + 2.14575i 0.266914 + 0.162669i
175175 −5.18111 −0.391655
176176 0 0
177177 −3.60087 −0.270658
178178 −6.51765 3.97214i −0.488518 0.297724i
179179 0.933676i 0.0697862i −0.999391 0.0348931i 0.988891π-0.988891\pi
0.999391 0.0348931i 0.0111091π-0.0111091\pi
180180 −3.03010 5.87570i −0.225850 0.437949i
181181 18.8395 1.40033 0.700163 0.713983i 0.253111π-0.253111\pi
0.700163 + 0.713983i 0.253111π0.253111\pi
182182 −4.26313 + 6.99512i −0.316004 + 0.518513i
183183 0.996967 0.0736979
184184 14.9805 + 1.06851i 1.10438 + 0.0787716i
185185 9.27521 0.681927
186186 3.30401 + 2.01361i 0.242262 + 0.147645i
187187 0 0
188188 17.4295 8.98840i 1.27118 0.655547i
189189 6.57490i 0.478253i
190190 −12.9480 7.89110i −0.939350 0.572480i
191191 20.4441i 1.47928i 0.673001 + 0.739641i 0.265005π0.265005\pi
−0.673001 + 0.739641i 0.734995π0.734995\pi
192192 −0.840998 + 5.86542i −0.0606938 + 0.423300i
193193 17.3409i 1.24823i 0.781333 + 0.624114i 0.214540π0.214540\pi
−0.781333 + 0.624114i 0.785460π0.785460\pi
194194 8.84730 + 5.39192i 0.635199 + 0.387118i
195195 −3.55274 −0.254417
196196 −3.98612 7.72953i −0.284723 0.552110i
197197 3.49133i 0.248747i 0.992235 + 0.124374i 0.0396921π0.0396921\pi
−0.992235 + 0.124374i 0.960308π0.960308\pi
198198 0 0
199199 11.2660i 0.798625i 0.916815 + 0.399313i 0.130751π0.130751\pi
−0.916815 + 0.399313i 0.869249π0.869249\pi
200200 0.640271 8.97663i 0.0452740 0.634743i
201201 3.63896 0.256673
202202 −7.04524 + 11.5601i −0.495701 + 0.813368i
203203 6.40974i 0.449876i
204204 −0.0475041 0.0921159i −0.00332595 0.00644940i
205205 7.80226i 0.544933i
206206 7.59635 12.4644i 0.529263 0.868436i
207207 13.0166i 0.904718i
208208 −11.5927 8.25060i −0.803808 0.572076i
209209 0 0
210210 −1.19693 + 1.96397i −0.0825957 + 0.135526i
211211 2.74295 0.188833 0.0944163 0.995533i 0.469902π-0.469902\pi
0.0944163 + 0.995533i 0.469902π0.469902\pi
212212 −3.56375 6.91051i −0.244759 0.474616i
213213 −5.16663 −0.354012
214214 −13.3770 8.15251i −0.914431 0.557294i
215215 −2.55546 −0.174281
216216 11.3915 + 0.812513i 0.775090 + 0.0552845i
217217 6.01501i 0.408325i
218218 −6.59384 + 10.8195i −0.446591 + 0.732786i
219219 −7.49726 −0.506618
220220 0 0
221221 0.248884 0.0167417
222222 −3.74966 + 6.15259i −0.251660 + 0.412935i
223223 23.7258i 1.58880i 0.607398 + 0.794398i 0.292213π0.292213\pi
−0.607398 + 0.794398i 0.707787π0.707787\pi
224224 −8.46655 + 3.62882i −0.565695 + 0.242461i
225225 −7.79981 −0.519988
226226 13.3117 + 8.11270i 0.885478 + 0.539649i
227227 0.800839 0.0531536 0.0265768 0.999647i 0.491539π-0.491539\pi
0.0265768 + 0.999647i 0.491539π0.491539\pi
228228 10.4689 5.39881i 0.693321 0.357545i
229229 −23.5889 −1.55880 −0.779401 0.626526i 0.784476π-0.784476\pi
−0.779401 + 0.626526i 0.784476π0.784476\pi
230230 −5.26951 + 8.64644i −0.347461 + 0.570129i
231231 0 0
232232 −11.1053 0.792103i −0.729100 0.0520041i
233233 17.4915i 1.14591i −0.819588 0.572953i 0.805798π-0.805798\pi
0.819588 0.572953i 0.194202π-0.194202\pi
234234 −6.41785 + 10.5307i −0.419548 + 0.688412i
235235 13.2217i 0.862487i
236236 8.64176 4.45655i 0.562531 0.290097i
237237 4.44743i 0.288892i
238238 0.0838493 0.137584i 0.00543515 0.00891822i
239239 −6.68497 −0.432415 −0.216207 0.976347i 0.569369π-0.569369\pi
−0.216207 + 0.976347i 0.569369π0.569369\pi
240240 −3.25479 2.31646i −0.210096 0.149527i
241241 4.28655i 0.276121i −0.990424 0.138061i 0.955913π-0.955913\pi
0.990424 0.138061i 0.0440868π-0.0440868\pi
242242 0 0
243243 15.3451i 0.984391i
244244 −2.39263 + 1.23388i −0.153172 + 0.0789909i
245245 5.86346 0.374603
246246 −5.17553 3.15419i −0.329980 0.201104i
247247 28.2855i 1.79976i
248248 −10.4214 0.743323i −0.661760 0.0472010i
249249 2.67527i 0.169538i
250250 13.3230 + 8.11959i 0.842618 + 0.513528i
251251 4.89768i 0.309139i 0.987982 + 0.154569i 0.0493990π0.0493990\pi
−0.987982 + 0.154569i 0.950601π0.950601\pi
252252 3.65920 + 7.09560i 0.230508 + 0.446981i
253253 0 0
254254 −12.4292 7.57491i −0.779879 0.475292i
255255 0.0698772 0.00437588
256256 −5.24091 15.1173i −0.327557 0.944832i
257257 −12.3843 −0.772511 −0.386256 0.922392i 0.626232π-0.626232\pi
−0.386256 + 0.922392i 0.626232π0.626232\pi
258258 1.03309 1.69513i 0.0643171 0.105534i
259259 −11.2009 −0.695991
260260 8.52625 4.39698i 0.528776 0.272689i
261261 9.64944i 0.597285i
262262 2.25545 + 1.37457i 0.139342 + 0.0849211i
263263 −16.9489 −1.04511 −0.522556 0.852605i 0.675021π-0.675021\pi
−0.522556 + 0.852605i 0.675021π0.675021\pi
264264 0 0
265265 5.24217 0.322024
266266 15.6363 + 9.52943i 0.958722 + 0.584287i
267267 3.99751i 0.244644i
268268 −8.73318 + 4.50369i −0.533464 + 0.275107i
269269 3.95476 0.241126 0.120563 0.992706i 0.461530π-0.461530\pi
0.120563 + 0.992706i 0.461530π0.461530\pi
270270 −4.00703 + 6.57490i −0.243860 + 0.400135i
271271 23.7375 1.44195 0.720974 0.692962i 0.243695π-0.243695\pi
0.720974 + 0.692962i 0.243695π0.243695\pi
272272 0.228011 + 0.162277i 0.0138252 + 0.00983949i
273273 4.29036 0.259664
274274 −1.51493 0.923261i −0.0915200 0.0557763i
275275 0 0
276276 −3.60522 6.99093i −0.217009 0.420804i
277277 15.0111i 0.901928i 0.892542 + 0.450964i 0.148920π0.148920\pi
−0.892542 + 0.450964i 0.851080π0.851080\pi
278278 7.59730 + 4.63012i 0.455656 + 0.277696i
279279 9.05519i 0.542120i
280280 0.441845 6.19468i 0.0264053 0.370203i
281281 5.74135i 0.342500i 0.985228 + 0.171250i 0.0547806π0.0547806\pi
−0.985228 + 0.171250i 0.945219π0.945219\pi
282282 −8.77043 5.34508i −0.522272 0.318295i
283283 11.1948 0.665460 0.332730 0.943022i 0.392030π-0.392030\pi
0.332730 + 0.943022i 0.392030π0.392030\pi
284284 12.3994 6.39439i 0.735771 0.379437i
285285 7.94150i 0.470414i
286286 0 0
287287 9.42215i 0.556172i
288288 −12.7458 + 5.46295i −0.751054 + 0.321907i
289289 16.9951 0.999712
290290 3.90637 6.40974i 0.229390 0.376393i
291291 5.42637i 0.318099i
292292 17.9927 9.27883i 1.05294 0.543003i
293293 5.30290i 0.309799i 0.987930 + 0.154899i 0.0495053π0.0495053\pi
−0.987930 + 0.154899i 0.950495π0.950495\pi
294294 −2.37040 + 3.88945i −0.138245 + 0.226838i
295295 6.55546i 0.381674i
296296 1.38419 19.4063i 0.0804542 1.12797i
297297 0 0
298298 12.6261 20.7175i 0.731413 1.20013i
299299 18.8885 1.09235
300300 −4.18910 + 2.16032i −0.241858 + 0.124726i
301301 3.08602 0.177875
302302 −14.6826 8.94819i −0.844887 0.514911i
303303 7.09024 0.407324
304304 −18.4427 + 25.9133i −1.05776 + 1.48623i
305305 1.81500i 0.103926i
306306 0.126230 0.207123i 0.00721606 0.0118404i
307307 −2.27014 −0.129564 −0.0647820 0.997899i 0.520635π-0.520635\pi
−0.0647820 + 0.997899i 0.520635π0.520635\pi
308308 0 0
309309 −7.64487 −0.434901
310310 3.66581 6.01501i 0.208204 0.341630i
311311 20.1665i 1.14354i −0.820414 0.571770i 0.806257π-0.806257\pi
0.820414 0.571770i 0.193743π-0.193743\pi
312312 −0.530194 + 7.43333i −0.0300163 + 0.420830i
313313 1.54188 0.0871524 0.0435762 0.999050i 0.486125π-0.486125\pi
0.0435762 + 0.999050i 0.486125π0.486125\pi
314314 −6.40247 3.90194i −0.361312 0.220199i
315315 −5.38258 −0.303274
316316 −5.50428 10.6734i −0.309640 0.600427i
317317 −16.8622 −0.947076 −0.473538 0.880773i 0.657023π-0.657023\pi
−0.473538 + 0.880773i 0.657023π0.657023\pi
318318 −2.11923 + 3.47732i −0.118841 + 0.194999i
319319 0 0
320320 10.6781 + 1.53105i 0.596924 + 0.0855885i
321321 8.20458i 0.457935i
322322 6.36356 10.4416i 0.354627 0.581887i
323323 0.556334i 0.0309552i
324324 4.00000 + 7.75646i 0.222222 + 0.430914i
325325 11.3183i 0.627828i
326326 7.40210 12.1457i 0.409965 0.672687i
327327 6.63596 0.366969
328328 16.3245 + 1.16437i 0.901370 + 0.0642916i
329329 15.9667i 0.880275i
330330 0 0
331331 33.9735i 1.86735i 0.358115 + 0.933677i 0.383419π0.383419\pi
−0.358115 + 0.933677i 0.616581π0.616581\pi
332332 −3.31099 6.42039i −0.181714 0.352365i
333333 −16.8622 −0.924044
334334 26.4561 + 16.1235i 1.44761 + 0.882237i
335335 6.62480i 0.361952i
336336 3.93054 + 2.79739i 0.214429 + 0.152610i
337337 17.0957i 0.931262i −0.884979 0.465631i 0.845827π-0.845827\pi
0.884979 0.465631i 0.154173π-0.154173\pi
338338 0.417938 + 0.254709i 0.0227328 + 0.0138544i
339339 8.16452i 0.443436i
340340 −0.167699 + 0.0864821i −0.00909474 + 0.00469015i
341341 0 0
342342 23.5394 + 14.3459i 1.27286 + 0.775738i
343343 −18.4794 −0.997794
344344 −0.381364 + 5.34674i −0.0205618 + 0.288277i
345345 5.30317 0.285513
346346 −8.70820 + 14.2888i −0.468156 + 0.768170i
347347 2.49909 0.134158 0.0670790 0.997748i 0.478632π-0.478632\pi
0.0670790 + 0.997748i 0.478632π0.478632\pi
348348 2.67261 + 5.18249i 0.143267 + 0.277810i
349349 7.01126i 0.375304i 0.982236 + 0.187652i 0.0600878π0.0600878\pi
−0.982236 + 0.187652i 0.939912π0.939912\pi
350350 −6.25680 3.81317i −0.334440 0.203822i
351351 14.3631 0.766646
352352 0 0
353353 17.9431 0.955017 0.477509 0.878627i 0.341540π-0.341540\pi
0.477509 + 0.878627i 0.341540π0.341540\pi
354354 −4.34848 2.65015i −0.231119 0.140854i
355355 9.40596i 0.499216i
356356 −4.94744 9.59365i −0.262214 0.508462i
357357 −0.0843849 −0.00446612
358358 0.687162 1.12752i 0.0363176 0.0595915i
359359 −9.67947 −0.510863 −0.255431 0.966827i 0.582217π-0.582217\pi
−0.255431 + 0.966827i 0.582217π0.582217\pi
360360 0.665168 9.32568i 0.0350574 0.491506i
361361 44.2270 2.32774
362362 22.7509 + 13.8654i 1.19576 + 0.728748i
363363 0 0
364364 −10.2965 + 5.30988i −0.539681 + 0.278313i
365365 13.6489i 0.714416i
366366 1.20396 + 0.733743i 0.0629318 + 0.0383533i
367367 30.9471i 1.61543i −0.589575 0.807713i 0.700705π-0.700705\pi
0.589575 0.807713i 0.299295π-0.299295\pi
368368 17.3044 + 12.3156i 0.902053 + 0.641998i
369369 14.1844i 0.738411i
370370 11.2009 + 6.82632i 0.582308 + 0.354883i
371371 −6.33054 −0.328665
372372 2.50802 + 4.86333i 0.130035 + 0.252152i
373373 4.92658i 0.255088i −0.991833 0.127544i 0.959291π-0.959291\pi
0.991833 0.127544i 0.0407095π-0.0407095\pi
374374 0 0
375375 8.17145i 0.421972i
376376 27.6635 + 1.97314i 1.42663 + 0.101757i
377377 −14.0023 −0.721157
378378 4.83896 7.93996i 0.248889 0.408388i
379379 4.02515i 0.206758i −0.994642 0.103379i 0.967035π-0.967035\pi
0.994642 0.103379i 0.0329655π-0.0329655\pi
380380 −9.82864 19.0589i −0.504199 0.977699i
381381 7.62329i 0.390553i
382382 −15.0463 + 24.6887i −0.769837 + 1.26318i
383383 11.9889i 0.612604i 0.951934 + 0.306302i 0.0990918π0.0990918\pi
−0.951934 + 0.306302i 0.900908π0.900908\pi
384384 −5.33240 + 6.46423i −0.272118 + 0.329877i
385385 0 0
386386 −12.7625 + 20.9412i −0.649594 + 1.06588i
387387 4.64579 0.236159
388388 6.71584 + 13.0228i 0.340945 + 0.661131i
389389 13.7371 0.696496 0.348248 0.937402i 0.386777π-0.386777\pi
0.348248 + 0.937402i 0.386777π0.386777\pi
390390 −4.29036 2.61473i −0.217251 0.132402i
391391 −0.371508 −0.0187880
392392 0.875034 12.2680i 0.0441959 0.619628i
393393 1.38335i 0.0697807i
394394 −2.56953 + 4.21619i −0.129451 + 0.212409i
395395 8.09663 0.407386
396396 0 0
397397 −12.1547 −0.610027 −0.305014 0.952348i 0.598661π-0.598661\pi
−0.305014 + 0.952348i 0.598661π0.598661\pi
398398 −8.29149 + 13.6050i −0.415615 + 0.681958i
399399 9.59030i 0.480115i
400400 7.37977 10.3691i 0.368989 0.518456i
401401 −28.7805 −1.43723 −0.718614 0.695409i 0.755223π-0.755223\pi
−0.718614 + 0.695409i 0.755223π0.755223\pi
402402 4.39448 + 2.67819i 0.219177 + 0.133576i
403403 −13.1400 −0.654551
404404 −17.0159 + 8.77510i −0.846574 + 0.436578i
405405 −5.88388 −0.292373
406406 −4.71741 + 7.74052i −0.234121 + 0.384156i
407407 0 0
408408 0.0104281 0.146203i 0.000516269 0.00723811i
409409 18.9552i 0.937276i −0.883390 0.468638i 0.844745π-0.844745\pi
0.883390 0.468638i 0.155255π-0.155255\pi
410410 −5.74226 + 9.42215i −0.283590 + 0.465327i
411411 0.929159i 0.0458320i
412412 18.3470 9.46152i 0.903891 0.466136i
413413 7.91649i 0.389545i
414414 9.57991 15.7191i 0.470827 0.772552i
415415 4.87038 0.239077
416416 −7.92731 18.4955i −0.388668 0.906816i
417417 4.65970i 0.228186i
418418 0 0
419419 15.3705i 0.750898i −0.926843 0.375449i 0.877488π-0.877488\pi
0.926843 0.375449i 0.122512π-0.122512\pi
420420 −2.89086 + 1.49081i −0.141059 + 0.0727442i
421421 19.3208 0.941640 0.470820 0.882229i 0.343958π-0.343958\pi
0.470820 + 0.882229i 0.343958π0.343958\pi
422422 3.31244 + 2.01874i 0.161247 + 0.0982709i
423423 24.0369i 1.16871i
424424 0.782315 10.9681i 0.0379926 0.532657i
425425 0.222615i 0.0107984i
426426 −6.23932 3.80251i −0.302296 0.184232i
427427 2.19182i 0.106070i
428428 −10.1542 19.6902i −0.490824 0.951763i
429429 0 0
430430 −3.08602 1.88075i −0.148821 0.0906980i
431431 −27.1040 −1.30555 −0.652777 0.757550i 0.726396π-0.726396\pi
−0.652777 + 0.757550i 0.726396π0.726396\pi
432432 13.1585 + 9.36502i 0.633090 + 0.450575i
433433 4.35614 0.209343 0.104671 0.994507i 0.466621π-0.466621\pi
0.104671 + 0.994507i 0.466621π0.466621\pi
434434 −4.42689 + 7.26383i −0.212498 + 0.348675i
435435 −3.93133 −0.188493
436436 −15.9257 + 8.21287i −0.762702 + 0.393325i
437437 42.2217i 2.01974i
438438 −9.05382 5.51779i −0.432608 0.263650i
439439 24.0996 1.15021 0.575105 0.818080i 0.304961π-0.304961\pi
0.575105 + 0.818080i 0.304961π0.304961\pi
440440 0 0
441441 −10.6597 −0.507605
442442 0.300556 + 0.183172i 0.0142960 + 0.00871261i
443443 23.0448i 1.09489i −0.836841 0.547446i 0.815600π-0.815600\pi
0.836841 0.547446i 0.184400π-0.184400\pi
444444 −9.05630 + 4.67033i −0.429793 + 0.221644i
445445 7.27754 0.344989
446446 −17.4616 + 28.6517i −0.826829 + 1.35670i
447447 −12.7068 −0.601011
448448 −12.8951 1.84893i −0.609235 0.0873536i
449449 −3.77349 −0.178082 −0.0890409 0.996028i 0.528380π-0.528380\pi
−0.0890409 + 0.996028i 0.528380π0.528380\pi
450450 −9.41920 5.74046i −0.444025 0.270608i
451451 0 0
452452 10.1047 + 19.5941i 0.475283 + 0.921628i
453453 9.00535i 0.423108i
454454 0.967108 + 0.589397i 0.0453886 + 0.0276618i
455455 7.81068i 0.366170i
456456 16.6158 + 1.18515i 0.778108 + 0.0554997i
457457 35.2571i 1.64926i 0.565674 + 0.824629i 0.308616π0.308616\pi
−0.565674 + 0.824629i 0.691384π0.691384\pi
458458 −28.4864 17.3609i −1.33108 0.811220i
459459 −0.282501 −0.0131860
460460 −12.7271 + 6.56337i −0.593405 + 0.306019i
461461 38.5074i 1.79347i 0.442571 + 0.896734i 0.354067π0.354067\pi
−0.442571 + 0.896734i 0.645933π0.645933\pi
462462 0 0
463463 10.7672i 0.500394i −0.968195 0.250197i 0.919505π-0.919505\pi
0.968195 0.250197i 0.0804954π-0.0804954\pi
464464 −12.8280 9.12979i −0.595525 0.423840i
465465 −3.68922 −0.171084
466466 12.8733 21.1231i 0.596344 0.978507i
467467 20.6799i 0.956950i −0.878101 0.478475i 0.841190π-0.841190\pi
0.878101 0.478475i 0.158810π-0.158810\pi
468468 −15.5006 + 7.99366i −0.716516 + 0.369507i
469469 8.00023i 0.369416i
470470 −9.73082 + 15.9667i −0.448849 + 0.736491i
471471 3.92686i 0.180940i
472472 13.7159 + 0.978304i 0.631323 + 0.0450301i
473473 0 0
474474 −3.27320 + 5.37080i −0.150343 + 0.246689i
475475 −25.3000 −1.16085
476476 0.202516 0.104437i 0.00928230 0.00478688i
477477 −9.53019 −0.436358
478478 −8.07289 4.91997i −0.369245 0.225034i
479479 11.4138 0.521511 0.260756 0.965405i 0.416028π-0.416028\pi
0.260756 + 0.965405i 0.416028π0.416028\pi
480480 −2.22569 5.19284i −0.101588 0.237019i
481481 24.4688i 1.11568i
482482 3.15479 5.17652i 0.143697 0.235784i
483483 −6.40421 −0.291401
484484 0 0
485485 −9.87880 −0.448573
486486 11.2936 18.5311i 0.512290 0.840586i
487487 4.00496i 0.181482i −0.995875 0.0907410i 0.971076π-0.971076\pi
0.995875 0.0907410i 0.0289235π-0.0289235\pi
488488 −3.79748 0.270861i −0.171904 0.0122613i
489489 −7.44938 −0.336873
490490 7.08082 + 4.31536i 0.319879 + 0.194948i
491491 −11.1940 −0.505179 −0.252589 0.967574i 0.581282π-0.581282\pi
−0.252589 + 0.967574i 0.581282π0.581282\pi
492492 −3.92866 7.61812i −0.177118 0.343451i
493493 0.275405 0.0124036
494494 −20.8174 + 34.1581i −0.936619 + 1.53684i
495495 0 0
496496 −12.0380 8.56754i −0.540523 0.384694i
497497 11.3588i 0.509512i
498498 −1.96893 + 3.23070i −0.0882298 + 0.144771i
499499 39.3656i 1.76224i −0.472888 0.881122i 0.656789π-0.656789\pi
0.472888 0.881122i 0.343211π-0.343211\pi
500500 10.1132 + 19.6107i 0.452278 + 0.877018i
501501 16.2265i 0.724944i
502502 −3.60456 + 5.91452i −0.160880 + 0.263978i
503503 19.3369 0.862191 0.431096 0.902306i 0.358127π-0.358127\pi
0.431096 + 0.902306i 0.358127π0.358127\pi
504504 −0.803269 + 11.2619i −0.0357804 + 0.501643i
505505 12.9079i 0.574395i
506506 0 0
507507 0.256336i 0.0113843i
508508 −9.43482 18.2952i −0.418602 0.811718i
509509 −42.9965 −1.90579 −0.952893 0.303306i 0.901910π-0.901910\pi
−0.952893 + 0.303306i 0.901910π0.901910\pi
510510 0.0843849 + 0.0514278i 0.00373663 + 0.00227726i
511511 16.4827i 0.729150i
512512 4.79694 22.1131i 0.211997 0.977270i
513513 32.1061i 1.41752i
514514 −14.9555 9.11453i −0.659659 0.402025i
515515 13.9176i 0.613284i
516516 2.49515 1.28675i 0.109843 0.0566458i
517517 0 0
518518 −13.5264 8.24359i −0.594317 0.362202i
519519 8.76383 0.384689
520520 13.5325 + 0.965228i 0.593440 + 0.0423280i
521521 −14.7313 −0.645389 −0.322694 0.946503i 0.604589π-0.604589\pi
−0.322694 + 0.946503i 0.604589π0.604589\pi
522522 −7.10174 + 11.6528i −0.310835 + 0.510031i
523523 −40.4528 −1.76888 −0.884440 0.466655i 0.845459π-0.845459\pi
−0.884440 + 0.466655i 0.845459π0.845459\pi
524524 1.71207 + 3.31991i 0.0747923 + 0.145031i
525525 3.83752i 0.167483i
526526 −20.4677 12.4739i −0.892436 0.543889i
527527 0.258445 0.0112580
528528 0 0
529529 −5.19479 −0.225860
530530 6.33054 + 3.85810i 0.274981 + 0.167585i
531531 11.9177i 0.517186i
532532 11.8692 + 23.0158i 0.514597 + 0.997862i
533533 20.5830 0.891551
534534 −2.94206 + 4.82746i −0.127316 + 0.208905i
535535 14.9366 0.645765
536536 −13.8609 0.988653i −0.598702 0.0427033i
537537 −0.691551 −0.0298426
538538 4.77584 + 2.91060i 0.205901 + 0.125485i
539539 0 0
540540 −9.67791 + 4.99089i −0.416471 + 0.214774i
541541 16.7350i 0.719496i 0.933050 + 0.359748i 0.117137π0.117137\pi
−0.933050 + 0.359748i 0.882863π0.882863\pi
542542 28.6658 + 17.4702i 1.23130 + 0.750408i
543543 13.9539i 0.598821i
544544 0.155918 + 0.363779i 0.00668494 + 0.0155969i
545545 12.0809i 0.517489i
546546 5.18111 + 3.15759i 0.221731 + 0.135133i
547547 9.29004 0.397214 0.198607 0.980079i 0.436358π-0.436358\pi
0.198607 + 0.980079i 0.436358π0.436358\pi
548548 −1.14996 2.22989i −0.0491237 0.0952564i
549549 3.29964i 0.140825i
550550 0 0
551551 31.2996i 1.33341i
552552 0.791419 11.0957i 0.0336850 0.472265i
553553 −9.77764 −0.415787
554554 −11.0478 + 18.1276i −0.469375 + 0.770170i
555555 6.86992i 0.291612i
556556 5.76698 + 11.1828i 0.244575 + 0.474258i
557557 13.2620i 0.561928i 0.959718 + 0.280964i 0.0906541π0.0906541\pi
−0.959718 + 0.280964i 0.909346π0.909346\pi
558558 −6.66439 + 10.9352i −0.282126 + 0.462924i
559559 6.74153i 0.285136i
560560 5.09271 7.15563i 0.215206 0.302380i
561561 0 0
562562 −4.22549 + 6.93336i −0.178241 + 0.292466i
563563 −23.5044 −0.990594 −0.495297 0.868724i 0.664941π-0.664941\pi
−0.495297 + 0.868724i 0.664941π0.664941\pi
564564 −6.65749 12.9096i −0.280331 0.543594i
565565 −14.8637 −0.625319
566566 13.5190 + 8.23907i 0.568246 + 0.346314i
567567 7.10549 0.298402
568568 19.6799 + 1.40370i 0.825750 + 0.0588979i
569569 12.8798i 0.539950i 0.962867 + 0.269975i 0.0870154π0.0870154\pi
−0.962867 + 0.269975i 0.912985π0.912985\pi
570570 −5.84474 + 9.59030i −0.244809 + 0.401693i
571571 20.4261 0.854806 0.427403 0.904061i 0.359429π-0.359429\pi
0.427403 + 0.904061i 0.359429π0.359429\pi
572572 0 0
573573 15.1424 0.632585
574574 6.93446 11.3784i 0.289439 0.474923i
575575 16.8949i 0.704564i
576576 −19.4127 2.78344i −0.808861 0.115976i
577577 6.84506 0.284963 0.142482 0.989797i 0.454492π-0.454492\pi
0.142482 + 0.989797i 0.454492π0.454492\pi
578578 20.5236 + 12.5080i 0.853669 + 0.520263i
579579 12.8440 0.533779
580580 9.43482 4.86553i 0.391759 0.202030i
581581 −5.88155 −0.244008
582582 3.99367 6.55298i 0.165543 0.271630i
583583 0 0
584584 28.5573 + 2.03689i 1.18171 + 0.0842873i
585585 11.7584i 0.486152i
586586 −3.90280 + 6.40388i −0.161223 + 0.264542i
587587 0.638798i 0.0263660i −0.999913 0.0131830i 0.995804π-0.995804\pi
0.999913 0.0131830i 0.00419640π-0.00419640\pi
588588 −5.72508 + 2.95242i −0.236098 + 0.121756i
589589 29.3721i 1.21026i
590590 −4.82465 + 7.91649i −0.198628 + 0.325917i
591591 2.58594 0.106372
592592 15.9541 22.4167i 0.655711 0.921321i
593593 17.0480i 0.700077i −0.936735 0.350039i 0.886168π-0.886168\pi
0.936735 0.350039i 0.113832π-0.113832\pi
594594 0 0
595595 0.153624i 0.00629799i
596596 30.4951 15.7263i 1.24913 0.644175i
597597 8.34445 0.341516
598598 22.8101 + 13.9014i 0.932773 + 0.568472i
599599 1.98468i 0.0810916i −0.999178 0.0405458i 0.987090π-0.987090\pi
0.999178 0.0405458i 0.0129097π-0.0129097\pi
600600 −6.64877 0.474233i −0.271435 0.0193605i
601601 16.4628i 0.671532i 0.941945 + 0.335766i 0.108995π0.108995\pi
−0.941945 + 0.335766i 0.891005π0.891005\pi
602602 3.72673 + 2.27123i 0.151890 + 0.0925685i
603603 12.0438i 0.490462i
604604 −11.1453 21.6120i −0.453496 0.879380i
605605 0 0
606606 8.56231 + 5.21824i 0.347820 + 0.211976i
607607 28.7204 1.16573 0.582863 0.812571i 0.301933π-0.301933\pi
0.582863 + 0.812571i 0.301933π0.301933\pi
608608 −41.3432 + 17.7200i −1.67669 + 0.718642i
609609 4.74754 0.192380
610610 1.33579 2.19182i 0.0540847 0.0887444i
611611 34.8800 1.41109
612612 0.304874 0.157223i 0.0123238 0.00635538i
613613 6.65378i 0.268744i −0.990931 0.134372i 0.957098π-0.957098\pi
0.990931 0.134372i 0.0429017π-0.0429017\pi
614614 −2.74147 1.67077i −0.110637 0.0674267i
615615 5.77894 0.233029
616616 0 0
617617 −17.8948 −0.720416 −0.360208 0.932872i 0.617294π-0.617294\pi
−0.360208 + 0.932872i 0.617294π0.617294\pi
618618 −9.23208 5.62643i −0.371369 0.226328i
619619 23.2378i 0.934007i −0.884256 0.467003i 0.845334π-0.845334\pi
0.884256 0.467003i 0.154666π-0.154666\pi
620620 8.85379 4.56589i 0.355577 0.183371i
621621 −21.4398 −0.860349
622622 14.8421 24.3535i 0.595112 0.976485i
623623 −8.78849 −0.352103
624624 −6.11102 + 8.58642i −0.244636 + 0.343732i
625625 1.03262 0.0413048
626626 1.86201 + 1.13479i 0.0744208 + 0.0453552i
627627 0 0
628628 −4.86001 9.42411i −0.193935 0.376063i
629629 0.481265i 0.0191893i
630630 −6.50010 3.96144i −0.258970 0.157828i
631631 46.3216i 1.84404i 0.387148 + 0.922018i 0.373460π0.373460\pi
−0.387148 + 0.922018i 0.626540π0.626540\pi
632632 1.20830 16.9404i 0.0480636 0.673854i
633633 2.03164i 0.0807503i
634634 −20.3631 12.4102i −0.808723 0.492871i
635635 13.8783 0.550745
636636 −5.11845 + 2.63958i −0.202960 + 0.104666i
637637 15.4683i 0.612877i
638638 0 0
639639 17.0999i 0.676462i
640640 11.7683 + 9.70774i 0.465181 + 0.383732i
641641 27.1756 1.07337 0.536687 0.843782i 0.319676π-0.319676\pi
0.536687 + 0.843782i 0.319676π0.319676\pi
642642 −6.03836 + 9.90800i −0.238315 + 0.391038i
643643 31.0236i 1.22345i 0.791069 + 0.611726i 0.209525π0.209525\pi
−0.791069 + 0.611726i 0.790475π0.790475\pi
644644 15.3695 7.92604i 0.605643 0.312330i
645645 1.89277i 0.0745276i
646646 0.409447 0.671838i 0.0161095 0.0264331i
647647 42.1713i 1.65793i −0.559303 0.828963i 0.688931π-0.688931\pi
0.559303 0.828963i 0.311069π-0.311069\pi
648648 −0.878082 + 12.3107i −0.0344943 + 0.483611i
649649 0 0
650650 8.33001 13.6682i 0.326730 0.536112i
651651 4.45517 0.174612
652652 17.8778 9.21959i 0.700150 0.361067i
653653 −4.04757 −0.158394 −0.0791969 0.996859i 0.525236π-0.525236\pi
−0.0791969 + 0.996859i 0.525236π0.525236\pi
654654 8.01371 + 4.88390i 0.313361 + 0.190976i
655655 −2.51841 −0.0984025
656656 18.8568 + 13.4205i 0.736235 + 0.523984i
657657 24.8135i 0.968068i
658658 11.7511 19.2817i 0.458106 0.751680i
659659 −6.46292 −0.251760 −0.125880 0.992045i 0.540175π-0.540175\pi
−0.125880 + 0.992045i 0.540175π0.540175\pi
660660 0 0
661661 26.6232 1.03552 0.517761 0.855525i 0.326766π-0.326766\pi
0.517761 + 0.855525i 0.326766π0.326766\pi
662662 −25.0037 + 41.0271i −0.971795 + 1.59456i
663663 0.184342i 0.00715925i
664664 0.726831 10.1902i 0.0282065 0.395456i
665665 −17.4593 −0.677043
666666 −20.3631 12.4102i −0.789055 0.480884i
667667 20.9012 0.809300
668668 20.0824 + 38.9420i 0.777010 + 1.50671i
669669 17.5731 0.679416
670670 4.87569 8.00023i 0.188364 0.309076i
671671 0 0
672672 2.68778 + 6.27096i 0.103683 + 0.241908i
673673 8.31993i 0.320710i 0.987059 + 0.160355i 0.0512639π0.0512639\pi
−0.987059 + 0.160355i 0.948736π0.948736\pi
674674 12.5820 20.6451i 0.484641 0.795219i
675675 12.8471i 0.494486i
676676 0.317250 + 0.615183i 0.0122019 + 0.0236609i
677677 15.2629i 0.586602i −0.956020 0.293301i 0.905246π-0.905246\pi
0.956020 0.293301i 0.0947538π-0.0947538\pi
678678 6.00888 9.85962i 0.230769 0.378656i
679679 11.9298 0.457824
680680 −0.266165 0.0189846i −0.0102069 0.000728026i
681681 0.593162i 0.0227300i
682682 0 0
683683 32.9156i 1.25948i −0.776806 0.629740i 0.783161π-0.783161\pi
0.776806 0.629740i 0.216839π-0.216839\pi
684684 17.8683 + 34.6488i 0.683213 + 1.32483i
685685 1.69155 0.0646308
686686 −22.3161 13.6004i −0.852031 0.519265i
687687 17.4718i 0.666589i
688688 −4.39560 + 6.17614i −0.167581 + 0.235463i
689689 13.8293i 0.526854i
690690 6.40421 + 3.90300i 0.243804 + 0.148585i
691691 45.5175i 1.73157i 0.500419 + 0.865783i 0.333179π0.333179\pi
−0.500419 + 0.865783i 0.666821π0.666821\pi
692692 −21.0324 + 10.8464i −0.799531 + 0.412318i
693693 0 0
694694 3.01794 + 1.83926i 0.114559 + 0.0698175i
695695 −8.48306 −0.321781
696696 −0.586692 + 8.22544i −0.0222385 + 0.311784i
697697 −0.404838 −0.0153343
698698 −5.16011 + 8.46693i −0.195313 + 0.320478i
699699 −12.9555 −0.490023
700700 −4.74944 9.20970i −0.179512 0.348094i
701701 50.0843i 1.89166i 0.324665 + 0.945829i 0.394748π0.394748\pi
−0.324665 + 0.945829i 0.605252π0.605252\pi
702702 17.3452 + 10.5709i 0.654651 + 0.398972i
703703 −54.6955 −2.06288
704704 0 0
705705 9.79298 0.368825
706706 21.6685 + 13.2057i 0.815504 + 0.497003i
707707 15.5878i 0.586241i
708708 −3.30086 6.40074i −0.124054 0.240555i
709709 −8.49866 −0.319174 −0.159587 0.987184i 0.551016π-0.551016\pi
−0.159587 + 0.987184i 0.551016π0.551016\pi
710710 −6.92254 + 11.3588i −0.259798 + 0.426288i
711711 −14.7196 −0.552027
712712 1.08606 15.2267i 0.0407020 0.570643i
713713 19.6141 0.734553
714714 −0.101905 0.0621052i −0.00381369 0.00232423i
715715 0 0
716716 1.65966 0.855885i 0.0620243 0.0319859i
717717 4.95139i 0.184913i
718718 −11.6891 7.12384i −0.436233 0.265859i
719719 7.29734i 0.272145i 0.990699 + 0.136072i 0.0434480π0.0434480\pi
−0.990699 + 0.136072i 0.956552π0.956552\pi
720720 7.66673 10.7723i 0.285722 0.401460i
721721 16.8072i 0.625932i
722722 53.4093 + 32.5499i 1.98769 + 1.21138i
723723 −3.17494 −0.118077
724724 17.2698 + 33.4881i 0.641828 + 1.24458i
725725 12.5244i 0.465146i
726726 0 0
727727 1.85004i 0.0686140i −0.999411 0.0343070i 0.989078π-0.989078\pi
0.999411 0.0343070i 0.0109224π-0.0109224\pi
728728 −16.3421 1.16563i −0.605679 0.0432010i
729729 1.72491 0.0638855
730730 −10.0452 + 16.4827i −0.371791 + 0.610050i
731731 0.132596i 0.00490423i
732732 0.913903 + 1.77216i 0.0337788 + 0.0655010i
733733 18.8938i 0.697857i 0.937149 + 0.348928i 0.113454π0.113454\pi
−0.937149 + 0.348928i 0.886546π0.886546\pi
734734 22.7763 37.3723i 0.840689 1.37944i
735735 4.34292i 0.160191i
736736 11.8331 + 27.6082i 0.436173 + 1.01765i
737737 0 0
738738 10.4394 17.1293i 0.384278 0.630540i
739739 15.7186 0.578218 0.289109 0.957296i 0.406641π-0.406641\pi
0.289109 + 0.957296i 0.406641π0.406641\pi
740740 8.50243 + 16.4872i 0.312555 + 0.606081i
741741 20.9504 0.769631
742742 −7.64487 4.65911i −0.280652 0.171041i
743743 5.80638 0.213015 0.106508 0.994312i 0.466033π-0.466033\pi
0.106508 + 0.994312i 0.466033π0.466033\pi
744744 −0.550561 + 7.71888i −0.0201845 + 0.282988i
745745 23.1330i 0.847526i
746746 3.62583 5.94942i 0.132751 0.217824i
747747 −8.85428 −0.323961
748748 0 0
749749 −18.0377 −0.659083
750750 6.01398 9.86799i 0.219599 0.360328i
751751 3.00343i 0.109597i 0.998497 + 0.0547983i 0.0174516π0.0174516\pi
−0.998497 + 0.0547983i 0.982548π0.982548\pi
752752 31.9547 + 22.7424i 1.16527 + 0.829330i
753753 3.62759 0.132197
754754 −16.9095 10.3054i −0.615806 0.375299i
755755 16.3944 0.596654
756756 11.6872 6.02709i 0.425060 0.219203i
757757 −26.0871 −0.948152 −0.474076 0.880484i 0.657218π-0.657218\pi
−0.474076 + 0.880484i 0.657218π0.657218\pi
758758 2.96241 4.86085i 0.107600 0.176554i
759759 0 0
760760 2.15759 30.2495i 0.0782639 1.09726i
761761 31.9526i 1.15828i 0.815228 + 0.579140i 0.196612π0.196612\pi
−0.815228 + 0.579140i 0.803388π0.803388\pi
762762 −5.61055 + 9.20602i −0.203249 + 0.333499i
763763 14.5891i 0.528161i
764764 −36.3405 + 18.7408i −1.31475 + 0.678017i
765765 0.231271i 0.00836162i
766766 −8.82353 + 14.4780i −0.318807 + 0.523112i
767767 17.2939 0.624446
768768 −11.1970 + 3.88181i −0.404038 + 0.140073i
769769 22.3560i 0.806176i 0.915161 + 0.403088i 0.132063π0.132063\pi
−0.915161 + 0.403088i 0.867937π0.867937\pi
770770 0 0
771771 9.17275i 0.330348i
772772 −30.8244 + 15.8961i −1.10940 + 0.572115i
773773 5.07704 0.182608 0.0913042 0.995823i 0.470896π-0.470896\pi
0.0913042 + 0.995823i 0.470896π0.470896\pi
774774 5.61034 + 3.41919i 0.201660 + 0.122900i
775775 11.7531i 0.422185i
776776 −1.47426 + 20.6692i −0.0529230 + 0.741982i
777777 8.29624i 0.297626i
778778 16.5891 + 10.1101i 0.594749 + 0.362465i
779779 46.0096i 1.64846i
780780 −3.25674 6.31519i −0.116610 0.226120i
781781 0 0
782782 −0.448640 0.273421i −0.0160433 0.00977750i
783783 15.8937 0.567993
784784 10.0856 14.1711i 0.360202 0.506109i
785785 7.14893 0.255156
786786 1.01811 1.67056i 0.0363147 0.0595867i
787787 2.94375 0.104933 0.0524667 0.998623i 0.483292π-0.483292\pi
0.0524667 + 0.998623i 0.483292π0.483292\pi
788788 −6.20602 + 3.20044i −0.221080 + 0.114011i
789789 12.5536i 0.446920i
790790 9.77764 + 5.95891i 0.347873 + 0.212009i
791791 17.9496 0.638215
792792 0 0
793793 −4.78812 −0.170031
794794 −14.6782 8.94556i −0.520911 0.317466i
795795 3.88275i 0.137707i
796796 −20.0259 + 10.3273i −0.709799 + 0.366043i
797797 7.49194 0.265378 0.132689 0.991158i 0.457639π-0.457639\pi
0.132689 + 0.991158i 0.457639π0.457639\pi
798798 7.05822 11.5814i 0.249858 0.409978i
799799 −0.686037 −0.0242702
800800 16.5434 7.09060i 0.584896 0.250691i
801801 −13.2305 −0.467476
802802 −34.7558 21.1817i −1.22727 0.747952i
803803 0 0
804804 3.33578 + 6.46845i 0.117644 + 0.228125i
805805 11.6590i 0.410925i
806806 −15.8681 9.67072i −0.558931 0.340637i
807807 2.92919i 0.103112i
808808 −27.0070 1.92631i −0.950103 0.0677675i
809809 39.8260i 1.40021i 0.714041 + 0.700104i 0.246863π0.246863\pi
−0.714041 + 0.700104i 0.753137π0.753137\pi
810810 −7.10549 4.33039i −0.249661 0.152154i
811811 −42.6481 −1.49758 −0.748788 0.662809i 0.769364π-0.769364\pi
−0.748788 + 0.662809i 0.769364π0.769364\pi
812812 −11.3937 + 5.87570i −0.399839 + 0.206197i
813813 17.5818i 0.616619i
814814 0 0
815815 13.5617i 0.475047i
816816 0.120195 0.168882i 0.00420765 0.00591205i
817817 15.0694 0.527213
818818 13.9506 22.8907i 0.487770 0.800354i
819819 14.1997i 0.496178i
820820 −13.8689 + 7.15220i −0.484324 + 0.249766i
821821 19.3110i 0.673958i −0.941512 0.336979i 0.890595π-0.890595\pi
0.941512 0.336979i 0.109405π-0.109405\pi
822822 −0.683837 + 1.12207i −0.0238516 + 0.0391366i
823823 9.91929i 0.345765i −0.984942 0.172882i 0.944692π-0.944692\pi
0.984942 0.172882i 0.0553080π-0.0553080\pi
824824 29.1196 + 2.07700i 1.01443 + 0.0723557i
825825 0 0
826826 5.82633 9.56010i 0.202724 0.332638i
827827 43.6308 1.51719 0.758596 0.651562i 0.225886π-0.225886\pi
0.758596 + 0.651562i 0.225886π0.225886\pi
828828 23.1377 11.9321i 0.804092 0.414670i
829829 −28.1496 −0.977677 −0.488838 0.872374i 0.662579π-0.662579\pi
−0.488838 + 0.872374i 0.662579π0.662579\pi
830830 5.88155 + 3.58447i 0.204152 + 0.124419i
831831 11.1183 0.385691
832832 4.03905 28.1698i 0.140029 0.976611i
833833 0.304239i 0.0105413i
834834 3.42942 5.62713i 0.118751 0.194852i
835835 −29.5406 −1.02229
836836 0 0
837837 14.9149 0.515533
838838 11.3123 18.5617i 0.390777 0.641203i
839839 34.9528i 1.20670i 0.797475 + 0.603352i 0.206169π0.206169\pi
−0.797475 + 0.603352i 0.793831π0.793831\pi
840840 −4.58825 0.327264i −0.158310 0.0112917i
841841 13.5056 0.465709
842842 23.3322 + 14.2196i 0.804081 + 0.490041i
843843 4.25248 0.146463
844844 2.51442 + 4.87574i 0.0865498 + 0.167830i
845845 −0.466665 −0.0160538
846846 17.6905 29.0273i 0.608212 0.997980i
847847 0 0
848848 9.01697 12.6695i 0.309644 0.435072i
849849 8.29170i 0.284570i
850850 −0.163839 + 0.268834i −0.00561963 + 0.00922092i
851851 36.5246i 1.25205i
852852 −4.73617 9.18396i −0.162258 0.314637i
853853 27.2162i 0.931864i −0.884821 0.465932i 0.845719π-0.845719\pi
0.884821 0.465932i 0.154281π-0.154281\pi
854854 −1.61313 + 2.64689i −0.0552001 + 0.0905746i
855855 −26.2838 −0.898888
856856 2.22906 31.2515i 0.0761878 1.06816i
857857 37.5541i 1.28282i 0.767197 + 0.641412i 0.221651π0.221651\pi
−0.767197 + 0.641412i 0.778349π0.778349\pi
858858 0 0
859859 4.50293i 0.153638i 0.997045 + 0.0768190i 0.0244764π0.0244764\pi
−0.997045 + 0.0768190i 0.975524π0.975524\pi
860860 −2.34255 4.54246i −0.0798801 0.154897i
861861 −6.97876 −0.237835
862862 −32.7313 19.9478i −1.11483 0.679426i
863863 18.0361i 0.613958i 0.951716 + 0.306979i 0.0993181π0.0993181\pi
−0.951716 + 0.306979i 0.900682π0.900682\pi
864864 8.99807 + 20.9937i 0.306120 + 0.714221i
865865 15.9547i 0.542477i
866866 5.26055 + 3.20601i 0.178761 + 0.108945i
867867 12.5879i 0.427506i
868868 −10.6920 + 5.51386i −0.362910 + 0.187152i
869869 0 0
870870 −4.74754 2.89336i −0.160957 0.0980940i
871871 −17.4768 −0.592179
872872 −25.2766 1.80289i −0.855974 0.0610536i
873873 17.9595 0.607838
874874 31.0741 50.9877i 1.05110 1.72468i
875875 17.9649 0.607323
876876 −6.87261 13.3268i −0.232204 0.450270i
877877 13.6207i 0.459939i 0.973198 + 0.229970i 0.0738627π0.0738627\pi
−0.973198 + 0.229970i 0.926137π0.926137\pi
878878 29.1031 + 17.7367i 0.982181 + 0.598583i
879879 3.92773 0.132479
880880 0 0
881881 5.44549 0.183463 0.0917317 0.995784i 0.470760π-0.470760\pi
0.0917317 + 0.995784i 0.470760π0.470760\pi
882882 −12.8728 7.84527i −0.433451 0.264164i
883883 28.2297i 0.950005i 0.879985 + 0.475002i 0.157553π0.157553\pi
−0.879985 + 0.475002i 0.842447π0.842447\pi
884884 0.228147 + 0.442404i 0.00767343 + 0.0148797i
885885 4.85547 0.163215
886886 16.9604 27.8293i 0.569796 0.934945i
887887 42.4394 1.42498 0.712488 0.701684i 0.247568π-0.247568\pi
0.712488 + 0.701684i 0.247568π0.247568\pi
888888 −14.3738 1.02523i −0.482353 0.0344046i
889889 −16.7597 −0.562104
890890 8.78849 + 5.35608i 0.294591 + 0.179536i
891891 0 0
892892 −42.1738 + 21.7490i −1.41208 + 0.728211i
893893 77.9677i 2.60909i
894894 −15.3450 9.35188i −0.513212 0.312774i
895895 1.25898i 0.0420831i
896896 −14.2116 11.7232i −0.474775 0.391646i
897897 13.9902i 0.467120i
898898 −4.55693 2.77719i −0.152067 0.0926760i
899899 −14.5402 −0.484944
900900 −7.14996 13.8646i −0.238332 0.462153i
901901 0.272002i 0.00906169i
902902 0 0
903903 2.28574i 0.0760646i
904904 −2.21818 + 31.0989i −0.0737755 + 1.03434i
905905 −25.4034 −0.844438
906906 −6.62771 + 10.8750i −0.220191 + 0.361298i
907907 34.6899i 1.15186i 0.817500 + 0.575929i 0.195360π0.195360\pi
−0.817500 + 0.575929i 0.804640π0.804640\pi
908908 0.734116 + 1.42353i 0.0243625 + 0.0472416i
909909 23.4664i 0.778333i
910910 5.74846 9.43231i 0.190560 0.312678i
911911 29.6674i 0.982924i 0.870899 + 0.491462i 0.163537π0.163537\pi
−0.870899 + 0.491462i 0.836463π0.836463\pi
912912 19.1933 + 13.6600i 0.635555 + 0.452329i
913913 0 0
914914 −25.9483 + 42.5771i −0.858294 + 1.40833i
915915 −1.34432 −0.0444420
916916 −21.6236 41.9306i −0.714463 1.38543i
917917 3.04128 0.100432
918918 −0.341153 0.207914i −0.0112597 0.00686217i
919919 −21.6093 −0.712825 −0.356412 0.934329i 0.616000π-0.616000\pi
−0.356412 + 0.934329i 0.616000π0.616000\pi
920920 −20.2000 1.44079i −0.665973 0.0475016i
921921 1.68144i 0.0554054i
922922 −28.3405 + 46.5022i −0.933343 + 1.53147i
923923 24.8137 0.816754
924924 0 0
925925 21.8862 0.719614
926926 7.92438 13.0027i 0.260411 0.427294i
927927 25.3021i 0.831029i
928928 −8.77205 20.4664i −0.287957 0.671842i
929929 47.2208 1.54926 0.774632 0.632412i 0.217935π-0.217935\pi
0.774632 + 0.632412i 0.217935π0.217935\pi
930930 −4.45517 2.71517i −0.146091 0.0890340i
931931 −34.5766 −1.13320
932932 31.0921 16.0342i 1.01845 0.525217i
933933 −14.9369 −0.489011
934934 15.2199 24.9734i 0.498009 0.817154i
935935 0 0
936936 −24.6020 1.75477i −0.804140 0.0573565i
937937 46.3875i 1.51541i −0.652595 0.757707i 0.726320π-0.726320\pi
0.652595 0.757707i 0.273680π-0.273680\pi
938938 −5.88797 + 9.66123i −0.192249 + 0.315450i
939939 1.14204i 0.0372689i
940940 −23.5022 + 12.1201i −0.766558 + 0.395314i
941941 39.4205i 1.28507i 0.766255 + 0.642536i 0.222118π0.222118\pi
−0.766255 + 0.642536i 0.777882π0.777882\pi
942942 −2.89007 + 4.74215i −0.0941636 + 0.154508i
943943 −30.7243 −1.00052
944944 15.8435 + 11.2759i 0.515662 + 0.367000i
945945 8.86568i 0.288401i
946946 0 0
947947 24.9488i 0.810725i 0.914156 + 0.405363i 0.132855π0.132855\pi
−0.914156 + 0.405363i 0.867145π0.867145\pi
948948 −7.90554 + 4.07688i −0.256760 + 0.132411i
949949 36.0070 1.16884
950950 −30.5528 18.6202i −0.991264 0.604119i
951951 12.4894i 0.404998i
952952 0.321425 + 0.0229261i 0.0104175 + 0.000743040i
953953 40.9113i 1.32525i 0.748952 + 0.662624i 0.230557π0.230557\pi
−0.748952 + 0.662624i 0.769443π0.769443\pi
954954 −11.5088 7.01398i −0.372612 0.227086i
955955 27.5671i 0.892051i
956956 −6.12800 11.8829i −0.198194 0.384320i
957957 0 0
958958 13.7835 + 8.40029i 0.445326 + 0.271401i
959959 −2.04275 −0.0659638
960960 1.13401 7.90901i 0.0366001 0.255262i
961961 17.3552 0.559845
962962 18.0084 29.5490i 0.580615 0.952698i
963963 −27.1545 −0.875043
964964 7.61957 3.92941i 0.245410 0.126558i
965965 23.3828i 0.752718i
966966 −7.73384 4.71333i −0.248832 0.151649i
967967 23.6696 0.761164 0.380582 0.924747i 0.375724π-0.375724\pi
0.380582 + 0.924747i 0.375724π0.375724\pi
968968 0 0
969969 −0.412063 −0.0132374
970970 −11.9298 7.27055i −0.383043 0.233443i
971971 53.9321i 1.73076i 0.501112 + 0.865382i 0.332924π0.332924\pi
−0.501112 + 0.865382i 0.667076π0.667076\pi
972972 27.2768 14.0666i 0.874903 0.451187i
973973 10.2443 0.328417
974974 2.94755 4.83646i 0.0944455 0.154970i
975975 −8.38321 −0.268478
976976 −4.38656 3.12195i −0.140410 0.0999311i
977977 −9.59586 −0.306999 −0.153499 0.988149i 0.549054π-0.549054\pi
−0.153499 + 0.988149i 0.549054π0.549054\pi
978978 −8.99601 5.48256i −0.287661 0.175313i
979979 0 0
980980 5.37494 + 10.4226i 0.171696 + 0.332938i
981981 21.9629i 0.701222i
982982 −13.5181 8.23851i −0.431380 0.262901i
983983 35.3025i 1.12597i −0.826466 0.562987i 0.809652π-0.809652\pi
0.826466 0.562987i 0.190348π-0.190348\pi
984984 0.862421 12.0912i 0.0274930 0.385452i
985985 4.70776i 0.150002i
986986 0.332584 + 0.202691i 0.0105916 + 0.00645500i
987987 −11.8262 −0.376431
988988 −50.2789 + 25.9288i −1.59959 + 0.824906i
989989 10.0631i 0.319987i
990990 0 0
991991 17.8021i 0.565502i 0.959193 + 0.282751i 0.0912471π0.0912471\pi
−0.959193 + 0.282751i 0.908753π0.908753\pi
992992 −8.23183 19.2060i −0.261361 0.609791i
993993 25.1634 0.798536
994994 8.35979 13.7171i 0.265156 0.435080i
995995 15.1912i 0.481594i
996996 −4.75543 + 2.45237i −0.150682 + 0.0777064i
997997 62.9390i 1.99330i −0.0817877 0.996650i 0.526063π-0.526063\pi
0.0817877 0.996650i 0.473937π-0.473937\pi
998998 28.9721 47.5386i 0.917094 1.50481i
999999 27.7739i 0.878727i
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 484.2.c.d.483.14 16
4.3 odd 2 inner 484.2.c.d.483.4 16
11.2 odd 10 44.2.g.a.7.3 yes 16
11.3 even 5 484.2.g.f.475.4 16
11.4 even 5 484.2.g.j.215.2 16
11.5 even 5 44.2.g.a.19.1 yes 16
11.6 odd 10 484.2.g.i.239.4 16
11.7 odd 10 484.2.g.f.215.3 16
11.8 odd 10 484.2.g.j.475.1 16
11.9 even 5 484.2.g.i.403.2 16
11.10 odd 2 inner 484.2.c.d.483.3 16
33.2 even 10 396.2.r.a.271.2 16
33.5 odd 10 396.2.r.a.19.4 16
44.3 odd 10 484.2.g.f.475.3 16
44.7 even 10 484.2.g.f.215.4 16
44.15 odd 10 484.2.g.j.215.1 16
44.19 even 10 484.2.g.j.475.2 16
44.27 odd 10 44.2.g.a.19.3 yes 16
44.31 odd 10 484.2.g.i.403.4 16
44.35 even 10 44.2.g.a.7.1 16
44.39 even 10 484.2.g.i.239.2 16
44.43 even 2 inner 484.2.c.d.483.13 16
88.5 even 10 704.2.u.c.63.2 16
88.13 odd 10 704.2.u.c.447.3 16
88.27 odd 10 704.2.u.c.63.3 16
88.35 even 10 704.2.u.c.447.2 16
132.35 odd 10 396.2.r.a.271.4 16
132.71 even 10 396.2.r.a.19.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
44.2.g.a.7.1 16 44.35 even 10
44.2.g.a.7.3 yes 16 11.2 odd 10
44.2.g.a.19.1 yes 16 11.5 even 5
44.2.g.a.19.3 yes 16 44.27 odd 10
396.2.r.a.19.2 16 132.71 even 10
396.2.r.a.19.4 16 33.5 odd 10
396.2.r.a.271.2 16 33.2 even 10
396.2.r.a.271.4 16 132.35 odd 10
484.2.c.d.483.3 16 11.10 odd 2 inner
484.2.c.d.483.4 16 4.3 odd 2 inner
484.2.c.d.483.13 16 44.43 even 2 inner
484.2.c.d.483.14 16 1.1 even 1 trivial
484.2.g.f.215.3 16 11.7 odd 10
484.2.g.f.215.4 16 44.7 even 10
484.2.g.f.475.3 16 44.3 odd 10
484.2.g.f.475.4 16 11.3 even 5
484.2.g.i.239.2 16 44.39 even 10
484.2.g.i.239.4 16 11.6 odd 10
484.2.g.i.403.2 16 11.9 even 5
484.2.g.i.403.4 16 44.31 odd 10
484.2.g.j.215.1 16 44.15 odd 10
484.2.g.j.215.2 16 11.4 even 5
484.2.g.j.475.1 16 11.8 odd 10
484.2.g.j.475.2 16 44.19 even 10
704.2.u.c.63.2 16 88.5 even 10
704.2.u.c.63.3 16 88.27 odd 10
704.2.u.c.447.2 16 88.35 even 10
704.2.u.c.447.3 16 88.13 odd 10