Properties

Label 630.2.bo.a.89.3
Level 630630
Weight 22
Character 630.89
Analytic conductor 5.0315.031
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] = [630,2,Mod(89,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 630=23257 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 630.bo (of order 66, degree 22, 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: 5.030575327345.03057532734
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ6)\Q(\zeta_{6})
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: x166x15+21x1454x13+113x12168x11+186x1084x9++390625 x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 89.3
Root 1.687601.46697i1.68760 - 1.46697i of defining polynomial
Character χ\chi == 630.89
Dual form 630.2.bo.a.269.3

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+(0.500000+0.866025i)q2+(0.5000000.866025i)q4+(1.687601.46697i)q5+(2.30608+1.29693i)q7+1.00000q8+(2.114230.728019i)q10+(1.111200.641550i)q11+6.14864q13+(0.02986662.64558i)q14+(0.500000+0.866025i)q16+(5.64871+3.26128i)q17+(5.22868+3.01878i)q19+(0.426635+2.19499i)q20+1.28310iq22+(1.43958+2.49343i)q23+(0.695987+4.95132i)q25+(3.07432+5.32488i)q26+(2.27621+1.34866i)q28+1.35052iq29+(7.49558+4.32758i)q31+(0.5000000.866025i)q326.52257iq34+(5.79429+1.19425i)q35+(8.25652+4.76690i)q37+(5.22868+3.01878i)q38+(1.687601.46697i)q40+8.71759q41+5.35859iq43+(1.111200.641550i)q44+(1.439582.49343i)q46+(0.698165+0.403086i)q47+(3.635975.98162i)q49+(4.635971.87292i)q50+(3.074325.32488i)q52+(3.33413+5.77488i)q53+(2.816390.547415i)q55+(2.30608+1.29693i)q56+(1.169590.675260i)q58+(0.7981101.38237i)q59+(5.502393.17681i)q618.65515iq62+1.00000q64+(10.37649.01988i)q65+(4.671882.69731i)q67+(5.64871+3.26128i)q68+(3.93140+4.42087i)q70+15.6787iq71+(6.2083710.7532i)q73+(8.25652+4.76690i)q746.03756iq76+(1.73046+2.92060i)q77+(5.59093+9.68377i)q79+(2.114230.728019i)q80+(4.35880+7.54966i)q823.74493iq83+(14.3170+2.78275i)q85+(4.640672.67929i)q86+(1.111200.641550i)q88+(1.819713.15183i)q89+(14.1792+7.97433i)q91+2.87917q92+(0.698165+0.403086i)q94+(4.3954512.7648i)q958.76818q97+(3.36225+6.13965i)q98+O(q100)q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.68760 - 1.46697i) q^{5} +(-2.30608 + 1.29693i) q^{7} +1.00000 q^{8} +(2.11423 - 0.728019i) q^{10} +(1.11120 - 0.641550i) q^{11} +6.14864 q^{13} +(0.0298666 - 2.64558i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.64871 + 3.26128i) q^{17} +(5.22868 + 3.01878i) q^{19} +(-0.426635 + 2.19499i) q^{20} +1.28310i q^{22} +(-1.43958 + 2.49343i) q^{23} +(0.695987 + 4.95132i) q^{25} +(-3.07432 + 5.32488i) q^{26} +(2.27621 + 1.34866i) q^{28} +1.35052i q^{29} +(-7.49558 + 4.32758i) q^{31} +(-0.500000 - 0.866025i) q^{32} -6.52257i q^{34} +(5.79429 + 1.19425i) q^{35} +(8.25652 + 4.76690i) q^{37} +(-5.22868 + 3.01878i) q^{38} +(-1.68760 - 1.46697i) q^{40} +8.71759 q^{41} +5.35859i q^{43} +(-1.11120 - 0.641550i) q^{44} +(-1.43958 - 2.49343i) q^{46} +(0.698165 + 0.403086i) q^{47} +(3.63597 - 5.98162i) q^{49} +(-4.63597 - 1.87292i) q^{50} +(-3.07432 - 5.32488i) q^{52} +(3.33413 + 5.77488i) q^{53} +(-2.81639 - 0.547415i) q^{55} +(-2.30608 + 1.29693i) q^{56} +(-1.16959 - 0.675260i) q^{58} +(-0.798110 - 1.38237i) q^{59} +(-5.50239 - 3.17681i) q^{61} -8.65515i q^{62} +1.00000 q^{64} +(-10.3764 - 9.01988i) q^{65} +(4.67188 - 2.69731i) q^{67} +(5.64871 + 3.26128i) q^{68} +(-3.93140 + 4.42087i) q^{70} +15.6787i q^{71} +(-6.20837 - 10.7532i) q^{73} +(-8.25652 + 4.76690i) q^{74} -6.03756i q^{76} +(-1.73046 + 2.92060i) q^{77} +(-5.59093 + 9.68377i) q^{79} +(2.11423 - 0.728019i) q^{80} +(-4.35880 + 7.54966i) q^{82} -3.74493i q^{83} +(14.3170 + 2.78275i) q^{85} +(-4.64067 - 2.67929i) q^{86} +(1.11120 - 0.641550i) q^{88} +(1.81971 - 3.15183i) q^{89} +(-14.1792 + 7.97433i) q^{91} +2.87917 q^{92} +(-0.698165 + 0.403086i) q^{94} +(-4.39545 - 12.7648i) q^{95} -8.76818 q^{97} +(3.36225 + 6.13965i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q8q28q46q5+16q8+6q108q16+24q198q236q25+12q318q32+4q3524q386q408q46+60q4728q49+12q50++20q98+O(q100) 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8} + 6 q^{10} - 8 q^{16} + 24 q^{19} - 8 q^{23} - 6 q^{25} + 12 q^{31} - 8 q^{32} + 4 q^{35} - 24 q^{38} - 6 q^{40} - 8 q^{46} + 60 q^{47} - 28 q^{49} + 12 q^{50}+ \cdots + 20 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/630Z)×\left(\mathbb{Z}/630\mathbb{Z}\right)^\times.

nn 127127 281281 451451
χ(n)\chi(n) 1-1 1-1 e(56)e\left(\frac{5}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.500000 + 0.866025i −0.353553 + 0.612372i
33 0 0
44 −0.500000 0.866025i −0.250000 0.433013i
55 −1.68760 1.46697i −0.754718 0.656050i
66 0 0
77 −2.30608 + 1.29693i −0.871614 + 0.490192i
88 1.00000 0.353553
99 0 0
1010 2.11423 0.728019i 0.668580 0.230220i
1111 1.11120 0.641550i 0.335038 0.193435i −0.323037 0.946386i 0.604704π-0.604704\pi
0.658076 + 0.752952i 0.271371π0.271371\pi
1212 0 0
1313 6.14864 1.70533 0.852663 0.522462i 0.174986π-0.174986\pi
0.852663 + 0.522462i 0.174986π0.174986\pi
1414 0.0298666 2.64558i 0.00798219 0.707062i
1515 0 0
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 −5.64871 + 3.26128i −1.37001 + 0.790977i −0.990929 0.134385i 0.957094π-0.957094\pi
−0.379084 + 0.925362i 0.623761π0.623761\pi
1818 0 0
1919 5.22868 + 3.01878i 1.19954 + 0.692555i 0.960453 0.278443i 0.0898183π-0.0898183\pi
0.239088 + 0.970998i 0.423152π0.423152\pi
2020 −0.426635 + 2.19499i −0.0953985 + 0.490815i
2121 0 0
2222 1.28310i 0.273558i
2323 −1.43958 + 2.49343i −0.300174 + 0.519917i −0.976175 0.216984i 0.930378π-0.930378\pi
0.676001 + 0.736901i 0.263711π0.263711\pi
2424 0 0
2525 0.695987 + 4.95132i 0.139197 + 0.990265i
2626 −3.07432 + 5.32488i −0.602923 + 1.04429i
2727 0 0
2828 2.27621 + 1.34866i 0.430163 + 0.254872i
2929 1.35052i 0.250785i 0.992107 + 0.125393i 0.0400191π0.0400191\pi
−0.992107 + 0.125393i 0.959981π0.959981\pi
3030 0 0
3131 −7.49558 + 4.32758i −1.34625 + 0.777255i −0.987716 0.156263i 0.950055π-0.950055\pi
−0.358530 + 0.933518i 0.616722π0.616722\pi
3232 −0.500000 0.866025i −0.0883883 0.153093i
3333 0 0
3434 6.52257i 1.11861i
3535 5.79429 + 1.19425i 0.979413 + 0.201866i
3636 0 0
3737 8.25652 + 4.76690i 1.35736 + 0.783674i 0.989268 0.146114i 0.0466766π-0.0466766\pi
0.368095 + 0.929788i 0.380010π0.380010\pi
3838 −5.22868 + 3.01878i −0.848203 + 0.489710i
3939 0 0
4040 −1.68760 1.46697i −0.266833 0.231949i
4141 8.71759 1.36146 0.680730 0.732535i 0.261663π-0.261663\pi
0.680730 + 0.732535i 0.261663π0.261663\pi
4242 0 0
4343 5.35859i 0.817177i 0.912719 + 0.408588i 0.133979π0.133979\pi
−0.912719 + 0.408588i 0.866021π0.866021\pi
4444 −1.11120 0.641550i −0.167519 0.0967173i
4545 0 0
4646 −1.43958 2.49343i −0.212255 0.367637i
4747 0.698165 + 0.403086i 0.101838 + 0.0587961i 0.550054 0.835129i 0.314607π-0.314607\pi
−0.448216 + 0.893925i 0.647940π0.647940\pi
4848 0 0
4949 3.63597 5.98162i 0.519424 0.854517i
5050 −4.63597 1.87292i −0.655625 0.264871i
5151 0 0
5252 −3.07432 5.32488i −0.426331 0.738427i
5353 3.33413 + 5.77488i 0.457978 + 0.793241i 0.998854 0.0478611i 0.0152405π-0.0152405\pi
−0.540876 + 0.841102i 0.681907π0.681907\pi
5454 0 0
5555 −2.81639 0.547415i −0.379762 0.0738134i
5656 −2.30608 + 1.29693i −0.308162 + 0.173309i
5757 0 0
5858 −1.16959 0.675260i −0.153574 0.0886660i
5959 −0.798110 1.38237i −0.103905 0.179969i 0.809385 0.587278i 0.199800π-0.199800\pi
−0.913290 + 0.407309i 0.866467π0.866467\pi
6060 0 0
6161 −5.50239 3.17681i −0.704509 0.406748i 0.104516 0.994523i 0.466671π-0.466671\pi
−0.809025 + 0.587775i 0.800004π0.800004\pi
6262 8.65515i 1.09921i
6363 0 0
6464 1.00000 0.125000
6565 −10.3764 9.01988i −1.28704 1.11878i
6666 0 0
6767 4.67188 2.69731i 0.570761 0.329529i −0.186692 0.982418i 0.559777π-0.559777\pi
0.757453 + 0.652889i 0.226443π0.226443\pi
6868 5.64871 + 3.26128i 0.685006 + 0.395489i
6969 0 0
7070 −3.93140 + 4.42087i −0.469892 + 0.528395i
7171 15.6787i 1.86072i 0.366650 + 0.930359i 0.380505π0.380505\pi
−0.366650 + 0.930359i 0.619495π0.619495\pi
7272 0 0
7373 −6.20837 10.7532i −0.726635 1.25857i −0.958298 0.285772i 0.907750π-0.907750\pi
0.231663 0.972796i 0.425583π-0.425583\pi
7474 −8.25652 + 4.76690i −0.959801 + 0.554141i
7575 0 0
7676 6.03756i 0.692555i
7777 −1.73046 + 2.92060i −0.197204 + 0.332834i
7878 0 0
7979 −5.59093 + 9.68377i −0.629028 + 1.08951i 0.358719 + 0.933446i 0.383214π0.383214\pi
−0.987747 + 0.156064i 0.950120π0.950120\pi
8080 2.11423 0.728019i 0.236379 0.0813949i
8181 0 0
8282 −4.35880 + 7.54966i −0.481349 + 0.833720i
8383 3.74493i 0.411059i −0.978651 0.205530i 0.934108π-0.934108\pi
0.978651 0.205530i 0.0658917π-0.0658917\pi
8484 0 0
8585 14.3170 + 2.78275i 1.55289 + 0.301832i
8686 −4.64067 2.67929i −0.500417 0.288916i
8787 0 0
8888 1.11120 0.641550i 0.118454 0.0683894i
8989 1.81971 3.15183i 0.192889 0.334093i −0.753318 0.657657i 0.771548π-0.771548\pi
0.946206 + 0.323564i 0.104881π0.104881\pi
9090 0 0
9191 −14.1792 + 7.97433i −1.48639 + 0.835937i
9292 2.87917 0.300174
9393 0 0
9494 −0.698165 + 0.403086i −0.0720102 + 0.0415751i
9595 −4.39545 12.7648i −0.450964 1.30964i
9696 0 0
9797 −8.76818 −0.890274 −0.445137 0.895463i 0.646845π-0.646845\pi
−0.445137 + 0.895463i 0.646845π0.646845\pi
9898 3.36225 + 6.13965i 0.339639 + 0.620198i
9999 0 0
100100 3.93998 3.07840i 0.393998 0.307840i
101101 0.853270 + 1.47791i 0.0849035 + 0.147057i 0.905350 0.424666i 0.139608π-0.139608\pi
−0.820447 + 0.571723i 0.806275π0.806275\pi
102102 0 0
103103 5.18220 8.97583i 0.510617 0.884415i −0.489307 0.872112i 0.662750π-0.662750\pi
0.999924 0.0123035i 0.00391643π-0.00391643\pi
104104 6.14864 0.602923
105105 0 0
106106 −6.66826 −0.647679
107107 5.75680 9.97106i 0.556531 0.963939i −0.441252 0.897383i 0.645466π-0.645466\pi
0.997783 0.0665560i 0.0212011π-0.0212011\pi
108108 0 0
109109 −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i 0.197202π-0.197202\pi
−0.909935 + 0.414751i 0.863869π0.863869\pi
110110 1.88227 2.16536i 0.179468 0.206459i
111111 0 0
112112 0.0298666 2.64558i 0.00282213 0.249984i
113113 13.3875 1.25939 0.629695 0.776843i 0.283180π-0.283180\pi
0.629695 + 0.776843i 0.283180π0.283180\pi
114114 0 0
115115 6.08724 2.09609i 0.567638 0.195461i
116116 1.16959 0.675260i 0.108593 0.0626963i
117117 0 0
118118 1.59622 0.146944
119119 8.79670 14.8467i 0.806392 1.36100i
120120 0 0
121121 −4.67683 + 8.10050i −0.425166 + 0.736409i
122122 5.50239 3.17681i 0.498163 0.287615i
123123 0 0
124124 7.49558 + 4.32758i 0.673123 + 0.388628i
125125 6.08890 9.37685i 0.544608 0.838691i
126126 0 0
127127 5.65313i 0.501634i −0.968035 0.250817i 0.919301π-0.919301\pi
0.968035 0.250817i 0.0806992π-0.0806992\pi
128128 −0.500000 + 0.866025i −0.0441942 + 0.0765466i
129129 0 0
130130 12.9997 4.47632i 1.14015 0.392599i
131131 −6.23366 + 10.7970i −0.544638 + 0.943340i 0.453992 + 0.891006i 0.349999π0.349999\pi
−0.998630 + 0.0523344i 0.983334π0.983334\pi
132132 0 0
133133 −15.9729 0.180321i −1.38502 0.0156358i
134134 5.39463i 0.466025i
135135 0 0
136136 −5.64871 + 3.26128i −0.484373 + 0.279653i
137137 0.0254843 + 0.0441401i 0.00217727 + 0.00377114i 0.867112 0.498113i 0.165974π-0.165974\pi
−0.864935 + 0.501884i 0.832640π0.832640\pi
138138 0 0
139139 1.05069i 0.0891184i −0.999007 0.0445592i 0.985812π-0.985812\pi
0.999007 0.0445592i 0.0141883π-0.0141883\pi
140140 −1.86289 5.61513i −0.157443 0.474565i
141141 0 0
142142 −13.5781 7.83934i −1.13945 0.657863i
143143 6.83235 3.94466i 0.571350 0.329869i
144144 0 0
145145 1.98118 2.27914i 0.164528 0.189272i
146146 12.4167 1.02762
147147 0 0
148148 9.53381i 0.783674i
149149 −7.12137 4.11153i −0.583406 0.336829i 0.179080 0.983835i 0.442688π-0.442688\pi
−0.762486 + 0.647005i 0.776021π0.776021\pi
150150 0 0
151151 2.13357 + 3.69546i 0.173628 + 0.300732i 0.939686 0.342040i 0.111118π-0.111118\pi
−0.766058 + 0.642772i 0.777784π0.777784\pi
152152 5.22868 + 3.01878i 0.424102 + 0.244855i
153153 0 0
154154 −1.66409 2.95892i −0.134096 0.238437i
155155 18.9980 + 3.69259i 1.52595 + 0.296596i
156156 0 0
157157 2.41601 + 4.18466i 0.192819 + 0.333972i 0.946183 0.323631i 0.104904π-0.104904\pi
−0.753364 + 0.657603i 0.771570π0.771570\pi
158158 −5.59093 9.68377i −0.444790 0.770399i
159159 0 0
160160 −0.426635 + 2.19499i −0.0337285 + 0.173529i
161161 0.0859910 7.61708i 0.00677704 0.600310i
162162 0 0
163163 9.31256 + 5.37661i 0.729416 + 0.421128i 0.818208 0.574922i 0.194968π-0.194968\pi
−0.0887927 + 0.996050i 0.528301π0.528301\pi
164164 −4.35880 7.54966i −0.340365 0.589529i
165165 0 0
166166 3.24320 + 1.87246i 0.251721 + 0.145331i
167167 18.9267i 1.46459i 0.680988 + 0.732295i 0.261551π0.261551\pi
−0.680988 + 0.732295i 0.738449π0.738449\pi
168168 0 0
169169 24.8057 1.90813
170170 −9.56842 + 11.0075i −0.733864 + 0.844235i
171171 0 0
172172 4.64067 2.67929i 0.353848 0.204294i
173173 −10.2568 5.92176i −0.779810 0.450223i 0.0565531 0.998400i 0.481989π-0.481989\pi
−0.836363 + 0.548176i 0.815322π0.815322\pi
174174 0 0
175175 −8.02650 10.5155i −0.606746 0.794896i
176176 1.28310i 0.0967173i
177177 0 0
178178 1.81971 + 3.15183i 0.136393 + 0.236239i
179179 −3.27843 + 1.89280i −0.245041 + 0.141475i −0.617492 0.786577i 0.711851π-0.711851\pi
0.372450 + 0.928052i 0.378518π0.378518\pi
180180 0 0
181181 19.0033i 1.41251i −0.707960 0.706253i 0.750384π-0.750384\pi
0.707960 0.706253i 0.249616π-0.249616\pi
182182 0.183639 16.2667i 0.0136122 1.20577i
183183 0 0
184184 −1.43958 + 2.49343i −0.106128 + 0.183818i
185185 −6.94079 20.1567i −0.510297 1.48195i
186186 0 0
187187 −4.18455 + 7.24785i −0.306005 + 0.530016i
188188 0.806172i 0.0587961i
189189 0 0
190190 13.2524 + 2.57583i 0.961428 + 0.186871i
191191 −2.44949 1.41421i −0.177239 0.102329i 0.408756 0.912644i 0.365963π-0.365963\pi
−0.585995 + 0.810315i 0.699296π0.699296\pi
192192 0 0
193193 3.06479 1.76946i 0.220608 0.127368i −0.385623 0.922656i 0.626014π-0.626014\pi
0.606232 + 0.795288i 0.292680π0.292680\pi
194194 4.38409 7.59347i 0.314759 0.545179i
195195 0 0
196196 −6.99822 0.158029i −0.499873 0.0112878i
197197 −2.36728 −0.168662 −0.0843308 0.996438i 0.526875π-0.526875\pi
−0.0843308 + 0.996438i 0.526875π0.526875\pi
198198 0 0
199199 −3.00000 + 1.73205i −0.212664 + 0.122782i −0.602549 0.798082i 0.705848π-0.705848\pi
0.389885 + 0.920864i 0.372515π0.372515\pi
200200 0.695987 + 4.95132i 0.0492137 + 0.350111i
201201 0 0
202202 −1.70654 −0.120072
203203 −1.75153 3.11440i −0.122933 0.218588i
204204 0 0
205205 −14.7118 12.7885i −1.02752 0.893185i
206206 5.18220 + 8.97583i 0.361061 + 0.625376i
207207 0 0
208208 −3.07432 + 5.32488i −0.213166 + 0.369214i
209209 7.74679 0.535856
210210 0 0
211211 −14.3620 −0.988721 −0.494361 0.869257i 0.664598π-0.664598\pi
−0.494361 + 0.869257i 0.664598π0.664598\pi
212212 3.33413 5.77488i 0.228989 0.396621i
213213 0 0
214214 5.75680 + 9.97106i 0.393527 + 0.681608i
215215 7.86090 9.04315i 0.536109 0.616738i
216216 0 0
217217 11.6728 19.7009i 0.792403 1.33739i
218218 2.00000 0.135457
219219 0 0
220220 0.934120 + 2.71277i 0.0629784 + 0.182895i
221221 −34.7319 + 20.0524i −2.33632 + 1.34887i
222222 0 0
223223 −13.5975 −0.910557 −0.455279 0.890349i 0.650460π-0.650460\pi
−0.455279 + 0.890349i 0.650460π0.650460\pi
224224 2.27621 + 1.34866i 0.152086 + 0.0901109i
225225 0 0
226226 −6.69375 + 11.5939i −0.445261 + 0.771215i
227227 −10.7006 + 6.17797i −0.710221 + 0.410046i −0.811143 0.584848i 0.801154π-0.801154\pi
0.100922 + 0.994894i 0.467821π0.467821\pi
228228 0 0
229229 −2.09008 1.20671i −0.138116 0.0797414i 0.429350 0.903138i 0.358743π-0.358743\pi
−0.567466 + 0.823397i 0.692076π0.692076\pi
230230 −1.22835 + 6.31975i −0.0809952 + 0.416712i
231231 0 0
232232 1.35052i 0.0886660i
233233 6.43780 11.1506i 0.421754 0.730500i −0.574357 0.818605i 0.694748π-0.694748\pi
0.996111 + 0.0881051i 0.0280811π0.0280811\pi
234234 0 0
235235 −0.586908 1.70444i −0.0382857 0.111185i
236236 −0.798110 + 1.38237i −0.0519525 + 0.0899844i
237237 0 0
238238 8.45929 + 15.0415i 0.548334 + 0.974997i
239239 27.2546i 1.76296i 0.472226 + 0.881478i 0.343451π0.343451\pi
−0.472226 + 0.881478i 0.656549π0.656549\pi
240240 0 0
241241 2.26690 1.30880i 0.146024 0.0843070i −0.425208 0.905096i 0.639799π-0.639799\pi
0.571232 + 0.820789i 0.306466π0.306466\pi
242242 −4.67683 8.10050i −0.300638 0.520720i
243243 0 0
244244 6.35361i 0.406748i
245245 −14.9109 + 4.76072i −0.952624 + 0.304151i
246246 0 0
247247 32.1492 + 18.5614i 2.04561 + 1.18103i
248248 −7.49558 + 4.32758i −0.475970 + 0.274801i
249249 0 0
250250 5.07614 + 9.96157i 0.321043 + 0.630025i
251251 26.7173 1.68638 0.843190 0.537615i 0.180675π-0.180675\pi
0.843190 + 0.537615i 0.180675π0.180675\pi
252252 0 0
253253 3.69426i 0.232256i
254254 4.89575 + 2.82656i 0.307187 + 0.177354i
255255 0 0
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 9.14632 + 5.28063i 0.570532 + 0.329397i 0.757362 0.652996i 0.226488π-0.226488\pi
−0.186830 + 0.982392i 0.559821π0.559821\pi
258258 0 0
259259 −25.2225 0.284743i −1.56725 0.0176930i
260260 −2.62322 + 13.4962i −0.162685 + 0.836999i
261261 0 0
262262 −6.23366 10.7970i −0.385117 0.667042i
263263 4.16587 + 7.21550i 0.256879 + 0.444927i 0.965404 0.260759i 0.0839726π-0.0839726\pi
−0.708526 + 0.705685i 0.750639π0.750639\pi
264264 0 0
265265 2.84491 14.6368i 0.174762 0.899130i
266266 8.14259 13.7427i 0.499254 0.842621i
267267 0 0
268268 −4.67188 2.69731i −0.285381 0.164765i
269269 −7.14171 12.3698i −0.435438 0.754201i 0.561893 0.827210i 0.310073π-0.310073\pi
−0.997331 + 0.0730091i 0.976740π0.976740\pi
270270 0 0
271271 −6.58566 3.80223i −0.400050 0.230969i 0.286456 0.958094i 0.407523π-0.407523\pi
−0.686506 + 0.727125i 0.740856π0.740856\pi
272272 6.52257i 0.395489i
273273 0 0
274274 −0.0509686 −0.00307912
275275 3.94990 + 5.05538i 0.238188 + 0.304851i
276276 0 0
277277 −10.4270 + 6.02002i −0.626497 + 0.361708i −0.779394 0.626534i 0.784473π-0.784473\pi
0.152897 + 0.988242i 0.451140π0.451140\pi
278278 0.909924 + 0.525345i 0.0545736 + 0.0315081i
279279 0 0
280280 5.79429 + 1.19425i 0.346275 + 0.0713704i
281281 12.7879i 0.762861i −0.924397 0.381431i 0.875431π-0.875431\pi
0.924397 0.381431i 0.124569π-0.124569\pi
282282 0 0
283283 7.77607 + 13.4685i 0.462239 + 0.800622i 0.999072 0.0430666i 0.0137128π-0.0137128\pi
−0.536833 + 0.843689i 0.680379π0.680379\pi
284284 13.5781 7.83934i 0.805715 0.465180i
285285 0 0
286286 7.88931i 0.466505i
287287 −20.1034 + 11.3061i −1.18667 + 0.667376i
288288 0 0
289289 12.7719 22.1216i 0.751290 1.30127i
290290 0.983204 + 2.85532i 0.0577357 + 0.167670i
291291 0 0
292292 −6.20837 + 10.7532i −0.363317 + 0.629284i
293293 11.5536i 0.674967i −0.941331 0.337483i 0.890424π-0.890424\pi
0.941331 0.337483i 0.109576π-0.109576\pi
294294 0 0
295295 −0.681003 + 3.50369i −0.0396495 + 0.203993i
296296 8.25652 + 4.76690i 0.479900 + 0.277071i
297297 0 0
298298 7.12137 4.11153i 0.412530 0.238174i
299299 −8.85148 + 15.3312i −0.511894 + 0.886627i
300300 0 0
301301 −6.94969 12.3573i −0.400573 0.712263i
302302 −4.26715 −0.245547
303303 0 0
304304 −5.22868 + 3.01878i −0.299885 + 0.173139i
305305 4.62555 + 13.4330i 0.264858 + 0.769173i
306306 0 0
307307 −2.57617 −0.147030 −0.0735150 0.997294i 0.523422π-0.523422\pi
−0.0735150 + 0.997294i 0.523422π0.523422\pi
308308 3.39455 + 0.0383219i 0.193422 + 0.00218359i
309309 0 0
310310 −12.6969 + 14.6064i −0.721133 + 0.829590i
311311 12.3570 + 21.4030i 0.700702 + 1.21365i 0.968220 + 0.250098i 0.0804629π0.0804629\pi
−0.267519 + 0.963553i 0.586204π0.586204\pi
312312 0 0
313313 4.50087 7.79573i 0.254404 0.440641i −0.710329 0.703869i 0.751454π-0.751454\pi
0.964733 + 0.263229i 0.0847874π0.0847874\pi
314314 −4.83203 −0.272687
315315 0 0
316316 11.1819 0.629028
317317 −11.9529 + 20.7031i −0.671344 + 1.16280i 0.306180 + 0.951974i 0.400949π0.400949\pi
−0.977523 + 0.210828i 0.932384π0.932384\pi
318318 0 0
319319 0.866426 + 1.50069i 0.0485106 + 0.0840227i
320320 −1.68760 1.46697i −0.0943397 0.0820062i
321321 0 0
322322 6.55359 + 3.88301i 0.365217 + 0.216392i
323323 −39.3804 −2.19118
324324 0 0
325325 4.27937 + 30.4439i 0.237377 + 1.68872i
326326 −9.31256 + 5.37661i −0.515775 + 0.297783i
327327 0 0
328328 8.71759 0.481349
329329 −2.13279 0.0240776i −0.117585 0.00132744i
330330 0 0
331331 −2.18364 + 3.78217i −0.120024 + 0.207887i −0.919777 0.392442i 0.871630π-0.871630\pi
0.799753 + 0.600329i 0.204964π0.204964\pi
332332 −3.24320 + 1.87246i −0.177994 + 0.102765i
333333 0 0
334334 −16.3910 9.46334i −0.896874 0.517811i
335335 −11.8412 2.30154i −0.646951 0.125746i
336336 0 0
337337 19.5159i 1.06310i 0.847028 + 0.531549i 0.178390π0.178390\pi
−0.847028 + 0.531549i 0.821610π0.821610\pi
338338 −12.4029 + 21.4824i −0.674627 + 1.16849i
339339 0 0
340340 −4.74855 13.7902i −0.257526 0.747881i
341341 −5.55271 + 9.61758i −0.300696 + 0.520821i
342342 0 0
343343 −0.627092 + 18.5096i −0.0338598 + 0.999427i
344344 5.35859i 0.288916i
345345 0 0
346346 10.2568 5.92176i 0.551409 0.318356i
347347 13.4574 + 23.3088i 0.722429 + 1.25128i 0.960024 + 0.279919i 0.0903075π0.0903075\pi
−0.237595 + 0.971364i 0.576359π0.576359\pi
348348 0 0
349349 10.3821i 0.555741i −0.960619 0.277870i 0.910371π-0.910371\pi
0.960619 0.277870i 0.0896286π-0.0896286\pi
350350 13.1199 1.69341i 0.701289 0.0905167i
351351 0 0
352352 −1.11120 0.641550i −0.0592270 0.0341947i
353353 −0.146316 + 0.0844756i −0.00778761 + 0.00449618i −0.503889 0.863769i 0.668098π-0.668098\pi
0.496101 + 0.868265i 0.334765π0.334765\pi
354354 0 0
355355 23.0002 26.4594i 1.22072 1.40432i
356356 −3.63941 −0.192889
357357 0 0
358358 3.78561i 0.200075i
359359 −32.6198 18.8330i −1.72161 0.993970i −0.915631 0.402021i 0.868308π-0.868308\pi
−0.805975 0.591949i 0.798359π-0.798359\pi
360360 0 0
361361 8.72604 + 15.1139i 0.459265 + 0.795471i
362362 16.4574 + 9.50166i 0.864979 + 0.499396i
363363 0 0
364364 13.9956 + 8.29240i 0.733568 + 0.434640i
365365 −5.29741 + 27.2546i −0.277279 + 1.42657i
366366 0 0
367367 −7.57787 13.1253i −0.395562 0.685133i 0.597611 0.801786i 0.296117π-0.296117\pi
−0.993173 + 0.116653i 0.962783π0.962783\pi
368368 −1.43958 2.49343i −0.0750435 0.129979i
369369 0 0
370370 20.9266 + 4.06745i 1.08792 + 0.211457i
371371 −15.1784 8.99319i −0.788021 0.466903i
372372 0 0
373373 −10.4270 6.02002i −0.539889 0.311705i 0.205145 0.978732i 0.434233π-0.434233\pi
−0.745034 + 0.667027i 0.767567π0.767567\pi
374374 −4.18455 7.24785i −0.216378 0.374778i
375375 0 0
376376 0.698165 + 0.403086i 0.0360051 + 0.0207876i
377377 8.30386i 0.427671i
378378 0 0
379379 18.0918 0.929312 0.464656 0.885491i 0.346178π-0.346178\pi
0.464656 + 0.885491i 0.346178π0.346178\pi
380380 −8.85692 + 10.1890i −0.454351 + 0.522684i
381381 0 0
382382 2.44949 1.41421i 0.125327 0.0723575i
383383 −25.2480 14.5769i −1.29011 0.744846i −0.311437 0.950267i 0.600810π-0.600810\pi
−0.978674 + 0.205421i 0.934144π0.934144\pi
384384 0 0
385385 7.20477 2.39027i 0.367189 0.121819i
386386 3.53892i 0.180126i
387387 0 0
388388 4.38409 + 7.59347i 0.222568 + 0.385500i
389389 17.0297 9.83207i 0.863438 0.498506i −0.00172432 0.999999i 0.500549π-0.500549\pi
0.865162 + 0.501493i 0.167216π0.167216\pi
390390 0 0
391391 18.7796i 0.949723i
392392 3.63597 5.98162i 0.183644 0.302117i
393393 0 0
394394 1.18364 2.05012i 0.0596309 0.103284i
395395 23.6411 8.14060i 1.18951 0.409598i
396396 0 0
397397 2.84227 4.92295i 0.142649 0.247076i −0.785844 0.618425i 0.787771π-0.787771\pi
0.928493 + 0.371349i 0.121105π0.121105\pi
398398 3.46410i 0.173640i
399399 0 0
400400 −4.63597 1.87292i −0.231798 0.0936460i
401401 −8.84787 5.10832i −0.441842 0.255097i 0.262537 0.964922i 0.415441π-0.415441\pi
−0.704378 + 0.709825i 0.748774π0.748774\pi
402402 0 0
403403 −46.0876 + 26.6087i −2.29579 + 1.32547i
404404 0.853270 1.47791i 0.0424518 0.0735286i
405405 0 0
406406 3.57291 + 0.0403355i 0.177321 + 0.00200182i
407407 12.2328 0.606359
408408 0 0
409409 12.0969 6.98414i 0.598153 0.345344i −0.170162 0.985416i 0.554429π-0.554429\pi
0.768314 + 0.640073i 0.221096π0.221096\pi
410410 18.4310 6.34657i 0.910244 0.313435i
411411 0 0
412412 −10.3644 −0.510617
413413 3.63333 + 2.15275i 0.178784 + 0.105930i
414414 0 0
415415 −5.49370 + 6.31994i −0.269675 + 0.310234i
416416 −3.07432 5.32488i −0.150731 0.261074i
417417 0 0
418418 −3.87339 + 6.70891i −0.189454 + 0.328144i
419419 11.3181 0.552924 0.276462 0.961025i 0.410838π-0.410838\pi
0.276462 + 0.961025i 0.410838π0.410838\pi
420420 0 0
421421 −13.9099 −0.677928 −0.338964 0.940799i 0.610077π-0.610077\pi
−0.338964 + 0.940799i 0.610077π0.610077\pi
422422 7.18100 12.4379i 0.349566 0.605466i
423423 0 0
424424 3.33413 + 5.77488i 0.161920 + 0.280453i
425425 −20.0791 25.6988i −0.973979 1.24657i
426426 0 0
427427 16.8090 + 0.189761i 0.813445 + 0.00918318i
428428 −11.5136 −0.556531
429429 0 0
430430 3.90115 + 11.3293i 0.188130 + 0.546348i
431431 22.5947 13.0451i 1.08835 0.628359i 0.155213 0.987881i 0.450394π-0.450394\pi
0.933137 + 0.359522i 0.117060π0.117060\pi
432432 0 0
433433 8.42614 0.404935 0.202467 0.979289i 0.435104π-0.435104\pi
0.202467 + 0.979289i 0.435104π0.435104\pi
434434 11.2251 + 19.9594i 0.538822 + 0.958083i
435435 0 0
436436 −1.00000 + 1.73205i −0.0478913 + 0.0829502i
437437 −15.0542 + 8.69157i −0.720142 + 0.415774i
438438 0 0
439439 −23.9529 13.8292i −1.14321 0.660033i −0.195987 0.980606i 0.562791π-0.562791\pi
−0.947224 + 0.320573i 0.896125π0.896125\pi
440440 −2.81639 0.547415i −0.134266 0.0260970i
441441 0 0
442442 40.1049i 1.90759i
443443 −1.17861 + 2.04142i −0.0559975 + 0.0969906i −0.892665 0.450720i 0.851167π-0.851167\pi
0.836668 + 0.547711i 0.184501π0.184501\pi
444444 0 0
445445 −7.69458 + 2.64956i −0.364758 + 0.125601i
446446 6.79876 11.7758i 0.321931 0.557600i
447447 0 0
448448 −2.30608 + 1.29693i −0.108952 + 0.0612740i
449449 12.8021i 0.604169i −0.953281 0.302084i 0.902318π-0.902318\pi
0.953281 0.302084i 0.0976824π-0.0976824\pi
450450 0 0
451451 9.68696 5.59277i 0.456141 0.263353i
452452 −6.69375 11.5939i −0.314847 0.545332i
453453 0 0
454454 12.3559i 0.579893i
455455 35.6270 + 7.34304i 1.67022 + 0.344247i
456456 0 0
457457 29.8989 + 17.2621i 1.39861 + 0.807488i 0.994247 0.107111i 0.0341601π-0.0341601\pi
0.404363 + 0.914599i 0.367493π0.367493\pi
458458 2.09008 1.20671i 0.0976628 0.0563857i
459459 0 0
460460 −4.85888 4.22366i −0.226547 0.196929i
461461 20.2692 0.944032 0.472016 0.881590i 0.343526π-0.343526\pi
0.472016 + 0.881590i 0.343526π0.343526\pi
462462 0 0
463463 13.1246i 0.609952i −0.952360 0.304976i 0.901352π-0.901352\pi
0.952360 0.304976i 0.0986485π-0.0986485\pi
464464 −1.16959 0.675260i −0.0542966 0.0313482i
465465 0 0
466466 6.43780 + 11.1506i 0.298225 + 0.516541i
467467 1.32647 + 0.765836i 0.0613816 + 0.0354387i 0.530377 0.847762i 0.322050π-0.322050\pi
−0.468995 + 0.883201i 0.655384π0.655384\pi
468468 0 0
469469 −7.27550 + 12.2793i −0.335951 + 0.567005i
470470 1.76954 + 0.343941i 0.0816228 + 0.0158648i
471471 0 0
472472 −0.798110 1.38237i −0.0367360 0.0636286i
473473 3.43780 + 5.95444i 0.158070 + 0.273786i
474474 0 0
475475 −11.3079 + 27.9899i −0.518840 + 1.28426i
476476 −17.2560 0.194807i −0.790927 0.00892896i
477477 0 0
478478 −23.6032 13.6273i −1.07959 0.623299i
479479 14.6585 + 25.3893i 0.669764 + 1.16007i 0.977970 + 0.208746i 0.0669382π0.0669382\pi
−0.308205 + 0.951320i 0.599728π0.599728\pi
480480 0 0
481481 50.7663 + 29.3100i 2.31475 + 1.33642i
482482 2.61759i 0.119228i
483483 0 0
484484 9.35366 0.425166
485485 14.7972 + 12.8627i 0.671905 + 0.584064i
486486 0 0
487487 −7.09743 + 4.09770i −0.321615 + 0.185685i −0.652112 0.758122i 0.726117π-0.726117\pi
0.330497 + 0.943807i 0.392784π0.392784\pi
488488 −5.50239 3.17681i −0.249082 0.143807i
489489 0 0
490490 3.33256 15.2936i 0.150550 0.690894i
491491 40.4383i 1.82495i −0.409129 0.912477i 0.634167π-0.634167\pi
0.409129 0.912477i 0.365833π-0.365833\pi
492492 0 0
493493 −4.40443 7.62869i −0.198366 0.343579i
494494 −32.1492 + 18.5614i −1.44646 + 0.835116i
495495 0 0
496496 8.65515i 0.388628i
497497 −20.3341 36.1562i −0.912109 1.62183i
498498 0 0
499499 −8.72450 + 15.1113i −0.390562 + 0.676474i −0.992524 0.122051i 0.961053π-0.961053\pi
0.601961 + 0.798525i 0.294386π0.294386\pi
500500 −11.1650 0.584722i −0.499316 0.0261496i
501501 0 0
502502 −13.3586 + 23.1379i −0.596226 + 1.03269i
503503 1.91949i 0.0855860i −0.999084 0.0427930i 0.986374π-0.986374\pi
0.999084 0.0427930i 0.0136256π-0.0136256\pi
504504 0 0
505505 0.728069 3.74584i 0.0323987 0.166688i
506506 −3.19932 1.84713i −0.142227 0.0821149i
507507 0 0
508508 −4.89575 + 2.82656i −0.217214 + 0.125408i
509509 −5.54549 + 9.60508i −0.245800 + 0.425737i −0.962356 0.271792i 0.912384π-0.912384\pi
0.716556 + 0.697529i 0.245717π0.245717\pi
510510 0 0
511511 28.2631 + 16.7459i 1.25029 + 0.740796i
512512 1.00000 0.0441942
513513 0 0
514514 −9.14632 + 5.28063i −0.403427 + 0.232919i
515515 −21.9128 + 7.54547i −0.965592 + 0.332493i
516516 0 0
517517 1.03440 0.0454928
518518 12.8578 21.7009i 0.564941 0.953484i
519519 0 0
520520 −10.3764 9.01988i −0.455037 0.395548i
521521 −19.8706 34.4168i −0.870546 1.50783i −0.861433 0.507871i 0.830433π-0.830433\pi
−0.00911254 0.999958i 0.502901π-0.502901\pi
522522 0 0
523523 15.6404 27.0900i 0.683907 1.18456i −0.289872 0.957065i 0.593613π-0.593613\pi
0.973779 0.227496i 0.0730538π-0.0730538\pi
524524 12.4673 0.544638
525525 0 0
526526 −8.33174 −0.363281
527527 28.2269 48.8904i 1.22958 2.12970i
528528 0 0
529529 7.35519 + 12.7396i 0.319791 + 0.553894i
530530 11.2534 + 9.78215i 0.488815 + 0.424909i
531531 0 0
532532 7.83026 + 13.9231i 0.339485 + 0.603641i
533533 53.6013 2.32173
534534 0 0
535535 −24.3424 + 8.38211i −1.05242 + 0.362390i
536536 4.67188 2.69731i 0.201795 0.116506i
537537 0 0
538538 14.2834 0.615802
539539 0.202767 8.97941i 0.00873380 0.386771i
540540 0 0
541541 12.3987 21.4752i 0.533061 0.923290i −0.466193 0.884683i 0.654375π-0.654375\pi
0.999254 0.0386065i 0.0122919π-0.0122919\pi
542542 6.58566 3.80223i 0.282878 0.163320i
543543 0 0
544544 5.64871 + 3.26128i 0.242186 + 0.139826i
545545 −0.853270 + 4.38998i −0.0365501 + 0.188046i
546546 0 0
547547 40.5380i 1.73328i −0.498934 0.866640i 0.666275π-0.666275\pi
0.498934 0.866640i 0.333725π-0.333725\pi
548548 0.0254843 0.0441401i 0.00108863 0.00188557i
549549 0 0
550550 −6.35304 + 0.893021i −0.270895 + 0.0380785i
551551 −4.07692 + 7.06144i −0.173683 + 0.300827i
552552 0 0
553553 0.333964 29.5825i 0.0142016 1.25798i
554554 12.0400i 0.511532i
555555 0 0
556556 −0.909924 + 0.525345i −0.0385894 + 0.0222796i
557557 11.8732 + 20.5650i 0.503084 + 0.871367i 0.999994 + 0.00356477i 0.00113470π0.00113470\pi
−0.496910 + 0.867802i 0.665532π0.665532\pi
558558 0 0
559559 32.9480i 1.39355i
560560 −3.93140 + 4.42087i −0.166132 + 0.186816i
561561 0 0
562562 11.0746 + 6.39394i 0.467155 + 0.269712i
563563 7.29944 4.21434i 0.307635 0.177613i −0.338233 0.941062i 0.609829π-0.609829\pi
0.645868 + 0.763449i 0.276496π0.276496\pi
564564 0 0
565565 −22.5927 19.6391i −0.950483 0.826222i
566566 −15.5521 −0.653705
567567 0 0
568568 15.6787i 0.657863i
569569 20.3139 + 11.7283i 0.851605 + 0.491674i 0.861192 0.508280i 0.169718π-0.169718\pi
−0.00958727 + 0.999954i 0.503052π0.503052\pi
570570 0 0
571571 −7.67946 13.3012i −0.321376 0.556639i 0.659397 0.751795i 0.270812π-0.270812\pi
−0.980772 + 0.195157i 0.937479π0.937479\pi
572572 −6.83235 3.94466i −0.285675 0.164934i
573573 0 0
574574 0.260365 23.0631i 0.0108674 0.962636i
575575 −13.3477 5.39245i −0.556639 0.224881i
576576 0 0
577577 −7.12041 12.3329i −0.296426 0.513426i 0.678889 0.734241i 0.262462π-0.262462\pi
−0.975316 + 0.220815i 0.929128π0.929128\pi
578578 12.7719 + 22.1216i 0.531242 + 0.920139i
579579 0 0
580580 −2.96438 0.576179i −0.123089 0.0239245i
581581 4.85690 + 8.63609i 0.201498 + 0.358285i
582582 0 0
583583 7.40975 + 4.27802i 0.306881 + 0.177178i
584584 −6.20837 10.7532i −0.256904 0.444971i
585585 0 0
586586 10.0057 + 5.77679i 0.413331 + 0.238637i
587587 12.5249i 0.516958i 0.966017 + 0.258479i 0.0832212π0.0832212\pi
−0.966017 + 0.258479i 0.916779π0.916779\pi
588588 0 0
589589 −52.2560 −2.15317
590590 −2.69378 2.34161i −0.110901 0.0964025i
591591 0 0
592592 −8.25652 + 4.76690i −0.339341 + 0.195919i
593593 12.7436 + 7.35750i 0.523316 + 0.302136i 0.738290 0.674483i 0.235634π-0.235634\pi
−0.214975 + 0.976620i 0.568967π0.568967\pi
594594 0 0
595595 −36.6250 + 12.1508i −1.50148 + 0.498135i
596596 8.22305i 0.336829i
597597 0 0
598598 −8.85148 15.3312i −0.361964 0.626940i
599599 23.9304 13.8162i 0.977769 0.564515i 0.0761732 0.997095i 0.475730π-0.475730\pi
0.901596 + 0.432579i 0.142396π0.142396\pi
600600 0 0
601601 8.82137i 0.359831i −0.983682 0.179916i 0.942418π-0.942418\pi
0.983682 0.179916i 0.0575825π-0.0575825\pi
602602 14.1766 + 0.160043i 0.577794 + 0.00652286i
603603 0 0
604604 2.13357 3.69546i 0.0868139 0.150366i
605605 19.7758 6.80963i 0.804002 0.276851i
606606 0 0
607607 −13.2677 + 22.9803i −0.538519 + 0.932743i 0.460465 + 0.887678i 0.347683π0.347683\pi
−0.998984 + 0.0450649i 0.985651π0.985651\pi
608608 6.03756i 0.244855i
609609 0 0
610610 −13.9461 2.71067i −0.564662 0.109752i
611611 4.29276 + 2.47843i 0.173667 + 0.100266i
612612 0 0
613613 0.791273 0.456842i 0.0319592 0.0184517i −0.483935 0.875104i 0.660793π-0.660793\pi
0.515894 + 0.856652i 0.327460π0.327460\pi
614614 1.28809 2.23103i 0.0519830 0.0900371i
615615 0 0
616616 −1.73046 + 2.92060i −0.0697223 + 0.117674i
617617 −35.0558 −1.41129 −0.705646 0.708565i 0.749343π-0.749343\pi
−0.705646 + 0.708565i 0.749343π0.749343\pi
618618 0 0
619619 16.5382 9.54835i 0.664727 0.383781i −0.129348 0.991599i 0.541289π-0.541289\pi
0.794076 + 0.607819i 0.207955π0.207955\pi
620620 −6.30111 18.2990i −0.253059 0.734906i
621621 0 0
622622 −24.7140 −0.990942
623623 −0.108697 + 9.62837i −0.00435485 + 0.385753i
624624 0 0
625625 −24.0312 + 6.89212i −0.961248 + 0.275685i
626626 4.50087 + 7.79573i 0.179891 + 0.311580i
627627 0 0
628628 2.41601 4.18466i 0.0964095 0.166986i
629629 −62.1849 −2.47947
630630 0 0
631631 21.5350 0.857296 0.428648 0.903472i 0.358990π-0.358990\pi
0.428648 + 0.903472i 0.358990π0.358990\pi
632632 −5.59093 + 9.68377i −0.222395 + 0.385200i
633633 0 0
634634 −11.9529 20.7031i −0.474712 0.822225i
635635 −8.29298 + 9.54022i −0.329097 + 0.378592i
636636 0 0
637637 22.3562 36.7788i 0.885786 1.45723i
638638 −1.73285 −0.0686043
639639 0 0
640640 2.11423 0.728019i 0.0835725 0.0287775i
641641 28.6767 16.5565i 1.13266 0.653943i 0.188060 0.982158i 0.439780π-0.439780\pi
0.944603 + 0.328214i 0.106447π0.106447\pi
642642 0 0
643643 −3.31191 −0.130609 −0.0653044 0.997865i 0.520802π-0.520802\pi
−0.0653044 + 0.997865i 0.520802π0.520802\pi
644644 −6.63958 + 3.73407i −0.261636 + 0.147143i
645645 0 0
646646 19.6902 34.1044i 0.774700 1.34182i
647647 20.2077 11.6669i 0.794447 0.458674i −0.0470789 0.998891i 0.514991π-0.514991\pi
0.841526 + 0.540217i 0.181658π0.181658\pi
648648 0 0
649649 −1.77371 1.02405i −0.0696244 0.0401977i
650650 −28.5049 11.5159i −1.11805 0.451691i
651651 0 0
652652 10.7532i 0.421128i
653653 8.73019 15.1211i 0.341639 0.591735i −0.643099 0.765783i 0.722351π-0.722351\pi
0.984737 + 0.174048i 0.0556848π0.0556848\pi
654654 0 0
655655 26.3589 9.07644i 1.02993 0.354646i
656656 −4.35880 + 7.54966i −0.170182 + 0.294765i
657657 0 0
658658 1.08725 1.83501i 0.0423854 0.0715363i
659659 1.29864i 0.0505877i 0.999680 + 0.0252939i 0.00805215π0.00805215\pi
−0.999680 + 0.0252939i 0.991948π0.991948\pi
660660 0 0
661661 4.39869 2.53959i 0.171089 0.0987785i −0.412010 0.911179i 0.635173π-0.635173\pi
0.583099 + 0.812401i 0.301840π0.301840\pi
662662 −2.18364 3.78217i −0.0848695 0.146998i
663663 0 0
664664 3.74493i 0.145331i
665665 26.6913 + 23.7360i 1.03504 + 0.920444i
666666 0 0
667667 −3.36743 1.94419i −0.130387 0.0752793i
668668 16.3910 9.46334i 0.634186 0.366147i
669669 0 0
670670 7.91377 9.10397i 0.305735 0.351717i
671671 −8.15232 −0.314717
672672 0 0
673673 18.4124i 0.709747i 0.934914 + 0.354873i 0.115476π0.115476\pi
−0.934914 + 0.354873i 0.884524π0.884524\pi
674674 −16.9012 9.75794i −0.651012 0.375862i
675675 0 0
676676 −12.4029 21.4824i −0.477033 0.826246i
677677 35.7491 + 20.6397i 1.37395 + 0.793250i 0.991423 0.130695i 0.0417208π-0.0417208\pi
0.382526 + 0.923945i 0.375054π0.375054\pi
678678 0 0
679679 20.2201 11.3717i 0.775976 0.436405i
680680 14.3170 + 2.78275i 0.549031 + 0.106714i
681681 0 0
682682 −5.55271 9.61758i −0.212624 0.368276i
683683 −11.4896 19.9007i −0.439639 0.761477i 0.558022 0.829826i 0.311560π-0.311560\pi
−0.997662 + 0.0683485i 0.978227π0.978227\pi
684684 0 0
685685 0.0217450 0.111876i 0.000830833 0.00427454i
686686 −15.7163 9.79790i −0.600050 0.374085i
687687 0 0
688688 −4.64067 2.67929i −0.176924 0.102147i
689689 20.5004 + 35.5077i 0.781001 + 1.35273i
690690 0 0
691691 11.0048 + 6.35361i 0.418642 + 0.241703i 0.694496 0.719497i 0.255627π-0.255627\pi
−0.275854 + 0.961199i 0.588961π0.588961\pi
692692 11.8435i 0.450223i
693693 0 0
694694 −26.9147 −1.02167
695695 −1.54133 + 1.77314i −0.0584661 + 0.0672592i
696696 0 0
697697 −49.2431 + 28.4305i −1.86522 + 1.07688i
698698 8.99116 + 5.19105i 0.340320 + 0.196484i
699699 0 0
700700 −5.09342 + 12.2089i −0.192513 + 0.461453i
701701 26.5441i 1.00256i −0.865286 0.501279i 0.832863π-0.832863\pi
0.865286 0.501279i 0.167137π-0.167137\pi
702702 0 0
703703 28.7804 + 49.8492i 1.08548 + 1.88010i
704704 1.11120 0.641550i 0.0418798 0.0241793i
705705 0 0
706706 0.168951i 0.00635856i
707707 −3.88444 2.30154i −0.146089 0.0865582i
708708 0 0
709709 −21.1766 + 36.6789i −0.795303 + 1.37751i 0.127343 + 0.991859i 0.459355π0.459355\pi
−0.922646 + 0.385647i 0.873978π0.873978\pi
710710 11.4144 + 33.1484i 0.428374 + 1.24404i
711711 0 0
712712 1.81971 3.15183i 0.0681964 0.118120i
713713 24.9196i 0.933248i
714714 0 0
715715 −17.3170 3.36586i −0.647618 0.125876i
716716 3.27843 + 1.89280i 0.122521 + 0.0707374i
717717 0 0
718718 32.6198 18.8330i 1.21736 0.702843i
719719 11.9507 20.6992i 0.445686 0.771951i −0.552413 0.833570i 0.686293π-0.686293\pi
0.998100 + 0.0616189i 0.0196263π0.0196263\pi
720720 0 0
721721 −0.309550 + 27.4199i −0.0115282 + 1.02117i
722722 −17.4521 −0.649499
723723 0 0
724724 −16.4574 + 9.50166i −0.611633 + 0.353126i
725725 −6.68686 + 0.939945i −0.248344 + 0.0349087i
726726 0 0
727727 −22.4529 −0.832731 −0.416365 0.909197i 0.636696π-0.636696\pi
−0.416365 + 0.909197i 0.636696π0.636696\pi
728728 −14.1792 + 7.97433i −0.525517 + 0.295548i
729729 0 0
730730 −20.9545 18.2150i −0.775560 0.674168i
731731 −17.4759 30.2691i −0.646368 1.11954i
732732 0 0
733733 13.7725 23.8547i 0.508700 0.881094i −0.491249 0.871019i 0.663460π-0.663460\pi
0.999949 0.0100750i 0.00320702π-0.00320702\pi
734734 15.1557 0.559409
735735 0 0
736736 2.87917 0.106128
737737 3.46092 5.99449i 0.127485 0.220810i
738738 0 0
739739 −15.5456 26.9258i −0.571856 0.990483i −0.996375 0.0850646i 0.972890π-0.972890\pi
0.424520 0.905419i 0.360443π-0.360443\pi
740740 −13.9858 + 16.0893i −0.514129 + 0.591453i
741741 0 0
742742 15.3775 8.64824i 0.564526 0.317487i
743743 1.12610 0.0413127 0.0206564 0.999787i 0.493424π-0.493424\pi
0.0206564 + 0.999787i 0.493424π0.493424\pi
744744 0 0
745745 5.98654 + 17.3855i 0.219330 + 0.636954i
746746 10.4270 6.02002i 0.381759 0.220409i
747747 0 0
748748 8.36910 0.306005
749749 −0.343872 + 30.4602i −0.0125648 + 1.11299i
750750 0 0
751751 4.77108 8.26375i 0.174099 0.301549i −0.765750 0.643138i 0.777632π-0.777632\pi
0.939849 + 0.341590i 0.110965π0.110965\pi
752752 −0.698165 + 0.403086i −0.0254595 + 0.0146990i
753753 0 0
754754 −7.19135 4.15193i −0.261894 0.151204i
755755 1.82051 9.36635i 0.0662553 0.340876i
756756 0 0
757757 33.1687i 1.20554i 0.797917 + 0.602768i 0.205935π0.205935\pi
−0.797917 + 0.602768i 0.794065π0.794065\pi
758758 −9.04589 + 15.6679i −0.328562 + 0.569085i
759759 0 0
760760 −4.39545 12.7648i −0.159440 0.463028i
761761 −2.17122 + 3.76067i −0.0787068 + 0.136324i −0.902692 0.430287i 0.858412π-0.858412\pi
0.823985 + 0.566611i 0.191746π0.191746\pi
762762 0 0
763763 4.55242 + 2.69731i 0.164809 + 0.0976493i
764764 2.82843i 0.102329i
765765 0 0
766766 25.2480 14.5769i 0.912246 0.526685i
767767 −4.90729 8.49967i −0.177192 0.306905i
768768 0 0
769769 46.1795i 1.66528i 0.553818 + 0.832638i 0.313170π0.313170\pi
−0.553818 + 0.832638i 0.686830π0.686830\pi
770770 −1.53235 + 7.43465i −0.0552220 + 0.267926i
771771 0 0
772772 −3.06479 1.76946i −0.110304 0.0636842i
773773 15.5663 8.98723i 0.559883 0.323248i −0.193216 0.981156i 0.561892π-0.561892\pi
0.753098 + 0.657908i 0.228558π0.228558\pi
774774 0 0
775775 −26.6441 34.1011i −0.957083 1.22495i
776776 −8.76818 −0.314759
777777 0 0
778778 19.6641i 0.704994i
779779 45.5815 + 26.3165i 1.63313 + 0.942886i
780780 0 0
781781 10.0587 + 17.4221i 0.359927 + 0.623412i
782782 16.2636 + 9.38978i 0.581584 + 0.335778i
783783 0 0
784784 3.36225 + 6.13965i 0.120080 + 0.219273i
785785 2.06151 10.6063i 0.0735785 0.378554i
786786 0 0
787787 −6.92087 11.9873i −0.246702 0.427301i 0.715907 0.698196i 0.246014π-0.246014\pi
−0.962609 + 0.270895i 0.912680π0.912680\pi
788788 1.18364 + 2.05012i 0.0421654 + 0.0730326i
789789 0 0
790790 −4.77057 + 24.5441i −0.169729 + 0.873239i
791791 −30.8726 + 17.3626i −1.09770 + 0.617342i
792792 0 0
793793 −33.8322 19.5330i −1.20142 0.693638i
794794 2.84227 + 4.92295i 0.100868 + 0.174709i
795795 0 0
796796 3.00000 + 1.73205i 0.106332 + 0.0613909i
797797 7.46138i 0.264296i −0.991230 0.132148i 0.957813π-0.957813\pi
0.991230 0.132148i 0.0421874π-0.0421874\pi
798798 0 0
799799 −5.25831 −0.186026
800800 3.93998 3.07840i 0.139299 0.108838i
801801 0 0
802802 8.84787 5.10832i 0.312429 0.180381i
803803 −13.7974 7.96596i −0.486901 0.281113i
804804 0 0
805805 −11.3192 + 12.7284i −0.398948 + 0.448618i
806806 53.2174i 1.87450i
807807 0 0
808808 0.853270 + 1.47791i 0.0300179 + 0.0519926i
809809 1.28750 0.743340i 0.0452662 0.0261344i −0.477196 0.878797i 0.658347π-0.658347\pi
0.522462 + 0.852662i 0.325014π0.325014\pi
810810 0 0
811811 31.5494i 1.10785i 0.832567 + 0.553925i 0.186871π0.186871\pi
−0.832567 + 0.553925i 0.813129π0.813129\pi
812812 −1.82139 + 3.07407i −0.0639182 + 0.107879i
813813 0 0
814814 −6.11641 + 10.5939i −0.214380 + 0.371317i
815815 −7.82854 22.7348i −0.274222 0.796366i
816816 0 0
817817 −16.1764 + 28.0183i −0.565940 + 0.980237i
818818 13.9683i 0.488390i
819819 0 0
820820 −3.71923 + 19.1350i −0.129881 + 0.668224i
821821 27.5430 + 15.9020i 0.961257 + 0.554982i 0.896560 0.442923i 0.146058π-0.146058\pi
0.0646976 + 0.997905i 0.479392π0.479392\pi
822822 0 0
823823 31.7287 18.3186i 1.10599 0.638545i 0.168204 0.985752i 0.446203π-0.446203\pi
0.937788 + 0.347207i 0.112870π0.112870\pi
824824 5.18220 8.97583i 0.180530 0.312688i
825825 0 0
826826 −3.68100 + 2.07018i −0.128078 + 0.0720308i
827827 −21.9864 −0.764541 −0.382271 0.924050i 0.624858π-0.624858\pi
−0.382271 + 0.924050i 0.624858π0.624858\pi
828828 0 0
829829 −21.0498 + 12.1531i −0.731090 + 0.422095i −0.818821 0.574049i 0.805372π-0.805372\pi
0.0877305 + 0.996144i 0.472039π0.472039\pi
830830 −2.72638 7.91766i −0.0946339 0.274826i
831831 0 0
832832 6.14864 0.213166
833833 −1.03076 + 45.6463i −0.0357136 + 1.58155i
834834 0 0
835835 27.7649 31.9406i 0.960844 1.10535i
836836 −3.87339 6.70891i −0.133964 0.232033i
837837 0 0
838838 −5.65904 + 9.80175i −0.195488 + 0.338596i
839839 −27.3914 −0.945655 −0.472827 0.881155i 0.656767π-0.656767\pi
−0.472827 + 0.881155i 0.656767π0.656767\pi
840840 0 0
841841 27.1761 0.937107
842842 6.95496 12.0463i 0.239684 0.415145i
843843 0 0
844844 7.18100 + 12.4379i 0.247180 + 0.428129i
845845 −41.8622 36.3893i −1.44010 1.25183i
846846 0 0
847847 0.279362 24.7459i 0.00959899 0.850278i
848848 −6.66826 −0.228989
849849 0 0
850850 32.2953 4.53962i 1.10772 0.155708i
851851 −23.7719 + 13.7247i −0.814890 + 0.470477i
852852 0 0
853853 22.6073 0.774060 0.387030 0.922067i 0.373501π-0.373501\pi
0.387030 + 0.922067i 0.373501π0.373501\pi
854854 −8.56884 + 14.4622i −0.293220 + 0.494885i
855855 0 0
856856 5.75680 9.97106i 0.196763 0.340804i
857857 −41.4461 + 23.9289i −1.41577 + 0.817396i −0.995924 0.0901984i 0.971250π-0.971250\pi
−0.419848 + 0.907595i 0.637917π0.637917\pi
858858 0 0
859859 41.5770 + 24.0045i 1.41859 + 0.819022i 0.996175 0.0873810i 0.0278498π-0.0278498\pi
0.422413 + 0.906403i 0.361183π0.361183\pi
860860 −11.7620 2.28616i −0.401082 0.0779574i
861861 0 0
862862 26.0901i 0.888634i
863863 −23.7785 + 41.1855i −0.809428 + 1.40197i 0.103832 + 0.994595i 0.466890π0.466890\pi
−0.913260 + 0.407376i 0.866444π0.866444\pi
864864 0 0
865865 8.62231 + 25.0400i 0.293167 + 0.851386i
866866 −4.21307 + 7.29726i −0.143166 + 0.247971i
867867 0 0
868868 −22.8979 0.258500i −0.777206 0.00877406i
869869 14.3474i 0.486703i
870870 0 0
871871 28.7257 16.5848i 0.973334 0.561955i
872872 −1.00000 1.73205i −0.0338643 0.0586546i
873873 0 0
874874 17.3831i 0.587993i
875875 −1.88039 + 29.5206i −0.0635689 + 0.997977i
876876 0 0
877877 32.0433 + 18.5002i 1.08202 + 0.624707i 0.931442 0.363890i 0.118552π-0.118552\pi
0.150583 + 0.988597i 0.451885π0.451885\pi
878878 23.9529 13.8292i 0.808372 0.466714i
879879 0 0
880880 1.88227 2.16536i 0.0634513 0.0729942i
881881 5.97213 0.201206 0.100603 0.994927i 0.467923π-0.467923\pi
0.100603 + 0.994927i 0.467923π0.467923\pi
882882 0 0
883883 11.0589i 0.372163i −0.982534 0.186081i 0.940421π-0.940421\pi
0.982534 0.186081i 0.0595788π-0.0595788\pi
884884 34.7319 + 20.0524i 1.16816 + 0.674437i
885885 0 0
886886 −1.17861 2.04142i −0.0395962 0.0685827i
887887 −5.15346 2.97535i −0.173036 0.0999026i 0.410980 0.911644i 0.365186π-0.365186\pi
−0.584017 + 0.811742i 0.698520π0.698520\pi
888888 0 0
889889 7.33169 + 13.0365i 0.245897 + 0.437231i
890890 1.55270 7.98848i 0.0520467 0.267774i
891891 0 0
892892 6.79876 + 11.7758i 0.227639 + 0.394283i
893893 2.43365 + 4.21521i 0.0814391 + 0.141057i
894894 0 0
895895 8.30937 + 1.61507i 0.277752 + 0.0539859i
896896 0.0298666 2.64558i 0.000997774 0.0883827i
897897 0 0
898898 11.0869 + 6.40105i 0.369976 + 0.213606i
899899 −5.84448 10.1229i −0.194924 0.337619i
900900 0 0
901901 −37.6671 21.7471i −1.25487 0.724500i
902902 11.1855i 0.372438i
903903 0 0
904904 13.3875 0.445261
905905 −27.8773 + 32.0700i −0.926674 + 1.06604i
906906 0 0
907907 47.9037 27.6572i 1.59062 0.918343i 0.597415 0.801932i 0.296195π-0.296195\pi
0.993201 0.116411i 0.0371388π-0.0371388\pi
908908 10.7006 + 6.17797i 0.355110 + 0.205023i
909909 0 0
910910 −24.1727 + 27.1823i −0.801319 + 0.901086i
911911 35.2080i 1.16649i −0.812295 0.583246i 0.801782π-0.801782\pi
0.812295 0.583246i 0.198218π-0.198218\pi
912912 0 0
913913 −2.40256 4.16135i −0.0795131 0.137721i
914914 −29.8989 + 17.2621i −0.988966 + 0.570980i
915915 0 0
916916 2.41341i 0.0797414i
917917 0.372357 32.9833i 0.0122963 1.08921i
918918 0 0
919919 25.4437 44.0698i 0.839311 1.45373i −0.0511601 0.998690i 0.516292π-0.516292\pi
0.890471 0.455039i 0.150375π-0.150375\pi
920920 6.08724 2.09609i 0.200690 0.0691060i
921921 0 0
922922 −10.1346 + 17.5537i −0.333766 + 0.578099i
923923 96.4026i 3.17313i
924924 0 0
925925 −17.8560 + 44.1984i −0.587103 + 1.45323i
926926 11.3662 + 6.56230i 0.373518 + 0.215651i
927927 0 0
928928 1.16959 0.675260i 0.0383935 0.0221665i
929929 29.8405 51.6853i 0.979036 1.69574i 0.313118 0.949714i 0.398627π-0.398627\pi
0.665918 0.746025i 0.268040π-0.268040\pi
930930 0 0
931931 37.0685 20.2998i 1.21487 0.665298i
932932 −12.8756 −0.421754
933933 0 0
934934 −1.32647 + 0.765836i −0.0434033 + 0.0250589i
935935 17.6942 6.09286i 0.578664 0.199258i
936936 0 0
937937 24.2579 0.792471 0.396235 0.918149i 0.370316π-0.370316\pi
0.396235 + 0.918149i 0.370316π0.370316\pi
938938 −6.99643 12.4404i −0.228442 0.406194i
939939 0 0
940940 −1.18263 + 1.36050i −0.0385732 + 0.0443745i
941941 15.0539 + 26.0742i 0.490744 + 0.849994i 0.999943 0.0106549i 0.00339164π-0.00339164\pi
−0.509199 + 0.860649i 0.670058π0.670058\pi
942942 0 0
943943 −12.5497 + 21.7367i −0.408675 + 0.707845i
944944 1.59622 0.0519525
945945 0 0
946946 −6.87560 −0.223545
947947 23.0812 39.9779i 0.750039 1.29911i −0.197764 0.980250i 0.563368π-0.563368\pi
0.947803 0.318857i 0.103299π-0.103299\pi
948948 0 0
949949 −38.1730 66.1176i −1.23915 2.14627i
950950 −18.5860 23.7878i −0.603011 0.771779i
951951 0 0
952952 8.79670 14.8467i 0.285103 0.481185i
953953 23.7121 0.768110 0.384055 0.923310i 0.374527π-0.374527\pi
0.384055 + 0.923310i 0.374527π0.374527\pi
954954 0 0
955955 2.05915 + 5.97996i 0.0666324 + 0.193507i
956956 23.6032 13.6273i 0.763382 0.440739i
957957 0 0
958958 −29.3170 −0.947190
959959 −0.116015 0.0687391i −0.00374632 0.00221970i
960960 0 0
961961 21.9558 38.0286i 0.708252 1.22673i
962962 −50.7663 + 29.3100i −1.63677 + 0.944991i
963963 0 0
964964 −2.26690 1.30880i −0.0730120 0.0421535i
965965 −7.76789 1.50983i −0.250057 0.0486030i
966966 0 0
967967 0.0922780i 0.00296746i 0.999999 + 0.00148373i 0.000472286π0.000472286\pi
−0.999999 + 0.00148373i 0.999528π0.999528\pi
968968 −4.67683 + 8.10050i −0.150319 + 0.260360i
969969 0 0
970970 −18.5380 + 6.38340i −0.595219 + 0.204959i
971971 19.8502 34.3816i 0.637024 1.10336i −0.349058 0.937101i 0.613498π-0.613498\pi
0.986082 0.166257i 0.0531683π-0.0531683\pi
972972 0 0
973973 1.36267 + 2.42297i 0.0436851 + 0.0776769i
974974 8.19540i 0.262598i
975975 0 0
976976 5.50239 3.17681i 0.176127 0.101687i
977977 −18.4035 31.8758i −0.588779 1.01980i −0.994393 0.105751i 0.966275π-0.966275\pi
0.405613 0.914045i 0.367058π-0.367058\pi
978978 0 0
979979 4.66973i 0.149245i
980980 11.5784 + 10.5329i 0.369857 + 0.336460i
981981 0 0
982982 35.0206 + 20.2191i 1.11755 + 0.645218i
983983 −54.1899 + 31.2865i −1.72839 + 0.997885i −0.831693 + 0.555235i 0.812628π0.812628\pi
−0.896694 + 0.442650i 0.854038π0.854038\pi
984984 0 0
985985 3.99502 + 3.47273i 0.127292 + 0.110650i
986986 8.80886 0.280531
987987 0 0
988988 37.1227i 1.18103i
989989 −13.3613 7.71414i −0.424864 0.245295i
990990 0 0
991991 17.4019 + 30.1410i 0.552791 + 0.957462i 0.998072 + 0.0620708i 0.0197704π0.0197704\pi
−0.445281 + 0.895391i 0.646896π0.646896\pi
992992 7.49558 + 4.32758i 0.237985 + 0.137401i
993993 0 0
994994 41.4793 + 0.468269i 1.31564 + 0.0148526i
995995 7.60367 + 1.47791i 0.241053 + 0.0468528i
996996 0 0
997997 −24.4316 42.3167i −0.773755 1.34018i −0.935492 0.353349i 0.885043π-0.885043\pi
0.161736 0.986834i 0.448291π-0.448291\pi
998998 −8.72450 15.1113i −0.276169 0.478339i
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 630.2.bo.a.89.3 yes 16
3.2 odd 2 630.2.bo.b.89.6 yes 16
5.2 odd 4 3150.2.bf.f.1601.7 32
5.3 odd 4 3150.2.bf.f.1601.10 32
5.4 even 2 630.2.bo.b.89.8 yes 16
7.2 even 3 4410.2.d.b.4409.8 16
7.3 odd 6 inner 630.2.bo.a.269.1 yes 16
7.5 odd 6 4410.2.d.b.4409.9 16
15.2 even 4 3150.2.bf.f.1601.9 32
15.8 even 4 3150.2.bf.f.1601.8 32
15.14 odd 2 inner 630.2.bo.a.89.1 16
21.2 odd 6 4410.2.d.a.4409.9 16
21.5 even 6 4410.2.d.a.4409.8 16
21.17 even 6 630.2.bo.b.269.8 yes 16
35.3 even 12 3150.2.bf.f.1151.8 32
35.9 even 6 4410.2.d.a.4409.7 16
35.17 even 12 3150.2.bf.f.1151.9 32
35.19 odd 6 4410.2.d.a.4409.10 16
35.24 odd 6 630.2.bo.b.269.6 yes 16
105.17 odd 12 3150.2.bf.f.1151.7 32
105.38 odd 12 3150.2.bf.f.1151.10 32
105.44 odd 6 4410.2.d.b.4409.10 16
105.59 even 6 inner 630.2.bo.a.269.3 yes 16
105.89 even 6 4410.2.d.b.4409.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.bo.a.89.1 16 15.14 odd 2 inner
630.2.bo.a.89.3 yes 16 1.1 even 1 trivial
630.2.bo.a.269.1 yes 16 7.3 odd 6 inner
630.2.bo.a.269.3 yes 16 105.59 even 6 inner
630.2.bo.b.89.6 yes 16 3.2 odd 2
630.2.bo.b.89.8 yes 16 5.4 even 2
630.2.bo.b.269.6 yes 16 35.24 odd 6
630.2.bo.b.269.8 yes 16 21.17 even 6
3150.2.bf.f.1151.7 32 105.17 odd 12
3150.2.bf.f.1151.8 32 35.3 even 12
3150.2.bf.f.1151.9 32 35.17 even 12
3150.2.bf.f.1151.10 32 105.38 odd 12
3150.2.bf.f.1601.7 32 5.2 odd 4
3150.2.bf.f.1601.8 32 15.8 even 4
3150.2.bf.f.1601.9 32 15.2 even 4
3150.2.bf.f.1601.10 32 5.3 odd 4
4410.2.d.a.4409.7 16 35.9 even 6
4410.2.d.a.4409.8 16 21.5 even 6
4410.2.d.a.4409.9 16 21.2 odd 6
4410.2.d.a.4409.10 16 35.19 odd 6
4410.2.d.b.4409.7 16 105.89 even 6
4410.2.d.b.4409.8 16 7.2 even 3
4410.2.d.b.4409.9 16 7.5 odd 6
4410.2.d.b.4409.10 16 105.44 odd 6