Properties

Label 243.2.e.d.28.1
Level 243243
Weight 22
Character 243.28
Analytic conductor 1.9401.940
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [243,2,Mod(28,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("243.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 243=35 243 = 3^{5}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 243.e (of order 99, degree 66, not 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: 1.940364769121.94036476912
Analytic rank: 00
Dimension: 1212
Relative dimension: 22 over Q(ζ9)\Q(\zeta_{9})
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x126x11+27x1080x9+186x8330x7+463x6504x5+420x4++3 x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 3 3
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: SU(2)[C9]\mathrm{SU}(2)[C_{9}]

Embedding invariants

Embedding label 28.1
Root 0.5000002.22827i0.500000 - 2.22827i of defining polynomial
Character χ\chi == 243.28
Dual form 243.2.e.d.217.1

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+(0.3675482.08447i)q2+(2.33052+0.848241i)q4+(2.055371.72466i)q5+(0.9136940.332557i)q7+(0.508086+0.880031i)q8+(2.83955+4.91825i)q10+(0.242761+0.203701i)q11+(0.262909+1.49103i)q13+(0.357379+2.02679i)q14+(2.15207+1.80580i)q16+(0.587342+1.01731i)q17+(3.110405.38737i)q19+(6.25302+2.27591i)q20+(0.513834+0.431158i)q22+(2.03231+0.739701i)q23+(0.381855+2.16561i)q25+3.20463q26+2.41147q28+(0.7649054.33799i)q29+(8.150172.96642i)q31+(6.11199+5.12857i)q32+(2.33642+0.850386i)q34+(1.30443+2.25934i)q35+(2.233323.86823i)q37+(10.0866+8.46364i)q38+(0.4734502.68507i)q40+(1.015015.75638i)q41+(4.282953.59382i)q43+(0.3929730.680649i)q44+(2.28885+3.96441i)q46+(2.32674+0.846865i)q47+(4.638073.89180i)q49+(4.373781.59193i)q50+(0.6520373.69789i)q5210.8920q53+0.850279q55+(0.1715740.973047i)q56+(8.76126+3.18884i)q58+(1.320821.10830i)q59+(0.9535790.347074i)q61+(9.1789815.8985i)q62+(5.634559.75933i)q64+(3.111902.61119i)q65+(0.1487390.843538i)q67+(0.5058932.86906i)q68+(4.230083.54946i)q70+(4.797888.31018i)q71+(7.62091+13.1998i)q73+(8.884053.23353i)q74+(11.8187+9.91703i)q76+(0.2895520.105388i)q77+(1.9472511.0434i)q79+7.53771q8012.3721q82+(0.813530+4.61376i)q83+(2.961721.07798i)q85+(9.065387.60676i)q86+(0.3026070.110140i)q88+(7.74976+13.4230i)q89+(0.7360711.27491i)q91+(4.108913.44778i)q92+(0.9100735.16128i)q94+(2.89837+16.4375i)q95+(4.25115+3.56714i)q97+(6.40762+11.0983i)q98+O(q100)q+(-0.367548 - 2.08447i) q^{2} +(-2.33052 + 0.848241i) q^{4} +(-2.05537 - 1.72466i) q^{5} +(-0.913694 - 0.332557i) q^{7} +(0.508086 + 0.880031i) q^{8} +(-2.83955 + 4.91825i) q^{10} +(-0.242761 + 0.203701i) q^{11} +(-0.262909 + 1.49103i) q^{13} +(-0.357379 + 2.02679i) q^{14} +(-2.15207 + 1.80580i) q^{16} +(-0.587342 + 1.01731i) q^{17} +(-3.11040 - 5.38737i) q^{19} +(6.25302 + 2.27591i) q^{20} +(0.513834 + 0.431158i) q^{22} +(-2.03231 + 0.739701i) q^{23} +(0.381855 + 2.16561i) q^{25} +3.20463 q^{26} +2.41147 q^{28} +(-0.764905 - 4.33799i) q^{29} +(8.15017 - 2.96642i) q^{31} +(6.11199 + 5.12857i) q^{32} +(2.33642 + 0.850386i) q^{34} +(1.30443 + 2.25934i) q^{35} +(2.23332 - 3.86823i) q^{37} +(-10.0866 + 8.46364i) q^{38} +(0.473450 - 2.68507i) q^{40} +(1.01501 - 5.75638i) q^{41} +(4.28295 - 3.59382i) q^{43} +(0.392973 - 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(2.32674 + 0.846865i) q^{47} +(-4.63807 - 3.89180i) q^{49} +(4.37378 - 1.59193i) q^{50} +(-0.652037 - 3.69789i) q^{52} -10.8920 q^{53} +0.850279 q^{55} +(-0.171574 - 0.973047i) q^{56} +(-8.76126 + 3.18884i) q^{58} +(-1.32082 - 1.10830i) q^{59} +(-0.953579 - 0.347074i) q^{61} +(-9.17898 - 15.8985i) q^{62} +(5.63455 - 9.75933i) q^{64} +(3.11190 - 2.61119i) q^{65} +(0.148739 - 0.843538i) q^{67} +(0.505893 - 2.86906i) q^{68} +(4.23008 - 3.54946i) q^{70} +(4.79788 - 8.31018i) q^{71} +(7.62091 + 13.1998i) q^{73} +(-8.88405 - 3.23353i) q^{74} +(11.8187 + 9.91703i) q^{76} +(0.289552 - 0.105388i) q^{77} +(-1.94725 - 11.0434i) q^{79} +7.53771 q^{80} -12.3721 q^{82} +(0.813530 + 4.61376i) q^{83} +(2.96172 - 1.07798i) q^{85} +(-9.06538 - 7.60676i) q^{86} +(-0.302607 - 0.110140i) q^{88} +(7.74976 + 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(4.10891 - 3.44778i) q^{92} +(0.910073 - 5.16128i) q^{94} +(-2.89837 + 16.4375i) q^{95} +(-4.25115 + 3.56714i) q^{97} +(-6.40762 + 11.0983i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+3q2+3q4+6q5+3q7+6q83q106q11+3q1321q14+9q16+9q173q19+24q20+12q2212q23+12q2530q2612q28+45q98+O(q100) 12 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} + 3 q^{13} - 21 q^{14} + 9 q^{16} + 9 q^{17} - 3 q^{19} + 24 q^{20} + 12 q^{22} - 12 q^{23} + 12 q^{25} - 30 q^{26} - 12 q^{28}+ \cdots - 45 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/243Z)×\left(\mathbb{Z}/243\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(49)e\left(\frac{4}{9}\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 −0.367548 2.08447i −0.259895 1.47394i −0.783187 0.621786i 0.786407π-0.786407\pi
0.523291 0.852154i 0.324704π-0.324704\pi
33 0 0
44 −2.33052 + 0.848241i −1.16526 + 0.424121i
55 −2.05537 1.72466i −0.919190 0.771292i 0.0546547 0.998505i 0.482594π-0.482594\pi
−0.973845 + 0.227213i 0.927039π0.927039\pi
66 0 0
77 −0.913694 0.332557i −0.345344 0.125695i 0.163524 0.986539i 0.447714π-0.447714\pi
−0.508868 + 0.860844i 0.669936π0.669936\pi
88 0.508086 + 0.880031i 0.179636 + 0.311138i
99 0 0
1010 −2.83955 + 4.91825i −0.897945 + 1.55529i
1111 −0.242761 + 0.203701i −0.0731952 + 0.0614181i −0.678651 0.734461i 0.737435π-0.737435\pi
0.605456 + 0.795879i 0.292991π0.292991\pi
1212 0 0
1313 −0.262909 + 1.49103i −0.0729177 + 0.413537i 0.926398 + 0.376546i 0.122888π0.122888\pi
−0.999316 + 0.0369909i 0.988223π0.988223\pi
1414 −0.357379 + 2.02679i −0.0955135 + 0.541684i
1515 0 0
1616 −2.15207 + 1.80580i −0.538018 + 0.451451i
1717 −0.587342 + 1.01731i −0.142451 + 0.246733i −0.928419 0.371534i 0.878832π-0.878832\pi
0.785968 + 0.618267i 0.212165π0.212165\pi
1818 0 0
1919 −3.11040 5.38737i −0.713575 1.23595i −0.963507 0.267685i 0.913741π-0.913741\pi
0.249931 0.968264i 0.419592π-0.419592\pi
2020 6.25302 + 2.27591i 1.39822 + 0.508910i
2121 0 0
2222 0.513834 + 0.431158i 0.109550 + 0.0919231i
2323 −2.03231 + 0.739701i −0.423766 + 0.154238i −0.545095 0.838374i 0.683507π-0.683507\pi
0.121329 + 0.992612i 0.461284π0.461284\pi
2424 0 0
2525 0.381855 + 2.16561i 0.0763710 + 0.433121i
2626 3.20463 0.628480
2727 0 0
2828 2.41147 0.455726
2929 −0.764905 4.33799i −0.142039 0.805545i −0.969697 0.244311i 0.921438π-0.921438\pi
0.827658 0.561233i 0.189673π-0.189673\pi
3030 0 0
3131 8.15017 2.96642i 1.46381 0.532784i 0.517400 0.855743i 0.326900π-0.326900\pi
0.946413 + 0.322959i 0.104678π0.104678\pi
3232 6.11199 + 5.12857i 1.08046 + 0.906611i
3333 0 0
3434 2.33642 + 0.850386i 0.400692 + 0.145840i
3535 1.30443 + 2.25934i 0.220489 + 0.381899i
3636 0 0
3737 2.23332 3.86823i 0.367156 0.635933i −0.621964 0.783046i 0.713665π-0.713665\pi
0.989120 + 0.147113i 0.0469982π0.0469982\pi
3838 −10.0866 + 8.46364i −1.63626 + 1.37298i
3939 0 0
4040 0.473450 2.68507i 0.0748590 0.424547i
4141 1.01501 5.75638i 0.158517 0.898996i −0.796982 0.604003i 0.793572π-0.793572\pi
0.955499 0.294993i 0.0953174π-0.0953174\pi
4242 0 0
4343 4.28295 3.59382i 0.653143 0.548052i −0.254880 0.966973i 0.582036π-0.582036\pi
0.908023 + 0.418920i 0.137591π0.137591\pi
4444 0.392973 0.680649i 0.0592429 0.102612i
4545 0 0
4646 2.28885 + 3.96441i 0.337473 + 0.584521i
4747 2.32674 + 0.846865i 0.339390 + 0.123528i 0.506092 0.862479i 0.331090π-0.331090\pi
−0.166702 + 0.986007i 0.553312π0.553312\pi
4848 0 0
4949 −4.63807 3.89180i −0.662581 0.555972i
5050 4.37378 1.59193i 0.618546 0.225132i
5151 0 0
5252 −0.652037 3.69789i −0.0904213 0.512805i
5353 −10.8920 −1.49613 −0.748063 0.663628i 0.769016π-0.769016\pi
−0.748063 + 0.663628i 0.769016π0.769016\pi
5454 0 0
5555 0.850279 0.114652
5656 −0.171574 0.973047i −0.0229276 0.130029i
5757 0 0
5858 −8.76126 + 3.18884i −1.15041 + 0.418715i
5959 −1.32082 1.10830i −0.171956 0.144289i 0.552748 0.833348i 0.313579π-0.313579\pi
−0.724704 + 0.689060i 0.758024π0.758024\pi
6060 0 0
6161 −0.953579 0.347074i −0.122093 0.0444383i 0.280251 0.959927i 0.409582π-0.409582\pi
−0.402344 + 0.915488i 0.631805π0.631805\pi
6262 −9.17898 15.8985i −1.16573 2.01911i
6363 0 0
6464 5.63455 9.75933i 0.704319 1.21992i
6565 3.11190 2.61119i 0.385983 0.323878i
6666 0 0
6767 0.148739 0.843538i 0.0181713 0.103055i −0.974373 0.224938i 0.927782π-0.927782\pi
0.992544 + 0.121883i 0.0388933π0.0388933\pi
6868 0.505893 2.86906i 0.0613486 0.347925i
6969 0 0
7070 4.23008 3.54946i 0.505592 0.424242i
7171 4.79788 8.31018i 0.569404 0.986237i −0.427221 0.904147i 0.640507π-0.640507\pi
0.996625 0.0820894i 0.0261593π-0.0261593\pi
7272 0 0
7373 7.62091 + 13.1998i 0.891960 + 1.54492i 0.837522 + 0.546404i 0.184004π0.184004\pi
0.0544385 + 0.998517i 0.482663π0.482663\pi
7474 −8.88405 3.23353i −1.03275 0.375890i
7575 0 0
7676 11.8187 + 9.91703i 1.35569 + 1.13756i
7777 0.289552 0.105388i 0.0329975 0.0120101i
7878 0 0
7979 −1.94725 11.0434i −0.219083 1.24248i −0.873680 0.486502i 0.838273π-0.838273\pi
0.654597 0.755978i 0.272838π-0.272838\pi
8080 7.53771 0.842741
8181 0 0
8282 −12.3721 −1.36626
8383 0.813530 + 4.61376i 0.0892965 + 0.506425i 0.996347 + 0.0854026i 0.0272177π0.0272177\pi
−0.907050 + 0.421023i 0.861671π0.861671\pi
8484 0 0
8585 2.96172 1.07798i 0.321243 0.116923i
8686 −9.06538 7.60676i −0.977546 0.820258i
8787 0 0
8888 −0.302607 0.110140i −0.0322580 0.0117409i
8989 7.74976 + 13.4230i 0.821473 + 1.42283i 0.904586 + 0.426292i 0.140180π0.140180\pi
−0.0831130 + 0.996540i 0.526486π0.526486\pi
9090 0 0
9191 0.736071 1.27491i 0.0771612 0.133647i
9292 4.10891 3.44778i 0.428383 0.359456i
9393 0 0
9494 0.910073 5.16128i 0.0938669 0.532346i
9595 −2.89837 + 16.4375i −0.297366 + 1.68645i
9696 0 0
9797 −4.25115 + 3.56714i −0.431639 + 0.362188i −0.832570 0.553920i 0.813131π-0.813131\pi
0.400931 + 0.916108i 0.368687π0.368687\pi
9898 −6.40762 + 11.0983i −0.647267 + 1.12110i
9999 0 0
100100 −2.72688 4.72309i −0.272688 0.472309i
101101 9.52759 + 3.46776i 0.948030 + 0.345055i 0.769332 0.638849i 0.220589π-0.220589\pi
0.178698 + 0.983904i 0.442811π0.442811\pi
102102 0 0
103103 −7.54806 6.33357i −0.743732 0.624065i 0.190105 0.981764i 0.439117π-0.439117\pi
−0.933837 + 0.357698i 0.883562π0.883562\pi
104104 −1.44573 + 0.526203i −0.141766 + 0.0515985i
105105 0 0
106106 4.00331 + 22.7039i 0.388836 + 2.20520i
107107 5.17080 0.499880 0.249940 0.968261i 0.419589π-0.419589\pi
0.249940 + 0.968261i 0.419589π0.419589\pi
108108 0 0
109109 −7.31065 −0.700234 −0.350117 0.936706i 0.613858π-0.613858\pi
−0.350117 + 0.936706i 0.613858π0.613858\pi
110110 −0.312518 1.77238i −0.0297974 0.168990i
111111 0 0
112112 2.56687 0.934263i 0.242546 0.0882796i
113113 7.94820 + 6.66933i 0.747704 + 0.627398i 0.934895 0.354925i 0.115494π-0.115494\pi
−0.187191 + 0.982324i 0.559938π0.559938\pi
114114 0 0
115115 5.45289 + 1.98469i 0.508485 + 0.185073i
116116 5.46229 + 9.46096i 0.507161 + 0.878428i
117117 0 0
118118 −1.82475 + 3.16056i −0.167982 + 0.290953i
119119 0.874964 0.734182i 0.0802078 0.0673023i
120120 0 0
121121 −1.89269 + 10.7340i −0.172063 + 0.975817i
122122 −0.372979 + 2.11527i −0.0337680 + 0.191508i
123123 0 0
124124 −16.4779 + 13.8266i −1.47976 + 1.24167i
125125 −3.75766 + 6.50846i −0.336095 + 0.582134i
126126 0 0
127127 −2.61372 4.52709i −0.231930 0.401714i 0.726446 0.687223i 0.241171π-0.241171\pi
−0.958376 + 0.285509i 0.907837π0.907837\pi
128128 −7.41903 2.70031i −0.655756 0.238676i
129129 0 0
130130 −6.58671 5.52691i −0.577693 0.484742i
131131 6.79802 2.47428i 0.593946 0.216179i −0.0275183 0.999621i 0.508760π-0.508760\pi
0.621464 + 0.783443i 0.286538π0.286538\pi
132132 0 0
133133 1.05034 + 5.95680i 0.0910764 + 0.516520i
134134 −1.81300 −0.156619
135135 0 0
136136 −1.19368 −0.102357
137137 1.95342 + 11.0784i 0.166892 + 0.946493i 0.947092 + 0.320962i 0.104006π0.104006\pi
−0.780200 + 0.625531i 0.784883π0.784883\pi
138138 0 0
139139 −8.81447 + 3.20820i −0.747634 + 0.272116i −0.687610 0.726081i 0.741340π-0.741340\pi
−0.0600240 + 0.998197i 0.519118π0.519118\pi
140140 −4.95648 4.15898i −0.418899 0.351498i
141141 0 0
142142 −19.0857 6.94664i −1.60164 0.582949i
143143 −0.239900 0.415518i −0.0200614 0.0347474i
144144 0 0
145145 −5.90940 + 10.2354i −0.490749 + 0.850003i
146146 24.7135 20.7371i 2.04530 1.71621i
147147 0 0
148148 −1.92362 + 10.9094i −0.158121 + 0.896747i
149149 3.30821 18.7618i 0.271019 1.53703i −0.480309 0.877099i 0.659475π-0.659475\pi
0.751328 0.659928i 0.229413π-0.229413\pi
150150 0 0
151151 3.07490 2.58015i 0.250232 0.209970i −0.509040 0.860743i 0.670000π-0.670000\pi
0.759272 + 0.650773i 0.225555π0.225555\pi
152152 3.16070 5.47450i 0.256367 0.444041i
153153 0 0
154154 −0.326102 0.564825i −0.0262780 0.0455149i
155155 −21.8677 7.95919i −1.75646 0.639298i
156156 0 0
157157 5.57368 + 4.67687i 0.444828 + 0.373255i 0.837512 0.546418i 0.184009π-0.184009\pi
−0.392685 + 0.919673i 0.628454π0.628454\pi
158158 −22.3039 + 8.11795i −1.77440 + 0.645830i
159159 0 0
160160 −3.71737 21.0822i −0.293884 1.66670i
161161 2.10290 0.165732
162162 0 0
163163 12.4492 0.975094 0.487547 0.873097i 0.337892π-0.337892\pi
0.487547 + 0.873097i 0.337892π0.337892\pi
164164 2.51731 + 14.2764i 0.196569 + 1.11480i
165165 0 0
166166 9.31821 3.39155i 0.723233 0.263235i
167167 −1.78633 1.49891i −0.138230 0.115989i 0.571051 0.820915i 0.306536π-0.306536\pi
−0.709281 + 0.704926i 0.750980π0.750980\pi
168168 0 0
169169 10.0620 + 3.66225i 0.773997 + 0.281712i
170170 −3.33558 5.77739i −0.255827 0.443106i
171171 0 0
172172 −6.93308 + 12.0085i −0.528643 + 0.915636i
173173 −2.74418 + 2.30264i −0.208636 + 0.175066i −0.741118 0.671375i 0.765704π-0.765704\pi
0.532482 + 0.846442i 0.321260π0.321260\pi
174174 0 0
175175 0.371290 2.10569i 0.0280669 0.159175i
176176 0.154596 0.876757i 0.0116531 0.0660880i
177177 0 0
178178 25.1313 21.0877i 1.88367 1.58059i
179179 9.99785 17.3168i 0.747275 1.29432i −0.201850 0.979416i 0.564695π-0.564695\pi
0.949124 0.314901i 0.101971π-0.101971\pi
180180 0 0
181181 −4.86616 8.42844i −0.361699 0.626481i 0.626542 0.779388i 0.284470π-0.284470\pi
−0.988241 + 0.152907i 0.951136π0.951136\pi
182182 −2.92805 1.06572i −0.217042 0.0789967i
183183 0 0
184184 −1.68355 1.41267i −0.124113 0.104143i
185185 −11.2617 + 4.09892i −0.827976 + 0.301359i
186186 0 0
187187 −0.0646422 0.366604i −0.00472711 0.0268088i
188188 −6.14088 −0.447869
189189 0 0
190190 35.3286 2.56301
191191 −3.08339 17.4868i −0.223106 1.26530i −0.866273 0.499571i 0.833491π-0.833491\pi
0.643167 0.765726i 0.277620π-0.277620\pi
192192 0 0
193193 −9.94602 + 3.62006i −0.715930 + 0.260577i −0.674197 0.738551i 0.735510π-0.735510\pi
−0.0417333 + 0.999129i 0.513288π0.513288\pi
194194 8.99809 + 7.55029i 0.646025 + 0.542079i
195195 0 0
196196 14.1103 + 5.13574i 1.00788 + 0.366838i
197197 −7.07945 12.2620i −0.504390 0.873628i −0.999987 0.00507615i 0.998384π-0.998384\pi
0.495597 0.868552i 0.334949π-0.334949\pi
198198 0 0
199199 −3.77010 + 6.53000i −0.267255 + 0.462899i −0.968152 0.250363i 0.919450π-0.919450\pi
0.700897 + 0.713263i 0.252783π0.252783\pi
200200 −1.71179 + 1.43636i −0.121042 + 0.101566i
201201 0 0
202202 3.72658 21.1345i 0.262201 1.48702i
203203 −0.743742 + 4.21797i −0.0522004 + 0.296043i
204204 0 0
205205 −12.0140 + 10.0810i −0.839096 + 0.704085i
206206 −10.4278 + 18.0616i −0.726543 + 1.25841i
207207 0 0
208208 −2.12670 3.68356i −0.147460 0.255409i
209209 1.85250 + 0.674254i 0.128140 + 0.0466391i
210210 0 0
211211 3.99388 + 3.35126i 0.274950 + 0.230710i 0.769827 0.638253i 0.220342π-0.220342\pi
−0.494877 + 0.868963i 0.664787π0.664787\pi
212212 25.3840 9.23901i 1.74338 0.634538i
213213 0 0
214214 −1.90052 10.7784i −0.129917 0.736794i
215215 −15.0012 −1.02307
216216 0 0
217217 −8.43326 −0.572487
218218 2.68701 + 15.2388i 0.181988 + 1.03210i
219219 0 0
220220 −1.98160 + 0.721242i −0.133599 + 0.0486261i
221221 −1.36242 1.14320i −0.0916460 0.0769001i
222222 0 0
223223 −16.6267 6.05164i −1.11341 0.405248i −0.281166 0.959659i 0.590721π-0.590721\pi
−0.832243 + 0.554412i 0.812943π0.812943\pi
224224 −3.87894 6.71853i −0.259173 0.448901i
225225 0 0
226226 10.9807 19.0191i 0.730423 1.26513i
227227 −12.0820 + 10.1380i −0.801913 + 0.672885i −0.948663 0.316289i 0.897563π-0.897563\pi
0.146750 + 0.989174i 0.453119π0.453119\pi
228228 0 0
229229 −0.306813 + 1.74002i −0.0202748 + 0.114984i −0.993266 0.115860i 0.963038π-0.963038\pi
0.972991 + 0.230844i 0.0741487π0.0741487\pi
230230 2.13282 12.0958i 0.140634 0.797576i
231231 0 0
232232 3.42893 2.87721i 0.225120 0.188898i
233233 6.94920 12.0364i 0.455257 0.788529i −0.543446 0.839444i 0.682881π-0.682881\pi
0.998703 + 0.0509157i 0.0162140π0.0162140\pi
234234 0 0
235235 −3.32177 5.75347i −0.216688 0.375315i
236236 4.01831 + 1.46255i 0.261570 + 0.0952037i
237237 0 0
238238 −1.85197 1.55399i −0.120045 0.100730i
239239 18.6366 6.78318i 1.20550 0.438767i 0.340362 0.940295i 0.389451π-0.389451\pi
0.865142 + 0.501527i 0.167228π0.167228\pi
240240 0 0
241241 3.36438 + 19.0804i 0.216719 + 1.22907i 0.877899 + 0.478846i 0.158945π0.158945\pi
−0.661180 + 0.750227i 0.729944π0.729944\pi
242242 23.0703 1.48301
243243 0 0
244244 2.51674 0.161118
245245 2.82091 + 15.9982i 0.180222 + 1.02209i
246246 0 0
247247 8.85048 3.22131i 0.563143 0.204967i
248248 6.75153 + 5.66521i 0.428723 + 0.359741i
249249 0 0
250250 14.9478 + 5.44055i 0.945381 + 0.344090i
251251 2.73786 + 4.74212i 0.172812 + 0.299320i 0.939402 0.342818i 0.111381π-0.111381\pi
−0.766590 + 0.642137i 0.778048π0.778048\pi
252252 0 0
253253 0.342689 0.593554i 0.0215447 0.0373164i
254254 −8.47590 + 7.11212i −0.531825 + 0.446254i
255255 0 0
256256 1.01187 5.73859i 0.0632418 0.358662i
257257 −2.00827 + 11.3895i −0.125272 + 0.710455i 0.855873 + 0.517186i 0.173020π0.173020\pi
−0.981146 + 0.193270i 0.938091π0.938091\pi
258258 0 0
259259 −3.32698 + 2.79167i −0.206729 + 0.173466i
260260 −5.03743 + 8.72508i −0.312408 + 0.541107i
261261 0 0
262262 −7.65614 13.2608i −0.472998 0.819257i
263263 −6.08727 2.21558i −0.375357 0.136619i 0.147451 0.989069i 0.452893π-0.452893\pi
−0.522808 + 0.852451i 0.675115π0.675115\pi
264264 0 0
265265 22.3870 + 18.7849i 1.37522 + 1.15395i
266266 12.0307 4.37881i 0.737649 0.268482i
267267 0 0
268268 0.368885 + 2.09205i 0.0225332 + 0.127792i
269269 −13.8387 −0.843758 −0.421879 0.906652i 0.638629π-0.638629\pi
−0.421879 + 0.906652i 0.638629π0.638629\pi
270270 0 0
271271 1.94536 0.118172 0.0590860 0.998253i 0.481181π-0.481181\pi
0.0590860 + 0.998253i 0.481181π0.481181\pi
272272 −0.573052 3.24994i −0.0347464 0.197057i
273273 0 0
274274 22.3746 8.14369i 1.35170 0.491978i
275275 −0.533835 0.447941i −0.0321915 0.0270118i
276276 0 0
277277 −11.7205 4.26591i −0.704216 0.256314i −0.0350062 0.999387i 0.511145π-0.511145\pi
−0.669210 + 0.743073i 0.733367π0.733367\pi
278278 9.92713 + 17.1943i 0.595390 + 1.03125i
279279 0 0
280280 −1.32553 + 2.29588i −0.0792154 + 0.137205i
281281 7.47343 6.27095i 0.445827 0.374094i −0.392057 0.919941i 0.628237π-0.628237\pi
0.837885 + 0.545847i 0.183792π0.183792\pi
282282 0 0
283283 4.61405 26.1676i 0.274277 1.55550i −0.466974 0.884271i 0.654656π-0.654656\pi
0.741250 0.671229i 0.234233π-0.234233\pi
284284 −4.13255 + 23.4368i −0.245221 + 1.39072i
285285 0 0
286286 −0.777960 + 0.652786i −0.0460017 + 0.0386000i
287287 −2.84173 + 4.92202i −0.167742 + 0.290538i
288288 0 0
289289 7.81006 + 13.5274i 0.459415 + 0.795730i
290290 23.5073 + 8.55596i 1.38040 + 0.502423i
291291 0 0
292292 −28.9573 24.2981i −1.69460 1.42194i
293293 −11.5182 + 4.19230i −0.672903 + 0.244917i −0.655797 0.754937i 0.727667π-0.727667\pi
−0.0171059 + 0.999854i 0.505445π0.505445\pi
294294 0 0
295295 0.803336 + 4.55594i 0.0467720 + 0.265257i
296296 4.53888 0.263817
297297 0 0
298298 −40.3243 −2.33592
299299 −0.568603 3.22471i −0.0328832 0.186490i
300300 0 0
301301 −5.10845 + 1.85933i −0.294446 + 0.107170i
302302 −6.50841 5.46121i −0.374517 0.314257i
303303 0 0
304304 16.4223 + 5.97724i 0.941886 + 0.342818i
305305 1.36137 + 2.35797i 0.0779521 + 0.135017i
306306 0 0
307307 13.2370 22.9271i 0.755475 1.30852i −0.189663 0.981849i 0.560740π-0.560740\pi
0.945138 0.326671i 0.105927π-0.105927\pi
308308 −0.585412 + 0.491219i −0.0333569 + 0.0279898i
309309 0 0
310310 −8.55325 + 48.5079i −0.485792 + 2.75506i
311311 −3.06654 + 17.3912i −0.173887 + 0.986164i 0.765533 + 0.643397i 0.222475π0.222475\pi
−0.939420 + 0.342768i 0.888636π0.888636\pi
312312 0 0
313313 7.39019 6.20111i 0.417718 0.350507i −0.409576 0.912276i 0.634323π-0.634323\pi
0.827294 + 0.561769i 0.189879π0.189879\pi
314314 7.70019 13.3371i 0.434547 0.752657i
315315 0 0
316316 13.9056 + 24.0852i 0.782250 + 1.35490i
317317 3.48672 + 1.26906i 0.195834 + 0.0712777i 0.438075 0.898938i 0.355660π-0.355660\pi
−0.242241 + 0.970216i 0.577883π0.577883\pi
318318 0 0
319319 1.06934 + 0.897284i 0.0598716 + 0.0502382i
320320 −28.4126 + 10.3414i −1.58831 + 0.578099i
321321 0 0
322322 −0.772918 4.38343i −0.0430730 0.244279i
323323 7.30748 0.406599
324324 0 0
325325 −3.32937 −0.184680
326326 −4.57566 25.9499i −0.253422 1.43723i
327327 0 0
328328 5.58151 2.03150i 0.308187 0.112171i
329329 −1.84430 1.54755i −0.101680 0.0853193i
330330 0 0
331331 1.32759 + 0.483205i 0.0729712 + 0.0265593i 0.378248 0.925704i 0.376527π-0.376527\pi
−0.305277 + 0.952264i 0.598749π0.598749\pi
332332 −5.80953 10.0624i −0.318839 0.552246i
333333 0 0
334334 −2.46786 + 4.27446i −0.135035 + 0.233888i
335335 −1.76053 + 1.47726i −0.0961881 + 0.0807114i
336336 0 0
337337 −2.25570 + 12.7927i −0.122876 + 0.696864i 0.859671 + 0.510848i 0.170669π0.170669\pi
−0.982547 + 0.186016i 0.940442π0.940442\pi
338338 3.93559 22.3199i 0.214068 1.21404i
339339 0 0
340340 −5.98797 + 5.02450i −0.324743 + 0.272492i
341341 −1.37428 + 2.38033i −0.0744215 + 0.128902i
342342 0 0
343343 6.34669 + 10.9928i 0.342689 + 0.593555i
344344 5.33878 + 1.94316i 0.287848 + 0.104768i
345345 0 0
346346 5.80839 + 4.87382i 0.312261 + 0.262018i
347347 4.51096 1.64185i 0.242161 0.0881394i −0.218089 0.975929i 0.569982π-0.569982\pi
0.460250 + 0.887790i 0.347760π0.347760\pi
348348 0 0
349349 −3.92055 22.2346i −0.209862 1.19019i −0.889602 0.456736i 0.849018π-0.849018\pi
0.679740 0.733453i 0.262093π-0.262093\pi
350350 −4.52571 −0.241909
351351 0 0
352352 −2.52845 −0.134767
353353 −5.15849 29.2553i −0.274559 1.55710i −0.740360 0.672211i 0.765345π-0.765345\pi
0.465801 0.884889i 0.345766π-0.345766\pi
354354 0 0
355355 −24.1937 + 8.80578i −1.28407 + 0.467362i
356356 −29.4469 24.7089i −1.56068 1.30957i
357357 0 0
358358 −39.7710 14.4754i −2.10196 0.765051i
359359 −6.70991 11.6219i −0.354136 0.613381i 0.632834 0.774288i 0.281892π-0.281892\pi
−0.986970 + 0.160906i 0.948558π0.948558\pi
360360 0 0
361361 −9.84920 + 17.0593i −0.518379 + 0.897858i
362362 −15.7802 + 13.2412i −0.829392 + 0.695942i
363363 0 0
364364 −0.633997 + 3.59558i −0.0332305 + 0.188459i
365365 7.10140 40.2740i 0.371704 2.10804i
366366 0 0
367367 −6.09004 + 5.11015i −0.317897 + 0.266748i −0.787747 0.615999i 0.788753π-0.788753\pi
0.469850 + 0.882746i 0.344308π0.344308\pi
368368 3.03793 5.26184i 0.158363 0.274293i
369369 0 0
370370 12.6833 + 21.9681i 0.659372 + 1.14207i
371371 9.95192 + 3.62220i 0.516678 + 0.188055i
372372 0 0
373373 −8.74862 7.34096i −0.452986 0.380101i 0.387556 0.921846i 0.373319π-0.373319\pi
−0.840543 + 0.541745i 0.817764π0.817764\pi
374374 −0.740415 + 0.269489i −0.0382860 + 0.0139350i
375375 0 0
376376 0.436918 + 2.47789i 0.0225323 + 0.127787i
377377 6.66917 0.343480
378378 0 0
379379 −24.1705 −1.24155 −0.620777 0.783987i 0.713183π-0.713183\pi
−0.620777 + 0.783987i 0.713183π0.713183\pi
380380 −7.18821 40.7664i −0.368748 2.09127i
381381 0 0
382382 −35.3173 + 12.8544i −1.80699 + 0.657690i
383383 7.23397 + 6.07003i 0.369639 + 0.310164i 0.808619 0.588333i 0.200216π-0.200216\pi
−0.438980 + 0.898497i 0.644660π0.644660\pi
384384 0 0
385385 −0.776895 0.282767i −0.0395942 0.0144111i
386386 11.2015 + 19.4016i 0.570143 + 0.987516i
387387 0 0
388388 6.88162 11.9193i 0.349361 0.605111i
389389 −1.95166 + 1.63763i −0.0989529 + 0.0830314i −0.690922 0.722929i 0.742795π-0.742795\pi
0.591969 + 0.805961i 0.298351π0.298351\pi
390390 0 0
391391 0.441160 2.50194i 0.0223104 0.126529i
392392 1.06837 6.05902i 0.0539607 0.306027i
393393 0 0
394394 −22.9576 + 19.2637i −1.15659 + 0.970492i
395395 −15.0438 + 26.0567i −0.756937 + 1.31105i
396396 0 0
397397 −1.83759 3.18279i −0.0922258 0.159740i 0.816222 0.577739i 0.196065π-0.196065\pi
−0.908447 + 0.417999i 0.862731π0.862731\pi
398398 14.9973 + 5.45855i 0.751744 + 0.273613i
399399 0 0
400400 −4.73244 3.97098i −0.236622 0.198549i
401401 −15.1748 + 5.52319i −0.757795 + 0.275815i −0.691882 0.722010i 0.743218π-0.743218\pi
−0.0659131 + 0.997825i 0.520996π0.520996\pi
402402 0 0
403403 2.28027 + 12.9320i 0.113588 + 0.644190i
404404 −25.1458 −1.25105
405405 0 0
406406 9.06558 0.449917
407407 0.245797 + 1.39399i 0.0121837 + 0.0690973i
408408 0 0
409409 −8.62823 + 3.14042i −0.426639 + 0.155284i −0.546410 0.837518i 0.684006π-0.684006\pi
0.119772 + 0.992801i 0.461784π0.461784\pi
410410 25.4292 + 21.3376i 1.25586 + 1.05379i
411411 0 0
412412 22.9633 + 8.35797i 1.13132 + 0.411767i
413413 0.838253 + 1.45190i 0.0412477 + 0.0714432i
414414 0 0
415415 6.28506 10.8860i 0.308522 0.534375i
416416 −9.25374 + 7.76481i −0.453702 + 0.380701i
417417 0 0
418418 0.724578 4.10929i 0.0354403 0.200992i
419419 −1.21187 + 6.87285i −0.0592037 + 0.335761i −0.999995 0.00322608i 0.998973π-0.998973\pi
0.940791 + 0.338987i 0.110084π0.110084\pi
420420 0 0
421421 23.6023 19.8047i 1.15031 0.965221i 0.150579 0.988598i 0.451886π-0.451886\pi
0.999727 + 0.0233767i 0.00744170π0.00744170\pi
422422 5.51765 9.55686i 0.268595 0.465221i
423423 0 0
424424 −5.53405 9.58526i −0.268757 0.465502i
425425 −2.42736 0.883488i −0.117744 0.0428555i
426426 0 0
427427 0.755857 + 0.634240i 0.0365785 + 0.0306930i
428428 −12.0507 + 4.38609i −0.582491 + 0.212010i
429429 0 0
430430 5.51365 + 31.2694i 0.265892 + 1.50795i
431431 27.8971 1.34376 0.671879 0.740661i 0.265487π-0.265487\pi
0.671879 + 0.740661i 0.265487π0.265487\pi
432432 0 0
433433 19.1706 0.921278 0.460639 0.887588i 0.347620π-0.347620\pi
0.460639 + 0.887588i 0.347620π0.347620\pi
434434 3.09963 + 17.5789i 0.148787 + 0.843812i
435435 0 0
436436 17.0377 6.20120i 0.815956 0.296984i
437437 10.3064 + 8.64806i 0.493020 + 0.413693i
438438 0 0
439439 22.3167 + 8.12263i 1.06512 + 0.387672i 0.814350 0.580375i 0.197094π-0.197094\pi
0.250770 + 0.968047i 0.419316π0.419316\pi
440440 0.432015 + 0.748272i 0.0205955 + 0.0356725i
441441 0 0
442442 −1.88221 + 3.26009i −0.0895278 + 0.155067i
443443 17.8935 15.0144i 0.850144 0.713356i −0.109677 0.993967i 0.534982π-0.534982\pi
0.959821 + 0.280612i 0.0905373π0.0905373\pi
444444 0 0
445445 7.22146 40.9549i 0.342330 1.94145i
446446 −6.50332 + 36.8821i −0.307941 + 1.74642i
447447 0 0
448448 −8.39379 + 7.04323i −0.396569 + 0.332761i
449449 −2.40953 + 4.17343i −0.113713 + 0.196956i −0.917264 0.398279i 0.869608π-0.869608\pi
0.803552 + 0.595235i 0.202941π0.202941\pi
450450 0 0
451451 0.926176 + 1.60418i 0.0436119 + 0.0755380i
452452 −24.1807 8.80105i −1.13736 0.413966i
453453 0 0
454454 25.5731 + 21.4584i 1.20021 + 1.00709i
455455 −3.71169 + 1.35095i −0.174007 + 0.0633333i
456456 0 0
457457 −0.849765 4.81926i −0.0397503 0.225435i 0.958461 0.285225i 0.0920682π-0.0920682\pi
−0.998211 + 0.0597894i 0.980957π0.980957\pi
458458 3.73978 0.174749
459459 0 0
460460 −14.3916 −0.671012
461461 4.86049 + 27.5652i 0.226376 + 1.28384i 0.860038 + 0.510230i 0.170440π0.170440\pi
−0.633662 + 0.773610i 0.718449π0.718449\pi
462462 0 0
463463 25.8184 9.39712i 1.19988 0.436721i 0.336699 0.941612i 0.390690π-0.390690\pi
0.863183 + 0.504891i 0.168467π0.168467\pi
464464 9.47968 + 7.95440i 0.440083 + 0.369274i
465465 0 0
466466 −27.6436 10.0614i −1.28056 0.466087i
467467 10.6232 + 18.4000i 0.491585 + 0.851450i 0.999953 0.00968963i 0.00308435π-0.00308435\pi
−0.508368 + 0.861140i 0.669751π0.669751\pi
468468 0 0
469469 −0.416426 + 0.721272i −0.0192288 + 0.0333052i
470470 −10.7720 + 9.03879i −0.496876 + 0.416928i
471471 0 0
472472 0.304248 1.72548i 0.0140042 0.0794215i
473473 −0.307669 + 1.74488i −0.0141466 + 0.0802296i
474474 0 0
475475 10.4792 8.79310i 0.480819 0.403455i
476476 −1.41636 + 2.45321i −0.0649188 + 0.112443i
477477 0 0
478478 −20.9892 36.3543i −0.960022 1.66281i
479479 39.1653 + 14.2550i 1.78951 + 0.651328i 0.999257 + 0.0385448i 0.0122722π0.0122722\pi
0.790251 + 0.612783i 0.209950π0.209950\pi
480480 0 0
481481 5.18048 + 4.34694i 0.236210 + 0.198203i
482482 38.5358 14.0259i 1.75526 0.638861i
483483 0 0
484484 −4.69405 26.6213i −0.213366 1.21006i
485485 14.8898 0.676112
486486 0 0
487487 4.02801 0.182527 0.0912634 0.995827i 0.470909π-0.470909\pi
0.0912634 + 0.995827i 0.470909π0.470909\pi
488488 −0.179064 1.01552i −0.00810585 0.0459706i
489489 0 0
490490 32.3109 11.7602i 1.45966 0.531272i
491491 −29.5857 24.8253i −1.33518 1.12035i −0.982836 0.184482i 0.940939π-0.940939\pi
−0.352347 0.935869i 0.614616π-0.614616\pi
492492 0 0
493493 4.86233 + 1.76974i 0.218988 + 0.0797052i
494494 −9.96769 17.2645i −0.448468 0.776769i
495495 0 0
496496 −12.1830 + 21.1015i −0.547032 + 0.947487i
497497 −7.14741 + 5.99739i −0.320605 + 0.269020i
498498 0 0
499499 −0.707071 + 4.01000i −0.0316528 + 0.179512i −0.996535 0.0831694i 0.973496π-0.973496\pi
0.964883 + 0.262682i 0.0846069π0.0846069\pi
500500 3.23657 18.3555i 0.144744 0.820884i
501501 0 0
502502 8.87849 7.44994i 0.396266 0.332507i
503503 1.71297 2.96695i 0.0763775 0.132290i −0.825307 0.564684i 0.808998π-0.808998\pi
0.901684 + 0.432395i 0.142331π0.142331\pi
504504 0 0
505505 −13.6020 23.5594i −0.605282 1.04838i
506506 −1.36320 0.496164i −0.0606016 0.0220572i
507507 0 0
508508 9.93139 + 8.33343i 0.440634 + 0.369736i
509509 11.5238 4.19434i 0.510785 0.185911i −0.0737534 0.997277i 0.523498π-0.523498\pi
0.584539 + 0.811366i 0.301276π0.301276\pi
510510 0 0
511511 −2.57349 14.5950i −0.113844 0.645644i
512512 −28.1241 −1.24292
513513 0 0
514514 24.4791 1.07973
515515 4.59080 + 26.0357i 0.202295 + 1.14727i
516516 0 0
517517 −0.737350 + 0.268373i −0.0324286 + 0.0118030i
518518 7.04196 + 5.90891i 0.309406 + 0.259623i
519519 0 0
520520 3.87904 + 1.41186i 0.170107 + 0.0619140i
521521 −7.04117 12.1957i −0.308479 0.534302i 0.669551 0.742766i 0.266487π-0.266487\pi
−0.978030 + 0.208465i 0.933153π0.933153\pi
522522 0 0
523523 −4.88956 + 8.46897i −0.213806 + 0.370322i −0.952902 0.303277i 0.901919π-0.901919\pi
0.739097 + 0.673599i 0.235253π0.235253\pi
524524 −13.7442 + 11.5327i −0.600416 + 0.503809i
525525 0 0
526526 −2.38095 + 13.5030i −0.103814 + 0.588761i
527527 −1.76918 + 10.0335i −0.0770667 + 0.437067i
528528 0 0
529529 −14.0359 + 11.7775i −0.610256 + 0.512065i
530530 30.9283 53.5694i 1.34344 2.32691i
531531 0 0
532532 −7.50065 12.9915i −0.325195 0.563254i
533533 8.31608 + 3.02681i 0.360209 + 0.131105i
534534 0 0
535535 −10.6279 8.91789i −0.459485 0.385554i
536536 0.817912 0.297696i 0.0353284 0.0128585i
537537 0 0
538538 5.08637 + 28.8462i 0.219289 + 1.24365i
539539 1.91871 0.0826445
540540 0 0
541541 40.9454 1.76038 0.880189 0.474623i 0.157416π-0.157416\pi
0.880189 + 0.474623i 0.157416π0.157416\pi
542542 −0.715012 4.05503i −0.0307124 0.174179i
543543 0 0
544544 −8.80715 + 3.20554i −0.377604 + 0.137436i
545545 15.0261 + 12.6084i 0.643648 + 0.540085i
546546 0 0
547547 −1.04332 0.379737i −0.0446091 0.0162364i 0.319619 0.947546i 0.396445π-0.396445\pi
−0.364228 + 0.931310i 0.618667π0.618667\pi
548548 −13.9497 24.1615i −0.595900 1.03213i
549549 0 0
550550 −0.737508 + 1.27740i −0.0314474 + 0.0544686i
551551 −20.9912 + 17.6137i −0.894256 + 0.750370i
552552 0 0
553553 −1.89338 + 10.7379i −0.0805145 + 0.456620i
554554 −4.58431 + 25.9989i −0.194769 + 1.10459i
555555 0 0
556556 17.8210 14.9536i 0.755779 0.634174i
557557 −17.5201 + 30.3458i −0.742352 + 1.28579i 0.209070 + 0.977901i 0.432956π0.432956\pi
−0.951422 + 0.307890i 0.900377π0.900377\pi
558558 0 0
559559 4.23247 + 7.33084i 0.179014 + 0.310062i
560560 −6.88716 2.50672i −0.291035 0.105928i
561561 0 0
562562 −15.8184 13.2732i −0.667260 0.559898i
563563 36.4330 13.2605i 1.53547 0.558865i 0.570515 0.821287i 0.306744π-0.306744\pi
0.964953 + 0.262423i 0.0845215π0.0845215\pi
564564 0 0
565565 −4.83417 27.4159i −0.203375 1.15340i
566566 −56.2413 −2.36400
567567 0 0
568568 9.75095 0.409141
569569 −5.89854 33.4523i −0.247280 1.40239i −0.815138 0.579266i 0.803339π-0.803339\pi
0.567859 0.823126i 0.307772π-0.307772\pi
570570 0 0
571571 −9.48043 + 3.45060i −0.396744 + 0.144403i −0.532684 0.846314i 0.678817π-0.678817\pi
0.135940 + 0.990717i 0.456594π0.456594\pi
572572 0.911552 + 0.764883i 0.0381139 + 0.0319814i
573573 0 0
574574 11.3043 + 4.11442i 0.471831 + 0.171732i
575575 −2.37795 4.11873i −0.0991674 0.171763i
576576 0 0
577577 6.06615 10.5069i 0.252537 0.437407i −0.711687 0.702497i 0.752068π-0.752068\pi
0.964224 + 0.265090i 0.0854017π0.0854017\pi
578578 25.3269 21.2518i 1.05346 0.883957i
579579 0 0
580580 5.08993 28.8664i 0.211348 1.19861i
581581 0.791021 4.48611i 0.0328171 0.186115i
582582 0 0
583583 2.64414 2.21870i 0.109509 0.0918892i
584584 −7.74416 + 13.4133i −0.320456 + 0.555046i
585585 0 0
586586 12.9722 + 22.4685i 0.535877 + 0.928167i
587587 −29.8345 10.8589i −1.23140 0.448193i −0.357324 0.933981i 0.616311π-0.616311\pi
−0.874077 + 0.485787i 0.838533π0.838533\pi
588588 0 0
589589 −41.3315 34.6812i −1.70303 1.42902i
590590 9.20145 3.34905i 0.378818 0.137878i
591591 0 0
592592 2.17899 + 12.3576i 0.0895558 + 0.507896i
593593 13.4906 0.553993 0.276996 0.960871i 0.410661π-0.410661\pi
0.276996 + 0.960871i 0.410661π0.410661\pi
594594 0 0
595595 −3.06459 −0.125636
596596 8.20467 + 46.5310i 0.336077 + 1.90598i
597597 0 0
598598 −6.51281 + 2.37047i −0.266329 + 0.0969357i
599599 −32.5036 27.2737i −1.32806 1.11437i −0.984527 0.175233i 0.943932π-0.943932\pi
−0.343532 0.939141i 0.611623π-0.611623\pi
600600 0 0
601601 18.6104 + 6.77362i 0.759133 + 0.276302i 0.692444 0.721472i 0.256534π-0.256534\pi
0.0666892 + 0.997774i 0.478756π0.478756\pi
602602 5.75330 + 9.96501i 0.234487 + 0.406144i
603603 0 0
604604 −4.97755 + 8.62136i −0.202533 + 0.350798i
605605 22.4027 18.7981i 0.910798 0.764251i
606606 0 0
607607 −6.25117 + 35.4521i −0.253727 + 1.43896i 0.545592 + 0.838051i 0.316305π0.316305\pi
−0.799319 + 0.600906i 0.794806π0.794806\pi
608608 8.61877 48.8795i 0.349537 1.98232i
609609 0 0
610610 4.41474 3.70441i 0.178748 0.149987i
611611 −1.87442 + 3.24659i −0.0758310 + 0.131343i
612612 0 0
613613 −13.2314 22.9175i −0.534411 0.925627i −0.999192 0.0402013i 0.987200π-0.987200\pi
0.464780 0.885426i 0.346133π-0.346133\pi
614614 −52.6561 19.1652i −2.12503 0.773446i
615615 0 0
616616 0.239862 + 0.201268i 0.00966431 + 0.00810932i
617617 −46.1546 + 16.7989i −1.85812 + 0.676299i −0.877747 + 0.479124i 0.840955π0.840955\pi
−0.980368 + 0.197175i 0.936823π0.936823\pi
618618 0 0
619619 −4.20336 23.8385i −0.168947 0.958149i −0.944900 0.327358i 0.893842π-0.893842\pi
0.775953 0.630791i 0.217269π-0.217269\pi
620620 57.7145 2.31787
621621 0 0
622622 37.3785 1.49874
623623 −2.61700 14.8417i −0.104848 0.594621i
624624 0 0
625625 29.2803 10.6571i 1.17121 0.426286i
626626 −15.6422 13.1254i −0.625190 0.524597i
627627 0 0
628628 −16.9567 6.17173i −0.676646 0.246279i
629629 2.62345 + 4.54395i 0.104604 + 0.181179i
630630 0 0
631631 −8.84842 + 15.3259i −0.352250 + 0.610115i −0.986643 0.162895i 0.947917π-0.947917\pi
0.634393 + 0.773010i 0.281250π0.281250\pi
632632 8.72917 7.32464i 0.347228 0.291359i
633633 0 0
634634 1.36378 7.73439i 0.0541627 0.307172i
635635 −2.43554 + 13.8126i −0.0966514 + 0.548137i
636636 0 0
637637 7.02218 5.89231i 0.278229 0.233462i
638638 1.47732 2.55880i 0.0584878 0.101304i
639639 0 0
640640 10.5917 + 18.3454i 0.418676 + 0.725167i
641641 −35.7557 13.0140i −1.41226 0.514022i −0.480471 0.877011i 0.659534π-0.659534\pi
−0.931794 + 0.362988i 0.881757π0.881757\pi
642642 0 0
643643 35.9600 + 30.1741i 1.41813 + 1.18995i 0.952335 + 0.305053i 0.0986743π0.0986743\pi
0.465790 + 0.884895i 0.345770π0.345770\pi
644644 −4.90087 + 1.78377i −0.193121 + 0.0702904i
645645 0 0
646646 −2.68585 15.2322i −0.105673 0.599303i
647647 −28.2333 −1.10997 −0.554983 0.831862i 0.687275π-0.687275\pi
−0.554983 + 0.831862i 0.687275π0.687275\pi
648648 0 0
649649 0.546406 0.0214483
650650 1.22370 + 6.93997i 0.0479976 + 0.272208i
651651 0 0
652652 −29.0131 + 10.5599i −1.13624 + 0.413557i
653653 27.0469 + 22.6950i 1.05843 + 0.888125i 0.993954 0.109794i 0.0350192π-0.0350192\pi
0.0644721 + 0.997920i 0.479464π0.479464\pi
654654 0 0
655655 −18.2398 6.63873i −0.712686 0.259397i
656656 8.21052 + 14.2210i 0.320567 + 0.555239i
657657 0 0
658658 −2.54795 + 4.41318i −0.0993295 + 0.172044i
659659 31.9392 26.8002i 1.24418 1.04399i 0.246990 0.969018i 0.420558π-0.420558\pi
0.997186 0.0749700i 0.0238861π-0.0238861\pi
660660 0 0
661661 0.221213 1.25456i 0.00860418 0.0487967i −0.980203 0.197993i 0.936558π-0.936558\pi
0.988808 + 0.149197i 0.0476687π0.0476687\pi
662662 0.519270 2.94493i 0.0201820 0.114458i
663663 0 0
664664 −3.64691 + 3.06012i −0.141527 + 0.118756i
665665 8.11461 14.0549i 0.314671 0.545027i
666666 0 0
667667 4.76334 + 8.25035i 0.184437 + 0.319455i
668668 5.43452 + 1.97800i 0.210268 + 0.0765312i
669669 0 0
670670 3.72638 + 3.12680i 0.143963 + 0.120799i
671671 0.302191 0.109989i 0.0116660 0.00424606i
672672 0 0
673673 6.18756 + 35.0914i 0.238513 + 1.35267i 0.835088 + 0.550117i 0.185417π0.185417\pi
−0.596575 + 0.802558i 0.703472π0.703472\pi
674674 27.4951 1.05907
675675 0 0
676676 −26.5561 −1.02139
677677 3.12600 + 17.7284i 0.120142 + 0.681358i 0.984075 + 0.177752i 0.0568825π0.0568825\pi
−0.863934 + 0.503606i 0.832006π0.832006\pi
678678 0 0
679679 5.07053 1.84552i 0.194589 0.0708246i
680680 2.45346 + 2.05870i 0.0940859 + 0.0789474i
681681 0 0
682682 5.46682 + 1.98976i 0.209336 + 0.0761919i
683683 −19.8807 34.4344i −0.760715 1.31760i −0.942483 0.334255i 0.891515π-0.891515\pi
0.181768 0.983341i 0.441818π-0.441818\pi
684684 0 0
685685 15.0915 26.1393i 0.576617 0.998730i
686686 20.5814 17.2698i 0.785801 0.659366i
687687 0 0
688688 −2.72748 + 15.4683i −0.103984 + 0.589724i
689689 2.86359 16.2402i 0.109094 0.618703i
690690 0 0
691691 −12.9007 + 10.8250i −0.490767 + 0.411802i −0.854301 0.519779i 0.826014π-0.826014\pi
0.363534 + 0.931581i 0.381570π0.381570\pi
692692 4.44218 7.69408i 0.168866 0.292485i
693693 0 0
694694 −5.08038 8.79948i −0.192849 0.334024i
695695 23.6501 + 8.60793i 0.897099 + 0.326517i
696696 0 0
697697 5.25985 + 4.41354i 0.199231 + 0.167175i
698698 −44.9062 + 16.3445i −1.69973 + 0.618649i
699699 0 0
700700 0.920833 + 5.22230i 0.0348042 + 0.197385i
701701 −8.96921 −0.338762 −0.169381 0.985551i 0.554177π-0.554177\pi
−0.169381 + 0.985551i 0.554177π0.554177\pi
702702 0 0
703703 −27.7861 −1.04797
704704 0.620133 + 3.51695i 0.0233721 + 0.132550i
705705 0 0
706706 −59.0856 + 21.5054i −2.22372 + 0.809366i
707707 −7.55207 6.33694i −0.284025 0.238325i
708708 0 0
709709 −17.0476 6.20480i −0.640235 0.233026i 0.00144523 0.999999i 0.499540π-0.499540\pi
−0.641680 + 0.766973i 0.721762π0.721762\pi
710710 27.2477 + 47.1944i 1.02259 + 1.77117i
711711 0 0
712712 −7.87509 + 13.6401i −0.295131 + 0.511183i
713713 −14.3694 + 12.0574i −0.538139 + 0.451552i
714714 0 0
715715 −0.223546 + 1.26779i −0.00836014 + 0.0474127i
716716 −8.61142 + 48.8378i −0.321824 + 1.82515i
717717 0 0
718718 −21.7593 + 18.2582i −0.812049 + 0.681390i
719719 −15.7860 + 27.3421i −0.588718 + 1.01969i 0.405683 + 0.914014i 0.367034π0.367034\pi
−0.994401 + 0.105675i 0.966300π0.966300\pi
720720 0 0
721721 4.79034 + 8.29711i 0.178402 + 0.309001i
722722 39.1796 + 14.2602i 1.45811 + 0.530710i
723723 0 0
724724 18.4901 + 15.5150i 0.687177 + 0.576610i
725725 9.10230 3.31296i 0.338051 0.123040i
726726 0 0
727727 6.66970 + 37.8257i 0.247365 + 1.40288i 0.814934 + 0.579553i 0.196773π0.196773\pi
−0.567569 + 0.823326i 0.692116π0.692116\pi
728728 1.49595 0.0554436
729729 0 0
730730 −86.5599 −3.20373
731731 1.14046 + 6.46787i 0.0421814 + 0.239223i
732732 0 0
733733 28.5012 10.3736i 1.05271 0.383157i 0.243028 0.970019i 0.421859π-0.421859\pi
0.809686 + 0.586863i 0.199637π0.199637\pi
734734 12.8903 + 10.8163i 0.475790 + 0.399235i
735735 0 0
736736 −16.2151 5.90181i −0.597696 0.217543i
737737 0.135721 + 0.235076i 0.00499936 + 0.00865915i
738738 0 0
739739 −5.00127 + 8.66245i −0.183975 + 0.318653i −0.943230 0.332139i 0.892230π-0.892230\pi
0.759256 + 0.650792i 0.225563π0.225563\pi
740740 22.7688 19.1053i 0.836997 0.702324i
741741 0 0
742742 3.89255 22.0758i 0.142900 0.810427i
743743 6.29888 35.7227i 0.231083 1.31054i −0.619624 0.784899i 0.712715π-0.712715\pi
0.850707 0.525640i 0.176174π-0.176174\pi
744744 0 0
745745 −39.1574 + 32.8570i −1.43462 + 1.20379i
746746 −12.0865 + 20.9344i −0.442517 + 0.766461i
747747 0 0
748748 0.461619 + 0.799548i 0.0168785 + 0.0292344i
749749 −4.72453 1.71959i −0.172631 0.0628324i
750750 0 0
751751 −11.1493 9.35536i −0.406843 0.341382i 0.416288 0.909233i 0.363331π-0.363331\pi
−0.823132 + 0.567851i 0.807775π0.807775\pi
752752 −6.53659 + 2.37912i −0.238365 + 0.0867577i
753753 0 0
754754 −2.45124 13.9017i −0.0892688 0.506268i
755755 −10.7700 −0.391959
756756 0 0
757757 −45.5754 −1.65646 −0.828232 0.560385i 0.810653π-0.810653\pi
−0.828232 + 0.560385i 0.810653π0.810653\pi
758758 8.88380 + 50.3826i 0.322674 + 1.82998i
759759 0 0
760760 −15.9381 + 5.80099i −0.578135 + 0.210424i
761761 17.0411 + 14.2992i 0.617739 + 0.518344i 0.897092 0.441844i 0.145676π-0.145676\pi
−0.279353 + 0.960188i 0.590120π0.590120\pi
762762 0 0
763763 6.67970 + 2.43121i 0.241821 + 0.0880158i
764764 22.0189 + 38.1379i 0.796616 + 1.37978i
765765 0 0
766766 9.99393 17.3100i 0.361096 0.625436i
767767 1.99976 1.67800i 0.0722073 0.0605891i
768768 0 0
769769 2.37289 13.4573i 0.0855686 0.485284i −0.911664 0.410937i 0.865202π-0.865202\pi
0.997232 0.0743470i 0.0236872π-0.0236872\pi
770770 −0.303872 + 1.72334i −0.0109508 + 0.0621049i
771771 0 0
772772 20.1088 16.8733i 0.723730 0.607282i
773773 10.3270 17.8869i 0.371436 0.643345i −0.618351 0.785902i 0.712199π-0.712199\pi
0.989787 + 0.142557i 0.0455323π0.0455323\pi
774774 0 0
775775 9.53628 + 16.5173i 0.342553 + 0.593319i
776776 −5.29915 1.92873i −0.190228 0.0692374i
777777 0 0
778778 4.13092 + 3.46625i 0.148101 + 0.124271i
779779 −34.1689 + 12.4364i −1.22423 + 0.445582i
780780 0 0
781781 0.528050 + 2.99472i 0.0188951 + 0.107160i
782782 −5.37736 −0.192294
783783 0 0
784784 17.0093 0.607474
785785 −3.38996 19.2254i −0.120993 0.686185i
786786 0 0
787787 23.2136 8.44905i 0.827475 0.301176i 0.106653 0.994296i 0.465987π-0.465987\pi
0.720822 + 0.693120i 0.243764π0.243764\pi
788788 26.8999 + 22.5717i 0.958270 + 0.804084i
789789 0 0
790790 59.8435 + 21.7813i 2.12914 + 0.774943i
791791 −5.04429 8.73696i −0.179354 0.310651i
792792 0 0
793793 0.768202 1.33057i 0.0272797 0.0472498i
794794 −5.95902 + 5.00022i −0.211478 + 0.177451i
795795 0 0
796796 3.24728 18.4163i 0.115097 0.652747i
797797 −5.30769 + 30.1014i −0.188008 + 1.06625i 0.734021 + 0.679127i 0.237641π0.237641\pi
−0.922029 + 0.387120i 0.873470π0.873470\pi
798798 0 0
799799 −2.22812 + 1.86961i −0.0788251 + 0.0661421i
800800 −8.77257 + 15.1945i −0.310157 + 0.537208i
801801 0 0
802802 17.0904 + 29.6014i 0.603482 + 1.04526i
803803 −4.53887 1.65201i −0.160173 0.0582983i
804804 0 0
805805 −4.32225 3.62680i −0.152339 0.127828i
806806 26.1183 9.50628i 0.919977 0.334844i
807807 0 0
808808 1.78910 + 10.1465i 0.0629403 + 0.356952i
809809 46.8599 1.64751 0.823753 0.566949i 0.191876π-0.191876\pi
0.823753 + 0.566949i 0.191876π0.191876\pi
810810 0 0
811811 10.9984 0.386206 0.193103 0.981178i 0.438145π-0.438145\pi
0.193103 + 0.981178i 0.438145π0.438145\pi
812812 −1.84455 10.4610i −0.0647309 0.367107i
813813 0 0
814814 2.81537 1.02471i 0.0986788 0.0359161i
815815 −25.5877 21.4706i −0.896297 0.752082i
816816 0 0
817817 −32.6829 11.8956i −1.14343 0.416175i
818818 9.71738 + 16.8310i 0.339760 + 0.588482i
819819 0 0
820820 19.4479 33.6847i 0.679150 1.17632i
821821 −27.5648 + 23.1296i −0.962019 + 0.807230i −0.981280 0.192585i 0.938313π-0.938313\pi
0.0192613 + 0.999814i 0.493869π0.493869\pi
822822 0 0
823823 −8.50644 + 48.2424i −0.296516 + 1.68163i 0.364461 + 0.931219i 0.381253π0.381253\pi
−0.660977 + 0.750406i 0.729858π0.729858\pi
824824 1.73868 9.86053i 0.0605697 0.343508i
825825 0 0
826826 2.71833 2.28095i 0.0945829 0.0793645i
827827 7.80533 13.5192i 0.271418 0.470109i −0.697807 0.716286i 0.745841π-0.745841\pi
0.969225 + 0.246176i 0.0791742π0.0791742\pi
828828 0 0
829829 −5.73541 9.93401i −0.199199 0.345023i 0.749070 0.662491i 0.230501π-0.230501\pi
−0.948269 + 0.317468i 0.897167π0.897167\pi
830830 −25.0017 9.09986i −0.867820 0.315861i
831831 0 0
832832 13.0701 + 10.9671i 0.453123 + 0.380215i
833833 6.68329 2.43252i 0.231562 0.0842817i
834834 0 0
835835 1.08646 + 6.16163i 0.0375986 + 0.213232i
836836 −4.88922 −0.169097
837837 0 0
838838 14.7716 0.510278
839839 −0.117269 0.665065i −0.00404857 0.0229606i 0.982717 0.185117i 0.0592663π-0.0592663\pi
−0.986765 + 0.162156i 0.948155π0.948155\pi
840840 0 0
841841 9.01801 3.28229i 0.310966 0.113182i
842842 −49.9572 41.9190i −1.72164 1.44463i
843843 0 0
844844 −12.1505 4.42242i −0.418238 0.152226i
845845 −14.3649 24.8808i −0.494168 0.855925i
846846 0 0
847847 5.29901 9.17815i 0.182076 0.315365i
848848 23.4403 19.6687i 0.804942 0.675427i
849849 0 0
850850 −0.949430 + 5.38448i −0.0325652 + 0.184686i
851851 −1.67748 + 9.51344i −0.0575032 + 0.326117i
852852 0 0
853853 30.1483 25.2974i 1.03226 0.866166i 0.0411388 0.999153i 0.486901π-0.486901\pi
0.991118 + 0.132987i 0.0424570π0.0424570\pi
854854 1.04424 1.80867i 0.0357331 0.0618915i
855855 0 0
856856 2.62721 + 4.55047i 0.0897963 + 0.155532i
857857 −30.6923 11.1711i −1.04843 0.381598i −0.240360 0.970684i 0.577266π-0.577266\pi
−0.808070 + 0.589086i 0.799488π0.799488\pi
858858 0 0
859859 −25.4301 21.3384i −0.867664 0.728056i 0.0959411 0.995387i 0.469414π-0.469414\pi
−0.963605 + 0.267331i 0.913858π0.913858\pi
860860 34.9606 12.7246i 1.19215 0.433906i
861861 0 0
862862 −10.2535 58.1507i −0.349237 1.98062i
863863 22.6796 0.772024 0.386012 0.922494i 0.373852π-0.373852\pi
0.386012 + 0.922494i 0.373852π0.373852\pi
864864 0 0
865865 9.61158 0.326804
866866 −7.04609 39.9604i −0.239436 1.35791i
867867 0 0
868868 19.6539 7.15344i 0.667097 0.242804i
869869 2.72227 + 2.28425i 0.0923466 + 0.0774880i
870870 0 0
871871 1.21863 + 0.443547i 0.0412919 + 0.0150290i
872872 −3.71444 6.43360i −0.125787 0.217869i
873873 0 0
874874 14.2385 24.6618i 0.481625 0.834199i
875875 5.59779 4.69710i 0.189240 0.158791i
876876 0 0
877877 1.60516 9.10333i 0.0542025 0.307398i −0.945639 0.325219i 0.894562π-0.894562\pi
0.999841 + 0.0178215i 0.00567306π0.00567306\pi
878878 8.72888 49.5040i 0.294586 1.67068i
879879 0 0
880880 −1.82986 + 1.53544i −0.0616846 + 0.0517595i
881881 −3.89378 + 6.74422i −0.131185 + 0.227219i −0.924134 0.382070i 0.875211π-0.875211\pi
0.792949 + 0.609288i 0.208545π0.208545\pi
882882 0 0
883883 16.2309 + 28.1127i 0.546213 + 0.946068i 0.998530 + 0.0542106i 0.0172642π0.0172642\pi
−0.452317 + 0.891857i 0.649402π0.649402\pi
884884 4.14485 + 1.50860i 0.139407 + 0.0507398i
885885 0 0
886886 −37.8737 31.7798i −1.27239 1.06766i
887887 31.8064 11.5766i 1.06795 0.388704i 0.252543 0.967586i 0.418733π-0.418733\pi
0.815411 + 0.578882i 0.196511π0.196511\pi
888888 0 0
889889 0.882619 + 5.00558i 0.0296021 + 0.167882i
890890 −88.0234 −2.95055
891891 0 0
892892 43.8822 1.46929
893893 −2.67473 15.1691i −0.0895063 0.507616i
894894 0 0
895895 −50.4149 + 18.3495i −1.68518 + 0.613357i
896896 5.88071 + 4.93450i 0.196461 + 0.164850i
897897 0 0
898898 9.58500 + 3.48865i 0.319855 + 0.116418i
899899 −19.1024 33.0863i −0.637101 1.10349i
900900 0 0
901901 6.39731 11.0805i 0.213125 0.369144i
902902 3.00345 2.52020i 0.100004 0.0839133i
903903 0 0
904904 −1.83085 + 10.3833i −0.0608931 + 0.345342i
905905 −4.53444 + 25.7161i −0.150730 + 0.854831i
906906 0 0
907907 −8.47233 + 7.10913i −0.281319 + 0.236055i −0.772518 0.634992i 0.781003π-0.781003\pi
0.491199 + 0.871047i 0.336559π0.336559\pi
908908 19.5580 33.8754i 0.649054 1.12420i
909909 0 0
910910 4.18022 + 7.24036i 0.138573 + 0.240016i
911911 −11.7886 4.29070i −0.390574 0.142157i 0.139266 0.990255i 0.455526π-0.455526\pi
−0.529840 + 0.848098i 0.677748π0.677748\pi
912912 0 0
913913 −1.13732 0.954324i −0.0376398 0.0315835i
914914 −9.73325 + 3.54261i −0.321947 + 0.117179i
915915 0 0
916916 −0.760923 4.31541i −0.0251416 0.142585i
917917 −7.03415 −0.232288
918918 0 0
919919 −5.92909 −0.195583 −0.0977913 0.995207i 0.531178π-0.531178\pi
−0.0977913 + 0.995207i 0.531178π0.531178\pi
920920 1.02395 + 5.80711i 0.0337586 + 0.191455i
921921 0 0
922922 55.6723 20.2631i 1.83347 0.667328i
923923 11.1293 + 9.33860i 0.366326 + 0.307384i
924924 0 0
925925 9.22987 + 3.35940i 0.303476 + 0.110456i
926926 −29.0775 50.3636i −0.955545 1.65505i
927927 0 0
928928 17.5726 30.4366i 0.576848 0.999131i
929929 −7.68555 + 6.44894i −0.252155 + 0.211583i −0.760100 0.649807i 0.774850π-0.774850\pi
0.507945 + 0.861390i 0.330405π0.330405\pi
930930 0 0
931931 −6.54033 + 37.0921i −0.214351 + 1.21564i
932932 −5.98553 + 33.9456i −0.196063 + 1.11193i
933933 0 0
934934 34.4496 28.9067i 1.12723 0.945855i
935935 −0.499405 + 0.864995i −0.0163323 + 0.0282883i
936936 0 0
937937 11.7671 + 20.3811i 0.384413 + 0.665823i 0.991688 0.128669i 0.0410705π-0.0410705\pi
−0.607274 + 0.794492i 0.707737π0.707737\pi
938938 1.65652 + 0.602925i 0.0540874 + 0.0196862i
939939 0 0
940940 12.6218 + 10.5909i 0.411677 + 0.345438i
941941 27.5326 10.0210i 0.897536 0.326676i 0.148271 0.988947i 0.452629π-0.452629\pi
0.749265 + 0.662270i 0.230407π0.230407\pi
942942 0 0
943943 2.19520 + 12.4496i 0.0714854 + 0.405414i
944944 4.84388 0.157655
945945 0 0
946946 3.75023 0.121930
947947 9.31829 + 52.8467i 0.302804 + 1.71729i 0.633666 + 0.773607i 0.281549π0.281549\pi
−0.330862 + 0.943679i 0.607340π0.607340\pi
948948 0 0
949949 −21.6849 + 7.89266i −0.703922 + 0.256207i
950950 −22.1805 18.6117i −0.719631 0.603842i
951951 0 0
952952 1.09066 + 0.396968i 0.0353485 + 0.0128658i
953953 2.44828 + 4.24055i 0.0793076 + 0.137365i 0.902951 0.429743i 0.141396π-0.141396\pi
−0.823644 + 0.567108i 0.808062π0.808062\pi
954954 0 0
955955 −23.8212 + 41.2596i −0.770837 + 1.33513i
956956 −37.6793 + 31.6167i −1.21864 + 1.02256i
957957 0 0
958958 15.3190 86.8781i 0.494933 2.80691i
959959 1.89938 10.7719i 0.0613341 0.347843i
960960 0 0
961961 33.8782 28.4272i 1.09285 0.917007i
962962 7.15698 12.3962i 0.230750 0.399671i
963963 0 0
964964 −24.0255 41.6134i −0.773810 1.34028i
965965 26.6862 + 9.71297i 0.859058 + 0.312671i
966966 0 0
967967 13.0175 + 10.9230i 0.418615 + 0.351259i 0.827636 0.561266i 0.189685π-0.189685\pi
−0.409021 + 0.912525i 0.634130π0.634130\pi
968968 −10.4079 + 3.78816i −0.334522 + 0.121756i
969969 0 0
970970 −5.47272 31.0373i −0.175718 0.996548i
971971 −2.68374 −0.0861253 −0.0430627 0.999072i 0.513712π-0.513712\pi
−0.0430627 + 0.999072i 0.513712π0.513712\pi
972972 0 0
973973 9.12064 0.292394
974974 −1.48049 8.39626i −0.0474379 0.269034i
975975 0 0
976976 2.67892 0.975047i 0.0857501 0.0312105i
977977 8.42115 + 7.06619i 0.269417 + 0.226067i 0.767479 0.641074i 0.221511π-0.221511\pi
−0.498063 + 0.867141i 0.665955π0.665955\pi
978978 0 0
979979 −4.61561 1.67994i −0.147515 0.0536912i
980980 −20.1445 34.8914i −0.643494 1.11456i
981981 0 0
982982 −40.8734 + 70.7948i −1.30432 + 2.25915i
983983 −36.5983 + 30.7096i −1.16730 + 0.979484i −0.999979 0.00641835i 0.997957π-0.997957\pi
−0.167324 + 0.985902i 0.553513π0.553513\pi
984984 0 0
985985 −6.59684 + 37.4125i −0.210193 + 1.19206i
986986 1.90183 10.7858i 0.0605666 0.343490i
987987 0 0
988988 −17.8938 + 15.0147i −0.569278 + 0.477681i
989989 −6.04594 + 10.4719i −0.192250 + 0.332986i
990990 0 0
991991 −27.7503 48.0649i −0.881517 1.52683i −0.849654 0.527340i 0.823189π-0.823189\pi
−0.0318627 0.999492i 0.510144π-0.510144\pi
992992 65.0272 + 23.6680i 2.06462 + 0.751459i
993993 0 0
994994 15.1284 + 12.6942i 0.479843 + 0.402636i
995995 19.0110 6.91944i 0.602689 0.219361i
996996 0 0
997997 −7.82228 44.3624i −0.247734 1.40497i −0.814056 0.580786i 0.802745π-0.802745\pi
0.566322 0.824184i 0.308366π-0.308366\pi
998998 8.61859 0.272817
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 243.2.e.d.28.1 12
3.2 odd 2 243.2.e.a.28.2 12
9.2 odd 6 81.2.e.a.37.2 12
9.4 even 3 243.2.e.c.190.2 12
9.5 odd 6 243.2.e.b.190.1 12
9.7 even 3 27.2.e.a.22.1 yes 12
27.2 odd 18 243.2.e.a.217.2 12
27.4 even 9 729.2.c.e.487.5 12
27.5 odd 18 729.2.a.d.1.5 6
27.7 even 9 27.2.e.a.16.1 12
27.11 odd 18 243.2.e.b.55.1 12
27.13 even 9 729.2.c.e.244.5 12
27.14 odd 18 729.2.c.b.244.2 12
27.16 even 9 243.2.e.c.55.2 12
27.20 odd 18 81.2.e.a.46.2 12
27.22 even 9 729.2.a.a.1.2 6
27.23 odd 18 729.2.c.b.487.2 12
27.25 even 9 inner 243.2.e.d.217.1 12
36.7 odd 6 432.2.u.c.49.2 12
45.7 odd 12 675.2.u.b.49.1 24
45.34 even 6 675.2.l.c.76.2 12
45.43 odd 12 675.2.u.b.49.4 24
108.7 odd 18 432.2.u.c.97.2 12
135.7 odd 36 675.2.u.b.124.4 24
135.34 even 18 675.2.l.c.151.2 12
135.88 odd 36 675.2.u.b.124.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.16.1 12 27.7 even 9
27.2.e.a.22.1 yes 12 9.7 even 3
81.2.e.a.37.2 12 9.2 odd 6
81.2.e.a.46.2 12 27.20 odd 18
243.2.e.a.28.2 12 3.2 odd 2
243.2.e.a.217.2 12 27.2 odd 18
243.2.e.b.55.1 12 27.11 odd 18
243.2.e.b.190.1 12 9.5 odd 6
243.2.e.c.55.2 12 27.16 even 9
243.2.e.c.190.2 12 9.4 even 3
243.2.e.d.28.1 12 1.1 even 1 trivial
243.2.e.d.217.1 12 27.25 even 9 inner
432.2.u.c.49.2 12 36.7 odd 6
432.2.u.c.97.2 12 108.7 odd 18
675.2.l.c.76.2 12 45.34 even 6
675.2.l.c.151.2 12 135.34 even 18
675.2.u.b.49.1 24 45.7 odd 12
675.2.u.b.49.4 24 45.43 odd 12
675.2.u.b.124.1 24 135.88 odd 36
675.2.u.b.124.4 24 135.7 odd 36
729.2.a.a.1.2 6 27.22 even 9
729.2.a.d.1.5 6 27.5 odd 18
729.2.c.b.244.2 12 27.14 odd 18
729.2.c.b.487.2 12 27.23 odd 18
729.2.c.e.244.5 12 27.13 even 9
729.2.c.e.487.5 12 27.4 even 9