Properties

Label 273.2.j.c.172.3
Level 273273
Weight 22
Character 273.172
Analytic conductor 2.1802.180
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(100,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 273=3713 273 = 3 \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 273.j (of order 33, 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: 2.179915975182.17991597518
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20+18x184x17+211x1659x15+1458x14526x13+7324x12++1369 x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 172.3
Root 0.904928+1.56738i0.904928 + 1.56738i of defining polynomial
Character χ\chi == 273.172
Dual form 273.2.j.c.100.3

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+(0.904928+1.56738i)q2+1.00000q3+(0.6377891.10468i)q4+(1.98776+3.44291i)q5+(0.904928+1.56738i)q6+(2.603840.469078i)q71.31110q8+1.00000q97.19513q100.286654q11+(0.6377891.10468i)q12+(3.60075+0.185985i)q13+(3.091513.65672i)q14+(1.98776+3.44291i)q15+(2.462034.26436i)q16+(2.30091+3.98530i)q17+(0.904928+1.56738i)q186.96749q19+(2.535554.39170i)q20+(2.603840.469078i)q21+(0.2594020.449297i)q22+(3.619296.26879i)q231.31110q24+(5.40240+9.35723i)q25+(3.54993+5.47545i)q26+1.00000q27+(1.14252+3.17559i)q28+(0.421754+0.730500i)q297.19513q30+(0.212854+0.368675i)q31+(3.14482+5.44698i)q320.286654q338.32864q34+(3.560829.89718i)q35+(0.6377891.10468i)q36+(2.182083.77948i)q37+(6.3050710.9207i)q38+(3.60075+0.185985i)q39+(2.606154.51399i)q40+(0.5098850.883147i)q41+(3.091513.65672i)q42+(0.5852911.01375i)q43+(0.182825+0.316662i)q44+(1.98776+3.44291i)q45+(6.55039+11.3456i)q46+(2.71264+4.69843i)q47+(2.462034.26436i)q48+(6.55993+2.44280i)q49+(9.7775616.9352i)q50+(2.30091+3.98530i)q51+(2.091074.09631i)q52+(0.574226+0.994589i)q53+(0.904928+1.56738i)q54+(0.5698010.986924i)q55+(3.41389+0.615007i)q566.96749q571.52663q58+(2.42927+4.20762i)q59+(2.535554.39170i)q60+8.16848q61+(0.3852360.667248i)q62+(2.603840.469078i)q631.53522q64+(6.51711+12.7667i)q65+(0.2594020.449297i)q66+1.57387q67+(2.934995.08356i)q68+(3.619296.26879i)q69+(18.7349+3.37507i)q70+(3.22369+5.58359i)q711.31110q72+(8.2484514.2867i)q73+(3.94925+6.84031i)q74+(5.40240+9.35723i)q75+(4.44379+7.69686i)q76+(0.746401+0.134463i)q77+(3.54993+5.47545i)q78+(3.844126.65821i)q79+19.5757q80+1.00000q81+1.84564q82+13.3888q83+(1.14252+3.17559i)q84+(9.14733+15.8436i)q85+(1.05929+1.83475i)q86+(0.421754+0.730500i)q87+0.375832q88+(1.107861.91886i)q897.19513q90+(9.288532.17331i)q919.23336q92+(0.212854+0.368675i)q939.81898q94+(13.849723.9884i)q95+(3.14482+5.44698i)q96+(9.5224116.4933i)q97+(9.76507+8.07135i)q980.286654q99+O(q100)q+(-0.904928 + 1.56738i) q^{2} +1.00000 q^{3} +(-0.637789 - 1.10468i) q^{4} +(1.98776 + 3.44291i) q^{5} +(-0.904928 + 1.56738i) q^{6} +(-2.60384 - 0.469078i) q^{7} -1.31110 q^{8} +1.00000 q^{9} -7.19513 q^{10} -0.286654 q^{11} +(-0.637789 - 1.10468i) q^{12} +(3.60075 + 0.185985i) q^{13} +(3.09151 - 3.65672i) q^{14} +(1.98776 + 3.44291i) q^{15} +(2.46203 - 4.26436i) q^{16} +(2.30091 + 3.98530i) q^{17} +(-0.904928 + 1.56738i) q^{18} -6.96749 q^{19} +(2.53555 - 4.39170i) q^{20} +(-2.60384 - 0.469078i) q^{21} +(0.259402 - 0.449297i) q^{22} +(3.61929 - 6.26879i) q^{23} -1.31110 q^{24} +(-5.40240 + 9.35723i) q^{25} +(-3.54993 + 5.47545i) q^{26} +1.00000 q^{27} +(1.14252 + 3.17559i) q^{28} +(0.421754 + 0.730500i) q^{29} -7.19513 q^{30} +(-0.212854 + 0.368675i) q^{31} +(3.14482 + 5.44698i) q^{32} -0.286654 q^{33} -8.32864 q^{34} +(-3.56082 - 9.89718i) q^{35} +(-0.637789 - 1.10468i) q^{36} +(2.18208 - 3.77948i) q^{37} +(6.30507 - 10.9207i) q^{38} +(3.60075 + 0.185985i) q^{39} +(-2.60615 - 4.51399i) q^{40} +(-0.509885 - 0.883147i) q^{41} +(3.09151 - 3.65672i) q^{42} +(0.585291 - 1.01375i) q^{43} +(0.182825 + 0.316662i) q^{44} +(1.98776 + 3.44291i) q^{45} +(6.55039 + 11.3456i) q^{46} +(2.71264 + 4.69843i) q^{47} +(2.46203 - 4.26436i) q^{48} +(6.55993 + 2.44280i) q^{49} +(-9.77756 - 16.9352i) q^{50} +(2.30091 + 3.98530i) q^{51} +(-2.09107 - 4.09631i) q^{52} +(-0.574226 + 0.994589i) q^{53} +(-0.904928 + 1.56738i) q^{54} +(-0.569801 - 0.986924i) q^{55} +(3.41389 + 0.615007i) q^{56} -6.96749 q^{57} -1.52663 q^{58} +(2.42927 + 4.20762i) q^{59} +(2.53555 - 4.39170i) q^{60} +8.16848 q^{61} +(-0.385236 - 0.667248i) q^{62} +(-2.60384 - 0.469078i) q^{63} -1.53522 q^{64} +(6.51711 + 12.7667i) q^{65} +(0.259402 - 0.449297i) q^{66} +1.57387 q^{67} +(2.93499 - 5.08356i) q^{68} +(3.61929 - 6.26879i) q^{69} +(18.7349 + 3.37507i) q^{70} +(-3.22369 + 5.58359i) q^{71} -1.31110 q^{72} +(8.24845 - 14.2867i) q^{73} +(3.94925 + 6.84031i) q^{74} +(-5.40240 + 9.35723i) q^{75} +(4.44379 + 7.69686i) q^{76} +(0.746401 + 0.134463i) q^{77} +(-3.54993 + 5.47545i) q^{78} +(-3.84412 - 6.65821i) q^{79} +19.5757 q^{80} +1.00000 q^{81} +1.84564 q^{82} +13.3888 q^{83} +(1.14252 + 3.17559i) q^{84} +(-9.14733 + 15.8436i) q^{85} +(1.05929 + 1.83475i) q^{86} +(0.421754 + 0.730500i) q^{87} +0.375832 q^{88} +(1.10786 - 1.91886i) q^{89} -7.19513 q^{90} +(-9.28853 - 2.17331i) q^{91} -9.23336 q^{92} +(-0.212854 + 0.368675i) q^{93} -9.81898 q^{94} +(-13.8497 - 23.9884i) q^{95} +(3.14482 + 5.44698i) q^{96} +(9.52241 - 16.4933i) q^{97} +(-9.76507 + 8.07135i) q^{98} -0.286654 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+20q316q49q712q8+20q9+8q10+16q1116q125q139q1420q1614q19+12q209q219q2214q2312q2432q25++16q99+O(q100) 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/273Z)×\left(\mathbb{Z}/273\mathbb{Z}\right)^\times.

nn 9292 106106 157157
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\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 −0.904928 + 1.56738i −0.639881 + 1.10831i 0.345578 + 0.938390i 0.387683π0.387683\pi
−0.985459 + 0.169916i 0.945650π0.945650\pi
33 1.00000 0.577350
44 −0.637789 1.10468i −0.318895 0.552342i
55 1.98776 + 3.44291i 0.888954 + 1.53971i 0.841113 + 0.540859i 0.181901π0.181901\pi
0.0478412 + 0.998855i 0.484766π0.484766\pi
66 −0.904928 + 1.56738i −0.369435 + 0.639881i
77 −2.60384 0.469078i −0.984158 0.177295i
88 −1.31110 −0.463543
99 1.00000 0.333333
1010 −7.19513 −2.27530
1111 −0.286654 −0.0864295 −0.0432148 0.999066i 0.513760π-0.513760\pi
−0.0432148 + 0.999066i 0.513760π0.513760\pi
1212 −0.637789 1.10468i −0.184114 0.318895i
1313 3.60075 + 0.185985i 0.998669 + 0.0515830i
1414 3.09151 3.65672i 0.826240 0.977300i
1515 1.98776 + 3.44291i 0.513238 + 0.888954i
1616 2.46203 4.26436i 0.615507 1.06609i
1717 2.30091 + 3.98530i 0.558053 + 0.966577i 0.997659 + 0.0683857i 0.0217848π0.0217848\pi
−0.439606 + 0.898191i 0.644882π0.644882\pi
1818 −0.904928 + 1.56738i −0.213294 + 0.369435i
1919 −6.96749 −1.59845 −0.799225 0.601031i 0.794757π-0.794757\pi
−0.799225 + 0.601031i 0.794757π0.794757\pi
2020 2.53555 4.39170i 0.566965 0.982013i
2121 −2.60384 0.469078i −0.568204 0.102361i
2222 0.259402 0.449297i 0.0553046 0.0957904i
2323 3.61929 6.26879i 0.754673 1.30713i −0.190863 0.981617i 0.561129π-0.561129\pi
0.945537 0.325516i 0.105538π-0.105538\pi
2424 −1.31110 −0.267627
2525 −5.40240 + 9.35723i −1.08048 + 1.87145i
2626 −3.54993 + 5.47545i −0.696199 + 1.07382i
2727 1.00000 0.192450
2828 1.14252 + 3.17559i 0.215915 + 0.600130i
2929 0.421754 + 0.730500i 0.0783178 + 0.135650i 0.902524 0.430639i 0.141712π-0.141712\pi
−0.824206 + 0.566289i 0.808378π0.808378\pi
3030 −7.19513 −1.31364
3131 −0.212854 + 0.368675i −0.0382298 + 0.0662159i −0.884507 0.466527i 0.845505π-0.845505\pi
0.846277 + 0.532742i 0.178839π0.178839\pi
3232 3.14482 + 5.44698i 0.555930 + 0.962900i
3333 −0.286654 −0.0499001
3434 −8.32864 −1.42835
3535 −3.56082 9.89718i −0.601888 1.67293i
3636 −0.637789 1.10468i −0.106298 0.184114i
3737 2.18208 3.77948i 0.358732 0.621342i −0.629017 0.777391i 0.716542π-0.716542\pi
0.987749 + 0.156049i 0.0498758π0.0498758\pi
3838 6.30507 10.9207i 1.02282 1.77157i
3939 3.60075 + 0.185985i 0.576582 + 0.0297814i
4040 −2.60615 4.51399i −0.412069 0.713724i
4141 −0.509885 0.883147i −0.0796307 0.137924i 0.823460 0.567374i 0.192041π-0.192041\pi
−0.903091 + 0.429450i 0.858707π0.858707\pi
4242 3.09151 3.65672i 0.477030 0.564245i
4343 0.585291 1.01375i 0.0892560 0.154596i −0.817941 0.575302i 0.804884π-0.804884\pi
0.907197 + 0.420706i 0.138218π0.138218\pi
4444 0.182825 + 0.316662i 0.0275619 + 0.0477386i
4545 1.98776 + 3.44291i 0.296318 + 0.513238i
4646 6.55039 + 11.3456i 0.965802 + 1.67282i
4747 2.71264 + 4.69843i 0.395680 + 0.685337i 0.993188 0.116526i 0.0371758π-0.0371758\pi
−0.597508 + 0.801863i 0.703842π0.703842\pi
4848 2.46203 4.26436i 0.355363 0.615507i
4949 6.55993 + 2.44280i 0.937133 + 0.348972i
5050 −9.77756 16.9352i −1.38276 2.39500i
5151 2.30091 + 3.98530i 0.322192 + 0.558053i
5252 −2.09107 4.09631i −0.289979 0.568056i
5353 −0.574226 + 0.994589i −0.0788760 + 0.136617i −0.902765 0.430134i 0.858466π-0.858466\pi
0.823889 + 0.566751i 0.191800π0.191800\pi
5454 −0.904928 + 1.56738i −0.123145 + 0.213294i
5555 −0.569801 0.986924i −0.0768319 0.133077i
5656 3.41389 + 0.615007i 0.456200 + 0.0821838i
5757 −6.96749 −0.922866
5858 −1.52663 −0.200456
5959 2.42927 + 4.20762i 0.316264 + 0.547785i 0.979705 0.200443i 0.0642381π-0.0642381\pi
−0.663441 + 0.748228i 0.730905π0.730905\pi
6060 2.53555 4.39170i 0.327338 0.566965i
6161 8.16848 1.04587 0.522933 0.852374i 0.324838π-0.324838\pi
0.522933 + 0.852374i 0.324838π0.324838\pi
6262 −0.385236 0.667248i −0.0489250 0.0847406i
6363 −2.60384 0.469078i −0.328053 0.0590983i
6464 −1.53522 −0.191902
6565 6.51711 + 12.7667i 0.808348 + 1.58352i
6666 0.259402 0.449297i 0.0319301 0.0553046i
6767 1.57387 0.192279 0.0961397 0.995368i 0.469350π-0.469350\pi
0.0961397 + 0.995368i 0.469350π0.469350\pi
6868 2.93499 5.08356i 0.355920 0.616472i
6969 3.61929 6.26879i 0.435711 0.754673i
7070 18.7349 + 3.37507i 2.23925 + 0.403399i
7171 −3.22369 + 5.58359i −0.382581 + 0.662650i −0.991430 0.130636i 0.958298π-0.958298\pi
0.608849 + 0.793286i 0.291631π0.291631\pi
7272 −1.31110 −0.154514
7373 8.24845 14.2867i 0.965408 1.67214i 0.256893 0.966440i 0.417301π-0.417301\pi
0.708515 0.705696i 0.249365π-0.249365\pi
7474 3.94925 + 6.84031i 0.459092 + 0.795170i
7575 −5.40240 + 9.35723i −0.623815 + 1.08048i
7676 4.44379 + 7.69686i 0.509737 + 0.882891i
7777 0.746401 + 0.134463i 0.0850603 + 0.0153235i
7878 −3.54993 + 5.47545i −0.401950 + 0.619972i
7979 −3.84412 6.65821i −0.432497 0.749107i 0.564590 0.825371i 0.309034π-0.309034\pi
−0.997088 + 0.0762639i 0.975701π0.975701\pi
8080 19.5757 2.18863
8181 1.00000 0.111111
8282 1.84564 0.203817
8383 13.3888 1.46961 0.734805 0.678279i 0.237274π-0.237274\pi
0.734805 + 0.678279i 0.237274π0.237274\pi
8484 1.14252 + 3.17559i 0.124659 + 0.346485i
8585 −9.14733 + 15.8436i −0.992168 + 1.71848i
8686 1.05929 + 1.83475i 0.114226 + 0.197846i
8787 0.421754 + 0.730500i 0.0452168 + 0.0783178i
8888 0.375832 0.0400639
8989 1.10786 1.91886i 0.117433 0.203399i −0.801317 0.598240i 0.795867π-0.795867\pi
0.918750 + 0.394841i 0.129200π0.129200\pi
9090 −7.19513 −0.758433
9191 −9.28853 2.17331i −0.973702 0.227825i
9292 −9.23336 −0.962645
9393 −0.212854 + 0.368675i −0.0220720 + 0.0382298i
9494 −9.81898 −1.01275
9595 −13.8497 23.9884i −1.42095 2.46116i
9696 3.14482 + 5.44698i 0.320967 + 0.555930i
9797 9.52241 16.4933i 0.966854 1.67464i 0.262306 0.964985i 0.415517π-0.415517\pi
0.704549 0.709656i 0.251150π-0.251150\pi
9898 −9.76507 + 8.07135i −0.986421 + 0.815330i
9999 −0.286654 −0.0288098
100100 13.7824 1.37824
101101 −9.08855 −0.904344 −0.452172 0.891931i 0.649351π-0.649351\pi
−0.452172 + 0.891931i 0.649351π0.649351\pi
102102 −8.32864 −0.824658
103103 2.34421 + 4.06029i 0.230982 + 0.400072i 0.958097 0.286443i 0.0924729π-0.0924729\pi
−0.727116 + 0.686515i 0.759140π0.759140\pi
104104 −4.72094 0.243845i −0.462926 0.0239109i
105105 −3.56082 9.89718i −0.347500 0.965866i
106106 −1.03927 1.80006i −0.100943 0.174838i
107107 −7.25279 + 12.5622i −0.701154 + 1.21443i 0.266908 + 0.963722i 0.413998π0.413998\pi
−0.968062 + 0.250712i 0.919335π0.919335\pi
108108 −0.637789 1.10468i −0.0613713 0.106298i
109109 2.09694 3.63200i 0.200850 0.347883i −0.747952 0.663752i 0.768963π-0.768963\pi
0.948803 + 0.315870i 0.102296π0.102296\pi
110110 2.06251 0.196653
111111 2.18208 3.77948i 0.207114 0.358732i
112112 −8.41104 + 9.94881i −0.794768 + 0.940074i
113113 4.12305 7.14133i 0.387864 0.671800i −0.604298 0.796758i 0.706546π-0.706546\pi
0.992162 + 0.124958i 0.0398797π0.0398797\pi
114114 6.30507 10.9207i 0.590524 1.02282i
115115 28.7771 2.68348
116116 0.537981 0.931810i 0.0499503 0.0865164i
117117 3.60075 + 0.185985i 0.332890 + 0.0171943i
118118 −8.79326 −0.809485
119119 −4.12179 11.4564i −0.377843 1.05020i
120120 −2.60615 4.51399i −0.237908 0.412069i
121121 −10.9178 −0.992530
122122 −7.39189 + 12.8031i −0.669230 + 1.15914i
123123 −0.509885 0.883147i −0.0459748 0.0796307i
124124 0.543025 0.0487651
125125 −23.0771 −2.06408
126126 3.09151 3.65672i 0.275413 0.325767i
127127 −3.92173 6.79263i −0.347997 0.602748i 0.637897 0.770122i 0.279805π-0.279805\pi
−0.985894 + 0.167374i 0.946471π0.946471\pi
128128 −4.90037 + 8.48769i −0.433136 + 0.750213i
129129 0.585291 1.01375i 0.0515320 0.0892560i
130130 −25.9079 1.33819i −2.27227 0.117367i
131131 −4.04277 7.00228i −0.353218 0.611792i 0.633593 0.773666i 0.281579π-0.281579\pi
−0.986811 + 0.161874i 0.948246π0.948246\pi
132132 0.182825 + 0.316662i 0.0159129 + 0.0275619i
133133 18.1422 + 3.26829i 1.57313 + 0.283397i
134134 −1.42424 + 2.46686i −0.123036 + 0.213104i
135135 1.98776 + 3.44291i 0.171079 + 0.296318i
136136 −3.01672 5.22512i −0.258682 0.448050i
137137 −0.754841 1.30742i −0.0644904 0.111701i 0.831977 0.554809i 0.187209π-0.187209\pi
−0.896468 + 0.443109i 0.853876π0.853876\pi
138138 6.55039 + 11.3456i 0.557606 + 0.965802i
139139 2.02132 3.50104i 0.171446 0.296954i −0.767479 0.641074i 0.778489π-0.778489\pi
0.938926 + 0.344120i 0.111823π0.111823\pi
140140 −8.66220 + 10.2459i −0.732089 + 0.865936i
141141 2.71264 + 4.69843i 0.228446 + 0.395680i
142142 −5.83441 10.1055i −0.489613 0.848034i
143143 −1.03217 0.0533134i −0.0863145 0.00445829i
144144 2.46203 4.26436i 0.205169 0.355363i
145145 −1.67670 + 2.90412i −0.139242 + 0.241174i
146146 14.9285 + 25.8569i 1.23549 + 2.13993i
147147 6.55993 + 2.44280i 0.541054 + 0.201479i
148148 −5.56683 −0.457591
149149 −19.1947 −1.57249 −0.786247 0.617912i 0.787979π-0.787979\pi
−0.786247 + 0.617912i 0.787979π0.787979\pi
150150 −9.77756 16.9352i −0.798335 1.38276i
151151 −9.47334 + 16.4083i −0.770929 + 1.33529i 0.166125 + 0.986105i 0.446874π0.446874\pi
−0.937054 + 0.349184i 0.886459π0.886459\pi
152152 9.13506 0.740951
153153 2.30091 + 3.98530i 0.186018 + 0.322192i
154154 −0.886194 + 1.04822i −0.0714116 + 0.0844676i
155155 −1.69242 −0.135938
156156 −2.09107 4.09631i −0.167419 0.327967i
157157 −9.31770 + 16.1387i −0.743633 + 1.28801i 0.207197 + 0.978299i 0.433566π0.433566\pi
−0.950831 + 0.309711i 0.899768π0.899768\pi
158158 13.9146 1.10699
159159 −0.574226 + 0.994589i −0.0455391 + 0.0788760i
160160 −12.5023 + 21.6546i −0.988394 + 1.71195i
161161 −12.3646 + 14.6252i −0.974465 + 1.15262i
162162 −0.904928 + 1.56738i −0.0710979 + 0.123145i
163163 10.7052 0.838500 0.419250 0.907871i 0.362293π-0.362293\pi
0.419250 + 0.907871i 0.362293π0.362293\pi
164164 −0.650398 + 1.12652i −0.0507876 + 0.0879667i
165165 −0.569801 0.986924i −0.0443589 0.0768319i
166166 −12.1159 + 20.9853i −0.940375 + 1.62878i
167167 0.0240620 + 0.0416766i 0.00186197 + 0.00322503i 0.866955 0.498387i 0.166074π-0.166074\pi
−0.865093 + 0.501612i 0.832741π0.832741\pi
168168 3.41389 + 0.615007i 0.263387 + 0.0474489i
169169 12.9308 + 1.33937i 0.994678 + 0.103029i
170170 −16.5554 28.6747i −1.26974 2.19925i
171171 −6.96749 −0.532817
172172 −1.49317 −0.113853
173173 −14.0297 −1.06666 −0.533330 0.845907i 0.679060π-0.679060\pi
−0.533330 + 0.845907i 0.679060π0.679060\pi
174174 −1.52663 −0.115733
175175 18.4562 21.8306i 1.39516 1.65023i
176176 −0.705751 + 1.22240i −0.0531980 + 0.0921416i
177177 2.42927 + 4.20762i 0.182595 + 0.316264i
178178 2.00506 + 3.47287i 0.150286 + 0.260302i
179179 4.69863 0.351192 0.175596 0.984462i 0.443815π-0.443815\pi
0.175596 + 0.984462i 0.443815π0.443815\pi
180180 2.53555 4.39170i 0.188988 0.327338i
181181 −22.0382 −1.63809 −0.819044 0.573730i 0.805496π-0.805496\pi
−0.819044 + 0.573730i 0.805496π0.805496\pi
182182 11.8118 12.5920i 0.875552 0.933379i
183183 8.16848 0.603832
184184 −4.74524 + 8.21900i −0.349824 + 0.605913i
185185 17.3498 1.27559
186186 −0.385236 0.667248i −0.0282469 0.0489250i
187187 −0.659567 1.14240i −0.0482323 0.0835408i
188188 3.46019 5.99322i 0.252360 0.437101i
189189 −2.60384 0.469078i −0.189401 0.0341204i
190190 50.1319 3.63695
191191 11.0974 0.802982 0.401491 0.915863i 0.368492π-0.368492\pi
0.401491 + 0.915863i 0.368492π0.368492\pi
192192 −1.53522 −0.110795
193193 −0.486230 −0.0349996 −0.0174998 0.999847i 0.505571π-0.505571\pi
−0.0174998 + 0.999847i 0.505571π0.505571\pi
194194 17.2342 + 29.8505i 1.23734 + 2.14314i
195195 6.51711 + 12.7667i 0.466700 + 0.914245i
196196 −1.48533 8.80464i −0.106095 0.628903i
197197 −8.53814 14.7885i −0.608317 1.05364i −0.991518 0.129971i 0.958511π-0.958511\pi
0.383200 0.923665i 0.374822π-0.374822\pi
198198 0.259402 0.449297i 0.0184349 0.0319301i
199199 −11.5849 20.0656i −0.821230 1.42241i −0.904766 0.425908i 0.859955π-0.859955\pi
0.0835360 0.996505i 0.473379π-0.473379\pi
200200 7.08308 12.2683i 0.500849 0.867497i
201201 1.57387 0.111013
202202 8.22448 14.2452i 0.578673 1.00229i
203203 −0.755518 2.09994i −0.0530270 0.147387i
204204 2.93499 5.08356i 0.205491 0.355920i
205205 2.02706 3.51097i 0.141576 0.245217i
206206 −8.48536 −0.591203
207207 3.61929 6.26879i 0.251558 0.435711i
208208 9.65826 14.8970i 0.669680 1.03292i
209209 1.99726 0.138153
210210 18.7349 + 3.37507i 1.29283 + 0.232902i
211211 1.40788 + 2.43852i 0.0969224 + 0.167874i 0.910409 0.413709i 0.135767π-0.135767\pi
−0.813487 + 0.581583i 0.802433π0.802433\pi
212212 1.46494 0.100613
213213 −3.22369 + 5.58359i −0.220883 + 0.382581i
214214 −13.1265 22.7358i −0.897310 1.55419i
215215 4.65368 0.317378
216216 −1.31110 −0.0892090
217217 0.727175 0.860123i 0.0493639 0.0583890i
218218 3.79515 + 6.57340i 0.257040 + 0.445207i
219219 8.24845 14.2867i 0.557379 0.965408i
220220 −0.726825 + 1.25890i −0.0490026 + 0.0848749i
221221 7.54381 + 14.7780i 0.507451 + 0.994076i
222222 3.94925 + 6.84031i 0.265057 + 0.459092i
223223 −8.16232 14.1375i −0.546589 0.946720i −0.998505 0.0546597i 0.982593π-0.982593\pi
0.451916 0.892061i 0.350741π-0.350741\pi
224224 −5.63353 15.6582i −0.376406 1.04621i
225225 −5.40240 + 9.35723i −0.360160 + 0.623815i
226226 7.46213 + 12.9248i 0.496373 + 0.859744i
227227 3.10289 + 5.37436i 0.205946 + 0.356709i 0.950434 0.310927i 0.100640π-0.100640\pi
−0.744488 + 0.667636i 0.767306π0.767306\pi
228228 4.44379 + 7.69686i 0.294297 + 0.509737i
229229 0.261463 + 0.452867i 0.0172779 + 0.0299263i 0.874535 0.484962i 0.161167π-0.161167\pi
−0.857257 + 0.514889i 0.827833π0.827833\pi
230230 −26.0412 + 45.1047i −1.71711 + 2.97412i
231231 0.746401 + 0.134463i 0.0491096 + 0.00884703i
232232 −0.552962 0.957758i −0.0363037 0.0628799i
233233 −6.48273 11.2284i −0.424697 0.735598i 0.571695 0.820466i 0.306286π-0.306286\pi
−0.996392 + 0.0848689i 0.972953π0.972953\pi
234234 −3.54993 + 5.47545i −0.232066 + 0.357941i
235235 −10.7842 + 18.6787i −0.703482 + 1.21847i
236236 3.09872 5.36715i 0.201710 0.349371i
237237 −3.84412 6.65821i −0.249702 0.432497i
238238 21.6864 + 3.90678i 1.40572 + 0.253239i
239239 −4.79605 −0.310231 −0.155116 0.987896i 0.549575π-0.549575\pi
−0.155116 + 0.987896i 0.549575π0.549575\pi
240240 19.5757 1.26361
241241 −5.20975 9.02355i −0.335589 0.581258i 0.648008 0.761633i 0.275602π-0.275602\pi
−0.983598 + 0.180375i 0.942269π0.942269\pi
242242 9.87985 17.1124i 0.635101 1.10003i
243243 1.00000 0.0641500
244244 −5.20977 9.02358i −0.333521 0.577676i
245245 4.62924 + 27.4409i 0.295751 + 1.75314i
246246 1.84564 0.117674
247247 −25.0882 1.29585i −1.59632 0.0824529i
248248 0.279073 0.483369i 0.0177212 0.0306940i
249249 13.3888 0.848479
250250 20.8831 36.1706i 1.32077 2.28763i
251251 −5.10645 + 8.84463i −0.322316 + 0.558268i −0.980966 0.194182i 0.937795π-0.937795\pi
0.658649 + 0.752450i 0.271128π0.271128\pi
252252 1.14252 + 3.17559i 0.0719718 + 0.200043i
253253 −1.03748 + 1.79698i −0.0652261 + 0.112975i
254254 14.1955 0.890706
255255 −9.14733 + 15.8436i −0.572828 + 0.992168i
256256 −10.4042 18.0206i −0.650262 1.12629i
257257 3.18140 5.51035i 0.198450 0.343726i −0.749576 0.661919i 0.769742π-0.769742\pi
0.948026 + 0.318192i 0.103076π0.103076\pi
258258 1.05929 + 1.83475i 0.0659486 + 0.114226i
259259 −7.45466 + 8.81758i −0.463210 + 0.547898i
260260 9.94666 15.3418i 0.616866 0.951460i
261261 0.421754 + 0.730500i 0.0261059 + 0.0452168i
262262 14.6337 0.904070
263263 −17.0135 −1.04910 −0.524550 0.851380i 0.675766π-0.675766\pi
−0.524550 + 0.851380i 0.675766π0.675766\pi
264264 0.375832 0.0231309
265265 −4.56570 −0.280469
266266 −21.5400 + 25.4782i −1.32070 + 1.56217i
267267 1.10786 1.91886i 0.0677997 0.117433i
268268 −1.00380 1.73863i −0.0613168 0.106204i
269269 4.53019 + 7.84653i 0.276211 + 0.478411i 0.970440 0.241343i 0.0775879π-0.0775879\pi
−0.694229 + 0.719754i 0.744255π0.744255\pi
270270 −7.19513 −0.437881
271271 −1.11398 + 1.92947i −0.0676696 + 0.117207i −0.897875 0.440250i 0.854890π-0.854890\pi
0.830206 + 0.557457i 0.188223π0.188223\pi
272272 22.6596 1.37394
273273 −9.28853 2.17331i −0.562167 0.131535i
274274 2.73231 0.165065
275275 1.54862 2.68229i 0.0933854 0.161748i
276276 −9.23336 −0.555783
277277 3.90377 + 6.76153i 0.234555 + 0.406261i 0.959143 0.282921i 0.0913034π-0.0913034\pi
−0.724588 + 0.689182i 0.757970π0.757970\pi
278278 3.65830 + 6.33637i 0.219411 + 0.380030i
279279 −0.212854 + 0.368675i −0.0127433 + 0.0220720i
280280 4.66858 + 12.9762i 0.279001 + 0.775475i
281281 −12.7531 −0.760789 −0.380394 0.924824i 0.624212π-0.624212\pi
−0.380394 + 0.924824i 0.624212π0.624212\pi
282282 −9.81898 −0.584712
283283 16.3439 0.971542 0.485771 0.874086i 0.338539π-0.338539\pi
0.485771 + 0.874086i 0.338539π0.338539\pi
284284 8.22413 0.488012
285285 −13.8497 23.9884i −0.820386 1.42095i
286286 1.01760 1.56956i 0.0601721 0.0928101i
287287 0.913393 + 2.53875i 0.0539159 + 0.149857i
288288 3.14482 + 5.44698i 0.185310 + 0.320967i
289289 −2.08840 + 3.61721i −0.122847 + 0.212777i
290290 −3.03458 5.25604i −0.178196 0.308645i
291291 9.52241 16.4933i 0.558214 0.966854i
292292 −21.0431 −1.23145
293293 11.8319 20.4935i 0.691227 1.19724i −0.280209 0.959939i 0.590404π-0.590404\pi
0.971436 0.237302i 0.0762630π-0.0762630\pi
294294 −9.76507 + 8.07135i −0.569511 + 0.470731i
295295 −9.65762 + 16.7275i −0.562288 + 0.973912i
296296 −2.86093 + 4.95527i −0.166288 + 0.288019i
297297 −0.286654 −0.0166334
298298 17.3699 30.0855i 1.00621 1.74280i
299299 14.1980 21.8992i 0.821094 1.26646i
300300 13.7824 0.795725
301301 −1.99953 + 2.36510i −0.115251 + 0.136322i
302302 −17.1454 29.6967i −0.986605 1.70885i
303303 −9.08855 −0.522124
304304 −17.1541 + 29.7119i −0.983858 + 1.70409i
305305 16.2370 + 28.1233i 0.929728 + 1.61034i
306306 −8.32864 −0.476117
307307 8.99691 0.513481 0.256740 0.966480i 0.417351π-0.417351\pi
0.256740 + 0.966480i 0.417351π0.417351\pi
308308 −0.327507 0.910296i −0.0186615 0.0518689i
309309 2.34421 + 4.06029i 0.133357 + 0.230982i
310310 1.53151 2.65266i 0.0869842 0.150661i
311311 15.4498 26.7598i 0.876077 1.51741i 0.0204655 0.999791i 0.493485π-0.493485\pi
0.855611 0.517619i 0.173181π-0.173181\pi
312312 −4.72094 0.243845i −0.267271 0.0138050i
313313 3.74574 + 6.48782i 0.211722 + 0.366713i 0.952254 0.305308i 0.0987595π-0.0987595\pi
−0.740532 + 0.672022i 0.765426π0.765426\pi
314314 −16.8637 29.2088i −0.951673 1.64835i
315315 −3.56082 9.89718i −0.200629 0.557643i
316316 −4.90348 + 8.49307i −0.275842 + 0.477773i
317317 8.11402 + 14.0539i 0.455729 + 0.789346i 0.998730 0.0503864i 0.0160453π-0.0160453\pi
−0.543001 + 0.839732i 0.682712π0.682712\pi
318318 −1.03927 1.80006i −0.0582792 0.100943i
319319 −0.120898 0.209401i −0.00676897 0.0117242i
320320 −3.05165 5.28562i −0.170593 0.295475i
321321 −7.25279 + 12.5622i −0.404811 + 0.701154i
322322 −11.7342 32.6147i −0.653919 1.81755i
323323 −16.0316 27.7675i −0.892021 1.54503i
324324 −0.637789 1.10468i −0.0354327 0.0613713i
325325 −21.1930 + 32.6883i −1.17558 + 1.81322i
326326 −9.68748 + 16.7792i −0.536540 + 0.929314i
327327 2.09694 3.63200i 0.115961 0.200850i
328328 0.668510 + 1.15789i 0.0369123 + 0.0639340i
329329 −4.85935 13.5064i −0.267904 0.744632i
330330 2.06251 0.113538
331331 5.58434 0.306943 0.153472 0.988153i 0.450955π-0.450955\pi
0.153472 + 0.988153i 0.450955π0.450955\pi
332332 −8.53922 14.7904i −0.468650 0.811726i
333333 2.18208 3.77948i 0.119577 0.207114i
334334 −0.0870976 −0.00476577
335335 3.12849 + 5.41870i 0.170928 + 0.296055i
336336 −8.41104 + 9.94881i −0.458860 + 0.542752i
337337 −0.504097 −0.0274599 −0.0137299 0.999906i 0.504371π-0.504371\pi
−0.0137299 + 0.999906i 0.504371π0.504371\pi
338338 −13.8008 + 19.0555i −0.750663 + 1.03648i
339339 4.12305 7.14133i 0.223933 0.387864i
340340 23.3363 1.26559
341341 0.0610156 0.105682i 0.00330418 0.00572301i
342342 6.30507 10.9207i 0.340939 0.590524i
343343 −15.9351 9.43778i −0.860416 0.509592i
344344 −0.767374 + 1.32913i −0.0413740 + 0.0716619i
345345 28.7771 1.54931
346346 12.6959 21.9899i 0.682535 1.18219i
347347 6.06672 + 10.5079i 0.325678 + 0.564092i 0.981649 0.190694i 0.0610740π-0.0610740\pi
−0.655971 + 0.754786i 0.727741π0.727741\pi
348348 0.537981 0.931810i 0.0288388 0.0499503i
349349 10.9086 + 18.8943i 0.583924 + 1.01139i 0.995009 + 0.0997893i 0.0318169π0.0318169\pi
−0.411084 + 0.911597i 0.634850π0.634850\pi
350350 17.5152 + 48.6830i 0.936229 + 2.60222i
351351 3.60075 + 0.185985i 0.192194 + 0.00992715i
352352 −0.901476 1.56140i −0.0480488 0.0832230i
353353 −12.0879 −0.643375 −0.321688 0.946846i 0.604250π-0.604250\pi
−0.321688 + 0.946846i 0.604250π0.604250\pi
354354 −8.79326 −0.467356
355355 −25.6317 −1.36039
356356 −2.82631 −0.149794
357357 −4.12179 11.4564i −0.218148 0.606335i
358358 −4.25192 + 7.36454i −0.224721 + 0.389228i
359359 −7.22027 12.5059i −0.381071 0.660035i 0.610144 0.792290i 0.291111π-0.291111\pi
−0.991216 + 0.132255i 0.957778π0.957778\pi
360360 −2.60615 4.51399i −0.137356 0.237908i
361361 29.5459 1.55505
362362 19.9430 34.5423i 1.04818 1.81550i
363363 −10.9178 −0.573037
364364 3.52331 + 11.6470i 0.184671 + 0.610468i
365365 65.5838 3.43281
366366 −7.39189 + 12.8031i −0.386380 + 0.669230i
367367 24.3787 1.27256 0.636280 0.771459i 0.280472π-0.280472\pi
0.636280 + 0.771459i 0.280472π0.280472\pi
368368 −17.8216 30.8679i −0.929013 1.60910i
369369 −0.509885 0.883147i −0.0265436 0.0459748i
370370 −15.7004 + 27.1938i −0.816223 + 1.41374i
371371 1.96173 2.32039i 0.101848 0.120469i
372372 0.543025 0.0281545
373373 −8.40033 −0.434953 −0.217476 0.976066i 0.569782π-0.569782\pi
−0.217476 + 0.976066i 0.569782π0.569782\pi
374374 2.38744 0.123452
375375 −23.0771 −1.19170
376376 −3.55654 6.16011i −0.183415 0.317684i
377377 1.38277 + 2.70879i 0.0712163 + 0.139510i
378378 3.09151 3.65672i 0.159010 0.188082i
379379 −1.82895 3.16783i −0.0939467 0.162720i 0.815222 0.579149i 0.196615π-0.196615\pi
−0.909169 + 0.416428i 0.863282π0.863282\pi
380380 −17.6664 + 30.5991i −0.906266 + 1.56970i
381381 −3.92173 6.79263i −0.200916 0.347997i
382382 −10.0424 + 17.3939i −0.513812 + 0.889949i
383383 −30.7052 −1.56896 −0.784481 0.620152i 0.787071π-0.787071\pi
−0.784481 + 0.620152i 0.787071π0.787071\pi
384384 −4.90037 + 8.48769i −0.250071 + 0.433136i
385385 1.02072 + 2.83707i 0.0520209 + 0.144590i
386386 0.440003 0.762108i 0.0223956 0.0387903i
387387 0.585291 1.01375i 0.0297520 0.0515320i
388388 −24.2932 −1.23330
389389 −9.21889 + 15.9676i −0.467416 + 0.809589i −0.999307 0.0372241i 0.988148π-0.988148\pi
0.531890 + 0.846813i 0.321482π0.321482\pi
390390 −25.9079 1.33819i −1.31190 0.0677617i
391391 33.3106 1.68459
392392 −8.60072 3.20276i −0.434402 0.161764i
393393 −4.04277 7.00228i −0.203931 0.353218i
394394 30.9056 1.55700
395395 15.2824 26.4699i 0.768941 1.33184i
396396 0.182825 + 0.316662i 0.00918730 + 0.0159129i
397397 −2.26064 −0.113458 −0.0567290 0.998390i 0.518067π-0.518067\pi
−0.0567290 + 0.998390i 0.518067π0.518067\pi
398398 41.9339 2.10196
399399 18.1422 + 3.26829i 0.908246 + 0.163619i
400400 26.6017 + 46.0755i 1.33009 + 2.30378i
401401 −14.2609 + 24.7005i −0.712153 + 1.23349i 0.251894 + 0.967755i 0.418947π0.418947\pi
−0.964047 + 0.265731i 0.914387π0.914387\pi
402402 −1.42424 + 2.46686i −0.0710348 + 0.123036i
403403 −0.835004 + 1.28792i −0.0415945 + 0.0641558i
404404 5.79658 + 10.0400i 0.288391 + 0.499507i
405405 1.98776 + 3.44291i 0.0987727 + 0.171079i
406406 3.97509 + 0.716108i 0.197281 + 0.0355398i
407407 −0.625503 + 1.08340i −0.0310051 + 0.0537023i
408408 −3.01672 5.22512i −0.149350 0.258682i
409409 −5.42700 9.39983i −0.268348 0.464792i 0.700088 0.714057i 0.253144π-0.253144\pi
−0.968435 + 0.249265i 0.919811π0.919811\pi
410410 3.66869 + 6.35436i 0.181184 + 0.313819i
411411 −0.754841 1.30742i −0.0372335 0.0644904i
412412 2.99022 5.17921i 0.147318 0.255162i
413413 −4.35172 12.0955i −0.214134 0.595179i
414414 6.55039 + 11.3456i 0.321934 + 0.557606i
415415 26.6137 + 46.0963i 1.30642 + 2.26278i
416416 10.3106 + 20.1981i 0.505521 + 0.990294i
417417 2.02132 3.50104i 0.0989846 0.171446i
418418 −1.80738 + 3.13047i −0.0884017 + 0.153116i
419419 −7.68279 13.3070i −0.375329 0.650089i 0.615047 0.788490i 0.289137π-0.289137\pi
−0.990376 + 0.138401i 0.955804π0.955804\pi
420420 −8.66220 + 10.2459i −0.422672 + 0.499948i
421421 −3.33695 −0.162633 −0.0813166 0.996688i 0.525912π-0.525912\pi
−0.0813166 + 0.996688i 0.525912π0.525912\pi
422422 −5.09612 −0.248075
423423 2.71264 + 4.69843i 0.131893 + 0.228446i
424424 0.752867 1.30400i 0.0365625 0.0633281i
425425 −49.7218 −2.41186
426426 −5.83441 10.1055i −0.282678 0.489613i
427427 −21.2694 3.83165i −1.02930 0.185427i
428428 18.5030 0.894377
429429 −1.03217 0.0533134i −0.0498337 0.00257400i
430430 −4.21124 + 7.29408i −0.203084 + 0.351752i
431431 −4.26093 −0.205242 −0.102621 0.994721i 0.532723π-0.532723\pi
−0.102621 + 0.994721i 0.532723π0.532723\pi
432432 2.46203 4.26436i 0.118454 0.205169i
433433 −5.56416 + 9.63741i −0.267396 + 0.463144i −0.968189 0.250221i 0.919497π-0.919497\pi
0.700792 + 0.713365i 0.252830π0.252830\pi
434434 0.690100 + 1.91811i 0.0331259 + 0.0920722i
435435 −1.67670 + 2.90412i −0.0803914 + 0.139242i
436436 −5.34961 −0.256200
437437 −25.2173 + 43.6777i −1.20631 + 2.08939i
438438 14.9285 + 25.8569i 0.713312 + 1.23549i
439439 −20.5012 + 35.5092i −0.978470 + 1.69476i −0.310497 + 0.950574i 0.600496π0.600496\pi
−0.667973 + 0.744186i 0.732838π0.732838\pi
440440 0.747065 + 1.29395i 0.0356149 + 0.0616869i
441441 6.55993 + 2.44280i 0.312378 + 0.116324i
442442 −29.9894 1.54900i −1.42645 0.0736785i
443443 −7.92693 13.7298i −0.376620 0.652325i 0.613948 0.789346i 0.289580π-0.289580\pi
−0.990568 + 0.137022i 0.956247π0.956247\pi
444444 −5.56683 −0.264190
445445 8.80862 0.417569
446446 29.5452 1.39901
447447 −19.1947 −0.907880
448448 3.99746 + 0.720137i 0.188862 + 0.0340233i
449449 −7.54997 + 13.0769i −0.356305 + 0.617139i −0.987340 0.158616i 0.949297π-0.949297\pi
0.631035 + 0.775754i 0.282630π0.282630\pi
450450 −9.77756 16.9352i −0.460919 0.798335i
451451 0.146161 + 0.253158i 0.00688244 + 0.0119207i
452452 −10.5185 −0.494751
453453 −9.47334 + 16.4083i −0.445096 + 0.770929i
454454 −11.2316 −0.527123
455455 −10.9809 36.2995i −0.514792 1.70175i
456456 9.13506 0.427789
457457 0.0139240 0.0241170i 0.000651335 0.00112815i −0.865700 0.500564i 0.833126π-0.833126\pi
0.866351 + 0.499436i 0.166459π0.166459\pi
458458 −0.946420 −0.0442233
459459 2.30091 + 3.98530i 0.107397 + 0.186018i
460460 −18.3537 31.7896i −0.855747 1.48220i
461461 14.0543 24.3428i 0.654575 1.13376i −0.327425 0.944877i 0.606181π-0.606181\pi
0.982000 0.188880i 0.0604859π-0.0604859\pi
462462 −0.886194 + 1.04822i −0.0412295 + 0.0487674i
463463 −0.266538 −0.0123871 −0.00619354 0.999981i 0.501971π-0.501971\pi
−0.00619354 + 0.999981i 0.501971π0.501971\pi
464464 4.15349 0.192821
465465 −1.69242 −0.0784839
466466 23.4656 1.08702
467467 −18.5400 32.1123i −0.857931 1.48598i −0.873899 0.486107i 0.838417π-0.838417\pi
0.0159687 0.999872i 0.494917π-0.494917\pi
468468 −2.09107 4.09631i −0.0966595 0.189352i
469469 −4.09811 0.738270i −0.189233 0.0340901i
470470 −19.5178 33.8058i −0.900289 1.55935i
471471 −9.31770 + 16.1387i −0.429337 + 0.743633i
472472 −3.18501 5.51660i −0.146602 0.253922i
473473 −0.167776 + 0.290597i −0.00771436 + 0.0133617i
474474 13.9146 0.639119
475475 37.6411 65.1964i 1.72709 2.99141i
476476 −10.0268 + 11.8600i −0.459579 + 0.543603i
477477 −0.574226 + 0.994589i −0.0262920 + 0.0455391i
478478 4.34008 7.51725i 0.198511 0.343831i
479479 28.7986 1.31584 0.657922 0.753086i 0.271436π-0.271436\pi
0.657922 + 0.753086i 0.271436π0.271436\pi
480480 −12.5023 + 21.6546i −0.570649 + 0.988394i
481481 8.56006 13.2031i 0.390305 0.602011i
482482 18.8578 0.858949
483483 −12.3646 + 14.6252i −0.562608 + 0.665468i
484484 6.96327 + 12.0607i 0.316512 + 0.548216i
485485 75.7132 3.43796
486486 −0.904928 + 1.56738i −0.0410484 + 0.0710979i
487487 6.86516 + 11.8908i 0.311090 + 0.538824i 0.978599 0.205778i 0.0659725π-0.0659725\pi
−0.667508 + 0.744602i 0.732639π0.732639\pi
488488 −10.7097 −0.484805
489489 10.7052 0.484108
490490 −47.1995 17.5763i −2.13226 0.794016i
491491 13.7632 + 23.8386i 0.621126 + 1.07582i 0.989276 + 0.146056i 0.0466579π0.0466579\pi
−0.368150 + 0.929766i 0.620009π0.620009\pi
492492 −0.650398 + 1.12652i −0.0293222 + 0.0507876i
493493 −1.94084 + 3.36163i −0.0874110 + 0.151400i
494494 24.7341 38.1501i 1.11284 1.71645i
495495 −0.569801 0.986924i −0.0256106 0.0443589i
496496 1.04811 + 1.81537i 0.0470614 + 0.0815127i
497497 11.0131 13.0266i 0.494005 0.584323i
498498 −12.1159 + 20.9853i −0.542925 + 0.940375i
499499 1.94567 + 3.37000i 0.0871001 + 0.150862i 0.906284 0.422669i 0.138907π-0.138907\pi
−0.819184 + 0.573531i 0.805573π0.805573\pi
500500 14.7183 + 25.4929i 0.658224 + 1.14008i
501501 0.0240620 + 0.0416766i 0.00107501 + 0.00186197i
502502 −9.24194 16.0075i −0.412488 0.714450i
503503 −1.87991 + 3.25610i −0.0838212 + 0.145183i −0.904888 0.425649i 0.860046π-0.860046\pi
0.821067 + 0.570832i 0.193379π0.193379\pi
504504 3.41389 + 0.615007i 0.152067 + 0.0273946i
505505 −18.0659 31.2910i −0.803921 1.39243i
506506 −1.87770 3.25227i −0.0834738 0.144581i
507507 12.9308 + 1.33937i 0.574278 + 0.0594836i
508508 −5.00247 + 8.66453i −0.221949 + 0.384426i
509509 19.2740 33.3836i 0.854307 1.47970i −0.0229793 0.999736i 0.507315π-0.507315\pi
0.877286 0.479967i 0.159351π-0.159351\pi
510510 −16.5554 28.6747i −0.733084 1.26974i
511511 −28.1792 + 33.3312i −1.24657 + 1.47448i
512512 18.0587 0.798088
513513 −6.96749 −0.307622
514514 5.75788 + 9.97294i 0.253969 + 0.439888i
515515 −9.31946 + 16.1418i −0.410664 + 0.711291i
516516 −1.49317 −0.0657331
517517 −0.777591 1.34683i −0.0341984 0.0592334i
518518 −7.07458 19.6636i −0.310839 0.863967i
519519 −14.0297 −0.615837
520520 −8.54457 16.7385i −0.374704 0.734030i
521521 −6.92277 + 11.9906i −0.303292 + 0.525318i −0.976880 0.213790i 0.931419π-0.931419\pi
0.673587 + 0.739108i 0.264753π0.264753\pi
522522 −1.52663 −0.0668188
523523 −10.0335 + 17.3786i −0.438736 + 0.759913i −0.997592 0.0693515i 0.977907π-0.977907\pi
0.558856 + 0.829265i 0.311240π0.311240\pi
524524 −5.15687 + 8.93196i −0.225279 + 0.390194i
525525 18.4562 21.8306i 0.805496 0.952763i
526526 15.3960 26.6667i 0.671299 1.16272i
527527 −1.95904 −0.0853370
528528 −0.705751 + 1.22240i −0.0307139 + 0.0531980i
529529 −14.6985 25.4585i −0.639063 1.10689i
530530 4.13163 7.15619i 0.179467 0.310845i
531531 2.42927 + 4.20762i 0.105421 + 0.182595i
532532 −7.96047 22.1259i −0.345130 0.959278i
533533 −1.67172 3.27482i −0.0724101 0.141848i
534534 2.00506 + 3.47287i 0.0867674 + 0.150286i
535535 −57.6673 −2.49318
536536 −2.06351 −0.0891298
537537 4.69863 0.202761
538538 −16.3980 −0.706968
539539 −1.88043 0.700240i −0.0809960 0.0301615i
540540 2.53555 4.39170i 0.109113 0.188988i
541541 −18.9415 32.8076i −0.814357 1.41051i −0.909788 0.415072i 0.863756π-0.863756\pi
0.0954310 0.995436i 0.469577π-0.469577\pi
542542 −2.01615 3.49207i −0.0866009 0.149997i
543543 −22.0382 −0.945751
544544 −14.4719 + 25.0661i −0.620478 + 1.07470i
545545 16.6728 0.714186
546546 11.8118 12.5920i 0.505500 0.538887i
547547 29.3783 1.25613 0.628063 0.778162i 0.283848π-0.283848\pi
0.628063 + 0.778162i 0.283848π0.283848\pi
548548 −0.962858 + 1.66772i −0.0411313 + 0.0712415i
549549 8.16848 0.348622
550550 2.80278 + 4.85456i 0.119511 + 0.206999i
551551 −2.93857 5.08975i −0.125187 0.216831i
552552 −4.74524 + 8.21900i −0.201971 + 0.349824i
553553 6.88624 + 19.1401i 0.292833 + 0.813919i
554554 −14.1305 −0.600349
555555 17.3498 0.736460
556556 −5.15671 −0.218693
557557 1.02608 0.0434763 0.0217381 0.999764i 0.493080π-0.493080\pi
0.0217381 + 0.999764i 0.493080π0.493080\pi
558558 −0.385236 0.667248i −0.0163083 0.0282469i
559559 2.29603 3.54142i 0.0971117 0.149786i
560560 −50.9720 9.18253i −2.15396 0.388033i
561561 −0.659567 1.14240i −0.0278469 0.0482323i
562562 11.5407 19.9890i 0.486814 0.843187i
563563 18.1124 + 31.3716i 0.763348 + 1.32216i 0.941116 + 0.338085i 0.109779π0.109779\pi
−0.177768 + 0.984072i 0.556888π0.556888\pi
564564 3.46019 5.99322i 0.145700 0.252360i
565565 32.7826 1.37917
566566 −14.7900 + 25.6171i −0.621671 + 1.07677i
567567 −2.60384 0.469078i −0.109351 0.0196994i
568568 4.22657 7.32064i 0.177343 0.307167i
569569 −1.41835 + 2.45666i −0.0594605 + 0.102989i −0.894223 0.447621i 0.852271π-0.852271\pi
0.834763 + 0.550610i 0.185605π0.185605\pi
570570 50.1319 2.09980
571571 2.29825 3.98069i 0.0961789 0.166587i −0.813921 0.580975i 0.802671π-0.802671\pi
0.910100 + 0.414389i 0.136005π0.136005\pi
572572 0.599413 + 1.17422i 0.0250627 + 0.0490968i
573573 11.0974 0.463602
574574 −4.80574 0.865748i −0.200588 0.0361356i
575575 39.1057 + 67.7330i 1.63082 + 2.82466i
576576 −1.53522 −0.0639675
577577 8.75176 15.1585i 0.364341 0.631056i −0.624329 0.781161i 0.714628π-0.714628\pi
0.988670 + 0.150105i 0.0479611π0.0479611\pi
578578 −3.77970 6.54662i −0.157215 0.272304i
579579 −0.486230 −0.0202070
580580 4.27751 0.177614
581581 −34.8622 6.28038i −1.44633 0.260554i
582582 17.2342 + 29.8505i 0.714380 + 1.23734i
583583 0.164604 0.285103i 0.00681722 0.0118078i
584584 −10.8145 + 18.7313i −0.447509 + 0.775108i
585585 6.51711 + 12.7667i 0.269449 + 0.527840i
586586 21.4140 + 37.0902i 0.884606 + 1.53218i
587587 −0.671155 1.16247i −0.0277015 0.0479805i 0.851842 0.523798i 0.175485π-0.175485\pi
−0.879544 + 0.475818i 0.842152π0.842152\pi
588588 −1.48533 8.80464i −0.0612539 0.363097i
589589 1.48306 2.56874i 0.0611084 0.105843i
590590 −17.4789 30.2743i −0.719595 1.24638i
591591 −8.53814 14.7885i −0.351212 0.608317i
592592 −10.7447 18.6104i −0.441604 0.764881i
593593 22.0843 + 38.2512i 0.906895 + 1.57079i 0.818353 + 0.574716i 0.194888π0.194888\pi
0.0885427 + 0.996072i 0.471779π0.471779\pi
594594 0.259402 0.449297i 0.0106434 0.0184349i
595595 31.2501 36.9635i 1.28113 1.51535i
596596 12.2422 + 21.2041i 0.501460 + 0.868554i
597597 −11.5849 20.0656i −0.474138 0.821230i
598598 21.4762 + 42.0710i 0.878227 + 1.72041i
599599 8.46583 14.6632i 0.345904 0.599124i −0.639613 0.768697i 0.720905π-0.720905\pi
0.985518 + 0.169573i 0.0542388π0.0542388\pi
600600 7.08308 12.2683i 0.289166 0.500849i
601601 7.56311 + 13.0997i 0.308506 + 0.534348i 0.978036 0.208437i 0.0668378π-0.0668378\pi
−0.669530 + 0.742785i 0.733504π0.733504\pi
602602 −1.89758 5.27427i −0.0773398 0.214963i
603603 1.57387 0.0640931
604604 24.1680 0.983381
605605 −21.7021 37.5891i −0.882314 1.52821i
606606 8.22448 14.2452i 0.334097 0.578673i
607607 47.7239 1.93705 0.968527 0.248910i 0.0800722π-0.0800722\pi
0.968527 + 0.248910i 0.0800722π0.0800722\pi
608608 −21.9115 37.9518i −0.888628 1.53915i
609609 −0.755518 2.09994i −0.0306151 0.0850938i
610610 −58.7733 −2.37966
611611 8.89371 + 17.4224i 0.359801 + 0.704835i
612612 2.93499 5.08356i 0.118640 0.205491i
613613 23.9708 0.968173 0.484086 0.875020i 0.339152π-0.339152\pi
0.484086 + 0.875020i 0.339152π0.339152\pi
614614 −8.14155 + 14.1016i −0.328566 + 0.569094i
615615 2.02706 3.51097i 0.0817390 0.141576i
616616 −0.978606 0.176295i −0.0394292 0.00710311i
617617 −1.41810 + 2.45623i −0.0570907 + 0.0988839i −0.893158 0.449743i 0.851516π-0.851516\pi
0.836068 + 0.548626i 0.184849π0.184849\pi
618618 −8.48536 −0.341331
619619 0.658494 1.14055i 0.0264671 0.0458424i −0.852488 0.522746i 0.824908π-0.824908\pi
0.878956 + 0.476904i 0.158241π0.158241\pi
620620 1.07940 + 1.86958i 0.0433499 + 0.0750843i
621621 3.61929 6.26879i 0.145237 0.251558i
622622 27.9619 + 48.4314i 1.12117 + 1.94192i
623623 −3.78477 + 4.47674i −0.151634 + 0.179357i
624624 9.65826 14.8970i 0.386640 0.596357i
625625 −18.8598 32.6662i −0.754393 1.30665i
626626 −13.5585 −0.541907
627627 1.99726 0.0797629
628628 23.7709 0.948562
629629 20.0831 0.800766
630630 18.7349 + 3.37507i 0.746418 + 0.134466i
631631 −11.5676 + 20.0356i −0.460497 + 0.797604i −0.998986 0.0450286i 0.985662π-0.985662\pi
0.538489 + 0.842633i 0.318995π0.318995\pi
632632 5.04002 + 8.72957i 0.200481 + 0.347244i
633633 1.40788 + 2.43852i 0.0559582 + 0.0969224i
634634 −29.3704 −1.16645
635635 15.5909 27.0043i 0.618707 1.07163i
636636 1.46494 0.0580887
637637 23.1664 + 10.0160i 0.917885 + 0.396848i
638638 0.437615 0.0173253
639639 −3.22369 + 5.58359i −0.127527 + 0.220883i
640640 −38.9631 −1.54015
641641 18.3262 + 31.7420i 0.723843 + 1.25373i 0.959448 + 0.281884i 0.0909594π0.0909594\pi
−0.235605 + 0.971849i 0.575707π0.575707\pi
642642 −13.1265 22.7358i −0.518062 0.897310i
643643 −1.86917 + 3.23749i −0.0737127 + 0.127674i −0.900526 0.434803i 0.856818π-0.856818\pi
0.826813 + 0.562477i 0.190151π0.190151\pi
644644 24.0422 + 4.33117i 0.947394 + 0.170672i
645645 4.65368 0.183238
646646 58.0297 2.28315
647647 −1.52619 −0.0600006 −0.0300003 0.999550i 0.509551π-0.509551\pi
−0.0300003 + 0.999550i 0.509551π0.509551\pi
648648 −1.31110 −0.0515048
649649 −0.696361 1.20613i −0.0273345 0.0473448i
650650 −32.0569 62.7981i −1.25737 2.46314i
651651 0.727175 0.860123i 0.0285002 0.0337109i
652652 −6.82769 11.8259i −0.267393 0.463138i
653653 −4.47546 + 7.75172i −0.175138 + 0.303348i −0.940209 0.340598i 0.889371π-0.889371\pi
0.765071 + 0.643946i 0.222704π0.222704\pi
654654 3.79515 + 6.57340i 0.148402 + 0.257040i
655655 16.0721 27.8377i 0.627990 1.08771i
656656 −5.02141 −0.196053
657657 8.24845 14.2867i 0.321803 0.557379i
658658 25.5670 + 4.60587i 0.996707 + 0.179555i
659659 4.30599 7.45819i 0.167737 0.290530i −0.769887 0.638181i 0.779687π-0.779687\pi
0.937624 + 0.347651i 0.113021π0.113021\pi
660660 −0.726825 + 1.25890i −0.0282916 + 0.0490026i
661661 −40.0783 −1.55887 −0.779433 0.626486i 0.784493π-0.784493\pi
−0.779433 + 0.626486i 0.784493π0.784493\pi
662662 −5.05343 + 8.75279i −0.196407 + 0.340187i
663663 7.54381 + 14.7780i 0.292977 + 0.573930i
664664 −17.5540 −0.681228
665665 24.8100 + 68.9585i 0.962089 + 2.67409i
666666 3.94925 + 6.84031i 0.153031 + 0.265057i
667667 6.10580 0.236417
668668 0.0306930 0.0531618i 0.00118755 0.00205689i
669669 −8.16232 14.1375i −0.315573 0.546589i
670670 −11.3242 −0.437493
671671 −2.34153 −0.0903938
672672 −5.63353 15.6582i −0.217318 0.604029i
673673 −22.0131 38.1277i −0.848541 1.46972i −0.882510 0.470294i 0.844148π-0.844148\pi
0.0339689 0.999423i 0.489185π-0.489185\pi
674674 0.456171 0.790112i 0.0175711 0.0304340i
675675 −5.40240 + 9.35723i −0.207938 + 0.360160i
676676 −6.76755 15.1387i −0.260291 0.582258i
677677 −12.0556 20.8809i −0.463334 0.802518i 0.535791 0.844351i 0.320014π-0.320014\pi
−0.999125 + 0.0418328i 0.986680π0.986680\pi
678678 7.46213 + 12.9248i 0.286581 + 0.496373i
679679 −32.5314 + 38.4791i −1.24844 + 1.47669i
680680 11.9931 20.7726i 0.459913 0.796592i
681681 3.10289 + 5.37436i 0.118903 + 0.205946i
682682 0.110430 + 0.191270i 0.00422856 + 0.00732409i
683683 9.29276 + 16.0955i 0.355578 + 0.615878i 0.987217 0.159384i 0.0509508π-0.0509508\pi
−0.631639 + 0.775263i 0.717618π0.717618\pi
684684 4.44379 + 7.69686i 0.169912 + 0.294297i
685685 3.00089 5.19769i 0.114658 0.198594i
686686 29.2127 16.4359i 1.11535 0.627526i
687687 0.261463 + 0.452867i 0.00997543 + 0.0172779i
688688 −2.88201 4.99178i −0.109875 0.190310i
689689 −2.25262 + 3.47447i −0.0858182 + 0.132367i
690690 −26.0412 + 45.1047i −0.991372 + 1.71711i
691691 11.3187 19.6045i 0.430583 0.745792i −0.566340 0.824171i 0.691641π-0.691641\pi
0.996924 + 0.0783796i 0.0249746π0.0249746\pi
692692 8.94801 + 15.4984i 0.340152 + 0.589161i
693693 0.746401 + 0.134463i 0.0283534 + 0.00510783i
694694 −21.9598 −0.833581
695695 16.0716 0.609632
696696 −0.552962 0.957758i −0.0209600 0.0363037i
697697 2.34640 4.06409i 0.0888763 0.153938i
698698 −39.4860 −1.49457
699699 −6.48273 11.2284i −0.245199 0.424697i
700700 −35.8870 6.46500i −1.35640 0.244354i
701701 50.1432 1.89388 0.946941 0.321407i 0.104156π-0.104156\pi
0.946941 + 0.321407i 0.104156π0.104156\pi
702702 −3.54993 + 5.47545i −0.133983 + 0.206657i
703703 −15.2036 + 26.3335i −0.573416 + 0.993185i
704704 0.440077 0.0165860
705705 −10.7842 + 18.6787i −0.406156 + 0.703482i
706706 10.9387 18.9464i 0.411683 0.713056i
707707 23.6651 + 4.26324i 0.890018 + 0.160336i
708708 3.09872 5.36715i 0.116457 0.201710i
709709 −29.7112 −1.11583 −0.557913 0.829899i 0.688398π-0.688398\pi
−0.557913 + 0.829899i 0.688398π0.688398\pi
710710 23.1948 40.1746i 0.870487 1.50773i
711711 −3.84412 6.65821i −0.144166 0.249702i
712712 −1.45251 + 2.51582i −0.0544351 + 0.0942843i
713713 1.54076 + 2.66868i 0.0577020 + 0.0999428i
714714 21.6864 + 3.90678i 0.811594 + 0.146208i
715715 −1.86816 3.65964i −0.0698651 0.136863i
716716 −2.99673 5.19049i −0.111993 0.193978i
717717 −4.79605 −0.179112
718718 26.1353 0.975361
719719 −29.8693 −1.11394 −0.556968 0.830534i 0.688035π-0.688035\pi
−0.556968 + 0.830534i 0.688035π0.688035\pi
720720 19.5757 0.729544
721721 −4.19934 11.6719i −0.156392 0.434686i
722722 −26.7369 + 46.3096i −0.995044 + 1.72347i
723723 −5.20975 9.02355i −0.193753 0.335589i
724724 14.0557 + 24.3453i 0.522378 + 0.904785i
725725 −9.11394 −0.338483
726726 9.87985 17.1124i 0.366676 0.635101i
727727 36.0210 1.33594 0.667972 0.744186i 0.267163π-0.267163\pi
0.667972 + 0.744186i 0.267163π0.267163\pi
728728 12.1782 + 2.84942i 0.451353 + 0.105607i
729729 1.00000 0.0370370
730730 −59.3486 + 102.795i −2.19659 + 3.80461i
731731 5.38681 0.199238
732732 −5.20977 9.02358i −0.192559 0.333521i
733733 8.97642 + 15.5476i 0.331552 + 0.574265i 0.982816 0.184586i 0.0590945π-0.0590945\pi
−0.651265 + 0.758851i 0.725761π0.725761\pi
734734 −22.0610 + 38.2108i −0.814286 + 1.41038i
735735 4.62924 + 27.4409i 0.170752 + 1.01217i
736736 45.5280 1.67818
737737 −0.451158 −0.0166186
738738 1.84564 0.0679388
739739 44.4938 1.63673 0.818366 0.574698i 0.194880π-0.194880\pi
0.818366 + 0.574698i 0.194880π0.194880\pi
740740 −11.0655 19.1661i −0.406777 0.704559i
741741 −25.0882 1.29585i −0.921637 0.0476042i
742742 1.86171 + 5.17457i 0.0683456 + 0.189964i
743743 −10.7390 18.6004i −0.393975 0.682384i 0.598995 0.800753i 0.295567π-0.295567\pi
−0.992970 + 0.118368i 0.962234π0.962234\pi
744744 0.279073 0.483369i 0.0102313 0.0177212i
745745 −38.1546 66.0857i −1.39788 2.42119i
746746 7.60169 13.1665i 0.278318 0.482061i
747747 13.3888 0.489870
748748 −0.841329 + 1.45722i −0.0307620 + 0.0532814i
749749 24.7777 29.3078i 0.905359 1.07088i
750750 20.8831 36.1706i 0.762544 1.32077i
751751 −1.60018 + 2.77159i −0.0583913 + 0.101137i −0.893743 0.448579i 0.851930π-0.851930\pi
0.835352 + 0.549715i 0.185264π0.185264\pi
752752 26.7144 0.974174
753753 −5.10645 + 8.84463i −0.186089 + 0.322316i
754754 −5.49701 0.283930i −0.200189 0.0103401i
755755 −75.3230 −2.74128
756756 1.14252 + 3.17559i 0.0415529 + 0.115495i
757757 −12.8640 22.2811i −0.467550 0.809821i 0.531762 0.846894i 0.321530π-0.321530\pi
−0.999313 + 0.0370727i 0.988197π0.988197\pi
758758 6.62026 0.240459
759759 −1.03748 + 1.79698i −0.0376583 + 0.0652261i
760760 18.1583 + 31.4512i 0.658672 + 1.14085i
761761 28.7496 1.04217 0.521087 0.853504i 0.325527π-0.325527\pi
0.521087 + 0.853504i 0.325527π0.325527\pi
762762 14.1955 0.514249
763763 −7.16377 + 8.47351i −0.259346 + 0.306762i
764764 −7.07782 12.2591i −0.256066 0.443520i
765765 −9.14733 + 15.8436i −0.330723 + 0.572828i
766766 27.7860 48.1268i 1.00395 1.73889i
767767 7.96464 + 15.6024i 0.287587 + 0.563370i
768768 −10.4042 18.0206i −0.375429 0.650262i
769769 8.98213 + 15.5575i 0.323904 + 0.561018i 0.981290 0.192536i 0.0616712π-0.0616712\pi
−0.657386 + 0.753554i 0.728338π0.728338\pi
770770 −5.37045 0.967480i −0.193538 0.0348656i
771771 3.18140 5.51035i 0.114575 0.198450i
772772 0.310112 + 0.537131i 0.0111612 + 0.0193318i
773773 −19.8326 34.3511i −0.713329 1.23552i −0.963601 0.267346i 0.913853π-0.913853\pi
0.250272 0.968176i 0.419480π-0.419480\pi
774774 1.05929 + 1.83475i 0.0380755 + 0.0659486i
775775 −2.29985 3.98345i −0.0826130 0.143090i
776776 −12.4848 + 21.6243i −0.448179 + 0.776269i
777777 −7.45466 + 8.81758i −0.267434 + 0.316329i
778778 −16.6849 28.8990i −0.598182 1.03608i
779779 3.55262 + 6.15331i 0.127286 + 0.220465i
780780 9.94666 15.3418i 0.356148 0.549326i
781781 0.924084 1.60056i 0.0330663 0.0572725i
782782 −30.1437 + 52.2105i −1.07794 + 1.86704i
783783 0.421754 + 0.730500i 0.0150723 + 0.0261059i
784784 26.5677 21.9596i 0.948848 0.784273i
785785 −74.0855 −2.64422
786786 14.6337 0.521965
787787 19.7833 + 34.2657i 0.705199 + 1.22144i 0.966620 + 0.256215i 0.0824756π0.0824756\pi
−0.261421 + 0.965225i 0.584191π0.584191\pi
788788 −10.8911 + 18.8639i −0.387978 + 0.671998i
789789 −17.0135 −0.605698
790790 27.6589 + 47.9067i 0.984061 + 1.70444i
791791 −14.0856 + 16.6608i −0.500826 + 0.592391i
792792 0.375832 0.0133546
793793 29.4127 + 1.51922i 1.04447 + 0.0539489i
794794 2.04571 3.54328i 0.0725996 0.125746i
795795 −4.56570 −0.161929
796796 −14.7774 + 25.5952i −0.523772 + 0.907199i
797797 −9.72309 + 16.8409i −0.344409 + 0.596535i −0.985246 0.171142i 0.945254π-0.945254\pi
0.640837 + 0.767677i 0.278588π0.278588\pi
798798 −21.5400 + 25.4782i −0.762509 + 0.901917i
799799 −12.4831 + 21.6214i −0.441621 + 0.764909i
800800 −67.9582 −2.40269
801801 1.10786 1.91886i 0.0391442 0.0677997i
802802 −25.8101 44.7044i −0.911386 1.57857i
803803 −2.36445 + 4.09535i −0.0834398 + 0.144522i
804804 −1.00380 1.73863i −0.0354013 0.0613168i
805805 −74.9309 13.4987i −2.64097 0.475767i
806806 −1.26304 2.47424i −0.0444887 0.0871515i
807807 4.53019 + 7.84653i 0.159470 + 0.276211i
808808 11.9160 0.419203
809809 −17.3084 −0.608531 −0.304265 0.952587i 0.598411π-0.598411\pi
−0.304265 + 0.952587i 0.598411π0.598411\pi
810810 −7.19513 −0.252811
811811 −2.62646 −0.0922275 −0.0461138 0.998936i 0.514684π-0.514684\pi
−0.0461138 + 0.998936i 0.514684π0.514684\pi
812812 −1.83791 + 2.17393i −0.0644978 + 0.0762899i
813813 −1.11398 + 1.92947i −0.0390690 + 0.0676696i
814814 −1.13207 1.96080i −0.0396791 0.0687262i
815815 21.2795 + 36.8572i 0.745388 + 1.29105i
816816 22.6596 0.793246
817817 −4.07801 + 7.06331i −0.142671 + 0.247114i
818818 19.6442 0.686842
819819 −9.28853 2.17331i −0.324567 0.0759415i
820820 −5.17135 −0.180591
821821 16.1977 28.0553i 0.565305 0.979137i −0.431716 0.902009i 0.642092π-0.642092\pi
0.997021 0.0771274i 0.0245748π-0.0245748\pi
822822 2.73231 0.0953001
823823 20.5081 + 35.5210i 0.714866 + 1.23818i 0.963011 + 0.269461i 0.0868457π0.0868457\pi
−0.248145 + 0.968723i 0.579821π0.579821\pi
824824 −3.07349 5.32344i −0.107070 0.185451i
825825 1.54862 2.68229i 0.0539161 0.0933854i
826826 22.8962 + 4.12472i 0.796661 + 0.143517i
827827 −44.2260 −1.53789 −0.768944 0.639316i 0.779218π-0.779218\pi
−0.768944 + 0.639316i 0.779218π0.779218\pi
828828 −9.23336 −0.320882
829829 −5.49562 −0.190871 −0.0954354 0.995436i 0.530424π-0.530424\pi
−0.0954354 + 0.995436i 0.530424π0.530424\pi
830830 −96.3339 −3.34380
831831 3.90377 + 6.76153i 0.135420 + 0.234555i
832832 −5.52794 0.285528i −0.191647 0.00989890i
833833 5.35853 + 31.7640i 0.185662 + 1.10056i
834834 3.65830 + 6.33637i 0.126677 + 0.219411i
835835 −0.0956591 + 0.165686i −0.00331042 + 0.00573382i
836836 −1.27383 2.20634i −0.0440564 0.0763079i
837837 −0.212854 + 0.368675i −0.00735732 + 0.0127433i
838838 27.8095 0.960663
839839 −21.4269 + 37.1125i −0.739739 + 1.28127i 0.212873 + 0.977080i 0.431718π0.431718\pi
−0.952612 + 0.304186i 0.901615π0.901615\pi
840840 4.66858 + 12.9762i 0.161081 + 0.447721i
841841 14.1442 24.4986i 0.487733 0.844778i
842842 3.01970 5.23028i 0.104066 0.180247i
843843 −12.7531 −0.439242
844844 1.79586 3.11052i 0.0618160 0.107069i
845845 21.0921 + 47.1819i 0.725589 + 1.62311i
846846 −9.81898 −0.337584
847847 28.4282 + 5.12131i 0.976806 + 0.175970i
848848 2.82752 + 4.89741i 0.0970975 + 0.168178i
849849 16.3439 0.560920
850850 44.9946 77.9330i 1.54330 2.67308i
851851 −15.7952 27.3580i −0.541451 0.937821i
852852 8.22413 0.281754
853853 −46.0876 −1.57801 −0.789004 0.614388i 0.789403π-0.789403\pi
−0.789004 + 0.614388i 0.789403π0.789403\pi
854854 25.2529 29.8699i 0.864137 1.02213i
855855 −13.8497 23.9884i −0.473650 0.820386i
856856 9.50913 16.4703i 0.325015 0.562943i
857857 3.33662 5.77919i 0.113977 0.197413i −0.803394 0.595448i 0.796974π-0.796974\pi
0.917370 + 0.398035i 0.130308π0.130308\pi
858858 1.01760 1.56956i 0.0347404 0.0535839i
859859 8.20940 + 14.2191i 0.280101 + 0.485149i 0.971409 0.237411i 0.0762987π-0.0762987\pi
−0.691308 + 0.722560i 0.742965π0.742965\pi
860860 −2.96806 5.14084i −0.101210 0.175301i
861861 0.913393 + 2.53875i 0.0311284 + 0.0865203i
862862 3.85584 6.67851i 0.131330 0.227471i
863863 4.92500 + 8.53035i 0.167649 + 0.290377i 0.937593 0.347735i 0.113049π-0.113049\pi
−0.769944 + 0.638112i 0.779716π0.779716\pi
864864 3.14482 + 5.44698i 0.106989 + 0.185310i
865865 −27.8878 48.3030i −0.948213 1.64235i
866866 −10.0703 17.4423i −0.342204 0.592714i
867867 −2.08840 + 3.61721i −0.0709256 + 0.122847i
868868 −1.41395 0.254721i −0.0479925 0.00864579i
869869 1.10193 + 1.90861i 0.0373805 + 0.0647450i
870870 −3.03458 5.25604i −0.102882 0.178196i
871871 5.66713 + 0.292717i 0.192023 + 0.00991834i
872872 −2.74929 + 4.76191i −0.0931027 + 0.161259i
873873 9.52241 16.4933i 0.322285 0.558214i
874874 −45.6397 79.0503i −1.54379 2.67392i
875875 60.0890 + 10.8250i 2.03138 + 0.365951i
876876 −21.0431 −0.710980
877877 6.04112 0.203994 0.101997 0.994785i 0.467477π-0.467477\pi
0.101997 + 0.994785i 0.467477π0.467477\pi
878878 −37.1043 64.2665i −1.25221 2.16889i
879879 11.8319 20.4935i 0.399080 0.691227i
880880 −5.61146 −0.189162
881881 15.5861 + 26.9959i 0.525109 + 0.909516i 0.999572 + 0.0292404i 0.00930885π0.00930885\pi
−0.474463 + 0.880275i 0.657358π0.657358\pi
882882 −9.76507 + 8.07135i −0.328807 + 0.271777i
883883 −18.2205 −0.613169 −0.306584 0.951844i 0.599186π-0.599186\pi
−0.306584 + 0.951844i 0.599186π0.599186\pi
884884 11.5136 17.7588i 0.387246 0.597292i
885885 −9.65762 + 16.7275i −0.324637 + 0.562288i
886886 28.6932 0.963967
887887 −3.70842 + 6.42317i −0.124517 + 0.215669i −0.921544 0.388274i 0.873071π-0.873071\pi
0.797027 + 0.603943i 0.206405π0.206405\pi
888888 −2.86093 + 4.95527i −0.0960064 + 0.166288i
889889 7.02526 + 19.5265i 0.235620 + 0.654898i
890890 −7.97117 + 13.8065i −0.267194 + 0.462794i
891891 −0.286654 −0.00960328
892892 −10.4117 + 18.0336i −0.348609 + 0.603808i
893893 −18.9003 32.7363i −0.632474 1.09548i
894894 17.3699 30.0855i 0.580935 1.00621i
895895 9.33975 + 16.1769i 0.312194 + 0.540735i
896896 16.7412 19.8019i 0.559283 0.661535i
897897 14.1980 21.8992i 0.474059 0.731193i
898898 −13.6644 23.6674i −0.455986 0.789790i
899899 −0.359089 −0.0119763
900900 13.7824 0.459412
901901 −5.28498 −0.176068
902902 −0.529060 −0.0176158
903903 −1.99953 + 2.36510i −0.0665402 + 0.0787056i
904904 −5.40573 + 9.36299i −0.179792 + 0.311409i
905905 −43.8068 75.8756i −1.45619 2.52219i
906906 −17.1454 29.6967i −0.569617 0.986605i
907907 −17.4144 −0.578234 −0.289117 0.957294i 0.593362π-0.593362\pi
−0.289117 + 0.957294i 0.593362π0.593362\pi
908908 3.95797 6.85541i 0.131350 0.227505i
909909 −9.08855 −0.301448
910910 66.8321 + 15.6372i 2.21546 + 0.518369i
911911 −40.5753 −1.34432 −0.672159 0.740407i 0.734633π-0.734633\pi
−0.672159 + 0.740407i 0.734633π0.734633\pi
912912 −17.1541 + 29.7119i −0.568031 + 0.983858i
913913 −3.83795 −0.127018
914914 0.0252004 + 0.0436483i 0.000833554 + 0.00144376i
915915 16.2370 + 28.1233i 0.536779 + 0.929728i
916916 0.333516 0.577667i 0.0110197 0.0190867i
917917 7.24209 + 20.1292i 0.239155 + 0.664724i
918918 −8.32864 −0.274886
919919 −48.5466 −1.60140 −0.800702 0.599062i 0.795540π-0.795540\pi
−0.800702 + 0.599062i 0.795540π0.795540\pi
920920 −37.7297 −1.24391
921921 8.99691 0.296458
922922 25.4363 + 44.0570i 0.837700 + 1.45094i
923923 −12.6462 + 19.5056i −0.416253 + 0.642033i
924924 −0.327507 0.910296i −0.0107742 0.0299465i
925925 23.5770 + 40.8365i 0.775206 + 1.34270i
926926 0.241198 0.417767i 0.00792625 0.0137287i
927927 2.34421 + 4.06029i 0.0769939 + 0.133357i
928928 −2.65268 + 4.59458i −0.0870785 + 0.150824i
929929 −8.13928 −0.267041 −0.133521 0.991046i 0.542628π-0.542628\pi
−0.133521 + 0.991046i 0.542628π0.542628\pi
930930 1.53151 2.65266i 0.0502203 0.0869842i
931931 −45.7062 17.0202i −1.49796 0.557815i
932932 −8.26922 + 14.3227i −0.270867 + 0.469156i
933933 15.4498 26.7598i 0.505803 0.876077i
934934 67.1096 2.19589
935935 2.62212 4.54165i 0.0857526 0.148528i
936936 −4.72094 0.243845i −0.154309 0.00797032i
937937 30.6536 1.00141 0.500705 0.865618i 0.333074π-0.333074\pi
0.500705 + 0.865618i 0.333074π0.333074\pi
938938 4.86565 5.75522i 0.158869 0.187915i
939939 3.74574 + 6.48782i 0.122238 + 0.211722i
940940 27.5121 0.897347
941941 4.34815 7.53122i 0.141746 0.245511i −0.786408 0.617707i 0.788062π-0.788062\pi
0.928154 + 0.372196i 0.121395π0.121395\pi
942942 −16.8637 29.2088i −0.549449 0.951673i
943943 −7.38168 −0.240381
944944 23.9237 0.778651
945945 −3.56082 9.89718i −0.115833 0.321955i
946946 −0.303651 0.525938i −0.00987254 0.0170997i
947947 5.73610 9.93522i 0.186398 0.322851i −0.757649 0.652663i 0.773652π-0.773652\pi
0.944047 + 0.329812i 0.106985π0.106985\pi
948948 −4.90348 + 8.49307i −0.159258 + 0.275842i
949949 32.3577 49.9089i 1.05038 1.62011i
950950 68.1250 + 117.996i 2.21027 + 3.82830i
951951 8.11402 + 14.0539i 0.263115 + 0.455729i
952952 5.40407 + 15.0204i 0.175147 + 0.486815i
953953 −23.1731 + 40.1370i −0.750650 + 1.30016i 0.196859 + 0.980432i 0.436926π0.436926\pi
−0.947508 + 0.319731i 0.896407π0.896407\pi
954954 −1.03927 1.80006i −0.0336475 0.0582792i
955955 22.0590 + 38.2074i 0.713814 + 1.23636i
956956 3.05887 + 5.29812i 0.0989310 + 0.171353i
957957 −0.120898 0.209401i −0.00390807 0.00676897i
958958 −26.0607 + 45.1384i −0.841983 + 1.45836i
959959 1.35220 + 3.75839i 0.0436648 + 0.121365i
960960 −3.05165 5.28562i −0.0984916 0.170593i
961961 15.4094 + 26.6898i 0.497077 + 0.860963i
962962 12.9481 + 25.3648i 0.417463 + 0.817793i
963963 −7.25279 + 12.5622i −0.233718 + 0.404811i
964964 −6.64544 + 11.5102i −0.214035 + 0.370720i
965965 −0.966511 1.67405i −0.0311131 0.0538894i
966966 −11.7342 32.6147i −0.377541 1.04936i
967967 8.71419 0.280229 0.140115 0.990135i 0.455253π-0.455253\pi
0.140115 + 0.990135i 0.455253π0.455253\pi
968968 14.3144 0.460081
969969 −16.0316 27.7675i −0.515008 0.892021i
970970 −68.5149 + 118.671i −2.19988 + 3.81031i
971971 40.0563 1.28547 0.642733 0.766090i 0.277800π-0.277800\pi
0.642733 + 0.766090i 0.277800π0.277800\pi
972972 −0.637789 1.10468i −0.0204571 0.0354327i
973973 −6.90545 + 8.16797i −0.221379 + 0.261853i
974974 −24.8499 −0.796243
975975 −21.1930 + 32.6883i −0.678719 + 1.04686i
976976 20.1110 34.8333i 0.643738 1.11499i
977977 −42.3067 −1.35351 −0.676755 0.736208i 0.736614π-0.736614\pi
−0.676755 + 0.736208i 0.736614π0.736614\pi
978978 −9.68748 + 16.7792i −0.309771 + 0.536540i
979979 −0.317572 + 0.550050i −0.0101496 + 0.0175797i
980980 27.3611 22.6154i 0.874017 0.722422i
981981 2.09694 3.63200i 0.0669500 0.115961i
982982 −49.8189 −1.58979
983983 2.44395 4.23305i 0.0779501 0.135013i −0.824415 0.565985i 0.808496π-0.808496\pi
0.902365 + 0.430972i 0.141829π0.141829\pi
984984 0.668510 + 1.15789i 0.0213113 + 0.0369123i
985985 33.9436 58.7920i 1.08153 1.87327i
986986 −3.51264 6.08407i −0.111865 0.193756i
987987 −4.85935 13.5064i −0.154675 0.429913i
988988 14.5695 + 28.5410i 0.463517 + 0.908009i
989989 −4.23667 7.33813i −0.134718 0.233339i
990990 2.06251 0.0655510
991991 −18.5959 −0.590718 −0.295359 0.955386i 0.595439π-0.595439\pi
−0.295359 + 0.955386i 0.595439π0.595439\pi
992992 −2.67755 −0.0850124
993993 5.58434 0.177214
994994 10.4516 + 29.0498i 0.331504 + 0.921405i
995995 46.0560 79.7713i 1.46007 2.52892i
996996 −8.53922 14.7904i −0.270575 0.468650i
997997 12.8181 + 22.2017i 0.405954 + 0.703133i 0.994432 0.105380i 0.0336059π-0.0336059\pi
−0.588478 + 0.808513i 0.700273π0.700273\pi
998998 −7.04276 −0.222935
999999 2.18208 3.77948i 0.0690380 0.119577i
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 273.2.j.c.172.3 yes 20
3.2 odd 2 819.2.n.f.172.8 20
7.2 even 3 273.2.l.c.16.8 yes 20
13.9 even 3 273.2.l.c.256.8 yes 20
21.2 odd 6 819.2.s.f.289.3 20
39.35 odd 6 819.2.s.f.802.3 20
91.9 even 3 inner 273.2.j.c.100.3 20
273.191 odd 6 819.2.n.f.100.8 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.j.c.100.3 20 91.9 even 3 inner
273.2.j.c.172.3 yes 20 1.1 even 1 trivial
273.2.l.c.16.8 yes 20 7.2 even 3
273.2.l.c.256.8 yes 20 13.9 even 3
819.2.n.f.100.8 20 273.191 odd 6
819.2.n.f.172.8 20 3.2 odd 2
819.2.s.f.289.3 20 21.2 odd 6
819.2.s.f.802.3 20 39.35 odd 6