Properties

Label 1338.2.e.j.1075.3
Level 13381338
Weight 22
Character 1338.1075
Analytic conductor 10.68410.684
Analytic rank 00
Dimension 1818
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1338,2,Mod(931,1338)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1338, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1338.931");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1338=23223 1338 = 2 \cdot 3 \cdot 223
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1338.e (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: 10.683983790410.6839837904
Analytic rank: 00
Dimension: 1818
Relative dimension: 99 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x18x17+23x16+4x15+377x14+11x13+2342x12+157x11+10694x10++64 x^{18} - x^{17} + 23 x^{16} + 4 x^{15} + 377 x^{14} + 11 x^{13} + 2342 x^{12} + 157 x^{11} + 10694 x^{10} + \cdots + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 24 2^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 1075.3
Root 0.3559610.616542i-0.355961 - 0.616542i of defining polynomial
Character χ\chi == 1338.1075
Dual form 1338.2.e.j.931.3

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+1.00000q2+(0.5000000.866025i)q3+1.00000q4+(0.355961+0.616542i)q5+(0.5000000.866025i)q60.0500871q7+1.00000q8+(0.500000+0.866025i)q9+(0.355961+0.616542i)q10+(0.119016+0.206142i)q11+(0.5000000.866025i)q12+6.08940q130.0500871q14+0.711921q15+1.00000q162.89113q17+(0.500000+0.866025i)q18+(2.64073+4.57387i)q19+(0.355961+0.616542i)q20+(0.0250435+0.0433767i)q21+(0.119016+0.206142i)q22+(1.638872.83860i)q23+(0.5000000.866025i)q24+(2.24658+3.89120i)q25+6.08940q26+1.00000q270.0500871q28+(4.041857.00069i)q29+0.711921q30+(1.00721+1.74455i)q31+1.00000q32+0.238032q332.89113q34+(0.01782900.0308808i)q35+(0.500000+0.866025i)q36+(2.183583.78207i)q37+(2.64073+4.57387i)q38+(3.044705.27358i)q39+(0.355961+0.616542i)q40+10.3734q41+(0.0250435+0.0433767i)q42+(0.543104+0.940683i)q43+(0.119016+0.206142i)q44+(0.3559610.616542i)q45+(1.638872.83860i)q46+(1.00392+1.73883i)q47+(0.5000000.866025i)q486.99749q49+(2.24658+3.89120i)q50+(1.44557+2.50380i)q51+6.08940q52+(2.232843.86739i)q53+1.00000q54+(0.08473010.146757i)q550.0500871q56+(2.640734.57387i)q57+(4.041857.00069i)q58+9.30639q59+0.711921q60+(0.798509+1.38306i)q61+(1.00721+1.74455i)q62+(0.02504350.0433767i)q63+1.00000q64+(2.16759+3.75437i)q65+0.238032q66+(2.18092+3.77746i)q672.89113q68+(1.63887+2.83860i)q69+(0.01782900.0308808i)q70+(1.74602+3.02420i)q71+(0.500000+0.866025i)q72+(0.369119+0.639334i)q73+(2.183583.78207i)q74+(2.246583.89120i)q75+(2.64073+4.57387i)q76+(0.005961170.0103250i)q77+(3.044705.27358i)q78+(4.024596.97079i)q79+(0.355961+0.616542i)q80+(0.5000000.866025i)q81+10.3734q82+(4.53232+7.85020i)q83+(0.0250435+0.0433767i)q84+(1.029131.78250i)q85+(0.543104+0.940683i)q868.08370q87+(0.119016+0.206142i)q88+(4.615287.99390i)q89+(0.3559610.616542i)q900.305000q91+(1.638872.83860i)q92+(1.007211.74455i)q93+(1.00392+1.73883i)q943.75998q95+(0.5000000.866025i)q96+(1.071751.85633i)q976.99749q98+(0.1190160.206142i)q99+O(q100)q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.355961 + 0.616542i) q^{5} +(-0.500000 - 0.866025i) q^{6} -0.0500871 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.355961 + 0.616542i) q^{10} +(-0.119016 + 0.206142i) q^{11} +(-0.500000 - 0.866025i) q^{12} +6.08940 q^{13} -0.0500871 q^{14} +0.711921 q^{15} +1.00000 q^{16} -2.89113 q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.64073 + 4.57387i) q^{19} +(-0.355961 + 0.616542i) q^{20} +(0.0250435 + 0.0433767i) q^{21} +(-0.119016 + 0.206142i) q^{22} +(-1.63887 - 2.83860i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.24658 + 3.89120i) q^{25} +6.08940 q^{26} +1.00000 q^{27} -0.0500871 q^{28} +(4.04185 - 7.00069i) q^{29} +0.711921 q^{30} +(1.00721 + 1.74455i) q^{31} +1.00000 q^{32} +0.238032 q^{33} -2.89113 q^{34} +(0.0178290 - 0.0308808i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(2.18358 - 3.78207i) q^{37} +(2.64073 + 4.57387i) q^{38} +(-3.04470 - 5.27358i) q^{39} +(-0.355961 + 0.616542i) q^{40} +10.3734 q^{41} +(0.0250435 + 0.0433767i) q^{42} +(0.543104 + 0.940683i) q^{43} +(-0.119016 + 0.206142i) q^{44} +(-0.355961 - 0.616542i) q^{45} +(-1.63887 - 2.83860i) q^{46} +(-1.00392 + 1.73883i) q^{47} +(-0.500000 - 0.866025i) q^{48} -6.99749 q^{49} +(2.24658 + 3.89120i) q^{50} +(1.44557 + 2.50380i) q^{51} +6.08940 q^{52} +(2.23284 - 3.86739i) q^{53} +1.00000 q^{54} +(-0.0847301 - 0.146757i) q^{55} -0.0500871 q^{56} +(2.64073 - 4.57387i) q^{57} +(4.04185 - 7.00069i) q^{58} +9.30639 q^{59} +0.711921 q^{60} +(0.798509 + 1.38306i) q^{61} +(1.00721 + 1.74455i) q^{62} +(0.0250435 - 0.0433767i) q^{63} +1.00000 q^{64} +(-2.16759 + 3.75437i) q^{65} +0.238032 q^{66} +(2.18092 + 3.77746i) q^{67} -2.89113 q^{68} +(-1.63887 + 2.83860i) q^{69} +(0.0178290 - 0.0308808i) q^{70} +(1.74602 + 3.02420i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.369119 + 0.639334i) q^{73} +(2.18358 - 3.78207i) q^{74} +(2.24658 - 3.89120i) q^{75} +(2.64073 + 4.57387i) q^{76} +(0.00596117 - 0.0103250i) q^{77} +(-3.04470 - 5.27358i) q^{78} +(4.02459 - 6.97079i) q^{79} +(-0.355961 + 0.616542i) q^{80} +(-0.500000 - 0.866025i) q^{81} +10.3734 q^{82} +(-4.53232 + 7.85020i) q^{83} +(0.0250435 + 0.0433767i) q^{84} +(1.02913 - 1.78250i) q^{85} +(0.543104 + 0.940683i) q^{86} -8.08370 q^{87} +(-0.119016 + 0.206142i) q^{88} +(-4.61528 - 7.99390i) q^{89} +(-0.355961 - 0.616542i) q^{90} -0.305000 q^{91} +(-1.63887 - 2.83860i) q^{92} +(1.00721 - 1.74455i) q^{93} +(-1.00392 + 1.73883i) q^{94} -3.75998 q^{95} +(-0.500000 - 0.866025i) q^{96} +(1.07175 - 1.85633i) q^{97} -6.99749 q^{98} +(-0.119016 - 0.206142i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 18q+18q29q3+18q4+q59q6+4q7+18q89q9+q10+6q119q12+4q13+4q142q15+18q16+12q179q18q19+q20++6q99+O(q100) 18 q + 18 q^{2} - 9 q^{3} + 18 q^{4} + q^{5} - 9 q^{6} + 4 q^{7} + 18 q^{8} - 9 q^{9} + q^{10} + 6 q^{11} - 9 q^{12} + 4 q^{13} + 4 q^{14} - 2 q^{15} + 18 q^{16} + 12 q^{17} - 9 q^{18} - q^{19} + q^{20}+ \cdots + 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1338Z)×\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times.

nn 893893 895895
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{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 1.00000 0.707107
33 −0.500000 0.866025i −0.288675 0.500000i
44 1.00000 0.500000
55 −0.355961 + 0.616542i −0.159190 + 0.275726i −0.934577 0.355761i 0.884222π-0.884222\pi
0.775387 + 0.631487i 0.217555π0.217555\pi
66 −0.500000 0.866025i −0.204124 0.353553i
77 −0.0500871 −0.0189311 −0.00946556 0.999955i 0.503013π-0.503013\pi
−0.00946556 + 0.999955i 0.503013π0.503013\pi
88 1.00000 0.353553
99 −0.500000 + 0.866025i −0.166667 + 0.288675i
1010 −0.355961 + 0.616542i −0.112565 + 0.194968i
1111 −0.119016 + 0.206142i −0.0358847 + 0.0621541i −0.883410 0.468601i 0.844758π-0.844758\pi
0.847525 + 0.530755i 0.178092π0.178092\pi
1212 −0.500000 0.866025i −0.144338 0.250000i
1313 6.08940 1.68890 0.844449 0.535637i 0.179928π-0.179928\pi
0.844449 + 0.535637i 0.179928π0.179928\pi
1414 −0.0500871 −0.0133863
1515 0.711921 0.183817
1616 1.00000 0.250000
1717 −2.89113 −0.701203 −0.350602 0.936525i 0.614023π-0.614023\pi
−0.350602 + 0.936525i 0.614023π0.614023\pi
1818 −0.500000 + 0.866025i −0.117851 + 0.204124i
1919 2.64073 + 4.57387i 0.605824 + 1.04932i 0.991921 + 0.126860i 0.0404899π0.0404899\pi
−0.386096 + 0.922458i 0.626177π0.626177\pi
2020 −0.355961 + 0.616542i −0.0795952 + 0.137863i
2121 0.0250435 + 0.0433767i 0.00546495 + 0.00946556i
2222 −0.119016 + 0.206142i −0.0253743 + 0.0439496i
2323 −1.63887 2.83860i −0.341728 0.591890i 0.643026 0.765844i 0.277679π-0.277679\pi
−0.984754 + 0.173955i 0.944345π0.944345\pi
2424 −0.500000 0.866025i −0.102062 0.176777i
2525 2.24658 + 3.89120i 0.449317 + 0.778240i
2626 6.08940 1.19423
2727 1.00000 0.192450
2828 −0.0500871 −0.00946556
2929 4.04185 7.00069i 0.750553 1.30000i −0.197003 0.980403i 0.563121π-0.563121\pi
0.947555 0.319592i 0.103546π-0.103546\pi
3030 0.711921 0.129978
3131 1.00721 + 1.74455i 0.180901 + 0.313330i 0.942188 0.335086i 0.108765π-0.108765\pi
−0.761287 + 0.648416i 0.775432π0.775432\pi
3232 1.00000 0.176777
3333 0.238032 0.0414361
3434 −2.89113 −0.495825
3535 0.0178290 0.0308808i 0.00301365 0.00521980i
3636 −0.500000 + 0.866025i −0.0833333 + 0.144338i
3737 2.18358 3.78207i 0.358978 0.621769i −0.628812 0.777557i 0.716459π-0.716459\pi
0.987790 + 0.155789i 0.0497919π0.0497919\pi
3838 2.64073 + 4.57387i 0.428382 + 0.741980i
3939 −3.04470 5.27358i −0.487543 0.844449i
4040 −0.355961 + 0.616542i −0.0562823 + 0.0974838i
4141 10.3734 1.62005 0.810026 0.586393i 0.199453π-0.199453\pi
0.810026 + 0.586393i 0.199453π0.199453\pi
4242 0.0250435 + 0.0433767i 0.00386430 + 0.00669317i
4343 0.543104 + 0.940683i 0.0828225 + 0.143453i 0.904461 0.426556i 0.140273π-0.140273\pi
−0.821639 + 0.570009i 0.806940π0.806940\pi
4444 −0.119016 + 0.206142i −0.0179424 + 0.0310771i
4545 −0.355961 0.616542i −0.0530635 0.0919086i
4646 −1.63887 2.83860i −0.241638 0.418529i
4747 −1.00392 + 1.73883i −0.146436 + 0.253635i −0.929908 0.367793i 0.880114π-0.880114\pi
0.783472 + 0.621428i 0.213447π0.213447\pi
4848 −0.500000 0.866025i −0.0721688 0.125000i
4949 −6.99749 −0.999642
5050 2.24658 + 3.89120i 0.317715 + 0.550299i
5151 1.44557 + 2.50380i 0.202420 + 0.350602i
5252 6.08940 0.844449
5353 2.23284 3.86739i 0.306704 0.531228i −0.670935 0.741516i 0.734107π-0.734107\pi
0.977639 + 0.210289i 0.0674404π0.0674404\pi
5454 1.00000 0.136083
5555 −0.0847301 0.146757i −0.0114250 0.0197887i
5656 −0.0500871 −0.00669317
5757 2.64073 4.57387i 0.349773 0.605824i
5858 4.04185 7.00069i 0.530721 0.919235i
5959 9.30639 1.21159 0.605794 0.795621i 0.292855π-0.292855\pi
0.605794 + 0.795621i 0.292855π0.292855\pi
6060 0.711921 0.0919086
6161 0.798509 + 1.38306i 0.102239 + 0.177083i 0.912607 0.408839i 0.134066π-0.134066\pi
−0.810368 + 0.585921i 0.800733π0.800733\pi
6262 1.00721 + 1.74455i 0.127916 + 0.221558i
6363 0.0250435 0.0433767i 0.00315519 0.00546495i
6464 1.00000 0.125000
6565 −2.16759 + 3.75437i −0.268856 + 0.465673i
6666 0.238032 0.0292997
6767 2.18092 + 3.77746i 0.266441 + 0.461490i 0.967940 0.251181i 0.0808188π-0.0808188\pi
−0.701499 + 0.712671i 0.747485π0.747485\pi
6868 −2.89113 −0.350602
6969 −1.63887 + 2.83860i −0.197297 + 0.341728i
7070 0.0178290 0.0308808i 0.00213097 0.00369096i
7171 1.74602 + 3.02420i 0.207215 + 0.358907i 0.950836 0.309694i 0.100227π-0.100227\pi
−0.743621 + 0.668601i 0.766893π0.766893\pi
7272 −0.500000 + 0.866025i −0.0589256 + 0.102062i
7373 −0.369119 + 0.639334i −0.0432022 + 0.0748283i −0.886818 0.462119i 0.847089π-0.847089\pi
0.843616 + 0.536947i 0.180423π0.180423\pi
7474 2.18358 3.78207i 0.253836 0.439657i
7575 2.24658 3.89120i 0.259413 0.449317i
7676 2.64073 + 4.57387i 0.302912 + 0.524659i
7777 0.00596117 0.0103250i 0.000679338 0.00117665i
7878 −3.04470 5.27358i −0.344745 0.597115i
7979 4.02459 6.97079i 0.452801 0.784275i −0.545757 0.837943i 0.683758π-0.683758\pi
0.998559 + 0.0536681i 0.0170913π0.0170913\pi
8080 −0.355961 + 0.616542i −0.0397976 + 0.0689315i
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 10.3734 1.14555
8383 −4.53232 + 7.85020i −0.497486 + 0.861672i −0.999996 0.00289998i 0.999077π-0.999077\pi
0.502509 + 0.864572i 0.332410π0.332410\pi
8484 0.0250435 + 0.0433767i 0.00273247 + 0.00473278i
8585 1.02913 1.78250i 0.111625 0.193340i
8686 0.543104 + 0.940683i 0.0585644 + 0.101436i
8787 −8.08370 −0.866663
8888 −0.119016 + 0.206142i −0.0126872 + 0.0219748i
8989 −4.61528 7.99390i −0.489219 0.847351i 0.510704 0.859756i 0.329385π-0.329385\pi
−0.999923 + 0.0124049i 0.996051π0.996051\pi
9090 −0.355961 0.616542i −0.0375215 0.0649892i
9191 −0.305000 −0.0319727
9292 −1.63887 2.83860i −0.170864 0.295945i
9393 1.00721 1.74455i 0.104443 0.180901i
9494 −1.00392 + 1.73883i −0.103546 + 0.179347i
9595 −3.75998 −0.385766
9696 −0.500000 0.866025i −0.0510310 0.0883883i
9797 1.07175 1.85633i 0.108820 0.188482i −0.806472 0.591272i 0.798626π-0.798626\pi
0.915293 + 0.402790i 0.131959π0.131959\pi
9898 −6.99749 −0.706853
9999 −0.119016 0.206142i −0.0119616 0.0207180i
100100 2.24658 + 3.89120i 0.224658 + 0.389120i
101101 −7.67946 13.3012i −0.764134 1.32352i −0.940703 0.339231i 0.889833π-0.889833\pi
0.176568 0.984288i 0.443500π-0.443500\pi
102102 1.44557 + 2.50380i 0.143132 + 0.247913i
103103 −13.9141 −1.37100 −0.685499 0.728073i 0.740416π-0.740416\pi
−0.685499 + 0.728073i 0.740416π0.740416\pi
104104 6.08940 0.597115
105105 −0.0356580 −0.00347987
106106 2.23284 3.86739i 0.216873 0.375635i
107107 −3.45333 + 5.98134i −0.333846 + 0.578238i −0.983262 0.182195i 0.941680π-0.941680\pi
0.649417 + 0.760433i 0.275013π0.275013\pi
108108 1.00000 0.0962250
109109 −1.91519 + 3.31720i −0.183442 + 0.317730i −0.943050 0.332650i 0.892057π-0.892057\pi
0.759609 + 0.650380i 0.225391π0.225391\pi
110110 −0.0847301 0.146757i −0.00807870 0.0139927i
111111 −4.36716 −0.414512
112112 −0.0500871 −0.00473278
113113 2.03896 + 3.53159i 0.191810 + 0.332224i 0.945850 0.324604i 0.105231π-0.105231\pi
−0.754040 + 0.656828i 0.771898π0.771898\pi
114114 2.64073 4.57387i 0.247327 0.428382i
115115 2.33349 0.217599
116116 4.04185 7.00069i 0.375276 0.649998i
117117 −3.04470 + 5.27358i −0.281483 + 0.487543i
118118 9.30639 0.856723
119119 0.144808 0.0132746
120120 0.711921 0.0649892
121121 5.47167 + 9.47721i 0.497425 + 0.861565i
122122 0.798509 + 1.38306i 0.0722936 + 0.125216i
123123 −5.18670 8.98363i −0.467669 0.810026i
124124 1.00721 + 1.74455i 0.0904505 + 0.156665i
125125 −6.75839 −0.604488
126126 0.0250435 0.0433767i 0.00223106 0.00386430i
127127 2.66370 + 4.61366i 0.236365 + 0.409396i 0.959669 0.281134i 0.0907106π-0.0907106\pi
−0.723303 + 0.690530i 0.757377π0.757377\pi
128128 1.00000 0.0883883
129129 0.543104 0.940683i 0.0478176 0.0828225i
130130 −2.16759 + 3.75437i −0.190110 + 0.329280i
131131 −1.75869 3.04614i −0.153657 0.266142i 0.778912 0.627133i 0.215772π-0.215772\pi
−0.932569 + 0.360991i 0.882438π0.882438\pi
132132 0.238032 0.0207180
133133 −0.132266 0.229092i −0.0114689 0.0198648i
134134 2.18092 + 3.77746i 0.188402 + 0.326323i
135135 −0.355961 + 0.616542i −0.0306362 + 0.0530635i
136136 −2.89113 −0.247913
137137 −6.77141 11.7284i −0.578520 1.00203i −0.995649 0.0931793i 0.970297π-0.970297\pi
0.417129 0.908847i 0.363036π-0.363036\pi
138138 −1.63887 + 2.83860i −0.139510 + 0.241638i
139139 −1.31959 2.28560i −0.111926 0.193862i 0.804621 0.593789i 0.202369π-0.202369\pi
−0.916547 + 0.399927i 0.869035π0.869035\pi
140140 0.0178290 0.0308808i 0.00150683 0.00260990i
141141 2.00783 0.169090
142142 1.74602 + 3.02420i 0.146523 + 0.253785i
143143 −0.724737 + 1.25528i −0.0606056 + 0.104972i
144144 −0.500000 + 0.866025i −0.0416667 + 0.0721688i
145145 2.87748 + 4.98394i 0.238962 + 0.413893i
146146 −0.369119 + 0.639334i −0.0305485 + 0.0529116i
147147 3.49875 + 6.06001i 0.288572 + 0.499821i
148148 2.18358 3.78207i 0.179489 0.310884i
149149 3.80880 6.59703i 0.312029 0.540450i −0.666773 0.745261i 0.732325π-0.732325\pi
0.978801 + 0.204811i 0.0656581π0.0656581\pi
150150 2.24658 3.89120i 0.183433 0.317715i
151151 −9.54177 + 16.5268i −0.776498 + 1.34493i 0.157451 + 0.987527i 0.449672π0.449672\pi
−0.933949 + 0.357407i 0.883661π0.883661\pi
152152 2.64073 + 4.57387i 0.214191 + 0.370990i
153153 1.44557 2.50380i 0.116867 0.202420i
154154 0.00596117 0.0103250i 0.000480365 0.000832016i
155155 −1.43411 −0.115191
156156 −3.04470 5.27358i −0.243771 0.422224i
157157 6.48492 0.517553 0.258776 0.965937i 0.416681π-0.416681\pi
0.258776 + 0.965937i 0.416681π0.416681\pi
158158 4.02459 6.97079i 0.320179 0.554566i
159159 −4.46568 −0.354152
160160 −0.355961 + 0.616542i −0.0281411 + 0.0487419i
161161 0.0820861 + 0.142177i 0.00646929 + 0.0112051i
162162 −0.500000 0.866025i −0.0392837 0.0680414i
163163 −5.53504 −0.433538 −0.216769 0.976223i 0.569552π-0.569552\pi
−0.216769 + 0.976223i 0.569552π0.569552\pi
164164 10.3734 0.810026
165165 −0.0847301 + 0.146757i −0.00659623 + 0.0114250i
166166 −4.53232 + 7.85020i −0.351776 + 0.609294i
167167 3.84736 0.297717 0.148859 0.988858i 0.452440π-0.452440\pi
0.148859 + 0.988858i 0.452440π0.452440\pi
168168 0.0250435 + 0.0433767i 0.00193215 + 0.00334658i
169169 24.0809 1.85237
170170 1.02913 1.78250i 0.0789306 0.136712i
171171 −5.28145 −0.403883
172172 0.543104 + 0.940683i 0.0414113 + 0.0717264i
173173 0.646627 + 1.11999i 0.0491621 + 0.0851513i 0.889559 0.456820i 0.151012π-0.151012\pi
−0.840397 + 0.541971i 0.817678π0.817678\pi
174174 −8.08370 −0.612824
175175 −0.112525 0.194899i −0.00850608 0.0147330i
176176 −0.119016 + 0.206142i −0.00897118 + 0.0155385i
177177 −4.65320 8.05957i −0.349756 0.605794i
178178 −4.61528 7.99390i −0.345930 0.599168i
179179 −10.4033 + 18.0190i −0.777579 + 1.34681i 0.155754 + 0.987796i 0.450219π0.450219\pi
−0.933333 + 0.359011i 0.883114π0.883114\pi
180180 −0.355961 0.616542i −0.0265317 0.0459543i
181181 10.6949 + 18.5241i 0.794944 + 1.37688i 0.922875 + 0.385100i 0.125833π0.125833\pi
−0.127932 + 0.991783i 0.540834π0.540834\pi
182182 −0.305000 −0.0226081
183183 0.798509 1.38306i 0.0590275 0.102239i
184184 −1.63887 2.83860i −0.120819 0.209265i
185185 1.55454 + 2.69254i 0.114292 + 0.197959i
186186 1.00721 1.74455i 0.0738526 0.127916i
187187 0.344092 0.595984i 0.0251625 0.0435827i
188188 −1.00392 + 1.73883i −0.0732181 + 0.126818i
189189 −0.0500871 −0.00364330
190190 −3.75998 −0.272777
191191 −21.0306 −1.52172 −0.760862 0.648914i 0.775224π-0.775224\pi
−0.760862 + 0.648914i 0.775224π0.775224\pi
192192 −0.500000 0.866025i −0.0360844 0.0625000i
193193 −22.9321 −1.65069 −0.825344 0.564630i 0.809019π-0.809019\pi
−0.825344 + 0.564630i 0.809019π0.809019\pi
194194 1.07175 1.85633i 0.0769474 0.133277i
195195 4.33518 0.310448
196196 −6.99749 −0.499821
197197 −7.87651 −0.561178 −0.280589 0.959828i 0.590530π-0.590530\pi
−0.280589 + 0.959828i 0.590530π0.590530\pi
198198 −0.119016 0.206142i −0.00845811 0.0146499i
199199 −11.8545 20.5326i −0.840342 1.45551i −0.889606 0.456728i 0.849021π-0.849021\pi
0.0492647 0.998786i 0.484312π-0.484312\pi
200200 2.24658 + 3.89120i 0.158857 + 0.275149i
201201 2.18092 3.77746i 0.153830 0.266441i
202202 −7.67946 13.3012i −0.540325 0.935870i
203203 −0.202444 + 0.350644i −0.0142088 + 0.0246104i
204204 1.44557 + 2.50380i 0.101210 + 0.175301i
205205 −3.69252 + 6.39563i −0.257897 + 0.446690i
206206 −13.9141 −0.969442
207207 3.27774 0.227819
208208 6.08940 0.422224
209209 −1.25716 −0.0869593
210210 −0.0356580 −0.00246064
211211 −5.37153 9.30377i −0.369792 0.640498i 0.619741 0.784806i 0.287238π-0.287238\pi
−0.989533 + 0.144308i 0.953904π0.953904\pi
212212 2.23284 3.86739i 0.153352 0.265614i
213213 1.74602 3.02420i 0.119636 0.207215i
214214 −3.45333 + 5.98134i −0.236065 + 0.408876i
215215 −0.773294 −0.0527382
216216 1.00000 0.0680414
217217 −0.0504484 0.0873792i −0.00342466 0.00593169i
218218 −1.91519 + 3.31720i −0.129713 + 0.224669i
219219 0.738239 0.0498856
220220 −0.0847301 0.146757i −0.00571250 0.00989434i
221221 −17.6053 −1.18426
222222 −4.36716 −0.293104
223223 3.73581 + 14.4583i 0.250168 + 0.968202i
224224 −0.0500871 −0.00334658
225225 −4.49317 −0.299545
226226 2.03896 + 3.53159i 0.135630 + 0.234918i
227227 −9.78329 −0.649339 −0.324670 0.945827i 0.605253π-0.605253\pi
−0.324670 + 0.945827i 0.605253π0.605253\pi
228228 2.64073 4.57387i 0.174886 0.302912i
229229 2.54981 + 4.41641i 0.168496 + 0.291844i 0.937891 0.346929i 0.112775π-0.112775\pi
−0.769395 + 0.638773i 0.779442π0.779442\pi
230230 2.33349 0.153866
231231 −0.0119223 −0.000784432
232232 4.04185 7.00069i 0.265360 0.459618i
233233 −4.65509 + 8.06286i −0.304965 + 0.528215i −0.977254 0.212074i 0.931978π-0.931978\pi
0.672288 + 0.740289i 0.265312π0.265312\pi
234234 −3.04470 + 5.27358i −0.199038 + 0.344745i
235235 −0.714709 1.23791i −0.0466225 0.0807525i
236236 9.30639 0.605794
237237 −8.04918 −0.522850
238238 0.144808 0.00938654
239239 13.6826 0.885056 0.442528 0.896755i 0.354082π-0.354082\pi
0.442528 + 0.896755i 0.354082π0.354082\pi
240240 0.711921 0.0459543
241241 8.23257 14.2592i 0.530306 0.918518i −0.469068 0.883162i 0.655410π-0.655410\pi
0.999375 0.0353559i 0.0112565π-0.0112565\pi
242242 5.47167 + 9.47721i 0.351732 + 0.609218i
243243 −0.500000 + 0.866025i −0.0320750 + 0.0555556i
244244 0.798509 + 1.38306i 0.0511193 + 0.0885413i
245245 2.49083 4.31425i 0.159133 0.275627i
246246 −5.18670 8.98363i −0.330692 0.572775i
247247 16.0805 + 27.8522i 1.02317 + 1.77219i
248248 1.00721 + 1.74455i 0.0639582 + 0.110779i
249249 9.06463 0.574448
250250 −6.75839 −0.427438
251251 11.6521 0.735474 0.367737 0.929930i 0.380133π-0.380133\pi
0.367737 + 0.929930i 0.380133π0.380133\pi
252252 0.0250435 0.0433767i 0.00157759 0.00273247i
253253 0.780207 0.0490512
254254 2.66370 + 4.61366i 0.167135 + 0.289487i
255255 −2.05826 −0.128893
256256 1.00000 0.0625000
257257 −11.2746 −0.703292 −0.351646 0.936133i 0.614378π-0.614378\pi
−0.351646 + 0.936133i 0.614378π0.614378\pi
258258 0.543104 0.940683i 0.0338122 0.0585644i
259259 −0.109369 + 0.189433i −0.00679586 + 0.0117708i
260260 −2.16759 + 3.75437i −0.134428 + 0.232836i
261261 4.04185 + 7.00069i 0.250184 + 0.433332i
262262 −1.75869 3.04614i −0.108652 0.188191i
263263 −6.15272 + 10.6568i −0.379393 + 0.657128i −0.990974 0.134054i 0.957201π-0.957201\pi
0.611581 + 0.791182i 0.290534π0.290534\pi
264264 0.238032 0.0146499
265265 1.58961 + 2.75328i 0.0976488 + 0.169133i
266266 −0.132266 0.229092i −0.00810976 0.0140465i
267267 −4.61528 + 7.99390i −0.282450 + 0.489219i
268268 2.18092 + 3.77746i 0.133221 + 0.230745i
269269 −5.20507 9.01544i −0.317359 0.549681i 0.662577 0.748993i 0.269463π-0.269463\pi
−0.979936 + 0.199312i 0.936129π0.936129\pi
270270 −0.355961 + 0.616542i −0.0216631 + 0.0375215i
271271 −8.72371 15.1099i −0.529927 0.917861i −0.999390 0.0349092i 0.988886π-0.988886\pi
0.469463 0.882952i 0.344448π-0.344448\pi
272272 −2.89113 −0.175301
273273 0.152500 + 0.264138i 0.00922973 + 0.0159864i
274274 −6.77141 11.7284i −0.409076 0.708540i
275275 −1.06952 −0.0644944
276276 −1.63887 + 2.83860i −0.0986483 + 0.170864i
277277 −21.5632 −1.29561 −0.647804 0.761807i 0.724312π-0.724312\pi
−0.647804 + 0.761807i 0.724312π0.724312\pi
278278 −1.31959 2.28560i −0.0791438 0.137081i
279279 −2.01443 −0.120601
280280 0.0178290 0.0308808i 0.00106549 0.00184548i
281281 2.83723 4.91422i 0.169255 0.293158i −0.768903 0.639365i 0.779197π-0.779197\pi
0.938158 + 0.346207i 0.112531π0.112531\pi
282282 2.00783 0.119565
283283 0.879276 0.0522676 0.0261338 0.999658i 0.491680π-0.491680\pi
0.0261338 + 0.999658i 0.491680π0.491680\pi
284284 1.74602 + 3.02420i 0.103607 + 0.179453i
285285 1.87999 + 3.25624i 0.111361 + 0.192883i
286286 −0.724737 + 1.25528i −0.0428546 + 0.0742264i
287287 −0.519573 −0.0306694
288288 −0.500000 + 0.866025i −0.0294628 + 0.0510310i
289289 −8.64134 −0.508314
290290 2.87748 + 4.98394i 0.168971 + 0.292667i
291291 −2.14351 −0.125655
292292 −0.369119 + 0.639334i −0.0216011 + 0.0374142i
293293 −0.695703 + 1.20499i −0.0406434 + 0.0703964i −0.885632 0.464389i 0.846274π-0.846274\pi
0.844988 + 0.534785i 0.179607π0.179607\pi
294294 3.49875 + 6.06001i 0.204051 + 0.353427i
295295 −3.31271 + 5.73778i −0.192873 + 0.334066i
296296 2.18358 3.78207i 0.126918 0.219828i
297297 −0.119016 + 0.206142i −0.00690602 + 0.0119616i
298298 3.80880 6.59703i 0.220638 0.382156i
299299 −9.97974 17.2854i −0.577143 0.999641i
300300 2.24658 3.89120i 0.129707 0.224658i
301301 −0.0272025 0.0471161i −0.00156792 0.00271572i
302302 −9.54177 + 16.5268i −0.549067 + 0.951012i
303303 −7.67946 + 13.3012i −0.441173 + 0.764134i
304304 2.64073 + 4.57387i 0.151456 + 0.262330i
305305 −1.13695 −0.0651016
306306 1.44557 2.50380i 0.0826376 0.143132i
307307 0.860812 + 1.49097i 0.0491292 + 0.0850942i 0.889544 0.456849i 0.151022π-0.151022\pi
−0.840415 + 0.541943i 0.817689π0.817689\pi
308308 0.00596117 0.0103250i 0.000339669 0.000588324i
309309 6.95706 + 12.0500i 0.395773 + 0.685499i
310310 −1.43411 −0.0814522
311311 −0.323617 + 0.560522i −0.0183507 + 0.0317843i −0.875055 0.484024i 0.839175π-0.839175\pi
0.856704 + 0.515808i 0.172508π0.172508\pi
312312 −3.04470 5.27358i −0.172372 0.298558i
313313 14.0059 + 24.2589i 0.791661 + 1.37120i 0.924938 + 0.380118i 0.124117π0.124117\pi
−0.133277 + 0.991079i 0.542550π0.542550\pi
314314 6.48492 0.365965
315315 0.0178290 + 0.0308808i 0.00100455 + 0.00173993i
316316 4.02459 6.97079i 0.226401 0.392138i
317317 6.48625 11.2345i 0.364304 0.630993i −0.624360 0.781137i 0.714640π-0.714640\pi
0.988664 + 0.150144i 0.0479736π0.0479736\pi
318318 −4.46568 −0.250423
319319 0.962091 + 1.66639i 0.0538667 + 0.0932999i
320320 −0.355961 + 0.616542i −0.0198988 + 0.0344657i
321321 6.90666 0.385492
322322 0.0820861 + 0.142177i 0.00457448 + 0.00792323i
323323 −7.63470 13.2237i −0.424806 0.735785i
324324 −0.500000 0.866025i −0.0277778 0.0481125i
325325 13.6804 + 23.6951i 0.758850 + 1.31437i
326326 −5.53504 −0.306557
327327 3.83038 0.211820
328328 10.3734 0.572775
329329 0.0502832 0.0870931i 0.00277220 0.00480160i
330330 −0.0847301 + 0.146757i −0.00466424 + 0.00807870i
331331 −19.4415 −1.06860 −0.534301 0.845294i 0.679425π-0.679425\pi
−0.534301 + 0.845294i 0.679425π0.679425\pi
332332 −4.53232 + 7.85020i −0.248743 + 0.430836i
333333 2.18358 + 3.78207i 0.119659 + 0.207256i
334334 3.84736 0.210518
335335 −3.10528 −0.169660
336336 0.0250435 + 0.0433767i 0.00136624 + 0.00236639i
337337 −7.49038 + 12.9737i −0.408027 + 0.706723i −0.994669 0.103123i 0.967116π-0.967116\pi
0.586642 + 0.809847i 0.300450π0.300450\pi
338338 24.0809 1.30983
339339 2.03896 3.53159i 0.110741 0.191810i
340340 1.02913 1.78250i 0.0558124 0.0966699i
341341 −0.479499 −0.0259663
342342 −5.28145 −0.285588
343343 0.701093 0.0378555
344344 0.543104 + 0.940683i 0.0292822 + 0.0507182i
345345 −1.16675 2.02086i −0.0628154 0.108800i
346346 0.646627 + 1.11999i 0.0347629 + 0.0602111i
347347 −16.2473 28.1412i −0.872201 1.51070i −0.859715 0.510775i 0.829359π-0.829359\pi
−0.0124867 0.999922i 0.503975π-0.503975\pi
348348 −8.08370 −0.433332
349349 16.7922 29.0849i 0.898864 1.55688i 0.0699153 0.997553i 0.477727π-0.477727\pi
0.828949 0.559325i 0.188940π-0.188940\pi
350350 −0.112525 0.194899i −0.00601470 0.0104178i
351351 6.08940 0.325028
352352 −0.119016 + 0.206142i −0.00634358 + 0.0109874i
353353 7.62705 13.2104i 0.405947 0.703120i −0.588484 0.808509i 0.700275π-0.700275\pi
0.994431 + 0.105388i 0.0336085π0.0336085\pi
354354 −4.65320 8.05957i −0.247315 0.428361i
355355 −2.48606 −0.131946
356356 −4.61528 7.99390i −0.244609 0.423676i
357357 −0.0724042 0.125408i −0.00383204 0.00663728i
358358 −10.4033 + 18.0190i −0.549831 + 0.952336i
359359 −27.3141 −1.44159 −0.720793 0.693151i 0.756222π-0.756222\pi
−0.720793 + 0.693151i 0.756222π0.756222\pi
360360 −0.355961 0.616542i −0.0187608 0.0324946i
361361 −4.44688 + 7.70222i −0.234046 + 0.405380i
362362 10.6949 + 18.5241i 0.562110 + 0.973603i
363363 5.47167 9.47721i 0.287188 0.497425i
364364 −0.305000 −0.0159864
365365 −0.262784 0.455155i −0.0137547 0.0238239i
366366 0.798509 1.38306i 0.0417387 0.0722936i
367367 3.19056 5.52621i 0.166546 0.288466i −0.770657 0.637250i 0.780072π-0.780072\pi
0.937203 + 0.348784i 0.113405π0.113405\pi
368368 −1.63887 2.83860i −0.0854319 0.147972i
369369 −5.18670 + 8.98363i −0.270009 + 0.467669i
370370 1.55454 + 2.69254i 0.0808165 + 0.139978i
371371 −0.111836 + 0.193706i −0.00580626 + 0.0100567i
372372 1.00721 1.74455i 0.0522216 0.0904505i
373373 2.70078 4.67788i 0.139841 0.242211i −0.787595 0.616193i 0.788674π-0.788674\pi
0.927436 + 0.373981i 0.122008π0.122008\pi
374374 0.344092 0.595984i 0.0177926 0.0308176i
375375 3.37919 + 5.85293i 0.174501 + 0.302244i
376376 −1.00392 + 1.73883i −0.0517730 + 0.0896735i
377377 24.6125 42.6300i 1.26761 2.19556i
378378 −0.0500871 −0.00257620
379379 −2.14889 3.72199i −0.110381 0.191186i 0.805543 0.592538i 0.201874π-0.201874\pi
−0.915924 + 0.401352i 0.868541π0.868541\pi
380380 −3.75998 −0.192883
381381 2.66370 4.61366i 0.136465 0.236365i
382382 −21.0306 −1.07602
383383 4.19654 7.26862i 0.214433 0.371409i −0.738664 0.674074i 0.764543π-0.764543\pi
0.953097 + 0.302665i 0.0978763π0.0978763\pi
384384 −0.500000 0.866025i −0.0255155 0.0441942i
385385 0.00424388 + 0.00735062i 0.000216288 + 0.000374622i
386386 −22.9321 −1.16721
387387 −1.08621 −0.0552150
388388 1.07175 1.85633i 0.0544101 0.0942410i
389389 −17.4688 + 30.2568i −0.885703 + 1.53408i −0.0407968 + 0.999167i 0.512990π0.512990\pi
−0.844906 + 0.534915i 0.820344π0.820344\pi
390390 4.33518 0.219520
391391 4.73819 + 8.20679i 0.239621 + 0.415035i
392392 −6.99749 −0.353427
393393 −1.75869 + 3.04614i −0.0887140 + 0.153657i
394394 −7.87651 −0.396813
395395 2.86519 + 4.96265i 0.144163 + 0.249698i
396396 −0.119016 0.206142i −0.00598079 0.0103590i
397397 −10.0967 −0.506740 −0.253370 0.967369i 0.581539π-0.581539\pi
−0.253370 + 0.967369i 0.581539π0.581539\pi
398398 −11.8545 20.5326i −0.594211 1.02920i
399399 −0.132266 + 0.229092i −0.00662159 + 0.0114689i
400400 2.24658 + 3.89120i 0.112329 + 0.194560i
401401 3.37268 + 5.84166i 0.168424 + 0.291719i 0.937866 0.346998i 0.112799π-0.112799\pi
−0.769442 + 0.638717i 0.779466π0.779466\pi
402402 2.18092 3.77746i 0.108774 0.188402i
403403 6.13334 + 10.6233i 0.305523 + 0.529182i
404404 −7.67946 13.3012i −0.382067 0.661760i
405405 0.711921 0.0353756
406406 −0.202444 + 0.350644i −0.0100471 + 0.0174022i
407407 0.519762 + 0.900255i 0.0257637 + 0.0446240i
408408 1.44557 + 2.50380i 0.0715662 + 0.123956i
409409 16.4609 28.5112i 0.813940 1.40979i −0.0961459 0.995367i 0.530652π-0.530652\pi
0.910086 0.414419i 0.136015π-0.136015\pi
410410 −3.69252 + 6.39563i −0.182361 + 0.315858i
411411 −6.77141 + 11.7284i −0.334009 + 0.578520i
412412 −13.9141 −0.685499
413413 −0.466130 −0.0229367
414414 3.27774 0.161092
415415 −3.22665 5.58872i −0.158390 0.274340i
416416 6.08940 0.298558
417417 −1.31959 + 2.28560i −0.0646207 + 0.111926i
418418 −1.25716 −0.0614895
419419 −21.4045 −1.04568 −0.522839 0.852431i 0.675127π-0.675127\pi
−0.522839 + 0.852431i 0.675127π0.675127\pi
420420 −0.0356580 −0.00173993
421421 10.2834 + 17.8114i 0.501183 + 0.868074i 0.999999 + 0.00136603i 0.000434822π0.000434822\pi
−0.498817 + 0.866708i 0.666232π0.666232\pi
422422 −5.37153 9.30377i −0.261482 0.452900i
423423 −1.00392 1.73883i −0.0488121 0.0845450i
424424 2.23284 3.86739i 0.108436 0.187817i
425425 −6.49518 11.2500i −0.315062 0.545704i
426426 1.74602 3.02420i 0.0845951 0.146523i
427427 −0.0399950 0.0692733i −0.00193549 0.00335237i
428428 −3.45333 + 5.98134i −0.166923 + 0.289119i
429429 1.44947 0.0699813
430430 −0.773294 −0.0372915
431431 −3.62208 −0.174470 −0.0872348 0.996188i 0.527803π-0.527803\pi
−0.0872348 + 0.996188i 0.527803π0.527803\pi
432432 1.00000 0.0481125
433433 23.5556 1.13201 0.566005 0.824402i 0.308488π-0.308488\pi
0.566005 + 0.824402i 0.308488π0.308488\pi
434434 −0.0504484 0.0873792i −0.00242160 0.00419434i
435435 2.87748 4.98394i 0.137964 0.238962i
436436 −1.91519 + 3.31720i −0.0917208 + 0.158865i
437437 8.65561 14.9920i 0.414054 0.717163i
438438 0.738239 0.0352744
439439 16.0295 0.765047 0.382523 0.923946i 0.375055π-0.375055\pi
0.382523 + 0.923946i 0.375055π0.375055\pi
440440 −0.0847301 0.146757i −0.00403935 0.00699636i
441441 3.49875 6.06001i 0.166607 0.288572i
442442 −17.6053 −0.837398
443443 7.41778 + 12.8480i 0.352429 + 0.610426i 0.986675 0.162706i 0.0520223π-0.0520223\pi
−0.634245 + 0.773132i 0.718689π0.718689\pi
444444 −4.36716 −0.207256
445445 6.57143 0.311516
446446 3.73581 + 14.4583i 0.176896 + 0.684622i
447447 −7.61759 −0.360300
448448 −0.0500871 −0.00236639
449449 −0.0524197 0.0907936i −0.00247384 0.00428482i 0.864786 0.502141i 0.167454π-0.167454\pi
−0.867260 + 0.497856i 0.834121π0.834121\pi
450450 −4.49317 −0.211810
451451 −1.23460 + 2.13839i −0.0581351 + 0.100693i
452452 2.03896 + 3.53159i 0.0959048 + 0.166112i
453453 19.0835 0.896623
454454 −9.78329 −0.459152
455455 0.108568 0.188045i 0.00508975 0.00881571i
456456 2.64073 4.57387i 0.123663 0.214191i
457457 15.2865 26.4770i 0.715073 1.23854i −0.247858 0.968796i 0.579727π-0.579727\pi
0.962931 0.269747i 0.0869400π-0.0869400\pi
458458 2.54981 + 4.41641i 0.119145 + 0.206365i
459459 −2.89113 −0.134947
460460 2.33349 0.108800
461461 27.9212 1.30042 0.650209 0.759755i 0.274681π-0.274681\pi
0.650209 + 0.759755i 0.274681π0.274681\pi
462462 −0.0119223 −0.000554677
463463 −3.93371 −0.182815 −0.0914076 0.995814i 0.529137π-0.529137\pi
−0.0914076 + 0.995814i 0.529137π0.529137\pi
464464 4.04185 7.00069i 0.187638 0.324999i
465465 0.717057 + 1.24198i 0.0332527 + 0.0575954i
466466 −4.65509 + 8.06286i −0.215643 + 0.373505i
467467 −8.19816 14.1996i −0.379365 0.657080i 0.611605 0.791164i 0.290524π-0.290524\pi
−0.990970 + 0.134083i 0.957191π0.957191\pi
468468 −3.04470 + 5.27358i −0.140741 + 0.243771i
469469 −0.109236 0.189202i −0.00504404 0.00873653i
470470 −0.714709 1.23791i −0.0329671 0.0571006i
471471 −3.24246 5.61610i −0.149405 0.258776i
472472 9.30639 0.428361
473473 −0.258552 −0.0118883
474474 −8.04918 −0.369711
475475 −11.8652 + 20.5512i −0.544414 + 0.942953i
476476 0.144808 0.00663728
477477 2.23284 + 3.86739i 0.102235 + 0.177076i
478478 13.6826 0.625829
479479 30.4075 1.38936 0.694678 0.719321i 0.255547π-0.255547\pi
0.694678 + 0.719321i 0.255547π0.255547\pi
480480 0.711921 0.0324946
481481 13.2967 23.0306i 0.606277 1.05010i
482482 8.23257 14.2592i 0.374983 0.649490i
483483 0.0820861 0.142177i 0.00373505 0.00646929i
484484 5.47167 + 9.47721i 0.248712 + 0.430782i
485485 0.763004 + 1.32156i 0.0346462 + 0.0600090i
486486 −0.500000 + 0.866025i −0.0226805 + 0.0392837i
487487 39.0435 1.76923 0.884615 0.466321i 0.154421π-0.154421\pi
0.884615 + 0.466321i 0.154421π0.154421\pi
488488 0.798509 + 1.38306i 0.0361468 + 0.0626081i
489489 2.76752 + 4.79348i 0.125152 + 0.216769i
490490 2.49083 4.31425i 0.112524 0.194898i
491491 −16.1006 27.8871i −0.726611 1.25853i −0.958307 0.285740i 0.907761π-0.907761\pi
0.231696 0.972788i 0.425573π-0.425573\pi
492492 −5.18670 8.98363i −0.233834 0.405013i
493493 −11.6855 + 20.2399i −0.526290 + 0.911561i
494494 16.0805 + 27.8522i 0.723494 + 1.25313i
495495 0.169460 0.00761667
496496 1.00721 + 1.74455i 0.0452253 + 0.0783325i
497497 −0.0874532 0.151473i −0.00392281 0.00679451i
498498 9.06463 0.406196
499499 −8.88900 + 15.3962i −0.397926 + 0.689229i −0.993470 0.114094i 0.963603π-0.963603\pi
0.595544 + 0.803323i 0.296937π0.296937\pi
500500 −6.75839 −0.302244
501501 −1.92368 3.33191i −0.0859436 0.148859i
502502 11.6521 0.520059
503503 10.2168 17.6960i 0.455544 0.789025i −0.543175 0.839619i 0.682778π-0.682778\pi
0.998719 + 0.0505941i 0.0161115π0.0161115\pi
504504 0.0250435 0.0433767i 0.00111553 0.00193215i
505505 10.9343 0.486571
506506 0.780207 0.0346844
507507 −12.0404 20.8546i −0.534734 0.926187i
508508 2.66370 + 4.61366i 0.118183 + 0.204698i
509509 2.19511 3.80203i 0.0972963 0.168522i −0.813268 0.581889i 0.802314π-0.802314\pi
0.910565 + 0.413367i 0.135647π0.135647\pi
510510 −2.05826 −0.0911413
511511 0.0184881 0.0320223i 0.000817866 0.00141658i
512512 1.00000 0.0441942
513513 2.64073 + 4.57387i 0.116591 + 0.201941i
514514 −11.2746 −0.497303
515515 4.95288 8.57863i 0.218250 0.378020i
516516 0.543104 0.940683i 0.0239088 0.0414113i
517517 −0.238964 0.413899i −0.0105096 0.0182032i
518518 −0.109369 + 0.189433i −0.00480540 + 0.00832320i
519519 0.646627 1.11999i 0.0283838 0.0491621i
520520 −2.16759 + 3.75437i −0.0950550 + 0.164640i
521521 −6.80779 + 11.7914i −0.298255 + 0.516592i −0.975737 0.218947i 0.929738π-0.929738\pi
0.677482 + 0.735539i 0.263071π0.263071\pi
522522 4.04185 + 7.00069i 0.176907 + 0.306412i
523523 −4.91739 + 8.51717i −0.215022 + 0.372430i −0.953280 0.302090i 0.902316π-0.902316\pi
0.738257 + 0.674519i 0.235649π0.235649\pi
524524 −1.75869 3.04614i −0.0768286 0.133071i
525525 −0.112525 + 0.194899i −0.00491098 + 0.00850608i
526526 −6.15272 + 10.6568i −0.268271 + 0.464660i
527527 −2.91199 5.04372i −0.126848 0.219708i
528528 0.238032 0.0103590
529529 6.12822 10.6144i 0.266444 0.461495i
530530 1.58961 + 2.75328i 0.0690481 + 0.119595i
531531 −4.65320 + 8.05957i −0.201931 + 0.349756i
532532 −0.132266 0.229092i −0.00573447 0.00993239i
533533 63.1678 2.73610
534534 −4.61528 + 7.99390i −0.199723 + 0.345930i
535535 −2.45850 4.25824i −0.106290 0.184100i
536536 2.18092 + 3.77746i 0.0942012 + 0.163161i
537537 20.8066 0.897871
538538 −5.20507 9.01544i −0.224406 0.388683i
539539 0.832814 1.44248i 0.0358719 0.0621319i
540540 −0.355961 + 0.616542i −0.0153181 + 0.0265317i
541541 27.2969 1.17359 0.586794 0.809736i 0.300390π-0.300390\pi
0.586794 + 0.809736i 0.300390π0.300390\pi
542542 −8.72371 15.1099i −0.374715 0.649026i
543543 10.6949 18.5241i 0.458961 0.794944i
544544 −2.89113 −0.123956
545545 −1.36346 2.36159i −0.0584043 0.101159i
546546 0.152500 + 0.264138i 0.00652641 + 0.0113041i
547547 −20.8949 36.1911i −0.893403 1.54742i −0.835769 0.549081i 0.814978π-0.814978\pi
−0.0576332 0.998338i 0.518355π-0.518355\pi
548548 −6.77141 11.7284i −0.289260 0.501013i
549549 −1.59702 −0.0681591
550550 −1.06952 −0.0456044
551551 42.6937 1.81881
552552 −1.63887 + 2.83860i −0.0697549 + 0.120819i
553553 −0.201580 + 0.349146i −0.00857204 + 0.0148472i
554554 −21.5632 −0.916133
555555 1.55454 2.69254i 0.0659864 0.114292i
556556 −1.31959 2.28560i −0.0559631 0.0969310i
557557 −41.7961 −1.77096 −0.885478 0.464681i 0.846169π-0.846169\pi
−0.885478 + 0.464681i 0.846169π0.846169\pi
558558 −2.01443 −0.0852776
559559 3.30718 + 5.72820i 0.139879 + 0.242277i
560560 0.0178290 0.0308808i 0.000753413 0.00130495i
561561 −0.688183 −0.0290551
562562 2.83723 4.91422i 0.119681 0.207294i
563563 −15.7610 + 27.2989i −0.664249 + 1.15051i 0.315240 + 0.949012i 0.397915π0.397915\pi
−0.979488 + 0.201501i 0.935418π0.935418\pi
564564 2.00783 0.0845450
565565 −2.90316 −0.122137
566566 0.879276 0.0369587
567567 0.0250435 + 0.0433767i 0.00105173 + 0.00182165i
568568 1.74602 + 3.02420i 0.0732615 + 0.126893i
569569 9.51908 + 16.4875i 0.399061 + 0.691194i 0.993610 0.112865i 0.0360029π-0.0360029\pi
−0.594550 + 0.804059i 0.702670π0.702670\pi
570570 1.87999 + 3.25624i 0.0787441 + 0.136389i
571571 2.31163 0.0967388 0.0483694 0.998830i 0.484598π-0.484598\pi
0.0483694 + 0.998830i 0.484598π0.484598\pi
572572 −0.724737 + 1.25528i −0.0303028 + 0.0524860i
573573 10.5153 + 18.2131i 0.439284 + 0.760862i
574574 −0.519573 −0.0216866
575575 7.36371 12.7543i 0.307088 0.531892i
576576 −0.500000 + 0.866025i −0.0208333 + 0.0360844i
577577 −1.54212 2.67103i −0.0641992 0.111196i 0.832139 0.554567i 0.187116π-0.187116\pi
−0.896338 + 0.443370i 0.853783π0.853783\pi
578578 −8.64134 −0.359432
579579 11.4660 + 19.8598i 0.476513 + 0.825344i
580580 2.87748 + 4.98394i 0.119481 + 0.206947i
581581 0.227010 0.393194i 0.00941798 0.0163124i
582582 −2.14351 −0.0888512
583583 0.531488 + 0.920565i 0.0220120 + 0.0381259i
584584 −0.369119 + 0.639334i −0.0152743 + 0.0264558i
585585 −2.16759 3.75437i −0.0896187 0.155224i
586586 −0.695703 + 1.20499i −0.0287392 + 0.0497778i
587587 −26.0777 −1.07634 −0.538170 0.842836i 0.680884π-0.680884\pi
−0.538170 + 0.842836i 0.680884π0.680884\pi
588588 3.49875 + 6.06001i 0.144286 + 0.249910i
589589 −5.31956 + 9.21374i −0.219189 + 0.379646i
590590 −3.31271 + 5.73778i −0.136382 + 0.236221i
591591 3.93825 + 6.82125i 0.161998 + 0.280589i
592592 2.18358 3.78207i 0.0897446 0.155442i
593593 −8.68051 15.0351i −0.356466 0.617417i 0.630902 0.775863i 0.282685π-0.282685\pi
−0.987368 + 0.158446i 0.949352π0.949352\pi
594594 −0.119016 + 0.206142i −0.00488329 + 0.00845811i
595595 −0.0515461 + 0.0892804i −0.00211318 + 0.00366014i
596596 3.80880 6.59703i 0.156014 0.270225i
597597 −11.8545 + 20.5326i −0.485171 + 0.840342i
598598 −9.97974 17.2854i −0.408102 0.706853i
599599 −2.13484 + 3.69765i −0.0872271 + 0.151082i −0.906338 0.422553i 0.861134π-0.861134\pi
0.819111 + 0.573635i 0.194467π0.194467\pi
600600 2.24658 3.89120i 0.0917164 0.158857i
601601 23.9511 0.976984 0.488492 0.872568i 0.337547π-0.337547\pi
0.488492 + 0.872568i 0.337547π0.337547\pi
602602 −0.0272025 0.0471161i −0.00110869 0.00192031i
603603 −4.36183 −0.177628
604604 −9.54177 + 16.5268i −0.388249 + 0.672467i
605605 −7.79079 −0.316741
606606 −7.67946 + 13.3012i −0.311957 + 0.540325i
607607 −16.4245 28.4481i −0.666651 1.15467i −0.978835 0.204652i 0.934394π-0.934394\pi
0.312184 0.950022i 0.398939π-0.398939\pi
608608 2.64073 + 4.57387i 0.107096 + 0.185495i
609609 0.404889 0.0164069
610610 −1.13695 −0.0460338
611611 −6.11325 + 10.5885i −0.247316 + 0.428363i
612612 1.44557 2.50380i 0.0584336 0.101210i
613613 14.7764 0.596811 0.298406 0.954439i 0.403545π-0.403545\pi
0.298406 + 0.954439i 0.403545π0.403545\pi
614614 0.860812 + 1.49097i 0.0347396 + 0.0601707i
615615 7.38504 0.297794
616616 0.00596117 0.0103250i 0.000240182 0.000416008i
617617 −19.3305 −0.778217 −0.389108 0.921192i 0.627217π-0.627217\pi
−0.389108 + 0.921192i 0.627217π0.627217\pi
618618 6.95706 + 12.0500i 0.279854 + 0.484721i
619619 21.9517 + 38.0215i 0.882313 + 1.52821i 0.848762 + 0.528775i 0.177348π0.177348\pi
0.0335510 + 0.999437i 0.489318π0.489318\pi
620620 −1.43411 −0.0575954
621621 −1.63887 2.83860i −0.0657655 0.113909i
622622 −0.323617 + 0.560522i −0.0129759 + 0.0224749i
623623 0.231166 + 0.400391i 0.00926146 + 0.0160413i
624624 −3.04470 5.27358i −0.121886 0.211112i
625625 −8.82720 + 15.2892i −0.353088 + 0.611567i
626626 14.0059 + 24.2589i 0.559789 + 0.969582i
627627 0.628578 + 1.08873i 0.0251030 + 0.0434797i
628628 6.48492 0.258776
629629 −6.31302 + 10.9345i −0.251717 + 0.435986i
630630 0.0178290 + 0.0308808i 0.000710325 + 0.00123032i
631631 −8.09263 14.0169i −0.322163 0.558002i 0.658771 0.752343i 0.271076π-0.271076\pi
−0.980934 + 0.194341i 0.937743π0.937743\pi
632632 4.02459 6.97079i 0.160089 0.277283i
633633 −5.37153 + 9.30377i −0.213499 + 0.369792i
634634 6.48625 11.2345i 0.257602 0.446179i
635635 −3.79269 −0.150508
636636 −4.46568 −0.177076
637637 −42.6106 −1.68829
638638 0.962091 + 1.66639i 0.0380895 + 0.0659730i
639639 −3.49205 −0.138143
640640 −0.355961 + 0.616542i −0.0140706 + 0.0243710i
641641 4.86958 0.192337 0.0961685 0.995365i 0.469341π-0.469341\pi
0.0961685 + 0.995365i 0.469341π0.469341\pi
642642 6.90666 0.272584
643643 −30.1091 −1.18739 −0.593693 0.804691i 0.702331π-0.702331\pi
−0.593693 + 0.804691i 0.702331π0.702331\pi
644644 0.0820861 + 0.142177i 0.00323465 + 0.00560257i
645645 0.386647 + 0.669692i 0.0152242 + 0.0263691i
646646 −7.63470 13.2237i −0.300383 0.520279i
647647 −12.0345 + 20.8443i −0.473123 + 0.819473i −0.999527 0.0307615i 0.990207π-0.990207\pi
0.526404 + 0.850235i 0.323540π0.323540\pi
648648 −0.500000 0.866025i −0.0196419 0.0340207i
649649 −1.10761 + 1.91844i −0.0434775 + 0.0753053i
650650 13.6804 + 23.6951i 0.536588 + 0.929397i
651651 −0.0504484 + 0.0873792i −0.00197723 + 0.00342466i
652652 −5.53504 −0.216769
653653 19.1985 0.751294 0.375647 0.926763i 0.377421π-0.377421\pi
0.375647 + 0.926763i 0.377421π0.377421\pi
654654 3.83038 0.149780
655655 2.50409 0.0978430
656656 10.3734 0.405013
657657 −0.369119 0.639334i −0.0144007 0.0249428i
658658 0.0502832 0.0870931i 0.00196024 0.00339524i
659659 −19.0439 + 32.9849i −0.741843 + 1.28491i 0.209812 + 0.977742i 0.432715π0.432715\pi
−0.951655 + 0.307169i 0.900618π0.900618\pi
660660 −0.0847301 + 0.146757i −0.00329811 + 0.00571250i
661661 −24.0288 −0.934614 −0.467307 0.884095i 0.654776π-0.654776\pi
−0.467307 + 0.884095i 0.654776π0.654776\pi
662662 −19.4415 −0.755616
663663 8.80264 + 15.2466i 0.341866 + 0.592130i
664664 −4.53232 + 7.85020i −0.175888 + 0.304647i
665665 0.188326 0.00730298
666666 2.18358 + 3.78207i 0.0846120 + 0.146552i
667667 −26.4962 −1.02594
668668 3.84736 0.148859
669669 10.6534 10.4645i 0.411884 0.404580i
670670 −3.10528 −0.119967
671671 −0.380142 −0.0146752
672672 0.0250435 + 0.0433767i 0.000966075 + 0.00167329i
673673 10.8852 0.419592 0.209796 0.977745i 0.432720π-0.432720\pi
0.209796 + 0.977745i 0.432720π0.432720\pi
674674 −7.49038 + 12.9737i −0.288519 + 0.499729i
675675 2.24658 + 3.89120i 0.0864711 + 0.149772i
676676 24.0809 0.926187
677677 30.3616 1.16689 0.583445 0.812152i 0.301704π-0.301704\pi
0.583445 + 0.812152i 0.301704π0.301704\pi
678678 2.03896 3.53159i 0.0783059 0.135630i
679679 −0.0536810 + 0.0929782i −0.00206009 + 0.00356818i
680680 1.02913 1.78250i 0.0394653 0.0683559i
681681 4.89164 + 8.47257i 0.187448 + 0.324670i
682682 −0.479499 −0.0183610
683683 21.3729 0.817812 0.408906 0.912577i 0.365910π-0.365910\pi
0.408906 + 0.912577i 0.365910π0.365910\pi
684684 −5.28145 −0.201941
685685 9.64141 0.368379
686686 0.701093 0.0267679
687687 2.54981 4.41641i 0.0972815 0.168496i
688688 0.543104 + 0.940683i 0.0207056 + 0.0358632i
689689 13.5967 23.5501i 0.517992 0.897189i
690690 −1.16675 2.02086i −0.0444172 0.0769329i
691691 13.3532 23.1284i 0.507979 0.879846i −0.491978 0.870608i 0.663726π-0.663726\pi
0.999957 0.00923827i 0.00294067π-0.00294067\pi
692692 0.646627 + 1.11999i 0.0245811 + 0.0425756i
693693 0.00596117 + 0.0103250i 0.000226446 + 0.000392216i
694694 −16.2473 28.1412i −0.616739 1.06822i
695695 1.87889 0.0712704
696696 −8.08370 −0.306412
697697 −29.9909 −1.13599
698698 16.7922 29.0849i 0.635593 1.10088i
699699 9.31019 0.352144
700700 −0.112525 0.194899i −0.00425304 0.00736648i
701701 −40.3493 −1.52397 −0.761986 0.647594i 0.775775π-0.775775\pi
−0.761986 + 0.647594i 0.775775π0.775775\pi
702702 6.08940 0.229830
703703 23.0649 0.869911
704704 −0.119016 + 0.206142i −0.00448559 + 0.00776927i
705705 −0.714709 + 1.23791i −0.0269175 + 0.0466225i
706706 7.62705 13.2104i 0.287048 0.497181i
707707 0.384641 + 0.666218i 0.0144659 + 0.0250557i
708708 −4.65320 8.05957i −0.174878 0.302897i
709709 25.0533 43.3937i 0.940898 1.62968i 0.177135 0.984187i 0.443317π-0.443317\pi
0.763763 0.645496i 0.223349π-0.223349\pi
710710 −2.48606 −0.0933002
711711 4.02459 + 6.97079i 0.150934 + 0.261425i
712712 −4.61528 7.99390i −0.172965 0.299584i
713713 3.30138 5.71817i 0.123638 0.214147i
714714 −0.0724042 0.125408i −0.00270966 0.00469327i
715715 −0.515956 0.893662i −0.0192957 0.0334211i
716716 −10.4033 + 18.0190i −0.388790 + 0.673403i
717717 −6.84131 11.8495i −0.255494 0.442528i
718718 −27.3141 −1.01935
719719 26.0177 + 45.0639i 0.970296 + 1.68060i 0.694659 + 0.719339i 0.255555π0.255555\pi
0.275637 + 0.961262i 0.411111π0.411111\pi
720720 −0.355961 0.616542i −0.0132659 0.0229772i
721721 0.696917 0.0259545
722722 −4.44688 + 7.70222i −0.165496 + 0.286647i
723723 −16.4651 −0.612345
724724 10.6949 + 18.5241i 0.397472 + 0.688441i
725725 36.3214 1.34894
726726 5.47167 9.47721i 0.203073 0.351732i
727727 21.4731 37.1925i 0.796393 1.37939i −0.125557 0.992086i 0.540072π-0.540072\pi
0.921951 0.387307i 0.126595π-0.126595\pi
728728 −0.305000 −0.0113041
729729 1.00000 0.0370370
730730 −0.262784 0.455155i −0.00972607 0.0168460i
731731 −1.57019 2.71964i −0.0580754 0.100590i
732732 0.798509 1.38306i 0.0295138 0.0511193i
733733 −2.15962 −0.0797672 −0.0398836 0.999204i 0.512699π-0.512699\pi
−0.0398836 + 0.999204i 0.512699π0.512699\pi
734734 3.19056 5.52621i 0.117766 0.203976i
735735 −4.98166 −0.183751
736736 −1.63887 2.83860i −0.0604095 0.104632i
737737 −1.03826 −0.0382447
738738 −5.18670 + 8.98363i −0.190925 + 0.330692i
739739 9.95834 17.2484i 0.366324 0.634491i −0.622664 0.782489i 0.713950π-0.713950\pi
0.988988 + 0.147998i 0.0472830π0.0472830\pi
740740 1.55454 + 2.69254i 0.0571459 + 0.0989796i
741741 16.0805 27.8522i 0.590730 1.02317i
742742 −0.111836 + 0.193706i −0.00410565 + 0.00711119i
743743 9.20375 15.9414i 0.337653 0.584832i −0.646338 0.763051i 0.723700π-0.723700\pi
0.983991 + 0.178220i 0.0570337π0.0570337\pi
744744 1.00721 1.74455i 0.0369263 0.0639582i
745745 2.71156 + 4.69656i 0.0993440 + 0.172069i
746746 2.70078 4.67788i 0.0988824 0.171269i
747747 −4.53232 7.85020i −0.165829 0.287224i
748748 0.344092 0.595984i 0.0125812 0.0217913i
749749 0.172967 0.299588i 0.00632008 0.0109467i
750750 3.37919 + 5.85293i 0.123391 + 0.213719i
751751 −14.4658 −0.527866 −0.263933 0.964541i 0.585020π-0.585020\pi
−0.263933 + 0.964541i 0.585020π0.585020\pi
752752 −1.00392 + 1.73883i −0.0366091 + 0.0634088i
753753 −5.82605 10.0910i −0.212313 0.367737i
754754 24.6125 42.6300i 0.896333 1.55249i
755755 −6.79298 11.7658i −0.247222 0.428201i
756756 −0.0500871 −0.00182165
757757 1.17056 2.02747i 0.0425448 0.0736898i −0.843969 0.536392i 0.819787π-0.819787\pi
0.886514 + 0.462702i 0.153120π0.153120\pi
758758 −2.14889 3.72199i −0.0780513 0.135189i
759759 −0.390104 0.675679i −0.0141599 0.0245256i
760760 −3.75998 −0.136389
761761 16.6798 + 28.8903i 0.604643 + 1.04727i 0.992108 + 0.125388i 0.0400175π0.0400175\pi
−0.387465 + 0.921884i 0.626649π0.626649\pi
762762 2.66370 4.61366i 0.0964956 0.167135i
763763 0.0959261 0.166149i 0.00347276 0.00601499i
764764 −21.0306 −0.760862
765765 1.02913 + 1.78250i 0.0372083 + 0.0644466i
766766 4.19654 7.26862i 0.151627 0.262626i
767767 56.6704 2.04625
768768 −0.500000 0.866025i −0.0180422 0.0312500i
769769 16.9215 + 29.3089i 0.610206 + 1.05691i 0.991205 + 0.132332i 0.0422466π0.0422466\pi
−0.381000 + 0.924575i 0.624420π0.624420\pi
770770 0.00424388 + 0.00735062i 0.000152939 + 0.000264898i
771771 5.63732 + 9.76412i 0.203023 + 0.351646i
772772 −22.9321 −0.825344
773773 −2.06534 −0.0742852 −0.0371426 0.999310i 0.511826π-0.511826\pi
−0.0371426 + 0.999310i 0.511826π0.511826\pi
774774 −1.08621 −0.0390429
775775 −4.52558 + 7.83854i −0.162564 + 0.281569i
776776 1.07175 1.85633i 0.0384737 0.0666384i
777777 0.218738 0.00784719
778778 −17.4688 + 30.2568i −0.626286 + 1.08476i
779779 27.3933 + 47.4466i 0.981467 + 1.69995i
780780 4.33518 0.155224
781781 −0.831220 −0.0297434
782782 4.73819 + 8.20679i 0.169437 + 0.293474i
783783 4.04185 7.00069i 0.144444 0.250184i
784784 −6.99749 −0.249910
785785 −2.30837 + 3.99822i −0.0823894 + 0.142703i
786786 −1.75869 + 3.04614i −0.0627303 + 0.108652i
787787 −44.3100 −1.57948 −0.789740 0.613442i 0.789785π-0.789785\pi
−0.789740 + 0.613442i 0.789785π0.789785\pi
788788 −7.87651 −0.280589
789789 12.3054 0.438085
790790 2.86519 + 4.96265i 0.101939 + 0.176563i
791791 −0.102126 0.176887i −0.00363117 0.00628937i
792792 −0.119016 0.206142i −0.00422905 0.00732494i
793793 4.86245 + 8.42200i 0.172671 + 0.299074i
794794 −10.0967 −0.358319
795795 1.58961 2.75328i 0.0563775 0.0976488i
796796 −11.8545 20.5326i −0.420171 0.727757i
797797 −47.5531 −1.68442 −0.842209 0.539151i 0.818745π-0.818745\pi
−0.842209 + 0.539151i 0.818745π0.818745\pi
798798 −0.132266 + 0.229092i −0.00468217 + 0.00810976i
799799 2.90246 5.02720i 0.102682 0.177850i
800800 2.24658 + 3.89120i 0.0794287 + 0.137575i
801801 9.23056 0.326146
802802 3.37268 + 5.84166i 0.119094 + 0.206276i
803803 −0.0878623 0.152182i −0.00310059 0.00537039i
804804 2.18092 3.77746i 0.0769150 0.133221i
805805 −0.116878 −0.00411940
806806 6.13334 + 10.6233i 0.216038 + 0.374188i
807807 −5.20507 + 9.01544i −0.183227 + 0.317359i
808808 −7.67946 13.3012i −0.270162 0.467935i
809809 −3.83432 + 6.64124i −0.134808 + 0.233494i −0.925524 0.378689i 0.876375π-0.876375\pi
0.790716 + 0.612183i 0.209708π0.209708\pi
810810 0.711921 0.0250144
811811 6.22974 + 10.7902i 0.218756 + 0.378896i 0.954428 0.298442i 0.0964668π-0.0964668\pi
−0.735672 + 0.677338i 0.763134π0.763134\pi
812812 −0.202444 + 0.350644i −0.00710440 + 0.0123052i
813813 −8.72371 + 15.1099i −0.305954 + 0.529927i
814814 0.519762 + 0.900255i 0.0182177 + 0.0315539i
815815 1.97025 3.41258i 0.0690150 0.119538i
816816 1.44557 + 2.50380i 0.0506050 + 0.0876504i
817817 −2.86838 + 4.96818i −0.100352 + 0.173814i
818818 16.4609 28.5112i 0.575543 0.996869i
819819 0.152500 0.264138i 0.00532879 0.00922973i
820820 −3.69252 + 6.39563i −0.128948 + 0.223345i
821821 24.1305 + 41.7952i 0.842160 + 1.45866i 0.888065 + 0.459718i 0.152050π0.152050\pi
−0.0459049 + 0.998946i 0.514617π0.514617\pi
822822 −6.77141 + 11.7284i −0.236180 + 0.409076i
823823 13.4462 23.2895i 0.468705 0.811822i −0.530655 0.847588i 0.678054π-0.678054\pi
0.999360 + 0.0357664i 0.0113872π0.0113872\pi
824824 −13.9141 −0.484721
825825 0.534760 + 0.926231i 0.0186179 + 0.0322472i
826826 −0.466130 −0.0162187
827827 7.28594 12.6196i 0.253357 0.438827i −0.711091 0.703100i 0.751799π-0.751799\pi
0.964448 + 0.264273i 0.0851319π0.0851319\pi
828828 3.27774 0.113909
829829 4.27916 7.41173i 0.148621 0.257420i −0.782097 0.623157i 0.785850π-0.785850\pi
0.930718 + 0.365737i 0.119183π0.119183\pi
830830 −3.22665 5.58872i −0.111999 0.193987i
831831 10.7816 + 18.6743i 0.374010 + 0.647804i
832832 6.08940 0.211112
833833 20.2307 0.700952
834834 −1.31959 + 2.28560i −0.0456937 + 0.0791438i
835835 −1.36951 + 2.37206i −0.0473937 + 0.0820884i
836836 −1.25716 −0.0434797
837837 1.00721 + 1.74455i 0.0348144 + 0.0603004i
838838 −21.4045 −0.739406
839839 26.4520 45.8162i 0.913224 1.58175i 0.103743 0.994604i 0.466918π-0.466918\pi
0.809481 0.587146i 0.199749π-0.199749\pi
840840 −0.0356580 −0.00123032
841841 −18.1731 31.4767i −0.626658 1.08540i
842842 10.2834 + 17.8114i 0.354390 + 0.613821i
843843 −5.67445 −0.195439
844844 −5.37153 9.30377i −0.184896 0.320249i
845845 −8.57183 + 14.8468i −0.294880 + 0.510747i
846846 −1.00392 1.73883i −0.0345154 0.0597823i
847847 −0.274060 0.474686i −0.00941681 0.0163104i
848848 2.23284 3.86739i 0.0766761 0.132807i
849849 −0.439638 0.761476i −0.0150883 0.0261338i
850850 −6.49518 11.2500i −0.222783 0.385871i
851851 −14.3144 −0.490691
852852 1.74602 3.02420i 0.0598178 0.103607i
853853 17.0838 + 29.5900i 0.584938 + 1.01314i 0.994883 + 0.101033i 0.0322146π0.0322146\pi
−0.409945 + 0.912110i 0.634452π0.634452\pi
854854 −0.0399950 0.0692733i −0.00136860 0.00237049i
855855 1.87999 3.25624i 0.0642943 0.111361i
856856 −3.45333 + 5.98134i −0.118032 + 0.204438i
857857 22.5276 39.0190i 0.769529 1.33286i −0.168290 0.985738i 0.553824π-0.553824\pi
0.937819 0.347126i 0.112842π-0.112842\pi
858858 1.44947 0.0494843
859859 35.3463 1.20600 0.602999 0.797742i 0.293972π-0.293972\pi
0.602999 + 0.797742i 0.293972π0.293972\pi
860860 −0.773294 −0.0263691
861861 0.259787 + 0.449963i 0.00885350 + 0.0153347i
862862 −3.62208 −0.123369
863863 −14.0683 + 24.3669i −0.478889 + 0.829460i −0.999707 0.0242075i 0.992294π-0.992294\pi
0.520818 + 0.853668i 0.325627π0.325627\pi
864864 1.00000 0.0340207
865865 −0.920694 −0.0313045
866866 23.5556 0.800452
867867 4.32067 + 7.48362i 0.146738 + 0.254157i
868868 −0.0504484 0.0873792i −0.00171233 0.00296584i
869869 0.957982 + 1.65927i 0.0324973 + 0.0562870i
870870 2.87748 4.98394i 0.0975556 0.168971i
871871 13.2805 + 23.0025i 0.449992 + 0.779409i
872872 −1.91519 + 3.31720i −0.0648564 + 0.112335i
873873 1.07175 + 1.85633i 0.0362734 + 0.0628273i
874874 8.65561 14.9920i 0.292780 0.507110i
875875 0.338508 0.0114436
876876 0.738239 0.0249428
877877 −35.0531 −1.18366 −0.591829 0.806064i 0.701594π-0.701594\pi
−0.591829 + 0.806064i 0.701594π0.701594\pi
878878 16.0295 0.540970
879879 1.39141 0.0469309
880880 −0.0847301 0.146757i −0.00285625 0.00494717i
881881 12.0494 20.8702i 0.405955 0.703134i −0.588477 0.808514i 0.700272π-0.700272\pi
0.994432 + 0.105380i 0.0336057π0.0336057\pi
882882 3.49875 6.06001i 0.117809 0.204051i
883883 12.8255 22.2144i 0.431612 0.747573i −0.565401 0.824816i 0.691278π-0.691278\pi
0.997012 + 0.0772431i 0.0246117π0.0246117\pi
884884 −17.6053 −0.592130
885885 6.62542 0.222711
886886 7.41778 + 12.8480i 0.249205 + 0.431636i
887887 3.49064 6.04597i 0.117204 0.203004i −0.801454 0.598056i 0.795940π-0.795940\pi
0.918659 + 0.395052i 0.129273π0.129273\pi
888888 −4.36716 −0.146552
889889 −0.133417 0.231085i −0.00447466 0.00775033i
890890 6.57143 0.220275
891891 0.238032 0.00797438
892892 3.73581 + 14.4583i 0.125084 + 0.484101i
893893 −10.6043 −0.354859
894894 −7.61759 −0.254770
895895 −7.40633 12.8281i −0.247566 0.428797i
896896 −0.0500871 −0.00167329
897897 −9.97974 + 17.2854i −0.333214 + 0.577143i
898898 −0.0524197 0.0907936i −0.00174927 0.00302982i
899899 16.2840 0.543103
900900 −4.49317 −0.149772
901901 −6.45544 + 11.1812i −0.215062 + 0.372498i
902902 −1.23460 + 2.13839i −0.0411077 + 0.0712007i
903903 −0.0272025 + 0.0471161i −0.000905242 + 0.00156792i
904904 2.03896 + 3.53159i 0.0678149 + 0.117459i
905905 −15.2278 −0.506189
906906 19.0835 0.634008
907907 −51.4319 −1.70777 −0.853885 0.520462i 0.825760π-0.825760\pi
−0.853885 + 0.520462i 0.825760π0.825760\pi
908908 −9.78329 −0.324670
909909 15.3589 0.509423
910910 0.108568 0.188045i 0.00359900 0.00623365i
911911 2.90709 + 5.03522i 0.0963161 + 0.166824i 0.910157 0.414263i 0.135961π-0.135961\pi
−0.813841 + 0.581088i 0.802627π0.802627\pi
912912 2.64073 4.57387i 0.0874432 0.151456i
913913 −1.07884 1.86860i −0.0357043 0.0618417i
914914 15.2865 26.4770i 0.505633 0.875782i
915915 0.568476 + 0.984629i 0.0187932 + 0.0325508i
916916 2.54981 + 4.41641i 0.0842482 + 0.145922i
917917 0.0880875 + 0.152572i 0.00290890 + 0.00503837i
918918 −2.89113 −0.0954217
919919 9.40255 0.310162 0.155081 0.987902i 0.450436π-0.450436\pi
0.155081 + 0.987902i 0.450436π0.450436\pi
920920 2.33349 0.0769329
921921 0.860812 1.49097i 0.0283647 0.0491292i
922922 27.9212 0.919535
923923 10.6322 + 18.4156i 0.349965 + 0.606156i
924924 −0.0119223 −0.000392216
925925 19.6224 0.645180
926926 −3.93371 −0.129270
927927 6.95706 12.0500i 0.228500 0.395773i
928928 4.04185 7.00069i 0.132680 0.229809i
929929 10.4614 18.1197i 0.343228 0.594489i −0.641802 0.766870i 0.721813π-0.721813\pi
0.985030 + 0.172382i 0.0551462π0.0551462\pi
930930 0.717057 + 1.24198i 0.0235132 + 0.0407261i
931931 −18.4785 32.0056i −0.605607 1.04894i
932932 −4.65509 + 8.06286i −0.152483 + 0.264108i
933933 0.647235 0.0211895
934934 −8.19816 14.1996i −0.268252 0.464626i
935935 0.244966 + 0.424294i 0.00801125 + 0.0138759i
936936 −3.04470 + 5.27358i −0.0995192 + 0.172372i
937937 −0.499929 0.865903i −0.0163320 0.0282878i 0.857744 0.514077i 0.171866π-0.171866\pi
−0.874076 + 0.485789i 0.838532π0.838532\pi
938938 −0.109236 0.189202i −0.00356667 0.00617766i
939939 14.0059 24.2589i 0.457066 0.791661i
940940 −0.714709 1.23791i −0.0233112 0.0403763i
941941 −31.9629 −1.04196 −0.520980 0.853569i 0.674433π-0.674433\pi
−0.520980 + 0.853569i 0.674433π0.674433\pi
942942 −3.24246 5.61610i −0.105645 0.182983i
943943 −17.0006 29.4460i −0.553617 0.958893i
944944 9.30639 0.302897
945945 0.0178290 0.0308808i 0.000579978 0.00100455i
946946 −0.258552 −0.00840626
947947 −1.48187 2.56668i −0.0481544 0.0834058i 0.840944 0.541123i 0.182001π-0.182001\pi
−0.889098 + 0.457717i 0.848667π0.848667\pi
948948 −8.04918 −0.261425
949949 −2.24772 + 3.89316i −0.0729640 + 0.126377i
950950 −11.8652 + 20.5512i −0.384959 + 0.666768i
951951 −12.9725 −0.420662
952952 0.144808 0.00469327
953953 −7.57833 13.1261i −0.245486 0.425195i 0.716782 0.697297i 0.245614π-0.245614\pi
−0.962268 + 0.272103i 0.912281π0.912281\pi
954954 2.23284 + 3.86739i 0.0722909 + 0.125212i
955955 7.48608 12.9663i 0.242244 0.419579i
956956 13.6826 0.442528
957957 0.962091 1.66639i 0.0311000 0.0538667i
958958 30.4075 0.982423
959959 0.339160 + 0.587442i 0.0109520 + 0.0189695i
960960 0.711921 0.0229772
961961 13.4710 23.3325i 0.434550 0.752662i
962962 13.2967 23.0306i 0.428703 0.742535i
963963 −3.45333 5.98134i −0.111282 0.192746i
964964 8.23257 14.2592i 0.265153 0.459259i
965965 8.16292 14.1386i 0.262774 0.455137i
966966 0.0820861 0.142177i 0.00264108 0.00457448i
967967 15.1835 26.2987i 0.488270 0.845708i −0.511639 0.859200i 0.670962π-0.670962\pi
0.999909 + 0.0134925i 0.00429492π0.00429492\pi
968968 5.47167 + 9.47721i 0.175866 + 0.304609i
969969 −7.63470 + 13.2237i −0.245262 + 0.424806i
970970 0.763004 + 1.32156i 0.0244986 + 0.0424328i
971971 −21.6894 + 37.5671i −0.696045 + 1.20559i 0.273782 + 0.961792i 0.411725π0.411725\pi
−0.969827 + 0.243794i 0.921608π0.921608\pi
972972 −0.500000 + 0.866025i −0.0160375 + 0.0277778i
973973 0.0660945 + 0.114479i 0.00211889 + 0.00367003i
974974 39.0435 1.25104
975975 13.6804 23.6951i 0.438122 0.758850i
976976 0.798509 + 1.38306i 0.0255597 + 0.0442706i
977977 −12.9093 + 22.3595i −0.413004 + 0.715343i −0.995217 0.0976932i 0.968854π-0.968854\pi
0.582213 + 0.813036i 0.302187π0.302187\pi
978978 2.76752 + 4.79348i 0.0884955 + 0.153279i
979979 2.19717 0.0702219
980980 2.49083 4.31425i 0.0795667 0.137814i
981981 −1.91519 3.31720i −0.0611472 0.105910i
982982 −16.1006 27.8871i −0.513792 0.889914i
983983 17.3761 0.554211 0.277106 0.960839i 0.410625π-0.410625\pi
0.277106 + 0.960839i 0.410625π0.410625\pi
984984 −5.18670 8.98363i −0.165346 0.286388i
985985 2.80373 4.85619i 0.0893341 0.154731i
986986 −11.6855 + 20.2399i −0.372143 + 0.644571i
987987 −0.100566 −0.00320107
988988 16.0805 + 27.8522i 0.511587 + 0.886095i
989989 1.78015 3.08331i 0.0566055 0.0980436i
990990 0.169460 0.00538580
991991 2.59261 + 4.49053i 0.0823569 + 0.142646i 0.904262 0.426978i 0.140422π-0.140422\pi
−0.821905 + 0.569625i 0.807089π0.807089\pi
992992 1.00721 + 1.74455i 0.0319791 + 0.0553894i
993993 9.72076 + 16.8369i 0.308479 + 0.534301i
994994 −0.0874532 0.151473i −0.00277385 0.00480444i
995995 16.8789 0.535097
996996 9.06463 0.287224
997997 −13.7049 −0.434038 −0.217019 0.976167i 0.569633π-0.569633\pi
−0.217019 + 0.976167i 0.569633π0.569633\pi
998998 −8.88900 + 15.3962i −0.281376 + 0.487358i
999999 2.18358 3.78207i 0.0690854 0.119659i
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 1338.2.e.j.1075.3 yes 18
223.39 even 3 inner 1338.2.e.j.931.3 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1338.2.e.j.931.3 18 223.39 even 3 inner
1338.2.e.j.1075.3 yes 18 1.1 even 1 trivial