Properties

Label 460.2.e.a.91.8
Level 460460
Weight 22
Character 460.91
Analytic conductor 3.6733.673
Analytic rank 00
Dimension 1616
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(91,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 460=22523 460 = 2^{2} \cdot 5 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 460.e (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.673118492983.67311849298
Analytic rank: 00
Dimension: 1616
Coefficient field: 16.0.7465802011608416256.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16x14+x12+8x1020x8+32x6+16x464x2+256 x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 28 2^{8}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 91.8
Root 1.37379+0.335728i1.37379 + 0.335728i of defining polynomial
Character χ\chi == 460.91
Dual form 460.2.e.a.91.5

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+(0.637910+1.26217i)q22.87247iq3+(1.186141.61030i)q4+1.00000iq5+(3.62554+1.83238i)q62.68161q7+(2.789120.469882i)q85.25109q9+(1.262170.637910i)q104.89140q11+(4.62554+3.40715i)q12+0.727591q13+(1.710633.38465i)q14+2.87247q15+(1.18614+3.82009i)q16+6.34755iq17+(3.349726.62776i)q18+2.68161q19+(1.610301.18614i)q20+7.70285iq21+(3.120276.17377i)q22+(2.20979+4.25639i)q23+(1.349728.01167i)q241.00000q25+(0.464138+0.918342i)q26+6.46618iq27+(3.18077+4.31821i)q284.27582q29+(1.83238+3.62554i)q306.13645iq31+(4.064943.93398i)q32+14.0504iq33+(8.011674.04917i)q342.68161iq35+(6.22853+8.45583i)q36+3.87539iq37+(1.71063+3.38465i)q382.08998iq39+(0.469882+2.78912i)q408.07172q41+(9.722304.91373i)q4211.1319q43+(5.80189+7.87663i)q445.25109iq45+(6.78193+0.0739292i)q46+9.80928iq47+(10.9731+3.40715i)q48+0.191051q49+(0.6379101.26217i)q50+18.2331q51+(0.8630251.17164i)q5211.1565iq53+(8.161414.12484i)q544.89140iq55+(7.47935+1.26004i)q567.70285iq57+(2.727595.39681i)q58+1.87953iq59+(3.407154.62554i)q606.93356iq61+(7.74524+3.91451i)q62+14.0814q63+(7.558422.62112i)q64+0.727591iq65+(17.73408.96290i)q6610.5224q67+(10.22157.52908i)q68+(12.22636.34755i)q69+(3.38465+1.71063i)q707.24866iq71+(14.6459+2.46739i)q72+7.90882q73+(4.891402.47215i)q74+2.87247iq75+(3.180774.31821i)q76+13.1168q77+(2.63791+1.33322i)q783.67993q79+(3.820091.18614i)q80+2.82064q81+(5.1490410.1879i)q82+4.75372q83+(12.40399.13667i)q846.34755q85+(7.1011914.0504i)q86+12.2822iq87+(13.6427+2.29838i)q88+8.12461iq89+(6.62776+3.34972i)q901.95112q91+(4.232958.60710i)q9217.6268q93+(12.38106.25744i)q94+2.68161iq95+(11.3003+11.6764i)q96+2.68434iq97+(0.121873+0.241138i)q98+25.6852q99+O(q100)q+(-0.637910 + 1.26217i) q^{2} -2.87247i q^{3} +(-1.18614 - 1.61030i) q^{4} +1.00000i q^{5} +(3.62554 + 1.83238i) q^{6} -2.68161 q^{7} +(2.78912 - 0.469882i) q^{8} -5.25109 q^{9} +(-1.26217 - 0.637910i) q^{10} -4.89140 q^{11} +(-4.62554 + 3.40715i) q^{12} +0.727591 q^{13} +(1.71063 - 3.38465i) q^{14} +2.87247 q^{15} +(-1.18614 + 3.82009i) q^{16} +6.34755i q^{17} +(3.34972 - 6.62776i) q^{18} +2.68161 q^{19} +(1.61030 - 1.18614i) q^{20} +7.70285i q^{21} +(3.12027 - 6.17377i) q^{22} +(2.20979 + 4.25639i) q^{23} +(-1.34972 - 8.01167i) q^{24} -1.00000 q^{25} +(-0.464138 + 0.918342i) q^{26} +6.46618i q^{27} +(3.18077 + 4.31821i) q^{28} -4.27582 q^{29} +(-1.83238 + 3.62554i) q^{30} -6.13645i q^{31} +(-4.06494 - 3.93398i) q^{32} +14.0504i q^{33} +(-8.01167 - 4.04917i) q^{34} -2.68161i q^{35} +(6.22853 + 8.45583i) q^{36} +3.87539i q^{37} +(-1.71063 + 3.38465i) q^{38} -2.08998i q^{39} +(0.469882 + 2.78912i) q^{40} -8.07172 q^{41} +(-9.72230 - 4.91373i) q^{42} -11.1319 q^{43} +(5.80189 + 7.87663i) q^{44} -5.25109i q^{45} +(-6.78193 + 0.0739292i) q^{46} +9.80928i q^{47} +(10.9731 + 3.40715i) q^{48} +0.191051 q^{49} +(0.637910 - 1.26217i) q^{50} +18.2331 q^{51} +(-0.863025 - 1.17164i) q^{52} -11.1565i q^{53} +(-8.16141 - 4.12484i) q^{54} -4.89140i q^{55} +(-7.47935 + 1.26004i) q^{56} -7.70285i q^{57} +(2.72759 - 5.39681i) q^{58} +1.87953i q^{59} +(-3.40715 - 4.62554i) q^{60} -6.93356i q^{61} +(7.74524 + 3.91451i) q^{62} +14.0814 q^{63} +(7.55842 - 2.62112i) q^{64} +0.727591i q^{65} +(-17.7340 - 8.96290i) q^{66} -10.5224 q^{67} +(10.2215 - 7.52908i) q^{68} +(12.2263 - 6.34755i) q^{69} +(3.38465 + 1.71063i) q^{70} -7.24866i q^{71} +(-14.6459 + 2.46739i) q^{72} +7.90882 q^{73} +(-4.89140 - 2.47215i) q^{74} +2.87247i q^{75} +(-3.18077 - 4.31821i) q^{76} +13.1168 q^{77} +(2.63791 + 1.33322i) q^{78} -3.67993 q^{79} +(-3.82009 - 1.18614i) q^{80} +2.82064 q^{81} +(5.14904 - 10.1879i) q^{82} +4.75372 q^{83} +(12.4039 - 9.13667i) q^{84} -6.34755 q^{85} +(7.10119 - 14.0504i) q^{86} +12.2822i q^{87} +(-13.6427 + 2.29838i) q^{88} +8.12461i q^{89} +(6.62776 + 3.34972i) q^{90} -1.95112 q^{91} +(4.23295 - 8.60710i) q^{92} -17.6268 q^{93} +(-12.3810 - 6.25744i) q^{94} +2.68161i q^{95} +(-11.3003 + 11.6764i) q^{96} +2.68434i q^{97} +(-0.121873 + 0.241138i) q^{98} +25.6852 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+4q4+14q6+4q930q12+4q13+4q16+30q18+2q2416q2554q2648q29+34q3636q4140q46+18q48+68q49+34q5240q54+18q98+O(q100) 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9} - 30 q^{12} + 4 q^{13} + 4 q^{16} + 30 q^{18} + 2 q^{24} - 16 q^{25} - 54 q^{26} - 48 q^{29} + 34 q^{36} - 36 q^{41} - 40 q^{46} + 18 q^{48} + 68 q^{49} + 34 q^{52} - 40 q^{54}+ \cdots - 18 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/460Z)×\left(\mathbb{Z}/460\mathbb{Z}\right)^\times.

nn 231231 277277 281281
χ(n)\chi(n) 1-1 11 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.637910 + 1.26217i −0.451071 + 0.892488i
33 2.87247i 1.65842i −0.558936 0.829211i 0.688790π-0.688790\pi
0.558936 0.829211i 0.311210π-0.311210\pi
44 −1.18614 1.61030i −0.593070 0.805151i
55 1.00000i 0.447214i
66 3.62554 + 1.83238i 1.48012 + 0.748065i
77 −2.68161 −1.01355 −0.506777 0.862077i 0.669163π-0.669163\pi
−0.506777 + 0.862077i 0.669163π0.669163\pi
88 2.78912 0.469882i 0.986104 0.166128i
99 −5.25109 −1.75036
1010 −1.26217 0.637910i −0.399133 0.201725i
1111 −4.89140 −1.47481 −0.737406 0.675449i 0.763950π-0.763950\pi
−0.737406 + 0.675449i 0.763950π0.763950\pi
1212 −4.62554 + 3.40715i −1.33528 + 0.983561i
1313 0.727591 0.201797 0.100899 0.994897i 0.467828π-0.467828\pi
0.100899 + 0.994897i 0.467828π0.467828\pi
1414 1.71063 3.38465i 0.457185 0.904586i
1515 2.87247 0.741669
1616 −1.18614 + 3.82009i −0.296535 + 0.955022i
1717 6.34755i 1.53951i 0.638342 + 0.769753i 0.279621π0.279621\pi
−0.638342 + 0.769753i 0.720379π0.720379\pi
1818 3.34972 6.62776i 0.789537 1.56218i
1919 2.68161 0.615204 0.307602 0.951515i 0.400473π-0.400473\pi
0.307602 + 0.951515i 0.400473π0.400473\pi
2020 1.61030 1.18614i 0.360074 0.265229i
2121 7.70285i 1.68090i
2222 3.12027 6.17377i 0.665245 1.31625i
2323 2.20979 + 4.25639i 0.460772 + 0.887518i
2424 −1.34972 8.01167i −0.275511 1.63538i
2525 −1.00000 −0.200000
2626 −0.464138 + 0.918342i −0.0910249 + 0.180102i
2727 6.46618i 1.24442i
2828 3.18077 + 4.31821i 0.601109 + 0.816064i
2929 −4.27582 −0.794000 −0.397000 0.917819i 0.629949π-0.629949\pi
−0.397000 + 0.917819i 0.629949π0.629949\pi
3030 −1.83238 + 3.62554i −0.334545 + 0.661930i
3131 6.13645i 1.10214i −0.834459 0.551070i 0.814220π-0.814220\pi
0.834459 0.551070i 0.185780π-0.185780\pi
3232 −4.06494 3.93398i −0.718587 0.695437i
3333 14.0504i 2.44586i
3434 −8.01167 4.04917i −1.37399 0.694426i
3535 2.68161i 0.453275i
3636 6.22853 + 8.45583i 1.03809 + 1.40930i
3737 3.87539i 0.637111i 0.947904 + 0.318555i 0.103198π0.103198\pi
−0.947904 + 0.318555i 0.896802π0.896802\pi
3838 −1.71063 + 3.38465i −0.277501 + 0.549063i
3939 2.08998i 0.334665i
4040 0.469882 + 2.78912i 0.0742949 + 0.440999i
4141 −8.07172 −1.26059 −0.630296 0.776355i 0.717066π-0.717066\pi
−0.630296 + 0.776355i 0.717066π0.717066\pi
4242 −9.72230 4.91373i −1.50018 0.758205i
4343 −11.1319 −1.69761 −0.848803 0.528709i 0.822676π-0.822676\pi
−0.848803 + 0.528709i 0.822676π0.822676\pi
4444 5.80189 + 7.87663i 0.874668 + 1.18745i
4545 5.25109i 0.782786i
4646 −6.78193 + 0.0739292i −0.999941 + 0.0109003i
4747 9.80928i 1.43083i 0.698699 + 0.715416i 0.253763π0.253763\pi
−0.698699 + 0.715416i 0.746237π0.746237\pi
4848 10.9731 + 3.40715i 1.58383 + 0.491780i
4949 0.191051 0.0272930
5050 0.637910 1.26217i 0.0902142 0.178498i
5151 18.2331 2.55315
5252 −0.863025 1.17164i −0.119680 0.162477i
5353 11.1565i 1.53246i −0.642565 0.766231i 0.722130π-0.722130\pi
0.642565 0.766231i 0.277870π-0.277870\pi
5454 −8.16141 4.12484i −1.11063 0.561320i
5555 4.89140i 0.659556i
5656 −7.47935 + 1.26004i −0.999470 + 0.168380i
5757 7.70285i 1.02027i
5858 2.72759 5.39681i 0.358150 0.708636i
5959 1.87953i 0.244694i 0.992487 + 0.122347i 0.0390420π0.0390420\pi
−0.992487 + 0.122347i 0.960958π0.960958\pi
6060 −3.40715 4.62554i −0.439862 0.597155i
6161 6.93356i 0.887751i −0.896088 0.443875i 0.853603π-0.853603\pi
0.896088 0.443875i 0.146397π-0.146397\pi
6262 7.74524 + 3.91451i 0.983646 + 0.497143i
6363 14.0814 1.77409
6464 7.55842 2.62112i 0.944803 0.327640i
6565 0.727591i 0.0902465i
6666 −17.7340 8.96290i −2.18290 1.10326i
6767 −10.5224 −1.28552 −0.642761 0.766067i 0.722211π-0.722211\pi
−0.642761 + 0.766067i 0.722211π0.722211\pi
6868 10.2215 7.52908i 1.23953 0.913035i
6969 12.2263 6.34755i 1.47188 0.764155i
7070 3.38465 + 1.71063i 0.404543 + 0.204459i
7171 7.24866i 0.860258i −0.902767 0.430129i 0.858468π-0.858468\pi
0.902767 0.430129i 0.141532π-0.141532\pi
7272 −14.6459 + 2.46739i −1.72604 + 0.290785i
7373 7.90882 0.925657 0.462829 0.886448i 0.346834π-0.346834\pi
0.462829 + 0.886448i 0.346834π0.346834\pi
7474 −4.89140 2.47215i −0.568614 0.287382i
7575 2.87247i 0.331684i
7676 −3.18077 4.31821i −0.364859 0.495332i
7777 13.1168 1.49480
7878 2.63791 + 1.33322i 0.298685 + 0.150958i
7979 −3.67993 −0.414024 −0.207012 0.978338i 0.566374π-0.566374\pi
−0.207012 + 0.978338i 0.566374π0.566374\pi
8080 −3.82009 1.18614i −0.427099 0.132615i
8181 2.82064 0.313404
8282 5.14904 10.1879i 0.568616 1.12506i
8383 4.75372 0.521789 0.260894 0.965367i 0.415983π-0.415983\pi
0.260894 + 0.965367i 0.415983π0.415983\pi
8484 12.4039 9.13667i 1.35338 0.996892i
8585 −6.34755 −0.688488
8686 7.10119 14.0504i 0.765741 1.51509i
8787 12.2822i 1.31679i
8888 −13.6427 + 2.29838i −1.45432 + 0.245008i
8989 8.12461i 0.861207i 0.902541 + 0.430603i 0.141699π0.141699\pi
−0.902541 + 0.430603i 0.858301π0.858301\pi
9090 6.62776 + 3.34972i 0.698627 + 0.353092i
9191 −1.95112 −0.204533
9292 4.23295 8.60710i 0.441316 0.897352i
9393 −17.6268 −1.82781
9494 −12.3810 6.25744i −1.27700 0.645406i
9595 2.68161i 0.275128i
9696 −11.3003 + 11.6764i −1.15333 + 1.19172i
9797 2.68434i 0.272554i 0.990671 + 0.136277i 0.0435137π0.0435137\pi
−0.990671 + 0.136277i 0.956486π0.956486\pi
9898 −0.121873 + 0.241138i −0.0123111 + 0.0243587i
9999 25.6852 2.58146
100100 1.18614 + 1.61030i 0.118614 + 0.161030i
101101 1.53860 0.153096 0.0765480 0.997066i 0.475610π-0.475610\pi
0.0765480 + 0.997066i 0.475610π0.475610\pi
102102 −11.6311 + 23.0133i −1.15165 + 2.27866i
103103 −18.1121 −1.78464 −0.892321 0.451401i 0.850924π-0.850924\pi
−0.892321 + 0.451401i 0.850924π0.850924\pi
104104 2.02934 0.341882i 0.198993 0.0335243i
105105 −7.70285 −0.751722
106106 14.0814 + 7.11684i 1.36770 + 0.691249i
107107 11.1319 1.07617 0.538083 0.842892i 0.319149π-0.319149\pi
0.538083 + 0.842892i 0.319149π0.319149\pi
108108 10.4125 7.66979i 1.00194 0.738026i
109109 10.6447i 1.01958i −0.860300 0.509788i 0.829724π-0.829724\pi
0.860300 0.509788i 0.170276π-0.170276\pi
110110 6.17377 + 3.12027i 0.588646 + 0.297507i
111111 11.1319 1.05660
112112 3.18077 10.2440i 0.300555 0.967967i
113113 5.41399i 0.509305i 0.967033 + 0.254653i 0.0819611π0.0819611\pi
−0.967033 + 0.254653i 0.918039π0.918039\pi
114114 9.72230 + 4.91373i 0.910577 + 0.460213i
115115 −4.25639 + 2.20979i −0.396910 + 0.206064i
116116 5.07172 + 6.88536i 0.470898 + 0.639290i
117117 −3.82064 −0.353218
118118 −2.37228 1.19897i −0.218386 0.110374i
119119 17.0217i 1.56037i
120120 8.01167 1.34972i 0.731362 0.123212i
121121 12.9258 1.17507
122122 8.75132 + 4.42299i 0.792307 + 0.400439i
123123 23.1858i 2.09059i
124124 −9.88154 + 7.27870i −0.887388 + 0.653646i
125125 1.00000i 0.0894427i
126126 −8.98266 + 17.7731i −0.800239 + 1.58335i
127127 3.05353i 0.270957i −0.990780 0.135478i 0.956743π-0.956743\pi
0.990780 0.135478i 0.0432571π-0.0432571\pi
128128 −1.51330 + 11.2120i −0.133758 + 0.991014i
129129 31.9762i 2.81535i
130130 −0.918342 0.464138i −0.0805439 0.0407076i
131131 3.09691i 0.270578i −0.990806 0.135289i 0.956804π-0.956804\pi
0.990806 0.135289i 0.0431963π-0.0431963\pi
132132 22.6254 16.6658i 1.96929 1.45057i
133133 −7.19105 −0.623543
134134 6.71238 13.2811i 0.579861 1.14731i
135135 −6.46618 −0.556520
136136 2.98260 + 17.7041i 0.255756 + 1.51811i
137137 5.92579i 0.506275i −0.967430 0.253137i 0.918538π-0.918538\pi
0.967430 0.253137i 0.0814625π-0.0814625\pi
138138 0.212359 + 19.4809i 0.0180772 + 1.65832i
139139 3.32470i 0.281997i −0.990010 0.140999i 0.954969π-0.954969\pi
0.990010 0.140999i 0.0450313π-0.0450313\pi
140140 −4.31821 + 3.18077i −0.364955 + 0.268824i
141141 28.1769 2.37292
142142 9.14904 + 4.62400i 0.767770 + 0.388037i
143143 −3.55894 −0.297613
144144 6.22853 20.0596i 0.519044 1.67163i
145145 4.27582i 0.355088i
146146 −5.04512 + 9.98227i −0.417537 + 0.826138i
147147 0.548788i 0.0452633i
148148 6.24055 4.59676i 0.512970 0.377851i
149149 14.4242i 1.18168i −0.806789 0.590839i 0.798797π-0.798797\pi
0.806789 0.590839i 0.201203π-0.201203\pi
150150 −3.62554 1.83238i −0.296024 0.149613i
151151 13.3082i 1.08300i −0.840700 0.541501i 0.817856π-0.817856\pi
0.840700 0.541501i 0.182144π-0.182144\pi
152152 7.47935 1.26004i 0.606656 0.102203i
153153 33.3315i 2.69469i
154154 −8.36737 + 16.5557i −0.674262 + 1.33409i
155155 6.13645 0.492892
156156 −3.36550 + 2.47901i −0.269456 + 0.198480i
157157 3.66320i 0.292356i 0.989258 + 0.146178i 0.0466971π0.0466971\pi
−0.989258 + 0.146178i 0.953303π0.953303\pi
158158 2.34746 4.64469i 0.186754 0.369512i
159159 −32.0467 −2.54147
160160 3.93398 4.06494i 0.311009 0.321362i
161161 −5.92579 11.4140i −0.467018 0.899548i
162162 −1.79932 + 3.56012i −0.141368 + 0.279710i
163163 16.6589i 1.30483i 0.757864 + 0.652413i 0.226243π0.226243\pi
−0.757864 + 0.652413i 0.773757π0.773757\pi
164164 9.57420 + 12.9979i 0.747620 + 1.01497i
165165 −14.0504 −1.09382
166166 −3.03245 + 6.00000i −0.235364 + 0.465690i
167167 1.87953i 0.145442i −0.997352 0.0727211i 0.976832π-0.976832\pi
0.997352 0.0727211i 0.0231683π-0.0231683\pi
168168 3.61943 + 21.4842i 0.279245 + 1.65754i
169169 −12.4706 −0.959278
170170 4.04917 8.01167i 0.310557 0.614467i
171171 −14.0814 −1.07683
172172 13.2041 + 17.9258i 1.00680 + 1.36683i
173173 6.34755 0.482595 0.241297 0.970451i 0.422427π-0.422427\pi
0.241297 + 0.970451i 0.422427π0.422427\pi
174174 −15.5022 7.83492i −1.17522 0.593964i
175175 2.68161 0.202711
176176 5.80189 18.6856i 0.437334 1.40848i
177177 5.39889 0.405805
178178 −10.2546 5.18277i −0.768617 0.388465i
179179 3.09691i 0.231474i 0.993280 + 0.115737i 0.0369229π0.0369229\pi
−0.993280 + 0.115737i 0.963077π0.963077\pi
180180 −8.45583 + 6.22853i −0.630260 + 0.464247i
181181 10.7610i 0.799860i 0.916546 + 0.399930i 0.130966π0.130966\pi
−0.916546 + 0.399930i 0.869034π0.869034\pi
182182 1.24464 2.46264i 0.0922587 0.182543i
183183 −19.9164 −1.47227
184184 8.16337 + 10.8333i 0.601811 + 0.798638i
185185 −3.87539 −0.284925
186186 11.2443 22.2480i 0.824472 1.63130i
187187 31.0484i 2.27048i
188188 15.7959 11.6352i 1.15203 0.848584i
189189 17.3398i 1.26128i
190190 −3.38465 1.71063i −0.245548 0.124102i
191191 −4.75372 −0.343967 −0.171984 0.985100i 0.555018π-0.555018\pi
−0.171984 + 0.985100i 0.555018π0.555018\pi
192192 −7.52908 21.7113i −0.543365 1.56688i
193193 21.3640 1.53781 0.768907 0.639360i 0.220801π-0.220801\pi
0.768907 + 0.639360i 0.220801π0.220801\pi
194194 −3.38809 1.71237i −0.243251 0.122941i
195195 2.08998 0.149667
196196 −0.226613 0.307650i −0.0161867 0.0219750i
197197 20.4988 1.46048 0.730238 0.683193i 0.239409π-0.239409\pi
0.730238 + 0.683193i 0.239409π0.239409\pi
198198 −16.3848 + 32.4190i −1.16442 + 2.30392i
199199 −15.2762 −1.08290 −0.541449 0.840733i 0.682124π-0.682124\pi
−0.541449 + 0.840733i 0.682124π0.682124\pi
200200 −2.78912 + 0.469882i −0.197221 + 0.0332257i
201201 30.2254i 2.13194i
202202 −0.981487 + 1.94197i −0.0690572 + 0.136636i
203203 11.4661 0.804762
204204 −21.6271 29.3608i −1.51420 2.05567i
205205 8.07172i 0.563754i
206206 11.5539 22.8606i 0.805000 1.59277i
207207 −11.6038 22.3507i −0.806518 1.55348i
208208 −0.863025 + 2.77946i −0.0598400 + 0.192721i
209209 −13.1168 −0.907311
210210 4.91373 9.72230i 0.339080 0.670903i
211211 26.0740i 1.79501i 0.441008 + 0.897503i 0.354621π0.354621\pi
−0.441008 + 0.897503i 0.645379π0.645379\pi
212212 −17.9653 + 13.2332i −1.23386 + 0.908858i
213213 −20.8216 −1.42667
214214 −7.10119 + 14.0504i −0.485427 + 0.960466i
215215 11.1319i 0.759193i
216216 3.03834 + 18.0350i 0.206733 + 1.22712i
217217 16.4556i 1.11708i
218218 13.4354 + 6.79036i 0.909960 + 0.459901i
219219 22.7179i 1.53513i
220220 −7.87663 + 5.80189i −0.531042 + 0.391163i
221221 4.61841i 0.310668i
222222 −7.10119 + 14.0504i −0.476600 + 0.943001i
223223 1.47929i 0.0990606i 0.998773 + 0.0495303i 0.0157724π0.0157724\pi
−0.998773 + 0.0495303i 0.984228π0.984228\pi
224224 10.9006 + 10.5494i 0.728328 + 0.704863i
225225 5.25109 0.350072
226226 −6.83337 3.45364i −0.454549 0.229733i
227227 2.20064 0.146062 0.0730308 0.997330i 0.476733π-0.476733\pi
0.0730308 + 0.997330i 0.476733π0.476733\pi
228228 −12.4039 + 9.13667i −0.821469 + 0.605091i
229229 17.4140i 1.15075i −0.817890 0.575374i 0.804856π-0.804856\pi
0.817890 0.575374i 0.195144π-0.195144\pi
230230 −0.0739292 6.78193i −0.00487475 0.447187i
231231 37.6777i 2.47901i
232232 −11.9258 + 2.00913i −0.782967 + 0.131906i
233233 −26.7931 −1.75527 −0.877637 0.479326i 0.840881π-0.840881\pi
−0.877637 + 0.479326i 0.840881π0.840881\pi
234234 2.43723 4.82229i 0.159326 0.315243i
235235 −9.80928 −0.639887
236236 3.02661 2.22938i 0.197015 0.145121i
237237 10.5705i 0.686627i
238238 21.4842 + 10.8583i 1.39261 + 0.703839i
239239 23.5866i 1.52569i 0.646583 + 0.762844i 0.276198π0.276198\pi
−0.646583 + 0.762844i 0.723802π0.723802\pi
240240 −3.40715 + 10.9731i −0.219931 + 0.708310i
241241 0.212188i 0.0136683i 0.999977 + 0.00683413i 0.00217539π0.00217539\pi
−0.999977 + 0.00683413i 0.997825π0.997825\pi
242242 −8.24550 + 16.3145i −0.530041 + 1.04874i
243243 11.2963i 0.724659i
244244 −11.1651 + 8.22417i −0.714773 + 0.526499i
245245 0.191051i 0.0122058i
246246 −29.2644 14.7905i −1.86583 0.943005i
247247 1.95112 0.124147
248248 −2.88341 17.1153i −0.183097 1.08682i
249249 13.6549i 0.865346i
250250 1.26217 + 0.637910i 0.0798266 + 0.0403450i
251251 −11.1153 −0.701589 −0.350795 0.936452i 0.614088π-0.614088\pi
−0.350795 + 0.936452i 0.614088π0.614088\pi
252252 −16.7025 22.6753i −1.05216 1.42841i
253253 −10.8089 20.8197i −0.679553 1.30892i
254254 3.85407 + 1.94788i 0.241826 + 0.122221i
255255 18.2331i 1.14180i
256256 −13.1861 9.06232i −0.824134 0.566395i
257257 1.25450 0.0782533 0.0391267 0.999234i 0.487542π-0.487542\pi
0.0391267 + 0.999234i 0.487542π0.487542\pi
258258 −40.3594 20.3979i −2.51266 1.26992i
259259 10.3923i 0.645746i
260260 1.17164 0.863025i 0.0726620 0.0535225i
261261 22.4527 1.38979
262262 3.90882 + 1.97555i 0.241488 + 0.122050i
263263 −25.6760 −1.58325 −0.791625 0.611007i 0.790765π-0.790765\pi
−0.791625 + 0.611007i 0.790765π0.790765\pi
264264 6.60203 + 39.1883i 0.406327 + 2.41187i
265265 11.1565 0.685338
266266 4.58725 9.07632i 0.281262 0.556505i
267267 23.3377 1.42824
268268 12.4811 + 16.9443i 0.762404 + 1.03504i
269269 20.4193 1.24498 0.622492 0.782626i 0.286120π-0.286120\pi
0.622492 + 0.782626i 0.286120π0.286120\pi
270270 4.12484 8.16141i 0.251030 0.496687i
271271 3.08711i 0.187529i −0.995594 0.0937643i 0.970110π-0.970110\pi
0.995594 0.0937643i 0.0298900π-0.0298900\pi
272272 −24.2482 7.52908i −1.47026 0.456518i
273273 5.60452i 0.339201i
274274 7.47935 + 3.78012i 0.451844 + 0.228366i
275275 4.89140 0.294963
276276 −24.7236 12.1590i −1.48819 0.731887i
277277 2.96451 0.178120 0.0890602 0.996026i 0.471614π-0.471614\pi
0.0890602 + 0.996026i 0.471614π0.471614\pi
278278 4.19633 + 2.12086i 0.251679 + 0.127201i
279279 32.2230i 1.92914i
280280 −1.26004 7.47935i −0.0753019 0.446977i
281281 8.93603i 0.533079i −0.963824 0.266539i 0.914120π-0.914120\pi
0.963824 0.266539i 0.0858802π-0.0858802\pi
282282 −17.9743 + 35.5640i −1.07036 + 2.11780i
283283 17.2348 1.02450 0.512252 0.858835i 0.328811π-0.328811\pi
0.512252 + 0.858835i 0.328811π0.328811\pi
284284 −11.6725 + 8.59793i −0.692637 + 0.510194i
285285 7.70285 0.456278
286286 2.27028 4.49198i 0.134245 0.265616i
287287 21.6452 1.27768
288288 21.3454 + 20.6577i 1.25779 + 1.21727i
289289 −23.2913 −1.37008
290290 5.39681 + 2.72759i 0.316911 + 0.160170i
291291 7.71069 0.452009
292292 −9.38097 12.7356i −0.548980 0.745294i
293293 20.3500i 1.18886i 0.804147 + 0.594430i 0.202622π0.202622\pi
−0.804147 + 0.594430i 0.797378π0.797378\pi
294294 0.692663 + 0.350078i 0.0403969 + 0.0204169i
295295 −1.87953 −0.109430
296296 1.82098 + 10.8089i 0.105842 + 0.628257i
297297 31.6286i 1.83528i
298298 18.2058 + 9.20136i 1.05463 + 0.533021i
299299 1.60782 + 3.09691i 0.0929826 + 0.179099i
300300 4.62554 3.40715i 0.267056 0.196712i
301301 29.8516 1.72062
302302 16.7971 + 8.48941i 0.966567 + 0.488511i
303303 4.41957i 0.253898i
304304 −3.18077 + 10.2440i −0.182430 + 0.587534i
305305 6.93356 0.397014
306306 42.0700 + 21.2625i 2.40498 + 1.21550i
307307 32.9240i 1.87907i −0.342449 0.939537i 0.611256π-0.611256\pi
0.342449 0.939537i 0.388744π-0.388744\pi
308308 −15.5584 21.1221i −0.886523 1.20354i
309309 52.0266i 2.95969i
310310 −3.91451 + 7.74524i −0.222329 + 0.439900i
311311 31.6677i 1.79571i 0.440291 + 0.897855i 0.354875π0.354875\pi
−0.440291 + 0.897855i 0.645125π0.645125\pi
312312 −0.982045 5.82922i −0.0555973 0.330015i
313313 5.92579i 0.334946i 0.985877 + 0.167473i 0.0535606π0.0535606\pi
−0.985877 + 0.167473i 0.946439π0.946439\pi
314314 −4.62358 2.33680i −0.260924 0.131873i
315315 14.0814i 0.793396i
316316 4.36491 + 5.92579i 0.245546 + 0.333352i
317317 14.3079 0.803611 0.401806 0.915725i 0.368383π-0.368383\pi
0.401806 + 0.915725i 0.368383π0.368383\pi
318318 20.4429 40.4483i 1.14638 2.26823i
319319 20.9147 1.17100
320320 2.62112 + 7.55842i 0.146525 + 0.422529i
321321 31.9762i 1.78474i
322322 18.1865 0.198249i 1.01349 0.0110480i
323323 17.0217i 0.947111i
324324 −3.34568 4.54208i −0.185871 0.252338i
325325 −0.727591 −0.0403595
326326 −21.0263 10.6269i −1.16454 0.588569i
327327 −30.5766 −1.69089
328328 −22.5130 + 3.79276i −1.24307 + 0.209420i
329329 26.3047i 1.45023i
330330 8.96290 17.7340i 0.493391 0.976223i
331331 15.1629i 0.833430i 0.909037 + 0.416715i 0.136819π0.136819\pi
−0.909037 + 0.416715i 0.863181π0.863181\pi
332332 −5.63858 7.65492i −0.309457 0.420119i
333333 20.3500i 1.11517i
334334 2.37228 + 1.19897i 0.129805 + 0.0656047i
335335 10.5224i 0.574903i
336336 −29.4256 9.13667i −1.60530 0.498446i
337337 11.5520i 0.629276i −0.949212 0.314638i 0.898117π-0.898117\pi
0.949212 0.314638i 0.101883π-0.101883\pi
338338 7.95513 15.7400i 0.432702 0.856144i
339339 15.5515 0.844643
340340 7.52908 + 10.2215i 0.408322 + 0.554337i
341341 30.0158i 1.62545i
342342 8.98266 17.7731i 0.485727 0.961058i
343343 18.2590 0.985892
344344 −31.0484 + 5.23070i −1.67402 + 0.282021i
345345 6.34755 + 12.2263i 0.341740 + 0.658245i
346346 −4.04917 + 8.01167i −0.217684 + 0.430710i
347347 3.94249i 0.211644i 0.994385 + 0.105822i 0.0337474π0.0337474\pi
−0.994385 + 0.105822i 0.966253π0.966253\pi
348348 19.7780 14.5684i 1.06021 0.780947i
349349 −14.2826 −0.764532 −0.382266 0.924052i 0.624856π-0.624856\pi
−0.382266 + 0.924052i 0.624856π0.624856\pi
350350 −1.71063 + 3.38465i −0.0914370 + 0.180917i
351351 4.70473i 0.251120i
352352 19.8833 + 19.2427i 1.05978 + 1.02564i
353353 −24.2520 −1.29080 −0.645402 0.763843i 0.723310π-0.723310\pi
−0.645402 + 0.763843i 0.723310π0.723310\pi
354354 −3.44401 + 6.81431i −0.183047 + 0.362176i
355355 7.24866 0.384719
356356 13.0831 9.63693i 0.693401 0.510756i
357357 −48.8942 −2.58776
358358 −3.90882 1.97555i −0.206588 0.104411i
359359 35.2093 1.85828 0.929138 0.369734i 0.120551π-0.120551\pi
0.929138 + 0.369734i 0.120551π0.120551\pi
360360 −2.46739 14.6459i −0.130043 0.771908i
361361 −11.8089 −0.621524
362362 −13.5822 6.86457i −0.713866 0.360794i
363363 37.1290i 1.94876i
364364 2.31430 + 3.14189i 0.121302 + 0.164680i
365365 7.90882i 0.413967i
366366 12.7049 25.1379i 0.664096 1.31398i
367367 4.51174 0.235511 0.117755 0.993043i 0.462430π-0.462430\pi
0.117755 + 0.993043i 0.462430π0.462430\pi
368368 −18.8809 + 3.39290i −0.984235 + 0.176867i
369369 42.3853 2.20649
370370 2.47215 4.89140i 0.128521 0.254292i
371371 29.9174i 1.55323i
372372 20.9078 + 28.3844i 1.08402 + 1.47166i
373373 1.05569i 0.0546617i 0.999626 + 0.0273309i 0.00870077π0.00870077\pi
−0.999626 + 0.0273309i 0.991299π0.991299\pi
374374 39.1883 + 19.8061i 2.02638 + 1.02415i
375375 −2.87247 −0.148334
376376 4.60921 + 27.3593i 0.237702 + 1.41095i
377377 −3.11105 −0.160227
378378 21.8857 + 11.0612i 1.12568 + 0.568928i
379379 6.48253 0.332985 0.166493 0.986043i 0.446756π-0.446756\pi
0.166493 + 0.986043i 0.446756π0.446756\pi
380380 4.31821 3.18077i 0.221519 0.163170i
381381 −8.77117 −0.449361
382382 3.03245 6.00000i 0.155154 0.306987i
383383 −1.34915 −0.0689383 −0.0344692 0.999406i 0.510974π-0.510974\pi
−0.0344692 + 0.999406i 0.510974π0.510974\pi
384384 32.2063 + 4.34692i 1.64352 + 0.221828i
385385 13.1168i 0.668496i
386386 −13.6283 + 26.9650i −0.693663 + 1.37248i
387387 58.4548 2.97143
388388 4.32260 3.18401i 0.219447 0.161643i
389389 10.3846i 0.526519i 0.964725 + 0.263259i 0.0847975π0.0847975\pi
−0.964725 + 0.263259i 0.915203π0.915203\pi
390390 −1.33322 + 2.63791i −0.0675103 + 0.133576i
391391 −27.0176 + 14.0267i −1.36634 + 0.709362i
392392 0.532865 0.0897714i 0.0269137 0.00453414i
393393 −8.89578 −0.448733
394394 −13.0764 + 25.8729i −0.658778 + 1.30346i
395395 3.67993i 0.185157i
396396 −30.4662 41.3608i −1.53098 2.07846i
397397 −23.4623 −1.17754 −0.588770 0.808300i 0.700388π-0.700388\pi
−0.588770 + 0.808300i 0.700388π0.700388\pi
398398 9.74483 19.2811i 0.488464 0.966474i
399399 20.6561i 1.03410i
400400 1.18614 3.82009i 0.0593070 0.191004i
401401 26.3500i 1.31586i 0.753080 + 0.657929i 0.228567π0.228567\pi
−0.753080 + 0.657929i 0.771433π0.771433\pi
402402 −38.1496 19.2811i −1.90273 0.961654i
403403 4.46482i 0.222409i
404404 −1.82499 2.47760i −0.0907967 0.123265i
405405 2.82064i 0.140159i
406406 −7.31434 + 14.4722i −0.363005 + 0.718241i
407407 18.9561i 0.939619i
408408 50.8545 8.56742i 2.51767 0.424151i
409409 18.3538 0.907535 0.453768 0.891120i 0.350080π-0.350080\pi
0.453768 + 0.891120i 0.350080π0.350080\pi
410410 10.1879 + 5.14904i 0.503144 + 0.254293i
411411 −17.0217 −0.839617
412412 21.4836 + 29.1660i 1.05842 + 1.43691i
413413 5.04017i 0.248010i
414414 35.6125 0.388208i 1.75026 0.0190794i
415415 4.75372i 0.233351i
416416 −2.95762 2.86233i −0.145009 0.140337i
417417 −9.55010 −0.467670
418418 8.36737 16.5557i 0.409261 0.809764i
419419 −20.3386 −0.993606 −0.496803 0.867863i 0.665493π-0.665493\pi
−0.496803 + 0.867863i 0.665493π0.665493\pi
420420 9.13667 + 12.4039i 0.445824 + 0.605249i
421421 9.22242i 0.449473i −0.974420 0.224737i 0.927848π-0.927848\pi
0.974420 0.224737i 0.0721522π-0.0721522\pi
422422 −32.9098 16.6329i −1.60202 0.809675i
423423 51.5094i 2.50447i
424424 −5.24224 31.1168i −0.254585 1.51117i
425425 6.34755i 0.307901i
426426 13.2823 26.2803i 0.643529 1.27329i
427427 18.5931i 0.899784i
428428 −13.2041 17.9258i −0.638242 0.866476i
429429 10.2229i 0.493568i
430430 14.0504 + 7.10119i 0.677570 + 0.342450i
431431 10.2805 0.495192 0.247596 0.968863i 0.420359π-0.420359\pi
0.247596 + 0.968863i 0.420359π0.420359\pi
432432 −24.7014 7.66979i −1.18844 0.369013i
433433 17.8095i 0.855868i 0.903810 + 0.427934i 0.140758π0.140758\pi
−0.903810 + 0.427934i 0.859242π0.859242\pi
434434 −20.7697 10.4972i −0.996979 0.503881i
435435 −12.2822 −0.588885
436436 −17.1412 + 12.6261i −0.820913 + 0.604681i
437437 5.92579 + 11.4140i 0.283469 + 0.546005i
438438 28.6738 + 14.4920i 1.37009 + 0.692452i
439439 14.9756i 0.714746i −0.933962 0.357373i 0.883672π-0.883672\pi
0.933962 0.357373i 0.116328π-0.116328\pi
440440 −2.29838 13.6427i −0.109571 0.650391i
441441 −1.00322 −0.0477726
442442 −5.82922 2.94613i −0.277268 0.140133i
443443 14.0082i 0.665548i −0.943007 0.332774i 0.892015π-0.892015\pi
0.943007 0.332774i 0.107985π-0.107985\pi
444444 −13.2041 17.9258i −0.626637 0.850720i
445445 −8.12461 −0.385143
446446 −1.86711 0.943654i −0.0884104 0.0446833i
447447 −41.4332 −1.95972
448448 −20.2688 + 7.02882i −0.957609 + 0.332081i
449449 −28.3872 −1.33967 −0.669837 0.742508i 0.733636π-0.733636\pi
−0.669837 + 0.742508i 0.733636π0.733636\pi
450450 −3.34972 + 6.62776i −0.157907 + 0.312435i
451451 39.4820 1.85914
452452 8.71815 6.42175i 0.410067 0.302054i
453453 −38.2273 −1.79607
454454 −1.40381 + 2.77758i −0.0658841 + 0.130358i
455455 1.95112i 0.0914698i
456456 −3.61943 21.4842i −0.169495 1.00609i
457457 35.6394i 1.66714i −0.552413 0.833570i 0.686293π-0.686293\pi
0.552413 0.833570i 0.313707π-0.313707\pi
458458 21.9794 + 11.1086i 1.02703 + 0.519069i
459459 −41.0443 −1.91579
460460 8.60710 + 4.23295i 0.401308 + 0.197362i
461461 −1.09286 −0.0508997 −0.0254498 0.999676i 0.508102π-0.508102\pi
−0.0254498 + 0.999676i 0.508102π0.508102\pi
462462 47.5557 + 24.0350i 2.21249 + 1.11821i
463463 20.3766i 0.946980i −0.880799 0.473490i 0.842994π-0.842994\pi
0.880799 0.473490i 0.157006π-0.157006\pi
464464 5.07172 16.3340i 0.235449 0.758287i
465465 17.6268i 0.817422i
466466 17.0916 33.8174i 0.791753 1.56656i
467467 −30.8277 −1.42654 −0.713268 0.700892i 0.752786π-0.752786\pi
−0.713268 + 0.700892i 0.752786π0.752786\pi
468468 4.53182 + 6.15238i 0.209483 + 0.284394i
469469 28.2171 1.30295
470470 6.25744 12.3810i 0.288634 0.571092i
471471 10.5224 0.484849
472472 0.883156 + 5.24224i 0.0406506 + 0.241293i
473473 54.4508 2.50365
474474 −13.3417 6.74302i −0.612806 0.309717i
475475 −2.68161 −0.123041
476476 −27.4100 + 20.1901i −1.25634 + 0.925411i
477477 58.5837i 2.68236i
478478 −29.7702 15.0461i −1.36166 0.688193i
479479 −14.5699 −0.665715 −0.332858 0.942977i 0.608013π-0.608013\pi
−0.332858 + 0.942977i 0.608013π0.608013\pi
480480 −11.6764 11.3003i −0.532954 0.515784i
481481 2.81970i 0.128567i
482482 −0.267818 0.135357i −0.0121988 0.00616535i
483483 −32.7863 + 17.0217i −1.49183 + 0.774513i
484484 −15.3318 20.8144i −0.696900 0.946110i
485485 −2.68434 −0.121890
486486 −14.2579 7.20604i −0.646750 0.326873i
487487 2.18374i 0.0989549i 0.998775 + 0.0494774i 0.0157556π0.0157556\pi
−0.998775 + 0.0494774i 0.984244π0.984244\pi
488488 −3.25795 19.3385i −0.147481 0.875415i
489489 47.8522 2.16395
490490 −0.241138 0.121873i −0.0108935 0.00550568i
491491 7.55568i 0.340983i −0.985359 0.170491i 0.945464π-0.945464\pi
0.985359 0.170491i 0.0545355π-0.0545355\pi
492492 37.3361 27.5016i 1.68324 1.23987i
493493 27.1410i 1.22237i
494494 −1.24464 + 2.46264i −0.0559989 + 0.110799i
495495 25.6852i 1.15446i
496496 23.4418 + 7.27870i 1.05257 + 0.326823i
497497 19.4381i 0.871919i
498498 17.2348 + 8.71062i 0.772311 + 0.390332i
499499 10.0079i 0.448015i 0.974587 + 0.224007i 0.0719140π0.0719140\pi
−0.974587 + 0.224007i 0.928086π0.928086\pi
500500 −1.61030 + 1.18614i −0.0720149 + 0.0530458i
501501 −5.39889 −0.241204
502502 7.09054 14.0293i 0.316466 0.626160i
503503 32.7697 1.46113 0.730563 0.682845i 0.239258π-0.239258\pi
0.730563 + 0.682845i 0.239258π0.239258\pi
504504 39.2747 6.61659i 1.74943 0.294726i
505505 1.53860i 0.0684666i
506506 33.1731 0.361617i 1.47472 0.0160758i
507507 35.8215i 1.59089i
508508 −4.91710 + 3.62191i −0.218161 + 0.160696i
509509 −4.89723 −0.217066 −0.108533 0.994093i 0.534615π-0.534615\pi
−0.108533 + 0.994093i 0.534615π0.534615\pi
510510 −23.0133 11.6311i −1.01905 0.515034i
511511 −21.2084 −0.938204
512512 19.8498 10.8622i 0.877244 0.480045i
513513 17.3398i 0.765570i
514514 −0.800256 + 1.58339i −0.0352978 + 0.0698402i
515515 18.1121i 0.798116i
516516 51.4913 37.9283i 2.26678 1.66970i
517517 47.9811i 2.11021i
518518 13.1168 + 6.62936i 0.576321 + 0.291277i
519519 18.2331i 0.800346i
520520 0.341882 + 2.02934i 0.0149925 + 0.0889924i
521521 31.5065i 1.38033i −0.723654 0.690163i 0.757539π-0.757539\pi
0.723654 0.690163i 0.242461π-0.242461\pi
522522 −14.3228 + 28.3391i −0.626892 + 1.24037i
523523 −29.1444 −1.27440 −0.637198 0.770700i 0.719906π-0.719906\pi
−0.637198 + 0.770700i 0.719906π0.719906\pi
524524 −4.98696 + 3.67337i −0.217856 + 0.160472i
525525 7.70285i 0.336180i
526526 16.3790 32.4075i 0.714158 1.41303i
527527 38.9514 1.69675
528528 −53.6738 16.6658i −2.33585 0.725284i
529529 −13.2337 + 18.8114i −0.575378 + 0.817888i
530530 −7.11684 + 14.0814i −0.309136 + 0.611656i
531531 9.86956i 0.428302i
532532 8.52960 + 11.5798i 0.369805 + 0.502046i
533533 −5.87291 −0.254384
534534 −14.8874 + 29.4561i −0.644239 + 1.27469i
535535 11.1319i 0.481276i
536536 −29.3484 + 4.94431i −1.26766 + 0.213562i
537537 8.89578 0.383881
538538 −13.0257 + 25.7726i −0.561576 + 1.11113i
539539 −0.934506 −0.0402520
540540 7.66979 + 10.4125i 0.330055 + 0.448082i
541541 10.0459 0.431906 0.215953 0.976404i 0.430714π-0.430714\pi
0.215953 + 0.976404i 0.430714π0.430714\pi
542542 3.89645 + 1.96930i 0.167367 + 0.0845886i
543543 30.9107 1.32651
544544 24.9711 25.8024i 1.07063 1.10627i
545545 10.6447 0.455968
546546 −7.07386 3.57518i −0.302733 0.153004i
547547 40.9194i 1.74959i 0.484495 + 0.874794i 0.339003π0.339003\pi
−0.484495 + 0.874794i 0.660997π0.660997\pi
548548 −9.54231 + 7.02882i −0.407627 + 0.300256i
549549 36.4087i 1.55389i
550550 −3.12027 + 6.17377i −0.133049 + 0.263251i
551551 −11.4661 −0.488472
552552 31.1182 23.4490i 1.32448 0.998057i
553553 9.86814 0.419636
554554 −1.89109 + 3.74172i −0.0803449 + 0.158970i
555555 11.1319i 0.472525i
556556 −5.35377 + 3.94356i −0.227050 + 0.167244i
557557 5.20180i 0.220407i −0.993909 0.110204i 0.964850π-0.964850\pi
0.993909 0.110204i 0.0351503π-0.0351503\pi
558558 −40.6709 20.5554i −1.72174 0.870180i
559559 −8.09950 −0.342572
560560 10.2440 + 3.18077i 0.432888 + 0.134412i
561561 −89.1856 −3.76542
562562 11.2788 + 5.70038i 0.475766 + 0.240456i
563563 22.2639 0.938311 0.469156 0.883115i 0.344558π-0.344558\pi
0.469156 + 0.883115i 0.344558π0.344558\pi
564564 −33.4217 45.3733i −1.40731 1.91056i
565565 −5.41399 −0.227768
566566 −10.9943 + 21.7533i −0.462124 + 0.914358i
567567 −7.56387 −0.317652
568568 −3.40602 20.2174i −0.142913 0.848304i
569569 33.1614i 1.39020i 0.718913 + 0.695100i 0.244640π0.244640\pi
−0.718913 + 0.695100i 0.755360π0.755360\pi
570570 −4.91373 + 9.72230i −0.205814 + 0.407222i
571571 −3.20810 −0.134255 −0.0671274 0.997744i 0.521383π-0.521383\pi
−0.0671274 + 0.997744i 0.521383π0.521383\pi
572572 4.22140 + 5.73096i 0.176506 + 0.239623i
573573 13.6549i 0.570443i
574574 −13.8077 + 27.3200i −0.576323 + 1.14031i
575575 −2.20979 4.25639i −0.0921545 0.177504i
576576 −39.6899 + 13.7637i −1.65375 + 0.573488i
577577 12.3249 0.513091 0.256545 0.966532i 0.417416π-0.417416\pi
0.256545 + 0.966532i 0.417416π0.417416\pi
578578 14.8578 29.3976i 0.618002 1.22278i
579579 61.3675i 2.55034i
580580 −6.88536 + 5.07172i −0.285899 + 0.210592i
581581 −12.7476 −0.528861
582582 −4.91873 + 9.73219i −0.203888 + 0.403412i
583583 54.5709i 2.26009i
584584 22.0587 3.71621i 0.912795 0.153778i
585585 3.82064i 0.157964i
586586 −25.6852 12.9815i −1.06104 0.536260i
587587 8.83980i 0.364857i −0.983219 0.182429i 0.941604π-0.941604\pi
0.983219 0.182429i 0.0583959π-0.0583959\pi
588588 −0.883714 + 0.650940i −0.0364438 + 0.0268443i
589589 16.4556i 0.678041i
590590 1.19897 2.37228i 0.0493608 0.0976653i
591591 58.8821i 2.42208i
592592 −14.8043 4.59676i −0.608455 0.188926i
593593 2.38210 0.0978212 0.0489106 0.998803i 0.484425π-0.484425\pi
0.0489106 + 0.998803i 0.484425π0.484425\pi
594594 39.9207 + 20.1762i 1.63797 + 0.827841i
595595 17.0217 0.697820
596596 −23.2273 + 17.1092i −0.951429 + 0.700818i
597597 43.8803i 1.79590i
598598 −4.93447 + 0.0537902i −0.201785 + 0.00219964i
599599 8.38036i 0.342412i −0.985235 0.171206i 0.945234π-0.945234\pi
0.985235 0.171206i 0.0547664π-0.0547664\pi
600600 1.34972 + 8.01167i 0.0551022 + 0.327075i
601601 29.2981 1.19509 0.597547 0.801834i 0.296142π-0.296142\pi
0.597547 + 0.801834i 0.296142π0.296142\pi
602602 −19.0426 + 37.6777i −0.776120 + 1.53563i
603603 55.2543 2.25013
604604 −21.4301 + 15.7853i −0.871980 + 0.642297i
605605 12.9258i 0.525508i
606606 5.57825 + 2.81929i 0.226601 + 0.114526i
607607 6.58224i 0.267165i −0.991038 0.133582i 0.957352π-0.957352\pi
0.991038 0.133582i 0.0426481π-0.0426481\pi
608608 −10.9006 10.5494i −0.442078 0.427836i
609609 32.9360i 1.33464i
610610 −4.42299 + 8.75132i −0.179082 + 0.354331i
611611 7.13714i 0.288738i
612612 −53.6738 + 39.5359i −2.16963 + 1.59814i
613613 31.7187i 1.28111i 0.767914 + 0.640553i 0.221295π0.221295\pi
−0.767914 + 0.640553i 0.778705π0.778705\pi
614614 41.5557 + 21.0026i 1.67705 + 0.847595i
615615 −23.1858 −0.934941
616616 36.5845 6.16337i 1.47403 0.248329i
617617 41.9737i 1.68980i 0.534925 + 0.844899i 0.320340π0.320340\pi
−0.534925 + 0.844899i 0.679660π0.679660\pi
618618 −65.6663 33.1883i −2.64149 1.33503i
619619 40.4232 1.62474 0.812372 0.583139i 0.198176π-0.198176\pi
0.812372 + 0.583139i 0.198176π0.198176\pi
620620 −7.27870 9.88154i −0.292319 0.396852i
621621 −27.5226 + 14.2889i −1.10444 + 0.573392i
622622 −39.9700 20.2011i −1.60265 0.809992i
623623 21.7871i 0.872880i
624624 7.98391 + 2.47901i 0.319612 + 0.0992399i
625625 1.00000 0.0400000
626626 −7.47935 3.78012i −0.298935 0.151084i
627627 37.6777i 1.50470i
628628 5.89886 4.34508i 0.235390 0.173387i
629629 −24.5992 −0.980836
630630 −17.7731 8.98266i −0.708096 0.357878i
631631 3.27191 0.130253 0.0651263 0.997877i 0.479255π-0.479255\pi
0.0651263 + 0.997877i 0.479255π0.479255\pi
632632 −10.2638 + 1.72913i −0.408271 + 0.0687812i
633633 74.8967 2.97688
634634 −9.12715 + 18.0590i −0.362486 + 0.717214i
635635 3.05353 0.121176
636636 38.0119 + 51.6048i 1.50727 + 2.04627i
637637 0.139007 0.00550765
638638 −13.3417 + 26.3979i −0.528204 + 1.04510i
639639 38.0633i 1.50576i
640640 −11.2120 1.51330i −0.443195 0.0598185i
641641 2.70337i 0.106777i −0.998574 0.0533884i 0.982998π-0.982998\pi
0.998574 0.0533884i 0.0170021π-0.0170021\pi
642642 40.3594 + 20.3979i 1.59286 + 0.805043i
643643 −3.81007 −0.150254 −0.0751272 0.997174i 0.523936π-0.523936\pi
−0.0751272 + 0.997174i 0.523936π0.523936\pi
644644 −11.3511 + 23.0809i −0.447297 + 0.909515i
645645 −31.9762 −1.25906
646646 −21.4842 10.8583i −0.845285 0.427214i
647647 5.11436i 0.201066i 0.994934 + 0.100533i 0.0320548π0.0320548\pi
−0.994934 + 0.100533i 0.967945π0.967945\pi
648648 7.86711 1.32537i 0.309049 0.0520654i
649649 9.19352i 0.360877i
650650 0.464138 0.918342i 0.0182050 0.0360203i
651651 47.2682 1.85259
652652 26.8258 19.7598i 1.05058 0.773853i
653653 −27.5197 −1.07693 −0.538465 0.842648i 0.680996π-0.680996\pi
−0.538465 + 0.842648i 0.680996π0.680996\pi
654654 19.5051 38.5928i 0.762710 1.50910i
655655 3.09691 0.121006
656656 9.57420 30.8347i 0.373810 1.20389i
657657 −41.5299 −1.62024
658658 33.2010 + 16.7800i 1.29431 + 0.654154i
659659 31.4372 1.22462 0.612310 0.790618i 0.290241π-0.290241\pi
0.612310 + 0.790618i 0.290241π0.290241\pi
660660 16.6658 + 22.6254i 0.648713 + 0.880692i
661661 0.251685i 0.00978943i 0.999988 + 0.00489471i 0.00155804π0.00155804\pi
−0.999988 + 0.00489471i 0.998442π0.998442\pi
662662 −19.1382 9.67259i −0.743826 0.375936i
663663 13.2663 0.515219
664664 13.2587 2.23369i 0.514538 0.0866839i
665665 7.19105i 0.278857i
666666 25.6852 + 12.9815i 0.995280 + 0.503022i
667667 −9.44865 18.1996i −0.365853 0.704690i
668668 −3.02661 + 2.22938i −0.117103 + 0.0862575i
669669 4.24921 0.164284
670670 13.2811 + 6.71238i 0.513094 + 0.259322i
671671 33.9148i 1.30927i
672672 30.3029 31.3117i 1.16896 1.20787i
673673 −9.56375 −0.368655 −0.184328 0.982865i 0.559011π-0.559011\pi
−0.184328 + 0.982865i 0.559011π0.559011\pi
674674 14.5805 + 7.36912i 0.561621 + 0.283848i
675675 6.46618i 0.248883i
676676 14.7919 + 20.0814i 0.568919 + 0.772363i
677677 48.6951i 1.87150i −0.352658 0.935752i 0.614722π-0.614722\pi
0.352658 0.935752i 0.385278π-0.385278\pi
678678 −9.92048 + 19.6286i −0.380994 + 0.753834i
679679 7.19837i 0.276248i
680680 −17.7041 + 2.98260i −0.678921 + 0.114377i
681681 6.32127i 0.242232i
682682 −37.8851 19.1474i −1.45069 0.733193i
683683 23.9040i 0.914662i 0.889297 + 0.457331i 0.151195π0.151195\pi
−0.889297 + 0.457331i 0.848805π0.848805\pi
684684 16.7025 + 22.6753i 0.638636 + 0.867010i
685685 5.92579 0.226413
686686 −11.6476 + 23.0459i −0.444707 + 0.879897i
687687 −50.0212 −1.90843
688688 13.2041 42.5250i 0.503400 1.62125i
689689 8.11736i 0.309247i
690690 −19.4809 + 0.212359i −0.741625 + 0.00808438i
691691 32.6562i 1.24230i −0.783691 0.621150i 0.786666π-0.786666\pi
0.783691 0.621150i 0.213334π-0.213334\pi
692692 −7.52908 10.2215i −0.286213 0.388562i
693693 −68.8777 −2.61645
694694 −4.97609 2.51495i −0.188890 0.0954664i
695695 3.32470 0.126113
696696 5.77117 + 34.2565i 0.218756 + 1.29849i
697697 51.2356i 1.94069i
698698 9.11105 18.0271i 0.344858 0.682336i
699699 76.9624i 2.91098i
700700 −3.18077 4.31821i −0.120222 0.163213i
701701 6.51180i 0.245947i −0.992410 0.122974i 0.960757π-0.960757\pi
0.992410 0.122974i 0.0392431π-0.0392431\pi
702702 −5.93816 3.00119i −0.224121 0.113273i
703703 10.3923i 0.391953i
704704 −36.9713 + 12.8209i −1.39341 + 0.483207i
705705 28.1769i 1.06120i
706706 15.4706 30.6101i 0.582244 1.15203i
707707 −4.12592 −0.155171
708708 −6.40384 8.69384i −0.240671 0.326734i
709709 8.35583i 0.313810i −0.987614 0.156905i 0.949848π-0.949848\pi
0.987614 0.156905i 0.0501516π-0.0501516\pi
710710 −4.62400 + 9.14904i −0.173536 + 0.343357i
711711 19.3236 0.724692
712712 3.81761 + 22.6605i 0.143071 + 0.849239i
713713 26.1191 13.5602i 0.978169 0.507835i
714714 31.1901 61.7128i 1.16726 2.30954i
715715 3.55894i 0.133097i
716716 4.98696 3.67337i 0.186371 0.137280i
717717 67.7517 2.53023
718718 −22.4604 + 44.4401i −0.838214 + 1.65849i
719719 3.98961i 0.148787i 0.997229 + 0.0743937i 0.0237021π0.0237021\pi
−0.997229 + 0.0743937i 0.976298π0.976298\pi
720720 20.0596 + 6.22853i 0.747577 + 0.232123i
721721 48.5698 1.80883
722722 7.53305 14.9049i 0.280351 0.554703i
723723 0.609505 0.0226677
724724 17.3285 12.7641i 0.644008 0.474373i
725725 4.27582 0.158800
726726 46.8630 + 23.6849i 1.73925 + 0.879031i
727727 26.1403 0.969490 0.484745 0.874656i 0.338912π-0.338912\pi
0.484745 + 0.874656i 0.338912π0.338912\pi
728728 −5.44191 + 0.916794i −0.201690 + 0.0339787i
729729 40.9103 1.51520
730730 −9.98227 5.04512i −0.369460 0.186728i
731731 70.6606i 2.61348i
732732 23.6237 + 32.0715i 0.873157 + 1.18540i
733733 46.1008i 1.70277i −0.524540 0.851386i 0.675763π-0.675763\pi
0.524540 0.851386i 0.324237π-0.324237\pi
734734 −2.87808 + 5.69458i −0.106232 + 0.210191i
735735 0.548788 0.0202424
736736 7.76190 25.9952i 0.286108 0.958198i
737737 51.4695 1.89590
738738 −27.0380 + 53.4974i −0.995284 + 1.96927i
739739 32.2296i 1.18559i −0.805355 0.592793i 0.798025π-0.798025\pi
0.805355 0.592793i 0.201975π-0.201975\pi
740740 4.59676 + 6.24055i 0.168980 + 0.229407i
741741 5.60452i 0.205887i
742742 −37.7608 19.0846i −1.38624 0.700619i
743743 −33.3792 −1.22456 −0.612281 0.790640i 0.709748π-0.709748\pi
−0.612281 + 0.790640i 0.709748π0.709748\pi
744744 −49.1633 + 8.28250i −1.80241 + 0.303651i
745745 14.4242 0.528463
746746 −1.33246 0.673438i −0.0487850 0.0246563i
747747 −24.9622 −0.913319
748748 −49.9973 + 36.8278i −1.82808 + 1.34656i
749749 −29.8516 −1.09075
750750 1.83238 3.62554i 0.0669090 0.132386i
751751 −1.95865 −0.0714723 −0.0357362 0.999361i 0.511378π-0.511378\pi
−0.0357362 + 0.999361i 0.511378π0.511378\pi
752752 −37.4723 11.6352i −1.36648 0.424292i
753753 31.9283i 1.16353i
754754 1.98457 3.92667i 0.0722737 0.143001i
755755 13.3082 0.484333
756756 −27.9223 + 20.5674i −1.01552 + 0.748030i
757757 16.8031i 0.610721i 0.952237 + 0.305360i 0.0987769π0.0987769\pi
−0.952237 + 0.305360i 0.901223π0.901223\pi
758758 −4.13528 + 8.18205i −0.150200 + 0.297186i
759759 −59.8040 + 31.0484i −2.17075 + 1.12698i
760760 1.26004 + 7.47935i 0.0457065 + 0.271305i
761761 −44.9975 −1.63116 −0.815579 0.578646i 0.803581π-0.803581\pi
−0.815579 + 0.578646i 0.803581π0.803581\pi
762762 5.59522 11.0707i 0.202693 0.401049i
763763 28.5449i 1.03340i
764764 5.63858 + 7.65492i 0.203997 + 0.276945i
765765 33.3315 1.20510
766766 0.860637 1.70285i 0.0310961 0.0615266i
767767 1.36753i 0.0493785i
768768 −26.0313 + 37.8768i −0.939322 + 1.36676i
769769 19.8146i 0.714531i −0.934003 0.357266i 0.883709π-0.883709\pi
0.934003 0.357266i 0.116291π-0.116291\pi
770770 −16.5557 8.36737i −0.596625 0.301539i
771771 3.60350i 0.129777i
772772 −25.3407 34.4025i −0.912032 1.23817i
773773 47.4024i 1.70494i −0.522772 0.852472i 0.675102π-0.675102\pi
0.522772 0.852472i 0.324898π-0.324898\pi
774774 −37.2889 + 73.7798i −1.34032 + 2.65196i
775775 6.13645i 0.220428i
776776 1.26132 + 7.48696i 0.0452789 + 0.268766i
777777 −29.8516 −1.07092
778778 −13.1071 6.62443i −0.469912 0.237497i
779779 −21.6452 −0.775521
780780 −2.47901 3.36550i −0.0887629 0.120504i
781781 35.4561i 1.26872i
782782 −0.469269 43.0486i −0.0167810 1.53941i
783783 27.6482i 0.988066i
784784 −0.226613 + 0.729831i −0.00809333 + 0.0260654i
785785 −3.66320 −0.130745
786786 5.67471 11.2280i 0.202410 0.400488i
787787 28.8128 1.02706 0.513532 0.858070i 0.328337π-0.328337\pi
0.513532 + 0.858070i 0.328337π0.328337\pi
788788 −24.3144 33.0092i −0.866165 1.17590i
789789 73.7536i 2.62570i
790790 4.64469 + 2.34746i 0.165251 + 0.0835190i
791791 14.5182i 0.516209i
792792 71.6391 12.0690i 2.54558 0.428853i
793793 5.04479i 0.179146i
794794 14.9669 29.6134i 0.531154 1.05094i
795795 32.0467i 1.13658i
796796 18.1197 + 24.5992i 0.642235 + 0.871897i
797797 29.1492i 1.03252i 0.856432 + 0.516260i 0.172676π0.172676\pi
−0.856432 + 0.516260i 0.827324π0.827324\pi
798798 −26.0715 13.1767i −0.922920 0.466451i
799799 −62.2649 −2.20277
800800 4.06494 + 3.93398i 0.143717 + 0.139087i
801801 42.6630i 1.50742i
802802 −33.2582 16.8089i −1.17439 0.593545i
803803 −38.6852 −1.36517
804804 48.6720 35.8516i 1.71653 1.26439i
805805 11.4140 5.92579i 0.402290 0.208857i
806806 5.63536 + 2.84816i 0.198497 + 0.100322i
807807 58.6537i 2.06471i
808808 4.29134 0.722959i 0.150969 0.0254336i
809809 −39.3289 −1.38273 −0.691365 0.722506i 0.742990π-0.742990\pi
−0.691365 + 0.722506i 0.742990π0.742990\pi
810810 −3.56012 1.79932i −0.125090 0.0632215i
811811 25.2461i 0.886510i 0.896396 + 0.443255i 0.146176π0.146176\pi
−0.896396 + 0.443255i 0.853824π0.853824\pi
812812 −13.6004 18.4639i −0.477281 0.647955i
813813 −8.86763 −0.311001
814814 23.9258 + 12.0923i 0.838599 + 0.423835i
815815 −16.6589 −0.583536
816816 −21.6271 + 69.6522i −0.757099 + 2.43831i
817817 −29.8516 −1.04437
818818 −11.7081 + 23.1656i −0.409363 + 0.809965i
819819 10.2455 0.358006
820820 −12.9979 + 9.57420i −0.453907 + 0.334346i
821821 11.0606 0.386019 0.193009 0.981197i 0.438175π-0.438175\pi
0.193009 + 0.981197i 0.438175π0.438175\pi
822822 10.8583 21.4842i 0.378727 0.749348i
823823 9.36041i 0.326283i 0.986603 + 0.163142i 0.0521628π0.0521628\pi
−0.986603 + 0.163142i 0.947837π0.947837\pi
824824 −50.5170 + 8.51057i −1.75984 + 0.296480i
825825 14.0504i 0.489172i
826826 6.36154 + 3.21517i 0.221346 + 0.111870i
827827 −50.8347 −1.76770 −0.883848 0.467775i 0.845056π-0.845056\pi
−0.883848 + 0.467775i 0.845056π0.845056\pi
828828 −22.2276 + 45.1966i −0.772462 + 1.57069i
829829 6.23369 0.216505 0.108252 0.994123i 0.465475π-0.465475\pi
0.108252 + 0.994123i 0.465475π0.465475\pi
830830 −6.00000 3.03245i −0.208263 0.105258i
831831 8.51548i 0.295399i
832832 5.49944 1.90710i 0.190659 0.0661168i
833833 1.21270i 0.0420177i
834834 6.09211 12.0538i 0.210952 0.417390i
835835 1.87953 0.0650437
836836 15.5584 + 21.1221i 0.538099 + 0.730522i
837837 39.6794 1.37152
838838 12.9742 25.6708i 0.448187 0.886782i
839839 −14.6079 −0.504320 −0.252160 0.967686i 0.581141π-0.581141\pi
−0.252160 + 0.967686i 0.581141π0.581141\pi
840840 −21.4842 + 3.61943i −0.741276 + 0.124882i
841841 −10.7174 −0.369564
842842 11.6403 + 5.88308i 0.401150 + 0.202744i
843843 −25.6685 −0.884069
844844 41.9869 30.9274i 1.44525 1.06456i
845845 12.4706i 0.429002i
846846 65.0135 + 32.8584i 2.23521 + 1.12969i
847847 −34.6620 −1.19100
848848 42.6188 + 13.2332i 1.46354 + 0.454429i
849849 49.5065i 1.69906i
850850 8.01167 + 4.04917i 0.274798 + 0.138885i
851851 −16.4952 + 8.56379i −0.565447 + 0.293563i
852852 24.6973 + 33.5290i 0.846116 + 1.14868i
853853 33.5602 1.14908 0.574541 0.818476i 0.305181π-0.305181\pi
0.574541 + 0.818476i 0.305181π0.305181\pi
854854 −23.4677 11.8607i −0.803047 0.405866i
855855 14.0814i 0.481573i
856856 31.0484 5.23070i 1.06121 0.178782i
857857 −51.6052 −1.76280 −0.881400 0.472372i 0.843398π-0.843398\pi
−0.881400 + 0.472372i 0.843398π0.843398\pi
858858 −12.9031 6.52132i −0.440504 0.222634i
859859 27.1505i 0.926365i −0.886263 0.463182i 0.846708π-0.846708\pi
0.886263 0.463182i 0.153292π-0.153292\pi
860860 −17.9258 + 13.2041i −0.611264 + 0.450255i
861861 62.1753i 2.11893i
862862 −6.55801 + 12.9757i −0.223367 + 0.441953i
863863 8.73671i 0.297401i −0.988882 0.148701i 0.952491π-0.952491\pi
0.988882 0.148701i 0.0475091π-0.0475091\pi
864864 25.4378 26.2846i 0.865412 0.894222i
865865 6.34755i 0.215823i
866866 −22.4786 11.3608i −0.763852 0.386057i
867867 66.9037i 2.27217i
868868 26.4985 19.5186i 0.899417 0.662506i
869869 18.0000 0.610608
870870 7.83492 15.5022i 0.265629 0.525573i
871871 −7.65603 −0.259415
872872 −5.00175 29.6894i −0.169381 1.00541i
873873 14.0957i 0.477067i
874874 −18.1865 + 0.198249i −0.615168 + 0.00670589i
875875 2.68161i 0.0906551i
876876 −36.5826 + 26.9466i −1.23601 + 0.910440i
877877 15.0426 0.507954 0.253977 0.967210i 0.418261π-0.418261\pi
0.253977 + 0.967210i 0.418261π0.418261\pi
878878 18.9017 + 9.55309i 0.637903 + 0.322401i
879879 58.4548 1.97163
880880 18.6856 + 5.80189i 0.629891 + 0.195582i
881881 18.6951i 0.629854i −0.949116 0.314927i 0.898020π-0.898020\pi
0.949116 0.314927i 0.101980π-0.101980\pi
882882 0.639967 1.26624i 0.0215488 0.0426365i
883883 0.220695i 0.00742699i 0.999993 + 0.00371350i 0.00118205π0.00118205\pi
−0.999993 + 0.00371350i 0.998818π0.998818\pi
884884 7.43704 5.47809i 0.250135 0.184248i
885885 5.39889i 0.181482i
886886 17.6807 + 8.93595i 0.593994 + 0.300209i
887887 36.1252i 1.21297i 0.795096 + 0.606483i 0.207420π0.207420\pi
−0.795096 + 0.606483i 0.792580π0.792580\pi
888888 31.0484 5.23070i 1.04192 0.175531i
889889 8.18838i 0.274630i
890890 5.18277 10.2546i 0.173727 0.343736i
891891 −13.7969 −0.462213
892892 2.38210 1.75465i 0.0797587 0.0587499i
893893 26.3047i 0.880254i
894894 26.4306 52.2956i 0.883973 1.74903i
895895 −3.09691 −0.103518
896896 4.05809 30.0664i 0.135571 1.00445i
897897 8.89578 4.61841i 0.297021 0.154204i
898898 18.1085 35.8294i 0.604288 1.19564i
899899 26.2384i 0.875099i
900900 −6.22853 8.45583i −0.207618 0.281861i
901901 70.8164 2.35924
902902 −25.1860 + 49.8330i −0.838602 + 1.65926i
903903 85.7478i 2.85351i
904904 2.54394 + 15.1003i 0.0846100 + 0.502228i
905905 −10.7610 −0.357708
906906 24.3856 48.2493i 0.810157 1.60298i
907907 17.3062 0.574642 0.287321 0.957834i 0.407235π-0.407235\pi
0.287321 + 0.957834i 0.407235π0.407235\pi
908908 −2.61027 3.54369i −0.0866248 0.117602i
909909 −8.07930 −0.267974
910910 2.46264 + 1.24464i 0.0816357 + 0.0412593i
911911 36.3949 1.20582 0.602909 0.797810i 0.294008π-0.294008\pi
0.602909 + 0.797810i 0.294008π0.294008\pi
912912 29.4256 + 9.13667i 0.974378 + 0.302545i
913913 −23.2524 −0.769541
914914 44.9829 + 22.7347i 1.48790 + 0.751998i
915915 19.9164i 0.658417i
916916 −28.0418 + 20.6554i −0.926526 + 0.682475i
917917 8.30471i 0.274246i
918918 26.1826 51.8049i 0.864155 1.70982i
919919 11.5400 0.380668 0.190334 0.981719i 0.439043π-0.439043\pi
0.190334 + 0.981719i 0.439043π0.439043\pi
920920 −10.8333 + 8.16337i −0.357162 + 0.269138i
921921 −94.5733 −3.11630
922922 0.697148 1.37938i 0.0229594 0.0454274i
923923 5.27406i 0.173598i
924924 −60.6725 + 44.6911i −1.99598 + 1.47023i
925925 3.87539i 0.127422i
926926 25.7187 + 12.9984i 0.845169 + 0.427155i
927927 95.1084 3.12377
928928 17.3810 + 16.8210i 0.570558 + 0.552177i
929929 14.6414 0.480368 0.240184 0.970727i 0.422792π-0.422792\pi
0.240184 + 0.970727i 0.422792π0.422792\pi
930930 22.2480 + 11.2443i 0.729540 + 0.368715i
931931 0.512325 0.0167908
932932 31.7804 + 43.1450i 1.04100 + 1.41326i
933933 90.9645 2.97804
934934 19.6653 38.9098i 0.643468 1.27317i
935935 31.0484 1.01539
936936 −10.6562 + 1.79525i −0.348310 + 0.0586796i
937937 10.9207i 0.356762i −0.983961 0.178381i 0.942914π-0.942914\pi
0.983961 0.178381i 0.0570860π-0.0570860\pi
938938 −18.0000 + 35.6148i −0.587721 + 1.16286i
939939 17.0217 0.555481
940940 11.6352 + 15.7959i 0.379498 + 0.515206i
941941 24.4113i 0.795786i −0.917432 0.397893i 0.869741π-0.869741\pi
0.917432 0.397893i 0.130259π-0.130259\pi
942942 −6.71238 + 13.2811i −0.218701 + 0.432722i
943943 −17.8368 34.3564i −0.580846 1.11880i
944944 −7.17996 2.22938i −0.233688 0.0725603i
945945 17.3398 0.564063
946946 −34.7347 + 68.7261i −1.12932 + 2.23448i
947947 11.9194i 0.387327i 0.981068 + 0.193664i 0.0620371π0.0620371\pi
−0.981068 + 0.193664i 0.937963π0.937963\pi
948948 17.0217 12.5381i 0.552838 0.407218i
949949 5.75438 0.186795
950950 1.71063 3.38465i 0.0555001 0.109813i
951951 41.0990i 1.33273i
952952 −7.99817 47.4755i −0.259222 1.53869i
953953 56.4533i 1.82870i 0.404923 + 0.914351i 0.367298π0.367298\pi
−0.404923 + 0.914351i 0.632702π0.632702\pi
954954 −73.9425 37.3712i −2.39398 1.20994i
955955 4.75372i 0.153827i
956956 37.9815 27.9770i 1.22841 0.904840i
957957 60.0770i 1.94201i
958958 9.29429 18.3897i 0.300285 0.594143i
959959 15.8907i 0.513137i
960960 21.7113 7.52908i 0.700731 0.243000i
961961 −6.65605 −0.214711
962962 −3.55894 1.79872i −0.114745 0.0579929i
963963 −58.4548 −1.88368
964964 0.341687 0.251685i 0.0110050 0.00810624i
965965 21.3640i 0.687732i
966966 −0.569466 52.2402i −0.0183223 1.68080i
967967 23.1460i 0.744324i 0.928168 + 0.372162i 0.121383π0.121383\pi
−0.928168 + 0.372162i 0.878617π0.878617\pi
968968 36.0516 6.07360i 1.15874 0.195213i
969969 48.8942 1.57071
970970 1.71237 3.38809i 0.0549809 0.108785i
971971 −9.18083 −0.294627 −0.147313 0.989090i 0.547063π-0.547063\pi
−0.147313 + 0.989090i 0.547063π0.547063\pi
972972 18.1905 13.3990i 0.583460 0.429774i
973973 8.91556i 0.285820i
974974 −2.75625 1.39303i −0.0883161 0.0446356i
975975 2.08998i 0.0669330i
976976 26.4868 + 8.22417i 0.847822 + 0.263249i
977977 56.3849i 1.80391i 0.431827 + 0.901956i 0.357869π0.357869\pi
−0.431827 + 0.901956i 0.642131π0.642131\pi
978978 −30.5254 + 60.3975i −0.976095 + 1.93130i
979979 39.7407i 1.27012i
980980 0.307650 0.226613i 0.00982750 0.00723889i
981981 55.8962i 1.78463i
982982 9.53654 + 4.81984i 0.304323 + 0.153807i
983983 −22.0549 −0.703441 −0.351721 0.936105i 0.614403π-0.614403\pi
−0.351721 + 0.936105i 0.614403π0.614403\pi
984984 10.8946 + 64.6680i 0.347307 + 2.06154i
985985 20.4988i 0.653145i
986986 34.2565 + 17.3135i 1.09095 + 0.551374i
987987 −75.5595 −2.40509
988988 −2.31430 3.14189i −0.0736276 0.0999567i
989989 −24.5992 47.3819i −0.782210 1.50666i
990990 −32.4190 16.3848i −1.03034 0.520744i
991991 14.4702i 0.459661i 0.973231 + 0.229830i 0.0738171π0.0738171\pi
−0.973231 + 0.229830i 0.926183π0.926183\pi
992992 −24.1407 + 24.9443i −0.766468 + 0.791984i
993993 43.5550 1.38218
994994 −24.5342 12.3998i −0.778177 0.393297i
995995 15.2762i 0.484287i
996996 −21.9885 + 16.1967i −0.696734 + 0.513211i
997997 −33.2358 −1.05259 −0.526294 0.850303i 0.676419π-0.676419\pi
−0.526294 + 0.850303i 0.676419π0.676419\pi
998998 −12.6316 6.38414i −0.399848 0.202086i
999999 −25.0590 −0.792831
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 460.2.e.a.91.8 yes 16
4.3 odd 2 inner 460.2.e.a.91.6 yes 16
23.22 odd 2 inner 460.2.e.a.91.7 yes 16
92.91 even 2 inner 460.2.e.a.91.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.e.a.91.5 16 92.91 even 2 inner
460.2.e.a.91.6 yes 16 4.3 odd 2 inner
460.2.e.a.91.7 yes 16 23.22 odd 2 inner
460.2.e.a.91.8 yes 16 1.1 even 1 trivial