Properties

Label 48.3.l.a.43.3
Level 4848
Weight 33
Character 48.43
Analytic conductor 1.3081.308
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,3,Mod(19,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 48=243 48 = 2^{4} \cdot 3
Weight: k k == 3 3
Character orbit: [χ][\chi] == 48.l (of order 44, 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: 1.307905268931.30790526893
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(i)\Q(i)
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x166x144x13+10x12+56x11+88x10128x9496x8512x7++65536 x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 29 2^{9}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 43.3
Root 1.780120.911682i1.78012 - 0.911682i of defining polynomial
Character χ\chi == 48.43
Dual form 48.3.l.a.19.3

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+(1.780120.911682i)q2+(1.22474+1.22474i)q3+(2.33767+3.24581i)q4+(1.00772+1.00772i)q5+(1.063623.29677i)q6+10.0236q7+(1.202207.90915i)q8+3.00000iq9+(0.8751462.71259i)q10+(2.265172.26517i)q11+(1.11224+6.83834i)q12+(6.88229+6.88229i)q13+(17.84329.13830i)q14+2.46840iq15+(5.07058+15.1753i)q1622.3801q17+(2.735055.34037i)q18+(16.891816.8918i)q19+(0.915151+5.62660i)q20+(12.2763+12.2763i)q21+(6.09740+1.96717i)q22+33.2007q23+(8.2143111.1591i)q2422.9690iq25+(18.52585.97686i)q26+(3.67423+3.67423i)q27+(23.4318+32.5346i)q28+(24.6412+24.6412i)q29+(2.250404.39406i)q3041.3761iq31+(22.861322.3911i)q32+5.54852q33+(39.8394+20.4036i)q34+(10.1010+10.1010i)q35+(9.73743+7.01302i)q36+(6.600316.60031i)q37+(14.6695+45.4693i)q3816.8581q39+(6.758759.18170i)q4047.1477iq41+(10.661233.0454i)q42+(48.8218+48.8218i)q43+(12.6475+2.05709i)q44+(3.02316+3.02316i)q45+(59.101330.2685i)q46+45.6048iq47+(24.7960+12.3757i)q48+51.4717q49+(20.9404+40.8876i)q50+(27.410027.4100i)q51+(38.42716.25007i)q52+(25.1401+25.1401i)q53+(9.890323.19085i)q54+4.56532q55+(12.050379.2779i)q5641.3762iq57+(66.329221.3994i)q58+(6.239746.23974i)q59+(8.01197+5.77032i)q60+(35.951335.9513i)q61+(37.7219+73.6546i)q62+30.0707iq63+(61.1095+19.0167i)q6413.8709q65+(9.877045.05848i)q66+(10.2045+10.2045i)q67+(52.317472.6417i)q68+(40.6624+40.6624i)q69+(8.7720827.1898i)q70+11.9529q71+(23.72753.60659i)q72+111.332iq73+(5.73197+17.7667i)q74+(28.131228.1312i)q75+(15.340194.3149i)q76+(22.705122.7051i)q77+(30.0095+15.3692i)q78+4.46031iq79+(20.4022+10.1827i)q809.00000q81+(42.9837+83.9287i)q82+(10.1751+10.1751i)q83+(11.1486+68.5445i)q84+(22.553022.5530i)q85+(131.41942.3988i)q8660.3583q87+(20.638815.1924i)q8821.9364iq89+(8.137772.62544i)q90+(68.9850+68.9850i)q91+(77.6124+107.763i)q92+(50.675250.6752i)q93+(41.577181.1821i)q9434.0444iq95+(55.4226+0.575837i)q96+107.309q97+(91.626046.9259i)q98+(6.79552+6.79552i)q99+O(q100)q+(-1.78012 - 0.911682i) q^{2} +(1.22474 + 1.22474i) q^{3} +(2.33767 + 3.24581i) q^{4} +(1.00772 + 1.00772i) q^{5} +(-1.06362 - 3.29677i) q^{6} +10.0236 q^{7} +(-1.20220 - 7.90915i) q^{8} +3.00000i q^{9} +(-0.875146 - 2.71259i) q^{10} +(2.26517 - 2.26517i) q^{11} +(-1.11224 + 6.83834i) q^{12} +(-6.88229 + 6.88229i) q^{13} +(-17.8432 - 9.13830i) q^{14} +2.46840i q^{15} +(-5.07058 + 15.1753i) q^{16} -22.3801 q^{17} +(2.73505 - 5.34037i) q^{18} +(-16.8918 - 16.8918i) q^{19} +(-0.915151 + 5.62660i) q^{20} +(12.2763 + 12.2763i) q^{21} +(-6.09740 + 1.96717i) q^{22} +33.2007 q^{23} +(8.21431 - 11.1591i) q^{24} -22.9690i q^{25} +(18.5258 - 5.97686i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(23.4318 + 32.5346i) q^{28} +(-24.6412 + 24.6412i) q^{29} +(2.25040 - 4.39406i) q^{30} -41.3761i q^{31} +(22.8613 - 22.3911i) q^{32} +5.54852 q^{33} +(39.8394 + 20.4036i) q^{34} +(10.1010 + 10.1010i) q^{35} +(-9.73743 + 7.01302i) q^{36} +(-6.60031 - 6.60031i) q^{37} +(14.6695 + 45.4693i) q^{38} -16.8581 q^{39} +(6.75875 - 9.18170i) q^{40} -47.1477i q^{41} +(-10.6612 - 33.0454i) q^{42} +(-48.8218 + 48.8218i) q^{43} +(12.6475 + 2.05709i) q^{44} +(-3.02316 + 3.02316i) q^{45} +(-59.1013 - 30.2685i) q^{46} +45.6048i q^{47} +(-24.7960 + 12.3757i) q^{48} +51.4717 q^{49} +(-20.9404 + 40.8876i) q^{50} +(-27.4100 - 27.4100i) q^{51} +(-38.4271 - 6.25007i) q^{52} +(25.1401 + 25.1401i) q^{53} +(9.89032 - 3.19085i) q^{54} +4.56532 q^{55} +(-12.0503 - 79.2779i) q^{56} -41.3762i q^{57} +(66.3292 - 21.3994i) q^{58} +(6.23974 - 6.23974i) q^{59} +(-8.01197 + 5.77032i) q^{60} +(35.9513 - 35.9513i) q^{61} +(-37.7219 + 73.6546i) q^{62} +30.0707i q^{63} +(-61.1095 + 19.0167i) q^{64} -13.8709 q^{65} +(-9.87704 - 5.05848i) q^{66} +(10.2045 + 10.2045i) q^{67} +(-52.3174 - 72.6417i) q^{68} +(40.6624 + 40.6624i) q^{69} +(-8.77208 - 27.1898i) q^{70} +11.9529 q^{71} +(23.7275 - 3.60659i) q^{72} +111.332i q^{73} +(5.73197 + 17.7667i) q^{74} +(28.1312 - 28.1312i) q^{75} +(15.3401 - 94.3149i) q^{76} +(22.7051 - 22.7051i) q^{77} +(30.0095 + 15.3692i) q^{78} +4.46031i q^{79} +(-20.4022 + 10.1827i) q^{80} -9.00000 q^{81} +(-42.9837 + 83.9287i) q^{82} +(10.1751 + 10.1751i) q^{83} +(-11.1486 + 68.5445i) q^{84} +(-22.5530 - 22.5530i) q^{85} +(131.419 - 42.3988i) q^{86} -60.3583 q^{87} +(-20.6388 - 15.1924i) q^{88} -21.9364i q^{89} +(8.13777 - 2.62544i) q^{90} +(-68.9850 + 68.9850i) q^{91} +(77.6124 + 107.763i) q^{92} +(50.6752 - 50.6752i) q^{93} +(41.5771 - 81.1821i) q^{94} -34.0444i q^{95} +(55.4226 + 0.575837i) q^{96} +107.309 q^{97} +(-91.6260 - 46.9259i) q^{98} +(6.79552 + 6.79552i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+12q412q856q10+32q1124q1244q14+32q16+12q1832q19+80q20+32q22128q23+36q24100q26120q28+32q29+72q30++96q99+O(q100) 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30}+ \cdots + 96 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/48Z)×\left(\mathbb{Z}/48\mathbb{Z}\right)^\times.

nn 1717 3131 3737
χ(n)\chi(n) 11 1-1 e(14)e\left(\frac{1}{4}\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 −1.78012 0.911682i −0.890061 0.455841i
33 1.22474 + 1.22474i 0.408248 + 0.408248i
44 2.33767 + 3.24581i 0.584418 + 0.811453i
55 1.00772 + 1.00772i 0.201544 + 0.201544i 0.800661 0.599117i 0.204482π-0.204482\pi
−0.599117 + 0.800661i 0.704482π0.704482\pi
66 −1.06362 3.29677i −0.177270 0.549462i
77 10.0236 1.43194 0.715969 0.698133i 0.245985π-0.245985\pi
0.715969 + 0.698133i 0.245985π0.245985\pi
88 −1.20220 7.90915i −0.150274 0.988644i
99 3.00000i 0.333333i
1010 −0.875146 2.71259i −0.0875146 0.271259i
1111 2.26517 2.26517i 0.205925 0.205925i −0.596608 0.802533i 0.703485π-0.703485\pi
0.802533 + 0.596608i 0.203485π0.203485\pi
1212 −1.11224 + 6.83834i −0.0926865 + 0.569862i
1313 −6.88229 + 6.88229i −0.529407 + 0.529407i −0.920395 0.390989i 0.872133π-0.872133\pi
0.390989 + 0.920395i 0.372133π0.372133\pi
1414 −17.8432 9.13830i −1.27451 0.652736i
1515 2.46840i 0.164560i
1616 −5.07058 + 15.1753i −0.316911 + 0.948455i
1717 −22.3801 −1.31648 −0.658240 0.752809i 0.728699π-0.728699\pi
−0.658240 + 0.752809i 0.728699π0.728699\pi
1818 2.73505 5.34037i 0.151947 0.296687i
1919 −16.8918 16.8918i −0.889041 0.889041i 0.105390 0.994431i 0.466391π-0.466391\pi
−0.994431 + 0.105390i 0.966391π0.966391\pi
2020 −0.915151 + 5.62660i −0.0457575 + 0.281330i
2121 12.2763 + 12.2763i 0.584586 + 0.584586i
2222 −6.09740 + 1.96717i −0.277155 + 0.0894167i
2323 33.2007 1.44351 0.721755 0.692149i 0.243336π-0.243336\pi
0.721755 + 0.692149i 0.243336π0.243336\pi
2424 8.21431 11.1591i 0.342263 0.464962i
2525 22.9690i 0.918760i
2626 18.5258 5.97686i 0.712530 0.229879i
2727 −3.67423 + 3.67423i −0.136083 + 0.136083i
2828 23.4318 + 32.5346i 0.836850 + 1.16195i
2929 −24.6412 + 24.6412i −0.849696 + 0.849696i −0.990095 0.140399i 0.955161π-0.955161\pi
0.140399 + 0.990095i 0.455161π0.455161\pi
3030 2.25040 4.39406i 0.0750133 0.146469i
3131 41.3761i 1.33471i −0.744738 0.667357i 0.767426π-0.767426\pi
0.744738 0.667357i 0.232574π-0.232574\pi
3232 22.8613 22.3911i 0.714415 0.699722i
3333 5.54852 0.168137
3434 39.8394 + 20.4036i 1.17175 + 0.600105i
3535 10.1010 + 10.1010i 0.288599 + 0.288599i
3636 −9.73743 + 7.01302i −0.270484 + 0.194806i
3737 −6.60031 6.60031i −0.178387 0.178387i 0.612266 0.790652i 0.290258π-0.290258\pi
−0.790652 + 0.612266i 0.790258π0.790258\pi
3838 14.6695 + 45.4693i 0.386039 + 1.19656i
3939 −16.8581 −0.432259
4040 6.75875 9.18170i 0.168969 0.229543i
4141 47.1477i 1.14994i −0.818173 0.574972i 0.805013π-0.805013\pi
0.818173 0.574972i 0.194987π-0.194987\pi
4242 −10.6612 33.0454i −0.253839 0.786795i
4343 −48.8218 + 48.8218i −1.13539 + 1.13539i −0.146124 + 0.989266i 0.546680π0.546680\pi
−0.989266 + 0.146124i 0.953320π0.953320\pi
4444 12.6475 + 2.05709i 0.287444 + 0.0467521i
4545 −3.02316 + 3.02316i −0.0671814 + 0.0671814i
4646 −59.1013 30.2685i −1.28481 0.658011i
4747 45.6048i 0.970315i 0.874427 + 0.485157i 0.161238π0.161238\pi
−0.874427 + 0.485157i 0.838762π0.838762\pi
4848 −24.7960 + 12.3757i −0.516584 + 0.257827i
4949 51.4717 1.05044
5050 −20.9404 + 40.8876i −0.418808 + 0.817752i
5151 −27.4100 27.4100i −0.537450 0.537450i
5252 −38.4271 6.25007i −0.738983 0.120194i
5353 25.1401 + 25.1401i 0.474341 + 0.474341i 0.903316 0.428975i 0.141125π-0.141125\pi
−0.428975 + 0.903316i 0.641125π0.641125\pi
5454 9.89032 3.19085i 0.183154 0.0590899i
5555 4.56532 0.0830059
5656 −12.0503 79.2779i −0.215184 1.41568i
5757 41.3762i 0.725899i
5858 66.3292 21.3994i 1.14361 0.368955i
5959 6.23974 6.23974i 0.105758 0.105758i −0.652248 0.758006i 0.726174π-0.726174\pi
0.758006 + 0.652248i 0.226174π0.226174\pi
6060 −8.01197 + 5.77032i −0.133533 + 0.0961720i
6161 35.9513 35.9513i 0.589366 0.589366i −0.348093 0.937460i 0.613171π-0.613171\pi
0.937460 + 0.348093i 0.113171π0.113171\pi
6262 −37.7219 + 73.6546i −0.608417 + 1.18798i
6363 30.0707i 0.477312i
6464 −61.1095 + 19.0167i −0.954835 + 0.297136i
6565 −13.8709 −0.213398
6666 −9.87704 5.05848i −0.149652 0.0766437i
6767 10.2045 + 10.2045i 0.152307 + 0.152307i 0.779147 0.626841i 0.215652π-0.215652\pi
−0.626841 + 0.779147i 0.715652π0.715652\pi
6868 −52.3174 72.6417i −0.769374 1.06826i
6969 40.6624 + 40.6624i 0.589310 + 0.589310i
7070 −8.77208 27.1898i −0.125315 0.388426i
7171 11.9529 0.168350 0.0841752 0.996451i 0.473174π-0.473174\pi
0.0841752 + 0.996451i 0.473174π0.473174\pi
7272 23.7275 3.60659i 0.329548 0.0500915i
7373 111.332i 1.52510i 0.646929 + 0.762550i 0.276053π0.276053\pi
−0.646929 + 0.762550i 0.723947π0.723947\pi
7474 5.73197 + 17.7667i 0.0774591 + 0.240091i
7575 28.1312 28.1312i 0.375082 0.375082i
7676 15.3401 94.3149i 0.201843 1.24099i
7777 22.7051 22.7051i 0.294871 0.294871i
7878 30.0095 + 15.3692i 0.384737 + 0.197041i
7979 4.46031i 0.0564596i 0.999601 + 0.0282298i 0.00898702π0.00898702\pi
−0.999601 + 0.0282298i 0.991013π0.991013\pi
8080 −20.4022 + 10.1827i −0.255027 + 0.127284i
8181 −9.00000 −0.111111
8282 −42.9837 + 83.9287i −0.524192 + 1.02352i
8383 10.1751 + 10.1751i 0.122592 + 0.122592i 0.765741 0.643149i 0.222373π-0.222373\pi
−0.643149 + 0.765741i 0.722373π0.722373\pi
8484 −11.1486 + 68.5445i −0.132721 + 0.816006i
8585 −22.5530 22.5530i −0.265329 0.265329i
8686 131.419 42.3988i 1.52812 0.493010i
8787 −60.3583 −0.693774
8888 −20.6388 15.1924i −0.234532 0.172641i
8989 21.9364i 0.246476i −0.992377 0.123238i 0.960672π-0.960672\pi
0.992377 0.123238i 0.0393279π-0.0393279\pi
9090 8.13777 2.62544i 0.0904196 0.0291715i
9191 −68.9850 + 68.9850i −0.758077 + 0.758077i
9292 77.6124 + 107.763i 0.843613 + 1.17134i
9393 50.6752 50.6752i 0.544895 0.544895i
9494 41.5771 81.1821i 0.442309 0.863640i
9595 34.0444i 0.358362i
9696 55.4226 + 0.575837i 0.577319 + 0.00599830i
9797 107.309 1.10628 0.553140 0.833088i 0.313429π-0.313429\pi
0.553140 + 0.833088i 0.313429π0.313429\pi
9898 −91.6260 46.9259i −0.934959 0.478835i
9999 6.79552 + 6.79552i 0.0686416 + 0.0686416i
100100 74.5530 53.6940i 0.745530 0.536940i
101101 −100.780 100.780i −0.997824 0.997824i 0.00217389 0.999998i 0.499308π-0.499308\pi
−0.999998 + 0.00217389i 0.999308π0.999308\pi
102102 23.8039 + 73.7823i 0.233372 + 0.723356i
103103 58.0562 0.563653 0.281826 0.959465i 0.409060π-0.409060\pi
0.281826 + 0.959465i 0.409060π0.409060\pi
104104 62.7069 + 46.1592i 0.602951 + 0.443839i
105105 24.7422i 0.235640i
106106 −21.8327 67.6722i −0.205968 0.638417i
107107 112.747 112.747i 1.05371 1.05371i 0.0552381 0.998473i 0.482408π-0.482408\pi
0.998473 0.0552381i 0.0175918π-0.0175918\pi
108108 −20.5150 3.33671i −0.189954 0.0308955i
109109 −81.1384 + 81.1384i −0.744389 + 0.744389i −0.973419 0.229030i 0.926445π-0.926445\pi
0.229030 + 0.973419i 0.426445π0.426445\pi
110110 −8.12684 4.16212i −0.0738803 0.0378375i
111111 16.1674i 0.145652i
112112 −50.8252 + 152.110i −0.453797 + 1.35813i
113113 −171.844 −1.52074 −0.760371 0.649489i 0.774983π-0.774983\pi
−0.760371 + 0.649489i 0.774983π0.774983\pi
114114 −37.7219 + 73.6547i −0.330894 + 0.646094i
115115 33.4571 + 33.4571i 0.290931 + 0.290931i
116116 −137.584 22.3776i −1.18607 0.192910i
117117 −20.6469 20.6469i −0.176469 0.176469i
118118 −16.7962 + 5.41884i −0.142340 + 0.0459224i
119119 −224.329 −1.88512
120120 19.5230 2.96750i 0.162692 0.0247292i
121121 110.738i 0.915190i
122122 −96.7740 + 31.2216i −0.793230 + 0.255915i
123123 57.7439 57.7439i 0.469463 0.469463i
124124 134.299 96.7238i 1.08306 0.780031i
125125 48.3394 48.3394i 0.386715 0.386715i
126126 27.4149 53.5295i 0.217579 0.424837i
127127 36.8333i 0.290026i −0.989430 0.145013i 0.953678π-0.953678\pi
0.989430 0.145013i 0.0463224π-0.0463224\pi
128128 126.119 + 21.8603i 0.985309 + 0.170784i
129129 −119.588 −0.927042
130130 24.6918 + 12.6458i 0.189937 + 0.0972754i
131131 −12.3686 12.3686i −0.0944170 0.0944170i 0.658321 0.752738i 0.271267π-0.271267\pi
−0.752738 + 0.658321i 0.771267π0.771267\pi
132132 12.9706 + 18.0094i 0.0982622 + 0.136435i
133133 −169.316 169.316i −1.27305 1.27305i
134134 −8.86204 27.4686i −0.0661347 0.204990i
135135 −7.40521 −0.0548534
136136 26.9053 + 177.008i 0.197833 + 1.30153i
137137 145.679i 1.06335i 0.846949 + 0.531674i 0.178437π0.178437\pi
−0.846949 + 0.531674i 0.821563π0.821563\pi
138138 −35.3129 109.455i −0.255890 0.793154i
139139 82.5709 82.5709i 0.594035 0.594035i −0.344684 0.938719i 0.612014π-0.612014\pi
0.938719 + 0.344684i 0.112014π0.112014\pi
140140 −9.17307 + 56.3985i −0.0655219 + 0.402847i
141141 −55.8542 + 55.8542i −0.396129 + 0.396129i
142142 −21.2776 10.8972i −0.149842 0.0767410i
143143 31.1791i 0.218036i
144144 −45.5259 15.2117i −0.316152 0.105637i
145145 −49.6629 −0.342503
146146 101.500 198.185i 0.695203 1.35743i
147147 63.0398 + 63.0398i 0.428842 + 0.428842i
148148 5.99399 36.8527i 0.0405000 0.249005i
149149 196.248 + 196.248i 1.31710 + 1.31710i 0.916059 + 0.401043i 0.131352π0.131352\pi
0.401043 + 0.916059i 0.368648π0.368648\pi
150150 −75.7236 + 24.4302i −0.504824 + 0.162868i
151151 64.5007 0.427157 0.213578 0.976926i 0.431488π-0.431488\pi
0.213578 + 0.976926i 0.431488π0.431488\pi
152152 −113.292 + 153.907i −0.745345 + 1.01254i
153153 67.1404i 0.438826i
154154 −61.1177 + 19.7180i −0.396868 + 0.128039i
155155 41.6956 41.6956i 0.269004 0.269004i
156156 −39.4087 54.7182i −0.252620 0.350758i
157157 54.4202 54.4202i 0.346625 0.346625i −0.512226 0.858851i 0.671179π-0.671179\pi
0.858851 + 0.512226i 0.171179π0.171179\pi
158158 4.06638 7.93990i 0.0257366 0.0502525i
159159 61.5803i 0.387298i
160160 45.6018 + 0.473799i 0.285011 + 0.00296124i
161161 332.789 2.06701
162162 16.0211 + 8.20514i 0.0988957 + 0.0506490i
163163 104.803 + 104.803i 0.642961 + 0.642961i 0.951282 0.308321i 0.0997671π-0.0997671\pi
−0.308321 + 0.951282i 0.599767π0.599767\pi
164164 153.033 110.216i 0.933126 0.672048i
165165 5.59136 + 5.59136i 0.0338870 + 0.0338870i
166166 −8.83647 27.3894i −0.0532317 0.164996i
167167 53.3110 0.319228 0.159614 0.987180i 0.448975π-0.448975\pi
0.159614 + 0.987180i 0.448975π0.448975\pi
168168 82.3367 111.854i 0.490099 0.665796i
169169 74.2683i 0.439457i
170170 19.5859 + 60.7081i 0.115211 + 0.357107i
171171 50.6753 50.6753i 0.296347 0.296347i
172172 −272.596 44.3370i −1.58486 0.257773i
173173 −41.5780 + 41.5780i −0.240335 + 0.240335i −0.816989 0.576654i 0.804358π-0.804358\pi
0.576654 + 0.816989i 0.304358π0.304358\pi
174174 107.445 + 55.0276i 0.617501 + 0.316251i
175175 230.231i 1.31561i
176176 22.8889 + 45.8604i 0.130051 + 0.260570i
177177 15.2842 0.0863513
178178 −19.9990 + 39.0495i −0.112354 + 0.219379i
179179 53.0709 + 53.0709i 0.296486 + 0.296486i 0.839636 0.543150i 0.182769π-0.182769\pi
−0.543150 + 0.839636i 0.682769π0.682769\pi
180180 −16.8798 2.74545i −0.0937766 0.0152525i
181181 −66.6042 66.6042i −0.367979 0.367979i 0.498761 0.866740i 0.333789π-0.333789\pi
−0.866740 + 0.498761i 0.833789π0.833789\pi
182182 185.694 59.9094i 1.02030 0.329172i
183183 88.0625 0.481216
184184 −39.9138 262.590i −0.216923 1.42712i
185185 13.3025i 0.0719056i
186186 −136.408 + 44.0084i −0.733375 + 0.236604i
187187 −50.6949 + 50.6949i −0.271096 + 0.271096i
188188 −148.025 + 106.609i −0.787365 + 0.567070i
189189 −36.8289 + 36.8289i −0.194862 + 0.194862i
190190 −31.0377 + 60.6032i −0.163356 + 0.318964i
191191 113.753i 0.595567i 0.954633 + 0.297784i 0.0962474π0.0962474\pi
−0.954633 + 0.297784i 0.903753π0.903753\pi
192192 −98.1341 51.5529i −0.511115 0.268505i
193193 −26.5596 −0.137615 −0.0688073 0.997630i 0.521919π-0.521919\pi
−0.0688073 + 0.997630i 0.521919π0.521919\pi
194194 −191.023 97.8318i −0.984657 0.504288i
195195 −16.9883 16.9883i −0.0871193 0.0871193i
196196 120.324 + 167.068i 0.613898 + 0.852386i
197197 51.8935 + 51.8935i 0.263419 + 0.263419i 0.826442 0.563023i 0.190362π-0.190362\pi
−0.563023 + 0.826442i 0.690362π0.690362\pi
198198 −5.90150 18.2922i −0.0298056 0.0923848i
199199 −136.741 −0.687140 −0.343570 0.939127i 0.611636π-0.611636\pi
−0.343570 + 0.939127i 0.611636π0.611636\pi
200200 −181.665 + 27.6132i −0.908327 + 0.138066i
201201 24.9959i 0.124358i
202202 87.5216 + 271.281i 0.433275 + 1.34297i
203203 −246.992 + 246.992i −1.21671 + 1.21671i
204204 24.8921 153.043i 0.122020 0.750211i
205205 47.5118 47.5118i 0.231765 0.231765i
206206 −103.347 52.9288i −0.501686 0.256936i
207207 99.6022i 0.481170i
208208 −69.5435 139.338i −0.334344 0.669893i
209209 −76.5255 −0.366151
210210 22.5570 44.0441i 0.107414 0.209734i
211211 −141.171 141.171i −0.669057 0.669057i 0.288441 0.957498i 0.406863π-0.406863\pi
−0.957498 + 0.288441i 0.906863π0.906863\pi
212212 −22.8307 + 140.369i −0.107692 + 0.662119i
213213 14.6392 + 14.6392i 0.0687288 + 0.0687288i
214214 −303.493 + 97.9142i −1.41819 + 0.457543i
215215 −98.3975 −0.457663
216216 33.4772 + 24.6429i 0.154987 + 0.114088i
217217 414.736i 1.91123i
218218 218.409 70.4639i 1.00188 0.323229i
219219 −136.354 + 136.354i −0.622620 + 0.622620i
220220 10.6722 + 14.8182i 0.0485101 + 0.0673554i
221221 154.027 154.027i 0.696953 0.696953i
222222 −14.7395 + 28.7799i −0.0663942 + 0.129639i
223223 122.607i 0.549806i 0.961472 + 0.274903i 0.0886457π0.0886457\pi
−0.961472 + 0.274903i 0.911354π0.911354\pi
224224 229.151 224.439i 1.02300 1.00196i
225225 68.9070 0.306253
226226 305.903 + 156.667i 1.35355 + 0.693216i
227227 −295.844 295.844i −1.30328 1.30328i −0.926168 0.377112i 0.876917π-0.876917\pi
−0.377112 0.926168i 0.623083π-0.623083\pi
228228 134.299 96.7240i 0.589032 0.424228i
229229 73.3817 + 73.3817i 0.320444 + 0.320444i 0.848937 0.528493i 0.177243π-0.177243\pi
−0.528493 + 0.848937i 0.677243π0.677243\pi
230230 −29.0555 90.0599i −0.126328 0.391565i
231231 55.6159 0.240761
232232 224.514 + 165.267i 0.967735 + 0.712359i
233233 156.229i 0.670509i −0.942128 0.335255i 0.891178π-0.891178\pi
0.942128 0.335255i 0.108822π-0.108822\pi
234234 17.9306 + 55.5773i 0.0766264 + 0.237510i
235235 −45.9569 + 45.9569i −0.195561 + 0.195561i
236236 34.8395 + 5.66655i 0.147625 + 0.0240108i
237237 −5.46274 + 5.46274i −0.0230495 + 0.0230495i
238238 399.333 + 204.516i 1.67787 + 0.859313i
239239 13.1716i 0.0551113i 0.999620 + 0.0275557i 0.00877235π0.00877235\pi
−0.999620 + 0.0275557i 0.991228π0.991228\pi
240240 −37.4587 12.5162i −0.156078 0.0521510i
241241 −189.519 −0.786386 −0.393193 0.919456i 0.628630π-0.628630\pi
−0.393193 + 0.919456i 0.628630π0.628630\pi
242242 100.958 197.127i 0.417181 0.814575i
243243 −11.0227 11.0227i −0.0453609 0.0453609i
244244 200.734 + 32.6488i 0.822679 + 0.133807i
245245 51.8692 + 51.8692i 0.211711 + 0.211711i
246246 −155.435 + 50.1472i −0.631851 + 0.203850i
247247 232.508 0.941328
248248 −327.250 + 49.7422i −1.31956 + 0.200573i
249249 24.9238i 0.100096i
250250 −130.120 + 41.9799i −0.520481 + 0.167920i
251251 −27.4434 + 27.4434i −0.109336 + 0.109336i −0.759658 0.650322i 0.774634π-0.774634\pi
0.650322 + 0.759658i 0.274634π0.274634\pi
252252 −97.6037 + 70.2954i −0.387316 + 0.278950i
253253 75.2053 75.2053i 0.297254 0.297254i
254254 −33.5802 + 65.5678i −0.132206 + 0.258141i
255255 55.2432i 0.216640i
256256 −204.578 153.895i −0.799135 0.601152i
257257 135.375 0.526752 0.263376 0.964693i 0.415164π-0.415164\pi
0.263376 + 0.964693i 0.415164π0.415164\pi
258258 212.882 + 109.027i 0.825125 + 0.422584i
259259 −66.1586 66.1586i −0.255438 0.255438i
260260 −32.4255 45.0222i −0.124714 0.173162i
261261 −73.9236 73.9236i −0.283232 0.283232i
262262 10.7414 + 33.2939i 0.0409978 + 0.127076i
263263 31.6123 0.120199 0.0600994 0.998192i 0.480858π-0.480858\pi
0.0600994 + 0.998192i 0.480858π0.480858\pi
264264 −6.67040 43.8841i −0.0252667 0.166228i
265265 50.6684i 0.191201i
266266 147.041 + 455.765i 0.552784 + 1.71340i
267267 26.8665 26.8665i 0.100624 0.100624i
268268 −9.26715 + 56.9769i −0.0345789 + 0.212600i
269269 −194.213 + 194.213i −0.721981 + 0.721981i −0.969008 0.247028i 0.920546π-0.920546\pi
0.247028 + 0.969008i 0.420546π0.420546\pi
270270 13.1822 + 6.75120i 0.0488229 + 0.0250044i
271271 291.647i 1.07619i 0.842884 + 0.538095i 0.180856π0.180856\pi
−0.842884 + 0.538095i 0.819144π0.819144\pi
272272 113.480 339.625i 0.417207 1.24862i
273273 −168.978 −0.618967
274274 132.813 259.326i 0.484717 0.946444i
275275 −52.0287 52.0287i −0.189195 0.189195i
276276 −36.9271 + 227.038i −0.133794 + 0.822601i
277277 305.166 + 305.166i 1.10168 + 1.10168i 0.994208 + 0.107475i 0.0342765π0.0342765\pi
0.107475 + 0.994208i 0.465723π0.465723\pi
278278 −222.265 + 71.7079i −0.799513 + 0.257942i
279279 124.128 0.444905
280280 67.7467 92.0333i 0.241952 0.328691i
281281 211.861i 0.753955i −0.926222 0.376978i 0.876963π-0.876963\pi
0.926222 0.376978i 0.123037π-0.123037\pi
282282 150.349 48.5061i 0.533151 0.172007i
283283 105.325 105.325i 0.372175 0.372175i −0.496094 0.868269i 0.665233π-0.665233\pi
0.868269 + 0.496094i 0.165233π0.165233\pi
284284 27.9419 + 38.7968i 0.0983870 + 0.136608i
285285 41.6957 41.6957i 0.146301 0.146301i
286286 28.4254 55.5027i 0.0993897 0.194065i
287287 472.588i 1.64665i
288288 67.1733 + 68.5838i 0.233241 + 0.238138i
289289 211.871 0.733117
290290 88.4060 + 45.2768i 0.304848 + 0.156127i
291291 131.426 + 131.426i 0.451637 + 0.451637i
292292 −361.364 + 260.258i −1.23755 + 0.891296i
293293 −171.289 171.289i −0.584603 0.584603i 0.351562 0.936165i 0.385651π-0.385651\pi
−0.936165 + 0.351562i 0.885651π0.885651\pi
294294 −54.7463 169.691i −0.186212 0.577179i
295295 12.5758 0.0426300
296296 −44.2680 + 60.1377i −0.149554 + 0.203168i
297297 16.6455i 0.0560456i
298298 −170.430 528.262i −0.571912 1.77269i
299299 −228.497 + 228.497i −0.764204 + 0.764204i
300300 157.070 + 25.5470i 0.523566 + 0.0851566i
301301 −489.368 + 489.368i −1.62581 + 1.62581i
302302 −114.819 58.8041i −0.380196 0.194716i
303303 246.860i 0.814720i
304304 341.988 170.686i 1.12496 0.561468i
305305 72.4579 0.237567
306306 −61.2107 + 119.518i −0.200035 + 0.390582i
307307 −27.1124 27.1124i −0.0883140 0.0883140i 0.661570 0.749884i 0.269891π-0.269891\pi
−0.749884 + 0.661570i 0.769891π0.769891\pi
308308 126.773 + 20.6194i 0.411602 + 0.0669460i
309309 71.1041 + 71.1041i 0.230110 + 0.230110i
310310 −112.236 + 36.2102i −0.362053 + 0.116807i
311311 371.124 1.19333 0.596663 0.802492i 0.296493π-0.296493\pi
0.596663 + 0.802492i 0.296493π0.296493\pi
312312 20.2667 + 133.333i 0.0649575 + 0.427350i
313313 374.501i 1.19649i −0.801313 0.598245i 0.795865π-0.795865\pi
0.801313 0.598245i 0.204135π-0.204135\pi
314314 −146.488 + 47.2607i −0.466524 + 0.150512i
315315 −30.3029 + 30.3029i −0.0961996 + 0.0961996i
316316 −14.4773 + 10.4267i −0.0458143 + 0.0329960i
317317 −48.5840 + 48.5840i −0.153262 + 0.153262i −0.779573 0.626311i 0.784564π-0.784564\pi
0.626311 + 0.779573i 0.284564π0.284564\pi
318318 56.1417 109.621i 0.176546 0.344719i
319319 111.633i 0.349947i
320320 −80.7448 42.4178i −0.252328 0.132555i
321321 276.173 0.860352
322322 −592.406 303.398i −1.83977 0.942230i
323323 378.040 + 378.040i 1.17040 + 1.17040i
324324 −21.0391 29.2123i −0.0649353 0.0901614i
325325 158.079 + 158.079i 0.486398 + 0.486398i
326326 −91.0149 282.108i −0.279187 0.865363i
327327 −198.748 −0.607791
328328 −372.899 + 56.6808i −1.13689 + 0.172807i
329329 457.122i 1.38943i
330330 −4.85576 15.0508i −0.0147144 0.0456086i
331331 −1.88883 + 1.88883i −0.00570644 + 0.00570644i −0.709954 0.704248i 0.751284π-0.751284\pi
0.704248 + 0.709954i 0.251284π0.251284\pi
332332 −9.24040 + 56.8125i −0.0278325 + 0.171122i
333333 19.8009 19.8009i 0.0594622 0.0594622i
334334 −94.9001 48.6027i −0.284132 0.145517i
335335 20.5667i 0.0613931i
336336 −248.544 + 124.048i −0.739715 + 0.369192i
337337 −386.980 −1.14831 −0.574154 0.818747i 0.694669π-0.694669\pi
−0.574154 + 0.818747i 0.694669π0.694669\pi
338338 67.7090 132.207i 0.200323 0.391144i
339339 −210.465 210.465i −0.620840 0.620840i
340340 20.4812 125.924i 0.0602388 0.370365i
341341 −93.7240 93.7240i −0.274851 0.274851i
342342 −136.408 + 44.0085i −0.398854 + 0.128680i
343343 24.7757 0.0722325
344344 444.832 + 327.446i 1.29312 + 0.951877i
345345 81.9528i 0.237544i
346346 111.920 36.1080i 0.323468 0.104358i
347347 441.887 441.887i 1.27345 1.27345i 0.329183 0.944266i 0.393227π-0.393227\pi
0.944266 0.329183i 0.106773π-0.106773\pi
348348 −141.098 195.912i −0.405454 0.562965i
349349 119.382 119.382i 0.342068 0.342068i −0.515076 0.857144i 0.672236π-0.672236\pi
0.857144 + 0.515076i 0.172236π0.172236\pi
350350 −209.898 + 409.840i −0.599707 + 1.17097i
351351 50.5743i 0.144086i
352352 1.06501 102.504i 0.00302560 0.291206i
353353 −515.642 −1.46074 −0.730371 0.683050i 0.760653π-0.760653\pi
−0.730371 + 0.683050i 0.760653π0.760653\pi
354354 −27.2077 13.9343i −0.0768580 0.0393625i
355355 12.0452 + 12.0452i 0.0339301 + 0.0339301i
356356 71.2014 51.2801i 0.200004 0.144045i
357357 −274.745 274.745i −0.769595 0.769595i
358358 −46.0890 142.857i −0.128740 0.399041i
359359 428.264 1.19294 0.596468 0.802637i 0.296570π-0.296570\pi
0.596468 + 0.802637i 0.296570π0.296570\pi
360360 27.5451 + 20.2762i 0.0765142 + 0.0563229i
361361 209.664i 0.580786i
362362 57.8418 + 179.286i 0.159784 + 0.495264i
363363 −135.626 + 135.626i −0.373625 + 0.373625i
364364 −385.177 62.6480i −1.05818 0.172110i
365365 −112.192 + 112.192i −0.307375 + 0.307375i
366366 −156.762 80.2850i −0.428311 0.219358i
367367 219.482i 0.598043i 0.954246 + 0.299021i 0.0966602π0.0966602\pi
−0.954246 + 0.299021i 0.903340π0.903340\pi
368368 −168.347 + 503.830i −0.457464 + 1.36910i
369369 141.443 0.383315
370370 −12.1277 + 23.6802i −0.0327775 + 0.0640004i
371371 251.993 + 251.993i 0.679226 + 0.679226i
372372 282.944 + 46.0201i 0.760602 + 0.123710i
373373 425.005 + 425.005i 1.13942 + 1.13942i 0.988554 + 0.150870i 0.0482075π0.0482075\pi
0.150870 + 0.988554i 0.451793π0.451793\pi
374374 136.461 44.0255i 0.364868 0.117715i
375375 118.407 0.315752
376376 360.695 54.8259i 0.959296 0.145814i
377377 339.175i 0.899669i
378378 99.1362 31.9837i 0.262265 0.0846130i
379379 365.916 365.916i 0.965476 0.965476i −0.0339473 0.999424i 0.510808π-0.510808\pi
0.999424 + 0.0339473i 0.0108078π0.0108078\pi
380380 110.502 79.5846i 0.290794 0.209433i
381381 45.1114 45.1114i 0.118403 0.118403i
382382 103.707 202.495i 0.271484 0.530091i
383383 213.276i 0.556857i 0.960457 + 0.278428i 0.0898135π0.0898135\pi
−0.960457 + 0.278428i 0.910187π0.910187\pi
384384 127.691 + 181.238i 0.332528 + 0.471973i
385385 45.7608 0.118859
386386 47.2793 + 24.2139i 0.122485 + 0.0627303i
387387 −146.465 146.465i −0.378464 0.378464i
388388 250.854 + 348.305i 0.646530 + 0.897694i
389389 −210.798 210.798i −0.541898 0.541898i 0.382187 0.924085i 0.375171π-0.375171\pi
−0.924085 + 0.382187i 0.875171π0.875171\pi
390390 14.7533 + 45.7291i 0.0378290 + 0.117254i
391391 −743.037 −1.90035
392392 −61.8791 407.098i −0.157855 1.03852i
393393 30.2968i 0.0770912i
394394 −45.0665 139.687i −0.114382 0.354536i
395395 −4.49475 + 4.49475i −0.0113791 + 0.0113791i
396396 −6.17127 + 37.9426i −0.0155840 + 0.0958148i
397397 392.907 392.907i 0.989690 0.989690i −0.0102579 0.999947i 0.503265π-0.503265\pi
0.999947 + 0.0102579i 0.00326524π0.00326524\pi
398398 243.415 + 124.664i 0.611597 + 0.313226i
399399 414.737i 1.03944i
400400 348.561 + 116.466i 0.871403 + 0.291165i
401401 29.3290 0.0731396 0.0365698 0.999331i 0.488357π-0.488357\pi
0.0365698 + 0.999331i 0.488357π0.488357\pi
402402 22.7883 44.4958i 0.0566874 0.110686i
403403 284.762 + 284.762i 0.706606 + 0.706606i
404404 91.5224 562.705i 0.226541 1.39283i
405405 −9.06949 9.06949i −0.0223938 0.0223938i
406406 664.855 214.498i 1.63757 0.528321i
407407 −29.9017 −0.0734684
408408 −183.838 + 249.742i −0.450582 + 0.612112i
409409 601.115i 1.46972i 0.678219 + 0.734860i 0.262752π0.262752\pi
−0.678219 + 0.734860i 0.737248π0.737248\pi
410410 −127.892 + 41.2612i −0.311933 + 0.100637i
411411 −178.419 + 178.419i −0.434110 + 0.434110i
412412 135.716 + 188.440i 0.329409 + 0.457378i
413413 62.5444 62.5444i 0.151439 0.151439i
414414 90.8055 177.304i 0.219337 0.428271i
415415 20.5073i 0.0494153i
416416 −3.23584 + 311.440i −0.00777845 + 0.748654i
417417 202.257 0.485028
418418 136.225 + 69.7669i 0.325897 + 0.166907i
419419 −518.885 518.885i −1.23839 1.23839i −0.960659 0.277729i 0.910418π-0.910418\pi
−0.277729 0.960659i 0.589582π-0.589582\pi
420420 −80.3085 + 57.8391i −0.191211 + 0.137712i
421421 −411.213 411.213i −0.976754 0.976754i 0.0229817 0.999736i 0.492684π-0.492684\pi
−0.999736 + 0.0229817i 0.992684π0.992684\pi
422422 122.599 + 380.005i 0.290518 + 0.900485i
423423 −136.814 −0.323438
424424 168.613 229.060i 0.397673 0.540236i
425425 514.049i 1.20953i
426426 −12.7133 39.4059i −0.0298434 0.0925022i
427427 360.360 360.360i 0.843936 0.843936i
428428 629.522 + 102.390i 1.47084 + 0.239229i
429429 −38.1865 + 38.1865i −0.0890128 + 0.0890128i
430430 175.160 + 89.7072i 0.407348 + 0.208622i
431431 41.1083i 0.0953789i 0.998862 + 0.0476895i 0.0151858π0.0151858\pi
−0.998862 + 0.0476895i 0.984814π0.984814\pi
432432 −37.1271 74.3880i −0.0859423 0.172195i
433433 −351.682 −0.812199 −0.406100 0.913829i 0.633111π-0.633111\pi
−0.406100 + 0.913829i 0.633111π0.633111\pi
434434 −378.107 + 738.281i −0.871215 + 1.70111i
435435 −60.8244 60.8244i −0.139826 0.139826i
436436 −453.035 73.6850i −1.03907 0.169002i
437437 −560.819 560.819i −1.28334 1.28334i
438438 367.037 118.415i 0.837985 0.270354i
439439 −775.613 −1.76677 −0.883386 0.468646i 0.844742π-0.844742\pi
−0.883386 + 0.468646i 0.844742π0.844742\pi
440440 −5.48841 36.1079i −0.0124737 0.0820633i
441441 154.415i 0.350148i
442442 −414.609 + 133.763i −0.938030 + 0.302631i
443443 −241.372 + 241.372i −0.544858 + 0.544858i −0.924949 0.380091i 0.875893π-0.875893\pi
0.380091 + 0.924949i 0.375893π0.375893\pi
444444 52.4763 37.7940i 0.118190 0.0851217i
445445 22.1058 22.1058i 0.0496759 0.0496759i
446446 111.778 218.255i 0.250624 0.489361i
447447 480.708i 1.07541i
448448 −612.534 + 190.615i −1.36726 + 0.425480i
449449 266.360 0.593228 0.296614 0.954997i 0.404142π-0.404142\pi
0.296614 + 0.954997i 0.404142π0.404142\pi
450450 −122.663 62.8213i −0.272584 0.139603i
451451 −106.798 106.798i −0.236802 0.236802i
452452 −401.714 557.772i −0.888749 1.23401i
453453 78.9969 + 78.9969i 0.174386 + 0.174386i
454454 256.923 + 796.355i 0.565910 + 1.75409i
455455 −139.035 −0.305572
456456 −327.251 + 49.7423i −0.717655 + 0.109084i
457457 515.244i 1.12745i −0.825963 0.563725i 0.809368π-0.809368\pi
0.825963 0.563725i 0.190632π-0.190632\pi
458458 −63.7277 197.529i −0.139143 0.431287i
459459 82.2299 82.2299i 0.179150 0.179150i
460460 −30.3837 + 186.807i −0.0660514 + 0.406102i
461461 5.67717 5.67717i 0.0123149 0.0123149i −0.700923 0.713237i 0.747228π-0.747228\pi
0.713237 + 0.700923i 0.247228π0.247228\pi
462462 −99.0031 50.7040i −0.214292 0.109749i
463463 464.510i 1.00326i −0.865082 0.501631i 0.832733π-0.832733\pi
0.865082 0.501631i 0.167267π-0.167267\pi
464464 −248.992 498.882i −0.536621 1.07518i
465465 102.133 0.219641
466466 −142.431 + 278.106i −0.305646 + 0.596794i
467467 495.985 + 495.985i 1.06207 + 1.06207i 0.997942 + 0.0641248i 0.0204256π0.0204256\pi
0.0641248 + 0.997942i 0.479574π0.479574\pi
468468 18.7502 115.281i 0.0400646 0.246328i
469469 102.286 + 102.286i 0.218094 + 0.218094i
470470 123.707 39.9109i 0.263207 0.0849167i
471471 133.302 0.283018
472472 −56.8525 41.8497i −0.120450 0.0886646i
473473 221.180i 0.467610i
474474 14.7046 4.74407i 0.0310224 0.0100086i
475475 −387.987 + 387.987i −0.816815 + 0.816815i
476476 −524.407 728.129i −1.10170 1.52968i
477477 −75.4202 + 75.4202i −0.158114 + 0.158114i
478478 12.0083 23.4471i 0.0251220 0.0490525i
479479 378.802i 0.790818i −0.918505 0.395409i 0.870603π-0.870603\pi
0.918505 0.395409i 0.129397π-0.129397\pi
480480 55.2703 + 56.4309i 0.115146 + 0.117564i
481481 90.8504 0.188878
482482 337.367 + 172.781i 0.699932 + 0.358467i
483483 407.582 + 407.582i 0.843855 + 0.843855i
484484 −359.435 + 258.869i −0.742633 + 0.534854i
485485 108.138 + 108.138i 0.222964 + 0.222964i
486486 9.57256 + 29.6710i 0.0196966 + 0.0610514i
487487 147.446 0.302764 0.151382 0.988475i 0.451628π-0.451628\pi
0.151382 + 0.988475i 0.451628π0.451628\pi
488488 −327.565 241.124i −0.671240 0.494107i
489489 256.713i 0.524976i
490490 −45.0453 139.622i −0.0919292 0.284942i
491491 109.547 109.547i 0.223110 0.223110i −0.586697 0.809807i 0.699572π-0.699572\pi
0.809807 + 0.586697i 0.199572π0.199572\pi
492492 322.412 + 52.4395i 0.655310 + 0.106584i
493493 551.473 551.473i 1.11861 1.11861i
494494 −413.893 211.973i −0.837840 0.429096i
495495 13.6960i 0.0276686i
496496 627.894 + 209.801i 1.26592 + 0.422985i
497497 119.810 0.241067
498498 22.7226 44.3674i 0.0456277 0.0890912i
499499 −360.523 360.523i −0.722491 0.722491i 0.246621 0.969112i 0.420680π-0.420680\pi
−0.969112 + 0.246621i 0.920680π0.920680\pi
500500 269.902 + 43.8989i 0.539804 + 0.0877977i
501501 65.2924 + 65.2924i 0.130324 + 0.130324i
502502 73.8722 23.8329i 0.147156 0.0474760i
503503 −927.420 −1.84378 −0.921889 0.387454i 0.873355π-0.873355\pi
−0.921889 + 0.387454i 0.873355π0.873355\pi
504504 237.834 36.1508i 0.471892 0.0717279i
505505 203.117i 0.402211i
506506 −202.438 + 65.3114i −0.400075 + 0.129074i
507507 −90.9597 + 90.9597i −0.179408 + 0.179408i
508508 119.554 86.1042i 0.235342 0.169496i
509509 677.931 677.931i 1.33189 1.33189i 0.428208 0.903680i 0.359145π-0.359145\pi
0.903680 0.428208i 0.140855π-0.140855\pi
510510 −50.3642 + 98.3397i −0.0987534 + 0.192823i
511511 1115.95i 2.18385i
512512 223.872 + 460.462i 0.437249 + 0.899340i
513513 124.129 0.241966
514514 −240.984 123.419i −0.468841 0.240115i
515515 58.5045 + 58.5045i 0.113601 + 0.113601i
516516 −279.559 388.162i −0.541780 0.752251i
517517 103.303 + 103.303i 0.199812 + 0.199812i
518518 57.4548 + 178.086i 0.110917 + 0.343795i
519519 −101.845 −0.196233
520520 16.6755 + 109.707i 0.0320682 + 0.210974i
521521 143.173i 0.274804i −0.990515 0.137402i 0.956125π-0.956125\pi
0.990515 0.137402i 0.0438753π-0.0438753\pi
522522 64.1982 + 198.988i 0.122985 + 0.381203i
523523 226.187 226.187i 0.432481 0.432481i −0.456991 0.889471i 0.651073π-0.651073\pi
0.889471 + 0.456991i 0.151073π0.151073\pi
524524 11.2324 69.0600i 0.0214359 0.131794i
525525 281.974 281.974i 0.537094 0.537094i
526526 −56.2738 28.8204i −0.106984 0.0547916i
527527 926.004i 1.75712i
528528 −28.1342 + 84.2003i −0.0532844 + 0.159470i
529529 573.288 1.08372
530530 46.1934 90.1959i 0.0871574 0.170181i
531531 18.7192 + 18.7192i 0.0352528 + 0.0352528i
532532 153.762 945.371i 0.289027 1.77701i
533533 324.484 + 324.484i 0.608788 + 0.608788i
534534 −72.3193 + 23.3319i −0.135429 + 0.0436928i
535535 227.235 0.424739
536536 68.4415 92.9772i 0.127689 0.173465i
537537 129.997i 0.242080i
538538 522.783 168.662i 0.971716 0.313499i
539539 116.592 116.592i 0.216312 0.216312i
540540 −17.3110 24.0359i −0.0320573 0.0445109i
541541 −156.708 + 156.708i −0.289663 + 0.289663i −0.836947 0.547284i 0.815662π-0.815662\pi
0.547284 + 0.836947i 0.315662π0.315662\pi
542542 265.890 519.168i 0.490571 0.957875i
543543 163.146i 0.300454i
544544 −511.639 + 501.116i −0.940512 + 0.921170i
545545 −163.530 −0.300055
546546 300.802 + 154.054i 0.550919 + 0.282151i
547547 247.357 + 247.357i 0.452207 + 0.452207i 0.896086 0.443880i 0.146398π-0.146398\pi
−0.443880 + 0.896086i 0.646398π0.646398\pi
548548 −472.845 + 340.549i −0.862856 + 0.621440i
549549 107.854 + 107.854i 0.196455 + 0.196455i
550550 45.1839 + 140.051i 0.0821525 + 0.254638i
551551 832.466 1.51083
552552 272.721 370.489i 0.494060 0.671177i
553553 44.7082i 0.0808466i
554554 −265.019 821.447i −0.478373 1.48276i
555555 16.2922 16.2922i 0.0293553 0.0293553i
556556 461.033 + 74.9858i 0.829196 + 0.134867i
557557 −661.193 + 661.193i −1.18706 + 1.18706i −0.209184 + 0.977876i 0.567081π0.567081\pi
−0.977876 + 0.209184i 0.932919π0.932919\pi
558558 −220.964 113.166i −0.395992 0.202806i
559559 672.011i 1.20217i
560560 −204.503 + 102.067i −0.365183 + 0.182263i
561561 −124.177 −0.221349
562562 −193.150 + 377.139i −0.343684 + 0.671066i
563563 246.685 + 246.685i 0.438162 + 0.438162i 0.891393 0.453231i 0.149729π-0.149729\pi
−0.453231 + 0.891393i 0.649729π0.649729\pi
564564 −311.861 50.7234i −0.552945 0.0899351i
565565 −173.171 173.171i −0.306497 0.306497i
566566 −283.516 + 91.4689i −0.500911 + 0.161606i
567567 −90.2120 −0.159104
568568 −14.3697 94.5372i −0.0252988 0.166439i
569569 243.567i 0.428061i −0.976827 0.214030i 0.931341π-0.931341\pi
0.976827 0.214030i 0.0686592π-0.0686592\pi
570570 −112.237 + 36.2102i −0.196906 + 0.0635267i
571571 59.9229 59.9229i 0.104944 0.104944i −0.652685 0.757629i 0.726358π-0.726358\pi
0.757629 + 0.652685i 0.226358π0.226358\pi
572572 −101.202 + 72.8866i −0.176926 + 0.127424i
573573 −139.319 + 139.319i −0.243139 + 0.243139i
574574 −430.850 + 841.265i −0.750610 + 1.46562i
575575 762.587i 1.32624i
576576 −57.0501 183.328i −0.0990453 0.318278i
577577 136.609 0.236757 0.118378 0.992969i 0.462230π-0.462230\pi
0.118378 + 0.992969i 0.462230π0.462230\pi
578578 −377.156 193.159i −0.652519 0.334185i
579579 −32.5287 32.5287i −0.0561809 0.0561809i
580580 −116.096 161.196i −0.200165 0.277925i
581581 101.991 + 101.991i 0.175543 + 0.175543i
582582 −114.136 353.774i −0.196110 0.607859i
583583 113.893 0.195357
584584 880.544 133.843i 1.50778 0.229184i
585585 41.6126i 0.0711326i
586586 148.754 + 461.076i 0.253846 + 0.786818i
587587 −331.817 + 331.817i −0.565276 + 0.565276i −0.930801 0.365525i 0.880889π-0.880889\pi
0.365525 + 0.930801i 0.380889π0.380889\pi
588588 −57.2488 + 351.981i −0.0973620 + 0.598608i
589589 −698.916 + 698.916i −1.18661 + 1.18661i
590590 −22.3865 11.4652i −0.0379433 0.0194325i
591591 127.113i 0.215081i
592592 133.629 66.6942i 0.225724 0.112659i
593593 131.285 0.221391 0.110695 0.993854i 0.464692π-0.464692\pi
0.110695 + 0.993854i 0.464692π0.464692\pi
594594 15.1754 29.6311i 0.0255479 0.0498840i
595595 −226.061 226.061i −0.379934 0.379934i
596596 −178.221 + 1095.75i −0.299028 + 1.83850i
597597 −167.473 167.473i −0.280524 0.280524i
598598 615.069 198.436i 1.02854 0.331833i
599599 −136.119 −0.227243 −0.113621 0.993524i 0.536245π-0.536245\pi
−0.113621 + 0.993524i 0.536245π0.536245\pi
600600 −256.313 188.675i −0.427188 0.314458i
601601 498.566i 0.829561i −0.909922 0.414780i 0.863858π-0.863858\pi
0.909922 0.414780i 0.136142π-0.136142\pi
602602 1317.28 424.987i 2.18818 0.705959i
603603 −30.6136 + 30.6136i −0.0507689 + 0.0507689i
604604 150.781 + 209.357i 0.249638 + 0.346617i
605605 −111.593 + 111.593i −0.184451 + 0.184451i
606606 −225.058 + 439.441i −0.371383 + 0.725150i
607607 568.740i 0.936969i −0.883472 0.468484i 0.844800π-0.844800\pi
0.883472 0.468484i 0.155200π-0.155200\pi
608608 −764.393 7.94198i −1.25723 0.0130625i
609609 −605.005 −0.993441
610610 −128.984 66.0585i −0.211449 0.108293i
611611 −313.865 313.865i −0.513691 0.513691i
612612 217.925 156.952i 0.356087 0.256458i
613613 −168.441 168.441i −0.274782 0.274782i 0.556240 0.831022i 0.312244π-0.312244\pi
−0.831022 + 0.556240i 0.812244π0.812244\pi
614614 23.5455 + 72.9813i 0.0383478 + 0.118862i
615615 116.380 0.189235
616616 −206.874 152.282i −0.335834 0.247211i
617617 599.157i 0.971081i 0.874214 + 0.485541i 0.161377π0.161377\pi
−0.874214 + 0.485541i 0.838623π0.838623\pi
618618 −61.7497 191.398i −0.0999186 0.309706i
619619 126.719 126.719i 0.204715 0.204715i −0.597301 0.802017i 0.703760π-0.703760\pi
0.802017 + 0.597301i 0.203760π0.203760\pi
620620 232.807 + 37.8654i 0.375495 + 0.0610732i
621621 −121.987 + 121.987i −0.196437 + 0.196437i
622622 −660.647 338.347i −1.06213 0.543967i
623623 219.881i 0.352939i
624624 85.4802 255.826i 0.136988 0.409978i
625625 −476.800 −0.762879
626626 −341.426 + 666.658i −0.545409 + 1.06495i
627627 −93.7242 93.7242i −0.149480 0.149480i
628628 303.854 + 49.4210i 0.483844 + 0.0786959i
629629 147.716 + 147.716i 0.234842 + 0.234842i
630630 81.5694 26.3162i 0.129475 0.0417718i
631631 668.283 1.05909 0.529543 0.848283i 0.322363π-0.322363\pi
0.529543 + 0.848283i 0.322363π0.322363\pi
632632 35.2773 5.36216i 0.0558185 0.00848444i
633633 345.797i 0.546283i
634634 130.779 42.1923i 0.206275 0.0665494i
635635 37.1177 37.1177i 0.0584531 0.0584531i
636636 −199.878 + 143.955i −0.314274 + 0.226344i
637637 −354.243 + 354.243i −0.556112 + 0.556112i
638638 101.774 198.720i 0.159520 0.311474i
639639 35.8586i 0.0561168i
640640 105.064 + 149.122i 0.164163 + 0.233004i
641641 484.574 0.755966 0.377983 0.925813i 0.376618π-0.376618\pi
0.377983 + 0.925813i 0.376618π0.376618\pi
642642 −491.622 251.782i −0.765766 0.392184i
643643 75.2980 + 75.2980i 0.117104 + 0.117104i 0.763230 0.646126i 0.223612π-0.223612\pi
−0.646126 + 0.763230i 0.723612π0.723612\pi
644644 777.952 + 1080.17i 1.20800 + 1.67728i
645645 −120.512 120.512i −0.186840 0.186840i
646646 −328.306 1017.61i −0.508213 1.57525i
647647 −582.307 −0.900011 −0.450006 0.893026i 0.648578π-0.648578\pi
−0.450006 + 0.893026i 0.648578π0.648578\pi
648648 10.8198 + 71.1824i 0.0166972 + 0.109849i
649649 28.2682i 0.0435565i
650650 −137.282 425.518i −0.211204 0.654644i
651651 507.946 507.946i 0.780255 0.780255i
652652 −95.1754 + 585.164i −0.145974 + 0.897491i
653653 457.453 457.453i 0.700541 0.700541i −0.263986 0.964527i 0.585037π-0.585037\pi
0.964527 + 0.263986i 0.0850371π0.0850371\pi
654654 353.795 + 181.195i 0.540972 + 0.277056i
655655 24.9283i 0.0380584i
656656 715.480 + 239.066i 1.09067 + 0.364430i
657657 −333.997 −0.508367
658658 416.750 813.734i 0.633359 1.23668i
659659 −430.079 430.079i −0.652623 0.652623i 0.301001 0.953624i 0.402679π-0.402679\pi
−0.953624 + 0.301001i 0.902679π0.902679\pi
660660 −5.07773 + 31.2193i −0.00769353 + 0.0473019i
661661 −513.622 513.622i −0.777038 0.777038i 0.202288 0.979326i 0.435162π-0.435162\pi
−0.979326 + 0.202288i 0.935162π0.935162\pi
662662 5.08436 1.64034i 0.00768031 0.00247785i
663663 377.287 0.569060
664664 68.2440 92.7089i 0.102777 0.139622i
665665 341.246i 0.513152i
666666 −53.3002 + 17.1959i −0.0800303 + 0.0258197i
667667 −818.105 + 818.105i −1.22654 + 1.22654i
668668 124.624 + 173.037i 0.186562 + 0.259038i
669669 −150.162 + 150.162i −0.224457 + 0.224457i
670670 18.7503 36.6112i 0.0279855 0.0546436i
671671 162.872i 0.242730i
672672 555.532 + 5.77193i 0.826685 + 0.00858919i
673673 −1112.68 −1.65332 −0.826659 0.562703i 0.809761π-0.809761\pi
−0.826659 + 0.562703i 0.809761π0.809761\pi
674674 688.871 + 352.802i 1.02206 + 0.523446i
675675 84.3935 + 84.3935i 0.125027 + 0.125027i
676676 −241.061 + 173.615i −0.356599 + 0.256827i
677677 633.271 + 633.271i 0.935408 + 0.935408i 0.998037 0.0626291i 0.0199485π-0.0199485\pi
−0.0626291 + 0.998037i 0.519949π0.519949\pi
678678 182.776 + 566.530i 0.269581 + 0.835590i
679679 1075.62 1.58412
680680 −151.262 + 205.488i −0.222444 + 0.302188i
681681 724.668i 1.06412i
682682 81.3937 + 252.287i 0.119346 + 0.369922i
683683 −429.651 + 429.651i −0.629065 + 0.629065i −0.947833 0.318768i 0.896731π-0.896731\pi
0.318768 + 0.947833i 0.396731π0.396731\pi
684684 282.945 + 46.0202i 0.413662 + 0.0672810i
685685 −146.803 + 146.803i −0.214312 + 0.214312i
686686 −44.1038 22.5876i −0.0642913 0.0329265i
687687 179.748i 0.261642i
688688 −493.330 988.439i −0.717049 1.43668i
689689 −346.042 −0.502239
690690 74.7148 145.886i 0.108282 0.211429i
691691 −151.617 151.617i −0.219417 0.219417i 0.588836 0.808253i 0.299586π-0.299586\pi
−0.808253 + 0.588836i 0.799586π0.799586\pi
692692 −232.150 37.7586i −0.335477 0.0545644i
693693 68.1153 + 68.1153i 0.0982904 + 0.0982904i
694694 −1189.47 + 383.753i −1.71394 + 0.552958i
695695 166.417 0.239449
696696 72.5625 + 477.383i 0.104257 + 0.685896i
697697 1055.17i 1.51388i
698698 −321.353 + 103.676i −0.460391 + 0.148533i
699699 191.340 191.340i 0.273734 0.273734i
700700 747.287 538.205i 1.06755 0.768864i
701701 −920.704 + 920.704i −1.31341 + 1.31341i −0.394533 + 0.918882i 0.629094π0.629094\pi
−0.918882 + 0.394533i 0.870906π0.870906\pi
702702 −46.1076 + 90.0284i −0.0656804 + 0.128246i
703703 222.982i 0.317186i
704704 −95.3473 + 181.500i −0.135437 + 0.257812i
705705 −112.571 −0.159675
706706 917.906 + 470.102i 1.30015 + 0.665866i
707707 −1010.18 1010.18i −1.42882 1.42882i
708708 35.7294 + 49.6096i 0.0504653 + 0.0700700i
709709 405.348 + 405.348i 0.571718 + 0.571718i 0.932608 0.360890i 0.117527π-0.117527\pi
−0.360890 + 0.932608i 0.617527π0.617527\pi
710710 −10.4605 32.4233i −0.0147331 0.0456666i
711711 −13.3809 −0.0188199
712712 −173.498 + 26.3718i −0.243677 + 0.0370391i
713713 1373.72i 1.92667i
714714 238.600 + 739.561i 0.334174 + 1.03580i
715715 −31.4199 + 31.4199i −0.0439439 + 0.0439439i
716716 −48.1958 + 296.321i −0.0673125 + 0.413856i
717717 −16.1319 + 16.1319i −0.0224991 + 0.0224991i
718718 −762.363 390.441i −1.06179 0.543789i
719719 880.704i 1.22490i 0.790509 + 0.612450i 0.209816π0.209816\pi
−0.790509 + 0.612450i 0.790184π0.790184\pi
720720 −30.5482 61.2066i −0.0424280 0.0850091i
721721 581.930 0.807115
722722 191.147 373.227i 0.264746 0.516935i
723723 −232.112 232.112i −0.321041 0.321041i
724724 60.4859 371.884i 0.0835440 0.513651i
725725 565.983 + 565.983i 0.780667 + 0.780667i
726726 365.078 117.783i 0.502862 0.162235i
727727 1000.46 1.37615 0.688077 0.725637i 0.258455π-0.258455\pi
0.688077 + 0.725637i 0.258455π0.258455\pi
728728 628.547 + 462.680i 0.863388 + 0.635549i
729729 27.0000i 0.0370370i
730730 301.999 97.4320i 0.413697 0.133469i
731731 1092.64 1092.64i 1.49472 1.49472i
732732 205.861 + 285.834i 0.281231 + 0.390484i
733733 540.306 540.306i 0.737116 0.737116i −0.234903 0.972019i 0.575477π-0.575477\pi
0.972019 + 0.234903i 0.0754772π0.0754772\pi
734734 200.097 390.704i 0.272612 0.532295i
735735 127.053i 0.172861i
736736 759.011 743.401i 1.03126 1.01006i
737737 46.2301 0.0627274
738738 −251.786 128.951i −0.341174 0.174731i
739739 893.726 + 893.726i 1.20937 + 1.20937i 0.971230 + 0.238142i 0.0765384π0.0765384\pi
0.238142 + 0.971230i 0.423462π0.423462\pi
740740 43.1775 31.0970i 0.0583480 0.0420229i
741741 284.763 + 284.763i 0.384296 + 0.384296i
742742 −218.841 678.316i −0.294934 0.914172i
743743 1295.75 1.74394 0.871969 0.489561i 0.162843π-0.162843\pi
0.871969 + 0.489561i 0.162843π0.162843\pi
744744 −461.719 339.876i −0.620591 0.456823i
745745 395.527i 0.530909i
746746 −369.092 1144.03i −0.494761 1.53355i
747747 −30.5253 + 30.5253i −0.0408639 + 0.0408639i
748748 −283.054 46.0380i −0.378414 0.0615481i
749749 1130.13 1130.13i 1.50885 1.50885i
750750 −210.779 107.949i −0.281038 0.143932i
751751 229.818i 0.306016i −0.988225 0.153008i 0.951104π-0.951104\pi
0.988225 0.153008i 0.0488961π-0.0488961\pi
752752 −692.066 231.243i −0.920300 0.307504i
753753 −67.2223 −0.0892726
754754 −309.220 + 603.774i −0.410106 + 0.800761i
755755 64.9987 + 64.9987i 0.0860910 + 0.0860910i
756756 −205.634 33.4458i −0.272002 0.0442404i
757757 −373.678 373.678i −0.493630 0.493630i 0.415818 0.909448i 0.363495π-0.363495\pi
−0.909448 + 0.415818i 0.863495π0.863495\pi
758758 −984.973 + 317.776i −1.29944 + 0.419229i
759759 184.215 0.242707
760760 −269.262 + 40.9280i −0.354293 + 0.0538527i
761761 384.012i 0.504615i 0.967647 + 0.252307i 0.0811894π0.0811894\pi
−0.967647 + 0.252307i 0.918811π0.918811\pi
762762 −121.431 + 39.1766i −0.159358 + 0.0514128i
763763 −813.296 + 813.296i −1.06592 + 1.06592i
764764 −369.222 + 265.918i −0.483275 + 0.348060i
765765 67.6589 67.6589i 0.0884429 0.0884429i
766766 194.440 379.658i 0.253838 0.495637i
767767 85.8874i 0.111978i
768768 −62.0745 439.038i −0.0808261 0.571665i
769769 865.026 1.12487 0.562436 0.826841i 0.309864π-0.309864\pi
0.562436 + 0.826841i 0.309864π0.309864\pi
770770 −81.4598 41.7193i −0.105792 0.0541809i
771771 165.800 + 165.800i 0.215045 + 0.215045i
772772 −62.0876 86.2074i −0.0804244 0.111668i
773773 −1.78859 1.78859i −0.00231383 0.00231383i 0.705949 0.708263i 0.250521π-0.250521\pi
−0.708263 + 0.705949i 0.750521π0.750521\pi
774774 127.196 + 394.256i 0.164337 + 0.509375i
775775 −950.368 −1.22628
776776 −129.007 848.725i −0.166246 1.09372i
777777 162.055i 0.208565i
778778 183.066 + 567.428i 0.235303 + 0.729341i
779779 −796.409 + 796.409i −1.02235 + 1.02235i
780780 15.4277 94.8537i 0.0197791 0.121607i
781781 27.0753 27.0753i 0.0346675 0.0346675i
782782 1322.70 + 677.413i 1.69143 + 0.866257i
783783 181.075i 0.231258i
784784 −260.991 + 781.098i −0.332897 + 0.996299i
785785 109.681 0.139721
786786 −27.6211 + 53.9321i −0.0351413 + 0.0686159i
787787 143.702 + 143.702i 0.182595 + 0.182595i 0.792485 0.609891i 0.208787π-0.208787\pi
−0.609891 + 0.792485i 0.708787π0.708787\pi
788788 −47.1265 + 289.747i −0.0598052 + 0.367699i
789789 38.7170 + 38.7170i 0.0490710 + 0.0490710i
790790 12.0990 3.90342i 0.0153152 0.00494104i
791791 −1722.49 −2.17761
792792 45.5772 61.9163i 0.0575470 0.0781772i
793793 494.855i 0.624029i
794794 −1057.63 + 341.216i −1.33203 + 0.429743i
795795 −62.0558 + 62.0558i −0.0780577 + 0.0780577i
796796 −319.655 443.835i −0.401577 0.557582i
797797 −477.929 + 477.929i −0.599660 + 0.599660i −0.940222 0.340562i 0.889383π-0.889383\pi
0.340562 + 0.940222i 0.389383π0.389383\pi
798798 −378.108 + 738.283i −0.473820 + 0.925166i
799799 1020.64i 1.27740i
800800 −514.301 525.101i −0.642877 0.656376i
801801 65.8092 0.0821588
802802 −52.2091 26.7387i −0.0650987 0.0333400i
803803 252.187 + 252.187i 0.314056 + 0.314056i
804804 −81.1321 + 58.4323i −0.100911 + 0.0726770i
805805 335.359 + 335.359i 0.416595 + 0.416595i
806806 −247.299 766.524i −0.306823 0.951023i
807807 −475.722 −0.589495
808808 −675.929 + 918.244i −0.836545 + 1.13644i
809809 1524.96i 1.88500i −0.334212 0.942498i 0.608470π-0.608470\pi
0.334212 0.942498i 0.391530π-0.391530\pi
810810 7.87632 + 24.4133i 0.00972385 + 0.0301399i
811811 −576.427 + 576.427i −0.710761 + 0.710761i −0.966694 0.255933i 0.917617π-0.917617\pi
0.255933 + 0.966694i 0.417617π0.417617\pi
812812 −1379.08 224.303i −1.69837 0.276236i
813813 −357.194 + 357.194i −0.439353 + 0.439353i
814814 53.2286 + 27.2608i 0.0653914 + 0.0334899i
815815 211.224i 0.259170i
816816 554.938 276.970i 0.680072 0.339424i
817817 1649.37 2.01882
818818 548.026 1070.06i 0.669958 1.30814i
819819 −206.955 206.955i −0.252692 0.252692i
820820 265.281 + 43.1473i 0.323514 + 0.0526186i
821821 −386.324 386.324i −0.470552 0.470552i 0.431541 0.902093i 0.357970π-0.357970\pi
−0.902093 + 0.431541i 0.857970π0.857970\pi
822822 480.269 154.946i 0.584269 0.188499i
823823 377.870 0.459138 0.229569 0.973292i 0.426268π-0.426268\pi
0.229569 + 0.973292i 0.426268π0.426268\pi
824824 −69.7950 459.176i −0.0847026 0.557252i
825825 127.444i 0.154477i
826826 −168.357 + 54.3161i −0.203822 + 0.0657580i
827827 140.900 140.900i 0.170375 0.170375i −0.616769 0.787144i 0.711559π-0.711559\pi
0.787144 + 0.616769i 0.211559π0.211559\pi
828828 −323.290 + 232.837i −0.390447 + 0.281204i
829829 −522.203 + 522.203i −0.629919 + 0.629919i −0.948048 0.318128i 0.896946π-0.896946\pi
0.318128 + 0.948048i 0.396946π0.396946\pi
830830 18.6962 36.5056i 0.0225255 0.0439826i
831831 747.501i 0.899520i
832832 289.694 551.451i 0.348190 0.662802i
833833 −1151.95 −1.38289
834834 −360.041 184.394i −0.431704 0.221095i
835835 53.7226 + 53.7226i 0.0643385 + 0.0643385i
836836 −178.892 248.387i −0.213985 0.297114i
837837 152.026 + 152.026i 0.181632 + 0.181632i
838838 450.621 + 1396.74i 0.537734 + 1.66675i
839839 −442.133 −0.526976 −0.263488 0.964663i 0.584873π-0.584873\pi
−0.263488 + 0.964663i 0.584873π0.584873\pi
840840 195.690 29.7450i 0.232964 0.0354107i
841841 373.376i 0.443967i
842842 357.114 + 1106.91i 0.424126 + 1.31462i
843843 259.476 259.476i 0.307801 0.307801i
844844 128.203 788.226i 0.151899 0.933917i
845845 −74.8417 + 74.8417i −0.0885701 + 0.0885701i
846846 243.546 + 124.731i 0.287880 + 0.147436i
847847 1109.99i 1.31049i
848848 −508.982 + 254.033i −0.600215 + 0.299567i
849849 257.994 0.303879
850850 468.650 915.071i 0.551352 1.07655i
851851 −219.135 219.135i −0.257503 0.257503i
852852 −13.2945 + 81.7379i −0.0156038 + 0.0959365i
853853 −494.617 494.617i −0.579856 0.579856i 0.355007 0.934863i 0.384478π-0.384478\pi
−0.934863 + 0.355007i 0.884478π0.884478\pi
854854 −970.020 + 312.952i −1.13585 + 0.366454i
855855 102.133 0.119454
856856 −1027.28 756.190i −1.20009 0.883400i
857857 1676.75i 1.95654i 0.207340 + 0.978269i 0.433519π0.433519\pi
−0.207340 + 0.978269i 0.566481π0.566481\pi
858858 102.791 33.1627i 0.119802 0.0386511i
859859 228.948 228.948i 0.266529 0.266529i −0.561171 0.827700i 0.689649π-0.689649\pi
0.827700 + 0.561171i 0.189649π0.189649\pi
860860 −230.021 319.380i −0.267466 0.371372i
861861 578.800 578.800i 0.672241 0.672241i
862862 37.4777 73.1778i 0.0434776 0.0848931i
863863 1603.23i 1.85774i −0.370401 0.928872i 0.620780π-0.620780\pi
0.370401 0.928872i 0.379220π-0.379220\pi
864864 −1.72751 + 166.268i −0.00199943 + 0.192440i
865865 −83.7981 −0.0968764
866866 626.038 + 320.622i 0.722907 + 0.370234i
867867 259.488 + 259.488i 0.299294 + 0.299294i
868868 1346.15 969.517i 1.55087 1.11695i
869869 10.1034 + 10.1034i 0.0116264 + 0.0116264i
870870 52.8224 + 163.727i 0.0607154 + 0.188192i
871871 −140.461 −0.161264
872872 739.281 + 544.192i 0.847799 + 0.624074i
873873 321.927i 0.368760i
874874 487.038 + 1509.61i 0.557252 + 1.72725i
875875 484.533 484.533i 0.553752 0.553752i
876876 −761.328 123.828i −0.869096 0.141356i
877877 289.017 289.017i 0.329552 0.329552i −0.522864 0.852416i 0.675136π-0.675136\pi
0.852416 + 0.522864i 0.175136π0.175136\pi
878878 1380.69 + 707.113i 1.57254 + 0.805367i
879879 419.570i 0.477326i
880880 −23.1488 + 69.2801i −0.0263055 + 0.0787274i
881881 937.450 1.06408 0.532038 0.846721i 0.321426π-0.321426\pi
0.532038 + 0.846721i 0.321426π0.321426\pi
882882 140.778 274.878i 0.159612 0.311653i
883883 −485.966 485.966i −0.550357 0.550357i 0.376187 0.926544i 0.377235π-0.377235\pi
−0.926544 + 0.376187i 0.877235π0.877235\pi
884884 860.005 + 139.877i 0.972856 + 0.158232i
885885 15.4022 + 15.4022i 0.0174036 + 0.0174036i
886886 649.726 209.617i 0.733326 0.236588i
887887 −534.193 −0.602247 −0.301123 0.953585i 0.597362π-0.597362\pi
−0.301123 + 0.953585i 0.597362π0.597362\pi
888888 −127.870 + 19.4364i −0.143998 + 0.0218878i
889889 369.201i 0.415299i
890890 −59.5044 + 19.1976i −0.0668589 + 0.0215703i
891891 −20.3865 + 20.3865i −0.0228805 + 0.0228805i
892892 −397.958 + 286.614i −0.446142 + 0.321316i
893893 770.346 770.346i 0.862649 0.862649i
894894 438.253 855.719i 0.490216 0.957180i
895895 106.961i 0.119510i
896896 1264.17 + 219.118i 1.41090 + 0.244552i
897897 −559.701 −0.623970
898898 −474.153 242.835i −0.528010 0.270418i
899899 1019.56 + 1019.56i 1.13410 + 1.13410i
900900 161.082 + 223.659i 0.178980 + 0.248510i
901901 −562.638 562.638i −0.624460 0.624460i
902902 92.7475 + 287.479i 0.102824 + 0.318712i
903903 −1198.70 −1.32747
904904 206.590 + 1359.14i 0.228529 + 1.50347i
905905 134.237i 0.148328i
906906 −68.6041 212.644i −0.0757219 0.234706i
907907 368.669 368.669i 0.406471 0.406471i −0.474035 0.880506i 0.657203π-0.657203\pi
0.880506 + 0.474035i 0.157203π0.157203\pi
908908 268.668 1651.84i 0.295890 1.81921i
909909 302.341 302.341i 0.332608 0.332608i
910910 247.500 + 126.756i 0.271978 + 0.139292i
911911 1592.43i 1.74800i 0.485927 + 0.873999i 0.338482π0.338482\pi
−0.485927 + 0.873999i 0.661518π0.661518\pi
912912 627.896 + 209.801i 0.688482 + 0.230045i
913913 46.0967 0.0504893
914914 −469.739 + 917.198i −0.513938 + 1.00350i
915915 88.7424 + 88.7424i 0.0969863 + 0.0969863i
916916 −66.6408 + 409.726i −0.0727519 + 0.447299i
917917 −123.978 123.978i −0.135199 0.135199i
918918 −221.347 + 71.4118i −0.241119 + 0.0777906i
919919 −403.500 −0.439064 −0.219532 0.975605i 0.570453π-0.570453\pi
−0.219532 + 0.975605i 0.570453π0.570453\pi
920920 224.395 304.839i 0.243908 0.331347i
921921 66.4116i 0.0721081i
922922 −15.2818 + 4.93029i −0.0165747 + 0.00534738i
923923 −82.2632 + 82.2632i −0.0891258 + 0.0891258i
924924 130.012 + 180.519i 0.140705 + 0.195366i
925925 −151.602 + 151.602i −0.163894 + 0.163894i
926926 −423.486 + 826.886i −0.457328 + 0.892965i
927927 174.169i 0.187884i
928928 −11.5855 + 1115.07i −0.0124844 + 1.20159i
929929 348.546 0.375184 0.187592 0.982247i 0.439932π-0.439932\pi
0.187592 + 0.982247i 0.439932π0.439932\pi
930930 −181.809 93.1128i −0.195494 0.100121i
931931 −869.449 869.449i −0.933887 0.933887i
932932 507.089 365.211i 0.544087 0.391858i
933933 454.533 + 454.533i 0.487173 + 0.487173i
934934 −430.734 1335.10i −0.461171 1.42944i
935935 −102.173 −0.109276
936936 −138.478 + 188.121i −0.147946 + 0.200984i
937937 248.875i 0.265609i −0.991142 0.132804i 0.957602π-0.957602\pi
0.991142 0.132804i 0.0423982π-0.0423982\pi
938938 −88.8292 275.334i −0.0947007 0.293533i
939939 458.669 458.669i 0.488465 0.488465i
940940 −256.600 41.7353i −0.272978 0.0443992i
941941 884.188 884.188i 0.939626 0.939626i −0.0586528 0.998278i 0.518681π-0.518681\pi
0.998278 + 0.0586528i 0.0186805π0.0186805\pi
942942 −237.293 121.529i −0.251904 0.129011i
943943 1565.34i 1.65996i
944944 63.0508 + 126.329i 0.0667911 + 0.133823i
945945 −74.2266 −0.0785466
946946 201.645 393.727i 0.213156 0.416202i
947947 462.279 + 462.279i 0.488151 + 0.488151i 0.907722 0.419571i 0.137820π-0.137820\pi
−0.419571 + 0.907722i 0.637820π0.637820\pi
948948 −30.5011 4.96093i −0.0321742 0.00523304i
949949 −766.221 766.221i −0.807398 0.807398i
950950 1044.39 336.944i 1.09935 0.354678i
951951 −119.006 −0.125138
952952 269.687 + 1774.25i 0.283285 + 1.86371i
953953 707.656i 0.742556i 0.928522 + 0.371278i 0.121080π0.121080\pi
−0.928522 + 0.371278i 0.878920π0.878920\pi
954954 203.016 65.4980i 0.212806 0.0686562i
955955 −114.632 + 114.632i −0.120033 + 0.120033i
956956 −42.7525 + 30.7909i −0.0447202 + 0.0322081i
957957 −136.722 + 136.722i −0.142865 + 0.142865i
958958 −345.347 + 674.314i −0.360487 + 0.703877i
959959 1460.22i 1.52265i
960960 −46.9409 150.843i −0.0488968 0.157128i
961961 −750.983 −0.781460
962962 −161.725 82.8267i −0.168113 0.0860984i
963963 338.241 + 338.241i 0.351237 + 0.351237i
964964 −443.033 615.143i −0.459578 0.638115i
965965 −26.7647 26.7647i −0.0277354 0.0277354i
966966 −353.961 1097.13i −0.366419 1.13575i
967967 −841.240 −0.869949 −0.434974 0.900443i 0.643243π-0.643243\pi
−0.434974 + 0.900443i 0.643243π0.643243\pi
968968 875.844 133.129i 0.904797 0.137530i
969969 926.006i 0.955630i
970970 −93.9112 291.086i −0.0968157 0.300088i
971971 308.415 308.415i 0.317626 0.317626i −0.530229 0.847855i 0.677894π-0.677894\pi
0.847855 + 0.530229i 0.177894π0.177894\pi
972972 10.0101 61.5451i 0.0102985 0.0633180i
973973 827.654 827.654i 0.850621 0.850621i
974974 −262.472 134.424i −0.269478 0.138012i
975975 387.213i 0.397142i
976976 363.278 + 727.866i 0.372211 + 0.745764i
977977 −1316.85 −1.34786 −0.673928 0.738797i 0.735394π-0.735394\pi
−0.673928 + 0.738797i 0.735394π0.735394\pi
978978 234.041 456.981i 0.239305 0.467260i
979979 −49.6897 49.6897i −0.0507556 0.0507556i
980980 −47.1044 + 289.611i −0.0480657 + 0.295521i
981981 −243.415 243.415i −0.248130 0.248130i
982982 −294.880 + 95.1352i −0.300285 + 0.0968791i
983983 504.538 0.513263 0.256632 0.966509i 0.417387π-0.417387\pi
0.256632 + 0.966509i 0.417387π0.417387\pi
984984 −526.125 387.286i −0.534680 0.393584i
985985 104.588i 0.106181i
986986 −1484.46 + 478.922i −1.50554 + 0.485722i
987987 −559.858 + 559.858i −0.567232 + 0.567232i
988988 543.528 + 754.677i 0.550129 + 0.763843i
989989 −1620.92 + 1620.92i −1.63895 + 1.63895i
990990 12.4864 24.3805i 0.0126125 0.0246268i
991991 436.650i 0.440616i −0.975430 0.220308i 0.929294π-0.929294\pi
0.975430 0.220308i 0.0707062π-0.0707062\pi
992992 −926.457 945.911i −0.933929 0.953539i
993993 −4.62667 −0.00465929
994994 −213.277 109.229i −0.214565 0.109888i
995995 −137.797 137.797i −0.138489 0.138489i
996996 −80.8979 + 58.2637i −0.0812228 + 0.0584977i
997997 −383.801 383.801i −0.384956 0.384956i 0.487928 0.872884i 0.337753π-0.337753\pi
−0.872884 + 0.487928i 0.837753π0.837753\pi
998998 313.093 + 970.458i 0.313720 + 0.972403i
999999 48.5021 0.0485507
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 48.3.l.a.43.3 yes 16
3.2 odd 2 144.3.m.c.91.6 16
4.3 odd 2 192.3.l.a.79.3 16
8.3 odd 2 384.3.l.b.31.6 16
8.5 even 2 384.3.l.a.31.2 16
12.11 even 2 576.3.m.c.271.4 16
16.3 odd 4 inner 48.3.l.a.19.3 16
16.5 even 4 384.3.l.b.223.6 16
16.11 odd 4 384.3.l.a.223.2 16
16.13 even 4 192.3.l.a.175.3 16
24.5 odd 2 1152.3.m.f.415.5 16
24.11 even 2 1152.3.m.c.415.5 16
48.5 odd 4 1152.3.m.c.991.5 16
48.11 even 4 1152.3.m.f.991.5 16
48.29 odd 4 576.3.m.c.559.4 16
48.35 even 4 144.3.m.c.19.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.3.l.a.19.3 16 16.3 odd 4 inner
48.3.l.a.43.3 yes 16 1.1 even 1 trivial
144.3.m.c.19.6 16 48.35 even 4
144.3.m.c.91.6 16 3.2 odd 2
192.3.l.a.79.3 16 4.3 odd 2
192.3.l.a.175.3 16 16.13 even 4
384.3.l.a.31.2 16 8.5 even 2
384.3.l.a.223.2 16 16.11 odd 4
384.3.l.b.31.6 16 8.3 odd 2
384.3.l.b.223.6 16 16.5 even 4
576.3.m.c.271.4 16 12.11 even 2
576.3.m.c.559.4 16 48.29 odd 4
1152.3.m.c.415.5 16 24.11 even 2
1152.3.m.c.991.5 16 48.5 odd 4
1152.3.m.f.415.5 16 24.5 odd 2
1152.3.m.f.991.5 16 48.11 even 4