Properties

Label 85.2.e.a.81.3
Level 8585
Weight 22
Character 85.81
Analytic conductor 0.6790.679
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [85,2,Mod(21,85)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(85, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("85.21");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 85=517 85 = 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 85.e (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: 0.6787284171810.678728417181
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(i)\Q(i)
Coefficient field: Q[x]/(x12+)\mathbb{Q}[x]/(x^{12} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12+18x10+83x8+152x6+111x4+22x2+1 x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 81.3
Root 3.48265i3.48265i of defining polynomial
Character χ\chi == 85.81
Dual form 85.2.e.a.21.4

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) == q1.12708iq2+(1.755501.75550i)q3+0.729699q4+(0.7071070.707107i)q5+(1.97858+1.97858i)q6+(1.72715+1.72715i)q73.07658iq8+3.16356iq9+(0.796963+0.796963i)q10+(2.572512.57251i)q11+(1.280991.28099i)q12+3.64168q13+(1.94663+1.94663i)q14+2.48265iq152.00814q16+(3.03394+2.79199i)q17+3.56558q18+2.61358iq19+(0.5159750.515975i)q20+6.06403q21+(2.899412.89941i)q22+(0.9938500.993850i)q23+(5.40094+5.40094i)q24+1.00000iq254.10445iq26+(0.2871370.287137i)q27+(1.26030+1.26030i)q28+(0.601589+0.601589i)q29+2.79814q30+(6.677446.67744i)q313.88983iq329.03208q33+(3.146783.41948i)q34+2.44256q35+2.30845iq36+(7.78199+7.78199i)q37+2.94570q38+(6.392976.39297i)q39+(2.17547+2.17547i)q40+(6.74550+6.74550i)q416.83463iq42+7.47280iq43+(1.877161.87716i)q44+(2.236982.23698i)q45+(1.120141.12014i)q465.42683q47+(3.52529+3.52529i)q48+1.03389iq49+1.12708q50+(0.42474710.2274i)q51+2.65733q5212.9453iq53+(0.3236260.323626i)q543.63808q55+(5.31372+5.31372i)q56+(4.588144.58814i)q57+(0.6780370.678037i)q58+1.40270iq59+1.81159iq60+(0.8044850.804485i)q61+(7.52598+7.52598i)q62+(5.463965.46396i)q638.40042q64+(2.575062.57506i)q65+10.1798iq662.07908q67+(2.21387+2.03731i)q683.48941q692.75295iq70+(8.69168+8.69168i)q71+9.73296q72+(1.04359+1.04359i)q73+(8.770908.77090i)q74+(1.755501.75550i)q75+1.90713iq76+8.88623iq77+(7.20536+7.20536i)q78+(6.344706.34470i)q79+(1.41997+1.41997i)q80+8.48255q81+(7.60269+7.60269i)q82+2.52680iq83+4.42492q84+(0.1710864.11955i)q85+8.42242q862.11218iq87+(7.914537.91453i)q881.66373q89+(2.521242.52124i)q90+(6.28973+6.28973i)q91+(0.7252120.725212i)q92+23.4445iq93+6.11645iq94+(1.848081.84808i)q95+(6.82860+6.82860i)q96+(8.674328.67432i)q97+1.16527q98+(8.13830+8.13830i)q99+O(q100)q-1.12708i q^{2} +(-1.75550 - 1.75550i) q^{3} +0.729699 q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.97858 + 1.97858i) q^{6} +(-1.72715 + 1.72715i) q^{7} -3.07658i q^{8} +3.16356i q^{9} +(-0.796963 + 0.796963i) q^{10} +(2.57251 - 2.57251i) q^{11} +(-1.28099 - 1.28099i) q^{12} +3.64168 q^{13} +(1.94663 + 1.94663i) q^{14} +2.48265i q^{15} -2.00814 q^{16} +(3.03394 + 2.79199i) q^{17} +3.56558 q^{18} +2.61358i q^{19} +(-0.515975 - 0.515975i) q^{20} +6.06403 q^{21} +(-2.89941 - 2.89941i) q^{22} +(0.993850 - 0.993850i) q^{23} +(-5.40094 + 5.40094i) q^{24} +1.00000i q^{25} -4.10445i q^{26} +(0.287137 - 0.287137i) q^{27} +(-1.26030 + 1.26030i) q^{28} +(0.601589 + 0.601589i) q^{29} +2.79814 q^{30} +(-6.67744 - 6.67744i) q^{31} -3.88983i q^{32} -9.03208 q^{33} +(3.14678 - 3.41948i) q^{34} +2.44256 q^{35} +2.30845i q^{36} +(7.78199 + 7.78199i) q^{37} +2.94570 q^{38} +(-6.39297 - 6.39297i) q^{39} +(-2.17547 + 2.17547i) q^{40} +(-6.74550 + 6.74550i) q^{41} -6.83463i q^{42} +7.47280i q^{43} +(1.87716 - 1.87716i) q^{44} +(2.23698 - 2.23698i) q^{45} +(-1.12014 - 1.12014i) q^{46} -5.42683 q^{47} +(3.52529 + 3.52529i) q^{48} +1.03389i q^{49} +1.12708 q^{50} +(-0.424747 - 10.2274i) q^{51} +2.65733 q^{52} -12.9453i q^{53} +(-0.323626 - 0.323626i) q^{54} -3.63808 q^{55} +(5.31372 + 5.31372i) q^{56} +(4.58814 - 4.58814i) q^{57} +(0.678037 - 0.678037i) q^{58} +1.40270i q^{59} +1.81159i q^{60} +(0.804485 - 0.804485i) q^{61} +(-7.52598 + 7.52598i) q^{62} +(-5.46396 - 5.46396i) q^{63} -8.40042 q^{64} +(-2.57506 - 2.57506i) q^{65} +10.1798i q^{66} -2.07908 q^{67} +(2.21387 + 2.03731i) q^{68} -3.48941 q^{69} -2.75295i q^{70} +(8.69168 + 8.69168i) q^{71} +9.73296 q^{72} +(1.04359 + 1.04359i) q^{73} +(8.77090 - 8.77090i) q^{74} +(1.75550 - 1.75550i) q^{75} +1.90713i q^{76} +8.88623i q^{77} +(-7.20536 + 7.20536i) q^{78} +(6.34470 - 6.34470i) q^{79} +(1.41997 + 1.41997i) q^{80} +8.48255 q^{81} +(7.60269 + 7.60269i) q^{82} +2.52680i q^{83} +4.42492 q^{84} +(-0.171086 - 4.11955i) q^{85} +8.42242 q^{86} -2.11218i q^{87} +(-7.91453 - 7.91453i) q^{88} -1.66373 q^{89} +(-2.52124 - 2.52124i) q^{90} +(-6.28973 + 6.28973i) q^{91} +(0.725212 - 0.725212i) q^{92} +23.4445i q^{93} +6.11645i q^{94} +(1.84808 - 1.84808i) q^{95} +(-6.82860 + 6.82860i) q^{96} +(-8.67432 - 8.67432i) q^{97} +1.16527 q^{98} +(8.13830 + 8.13830i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q4q312q44q104q118q124q14+4q16+12q17+28q188q2016q21+20q22+12q23+4q244q27+4q2812q298q30++44q98+O(q100) 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/85Z)×\left(\mathbb{Z}/85\mathbb{Z}\right)^\times.

nn 5252 7171
χ(n)\chi(n) 11 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 1.12708i 0.796963i −0.917176 0.398482i 0.869537π-0.869537\pi
0.917176 0.398482i 0.130463π-0.130463\pi
33 −1.75550 1.75550i −1.01354 1.01354i −0.999907 0.0136316i 0.995661π-0.995661\pi
−0.0136316 0.999907i 0.504339π-0.504339\pi
44 0.729699 0.364850
55 −0.707107 0.707107i −0.316228 0.316228i
66 −1.97858 + 1.97858i −0.807753 + 0.807753i
77 −1.72715 + 1.72715i −0.652802 + 0.652802i −0.953667 0.300865i 0.902725π-0.902725\pi
0.300865 + 0.953667i 0.402725π0.402725\pi
88 3.07658i 1.08773i
99 3.16356i 1.05452i
1010 −0.796963 + 0.796963i −0.252022 + 0.252022i
1111 2.57251 2.57251i 0.775641 0.775641i −0.203446 0.979086i 0.565214π-0.565214\pi
0.979086 + 0.203446i 0.0652140π0.0652140\pi
1212 −1.28099 1.28099i −0.369789 0.369789i
1313 3.64168 1.01002 0.505010 0.863113i 0.331489π-0.331489\pi
0.505010 + 0.863113i 0.331489π0.331489\pi
1414 1.94663 + 1.94663i 0.520259 + 0.520259i
1515 2.48265i 0.641018i
1616 −2.00814 −0.502035
1717 3.03394 + 2.79199i 0.735839 + 0.677157i
1818 3.56558 0.840415
1919 2.61358i 0.599596i 0.954003 + 0.299798i 0.0969193π0.0969193\pi
−0.954003 + 0.299798i 0.903081π0.903081\pi
2020 −0.515975 0.515975i −0.115376 0.115376i
2121 6.06403 1.32328
2222 −2.89941 2.89941i −0.618157 0.618157i
2323 0.993850 0.993850i 0.207232 0.207232i −0.595858 0.803090i 0.703188π-0.703188\pi
0.803090 + 0.595858i 0.203188π0.203188\pi
2424 −5.40094 + 5.40094i −1.10246 + 1.10246i
2525 1.00000i 0.200000i
2626 4.10445i 0.804949i
2727 0.287137 0.287137i 0.0552596 0.0552596i
2828 −1.26030 + 1.26030i −0.238175 + 0.238175i
2929 0.601589 + 0.601589i 0.111712 + 0.111712i 0.760753 0.649041i 0.224830π-0.224830\pi
−0.649041 + 0.760753i 0.724830π0.724830\pi
3030 2.79814 0.510868
3131 −6.67744 6.67744i −1.19930 1.19930i −0.974376 0.224928i 0.927785π-0.927785\pi
−0.224928 0.974376i 0.572215π-0.572215\pi
3232 3.88983i 0.687632i
3333 −9.03208 −1.57228
3434 3.14678 3.41948i 0.539669 0.586436i
3535 2.44256 0.412868
3636 2.30845i 0.384742i
3737 7.78199 + 7.78199i 1.27935 + 1.27935i 0.941031 + 0.338320i 0.109859π0.109859\pi
0.338320 + 0.941031i 0.390141π0.390141\pi
3838 2.94570 0.477856
3939 −6.39297 6.39297i −1.02369 1.02369i
4040 −2.17547 + 2.17547i −0.343972 + 0.343972i
4141 −6.74550 + 6.74550i −1.05347 + 1.05347i −0.0549831 + 0.998487i 0.517511π0.517511\pi
−0.998487 + 0.0549831i 0.982489π0.982489\pi
4242 6.83463i 1.05461i
4343 7.47280i 1.13959i 0.821786 + 0.569796i 0.192978π0.192978\pi
−0.821786 + 0.569796i 0.807022π0.807022\pi
4444 1.87716 1.87716i 0.282992 0.282992i
4545 2.23698 2.23698i 0.333469 0.333469i
4646 −1.12014 1.12014i −0.165156 0.165156i
4747 −5.42683 −0.791585 −0.395792 0.918340i 0.629530π-0.629530\pi
−0.395792 + 0.918340i 0.629530π0.629530\pi
4848 3.52529 + 3.52529i 0.508832 + 0.508832i
4949 1.03389i 0.147699i
5050 1.12708 0.159393
5151 −0.424747 10.2274i −0.0594765 1.43213i
5252 2.65733 0.368506
5353 12.9453i 1.77817i −0.457737 0.889087i 0.651340π-0.651340\pi
0.457737 0.889087i 0.348660π-0.348660\pi
5454 −0.323626 0.323626i −0.0440399 0.0440399i
5555 −3.63808 −0.490558
5656 5.31372 + 5.31372i 0.710076 + 0.710076i
5757 4.58814 4.58814i 0.607714 0.607714i
5858 0.678037 0.678037i 0.0890306 0.0890306i
5959 1.40270i 0.182616i 0.995823 + 0.0913081i 0.0291048π0.0291048\pi
−0.995823 + 0.0913081i 0.970895π0.970895\pi
6060 1.81159i 0.233875i
6161 0.804485 0.804485i 0.103004 0.103004i −0.653727 0.756731i 0.726795π-0.726795\pi
0.756731 + 0.653727i 0.226795π0.226795\pi
6262 −7.52598 + 7.52598i −0.955800 + 0.955800i
6363 −5.46396 5.46396i −0.688394 0.688394i
6464 −8.40042 −1.05005
6565 −2.57506 2.57506i −0.319396 0.319396i
6666 10.1798i 1.25305i
6767 −2.07908 −0.254000 −0.127000 0.991903i 0.540535π-0.540535\pi
−0.127000 + 0.991903i 0.540535π0.540535\pi
6868 2.21387 + 2.03731i 0.268471 + 0.247060i
6969 −3.48941 −0.420076
7070 2.75295i 0.329041i
7171 8.69168 + 8.69168i 1.03151 + 1.03151i 0.999487 + 0.0320251i 0.0101957π0.0101957\pi
0.0320251 + 0.999487i 0.489804π0.489804\pi
7272 9.73296 1.14704
7373 1.04359 + 1.04359i 0.122143 + 0.122143i 0.765536 0.643393i 0.222474π-0.222474\pi
−0.643393 + 0.765536i 0.722474π0.722474\pi
7474 8.77090 8.77090i 1.01960 1.01960i
7575 1.75550 1.75550i 0.202708 0.202708i
7676 1.90713i 0.218762i
7777 8.88623i 1.01268i
7878 −7.20536 + 7.20536i −0.815847 + 0.815847i
7979 6.34470 6.34470i 0.713834 0.713834i −0.253501 0.967335i 0.581582π-0.581582\pi
0.967335 + 0.253501i 0.0815821π0.0815821\pi
8080 1.41997 + 1.41997i 0.158757 + 0.158757i
8181 8.48255 0.942506
8282 7.60269 + 7.60269i 0.839577 + 0.839577i
8383 2.52680i 0.277353i 0.990338 + 0.138676i 0.0442848π0.0442848\pi
−0.990338 + 0.138676i 0.955715π0.955715\pi
8484 4.42492 0.482799
8585 −0.171086 4.11955i −0.0185569 0.446828i
8686 8.42242 0.908213
8787 2.11218i 0.226449i
8888 −7.91453 7.91453i −0.843691 0.843691i
8989 −1.66373 −0.176355 −0.0881775 0.996105i 0.528104π-0.528104\pi
−0.0881775 + 0.996105i 0.528104π0.528104\pi
9090 −2.52124 2.52124i −0.265762 0.265762i
9191 −6.28973 + 6.28973i −0.659343 + 0.659343i
9292 0.725212 0.725212i 0.0756086 0.0756086i
9393 23.4445i 2.43108i
9494 6.11645i 0.630864i
9595 1.84808 1.84808i 0.189609 0.189609i
9696 −6.82860 + 6.82860i −0.696941 + 0.696941i
9797 −8.67432 8.67432i −0.880744 0.880744i 0.112867 0.993610i 0.463997π-0.463997\pi
−0.993610 + 0.112867i 0.963997π0.963997\pi
9898 1.16527 0.117710
9999 8.13830 + 8.13830i 0.817930 + 0.817930i
100100 0.729699i 0.0729699i
101101 −4.18131 −0.416056 −0.208028 0.978123i 0.566704π-0.566704\pi
−0.208028 + 0.978123i 0.566704π0.566704\pi
102102 −11.5271 + 0.478722i −1.14135 + 0.0474006i
103103 8.08417 0.796557 0.398279 0.917265i 0.369608π-0.369608\pi
0.398279 + 0.917265i 0.369608π0.369608\pi
104104 11.2039i 1.09863i
105105 −4.28792 4.28792i −0.418458 0.418458i
106106 −14.5903 −1.41714
107107 −6.22304 6.22304i −0.601604 0.601604i 0.339134 0.940738i 0.389866π-0.389866\pi
−0.940738 + 0.339134i 0.889866π0.889866\pi
108108 0.209524 0.209524i 0.0201615 0.0201615i
109109 10.1218 10.1218i 0.969496 0.969496i −0.0300524 0.999548i 0.509567π-0.509567\pi
0.999548 + 0.0300524i 0.00956740π0.00956740\pi
110110 4.10039i 0.390957i
111111 27.3226i 2.59334i
112112 3.46836 3.46836i 0.327730 0.327730i
113113 −8.10334 + 8.10334i −0.762298 + 0.762298i −0.976737 0.214440i 0.931208π-0.931208\pi
0.214440 + 0.976737i 0.431208π0.431208\pi
114114 −5.17118 5.17118i −0.484325 0.484325i
115115 −1.40552 −0.131065
116116 0.438979 + 0.438979i 0.0407582 + 0.0407582i
117117 11.5207i 1.06509i
118118 1.58095 0.145538
119119 −10.0623 + 0.417888i −0.922407 + 0.0383077i
120120 7.63808 0.697258
121121 2.23561i 0.203237i
122122 −0.906716 0.906716i −0.0820902 0.0820902i
123123 23.6835 2.13547
124124 −4.87252 4.87252i −0.437565 0.437565i
125125 0.707107 0.707107i 0.0632456 0.0632456i
126126 −6.15830 + 6.15830i −0.548625 + 0.548625i
127127 2.51562i 0.223225i −0.993752 0.111613i 0.964398π-0.964398\pi
0.993752 0.111613i 0.0356015π-0.0356015\pi
128128 1.68825i 0.149221i
129129 13.1185 13.1185i 1.15502 1.15502i
130130 −2.90228 + 2.90228i −0.254547 + 0.254547i
131131 −1.57140 1.57140i −0.137294 0.137294i 0.635120 0.772414i 0.280951π-0.280951\pi
−0.772414 + 0.635120i 0.780951π0.780951\pi
132132 −6.59071 −0.573647
133133 −4.51405 4.51405i −0.391417 0.391417i
134134 2.34328i 0.202428i
135135 −0.406074 −0.0349493
136136 8.58977 9.33416i 0.736567 0.800398i
137137 −22.1633 −1.89354 −0.946771 0.321908i 0.895676π-0.895676\pi
−0.946771 + 0.321908i 0.895676π0.895676\pi
138138 3.93283i 0.334785i
139139 9.81865 + 9.81865i 0.832807 + 0.832807i 0.987900 0.155093i 0.0495676π-0.0495676\pi
−0.155093 + 0.987900i 0.549568π0.549568\pi
140140 1.78234 0.150635
141141 9.52680 + 9.52680i 0.802302 + 0.802302i
142142 9.79618 9.79618i 0.822077 0.822077i
143143 9.36825 9.36825i 0.783413 0.783413i
144144 6.35288i 0.529407i
145145 0.850775i 0.0706530i
146146 1.17621 1.17621i 0.0973438 0.0973438i
147147 1.81500 1.81500i 0.149698 0.149698i
148148 5.67851 + 5.67851i 0.466771 + 0.466771i
149149 −11.6461 −0.954087 −0.477044 0.878880i 0.658292π-0.658292\pi
−0.477044 + 0.878880i 0.658292π0.658292\pi
150150 −1.97858 1.97858i −0.161551 0.161551i
151151 2.82731i 0.230083i −0.993361 0.115042i 0.963300π-0.963300\pi
0.993361 0.115042i 0.0367002π-0.0367002\pi
152152 8.04088 0.652201
153153 −8.83264 + 9.59807i −0.714076 + 0.775958i
154154 10.0155 0.807068
155155 9.44332i 0.758506i
156156 −4.66495 4.66495i −0.373495 0.373495i
157157 1.36913 0.109268 0.0546342 0.998506i 0.482601π-0.482601\pi
0.0546342 + 0.998506i 0.482601π0.482601\pi
158158 −7.15096 7.15096i −0.568900 0.568900i
159159 −22.7255 + 22.7255i −1.80225 + 1.80225i
160160 −2.75053 + 2.75053i −0.217448 + 0.217448i
161161 3.43306i 0.270563i
162162 9.56048i 0.751143i
163163 −8.54984 + 8.54984i −0.669675 + 0.669675i −0.957641 0.287966i 0.907021π-0.907021\pi
0.287966 + 0.957641i 0.407021π0.407021\pi
164164 −4.92219 + 4.92219i −0.384358 + 0.384358i
165165 6.38665 + 6.38665i 0.497200 + 0.497200i
166166 2.84790 0.221040
167167 4.16611 + 4.16611i 0.322383 + 0.322383i 0.849681 0.527297i 0.176795π-0.176795\pi
−0.527297 + 0.849681i 0.676795π0.676795\pi
168168 18.6565i 1.43938i
169169 0.261831 0.0201408
170170 −4.64305 + 0.192827i −0.356106 + 0.0147892i
171171 −8.26822 −0.632287
172172 5.45290i 0.415780i
173173 1.46761 + 1.46761i 0.111580 + 0.111580i 0.760693 0.649112i 0.224859π-0.224859\pi
−0.649112 + 0.760693i 0.724859π0.724859\pi
174174 −2.38059 −0.180472
175175 −1.72715 1.72715i −0.130560 0.130560i
176176 −5.16596 + 5.16596i −0.389399 + 0.389399i
177177 2.46244 2.46244i 0.185089 0.185089i
178178 1.87515i 0.140548i
179179 10.5373i 0.787597i 0.919197 + 0.393799i 0.128839π0.128839\pi
−0.919197 + 0.393799i 0.871161π0.871161\pi
180180 1.63232 1.63232i 0.121666 0.121666i
181181 −2.39758 + 2.39758i −0.178210 + 0.178210i −0.790575 0.612365i 0.790218π-0.790218\pi
0.612365 + 0.790575i 0.290218π0.290218\pi
182182 7.08901 + 7.08901i 0.525472 + 0.525472i
183183 −2.82455 −0.208797
184184 −3.05766 3.05766i −0.225414 0.225414i
185185 11.0054i 0.809133i
186186 26.4237 1.93748
187187 14.9873 0.622424i 1.09598 0.0455162i
188188 −3.95995 −0.288809
189189 0.991860i 0.0721472i
190190 −2.08293 2.08293i −0.151111 0.151111i
191191 −12.3426 −0.893077 −0.446538 0.894764i 0.647343π-0.647343\pi
−0.446538 + 0.894764i 0.647343π0.647343\pi
192192 14.7469 + 14.7469i 1.06427 + 1.06427i
193193 8.45396 8.45396i 0.608529 0.608529i −0.334032 0.942562i 0.608409π-0.608409\pi
0.942562 + 0.334032i 0.108409π0.108409\pi
194194 −9.77662 + 9.77662i −0.701920 + 0.701920i
195195 9.04103i 0.647441i
196196 0.754430i 0.0538878i
197197 0.864156 0.864156i 0.0615686 0.0615686i −0.675652 0.737221i 0.736138π-0.736138\pi
0.737221 + 0.675652i 0.236138π0.236138\pi
198198 9.17248 9.17248i 0.651860 0.651860i
199199 15.3689 + 15.3689i 1.08947 + 1.08947i 0.995583 + 0.0938906i 0.0299304π0.0299304\pi
0.0938906 + 0.995583i 0.470070π0.470070\pi
200200 3.07658 0.217547
201201 3.64982 + 3.64982i 0.257438 + 0.257438i
202202 4.71265i 0.331581i
203203 −2.07807 −0.145852
204204 −0.309938 7.46294i −0.0217000 0.522511i
205205 9.53958 0.666273
206206 9.11148i 0.634827i
207207 3.14411 + 3.14411i 0.218531 + 0.218531i
208208 −7.31300 −0.507065
209209 6.72345 + 6.72345i 0.465071 + 0.465071i
210210 −4.83281 + 4.83281i −0.333496 + 0.333496i
211211 −11.9397 + 11.9397i −0.821965 + 0.821965i −0.986390 0.164425i 0.947423π-0.947423\pi
0.164425 + 0.986390i 0.447423π0.447423\pi
212212 9.44618i 0.648767i
213213 30.5165i 2.09096i
214214 −7.01384 + 7.01384i −0.479456 + 0.479456i
215215 5.28407 5.28407i 0.360371 0.360371i
216216 −0.883401 0.883401i −0.0601078 0.0601078i
217217 23.0659 1.56582
218218 −11.4081 11.4081i −0.772653 0.772653i
219219 3.66406i 0.247594i
220220 −2.65470 −0.178980
221221 11.0486 + 10.1675i 0.743212 + 0.683942i
222222 −30.7946 −2.06680
223223 9.61320i 0.643748i −0.946783 0.321874i 0.895687π-0.895687\pi
0.946783 0.321874i 0.104313π-0.104313\pi
224224 6.71833 + 6.71833i 0.448887 + 0.448887i
225225 −3.16356 −0.210904
226226 9.13308 + 9.13308i 0.607523 + 0.607523i
227227 1.25815 1.25815i 0.0835064 0.0835064i −0.664120 0.747626i 0.731194π-0.731194\pi
0.747626 + 0.664120i 0.231194π0.231194\pi
228228 3.34796 3.34796i 0.221724 0.221724i
229229 16.7429i 1.10640i −0.833048 0.553201i 0.813406π-0.813406\pi
0.833048 0.553201i 0.186594π-0.186594\pi
230230 1.58412i 0.104454i
231231 15.5998 15.5998i 1.02639 1.02639i
232232 1.85084 1.85084i 0.121513 0.121513i
233233 9.25323 + 9.25323i 0.606199 + 0.606199i 0.941951 0.335751i 0.108990π-0.108990\pi
−0.335751 + 0.941951i 0.608990π0.608990\pi
234234 12.9847 0.848836
235235 3.83735 + 3.83735i 0.250321 + 0.250321i
236236 1.02355i 0.0666275i
237237 −22.2762 −1.44700
238238 0.470992 + 11.3409i 0.0305299 + 0.735124i
239239 −23.9469 −1.54900 −0.774498 0.632577i 0.781997π-0.781997\pi
−0.774498 + 0.632577i 0.781997π0.781997\pi
240240 4.98551i 0.321814i
241241 −12.2266 12.2266i −0.787587 0.787587i 0.193511 0.981098i 0.438012π-0.438012\pi
−0.981098 + 0.193511i 0.938012π0.938012\pi
242242 −2.51970 −0.161972
243243 −15.7525 15.7525i −1.01053 1.01053i
244244 0.587032 0.587032i 0.0375809 0.0375809i
245245 0.731071 0.731071i 0.0467064 0.0467064i
246246 26.6931i 1.70189i
247247 9.51781i 0.605604i
248248 −20.5437 + 20.5437i −1.30452 + 1.30452i
249249 4.43581 4.43581i 0.281108 0.281108i
250250 −0.796963 0.796963i −0.0504044 0.0504044i
251251 18.2106 1.14944 0.574722 0.818349i 0.305110π-0.305110\pi
0.574722 + 0.818349i 0.305110π0.305110\pi
252252 −3.98705 3.98705i −0.251160 0.251160i
253253 5.11338i 0.321475i
254254 −2.83529 −0.177902
255255 −6.93154 + 7.53222i −0.434070 + 0.471686i
256256 −14.8981 −0.931128
257257 2.58018i 0.160947i −0.996757 0.0804735i 0.974357π-0.974357\pi
0.996757 0.0804735i 0.0256432π-0.0256432\pi
258258 −14.7856 14.7856i −0.920509 0.920509i
259259 −26.8814 −1.67033
260260 −1.87902 1.87902i −0.116532 0.116532i
261261 −1.90317 + 1.90317i −0.117803 + 0.117803i
262262 −1.77109 + 1.77109i −0.109418 + 0.109418i
263263 9.58787i 0.591213i 0.955310 + 0.295607i 0.0955218π0.0955218\pi
−0.955310 + 0.295607i 0.904478π0.904478\pi
264264 27.7879i 1.71023i
265265 −9.15372 + 9.15372i −0.562308 + 0.562308i
266266 −5.08767 + 5.08767i −0.311945 + 0.311945i
267267 2.92068 + 2.92068i 0.178743 + 0.178743i
268268 −1.51710 −0.0926717
269269 −5.01049 5.01049i −0.305495 0.305495i 0.537664 0.843159i 0.319307π-0.319307\pi
−0.843159 + 0.537664i 0.819307π0.819307\pi
270270 0.457676i 0.0278533i
271271 −13.7773 −0.836909 −0.418454 0.908238i 0.637428π-0.637428\pi
−0.418454 + 0.908238i 0.637428π0.637428\pi
272272 −6.09258 5.60670i −0.369417 0.339956i
273273 22.0833 1.33654
274274 24.9798i 1.50908i
275275 2.57251 + 2.57251i 0.155128 + 0.155128i
276276 −2.54622 −0.153264
277277 3.19263 + 3.19263i 0.191827 + 0.191827i 0.796485 0.604658i 0.206690π-0.206690\pi
−0.604658 + 0.796485i 0.706690π0.706690\pi
278278 11.0664 11.0664i 0.663717 0.663717i
279279 21.1245 21.1245i 1.26469 1.26469i
280280 7.51473i 0.449091i
281281 3.44172i 0.205316i −0.994717 0.102658i 0.967265π-0.967265\pi
0.994717 0.102658i 0.0327347π-0.0327347\pi
282282 10.7374 10.7374i 0.639405 0.639405i
283283 16.6458 16.6458i 0.989493 0.989493i −0.0104528 0.999945i 0.503327π-0.503327\pi
0.999945 + 0.0104528i 0.00332730π0.00332730\pi
284284 6.34231 + 6.34231i 0.376347 + 0.376347i
285285 −6.48861 −0.384352
286286 −10.5587 10.5587i −0.624351 0.624351i
287287 23.3010i 1.37542i
288288 12.3057 0.725122
289289 1.40960 + 16.9415i 0.0829174 + 0.996556i
290290 −0.958888 −0.0563079
291291 30.4555i 1.78534i
292292 0.761510 + 0.761510i 0.0445640 + 0.0445640i
293293 15.5924 0.910918 0.455459 0.890257i 0.349475π-0.349475\pi
0.455459 + 0.890257i 0.349475π0.349475\pi
294294 −2.04564 2.04564i −0.119304 0.119304i
295295 0.991860 0.991860i 0.0577483 0.0577483i
296296 23.9419 23.9419i 1.39160 1.39160i
297297 1.47733i 0.0857232i
298298 13.1261i 0.760372i
299299 3.61928 3.61928i 0.209309 0.209309i
300300 1.28099 1.28099i 0.0739579 0.0739579i
301301 −12.9067 12.9067i −0.743928 0.743928i
302302 −3.18660 −0.183368
303303 7.34029 + 7.34029i 0.421688 + 0.421688i
304304 5.24843i 0.301018i
305305 −1.13771 −0.0651453
306306 10.8178 + 9.95505i 0.618410 + 0.569093i
307307 21.6549 1.23591 0.617955 0.786214i 0.287962π-0.287962\pi
0.617955 + 0.786214i 0.287962π0.287962\pi
308308 6.48428i 0.369476i
309309 −14.1918 14.1918i −0.807341 0.807341i
310310 10.6433 0.604501
311311 −6.26814 6.26814i −0.355434 0.355434i 0.506693 0.862127i 0.330868π-0.330868\pi
−0.862127 + 0.506693i 0.830868π0.830868\pi
312312 −19.6685 + 19.6685i −1.11351 + 1.11351i
313313 −12.1015 + 12.1015i −0.684016 + 0.684016i −0.960903 0.276887i 0.910697π-0.910697\pi
0.276887 + 0.960903i 0.410697π0.410697\pi
314314 1.54311i 0.0870828i
315315 7.72720i 0.435379i
316316 4.62972 4.62972i 0.260442 0.260442i
317317 7.30027 7.30027i 0.410024 0.410024i −0.471723 0.881747i 0.656368π-0.656368\pi
0.881747 + 0.471723i 0.156368π0.156368\pi
318318 25.6134 + 25.6134i 1.43633 + 1.43633i
319319 3.09519 0.173297
320320 5.93999 + 5.93999i 0.332056 + 0.332056i
321321 21.8491i 1.21950i
322322 3.86932 0.215629
323323 −7.29708 + 7.92944i −0.406020 + 0.441206i
324324 6.18971 0.343873
325325 3.64168i 0.202004i
326326 9.63632 + 9.63632i 0.533706 + 0.533706i
327327 −35.5378 −1.96524
328328 20.7531 + 20.7531i 1.14590 + 1.14590i
329329 9.37296 9.37296i 0.516748 0.516748i
330330 7.19824 7.19824i 0.396250 0.396250i
331331 6.56727i 0.360970i −0.983578 0.180485i 0.942233π-0.942233\pi
0.983578 0.180485i 0.0577667π-0.0577667\pi
332332 1.84381i 0.101192i
333333 −24.6188 + 24.6188i −1.34910 + 1.34910i
334334 4.69553 4.69553i 0.256928 0.256928i
335335 1.47013 + 1.47013i 0.0803217 + 0.0803217i
336336 −12.1774 −0.664333
337337 −21.3377 21.3377i −1.16234 1.16234i −0.983962 0.178379i 0.942915π-0.942915\pi
−0.178379 0.983962i 0.557085π-0.557085\pi
338338 0.295103i 0.0160515i
339339 28.4508 1.54524
340340 −0.124841 3.00604i −0.00677047 0.163025i
341341 −34.3555 −1.86046
342342 9.31892i 0.503909i
343343 −13.8758 13.8758i −0.749220 0.749220i
344344 22.9907 1.23957
345345 2.46739 + 2.46739i 0.132840 + 0.132840i
346346 1.65411 1.65411i 0.0889254 0.0889254i
347347 4.97815 4.97815i 0.267241 0.267241i −0.560746 0.827988i 0.689486π-0.689486\pi
0.827988 + 0.560746i 0.189486π0.189486\pi
348348 1.54126i 0.0826200i
349349 35.4396i 1.89704i −0.316723 0.948518i 0.602583π-0.602583\pi
0.316723 0.948518i 0.397417π-0.397417\pi
350350 −1.94663 + 1.94663i −0.104052 + 0.104052i
351351 1.04566 1.04566i 0.0558133 0.0558133i
352352 −10.0066 10.0066i −0.533355 0.533355i
353353 −8.54669 −0.454895 −0.227447 0.973790i 0.573038π-0.573038\pi
−0.227447 + 0.973790i 0.573038π0.573038\pi
354354 −2.77536 2.77536i −0.147509 0.147509i
355355 12.2919i 0.652386i
356356 −1.21402 −0.0643430
357357 18.3979 + 16.9307i 0.973721 + 0.896068i
358358 11.8764 0.627686
359359 20.2839i 1.07054i 0.844681 + 0.535271i 0.179790π0.179790\pi
−0.844681 + 0.535271i 0.820210π0.820210\pi
360360 −6.88224 6.88224i −0.362726 0.362726i
361361 12.1692 0.640485
362362 2.70225 + 2.70225i 0.142027 + 0.142027i
363363 −3.92461 + 3.92461i −0.205988 + 0.205988i
364364 −4.58962 + 4.58962i −0.240561 + 0.240561i
365365 1.47586i 0.0772503i
366366 3.18348i 0.166403i
367367 −8.99600 + 8.99600i −0.469587 + 0.469587i −0.901781 0.432193i 0.857740π-0.857740\pi
0.432193 + 0.901781i 0.357740π0.357740\pi
368368 −1.99579 + 1.99579i −0.104038 + 0.104038i
369369 −21.3398 21.3398i −1.11091 1.11091i
370370 −12.4039 −0.644849
371371 22.3585 + 22.3585i 1.16080 + 1.16080i
372372 17.1074i 0.886979i
373373 −11.1454 −0.577086 −0.288543 0.957467i 0.593171π-0.593171\pi
−0.288543 + 0.957467i 0.593171π0.593171\pi
374374 −0.701519 16.8918i −0.0362747 0.873453i
375375 −2.48265 −0.128204
376376 16.6961i 0.861034i
377377 2.19079 + 2.19079i 0.112832 + 0.112832i
378378 1.11790 0.0574987
379379 8.96691 + 8.96691i 0.460599 + 0.460599i 0.898852 0.438253i 0.144402π-0.144402\pi
−0.438253 + 0.898852i 0.644402π0.644402\pi
380380 1.34854 1.34854i 0.0691787 0.0691787i
381381 −4.41617 + 4.41617i −0.226247 + 0.226247i
382382 13.9110i 0.711749i
383383 17.3523i 0.886661i 0.896358 + 0.443331i 0.146203π0.146203\pi
−0.896358 + 0.443331i 0.853797π0.853797\pi
384384 2.96372 2.96372i 0.151241 0.151241i
385385 6.28351 6.28351i 0.320237 0.320237i
386386 −9.52825 9.52825i −0.484975 0.484975i
387387 −23.6407 −1.20172
388388 −6.32965 6.32965i −0.321339 0.321339i
389389 19.4510i 0.986205i −0.869971 0.493103i 0.835863π-0.835863\pi
0.869971 0.493103i 0.164137π-0.164137\pi
390390 10.1899 0.515987
391391 5.79010 0.240464i 0.292818 0.0121608i
392392 3.18085 0.160657
393393 5.51720i 0.278306i
394394 −0.973970 0.973970i −0.0490679 0.0490679i
395395 −8.97276 −0.451468
396396 5.93851 + 5.93851i 0.298421 + 0.298421i
397397 −3.36574 + 3.36574i −0.168922 + 0.168922i −0.786505 0.617584i 0.788112π-0.788112\pi
0.617584 + 0.786505i 0.288112π0.288112\pi
398398 17.3219 17.3219i 0.868270 0.868270i
399399 15.8488i 0.793434i
400400 2.00814i 0.100407i
401401 17.1148 17.1148i 0.854672 0.854672i −0.136032 0.990704i 0.543435π-0.543435\pi
0.990704 + 0.136032i 0.0434350π0.0434350\pi
402402 4.11362 4.11362i 0.205169 0.205169i
403403 −24.3171 24.3171i −1.21132 1.21132i
404404 −3.05110 −0.151798
405405 −5.99807 5.99807i −0.298047 0.298047i
406406 2.34214i 0.116239i
407407 40.0385 1.98463
408408 −31.4655 + 1.30677i −1.55777 + 0.0646947i
409409 18.2463 0.902221 0.451111 0.892468i 0.351028π-0.351028\pi
0.451111 + 0.892468i 0.351028π0.351028\pi
410410 10.7518i 0.530995i
411411 38.9078 + 38.9078i 1.91918 + 1.91918i
412412 5.89901 0.290624
413413 −2.42268 2.42268i −0.119212 0.119212i
414414 3.54365 3.54365i 0.174161 0.174161i
415415 1.78672 1.78672i 0.0877066 0.0877066i
416416 14.1655i 0.694522i
417417 34.4733i 1.68816i
418418 7.57784 7.57784i 0.370644 0.370644i
419419 1.23229 1.23229i 0.0602015 0.0602015i −0.676365 0.736567i 0.736446π-0.736446\pi
0.736567 + 0.676365i 0.236446π0.236446\pi
420420 −3.12889 3.12889i −0.152674 0.152674i
421421 −37.0251 −1.80449 −0.902247 0.431220i 0.858083π-0.858083\pi
−0.902247 + 0.431220i 0.858083π0.858083\pi
422422 13.4570 + 13.4570i 0.655076 + 0.655076i
423423 17.1681i 0.834743i
424424 −39.8273 −1.93418
425425 −2.79199 + 3.03394i −0.135431 + 0.147168i
426426 −34.3944 −1.66641
427427 2.77894i 0.134482i
428428 −4.54095 4.54095i −0.219495 0.219495i
429429 −32.8920 −1.58804
430430 −5.95555 5.95555i −0.287202 0.287202i
431431 21.4877 21.4877i 1.03503 1.03503i 0.0356645 0.999364i 0.488645π-0.488645\pi
0.999364 0.0356645i 0.0113548π-0.0113548\pi
432432 −0.576612 + 0.576612i −0.0277423 + 0.0277423i
433433 15.8246i 0.760483i 0.924887 + 0.380242i 0.124159π0.124159\pi
−0.924887 + 0.380242i 0.875841π0.875841\pi
434434 25.9970i 1.24790i
435435 −1.49354 + 1.49354i −0.0716096 + 0.0716096i
436436 7.38590 7.38590i 0.353720 0.353720i
437437 2.59751 + 2.59751i 0.124256 + 0.124256i
438438 −4.12967 −0.197323
439439 −2.94661 2.94661i −0.140634 0.140634i 0.633285 0.773919i 0.281706π-0.281706\pi
−0.773919 + 0.633285i 0.781706π0.781706\pi
440440 11.1928i 0.533597i
441441 −3.27078 −0.155751
442442 11.4596 12.4527i 0.545077 0.592313i
443443 15.7201 0.746884 0.373442 0.927654i 0.378177π-0.378177\pi
0.373442 + 0.927654i 0.378177π0.378177\pi
444444 19.9373i 0.946181i
445445 1.17643 + 1.17643i 0.0557683 + 0.0557683i
446446 −10.8348 −0.513043
447447 20.4448 + 20.4448i 0.967004 + 0.967004i
448448 14.5088 14.5088i 0.685476 0.685476i
449449 −11.7004 + 11.7004i −0.552176 + 0.552176i −0.927068 0.374892i 0.877680π-0.877680\pi
0.374892 + 0.927068i 0.377680π0.377680\pi
450450 3.56558i 0.168083i
451451 34.7057i 1.63423i
452452 −5.91300 + 5.91300i −0.278124 + 0.278124i
453453 −4.96335 + 4.96335i −0.233199 + 0.233199i
454454 −1.41803 1.41803i −0.0665515 0.0665515i
455455 8.89503 0.417005
456456 −14.1158 14.1158i −0.661031 0.661031i
457457 1.42830i 0.0668131i 0.999442 + 0.0334066i 0.0106356π0.0106356\pi
−0.999442 + 0.0334066i 0.989364π0.989364\pi
458458 −18.8705 −0.881761
459459 1.67284 0.0694735i 0.0780816 0.00324275i
460460 −1.02560 −0.0478191
461461 11.1662i 0.520062i −0.965600 0.260031i 0.916267π-0.916267\pi
0.965600 0.260031i 0.0837327π-0.0837327\pi
462462 −17.5821 17.5821i −0.817995 0.817995i
463463 −29.2204 −1.35799 −0.678994 0.734144i 0.737584π-0.737584\pi
−0.678994 + 0.734144i 0.737584π0.737584\pi
464464 −1.20807 1.20807i −0.0560835 0.0560835i
465465 16.5778 16.5778i 0.768775 0.768775i
466466 10.4291 10.4291i 0.483119 0.483119i
467467 10.9388i 0.506187i −0.967442 0.253093i 0.918552π-0.918552\pi
0.967442 0.253093i 0.0814480π-0.0814480\pi
468468 8.40664i 0.388597i
469469 3.59088 3.59088i 0.165811 0.165811i
470470 4.32498 4.32498i 0.199497 0.199497i
471471 −2.40351 2.40351i −0.110748 0.110748i
472472 4.31552 0.198638
473473 19.2239 + 19.2239i 0.883914 + 0.883914i
474474 25.1070i 1.15320i
475475 −2.61358 −0.119919
476476 −7.34243 + 0.304933i −0.336540 + 0.0139766i
477477 40.9533 1.87512
478478 26.9900i 1.23449i
479479 −12.1620 12.1620i −0.555695 0.555695i 0.372384 0.928079i 0.378540π-0.378540\pi
−0.928079 + 0.372384i 0.878540π0.878540\pi
480480 9.65710 0.440784
481481 28.3395 + 28.3395i 1.29217 + 1.29217i
482482 −13.7803 + 13.7803i −0.627678 + 0.627678i
483483 6.02674 6.02674i 0.274226 0.274226i
484484 1.63132i 0.0741509i
485485 12.2673i 0.557031i
486486 −17.7543 + 17.7543i −0.805352 + 0.805352i
487487 −18.2749 + 18.2749i −0.828113 + 0.828113i −0.987256 0.159143i 0.949127π-0.949127\pi
0.159143 + 0.987256i 0.449127π0.449127\pi
488488 −2.47506 2.47506i −0.112041 0.112041i
489489 30.0185 1.35748
490490 −0.823973 0.823973i −0.0372233 0.0372233i
491491 12.2373i 0.552261i −0.961120 0.276131i 0.910948π-0.910948\pi
0.961120 0.276131i 0.0890523π-0.0890523\pi
492492 17.2818 0.779124
493493 0.145556 + 3.50481i 0.00655550 + 0.157849i
494494 10.7273 0.482644
495495 11.5093i 0.517304i
496496 13.4092 + 13.4092i 0.602092 + 0.602092i
497497 −30.0237 −1.34675
498498 −4.99949 4.99949i −0.224033 0.224033i
499499 4.53684 4.53684i 0.203097 0.203097i −0.598229 0.801325i 0.704129π-0.704129\pi
0.801325 + 0.598229i 0.204129π0.204129\pi
500500 0.515975 0.515975i 0.0230751 0.0230751i
501501 14.6272i 0.653496i
502502 20.5248i 0.916065i
503503 15.0825 15.0825i 0.672497 0.672497i −0.285794 0.958291i 0.592257π-0.592257\pi
0.958291 + 0.285794i 0.0922574π0.0922574\pi
504504 −16.8103 + 16.8103i −0.748790 + 0.748790i
505505 2.95663 + 2.95663i 0.131568 + 0.131568i
506506 −5.76317 −0.256204
507507 −0.459644 0.459644i −0.0204135 0.0204135i
508508 1.83565i 0.0814436i
509509 14.2265 0.630577 0.315289 0.948996i 0.397899π-0.397899\pi
0.315289 + 0.948996i 0.397899π0.397899\pi
510510 8.48939 + 7.81237i 0.375916 + 0.345938i
511511 −3.60489 −0.159471
512512 20.1677i 0.891296i
513513 0.750456 + 0.750456i 0.0331334 + 0.0331334i
514514 −2.90805 −0.128269
515515 −5.71637 5.71637i −0.251893 0.251893i
516516 9.57257 9.57257i 0.421409 0.421409i
517517 −13.9606 + 13.9606i −0.613985 + 0.613985i
518518 30.2973i 1.33119i
519519 5.15278i 0.226182i
520520 −7.92236 + 7.92236i −0.347419 + 0.347419i
521521 −17.3636 + 17.3636i −0.760714 + 0.760714i −0.976451 0.215738i 0.930784π-0.930784\pi
0.215738 + 0.976451i 0.430784π0.430784\pi
522522 2.14501 + 2.14501i 0.0938846 + 0.0938846i
523523 39.8642 1.74314 0.871570 0.490271i 0.163102π-0.163102\pi
0.871570 + 0.490271i 0.163102π0.163102\pi
524524 −1.14665 1.14665i −0.0500917 0.0500917i
525525 6.06403i 0.264656i
526526 10.8063 0.471175
527527 −1.61562 38.9023i −0.0703775 1.69461i
528528 18.1377 0.789341
529529 21.0245i 0.914110i
530530 10.3169 + 10.3169i 0.448139 + 0.448139i
531531 −4.43754 −0.192573
532532 −3.29390 3.29390i −0.142809 0.142809i
533533 −24.5650 + 24.5650i −1.06403 + 1.06403i
534534 3.29183 3.29183i 0.142451 0.142451i
535535 8.80071i 0.380488i
536536 6.39644i 0.276284i
537537 18.4983 18.4983i 0.798260 0.798260i
538538 −5.64720 + 5.64720i −0.243468 + 0.243468i
539539 2.65969 + 2.65969i 0.114561 + 0.114561i
540540 −0.296312 −0.0127512
541541 16.1805 + 16.1805i 0.695654 + 0.695654i 0.963470 0.267816i 0.0863020π-0.0863020\pi
−0.267816 + 0.963470i 0.586302π0.586302\pi
542542 15.5280i 0.666985i
543543 8.41789 0.361246
544544 10.8604 11.8015i 0.465634 0.505986i
545545 −14.3144 −0.613163
546546 24.8895i 1.06517i
547547 10.9849 + 10.9849i 0.469682 + 0.469682i 0.901812 0.432130i 0.142238π-0.142238\pi
−0.432130 + 0.901812i 0.642238π0.642238\pi
548548 −16.1726 −0.690858
549549 2.54504 + 2.54504i 0.108620 + 0.108620i
550550 2.89941 2.89941i 0.123631 0.123631i
551551 −1.57230 + 1.57230i −0.0669822 + 0.0669822i
552552 10.7354i 0.456931i
553553 21.9165i 0.931985i
554554 3.59834 3.59834i 0.152879 0.152879i
555555 −19.3200 + 19.3200i −0.820087 + 0.820087i
556556 7.16467 + 7.16467i 0.303849 + 0.303849i
557557 −0.980081 −0.0415274 −0.0207637 0.999784i 0.506610π-0.506610\pi
−0.0207637 + 0.999784i 0.506610π0.506610\pi
558558 −23.8089 23.8089i −1.00791 1.00791i
559559 27.2136i 1.15101i
560560 −4.90501 −0.207274
561561 −27.4028 25.2175i −1.15695 1.06468i
562562 −3.87908 −0.163629
563563 28.8837i 1.21730i −0.793437 0.608652i 0.791711π-0.791711\pi
0.793437 0.608652i 0.208289π-0.208289\pi
564564 6.95170 + 6.95170i 0.292720 + 0.292720i
565565 11.4598 0.482119
566566 −18.7611 18.7611i −0.788589 0.788589i
567567 −14.6507 + 14.6507i −0.615270 + 0.615270i
568568 26.7406 26.7406i 1.12201 1.12201i
569569 18.2893i 0.766729i 0.923597 + 0.383365i 0.125235π0.125235\pi
−0.923597 + 0.383365i 0.874765π0.874765\pi
570570 7.31315i 0.306314i
571571 −7.35702 + 7.35702i −0.307882 + 0.307882i −0.844087 0.536206i 0.819857π-0.819857\pi
0.536206 + 0.844087i 0.319857π0.319857\pi
572572 6.83601 6.83601i 0.285828 0.285828i
573573 21.6674 + 21.6674i 0.905168 + 0.905168i
574574 −26.2620 −1.09616
575575 0.993850 + 0.993850i 0.0414464 + 0.0414464i
576576 26.5753i 1.10730i
577577 −28.3066 −1.17842 −0.589209 0.807980i 0.700561π-0.700561\pi
−0.589209 + 0.807980i 0.700561π0.700561\pi
578578 19.0943 1.58872i 0.794219 0.0660821i
579579 −29.6819 −1.23354
580580 0.620810i 0.0257777i
581581 −4.36417 4.36417i −0.181056 0.181056i
582582 34.3257 1.42285
583583 −33.3019 33.3019i −1.37922 1.37922i
584584 3.21070 3.21070i 0.132860 0.132860i
585585 8.14636 8.14636i 0.336810 0.336810i
586586 17.5738i 0.725968i
587587 2.68137i 0.110672i 0.998468 + 0.0553360i 0.0176230π0.0176230\pi
−0.998468 + 0.0553360i 0.982377π0.982377\pi
588588 1.32440 1.32440i 0.0546174 0.0546174i
589589 17.4520 17.4520i 0.719097 0.719097i
590590 −1.11790 1.11790i −0.0460233 0.0460233i
591591 −3.03405 −0.124804
592592 −15.6273 15.6273i −0.642279 0.642279i
593593 15.3155i 0.628934i 0.949268 + 0.314467i 0.101826π0.101826\pi
−0.949268 + 0.314467i 0.898174π0.898174\pi
594594 −1.66506 −0.0683183
595595 7.41059 + 6.81961i 0.303805 + 0.279577i
596596 −8.49817 −0.348098
597597 53.9603i 2.20845i
598598 −4.07921 4.07921i −0.166811 0.166811i
599599 43.5243 1.77836 0.889178 0.457561i 0.151277π-0.151277\pi
0.889178 + 0.457561i 0.151277π0.151277\pi
600600 −5.40094 5.40094i −0.220492 0.220492i
601601 21.7299 21.7299i 0.886381 0.886381i −0.107792 0.994173i 0.534378π-0.534378\pi
0.994173 + 0.107792i 0.0343782π0.0343782\pi
602602 −14.5468 + 14.5468i −0.592883 + 0.592883i
603603 6.57729i 0.267848i
604604 2.06309i 0.0839459i
605605 −1.58081 + 1.58081i −0.0642692 + 0.0642692i
606606 8.27306 8.27306i 0.336070 0.336070i
607607 −10.3997 10.3997i −0.422112 0.422112i 0.463818 0.885930i 0.346479π-0.346479\pi
−0.885930 + 0.463818i 0.846479π0.846479\pi
608608 10.1664 0.412301
609609 3.64806 + 3.64806i 0.147827 + 0.147827i
610610 1.28229i 0.0519184i
611611 −19.7628 −0.799516
612612 −6.44517 + 7.00370i −0.260531 + 0.283108i
613613 23.6535 0.955354 0.477677 0.878535i 0.341479π-0.341479\pi
0.477677 + 0.878535i 0.341479π0.341479\pi
614614 24.4067i 0.984974i
615615 −16.7467 16.7467i −0.675294 0.675294i
616616 27.3392 1.10153
617617 7.10492 + 7.10492i 0.286033 + 0.286033i 0.835509 0.549476i 0.185173π-0.185173\pi
−0.549476 + 0.835509i 0.685173π0.685173\pi
618618 −15.9952 + 15.9952i −0.643421 + 0.643421i
619619 −24.3145 + 24.3145i −0.977281 + 0.977281i −0.999748 0.0224668i 0.992848π-0.992848\pi
0.0224668 + 0.999748i 0.492848π0.492848\pi
620620 6.89079i 0.276741i
621621 0.570743i 0.0229031i
622622 −7.06467 + 7.06467i −0.283268 + 0.283268i
623623 2.87351 2.87351i 0.115125 0.115125i
624624 12.8380 + 12.8380i 0.513930 + 0.513930i
625625 −1.00000 −0.0400000
626626 13.6393 + 13.6393i 0.545136 + 0.545136i
627627 23.6060i 0.942735i
628628 0.999052 0.0398665
629629 1.88287 + 45.3373i 0.0750749 + 1.80772i
630630 8.70915 0.346981
631631 8.25061i 0.328451i −0.986423 0.164226i 0.947487π-0.947487\pi
0.986423 0.164226i 0.0525125π-0.0525125\pi
632632 −19.5200 19.5200i −0.776462 0.776462i
633633 41.9204 1.66619
634634 −8.22796 8.22796i −0.326774 0.326774i
635635 −1.77881 + 1.77881i −0.0705900 + 0.0705900i
636636 −16.5828 + 16.5828i −0.657550 + 0.657550i
637637 3.76510i 0.149179i
638638 3.48851i 0.138111i
639639 −27.4967 + 27.4967i −1.08775 + 1.08775i
640640 1.19377 1.19377i 0.0471879 0.0471879i
641641 12.1786 + 12.1786i 0.481024 + 0.481024i 0.905459 0.424434i 0.139527π-0.139527\pi
−0.424434 + 0.905459i 0.639527π0.639527\pi
642642 24.6256 0.971895
643643 −8.88071 8.88071i −0.350221 0.350221i 0.509971 0.860192i 0.329656π-0.329656\pi
−0.860192 + 0.509971i 0.829656π0.829656\pi
644644 2.50510i 0.0987149i
645645 −18.5524 −0.730499
646646 8.93708 + 8.22436i 0.351625 + 0.323583i
647647 −3.62337 −0.142449 −0.0712247 0.997460i 0.522691π-0.522691\pi
−0.0712247 + 0.997460i 0.522691π0.522691\pi
648648 26.0972i 1.02520i
649649 3.60846 + 3.60846i 0.141645 + 0.141645i
650650 4.10445 0.160990
651651 −40.4922 40.4922i −1.58701 1.58701i
652652 −6.23881 + 6.23881i −0.244331 + 0.244331i
653653 6.89142 6.89142i 0.269682 0.269682i −0.559290 0.828972i 0.688926π-0.688926\pi
0.828972 + 0.559290i 0.188926π0.188926\pi
654654 40.0538i 1.56623i
655655 2.22230i 0.0868325i
656656 13.5459 13.5459i 0.528879 0.528879i
657657 −3.30148 + 3.30148i −0.128803 + 0.128803i
658658 −10.5640 10.5640i −0.411829 0.411829i
659659 −7.19930 −0.280445 −0.140222 0.990120i 0.544782π-0.544782\pi
−0.140222 + 0.990120i 0.544782π0.544782\pi
660660 4.66033 + 4.66033i 0.181403 + 0.181403i
661661 11.0362i 0.429258i 0.976696 + 0.214629i 0.0688542π0.0688542\pi
−0.976696 + 0.214629i 0.931146π0.931146\pi
662662 −7.40181 −0.287680
663663 −1.54679 37.2450i −0.0600725 1.44648i
664664 7.77391 0.301686
665665 6.38383i 0.247554i
666666 27.7473 + 27.7473i 1.07519 + 1.07519i
667667 1.19578 0.0463007
668668 3.04001 + 3.04001i 0.117621 + 0.117621i
669669 −16.8760 + 16.8760i −0.652463 + 0.652463i
670670 1.65695 1.65695i 0.0640135 0.0640135i
671671 4.13909i 0.159788i
672672 23.5881i 0.909929i
673673 20.8675 20.8675i 0.804382 0.804382i −0.179395 0.983777i 0.557414π-0.557414\pi
0.983777 + 0.179395i 0.0574141π0.0574141\pi
674674 −24.0493 + 24.0493i −0.926343 + 0.926343i
675675 0.287137 + 0.287137i 0.0110519 + 0.0110519i
676676 0.191058 0.00734837
677677 0.394531 + 0.394531i 0.0151631 + 0.0151631i 0.714648 0.699485i 0.246587π-0.246587\pi
−0.699485 + 0.714648i 0.746587π0.746587\pi
678678 32.0662i 1.23150i
679679 29.9637 1.14990
680680 −12.6741 + 0.526360i −0.486031 + 0.0201850i
681681 −4.41737 −0.169274
682682 38.7213i 1.48272i
683683 −25.5664 25.5664i −0.978272 0.978272i 0.0214974 0.999769i 0.493157π-0.493157\pi
−0.999769 + 0.0214974i 0.993157π0.993157\pi
684684 −6.03332 −0.230690
685685 15.6718 + 15.6718i 0.598790 + 0.598790i
686686 −15.6390 + 15.6390i −0.597101 + 0.597101i
687687 −29.3922 + 29.3922i −1.12138 + 1.12138i
688688 15.0064i 0.572115i
689689 47.1427i 1.79599i
690690 2.78093 2.78093i 0.105868 0.105868i
691691 28.1588 28.1588i 1.07121 1.07121i 0.0739501 0.997262i 0.476439π-0.476439\pi
0.997262 0.0739501i 0.0235606π-0.0235606\pi
692692 1.07091 + 1.07091i 0.0407100 + 0.0407100i
693693 −28.1122 −1.06789
694694 −5.61075 5.61075i −0.212981 0.212981i
695695 13.8857i 0.526714i
696696 −6.49829 −0.246317
697697 −39.2988 + 1.63209i −1.48855 + 0.0618198i
698698 −39.9431 −1.51187
699699 32.4881i 1.22881i
700700 −1.26030 1.26030i −0.0476349 0.0476349i
701701 20.0299 0.756520 0.378260 0.925699i 0.376522π-0.376522\pi
0.378260 + 0.925699i 0.376522π0.376522\pi
702702 −1.17854 1.17854i −0.0444812 0.0444812i
703703 −20.3388 + 20.3388i −0.767094 + 0.767094i
704704 −21.6101 + 21.6101i −0.814463 + 0.814463i
705705 13.4729i 0.507420i
706706 9.63277i 0.362534i
707707 7.22175 7.22175i 0.271602 0.271602i
708708 1.79684 1.79684i 0.0675295 0.0675295i
709709 −6.86493 6.86493i −0.257818 0.257818i 0.566348 0.824166i 0.308356π-0.308356\pi
−0.824166 + 0.566348i 0.808356π0.808356\pi
710710 −13.8539 −0.519927
711711 20.0719 + 20.0719i 0.752753 + 0.752753i
712712 5.11859i 0.191827i
713713 −13.2727 −0.497068
714714 19.0822 20.7359i 0.714133 0.776020i
715715 −13.2487 −0.495474
716716 7.68909i 0.287355i
717717 42.0388 + 42.0388i 1.56997 + 1.56997i
718718 22.8615 0.853182
719719 14.7143 + 14.7143i 0.548750 + 0.548750i 0.926079 0.377329i 0.123157π-0.123157\pi
−0.377329 + 0.926079i 0.623157π0.623157\pi
720720 −4.49216 + 4.49216i −0.167413 + 0.167413i
721721 −13.9626 + 13.9626i −0.519994 + 0.519994i
722722 13.7156i 0.510443i
723723 42.9277i 1.59650i
724724 −1.74951 + 1.74951i −0.0650200 + 0.0650200i
725725 −0.601589 + 0.601589i −0.0223425 + 0.0223425i
726726 4.42333 + 4.42333i 0.164165 + 0.164165i
727727 39.1557 1.45220 0.726102 0.687587i 0.241330π-0.241330\pi
0.726102 + 0.687587i 0.241330π0.241330\pi
728728 19.3509 + 19.3509i 0.717191 + 0.717191i
729729 29.8595i 1.10591i
730730 −1.66341 −0.0615656
731731 −20.8640 + 22.6720i −0.771682 + 0.838556i
732732 −2.06107 −0.0761793
733733 12.9215i 0.477265i −0.971110 0.238633i 0.923301π-0.923301\pi
0.971110 0.238633i 0.0766992π-0.0766992\pi
734734 10.1392 + 10.1392i 0.374244 + 0.374244i
735735 −2.56679 −0.0946776
736736 −3.86591 3.86591i −0.142499 0.142499i
737737 −5.34844 + 5.34844i −0.197012 + 0.197012i
738738 −24.0516 + 24.0516i −0.885352 + 0.885352i
739739 37.9866i 1.39736i −0.715434 0.698680i 0.753771π-0.753771\pi
0.715434 0.698680i 0.246229π-0.246229\pi
740740 8.03063i 0.295212i
741741 16.7085 16.7085i 0.613803 0.613803i
742742 25.1998 25.1998i 0.925112 0.925112i
743743 8.65513 + 8.65513i 0.317526 + 0.317526i 0.847816 0.530290i 0.177917π-0.177917\pi
−0.530290 + 0.847816i 0.677917π0.677917\pi
744744 72.1288 2.64437
745745 8.23505 + 8.23505i 0.301709 + 0.301709i
746746 12.5617i 0.459916i
747747 −7.99371 −0.292474
748748 10.9362 0.454183i 0.399867 0.0166066i
749749 21.4963 0.785457
750750 2.79814i 0.102174i
751751 −9.97504 9.97504i −0.363995 0.363995i 0.501287 0.865281i 0.332860π-0.332860\pi
−0.865281 + 0.501287i 0.832860π0.832860\pi
752752 10.8978 0.397403
753753 −31.9688 31.9688i −1.16501 1.16501i
754754 2.46919 2.46919i 0.0899227 0.0899227i
755755 −1.99921 + 1.99921i −0.0727588 + 0.0727588i
756756 0.723760i 0.0263229i
757757 0.782070i 0.0284248i −0.999899 0.0142124i 0.995476π-0.995476\pi
0.999899 0.0142124i 0.00452410π-0.00452410\pi
758758 10.1064 10.1064i 0.367081 0.367081i
759759 −8.97654 + 8.97654i −0.325828 + 0.325828i
760760 −5.68576 5.68576i −0.206244 0.206244i
761761 2.86350 0.103802 0.0519009 0.998652i 0.483472π-0.483472\pi
0.0519009 + 0.998652i 0.483472π0.483472\pi
762762 4.97736 + 4.97736i 0.180311 + 0.180311i
763763 34.9639i 1.26578i
764764 −9.00636 −0.325839
765765 13.0325 0.541242i 0.471190 0.0195686i
766766 19.5574 0.706636
767767 5.10819i 0.184446i
768768 26.1535 + 26.1535i 0.943734 + 0.943734i
769769 38.6633 1.39423 0.697117 0.716957i 0.254466π-0.254466\pi
0.697117 + 0.716957i 0.254466π0.254466\pi
770770 −7.08200 7.08200i −0.255217 0.255217i
771771 −4.52950 + 4.52950i −0.163126 + 0.163126i
772772 6.16885 6.16885i 0.222022 0.222022i
773773 37.9989i 1.36672i −0.730080 0.683362i 0.760517π-0.760517\pi
0.730080 0.683362i 0.239483π-0.239483\pi
774774 26.6449i 0.957730i
775775 6.67744 6.67744i 0.239861 0.239861i
776776 −26.6872 + 26.6872i −0.958016 + 0.958016i
777777 47.1902 + 47.1902i 1.69294 + 1.69294i
778778 −21.9228 −0.785969
779779 −17.6299 17.6299i −0.631656 0.631656i
780780 6.59723i 0.236219i
781781 44.7188 1.60017
782782 −0.271021 6.52589i −0.00969171 0.233365i
783783 0.345477 0.0123464
784784 2.07620i 0.0741499i
785785 −0.968120 0.968120i −0.0345537 0.0345537i
786786 6.21831 0.221800
787787 −25.0127 25.0127i −0.891606 0.891606i 0.103068 0.994674i 0.467134π-0.467134\pi
−0.994674 + 0.103068i 0.967134π0.967134\pi
788788 0.630574 0.630574i 0.0224633 0.0224633i
789789 16.8315 16.8315i 0.599217 0.599217i
790790 10.1130i 0.359804i
791791 27.9914i 0.995259i
792792 25.0381 25.0381i 0.889691 0.889691i
793793 2.92968 2.92968i 0.104036 0.104036i
794794 3.79344 + 3.79344i 0.134624 + 0.134624i
795795 32.1387 1.13984
796796 11.2147 + 11.2147i 0.397494 + 0.397494i
797797 26.7826i 0.948688i 0.880340 + 0.474344i 0.157315π0.157315\pi
−0.880340 + 0.474344i 0.842685π0.842685\pi
798798 17.8628 0.632337
799799 −16.4647 15.1516i −0.582479 0.536027i
800800 3.88983 0.137526
801801 5.26331i 0.185970i
802802 −19.2897 19.2897i −0.681142 0.681142i
803803 5.36931 0.189479
804804 2.66327 + 2.66327i 0.0939263 + 0.0939263i
805805 2.42754 2.42754i 0.0855596 0.0855596i
806806 −27.4072 + 27.4072i −0.965378 + 0.965378i
807807 17.5918i 0.619262i
808808 12.8641i 0.452558i
809809 −38.1898 + 38.1898i −1.34268 + 1.34268i −0.449303 + 0.893379i 0.648328π0.648328\pi
−0.893379 + 0.449303i 0.851672π0.851672\pi
810810 −6.76028 + 6.76028i −0.237532 + 0.237532i
811811 −37.3327 37.3327i −1.31093 1.31093i −0.920730 0.390200i 0.872406π-0.872406\pi
−0.390200 0.920730i 0.627594π-0.627594\pi
812812 −1.51637 −0.0532141
813813 24.1860 + 24.1860i 0.848239 + 0.848239i
814814 45.1264i 1.58168i
815815 12.0913 0.423540
816816 0.852952 + 20.5381i 0.0298593 + 0.718977i
817817 −19.5308 −0.683295
818818 20.5650i 0.719037i
819819 −19.8980 19.8980i −0.695292 0.695292i
820820 6.96103 0.243090
821821 −8.42042 8.42042i −0.293875 0.293875i 0.544734 0.838609i 0.316631π-0.316631\pi
−0.838609 + 0.544734i 0.816631π0.816631\pi
822822 43.8520 43.8520i 1.52951 1.52951i
823823 −27.9601 + 27.9601i −0.974627 + 0.974627i −0.999686 0.0250590i 0.992023π-0.992023\pi
0.0250590 + 0.999686i 0.492023π0.492023\pi
824824 24.8716i 0.866443i
825825 9.03208i 0.314457i
826826 −2.73054 + 2.73054i −0.0950078 + 0.0950078i
827827 −12.9612 + 12.9612i −0.450704 + 0.450704i −0.895588 0.444884i 0.853245π-0.853245\pi
0.444884 + 0.895588i 0.353245π0.353245\pi
828828 2.29425 + 2.29425i 0.0797309 + 0.0797309i
829829 −39.4065 −1.36864 −0.684322 0.729180i 0.739902π-0.739902\pi
−0.684322 + 0.729180i 0.739902π0.739902\pi
830830 −2.01377 2.01377i −0.0698990 0.0698990i
831831 11.2093i 0.388847i
832832 −30.5916 −1.06057
833833 −2.88661 + 3.13676i −0.100015 + 0.108682i
834834 −38.8540 −1.34541
835835 5.89177i 0.203893i
836836 4.90610 + 4.90610i 0.169681 + 0.169681i
837837 −3.83468 −0.132546
838838 −1.38889 1.38889i −0.0479783 0.0479783i
839839 −14.5709 + 14.5709i −0.503043 + 0.503043i −0.912382 0.409339i 0.865759π-0.865759\pi
0.409339 + 0.912382i 0.365759π0.365759\pi
840840 −13.1921 + 13.1921i −0.455171 + 0.455171i
841841 28.2762i 0.975041i
842842 41.7301i 1.43812i
843843 −6.04194 + 6.04194i −0.208095 + 0.208095i
844844 −8.71241 + 8.71241i −0.299894 + 0.299894i
845845 −0.185142 0.185142i −0.00636909 0.00636909i
846846 −19.3498 −0.665259
847847 3.86123 + 3.86123i 0.132673 + 0.132673i
848848 25.9960i 0.892706i
849849 −58.4436 −2.00578
850850 3.41948 + 3.14678i 0.117287 + 0.107934i
851851 15.4683 0.530245
852852 22.2679i 0.762884i
853853 5.82880 + 5.82880i 0.199574 + 0.199574i 0.799817 0.600243i 0.204930π-0.204930\pi
−0.600243 + 0.799817i 0.704930π0.704930\pi
854854 3.13207 0.107177
855855 5.84652 + 5.84652i 0.199947 + 0.199947i
856856 −19.1457 + 19.1457i −0.654386 + 0.654386i
857857 19.6053 19.6053i 0.669703 0.669703i −0.287944 0.957647i 0.592972π-0.592972\pi
0.957647 + 0.287944i 0.0929716π0.0929716\pi
858858 37.0717i 1.26561i
859859 7.00671i 0.239066i −0.992830 0.119533i 0.961860π-0.961860\pi
0.992830 0.119533i 0.0381397π-0.0381397\pi
860860 3.85578 3.85578i 0.131481 0.131481i
861861 −40.9049 + 40.9049i −1.39404 + 1.39404i
862862 −24.2183 24.2183i −0.824879 0.824879i
863863 29.4176 1.00139 0.500693 0.865625i 0.333079π-0.333079\pi
0.500693 + 0.865625i 0.333079π0.333079\pi
864864 −1.11692 1.11692i −0.0379983 0.0379983i
865865 2.07551i 0.0705696i
866866 17.8356 0.606077
867867 27.2662 32.2153i 0.926008 1.09409i
868868 16.8312 0.571287
869869 32.6436i 1.10736i
870870 1.68333 + 1.68333i 0.0570702 + 0.0570702i
871871 −7.57133 −0.256545
872872 −31.1406 31.1406i −1.05455 1.05455i
873873 27.4418 27.4418i 0.928763 0.928763i
874874 2.92759 2.92759i 0.0990271 0.0990271i
875875 2.44256i 0.0825737i
876876 2.67366i 0.0903347i
877877 −36.4433 + 36.4433i −1.23060 + 1.23060i −0.266872 + 0.963732i 0.585990π0.585990\pi
−0.963732 + 0.266872i 0.914010π0.914010\pi
878878 −3.32106 + 3.32106i −0.112080 + 0.112080i
879879 −27.3725 27.3725i −0.923250 0.923250i
880880 7.30577 0.246277
881881 −33.0055 33.0055i −1.11198 1.11198i −0.992882 0.119102i 0.961998π-0.961998\pi
−0.119102 0.992882i 0.538002π-0.538002\pi
882882 3.68642i 0.124128i
883883 9.95880 0.335140 0.167570 0.985860i 0.446408π-0.446408\pi
0.167570 + 0.985860i 0.446408π0.446408\pi
884884 8.06219 + 7.41924i 0.271161 + 0.249536i
885885 −3.48242 −0.117060
886886 17.7177i 0.595239i
887887 13.3201 + 13.3201i 0.447246 + 0.447246i 0.894438 0.447192i 0.147576π-0.147576\pi
−0.447192 + 0.894438i 0.647576π0.647576\pi
888888 −84.0601 −2.82087
889889 4.34486 + 4.34486i 0.145722 + 0.145722i
890890 1.32593 1.32593i 0.0444453 0.0444453i
891891 21.8214 21.8214i 0.731046 0.731046i
892892 7.01475i 0.234871i
893893 14.1834i 0.474631i
894894 23.0428 23.0428i 0.770667 0.770667i
895895 7.45102 7.45102i 0.249060 0.249060i
896896 −2.91586 2.91586i −0.0974119 0.0974119i
897897 −12.7073 −0.424285
898898 13.1872 + 13.1872i 0.440064 + 0.440064i
899899 8.03414i 0.267954i
900900 −2.30845 −0.0769484
901901 36.1432 39.2753i 1.20410 1.30845i
902902 39.1160 1.30242
903903 45.3153i 1.50800i
904904 24.9306 + 24.9306i 0.829178 + 0.829178i
905905 3.39068 0.112710
906906 5.59407 + 5.59407i 0.185851 + 0.185851i
907907 18.9094 18.9094i 0.627876 0.627876i −0.319658 0.947533i 0.603568π-0.603568\pi
0.947533 + 0.319658i 0.103568π0.103568\pi
908908 0.918072 0.918072i 0.0304673 0.0304673i
909909 13.2278i 0.438740i
910910 10.0254i 0.332338i
911911 7.34196 7.34196i 0.243250 0.243250i −0.574943 0.818193i 0.694976π-0.694976\pi
0.818193 + 0.574943i 0.194976π0.194976\pi
912912 −9.21362 + 9.21362i −0.305093 + 0.305093i
913913 6.50023 + 6.50023i 0.215126 + 0.215126i
914914 1.60980 0.0532476
915915 1.99726 + 1.99726i 0.0660273 + 0.0660273i
916916 12.2173i 0.403670i
917917 5.42811 0.179252
918918 −0.0783019 1.88542i −0.00258435 0.0622282i
919919 20.4602 0.674919 0.337460 0.941340i 0.390432π-0.390432\pi
0.337460 + 0.941340i 0.390432π0.390432\pi
920920 4.32418i 0.142564i
921921 −38.0151 38.0151i −1.25264 1.25264i
922922 −12.5852 −0.414470
923923 31.6523 + 31.6523i 1.04185 + 1.04185i
924924 11.3832 11.3832i 0.374478 0.374478i
925925 −7.78199 + 7.78199i −0.255870 + 0.255870i
926926 32.9337i 1.08227i
927927 25.5748i 0.839986i
928928 2.34008 2.34008i 0.0768169 0.0768169i
929929 3.22981 3.22981i 0.105966 0.105966i −0.652136 0.758102i 0.726127π-0.726127\pi
0.758102 + 0.652136i 0.226127π0.226127\pi
930930 −18.6844 18.6844i −0.612685 0.612685i
931931 −2.70215 −0.0885595
932932 6.75208 + 6.75208i 0.221172 + 0.221172i
933933 22.0075i 0.720492i
934934 −12.3288 −0.403412
935935 −11.0377 10.1575i −0.360972 0.332185i
936936 35.4443 1.15853
937937 2.90874i 0.0950243i −0.998871 0.0475122i 0.984871π-0.984871\pi
0.998871 0.0475122i 0.0151293π-0.0151293\pi
938938 −4.04720 4.04720i −0.132146 0.132146i
939939 42.4883 1.38655
940940 2.80011 + 2.80011i 0.0913296 + 0.0913296i
941941 −10.8860 + 10.8860i −0.354872 + 0.354872i −0.861919 0.507046i 0.830737π-0.830737\pi
0.507046 + 0.861919i 0.330737π0.330737\pi
942942 −2.70893 + 2.70893i −0.0882618 + 0.0882618i
943943 13.4080i 0.436626i
944944 2.81682i 0.0916797i
945945 0.701351 0.701351i 0.0228149 0.0228149i
946946 21.6667 21.6667i 0.704447 0.704447i
947947 16.9623 + 16.9623i 0.551200 + 0.551200i 0.926787 0.375587i 0.122559π-0.122559\pi
−0.375587 + 0.926787i 0.622559π0.622559\pi
948948 −16.2550 −0.527937
949949 3.80043 + 3.80043i 0.123367 + 0.123367i
950950 2.94570i 0.0955712i
951951 −25.6313 −0.831151
952952 1.28567 + 30.9574i 0.0416687 + 1.00333i
953953 −9.31030 −0.301590 −0.150795 0.988565i 0.548183π-0.548183\pi
−0.150795 + 0.988565i 0.548183π0.548183\pi
954954 46.1575i 1.49440i
955955 8.72751 + 8.72751i 0.282416 + 0.282416i
956956 −17.4740 −0.565151
957957 −5.43360 5.43360i −0.175643 0.175643i
958958 −13.7075 + 13.7075i −0.442868 + 0.442868i
959959 38.2795 38.2795i 1.23611 1.23611i
960960 20.8553i 0.673102i
961961 58.1763i 1.87666i
962962 31.9408 31.9408i 1.02981 1.02981i
963963 19.6870 19.6870i 0.634404 0.634404i
964964 −8.92177 8.92177i −0.287351 0.287351i
965965 −11.9557 −0.384868
966966 −6.79260 6.79260i −0.218548 0.218548i
967967 1.29315i 0.0415848i 0.999784 + 0.0207924i 0.00661890π0.00661890\pi
−0.999784 + 0.0207924i 0.993381π0.993381\pi
968968 −6.87802 −0.221068
969969 26.7302 1.11011i 0.858697 0.0356619i
970970 13.8262 0.443933
971971 39.3251i 1.26200i 0.775781 + 0.631002i 0.217356π0.217356\pi
−0.775781 + 0.631002i 0.782644π0.782644\pi
972972 −11.4946 11.4946i −0.368690 0.368690i
973973 −33.9166 −1.08732
974974 20.5972 + 20.5972i 0.659976 + 0.659976i
975975 6.39297 6.39297i 0.204739 0.204739i
976976 −1.61552 + 1.61552i −0.0517115 + 0.0517115i
977977 53.3750i 1.70762i 0.520586 + 0.853809i 0.325714π0.325714\pi
−0.520586 + 0.853809i 0.674286π0.674286\pi
978978 33.8331i 1.08186i
979979 −4.27996 + 4.27996i −0.136788 + 0.136788i
980980 0.533462 0.533462i 0.0170408 0.0170408i
981981 32.0211 + 32.0211i 1.02235 + 1.02235i
982982 −13.7924 −0.440132
983983 −36.1157 36.1157i −1.15191 1.15191i −0.986169 0.165742i 0.946998π-0.946998\pi
−0.165742 0.986169i 0.553002π-0.553002\pi
984984 72.8641i 2.32282i
985985 −1.22210 −0.0389394
986986 3.95019 0.164052i 0.125800 0.00522449i
987987 −32.9085 −1.04749
988988 6.94514i 0.220954i
989989 7.42685 + 7.42685i 0.236160 + 0.236160i
990990 −12.9718 −0.412272
991991 7.48752 + 7.48752i 0.237849 + 0.237849i 0.815959 0.578110i 0.196210π-0.196210\pi
−0.578110 + 0.815959i 0.696210π0.696210\pi
992992 −25.9741 + 25.9741i −0.824679 + 0.824679i
993993 −11.5288 + 11.5288i −0.365857 + 0.365857i
994994 33.8390i 1.07331i
995995 21.7349i 0.689043i
996996 3.23680 3.23680i 0.102562 0.102562i
997997 −2.43619 + 2.43619i −0.0771550 + 0.0771550i −0.744631 0.667476i 0.767375π-0.767375\pi
0.667476 + 0.744631i 0.267375π0.267375\pi
998998 −5.11336 5.11336i −0.161861 0.161861i
999999 4.46900 0.141393
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 85.2.e.a.81.3 yes 12
3.2 odd 2 765.2.k.b.676.4 12
4.3 odd 2 1360.2.bt.d.81.6 12
5.2 odd 4 425.2.j.c.149.4 12
5.3 odd 4 425.2.j.b.149.3 12
5.4 even 2 425.2.e.f.251.4 12
17.2 even 8 1445.2.a.o.1.4 6
17.4 even 4 inner 85.2.e.a.21.4 12
17.8 even 8 1445.2.d.g.866.6 12
17.9 even 8 1445.2.d.g.866.5 12
17.15 even 8 1445.2.a.n.1.4 6
51.38 odd 4 765.2.k.b.361.3 12
68.55 odd 4 1360.2.bt.d.1041.6 12
85.4 even 4 425.2.e.f.276.3 12
85.19 even 8 7225.2.a.z.1.3 6
85.38 odd 4 425.2.j.c.174.4 12
85.49 even 8 7225.2.a.bb.1.3 6
85.72 odd 4 425.2.j.b.174.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
85.2.e.a.21.4 12 17.4 even 4 inner
85.2.e.a.81.3 yes 12 1.1 even 1 trivial
425.2.e.f.251.4 12 5.4 even 2
425.2.e.f.276.3 12 85.4 even 4
425.2.j.b.149.3 12 5.3 odd 4
425.2.j.b.174.3 12 85.72 odd 4
425.2.j.c.149.4 12 5.2 odd 4
425.2.j.c.174.4 12 85.38 odd 4
765.2.k.b.361.3 12 51.38 odd 4
765.2.k.b.676.4 12 3.2 odd 2
1360.2.bt.d.81.6 12 4.3 odd 2
1360.2.bt.d.1041.6 12 68.55 odd 4
1445.2.a.n.1.4 6 17.15 even 8
1445.2.a.o.1.4 6 17.2 even 8
1445.2.d.g.866.5 12 17.9 even 8
1445.2.d.g.866.6 12 17.8 even 8
7225.2.a.z.1.3 6 85.19 even 8
7225.2.a.bb.1.3 6 85.49 even 8