Properties

Label 196.4.f.d.19.9
Level 196196
Weight 44
Character 196.19
Analytic conductor 11.56411.564
Analytic rank 00
Dimension 2020
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [196,4,Mod(19,196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(196, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("196.19");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 196=2272 196 = 2^{2} \cdot 7^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 196.f (of order 66, degree 22, not 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: 11.564374361111.5643743611
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x202x1824x17+28x16+56x15192x14+352x13448x12++1073741824 x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 224 2^{24}
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 19.9
Root 2.265101.69390i-2.26510 - 1.69390i of defining polynomial
Character χ\chi == 196.19
Dual form 196.4.f.d.31.9

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+(2.59951+1.11469i)q2+(1.671342.89484i)q3+(5.51494+5.79529i)q4+(15.9583+9.21354i)q5+(1.117829.38820i)q6+(7.87623+21.2124i)q8+(7.9132713.7062i)q9+(31.2137+41.7393i)q10+(35.6274+20.5695i)q11+(7.5591125.6508i)q12+24.8455iq1361.5957iq15+(3.17079+63.9214i)q16+(41.382623.8923i)q17+(35.848726.8086i)q18+(30.915053.5464i)q19+(34.6141+143.295i)q20+(115.542+13.7572i)q22+(64.3994+37.1810i)q23+(48.242658.2535i)q24+(107.279+185.812i)q25+(27.6950+64.5862i)q26143.155q27+28.8513q29+(68.6600160.119i)q30+(11.5660+20.0328i)q31+(79.4949+162.630i)q32+(119.091+68.7571i)q33+(134.20715.9796i)q34+(123.07229.7291i)q36+(51.890089.8761i)q37+(140.052104.734i)q38+(71.923741.5252i)q39+(69.7496+411.082i)q40+96.1780iq41195.747iq43+(315.68993.0315i)q44+(252.565145.818i)q45+(125.962+168.438i)q46+(89.8186155.570i)q47+(190.34297.6553i)q48+(71.7499+602.603i)q50+(138.32979.8641i)q51+(143.987+137.021i)q52+(218.681378.767i)q53+(372.134159.573i)q54758.071q55206.678q57+(74.9993+32.1601i)q58+(286.640496.475i)q59+(356.965339.697i)q60+(368.470212.736i)q61+(7.73553+64.9681i)q62+(387.930+334.147i)q64+(228.915+396.492i)q65+(232.935+311.484i)q66+(728.093+420.365i)q67+(366.686+108.060i)q68248.568iq691179.04iq71+(353.067+59.9061i)q72+(716.185+413.489i)q73+(235.072175.793i)q74+(358.597621.109i)q75+(480.812116.144i)q76+(233.25427.7728i)q78+(282.007+162.817i)q79+(639.543+990.864i)q80+(25.6023+44.3445i)q81+(107.208+250.016i)q82+507.854q83+880.530q85+(218.197508.848i)q86+(48.220283.5198i)q87+(716.937593.731i)q88+(176.826+102.090i)q89+(819.08897.5260i)q90+(139.684+578.264i)q92+(38.661266.9632i)q93+(406.897304.288i)q94+(986.704569.674i)q95+(603.65141.6847i)q961116.33iq97+651.087iq99+O(q100)q+(2.59951 + 1.11469i) q^{2} +(-1.67134 - 2.89484i) q^{3} +(5.51494 + 5.79529i) q^{4} +(15.9583 + 9.21354i) q^{5} +(-1.11782 - 9.38820i) q^{6} +(7.87623 + 21.2124i) q^{8} +(7.91327 - 13.7062i) q^{9} +(31.2137 + 41.7393i) q^{10} +(-35.6274 + 20.5695i) q^{11} +(7.55911 - 25.6508i) q^{12} +24.8455i q^{13} -61.5957i q^{15} +(-3.17079 + 63.9214i) q^{16} +(41.3826 - 23.8923i) q^{17} +(35.8487 - 26.8086i) q^{18} +(30.9150 - 53.5464i) q^{19} +(34.6141 + 143.295i) q^{20} +(-115.542 + 13.7572i) q^{22} +(64.3994 + 37.1810i) q^{23} +(48.2426 - 58.2535i) q^{24} +(107.279 + 185.812i) q^{25} +(-27.6950 + 64.5862i) q^{26} -143.155 q^{27} +28.8513 q^{29} +(68.6600 - 160.119i) q^{30} +(11.5660 + 20.0328i) q^{31} +(-79.4949 + 162.630i) q^{32} +(119.091 + 68.7571i) q^{33} +(134.207 - 15.9796i) q^{34} +(123.072 - 29.7291i) q^{36} +(51.8900 - 89.8761i) q^{37} +(140.052 - 104.734i) q^{38} +(71.9237 - 41.5252i) q^{39} +(-69.7496 + 411.082i) q^{40} +96.1780i q^{41} -195.747i q^{43} +(-315.689 - 93.0315i) q^{44} +(252.565 - 145.818i) q^{45} +(125.962 + 168.438i) q^{46} +(89.8186 - 155.570i) q^{47} +(190.342 - 97.6553i) q^{48} +(71.7499 + 602.603i) q^{50} +(-138.329 - 79.8641i) q^{51} +(-143.987 + 137.021i) q^{52} +(-218.681 - 378.767i) q^{53} +(-372.134 - 159.573i) q^{54} -758.071 q^{55} -206.678 q^{57} +(74.9993 + 32.1601i) q^{58} +(-286.640 - 496.475i) q^{59} +(356.965 - 339.697i) q^{60} +(-368.470 - 212.736i) q^{61} +(7.73553 + 64.9681i) q^{62} +(-387.930 + 334.147i) q^{64} +(-228.915 + 396.492i) q^{65} +(232.935 + 311.484i) q^{66} +(-728.093 + 420.365i) q^{67} +(366.686 + 108.060i) q^{68} -248.568i q^{69} -1179.04i q^{71} +(353.067 + 59.9061i) q^{72} +(-716.185 + 413.489i) q^{73} +(235.072 - 175.793i) q^{74} +(358.597 - 621.109i) q^{75} +(480.812 - 116.144i) q^{76} +(233.254 - 27.7728i) q^{78} +(282.007 + 162.817i) q^{79} +(-639.543 + 990.864i) q^{80} +(25.6023 + 44.3445i) q^{81} +(-107.208 + 250.016i) q^{82} +507.854 q^{83} +880.530 q^{85} +(218.197 - 508.848i) q^{86} +(-48.2202 - 83.5198i) q^{87} +(-716.937 - 593.731i) q^{88} +(176.826 + 102.090i) q^{89} +(819.088 - 97.5260i) q^{90} +(139.684 + 578.264i) q^{92} +(38.6612 - 66.9632i) q^{93} +(406.897 - 304.288i) q^{94} +(986.704 - 569.674i) q^{95} +(603.651 - 41.6847i) q^{96} -1116.33i q^{97} +651.087i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+4q4+6q5+72q856q9+12q10+168q12104q16+6q17+68q18184q22348q2436q25396q26352q29+644q3040q3230q33++11784q96+O(q100) 20 q + 4 q^{4} + 6 q^{5} + 72 q^{8} - 56 q^{9} + 12 q^{10} + 168 q^{12} - 104 q^{16} + 6 q^{17} + 68 q^{18} - 184 q^{22} - 348 q^{24} - 36 q^{25} - 396 q^{26} - 352 q^{29} + 644 q^{30} - 40 q^{32} - 30 q^{33}+ \cdots + 11784 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/196Z)×\left(\mathbb{Z}/196\mathbb{Z}\right)^\times.

nn 9999 101101
χ(n)\chi(n) 1-1 e(56)e\left(\frac{5}{6}\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 2.59951 + 1.11469i 0.919067 + 0.394102i
33 −1.67134 2.89484i −0.321649 0.557112i 0.659179 0.751986i 0.270904π-0.270904\pi
−0.980828 + 0.194873i 0.937570π0.937570\pi
44 5.51494 + 5.79529i 0.689368 + 0.724411i
55 15.9583 + 9.21354i 1.42736 + 0.824084i 0.996911 0.0785333i 0.0250237π-0.0250237\pi
0.430444 + 0.902617i 0.358357π0.358357\pi
66 −1.11782 9.38820i −0.0760581 0.638786i
77 0 0
88 7.87623 + 21.2124i 0.348084 + 0.937463i
99 7.91327 13.7062i 0.293084 0.507636i
1010 31.2137 + 41.7393i 0.987062 + 1.31991i
1111 −35.6274 + 20.5695i −0.976551 + 0.563812i −0.901227 0.433347i 0.857332π-0.857332\pi
−0.0753237 + 0.997159i 0.523999π0.523999\pi
1212 7.55911 25.6508i 0.181844 0.617062i
1313 24.8455i 0.530069i 0.964239 + 0.265035i 0.0853834π0.0853834\pi
−0.964239 + 0.265035i 0.914617π0.914617\pi
1414 0 0
1515 61.5957i 1.06026i
1616 −3.17079 + 63.9214i −0.0495436 + 0.998772i
1717 41.3826 23.8923i 0.590398 0.340866i −0.174857 0.984594i 0.555946π-0.555946\pi
0.765255 + 0.643728i 0.222613π0.222613\pi
1818 35.8487 26.8086i 0.469424 0.351047i
1919 30.9150 53.5464i 0.373284 0.646547i −0.616785 0.787132i 0.711565π-0.711565\pi
0.990069 + 0.140585i 0.0448984π0.0448984\pi
2020 34.6141 + 143.295i 0.386997 + 1.60209i
2121 0 0
2222 −115.542 + 13.7572i −1.11971 + 0.133321i
2323 64.3994 + 37.1810i 0.583835 + 0.337077i 0.762656 0.646804i 0.223895π-0.223895\pi
−0.178821 + 0.983882i 0.557228π0.557228\pi
2424 48.2426 58.2535i 0.410312 0.495456i
2525 107.279 + 185.812i 0.858229 + 1.48650i
2626 −27.6950 + 64.5862i −0.208901 + 0.487169i
2727 −143.155 −1.02038
2828 0 0
2929 28.8513 0.184743 0.0923715 0.995725i 0.470555π-0.470555\pi
0.0923715 + 0.995725i 0.470555π0.470555\pi
3030 68.6600 160.119i 0.417851 0.974453i
3131 11.5660 + 20.0328i 0.0670099 + 0.116065i 0.897584 0.440844i 0.145321π-0.145321\pi
−0.830574 + 0.556908i 0.811987π0.811987\pi
3232 −79.4949 + 162.630i −0.439151 + 0.898413i
3333 119.091 + 68.7571i 0.628213 + 0.362699i
3434 134.207 15.9796i 0.676951 0.0806023i
3535 0 0
3636 123.072 29.7291i 0.569780 0.137635i
3737 51.8900 89.8761i 0.230558 0.399339i −0.727414 0.686199i 0.759278π-0.759278\pi
0.957973 + 0.286860i 0.0926114π0.0926114\pi
3838 140.052 104.734i 0.597878 0.447108i
3939 71.9237 41.5252i 0.295308 0.170496i
4040 −69.7496 + 411.082i −0.275710 + 1.62494i
4141 96.1780i 0.366353i 0.983080 + 0.183177i 0.0586380π0.0586380\pi
−0.983080 + 0.183177i 0.941362π0.941362\pi
4242 0 0
4343 195.747i 0.694213i −0.937826 0.347107i 0.887164π-0.887164\pi
0.937826 0.347107i 0.112836π-0.112836\pi
4444 −315.689 93.0315i −1.08163 0.318751i
4545 252.565 145.818i 0.836670 0.483052i
4646 125.962 + 168.438i 0.403741 + 0.539887i
4747 89.8186 155.570i 0.278753 0.482815i −0.692322 0.721589i 0.743412π-0.743412\pi
0.971075 + 0.238774i 0.0767456π0.0767456\pi
4848 190.342 97.6553i 0.572364 0.293653i
4949 0 0
5050 71.7499 + 602.603i 0.202939 + 1.70442i
5151 −138.329 79.8641i −0.379802 0.219279i
5252 −143.987 + 137.021i −0.383988 + 0.365413i
5353 −218.681 378.767i −0.566758 0.981654i −0.996884 0.0788851i 0.974864π-0.974864\pi
0.430125 0.902769i 0.358469π-0.358469\pi
5454 −372.134 159.573i −0.937796 0.402133i
5555 −758.071 −1.85851
5656 0 0
5757 −206.678 −0.480266
5858 74.9993 + 32.1601i 0.169791 + 0.0728075i
5959 −286.640 496.475i −0.632497 1.09552i −0.987040 0.160477i 0.948697π-0.948697\pi
0.354542 0.935040i 0.384637π-0.384637\pi
6060 356.965 339.697i 0.768067 0.730911i
6161 −368.470 212.736i −0.773405 0.446526i 0.0606829 0.998157i 0.480672π-0.480672\pi
−0.834088 + 0.551632i 0.814005π0.814005\pi
6262 7.73553 + 64.9681i 0.0158454 + 0.133080i
6363 0 0
6464 −387.930 + 334.147i −0.757675 + 0.652631i
6565 −228.915 + 396.492i −0.436822 + 0.756597i
6666 232.935 + 311.484i 0.434430 + 0.580924i
6767 −728.093 + 420.365i −1.32762 + 0.766504i −0.984932 0.172944i 0.944672π-0.944672\pi
−0.342692 + 0.939448i 0.611339π0.611339\pi
6868 366.686 + 108.060i 0.653929 + 0.192709i
6969 248.568i 0.433682i
7070 0 0
7171 1179.04i 1.97079i −0.170279 0.985396i 0.554467π-0.554467\pi
0.170279 0.985396i 0.445533π-0.445533\pi
7272 353.067 + 59.9061i 0.577908 + 0.0980556i
7373 −716.185 + 413.489i −1.14826 + 0.662949i −0.948463 0.316888i 0.897362π-0.897362\pi
−0.199798 + 0.979837i 0.564029π0.564029\pi
7474 235.072 175.793i 0.369279 0.276156i
7575 358.597 621.109i 0.552097 0.956260i
7676 480.812 116.144i 0.725696 0.175297i
7777 0 0
7878 233.254 27.7728i 0.338601 0.0403160i
7979 282.007 + 162.817i 0.401623 + 0.231877i 0.687184 0.726483i 0.258847π-0.258847\pi
−0.285561 + 0.958361i 0.592180π0.592180\pi
8080 −639.543 + 990.864i −0.893788 + 1.38477i
8181 25.6023 + 44.3445i 0.0351198 + 0.0608292i
8282 −107.208 + 250.016i −0.144380 + 0.336703i
8383 507.854 0.671617 0.335808 0.941930i 0.390991π-0.390991\pi
0.335808 + 0.941930i 0.390991π0.390991\pi
8484 0 0
8585 880.530 1.12361
8686 218.197 508.848i 0.273591 0.638029i
8787 −48.2202 83.5198i −0.0594224 0.102923i
8888 −716.937 593.731i −0.868474 0.719227i
8989 176.826 + 102.090i 0.210601 + 0.121590i 0.601591 0.798805i 0.294534π-0.294534\pi
−0.390990 + 0.920395i 0.627867π0.627867\pi
9090 819.088 97.5260i 0.959327 0.114224i
9191 0 0
9292 139.684 + 578.264i 0.158295 + 0.655307i
9393 38.6612 66.9632i 0.0431074 0.0746641i
9494 406.897 304.288i 0.446471 0.333882i
9595 986.704 569.674i 1.06562 0.615235i
9696 603.651 41.6847i 0.641770 0.0443170i
9797 1116.33i 1.16852i −0.811566 0.584261i 0.801385π-0.801385\pi
0.811566 0.584261i 0.198615π-0.198615\pi
9898 0 0
9999 651.087i 0.660977i
100100 −485.199 + 1646.45i −0.485199 + 1.64645i
101101 3.43081 1.98078i 0.00337999 0.00195144i −0.498309 0.866999i 0.666046π-0.666046\pi
0.501689 + 0.865048i 0.332712π0.332712\pi
102102 −270.564 361.801i −0.262645 0.351212i
103103 179.406 310.741i 0.171626 0.297264i −0.767363 0.641213i 0.778431π-0.778431\pi
0.938988 + 0.343949i 0.111765π0.111765\pi
104104 −527.032 + 195.689i −0.496920 + 0.184508i
105105 0 0
106106 −146.258 1228.37i −0.134017 1.12557i
107107 803.472 + 463.885i 0.725931 + 0.419116i 0.816932 0.576735i 0.195673π-0.195673\pi
−0.0910010 + 0.995851i 0.529007π0.529007\pi
108108 −789.493 829.626i −0.703416 0.739174i
109109 −594.270 1029.31i −0.522209 0.904492i −0.999666 0.0258371i 0.991775π-0.991775\pi
0.477458 0.878655i 0.341558π-0.341558\pi
110110 −1970.62 845.012i −1.70810 0.732443i
111111 −346.903 −0.296635
112112 0 0
113113 −662.367 −0.551418 −0.275709 0.961241i 0.588913π-0.588913\pi
−0.275709 + 0.961241i 0.588913π0.588913\pi
114114 −537.262 230.381i −0.441396 0.189273i
115115 685.137 + 1186.69i 0.555560 + 0.962258i
116116 159.113 + 167.201i 0.127356 + 0.133830i
117117 340.537 + 196.609i 0.269082 + 0.155355i
118118 −191.710 1610.11i −0.149562 1.25612i
119119 0 0
120120 1306.59 485.142i 0.993958 0.369060i
121121 180.707 312.993i 0.135768 0.235156i
122122 −720.708 963.739i −0.534835 0.715187i
123123 278.420 160.746i 0.204100 0.117837i
124124 −52.3105 + 177.508i −0.0378840 + 0.128554i
125125 1650.28i 1.18084i
126126 0 0
127127 1496.04i 1.04529i 0.852549 + 0.522647i 0.175055π0.175055\pi
−0.852549 + 0.522647i 0.824945π0.824945\pi
128128 −1380.90 + 436.200i −0.953558 + 0.301211i
129129 −566.657 + 327.160i −0.386755 + 0.223293i
130130 −1037.03 + 775.518i −0.699644 + 0.523211i
131131 −984.794 + 1705.71i −0.656808 + 1.13762i 0.324630 + 0.945841i 0.394760π0.394760\pi
−0.981437 + 0.191783i 0.938573π0.938573\pi
132132 258.311 + 1069.36i 0.170327 + 0.705118i
133133 0 0
134134 −2361.26 + 281.148i −1.52225 + 0.181250i
135135 −2284.52 1318.97i −1.45644 0.840878i
136136 832.751 + 689.643i 0.525058 + 0.434826i
137137 896.791 + 1553.29i 0.559256 + 0.968660i 0.997559 + 0.0698322i 0.0222464π0.0222464\pi
−0.438303 + 0.898827i 0.644420π0.644420\pi
138138 277.076 646.156i 0.170915 0.398583i
139139 306.409 0.186973 0.0934867 0.995621i 0.470199π-0.470199\pi
0.0934867 + 0.995621i 0.470199π0.470199\pi
140140 0 0
141141 −600.469 −0.358643
142142 1314.26 3064.93i 0.776692 1.81129i
143143 −511.059 885.180i −0.298859 0.517639i
144144 851.027 + 549.286i 0.492492 + 0.317874i
145145 460.418 + 265.822i 0.263694 + 0.152244i
146146 −2322.64 + 276.549i −1.31660 + 0.156763i
147147 0 0
148148 807.028 194.944i 0.448225 0.108272i
149149 714.928 1238.29i 0.393082 0.680838i −0.599773 0.800171i 0.704742π-0.704742\pi
0.992854 + 0.119333i 0.0380756π0.0380756\pi
150150 1624.52 1214.86i 0.884277 0.661285i
151151 −1079.16 + 623.054i −0.581595 + 0.335784i −0.761767 0.647851i 0.775668π-0.775668\pi
0.180172 + 0.983635i 0.442335π0.442335\pi
152152 1379.34 + 234.037i 0.736048 + 0.124888i
153153 756.264i 0.399610i
154154 0 0
155155 426.254i 0.220887i
156156 637.306 + 187.810i 0.327085 + 0.0963899i
157157 2201.64 1271.12i 1.11917 0.646154i 0.177982 0.984034i 0.443043π-0.443043\pi
0.941189 + 0.337880i 0.109710π0.109710\pi
158158 551.591 + 737.594i 0.277736 + 0.371391i
159159 −730.980 + 1266.10i −0.364594 + 0.631496i
160160 −2767.00 + 1862.87i −1.36719 + 0.920457i
161161 0 0
162162 17.1233 + 143.813i 0.00830453 + 0.0697469i
163163 637.434 + 368.022i 0.306305 + 0.176845i 0.645272 0.763953i 0.276744π-0.276744\pi
−0.338967 + 0.940798i 0.610078π0.610078\pi
164164 −557.379 + 530.416i −0.265390 + 0.252552i
165165 1266.99 + 2194.49i 0.597789 + 1.03540i
166166 1320.17 + 566.098i 0.617261 + 0.264685i
167167 3110.82 1.44145 0.720726 0.693220i 0.243809π-0.243809\pi
0.720726 + 0.693220i 0.243809π0.243809\pi
168168 0 0
169169 1579.70 0.719027
170170 2288.95 + 981.515i 1.03267 + 0.442816i
171171 −489.278 847.454i −0.218807 0.378985i
172172 1134.41 1079.54i 0.502896 0.478569i
173173 −2719.50 1570.10i −1.19514 0.690015i −0.235674 0.971832i 0.575730π-0.575730\pi
−0.959468 + 0.281817i 0.909063π0.909063\pi
174174 −32.2506 270.861i −0.0140512 0.118011i
175175 0 0
176176 −1201.86 2342.57i −0.514738 1.00328i
177177 −958.144 + 1659.55i −0.406884 + 0.704744i
178178 345.862 + 462.491i 0.145637 + 0.194748i
179179 206.742 119.362i 0.0863274 0.0498411i −0.456215 0.889870i 0.650795π-0.650795\pi
0.542542 + 0.840028i 0.317462π0.317462\pi
180180 2237.94 + 659.506i 0.926701 + 0.273093i
181181 1947.09i 0.799591i 0.916604 + 0.399796i 0.130919π0.130919\pi
−0.916604 + 0.399796i 0.869081π0.869081\pi
182182 0 0
183183 1422.21i 0.574498i
184184 −281.473 + 1658.91i −0.112774 + 0.664655i
185185 1656.15 956.181i 0.658177 0.379999i
186186 175.143 130.977i 0.0690438 0.0516327i
187187 −982.903 + 1702.44i −0.384369 + 0.665746i
188188 1396.92 337.437i 0.541920 0.130905i
189189 0 0
190190 3199.96 381.008i 1.22184 0.145480i
191191 −393.391 227.124i −0.149030 0.0860427i 0.423631 0.905835i 0.360755π-0.360755\pi
−0.572661 + 0.819792i 0.694089π0.694089\pi
192192 1615.66 + 564.522i 0.607295 + 0.212192i
193193 −1605.08 2780.08i −0.598634 1.03686i −0.993023 0.117921i 0.962377π-0.962377\pi
0.394389 0.918944i 0.370956π-0.370956\pi
194194 1244.36 2901.93i 0.460516 1.07395i
195195 1530.38 0.562013
196196 0 0
197197 −4173.52 −1.50940 −0.754698 0.656073i 0.772216π-0.772216\pi
−0.754698 + 0.656073i 0.772216π0.772216\pi
198198 −725.758 + 1692.51i −0.260492 + 0.607482i
199199 2639.30 + 4571.40i 0.940176 + 1.62843i 0.765134 + 0.643871i 0.222673π0.222673\pi
0.175042 + 0.984561i 0.443994π0.443994\pi
200200 −3096.56 + 3739.13i −1.09480 + 1.32198i
201201 2433.78 + 1405.14i 0.854057 + 0.493090i
202202 11.1264 1.32478i 0.00387550 0.000461443i
203203 0 0
204204 −300.039 1242.10i −0.102975 0.426296i
205205 −886.140 + 1534.84i −0.301906 + 0.522916i
206206 812.748 607.793i 0.274888 0.205568i
207207 1019.22 588.446i 0.342225 0.197584i
208208 −1588.16 78.7798i −0.529418 0.0262615i
209209 2543.62i 0.841848i
210210 0 0
211211 871.583i 0.284371i 0.989840 + 0.142185i 0.0454130π0.0454130\pi
−0.989840 + 0.142185i 0.954587π0.954587\pi
212212 989.051 3356.20i 0.320416 1.08729i
213213 −3413.13 + 1970.57i −1.09795 + 0.633903i
214214 1571.55 + 2101.49i 0.502004 + 0.671286i
215215 1803.53 3123.80i 0.572090 0.990889i
216216 −1127.52 3036.66i −0.355177 0.956568i
217217 0 0
218218 −397.459 3338.12i −0.123483 1.03709i
219219 2393.97 + 1382.16i 0.738674 + 0.426474i
220220 −4180.72 4393.24i −1.28120 1.34633i
221221 593.615 + 1028.17i 0.180683 + 0.312952i
222222 −901.778 386.688i −0.272628 0.116904i
223223 1930.21 0.579624 0.289812 0.957084i 0.406407π-0.406407\pi
0.289812 + 0.957084i 0.406407π0.406407\pi
224224 0 0
225225 3395.70 1.00613
226226 −1721.83 738.333i −0.506790 0.217315i
227227 988.231 + 1711.67i 0.288948 + 0.500473i 0.973559 0.228436i 0.0733612π-0.0733612\pi
−0.684611 + 0.728909i 0.740028π0.740028\pi
228228 −1139.82 1197.76i −0.331080 0.347910i
229229 2237.66 + 1291.92i 0.645716 + 0.372804i 0.786813 0.617192i 0.211730π-0.211730\pi
−0.141097 + 0.989996i 0.545063π0.545063\pi
230230 458.233 + 3848.54i 0.131369 + 1.10333i
231231 0 0
232232 227.239 + 612.004i 0.0643060 + 0.173190i
233233 1724.22 2986.43i 0.484795 0.839690i −0.515052 0.857159i 0.672227π-0.672227\pi
0.999847 + 0.0174686i 0.00556071π0.00556071\pi
234234 666.072 + 890.680i 0.186079 + 0.248827i
235235 2866.71 1655.10i 0.795759 0.459432i
236236 1296.41 4399.19i 0.357582 1.21340i
237237 1088.49i 0.298333i
238238 0 0
239239 3647.94i 0.987304i 0.869659 + 0.493652i 0.164338π0.164338\pi
−0.869659 + 0.493652i 0.835662π0.835662\pi
240240 3937.28 + 195.307i 1.05896 + 0.0525292i
241241 2194.49 1266.99i 0.586553 0.338646i −0.177180 0.984178i 0.556698π-0.556698\pi
0.763733 + 0.645532i 0.223364π0.223364\pi
242242 818.639 612.198i 0.217455 0.162618i
243243 −1847.01 + 3199.12i −0.487597 + 0.844542i
244244 −799.222 3308.62i −0.209692 0.868084i
245245 0 0
246246 902.938 107.510i 0.234021 0.0278641i
247247 1330.39 + 768.099i 0.342714 + 0.197866i
248248 −333.848 + 403.125i −0.0854813 + 0.103220i
249249 −848.795 1470.16i −0.216025 0.374166i
250250 −1839.54 + 4289.92i −0.465372 + 1.08527i
251251 −5658.23 −1.42289 −0.711443 0.702744i 0.751958π-0.751958\pi
−0.711443 + 0.702744i 0.751958π0.751958\pi
252252 0 0
253253 −3059.18 −0.760193
254254 −1667.62 + 3888.98i −0.411952 + 0.960695i
255255 −1471.66 2548.99i −0.361408 0.625977i
256256 −4075.89 405.362i −0.995091 0.0989655i
257257 −4328.82 2499.25i −1.05068 0.606610i −0.127840 0.991795i 0.540804π-0.540804\pi
−0.922840 + 0.385185i 0.874138π0.874138\pi
258258 −1837.71 + 218.810i −0.443454 + 0.0528006i
259259 0 0
260260 −3560.24 + 860.004i −0.849218 + 0.205135i
261261 228.308 395.441i 0.0541452 0.0937822i
262262 −4461.32 + 3336.29i −1.05199 + 0.786704i
263263 −1646.99 + 950.892i −0.386152 + 0.222945i −0.680491 0.732756i 0.738234π-0.738234\pi
0.294340 + 0.955701i 0.404900π0.404900\pi
264264 −520.514 + 3067.74i −0.121346 + 0.715176i
265265 8059.32i 1.86823i
266266 0 0
267267 682.509i 0.156438i
268268 −6451.53 1901.22i −1.47048 0.433342i
269269 −6976.20 + 4027.71i −1.58121 + 0.912913i −0.586530 + 0.809928i 0.699506π0.699506\pi
−0.994683 + 0.102986i 0.967160π0.967160\pi
270270 −4468.39 5975.19i −1.00718 1.34681i
271271 2189.04 3791.53i 0.490682 0.849886i −0.509261 0.860612i 0.670081π-0.670081\pi
0.999942 + 0.0107264i 0.00341438π0.00341438\pi
272272 1396.01 + 2720.99i 0.311197 + 0.606560i
273273 0 0
274274 599.791 + 5037.44i 0.132243 + 1.11067i
275275 −7644.11 4413.33i −1.67621 0.967759i
276276 1440.52 1370.84i 0.314164 0.298967i
277277 1602.26 + 2775.19i 0.347547 + 0.601968i 0.985813 0.167847i 0.0536815π-0.0536815\pi
−0.638266 + 0.769815i 0.720348π0.720348\pi
278278 796.515 + 341.551i 0.171841 + 0.0736865i
279279 366.098 0.0785581
280280 0 0
281281 6258.33 1.32861 0.664307 0.747460i 0.268727π-0.268727\pi
0.664307 + 0.747460i 0.268727π0.268727\pi
282282 −1560.93 669.335i −0.329617 0.141342i
283283 −3029.37 5247.02i −0.636316 1.10213i −0.986235 0.165351i 0.947124π-0.947124\pi
0.349919 0.936780i 0.386209π-0.386209\pi
284284 6832.87 6502.33i 1.42766 1.35860i
285285 −3298.23 1904.23i −0.685510 0.395779i
286286 −341.806 2870.71i −0.0706692 0.593526i
287287 0 0
288288 1599.97 + 2376.51i 0.327359 + 0.486240i
289289 −1314.82 + 2277.33i −0.267620 + 0.463532i
290290 900.554 + 1204.23i 0.182353 + 0.243844i
291291 −3231.61 + 1865.77i −0.650998 + 0.375854i
292292 −6346.01 1870.13i −1.27182 0.374798i
293293 457.644i 0.0912486i 0.998959 + 0.0456243i 0.0145277π0.0145277\pi
−0.998959 + 0.0456243i 0.985472π0.985472\pi
294294 0 0
295295 10563.9i 2.08492i
296296 2315.18 + 392.825i 0.454619 + 0.0771367i
297297 5100.24 2944.63i 0.996451 0.575301i
298298 3238.77 2422.03i 0.629588 0.470821i
299299 −923.780 + 1600.03i −0.178674 + 0.309473i
300300 5577.15 1347.20i 1.07332 0.259270i
301301 0 0
302302 −3499.80 + 416.710i −0.666858 + 0.0794005i
303303 −11.4681 6.62110i −0.00217434 0.00125535i
304304 3324.74 + 2145.92i 0.627259 + 0.404858i
305305 −3920.10 6789.82i −0.735949 1.27470i
306306 842.997 1965.92i 0.157487 0.367268i
307307 4195.62 0.779989 0.389995 0.920817i 0.372477π-0.372477\pi
0.389995 + 0.920817i 0.372477π0.372477\pi
308308 0 0
309309 −1199.39 −0.220813
310310 −475.140 + 1108.05i −0.0870520 + 0.203010i
311311 −3254.20 5636.44i −0.593341 1.02770i −0.993779 0.111372i 0.964475π-0.964475\pi
0.400438 0.916324i 0.368858π-0.368858\pi
312312 1447.34 + 1198.61i 0.262626 + 0.217494i
313313 7481.59 + 4319.50i 1.35107 + 0.780040i 0.988399 0.151878i 0.0485320π-0.0485320\pi
0.362670 + 0.931918i 0.381865π0.381865\pi
314314 7140.09 850.146i 1.28324 0.152792i
315315 0 0
316316 611.682 + 2532.24i 0.108892 + 0.450789i
317317 −463.165 + 802.226i −0.0820629 + 0.142137i −0.904136 0.427245i 0.859484π-0.859484\pi
0.822073 + 0.569382i 0.192818π0.192818\pi
318318 −3311.49 + 2476.42i −0.583960 + 0.436700i
319319 −1027.90 + 593.455i −0.180411 + 0.104160i
320320 −9269.39 + 1758.22i −1.61930 + 0.307149i
321321 3101.23i 0.539233i
322322 0 0
323323 2954.52i 0.508960i
324324 −115.794 + 392.930i −0.0198549 + 0.0673749i
325325 −4616.59 + 2665.39i −0.787946 + 0.454921i
326326 1246.79 + 1667.22i 0.211820 + 0.283248i
327327 −1986.45 + 3440.63i −0.335936 + 0.581858i
328328 −2040.16 + 757.520i −0.343443 + 0.127522i
329329 0 0
330330 847.387 + 7116.92i 0.141355 + 1.18719i
331331 8260.72 + 4769.33i 1.37175 + 0.791982i 0.991149 0.132756i 0.0423828π-0.0423828\pi
0.380604 + 0.924738i 0.375716π0.375716\pi
332332 2800.79 + 2943.16i 0.462991 + 0.486527i
333333 −821.238 1422.43i −0.135146 0.234080i
334334 8086.62 + 3467.59i 1.32479 + 0.568078i
335335 −15492.2 −2.52665
336336 0 0
337337 4736.32 0.765589 0.382795 0.923833i 0.374962π-0.374962\pi
0.382795 + 0.923833i 0.374962π0.374962\pi
338338 4106.46 + 1760.87i 0.660834 + 0.283370i
339339 1107.04 + 1917.45i 0.177363 + 0.307202i
340340 4856.07 + 5102.92i 0.774581 + 0.813956i
341341 −824.130 475.812i −0.130877 0.0755620i
342342 −327.238 2748.36i −0.0517398 0.434545i
343343 0 0
344344 4152.26 1541.75i 0.650800 0.241644i
345345 2290.19 3966.73i 0.357391 0.619019i
346346 −5319.20 7112.89i −0.826479 1.10518i
347347 −1694.40 + 978.260i −0.262133 + 0.151342i −0.625307 0.780379i 0.715026π-0.715026\pi
0.363174 + 0.931721i 0.381693π0.381693\pi
348348 218.090 740.057i 0.0335944 0.113998i
349349 9739.50i 1.49382i 0.664924 + 0.746911i 0.268464π0.268464\pi
−0.664924 + 0.746911i 0.731536π0.731536\pi
350350 0 0
351351 3556.76i 0.540871i
352352 −513.022 7429.25i −0.0776823 1.12494i
353353 2590.09 1495.39i 0.390528 0.225471i −0.291861 0.956461i 0.594274π-0.594274\pi
0.682389 + 0.730989i 0.260941π0.260941\pi
354354 −4340.59 + 3246.00i −0.651695 + 0.487353i
355355 10863.1 18815.5i 1.62410 2.81302i
356356 383.540 + 1587.78i 0.0571000 + 0.236382i
357357 0 0
358358 670.480 79.8318i 0.0989831 0.0117856i
359359 1144.24 + 660.628i 0.168219 + 0.0971215i 0.581746 0.813371i 0.302370π-0.302370\pi
−0.413527 + 0.910492i 0.635703π0.635703\pi
360360 5082.41 + 4209.00i 0.744074 + 0.616205i
361361 1518.02 + 2629.29i 0.221318 + 0.383334i
362362 −2170.40 + 5061.49i −0.315120 + 0.734878i
363363 −1208.09 −0.174678
364364 0 0
365365 −15238.8 −2.18530
366366 −1585.32 + 3697.07i −0.226411 + 0.528002i
367367 3367.76 + 5833.14i 0.479008 + 0.829666i 0.999710 0.0240726i 0.00766327π-0.00766327\pi
−0.520703 + 0.853738i 0.674330π0.674330\pi
368368 −2580.86 + 3998.61i −0.365589 + 0.566418i
369369 1318.23 + 761.082i 0.185974 + 0.107372i
370370 5371.04 639.511i 0.754667 0.0898557i
371371 0 0
372372 601.286 145.245i 0.0838044 0.0202436i
373373 −104.742 + 181.419i −0.0145398 + 0.0251837i −0.873204 0.487355i 0.837962π-0.837962\pi
0.858664 + 0.512539i 0.171295π0.171295\pi
374374 −4452.76 + 3329.88i −0.615632 + 0.460385i
375375 4777.29 2758.17i 0.657862 0.379817i
376376 4007.45 + 679.957i 0.549650 + 0.0932610i
377377 716.824i 0.0979265i
378378 0 0
379379 1205.99i 0.163450i −0.996655 0.0817250i 0.973957π-0.973957\pi
0.996655 0.0817250i 0.0260429π-0.0260429\pi
380380 8743.04 + 2576.52i 1.18029 + 0.347822i
381381 4330.81 2500.39i 0.582346 0.336218i
382382 −769.453 1028.92i −0.103059 0.137812i
383383 −1590.45 + 2754.73i −0.212188 + 0.367520i −0.952399 0.304854i 0.901392π-0.901392\pi
0.740211 + 0.672375i 0.234726π0.234726\pi
384384 3570.68 + 3268.44i 0.474519 + 0.434354i
385385 0 0
386386 −1073.51 9016.03i −0.141555 1.18887i
387387 −2682.95 1549.00i −0.352408 0.203463i
388388 6469.48 6156.52i 0.846490 0.805541i
389389 4006.02 + 6938.63i 0.522142 + 0.904377i 0.999668 + 0.0257595i 0.00820040π0.00820040\pi
−0.477526 + 0.878618i 0.658466π0.658466\pi
390390 3978.23 + 1705.89i 0.516527 + 0.221490i
391391 3553.36 0.459593
392392 0 0
393393 6583.69 0.845046
394394 −10849.1 4652.17i −1.38724 0.594855i
395395 3000.24 + 5196.56i 0.382173 + 0.661943i
396396 −3773.24 + 3590.71i −0.478819 + 0.455656i
397397 −10496.5 6060.15i −1.32696 0.766121i −0.342132 0.939652i 0.611149π-0.611149\pi
−0.984828 + 0.173531i 0.944482π0.944482\pi
398398 1765.21 + 14825.4i 0.222317 + 1.86716i
399399 0 0
400400 −12217.5 + 6268.23i −1.52719 + 0.783529i
401401 −5497.13 + 9521.31i −0.684573 + 1.18571i 0.288998 + 0.957330i 0.406678π0.406678\pi
−0.973571 + 0.228385i 0.926655π0.926655\pi
402402 4760.35 + 6365.59i 0.590608 + 0.789768i
403403 −497.726 + 287.362i −0.0615223 + 0.0355199i
404404 30.3999 + 8.95866i 0.00374370 + 0.00110324i
405405 943.552i 0.115767i
406406 0 0
407407 4269.40i 0.519966i
408408 604.598 3563.31i 0.0733629 0.432377i
409409 1739.78 1004.46i 0.210333 0.121436i −0.391133 0.920334i 0.627917π-0.627917\pi
0.601466 + 0.798898i 0.294583π0.294583\pi
410410 −4014.40 + 3002.07i −0.483554 + 0.361613i
411411 2997.68 5192.14i 0.359768 0.623137i
412412 2790.25 674.007i 0.333655 0.0805969i
413413 0 0
414414 3305.41 393.564i 0.392396 0.0467213i
415415 8104.49 + 4679.13i 0.958636 + 0.553469i
416416 −4040.63 1975.09i −0.476221 0.232781i
417417 −512.113 887.006i −0.0601398 0.104165i
418418 −2835.35 + 6612.18i −0.331773 + 0.773714i
419419 −6662.83 −0.776850 −0.388425 0.921480i 0.626981π-0.626981\pi
−0.388425 + 0.921480i 0.626981π0.626981\pi
420420 0 0
421421 5859.67 0.678344 0.339172 0.940724i 0.389853π-0.389853\pi
0.339172 + 0.940724i 0.389853π0.389853\pi
422422 −971.543 + 2265.69i −0.112071 + 0.261356i
423423 −1421.52 2462.14i −0.163396 0.283010i
424424 6312.17 7622.01i 0.722986 0.873013i
425425 8878.94 + 5126.26i 1.01339 + 0.585083i
426426 −11069.1 + 1317.95i −1.25891 + 0.149895i
427427 0 0
428428 1742.76 + 7214.65i 0.196821 + 0.814798i
429429 −1708.30 + 2958.87i −0.192256 + 0.332996i
430430 8170.35 6109.99i 0.916300 0.685232i
431431 −3178.02 + 1834.83i −0.355174 + 0.205060i −0.666962 0.745092i 0.732406π-0.732406\pi
0.311788 + 0.950152i 0.399072π0.399072\pi
432432 453.915 9150.68i 0.0505532 1.01913i
433433 8282.34i 0.919224i −0.888120 0.459612i 0.847989π-0.847989\pi
0.888120 0.459612i 0.152011π-0.152011\pi
434434 0 0
435435 1777.11i 0.195876i
436436 2687.76 9120.53i 0.295230 1.00182i
437437 3981.82 2298.90i 0.435872 0.251651i
438438 4682.49 + 6261.47i 0.510817 + 0.683070i
439439 −4840.93 + 8384.73i −0.526298 + 0.911575i 0.473233 + 0.880938i 0.343087π0.343087\pi
−0.999531 + 0.0306374i 0.990246π0.990246\pi
440440 −5970.74 16080.5i −0.646918 1.74229i
441441 0 0
442442 397.021 + 3334.44i 0.0427248 + 0.358831i
443443 −7154.34 4130.56i −0.767298 0.443000i 0.0646117 0.997910i 0.479419π-0.479419\pi
−0.831910 + 0.554911i 0.812752π0.812752\pi
444444 −1913.15 2010.40i −0.204491 0.214886i
445445 1881.23 + 3258.38i 0.200402 + 0.347106i
446446 5017.60 + 2151.58i 0.532713 + 0.228431i
447447 −4779.54 −0.505737
448448 0 0
449449 −73.1562 −0.00768921 −0.00384461 0.999993i 0.501224π-0.501224\pi
−0.00384461 + 0.999993i 0.501224π0.501224\pi
450450 8827.16 + 3785.14i 0.924703 + 0.396518i
451451 −1978.33 3426.57i −0.206554 0.357762i
452452 −3652.92 3838.61i −0.380130 0.399454i
453453 3607.28 + 2082.67i 0.374139 + 0.216009i
454454 660.948 + 5551.07i 0.0683256 + 0.573843i
455455 0 0
456456 −1627.84 4384.13i −0.167173 0.450231i
457457 6586.17 11407.6i 0.674153 1.16767i −0.302563 0.953129i 0.597842π-0.597842\pi
0.976716 0.214538i 0.0688245π-0.0688245\pi
458458 4376.75 + 5852.65i 0.446533 + 0.597110i
459459 −5924.14 + 3420.30i −0.602429 + 0.347813i
460460 −3098.74 + 10515.1i −0.314085 + 1.06580i
461461 12655.0i 1.27853i 0.768985 + 0.639267i 0.220762π0.220762\pi
−0.768985 + 0.639267i 0.779238π0.779238\pi
462462 0 0
463463 852.596i 0.0855799i 0.999084 + 0.0427899i 0.0136246π0.0136246\pi
−0.999084 + 0.0427899i 0.986375π0.986375\pi
464464 −91.4813 + 1844.21i −0.00915283 + 0.184516i
465465 1233.94 712.414i 0.123059 0.0710482i
466466 7811.07 5841.31i 0.776483 0.580673i
467467 −5462.60 + 9461.49i −0.541282 + 0.937528i 0.457549 + 0.889185i 0.348728π0.348728\pi
−0.998831 + 0.0483436i 0.984606π0.984606\pi
468468 738.635 + 3057.80i 0.0729560 + 0.302023i
469469 0 0
470470 9296.96 1106.96i 0.912419 0.108639i
471471 −7359.36 4248.93i −0.719961 0.415669i
472472 8273.77 9990.67i 0.806846 0.974275i
473473 4026.42 + 6973.96i 0.391406 + 0.677935i
474474 1213.32 2829.54i 0.117573 0.274188i
475475 13266.1 1.28145
476476 0 0
477477 −6921.93 −0.664431
478478 −4066.32 + 9482.88i −0.389098 + 0.907399i
479479 −5330.56 9232.81i −0.508475 0.880705i −0.999952 0.00981425i 0.996876π-0.996876\pi
0.491477 0.870891i 0.336457π-0.336457\pi
480480 10017.3 + 4896.55i 0.952554 + 0.465616i
481481 2233.01 + 1289.23i 0.211677 + 0.122212i
482482 7116.89 847.384i 0.672542 0.0800774i
483483 0 0
484484 2810.47 678.892i 0.263944 0.0637577i
485485 10285.4 17814.8i 0.962960 1.66789i
486486 −8367.36 + 6257.32i −0.780969 + 0.584028i
487487 46.9282 27.0940i 0.00436657 0.00252104i −0.497815 0.867283i 0.665864π-0.665864\pi
0.502182 + 0.864762i 0.332531π0.332531\pi
488488 1610.48 9491.68i 0.149392 0.880467i
489489 2460.36i 0.227528i
490490 0 0
491491 5628.07i 0.517294i −0.965972 0.258647i 0.916723π-0.916723\pi
0.965972 0.258647i 0.0832766π-0.0832766\pi
492492 2467.04 + 727.020i 0.226062 + 0.0666191i
493493 1193.94 689.322i 0.109072 0.0629727i
494494 2602.17 + 3479.65i 0.236998 + 0.316917i
495495 −5998.81 + 10390.3i −0.544700 + 0.943449i
496496 −1317.20 + 675.793i −0.119242 + 0.0611774i
497497 0 0
498498 −567.690 4767.83i −0.0510819 0.429019i
499499 −536.728 309.880i −0.0481508 0.0277999i 0.475731 0.879591i 0.342183π-0.342183\pi
−0.523882 + 0.851791i 0.675517π0.675517\pi
500500 −9563.84 + 9101.19i −0.855416 + 0.814035i
501501 −5199.23 9005.33i −0.463641 0.803050i
502502 −14708.7 6307.16i −1.30773 0.560762i
503503 18680.1 1.65587 0.827935 0.560823i 0.189515π-0.189515\pi
0.827935 + 0.560823i 0.189515π0.189515\pi
504504 0 0
505505 73.0000 0.00643259
506506 −7952.37 3410.02i −0.698668 0.299593i
507507 −2640.21 4572.98i −0.231274 0.400579i
508508 −8670.00 + 8250.59i −0.757223 + 0.720592i
509509 −3084.16 1780.64i −0.268572 0.155060i 0.359667 0.933081i 0.382890π-0.382890\pi
−0.628238 + 0.778021i 0.716224π0.716224\pi
510510 −984.275 8266.58i −0.0854596 0.717746i
511511 0 0
512512 −10143.5 5597.09i −0.875553 0.483123i
513513 −4425.65 + 7665.44i −0.380891 + 0.659722i
514514 −8466.96 11322.1i −0.726579 0.971590i
515515 5726.05 3305.93i 0.489941 0.282868i
516516 −5021.07 1479.68i −0.428372 0.126239i
517517 7390.09i 0.628657i
518518 0 0
519519 10496.7i 0.887771i
520520 −10213.5 1732.96i −0.861333 0.146145i
521521 −10004.0 + 5775.82i −0.841235 + 0.485687i −0.857684 0.514177i 0.828097π-0.828097\pi
0.0164486 + 0.999865i 0.494764π0.494764\pi
522522 1034.28 773.462i 0.0867228 0.0648534i
523523 2135.62 3699.00i 0.178554 0.309265i −0.762831 0.646598i 0.776191π-0.776191\pi
0.941386 + 0.337332i 0.109525π0.109525\pi
524524 −15316.2 + 3699.74i −1.27689 + 0.308443i
525525 0 0
526526 −5341.33 + 635.974i −0.442762 + 0.0527182i
527527 957.260 + 552.674i 0.0791250 + 0.0456829i
528528 −4772.66 + 7394.43i −0.393377 + 0.609472i
529529 −3318.65 5748.06i −0.272758 0.472431i
530530 8983.62 20950.3i 0.736271 1.71702i
531531 −9073.03 −0.741499
532532 0 0
533533 −2389.59 −0.194192
534534 760.785 1774.19i 0.0616524 0.143777i
535535 8548.04 + 14805.6i 0.690774 + 1.19646i
536536 −14651.6 12133.7i −1.18069 0.977791i
537537 −691.070 398.990i −0.0555342 0.0320627i
538538 −22624.4 + 2693.81i −1.81302 + 0.215870i
539539 0 0
540540 −4955.18 20513.5i −0.394884 1.63474i
541541 −4878.48 + 8449.78i −0.387694 + 0.671505i −0.992139 0.125142i 0.960061π-0.960061\pi
0.604445 + 0.796647i 0.293395π0.293395\pi
542542 9916.82 7416.04i 0.785911 0.587724i
543543 5636.51 3254.24i 0.445462 0.257188i
544544 595.896 + 8629.38i 0.0469647 + 0.680113i
545545 21901.3i 1.72138i
546546 0 0
547547 19891.0i 1.55480i 0.629005 + 0.777401i 0.283463π0.283463\pi
−0.629005 + 0.777401i 0.716537π0.716537\pi
548548 −4056.00 + 13763.5i −0.316175 + 1.07289i
549549 −5831.60 + 3366.87i −0.453345 + 0.261739i
550550 −14951.5 19993.3i −1.15915 1.55003i
551551 891.938 1544.88i 0.0689616 0.119445i
552552 5272.72 1957.78i 0.406561 0.150958i
553553 0 0
554554 1071.62 + 9000.17i 0.0821819 + 0.690218i
555555 −5535.98 3196.20i −0.423404 0.244453i
556556 1689.83 + 1775.73i 0.128893 + 0.135446i
557557 −3043.39 5271.30i −0.231513 0.400992i 0.726741 0.686912i 0.241034π-0.241034\pi
−0.958253 + 0.285920i 0.907701π0.907701\pi
558558 951.677 + 408.085i 0.0722002 + 0.0309599i
559559 4863.44 0.367981
560560 0 0
561561 6571.05 0.494527
562562 16268.6 + 6976.08i 1.22108 + 0.523609i
563563 4067.94 + 7045.87i 0.304517 + 0.527439i 0.977154 0.212534i 0.0681716π-0.0681716\pi
−0.672637 + 0.739973i 0.734838π0.734838\pi
564564 −3311.55 3479.89i −0.247237 0.259805i
565565 −10570.3 6102.75i −0.787070 0.454415i
566566 −2026.10 17016.5i −0.150465 1.26371i
567567 0 0
568568 25010.2 9286.39i 1.84755 0.686000i
569569 −11495.9 + 19911.5i −0.846985 + 1.46702i 0.0369008 + 0.999319i 0.488251π0.488251\pi
−0.883886 + 0.467702i 0.845082π0.845082\pi
570570 −6451.17 8626.58i −0.474052 0.633908i
571571 16493.6 9522.59i 1.20882 0.697912i 0.246318 0.969189i 0.420779π-0.420779\pi
0.962501 + 0.271277i 0.0874459π0.0874459\pi
572572 2311.41 7843.45i 0.168960 0.573341i
573573 1518.41i 0.110702i
574574 0 0
575575 15954.9i 1.15716i
576576 1510.09 + 7961.23i 0.109237 + 0.575899i
577577 −13902.1 + 8026.36i −1.00303 + 0.579102i −0.909144 0.416481i 0.863263π-0.863263\pi
−0.0938892 + 0.995583i 0.529930π0.529930\pi
578578 −5956.40 + 4454.35i −0.428640 + 0.320547i
579579 −5365.27 + 9292.92i −0.385100 + 0.667013i
580580 998.660 + 4134.25i 0.0714950 + 0.295975i
581581 0 0
582582 −10480.4 + 1247.86i −0.746435 + 0.0888755i
583583 15582.1 + 8996.32i 1.10694 + 0.639090i
584584 −14411.9 11935.2i −1.02118 0.845691i
585585 3622.93 + 6275.10i 0.256051 + 0.443493i
586586 −510.130 + 1189.65i −0.0359612 + 0.0838635i
587587 21155.6 1.48754 0.743770 0.668436i 0.233036π-0.233036\pi
0.743770 + 0.668436i 0.233036π0.233036\pi
588588 0 0
589589 1430.25 0.100055
590590 11775.4 27460.9i 0.821672 1.91618i
591591 6975.36 + 12081.7i 0.485495 + 0.840903i
592592 5580.47 + 3601.86i 0.387426 + 0.250060i
593593 1240.18 + 716.018i 0.0858821 + 0.0495840i 0.542326 0.840168i 0.317544π-0.317544\pi
−0.456444 + 0.889752i 0.650877π0.650877\pi
594594 16540.5 1969.42i 1.14253 0.136038i
595595 0 0
596596 11119.0 2685.89i 0.764184 0.184595i
597597 8822.32 15280.7i 0.604813 1.04757i
598598 −4184.92 + 3129.59i −0.286177 + 0.214010i
599599 −4611.09 + 2662.21i −0.314531 + 0.181595i −0.648952 0.760829i 0.724793π-0.724793\pi
0.334421 + 0.942424i 0.391459π0.391459\pi
600600 15999.6 + 2714.70i 1.08863 + 0.184712i
601601 8711.39i 0.591256i −0.955303 0.295628i 0.904471π-0.904471\pi
0.955303 0.295628i 0.0955289π-0.0955289\pi
602602 0 0
603603 13305.8i 0.898599i
604604 −9562.29 2817.94i −0.644179 0.189835i
605605 5767.55 3329.90i 0.387577 0.223768i
606606 −22.4310 29.9950i −0.00150363 0.00201067i
607607 12379.6 21442.1i 0.827796 1.43378i −0.0719681 0.997407i 0.522928π-0.522928\pi
0.899764 0.436377i 0.143739π-0.143739\pi
608608 6250.67 + 9284.38i 0.416938 + 0.619295i
609609 0 0
610610 −2621.84 22019.9i −0.174025 1.46157i
611611 3865.22 + 2231.59i 0.255925 + 0.147758i
612612 4382.77 4170.75i 0.289482 0.275478i
613613 −3167.74 5486.69i −0.208717 0.361509i 0.742593 0.669743i 0.233596π-0.233596\pi
−0.951311 + 0.308233i 0.900262π0.900262\pi
614614 10906.6 + 4676.81i 0.716862 + 0.307395i
615615 5924.15 0.388431
616616 0 0
617617 12720.7 0.830013 0.415006 0.909819i 0.363779π-0.363779\pi
0.415006 + 0.909819i 0.363779π0.363779\pi
618618 −3117.84 1336.95i −0.202942 0.0870226i
619619 11135.8 + 19287.7i 0.723077 + 1.25241i 0.959761 + 0.280820i 0.0906063π0.0906063\pi
−0.236683 + 0.971587i 0.576060π0.576060\pi
620620 −2470.26 + 2350.77i −0.160013 + 0.152273i
621621 −9219.10 5322.65i −0.595733 0.343946i
622622 −2176.47 18279.4i −0.140303 1.17836i
623623 0 0
624624 2426.29 + 4729.13i 0.155656 + 0.303392i
625625 −1795.08 + 3109.16i −0.114885 + 0.198987i
626626 14633.6 + 19568.2i 0.934308 + 1.24937i
627627 7363.39 4251.25i 0.469004 0.270779i
628628 19508.4 + 5749.00i 1.23960 + 0.365303i
629629 4959.08i 0.314358i
630630 0 0
631631 7895.30i 0.498110i −0.968489 0.249055i 0.919880π-0.919880\pi
0.968489 0.249055i 0.0801199π-0.0801199\pi
632632 −1232.58 + 7264.42i −0.0775780 + 0.457220i
633633 2523.10 1456.71i 0.158427 0.0914676i
634634 −2098.23 + 1569.11i −0.131438 + 0.0982924i
635635 −13783.8 + 23874.3i −0.861410 + 1.49201i
636636 −11368.7 + 2746.20i −0.708803 + 0.171217i
637637 0 0
638638 −3333.54 + 396.914i −0.206859 + 0.0246301i
639639 −16160.1 9330.05i −1.00045 0.577607i
640640 −26055.8 5761.95i −1.60929 0.355876i
641641 −4213.92 7298.73i −0.259657 0.449739i 0.706493 0.707720i 0.250276π-0.250276\pi
−0.966150 + 0.257981i 0.916943π0.916943\pi
642642 3456.90 8061.69i 0.212513 0.495591i
643643 −12838.8 −0.787424 −0.393712 0.919234i 0.628809π-0.628809\pi
−0.393712 + 0.919234i 0.628809π0.628809\pi
644644 0 0
645645 −12057.2 −0.736049
646646 3293.37 7680.32i 0.200582 0.467768i
647647 −11376.3 19704.4i −0.691267 1.19731i −0.971423 0.237355i 0.923719π-0.923719\pi
0.280156 0.959955i 0.409614π-0.409614\pi
648648 −739.003 + 892.354i −0.0448006 + 0.0540972i
649649 20424.5 + 11792.1i 1.23533 + 0.713219i
650650 −14972.0 + 1782.66i −0.903460 + 0.107572i
651651 0 0
652652 1382.61 + 5723.74i 0.0830480 + 0.343802i
653653 −430.103 + 744.961i −0.0257753 + 0.0446441i −0.878625 0.477512i 0.841539π-0.841539\pi
0.852850 + 0.522156i 0.174872π0.174872\pi
654654 −8999.04 + 6729.70i −0.538058 + 0.402373i
655655 −31431.3 + 18146.9i −1.87500 + 1.08253i
656656 −6147.83 304.960i −0.365903 0.0181504i
657657 13088.2i 0.777199i
658658 0 0
659659 19262.8i 1.13865i −0.822111 0.569327i 0.807204π-0.807204\pi
0.822111 0.569327i 0.192796π-0.192796\pi
660660 −5730.34 + 19445.1i −0.337959 + 1.14682i
661661 −3499.64 + 2020.52i −0.205931 + 0.118894i −0.599419 0.800436i 0.704602π-0.704602\pi
0.393488 + 0.919330i 0.371268π0.371268\pi
662662 16157.5 + 21606.1i 0.948611 + 1.26849i
663663 1984.26 3436.84i 0.116233 0.201321i
664664 3999.98 + 10772.8i 0.233779 + 0.629616i
665665 0 0
666666 −549.259 4613.04i −0.0319570 0.268396i
667667 1858.00 + 1072.72i 0.107859 + 0.0622727i
668668 17156.0 + 18028.1i 0.993691 + 1.04420i
669669 −3226.03 5587.64i −0.186435 0.322916i
670670 −40272.2 17269.0i −2.32216 0.995758i
671671 17503.5 1.00703
672672 0 0
673673 −30094.8 −1.72373 −0.861863 0.507141i 0.830702π-0.830702\pi
−0.861863 + 0.507141i 0.830702π0.830702\pi
674674 12312.1 + 5279.51i 0.703628 + 0.301720i
675675 −15357.5 26599.9i −0.875718 1.51679i
676676 8711.97 + 9154.83i 0.495674 + 0.520871i
677677 −16898.8 9756.55i −0.959343 0.553877i −0.0633724 0.997990i 0.520186π-0.520186\pi
−0.895971 + 0.444113i 0.853519π0.853519\pi
678678 740.408 + 6218.43i 0.0419398 + 0.352238i
679679 0 0
680680 6935.26 + 18678.1i 0.391110 + 1.05334i
681681 3303.34 5721.55i 0.185880 0.321953i
682682 −1611.96 2155.53i −0.0905058 0.121025i
683683 19594.6 11312.9i 1.09775 0.633788i 0.162123 0.986771i 0.448166π-0.448166\pi
0.935630 + 0.352982i 0.114832π0.114832\pi
684684 2212.90 7509.17i 0.123702 0.419766i
685685 33050.5i 1.84350i
686686 0 0
687687 8636.90i 0.479648i
688688 12512.4 + 620.673i 0.693361 + 0.0343938i
689689 9410.66 5433.24i 0.520345 0.300421i
690690 10375.0 7758.71i 0.572422 0.428071i
691691 −102.478 + 177.498i −0.00564177 + 0.00977182i −0.868833 0.495106i 0.835129π-0.835129\pi
0.863191 + 0.504878i 0.168463π0.168463\pi
692692 −5898.67 24419.3i −0.324037 1.34145i
693693 0 0
694694 −5495.06 + 654.279i −0.300562 + 0.0357869i
695695 4889.78 + 2823.11i 0.266877 + 0.154082i
696696 1391.86 1680.69i 0.0758022 0.0915320i
697697 2297.91 + 3980.10i 0.124877 + 0.216294i
698698 −10856.5 + 25318.0i −0.588717 + 1.37292i
699699 −11527.0 −0.623736
700700 0 0
701701 9946.71 0.535923 0.267962 0.963430i 0.413650π-0.413650\pi
0.267962 + 0.963430i 0.413650π0.413650\pi
702702 3964.67 9245.84i 0.213158 0.497097i
703703 −3208.36 5557.04i −0.172127 0.298133i
704704 6947.69 19884.3i 0.371947 1.06451i
705705 −9582.47 5532.44i −0.511910 0.295552i
706706 8399.85 1000.14i 0.447780 0.0533157i
707707 0 0
708708 −14901.7 + 3599.62i −0.791018 + 0.191076i
709709 −14432.4 + 24997.6i −0.764484 + 1.32412i 0.176035 + 0.984384i 0.443673π0.443673\pi
−0.940519 + 0.339741i 0.889661π0.889661\pi
710710 49212.2 36802.1i 2.60127 1.94529i
711711 4463.19 2576.82i 0.235419 0.135919i
712712 −772.858 + 4554.98i −0.0406799 + 0.239754i
713713 1720.14i 0.0903501i
714714 0 0
715715 18834.6i 0.985141i
716716 1831.91 + 539.852i 0.0956168 + 0.0281777i
717717 10560.2 6096.94i 0.550039 0.317565i
718718 2238.08 + 2992.78i 0.116329 + 0.155557i
719719 −3063.07 + 5305.39i −0.158878 + 0.275185i −0.934464 0.356057i 0.884121π-0.884121\pi
0.775586 + 0.631241i 0.217454π0.217454\pi
720720 8520.09 + 16606.7i 0.441007 + 0.859574i
721721 0 0
722722 1015.28 + 8527.00i 0.0523336 + 0.439532i
723723 −7335.45 4235.12i −0.377328 0.217851i
724724 −11283.9 + 10738.1i −0.579233 + 0.551213i
725725 3095.12 + 5360.91i 0.158552 + 0.274620i
726726 −3140.44 1346.64i −0.160541 0.0688409i
727727 −20742.9 −1.05820 −0.529101 0.848559i 0.677471π-0.677471\pi
−0.529101 + 0.848559i 0.677471π0.677471\pi
728728 0 0
729729 13730.5 0.697579
730730 −39613.5 16986.5i −2.00844 0.861231i
731731 −4676.85 8100.54i −0.236634 0.409862i
732732 −8242.15 + 7843.43i −0.416173 + 0.396040i
733733 15694.9 + 9061.44i 0.790864 + 0.456606i 0.840267 0.542173i 0.182398π-0.182398\pi
−0.0494026 + 0.998779i 0.515732π0.515732\pi
734734 2252.42 + 18917.3i 0.113268 + 0.951296i
735735 0 0
736736 −11166.2 + 7517.58i −0.559227 + 0.376497i
737737 17293.4 29953.0i 0.864328 1.49706i
738738 2578.40 + 3447.86i 0.128607 + 0.171975i
739739 −32754.4 + 18910.8i −1.63043 + 0.941332i −0.646476 + 0.762934i 0.723758π0.723758\pi
−0.983958 + 0.178398i 0.942909π0.942909\pi
740740 14674.9 + 4324.61i 0.729002 + 0.214832i
741741 5135.01i 0.254574i
742742 0 0
743743 4974.35i 0.245614i 0.992431 + 0.122807i 0.0391896π0.0391896\pi
−0.992431 + 0.122807i 0.960810π0.960810\pi
744744 1724.95 + 292.679i 0.0849999 + 0.0144222i
745745 22818.1 13174.0i 1.12213 0.647865i
746746 −474.504 + 354.846i −0.0232880 + 0.0174153i
747747 4018.78 6960.73i 0.196840 0.340937i
748748 −15286.8 + 3692.64i −0.747246 + 0.180503i
749749 0 0
750750 15493.1 1844.72i 0.754306 0.0898127i
751751 −19034.7 10989.7i −0.924884 0.533982i −0.0396939 0.999212i 0.512638π-0.512638\pi
−0.885190 + 0.465230i 0.845972π0.845972\pi
752752 9659.49 + 6234.61i 0.468411 + 0.302331i
753753 9456.81 + 16379.7i 0.457670 + 0.792707i
754754 −799.035 + 1863.39i −0.0385930 + 0.0900011i
755755 −22962.1 −1.10686
756756 0 0
757757 −10241.5 −0.491722 −0.245861 0.969305i 0.579071π-0.579071\pi
−0.245861 + 0.969305i 0.579071π0.579071\pi
758758 1344.30 3134.99i 0.0644159 0.150221i
759759 5112.91 + 8855.83i 0.244515 + 0.423513i
760760 19855.6 + 16443.4i 0.947684 + 0.784824i
761761 18578.2 + 10726.2i 0.884968 + 0.510937i 0.872293 0.488983i 0.162632π-0.162632\pi
0.0126751 + 0.999920i 0.495965π0.495965\pi
762762 14045.1 1672.31i 0.667719 0.0795031i
763763 0 0
764764 −853.278 3532.39i −0.0404064 0.167274i
765765 6967.86 12068.7i 0.329312 0.570385i
766766 −7205.05 + 5388.12i −0.339855 + 0.254152i
767767 12335.2 7121.71i 0.580700 0.335267i
768768 5638.73 + 12476.6i 0.264935 + 0.586210i
769769 26466.5i 1.24110i −0.784166 0.620551i 0.786909π-0.786909\pi
0.784166 0.620551i 0.213091π-0.213091\pi
770770 0 0
771771 16708.3i 0.780462i
772772 7259.46 24633.9i 0.338437 1.14844i
773773 −9692.09 + 5595.73i −0.450971 + 0.260368i −0.708240 0.705972i 0.750511π-0.750511\pi
0.257269 + 0.966340i 0.417177π0.417177\pi
774774 −5247.71 7017.29i −0.243701 0.325880i
775775 −2481.56 + 4298.19i −0.115020 + 0.199220i
776776 23680.1 8792.51i 1.09545 0.406743i
777777 0 0
778778 2679.30 + 22502.5i 0.123467 + 1.03696i
779779 5149.99 + 2973.35i 0.236864 + 0.136754i
780780 8439.94 + 8868.97i 0.387434 + 0.407128i
781781 24252.2 + 42006.1i 1.11116 + 1.92458i
782782 9237.00 + 3960.88i 0.422397 + 0.181126i
783783 −4130.21 −0.188508
784784 0 0
785785 46845.9 2.12994
786786 17114.4 + 7338.75i 0.776654 + 0.333034i
787787 15026.0 + 26025.7i 0.680582 + 1.17880i 0.974804 + 0.223065i 0.0716062π0.0716062\pi
−0.294222 + 0.955737i 0.595061π0.595061\pi
788788 −23016.7 24186.8i −1.04053 1.09342i
789789 5505.36 + 3178.52i 0.248411 + 0.143420i
790790 2006.61 + 16852.9i 0.0903698 + 0.758985i
791791 0 0
792792 −13811.1 + 5128.11i −0.619641 + 0.230075i
793793 5285.53 9154.81i 0.236689 0.409958i
794794 −20530.6 27453.7i −0.917636 1.22707i
795795 −23330.4 + 13469.8i −1.04081 + 0.600913i
796796 −11937.0 + 40506.5i −0.531528 + 1.80366i
797797 26567.8i 1.18078i −0.807119 0.590389i 0.798974π-0.798974\pi
0.807119 0.590389i 0.201026π-0.201026\pi
798798 0 0
799799 8583.89i 0.380070i
800800 −38746.7 + 2675.63i −1.71238 + 0.118247i
801801 2798.54 1615.74i 0.123447 0.0712724i
802802 −24903.2 + 18623.2i −1.09646 + 0.819960i
803803 17010.5 29463.1i 0.747557 1.29481i
804804 5278.94 + 21853.7i 0.231560 + 0.958609i
805805 0 0
806806 −1614.16 + 192.193i −0.0705415 + 0.00839914i
807807 23319.1 + 13463.3i 1.01719 + 0.587275i
808808 69.0390 + 57.1746i 0.00300592 + 0.00248935i
809809 980.413 + 1698.13i 0.0426075 + 0.0737984i 0.886543 0.462647i 0.153100π-0.153100\pi
−0.843935 + 0.536445i 0.819767π0.819767\pi
810810 −1051.77 + 2452.78i −0.0456238 + 0.106397i
811811 2633.82 0.114040 0.0570198 0.998373i 0.481840π-0.481840\pi
0.0570198 + 0.998373i 0.481840π0.481840\pi
812812 0 0
813813 −14634.5 −0.631309
814814 −4759.04 + 11098.4i −0.204919 + 0.477884i
815815 6781.58 + 11746.0i 0.291470 + 0.504841i
816816 5543.63 8588.93i 0.237826 0.368471i
817817 −10481.6 6051.53i −0.448841 0.259139i
818818 5642.23 671.801i 0.241169 0.0287151i
819819 0 0
820820 −13781.8 + 3329.11i −0.586931 + 0.141778i
821821 −5333.16 + 9237.30i −0.226710 + 0.392672i −0.956831 0.290645i 0.906130π-0.906130\pi
0.730121 + 0.683317i 0.239463π0.239463\pi
822822 13580.1 10155.6i 0.576230 0.430919i
823823 32943.1 19019.7i 1.39529 0.805571i 0.401395 0.915905i 0.368525π-0.368525\pi
0.993895 + 0.110334i 0.0351922π0.0351922\pi
824824 8004.60 + 1358.17i 0.338414 + 0.0574199i
825825 29504.6i 1.24512i
826826 0 0
827827 22277.0i 0.936697i −0.883544 0.468349i 0.844849π-0.844849\pi
0.883544 0.468349i 0.155151π-0.155151\pi
828828 9031.15 + 2661.42i 0.379051 + 0.111704i
829829 −18752.2 + 10826.6i −0.785633 + 0.453585i −0.838423 0.545020i 0.816522π-0.816522\pi
0.0527901 + 0.998606i 0.483189π0.483189\pi
830830 15852.0 + 21197.4i 0.662928 + 0.886475i
831831 5355.83 9276.57i 0.223576 0.387245i
832832 −8302.05 9638.31i −0.345940 0.401620i
833833 0 0
834834 −342.511 2876.63i −0.0142208 0.119436i
835835 49643.4 + 28661.7i 2.05746 + 1.18788i
836836 −14741.0 + 14027.9i −0.609844 + 0.580343i
837837 −1655.73 2867.80i −0.0683755 0.118430i
838838 −17320.1 7426.97i −0.713977 0.306158i
839839 −47337.4 −1.94788 −0.973939 0.226811i 0.927170π-0.927170\pi
−0.973939 + 0.226811i 0.927170π0.927170\pi
840840 0 0
841841 −23556.6 −0.965870
842842 15232.3 + 6531.70i 0.623443 + 0.267336i
843843 −10459.8 18116.9i −0.427347 0.740187i
844844 −5051.08 + 4806.73i −0.206002 + 0.196036i
845845 25209.4 + 14554.6i 1.02631 + 0.592538i
846846 −950.737 7984.92i −0.0386371 0.324500i
847847 0 0
848848 24904.7 12777.4i 1.00853 0.517428i
849849 −10126.2 + 17539.1i −0.409341 + 0.708999i
850850 17366.8 + 23223.0i 0.700794 + 0.937110i
851851 6683.37 3858.64i 0.269216 0.155432i
852852 −30243.3 8912.49i −1.21610 0.358377i
853853 16562.9i 0.664833i 0.943133 + 0.332417i 0.107864π0.107864\pi
−0.943133 + 0.332417i 0.892136π0.892136\pi
854854 0 0
855855 18031.9i 0.721261i
856856 −3511.76 + 20697.2i −0.140222 + 0.826421i
857857 28076.8 16210.2i 1.11912 0.646124i 0.177944 0.984041i 0.443056π-0.443056\pi
0.941176 + 0.337917i 0.109722π0.109722\pi
858858 −7738.97 + 5787.39i −0.307930 + 0.230278i
859859 16065.2 27825.8i 0.638112 1.10524i −0.347735 0.937593i 0.613049π-0.613049\pi
0.985847 0.167649i 0.0536177π-0.0536177\pi
860860 28049.7 6775.61i 1.11219 0.268659i
861861 0 0
862862 −10306.6 + 1227.17i −0.407243 + 0.0484891i
863863 −33292.7 19221.5i −1.31320 0.758179i −0.330579 0.943778i 0.607244π-0.607244\pi
−0.982625 + 0.185600i 0.940577π0.940577\pi
864864 11380.1 23281.3i 0.448101 0.916721i
865865 −28932.4 50112.4i −1.13726 1.96979i
866866 9232.22 21530.1i 0.362267 0.844828i
867867 8790.02 0.344319
868868 0 0
869869 −13396.2 −0.522941
870870 1980.93 4619.63i 0.0771951 0.180023i
871871 −10444.2 18089.8i −0.406300 0.703732i
872872 17153.4 20712.9i 0.666156 0.804390i
873873 −15300.7 8833.85i −0.593184 0.342475i
874874 12913.4 1537.55i 0.499772 0.0595062i
875875 0 0
876876 5192.60 + 21496.3i 0.200276 + 0.829101i
877877 10742.3 18606.2i 0.413616 0.716404i −0.581666 0.813428i 0.697599π-0.697599\pi
0.995282 + 0.0970237i 0.0309323π0.0309323\pi
878878 −21930.4 + 16400.1i −0.842956 + 0.630383i
879879 1324.81 764.877i 0.0508357 0.0293500i
880880 2403.68 48456.9i 0.0920774 1.85623i
881881 17193.8i 0.657517i 0.944414 + 0.328759i 0.106630π0.106630\pi
−0.944414 + 0.328759i 0.893370π0.893370\pi
882882 0 0
883883 16514.2i 0.629384i −0.949194 0.314692i 0.898099π-0.898099\pi
0.949194 0.314692i 0.101901π-0.101901\pi
884884 −2684.80 + 9110.48i −0.102149 + 0.346627i
885885 −30580.7 + 17655.8i −1.16154 + 0.670614i
886886 −13993.5 18712.3i −0.530612 0.709540i
887887 10239.6 17735.5i 0.387612 0.671364i −0.604516 0.796593i 0.706633π-0.706633\pi
0.992128 + 0.125229i 0.0399667π0.0399667\pi
888888 −2732.29 7358.63i −0.103254 0.278085i
889889 0 0
890890 1258.20 + 10567.2i 0.0473876 + 0.397992i
891891 −1824.29 1053.25i −0.0685925 0.0396019i
892892 10645.0 + 11186.1i 0.399574 + 0.419886i
893893 −5553.49 9618.93i −0.208108 0.360454i
894894 −12424.5 5327.70i −0.464806 0.199312i
895895 4399.00 0.164293
896896 0 0
897897 6175.79 0.229882
898898 −190.171 81.5463i −0.00706690 0.00303033i
899899 333.693 + 577.973i 0.0123796 + 0.0214421i
900900 18727.1 + 19679.0i 0.693595 + 0.728854i
901901 −18099.2 10449.6i −0.669226 0.386378i
902902 −1323.14 11112.6i −0.0488424 0.410211i
903903 0 0
904904 −5216.96 14050.4i −0.191940 0.516935i
905905 −17939.6 + 31072.3i −0.658930 + 1.14130i
906906 7055.66 + 9434.91i 0.258729 + 0.345976i
907907 −26983.7 + 15579.0i −0.987848 + 0.570334i −0.904630 0.426197i 0.859853π-0.859853\pi
−0.0832177 + 0.996531i 0.526520π0.526520\pi
908908 −4469.57 + 15166.8i −0.163357 + 0.554327i
909909 62.6978i 0.00228774i
910910 0 0
911911 412.348i 0.0149964i 0.999972 + 0.00749818i 0.00238677π0.00238677\pi
−0.999972 + 0.00749818i 0.997613π0.997613\pi
912912 655.331 13211.1i 0.0237941 0.479676i
913913 −18093.5 + 10446.3i −0.655868 + 0.378666i
914914 29836.7 22312.6i 1.07977 0.807480i
915915 −13103.6 + 22696.2i −0.473435 + 0.820013i
916916 4853.56 + 20092.7i 0.175072 + 0.724763i
917917 0 0
918918 −19212.4 + 2287.56i −0.690746 + 0.0822448i
919919 8444.08 + 4875.19i 0.303095 + 0.174992i 0.643832 0.765166i 0.277343π-0.277343\pi
−0.340737 + 0.940159i 0.610677π0.610677\pi
920920 −19776.3 + 23880.1i −0.708700 + 0.855763i
921921 −7012.30 12145.7i −0.250883 0.434542i
922922 −14106.4 + 32897.0i −0.503872 + 1.17506i
923923 29293.8 1.04466
924924 0 0
925925 22266.7 0.791487
926926 −950.378 + 2216.33i −0.0337272 + 0.0786536i
927927 −2839.38 4917.95i −0.100601 0.174247i
928928 −2293.53 + 4692.09i −0.0811301 + 0.165976i
929929 19036.4 + 10990.7i 0.672297 + 0.388151i 0.796946 0.604050i 0.206447π-0.206447\pi
−0.124650 + 0.992201i 0.539781π0.539781\pi
930930 4001.75 476.475i 0.141100 0.0168003i
931931 0 0
932932 26816.2 6477.67i 0.942484 0.227664i
933933 −10877.7 + 18840.8i −0.381695 + 0.661115i
934934 −24746.7 + 18506.2i −0.866956 + 0.648331i
935935 −31371.0 + 18112.0i −1.09726 + 0.633505i
936936 −1488.40 + 8772.13i −0.0519762 + 0.306331i
937937 19723.5i 0.687662i −0.939032 0.343831i 0.888275π-0.888275\pi
0.939032 0.343831i 0.111725π-0.111725\pi
938938 0 0
939939 28877.4i 1.00360i
940940 25401.5 + 7485.65i 0.881389 + 0.259739i
941941 9773.15 5642.53i 0.338571 0.195474i −0.321069 0.947056i 0.604042π-0.604042\pi
0.659640 + 0.751582i 0.270709π0.270709\pi
942942 −14394.5 19248.5i −0.497876 0.665766i
943943 −3575.99 + 6193.80i −0.123489 + 0.213890i
944944 32644.2 16748.2i 1.12551 0.577445i
945945 0 0
946946 2692.94 + 22617.1i 0.0925530 + 0.777321i
947947 −26386.0 15234.0i −0.905417 0.522743i −0.0264635 0.999650i 0.508425π-0.508425\pi
−0.878954 + 0.476907i 0.841758π0.841758\pi
948948 6308.10 6002.94i 0.216115 0.205661i
949949 −10273.3 17794.0i −0.351409 0.608658i
950950 34485.4 + 14787.5i 1.17774 + 0.505022i
951951 3096.42 0.105582
952952 0 0
953953 11791.2 0.400791 0.200395 0.979715i 0.435777π-0.435777\pi
0.200395 + 0.979715i 0.435777π0.435777\pi
954954 −17993.7 7715.79i −0.610657 0.261853i
955955 −4185.24 7249.05i −0.141813 0.245627i
956956 −21140.9 + 20118.2i −0.715215 + 0.680616i
957957 3435.92 + 1983.73i 0.116058 + 0.0670061i
958958 −3565.18 29942.7i −0.120236 1.00982i
959959 0 0
960960 20582.0 + 23894.8i 0.691961 + 0.803335i
961961 14628.0 25336.4i 0.491019 0.850470i
962962 4367.66 + 5840.49i 0.146382 + 0.195743i
963963 12716.2 7341.69i 0.425517 0.245672i
964964 19445.0 + 5730.32i 0.649670 + 0.191454i
965965 59154.0i 1.97330i
966966 0 0
967967 40914.1i 1.36061i −0.732929 0.680305i 0.761847π-0.761847\pi
0.732929 0.680305i 0.238153π-0.238153\pi
968968 8062.61 + 1368.01i 0.267709 + 0.0454230i
969969 −8552.87 + 4938.00i −0.283548 + 0.163706i
970970 46595.0 34844.9i 1.54234 1.15340i
971971 −9276.00 + 16066.5i −0.306572 + 0.530997i −0.977610 0.210425i 0.932515π-0.932515\pi
0.671038 + 0.741423i 0.265849π0.265849\pi
972972 −28726.0 + 6939.00i −0.947930 + 0.228980i
973973 0 0
974974 152.192 18.1210i 0.00500671 0.000596133i
975975 15431.8 + 8909.53i 0.506884 + 0.292650i
976976 14766.7 22878.6i 0.484294 0.750333i
977977 1455.74 + 2521.42i 0.0476697 + 0.0825664i 0.888876 0.458148i 0.151487π-0.151487\pi
−0.841206 + 0.540715i 0.818154π0.818154\pi
978978 2742.53 6395.74i 0.0896692 0.209114i
979979 −8399.78 −0.274217
980980 0 0
981981 −18810.5 −0.612204
982982 6273.54 14630.3i 0.203866 0.475428i
983983 −18251.1 31611.8i −0.592186 1.02570i −0.993937 0.109947i 0.964932π-0.964932\pi
0.401752 0.915749i 0.368402π-0.368402\pi
984984 5602.70 + 4639.88i 0.181512 + 0.150319i
985985 −66602.3 38452.9i −2.15444 1.24387i
986986 3872.05 461.032i 0.125062 0.0148907i
987987 0 0
988988 2885.65 + 11946.0i 0.0929198 + 0.384669i
989989 7278.08 12606.0i 0.234004 0.405306i
990990 −27175.9 + 20322.8i −0.872431 + 0.652425i
991991 31879.7 18405.7i 1.02189 0.589987i 0.107238 0.994233i 0.465799π-0.465799\pi
0.914650 + 0.404246i 0.132466π0.132466\pi
992992 −4177.38 + 288.466i −0.133701 + 0.00923266i
993993 31884.6i 1.01896i
994994 0 0
995995 97269.2i 3.09914i
996996 3838.92 13026.8i 0.122129 0.414429i
997997 10060.1 5808.18i 0.319564 0.184500i −0.331634 0.943408i 0.607600π-0.607600\pi
0.651198 + 0.758908i 0.274267π0.274267\pi
998998 −1049.81 1403.82i −0.0332978 0.0445262i
999999 −7428.32 + 12866.2i −0.235257 + 0.407477i
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 196.4.f.d.19.9 20
4.3 odd 2 inner 196.4.f.d.19.2 20
7.2 even 3 196.4.d.b.195.10 20
7.3 odd 6 inner 196.4.f.d.31.2 20
7.4 even 3 28.4.f.a.3.2 20
7.5 odd 6 196.4.d.b.195.9 20
7.6 odd 2 28.4.f.a.19.9 yes 20
28.3 even 6 inner 196.4.f.d.31.9 20
28.11 odd 6 28.4.f.a.3.9 yes 20
28.19 even 6 196.4.d.b.195.12 20
28.23 odd 6 196.4.d.b.195.11 20
28.27 even 2 28.4.f.a.19.2 yes 20
56.11 odd 6 448.4.p.h.255.4 20
56.13 odd 2 448.4.p.h.383.4 20
56.27 even 2 448.4.p.h.383.7 20
56.53 even 6 448.4.p.h.255.7 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.4.f.a.3.2 20 7.4 even 3
28.4.f.a.3.9 yes 20 28.11 odd 6
28.4.f.a.19.2 yes 20 28.27 even 2
28.4.f.a.19.9 yes 20 7.6 odd 2
196.4.d.b.195.9 20 7.5 odd 6
196.4.d.b.195.10 20 7.2 even 3
196.4.d.b.195.11 20 28.23 odd 6
196.4.d.b.195.12 20 28.19 even 6
196.4.f.d.19.2 20 4.3 odd 2 inner
196.4.f.d.19.9 20 1.1 even 1 trivial
196.4.f.d.31.2 20 7.3 odd 6 inner
196.4.f.d.31.9 20 28.3 even 6 inner
448.4.p.h.255.4 20 56.11 odd 6
448.4.p.h.255.7 20 56.53 even 6
448.4.p.h.383.4 20 56.13 odd 2
448.4.p.h.383.7 20 56.27 even 2