Properties

Label 84.4.e.a.71.17
Level 8484
Weight 44
Character 84.71
Analytic conductor 4.9564.956
Analytic rank 00
Dimension 3636
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [84,4,Mod(71,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.71");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 84=2237 84 = 2^{2} \cdot 3 \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 84.e (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.956160440484.95616044048
Analytic rank: 00
Dimension: 3636
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 71.17
Character χ\chi == 84.71
Dual form 84.4.e.a.71.18

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.08787672.82706i)q2+(0.849945+5.12617i)q3+(7.98456+0.496866i)q411.8826iq5+(14.5667+1.95238i)q67.00000iq7+(2.10633+22.5292i)q8+(25.55528.71392i)q9+(33.5929+1.04421i)q1057.5490q11+(4.2394241.3525i)q1259.9367q13+(19.7894+0.615137i)q14+(60.9123+10.0996i)q15+(63.50627.93450i)q1651.9634iq17+(22.3891+73.0118i)q1820.5454iq19+(5.90407+94.8774i)q20+(35.8832+5.94962i)q21+(5.05721+162.694i)q22+53.7192q23+(117.2798.35118i)q2416.1967q25+(5.26704+169.445i)q26+(66.3895123.594i)q27+(3.47806+55.8919i)q28158.741iq29+(23.1994173.090i)q30+302.431iq31+(28.0120178.839i)q32+(48.9135295.006i)q33+(146.904+4.56637i)q3483.1783q35+(208.376+56.8793i)q36+284.534q37+(58.0830+1.80546i)q38+(50.9429307.245i)q39+(267.70625.0287i)q40157.215iq41+(13.6666101.967i)q4283.6549iq43+(459.50328.5941i)q44+(103.544+303.663i)q45+(4.72067151.868i)q46479.631q47+(13.3032+332.288i)q4849.0000q49+(1.42331+45.7890i)q50+(266.373+44.1660i)q51+(478.56829.7805i)q52+265.944iq53+(355.241176.826i)q54+683.832iq55+(157.70414.7443i)q56+(105.319+17.4624i)q57+(448.770+13.9496i)q58148.259q59+(491.37650.3754i)q60476.710q61+(854.99126.5766i)q62+(60.9975+178.886i)q63+(503.127+94.9075i)q64+712.205iq65+(838.297112.357i)q66779.619iq67+(25.8188+414.905i)q68+(45.6584+275.374i)q69+(7.30944+235.150i)q70+615.023q71+(142.490594.091i)q72+327.327q73+(25.0039804.395i)q74+(13.766383.0269i)q75+(10.2083+164.046i)q76+402.843iq77+(873.079117.019i)q78448.606iq79+(94.2827754.621i)q80+(577.135+445.372i)q81+(444.456+13.8155i)q82680.159q83+(289.46729.6759i)q84617.461q85+(236.498+7.35132i)q86+(813.732+134.921i)q87+(121.2171296.53i)q88413.171iq89+(867.572+266.041i)q90+419.557iq91+(428.924+26.6912i)q92+(1550.31257.050i)q93+(42.1483+1355.95i)q94244.133q95+(940.566+8.40876i)q96+552.922q97+(4.30596+138.526i)q98+(1470.67+501.477i)q99+O(q100)q+(-0.0878767 - 2.82706i) q^{2} +(-0.849945 + 5.12617i) q^{3} +(-7.98456 + 0.496866i) q^{4} -11.8826i q^{5} +(14.5667 + 1.95238i) q^{6} -7.00000i q^{7} +(2.10633 + 22.5292i) q^{8} +(-25.5552 - 8.71392i) q^{9} +(-33.5929 + 1.04421i) q^{10} -57.5490 q^{11} +(4.23942 - 41.3525i) q^{12} -59.9367 q^{13} +(-19.7894 + 0.615137i) q^{14} +(60.9123 + 10.0996i) q^{15} +(63.5062 - 7.93450i) q^{16} -51.9634i q^{17} +(-22.3891 + 73.0118i) q^{18} -20.5454i q^{19} +(5.90407 + 94.8774i) q^{20} +(35.8832 + 5.94962i) q^{21} +(5.05721 + 162.694i) q^{22} +53.7192 q^{23} +(-117.279 - 8.35118i) q^{24} -16.1967 q^{25} +(5.26704 + 169.445i) q^{26} +(66.3895 - 123.594i) q^{27} +(3.47806 + 55.8919i) q^{28} -158.741i q^{29} +(23.1994 - 173.090i) q^{30} +302.431i q^{31} +(-28.0120 - 178.839i) q^{32} +(48.9135 - 295.006i) q^{33} +(-146.904 + 4.56637i) q^{34} -83.1783 q^{35} +(208.376 + 56.8793i) q^{36} +284.534 q^{37} +(-58.0830 + 1.80546i) q^{38} +(50.9429 - 307.245i) q^{39} +(267.706 - 25.0287i) q^{40} -157.215i q^{41} +(13.6666 - 101.967i) q^{42} -83.6549i q^{43} +(459.503 - 28.5941i) q^{44} +(-103.544 + 303.663i) q^{45} +(-4.72067 - 151.868i) q^{46} -479.631 q^{47} +(-13.3032 + 332.288i) q^{48} -49.0000 q^{49} +(1.42331 + 45.7890i) q^{50} +(266.373 + 44.1660i) q^{51} +(478.568 - 29.7805i) q^{52} +265.944i q^{53} +(-355.241 - 176.826i) q^{54} +683.832i q^{55} +(157.704 - 14.7443i) q^{56} +(105.319 + 17.4624i) q^{57} +(-448.770 + 13.9496i) q^{58} -148.259 q^{59} +(-491.376 - 50.3754i) q^{60} -476.710 q^{61} +(854.991 - 26.5766i) q^{62} +(-60.9975 + 178.886i) q^{63} +(-503.127 + 94.9075i) q^{64} +712.205i q^{65} +(-838.297 - 112.357i) q^{66} -779.619i q^{67} +(25.8188 + 414.905i) q^{68} +(-45.6584 + 275.374i) q^{69} +(7.30944 + 235.150i) q^{70} +615.023 q^{71} +(142.490 - 594.091i) q^{72} +327.327 q^{73} +(-25.0039 - 804.395i) q^{74} +(13.7663 - 83.0269i) q^{75} +(10.2083 + 164.046i) q^{76} +402.843i q^{77} +(-873.079 - 117.019i) q^{78} -448.606i q^{79} +(-94.2827 - 754.621i) q^{80} +(577.135 + 445.372i) q^{81} +(-444.456 + 13.8155i) q^{82} -680.159 q^{83} +(-289.467 - 29.6759i) q^{84} -617.461 q^{85} +(-236.498 + 7.35132i) q^{86} +(813.732 + 134.921i) q^{87} +(-121.217 - 1296.53i) q^{88} -413.171i q^{89} +(867.572 + 266.041i) q^{90} +419.557i q^{91} +(-428.924 + 26.6912i) q^{92} +(-1550.31 - 257.050i) q^{93} +(42.1483 + 1355.95i) q^{94} -244.133 q^{95} +(940.566 + 8.40876i) q^{96} +552.922 q^{97} +(4.30596 + 138.526i) q^{98} +(1470.67 + 501.477i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 36q+12q4+30q6+20q9132q1078q12+324q16+424q18240q22382q24900q25+168q28+476q30+848q33576q34+412q36+528q37+72q97+O(q100) 36 q + 12 q^{4} + 30 q^{6} + 20 q^{9} - 132 q^{10} - 78 q^{12} + 324 q^{16} + 424 q^{18} - 240 q^{22} - 382 q^{24} - 900 q^{25} + 168 q^{28} + 476 q^{30} + 848 q^{33} - 576 q^{34} + 412 q^{36} + 528 q^{37}+ \cdots - 72 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/84Z)×\left(\mathbb{Z}/84\mathbb{Z}\right)^\times.

nn 2929 4343 7373
χ(n)\chi(n) 1-1 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.0878767 2.82706i −0.0310691 0.999517i
33 −0.849945 + 5.12617i −0.163572 + 0.986531i
44 −7.98456 + 0.496866i −0.998069 + 0.0621082i
55 11.8826i 1.06281i −0.847117 0.531407i 0.821664π-0.821664\pi
0.847117 0.531407i 0.178336π-0.178336\pi
66 14.5667 + 1.95238i 0.991137 + 0.132842i
77 7.00000i 0.377964i
88 2.10633 + 22.5292i 0.0930873 + 0.995658i
99 −25.5552 8.71392i −0.946488 0.322738i
1010 −33.5929 + 1.04421i −1.06230 + 0.0330207i
1111 −57.5490 −1.57742 −0.788712 0.614763i 0.789252π-0.789252\pi
−0.788712 + 0.614763i 0.789252π0.789252\pi
1212 4.23942 41.3525i 0.101985 0.994786i
1313 −59.9367 −1.27873 −0.639363 0.768905i 0.720802π-0.720802\pi
−0.639363 + 0.768905i 0.720802π0.720802\pi
1414 −19.7894 + 0.615137i −0.377782 + 0.0117430i
1515 60.9123 + 10.0996i 1.04850 + 0.173847i
1616 63.5062 7.93450i 0.992285 0.123977i
1717 51.9634i 0.741351i −0.928762 0.370676i 0.879126π-0.879126\pi
0.928762 0.370676i 0.120874π-0.120874\pi
1818 −22.3891 + 73.0118i −0.293175 + 0.956059i
1919 20.5454i 0.248075i −0.992278 0.124038i 0.960416π-0.960416\pi
0.992278 0.124038i 0.0395843π-0.0395843\pi
2020 5.90407 + 94.8774i 0.0660095 + 1.06076i
2121 35.8832 + 5.94962i 0.372874 + 0.0618244i
2222 5.05721 + 162.694i 0.0490091 + 1.57666i
2323 53.7192 0.487010 0.243505 0.969900i 0.421703π-0.421703\pi
0.243505 + 0.969900i 0.421703π0.421703\pi
2424 −117.279 8.35118i −0.997474 0.0710282i
2525 −16.1967 −0.129573
2626 5.26704 + 169.445i 0.0397289 + 1.27811i
2727 66.3895 123.594i 0.473210 0.880950i
2828 3.47806 + 55.8919i 0.0234747 + 0.377235i
2929 158.741i 1.01646i −0.861220 0.508232i 0.830299π-0.830299\pi
0.861220 0.508232i 0.169701π-0.169701\pi
3030 23.1994 173.090i 0.141187 1.05339i
3131 302.431i 1.75220i 0.482129 + 0.876100i 0.339864π0.339864\pi
−0.482129 + 0.876100i 0.660136π0.660136\pi
3232 −28.0120 178.839i −0.154746 0.987954i
3333 48.9135 295.006i 0.258022 1.55618i
3434 −146.904 + 4.56637i −0.740993 + 0.0230331i
3535 −83.1783 −0.401706
3636 208.376 + 56.8793i 0.964706 + 0.263330i
3737 284.534 1.26425 0.632123 0.774868i 0.282184π-0.282184\pi
0.632123 + 0.774868i 0.282184π0.282184\pi
3838 −58.0830 + 1.80546i −0.247955 + 0.00770747i
3939 50.9429 307.245i 0.209164 1.26150i
4040 267.706 25.0287i 1.05820 0.0989345i
4141 157.215i 0.598849i −0.954120 0.299425i 0.903205π-0.903205\pi
0.954120 0.299425i 0.0967947π-0.0967947\pi
4242 13.6666 101.967i 0.0502097 0.374615i
4343 83.6549i 0.296680i −0.988936 0.148340i 0.952607π-0.952607\pi
0.988936 0.148340i 0.0473931π-0.0473931\pi
4444 459.503 28.5941i 1.57438 0.0979710i
4545 −103.544 + 303.663i −0.343010 + 1.00594i
4646 −4.72067 151.868i −0.0151310 0.486775i
4747 −479.631 −1.48854 −0.744269 0.667880i 0.767202π-0.767202\pi
−0.744269 + 0.667880i 0.767202π0.767202\pi
4848 −13.3032 + 332.288i −0.0400033 + 0.999200i
4949 −49.0000 −0.142857
5050 1.42331 + 45.7890i 0.00402573 + 0.129511i
5151 266.373 + 44.1660i 0.731366 + 0.121264i
5252 478.568 29.7805i 1.27626 0.0794194i
5353 265.944i 0.689251i 0.938740 + 0.344625i 0.111994π0.111994\pi
−0.938740 + 0.344625i 0.888006π0.888006\pi
5454 −355.241 176.826i −0.895227 0.445611i
5555 683.832i 1.67651i
5656 157.704 14.7443i 0.376323 0.0351837i
5757 105.319 + 17.4624i 0.244734 + 0.0405782i
5858 −448.770 + 13.9496i −1.01597 + 0.0315806i
5959 −148.259 −0.327148 −0.163574 0.986531i 0.552302π-0.552302\pi
−0.163574 + 0.986531i 0.552302π0.552302\pi
6060 −491.376 50.3754i −1.05727 0.108391i
6161 −476.710 −1.00060 −0.500299 0.865853i 0.666776π-0.666776\pi
−0.500299 + 0.865853i 0.666776π0.666776\pi
6262 854.991 26.5766i 1.75136 0.0544393i
6363 −60.9975 + 178.886i −0.121983 + 0.357739i
6464 −503.127 + 94.9075i −0.982670 + 0.185366i
6565 712.205i 1.35905i
6666 −838.297 112.357i −1.56344 0.209549i
6767 779.619i 1.42158i −0.703406 0.710788i 0.748338π-0.748338\pi
0.703406 0.710788i 0.251662π-0.251662\pi
6868 25.8188 + 414.905i 0.0460440 + 0.739920i
6969 −45.6584 + 275.374i −0.0796613 + 0.480451i
7070 7.30944 + 235.150i 0.0124806 + 0.401512i
7171 615.023 1.02803 0.514013 0.857782i 0.328158π-0.328158\pi
0.514013 + 0.857782i 0.328158π0.328158\pi
7272 142.490 594.091i 0.233230 0.972421i
7373 327.327 0.524805 0.262403 0.964958i 0.415485π-0.415485\pi
0.262403 + 0.964958i 0.415485π0.415485\pi
7474 −25.0039 804.395i −0.0392790 1.26364i
7575 13.7663 83.0269i 0.0211946 0.127828i
7676 10.2083 + 164.046i 0.0154075 + 0.247596i
7777 402.843i 0.596210i
7878 −873.079 117.019i −1.26739 0.169869i
7979 448.606i 0.638887i −0.947605 0.319444i 0.896504π-0.896504\pi
0.947605 0.319444i 0.103496π-0.103496\pi
8080 −94.2827 754.621i −0.131764 1.05461i
8181 577.135 + 445.372i 0.791681 + 0.610935i
8282 −444.456 + 13.8155i −0.598560 + 0.0186057i
8383 −680.159 −0.899484 −0.449742 0.893159i 0.648484π-0.648484\pi
−0.449742 + 0.893159i 0.648484π0.648484\pi
8484 −289.467 29.6759i −0.375994 0.0385465i
8585 −617.461 −0.787919
8686 −236.498 + 7.35132i −0.296537 + 0.00921759i
8787 813.732 + 134.921i 1.00277 + 0.166265i
8888 −121.217 1296.53i −0.146838 1.57057i
8989 413.171i 0.492090i −0.969258 0.246045i 0.920869π-0.920869\pi
0.969258 0.246045i 0.0791312π-0.0791312\pi
9090 867.572 + 266.041i 1.01611 + 0.311591i
9191 419.557i 0.483313i
9292 −428.924 + 26.6912i −0.486070 + 0.0302473i
9393 −1550.31 257.050i −1.72860 0.286611i
9494 42.1483 + 1355.95i 0.0462476 + 1.48782i
9595 −244.133 −0.263658
9696 940.566 + 8.40876i 0.999960 + 0.00893975i
9797 552.922 0.578771 0.289385 0.957213i 0.406549π-0.406549\pi
0.289385 + 0.957213i 0.406549π0.406549\pi
9898 4.30596 + 138.526i 0.00443844 + 0.142788i
9999 1470.67 + 501.477i 1.49301 + 0.509094i
100100 129.323 8.04757i 0.129323 0.00804757i
101101 81.5446i 0.0803366i −0.999193 0.0401683i 0.987211π-0.987211\pi
0.999193 0.0401683i 0.0127894π-0.0127894\pi
102102 101.452 756.934i 0.0984829 0.734781i
103103 1015.94i 0.971881i −0.873992 0.485940i 0.838477π-0.838477\pi
0.873992 0.485940i 0.161523π-0.161523\pi
104104 −126.246 1350.32i −0.119033 1.27317i
105105 70.6970 426.386i 0.0657078 0.396295i
106106 751.841 23.3703i 0.688918 0.0214144i
107107 −2141.69 −1.93500 −0.967499 0.252874i 0.918624π-0.918624\pi
−0.967499 + 0.252874i 0.918624π0.918624\pi
108108 −468.681 + 1019.83i −0.417582 + 0.908639i
109109 67.7332 0.0595199 0.0297599 0.999557i 0.490526π-0.490526\pi
0.0297599 + 0.999557i 0.490526π0.490526\pi
110110 1933.24 60.0929i 1.67570 0.0520876i
111111 −241.838 + 1458.57i −0.206795 + 1.24722i
112112 −55.5415 444.544i −0.0468587 0.375049i
113113 1228.08i 1.02237i 0.859471 + 0.511185i 0.170793π0.170793\pi
−0.859471 + 0.511185i 0.829207π0.829207\pi
114114 40.1123 299.278i 0.0329549 0.245877i
115115 638.325i 0.517601i
116116 78.8729 + 1267.48i 0.0631307 + 1.01450i
117117 1531.69 + 522.284i 1.21030 + 0.412693i
118118 13.0285 + 419.138i 0.0101642 + 0.326990i
119119 −363.744 −0.280204
120120 −99.2339 + 1393.58i −0.0754898 + 1.06013i
121121 1980.88 1.48827
122122 41.8917 + 1347.69i 0.0310877 + 1.00011i
123123 805.909 + 133.624i 0.590784 + 0.0979550i
124124 −150.268 2414.78i −0.108826 1.74882i
125125 1292.87i 0.925101i
126126 511.083 + 156.724i 0.361356 + 0.110810i
127127 1138.85i 0.795724i 0.917445 + 0.397862i 0.130248π0.130248\pi
−0.917445 + 0.397862i 0.869752π0.869752\pi
128128 312.523 + 1414.03i 0.215807 + 0.976436i
129129 428.829 + 71.1021i 0.292684 + 0.0485286i
130130 2013.45 62.5862i 1.35839 0.0422244i
131131 −1538.22 −1.02591 −0.512956 0.858415i 0.671450π-0.671450\pi
−0.512956 + 0.858415i 0.671450π0.671450\pi
132132 −243.974 + 2379.79i −0.160873 + 1.56920i
133133 −143.817 −0.0937636
134134 −2204.03 + 68.5103i −1.42089 + 0.0441671i
135135 −1468.62 788.882i −0.936286 0.502934i
136136 1170.69 109.452i 0.738132 0.0690104i
137137 1885.75i 1.17599i −0.808866 0.587993i 0.799918π-0.799918\pi
0.808866 0.587993i 0.200082π-0.200082\pi
138138 782.511 + 104.880i 0.482694 + 0.0646956i
139139 704.823i 0.430089i −0.976604 0.215044i 0.931010π-0.931010\pi
0.976604 0.215044i 0.0689896π-0.0689896\pi
140140 664.142 41.3285i 0.400930 0.0249492i
141141 407.660 2458.67i 0.243483 1.46849i
142142 −54.0462 1738.71i −0.0319398 1.02753i
143143 3449.29 2.01709
144144 −1692.05 350.621i −0.979198 0.202906i
145145 −1886.26 −1.08031
146146 −28.7644 925.375i −0.0163052 0.524552i
147147 41.6473 251.182i 0.0233674 0.140933i
148148 −2271.88 + 141.375i −1.26181 + 0.0785201i
149149 2025.45i 1.11363i −0.830636 0.556816i 0.812023π-0.812023\pi
0.830636 0.556816i 0.187977π-0.187977\pi
150150 −235.932 31.6220i −0.128425 0.0172129i
151151 1333.21i 0.718513i −0.933239 0.359256i 0.883030π-0.883030\pi
0.933239 0.359256i 0.116970π-0.116970\pi
152152 462.870 43.2752i 0.246998 0.0230927i
153153 −452.805 + 1327.93i −0.239262 + 0.701680i
154154 1138.86 35.4005i 0.595922 0.0185237i
155155 3593.67 1.86226
156156 −254.097 + 2478.53i −0.130410 + 1.27206i
157157 −1977.17 −1.00506 −0.502532 0.864558i 0.667598π-0.667598\pi
−0.502532 + 0.864558i 0.667598π0.667598\pi
158158 −1268.24 + 39.4220i −0.638579 + 0.0198497i
159159 −1363.28 226.038i −0.679967 0.112742i
160160 −2125.07 + 332.856i −1.05001 + 0.164466i
161161 376.035i 0.184073i
162162 1208.38 1670.73i 0.586044 0.810280i
163163 1678.40i 0.806516i 0.915086 + 0.403258i 0.132122π0.132122\pi
−0.915086 + 0.403258i 0.867878π0.867878\pi
164164 78.1146 + 1255.29i 0.0371935 + 0.597693i
165165 −3505.44 581.220i −1.65393 0.274230i
166166 59.7701 + 1922.85i 0.0279462 + 0.899050i
167167 −2933.39 −1.35924 −0.679619 0.733565i 0.737855π-0.737855\pi
−0.679619 + 0.733565i 0.737855π0.737855\pi
168168 −58.4582 + 820.950i −0.0268461 + 0.377010i
169169 1395.41 0.635141
170170 54.2604 + 1745.60i 0.0244799 + 0.787538i
171171 −179.031 + 525.040i −0.0800632 + 0.234800i
172172 41.5652 + 667.947i 0.0184263 + 0.296108i
173173 2035.22i 0.894420i 0.894429 + 0.447210i 0.147582π0.147582\pi
−0.894429 + 0.447210i 0.852418π0.852418\pi
174174 309.922 2312.33i 0.135029 1.00745i
175175 113.377i 0.0489742i
176176 −3654.72 + 456.622i −1.56525 + 0.195564i
177177 126.012 760.002i 0.0535122 0.322742i
178178 −1168.06 + 36.3081i −0.491853 + 0.0152888i
179179 3632.86 1.51694 0.758472 0.651706i 0.225946π-0.225946\pi
0.758472 + 0.651706i 0.225946π0.225946\pi
180180 675.875 2476.06i 0.279871 1.02530i
181181 −2086.31 −0.856762 −0.428381 0.903598i 0.640916π-0.640916\pi
−0.428381 + 0.903598i 0.640916π0.640916\pi
182182 1186.11 36.8693i 0.483080 0.0150161i
183183 405.177 2443.69i 0.163670 0.987121i
184184 113.150 + 1210.25i 0.0453345 + 0.484896i
185185 3381.01i 1.34366i
186186 −590.459 + 4405.42i −0.232767 + 1.73667i
187187 2990.44i 1.16943i
188188 3829.64 238.312i 1.48567 0.0924505i
189189 −865.157 464.727i −0.332968 0.178857i
190190 21.4536 + 690.178i 0.00819161 + 0.263530i
191191 1170.52 0.443433 0.221716 0.975111i 0.428834π-0.428834\pi
0.221716 + 0.975111i 0.428834π0.428834\pi
192192 −58.8818 2659.78i −0.0221324 0.999755i
193193 2386.62 0.890116 0.445058 0.895502i 0.353183π-0.353183\pi
0.445058 + 0.895502i 0.353183π0.353183\pi
194194 −48.5890 1563.15i −0.0179819 0.578491i
195195 −3650.88 605.335i −1.34074 0.222302i
196196 391.243 24.3464i 0.142581 0.00887260i
197197 4598.82i 1.66321i 0.555369 + 0.831604i 0.312577π0.312577\pi
−0.555369 + 0.831604i 0.687423π0.687423\pi
198198 1288.47 4201.76i 0.462462 1.50811i
199199 1007.78i 0.358992i 0.983759 + 0.179496i 0.0574467π0.0574467\pi
−0.983759 + 0.179496i 0.942553π0.942553\pi
200200 −34.1155 364.898i −0.0120616 0.129011i
201201 3996.46 + 662.633i 1.40243 + 0.232530i
202202 −230.532 + 7.16587i −0.0802978 + 0.00249598i
203203 −1111.19 −0.384187
204204 −2148.81 220.294i −0.737486 0.0756064i
205205 −1868.12 −0.636466
206206 −2872.13 + 89.2776i −0.971411 + 0.0301955i
207207 −1372.81 468.105i −0.460950 0.157177i
208208 −3806.35 + 475.568i −1.26886 + 0.158532i
209209 1182.36i 0.391320i
210210 −1211.63 162.395i −0.398146 0.0533636i
211211 4982.89i 1.62576i −0.582429 0.812881i 0.697898π-0.697898\pi
0.582429 0.812881i 0.302102π-0.302102\pi
212212 −132.139 2123.45i −0.0428081 0.687920i
213213 −522.736 + 3152.71i −0.168156 + 1.01418i
214214 188.204 + 6054.69i 0.0601187 + 1.93406i
215215 −994.040 −0.315316
216216 2924.30 + 1235.37i 0.921174 + 0.389150i
217217 2117.02 0.662270
218218 −5.95217 191.486i −0.00184923 0.0594911i
219219 −278.210 + 1677.94i −0.0858434 + 0.517737i
220220 −339.773 5460.10i −0.104125 1.67327i
221221 3114.51i 0.947986i
222222 4144.72 + 555.518i 1.25304 + 0.167946i
223223 341.997i 0.102699i −0.998681 0.0513493i 0.983648π-0.983648\pi
0.998681 0.0513493i 0.0163522π-0.0163522\pi
224224 −1251.87 + 196.084i −0.373412 + 0.0584885i
225225 413.909 + 141.137i 0.122640 + 0.0418183i
226226 3471.85 107.919i 1.02188 0.0317641i
227227 −1179.18 −0.344779 −0.172389 0.985029i 0.555149π-0.555149\pi
−0.172389 + 0.985029i 0.555149π0.555149\pi
228228 −849.601 87.1003i −0.246782 0.0252998i
229229 −1424.43 −0.411043 −0.205522 0.978653i 0.565889π-0.565889\pi
−0.205522 + 0.978653i 0.565889π0.565889\pi
230230 −1804.59 + 56.0939i −0.517351 + 0.0160814i
231231 −2065.04 342.394i −0.588180 0.0975233i
232232 3576.30 334.360i 1.01205 0.0946199i
233233 573.154i 0.161153i 0.996748 + 0.0805763i 0.0256761π0.0256761\pi
−0.996748 + 0.0805763i 0.974324π0.974324\pi
234234 1341.93 4376.09i 0.374891 1.22254i
235235 5699.27i 1.58204i
236236 1183.78 73.6650i 0.326516 0.0203186i
237237 2299.63 + 381.290i 0.630283 + 0.104504i
238238 31.9646 + 1028.33i 0.00870570 + 0.280069i
239239 5563.85 1.50584 0.752920 0.658112i 0.228645π-0.228645\pi
0.752920 + 0.658112i 0.228645π0.228645\pi
240240 3948.45 + 158.077i 1.06196 + 0.0425161i
241241 4691.92 1.25408 0.627039 0.778988i 0.284267π-0.284267\pi
0.627039 + 0.778988i 0.284267π0.284267\pi
242242 −174.073 5600.08i −0.0462391 1.48755i
243243 −2773.58 + 2579.95i −0.732204 + 0.681086i
244244 3806.32 236.861i 0.998666 0.0621453i
245245 582.248i 0.151831i
246246 306.943 2290.10i 0.0795526 0.593542i
247247 1231.42i 0.317220i
248248 −6813.52 + 637.018i −1.74459 + 0.163108i
249249 578.098 3486.61i 0.147130 0.887369i
250250 −3655.02 + 113.613i −0.924655 + 0.0287421i
251251 4505.81 1.13308 0.566542 0.824033i 0.308281π-0.308281\pi
0.566542 + 0.824033i 0.308281π0.308281\pi
252252 398.155 1458.64i 0.0995294 0.364625i
253253 −3091.49 −0.768222
254254 3219.61 100.079i 0.795339 0.0247224i
255255 524.808 3165.21i 0.128881 0.777306i
256256 3970.09 1007.78i 0.969260 0.246040i
257257 1625.67i 0.394578i 0.980345 + 0.197289i 0.0632137π0.0632137\pi
−0.980345 + 0.197289i 0.936786π0.936786\pi
258258 163.326 1218.57i 0.0394117 0.294051i
259259 1991.74i 0.477840i
260260 −353.870 5686.64i −0.0844080 1.35642i
261261 −1383.26 + 4056.65i −0.328051 + 0.962071i
262262 135.173 + 4348.63i 0.0318742 + 1.02542i
263263 −2356.53 −0.552509 −0.276254 0.961085i 0.589093π-0.589093\pi
−0.276254 + 0.961085i 0.589093π0.589093\pi
264264 6749.26 + 480.602i 1.57344 + 0.112042i
265265 3160.12 0.732545
266266 12.6382 + 406.581i 0.00291315 + 0.0937183i
267267 2117.98 + 351.173i 0.485463 + 0.0804922i
268268 387.366 + 6224.91i 0.0882916 + 1.41883i
269269 2337.79i 0.529880i −0.964265 0.264940i 0.914648π-0.914648\pi
0.964265 0.264940i 0.0853521π-0.0853521\pi
270270 −2101.16 + 4221.20i −0.473602 + 0.951459i
271271 1373.37i 0.307846i 0.988083 + 0.153923i 0.0491908π0.0491908\pi
−0.988083 + 0.153923i 0.950809π0.950809\pi
272272 −412.304 3300.00i −0.0919102 0.735632i
273273 −2150.72 356.600i −0.476804 0.0790565i
274274 −5331.12 + 165.713i −1.17542 + 0.0365368i
275275 932.102 0.204392
276276 227.738 2221.42i 0.0496675 0.484471i
277277 1893.14 0.410642 0.205321 0.978695i 0.434176π-0.434176\pi
0.205321 + 0.978695i 0.434176π0.434176\pi
278278 −1992.58 + 61.9375i −0.429881 + 0.0133625i
279279 2635.36 7728.68i 0.565502 1.65844i
280280 −175.201 1873.94i −0.0373937 0.399962i
281281 3960.77i 0.840852i −0.907327 0.420426i 0.861881π-0.861881\pi
0.907327 0.420426i 0.138119π-0.138119\pi
282282 −6986.63 936.420i −1.47535 0.197741i
283283 3479.48i 0.730860i −0.930839 0.365430i 0.880922π-0.880922\pi
0.930839 0.365430i 0.119078π-0.119078\pi
284284 −4910.69 + 305.584i −1.02604 + 0.0638488i
285285 207.499 1251.47i 0.0431270 0.260107i
286286 −303.112 9751.37i −0.0626693 2.01612i
287287 −1100.50 −0.226344
288288 −842.535 + 4814.35i −0.172385 + 0.985030i
289289 2212.81 0.450398
290290 165.758 + 5332.57i 0.0335643 + 1.07979i
291291 −469.954 + 2834.37i −0.0946707 + 0.570975i
292292 −2613.56 + 162.638i −0.523792 + 0.0325947i
293293 1778.78i 0.354667i 0.984151 + 0.177334i 0.0567471π0.0567471\pi
−0.984151 + 0.177334i 0.943253π0.943253\pi
294294 −713.767 95.6665i −0.141591 0.0189775i
295295 1761.71i 0.347697i
296296 599.322 + 6410.32i 0.117685 + 1.25876i
297297 −3820.65 + 7112.69i −0.746453 + 1.38963i
298298 −5726.07 + 177.990i −1.11309 + 0.0345995i
299299 −3219.75 −0.622753
300300 −68.6645 + 669.773i −0.0132145 + 0.128898i
301301 −585.584 −0.112135
302302 −3769.08 + 117.158i −0.718166 + 0.0223235i
303303 418.011 + 69.3084i 0.0792545 + 0.0131408i
304304 −163.017 1304.76i −0.0307555 0.246161i
305305 5664.56i 1.06345i
306306 3793.94 + 1163.41i 0.708775 + 0.217346i
307307 25.4001i 0.00472203i −0.999997 0.00236101i 0.999248π-0.999248\pi
0.999997 0.00236101i 0.000751534π-0.000751534\pi
308308 −200.159 3216.52i −0.0370295 0.595059i
309309 5207.89 + 863.495i 0.958791 + 0.158972i
310310 −315.800 10159.5i −0.0578588 1.86136i
311311 3038.33 0.553981 0.276991 0.960873i 0.410663π-0.410663\pi
0.276991 + 0.960873i 0.410663π0.410663\pi
312312 7029.29 + 500.542i 1.27550 + 0.0908256i
313313 −8947.92 −1.61587 −0.807934 0.589274i 0.799414π-0.799414\pi
−0.807934 + 0.589274i 0.799414π0.799414\pi
314314 173.747 + 5589.58i 0.0312265 + 1.00458i
315315 2125.64 + 724.810i 0.380210 + 0.129646i
316316 222.897 + 3581.92i 0.0396801 + 0.637654i
317317 10.5693i 0.00187266i 1.00000 0.000936328i 0.000298043π0.000298043\pi
−1.00000 0.000936328i 0.999702π0.999702\pi
318318 −519.224 + 3873.93i −0.0915617 + 0.683142i
319319 9135.37i 1.60339i
320320 1127.75 + 5978.46i 0.197010 + 1.04439i
321321 1820.32 10978.7i 0.316512 1.90894i
322322 −1063.07 + 33.0447i −0.183984 + 0.00571897i
323323 −1067.61 −0.183911
324324 −4829.46 3269.34i −0.828096 0.560586i
325325 970.775 0.165689
326326 4744.93 147.492i 0.806127 0.0250577i
327327 −57.5695 + 347.212i −0.00973579 + 0.0587182i
328328 3541.92 331.146i 0.596249 0.0557453i
329329 3357.41i 0.562615i
330330 −1335.10 + 9961.17i −0.222711 + 1.66165i
331331 7153.70i 1.18792i −0.804493 0.593962i 0.797563π-0.797563\pi
0.804493 0.593962i 0.202437π-0.202437\pi
332332 5430.77 337.948i 0.897747 0.0558653i
333333 −7271.32 2479.41i −1.19659 0.408020i
334334 257.777 + 8292.89i 0.0422303 + 1.35858i
335335 −9263.92 −1.51087
336336 2326.01 + 93.1227i 0.377662 + 0.0151198i
337337 −8329.05 −1.34633 −0.673163 0.739494i 0.735065π-0.735065\pi
−0.673163 + 0.739494i 0.735065π0.735065\pi
338338 −122.624 3944.90i −0.0197333 0.634835i
339339 −6295.33 1043.80i −1.00860 0.167231i
340340 4930.15 306.795i 0.786397 0.0489362i
341341 17404.6i 2.76396i
342342 1500.05 + 459.992i 0.237174 + 0.0727296i
343343 343.000i 0.0539949i
344344 1884.68 176.205i 0.295392 0.0276172i
345345 3272.16 + 542.542i 0.510630 + 0.0846651i
346346 5753.68 178.848i 0.893988 0.0277888i
347347 4245.62 0.656821 0.328411 0.944535i 0.393487π-0.393487\pi
0.328411 + 0.944535i 0.393487π0.393487\pi
348348 −6564.33 672.969i −1.01116 0.103664i
349349 −6998.42 −1.07340 −0.536700 0.843773i 0.680329π-0.680329\pi
−0.536700 + 0.843773i 0.680329π0.680329\pi
350350 320.523 9.96317i 0.0489505 0.00152158i
351351 −3979.17 + 7407.80i −0.605106 + 1.12649i
352352 1612.06 + 10292.0i 0.244100 + 1.55842i
353353 6706.36i 1.01117i −0.862776 0.505586i 0.831276π-0.831276\pi
0.862776 0.505586i 0.168724π-0.168724\pi
354354 −2159.65 289.458i −0.324248 0.0434591i
355355 7308.09i 1.09260i
356356 205.290 + 3298.99i 0.0305628 + 0.491140i
357357 309.162 1864.61i 0.0458336 0.276431i
358358 −319.244 10270.3i −0.0471301 1.51621i
359359 2823.78 0.415135 0.207567 0.978221i 0.433445π-0.433445\pi
0.207567 + 0.978221i 0.433445π0.433445\pi
360360 −7059.36 1693.15i −1.03350 0.247881i
361361 6436.89 0.938459
362362 183.338 + 5898.12i 0.0266188 + 0.856348i
363363 −1683.64 + 10154.3i −0.243439 + 1.46822i
364364 −208.463 3349.97i −0.0300177 0.482380i
365365 3889.51i 0.557770i
366366 −6944.08 930.717i −0.991729 0.132922i
367367 4911.38i 0.698561i −0.937018 0.349280i 0.886426π-0.886426\pi
0.937018 0.349280i 0.113574π-0.113574\pi
368368 3411.51 426.235i 0.483253 0.0603779i
369369 −1369.96 + 4017.65i −0.193271 + 0.566804i
370370 −9558.33 + 297.112i −1.34301 + 0.0417463i
371371 1861.61 0.260512
372372 12506.3 + 1282.13i 1.74306 + 0.178697i
373373 −1837.65 −0.255094 −0.127547 0.991833i 0.540710π-0.540710\pi
−0.127547 + 0.991833i 0.540710π0.540710\pi
374374 8454.15 262.790i 1.16886 0.0363330i
375375 6627.46 + 1098.87i 0.912642 + 0.151321i
376376 −1010.26 10805.7i −0.138564 1.48208i
377377 9514.40i 1.29978i
378378 −1237.78 + 2486.69i −0.168425 + 0.338364i
379379 2325.05i 0.315118i −0.987510 0.157559i 0.949638π-0.949638\pi
0.987510 0.157559i 0.0503624π-0.0503624\pi
380380 1949.29 121.301i 0.263149 0.0163753i
381381 −5837.95 967.963i −0.785006 0.130158i
382382 −102.861 3309.12i −0.0137770 0.443218i
383383 9467.13 1.26305 0.631525 0.775356i 0.282429π-0.282429\pi
0.631525 + 0.775356i 0.282429π0.282429\pi
384384 −7514.18 + 400.195i −0.998585 + 0.0531832i
385385 4786.83 0.633661
386386 −209.728 6747.11i −0.0276551 0.889686i
387387 −728.962 + 2137.82i −0.0957500 + 0.280805i
388388 −4414.84 + 274.728i −0.577653 + 0.0359464i
389389 3593.30i 0.468348i 0.972195 + 0.234174i 0.0752386π0.0752386\pi
−0.972195 + 0.234174i 0.924761π0.924761\pi
390390 −1390.49 + 10374.5i −0.180539 + 1.34700i
391391 2791.43i 0.361046i
392392 −103.210 1103.93i −0.0132982 0.142237i
393393 1307.40 7885.15i 0.167811 1.01210i
394394 13001.1 404.129i 1.66241 0.0516744i
395395 −5330.61 −0.679019
396396 −11991.8 3273.34i −1.52175 0.415383i
397397 12570.5 1.58916 0.794578 0.607163i 0.207692π-0.207692\pi
0.794578 + 0.607163i 0.207692π0.207692\pi
398398 2849.05 88.5600i 0.358819 0.0111536i
399399 122.237 737.233i 0.0153371 0.0925007i
400400 −1028.59 + 128.513i −0.128574 + 0.0160641i
401401 12634.4i 1.57340i −0.617338 0.786698i 0.711789π-0.711789\pi
0.617338 0.786698i 0.288211π-0.288211\pi
402402 1522.11 11356.5i 0.188846 1.40898i
403403 18126.7i 2.24059i
404404 40.5167 + 651.097i 0.00498956 + 0.0801815i
405405 5292.18 6857.88i 0.649310 0.841409i
406406 97.6474 + 3141.39i 0.0119363 + 0.384002i
407407 −16374.6 −1.99425
408408 −433.955 + 6094.19i −0.0526569 + 0.739479i
409409 12338.3 1.49167 0.745834 0.666132i 0.232051π-0.232051\pi
0.745834 + 0.666132i 0.232051π0.232051\pi
410410 164.165 + 5281.30i 0.0197744 + 0.636158i
411411 9666.65 + 1602.78i 1.16015 + 0.192359i
412412 504.786 + 8111.84i 0.0603618 + 0.970004i
413413 1037.82i 0.123650i
414414 −1202.73 + 3922.14i −0.142779 + 0.465610i
415415 8082.07i 0.955984i
416416 1678.95 + 10719.0i 0.197878 + 1.26332i
417417 3613.04 + 599.061i 0.424296 + 0.0703505i
418418 3342.62 103.902i 0.391131 0.0121579i
419419 10572.5 1.23270 0.616348 0.787474i 0.288611π-0.288611\pi
0.616348 + 0.787474i 0.288611π0.288611\pi
420420 −352.628 + 3439.63i −0.0409678 + 0.399611i
421421 6245.67 0.723030 0.361515 0.932366i 0.382260π-0.382260\pi
0.361515 + 0.932366i 0.382260π0.382260\pi
422422 −14086.9 + 437.879i −1.62498 + 0.0505110i
423423 12257.1 + 4179.46i 1.40888 + 0.480408i
424424 −5991.51 + 560.166i −0.686258 + 0.0641605i
425425 841.635i 0.0960595i
426426 8958.85 + 1200.76i 1.01891 + 0.136565i
427427 3336.97i 0.378190i
428428 17100.4 1064.13i 1.93126 0.120179i
429429 −2931.71 + 17681.7i −0.329940 + 1.98993i
430430 87.3529 + 2810.21i 0.00979658 + 0.315164i
431431 −9318.09 −1.04138 −0.520692 0.853745i 0.674326π-0.674326\pi
−0.520692 + 0.853745i 0.674326π0.674326\pi
432432 3235.49 8375.75i 0.360342 0.932820i
433433 −13699.1 −1.52041 −0.760204 0.649685i 0.774901π-0.774901\pi
−0.760204 + 0.649685i 0.774901π0.774901\pi
434434 −186.036 5984.94i −0.0205761 0.661950i
435435 1603.22 9669.27i 0.176709 1.06576i
436436 −540.820 + 33.6543i −0.0594050 + 0.00369667i
437437 1103.68i 0.120815i
438438 4768.07 + 639.066i 0.520154 + 0.0697164i
439439 7199.35i 0.782702i 0.920242 + 0.391351i 0.127992π0.127992\pi
−0.920242 + 0.391351i 0.872008π0.872008\pi
440440 −15406.2 + 1440.37i −1.66923 + 0.156062i
441441 1252.20 + 426.982i 0.135213 + 0.0461054i
442442 8804.92 273.693i 0.947528 0.0294531i
443443 −15697.3 −1.68353 −0.841763 0.539847i 0.818482π-0.818482\pi
−0.841763 + 0.539847i 0.818482π0.818482\pi
444444 1206.26 11766.2i 0.128934 1.25765i
445445 −4909.55 −0.523000
446446 −966.846 + 30.0535i −0.102649 + 0.00319075i
447447 10382.8 + 1721.52i 1.09863 + 0.182159i
448448 664.353 + 3521.89i 0.0700619 + 0.371414i
449449 16461.7i 1.73024i 0.501567 + 0.865119i 0.332757π0.332757\pi
−0.501567 + 0.865119i 0.667243π0.667243\pi
450450 362.629 1182.55i 0.0379878 0.123880i
451451 9047.55i 0.944639i
452452 −610.189 9805.65i −0.0634975 1.02040i
453453 6834.28 + 1133.16i 0.708836 + 0.117529i
454454 103.622 + 3333.61i 0.0107120 + 0.344612i
455455 4985.43 0.513672
456456 −171.578 + 2409.53i −0.0176203 + 0.247449i
457457 4880.98 0.499612 0.249806 0.968296i 0.419633π-0.419633\pi
0.249806 + 0.968296i 0.419633π0.419633\pi
458458 125.174 + 4026.95i 0.0127707 + 0.410845i
459459 −6422.35 3449.82i −0.653093 0.350815i
460460 317.162 + 5096.75i 0.0321473 + 0.516602i
461461 10228.4i 1.03337i 0.856176 + 0.516685i 0.172834π0.172834\pi
−0.856176 + 0.516685i 0.827166π0.827166\pi
462462 −786.501 + 5868.08i −0.0792020 + 0.590926i
463463 10248.4i 1.02869i 0.857584 + 0.514345i 0.171965π0.171965\pi
−0.857584 + 0.514345i 0.828035π0.828035\pi
464464 −1259.53 10081.0i −0.126018 1.00862i
465465 −3054.43 + 18421.8i −0.304614 + 1.83718i
466466 1620.34 50.3669i 0.161075 0.00500687i
467467 4813.88 0.477002 0.238501 0.971142i 0.423344π-0.423344\pi
0.238501 + 0.971142i 0.423344π0.423344\pi
468468 −12489.4 3409.16i −1.23359 0.336727i
469469 −5457.33 −0.537305
470470 16112.2 500.833i 1.58128 0.0491525i
471471 1680.48 10135.3i 0.164400 0.991528i
472472 −312.282 3340.16i −0.0304533 0.325727i
473473 4814.25i 0.467991i
474474 875.848 6534.70i 0.0848714 0.633225i
475475 332.767i 0.0321440i
476476 2904.33 180.732i 0.279664 0.0174030i
477477 2317.42 6796.26i 0.222447 0.652368i
478478 −488.933 15729.4i −0.0467851 1.50511i
479479 −11369.2 −1.08450 −0.542249 0.840218i 0.682427π-0.682427\pi
−0.542249 + 0.840218i 0.682427π0.682427\pi
480480 99.9182 11176.4i 0.00950129 1.06277i
481481 −17054.0 −1.61663
482482 −412.310 13264.3i −0.0389631 1.25347i
483483 1927.62 + 319.609i 0.181593 + 0.0301091i
484484 −15816.5 + 984.232i −1.48539 + 0.0924335i
485485 6570.17i 0.615125i
486486 7537.41 + 7614.37i 0.703506 + 0.710689i
487487 4160.42i 0.387118i −0.981089 0.193559i 0.937997π-0.937997\pi
0.981089 0.193559i 0.0620031π-0.0620031\pi
488488 −1004.11 10739.9i −0.0931429 0.996253i
489489 −8603.74 1426.54i −0.795653 0.131923i
490490 1646.05 51.1661i 0.151757 0.00471724i
491491 −15620.4 −1.43572 −0.717862 0.696185i 0.754879π-0.754879\pi
−0.717862 + 0.696185i 0.754879π0.754879\pi
492492 −6501.22 666.499i −0.595727 0.0610734i
493493 −8248.72 −0.753557
494494 3481.30 108.213i 0.317067 0.00985575i
495495 5958.86 17475.5i 0.541073 1.58680i
496496 2399.64 + 19206.3i 0.217232 + 1.73868i
497497 4305.16i 0.388557i
498498 −9907.66 1327.93i −0.891512 0.119490i
499499 4722.33i 0.423648i 0.977308 + 0.211824i 0.0679404π0.0679404\pi
−0.977308 + 0.211824i 0.932060π0.932060\pi
500500 642.382 + 10323.0i 0.0574564 + 0.923315i
501501 2493.22 15037.1i 0.222333 1.34093i
502502 −395.956 12738.2i −0.0352039 1.13254i
503503 −647.849 −0.0574278 −0.0287139 0.999588i 0.509141π-0.509141\pi
−0.0287139 + 0.999588i 0.509141π0.509141\pi
504504 −4158.64 997.429i −0.367541 0.0881528i
505505 −968.964 −0.0853828
506506 271.670 + 8739.82i 0.0238680 + 0.767851i
507507 −1186.02 + 7153.08i −0.103891 + 0.626587i
508508 −565.857 9093.24i −0.0494210 0.794187i
509509 17395.7i 1.51483i 0.652932 + 0.757417i 0.273539π0.273539\pi
−0.652932 + 0.757417i 0.726461π0.726461\pi
510510 −8994.36 1205.52i −0.780935 0.104669i
511511 2291.29i 0.198358i
512512 −3197.94 11135.1i −0.276035 0.961147i
513513 −2539.28 1364.00i −0.218542 0.117392i
514514 4595.87 142.858i 0.394387 0.0122592i
515515 −12072.1 −1.03293
516516 −3459.34 354.648i −0.295133 0.0302568i
517517 27602.2 2.34806
518518 −5630.77 + 175.027i −0.477610 + 0.0148461i
519519 −10432.9 1729.82i −0.882373 0.146302i
520520 −16045.4 + 1500.14i −1.35315 + 0.126510i
521521 15959.1i 1.34200i −0.741458 0.670999i 0.765866π-0.765866\pi
0.741458 0.670999i 0.234134π-0.234134\pi
522522 11590.0 + 3554.06i 0.971799 + 0.298002i
523523 5571.06i 0.465784i −0.972503 0.232892i 0.925181π-0.925181\pi
0.972503 0.232892i 0.0748189π-0.0748189\pi
524524 12282.0 764.287i 1.02393 0.0637176i
525525 −581.188 96.3640i −0.0483146 0.00801080i
526526 207.084 + 6662.05i 0.0171659 + 0.552242i
527527 15715.3 1.29900
528528 765.588 19122.8i 0.0631021 1.57616i
529529 −9281.24 −0.762821
530530 −277.701 8933.85i −0.0227595 0.732192i
531531 3788.80 + 1291.92i 0.309642 + 0.105583i
532532 1148.32 71.4580i 0.0935826 0.00582349i
533533 9422.93i 0.765765i
534534 806.665 6018.53i 0.0653705 0.487729i
535535 25448.9i 2.05654i
536536 17564.2 1642.13i 1.41540 0.132331i
537537 −3087.73 + 18622.7i −0.248130 + 1.49651i
538538 −6609.08 + 205.437i −0.529624 + 0.0164629i
539539 2819.90 0.225346
540540 12118.2 + 5569.16i 0.965714 + 0.443812i
541541 4627.15 0.367721 0.183860 0.982952i 0.441141π-0.441141\pi
0.183860 + 0.982952i 0.441141π0.441141\pi
542542 3882.60 120.687i 0.307698 0.00956450i
543543 1773.25 10694.8i 0.140142 0.845223i
544544 −9293.07 + 1455.60i −0.732421 + 0.114721i
545545 804.848i 0.0632586i
546546 −819.133 + 6111.55i −0.0642045 + 0.479030i
547547 4288.22i 0.335194i 0.985856 + 0.167597i 0.0536007π0.0536007\pi
−0.985856 + 0.167597i 0.946399π0.946399\pi
548548 936.962 + 15056.8i 0.0730384 + 1.17372i
549549 12182.4 + 4154.01i 0.947054 + 0.322931i
550550 −81.9100 2635.11i −0.00635028 0.204294i
551551 −3261.39 −0.252159
552552 −6300.12 448.619i −0.485780 0.0345915i
553553 −3140.24 −0.241477
554554 −166.363 5352.02i −0.0127583 0.410443i
555555 17331.6 + 2873.67i 1.32556 + 0.219785i
556556 350.202 + 5627.70i 0.0267120 + 0.429258i
557557 13183.7i 1.00289i 0.865189 + 0.501446i 0.167199π0.167199\pi
−0.865189 + 0.501446i 0.832801π0.832801\pi
558558 −22081.1 6771.16i −1.67521 0.513702i
559559 5014.00i 0.379373i
560560 −5282.34 + 659.979i −0.398607 + 0.0498021i
561561 −15329.5 2541.71i −1.15367 0.191285i
562562 −11197.3 + 348.059i −0.840446 + 0.0261245i
563563 5054.25 0.378350 0.189175 0.981943i 0.439419π-0.439419\pi
0.189175 + 0.981943i 0.439419π0.439419\pi
564564 −2033.35 + 19833.9i −0.151808 + 1.48078i
565565 14592.8 1.08659
566566 −9836.70 + 305.765i −0.730508 + 0.0227072i
567567 3117.60 4039.95i 0.230912 0.299227i
568568 1295.44 + 13856.0i 0.0956962 + 1.02356i
569569 1790.71i 0.131934i −0.997822 0.0659671i 0.978987π-0.978987\pi
0.997822 0.0659671i 0.0210132π-0.0210132\pi
570570 −3556.20 476.639i −0.261321 0.0350249i
571571 10998.7i 0.806099i −0.915178 0.403049i 0.867950π-0.867950\pi
0.915178 0.403049i 0.132050π-0.132050\pi
572572 −27541.1 + 1713.84i −2.01320 + 0.125278i
573573 −994.875 + 6000.26i −0.0725332 + 0.437460i
574574 96.7086 + 3111.19i 0.00703230 + 0.226235i
575575 −870.074 −0.0631036
576576 13684.5 + 1958.83i 0.989910 + 0.141698i
577577 −25965.2 −1.87339 −0.936695 0.350147i 0.886132π-0.886132\pi
−0.936695 + 0.350147i 0.886132π0.886132\pi
578578 −194.454 6255.74i −0.0139935 0.450181i
579579 −2028.49 + 12234.2i −0.145598 + 0.878127i
580580 15060.9 937.217i 1.07823 0.0670962i
581581 4761.11i 0.339973i
582582 8054.24 + 1079.51i 0.573641 + 0.0768853i
583583 15304.8i 1.08724i
584584 689.458 + 7374.41i 0.0488527 + 0.522526i
585585 6206.10 18200.5i 0.438616 1.28632i
586586 5028.72 156.313i 0.354496 0.0110192i
587587 11193.8 0.787084 0.393542 0.919307i 0.371250π-0.371250\pi
0.393542 + 0.919307i 0.371250π0.371250\pi
588588 −207.731 + 2026.27i −0.0145692 + 0.142112i
589589 6213.55 0.434678
590590 4980.46 154.813i 0.347529 0.0108026i
591591 −23574.3 3908.74i −1.64081 0.272054i
592592 18069.7 2257.64i 1.25449 0.156737i
593593 14750.7i 1.02148i −0.859735 0.510740i 0.829371π-0.829371\pi
0.859735 0.510740i 0.170629π-0.170629\pi
594594 20443.8 + 10176.2i 1.41215 + 0.702918i
595595 4322.23i 0.297805i
596596 1006.38 + 16172.3i 0.0691657 + 1.11148i
597597 −5166.03 856.555i −0.354157 0.0587210i
598598 282.941 + 9102.44i 0.0193484 + 0.622452i
599599 5736.96 0.391329 0.195664 0.980671i 0.437314π-0.437314\pi
0.195664 + 0.980671i 0.437314π0.437314\pi
600600 1899.52 + 135.261i 0.129246 + 0.00920337i
601601 11522.6 0.782054 0.391027 0.920379i 0.372120π-0.372120\pi
0.391027 + 0.920379i 0.372120π0.372120\pi
602602 51.4592 + 1655.48i 0.00348392 + 0.112081i
603603 −6793.54 + 19923.3i −0.458797 + 1.34551i
604604 662.428 + 10645.1i 0.0446255 + 0.717126i
605605 23538.1i 1.58175i
606606 159.206 1187.83i 0.0106721 0.0796245i
607607 18497.3i 1.23687i −0.785835 0.618436i 0.787766π-0.787766\pi
0.785835 0.618436i 0.212234π-0.212234\pi
608608 −3674.31 + 575.517i −0.245087 + 0.0383887i
609609 944.447 5696.13i 0.0628423 0.379013i
610610 16014.1 497.783i 1.06294 0.0330404i
611611 28747.5 1.90343
612612 2955.64 10827.9i 0.195220 0.715186i
613613 8751.26 0.576607 0.288304 0.957539i 0.406909π-0.406909\pi
0.288304 + 0.957539i 0.406909π0.406909\pi
614614 −71.8077 + 2.23208i −0.00471975 + 0.000146709i
615615 1587.80 9576.32i 0.104108 0.627893i
616616 −9075.71 + 848.518i −0.593621 + 0.0554996i
617617 14023.7i 0.915030i 0.889202 + 0.457515i 0.151260π0.151260\pi
−0.889202 + 0.457515i 0.848740π0.848740\pi
618618 1983.50 14798.9i 0.129107 0.963267i
619619 20122.5i 1.30661i −0.757096 0.653304i 0.773382π-0.773382\pi
0.757096 0.653304i 0.226618π-0.226618\pi
620620 −28693.9 + 1785.57i −1.85867 + 0.115662i
621621 3566.40 6639.37i 0.230458 0.429032i
622622 −266.999 8589.56i −0.0172117 0.553714i
623623 −2892.20 −0.185993
624624 797.352 19916.2i 0.0511533 1.27770i
625625 −17387.3 −1.11278
626626 786.314 + 25296.3i 0.0502035 + 1.61509i
627627 −6060.99 1004.94i −0.386049 0.0640089i
628628 15786.8 982.387i 1.00312 0.0624228i
629629 14785.4i 0.937251i
630630 1862.29 6073.00i 0.117770 0.384054i
631631 15050.4i 0.949523i 0.880115 + 0.474761i 0.157466π0.157466\pi
−0.880115 + 0.474761i 0.842534π0.842534\pi
632632 10106.7 944.910i 0.636113 0.0594723i
633633 25543.1 + 4235.18i 1.60387 + 0.265929i
634634 29.8801 0.928797i 0.00187175 5.81817e-5i
635635 13532.6 0.845706
636636 10997.5 + 1127.45i 0.685657 + 0.0702929i
637637 2936.90 0.182675
638638 25826.3 802.786i 1.60262 0.0498160i
639639 −15717.0 5359.27i −0.973015 0.331783i
640640 16802.4 3713.59i 1.03777 0.229363i
641641 12990.3i 0.800444i −0.916418 0.400222i 0.868933π-0.868933\pi
0.916418 0.400222i 0.131067π-0.131067\pi
642642 −31197.3 4181.38i −1.91785 0.257050i
643643 13304.0i 0.815956i 0.912992 + 0.407978i 0.133766π0.133766\pi
−0.912992 + 0.407978i 0.866234π0.866234\pi
644644 186.839 + 3002.47i 0.0114324 + 0.183717i
645645 844.879 5095.61i 0.0515769 0.311069i
646646 93.8177 + 3018.19i 0.00571394 + 0.183822i
647647 −11304.7 −0.686912 −0.343456 0.939169i 0.611598π-0.611598\pi
−0.343456 + 0.939169i 0.611598π0.611598\pi
648648 −8818.22 + 13940.5i −0.534587 + 0.845113i
649649 8532.17 0.516051
650650 −85.3085 2744.44i −0.00514781 0.165609i
651651 −1799.35 + 10852.2i −0.108329 + 0.653350i
652652 −833.937 13401.2i −0.0500912 0.804959i
653653 19130.0i 1.14643i −0.819407 0.573213i 0.805697π-0.805697\pi
0.819407 0.573213i 0.194303π-0.194303\pi
654654 986.648 + 132.241i 0.0589924 + 0.00790676i
655655 18278.0i 1.09035i
656656 −1247.42 9984.12i −0.0742433 0.594229i
657657 −8364.91 2852.31i −0.496722 0.169374i
658658 9491.62 295.038i 0.562343 0.0174799i
659659 −23752.1 −1.40402 −0.702011 0.712166i 0.747714π-0.747714\pi
−0.702011 + 0.712166i 0.747714π0.747714\pi
660660 28278.2 + 2899.05i 1.66777 + 0.170978i
661661 7980.69 0.469611 0.234805 0.972042i 0.424555π-0.424555\pi
0.234805 + 0.972042i 0.424555π0.424555\pi
662662 −20224.0 + 628.643i −1.18735 + 0.0369077i
663663 −15965.5 2647.16i −0.935218 0.155064i
664664 −1432.64 15323.4i −0.0837306 0.895578i
665665 1708.93i 0.0996533i
666666 −6370.46 + 20774.4i −0.370646 + 1.20869i
667667 8527.44i 0.495028i
668668 23421.8 1457.50i 1.35661 0.0844199i
669669 1753.13 + 290.678i 0.101315 + 0.0167986i
670670 814.082 + 26189.7i 0.0469414 + 1.51014i
671671 27434.2 1.57837
672672 58.8614 6583.97i 0.00337891 0.377949i
673673 8141.43 0.466313 0.233157 0.972439i 0.425094π-0.425094\pi
0.233157 + 0.972439i 0.425094π0.425094\pi
674674 731.929 + 23546.7i 0.0418292 + 1.34568i
675675 −1075.29 + 2001.81i −0.0613155 + 0.114148i
676676 −11141.7 + 693.329i −0.633915 + 0.0394475i
677677 8089.20i 0.459222i 0.973283 + 0.229611i 0.0737454π0.0737454\pi
−0.973283 + 0.229611i 0.926255π0.926255\pi
678678 −2397.67 + 17889.0i −0.135814 + 1.01331i
679679 3870.46i 0.218755i
680680 −1300.57 13910.9i −0.0733452 0.784497i
681681 1002.24 6044.66i 0.0563961 0.340135i
682682 −49203.9 + 1529.46i −2.76263 + 0.0858739i
683683 −1228.57 −0.0688287 −0.0344143 0.999408i 0.510957π-0.510957\pi
−0.0344143 + 0.999408i 0.510957π0.510957\pi
684684 1168.61 4281.17i 0.0653257 0.239320i
685685 −22407.6 −1.24986
686686 969.682 30.1417i 0.0539689 0.00167757i
687687 1210.69 7301.86i 0.0672351 0.405507i
688688 −663.760 5312.61i −0.0367814 0.294392i
689689 15939.8i 0.881363i
690690 1246.25 9298.28i 0.0687594 0.513014i
691691 16599.3i 0.913844i 0.889507 + 0.456922i 0.151048π0.151048\pi
−0.889507 + 0.456922i 0.848952π0.848952\pi
692692 −1011.23 16250.3i −0.0555508 0.892693i
693693 3510.34 10294.7i 0.192420 0.564306i
694694 −373.091 12002.6i −0.0204068 0.656504i
695695 −8375.15 −0.457104
696696 −1325.67 + 18616.9i −0.0721976 + 1.01390i
697697 −8169.41 −0.443958
698698 614.998 + 19785.0i 0.0333496 + 1.07288i
699699 −2938.08 487.150i −0.158982 0.0263601i
700700 −56.3330 905.263i −0.00304170 0.0488796i
701701 23398.3i 1.26069i −0.776316 0.630344i 0.782914π-0.782914\pi
0.776316 0.630344i 0.217086π-0.217086\pi
702702 21292.0 + 10598.4i 1.14475 + 0.569815i
703703 5845.85i 0.313628i
704704 28954.4 5461.83i 1.55009 0.292401i
705705 −29215.4 4844.07i −1.56073 0.258777i
706706 −18959.3 + 589.333i −1.01068 + 0.0314162i
707707 −570.812 −0.0303644
708708 −628.533 + 6130.89i −0.0333640 + 0.325442i
709709 4729.80 0.250538 0.125269 0.992123i 0.460021π-0.460021\pi
0.125269 + 0.992123i 0.460021π0.460021\pi
710710 −20660.4 + 642.211i −1.09207 + 0.0339461i
711711 −3909.12 + 11464.2i −0.206193 + 0.604700i
712712 9308.40 870.273i 0.489954 0.0458074i
713713 16246.4i 0.853340i
714714 −5298.54 710.165i −0.277721 0.0372230i
715715 40986.6i 2.14380i
716716 −29006.8 + 1805.04i −1.51402 + 0.0942147i
717717 −4728.97 + 28521.2i −0.246313 + 1.48556i
718718 −248.144 7983.00i −0.0128979 0.414934i
719719 17392.3 0.902120 0.451060 0.892494i 0.351046π-0.351046\pi
0.451060 + 0.892494i 0.351046π0.351046\pi
720720 −4166.29 + 20106.0i −0.215651 + 1.04071i
721721 −7111.59 −0.367336
722722 −565.652 18197.5i −0.0291571 0.938006i
723723 −3987.87 + 24051.5i −0.205132 + 1.23719i
724724 16658.2 1036.61i 0.855108 0.0532119i
725725 2571.08i 0.131707i
726726 28854.9 + 3867.43i 1.47508 + 0.197705i
727727 2259.30i 0.115258i 0.998338 + 0.0576292i 0.0183541π0.0183541\pi
−0.998338 + 0.0576292i 0.981646π0.981646\pi
728728 −9452.26 + 883.723i −0.481215 + 0.0449903i
729729 −10867.9 16410.7i −0.552145 0.833748i
730730 −10995.9 + 341.797i −0.557501 + 0.0173294i
731731 −4346.99 −0.219944
732732 −2020.97 + 19713.1i −0.102045 + 0.995380i
733733 9477.23 0.477557 0.238779 0.971074i 0.423253π-0.423253\pi
0.238779 + 0.971074i 0.423253π0.423253\pi
734734 −13884.8 + 431.595i −0.698223 + 0.0217036i
735735 −2984.70 494.879i −0.149786 0.0248352i
736736 −1504.79 9607.09i −0.0753630 0.481144i
737737 44866.3i 2.24243i
738738 11478.5 + 3519.90i 0.572535 + 0.175568i
739739 11228.4i 0.558922i 0.960157 + 0.279461i 0.0901558π0.0901558\pi
−0.960157 + 0.279461i 0.909844π0.909844\pi
740740 1679.91 + 26995.9i 0.0834522 + 1.34106i
741741 −6312.47 1046.64i −0.312948 0.0518884i
742742 −163.592 5262.89i −0.00809388 0.260386i
743743 32368.4 1.59822 0.799112 0.601182i 0.205303π-0.205303\pi
0.799112 + 0.601182i 0.205303π0.205303\pi
744744 2525.66 35468.7i 0.124456 1.74778i
745745 −24067.6 −1.18358
746746 161.487 + 5195.16i 0.00792554 + 0.254971i
747747 17381.6 + 5926.85i 0.851351 + 0.290298i
748748 −1485.85 23877.3i −0.0726309 1.16717i
749749 14991.8i 0.731361i
750750 2524.17 18832.8i 0.122893 0.916902i
751751 6776.22i 0.329251i −0.986356 0.164626i 0.947358π-0.947358\pi
0.986356 0.164626i 0.0526416π-0.0526416\pi
752752 −30459.5 + 3805.63i −1.47705 + 0.184544i
753753 −3829.69 + 23097.5i −0.185341 + 1.11782i
754754 26897.8 836.094i 1.29915 0.0403830i
755755 −15842.1 −0.763646
756756 7138.80 + 3280.77i 0.343433 + 0.157831i
757757 16374.4 0.786180 0.393090 0.919500i 0.371406π-0.371406\pi
0.393090 + 0.919500i 0.371406π0.371406\pi
758758 −6573.05 + 204.317i −0.314966 + 0.00979042i
759759 2627.59 15847.5i 0.125660 0.757875i
760760 −514.223 5500.11i −0.0245432 0.262513i
761761 6365.36i 0.303212i −0.988441 0.151606i 0.951556π-0.951556\pi
0.988441 0.151606i 0.0484445π-0.0484445\pi
762762 −2223.47 + 16589.3i −0.105706 + 0.788671i
763763 474.133i 0.0224964i
764764 −9346.06 + 581.589i −0.442576 + 0.0275408i
765765 15779.3 + 5380.51i 0.745756 + 0.254291i
766766 −831.940 26764.2i −0.0392418 1.26244i
767767 8886.17 0.418333
768768 1791.70 + 21207.9i 0.0841827 + 0.996450i
769769 −540.012 −0.0253229 −0.0126615 0.999920i 0.504030π-0.504030\pi
−0.0126615 + 0.999920i 0.504030π0.504030\pi
770770 −420.650 13532.7i −0.0196873 0.633355i
771771 −8333.45 1381.73i −0.389263 0.0645418i
772772 −19056.1 + 1185.83i −0.888398 + 0.0552835i
773773 20167.6i 0.938394i 0.883094 + 0.469197i 0.155457π0.155457\pi
−0.883094 + 0.469197i 0.844543π0.844543\pi
774774 6107.80 + 1872.96i 0.283644 + 0.0869794i
775775 4898.38i 0.227039i
776776 1164.63 + 12456.9i 0.0538762 + 0.576258i
777777 10210.0 + 1692.87i 0.471404 + 0.0781613i
778778 10158.5 315.767i 0.468122 0.0145512i
779779 −3230.03 −0.148560
780780 29451.4 + 3019.33i 1.35196 + 0.138602i
781781 −35394.0 −1.62163
782782 −7891.56 + 245.302i −0.360871 + 0.0112174i
783783 −19619.4 10538.7i −0.895453 0.481001i
784784 −3111.81 + 388.791i −0.141755 + 0.0177109i
785785 23493.9i 1.06820i
786786 −22406.7 3003.18i −1.01682 0.136285i
787787 39007.0i 1.76677i −0.468646 0.883386i 0.655258π-0.655258\pi
0.468646 0.883386i 0.344742π-0.344742\pi
788788 −2284.99 36719.5i −0.103299 1.66000i
789789 2002.92 12080.0i 0.0903750 0.545067i
790790 468.437 + 15070.0i 0.0210965 + 0.678691i
791791 8596.54 0.386419
792792 −8200.14 + 34189.3i −0.367903 + 1.53392i
793793 28572.4 1.27949
794794 −1104.65 35537.5i −0.0493736 1.58839i
795795 −2685.93 + 16199.3i −0.119824 + 0.722679i
796796 −500.729 8046.65i −0.0222963 0.358299i
797797 9334.99i 0.414884i −0.978247 0.207442i 0.933486π-0.933486\pi
0.978247 0.207442i 0.0665138π-0.0665138\pi
798798 −2094.94 280.786i −0.0929326 0.0124558i
799799 24923.2i 1.10353i
800800 453.702 + 2896.60i 0.0200510 + 0.128013i
801801 −3600.34 + 10558.7i −0.158816 + 0.465758i
802802 −35718.2 + 1110.27i −1.57264 + 0.0488840i
803803 −18837.3 −0.827840
804804 −32239.2 3305.13i −1.41416 0.144979i
805805 −4468.28 −0.195635
806806 −51245.3 + 1592.92i −2.23950 + 0.0696130i
807807 11983.9 + 1986.99i 0.522743 + 0.0866735i
808808 1837.13 171.760i 0.0799877 0.00747831i
809809 11699.2i 0.508433i 0.967147 + 0.254217i 0.0818176π0.0818176\pi
−0.967147 + 0.254217i 0.918182π0.918182\pi
810810 −19852.7 14358.7i −0.861176 0.622855i
811811 27172.5i 1.17652i −0.808673 0.588258i 0.799814π-0.799814\pi
0.808673 0.588258i 0.200186π-0.200186\pi
812812 8872.33 552.110i 0.383445 0.0238612i
813813 −7040.13 1167.29i −0.303700 0.0503550i
814814 1438.95 + 46292.1i 0.0619596 + 1.99329i
815815 19943.7 0.857176
816816 17266.8 + 691.282i 0.740758 + 0.0296565i
817817 −1718.72 −0.0735990
818818 −1084.25 34881.3i −0.0463448 1.49095i
819819 3655.98 10721.9i 0.155983 0.457450i
820820 14916.1 928.206i 0.635237 0.0395297i
821821 25582.6i 1.08750i −0.839247 0.543751i 0.817004π-0.817004\pi
0.839247 0.543751i 0.182996π-0.182996\pi
822822 3681.69 27469.1i 0.156221 1.16556i
823823 14407.8i 0.610237i 0.952314 + 0.305119i 0.0986961π0.0986961\pi
−0.952314 + 0.305119i 0.901304π0.901304\pi
824824 22888.3 2139.90i 0.967661 0.0904698i
825825 −792.236 + 4778.11i −0.0334329 + 0.201639i
826826 2933.97 91.1998i 0.123591 0.00384170i
827827 15273.7 0.642225 0.321113 0.947041i 0.395943π-0.395943\pi
0.321113 + 0.947041i 0.395943π0.395943\pi
828828 11193.8 + 3055.51i 0.469822 + 0.128244i
829829 13333.4 0.558610 0.279305 0.960202i 0.409896π-0.409896\pi
0.279305 + 0.960202i 0.409896π0.409896\pi
830830 22848.5 710.226i 0.955523 0.0297016i
831831 −1609.06 + 9704.55i −0.0671695 + 0.405111i
832832 30155.7 5688.44i 1.25657 0.237033i
833833 2546.21i 0.105907i
834834 1376.08 10266.9i 0.0571340 0.426277i
835835 34856.4i 1.44462i
836836 −587.476 9440.65i −0.0243042 0.390564i
837837 37378.6 + 20078.3i 1.54360 + 0.829159i
838838 −929.075 29889.1i −0.0382988 1.23210i
839839 −18346.1 −0.754919 −0.377460 0.926026i 0.623202π-0.623202\pi
−0.377460 + 0.926026i 0.623202π0.623202\pi
840840 9755.04 + 694.637i 0.400691 + 0.0285324i
841841 −809.675 −0.0331984
842842 −548.849 17656.9i −0.0224639 0.722681i
843843 20303.6 + 3366.43i 0.829527 + 0.137540i
844844 2475.82 + 39786.1i 0.100973 + 1.62262i
845845 16581.1i 0.675037i
846846 10738.5 35018.7i 0.436403 1.42313i
847847 13866.2i 0.562512i
848848 2110.14 + 16889.1i 0.0854509 + 0.683933i
849849 17836.4 + 2957.37i 0.721017 + 0.119548i
850850 2379.35 73.9600i 0.0960131 0.00298448i
851851 15285.0 0.615701
852852 2607.34 25432.7i 0.104843 1.02267i
853853 35153.2 1.41105 0.705524 0.708686i 0.250712π-0.250712\pi
0.705524 + 0.708686i 0.250712π0.250712\pi
854854 9433.82 293.242i 0.378008 0.0117500i
855855 6238.86 + 2127.35i 0.249549 + 0.0850923i
856856 −4511.09 48250.5i −0.180124 1.92660i
857857 15229.6i 0.607041i −0.952825 0.303521i 0.901838π-0.901838\pi
0.952825 0.303521i 0.0981621π-0.0981621\pi
858858 50244.8 + 6734.32i 1.99922 + 0.267956i
859859 33945.5i 1.34832i 0.738585 + 0.674160i 0.235494π0.235494\pi
−0.738585 + 0.674160i 0.764506π0.764506\pi
860860 7936.97 493.904i 0.314707 0.0195837i
861861 935.368 5641.37i 0.0370235 0.223295i
862862 818.842 + 26342.8i 0.0323549 + 1.04088i
863863 −43822.0 −1.72853 −0.864264 0.503039i 0.832215π-0.832215\pi
−0.864264 + 0.503039i 0.832215π0.832215\pi
864864 −23963.1 8410.91i −0.943565 0.331186i
865865 24183.7 0.950602
866866 1203.83 + 38728.2i 0.0472377 + 1.51967i
867867 −1880.76 + 11343.2i −0.0736725 + 0.444332i
868868 −16903.4 + 1051.87i −0.660991 + 0.0411324i
869869 25816.8i 1.00780i
870870 −27476.5 3682.69i −1.07074 0.143511i
871871 46727.8i 1.81781i
872872 142.668 + 1525.97i 0.00554055 + 0.0592614i
873873 −14130.0 4818.12i −0.547800 0.186791i
874874 −3120.17 + 96.9878i −0.120757 + 0.00375362i
875875 −9050.08 −0.349655
876876 1387.68 13535.8i 0.0535220 0.522069i
877877 −37852.1 −1.45744 −0.728719 0.684813i 0.759884π-0.759884\pi
−0.728719 + 0.684813i 0.759884π0.759884\pi
878878 20353.0 632.655i 0.782324 0.0243178i
879879 −9118.33 1511.87i −0.349890 0.0580136i
880880 5425.87 + 43427.6i 0.207848 + 1.66357i
881881 3600.18i 0.137677i 0.997628 + 0.0688384i 0.0219293π0.0219293\pi
−0.997628 + 0.0688384i 0.978071π0.978071\pi
882882 1097.07 3577.58i 0.0418822 0.136580i
883883 43272.5i 1.64919i −0.565722 0.824596i 0.691403π-0.691403\pi
0.565722 0.824596i 0.308597π-0.308597\pi
884884 −1547.49 24868.0i −0.0588777 0.946155i
885885 −9030.82 1497.36i −0.343014 0.0568735i
886886 1379.43 + 44377.3i 0.0523057 + 1.68271i
887887 −24028.0 −0.909562 −0.454781 0.890603i 0.650283π-0.650283\pi
−0.454781 + 0.890603i 0.650283π0.650283\pi
888888 −33369.7 2376.19i −1.26105 0.0897972i
889889 7971.97 0.300755
890890 431.435 + 13879.6i 0.0162492 + 0.522748i
891891 −33213.5 25630.7i −1.24882 0.963704i
892892 169.926 + 2730.69i 0.00637843 + 0.102500i
893893 9854.18i 0.369269i
894894 3954.44 29504.1i 0.147938 1.10376i
895895 43167.9i 1.61223i
896896 9898.21 2187.66i 0.369058 0.0815675i
897897 2736.61 16505.0i 0.101865 0.614365i
898898 46538.3 1446.60i 1.72940 0.0537569i
899899 48008.2 1.78105
900900 −3375.01 921.256i −0.125000 0.0341206i
901901 13819.4 0.510977
902902 25578.0 795.068i 0.944183 0.0293491i
903903 497.715 3001.80i 0.0183421 0.110624i
904904 −27667.5 + 2586.73i −1.01793 + 0.0951696i
905905 24790.8i 0.910579i
906906 2602.94 19420.5i 0.0954490 0.712145i
907907 3259.12i 0.119313i 0.998219 + 0.0596567i 0.0190006π0.0190006\pi
−0.998219 + 0.0596567i 0.980999π0.980999\pi
908908 9415.21 585.893i 0.344113 0.0214136i
909909 −710.573 + 2083.89i −0.0259276 + 0.0760376i
910910 −438.103 14094.1i −0.0159593 0.513424i
911911 4957.30 0.180288 0.0901441 0.995929i 0.471267π-0.471267\pi
0.0901441 + 0.995929i 0.471267π0.471267\pi
912912 6826.97 + 273.320i 0.247877 + 0.00992382i
913913 39142.5 1.41887
914914 −428.924 13798.8i −0.0155225 0.499371i
915915 −29037.5 4814.57i −1.04913 0.173950i
916916 11373.4 707.749i 0.410250 0.0255291i
917917 10767.5i 0.387759i
918918 −9188.49 + 18459.5i −0.330355 + 0.663677i
919919 14412.7i 0.517334i 0.965967 + 0.258667i 0.0832832π0.0832832\pi
−0.965967 + 0.258667i 0.916717π0.916717\pi
920920 14380.9 1344.52i 0.515354 0.0481821i
921921 130.205 + 21.5887i 0.00465843 + 0.000772391i
922922 28916.3 898.837i 1.03287 0.0321059i
923923 −36862.5 −1.31456
924924 16658.5 + 1707.82i 0.593102 + 0.0608042i
925925 −4608.51 −0.163813
926926 28972.8 900.595i 1.02819 0.0319604i
927927 −8852.84 + 25962.6i −0.313663 + 0.919874i
928928 −28389.0 + 4446.66i −1.00422 + 0.157294i
929929 3928.90i 0.138755i 0.997590 + 0.0693774i 0.0221013π0.0221013\pi
−0.997590 + 0.0693774i 0.977899π0.977899\pi
930930 52347.9 + 7016.21i 1.84576 + 0.247388i
931931 1006.72i 0.0354393i
932932 −284.781 4576.38i −0.0100089 0.160842i
933933 −2582.42 + 15575.0i −0.0906158 + 0.546520i
934934 −423.028 13609.1i −0.0148200 0.476771i
935935 35534.2 1.24288
936936 −8540.37 + 35607.9i −0.298238 + 1.24346i
937937 −22929.1 −0.799426 −0.399713 0.916640i 0.630890π-0.630890\pi
−0.399713 + 0.916640i 0.630890π0.630890\pi
938938 479.572 + 15428.2i 0.0166936 + 0.537046i
939939 7605.24 45868.5i 0.264311 1.59410i
940940 −2831.77 45506.1i −0.0982576 1.57899i
941941 5458.91i 0.189113i 0.995519 + 0.0945565i 0.0301433π0.0301433\pi
−0.995519 + 0.0945565i 0.969857π0.969857\pi
942942 −28800.8 3860.18i −0.996157 0.133515i
943943 8445.46i 0.291646i
944944 −9415.39 + 1176.36i −0.324624 + 0.0405587i
945945 −5522.17 + 10280.3i −0.190091 + 0.353883i
946946 13610.2 423.061i 0.467765 0.0145400i
947947 9864.40 0.338490 0.169245 0.985574i 0.445867π-0.445867\pi
0.169245 + 0.985574i 0.445867π0.445867\pi
948948 −18551.0 1901.83i −0.635556 0.0651566i
949949 −19618.9 −0.671082
950950 940.752 29.2424i 0.0321284 0.000998684i
951951 −54.1801 8.98334i −0.00184743 0.000306314i
952952 −766.163 8194.84i −0.0260835 0.278988i
953953 39622.9i 1.34681i −0.739273 0.673406i 0.764831π-0.764831\pi
0.739273 0.673406i 0.235169π-0.235169\pi
954954 −19417.1 5954.25i −0.658964 0.202071i
955955 13908.8i 0.471286i
956956 −44424.9 + 2764.49i −1.50293 + 0.0935250i
957957 −46829.5 7764.57i −1.58180 0.262270i
958958 999.092 + 32141.6i 0.0336943 + 1.08397i
959959 −13200.2 −0.444481
960960 −31605.1 + 699.670i −1.06255 + 0.0235226i
961961 −61673.6 −2.07021
962962 1498.65 + 48212.8i 0.0502271 + 1.61585i
963963 54731.2 + 18662.5i 1.83145 + 0.624497i
964964 −37462.9 + 2331.25i −1.25166 + 0.0778885i
965965 28359.3i 0.946028i
966966 734.161 5477.58i 0.0244526 0.182441i
967967 58502.3i 1.94551i 0.231838 + 0.972754i 0.425526π0.425526\pi
−0.231838 + 0.972754i 0.574474π0.574474\pi
968968 4172.38 + 44627.6i 0.138539 + 1.48180i
969969 907.407 5472.73i 0.0300827 0.181434i
970970 −18574.3 + 577.364i −0.614828 + 0.0191114i
971971 23211.9 0.767154 0.383577 0.923509i 0.374692π-0.374692\pi
0.383577 + 0.923509i 0.374692π0.374692\pi
972972 20863.9 21977.9i 0.688489 0.725247i
973973 −4933.76 −0.162558
974974 −11761.8 + 365.604i −0.386931 + 0.0120274i
975975 −825.106 + 4976.36i −0.0271021 + 0.163457i
976976 −30274.1 + 3782.46i −0.992878 + 0.124051i
977977 29085.1i 0.952421i −0.879331 0.476210i 0.842010π-0.842010\pi
0.879331 0.476210i 0.157990π-0.157990\pi
978978 −3276.86 + 24448.7i −0.107140 + 0.799368i
979979 23777.6i 0.776235i
980980 −289.299 4648.99i −0.00942992 0.151537i
981981 −1730.94 590.222i −0.0563349 0.0192093i
982982 1372.67 + 44160.0i 0.0446067 + 1.43503i
983983 −13441.3 −0.436125 −0.218063 0.975935i 0.569974π-0.569974\pi
−0.218063 + 0.975935i 0.569974π0.569974\pi
984984 −1312.93 + 18437.9i −0.0425352 + 0.597337i
985985 54646.0 1.76768
986986 724.870 + 23319.6i 0.0234123 + 0.753193i
987987 −17210.7 2853.62i −0.555037 0.0920280i
988988 −611.850 9832.34i −0.0197020 0.316608i
989989 4493.88i 0.144486i
990990 −49927.9 15310.4i −1.60284 0.491511i
991991 18843.6i 0.604022i −0.953304 0.302011i 0.902342π-0.902342\pi
0.953304 0.302011i 0.0976580π-0.0976580\pi
992992 54086.4 8471.71i 1.73109 0.271146i
993993 36671.1 + 6080.25i 1.17192 + 0.194311i
994994 −12171.0 + 378.324i −0.388370 + 0.0120721i
995995 11975.0 0.381542
996996 −2883.48 + 28126.3i −0.0917335 + 0.894794i
997997 3446.16 0.109469 0.0547346 0.998501i 0.482569π-0.482569\pi
0.0547346 + 0.998501i 0.482569π0.482569\pi
998998 13350.3 414.982i 0.423443 0.0131624i
999999 18890.1 35166.7i 0.598254 1.11374i
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 84.4.e.a.71.17 36
3.2 odd 2 inner 84.4.e.a.71.20 yes 36
4.3 odd 2 inner 84.4.e.a.71.19 yes 36
12.11 even 2 inner 84.4.e.a.71.18 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.4.e.a.71.17 36 1.1 even 1 trivial
84.4.e.a.71.18 yes 36 12.11 even 2 inner
84.4.e.a.71.19 yes 36 4.3 odd 2 inner
84.4.e.a.71.20 yes 36 3.2 odd 2 inner