Properties

Label 56.4.p.a.53.20
Level 5656
Weight 44
Character 56.53
Analytic conductor 3.3043.304
Analytic rank 00
Dimension 4444
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [56,4,Mod(37,56)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(56, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("56.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 56=237 56 = 2^{3} \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 56.p (of order 66, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.304106960323.30410696032
Analytic rank: 00
Dimension: 4444
Relative dimension: 2222 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 53.20
Character χ\chi == 56.53
Dual form 56.4.p.a.37.20

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+(2.53540+1.25369i)q2+(7.079964.08762i)q3+(4.85654+6.35720i)q4+(17.02289.82813i)q5+(12.826019.2398i)q6+(15.69319.83491i)q7+(4.34335+22.2066i)q8+(19.9172+34.4977i)q9+(55.48113.57700i)q10+(29.714117.1555i)q11+(8.3983164.8604i)q123.09910iq13+(52.11835.26121i)q14160.695q15+(16.8280+61.7480i)q16+(14.8109+25.6532i)q17+(7.24898+112.435i)q18+(40.0355+23.1145i)q19+(145.151+60.4868i)q20+(151.308+5.48329i)q21+(53.829780.7482i)q22+(49.7004+86.0836i)q23+(60.0215174.976i)q24+(130.684226.352i)q25+(3.885307.85747i)q26104.925iq27+(138.737+52.0007i)q28+136.943iq29+(407.425201.461i)q30+(0.290223+0.502681i)q31+(120.078+135.459i)q32+(140.250+242.920i)q33+(69.7127+46.4730i)q34+(170.483321.652i)q35+(122.580+294.157i)q36+(128.221+74.0282i)q37+(130.484+8.41263i)q38+(12.6679+21.9415i)q39+(292.186+335.333i)q40141.194q41+(390.502175.791i)q42+259.780iq43+(35.2472272.215i)q44+(678.095+391.498i)q45+(18.0887+280.565i)q46+(174.311301.916i)q47+(371.544368.387i)q48+(149.549308.681i)q49+(615.111410.056i)q50+(209.721121.083i)q51+(19.701615.0509i)q52+(184.884106.743i)q53+(131.543266.027i)q54674.424q55+(286.561+305.775i)q56+377.933q57+(171.683+347.205i)q58+(100.39857.9647i)q59+(780.4201021.57i)q60+(345.954199.737i)q61+(1.36604+0.910650i)q62+(651.846+345.492i)q63+(474.271+192.903i)q64+(30.458452.7554i)q65+(51.0446+791.730i)q66+(893.014+515.582i)q67+(235.012+30.4301i)q68812.625iq69+(835.493601.786i)q70+476.543q71+(679.570+592.131i)q72+(554.624+960.638i)q73+(417.899+26.9429i)q74+(1850.48+1068.37i)q75+(341.377142.257i)q76+(635.030+23.0130i)q77+(59.6261+39.7490i)q78+(225.997391.439i)q79+(320.407+1216.51i)q80+(108.872188.573i)q81+(357.984177.013i)q82770.316iq83+(769.693935.267i)q84+582.253iq85+(325.683+658.648i)q86+(559.769969.549i)q87+(251.906734.363i)q88+(615.3891065.88i)q89+(1228.43+1842.73i)q90+(30.479448.6346i)q91+(305.879+734.024i)q92+(4.109532.37264i)q93+(63.4414984.010i)q94+(454.344+786.948i)q95+(1403.86468.210i)q96+706.293q97+(766.156595.144i)q981366.76iq99+O(q100)q+(2.53540 + 1.25369i) q^{2} +(-7.07996 - 4.08762i) q^{3} +(4.85654 + 6.35720i) q^{4} +(17.0228 - 9.82813i) q^{5} +(-12.8260 - 19.2398i) q^{6} +(15.6931 - 9.83491i) q^{7} +(4.34335 + 22.2066i) q^{8} +(19.9172 + 34.4977i) q^{9} +(55.4811 - 3.57700i) q^{10} +(-29.7141 - 17.1555i) q^{11} +(-8.39831 - 64.8604i) q^{12} -3.09910i q^{13} +(52.1183 - 5.26121i) q^{14} -160.695 q^{15} +(-16.8280 + 61.7480i) q^{16} +(-14.8109 + 25.6532i) q^{17} +(7.24898 + 112.435i) q^{18} +(-40.0355 + 23.1145i) q^{19} +(145.151 + 60.4868i) q^{20} +(-151.308 + 5.48329i) q^{21} +(-53.8297 - 80.7482i) q^{22} +(49.7004 + 86.0836i) q^{23} +(60.0215 - 174.976i) q^{24} +(130.684 - 226.352i) q^{25} +(3.88530 - 7.85747i) q^{26} -104.925i q^{27} +(138.737 + 52.0007i) q^{28} +136.943i q^{29} +(-407.425 - 201.461i) q^{30} +(-0.290223 + 0.502681i) q^{31} +(-120.078 + 135.459i) q^{32} +(140.250 + 242.920i) q^{33} +(-69.7127 + 46.4730i) q^{34} +(170.483 - 321.652i) q^{35} +(-122.580 + 294.157i) q^{36} +(-128.221 + 74.0282i) q^{37} +(-130.484 + 8.41263i) q^{38} +(-12.6679 + 21.9415i) q^{39} +(292.186 + 335.333i) q^{40} -141.194 q^{41} +(-390.502 - 175.791i) q^{42} +259.780i q^{43} +(-35.2472 - 272.215i) q^{44} +(678.095 + 391.498i) q^{45} +(18.0887 + 280.565i) q^{46} +(-174.311 - 301.916i) q^{47} +(371.544 - 368.387i) q^{48} +(149.549 - 308.681i) q^{49} +(615.111 - 410.056i) q^{50} +(209.721 - 121.083i) q^{51} +(19.7016 - 15.0509i) q^{52} +(-184.884 - 106.743i) q^{53} +(131.543 - 266.027i) q^{54} -674.424 q^{55} +(286.561 + 305.775i) q^{56} +377.933 q^{57} +(-171.683 + 347.205i) q^{58} +(-100.398 - 57.9647i) q^{59} +(-780.420 - 1021.57i) q^{60} +(345.954 - 199.737i) q^{61} +(-1.36604 + 0.910650i) q^{62} +(651.846 + 345.492i) q^{63} +(-474.271 + 192.903i) q^{64} +(-30.4584 - 52.7554i) q^{65} +(51.0446 + 791.730i) q^{66} +(893.014 + 515.582i) q^{67} +(-235.012 + 30.4301i) q^{68} -812.625i q^{69} +(835.493 - 601.786i) q^{70} +476.543 q^{71} +(-679.570 + 592.131i) q^{72} +(-554.624 + 960.638i) q^{73} +(-417.899 + 26.9429i) q^{74} +(-1850.48 + 1068.37i) q^{75} +(-341.377 - 142.257i) q^{76} +(-635.030 + 23.0130i) q^{77} +(-59.6261 + 39.7490i) q^{78} +(-225.997 - 391.439i) q^{79} +(320.407 + 1216.51i) q^{80} +(108.872 - 188.573i) q^{81} +(-357.984 - 177.013i) q^{82} -770.316i q^{83} +(-769.693 - 935.267i) q^{84} +582.253i q^{85} +(-325.683 + 658.648i) q^{86} +(559.769 - 969.549i) q^{87} +(251.906 - 734.363i) q^{88} +(-615.389 - 1065.88i) q^{89} +(1228.43 + 1842.73i) q^{90} +(-30.4794 - 48.6346i) q^{91} +(-305.879 + 734.024i) q^{92} +(4.10953 - 2.37264i) q^{93} +(-63.4414 - 984.010i) q^{94} +(-454.344 + 786.948i) q^{95} +(1403.86 - 468.210i) q^{96} +706.293 q^{97} +(766.156 - 595.144i) q^{98} -1366.76i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 44q+4q420q64q712q8+160q914q10110q12+102q14116q15104q162q1738q18+256q20360q22+162q23+186q24+348q25+2670q98+O(q100) 44 q + 4 q^{4} - 20 q^{6} - 4 q^{7} - 12 q^{8} + 160 q^{9} - 14 q^{10} - 110 q^{12} + 102 q^{14} - 116 q^{15} - 104 q^{16} - 2 q^{17} - 38 q^{18} + 256 q^{20} - 360 q^{22} + 162 q^{23} + 186 q^{24} + 348 q^{25}+ \cdots - 2670 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/56Z)×\left(\mathbb{Z}/56\mathbb{Z}\right)^\times.

nn 1515 1717 2929
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right) 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 2.53540 + 1.25369i 0.896400 + 0.443245i
33 −7.07996 4.08762i −1.36254 0.786662i −0.372578 0.928001i 0.621526π-0.621526\pi
−0.989961 + 0.141338i 0.954859π0.954859\pi
44 4.85654 + 6.35720i 0.607068 + 0.794650i
55 17.0228 9.82813i 1.52257 0.879055i 0.522923 0.852380i 0.324842π-0.324842\pi
0.999644 0.0266746i 0.00849178π-0.00849178\pi
66 −12.8260 19.2398i −0.872697 1.30910i
77 15.6931 9.83491i 0.847350 0.531035i
88 4.34335 + 22.2066i 0.191951 + 0.981405i
99 19.9172 + 34.4977i 0.737676 + 1.27769i
1010 55.4811 3.57700i 1.75447 0.113115i
1111 −29.7141 17.1555i −0.814468 0.470233i 0.0340372 0.999421i 0.489164π-0.489164\pi
−0.848505 + 0.529187i 0.822497π0.822497\pi
1212 −8.39831 64.8604i −0.202032 1.56030i
1313 3.09910i 0.0661182i −0.999453 0.0330591i 0.989475π-0.989475\pi
0.999453 0.0330591i 0.0105249π-0.0105249\pi
1414 52.1183 5.26121i 0.994943 0.100437i
1515 −160.695 −2.76608
1616 −16.8280 + 61.7480i −0.262938 + 0.964813i
1717 −14.8109 + 25.6532i −0.211304 + 0.365989i −0.952123 0.305716i 0.901104π-0.901104\pi
0.740819 + 0.671705i 0.234438π0.234438\pi
1818 7.24898 + 112.435i 0.0949222 + 1.47229i
1919 −40.0355 + 23.1145i −0.483409 + 0.279096i −0.721836 0.692064i 0.756702π-0.756702\pi
0.238427 + 0.971160i 0.423368π0.423368\pi
2020 145.151 + 60.4868i 1.62284 + 0.676263i
2121 −151.308 + 5.48329i −1.57229 + 0.0569786i
2222 −53.8297 80.7482i −0.521661 0.782526i
2323 49.7004 + 86.0836i 0.450576 + 0.780420i 0.998422 0.0561589i 0.0178854π-0.0178854\pi
−0.547846 + 0.836579i 0.684552π0.684552\pi
2424 60.0215 174.976i 0.510493 1.48820i
2525 130.684 226.352i 1.04547 1.81081i
2626 3.88530 7.85747i 0.0293065 0.0592683i
2727 104.925i 0.747882i
2828 138.737 + 52.0007i 0.936386 + 0.350972i
2929 136.943i 0.876883i 0.898760 + 0.438442i 0.144469π0.144469\pi
−0.898760 + 0.438442i 0.855531π0.855531\pi
3030 −407.425 201.461i −2.47951 1.22605i
3131 −0.290223 + 0.502681i −0.00168147 + 0.00291239i −0.866865 0.498543i 0.833869π-0.833869\pi
0.865183 + 0.501455i 0.167202π0.167202\pi
3232 −120.078 + 135.459i −0.663346 + 0.748313i
3333 140.250 + 242.920i 0.739830 + 1.28142i
3434 −69.7127 + 46.4730i −0.351636 + 0.234414i
3535 170.483 321.652i 0.823337 1.55340i
3636 −122.580 + 294.157i −0.567499 + 1.36184i
3737 −128.221 + 74.0282i −0.569712 + 0.328923i −0.757034 0.653375i 0.773352π-0.773352\pi
0.187322 + 0.982299i 0.440019π0.440019\pi
3838 −130.484 + 8.41263i −0.557036 + 0.0359134i
3939 −12.6679 + 21.9415i −0.0520127 + 0.0900886i
4040 292.186 + 335.333i 1.15497 + 1.32552i
4141 −141.194 −0.537825 −0.268913 0.963165i 0.586664π-0.586664\pi
−0.268913 + 0.963165i 0.586664π0.586664\pi
4242 −390.502 175.791i −1.43466 0.645835i
4343 259.780i 0.921306i 0.887580 + 0.460653i 0.152385π0.152385\pi
−0.887580 + 0.460653i 0.847615π0.847615\pi
4444 −35.2472 272.215i −0.120766 0.932680i
4545 678.095 + 391.498i 2.24632 + 1.29691i
4646 18.0887 + 280.565i 0.0579790 + 0.899285i
4747 −174.311 301.916i −0.540977 0.936999i −0.998848 0.0479808i 0.984721π-0.984721\pi
0.457872 0.889018i 0.348612π-0.348612\pi
4848 371.544 368.387i 1.11725 1.10775i
4949 149.549 308.681i 0.436003 0.899945i
5050 615.111 410.056i 1.73980 1.15981i
5151 209.721 121.083i 0.575820 0.332450i
5252 19.7016 15.0509i 0.0525408 0.0401382i
5353 −184.884 106.743i −0.479165 0.276646i 0.240904 0.970549i 0.422556π-0.422556\pi
−0.720068 + 0.693903i 0.755890π0.755890\pi
5454 131.543 266.027i 0.331495 0.670402i
5555 −674.424 −1.65344
5656 286.561 + 305.775i 0.683810 + 0.729660i
5757 377.933 0.878218
5858 −171.683 + 347.205i −0.388674 + 0.786039i
5959 −100.398 57.9647i −0.221537 0.127904i 0.385125 0.922864i 0.374158π-0.374158\pi
−0.606662 + 0.794960i 0.707492π0.707492\pi
6060 −780.420 1021.57i −1.67920 2.19806i
6161 345.954 199.737i 0.726146 0.419240i −0.0908649 0.995863i 0.528963π-0.528963\pi
0.817010 + 0.576623i 0.195630π0.195630\pi
6262 −1.36604 + 0.910650i −0.00279817 + 0.00186537i
6363 651.846 + 345.492i 1.30357 + 0.690920i
6464 −474.271 + 192.903i −0.926310 + 0.376763i
6565 −30.4584 52.7554i −0.0581215 0.100669i
6666 51.0446 + 791.730i 0.0951994 + 1.47659i
6767 893.014 + 515.582i 1.62834 + 0.940125i 0.984587 + 0.174895i 0.0559586π0.0559586\pi
0.643757 + 0.765230i 0.277375π0.277375\pi
6868 −235.012 + 30.4301i −0.419109 + 0.0542675i
6969 812.625i 1.41780i
7070 835.493 601.786i 1.42658 1.02753i
7171 476.543 0.796553 0.398276 0.917265i 0.369608π-0.369608\pi
0.398276 + 0.917265i 0.369608π0.369608\pi
7272 −679.570 + 592.131i −1.11233 + 0.969212i
7373 −554.624 + 960.638i −0.889231 + 1.54019i −0.0484453 + 0.998826i 0.515427π0.515427\pi
−0.840786 + 0.541368i 0.817907π0.817907\pi
7474 −417.899 + 26.9429i −0.656484 + 0.0423250i
7575 −1850.48 + 1068.37i −2.84900 + 1.64487i
7676 −341.377 142.257i −0.515246 0.214711i
7777 −635.030 + 23.0130i −0.939850 + 0.0340594i
7878 −59.6261 + 39.7490i −0.0865555 + 0.0577011i
7979 −225.997 391.439i −0.321857 0.557472i 0.659014 0.752130i 0.270974π-0.270974\pi
−0.980871 + 0.194658i 0.937640π0.937640\pi
8080 320.407 + 1216.51i 0.447783 + 1.70013i
8181 108.872 188.573i 0.149345 0.258673i
8282 −357.984 177.013i −0.482107 0.238388i
8383 770.316i 1.01871i −0.860556 0.509356i 0.829883π-0.829883\pi
0.860556 0.509356i 0.170117π-0.170117\pi
8484 −769.693 935.267i −0.999766 1.21483i
8585 582.253i 0.742991i
8686 −325.683 + 658.648i −0.408364 + 0.825859i
8787 559.769 969.549i 0.689811 1.19479i
8888 251.906 734.363i 0.305151 0.889584i
8989 −615.389 1065.88i −0.732934 1.26948i −0.955624 0.294589i 0.904817π-0.904817\pi
0.222690 0.974889i 0.428516π-0.428516\pi
9090 1228.43 + 1842.73i 1.43875 + 2.15823i
9191 −30.4794 48.6346i −0.0351111 0.0560252i
9292 −305.879 + 734.024i −0.346631 + 0.831818i
9393 4.10953 2.37264i 0.00458214 0.00264550i
9494 −63.4414 984.010i −0.0696115 1.07971i
9595 −454.344 + 786.948i −0.490682 + 0.849885i
9696 1403.86 468.210i 1.49250 0.497776i
9797 706.293 0.739311 0.369656 0.929169i 0.379476π-0.379476\pi
0.369656 + 0.929169i 0.379476π0.379476\pi
9898 766.156 595.144i 0.789729 0.613455i
9999 1366.76i 1.38752i
100100 2073.64 268.500i 2.07364 0.268500i
101101 −760.005 438.789i −0.748745 0.432288i 0.0764951 0.997070i 0.475627π-0.475627\pi
−0.825240 + 0.564782i 0.808960π0.808960\pi
102102 683.527 44.0686i 0.663522 0.0427788i
103103 808.543 + 1400.44i 0.773477 + 1.33970i 0.935646 + 0.352939i 0.114818π0.114818\pi
−0.162169 + 0.986763i 0.551849π0.551849\pi
104104 68.8207 13.4605i 0.0648887 0.0126914i
105105 −2521.80 + 1580.42i −2.34383 + 1.46888i
106106 −334.933 502.422i −0.306901 0.460373i
107107 −544.209 + 314.199i −0.491688 + 0.283876i −0.725275 0.688460i 0.758287π-0.758287\pi
0.233586 + 0.972336i 0.424954π0.424954\pi
108108 667.029 509.572i 0.594305 0.454015i
109109 −398.630 230.149i −0.350292 0.202241i 0.314522 0.949250i 0.398156π-0.398156\pi
−0.664814 + 0.747009i 0.731489π0.731489\pi
110110 −1709.94 845.516i −1.48215 0.732880i
111111 1210.40 1.03501
112112 343.202 + 1134.52i 0.289550 + 0.957163i
113113 −1015.23 −0.845171 −0.422586 0.906323i 0.638877π-0.638877\pi
−0.422586 + 0.906323i 0.638877π0.638877\pi
114114 958.212 + 473.809i 0.787235 + 0.389266i
115115 1692.08 + 976.923i 1.37206 + 0.792161i
116116 −870.572 + 665.068i −0.696816 + 0.532328i
117117 106.912 61.7256i 0.0844786 0.0487738i
118118 −181.879 272.831i −0.141893 0.212849i
119119 19.8679 + 548.243i 0.0153049 + 0.422331i
120120 −697.953 3568.49i −0.530951 2.71464i
121121 −76.8805 133.161i −0.0577614 0.100046i
122122 1127.54 72.6951i 0.836743 0.0539468i
123123 999.650 + 577.148i 0.732808 + 0.423087i
124124 −4.60512 + 0.596284i −0.00333510 + 0.000431838i
125125 2680.49i 1.91800i
126126 1219.55 + 1693.17i 0.862273 + 1.19714i
127127 112.340 0.0784925 0.0392463 0.999230i 0.487504π-0.487504\pi
0.0392463 + 0.999230i 0.487504π0.487504\pi
128128 −1444.31 105.501i −0.997343 0.0728517i
129129 1061.88 1839.24i 0.724757 1.25532i
130130 −11.0855 171.942i −0.00747892 0.116002i
131131 475.899 274.760i 0.317400 0.183251i −0.332833 0.942986i 0.608004π-0.608004\pi
0.650233 + 0.759735i 0.274671π0.274671\pi
132132 −863.162 + 2071.35i −0.569156 + 1.36582i
133133 −400.953 + 756.484i −0.261406 + 0.493199i
134134 1617.77 + 2426.77i 1.04294 + 1.56448i
135135 −1031.22 1786.12i −0.657429 1.13870i
136136 −634.001 217.479i −0.399744 0.137123i
137137 927.547 1606.56i 0.578436 1.00188i −0.417223 0.908804i 0.636997π-0.636997\pi
0.995659 0.0930760i 0.0296700π-0.0296700\pi
138138 1018.78 2060.33i 0.628435 1.27092i
139139 150.835i 0.0920405i −0.998941 0.0460203i 0.985346π-0.985346\pi
0.998941 0.0460203i 0.0146539π-0.0146539\pi
140140 2872.76 478.325i 1.73423 0.288756i
141141 2850.07i 1.70226i
142142 1208.23 + 597.436i 0.714030 + 0.353068i
143143 −53.1665 + 92.0871i −0.0310910 + 0.0538511i
144144 −2465.33 + 649.323i −1.42670 + 0.375765i
145145 1345.89 + 2331.15i 0.770828 + 1.33511i
146146 −2610.53 + 1740.28i −1.47979 + 0.986483i
147147 −2320.57 + 1574.15i −1.30202 + 0.883224i
148148 −1093.32 455.603i −0.607233 0.253043i
149149 2697.57 1557.44i 1.48318 0.856312i 0.483359 0.875422i 0.339417π-0.339417\pi
0.999817 + 0.0191102i 0.00608335π0.00608335\pi
150150 −6031.12 + 388.840i −3.28292 + 0.211658i
151151 448.845 777.422i 0.241897 0.418978i −0.719357 0.694640i 0.755564π-0.755564\pi
0.961255 + 0.275662i 0.0888970π0.0888970\pi
152152 −687.184 788.659i −0.366697 0.420847i
153153 −1179.97 −0.623495
154154 −1638.91 737.782i −0.857578 0.386053i
155155 11.4094i 0.00591241i
156156 −201.009 + 26.0272i −0.103164 + 0.0133580i
157157 −1805.49 1042.40i −0.917794 0.529889i −0.0348634 0.999392i 0.511100π-0.511100\pi
−0.882931 + 0.469503i 0.844433π0.844433\pi
158158 −82.2529 1275.79i −0.0414157 0.642380i
159159 872.646 + 1511.47i 0.435254 + 0.753881i
160160 −712.765 + 3486.04i −0.352181 + 1.72247i
161161 1626.58 + 862.122i 0.796226 + 0.422017i
162162 512.447 341.616i 0.248528 0.165678i
163163 470.091 271.407i 0.225892 0.130419i −0.382784 0.923838i 0.625035π-0.625035\pi
0.608675 + 0.793419i 0.291701π0.291701\pi
164164 −685.716 897.600i −0.326496 0.427383i
165165 4774.90 + 2756.79i 2.25288 + 1.30070i
166166 965.735 1953.06i 0.451539 0.913175i
167167 −2401.40 −1.11273 −0.556366 0.830938i 0.687805π-0.687805\pi
−0.556366 + 0.830938i 0.687805π0.687805\pi
168168 −778.950 3336.23i −0.357722 1.53212i
169169 2187.40 0.995628
170170 −729.963 + 1476.25i −0.329327 + 0.666017i
171171 −1594.79 920.754i −0.713198 0.411765i
172172 −1651.48 + 1261.63i −0.732116 + 0.559295i
173173 67.3790 38.9013i 0.0296111 0.0170960i −0.485121 0.874447i 0.661225π-0.661225\pi
0.514732 + 0.857351i 0.327891π0.327891\pi
174174 2634.75 1756.42i 1.14793 0.765253i
175175 −175.305 4837.44i −0.0757245 2.08958i
176176 1559.35 1546.10i 0.667841 0.662167i
177177 473.875 + 820.775i 0.201235 + 0.348549i
178178 −223.974 3473.95i −0.0943121 1.46283i
179179 −648.975 374.686i −0.270987 0.156454i 0.358349 0.933588i 0.383340π-0.383340\pi
−0.629336 + 0.777133i 0.716673π0.716673\pi
180180 804.363 + 6212.12i 0.333076 + 2.57235i
181181 3814.83i 1.56660i 0.621647 + 0.783298i 0.286464π0.286464\pi
−0.621647 + 0.783298i 0.713536π0.713536\pi
182182 −16.3050 161.520i −0.00664070 0.0657838i
183183 −3265.79 −1.31920
184184 −1695.76 + 1477.57i −0.679420 + 0.592000i
185185 −1455.12 + 2520.34i −0.578283 + 1.00162i
186186 13.3939 0.863534i 0.00528003 0.000340416i
187187 880.185 508.175i 0.344201 0.198724i
188188 1072.79 2574.40i 0.416177 0.998709i
189189 −1031.93 1646.60i −0.397152 0.633717i
190190 −2138.53 + 1425.62i −0.816555 + 0.544346i
191191 499.858 + 865.779i 0.189364 + 0.327987i 0.945038 0.326960i 0.106024π-0.106024\pi
−0.755675 + 0.654947i 0.772691π0.772691\pi
192192 4146.33 + 572.893i 1.55852 + 0.215339i
193193 406.904 704.779i 0.151760 0.262855i −0.780115 0.625636i 0.784839π-0.784839\pi
0.931874 + 0.362781i 0.118173π0.118173\pi
194194 1790.74 + 885.470i 0.662719 + 0.327696i
195195 498.009i 0.182888i
196196 2688.64 548.411i 0.979825 0.199858i
197197 12.8192i 0.00463618i 0.999997 + 0.00231809i 0.000737872π0.000737872\pi
−0.999997 + 0.00231809i 0.999262π0.999262\pi
198198 1713.49 3465.28i 0.615011 1.24377i
199199 75.7989 131.288i 0.0270012 0.0467675i −0.852209 0.523201i 0.824738π-0.824738\pi
0.879210 + 0.476434i 0.158071π0.158071\pi
200200 5594.12 + 1918.93i 1.97782 + 0.678445i
201201 −4215.00 7300.60i −1.47912 2.56191i
202202 −1376.81 2065.31i −0.479566 0.719381i
203203 1346.82 + 2149.06i 0.465656 + 0.743027i
204204 1788.26 + 745.197i 0.613743 + 0.255756i
205205 −2403.52 + 1387.68i −0.818875 + 0.472778i
206206 294.273 + 4564.34i 0.0995291 + 1.54375i
207207 −1979.79 + 3429.09i −0.664758 + 1.15139i
208208 191.363 + 52.1517i 0.0637916 + 0.0173850i
209209 1586.16 0.524961
210210 −8375.13 + 845.447i −2.75209 + 0.277816i
211211 4630.42i 1.51077i −0.655284 0.755383i 0.727451π-0.727451\pi
0.655284 0.755383i 0.272549π-0.272549\pi
212212 −219.311 1693.74i −0.0710487 0.548711i
213213 −3373.91 1947.93i −1.08533 0.626618i
214214 −1773.70 + 114.354i −0.566577 + 0.0365285i
215215 2553.16 + 4422.19i 0.809878 + 1.40275i
216216 2330.03 455.726i 0.733975 0.143557i
217217 0.389316 + 10.7430i 0.000121790 + 0.00336073i
218218 −722.152 1083.28i −0.224359 0.336554i
219219 7853.44 4534.19i 2.42322 1.39905i
220220 −3275.37 4287.45i −1.00375 1.31391i
221221 79.5019 + 45.9004i 0.0241985 + 0.0139710i
222222 3068.84 + 1517.46i 0.927781 + 0.458762i
223223 −3007.58 −0.903151 −0.451575 0.892233i 0.649138π-0.649138\pi
−0.451575 + 0.892233i 0.649138π0.649138\pi
224224 −552.179 + 3306.74i −0.164705 + 0.986343i
225225 10411.5 3.08488
226226 −2574.01 1272.77i −0.757612 0.374618i
227227 1846.41 + 1066.03i 0.539870 + 0.311694i 0.745026 0.667035i 0.232437π-0.232437\pi
−0.205156 + 0.978729i 0.565770π0.565770\pi
228228 1835.45 + 2402.60i 0.533138 + 0.697876i
229229 −1627.50 + 939.637i −0.469643 + 0.271148i −0.716090 0.698008i 0.754070π-0.754070\pi
0.246447 + 0.969156i 0.420737π0.420737\pi
230230 3065.35 + 4598.23i 0.878797 + 1.31825i
231231 4590.06 + 2432.83i 1.30738 + 0.692937i
232232 −3041.04 + 594.791i −0.860577 + 0.168319i
233233 1664.34 + 2882.72i 0.467959 + 0.810528i 0.999330 0.0366112i 0.0116563π-0.0116563\pi
−0.531371 + 0.847139i 0.678323π0.678323\pi
234234 348.449 22.4653i 0.0973454 0.00627608i
235235 −5934.54 3426.31i −1.64735 0.951096i
236236 −119.093 919.757i −0.0328486 0.253691i
237237 3695.16i 1.01277i
238238 −636.952 + 1414.93i −0.173477 + 0.385361i
239239 −5724.47 −1.54931 −0.774655 0.632384i 0.782077π-0.782077\pi
−0.774655 + 0.632384i 0.782077π0.782077\pi
240240 2704.17 9922.57i 0.727306 2.66875i
241241 −921.960 + 1596.88i −0.246426 + 0.426822i −0.962532 0.271170i 0.912590π-0.912590\pi
0.716106 + 0.697992i 0.245923π0.245923\pi
242242 −27.9810 434.001i −0.00743260 0.115284i
243243 −3995.05 + 2306.54i −1.05466 + 0.608909i
244244 2949.91 + 1229.27i 0.773969 + 0.322524i
245245 −488.015 6724.41i −0.127258 1.75350i
246246 1810.95 + 2716.55i 0.469358 + 0.704069i
247247 71.6342 + 124.074i 0.0184533 + 0.0319621i
248248 −12.4234 4.26156i −0.00318099 0.00109117i
249249 −3148.76 + 5453.81i −0.801383 + 1.38804i
250250 3360.50 6796.13i 0.850146 1.71930i
251251 6537.91i 1.64410i −0.569415 0.822050i 0.692830π-0.692830\pi
0.569415 0.822050i 0.307170π-0.307170\pi
252252 969.351 + 5821.81i 0.242315 + 1.45532i
253253 3410.53i 0.847503i
254254 284.827 + 140.839i 0.0703608 + 0.0347914i
255255 2380.03 4122.33i 0.584483 1.01235i
256256 −3529.64 2078.19i −0.861727 0.507372i
257257 −3492.66 6049.46i −0.847727 1.46831i −0.883231 0.468937i 0.844637π-0.844637\pi
0.0355040 0.999370i 0.488696π-0.488696\pi
258258 4998.13 3331.94i 1.20608 0.804020i
259259 −1284.12 + 2422.77i −0.308075 + 0.581251i
260260 187.455 449.839i 0.0447132 0.107299i
261261 −4724.20 + 2727.52i −1.12039 + 0.646856i
262262 1551.06 100.000i 0.365743 0.0235803i
263263 3530.99 6115.85i 0.827870 1.43391i −0.0718353 0.997417i 0.522886π-0.522886\pi
0.899706 0.436497i 0.143781π-0.143781\pi
264264 −4785.28 + 4169.57i −1.11558 + 0.972042i
265265 −4196.32 −0.972747
266266 −1964.97 + 1415.32i −0.452933 + 0.326237i
267267 10061.9i 2.30629i
268268 1059.30 + 8181.02i 0.241445 + 1.86468i
269269 4770.05 + 2753.99i 1.08117 + 0.624214i 0.931212 0.364478i 0.118753π-0.118753\pi
0.149959 + 0.988692i 0.452086π0.452086\pi
270270 −375.316 5821.35i −0.0845963 1.31213i
271271 −1142.36 1978.63i −0.256065 0.443517i 0.709120 0.705088i 0.249093π-0.249093\pi
−0.965184 + 0.261571i 0.915759π0.915759\pi
272272 −1334.80 1346.24i −0.297551 0.300101i
273273 16.9933 + 468.919i 0.00376732 + 0.103957i
274274 4365.83 2910.42i 0.962588 0.641697i
275275 −7766.33 + 4483.90i −1.70301 + 0.983233i
276276 5166.02 3946.54i 1.12666 0.860703i
277277 1467.21 + 847.095i 0.318253 + 0.183744i 0.650614 0.759409i 0.274512π-0.274512\pi
−0.332360 + 0.943152i 0.607845π0.607845\pi
278278 189.099 382.427i 0.0407965 0.0825052i
279279 −23.1218 −0.00496152
280280 7883.28 + 2388.80i 1.68256 + 0.509850i
281281 −7993.95 −1.69708 −0.848539 0.529133i 0.822517π-0.822517\pi
−0.848539 + 0.529133i 0.822517π0.822517\pi
282282 −3573.10 + 7226.08i −0.754520 + 1.52591i
283283 565.457 + 326.467i 0.118774 + 0.0685740i 0.558210 0.829700i 0.311488π-0.311488\pi
−0.439436 + 0.898274i 0.644822π0.644822\pi
284284 2314.35 + 3029.48i 0.483561 + 0.632981i
285285 6433.48 3714.37i 1.33715 0.772002i
286286 −250.247 + 166.824i −0.0517392 + 0.0344913i
287287 −2215.78 + 1388.63i −0.455726 + 0.285604i
288288 −7064.65 1444.46i −1.44545 0.295540i
289289 2017.78 + 3494.89i 0.410701 + 0.711355i
290290 489.843 + 7597.73i 0.0991883 + 1.53846i
291291 −5000.53 2887.06i −1.00734 0.581589i
292292 −8800.52 + 1139.52i −1.76374 + 0.228374i
293293 4866.56i 0.970332i 0.874422 + 0.485166i 0.161241π0.161241\pi
−0.874422 + 0.485166i 0.838759π0.838759\pi
294294 −7857.08 + 1081.84i −1.55862 + 0.214607i
295295 −2278.74 −0.449740
296296 −2200.83 2525.82i −0.432164 0.495981i
297297 −1800.04 + 3117.75i −0.351679 + 0.609126i
298298 8791.96 566.838i 1.70908 0.110188i
299299 266.782 154.027i 0.0516000 0.0297912i
300300 −15778.8 6575.26i −3.03663 1.26541i
301301 2554.92 + 4076.77i 0.489246 + 0.780668i
302302 2112.65 1408.37i 0.402547 0.268353i
303303 3587.20 + 6213.22i 0.680130 + 1.17802i
304304 −753.556 2861.08i −0.142169 0.539784i
305305 3926.08 6800.16i 0.737070 1.27664i
306306 −2991.70 1479.31i −0.558901 0.276361i
307307 8098.28i 1.50552i 0.658297 + 0.752758i 0.271277π0.271277\pi
−0.658297 + 0.752758i 0.728723π0.728723\pi
308308 −3230.35 3925.25i −0.597617 0.726175i
309309 13220.1i 2.43386i
310310 −14.3038 + 28.9274i −0.00262065 + 0.00529989i
311311 221.066 382.897i 0.0403071 0.0698139i −0.845168 0.534501i 0.820500π-0.820500\pi
0.885475 + 0.464687i 0.153833π0.153833\pi
312312 −542.269 186.013i −0.0983972 0.0337529i
313313 2747.89 + 4759.48i 0.496230 + 0.859495i 0.999991 0.00434826i 0.00138410π-0.00138410\pi
−0.503761 + 0.863843i 0.668051π0.668051\pi
314314 −3270.80 4906.42i −0.587841 0.881800i
315315 14491.8 525.171i 2.59213 0.0939366i
316316 1390.89 3337.75i 0.247607 0.594187i
317317 2494.51 1440.21i 0.441974 0.255174i −0.262461 0.964943i 0.584534π-0.584534\pi
0.704435 + 0.709769i 0.251201π0.251201\pi
318318 317.604 + 4926.20i 0.0560073 + 0.868704i
319319 2349.31 4069.13i 0.412340 0.714193i
320320 −6177.55 + 7944.94i −1.07917 + 1.38792i
321321 5137.30 0.893260
322322 3043.20 + 4225.05i 0.526680 + 0.731220i
323323 1369.38i 0.235897i
324324 1727.54 223.687i 0.296217 0.0383550i
325325 −701.487 405.004i −0.119728 0.0691248i
326326 1532.13 98.7799i 0.260297 0.0167819i
327327 1881.52 + 3258.89i 0.318191 + 0.551123i
328328 −613.256 3135.45i −0.103236 0.527824i
329329 −5704.81 3023.67i −0.955976 0.506688i
330330 8650.14 + 12975.8i 1.44295 + 2.16453i
331331 3370.95 1946.22i 0.559771 0.323184i −0.193283 0.981143i 0.561913π-0.561913\pi
0.753053 + 0.657959i 0.228580π0.228580\pi
332332 4897.05 3741.07i 0.809520 0.618428i
333333 −5107.60 2948.88i −0.840526 0.485278i
334334 −6088.52 3010.61i −0.997453 0.493213i
335335 20268.8 3.30568
336336 2207.63 9435.25i 0.358442 1.53195i
337337 7323.86 1.18385 0.591923 0.805994i 0.298369π-0.298369\pi
0.591923 + 0.805994i 0.298369π0.298369\pi
338338 5545.93 + 2742.31i 0.892482 + 0.441307i
339339 7187.76 + 4149.85i 1.15158 + 0.664865i
340340 −3701.50 + 2827.74i −0.590418 + 0.451046i
341341 17.2474 9.95781i 0.00273901 0.00158137i
342342 −2889.11 4333.85i −0.456798 0.685228i
343343 −688.963 6314.98i −0.108456 0.994101i
344344 −5768.85 + 1128.32i −0.904174 + 0.176845i
345345 −7986.58 13833.2i −1.24633 2.15870i
346346 219.603 14.1583i 0.0341212 0.00219987i
347347 1255.10 + 724.632i 0.194171 + 0.112105i 0.593934 0.804514i 0.297574π-0.297574\pi
−0.399763 + 0.916619i 0.630908π0.630908\pi
348348 8882.16 1150.09i 1.36820 0.177159i
349349 6471.81i 0.992630i −0.868142 0.496315i 0.834686π-0.834686\pi
0.868142 0.496315i 0.165314π-0.165314\pi
350350 5620.16 12484.6i 0.858315 1.90666i
351351 −325.173 −0.0494486
352352 5891.89 1965.05i 0.892156 0.297549i
353353 −2516.41 + 4358.55i −0.379419 + 0.657173i −0.990978 0.134026i 0.957209π-0.957209\pi
0.611559 + 0.791199i 0.290543π0.290543\pi
354354 172.469 + 2675.09i 0.0258944 + 0.401636i
355355 8112.11 4683.53i 1.21281 0.700213i
356356 3787.38 9088.66i 0.563851 1.35309i
357357 2100.34 3962.75i 0.311378 0.587482i
358358 −1175.68 1763.59i −0.173565 0.260360i
359359 −5022.83 8699.80i −0.738426 1.27899i −0.953204 0.302329i 0.902236π-0.902236\pi
0.214777 0.976663i 0.431097π-0.431097\pi
360360 −5748.66 + 16758.6i −0.841614 + 2.45349i
361361 −2360.94 + 4089.27i −0.344211 + 0.596190i
362362 −4782.60 + 9672.12i −0.694386 + 1.40430i
363363 1257.03i 0.181755i
364364 161.156 429.960i 0.0232056 0.0619121i
365365 21803.7i 3.12673i
366366 −8280.09 4094.27i −1.18253 0.584730i
367367 −2105.38 + 3646.63i −0.299455 + 0.518672i −0.976011 0.217719i 0.930138π-0.930138\pi
0.676556 + 0.736391i 0.263472π0.263472\pi
368368 −6151.85 + 1620.28i −0.871433 + 0.229519i
369369 −2812.20 4870.87i −0.396741 0.687175i
370370 −6849.03 + 4565.81i −0.962335 + 0.641528i
371371 −3951.21 + 143.189i −0.552929 + 0.0200377i
372372 35.0415 + 14.6023i 0.00488391 + 0.00203520i
373373 −10289.1 + 5940.41i −1.42828 + 0.824619i −0.996985 0.0775918i 0.975277π-0.975277\pi
−0.431296 + 0.902210i 0.641944π0.641944\pi
374374 2868.72 184.953i 0.396625 0.0255713i
375375 −10956.8 + 18977.8i −1.50882 + 2.61336i
376376 5947.45 5182.20i 0.815734 0.710775i
377377 424.399 0.0579779
378378 −552.032 5468.51i −0.0751150 0.744100i
379379 6238.70i 0.845543i −0.906236 0.422771i 0.861057π-0.861057\pi
0.906236 0.422771i 0.138943π-0.138943\pi
380380 −7209.33 + 933.484i −0.973239 + 0.126018i
381381 −795.362 459.203i −0.106949 0.0617471i
382382 181.926 + 2821.77i 0.0243668 + 0.377943i
383383 3360.68 + 5820.87i 0.448363 + 0.776587i 0.998280 0.0586324i 0.0186740π-0.0186740\pi
−0.549917 + 0.835219i 0.685341π0.685341\pi
384384 9794.39 + 6650.71i 1.30161 + 0.883835i
385385 −10583.8 + 6632.90i −1.40104 + 0.878037i
386386 1915.24 1276.77i 0.252547 0.168357i
387387 −8961.82 + 5174.11i −1.17714 + 0.679625i
388388 3430.14 + 4490.05i 0.448812 + 0.587494i
389389 −351.685 203.046i −0.0458385 0.0264648i 0.476906 0.878954i 0.341758π-0.341758\pi
−0.522744 + 0.852490i 0.675092π0.675092\pi
390390 −624.347 + 1262.65i −0.0810642 + 0.163941i
391391 −2944.43 −0.380834
392392 7504.32 + 1980.27i 0.966902 + 0.255150i
393393 −4492.46 −0.576627
394394 −16.0712 + 32.5017i −0.00205496 + 0.00415587i
395395 −7694.23 4442.26i −0.980097 0.565860i
396396 8688.75 6637.71i 1.10259 0.842317i
397397 11599.8 6697.13i 1.46644 0.846648i 0.467143 0.884182i 0.345283π-0.345283\pi
0.999295 + 0.0375335i 0.0119501π0.0119501\pi
398398 356.774 237.839i 0.0449334 0.0299542i
399399 5930.95 3716.94i 0.744158 0.466365i
400400 11777.6 + 11878.5i 1.47220 + 1.48482i
401401 2639.24 + 4571.30i 0.328672 + 0.569277i 0.982249 0.187584i 0.0600656π-0.0600656\pi
−0.653577 + 0.756860i 0.726732π0.726732\pi
402402 −1534.07 23794.3i −0.190330 2.95211i
403403 1.55786 + 0.899430i 0.000192562 + 0.000111176i
404404 −901.524 6962.50i −0.111021 0.857419i
405405 4280.05i 0.525130i
406406 720.484 + 7137.22i 0.0880715 + 0.872449i
407407 5079.95 0.618683
408408 3599.73 + 4131.30i 0.436797 + 0.501298i
409409 3940.94 6825.91i 0.476447 0.825231i −0.523189 0.852217i 0.675258π-0.675258\pi
0.999636 + 0.0269860i 0.00859097π0.00859097\pi
410410 −7833.61 + 505.051i −0.943596 + 0.0608359i
411411 −13134.0 + 7582.92i −1.57628 + 0.910067i
412412 −4976.14 + 11941.4i −0.595041 + 1.42793i
413413 −2145.63 + 77.7560i −0.255641 + 0.00926422i
414414 −9318.57 + 6212.10i −1.10624 + 0.737460i
415415 −7570.76 13112.9i −0.895504 1.55106i
416416 419.801 + 372.135i 0.0494771 + 0.0438592i
417417 −616.555 + 1067.90i −0.0724048 + 0.125409i
418418 4021.55 + 1988.55i 0.470576 + 0.232686i
419419 3028.37i 0.353092i 0.984292 + 0.176546i 0.0564924π0.0564924\pi
−0.984292 + 0.176546i 0.943508π0.943508\pi
420420 −22294.3 8356.24i −2.59012 0.970816i
421421 10492.4i 1.21465i 0.794452 + 0.607327i 0.207758π0.207758\pi
−0.794452 + 0.607327i 0.792242π0.792242\pi
422422 5805.10 11740.0i 0.669639 1.35425i
423423 6943.60 12026.7i 0.798131 1.38240i
424424 1567.38 4569.27i 0.179525 0.523357i
425425 3871.10 + 6704.94i 0.441826 + 0.765264i
426426 −6112.13 9168.60i −0.695149 1.04277i
427427 3464.71 6536.92i 0.392668 0.740852i
428428 −4640.40 1933.72i −0.524071 0.218388i
429429 752.834 434.649i 0.0847253 0.0489162i
430430 929.233 + 14412.9i 0.104213 + 1.61640i
431431 −6466.81 + 11200.8i −0.722727 + 1.25180i 0.237176 + 0.971467i 0.423778π0.423778\pi
−0.959903 + 0.280333i 0.909555π0.909555\pi
432432 6478.91 + 1765.68i 0.721566 + 0.196646i
433433 15739.7 1.74689 0.873444 0.486925i 0.161881π-0.161881\pi
0.873444 + 0.486925i 0.161881π0.161881\pi
434434 −12.4812 + 27.7258i −0.00138046 + 0.00306655i
435435 22005.9i 2.42553i
436436 −472.858 3651.90i −0.0519399 0.401133i
437437 −3979.56 2297.60i −0.435625 0.251508i
438438 25596.1 1650.24i 2.79230 0.180026i
439439 −2252.15 3900.84i −0.244850 0.424093i 0.717239 0.696827i 0.245405π-0.245405\pi
−0.962090 + 0.272734i 0.912072π0.912072\pi
440440 −2929.26 14976.7i −0.317380 1.62270i
441441 13627.4 988.990i 1.47148 0.106791i
442442 144.025 + 216.047i 0.0154990 + 0.0232495i
443443 −13011.1 + 7511.96i −1.39543 + 0.805653i −0.993910 0.110197i 0.964852π-0.964852\pi
−0.401521 + 0.915850i 0.631518π0.631518\pi
444444 5878.34 + 7694.74i 0.628319 + 0.822468i
445445 −20951.3 12096.2i −2.23188 1.28858i
446446 −7625.44 3770.57i −0.809585 0.400317i
447447 −25464.9 −2.69451
448448 −5545.61 + 7691.66i −0.584834 + 0.811153i
449449 −1550.44 −0.162962 −0.0814809 0.996675i 0.525965π-0.525965\pi
−0.0814809 + 0.996675i 0.525965π0.525965\pi
450450 26397.3 + 13052.7i 2.76529 + 1.36736i
451451 4195.46 + 2422.25i 0.438041 + 0.252903i
452452 −4930.48 6453.99i −0.513076 0.671616i
453453 −6355.61 + 3669.41i −0.659189 + 0.380583i
454454 3344.93 + 5017.62i 0.345783 + 0.518698i
455455 −996.832 528.343i −0.102708 0.0544376i
456456 1641.50 + 8392.62i 0.168575 + 0.861887i
457457 6335.06 + 10972.7i 0.648450 + 1.12315i 0.983493 + 0.180946i 0.0579159π0.0579159\pi
−0.335043 + 0.942203i 0.608751π0.608751\pi
458458 −5304.38 + 341.985i −0.541173 + 0.0348907i
459459 2691.66 + 1554.03i 0.273717 + 0.158030i
460460 2007.16 + 15501.4i 0.203444 + 1.57121i
461461 4811.69i 0.486123i 0.970011 + 0.243062i 0.0781518π0.0781518\pi
−0.970011 + 0.243062i 0.921848π0.921848\pi
462462 8587.64 + 11922.7i 0.864791 + 1.20064i
463463 5222.12 0.524174 0.262087 0.965044i 0.415589π-0.415589\pi
0.262087 + 0.965044i 0.415589π0.415589\pi
464464 −8455.94 2304.47i −0.846028 0.230566i
465465 46.6372 80.7781i 0.00465107 0.00805590i
466466 605.744 + 9395.41i 0.0602157 + 0.933978i
467467 10536.9 6083.50i 1.04409 0.602807i 0.123103 0.992394i 0.460716π-0.460716\pi
0.920990 + 0.389587i 0.127382π0.127382\pi
468468 911.623 + 379.887i 0.0900423 + 0.0375220i
469469 19084.9 691.621i 1.87902 0.0680940i
470470 −10750.9 16127.1i −1.05511 1.58274i
471471 8521.86 + 14760.3i 0.833687 + 1.44399i
472472 851.138 2481.26i 0.0830017 0.241969i
473473 4456.65 7719.15i 0.433229 0.750374i
474474 −4632.58 + 9368.73i −0.448906 + 0.907848i
475475 12082.8i 1.16715i
476476 −3388.80 + 2788.87i −0.326314 + 0.268545i
477477 8504.07i 0.816299i
478478 −14513.8 7176.69i −1.38880 0.686724i
479479 −6773.05 + 11731.3i −0.646072 + 1.11903i 0.337981 + 0.941153i 0.390256π0.390256\pi
−0.984053 + 0.177877i 0.943077π0.943077\pi
480480 19296.0 21767.5i 1.83487 2.06989i
481481 229.421 + 397.369i 0.0217478 + 0.0376683i
482482 −4339.53 + 2892.89i −0.410083 + 0.273377i
483483 −7992.09 12752.6i −0.752904 1.20138i
484484 473.157 1135.45i 0.0444363 0.106635i
485485 12023.1 6941.54i 1.12565 0.649895i
486486 −13020.8 + 839.478i −1.21530 + 0.0783529i
487487 3537.94 6127.89i 0.329198 0.570187i −0.653155 0.757224i 0.726555π-0.726555\pi
0.982353 + 0.187037i 0.0598884π0.0598884\pi
488488 5938.08 + 6814.95i 0.550829 + 0.632169i
489489 −4437.63 −0.410382
490490 7192.99 17660.9i 0.663155 1.62824i
491491 6617.13i 0.608202i 0.952640 + 0.304101i 0.0983560π0.0983560\pi
−0.952640 + 0.304101i 0.901644π0.901644\pi
492492 1185.79 + 9157.92i 0.108658 + 0.839168i
493493 −3513.02 2028.24i −0.320930 0.185289i
494494 26.0716 + 404.384i 0.00237453 + 0.0368302i
495495 −13432.7 23266.1i −1.21970 2.11259i
496496 −26.1557 26.3798i −0.00236779 0.00238808i
497497 7478.45 4686.76i 0.674959 0.422998i
498498 −14820.7 + 9880.05i −1.33360 + 0.889027i
499499 11245.8 6492.78i 1.00888 0.582478i 0.0980181 0.995185i 0.468750π-0.468750\pi
0.910864 + 0.412706i 0.135416π0.135416\pi
500500 17040.4 13017.9i 1.52414 1.16436i
501501 17001.8 + 9816.02i 1.51614 + 0.875344i
502502 8196.49 16576.2i 0.728739 1.47377i
503503 −1755.69 −0.155631 −0.0778154 0.996968i 0.524794π-0.524794\pi
−0.0778154 + 0.996968i 0.524794π0.524794\pi
504504 −4841.03 + 15975.9i −0.427850 + 1.41195i
505505 −17249.9 −1.52002
506506 4275.74 8647.07i 0.375651 0.759702i
507507 −15486.7 8941.24i −1.35658 0.783223i
508508 545.583 + 714.167i 0.0476503 + 0.0623741i
509509 4198.62 2424.08i 0.365620 0.211091i −0.305923 0.952056i 0.598965π-0.598965\pi
0.671543 + 0.740965i 0.265632π0.265632\pi
510510 11202.4 7467.96i 0.972652 0.648406i
511511 743.994 + 20530.1i 0.0644078 + 1.77730i
512512 −6343.65 9694.12i −0.547563 0.836765i
513513 2425.29 + 4200.72i 0.208731 + 0.361533i
514514 −1271.17 19716.5i −0.109083 1.69194i
515515 27527.4 + 15892.9i 2.35534 + 1.35986i
516516 16849.5 2181.72i 1.43751 0.186133i
517517 11961.6i 1.01754i
518518 −6293.17 + 4532.82i −0.533795 + 0.384480i
519519 −636.054 −0.0537951
520520 1039.23 905.514i 0.0876409 0.0763642i
521521 6337.65 10977.1i 0.532932 0.923066i −0.466328 0.884612i 0.654423π-0.654423\pi
0.999260 0.0384538i 0.0122432π-0.0122432\pi
522522 −15397.2 + 992.695i −1.29103 + 0.0832357i
523523 −2491.10 + 1438.24i −0.208276 + 0.120248i −0.600510 0.799617i 0.705036π-0.705036\pi
0.392234 + 0.919865i 0.371702π0.371702\pi
524524 4057.93 + 1691.00i 0.338304 + 0.140976i
525525 −18532.4 + 34965.4i −1.54061 + 2.90670i
526526 16619.8 11079.4i 1.37768 0.918411i
527527 −8.59692 14.8903i −0.000710603 0.00123080i
528528 −17360.0 + 4572.29i −1.43086 + 0.376863i
529529 1143.25 1980.16i 0.0939628 0.162748i
530530 −10639.4 5260.87i −0.871971 0.431165i
531531 4617.99i 0.377408i
532532 −6756.37 + 1124.96i −0.550612 + 0.0916788i
533533 437.575i 0.0355600i
534534 −12614.5 + 25511.0i −1.02225 + 2.06736i
535535 −6175.98 + 10697.1i −0.499086 + 0.864442i
536536 −7570.67 + 22070.2i −0.610081 + 1.77852i
537537 3063.15 + 5305.53i 0.246154 + 0.426351i
538538 8641.36 + 12962.6i 0.692482 + 1.03877i
539539 −9739.28 + 6606.61i −0.778294 + 0.527954i
540540 6346.57 15230.0i 0.505765 1.21369i
541541 14454.9 8345.57i 1.14874 0.663224i 0.200158 0.979764i 0.435855π-0.435855\pi
0.948579 + 0.316540i 0.102521π0.102521\pi
542542 −415.768 6448.78i −0.0329497 0.511068i
543543 15593.6 27008.8i 1.23238 2.13455i
544544 −1696.49 5086.67i −0.133707 0.400899i
545545 −9047.73 −0.711123
546546 −544.793 + 1210.20i −0.0427014 + 0.0948570i
547547 13392.5i 1.04684i −0.852074 0.523422i 0.824655π-0.824655\pi
0.852074 0.523422i 0.175345π-0.175345\pi
548548 14717.9 1905.71i 1.14729 0.148555i
549549 13780.9 + 7956.41i 1.07132 + 0.618527i
550550 −25312.2 + 1631.94i −1.96239 + 0.126520i
551551 −3165.36 5482.57i −0.244735 0.423893i
552552 18045.7 3529.52i 1.39144 0.272149i
553553 −7396.38 3920.24i −0.568763 0.301457i
554554 2657.98 + 3987.15i 0.203839 + 0.305772i
555555 20604.4 11895.9i 1.57587 0.909828i
556556 958.887 732.535i 0.0731400 0.0558748i
557557 −17896.2 10332.4i −1.36138 0.785992i −0.371571 0.928405i 0.621181π-0.621181\pi
−0.989807 + 0.142413i 0.954514π0.954514\pi
558558 −58.6230 28.9874i −0.00444751 0.00219917i
559559 805.086 0.0609150
560560 16992.5 + 15939.7i 1.28226 + 1.20282i
561561 −8308.90 −0.625316
562562 −20267.9 10021.9i −1.52126 0.752221i
563563 10428.6 + 6020.95i 0.780662 + 0.450715i 0.836665 0.547715i 0.184502π-0.184502\pi
−0.0560031 + 0.998431i 0.517836π0.517836\pi
564564 −18118.5 + 13841.5i −1.35270 + 1.03339i
565565 −17282.0 + 9977.77i −1.28683 + 0.742952i
566566 1024.37 + 1536.63i 0.0760736 + 0.114116i
567567 −146.046 4030.05i −0.0108172 0.298494i
568568 2069.79 + 10582.4i 0.152899 + 0.781741i
569569 3066.49 + 5311.31i 0.225929 + 0.391321i 0.956598 0.291411i 0.0941248π-0.0941248\pi
−0.730669 + 0.682732i 0.760792π0.760792\pi
570570 20968.1 1351.86i 1.54080 0.0993392i
571571 −9727.66 5616.27i −0.712942 0.411617i 0.0992074 0.995067i 0.468369π-0.468369\pi
−0.812149 + 0.583450i 0.801703π0.801703\pi
572572 −843.622 + 109.235i −0.0616671 + 0.00798483i
573573 8172.91i 0.595861i
574574 −7358.81 + 742.852i −0.535106 + 0.0540175i
575575 25980.2 1.88426
576576 −16100.9 12519.1i −1.16470 0.905609i
577577 3029.04 5246.45i 0.218545 0.378531i −0.735818 0.677179i 0.763202π-0.763202\pi
0.954363 + 0.298648i 0.0965356π0.0965356\pi
578578 734.379 + 11390.6i 0.0528480 + 0.819701i
579579 −5761.74 + 3326.54i −0.413557 + 0.238767i
580580 −8283.22 + 19877.4i −0.593004 + 1.42304i
581581 −7575.99 12088.7i −0.540973 0.863206i
582582 −9058.89 13588.9i −0.645195 0.967835i
583583 3662.44 + 6343.53i 0.260176 + 0.450638i
584584 −23741.5 8143.96i −1.68224 0.577054i
585585 1213.29 2101.49i 0.0857496 0.148523i
586586 −6101.14 + 12338.7i −0.430095 + 0.869806i
587587 6644.32i 0.467190i −0.972334 0.233595i 0.924951π-0.924951\pi
0.972334 0.233595i 0.0750489π-0.0750489\pi
588588 −21277.2 7107.40i −1.49227 0.498477i
589589 26.8334i 0.00187717i
590590 −5777.52 2856.82i −0.403147 0.199345i
591591 52.3998 90.7592i 0.00364711 0.00631698i
592592 −2413.40 9163.12i −0.167551 0.636152i
593593 2137.96 + 3703.05i 0.148053 + 0.256435i 0.930508 0.366272i 0.119366π-0.119366\pi
−0.782455 + 0.622707i 0.786033π0.786033\pi
594594 −8472.50 + 5648.08i −0.585237 + 0.390141i
595595 5726.41 + 9137.38i 0.394555 + 0.629573i
596596 23001.8 + 9585.20i 1.58086 + 0.658767i
597597 −1073.31 + 619.674i −0.0735805 + 0.0424817i
598598 869.500 56.0587i 0.0594590 0.00383346i
599599 −3875.72 + 6712.95i −0.264370 + 0.457903i −0.967398 0.253259i 0.918497π-0.918497\pi
0.703028 + 0.711162i 0.251831π0.251831\pi
600600 −31762.3 36452.6i −2.16115 2.48029i
601601 3307.77 0.224504 0.112252 0.993680i 0.464194π-0.464194\pi
0.112252 + 0.993680i 0.464194π0.464194\pi
602602 1366.76 + 13539.3i 0.0925331 + 0.916647i
603603 41075.9i 2.77403i
604604 7122.07 922.185i 0.479789 0.0621245i
605605 −2617.44 1511.18i −0.175891 0.101551i
606606 1305.58 + 20250.2i 0.0875174 + 1.35744i
607607 9431.37 + 16335.6i 0.630655 + 1.09233i 0.987418 + 0.158131i 0.0505469π0.0505469\pi
−0.356764 + 0.934195i 0.616120π0.616120\pi
608608 1676.33 8198.72i 0.111816 0.546878i
609609 −750.896 20720.5i −0.0499636 1.37872i
610610 18479.5 12319.1i 1.22658 0.817681i
611611 −935.668 + 540.208i −0.0619527 + 0.0357684i
612612 −5730.56 7501.30i −0.378504 0.495461i
613613 9142.16 + 5278.23i 0.602363 + 0.347774i 0.769971 0.638079i 0.220271π-0.220271\pi
−0.167608 + 0.985854i 0.553604π0.553604\pi
614614 −10152.7 + 20532.4i −0.667313 + 1.34955i
615615 22689.1 1.48767
616616 −3269.20 14001.9i −0.213831 0.915835i
617617 29924.7 1.95255 0.976274 0.216541i 0.0694775π-0.0694775\pi
0.976274 + 0.216541i 0.0694775π0.0694775\pi
618618 16573.8 33518.2i 1.07880 2.18171i
619619 −2646.83 1528.15i −0.171866 0.0992270i 0.411599 0.911365i 0.364970π-0.364970\pi
−0.583466 + 0.812138i 0.698304π0.698304\pi
620620 −72.5318 + 55.4102i −0.00469830 + 0.00358924i
621621 9032.31 5214.81i 0.583662 0.336978i
622622 1040.52 693.652i 0.0670759 0.0447153i
623623 −20140.3 10674.8i −1.29519 0.686478i
624624 −1141.67 1151.45i −0.0732425 0.0738702i
625625 −10008.7 17335.6i −0.640557 1.10948i
626626 1000.11 + 15512.2i 0.0638536 + 0.990403i
627627 −11229.9 6483.61i −0.715280 0.412967i
628628 −2141.69 16540.3i −0.136087 1.05100i
629629 4385.70i 0.278011i
630630 37400.9 + 16836.6i 2.36522 + 1.06474i
631631 −27891.8 −1.75968 −0.879838 0.475274i 0.842349π-0.842349\pi
−0.879838 + 0.475274i 0.842349π0.842349\pi
632632 7710.96 6718.80i 0.485325 0.422879i
633633 −18927.4 + 32783.2i −1.18846 + 2.05848i
634634 8130.16 524.170i 0.509290 0.0328351i
635635 1912.34 1104.09i 0.119510 0.0689992i
636636 −5370.66 + 12888.1i −0.334844 + 0.803531i
637637 −956.635 463.467i −0.0595027 0.0288277i
638638 11057.9 7371.59i 0.686184 0.457436i
639639 9491.42 + 16439.6i 0.587598 + 1.01775i
640640 −25623.0 + 12398.9i −1.58256 + 0.765797i
641641 −3917.07 + 6784.57i −0.241365 + 0.418057i −0.961103 0.276189i 0.910928π-0.910928\pi
0.719738 + 0.694245i 0.244262π0.244262\pi
642642 13025.1 + 6440.57i 0.800718 + 0.395933i
643643 5261.50i 0.322695i 0.986898 + 0.161348i 0.0515841π0.0515841\pi
−0.986898 + 0.161348i 0.948416π0.948416\pi
644644 2418.86 + 14527.4i 0.148007 + 0.888914i
645645 41745.3i 2.54840i
646646 1716.78 3471.94i 0.104560 0.211458i
647647 3563.73 6172.57i 0.216545 0.375067i −0.737204 0.675670i 0.763854π-0.763854\pi
0.953749 + 0.300603i 0.0971878π0.0971878\pi
648648 4660.44 + 1598.66i 0.282530 + 0.0969153i
649649 1988.82 + 3444.74i 0.120290 + 0.208348i
650650 −1270.80 1906.29i −0.0766847 0.115032i
651651 41.1567 77.6511i 0.00247782 0.00467494i
652652 4008.40 + 1670.36i 0.240769 + 0.100332i
653653 5945.31 3432.52i 0.356291 0.205705i −0.311162 0.950357i 0.600718π-0.600718\pi
0.667452 + 0.744652i 0.267385π0.267385\pi
654654 684.789 + 10621.4i 0.0409440 + 0.635063i
655655 5400.76 9354.38i 0.322176 0.558024i
656656 2376.02 8718.46i 0.141415 0.518901i
657657 −44186.4 −2.62386
658658 −10673.3 14818.3i −0.632351 0.877927i
659659 19567.2i 1.15665i 0.815807 + 0.578324i 0.196293π0.196293\pi
−0.815807 + 0.578324i 0.803707π0.803707\pi
660660 5664.03 + 43743.4i 0.334048 + 2.57987i
661661 −6568.19 3792.15i −0.386495 0.223143i 0.294146 0.955761i 0.404965π-0.404965\pi
−0.680640 + 0.732618i 0.738298π0.738298\pi
662662 10986.7 708.336i 0.645028 0.0415865i
663663 −375.247 649.947i −0.0219810 0.0380722i
664664 17106.1 3345.75i 0.999769 0.195543i
665665 609.475 + 16818.1i 0.0355405 + 0.980719i
666666 −9252.87 13879.9i −0.538351 0.807562i
667667 −11788.5 + 6806.10i −0.684338 + 0.395103i
668668 −11662.5 15266.2i −0.675503 0.884232i
669669 21293.6 + 12293.8i 1.23058 + 0.710475i
670670 51389.7 + 25410.8i 2.96322 + 1.46523i
671671 −13706.3 −0.788563
672672 17426.1 21154.5i 1.00034 1.21436i
673673 −31020.7 −1.77676 −0.888379 0.459110i 0.848168π-0.848168\pi
−0.888379 + 0.459110i 0.848168π0.848168\pi
674674 18569.0 + 9181.83i 1.06120 + 0.524734i
675675 −23749.9 13712.0i −1.35427 0.781891i
676676 10623.2 + 13905.7i 0.604414 + 0.791176i
677677 −19466.4 + 11238.9i −1.10510 + 0.638032i −0.937557 0.347832i 0.886918π-0.886918\pi
−0.167547 + 0.985864i 0.553585π0.553585\pi
678678 13021.2 + 19532.7i 0.737578 + 1.10642i
679679 11084.0 6946.33i 0.626455 0.392601i
680680 −12929.9 + 2528.93i −0.729175 + 0.142618i
681681 −8715.01 15094.8i −0.490396 0.849391i
682682 56.2132 3.62419i 0.00315618 0.000203486i
683683 7487.89 + 4323.14i 0.419497 + 0.242196i 0.694862 0.719143i 0.255465π-0.255465\pi
−0.275365 + 0.961340i 0.588799π0.588799\pi
684684 −1891.76 14610.1i −0.105750 0.816712i
685685 36464.2i 2.03391i
686686 6170.20 16874.8i 0.343410 0.939186i
687687 15363.5 0.853209
688688 −16040.9 4371.59i −0.888887 0.242246i
689689 −330.806 + 572.973i −0.0182913 + 0.0316815i
690690 −2906.75 45085.3i −0.160374 2.48749i
691691 −2663.91 + 1538.01i −0.146657 + 0.0846724i −0.571533 0.820579i 0.693651π-0.693651\pi
0.424876 + 0.905252i 0.360318π0.360318\pi
692692 574.532 + 239.416i 0.0315613 + 0.0131521i
693693 −13441.9 21448.7i −0.736821 1.17571i
694694 2273.72 + 3410.74i 0.124365 + 0.186556i
695695 −1482.42 2567.63i −0.0809087 0.140138i
696696 23961.7 + 8219.51i 1.30498 + 0.447643i
697697 2091.21 3622.09i 0.113645 0.196838i
698698 8113.62 16408.6i 0.439979 0.889794i
699699 27212.7i 1.47250i
700700 29901.2 24607.7i 1.61451 1.32869i
701701 1052.30i 0.0566972i 0.999598 + 0.0283486i 0.00902485π0.00902485\pi
−0.999598 + 0.0283486i 0.990975π0.990975\pi
702702 −824.445 407.665i −0.0443257 0.0219178i
703703 3422.25 5927.51i 0.183603 0.318009i
704704 17401.9 + 2404.40i 0.931616 + 0.128720i
705705 28010.9 + 48516.2i 1.49638 + 2.59181i
706706 −11844.4 + 7895.89i −0.631400 + 0.420915i
707707 −16242.3 + 588.608i −0.864009 + 0.0313110i
708708 −2916.44 + 6998.65i −0.154812 + 0.371505i
709709 −14804.1 + 8547.16i −0.784175 + 0.452744i −0.837908 0.545812i 0.816221π-0.816221\pi
0.0537327 + 0.998555i 0.482888π0.482888\pi
710710 26439.1 1704.59i 1.39753 0.0901017i
711711 9002.49 15592.8i 0.474852 0.822468i
712712 20996.9 18295.2i 1.10518 0.962982i
713713 −57.6967 −0.00303052
714714 10293.3 7414.00i 0.539518 0.388602i
715715 2090.11i 0.109323i
716716 −769.820 5945.34i −0.0401809 0.310318i
717717 40529.0 + 23399.5i 2.11100 + 1.21878i
718718 −1828.09 28354.6i −0.0950188 1.47379i
719719 −11239.8 19467.9i −0.582995 1.00978i −0.995122 0.0986507i 0.968547π-0.968547\pi
0.412127 0.911126i 0.364786π-0.364786\pi
720720 −35585.3 + 35282.9i −1.84192 + 1.82627i
721721 26461.8 + 14025.3i 1.36683 + 0.724452i
722722 −11112.6 + 7408.07i −0.572809 + 0.381856i
723723 13054.9 7537.24i 0.671530 0.387708i
724724 −24251.6 + 18526.9i −1.24490 + 0.951030i
725725 30997.2 + 17896.2i 1.58787 + 0.916759i
726726 −1575.92 + 3187.08i −0.0805620 + 0.162925i
727727 26355.5 1.34453 0.672265 0.740311i 0.265322π-0.265322\pi
0.672265 + 0.740311i 0.265322π0.265322\pi
728728 947.629 888.083i 0.0482438 0.0452123i
729729 31834.0 1.61733
730730 −27335.0 + 55281.1i −1.38591 + 2.80280i
731731 −6664.20 3847.58i −0.337188 0.194676i
732732 −15860.4 20761.3i −0.800845 1.04830i
733733 −19348.2 + 11170.7i −0.974954 + 0.562890i −0.900743 0.434353i 0.856977π-0.856977\pi
−0.0742108 + 0.997243i 0.523644π0.523644\pi
734734 −9909.72 + 6606.19i −0.498330 + 0.332205i
735735 −24031.7 + 49603.4i −1.20602 + 2.48932i
736736 −17628.7 3604.42i −0.882886 0.180517i
737737 −17690.1 30640.1i −0.884156 1.53140i
738738 −1023.51 15875.2i −0.0510516 0.791837i
739739 −7009.10 4046.71i −0.348896 0.201435i 0.315303 0.948991i 0.397894π-0.397894\pi
−0.664199 + 0.747556i 0.731227π0.731227\pi
740740 −23089.1 + 2989.65i −1.14699 + 0.148516i
741741 1171.25i 0.0580662i
742742 −10197.4 4590.53i −0.504527 0.227121i
743743 17583.7 0.868214 0.434107 0.900861i 0.357064π-0.357064\pi
0.434107 + 0.900861i 0.357064π0.357064\pi
744744 70.5376 + 80.9538i 0.00347585 + 0.00398912i
745745 30613.5 53024.1i 1.50549 2.60759i
746746 −33534.4 + 2162.04i −1.64582 + 0.106110i
747747 26574.1 15342.6i 1.30160 0.751480i
748748 7505.23 + 3127.54i 0.366869 + 0.152880i
749749 −5450.22 + 10283.0i −0.265883 + 0.501647i
750750 −51572.2 + 34379.9i −2.51087 + 1.67384i
751751 1665.58 + 2884.86i 0.0809291 + 0.140173i 0.903649 0.428273i 0.140878π-0.140878\pi
−0.822720 + 0.568447i 0.807545π0.807545\pi
752752 21576.0 5682.73i 1.04627 0.275569i
753753 −26724.5 + 46288.1i −1.29335 + 2.24015i
754754 1076.02 + 532.064i 0.0519714 + 0.0256984i
755755 17645.2i 0.850564i
756756 5456.17 14557.0i 0.262486 0.700306i
757757 20862.2i 1.00165i −0.865548 0.500826i 0.833030π-0.833030\pi
0.865548 0.500826i 0.166970π-0.166970\pi
758758 7821.38 15817.6i 0.374783 0.757945i
759759 −13940.9 + 24146.4i −0.666699 + 1.15476i
760760 −19448.8 6671.48i −0.928268 0.318421i
761761 −15284.5 26473.6i −0.728074 1.26106i −0.957696 0.287782i 0.907082π-0.907082\pi
0.229622 0.973280i 0.426251π-0.426251\pi
762762 −1440.87 2161.40i −0.0685002 0.102755i
763763 −8519.24 + 308.730i −0.404217 + 0.0146485i
764764 −3076.35 + 7382.39i −0.145679 + 0.349588i
765765 −20086.4 + 11596.9i −0.949313 + 0.548086i
766766 1223.14 + 18971.5i 0.0576942 + 0.894867i
767767 −179.638 + 311.143i −0.00845680 + 0.0146476i
768768 16494.8 + 29141.3i 0.775007 + 1.36920i
769769 −20444.9 −0.958729 −0.479365 0.877616i 0.659133π-0.659133\pi
−0.479365 + 0.877616i 0.659133π0.659133\pi
770770 −35149.9 + 3548.29i −1.64508 + 0.166067i
771771 57106.6i 2.66750i
772772 6456.57 836.015i 0.301007 0.0389752i
773773 −30330.4 17511.3i −1.41127 0.814796i −0.415760 0.909474i 0.636484π-0.636484\pi
−0.995508 + 0.0946782i 0.969818π0.969818\pi
774774 −29208.5 + 1883.14i −1.35643 + 0.0874524i
775775 75.8551 + 131.385i 0.00351587 + 0.00608966i
776776 3067.68 + 15684.4i 0.141912 + 0.725564i
777777 18994.9 11904.1i 0.877013 0.549625i
778778 −637.109 955.706i −0.0293592 0.0440408i
779779 5652.78 3263.63i 0.259989 0.150105i
780780 −3165.94 + 2418.60i −0.145332 + 0.111025i
781781 −14160.1 8175.31i −0.648767 0.374566i
782782 −7465.31 3691.39i −0.341380 0.168803i
783783 14368.7 0.655805
784784 16543.8 + 14428.8i 0.753637 + 0.657291i
785785 −40979.3 −1.86320
786786 −11390.2 5632.13i −0.516889 0.255587i
787787 5306.74 + 3063.85i 0.240362 + 0.138773i 0.615343 0.788259i 0.289018π-0.289018\pi
−0.374981 + 0.927032i 0.622351π0.622351\pi
788788 −81.4940 + 62.2568i −0.00368414 + 0.00281447i
789789 −49998.5 + 28866.6i −2.25601 + 1.30251i
790790 −13938.8 20909.1i −0.627745 0.941660i
791791 −15932.1 + 9984.66i −0.716156 + 0.448816i
792792 30351.1 5936.31i 1.36172 0.266335i
793793 −619.004 1072.15i −0.0277194 0.0480114i
794794 37806.2 2437.45i 1.68979 0.108945i
795795 29709.8 + 17153.0i 1.32541 + 0.765223i
796796 1202.74 155.735i 0.0535554 0.00693450i
797797 23892.7i 1.06189i 0.847407 + 0.530944i 0.178162π0.178162\pi
−0.847407 + 0.530944i 0.821838π0.821838\pi
798798 19697.2 1988.38i 0.873777 0.0882055i
799799 10326.8 0.457242
800800 14969.0 + 44882.3i 0.661544 + 1.98354i
801801 24513.7 42459.0i 1.08133 1.87293i
802802 960.565 + 14898.9i 0.0422927 + 0.655982i
803803 32960.4 19029.7i 1.44850 0.836292i
804804 25941.1 62251.3i 1.13790 2.73064i
805805 36162.0 1310.48i 1.58328 0.0573769i
806806 2.82220 + 4.23348i 0.000123335 + 0.000185010i
807807 −22514.5 38996.3i −0.982092 1.70103i
808808 6443.06 18783.0i 0.280527 0.817800i
809809 −12610.4 + 21841.8i −0.548030 + 0.949216i 0.450379 + 0.892837i 0.351289π0.351289\pi
−0.998409 + 0.0563787i 0.982045π0.982045\pi
810810 5365.84 10851.7i 0.232761 0.470726i
811811 1732.97i 0.0750345i 0.999296 + 0.0375172i 0.0119449π0.0119449\pi
−0.999296 + 0.0375172i 0.988055π0.988055\pi
812812 −7121.12 + 18999.0i −0.307762 + 0.821101i
813813 18678.1i 0.805746i
814814 12879.7 + 6368.67i 0.554588 + 0.274228i
815815 5334.84 9240.22i 0.229290 0.397142i
816816 3947.41 + 14987.4i 0.169347 + 0.642972i
817817 −6004.69 10400.4i −0.257133 0.445367i
818818 18549.4 12365.7i 0.792867 0.528554i
819819 1070.72 2020.14i 0.0456823 0.0861896i
820820 −20494.5 8540.38i −0.872805 0.363711i
821821 5968.24 3445.76i 0.253706 0.146477i −0.367754 0.929923i 0.619873π-0.619873\pi
0.621460 + 0.783446i 0.286540π0.286540\pi
822822 −42806.6 + 2759.84i −1.81636 + 0.117105i
823823 −12426.4 + 21523.1i −0.526314 + 0.911602i 0.473216 + 0.880946i 0.343093π0.343093\pi
−0.999530 + 0.0306558i 0.990240π0.990240\pi
824824 −27587.2 + 24037.6i −1.16632 + 1.01625i
825825 73313.8 3.09389
826826 −5537.53 2492.81i −0.233263 0.105007i
827827 40056.0i 1.68426i −0.539274 0.842130i 0.681301π-0.681301\pi
0.539274 0.842130i 0.318699π-0.318699\pi
828828 −31414.4 + 4067.62i −1.31851 + 0.170724i
829829 17833.4 + 10296.1i 0.747143 + 0.431363i 0.824661 0.565628i 0.191366π-0.191366\pi
−0.0775180 + 0.996991i 0.524700π0.524700\pi
830830 −2755.42 42738.0i −0.115231 1.78730i
831831 −6925.20 11994.8i −0.289089 0.500716i
832832 597.825 + 1469.81i 0.0249109 + 0.0612459i
833833 5703.71 + 8408.25i 0.237241 + 0.349734i
834834 −2902.03 + 1934.60i −0.120491 + 0.0803235i
835835 −40878.6 + 23601.3i −1.69421 + 0.978151i
836836 7703.25 + 10083.5i 0.318687 + 0.417161i
837837 52.7437 + 30.4516i 0.00217812 + 0.00125754i
838838 −3796.62 + 7678.13i −0.156506 + 0.316511i
839839 −28341.7 −1.16622 −0.583112 0.812392i 0.698165π-0.698165\pi
−0.583112 + 0.812392i 0.698165π0.698165\pi
840840 −46048.8 49136.4i −1.89147 2.01830i
841841 5635.70 0.231075
842842 −13154.2 + 26602.5i −0.538389 + 1.08882i
843843 56596.8 + 32676.2i 2.31233 + 1.33503i
844844 29436.5 22487.8i 1.20053 0.917137i
845845 37235.6 21498.0i 1.51591 0.875212i
846846 32682.5 21787.4i 1.32819 0.885419i
847847 −2516.12 1333.60i −0.102072 0.0541003i
848848 9702.37 9619.93i 0.392902 0.389563i
849849 −2668.94 4622.74i −0.107889 0.186869i
850850 1408.91 + 21852.9i 0.0568530 + 0.881820i
851851 −12745.2 7358.46i −0.513397 0.296410i
852852 −4002.16 30908.8i −0.160929 1.24286i
853853 15664.3i 0.628763i 0.949297 + 0.314382i 0.101797π0.101797\pi
−0.949297 + 0.314382i 0.898203π0.898203\pi
854854 16979.7 12230.1i 0.680367 0.490052i
855855 −36197.1 −1.44786
856856 −9341.00 10720.4i −0.372978 0.428055i
857857 −12500.5 + 21651.5i −0.498260 + 0.863011i −0.999998 0.00200842i 0.999361π-0.999361\pi
0.501738 + 0.865019i 0.332694π0.332694\pi
858858 2453.65 158.193i 0.0976297 0.00629441i
859859 2767.80 1597.99i 0.109937 0.0634724i −0.444023 0.896015i 0.646449π-0.646449\pi
0.553960 + 0.832543i 0.313116π0.313116\pi
860860 −15713.3 + 37707.5i −0.623045 + 1.49513i
861861 21363.8 774.208i 0.845619 0.0306445i
862862 −30438.3 + 20291.3i −1.20271 + 0.801769i
863863 1905.67 + 3300.72i 0.0751677 + 0.130194i 0.901159 0.433488i 0.142717π-0.142717\pi
−0.825991 + 0.563683i 0.809384π0.809384\pi
864864 14213.0 + 12599.2i 0.559650 + 0.496105i
865865 764.653 1324.42i 0.0300566 0.0520596i
866866 39906.5 + 19732.7i 1.56591 + 0.774299i
867867 32991.6i 1.29233i
868868 −66.4044 + 54.6486i −0.00259667 + 0.00213697i
869869 15508.4i 0.605391i
870870 27588.6 55793.9i 1.07510 2.17424i
871871 1597.84 2767.54i 0.0621593 0.107663i
872872 3379.45 9851.85i 0.131241 0.382598i
873873 14067.4 + 24365.5i 0.545372 + 0.944612i
874874 −7209.31 10814.5i −0.279014 0.418540i
875875 −26362.4 42065.3i −1.01853 1.62522i
876876 66965.3 + 27905.4i 2.58282 + 1.07630i
877877 29051.2 16772.7i 1.11858 0.645810i 0.177538 0.984114i 0.443187π-0.443187\pi
0.941037 + 0.338304i 0.109853π0.109853\pi
878878 −819.681 12713.7i −0.0315067 0.488686i
879879 19892.6 34455.0i 0.763324 1.32212i
880880 11349.2 41644.4i 0.434753 1.59526i
881881 27593.4 1.05522 0.527608 0.849488i 0.323089π-0.323089\pi
0.527608 + 0.849488i 0.323089π0.323089\pi
882882 35790.8 + 14577.0i 1.36637 + 0.556499i
883883 6231.84i 0.237506i 0.992924 + 0.118753i 0.0378897π0.0378897\pi
−0.992924 + 0.118753i 0.962110π0.962110\pi
884884 94.3059 + 728.327i 0.00358807 + 0.0277107i
885885 16133.4 + 9314.61i 0.612788 + 0.353793i
886886 −42406.0 + 2734.02i −1.60797 + 0.103669i
887887 15706.2 + 27203.9i 0.594546 + 1.02978i 0.993611 + 0.112862i 0.0360017π0.0360017\pi
−0.399064 + 0.916923i 0.630665π0.630665\pi
888888 5257.18 + 26878.9i 0.198671 + 1.01576i
889889 1762.96 1104.85i 0.0665106 0.0416823i
890890 −37955.1 56935.2i −1.42950 2.14435i
891891 −6470.10 + 3735.52i −0.243273 + 0.140454i
892892 −14606.4 19119.8i −0.548274 0.717689i
893893 13957.3 + 8058.23i 0.523026 + 0.301969i
894894 −64563.8 31925.0i −2.41536 1.19433i
895895 −14729.8 −0.550128
896896 −23703.3 + 12549.0i −0.883785 + 0.467894i
897897 −2518.41 −0.0937426
898898 −3930.99 1943.77i −0.146079 0.0722320i
899899 −68.8385 39.7439i −0.00255383 0.00147445i
900900 50563.8 + 66187.9i 1.87273 + 2.45140i
901901 5476.58 3161.91i 0.202499 0.116913i
902902 7600.45 + 11401.2i 0.280562 + 0.420862i
903903 −1424.45 39306.9i −0.0524947 1.44856i
904904 −4409.48 22544.8i −0.162231 0.829455i
905905 37492.6 + 64939.1i 1.37712 + 2.38525i
906906 −20714.3 + 1335.50i −0.759589 + 0.0489725i
907907 −19169.5 11067.5i −0.701778 0.405172i 0.106231 0.994341i 0.466122π-0.466122\pi
−0.808009 + 0.589170i 0.799455π0.799455\pi
908908 2190.23 + 16915.2i 0.0800499 + 0.618228i
909909 34957.9i 1.27555i
910910 −1865.00 2589.28i −0.0679385 0.0943228i
911911 9718.26 0.353436 0.176718 0.984262i 0.443452π-0.443452\pi
0.176718 + 0.984262i 0.443452π0.443452\pi
912912 −6359.86 + 23336.6i −0.230917 + 0.847316i
913913 −13215.1 + 22889.3i −0.479033 + 0.829709i
914914 2305.68 + 35762.3i 0.0834409 + 1.29421i
915915 −55592.9 + 32096.6i −2.00857 + 1.15965i
916916 −13877.5 5782.95i −0.500573 0.208596i
917917 4766.10 8992.27i 0.171636 0.323829i
918918 4876.18 + 7314.60i 0.175314 + 0.262982i
919919 4150.94 + 7189.64i 0.148996 + 0.258068i 0.930857 0.365385i 0.119063π-0.119063\pi
−0.781861 + 0.623453i 0.785729π0.785729\pi
920920 −14344.9 + 41818.6i −0.514062 + 1.49861i
921921 33102.7 57335.5i 1.18433 2.05133i
922922 −6032.35 + 12199.6i −0.215472 + 0.435761i
923923 1476.86i 0.0526666i
924924 6825.82 + 40995.1i 0.243023 + 1.45957i
925925 38697.3i 1.37552i
926926 13240.2 + 6546.90i 0.469870 + 0.232337i
927927 −32207.9 + 55785.7i −1.14115 + 1.97653i
928928 −18550.1 16443.9i −0.656183 0.581677i
929929 −8647.88 14978.6i −0.305412 0.528989i 0.671941 0.740605i 0.265461π-0.265461\pi
−0.977353 + 0.211615i 0.932128π0.932128\pi
930930 219.515 146.336i 0.00773996 0.00515974i
931931 1147.75 + 15814.9i 0.0404038 + 0.556728i
932932 −10243.1 + 24580.6i −0.360004 + 0.863909i
933933 −3130.28 + 1807.27i −0.109840 + 0.0634161i
934934 34342.2 2214.12i 1.20312 0.0775677i
935935 9988.82 17301.1i 0.349379 0.605142i
936936 1835.07 + 2106.06i 0.0640825 + 0.0735455i
937937 −43100.4 −1.50270 −0.751350 0.659904i 0.770597π-0.770597\pi
−0.751350 + 0.659904i 0.770597π0.770597\pi
938938 49255.0 + 22172.9i 1.71453 + 0.771825i
939939 44929.3i 1.56146i
940940 −7039.60 54367.0i −0.244262 1.88644i
941941 −39293.0 22685.8i −1.36123 0.785904i −0.371439 0.928457i 0.621135π-0.621135\pi
−0.989787 + 0.142553i 0.954469π0.954469\pi
942942 3101.57 + 48107.0i 0.107277 + 1.66392i
943943 −7017.41 12154.5i −0.242331 0.419730i
944944 5268.70 5223.93i 0.181654 0.180111i
945945 −33749.3 17887.9i −1.16176 0.615759i
946946 20976.8 13983.9i 0.720946 0.480609i
947947 3279.36 1893.34i 0.112529 0.0649687i −0.442679 0.896680i 0.645972π-0.645972\pi
0.555208 + 0.831711i 0.312639π0.312639\pi
948948 −23490.9 + 17945.7i −0.804799 + 0.614820i
949949 2977.11 + 1718.84i 0.101835 + 0.0587943i
950950 −15148.0 + 30634.8i −0.517334 + 1.04623i
951951 −23548.1 −0.802942
952952 −12088.3 + 2822.41i −0.411540 + 0.0960871i
953953 7167.42 0.243626 0.121813 0.992553i 0.461129π-0.461129\pi
0.121813 + 0.992553i 0.461129π0.461129\pi
954954 10661.4 21561.3i 0.361821 0.731731i
955955 17018.0 + 9825.34i 0.576638 + 0.332922i
956956 −27801.1 36391.6i −0.940536 1.23116i
957957 −33266.1 + 19206.2i −1.12366 + 0.648744i
958958 −31879.7 + 21252.2i −1.07514 + 0.716730i
959959 −1244.25 34334.3i −0.0418966 1.15611i
960960 76212.7 30998.4i 2.56224 1.04216i
961961 14895.3 + 25799.5i 0.499994 + 0.866016i
962962 83.4989 + 1295.11i 0.00279845 + 0.0434055i
963963 −21678.3 12516.0i −0.725413 0.418817i
964964 −14629.2 + 1894.24i −0.488772 + 0.0632876i
965965 15996.4i 0.533620i
966966 −4275.39 42352.6i −0.142400 1.41064i
967967 41487.5 1.37968 0.689838 0.723963i 0.257682π-0.257682\pi
0.689838 + 0.723963i 0.257682π0.257682\pi
968968 2623.14 2285.62i 0.0870980 0.0758912i
969969 −5597.52 + 9695.19i −0.185571 + 0.321418i
970970 39185.9 2526.41i 1.29710 0.0836269i
971971 24879.2 14364.0i 0.822258 0.474731i −0.0289362 0.999581i 0.509212π-0.509212\pi
0.851195 + 0.524850i 0.175879π0.175879\pi
972972 −34065.3 14195.5i −1.12412 0.468438i
973973 −1483.45 2367.07i −0.0488768 0.0779905i
974974 16652.6 11101.2i 0.547826 0.365201i
975975 3311.00 + 5734.82i 0.108756 + 0.188371i
976976 6511.62 + 24723.1i 0.213557 + 0.810829i
977977 21126.3 36591.9i 0.691803 1.19824i −0.279444 0.960162i 0.590150π-0.590150\pi
0.971247 0.238075i 0.0765165π-0.0765165\pi
978978 −11251.2 5563.40i −0.367866 0.181900i
979979 42229.1i 1.37860i
980980 40378.4 35759.8i 1.31616 1.16562i
981981 18335.7i 0.596753i
982982 −8295.81 + 16777.1i −0.269582 + 0.545192i
983983 −2241.94 + 3883.16i −0.0727435 + 0.125995i −0.900103 0.435678i 0.856509π-0.856509\pi
0.827359 + 0.561673i 0.189842π0.189842\pi
984984 −8474.69 + 24705.6i −0.274556 + 0.800393i
985985 125.988 + 218.218i 0.00407545 + 0.00705889i
986986 −6364.14 9546.64i −0.205553 0.308344i
987987 28030.2 + 44726.5i 0.903963 + 1.44241i
988988 −440.869 + 1057.96i −0.0141963 + 0.0340671i
989989 −22362.8 + 12911.2i −0.719006 + 0.415118i
990990 −4888.89 75829.2i −0.156948 2.43435i
991991 −10162.7 + 17602.3i −0.325761 + 0.564235i −0.981666 0.190609i 0.938954π-0.938954\pi
0.655905 + 0.754844i 0.272287π0.272287\pi
992992 −33.2432 99.6745i −0.00106398 0.00319019i
993993 −31821.6 −1.01695
994994 24836.6 2507.19i 0.792525 0.0800033i
995995 2979.85i 0.0949422i
996996 −49963.0 + 6469.36i −1.58950 + 0.205813i
997997 14049.1 + 8111.27i 0.446279 + 0.257659i 0.706258 0.707955i 0.250382π-0.250382\pi
−0.259978 + 0.965614i 0.583715π0.583715\pi
998998 36652.6 2363.08i 1.16254 0.0749519i
999999 7767.41 + 13453.5i 0.245996 + 0.426077i
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 56.4.p.a.53.20 yes 44
4.3 odd 2 224.4.t.a.81.21 44
7.2 even 3 inner 56.4.p.a.37.11 44
8.3 odd 2 224.4.t.a.81.2 44
8.5 even 2 inner 56.4.p.a.53.11 yes 44
28.23 odd 6 224.4.t.a.177.2 44
56.37 even 6 inner 56.4.p.a.37.20 yes 44
56.51 odd 6 224.4.t.a.177.21 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.4.p.a.37.11 44 7.2 even 3 inner
56.4.p.a.37.20 yes 44 56.37 even 6 inner
56.4.p.a.53.11 yes 44 8.5 even 2 inner
56.4.p.a.53.20 yes 44 1.1 even 1 trivial
224.4.t.a.81.2 44 8.3 odd 2
224.4.t.a.81.21 44 4.3 odd 2
224.4.t.a.177.2 44 28.23 odd 6
224.4.t.a.177.21 44 56.51 odd 6