Properties

Label 126.3.i.a.65.6
Level 126126
Weight 33
Character 126.65
Analytic conductor 3.4333.433
Analytic rank 00
Dimension 3232
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,3,Mod(65,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.65");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 126=2327 126 = 2 \cdot 3^{2} \cdot 7
Weight: k k == 3 3
Character orbit: [χ][\chi] == 126.i (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: 3.433251330943.43325133094
Analytic rank: 00
Dimension: 3232
Relative dimension: 1616 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 65.6
Character χ\chi == 126.65
Dual form 126.3.i.a.95.6

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.22474+0.707107i)q2+(0.8940732.86367i)q3+(1.000001.73205i)q43.35218iq5+(0.929913+4.13948i)q6+(6.403952.82655i)q7+2.82843iq8+(7.401275.12067i)q9+(2.37035+4.10556i)q10+14.1890iq11+(4.065964.41225i)q12+(8.3190814.4091i)q13+(9.841881.06647i)q14+(9.599542.99709i)q15+(2.000003.46410i)q16+(13.5532+7.82495i)q17+(12.6855+1.03802i)q18+(17.316229.9925i)q19+(5.806143.35218i)q20+(13.8199+15.8117i)q21+(10.033117.3779i)q2226.2640iq23+(8.09970+2.52882i)q24+13.7629q25+(20.3775+11.7650i)q26+(21.2812+16.6166i)q27+(11.2997+8.26542i)q28+(18.2368+10.5290i)q29+(13.87633.11723i)q30+(16.873829.2264i)q31+(4.89898+2.82843i)q32+(40.6326+12.6860i)q33+(11.066219.1671i)q34+(9.47510+21.4672i)q35+(16.2705+7.69871i)q36+(31.9815+55.3936i)q37+48.9776iq38+(48.7008+10.9404i)q39+9.48139q40+(5.442003.14194i)q41+(5.7453229.1375i)q42+(0.07426270.128627i)q43+(24.5760+14.1890i)q44+(17.1654+24.8104i)q45+(18.5715+32.1667i)q46+(36.355220.9897i)q47+(11.7082+2.63019i)q48+(33.0212+36.2022i)q49+(16.8561+9.73185i)q50+(10.2906+45.8081i)q5133.2763q52+(38.607422.2900i)q53+(14.314335.3991i)q54+47.5639q55+(7.9946918.1131i)q56+(70.406976.4034i)q5729.7805q58+(35.9038+20.7290i)q59+(14.7907+13.6298i)q60+(7.9997613.8560i)q61+47.7264iq62+(32.9235+53.7126i)q638.00000q64+(48.3018+27.8870i)q65+(58.7349+13.1945i)q66+(42.662573.8936i)q67+31.2998iq68+(75.211623.4819i)q69+(3.5750132.9917i)q7056.4376iq71+(14.483420.9339i)q72+(4.42855+7.67047i)q7390.4573iq74+(12.305039.4125i)q75+(34.632459.9850i)q76+(40.105890.8654i)q77+(51.910047.8358i)q78+(14.570425.2366i)q79+(11.6123+6.70435i)q80+(28.5576+75.7989i)q81+(4.44338+7.69616i)q82+(48.853128.2054i)q83+(13.5667+39.7485i)q84+(26.2306+45.4328i)q85+0.210047iq86+(46.456742.8105i)q8740.1324q88+(5.43082+3.13549i)q89+(3.4796342.5241i)q90+(12.5470+115.789i)q91+(45.490626.2640i)q92+(68.608374.4517i)q93+(29.6839+51.4141i)q94+(100.54058.0469i)q95+(12.479711.5003i)q96+(32.1934+55.7605i)q97+(66.041420.9889i)q98+(72.6569105.016i)q99+O(q100)q+(-1.22474 + 0.707107i) q^{2} +(0.894073 - 2.86367i) q^{3} +(1.00000 - 1.73205i) q^{4} -3.35218i q^{5} +(0.929913 + 4.13948i) q^{6} +(-6.40395 - 2.82655i) q^{7} +2.82843i q^{8} +(-7.40127 - 5.12067i) q^{9} +(2.37035 + 4.10556i) q^{10} +14.1890i q^{11} +(-4.06596 - 4.41225i) q^{12} +(-8.31908 - 14.4091i) q^{13} +(9.84188 - 1.06647i) q^{14} +(-9.59954 - 2.99709i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-13.5532 + 7.82495i) q^{17} +(12.6855 + 1.03802i) q^{18} +(17.3162 - 29.9925i) q^{19} +(-5.80614 - 3.35218i) q^{20} +(-13.8199 + 15.8117i) q^{21} +(-10.0331 - 17.3779i) q^{22} -26.2640i q^{23} +(8.09970 + 2.52882i) q^{24} +13.7629 q^{25} +(20.3775 + 11.7650i) q^{26} +(-21.2812 + 16.6166i) q^{27} +(-11.2997 + 8.26542i) q^{28} +(18.2368 + 10.5290i) q^{29} +(13.8763 - 3.11723i) q^{30} +(16.8738 - 29.2264i) q^{31} +(4.89898 + 2.82843i) q^{32} +(40.6326 + 12.6860i) q^{33} +(11.0662 - 19.1671i) q^{34} +(-9.47510 + 21.4672i) q^{35} +(-16.2705 + 7.69871i) q^{36} +(-31.9815 + 55.3936i) q^{37} +48.9776i q^{38} +(-48.7008 + 10.9404i) q^{39} +9.48139 q^{40} +(5.44200 - 3.14194i) q^{41} +(5.74532 - 29.1375i) q^{42} +(0.0742627 - 0.128627i) q^{43} +(24.5760 + 14.1890i) q^{44} +(-17.1654 + 24.8104i) q^{45} +(18.5715 + 32.1667i) q^{46} +(36.3552 - 20.9897i) q^{47} +(-11.7082 + 2.63019i) q^{48} +(33.0212 + 36.2022i) q^{49} +(-16.8561 + 9.73185i) q^{50} +(10.2906 + 45.8081i) q^{51} -33.2763 q^{52} +(38.6074 - 22.2900i) q^{53} +(14.3143 - 35.3991i) q^{54} +47.5639 q^{55} +(7.99469 - 18.1131i) q^{56} +(-70.4069 - 76.4034i) q^{57} -29.7805 q^{58} +(35.9038 + 20.7290i) q^{59} +(-14.7907 + 13.6298i) q^{60} +(-7.99976 - 13.8560i) q^{61} +47.7264i q^{62} +(32.9235 + 53.7126i) q^{63} -8.00000 q^{64} +(-48.3018 + 27.8870i) q^{65} +(-58.7349 + 13.1945i) q^{66} +(42.6625 - 73.8936i) q^{67} +31.2998i q^{68} +(-75.2116 - 23.4819i) q^{69} +(-3.57501 - 32.9917i) q^{70} -56.4376i q^{71} +(14.4834 - 20.9339i) q^{72} +(4.42855 + 7.67047i) q^{73} -90.4573i q^{74} +(12.3050 - 39.4125i) q^{75} +(-34.6324 - 59.9850i) q^{76} +(40.1058 - 90.8654i) q^{77} +(51.9100 - 47.8358i) q^{78} +(-14.5704 - 25.2366i) q^{79} +(-11.6123 + 6.70435i) q^{80} +(28.5576 + 75.7989i) q^{81} +(-4.44338 + 7.69616i) q^{82} +(-48.8531 - 28.2054i) q^{83} +(13.5667 + 39.7485i) q^{84} +(26.2306 + 45.4328i) q^{85} +0.210047i q^{86} +(46.4567 - 42.8105i) q^{87} -40.1324 q^{88} +(5.43082 + 3.13549i) q^{89} +(3.47963 - 42.5241i) q^{90} +(12.5470 + 115.789i) q^{91} +(-45.4906 - 26.2640i) q^{92} +(-68.6083 - 74.4517i) q^{93} +(-29.6839 + 51.4141i) q^{94} +(-100.540 - 58.0469i) q^{95} +(12.4797 - 11.5003i) q^{96} +(-32.1934 + 55.7605i) q^{97} +(-66.0414 - 20.9889i) q^{98} +(72.6569 - 105.016i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+32q4+8q6+2q7+4q9+10q13+36q14+10q1564q16+54q17+24q18+28q19+16q21+8q24160q25+72q26126q274q28++394q99+O(q100) 32 q + 32 q^{4} + 8 q^{6} + 2 q^{7} + 4 q^{9} + 10 q^{13} + 36 q^{14} + 10 q^{15} - 64 q^{16} + 54 q^{17} + 24 q^{18} + 28 q^{19} + 16 q^{21} + 8 q^{24} - 160 q^{25} + 72 q^{26} - 126 q^{27} - 4 q^{28}+ \cdots + 394 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/126Z)×\left(\mathbb{Z}/126\mathbb{Z}\right)^\times.

nn 2929 7373
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.22474 + 0.707107i −0.612372 + 0.353553i
33 0.894073 2.86367i 0.298024 0.954558i
44 1.00000 1.73205i 0.250000 0.433013i
55 3.35218i 0.670435i −0.942141 0.335218i 0.891190π-0.891190\pi
0.942141 0.335218i 0.108810π-0.108810\pi
66 0.929913 + 4.13948i 0.154986 + 0.689913i
77 −6.40395 2.82655i −0.914850 0.403793i
88 2.82843i 0.353553i
99 −7.40127 5.12067i −0.822363 0.568963i
1010 2.37035 + 4.10556i 0.237035 + 0.410556i
1111 14.1890i 1.28991i 0.764222 + 0.644953i 0.223123π0.223123\pi
−0.764222 + 0.644953i 0.776877π0.776877\pi
1212 −4.06596 4.41225i −0.338830 0.367688i
1313 −8.31908 14.4091i −0.639930 1.10839i −0.985448 0.169978i 0.945630π-0.945630\pi
0.345518 0.938412i 0.387703π-0.387703\pi
1414 9.84188 1.06647i 0.702992 0.0761767i
1515 −9.59954 2.99709i −0.639970 0.199806i
1616 −2.00000 3.46410i −0.125000 0.216506i
1717 −13.5532 + 7.82495i −0.797248 + 0.460291i −0.842508 0.538684i 0.818922π-0.818922\pi
0.0452601 + 0.998975i 0.485588π0.485588\pi
1818 12.6855 + 1.03802i 0.704751 + 0.0576679i
1919 17.3162 29.9925i 0.911378 1.57855i 0.0992583 0.995062i 0.468353π-0.468353\pi
0.812120 0.583491i 0.198314π-0.198314\pi
2020 −5.80614 3.35218i −0.290307 0.167609i
2121 −13.8199 + 15.8117i −0.658092 + 0.752938i
2222 −10.0331 17.3779i −0.456050 0.789903i
2323 26.2640i 1.14191i −0.820980 0.570956i 0.806572π-0.806572\pi
0.820980 0.570956i 0.193428π-0.193428\pi
2424 8.09970 + 2.52882i 0.337487 + 0.105367i
2525 13.7629 0.550517
2626 20.3775 + 11.7650i 0.783750 + 0.452499i
2727 −21.2812 + 16.6166i −0.788192 + 0.615429i
2828 −11.2997 + 8.26542i −0.403560 + 0.295194i
2929 18.2368 + 10.5290i 0.628855 + 0.363069i 0.780308 0.625395i 0.215062π-0.215062\pi
−0.151454 + 0.988464i 0.548395π0.548395\pi
3030 13.8763 3.11723i 0.462542 0.103908i
3131 16.8738 29.2264i 0.544317 0.942785i −0.454332 0.890832i 0.650122π-0.650122\pi
0.998650 0.0519531i 0.0165446π-0.0165446\pi
3232 4.89898 + 2.82843i 0.153093 + 0.0883883i
3333 40.6326 + 12.6860i 1.23129 + 0.384423i
3434 11.0662 19.1671i 0.325475 0.563739i
3535 −9.47510 + 21.4672i −0.270717 + 0.613348i
3636 −16.2705 + 7.69871i −0.451959 + 0.213853i
3737 −31.9815 + 55.3936i −0.864365 + 1.49712i 0.00331203 + 0.999995i 0.498946π0.498946\pi
−0.867677 + 0.497129i 0.834388π0.834388\pi
3838 48.9776i 1.28888i
3939 −48.7008 + 10.9404i −1.24874 + 0.280523i
4040 9.48139 0.237035
4141 5.44200 3.14194i 0.132732 0.0766328i −0.432164 0.901795i 0.642250π-0.642250\pi
0.564896 + 0.825162i 0.308916π0.308916\pi
4242 5.74532 29.1375i 0.136793 0.693749i
4343 0.0742627 0.128627i 0.00172704 0.00299132i −0.865161 0.501495i 0.832784π-0.832784\pi
0.866888 + 0.498504i 0.166117π0.166117\pi
4444 24.5760 + 14.1890i 0.558545 + 0.322476i
4545 −17.1654 + 24.8104i −0.381453 + 0.551341i
4646 18.5715 + 32.1667i 0.403727 + 0.699276i
4747 36.3552 20.9897i 0.773516 0.446590i −0.0606115 0.998161i 0.519305π-0.519305\pi
0.834127 + 0.551572i 0.185972π0.185972\pi
4848 −11.7082 + 2.63019i −0.243921 + 0.0547957i
4949 33.0212 + 36.2022i 0.673902 + 0.738820i
5050 −16.8561 + 9.73185i −0.337121 + 0.194637i
5151 10.2906 + 45.8081i 0.201776 + 0.898197i
5252 −33.2763 −0.639930
5353 38.6074 22.2900i 0.728442 0.420566i −0.0894100 0.995995i 0.528498π-0.528498\pi
0.817852 + 0.575429i 0.195165π0.195165\pi
5454 14.3143 35.3991i 0.265080 0.655540i
5555 47.5639 0.864798
5656 7.99469 18.1131i 0.142762 0.323448i
5757 −70.4069 76.4034i −1.23521 1.34041i
5858 −29.7805 −0.513458
5959 35.9038 + 20.7290i 0.608538 + 0.351340i 0.772393 0.635145i 0.219060π-0.219060\pi
−0.163855 + 0.986484i 0.552393π0.552393\pi
6060 −14.7907 + 13.6298i −0.246511 + 0.227163i
6161 −7.99976 13.8560i −0.131144 0.227147i 0.792974 0.609255i 0.208532π-0.208532\pi
−0.924118 + 0.382108i 0.875198π0.875198\pi
6262 47.7264i 0.769781i
6363 32.9235 + 53.7126i 0.522596 + 0.852580i
6464 −8.00000 −0.125000
6565 −48.3018 + 27.8870i −0.743104 + 0.429031i
6666 −58.7349 + 13.1945i −0.889922 + 0.199917i
6767 42.6625 73.8936i 0.636753 1.10289i −0.349387 0.936978i 0.613610π-0.613610\pi
0.986141 0.165911i 0.0530564π-0.0530564\pi
6868 31.2998i 0.460291i
6969 −75.2116 23.4819i −1.09002 0.340318i
7070 −3.57501 32.9917i −0.0510716 0.471310i
7171 56.4376i 0.794896i −0.917625 0.397448i 0.869896π-0.869896\pi
0.917625 0.397448i 0.130104π-0.130104\pi
7272 14.4834 20.9339i 0.201159 0.290749i
7373 4.42855 + 7.67047i 0.0606650 + 0.105075i 0.894763 0.446542i 0.147345π-0.147345\pi
−0.834098 + 0.551617i 0.814011π0.814011\pi
7474 90.4573i 1.22240i
7575 12.3050 39.4125i 0.164067 0.525500i
7676 −34.6324 59.9850i −0.455689 0.789276i
7777 40.1058 90.8654i 0.520855 1.18007i
7878 51.9100 47.8358i 0.665513 0.613280i
7979 −14.5704 25.2366i −0.184435 0.319451i 0.758951 0.651148i 0.225712π-0.225712\pi
−0.943386 + 0.331697i 0.892379π0.892379\pi
8080 −11.6123 + 6.70435i −0.145153 + 0.0838044i
8181 28.5576 + 75.7989i 0.352562 + 0.935788i
8282 −4.44338 + 7.69616i −0.0541875 + 0.0938556i
8383 −48.8531 28.2054i −0.588592 0.339824i 0.175949 0.984399i 0.443701π-0.443701\pi
−0.764540 + 0.644576i 0.777034π0.777034\pi
8484 13.5667 + 39.7485i 0.161509 + 0.473196i
8585 26.2306 + 45.4328i 0.308595 + 0.534503i
8686 0.210047i 0.00244240i
8787 46.4567 42.8105i 0.533985 0.492075i
8888 −40.1324 −0.456050
8989 5.43082 + 3.13549i 0.0610205 + 0.0352302i 0.530200 0.847873i 0.322117π-0.322117\pi
−0.469179 + 0.883103i 0.655450π0.655450\pi
9090 3.47963 42.5241i 0.0386626 0.472490i
9191 12.5470 + 115.789i 0.137879 + 1.27241i
9292 −45.4906 26.2640i −0.494463 0.285478i
9393 −68.6083 74.4517i −0.737724 0.800556i
9494 −29.6839 + 51.4141i −0.315787 + 0.546958i
9595 −100.540 58.0469i −1.05832 0.611020i
9696 12.4797 11.5003i 0.129997 0.119794i
9797 −32.1934 + 55.7605i −0.331890 + 0.574851i −0.982883 0.184233i 0.941020π-0.941020\pi
0.650992 + 0.759084i 0.274353π0.274353\pi
9898 −66.0414 20.9889i −0.673892 0.214173i
9999 72.6569 105.016i 0.733908 1.06077i
100100 13.7629 23.8381i 0.137629 0.238381i
101101 93.2173i 0.922943i 0.887155 + 0.461472i 0.152678π0.152678\pi
−0.887155 + 0.461472i 0.847322π0.847322\pi
102102 −44.9945 48.8267i −0.441123 0.478693i
103103 129.105 1.25344 0.626721 0.779243i 0.284396π-0.284396\pi
0.626721 + 0.779243i 0.284396π0.284396\pi
104104 40.7550 23.5299i 0.391875 0.226249i
105105 53.0036 + 46.3268i 0.504796 + 0.441208i
106106 −31.5228 + 54.5991i −0.297385 + 0.515086i
107107 −92.8758 53.6219i −0.867998 0.501139i −0.00131550 0.999999i 0.500419π-0.500419\pi
−0.866682 + 0.498860i 0.833752π0.833752\pi
108108 7.49957 + 53.4767i 0.0694404 + 0.495155i
109109 −16.5505 28.6662i −0.151839 0.262993i 0.780064 0.625699i 0.215186π-0.215186\pi
−0.931904 + 0.362706i 0.881853π0.881853\pi
110110 −58.2536 + 33.6328i −0.529579 + 0.305752i
111111 130.035 + 141.110i 1.17149 + 1.27127i
112112 3.01644 + 27.8370i 0.0269325 + 0.248545i
113113 −146.122 + 84.3635i −1.29311 + 0.746580i −0.979205 0.202874i 0.934972π-0.934972\pi
−0.313909 + 0.949453i 0.601639π0.601639\pi
114114 140.256 + 43.7895i 1.23031 + 0.384118i
115115 −88.0416 −0.765579
116116 36.4736 21.0580i 0.314427 0.181535i
117117 −12.2123 + 149.245i −0.104379 + 1.27560i
118118 −58.6306 −0.496869
119119 108.912 11.8018i 0.915225 0.0991745i
120120 8.47705 27.1516i 0.0706421 0.226263i
121121 −80.3266 −0.663856
122122 19.5953 + 11.3134i 0.160618 + 0.0927326i
123123 −4.13196 18.3933i −0.0335931 0.149539i
124124 −33.7477 58.4527i −0.272159 0.471393i
125125 129.940i 1.03952i
126126 −78.3035 42.5037i −0.621456 0.337331i
127127 75.2845 0.592792 0.296396 0.955065i 0.404215π-0.404215\pi
0.296396 + 0.955065i 0.404215π0.404215\pi
128128 9.79796 5.65685i 0.0765466 0.0441942i
129129 −0.301949 0.327666i −0.00234069 0.00254004i
130130 39.4382 68.3090i 0.303371 0.525454i
131131 156.493i 1.19461i 0.802015 + 0.597303i 0.203761π0.203761\pi
−0.802015 + 0.597303i 0.796239π0.796239\pi
132132 62.6053 57.6917i 0.474283 0.437058i
133133 −195.667 + 143.125i −1.47118 + 1.07613i
134134 120.668i 0.900505i
135135 55.7017 + 71.3383i 0.412605 + 0.528432i
136136 −22.1323 38.3343i −0.162738 0.281870i
137137 82.6934i 0.603601i −0.953371 0.301801i 0.902412π-0.902412\pi
0.953371 0.301801i 0.0975877π-0.0975877\pi
138138 108.719 24.4232i 0.787820 0.176980i
139139 50.4535 + 87.3880i 0.362975 + 0.628690i 0.988449 0.151554i 0.0484279π-0.0484279\pi
−0.625474 + 0.780245i 0.715095π0.715095\pi
140140 27.7071 + 37.8785i 0.197908 + 0.270561i
141141 −27.6035 122.876i −0.195769 0.871461i
142142 39.9074 + 69.1217i 0.281038 + 0.486772i
143143 204.450 118.039i 1.42972 0.825449i
144144 −2.93597 + 35.8801i −0.0203887 + 0.249167i
145145 35.2951 61.1329i 0.243415 0.421606i
146146 −10.8477 6.26291i −0.0742992 0.0428967i
147147 133.195 62.1946i 0.906086 0.423093i
148148 63.9630 + 110.787i 0.432182 + 0.748562i
149149 120.298i 0.807370i −0.914898 0.403685i 0.867729π-0.867729\pi
0.914898 0.403685i 0.132271π-0.132271\pi
150150 12.7983 + 56.9712i 0.0853221 + 0.379808i
151151 73.7142 0.488174 0.244087 0.969753i 0.421512π-0.421512\pi
0.244087 + 0.969753i 0.421512π0.421512\pi
152152 84.8316 + 48.9776i 0.558103 + 0.322221i
153153 140.380 + 11.4869i 0.917516 + 0.0750779i
154154 15.1322 + 139.646i 0.0982608 + 0.906793i
155155 −97.9719 56.5641i −0.632077 0.364930i
156156 −29.7515 + 95.2926i −0.190714 + 0.610850i
157157 131.796 228.277i 0.839463 1.45399i −0.0508817 0.998705i 0.516203π-0.516203\pi
0.890344 0.455287i 0.150464π-0.150464\pi
158158 35.6900 + 20.6056i 0.225886 + 0.130415i
159159 −29.3135 130.488i −0.184362 0.820679i
160160 9.48139 16.4222i 0.0592587 0.102639i
161161 −74.2365 + 168.193i −0.461097 + 1.04468i
162162 −88.5736 72.6410i −0.546751 0.448401i
163163 −36.3832 + 63.0176i −0.223210 + 0.386611i −0.955781 0.294080i 0.904987π-0.904987\pi
0.732571 + 0.680691i 0.238320π0.238320\pi
164164 12.5678i 0.0766328i
165165 42.5256 136.208i 0.257731 0.825500i
166166 79.7768 0.480583
167167 −172.653 + 99.6811i −1.03385 + 0.596893i −0.918085 0.396384i 0.870265π-0.870265\pi
−0.115764 + 0.993277i 0.536932π0.536932\pi
168168 −44.7222 39.0886i −0.266204 0.232670i
169169 −53.9143 + 93.3824i −0.319020 + 0.552558i
170170 −64.2516 37.0957i −0.377951 0.218210i
171171 −281.743 + 133.312i −1.64762 + 0.779603i
172172 −0.148525 0.257253i −0.000863519 0.00149566i
173173 −216.071 + 124.749i −1.24897 + 0.721090i −0.970903 0.239473i 0.923025π-0.923025\pi
−0.278062 + 0.960563i 0.589692π0.589692\pi
174174 −26.6260 + 85.2818i −0.153023 + 0.490125i
175175 −88.1370 38.9016i −0.503640 0.222295i
176176 49.1520 28.3779i 0.279273 0.161238i
177177 91.4618 84.2834i 0.516733 0.476177i
178178 −8.86850 −0.0498230
179179 −178.420 + 103.011i −0.996760 + 0.575479i −0.907288 0.420510i 0.861851π-0.861851\pi
−0.0894717 + 0.995989i 0.528518π0.528518\pi
180180 25.8074 + 54.5417i 0.143375 + 0.303009i
181181 −68.0662 −0.376056 −0.188028 0.982164i 0.560210π-0.560210\pi
−0.188028 + 0.982164i 0.560210π0.560210\pi
182182 −97.2423 132.940i −0.534299 0.730441i
183183 −46.8314 + 10.5205i −0.255909 + 0.0574888i
184184 74.2858 0.403727
185185 185.689 + 107.208i 1.00372 + 0.579501i
186186 136.673 + 42.6709i 0.734801 + 0.229413i
187187 −111.028 192.306i −0.593732 1.02837i
188188 83.9588i 0.446590i
189189 183.251 46.2594i 0.969584 0.244759i
190190 164.181 0.864113
191191 223.558 129.071i 1.17046 0.675765i 0.216671 0.976245i 0.430480π-0.430480\pi
0.953788 + 0.300480i 0.0971467π0.0971467\pi
192192 −7.15258 + 22.9094i −0.0372530 + 0.119320i
193193 −79.8002 + 138.218i −0.413473 + 0.716156i −0.995267 0.0971803i 0.969018π-0.969018\pi
0.581794 + 0.813336i 0.302351π0.302351\pi
194194 91.0566i 0.469364i
195195 36.6741 + 163.254i 0.188072 + 0.837198i
196196 95.7253 20.9922i 0.488394 0.107103i
197197 173.797i 0.882219i −0.897453 0.441109i 0.854585π-0.854585\pi
0.897453 0.441109i 0.145415π-0.145415\pi
198198 −14.7285 + 179.994i −0.0743862 + 0.909063i
199199 48.3082 + 83.6723i 0.242755 + 0.420464i 0.961498 0.274812i 0.0886156π-0.0886156\pi
−0.718743 + 0.695276i 0.755282π0.755282\pi
200200 38.9274i 0.194637i
201201 −173.464 188.238i −0.863004 0.936506i
202202 −65.9146 114.167i −0.326310 0.565185i
203203 −87.0267 118.974i −0.428703 0.586081i
204204 89.6325 + 27.9843i 0.439375 + 0.137178i
205205 −10.5323 18.2426i −0.0513773 0.0889881i
206206 −158.120 + 91.2907i −0.767574 + 0.443159i
207207 −134.489 + 194.387i −0.649706 + 0.939067i
208208 −33.2763 + 57.6363i −0.159982 + 0.277098i
209209 425.562 + 245.699i 2.03618 + 1.17559i
210210 −97.6739 19.2593i −0.465114 0.0917111i
211211 8.68169 + 15.0371i 0.0411455 + 0.0712660i 0.885865 0.463944i 0.153566π-0.153566\pi
−0.844719 + 0.535210i 0.820233π0.820233\pi
212212 89.1600i 0.420566i
213213 −161.619 50.4593i −0.758774 0.236898i
214214 151.666 0.708717
215215 −0.431179 0.248942i −0.00200549 0.00115787i
216216 −46.9988 60.1923i −0.217587 0.278668i
217217 −190.669 + 139.469i −0.878659 + 0.642716i
218218 40.5402 + 23.4059i 0.185964 + 0.107366i
219219 25.9252 5.82397i 0.118380 0.0265934i
220220 47.5639 82.3831i 0.216200 0.374469i
221221 225.501 + 130.193i 1.02036 + 0.589108i
222222 −259.040 80.8754i −1.16685 0.364304i
223223 147.273 255.085i 0.660418 1.14388i −0.320088 0.947388i 0.603713π-0.603713\pi
0.980506 0.196489i 0.0629541π-0.0629541\pi
224224 −23.3781 31.9603i −0.104367 0.142680i
225225 −101.863 70.4753i −0.452725 0.313223i
226226 119.308 206.648i 0.527912 0.914370i
227227 224.271i 0.987976i −0.869469 0.493988i 0.835539π-0.835539\pi
0.869469 0.493988i 0.164461π-0.164461\pi
228228 −202.741 + 45.5449i −0.889217 + 0.199758i
229229 −103.470 −0.451833 −0.225916 0.974147i 0.572538π-0.572538\pi
−0.225916 + 0.974147i 0.572538π0.572538\pi
230230 107.828 62.2548i 0.468819 0.270673i
231231 −224.352 196.090i −0.971219 0.848876i
232232 −29.7805 + 51.5814i −0.128364 + 0.222334i
233233 187.439 + 108.218i 0.804457 + 0.464454i 0.845027 0.534723i 0.179584π-0.179584\pi
−0.0405700 + 0.999177i 0.512917π0.512917\pi
234234 −90.5750 191.422i −0.387073 0.818043i
235235 −70.3612 121.869i −0.299409 0.518592i
236236 71.8075 41.4581i 0.304269 0.175670i
237237 −85.2965 + 19.1614i −0.359901 + 0.0808500i
238238 −125.044 + 91.4664i −0.525395 + 0.384313i
239239 −387.074 + 223.477i −1.61956 + 0.935052i −0.632524 + 0.774541i 0.717981π0.717981\pi
−0.987034 + 0.160511i 0.948686π0.948686\pi
240240 8.81687 + 39.2480i 0.0367369 + 0.163533i
241241 −82.7511 −0.343365 −0.171683 0.985152i 0.554920π-0.554920\pi
−0.171683 + 0.985152i 0.554920π0.554920\pi
242242 98.3796 56.7995i 0.406527 0.234709i
243243 242.596 14.0099i 0.998337 0.0576538i
244244 −31.9991 −0.131144
245245 121.356 110.693i 0.495331 0.451808i
246246 18.0666 + 19.6053i 0.0734414 + 0.0796964i
247247 −576.219 −2.33287
248248 82.6646 + 47.7264i 0.333325 + 0.192445i
249249 −124.449 + 114.682i −0.499796 + 0.460569i
250250 91.8815 + 159.143i 0.367526 + 0.636574i
251251 228.368i 0.909831i −0.890535 0.454916i 0.849669π-0.849669\pi
0.890535 0.454916i 0.150331π-0.150331\pi
252252 125.956 3.31269i 0.499827 0.0131456i
253253 372.659 1.47296
254254 −92.2044 + 53.2342i −0.363009 + 0.209584i
255255 153.557 34.4958i 0.602183 0.135278i
256256 −8.00000 + 13.8564i −0.0312500 + 0.0541266i
257257 76.6580i 0.298280i −0.988816 0.149140i 0.952349π-0.952349\pi
0.988816 0.149140i 0.0476505π-0.0476505\pi
258258 0.601505 + 0.187797i 0.00233142 + 0.000727895i
259259 361.381 264.340i 1.39529 1.02062i
260260 111.548i 0.429031i
261261 −81.0598 171.313i −0.310574 0.656370i
262262 −110.658 191.665i −0.422357 0.731544i
263263 354.445i 1.34770i 0.738869 + 0.673849i 0.235360π0.235360\pi
−0.738869 + 0.673849i 0.764640π0.764640\pi
264264 −35.8813 + 114.926i −0.135914 + 0.435327i
265265 −74.7200 129.419i −0.281962 0.488373i
266266 138.438 313.650i 0.520442 1.17913i
267267 13.8346 12.7488i 0.0518149 0.0477482i
268268 −85.3249 147.787i −0.318377 0.551445i
269269 87.8658 50.7294i 0.326639 0.188585i −0.327709 0.944779i 0.606277π-0.606277\pi
0.654348 + 0.756194i 0.272943π0.272943\pi
270270 −118.664 47.9842i −0.439497 0.177719i
271271 −37.9220 + 65.6829i −0.139934 + 0.242372i −0.927471 0.373894i 0.878022π-0.878022\pi
0.787538 + 0.616267i 0.211356π0.211356\pi
272272 54.2129 + 31.2998i 0.199312 + 0.115073i
273273 342.801 + 67.5935i 1.25568 + 0.247595i
274274 58.4731 + 101.278i 0.213405 + 0.369629i
275275 195.281i 0.710114i
276276 −115.883 + 106.788i −0.419868 + 0.386914i
277277 268.121 0.967946 0.483973 0.875083i 0.339193π-0.339193\pi
0.483973 + 0.875083i 0.339193π0.339193\pi
278278 −123.585 71.3520i −0.444551 0.256662i
279279 −274.546 + 129.907i −0.984037 + 0.465616i
280280 −60.7183 26.7996i −0.216851 0.0957130i
281281 423.951 + 244.768i 1.50872 + 0.871060i 0.999948 + 0.0101594i 0.00323390π0.00323390\pi
0.508773 + 0.860901i 0.330099π0.330099\pi
282282 120.694 + 130.973i 0.427992 + 0.464443i
283283 261.618 453.136i 0.924446 1.60119i 0.131997 0.991250i 0.457861π-0.457861\pi
0.792449 0.609938i 0.208806π-0.208806\pi
284284 −97.7528 56.4376i −0.344200 0.198724i
285285 −256.118 + 236.016i −0.898658 + 0.828127i
286286 −166.933 + 289.136i −0.583680 + 1.01096i
287287 −43.7312 + 4.73875i −0.152374 + 0.0165113i
288288 −21.7752 46.0200i −0.0756084 0.159792i
289289 −22.0403 + 38.1749i −0.0762639 + 0.132093i
290290 99.8296i 0.344240i
291291 130.897 + 142.045i 0.449817 + 0.488128i
292292 17.7142 0.0606650
293293 64.1639 37.0450i 0.218989 0.126434i −0.386493 0.922292i 0.626314π-0.626314\pi
0.605482 + 0.795859i 0.292980π0.292980\pi
294294 −119.151 + 170.355i −0.405276 + 0.579440i
295295 69.4874 120.356i 0.235551 0.407985i
296296 −156.677 90.4573i −0.529313 0.305599i
297297 −235.772 301.958i −0.793845 1.01669i
298298 85.0636 + 147.334i 0.285448 + 0.494411i
299299 −378.440 + 218.492i −1.26569 + 0.730744i
300300 −55.9594 60.7255i −0.186531 0.202418i
301301 −0.839145 + 0.613812i −0.00278786 + 0.00203924i
302302 −90.2811 + 52.1238i −0.298944 + 0.172596i
303303 266.944 + 83.3430i 0.881003 + 0.275059i
304304 −138.529 −0.455689
305305 −46.4477 + 26.8166i −0.152288 + 0.0879233i
306306 −180.052 + 85.1951i −0.588405 + 0.278415i
307307 −159.112 −0.518280 −0.259140 0.965840i 0.583439π-0.583439\pi
−0.259140 + 0.965840i 0.583439π0.583439\pi
308308 −117.278 160.331i −0.380772 0.520554i
309309 115.429 369.714i 0.373556 1.19648i
310310 159.987 0.516088
311311 386.729 + 223.278i 1.24350 + 0.717936i 0.969805 0.243880i 0.0784204π-0.0784204\pi
0.273696 + 0.961816i 0.411754π0.411754\pi
312312 −30.9441 137.747i −0.0991798 0.441496i
313313 98.1534 + 170.007i 0.313589 + 0.543152i 0.979137 0.203203i 0.0651352π-0.0651352\pi
−0.665548 + 0.746355i 0.731802π0.731802\pi
314314 372.774i 1.18718i
315315 180.054 110.366i 0.571600 0.350367i
316316 −58.2815 −0.184435
317317 295.123 170.389i 0.930987 0.537506i 0.0438635 0.999038i 0.486033π-0.486033\pi
0.887124 + 0.461532i 0.152700π0.152700\pi
318318 128.170 + 139.087i 0.403052 + 0.437380i
319319 −149.396 + 258.761i −0.468325 + 0.811163i
320320 26.8174i 0.0838044i
321321 −236.593 + 218.024i −0.737051 + 0.679203i
322322 −28.0099 258.487i −0.0869872 0.802755i
323323 541.993i 1.67800i
324324 159.845 + 26.3357i 0.493349 + 0.0812831i
325325 −114.495 198.311i −0.352292 0.610187i
326326 102.907i 0.315667i
327327 −96.8881 + 21.7654i −0.296294 + 0.0665610i
328328 8.88676 + 15.3923i 0.0270938 + 0.0469278i
329329 −292.146 + 31.6571i −0.887981 + 0.0962223i
330330 44.2303 + 196.890i 0.134031 + 0.596635i
331331 281.789 + 488.072i 0.851326 + 1.47454i 0.880012 + 0.474951i 0.157534π0.157534\pi
−0.0286868 + 0.999588i 0.509133π0.509133\pi
332332 −97.7062 + 56.4107i −0.294296 + 0.169912i
333333 520.356 246.216i 1.56263 0.739388i
334334 140.970 244.168i 0.422067 0.731041i
335335 −247.704 143.012i −0.739416 0.426902i
336336 82.4132 + 16.2502i 0.245277 + 0.0483638i
337337 303.340 + 525.401i 0.900119 + 1.55905i 0.827338 + 0.561704i 0.189854π0.189854\pi
0.0727808 + 0.997348i 0.476813π0.476813\pi
338338 152.493i 0.451162i
339339 110.946 + 493.873i 0.327275 + 1.45685i
340340 104.922 0.308595
341341 414.692 + 239.422i 1.21610 + 0.702118i
342342 250.798 362.496i 0.733327 1.05993i
343343 −109.139 325.173i −0.318189 0.948027i
344344 0.363811 + 0.210047i 0.00105759 + 0.000610600i
345345 −78.7155 + 252.122i −0.228161 + 0.730790i
346346 176.421 305.570i 0.509888 0.883152i
347347 −45.3661 26.1921i −0.130738 0.0754816i 0.433205 0.901296i 0.357383π-0.357383\pi
−0.563943 + 0.825814i 0.690716π0.690716\pi
348348 −27.6933 123.276i −0.0795785 0.354241i
349349 −4.33946 + 7.51616i −0.0124340 + 0.0215363i −0.872175 0.489193i 0.837291π-0.837291\pi
0.859741 + 0.510729i 0.170625π0.170625\pi
350350 135.453 14.6778i 0.387008 0.0419365i
351351 416.470 + 168.408i 1.18652 + 0.479794i
352352 −40.1324 + 69.5114i −0.114013 + 0.197476i
353353 120.078i 0.340163i 0.985430 + 0.170082i 0.0544031π0.0544031\pi
−0.985430 + 0.170082i 0.945597π0.945597\pi
354354 −52.4200 + 167.899i −0.148079 + 0.474291i
355355 −189.189 −0.532926
356356 10.8616 6.27097i 0.0305102 0.0176151i
357357 63.5786 322.440i 0.178091 0.903192i
358358 145.679 252.324i 0.406925 0.704816i
359359 −101.066 58.3503i −0.281520 0.162536i 0.352591 0.935777i 0.385301π-0.385301\pi
−0.634111 + 0.773242i 0.718634π0.718634\pi
360360 −70.1743 48.5510i −0.194929 0.134864i
361361 −419.200 726.076i −1.16122 2.01129i
362362 83.3637 48.1301i 0.230287 0.132956i
363363 −71.8178 + 230.029i −0.197845 + 0.633690i
364364 213.100 + 94.0573i 0.585440 + 0.258399i
365365 25.7128 14.8453i 0.0704459 0.0406720i
366366 49.9175 45.9997i 0.136387 0.125682i
367367 296.598 0.808169 0.404085 0.914722i 0.367590π-0.367590\pi
0.404085 + 0.914722i 0.367590π0.367590\pi
368368 −90.9812 + 52.5280i −0.247231 + 0.142739i
369369 −56.3666 4.61233i −0.152755 0.0124995i
370370 −303.229 −0.819538
371371 −310.244 + 33.6183i −0.836237 + 0.0906153i
372372 −197.562 + 44.3814i −0.531082 + 0.119305i
373373 −416.106 −1.11557 −0.557783 0.829987i 0.688348π-0.688348\pi
−0.557783 + 0.829987i 0.688348π0.688348\pi
374374 271.962 + 157.017i 0.727171 + 0.419832i
375375 −372.106 116.176i −0.992283 0.309802i
376376 59.3679 + 102.828i 0.157893 + 0.273479i
377377 350.367i 0.929355i
378378 −191.726 + 186.234i −0.507211 + 0.492683i
379379 315.897 0.833501 0.416750 0.909021i 0.363169π-0.363169\pi
0.416750 + 0.909021i 0.363169π0.363169\pi
380380 −201.080 + 116.094i −0.529159 + 0.305510i
381381 67.3098 215.590i 0.176666 0.565854i
382382 −182.534 + 316.158i −0.477838 + 0.827640i
383383 402.775i 1.05163i −0.850598 0.525816i 0.823760π-0.823760\pi
0.850598 0.525816i 0.176240π-0.176240\pi
384384 −7.43931 33.1158i −0.0193732 0.0862391i
385385 −304.597 134.442i −0.791161 0.349200i
386386 225.709i 0.584739i
387387 −1.20829 + 0.571727i −0.00312220 + 0.00147733i
388388 64.3867 + 111.521i 0.165945 + 0.287425i
389389 363.489i 0.934420i 0.884146 + 0.467210i 0.154741π0.154741\pi
−0.884146 + 0.467210i 0.845259π0.845259\pi
390390 −160.354 174.011i −0.411165 0.446183i
391391 205.515 + 355.962i 0.525613 + 0.910388i
392392 −102.395 + 93.3981i −0.261212 + 0.238260i
393393 448.146 + 139.916i 1.14032 + 0.356022i
394394 122.893 + 212.857i 0.311911 + 0.540246i
395395 −84.5977 + 48.8425i −0.214171 + 0.123652i
396396 −109.237 230.862i −0.275850 0.582984i
397397 32.4146 56.1437i 0.0816489 0.141420i −0.822309 0.569041i 0.807315π-0.807315\pi
0.903958 + 0.427621i 0.140648π0.140648\pi
398398 −118.330 68.3181i −0.297313 0.171654i
399399 234.924 + 688.292i 0.588782 + 1.72504i
400400 −27.5258 47.6761i −0.0688146 0.119190i
401401 496.964i 1.23931i −0.784874 0.619656i 0.787272π-0.787272\pi
0.784874 0.619656i 0.212728π-0.212728\pi
402402 345.553 + 107.886i 0.859585 + 0.268372i
403403 −561.500 −1.39330
404404 161.457 + 93.2173i 0.399646 + 0.230736i
405405 254.091 95.7300i 0.627385 0.236370i
406406 190.713 + 84.1762i 0.469737 + 0.207331i
407407 −785.977 453.784i −1.93115 1.11495i
408408 −129.565 + 29.1061i −0.317561 + 0.0713385i
409409 −246.997 + 427.811i −0.603905 + 1.04599i 0.388319 + 0.921525i 0.373056π0.373056\pi
−0.992224 + 0.124469i 0.960277π0.960277\pi
410410 25.7989 + 14.8950i 0.0629241 + 0.0363292i
411411 −236.807 73.9339i −0.576173 0.179888i
412412 129.105 223.616i 0.313361 0.542757i
413413 −171.334 234.232i −0.414853 0.567147i
414414 27.2626 333.173i 0.0658517 0.804765i
415415 −94.5493 + 163.764i −0.227830 + 0.394613i
416416 94.1197i 0.226249i
417417 295.360 66.3511i 0.708297 0.159115i
418418 −694.941 −1.66254
419419 229.187 132.321i 0.546987 0.315803i −0.200919 0.979608i 0.564393π-0.564393\pi
0.747906 + 0.663805i 0.231060π0.231060\pi
420420 133.244 45.4781i 0.317248 0.108281i
421421 −41.2156 + 71.3876i −0.0978994 + 0.169567i −0.910815 0.412815i 0.864546π-0.864546\pi
0.812916 + 0.582382i 0.197879π0.197879\pi
422422 −21.2657 12.2778i −0.0503927 0.0290942i
423423 −376.556 30.8126i −0.890204 0.0728430i
424424 63.0456 + 109.198i 0.148693 + 0.257543i
425425 −186.532 + 107.694i −0.438898 + 0.253398i
426426 233.622 52.4821i 0.548409 0.123197i
427427 12.0654 + 111.345i 0.0282562 + 0.260761i
428428 −185.752 + 107.244i −0.433999 + 0.250569i
429429 −155.233 691.013i −0.361848 1.61075i
430430 0.704113 0.00163747
431431 409.848 236.626i 0.950924 0.549016i 0.0575561 0.998342i 0.481669π-0.481669\pi
0.893368 + 0.449326i 0.148336π0.148336\pi
432432 100.124 + 40.4871i 0.231768 + 0.0937200i
433433 140.867 0.325328 0.162664 0.986681i 0.447991π-0.447991\pi
0.162664 + 0.986681i 0.447991π0.447991\pi
434434 134.901 305.638i 0.310832 0.704235i
435435 −143.508 155.731i −0.329904 0.358002i
436436 −66.2018 −0.151839
437437 −787.723 454.792i −1.80257 1.04071i
438438 −27.6336 + 25.4647i −0.0630903 + 0.0581387i
439439 127.577 + 220.970i 0.290609 + 0.503349i 0.973954 0.226746i 0.0728088π-0.0728088\pi
−0.683345 + 0.730096i 0.739475π0.739475\pi
440440 134.531i 0.305752i
441441 −59.0195 437.033i −0.133831 0.991004i
442442 −368.241 −0.833124
443443 403.897 233.190i 0.911732 0.526388i 0.0307437 0.999527i 0.490212π-0.490212\pi
0.880988 + 0.473139i 0.156879π0.156879\pi
444444 374.446 84.1175i 0.843347 0.189454i
445445 10.5107 18.2051i 0.0236196 0.0409103i
446446 416.551i 0.933972i
447447 −344.495 107.555i −0.770681 0.240616i
448448 51.2316 + 22.6124i 0.114356 + 0.0504741i
449449 383.226i 0.853509i −0.904367 0.426755i 0.859657π-0.859657\pi
0.904367 0.426755i 0.140343π-0.140343\pi
450450 174.590 + 14.2862i 0.387977 + 0.0317471i
451451 44.5809 + 77.2164i 0.0988490 + 0.171212i
452452 337.454i 0.746580i
453453 65.9059 211.094i 0.145488 0.465990i
454454 158.583 + 274.674i 0.349302 + 0.605009i
455455 388.146 42.0598i 0.853069 0.0924392i
456456 216.101 199.141i 0.473907 0.436712i
457457 241.747 + 418.718i 0.528987 + 0.916233i 0.999429 + 0.0338015i 0.0107614π0.0107614\pi
−0.470441 + 0.882431i 0.655905π0.655905\pi
458458 126.724 73.1641i 0.276690 0.159747i
459459 158.405 391.732i 0.345108 0.853447i
460460 −88.0416 + 152.492i −0.191395 + 0.331505i
461461 −391.665 226.128i −0.849599 0.490516i 0.0109166 0.999940i 0.496525π-0.496525\pi
−0.860516 + 0.509424i 0.829858π0.829858\pi
462462 413.430 + 81.5201i 0.894871 + 0.176451i
463463 −157.167 272.221i −0.339454 0.587951i 0.644876 0.764287i 0.276909π-0.276909\pi
−0.984330 + 0.176336i 0.943575π0.943575\pi
464464 84.2321i 0.181535i
465465 −249.575 + 229.987i −0.536721 + 0.494596i
466466 −306.086 −0.656837
467467 −258.779 149.406i −0.554130 0.319927i 0.196656 0.980473i 0.436992π-0.436992\pi
−0.750786 + 0.660545i 0.770325π0.770325\pi
468468 246.287 + 170.397i 0.526255 + 0.364096i
469469 −482.072 + 352.623i −1.02787 + 0.751862i
470470 172.349 + 99.5058i 0.366700 + 0.211714i
471471 −535.876 581.516i −1.13774 1.23464i
472472 −58.6306 + 101.551i −0.124217 + 0.215151i
473473 1.82508 + 1.05371i 0.00385852 + 0.00222772i
474474 90.9173 83.7816i 0.191809 0.176754i
475475 238.321 412.784i 0.501729 0.869019i
476476 88.4705 200.442i 0.185862 0.421098i
477477 −399.884 32.7214i −0.838330 0.0685983i
478478 316.045 547.406i 0.661182 1.14520i
479479 503.953i 1.05209i −0.850456 0.526047i 0.823674π-0.823674\pi
0.850456 0.526047i 0.176326π-0.176326\pi
480480 −38.5509 41.8343i −0.0803144 0.0871548i
481481 1064.23 2.21253
482482 101.349 58.5138i 0.210267 0.121398i
483483 415.278 + 362.966i 0.859790 + 0.751483i
484484 −80.3266 + 139.130i −0.165964 + 0.287458i
485485 186.919 + 107.918i 0.385400 + 0.222511i
486486 −287.211 + 188.700i −0.590970 + 0.388271i
487487 146.436 + 253.634i 0.300690 + 0.520810i 0.976292 0.216456i 0.0694498π-0.0694498\pi
−0.675603 + 0.737266i 0.736116π0.736116\pi
488488 39.1907 22.6267i 0.0803088 0.0463663i
489489 147.933 + 160.532i 0.302521 + 0.328287i
490490 −70.3586 + 221.382i −0.143589 + 0.451801i
491491 −370.452 + 213.881i −0.754485 + 0.435602i −0.827312 0.561743i 0.810131π-0.810131\pi
0.0728274 + 0.997345i 0.476798π0.476798\pi
492492 −35.9900 11.2365i −0.0731504 0.0228384i
493493 −329.556 −0.668471
494494 705.721 407.448i 1.42859 0.824794i
495495 −352.033 243.559i −0.711178 0.492038i
496496 −134.991 −0.272159
497497 −159.524 + 361.424i −0.320973 + 0.727211i
498498 71.3262 228.455i 0.143225 0.458745i
499499 206.391 0.413609 0.206804 0.978382i 0.433694π-0.433694\pi
0.206804 + 0.978382i 0.433694π0.433694\pi
500500 −225.063 129.940i −0.450126 0.259880i
501501 131.090 + 583.543i 0.261657 + 1.16476i
502502 161.480 + 279.692i 0.321674 + 0.557156i
503503 415.249i 0.825546i 0.910834 + 0.412773i 0.135440π0.135440\pi
−0.910834 + 0.412773i 0.864560π0.864560\pi
504504 −151.922 + 93.1219i −0.301433 + 0.184766i
505505 312.481 0.618774
506506 −456.412 + 263.510i −0.902000 + 0.520770i
507507 219.213 + 237.884i 0.432374 + 0.469199i
508508 75.2845 130.397i 0.148198 0.256686i
509509 384.889i 0.756168i −0.925771 0.378084i 0.876583π-0.876583\pi
0.925771 0.378084i 0.123417π-0.123417\pi
510510 −163.676 + 150.830i −0.320933 + 0.295744i
511511 −6.67923 61.6388i −0.0130709 0.120624i
512512 22.6274i 0.0441942i
513513 129.864 + 926.012i 0.253146 + 1.80509i
514514 54.2054 + 93.8865i 0.105458 + 0.182659i
515515 432.781i 0.840352i
516516 −0.869483 + 0.195325i −0.00168504 + 0.000378537i
517517 297.822 + 515.843i 0.576058 + 0.997762i
518518 −255.682 + 579.284i −0.493595 + 1.11831i
519519 164.056 + 730.291i 0.316101 + 1.40711i
520520 −78.8765 136.618i −0.151685 0.262727i
521521 −191.141 + 110.355i −0.366874 + 0.211815i −0.672092 0.740468i 0.734604π-0.734604\pi
0.305218 + 0.952282i 0.401271π0.401271\pi
522522 220.414 + 152.496i 0.422249 + 0.292138i
523523 389.796 675.146i 0.745308 1.29091i −0.204743 0.978816i 0.565636π-0.565636\pi
0.950051 0.312095i 0.101031π-0.101031\pi
524524 271.055 + 156.493i 0.517280 + 0.298652i
525525 −190.202 + 217.615i −0.362290 + 0.414505i
526526 −250.630 434.104i −0.476483 0.825293i
527527 528.148i 1.00218i
528528 −37.3197 166.127i −0.0706812 0.314635i
529529 −160.798 −0.303965
530530 183.026 + 105.670i 0.345332 + 0.199377i
531531 −159.587 337.272i −0.300540 0.635164i
532532 52.2333 + 482.031i 0.0981829 + 0.906074i
533533 −90.5450 52.2762i −0.169878 0.0980791i
534534 −7.92908 + 25.3965i −0.0148485 + 0.0475590i
535535 −179.750 + 311.336i −0.335981 + 0.581936i
536536 209.003 + 120.668i 0.389930 + 0.225126i
537537 135.469 + 603.036i 0.252270 + 1.12297i
538538 −71.7422 + 124.261i −0.133350 + 0.230969i
539539 −513.672 + 468.537i −0.953009 + 0.869270i
540540 179.263 25.1399i 0.331969 0.0465553i
541541 108.437 187.818i 0.200437 0.347168i −0.748232 0.663437i 0.769097π-0.769097\pi
0.948669 + 0.316269i 0.102430π0.102430\pi
542542 107.260i 0.197896i
543543 −60.8561 + 194.920i −0.112074 + 0.358968i
544544 −88.5292 −0.162738
545545 −96.0943 + 55.4801i −0.176320 + 0.101798i
546546 −467.640 + 159.612i −0.856483 + 0.292330i
547547 −330.752 + 572.879i −0.604665 + 1.04731i 0.387440 + 0.921895i 0.373360π0.373360\pi
−0.992104 + 0.125415i 0.959974π0.959974\pi
548548 −143.229 82.6934i −0.261367 0.150900i
549549 −11.7435 + 143.516i −0.0213908 + 0.261414i
550550 −138.085 239.170i −0.251063 0.434854i
551551 631.583 364.644i 1.14625 0.661787i
552552 66.4169 212.730i 0.120320 0.385381i
553553 21.9754 + 202.798i 0.0397385 + 0.366724i
554554 −328.380 + 189.590i −0.592744 + 0.342221i
555555 473.027 435.902i 0.852301 0.785408i
556556 201.814 0.362975
557557 −159.762 + 92.2387i −0.286826 + 0.165599i −0.636510 0.771269i 0.719622π-0.719622\pi
0.349684 + 0.936868i 0.386289π0.386289\pi
558558 244.391 353.236i 0.437977 0.633040i
559559 −2.47119 −0.00442073
560560 93.3147 10.1117i 0.166633 0.0180565i
561561 −649.969 + 146.012i −1.15859 + 0.260272i
562562 −692.308 −1.23187
563563 903.991 + 521.919i 1.60567 + 0.927033i 0.990324 + 0.138774i 0.0443160π0.0443160\pi
0.615344 + 0.788259i 0.289017π0.289017\pi
564564 −240.431 75.0653i −0.426296 0.133094i
565565 282.801 + 489.826i 0.500533 + 0.866949i
566566 739.968i 1.30736i
567567 31.3681 566.132i 0.0553230 0.998469i
568568 159.630 0.281038
569569 65.6788 37.9197i 0.115428 0.0666427i −0.441174 0.897421i 0.645438π-0.645438\pi
0.556603 + 0.830779i 0.312105π0.312105\pi
570570 146.790 470.162i 0.257526 0.824846i
571571 385.418 667.564i 0.674988 1.16911i −0.301484 0.953471i 0.597482π-0.597482\pi
0.976472 0.215643i 0.0691846π-0.0691846\pi
572572 472.157i 0.825449i
573573 −169.741 755.596i −0.296232 1.31867i
574574 50.2088 36.7264i 0.0874717 0.0639832i
575575 361.469i 0.628642i
576576 59.2101 + 40.9653i 0.102795 + 0.0711204i
577577 435.383 + 754.105i 0.754563 + 1.30694i 0.945591 + 0.325357i 0.105484π0.105484\pi
−0.191028 + 0.981585i 0.561182π0.561182\pi
578578 62.3393i 0.107853i
579579 324.464 + 352.099i 0.560388 + 0.608116i
580580 −70.5902 122.266i −0.121707 0.210803i
581581 233.129 + 318.712i 0.401255 + 0.548557i
582582 −260.756 81.4112i −0.448035 0.139882i
583583 316.272 + 547.799i 0.542491 + 0.939621i
584584 −21.6954 + 12.5258i −0.0371496 + 0.0214483i
585585 500.295 + 40.9378i 0.855204 + 0.0699791i
586586 −52.3896 + 90.7414i −0.0894020 + 0.154849i
587587 520.453 + 300.484i 0.886633 + 0.511898i 0.872840 0.488007i 0.162276π-0.162276\pi
0.0137932 + 0.999905i 0.495609π0.495609\pi
588588 25.4704 292.895i 0.0433171 0.498120i
589589 −584.381 1012.18i −0.992158 1.71847i
590590 196.540i 0.333119i
591591 −497.698 155.387i −0.842129 0.262922i
592592 255.852 0.432182
593593 288.796 + 166.736i 0.487008 + 0.281174i 0.723332 0.690500i 0.242609π-0.242609\pi
−0.236324 + 0.971674i 0.575943π0.575943\pi
594594 502.277 + 203.106i 0.845584 + 0.341929i
595595 −39.5616 365.091i −0.0664901 0.613599i
596596 −208.362 120.298i −0.349601 0.201842i
597597 282.801 63.5299i 0.473704 0.106415i
598598 308.995 535.195i 0.516714 0.894975i
599599 −355.388 205.183i −0.593302 0.342543i 0.173100 0.984904i 0.444622π-0.444622\pi
−0.766402 + 0.642361i 0.777955π0.777955\pi
600600 111.475 + 34.8039i 0.185792 + 0.0580065i
601601 204.315 353.884i 0.339958 0.588825i −0.644466 0.764633i 0.722920π-0.722920\pi
0.984424 + 0.175808i 0.0562538π0.0562538\pi
602602 0.593707 1.34513i 0.000986225 0.00223443i
603603 −694.141 + 328.446i −1.15115 + 0.544686i
604604 73.7142 127.677i 0.122043 0.211385i
605605 269.269i 0.445073i
606606 −385.871 + 86.6840i −0.636750 + 0.143043i
607607 −228.162 −0.375885 −0.187942 0.982180i 0.560182π-0.560182\pi
−0.187942 + 0.982180i 0.560182π0.560182\pi
608608 169.663 97.9551i 0.279051 0.161110i
609609 −418.512 + 142.844i −0.687213 + 0.234556i
610610 37.9244 65.6870i 0.0621712 0.107684i
611611 −604.885 349.230i −0.989991 0.571572i
612612 160.276 231.658i 0.261889 0.378527i
613613 −59.5738 103.185i −0.0971840 0.168328i 0.813334 0.581797i 0.197650π-0.197650\pi
−0.910518 + 0.413469i 0.864317π0.864317\pi
614614 194.872 112.509i 0.317381 0.183240i
615615 −61.6574 + 13.8510i −0.100256 + 0.0225220i
616616 257.006 + 113.436i 0.417218 + 0.184150i
617617 1004.18 579.761i 1.62751 0.939645i 0.642682 0.766133i 0.277822π-0.277822\pi
0.984832 0.173512i 0.0555116π-0.0555116\pi
618618 120.056 + 534.425i 0.194265 + 0.864766i
619619 −765.830 −1.23721 −0.618603 0.785704i 0.712301π-0.712301\pi
−0.618603 + 0.785704i 0.712301π0.712301\pi
620620 −195.944 + 113.128i −0.316038 + 0.182465i
621621 436.418 + 558.929i 0.702766 + 0.900047i
622622 −631.526 −1.01531
623623 −25.9161 35.4300i −0.0415989 0.0568700i
624624 135.300 + 146.824i 0.216827 + 0.235294i
625625 −91.5094 −0.146415
626626 −240.426 138.810i −0.384067 0.221741i
627627 1084.08 999.000i 1.72900 1.59330i
628628 −263.591 456.554i −0.419731 0.726996i
629629 1001.01i 1.59144i
630630 −142.480 + 262.487i −0.226159 + 0.416646i
631631 −562.217 −0.890994 −0.445497 0.895283i 0.646973π-0.646973\pi
−0.445497 + 0.895283i 0.646973π0.646973\pi
632632 71.3800 41.2113i 0.112943 0.0652077i
633633 50.8235 11.4173i 0.0802899 0.0180367i
634634 −240.967 + 417.367i −0.380074 + 0.658307i
635635 252.367i 0.397428i
636636 −255.325 79.7155i −0.401455 0.125339i
637637 246.934 776.974i 0.387652 1.21974i
638638 422.555i 0.662312i
639639 −288.998 + 417.710i −0.452266 + 0.653693i
640640 −18.9628 32.8445i −0.0296293 0.0513195i
641641 702.181i 1.09545i 0.836660 + 0.547723i 0.184505π0.184505\pi
−0.836660 + 0.547723i 0.815495π0.815495\pi
642642 135.600 434.321i 0.211215 0.676512i
643643 110.674 + 191.694i 0.172122 + 0.298124i 0.939161 0.343476i 0.111604π-0.111604\pi
−0.767040 + 0.641600i 0.778271π0.778271\pi
644644 217.083 + 296.775i 0.337085 + 0.460831i
645645 −1.09839 + 1.01219i −0.00170294 + 0.00156928i
646646 −383.247 663.803i −0.593262 1.02756i
647647 −501.744 + 289.682i −0.775494 + 0.447731i −0.834831 0.550507i 0.814435π-0.814435\pi
0.0593372 + 0.998238i 0.481101π0.481101\pi
648648 −214.392 + 80.7730i −0.330851 + 0.124650i
649649 −294.124 + 509.437i −0.453195 + 0.784957i
650650 280.454 + 161.920i 0.431468 + 0.249108i
651651 228.923 + 670.710i 0.351648 + 1.03028i
652652 72.7665 + 126.035i 0.111605 + 0.193306i
653653 1069.79i 1.63827i 0.573602 + 0.819134i 0.305545π0.305545\pi
−0.573602 + 0.819134i 0.694455π0.694455\pi
654654 103.273 95.1673i 0.157909 0.145516i
655655 524.594 0.800906
656656 −21.7680 12.5678i −0.0331830 0.0191582i
657657 6.50104 79.4483i 0.00989504 0.120926i
658658 335.419 245.350i 0.509755 0.372873i
659659 740.124 + 427.311i 1.12310 + 0.648423i 0.942191 0.335076i 0.108762π-0.108762\pi
0.180911 + 0.983499i 0.442095π0.442095\pi
660660 −193.393 209.864i −0.293019 0.317976i
661661 590.335 1022.49i 0.893094 1.54688i 0.0569477 0.998377i 0.481863π-0.481863\pi
0.836146 0.548507i 0.184803π-0.184803\pi
662662 −690.239 398.509i −1.04266 0.601978i
663663 574.444 529.359i 0.866431 0.798429i
664664 79.7768 138.177i 0.120146 0.208099i
665665 479.782 + 655.911i 0.721477 + 0.986333i
666666 −463.202 + 669.499i −0.695498 + 1.00525i
667667 276.534 478.971i 0.414594 0.718097i
668668 398.724i 0.596893i
669669 −598.807 649.807i −0.895077 0.971310i
670670 404.499 0.603730
671671 196.602 113.508i 0.292999 0.169163i
672672 −112.426 + 38.3725i −0.167300 + 0.0571020i
673673 232.243 402.257i 0.345086 0.597707i −0.640283 0.768139i 0.721183π-0.721183\pi
0.985369 + 0.170432i 0.0545163π0.0545163\pi
674674 −743.029 428.988i −1.10242 0.636480i
675675 −292.891 + 228.693i −0.433913 + 0.338804i
676676 107.829 + 186.765i 0.159510 + 0.276279i
677677 −158.446 + 91.4789i −0.234042 + 0.135124i −0.612435 0.790521i 0.709810π-0.709810\pi
0.378394 + 0.925645i 0.376477π0.376477\pi
678678 −485.101 526.417i −0.715489 0.776427i
679679 363.775 266.092i 0.535751 0.391888i
680680 −128.503 + 74.1914i −0.188975 + 0.109105i
681681 −642.238 200.514i −0.943081 0.294441i
682682 −677.188 −0.992945
683683 −878.043 + 506.938i −1.28557 + 0.742223i −0.977861 0.209258i 0.932895π-0.932895\pi
−0.307708 + 0.951481i 0.599562π0.599562\pi
684684 −50.8398 + 621.306i −0.0743272 + 0.908342i
685685 −277.203 −0.404676
686686 363.600 + 321.082i 0.530029 + 0.468049i
687687 −92.5094 + 296.304i −0.134657 + 0.431301i
688688 −0.594101 −0.000863519
689689 −642.357 370.865i −0.932303 0.538265i
690690 −81.8710 364.446i −0.118654 0.528182i
691691 −501.204 868.111i −0.725331 1.25631i −0.958837 0.283955i 0.908353π-0.908353\pi
0.233506 0.972355i 0.424980π-0.424980\pi
692692 498.995i 0.721090i
693693 −762.126 + 467.151i −1.09975 + 0.674099i
694694 74.0825 0.106747
695695 292.940 169.129i 0.421496 0.243351i
696696 121.086 + 131.399i 0.173975 + 0.188792i
697697 −49.1711 + 85.1668i −0.0705468 + 0.122191i
698698 12.2738i 0.0175843i
699699 477.484 440.009i 0.683096 0.629483i
700700 −155.517 + 113.756i −0.222167 + 0.162509i
701701 77.0590i 0.109927i −0.998488 0.0549636i 0.982496π-0.982496\pi
0.998488 0.0549636i 0.0175043π-0.0175043\pi
702702 −629.151 + 88.2321i −0.896227 + 0.125687i
703703 1107.59 + 1918.41i 1.57553 + 2.72889i
704704 113.512i 0.161238i
705705 −411.902 + 92.5317i −0.584258 + 0.131251i
706706 −84.9077 147.064i −0.120266 0.208306i
707707 263.483 596.959i 0.372678 0.844355i
708708 −54.5214 242.700i −0.0770076 0.342796i
709709 −453.117 784.822i −0.639093 1.10694i −0.985632 0.168907i 0.945976π-0.945976\pi
0.346539 0.938036i 0.387357π-0.387357\pi
710710 231.708 133.777i 0.326349 0.188418i
711711 −21.3891 + 261.393i −0.0300831 + 0.367642i
712712 −8.86850 + 15.3607i −0.0124558 + 0.0215740i
713713 −767.601 443.175i −1.07658 0.621563i
714714 150.132 + 439.863i 0.210268 + 0.616055i
715715 −395.688 685.352i −0.553410 0.958534i
716716 412.043i 0.575479i
717717 293.894 + 1308.26i 0.409894 + 1.82463i
718718 165.040 0.229860
719719 −20.7034 11.9531i −0.0287947 0.0166246i 0.485534 0.874218i 0.338625π-0.338625\pi
−0.514328 + 0.857593i 0.671959π0.671959\pi
720720 120.276 + 9.84189i 0.167050 + 0.0136693i
721721 −826.780 364.921i −1.14671 0.506131i
722722 1026.83 + 592.838i 1.42220 + 0.821106i
723723 −73.9854 + 236.972i −0.102331 + 0.327762i
724724 −68.0662 + 117.894i −0.0940141 + 0.162837i
725725 250.991 + 144.910i 0.346195 + 0.199876i
726726 −74.6968 332.510i −0.102888 0.458003i
727727 185.455 321.217i 0.255096 0.441839i −0.709826 0.704377i 0.751226π-0.751226\pi
0.964921 + 0.262539i 0.0845597π0.0845597\pi
728728 −327.502 + 35.4883i −0.449865 + 0.0487477i
729729 176.778 707.241i 0.242494 0.970153i
730730 −20.9944 + 36.3633i −0.0287594 + 0.0498128i
731731 2.32441i 0.00317976i
732732 −28.6095 + 91.6349i −0.0390840 + 0.125184i
733733 −619.897 −0.845698 −0.422849 0.906200i 0.638970π-0.638970\pi
−0.422849 + 0.906200i 0.638970π0.638970\pi
734734 −363.257 + 209.726i −0.494900 + 0.285731i
735735 −208.487 446.492i −0.283656 0.607472i
736736 74.2858 128.667i 0.100932 0.174819i
737737 1048.47 + 605.336i 1.42262 + 0.821352i
738738 72.2961 34.2083i 0.0979622 0.0463527i
739739 −304.105 526.725i −0.411508 0.712754i 0.583546 0.812080i 0.301665π-0.301665\pi
−0.995055 + 0.0993262i 0.968331π0.968331\pi
740740 371.378 214.415i 0.501862 0.289750i
741741 −515.182 + 1650.10i −0.695252 + 2.22686i
742742 356.198 260.549i 0.480051 0.351145i
743743 723.866 417.924i 0.974248 0.562482i 0.0737195 0.997279i 0.476513π-0.476513\pi
0.900529 + 0.434797i 0.143180π0.143180\pi
744744 210.581 194.054i 0.283039 0.260825i
745745 −403.260 −0.541289
746746 509.624 294.232i 0.683142 0.394412i
747747 217.145 + 458.916i 0.290689 + 0.614345i
748748 −444.112 −0.593732
749749 443.207 + 605.910i 0.591732 + 0.808959i
750750 537.884 120.833i 0.717179 0.161111i
751751 1043.24 1.38913 0.694566 0.719429i 0.255597π-0.255597\pi
0.694566 + 0.719429i 0.255597π0.255597\pi
752752 −145.421 83.9588i −0.193379 0.111647i
753753 −653.971 204.177i −0.868487 0.271152i
754754 247.747 + 429.110i 0.328577 + 0.569112i
755755 247.103i 0.327289i
756756 103.128 363.660i 0.136412 0.481032i
757757 441.367 0.583047 0.291524 0.956564i 0.405838π-0.405838\pi
0.291524 + 0.956564i 0.405838π0.405838\pi
758758 −386.893 + 223.373i −0.510413 + 0.294687i
759759 333.184 1067.17i 0.438978 1.40603i
760760 164.181 284.371i 0.216028 0.374172i
761761 297.170i 0.390499i 0.980754 + 0.195249i 0.0625517π0.0625517\pi
−0.980754 + 0.195249i 0.937448π0.937448\pi
762762 70.0081 + 311.639i 0.0918741 + 0.408975i
763763 24.9618 + 230.358i 0.0327153 + 0.301911i
764764 516.285i 0.675765i
765765 38.5062 470.578i 0.0503349 0.615135i
766766 284.805 + 493.297i 0.371808 + 0.643990i
767767 689.787i 0.899331i
768768 32.5277 + 35.2980i 0.0423537 + 0.0459610i
769769 −79.6447 137.949i −0.103569 0.179387i 0.809584 0.587005i 0.199693π-0.199693\pi
−0.913153 + 0.407618i 0.866360π0.866360\pi
770770 468.118 50.7257i 0.607946 0.0658775i
771771 −219.524 68.5378i −0.284726 0.0888947i
772772 159.600 + 276.436i 0.206736 + 0.358078i
773773 −767.592 + 443.170i −0.993004 + 0.573311i −0.906171 0.422912i 0.861008π-0.861008\pi
−0.0868334 + 0.996223i 0.527675π0.527675\pi
774774 1.07558 1.55461i 0.00138964 0.00200854i
775775 232.233 402.240i 0.299656 0.519019i
776776 −157.715 91.0566i −0.203241 0.117341i
777777 −433.885 1271.22i −0.558410 1.63606i
778778 −257.026 445.182i −0.330367 0.572213i
779779 217.626i 0.279366i
780780 319.438 + 99.7321i 0.409535 + 0.127862i
781781 800.791 1.02534
782782 −503.406 290.641i −0.643741 0.371664i
783783 −563.057 + 78.9630i −0.719102 + 0.100847i
784784 59.3657 186.793i 0.0757215 0.238257i
785785 −765.224 441.802i −0.974808 0.562805i
786786 −647.801 + 145.525i −0.824174 + 0.185147i
787787 −494.657 + 856.771i −0.628535 + 1.08865i 0.359311 + 0.933218i 0.383012π0.383012\pi
−0.987846 + 0.155437i 0.950322π0.950322\pi
788788 −301.025 173.797i −0.382012 0.220555i
789789 1015.01 + 316.899i 1.28646 + 0.401647i
790790 69.0737 119.639i 0.0874351 0.151442i
791791 1174.22 127.239i 1.48447 0.160858i
792792 297.031 + 205.505i 0.375039 + 0.259476i
793793 −133.101 + 230.538i −0.167845 + 0.290717i
794794 91.6824i 0.115469i
795795 −437.419 + 98.2640i −0.550212 + 0.123603i
796796 193.233 0.242755
797797 −1020.06 + 588.934i −1.27988 + 0.738939i −0.976826 0.214034i 0.931340π-0.931340\pi
−0.303054 + 0.952973i 0.598006π0.598006\pi
798798 −774.418 676.866i −0.970449 0.848203i
799799 −328.487 + 568.956i −0.411123 + 0.712085i
800800 67.4242 + 38.9274i 0.0842803 + 0.0486592i
801801 −24.1392 51.0160i −0.0301363 0.0636904i
802802 351.407 + 608.654i 0.438163 + 0.758920i
803803 −108.836 + 62.8365i −0.135537 + 0.0782522i
804804 −499.501 + 112.210i −0.621270 + 0.139565i
805805 563.814 + 248.854i 0.700390 + 0.309135i
806806 687.694 397.040i 0.853218 0.492606i
807807 −66.7140 296.975i −0.0826691 0.367999i
808808 −263.658 −0.326310
809809 −240.690 + 138.963i −0.297516 + 0.171771i −0.641326 0.767268i 0.721616π-0.721616\pi
0.343810 + 0.939039i 0.388282π0.388282\pi
810810 −243.505 + 296.914i −0.300624 + 0.366561i
811811 −594.387 −0.732906 −0.366453 0.930437i 0.619428π-0.619428\pi
−0.366453 + 0.930437i 0.619428π0.619428\pi
812812 −293.097 + 31.7602i −0.360956 + 0.0391135i
813813 154.189 + 167.322i 0.189655 + 0.205808i
814814 1283.50 1.57678
815815 211.246 + 121.963i 0.259198 + 0.149648i
816816 138.103 127.264i 0.169243 0.155960i
817817 −2.57189 4.45465i −0.00314797 0.00545244i
818818 698.613i 0.854050i
819819 500.055 921.237i 0.610567 1.12483i
820820 −42.1294 −0.0513773
821821 −116.955 + 67.5240i −0.142454 + 0.0822460i −0.569533 0.821968i 0.692876π-0.692876\pi
0.427079 + 0.904214i 0.359543π0.359543\pi
822822 342.307 76.8977i 0.416432 0.0935495i
823823 −191.577 + 331.820i −0.232778 + 0.403184i −0.958625 0.284673i 0.908115π-0.908115\pi
0.725846 + 0.687857i 0.241448π0.241448\pi
824824 365.163i 0.443159i
825825 559.223 + 174.596i 0.677846 + 0.211631i
826826 375.467 + 165.722i 0.454561 + 0.200632i
827827 1194.80i 1.44474i 0.691504 + 0.722372i 0.256948π0.256948\pi
−0.691504 + 0.722372i 0.743052π0.743052\pi
828828 202.199 + 427.329i 0.244201 + 0.516098i
829829 484.580 + 839.318i 0.584536 + 1.01245i 0.994933 + 0.100539i 0.0320567π0.0320567\pi
−0.410397 + 0.911907i 0.634610π0.634610\pi
830830 267.426i 0.322200i
831831 239.720 767.812i 0.288471 0.923961i
832832 66.5527 + 115.273i 0.0799912 + 0.138549i
833833 −730.824 232.267i −0.877340 0.278832i
834834 −314.823 + 290.114i −0.377486 + 0.347859i
835835 334.149 + 578.762i 0.400178 + 0.693128i
836836 851.125 491.397i 1.01809 0.587796i
837837 126.547 + 902.357i 0.151191 + 1.07809i
838838 −187.131 + 324.120i −0.223306 + 0.386778i
839839 −766.287 442.416i −0.913334 0.527314i −0.0318317 0.999493i 0.510134π-0.510134\pi
−0.881502 + 0.472180i 0.843467π0.843467\pi
840840 −131.032 + 149.917i −0.155991 + 0.178472i
841841 −198.780 344.297i −0.236361 0.409390i
842842 116.575i 0.138451i
843843 1079.98 995.216i 1.28111 1.18057i
844844 34.7268 0.0411455
845845 313.034 + 180.730i 0.370455 + 0.213882i
846846 482.973 228.528i 0.570890 0.270128i
847847 514.408 + 227.047i 0.607329 + 0.268061i
848848 −154.430 89.1600i −0.182110 0.105142i
849849 −1063.73 1154.33i −1.25292 1.35963i
850850 152.302 263.796i 0.179179 0.310348i
851851 1454.86 + 839.962i 1.70958 + 0.987029i
852852 −249.017 + 229.473i −0.292274 + 0.269334i
853853 −91.3479 + 158.219i −0.107090 + 0.185486i −0.914590 0.404382i 0.867487π-0.867487\pi
0.807500 + 0.589867i 0.200820π0.200820\pi
854854 −93.5098 127.838i −0.109496 0.149693i
855855 446.886 + 944.453i 0.522674 + 1.10462i
856856 151.666 262.692i 0.177179 0.306884i
857857 1205.39i 1.40652i −0.710934 0.703259i 0.751728π-0.751728\pi
0.710934 0.703259i 0.248272π-0.248272\pi
858858 678.741 + 736.549i 0.791073 + 0.858449i
859859 −1037.49 −1.20778 −0.603892 0.797066i 0.706384π-0.706384\pi
−0.603892 + 0.797066i 0.706384π0.706384\pi
860860 −0.862359 + 0.497883i −0.00100274 + 0.000578934i
861861 −25.5286 + 129.469i −0.0296500 + 0.150370i
862862 −334.640 + 579.613i −0.388213 + 0.672405i
863863 908.692 + 524.634i 1.05295 + 0.607919i 0.923473 0.383664i 0.125338π-0.125338\pi
0.129473 + 0.991583i 0.458671π0.458671\pi
864864 −151.255 + 21.2120i −0.175064 + 0.0245509i
865865 418.179 + 724.308i 0.483444 + 0.837350i
866866 −172.526 + 99.6082i −0.199222 + 0.115021i
867867 89.6148 + 97.2473i 0.103362 + 0.112165i
868868 50.8990 + 469.718i 0.0586394 + 0.541150i
869869 358.082 206.739i 0.412062 0.237904i
870870 285.880 + 89.2549i 0.328597 + 0.102592i
871871 −1419.65 −1.62991
872872 81.0804 46.8118i 0.0929821 0.0536832i
873873 523.803 247.847i 0.600003 0.283903i
874874 1286.35 1.47179
875875 −367.282 + 832.130i −0.419751 + 0.951006i
876876 15.8378 50.7277i 0.0180796 0.0579083i
877877 −1065.07 −1.21445 −0.607224 0.794530i 0.707717π-0.707717\pi
−0.607224 + 0.794530i 0.707717π0.707717\pi
878878 −312.499 180.422i −0.355922 0.205491i
879879 −48.7178 216.865i −0.0554241 0.246718i
880880 −95.1278 164.766i −0.108100 0.187234i
881881 963.331i 1.09345i 0.837312 + 0.546726i 0.184126π0.184126\pi
−0.837312 + 0.546726i 0.815874π0.815874\pi
882882 381.313 + 493.521i 0.432327 + 0.559547i
883883 −1212.68 −1.37336 −0.686681 0.726959i 0.740933π-0.740933\pi
−0.686681 + 0.726959i 0.740933π0.740933\pi
884884 451.001 260.386i 0.510182 0.294554i
885885 −282.533 306.596i −0.319246 0.346436i
886886 −329.781 + 571.197i −0.372213 + 0.644692i
887887 467.361i 0.526901i −0.964673 0.263450i 0.915139π-0.915139\pi
0.964673 0.263450i 0.0848606π-0.0848606\pi
888888 −399.121 + 367.796i −0.449460 + 0.414184i
889889 −482.119 212.796i −0.542316 0.239365i
890890 29.7288i 0.0334031i
891891 −1075.51 + 405.202i −1.20708 + 0.454772i
892892 −294.546 510.169i −0.330209 0.571939i
893893 1453.85i 1.62805i
894894 497.971 111.867i 0.557015 0.125131i
895895 345.310 + 598.095i 0.385822 + 0.668263i
896896 −78.7351 + 8.53179i −0.0878739 + 0.00952209i
897897 287.338 + 1279.08i 0.320333 + 1.42595i
898898 270.981 + 469.354i 0.301761 + 0.522665i
899899 615.449 355.330i 0.684593 0.395250i
900900 −223.930 + 105.957i −0.248811 + 0.117730i
901901 −348.836 + 604.202i −0.387166 + 0.670591i
902902 −109.200 63.0469i −0.121065 0.0698968i
903903 1.00750 + 2.95183i 0.00111573 + 0.00326892i
904904 −238.616 413.295i −0.263956 0.457185i
905905 228.170i 0.252121i
906906 68.5479 + 305.138i 0.0756599 + 0.336797i
907907 −1051.14 −1.15892 −0.579461 0.815000i 0.696737π-0.696737\pi
−0.579461 + 0.815000i 0.696737π0.696737\pi
908908 −388.448 224.271i −0.427806 0.246994i
909909 477.334 689.926i 0.525120 0.758994i
910910 −445.639 + 325.973i −0.489714 + 0.358213i
911911 1182.79 + 682.886i 1.29835 + 0.749601i 0.980118 0.198413i 0.0635788π-0.0635788\pi
0.318228 + 0.948014i 0.396912π0.396912\pi
912912 −123.855 + 396.703i −0.135806 + 0.434982i
913913 400.205 693.175i 0.438340 0.759228i
914914 −592.157 341.882i −0.647874 0.374050i
915915 35.2664 + 156.987i 0.0385425 + 0.171571i
916916 −103.470 + 179.215i −0.112958 + 0.195649i
917917 442.337 1002.18i 0.482374 1.09289i
918918 82.9914 + 591.781i 0.0904045 + 0.644642i
919919 87.7536 151.994i 0.0954881 0.165390i −0.814324 0.580410i 0.802892π-0.802892\pi
0.909812 + 0.415020i 0.136225π0.136225\pi
920920 249.019i 0.270673i
921921 −142.258 + 455.645i −0.154460 + 0.494729i
922922 639.586 0.693695
923923 −813.214 + 469.509i −0.881055 + 0.508677i
924924 −563.990 + 192.498i −0.610379 + 0.208331i
925925 −440.158 + 762.377i −0.475847 + 0.824191i
926926 384.979 + 222.268i 0.415744 + 0.240030i
927927 −955.538 661.102i −1.03079 0.713162i
928928 59.5611 + 103.163i 0.0641822 + 0.111167i
929929 −911.266 + 526.120i −0.980910 + 0.566329i −0.902545 0.430596i 0.858303π-0.858303\pi
−0.0783655 + 0.996925i 0.524970π0.524970\pi
930930 143.040 458.152i 0.153807 0.492637i
931931 1657.60 363.505i 1.78045 0.390446i
932932 374.877 216.435i 0.402229 0.232227i
933933 985.160 907.839i 1.05591 0.973032i
934934 422.584 0.452446
935935 −644.644 + 372.185i −0.689458 + 0.398059i
936936 −422.128 34.5416i −0.450991 0.0369034i
937937 1548.61 1.65274 0.826368 0.563131i 0.190403π-0.190403\pi
0.826368 + 0.563131i 0.190403π0.190403\pi
938938 341.073 772.750i 0.363618 0.823827i
939939 574.600 129.081i 0.611927 0.137467i
940940 −281.445 −0.299409
941941 −495.455 286.051i −0.526519 0.303986i 0.213079 0.977035i 0.431651π-0.431651\pi
−0.739598 + 0.673049i 0.764984π0.764984\pi
942942 1067.50 + 333.287i 1.13323 + 0.353808i
943943 −82.5200 142.929i −0.0875079 0.151568i
944944 165.832i 0.175670i
945945 −155.070 614.291i −0.164095 0.650043i
946946 −2.98034 −0.00315047
947947 −830.937 + 479.742i −0.877442 + 0.506591i −0.869814 0.493380i 0.835761π-0.835761\pi
−0.00762758 + 0.999971i 0.502428π0.502428\pi
948948 −52.1079 + 166.899i −0.0549662 + 0.176054i
949949 73.6829 127.623i 0.0776427 0.134481i
950950 674.074i 0.709551i
951951 −224.078 997.477i −0.235624 1.04887i
952952 33.3804 + 308.049i 0.0350635 + 0.323581i
953953 1308.52i 1.37305i −0.727104 0.686527i 0.759134π-0.759134\pi
0.727104 0.686527i 0.240866π-0.240866\pi
954954 512.893 242.685i 0.537624 0.254387i
955955 −432.669 749.405i −0.453057 0.784717i
956956 893.910i 0.935052i
957957 607.437 + 659.172i 0.634730 + 0.688790i
958958 356.348 + 617.213i 0.371971 + 0.644273i
959959 −233.737 + 529.565i −0.243730 + 0.552205i
960960 76.7963 + 23.9767i 0.0799962 + 0.0249757i
961961 −88.9530 154.071i −0.0925630 0.160324i
962962 −1303.41 + 752.522i −1.35489 + 0.782247i
963963 412.819 + 872.456i 0.428680 + 0.905977i
964964 −82.7511 + 143.329i −0.0858413 + 0.148682i
965965 463.331 + 267.504i 0.480136 + 0.277207i
966966 −765.266 150.895i −0.792201 0.156206i
967967 85.8474 + 148.692i 0.0887770 + 0.153766i 0.906994 0.421143i 0.138371π-0.138371\pi
−0.818217 + 0.574909i 0.805037π0.805037\pi
968968 227.198i 0.234709i
969969 1552.09 + 484.581i 1.60175 + 0.500084i
970970 −305.238 −0.314678
971971 −803.642 463.983i −0.827644 0.477840i 0.0254013 0.999677i 0.491914π-0.491914\pi
−0.853045 + 0.521837i 0.825247π0.825247\pi
972972 218.330 434.198i 0.224619 0.446706i
973973 −76.0950 702.238i −0.0782066 0.721724i
974974 −358.693 207.092i −0.368268 0.212620i
975975 −670.265 + 150.572i −0.687451 + 0.154433i
976976 −31.9991 + 55.4240i −0.0327859 + 0.0567869i
977977 −1232.02 711.306i −1.26102 0.728051i −0.287749 0.957706i 0.592907π-0.592907\pi
−0.973272 + 0.229655i 0.926240π0.926240\pi
978978 −294.693 92.0067i −0.301322 0.0940763i
979979 −44.4893 + 77.0577i −0.0454436 + 0.0787107i
980980 −70.3696 320.888i −0.0718057 0.327437i
981981 −24.2958 + 296.916i −0.0247664 + 0.302667i
982982 302.473 523.898i 0.308017 0.533501i
983983 282.456i 0.287341i −0.989626 0.143670i 0.954110π-0.954110\pi
0.989626 0.143670i 0.0458905π-0.0458905\pi
984984 52.0240 11.6869i 0.0528699 0.0118770i
985985 −582.598 −0.591470
986986 403.622 233.031i 0.409353 0.236340i
987987 −170.544 + 864.914i −0.172790 + 0.876306i
988988 −576.219 + 998.041i −0.583218 + 1.01016i
989989 −3.37825 1.95043i −0.00341583 0.00197213i
990990 603.373 + 49.3724i 0.609468 + 0.0498711i
991991 587.805 + 1018.11i 0.593143 + 1.02735i 0.993806 + 0.111129i 0.0354465π0.0354465\pi
−0.400663 + 0.916226i 0.631220π0.631220\pi
992992 165.329 95.4529i 0.166663 0.0962226i
993993 1649.62 370.579i 1.66125 0.373192i
994994 −60.1892 555.452i −0.0605525 0.558805i
995995 280.484 161.938i 0.281894 0.162751i
996996 74.1855 + 330.234i 0.0744834 + 0.331560i
997997 −715.860 −0.718014 −0.359007 0.933335i 0.616885π-0.616885\pi
−0.359007 + 0.933335i 0.616885π0.616885\pi
998998 −252.776 + 145.940i −0.253283 + 0.146233i
999999 −239.847 1710.26i −0.240087 1.71198i
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 126.3.i.a.65.6 32
3.2 odd 2 378.3.i.a.359.15 32
7.4 even 3 126.3.r.a.11.1 yes 32
9.4 even 3 378.3.r.a.233.2 32
9.5 odd 6 126.3.r.a.23.9 yes 32
21.11 odd 6 378.3.r.a.305.10 32
63.4 even 3 378.3.i.a.179.10 32
63.32 odd 6 inner 126.3.i.a.95.6 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.3.i.a.65.6 32 1.1 even 1 trivial
126.3.i.a.95.6 yes 32 63.32 odd 6 inner
126.3.r.a.11.1 yes 32 7.4 even 3
126.3.r.a.23.9 yes 32 9.5 odd 6
378.3.i.a.179.10 32 63.4 even 3
378.3.i.a.359.15 32 3.2 odd 2
378.3.r.a.233.2 32 9.4 even 3
378.3.r.a.305.10 32 21.11 odd 6