Properties

Label 182.3.r.a.17.17
Level 182182
Weight 33
Character 182.17
Analytic conductor 4.9594.959
Analytic rank 00
Dimension 3636
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [182,3,Mod(17,182)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(182, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("182.17"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 182=2713 182 = 2 \cdot 7 \cdot 13
Weight: k k == 3 3
Character orbit: [χ][\chi] == 182.r (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.959140811364.95914081136
Analytic rank: 00
Dimension: 3636
Relative dimension: 1818 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 17.17
Character χ\chi == 182.17
Dual form 182.3.r.a.75.8

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.41421iq2+(3.489432.01462i)q32.00000q4+(4.597027.96227i)q5+(2.84911+4.93480i)q6+(6.55840+2.44692i)q72.82843iq8+(3.617426.26555i)q9+(11.26036.50116i)q10+(14.87248.58660i)q11+(6.97886+4.02925i)q12+(9.513388.85977i)q13+(3.460479.27497i)q14+(32.081918.5225i)q15+4.00000q16+3.67858iq17+(8.86083+5.11580i)q18+(8.6146914.9211i)q19+(9.19403+15.9245i)q20+(17.9554+21.7511i)q21+(12.1433+21.0328i)q22+7.00175q23+(5.698229.86960i)q24+(29.7651+51.5547i)q25+(12.529613.4540i)q26+7.11227iq27+(13.11684.89384i)q28+(0.3597810.623160i)q29+(26.194845.3707i)q30+(22.210138.4690i)q31+5.65685iq32+(34.597659.9247i)q335.20230q34+(49.6321+40.9712i)q35+(7.23484+12.5311i)q36+30.5131iq37+(21.1016+12.1830i)q38+(51.045411.7497i)q39+(22.5207+13.0023i)q40+(16.253028.1511i)q41+(30.760725.3928i)q42+(26.8250+46.4622i)q43+(29.7449+17.1732i)q4466.5173q45+9.90197iq46+(36.6987+63.5641i)q47+(13.95778.05850i)q48+(37.025132.0958i)q49+(72.909342.0942i)q50+(7.41096+12.8362i)q51+(19.0268+17.7195i)q52+(4.39981+7.62069i)q5310.0583q54+(136.73878.9455i)q55+(6.92094+18.5499i)q5669.4215iq57+(0.881281+0.508808i)q5813.1679q59+(64.1639+37.0450i)q60+(10.04855.80148i)q61+(54.4034+31.4098i)q62+(8.39315+49.9435i)q638.00000q64+(26.8107+116.477i)q65+(84.7464+48.9283i)q66+(24.061013.8916i)q677.35717iq68+(24.432114.1059i)q69+(57.9420+70.1904i)q70+(25.6313+14.7983i)q71+(17.721710.2316i)q72+(30.127952.1831i)q7343.1520q74+239.862iq75+(17.2294+29.8422i)q76+(76.5286+92.7060i)q77+(16.616572.1891i)q78+(66.3791114.972i)q79+(18.388131.8491i)q80+(46.8853+81.2078i)q81+(39.8117+22.9853i)q82108.148q83+(35.910943.5021i)q84+(29.289916.9105i)q85+(65.7075+37.9363i)q862.89930iq87+(24.286642.0656i)q88+97.2426q8994.0697iq90+(84.0717+34.8274i)q9114.0035q92178.980iq93+(89.8932+51.8998i)q94158.408q95+(11.3964+19.7392i)q96+(39.572868.5420i)q97+(45.3903+52.3615i)q98124.245iq99+O(q100)q+1.41421i q^{2} +(3.48943 - 2.01462i) q^{3} -2.00000 q^{4} +(-4.59702 - 7.96227i) q^{5} +(2.84911 + 4.93480i) q^{6} +(-6.55840 + 2.44692i) q^{7} -2.82843i q^{8} +(3.61742 - 6.26555i) q^{9} +(11.2603 - 6.50116i) q^{10} +(14.8724 - 8.58660i) q^{11} +(-6.97886 + 4.02925i) q^{12} +(-9.51338 - 8.85977i) q^{13} +(-3.46047 - 9.27497i) q^{14} +(-32.0819 - 18.5225i) q^{15} +4.00000 q^{16} +3.67858i q^{17} +(8.86083 + 5.11580i) q^{18} +(8.61469 - 14.9211i) q^{19} +(9.19403 + 15.9245i) q^{20} +(-17.9554 + 21.7511i) q^{21} +(12.1433 + 21.0328i) q^{22} +7.00175 q^{23} +(-5.69822 - 9.86960i) q^{24} +(-29.7651 + 51.5547i) q^{25} +(12.5296 - 13.4540i) q^{26} +7.11227i q^{27} +(13.1168 - 4.89384i) q^{28} +(0.359781 - 0.623160i) q^{29} +(26.1948 - 45.3707i) q^{30} +(22.2101 - 38.4690i) q^{31} +5.65685i q^{32} +(34.5976 - 59.9247i) q^{33} -5.20230 q^{34} +(49.6321 + 40.9712i) q^{35} +(-7.23484 + 12.5311i) q^{36} +30.5131i q^{37} +(21.1016 + 12.1830i) q^{38} +(-51.0454 - 11.7497i) q^{39} +(-22.5207 + 13.0023i) q^{40} +(16.2530 - 28.1511i) q^{41} +(-30.7607 - 25.3928i) q^{42} +(26.8250 + 46.4622i) q^{43} +(-29.7449 + 17.1732i) q^{44} -66.5173 q^{45} +9.90197i q^{46} +(36.6987 + 63.5641i) q^{47} +(13.9577 - 8.05850i) q^{48} +(37.0251 - 32.0958i) q^{49} +(-72.9093 - 42.0942i) q^{50} +(7.41096 + 12.8362i) q^{51} +(19.0268 + 17.7195i) q^{52} +(-4.39981 + 7.62069i) q^{53} -10.0583 q^{54} +(-136.738 - 78.9455i) q^{55} +(6.92094 + 18.5499i) q^{56} -69.4215i q^{57} +(0.881281 + 0.508808i) q^{58} -13.1679 q^{59} +(64.1639 + 37.0450i) q^{60} +(-10.0485 - 5.80148i) q^{61} +(54.4034 + 31.4098i) q^{62} +(-8.39315 + 49.9435i) q^{63} -8.00000 q^{64} +(-26.8107 + 116.477i) q^{65} +(84.7464 + 48.9283i) q^{66} +(24.0610 - 13.8916i) q^{67} -7.35717i q^{68} +(24.4321 - 14.1059i) q^{69} +(-57.9420 + 70.1904i) q^{70} +(-25.6313 + 14.7983i) q^{71} +(-17.7217 - 10.2316i) q^{72} +(30.1279 - 52.1831i) q^{73} -43.1520 q^{74} +239.862i q^{75} +(-17.2294 + 29.8422i) q^{76} +(-76.5286 + 92.7060i) q^{77} +(16.6165 - 72.1891i) q^{78} +(-66.3791 - 114.972i) q^{79} +(-18.3881 - 31.8491i) q^{80} +(46.8853 + 81.2078i) q^{81} +(39.8117 + 22.9853i) q^{82} -108.148 q^{83} +(35.9109 - 43.5021i) q^{84} +(29.2899 - 16.9105i) q^{85} +(-65.7075 + 37.9363i) q^{86} -2.89930i q^{87} +(-24.2866 - 42.0656i) q^{88} +97.2426 q^{89} -94.0697i q^{90} +(84.0717 + 34.8274i) q^{91} -14.0035 q^{92} -178.980i q^{93} +(-89.8932 + 51.8998i) q^{94} -158.408 q^{95} +(11.3964 + 19.7392i) q^{96} +(-39.5728 - 68.5420i) q^{97} +(45.3903 + 52.3615i) q^{98} -124.245i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 36q+6q372q4+8q7+44q9+12q1112q12+4q1312q14+60q15+144q16+24q18+50q19+42q21+12q2256q2382q25+48q26+24q98+O(q100) 36 q + 6 q^{3} - 72 q^{4} + 8 q^{7} + 44 q^{9} + 12 q^{11} - 12 q^{12} + 4 q^{13} - 12 q^{14} + 60 q^{15} + 144 q^{16} + 24 q^{18} + 50 q^{19} + 42 q^{21} + 12 q^{22} - 56 q^{23} - 82 q^{25} + 48 q^{26}+ \cdots - 24 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/182Z)×\left(\mathbb{Z}/182\mathbb{Z}\right)^\times.

nn 1515 157157
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) e(16)e\left(\frac{1}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.41421i 0.707107i
33 3.48943 2.01462i 1.16314 0.671541i 0.211088 0.977467i 0.432299π-0.432299\pi
0.952055 + 0.305926i 0.0989659π0.0989659\pi
44 −2.00000 −0.500000
55 −4.59702 7.96227i −0.919403 1.59245i −0.800324 0.599568i 0.795339π-0.795339\pi
−0.119080 0.992885i 0.537994π-0.537994\pi
66 2.84911 + 4.93480i 0.474851 + 0.822467i
77 −6.55840 + 2.44692i −0.936914 + 0.349560i
88 2.82843i 0.353553i
99 3.61742 6.26555i 0.401936 0.696173i
1010 11.2603 6.50116i 1.12603 0.650116i
1111 14.8724 8.58660i 1.35204 0.780600i 0.363505 0.931592i 0.381580π-0.381580\pi
0.988535 + 0.150992i 0.0482468π0.0482468\pi
1212 −6.97886 + 4.02925i −0.581572 + 0.335771i
1313 −9.51338 8.85977i −0.731799 0.681521i
1414 −3.46047 9.27497i −0.247176 0.662498i
1515 −32.0819 18.5225i −2.13880 1.23483i
1616 4.00000 0.250000
1717 3.67858i 0.216387i 0.994130 + 0.108194i 0.0345067π0.0345067\pi
−0.994130 + 0.108194i 0.965493π0.965493\pi
1818 8.86083 + 5.11580i 0.492268 + 0.284211i
1919 8.61469 14.9211i 0.453405 0.785320i −0.545190 0.838312i 0.683543π-0.683543\pi
0.998595 + 0.0529922i 0.0168759π0.0168759\pi
2020 9.19403 + 15.9245i 0.459702 + 0.796227i
2121 −17.9554 + 21.7511i −0.855021 + 1.03577i
2222 12.1433 + 21.0328i 0.551968 + 0.956036i
2323 7.00175 0.304424 0.152212 0.988348i 0.451360π-0.451360\pi
0.152212 + 0.988348i 0.451360π0.451360\pi
2424 −5.69822 9.86960i −0.237426 0.411233i
2525 −29.7651 + 51.5547i −1.19060 + 2.06219i
2626 12.5296 13.4540i 0.481908 0.517460i
2727 7.11227i 0.263417i
2828 13.1168 4.89384i 0.468457 0.174780i
2929 0.359781 0.623160i 0.0124063 0.0214883i −0.859756 0.510706i 0.829384π-0.829384\pi
0.872162 + 0.489217i 0.162718π0.162718\pi
3030 26.1948 45.3707i 0.873160 1.51236i
3131 22.2101 38.4690i 0.716455 1.24094i −0.245941 0.969285i 0.579097π-0.579097\pi
0.962396 0.271651i 0.0875696π-0.0875696\pi
3232 5.65685i 0.176777i
3333 34.5976 59.9247i 1.04841 1.81590i
3434 −5.20230 −0.153009
3535 49.6321 + 40.9712i 1.41806 + 1.17060i
3636 −7.23484 + 12.5311i −0.200968 + 0.348086i
3737 30.5131i 0.824677i 0.911031 + 0.412339i 0.135288π0.135288\pi
−0.911031 + 0.412339i 0.864712π0.864712\pi
3838 21.1016 + 12.1830i 0.555305 + 0.320606i
3939 −51.0454 11.7497i −1.30886 0.301274i
4040 −22.5207 + 13.0023i −0.563017 + 0.325058i
4141 16.2530 28.1511i 0.396416 0.686612i −0.596865 0.802342i 0.703587π-0.703587\pi
0.993281 + 0.115729i 0.0369206π0.0369206\pi
4242 −30.7607 25.3928i −0.732397 0.604591i
4343 26.8250 + 46.4622i 0.623837 + 1.08052i 0.988765 + 0.149481i 0.0477604π0.0477604\pi
−0.364928 + 0.931036i 0.618906π0.618906\pi
4444 −29.7449 + 17.1732i −0.676020 + 0.390300i
4545 −66.5173 −1.47816
4646 9.90197i 0.215260i
4747 36.6987 + 63.5641i 0.780824 + 1.35243i 0.931462 + 0.363838i 0.118534π0.118534\pi
−0.150638 + 0.988589i 0.548133π0.548133\pi
4848 13.9577 8.05850i 0.290786 0.167885i
4949 37.0251 32.0958i 0.755615 0.655016i
5050 −72.9093 42.0942i −1.45819 0.841884i
5151 7.41096 + 12.8362i 0.145313 + 0.251690i
5252 19.0268 + 17.7195i 0.365899 + 0.340760i
5353 −4.39981 + 7.62069i −0.0830153 + 0.143787i −0.904544 0.426381i 0.859788π-0.859788\pi
0.821528 + 0.570167i 0.193122π0.193122\pi
5454 −10.0583 −0.186264
5555 −136.738 78.9455i −2.48614 1.43537i
5656 6.92094 + 18.5499i 0.123588 + 0.331249i
5757 69.4215i 1.21792i
5858 0.881281 + 0.508808i 0.0151945 + 0.00877255i
5959 −13.1679 −0.223185 −0.111592 0.993754i 0.535595π-0.535595\pi
−0.111592 + 0.993754i 0.535595π0.535595\pi
6060 64.1639 + 37.0450i 1.06940 + 0.617417i
6161 −10.0485 5.80148i −0.164729 0.0951062i 0.415369 0.909653i 0.363652π-0.363652\pi
−0.580098 + 0.814547i 0.696986π0.696986\pi
6262 54.4034 + 31.4098i 0.877474 + 0.506610i
6363 −8.39315 + 49.9435i −0.133225 + 0.792755i
6464 −8.00000 −0.125000
6565 −26.8107 + 116.477i −0.412472 + 1.79195i
6666 84.7464 + 48.9283i 1.28404 + 0.741338i
6767 24.0610 13.8916i 0.359119 0.207338i −0.309575 0.950875i 0.600187π-0.600187\pi
0.668694 + 0.743537i 0.266854π0.266854\pi
6868 7.35717i 0.108194i
6969 24.4321 14.1059i 0.354089 0.204433i
7070 −57.9420 + 70.1904i −0.827742 + 1.00272i
7171 −25.6313 + 14.7983i −0.361005 + 0.208426i −0.669521 0.742793i 0.733501π-0.733501\pi
0.308517 + 0.951219i 0.400167π0.400167\pi
7272 −17.7217 10.2316i −0.246134 0.142106i
7373 30.1279 52.1831i 0.412711 0.714836i −0.582474 0.812849i 0.697915π-0.697915\pi
0.995185 + 0.0980129i 0.0312486π0.0312486\pi
7474 −43.1520 −0.583135
7575 239.862i 3.19816i
7676 −17.2294 + 29.8422i −0.226702 + 0.392660i
7777 −76.5286 + 92.7060i −0.993878 + 1.20397i
7878 16.6165 72.1891i 0.213033 0.925501i
7979 −66.3791 114.972i −0.840242 1.45534i −0.889690 0.456565i 0.849080π-0.849080\pi
0.0494485 0.998777i 0.484254π-0.484254\pi
8080 −18.3881 31.8491i −0.229851 0.398113i
8181 46.8853 + 81.2078i 0.578831 + 1.00257i
8282 39.8117 + 22.9853i 0.485508 + 0.280308i
8383 −108.148 −1.30299 −0.651493 0.758654i 0.725857π-0.725857\pi
−0.651493 + 0.758654i 0.725857π0.725857\pi
8484 35.9109 43.5021i 0.427511 0.517883i
8585 29.2899 16.9105i 0.344587 0.198947i
8686 −65.7075 + 37.9363i −0.764041 + 0.441119i
8787 2.89930i 0.0333253i
8888 −24.2866 42.0656i −0.275984 0.478018i
8989 97.2426 1.09261 0.546307 0.837585i 0.316033π-0.316033\pi
0.546307 + 0.837585i 0.316033π0.316033\pi
9090 94.0697i 1.04522i
9191 84.0717 + 34.8274i 0.923865 + 0.382719i
9292 −14.0035 −0.152212
9393 178.980i 1.92452i
9494 −89.8932 + 51.8998i −0.956310 + 0.552126i
9595 −158.408 −1.66745
9696 11.3964 + 19.7392i 0.118713 + 0.205617i
9797 −39.5728 68.5420i −0.407967 0.706619i 0.586695 0.809808i 0.300429π-0.300429\pi
−0.994662 + 0.103189i 0.967095π0.967095\pi
9898 45.3903 + 52.3615i 0.463166 + 0.534301i
9999 124.245i 1.25500i
100100 59.5302 103.109i 0.595302 1.03109i
101101 −9.55534 + 5.51678i −0.0946073 + 0.0546216i −0.546557 0.837422i 0.684062π-0.684062\pi
0.451950 + 0.892043i 0.350729π0.350729\pi
102102 −18.1531 + 10.4807i −0.177971 + 0.102752i
103103 139.106 80.3127i 1.35054 0.779735i 0.362215 0.932094i 0.382020π-0.382020\pi
0.988325 + 0.152360i 0.0486872π0.0486872\pi
104104 −25.0592 + 26.9079i −0.240954 + 0.258730i
105105 255.729 + 42.9760i 2.43552 + 0.409296i
106106 −10.7773 6.22227i −0.101673 0.0587007i
107107 134.060 1.25290 0.626450 0.779461i 0.284507π-0.284507\pi
0.626450 + 0.779461i 0.284507π0.284507\pi
108108 14.2245i 0.131709i
109109 −53.7515 31.0334i −0.493133 0.284710i 0.232740 0.972539i 0.425231π-0.425231\pi
−0.725873 + 0.687829i 0.758564π0.758564\pi
110110 111.646 193.376i 1.01496 1.75797i
111111 61.4723 + 106.473i 0.553805 + 0.959218i
112112 −26.2336 + 9.78769i −0.234228 + 0.0873901i
113113 −15.4838 26.8187i −0.137024 0.237333i 0.789345 0.613950i 0.210421π-0.210421\pi
−0.926369 + 0.376617i 0.877087π0.877087\pi
114114 98.1768 0.861200
115115 −32.1872 55.7498i −0.279888 0.484781i
116116 −0.719563 + 1.24632i −0.00620313 + 0.0107441i
117117 −89.9253 + 27.5571i −0.768592 + 0.235531i
118118 18.6222i 0.157815i
119119 −9.00121 24.1256i −0.0756404 0.202736i
120120 −52.3896 + 90.7414i −0.436580 + 0.756179i
121121 86.9596 150.618i 0.718674 1.24478i
122122 8.20453 14.2107i 0.0672502 0.116481i
123123 130.975i 1.06484i
124124 −44.4202 + 76.9380i −0.358227 + 0.620468i
125125 317.472 2.53978
126126 −70.6308 11.8697i −0.560562 0.0942041i
127127 24.8316 43.0096i 0.195524 0.338658i −0.751548 0.659678i 0.770692π-0.770692\pi
0.947072 + 0.321020i 0.104026π0.104026\pi
128128 11.3137i 0.0883883i
129129 187.208 + 108.085i 1.45122 + 0.837865i
130130 −164.723 37.9160i −1.26710 0.291662i
131131 −148.863 + 85.9460i −1.13636 + 0.656076i −0.945526 0.325547i 0.894452π-0.894452\pi
−0.190831 + 0.981623i 0.561118π0.561118\pi
132132 −69.1951 + 119.849i −0.524205 + 0.907950i
133133 −19.9878 + 118.938i −0.150285 + 0.894270i
134134 19.6457 + 34.0274i 0.146610 + 0.253936i
135135 56.6298 32.6952i 0.419480 0.242187i
136136 10.4046 0.0765045
137137 43.5477i 0.317866i −0.987289 0.158933i 0.949195π-0.949195\pi
0.987289 0.158933i 0.0508054π-0.0508054\pi
138138 19.9487 + 34.5522i 0.144556 + 0.250379i
139139 −21.7494 + 12.5570i −0.156471 + 0.0903384i −0.576191 0.817315i 0.695462π-0.695462\pi
0.419720 + 0.907654i 0.362128π0.362128\pi
140140 −99.2642 81.9423i −0.709030 0.585302i
141141 256.115 + 147.868i 1.81642 + 1.04871i
142142 −20.9279 36.2482i −0.147380 0.255269i
143143 −217.563 50.0787i −1.52142 0.350201i
144144 14.4697 25.0622i 0.100484 0.174043i
145145 −6.61568 −0.0456254
146146 73.7980 + 42.6073i 0.505466 + 0.291831i
147147 64.5358 186.588i 0.439019 1.26930i
148148 61.0261i 0.412339i
149149 133.539 + 77.0987i 0.896233 + 0.517441i 0.875976 0.482354i 0.160218π-0.160218\pi
0.0202572 + 0.999795i 0.493551π0.493551\pi
150150 −339.216 −2.26144
151151 −38.2961 22.1103i −0.253617 0.146426i 0.367802 0.929904i 0.380110π-0.380110\pi
−0.621419 + 0.783478i 0.713444π0.713444\pi
152152 −42.2032 24.3660i −0.277653 0.160303i
153153 23.0484 + 13.3070i 0.150643 + 0.0869738i
154154 −131.106 108.228i −0.851339 0.702778i
155155 −408.401 −2.63484
156156 102.091 + 23.4993i 0.654428 + 0.150637i
157157 112.372 + 64.8778i 0.715743 + 0.413235i 0.813184 0.582007i 0.197732π-0.197732\pi
−0.0974406 + 0.995241i 0.531066π0.531066\pi
158158 162.595 93.8742i 1.02908 0.594141i
159159 35.4559i 0.222993i
160160 45.0414 26.0046i 0.281509 0.162529i
161161 −45.9203 + 17.1327i −0.285219 + 0.106414i
162162 −114.845 + 66.3059i −0.708921 + 0.409295i
163163 −185.626 107.171i −1.13881 0.657494i −0.192676 0.981262i 0.561717π-0.561717\pi
−0.946136 + 0.323769i 0.895050π0.895050\pi
164164 −32.5061 + 56.3022i −0.198208 + 0.343306i
165165 −636.182 −3.85565
166166 152.944i 0.921351i
167167 −70.0407 + 121.314i −0.419405 + 0.726431i −0.995880 0.0906838i 0.971095π-0.971095\pi
0.576474 + 0.817115i 0.304428π0.304428\pi
168168 61.5213 + 50.7857i 0.366198 + 0.302296i
169169 12.0089 + 168.573i 0.0710587 + 0.997472i
170170 23.9151 + 41.4221i 0.140677 + 0.243660i
171171 −62.3259 107.952i −0.364479 0.631296i
172172 −53.6500 92.9245i −0.311918 0.540259i
173173 261.813 + 151.158i 1.51337 + 0.873746i 0.999877 + 0.0156530i 0.00498271π0.00498271\pi
0.513495 + 0.858093i 0.328351π0.328351\pi
174174 4.10023 0.0235645
175175 69.0611 410.949i 0.394635 2.34828i
176176 59.4897 34.3464i 0.338010 0.195150i
177177 −45.9484 + 26.5283i −0.259596 + 0.149878i
178178 137.522i 0.772594i
179179 91.7087 + 158.844i 0.512339 + 0.887398i 0.999898 + 0.0143073i 0.00455430π0.00455430\pi
−0.487558 + 0.873090i 0.662112π0.662112\pi
180180 133.035 0.739082
181181 220.794i 1.21986i 0.792456 + 0.609929i 0.208802π0.208802\pi
−0.792456 + 0.609929i 0.791198π0.791198\pi
182182 −49.2534 + 118.895i −0.270623 + 0.653271i
183183 −46.7512 −0.255471
184184 19.8039i 0.107630i
185185 242.953 140.269i 1.31326 0.758211i
186186 253.116 1.36084
187187 31.5866 + 54.7095i 0.168912 + 0.292564i
188188 −73.3975 127.128i −0.390412 0.676214i
189189 −17.4032 46.6451i −0.0920803 0.246799i
190190 224.022i 1.17906i
191191 4.70861 8.15555i 0.0246524 0.0426992i −0.853436 0.521198i 0.825485π-0.825485\pi
0.878088 + 0.478498i 0.158819π0.158819\pi
192192 −27.9154 + 16.1170i −0.145393 + 0.0839427i
193193 −29.7773 + 17.1919i −0.154287 + 0.0890774i −0.575156 0.818044i 0.695059π-0.695059\pi
0.420869 + 0.907121i 0.361725π0.361725\pi
194194 96.9331 55.9643i 0.499655 0.288476i
195195 141.103 + 460.450i 0.723603 + 2.36128i
196196 −74.0503 + 64.1915i −0.377808 + 0.327508i
197197 100.680 + 58.1276i 0.511065 + 0.295064i 0.733271 0.679936i 0.237992π-0.237992\pi
−0.222206 + 0.975000i 0.571326π0.571326\pi
198198 175.710 0.887422
199199 99.9665i 0.502344i −0.967942 0.251172i 0.919184π-0.919184\pi
0.967942 0.251172i 0.0808160π-0.0808160\pi
200200 145.819 + 84.1884i 0.729093 + 0.420942i
201201 55.9728 96.9477i 0.278471 0.482327i
202202 −7.80190 13.5133i −0.0386233 0.0668975i
203203 −0.834767 + 4.96729i −0.00411215 + 0.0244694i
204204 −14.8219 25.6723i −0.0726565 0.125845i
205205 −298.862 −1.45786
206206 113.579 + 196.725i 0.551356 + 0.954976i
207207 25.3283 43.8698i 0.122359 0.211932i
208208 −38.0535 35.4391i −0.182950 0.170380i
209209 295.884i 1.41571i
210210 −60.7773 + 361.656i −0.289416 + 1.72217i
211211 −160.266 + 277.589i −0.759555 + 1.31559i 0.183522 + 0.983016i 0.441250π0.441250\pi
−0.943078 + 0.332573i 0.892083π0.892083\pi
212212 8.79962 15.2414i 0.0415076 0.0718933i
213213 −59.6259 + 103.275i −0.279934 + 0.484859i
214214 189.590i 0.885935i
215215 246.630 427.175i 1.14712 1.98686i
216216 20.1165 0.0931321
217217 −51.5320 + 306.641i −0.237474 + 1.41309i
218218 43.8879 76.0161i 0.201321 0.348698i
219219 242.786i 1.10861i
220220 273.475 + 157.891i 1.24307 + 0.717687i
221221 32.5914 34.9958i 0.147472 0.158352i
222222 −150.576 + 86.9350i −0.678270 + 0.391599i
223223 −158.432 + 274.412i −0.710458 + 1.23055i 0.254228 + 0.967144i 0.418179π0.418179\pi
−0.964686 + 0.263404i 0.915155π0.915155\pi
224224 −13.8419 37.0999i −0.0617941 0.165625i
225225 215.346 + 372.990i 0.957092 + 1.65773i
226226 37.9273 21.8973i 0.167820 0.0968909i
227227 141.103 0.621597 0.310799 0.950476i 0.399404π-0.399404\pi
0.310799 + 0.950476i 0.399404π0.399404\pi
228228 138.843i 0.608960i
229229 −38.3046 66.3454i −0.167269 0.289718i 0.770190 0.637815i 0.220161π-0.220161\pi
−0.937459 + 0.348097i 0.886828π0.886828\pi
230230 78.8421 45.5195i 0.342792 0.197911i
231231 −80.2734 + 477.668i −0.347504 + 2.06783i
232232 −1.76256 1.01762i −0.00759725 0.00438627i
233233 −137.436 238.046i −0.589853 1.02166i −0.994251 0.107073i 0.965852π-0.965852\pi
0.404398 0.914583i 0.367481π-0.367481\pi
234234 −38.9716 127.174i −0.166545 0.543477i
235235 337.409 584.410i 1.43578 2.48685i
236236 26.3358 0.111592
237237 −463.251 267.458i −1.95464 1.12851i
238238 34.1188 12.7296i 0.143356 0.0534858i
239239 177.253i 0.741646i −0.928704 0.370823i 0.879076π-0.879076\pi
0.928704 0.370823i 0.120924π-0.120924\pi
240240 −128.328 74.0901i −0.534699 0.308709i
241241 −319.864 −1.32723 −0.663617 0.748072i 0.730980π-0.730980\pi
−0.663617 + 0.748072i 0.730980π0.730980\pi
242242 213.007 + 122.979i 0.880192 + 0.508179i
243243 271.772 + 156.907i 1.11840 + 0.645709i
244244 20.0969 + 11.6030i 0.0823644 + 0.0475531i
245245 −425.760 147.259i −1.73780 0.601058i
246246 185.227 0.752954
247247 −214.152 + 65.6258i −0.867013 + 0.265691i
248248 −108.807 62.8196i −0.438737 0.253305i
249249 −377.375 + 217.877i −1.51556 + 0.875010i
250250 448.973i 1.79589i
251251 27.6527 15.9653i 0.110170 0.0636067i −0.443902 0.896075i 0.646406π-0.646406\pi
0.554073 + 0.832468i 0.313073π0.313073\pi
252252 16.7863 99.8871i 0.0666123 0.396377i
253253 104.133 60.1212i 0.411593 0.237633i
254254 60.8247 + 35.1172i 0.239467 + 0.138257i
255255 68.1366 118.016i 0.267203 0.462808i
256256 16.0000 0.0625000
257257 36.6300i 0.142529i −0.997457 0.0712646i 0.977297π-0.977297\pi
0.997457 0.0712646i 0.0227035π-0.0227035\pi
258258 −152.855 + 264.752i −0.592460 + 1.02617i
259259 −74.6631 200.117i −0.288274 0.772652i
260260 53.6213 232.953i 0.206236 0.895974i
261261 −2.60296 4.50846i −0.00997303 0.0172738i
262262 −121.546 210.524i −0.463916 0.803526i
263263 211.204 + 365.815i 0.803056 + 1.39093i 0.917596 + 0.397515i 0.130127π0.130127\pi
−0.114540 + 0.993419i 0.536539π0.536539\pi
264264 −169.493 97.8567i −0.642018 0.370669i
265265 80.9040 0.305298
266266 −168.204 28.2671i −0.632344 0.106267i
267267 339.321 195.907i 1.27087 0.733735i
268268 −48.1220 + 27.7832i −0.179560 + 0.103669i
269269 445.620i 1.65658i −0.560300 0.828290i 0.689314π-0.689314\pi
0.560300 0.828290i 0.310686π-0.310686\pi
270270 46.2380 + 80.0866i 0.171252 + 0.296617i
271271 −368.469 −1.35967 −0.679833 0.733367i 0.737948π-0.737948\pi
−0.679833 + 0.733367i 0.737948π0.737948\pi
272272 14.7143i 0.0540968i
273273 363.527 47.8451i 1.33160 0.175257i
274274 61.5857 0.224765
275275 1022.32i 3.71755i
276276 −48.8642 + 28.2118i −0.177044 + 0.102217i
277277 333.166 1.20276 0.601382 0.798962i 0.294617π-0.294617\pi
0.601382 + 0.798962i 0.294617π0.294617\pi
278278 −17.7583 30.7583i −0.0638789 0.110641i
279279 −160.686 278.317i −0.575937 0.997552i
280280 115.884 140.381i 0.413871 0.501360i
281281 289.853i 1.03151i 0.856738 + 0.515753i 0.172488π0.172488\pi
−0.856738 + 0.515753i 0.827512π0.827512\pi
282282 −209.117 + 362.202i −0.741551 + 1.28440i
283283 13.4673 7.77535i 0.0475876 0.0274747i −0.476017 0.879436i 0.657920π-0.657920\pi
0.523605 + 0.851961i 0.324587π0.324587\pi
284284 51.2627 29.5965i 0.180502 0.104213i
285285 −552.752 + 319.132i −1.93948 + 1.11976i
286286 70.8220 307.680i 0.247629 1.07580i
287287 −37.7104 + 224.396i −0.131395 + 0.781868i
288288 35.4433 + 20.4632i 0.123067 + 0.0710528i
289289 275.468 0.953177
290290 9.35599i 0.0322620i
291291 −276.173 159.448i −0.949048 0.547933i
292292 −60.2558 + 104.366i −0.206355 + 0.357418i
293293 126.969 + 219.916i 0.433340 + 0.750566i 0.997159 0.0753321i 0.0240017π-0.0240017\pi
−0.563819 + 0.825899i 0.690668π0.690668\pi
294294 263.875 + 91.2674i 0.897534 + 0.310433i
295295 60.5330 + 104.846i 0.205197 + 0.355411i
296296 86.3040 0.291567
297297 61.0703 + 105.777i 0.205624 + 0.356151i
298298 −109.034 + 188.852i −0.365886 + 0.633733i
299299 −66.6103 62.0339i −0.222777 0.207471i
300300 479.724i 1.59908i
301301 −289.618 239.079i −0.962187 0.794283i
302302 31.2687 54.1589i 0.103539 0.179334i
303303 −22.2285 + 38.5008i −0.0733613 + 0.127065i
304304 34.4588 59.6843i 0.113351 0.196330i
305305 106.678i 0.349764i
306306 −18.8189 + 32.5953i −0.0614997 + 0.106521i
307307 −272.611 −0.887982 −0.443991 0.896031i 0.646438π-0.646438\pi
−0.443991 + 0.896031i 0.646438π0.646438\pi
308308 153.057 185.412i 0.496939 0.601987i
309309 323.600 560.491i 1.04725 1.81389i
310310 577.566i 1.86312i
311311 −250.624 144.698i −0.805866 0.465267i 0.0396525 0.999214i 0.487375π-0.487375\pi
−0.845518 + 0.533947i 0.820708π0.820708\pi
312312 −33.2331 + 144.378i −0.106516 + 0.462751i
313313 248.246 143.325i 0.793117 0.457906i −0.0479417 0.998850i 0.515266π-0.515266\pi
0.841059 + 0.540944i 0.181933π0.181933\pi
314314 −91.7511 + 158.918i −0.292201 + 0.506107i
315315 436.247 162.763i 1.38491 0.516707i
316316 132.758 + 229.944i 0.420121 + 0.727671i
317317 72.1894 41.6786i 0.227727 0.131478i −0.381796 0.924247i 0.624694π-0.624694\pi
0.609523 + 0.792768i 0.291361π0.291361\pi
318318 −50.1421 −0.157680
319319 12.3572i 0.0387373i
320320 36.7761 + 63.6981i 0.114925 + 0.199057i
321321 467.794 270.081i 1.45730 0.841375i
322322 −24.2293 64.9410i −0.0752464 0.201680i
323323 54.8885 + 31.6899i 0.169933 + 0.0981111i
324324 −93.7707 162.416i −0.289416 0.501283i
325325 739.930 226.747i 2.27671 0.697684i
326326 151.563 262.515i 0.464918 0.805262i
327327 −250.083 −0.764779
328328 −79.6233 45.9706i −0.242754 0.140154i
329329 −396.221 327.079i −1.20432 0.994163i
330330 899.697i 2.72636i
331331 259.200 + 149.649i 0.783082 + 0.452113i 0.837521 0.546404i 0.184004π-0.184004\pi
−0.0544394 + 0.998517i 0.517337π0.517337\pi
332332 216.296 0.651493
333333 191.181 + 110.379i 0.574118 + 0.331467i
334334 −171.564 99.0525i −0.513665 0.296564i
335335 −221.217 127.720i −0.660351 0.381254i
336336 −71.8218 + 87.0043i −0.213755 + 0.258941i
337337 −605.486 −1.79669 −0.898347 0.439286i 0.855232π-0.855232\pi
−0.898347 + 0.439286i 0.855232π0.855232\pi
338338 −238.398 + 16.9832i −0.705319 + 0.0502461i
339339 −108.059 62.3879i −0.318758 0.184035i
340340 −58.5797 + 33.8210i −0.172293 + 0.0994736i
341341 762.837i 2.23706i
342342 152.667 88.1421i 0.446394 0.257726i
343343 −164.290 + 301.094i −0.478979 + 0.877826i
344344 131.415 75.8725i 0.382021 0.220560i
345345 −224.630 129.690i −0.651101 0.375913i
346346 −213.770 + 370.260i −0.617832 + 1.07012i
347347 25.2726 0.0728318 0.0364159 0.999337i 0.488406π-0.488406\pi
0.0364159 + 0.999337i 0.488406π0.488406\pi
348348 5.79859i 0.0166626i
349349 −276.022 + 478.084i −0.790894 + 1.36987i 0.134520 + 0.990911i 0.457051π0.457051\pi
−0.925414 + 0.378958i 0.876283π0.876283\pi
350350 581.170 + 97.6672i 1.66048 + 0.279049i
351351 63.0131 67.6618i 0.179524 0.192769i
352352 48.5732 + 84.1312i 0.137992 + 0.239009i
353353 75.4148 + 130.622i 0.213640 + 0.370035i 0.952851 0.303439i 0.0981349π-0.0981349\pi
−0.739211 + 0.673474i 0.764802π0.764802\pi
354354 −37.5167 64.9809i −0.105979 0.183562i
355355 235.655 + 136.056i 0.663818 + 0.383255i
356356 −194.485 −0.546307
357357 −80.0131 66.0506i −0.224126 0.185016i
358358 −224.640 + 129.696i −0.627485 + 0.362279i
359359 −53.1461 + 30.6839i −0.148039 + 0.0854705i −0.572190 0.820121i 0.693906π-0.693906\pi
0.424151 + 0.905592i 0.360573π0.360573\pi
360360 188.139i 0.522610i
361361 32.0742 + 55.5541i 0.0888481 + 0.153889i
362362 −312.250 −0.862570
363363 700.763i 1.93048i
364364 −168.143 69.6548i −0.461932 0.191359i
365365 −553.994 −1.51779
366366 66.1162i 0.180645i
367367 356.970 206.097i 0.972670 0.561572i 0.0726211 0.997360i 0.476864π-0.476864\pi
0.900049 + 0.435788i 0.143530π0.143530\pi
368368 28.0070 0.0761060
369369 −117.588 203.669i −0.318667 0.551948i
370370 198.370 + 343.588i 0.536136 + 0.928615i
371371 10.2085 60.7455i 0.0275161 0.163735i
372372 357.960i 0.962258i
373373 −83.9583 + 145.420i −0.225089 + 0.389866i −0.956346 0.292236i 0.905601π-0.905601\pi
0.731257 + 0.682102i 0.238934π0.238934\pi
374374 −77.3709 + 44.6701i −0.206874 + 0.119439i
375375 1107.80 639.587i 2.95412 1.70556i
376376 179.786 103.800i 0.478155 0.276063i
377377 −8.94379 + 2.74078i −0.0237236 + 0.00726996i
378378 65.9661 24.6118i 0.174514 0.0651106i
379379 −180.041 103.947i −0.475042 0.274266i 0.243306 0.969950i 0.421768π-0.421768\pi
−0.718348 + 0.695684i 0.755101π0.755101\pi
380380 316.815 0.833724
381381 200.105i 0.525211i
382382 11.5337 + 6.65898i 0.0301929 + 0.0174319i
383383 −253.134 + 438.440i −0.660924 + 1.14475i 0.319450 + 0.947603i 0.396502π0.396502\pi
−0.980373 + 0.197150i 0.936831π0.936831\pi
384384 −22.7929 39.4784i −0.0593564 0.102808i
385385 1089.95 + 183.170i 2.83105 + 0.475766i
386386 −24.3131 42.1115i −0.0629873 0.109097i
387387 388.149 1.00297
388388 79.1455 + 137.084i 0.203983 + 0.353309i
389389 −132.829 + 230.066i −0.341462 + 0.591429i −0.984704 0.174233i 0.944255π-0.944255\pi
0.643243 + 0.765662i 0.277589π0.277589\pi
390390 −651.175 + 199.549i −1.66968 + 0.511664i
391391 25.7565i 0.0658735i
392392 −90.7805 104.723i −0.231583 0.267150i
393393 −346.298 + 599.805i −0.881165 + 1.52622i
394394 −82.2048 + 142.383i −0.208642 + 0.361378i
395395 −610.292 + 1057.06i −1.54504 + 2.67609i
396396 248.491i 0.627502i
397397 98.2478 170.170i 0.247476 0.428640i −0.715349 0.698767i 0.753732π-0.753732\pi
0.962825 + 0.270127i 0.0870656π0.0870656\pi
398398 141.374 0.355211
399399 169.869 + 455.294i 0.425737 + 1.14109i
400400 −119.060 + 206.219i −0.297651 + 0.515547i
401401 18.3343i 0.0457213i −0.999739 0.0228607i 0.992723π-0.992723\pi
0.999739 0.0228607i 0.00727741π-0.00727741\pi
402402 137.105 + 79.1574i 0.341056 + 0.196909i
403403 −552.120 + 169.194i −1.37002 + 0.419836i
404404 19.1107 11.0336i 0.0473037 0.0273108i
405405 431.065 746.627i 1.06436 1.84352i
406406 −7.02480 1.18054i −0.0173025 0.00290773i
407407 262.004 + 453.804i 0.643743 + 1.11500i
408408 36.3062 20.9614i 0.0889857 0.0513759i
409409 55.2062 0.134979 0.0674893 0.997720i 0.478501π-0.478501\pi
0.0674893 + 0.997720i 0.478501π0.478501\pi
410410 422.655i 1.03087i
411411 −87.7321 151.957i −0.213460 0.369724i
412412 −278.211 + 160.625i −0.675270 + 0.389867i
413413 86.3602 32.2208i 0.209105 0.0780164i
414414 62.0413 + 35.8196i 0.149858 + 0.0865207i
415415 497.158 + 861.102i 1.19797 + 2.07495i
416416 50.1184 53.8158i 0.120477 0.129365i
417417 −50.5954 + 87.6338i −0.121332 + 0.210153i
418418 418.443 1.00106
419419 595.399 + 343.754i 1.42100 + 0.820415i 0.996384 0.0849586i 0.0270758π-0.0270758\pi
0.424616 + 0.905374i 0.360409π0.360409\pi
420420 −511.459 85.9521i −1.21776 0.204648i
421421 584.326i 1.38795i 0.720001 + 0.693973i 0.244141π0.244141\pi
−0.720001 + 0.693973i 0.755859π0.755859\pi
422422 −392.570 226.651i −0.930261 0.537087i
423423 531.019 1.25536
424424 21.5546 + 12.4445i 0.0508363 + 0.0293503i
425425 −189.648 109.493i −0.446231 0.257632i
426426 −146.053 84.3237i −0.342847 0.197943i
427427 80.0975 + 13.4606i 0.187582 + 0.0315237i
428428 −268.121 −0.626450
429429 −860.059 + 263.560i −2.00480 + 0.614360i
430430 604.117 + 348.787i 1.40492 + 0.811133i
431431 −2.84514 + 1.64264i −0.00660126 + 0.00381124i −0.503297 0.864113i 0.667880π-0.667880\pi
0.496696 + 0.867925i 0.334546π0.334546\pi
432432 28.4491i 0.0658544i
433433 244.440 141.128i 0.564527 0.325930i −0.190434 0.981700i 0.560989π-0.560989\pi
0.754960 + 0.655770i 0.227656π0.227656\pi
434434 −433.656 72.8772i −0.999208 0.167920i
435435 −23.0850 + 13.3281i −0.0530689 + 0.0306393i
436436 107.503 + 62.0668i 0.246566 + 0.142355i
437437 60.3179 104.474i 0.138027 0.239070i
438438 343.351 0.783906
439439 350.600i 0.798634i −0.916813 0.399317i 0.869247π-0.869247\pi
0.916813 0.399317i 0.130753π-0.130753\pi
440440 −223.292 + 386.752i −0.507481 + 0.878983i
441441 −67.1623 348.087i −0.152295 0.789313i
442442 49.4915 + 46.0912i 0.111972 + 0.104279i
443443 15.8959 + 27.5325i 0.0358824 + 0.0621501i 0.883409 0.468603i 0.155243π-0.155243\pi
−0.847527 + 0.530753i 0.821909π0.821909\pi
444444 −122.945 212.946i −0.276902 0.479609i
445445 −447.026 774.271i −1.00455 1.73994i
446446 −388.078 224.057i −0.870129 0.502369i
447447 621.299 1.38993
448448 52.4672 19.5754i 0.117114 0.0436950i
449449 −271.586 + 156.800i −0.604868 + 0.349221i −0.770954 0.636891i 0.780220π-0.780220\pi
0.166086 + 0.986111i 0.446887π0.446887\pi
450450 −527.487 + 304.545i −1.17219 + 0.676767i
451451 558.234i 1.23777i
452452 30.9675 + 53.6373i 0.0685122 + 0.118667i
453453 −178.176 −0.393324
454454 199.549i 0.439536i
455455 −109.174 829.503i −0.239943 1.82308i
456456 −196.354 −0.430600
457457 97.0336i 0.212327i 0.994349 + 0.106164i 0.0338567π0.0338567\pi
−0.994349 + 0.106164i 0.966143π0.966143\pi
458458 93.8266 54.1708i 0.204862 0.118277i
459459 −26.1631 −0.0570002
460460 64.3743 + 111.500i 0.139944 + 0.242390i
461461 −244.363 423.249i −0.530071 0.918110i −0.999385 0.0350783i 0.988832π-0.988832\pi
0.469314 0.883032i 0.344501π-0.344501\pi
462462 −675.524 113.524i −1.46217 0.245722i
463463 570.309i 1.23177i −0.787837 0.615884i 0.788799π-0.788799\pi
0.787837 0.615884i 0.211201π-0.211201\pi
464464 1.43913 2.49264i 0.00310156 0.00537207i
465465 −1425.09 + 822.774i −3.06470 + 1.76941i
466466 336.648 194.364i 0.722420 0.417089i
467467 −92.0182 + 53.1267i −0.197041 + 0.113762i −0.595275 0.803522i 0.702957π-0.702957\pi
0.398233 + 0.917284i 0.369623π0.369623\pi
468468 179.851 55.1142i 0.384296 0.117765i
469469 −123.810 + 149.982i −0.263987 + 0.319791i
470470 826.481 + 477.169i 1.75847 + 1.01525i
471471 522.818 1.11002
472472 37.2444i 0.0789076i
473473 797.906 + 460.671i 1.68690 + 0.973935i
474474 378.243 655.135i 0.797980 1.38214i
475475 512.835 + 888.255i 1.07965 + 1.87001i
476476 18.0024 + 48.2512i 0.0378202 + 0.101368i
477477 31.8319 + 55.1345i 0.0667336 + 0.115586i
478478 250.674 0.524423
479479 16.6219 + 28.7900i 0.0347012 + 0.0601043i 0.882854 0.469647i 0.155619π-0.155619\pi
−0.848153 + 0.529751i 0.822285π0.822285\pi
480480 104.779 181.483i 0.218290 0.378089i
481481 270.339 290.282i 0.562035 0.603498i
482482 452.355i 0.938497i
483483 −125.720 + 152.296i −0.260289 + 0.315312i
484484 −173.919 + 301.237i −0.359337 + 0.622390i
485485 −363.833 + 630.178i −0.750172 + 1.29934i
486486 −221.901 + 384.343i −0.456586 + 0.790829i
487487 360.023i 0.739266i −0.929178 0.369633i 0.879483π-0.879483\pi
0.929178 0.369633i 0.120517π-0.120517\pi
488488 −16.4091 + 28.4213i −0.0336251 + 0.0582404i
489489 −863.641 −1.76614
490490 208.256 602.116i 0.425012 1.22881i
491491 242.721 420.404i 0.494339 0.856221i −0.505639 0.862745i 0.668743π-0.668743\pi
0.999979 + 0.00652400i 0.00207667π0.00207667\pi
492492 261.950i 0.532419i
493493 2.29235 + 1.32349i 0.00464979 + 0.00268456i
494494 −92.8089 302.857i −0.187872 0.613071i
495495 −989.275 + 571.158i −1.99854 + 1.15385i
496496 88.8404 153.876i 0.179114 0.310234i
497497 131.890 159.771i 0.265373 0.321470i
498498 −308.125 533.688i −0.618725 1.07166i
499499 −295.490 + 170.601i −0.592164 + 0.341886i −0.765953 0.642897i 0.777732π-0.777732\pi
0.173789 + 0.984783i 0.444399π0.444399\pi
500500 −634.944 −1.26989
501501 564.423i 1.12659i
502502 22.5783 + 39.1068i 0.0449767 + 0.0779020i
503503 −227.952 + 131.608i −0.453184 + 0.261646i −0.709174 0.705034i 0.750932π-0.750932\pi
0.255990 + 0.966679i 0.417599π0.417599\pi
504504 141.262 + 23.7394i 0.280281 + 0.0471020i
505505 87.8521 + 50.7214i 0.173965 + 0.100438i
506506 85.0243 + 147.266i 0.168032 + 0.291040i
507507 381.515 + 564.030i 0.752495 + 1.11248i
508508 −49.6632 + 86.0192i −0.0977622 + 0.169329i
509509 159.836 0.314019 0.157009 0.987597i 0.449815π-0.449815\pi
0.157009 + 0.987597i 0.449815π0.449815\pi
510510 166.900 + 96.3598i 0.327255 + 0.188941i
511511 −69.9029 + 415.958i −0.136796 + 0.814007i
512512 22.6274i 0.0441942i
513513 106.123 + 61.2700i 0.206867 + 0.119435i
514514 51.8027 0.100783
515515 −1278.94 738.397i −2.48338 1.43378i
516516 −374.416 216.169i −0.725612 0.418932i
517517 1091.60 + 630.235i 2.11141 + 1.21902i
518518 283.008 105.590i 0.546347 0.203841i
519519 1218.11 2.34703
520520 329.446 + 75.8320i 0.633549 + 0.145831i
521521 676.625 + 390.650i 1.29870 + 0.749808i 0.980180 0.198107i 0.0634793π-0.0634793\pi
0.318525 + 0.947915i 0.396813π0.396813\pi
522522 6.37593 3.68114i 0.0122144 0.00705200i
523523 830.732i 1.58840i 0.607658 + 0.794199i 0.292109π0.292109\pi
−0.607658 + 0.794199i 0.707891π0.707891\pi
524524 297.726 171.892i 0.568179 0.328038i
525525 −586.924 1573.11i −1.11795 2.99640i
526526 −517.341 + 298.687i −0.983538 + 0.567846i
527527 141.512 + 81.7017i 0.268523 + 0.155032i
528528 138.390 239.699i 0.262103 0.453975i
529529 −479.976 −0.907326
530530 114.416i 0.215878i
531531 −47.6338 + 82.5041i −0.0897058 + 0.155375i
532532 39.9757 237.876i 0.0751423 0.447135i
533533 −404.034 + 123.814i −0.758037 + 0.232296i
534534 277.055 + 479.873i 0.518829 + 0.898638i
535535 −616.278 1067.42i −1.15192 1.99519i
536536 −39.2914 68.0547i −0.0733049 0.126968i
537537 640.023 + 369.517i 1.19185 + 0.688114i
538538 630.202 1.17138
539539 275.060 795.263i 0.510316 1.47544i
540540 −113.260 + 65.3904i −0.209740 + 0.121093i
541541 55.8428 32.2408i 0.103221 0.0595949i −0.447501 0.894284i 0.647686π-0.647686\pi
0.550722 + 0.834689i 0.314352π0.314352\pi
542542 521.094i 0.961428i
543543 444.817 + 770.446i 0.819185 + 1.41887i
544544 −20.8092 −0.0382522
545545 570.645i 1.04705i
546546 67.6632 + 514.104i 0.123925 + 0.941583i
547547 −196.545 −0.359314 −0.179657 0.983729i 0.557499π-0.557499\pi
−0.179657 + 0.983729i 0.557499π0.557499\pi
548548 87.0953i 0.158933i
549549 −72.6990 + 41.9728i −0.132421 + 0.0764531i
550550 −1445.79 −2.62870
551551 −6.19881 10.7367i −0.0112501 0.0194858i
552552 −39.8975 69.1045i −0.0722781 0.125189i
553553 716.668 + 591.607i 1.29596 + 1.06981i
554554 471.167i 0.850483i
555555 565.179 978.918i 1.01834 1.76382i
556556 43.4988 25.1141i 0.0782353 0.0451692i
557557 388.499 224.300i 0.697485 0.402693i −0.108925 0.994050i 0.534741π-0.534741\pi
0.806410 + 0.591357i 0.201408π0.201408\pi
558558 393.600 227.245i 0.705376 0.407249i
559559 156.448 679.676i 0.279872 1.21588i
560560 198.528 + 163.885i 0.354515 + 0.292651i
561561 220.438 + 127.270i 0.392938 + 0.226863i
562562 −409.914 −0.729384
563563 518.144i 0.920327i 0.887834 + 0.460164i 0.152209π0.152209\pi
−0.887834 + 0.460164i 0.847791π0.847791\pi
564564 −512.231 295.737i −0.908211 0.524356i
565565 −142.358 + 246.572i −0.251961 + 0.436410i
566566 10.9960 + 19.0456i 0.0194276 + 0.0336495i
567567 −506.202 417.868i −0.892772 0.736981i
568568 41.8558 + 72.4964i 0.0736898 + 0.127634i
569569 −686.901 −1.20721 −0.603604 0.797285i 0.706269π-0.706269\pi
−0.603604 + 0.797285i 0.706269π0.706269\pi
570570 −451.320 781.709i −0.791790 1.37142i
571571 321.533 556.911i 0.563105 0.975326i −0.434118 0.900856i 0.642940π-0.642940\pi
0.997223 0.0744705i 0.0237267π-0.0237267\pi
572572 435.125 + 100.157i 0.760708 + 0.175100i
573573 37.9443i 0.0662205i
574574 −317.344 53.3305i −0.552864 0.0929104i
575575 −208.408 + 360.973i −0.362448 + 0.627779i
576576 −28.9394 + 50.1244i −0.0502419 + 0.0870216i
577577 −139.909 + 242.329i −0.242476 + 0.419981i −0.961419 0.275088i 0.911293π-0.911293\pi
0.718943 + 0.695069i 0.244626π0.244626\pi
578578 389.571i 0.673998i
579579 −69.2706 + 119.980i −0.119638 + 0.207220i
580580 13.2314 0.0228127
581581 709.277 264.629i 1.22079 0.455472i
582582 225.494 390.567i 0.387447 0.671078i
583583 151.118i 0.259207i
584584 −147.596 85.2146i −0.252733 0.145915i
585585 632.805 + 589.328i 1.08172 + 1.00740i
586586 −311.008 + 179.561i −0.530731 + 0.306417i
587587 522.694 905.332i 0.890449 1.54230i 0.0511114 0.998693i 0.483724π-0.483724\pi
0.839338 0.543610i 0.182943π-0.182943\pi
588588 −129.072 + 373.175i −0.219510 + 0.634652i
589589 −382.666 662.797i −0.649688 1.12529i
590590 −148.275 + 85.6066i −0.251313 + 0.145096i
591591 468.421 0.792590
592592 122.052i 0.206169i
593593 300.390 + 520.290i 0.506559 + 0.877387i 0.999971 + 0.00759089i 0.00241628π0.00241628\pi
−0.493412 + 0.869796i 0.664250π0.664250\pi
594594 −149.591 + 86.3664i −0.251837 + 0.145398i
595595 −150.716 + 182.576i −0.253304 + 0.306850i
596596 −267.078 154.197i −0.448117 0.258720i
597597 −201.395 348.826i −0.337345 0.584299i
598598 87.7292 94.2012i 0.146704 0.157527i
599599 −158.885 + 275.197i −0.265251 + 0.459428i −0.967629 0.252376i 0.918788π-0.918788\pi
0.702378 + 0.711804i 0.252121π0.252121\pi
600600 678.432 1.13072
601601 −906.763 523.520i −1.50876 0.871082i −0.999948 0.0102029i 0.996752π-0.996752\pi
−0.508810 0.860879i 0.669914π-0.669914\pi
602602 338.109 409.582i 0.561643 0.680369i
603603 201.007i 0.333345i
604604 76.5923 + 44.2206i 0.126808 + 0.0732129i
605605 −1599.02 −2.64300
606606 −54.4484 31.4358i −0.0898489 0.0518743i
607607 −103.899 59.9859i −0.171167 0.0988235i 0.411969 0.911198i 0.364841π-0.364841\pi
−0.583136 + 0.812374i 0.698175π0.698175\pi
608608 84.4064 + 48.7321i 0.138826 + 0.0801514i
609609 7.09435 + 19.0147i 0.0116492 + 0.0312229i
610610 −150.865 −0.247320
611611 214.034 929.852i 0.350301 1.52185i
612612 −46.0967 26.6140i −0.0753215 0.0434869i
613613 11.5933 6.69339i 0.0189124 0.0109191i −0.490514 0.871433i 0.663191π-0.663191\pi
0.509426 + 0.860514i 0.329858π0.329858\pi
614614 385.530i 0.627898i
615615 −1042.86 + 602.095i −1.69570 + 0.979016i
616616 262.212 + 216.456i 0.425669 + 0.351389i
617617 602.948 348.112i 0.977225 0.564201i 0.0757935 0.997124i 0.475851π-0.475851\pi
0.901431 + 0.432923i 0.142518π0.142518\pi
618618 792.654 + 457.639i 1.28261 + 0.740516i
619619 459.302 795.534i 0.742006 1.28519i −0.209574 0.977793i 0.567208π-0.567208\pi
0.951580 0.307400i 0.0994589π-0.0994589\pi
620620 816.801 1.31742
621621 49.7983i 0.0801906i
622622 204.634 354.436i 0.328993 0.569833i
623623 −637.755 + 237.945i −1.02368 + 0.381934i
624624 −204.182 46.9987i −0.327214 0.0753184i
625625 −715.296 1238.93i −1.14447 1.98229i
626626 202.692 + 351.072i 0.323789 + 0.560818i
627627 −596.095 1032.47i −0.950709 1.64668i
628628 −224.743 129.756i −0.357872 0.206617i
629629 −112.245 −0.178450
630630 230.181 + 616.947i 0.365367 + 0.979280i
631631 610.860 352.680i 0.968082 0.558922i 0.0694309 0.997587i 0.477882π-0.477882\pi
0.898651 + 0.438664i 0.144548π0.144548\pi
632632 −325.190 + 187.748i −0.514541 + 0.297070i
633633 1291.50i 2.04029i
634634 58.9424 + 102.091i 0.0929691 + 0.161027i
635635 −456.605 −0.719063
636636 70.9117i 0.111496i
637637 −636.596 22.6950i −0.999365 0.0356279i
638638 17.4757 0.0273914
639639 214.126i 0.335096i
640640 −90.0827 + 52.0093i −0.140754 + 0.0812645i
641641 792.995 1.23712 0.618560 0.785737i 0.287716π-0.287716\pi
0.618560 + 0.785737i 0.287716π0.287716\pi
642642 381.953 + 661.561i 0.594942 + 1.03047i
643643 −420.524 728.369i −0.654003 1.13277i −0.982143 0.188137i 0.939755π-0.939755\pi
0.328140 0.944629i 0.393578π-0.393578\pi
644644 91.8405 34.2655i 0.142609 0.0532072i
645645 1987.47i 3.08134i
646646 −44.8163 + 77.6240i −0.0693750 + 0.120161i
647647 518.738 299.493i 0.801759 0.462896i −0.0423272 0.999104i 0.513477π-0.513477\pi
0.844086 + 0.536208i 0.180144π0.180144\pi
648648 229.690 132.612i 0.354460 0.204648i
649649 −195.839 + 113.067i −0.301754 + 0.174218i
650650 320.669 + 1046.42i 0.493337 + 1.60987i
651651 437.950 + 1173.82i 0.672734 + 1.80311i
652652 371.253 + 214.343i 0.569406 + 0.328747i
653653 −413.536 −0.633286 −0.316643 0.948545i 0.602556π-0.602556\pi
−0.316643 + 0.948545i 0.602556π0.602556\pi
654654 353.670i 0.540780i
655655 1368.65 + 790.190i 2.08954 + 1.20640i
656656 65.0122 112.604i 0.0991039 0.171653i
657657 −217.970 377.536i −0.331766 0.574636i
658658 462.560 560.341i 0.702979 0.851583i
659659 9.17613 + 15.8935i 0.0139243 + 0.0241176i 0.872904 0.487893i 0.162234π-0.162234\pi
−0.858979 + 0.512010i 0.828901π0.828901\pi
660660 1272.36 1.92782
661661 487.981 + 845.208i 0.738246 + 1.27868i 0.953284 + 0.302075i 0.0976792π0.0976792\pi
−0.215038 + 0.976606i 0.568988π0.568988\pi
662662 −211.636 + 366.564i −0.319692 + 0.553723i
663663 43.2222 187.775i 0.0651918 0.283220i
664664 305.888i 0.460675i
665665 1038.90 387.611i 1.56225 0.582873i
666666 −156.099 + 270.371i −0.234383 + 0.405963i
667667 2.51910 4.36321i 0.00377676 0.00654154i
668668 140.081 242.628i 0.209703 0.363216i
669669 1276.72i 1.90841i
670670 180.623 312.849i 0.269587 0.466938i
671671 −199.260 −0.296960
672672 −123.043 101.571i −0.183099 0.151148i
673673 478.681 829.100i 0.711264 1.23195i −0.253119 0.967435i 0.581456π-0.581456\pi
0.964383 0.264511i 0.0852104π-0.0852104\pi
674674 856.287i 1.27045i
675675 −366.671 211.698i −0.543216 0.313626i
676676 −24.0179 337.146i −0.0355294 0.498736i
677677 −973.555 + 562.082i −1.43804 + 0.830255i −0.997714 0.0675817i 0.978472π-0.978472\pi
−0.440329 + 0.897836i 0.645138π0.645138\pi
678678 88.2298 152.819i 0.130132 0.225396i
679679 427.251 + 352.694i 0.629236 + 0.519432i
680680 −47.8302 82.8443i −0.0703385 0.121830i
681681 492.368 284.269i 0.723007 0.417428i
682682 1078.81 1.58184
683683 397.466i 0.581942i −0.956732 0.290971i 0.906022π-0.906022\pi
0.956732 0.290971i 0.0939783π-0.0939783\pi
684684 124.652 + 215.903i 0.182240 + 0.315648i
685685 −346.738 + 200.189i −0.506187 + 0.292247i
686686 −425.812 232.341i −0.620717 0.338689i
687687 −267.322 154.339i −0.389115 0.224656i
688688 107.300 + 185.849i 0.155959 + 0.270129i
689689 109.375 33.5173i 0.158744 0.0486463i
690690 183.409 317.674i 0.265811 0.460398i
691691 −422.080 −0.610825 −0.305413 0.952220i 0.598794π-0.598794\pi
−0.305413 + 0.952220i 0.598794π0.598794\pi
692692 −523.627 302.316i −0.756686 0.436873i
693693 304.019 + 814.851i 0.438700 + 1.17583i
694694 35.7409i 0.0514999i
695695 199.965 + 115.450i 0.287719 + 0.166115i
696696 −8.20045 −0.0117823
697697 103.556 + 59.7882i 0.148574 + 0.0857793i
698698 −676.113 390.354i −0.968643 0.559247i
699699 −959.146 553.763i −1.37217 0.792222i
700700 −138.122 + 821.898i −0.197318 + 1.17414i
701701 253.930 0.362240 0.181120 0.983461i 0.442028π-0.442028\pi
0.181120 + 0.983461i 0.442028π0.442028\pi
702702 95.6882 + 89.1140i 0.136308 + 0.126943i
703703 455.288 + 262.861i 0.647636 + 0.373913i
704704 −118.979 + 68.6928i −0.169005 + 0.0975751i
705705 2719.01i 3.85675i
706706 −184.728 + 106.653i −0.261654 + 0.151066i
707707 49.1686 59.5624i 0.0695454 0.0842467i
708708 91.8969 53.0567i 0.129798 0.0749388i
709709 780.741 + 450.761i 1.10119 + 0.635770i 0.936532 0.350581i 0.114016π-0.114016\pi
0.164654 + 0.986351i 0.447349π0.447349\pi
710710 −192.412 + 333.267i −0.271003 + 0.469390i
711711 −960.484 −1.35089
712712 275.044i 0.386297i
713713 155.509 269.350i 0.218106 0.377770i
714714 93.4097 113.156i 0.130826 0.158481i
715715 601.398 + 1962.50i 0.841117 + 2.74476i
716716 −183.417 317.688i −0.256170 0.443699i
717717 −357.099 618.513i −0.498046 0.862640i
718718 −43.3936 75.1599i −0.0604368 0.104680i
719719 −941.586 543.625i −1.30958 0.756085i −0.327552 0.944833i 0.606224π-0.606224\pi
−0.982025 + 0.188749i 0.939557π0.939557\pi
720720 −266.069 −0.369541
721721 −715.791 + 867.103i −0.992776 + 1.20264i
722722 −78.5653 + 45.3597i −0.108816 + 0.0628251i
723723 −1116.14 + 644.405i −1.54376 + 0.891293i
724724 441.588i 0.609929i
725725 21.4179 + 37.0968i 0.0295419 + 0.0511681i
726726 991.029 1.36505
727727 202.930i 0.279133i 0.990213 + 0.139566i 0.0445709π0.0445709\pi
−0.990213 + 0.139566i 0.955429π0.955429\pi
728728 98.5067 237.791i 0.135311 0.326636i
729729 420.502 0.576820
730730 783.465i 1.07324i
731731 −170.915 + 98.6780i −0.233810 + 0.134990i
732732 93.5024 0.127736
733733 270.224 + 468.041i 0.368654 + 0.638528i 0.989355 0.145519i 0.0464852π-0.0464852\pi
−0.620701 + 0.784047i 0.713152π0.713152\pi
734734 291.465 + 504.832i 0.397091 + 0.687782i
735735 −1782.33 + 343.896i −2.42494 + 0.467885i
736736 39.6079i 0.0538150i
737737 238.564 413.204i 0.323695 0.560657i
738738 288.031 166.295i 0.390286 0.225332i
739739 −538.883 + 311.124i −0.729206 + 0.421007i −0.818132 0.575031i 0.804990π-0.804990\pi
0.0889257 + 0.996038i 0.471657π0.471657\pi
740740 −485.906 + 280.538i −0.656630 + 0.379105i
741741 −615.058 + 660.433i −0.830038 + 0.891273i
742742 85.9072 + 14.4369i 0.115778 + 0.0194568i
743743 330.453 + 190.787i 0.444755 + 0.256780i 0.705613 0.708598i 0.250672π-0.250672\pi
−0.260857 + 0.965377i 0.584005π0.584005\pi
744744 −506.232 −0.680419
745745 1417.69i 1.90295i
746746 −205.655 118.735i −0.275677 0.159162i
747747 −391.216 + 677.607i −0.523717 + 0.907104i
748748 −63.1731 109.419i −0.0844560 0.146282i
749749 −879.221 + 328.035i −1.17386 + 0.437964i
750750 904.512 + 1566.66i 1.20602 + 2.08888i
751751 −241.806 −0.321979 −0.160989 0.986956i 0.551469π-0.551469\pi
−0.160989 + 0.986956i 0.551469π0.551469\pi
752752 146.795 + 254.256i 0.195206 + 0.338107i
753753 64.3281 111.420i 0.0854291 0.147968i
754754 −3.87604 12.6484i −0.00514064 0.0167751i
755755 406.565i 0.538497i
756756 34.8063 + 93.2902i 0.0460401 + 0.123400i
757757 −277.724 + 481.032i −0.366874 + 0.635445i −0.989075 0.147413i 0.952905π-0.952905\pi
0.622201 + 0.782858i 0.286239π0.286239\pi
758758 147.003 254.616i 0.193935 0.335906i
759759 242.243 419.578i 0.319161 0.552804i
760760 448.044i 0.589532i
761761 450.886 780.958i 0.592492 1.02623i −0.401404 0.915901i 0.631478π-0.631478\pi
0.993896 0.110325i 0.0351890π-0.0351890\pi
762762 282.992 0.371380
763763 428.460 + 72.0039i 0.561546 + 0.0943695i
764764 −9.41722 + 16.3111i −0.0123262 + 0.0213496i
765765 244.690i 0.319856i
766766 −620.048 357.985i −0.809463 0.467343i
767767 125.271 + 116.664i 0.163326 + 0.152105i
768768 55.8309 32.2340i 0.0726965 0.0419713i
769769 27.1659 47.0527i 0.0353263 0.0611869i −0.847822 0.530281i 0.822086π-0.822086\pi
0.883148 + 0.469094i 0.155420π0.155420\pi
770770 −259.041 + 1541.43i −0.336417 + 2.00185i
771771 −73.7957 127.818i −0.0957143 0.165782i
772772 59.5546 34.3839i 0.0771433 0.0445387i
773773 −484.904 −0.627301 −0.313651 0.949538i 0.601552π-0.601552\pi
−0.313651 + 0.949538i 0.601552π0.601552\pi
774774 548.925i 0.709206i
775775 1322.17 + 2290.07i 1.70603 + 2.95493i
776776 −193.866 + 111.929i −0.249828 + 0.144238i
777777 −663.692 547.876i −0.854172 0.705117i
778778 −325.362 187.848i −0.418203 0.241450i
779779 −280.030 485.026i −0.359474 0.622627i
780780 −282.205 920.901i −0.361801 1.18064i
781781 −254.134 + 440.172i −0.325395 + 0.563601i
782782 −36.4252 −0.0465796
783783 4.43208 + 2.55886i 0.00566038 + 0.00326802i
784784 148.101 128.383i 0.188904 0.163754i
785785 1192.98i 1.51972i
786786 −848.253 489.739i −1.07920 0.623077i
787787 −617.635 −0.784797 −0.392398 0.919795i 0.628354π-0.628354\pi
−0.392398 + 0.919795i 0.628354π0.628354\pi
788788 −201.360 116.255i −0.255533 0.147532i
789789 1473.96 + 850.992i 1.86814 + 1.07857i
790790 −1494.90 863.083i −1.89228 1.09251i
791791 167.172 + 138.000i 0.211342 + 0.174463i
792792 −351.419 −0.443711
793793 44.1950 + 144.219i 0.0557315 + 0.181865i
794794 240.657 + 138.943i 0.303095 + 0.174992i
795795 282.309 162.991i 0.355106 0.205020i
796796 199.933i 0.251172i
797797 −45.6634 + 26.3638i −0.0572941 + 0.0330788i −0.528373 0.849012i 0.677198π-0.677198\pi
0.471079 + 0.882091i 0.343865π0.343865\pi
798798 −643.882 + 240.231i −0.806870 + 0.301041i
799799 −233.826 + 134.999i −0.292648 + 0.168960i
800800 −291.637 168.377i −0.364547 0.210471i
801801 351.767 609.279i 0.439160 0.760648i
802802 25.9285 0.0323299
803803 1034.79i 1.28865i
804804 −111.946 + 193.895i −0.139236 + 0.241163i
805805 347.511 + 286.870i 0.431691 + 0.356360i
806806 −239.277 780.815i −0.296869 0.968753i
807807 −897.756 1554.96i −1.11246 1.92684i
808808 15.6038 + 27.0266i 0.0193116 + 0.0334487i
809809 311.964 + 540.338i 0.385617 + 0.667909i 0.991855 0.127375i 0.0406552π-0.0406552\pi
−0.606237 + 0.795284i 0.707322π0.707322\pi
810810 1055.89 + 609.618i 1.30357 + 0.752615i
811811 10.3713 0.0127882 0.00639412 0.999980i 0.497965π-0.497965\pi
0.00639412 + 0.999980i 0.497965π0.497965\pi
812812 1.66953 9.93457i 0.00205608 0.0122347i
813813 −1285.75 + 742.327i −1.58149 + 0.913071i
814814 −641.775 + 370.529i −0.788421 + 0.455195i
815815 1970.68i 2.41801i
816816 29.6439 + 51.3447i 0.0363283 + 0.0629224i
817817 924.356 1.13140
818818 78.0734i 0.0954442i
819819 522.336 400.771i 0.637772 0.489341i
820820 597.724 0.728932
821821 97.1595i 0.118343i 0.998248 + 0.0591715i 0.0188459π0.0188459\pi
−0.998248 + 0.0591715i 0.981154π0.981154\pi
822822 214.899 124.072i 0.261434 0.150939i
823823 −872.335 −1.05995 −0.529973 0.848015i 0.677798π-0.677798\pi
−0.529973 + 0.848015i 0.677798π0.677798\pi
824824 −227.159 393.450i −0.275678 0.477488i
825825 2059.60 + 3567.33i 2.49649 + 4.32404i
826826 45.5671 + 122.132i 0.0551659 + 0.147859i
827827 246.854i 0.298493i −0.988800 0.149247i 0.952315π-0.952315\pi
0.988800 0.149247i 0.0476848π-0.0476848\pi
828828 −50.6565 + 87.7397i −0.0611794 + 0.105966i
829829 511.303 295.201i 0.616771 0.356093i −0.158840 0.987304i 0.550775π-0.550775\pi
0.775611 + 0.631211i 0.217442π0.217442\pi
830830 −1217.78 + 703.087i −1.46721 + 0.847093i
831831 1162.56 671.203i 1.39899 0.807706i
832832 76.1071 + 70.8782i 0.0914748 + 0.0851901i
833833 118.067 + 136.200i 0.141737 + 0.163506i
834834 −123.933 71.5527i −0.148601 0.0857946i
835835 1287.91 1.54241
836836 591.768i 0.707856i
837837 273.602 + 157.964i 0.326884 + 0.188727i
838838 −486.141 + 842.022i −0.580121 + 1.00480i
839839 186.954 + 323.815i 0.222830 + 0.385953i 0.955666 0.294452i 0.0951372π-0.0951372\pi
−0.732836 + 0.680405i 0.761804π0.761804\pi
840840 121.555 723.312i 0.144708 0.861085i
841841 420.241 + 727.879i 0.499692 + 0.865492i
842842 −826.361 −0.981427
843843 583.945 + 1011.42i 0.692698 + 1.19979i
844844 320.532 555.178i 0.379778 0.657794i
845845 1287.02 870.550i 1.52310 1.03024i
846846 750.974i 0.887676i
847847 −201.764 + 1200.60i −0.238210 + 1.41747i
848848 −17.5992 + 30.4828i −0.0207538 + 0.0359467i
849849 31.3288 54.2631i 0.0369008 0.0639141i
850850 154.847 268.203i 0.182173 0.315533i
851851 213.645i 0.251051i
852852 119.252 206.550i 0.139967 0.242430i
853853 −1444.14 −1.69301 −0.846506 0.532379i 0.821298π-0.821298\pi
−0.846506 + 0.532379i 0.821298π0.821298\pi
854854 −19.0362 + 113.275i −0.0222906 + 0.132641i
855855 −573.026 + 992.511i −0.670206 + 1.16083i
856856 379.180i 0.442967i
857857 641.919 + 370.612i 0.749031 + 0.432453i 0.825344 0.564631i 0.190981π-0.190981\pi
−0.0763129 + 0.997084i 0.524315π0.524315\pi
858858 −372.731 1216.31i −0.434418 1.41761i
859859 898.862 518.958i 1.04641 0.604142i 0.124764 0.992186i 0.460183π-0.460183\pi
0.921641 + 0.388044i 0.126849π0.126849\pi
860860 −493.260 + 854.351i −0.573558 + 0.993431i
861861 320.486 + 858.987i 0.372225 + 0.997662i
862862 −2.32305 4.02364i −0.00269495 0.00466780i
863863 301.249 173.926i 0.349071 0.201536i −0.315205 0.949024i 0.602073π-0.602073\pi
0.664276 + 0.747487i 0.268740π0.268740\pi
864864 −40.2331 −0.0465661
865865 2779.50i 3.21330i
866866 199.584 + 345.690i 0.230467 + 0.399181i
867867 961.227 554.964i 1.10868 0.640097i
868868 103.064 613.283i 0.118737 0.706547i
869869 −1974.44 1139.94i −2.27208 1.31179i
870870 −18.8488 32.6471i −0.0216653 0.0375254i
871871 −351.978 81.0185i −0.404108 0.0930178i
872872 −87.7758 + 152.032i −0.100660 + 0.174349i
873873 −572.605 −0.655905
874874 147.748 + 85.3024i 0.169048 + 0.0976000i
875875 −2082.11 + 776.829i −2.37955 + 0.887805i
876876 485.571i 0.554305i
877877 779.140 + 449.837i 0.888415 + 0.512926i 0.873424 0.486961i 0.161895π-0.161895\pi
0.0149911 + 0.999888i 0.495228π0.495228\pi
878878 495.824 0.564720
879879 886.096 + 511.588i 1.00807 + 0.582011i
880880 −546.951 315.782i −0.621535 0.358843i
881881 −222.311 128.352i −0.252340 0.145688i 0.368495 0.929630i 0.379873π-0.379873\pi
−0.620835 + 0.783941i 0.713206π0.713206\pi
882882 492.269 94.9818i 0.558128 0.107689i
883883 −774.664 −0.877309 −0.438654 0.898656i 0.644545π-0.644545\pi
−0.438654 + 0.898656i 0.644545π0.644545\pi
884884 −65.1828 + 69.9916i −0.0737362 + 0.0791760i
885885 422.451 + 243.902i 0.477346 + 0.275596i
886886 −38.9368 + 22.4802i −0.0439467 + 0.0253727i
887887 604.756i 0.681800i −0.940100 0.340900i 0.889268π-0.889268\pi
0.940100 0.340900i 0.110732π-0.110732\pi
888888 301.152 173.870i 0.339135 0.195800i
889889 −57.6144 + 342.835i −0.0648081 + 0.385641i
890890 1094.98 632.190i 1.23032 0.710326i
891891 1394.60 + 805.172i 1.56521 + 0.903672i
892892 316.864 548.825i 0.355229 0.615274i
893893 1264.59 1.41612
894894 878.650i 0.982830i
895895 843.173 1460.42i 0.942093 1.63175i
896896 27.6838 + 74.1998i 0.0308971 + 0.0828123i
897897 −357.407 82.2682i −0.398447 0.0917149i
898898 −221.749 384.080i −0.246936 0.427706i
899899 −15.9816 27.6809i −0.0177770 0.0307907i
900900 −430.692 745.980i −0.478546 0.828866i
901901 −28.0334 16.1851i −0.0311136 0.0179635i
902902 789.462 0.875235
903903 −1492.26 250.778i −1.65256 0.277717i
904904 −75.8546 + 43.7947i −0.0839100 + 0.0484454i
905905 1758.02 1014.99i 1.94257 1.12154i
906906 251.978i 0.278122i
907907 62.1926 + 107.721i 0.0685696 + 0.118766i 0.898272 0.439440i 0.144823π-0.144823\pi
−0.829702 + 0.558206i 0.811490π0.811490\pi
908908 −282.205 −0.310799
909909 79.8260i 0.0878174i
910910 1173.09 154.395i 1.28912 0.169665i
911911 1162.26 1.27580 0.637902 0.770117i 0.279802π-0.279802\pi
0.637902 + 0.770117i 0.279802π0.279802\pi
912912 277.686i 0.304480i
913913 −1608.42 + 928.623i −1.76169 + 1.01711i
914914 −137.226 −0.150138
915915 214.916 + 372.245i 0.234881 + 0.406826i
916916 76.6091 + 132.691i 0.0836344 + 0.144859i
917917 765.998 927.923i 0.835331 1.01191i
918918 37.0002i 0.0403052i
919919 −143.941 + 249.312i −0.156627 + 0.271287i −0.933650 0.358186i 0.883396π-0.883396\pi
0.777023 + 0.629472i 0.216729π0.216729\pi
920920 −157.684 + 91.0390i −0.171396 + 0.0989554i
921921 −951.256 + 549.208i −1.03285 + 0.596317i
922922 598.564 345.581i 0.649202 0.374817i
923923 374.950 + 86.3063i 0.406230 + 0.0935063i
924924 160.547 955.335i 0.173752 1.03391i
925925 −1573.09 908.225i −1.70064 0.981864i
926926 806.539 0.870992
927927 1162.10i 1.25361i
928928 3.52512 + 2.03523i 0.00379862 + 0.00219314i
929929 −536.089 + 928.534i −0.577061 + 0.999498i 0.418754 + 0.908100i 0.362467π0.362467\pi
−0.995814 + 0.0913984i 0.970866π0.970866\pi
930930 −1163.58 2015.38i −1.25116 2.16707i
931931 −159.943 828.951i −0.171797 0.890387i
932932 274.872 + 476.092i 0.294927 + 0.510828i
933933 −1166.05 −1.24978
934934 −75.1325 130.133i −0.0804417 0.139329i
935935 290.408 503.001i 0.310597 0.537969i
936936 77.9433 + 254.347i 0.0832727 + 0.271738i
937937 980.365i 1.04628i 0.852247 + 0.523140i 0.175240π0.175240\pi
−0.852247 + 0.523140i 0.824760π0.824760\pi
938938 −212.107 175.093i −0.226126 0.186667i
939939 577.491 1000.24i 0.615006 1.06522i
940940 −674.819 + 1168.82i −0.717892 + 1.24343i
941941 355.761 616.197i 0.378067 0.654832i −0.612714 0.790305i 0.709922π-0.709922\pi
0.990781 + 0.135473i 0.0432554π0.0432554\pi
942942 739.376i 0.784900i
943943 113.800 197.107i 0.120678 0.209021i
944944 −52.6715 −0.0557961
945945 −291.398 + 352.997i −0.308358 + 0.373542i
946946 −651.487 + 1128.41i −0.688676 + 1.19282i
947947 1060.33i 1.11967i 0.828603 + 0.559836i 0.189136π0.189136\pi
−0.828603 + 0.559836i 0.810864π0.810864\pi
948948 926.501 + 534.916i 0.977322 + 0.564257i
949949 −748.948 + 229.511i −0.789197 + 0.241845i
950950 −1256.18 + 725.258i −1.32230 + 0.763429i
951951 167.933 290.869i 0.176586 0.305856i
952952 −68.2376 + 25.4593i −0.0716781 + 0.0267429i
953953 241.380 + 418.082i 0.253284 + 0.438701i 0.964428 0.264345i 0.0851559π-0.0851559\pi
−0.711144 + 0.703046i 0.751823π0.751823\pi
954954 −77.9720 + 45.0171i −0.0817316 + 0.0471878i
955955 −86.5822 −0.0906620
956956 354.507i 0.370823i
957957 −24.8951 43.1196i −0.0260137 0.0450571i
958958 −40.7151 + 23.5069i −0.0425001 + 0.0245375i
959959 106.558 + 285.603i 0.111113 + 0.297813i
960960 256.656 + 148.180i 0.267350 + 0.154354i
961961 −506.076 876.550i −0.526614 0.912123i
962962 410.521 + 382.317i 0.426737 + 0.397419i
963963 484.953 839.963i 0.503585 0.872235i
964964 639.727 0.663617
965965 273.774 + 158.063i 0.283703 + 0.163796i
966966 −215.378 177.794i −0.222959 0.184052i
967967 477.346i 0.493636i −0.969062 0.246818i 0.920615π-0.920615\pi
0.969062 0.246818i 0.0793849π-0.0793849\pi
968968 −426.013 245.959i −0.440096 0.254090i
969969 255.373 0.263543
970970 −891.206 514.538i −0.918769 0.530451i
971971 −622.642 359.482i −0.641237 0.370219i 0.143854 0.989599i 0.454051π-0.454051\pi
−0.785091 + 0.619380i 0.787384π0.787384\pi
972972 −543.543 313.815i −0.559201 0.322855i
973973 111.915 135.573i 0.115021 0.139335i
974974 509.149 0.522740
975975 2125.12 2281.90i 2.17961 2.34041i
976976 −40.1938 23.2059i −0.0411822 0.0237766i
977977 −272.518 + 157.338i −0.278933 + 0.161042i −0.632940 0.774201i 0.718152π-0.718152\pi
0.354007 + 0.935243i 0.384819π0.384819\pi
978978 1221.37i 1.24885i
979979 1446.23 834.984i 1.47726 0.852894i
980980 851.520 + 294.519i 0.868898 + 0.300529i
981981 −388.883 + 224.522i −0.396415 + 0.228870i
982982 594.542 + 343.259i 0.605440 + 0.349551i
983983 542.737 940.049i 0.552123 0.956306i −0.445998 0.895034i 0.647151π-0.647151\pi
0.998121 0.0612717i 0.0195156π-0.0195156\pi
984984 −370.454 −0.376477
985985 1068.85i 1.08513i
986986 −1.87169 + 3.24187i −0.00189827 + 0.00328790i
987987 −2041.53 343.085i −2.06842 0.347604i
988988 428.305 131.252i 0.433507 0.132846i
989989 187.822 + 325.317i 0.189911 + 0.328935i
990990 −807.740 1399.05i −0.815899 1.41318i
991991 71.7454 + 124.267i 0.0723970 + 0.125395i 0.899951 0.435990i 0.143602π-0.143602\pi
−0.827554 + 0.561386i 0.810268π0.810268\pi
992992 217.614 + 125.639i 0.219369 + 0.126652i
993993 1205.95 1.21445
994994 225.950 + 186.521i 0.227314 + 0.187647i
995995 −795.960 + 459.548i −0.799960 + 0.461857i
996996 754.749 435.755i 0.757780 0.437505i
997997 1390.84i 1.39502i −0.716574 0.697511i 0.754291π-0.754291\pi
0.716574 0.697511i 0.245709π-0.245709\pi
998998 −241.266 417.886i −0.241750 0.418723i
999999 −217.017 −0.217234
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 182.3.r.a.17.17 yes 36
7.5 odd 6 182.3.k.a.173.11 yes 36
13.10 even 6 182.3.k.a.101.17 36
91.75 odd 6 inner 182.3.r.a.75.8 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.3.k.a.101.17 36 13.10 even 6
182.3.k.a.173.11 yes 36 7.5 odd 6
182.3.r.a.17.17 yes 36 1.1 even 1 trivial
182.3.r.a.75.8 yes 36 91.75 odd 6 inner