Properties

Label 169.3.f.g.19.1
Level 169169
Weight 33
Character 169.19
Analytic conductor 4.6054.605
Analytic rank 00
Dimension 4848
Inner twists 88

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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] = [169,3,Mod(19,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([5])) 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("169.19"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 169=132 169 = 13^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 169.f (of order 1212, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.604916467694.60491646769
Analytic rank: 00
Dimension: 4848
Relative dimension: 1212 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 19.1
Character χ\chi == 169.19
Dual form 169.3.f.g.89.1

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+(0.8346433.11493i)q2+(1.023041.77195i)q3+(5.54206+3.19971i)q4+(5.50472+5.50472i)q5+(6.373361.70774i)q6+(0.846854+3.16050i)q7+(5.47136+5.47136i)q8+(2.40680+4.16870i)q9+(21.7413+12.5523i)q10+(4.90135+1.31331i)q11+13.0937iq12+10.5516q14+(4.12256+15.3856i)q15+(0.322570+0.558708i)q16+(8.72503+5.03740i)q17+(10.976410.9764i)q18+(11.48453.07725i)q19+(12.894048.1209i)q20+(4.73388+4.73388i)q21+(8.18176+14.1712i)q22+(27.578515.9225i)q23+(15.29244.09757i)q2435.6038iq25+28.2636q27+(5.4193720.2254i)q28+(16.3339+28.2912i)q29+(44.484225.6830i)q30+(8.05564+8.05564i)q31+(31.9056+8.54908i)q32+(2.68713+10.0285i)q33+(22.9734+22.9734i)q34+(12.736022.0593i)q35+(26.677215.4021i)q36+(42.793411.4664i)q37+38.3417iq3860.2365q40+(12.2352+45.6623i)q41+(10.794618.6968i)q42+(20.1558+11.6370i)q43+(22.961422.9614i)q44+(36.19629.69875i)q45+(26.5792+99.1947i)q46+(64.605764.6057i)q47+(0.660002+1.14316i)q48+(33.1636+19.1470i)q49+(110.903+29.7165i)q50+20.6138iq5148.7831q53+(23.590088.0391i)q54+(19.751134.2100i)q55+(21.9257+12.6588i)q56+(17.2018+17.2018i)q57+(101.758+27.2660i)q58+(6.31406+23.5644i)q59+(72.076872.0768i)q60+(6.3033510.9177i)q61+(31.8163+18.3692i)q62+(15.2134+4.07641i)q63103.939iq64+33.4809q66+(4.48316+16.7314i)q67+(32.236455.8351i)q68+(56.4276+32.5785i)q69+(58.0833+58.0833i)q70+(38.840410.4073i)q71+(9.63998+35.9769i)q72+(76.5080+76.5080i)q73+(71.4344123.728i)q74+(63.088136.4239i)q75+(73.493919.6926i)q7616.6029iq7794.0887q79+(1.299874.85119i)q80+(7.2534612.5634i)q81+(132.02376.2235i)q82+(33.617733.6177i)q83+(41.382511.0884i)q84+(20.299475.7583i)q85+(53.0713+53.0713i)q86+(33.4204+57.8858i)q87+(34.002719.6314i)q88+(35.0471+9.39084i)q89+120.844iq90+203.789q92+(6.03298+22.5154i)q93+(147.319+255.165i)q94+(80.158246.2793i)q95+(47.789147.7891i)q96+(40.1144+10.7486i)q97+(31.9619119.283i)q98+(17.271417.2714i)q99+O(q100)q+(-0.834643 - 3.11493i) q^{2} +(1.02304 - 1.77195i) q^{3} +(-5.54206 + 3.19971i) q^{4} +(-5.50472 + 5.50472i) q^{5} +(-6.37336 - 1.70774i) q^{6} +(-0.846854 + 3.16050i) q^{7} +(5.47136 + 5.47136i) q^{8} +(2.40680 + 4.16870i) q^{9} +(21.7413 + 12.5523i) q^{10} +(-4.90135 + 1.31331i) q^{11} +13.0937i q^{12} +10.5516 q^{14} +(4.12256 + 15.3856i) q^{15} +(-0.322570 + 0.558708i) q^{16} +(-8.72503 + 5.03740i) q^{17} +(10.9764 - 10.9764i) q^{18} +(-11.4845 - 3.07725i) q^{19} +(12.8940 - 48.1209i) q^{20} +(4.73388 + 4.73388i) q^{21} +(8.18176 + 14.1712i) q^{22} +(-27.5785 - 15.9225i) q^{23} +(15.2924 - 4.09757i) q^{24} -35.6038i q^{25} +28.2636 q^{27} +(-5.41937 - 20.2254i) q^{28} +(-16.3339 + 28.2912i) q^{29} +(44.4842 - 25.6830i) q^{30} +(-8.05564 + 8.05564i) q^{31} +(31.9056 + 8.54908i) q^{32} +(-2.68713 + 10.0285i) q^{33} +(22.9734 + 22.9734i) q^{34} +(-12.7360 - 22.0593i) q^{35} +(-26.6772 - 15.4021i) q^{36} +(42.7934 - 11.4664i) q^{37} +38.3417i q^{38} -60.2365 q^{40} +(12.2352 + 45.6623i) q^{41} +(10.7946 - 18.6968i) q^{42} +(-20.1558 + 11.6370i) q^{43} +(22.9614 - 22.9614i) q^{44} +(-36.1962 - 9.69875i) q^{45} +(-26.5792 + 99.1947i) q^{46} +(-64.6057 - 64.6057i) q^{47} +(0.660002 + 1.14316i) q^{48} +(33.1636 + 19.1470i) q^{49} +(-110.903 + 29.7165i) q^{50} +20.6138i q^{51} -48.7831 q^{53} +(-23.5900 - 88.0391i) q^{54} +(19.7511 - 34.2100i) q^{55} +(-21.9257 + 12.6588i) q^{56} +(-17.2018 + 17.2018i) q^{57} +(101.758 + 27.2660i) q^{58} +(-6.31406 + 23.5644i) q^{59} +(-72.0768 - 72.0768i) q^{60} +(-6.30335 - 10.9177i) q^{61} +(31.8163 + 18.3692i) q^{62} +(-15.2134 + 4.07641i) q^{63} -103.939i q^{64} +33.4809 q^{66} +(4.48316 + 16.7314i) q^{67} +(32.2364 - 55.8351i) q^{68} +(-56.4276 + 32.5785i) q^{69} +(-58.0833 + 58.0833i) q^{70} +(-38.8404 - 10.4073i) q^{71} +(-9.63998 + 35.9769i) q^{72} +(76.5080 + 76.5080i) q^{73} +(-71.4344 - 123.728i) q^{74} +(-63.0881 - 36.4239i) q^{75} +(73.4939 - 19.6926i) q^{76} -16.6029i q^{77} -94.0887 q^{79} +(-1.29987 - 4.85119i) q^{80} +(7.25346 - 12.5634i) q^{81} +(132.023 - 76.2235i) q^{82} +(33.6177 - 33.6177i) q^{83} +(-41.3825 - 11.0884i) q^{84} +(20.2994 - 75.7583i) q^{85} +(53.0713 + 53.0713i) q^{86} +(33.4204 + 57.8858i) q^{87} +(-34.0027 - 19.6314i) q^{88} +(-35.0471 + 9.39084i) q^{89} +120.844i q^{90} +203.789 q^{92} +(6.03298 + 22.5154i) q^{93} +(-147.319 + 255.165i) q^{94} +(80.1582 - 46.2793i) q^{95} +(47.7891 - 47.7891i) q^{96} +(40.1144 + 10.7486i) q^{97} +(31.9619 - 119.283i) q^{98} +(-17.2714 - 17.2714i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q12q384q9+376q14188q16+136q22+120q2784q29176q351048q40+368q42+368q4888q53+704q55+8q611480q66+168q68+1132q94+O(q100) 48 q - 12 q^{3} - 84 q^{9} + 376 q^{14} - 188 q^{16} + 136 q^{22} + 120 q^{27} - 84 q^{29} - 176 q^{35} - 1048 q^{40} + 368 q^{42} + 368 q^{48} - 88 q^{53} + 704 q^{55} + 8 q^{61} - 1480 q^{66} + 168 q^{68}+ \cdots - 1132 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/169Z)×\left(\mathbb{Z}/169\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(512)e\left(\frac{5}{12}\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 −0.834643 3.11493i −0.417321 1.55746i −0.780140 0.625605i 0.784852π-0.784852\pi
0.362819 0.931860i 0.381814π-0.381814\pi
33 1.02304 1.77195i 0.341012 0.590650i −0.643609 0.765354i 0.722564π-0.722564\pi
0.984621 + 0.174705i 0.0558971π0.0558971\pi
44 −5.54206 + 3.19971i −1.38551 + 0.799927i
55 −5.50472 + 5.50472i −1.10094 + 1.10094i −0.106646 + 0.994297i 0.534011π0.534011\pi
−0.994297 + 0.106646i 0.965989π0.965989\pi
66 −6.37336 1.70774i −1.06223 0.284623i
77 −0.846854 + 3.16050i −0.120979 + 0.451500i −0.999665 0.0259011i 0.991754π-0.991754\pi
0.878685 + 0.477401i 0.158421π0.158421\pi
88 5.47136 + 5.47136i 0.683920 + 0.683920i
99 2.40680 + 4.16870i 0.267422 + 0.463189i
1010 21.7413 + 12.5523i 2.17413 + 1.25523i
1111 −4.90135 + 1.31331i −0.445578 + 0.119392i −0.474629 0.880186i 0.657418π-0.657418\pi
0.0290518 + 0.999578i 0.490751π0.490751\pi
1212 13.0937i 1.09114i
1313 0 0
1414 10.5516 0.753683
1515 4.12256 + 15.3856i 0.274837 + 1.02571i
1616 −0.322570 + 0.558708i −0.0201607 + 0.0349193i
1717 −8.72503 + 5.03740i −0.513237 + 0.296318i −0.734163 0.678973i 0.762425π-0.762425\pi
0.220926 + 0.975291i 0.429092π0.429092\pi
1818 10.9764 10.9764i 0.609799 0.609799i
1919 −11.4845 3.07725i −0.604446 0.161961i −0.0563988 0.998408i 0.517962π-0.517962\pi
−0.548047 + 0.836448i 0.684629π0.684629\pi
2020 12.8940 48.1209i 0.644698 2.40605i
2121 4.73388 + 4.73388i 0.225423 + 0.225423i
2222 8.18176 + 14.1712i 0.371898 + 0.644147i
2323 −27.5785 15.9225i −1.19907 0.692281i −0.238719 0.971089i 0.576728π-0.576728\pi
−0.960347 + 0.278807i 0.910061π0.910061\pi
2424 15.2924 4.09757i 0.637181 0.170732i
2525 35.6038i 1.42415i
2626 0 0
2727 28.2636 1.04680
2828 −5.41937 20.2254i −0.193549 0.722334i
2929 −16.3339 + 28.2912i −0.563239 + 0.975559i 0.433972 + 0.900927i 0.357112π0.357112\pi
−0.997211 + 0.0746329i 0.976222π0.976222\pi
3030 44.4842 25.6830i 1.48281 0.856098i
3131 −8.05564 + 8.05564i −0.259859 + 0.259859i −0.824997 0.565137i 0.808823π-0.808823\pi
0.565137 + 0.824997i 0.308823π0.308823\pi
3232 31.9056 + 8.54908i 0.997050 + 0.267159i
3333 −2.68713 + 10.0285i −0.0814283 + 0.303894i
3434 22.9734 + 22.9734i 0.675689 + 0.675689i
3535 −12.7360 22.0593i −0.363885 0.630267i
3636 −26.6772 15.4021i −0.741034 0.427836i
3737 42.7934 11.4664i 1.15658 0.309904i 0.370979 0.928641i 0.379022π-0.379022\pi
0.785598 + 0.618737i 0.212355π0.212355\pi
3838 38.3417i 1.00899i
3939 0 0
4040 −60.2365 −1.50591
4141 12.2352 + 45.6623i 0.298419 + 1.11372i 0.938464 + 0.345378i 0.112249π0.112249\pi
−0.640045 + 0.768338i 0.721084π0.721084\pi
4242 10.7946 18.6968i 0.257015 0.445162i
4343 −20.1558 + 11.6370i −0.468740 + 0.270627i −0.715712 0.698395i 0.753898π-0.753898\pi
0.246972 + 0.969023i 0.420564π0.420564\pi
4444 22.9614 22.9614i 0.521849 0.521849i
4545 −36.1962 9.69875i −0.804361 0.215528i
4646 −26.5792 + 99.1947i −0.577808 + 2.15641i
4747 −64.6057 64.6057i −1.37459 1.37459i −0.853506 0.521082i 0.825528π-0.825528\pi
−0.521082 0.853506i 0.674472π-0.674472\pi
4848 0.660002 + 1.14316i 0.0137500 + 0.0238158i
4949 33.1636 + 19.1470i 0.676809 + 0.390756i
5050 −110.903 + 29.7165i −2.21807 + 0.594329i
5151 20.6138i 0.404191i
5252 0 0
5353 −48.7831 −0.920436 −0.460218 0.887806i 0.652229π-0.652229\pi
−0.460218 + 0.887806i 0.652229π0.652229\pi
5454 −23.5900 88.0391i −0.436852 1.63035i
5555 19.7511 34.2100i 0.359112 0.622000i
5656 −21.9257 + 12.6588i −0.391530 + 0.226050i
5757 −17.2018 + 17.2018i −0.301785 + 0.301785i
5858 101.758 + 27.2660i 1.75445 + 0.470104i
5959 −6.31406 + 23.5644i −0.107018 + 0.399397i −0.998566 0.0535290i 0.982953π-0.982953\pi
0.891548 + 0.452926i 0.149620π0.149620\pi
6060 −72.0768 72.0768i −1.20128 1.20128i
6161 −6.30335 10.9177i −0.103334 0.178979i 0.809723 0.586813i 0.199618π-0.199618\pi
−0.913056 + 0.407834i 0.866284π0.866284\pi
6262 31.8163 + 18.3692i 0.513167 + 0.296277i
6363 −15.2134 + 4.07641i −0.241482 + 0.0647049i
6464 103.939i 1.62404i
6565 0 0
6666 33.4809 0.507287
6767 4.48316 + 16.7314i 0.0669128 + 0.249722i 0.991278 0.131787i 0.0420714π-0.0420714\pi
−0.924365 + 0.381508i 0.875405π0.875405\pi
6868 32.2364 55.8351i 0.474065 0.821105i
6969 −56.4276 + 32.5785i −0.817791 + 0.472152i
7070 −58.0833 + 58.0833i −0.829762 + 0.829762i
7171 −38.8404 10.4073i −0.547048 0.146581i −0.0252987 0.999680i 0.508054π-0.508054\pi
−0.521749 + 0.853099i 0.674720π0.674720\pi
7272 −9.63998 + 35.9769i −0.133889 + 0.499679i
7373 76.5080 + 76.5080i 1.04806 + 1.04806i 0.998786 + 0.0492695i 0.0156893π0.0156893\pi
0.0492695 + 0.998786i 0.484311π0.484311\pi
7474 −71.4344 123.728i −0.965329 1.67200i
7575 −63.0881 36.4239i −0.841175 0.485653i
7676 73.4939 19.6926i 0.967025 0.259114i
7777 16.6029i 0.215622i
7878 0 0
7979 −94.0887 −1.19100 −0.595498 0.803357i 0.703045π-0.703045\pi
−0.595498 + 0.803357i 0.703045π0.703045\pi
8080 −1.29987 4.85119i −0.0162484 0.0606399i
8181 7.25346 12.5634i 0.0895489 0.155103i
8282 132.023 76.2235i 1.61004 0.929555i
8383 33.6177 33.6177i 0.405032 0.405032i −0.474970 0.880002i 0.657541π-0.657541\pi
0.880002 + 0.474970i 0.157541π0.157541\pi
8484 −41.3825 11.0884i −0.492649 0.132005i
8585 20.2994 75.7583i 0.238816 0.891274i
8686 53.0713 + 53.0713i 0.617108 + 0.617108i
8787 33.4204 + 57.8858i 0.384143 + 0.665354i
8888 −34.0027 19.6314i −0.386394 0.223085i
8989 −35.0471 + 9.39084i −0.393788 + 0.105515i −0.450279 0.892888i 0.648675π-0.648675\pi
0.0564911 + 0.998403i 0.482009π0.482009\pi
9090 120.844i 1.34271i
9191 0 0
9292 203.789 2.21510
9393 6.03298 + 22.5154i 0.0648708 + 0.242101i
9494 −147.319 + 255.165i −1.56723 + 2.71452i
9595 80.1582 46.2793i 0.843770 0.487151i
9696 47.7891 47.7891i 0.497803 0.497803i
9797 40.1144 + 10.7486i 0.413550 + 0.110810i 0.459594 0.888129i 0.347995π-0.347995\pi
−0.0460441 + 0.998939i 0.514661π0.514661\pi
9898 31.9619 119.283i 0.326142 1.21718i
9999 −17.2714 17.2714i −0.174458 0.174458i
100100 113.922 + 197.318i 1.13922 + 1.97318i
101101 −20.6108 11.8997i −0.204067 0.117818i 0.394484 0.918903i 0.370923π-0.370923\pi
−0.598551 + 0.801085i 0.704257π0.704257\pi
102102 64.2104 17.2051i 0.629514 0.168678i
103103 99.0034i 0.961198i 0.876940 + 0.480599i 0.159581π0.159581\pi
−0.876940 + 0.480599i 0.840419π0.840419\pi
104104 0 0
105105 −52.1174 −0.496356
106106 40.7165 + 151.956i 0.384118 + 1.43355i
107107 72.7606 126.025i 0.680006 1.17780i −0.294972 0.955506i 0.595310π-0.595310\pi
0.974978 0.222299i 0.0713562π-0.0713562\pi
108108 −156.638 + 90.4352i −1.45036 + 0.837363i
109109 104.897 104.897i 0.962359 0.962359i −0.0369580 0.999317i 0.511767π-0.511767\pi
0.999317 + 0.0369580i 0.0117668π0.0117668\pi
110110 −123.047 32.9703i −1.11861 0.299730i
111111 23.4612 87.5582i 0.211362 0.788813i
112112 −1.49263 1.49263i −0.0133270 0.0133270i
113113 20.4781 + 35.4690i 0.181222 + 0.313885i 0.942297 0.334778i 0.108661π-0.108661\pi
−0.761075 + 0.648664i 0.775328π0.775328\pi
114114 67.9396 + 39.2249i 0.595961 + 0.344078i
115115 239.461 64.1633i 2.08227 0.557942i
116116 209.055i 1.80220i
117117 0 0
118118 78.6714 0.666707
119119 −8.53188 31.8414i −0.0716965 0.267575i
120120 −61.6241 + 106.736i −0.513534 + 0.889467i
121121 −82.4906 + 47.6260i −0.681740 + 0.393603i
122122 −28.7469 + 28.7469i −0.235630 + 0.235630i
123123 93.4283 + 25.0340i 0.759580 + 0.203529i
124124 18.8691 70.4205i 0.152170 0.567907i
125125 58.3709 + 58.3709i 0.466967 + 0.466967i
126126 25.3955 + 43.9862i 0.201551 + 0.349097i
127127 100.148 + 57.8204i 0.788566 + 0.455279i 0.839457 0.543425i 0.182873π-0.182873\pi
−0.0508914 + 0.998704i 0.516206π0.516206\pi
128128 −196.139 + 52.5553i −1.53234 + 0.410588i
129129 47.6201i 0.369148i
130130 0 0
131131 55.6501 0.424810 0.212405 0.977182i 0.431870π-0.431870\pi
0.212405 + 0.977182i 0.431870π0.431870\pi
132132 −17.1961 64.1766i −0.130273 0.486187i
133133 19.4513 33.6907i 0.146251 0.253313i
134134 48.3752 27.9294i 0.361009 0.208429i
135135 −155.583 + 155.583i −1.15247 + 1.15247i
136136 −75.2992 20.1764i −0.553670 0.148356i
137137 8.17673 30.5160i 0.0596841 0.222744i −0.929642 0.368465i 0.879883π-0.879883\pi
0.989326 + 0.145721i 0.0465501π0.0465501\pi
138138 148.577 + 148.577i 1.07664 + 1.07664i
139139 −116.947 202.558i −0.841343 1.45725i −0.888759 0.458374i 0.848432π-0.848432\pi
0.0474162 0.998875i 0.484901π-0.484901\pi
140140 141.167 + 81.5028i 1.00834 + 0.582163i
141141 −180.572 + 48.3841i −1.28065 + 0.343149i
142142 129.671i 0.913180i
143143 0 0
144144 −3.10545 −0.0215656
145145 −65.8214 245.649i −0.453941 1.69413i
146146 174.460 302.174i 1.19493 2.06968i
147147 67.8551 39.1762i 0.461600 0.266505i
148148 −200.474 + 200.474i −1.35455 + 1.35455i
149149 −171.694 46.0054i −1.15231 0.308761i −0.368420 0.929659i 0.620101π-0.620101\pi
−0.783891 + 0.620899i 0.786768π0.786768\pi
150150 −60.8020 + 226.916i −0.405346 + 1.51277i
151151 −32.9910 32.9910i −0.218484 0.218484i 0.589376 0.807859i 0.299374π-0.299374\pi
−0.807859 + 0.589376i 0.799374π0.799374\pi
152152 −45.9989 79.6724i −0.302624 0.524160i
153153 −41.9988 24.2480i −0.274502 0.158484i
154154 −51.7169 + 13.8575i −0.335824 + 0.0899838i
155155 88.6880i 0.572181i
156156 0 0
157157 61.3344 0.390665 0.195332 0.980737i 0.437421π-0.437421\pi
0.195332 + 0.980737i 0.437421π0.437421\pi
158158 78.5305 + 293.080i 0.497028 + 1.85494i
159159 −49.9068 + 86.4411i −0.313879 + 0.543655i
160160 −222.692 + 128.571i −1.39182 + 0.803569i
161161 73.6779 73.6779i 0.457627 0.457627i
162162 −45.1880 12.1081i −0.278938 0.0747413i
163163 −41.6113 + 155.296i −0.255284 + 0.952734i 0.712648 + 0.701522i 0.247496π0.247496\pi
−0.967932 + 0.251212i 0.919171π0.919171\pi
164164 −213.914 213.914i −1.30435 1.30435i
165165 −40.4122 69.9960i −0.244923 0.424218i
166166 −132.775 76.6580i −0.799852 0.461795i
167167 −16.2249 + 4.34745i −0.0971551 + 0.0260326i −0.307069 0.951687i 0.599348π-0.599348\pi
0.209914 + 0.977720i 0.432682π0.432682\pi
168168 51.8015i 0.308342i
169169 0 0
170170 −252.925 −1.48779
171171 −14.8127 55.2816i −0.0866238 0.323284i
172172 74.4699 128.986i 0.432964 0.749916i
173173 −33.5017 + 19.3422i −0.193651 + 0.111805i −0.593691 0.804693i 0.702330π-0.702330\pi
0.400039 + 0.916498i 0.368996π0.368996\pi
174174 152.416 152.416i 0.875955 0.875955i
175175 112.526 + 30.1512i 0.643005 + 0.172293i
176176 0.847272 3.16206i 0.00481405 0.0179663i
177177 35.2954 + 35.2954i 0.199409 + 0.199409i
178178 58.5036 + 101.331i 0.328672 + 0.569277i
179179 240.631 + 138.929i 1.34431 + 0.776137i 0.987437 0.158016i 0.0505096π-0.0505096\pi
0.356873 + 0.934153i 0.383843π0.383843\pi
180180 231.635 62.0663i 1.28686 0.344813i
181181 13.3679i 0.0738556i 0.999318 + 0.0369278i 0.0117572π0.0117572\pi
−0.999318 + 0.0369278i 0.988243π0.988243\pi
182182 0 0
183183 −25.7942 −0.140952
184184 −63.7744 238.009i −0.346600 1.29353i
185185 −172.446 + 298.685i −0.932140 + 1.61451i
186186 65.0985 37.5846i 0.349992 0.202068i
187187 36.1488 36.1488i 0.193309 0.193309i
188188 564.768 + 151.329i 3.00408 + 0.804942i
189189 −23.9351 + 89.3271i −0.126641 + 0.472630i
190190 −211.060 211.060i −1.11084 1.11084i
191191 163.781 + 283.678i 0.857494 + 1.48522i 0.874312 + 0.485365i 0.161313π0.161313\pi
−0.0168172 + 0.999859i 0.505353π0.505353\pi
192192 −184.174 106.333i −0.959239 0.553817i
193193 −226.302 + 60.6375i −1.17255 + 0.314184i −0.791968 0.610563i 0.790943π-0.790943\pi
−0.380583 + 0.924747i 0.624277π0.624277\pi
194194 133.925i 0.690333i
195195 0 0
196196 −245.060 −1.25030
197197 25.1743 + 93.9516i 0.127788 + 0.476912i 0.999924 0.0123525i 0.00393201π-0.00393201\pi
−0.872136 + 0.489264i 0.837265π0.837265\pi
198198 −39.3837 + 68.2146i −0.198908 + 0.344518i
199199 231.474 133.641i 1.16318 0.671564i 0.211119 0.977460i 0.432289π-0.432289\pi
0.952065 + 0.305896i 0.0989560π0.0989560\pi
200200 194.801 194.801i 0.974005 0.974005i
201201 34.2335 + 9.17285i 0.170316 + 0.0456361i
202202 −19.8639 + 74.1332i −0.0983362 + 0.366996i
203203 −75.5820 75.5820i −0.372325 0.372325i
204204 −65.9580 114.243i −0.323323 0.560013i
205205 −318.709 184.007i −1.55468 0.897595i
206206 308.389 82.6325i 1.49703 0.401129i
207207 153.289i 0.740525i
208208 0 0
209209 60.3309 0.288664
210210 43.4994 + 162.342i 0.207140 + 0.773057i
211211 79.7306 138.097i 0.377870 0.654490i −0.612882 0.790174i 0.709990π-0.709990\pi
0.990752 + 0.135684i 0.0433233π0.0433233\pi
212212 270.359 156.092i 1.27528 0.736281i
213213 −58.1762 + 58.1762i −0.273128 + 0.273128i
214214 −453.289 121.458i −2.11817 0.567562i
215215 46.8939 175.010i 0.218111 0.814002i
216216 154.640 + 154.640i 0.715927 + 0.715927i
217217 −18.6379 32.2818i −0.0858890 0.148764i
218218 −414.299 239.195i −1.90045 1.09723i
219219 213.839 57.2979i 0.976432 0.261634i
220220 252.792i 1.14905i
221221 0 0
222222 −292.319 −1.31675
223223 47.7476 + 178.197i 0.214115 + 0.799088i 0.986476 + 0.163904i 0.0524088π0.0524088\pi
−0.772361 + 0.635183i 0.780925π0.780925\pi
224224 −54.0388 + 93.5979i −0.241244 + 0.417848i
225225 148.421 85.6912i 0.659651 0.380850i
226226 93.3917 93.3917i 0.413238 0.413238i
227227 215.806 + 57.8250i 0.950687 + 0.254736i 0.700654 0.713502i 0.252892π-0.252892\pi
0.250033 + 0.968237i 0.419559π0.419559\pi
228228 40.2925 150.374i 0.176722 0.659534i
229229 −7.86632 7.86632i −0.0343508 0.0343508i 0.689723 0.724074i 0.257732π-0.257732\pi
−0.724074 + 0.689723i 0.757732π0.757732\pi
230230 −399.728 692.350i −1.73795 3.01022i
231231 −29.4195 16.9854i −0.127357 0.0735297i
232232 −244.160 + 65.4225i −1.05241 + 0.281994i
233233 39.1708i 0.168115i −0.996461 0.0840575i 0.973212π-0.973212\pi
0.996461 0.0840575i 0.0267879π-0.0267879\pi
234234 0 0
235235 711.272 3.02669
236236 −40.4063 150.798i −0.171213 0.638976i
237237 −96.2561 + 166.720i −0.406144 + 0.703462i
238238 −92.0627 + 53.1524i −0.386818 + 0.223330i
239239 −274.654 + 274.654i −1.14918 + 1.14918i −0.162466 + 0.986714i 0.551945π0.551945\pi
−0.986714 + 0.162466i 0.948055π0.948055\pi
240240 −9.92588 2.65963i −0.0413578 0.0110818i
241241 −88.8999 + 331.779i −0.368879 + 1.37668i 0.493205 + 0.869913i 0.335825π0.335825\pi
−0.862085 + 0.506764i 0.830842π0.830842\pi
242242 217.202 + 217.202i 0.897528 + 0.897528i
243243 112.345 + 194.587i 0.462325 + 0.800771i
244244 69.8671 + 40.3378i 0.286340 + 0.165319i
245245 −287.955 + 77.1574i −1.17533 + 0.314928i
246246 311.917i 1.26796i
247247 0 0
248248 −88.1506 −0.355446
249249 −25.1767 93.9609i −0.101111 0.377353i
250250 133.102 230.540i 0.532410 0.922161i
251251 15.1070 8.72206i 0.0601874 0.0347492i −0.469604 0.882877i 0.655603π-0.655603\pi
0.529792 + 0.848128i 0.322270π0.322270\pi
252252 71.2701 71.2701i 0.282818 0.282818i
253253 156.083 + 41.8224i 0.616930 + 0.165306i
254254 96.5188 360.213i 0.379995 1.41816i
255255 −113.473 113.473i −0.444992 0.444992i
256256 119.535 + 207.040i 0.466933 + 0.808752i
257257 232.356 + 134.151i 0.904107 + 0.521986i 0.878530 0.477686i 0.158524π-0.158524\pi
0.0255766 + 0.999673i 0.491858π0.491858\pi
258258 148.333 39.7458i 0.574936 0.154054i
259259 144.959i 0.559687i
260260 0 0
261261 −157.250 −0.602491
262262 −46.4480 173.346i −0.177282 0.661626i
263263 6.06253 10.5006i 0.0230515 0.0399263i −0.854270 0.519830i 0.825995π-0.825995\pi
0.877321 + 0.479904i 0.159329π0.159329\pi
264264 −69.5718 + 40.1673i −0.263530 + 0.152149i
265265 268.537 268.537i 1.01335 1.01335i
266266 −121.179 32.4698i −0.455560 0.122067i
267267 −19.2143 + 71.7088i −0.0719638 + 0.268572i
268268 −78.3814 78.3814i −0.292468 0.292468i
269269 59.2202 + 102.572i 0.220150 + 0.381310i 0.954853 0.297078i 0.0960121π-0.0960121\pi
−0.734704 + 0.678388i 0.762679π0.762679\pi
270270 614.486 + 354.774i 2.27588 + 1.31398i
271271 −135.707 + 36.3626i −0.500764 + 0.134179i −0.500354 0.865821i 0.666797π-0.666797\pi
−0.000409306 1.00000i 0.500130π0.500130\pi
272272 6.49967i 0.0238958i
273273 0 0
274274 −101.880 −0.371824
275275 46.7590 + 174.507i 0.170033 + 0.634570i
276276 208.483 361.104i 0.755374 1.30835i
277277 −469.067 + 270.816i −1.69338 + 0.977676i −0.741632 + 0.670807i 0.765948π0.765948\pi
−0.951752 + 0.306869i 0.900719π0.900719\pi
278278 −533.344 + 533.344i −1.91850 + 1.91850i
279279 −52.9698 14.1932i −0.189856 0.0508718i
280280 51.0115 190.378i 0.182184 0.679920i
281281 57.5732 + 57.5732i 0.204887 + 0.204887i 0.802090 0.597203i 0.203721π-0.203721\pi
−0.597203 + 0.802090i 0.703721π0.703721\pi
282282 301.426 + 522.085i 1.06889 + 1.85137i
283283 132.682 + 76.6042i 0.468842 + 0.270686i 0.715755 0.698352i 0.246083π-0.246083\pi
−0.246913 + 0.969038i 0.579416π0.579416\pi
284284 248.556 66.6004i 0.875197 0.234508i
285285 189.382i 0.664497i
286286 0 0
287287 −154.677 −0.538945
288288 41.1518 + 153.581i 0.142888 + 0.533267i
289289 −93.7492 + 162.378i −0.324392 + 0.561863i
290290 −710.242 + 410.058i −2.44911 + 1.41399i
291291 60.0844 60.0844i 0.206476 0.206476i
292292 −668.815 179.208i −2.29046 0.613728i
293293 −60.5070 + 225.815i −0.206509 + 0.770700i 0.782476 + 0.622681i 0.213957π0.213957\pi
−0.988984 + 0.148020i 0.952710π0.952710\pi
294294 −178.666 178.666i −0.607707 0.607707i
295295 −94.9582 164.472i −0.321892 0.557534i
296296 296.875 + 171.401i 1.00296 + 0.579057i
297297 −138.530 + 37.1190i −0.466430 + 0.124980i
298298 573.214i 1.92354i
299299 0 0
300300 466.184 1.55395
301301 −19.7096 73.5573i −0.0654805 0.244377i
302302 −75.2290 + 130.300i −0.249103 + 0.431458i
303303 −42.1711 + 24.3475i −0.139179 + 0.0803549i
304304 5.42384 5.42384i 0.0178416 0.0178416i
305305 94.7972 + 25.4008i 0.310810 + 0.0832814i
306306 −40.4769 + 151.062i −0.132277 + 0.493666i
307307 115.257 + 115.257i 0.375429 + 0.375429i 0.869450 0.494021i 0.164473π-0.164473\pi
−0.494021 + 0.869450i 0.664473π0.664473\pi
308308 53.1245 + 92.0143i 0.172482 + 0.298748i
309309 175.429 + 101.284i 0.567731 + 0.327780i
310310 −276.257 + 74.0228i −0.891152 + 0.238783i
311311 511.349i 1.64421i 0.569336 + 0.822105i 0.307201π0.307201\pi
−0.569336 + 0.822105i 0.692799π0.692799\pi
312312 0 0
313313 59.4173 0.189832 0.0949158 0.995485i 0.469742π-0.469742\pi
0.0949158 + 0.995485i 0.469742π0.469742\pi
314314 −51.1923 191.052i −0.163033 0.608447i
315315 61.3058 106.185i 0.194622 0.337095i
316316 521.445 301.056i 1.65014 0.952710i
317317 115.961 115.961i 0.365808 0.365808i −0.500138 0.865946i 0.666717π-0.666717\pi
0.865946 + 0.500138i 0.166717π0.166717\pi
318318 310.912 + 83.3087i 0.977712 + 0.261977i
319319 42.9032 160.117i 0.134493 0.501934i
320320 572.153 + 572.153i 1.78798 + 1.78798i
321321 −148.873 257.856i −0.463780 0.803291i
322322 −290.996 168.007i −0.903715 0.521760i
323323 115.704 31.0027i 0.358216 0.0959837i
324324 92.8358i 0.286530i
325325 0 0
326326 518.466 1.59039
327327 −78.5589 293.186i −0.240241 0.896592i
328328 −182.892 + 316.778i −0.557597 + 0.965786i
329329 258.898 149.475i 0.786923 0.454330i
330330 −184.303 + 184.303i −0.558494 + 0.558494i
331331 −528.576 141.631i −1.59691 0.427890i −0.652800 0.757531i 0.726406π-0.726406\pi
−0.944106 + 0.329641i 0.893072π0.893072\pi
332332 −78.7443 + 293.878i −0.237182 + 0.885174i
333333 150.795 + 150.795i 0.452838 + 0.452838i
334334 27.0840 + 46.9109i 0.0810898 + 0.140452i
335335 −116.780 67.4229i −0.348597 0.201262i
336336 −4.17187 + 1.11785i −0.0124163 + 0.00332693i
337337 514.522i 1.52677i −0.645942 0.763386i 0.723535π-0.723535\pi
0.645942 0.763386i 0.276465π-0.276465\pi
338338 0 0
339339 83.7991 0.247195
340340 129.904 + 484.809i 0.382071 + 1.42591i
341341 28.9040 50.0631i 0.0847624 0.146813i
342342 −159.835 + 92.2808i −0.467354 + 0.269827i
343343 −201.968 + 201.968i −0.588827 + 0.588827i
344344 −173.950 46.6097i −0.505668 0.135493i
345345 131.283 489.953i 0.380529 1.42015i
346346 88.2116 + 88.2116i 0.254947 + 0.254947i
347347 86.2782 + 149.438i 0.248640 + 0.430658i 0.963149 0.268969i 0.0866829π-0.0866829\pi
−0.714508 + 0.699627i 0.753350π0.753350\pi
348348 −370.435 213.871i −1.06447 0.614572i
349349 634.579 170.035i 1.81828 0.487206i 0.821703 0.569916i 0.193024π-0.193024\pi
0.996574 + 0.0827101i 0.0263576π0.0263576\pi
350350 375.676i 1.07336i
351351 0 0
352352 −167.608 −0.476160
353353 −18.7227 69.8740i −0.0530388 0.197943i 0.934323 0.356429i 0.116006π-0.116006\pi
−0.987361 + 0.158485i 0.949339π0.949339\pi
354354 80.4836 139.402i 0.227355 0.393790i
355355 271.094 156.516i 0.763646 0.440891i
356356 164.185 164.185i 0.461194 0.461194i
357357 −65.1498 17.4568i −0.182492 0.0488987i
358358 231.912 865.506i 0.647798 2.41761i
359359 −336.848 336.848i −0.938295 0.938295i 0.0599089 0.998204i 0.480919π-0.480919\pi
−0.998204 + 0.0599089i 0.980919π0.980919\pi
360360 −144.977 251.108i −0.402714 0.697522i
361361 −190.212 109.819i −0.526902 0.304207i
362362 41.6399 11.1574i 0.115027 0.0308215i
363363 194.892i 0.536893i
364364 0 0
365365 −842.310 −2.30770
366366 21.5289 + 80.3471i 0.0588223 + 0.219528i
367367 24.9938 43.2905i 0.0681030 0.117958i −0.829963 0.557818i 0.811639π-0.811639\pi
0.898066 + 0.439860i 0.144972π0.144972\pi
368368 17.7920 10.2722i 0.0483479 0.0279137i
369369 −160.905 + 160.905i −0.436056 + 0.436056i
370370 1074.31 + 287.861i 2.90355 + 0.778004i
371371 41.3121 154.179i 0.111353 0.415577i
372372 −105.478 105.478i −0.283542 0.283542i
373373 −113.491 196.572i −0.304265 0.527003i 0.672832 0.739795i 0.265078π-0.265078\pi
−0.977097 + 0.212792i 0.931744π0.931744\pi
374374 −142.772 82.4296i −0.381744 0.220400i
375375 163.146 43.7148i 0.435055 0.116573i
376376 706.961i 1.88022i
377377 0 0
378378 298.225 0.788955
379379 2.45213 + 9.15147i 0.00647000 + 0.0241464i 0.969085 0.246726i 0.0793546π-0.0793546\pi
−0.962615 + 0.270872i 0.912688π0.912688\pi
380380 −296.161 + 512.965i −0.779370 + 1.34991i
381381 204.910 118.305i 0.537820 0.310511i
382382 746.937 746.937i 1.95533 1.95533i
383383 83.0919 + 22.2644i 0.216950 + 0.0581316i 0.365657 0.930750i 0.380844π-0.380844\pi
−0.148707 + 0.988881i 0.547511π0.547511\pi
384384 −107.532 + 401.314i −0.280031 + 1.04509i
385385 91.3943 + 91.3943i 0.237388 + 0.237388i
386386 377.763 + 654.305i 0.978661 + 1.69509i
387387 −97.0221 56.0157i −0.250703 0.144743i
388388 −256.709 + 68.7848i −0.661620 + 0.177281i
389389 34.7670i 0.0893754i 0.999001 + 0.0446877i 0.0142293π0.0142293\pi
−0.999001 + 0.0446877i 0.985771π0.985771\pi
390390 0 0
391391 320.831 0.820541
392392 76.6898 + 286.210i 0.195637 + 0.730128i
393393 56.9320 98.6091i 0.144865 0.250914i
394394 271.641 156.832i 0.689445 0.398051i
395395 517.932 517.932i 1.31122 1.31122i
396396 150.982 + 40.4556i 0.381268 + 0.102161i
397397 49.0156 182.929i 0.123465 0.460778i −0.876315 0.481738i 0.840006π-0.840006\pi
0.999780 + 0.0209602i 0.00667233π0.00667233\pi
398398 −609.481 609.481i −1.53136 1.53136i
399399 −39.7988 68.9335i −0.0997463 0.172766i
400400 19.8921 + 11.4847i 0.0497304 + 0.0287118i
401401 −233.635 + 62.6022i −0.582630 + 0.156115i −0.538083 0.842892i 0.680851π-0.680851\pi
−0.0445472 + 0.999007i 0.514185π0.514185\pi
402402 114.291i 0.284306i
403403 0 0
404404 152.302 0.376984
405405 29.2295 + 109.086i 0.0721716 + 0.269348i
406406 −172.349 + 298.516i −0.424504 + 0.735262i
407407 −194.686 + 112.402i −0.478345 + 0.276173i
408408 −112.785 + 112.785i −0.276434 + 0.276434i
409409 450.091 + 120.602i 1.10047 + 0.294869i 0.762955 0.646452i 0.223748π-0.223748\pi
0.337513 + 0.941321i 0.390414π0.390414\pi
410410 −307.160 + 1146.34i −0.749171 + 2.79594i
411411 −45.7076 45.7076i −0.111211 0.111211i
412412 −316.782 548.683i −0.768888 1.33175i
413413 −69.1282 39.9112i −0.167381 0.0966373i
414414 −477.483 + 127.941i −1.15334 + 0.309037i
415415 370.112i 0.891835i
416416 0 0
417417 −478.562 −1.14763
418418 −50.3547 187.926i −0.120466 0.449585i
419419 347.147 601.277i 0.828514 1.43503i −0.0706893 0.997498i 0.522520π-0.522520\pi
0.899204 0.437531i 0.144147π-0.144147\pi
420420 288.837 166.760i 0.687708 0.397049i
421421 −138.088 + 138.088i −0.328000 + 0.328000i −0.851826 0.523825i 0.824504π-0.824504\pi
0.523825 + 0.851826i 0.324504π0.324504\pi
422422 −496.710 133.093i −1.17704 0.315386i
423423 113.829 424.814i 0.269098 1.00429i
424424 −266.910 266.910i −0.629504 0.629504i
425425 179.351 + 310.644i 0.422001 + 0.730928i
426426 229.771 + 132.658i 0.539369 + 0.311405i
427427 39.8435 10.6760i 0.0933103 0.0250024i
428428 931.251i 2.17582i
429429 0 0
430430 −584.285 −1.35880
431431 −43.8570 163.677i −0.101756 0.379760i 0.896201 0.443649i 0.146316π-0.146316\pi
−0.997957 + 0.0638890i 0.979650π0.979650\pi
432432 −9.11700 + 15.7911i −0.0211042 + 0.0365535i
433433 −561.144 + 323.977i −1.29594 + 0.748214i −0.979701 0.200464i 0.935755π-0.935755\pi
−0.316244 + 0.948678i 0.602422π0.602422\pi
434434 −84.9996 + 84.9996i −0.195852 + 0.195852i
435435 −502.615 134.675i −1.15544 0.309598i
436436 −245.706 + 916.986i −0.563545 + 2.10318i
437437 267.727 + 267.727i 0.612648 + 0.612648i
438438 −356.958 618.269i −0.814972 1.41157i
439439 −203.421 117.445i −0.463374 0.267529i 0.250088 0.968223i 0.419541π-0.419541\pi
−0.713462 + 0.700694i 0.752874π0.752874\pi
440440 295.241 79.1095i 0.671001 0.179794i
441441 184.332i 0.417987i
442442 0 0
443443 −601.057 −1.35679 −0.678394 0.734698i 0.737324π-0.737324\pi
−0.678394 + 0.734698i 0.737324π0.737324\pi
444444 150.138 + 560.322i 0.338148 + 1.26199i
445445 141.230 244.618i 0.317372 0.549704i
446446 515.217 297.461i 1.15520 0.666953i
447447 −257.168 + 257.168i −0.575321 + 0.575321i
448448 328.498 + 88.0208i 0.733255 + 0.196475i
449449 −133.980 + 500.022i −0.298397 + 1.11363i 0.640084 + 0.768305i 0.278899π0.278899\pi
−0.938482 + 0.345329i 0.887767π0.887767\pi
450450 −390.801 390.801i −0.868446 0.868446i
451451 −119.938 207.739i −0.265938 0.460618i
452452 −226.981 131.048i −0.502171 0.289928i
453453 −92.2094 + 24.7074i −0.203553 + 0.0545418i
454454 720.483i 1.58697i
455455 0 0
456456 −188.234 −0.412794
457457 33.4099 + 124.688i 0.0731071 + 0.272839i 0.992797 0.119805i 0.0382270π-0.0382270\pi
−0.919690 + 0.392644i 0.871560π0.871560\pi
458458 −17.9375 + 31.0686i −0.0391648 + 0.0678354i
459459 −246.601 + 142.375i −0.537257 + 0.310185i
460460 −1121.80 + 1121.80i −2.43870 + 2.43870i
461461 −436.918 117.072i −0.947762 0.253952i −0.248349 0.968671i 0.579888π-0.579888\pi
−0.699412 + 0.714719i 0.746555π0.746555\pi
462462 −28.3534 + 105.816i −0.0613711 + 0.229040i
463463 315.336 + 315.336i 0.681072 + 0.681072i 0.960242 0.279170i 0.0900592π-0.0900592\pi
−0.279170 + 0.960242i 0.590059π0.590059\pi
464464 −10.5377 18.2518i −0.0227106 0.0393358i
465465 −157.151 90.7310i −0.337958 0.195120i
466466 −122.014 + 32.6936i −0.261833 + 0.0701580i
467467 578.767i 1.23933i −0.784866 0.619665i 0.787268π-0.787268\pi
0.784866 0.619665i 0.212732π-0.212732\pi
468468 0 0
469469 −56.6761 −0.120844
470470 −593.658 2215.56i −1.26310 4.71396i
471471 62.7472 108.681i 0.133221 0.230746i
472472 −163.476 + 94.3827i −0.346347 + 0.199963i
473473 83.5079 83.5079i 0.176549 0.176549i
474474 599.662 + 160.679i 1.26511 + 0.338985i
475475 −109.562 + 408.891i −0.230657 + 0.860823i
476476 149.167 + 149.167i 0.313377 + 0.313377i
477477 −117.411 203.362i −0.246145 0.426335i
478478 1084.77 + 626.290i 2.26939 + 1.31023i
479479 188.883 50.6111i 0.394328 0.105660i −0.0562058 0.998419i 0.517900π-0.517900\pi
0.450534 + 0.892759i 0.351234π0.351234\pi
480480 526.131i 1.09611i
481481 0 0
482482 1107.67 2.29807
483483 −55.1784 205.929i −0.114241 0.426353i
484484 304.778 527.892i 0.629707 1.09069i
485485 −279.986 + 161.650i −0.577291 + 0.333299i
486486 512.358 512.358i 1.05423 1.05423i
487487 643.217 + 172.350i 1.32077 + 0.353901i 0.849268 0.527962i 0.177044π-0.177044\pi
0.471507 + 0.881862i 0.343710π0.343710\pi
488488 25.2469 94.2227i 0.0517354 0.193079i
489489 232.606 + 232.606i 0.475677 + 0.475677i
490490 480.680 + 832.562i 0.980979 + 1.69911i
491491 −168.907 97.5186i −0.344006 0.198612i 0.318036 0.948079i 0.396977π-0.396977\pi
−0.662042 + 0.749466i 0.730310π0.730310\pi
492492 −597.887 + 160.203i −1.21522 + 0.325616i
493493 329.123i 0.667591i
494494 0 0
495495 190.148 0.384138
496496 −1.90224 7.09927i −0.00383517 0.0143130i
497497 65.7843 113.942i 0.132363 0.229259i
498498 −271.668 + 156.848i −0.545518 + 0.314955i
499499 −160.747 + 160.747i −0.322139 + 0.322139i −0.849587 0.527448i 0.823149π-0.823149\pi
0.527448 + 0.849587i 0.323149π0.323149\pi
500500 −510.265 136.725i −1.02053 0.273450i
501501 −8.89519 + 33.1973i −0.0177549 + 0.0662621i
502502 −39.7776 39.7776i −0.0792382 0.0792382i
503503 −247.660 428.960i −0.492366 0.852803i 0.507595 0.861596i 0.330534π-0.330534\pi
−0.999961 + 0.00879272i 0.997201π0.997201\pi
504504 −105.541 60.9343i −0.209407 0.120901i
505505 178.961 47.9524i 0.354378 0.0949553i
506506 521.095i 1.02983i
507507 0 0
508508 −740.034 −1.45676
509509 166.732 + 622.252i 0.327568 + 1.22250i 0.911705 + 0.410845i 0.134766π0.134766\pi
−0.584138 + 0.811655i 0.698567π0.698567\pi
510510 −258.751 + 448.169i −0.507354 + 0.878763i
511511 −306.595 + 177.013i −0.599990 + 0.346404i
512512 −29.1874 + 29.1874i −0.0570067 + 0.0570067i
513513 −324.592 86.9743i −0.632734 0.169540i
514514 223.936 835.739i 0.435672 1.62595i
515515 −544.986 544.986i −1.05822 1.05822i
516516 −152.371 263.914i −0.295292 0.511460i
517517 401.503 + 231.808i 0.776601 + 0.448371i
518518 451.537 120.989i 0.871692 0.233569i
519519 79.1511i 0.152507i
520520 0 0
521521 807.372 1.54966 0.774830 0.632170i 0.217836π-0.217836\pi
0.774830 + 0.632170i 0.217836π0.217836\pi
522522 131.248 + 489.823i 0.251432 + 0.938358i
523523 −168.756 + 292.295i −0.322670 + 0.558881i −0.981038 0.193815i 0.937914π-0.937914\pi
0.658368 + 0.752696i 0.271247π0.271247\pi
524524 −308.416 + 178.064i −0.588580 + 0.339817i
525525 168.544 168.544i 0.321037 0.321037i
526526 −37.7687 10.1201i −0.0718036 0.0192397i
527527 29.7063 110.865i 0.0563686 0.210370i
528528 −4.73623 4.73623i −0.00897012 0.00897012i
529529 242.550 + 420.109i 0.458507 + 0.794157i
530530 −1060.61 612.342i −2.00114 1.15536i
531531 −113.430 + 30.3933i −0.213615 + 0.0572379i
532532 248.954i 0.467959i
533533 0 0
534534 239.405 0.448324
535535 293.206 + 1094.26i 0.548048 + 2.04534i
536536 −67.0143 + 116.072i −0.125027 + 0.216553i
537537 492.349 284.258i 0.916850 0.529344i
538538 270.078 270.078i 0.502004 0.502004i
539539 −187.693 50.2921i −0.348224 0.0933064i
540540 364.430 1360.07i 0.674870 2.51865i
541541 −532.661 532.661i −0.984586 0.984586i 0.0152973 0.999883i 0.495131π-0.495131\pi
−0.999883 + 0.0152973i 0.995131π0.995131\pi
542542 226.534 + 392.368i 0.417959 + 0.723926i
543543 23.6872 + 13.6758i 0.0436228 + 0.0251856i
544544 −321.443 + 86.1303i −0.590887 + 0.158328i
545545 1154.86i 2.11900i
546546 0 0
547547 −508.494 −0.929606 −0.464803 0.885414i 0.653875π-0.653875\pi
−0.464803 + 0.885414i 0.653875π0.653875\pi
548548 52.3263 + 195.284i 0.0954859 + 0.356358i
549549 30.3418 52.5535i 0.0552674 0.0957259i
550550 504.549 291.302i 0.917363 0.529640i
551551 274.646 274.646i 0.498450 0.498450i
552552 −486.984 130.487i −0.882217 0.236389i
553553 79.6794 297.367i 0.144086 0.537735i
554554 1235.08 + 1235.08i 2.22938 + 2.22938i
555555 352.836 + 611.130i 0.635741 + 1.10114i
556556 1296.25 + 748.391i 2.33139 + 1.34603i
557557 521.046 139.614i 0.935450 0.250653i 0.241273 0.970457i 0.422435π-0.422435\pi
0.694177 + 0.719804i 0.255768π0.255768\pi
558558 176.844i 0.316924i
559559 0 0
560560 16.4330 0.0293446
561561 −27.0723 101.035i −0.0482573 0.180099i
562562 131.283 227.389i 0.233600 0.404608i
563563 612.760 353.777i 1.08838 0.628379i 0.155238 0.987877i 0.450386π-0.450386\pi
0.933146 + 0.359498i 0.117052π0.117052\pi
564564 845.924 845.924i 1.49987 1.49987i
565565 −307.973 82.5211i −0.545085 0.146055i
566566 127.874 477.233i 0.225926 0.843168i
567567 33.5639 + 33.5639i 0.0591956 + 0.0591956i
568568 −155.568 269.452i −0.273887 0.474386i
569569 −75.1164 43.3685i −0.132015 0.0762188i 0.432538 0.901616i 0.357618π-0.357618\pi
−0.564553 + 0.825397i 0.690951π0.690951\pi
570570 −589.910 + 158.066i −1.03493 + 0.277309i
571571 819.215i 1.43470i −0.696712 0.717351i 0.745354π-0.745354\pi
0.696712 0.717351i 0.254646π-0.254646\pi
572572 0 0
573573 670.217 1.16966
574574 129.100 + 481.809i 0.224913 + 0.839388i
575575 −566.900 + 981.900i −0.985914 + 1.70765i
576576 433.289 250.159i 0.752237 0.434304i
577577 −280.814 + 280.814i −0.486679 + 0.486679i −0.907256 0.420578i 0.861827π-0.861827\pi
0.420578 + 0.907256i 0.361827π0.361827\pi
578578 584.044 + 156.494i 1.01046 + 0.270751i
579579 −124.069 + 463.030i −0.214281 + 0.799707i
580580 1150.79 + 1150.79i 1.98412 + 1.98412i
581581 77.7794 + 134.718i 0.133872 + 0.231873i
582582 −237.308 137.010i −0.407745 0.235412i
583583 239.103 64.0675i 0.410126 0.109893i
584584 837.205i 1.43357i
585585 0 0
586586 753.900 1.28652
587587 112.215 + 418.790i 0.191166 + 0.713442i 0.993226 + 0.116198i 0.0370708π0.0370708\pi
−0.802060 + 0.597244i 0.796263π0.796263\pi
588588 −250.705 + 434.233i −0.426369 + 0.738492i
589589 117.304 67.7255i 0.199158 0.114984i
590590 −433.064 + 433.064i −0.734007 + 0.734007i
591591 192.232 + 51.5083i 0.325265 + 0.0871545i
592592 −7.39748 + 27.6078i −0.0124957 + 0.0466347i
593593 −390.547 390.547i −0.658596 0.658596i 0.296452 0.955048i 0.404197π-0.404197\pi
−0.955048 + 0.296452i 0.904197π0.904197\pi
594594 231.246 + 400.530i 0.389303 + 0.674292i
595595 222.244 + 128.312i 0.373519 + 0.215651i
596596 1098.74 294.407i 1.84353 0.493972i
597597 546.879i 0.916045i
598598 0 0
599599 −315.242 −0.526281 −0.263140 0.964758i 0.584758π-0.584758\pi
−0.263140 + 0.964758i 0.584758π0.584758\pi
600600 −145.889 544.466i −0.243149 0.907443i
601601 −229.868 + 398.143i −0.382476 + 0.662468i −0.991416 0.130749i 0.958262π-0.958262\pi
0.608940 + 0.793217i 0.291595π0.291595\pi
602602 −212.675 + 122.788i −0.353281 + 0.203967i
603603 −58.9579 + 58.9579i −0.0977743 + 0.0977743i
604604 288.400 + 77.2765i 0.477483 + 0.127941i
605605 191.920 716.255i 0.317223 1.18389i
606606 111.039 + 111.039i 0.183232 + 0.183232i
607607 −448.920 777.551i −0.739571 1.28097i −0.952689 0.303948i 0.901695π-0.901695\pi
0.213118 0.977027i 0.431638π-0.431638\pi
608608 −340.111 196.363i −0.559394 0.322966i
609609 −211.250 + 56.6044i −0.346881 + 0.0929464i
610610 316.487i 0.518831i
611611 0 0
612612 310.346 0.507102
613613 −164.918 615.481i −0.269033 1.00405i −0.959735 0.280907i 0.909365π-0.909365\pi
0.690702 0.723140i 0.257302π-0.257302\pi
614614 262.819 455.215i 0.428043 0.741393i
615615 −652.102 + 376.491i −1.06033 + 0.612181i
616616 90.8405 90.8405i 0.147468 0.147468i
617617 −386.513 103.566i −0.626439 0.167854i −0.0683856 0.997659i 0.521785π-0.521785\pi
−0.558053 + 0.829805i 0.688451π0.688451\pi
618618 169.072 630.985i 0.273579 1.02101i
619619 524.800 + 524.800i 0.847819 + 0.847819i 0.989861 0.142041i 0.0453666π-0.0453666\pi
−0.142041 + 0.989861i 0.545367π0.545367\pi
620620 283.776 + 491.514i 0.457703 + 0.792765i
621621 −779.468 450.026i −1.25518 0.724680i
622622 1592.82 426.794i 2.56080 0.686164i
623623 118.719i 0.190560i
624624 0 0
625625 247.464 0.395943
626626 −49.5922 185.081i −0.0792208 0.295656i
627627 61.7206 106.903i 0.0984379 0.170500i
628628 −339.919 + 196.252i −0.541272 + 0.312503i
629629 −315.613 + 315.613i −0.501769 + 0.501769i
630630 −381.927 102.337i −0.606233 0.162440i
631631 −78.4079 + 292.622i −0.124260 + 0.463744i −0.999812 0.0193793i 0.993831π-0.993831\pi
0.875552 + 0.483123i 0.160498π0.160498\pi
632632 −514.793 514.793i −0.814546 0.814546i
633633 −163.134 282.557i −0.257716 0.446377i
634634 −457.997 264.424i −0.722392 0.417073i
635635 −869.571 + 233.001i −1.36940 + 0.366930i
636636 638.749i 1.00432i
637637 0 0
638638 −534.562 −0.837871
639639 −50.0963 186.962i −0.0783980 0.292585i
640640 790.388 1368.99i 1.23498 2.13905i
641641 −802.665 + 463.419i −1.25221 + 0.722962i −0.971547 0.236845i 0.923887π-0.923887\pi
−0.280660 + 0.959807i 0.590553π0.590553\pi
642642 −678.948 + 678.948i −1.05755 + 1.05755i
643643 −765.787 205.192i −1.19096 0.319117i −0.391695 0.920095i 0.628111π-0.628111\pi
−0.799265 + 0.600978i 0.794778π0.794778\pi
644644 −172.579 + 644.075i −0.267980 + 1.00012i
645645 −262.135 262.135i −0.406411 0.406411i
646646 −193.143 334.533i −0.298982 0.517853i
647647 565.632 + 326.568i 0.874238 + 0.504742i 0.868754 0.495243i 0.164921π-0.164921\pi
0.00548379 + 0.999985i 0.498254π0.498254\pi
648648 108.425 29.0524i 0.167322 0.0448339i
649649 123.790i 0.190739i
650650 0 0
651651 −76.2689 −0.117157
652652 −266.288 993.801i −0.408418 1.52423i
653653 −497.150 + 861.089i −0.761333 + 1.31867i 0.180831 + 0.983514i 0.442121π0.442121\pi
−0.942164 + 0.335152i 0.891212π0.891212\pi
654654 −847.684 + 489.411i −1.29615 + 0.748335i
655655 −306.338 + 306.338i −0.467692 + 0.467692i
656656 −29.4586 7.89342i −0.0449065 0.0120326i
657657 −134.799 + 503.078i −0.205174 + 0.765720i
658658 −681.690 681.690i −1.03600 1.03600i
659659 554.342 + 960.149i 0.841187 + 1.45698i 0.888892 + 0.458118i 0.151476π0.151476\pi
−0.0477042 + 0.998862i 0.515190π0.515190\pi
660660 447.934 + 258.615i 0.678687 + 0.391840i
661661 −697.517 + 186.899i −1.05525 + 0.282752i −0.744418 0.667714i 0.767273π-0.767273\pi
−0.310828 + 0.950466i 0.600606π0.600606\pi
662662 1764.69i 2.66569i
663663 0 0
664664 367.869 0.554019
665665 78.3836 + 292.532i 0.117870 + 0.439897i
666666 343.856 595.576i 0.516301 0.894259i
667667 900.932 520.153i 1.35072 0.779840i
668668 76.0088 76.0088i 0.113786 0.113786i
669669 364.603 + 97.6950i 0.544996 + 0.146031i
670670 −112.548 + 420.035i −0.167982 + 0.626918i
671671 45.2334 + 45.2334i 0.0674119 + 0.0674119i
672672 110.567 + 191.508i 0.164534 + 0.284982i
673673 201.737 + 116.473i 0.299757 + 0.173065i 0.642334 0.766425i 0.277966π-0.277966\pi
−0.342577 + 0.939490i 0.611300π0.611300\pi
674674 −1602.70 + 429.442i −2.37789 + 0.637155i
675675 1006.29i 1.49080i
676676 0 0
677677 759.119 1.12130 0.560649 0.828053i 0.310552π-0.310552\pi
0.560649 + 0.828053i 0.310552π0.310552\pi
678678 −69.9423 261.028i −0.103160 0.384998i
679679 −67.9420 + 117.679i −0.100062 + 0.173312i
680680 525.566 303.436i 0.772891 0.446229i
681681 323.240 323.240i 0.474655 0.474655i
682682 −180.068 48.2490i −0.264029 0.0707463i
683683 −205.332 + 766.309i −0.300632 + 1.12197i 0.636008 + 0.771682i 0.280584π0.280584\pi
−0.936640 + 0.350293i 0.886082π0.886082\pi
684684 258.978 + 258.978i 0.378622 + 0.378622i
685685 122.971 + 212.992i 0.179520 + 0.310938i
686686 797.686 + 460.544i 1.16281 + 0.671347i
687687 −21.9862 + 5.89120i −0.0320033 + 0.00857525i
688688 15.0150i 0.0218241i
689689 0 0
690690 −1635.74 −2.37064
691691 −238.407 889.748i −0.345018 1.28762i −0.892592 0.450866i 0.851115π-0.851115\pi
0.547574 0.836757i 0.315552π-0.315552\pi
692692 123.779 214.391i 0.178871 0.309814i
693693 69.2125 39.9599i 0.0998738 0.0576622i
694694 393.478 393.478i 0.566971 0.566971i
695695 1758.78 + 471.264i 2.53062 + 0.678078i
696696 −133.859 + 499.569i −0.192326 + 0.717771i
697697 −336.772 336.772i −0.483173 0.483173i
698698 −1059.29 1834.75i −1.51761 2.62858i
699699 −69.4087 40.0731i −0.0992971 0.0573292i
700700 −720.100 + 192.950i −1.02871 + 0.275643i
701701 1256.17i 1.79197i 0.444079 + 0.895987i 0.353531π0.353531\pi
−0.444079 + 0.895987i 0.646469π0.646469\pi
702702 0 0
703703 −526.744 −0.749281
704704 136.504 + 509.440i 0.193898 + 0.723636i
705705 727.656 1260.34i 1.03214 1.78771i
706706 −202.026 + 116.640i −0.286156 + 0.165212i
707707 55.0632 55.0632i 0.0778829 0.0778829i
708708 −308.544 82.6741i −0.435797 0.116771i
709709 −50.4214 + 188.175i −0.0711162 + 0.265409i −0.992325 0.123660i 0.960537π-0.960537\pi
0.921208 + 0.389070i 0.127203π0.127203\pi
710710 −713.805 713.805i −1.00536 1.00536i
711711 −226.453 392.227i −0.318499 0.551656i
712712 −243.136 140.375i −0.341483 0.197155i
713713 350.428 93.8970i 0.491484 0.131693i
714714 217.507i 0.304632i
715715 0 0
716716 −1778.12 −2.48341
717717 205.692 + 767.654i 0.286879 + 1.07065i
718718 −768.110 + 1330.41i −1.06979 + 1.85293i
719719 −847.432 + 489.265i −1.17863 + 0.680480i −0.955696 0.294355i 0.904895π-0.904895\pi
−0.222929 + 0.974835i 0.571562π0.571562\pi
720720 17.0946 17.0946i 0.0237425 0.0237425i
721721 −312.900 83.8414i −0.433981 0.116285i
722722 −183.319 + 684.155i −0.253904 + 0.947583i
723723 496.948 + 496.948i 0.687341 + 0.687341i
724724 −42.7732 74.0854i −0.0590791 0.102328i
725725 1007.28 + 581.551i 1.38934 + 0.802139i
726726 607.075 162.665i 0.836192 0.224057i
727727 470.571i 0.647278i 0.946181 + 0.323639i 0.104906π0.104906\pi
−0.946181 + 0.323639i 0.895094π0.895094\pi
728728 0 0
729729 590.294 0.809731
730730 703.028 + 2623.74i 0.963052 + 3.59416i
731731 117.240 203.066i 0.160383 0.277792i
732732 142.953 82.5339i 0.195291 0.112751i
733733 −113.014 + 113.014i −0.154181 + 0.154181i −0.779982 0.625802i 0.784772π-0.784772\pi
0.625802 + 0.779982i 0.284772π0.284772\pi
734734 −155.708 41.7218i −0.212136 0.0568417i
735735 −157.870 + 589.177i −0.214788 + 0.801601i
736736 −743.787 743.787i −1.01058 1.01058i
737737 −43.9471 76.1185i −0.0596297 0.103282i
738738 635.505 + 366.909i 0.861118 + 0.497167i
739739 −233.349 + 62.5256i −0.315763 + 0.0846084i −0.413220 0.910631i 0.635596π-0.635596\pi
0.0974569 + 0.995240i 0.468929π0.468929\pi
740740 2207.10i 2.98257i
741741 0 0
742742 −514.738 −0.693716
743743 −40.0554 149.489i −0.0539103 0.201196i 0.933718 0.358010i 0.116545π-0.116545\pi
−0.987628 + 0.156814i 0.949878π0.949878\pi
744744 −90.1811 + 156.198i −0.121211 + 0.209944i
745745 1198.38 691.882i 1.60856 0.928701i
746746 −517.583 + 517.583i −0.693812 + 0.693812i
747747 221.053 + 59.2309i 0.295921 + 0.0792918i
748748 −84.6731 + 316.004i −0.113199 + 0.422466i
749749 336.685 + 336.685i 0.449513 + 0.449513i
750750 −272.337 471.701i −0.363116 0.628935i
751751 −1009.94 583.090i −1.34480 0.776419i −0.357289 0.933994i 0.616299π-0.616299\pi
−0.987507 + 0.157575i 0.949632π0.949632\pi
752752 56.9356 15.2559i 0.0757123 0.0202870i
753753 35.6919i 0.0473996i
754754 0 0
755755 363.212 0.481076
756756 −153.171 571.641i −0.202607 0.756139i
757757 597.091 1034.19i 0.788759 1.36617i −0.137968 0.990437i 0.544057π-0.544057\pi
0.926727 0.375734i 0.122609π-0.122609\pi
758758 26.4595 15.2764i 0.0349071 0.0201536i
759759 233.786 233.786i 0.308018 0.308018i
760760 691.785 + 185.363i 0.910243 + 0.243899i
761761 248.434 927.170i 0.326458 1.21836i −0.586381 0.810036i 0.699448π-0.699448\pi
0.912838 0.408321i 0.133886π-0.133886\pi
762762 −539.537 539.537i −0.708054 0.708054i
763763 242.695 + 420.360i 0.318080 + 0.550930i
764764 −1815.37 1048.11i −2.37614 1.37187i
765765 364.670 97.7130i 0.476693 0.127729i
766766 277.408i 0.362152i
767767 0 0
768768 489.153 0.636918
769769 −292.755 1092.58i −0.380695 1.42077i −0.844842 0.535016i 0.820306π-0.820306\pi
0.464147 0.885758i 0.346361π-0.346361\pi
770770 208.405 360.969i 0.270656 0.468790i
771771 475.416 274.481i 0.616622 0.356007i
772772 1060.16 1060.16i 1.37326 1.37326i
773773 399.515 + 107.050i 0.516837 + 0.138486i 0.507803 0.861473i 0.330458π-0.330458\pi
0.00903396 + 0.999959i 0.497124π0.497124\pi
774774 −93.5062 + 348.970i −0.120809 + 0.450866i
775775 286.811 + 286.811i 0.370079 + 0.370079i
776776 160.670 + 278.289i 0.207050 + 0.358620i
777777 256.860 + 148.298i 0.330579 + 0.190860i
778778 108.297 29.0181i 0.139199 0.0372983i
779779 562.058i 0.721513i
780780 0 0
781781 204.039 0.261253
782782 −267.780 999.367i −0.342429 1.27796i
783783 −461.656 + 799.611i −0.589599 + 1.02122i
784784 −21.3952 + 12.3525i −0.0272898 + 0.0157558i
785785 −337.628 + 337.628i −0.430100 + 0.430100i
786786 −354.678 95.0358i −0.451245 0.120911i
787787 347.048 1295.20i 0.440975 1.64574i −0.285373 0.958416i 0.592118π-0.592118\pi
0.726349 0.687326i 0.241216π-0.241216\pi
788788 −440.135 440.135i −0.558547 0.558547i
789789 −12.4044 21.4850i −0.0157216 0.0272307i
790790 −2045.61 1181.03i −2.58938 1.49498i
791791 −129.442 + 34.6838i −0.163643 + 0.0438481i
792792 188.996i 0.238631i
793793 0 0
794794 −610.721 −0.769170
795795 −201.111 750.557i −0.252970 0.944097i
796796 −855.226 + 1481.30i −1.07440 + 1.86092i
797797 1133.61 654.489i 1.42234 0.821191i 0.425845 0.904796i 0.359977π-0.359977\pi
0.996499 + 0.0836053i 0.0266435π0.0266435\pi
798798 −181.505 + 181.505i −0.227450 + 0.227450i
799799 889.131 + 238.242i 1.11281 + 0.298175i
800800 304.380 1135.96i 0.380475 1.41995i
801801 −123.499 123.499i −0.154181 0.154181i
802802 390.003 + 675.505i 0.486288 + 0.842275i
803803 −475.472 274.514i −0.592119 0.341860i
804804 −219.075 + 58.7009i −0.272481 + 0.0730110i
805805 811.152i 1.00764i
806806 0 0
807807 242.337 0.300294
808808 −47.6618 177.876i −0.0589874 0.220144i
809809 12.0403 20.8545i 0.0148830 0.0257781i −0.858488 0.512834i 0.828596π-0.828596\pi
0.873371 + 0.487056i 0.161929π0.161929\pi
810810 315.399 182.096i 0.389381 0.224809i
811811 685.757 685.757i 0.845570 0.845570i −0.144007 0.989577i 0.545999π-0.545999\pi
0.989577 + 0.144007i 0.0459987π0.0459987\pi
812812 660.720 + 177.039i 0.813694 + 0.218029i
813813 −74.4004 + 277.666i −0.0915134 + 0.341533i
814814 512.619 + 512.619i 0.629753 + 0.629753i
815815 −625.800 1083.92i −0.767852 1.32996i
816816 −11.5171 6.64939i −0.0141141 0.00814876i
817817 267.289 71.6199i 0.327159 0.0876620i
818818 1502.66i 1.83700i
819819 0 0
820820 2355.07 2.87204
821821 −91.7762 342.513i −0.111786 0.417191i 0.887241 0.461307i 0.152619π-0.152619\pi
−0.999026 + 0.0441166i 0.985953π0.985953\pi
822822 −104.227 + 180.526i −0.126796 + 0.219618i
823823 −761.836 + 439.846i −0.925681 + 0.534442i −0.885443 0.464748i 0.846145π-0.846145\pi
−0.0402381 + 0.999190i 0.512812π0.512812\pi
824824 −541.683 + 541.683i −0.657382 + 0.657382i
825825 357.053 + 95.6721i 0.432792 + 0.115966i
826826 −66.6232 + 248.641i −0.0806576 + 0.301018i
827827 496.734 + 496.734i 0.600645 + 0.600645i 0.940484 0.339838i 0.110372π-0.110372\pi
−0.339838 + 0.940484i 0.610372π0.610372\pi
828828 490.479 + 849.535i 0.592366 + 1.02601i
829829 −841.504 485.843i −1.01508 0.586059i −0.102408 0.994743i 0.532655π-0.532655\pi
−0.912676 + 0.408684i 0.865988π0.865988\pi
830830 1152.87 308.911i 1.38900 0.372182i
831831 1108.22i 1.33360i
832832 0 0
833833 −385.805 −0.463152
834834 399.429 + 1490.69i 0.478931 + 1.78740i
835835 65.3820 113.245i 0.0783018 0.135623i
836836 −334.357 + 193.041i −0.399949 + 0.230910i
837837 −227.681 + 227.681i −0.272021 + 0.272021i
838838 −2162.68 579.488i −2.58076 0.691514i
839839 16.6003 61.9530i 0.0197858 0.0738415i −0.955327 0.295551i 0.904497π-0.904497\pi
0.975113 + 0.221709i 0.0711636π0.0711636\pi
840840 −285.153 285.153i −0.339468 0.339468i
841841 −113.096 195.887i −0.134477 0.232922i
842842 545.389 + 314.880i 0.647730 + 0.373967i
843843 160.916 43.1173i 0.190885 0.0511475i
844844 1020.46i 1.20907i
845845 0 0
846846 −1418.27 −1.67645
847847 −80.6644 301.044i −0.0952355 0.355424i
848848 15.7360 27.2555i 0.0185566 0.0321409i
849849 271.477 156.738i 0.319761 0.184614i
850850 817.942 817.942i 0.962284 0.962284i
851851 −1362.75 365.148i −1.60135 0.429081i
852852 136.269 508.563i 0.159940 0.596905i
853853 −118.160 118.160i −0.138523 0.138523i 0.634445 0.772968i 0.281229π-0.281229\pi
−0.772968 + 0.634445i 0.781229π0.781229\pi
854854 −66.5102 115.199i −0.0778808 0.134893i
855855 385.849 + 222.770i 0.451285 + 0.260550i
856856 1087.63 291.429i 1.27059 0.340454i
857857 1001.36i 1.16845i −0.811592 0.584225i 0.801399π-0.801399\pi
0.811592 0.584225i 0.198601π-0.198601\pi
858858 0 0
859859 −1088.25 −1.26688 −0.633438 0.773793i 0.718357π-0.718357\pi
−0.633438 + 0.773793i 0.718357π0.718357\pi
860860 300.094 + 1119.96i 0.348946 + 1.30228i
861861 −158.240 + 274.080i −0.183787 + 0.318328i
862862 −473.236 + 273.223i −0.548998 + 0.316964i
863863 1068.95 1068.95i 1.23864 1.23864i 0.278082 0.960557i 0.410301π-0.410301\pi
0.960557 0.278082i 0.0896989π-0.0896989\pi
864864 901.767 + 241.628i 1.04371 + 0.279662i
865865 77.9440 290.891i 0.0901086 0.336290i
866866 1477.52 + 1477.52i 1.70614 + 1.70614i
867867 191.817 + 332.238i 0.221243 + 0.383204i
868868 206.585 + 119.272i 0.238001 + 0.137410i
869869 461.162 123.568i 0.530681 0.142196i
870870 1678.02i 1.92875i
871871 0 0
872872 1147.86 1.31635
873873 51.7395 + 193.094i 0.0592663 + 0.221185i
874874 610.495 1057.41i 0.698507 1.20985i
875875 −233.913 + 135.050i −0.267329 + 0.154343i
876876 −1001.77 + 1001.77i −1.14357 + 1.14357i
877877 827.023 + 221.600i 0.943014 + 0.252680i 0.697395 0.716687i 0.254342π-0.254342\pi
0.245618 + 0.969367i 0.421009π0.421009\pi
878878 −196.050 + 731.668i −0.223291 + 0.833335i
879879 338.232 + 338.232i 0.384792 + 0.384792i
880880 12.7423 + 22.0703i 0.0144799 + 0.0250798i
881881 1223.50 + 706.388i 1.38876 + 0.801802i 0.993176 0.116626i 0.0372080π-0.0372080\pi
0.395587 + 0.918429i 0.370541π0.370541\pi
882882 574.182 153.852i 0.651000 0.174435i
883883 249.675i 0.282757i 0.989956 + 0.141379i 0.0451535π0.0451535\pi
−0.989956 + 0.141379i 0.954847π0.954847\pi
884884 0 0
885885 −388.582 −0.439076
886886 501.668 + 1872.25i 0.566217 + 2.11315i
887887 −407.874 + 706.459i −0.459836 + 0.796459i −0.998952 0.0457724i 0.985425π-0.985425\pi
0.539116 + 0.842232i 0.318758π0.318758\pi
888888 607.427 350.698i 0.684039 0.394930i
889889 −267.552 + 267.552i −0.300958 + 0.300958i
890890 −879.846 235.754i −0.988591 0.264892i
891891 −19.0521 + 71.1035i −0.0213829 + 0.0798019i
892892 −834.797 834.797i −0.935871 0.935871i
893893 543.154 + 940.770i 0.608235 + 1.05349i
894894 1015.71 + 586.418i 1.13614 + 0.655948i
895895 −2089.37 + 559.845i −2.33449 + 0.625525i
896896 664.404i 0.741522i
897897 0 0
898898 1669.36 1.85897
899899 −96.3235 359.484i −0.107145 0.399871i
900900 −548.373 + 949.811i −0.609304 + 1.05535i
901901 425.634 245.740i 0.472402 0.272741i
902902 −546.986 + 546.986i −0.606414 + 0.606414i
903903 −150.503 40.3273i −0.166671 0.0446592i
904904 −82.0210 + 306.107i −0.0907312 + 0.338613i
905905 −73.5863 73.5863i −0.0813108 0.0813108i
906906 153.924 + 266.604i 0.169894 + 0.294265i
907907 1119.16 + 646.145i 1.23391 + 0.712398i 0.967843 0.251556i 0.0809424π-0.0809424\pi
0.266067 + 0.963955i 0.414276π0.414276\pi
908908 −1381.03 + 370.046i −1.52096 + 0.407540i
909909 114.560i 0.126029i
910910 0 0
911911 −108.954 −0.119598 −0.0597992 0.998210i 0.519046π-0.519046\pi
−0.0597992 + 0.998210i 0.519046π0.519046\pi
912912 −4.06199 15.1595i −0.00445393 0.0166223i
913913 −120.622 + 208.923i −0.132116 + 0.228831i
914914 360.508 208.139i 0.394429 0.227723i
915915 141.990 141.990i 0.155180 0.155180i
916916 68.7655 + 18.4257i 0.0750715 + 0.0201154i
917917 −47.1275 + 175.882i −0.0513931 + 0.191802i
918918 649.312 + 649.312i 0.707311 + 0.707311i
919919 334.516 + 579.399i 0.364000 + 0.630467i 0.988615 0.150466i 0.0480774π-0.0480774\pi
−0.624615 + 0.780933i 0.714744π0.714744\pi
920920 1661.23 + 959.114i 1.80569 + 1.04252i
921921 322.141 86.3174i 0.349773 0.0937214i
922922 1458.68i 1.58209i
923923 0 0
924924 217.393 0.235274
925925 −408.249 1523.61i −0.441350 1.64714i
926926 719.057 1245.44i 0.776520 1.34497i
927927 −412.715 + 238.281i −0.445216 + 0.257046i
928928 −763.009 + 763.009i −0.822208 + 0.822208i
929929 531.264 + 142.352i 0.571866 + 0.153231i 0.533152 0.846019i 0.321007π-0.321007\pi
0.0387140 + 0.999250i 0.487674π0.487674\pi
930930 −151.456 + 565.241i −0.162856 + 0.607786i
931931 −321.947 321.947i −0.345807 0.345807i
932932 125.335 + 217.087i 0.134480 + 0.232926i
933933 906.085 + 523.128i 0.971152 + 0.560695i
934934 −1802.82 + 483.064i −1.93021 + 0.517199i
935935 397.978i 0.425645i
936936 0 0
937937 −1312.75 −1.40101 −0.700507 0.713646i 0.747043π-0.747043\pi
−0.700507 + 0.713646i 0.747043π0.747043\pi
938938 47.3043 + 176.542i 0.0504310 + 0.188211i
939939 60.7860 105.284i 0.0647348 0.112124i
940940 −3941.91 + 2275.86i −4.19352 + 2.42113i
941941 310.426 310.426i 0.329889 0.329889i −0.522655 0.852544i 0.675058π-0.675058\pi
0.852544 + 0.522655i 0.175058π0.175058\pi
942942 −390.906 104.743i −0.414975 0.111192i
943943 389.629 1454.11i 0.413180 1.54201i
944944 −11.1289 11.1289i −0.0117891 0.0117891i
945945 −359.964 623.476i −0.380915 0.659763i
946946 −329.820 190.422i −0.348647 0.201292i
947947 −750.497 + 201.095i −0.792499 + 0.212350i −0.632288 0.774733i 0.717884π-0.717884\pi
−0.160211 + 0.987083i 0.551217π0.551217\pi
948948 1231.97i 1.29954i
949949 0 0
950950 1365.11 1.43696
951951 −86.8448 324.109i −0.0913195 0.340809i
952952 127.535 220.897i 0.133965 0.232034i
953953 −147.254 + 85.0174i −0.154517 + 0.0892102i −0.575265 0.817967i 0.695101π-0.695101\pi
0.420748 + 0.907178i 0.361768π0.361768\pi
954954 −535.462 + 535.462i −0.561281 + 0.561281i
955955 −2463.14 659.995i −2.57920 0.691094i
956956 643.336 2400.96i 0.672945 2.51147i
957957 −239.827 239.827i −0.250603 0.250603i
958958 −315.300 546.116i −0.329123 0.570058i
959959 89.5212 + 51.6851i 0.0933485 + 0.0538948i
960960 1599.16 428.493i 1.66579 0.446347i
961961 831.213i 0.864946i
962962 0 0
963963 700.481 0.727394
964964 −568.908 2123.19i −0.590153 2.20248i
965965 911.938 1579.52i 0.945013 1.63681i
966966 −595.399 + 343.754i −0.616355 + 0.355853i
967967 −702.486 + 702.486i −0.726460 + 0.726460i −0.969913 0.243453i 0.921720π-0.921720\pi
0.243453 + 0.969913i 0.421720π0.421720\pi
968968 −711.914 190.757i −0.735448 0.197063i
969969 63.4338 236.738i 0.0654631 0.244312i
970970 737.217 + 737.217i 0.760018 + 0.760018i
971971 −521.890 903.939i −0.537476 0.930936i −0.999039 0.0438288i 0.986044π-0.986044\pi
0.461563 0.887108i 0.347289π-0.347289\pi
972972 −1245.25 718.943i −1.28112 0.739653i
973973 739.220 198.073i 0.759733 0.203570i
974974 2147.43i 2.20475i
975975 0 0
976976 8.13310 0.00833309
977977 314.547 + 1173.90i 0.321951 + 1.20154i 0.917341 + 0.398102i 0.130331π0.130331\pi
−0.595390 + 0.803437i 0.703002π0.703002\pi
978978 530.408 918.694i 0.542340 0.939360i
979979 159.445 92.0557i 0.162865 0.0940303i
980980 1348.98 1348.98i 1.37651 1.37651i
981981 689.750 + 184.818i 0.703110 + 0.188398i
982982 −162.786 + 607.527i −0.165770 + 0.618663i
983983 −511.256 511.256i −0.520098 0.520098i 0.397503 0.917601i 0.369877π-0.369877\pi
−0.917601 + 0.397503i 0.869877π0.869877\pi
984984 374.209 + 648.150i 0.380294 + 0.658689i
985985 −655.754 378.600i −0.665740 0.384365i
986986 −1025.19 + 274.700i −1.03975 + 0.278600i
987987 611.672i 0.619728i
988988 0 0
989989 741.158 0.749401
990990 −158.706 592.298i −0.160309 0.598281i
991991 2.60955 4.51988i 0.00263325 0.00456093i −0.864706 0.502279i 0.832495π-0.832495\pi
0.867339 + 0.497718i 0.165828π0.165828\pi
992992 −325.889 + 188.152i −0.328517 + 0.189669i
993993 −791.715 + 791.715i −0.797296 + 0.797296i
994994 −409.827 109.813i −0.412301 0.110476i
995995 −538.539 + 2009.85i −0.541245 + 2.01995i
996996 440.178 + 440.178i 0.441946 + 0.441946i
997997 136.426 + 236.297i 0.136836 + 0.237008i 0.926298 0.376793i 0.122973π-0.122973\pi
−0.789461 + 0.613801i 0.789640π0.789640\pi
998998 634.883 + 366.550i 0.636156 + 0.367285i
999999 1209.49 324.083i 1.21070 0.324407i
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 169.3.f.g.19.1 48
13.2 odd 12 inner 169.3.f.g.89.12 48
13.3 even 3 inner 169.3.f.g.80.12 48
13.4 even 6 169.3.d.e.70.12 yes 24
13.5 odd 4 inner 169.3.f.g.150.1 48
13.6 odd 12 169.3.d.e.99.12 yes 24
13.7 odd 12 169.3.d.e.99.1 yes 24
13.8 odd 4 inner 169.3.f.g.150.12 48
13.9 even 3 169.3.d.e.70.1 24
13.10 even 6 inner 169.3.f.g.80.1 48
13.11 odd 12 inner 169.3.f.g.89.1 48
13.12 even 2 inner 169.3.f.g.19.12 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.3.d.e.70.1 24 13.9 even 3
169.3.d.e.70.12 yes 24 13.4 even 6
169.3.d.e.99.1 yes 24 13.7 odd 12
169.3.d.e.99.12 yes 24 13.6 odd 12
169.3.f.g.19.1 48 1.1 even 1 trivial
169.3.f.g.19.12 48 13.12 even 2 inner
169.3.f.g.80.1 48 13.10 even 6 inner
169.3.f.g.80.12 48 13.3 even 3 inner
169.3.f.g.89.1 48 13.11 odd 12 inner
169.3.f.g.89.12 48 13.2 odd 12 inner
169.3.f.g.150.1 48 13.5 odd 4 inner
169.3.f.g.150.12 48 13.8 odd 4 inner