Properties

Label 171.4.e.a.58.19
Level 171171
Weight 44
Character 171.58
Analytic conductor 10.08910.089
Analytic rank 00
Dimension 5454
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [171,4,Mod(58,171)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(171, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.58");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 171=3219 171 = 3^{2} \cdot 19
Weight: k k == 4 4
Character orbit: [χ][\chi] == 171.e (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 10.089326611010.0893266110
Analytic rank: 00
Dimension: 5454
Relative dimension: 2727 over Q(ζ3)\Q(\zeta_{3})
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 58.19
Character χ\chi == 171.58
Dual form 171.4.e.a.115.19

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.989966+1.71467i)q2+(4.88583+1.76881i)q3+(2.039933.53327i)q4+(1.256502.17632i)q5+(1.80387+10.1287i)q6+(18.095031.3414i)q7+23.9173q8+(20.7426+17.2842i)q9+4.97556q10+(17.8332+30.8880i)q11+(16.216513.6547i)q12+(32.977457.1185i)q13+(35.826862.0539i)q14+(9.988548.41061i)q15+(7.35786+12.7442i)q16+27.0750q17+(9.10228+52.6775i)q1819.0000q19+(5.126358.87910i)q20+(32.9718185.135i)q21+(35.3085+61.1562i)q22+(78.7214+136.349i)q23+(116.856+42.3052i)q24+(59.3424+102.784i)q25+130.586q26+(70.7723+121.137i)q27147.650q28+(119.004206.121i)q29+(24.3097+8.80084i)q30+(37.5030+64.9570i)q31+(81.1012140.471i)q32+(32.4949+182.457i)q33+(26.8034+46.4248i)q3490.9452q35+(103.38338.0306i)q36+18.8827q37+(18.809432.5788i)q38+(262.154220.740i)q39+(30.052152.0517i)q40+(85.4586+148.019i)q41+(284.805239.813i)q42+(34.8186+60.3077i)q43+145.514q44+(63.679023.4249i)q45311.726q46+(254.788+441.305i)q47+(13.4072+75.2806i)q48+(483.356+837.197i)q49+(117.494+203.506i)q50+(132.284+47.8907i)q51+(134.543233.036i)q52+211.211q53+(137.649+241.273i)q54+89.6296q55+(432.783749.602i)q56+(92.830733.6074i)q57+(235.619408.105i)q58+(24.0526+41.6603i)q59+(9.3410052.4493i)q60+(320.221554.638i)q61148.507q62+(166.375962.860i)q63+438.876q64+(82.8721143.539i)q65+(280.685+236.344i)q66+(160.552278.084i)q67+(55.231395.6635i)q68+(625.796+526.937i)q69+(90.0327155.941i)q70564.580q71+(496.108+413.392i)q721223.30q73+(18.6932+32.3776i)q74+(108.131+607.151i)q75+(38.7588+67.1321i)q76+(645.3831117.84i)q77+(638.020+230.982i)q78+(527.668+913.948i)q79+36.9806q80+(131.512+717.040i)q81338.404q82+(408.359707.299i)q83+(721.393261.165i)q84+(34.019858.9240i)q85+(68.9386+119.405i)q86+(216.8431217.57i)q87+(426.523+738.759i)q88119.022q89+(103.206+85.9988i)q902386.90q91+(321.173+556.288i)q92+(298.130+251.033i)q93+(504.462+873.754i)q94+(23.8735+41.3501i)q95+(644.714542.866i)q96+(470.013+814.087i)q971914.02q98+(163.968+948.931i)q99+O(q100)q+(0.989966 + 1.71467i) q^{2} +(4.88583 + 1.76881i) q^{3} +(2.03993 - 3.53327i) q^{4} +(1.25650 - 2.17632i) q^{5} +(1.80387 + 10.1287i) q^{6} +(-18.0950 - 31.3414i) q^{7} +23.9173 q^{8} +(20.7426 + 17.2842i) q^{9} +4.97556 q^{10} +(17.8332 + 30.8880i) q^{11} +(16.2165 - 13.6547i) q^{12} +(32.9774 - 57.1185i) q^{13} +(35.8268 - 62.0539i) q^{14} +(9.98854 - 8.41061i) q^{15} +(7.35786 + 12.7442i) q^{16} +27.0750 q^{17} +(-9.10228 + 52.6775i) q^{18} -19.0000 q^{19} +(-5.12635 - 8.87910i) q^{20} +(-32.9718 - 185.135i) q^{21} +(-35.3085 + 61.1562i) q^{22} +(-78.7214 + 136.349i) q^{23} +(116.856 + 42.3052i) q^{24} +(59.3424 + 102.784i) q^{25} +130.586 q^{26} +(70.7723 + 121.137i) q^{27} -147.650 q^{28} +(-119.004 - 206.121i) q^{29} +(24.3097 + 8.80084i) q^{30} +(-37.5030 + 64.9570i) q^{31} +(81.1012 - 140.471i) q^{32} +(32.4949 + 182.457i) q^{33} +(26.8034 + 46.4248i) q^{34} -90.9452 q^{35} +(103.383 - 38.0306i) q^{36} +18.8827 q^{37} +(-18.8094 - 32.5788i) q^{38} +(262.154 - 220.740i) q^{39} +(30.0521 - 52.0517i) q^{40} +(-85.4586 + 148.019i) q^{41} +(284.805 - 239.813i) q^{42} +(34.8186 + 60.3077i) q^{43} +145.514 q^{44} +(63.6790 - 23.4249i) q^{45} -311.726 q^{46} +(254.788 + 441.305i) q^{47} +(13.4072 + 75.2806i) q^{48} +(-483.356 + 837.197i) q^{49} +(-117.494 + 203.506i) q^{50} +(132.284 + 47.8907i) q^{51} +(-134.543 - 233.036i) q^{52} +211.211 q^{53} +(-137.649 + 241.273i) q^{54} +89.6296 q^{55} +(-432.783 - 749.602i) q^{56} +(-92.8307 - 33.6074i) q^{57} +(235.619 - 408.105i) q^{58} +(-24.0526 + 41.6603i) q^{59} +(-9.34100 - 52.4493i) q^{60} +(-320.221 - 554.638i) q^{61} -148.507 q^{62} +(166.375 - 962.860i) q^{63} +438.876 q^{64} +(-82.8721 - 143.539i) q^{65} +(-280.685 + 236.344i) q^{66} +(160.552 - 278.084i) q^{67} +(55.2313 - 95.6635i) q^{68} +(-625.796 + 526.937i) q^{69} +(-90.0327 - 155.941i) q^{70} -564.580 q^{71} +(496.108 + 413.392i) q^{72} -1223.30 q^{73} +(18.6932 + 32.3776i) q^{74} +(108.131 + 607.151i) q^{75} +(-38.7588 + 67.1321i) q^{76} +(645.383 - 1117.84i) q^{77} +(638.020 + 230.982i) q^{78} +(527.668 + 913.948i) q^{79} +36.9806 q^{80} +(131.512 + 717.040i) q^{81} -338.404 q^{82} +(-408.359 - 707.299i) q^{83} +(-721.393 - 261.165i) q^{84} +(34.0198 - 58.9240i) q^{85} +(-68.9386 + 119.405i) q^{86} +(-216.843 - 1217.57i) q^{87} +(426.523 + 738.759i) q^{88} -119.022 q^{89} +(103.206 + 85.9988i) q^{90} -2386.90 q^{91} +(321.173 + 556.288i) q^{92} +(-298.130 + 251.033i) q^{93} +(-504.462 + 873.754i) q^{94} +(-23.8735 + 41.3501i) q^{95} +(644.714 - 542.866i) q^{96} +(470.013 + 814.087i) q^{97} -1914.02 q^{98} +(-163.968 + 948.931i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 54q6q2+2q3108q426q5+59q6+138q8102q970q11+256q12121q14+64q15468q16+136q17102q181026q19136q20+133q21++2690q99+O(q100) 54 q - 6 q^{2} + 2 q^{3} - 108 q^{4} - 26 q^{5} + 59 q^{6} + 138 q^{8} - 102 q^{9} - 70 q^{11} + 256 q^{12} - 121 q^{14} + 64 q^{15} - 468 q^{16} + 136 q^{17} - 102 q^{18} - 1026 q^{19} - 136 q^{20} + 133 q^{21}+ \cdots + 2690 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/171Z)×\left(\mathbb{Z}/171\mathbb{Z}\right)^\times.

nn 2020 154154
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.989966 + 1.71467i 0.350006 + 0.606228i 0.986250 0.165260i 0.0528463π-0.0528463\pi
−0.636244 + 0.771488i 0.719513π0.719513\pi
33 4.88583 + 1.76881i 0.940278 + 0.340408i
44 2.03993 3.53327i 0.254992 0.441659i
55 1.25650 2.17632i 0.112385 0.194656i −0.804347 0.594160i 0.797484π-0.797484\pi
0.916731 + 0.399504i 0.130818π0.130818\pi
66 1.80387 + 10.1287i 0.122738 + 0.689167i
77 −18.0950 31.3414i −0.977036 1.69228i −0.673044 0.739602i 0.735014π-0.735014\pi
−0.303992 0.952674i 0.598320π-0.598320\pi
88 23.9173 1.05701
99 20.7426 + 17.2842i 0.768245 + 0.640156i
1010 4.97556 0.157341
1111 17.8332 + 30.8880i 0.488810 + 0.846645i 0.999917 0.0128727i 0.00409763π-0.00409763\pi
−0.511107 + 0.859517i 0.670764π0.670764\pi
1212 16.2165 13.6547i 0.390107 0.328481i
1313 32.9774 57.1185i 0.703560 1.21860i −0.263649 0.964619i 0.584926π-0.584926\pi
0.967209 0.253983i 0.0817407π-0.0817407\pi
1414 35.8268 62.0539i 0.683937 1.18461i
1515 9.98854 8.41061i 0.171935 0.144774i
1616 7.35786 + 12.7442i 0.114967 + 0.199128i
1717 27.0750 0.386274 0.193137 0.981172i 0.438134π-0.438134\pi
0.193137 + 0.981172i 0.438134π0.438134\pi
1818 −9.10228 + 52.6775i −0.119190 + 0.689790i
1919 −19.0000 −0.229416
2020 −5.12635 8.87910i −0.0573143 0.0992713i
2121 −32.9718 185.135i −0.342621 1.92380i
2222 −35.3085 + 61.1562i −0.342173 + 0.592661i
2323 −78.7214 + 136.349i −0.713676 + 1.23612i 0.249792 + 0.968300i 0.419638π0.419638\pi
−0.963468 + 0.267824i 0.913696π0.913696\pi
2424 116.856 + 42.3052i 0.993879 + 0.359813i
2525 59.3424 + 102.784i 0.474739 + 0.822273i
2626 130.586 0.985000
2727 70.7723 + 121.137i 0.504449 + 0.863441i
2828 −147.650 −0.996545
2929 −119.004 206.121i −0.762016 1.31985i −0.941810 0.336146i 0.890877π-0.890877\pi
0.179794 0.983704i 0.442457π-0.442457\pi
3030 24.3097 + 8.80084i 0.147944 + 0.0535602i
3131 −37.5030 + 64.9570i −0.217282 + 0.376343i −0.953976 0.299883i 0.903052π-0.903052\pi
0.736694 + 0.676226i 0.236386π0.236386\pi
3232 81.1012 140.471i 0.448025 0.776002i
3333 32.4949 + 182.457i 0.171413 + 0.962476i
3434 26.8034 + 46.4248i 0.135198 + 0.234170i
3535 −90.9452 −0.439216
3636 103.383 38.0306i 0.478627 0.176067i
3737 18.8827 0.0839000 0.0419500 0.999120i 0.486643π-0.486643\pi
0.0419500 + 0.999120i 0.486643π0.486643\pi
3838 −18.8094 32.5788i −0.0802968 0.139078i
3939 262.154 220.740i 1.07636 0.906327i
4040 30.0521 52.0517i 0.118791 0.205753i
4141 −85.4586 + 148.019i −0.325522 + 0.563820i −0.981618 0.190857i 0.938873π-0.938873\pi
0.656096 + 0.754677i 0.272207π0.272207\pi
4242 284.805 239.813i 1.04634 0.881048i
4343 34.8186 + 60.3077i 0.123484 + 0.213880i 0.921139 0.389233i 0.127260π-0.127260\pi
−0.797656 + 0.603113i 0.793927π0.793927\pi
4444 145.514 0.498571
4545 63.6790 23.4249i 0.210949 0.0775997i
4646 −311.726 −0.999163
4747 254.788 + 441.305i 0.790736 + 1.36959i 0.925512 + 0.378719i 0.123635π0.123635\pi
−0.134776 + 0.990876i 0.543031π0.543031\pi
4848 13.4072 + 75.2806i 0.0403158 + 0.226371i
4949 −483.356 + 837.197i −1.40920 + 2.44081i
5050 −117.494 + 203.506i −0.332323 + 0.575601i
5151 132.284 + 47.8907i 0.363205 + 0.131491i
5252 −134.543 233.036i −0.358804 0.621467i
5353 211.211 0.547398 0.273699 0.961815i 0.411753π-0.411753\pi
0.273699 + 0.961815i 0.411753π0.411753\pi
5454 −137.649 + 241.273i −0.346882 + 0.608021i
5555 89.6296 0.219739
5656 −432.783 749.602i −1.03273 1.78875i
5757 −92.8307 33.6074i −0.215715 0.0780950i
5858 235.619 408.105i 0.533420 0.923910i
5959 −24.0526 + 41.6603i −0.0530742 + 0.0919272i −0.891342 0.453332i 0.850235π-0.850235\pi
0.838268 + 0.545259i 0.183569π0.183569\pi
6060 −9.34100 52.4493i −0.0200986 0.112853i
6161 −320.221 554.638i −0.672132 1.16417i −0.977298 0.211868i 0.932045π-0.932045\pi
0.305166 0.952299i 0.401288π-0.401288\pi
6262 −148.507 −0.304199
6363 166.375 962.860i 0.332718 1.92554i
6464 438.876 0.857179
6565 −82.8721 143.539i −0.158139 0.273904i
6666 −280.685 + 236.344i −0.523484 + 0.440788i
6767 160.552 278.084i 0.292754 0.507065i −0.681706 0.731626i 0.738762π-0.738762\pi
0.974460 + 0.224561i 0.0720949π0.0720949\pi
6868 55.2313 95.6635i 0.0984968 0.170601i
6969 −625.796 + 526.937i −1.09184 + 0.919358i
7070 −90.0327 155.941i −0.153728 0.266265i
7171 −564.580 −0.943709 −0.471855 0.881676i 0.656415π-0.656415\pi
−0.471855 + 0.881676i 0.656415π0.656415\pi
7272 496.108 + 413.392i 0.812039 + 0.676649i
7373 −1223.30 −1.96132 −0.980660 0.195717i 0.937297π-0.937297\pi
−0.980660 + 0.195717i 0.937297π0.937297\pi
7474 18.6932 + 32.3776i 0.0293655 + 0.0508625i
7575 108.131 + 607.151i 0.166479 + 0.934770i
7676 −38.7588 + 67.1321i −0.0584991 + 0.101323i
7777 645.383 1117.84i 0.955171 1.65441i
7878 638.020 + 230.982i 0.926174 + 0.335302i
7979 527.668 + 913.948i 0.751485 + 1.30161i 0.947103 + 0.320930i 0.103996π0.103996\pi
−0.195618 + 0.980680i 0.562671π0.562671\pi
8080 36.9806 0.0516819
8181 131.512 + 717.040i 0.180400 + 0.983593i
8282 −338.404 −0.455738
8383 −408.359 707.299i −0.540039 0.935376i −0.998901 0.0468679i 0.985076π-0.985076\pi
0.458862 0.888508i 0.348257π-0.348257\pi
8484 −721.393 261.165i −0.937029 0.339232i
8585 34.0198 58.9240i 0.0434113 0.0751906i
8686 −68.9386 + 119.405i −0.0864400 + 0.149718i
8787 −216.843 1217.57i −0.267219 1.50042i
8888 426.523 + 738.759i 0.516676 + 0.894909i
8989 −119.022 −0.141756 −0.0708782 0.997485i 0.522580π-0.522580\pi
−0.0708782 + 0.997485i 0.522580π0.522580\pi
9090 103.206 + 85.9988i 0.120877 + 0.100723i
9191 −2386.90 −2.74961
9292 321.173 + 556.288i 0.363963 + 0.630403i
9393 −298.130 + 251.033i −0.332415 + 0.279902i
9494 −504.462 + 873.754i −0.553524 + 0.958732i
9595 −23.8735 + 41.3501i −0.0257828 + 0.0446571i
9696 644.714 542.866i 0.685426 0.577146i
9797 470.013 + 814.087i 0.491986 + 0.852144i 0.999957 0.00922935i 0.00293784π-0.00293784\pi
−0.507972 + 0.861374i 0.669605π0.669605\pi
9898 −1914.02 −1.97291
9999 −163.968 + 948.931i −0.166459 + 0.963345i
100100 484.219 0.484219
101101 −607.124 1051.57i −0.598129 1.03599i −0.993097 0.117296i 0.962578π-0.962578\pi
0.394968 0.918695i 0.370756π-0.370756\pi
102102 48.8399 + 274.234i 0.0474105 + 0.266208i
103103 56.6910 98.1917i 0.0542324 0.0939332i −0.837635 0.546231i 0.816062π-0.816062\pi
0.891867 + 0.452298i 0.149395π0.149395\pi
104104 788.731 1366.12i 0.743667 1.28807i
105105 −444.343 160.865i −0.412985 0.149513i
106106 209.092 + 362.158i 0.191593 + 0.331848i
107107 1158.81 1.04697 0.523487 0.852034i 0.324631π-0.324631\pi
0.523487 + 0.852034i 0.324631π0.324631\pi
108108 572.382 2.94497i 0.509977 0.00262388i
109109 553.494 0.486377 0.243189 0.969979i 0.421807π-0.421807\pi
0.243189 + 0.969979i 0.421807π0.421807\pi
110110 88.7303 + 153.685i 0.0769100 + 0.133212i
111111 92.2577 + 33.4000i 0.0788893 + 0.0285602i
112112 266.280 461.211i 0.224653 0.389110i
113113 −146.584 + 253.890i −0.122030 + 0.211363i −0.920568 0.390582i 0.872274π-0.872274\pi
0.798538 + 0.601945i 0.205607π0.205607\pi
114114 −34.2735 192.444i −0.0281580 0.158106i
115115 197.827 + 342.646i 0.160413 + 0.277843i
116116 −971.040 −0.777231
117117 1671.29 614.798i 1.32060 0.485796i
118118 −95.2449 −0.0743051
119119 −489.922 848.570i −0.377404 0.653683i
120120 238.899 201.159i 0.181737 0.153027i
121121 29.4532 51.0145i 0.0221287 0.0383280i
122122 634.015 1098.15i 0.470500 0.814930i
123123 −679.353 + 572.033i −0.498010 + 0.419337i
124124 153.007 + 265.016i 0.110810 + 0.191929i
125125 612.379 0.438183
126126 1815.69 667.920i 1.28377 0.472247i
127127 567.894 0.396791 0.198395 0.980122i 0.436427π-0.436427\pi
0.198395 + 0.980122i 0.436427π0.436427\pi
128128 −214.338 371.244i −0.148008 0.256357i
129129 63.4450 + 356.240i 0.0433025 + 0.243141i
130130 164.081 284.197i 0.110699 0.191736i
131131 −778.288 + 1348.03i −0.519079 + 0.899071i 0.480675 + 0.876899i 0.340392π0.340392\pi
−0.999754 + 0.0221726i 0.992942π0.992942\pi
132132 710.958 + 257.387i 0.468795 + 0.169717i
133133 343.804 + 595.487i 0.224148 + 0.388235i
134134 635.763 0.409863
135135 352.559 1.81395i 0.224766 0.00115645i
136136 647.563 0.408294
137137 782.857 + 1355.95i 0.488204 + 0.845594i 0.999908 0.0135677i 0.00431886π-0.00431886\pi
−0.511704 + 0.859162i 0.670986π0.670986\pi
138138 −1523.04 551.385i −0.939491 0.340123i
139139 480.105 831.565i 0.292964 0.507428i −0.681546 0.731776i 0.738692π-0.738692\pi
0.974509 + 0.224348i 0.0720252π0.0720252\pi
140140 −185.522 + 321.334i −0.111996 + 0.193983i
141141 464.262 + 2606.81i 0.277290 + 1.55697i
142142 −558.915 968.070i −0.330304 0.572103i
143143 2352.37 1.37563
144144 −67.6521 + 391.522i −0.0391505 + 0.226576i
145145 −598.113 −0.342556
146146 −1211.03 2097.56i −0.686474 1.18901i
147147 −3842.44 + 3235.43i −2.15591 + 1.81533i
148148 38.5195 66.7177i 0.0213938 0.0370552i
149149 287.163 497.380i 0.157888 0.273470i −0.776219 0.630463i 0.782865π-0.782865\pi
0.934107 + 0.356994i 0.116198π0.116198\pi
150150 −934.018 + 786.468i −0.508415 + 0.428099i
151151 −576.757 998.973i −0.310833 0.538379i 0.667710 0.744422i 0.267275π-0.267275\pi
−0.978543 + 0.206043i 0.933941π0.933941\pi
152152 −454.429 −0.242494
153153 561.607 + 467.971i 0.296753 + 0.247276i
154154 2555.63 1.33726
155155 94.2448 + 163.237i 0.0488382 + 0.0845903i
156156 −245.159 1376.56i −0.125823 0.706491i
157157 −1033.02 + 1789.25i −0.525122 + 0.909537i 0.474450 + 0.880282i 0.342647π0.342647\pi
−0.999572 + 0.0292550i 0.990687π0.990687\pi
158158 −1044.75 + 1809.56i −0.526048 + 0.911143i
159159 1031.94 + 373.593i 0.514707 + 0.186339i
160160 −203.807 353.004i −0.100702 0.174422i
161161 5697.85 2.78915
162162 −1099.30 + 935.344i −0.533141 + 0.453627i
163163 672.746 0.323273 0.161637 0.986850i 0.448323π-0.448323\pi
0.161637 + 0.986850i 0.448323π0.448323\pi
164164 348.660 + 603.897i 0.166011 + 0.287539i
165165 437.915 + 158.538i 0.206616 + 0.0748010i
166166 808.524 1400.40i 0.378034 0.654774i
167167 −1985.68 + 3439.31i −0.920101 + 1.59366i −0.120845 + 0.992671i 0.538560π0.538560\pi
−0.799256 + 0.600991i 0.794773π0.794773\pi
168168 −788.598 4427.94i −0.362153 2.03347i
169169 −1076.52 1864.58i −0.489993 0.848693i
170170 134.714 0.0607769
171171 −394.110 328.400i −0.176247 0.146862i
172172 284.111 0.125949
173173 305.277 + 528.756i 0.134161 + 0.232373i 0.925277 0.379293i 0.123833π-0.123833\pi
−0.791116 + 0.611666i 0.790500π0.790500\pi
174174 1873.06 1577.16i 0.816069 0.687152i
175175 2147.60 3719.75i 0.927675 1.60678i
176176 −262.428 + 454.539i −0.112394 + 0.194672i
177177 −191.206 + 161.000i −0.0811973 + 0.0683703i
178178 −117.828 204.084i −0.0496155 0.0859366i
179179 3262.59 1.36233 0.681167 0.732128i 0.261473π-0.261473\pi
0.681167 + 0.732128i 0.261473π0.261473\pi
180180 47.1344 272.781i 0.0195177 0.112955i
181181 −781.862 −0.321079 −0.160540 0.987029i 0.551323π-0.551323\pi
−0.160540 + 0.987029i 0.551323π0.551323\pi
182182 −2362.95 4092.75i −0.962381 1.66689i
183183 −583.491 3276.28i −0.235699 1.32344i
184184 −1882.81 + 3261.11i −0.754360 + 1.30659i
185185 23.7261 41.0948i 0.00942907 0.0163316i
186186 −725.578 262.680i −0.286032 0.103552i
187187 482.835 + 836.295i 0.188815 + 0.327037i
188188 2079.00 0.806525
189189 2516.00 4410.08i 0.968317 1.69728i
190190 −94.5357 −0.0360965
191191 −638.536 1105.98i −0.241900 0.418983i 0.719356 0.694642i 0.244437π-0.244437\pi
−0.961255 + 0.275659i 0.911104π0.911104\pi
192192 2144.27 + 776.288i 0.805986 + 0.291791i
193193 310.504 537.809i 0.115806 0.200582i −0.802296 0.596927i 0.796388π-0.796388\pi
0.918102 + 0.396345i 0.129722π0.129722\pi
194194 −930.595 + 1611.84i −0.344396 + 0.596511i
195195 −151.006 847.890i −0.0554551 0.311378i
196196 1972.03 + 3415.65i 0.718669 + 1.24477i
197197 −1997.22 −0.722315 −0.361157 0.932505i 0.617618π-0.617618\pi
−0.361157 + 0.932505i 0.617618π0.617618\pi
198198 −1789.43 + 658.258i −0.642268 + 0.236265i
199199 1311.08 0.467036 0.233518 0.972352i 0.424976π-0.424976\pi
0.233518 + 0.972352i 0.424976π0.424976\pi
200200 1419.31 + 2458.32i 0.501802 + 0.869147i
201201 1276.31 1074.68i 0.447879 0.377126i
202202 1202.06 2082.04i 0.418698 0.725206i
203203 −4306.74 + 7459.49i −1.48903 + 2.57908i
204204 439.061 369.701i 0.150688 0.126884i
205205 214.757 + 371.970i 0.0731673 + 0.126729i
206206 224.489 0.0759266
207207 −3989.58 + 1467.61i −1.33959 + 0.492781i
208208 970.572 0.323543
209209 −338.831 586.872i −0.112141 0.194234i
210210 −164.053 921.153i −0.0539084 0.302693i
211211 −2225.01 + 3853.82i −0.725951 + 1.25738i 0.232630 + 0.972565i 0.425267π0.425267\pi
−0.958581 + 0.284819i 0.908066π0.908066\pi
212212 430.857 746.267i 0.139582 0.241763i
213213 −2758.44 998.637i −0.887349 0.321246i
214214 1147.18 + 1986.98i 0.366447 + 0.634705i
215215 174.998 0.0555106
216216 1692.68 + 2897.28i 0.533206 + 0.912663i
217217 2714.46 0.849168
218218 547.941 + 949.061i 0.170235 + 0.294856i
219219 −5976.83 2163.79i −1.84419 0.667649i
220220 182.839 316.686i 0.0560317 0.0970497i
221221 892.864 1546.49i 0.271767 0.470714i
222222 34.0620 + 191.256i 0.0102977 + 0.0578211i
223223 −2583.55 4474.83i −0.775816 1.34375i −0.934335 0.356397i 0.884005π-0.884005\pi
0.158518 0.987356i 0.449328π-0.449328\pi
224224 −5870.10 −1.75095
225225 −545.626 + 3157.70i −0.161667 + 0.935614i
226226 −580.451 −0.170845
227227 −1567.26 2714.58i −0.458251 0.793714i 0.540618 0.841268i 0.318191π-0.318191\pi
−0.998869 + 0.0475544i 0.984857π0.984857\pi
228228 −308.113 + 259.439i −0.0894968 + 0.0753586i
229229 1629.99 2823.22i 0.470361 0.814689i −0.529064 0.848582i 0.677457π-0.677457\pi
0.999425 + 0.0338924i 0.0107903π0.0107903\pi
230230 −391.684 + 678.416i −0.112291 + 0.194493i
231231 5130.47 4319.99i 1.46130 1.23045i
232232 −2846.25 4929.85i −0.805455 1.39509i
233233 −1191.36 −0.334973 −0.167486 0.985874i 0.553565π-0.553565\pi
−0.167486 + 0.985874i 0.553565π0.553565\pi
234234 2708.69 + 2257.08i 0.756721 + 0.630554i
235235 1280.56 0.355466
236236 98.1314 + 169.968i 0.0270670 + 0.0468814i
237237 961.493 + 5398.74i 0.263526 + 1.47969i
238238 970.012 1680.11i 0.264187 0.457586i
239239 −1259.92 + 2182.25i −0.340995 + 0.590620i −0.984618 0.174723i 0.944097π-0.944097\pi
0.643623 + 0.765343i 0.277430π0.277430\pi
240240 180.681 + 65.4117i 0.0485954 + 0.0175929i
241241 −107.572 186.320i −0.0287524 0.0498006i 0.851291 0.524694i 0.175820π-0.175820\pi
−0.880044 + 0.474893i 0.842487π0.842487\pi
242242 116.631 0.0309806
243243 −625.766 + 3735.95i −0.165197 + 0.986261i
244244 −2612.92 −0.685553
245245 1214.67 + 2103.87i 0.316745 + 0.548619i
246246 −1653.39 598.574i −0.428520 0.155137i
247247 −626.570 + 1085.25i −0.161408 + 0.279566i
248248 −896.970 + 1553.60i −0.229668 + 0.397797i
249249 −744.094 4178.05i −0.189378 1.06335i
250250 606.235 + 1050.03i 0.153367 + 0.265639i
251251 6911.40 1.73802 0.869012 0.494791i 0.164756π-0.164756\pi
0.869012 + 0.494791i 0.164756π0.164756\pi
252252 −3062.65 2552.02i −0.765591 0.637945i
253253 −5615.42 −1.39541
254254 562.196 + 973.751i 0.138879 + 0.240546i
255255 270.440 227.718i 0.0664142 0.0559225i
256256 2179.88 3775.66i 0.532196 0.921791i
257257 −152.177 + 263.579i −0.0369360 + 0.0639750i −0.883902 0.467671i 0.845093π-0.845093\pi
0.846966 + 0.531646i 0.178426π0.178426\pi
258258 −548.027 + 461.453i −0.132243 + 0.111352i
259259 −341.682 591.811i −0.0819733 0.141982i
260260 −676.214 −0.161296
261261 1094.19 6332.37i 0.259496 1.50178i
262262 −3081.92 −0.726723
263263 3271.54 + 5666.47i 0.767041 + 1.32855i 0.939161 + 0.343478i 0.111605π0.111605\pi
−0.172120 + 0.985076i 0.555062π0.555062\pi
264264 777.190 + 4363.89i 0.181185 + 1.01734i
265265 265.387 459.664i 0.0615192 0.106554i
266266 −680.709 + 1179.02i −0.156906 + 0.271769i
267267 −581.521 210.528i −0.133290 0.0482550i
268268 −655.030 1134.55i −0.149300 0.258595i
269269 −1680.21 −0.380833 −0.190417 0.981703i 0.560984π-0.560984\pi
−0.190417 + 0.981703i 0.560984π0.560984\pi
270270 352.132 + 602.727i 0.0793706 + 0.135855i
271271 −421.138 −0.0943996 −0.0471998 0.998885i 0.515030π-0.515030\pi
−0.0471998 + 0.998885i 0.515030π0.515030\pi
272272 199.214 + 345.049i 0.0444086 + 0.0769180i
273273 −11662.0 4221.98i −2.58540 0.935991i
274274 −1550.00 + 2684.68i −0.341749 + 0.591926i
275275 −2116.53 + 3665.94i −0.464115 + 0.803871i
276276 585.227 + 3286.02i 0.127632 + 0.716650i
277277 −348.391 603.431i −0.0755696 0.130890i 0.825764 0.564015i 0.190744π-0.190744\pi
−0.901334 + 0.433125i 0.857411π0.857411\pi
278278 1901.15 0.410156
279279 −1900.64 + 699.169i −0.407844 + 0.150029i
280280 −2175.17 −0.464254
281281 −965.771 1672.76i −0.205029 0.355120i 0.745113 0.666938i 0.232395π-0.232395\pi
−0.950142 + 0.311818i 0.899062π0.899062\pi
282282 −4010.22 + 3376.71i −0.846827 + 0.713051i
283283 3203.55 5548.72i 0.672903 1.16550i −0.304174 0.952616i 0.598381π-0.598381\pi
0.977077 0.212885i 0.0682861π-0.0682861\pi
284284 −1151.71 + 1994.82i −0.240638 + 0.416798i
285285 −189.782 + 159.802i −0.0394447 + 0.0332134i
286286 2328.77 + 4033.54i 0.481479 + 0.833945i
287287 6185.48 1.27219
288288 4110.19 1511.97i 0.840956 0.309354i
289289 −4179.94 −0.850792
290290 −592.111 1025.57i −0.119896 0.207667i
291291 856.437 + 4808.85i 0.172527 + 0.968728i
292292 −2495.45 + 4322.25i −0.500121 + 0.866234i
293293 −1741.85 + 3016.97i −0.347304 + 0.601548i −0.985770 0.168103i 0.946236π-0.946236\pi
0.638466 + 0.769650i 0.279569π0.279569\pi
294294 −9351.59 3385.55i −1.85509 0.671596i
295295 60.4441 + 104.692i 0.0119295 + 0.0206624i
296296 451.624 0.0886828
297297 −2479.60 + 4346.29i −0.484448 + 0.849148i
298298 1137.13 0.221047
299299 5192.05 + 8992.90i 1.00423 + 1.73937i
300300 2365.81 + 856.492i 0.455300 + 0.164832i
301301 1260.08 2182.53i 0.241296 0.417937i
302302 1141.94 1977.90i 0.217587 0.376872i
303303 −1106.27 6211.67i −0.209748 1.17773i
304304 −139.799 242.140i −0.0263751 0.0456831i
305305 −1609.43 −0.302149
306306 −246.445 + 1426.25i −0.0460402 + 0.266448i
307307 5195.75 0.965919 0.482959 0.875643i 0.339562π-0.339562\pi
0.482959 + 0.875643i 0.339562π0.339562\pi
308308 −2633.08 4560.62i −0.487122 0.843720i
309309 450.665 379.472i 0.0829691 0.0698622i
310310 −186.598 + 323.198i −0.0341873 + 0.0592142i
311311 2429.65 4208.28i 0.442999 0.767297i −0.554911 0.831910i 0.687248π-0.687248\pi
0.997910 + 0.0646123i 0.0205811π0.0205811\pi
312312 6270.01 5279.52i 1.13772 0.957993i
313313 −3796.70 6576.08i −0.685630 1.18755i −0.973238 0.229798i 0.926193π-0.926193\pi
0.287608 0.957748i 0.407140π-0.407140\pi
314314 −4090.62 −0.735182
315315 −1886.44 1571.92i −0.337425 0.281167i
316316 4305.64 0.766490
317317 −3502.14 6065.88i −0.620504 1.07474i −0.989392 0.145270i 0.953595π-0.953595\pi
0.368888 0.929474i 0.379739π-0.379739\pi
318318 380.998 + 2139.29i 0.0671865 + 0.377249i
319319 4244.44 7351.59i 0.744962 1.29031i
320320 551.447 955.134i 0.0963338 0.166855i
321321 5661.74 + 2049.71i 0.984446 + 0.356398i
322322 5640.67 + 9769.93i 0.976219 + 1.69086i
323323 −514.426 −0.0886174
324324 2801.77 + 998.048i 0.480413 + 0.171133i
325325 7827.83 1.33603
326326 665.995 + 1153.54i 0.113147 + 0.195977i
327327 2704.28 + 979.027i 0.457330 + 0.165567i
328328 −2043.94 + 3540.21i −0.344078 + 0.595961i
329329 9220.75 15970.8i 1.54516 2.67629i
330330 161.680 + 907.827i 0.0269703 + 0.151437i
331331 −1398.51 2422.29i −0.232232 0.402238i 0.726232 0.687449i 0.241270π-0.241270\pi
−0.958465 + 0.285211i 0.907936π0.907936\pi
332332 −3332.11 −0.550822
333333 391.677 + 326.373i 0.0644557 + 0.0537091i
334334 −7863.04 −1.28816
335335 −403.466 698.824i −0.0658021 0.113973i
336336 2116.80 1782.40i 0.343693 0.289398i
337337 −3481.07 + 6029.39i −0.562689 + 0.974605i 0.434572 + 0.900637i 0.356900π0.356900\pi
−0.997261 + 0.0739681i 0.976434π0.976434\pi
338338 2131.43 3691.74i 0.343001 0.594095i
339339 −1165.27 + 981.185i −0.186692 + 0.157200i
340340 −138.796 240.402i −0.0221391 0.0383460i
341341 −2675.19 −0.424838
342342 172.943 1000.87i 0.0273442 0.158249i
343343 22572.1 3.55329
344344 832.769 + 1442.40i 0.130523 + 0.226072i
345345 360.471 + 2024.03i 0.0562525 + 0.315855i
346346 −604.428 + 1046.90i −0.0939140 + 0.162664i
347347 943.257 1633.77i 0.145927 0.252753i −0.783791 0.621024i 0.786717π-0.786717\pi
0.929718 + 0.368271i 0.120050π0.120050\pi
348348 −4744.33 1717.59i −0.730813 0.264576i
349349 −4848.28 8397.47i −0.743618 1.28798i −0.950838 0.309689i 0.899775π-0.899775\pi
0.207220 0.978294i 0.433558π-0.433558\pi
350350 8504.20 1.29877
351351 9253.07 47.6080i 1.40710 0.00723968i
352352 5785.18 0.875998
353353 −2894.39 5013.24i −0.436411 0.755886i 0.560999 0.827817i 0.310417π-0.310417\pi
−0.997410 + 0.0719309i 0.977084π0.977084\pi
354354 −465.350 168.470i −0.0698675 0.0252941i
355355 −709.395 + 1228.71i −0.106058 + 0.183699i
356356 −242.797 + 420.537i −0.0361467 + 0.0626079i
357357 −892.714 5012.55i −0.132346 0.743115i
358358 3229.86 + 5594.28i 0.476825 + 0.825885i
359359 11197.3 1.64616 0.823081 0.567924i 0.192253π-0.192253\pi
0.823081 + 0.567924i 0.192253π0.192253\pi
360360 1523.03 560.262i 0.222975 0.0820233i
361361 361.000 0.0526316
362362 −774.017 1340.64i −0.112380 0.194647i
363363 234.139 197.151i 0.0338542 0.0285062i
364364 −4869.12 + 8433.56i −0.701129 + 1.21439i
365365 −1537.07 + 2662.29i −0.220422 + 0.381783i
366366 5040.10 4243.90i 0.719810 0.606099i
367367 794.879 + 1376.77i 0.113058 + 0.195822i 0.917002 0.398883i 0.130602π-0.130602\pi
−0.803944 + 0.594705i 0.797269π0.797269\pi
368368 −2316.88 −0.328196
369369 −4331.02 + 1593.21i −0.611013 + 0.224767i
370370 93.9522 0.0132009
371371 −3821.86 6619.66i −0.534828 0.926350i
372372 278.803 + 1565.46i 0.0388582 + 0.218187i
373373 −919.929 + 1593.36i −0.127700 + 0.221183i −0.922785 0.385315i 0.874093π-0.874093\pi
0.795085 + 0.606498i 0.207426π0.207426\pi
374374 −955.980 + 1655.81i −0.132173 + 0.228930i
375375 2991.98 + 1083.18i 0.412014 + 0.149161i
376376 6093.84 + 10554.8i 0.835813 + 1.44767i
377377 −15697.7 −2.14449
378378 10052.6 51.7216i 1.36786 0.00703776i
379379 −7320.77 −0.992196 −0.496098 0.868266i 0.665234π-0.665234\pi
−0.496098 + 0.868266i 0.665234π0.665234\pi
380380 97.4007 + 168.703i 0.0131488 + 0.0227744i
381381 2774.63 + 1004.50i 0.373094 + 0.135071i
382382 1264.26 2189.76i 0.169333 0.293293i
383383 691.918 1198.44i 0.0923116 0.159888i −0.816172 0.577809i 0.803908π-0.803908\pi
0.908483 + 0.417921i 0.137241π0.137241\pi
384384 −390.557 2192.96i −0.0519024 0.291429i
385385 −1621.85 2809.12i −0.214693 0.371860i
386386 1229.56 0.162131
387387 −320.141 + 1852.75i −0.0420509 + 0.243361i
388388 3835.19 0.501809
389389 449.284 + 778.182i 0.0585594 + 0.101428i 0.893819 0.448428i 0.148016π-0.148016\pi
−0.835260 + 0.549856i 0.814683π0.814683\pi
390390 1304.36 1098.31i 0.169356 0.142602i
391391 −2131.39 + 3691.67i −0.275675 + 0.477483i
392392 −11560.6 + 20023.5i −1.48953 + 2.57995i
393393 −6187.00 + 5209.62i −0.794130 + 0.668678i
394394 −1977.18 3424.58i −0.252814 0.437887i
395395 2652.06 0.337822
396396 3018.35 + 2515.10i 0.383024 + 0.319163i
397397 5636.84 0.712607 0.356303 0.934370i 0.384037π-0.384037\pi
0.356303 + 0.934370i 0.384037π0.384037\pi
398398 1297.93 + 2248.08i 0.163465 + 0.283130i
399399 626.465 + 3517.57i 0.0786027 + 0.441350i
400400 −873.266 + 1512.54i −0.109158 + 0.189068i
401401 997.797 1728.24i 0.124258 0.215222i −0.797184 0.603736i 0.793678π-0.793678\pi
0.921443 + 0.388514i 0.127011π0.127011\pi
402402 3106.23 + 1124.55i 0.385385 + 0.139521i
403403 2473.50 + 4284.23i 0.305741 + 0.529559i
404404 −4953.97 −0.610072
405405 1725.75 + 614.748i 0.211736 + 0.0754249i
406406 −17054.1 −2.08468
407407 336.739 + 583.250i 0.0410112 + 0.0710335i
408408 3163.88 + 1145.42i 0.383910 + 0.138987i
409409 4526.61 7840.32i 0.547253 0.947870i −0.451208 0.892419i 0.649007π-0.649007\pi
0.998461 0.0554514i 0.0176598π-0.0176598\pi
410410 −425.205 + 736.476i −0.0512180 + 0.0887121i
411411 1426.49 + 8009.65i 0.171200 + 0.961282i
412412 −231.292 400.609i −0.0276576 0.0479044i
413413 1740.92 0.207422
414414 −6466.01 5387.94i −0.767602 0.639621i
415415 −2052.41 −0.242769
416416 −5349.01 9264.76i −0.630425 1.09193i
417417 3816.59 3213.67i 0.448200 0.377396i
418418 670.862 1161.97i 0.0784999 0.135966i
419419 5505.54 9535.87i 0.641917 1.11183i −0.343087 0.939303i 0.611473π-0.611473\pi
0.985004 0.172529i 0.0551940π-0.0551940\pi
420420 −1474.81 + 1241.83i −0.171341 + 0.144274i
421421 −4521.01 7830.62i −0.523374 0.906511i −0.999630 0.0272039i 0.991340π-0.991340\pi
0.476256 0.879307i 0.341994π-0.341994\pi
422422 −8810.72 −1.01635
423423 −2342.65 + 13557.6i −0.269276 + 1.55838i
424424 5051.61 0.578604
425425 1606.70 + 2782.88i 0.183380 + 0.317623i
426426 −1018.43 5718.44i −0.115829 0.650374i
427427 −11588.8 + 20072.3i −1.31339 + 2.27487i
428428 2363.89 4094.38i 0.266970 0.462405i
429429 11493.3 + 4160.90i 1.29347 + 0.468275i
430430 173.242 + 300.065i 0.0194291 + 0.0336521i
431431 1224.90 0.136894 0.0684471 0.997655i 0.478196π-0.478196\pi
0.0684471 + 0.997655i 0.478196π0.478196\pi
432432 −1023.07 + 1793.25i −0.113941 + 0.199717i
433433 2132.79 0.236709 0.118355 0.992971i 0.462238π-0.462238\pi
0.118355 + 0.992971i 0.462238π0.462238\pi
434434 2687.22 + 4654.41i 0.297214 + 0.514789i
435435 −2922.27 1057.95i −0.322097 0.116609i
436436 1129.09 1955.64i 0.124022 0.214813i
437437 1495.71 2590.64i 0.163729 0.283586i
438438 −2206.68 12390.4i −0.240728 1.35168i
439439 3955.93 + 6851.87i 0.430082 + 0.744925i 0.996880 0.0789326i 0.0251512π-0.0251512\pi
−0.566798 + 0.823857i 0.691818π0.691818\pi
440440 2143.70 0.232266
441441 −24496.4 + 9011.22i −2.64511 + 0.973028i
442442 3535.62 0.380480
443443 −4198.99 7272.86i −0.450338 0.780009i 0.548068 0.836433i 0.315363π-0.315363\pi
−0.998407 + 0.0564245i 0.982030π0.982030\pi
444444 306.211 257.837i 0.0327300 0.0275595i
445445 −149.551 + 259.030i −0.0159312 + 0.0275937i
446446 5115.25 8859.86i 0.543080 0.940643i
447447 2282.80 1922.18i 0.241550 0.203391i
448448 −7941.44 13755.0i −0.837495 1.45058i
449449 13283.5 1.39619 0.698095 0.716005i 0.254031π-0.254031\pi
0.698095 + 0.716005i 0.254031π0.254031\pi
450450 −5954.57 + 2190.44i −0.623780 + 0.229463i
451451 −6096.00 −0.636474
452452 598.042 + 1035.84i 0.0622335 + 0.107792i
453453 −1050.94 5900.98i −0.109001 0.612036i
454454 3103.08 5374.69i 0.320781 0.555609i
455455 −2999.14 + 5194.65i −0.309015 + 0.535229i
456456 −2220.26 803.800i −0.228012 0.0825469i
457457 −6674.65 11560.8i −0.683210 1.18335i −0.973996 0.226566i 0.927250π-0.927250\pi
0.290786 0.956788i 0.406083π-0.406083\pi
458458 6454.53 0.658517
459459 1916.16 + 3279.80i 0.194856 + 0.333525i
460460 1614.21 0.163616
461461 −6239.00 10806.3i −0.630324 1.09175i −0.987485 0.157710i 0.949589π-0.949589\pi
0.357162 0.934042i 0.383744π-0.383744\pi
462462 12486.4 + 4520.43i 1.25740 + 0.455215i
463463 −6101.13 + 10567.5i −0.612406 + 1.06072i 0.378428 + 0.925631i 0.376465π0.376465\pi
−0.990834 + 0.135087i 0.956869π0.956869\pi
464464 1751.23 3033.21i 0.175213 0.303477i
465465 171.729 + 964.248i 0.0171263 + 0.0961633i
466466 −1179.41 2042.79i −0.117242 0.203070i
467467 7789.97 0.771899 0.385949 0.922520i 0.373874π-0.373874\pi
0.385949 + 0.922520i 0.373874π0.373874\pi
468468 1237.06 7159.25i 0.122187 0.707129i
469469 −11620.7 −1.14413
470470 1267.71 + 2195.74i 0.124415 + 0.215494i
471471 −8212.00 + 6914.72i −0.803374 + 0.676462i
472472 −575.273 + 996.402i −0.0560998 + 0.0971677i
473473 −1241.86 + 2150.96i −0.120720 + 0.209093i
474474 −8305.22 + 6993.21i −0.804792 + 0.677656i
475475 −1127.51 1952.90i −0.108913 0.188642i
476476 −3997.64 −0.384940
477477 4381.07 + 3650.62i 0.420536 + 0.350421i
478478 −4989.13 −0.477400
479479 −4699.45 8139.68i −0.448274 0.776433i 0.550000 0.835165i 0.314628π-0.314628\pi
−0.998274 + 0.0587316i 0.981294π0.981294\pi
480480 −371.368 2085.21i −0.0353137 0.198285i
481481 622.702 1078.55i 0.0590287 0.102241i
482482 212.986 368.902i 0.0201270 0.0348610i
483483 27838.7 + 10078.4i 2.62258 + 0.949449i
484484 −120.165 208.133i −0.0112853 0.0195466i
485485 2362.28 0.221167
486486 −7025.41 + 2625.48i −0.655719 + 0.245050i
487487 −18953.9 −1.76362 −0.881810 0.471604i 0.843675π-0.843675\pi
−0.881810 + 0.471604i 0.843675π0.843675\pi
488488 −7658.82 13265.5i −0.710448 1.23053i
489489 3286.92 + 1189.96i 0.303966 + 0.110045i
490490 −2404.97 + 4165.53i −0.221725 + 0.384039i
491491 −1761.16 + 3050.42i −0.161874 + 0.280374i −0.935541 0.353219i 0.885087π-0.885087\pi
0.773667 + 0.633592i 0.218420π0.218420\pi
492492 635.312 + 3567.25i 0.0582156 + 0.326878i
493493 −3222.03 5580.73i −0.294347 0.509824i
494494 −2481.13 −0.225975
495495 1859.15 + 1549.18i 0.168813 + 0.140667i
496496 −1103.77 −0.0999205
497497 10216.1 + 17694.7i 0.922039 + 1.59702i
498498 6427.36 5412.01i 0.578347 0.486984i
499499 1948.97 3375.72i 0.174846 0.302842i −0.765262 0.643719i 0.777391π-0.777391\pi
0.940108 + 0.340877i 0.110724π0.110724\pi
500500 1249.21 2163.70i 0.111733 0.193527i
501501 −15785.2 + 13291.6i −1.40765 + 1.18528i
502502 6842.05 + 11850.8i 0.608318 + 1.05364i
503503 −21465.3 −1.90276 −0.951382 0.308014i 0.900336π-0.900336\pi
−0.951382 + 0.308014i 0.900336π0.900336\pi
504504 3979.24 23029.0i 0.351686 2.03531i
505505 −3051.40 −0.268882
506506 −5559.08 9628.60i −0.488401 0.845936i
507507 −1961.58 11014.2i −0.171828 0.964805i
508508 1158.47 2006.52i 0.101178 0.175246i
509509 3861.76 6688.76i 0.336286 0.582464i −0.647445 0.762112i 0.724163π-0.724163\pi
0.983731 + 0.179648i 0.0574958π0.0574958\pi
510510 658.188 + 238.283i 0.0571471 + 0.0206889i
511511 22135.6 + 38339.9i 1.91628 + 3.31910i
512512 5202.61 0.449072
513513 −1344.67 2301.61i −0.115729 0.198087i
514514 −602.601 −0.0517113
515515 −142.464 246.756i −0.0121898 0.0211133i
516516 1388.12 + 502.539i 0.118427 + 0.0428741i
517517 −9087.36 + 15739.8i −0.773040 + 1.33894i
518518 676.507 1171.75i 0.0573823 0.0993890i
519519 556.262 + 3123.39i 0.0470466 + 0.264165i
520520 −1982.08 3433.06i −0.167154 0.289519i
521521 13201.5 1.11011 0.555055 0.831814i 0.312697π-0.312697\pi
0.555055 + 0.831814i 0.312697π0.312697\pi
522522 11941.1 4392.66i 1.00124 0.368317i
523523 −4723.73 −0.394941 −0.197471 0.980309i 0.563273π-0.563273\pi
−0.197471 + 0.980309i 0.563273π0.563273\pi
524524 3175.31 + 5499.81i 0.264722 + 0.458512i
525525 17072.3 14375.4i 1.41923 1.19503i
526526 −6477.43 + 11219.2i −0.536938 + 0.930003i
527527 −1015.39 + 1758.71i −0.0839303 + 0.145372i
528528 −2086.18 + 1756.61i −0.171949 + 0.144786i
529529 −6310.62 10930.3i −0.518667 0.898358i
530530 1050.90 0.0861283
531531 −1218.98 + 448.413i −0.0996218 + 0.0366468i
532532 2805.35 0.228623
533533 5636.40 + 9762.53i 0.458048 + 0.793363i
534534 −214.700 1205.53i −0.0173989 0.0976939i
535535 1456.04 2521.94i 0.117664 0.203800i
536536 3839.97 6651.02i 0.309443 0.535971i
537537 15940.5 + 5770.92i 1.28097 + 0.463749i
538538 −1663.35 2881.01i −0.133294 0.230872i
539539 −34479.1 −2.75533
540540 712.788 1249.39i 0.0568028 0.0995649i
541541 −699.631 −0.0555998 −0.0277999 0.999614i 0.508850π-0.508850\pi
−0.0277999 + 0.999614i 0.508850π0.508850\pi
542542 −416.912 722.113i −0.0330404 0.0572277i
543543 −3820.04 1382.97i −0.301904 0.109298i
544544 2195.82 3803.27i 0.173061 0.299750i
545545 695.465 1204.58i 0.0546614 0.0946763i
546546 −4305.66 24176.1i −0.337482 1.89495i
547547 −8548.87 14807.1i −0.668232 1.15741i −0.978398 0.206730i 0.933718π-0.933718\pi
0.310166 0.950683i 0.399616π-0.399616\pi
548548 6387.90 0.497952
549549 2944.28 17039.4i 0.228887 1.32463i
550550 −8381.18 −0.649772
551551 2261.07 + 3916.29i 0.174818 + 0.302794i
552552 −14967.4 + 12602.9i −1.15408 + 0.971767i
553553 19096.3 33075.7i 1.46846 2.54344i
554554 689.790 1194.75i 0.0528996 0.0916248i
555555 188.611 158.815i 0.0144254 0.0121465i
556556 −1958.76 3392.68i −0.149407 0.258780i
557557 2587.98 0.196869 0.0984347 0.995144i 0.468616π-0.468616\pi
0.0984347 + 0.995144i 0.468616π0.468616\pi
558558 −3080.41 2566.82i −0.233700 0.194735i
559559 4592.91 0.347512
560560 −669.162 1159.02i −0.0504951 0.0874601i
561561 879.800 + 4940.04i 0.0662124 + 0.371780i
562562 1912.16 3311.96i 0.143522 0.248588i
563563 −7421.26 + 12854.0i −0.555540 + 0.962223i 0.442322 + 0.896856i 0.354155π0.354155\pi
−0.997861 + 0.0653663i 0.979178π0.979178\pi
564564 10157.6 + 3677.36i 0.758357 + 0.274548i
565565 368.364 + 638.026i 0.0274287 + 0.0475079i
566566 12685.6 0.942080
567567 20093.3 17096.6i 1.48825 1.26629i
568568 −13503.3 −0.997507
569569 2753.27 + 4768.81i 0.202853 + 0.351351i 0.949446 0.313929i 0.101645π-0.101645\pi
−0.746594 + 0.665280i 0.768312π0.768312\pi
570570 −461.885 167.216i −0.0339408 0.0122876i
571571 −5624.72 + 9742.31i −0.412237 + 0.714016i −0.995134 0.0985305i 0.968586π-0.968586\pi
0.582897 + 0.812546i 0.301919π0.301919\pi
572572 4798.68 8311.56i 0.350774 0.607559i
573573 −1163.51 6533.06i −0.0848279 0.476305i
574574 6123.42 + 10606.1i 0.445273 + 0.771235i
575575 −18686.1 −1.35524
576576 9103.42 + 7585.62i 0.658523 + 0.548728i
577577 18667.6 1.34687 0.673435 0.739247i 0.264818π-0.264818\pi
0.673435 + 0.739247i 0.264818π0.264818\pi
578578 −4138.00 7167.23i −0.297782 0.515774i
579579 2468.35 2078.42i 0.177170 0.149182i
580580 −1220.11 + 2113.29i −0.0873488 + 0.151293i
581581 −14778.5 + 25597.1i −1.05528 + 1.82779i
582582 −7397.76 + 6229.11i −0.526885 + 0.443651i
583583 3766.58 + 6523.90i 0.267574 + 0.463452i
584584 −29258.1 −2.07313
585585 761.971 4409.75i 0.0538523 0.311659i
586586 −6897.49 −0.486233
587587 342.110 + 592.552i 0.0240552 + 0.0416648i 0.877802 0.479023i 0.159009π-0.159009\pi
−0.853747 + 0.520688i 0.825676π0.825676\pi
588588 3593.34 + 20176.4i 0.252018 + 1.41507i
589589 712.556 1234.18i 0.0498478 0.0863390i
590590 −119.675 + 207.283i −0.00835076 + 0.0144639i
591591 −9758.07 3532.71i −0.679177 0.245882i
592592 138.936 + 240.645i 0.00964569 + 0.0167068i
593593 −13876.6 −0.960952 −0.480476 0.877008i 0.659536π-0.659536\pi
−0.480476 + 0.877008i 0.659536π0.659536\pi
594594 −9907.17 + 50.9734i −0.684337 + 0.00352099i
595595 −2462.35 −0.169658
596596 −1171.59 2029.25i −0.0805202 0.139465i
597597 6405.72 + 2319.06i 0.439144 + 0.158983i
598598 −10279.9 + 17805.3i −0.702971 + 1.21758i
599599 −11727.7 + 20313.0i −0.799969 + 1.38559i 0.119667 + 0.992814i 0.461817π0.461817\pi
−0.919636 + 0.392773i 0.871516π0.871516\pi
600600 2586.21 + 14521.4i 0.175969 + 0.988058i
601601 −9321.09 16144.6i −0.632638 1.09576i −0.987010 0.160656i 0.948639π-0.948639\pi
0.354373 0.935104i 0.384694π-0.384694\pi
602602 4989.76 0.337820
603603 8136.73 2993.17i 0.549508 0.202142i
604604 −4706.19 −0.317040
605605 −74.0159 128.199i −0.00497384 0.00861495i
606606 9555.81 8046.24i 0.640558 0.539367i
607607 7140.81 12368.2i 0.477490 0.827037i −0.522177 0.852837i 0.674880π-0.674880\pi
0.999667 + 0.0258002i 0.00821337π0.00821337\pi
608608 −1540.92 + 2668.96i −0.102784 + 0.178027i
609609 −34236.4 + 28828.0i −2.27805 + 1.91818i
610610 −1593.28 2759.64i −0.105754 0.183171i
611611 33608.9 2.22532
612612 2799.11 1029.68i 0.184881 0.0680103i
613613 −16591.5 −1.09319 −0.546593 0.837398i 0.684076π-0.684076\pi
−0.546593 + 0.837398i 0.684076π0.684076\pi
614614 5143.62 + 8909.00i 0.338077 + 0.585567i
615615 391.321 + 2197.25i 0.0256579 + 0.144068i
616616 15435.8 26735.6i 1.00962 1.74872i
617617 9516.01 16482.2i 0.620908 1.07544i −0.368409 0.929664i 0.620097π-0.620097\pi
0.989317 0.145781i 0.0465693π-0.0465693\pi
618618 1096.81 + 397.078i 0.0713921 + 0.0258460i
619619 −7267.87 12588.3i −0.471923 0.817395i 0.527561 0.849517i 0.323107π-0.323107\pi
−0.999484 + 0.0321223i 0.989773π0.989773\pi
620620 769.013 0.0498134
621621 −22088.3 + 113.647i −1.42733 + 0.00734378i
622622 9621.08 0.620209
623623 2153.70 + 3730.32i 0.138501 + 0.239891i
624624 4742.05 + 1716.76i 0.304221 + 0.110137i
625625 −6648.35 + 11515.3i −0.425494 + 0.736978i
626626 7517.21 13020.2i 0.479949 0.831296i
627627 −617.402 3466.69i −0.0393248 0.220807i
628628 4214.59 + 7299.89i 0.267803 + 0.463849i
629629 511.250 0.0324084
630630 827.809 4790.77i 0.0523503 0.302967i
631631 −2527.57 −0.159463 −0.0797315 0.996816i 0.525406π-0.525406\pi
−0.0797315 + 0.996816i 0.525406π0.525406\pi
632632 12620.4 + 21859.2i 0.794324 + 1.37581i
633633 −17687.7 + 14893.5i −1.11062 + 0.935171i
634634 6934.00 12010.0i 0.434360 0.752334i
635635 713.558 1235.92i 0.0445932 0.0772377i
636636 3425.10 2884.03i 0.213544 0.179810i
637637 31879.6 + 55217.1i 1.98291 + 3.43451i
638638 16807.4 1.04296
639639 −11710.9 9758.33i −0.725000 0.604121i
640640 −1077.26 −0.0665351
641641 2707.40 + 4689.36i 0.166827 + 0.288953i 0.937303 0.348517i 0.113315π-0.113315\pi
−0.770476 + 0.637469i 0.779981π0.779981\pi
642642 2090.34 + 11737.2i 0.128503 + 0.721540i
643643 587.285 1017.21i 0.0360191 0.0623869i −0.847454 0.530869i 0.821866π-0.821866\pi
0.883473 + 0.468482i 0.155199π0.155199\pi
644644 11623.2 20132.0i 0.711210 1.23185i
645645 855.012 + 309.539i 0.0521954 + 0.0188963i
646646 −509.264 882.071i −0.0310166 0.0537223i
647647 9101.51 0.553040 0.276520 0.961008i 0.410819π-0.410819\pi
0.276520 + 0.961008i 0.410819π0.410819\pi
648648 3145.40 + 17149.7i 0.190684 + 1.03966i
649649 −1715.74 −0.103773
650650 7749.29 + 13422.2i 0.467618 + 0.809939i
651651 13262.4 + 4801.37i 0.798454 + 0.289064i
652652 1372.36 2376.99i 0.0824320 0.142776i
653653 2943.59 5098.44i 0.176404 0.305540i −0.764243 0.644929i 0.776887π-0.776887\pi
0.940646 + 0.339389i 0.110220π0.110220\pi
654654 998.432 + 5606.15i 0.0596969 + 0.335195i
655655 1955.84 + 3387.61i 0.116673 + 0.202084i
656656 −2515.17 −0.149696
657657 −25374.4 21143.8i −1.50677 1.25555i
658658 36512.9 2.16325
659659 −5108.58 8848.32i −0.301976 0.523037i 0.674608 0.738176i 0.264313π-0.264313\pi
−0.976583 + 0.215139i 0.930979π0.930979\pi
660660 1453.48 1223.86i 0.0857219 0.0721801i
661661 3050.88 5284.28i 0.179524 0.310945i −0.762193 0.647349i 0.775878π-0.775878\pi
0.941718 + 0.336404i 0.109211π0.109211\pi
662662 2768.95 4795.96i 0.162565 0.281572i
663663 7097.82 5976.55i 0.415772 0.350091i
664664 −9766.86 16916.7i −0.570825 0.988698i
665665 1727.96 0.100763
666666 −171.876 + 994.695i −0.0100001 + 0.0578733i
667667 37472.6 2.17533
668668 8101.33 + 14031.9i 0.469237 + 0.812742i
669669 −4707.62 26433.1i −0.272058 1.52760i
670670 798.836 1383.62i 0.0460623 0.0797822i
671671 11421.1 19782.0i 0.657090 1.13811i
672672 −28680.3 10383.1i −1.64638 0.596037i
673673 −1582.16 2740.38i −0.0906208 0.156960i 0.817152 0.576423i 0.195552π-0.195552\pi
−0.907773 + 0.419463i 0.862218π0.862218\pi
674674 −13784.6 −0.787777
675675 −8251.21 + 14462.9i −0.470502 + 0.824704i
676676 −8784.08 −0.499777
677677 14849.2 + 25719.6i 0.842987 + 1.46010i 0.887358 + 0.461082i 0.152539π0.152539\pi
−0.0443701 + 0.999015i 0.514128π0.514128\pi
678678 −2835.98 1026.71i −0.160642 0.0581571i
679679 17009.8 29461.8i 0.961376 1.66515i
680680 813.662 1409.30i 0.0458860 0.0794769i
681681 −2855.80 16035.2i −0.160697 0.902304i
682682 −2648.35 4587.08i −0.148696 0.257549i
683683 2998.31 0.167976 0.0839878 0.996467i 0.473234π-0.473234\pi
0.0839878 + 0.996467i 0.473234π0.473234\pi
684684 −1964.28 + 722.581i −0.109805 + 0.0403926i
685685 3934.63 0.219467
686686 22345.6 + 38703.7i 1.24367 + 2.15410i
687687 12957.6 10910.6i 0.719597 0.605920i
688688 −512.381 + 887.471i −0.0283930 + 0.0491781i
689689 6965.20 12064.1i 0.385128 0.667061i
690690 −3113.69 + 2621.81i −0.171791 + 0.144653i
691691 6508.85 + 11273.7i 0.358333 + 0.620651i 0.987683 0.156471i 0.0500119π-0.0500119\pi
−0.629349 + 0.777123i 0.716679π0.716679\pi
692692 2490.98 0.136839
693693 32707.8 12031.9i 1.79288 0.659529i
694694 3735.17 0.204301
695695 −1206.50 2089.72i −0.0658492 0.114054i
696696 −5186.31 29120.9i −0.282452 1.58596i
697697 −2313.80 + 4007.61i −0.125741 + 0.217789i
698698 9599.27 16626.4i 0.520541 0.901604i
699699 −5820.78 2107.29i −0.314967 0.114027i
700700 −8761.92 15176.1i −0.473099 0.819432i
701701 −28770.9 −1.55016 −0.775080 0.631863i 0.782291π-0.782291\pi
−0.775080 + 0.631863i 0.782291π0.782291\pi
702702 9241.86 + 15818.9i 0.496883 + 0.850490i
703703 −358.772 −0.0192480
704704 7826.56 + 13556.0i 0.418998 + 0.725726i
705705 6256.60 + 2265.07i 0.334237 + 0.121004i
706706 5730.70 9925.87i 0.305493 0.529129i
707707 −21971.8 + 38056.2i −1.16879 + 2.02440i
708708 178.810 + 1004.01i 0.00949168 + 0.0532953i
709709 7729.78 + 13388.4i 0.409447 + 0.709183i 0.994828 0.101575i 0.0323882π-0.0323882\pi
−0.585381 + 0.810759i 0.699055π0.699055\pi
710710 −2809.11 −0.148484
711711 −4851.67 + 28078.0i −0.255910 + 1.48102i
712712 −2846.69 −0.149837
713713 −5904.57 10227.0i −0.310137 0.537174i
714714 7711.11 6492.96i 0.404175 0.340326i
715715 2955.75 5119.51i 0.154600 0.267775i
716716 6655.48 11527.6i 0.347384 0.601687i
717717 −10015.8 + 8433.54i −0.521681 + 0.439270i
718718 11085.0 + 19199.7i 0.576166 + 0.997949i
719719 −7691.51 −0.398950 −0.199475 0.979903i 0.563924π-0.563924\pi
−0.199475 + 0.979903i 0.563924π0.563924\pi
720720 767.073 + 639.180i 0.0397044 + 0.0330845i
721721 −4103.29 −0.211948
722722 357.378 + 618.996i 0.0184214 + 0.0319067i
723723 −196.013 1100.60i −0.0100827 0.0566140i
724724 −1594.95 + 2762.53i −0.0818726 + 0.141807i
725725 14123.9 24463.4i 0.723518 1.25317i
726726 569.838 + 206.298i 0.0291304 + 0.0105461i
727727 −1915.06 3316.97i −0.0976967 0.169216i 0.813034 0.582216i 0.197814π-0.197814\pi
−0.910731 + 0.413000i 0.864481π0.864481\pi
728728 −57088.2 −2.90636
729729 −9665.58 + 17146.3i −0.491062 + 0.871125i
730730 −6086.61 −0.308596
731731 942.716 + 1632.83i 0.0476985 + 0.0826163i
732732 −12766.3 4621.76i −0.644610 0.233368i
733733 −2328.91 + 4033.79i −0.117354 + 0.203262i −0.918718 0.394914i 0.870774π-0.870774\pi
0.801365 + 0.598176i 0.204108π0.204108\pi
734734 −1573.81 + 2725.91i −0.0791420 + 0.137078i
735735 2213.32 + 12427.7i 0.111074 + 0.623676i
736736 12768.8 + 22116.2i 0.639490 + 1.10763i
737737 11452.6 0.572405
738738 −7019.39 5849.06i −0.350118 0.291744i
739739 37264.5 1.85493 0.927466 0.373907i 0.121982π-0.121982\pi
0.927466 + 0.373907i 0.121982π0.121982\pi
740740 −96.7994 167.661i −0.00480867 0.00832886i
741741 −4980.92 + 4194.07i −0.246935 + 0.207926i
742742 7567.03 13106.5i 0.374386 0.648456i
743743 −11479.4 + 19882.9i −0.566808 + 0.981741i 0.430071 + 0.902795i 0.358489π0.358489\pi
−0.996879 + 0.0789455i 0.974845π0.974845\pi
744744 −7130.46 + 6004.04i −0.351365 + 0.295859i
745745 −721.639 1249.92i −0.0354883 0.0614676i
746746 −3642.79 −0.178783
747747 3754.68 21729.4i 0.183904 1.06431i
748748 3939.81 0.192585
749749 −20968.6 36318.7i −1.02293 1.77177i
750750 1104.65 + 6202.58i 0.0537817 + 0.301982i
751751 −3623.63 + 6276.31i −0.176069 + 0.304961i −0.940531 0.339708i 0.889672π-0.889672\pi
0.764462 + 0.644669i 0.223005π0.223005\pi
752752 −3749.38 + 6494.12i −0.181816 + 0.314915i
753753 33767.9 + 12225.0i 1.63423 + 0.591637i
754754 −15540.2 26916.5i −0.750586 1.30005i
755755 −2898.78 −0.139732
756756 −10449.5 17886.0i −0.502706 0.860458i
757757 11767.6 0.564996 0.282498 0.959268i 0.408837π-0.408837\pi
0.282498 + 0.959268i 0.408837π0.408837\pi
758758 −7247.31 12552.7i −0.347275 0.601497i
759759 −27436.0 9932.63i −1.31207 0.475009i
760760 −570.990 + 988.983i −0.0272526 + 0.0472029i
761761 −2919.39 + 5056.52i −0.139064 + 0.240866i −0.927143 0.374709i 0.877743π-0.877743\pi
0.788079 + 0.615575i 0.211076π0.211076\pi
762762 1024.41 + 5752.00i 0.0487013 + 0.273455i
763763 −10015.5 17347.3i −0.475208 0.823085i
764764 −5210.29 −0.246730
765765 1724.11 634.231i 0.0814842 0.0299748i
766766 2739.90 0.129238
767767 1586.38 + 2747.69i 0.0746818 + 0.129353i
768768 17328.9 14591.4i 0.814198 0.685576i
769769 3340.04 5785.11i 0.156625 0.271283i −0.777024 0.629471i 0.783272π-0.783272\pi
0.933650 + 0.358188i 0.116605π0.116605\pi
770770 3211.14 5561.86i 0.150288 0.260306i
771771 −1209.73 + 1018.63i −0.0565077 + 0.0475810i
772772 −1266.82 2194.19i −0.0590593 0.102294i
773773 19676.9 0.915560 0.457780 0.889065i 0.348645π-0.348645\pi
0.457780 + 0.889065i 0.348645π0.348645\pi
774774 −3493.79 + 1285.22i −0.162250 + 0.0596853i
775775 −8902.06 −0.412609
776776 11241.5 + 19470.8i 0.520032 + 0.900722i
777777 −622.597 3495.86i −0.0287459 0.161407i
778778 −889.551 + 1540.75i −0.0409922 + 0.0710006i
779779 1623.71 2812.35i 0.0746798 0.129349i
780780 −3303.87 1196.10i −0.151663 0.0549066i
781781 −10068.3 17438.8i −0.461295 0.798986i
782782 −8440.00 −0.385951
783783 16546.8 29003.4i 0.755215 1.32375i
784784 −14225.9 −0.648044
785785 2595.98 + 4496.37i 0.118031 + 0.204436i
786786 −15057.7 5451.33i −0.683321 0.247382i
787787 −12842.8 + 22244.3i −0.581697 + 1.00753i 0.413582 + 0.910467i 0.364278π0.364278\pi
−0.995278 + 0.0970611i 0.969056π0.969056\pi
788788 −4074.20 + 7056.72i −0.184184 + 0.319017i
789789 5961.25 + 33472.1i 0.268981 + 1.51032i
790790 2625.45 + 4547.41i 0.118240 + 0.204797i
791791 10609.7 0.476912
792792 −3921.68 + 22695.9i −0.175948 + 1.01826i
793793 −42240.1 −1.89154
794794 5580.28 + 9665.33i 0.249417 + 0.432002i
795795 2109.69 1776.42i 0.0941171 0.0792491i
796796 2674.52 4632.41i 0.119090 0.206271i
797797 8628.46 14944.9i 0.383483 0.664211i −0.608075 0.793880i 0.708058π-0.708058\pi
0.991557 + 0.129668i 0.0413913π0.0413913\pi
798798 −5411.30 + 4556.46i −0.240047 + 0.202126i
799799 6898.39 + 11948.4i 0.305441 + 0.529039i
800800 19251.0 0.850781
801801 −2468.83 2057.20i −0.108904 0.0907462i
802802 3951.14 0.173965
803803 −21815.4 37785.3i −0.958714 1.66054i
804804 −1193.57 6701.82i −0.0523555 0.293974i
805805 7159.34 12400.3i 0.313458 0.542925i
806806 −4897.36 + 8482.47i −0.214022 + 0.370698i
807807 −8209.21 2971.97i −0.358089 0.129639i
808808 −14520.8 25150.7i −0.632227 1.09505i
809809 854.593 0.0371395 0.0185698 0.999828i 0.494089π-0.494089\pi
0.0185698 + 0.999828i 0.494089π0.494089\pi
810810 654.344 + 3567.68i 0.0283843 + 0.154760i
811811 14057.1 0.608646 0.304323 0.952569i 0.401570π-0.401570\pi
0.304323 + 0.952569i 0.401570π0.401570\pi
812812 17570.9 + 30433.8i 0.759383 + 1.31529i
813813 −2057.61 744.913i −0.0887618 0.0321344i
814814 −666.721 + 1154.79i −0.0287083 + 0.0497242i
815815 845.304 1464.11i 0.0363309 0.0629270i
816816 362.999 + 2038.22i 0.0155729 + 0.0874413i
817817 −661.554 1145.85i −0.0283291 0.0490674i
818818 17924.8 0.766167
819819 −49510.5 41255.7i −2.11238 1.76018i
820820 1752.36 0.0746282
821821 −8271.65 14326.9i −0.351623 0.609029i 0.634911 0.772585i 0.281037π-0.281037\pi
−0.986534 + 0.163556i 0.947703π0.947703\pi
822822 −12321.7 + 10375.2i −0.522835 + 0.440241i
823823 −20164.9 + 34926.7i −0.854078 + 1.47931i 0.0234206 + 0.999726i 0.492544π0.492544\pi
−0.877498 + 0.479580i 0.840789π0.840789\pi
824824 1355.90 2348.48i 0.0573239 0.0992880i
825825 −16825.4 + 14167.4i −0.710041 + 0.597874i
826826 1723.45 + 2985.11i 0.0725988 + 0.125745i
827827 −33819.0 −1.42201 −0.711005 0.703187i 0.751760π-0.751760\pi
−0.711005 + 0.703187i 0.751760π0.751760\pi
828828 −2953.04 + 17090.1i −0.123943 + 0.717297i
829829 −16608.2 −0.695812 −0.347906 0.937529i 0.613107π-0.613107\pi
−0.347906 + 0.937529i 0.613107π0.613107\pi
830830 −2031.82 3519.21i −0.0849704 0.147173i
831831 −634.822 3564.50i −0.0265003 0.148798i
832832 14473.0 25067.9i 0.603077 1.04456i
833833 −13086.9 + 22667.1i −0.544338 + 0.942821i
834834 9288.68 + 3362.78i 0.385660 + 0.139620i
835835 4990.02 + 8642.97i 0.206811 + 0.358206i
836836 −2764.77 −0.114380
837837 −10522.9 + 54.1414i −0.434557 + 0.00223584i
838838 21801.2 0.898699
839839 −2260.32 3914.98i −0.0930093 0.161097i 0.815767 0.578381i 0.196315π-0.196315\pi
−0.908776 + 0.417284i 0.862982π0.862982\pi
840840 −10627.5 3847.46i −0.436527 0.158036i
841841 −16129.3 + 27936.8i −0.661336 + 1.14547i
842842 8951.29 15504.1i 0.366368 0.634568i
843843 −1759.78 9881.10i −0.0718982 0.403705i
844844 9077.73 + 15723.1i 0.370223 + 0.641245i
845845 −5410.56 −0.220271
846846 −25566.0 + 9404.70i −1.03898 + 0.382199i
847847 −2131.82 −0.0864820
848848 1554.06 + 2691.72i 0.0629325 + 0.109002i
849849 25466.6 21443.6i 1.02946 0.866834i
850850 −3181.15 + 5509.92i −0.128368 + 0.222340i
851851 −1486.47 + 2574.65i −0.0598774 + 0.103711i
852852 −9155.49 + 7709.17i −0.368148 + 0.309990i
853853 −1911.61 3311.00i −0.0767318 0.132903i 0.825106 0.564978i 0.191115π-0.191115\pi
−0.901838 + 0.432074i 0.857782π0.857782\pi
854854 −45889.9 −1.83878
855855 −1209.90 + 445.074i −0.0483951 + 0.0178026i
856856 27715.6 1.10666
857857 10107.2 + 17506.2i 0.402865 + 0.697783i 0.994070 0.108738i 0.0346810π-0.0346810\pi
−0.591205 + 0.806521i 0.701348π0.701348\pi
858858 4243.37 + 23826.3i 0.168842 + 0.948039i
859859 9675.51 16758.5i 0.384312 0.665648i −0.607361 0.794426i 0.707772π-0.707772\pi
0.991674 + 0.128777i 0.0411053π0.0411053\pi
860860 356.985 618.316i 0.0141548 0.0245168i
861861 30221.2 + 10941.0i 1.19621 + 0.433062i
862862 1212.61 + 2100.30i 0.0479138 + 0.0829891i
863863 27462.6 1.08324 0.541620 0.840623i 0.317811π-0.317811\pi
0.541620 + 0.840623i 0.317811π0.317811\pi
864864 22756.1 117.082i 0.896038 0.00461021i
865865 1534.32 0.0603104
866866 2111.39 + 3657.03i 0.0828497 + 0.143500i
867867 −20422.5 7393.53i −0.799981 0.289616i
868868 5537.32 9590.92i 0.216531 0.375043i
869869 −18820.0 + 32597.3i −0.734668 + 1.27248i
870870 −1078.92 6058.07i −0.0420445 0.236078i
871871 −10589.2 18341.0i −0.411940 0.713501i
872872 13238.1 0.514104
873873 −4321.56 + 25010.1i −0.167540 + 0.969603i
874874 5922.80 0.229224
875875 −11081.0 19192.8i −0.428121 0.741527i
876876 −19837.6 + 16703.8i −0.765126 + 0.644256i
877877 −5196.63 + 9000.84i −0.200089 + 0.346564i −0.948557 0.316607i 0.897456π-0.897456\pi
0.748468 + 0.663171i 0.230790π0.230790\pi
878878 −7832.47 + 13566.2i −0.301063 + 0.521456i
879879 −13846.8 + 11659.4i −0.531334 + 0.447397i
880880 659.482 + 1142.26i 0.0252627 + 0.0437562i
881881 37813.2 1.44604 0.723018 0.690829i 0.242754π-0.242754\pi
0.723018 + 0.690829i 0.242754π0.242754\pi
882882 −39701.8 33082.4i −1.51568 1.26297i
883883 −19334.7 −0.736881 −0.368440 0.929651i 0.620108π-0.620108\pi
−0.368440 + 0.929651i 0.620108π0.620108\pi
884884 −3642.77 6309.46i −0.138597 0.240057i
885885 110.138 + 618.422i 0.00418335 + 0.0234893i
886886 8313.71 14399.8i 0.315242 0.546015i
887887 2792.24 4836.31i 0.105698 0.183075i −0.808325 0.588736i 0.799626π-0.799626\pi
0.914023 + 0.405662i 0.132959π0.132959\pi
888888 2206.56 + 798.838i 0.0833865 + 0.0301883i
889889 −10276.0 17798.6i −0.387679 0.671480i
890890 −592.202 −0.0223041
891891 −19802.7 + 16849.2i −0.744573 + 0.633525i
892892 −21081.1 −0.791307
893893 −4840.96 8384.80i −0.181407 0.314207i
894894 5555.80 + 2011.36i 0.207845 + 0.0752461i
895895 4099.45 7100.45i 0.153105 0.265186i
896896 −7756.87 + 13435.3i −0.289218 + 0.500940i
897897 9460.72 + 53121.5i 0.352156 + 1.97734i
898898 13150.3 + 22776.9i 0.488675 + 0.846409i
899899 17852.0 0.662288
900900 10044.0 + 8369.34i 0.371998 + 0.309976i
901901 5718.56 0.211446
902902 −6034.84 10452.6i −0.222770 0.385848i
903903 10017.0 8434.61i 0.369154 0.310838i
904904 −3505.89 + 6072.38i −0.128987 + 0.223412i
905905 −982.408 + 1701.58i −0.0360844 + 0.0625000i
906906 9077.85 7643.79i 0.332882 0.280296i
907907 14585.2 + 25262.3i 0.533951 + 0.924831i 0.999213 + 0.0396577i 0.0126267π0.0126267\pi
−0.465262 + 0.885173i 0.654040π0.654040\pi
908908 −12788.5 −0.467401
909909 5582.22 32305.9i 0.203686 1.17879i
910910 −11876.2 −0.432628
911911 25412.2 + 44015.2i 0.924198 + 1.60076i 0.792847 + 0.609421i 0.208598π0.208598\pi
0.131351 + 0.991336i 0.458069π0.458069\pi
912912 −254.736 1430.33i −0.00924907 0.0519331i
913913 14564.7 25226.8i 0.527954 0.914443i
914914 13215.4 22889.7i 0.478255 0.828362i
915915 −7863.38 2846.77i −0.284104 0.102854i
916916 −6650.14 11518.4i −0.239876 0.415478i
917917 56332.4 2.02864
918918 −3726.85 + 6532.48i −0.133992 + 0.234863i
919919 23089.0 0.828768 0.414384 0.910102i 0.363997π-0.363997\pi
0.414384 + 0.910102i 0.363997π0.363997\pi
920920 4731.49 + 8195.17i 0.169557 + 0.293681i
921921 25385.5 + 9190.30i 0.908232 + 0.328807i
922922 12352.8 21395.7i 0.441234 0.764239i
923923 −18618.4 + 32248.0i −0.663956 + 1.15001i
924924 −4797.87 26939.8i −0.170821 0.959151i
925925 1120.55 + 1940.84i 0.0398306 + 0.0689887i
926926 −24159.7 −0.857382
927927 2873.09 1056.89i 0.101796 0.0374465i
928928 −38605.4 −1.36561
929929 3259.82 + 5646.17i 0.115125 + 0.199403i 0.917830 0.396974i 0.129940π-0.129940\pi
−0.802705 + 0.596377i 0.796606π0.796606\pi
930930 −1483.36 + 1249.03i −0.0523026 + 0.0440402i
931931 9183.76 15906.7i 0.323293 0.559959i
932932 −2430.30 + 4209.40i −0.0854153 + 0.147944i
933933 19314.5 16263.3i 0.677737 0.570672i
934934 7711.80 + 13357.2i 0.270169 + 0.467947i
935935 2426.73 0.0848796
936936 39972.7 14704.3i 1.39588 0.513489i
937937 −15579.4 −0.543178 −0.271589 0.962413i 0.587549π-0.587549\pi
−0.271589 + 0.962413i 0.587549π0.587549\pi
938938 −11504.1 19925.7i −0.400451 0.693601i
939939 −6918.18 38845.2i −0.240433 1.35002i
940940 2612.26 4524.57i 0.0906410 0.156995i
941941 8944.32 15492.0i 0.309858 0.536690i −0.668473 0.743736i 0.733052π-0.733052\pi
0.978331 + 0.207046i 0.0663851π0.0663851\pi
942942 −19986.1 7235.55i −0.691276 0.250262i
943943 −13454.8 23304.5i −0.464634 0.804770i
944944 −707.902 −0.0244070
945945 −6436.40 11016.9i −0.221562 0.379237i
946946 −4917.58 −0.169011
947947 1193.79 + 2067.70i 0.0409640 + 0.0709518i 0.885780 0.464104i 0.153624π-0.153624\pi
−0.844816 + 0.535056i 0.820290π0.820290\pi
948948 21036.6 + 7615.86i 0.720714 + 0.260919i
949949 −40341.2 + 69873.0i −1.37991 + 2.39007i
950950 2232.39 3866.60i 0.0762402 0.132052i
951951 −6381.44 35831.5i −0.217594 1.22178i
952952 −11717.6 20295.5i −0.398918 0.690947i
953953 −50911.1 −1.73050 −0.865252 0.501337i 0.832842π-0.832842\pi
−0.865252 + 0.501337i 0.832842π0.832842\pi
954954 −1922.51 + 11126.1i −0.0652447 + 0.377590i
955955 −3209.28 −0.108743
956956 5140.32 + 8903.30i 0.173902 + 0.301207i
957957 33741.2 28411.0i 1.13970 0.959661i
958958 9304.58 16116.0i 0.313797 0.543512i
959959 28331.5 49071.6i 0.953986 1.65235i
960960 4383.72 3691.21i 0.147379 0.124097i
961961 12082.6 + 20927.6i 0.405577 + 0.702481i
962962 2465.82 0.0826415
963963 24036.7 + 20029.1i 0.804332 + 0.670227i
964964 −877.761 −0.0293265
965965 −780.297 1351.51i −0.0260297 0.0450847i
966966 10278.2 + 57711.5i 0.342334 + 1.92219i
967967 2938.71 5090.00i 0.0977277 0.169269i −0.813016 0.582241i 0.802176π-0.802176\pi
0.910744 + 0.412972i 0.135509π0.135509\pi
968968 704.443 1220.13i 0.0233901 0.0405129i
969969 −2513.40 909.923i −0.0833250 0.0301661i
970970 2338.58 + 4050.54i 0.0774096 + 0.134077i
971971 −29273.1 −0.967476 −0.483738 0.875213i 0.660721π-0.660721\pi
−0.483738 + 0.875213i 0.660721π0.660721\pi
972972 11923.6 + 9832.09i 0.393467 + 0.324449i
973973 −34749.9 −1.14494
974974 −18763.7 32499.7i −0.617277 1.06916i
975975 38245.4 + 13846.0i 1.25624 + 0.454796i
976976 4712.28 8161.90i 0.154545 0.267680i
977977 −20833.8 + 36085.1i −0.682222 + 1.18164i 0.292079 + 0.956394i 0.405653π0.405653\pi
−0.974301 + 0.225249i 0.927680π0.927680\pi
978978 1213.55 + 6814.01i 0.0396778 + 0.222789i
979979 −2122.55 3676.36i −0.0692920 0.120017i
980980 9911.40 0.323070
981981 11480.9 + 9566.72i 0.373657 + 0.311358i
982982 −6973.95 −0.226627
983983 24668.1 + 42726.4i 0.800396 + 1.38633i 0.919356 + 0.393428i 0.128711π0.128711\pi
−0.118959 + 0.992899i 0.537956π0.537956\pi
984984 −16248.3 + 13681.5i −0.526399 + 0.443242i
985985 −2509.50 + 4346.59i −0.0811771 + 0.140603i
986986 6379.41 11049.5i 0.206046 0.356883i
987987 73300.3 61720.8i 2.36391 1.99047i
988988 2556.32 + 4427.68i 0.0823153 + 0.142574i
989989 −10963.9 −0.352509
990990 −815.834 + 4721.47i −0.0261908 + 0.151574i
991991 −60404.6 −1.93624 −0.968121 0.250485i 0.919410π-0.919410\pi
−0.968121 + 0.250485i 0.919410π0.919410\pi
992992 6083.07 + 10536.2i 0.194695 + 0.337222i
993993 −2548.30 14308.6i −0.0814378 0.457270i
994994 −20227.1 + 35034.4i −0.645438 + 1.11793i
995995 1647.37 2853.33i 0.0524877 0.0909114i
996996 −16280.1 5893.87i −0.517926 0.187504i
997997 28168.3 + 48788.9i 0.894783 + 1.54981i 0.834073 + 0.551655i 0.186003π0.186003\pi
0.0607108 + 0.998155i 0.480663π0.480663\pi
998998 7717.67 0.244788
999999 1336.37 + 2287.40i 0.0423233 + 0.0724427i
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 171.4.e.a.58.19 54
9.4 even 3 1539.4.a.h.1.9 27
9.5 odd 6 1539.4.a.g.1.19 27
9.7 even 3 inner 171.4.e.a.115.19 yes 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.4.e.a.58.19 54 1.1 even 1 trivial
171.4.e.a.115.19 yes 54 9.7 even 3 inner
1539.4.a.g.1.19 27 9.5 odd 6
1539.4.a.h.1.9 27 9.4 even 3