Properties

Label 115.2.l.a.102.4
Level 115115
Weight 22
Character 115.102
Analytic conductor 0.9180.918
Analytic rank 00
Dimension 200200
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [115,2,Mod(7,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([11, 38]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("115.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 115=523 115 = 5 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 115.l (of order 4444, degree 2020, 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: 0.9182796232450.918279623245
Analytic rank: 00
Dimension: 200200
Relative dimension: 1010 over Q(ζ44)\Q(\zeta_{44})
Twist minimal: yes
Sato-Tate group: SU(2)[C44]\mathrm{SU}(2)[C_{44}]

Embedding invariants

Embedding label 102.4
Character χ\chi == 115.102
Dual form 115.2.l.a.53.4

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+(0.0452482+0.632652i)q2+(1.67360+0.364069i)q3+(1.58144+0.227377i)q4+(0.673353+2.13227i)q5+(0.1546021.07528i)q6+(0.171765+0.0937908i)q7+(0.485055+2.22976i)q8+(0.0605071+0.0276327i)q9+(1.318520.522480i)q10+(2.33306+2.02161i)q11+(2.72948+0.195216i)q12+(0.06820680.124911i)q13+(0.05156490.112911i)q14+(0.3506283.81372i)q15+(1.67726+0.492487i)q16+(0.702107+0.525590i)q17+(0.01474400.0395303i)q18+(1.073657.46738i)q19+(1.54970+3.21896i)q20+(0.2533200.219503i)q21+(1.38454+1.38454i)q22+(1.567654.53238i)q233.90832iq24+(4.093192.87155i)q25+(0.0759392+0.0488032i)q26+(4.204563.14750i)q27+(0.292962+0.109269i)q28+(3.418000.491434i)q29+(2.39689+0.394389i)q30+(0.282325+0.181439i)q31+(1.98236+5.31490i)q32+(4.640622.53397i)q33+(0.364285+0.420407i)q34+(0.08432920.429405i)q35+(0.101971+0.0299415i)q36+(7.03930+2.62552i)q37+(4.67567+1.01713i)q38+(0.0686744+0.233884i)q39+(4.427852.53569i)q40+(3.88633+8.50988i)q41+(0.127407+0.170195i)q42+(0.170122+0.782038i)q43+(3.22994+3.72754i)q44+(0.01817780.147624i)q45+(2.79649+1.19686i)q46+(4.494974.49497i)q47+(2.986360.213588i)q48+(3.76378+5.85655i)q49+(2.001902.45963i)q50+(1.366400.624012i)q51+(0.1362670.182031i)q52+(0.9556231.75009i)q53+(1.80102+2.80244i)q54+(5.88161+3.61347i)q55+(0.1258160.428489i)q56+(0.921788+12.8883i)q57+(0.156248+2.18464i)q58+(2.497688.50633i)q59+(1.421655.95145i)q60+(5.605578.72243i)q61+(0.1020130.186823i)q62+(0.007801320.0104213i)q63+(0.09259460.0422865i)q64+(0.220418+0.229545i)q65+(1.813102.82124i)q66+(8.30923+0.594288i)q67+(0.990833+0.990833i)q68+(0.973521+8.15612i)q69+(0.2754800.0339213i)q70+(4.40447+5.08303i)q71+(0.03226500.148320i)q72+(4.04711+5.40630i)q73+(1.97956+4.33463i)q74+(7.89580+3.31562i)q75+(3.3958211.5651i)q76+(0.5903470.128422i)q77+(0.1448600.0540298i)q78+(3.575171.04977i)q79+(2.17950+3.24475i)q80+(5.76017+6.64759i)q81+(5.207952.84375i)q82+(3.02763+8.11740i)q83+(0.4505200.289532i)q84+(1.59347+1.14318i)q85+(0.502456+0.0722422i)q86+(5.54144+2.06685i)q87+(5.63937+4.22158i)q88+(6.569774.22214i)q89+(0.09421730.00482048i)q90+0.0278526iq91+(3.509716.81125i)q92+(0.4064420.406442i)q93+(3.047142.64036i)q94+(15.1996+7.31749i)q95+(1.382689.61674i)q96+(4.5464312.1894i)q97+(3.534862.64616i)q98+(0.1970290.0578530i)q99+O(q100)q+(-0.0452482 + 0.632652i) q^{2} +(-1.67360 + 0.364069i) q^{3} +(1.58144 + 0.227377i) q^{4} +(-0.673353 + 2.13227i) q^{5} +(-0.154602 - 1.07528i) q^{6} +(-0.171765 + 0.0937908i) q^{7} +(-0.485055 + 2.22976i) q^{8} +(-0.0605071 + 0.0276327i) q^{9} +(-1.31852 - 0.522480i) q^{10} +(2.33306 + 2.02161i) q^{11} +(-2.72948 + 0.195216i) q^{12} +(0.0682068 - 0.124911i) q^{13} +(-0.0515649 - 0.112911i) q^{14} +(0.350628 - 3.81372i) q^{15} +(1.67726 + 0.492487i) q^{16} +(0.702107 + 0.525590i) q^{17} +(-0.0147440 - 0.0395303i) q^{18} +(1.07365 - 7.46738i) q^{19} +(-1.54970 + 3.21896i) q^{20} +(0.253320 - 0.219503i) q^{21} +(-1.38454 + 1.38454i) q^{22} +(1.56765 - 4.53238i) q^{23} -3.90832i q^{24} +(-4.09319 - 2.87155i) q^{25} +(0.0759392 + 0.0488032i) q^{26} +(4.20456 - 3.14750i) q^{27} +(-0.292962 + 0.109269i) q^{28} +(3.41800 - 0.491434i) q^{29} +(2.39689 + 0.394389i) q^{30} +(-0.282325 + 0.181439i) q^{31} +(-1.98236 + 5.31490i) q^{32} +(-4.64062 - 2.53397i) q^{33} +(-0.364285 + 0.420407i) q^{34} +(-0.0843292 - 0.429405i) q^{35} +(-0.101971 + 0.0299415i) q^{36} +(7.03930 + 2.62552i) q^{37} +(4.67567 + 1.01713i) q^{38} +(-0.0686744 + 0.233884i) q^{39} +(-4.42785 - 2.53569i) q^{40} +(-3.88633 + 8.50988i) q^{41} +(0.127407 + 0.170195i) q^{42} +(0.170122 + 0.782038i) q^{43} +(3.22994 + 3.72754i) q^{44} +(-0.0181778 - 0.147624i) q^{45} +(2.79649 + 1.19686i) q^{46} +(-4.49497 - 4.49497i) q^{47} +(-2.98636 - 0.213588i) q^{48} +(-3.76378 + 5.85655i) q^{49} +(2.00190 - 2.45963i) q^{50} +(-1.36640 - 0.624012i) q^{51} +(0.136267 - 0.182031i) q^{52} +(-0.955623 - 1.75009i) q^{53} +(1.80102 + 2.80244i) q^{54} +(-5.88161 + 3.61347i) q^{55} +(-0.125816 - 0.428489i) q^{56} +(0.921788 + 12.8883i) q^{57} +(0.156248 + 2.18464i) q^{58} +(-2.49768 - 8.50633i) q^{59} +(1.42165 - 5.95145i) q^{60} +(-5.60557 - 8.72243i) q^{61} +(-0.102013 - 0.186823i) q^{62} +(0.00780132 - 0.0104213i) q^{63} +(-0.0925946 - 0.0422865i) q^{64} +(0.220418 + 0.229545i) q^{65} +(1.81310 - 2.82124i) q^{66} +(8.30923 + 0.594288i) q^{67} +(0.990833 + 0.990833i) q^{68} +(-0.973521 + 8.15612i) q^{69} +(0.275480 - 0.0339213i) q^{70} +(4.40447 + 5.08303i) q^{71} +(-0.0322650 - 0.148320i) q^{72} +(4.04711 + 5.40630i) q^{73} +(-1.97956 + 4.33463i) q^{74} +(7.89580 + 3.31562i) q^{75} +(3.39582 - 11.5651i) q^{76} +(-0.590347 - 0.128422i) q^{77} +(-0.144860 - 0.0540298i) q^{78} +(3.57517 - 1.04977i) q^{79} +(-2.17950 + 3.24475i) q^{80} +(-5.76017 + 6.64759i) q^{81} +(-5.20795 - 2.84375i) q^{82} +(-3.02763 + 8.11740i) q^{83} +(0.450520 - 0.289532i) q^{84} +(-1.59347 + 1.14318i) q^{85} +(-0.502456 + 0.0722422i) q^{86} +(-5.54144 + 2.06685i) q^{87} +(-5.63937 + 4.22158i) q^{88} +(-6.56977 - 4.22214i) q^{89} +(0.0942173 - 0.00482048i) q^{90} +0.0278526i q^{91} +(3.50971 - 6.81125i) q^{92} +(0.406442 - 0.406442i) q^{93} +(3.04714 - 2.64036i) q^{94} +(15.1996 + 7.31749i) q^{95} +(1.38268 - 9.61674i) q^{96} +(-4.54643 - 12.1894i) q^{97} +(-3.53486 - 2.64616i) q^{98} +(-0.197029 - 0.0578530i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 200q18q214q322q536q622q726q822q1044q116q1226q1322q1552q1622q17+58q1822q2044q21+22q23+50q98+O(q100) 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/115Z)×\left(\mathbb{Z}/115\mathbb{Z}\right)^\times.

nn 4747 5151
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right) e(322)e\left(\frac{3}{22}\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 −0.0452482 + 0.632652i −0.0319953 + 0.447353i 0.956052 + 0.293199i 0.0947197π0.0947197\pi
−0.988047 + 0.154154i 0.950735π0.950735\pi
33 −1.67360 + 0.364069i −0.966253 + 0.210196i −0.667893 0.744258i 0.732803π-0.732803\pi
−0.298361 + 0.954453i 0.596440π0.596440\pi
44 1.58144 + 0.227377i 0.790721 + 0.113688i
55 −0.673353 + 2.13227i −0.301133 + 0.953582i
66 −0.154602 1.07528i −0.0631160 0.438981i
77 −0.171765 + 0.0937908i −0.0649211 + 0.0354496i −0.511382 0.859354i 0.670866π-0.670866\pi
0.446461 + 0.894803i 0.352684π0.352684\pi
88 −0.485055 + 2.22976i −0.171493 + 0.788339i
99 −0.0605071 + 0.0276327i −0.0201690 + 0.00921089i
1010 −1.31852 0.522480i −0.416953 0.165223i
1111 2.33306 + 2.02161i 0.703445 + 0.609539i 0.931342 0.364147i 0.118639π-0.118639\pi
−0.227897 + 0.973685i 0.573185π0.573185\pi
1212 −2.72948 + 0.195216i −0.787933 + 0.0563541i
1313 0.0682068 0.124911i 0.0189172 0.0346442i −0.868049 0.496478i 0.834626π-0.834626\pi
0.886967 + 0.461834i 0.152808π0.152808\pi
1414 −0.0515649 0.112911i −0.0137813 0.0301768i
1515 0.350628 3.81372i 0.0905317 0.984699i
1616 1.67726 + 0.492487i 0.419314 + 0.123122i
1717 0.702107 + 0.525590i 0.170286 + 0.127474i 0.681022 0.732263i 0.261536π-0.261536\pi
−0.510736 + 0.859738i 0.670627π0.670627\pi
1818 −0.0147440 0.0395303i −0.00347520 0.00931737i
1919 1.07365 7.46738i 0.246311 1.71313i −0.372868 0.927884i 0.621626π-0.621626\pi
0.619180 0.785249i 0.287465π-0.287465\pi
2020 −1.54970 + 3.21896i −0.346523 + 0.719782i
2121 0.253320 0.219503i 0.0552789 0.0478994i
2222 −1.38454 + 1.38454i −0.295186 + 0.295186i
2323 1.56765 4.53238i 0.326878 0.945067i
2424 3.90832i 0.797782i
2525 −4.09319 2.87155i −0.818638 0.574310i
2626 0.0759392 + 0.0488032i 0.0148929 + 0.00957109i
2727 4.20456 3.14750i 0.809169 0.605736i
2828 −0.292962 + 0.109269i −0.0553647 + 0.0206500i
2929 3.41800 0.491434i 0.634706 0.0912569i 0.182551 0.983196i 0.441565π-0.441565\pi
0.452155 + 0.891939i 0.350655π0.350655\pi
3030 2.39689 + 0.394389i 0.437611 + 0.0720053i
3131 −0.282325 + 0.181439i −0.0507070 + 0.0325874i −0.565749 0.824578i 0.691413π-0.691413\pi
0.515042 + 0.857165i 0.327776π0.327776\pi
3232 −1.98236 + 5.31490i −0.350434 + 0.939551i
3333 −4.64062 2.53397i −0.807828 0.441108i
3434 −0.364285 + 0.420407i −0.0624743 + 0.0720992i
3535 −0.0843292 0.429405i −0.0142542 0.0725826i
3636 −0.101971 + 0.0299415i −0.0169952 + 0.00499025i
3737 7.03930 + 2.62552i 1.15725 + 0.431633i 0.853487 0.521113i 0.174483π-0.174483\pi
0.303766 + 0.952747i 0.401756π0.401756\pi
3838 4.67567 + 1.01713i 0.758494 + 0.165000i
3939 −0.0686744 + 0.233884i −0.0109967 + 0.0374514i
4040 −4.42785 2.53569i −0.700104 0.400927i
4141 −3.88633 + 8.50988i −0.606943 + 1.32902i 0.317702 + 0.948191i 0.397089π0.397089\pi
−0.924645 + 0.380830i 0.875638π0.875638\pi
4242 0.127407 + 0.170195i 0.0196593 + 0.0262617i
4343 0.170122 + 0.782038i 0.0259433 + 0.119260i 0.988297 0.152539i 0.0487451π-0.0487451\pi
−0.962354 + 0.271799i 0.912381π0.912381\pi
4444 3.22994 + 3.72754i 0.486931 + 0.561948i
4545 −0.0181778 0.147624i −0.00270978 0.0220065i
4646 2.79649 + 1.19686i 0.412319 + 0.176467i
4747 −4.49497 4.49497i −0.655659 0.655659i 0.298691 0.954350i 0.403450π-0.403450\pi
−0.954350 + 0.298691i 0.903450π0.903450\pi
4848 −2.98636 0.213588i −0.431043 0.0308288i
4949 −3.76378 + 5.85655i −0.537683 + 0.836651i
5050 2.00190 2.45963i 0.283111 0.347845i
5151 −1.36640 0.624012i −0.191334 0.0873792i
5252 0.136267 0.182031i 0.0188968 0.0252432i
5353 −0.955623 1.75009i −0.131265 0.240394i 0.803777 0.594930i 0.202820π-0.202820\pi
−0.935042 + 0.354537i 0.884639π0.884639\pi
5454 1.80102 + 2.80244i 0.245088 + 0.381364i
5555 −5.88161 + 3.61347i −0.793075 + 0.487241i
5656 −0.125816 0.428489i −0.0168128 0.0572592i
5757 0.921788 + 12.8883i 0.122094 + 1.70709i
5858 0.156248 + 2.18464i 0.0205164 + 0.286857i
5959 −2.49768 8.50633i −0.325171 1.10743i −0.946184 0.323630i 0.895097π-0.895097\pi
0.621013 0.783800i 0.286721π-0.286721\pi
6060 1.42165 5.95145i 0.183534 0.768329i
6161 −5.60557 8.72243i −0.717719 1.11679i −0.988066 0.154030i 0.950775π-0.950775\pi
0.270347 0.962763i 0.412862π-0.412862\pi
6262 −0.102013 0.186823i −0.0129557 0.0237266i
6363 0.00780132 0.0104213i 0.000982873 0.00131297i
6464 −0.0925946 0.0422865i −0.0115743 0.00528582i
6565 0.220418 + 0.229545i 0.0273395 + 0.0284716i
6666 1.81310 2.82124i 0.223177 0.347271i
6767 8.30923 + 0.594288i 1.01513 + 0.0726038i 0.568979 0.822352i 0.307338π-0.307338\pi
0.446155 + 0.894956i 0.352793π0.352793\pi
6868 0.990833 + 0.990833i 0.120156 + 0.120156i
6969 −0.973521 + 8.15612i −0.117198 + 0.981882i
7070 0.275480 0.0339213i 0.0329261 0.00405437i
7171 4.40447 + 5.08303i 0.522714 + 0.603245i 0.954308 0.298823i 0.0965941π-0.0965941\pi
−0.431594 + 0.902068i 0.642049π0.642049\pi
7272 −0.0322650 0.148320i −0.00380246 0.0174796i
7373 4.04711 + 5.40630i 0.473678 + 0.632760i 0.972210 0.234112i 0.0752181π-0.0752181\pi
−0.498532 + 0.866872i 0.666127π0.666127\pi
7474 −1.97956 + 4.33463i −0.230119 + 0.503890i
7575 7.89580 + 3.31562i 0.911729 + 0.382854i
7676 3.39582 11.5651i 0.389527 1.32661i
7777 −0.590347 0.128422i −0.0672763 0.0146351i
7878 −0.144860 0.0540298i −0.0164021 0.00611767i
7979 3.57517 1.04977i 0.402239 0.118108i −0.0743546 0.997232i 0.523690π-0.523690\pi
0.476593 + 0.879124i 0.341871π0.341871\pi
8080 −2.17950 + 3.24475i −0.243676 + 0.362775i
8181 −5.76017 + 6.64759i −0.640019 + 0.738621i
8282 −5.20795 2.84375i −0.575121 0.314040i
8383 −3.02763 + 8.11740i −0.332326 + 0.891000i 0.658097 + 0.752933i 0.271362π0.271362\pi
−0.990423 + 0.138067i 0.955911π0.955911\pi
8484 0.450520 0.289532i 0.0491558 0.0315905i
8585 −1.59347 + 1.14318i −0.172836 + 0.123995i
8686 −0.502456 + 0.0722422i −0.0541812 + 0.00779008i
8787 −5.54144 + 2.06685i −0.594105 + 0.221590i
8888 −5.63937 + 4.22158i −0.601159 + 0.450022i
8989 −6.56977 4.22214i −0.696395 0.447546i 0.143959 0.989584i 0.454017π-0.454017\pi
−0.840354 + 0.542038i 0.817653π0.817653\pi
9090 0.0942173 0.00482048i 0.00993138 0.000508124i
9191 0.0278526i 0.00291974i
9292 3.50971 6.81125i 0.365912 0.710121i
9393 0.406442 0.406442i 0.0421461 0.0421461i
9494 3.04714 2.64036i 0.314289 0.272333i
9595 15.1996 + 7.31749i 1.55944 + 0.750759i
9696 1.38268 9.61674i 0.141119 0.981504i
9797 −4.54643 12.1894i −0.461620 1.23765i −0.934323 0.356428i 0.883994π-0.883994\pi
0.472703 0.881222i 0.343278π-0.343278\pi
9898 −3.53486 2.64616i −0.357075 0.267303i
9999 −0.197029 0.0578530i −0.0198022 0.00581445i
100100 −5.82022 5.47188i −0.582022 0.547188i
101101 4.62209 + 10.1210i 0.459915 + 1.00707i 0.987507 + 0.157575i 0.0503678π0.0503678\pi
−0.527592 + 0.849498i 0.676905π0.676905\pi
102102 0.456610 0.836218i 0.0452111 0.0827979i
103103 5.63058 0.402707i 0.554797 0.0396799i 0.208874 0.977943i 0.433020π-0.433020\pi
0.345924 + 0.938263i 0.387566π0.387566\pi
104104 0.245438 + 0.212674i 0.0240672 + 0.0208544i
105105 0.297466 + 0.687950i 0.0290298 + 0.0671370i
106106 1.15044 0.525389i 0.111741 0.0510303i
107107 3.70255 17.0203i 0.357939 1.64542i −0.348254 0.937400i 0.613225π-0.613225\pi
0.706193 0.708019i 0.250411π-0.250411\pi
108108 7.36494 4.02156i 0.708692 0.386975i
109109 −1.08276 7.53075i −0.103709 0.721315i −0.973632 0.228126i 0.926740π-0.926740\pi
0.869922 0.493189i 0.164169π-0.164169\pi
110110 −2.01994 3.88451i −0.192594 0.370374i
111111 −12.7368 1.83128i −1.20893 0.173817i
112112 −0.334285 + 0.0727192i −0.0315870 + 0.00687132i
113113 0.628483 8.78734i 0.0591227 0.826644i −0.878225 0.478248i 0.841272π-0.841272\pi
0.937348 0.348396i 0.113273π-0.113273\pi
114114 −8.19551 −0.767579
115115 8.60870 + 6.39456i 0.802765 + 0.596296i
116116 5.51710 0.512250
117117 −0.000675360 0.00944276i −6.24370e−5 0.000872983i
118118 5.49456 1.19527i 0.505816 0.110033i
119119 −0.169893 0.0244269i −0.0155741 0.00223921i
120120 8.33361 + 2.63168i 0.760751 + 0.240238i
121121 −0.209189 1.45494i −0.0190172 0.132268i
122122 5.77191 3.15170i 0.522564 0.285341i
123123 3.40598 15.6570i 0.307107 1.41175i
124124 −0.487735 + 0.222741i −0.0437999 + 0.0200028i
125125 8.87909 6.79424i 0.794170 0.607695i
126126 0.00624009 + 0.00540707i 0.000555911 + 0.000481700i
127127 −21.8775 + 1.56471i −1.94131 + 0.138845i −0.987080 0.160228i 0.948777π-0.948777\pi
−0.954230 + 0.299073i 0.903323π0.903323\pi
128128 −5.40620 + 9.90071i −0.477845 + 0.875107i
129129 −0.569432 1.24688i −0.0501357 0.109782i
130130 −0.155196 + 0.129062i −0.0136116 + 0.0113194i
131131 −17.6458 5.18128i −1.54172 0.452691i −0.603109 0.797659i 0.706071π-0.706071\pi
−0.938614 + 0.344968i 0.887890π0.887890\pi
132132 −6.76270 5.06250i −0.588618 0.440634i
133133 0.515956 + 1.38333i 0.0447391 + 0.119950i
134134 −0.751955 + 5.22996i −0.0649590 + 0.451800i
135135 3.88017 + 11.0847i 0.333952 + 0.954016i
136136 −1.51250 + 1.31059i −0.129696 + 0.112382i
137137 −5.31898 + 5.31898i −0.454431 + 0.454431i −0.896822 0.442391i 0.854130π-0.854130\pi
0.442391 + 0.896822i 0.354130π0.354130\pi
138138 −5.11594 0.984950i −0.435498 0.0838445i
139139 16.5816i 1.40643i 0.710975 + 0.703217i 0.248254π0.248254\pi
−0.710975 + 0.703217i 0.751746π0.751746\pi
140140 −0.0357250 0.698253i −0.00301932 0.0590132i
141141 9.15926 + 5.88630i 0.771349 + 0.495716i
142142 −3.41508 + 2.55650i −0.286587 + 0.214537i
143143 0.411653 0.153539i 0.0344241 0.0128395i
144144 −0.115095 + 0.0165481i −0.00959122 + 0.00137901i
145145 −1.25365 + 7.61901i −0.104110 + 0.632725i
146146 −3.60343 + 2.31579i −0.298222 + 0.191656i
147147 4.16687 11.1718i 0.343677 0.921435i
148148 10.5353 + 5.75268i 0.865993 + 0.472868i
149149 −8.33524 + 9.61937i −0.682849 + 0.788050i −0.986329 0.164788i 0.947306π-0.947306\pi
0.303480 + 0.952838i 0.401851π0.401851\pi
150150 −2.45490 + 4.84527i −0.200442 + 0.395615i
151151 0.986154 0.289561i 0.0802521 0.0235641i −0.241360 0.970436i 0.577593π-0.577593\pi
0.321612 + 0.946872i 0.395775π0.395775\pi
152152 16.1297 + 6.01606i 1.30829 + 0.487967i
153153 −0.0570059 0.0124009i −0.00460865 0.00100255i
154154 0.107959 0.367674i 0.00869956 0.0296280i
155155 −0.196774 0.724167i −0.0158052 0.0581665i
156156 −0.161784 + 0.354258i −0.0129531 + 0.0283634i
157157 10.2561 + 13.7006i 0.818526 + 1.09342i 0.994048 + 0.108948i 0.0347481π0.0347481\pi
−0.175521 + 0.984476i 0.556161π0.556161\pi
158158 0.502366 + 2.30934i 0.0399661 + 0.183721i
159159 2.23649 + 2.58104i 0.177365 + 0.204690i
160160 −9.99801 7.80574i −0.790412 0.617098i
161161 0.155828 + 0.925536i 0.0122810 + 0.0729425i
162162 −3.94497 3.94497i −0.309946 0.309946i
163163 −4.99602 0.357322i −0.391318 0.0279876i −0.125706 0.992068i 0.540120π-0.540120\pi
−0.265612 + 0.964080i 0.585574π0.585574\pi
164164 −8.08096 + 12.5742i −0.631017 + 0.981881i
165165 8.52790 8.18882i 0.663896 0.637499i
166166 −4.99849 2.28274i −0.387958 0.177175i
167167 4.90538 6.55282i 0.379590 0.507073i −0.569537 0.821965i 0.692878π-0.692878\pi
0.949127 + 0.314893i 0.101969π0.101969\pi
168168 0.366565 + 0.671313i 0.0282811 + 0.0517929i
169169 7.01738 + 10.9193i 0.539798 + 0.839943i
170170 −0.651131 1.05984i −0.0499395 0.0812859i
171171 0.141380 + 0.481497i 0.0108116 + 0.0368210i
172172 0.0912205 + 1.27543i 0.00695550 + 0.0972505i
173173 −1.23899 17.3233i −0.0941985 1.31707i −0.796262 0.604952i 0.793192π-0.793192\pi
0.702063 0.712114i 0.252262π-0.252262\pi
174174 −1.05686 3.59932i −0.0801201 0.272864i
175175 0.972392 + 0.109328i 0.0735059 + 0.00826442i
176176 2.91753 + 4.53976i 0.219917 + 0.342198i
177177 7.27702 + 13.3269i 0.546974 + 1.00171i
178178 2.96841 3.96534i 0.222492 0.297215i
179179 −11.4047 5.20834i −0.852425 0.389290i −0.0592208 0.998245i 0.518862π-0.518862\pi
−0.793205 + 0.608955i 0.791589π0.791589\pi
180180 0.00481926 0.237592i 0.000359207 0.0177091i
181181 14.0743 21.9000i 1.04613 1.62782i 0.310322 0.950631i 0.399563π-0.399563\pi
0.735812 0.677186i 0.236801π-0.236801\pi
182182 −0.0176210 0.00126028i −0.00130616 9.34181e-5i
183183 12.5570 + 12.5570i 0.928243 + 0.928243i
184184 9.34572 + 5.69394i 0.688976 + 0.419763i
185185 −10.3383 + 13.2418i −0.760085 + 0.973558i
186186 0.238746 + 0.275527i 0.0175057 + 0.0202026i
187187 0.575520 + 2.64562i 0.0420862 + 0.193467i
188188 −6.08648 8.13058i −0.443902 0.592984i
189189 −0.426991 + 0.934980i −0.0310590 + 0.0680098i
190190 −5.31718 + 9.28493i −0.385749 + 0.673599i
191191 3.50213 11.9272i 0.253406 0.863020i −0.730284 0.683144i 0.760612π-0.760612\pi
0.983689 0.179876i 0.0575697π-0.0575697\pi
192192 0.170362 + 0.0370599i 0.0122948 + 0.00267457i
193193 10.6245 + 3.96275i 0.764771 + 0.285245i 0.701422 0.712747i 0.252549π-0.252549\pi
0.0633493 + 0.997991i 0.479822π0.479822\pi
194194 7.91739 2.32476i 0.568436 0.166908i
195195 −0.452462 0.303919i −0.0324015 0.0217641i
196196 −7.28384 + 8.40600i −0.520274 + 0.600429i
197197 −6.09462 3.32791i −0.434224 0.237104i 0.247243 0.968954i 0.420476π-0.420476\pi
−0.681466 + 0.731850i 0.738657π0.738657\pi
198198 0.0455161 0.122033i 0.00323469 0.00867253i
199199 −17.0426 + 10.9526i −1.20812 + 0.776411i −0.980343 0.197302i 0.936782π-0.936782\pi
−0.227777 + 0.973713i 0.573146π0.573146\pi
200200 8.38829 7.73398i 0.593141 0.546875i
201201 −14.1227 + 2.03054i −0.996138 + 0.143223i
202202 −6.61219 + 2.46622i −0.465232 + 0.173523i
203203 −0.541000 + 0.404988i −0.0379708 + 0.0284246i
204204 −2.01899 1.29753i −0.141358 0.0908450i
205205 −15.5285 14.0169i −1.08456 0.978982i
206206 3.58042i 0.249460i
207207 0.0303877 + 0.317560i 0.00211209 + 0.0220719i
208208 0.175917 0.175917i 0.0121977 0.0121977i
209209 17.6010 15.2514i 1.21749 1.05496i
210210 −0.448693 + 0.157064i −0.0309627 + 0.0108385i
211211 −0.733595 + 5.10227i −0.0505028 + 0.351255i 0.948864 + 0.315684i 0.102234π0.102234\pi
−0.999367 + 0.0355706i 0.988675π0.988675\pi
212212 −1.11333 2.98496i −0.0764639 0.205008i
213213 −9.22189 6.90342i −0.631874 0.473015i
214214 10.6004 + 3.11257i 0.724630 + 0.212771i
215215 −1.78207 0.163841i −0.121536 0.0111739i
216216 4.97872 + 10.9019i 0.338759 + 0.741779i
217217 0.0314762 0.0576444i 0.00213674 0.00391316i
218218 4.81334 0.344257i 0.326000 0.0233160i
219219 −8.74151 7.57456i −0.590696 0.511841i
220220 −10.1230 + 4.37716i −0.682495 + 0.295108i
221221 0.113541 0.0518523i 0.00763757 0.00348796i
222222 1.73488 7.97513i 0.116438 0.535255i
223223 −10.7757 + 5.88395i −0.721591 + 0.394019i −0.797679 0.603083i 0.793939π-0.793939\pi
0.0760877 + 0.997101i 0.475757π0.475757\pi
224224 −0.157990 1.09884i −0.0105561 0.0734195i
225225 0.327016 + 0.0606433i 0.0218010 + 0.00404288i
226226 5.53089 + 0.795223i 0.367910 + 0.0528974i
227227 5.04440 1.09734i 0.334808 0.0728331i −0.0420184 0.999117i 0.513379π-0.513379\pi
0.376827 + 0.926284i 0.377015π0.377015\pi
228228 −1.47274 + 20.5917i −0.0975349 + 1.36372i
229229 16.5896 1.09627 0.548137 0.836389i 0.315337π-0.315337\pi
0.548137 + 0.836389i 0.315337π0.315337\pi
230230 −4.43506 + 5.15697i −0.292439 + 0.340040i
231231 1.03476 0.0680822
232232 −0.562136 + 7.85968i −0.0369060 + 0.516013i
233233 −9.08066 + 1.97538i −0.594894 + 0.129411i −0.499924 0.866069i 0.666639π-0.666639\pi
−0.0949691 + 0.995480i 0.530275π0.530275\pi
234234 −0.00594342 0.000854535i −0.000388534 5.58627e-5i
235235 12.6112 6.55781i 0.822665 0.427784i
236236 −2.01580 14.0202i −0.131217 0.912636i
237237 −5.60122 + 3.05850i −0.363838 + 0.198671i
238238 0.0231411 0.106378i 0.00150001 0.00689545i
239239 3.59581 1.64215i 0.232594 0.106222i −0.295709 0.955278i 0.595556π-0.595556\pi
0.528303 + 0.849056i 0.322829π0.322829\pi
240240 2.46630 6.22391i 0.159199 0.401752i
241241 4.61704 + 4.00069i 0.297409 + 0.257707i 0.790763 0.612122i 0.209684π-0.209684\pi
−0.493354 + 0.869829i 0.664229π0.664229\pi
242242 0.929939 0.0665106i 0.0597788 0.00427546i
243243 −0.331233 + 0.606607i −0.0212486 + 0.0389139i
244244 −6.88160 15.0686i −0.440549 0.964668i
245245 −9.95343 11.9689i −0.635901 0.764668i
246246 9.75134 + 2.86325i 0.621723 + 0.182554i
247247 −0.859530 0.643436i −0.0546906 0.0409409i
248248 −0.267623 0.717525i −0.0169941 0.0455629i
249249 2.11175 14.6875i 0.133827 0.930785i
250250 3.89663 + 5.92480i 0.246444 + 0.374718i
251251 4.28686 3.71459i 0.270584 0.234463i −0.508990 0.860772i 0.669981π-0.669981\pi
0.779574 + 0.626310i 0.215436π0.215436\pi
252252 0.0147069 0.0147069i 0.000926447 0.000926447i
253253 12.8201 7.40515i 0.805995 0.465558i
254254 13.9116i 0.872893i
255255 2.25063 2.49335i 0.140940 0.156140i
256256 −6.19035 3.97830i −0.386897 0.248644i
257257 −18.5185 + 13.8628i −1.15515 + 0.864737i −0.992536 0.121952i 0.961085π-0.961085\pi
−0.162618 + 0.986689i 0.551994π0.551994\pi
258258 0.814608 0.303833i 0.0507153 0.0189158i
259259 −1.45536 + 0.209249i −0.0904314 + 0.0130021i
260260 0.296385 + 0.413130i 0.0183810 + 0.0256212i
261261 −0.193233 + 0.124184i −0.0119608 + 0.00768677i
262262 4.07639 10.9292i 0.251840 0.675210i
263263 −22.9578 12.5359i −1.41564 0.772998i −0.424451 0.905451i 0.639533π-0.639533\pi
−0.991189 + 0.132453i 0.957715π0.957715\pi
264264 7.90110 9.11836i 0.486279 0.561196i
265265 4.37515 0.859220i 0.268763 0.0527815i
266266 −0.898514 + 0.263828i −0.0550915 + 0.0161763i
267267 12.5323 + 4.67431i 0.766966 + 0.286063i
268268 13.0054 + 2.82916i 0.794433 + 0.172818i
269269 5.70242 19.4206i 0.347683 1.18410i −0.581212 0.813752i 0.697421π-0.697421\pi
0.928894 0.370345i 0.120761π-0.120761\pi
270270 −7.18831 + 1.95324i −0.437466 + 0.118870i
271271 3.29990 7.22577i 0.200455 0.438934i −0.782532 0.622610i 0.786072π-0.786072\pi
0.982987 + 0.183676i 0.0587996π0.0587996\pi
272272 0.918766 + 1.22733i 0.0557084 + 0.0744177i
273273 −0.0101403 0.0466141i −0.000613717 0.00282121i
274274 −3.12439 3.60574i −0.188751 0.217831i
275275 −3.74452 14.9743i −0.225803 0.902987i
276276 −3.39408 + 12.6771i −0.204300 + 0.763070i
277277 2.42021 + 2.42021i 0.145416 + 0.145416i 0.776067 0.630651i 0.217212π-0.217212\pi
−0.630651 + 0.776067i 0.717212π0.717212\pi
278278 −10.4904 0.750288i −0.629172 0.0449993i
279279 0.0120690 0.0187797i 0.000722553 0.00112431i
280280 0.998374 + 0.0202508i 0.0596643 + 0.00121021i
281281 0.296073 + 0.135212i 0.0176623 + 0.00806608i 0.424227 0.905556i 0.360546π-0.360546\pi
−0.406564 + 0.913622i 0.633273π0.633273\pi
282282 −4.13842 + 5.52828i −0.246439 + 0.329204i
283283 12.8604 + 23.5521i 0.764471 + 1.40002i 0.911672 + 0.410918i 0.134792π0.134792\pi
−0.147201 + 0.989107i 0.547026π0.547026\pi
284284 5.80965 + 9.03999i 0.344739 + 0.536425i
285285 −28.1020 6.71286i −1.66462 0.397635i
286286 0.0785100 + 0.267380i 0.00464239 + 0.0158105i
287287 −0.130613 1.82620i −0.00770982 0.107797i
288288 −0.0269183 0.376367i −0.00158618 0.0221776i
289289 −4.57275 15.5733i −0.268985 0.916079i
290290 −4.76346 1.13787i −0.279720 0.0668180i
291291 12.0467 + 18.7450i 0.706190 + 1.09885i
292292 5.17100 + 9.46997i 0.302610 + 0.554188i
293293 −5.21528 + 6.96681i −0.304680 + 0.407005i −0.926584 0.376089i 0.877269π-0.877269\pi
0.621903 + 0.783094i 0.286360π0.286360\pi
294294 6.87932 + 3.14168i 0.401210 + 0.183227i
295295 19.8197 + 0.402017i 1.15395 + 0.0234063i
296296 −9.26873 + 14.4224i −0.538734 + 0.838287i
297297 16.1725 + 1.15668i 0.938425 + 0.0671175i
298298 −5.70856 5.70856i −0.330688 0.330688i
299299 −0.459221 0.504957i −0.0265575 0.0292024i
300300 11.7329 + 7.03878i 0.677397 + 0.406384i
301301 −0.102569 0.118371i −0.00591198 0.00682279i
302302 0.138570 + 0.636994i 0.00797379 + 0.0366549i
303303 −11.4203 15.2557i −0.656077 0.876416i
304304 5.47837 11.9959i 0.314206 0.688015i
305305 22.3731 6.07933i 1.28108 0.348101i
306306 0.0104248 0.0355038i 0.000595949 0.00202962i
307307 −21.2410 4.62069i −1.21229 0.263717i −0.439418 0.898283i 0.644815π-0.644815\pi
−0.772869 + 0.634566i 0.781179π0.781179\pi
308308 −0.904400 0.337324i −0.0515330 0.0192208i
309309 −9.27672 + 2.72389i −0.527734 + 0.154957i
310310 0.467049 0.0917221i 0.0265266 0.00520947i
311311 11.0480 12.7501i 0.626474 0.722990i −0.350449 0.936582i 0.613971π-0.613971\pi
0.976923 + 0.213592i 0.0685164π0.0685164\pi
312312 −0.488194 0.266574i −0.0276385 0.0150918i
313313 −8.81628 + 23.6374i −0.498326 + 1.33606i 0.407807 + 0.913068i 0.366294π0.366294\pi
−0.906132 + 0.422994i 0.860979π0.860979\pi
314314 −9.13175 + 5.86862i −0.515335 + 0.331186i
315315 0.0169681 + 0.0236518i 0.000956045 + 0.00133263i
316316 5.89262 0.847231i 0.331486 0.0476605i
317317 22.9628 8.56468i 1.28972 0.481040i 0.391334 0.920249i 0.372014π-0.372014\pi
0.898385 + 0.439208i 0.144741π0.144741\pi
318318 −1.73410 + 1.29813i −0.0972434 + 0.0727955i
319319 8.96789 + 5.76331i 0.502105 + 0.322683i
320320 0.152515 0.168963i 0.00852587 0.00944534i
321321 29.8332i 1.66513i
322322 −0.592593 + 0.0567060i −0.0330239 + 0.00316010i
323323 4.67859 4.67859i 0.260324 0.260324i
324324 −10.6209 + 9.20304i −0.590049 + 0.511280i
325325 −0.637872 + 0.315427i −0.0353828 + 0.0174967i
326326 0.452121 3.14457i 0.0250407 0.174162i
327327 4.55382 + 12.2093i 0.251827 + 0.675174i
328328 −17.0899 12.7933i −0.943633 0.706395i
329329 1.19367 + 0.350492i 0.0658089 + 0.0193232i
330330 4.79480 + 5.76572i 0.263945 + 0.317393i
331331 0.362741 + 0.794293i 0.0199381 + 0.0436583i 0.919339 0.393466i 0.128724π-0.128724\pi
−0.899401 + 0.437125i 0.855997π0.855997\pi
332332 −6.63373 + 12.1488i −0.364073 + 0.666751i
333333 −0.498478 + 0.0356518i −0.0273164 + 0.00195371i
334334 3.92370 + 3.39990i 0.214695 + 0.186034i
335335 −6.86223 + 17.3174i −0.374924 + 0.946150i
336336 0.532984 0.243406i 0.0290767 0.0132789i
337337 1.37093 6.30208i 0.0746795 0.343296i −0.924613 0.380908i 0.875611π-0.875611\pi
0.999292 + 0.0376120i 0.0119751π0.0119751\pi
338338 −7.22561 + 3.94548i −0.393022 + 0.214606i
339339 2.14737 + 14.9353i 0.116629 + 0.811174i
340340 −2.77991 + 1.44555i −0.150762 + 0.0783958i
341341 −1.02548 0.147442i −0.0555329 0.00798443i
342342 −0.311017 + 0.0676577i −0.0168179 + 0.00365851i
343343 0.194924 2.72540i 0.0105249 0.147158i
344344 −1.82628 −0.0984662
345345 −16.7356 7.56777i −0.901013 0.407435i
346346 11.0157 0.592207
347347 −1.02315 + 14.3054i −0.0549253 + 0.767956i 0.893120 + 0.449819i 0.148512π0.148512\pi
−0.948045 + 0.318137i 0.896943π0.896943\pi
348348 −9.23342 + 2.00861i −0.494963 + 0.107673i
349349 26.0154 + 3.74046i 1.39257 + 0.200222i 0.797437 0.603402i 0.206188π-0.206188\pi
0.595138 + 0.803624i 0.297098π0.297098\pi
350350 −0.113166 + 0.610239i −0.00604895 + 0.0326187i
351351 −0.106378 0.739879i −0.00567806 0.0394918i
352352 −15.3696 + 8.39245i −0.819204 + 0.447319i
353353 −3.12048 + 14.3446i −0.166086 + 0.763486i 0.816450 + 0.577416i 0.195939π0.195939\pi
−0.982536 + 0.186070i 0.940425π0.940425\pi
354354 −8.76054 + 4.00080i −0.465617 + 0.212640i
355355 −13.8042 + 5.96887i −0.732650 + 0.316795i
356356 −9.42970 8.17088i −0.499773 0.433056i
357357 0.293226 0.0209719i 0.0155192 0.00110995i
358358 3.81111 6.97952i 0.201423 0.368879i
359359 −6.34071 13.8842i −0.334650 0.732781i 0.665254 0.746617i 0.268323π-0.268323\pi
−0.999904 + 0.0138356i 0.995596π0.995596\pi
360360 0.337984 + 0.0310738i 0.0178133 + 0.00163773i
361361 −36.3786 10.6817i −1.91466 0.562196i
362362 13.2183 + 9.89507i 0.694737 + 0.520073i
363363 0.879800 + 2.35883i 0.0461775 + 0.123807i
364364 −0.00633304 + 0.0440472i −0.000331941 + 0.00230870i
365365 −14.2529 + 4.98919i −0.746029 + 0.261146i
366366 −8.51242 + 7.37606i −0.444951 + 0.385553i
367367 10.4062 10.4062i 0.543199 0.543199i −0.381266 0.924465i 0.624512π-0.624512\pi
0.924465 + 0.381266i 0.124512π0.124512\pi
368368 4.86149 6.82992i 0.253423 0.356034i
369369 0.622298i 0.0323955i
370370 −7.90967 7.13970i −0.411204 0.371175i
371371 0.328285 + 0.210976i 0.0170437 + 0.0109533i
372372 0.735180 0.550349i 0.0381173 0.0285343i
373373 −17.1142 + 6.38327i −0.886140 + 0.330513i −0.750991 0.660312i 0.770424π-0.770424\pi
−0.135149 + 0.990825i 0.543151π0.543151\pi
374374 −1.69980 + 0.244394i −0.0878945 + 0.0126373i
375375 −12.3865 + 14.6034i −0.639635 + 0.754119i
376376 12.2030 7.84240i 0.629322 0.404441i
377377 0.171745 0.460466i 0.00884531 0.0237152i
378378 −0.572196 0.312443i −0.0294306 0.0160703i
379379 2.12189 2.44879i 0.108994 0.125786i −0.698631 0.715482i 0.746207π-0.746207\pi
0.807625 + 0.589696i 0.200752π0.200752\pi
380380 22.3734 + 15.0282i 1.14773 + 0.770931i
381381 36.0444 10.5836i 1.84661 0.542214i
382382 7.38729 + 2.75532i 0.377967 + 0.140974i
383383 24.7699 + 5.38836i 1.26568 + 0.275332i 0.794804 0.606866i 0.207573π-0.207573\pi
0.470878 + 0.882198i 0.343937π0.343937\pi
384384 5.44326 18.5380i 0.277775 0.946016i
385385 0.671344 1.17231i 0.0342148 0.0597464i
386386 −2.98778 + 6.54233i −0.152074 + 0.332996i
387387 −0.0319034 0.0426179i −0.00162174 0.00216639i
388388 −4.41831 20.3106i −0.224306 1.03112i
389389 −8.46700 9.77144i −0.429294 0.495432i 0.499352 0.866399i 0.333572π-0.333572\pi
−0.928646 + 0.370968i 0.879026π0.879026\pi
390390 0.212748 0.272499i 0.0107729 0.0137985i
391391 3.48283 2.35827i 0.176134 0.119263i
392392 −11.2331 11.2331i −0.567356 0.567356i
393393 31.4184 + 2.24709i 1.58485 + 0.113351i
394394 2.38118 3.70519i 0.119962 0.186665i
395395 −0.168966 + 8.33012i −0.00850160 + 0.419134i
396396 −0.298436 0.136291i −0.0149970 0.00684889i
397397 −13.2178 + 17.6569i −0.663382 + 0.886174i −0.998429 0.0560269i 0.982157π-0.982157\pi
0.335047 + 0.942201i 0.391248π0.391248\pi
398398 −6.15806 11.2776i −0.308675 0.565297i
399399 −1.36713 2.12730i −0.0684423 0.106498i
400400 −5.45113 6.83217i −0.272557 0.341608i
401401 6.39755 + 21.7880i 0.319478 + 1.08804i 0.950098 + 0.311951i 0.100982π0.100982\pi
−0.630620 + 0.776092i 0.717199π0.717199\pi
402402 −0.645597 9.02663i −0.0321995 0.450207i
403403 0.00340735 + 0.0476410i 0.000169732 + 0.00237317i
404404 5.00829 + 17.0567i 0.249172 + 0.848601i
405405 −10.2959 16.7584i −0.511605 0.832733i
406406 −0.231737 0.360590i −0.0115009 0.0178958i
407407 11.1153 + 20.3562i 0.550967 + 1.00902i
408408 2.05417 2.74406i 0.101697 0.135851i
409409 9.91080 + 4.52611i 0.490058 + 0.223802i 0.645089 0.764108i 0.276820π-0.276820\pi
−0.155031 + 0.987910i 0.549548π0.549548\pi
410410 9.57045 9.18992i 0.472651 0.453858i
411411 6.96537 10.8383i 0.343576 0.534615i
412412 8.99600 + 0.643407i 0.443201 + 0.0316984i
413413 1.22683 + 1.22683i 0.0603684 + 0.0603684i
414414 −0.202280 + 0.00485584i −0.00994150 + 0.000238651i
415415 −15.2699 11.9216i −0.749568 0.585209i
416416 0.528682 + 0.610131i 0.0259208 + 0.0299142i
417417 −6.03686 27.7510i −0.295626 1.35897i
418418 8.85239 + 11.8254i 0.432985 + 0.578400i
419419 −13.3850 + 29.3090i −0.653898 + 1.43184i 0.234203 + 0.972188i 0.424752π0.424752\pi
−0.888101 + 0.459649i 0.847975π0.847975\pi
420420 0.314002 + 1.15559i 0.0153217 + 0.0563870i
421421 3.93444 13.3995i 0.191753 0.653050i −0.806348 0.591442i 0.798559π-0.798559\pi
0.998100 0.0616082i 0.0196229π-0.0196229\pi
422422 −3.19477 0.694979i −0.155519 0.0338310i
423423 0.396185 + 0.147770i 0.0192632 + 0.00718480i
424424 4.36582 1.28192i 0.212023 0.0622555i
425425 −1.36460 4.16747i −0.0661927 0.202152i
426426 4.78474 5.52188i 0.231821 0.267536i
427427 1.78092 + 0.972458i 0.0861850 + 0.0470606i
428428 9.72540 26.0748i 0.470095 1.26037i
429429 −0.633043 + 0.406832i −0.0305636 + 0.0196420i
430430 0.184290 1.12002i 0.00888725 0.0540121i
431431 2.74180 0.394211i 0.132068 0.0189885i −0.0759639 0.997111i 0.524203π-0.524203\pi
0.208032 + 0.978122i 0.433294π0.433294\pi
432432 8.60223 3.20847i 0.413875 0.154367i
433433 9.75986 7.30614i 0.469029 0.351111i −0.338473 0.940976i 0.609910π-0.609910\pi
0.807501 + 0.589866i 0.200819π0.200819\pi
434434 0.0350446 + 0.0225218i 0.00168219 + 0.00108108i
435435 −0.675746 13.2076i −0.0323995 0.633256i
436436 12.1556i 0.582149i
437437 −32.1619 16.5724i −1.53851 0.792766i
438438 5.18760 5.18760i 0.247873 0.247873i
439439 −16.0315 + 13.8914i −0.765140 + 0.662998i −0.947328 0.320266i 0.896228π-0.896228\pi
0.182187 + 0.983264i 0.441682π0.441682\pi
440440 −5.20428 14.8673i −0.248104 0.708771i
441441 0.0659031 0.458366i 0.00313824 0.0218270i
442442 0.0276669 + 0.0741780i 0.00131598 + 0.00352829i
443443 18.3197 + 13.7140i 0.870397 + 0.651571i 0.938187 0.346129i 0.112504π-0.112504\pi
−0.0677903 + 0.997700i 0.521595π0.521595\pi
444444 −19.7262 5.79213i −0.936163 0.274882i
445445 13.4265 11.1656i 0.636479 0.529299i
446446 −3.23492 7.08348i −0.153178 0.335412i
447447 10.4477 19.1336i 0.494161 0.904987i
448448 0.0198706 0.00142117i 0.000938798 6.71442e-5i
449449 21.0185 + 18.2126i 0.991925 + 0.859508i 0.990082 0.140490i 0.0448679π-0.0448679\pi
0.00184293 + 0.999998i 0.499413π0.499413\pi
450450 −0.0531630 + 0.204143i −0.00250613 + 0.00962340i
451451 −26.2707 + 11.9974i −1.23704 + 0.564937i
452452 2.99195 13.7538i 0.140729 0.646923i
453453 −1.54501 + 0.843637i −0.0725907 + 0.0396375i
454454 0.465986 + 3.24100i 0.0218698 + 0.152108i
455455 −0.0593894 0.0187546i −0.00278422 0.000879231i
456456 −29.1849 4.19615i −1.36671 0.196503i
457457 −39.4237 + 8.57611i −1.84416 + 0.401173i −0.992431 0.122802i 0.960812π-0.960812\pi
−0.851733 + 0.523976i 0.824448π0.824448\pi
458458 −0.750651 + 10.4955i −0.0350756 + 0.490421i
459459 4.60635 0.215006
460460 12.1602 + 12.0700i 0.566971 + 0.562768i
461461 9.74476 0.453859 0.226929 0.973911i 0.427131π-0.427131\pi
0.226929 + 0.973911i 0.427131π0.427131\pi
462462 −0.0468210 + 0.654643i −0.00217831 + 0.0304567i
463463 9.37152 2.03865i 0.435531 0.0947440i 0.0105462 0.999944i 0.496643π-0.496643\pi
0.424985 + 0.905200i 0.360279π0.360279\pi
464464 5.97488 + 0.859058i 0.277377 + 0.0398808i
465465 0.592967 + 1.14033i 0.0274982 + 0.0528813i
466466 −0.838843 5.83428i −0.0388586 0.270268i
467467 −5.69780 + 3.11123i −0.263663 + 0.143971i −0.605643 0.795736i 0.707084π-0.707084\pi
0.341981 + 0.939707i 0.388902π0.388902\pi
468468 −0.00321511 + 0.0147796i −0.000148618 + 0.000683188i
469469 −1.48297 + 0.677252i −0.0684774 + 0.0312726i
470470 3.57818 + 8.27524i 0.165049 + 0.381708i
471471 −22.1526 19.1953i −1.02074 0.884473i
472472 20.1786 1.44320i 0.928795 0.0664287i
473473 −1.18407 + 2.16846i −0.0544436 + 0.0997061i
474474 −1.68152 3.68202i −0.0772348 0.169121i
475475 −25.8376 + 27.4824i −1.18551 + 1.26098i
476476 −0.263122 0.0772595i −0.0120602 0.00354118i
477477 0.106182 + 0.0794867i 0.00486173 + 0.00363944i
478478 0.876207 + 2.34920i 0.0400768 + 0.107450i
479479 1.67535 11.6523i 0.0765487 0.532408i −0.915079 0.403275i 0.867872π-0.867872\pi
0.991627 0.129132i 0.0412192π-0.0412192\pi
480480 19.5745 + 9.42371i 0.893449 + 0.430132i
481481 0.808086 0.700210i 0.0368455 0.0319268i
482482 −2.73995 + 2.73995i −0.124802 + 0.124802i
483483 −0.597753 1.49224i −0.0271987 0.0678995i
484484 2.34847i 0.106749i
485485 29.0526 1.48643i 1.31921 0.0674953i
486486 −0.368784 0.237003i −0.0167284 0.0107507i
487487 −12.8124 + 9.59126i −0.580586 + 0.434621i −0.848782 0.528743i 0.822663π-0.822663\pi
0.268196 + 0.963364i 0.413573π0.413573\pi
488488 22.1679 8.26821i 1.00350 0.374284i
489489 8.49142 1.22088i 0.383996 0.0552102i
490490 8.02255 5.75549i 0.362422 0.260006i
491491 −4.32259 + 2.77796i −0.195076 + 0.125368i −0.634533 0.772896i 0.718807π-0.718807\pi
0.439457 + 0.898264i 0.355171π0.355171\pi
492492 8.94640 23.9862i 0.403335 1.08138i
493493 2.65809 + 1.45143i 0.119714 + 0.0653690i
494494 0.445964 0.514669i 0.0200648 0.0231561i
495495 0.256029 0.381165i 0.0115076 0.0171321i
496496 −0.562888 + 0.165279i −0.0252744 + 0.00742123i
497497 −1.23328 0.459988i −0.0553200 0.0206333i
498498 9.19655 + 2.00059i 0.412107 + 0.0896485i
499499 −9.59724 + 32.6852i −0.429631 + 1.46319i 0.405986 + 0.913879i 0.366928π0.366928\pi
−0.835618 + 0.549311i 0.814890π0.814890\pi
500500 15.5866 8.72579i 0.697055 0.390229i
501501 −5.82396 + 12.7527i −0.260196 + 0.569749i
502502 2.15607 + 2.88017i 0.0962300 + 0.128548i
503503 0.334058 + 1.53564i 0.0148949 + 0.0684709i 0.983994 0.178199i 0.0570272π-0.0570272\pi
−0.969099 + 0.246670i 0.920664π0.920664\pi
504504 0.0194530 + 0.0224500i 0.000866506 + 0.00100000i
505505 −24.6930 + 3.04058i −1.09882 + 0.135304i
506506 4.10479 + 8.44576i 0.182480 + 0.375460i
507507 −15.7196 15.7196i −0.698134 0.698134i
508508 −34.9537 2.49994i −1.55082 0.110917i
509509 10.9905 17.1015i 0.487145 0.758012i −0.507468 0.861670i 0.669419π-0.669419\pi
0.994613 + 0.103659i 0.0330549π0.0330549\pi
510510 1.47559 + 1.53669i 0.0653401 + 0.0680457i
511511 −1.20221 0.549032i −0.0531828 0.0242878i
512512 −10.7234 + 14.3248i −0.473911 + 0.633072i
513513 −18.9893 34.7764i −0.838399 1.53541i
514514 −7.93239 12.3430i −0.349883 0.544428i
515515 −2.93269 + 12.2771i −0.129230 + 0.540994i
516516 −0.617011 2.10135i −0.0271624 0.0925066i
517517 −1.39997 19.5741i −0.0615706 0.860869i
518518 −0.0665294 0.930202i −0.00292313 0.0408707i
519519 8.38045 + 28.5412i 0.367861 + 1.25282i
520520 −0.618745 + 0.380138i −0.0271338 + 0.0166701i
521521 19.6254 + 30.5377i 0.859804 + 1.33788i 0.940025 + 0.341104i 0.110801π0.110801\pi
−0.0802212 + 0.996777i 0.525563π0.525563\pi
522522 −0.0698215 0.127869i −0.00305600 0.00559666i
523523 1.45985 1.95013i 0.0638346 0.0852730i −0.767488 0.641064i 0.778493π-0.778493\pi
0.831322 + 0.555791i 0.187584π0.187584\pi
524524 −26.7277 12.2061i −1.16761 0.533228i
525525 −1.66720 + 0.171047i −0.0727625 + 0.00746510i
526526 8.96968 13.9571i 0.391096 0.608558i
527527 −0.293585 0.0209976i −0.0127888 0.000914670i
528528 −6.53556 6.53556i −0.284424 0.284424i
529529 −18.0849 14.2104i −0.786302 0.617843i
530530 0.345620 + 2.80683i 0.0150128 + 0.121921i
531531 0.386180 + 0.445676i 0.0167588 + 0.0193407i
532532 0.501417 + 2.30498i 0.0217392 + 0.0999334i
533533 0.797907 + 1.06588i 0.0345612 + 0.0461683i
534534 −3.52428 + 7.71709i −0.152510 + 0.333951i
535535 33.7989 + 19.3556i 1.46126 + 0.836814i
536536 −5.35555 + 18.2393i −0.231325 + 0.787819i
537537 20.9831 + 4.56458i 0.905486 + 0.196976i
538538 12.0285 + 4.48640i 0.518585 + 0.193422i
539539 −20.6208 + 6.05482i −0.888201 + 0.260799i
540540 3.61587 + 18.4120i 0.155602 + 0.792327i
541541 23.9206 27.6058i 1.02843 1.18687i 0.0462450 0.998930i 0.485275π-0.485275\pi
0.982181 0.187937i 0.0601800π-0.0601800\pi
542542 4.42208 + 2.41464i 0.189945 + 0.103718i
543543 −15.5816 + 41.7759i −0.668671 + 1.79278i
544544 −4.18529 + 2.68972i −0.179443 + 0.115321i
545545 16.7867 + 2.76212i 0.719064 + 0.118316i
546546 0.0299493 0.00430606i 0.00128171 0.000184282i
547547 38.6516 14.4163i 1.65262 0.616396i 0.661571 0.749883i 0.269890π-0.269890\pi
0.991051 + 0.133487i 0.0426175π0.0426175\pi
548548 −9.62107 + 7.20225i −0.410992 + 0.307665i
549549 0.580200 + 0.372872i 0.0247624 + 0.0159138i
550550 9.64298 1.69142i 0.411178 0.0721223i
551551 26.0511i 1.10981i
552552 −17.7140 6.12688i −0.753957 0.260777i
553553 −0.515632 + 0.515632i −0.0219269 + 0.0219269i
554554 −1.64066 + 1.42164i −0.0697050 + 0.0603997i
555555 12.4812 25.9253i 0.529797 1.10047i
556556 −3.77028 + 26.2229i −0.159895 + 1.11210i
557557 4.73958 + 12.7073i 0.200822 + 0.538426i 0.997852 0.0655152i 0.0208691π-0.0208691\pi
−0.797029 + 0.603941i 0.793596π0.793596\pi
558558 0.0113349 + 0.00848523i 0.000479846 + 0.000359208i
559559 0.109289 + 0.0320901i 0.00462243 + 0.00135727i
560560 0.0700345 0.761753i 0.00295950 0.0321899i
561561 −1.92638 4.21818i −0.0813318 0.178092i
562562 −0.0989391 + 0.181193i −0.00417349 + 0.00764318i
563563 −21.1473 + 1.51248i −0.891251 + 0.0637435i −0.509449 0.860501i 0.670151π-0.670151\pi
−0.381802 + 0.924244i 0.624696π0.624696\pi
564564 13.1464 + 11.3914i 0.553564 + 0.479666i
565565 18.3138 + 7.25709i 0.770469 + 0.305308i
566566 −15.4822 + 7.07047i −0.650764 + 0.297194i
567567 0.365913 1.68207i 0.0153669 0.0706405i
568568 −13.4703 + 7.35537i −0.565203 + 0.308624i
569569 0.120169 + 0.835792i 0.00503773 + 0.0350382i 0.992185 0.124773i 0.0398204π-0.0398204\pi
−0.987148 + 0.159812i 0.948911π0.948911\pi
570570 5.51847 17.4751i 0.231143 0.731950i
571571 −25.5215 3.66943i −1.06804 0.153561i −0.414194 0.910189i 0.635937π-0.635937\pi
−0.653846 + 0.756628i 0.726846π0.726846\pi
572572 0.685916 0.149212i 0.0286796 0.00623886i
573573 −1.51885 + 21.2363i −0.0634510 + 0.887161i
574574 1.16126 0.0484701
575575 −19.4316 + 14.0503i −0.810356 + 0.585938i
576576 0.00677112 0.000282130
577577 1.51556 21.1902i 0.0630934 0.882161i −0.863081 0.505066i 0.831468π-0.831468\pi
0.926174 0.377096i 0.123077π-0.123077\pi
578578 10.0594 2.18829i 0.418416 0.0910209i
579579 −19.2239 2.76398i −0.798919 0.114867i
580580 −3.71496 + 11.7640i −0.154255 + 0.488472i
581581 −0.241296 1.67825i −0.0100106 0.0696255i
582582 −12.4042 + 6.77319i −0.514170 + 0.280758i
583583 1.30848 6.01498i 0.0541916 0.249115i
584584 −14.0178 + 6.40173i −0.580062 + 0.264905i
585585 −0.0196798 0.00779836i −0.000813660 0.000322423i
586586 −4.17158 3.61470i −0.172326 0.149322i
587587 1.93346 0.138284i 0.0798026 0.00570759i −0.0313808 0.999508i 0.509990π-0.509990\pi
0.111183 + 0.993800i 0.464536π0.464536\pi
588588 9.12987 16.7201i 0.376509 0.689526i
589589 1.05176 + 2.30303i 0.0433369 + 0.0948946i
590590 −1.15114 + 12.5208i −0.0473917 + 0.515471i
591591 11.4115 + 3.35073i 0.469408 + 0.137831i
592592 10.5137 + 7.87044i 0.432109 + 0.323473i
593593 1.30615 + 3.50192i 0.0536371 + 0.143807i 0.961005 0.276530i 0.0891846π-0.0891846\pi
−0.907368 + 0.420337i 0.861912π0.861912\pi
594594 −1.46355 + 10.1792i −0.0600504 + 0.417660i
595595 0.166483 0.345811i 0.00682513 0.0141768i
596596 −15.3689 + 13.3172i −0.629535 + 0.545495i
597597 24.5350 24.5350i 1.00415 1.00415i
598598 0.340241 0.267679i 0.0139135 0.0109462i
599599 30.7152i 1.25499i 0.778622 + 0.627494i 0.215919π0.215919\pi
−0.778622 + 0.627494i 0.784081π0.784081\pi
600600 −11.2229 + 15.9975i −0.458174 + 0.653095i
601601 −5.73269 3.68418i −0.233841 0.150281i 0.418473 0.908229i 0.362565π-0.362565\pi
−0.652314 + 0.757949i 0.726202π0.726202\pi
602602 0.0795287 0.0595344i 0.00324135 0.00242644i
603603 −0.519189 + 0.193648i −0.0211430 + 0.00788594i
604604 1.62538 0.233695i 0.0661359 0.00950891i
605605 3.24320 + 0.533642i 0.131855 + 0.0216956i
606606 10.1683 6.53476i 0.413058 0.265456i
607607 5.35178 14.3487i 0.217222 0.582395i −0.781939 0.623355i 0.785769π-0.785769\pi
0.999161 + 0.0409605i 0.0130418π0.0130418\pi
608608 37.5600 + 20.5093i 1.52326 + 0.831763i
609609 0.757974 0.874749i 0.0307147 0.0354466i
610610 2.83376 + 14.4295i 0.114735 + 0.584233i
611611 −0.868060 + 0.254885i −0.0351180 + 0.0103116i
612612 −0.0873318 0.0325731i −0.00353018 0.00131669i
613613 −44.8300 9.75216i −1.81066 0.393886i −0.825348 0.564624i 0.809021π-0.809021\pi
−0.985316 + 0.170738i 0.945385π0.945385\pi
614614 3.88441 13.2291i 0.156762 0.533882i
615615 31.0917 + 17.8052i 1.25374 + 0.717975i
616616 0.572702 1.25404i 0.0230748 0.0505268i
617617 16.2881 + 21.7584i 0.655736 + 0.875961i 0.997972 0.0636532i 0.0202751π-0.0202751\pi
−0.342236 + 0.939614i 0.611184π0.611184\pi
618618 −1.30352 5.99219i −0.0524353 0.241041i
619619 −6.85826 7.91486i −0.275657 0.318125i 0.600993 0.799255i 0.294772π-0.294772\pi
−0.876650 + 0.481130i 0.840227π0.840227\pi
620620 −0.146527 1.18997i −0.00588468 0.0477903i
621621 −7.67436 23.9909i −0.307961 0.962720i
622622 7.56645 + 7.56645i 0.303387 + 0.303387i
623623 1.52446 + 0.109031i 0.0610760 + 0.00436824i
624624 −0.230369 + 0.358462i −0.00922215 + 0.0143499i
625625 8.50842 + 23.5076i 0.340337 + 0.940304i
626626 −14.5553 6.64719i −0.581747 0.265675i
627627 −23.9045 + 31.9327i −0.954653 + 1.27527i
628628 13.1042 + 23.9986i 0.522916 + 0.957649i
629629 3.56239 + 5.54318i 0.142042 + 0.221021i
630630 −0.0157311 + 0.00966471i −0.000626743 + 0.000385051i
631631 1.07019 + 3.64475i 0.0426037 + 0.145095i 0.978048 0.208379i 0.0668186π-0.0668186\pi
−0.935445 + 0.353474i 0.885000π0.885000\pi
632632 0.606571 + 8.48098i 0.0241281 + 0.337355i
633633 −0.629834 8.80623i −0.0250337 0.350016i
634634 4.37944 + 14.9150i 0.173930 + 0.592350i
635635 11.3949 47.7023i 0.452192 1.89301i
636636 2.95000 + 4.59029i 0.116975 + 0.182017i
637637 0.474835 + 0.869596i 0.0188137 + 0.0344546i
638638 −4.05195 + 5.41277i −0.160418 + 0.214294i
639639 −0.406959 0.185852i −0.0160991 0.00735220i
640640 −17.4707 18.1942i −0.690592 0.719188i
641641 −6.36323 + 9.90138i −0.251333 + 0.391081i −0.943879 0.330293i 0.892853π-0.892853\pi
0.692546 + 0.721374i 0.256489π0.256489\pi
642642 −18.8741 1.34990i −0.744900 0.0532763i
643643 12.7726 + 12.7726i 0.503701 + 0.503701i 0.912586 0.408885i 0.134082π-0.134082\pi
−0.408885 + 0.912586i 0.634082π0.634082\pi
644644 0.0359870 + 1.49911i 0.00141809 + 0.0590733i
645645 3.04212 0.374593i 0.119784 0.0147496i
646646 2.74823 + 3.17162i 0.108127 + 0.124786i
647647 −5.54103 25.4717i −0.217840 1.00140i −0.948037 0.318160i 0.896935π-0.896935\pi
0.730197 0.683237i 0.239428π-0.239428\pi
648648 −12.0285 16.0682i −0.472525 0.631220i
649649 11.3692 24.8952i 0.446282 0.977220i
650650 −0.170693 0.417824i −0.00669513 0.0163884i
651651 −0.0316920 + 0.107933i −0.00124211 + 0.00423023i
652652 −7.81966 1.70106i −0.306242 0.0666188i
653653 29.1500 + 10.8724i 1.14073 + 0.425469i 0.847617 0.530609i 0.178037π-0.178037\pi
0.293111 + 0.956079i 0.405310π0.405310\pi
654654 −7.93027 + 2.32854i −0.310098 + 0.0910530i
655655 22.9298 34.1369i 0.895941 1.33384i
656656 −10.7094 + 12.3593i −0.418131 + 0.482549i
657657 −0.394269 0.215287i −0.0153819 0.00839916i
658658 −0.275751 + 0.739316i −0.0107499 + 0.0288215i
659659 0.0162657 0.0104533i 0.000633622 0.000407204i −0.540324 0.841457i 0.681698π-0.681698\pi
0.540958 + 0.841050i 0.318062π0.318062\pi
660660 15.3483 11.0111i 0.597433 0.428606i
661661 35.4326 5.09444i 1.37817 0.198151i 0.586919 0.809646i 0.300341π-0.300341\pi
0.791248 + 0.611495i 0.209432π0.209432\pi
662662 −0.518924 + 0.193549i −0.0201686 + 0.00752249i
663663 −0.171144 + 0.128117i −0.00664667 + 0.00497564i
664664 −16.6313 10.6883i −0.645419 0.414786i
665665 −3.29707 + 0.168689i −0.127855 + 0.00654149i
666666 0.316976i 0.0122826i
667667 3.13086 16.2621i 0.121228 0.629669i
668668 9.24754 9.24754i 0.357798 0.357798i
669669 15.8920 13.7705i 0.614419 0.532397i
670670 −10.6454 5.12499i −0.411267 0.197996i
671671 4.55522 31.6823i 0.175852 1.22308i
672672 0.664466 + 1.78150i 0.0256323 + 0.0687229i
673673 −20.0631 15.0190i −0.773374 0.578940i 0.138042 0.990426i 0.455919π-0.455919\pi
−0.911416 + 0.411486i 0.865010π0.865010\pi
674674 3.92499 + 1.15248i 0.151185 + 0.0443919i
675675 −26.2483 + 0.809698i −1.01030 + 0.0311653i
676676 8.61479 + 18.8638i 0.331338 + 0.725529i
677677 −16.1282 + 29.5365i −0.619856 + 1.13518i 0.359521 + 0.933137i 0.382940π0.382940\pi
−0.979376 + 0.202044i 0.935242π0.935242\pi
678678 −9.54602 + 0.682745i −0.366613 + 0.0262207i
679679 1.92418 + 1.66731i 0.0738431 + 0.0639854i
680680 −1.77609 4.10756i −0.0681099 0.157518i
681681 −8.04279 + 3.67302i −0.308201 + 0.140750i
682682 0.139681 0.642101i 0.00534865 0.0245873i
683683 17.8768 9.76146i 0.684036 0.373512i −0.0993455 0.995053i 0.531675π-0.531675\pi
0.783382 + 0.621541i 0.213493π0.213493\pi
684684 0.114103 + 0.793606i 0.00436285 + 0.0303443i
685685 −7.75998 14.9231i −0.296494 0.570182i
686686 1.71541 + 0.246638i 0.0654946 + 0.00941670i
687687 −27.7644 + 6.03978i −1.05928 + 0.230432i
688688 −0.0998053 + 1.39546i −0.00380504 + 0.0532014i
689689 −0.283787 −0.0108114
690690 5.54502 10.2454i 0.211095 0.390034i
691691 −9.06622 −0.344895 −0.172448 0.985019i 0.555168π-0.555168\pi
−0.172448 + 0.985019i 0.555168π0.555168\pi
692692 1.97953 27.6775i 0.0752506 1.05214i
693693 0.0392689 0.00854242i 0.00149170 0.000324500i
694694 −9.00407 1.29459i −0.341790 0.0491420i
695695 −35.3566 11.1653i −1.34115 0.423523i
696696 −1.92068 13.3586i −0.0728032 0.506357i
697697 −7.20133 + 3.93222i −0.272770 + 0.148944i
698698 −3.54356 + 16.2895i −0.134126 + 0.616566i
699699 14.4782 6.61198i 0.547616 0.250088i
700700 1.51292 + 0.393995i 0.0571831 + 0.0148916i
701701 −2.88463 2.49955i −0.108951 0.0944066i 0.598682 0.800987i 0.295691π-0.295691\pi
−0.707633 + 0.706580i 0.750237π0.750237\pi
702702 0.472899 0.0338224i 0.0178484 0.00127654i
703703 27.1635 49.7462i 1.02449 1.87621i
704704 −0.130542 0.285847i −0.00491999 0.0107733i
705705 −18.7186 + 15.5665i −0.704984 + 0.586268i
706706 −8.93395 2.62324i −0.336234 0.0987271i
707707 −1.74317 1.30492i −0.0655585 0.0490765i
708708 8.47796 + 22.7303i 0.318621 + 0.854256i
709709 −0.496317 + 3.45196i −0.0186396 + 0.129641i −0.997016 0.0771888i 0.975406π-0.975406\pi
0.978377 + 0.206830i 0.0663147π0.0663147\pi
710710 −3.15160 9.00332i −0.118278 0.337889i
711711 −0.187316 + 0.162310i −0.00702488 + 0.00608710i
712712 12.6011 12.6011i 0.472244 0.472244i
713713 0.379764 + 1.56404i 0.0142223 + 0.0585736i
714714 0.186459i 0.00697805i
715715 0.0501986 + 0.981143i 0.00187732 + 0.0366927i
716716 −16.8516 10.8298i −0.629773 0.404730i
717717 −5.42009 + 4.05743i −0.202417 + 0.151528i
718718 9.07079 3.38323i 0.338519 0.126261i
719719 −1.41127 + 0.202910i −0.0526314 + 0.00756725i −0.168580 0.985688i 0.553918π-0.553918\pi
0.115949 + 0.993255i 0.463009π0.463009\pi
720720 0.0422142 0.256556i 0.00157323 0.00956128i
721721 −0.929367 + 0.597268i −0.0346114 + 0.0222434i
722722 8.40388 22.5317i 0.312760 0.838542i
723723 −9.18360 5.01462i −0.341542 0.186496i
724724 27.2372 31.4335i 1.01226 1.16822i
725725 −15.4017 7.80341i −0.572004 0.289811i
726726 −1.53213 + 0.449874i −0.0568627 + 0.0166964i
727727 6.16192 + 2.29828i 0.228533 + 0.0852384i 0.461122 0.887337i 0.347447π-0.347447\pi
−0.232589 + 0.972575i 0.574720π0.574720\pi
728728 −0.0621046 0.0135100i −0.00230175 0.000500715i
729729 7.76788 26.4550i 0.287699 0.979814i
730730 −2.51151 9.24285i −0.0929551 0.342093i
731731 −0.291588 + 0.638488i −0.0107848 + 0.0236153i
732732 17.0030 + 22.7134i 0.628451 + 0.839512i
733733 −2.58919 11.9023i −0.0956338 0.439621i −0.999919 0.0126935i 0.995959π-0.995959\pi
0.904286 0.426928i 0.140404π-0.140404\pi
734734 6.11264 + 7.05436i 0.225622 + 0.260381i
735735 21.0156 + 16.4075i 0.775171 + 0.605199i
736736 20.9815 + 17.3167i 0.773389 + 0.638302i
737737 18.1845 + 18.1845i 0.669836 + 0.669836i
738738 0.393698 + 0.0281578i 0.0144922 + 0.00103650i
739739 7.74807 12.0562i 0.285017 0.443496i −0.668993 0.743269i 0.733274π-0.733274\pi
0.954011 + 0.299773i 0.0969108π0.0969108\pi
740740 −19.3603 + 18.5905i −0.711697 + 0.683399i
741741 1.67276 + 0.763926i 0.0614506 + 0.0280635i
742742 −0.148329 + 0.198144i −0.00544533 + 0.00727410i
743743 −9.02949 16.5363i −0.331260 0.606657i 0.657967 0.753047i 0.271417π-0.271417\pi
−0.989227 + 0.146389i 0.953235π0.953235\pi
744744 0.709122 + 1.10342i 0.0259977 + 0.0404532i
745745 −14.8986 24.2502i −0.545842 0.888460i
746746 −3.26400 11.1162i −0.119504 0.406992i
747747 −0.0411121 0.574822i −0.00150421 0.0210316i
748748 0.308597 + 4.31476i 0.0112834 + 0.157763i
749749 0.960384 + 3.27077i 0.0350917 + 0.119511i
750750 −8.67843 8.49711i −0.316892 0.310270i
751751 15.9579 + 24.8310i 0.582313 + 0.906096i 0.999997 0.00249615i 0.000794549π-0.000794549\pi
−0.417684 + 0.908592i 0.637158π0.637158\pi
752752 −5.32550 9.75293i −0.194201 0.355653i
753753 −5.82212 + 7.77744i −0.212170 + 0.283426i
754754 0.283543 + 0.129490i 0.0103260 + 0.00471575i
755755 −0.0466065 + 2.29773i −0.00169619 + 0.0836229i
756756 −0.887854 + 1.38153i −0.0322909 + 0.0502457i
757757 −21.7294 1.55412i −0.789770 0.0564854i −0.329374 0.944199i 0.606838π-0.606838\pi
−0.460395 + 0.887714i 0.652292π0.652292\pi
758758 1.45322 + 1.45322i 0.0527834 + 0.0527834i
759759 −18.7598 + 17.0607i −0.680937 + 0.619263i
760760 −23.6889 + 30.3420i −0.859285 + 1.10062i
761761 −12.8439 14.8227i −0.465593 0.537323i 0.473588 0.880747i 0.342959π-0.342959\pi
−0.939180 + 0.343424i 0.888413π0.888413\pi
762762 5.06479 + 23.2825i 0.183478 + 0.843435i
763763 0.892296 + 1.19197i 0.0323033 + 0.0431521i
764764 8.25039 18.0658i 0.298488 0.653599i
765765 0.0648272 0.113202i 0.00234383 0.00409283i
766766 −4.52975 + 15.4269i −0.163667 + 0.557397i
767767 −1.23290 0.268200i −0.0445173 0.00968415i
768768 11.8085 + 4.40436i 0.426104 + 0.158929i
769769 −0.293488 + 0.0861757i −0.0105834 + 0.00310758i −0.287020 0.957925i 0.592665π-0.592665\pi
0.276437 + 0.961032i 0.410846π0.410846\pi
770770 0.711287 + 0.477772i 0.0256330 + 0.0172177i
771771 25.9456 29.9428i 0.934407 1.07836i
772772 15.9010 + 8.68263i 0.572291 + 0.312495i
773773 −7.03246 + 18.8547i −0.252940 + 0.678158i 0.746972 + 0.664856i 0.231507π0.231507\pi
−0.999912 + 0.0133021i 0.995766π0.995766\pi
774774 0.0284059 0.0182554i 0.00102103 0.000656175i
775775 1.67662 + 0.0680443i 0.0602260 + 0.00244422i
776776 29.3848 4.22490i 1.05485 0.151665i
777777 2.35950 0.880049i 0.0846467 0.0315716i
778778 6.56504 4.91453i 0.235368 0.176194i
779779 59.3739 + 38.1573i 2.12729 + 1.36713i
780780 −0.646438 0.583510i −0.0231462 0.0208930i
781781 20.7632i 0.742964i
782782 1.33437 + 2.31013i 0.0477171 + 0.0826101i
783783 12.8244 12.8244i 0.458306 0.458306i
784784 −9.19710 + 7.96933i −0.328468 + 0.284619i
785785 −36.1193 + 12.6435i −1.28915 + 0.451267i
786786 −2.84325 + 19.7752i −0.101415 + 0.705359i
787787 7.36810 + 19.7546i 0.262644 + 0.704177i 0.999601 + 0.0282370i 0.00898931π0.00898931\pi
−0.736957 + 0.675940i 0.763738π0.763738\pi
788788 −8.88159 6.64868i −0.316394 0.236849i
789789 42.9861 + 12.6219i 1.53035 + 0.449351i
790790 −5.26242 0.483819i −0.187229 0.0172135i
791791 0.716221 + 1.56830i 0.0254659 + 0.0557625i
792792 0.224568 0.411266i 0.00797969 0.0146137i
793793 −1.47187 + 0.105270i −0.0522676 + 0.00373825i
794794 −10.5726 9.16121i −0.375207 0.325119i
795795 −7.00944 + 3.03085i −0.248599 + 0.107493i
796796 −29.4423 + 13.4458i −1.04355 + 0.476575i
797797 4.78441 21.9936i 0.169472 0.779052i −0.811414 0.584471i 0.801302π-0.801302\pi
0.980887 0.194580i 0.0623345π-0.0623345\pi
798798 1.40770 0.768663i 0.0498321 0.0272104i
799799 −0.793435 5.51846i −0.0280697 0.195229i
800800 23.3762 16.0625i 0.826472 0.567895i
801801 0.514187 + 0.0739289i 0.0181679 + 0.00261215i
802802 −14.0737 + 3.06155i −0.496961 + 0.108107i
803803 −1.48728 + 20.7949i −0.0524850 + 0.733837i
804804 −22.7959 −0.803949
805805 −2.07842 0.290945i −0.0732548 0.0102545i
806806 −0.0302943 −0.00106707
807807 −2.47310 + 34.5785i −0.0870573 + 1.21722i
808808 −24.8093 + 5.39693i −0.872788 + 0.189863i
809809 −36.4611 5.24231i −1.28190 0.184310i −0.532504 0.846428i 0.678749π-0.678749\pi
−0.749400 + 0.662118i 0.769658π0.769658\pi
810810 11.0681 5.75541i 0.388894 0.202224i
811811 2.23766 + 15.5633i 0.0785750 + 0.546501i 0.990645 + 0.136466i 0.0435744π0.0435744\pi
−0.912070 + 0.410035i 0.865516π0.865516\pi
812812 −0.947645 + 0.517454i −0.0332558 + 0.0181591i
813813 −2.89203 + 13.2944i −0.101428 + 0.466256i
814814 −13.3814 + 6.11106i −0.469017 + 0.214193i
815815 4.12599 10.4123i 0.144527 0.364726i
816816 −1.98448 1.71956i −0.0694707 0.0601967i
817817 6.02242 0.430732i 0.210698 0.0150694i
818818 −3.31190 + 6.06529i −0.115798 + 0.212068i
819819 −0.000769641 0.00168528i −2.68934e−5 5.88884e-5i
820820 −21.3703 25.6977i −0.746285 0.897403i
821821 18.5294 + 5.44073i 0.646682 + 0.189883i 0.588594 0.808429i 0.299682π-0.299682\pi
0.0580876 + 0.998311i 0.481500π0.481500\pi
822822 6.54172 + 4.89707i 0.228169 + 0.170805i
823823 −5.33967 14.3162i −0.186129 0.499032i 0.810050 0.586360i 0.199440π-0.199440\pi
−0.996180 + 0.0873287i 0.972167π0.972167\pi
824824 −1.83320 + 12.7502i −0.0638625 + 0.444173i
825825 11.7185 + 23.6978i 0.407987 + 0.825051i
826826 −0.831669 + 0.720645i −0.0289375 + 0.0250745i
827827 15.0227 15.0227i 0.522391 0.522391i −0.395902 0.918293i 0.629568π-0.629568\pi
0.918293 + 0.395902i 0.129568π0.129568\pi
828828 −0.0241494 + 0.509111i −0.000839249 + 0.0176928i
829829 37.7158i 1.30992i 0.755661 + 0.654962i 0.227316π0.227316\pi
−0.755661 + 0.654962i 0.772684π0.772684\pi
830830 8.23317 9.12108i 0.285778 0.316597i
831831 −4.93159 3.16934i −0.171075 0.109943i
832832 −0.0115977 + 0.00868189i −0.000402076 + 0.000300991i
833833 −5.72072 + 2.13372i −0.198211 + 0.0739290i
834834 17.8299 2.56355i 0.617398 0.0887685i
835835 10.6694 + 14.8720i 0.369229 + 0.514666i
836836 31.3028 20.1171i 1.08263 0.695764i
837837 −0.615974 + 1.65149i −0.0212912 + 0.0570838i
838838 −17.9367 9.79420i −0.619614 0.338335i
839839 15.5246 17.9164i 0.535970 0.618543i −0.421586 0.906788i 0.638527π-0.638527\pi
0.957556 + 0.288246i 0.0930720π0.0930720\pi
840840 −1.67825 + 0.329586i −0.0579052 + 0.0113718i
841841 −16.3841 + 4.81081i −0.564969 + 0.165890i
842842 8.29918 + 3.09543i 0.286008 + 0.106676i
843843 −0.544735 0.118500i −0.0187617 0.00408135i
844844 −2.32028 + 7.90214i −0.0798672 + 0.272003i
845845 −28.0080 + 7.61046i −0.963506 + 0.261808i
846846 −0.111413 + 0.243961i −0.00383047 + 0.00838756i
847847 0.172392 + 0.230289i 0.00592346 + 0.00791281i
848848 −0.740927 3.40599i −0.0254435 0.116962i
849849 −30.0977 34.7346i −1.03295 1.19209i
850850 2.69831 0.674745i 0.0925512 0.0231436i
851851 22.9350 27.7889i 0.786203 0.952590i
852852 −13.0142 13.0142i −0.445859 0.445859i
853853 2.98919 + 0.213791i 0.102348 + 0.00732006i 0.122419 0.992478i 0.460935π-0.460935\pi
−0.0200713 + 0.999799i 0.506389π0.506389\pi
854854 −0.695811 + 1.08270i −0.0238102 + 0.0370494i
855855 −1.12188 0.0227560i −0.0383676 0.000778238i
856856 36.1554 + 16.5116i 1.23576 + 0.564355i
857857 −31.6373 + 42.2625i −1.08071 + 1.44366i −0.194193 + 0.980963i 0.562209π0.562209\pi
−0.886517 + 0.462696i 0.846882π0.846882\pi
858858 −0.228739 0.418905i −0.00780903 0.0143012i
859859 −28.8098 44.8289i −0.982977 1.52954i −0.841963 0.539535i 0.818600π-0.818600\pi
−0.141014 0.990008i 0.545036π-0.545036\pi
860860 −2.78099 0.664307i −0.0948309 0.0226527i
861861 0.883458 + 3.00878i 0.0301082 + 0.102539i
862862 0.125337 + 1.75244i 0.00426900 + 0.0596884i
863863 −3.32241 46.4534i −0.113096 1.58129i −0.664651 0.747154i 0.731420π-0.731420\pi
0.551555 0.834139i 0.314035π-0.314035\pi
864864 8.39370 + 28.5863i 0.285559 + 0.972526i
865865 37.7723 + 9.02284i 1.28430 + 0.306786i
866866 4.18063 + 6.50518i 0.142064 + 0.221055i
867867 13.3227 + 24.3987i 0.452463 + 0.828625i
868868 0.0628848 0.0840043i 0.00213445 0.00285129i
869869 10.4633 + 4.77844i 0.354944 + 0.162097i
870870 8.38639 + 0.170107i 0.284325 + 0.00576718i
871871 0.640979 0.997383i 0.0217188 0.0337950i
872872 17.3170 + 1.23853i 0.586426 + 0.0419420i
873873 0.611918 + 0.611918i 0.0207103 + 0.0207103i
874874 11.9398 19.5974i 0.403871 0.662892i
875875 −0.887881 + 1.99979i −0.0300158 + 0.0676053i
876876 −12.1019 13.9663i −0.408885 0.471879i
877877 7.42725 + 34.1425i 0.250801 + 1.15291i 0.914396 + 0.404820i 0.132666π0.132666\pi
−0.663596 + 0.748091i 0.730970π0.730970\pi
878878 −8.06300 10.7709i −0.272113 0.363500i
879879 6.19190 13.5584i 0.208848 0.457312i
880880 −11.6445 + 3.16411i −0.392538 + 0.106662i
881881 2.81610 9.59077i 0.0948769 0.323121i −0.898355 0.439271i 0.855237π-0.855237\pi
0.993232 + 0.116149i 0.0370551π0.0370551\pi
882882 0.287004 + 0.0624340i 0.00966394 + 0.00210226i
883883 19.9409 + 7.43756i 0.671064 + 0.250294i 0.661819 0.749664i 0.269785π-0.269785\pi
0.00924435 + 0.999957i 0.497057π0.497057\pi
884884 0.191348 0.0561848i 0.00643573 0.00188970i
885885 −33.3165 + 6.54291i −1.11992 + 0.219938i
886886 −9.50511 + 10.9695i −0.319331 + 0.368527i
887887 −15.3253 8.36823i −0.514572 0.280978i 0.200909 0.979610i 0.435610π-0.435610\pi
−0.715481 + 0.698632i 0.753792π0.753792\pi
888888 10.2614 27.5118i 0.344349 0.923236i
889889 3.61103 2.32067i 0.121110 0.0778327i
890890 6.45640 + 8.99955i 0.216419 + 0.301665i
891891 −26.8777 + 3.86443i −0.900436 + 0.129463i
892892 −18.3789 + 6.85499i −0.615372 + 0.229522i
893893 −38.3916 + 28.7396i −1.28473 + 0.961734i
894894 11.6322 + 7.47554i 0.389038 + 0.250019i
895895 18.7850 20.8108i 0.627913 0.695630i
896896 2.20765i 0.0737523i
897897 0.952392 + 0.677907i 0.0317994 + 0.0226346i
898898 −12.4733 + 12.4733i −0.416240 + 0.416240i
899899 −0.875820 + 0.758902i −0.0292102 + 0.0253108i
900900 0.503367 + 0.170260i 0.0167789 + 0.00567532i
901901 0.248883 1.73102i 0.00829149 0.0576686i
902902 −6.40150 17.1631i −0.213147 0.571469i
903903 0.214755 + 0.160763i 0.00714659 + 0.00534987i
904904 19.2888 + 5.66371i 0.641537 + 0.188372i
905905 37.2199 + 44.7567i 1.23723 + 1.48776i
906906 −0.463820 1.01562i −0.0154094 0.0337419i
907907 21.4410 39.2663i 0.711938 1.30382i −0.231683 0.972791i 0.574423π-0.574423\pi
0.943622 0.331026i 0.107395π-0.107395\pi
908908 8.22693 0.588402i 0.273020 0.0195268i
909909 −0.559338 0.484669i −0.0185521 0.0160755i
910910 0.0145524 0.0367242i 0.000482408 0.00121740i
911911 −22.6399 + 10.3393i −0.750095 + 0.342557i −0.753509 0.657437i 0.771640π-0.771640\pi
0.00341443 + 0.999994i 0.498913π0.498913\pi
912912 −4.80123 + 22.0709i −0.158985 + 0.730841i
913913 −23.4739 + 12.8177i −0.776872 + 0.424204i
914914 −3.64184 25.3296i −0.120461 0.837827i
915915 −35.2304 + 18.3197i −1.16468 + 0.605632i
916916 26.2355 + 3.77210i 0.866847 + 0.124634i
917917 3.51689 0.765053i 0.116138 0.0252643i
918918 −0.208429 + 2.91421i −0.00687917 + 0.0961834i
919919 −24.9235 −0.822150 −0.411075 0.911602i 0.634847π-0.634847\pi
−0.411075 + 0.911602i 0.634847π0.634847\pi
920920 −18.4340 + 16.0936i −0.607752 + 0.530591i
921921 37.2311 1.22681
922922 −0.440932 + 6.16504i −0.0145213 + 0.203035i
923923 0.935343 0.203471i 0.0307872 0.00669734i
924924 1.63641 + 0.235281i 0.0538340 + 0.00774016i
925925 −21.2739 30.9604i −0.699481 1.01797i
926926 0.865711 + 6.02115i 0.0284490 + 0.197867i
927927 −0.329562 + 0.179955i −0.0108242 + 0.00591048i
928928 −4.16376 + 19.1405i −0.136682 + 0.628318i
929929 −0.933878 + 0.426488i −0.0306395 + 0.0139926i −0.430676 0.902507i 0.641725π-0.641725\pi
0.400036 + 0.916499i 0.368998π0.368998\pi
930930 −0.748260 + 0.323544i −0.0245364 + 0.0106094i
931931 39.6921 + 34.3934i 1.30086 + 1.12720i
932932 −14.8097 + 1.05921i −0.485107 + 0.0346956i
933933 −13.8480 + 25.3607i −0.453363 + 0.830273i
934934 −1.71051 3.74550i −0.0559697 0.122557i
935935 −6.02872 0.554272i −0.197160 0.0181266i
936936 −0.0207275 0.00608614i −0.000677500 0.000198932i
937937 7.34182 + 5.49602i 0.239847 + 0.179547i 0.712439 0.701734i 0.247591π-0.247591\pi
−0.472592 + 0.881281i 0.656682π0.656682\pi
938938 −0.361363 0.968851i −0.0117989 0.0316341i
939939 6.14929 42.7692i 0.200674 1.39572i
940940 21.4350 7.50329i 0.699132 0.244730i
941941 −11.2095 + 9.71311i −0.365420 + 0.316638i −0.818145 0.575012i 0.804997π-0.804997\pi
0.452725 + 0.891650i 0.350452π0.350452\pi
942942 13.1463 13.1463i 0.428330 0.428330i
943943 32.4776 + 30.9549i 1.05762 + 1.00803i
944944 15.4974i 0.504397i
945945 −1.70612 1.54003i −0.0555000 0.0500973i
946946 −1.31831 0.847224i −0.0428618 0.0275456i
947947 3.87889 2.90370i 0.126047 0.0943577i −0.534394 0.845235i 0.679460π-0.679460\pi
0.660441 + 0.750878i 0.270369π0.270369\pi
948948 −9.55344 + 3.56325i −0.310281 + 0.115729i
949949 0.951349 0.136783i 0.0308821 0.00444017i
950950 −16.2177 17.5897i −0.526171 0.570686i
951951 −35.3124 + 22.6939i −1.14508 + 0.735900i
952952 0.136874 0.366972i 0.00443610 0.0118936i
953953 −22.1425 12.0907i −0.717267 0.391658i 0.0787799 0.996892i 0.474898π-0.474898\pi
−0.796047 + 0.605234i 0.793079π0.793079\pi
954954 −0.0550919 + 0.0635795i −0.00178367 + 0.00205846i
955955 23.0738 + 15.4987i 0.746652 + 0.501527i
956956 6.05996 1.77936i 0.195993 0.0575487i
957957 −17.1069 6.38054i −0.552987 0.206254i
958958 7.29605 + 1.58716i 0.235725 + 0.0512788i
959959 0.414744 1.41249i 0.0133928 0.0456116i
960960 −0.193735 + 0.338303i −0.00625278 + 0.0109187i
961961 −12.8311 + 28.0961i −0.413906 + 0.906327i
962962 0.406425 + 0.542920i 0.0131037 + 0.0175045i
963963 0.246287 + 1.13216i 0.00793649 + 0.0364834i
964964 6.39191 + 7.37666i 0.205870 + 0.237586i
965965 −15.6037 + 19.9861i −0.502302 + 0.643375i
966966 0.971119 0.310648i 0.0312452 0.00999494i
967967 −31.6406 31.6406i −1.01749 1.01749i −0.999844 0.0176482i 0.994382π-0.994382\pi
−0.0176482 0.999844i 0.505618π-0.505618\pi
968968 3.34565 + 0.239285i 0.107533 + 0.00769092i
969969 −6.12676 + 9.53343i −0.196820 + 0.306258i
970970 −0.374183 + 18.4474i −0.0120143 + 0.592312i
971971 3.89604 + 1.77926i 0.125030 + 0.0570993i 0.476948 0.878932i 0.341743π-0.341743\pi
−0.351918 + 0.936031i 0.614470π0.614470\pi
972972 −0.661753 + 0.883999i −0.0212257 + 0.0283543i
973973 −1.55520 2.84814i −0.0498575 0.0913073i
974974 −5.48819 8.53979i −0.175853 0.273633i
975975 0.952706 0.760128i 0.0305110 0.0243436i
976976 −5.10629 17.3904i −0.163448 0.556654i
977977 −0.917337 12.8260i −0.0293482 0.410342i −0.990797 0.135357i 0.956782π-0.956782\pi
0.961449 0.274984i 0.0886727π-0.0886727\pi
978978 0.388172 + 5.42736i 0.0124124 + 0.173548i
979979 −6.79218 23.1320i −0.217079 0.739303i
980980 −13.0193 21.1914i −0.415887 0.676933i
981981 0.273609 + 0.425744i 0.00873567 + 0.0135930i
982982 −1.56189 2.86040i −0.0498420 0.0912789i
983983 −3.07935 + 4.11353i −0.0982159 + 0.131201i −0.846957 0.531662i 0.821568π-0.821568\pi
0.748741 + 0.662863i 0.230659π0.230659\pi
984984 33.2593 + 15.1890i 1.06027 + 0.484209i
985985 11.1999 10.7545i 0.356857 0.342668i
986986 −1.03852 + 1.61597i −0.0330733 + 0.0514630i
987987 −2.12532 0.152006i −0.0676497 0.00483840i
988988 −1.21299 1.21299i −0.0385905 0.0385905i
989989 3.81118 + 0.454906i 0.121189 + 0.0144652i
990990 0.229560 + 0.179224i 0.00729590 + 0.00569612i
991991 2.02548 + 2.33753i 0.0643416 + 0.0742541i 0.787008 0.616943i 0.211629π-0.211629\pi
−0.722666 + 0.691197i 0.757084π0.757084\pi
992992 −0.404663 1.86021i −0.0128481 0.0590616i
993993 −0.896261 1.19726i −0.0284420 0.0379940i
994994 0.346816 0.759421i 0.0110003 0.0240874i
995995 −11.8783 43.7145i −0.376568 1.38584i
996996 6.67922 22.7473i 0.211639 0.720777i
997997 35.3791 + 7.69626i 1.12047 + 0.243743i 0.734393 0.678724i 0.237467π-0.237467\pi
0.386075 + 0.922467i 0.373830π0.373830\pi
998998 −20.2441 7.55066i −0.640816 0.239012i
999999 37.8610 11.1170i 1.19787 0.351726i
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 115.2.l.a.102.4 yes 200
5.2 odd 4 575.2.r.b.493.4 200
5.3 odd 4 inner 115.2.l.a.33.7 yes 200
5.4 even 2 575.2.r.b.332.7 200
23.7 odd 22 inner 115.2.l.a.7.7 200
115.7 even 44 575.2.r.b.168.7 200
115.53 even 44 inner 115.2.l.a.53.4 yes 200
115.99 odd 22 575.2.r.b.7.4 200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.2.l.a.7.7 200 23.7 odd 22 inner
115.2.l.a.33.7 yes 200 5.3 odd 4 inner
115.2.l.a.53.4 yes 200 115.53 even 44 inner
115.2.l.a.102.4 yes 200 1.1 even 1 trivial
575.2.r.b.7.4 200 115.99 odd 22
575.2.r.b.168.7 200 115.7 even 44
575.2.r.b.332.7 200 5.4 even 2
575.2.r.b.493.4 200 5.2 odd 4