Properties

Label 529.2.c.o.170.1
Level 529529
Weight 22
Character 529.170
Analytic conductor 4.2244.224
Analytic rank 00
Dimension 2020
Inner twists 1010

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [529,2,Mod(118,529)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(529, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("529.118");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 529=232 529 = 23^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 529.c (of order 1111, degree 1010, not 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: 4.224086266934.22408626693
Analytic rank: 00
Dimension: 2020
Relative dimension: 22 over Q(ζ11)\Q(\zeta_{11})
Coefficient field: 20.0.54296067514572573056640625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20x19+2x183x17+5x168x15+13x1421x13+34x12++1 x^{20} - x^{19} + 2 x^{18} - 3 x^{17} + 5 x^{16} - 8 x^{15} + 13 x^{14} - 21 x^{13} + 34 x^{12} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 23)
Sato-Tate group: SU(2)[C11]\mathrm{SU}(2)[C_{11}]

Embedding invariants

Embedding label 170.1
Root 0.256741+0.562183i0.256741 + 0.562183i of defining polynomial
Character χ\chi == 529.170
Dual form 529.2.c.o.501.1

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+(0.592999+0.174120i)q2+(1.46431+1.68991i)q3+(1.36118+0.874775i)q4+(0.1759111.22349i)q5+(1.162580.747147i)q6+(1.344312.94363i)q7+(1.464311.68991i)q8+(0.284630+1.97964i)q9+(0.317349+0.694897i)q10+(5.02397+1.47517i)q11+(3.471481.01932i)q12+(1.24625+2.72890i)q13+(0.284630+1.97964i)q14+(1.809992.08884i)q15+(0.7702221.68655i)q16+(0.642661+0.413013i)q17+(0.1759111.22349i)q18+(1.68251+1.08128i)q19+(1.30972+1.51150i)q20+(6.942962.03864i)q213.23607q22+5.00000q24+(3.331490.978214i)q25+(1.214181.40124i)q26+(1.881101.20891i)q27+(0.745170+5.18277i)q28+(2.523761.62192i)q29+(0.709614+1.55384i)q30+(4.39294+5.06972i)q31+(0.799530+5.56085i)q32+(4.86376+10.6502i)q33+(0.4530110.133016i)q34+(3.837971.12693i)q35+(1.344312.94363i)q36+(0.1759111.22349i)q37+(0.8094520.934158i)q38+(2.78669+6.10200i)q39+(2.325171.49429i)q40+(0.494136+3.43679i)q41+(3.76220+2.41782i)q42+(8.12895+2.38688i)q44+2.47214q452.23607q47+(3.977961.16803i)q48+(2.273772.62407i)q49+(1.80524+1.16016i)q50+(0.243103+1.69082i)q51+(4.083532.62433i)q52+(0.1961320.429470i)q53+(0.904995+1.04442i)q54+(0.9210816.40626i)q55+(3.005976.58216i)q56+(4.290981.25995i)q57+(1.77900+0.522361i)q58+(2.68862+5.88726i)q59+(0.636451+4.42662i)q60+(4.547535.24813i)q61+(1.722273.77124i)q62+(5.44471+3.49910i)q63+(0.0335960+0.233665i)q64+(3.119542.00481i)q65+(4.738625.46866i)q66+(2.651970.778690i)q671.23607q68+2.47214q70+(11.7404+3.44730i)q71+(2.92863+3.37981i)q72+(5.491593.52923i)q73+(0.108719+0.756156i)q74+(6.53144+4.19750i)q75+(1.344312.94363i)q76+(11.096112.8056i)q77+(0.5900234.10370i)q78+(4.546419.95526i)q79+(2.198960.645674i)q80+(10.5544+3.09906i)q81+(0.8914381.95198i)q82+(1.247248.67473i)q83+(7.66724+8.84847i)q84+(0.3922650.858940i)q85+(0.9546776.63992i)q87+(9.849576.32993i)q88+(6.85779+7.91431i)q89+(1.46597+0.430449i)q90+9.70820q9115.0000q93+(1.325990.389345i)q94+(1.61890+1.86832i)q95+(10.5681+6.79170i)q96+(2.5201417.5280i)q97+(1.80524+1.16016i)q98+(4.35028+9.52579i)q99+O(q100)q+(-0.592999 + 0.174120i) q^{2} +(1.46431 + 1.68991i) q^{3} +(-1.36118 + 0.874775i) q^{4} +(-0.175911 - 1.22349i) q^{5} +(-1.16258 - 0.747147i) q^{6} +(1.34431 - 2.94363i) q^{7} +(1.46431 - 1.68991i) q^{8} +(-0.284630 + 1.97964i) q^{9} +(0.317349 + 0.694897i) q^{10} +(5.02397 + 1.47517i) q^{11} +(-3.47148 - 1.01932i) q^{12} +(1.24625 + 2.72890i) q^{13} +(-0.284630 + 1.97964i) q^{14} +(1.80999 - 2.08884i) q^{15} +(0.770222 - 1.68655i) q^{16} +(0.642661 + 0.413013i) q^{17} +(-0.175911 - 1.22349i) q^{18} +(-1.68251 + 1.08128i) q^{19} +(1.30972 + 1.51150i) q^{20} +(6.94296 - 2.03864i) q^{21} -3.23607 q^{22} +5.00000 q^{24} +(3.33149 - 0.978214i) q^{25} +(-1.21418 - 1.40124i) q^{26} +(1.88110 - 1.20891i) q^{27} +(0.745170 + 5.18277i) q^{28} +(-2.52376 - 1.62192i) q^{29} +(-0.709614 + 1.55384i) q^{30} +(-4.39294 + 5.06972i) q^{31} +(-0.799530 + 5.56085i) q^{32} +(4.86376 + 10.6502i) q^{33} +(-0.453011 - 0.133016i) q^{34} +(-3.83797 - 1.12693i) q^{35} +(-1.34431 - 2.94363i) q^{36} +(0.175911 - 1.22349i) q^{37} +(0.809452 - 0.934158i) q^{38} +(-2.78669 + 6.10200i) q^{39} +(-2.32517 - 1.49429i) q^{40} +(0.494136 + 3.43679i) q^{41} +(-3.76220 + 2.41782i) q^{42} +(-8.12895 + 2.38688i) q^{44} +2.47214 q^{45} -2.23607 q^{47} +(3.97796 - 1.16803i) q^{48} +(-2.27377 - 2.62407i) q^{49} +(-1.80524 + 1.16016i) q^{50} +(0.243103 + 1.69082i) q^{51} +(-4.08353 - 2.62433i) q^{52} +(0.196132 - 0.429470i) q^{53} +(-0.904995 + 1.04442i) q^{54} +(0.921081 - 6.40626i) q^{55} +(-3.00597 - 6.58216i) q^{56} +(-4.29098 - 1.25995i) q^{57} +(1.77900 + 0.522361i) q^{58} +(2.68862 + 5.88726i) q^{59} +(-0.636451 + 4.42662i) q^{60} +(4.54753 - 5.24813i) q^{61} +(1.72227 - 3.77124i) q^{62} +(5.44471 + 3.49910i) q^{63} +(0.0335960 + 0.233665i) q^{64} +(3.11954 - 2.00481i) q^{65} +(-4.73862 - 5.46866i) q^{66} +(2.65197 - 0.778690i) q^{67} -1.23607 q^{68} +2.47214 q^{70} +(-11.7404 + 3.44730i) q^{71} +(2.92863 + 3.37981i) q^{72} +(5.49159 - 3.52923i) q^{73} +(0.108719 + 0.756156i) q^{74} +(6.53144 + 4.19750i) q^{75} +(1.34431 - 2.94363i) q^{76} +(11.0961 - 12.8056i) q^{77} +(0.590023 - 4.10370i) q^{78} +(-4.54641 - 9.95526i) q^{79} +(-2.19896 - 0.645674i) q^{80} +(10.5544 + 3.09906i) q^{81} +(-0.891438 - 1.95198i) q^{82} +(1.24724 - 8.67473i) q^{83} +(-7.66724 + 8.84847i) q^{84} +(0.392265 - 0.858940i) q^{85} +(-0.954677 - 6.63992i) q^{87} +(9.84957 - 6.32993i) q^{88} +(6.85779 + 7.91431i) q^{89} +(-1.46597 + 0.430449i) q^{90} +9.70820 q^{91} -15.0000 q^{93} +(1.32599 - 0.389345i) q^{94} +(1.61890 + 1.86832i) q^{95} +(-10.5681 + 6.79170i) q^{96} +(-2.52014 - 17.5280i) q^{97} +(1.80524 + 1.16016i) q^{98} +(-4.35028 + 9.52579i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+q2+q4+2q5+5q62q74q96q10+6q115q126q134q14+10q15+3q166q17+2q18+4q19+4q20+10q2120q22++12q99+O(q100) 20 q + q^{2} + q^{4} + 2 q^{5} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{11} - 5 q^{12} - 6 q^{13} - 4 q^{14} + 10 q^{15} + 3 q^{16} - 6 q^{17} + 2 q^{18} + 4 q^{19} + 4 q^{20} + 10 q^{21} - 20 q^{22}+ \cdots + 12 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/529Z)×\left(\mathbb{Z}/529\mathbb{Z}\right)^\times.

nn 55
χ(n)\chi(n) e(511)e\left(\frac{5}{11}\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 −0.592999 + 0.174120i −0.419314 + 0.123122i −0.484581 0.874746i 0.661028π-0.661028\pi
0.0652676 + 0.997868i 0.479210π0.479210\pi
33 1.46431 + 1.68991i 0.845422 + 0.975669i 0.999924 0.0123239i 0.00392292π-0.00392292\pi
−0.154502 + 0.987992i 0.549377π0.549377\pi
44 −1.36118 + 0.874775i −0.680588 + 0.437388i
55 −0.175911 1.22349i −0.0786697 0.547160i −0.990597 0.136809i 0.956315π-0.956315\pi
0.911928 0.410351i 0.134594π-0.134594\pi
66 −1.16258 0.747147i −0.474623 0.305022i
77 1.34431 2.94363i 0.508102 1.11259i −0.465649 0.884970i 0.654179π-0.654179\pi
0.973750 0.227618i 0.0730938π-0.0730938\pi
88 1.46431 1.68991i 0.517713 0.597472i
99 −0.284630 + 1.97964i −0.0948766 + 0.659881i
1010 0.317349 + 0.694897i 0.100355 + 0.219746i
1111 5.02397 + 1.47517i 1.51478 + 0.444781i 0.930354 0.366663i 0.119500π-0.119500\pi
0.584430 + 0.811444i 0.301318π0.301318\pi
1212 −3.47148 1.01932i −1.00213 0.294252i
1313 1.24625 + 2.72890i 0.345646 + 0.756860i 1.00000 0.000670851i 0.000213539π0.000213539\pi
−0.654354 + 0.756189i 0.727059π0.727059\pi
1414 −0.284630 + 1.97964i −0.0760705 + 0.529082i
1515 1.80999 2.08884i 0.467338 0.539336i
1616 0.770222 1.68655i 0.192555 0.421638i
1717 0.642661 + 0.413013i 0.155868 + 0.100170i 0.616250 0.787551i 0.288651π-0.288651\pi
−0.460382 + 0.887721i 0.652287π0.652287\pi
1818 −0.175911 1.22349i −0.0414626 0.288379i
1919 −1.68251 + 1.08128i −0.385994 + 0.248063i −0.719218 0.694785i 0.755500π-0.755500\pi
0.333224 + 0.942848i 0.391863π0.391863\pi
2020 1.30972 + 1.51150i 0.292863 + 0.337981i
2121 6.94296 2.03864i 1.51508 0.444867i
2222 −3.23607 −0.689932
2323 0 0
2424 5.00000 1.02062
2525 3.33149 0.978214i 0.666298 0.195643i
2626 −1.21418 1.40124i −0.238120 0.274805i
2727 1.88110 1.20891i 0.362018 0.232655i
2828 0.745170 + 5.18277i 0.140824 + 0.979452i
2929 −2.52376 1.62192i −0.468651 0.301183i 0.284919 0.958552i 0.408033π-0.408033\pi
−0.753570 + 0.657368i 0.771670π0.771670\pi
3030 −0.709614 + 1.55384i −0.129557 + 0.283691i
3131 −4.39294 + 5.06972i −0.788995 + 0.910549i −0.997724 0.0674245i 0.978522π-0.978522\pi
0.208729 + 0.977973i 0.433067π0.433067\pi
3232 −0.799530 + 5.56085i −0.141338 + 0.983029i
3333 4.86376 + 10.6502i 0.846673 + 1.85395i
3434 −0.453011 0.133016i −0.0776908 0.0228121i
3535 −3.83797 1.12693i −0.648736 0.190486i
3636 −1.34431 2.94363i −0.224052 0.490605i
3737 0.175911 1.22349i 0.0289196 0.201140i −0.970239 0.242148i 0.922148π-0.922148\pi
0.999159 + 0.0410084i 0.0130570π0.0130570\pi
3838 0.809452 0.934158i 0.131311 0.151540i
3939 −2.78669 + 6.10200i −0.446227 + 0.977102i
4040 −2.32517 1.49429i −0.367641 0.236269i
4141 0.494136 + 3.43679i 0.0771712 + 0.536737i 0.991331 + 0.131384i 0.0419422π0.0419422\pi
−0.914160 + 0.405353i 0.867149π0.867149\pi
4242 −3.76220 + 2.41782i −0.580520 + 0.373078i
4343 0 0 0.755750 0.654861i 0.227273π-0.227273\pi
−0.755750 + 0.654861i 0.772727π0.772727\pi
4444 −8.12895 + 2.38688i −1.22549 + 0.359835i
4545 2.47214 0.368524
4646 0 0
4747 −2.23607 −0.326164 −0.163082 0.986613i 0.552144π-0.552144\pi
−0.163082 + 0.986613i 0.552144π0.552144\pi
4848 3.97796 1.16803i 0.574169 0.168591i
4949 −2.27377 2.62407i −0.324824 0.374866i
5050 −1.80524 + 1.16016i −0.255300 + 0.164071i
5151 0.243103 + 1.69082i 0.0340412 + 0.236762i
5252 −4.08353 2.62433i −0.566284 0.363928i
5353 0.196132 0.429470i 0.0269409 0.0589922i −0.895683 0.444693i 0.853313π-0.853313\pi
0.922624 + 0.385700i 0.126040π0.126040\pi
5454 −0.904995 + 1.04442i −0.123154 + 0.142128i
5555 0.921081 6.40626i 0.124199 0.863820i
5656 −3.00597 6.58216i −0.401690 0.879578i
5757 −4.29098 1.25995i −0.568355 0.166884i
5858 1.77900 + 0.522361i 0.233594 + 0.0685893i
5959 2.68862 + 5.88726i 0.350029 + 0.766456i 0.999979 + 0.00647940i 0.00206247π0.00206247\pi
−0.649950 + 0.759977i 0.725210π0.725210\pi
6060 −0.636451 + 4.42662i −0.0821655 + 0.571474i
6161 4.54753 5.24813i 0.582252 0.671954i −0.385836 0.922568i 0.626087π-0.626087\pi
0.968087 + 0.250613i 0.0806323π0.0806323\pi
6262 1.72227 3.77124i 0.218728 0.478948i
6363 5.44471 + 3.49910i 0.685969 + 0.440845i
6464 0.0335960 + 0.233665i 0.00419950 + 0.0292081i
6565 3.11954 2.00481i 0.386931 0.248666i
6666 −4.73862 5.46866i −0.583283 0.673145i
6767 2.65197 0.778690i 0.323990 0.0951321i −0.115693 0.993285i 0.536909π-0.536909\pi
0.439683 + 0.898153i 0.355091π0.355091\pi
6868 −1.23607 −0.149895
6969 0 0
7070 2.47214 0.295477
7171 −11.7404 + 3.44730i −1.39333 + 0.409119i −0.890389 0.455201i 0.849568π-0.849568\pi
−0.502943 + 0.864320i 0.667749π0.667749\pi
7272 2.92863 + 3.37981i 0.345142 + 0.398315i
7373 5.49159 3.52923i 0.642742 0.413065i −0.178266 0.983982i 0.557049π-0.557049\pi
0.821008 + 0.570917i 0.193412π0.193412\pi
7474 0.108719 + 0.756156i 0.0126383 + 0.0879014i
7575 6.53144 + 4.19750i 0.754185 + 0.484685i
7676 1.34431 2.94363i 0.154203 0.337658i
7777 11.0961 12.8056i 1.26452 1.45934i
7878 0.590023 4.10370i 0.0668069 0.464652i
7979 −4.54641 9.95526i −0.511512 1.12005i −0.972554 0.232676i 0.925252π-0.925252\pi
0.461043 0.887378i 0.347476π-0.347476\pi
8080 −2.19896 0.645674i −0.245851 0.0721885i
8181 10.5544 + 3.09906i 1.17271 + 0.344340i
8282 −0.891438 1.95198i −0.0984429 0.215560i
8383 1.24724 8.67473i 0.136902 0.952175i −0.799355 0.600859i 0.794825π-0.794825\pi
0.936257 0.351316i 0.114266π-0.114266\pi
8484 −7.66724 + 8.84847i −0.836565 + 0.965447i
8585 0.392265 0.858940i 0.0425471 0.0931651i
8686 0 0
8787 −0.954677 6.63992i −0.102352 0.711875i
8888 9.84957 6.32993i 1.04997 0.674773i
8989 6.85779 + 7.91431i 0.726924 + 0.838915i 0.992122 0.125279i 0.0399825π-0.0399825\pi
−0.265197 + 0.964194i 0.585437π0.585437\pi
9090 −1.46597 + 0.430449i −0.154527 + 0.0453733i
9191 9.70820 1.01770
9292 0 0
9393 −15.0000 −1.55543
9494 1.32599 0.389345i 0.136765 0.0401579i
9595 1.61890 + 1.86832i 0.166096 + 0.191685i
9696 −10.5681 + 6.79170i −1.07860 + 0.693175i
9797 −2.52014 17.5280i −0.255881 1.77969i −0.561436 0.827520i 0.689751π-0.689751\pi
0.305555 0.952175i 0.401158π-0.401158\pi
9898 1.80524 + 1.16016i 0.182357 + 0.117194i
9999 −4.35028 + 9.52579i −0.437220 + 0.957378i
100100 −3.67903 + 4.24583i −0.367903 + 0.424583i
101101 −0.636451 + 4.42662i −0.0633293 + 0.440465i 0.933345 + 0.358980i 0.116875π0.116875\pi
−0.996675 + 0.0814849i 0.974034π0.974034\pi
102102 −0.438565 0.960324i −0.0434244 0.0950862i
103103 4.01101 + 1.17774i 0.395216 + 0.116046i 0.473301 0.880901i 0.343062π-0.343062\pi
−0.0780848 + 0.996947i 0.524880π0.524880\pi
104104 6.43647 + 1.88992i 0.631148 + 0.185322i
105105 −3.71558 8.13600i −0.362604 0.793992i
106106 −0.0415269 + 0.288826i −0.00403345 + 0.0280533i
107107 −8.78588 + 10.1394i −0.849363 + 0.980217i −0.999965 0.00837738i 0.997333π-0.997333\pi
0.150602 + 0.988594i 0.451879π0.451879\pi
108108 −1.50299 + 3.29108i −0.144625 + 0.316684i
109109 0 0 0.540641 0.841254i 0.318182π-0.318182\pi
−0.540641 + 0.841254i 0.681818π0.681818\pi
110110 0.569259 + 3.95929i 0.0542767 + 0.377503i
111111 2.32517 1.49429i 0.220695 0.141832i
112112 −3.92916 4.53450i −0.371271 0.428470i
113113 −8.40893 + 2.46908i −0.791046 + 0.232272i −0.652205 0.758043i 0.726156π-0.726156\pi
−0.138841 + 0.990315i 0.544338π0.544338\pi
114114 2.76393 0.258866
115115 0 0
116116 4.85410 0.450692
117117 −5.75696 + 1.69040i −0.532231 + 0.156277i
118118 −2.61944 3.02300i −0.241139 0.278290i
119119 2.07969 1.33654i 0.190645 0.122520i
120120 −0.879554 6.11743i −0.0802919 0.558443i
121121 13.8104 + 8.87538i 1.25549 + 0.806853i
122122 −1.78288 + 3.90396i −0.161414 + 0.353447i
123123 −5.08429 + 5.86759i −0.458435 + 0.529063i
124124 1.54470 10.7436i 0.138718 0.964806i
125125 −4.35028 9.52579i −0.389101 0.852013i
126126 −3.83797 1.12693i −0.341914 0.100395i
127127 6.99643 + 2.05434i 0.620833 + 0.182293i 0.576998 0.816746i 0.304224π-0.304224\pi
0.0438350 + 0.999039i 0.486042π0.486042\pi
128128 −4.72824 10.3534i −0.417921 0.915120i
129129 0 0
130130 −1.50081 + 1.73202i −0.131630 + 0.151909i
131131 7.77167 17.0176i 0.679014 1.48683i −0.184671 0.982800i 0.559122π-0.559122\pi
0.863685 0.504033i 0.168151π-0.168151\pi
132132 −15.9369 10.2420i −1.38713 0.891456i
133133 0.921081 + 6.40626i 0.0798679 + 0.555493i
134134 −1.43703 + 0.923525i −0.124141 + 0.0797804i
135135 −1.80999 2.08884i −0.155779 0.179779i
136136 1.63901 0.481257i 0.140544 0.0412674i
137137 −21.8885 −1.87006 −0.935032 0.354563i 0.884630π-0.884630\pi
−0.935032 + 0.354563i 0.884630π0.884630\pi
138138 0 0
139139 −10.7082 −0.908258 −0.454129 0.890936i 0.650049π-0.650049\pi
−0.454129 + 0.890936i 0.650049π0.650049\pi
140140 6.20997 1.82341i 0.524838 0.154106i
141141 −3.27430 3.77875i −0.275746 0.318228i
142142 6.36182 4.08849i 0.533872 0.343099i
143143 2.23551 + 15.5483i 0.186943 + 1.30022i
144144 3.11954 + 2.00481i 0.259962 + 0.167067i
145145 −1.54044 + 3.37310i −0.127927 + 0.280121i
146146 −2.64200 + 3.04903i −0.218653 + 0.252339i
147147 1.10492 7.68491i 0.0911325 0.633840i
148148 0.830830 + 1.81926i 0.0682938 + 0.149543i
149149 −22.9209 6.73018i −1.87775 0.551358i −0.996965 0.0778452i 0.975196π-0.975196\pi
−0.880787 0.473513i 0.842986π-0.842986\pi
150150 −4.60401 1.35186i −0.375916 0.110379i
151151 1.75973 + 3.85326i 0.143204 + 0.313574i 0.967620 0.252411i 0.0812234π-0.0812234\pi
−0.824416 + 0.565985i 0.808496π0.808496\pi
152152 −0.636451 + 4.42662i −0.0516230 + 0.359046i
153153 −1.00054 + 1.15468i −0.0808887 + 0.0933506i
154154 −4.35028 + 9.52579i −0.350556 + 0.767610i
155155 6.97550 + 4.48288i 0.560286 + 0.360074i
156156 −1.54470 10.7436i −0.123675 0.860178i
157157 −9.60409 + 6.17218i −0.766490 + 0.492593i −0.864525 0.502590i 0.832381π-0.832381\pi
0.0980350 + 0.995183i 0.468744π0.468744\pi
158158 4.42943 + 5.11184i 0.352387 + 0.406676i
159159 1.01296 0.297433i 0.0803332 0.0235880i
160160 6.94427 0.548993
161161 0 0
162162 −6.79837 −0.534131
163163 5.53045 1.62389i 0.433178 0.127193i −0.0578716 0.998324i 0.518431π-0.518431\pi
0.491050 + 0.871131i 0.336613π0.336613\pi
164164 −3.67903 4.24583i −0.287284 0.331543i
165165 12.1747 7.82423i 0.947802 0.609115i
166166 0.770835 + 5.36128i 0.0598284 + 0.416116i
167167 1.28532 + 0.826026i 0.0994611 + 0.0639198i 0.589426 0.807822i 0.299354π-0.299354\pi
−0.489965 + 0.871742i 0.662990π0.662990\pi
168168 6.72156 14.7182i 0.518579 1.13553i
169169 2.61944 3.02300i 0.201496 0.232538i
170170 −0.0830538 + 0.577652i −0.00636994 + 0.0443039i
171171 −1.66166 3.63853i −0.127070 0.278245i
172172 0 0
173173 −22.0149 6.46415i −1.67376 0.491460i −0.699076 0.715048i 0.746405π-0.746405\pi
−0.974684 + 0.223588i 0.928223π0.928223\pi
174174 1.72227 + 3.77124i 0.130565 + 0.285897i
175175 1.59906 11.1217i 0.120878 0.840722i
176176 6.35752 7.33697i 0.479216 0.553045i
177177 −6.01194 + 13.1643i −0.451885 + 0.989491i
178178 −5.44471 3.49910i −0.408098 0.262269i
179179 −0.100788 0.700995i −0.00753324 0.0523949i 0.985708 0.168462i 0.0538802π-0.0538802\pi
−0.993241 + 0.116068i 0.962971π0.962971\pi
180180 −3.36501 + 2.16256i −0.250813 + 0.161188i
181181 −10.9051 12.5851i −0.810566 0.935443i 0.188345 0.982103i 0.439688π-0.439688\pi
−0.998911 + 0.0466598i 0.985142π0.985142\pi
182182 −5.75696 + 1.69040i −0.426734 + 0.125300i
183183 15.5279 1.14785
184184 0 0
185185 −1.52786 −0.112331
186186 8.89499 2.61180i 0.652212 0.191507i
187187 2.61944 + 3.02300i 0.191553 + 0.221064i
188188 3.04368 1.95606i 0.221983 0.142660i
189189 −1.02980 7.16242i −0.0749069 0.520989i
190190 −1.28532 0.826026i −0.0932470 0.0599262i
191191 −10.8757 + 23.8145i −0.786938 + 1.72315i −0.101725 + 0.994813i 0.532436π0.532436\pi
−0.685213 + 0.728342i 0.740291π0.740291\pi
192192 −0.345677 + 0.398933i −0.0249471 + 0.0287905i
193193 −1.41522 + 9.84305i −0.101870 + 0.708518i 0.873320 + 0.487147i 0.161962π0.161962\pi
−0.975190 + 0.221371i 0.928947π0.928947\pi
194194 4.54641 + 9.95526i 0.326414 + 0.714746i
195195 7.95592 + 2.33607i 0.569735 + 0.167289i
196196 5.39046 + 1.58278i 0.385033 + 0.113056i
197197 −0.611547 1.33910i −0.0435709 0.0954071i 0.886595 0.462547i 0.153064π-0.153064\pi
−0.930166 + 0.367140i 0.880337π0.880337\pi
198198 0.921081 6.40626i 0.0654584 0.455273i
199199 8.04941 9.28952i 0.570608 0.658517i −0.394951 0.918702i 0.629238π-0.629238\pi
0.965559 + 0.260186i 0.0837838π0.0837838\pi
200200 3.22525 7.06232i 0.228060 0.499382i
201201 5.19923 + 3.34134i 0.366726 + 0.235680i
202202 −0.393349 2.73580i −0.0276759 0.192490i
203203 −8.16706 + 5.24865i −0.573215 + 0.368383i
204204 −1.80999 2.08884i −0.126725 0.146248i
205205 4.11795 1.20914i 0.287610 0.0844499i
206206 −2.58359 −0.180007
207207 0 0
208208 5.56231 0.385677
209209 −10.0479 + 2.95034i −0.695031 + 0.204079i
210210 3.61998 + 4.17768i 0.249802 + 0.288287i
211211 −19.6991 + 12.6599i −1.35614 + 0.871541i −0.998067 0.0621507i 0.980204π-0.980204\pi
−0.358078 + 0.933692i 0.616568π0.616568\pi
212212 0.108719 + 0.756156i 0.00746684 + 0.0519330i
213213 −23.0173 14.7923i −1.57712 1.01355i
214214 3.44454 7.54248i 0.235464 0.515594i
215215 0 0
216216 0.711574 4.94911i 0.0484165 0.336744i
217217 9.01791 + 19.7465i 0.612176 + 1.34048i
218218 0 0
219219 14.0055 + 4.11238i 0.946402 + 0.277889i
220220 4.35028 + 9.52579i 0.293296 + 0.642229i
221221 −0.326157 + 2.26847i −0.0219397 + 0.152594i
222222 −1.11864 + 1.29097i −0.0750779 + 0.0866445i
223223 1.66166 3.63853i 0.111273 0.243654i −0.845800 0.533499i 0.820877π-0.820877\pi
0.957073 + 0.289846i 0.0936039π0.0936039\pi
224224 15.2943 + 9.82903i 1.02189 + 0.656730i
225225 0.988273 + 6.87359i 0.0658849 + 0.458239i
226226 4.55657 2.92833i 0.303099 0.194790i
227227 7.97643 + 9.20529i 0.529414 + 0.610976i 0.955963 0.293488i 0.0948162π-0.0948162\pi
−0.426549 + 0.904465i 0.640271π0.640271\pi
228228 6.94296 2.03864i 0.459809 0.135012i
229229 −12.0000 −0.792982 −0.396491 0.918039i 0.629772π-0.629772\pi
−0.396491 + 0.918039i 0.629772π0.629772\pi
230230 0 0
231231 37.8885 2.49288
232232 −6.43647 + 1.88992i −0.422575 + 0.124079i
233233 4.27484 + 4.93343i 0.280054 + 0.323200i 0.878297 0.478115i 0.158680π-0.158680\pi
−0.598243 + 0.801315i 0.704134π0.704134\pi
234234 3.11954 2.00481i 0.203931 0.131058i
235235 0.393349 + 2.73580i 0.0256592 + 0.178464i
236236 −8.80972 5.66166i −0.573464 0.368543i
237237 10.1661 22.2606i 0.660359 1.44598i
238238 −1.00054 + 1.15468i −0.0648553 + 0.0748470i
239239 −1.95881 + 13.6238i −0.126705 + 0.881253i 0.822985 + 0.568062i 0.192307π0.192307\pi
−0.949690 + 0.313190i 0.898602π0.898602\pi
240240 −2.12884 4.66151i −0.137416 0.300899i
241241 22.1879 + 6.51496i 1.42925 + 0.419665i 0.902623 0.430432i 0.141639π-0.141639\pi
0.526626 + 0.850097i 0.323457π0.323457\pi
242242 −9.73492 2.85843i −0.625784 0.183747i
243243 7.43117 + 16.2720i 0.476710 + 1.04385i
244244 −1.59906 + 11.1217i −0.102369 + 0.711994i
245245 −2.81053 + 3.24352i −0.179558 + 0.207221i
246246 1.99332 4.36475i 0.127089 0.278287i
247247 −5.04752 3.24384i −0.321166 0.206401i
248248 2.13472 + 14.8473i 0.135555 + 0.942806i
249249 16.4858 10.5948i 1.04475 0.671418i
250250 4.23835 + 4.89131i 0.268057 + 0.309354i
251251 −2.19896 + 0.645674i −0.138797 + 0.0407546i −0.350393 0.936603i 0.613952π-0.613952\pi
0.211596 + 0.977357i 0.432134π0.432134\pi
252252 −10.4721 −0.659683
253253 0 0
254254 −4.50658 −0.282768
255255 2.02593 0.594866i 0.126868 0.0372520i
256256 4.29740 + 4.95946i 0.268587 + 0.309966i
257257 −6.28596 + 4.03974i −0.392107 + 0.251992i −0.721808 0.692093i 0.756689π-0.756689\pi
0.329700 + 0.944086i 0.393052π0.393052\pi
258258 0 0
259259 −3.36501 2.16256i −0.209092 0.134375i
260260 −2.49249 + 5.45779i −0.154578 + 0.338478i
261261 3.92916 4.53450i 0.243209 0.280678i
262262 −1.64549 + 11.4446i −0.101659 + 0.707051i
263263 1.22309 + 2.67820i 0.0754193 + 0.165145i 0.943586 0.331127i 0.107429π-0.107429\pi
−0.868167 + 0.496272i 0.834702π0.834702\pi
264264 25.1199 + 7.37585i 1.54602 + 0.453952i
265265 −0.559953 0.164417i −0.0343976 0.0101001i
266266 −1.66166 3.63853i −0.101883 0.223092i
267267 −3.33250 + 23.1781i −0.203946 + 1.41847i
268268 −2.92863 + 3.37981i −0.178894 + 0.206455i
269269 −3.30017 + 7.22636i −0.201215 + 0.440599i −0.983160 0.182749i 0.941501π-0.941501\pi
0.781945 + 0.623348i 0.214228π0.214228\pi
270270 1.43703 + 0.923525i 0.0874550 + 0.0562039i
271271 −1.13852 7.91857i −0.0691601 0.481019i −0.994737 0.102460i 0.967329π-0.967329\pi
0.925577 0.378559i 0.123580π-0.123580\pi
272272 1.19156 0.765768i 0.0722488 0.0464315i
273273 14.2159 + 16.4060i 0.860382 + 0.992934i
274274 12.9799 3.81124i 0.784144 0.230245i
275275 18.1803 1.09632
276276 0 0
277277 15.4721 0.929631 0.464815 0.885408i 0.346121π-0.346121\pi
0.464815 + 0.885408i 0.346121π0.346121\pi
278278 6.34996 1.86452i 0.380845 0.111826i
279279 −8.78588 10.1394i −0.525997 0.607033i
280280 −7.52440 + 4.83564i −0.449669 + 0.288985i
281281 1.24724 + 8.67473i 0.0744040 + 0.517491i 0.992606 + 0.121379i 0.0387317π0.0387317\pi
−0.918202 + 0.396112i 0.870359π0.870359\pi
282282 2.59962 + 1.67067i 0.154805 + 0.0994871i
283283 11.5104 25.2043i 0.684222 1.49824i −0.173884 0.984766i 0.555632π-0.555632\pi
0.858106 0.513472i 0.171641π-0.171641\pi
284284 12.9652 14.9626i 0.769342 0.887868i
285285 −0.786697 + 5.47160i −0.0465999 + 0.324110i
286286 −4.03293 8.83089i −0.238472 0.522182i
287287 10.7809 + 3.16557i 0.636378 + 0.186857i
288288 −10.7809 3.16557i −0.635272 0.186533i
289289 −6.81962 14.9329i −0.401154 0.878405i
290290 0.326157 2.26847i 0.0191526 0.133209i
291291 25.9304 29.9252i 1.52006 1.75425i
292292 −4.38774 + 9.60781i −0.256773 + 0.562255i
293293 −1.28532 0.826026i −0.0750893 0.0482569i 0.502558 0.864544i 0.332393π-0.332393\pi
−0.577647 + 0.816287i 0.696029π0.696029\pi
294294 0.682880 + 4.74953i 0.0398264 + 0.276998i
295295 6.73003 4.32513i 0.391837 0.251819i
296296 −1.80999 2.08884i −0.105204 0.121411i
297297 11.2339 3.29858i 0.651859 0.191403i
298298 14.7639 0.855252
299299 0 0
300300 −12.5623 −0.725285
301301 0 0
302302 −1.71445 1.97858i −0.0986554 0.113854i
303303 −8.41254 + 5.40641i −0.483288 + 0.310590i
304304 0.527732 + 3.67046i 0.0302675 + 0.210515i
305305 −7.22098 4.64064i −0.413472 0.265722i
306306 0.392265 0.858940i 0.0224243 0.0491023i
307307 −6.23942 + 7.20068i −0.356103 + 0.410964i −0.905330 0.424708i 0.860377π-0.860377\pi
0.549227 + 0.835673i 0.314922π0.314922\pi
308308 −3.90176 + 27.1373i −0.222324 + 1.54629i
309309 3.88310 + 8.50281i 0.220902 + 0.483708i
310310 −4.91703 1.44377i −0.279268 0.0820006i
311311 −12.6464 3.71333i −0.717114 0.210564i −0.0972354 0.995261i 0.531000π-0.531000\pi
−0.619879 + 0.784698i 0.712818π0.712818\pi
312312 6.23123 + 13.6445i 0.352774 + 0.772467i
313313 −3.46689 + 24.1127i −0.195960 + 1.36293i 0.619899 + 0.784681i 0.287173π0.287173\pi
−0.815859 + 0.578250i 0.803736π0.803736\pi
314314 4.62052 5.33236i 0.260751 0.300923i
315315 3.32332 7.27706i 0.187248 0.410016i
316316 14.8971 + 9.57378i 0.838027 + 0.538567i
317317 −3.61713 25.1577i −0.203158 1.41300i −0.794837 0.606823i 0.792444π-0.792444\pi
0.591678 0.806174i 0.298466π-0.298466\pi
318318 −0.548898 + 0.352755i −0.0307806 + 0.0197815i
319319 −10.2867 11.8715i −0.575944 0.664675i
320320 0.279976 0.0822085i 0.0156511 0.00459559i
321321 −30.0000 −1.67444
322322 0 0
323323 −1.52786 −0.0850126
324324 −17.0774 + 5.01438i −0.948745 + 0.278577i
325325 6.82130 + 7.87220i 0.378377 + 0.436671i
326326 −2.99680 + 1.92593i −0.165978 + 0.106667i
327327 0 0
328328 6.53144 + 4.19750i 0.360638 + 0.231768i
329329 −3.00597 + 6.58216i −0.165725 + 0.362886i
330330 −5.85725 + 6.75963i −0.322431 + 0.372105i
331331 2.79684 19.4524i 0.153728 1.06920i −0.756171 0.654374i 0.772932π-0.772932\pi
0.909899 0.414829i 0.136159π-0.136159\pi
332332 5.89073 + 12.8989i 0.323296 + 0.707919i
333333 2.37200 + 0.696481i 0.129985 + 0.0381669i
334334 −0.906022 0.266032i −0.0495753 0.0145566i
335335 −1.41923 3.10767i −0.0775407 0.169790i
336336 1.90935 13.2798i 0.104164 0.724475i
337337 −15.3345 + 17.6969i −0.835323 + 0.964014i −0.999750 0.0223755i 0.992877π-0.992877\pi
0.164427 + 0.986389i 0.447423π0.447423\pi
338338 −1.02696 + 2.24873i −0.0558594 + 0.122315i
339339 −16.4858 10.5948i −0.895388 0.575431i
340340 0.217438 + 1.51231i 0.0117922 + 0.0820167i
341341 −29.5487 + 18.9898i −1.60015 + 1.02836i
342342 1.61890 + 1.86832i 0.0875403 + 0.101027i
343343 10.9540 3.21637i 0.591458 0.173668i
344344 0 0
345345 0 0
346346 14.1803 0.762340
347347 9.48799 2.78592i 0.509342 0.149556i −0.0169565 0.999856i 0.505398π-0.505398\pi
0.526298 + 0.850300i 0.323579π0.323579\pi
348348 7.10793 + 8.20298i 0.381025 + 0.439726i
349349 20.5404 13.2005i 1.09950 0.706607i 0.140521 0.990078i 0.455122π-0.455122\pi
0.958981 + 0.283471i 0.0914859π0.0914859\pi
350350 0.988273 + 6.87359i 0.0528254 + 0.367409i
351351 5.64330 + 3.62673i 0.301217 + 0.193580i
352352 −12.2200 + 26.7581i −0.651329 + 1.42621i
353353 −6.12994 + 7.07433i −0.326264 + 0.376529i −0.895057 0.445952i 0.852865π-0.852865\pi
0.568793 + 0.822481i 0.307411π0.307411\pi
354354 1.27290 8.85323i 0.0676540 0.470544i
355355 6.28299 + 13.7578i 0.333467 + 0.730190i
356356 −16.2579 4.77375i −0.861667 0.253008i
357357 5.30395 + 1.55738i 0.280715 + 0.0824253i
358358 0.181825 + 0.398141i 0.00960973 + 0.0210424i
359359 2.83043 19.6861i 0.149385 1.03899i −0.767845 0.640635i 0.778671π-0.778671\pi
0.917230 0.398358i 0.130420π-0.130420\pi
360360 3.61998 4.17768i 0.190790 0.220183i
361361 −6.23123 + 13.6445i −0.327959 + 0.718131i
362362 8.65801 + 5.56417i 0.455055 + 0.292446i
363363 5.22412 + 36.3346i 0.274195 + 1.90707i
364364 −13.2146 + 8.49250i −0.692632 + 0.445128i
365365 −5.28400 6.09806i −0.276577 0.319187i
366366 −9.20801 + 2.70372i −0.481310 + 0.141326i
367367 −4.18034 −0.218212 −0.109106 0.994030i 0.534799π-0.534799\pi
−0.109106 + 0.994030i 0.534799π0.534799\pi
368368 0 0
369369 −6.94427 −0.361504
370370 0.906022 0.266032i 0.0471019 0.0138304i
371371 −1.00054 1.15468i −0.0519454 0.0599481i
372372 20.4177 13.1216i 1.05861 0.680325i
373373 −1.09699 7.62975i −0.0568001 0.395053i −0.998312 0.0580743i 0.981504π-0.981504\pi
0.941512 0.336979i 0.109405π-0.109405\pi
374374 −2.07969 1.33654i −0.107538 0.0691107i
375375 9.72753 21.3003i 0.502327 1.09994i
376376 −3.27430 + 3.77875i −0.168859 + 0.194874i
377377 1.28083 8.90839i 0.0659663 0.458806i
378378 1.85779 + 4.06800i 0.0955545 + 0.209235i
379379 −23.3739 6.86320i −1.20064 0.352539i −0.380540 0.924764i 0.624262π-0.624262\pi
−0.820096 + 0.572226i 0.806080π0.806080\pi
380380 −3.83797 1.12693i −0.196884 0.0578103i
381381 6.77332 + 14.8315i 0.347008 + 0.759841i
382382 2.30270 16.0156i 0.117817 0.819432i
383383 −4.62052 + 5.33236i −0.236098 + 0.272471i −0.861418 0.507897i 0.830423π-0.830423\pi
0.625320 + 0.780368i 0.284968π0.284968\pi
384384 10.5727 23.1509i 0.539534 1.18141i
385385 −17.6194 11.3233i −0.897970 0.577090i
386386 −0.874652 6.08334i −0.0445186 0.309634i
387387 0 0
388388 18.7634 + 21.6541i 0.952566 + 1.09932i
389389 −24.4938 + 7.19203i −1.24189 + 0.364650i −0.835723 0.549151i 0.814951π-0.814951\pi
−0.406162 + 0.913801i 0.633133π0.633133\pi
390390 −5.12461 −0.259495
391391 0 0
392392 −7.76393 −0.392138
393393 40.1383 11.7857i 2.02471 0.594508i
394394 0.595812 + 0.687604i 0.0300166 + 0.0346410i
395395 −11.3804 + 7.31372i −0.572608 + 0.367993i
396396 −2.41142 16.7718i −0.121178 0.842815i
397397 −20.5404 13.2005i −1.03089 0.662514i −0.0881745 0.996105i 0.528103π-0.528103\pi
−0.942718 + 0.333591i 0.891740π0.891740\pi
398398 −3.15580 + 6.91024i −0.158186 + 0.346379i
399399 −9.47723 + 10.9373i −0.474455 + 0.547550i
400400 0.916179 6.37217i 0.0458090 0.318608i
401401 −5.89073 12.8989i −0.294169 0.644140i 0.703622 0.710575i 0.251565π-0.251565\pi
−0.997791 + 0.0664346i 0.978838π0.978838\pi
402402 −3.66494 1.07612i −0.182790 0.0536721i
403403 −19.3094 5.66976i −0.961871 0.282431i
404404 −3.00597 6.58216i −0.149553 0.327475i
405405 1.93502 13.4584i 0.0961519 0.668751i
406406 3.92916 4.53450i 0.195001 0.225043i
407407 2.68862 5.88726i 0.133270 0.291821i
408408 3.21330 + 2.06506i 0.159082 + 0.102236i
409409 −3.03994 21.1433i −0.150315 1.04547i −0.915691 0.401883i 0.868356π-0.868356\pi
0.765376 0.643584i 0.222553π-0.222553\pi
410410 −2.23140 + 1.43404i −0.110201 + 0.0708220i
411411 −32.0517 36.9896i −1.58099 1.82456i
412412 −6.48995 + 1.90562i −0.319737 + 0.0938832i
413413 20.9443 1.03060
414414 0 0
415415 −10.8328 −0.531762
416416 −16.1714 + 4.74835i −0.792868 + 0.232807i
417417 −15.6802 18.0959i −0.767861 0.886159i
418418 5.44471 3.49910i 0.266309 0.171147i
419419 0.652313 + 4.53694i 0.0318676 + 0.221644i 0.999532 0.0305981i 0.00974119π-0.00974119\pi
−0.967664 + 0.252242i 0.918832π0.918832\pi
420420 12.1747 + 7.82423i 0.594066 + 0.381783i
421421 −4.27537 + 9.36175i −0.208369 + 0.456264i −0.984744 0.174007i 0.944329π-0.944329\pi
0.776376 + 0.630270i 0.217056π0.217056\pi
422422 9.47723 10.9373i 0.461345 0.532420i
423423 0.636451 4.42662i 0.0309453 0.215229i
424424 −0.438565 0.960324i −0.0212986 0.0466375i
425425 2.54503 + 0.747289i 0.123452 + 0.0362488i
426426 16.2249 + 4.76405i 0.786097 + 0.230819i
427427 −9.33526 20.4414i −0.451765 0.989227i
428428 3.08940 21.4872i 0.149332 1.03863i
429429 −23.0017 + 26.5454i −1.11053 + 1.28162i
430430 0 0
431431 −14.7454 9.47628i −0.710260 0.456456i 0.134977 0.990849i 0.456904π-0.456904\pi
−0.845236 + 0.534392i 0.820540π0.820540\pi
432432 −0.590023 4.10370i −0.0283875 0.197439i
433433 14.9909 9.63404i 0.720414 0.462982i −0.128367 0.991727i 0.540973π-0.540973\pi
0.848781 + 0.528745i 0.177337π0.177337\pi
434434 −8.78588 10.1394i −0.421736 0.486709i
435435 −7.95592 + 2.33607i −0.381457 + 0.112006i
436436 0 0
437437 0 0
438438 −9.02129 −0.431054
439439 17.9504 5.27071i 0.856725 0.251557i 0.176266 0.984343i 0.443598π-0.443598\pi
0.680460 + 0.732785i 0.261780π0.261780\pi
440440 −9.47723 10.9373i −0.451809 0.521416i
441441 5.84189 3.75436i 0.278185 0.178779i
442442 −0.201576 1.40199i −0.00958799 0.0666859i
443443 32.0725 + 20.6117i 1.52381 + 0.979292i 0.991118 + 0.132982i 0.0424553π0.0424553\pi
0.532690 + 0.846310i 0.321181π0.321181\pi
444444 −1.85779 + 4.06800i −0.0881669 + 0.193059i
445445 8.47670 9.78263i 0.401834 0.463741i
446446 −0.351822 + 2.44697i −0.0166592 + 0.115868i
447447 −22.1900 48.5893i −1.04955 2.29819i
448448 0.732987 + 0.215225i 0.0346304 + 0.0101684i
449449 14.3389 + 4.21029i 0.676696 + 0.198696i 0.601982 0.798509i 0.294378π-0.294378\pi
0.0747132 + 0.997205i 0.476196π0.476196\pi
450450 −1.78288 3.90396i −0.0840456 0.184034i
451451 −2.58733 + 17.9953i −0.121833 + 0.847365i
452452 9.28615 10.7168i 0.436784 0.504075i
453453 −3.93487 + 8.61616i −0.184876 + 0.404822i
454454 −6.33284 4.06987i −0.297215 0.191008i
455455 −1.70778 11.8779i −0.0800619 0.556843i
456456 −8.41254 + 5.40641i −0.393953 + 0.253178i
457457 3.35591 + 3.87292i 0.156983 + 0.181168i 0.828793 0.559556i 0.189028π-0.189028\pi
−0.671810 + 0.740724i 0.734483π0.734483\pi
458458 7.11599 2.08944i 0.332508 0.0976333i
459459 1.70820 0.0797321
460460 0 0
461461 −1.47214 −0.0685642 −0.0342821 0.999412i 0.510914π-0.510914\pi
−0.0342821 + 0.999412i 0.510914π0.510914\pi
462462 −22.4679 + 6.59716i −1.04530 + 0.306928i
463463 13.0972 + 15.1150i 0.608679 + 0.702453i 0.973516 0.228618i 0.0734207π-0.0734207\pi
−0.364837 + 0.931071i 0.618875π0.618875\pi
464464 −4.67931 + 3.00721i −0.217231 + 0.139606i
465465 2.63866 + 18.3523i 0.122365 + 0.851067i
466466 −3.39399 2.18118i −0.157223 0.101041i
467467 −5.42355 + 11.8759i −0.250972 + 0.549551i −0.992624 0.121233i 0.961315π-0.961315\pi
0.741652 + 0.670784i 0.234042π0.234042\pi
468468 6.35752 7.33697i 0.293877 0.339152i
469469 1.27290 8.85323i 0.0587772 0.408804i
470470 −0.709614 1.55384i −0.0327320 0.0716732i
471471 −24.4938 7.19203i −1.12862 0.331391i
472472 13.8859 + 4.07727i 0.639151 + 0.187672i
473473 0 0
474474 −2.15246 + 14.9707i −0.0988656 + 0.687625i
475475 −4.54753 + 5.24813i −0.208655 + 0.240801i
476476 −1.66166 + 3.63853i −0.0761621 + 0.166772i
477477 0.794372 + 0.510512i 0.0363718 + 0.0233747i
478478 −1.21061 8.41999i −0.0553721 0.385122i
479479 26.5809 17.0825i 1.21451 0.780519i 0.233103 0.972452i 0.425112π-0.425112\pi
0.981408 + 0.191933i 0.0614756π0.0614756\pi
480480 10.1686 + 11.7352i 0.464130 + 0.535635i
481481 3.55800 1.04472i 0.162231 0.0476352i
482482 −14.2918 −0.650973
483483 0 0
484484 −26.5623 −1.20738
485485 −21.0019 + 6.16672i −0.953647 + 0.280016i
486486 −7.23996 8.35536i −0.328411 0.379007i
487487 −12.3733 + 7.95186i −0.560689 + 0.360333i −0.790082 0.613001i 0.789962π-0.789962\pi
0.229393 + 0.973334i 0.426326π0.426326\pi
488488 −2.20985 15.3698i −0.100035 0.695759i
489489 10.8425 + 6.96807i 0.490316 + 0.315107i
490490 1.10188 2.41278i 0.0497778 0.108998i
491491 −5.46647 + 6.30864i −0.246698 + 0.284705i −0.865571 0.500786i 0.833044π-0.833044\pi
0.618873 + 0.785491i 0.287590π0.287590\pi
492492 1.78780 12.4344i 0.0806004 0.560588i
493493 −0.952046 2.08469i −0.0428780 0.0938898i
494494 3.55800 + 1.04472i 0.160082 + 0.0470043i
495495 12.4199 + 3.64682i 0.558235 + 0.163912i
496496 5.16680 + 11.3137i 0.231996 + 0.508001i
497497 −5.63520 + 39.1937i −0.252773 + 1.75808i
498498 −7.93132 + 9.15323i −0.355411 + 0.410166i
499499 8.01410 17.5484i 0.358760 0.785576i −0.641076 0.767478i 0.721512π-0.721512\pi
0.999836 0.0180982i 0.00576116π-0.00576116\pi
500500 14.2544 + 9.16077i 0.637477 + 0.409682i
501501 0.486206 + 3.38163i 0.0217221 + 0.151080i
502502 1.19156 0.765768i 0.0531818 0.0341779i
503503 17.6447 + 20.3631i 0.786740 + 0.907947i 0.997577 0.0695746i 0.0221642π-0.0221642\pi
−0.210836 + 0.977521i 0.567619π0.567619\pi
504504 13.8859 4.07727i 0.618528 0.181616i
505505 5.52786 0.245987
506506 0 0
507507 8.94427 0.397229
508508 −11.3205 + 3.32399i −0.502264 + 0.147478i
509509 18.5358 + 21.3915i 0.821585 + 0.948160i 0.999355 0.0359125i 0.0114338π-0.0114338\pi
−0.177770 + 0.984072i 0.556888π0.556888\pi
510510 −1.09780 + 0.705510i −0.0486112 + 0.0312405i
511511 −3.00635 20.9096i −0.132993 0.924986i
512512 15.7383 + 10.1144i 0.695543 + 0.446998i
513513 −1.85779 + 4.06800i −0.0820235 + 0.179606i
514514 3.02417 3.49008i 0.133390 0.153941i
515515 0.735367 5.11459i 0.0324041 0.225376i
516516 0 0
517517 −11.2339 3.29858i −0.494068 0.145071i
518518 2.37200 + 0.696481i 0.104220 + 0.0306016i
519519 −21.3128 46.6686i −0.935530 2.04853i
520520 1.18005 8.20740i 0.0517484 0.359918i
521521 −20.5734 + 23.7429i −0.901336 + 1.04020i 0.0976523 + 0.995221i 0.468867π0.468867\pi
−0.998988 + 0.0449764i 0.985679π0.985679\pi
522522 −1.54044 + 3.37310i −0.0674234 + 0.147637i
523523 34.5962 + 22.2336i 1.51279 + 0.972209i 0.993026 + 0.117898i 0.0376156π0.0376156\pi
0.519762 + 0.854311i 0.326021π0.326021\pi
524524 4.30794 + 29.9624i 0.188193 + 1.30891i
525525 21.1362 13.5834i 0.922458 0.592828i
526526 −1.19162 1.37521i −0.0519573 0.0599619i
527527 −4.91703 + 1.44377i −0.214189 + 0.0628916i
528528 21.7082 0.944728
529529 0 0
530530 0.360680 0.0156669
531531 −12.4199 + 3.64682i −0.538979 + 0.158259i
532532 −6.85779 7.91431i −0.297323 0.343129i
533533 −8.76284 + 5.63154i −0.379561 + 0.243929i
534534 −2.05960 14.3248i −0.0891276 0.619896i
535535 13.9510 + 8.96577i 0.603155 + 0.387624i
536536 2.56741 5.62183i 0.110895 0.242826i
537537 1.03703 1.19680i 0.0447512 0.0516457i
538538 0.698742 4.85986i 0.0301249 0.209523i
539539 −7.55239 16.5374i −0.325304 0.712317i
540540 4.29098 + 1.25995i 0.184655 + 0.0542195i
541541 33.0223 + 9.69622i 1.41974 + 0.416873i 0.899415 0.437095i 0.143993π-0.143993\pi
0.520325 + 0.853969i 0.325811π0.325811\pi
542542 2.05392 + 4.49747i 0.0882236 + 0.193183i
543543 5.29924 36.8571i 0.227412 1.58169i
544544 −2.81053 + 3.24352i −0.120500 + 0.139065i
545545 0 0
546546 −11.2866 7.25346i −0.483022 0.310419i
547547 4.20413 + 29.2403i 0.179755 + 1.25023i 0.857328 + 0.514771i 0.172123π0.172123\pi
−0.677573 + 0.735456i 0.736968π0.736968\pi
548548 29.7942 19.1476i 1.27274 0.817943i
549549 9.09506 + 10.4963i 0.388168 + 0.447970i
550550 −10.7809 + 3.16557i −0.459700 + 0.134980i
551551 6.00000 0.255609
552552 0 0
553553 −35.4164 −1.50606
554554 −9.17497 + 2.69401i −0.389807 + 0.114458i
555555 −2.23727 2.58195i −0.0949669 0.109598i
556556 14.5758 9.36727i 0.618150 0.397261i
557557 1.05546 + 7.34092i 0.0447215 + 0.311045i 0.999888 + 0.0149752i 0.00476693π0.00476693\pi
−0.955166 + 0.296070i 0.904324π0.904324\pi
558558 6.97550 + 4.48288i 0.295297 + 0.189776i
559559 0 0
560560 −4.85671 + 5.60495i −0.205234 + 0.236852i
561561 −1.27290 + 8.85323i −0.0537420 + 0.373784i
562562 −2.25006 4.92694i −0.0949129 0.207830i
563563 31.6098 + 9.28147i 1.33219 + 0.391167i 0.868878 0.495026i 0.164841π-0.164841\pi
0.463316 + 0.886193i 0.346660π0.346660\pi
564564 7.76246 + 2.27926i 0.326859 + 0.0959743i
565565 4.50011 + 9.85388i 0.189321 + 0.414556i
566566 −2.43709 + 16.9503i −0.102438 + 0.712475i
567567 23.3109 26.9022i 0.978966 1.12979i
568568 −11.3660 + 24.8881i −0.476908 + 1.04428i
569569 −18.6593 11.9916i −0.782238 0.502714i 0.0875376 0.996161i 0.472100π-0.472100\pi
−0.869776 + 0.493447i 0.835737π0.835737\pi
570570 −0.486206 3.38163i −0.0203649 0.141641i
571571 −12.0230 + 7.72673i −0.503148 + 0.323354i −0.767474 0.641080i 0.778487π-0.778487\pi
0.264326 + 0.964433i 0.414850π0.414850\pi
572572 −16.6442 19.2084i −0.695929 0.803145i
573573 −56.1697 + 16.4929i −2.34652 + 0.689001i
574574 −6.94427 −0.289848
575575 0 0
576576 −0.472136 −0.0196723
577577 −21.9614 + 6.44845i −0.914265 + 0.268452i −0.704835 0.709371i 0.748979π-0.748979\pi
−0.209430 + 0.977824i 0.567161π0.567161\pi
578578 6.64415 + 7.66776i 0.276360 + 0.318937i
579579 −18.7062 + 12.0217i −0.777402 + 0.499606i
580580 −0.853889 5.93893i −0.0354558 0.246601i
581581 −23.8585 15.3329i −0.989818 0.636118i
582582 −10.1661 + 22.2606i −0.421398 + 0.922733i
583583 1.61890 1.86832i 0.0670482 0.0773777i
584584 2.07733 14.4482i 0.0859607 0.597870i
585585 3.08089 + 6.74620i 0.127379 + 0.278921i
586586 0.906022 + 0.266032i 0.0374274 + 0.0109897i
587587 23.7073 + 6.96111i 0.978507 + 0.287316i 0.731608 0.681726i 0.238770π-0.238770\pi
0.246899 + 0.969041i 0.420588π0.420588\pi
588588 5.21857 + 11.4271i 0.215210 + 0.471245i
589589 1.90935 13.2798i 0.0786736 0.547187i
590590 −3.23781 + 3.73663i −0.133299 + 0.153835i
591591 1.36746 2.99432i 0.0562499 0.123170i
592592 −1.92798 1.23904i −0.0792396 0.0509242i
593593 0.419014 + 2.91430i 0.0172068 + 0.119676i 0.996614 0.0822165i 0.0261999π-0.0261999\pi
−0.979408 + 0.201893i 0.935291π0.935291\pi
594594 −6.08737 + 3.91211i −0.249768 + 0.160516i
595595 −2.00108 2.30937i −0.0820361 0.0946747i
596596 37.0868 10.8897i 1.51913 0.446058i
597597 27.4853 1.12490
598598 0 0
599599 33.8885 1.38465 0.692324 0.721587i 0.256587π-0.256587\pi
0.692324 + 0.721587i 0.256587π0.256587\pi
600600 16.6575 4.89107i 0.680038 0.199677i
601601 −30.7055 35.4360i −1.25250 1.44546i −0.847193 0.531285i 0.821710π-0.821710\pi
−0.405309 0.914180i 0.632836π-0.632836\pi
602602 0 0
603603 0.786697 + 5.47160i 0.0320368 + 0.222821i
604604 −5.76604 3.70561i −0.234617 0.150779i
605605 8.42952 18.4581i 0.342709 0.750427i
606606 4.04726 4.67079i 0.164409 0.189738i
607607 −3.76738 + 26.2027i −0.152913 + 1.06353i 0.758391 + 0.651800i 0.225986π0.225986\pi
−0.911304 + 0.411734i 0.864923π0.864923\pi
608608 −4.66763 10.2207i −0.189297 0.414504i
609609 −20.8289 6.11591i −0.844028 0.247829i
610610 5.09006 + 1.49458i 0.206091 + 0.0605137i
611611 −2.78669 6.10200i −0.112737 0.246860i
612612 0.351822 2.44697i 0.0142215 0.0989130i
613613 −3.73808 + 4.31397i −0.150980 + 0.174240i −0.826201 0.563375i 0.809503π-0.809503\pi
0.675222 + 0.737615i 0.264048π0.264048\pi
614614 2.44619 5.35641i 0.0987202 0.216167i
615615 8.07330 + 5.18839i 0.325547 + 0.209216i
616616 −5.39210 37.5029i −0.217254 1.51103i
617617 −6.33284 + 4.06987i −0.254951 + 0.163847i −0.661873 0.749616i 0.730238π-0.730238\pi
0.406923 + 0.913463i 0.366602π0.366602\pi
618618 −3.78319 4.36603i −0.152182 0.175628i
619619 −18.6299 + 5.47023i −0.748799 + 0.219867i −0.633799 0.773498i 0.718505π-0.718505\pi
−0.115001 + 0.993365i 0.536687π0.536687\pi
620620 −13.4164 −0.538816
621621 0 0
622622 8.14590 0.326621
623623 32.5158 9.54751i 1.30272 0.382513i
624624 8.14496 + 9.39978i 0.326059 + 0.376292i
625625 3.71532 2.38769i 0.148613 0.0955076i
626626 −2.14265 14.9025i −0.0856377 0.595623i
627627 −19.6991 12.6599i −0.786708 0.505586i
628628 7.67360 16.8028i 0.306210 0.670507i
629629 0.618367 0.713633i 0.0246559 0.0284544i
630630 −0.703643 + 4.89395i −0.0280338 + 0.194979i
631631 5.13481 + 11.2437i 0.204414 + 0.447603i 0.983877 0.178844i 0.0572357π-0.0572357\pi
−0.779464 + 0.626447i 0.784508π0.784508\pi
632632 −23.4808 6.89460i −0.934018 0.274252i
633633 −50.2397 14.7517i −1.99685 0.586328i
634634 6.52542 + 14.2887i 0.259158 + 0.567476i
635635 1.28271 8.92141i 0.0509026 0.354036i
636636 −1.11864 + 1.29097i −0.0443568 + 0.0511905i
637637 4.32713 9.47510i 0.171447 0.375417i
638638 8.16706 + 5.24865i 0.323337 + 0.207796i
639639 −3.48275 24.2230i −0.137775 0.958249i
640640 −11.8355 + 7.60621i −0.467839 + 0.300662i
641641 11.3323 + 13.0782i 0.447600 + 0.516558i 0.934046 0.357153i 0.116252π-0.116252\pi
−0.486446 + 0.873711i 0.661707π0.661707\pi
642642 17.7900 5.22361i 0.702114 0.206159i
643643 −29.5967 −1.16718 −0.583591 0.812048i 0.698353π-0.698353\pi
−0.583591 + 0.812048i 0.698353π0.698353\pi
644644 0 0
645645 0 0
646646 0.906022 0.266032i 0.0356470 0.0104669i
647647 −4.39294 5.06972i −0.172704 0.199311i 0.662798 0.748798i 0.269369π-0.269369\pi
−0.835502 + 0.549487i 0.814823π0.814823\pi
648648 20.6921 13.2980i 0.812862 0.522395i
649649 4.82284 + 33.5436i 0.189313 + 1.31670i
650650 −5.41573 3.48048i −0.212423 0.136516i
651651 −20.1647 + 44.1545i −0.790316 + 1.73055i
652652 −6.10739 + 7.04830i −0.239184 + 0.276033i
653653 5.45136 37.9151i 0.213328 1.48373i −0.548608 0.836079i 0.684842π-0.684842\pi
0.761937 0.647652i 0.224249π-0.224249\pi
654654 0 0
655655 −22.1879 6.51496i −0.866953 0.254560i
656656 6.17692 + 1.81371i 0.241168 + 0.0708134i
657657 5.42355 + 11.8759i 0.211593 + 0.463323i
658658 0.636451 4.42662i 0.0248115 0.172567i
659659 6.97589 8.05060i 0.271742 0.313607i −0.603433 0.797414i 0.706201π-0.706201\pi
0.875175 + 0.483807i 0.160746π0.160746\pi
660660 −9.72753 + 21.3003i −0.378643 + 0.829114i
661661 −19.3019 12.4046i −0.750759 0.482483i 0.108454 0.994101i 0.465410π-0.465410\pi
−0.859213 + 0.511618i 0.829046π0.829046\pi
662662 1.72854 + 12.0223i 0.0671817 + 0.467259i
663663 −4.31110 + 2.77057i −0.167429 + 0.107600i
664664 −12.8331 14.8102i −0.498022 0.574749i
665665 7.67594 2.25386i 0.297660 0.0874010i
666666 −1.52786 −0.0592035
667667 0 0
668668 −2.47214 −0.0956498
669669 8.58197 2.51989i 0.331798 0.0974247i
670670 1.38271 + 1.59573i 0.0534187 + 0.0616485i
671671 30.5886 19.6581i 1.18086 0.758891i
672672 5.78545 + 40.2387i 0.223179 + 1.55224i
673673 2.52376 + 1.62192i 0.0972838 + 0.0625205i 0.588378 0.808586i 0.299767π-0.299767\pi
−0.491094 + 0.871106i 0.663403π0.663403\pi
674674 6.01194 13.1643i 0.231571 0.507071i
675675 5.08429 5.86759i 0.195695 0.225844i
676676 −0.921081 + 6.40626i −0.0354262 + 0.246395i
677677 7.47747 + 16.3734i 0.287383 + 0.629280i 0.997174 0.0751323i 0.0239379π-0.0239379\pi
−0.709791 + 0.704412i 0.751211π0.751211\pi
678678 11.6209 + 3.41219i 0.446296 + 0.131044i
679679 −54.9837 16.1447i −2.11008 0.619576i
680680 −0.877131 1.92065i −0.0336364 0.0736535i
681681 −3.87610 + 26.9588i −0.148532 + 1.03307i
682682 14.2159 16.4060i 0.544353 0.628217i
683683 11.0487 24.1933i 0.422766 0.925729i −0.571679 0.820477i 0.693708π-0.693708\pi
0.994446 0.105252i 0.0335649π-0.0335649\pi
684684 5.44471 + 3.49910i 0.208184 + 0.133791i
685685 3.85043 + 26.7803i 0.147117 + 1.02322i
686686 −5.93566 + 3.81461i −0.226624 + 0.145643i
687687 −17.5718 20.2789i −0.670404 0.773688i
688688 0 0
689689 1.41641 0.0539608
690690 0 0
691691 7.05573 0.268413 0.134206 0.990953i 0.457152π-0.457152\pi
0.134206 + 0.990953i 0.457152π0.457152\pi
692692 35.6208 10.4592i 1.35410 0.397600i
693693 22.1923 + 25.6113i 0.843015 + 0.972891i
694694 −5.14128 + 3.30410i −0.195160 + 0.125422i
695695 1.88369 + 13.1013i 0.0714524 + 0.496962i
696696 −12.6188 8.10961i −0.478314 0.307394i
697697 −1.10188 + 2.41278i −0.0417366 + 0.0913904i
698698 −9.88196 + 11.4044i −0.374038 + 0.431663i
699699 −2.07733 + 14.4482i −0.0785720 + 0.546480i
700700 7.55239 + 16.5374i 0.285453 + 0.625056i
701701 3.66494 + 1.07612i 0.138423 + 0.0406446i 0.350210 0.936671i 0.386110π-0.386110\pi
−0.211787 + 0.977316i 0.567928π0.567928\pi
702702 −3.97796 1.16803i −0.150138 0.0440846i
703703 1.02696 + 2.24873i 0.0387326 + 0.0848126i
704704 −0.175911 + 1.22349i −0.00662989 + 0.0461119i
705705 −4.04726 + 4.67079i −0.152429 + 0.175912i
706706 2.40327 5.26242i 0.0904481 0.198054i
707707 12.1747 + 7.82423i 0.457878 + 0.294260i
708708 −3.33250 23.1781i −0.125243 0.871085i
709709 −35.3906 + 22.7442i −1.32912 + 0.854175i −0.996056 0.0887288i 0.971720π-0.971720\pi
−0.333066 + 0.942904i 0.608083π0.608083\pi
710710 −6.12133 7.06439i −0.229729 0.265122i
711711 21.0019 6.16672i 0.787633 0.231270i
712712 23.4164 0.877567
713713 0 0
714714 −3.41641 −0.127856
715715 18.6299 5.47023i 0.696719 0.204575i
716716 0.750404 + 0.866012i 0.0280439 + 0.0323644i
717717 −25.8913 + 16.6393i −0.966930 + 0.621408i
718718 1.74930 + 12.1667i 0.0652835 + 0.454057i
719719 −2.57064 1.65205i −0.0958688 0.0616111i 0.491828 0.870692i 0.336329π-0.336329\pi
−0.587697 + 0.809081i 0.699965π0.699965\pi
720720 1.90409 4.16938i 0.0709614 0.155384i
721721 8.85887 10.2237i 0.329921 0.380750i
722722 1.31933 9.17615i 0.0491004 0.341501i
723723 21.4804 + 47.0354i 0.798863 + 1.74927i
724724 25.8528 + 7.59108i 0.960813 + 0.282120i
725725 −9.99447 2.93464i −0.371185 0.108990i
726726 −9.42449 20.6367i −0.349775 0.765901i
727727 3.94329 27.4262i 0.146248 1.01718i −0.776041 0.630682i 0.782775π-0.782775\pi
0.922290 0.386499i 0.126316π-0.126316\pi
728728 14.2159 16.4060i 0.526874 0.608046i
729729 −2.90791 + 6.36742i −0.107700 + 0.235831i
730730 4.19520 + 2.69609i 0.155271 + 0.0997868i
731731 0 0
732732 −21.1362 + 13.5834i −0.781215 + 0.502057i
733733 20.4553 + 23.6066i 0.755533 + 0.871931i 0.995092 0.0989503i 0.0315485π-0.0315485\pi
−0.239560 + 0.970882i 0.577003π0.577003\pi
734734 2.47894 0.727882i 0.0914993 0.0268666i
735735 −9.59675 −0.353981
736736 0 0
737737 14.4721 0.533088
738738 4.11795 1.20914i 0.151584 0.0445090i
739739 −17.5631 20.2689i −0.646071 0.745605i 0.334365 0.942444i 0.391478π-0.391478\pi
−0.980436 + 0.196838i 0.936933π0.936933\pi
740740 2.07969 1.33654i 0.0764510 0.0491321i
741741 −1.90935 13.2798i −0.0701419 0.487847i
742742 0.794372 + 0.510512i 0.0291623 + 0.0187415i
743743 17.0838 37.4083i 0.626743 1.37238i −0.283769 0.958893i 0.591585π-0.591585\pi
0.910512 0.413483i 0.135688π-0.135688\pi
744744 −21.9647 + 25.3486i −0.805265 + 0.929325i
745745 −4.20225 + 29.2273i −0.153959 + 1.07081i
746746 1.97901 + 4.33342i 0.0724567 + 0.158658i
747747 16.8179 + 4.93817i 0.615333 + 0.180678i
748748 −6.20997 1.82341i −0.227059 0.0666705i
749749 18.0358 + 39.4930i 0.659015 + 1.44304i
750750 −2.05960 + 14.3248i −0.0752059 + 0.523069i
751751 −0.236195 + 0.272584i −0.00861888 + 0.00994672i −0.760043 0.649873i 0.774822π-0.774822\pi
0.751424 + 0.659820i 0.229367π0.229367\pi
752752 −1.72227 + 3.77124i −0.0628047 + 0.137523i
753753 −4.31110 2.77057i −0.157105 0.100965i
754754 0.791599 + 5.50569i 0.0288283 + 0.200505i
755755 4.40486 2.83083i 0.160309 0.103025i
756756 7.66724 + 8.84847i 0.278855 + 0.321816i
757757 −1.53207 + 0.449856i −0.0556840 + 0.0163503i −0.309456 0.950914i 0.600147π-0.600147\pi
0.253772 + 0.967264i 0.418329π0.418329\pi
758758 15.0557 0.546849
759759 0 0
760760 5.52786 0.200517
761761 −44.4293 + 13.0456i −1.61056 + 0.472903i −0.958459 0.285229i 0.907930π-0.907930\pi
−0.652101 + 0.758132i 0.726112π0.726112\pi
762762 −6.59904 7.61570i −0.239058 0.275888i
763763 0 0
764764 −6.02855 41.9295i −0.218105 1.51696i
765765 1.58874 + 1.02102i 0.0574412 + 0.0369152i
766766 1.81149 3.96661i 0.0654519 0.143320i
767767 −12.7150 + 14.6739i −0.459114 + 0.529845i
768768 −2.08829 + 14.5244i −0.0753548 + 0.524104i
769769 −9.60631 21.0349i −0.346412 0.758537i −0.999999 0.00168529i 0.999464π-0.999464\pi
0.653586 0.756852i 0.273264π-0.273264\pi
770770 12.4199 + 3.64682i 0.447583 + 0.131422i
771771 −16.0314 4.70725i −0.577357 0.169527i
772772 −6.68410 14.6361i −0.240566 0.526766i
773773 0.786697 5.47160i 0.0282955 0.196800i −0.970770 0.240010i 0.922849π-0.922849\pi
0.999066 + 0.0432100i 0.0137585π0.0137585\pi
774774 0 0
775775 −9.67576 + 21.1870i −0.347564 + 0.761058i
776776 −33.3109 21.4076i −1.19579 0.768489i
777777 −1.27290 8.85323i −0.0456651 0.317608i
778778 13.2725 8.52974i 0.475843 0.305806i
779779 −4.54753 5.24813i −0.162932 0.188034i
780780 −12.8729 + 3.77984i −0.460926 + 0.135340i
781781 −64.0689 −2.29256
782782 0 0
783783 −6.70820 −0.239732
784784 −6.17692 + 1.81371i −0.220604 + 0.0647753i
785785 9.24104 + 10.6647i 0.329827 + 0.380640i
786786 −21.7499 + 13.9778i −0.775792 + 0.498571i
787787 −3.49861 24.3334i −0.124712 0.867391i −0.952106 0.305769i 0.901087π-0.901087\pi
0.827394 0.561622i 0.189823π-0.189823\pi
788788 2.00384 + 1.28779i 0.0713837 + 0.0458755i
789789 −2.73492 + 5.98865i −0.0973658 + 0.213201i
790790 5.47508 6.31858i 0.194795 0.224805i
791791 −4.03615 + 28.0720i −0.143509 + 0.998126i
792792 9.72753 + 21.3003i 0.345653 + 0.756874i
793793 19.9889 + 5.86928i 0.709828 + 0.208424i
794794 14.4789 + 4.25139i 0.513837 + 0.150876i
795795 −0.542097 1.18703i −0.0192262 0.0420995i
796796 −2.83043 + 19.6861i −0.100322 + 0.697756i
797797 22.5015 25.9681i 0.797043 0.919836i −0.201173 0.979556i 0.564475π-0.564475\pi
0.998215 + 0.0597196i 0.0190207π0.0190207\pi
798798 3.71558 8.13600i 0.131530 0.288011i
799799 −1.43703 0.923525i −0.0508386 0.0326720i
800800 2.77608 + 19.3080i 0.0981491 + 0.682642i
801801 −17.6194 + 11.3233i −0.622552 + 0.400090i
802802 5.73915 + 6.62334i 0.202657 + 0.233878i
803803 32.7958 9.62971i 1.15734 0.339825i
804804 −10.0000 −0.352673
805805 0 0
806806 12.4377 0.438099
807807 −17.0444 + 5.00468i −0.599990 + 0.176173i
808808 6.54861 + 7.55750i 0.230379 + 0.265872i
809809 10.1888 6.54795i 0.358219 0.230214i −0.349135 0.937072i 0.613525π-0.613525\pi
0.707355 + 0.706859i 0.249888π0.249888\pi
810810 1.19591 + 8.31772i 0.0420199 + 0.292255i
811811 −20.4824 13.1633i −0.719236 0.462225i 0.129135 0.991627i 0.458780π-0.458780\pi
−0.848371 + 0.529402i 0.822416π0.822416\pi
812812 6.52542 14.2887i 0.228997 0.501435i
813813 11.7145 13.5193i 0.410846 0.474141i
814814 −0.569259 + 3.95929i −0.0199525 + 0.138773i
815815 −2.95967 6.48077i −0.103673 0.227012i
816816 3.03889 + 0.892299i 0.106382 + 0.0312367i
817817 0 0
818818 5.48415 + 12.0086i 0.191749 + 0.419872i
819819 −2.76324 + 19.2188i −0.0965555 + 0.671558i
820820 −4.54753 + 5.24813i −0.158807 + 0.183273i
821821 −16.1780 + 35.4250i −0.564617 + 1.23634i 0.384997 + 0.922918i 0.374203π0.374203\pi
−0.949614 + 0.313422i 0.898525π0.898525\pi
822822 25.4473 + 16.3540i 0.887575 + 0.570410i
823823 5.62727 + 39.1385i 0.196154 + 1.36428i 0.815314 + 0.579019i 0.196564π0.196564\pi
−0.619160 + 0.785265i 0.712527π0.712527\pi
824824 7.86364 5.05365i 0.273943 0.176052i
825825 26.6217 + 30.7231i 0.926849 + 1.06964i
826826 −12.4199 + 3.64682i −0.432145 + 0.126889i
827827 1.52786 0.0531290 0.0265645 0.999647i 0.491543π-0.491543\pi
0.0265645 + 0.999647i 0.491543π0.491543\pi
828828 0 0
829829 40.2492 1.39791 0.698957 0.715164i 0.253648π-0.253648\pi
0.698957 + 0.715164i 0.253648π0.253648\pi
830830 6.42385 1.88621i 0.222975 0.0654714i
831831 22.6561 + 26.1465i 0.785930 + 0.907011i
832832 −0.595779 + 0.382884i −0.0206549 + 0.0132741i
833833 −0.377487 2.62548i −0.0130791 0.0909674i
834834 12.4492 + 8.00060i 0.431080 + 0.277038i
835835 0.784529 1.71788i 0.0271498 0.0594497i
836836 11.0961 12.8056i 0.383768 0.442892i
837837 −2.13472 + 14.8473i −0.0737868 + 0.513199i
838838 −1.17679 2.57682i −0.0406517 0.0890148i
839839 39.4588 + 11.5861i 1.36227 + 0.399998i 0.879562 0.475784i 0.157836π-0.157836\pi
0.482706 + 0.875782i 0.339654π0.339654\pi
840840 −19.1899 5.63465i −0.662113 0.194414i
841841 −8.30830 18.1926i −0.286493 0.627332i
842842 0.905219 6.29594i 0.0311959 0.216972i
843843 −12.8331 + 14.8102i −0.441997 + 0.510092i
844844 15.7395 34.4646i 0.541775 1.18632i
845845 −4.15939 2.67308i −0.143087 0.0919566i
846846 0.393349 + 2.73580i 0.0135236 + 0.0940587i
847847 44.6913 28.7213i 1.53561 0.986877i
848848 −0.573257 0.661574i −0.0196857 0.0227186i
849849 59.4477 17.4554i 2.04024 0.599069i
850850 −1.63932 −0.0562282
851851 0 0
852852 44.2705 1.51668
853853 10.1549 2.98174i 0.347697 0.102093i −0.103221 0.994658i 0.532915π-0.532915\pi
0.450918 + 0.892566i 0.351097π0.351097\pi
854854 9.09506 + 10.4963i 0.311227 + 0.359175i
855855 −4.15939 + 2.67308i −0.142248 + 0.0914172i
856856 4.26945 + 29.6946i 0.145927 + 1.01494i
857857 1.23844 + 0.795897i 0.0423043 + 0.0271873i 0.561622 0.827394i 0.310178π-0.310178\pi
−0.519318 + 0.854581i 0.673814π0.673814\pi
858858 9.01791 19.7465i 0.307867 0.674134i
859859 10.9415 12.6272i 0.373321 0.430835i −0.537738 0.843112i 0.680721π-0.680721\pi
0.911059 + 0.412277i 0.135266π0.135266\pi
860860 0 0
861861 10.4371 + 22.8542i 0.355697 + 0.778867i
862862 10.3940 + 3.05196i 0.354021 + 0.103950i
863863 20.6685 + 6.06881i 0.703562 + 0.206585i 0.613896 0.789387i 0.289602π-0.289602\pi
0.0896669 + 0.995972i 0.471420π0.471420\pi
864864 5.21857 + 11.4271i 0.177539 + 0.388757i
865865 −4.03615 + 28.0720i −0.137233 + 0.954477i
866866 −7.21208 + 8.32319i −0.245077 + 0.282833i
867867 15.2491 33.3910i 0.517888 1.13402i
868868 −29.5487 18.9898i −1.00295 0.644556i
869869 −8.15534 56.7217i −0.276651 1.92415i
870870 4.31110 2.77057i 0.146160 0.0939313i
871871 5.42997 + 6.26652i 0.183988 + 0.212333i
872872 0 0
873873 35.4164 1.19866
874874 0 0
875875 −33.8885 −1.14564
876876 −22.6613 + 6.65397i −0.765656 + 0.224817i
877877 23.8842 + 27.5638i 0.806511 + 0.930763i 0.998719 0.0505907i 0.0161104π-0.0161104\pi
−0.192208 + 0.981354i 0.561565π0.561565\pi
878878 −9.72683 + 6.25105i −0.328265 + 0.210963i
879879 −0.486206 3.38163i −0.0163993 0.114060i
880880 −10.0950 6.48769i −0.340304 0.218700i
881881 18.3532 40.1879i 0.618334 1.35396i −0.298391 0.954444i 0.596450π-0.596450\pi
0.916725 0.399519i 0.130823π-0.130823\pi
882882 −2.81053 + 3.24352i −0.0946354 + 0.109215i
883883 −0.569259 + 3.95929i −0.0191571 + 0.133241i −0.997155 0.0753718i 0.975986π-0.975986\pi
0.977998 + 0.208612i 0.0668947π0.0668947\pi
884884 −1.54044 3.37310i −0.0518107 0.113450i
885885 17.1639 + 5.03979i 0.576959 + 0.169411i
886886 −22.6079 6.63827i −0.759526 0.223017i
887887 9.58316 + 20.9842i 0.321771 + 0.704580i 0.999528 0.0307053i 0.00977532π-0.00977532\pi
−0.677757 + 0.735286i 0.737048π0.737048\pi
888888 0.879554 6.11743i 0.0295159 0.205288i
889889 15.4526 17.8332i 0.518263 0.598107i
890890 −3.32332 + 7.27706i −0.111398 + 0.243927i
891891 48.4535 + 31.1392i 1.62325 + 1.04320i
892892 0.921081 + 6.40626i 0.0308401 + 0.214497i
893893 3.76220 2.41782i 0.125897 0.0809092i
894894 21.6190 + 24.9497i 0.723048 + 0.834442i
895895 −0.839929 + 0.246625i −0.0280757 + 0.00824378i
896896 −36.8328 −1.23050
897897 0 0
898898 −9.23607 −0.308212
899899 19.3094 5.66976i 0.644005 0.189097i
900900 −7.35806 8.49165i −0.245269 0.283055i
901901 0.303423 0.194998i 0.0101085 0.00649633i
902902 −1.59906 11.1217i −0.0532428 0.370312i
903903 0 0
904904 −8.14078 + 17.8258i −0.270758 + 0.592878i
905905 −13.4794 + 15.5560i −0.448070 + 0.517100i
906906 0.833126 5.79452i 0.0276787 0.192510i
907907 −16.7201 36.6120i −0.555183 1.21568i −0.954319 0.298789i 0.903417π-0.903417\pi
0.399136 0.916892i 0.369310π-0.369310\pi
908908 −18.9099 5.55244i −0.627547 0.184264i
909909 −8.58197 2.51989i −0.284646 0.0835796i
910910 3.08089 + 6.74620i 0.102130 + 0.223634i
911911 −4.45516 + 30.9863i −0.147606 + 1.02662i 0.772517 + 0.634994i 0.218997π0.218997\pi
−0.920123 + 0.391629i 0.871912π0.871912\pi
912912 −5.42997 + 6.26652i −0.179804 + 0.207505i
913913 19.0628 41.7417i 0.630886 1.38145i
914914 −2.66440 1.71231i −0.0881307 0.0566382i
915915 −2.73152 18.9981i −0.0903012 0.628059i
916916 16.3341 10.4973i 0.539695 0.346841i
917917 −39.6459 45.7538i −1.30922 1.51093i
918918 −1.01296 + 0.297433i −0.0334328 + 0.00981675i
919919 41.1246 1.35658 0.678288 0.734796i 0.262722π-0.262722\pi
0.678288 + 0.734796i 0.262722π0.262722\pi
920920 0 0
921921 −21.3050 −0.702022
922922 0.872976 0.256329i 0.0287499 0.00844174i
923923 −24.0388 27.7422i −0.791245 0.913146i
924924 −51.5730 + 33.1440i −1.69663 + 1.09036i
925925 −0.610786 4.24811i −0.0200825 0.139677i
926926 −10.3985 6.68269i −0.341715 0.219607i
927927 −3.47315 + 7.60514i −0.114073 + 0.249786i
928928 11.0371 12.7375i 0.362310 0.418128i
929929 3.42349 23.8109i 0.112321 0.781209i −0.853331 0.521370i 0.825421π-0.825421\pi
0.965652 0.259840i 0.0836697π-0.0836697\pi
930930 −4.76023 10.4235i −0.156094 0.341799i
931931 6.66298 + 1.95643i 0.218370 + 0.0641193i
932932 −10.1345 2.97575i −0.331965 0.0974738i
933933 −12.2432 26.8088i −0.400823 0.877681i
934934 1.14832 7.98675i 0.0375742 0.261335i
935935 3.23781 3.73663i 0.105888 0.122201i
936936 −5.57338 + 12.2040i −0.182172 + 0.398900i
937937 28.7543 + 18.4793i 0.939363 + 0.603692i 0.918214 0.396084i 0.129631π-0.129631\pi
0.0211489 + 0.999776i 0.493268π0.493268\pi
938938 0.786697 + 5.47160i 0.0256866 + 0.178654i
939939 −45.8249 + 29.4499i −1.49544 + 0.961060i
940940 −2.92863 3.37981i −0.0955213 0.110237i
941941 −6.38300 + 1.87422i −0.208080 + 0.0610978i −0.384111 0.923287i 0.625492π-0.625492\pi
0.176031 + 0.984385i 0.443674π0.443674\pi
942942 15.7771 0.514045
943943 0 0
944944 12.0000 0.390567
945945 −8.58197 + 2.51989i −0.279171 + 0.0819721i
946946 0 0
947947 −9.10208 + 5.84955i −0.295778 + 0.190085i −0.680110 0.733110i 0.738068π-0.738068\pi
0.384332 + 0.923195i 0.374432π0.374432\pi
948948 5.63520 + 39.1937i 0.183023 + 1.27295i
949949 16.4748 + 10.5877i 0.534794 + 0.343691i
950950 1.78288 3.90396i 0.0578442 0.126661i
951951 37.2176 42.9514i 1.20686 1.39279i
952952 0.786697 5.47160i 0.0254970 0.177336i
953953 8.50443 + 18.6221i 0.275486 + 0.603229i 0.995915 0.0902993i 0.0287824π-0.0287824\pi
−0.720429 + 0.693529i 0.756055π0.756055\pi
954954 −0.559953 0.164417i −0.0181291 0.00532319i
955955 31.0498 + 9.11706i 1.00475 + 0.295021i
956956 −9.25150 20.2580i −0.299215 0.655190i
957957 4.99875 34.7671i 0.161587 1.12386i
958958 −12.7880 + 14.7582i −0.413163 + 0.476815i
959959 −29.4250 + 64.4318i −0.950183 + 2.08061i
960960 0.548898 + 0.352755i 0.0177156 + 0.0113851i
961961 −1.99241 13.8575i −0.0642712 0.447016i
962962 −1.92798 + 1.23904i −0.0621606 + 0.0399482i
963963 −17.5718 20.2789i −0.566242 0.653478i
964964 −35.9008 + 10.5414i −1.15629 + 0.339516i
965965 12.2918 0.395687
966966 0 0
967967 27.5410 0.885659 0.442830 0.896606i 0.353975π-0.353975\pi
0.442830 + 0.896606i 0.353975π0.353975\pi
968968 35.2213 10.3419i 1.13205 0.332401i
969969 −2.23727 2.58195i −0.0718715 0.0829441i
970970 11.3804 7.31372i 0.365401 0.234829i
971971 −2.34423 16.3045i −0.0752299 0.523235i −0.992237 0.124364i 0.960311π-0.960311\pi
0.917007 0.398872i 0.130598π-0.130598\pi
972972 −24.3495 15.6485i −0.781010 0.501924i
973973 −14.3952 + 31.5210i −0.461488 + 1.01052i
974974 5.95280 6.86989i 0.190740 0.220126i
975975 −3.31477 + 23.0547i −0.106158 + 0.738342i
976976 −5.34863 11.7119i −0.171205 0.374888i
977977 22.4018 + 6.57776i 0.716697 + 0.210441i 0.619695 0.784843i 0.287256π-0.287256\pi
0.0970020 + 0.995284i 0.469075π0.469075\pi
978978 −7.64290 2.24416i −0.244393 0.0717602i
979979 22.7784 + 49.8777i 0.728000 + 1.59410i
980980 0.988273 6.87359i 0.0315692 0.219569i
981981 0 0
982982 2.14315 4.69284i 0.0683906 0.149755i
983983 −34.0473 21.8809i −1.08594 0.697892i −0.130019 0.991512i 0.541504π-0.541504\pi
−0.955922 + 0.293620i 0.905140π0.905140\pi
984984 2.47068 + 17.1840i 0.0787625 + 0.547805i
985985 −1.53080 + 0.983783i −0.0487752 + 0.0313459i
986986 0.927550 + 1.07045i 0.0295392 + 0.0340901i
987987 −15.5249 + 4.55853i −0.494164 + 0.145100i
988988 9.70820 0.308859
989989 0 0
990990 −8.00000 −0.254257
991991 −23.0278 + 6.76158i −0.731503 + 0.214789i −0.626212 0.779653i 0.715396π-0.715396\pi
−0.105291 + 0.994441i 0.533577π0.533577\pi
992992 −24.6797 28.4819i −0.783581 0.904300i
993993 36.9683 23.7581i 1.17315 0.753939i
994994 −3.48275 24.2230i −0.110466 0.768308i
995995 −12.7816 8.21422i −0.405203 0.260408i
996996 −13.1721 + 28.8428i −0.417373 + 0.913919i
997997 −11.0232 + 12.7214i −0.349107 + 0.402891i −0.902961 0.429723i 0.858611π-0.858611\pi
0.553854 + 0.832614i 0.313157π0.313157\pi
998998 −1.69682 + 11.8016i −0.0537118 + 0.373574i
999999 −1.14818 2.51416i −0.0363268 0.0795445i
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 529.2.c.o.170.1 20
23.2 even 11 inner 529.2.c.o.266.1 20
23.3 even 11 inner 529.2.c.o.334.2 20
23.4 even 11 inner 529.2.c.o.466.2 20
23.5 odd 22 529.2.c.n.501.1 20
23.6 even 11 inner 529.2.c.o.255.2 20
23.7 odd 22 529.2.c.n.487.2 20
23.8 even 11 23.2.a.a.1.2 2
23.9 even 11 inner 529.2.c.o.177.1 20
23.10 odd 22 529.2.c.n.118.1 20
23.11 odd 22 529.2.c.n.399.1 20
23.12 even 11 inner 529.2.c.o.399.1 20
23.13 even 11 inner 529.2.c.o.118.1 20
23.14 odd 22 529.2.c.n.177.1 20
23.15 odd 22 529.2.a.a.1.2 2
23.16 even 11 inner 529.2.c.o.487.2 20
23.17 odd 22 529.2.c.n.255.2 20
23.18 even 11 inner 529.2.c.o.501.1 20
23.19 odd 22 529.2.c.n.466.2 20
23.20 odd 22 529.2.c.n.334.2 20
23.21 odd 22 529.2.c.n.266.1 20
23.22 odd 2 529.2.c.n.170.1 20
69.8 odd 22 207.2.a.d.1.1 2
69.38 even 22 4761.2.a.w.1.1 2
92.15 even 22 8464.2.a.bb.1.2 2
92.31 odd 22 368.2.a.h.1.2 2
115.8 odd 44 575.2.b.d.24.2 4
115.54 even 22 575.2.a.f.1.1 2
115.77 odd 44 575.2.b.d.24.3 4
161.146 odd 22 1127.2.a.c.1.2 2
184.77 even 22 1472.2.a.t.1.2 2
184.123 odd 22 1472.2.a.s.1.1 2
253.54 odd 22 2783.2.a.c.1.1 2
276.215 even 22 3312.2.a.ba.1.1 2
299.77 even 22 3887.2.a.i.1.1 2
345.284 odd 22 5175.2.a.be.1.2 2
391.169 even 22 6647.2.a.b.1.2 2
437.284 odd 22 8303.2.a.e.1.1 2
460.399 odd 22 9200.2.a.bt.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.2.a.a.1.2 2 23.8 even 11
207.2.a.d.1.1 2 69.8 odd 22
368.2.a.h.1.2 2 92.31 odd 22
529.2.a.a.1.2 2 23.15 odd 22
529.2.c.n.118.1 20 23.10 odd 22
529.2.c.n.170.1 20 23.22 odd 2
529.2.c.n.177.1 20 23.14 odd 22
529.2.c.n.255.2 20 23.17 odd 22
529.2.c.n.266.1 20 23.21 odd 22
529.2.c.n.334.2 20 23.20 odd 22
529.2.c.n.399.1 20 23.11 odd 22
529.2.c.n.466.2 20 23.19 odd 22
529.2.c.n.487.2 20 23.7 odd 22
529.2.c.n.501.1 20 23.5 odd 22
529.2.c.o.118.1 20 23.13 even 11 inner
529.2.c.o.170.1 20 1.1 even 1 trivial
529.2.c.o.177.1 20 23.9 even 11 inner
529.2.c.o.255.2 20 23.6 even 11 inner
529.2.c.o.266.1 20 23.2 even 11 inner
529.2.c.o.334.2 20 23.3 even 11 inner
529.2.c.o.399.1 20 23.12 even 11 inner
529.2.c.o.466.2 20 23.4 even 11 inner
529.2.c.o.487.2 20 23.16 even 11 inner
529.2.c.o.501.1 20 23.18 even 11 inner
575.2.a.f.1.1 2 115.54 even 22
575.2.b.d.24.2 4 115.8 odd 44
575.2.b.d.24.3 4 115.77 odd 44
1127.2.a.c.1.2 2 161.146 odd 22
1472.2.a.s.1.1 2 184.123 odd 22
1472.2.a.t.1.2 2 184.77 even 22
2783.2.a.c.1.1 2 253.54 odd 22
3312.2.a.ba.1.1 2 276.215 even 22
3887.2.a.i.1.1 2 299.77 even 22
4761.2.a.w.1.1 2 69.38 even 22
5175.2.a.be.1.2 2 345.284 odd 22
6647.2.a.b.1.2 2 391.169 even 22
8303.2.a.e.1.1 2 437.284 odd 22
8464.2.a.bb.1.2 2 92.15 even 22
9200.2.a.bt.1.1 2 460.399 odd 22