Properties

Label 416.2.bd.a.411.5
Level 416416
Weight 22
Character 416.411
Analytic conductor 3.3223.322
Analytic rank 00
Dimension 216216
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [416,2,Mod(83,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 7, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.83");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 416=2513 416 = 2^{5} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 416.bd (of order 88, degree 44, 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: 3.321776724093.32177672409
Analytic rank: 00
Dimension: 216216
Relative dimension: 5454 over Q(ζ8)\Q(\zeta_{8})
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 411.5
Character χ\chi == 416.411
Dual form 416.2.bd.a.83.5

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+(1.351520.416401i)q2+(2.25523+0.934148i)q3+(1.65322+1.12555i)q4+(0.261748+0.631915i)q5+(3.436980.323439i)q6+4.76655iq7+(1.765682.20961i)q8+(2.092132.09213i)q9+(0.09062750.963039i)q10+(1.639780.679219i)q11+(4.779830.994027i)q12+(3.28393+1.48856i)q13+(1.984806.44209i)q14+(1.180611.18061i)q15+(1.46627+3.72157i)q162.74788q17+(3.69872+1.95639i)q18+(0.4143551.00034i)q19+(0.278526+1.33931i)q20+(4.4526610.7497i)q21+(2.49902+0.235173i)q22+(5.08603+5.08603i)q23+(6.04613+3.33378i)q24+(3.204733.20473i)q25+(3.818463.37925i)q26+(0.03856890.0931135i)q27+(5.36499+7.88015i)q28+(0.203632+0.491611i)q29+(1.10401+2.08722i)q30+(5.24354+5.24354i)q31+(0.4320335.64033i)q32+(3.06360+3.06360i)q33+(3.71382+1.14422i)q34+(3.01206+1.24763i)q35+(5.813541.10395i)q36+(4.94751+2.04933i)q37+(0.976552+1.17944i)q38+(8.796560.289375i)q39+(0.9341221.69412i)q402.97903q41+(1.54169+16.3825i)q42+(2.44549+5.90392i)q43+(3.47541+0.722757i)q44+(1.86966+0.774437i)q45+(8.991704.75604i)q46+(2.46927+2.46927i)q47+(6.783287.02328i)q4815.7200q49+(5.66571+2.99681i)q50+(6.197122.56693i)q51+(3.75361+6.15715i)q52+(1.107662.67412i)q53+(0.0908993+0.109785i)q54+(0.858418+0.858418i)q55+(10.53228.41621i)q56+2.64307iq57+(0.07050550.749215i)q58+(3.752249.05870i)q59+(0.6229693.28063i)q60+(4.090739.87589i)q61+(9.270174.90334i)q62+(9.97222+9.97222i)q63+(1.76474+7.80293i)q64+(0.0810828+2.46479i)q65+(5.416202.86483i)q66+(7.51832+3.11419i)q67+(4.542863.09288i)q68+(6.7190716.2213i)q69+(4.590370.431980i)q70+12.2690q71+(8.316810.928752i)q72+1.56983iq73+(7.540010.709558i)q74+(4.23372+10.2211i)q75+(1.810951.18741i)q76+(3.23753+7.81609i)q77+(11.7682+4.05400i)q784.45846q79+(1.96792+1.90067i)q80+9.12216iq81+(4.02623+1.24047i)q82+(5.7775813.9483i)q83+(4.7380822.7833i)q84+(0.7192531.73643i)q85+(5.763536.96098i)q86+(0.9184750.918475i)q87+(4.396142.42399i)q88+4.19672q89+(2.204401.82520i)q90+(7.09530+15.6530i)q91+(14.1329+2.68374i)q92+(6.9271616.7236i)q93+(4.365482.30906i)q94+0.740587q95+(6.24324+12.3167i)q96+(0.2453040.245304i)q97+(21.2459+6.54582i)q98+(2.009614.85164i)q99+O(q100)q+(-1.35152 - 0.416401i) q^{2} +(-2.25523 + 0.934148i) q^{3} +(1.65322 + 1.12555i) q^{4} +(0.261748 + 0.631915i) q^{5} +(3.43698 - 0.323439i) q^{6} +4.76655i q^{7} +(-1.76568 - 2.20961i) q^{8} +(2.09213 - 2.09213i) q^{9} +(-0.0906275 - 0.963039i) q^{10} +(1.63978 - 0.679219i) q^{11} +(-4.77983 - 0.994027i) q^{12} +(3.28393 + 1.48856i) q^{13} +(1.98480 - 6.44209i) q^{14} +(-1.18061 - 1.18061i) q^{15} +(1.46627 + 3.72157i) q^{16} -2.74788 q^{17} +(-3.69872 + 1.95639i) q^{18} +(0.414355 - 1.00034i) q^{19} +(-0.278526 + 1.33931i) q^{20} +(-4.45266 - 10.7497i) q^{21} +(-2.49902 + 0.235173i) q^{22} +(-5.08603 + 5.08603i) q^{23} +(6.04613 + 3.33378i) q^{24} +(3.20473 - 3.20473i) q^{25} +(-3.81846 - 3.37925i) q^{26} +(0.0385689 - 0.0931135i) q^{27} +(-5.36499 + 7.88015i) q^{28} +(0.203632 + 0.491611i) q^{29} +(1.10401 + 2.08722i) q^{30} +(-5.24354 + 5.24354i) q^{31} +(-0.432033 - 5.64033i) q^{32} +(-3.06360 + 3.06360i) q^{33} +(3.71382 + 1.14422i) q^{34} +(-3.01206 + 1.24763i) q^{35} +(5.81354 - 1.10395i) q^{36} +(-4.94751 + 2.04933i) q^{37} +(-0.976552 + 1.17944i) q^{38} +(-8.79656 - 0.289375i) q^{39} +(0.934122 - 1.69412i) q^{40} -2.97903 q^{41} +(1.54169 + 16.3825i) q^{42} +(-2.44549 + 5.90392i) q^{43} +(3.47541 + 0.722757i) q^{44} +(1.86966 + 0.774437i) q^{45} +(8.99170 - 4.75604i) q^{46} +(-2.46927 + 2.46927i) q^{47} +(-6.78328 - 7.02328i) q^{48} -15.7200 q^{49} +(-5.66571 + 2.99681i) q^{50} +(6.19712 - 2.56693i) q^{51} +(3.75361 + 6.15715i) q^{52} +(1.10766 - 2.67412i) q^{53} +(-0.0908993 + 0.109785i) q^{54} +(0.858418 + 0.858418i) q^{55} +(10.5322 - 8.41621i) q^{56} +2.64307i q^{57} +(-0.0705055 - 0.749215i) q^{58} +(-3.75224 - 9.05870i) q^{59} +(-0.622969 - 3.28063i) q^{60} +(-4.09073 - 9.87589i) q^{61} +(9.27017 - 4.90334i) q^{62} +(9.97222 + 9.97222i) q^{63} +(-1.76474 + 7.80293i) q^{64} +(-0.0810828 + 2.46479i) q^{65} +(5.41620 - 2.86483i) q^{66} +(7.51832 + 3.11419i) q^{67} +(-4.54286 - 3.09288i) q^{68} +(6.71907 - 16.2213i) q^{69} +(4.59037 - 0.431980i) q^{70} +12.2690 q^{71} +(-8.31681 - 0.928752i) q^{72} +1.56983i q^{73} +(7.54001 - 0.709558i) q^{74} +(-4.23372 + 10.2211i) q^{75} +(1.81095 - 1.18741i) q^{76} +(3.23753 + 7.81609i) q^{77} +(11.7682 + 4.05400i) q^{78} -4.45846 q^{79} +(-1.96792 + 1.90067i) q^{80} +9.12216i q^{81} +(4.02623 + 1.24047i) q^{82} +(5.77758 - 13.9483i) q^{83} +(4.73808 - 22.7833i) q^{84} +(-0.719253 - 1.73643i) q^{85} +(5.76353 - 6.96098i) q^{86} +(-0.918475 - 0.918475i) q^{87} +(-4.39614 - 2.42399i) q^{88} +4.19672 q^{89} +(-2.20440 - 1.82520i) q^{90} +(-7.09530 + 15.6530i) q^{91} +(-14.1329 + 2.68374i) q^{92} +(6.92716 - 16.7236i) q^{93} +(4.36548 - 2.30906i) q^{94} +0.740587 q^{95} +(6.24324 + 12.3167i) q^{96} +(-0.245304 - 0.245304i) q^{97} +(21.2459 + 6.54582i) q^{98} +(2.00961 - 4.85164i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 216q4q28q34q5+8q64q88q94q1124q124q13+24q148q158q1612q184q1920q20+8q2124q2236q24+44q99+O(q100) 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/416Z)×\left(\mathbb{Z}/416\mathbb{Z}\right)^\times.

nn 261261 287287 353353
χ(n)\chi(n) e(18)e\left(\frac{1}{8}\right) 1-1 e(14)e\left(\frac{1}{4}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.35152 0.416401i −0.955670 0.294440i
33 −2.25523 + 0.934148i −1.30206 + 0.539331i −0.922557 0.385860i 0.873905π-0.873905\pi
−0.379502 + 0.925191i 0.623905π0.623905\pi
44 1.65322 + 1.12555i 0.826610 + 0.562775i
55 0.261748 + 0.631915i 0.117057 + 0.282601i 0.971539 0.236881i 0.0761250π-0.0761250\pi
−0.854482 + 0.519482i 0.826125π0.826125\pi
66 3.43698 0.323439i 1.40314 0.132043i
77 4.76655i 1.80159i 0.434249 + 0.900793i 0.357014π0.357014\pi
−0.434249 + 0.900793i 0.642986π0.642986\pi
88 −1.76568 2.20961i −0.624263 0.781215i
99 2.09213 2.09213i 0.697375 0.697375i
1010 −0.0906275 0.963039i −0.0286589 0.304540i
1111 1.63978 0.679219i 0.494412 0.204792i −0.121524 0.992589i 0.538778π-0.538778\pi
0.615936 + 0.787796i 0.288778π0.288778\pi
1212 −4.77983 0.994027i −1.37982 0.286951i
1313 3.28393 + 1.48856i 0.910798 + 0.412852i
1414 1.98480 6.44209i 0.530459 1.72172i
1515 −1.18061 1.18061i −0.304831 0.304831i
1616 1.46627 + 3.72157i 0.366568 + 0.930391i
1717 −2.74788 −0.666460 −0.333230 0.942846i 0.608138π-0.608138\pi
−0.333230 + 0.942846i 0.608138π0.608138\pi
1818 −3.69872 + 1.95639i −0.871796 + 0.461125i
1919 0.414355 1.00034i 0.0950595 0.229494i −0.869196 0.494467i 0.835363π-0.835363\pi
0.964256 + 0.264973i 0.0853632π0.0853632\pi
2020 −0.278526 + 1.33931i −0.0622803 + 0.299478i
2121 −4.45266 10.7497i −0.971651 2.34577i
2222 −2.49902 + 0.235173i −0.532794 + 0.0501390i
2323 −5.08603 + 5.08603i −1.06051 + 1.06051i −0.0624623 + 0.998047i 0.519895π0.519895\pi
−0.998047 + 0.0624623i 0.980105π0.980105\pi
2424 6.04613 + 3.33378i 1.23416 + 0.680504i
2525 3.20473 3.20473i 0.640946 0.640946i
2626 −3.81846 3.37925i −0.748862 0.662726i
2727 0.0385689 0.0931135i 0.00742259 0.0179197i
2828 −5.36499 + 7.88015i −1.01389 + 1.48921i
2929 0.203632 + 0.491611i 0.0378135 + 0.0912899i 0.941658 0.336571i 0.109267π-0.109267\pi
−0.903845 + 0.427861i 0.859267π0.859267\pi
3030 1.10401 + 2.08722i 0.201563 + 0.381072i
3131 −5.24354 + 5.24354i −0.941767 + 0.941767i −0.998395 0.0566280i 0.981965π-0.981965\pi
0.0566280 + 0.998395i 0.481965π0.481965\pi
3232 −0.432033 5.64033i −0.0763734 0.997079i
3333 −3.06360 + 3.06360i −0.533303 + 0.533303i
3434 3.71382 + 1.14422i 0.636915 + 0.196233i
3535 −3.01206 + 1.24763i −0.509130 + 0.210889i
3636 5.81354 1.10395i 0.968923 0.183992i
3737 −4.94751 + 2.04933i −0.813366 + 0.336907i −0.750296 0.661102i 0.770089π-0.770089\pi
−0.0630697 + 0.998009i 0.520089π0.520089\pi
3838 −0.976552 + 1.17944i −0.158418 + 0.191331i
3939 −8.79656 0.289375i −1.40858 0.0463371i
4040 0.934122 1.69412i 0.147698 0.267864i
4141 −2.97903 −0.465247 −0.232623 0.972567i 0.574731π-0.574731\pi
−0.232623 + 0.972567i 0.574731π0.574731\pi
4242 1.54169 + 16.3825i 0.237888 + 2.52788i
4343 −2.44549 + 5.90392i −0.372933 + 0.900340i 0.620317 + 0.784351i 0.287004π0.287004\pi
−0.993250 + 0.115989i 0.962996π0.962996\pi
4444 3.47541 + 0.722757i 0.523938 + 0.108960i
4545 1.86966 + 0.774437i 0.278712 + 0.115446i
4646 8.99170 4.75604i 1.32575 0.701240i
4747 −2.46927 + 2.46927i −0.360180 + 0.360180i −0.863879 0.503699i 0.831972π-0.831972\pi
0.503699 + 0.863879i 0.331972π0.331972\pi
4848 −6.78328 7.02328i −0.979082 1.01372i
4949 −15.7200 −2.24571
5050 −5.66571 + 2.99681i −0.801253 + 0.423812i
5151 6.19712 2.56693i 0.867770 0.359442i
5252 3.75361 + 6.15715i 0.520531 + 0.853842i
5353 1.10766 2.67412i 0.152148 0.367318i −0.829367 0.558705i 0.811298π-0.811298\pi
0.981515 + 0.191387i 0.0612984π0.0612984\pi
5454 −0.0908993 + 0.109785i −0.0123698 + 0.0149398i
5555 0.858418 + 0.858418i 0.115749 + 0.115749i
5656 10.5322 8.41621i 1.40743 1.12466i
5757 2.64307i 0.350083i
5858 −0.0705055 0.749215i −0.00925782 0.0983768i
5959 −3.75224 9.05870i −0.488499 1.17934i −0.955475 0.295072i 0.904656π-0.904656\pi
0.466976 0.884270i 0.345344π-0.345344\pi
6060 −0.622969 3.28063i −0.0804250 0.423528i
6161 −4.09073 9.87589i −0.523764 1.26448i −0.935549 0.353197i 0.885095π-0.885095\pi
0.411785 0.911281i 0.364905π-0.364905\pi
6262 9.27017 4.90334i 1.17731 0.622725i
6363 9.97222 + 9.97222i 1.25638 + 1.25638i
6464 −1.76474 + 7.80293i −0.220592 + 0.975366i
6565 −0.0810828 + 2.46479i −0.0100571 + 0.305720i
6666 5.41620 2.86483i 0.666688 0.352636i
6767 7.51832 + 3.11419i 0.918509 + 0.380459i 0.791308 0.611418i 0.209401π-0.209401\pi
0.127201 + 0.991877i 0.459401π0.459401\pi
6868 −4.54286 3.09288i −0.550902 0.375067i
6969 6.71907 16.2213i 0.808881 1.95281i
7070 4.59037 0.431980i 0.548655 0.0516315i
7171 12.2690 1.45606 0.728028 0.685547i 0.240437π-0.240437\pi
0.728028 + 0.685547i 0.240437π0.240437\pi
7272 −8.31681 0.928752i −0.980145 0.109454i
7373 1.56983i 0.183734i 0.995771 + 0.0918672i 0.0292835π0.0292835\pi
−0.995771 + 0.0918672i 0.970716π0.970716\pi
7474 7.54001 0.709558i 0.876508 0.0824844i
7575 −4.23372 + 10.2211i −0.488868 + 1.18023i
7676 1.81095 1.18741i 0.207731 0.136205i
7777 3.23753 + 7.81609i 0.368951 + 0.890726i
7878 11.7682 + 4.05400i 1.33249 + 0.459025i
7979 −4.45846 −0.501616 −0.250808 0.968037i 0.580696π-0.580696\pi
−0.250808 + 0.968037i 0.580696π0.580696\pi
8080 −1.96792 + 1.90067i −0.220020 + 0.212502i
8181 9.12216i 1.01357i
8282 4.02623 + 1.24047i 0.444622 + 0.136987i
8383 5.77758 13.9483i 0.634172 1.53103i −0.200159 0.979763i 0.564146π-0.564146\pi
0.834331 0.551263i 0.185854π-0.185854\pi
8484 4.73808 22.7833i 0.516967 2.48586i
8585 −0.719253 1.73643i −0.0780139 0.188342i
8686 5.76353 6.96098i 0.621497 0.750621i
8787 −0.918475 0.918475i −0.0984709 0.0984709i
8888 −4.39614 2.42399i −0.468630 0.258398i
8989 4.19672 0.444851 0.222426 0.974950i 0.428603π-0.428603\pi
0.222426 + 0.974950i 0.428603π0.428603\pi
9090 −2.20440 1.82520i −0.232365 0.192392i
9191 −7.09530 + 15.6530i −0.743789 + 1.64088i
9292 −14.1329 + 2.68374i −1.47346 + 0.279799i
9393 6.92716 16.7236i 0.718313 1.73416i
9494 4.36548 2.30906i 0.450264 0.238162i
9595 0.740587 0.0759826
9696 6.24324 + 12.3167i 0.637198 + 1.25707i
9797 −0.245304 0.245304i −0.0249069 0.0249069i 0.694544 0.719451i 0.255606π-0.255606\pi
−0.719451 + 0.694544i 0.755606π0.755606\pi
9898 21.2459 + 6.54582i 2.14616 + 0.661228i
9999 2.00961 4.85164i 0.201974 0.487608i
100100 8.90521 1.69104i 0.890521 0.169104i
101101 −2.01267 + 4.85902i −0.200268 + 0.483490i −0.991825 0.127605i 0.959271π-0.959271\pi
0.791557 + 0.611096i 0.209271π0.209271\pi
102102 −9.44441 + 0.888773i −0.935136 + 0.0880017i
103103 −8.16643 8.16643i −0.804663 0.804663i 0.179158 0.983820i 0.442663π-0.442663\pi
−0.983820 + 0.179158i 0.942663π0.942663\pi
104104 −2.50924 9.88452i −0.246051 0.969257i
105105 5.62741 5.62741i 0.549179 0.549179i
106106 −2.61053 + 3.15290i −0.253557 + 0.306236i
107107 −0.342942 0.142051i −0.0331534 0.0137326i 0.366045 0.930597i 0.380712π-0.380712\pi
−0.399199 + 0.916865i 0.630712π0.630712\pi
108108 0.168567 0.110526i 0.0162204 0.0106354i
109109 19.0153 + 7.87639i 1.82133 + 0.754421i 0.975156 + 0.221520i 0.0711019π0.0711019\pi
0.846178 + 0.532901i 0.178898π0.178898\pi
110110 −0.802724 1.51762i −0.0765367 0.144699i
111111 9.24342 9.24342i 0.877346 0.877346i
112112 −17.7390 + 6.98906i −1.67618 + 0.660404i
113113 0.911688i 0.0857644i −0.999080 0.0428822i 0.986346π-0.986346\pi
0.999080 0.0428822i 0.0136540π-0.0136540\pi
114114 1.10058 3.57217i 0.103079 0.334564i
115115 −4.54519 1.88268i −0.423842 0.175561i
116116 −0.216685 + 1.04194i −0.0201187 + 0.0967416i
117117 9.98465 3.75614i 0.923081 0.347255i
118118 1.29917 + 13.8055i 0.119599 + 1.27090i
119119 13.0979i 1.20068i
120120 −0.524103 + 4.69325i −0.0478438 + 0.428433i
121121 −5.55064 + 5.55064i −0.504603 + 0.504603i
122122 1.41637 + 15.0509i 0.128232 + 1.36264i
123123 6.71842 2.78286i 0.605779 0.250922i
124124 −14.5706 + 2.76685i −1.30848 + 0.248471i
125125 6.02353 + 2.49503i 0.538761 + 0.223162i
126126 −9.32522 17.6301i −0.830757 1.57062i
127127 −19.1141 −1.69611 −0.848053 0.529911i 0.822225π-0.822225\pi
−0.848053 + 0.529911i 0.822225π0.822225\pi
128128 5.63423 9.81098i 0.498001 0.867177i
129129 15.5992i 1.37343i
130130 1.13593 3.29746i 0.0996275 0.289206i
131131 −12.2119 + 5.05835i −1.06696 + 0.441950i −0.845917 0.533314i 0.820946π-0.820946\pi
−0.221044 + 0.975264i 0.570946π0.570946\pi
132132 −8.51303 + 1.61657i −0.740964 + 0.140704i
133133 4.76817 + 1.97504i 0.413453 + 0.171258i
134134 −8.86442 7.33953i −0.765769 0.634039i
135135 0.0689352 0.00593300
136136 4.85189 + 6.07175i 0.416046 + 0.520648i
137137 13.5356i 1.15642i 0.815887 + 0.578212i 0.196249π0.196249\pi
−0.815887 + 0.578212i 0.803751π0.803751\pi
138138 −15.8355 + 19.1256i −1.34801 + 1.62808i
139139 −1.05909 0.438691i −0.0898311 0.0372093i 0.337315 0.941392i 0.390481π-0.390481\pi
−0.427146 + 0.904182i 0.640481π0.640481\pi
140140 −6.38387 1.32761i −0.539535 0.112203i
141141 3.26211 7.87544i 0.274720 0.663232i
142142 −16.5818 5.10881i −1.39151 0.428722i
143143 6.39598 + 0.210405i 0.534859 + 0.0175949i
144144 10.8536 + 4.71836i 0.904467 + 0.393196i
145145 −0.257356 + 0.257356i −0.0213723 + 0.0213723i
146146 0.653678 2.12165i 0.0540988 0.175589i
147147 35.4523 14.6848i 2.92405 1.21118i
148148 −10.4859 2.18069i −0.861939 0.179251i
149149 −16.1546 + 6.69145i −1.32344 + 0.548185i −0.928776 0.370643i 0.879137π-0.879137\pi
−0.394660 + 0.918827i 0.629137π0.629137\pi
150150 9.97804 12.0511i 0.814704 0.983969i
151151 21.8089 1.77478 0.887392 0.461016i 0.152515π-0.152515\pi
0.887392 + 0.461016i 0.152515π0.152515\pi
152152 −2.94198 + 0.850721i −0.238626 + 0.0690026i
153153 −5.74892 + 5.74892i −0.464772 + 0.464772i
154154 −1.12096 11.9117i −0.0903296 0.959874i
155155 −4.68596 1.94099i −0.376385 0.155904i
156156 −14.2169 10.3794i −1.13827 0.831015i
157157 4.63951 + 11.2008i 0.370273 + 0.893918i 0.993704 + 0.112040i 0.0357384π0.0357384\pi
−0.623431 + 0.781879i 0.714262π0.714262\pi
158158 6.02571 + 1.85651i 0.479380 + 0.147696i
159159 7.06547i 0.560329i
160160 3.45113 1.74935i 0.272836 0.138299i
161161 −24.2428 24.2428i −1.91060 1.91060i
162162 3.79848 12.3288i 0.298437 0.968641i
163163 1.91518 4.62366i 0.150009 0.362153i −0.830956 0.556338i 0.812206π-0.812206\pi
0.980965 + 0.194185i 0.0622061π0.0622061\pi
164164 −4.92500 3.35305i −0.384578 0.261829i
165165 −2.73782 1.13404i −0.213139 0.0882851i
166166 −13.6166 + 16.4457i −1.05685 + 1.27643i
167167 20.0885i 1.55450i 0.629195 + 0.777248i 0.283385π0.283385\pi
−0.629195 + 0.777248i 0.716615π0.716615\pi
168168 −15.8906 + 28.8192i −1.22599 + 2.22345i
169169 8.56837 + 9.77665i 0.659106 + 0.752050i
170170 0.249034 + 2.64632i 0.0191000 + 0.202963i
171171 −1.22596 2.95972i −0.0937512 0.226335i
172172 −10.6881 + 7.00797i −0.814959 + 0.534353i
173173 6.32717 + 15.2752i 0.481046 + 1.16135i 0.959113 + 0.283025i 0.0913378π0.0913378\pi
−0.478066 + 0.878324i 0.658662π0.658662\pi
174174 0.858885 + 1.62379i 0.0651119 + 0.123099i
175175 15.2755 + 15.2755i 1.15472 + 1.15472i
176176 4.93212 + 5.10663i 0.371773 + 0.384926i
177177 16.9243 + 16.9243i 1.27211 + 1.27211i
178178 −5.67195 1.74752i −0.425131 0.130982i
179179 −8.30332 + 3.43935i −0.620619 + 0.257069i −0.670761 0.741673i 0.734033π-0.734033\pi
0.0501422 + 0.998742i 0.484033π0.484033\pi
180180 2.21928 + 3.38471i 0.165416 + 0.252281i
181181 7.67585 + 3.17944i 0.570542 + 0.236326i 0.649254 0.760571i 0.275081π-0.275081\pi
−0.0787128 + 0.996897i 0.525081π0.525081\pi
182182 16.1074 18.2009i 1.19396 1.34914i
183183 18.4511 + 18.4511i 1.36394 + 1.36394i
184184 20.2184 + 2.25783i 1.49052 + 0.166449i
185185 −2.59000 2.59000i −0.190421 0.190421i
186186 −16.3260 + 19.7179i −1.19708 + 1.44579i
187187 −4.50592 + 1.86641i −0.329506 + 0.136486i
188188 −6.86153 + 1.30296i −0.500429 + 0.0950279i
189189 0.443830 + 0.183840i 0.0322839 + 0.0133724i
190190 −1.00092 0.308381i −0.0726143 0.0223723i
191191 7.74904i 0.560701i −0.959898 0.280350i 0.909549π-0.909549\pi
0.959898 0.280350i 0.0904507π-0.0904507\pi
192192 −3.30919 19.2460i −0.238820 1.38896i
193193 12.4434 12.4434i 0.895696 0.895696i −0.0993562 0.995052i 0.531678π-0.531678\pi
0.995052 + 0.0993562i 0.0316783π0.0316783\pi
194194 0.229389 + 0.433679i 0.0164692 + 0.0311363i
195195 −2.11962 5.63443i −0.151789 0.403490i
196196 −25.9886 17.6936i −1.85633 1.26383i
197197 2.23719 + 5.40104i 0.159393 + 0.384809i 0.983319 0.181889i 0.0582210π-0.0582210\pi
−0.823926 + 0.566697i 0.808221π0.808221\pi
198198 −4.73626 + 5.72028i −0.336592 + 0.406523i
199199 3.20031 + 3.20031i 0.226864 + 0.226864i 0.811381 0.584517i 0.198716π-0.198716\pi
−0.584517 + 0.811381i 0.698716π0.698716\pi
200200 −12.7397 1.42267i −0.900835 0.100598i
201201 −19.8647 −1.40115
202202 4.74347 5.72899i 0.333749 0.403090i
203203 −2.34329 + 0.970622i −0.164467 + 0.0681243i
204204 13.1344 + 2.73147i 0.919593 + 0.191241i
205205 −0.779756 1.88250i −0.0544605 0.131479i
206206 7.63660 + 14.4376i 0.532067 + 1.00592i
207207 21.2812i 1.47915i
208208 −0.724642 + 14.4040i −0.0502449 + 0.998737i
209209 1.92178i 0.132932i
210210 −9.94883 + 5.26231i −0.686535 + 0.363134i
211211 −0.961172 2.32047i −0.0661698 0.159748i 0.887335 0.461125i 0.152554π-0.152554\pi
−0.953505 + 0.301377i 0.902554π0.902554\pi
212212 4.84105 3.17418i 0.332485 0.218004i
213213 −27.6694 + 11.4610i −1.89587 + 0.785296i
214214 0.404343 + 0.334787i 0.0276403 + 0.0228855i
215215 −4.37088 −0.298092
216216 −0.273845 + 0.0791867i −0.0186328 + 0.00538797i
217217 −24.9936 24.9936i −1.69668 1.69668i
218218 −22.4198 18.5631i −1.51846 1.25725i
219219 −1.46645 3.54033i −0.0990936 0.239233i
220220 0.452961 + 2.38535i 0.0305386 + 0.160820i
221221 −9.02385 4.09039i −0.607010 0.275149i
222222 −16.3416 + 8.64371i −1.09678 + 0.580128i
223223 6.19432 6.19432i 0.414802 0.414802i −0.468605 0.883408i 0.655243π-0.655243\pi
0.883408 + 0.468605i 0.155243π0.155243\pi
224224 26.8849 2.05931i 1.79632 0.137593i
225225 13.4094i 0.893959i
226226 −0.379628 + 1.23217i −0.0252525 + 0.0819624i
227227 −19.9580 8.26686i −1.32466 0.548690i −0.395530 0.918453i 0.629439π-0.629439\pi
−0.929126 + 0.369763i 0.879439π0.879439\pi
228228 −2.97491 + 4.36958i −0.197018 + 0.289382i
229229 19.3325 8.00780i 1.27753 0.529170i 0.362285 0.932068i 0.381997π-0.381997\pi
0.915245 + 0.402897i 0.131997π0.131997\pi
230230 5.35898 + 4.43711i 0.353360 + 0.292574i
231231 −14.6028 14.6028i −0.960792 0.960792i
232232 0.726719 1.31798i 0.0477114 0.0865293i
233233 8.75627 + 8.75627i 0.573642 + 0.573642i 0.933144 0.359502i 0.117053π-0.117053\pi
−0.359502 + 0.933144i 0.617053π0.617053\pi
234234 −15.0585 + 0.918877i −0.984406 + 0.0600689i
235235 −2.20669 0.914043i −0.143949 0.0596256i
236236 3.99275 19.1993i 0.259906 1.24977i
237237 10.0549 4.16487i 0.653134 0.270537i
238238 −5.45399 + 17.7021i −0.353530 + 1.14746i
239239 15.7148 + 15.7148i 1.01651 + 1.01651i 0.999861 + 0.0166470i 0.00529915π0.00529915\pi
0.0166470 + 0.999861i 0.494701π0.494701\pi
240240 2.66261 6.12479i 0.171871 0.395353i
241241 3.57821 + 3.57821i 0.230493 + 0.230493i 0.812898 0.582405i 0.197888π-0.197888\pi
−0.582405 + 0.812898i 0.697888π0.697888\pi
242242 9.81309 5.19051i 0.630810 0.333659i
243243 −8.40574 20.2933i −0.539229 1.30181i
244244 4.35294 20.9313i 0.278668 1.33999i
245245 −4.11467 9.93370i −0.262877 0.634641i
246246 −10.2389 + 0.963536i −0.652806 + 0.0614328i
247247 2.84978 2.66826i 0.181327 0.169777i
248248 20.8446 + 2.32775i 1.32363 + 0.147812i
249249 36.8538i 2.33552i
250250 −7.10199 5.88028i −0.449169 0.371902i
251251 −9.20091 3.81114i −0.580756 0.240557i 0.0729119 0.997338i 0.476771π-0.476771\pi
−0.653668 + 0.756781i 0.726771π0.726771\pi
252252 5.26203 + 27.7105i 0.331477 + 1.74560i
253253 −4.88544 + 11.7945i −0.307145 + 0.741513i
254254 25.8332 + 7.95916i 1.62092 + 0.499402i
255255 3.24417 + 3.24417i 0.203158 + 0.203158i
256256 −11.7001 + 10.9137i −0.731256 + 0.682103i
257257 15.4585i 0.964276i 0.876095 + 0.482138i 0.160140π0.160140\pi
−0.876095 + 0.482138i 0.839860π0.839860\pi
258258 −6.49552 + 21.0826i −0.404393 + 1.31255i
259259 −9.76821 23.5826i −0.606967 1.46535i
260260 −2.90830 + 3.98358i −0.180365 + 0.247051i
261261 1.45454 + 0.602488i 0.0900335 + 0.0372931i
262262 18.6110 1.75140i 1.14979 0.108202i
263263 22.1324 22.1324i 1.36474 1.36474i 0.496981 0.867761i 0.334442π-0.334442\pi
0.867761 0.496981i 0.165558π-0.165558\pi
264264 12.1787 + 1.36001i 0.749546 + 0.0837030i
265265 1.97974 0.121615
266266 −5.62188 4.65478i −0.344699 0.285403i
267267 −9.46458 + 3.92036i −0.579223 + 0.239922i
268268 8.92426 + 13.6107i 0.545136 + 0.831405i
269269 21.4569 8.88775i 1.30825 0.541896i 0.383878 0.923384i 0.374588π-0.374588\pi
0.924374 + 0.381488i 0.124588π0.124588\pi
270270 −0.0931674 0.0287047i −0.00566999 0.00174691i
271271 −15.0473 + 15.0473i −0.914058 + 0.914058i −0.996589 0.0825308i 0.973700π-0.973700\pi
0.0825308 + 0.996589i 0.473700π0.473700\pi
272272 −4.02914 10.2264i −0.244303 0.620068i
273273 1.37932 41.9292i 0.0834804 2.53767i
274274 5.63624 18.2936i 0.340498 1.10516i
275275 3.07834 7.43176i 0.185631 0.448152i
276276 29.3660 19.2547i 1.76762 1.15900i
277277 −12.0846 5.00560i −0.726092 0.300757i −0.0111473 0.999938i 0.503548π-0.503548\pi
−0.714945 + 0.699181i 0.753548π0.753548\pi
278278 1.24872 + 1.03391i 0.0748930 + 0.0620097i
279279 21.9403i 1.31353i
280280 8.07511 + 4.45254i 0.482580 + 0.266090i
281281 18.2366 1.08791 0.543953 0.839116i 0.316927π-0.316927\pi
0.543953 + 0.839116i 0.316927π0.316927\pi
282282 −7.68816 + 9.28548i −0.457823 + 0.552942i
283283 5.24389 + 2.17209i 0.311717 + 0.129117i 0.533057 0.846079i 0.321043π-0.321043\pi
−0.221340 + 0.975197i 0.571043π0.571043\pi
284284 20.2833 + 13.8093i 1.20359 + 0.819433i
285285 −1.67020 + 0.691818i −0.0989339 + 0.0409798i
286286 −8.55669 2.94766i −0.505968 0.174299i
287287 14.1997i 0.838182i
288288 −12.7042 10.8964i −0.748599 0.642077i
289289 −9.44914 −0.555832
290290 0.454986 0.240659i 0.0267177 0.0141320i
291291 0.782369 + 0.324068i 0.0458633 + 0.0189972i
292292 −1.76692 + 2.59527i −0.103401 + 0.151877i
293293 −27.8685 + 11.5435i −1.62809 + 0.674379i −0.995017 0.0997101i 0.968208π-0.968208\pi
−0.633077 + 0.774089i 0.718208π0.718208\pi
294294 −54.0292 + 5.08446i −3.15105 + 0.296532i
295295 4.74219 4.74219i 0.276101 0.276101i
296296 13.2639 + 7.31361i 0.770951 + 0.425095i
297297 0.178882i 0.0103798i
298298 24.6196 2.31684i 1.42617 0.134211i
299299 −24.2730 + 9.13129i −1.40374 + 0.528076i
300300 −18.5036 + 12.1325i −1.06831 + 0.700468i
301301 −28.1413 11.6565i −1.62204 0.671871i
302302 −29.4752 9.08126i −1.69611 0.522568i
303303 12.8384i 0.737544i
304304 4.33039 + 0.0752764i 0.248365 + 0.00431740i
305305 5.16999 5.16999i 0.296033 0.296033i
306306 10.1636 5.37593i 0.581017 0.307321i
307307 13.0113 + 5.38945i 0.742593 + 0.307592i 0.721716 0.692190i 0.243354π-0.243354\pi
0.0208779 + 0.999782i 0.493354π0.493354\pi
308308 −3.44505 + 16.5657i −0.196300 + 0.943920i
309309 26.0459 + 10.7886i 1.48170 + 0.613739i
310310 5.52494 + 4.57453i 0.313796 + 0.259816i
311311 −14.0691 + 14.0691i −0.797786 + 0.797786i −0.982746 0.184960i 0.940784π-0.940784\pi
0.184960 + 0.982746i 0.440784π0.440784\pi
312312 14.8925 + 19.9479i 0.843123 + 1.12933i
313313 0.452439 + 0.452439i 0.0255734 + 0.0255734i 0.719778 0.694204i 0.244244π-0.244244\pi
−0.694204 + 0.719778i 0.744244π0.744244\pi
314314 −1.60638 17.0700i −0.0906534 0.963314i
315315 −3.69139 + 8.91181i −0.207986 + 0.502123i
316316 −7.37082 5.01823i −0.414641 0.282297i
317317 −5.13543 + 12.3980i −0.288435 + 0.696343i −0.999980 0.00629718i 0.997996π-0.997996\pi
0.711546 + 0.702640i 0.247996π0.247996\pi
318318 2.94207 9.54914i 0.164983 0.535489i
319319 0.667823 + 0.667823i 0.0373909 + 0.0373909i
320320 −5.39271 + 0.927234i −0.301462 + 0.0518340i
321321 0.906111 0.0505742
322322 22.6699 + 42.8594i 1.26335 + 2.38846i
323323 −1.13860 + 2.74882i −0.0633533 + 0.152948i
324324 −10.2675 + 15.0809i −0.570414 + 0.837830i
325325 15.2945 5.75367i 0.848388 0.319156i
326326 −4.51371 + 5.45149i −0.249991 + 0.301930i
327327 −50.2416 −2.77837
328328 5.26002 + 6.58250i 0.290436 + 0.363458i
329329 −11.7699 11.7699i −0.648895 0.648895i
330330 3.22801 + 2.67272i 0.177696 + 0.147128i
331331 6.46992 + 15.6198i 0.355619 + 0.858540i 0.995905 + 0.0904037i 0.0288157π0.0288157\pi
−0.640286 + 0.768136i 0.721184π0.721184\pi
332332 25.2511 16.5567i 1.38584 0.908665i
333333 −6.06337 + 14.6383i −0.332270 + 0.802172i
334334 8.36488 27.1500i 0.457706 1.48558i
335335 5.56608i 0.304107i
336336 33.4768 32.3328i 1.82631 1.76390i
337337 19.8195 1.07964 0.539819 0.841781i 0.318493π-0.318493\pi
0.539819 + 0.841781i 0.318493π0.318493\pi
338338 −7.50933 16.7812i −0.408454 0.912779i
339339 0.851652 + 2.05607i 0.0462554 + 0.111670i
340340 0.765357 3.68026i 0.0415073 0.199590i
341341 −5.03674 + 12.1598i −0.272755 + 0.658488i
342342 0.424475 + 4.51061i 0.0229530 + 0.243906i
343343 41.5643i 2.24426i
344344 17.3633 5.02088i 0.936167 0.270708i
345345 12.0092 0.646552
346346 −2.19072 23.2793i −0.117774 1.25150i
347347 −7.82618 + 18.8941i −0.420131 + 1.01429i 0.562177 + 0.827017i 0.309964π0.309964\pi
−0.982308 + 0.187270i 0.940036π0.940036\pi
348348 −0.484651 2.55223i −0.0259800 0.136814i
349349 −9.16581 3.79660i −0.490634 0.203227i 0.123629 0.992329i 0.460547π-0.460547\pi
−0.614263 + 0.789101i 0.710547π0.710547\pi
350350 −14.2844 27.0059i −0.763535 1.44353i
351351 0.265263 0.248366i 0.0141587 0.0132568i
352352 −4.53946 8.95546i −0.241954 0.477327i
353353 −2.03374 2.03374i −0.108245 0.108245i 0.650910 0.759155i 0.274388π-0.274388\pi
−0.759155 + 0.650910i 0.774388π0.774388\pi
354354 −15.8263 29.9209i −0.841158 1.59028i
355355 3.21137 + 7.75294i 0.170442 + 0.411483i
356356 6.93810 + 4.72362i 0.367718 + 0.250351i
357357 12.2354 + 29.5389i 0.647566 + 1.56336i
358358 12.6543 1.19084i 0.668799 0.0629378i
359359 5.77186i 0.304627i −0.988332 0.152314i 0.951328π-0.951328\pi
0.988332 0.152314i 0.0486724π-0.0486724\pi
360360 −1.59001 5.49862i −0.0838011 0.289803i
361361 12.6060 + 12.6060i 0.663476 + 0.663476i
362362 −9.05016 7.49332i −0.475666 0.393840i
363363 7.33286 17.7031i 0.384876 0.929172i
364364 −29.3483 + 17.8917i −1.53827 + 0.937782i
365365 −0.991998 + 0.410899i −0.0519235 + 0.0215074i
366366 −17.2540 32.6201i −0.901880 1.70508i
367367 5.52161 0.288226 0.144113 0.989561i 0.453967π-0.453967\pi
0.144113 + 0.989561i 0.453967π0.453967\pi
368368 −26.3855 11.4705i −1.37544 0.597940i
369369 −6.23251 + 6.23251i −0.324452 + 0.324452i
370370 2.42196 + 4.57892i 0.125912 + 0.238047i
371371 12.7463 + 5.27969i 0.661755 + 0.274108i
372372 30.2754 19.8510i 1.56971 1.02923i
373373 5.04449 12.1785i 0.261194 0.630577i −0.737819 0.674998i 0.764144π-0.764144\pi
0.999013 + 0.0444210i 0.0141443π0.0141443\pi
374374 6.86703 0.646227i 0.355086 0.0334156i
375375 −15.9152 −0.821856
376376 9.81606 + 1.09618i 0.506225 + 0.0565309i
377377 −0.0630800 + 1.91753i −0.00324878 + 0.0987580i
378378 −0.523295 0.433276i −0.0269154 0.0222853i
379379 25.0950 10.3947i 1.28904 0.533939i 0.370342 0.928895i 0.379240π-0.379240\pi
0.918700 + 0.394957i 0.129240π0.129240\pi
380380 1.22435 + 0.833568i 0.0628080 + 0.0427612i
381381 43.1069 17.8555i 2.20843 0.914762i
382382 −3.22671 + 10.4730i −0.165093 + 0.535845i
383383 18.8204 18.8204i 0.961679 0.961679i −0.0376130 0.999292i 0.511975π-0.511975\pi
0.999292 + 0.0376130i 0.0119754π0.0119754\pi
384384 −3.54160 + 27.3893i −0.180731 + 1.39770i
385385 −4.09169 + 4.09169i −0.208532 + 0.208532i
386386 −21.9990 + 11.6361i −1.11972 + 0.592261i
387387 7.23549 + 17.4680i 0.367801 + 0.887949i
388388 −0.129439 0.681644i −0.00657129 0.0346052i
389389 −1.64741 + 3.97720i −0.0835269 + 0.201652i −0.960125 0.279572i 0.909808π-0.909808\pi
0.876598 + 0.481224i 0.159808π0.159808\pi
390390 0.518531 + 8.49766i 0.0262568 + 0.430296i
391391 13.9758 13.9758i 0.706787 0.706787i
392392 27.7565 + 34.7350i 1.40191 + 1.75438i
393393 22.8155 22.8155i 1.15089 1.15089i
394394 −0.774602 8.23119i −0.0390239 0.414682i
395395 −1.16699 2.81737i −0.0587178 0.141757i
396396 8.78309 5.75890i 0.441367 0.289396i
397397 −6.18853 + 14.9404i −0.310593 + 0.749838i 0.689090 + 0.724676i 0.258010π0.258010\pi
−0.999683 + 0.0251627i 0.991990π0.991990\pi
398398 −2.99267 5.65790i −0.150009 0.283605i
399399 −12.5983 −0.630705
400400 16.6256 + 7.22760i 0.831281 + 0.361380i
401401 10.4619 + 10.4619i 0.522441 + 0.522441i 0.918308 0.395867i 0.129556π-0.129556\pi
−0.395867 + 0.918308i 0.629556π0.629556\pi
402402 26.8475 + 8.27168i 1.33903 + 0.412554i
403403 −25.0247 + 9.41408i −1.24657 + 0.468949i
404404 −8.79646 + 5.76766i −0.437640 + 0.286952i
405405 −5.76443 + 2.38771i −0.286437 + 0.118646i
406406 3.57117 0.336068i 0.177234 0.0166788i
407407 −6.72089 + 6.72089i −0.333142 + 0.333142i
408408 −16.6140 9.16083i −0.822518 0.453528i
409409 6.51944i 0.322366i 0.986925 + 0.161183i 0.0515309π0.0515309\pi
−0.986925 + 0.161183i 0.948469π0.948469\pi
410410 0.269982 + 2.86893i 0.0133335 + 0.141686i
411411 −12.6443 30.5259i −0.623695 1.50573i
412412 −4.30918 22.6926i −0.212298 1.11799i
413413 43.1787 17.8852i 2.12469 0.880074i
414414 8.86152 28.7620i 0.435520 1.41358i
415415 10.3264 0.506904
416416 6.97721 19.1656i 0.342086 0.939669i
417417 2.79831 0.137034
418418 −0.800230 + 2.59732i −0.0391405 + 0.127039i
419419 0.805740 0.333748i 0.0393630 0.0163047i −0.362915 0.931822i 0.618219π-0.618219\pi
0.402278 + 0.915518i 0.368219π0.368219\pi
420420 15.6373 2.96941i 0.763022 0.144893i
421421 −6.16886 14.8930i −0.300652 0.725838i −0.999940 0.0109977i 0.996499π-0.996499\pi
0.699287 0.714841i 0.253501π-0.253501\pi
422422 0.332796 + 3.53640i 0.0162002 + 0.172149i
423423 10.3320i 0.502361i
424424 −7.86452 + 2.27415i −0.381935 + 0.110443i
425425 −8.80622 + 8.80622i −0.427164 + 0.427164i
426426 42.1681 3.96826i 2.04305 0.192263i
427427 47.0739 19.4986i 2.27807 0.943606i
428428 −0.407073 0.620840i −0.0196766 0.0300094i
429429 −14.6210 + 5.50028i −0.705907 + 0.265556i
430430 5.90734 + 1.82004i 0.284877 + 0.0877702i
431431 1.57232 + 1.57232i 0.0757361 + 0.0757361i 0.743960 0.668224i 0.232945π-0.232945\pi
−0.668224 + 0.743960i 0.732945π0.732945\pi
432432 0.403081 + 0.00700686i 0.0193932 + 0.000337118i
433433 −27.0551 −1.30019 −0.650094 0.759854i 0.725270π-0.725270\pi
−0.650094 + 0.759854i 0.725270π0.725270\pi
434434 23.3720 + 44.1867i 1.12189 + 2.12103i
435435 0.339990 0.820808i 0.0163013 0.0393547i
436436 22.5712 + 34.4241i 1.08096 + 1.64861i
437437 2.98034 + 7.19518i 0.142569 + 0.344192i
438438 0.507743 + 5.39546i 0.0242609 + 0.257805i
439439 7.17594 7.17594i 0.342489 0.342489i −0.514813 0.857302i 0.672139π-0.672139\pi
0.857302 + 0.514813i 0.172139π0.172139\pi
440440 0.381075 3.41246i 0.0181670 0.162683i
441441 −32.8882 + 32.8882i −1.56610 + 1.56610i
442442 10.4927 + 9.28580i 0.499086 + 0.441680i
443443 9.17145 22.1418i 0.435749 1.05199i −0.541653 0.840602i 0.682201π-0.682201\pi
0.977402 0.211388i 0.0677985π-0.0677985\pi
444444 25.6853 4.87747i 1.21897 0.231474i
445445 1.09848 + 2.65197i 0.0520730 + 0.125715i
446446 −10.9511 + 5.79243i −0.518549 + 0.274280i
447447 30.1816 30.1816i 1.42754 1.42754i
448448 −37.1930 8.41172i −1.75721 0.397416i
449449 1.55890 1.55890i 0.0735689 0.0735689i −0.669365 0.742934i 0.733434π-0.733434\pi
0.742934 + 0.669365i 0.233434π0.233434\pi
450450 −5.58369 + 18.1231i −0.263218 + 0.854330i
451451 −4.88496 + 2.02342i −0.230024 + 0.0952789i
452452 1.02615 1.50722i 0.0482661 0.0708937i
453453 −49.1842 + 20.3728i −2.31087 + 0.957196i
454454 23.5313 + 19.4834i 1.10438 + 0.914399i
455455 −11.7486 0.386485i −0.550781 0.0181187i
456456 5.84015 4.66682i 0.273490 0.218544i
457457 −29.0570 −1.35923 −0.679614 0.733570i 0.737853π-0.737853\pi
−0.679614 + 0.733570i 0.737853π0.737853\pi
458458 −29.4628 + 2.77262i −1.37671 + 0.129556i
459459 −0.105983 + 0.255865i −0.00494685 + 0.0119428i
460460 −5.39515 8.22833i −0.251550 0.383648i
461461 8.58483 + 3.55595i 0.399835 + 0.165617i 0.573534 0.819182i 0.305572π-0.305572\pi
−0.173699 + 0.984799i 0.555572π0.555572\pi
462462 13.6553 + 25.8166i 0.635304 + 1.20110i
463463 16.3647 16.3647i 0.760534 0.760534i −0.215885 0.976419i 0.569263π-0.569263\pi
0.976419 + 0.215885i 0.0692635π0.0692635\pi
464464 −1.53098 + 1.47867i −0.0710741 + 0.0686453i
465465 12.3811 0.574160
466466 −8.18816 15.4804i −0.379309 0.717116i
467467 −31.2231 + 12.9330i −1.44483 + 0.598469i −0.960965 0.276671i 0.910769π-0.910769\pi
−0.483869 + 0.875141i 0.660769π0.660769\pi
468468 20.7345 + 5.02851i 0.958454 + 0.232443i
469469 −14.8439 + 35.8364i −0.685430 + 1.65477i
470470 2.60179 + 2.15422i 0.120011 + 0.0993667i
471471 −20.9264 20.9264i −0.964235 0.964235i
472472 −13.3909 + 24.2857i −0.616367 + 1.11784i
473473 11.3422i 0.521513i
474474 −15.3236 + 1.44204i −0.703838 + 0.0662352i
475475 −1.87793 4.53372i −0.0861652 0.208021i
476476 14.7424 21.6537i 0.675716 0.992498i
477477 −3.27723 7.91194i −0.150054 0.362263i
478478 −14.6953 27.7826i −0.672146 1.27075i
479479 10.5792 + 10.5792i 0.483375 + 0.483375i 0.906208 0.422832i 0.138964π-0.138964\pi
−0.422832 + 0.906208i 0.638964π0.638964\pi
480480 −6.14895 + 7.16907i −0.280660 + 0.327222i
481481 −19.2978 0.634829i −0.879905 0.0289457i
482482 −3.34606 6.32601i −0.152409 0.288142i
483483 77.3195 + 32.0268i 3.51816 + 1.45727i
484484 −15.4239 + 2.92890i −0.701088 + 0.133132i
485485 0.0908036 0.219219i 0.00412318 0.00995423i
486486 2.91040 + 30.9269i 0.132018 + 1.40287i
487487 −22.1275 −1.00269 −0.501346 0.865247i 0.667162π-0.667162\pi
−0.501346 + 0.865247i 0.667162π0.667162\pi
488488 −14.5989 + 26.4766i −0.660862 + 1.19854i
489489 12.2165i 0.552449i
490490 1.42466 + 15.1390i 0.0643597 + 0.683909i
491491 −10.8369 + 26.1627i −0.489064 + 1.18071i 0.466127 + 0.884718i 0.345649π0.345649\pi
−0.955192 + 0.295988i 0.904351π0.904351\pi
492492 14.2393 + 2.96124i 0.641956 + 0.133503i
493493 −0.559557 1.35089i −0.0252012 0.0608410i
494494 −4.96260 + 2.41955i −0.223278 + 0.108861i
495495 3.59184 0.161441
496496 −27.2026 11.8257i −1.22143 0.530990i
497497 58.4806i 2.62321i
498498 15.3460 49.8087i 0.687670 2.23198i
499499 −6.86454 + 16.5725i −0.307299 + 0.741886i 0.692492 + 0.721426i 0.256513π0.256513\pi
−0.999791 + 0.0204597i 0.993487π0.993487\pi
500500 7.14993 + 10.9046i 0.319755 + 0.487669i
501501 −18.7656 45.3043i −0.838387 2.02405i
502502 10.8483 + 8.98211i 0.484182 + 0.400891i
503503 14.1124 + 14.1124i 0.629242 + 0.629242i 0.947877 0.318636i 0.103225π-0.103225\pi
−0.318636 + 0.947877i 0.603225π0.603225\pi
504504 4.42694 39.6425i 0.197192 1.76582i
505505 −3.59730 −0.160078
506506 11.5140 13.9062i 0.511860 0.618206i
507507 −28.4565 14.0445i −1.26380 0.623738i
508508 −31.5999 21.5139i −1.40202 0.954527i
509509 8.34879 20.1558i 0.370054 0.893388i −0.623687 0.781674i 0.714366π-0.714366\pi
0.993740 0.111714i 0.0356341π-0.0356341\pi
510510 −3.03368 5.73544i −0.134334 0.253969i
511511 −7.48266 −0.331013
512512 20.3574 9.87810i 0.899678 0.436555i
513513 −0.0771641 0.0771641i −0.00340688 0.00340688i
514514 6.43695 20.8925i 0.283922 0.921530i
515515 3.02295 7.29804i 0.133207 0.321590i
516516 17.5577 25.7889i 0.772933 1.13529i
517517 −2.37188 + 5.72623i −0.104315 + 0.251839i
518518 3.38214 + 35.9398i 0.148603 + 1.57911i
519519 −28.5385 28.5385i −1.25270 1.25270i
520520 5.58939 4.17288i 0.245111 0.182993i
521521 −12.6505 + 12.6505i −0.554227 + 0.554227i −0.927658 0.373431i 0.878181π-0.878181\pi
0.373431 + 0.927658i 0.378181π0.378181\pi
522522 −1.71496 1.41995i −0.0750617 0.0621494i
523523 −4.54778 1.88375i −0.198860 0.0823707i 0.281031 0.959699i 0.409324π-0.409324\pi
−0.479891 + 0.877328i 0.659324π0.659324\pi
524524 −25.8824 5.38259i −1.13068 0.235139i
525525 −48.7194 20.1802i −2.12629 0.880738i
526526 −39.1284 + 20.6965i −1.70608 + 0.902408i
527527 14.4086 14.4086i 0.627650 0.627650i
528528 −15.8934 6.90930i −0.691673 0.300689i
529529 28.7353i 1.24936i
530530 −2.67566 0.824367i −0.116223 0.0358082i
531531 −26.8021 11.1018i −1.16311 0.481776i
532532 5.65983 + 8.63200i 0.245385 + 0.374245i
533533 −9.78293 4.43447i −0.423746 0.192078i
534534 14.4240 1.35738i 0.624188 0.0587397i
535535 0.253892i 0.0109767i
536536 −6.39382 22.1112i −0.276171 0.955059i
537537 15.5131 15.5131i 0.669438 0.669438i
538538 −32.7004 + 3.07729i −1.40981 + 0.132671i
539539 −25.7773 + 10.6773i −1.11031 + 0.459905i
540540 0.113965 + 0.0775901i 0.00490427 + 0.00333894i
541541 1.16123 + 0.480999i 0.0499253 + 0.0206797i 0.407506 0.913202i 0.366398π-0.366398\pi
−0.357581 + 0.933882i 0.616398π0.616398\pi
542542 26.6024 14.0710i 1.14267 0.604402i
543543 −20.2809 −0.870337
544544 1.18718 + 15.4990i 0.0508998 + 0.664513i
545545 14.0777i 0.603021i
546546 −19.3236 + 56.0939i −0.826973 + 2.40060i
547547 35.9252 14.8807i 1.53605 0.636253i 0.555324 0.831634i 0.312594π-0.312594\pi
0.980727 + 0.195381i 0.0625944π0.0625944\pi
548548 −15.2350 + 22.3773i −0.650807 + 0.955911i
549549 −29.2199 12.1033i −1.24708 0.516555i
550550 −7.25503 + 8.76236i −0.309356 + 0.373628i
551551 0.576154 0.0245450
552552 −47.7064 + 13.7951i −2.03052 + 0.587158i
553553 21.2515i 0.903705i
554554 14.2482 + 11.7972i 0.605350 + 0.501216i
555555 8.26050 + 3.42161i 0.350639 + 0.145239i
556556 −1.25715 1.91732i −0.0533149 0.0813123i
557557 −4.64040 + 11.2029i −0.196620 + 0.474683i −0.991183 0.132498i 0.957700π-0.957700\pi
0.794563 + 0.607182i 0.207700π0.207700\pi
558558 9.13596 29.6528i 0.386756 1.25530i
559559 −16.8192 + 15.7478i −0.711374 + 0.666062i
560560 −9.05965 9.38019i −0.382840 0.396385i
561561 8.41840 8.41840i 0.355425 0.355425i
562562 −24.6472 7.59375i −1.03968 0.320323i
563563 25.1805 10.4301i 1.06123 0.439577i 0.217344 0.976095i 0.430261π-0.430261\pi
0.843889 + 0.536518i 0.180261π0.180261\pi
564564 14.2572 9.34816i 0.600336 0.393629i
565565 0.576110 0.238632i 0.0242371 0.0100393i
566566 −6.18277 5.11919i −0.259881 0.215176i
567567 −43.4812 −1.82604
568568 −21.6631 27.1096i −0.908962 1.13749i
569569 −19.1179 + 19.1179i −0.801463 + 0.801463i −0.983324 0.181861i 0.941788π-0.941788\pi
0.181861 + 0.983324i 0.441788π0.441788\pi
570570 2.54538 0.239535i 0.106614 0.0100330i
571571 34.0120 + 14.0882i 1.42336 + 0.589574i 0.955702 0.294337i 0.0950987π-0.0950987\pi
0.467656 + 0.883911i 0.345099π0.345099\pi
572572 10.3371 + 7.54684i 0.432217 + 0.315549i
573573 7.23875 + 17.4759i 0.302403 + 0.730066i
574574 −5.91278 + 19.1912i −0.246795 + 0.801026i
575575 32.5987i 1.35946i
576576 12.6326 + 20.0168i 0.526360 + 0.834032i
577577 1.11287 + 1.11287i 0.0463293 + 0.0463293i 0.729892 0.683563i 0.239570π-0.239570\pi
−0.683563 + 0.729892i 0.739570π0.739570\pi
578578 12.7707 + 3.93463i 0.531191 + 0.163659i
579579 −16.4388 + 39.6868i −0.683173 + 1.64933i
580580 −0.715134 + 0.135799i −0.0296943 + 0.00563875i
581581 66.4853 + 27.5391i 2.75828 + 1.14252i
582582 −0.922446 0.763764i −0.0382366 0.0316590i
583583 5.13730i 0.212765i
584584 3.46870 2.77181i 0.143536 0.114698i
585585 4.98702 + 5.32629i 0.206188 + 0.220215i
586586 42.4716 3.99682i 1.75448 0.165107i
587587 −10.0510 24.2652i −0.414848 1.00153i −0.983818 0.179173i 0.942658π-0.942658\pi
0.568969 0.822359i 0.307342π-0.307342\pi
588588 75.1389 + 15.6261i 3.09867 + 0.644409i
589589 3.07264 + 7.41801i 0.126606 + 0.305654i
590590 −8.38383 + 4.43452i −0.345157 + 0.182566i
591591 −10.0908 10.0908i −0.415078 0.415078i
592592 −14.8811 15.4076i −0.611609 0.633249i
593593 0.990617 + 0.990617i 0.0406798 + 0.0406798i 0.727154 0.686474i 0.240843π-0.240843\pi
−0.686474 + 0.727154i 0.740843π0.740843\pi
594594 −0.0744869 + 0.241763i −0.00305623 + 0.00991967i
595595 8.27678 3.42835i 0.339315 0.140549i
596596 −34.2386 7.12037i −1.40247 0.291662i
597597 −10.2070 4.22788i −0.417745 0.173036i
598598 36.6078 2.23382i 1.49700 0.0913477i
599599 −12.7082 12.7082i −0.519242 0.519242i 0.398100 0.917342i 0.369670π-0.369670\pi
−0.917342 + 0.398100i 0.869670π0.869670\pi
600600 30.0600 8.69235i 1.22720 0.354864i
601601 10.1980 + 10.1980i 0.415983 + 0.415983i 0.883817 0.467833i 0.154965π-0.154965\pi
−0.467833 + 0.883817i 0.654965π0.654965\pi
602602 33.1798 + 27.4721i 1.35231 + 1.11968i
603603 22.2445 9.21399i 0.905868 0.375223i
604604 36.0549 + 24.5470i 1.46705 + 0.998805i
605605 −4.96040 2.05466i −0.201669 0.0835340i
606606 −5.34591 + 17.3513i −0.217163 + 0.704849i
607607 27.2432i 1.10577i 0.833259 + 0.552883i 0.186472π0.186472\pi
−0.833259 + 0.552883i 0.813528π0.813528\pi
608608 −5.82127 1.90492i −0.236084 0.0772546i
609609 4.37796 4.37796i 0.177404 0.177404i
610610 −9.14013 + 4.83456i −0.370073 + 0.195745i
611611 −11.7846 + 4.43325i −0.476752 + 0.179350i
612612 −15.9749 + 3.03353i −0.645748 + 0.122623i
613613 −1.02866 2.48341i −0.0415473 0.100304i 0.901744 0.432271i 0.142288π-0.142288\pi
−0.943291 + 0.331967i 0.892288π0.892288\pi
614614 −15.3409 12.7019i −0.619107 0.512606i
615615 3.51706 + 3.51706i 0.141822 + 0.141822i
616616 11.5541 20.9544i 0.465526 0.844277i
617617 0.0166708 0.000671140 0.000335570 1.00000i 0.499893π-0.499893\pi
0.000335570 1.00000i 0.499893π0.499893\pi
618618 −30.7092 25.4265i −1.23530 1.02280i
619619 −0.177010 + 0.0733199i −0.00711463 + 0.00294698i −0.386238 0.922399i 0.626226π-0.626226\pi
0.379123 + 0.925346i 0.376226π0.376226\pi
620620 −5.56224 8.48316i −0.223385 0.340692i
621621 0.277415 + 0.669740i 0.0111323 + 0.0268757i
622622 24.8731 13.1563i 0.997320 0.527520i
623623 20.0039i 0.801438i
624624 −11.8212 33.1613i −0.473228 1.32751i
625625 18.2014i 0.728057i
626626 −0.423085 0.799877i −0.0169099 0.0319695i
627627 1.79522 + 4.33405i 0.0716943 + 0.173085i
628628 −4.93690 + 23.7393i −0.197004 + 0.947302i
629629 13.5952 5.63131i 0.542075 0.224535i
630630 8.69988 10.5074i 0.346612 0.418625i
631631 3.70486 0.147488 0.0737440 0.997277i 0.476505π-0.476505\pi
0.0737440 + 0.997277i 0.476505π0.476505\pi
632632 7.87222 + 9.85146i 0.313140 + 0.391870i
633633 4.33534 + 4.33534i 0.172314 + 0.172314i
634634 12.1032 14.6178i 0.480680 0.580547i
635635 −5.00309 12.0785i −0.198542 0.479322i
636636 −7.95255 + 11.6808i −0.315339 + 0.463173i
637637 −51.6233 23.4002i −2.04539 0.927148i
638638 −0.624495 1.18066i −0.0247240 0.0467428i
639639 25.6682 25.6682i 1.01542 1.01542i
640640 7.67446 + 0.992354i 0.303360 + 0.0392262i
641641 22.9808i 0.907685i 0.891082 + 0.453843i 0.149947π0.149947\pi
−0.891082 + 0.453843i 0.850053π0.850053\pi
642642 −1.22463 0.377306i −0.0483322 0.0148911i
643643 −10.5208 4.35785i −0.414899 0.171857i 0.165462 0.986216i 0.447089π-0.447089\pi
−0.580361 + 0.814359i 0.697089π0.697089\pi
644644 −12.7922 67.3651i −0.504082 2.65456i
645645 9.85736 4.08305i 0.388133 0.160770i
646646 2.68345 3.24097i 0.105579 0.127514i
647647 −33.8281 33.8281i −1.32992 1.32992i −0.905436 0.424483i 0.860456π-0.860456\pi
−0.424483 0.905436i 0.639544π-0.639544\pi
648648 20.1564 16.1068i 0.791818 0.632736i
649649 −12.3057 12.3057i −0.483040 0.483040i
650650 −23.0667 + 1.40754i −0.904751 + 0.0552083i
651651 79.7141 + 33.0187i 3.12424 + 1.29410i
652652 8.37038 5.48829i 0.327810 0.214938i
653653 26.2471 10.8719i 1.02713 0.425451i 0.195453 0.980713i 0.437382π-0.437382\pi
0.831675 + 0.555263i 0.187382π0.187382\pi
654654 67.9026 + 20.9207i 2.65520 + 0.818063i
655655 −6.39290 6.39290i −0.249791 0.249791i
656656 −4.36807 11.0867i −0.170545 0.432862i
657657 3.28427 + 3.28427i 0.128132 + 0.128132i
658658 11.0063 + 20.8083i 0.429069 + 0.811190i
659659 10.8417 + 26.1741i 0.422332 + 1.01960i 0.981658 + 0.190651i 0.0610599π0.0610599\pi
−0.559326 + 0.828948i 0.688940π0.688940\pi
660660 −3.24980 4.95638i −0.126498 0.192927i
661661 −3.39761 8.20256i −0.132152 0.319043i 0.843928 0.536457i 0.180238π-0.180238\pi
−0.976079 + 0.217414i 0.930238π0.930238\pi
662662 −2.24014 23.8045i −0.0870656 0.925189i
663663 24.1719 + 0.795170i 0.938760 + 0.0308818i
664664 −41.0217 + 11.8621i −1.59195 + 0.460338i
665665 3.53005i 0.136889i
666666 14.2902 17.2591i 0.553732 0.668778i
667667 −3.53602 1.46467i −0.136915 0.0567122i
668668 −22.6106 + 33.2107i −0.874832 + 1.28496i
669669 −8.18323 + 19.7561i −0.316382 + 0.763813i
670670 2.31772 7.52267i 0.0895414 0.290626i
671671 −13.4158 13.4158i −0.517910 0.517910i
672672 −58.7081 + 29.7587i −2.26471 + 1.14797i
673673 32.8253i 1.26532i −0.774429 0.632661i 0.781963π-0.781963\pi
0.774429 0.632661i 0.218037π-0.218037\pi
674674 −26.7865 8.25288i −1.03178 0.317889i
675675 −0.174801 0.422006i −0.00672809 0.0162430i
676676 3.16129 + 25.8071i 0.121588 + 0.992581i
677677 −29.4862 12.2136i −1.13325 0.469406i −0.264363 0.964423i 0.585162π-0.585162\pi
−0.868883 + 0.495017i 0.835162π0.835162\pi
678678 −0.294876 3.13345i −0.0113246 0.120339i
679679 1.16925 1.16925i 0.0448719 0.0448719i
680680 −2.56686 + 4.65525i −0.0984346 + 0.178521i
681681 52.7323 2.02071
682682 11.8706 14.3369i 0.454549 0.548987i
683683 −22.7829 + 9.43698i −0.871763 + 0.361096i −0.773297 0.634044i 0.781394π-0.781394\pi
−0.0984662 + 0.995140i 0.531394π0.531394\pi
684684 1.30454 6.27294i 0.0498803 0.239852i
685685 −8.55335 + 3.54291i −0.326807 + 0.135368i
686686 −17.3074 + 56.1750i −0.660800 + 2.14477i
687687 −36.1189 + 36.1189i −1.37802 + 1.37802i
688688 −25.5576 0.444275i −0.974374 0.0169378i
689689 7.61805 7.13280i 0.290224 0.271738i
690690 −16.2307 5.00064i −0.617891 0.190371i
691691 3.99662 9.64869i 0.152039 0.367054i −0.829448 0.558584i 0.811345π-0.811345\pi
0.981487 + 0.191530i 0.0613450π0.0613450\pi
692692 −6.73274 + 32.3747i −0.255941 + 1.23070i
693693 23.1256 + 9.57892i 0.878467 + 0.363873i
694694 18.4448 22.2769i 0.700154 0.845620i
695695 0.784084i 0.0297420i
696696 −0.407736 + 3.65121i −0.0154552 + 0.138399i
697697 8.18604 0.310068
698698 10.8069 + 8.94784i 0.409046 + 0.338681i
699699 −27.9271 11.5678i −1.05630 0.437534i
700700 8.06041 + 42.4471i 0.304655 + 1.60435i
701701 2.60641 1.07961i 0.0984428 0.0407763i −0.332919 0.942956i 0.608033π-0.608033\pi
0.431361 + 0.902179i 0.358033π0.358033\pi
702702 −0.461928 + 0.225216i −0.0174343 + 0.00850024i
703703 5.79834i 0.218689i
704704 2.40611 + 13.9937i 0.0906838 + 0.527408i
705705 5.83046 0.219588
706706 1.90179 + 3.59550i 0.0715750 + 0.135318i
707707 −23.1608 9.59350i −0.871050 0.360801i
708708 8.93045 + 47.0288i 0.335627 + 1.76745i
709709 15.7303 6.51571i 0.590764 0.244703i −0.0672152 0.997739i 0.521411π-0.521411\pi
0.657979 + 0.753036i 0.271411π0.271411\pi
710710 −1.11190 11.8155i −0.0417290 0.443427i
711711 −9.32766 + 9.32766i −0.349815 + 0.349815i
712712 −7.41006 9.27310i −0.277704 0.347524i
713713 53.3375i 1.99751i
714714 −4.23638 45.0173i −0.158543 1.68473i
715715 1.54118 + 4.09679i 0.0576367 + 0.153211i
716716 −17.5984 3.65981i −0.657682 0.136773i
717717 −50.1206 20.7606i −1.87179 0.775320i
718718 −2.40341 + 7.80080i −0.0896945 + 0.291123i
719719 7.89011i 0.294252i −0.989118 0.147126i 0.952998π-0.952998\pi
0.989118 0.147126i 0.0470022π-0.0470022\pi
720720 −0.140693 + 8.09358i −0.00524332 + 0.301630i
721721 38.9257 38.9257i 1.44967 1.44967i
722722 −11.7882 22.2865i −0.438710 0.829418i
723723 −11.4123 4.72713i −0.424428 0.175804i
724724 9.11125 + 13.8959i 0.338617 + 0.516436i
725725 2.22807 + 0.922895i 0.0827483 + 0.0342755i
726726 −17.2821 + 20.8727i −0.641399 + 0.774659i
727727 25.8773 25.8773i 0.959735 0.959735i −0.0394856 0.999220i 0.512572π-0.512572\pi
0.999220 + 0.0394856i 0.0125719π0.0125719\pi
728728 47.1151 11.9604i 1.74620 0.443282i
729729 18.5628 + 18.5628i 0.687511 + 0.687511i
730730 1.51180 0.142269i 0.0559544 0.00526563i
731731 6.71991 16.2233i 0.248545 0.600040i
732732 9.73607 + 51.2713i 0.359856 + 1.89504i
733733 −5.72801 + 13.8286i −0.211569 + 0.510773i −0.993665 0.112386i 0.964151π-0.964151\pi
0.782096 + 0.623158i 0.214151π0.214151\pi
734734 −7.46257 2.29921i −0.275449 0.0848652i
735735 18.5591 + 18.5591i 0.684563 + 0.684563i
736736 30.8842 + 26.4895i 1.13841 + 0.976417i
737737 14.4436 0.532037
738738 11.0186 5.82815i 0.405600 0.214537i
739739 4.11332 9.93043i 0.151311 0.365297i −0.829990 0.557779i 0.811654π-0.811654\pi
0.981300 + 0.192482i 0.0616537π0.0616537\pi
740740 −1.36666 7.19702i −0.0502396 0.264568i
741741 −3.93437 + 8.67966i −0.144533 + 0.318855i
742742 −15.0284 12.4432i −0.551711 0.456804i
743743 34.0245 1.24824 0.624118 0.781330i 0.285458π-0.285458\pi
0.624118 + 0.781330i 0.285458π0.285458\pi
744744 −49.1839 + 14.2223i −1.80317 + 0.521415i
745745 −8.45686 8.45686i −0.309835 0.309835i
746746 −11.8889 + 14.3589i −0.435282 + 0.525718i
747747 −17.0942 41.2691i −0.625444 1.50996i
748748 −9.55003 1.98605i −0.349184 0.0726172i
749749 0.677094 1.63465i 0.0247405 0.0597288i
750750 21.5097 + 6.62710i 0.785424 + 0.241988i
751751 28.2172i 1.02966i 0.857292 + 0.514830i 0.172145π0.172145\pi
−0.857292 + 0.514830i 0.827855π0.827855\pi
752752 −12.8102 5.56892i −0.467139 0.203078i
753753 24.3104 0.885919
754754 0.883718 2.56532i 0.0321831 0.0934235i
755755 5.70844 + 13.7814i 0.207751 + 0.501556i
756756 0.526827 + 0.803482i 0.0191605 + 0.0292224i
757757 8.60430 20.7726i 0.312729 0.754994i −0.686873 0.726777i 0.741017π-0.741017\pi
0.999602 0.0282165i 0.00898279π-0.00898279\pi
758758 −38.2447 + 3.59905i −1.38911 + 0.130723i
759759 31.1630i 1.13115i
760760 −1.30764 1.63641i −0.0474331 0.0593587i
761761 −6.99161 −0.253446 −0.126723 0.991938i 0.540446π-0.540446\pi
−0.126723 + 0.991938i 0.540446π0.540446\pi
762762 −65.6949 + 6.18226i −2.37987 + 0.223960i
763763 −37.5432 + 90.6373i −1.35915 + 3.28129i
764764 8.72194 12.8109i 0.315549 0.463481i
765765 −5.13760 2.12806i −0.185750 0.0769402i
766766 −33.2731 + 17.5994i −1.20221 + 0.635891i
767767 1.16235 35.3335i 0.0419699 1.27582i
768768 16.1915 35.5425i 0.584259 1.28253i
769769 38.7943 + 38.7943i 1.39896 + 1.39896i 0.803064 + 0.595893i 0.203202π0.203202\pi
0.595893 + 0.803064i 0.296798π0.296798\pi
770770 7.23379 3.82622i 0.260688 0.137887i
771771 −14.4406 34.8626i −0.520064 1.25555i
772772 34.5774 6.56600i 1.24447 0.236316i
773773 −18.4367 44.5102i −0.663123 1.60092i −0.792883 0.609375i 0.791421π-0.791421\pi
0.129760 0.991545i 0.458579π-0.458579\pi
774774 −2.50521 26.6213i −0.0900480 0.956881i
775775 33.6082i 1.20724i
776776 −0.108897 + 0.975155i −0.00390918 + 0.0350060i
777777 44.0592 + 44.0592i 1.58062 + 1.58062i
778778 3.88262 4.68928i 0.139199 0.168119i
779779 −1.23438 + 2.98005i −0.0442261 + 0.106771i
780780 2.83763 11.7007i 0.101604 0.418952i
781781 20.1184 8.33331i 0.719892 0.298189i
782782 −24.7081 + 13.0691i −0.883561 + 0.467348i
783783 0.0536295 0.00191656
784784 −23.0498 58.5030i −0.823206 2.08939i
785785 −5.86355 + 5.86355i −0.209279 + 0.209279i
786786 −40.3361 + 21.3352i −1.43874 + 0.761003i
787787 47.2043 + 19.5527i 1.68265 + 0.696977i 0.999447 0.0332494i 0.0105856π-0.0105856\pi
0.683205 + 0.730227i 0.260586π0.260586\pi
788788 −2.38059 + 11.4472i −0.0848050 + 0.407789i
789789 −29.2388 + 70.5887i −1.04093 + 2.51302i
790790 0.404059 + 4.29368i 0.0143758 + 0.152762i
791791 4.34560 0.154512
792792 −14.2686 + 4.12598i −0.507011 + 0.146610i
793793 1.26720 38.5210i 0.0449997 1.36792i
794794 14.5851 17.6154i 0.517607 0.625147i
795795 −4.46478 + 1.84937i −0.158349 + 0.0655905i
796796 1.68871 + 8.89293i 0.0598546 + 0.315202i
797797 15.2942 6.33507i 0.541749 0.224400i −0.0949914 0.995478i 0.530282π-0.530282\pi
0.636740 + 0.771078i 0.280282π0.280282\pi
798798 17.0269 + 5.24596i 0.602746 + 0.185705i
799799 6.78526 6.78526i 0.240045 0.240045i
800800 −19.4603 16.6912i −0.688025 0.590123i
801801 8.78006 8.78006i 0.310228 0.310228i
802802 −9.78311 18.4958i −0.345454 0.653109i
803803 1.06626 + 2.57417i 0.0376274 + 0.0908405i
804804 −32.8407 22.3587i −1.15820 0.788531i
805805 8.97389 21.6649i 0.316288 0.763587i
806806 37.7415 2.30300i 1.32939 0.0811198i
807807 −40.0879 + 40.0879i −1.41116 + 1.41116i
808808 14.2903 4.13226i 0.502730 0.145372i
809809 −1.94906 + 1.94906i −0.0685251 + 0.0685251i −0.740539 0.672014i 0.765430π-0.765430\pi
0.672014 + 0.740539i 0.265430π0.265430\pi
810810 8.78500 0.826718i 0.308673 0.0290479i
811811 8.60460 + 20.7733i 0.302148 + 0.729450i 0.999914 + 0.0131243i 0.00417771π0.00417771\pi
−0.697766 + 0.716326i 0.745822π0.745822\pi
812812 −4.96645 1.03284i −0.174288 0.0362455i
813813 19.8788 47.9916i 0.697178 1.68314i
814814 11.8820 6.28484i 0.416464 0.220283i
815815 3.42306 0.119904
816816 18.6397 + 19.2992i 0.652519 + 0.675606i
817817 4.89264 + 4.89264i 0.171172 + 0.171172i
818818 2.71470 8.81117i 0.0949174 0.308075i
819819 17.9038 + 47.5923i 0.625610 + 1.66301i
820820 0.829738 3.98984i 0.0289757 0.139331i
821821 −1.48193 + 0.613835i −0.0517197 + 0.0214230i −0.408393 0.912806i 0.633911π-0.633911\pi
0.356674 + 0.934229i 0.383911π0.383911\pi
822822 4.37794 + 46.5215i 0.152698 + 1.62262i
823823 9.33507 9.33507i 0.325400 0.325400i −0.525434 0.850834i 0.676097π-0.676097\pi
0.850834 + 0.525434i 0.176097π0.176097\pi
824824 −3.62530 + 32.4639i −0.126293 + 1.13093i
825825 19.6360i 0.683637i
826826 −65.8044 + 6.19257i −2.28963 + 0.215467i
827827 19.7431 + 47.6641i 0.686536 + 1.65744i 0.751647 + 0.659566i 0.229260π0.229260\pi
−0.0651107 + 0.997878i 0.520740π0.520740\pi
828828 −23.9531 + 35.1825i −0.832427 + 1.22268i
829829 −3.28374 + 1.36017i −0.114049 + 0.0472406i −0.438978 0.898498i 0.644659π-0.644659\pi
0.324929 + 0.945738i 0.394659π0.394659\pi
830830 −13.9564 4.29994i −0.484433 0.149253i
831831 31.9295 1.10762
832832 −17.4104 + 22.9973i −0.603597 + 0.797289i
833833 43.1967 1.49668
834834 −3.78197 1.16522i −0.130959 0.0403482i
835835 −12.6942 + 5.25813i −0.439302 + 0.181965i
836836 2.16306 3.17712i 0.0748109 0.109883i
837837 0.286007 + 0.690482i 0.00988585 + 0.0238665i
838838 −1.22795 + 0.115557i −0.0424187 + 0.00399185i
839839 51.0263i 1.76162i 0.473466 + 0.880812i 0.343003π0.343003\pi
−0.473466 + 0.880812i 0.656997π0.656997\pi
840840 −22.3706 2.49816i −0.771859 0.0861948i
841841 20.3059 20.3059i 0.700203 0.700203i
842842 2.13591 + 22.6969i 0.0736082 + 0.782186i
843843 −41.1279 + 17.0357i −1.41652 + 0.586741i
844844 1.02278 4.91810i 0.0352056 0.169288i
845845 −3.93526 + 7.97351i −0.135377 + 0.274297i
846846 4.30227 13.9640i 0.147915 0.480091i
847847 −26.4574 26.4574i −0.909086 0.909086i
848848 11.5760 + 0.201229i 0.397522 + 0.00691024i
849849 −13.8553 −0.475511
850850 15.5687 8.23487i 0.534003 0.282454i
851851 14.7402 35.5861i 0.505289 1.21988i
852852 −58.6435 12.1957i −2.00909 0.417817i
853853 3.43022 + 8.28129i 0.117449 + 0.283546i 0.971661 0.236378i 0.0759603π-0.0759603\pi
−0.854213 + 0.519924i 0.825960π0.825960\pi
854854 −71.7406 + 6.75120i −2.45491 + 0.231021i
855855 1.54940 1.54940i 0.0529884 0.0529884i
856856 0.291649 + 1.00858i 0.00996834 + 0.0344727i
857857 −12.9270 + 12.9270i −0.441577 + 0.441577i −0.892542 0.450965i 0.851080π-0.851080\pi
0.450965 + 0.892542i 0.351080π0.351080\pi
858858 22.0509 1.34555i 0.752805 0.0459365i
859859 −8.50209 + 20.5259i −0.290087 + 0.700333i −0.999992 0.00396469i 0.998738π-0.998738\pi
0.709905 + 0.704298i 0.248738π0.248738\pi
860860 −7.22603 4.91965i −0.246406 0.167759i
861861 13.2646 + 32.0237i 0.452058 + 1.09136i
862862 −1.47031 2.77974i −0.0500790 0.0946785i
863863 −14.4774 + 14.4774i −0.492818 + 0.492818i −0.909193 0.416375i 0.863300π-0.863300\pi
0.416375 + 0.909193i 0.363300π0.363300\pi
864864 −0.541854 0.177313i −0.0184343 0.00603232i
865865 −7.99648 + 7.99648i −0.271888 + 0.271888i
866866 36.5656 + 11.2658i 1.24255 + 0.382827i
867867 21.3100 8.82690i 0.723726 0.299777i
868868 −13.1883 69.4514i −0.447642 2.35734i
869869 −7.31090 + 3.02827i −0.248005 + 0.102727i
870870 −0.801289 + 0.967767i −0.0271662 + 0.0328104i
871871 20.0540 + 21.4183i 0.679503 + 0.725730i
872872 −16.1712 55.9235i −0.547626 1.89381i
873873 −1.02641 −0.0347388
874874 −1.03191 10.9655i −0.0349049 0.370912i
875875 −11.8927 + 28.7114i −0.402045 + 0.970624i
876876 1.56045 7.50350i 0.0527227 0.253520i
877877 37.4110 + 15.4961i 1.26328 + 0.523268i 0.910915 0.412595i 0.135378π-0.135378\pi
0.352365 + 0.935863i 0.385378π0.385378\pi
878878 −12.6865 + 6.71036i −0.428149 + 0.226464i
879879 52.0666 52.0666i 1.75616 1.75616i
880880 −1.93598 + 4.45333i −0.0652620 + 0.150122i
881881 −28.3568 −0.955365 −0.477682 0.878533i 0.658523π-0.658523\pi
−0.477682 + 0.878533i 0.658523π0.658523\pi
882882 58.1438 30.7544i 1.95780 1.03555i
883883 −34.8429 + 14.4324i −1.17256 + 0.485688i −0.882037 0.471181i 0.843828π-0.843828\pi
−0.290519 + 0.956869i 0.593828π0.593828\pi
884884 −10.3145 16.9191i −0.346913 0.569052i
885885 −6.26484 + 15.1247i −0.210590 + 0.508410i
886886 −21.6153 + 26.1062i −0.726180 + 0.877054i
887887 14.3416 + 14.3416i 0.481545 + 0.481545i 0.905625 0.424080i 0.139402π-0.139402\pi
−0.424080 + 0.905625i 0.639402π0.639402\pi
888888 −36.7453 4.10341i −1.23309 0.137701i
889889 91.1085i 3.05568i
890890 −0.380338 4.04160i −0.0127490 0.135475i
891891 6.19594 + 14.9583i 0.207572 + 0.501123i
892892 17.2126 3.26855i 0.576320 0.109439i
893893 1.44696 + 3.49326i 0.0484206 + 0.116898i
894894 −53.3587 + 28.2234i −1.78458 + 0.943931i
895895 −4.34675 4.34675i −0.145296 0.145296i
896896 46.7645 + 26.8558i 1.56229 + 0.897191i
897897 46.2113 43.2678i 1.54295 1.44467i
898898 −2.75601 + 1.45776i −0.0919693 + 0.0486460i
899899 −3.64553 1.51003i −0.121585 0.0503623i
900900 15.0929 22.1687i 0.503098 0.738956i
901901 −3.04371 + 7.34816i −0.101401 + 0.244803i
902902 7.44468 0.700587i 0.247881 0.0233270i
903903 74.3542 2.47435
904904 −2.01447 + 1.60975i −0.0670004 + 0.0535395i
905905 5.68270i 0.188899i
906906 74.9567 7.05386i 2.49027 0.234349i
907907 22.1387 53.4474i 0.735102 1.77469i 0.110317 0.993897i 0.464814π-0.464814\pi
0.624785 0.780797i 0.285186π-0.285186\pi
908908 −23.6901 36.1306i −0.786184 1.19904i
909909 5.95492 + 14.3764i 0.197512 + 0.476836i
910910 15.7175 + 5.41446i 0.521030 + 0.179488i
911911 −35.7122 −1.18320 −0.591600 0.806232i 0.701503π-0.701503\pi
−0.591600 + 0.806232i 0.701503π0.701503\pi
912912 −9.83636 + 3.87546i −0.325714 + 0.128329i
913913 26.7964i 0.886832i
914914 39.2711 + 12.0994i 1.29897 + 0.400212i
915915 −6.82999 + 16.4891i −0.225793 + 0.545112i
916916 40.9741 + 8.52109i 1.35382 + 0.281545i
917917 −24.1109 58.2088i −0.796211 1.92222i
918918 0.249781 0.301676i 0.00824399 0.00995679i
919919 33.1467 + 33.1467i 1.09341 + 1.09341i 0.995162 + 0.0982462i 0.0313233π0.0313233\pi
0.0982462 + 0.995162i 0.468677π0.468677\pi
920920 3.86538 + 13.3673i 0.127438 + 0.440707i
921921 −34.3780 −1.13280
922922 −10.1219 8.38068i −0.333346 0.276003i
923923 40.2904 + 18.2631i 1.32617 + 0.601137i
924924 −7.70544 40.5778i −0.253490 1.33491i
925925 −9.28790 + 22.4230i −0.305384 + 0.737263i
926926 −28.9316 + 15.3030i −0.950752 + 0.502888i
927927 −34.1704 −1.12230
928928 2.68487 1.36094i 0.0881353 0.0446752i
929929 −28.8546 28.8546i −0.946690 0.946690i 0.0519589 0.998649i 0.483454π-0.483454\pi
−0.998649 + 0.0519589i 0.983454π0.983454\pi
930930 −16.7333 5.15551i −0.548707 0.169056i
931931 −6.51365 + 15.7253i −0.213476 + 0.515377i
932932 4.62042 + 24.3317i 0.151347 + 0.797010i
933933 18.5865 44.8718i 0.608494 1.46904i
934934 47.5840 4.47793i 1.55700 0.146522i
935935 −2.35883 2.35883i −0.0771421 0.0771421i
936936 −25.9293 15.4300i −0.847525 0.504346i
937937 16.1062 16.1062i 0.526167 0.526167i −0.393261 0.919427i 0.628653π-0.628653\pi
0.919427 + 0.393261i 0.128653π0.128653\pi
938938 34.9842 42.2527i 1.14228 1.37960i
939939 −1.44300 0.597710i −0.0470905 0.0195055i
940940 −2.61935 3.99486i −0.0854338 0.130298i
941941 −28.1343 11.6536i −0.917150 0.379896i −0.126361 0.991984i 0.540330π-0.540330\pi
−0.790790 + 0.612088i 0.790330π0.790330\pi
942942 19.5687 + 36.9962i 0.637581 + 1.20540i
943943 15.1514 15.1514i 0.493399 0.493399i
944944 28.2107 27.2467i 0.918181 0.886805i
945945 0.328583i 0.0106888i
946946 4.72289 15.3292i 0.153554 0.498394i
947947 20.6361 + 8.54775i 0.670583 + 0.277764i 0.691884 0.722009i 0.256781π-0.256781\pi
−0.0213014 + 0.999773i 0.506781π0.506781\pi
948948 21.3107 + 4.43183i 0.692139 + 0.143939i
949949 −2.33678 + 5.15520i −0.0758552 + 0.167345i
950950 0.650213 + 6.90938i 0.0210957 + 0.224170i
951951 32.7577i 1.06224i
952952 −28.9413 + 23.1268i −0.937992 + 0.749542i
953953 34.8685 34.8685i 1.12950 1.12950i 0.139243 0.990258i 0.455533π-0.455533\pi
0.990258 0.139243i 0.0444670π-0.0444670\pi
954954 1.13471 + 12.0578i 0.0367375 + 0.390386i
955955 4.89674 2.02830i 0.158455 0.0656341i
956956 8.29224 + 43.6679i 0.268190 + 1.41232i
957957 −2.12994 0.882251i −0.0688513 0.0285191i
958958 −9.89281 18.7032i −0.319622 0.604272i
959959 −64.5181 −2.08340
960960 11.2956 7.12872i 0.364565 0.230078i
961961 23.9894i 0.773851i
962962 25.8171 + 8.89362i 0.832376 + 0.286742i
963963 −1.01467 + 0.420289i −0.0326972 + 0.0135436i
964964 1.88811 + 9.94304i 0.0608121 + 0.320244i
965965 11.1202 + 4.60614i 0.357972 + 0.148277i
966966 −91.1630 75.4808i −2.93312 2.42856i
967967 26.6348 0.856518 0.428259 0.903656i 0.359127π-0.359127\pi
0.428259 + 0.903656i 0.359127π0.359127\pi
968968 22.0654 + 2.46408i 0.709208 + 0.0791985i
969969 7.26285i 0.233316i
970970 −0.214006 + 0.258469i −0.00687132 + 0.00829893i
971971 23.4336 + 9.70652i 0.752021 + 0.311497i 0.725566 0.688153i 0.241578π-0.241578\pi
0.0264550 + 0.999650i 0.491578π0.491578\pi
972972 8.94455 43.0103i 0.286896 1.37956i
973973 2.09104 5.04822i 0.0670357 0.161839i
974974 29.9057 + 9.21391i 0.958242 + 0.295233i
975975 −29.1180 + 27.2632i −0.932521 + 0.873122i
976976 30.7556 29.7046i 0.984464 0.950822i
977977 −19.4680 + 19.4680i −0.622838 + 0.622838i −0.946256 0.323418i 0.895168π-0.895168\pi
0.323418 + 0.946256i 0.395168π0.395168\pi
978978 5.08697 16.5109i 0.162663 0.527959i
979979 6.88169 2.85049i 0.219940 0.0911020i
980980 4.37842 21.0539i 0.139864 0.672541i
981981 56.2607 23.3040i 1.79627 0.744038i
982982 25.5405 30.8469i 0.815031 0.984365i
983983 −37.8510 −1.20726 −0.603629 0.797265i 0.706279π-0.706279\pi
−0.603629 + 0.797265i 0.706279π0.706279\pi
984984 −18.0116 9.93143i −0.574189 0.316602i
985985 −2.82742 + 2.82742i −0.0900892 + 0.0900892i
986986 0.193741 + 2.05876i 0.00616996 + 0.0655642i
987987 37.5387 + 15.5490i 1.19487 + 0.494931i
988988 7.71457 1.20364i 0.245433 0.0382930i
989989 −17.5897 42.4653i −0.559320 1.35032i
990990 −4.85444 1.49565i −0.154284 0.0475347i
991991 31.2350i 0.992212i 0.868262 + 0.496106i 0.165237π0.165237\pi
−0.868262 + 0.496106i 0.834763π0.834763\pi
992992 31.8407 + 27.3099i 1.01094 + 0.867091i
993993 −29.1824 29.1824i −0.926074 0.926074i
994994 24.3514 79.0377i 0.772379 2.50692i
995995 −1.18465 + 2.86000i −0.0375560 + 0.0906681i
996996 −41.4808 + 60.9275i −1.31437 + 1.93056i
997997 −23.4901 9.72991i −0.743938 0.308149i −0.0216727 0.999765i 0.506899π-0.506899\pi
−0.722266 + 0.691616i 0.756899π0.756899\pi
998998 16.1784 19.5396i 0.512117 0.618517i
999999 0.539720i 0.0170760i
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 416.2.bd.a.411.5 yes 216
13.5 odd 4 416.2.bi.a.187.24 yes 216
32.19 odd 8 416.2.bi.a.307.24 yes 216
416.83 even 8 inner 416.2.bd.a.83.5 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
416.2.bd.a.83.5 216 416.83 even 8 inner
416.2.bd.a.411.5 yes 216 1.1 even 1 trivial
416.2.bi.a.187.24 yes 216 13.5 odd 4
416.2.bi.a.307.24 yes 216 32.19 odd 8