Properties

Label 483.2.y.a.4.5
Level 483483
Weight 22
Character 483.4
Analytic conductor 3.8573.857
Analytic rank 00
Dimension 320320
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,2,Mod(4,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([0, 44, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 483=3723 483 = 3 \cdot 7 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 483.y (of order 3333, degree 2020, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.856774417633.85677441763
Analytic rank: 00
Dimension: 320320
Relative dimension: 1616 over Q(ζ33)\Q(\zeta_{33})
Twist minimal: yes
Sato-Tate group: SU(2)[C33]\mathrm{SU}(2)[C_{33}]

Embedding invariants

Embedding label 4.5
Character χ\chi == 483.4
Dual form 483.2.y.a.121.5

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+(0.957403+1.34448i)q2+(0.235759+0.971812i)q3+(0.2368820.684426i)q4+(0.1155702.42610i)q5+(1.080871.24739i)q6+(2.219641.43986i)q7+(2.020360.593231i)q8+(0.8888350.458227i)q9+(3.15121+2.47814i)q10+(0.2434780.341917i)q11+(0.7209800.0688452i)q12+(0.871137+6.05889i)q13+(0.189222+4.36280i)q14+(2.33047+0.684288i)q15+(3.870503.04379i)q16+(5.699181.09843i)q17+(1.467050.756318i)q18+(4.77961+0.921194i)q19+(1.68786+0.495602i)q20+(0.875972+2.49653i)q21+0.692809q22+(3.96736+2.69445i)q23+(1.052831.82355i)q24+(0.8952670.0854877i)q25+(7.312056.97203i)q26+(0.6548610.755750i)q27+(1.511271.17810i)q28+(0.4081460.471026i)q29+(3.15121+2.47814i)q30+(5.22627+4.98324i)q31+(0.186324+3.91143i)q32+(0.3896810.156005i)q33+(3.97960+8.71410i)q34+(3.236735.55148i)q35+(0.103073+0.716887i)q36+(6.81960+3.51575i)q37+(5.81454+5.54416i)q38+(5.682722.27502i)q39+(1.67273+4.83304i)q40+(3.15401+2.02696i)q41+(4.195211.21246i)q42+(0.780351+0.229132i)q43+(0.176341+0.247637i)q44+(1.21443+2.10345i)q45+(7.42101+2.75438i)q46+(4.233047.33184i)q47+(2.04549+4.47900i)q48+(2.853616.39194i)q49+(0.9720691.12183i)q50+(0.276169+5.79750i)q51+(4.353220.839014i)q52+(3.644741.45913i)q53+(0.389128+1.60401i)q54+(0.857666+0.551188i)q55+(5.33864+1.59227i)q56+(2.02206+4.42770i)q57+(1.024050.0977847i)q58+(2.864692.25282i)q59+(0.08370241.75713i)q60+(2.9074111.9845i)q61+(1.6962411.7976i)q62+(2.63268+0.262700i)q63+(2.84736+1.82989i)q64+(14.5988+2.81369i)q65+(0.163336+0.673280i)q66+(11.4516+1.09349i)q67+(2.101833.64047i)q68+(3.55384+3.22029i)q69+(10.5627+0.963278i)q70+(5.27225+11.5446i)q71+(1.52393+1.45307i)q72+(1.530394.42177i)q73+(11.2560+5.80286i)q74+(0.2941450.849877i)q75+(0.5017153.48950i)q76+(1.032750.408359i)q77+(8.499385.46222i)q78+(0.4490120.179757i)q79+(6.937259.74201i)q80+(0.580057+0.814576i)q81+(5.74488+2.29990i)q82+(7.46719+4.79887i)q83+(1.501191.19092i)q84+(2.0062513.9538i)q85+(0.4390461.26854i)q86+(0.5539730.285593i)q87+(0.289077+0.835234i)q88+(2.055701.96010i)q89+(1.665363.64663i)q90+(6.79034+14.7029i)q91+(0.9043523.35363i)q92+(3.610636.25380i)q93+(13.9103+1.32827i)q94+(2.7872911.4894i)q95+(3.845100.741083i)q96+(5.735133.68574i)q97+(5.86181+9.95630i)q98+(0.0597365+0.415476i)q99+O(q100)q+(-0.957403 + 1.34448i) q^{2} +(-0.235759 + 0.971812i) q^{3} +(-0.236882 - 0.684426i) q^{4} +(0.115570 - 2.42610i) q^{5} +(-1.08087 - 1.24739i) q^{6} +(2.21964 - 1.43986i) q^{7} +(-2.02036 - 0.593231i) q^{8} +(-0.888835 - 0.458227i) q^{9} +(3.15121 + 2.47814i) q^{10} +(-0.243478 - 0.341917i) q^{11} +(0.720980 - 0.0688452i) q^{12} +(-0.871137 + 6.05889i) q^{13} +(-0.189222 + 4.36280i) q^{14} +(2.33047 + 0.684288i) q^{15} +(3.87050 - 3.04379i) q^{16} +(5.69918 - 1.09843i) q^{17} +(1.46705 - 0.756318i) q^{18} +(4.77961 + 0.921194i) q^{19} +(-1.68786 + 0.495602i) q^{20} +(0.875972 + 2.49653i) q^{21} +0.692809 q^{22} +(3.96736 + 2.69445i) q^{23} +(1.05283 - 1.82355i) q^{24} +(-0.895267 - 0.0854877i) q^{25} +(-7.31205 - 6.97203i) q^{26} +(0.654861 - 0.755750i) q^{27} +(-1.51127 - 1.17810i) q^{28} +(-0.408146 - 0.471026i) q^{29} +(-3.15121 + 2.47814i) q^{30} +(-5.22627 + 4.98324i) q^{31} +(0.186324 + 3.91143i) q^{32} +(0.389681 - 0.156005i) q^{33} +(-3.97960 + 8.71410i) q^{34} +(-3.23673 - 5.55148i) q^{35} +(-0.103073 + 0.716887i) q^{36} +(6.81960 + 3.51575i) q^{37} +(-5.81454 + 5.54416i) q^{38} +(-5.68272 - 2.27502i) q^{39} +(-1.67273 + 4.83304i) q^{40} +(3.15401 + 2.02696i) q^{41} +(-4.19521 - 1.21246i) q^{42} +(-0.780351 + 0.229132i) q^{43} +(-0.176341 + 0.247637i) q^{44} +(-1.21443 + 2.10345i) q^{45} +(-7.42101 + 2.75438i) q^{46} +(-4.23304 - 7.33184i) q^{47} +(2.04549 + 4.47900i) q^{48} +(2.85361 - 6.39194i) q^{49} +(0.972069 - 1.12183i) q^{50} +(-0.276169 + 5.79750i) q^{51} +(4.35322 - 0.839014i) q^{52} +(-3.64474 - 1.45913i) q^{53} +(0.389128 + 1.60401i) q^{54} +(-0.857666 + 0.551188i) q^{55} +(-5.33864 + 1.59227i) q^{56} +(-2.02206 + 4.42770i) q^{57} +(1.02405 - 0.0977847i) q^{58} +(-2.86469 - 2.25282i) q^{59} +(-0.0837024 - 1.75713i) q^{60} +(-2.90741 - 11.9845i) q^{61} +(-1.69624 - 11.7976i) q^{62} +(-2.63268 + 0.262700i) q^{63} +(2.84736 + 1.82989i) q^{64} +(14.5988 + 2.81369i) q^{65} +(-0.163336 + 0.673280i) q^{66} +(11.4516 + 1.09349i) q^{67} +(-2.10183 - 3.64047i) q^{68} +(-3.55384 + 3.22029i) q^{69} +(10.5627 + 0.963278i) q^{70} +(5.27225 + 11.5446i) q^{71} +(1.52393 + 1.45307i) q^{72} +(-1.53039 - 4.42177i) q^{73} +(-11.2560 + 5.80286i) q^{74} +(0.294145 - 0.849877i) q^{75} +(-0.501715 - 3.48950i) q^{76} +(-1.03275 - 0.408359i) q^{77} +(8.49938 - 5.46222i) q^{78} +(0.449012 - 0.179757i) q^{79} +(-6.93725 - 9.74201i) q^{80} +(0.580057 + 0.814576i) q^{81} +(-5.74488 + 2.29990i) q^{82} +(-7.46719 + 4.79887i) q^{83} +(1.50119 - 1.19092i) q^{84} +(-2.00625 - 13.9538i) q^{85} +(0.439046 - 1.26854i) q^{86} +(0.553973 - 0.285593i) q^{87} +(0.289077 + 0.835234i) q^{88} +(-2.05570 - 1.96010i) q^{89} +(-1.66536 - 3.64663i) q^{90} +(6.79034 + 14.7029i) q^{91} +(0.904352 - 3.35363i) q^{92} +(-3.61063 - 6.25380i) q^{93} +(13.9103 + 1.32827i) q^{94} +(2.78729 - 11.4894i) q^{95} +(-3.84510 - 0.741083i) q^{96} +(-5.73513 - 3.68574i) q^{97} +(5.86181 + 9.95630i) q^{98} +(0.0597365 + 0.415476i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 320q+2q216q3+18q42q518q6+2q712q8+16q9+8q106q1118q1210q14+18q15+8q16+4q17+2q18+18q20+4q21+10q99+O(q100) 320 q + 2 q^{2} - 16 q^{3} + 18 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{7} - 12 q^{8} + 16 q^{9} + 8 q^{10} - 6 q^{11} - 18 q^{12} - 10 q^{14} + 18 q^{15} + 8 q^{16} + 4 q^{17} + 2 q^{18} + 18 q^{20} + 4 q^{21}+ \cdots - 10 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/483Z)×\left(\mathbb{Z}/483\mathbb{Z}\right)^\times.

nn 323323 346346 442442
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right) e(211)e\left(\frac{2}{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 −0.957403 + 1.34448i −0.676986 + 0.950694i 0.323005 + 0.946397i 0.395307π0.395307\pi
−0.999991 + 0.00429672i 0.998632π0.998632\pi
33 −0.235759 + 0.971812i −0.136115 + 0.561076i
44 −0.236882 0.684426i −0.118441 0.342213i
55 0.115570 2.42610i 0.0516843 1.08499i −0.812869 0.582446i 0.802096π-0.802096\pi
0.864554 0.502541i 0.167601π-0.167601\pi
66 −1.08087 1.24739i −0.441263 0.509245i
77 2.21964 1.43986i 0.838945 0.544216i
88 −2.02036 0.593231i −0.714305 0.209739i
99 −0.888835 0.458227i −0.296278 0.152742i
1010 3.15121 + 2.47814i 0.996501 + 0.783657i
1111 −0.243478 0.341917i −0.0734114 0.103092i 0.776238 0.630440i 0.217126π-0.217126\pi
−0.849649 + 0.527348i 0.823186π0.823186\pi
1212 0.720980 0.0688452i 0.208129 0.0198739i
1313 −0.871137 + 6.05889i −0.241610 + 1.68043i 0.402437 + 0.915448i 0.368163π0.368163\pi
−0.644047 + 0.764986i 0.722746π0.722746\pi
1414 −0.189222 + 4.36280i −0.0505716 + 1.16601i
1515 2.33047 + 0.684288i 0.601725 + 0.176682i
1616 3.87050 3.04379i 0.967625 0.760949i
1717 5.69918 1.09843i 1.38225 0.266408i 0.556692 0.830719i 0.312070π-0.312070\pi
0.825562 + 0.564311i 0.190858π0.190858\pi
1818 1.46705 0.756318i 0.345788 0.178266i
1919 4.77961 + 0.921194i 1.09652 + 0.211336i 0.705263 0.708946i 0.250829π-0.250829\pi
0.391255 + 0.920282i 0.372041π0.372041\pi
2020 −1.68786 + 0.495602i −0.377418 + 0.110820i
2121 0.875972 + 2.49653i 0.191153 + 0.544788i
2222 0.692809 0.147707
2323 3.96736 + 2.69445i 0.827252 + 0.561831i
2424 1.05283 1.82355i 0.214907 0.372230i
2525 −0.895267 0.0854877i −0.179053 0.0170975i
2626 −7.31205 6.97203i −1.43401 1.36733i
2727 0.654861 0.755750i 0.126028 0.145444i
2828 −1.51127 1.17810i −0.285603 0.222640i
2929 −0.408146 0.471026i −0.0757909 0.0874673i 0.716588 0.697497i 0.245703π-0.245703\pi
−0.792379 + 0.610030i 0.791158π0.791158\pi
3030 −3.15121 + 2.47814i −0.575330 + 0.452445i
3131 −5.22627 + 4.98324i −0.938667 + 0.895017i −0.994638 0.103416i 0.967023π-0.967023\pi
0.0559716 + 0.998432i 0.482174π0.482174\pi
3232 0.186324 + 3.91143i 0.0329378 + 0.691450i
3333 0.389681 0.156005i 0.0678348 0.0271570i
3434 −3.97960 + 8.71410i −0.682495 + 1.49446i
3535 −3.23673 5.55148i −0.547107 0.938372i
3636 −0.103073 + 0.716887i −0.0171788 + 0.119481i
3737 6.81960 + 3.51575i 1.12114 + 0.577986i 0.916173 0.400784i 0.131262π-0.131262\pi
0.204963 + 0.978770i 0.434292π0.434292\pi
3838 −5.81454 + 5.54416i −0.943244 + 0.899381i
3939 −5.68272 2.27502i −0.909964 0.364294i
4040 −1.67273 + 4.83304i −0.264482 + 0.764171i
4141 3.15401 + 2.02696i 0.492574 + 0.316558i 0.763240 0.646115i 0.223607π-0.223607\pi
−0.270666 + 0.962673i 0.587244π0.587244\pi
4242 −4.19521 1.21246i −0.647335 0.187086i
4343 −0.780351 + 0.229132i −0.119002 + 0.0349422i −0.340691 0.940175i 0.610661π-0.610661\pi
0.221689 + 0.975117i 0.428843π0.428843\pi
4444 −0.176341 + 0.247637i −0.0265845 + 0.0373327i
4545 −1.21443 + 2.10345i −0.181036 + 0.313564i
4646 −7.42101 + 2.75438i −1.09417 + 0.406112i
4747 −4.23304 7.33184i −0.617452 1.06946i −0.989949 0.141425i 0.954831π-0.954831\pi
0.372496 0.928034i 0.378502π-0.378502\pi
4848 2.04549 + 4.47900i 0.295241 + 0.646488i
4949 2.85361 6.39194i 0.407658 0.913135i
5050 0.972069 1.12183i 0.137471 0.158650i
5151 −0.276169 + 5.79750i −0.0386714 + 0.811812i
5252 4.35322 0.839014i 0.603682 0.116350i
5353 −3.64474 1.45913i −0.500643 0.200427i 0.107575 0.994197i 0.465691π-0.465691\pi
−0.608218 + 0.793770i 0.708116π0.708116\pi
5454 0.389128 + 1.60401i 0.0529536 + 0.218278i
5555 −0.857666 + 0.551188i −0.115648 + 0.0743222i
5656 −5.33864 + 1.59227i −0.713406 + 0.212777i
5757 −2.02206 + 4.42770i −0.267829 + 0.586463i
5858 1.02405 0.0977847i 0.134464 0.0128398i
5959 −2.86469 2.25282i −0.372951 0.293292i 0.414037 0.910260i 0.364118π-0.364118\pi
−0.786988 + 0.616968i 0.788361π0.788361\pi
6060 −0.0837024 1.75713i −0.0108059 0.226844i
6161 −2.90741 11.9845i −0.372255 1.53446i −0.782599 0.622526i 0.786107π-0.786107\pi
0.410344 0.911931i 0.365409π-0.365409\pi
6262 −1.69624 11.7976i −0.215423 1.49830i
6363 −2.63268 + 0.262700i −0.331686 + 0.0330971i
6464 2.84736 + 1.82989i 0.355920 + 0.228736i
6565 14.5988 + 2.81369i 1.81076 + 0.348996i
6666 −0.163336 + 0.673280i −0.0201053 + 0.0828750i
6767 11.4516 + 1.09349i 1.39903 + 0.133591i 0.767148 0.641471i 0.221675π-0.221675\pi
0.631885 + 0.775062i 0.282281π0.282281\pi
6868 −2.10183 3.64047i −0.254884 0.441472i
6969 −3.55384 + 3.22029i −0.427831 + 0.387677i
7070 10.5627 + 0.963278i 1.26249 + 0.115134i
7171 5.27225 + 11.5446i 0.625701 + 1.37009i 0.911299 + 0.411745i 0.135081π0.135081\pi
−0.285598 + 0.958350i 0.592192π0.592192\pi
7272 1.52393 + 1.45307i 0.179597 + 0.171246i
7373 −1.53039 4.42177i −0.179119 0.517529i 0.819323 0.573332i 0.194349π-0.194349\pi
−0.998442 + 0.0558028i 0.982228π0.982228\pi
7474 −11.2560 + 5.80286i −1.30848 + 0.674569i
7575 0.294145 0.849877i 0.0339650 0.0981353i
7676 −0.501715 3.48950i −0.0575506 0.400273i
7777 −1.03275 0.408359i −0.117692 0.0465368i
7878 8.49938 5.46222i 0.962365 0.618475i
7979 0.449012 0.179757i 0.0505178 0.0202243i −0.346266 0.938136i 0.612551π-0.612551\pi
0.396784 + 0.917912i 0.370126π0.370126\pi
8080 −6.93725 9.74201i −0.775608 1.08919i
8181 0.580057 + 0.814576i 0.0644508 + 0.0905084i
8282 −5.74488 + 2.29990i −0.634416 + 0.253982i
8383 −7.46719 + 4.79887i −0.819631 + 0.526745i −0.881967 0.471311i 0.843781π-0.843781\pi
0.0623367 + 0.998055i 0.480145π0.480145\pi
8484 1.50119 1.19092i 0.163793 0.129940i
8585 −2.00625 13.9538i −0.217608 1.51350i
8686 0.439046 1.26854i 0.0473436 0.136790i
8787 0.553973 0.285593i 0.0593921 0.0306188i
8888 0.289077 + 0.835234i 0.0308158 + 0.0890363i
8989 −2.05570 1.96010i −0.217903 0.207770i 0.573263 0.819371i 0.305677π-0.305677\pi
−0.791166 + 0.611601i 0.790526π0.790526\pi
9090 −1.66536 3.64663i −0.175544 0.384389i
9191 6.79034 + 14.7029i 0.711821 + 1.54128i
9292 0.904352 3.35363i 0.0942852 0.349640i
9393 −3.61063 6.25380i −0.374405 0.648489i
9494 13.9103 + 1.32827i 1.43474 + 0.137001i
9595 2.78729 11.4894i 0.285970 1.17878i
9696 −3.84510 0.741083i −0.392439 0.0756364i
9797 −5.73513 3.68574i −0.582314 0.374230i 0.216071 0.976378i 0.430676π-0.430676\pi
−0.798385 + 0.602147i 0.794312π0.794312\pi
9898 5.86181 + 9.95630i 0.592133 + 1.00574i
9999 0.0597365 + 0.415476i 0.00600374 + 0.0417569i
100100 0.153563 + 0.632995i 0.0153563 + 0.0632995i
101101 0.169940 + 3.56749i 0.0169097 + 0.354978i 0.991427 + 0.130664i 0.0417110π0.0417110\pi
−0.974517 + 0.224314i 0.927986π0.927986\pi
102102 −7.53024 5.92184i −0.745605 0.586350i
103103 19.7970 1.89039i 1.95066 0.186265i 0.956304 0.292375i 0.0944456π-0.0944456\pi
0.994354 + 0.106110i 0.0338395π0.0338395\pi
104104 5.35433 11.7243i 0.525035 1.14967i
105105 6.15808 1.83668i 0.600967 0.179241i
106106 5.45126 3.50331i 0.529473 0.340272i
107107 −0.794196 3.27372i −0.0767778 0.316483i 0.920453 0.390854i 0.127820π-0.127820\pi
−0.997231 + 0.0743712i 0.976305π0.976305\pi
108108 −0.672379 0.269180i −0.0646997 0.0259019i
109109 −10.5500 + 2.03335i −1.01051 + 0.194759i −0.667529 0.744584i 0.732648π-0.732648\pi
−0.342979 + 0.939343i 0.611436π0.611436\pi
110110 0.0800677 1.68083i 0.00763416 0.160261i
111111 −5.02443 + 5.79850i −0.476898 + 0.550369i
112112 4.20848 12.3291i 0.397664 1.16499i
113113 1.16459 + 2.55010i 0.109556 + 0.239893i 0.956467 0.291841i 0.0942678π-0.0942678\pi
−0.846911 + 0.531734i 0.821540π0.821540\pi
114114 −4.01704 6.95773i −0.376231 0.651651i
115115 6.99552 9.31384i 0.652335 0.868520i
116116 −0.225700 + 0.390923i −0.0209557 + 0.0362963i
117117 3.55064 4.98618i 0.328257 0.460972i
118118 5.77154 1.69468i 0.531313 0.156008i
119119 11.0686 10.6441i 1.01465 0.975746i
120120 −4.30244 2.76501i −0.392758 0.252410i
121121 3.54012 10.2285i 0.321829 0.929865i
122122 18.8965 + 7.56502i 1.71081 + 0.684905i
123123 −2.71341 + 2.58723i −0.244660 + 0.233283i
124124 4.64867 + 2.39656i 0.417463 + 0.215217i
125125 1.41744 9.85853i 0.126780 0.881774i
126126 2.16734 3.79110i 0.193082 0.337738i
127127 −3.21746 + 7.04526i −0.285504 + 0.625166i −0.996990 0.0775344i 0.975295π-0.975295\pi
0.711486 + 0.702700i 0.248023π0.248023\pi
128128 −12.4571 + 4.98706i −1.10106 + 0.440798i
129129 −0.0386981 0.812373i −0.00340718 0.0715255i
130130 −17.7599 + 16.9341i −1.55765 + 1.48521i
131131 −14.8350 + 11.6664i −1.29614 + 1.01930i −0.298243 + 0.954490i 0.596401π0.596401\pi
−0.997898 + 0.0648067i 0.979357π0.979357\pi
132132 −0.199082 0.229753i −0.0173279 0.0199974i
133133 11.9354 4.83725i 1.03493 0.419442i
134134 −12.4340 + 14.3496i −1.07413 + 1.23961i
135135 −1.75785 1.67610i −0.151291 0.144256i
136136 −12.1660 1.16171i −1.04323 0.0996161i
137137 4.81734 8.34388i 0.411573 0.712865i −0.583489 0.812121i 0.698313π-0.698313\pi
0.995062 + 0.0992557i 0.0316462π0.0316462\pi
138138 −0.927174 7.86119i −0.0789263 0.669189i
139139 −17.0999 −1.45040 −0.725199 0.688539i 0.758252π-0.758252\pi
−0.725199 + 0.688539i 0.758252π0.758252\pi
140140 −3.03286 + 3.53035i −0.256323 + 0.298369i
141141 8.12315 2.38517i 0.684092 0.200868i
142142 −20.5692 3.96440i −1.72613 0.332685i
143143 2.28374 1.17735i 0.190976 0.0984550i
144144 −4.83498 + 0.931867i −0.402915 + 0.0776556i
145145 −1.18993 + 0.935769i −0.0988181 + 0.0777114i
146146 7.41020 + 2.17583i 0.613272 + 0.180073i
147147 5.53900 + 4.28013i 0.456849 + 0.353019i
148148 0.790828 5.50033i 0.0650057 0.452124i
149149 4.67883 0.446774i 0.383304 0.0366011i 0.0983745 0.995149i 0.468636π-0.468636\pi
0.284930 + 0.958548i 0.408030π0.408030\pi
150150 0.861031 + 1.20915i 0.0703029 + 0.0987266i
151151 1.11189 + 0.874401i 0.0904844 + 0.0711577i 0.662376 0.749171i 0.269548π-0.269548\pi
−0.571892 + 0.820329i 0.693790π0.693790\pi
152152 −9.11004 4.69655i −0.738922 0.380941i
153153 −5.56896 1.63520i −0.450224 0.132198i
154154 1.53779 0.997548i 0.123918 0.0803847i
155155 11.4859 + 13.2554i 0.922567 + 1.06470i
156156 −0.210946 + 4.42831i −0.0168892 + 0.354549i
157157 1.61628 + 4.66995i 0.128994 + 0.372702i 0.990941 0.134294i 0.0428768π-0.0428768\pi
−0.861948 + 0.506997i 0.830756π0.830756\pi
158158 −0.188204 + 0.775789i −0.0149727 + 0.0617185i
159159 2.27728 3.19799i 0.180600 0.253617i
160160 9.51107 0.751916
161161 12.6857 + 0.268259i 0.999776 + 0.0211418i
162162 −1.65053 −0.129678
163163 5.08569 7.14186i 0.398342 0.559393i −0.565880 0.824487i 0.691464π-0.691464\pi
0.964223 + 0.265094i 0.0854030π0.0854030\pi
164164 0.640175 2.63884i 0.0499893 0.206059i
165165 −0.333449 0.963437i −0.0259590 0.0750035i
166166 0.697102 14.6340i 0.0541056 1.13582i
167167 8.59292 + 9.91676i 0.664940 + 0.767382i 0.983576 0.180495i 0.0577700π-0.0577700\pi
−0.318636 + 0.947877i 0.603225π0.603225\pi
168168 −0.288758 5.56354i −0.0222782 0.429237i
169169 −23.4779 6.89372i −1.80599 0.530286i
170170 20.6814 + 10.6620i 1.58619 + 0.817738i
171171 −3.82617 3.00893i −0.292595 0.230099i
172172 0.341675 + 0.479815i 0.0260524 + 0.0365855i
173173 6.31277 0.602797i 0.479951 0.0458298i 0.147723 0.989029i 0.452806π-0.452806\pi
0.332228 + 0.943199i 0.392200π0.392200\pi
174174 −0.146400 + 1.01823i −0.0110986 + 0.0771922i
175175 −2.11026 + 1.09931i −0.159521 + 0.0830998i
176176 −1.98311 0.582293i −0.149482 0.0438920i
177177 2.86469 2.25282i 0.215323 0.169332i
178178 4.60345 0.887243i 0.345044 0.0665017i
179179 −13.4941 + 6.95669i −1.00860 + 0.519967i −0.881631 0.471940i 0.843554π-0.843554\pi
−0.126965 + 0.991907i 0.540524π0.540524\pi
180180 1.72733 + 0.332916i 0.128748 + 0.0248141i
181181 −11.9736 + 3.51577i −0.889992 + 0.261325i −0.694597 0.719399i 0.744417π-0.744417\pi
−0.195395 + 0.980725i 0.562599π0.562599\pi
182182 −26.2689 4.94707i −1.94718 0.366701i
183183 12.3321 0.911616
184184 −6.41706 7.79731i −0.473072 0.574825i
185185 9.31772 16.1388i 0.685052 1.18655i
186186 11.8650 + 1.13297i 0.869981 + 0.0830732i
187187 −1.76320 1.68121i −0.128938 0.122942i
188188 −4.01537 + 4.63398i −0.292851 + 0.337968i
189189 0.365382 2.62040i 0.0265776 0.190606i
190190 12.7787 + 14.7474i 0.927066 + 1.06989i
191191 −0.396203 + 0.311578i −0.0286682 + 0.0225450i −0.632390 0.774650i 0.717926π-0.717926\pi
0.603722 + 0.797195i 0.293684π0.293684\pi
192192 −2.44960 + 2.33569i −0.176785 + 0.168564i
193193 −1.14655 24.0691i −0.0825307 1.73253i −0.538576 0.842577i 0.681037π-0.681037\pi
0.456045 0.889957i 0.349266π-0.349266\pi
194194 10.4462 4.18205i 0.749997 0.300254i
195195 −6.17618 + 13.5240i −0.442286 + 0.968470i
196196 −5.05078 0.438947i −0.360770 0.0313533i
197197 −2.69941 + 18.7748i −0.192325 + 1.33765i 0.633507 + 0.773737i 0.281615π0.281615\pi
−0.825833 + 0.563915i 0.809294π0.809294\pi
198198 −0.615793 0.317464i −0.0437625 0.0225612i
199199 −8.61200 + 8.21152i −0.610488 + 0.582100i −0.930943 0.365164i 0.881013π-0.881013\pi
0.320455 + 0.947264i 0.396164π0.396164\pi
200200 1.75805 + 0.703816i 0.124313 + 0.0497673i
201201 −3.76248 + 10.8710i −0.265385 + 0.766779i
202202 −4.95913 3.18704i −0.348923 0.224239i
203203 −1.58415 0.457835i −0.111185 0.0321337i
204204 4.03337 1.18431i 0.282393 0.0829180i
205205 5.28213 7.41771i 0.368920 0.518075i
206206 −16.4121 + 28.4266i −1.14349 + 1.98058i
207207 −2.29166 4.21287i −0.159282 0.292815i
208208 15.0703 + 26.1025i 1.04494 + 1.80988i
209209 −0.848758 1.85852i −0.0587098 0.128557i
210210 −3.42638 + 10.0379i −0.236443 + 0.692680i
211211 −8.72529 + 10.0695i −0.600674 + 0.693215i −0.971918 0.235321i 0.924386π-0.924386\pi
0.371244 + 0.928535i 0.378931π0.378931\pi
212212 −0.135295 + 2.84019i −0.00929210 + 0.195065i
213213 −12.4622 + 2.40189i −0.853895 + 0.164575i
214214 5.16183 + 2.06649i 0.352856 + 0.141262i
215215 0.465712 + 1.91969i 0.0317613 + 0.130922i
216216 −1.77139 + 1.13840i −0.120528 + 0.0774584i
217217 −4.42528 + 18.5861i −0.300408 + 1.26171i
218218 7.36681 16.1311i 0.498943 1.09253i
219219 4.65793 0.444778i 0.314754 0.0300553i
220220 0.580413 + 0.456442i 0.0391314 + 0.0307733i
221221 1.69048 + 35.4876i 0.113714 + 2.38715i
222222 −2.98559 12.3068i −0.200380 0.825976i
223223 −2.97284 20.6765i −0.199076 1.38460i −0.806974 0.590587i 0.798896π-0.798896\pi
0.607898 0.794015i 0.292013π-0.292013\pi
224224 6.04549 + 8.41369i 0.403931 + 0.562163i
225225 0.756573 + 0.486220i 0.0504382 + 0.0324147i
226226 −4.54356 0.875699i −0.302233 0.0582506i
227227 3.05516 12.5935i 0.202778 0.835862i −0.775966 0.630775i 0.782737π-0.782737\pi
0.978744 0.205087i 0.0657477π-0.0657477\pi
228228 3.50942 + 0.335109i 0.232417 + 0.0221931i
229229 0.441905 + 0.765402i 0.0292019 + 0.0505792i 0.880257 0.474497i 0.157370π-0.157370\pi
−0.851055 + 0.525076i 0.824037π0.824037\pi
230230 5.82478 + 18.3225i 0.384075 + 1.20815i
231231 0.640327 0.907361i 0.0421304 0.0597000i
232232 0.545175 + 1.19377i 0.0357925 + 0.0783746i
233233 5.04466 + 4.81007i 0.330487 + 0.315118i 0.837095 0.547058i 0.184252π-0.184252\pi
−0.506608 + 0.862177i 0.669101π0.669101\pi
234234 3.30444 + 9.54756i 0.216018 + 0.624144i
235235 −18.2770 + 9.42246i −1.19226 + 0.614654i
236236 −0.863292 + 2.49432i −0.0561955 + 0.162366i
237237 0.0688316 + 0.478734i 0.00447109 + 0.0310971i
238238 3.71381 + 25.0722i 0.240730 + 1.62519i
239239 11.6683 7.49879i 0.754762 0.485056i −0.105809 0.994386i 0.533743π-0.533743\pi
0.860571 + 0.509330i 0.170107π0.170107\pi
240240 11.1029 4.44494i 0.716690 0.286919i
241241 −8.91891 12.5249i −0.574518 0.806797i 0.420416 0.907331i 0.361884π-0.361884\pi
−0.994934 + 0.100534i 0.967945π0.967945\pi
242242 10.3628 + 14.5524i 0.666143 + 0.935467i
243243 −0.928368 + 0.371662i −0.0595548 + 0.0238422i
244244 −7.51378 + 4.82881i −0.481020 + 0.309133i
245245 −15.1777 7.66187i −0.969670 0.489499i
246246 −0.880665 6.12516i −0.0561492 0.390526i
247247 −9.74511 + 28.1566i −0.620066 + 1.79156i
248248 13.5152 6.96755i 0.858214 0.442440i
249249 −2.90314 8.38808i −0.183979 0.531573i
250250 11.8976 + 11.3443i 0.752469 + 0.717478i
251251 −6.82450 14.9436i −0.430759 0.943230i −0.993203 0.116395i 0.962866π-0.962866\pi
0.562444 0.826835i 0.309861π-0.309861\pi
252252 0.803433 + 1.73964i 0.0506115 + 0.109587i
253253 −0.0446882 2.01255i −0.00280952 0.126528i
254254 −6.39184 11.0710i −0.401060 0.694655i
255255 14.0334 + 1.34003i 0.878806 + 0.0839158i
256256 3.62548 14.9444i 0.226592 0.934027i
257257 −23.7273 4.57306i −1.48007 0.285260i −0.615645 0.788024i 0.711104π-0.711104\pi
−0.864424 + 0.502764i 0.832317π0.832317\pi
258258 1.12927 + 0.725740i 0.0703055 + 0.0451826i
259259 20.1993 2.01557i 1.25512 0.125241i
260260 −1.53244 10.6583i −0.0950376 0.661001i
261261 0.146938 + 0.605688i 0.00909525 + 0.0374911i
262262 −1.48218 31.1149i −0.0915696 1.92228i
263263 21.0145 + 16.5260i 1.29581 + 1.01904i 0.997922 + 0.0644361i 0.0205249π0.0205249\pi
0.297889 + 0.954601i 0.403718π0.403718\pi
264264 −0.879843 + 0.0840148i −0.0541506 + 0.00517075i
265265 −3.96123 + 8.67388i −0.243336 + 0.532832i
266266 −4.92339 + 20.6782i −0.301872 + 1.26786i
267267 2.38950 1.53564i 0.146235 0.0939795i
268268 −1.96426 8.09678i −0.119986 0.494590i
269269 −14.5579 5.82809i −0.887608 0.355345i −0.117360 0.993089i 0.537443π-0.537443\pi
−0.770248 + 0.637745i 0.779868π0.779868\pi
270270 3.93646 0.758691i 0.239565 0.0461724i
271271 −1.02814 + 21.5834i −0.0624553 + 1.31110i 0.722424 + 0.691450i 0.243028π0.243028\pi
−0.784879 + 0.619649i 0.787275π0.787275\pi
272272 18.7153 21.5986i 1.13478 1.30961i
273273 −15.8893 + 3.13260i −0.961664 + 0.189593i
274274 6.60608 + 14.4653i 0.399088 + 0.873880i
275275 0.188748 + 0.326922i 0.0113820 + 0.0197141i
276276 3.04589 + 1.66951i 0.183341 + 0.100493i
277277 −6.46923 + 11.2050i −0.388698 + 0.673245i −0.992275 0.124060i 0.960408π-0.960408\pi
0.603576 + 0.797305i 0.293742π0.293742\pi
278278 16.3715 22.9906i 0.981899 1.37888i
279279 6.92875 2.03447i 0.414814 0.121800i
280280 3.24604 + 13.1361i 0.193988 + 0.785033i
281281 −15.5930 10.0210i −0.930199 0.597803i −0.0145992 0.999893i 0.504647π-0.504647\pi
−0.915600 + 0.402091i 0.868284π0.868284\pi
282282 −4.57030 + 13.2050i −0.272157 + 0.786347i
283283 −3.25723 1.30400i −0.193622 0.0775147i 0.272825 0.962064i 0.412042π-0.412042\pi
−0.466447 + 0.884549i 0.654466π0.654466\pi
284284 6.65254 6.34318i 0.394755 0.376398i
285285 10.5084 + 5.41744i 0.622462 + 0.320902i
286286 −0.603532 + 4.19765i −0.0356876 + 0.248213i
287287 9.91931 0.0422112i 0.585519 0.00249165i
288288 1.62671 3.56200i 0.0958548 0.209893i
289289 15.4919 6.20201i 0.911287 0.364824i
290290 −0.118887 2.49575i −0.00698129 0.146555i
291291 4.93395 4.70451i 0.289233 0.275784i
292292 −2.66385 + 2.09488i −0.155890 + 0.122593i
293293 −9.08147 10.4806i −0.530545 0.612282i 0.425694 0.904867i 0.360030π-0.360030\pi
−0.956239 + 0.292585i 0.905485π0.905485\pi
294294 −11.0576 + 3.34929i −0.644893 + 0.195335i
295295 −5.79664 + 6.68968i −0.337493 + 0.389488i
296296 −11.6924 11.1487i −0.679606 0.648003i
297297 −0.417848 0.0398997i −0.0242460 0.00231521i
298298 −3.87884 + 6.71835i −0.224695 + 0.389184i
299299 −19.7815 + 21.6906i −1.14399 + 1.25440i
300300 −0.651355 −0.0376060
301301 −1.40218 + 1.63218i −0.0808203 + 0.0940776i
302302 −2.24015 + 0.657766i −0.128906 + 0.0378502i
303303 −3.50699 0.675917i −0.201471 0.0388304i
304304 21.3034 10.9827i 1.22183 0.629899i
305305 −29.4116 + 5.66863i −1.68411 + 0.324585i
306306 7.53024 5.92184i 0.430475 0.338529i
307307 −4.98939 1.46502i −0.284760 0.0836130i 0.136234 0.990677i 0.456500π-0.456500\pi
−0.420993 + 0.907064i 0.638318π0.638318\pi
308308 −0.0348522 + 0.803571i −0.00198589 + 0.0457877i
309309 −2.83022 + 19.6846i −0.161006 + 1.11982i
310310 −28.8183 + 2.75181i −1.63677 + 0.156292i
311311 15.3205 + 21.5146i 0.868743 + 1.21998i 0.974230 + 0.225558i 0.0724206π0.0724206\pi
−0.105487 + 0.994421i 0.533640π0.533640\pi
312312 10.1315 + 7.96752i 0.573584 + 0.451072i
313313 −23.8271 12.2837i −1.34679 0.694317i −0.374308 0.927305i 0.622120π-0.622120\pi
−0.972480 + 0.232987i 0.925150π0.925150\pi
314314 −7.82611 2.29795i −0.441653 0.129681i
315315 0.333081 + 6.41751i 0.0187670 + 0.361586i
316316 −0.229393 0.264734i −0.0129044 0.0148924i
317317 0.409460 8.59563i 0.0229976 0.482779i −0.957762 0.287561i 0.907156π-0.907156\pi
0.980760 0.195218i 0.0625414π-0.0625414\pi
318318 2.11938 + 6.12354i 0.118849 + 0.343391i
319319 −0.0616772 + 0.254237i −0.00345326 + 0.0142345i
320320 4.76857 6.69652i 0.266571 0.374347i
321321 3.36868 0.188021
322322 −12.5060 + 16.7990i −0.696934 + 0.936169i
323323 28.2517 1.57197
324324 0.420112 0.589964i 0.0233395 0.0327758i
325325 1.29786 5.34986i 0.0719924 0.296757i
326326 4.73306 + 13.6753i 0.262140 + 0.757403i
327327 0.511228 10.7320i 0.0282710 0.593481i
328328 −5.16978 5.96625i −0.285453 0.329431i
329329 −19.9527 10.1791i −1.10003 0.561190i
330330 1.61457 + 0.474081i 0.0888792 + 0.0260973i
331331 −14.5591 7.50576i −0.800242 0.412554i 0.00905041 0.999959i 0.497119π-0.497119\pi
−0.809293 + 0.587405i 0.800149π0.800149\pi
332332 5.05331 + 3.97397i 0.277337 + 0.218100i
333333 −4.45050 6.24985i −0.243886 0.342489i
334334 −21.5598 + 2.05871i −1.17970 + 0.112648i
335335 3.97638 27.6563i 0.217253 1.51103i
336336 10.9894 + 6.99655i 0.599520 + 0.381693i
337337 19.4752 + 5.71843i 1.06088 + 0.311503i 0.765206 0.643786i 0.222637π-0.222637\pi
0.295675 + 0.955289i 0.404455π0.404455\pi
338338 31.7463 24.9655i 1.72677 1.35795i
339339 −2.75278 + 0.530555i −0.149511 + 0.0288158i
340340 −9.07507 + 4.67852i −0.492165 + 0.253728i
341341 2.97634 + 0.573643i 0.161178 + 0.0310645i
342342 7.70865 2.26346i 0.416836 0.122394i
343343 −2.86952 18.2966i −0.154939 0.987924i
344344 1.71252 0.0923327
345345 7.40204 + 8.99414i 0.398512 + 0.484228i
346346 −5.23342 + 9.06454i −0.281350 + 0.487313i
347347 18.8789 + 1.80271i 1.01347 + 0.0967748i 0.588555 0.808457i 0.299697π-0.299697\pi
0.424917 + 0.905232i 0.360303π0.360303\pi
348348 −0.326693 0.311501i −0.0175126 0.0166982i
349349 1.30868 1.51030i 0.0700522 0.0808445i −0.719642 0.694346i 0.755694π-0.755694\pi
0.789694 + 0.613501i 0.210239π0.210239\pi
350350 0.542370 3.88970i 0.0289909 0.207913i
351351 4.00853 + 4.62609i 0.213959 + 0.246922i
352352 1.29202 1.01606i 0.0688649 0.0541559i
353353 −22.4209 + 21.3783i −1.19335 + 1.13785i −0.206119 + 0.978527i 0.566083π0.566083\pi
−0.987226 + 0.159326i 0.949068π0.949068\pi
354354 0.286215 + 6.00838i 0.0152121 + 0.319342i
355355 28.6178 11.4568i 1.51887 0.608065i
356356 −0.854587 + 1.87128i −0.0452930 + 0.0991778i
357357 7.73458 + 13.2660i 0.409358 + 0.702111i
358358 3.56613 24.8030i 0.188476 1.31088i
359359 −11.6998 6.03167i −0.617492 0.318339i 0.120947 0.992659i 0.461407π-0.461407\pi
−0.738440 + 0.674319i 0.764437π0.764437\pi
360360 3.70141 3.52929i 0.195081 0.186010i
361361 4.35708 + 1.74431i 0.229320 + 0.0918058i
362362 6.73668 19.4644i 0.354072 1.02302i
363363 9.10557 + 5.85179i 0.477918 + 0.307140i
364364 8.45451 8.13033i 0.443137 0.426145i
365365 −10.9045 + 3.20186i −0.570770 + 0.167593i
366366 −11.8068 + 16.5803i −0.617151 + 0.866668i
367367 9.17583 15.8930i 0.478974 0.829608i −0.520735 0.853718i 0.674342π-0.674342\pi
0.999709 + 0.0241105i 0.00767535π0.00767535\pi
368368 23.5570 1.64698i 1.22799 0.0858547i
369369 −1.87459 3.24689i −0.0975873 0.169026i
370370 12.7775 + 27.9788i 0.664271 + 1.45455i
371371 −10.1909 + 2.00916i −0.529088 + 0.104310i
372372 −3.42497 + 3.95262i −0.177576 + 0.204934i
373373 −0.347852 + 7.30231i −0.0180111 + 0.378099i 0.971808 + 0.235772i 0.0757617π0.0757617\pi
−0.989820 + 0.142328i 0.954541π0.954541\pi
374374 3.94845 0.761001i 0.204169 0.0393504i
375375 9.24646 + 3.70173i 0.477485 + 0.191156i
376376 4.20279 + 17.3241i 0.216742 + 0.893423i
377377 3.20944 2.06259i 0.165295 0.106229i
378378 3.17327 + 3.00003i 0.163215 + 0.154305i
379379 2.08203 4.55902i 0.106947 0.234181i −0.848591 0.529050i 0.822549π-0.822549\pi
0.955538 + 0.294868i 0.0952758π0.0952758\pi
380380 −8.52388 + 0.813932i −0.437266 + 0.0417538i
381381 −6.08812 4.78775i −0.311904 0.245284i
382382 −0.0395851 0.830994i −0.00202535 0.0425174i
383383 −7.01417 28.9128i −0.358407 1.47737i −0.810677 0.585493i 0.800901π-0.800901\pi
0.452270 0.891881i 0.350614π-0.350614\pi
384384 −1.90961 13.2817i −0.0974496 0.677777i
385385 −1.11008 + 2.45836i −0.0565747 + 0.125290i
386386 33.4583 + 21.5023i 1.70298 + 1.09444i
387387 0.798597 + 0.153917i 0.0405950 + 0.00782404i
388388 −1.16407 + 4.79835i −0.0590966 + 0.243599i
389389 24.5506 + 2.34430i 1.24477 + 0.118861i 0.696570 0.717489i 0.254709π-0.254709\pi
0.548197 + 0.836350i 0.315315π0.315315\pi
390390 −12.2696 21.2517i −0.621298 1.07612i
391391 25.5704 + 10.9983i 1.29315 + 0.556207i
392392 −9.55721 + 11.2212i −0.482712 + 0.566754i
393393 −7.84004 17.1673i −0.395478 0.865975i
394394 −22.6581 21.6044i −1.14150 1.08841i
395395 −0.384217 1.11012i −0.0193321 0.0558564i
396396 0.270212 0.139304i 0.0135787 0.00700029i
397397 11.3013 32.6530i 0.567196 1.63881i −0.187152 0.982331i 0.559926π-0.559926\pi
0.754348 0.656475i 0.227953π-0.227953\pi
398398 −2.79511 19.4404i −0.140106 0.974461i
399399 1.88701 + 12.7394i 0.0944689 + 0.637767i
400400 −3.72534 + 2.39413i −0.186267 + 0.119707i
401401 −16.4038 + 6.56708i −0.819165 + 0.327944i −0.743118 0.669160i 0.766654π-0.766654\pi
−0.0760469 + 0.997104i 0.524230π0.524230\pi
402402 −11.0136 15.4665i −0.549311 0.771399i
403403 −25.6401 36.0065i −1.27723 1.79361i
404404 2.40142 0.961385i 0.119475 0.0478307i
405405 2.04328 1.31314i 0.101532 0.0652504i
406406 2.13222 1.69153i 0.105820 0.0839493i
407407 −0.458329 3.18775i −0.0227185 0.158011i
408408 3.99721 11.5492i 0.197891 0.571770i
409409 14.4558 7.45248i 0.714793 0.368501i −0.0621547 0.998067i 0.519797π-0.519797\pi
0.776948 + 0.629565i 0.216767π0.216767\pi
410410 4.91587 + 14.2035i 0.242778 + 0.701460i
411411 6.97294 + 6.64869i 0.343950 + 0.327956i
412412 −5.98339 13.1018i −0.294780 0.645479i
413413 −9.60232 0.875692i −0.472499 0.0430900i
414414 7.85819 + 0.952307i 0.386209 + 0.0468033i
415415 10.7796 + 18.6708i 0.529149 + 0.916513i
416416 −23.8612 2.27847i −1.16989 0.111711i
417417 4.03146 16.6179i 0.197422 0.813783i
418418 3.31136 + 0.638212i 0.161964 + 0.0312160i
419419 −13.6232 8.75508i −0.665535 0.427714i 0.163778 0.986497i 0.447632π-0.447632\pi
−0.829314 + 0.558784i 0.811268π0.811268\pi
420420 −2.71581 3.77968i −0.132518 0.184429i
421421 0.118782 + 0.826150i 0.00578910 + 0.0402641i 0.992511 0.122153i 0.0389800π-0.0389800\pi
−0.986722 + 0.162417i 0.948071π0.948071\pi
422422 −5.18470 21.3716i −0.252387 1.04035i
423423 0.402832 + 8.45649i 0.0195864 + 0.411169i
424424 6.49807 + 5.11014i 0.315574 + 0.248170i
425425 −5.19619 + 0.496176i −0.252052 + 0.0240681i
426426 8.70203 19.0548i 0.421615 0.923207i
427427 −23.7094 22.4150i −1.14738 1.08474i
428428 −2.05249 + 1.31905i −0.0992108 + 0.0637589i
429429 0.605750 + 2.49694i 0.0292459 + 0.120553i
430430 −3.02687 1.21178i −0.145969 0.0584371i
431431 −16.0456 + 3.09253i −0.772889 + 0.148962i −0.560423 0.828206i 0.689362π-0.689362\pi
−0.212466 + 0.977169i 0.568149π0.568149\pi
432432 0.234292 4.91839i 0.0112724 0.236636i
433433 20.9897 24.2234i 1.00870 1.16410i 0.0222986 0.999751i 0.492902π-0.492902\pi
0.986402 0.164351i 0.0525530π-0.0525530\pi
434434 −20.7520 23.7441i −0.996126 1.13975i
435435 −0.628855 1.37700i −0.0301513 0.0660222i
436436 3.89078 + 6.73904i 0.186335 + 0.322741i
437437 16.4803 + 16.5331i 0.788361 + 0.790886i
438438 −3.86152 + 6.68835i −0.184510 + 0.319582i
439439 −17.4810 + 24.5487i −0.834324 + 1.17164i 0.148830 + 0.988863i 0.452449π0.452449\pi
−0.983154 + 0.182781i 0.941490π0.941490\pi
440440 2.05977 0.604804i 0.0981959 0.0288329i
441441 −5.46535 + 4.37379i −0.260255 + 0.208276i
442442 −49.3310 31.7031i −2.34644 1.50796i
443443 −12.4742 + 36.0418i −0.592666 + 1.71240i 0.103606 + 0.994618i 0.466962π0.466962\pi
−0.696272 + 0.717778i 0.745159π0.745159\pi
444444 5.15884 + 2.06529i 0.244828 + 0.0980142i
445445 −4.99299 + 4.76080i −0.236690 + 0.225684i
446446 30.6455 + 15.7988i 1.45111 + 0.748097i
447447 −0.668895 + 4.65227i −0.0316377 + 0.220045i
448448 8.95491 0.0381072i 0.423080 0.00180040i
449449 10.1949 22.3237i 0.481127 1.05352i −0.501025 0.865433i 0.667044π-0.667044\pi
0.982152 0.188088i 0.0602290π-0.0602290\pi
450450 −1.37806 + 0.551692i −0.0649624 + 0.0260070i
451451 −0.0748804 1.57193i −0.00352598 0.0740194i
452452 1.46948 1.40115i 0.0691187 0.0659046i
453453 −1.11189 + 0.874401i −0.0522412 + 0.0410829i
454454 14.0068 + 16.1647i 0.657371 + 0.758647i
455455 36.4555 14.7749i 1.70906 0.692657i
456456 6.71194 7.74599i 0.314315 0.362739i
457457 −10.5779 10.0860i −0.494815 0.471805i 0.401098 0.916035i 0.368629π-0.368629\pi
−0.895913 + 0.444230i 0.853477π0.853477\pi
458458 −1.45215 0.138664i −0.0678546 0.00647933i
459459 2.90203 5.02647i 0.135455 0.234616i
460460 −8.03174 2.58163i −0.374482 0.120369i
461461 −7.74020 −0.360497 −0.180249 0.983621i 0.557690π-0.557690\pi
−0.180249 + 0.983621i 0.557690π0.557690\pi
462462 0.606882 + 1.72962i 0.0282347 + 0.0804692i
463463 −7.13859 + 2.09608i −0.331759 + 0.0974131i −0.443370 0.896339i 0.646217π-0.646217\pi
0.111611 + 0.993752i 0.464399π0.464399\pi
464464 −3.01344 0.580792i −0.139895 0.0269626i
465465 −15.5896 + 8.03702i −0.722953 + 0.372708i
466466 −11.2968 + 2.17729i −0.523316 + 0.100861i
467467 −1.91720 + 1.50770i −0.0887176 + 0.0697683i −0.661533 0.749916i 0.730094π-0.730094\pi
0.572815 + 0.819685i 0.305851π0.305851\pi
468468 −4.25375 1.24901i −0.196630 0.0577357i
469469 26.9929 14.0615i 1.24641 0.649300i
470470 4.83013 33.5943i 0.222797 1.54959i
471471 −4.91936 + 0.469742i −0.226672 + 0.0216446i
472472 4.45126 + 6.25092i 0.204886 + 0.287722i
473473 0.268342 + 0.211027i 0.0123384 + 0.00970302i
474474 −0.709550 0.365798i −0.0325907 0.0168017i
475475 −4.20028 1.23331i −0.192722 0.0565883i
476476 −9.90706 5.05420i −0.454089 0.231659i
477477 2.57096 + 2.96704i 0.117716 + 0.135852i
478478 −1.08930 + 22.8673i −0.0498235 + 1.04592i
479479 −5.12407 14.8050i −0.234125 0.676459i −0.999461 0.0328286i 0.989548π-0.989548\pi
0.765336 0.643631i 0.222573π-0.222573\pi
480480 −2.24232 + 9.24297i −0.102347 + 0.421882i
481481 −27.2423 + 38.2565i −1.24214 + 1.74435i
482482 25.3785 1.15596
483483 −3.25147 + 12.2649i −0.147947 + 0.558073i
484484 −7.83925 −0.356329
485485 −9.60480 + 13.4881i −0.436132 + 0.612461i
486486 0.389128 1.60401i 0.0176512 0.0727592i
487487 −5.68985 16.4398i −0.257832 0.744956i −0.997413 0.0718885i 0.977097π-0.977097\pi
0.739581 0.673068i 0.235024π-0.235024\pi
488488 −1.23557 + 25.9377i −0.0559314 + 1.17415i
489489 5.74154 + 6.62609i 0.259641 + 0.299642i
490490 24.8325 13.0707i 1.12182 0.590475i
491491 20.1655 + 5.92112i 0.910055 + 0.267216i 0.703064 0.711127i 0.251815π-0.251815\pi
0.206991 + 0.978343i 0.433633π0.433633\pi
492492 2.41353 + 1.24426i 0.108810 + 0.0560955i
493493 −2.84349 2.23614i −0.128064 0.100711i
494494 −28.5262 40.0594i −1.28345 1.80236i
495495 1.01489 0.0969105i 0.0456160 0.00435580i
496496 −5.06033 + 35.1953i −0.227215 + 1.58032i
497497 28.3251 + 18.0336i 1.27056 + 0.808918i
498498 14.0571 + 4.12754i 0.629915 + 0.184960i
499499 9.68328 7.61501i 0.433483 0.340895i −0.377454 0.926028i 0.623200π-0.623200\pi
0.810937 + 0.585134i 0.198958π0.198958\pi
500500 −7.08320 + 1.36518i −0.316770 + 0.0610525i
501501 −11.6631 + 6.01274i −0.521068 + 0.268629i
502502 26.6252 + 5.13159i 1.18834 + 0.229034i
503503 23.4080 6.87321i 1.04371 0.306461i 0.285437 0.958397i 0.407861π-0.407861\pi
0.758274 + 0.651936i 0.226043π0.226043\pi
504504 5.47479 + 1.03104i 0.243867 + 0.0459260i
505505 8.67473 0.386020
506506 2.74862 + 1.86674i 0.122191 + 0.0829866i
507507 12.2345 21.1908i 0.543354 0.941116i
508508 5.58412 + 0.533219i 0.247755 + 0.0236578i
509509 6.92361 + 6.60165i 0.306883 + 0.292613i 0.827833 0.560975i 0.189574π-0.189574\pi
−0.520949 + 0.853588i 0.674422π0.674422\pi
510510 −15.2373 + 17.5848i −0.674718 + 0.778666i
511511 −9.76364 7.61119i −0.431918 0.336699i
512512 −0.952643 1.09941i −0.0421013 0.0485875i
513513 3.82617 3.00893i 0.168930 0.132848i
514514 28.8650 27.5227i 1.27318 1.21398i
515515 −2.29834 48.2481i −0.101277 2.12607i
516516 −0.546842 + 0.218923i −0.0240734 + 0.00963753i
517517 −1.47623 + 3.23249i −0.0649245 + 0.142165i
518518 −16.6289 + 29.0873i −0.730633 + 1.27802i
519519 −0.902488 + 6.27694i −0.0396148 + 0.275527i
520520 −27.8257 14.3451i −1.22024 0.629076i
521521 −19.8547 + 18.9314i −0.869849 + 0.829399i −0.986498 0.163774i 0.947633π-0.947633\pi
0.116649 + 0.993173i 0.462785π0.462785\pi
522522 −0.955017 0.382331i −0.0418000 0.0167342i
523523 −13.5888 + 39.2622i −0.594196 + 1.71682i 0.0980748 + 0.995179i 0.468732π0.468732\pi
−0.692271 + 0.721638i 0.743390π0.743390\pi
524524 11.4989 + 7.38991i 0.502333 + 0.322830i
525525 −0.570807 2.30995i −0.0249120 0.100814i
526526 −42.3383 + 12.4316i −1.84604 + 0.542046i
527527 −24.3118 + 34.1411i −1.05904 + 1.48721i
528528 1.03341 1.78993i 0.0449736 0.0778966i
529529 8.47991 + 21.3797i 0.368692 + 0.929552i
530530 −7.86940 13.6302i −0.341825 0.592058i
531531 1.51394 + 3.31506i 0.0656993 + 0.143861i
532532 −6.13802 7.02304i −0.266117 0.304487i
533533 −15.0287 + 17.3441i −0.650966 + 0.751254i
534534 −0.223072 + 4.68287i −0.00965329 + 0.202647i
535535 −8.03417 + 1.54846i −0.347348 + 0.0669458i
536536 −22.4876 9.00267i −0.971316 0.388856i
537537 −3.57924 14.7538i −0.154455 0.636674i
538538 21.7735 13.9930i 0.938723 0.603281i
539539 −2.88031 + 0.580601i −0.124064 + 0.0250082i
540540 −0.730765 + 1.60015i −0.0314471 + 0.0688596i
541541 31.3950 2.99786i 1.34978 0.128888i 0.605013 0.796215i 0.293168π-0.293168\pi
0.744765 + 0.667327i 0.232562π0.232562\pi
542542 −28.0342 22.0463i −1.20417 0.946972i
543543 −0.593780 12.4650i −0.0254815 0.534923i
544544 5.35832 + 22.0873i 0.229736 + 0.946985i
545545 3.71386 + 25.8304i 0.159084 + 1.10645i
546546 11.0007 24.3621i 0.470788 1.04260i
547547 −16.9316 10.8813i −0.723942 0.465250i 0.126064 0.992022i 0.459766π-0.459766\pi
−0.850006 + 0.526773i 0.823402π0.823402\pi
548548 −6.85190 1.32060i −0.292699 0.0564131i
549549 −2.90741 + 11.9845i −0.124085 + 0.511486i
550550 −0.620250 0.0592267i −0.0264475 0.00252543i
551551 −1.51687 2.62730i −0.0646210 0.111927i
552552 9.09039 4.39789i 0.386913 0.187187i
553553 0.737819 1.04551i 0.0313753 0.0444596i
554554 −8.87133 19.4255i −0.376907 0.825311i
555555 13.4871 + 12.8599i 0.572495 + 0.545873i
556556 4.05067 + 11.7036i 0.171787 + 0.496345i
557557 8.52210 4.39345i 0.361093 0.186156i −0.268127 0.963384i 0.586405π-0.586405\pi
0.629220 + 0.777227i 0.283374π0.283374\pi
558558 −3.89830 + 11.2634i −0.165028 + 0.476818i
559559 −0.708491 4.92766i −0.0299660 0.208418i
560560 −29.4253 11.6351i −1.24345 0.491672i
561561 2.04950 1.31714i 0.0865302 0.0556096i
562562 28.4018 11.3704i 1.19806 0.479631i
563563 22.0782 + 31.0044i 0.930484 + 1.30668i 0.951739 + 0.306908i 0.0992943π0.0992943\pi
−0.0212554 + 0.999774i 0.506766π0.506766\pi
564564 −3.55670 4.99469i −0.149764 0.210314i
565565 6.32141 2.53071i 0.265944 0.106468i
566566 4.87169 3.13085i 0.204772 0.131599i
567567 2.46039 + 0.972865i 0.103327 + 0.0408565i
568568 −3.80322 26.4519i −0.159579 1.10990i
569569 10.9849 31.7389i 0.460513 1.33056i −0.440882 0.897565i 0.645334π-0.645334\pi
0.901395 0.432999i 0.142545π-0.142545\pi
570570 −17.3444 + 8.94167i −0.726478 + 0.374525i
571571 12.5645 + 36.3028i 0.525808 + 1.51922i 0.825058 + 0.565049i 0.191143π0.191143\pi
−0.299249 + 0.954175i 0.596736π0.596736\pi
572572 −1.34679 1.28416i −0.0563120 0.0536934i
573573 −0.209386 0.458492i −0.00874724 0.0191538i
574574 −9.44003 + 13.3768i −0.394019 + 0.558336i
575575 −3.32151 2.75141i −0.138516 0.114742i
576576 −1.69233 2.93121i −0.0705139 0.122134i
577577 −27.3802 2.61449i −1.13985 0.108843i −0.491990 0.870601i 0.663730π-0.663730\pi
−0.647862 + 0.761758i 0.724337π0.724337\pi
578578 −6.49346 + 26.7664i −0.270092 + 1.11334i
579579 23.6610 + 4.56028i 0.983316 + 0.189519i
580580 0.922337 + 0.592750i 0.0382980 + 0.0246126i
581581 −9.66478 + 21.4035i −0.400962 + 0.887966i
582582 1.60137 + 11.1377i 0.0663787 + 0.461674i
583583 0.388511 + 1.60146i 0.0160905 + 0.0663259i
584584 0.468805 + 9.84143i 0.0193993 + 0.407241i
585585 −11.6866 9.19048i −0.483183 0.379979i
586586 22.7856 2.17576i 0.941265 0.0898799i
587587 −18.7751 + 41.1118i −0.774932 + 1.69686i −0.0594508 + 0.998231i 0.518935π0.518935\pi
−0.715481 + 0.698632i 0.753792π0.753792\pi
588588 1.61734 4.80492i 0.0666979 0.198152i
589589 −29.5701 + 19.0035i −1.21841 + 0.783027i
590590 −3.44445 14.1982i −0.141806 0.584531i
591591 −17.6092 7.04966i −0.724346 0.289984i
592592 37.0965 7.14976i 1.52466 0.293853i
593593 0.00432666 0.0908278i 0.000177675 0.00372985i −0.998777 0.0494468i 0.984254π-0.984254\pi
0.998954 + 0.0457169i 0.0145572π0.0145572\pi
594594 0.453694 0.523590i 0.0186153 0.0214832i
595595 −24.5446 28.0836i −1.00623 1.15132i
596596 −1.41411 3.09648i −0.0579244 0.126837i
597597 −5.94970 10.3052i −0.243505 0.421763i
598598 −10.2238 47.3625i −0.418082 1.93680i
599599 −6.93932 + 12.0193i −0.283533 + 0.491093i −0.972252 0.233935i 0.924840π-0.924840\pi
0.688719 + 0.725028i 0.258173π0.258173\pi
600600 −1.09845 + 1.54256i −0.0448441 + 0.0629747i
601601 −20.4507 + 6.00486i −0.834200 + 0.244943i −0.670820 0.741620i 0.734058π-0.734058\pi
−0.163380 + 0.986563i 0.552240π0.552240\pi
602602 −0.851996 3.44787i −0.0347248 0.140525i
603603 −9.67750 6.21935i −0.394098 0.253272i
604604 0.335075 0.968137i 0.0136340 0.0393929i
605605 −24.4063 9.77081i −0.992257 0.397240i
606606 4.26636 4.06797i 0.173309 0.165250i
607607 5.67239 + 2.92432i 0.230235 + 0.118695i 0.569485 0.822002i 0.307143π-0.307143\pi
−0.339249 + 0.940696i 0.610173π0.610173\pi
608608 −2.71263 + 18.8668i −0.110012 + 0.765148i
609609 0.818407 1.43156i 0.0331635 0.0580096i
610610 20.5374 44.9706i 0.831535 1.82081i
611611 48.1104 19.2605i 1.94634 0.779196i
612612 0.200018 + 4.19889i 0.00808524 + 0.169730i
613613 14.9884 14.2914i 0.605376 0.577225i −0.324139 0.946010i 0.605074π-0.605074\pi
0.929515 + 0.368784i 0.120226π0.120226\pi
614614 6.74655 5.30555i 0.272269 0.214115i
615615 5.96331 + 6.88202i 0.240464 + 0.277510i
616616 1.84427 + 1.43769i 0.0743077 + 0.0579261i
617617 −6.70943 + 7.74310i −0.270112 + 0.311725i −0.874558 0.484920i 0.838849π-0.838849\pi
0.604447 + 0.796645i 0.293394π0.293394\pi
618618 −23.7560 22.6513i −0.955608 0.911170i
619619 22.9858 + 2.19487i 0.923876 + 0.0882195i 0.546140 0.837694i 0.316097π-0.316097\pi
0.377736 + 0.925913i 0.376703π0.376703\pi
620620 6.35154 11.0012i 0.255084 0.441818i
621621 4.63440 1.23384i 0.185972 0.0495125i
622622 −43.5938 −1.74795
623623 −7.38518 1.39081i −0.295881 0.0557215i
624624 −28.9197 + 8.49158i −1.15771 + 0.339935i
625625 −28.1695 5.42922i −1.12678 0.217169i
626626 39.3274 20.2747i 1.57184 0.810340i
627627 2.00624 0.386670i 0.0801213 0.0154421i
628628 2.81336 2.21245i 0.112265 0.0882865i
629629 42.7280 + 12.5461i 1.70368 + 0.500244i
630630 −8.94714 5.69632i −0.356462 0.226947i
631631 −1.06854 + 7.43188i −0.0425381 + 0.295859i 0.957436 + 0.288646i 0.0932050π0.0932050\pi
−0.999974 + 0.00721280i 0.997704π0.997704\pi
632632 −1.01380 + 0.0968063i −0.0403269 + 0.00385075i
633633 −7.72861 10.8533i −0.307185 0.431381i
634634 11.1647 + 8.78000i 0.443406 + 0.348698i
635635 16.7207 + 8.62012i 0.663541 + 0.342079i
636636 −2.72824 0.801082i −0.108182 0.0317650i
637637 36.2422 + 22.8580i 1.43597 + 0.905665i
638638 −0.282768 0.326331i −0.0111949 0.0129196i
639639 0.603887 12.6772i 0.0238894 0.501501i
640640 10.6595 + 30.7985i 0.421352 + 1.21742i
641641 9.86705 40.6725i 0.389725 1.60647i −0.352160 0.935940i 0.614553π-0.614553\pi
0.741884 0.670528i 0.233932π-0.233932\pi
642642 −3.22518 + 4.52914i −0.127288 + 0.178751i
643643 12.0368 0.474684 0.237342 0.971426i 0.423724π-0.423724\pi
0.237342 + 0.971426i 0.423724π0.423724\pi
644644 −2.82142 8.74599i −0.111180 0.344640i
645645 −1.97538 −0.0777803
646646 −27.0483 + 37.9840i −1.06420 + 1.49446i
647647 −3.54640 + 14.6185i −0.139423 + 0.574711i 0.858644 + 0.512572i 0.171307π0.171307\pi
−0.998068 + 0.0621386i 0.980208π0.980208\pi
648648 −0.688691 1.98984i −0.0270544 0.0781684i
649649 −0.0727875 + 1.52800i −0.00285716 + 0.0599792i
650650 5.95022 + 6.86692i 0.233387 + 0.269343i
651651 −17.0189 8.68238i −0.667023 0.340289i
652652 −6.09278 1.78900i −0.238612 0.0700627i
653653 16.0481 + 8.27334i 0.628009 + 0.323761i 0.742684 0.669642i 0.233552π-0.233552\pi
−0.114675 + 0.993403i 0.536583π0.536583\pi
654654 13.9396 + 10.9622i 0.545080 + 0.428656i
655655 26.5894 + 37.3396i 1.03893 + 1.45898i
656656 18.3773 1.75482i 0.717511 0.0685140i
657657 −0.665908 + 4.63149i −0.0259795 + 0.180692i
658658 32.7883 17.0806i 1.27822 0.665870i
659659 −31.5862 9.27455i −1.23042 0.361285i −0.399014 0.916945i 0.630648π-0.630648\pi
−0.831410 + 0.555659i 0.812466π0.812466\pi
660660 −0.580413 + 0.456442i −0.0225925 + 0.0177670i
661661 −44.6021 + 8.59636i −1.73482 + 0.334359i −0.956107 0.293019i 0.905340π-0.905340\pi
−0.778715 + 0.627378i 0.784128π0.784128\pi
662662 24.0303 12.3885i 0.933965 0.481493i
663663 −34.8858 6.72369i −1.35485 0.261126i
664664 17.9332 5.26567i 0.695945 0.204348i
665665 −10.3563 29.5156i −0.401600 1.14457i
666666 12.6637 0.490710
667667 −0.350110 2.96846i −0.0135563 0.114939i
668668 4.75178 8.23032i 0.183852 0.318441i
669669 20.7946 + 1.98564i 0.803964 + 0.0767693i
670670 33.3765 + 31.8245i 1.28945 + 1.22949i
671671 −3.38981 + 3.91205i −0.130862 + 0.151023i
672672 −9.60180 + 3.89147i −0.370397 + 0.150117i
673673 29.3431 + 33.8637i 1.13109 + 1.30535i 0.946562 + 0.322523i 0.104531π0.104531\pi
0.184530 + 0.982827i 0.440924π0.440924\pi
674674 −26.3339 + 20.7092i −1.01435 + 0.797690i
675675 −0.650883 + 0.620615i −0.0250525 + 0.0238875i
676676 0.843243 + 17.7018i 0.0324324 + 0.680840i
677677 −4.90202 + 1.96247i −0.188400 + 0.0754240i −0.463944 0.885864i 0.653566π-0.653566\pi
0.275544 + 0.961288i 0.411142π0.411142\pi
678678 1.92220 4.20903i 0.0738216 0.161647i
679679 −18.0369 + 0.0767551i −0.692191 + 0.00294559i
680680 −4.22446 + 29.3818i −0.162001 + 1.12674i
681681 11.5183 + 5.93807i 0.441381 + 0.227548i
682682 −3.62081 + 3.45244i −0.138648 + 0.132201i
683683 14.7102 + 5.88909i 0.562871 + 0.225340i 0.635609 0.772012i 0.280749π-0.280749\pi
−0.0727374 + 0.997351i 0.523174π0.523174\pi
684684 −1.15304 + 3.33149i −0.0440876 + 0.127383i
685685 −19.6864 12.6517i −0.752178 0.483395i
686686 27.3468 + 13.6592i 1.04411 + 0.521511i
687687 −0.848009 + 0.248998i −0.0323536 + 0.00949987i
688688 −2.32292 + 3.26208i −0.0885604 + 0.124366i
689689 12.0158 20.8119i 0.457765 0.792872i
690690 −19.1792 + 1.34091i −0.730141 + 0.0510475i
691691 1.30635 + 2.26266i 0.0496957 + 0.0860755i 0.889803 0.456344i 0.150842π-0.150842\pi
−0.840107 + 0.542420i 0.817508π0.817508\pi
692692 −1.90795 4.17783i −0.0725294 0.158817i
693693 0.730821 + 0.836196i 0.0277616 + 0.0317645i
694694 −20.4984 + 23.6564i −0.778110 + 0.897986i
695695 −1.97623 + 41.4862i −0.0749628 + 1.57366i
696696 −1.28865 + 0.248366i −0.0488460 + 0.00941429i
697697 20.2018 + 8.08757i 0.765196 + 0.306338i
698698 0.777639 + 3.20547i 0.0294341 + 0.121329i
699699 −5.86381 + 3.76844i −0.221790 + 0.142536i
700700 1.25228 + 1.18391i 0.0473316 + 0.0447476i
701701 −10.2584 + 22.4628i −0.387455 + 0.848408i 0.610935 + 0.791681i 0.290794π0.290794\pi
−0.998390 + 0.0567272i 0.981933π0.981933\pi
702702 −10.0575 + 0.960373i −0.379595 + 0.0362470i
703703 29.3564 + 23.0861i 1.10720 + 0.870708i
704704 −0.0676001 1.41910i −0.00254777 0.0534844i
705705 −4.84788 19.9833i −0.182582 0.752613i
706706 −7.27694 50.6122i −0.273871 1.90482i
707707 5.51388 + 7.67384i 0.207371 + 0.288605i
708708 −2.22048 1.42702i −0.0834507 0.0536305i
709709 35.8104 + 6.90189i 1.34489 + 0.259206i 0.810354 0.585941i 0.199275π-0.199275\pi
0.534534 + 0.845147i 0.320487π0.320487\pi
710710 −11.9952 + 49.4450i −0.450173 + 1.85564i
711711 −0.481467 0.0459745i −0.0180564 0.00172418i
712712 2.99045 + 5.17961i 0.112072 + 0.194114i
713713 −34.1616 + 5.68841i −1.27936 + 0.213033i
714714 −25.2410 2.30188i −0.944622 0.0861457i
715715 −2.59244 5.67666i −0.0969519 0.212295i
716716 7.95784 + 7.58779i 0.297399 + 0.283569i
717717 4.53649 + 13.1073i 0.169418 + 0.489502i
718718 19.3109 9.95547i 0.720677 0.371535i
719719 2.18837 6.32287i 0.0816123 0.235803i −0.896811 0.442414i 0.854122π-0.854122\pi
0.978423 + 0.206611i 0.0662434π0.0662434\pi
720720 1.70203 + 11.8379i 0.0634309 + 0.441172i
721721 41.2204 32.7009i 1.53513 1.21785i
722722 −6.51668 + 4.18801i −0.242526 + 0.155862i
723723 14.2745 5.71465i 0.530875 0.212530i
724724 5.24262 + 7.36223i 0.194840 + 0.273615i
725725 0.325133 + 0.456586i 0.0120751 + 0.0169572i
726726 −16.5853 + 6.63977i −0.615540 + 0.246425i
727727 16.0819 10.3352i 0.596443 0.383311i −0.207309 0.978276i 0.566470π-0.566470\pi
0.803752 + 0.594965i 0.202834π0.202834\pi
728728 −4.99673 33.7333i −0.185191 1.25024i
729729 −0.142315 0.989821i −0.00527092 0.0366601i
730730 6.13519 17.7265i 0.227073 0.656086i
731731 −4.19568 + 2.16302i −0.155183 + 0.0800022i
732732 −2.92126 8.44041i −0.107973 0.311967i
733733 −17.3366 16.5304i −0.640343 0.610566i 0.298707 0.954345i 0.403445π-0.403445\pi
−0.939051 + 0.343779i 0.888293π0.888293\pi
734734 12.5829 + 27.5528i 0.464444 + 1.01699i
735735 11.0242 12.9435i 0.406633 0.477430i
736736 −9.79993 + 16.0201i −0.361230 + 0.590509i
737737 −2.41432 4.18173i −0.0889328 0.154036i
738738 6.16013 + 0.588221i 0.226757 + 0.0216527i
739739 −1.75981 + 7.25403i −0.0647356 + 0.266844i −0.994977 0.100104i 0.968082π-0.968082\pi
0.930241 + 0.366948i 0.119597π0.119597\pi
740740 −13.2530 2.55430i −0.487189 0.0938980i
741741 −25.0654 16.1086i −0.920802 0.591764i
742742 7.05556 15.6251i 0.259018 0.573617i
743743 −0.222916 1.55042i −0.00817801 0.0568793i 0.985324 0.170696i 0.0546015π-0.0546015\pi
−0.993502 + 0.113816i 0.963692π0.963692\pi
744744 3.58483 + 14.7769i 0.131426 + 0.541746i
745745 −0.543190 11.4030i −0.0199009 0.417772i
746746 −9.48481 7.45894i −0.347264 0.273091i
747747 8.83607 0.843743i 0.323295 0.0308709i
748748 −0.732991 + 1.60503i −0.0268008 + 0.0586855i
749749 −6.47653 6.12295i −0.236647 0.223728i
750750 −13.8295 + 8.88768i −0.504982 + 0.324532i
751751 −4.98511 20.5489i −0.181909 0.749840i −0.987533 0.157413i 0.949685π-0.949685\pi
0.805624 0.592428i 0.201830π-0.201830\pi
752752 −38.7006 15.4934i −1.41127 0.564986i
753753 16.1313 3.10905i 0.587856 0.113300i
754754 −0.299619 + 6.28977i −0.0109115 + 0.229060i
755755 2.24989 2.59651i 0.0818819 0.0944967i
756756 −1.88002 + 0.370649i −0.0683757 + 0.0134804i
757757 5.80833 + 12.7185i 0.211107 + 0.462260i 0.985332 0.170651i 0.0545870π-0.0545870\pi
−0.774224 + 0.632911i 0.781860π0.781860\pi
758758 4.13618 + 7.16408i 0.150233 + 0.260211i
759759 1.96635 + 0.431048i 0.0713741 + 0.0156460i
760760 −12.4472 + 21.5591i −0.451506 + 0.782032i
761761 1.04304 1.46475i 0.0378103 0.0530971i −0.795238 0.606297i 0.792654π-0.792654\pi
0.833048 + 0.553200i 0.186594π0.186594\pi
762762 12.2658 3.60158i 0.444345 0.130471i
763763 −20.4895 + 19.7038i −0.741770 + 0.713327i
764764 0.307105 + 0.197364i 0.0111107 + 0.00714039i
765765 −4.61076 + 13.3219i −0.166702 + 0.481655i
766766 45.5882 + 18.2508i 1.64717 + 0.659426i
767767 16.1451 15.3943i 0.582966 0.555857i
768768 13.6684 + 7.04657i 0.493217 + 0.254271i
769769 4.97179 34.5796i 0.179287 1.24697i −0.679129 0.734019i 0.737642π-0.737642\pi
0.858417 0.512953i 0.171448π-0.171448\pi
770770 −2.24243 3.84612i −0.0808117 0.138605i
771771 10.0381 21.9803i 0.361513 0.791602i
772772 −16.2019 + 6.48627i −0.583120 + 0.233446i
773773 1.27081 + 26.6776i 0.0457079 + 0.959527i 0.898961 + 0.438030i 0.144323π0.144323\pi
−0.853253 + 0.521498i 0.825373π0.825373\pi
774774 −0.971519 + 0.926341i −0.0349205 + 0.0332966i
775775 5.10492 4.01455i 0.183374 0.144207i
776776 9.40051 + 10.8488i 0.337459 + 0.389448i
777777 −2.80340 + 20.1051i −0.100571 + 0.721265i
778778 −26.6567 + 30.7635i −0.955690 + 1.10293i
779779 13.2077 + 12.5935i 0.473216 + 0.451210i
780780 10.7192 + 1.02356i 0.383808 + 0.0366492i
781781 2.66363 4.61354i 0.0953121 0.165085i
782782 −39.2682 + 23.8492i −1.40423 + 0.852845i
783783 −0.623257 −0.0222734
784784 −8.41087 33.4258i −0.300388 1.19378i
785785 11.5166 3.38157i 0.411044 0.120693i
786786 30.5872 + 5.89521i 1.09101 + 0.210275i
787787 11.8479 6.10800i 0.422331 0.217727i −0.233942 0.972251i 0.575162π-0.575162\pi
0.656273 + 0.754524i 0.272132π0.272132\pi
788788 13.4894 2.59987i 0.480541 0.0926167i
789789 −21.0145 + 16.5260i −0.748137 + 0.588341i
790790 1.86039 + 0.546261i 0.0661899 + 0.0194351i
791791 6.25677 + 3.98346i 0.222465 + 0.141636i
792792 0.125784 0.874849i 0.00446955 0.0310864i
793793 75.1454 7.17552i 2.66849 0.254810i
794794 33.0815 + 46.4565i 1.17402 + 1.64868i
795795 −7.49548 5.89451i −0.265837 0.209057i
796796 7.66021 + 3.94911i 0.271509 + 0.139973i
797797 −3.67526 1.07915i −0.130184 0.0382256i 0.215991 0.976395i 0.430702π-0.430702\pi
−0.346176 + 0.938170i 0.612520π0.612520\pi
798798 −18.9345 9.65967i −0.670276 0.341949i
799799 −32.1784 37.1358i −1.13839 1.31377i
800800 0.167569 3.51771i 0.00592446 0.124370i
801801 0.929004 + 2.68418i 0.0328248 + 0.0948409i
802802 6.87569 28.3420i 0.242789 1.00079i
803803 −1.13926 + 1.59987i −0.0402037 + 0.0564582i
804804 8.33164 0.293834
805805 2.11691 30.7459i 0.0746113 1.08365i
806806 72.9581 2.56984
807807 9.09595 12.7735i 0.320193 0.449648i
808808 1.77300 7.30841i 0.0623740 0.257109i
809809 −10.0343 28.9923i −0.352789 1.01932i −0.972180 0.234234i 0.924742π-0.924742\pi
0.619392 0.785082i 0.287379π-0.287379\pi
810810 −0.190751 + 4.00437i −0.00670232 + 0.140699i
811811 −0.412673 0.476250i −0.0144909 0.0167234i 0.748458 0.663182i 0.230795π-0.230795\pi
−0.762949 + 0.646459i 0.776249π0.776249\pi
812812 0.0619026 + 1.19269i 0.00217235 + 0.0418550i
813813 −20.7326 6.08764i −0.727124 0.213503i
814814 4.72468 + 2.43574i 0.165600 + 0.0853728i
815815 −16.7391 13.1638i −0.586346 0.461108i
816816 16.5775 + 23.2798i 0.580328 + 0.814956i
817817 −3.94085 + 0.376305i −0.137873 + 0.0131652i
818818 −3.82028 + 26.5706i −0.133573 + 0.929020i
819819 0.701750 16.1799i 0.0245211 0.565373i
820820 −6.32811 1.85810i −0.220987 0.0648877i
821821 16.5765 13.0359i 0.578524 0.454956i −0.285520 0.958373i 0.592166π-0.592166\pi
0.864044 + 0.503417i 0.167924π0.167924\pi
822822 −15.6150 + 3.00954i −0.544635 + 0.104970i
823823 −30.6644 + 15.8086i −1.06889 + 0.551053i −0.900584 0.434681i 0.856861π-0.856861\pi
−0.168310 + 0.985734i 0.553831π0.553831\pi
824824 −41.1185 7.92494i −1.43243 0.276078i
825825 −0.362206 + 0.106353i −0.0126104 + 0.00370274i
826826 10.3706 12.0718i 0.360841 0.420031i
827827 −20.0136 −0.695939 −0.347970 0.937506i 0.613129π-0.613129\pi
−0.347970 + 0.937506i 0.613129π0.613129\pi
828828 −2.34054 + 2.56643i −0.0813395 + 0.0891895i
829829 3.62610 6.28059i 0.125940 0.218134i −0.796160 0.605086i 0.793139π-0.793139\pi
0.922100 + 0.386952i 0.126472π0.126472\pi
830830 −35.4230 3.38249i −1.22955 0.117408i
831831 −9.36400 8.92856i −0.324834 0.309728i
832832 −13.5675 + 15.6578i −0.470370 + 0.542836i
833833 9.24215 39.5633i 0.320221 1.37079i
834834 18.4828 + 21.3303i 0.640007 + 0.738607i
835835 25.0522 19.7013i 0.866966 0.681790i
836836 −1.07096 + 1.02116i −0.0370401 + 0.0353176i
837837 0.343602 + 7.21308i 0.0118766 + 0.249321i
838838 24.8139 9.93400i 0.857183 0.343164i
839839 3.06372 6.70860i 0.105771 0.231607i −0.849345 0.527838i 0.823003π-0.823003\pi
0.955116 + 0.296232i 0.0957300π0.0957300\pi
840840 −13.5311 + 0.0575811i −0.466868 + 0.00198674i
841841 4.07185 28.3203i 0.140409 0.976563i
842842 −1.22447 0.631257i −0.0421980 0.0217546i
843843 13.4147 12.7909i 0.462027 0.440542i
844844 8.95871 + 3.58652i 0.308371 + 0.123453i
845845 −19.4382 + 56.1630i −0.668695 + 1.93207i
846846 −11.7553 7.55467i −0.404155 0.259735i
847847 −6.86982 27.8009i −0.236050 0.955250i
848848 −18.5482 + 5.44626i −0.636949 + 0.187025i
849849 2.03516 2.85799i 0.0698466 0.0980858i
850850 4.30775 7.46124i 0.147755 0.255919i
851851 17.5828 + 32.3233i 0.602732 + 1.10803i
852852 4.59598 + 7.96047i 0.157456 + 0.272721i
853853 7.22512 + 15.8208i 0.247384 + 0.541694i 0.992065 0.125726i 0.0401259π-0.0401259\pi
−0.744682 + 0.667420i 0.767399π0.767399\pi
854854 52.8361 10.4167i 1.80801 0.356452i
855855 −7.74218 + 8.93495i −0.264777 + 0.305569i
856856 −0.337511 + 7.08523i −0.0115359 + 0.242168i
857857 24.2702 4.67770i 0.829055 0.159787i 0.242967 0.970035i 0.421879π-0.421879\pi
0.586088 + 0.810247i 0.300667π0.300667\pi
858858 −3.93704 1.57615i −0.134408 0.0538090i
859859 −3.26353 13.4525i −0.111350 0.458992i −1.00000 0.000405202i 0.999871π-0.999871\pi
0.888650 0.458587i 0.151644π-0.151644\pi
860860 1.20357 0.773486i 0.0410413 0.0263757i
861861 −2.29755 + 9.64966i −0.0783001 + 0.328859i
862862 11.2042 24.5339i 0.381618 0.835626i
863863 −12.9177 + 1.23349i −0.439722 + 0.0419884i −0.312570 0.949895i 0.601190π-0.601190\pi
−0.127152 + 0.991883i 0.540584π0.540584\pi
864864 3.07808 + 2.42063i 0.104718 + 0.0823514i
865865 −0.732883 15.3851i −0.0249188 0.523109i
866866 12.4724 + 51.4119i 0.423829 + 1.74705i
867867 2.37484 + 16.5174i 0.0806538 + 0.560959i
868868 13.7691 1.37394i 0.467353 0.0466346i
869869 −0.170787 0.109758i −0.00579354 0.00372328i
870870 2.45342 + 0.472859i 0.0831789 + 0.0160314i
871871 −16.6012 + 68.4312i −0.562512 + 2.31870i
872872 22.5211 + 2.15050i 0.762659 + 0.0728251i
873873 3.40868 + 5.90400i 0.115366 + 0.199820i
874874 −38.0068 + 6.32869i −1.28560 + 0.214071i
875875 −11.0487 23.9233i −0.373514 0.808756i
876876 −1.40780 3.08265i −0.0475651 0.104153i
877877 0.562643 + 0.536479i 0.0189991 + 0.0181156i 0.699519 0.714614i 0.253398π-0.253398\pi
−0.680520 + 0.732729i 0.738246π0.738246\pi
878878 −16.2689 47.0060i −0.549049 1.58637i
879879 12.3262 6.35459i 0.415752 0.214335i
880880 −1.64189 + 4.74393i −0.0553481 + 0.159918i
881881 1.63620 + 11.3800i 0.0551249 + 0.383402i 0.998643 + 0.0520807i 0.0165853π0.0165853\pi
−0.943518 + 0.331321i 0.892506π0.892506\pi
882882 −0.647948 11.5355i −0.0218176 0.388422i
883883 −40.5463 + 26.0575i −1.36449 + 0.876906i −0.998555 0.0537334i 0.982888π-0.982888\pi
−0.365937 + 0.930640i 0.619252π0.619252\pi
884884 23.8882 9.56338i 0.803446 0.321651i
885885 −5.13450 7.21039i −0.172594 0.242375i
886886 −36.5148 51.2779i −1.22674 1.72271i
887887 30.3482 12.1496i 1.01899 0.407943i 0.198806 0.980039i 0.436294π-0.436294\pi
0.820187 + 0.572096i 0.193869π0.193869\pi
888888 13.5910 8.73440i 0.456084 0.293107i
889889 3.00258 + 20.2706i 0.100703 + 0.679856i
890890 −1.62053 11.2710i −0.0543201 0.377805i
891891 0.137286 0.396663i 0.00459927 0.0132887i
892892 −13.4473 + 6.93258i −0.450250 + 0.232120i
893893 −13.4782 38.9428i −0.451032 1.30317i
894894 −5.61450 5.35342i −0.187777 0.179045i
895895 15.3181 + 33.5421i 0.512029 + 1.12119i
896896 −20.4695 + 29.0059i −0.683839 + 0.969019i
897897 −16.4155 24.3376i −0.548097 0.812609i
898898 20.2532 + 35.0797i 0.675860 + 1.17062i
899899 4.48032 + 0.427819i 0.149427 + 0.0142686i
900900 0.153563 0.632995i 0.00511876 0.0210998i
901901 −22.3748 4.31238i −0.745411 0.143666i
902902 2.18513 + 1.40430i 0.0727569 + 0.0467580i
903903 −1.25560 1.74746i −0.0417837 0.0581517i
904904 −0.840095 5.84299i −0.0279412 0.194335i
905905 7.14584 + 29.4556i 0.237536 + 0.979136i
906906 −0.111090 2.33208i −0.00369073 0.0774780i
907907 −24.7398 19.4556i −0.821472 0.646013i 0.116320 0.993212i 0.462890π-0.462890\pi
−0.937791 + 0.347199i 0.887133π0.887133\pi
908908 −9.34305 + 0.892153i −0.310060 + 0.0296071i
909909 1.48367 3.24878i 0.0492101 0.107755i
910910 −15.0380 + 63.1593i −0.498504 + 2.09371i
911911 12.6120 8.10523i 0.417854 0.268538i −0.314776 0.949166i 0.601929π-0.601929\pi
0.732629 + 0.680628i 0.238293π0.238293\pi
912912 5.65062 + 23.2922i 0.187111 + 0.771280i
913913 3.45891 + 1.38474i 0.114473 + 0.0458282i
914914 23.6879 4.56546i 0.783525 0.151012i
915915 1.42522 29.9190i 0.0471162 0.989091i
916916 0.419181 0.483761i 0.0138501 0.0159839i
917917 −16.1304 + 47.2555i −0.532674 + 1.56051i
918918 3.97960 + 8.71410i 0.131346 + 0.287608i
919919 10.1177 + 17.5244i 0.333753 + 0.578077i 0.983244 0.182292i 0.0583516π-0.0583516\pi
−0.649492 + 0.760369i 0.725018π0.725018\pi
920920 −19.6587 + 14.6673i −0.648128 + 0.483568i
921921 2.60002 4.50336i 0.0856734 0.148391i
922922 7.41050 10.4066i 0.244052 0.342723i
923923 −74.5405 + 21.8871i −2.45353 + 0.720421i
924924 −0.772703 0.223319i −0.0254201 0.00734665i
925925 −5.80482 3.73053i −0.190861 0.122659i
926926 4.01636 11.6045i 0.131986 0.381348i
927927 −18.4625 7.39128i −0.606389 0.242761i
928928 1.76634 1.68420i 0.0579829 0.0552866i
929929 −21.9701 11.3264i −0.720817 0.371607i 0.0584574 0.998290i 0.481382π-0.481382\pi
−0.779274 + 0.626683i 0.784412π0.784412\pi
930930 4.11993 28.6547i 0.135098 0.939625i
931931 19.5274 27.9223i 0.639983 0.915115i
932932 2.09715 4.59211i 0.0686944 0.150420i
933933 −24.5200 + 9.81634i −0.802750 + 0.321373i
934934 −0.191550 4.02113i −0.00626771 0.131575i
935935 −4.28255 + 4.08341i −0.140054 + 0.133542i
936936 −10.1315 + 7.96752i −0.331159 + 0.260426i
937937 13.8663 + 16.0026i 0.452992 + 0.522781i 0.935603 0.353054i 0.114857π-0.114857\pi
−0.482611 + 0.875835i 0.660311π0.660311\pi
938938 −6.93758 + 49.7540i −0.226520 + 1.62453i
939939 17.5549 20.2595i 0.572883 0.661142i
940940 10.7785 + 10.2773i 0.351555 + 0.335207i
941941 2.31598 + 0.221149i 0.0754988 + 0.00720926i 0.132737 0.991151i 0.457623π-0.457623\pi
−0.0572383 + 0.998361i 0.518229π0.518229\pi
942942 4.07825 7.06374i 0.132877 0.230149i
943943 7.05157 + 16.5400i 0.229631 + 0.538617i
944944 −17.9449 −0.584056
945945 −6.31514 1.18929i −0.205431 0.0386877i
946946 −0.540634 + 0.158744i −0.0175775 + 0.00516123i
947947 −21.0707 4.06105i −0.684706 0.131966i −0.164977 0.986297i 0.552755π-0.552755\pi
−0.519729 + 0.854331i 0.673967π0.673967\pi
948948 0.311353 0.160514i 0.0101123 0.00521324i
949949 28.1242 5.42049i 0.912950 0.175957i
950950 5.67953 4.46643i 0.184268 0.144910i
951951 8.25680 + 2.42442i 0.267745 + 0.0786171i
952952 −28.6769 + 14.9388i −0.929423 + 0.484168i
953953 −1.78221 + 12.3956i −0.0577315 + 0.401531i 0.940381 + 0.340122i 0.110468π0.110468\pi
−0.998113 + 0.0614090i 0.980441π0.980441\pi
954954 −6.45058 + 0.615956i −0.208845 + 0.0199423i
955955 0.710131 + 0.997239i 0.0229793 + 0.0322699i
956956 −7.89638 6.20978i −0.255387 0.200839i
957957 −0.232529 0.119877i −0.00751661 0.00387508i
958958 24.8109 + 7.28515i 0.801605 + 0.235373i
959959 −1.32125 25.4567i −0.0426654 0.822040i
960960 5.38352 + 6.21292i 0.173752 + 0.200521i
961961 1.00620 21.1227i 0.0324580 0.681377i
962962 −25.3534 73.2538i −0.817426 2.36180i
963963 −0.794196 + 3.27372i −0.0255926 + 0.105494i
964964 −6.45961 + 9.07125i −0.208050 + 0.292165i
965965 −58.5267 −1.88404
966966 −13.3770 16.1140i −0.430398 0.518460i
967967 23.0935 0.742638 0.371319 0.928505i 0.378906π-0.378906\pi
0.371319 + 0.928505i 0.378906π0.378906\pi
968968 −13.2202 + 18.5651i −0.424913 + 0.596706i
969969 −6.66060 + 27.4554i −0.213969 + 0.881993i
970970 −8.93882 25.8270i −0.287008 0.829255i
971971 1.75839 36.9132i 0.0564295 1.18460i −0.776096 0.630614i 0.782803π-0.782803\pi
0.832526 0.553986i 0.186894π-0.186894\pi
972972 0.474289 + 0.547359i 0.0152128 + 0.0175565i
973973 −37.9557 + 24.6215i −1.21680 + 0.789329i
974974 27.5505 + 8.08955i 0.882774 + 0.259206i
975975 4.89307 + 2.52255i 0.156704 + 0.0807863i
976976 −47.7314 37.5364i −1.52785 1.20151i
977977 −22.1259 31.0714i −0.707869 0.994063i −0.999298 0.0374707i 0.988070π-0.988070\pi
0.291428 0.956593i 0.405869π-0.405869\pi
978978 −14.4056 + 1.37557i −0.460642 + 0.0439860i
979979 −0.169676 + 1.18012i −0.00542286 + 0.0377168i
980980 −1.64865 + 12.2030i −0.0526641 + 0.389810i
981981 10.3090 + 3.02698i 0.329140 + 0.0966442i
982982 −27.2673 + 21.4433i −0.870136 + 0.684282i
983983 0.101990 0.0196570i 0.00325299 0.000626962i −0.187624 0.982241i 0.560079π-0.560079\pi
0.190877 + 0.981614i 0.438867π0.438867\pi
984984 7.01689 3.61746i 0.223690 0.115320i
985985 45.2378 + 8.71886i 1.44139 + 0.277806i
986986 5.72882 1.68213i 0.182443 0.0535701i
987987 14.5962 16.9904i 0.464601 0.540811i
988988 21.5796 0.686537
989989 −3.71332 1.19356i −0.118077 0.0379532i
990990 −0.841367 + 1.45729i −0.0267404 + 0.0463157i
991991 19.3310 + 1.84588i 0.614069 + 0.0586365i 0.397456 0.917621i 0.369893π-0.369893\pi
0.216613 + 0.976258i 0.430499π0.430499\pi
992992 −20.4654 19.5137i −0.649777 0.619561i
993993 10.7266 12.3792i 0.340399 0.392842i
994994 −51.3645 + 20.8173i −1.62918 + 0.660284i
995995 18.9267 + 21.8426i 0.600018 + 0.692457i
996996 −5.05331 + 3.97397i −0.160120 + 0.125920i
997997 −19.8777 + 18.9533i −0.629533 + 0.600258i −0.936161 0.351571i 0.885648π-0.885648\pi
0.306628 + 0.951829i 0.400799π0.400799\pi
998998 0.967468 + 20.3097i 0.0306247 + 0.642891i
999999 7.12292 2.85159i 0.225359 0.0902202i
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 483.2.y.a.4.5 320
7.2 even 3 inner 483.2.y.a.142.12 yes 320
23.6 even 11 inner 483.2.y.a.466.12 yes 320
161.121 even 33 inner 483.2.y.a.121.5 yes 320
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.y.a.4.5 320 1.1 even 1 trivial
483.2.y.a.121.5 yes 320 161.121 even 33 inner
483.2.y.a.142.12 yes 320 7.2 even 3 inner
483.2.y.a.466.12 yes 320 23.6 even 11 inner