LMFDB - Embedded newform 512.2.o.a.117.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			117.11
Character	$\chi$	$=$	512.117
Dual form			512.2.o.a.477.11

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25412 - 0.653597i) q^{2} +(0.0781181 + 3.18218i) q^{3} +(1.14562 + 1.63937i) q^{4} +(-0.0822049 - 0.297050i) q^{5} +(1.98189 - 4.04188i) q^{6} +(0.751910 - 1.58978i) q^{7} +(-0.365254 - 2.80474i) q^{8} +(-7.12377 + 0.349968i) q^{9} +O(q^{10})$	\(q+(-1.25412 - 0.653597i) q^{2} +(0.0781181 + 3.18218i) q^{3} +(1.14562 + 1.63937i) q^{4} +(-0.0822049 - 0.297050i) q^{5} +(1.98189 - 4.04188i) q^{6} +(0.751910 - 1.58978i) q^{7} +(-0.365254 - 2.80474i) q^{8} +(-7.12377 + 0.349968i) q^{9} +(-0.0910565 + 0.426265i) q^{10} +(-3.37483 - 2.37683i) q^{11} +(-5.12729 + 3.77364i) q^{12} +(-4.35772 + 0.537473i) q^{13} +(-1.98206 + 1.50233i) q^{14} +(0.938845 - 0.284795i) q^{15} +(-1.37510 + 3.75621i) q^{16} +(-0.773749 + 2.55071i) q^{17} +(9.16278 + 4.21717i) q^{18} +(0.456645 - 6.19058i) q^{19} +(0.392801 - 0.475072i) q^{20} +(5.11770 + 2.26852i) q^{21} +(2.67895 + 5.18660i) q^{22} +(-6.74306 + 5.00099i) q^{23} +(8.89666 - 1.38141i) q^{24} +(4.20716 - 2.52168i) q^{25} +(5.81638 + 2.17414i) q^{26} +(-0.967658 - 13.1182i) q^{27} +(3.46765 - 0.588625i) q^{28} +(-10.3606 + 2.32656i) q^{29} +(-1.36356 - 0.256459i) q^{30} +(1.03298 + 1.54596i) q^{31} +(4.17958 - 3.81197i) q^{32} +(7.29985 - 10.9250i) q^{33} +(2.63751 - 2.69317i) q^{34} +(-0.534055 - 0.0926673i) q^{35} +(-8.73487 - 11.2776i) q^{36} +(2.04886 + 4.07038i) q^{37} +(-4.61883 + 7.46526i) q^{38} +(-2.05075 - 13.8250i) q^{39} +(-0.803124 + 0.339062i) q^{40} +(2.56194 + 1.53557i) q^{41} +(-4.93550 - 6.18991i) q^{42} +(-8.30756 - 8.72570i) q^{43} +(0.0302252 - 8.25556i) q^{44} +(0.689566 + 2.08735i) q^{45} +(11.7252 - 1.86459i) q^{46} +(3.25239 + 2.66917i) q^{47} +(-12.0603 - 4.08239i) q^{48} +(2.47872 + 3.02033i) q^{49} +(-6.92444 + 0.412690i) q^{50} +(-8.17726 - 2.26295i) q^{51} +(-5.87341 - 6.52819i) q^{52} +(1.89510 + 0.425560i) q^{53} +(-7.36047 + 17.0843i) q^{54} +(-0.428609 + 1.19788i) q^{55} +(-4.73356 - 1.52824i) q^{56} +(19.7352 + 0.969529i) q^{57} +(14.5141 + 3.85390i) q^{58} +(0.455138 - 3.69016i) q^{59} +(1.54245 + 1.21285i) q^{60} +(1.47715 + 3.33240i) q^{61} +(-0.285041 - 2.61397i) q^{62} +(-4.80006 + 11.5884i) q^{63} +(-7.73318 + 2.04889i) q^{64} +(0.517882 + 1.25028i) q^{65} +(-16.2954 + 8.93007i) q^{66} +(-2.88825 + 7.48751i) q^{67} +(-5.06799 + 1.65368i) q^{68} +(-16.4408 - 21.0669i) q^{69} +(0.609201 + 0.465273i) q^{70} +(-0.990371 - 1.09271i) q^{71} +(3.58356 + 19.8525i) q^{72} +(5.22880 + 11.0554i) q^{73} +(0.0908802 - 6.44387i) q^{74} +(8.35308 + 13.1909i) q^{75} +(10.6718 - 6.34346i) q^{76} +(-6.31620 + 3.57808i) q^{77} +(-6.46412 + 18.6786i) q^{78} +(-0.267875 + 2.71978i) q^{79} +(1.22882 + 0.0996952i) q^{80} +(20.3749 - 2.00675i) q^{81} +(-2.20933 - 3.60025i) q^{82} +(3.29826 - 6.55251i) q^{83} +(2.14399 + 10.9887i) q^{84} +(0.821295 + 0.0201617i) q^{85} +(4.71556 + 16.3728i) q^{86} +(-8.21288 - 32.7877i) q^{87} +(-5.43371 + 10.3337i) q^{88} +(-13.8242 - 10.2527i) q^{89} +(0.499486 - 3.06848i) q^{90} +(-2.42215 + 7.33194i) q^{91} +(-15.9235 - 5.32515i) q^{92} +(-4.83884 + 3.40789i) q^{93} +(-2.33432 - 5.47321i) q^{94} +(-1.87645 + 0.373250i) q^{95} +(12.4569 + 13.0024i) q^{96} +(-0.974057 - 0.193752i) q^{97} +(-1.13453 - 5.40793i) q^{98} +(24.8733 + 15.7509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{53}{128}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.25412	−	0.653597i	−0.886795	−	0.462163i
$2$	−1.25412	−	0.653597i	−0.886795	−	0.462163i
$3$	0.0781181	+	3.18218i	0.0451015	+	1.83723i	0.416940	+	0.908934i	$0.363102\pi$
$3$	0.0781181	+	3.18218i	0.0451015	+	1.83723i	−0.371839	+	0.928297i	$0.621273\pi$
$4$	1.14562	+	1.63937i	0.572811	+	0.819687i
$5$	−0.0822049	−	0.297050i	−0.0367631	−	0.132845i	0.943103	−	0.332501i	$-0.107892\pi$
$5$	−0.0822049	−	0.297050i	−0.0367631	−	0.132845i	−0.979866	+	0.199656i	$0.936017\pi$
$6$	1.98189	−	4.04188i	0.809104	−	1.65009i
$7$	0.751910	−	1.58978i	0.284195	−	0.600880i	−0.710506	−	0.703691i	$-0.751534\pi$
$7$	0.751910	−	1.58978i	0.284195	−	0.600880i	0.994701	+	0.102811i	$0.0327837\pi$
$8$	−0.365254	−	2.80474i	−0.129137	−	0.991627i
$9$	−7.12377	+	0.349968i	−2.37459	+	0.116656i
$10$	−0.0910565	+	0.426265i	−0.0287946	+	0.134797i
$11$	−3.37483	−	2.37683i	−1.01755	−	0.716640i	−0.0580403	−	0.998314i	$-0.518485\pi$
$11$	−3.37483	−	2.37683i	−1.01755	−	0.716640i	−0.959510	+	0.281674i	$0.909110\pi$
$12$	−5.12729	+	3.77364i	−1.48012	+	1.08936i
$13$	−4.35772	+	0.537473i	−1.20861	+	0.149068i	−0.701410	−	0.712758i	$-0.747446\pi$
$13$	−4.35772	+	0.537473i	−1.20861	+	0.149068i	−0.507203	+	0.861827i	$0.669321\pi$
$14$	−1.98206	+	1.50233i	−0.529728	+	0.401513i
$15$	0.938845	−	0.284795i	0.242409	−	0.0735339i
$16$	−1.37510	+	3.75621i	−0.343775	+	0.939052i
$17$	−0.773749	+	2.55071i	−0.187662	+	0.618638i	0.811739	+	0.584021i	$0.198521\pi$
$17$	−0.773749	+	2.55071i	−0.187662	+	0.618638i	−0.999401	+	0.0346174i	$0.988979\pi$
$18$	9.16278	+	4.21717i	2.15969	+	0.993997i
$19$	0.456645	−	6.19058i	0.104762	−	1.42022i	−0.647858	−	0.761761i	$-0.724335\pi$
$19$	0.456645	−	6.19058i	0.104762	−	1.42022i	0.752619	−	0.658456i	$-0.228790\pi$
$20$	0.392801	−	0.475072i	0.0878330	−	0.106229i
$21$	5.11770	+	2.26852i	1.11677	+	0.495032i
$22$	2.67895	+	5.18660i	0.571154	+	1.10579i
$23$	−6.74306	+	5.00099i	−1.40602	+	1.04278i	−0.414896	+	0.909869i	$0.636182\pi$
$23$	−6.74306	+	5.00099i	−1.40602	+	1.04278i	−0.991128	+	0.132910i	$0.957568\pi$
$24$	8.89666	−	1.38141i	1.81602	−	0.281978i
$25$	4.20716	−	2.52168i	0.841432	−	0.504335i
$26$	5.81638	+	2.17414i	1.14069	+	0.426383i
$27$	−0.967658	−	13.1182i	−0.186226	−	2.52460i
$28$	3.46765	−	0.588625i	0.655324	−	0.111240i
$29$	−10.3606	+	2.32656i	−1.92392	+	0.432031i	−0.925321	+	0.379186i	$0.876204\pi$
$29$	−10.3606	+	2.32656i	−1.92392	+	0.432031i	−0.998603	+	0.0528456i	$0.983171\pi$
$30$	−1.36356	−	0.256459i	−0.248951	−	0.0468228i
$31$	1.03298	+	1.54596i	0.185529	+	0.277663i	0.912562	−	0.408939i	$-0.134101\pi$
$31$	1.03298	+	1.54596i	0.185529	+	0.277663i	−0.727033	+	0.686603i	$0.759101\pi$
$32$	4.17958	−	3.81197i	0.738853	−	0.673867i
$33$	7.29985	−	10.9250i	1.27074	−	1.90180i
$34$	2.63751	−	2.69317i	0.452329	−	0.461875i
$35$	−0.534055	−	0.0926673i	−0.0902718	−	0.0156636i
$36$	−8.73487	−	11.2776i	−1.45581	−	1.87960i
$37$	2.04886	+	4.07038i	0.336830	+	0.669167i	0.996608	−	0.0822940i	$-0.0262246\pi$
$37$	2.04886	+	4.07038i	0.336830	+	0.669167i	−0.659778	+	0.751461i	$0.729350\pi$
$38$	−4.61883	+	7.46526i	−0.749274	+	1.21102i
$39$	−2.05075	−	13.8250i	−0.328383	−	2.21378i
$40$	−0.803124	+	0.339062i	−0.126985	+	0.0536105i
$41$	2.56194	+	1.53557i	0.400107	+	0.239815i	0.699977	−	0.714165i	$-0.253193\pi$
$41$	2.56194	+	1.53557i	0.400107	+	0.239815i	−0.299870	+	0.953980i	$0.596943\pi$
$42$	−4.93550	−	6.18991i	−0.761564	−	0.955123i
$43$	−8.30756	−	8.72570i	−1.26689	−	1.33066i	−0.919578	−	0.392907i	$-0.871469\pi$
$43$	−8.30756	−	8.72570i	−1.26689	−	1.33066i	−0.347313	−	0.937749i	$-0.612906\pi$
$44$	0.0302252	−	8.25556i	0.00455662	−	1.24457i
$45$	0.689566	+	2.08735i	0.102794	+	0.311163i
$46$	11.7252	−	1.86459i	1.72879	−	0.274919i
$47$	3.25239	+	2.66917i	0.474410	+	0.389338i	0.840992	−	0.541047i	$-0.181972\pi$
$47$	3.25239	+	2.66917i	0.474410	+	0.389338i	−0.366582	+	0.930386i	$0.619472\pi$
$48$	−12.0603	−	4.08239i	−1.74076	−	0.589242i
$49$	2.47872	+	3.02033i	0.354103	+	0.431476i
$50$	−6.92444	+	0.412690i	−0.979263	+	0.0583632i
$51$	−8.17726	−	2.26295i	−1.14504	−	0.316877i
$52$	−5.87341	−	6.52819i	−0.814496	−	0.905297i
$53$	1.89510	+	0.425560i	0.260313	+	0.0584551i	0.347299	−	0.937754i	$-0.387099\pi$
$53$	1.89510	+	0.425560i	0.260313	+	0.0584551i	−0.0869868	+	0.996209i	$0.527724\pi$
$54$	−7.36047	+	17.0843i	−1.00163	+	2.32487i
$55$	−0.428609	+	1.19788i	−0.0577936	+	0.161522i
$56$	−4.73356	−	1.52824i	−0.632549	−	0.204220i
$57$	19.7352	+	0.969529i	2.61399	+	0.128417i
$58$	14.5141	+	3.85390i	1.90579	+	0.506042i
$59$	0.455138	−	3.69016i	0.0592539	−	0.480418i	−0.933345	−	0.358980i	$-0.883125\pi$
$59$	0.455138	−	3.69016i	0.0592539	−	0.480418i	0.992599	−	0.121438i	$-0.0387504\pi$
$60$	1.54245	+	1.21285i	0.199129	+	0.156578i
$61$	1.47715	+	3.33240i	0.189130	+	0.426670i	0.983535	−	0.180718i	$-0.0578422\pi$
$61$	1.47715	+	3.33240i	0.189130	+	0.426670i	−0.794405	+	0.607388i	$0.792217\pi$
$62$	−0.285041	−	2.61397i	−0.0362003	−	0.331975i
$63$	−4.80006	+	11.5884i	−0.604751	+	1.46000i
$64$	−7.73318	+	2.04889i	−0.966647	+	0.256111i
$65$	0.517882	+	1.25028i	0.0642353	+	0.155078i
$66$	−16.2954	+	8.93007i	−2.00583	+	1.09922i
$67$	−2.88825	+	7.48751i	−0.352856	+	0.914744i	0.636767	+	0.771056i	$0.280271\pi$
$67$	−2.88825	+	7.48751i	−0.352856	+	0.914744i	−0.989623	+	0.143688i	$0.954104\pi$
$68$	−5.06799	+	1.65368i	−0.614585	+	0.200539i
$69$	−16.4408	−	21.0669i	−1.97924	−	2.53616i
$70$	0.609201	+	0.465273i	0.0728134	+	0.0556107i
$71$	−0.990371	−	1.09271i	−0.117535	−	0.129680i	0.679341	−	0.733823i	$-0.262266\pi$
$71$	−0.990371	−	1.09271i	−0.117535	−	0.129680i	−0.796876	+	0.604142i	$0.793516\pi$
$72$	3.58356	+	19.8525i	0.422326	+	2.33964i
$73$	5.22880	+	11.0554i	0.611985	+	1.29393i	0.937364	+	0.348350i	$0.113258\pi$
$73$	5.22880	+	11.0554i	0.611985	+	1.29393i	−0.325379	+	0.945584i	$0.605492\pi$
$74$	0.0908802	−	6.44387i	0.0105646	−	0.749084i
$75$	8.35308	+	13.1909i	0.964530	+	1.52316i
$76$	10.6718	−	6.34346i	1.22414	−	0.727644i
$77$	−6.31620	+	3.57808i	−0.719798	+	0.407760i
$78$	−6.46412	+	18.6786i	−0.731918	+	2.11493i
$79$	−0.267875	+	2.71978i	−0.0301382	+	0.305999i	0.968284	+	0.249851i	$0.0803817\pi$
$79$	−0.267875	+	2.71978i	−0.0301382	+	0.305999i	−0.998422	+	0.0561475i	$0.982118\pi$
$80$	1.22882	+	0.0996952i	0.137387	+	0.0111463i
$81$	20.3749	−	2.00675i	2.26388	−	0.222972i
$82$	−2.20933	−	3.60025i	−0.243980	−	0.397582i
$83$	3.29826	−	6.55251i	0.362031	−	0.719232i	−0.636619	−	0.771178i	$-0.719668\pi$
$83$	3.29826	−	6.55251i	0.362031	−	0.719232i	0.998650	+	0.0519468i	$0.0165426\pi$
$84$	2.14399	+	10.9887i	0.233929	+	1.19897i
$85$	0.821295	+	0.0201617i	0.0890819	+	0.00218684i
$86$	4.71556	+	16.3728i	0.508492	+	1.76553i
$87$	−8.21288	−	32.7877i	−0.880513	−	3.51521i
$88$	−5.43371	+	10.3337i	−0.579236	+	1.10157i
$89$	−13.8242	−	10.2527i	−1.46536	−	1.08679i	−0.976774	−	0.214271i	$-0.931263\pi$
$89$	−13.8242	−	10.2527i	−1.46536	−	1.08679i	−0.488587	−	0.872515i	$-0.662487\pi$
$90$	0.499486	−	3.06848i	0.0526505	−	0.323446i
$91$	−2.42215	+	7.33194i	−0.253910	+	0.768596i
$92$	−15.9235	−	5.32515i	−1.66014	−	0.555185i
$93$	−4.83884	+	3.40789i	−0.501764	+	0.353382i
$94$	−2.33432	−	5.47321i	−0.240767	−	0.564518i
$95$	−1.87645	+	0.373250i	−0.192520	+	0.0382946i
$96$	12.4569	+	13.0024i	1.27137	+	1.32705i
$97$	−0.974057	−	0.193752i	−0.0989005	−	0.0196725i	0.145392	−	0.989374i	$-0.453556\pi$
$97$	−0.974057	−	0.193752i	−0.0989005	−	0.0196725i	−0.244292	+	0.969702i	$0.578556\pi$
$98$	−1.13453	−	5.40793i	−0.114605	−	0.546284i
$99$	24.8733	+	15.7509i	2.49986	+	1.58302i
$100$	8.95379	+	4.00823i	0.895379	+	0.400823i
$101$	3.55297	+	3.06481i	0.353534	+	0.304960i	0.811893	−	0.583807i	$-0.198437\pi$
$101$	3.55297	+	3.06481i	0.353534	+	0.304960i	−0.458359	+	0.888767i	$0.651562\pi$
$102$	8.77618	+	8.18264i	0.868972	+	0.810202i
$103$	6.74516	+	1.68957i	0.664620	+	0.166479i	0.560588	−	0.828095i	$-0.310575\pi$
$103$	6.74516	+	1.68957i	0.664620	+	0.166479i	0.104033	+	0.994574i	$0.466825\pi$
$104$	3.09915	+	12.0260i	0.303897	+	1.17924i
$105$	0.253165	−	1.70670i	0.0247063	−	0.166557i
$106$	−2.09854	−	1.77234i	−0.203828	−	0.172144i
$107$	−1.96493	−	5.09388i	−0.189957	−	0.492444i	0.804938	−	0.593358i	$-0.202198\pi$
$107$	−1.96493	−	5.09388i	−0.189957	−	0.492444i	−0.994895	+	0.100914i	$0.967823\pi$
$108$	20.3971	−	16.6149i	1.96271	−	1.59877i
$109$	−3.80061	−	4.40597i	−0.364033	−	0.422015i	0.545198	−	0.838307i	$-0.316454\pi$
$109$	−3.80061	−	4.40597i	−0.364033	−	0.422015i	−0.909231	+	0.416292i	$0.863329\pi$
$110$	1.32046	−	1.22215i	0.125901	−	0.116527i
$111$	−12.7926	+	6.83780i	−1.21422	+	0.649015i
$112$	4.93759	+	5.01044i	0.466559	+	0.473442i
$113$	−3.73390	+	6.98563i	−0.351256	+	0.657153i	−0.994055	−	0.108882i	$-0.965273\pi$
$113$	−3.73390	+	6.98563i	−0.351256	+	0.657153i	0.642799	+	0.766035i	$0.277773\pi$
$114$	−24.1166	−	14.1148i	−2.25873	−	1.32197i
$115$	2.03986	+	1.59192i	0.190218	+	0.148447i
$116$	−15.6835	−	14.3196i	−1.45618	−	1.32954i
$117$	30.8553	−	5.35389i	2.85257	−	0.494968i
$118$	−2.98267	+	4.33042i	−0.274577	+	0.398647i
$119$	3.47328	+	3.14800i	0.318395	+	0.288576i
$120$	−1.14170	−	2.52920i	−0.104222	−	0.230883i
$121$	2.03441	+	5.68579i	0.184946	+	0.516890i
$122$	0.325525	−	5.14468i	0.0294716	−	0.465778i
$123$	−4.68631	+	8.27250i	−0.422550	+	0.745906i
$124$	−1.35101	+	3.46453i	−0.121324	+	0.311124i
$125$	−2.21103	−	2.10508i	−0.197761	−	0.188284i
$126$	13.5940	−	11.3959i	1.21105	−	1.01522i
$127$	4.90343	+	4.90343i	0.435109	+	0.435109i	0.890362	−	0.455253i	$-0.150451\pi$
$127$	4.90343	+	4.90343i	0.435109	+	0.435109i	−0.455253	+	0.890362i	$0.650451\pi$
$128$	11.0375	+	2.48483i	0.975583	+	0.219630i
$129$	27.1178	−	27.1178i	2.38759	−	2.38759i
$130$	0.167693	−	1.90648i	0.0147076	−	0.167209i
$131$	−5.29834	+	5.56502i	−0.462918	+	0.486218i	−0.913685	−	0.406424i	$-0.866776\pi$
$131$	−5.29834	+	5.56502i	−0.462918	+	0.486218i	0.450766	+	0.892642i	$0.351151\pi$
$132$	26.2730	−	0.548727i	2.28677	−	0.0477605i
$133$	−9.49831	−	5.38073i	−0.823608	−	0.466568i
$134$	8.51602	−	7.50246i	0.735672	−	0.648114i
$135$	−3.81722	+	1.36582i	−0.328534	+	0.117551i
$136$	7.43670	+	1.23851i	0.637692	+	0.106201i
$137$	−1.73828	+	1.91789i	−0.148511	+	0.163856i	−0.810663	−	0.585513i	$-0.800893\pi$
$137$	−1.73828	+	1.91789i	−0.148511	+	0.163856i	0.662152	+	0.749369i	$0.269643\pi$
$138$	6.84941	+	37.1661i	0.583060	+	3.16379i
$139$	−0.937373	−	5.40222i	−0.0795070	−	0.458210i	−0.998024	−	0.0628292i	$-0.979988\pi$
$139$	−0.937373	−	5.40222i	−0.0795070	−	0.458210i	0.918517	−	0.395381i	$-0.129387\pi$
$140$	−0.459909	−	0.981678i	−0.0388694	−	0.0829670i
$141$	−8.23970	+	10.5582i	−0.693908	+	0.889161i
$142$	0.527853	+	2.01769i	0.0442964	+	0.169320i
$143$	15.9840	+	8.54365i	1.33665	+	0.714456i
$144$	8.48134	−	27.2396i	0.706778	−	2.26997i
$145$	1.54280	+	2.88638i	0.128123	+	0.239701i
$146$	0.668226	−	17.2823i	0.0553027	−	1.43029i
$147$	−9.41760	+	8.12367i	−0.776750	+	0.670029i
$148$	−4.32567	+	8.02197i	−0.355567	+	0.659402i
$149$	−5.22244	+	2.01452i	−0.427839	+	0.165036i	−0.564227	−	0.825620i	$-0.690826\pi$
$149$	−5.22244	+	2.01452i	−0.427839	+	0.165036i	0.136388	+	0.990656i	$0.456451\pi$
$150$	−1.85418	−	22.0025i	−0.151393	−	1.79650i
$151$	−5.52909	−	0.820164i	−0.449951	−	0.0667440i	−0.0820906	−	0.996625i	$-0.526160\pi$
$151$	−5.52909	−	0.820164i	−0.449951	−	0.0667440i	−0.367861	+	0.929881i	$0.619910\pi$
$152$	−17.5298	+	0.980365i	−1.42185	+	0.0795181i
$153$	4.61934	−	18.4415i	0.373452	−	1.49090i
$154$	10.2599	−	0.359088i	0.826765	−	0.0289361i
$155$	0.374313	−	0.433933i	0.0300655	−	0.0348543i
$156$	20.3150	−	19.2002i	1.62650	−	1.53725i
$157$	−4.13118	+	6.52384i	−0.329704	+	0.520659i	−0.968597	−	0.248636i	$-0.920018\pi$
$157$	−4.13118	+	6.52384i	−0.329704	+	0.520659i	0.638893	+	0.769296i	$0.279393\pi$
$158$	2.11358	−	3.23584i	0.168148	−	0.257429i
$159$	−1.20617	+	6.06380i	−0.0956551	+	0.480891i
$160$	−1.47593	−	0.928184i	−0.116682	−	0.0733794i
$161$	2.88030	+	14.4803i	0.227000	+	1.14121i
$162$	−26.8641	−	10.8003i	−2.11064	−	0.848548i
$163$	−1.31535	−	1.86766i	−0.103027	−	0.146286i	0.762793	−	0.646643i	$-0.223827\pi$
$163$	−1.31535	−	1.86766i	−0.103027	−	0.146286i	−0.865820	+	0.500356i	$0.833202\pi$
$164$	0.417643	+	5.95915i	0.0326125	+	0.465332i
$165$	−3.84535	−	1.27033i	−0.299360	−	0.0988953i
$166$	−8.41910	+	6.06189i	−0.653449	+	0.470494i
$167$	−2.06057	+	2.77836i	−0.159452	+	0.214996i	−0.875707	−	0.482842i	$-0.839605\pi$
$167$	−2.06057	+	2.77836i	−0.159452	+	0.214996i	0.716256	+	0.697838i	$0.245855\pi$
$168$	4.49336	−	15.1824i	0.346670	−	1.17135i
$169$	6.09040	−	1.52557i	0.468492	−	0.117351i
$170$	−1.01682	−	0.562081i	−0.0779867	−	0.0431096i
$171$	−1.08652	+	44.2601i	−0.0830886	+	3.38465i
$172$	4.78737	−	23.6156i	0.365034	−	1.80067i
$173$	23.3163	+	11.7365i	1.77271	+	0.892307i	0.942010	+	0.335583i	$0.108933\pi$
$173$	23.3163	+	11.7365i	1.77271	+	0.892307i	0.830698	+	0.556723i	$0.187942\pi$
$174$	−11.1300	+	46.4875i	−0.843763	+	3.52421i
$175$	−0.845503	−	8.58453i	−0.0639140	−	0.648930i
$176$	13.5686	−	9.40820i	1.02277	−	0.709170i
$177$	11.7783	+	1.16006i	0.885311	+	0.0871955i
$178$	10.6360	+	21.8936i	0.797203	+	1.64099i
$179$	−0.562944	−	0.993735i	−0.0420764	−	0.0742753i	0.848256	−	0.529587i	$-0.177653\pi$
$179$	−0.562944	−	0.993735i	−0.0420764	−	0.0742753i	−0.890332	+	0.455311i	$0.849528\pi$
$180$	−2.63196	+	3.52177i	−0.196175	+	0.262497i
$181$	−8.12900	+	5.14763i	−0.604224	+	0.382620i	−0.801735	−	0.597680i	$-0.796089\pi$
$181$	−8.12900	+	5.14763i	−0.604224	+	0.382620i	0.197511	+	0.980301i	$0.436714\pi$
$182$	7.82979	−	7.61201i	0.580383	−	0.564240i
$183$	−10.4889	+	4.96088i	−0.775361	+	0.366719i
$184$	16.4894	+	17.0859i	1.21562	+	1.25959i
$185$	1.04068	−	0.943219i	0.0765124	−	0.0693468i
$186$	8.29586	−	1.11125i	0.608282	−	0.0814808i
$187$	8.67387	−	6.76915i	0.634296	−	0.495009i
$188$	−0.649757	+	8.38975i	−0.0473884	+	0.611886i
$189$	−21.5827	−	8.32536i	−1.56991	−	0.605581i
$190$	2.59725	+	0.758345i	0.188424	+	0.0550161i
$191$	−15.1845	+	6.28961i	−1.09871	+	0.455100i	−0.857035	−	0.515257i	$-0.827696\pi$
$191$	−15.1845	+	6.28961i	−1.09871	+	0.455100i	−0.241674	+	0.970358i	$0.577696\pi$
$192$	−7.12403	−	24.4483i	−0.514133	−	1.76440i
$193$	−1.86451	−	0.772307i	−0.134211	−	0.0555918i	0.314567	−	0.949235i	$-0.398141\pi$
$193$	−1.86451	−	0.772307i	−0.134211	−	0.0555918i	−0.448778	+	0.893643i	$0.648141\pi$
$194$	1.09495	+	0.879628i	0.0786126	+	0.0631536i
$195$	−3.93815	+	1.74566i	−0.282017	+	0.125009i
$196$	−2.11178	+	7.52371i	−0.150841	+	0.537408i
$197$	6.27822	+	0.774345i	0.447305	+	0.0551698i	0.342914	−	0.939367i	$-0.388586\pi$
$197$	6.27822	+	0.774345i	0.447305	+	0.0551698i	0.104390	+	0.994536i	$0.466711\pi$
$198$	−20.8994	−	36.0106i	−1.48525	−	2.55916i
$199$	0.178968	−	3.64297i	0.0126867	−	0.258243i	−0.984071	−	0.177777i	$-0.943109\pi$
$199$	0.178968	−	3.64297i	0.0126867	−	0.258243i	0.996757	−	0.0804656i	$-0.0256407\pi$
$200$	−8.60934	−	10.8790i	−0.608772	−	0.769259i
$201$	−24.0522	−	8.60602i	−1.69651	−	0.607022i
$202$	−2.45269	−	6.16585i	−0.172571	−	0.433828i
$203$	−4.09155	+	18.2205i	−0.287171	+	1.27883i
$204$	−5.65822	−	15.9981i	−0.396155	−	1.12009i
$205$	0.245536	−	0.887255i	0.0171490	−	0.0619686i
$206$	−7.35492	−	6.52754i	−0.512442	−	0.454795i
$207$	46.2858	−	37.9858i	3.21708	−	2.64019i
$208$	3.97344	−	17.1076i	0.275508	−	1.18620i
$209$	−16.2550	+	19.8068i	−1.12438	+	1.37007i
$210$	−1.43299	+	1.97493i	−0.0988857	+	0.136283i
$211$	11.0964	−	3.66577i	0.763910	−	0.252362i	0.0947710	−	0.995499i	$-0.469788\pi$
$211$	11.0964	−	3.66577i	0.763910	−	0.252362i	0.669139	+	0.743137i	$0.266663\pi$
$212$	1.47342	+	3.59432i	0.101195	+	0.246859i
$213$	3.39982	−	3.23690i	0.232952	−	0.221789i
$214$	−0.865096	+	7.67260i	−0.0591368	+	0.524488i
$215$	−1.90905	+	3.18506i	−0.130196	+	0.217219i
$216$	−36.4398	+	7.50552i	−2.47942	+	0.510686i
$217$	3.23445	−	0.479785i	0.219569	−	0.0325700i
$218$	1.88669	+	8.00967i	0.127783	+	0.542483i
$219$	−34.7717	+	17.5026i	−2.34965	+	1.18272i
$220$	−2.45480	+	0.669669i	−0.165503	+	0.0451491i
$221$	2.00084	−	11.5311i	0.134591	−	0.775668i
$222$	20.5126	−	0.214185i	1.37672	−	0.0143752i
$223$	−11.5260	−	7.70140i	−0.771835	−	0.515724i	0.106186	−	0.994346i	$-0.466136\pi$
$223$	−11.5260	−	7.70140i	−0.771835	−	0.515724i	−0.878021	+	0.478623i	$0.841136\pi$
$224$	−2.91752	−	9.51087i	−0.194935	−	0.635472i
$225$	−29.0883	+	19.4362i	−1.93922	+	1.29575i
$226$	9.24853	−	6.32034i	0.615203	−	0.420423i
$227$	−2.71727	−	12.1005i	−0.180351	−	0.803141i	−0.979409	−	0.201887i	$-0.935293\pi$
$227$	−2.71727	−	12.1005i	−0.180351	−	0.803141i	0.799058	−	0.601255i	$-0.205332\pi$
$228$	21.0197	+	33.4641i	1.39206	+	2.21622i
$229$	−27.6517	+	2.03971i	−1.82727	+	0.134788i	−0.943129	−	0.332427i	$-0.892133\pi$
$229$	−27.6517	+	2.03971i	−1.82727	+	0.134788i	−0.884144	+	0.467215i	$0.845258\pi$
$230$	−1.51775	−	3.32970i	−0.100077	−	0.219554i
$231$	−11.8795	−	19.8198i	−0.781614	−	1.30404i
$232$	10.3097	+	28.2092i	0.676863	+	1.85202i
$233$	−3.05678	−	4.12159i	−0.200256	−	0.270014i	0.691652	−	0.722231i	$-0.256883\pi$
$233$	−3.05678	−	4.12159i	−0.200256	−	0.270014i	−0.891908	+	0.452217i	$0.850633\pi$
$234$	−42.1954	−	13.4525i	−2.75840	−	0.879417i
$235$	0.525515	−	1.18554i	0.0342808	−	0.0773363i
$236$	6.57097	−	3.48138i	0.427734	−	0.226619i
$237$	−8.67574	−	0.639961i	−0.563550	−	0.0415699i
$238$	−2.29838	−	6.21808i	−0.148982	−	0.403058i
$239$	−26.6638	−	8.08839i	−1.72474	−	0.523194i	−0.736545	−	0.676389i	$-0.763544\pi$
$239$	−26.6638	−	8.08839i	−1.72474	−	0.523194i	−0.988196	+	0.153194i	$0.951044\pi$
$240$	−0.221255	+	3.91812i	−0.0142819	+	0.252913i
$241$	−3.72457	−	12.2783i	−0.239920	−	0.790912i	−0.991367	−	0.131118i	$-0.958143\pi$
$241$	−3.72457	−	12.2783i	−0.239920	−	0.790912i	0.751446	−	0.659794i	$-0.229357\pi$
$242$	1.16483	−	8.46033i	0.0748780	−	0.543851i
$243$	3.14696	+	25.5149i	0.201878	+	1.63678i
$244$	−3.77079	+	6.23927i	−0.241400	+	0.399429i
$245$	0.693427	−	0.984590i	0.0443014	−	0.0629032i
$246$	11.2841	−	7.31172i	0.719446	−	0.466178i
$247$	1.33734	+	27.2222i	0.0850931	+	1.73211i
$248$	3.95873	−	3.46191i	0.251380	−	0.219832i
$249$	21.1089	+	9.98377i	1.33772	+	0.632696i
$250$	1.39702	+	4.08514i	0.0883554	+	0.258367i
$251$	−21.9677	+	6.07928i	−1.38659	+	0.383721i	−0.878565	−	0.477623i	$-0.841499\pi$
$251$	−21.9677	+	6.07928i	−1.38659	+	0.383721i	−0.508023	+	0.861343i	$0.669624\pi$
$252$	−24.4967	+	5.40679i	−1.54315	+	0.340596i
$253$	34.6432	−	0.850442i	2.17800	−	0.0534668i
$254$	−2.94461	−	9.35434i	−0.184761	−	0.586944i
$255$			2.61508i			0.163763i
$256$	−12.2182	−	10.3303i	−0.763637	−	0.645645i
$257$		−	11.1663i		−	0.696538i	−0.937395	−	0.348269i	$-0.886770\pi$
$257$		−	11.1663i		−	0.696538i	0.937395	−	0.348269i	$-0.113230\pi$
$258$	−51.7329	+	16.2848i	−3.22075	+	1.01385i
$259$	8.01157	−	0.196673i	0.497815	−	0.0122207i
$260$	−1.45638	+	2.28135i	−0.0903206	+	0.141483i
$261$	72.9926	−	20.1998i	4.51813	−	1.25033i
$262$	10.2820	−	3.51621i	0.635226	−	0.217232i
$263$	11.6743	+	5.52152i	0.719866	+	0.340471i	0.752136	−	0.659008i	$-0.229024\pi$
$263$	11.6743	+	5.52152i	0.719866	+	0.340471i	−0.0322700	+	0.999479i	$0.510274\pi$
$264$	−33.3081	−	16.4838i	−2.04997	−	1.01451i
$265$	−0.0293741	−	0.597924i	−0.00180444	−	0.0367302i
$266$	8.39517	+	12.9561i	0.514741	+	0.794391i
$267$	31.5461	−	44.7920i	1.93059	−	2.74122i
$268$	−15.5837	+	3.84293i	−0.951924	+	0.234744i
$269$	3.57821	+	29.0114i	0.218167	+	1.76885i	0.559421	+	0.828884i	$0.311024\pi$
$269$	3.57821	+	29.0114i	0.218167	+	1.76885i	−0.341254	+	0.939971i	$0.610851\pi$
$270$	5.67995	+	0.782021i	0.345671	+	0.0475923i
$271$	−5.73577	−	18.9083i	−0.348424	−	1.14860i	−0.939663	−	0.342102i	$-0.888861\pi$
$271$	−5.73577	−	18.9083i	−0.348424	−	1.14860i	0.591239	−	0.806496i	$-0.298639\pi$
$272$	−8.51701	−	6.41385i	−0.516420	−	0.388896i
$273$	−23.5208	−	7.13494i	−1.42354	−	0.431826i
$274$	3.43353	−	1.26913i	0.207427	−	0.0766709i
$275$	−20.1920	−	1.48946i	−1.21763	−	0.0898175i
$276$	15.7017	−	51.0874i	0.945129	−	3.07510i
$277$	−8.47492	+	19.1191i	−0.509208	+	1.14876i	0.456641	+	0.889651i	$0.349052\pi$
$277$	−8.47492	+	19.1191i	−0.509208	+	1.14876i	−0.965849	+	0.259104i	$0.916573\pi$
$278$	−2.35530	+	7.38768i	−0.141261	+	0.443083i
$279$	−7.89975	−	10.6516i	−0.472946	−	0.637693i
$280$	−0.0648423	+	1.53174i	−0.00387507	+	0.0915387i
$281$	−4.02711	−	6.71883i	−0.240237	−	0.400812i	0.713869	−	0.700279i	$-0.246941\pi$
$281$	−4.02711	−	6.71883i	−0.240237	−	0.400812i	−0.954107	+	0.299467i	$0.903191\pi$
$282$	17.2344	−	7.85578i	1.02629	−	0.467805i
$283$	17.7679	−	1.31064i	1.05619	−	0.0779094i	0.465692	−	0.884947i	$-0.345805\pi$
$283$	17.7679	−	1.31064i	1.05619	−	0.0779094i	0.590500	+	0.807037i	$0.298930\pi$
$284$	0.656764	−	2.87542i	0.0389718	−	0.170625i
$285$	−1.33433	−	5.94205i	−0.0790390	−	0.351977i
$286$	−14.4618	−	21.1619i	−0.855142	−	1.25133i
$287$	4.36756	−	2.91831i	0.257809	−	0.172262i
$288$	−28.4403	+	28.6183i	−1.67586	+	1.68635i
$289$	8.22755	+	5.49747i	0.483974	+	0.323381i
$290$	−0.0483263	−	4.62823i	−0.00283782	−	0.271779i
$291$	0.540462	−	3.11476i	0.0316824	−	0.182590i
$292$	−12.1337	+	21.2373i	−0.710070	+	1.24282i
$293$	18.7349	−	9.43035i	1.09450	−	0.550927i	0.191906	−	0.981413i	$-0.438533\pi$
$293$	18.7349	−	9.43035i	1.09450	−	0.550927i	0.902597	+	0.430486i	$0.141658\pi$
$294$	17.1204	−	4.03273i	0.998481	−	0.235194i
$295$	−1.13358	+	0.168150i	−0.0659994	+	0.00979008i
$296$	10.6680	−	7.23325i	0.620066	−	0.420424i
$297$	−27.9140	+	46.5718i	−1.61974	+	2.70237i
$298$	7.86623	+	0.886929i	0.455679	+	0.0513784i
$299$	26.6964	−	25.4171i	1.54389	−	1.46991i
$300$	−12.0554	+	28.8057i	−0.696021	+	1.66310i
$301$	−20.1185	+	6.64625i	−1.15961	+	0.383083i
$302$	6.39808	+	4.64238i	0.368168	+	0.267139i
$303$	−9.47523	+	11.5456i	−0.544338	+	0.663278i
$304$	22.6252	+	10.2279i	1.29764	+	0.586612i
$305$	0.868461	−	0.712727i	0.0497279	−	0.0408106i
$306$	−17.8465	+	20.1086i	−1.02022	+	1.14953i
$307$	−4.29747	+	15.5291i	−0.245269	+	0.886290i	0.733220	+	0.679992i	$0.238017\pi$
$307$	−4.29747	+	15.5291i	−0.245269	+	0.886290i	−0.978489	+	0.206298i	$0.933858\pi$
$308$	−13.1018	−	6.25549i	−0.746544	−	0.356440i
$309$	−4.84961	+	21.5963i	−0.275885	+	1.22857i
$310$	−0.753049	+	0.299553i	−0.0427703	+	0.0170135i
$311$	−12.0101	−	4.29727i	−0.681028	−	0.243676i	−0.0264276	−	0.999651i	$-0.508413\pi$
$311$	−12.0101	−	4.29727i	−0.681028	−	0.243676i	−0.654601	+	0.755975i	$0.727163\pi$
$312$	−38.0267	+	10.8015i	−2.15284	+	0.611514i
$313$	−1.52001	+	30.9406i	−0.0859162	+	1.74887i	0.439701	+	0.898144i	$0.355084\pi$
$313$	−1.52001	+	30.9406i	−0.0859162	+	1.74887i	−0.525618	+	0.850721i	$0.676166\pi$
$314$	9.44495	−	5.48154i	0.533009	−	0.309341i
$315$	3.83691	+	0.473238i	0.216186	+	0.0266640i
$316$	−4.76562	+	2.67669i	−0.268087	+	0.150575i
$317$	5.51670	−	2.44539i	0.309849	−	0.137347i	−0.244456	−	0.969660i	$-0.578609\pi$
$317$	5.51670	−	2.44539i	0.309849	−	0.137347i	0.554305	+	0.832314i	$0.312984\pi$
$318$	5.47595	−	6.81637i	0.307076	−	0.382243i
$319$	40.4953	+	16.7737i	2.26730	+	0.939146i
$320$	1.24433	+	2.12871i	0.0695600	+	0.118999i
$321$	16.0562	−	6.65068i	0.896167	−	0.371205i
$322$	5.85202	−	20.0425i	0.326120	−	1.11693i
$323$	15.4371	+	5.95473i	0.858941	+	0.331330i
$324$	26.6317	+	31.1031i	1.47954	+	1.72795i
$325$	−16.9783	+	13.2500i	−0.941786	+	0.734977i
$326$	0.428912	+	3.20198i	0.0237553	+	0.177341i
$327$	13.7237	−	12.4384i	0.758921	−	0.687846i
$328$	3.37111	−	7.74645i	0.186138	−	0.427726i
$329$	6.68890	−	3.16361i	0.368771	−	0.174416i
$330$	3.99224	+	4.10646i	0.219766	+	0.226053i
$331$	24.6069	−	15.5822i	1.35252	−	0.856473i	0.355578	−	0.934646i	$-0.384284\pi$
$331$	24.6069	−	15.5822i	1.35252	−	0.856473i	0.996940	+	0.0781739i	$0.0249089\pi$
$332$	14.5206	−	2.09962i	0.796920	−	0.115232i
$333$	−16.0201	−	28.2794i	−0.877896	−	1.54970i
$334$	4.40013	−	2.13761i	0.240764	−	0.116965i
$335$	2.46159	+	0.242446i	0.134491	+	0.0132462i
$336$	−15.5584	+	16.1037i	−0.848780	+	0.878529i
$337$	−3.13561	−	31.8364i	−0.170807	−	1.73424i	−0.573767	−	0.819019i	$-0.694518\pi$
$337$	−3.13561	−	31.8364i	−0.170807	−	1.73424i	0.402959	−	0.915218i	$-0.367982\pi$
$338$	−8.63518	−	2.06743i	−0.469692	−	0.112453i
$339$	−22.5212	−	11.3362i	−1.22318	−	0.615699i
$340$	0.907841	+	1.36951i	0.0492346	+	0.0742720i
$341$	0.188351	−	7.67258i	0.0101998	−	0.415494i
$342$	30.2909	−	54.7972i	1.63794	−	2.96309i
$343$	18.6069	−	4.66079i	1.00468	−	0.251659i
$344$	−21.4390	+	26.4877i	−1.15591	+	1.42812i
$345$	−4.90642	+	6.61555i	−0.264153	+	0.356169i
$346$	−21.5705	−	29.9584i	−1.15964	−	1.61057i
$347$	5.44966	+	1.80033i	0.292553	+	0.0966466i	0.456214	−	0.889870i	$-0.349205\pi$
$347$	5.44966	+	1.80033i	0.292553	+	0.0966466i	−0.163661	+	0.986517i	$0.552330\pi$
$348$	44.3424	−	51.0263i	2.37700	−	2.73529i
$349$	−12.3903	−	17.5928i	−0.663235	−	0.941722i	−1.00000		0.000133068i	$-0.999958\pi$
$349$	−12.3903	−	17.5928i	−0.663235	−	0.941722i	0.336765	−	0.941589i	$-0.390667\pi$
$350$	−4.55047	+	11.3186i	−0.243233	+	0.605006i
$351$	11.2675	+	56.6454i	0.601413	+	3.02351i
$352$	−23.1658	+	2.93060i	−1.23474	+	0.156202i
$353$	−3.93577	+	19.7864i	−0.209480	+	1.05313i	0.722709	+	0.691153i	$0.242897\pi$
$353$	−3.93577	+	19.7864i	−0.209480	+	1.05313i	−0.932189	+	0.361973i	$0.882103\pi$
$354$	−14.0132	−	9.15311i	−0.744791	−	0.486482i
$355$	−0.243175	+	0.384016i	−0.0129064	+	0.0203814i
$356$	0.970752	−	34.4088i	0.0514498	−	1.82366i
$357$	−9.74615	+	11.2985i	−0.515821	+	0.597980i
$358$	0.0564957	+	1.61420i	0.00298589	+	0.0853131i
$359$	5.58589	−	22.3001i	0.294812	−	1.17696i	−0.623732	−	0.781638i	$-0.714385\pi$
$359$	5.58589	−	22.3001i	0.294812	−	1.17696i	0.918544	−	0.395318i	$-0.129365\pi$
$360$	5.60261	−	2.69647i	0.295283	−	0.142116i
$361$	−19.3204	−	2.86592i	−1.01687	−	0.150838i
$362$	13.5592	−	1.14265i	0.712656	−	0.0600562i
$363$	−17.9343	+	6.91801i	−0.941305	+	0.363101i
$364$	−14.7947	+	4.42883i	−0.775451	+	0.232134i
$365$	2.85417	−	2.46202i	0.149394	−	0.128868i
$366$	16.3967	+	0.633985i	0.857070	+	0.0331389i
$367$	−12.1947	−	22.8148i	−0.636560	−	1.19092i	−0.968828	−	0.247736i	$-0.920314\pi$
$367$	−12.1947	−	22.8148i	−0.636560	−	1.19092i	0.332267	−	0.943185i	$-0.392186\pi$
$368$	−9.51239	−	32.2052i	−0.495867	−	1.67881i
$369$	−18.7880	−	10.0424i	−0.978066	−	0.522787i
$370$	−1.92162	+	0.502721i	−0.0999004	+	0.0261352i
$371$	2.10149	−	2.69282i	0.109104	−	0.139804i
$372$	−11.1303	−	4.02851i	−0.577079	−	0.208869i
$373$	−1.34999	−	7.78020i	−0.0699000	−	0.402844i	−0.999419	−	0.0340705i	$-0.989153\pi$
$373$	−1.34999	−	7.78020i	−0.0699000	−	0.402844i	0.929519	−	0.368773i	$-0.120222\pi$
$374$	−15.3023	+	2.82010i	−0.791265	+	0.145824i
$375$	6.52601	−	7.20034i	0.337002	−	0.371824i
$376$	6.29839	−	10.0971i	0.324815	−	0.520716i
$377$	43.8983	−	15.7071i	2.26088	−	0.808954i
$378$	21.6258	+	24.5473i	1.11231	+	1.26258i
$379$	20.5435	+	11.6377i	1.05525	+	0.597790i	0.919555	−	0.392962i	$-0.128549\pi$
$379$	20.5435	+	11.6377i	1.05525	+	0.597790i	0.135691	+	0.990751i	$0.456674\pi$
$380$	−2.76160	−	2.64861i	−0.141667	−	0.135871i
$381$	−15.2205	+	15.9866i	−0.779772	+	0.819020i
$382$	23.1540	+	2.03661i	1.18466	+	0.104202i
$383$	11.9751	−	11.9751i	0.611900	−	0.611900i	−0.331541	−	0.943441i	$-0.607569\pi$
$383$	11.9751	−	11.9751i	0.611900	−	0.611900i	0.943441	+	0.331541i	$0.107569\pi$
$384$	−7.04496	+	35.3173i	−0.359511	+	1.80228i
$385$	1.58209	+	1.58209i	0.0806309	+	0.0806309i
$386$	1.83354	+	2.18720i	0.0933248	+	0.111326i
$387$	62.2348	+	59.2525i	3.16357	+	3.01197i
$388$	−0.798269	−	1.81881i	−0.0405260	−	0.0923361i
$389$	2.21389	−	3.90807i	0.112249	−	0.198147i	−0.808304	−	0.588766i	$-0.799614\pi$
$389$	2.21389	−	3.90807i	0.112249	−	0.198147i	0.920552	+	0.390619i	$0.127739\pi$
$390$	6.07986	+	0.384697i	0.307866	+	0.0194799i
$391$	−7.53864	−	21.0691i	−0.381245	−	1.06551i
$392$	7.56589	−	8.05537i	0.382135	−	0.406857i
$393$	−18.1228	−	16.4255i	−0.914174	−	0.828559i
$394$	−7.36752	−	5.07455i	−0.371170	−	0.255652i
$395$	0.829931	−	0.144007i	0.0417583	−	0.00724576i
$396$	2.67387	+	58.8213i	0.134367	+	2.95588i
$397$	−13.4772	−	10.5177i	−0.676402	−	0.527869i	0.217540	−	0.976051i	$-0.430197\pi$
$397$	−13.4772	−	10.5177i	−0.676402	−	0.527869i	−0.893942	+	0.448182i	$0.852072\pi$
$398$	−2.60548	+	4.45174i	−0.130601	+	0.223145i
$399$	16.3804	−	30.6456i	0.820048	−	1.53420i
$400$	3.68667	+	19.2705i	0.184333	+	0.963527i
$401$	18.8777	−	10.0903i	0.942706	−	0.503887i	0.0729317	−	0.997337i	$-0.476764\pi$
$401$	18.8777	−	10.0903i	0.942706	−	0.503887i	0.869774	+	0.493450i	$0.164264\pi$
$402$	24.5394	+	26.5134i	1.22392	+	1.32237i
$403$	−5.33235	−	6.18167i	−0.265623	−	0.307931i
$404$	−0.954017	+	9.33577i	−0.0474641	+	0.464472i
$405$	−2.27102	−	5.88740i	−0.112848	−	0.292547i
$406$	17.0402	−	20.1764i	0.845689	−	1.00134i
$407$	2.76003	−	18.6066i	0.136810	−	0.922297i
$408$	−3.36022	+	23.7617i	−0.166356	+	1.17638i
$409$	12.6441	+	3.16718i	0.625211	+	0.156607i	0.542623	−	0.839977i	$-0.317431\pi$
$409$	12.6441	+	3.16718i	0.625211	+	0.156607i	0.0825881	+	0.996584i	$0.473681\pi$
$410$	−0.887839	+	0.952240i	−0.0438472	+	0.0470278i
$411$	−6.23886	−	5.38168i	−0.307740	−	0.265459i
$412$	4.95756	+	12.9935i	0.244241	+	0.640142i
$413$	−5.52432	−	3.49823i	−0.271834	−	0.172137i
$414$	−82.8752	+	17.3864i	−4.07309	+	0.854493i
$415$	−2.21756	−	0.441100i	−0.108856	−	0.0216527i
$416$	−16.1646	+	18.8579i	−0.792535	+	0.924583i
$417$	17.1176	−	3.40490i	0.838252	−	0.166739i
$418$	33.3314	−	14.2158i	1.63029	−	0.695319i
$419$	−1.90524	+	1.34182i	−0.0930772	+	0.0655523i	−0.621413	−	0.783483i	$-0.713441\pi$
$419$	−1.90524	+	1.34182i	−0.0930772	+	0.0655523i	0.528336	+	0.849035i	$0.322816\pi$
$420$	3.08795	−	1.54020i	0.150676	−	0.0751540i
$421$	−2.00434	+	6.06723i	−0.0976857	+	0.295699i	−0.986790	−	0.162006i	$-0.948203\pi$
$421$	−2.00434	+	6.06723i	−0.0976857	+	0.295699i	0.889104	+	0.457705i	$0.151328\pi$
$422$	−16.3122	−	2.65529i	−0.794064	−	0.129258i
$423$	−24.1034	−	17.8763i	−1.17195	−	0.869176i
$424$	0.501391	−	5.47072i	0.0243497	−	0.265682i
$425$	3.17677	+	12.6824i	0.154096	+	0.615186i
$426$	−6.37940	+	1.83734i	−0.309083	+	0.0890193i
$427$	6.40846	+	0.157319i	0.310127	+	0.00761320i
$428$	6.09972	−	9.05692i	0.294841	−	0.437783i
$429$	−25.9388	+	51.5315i	−1.25234	+	2.48796i
$430$	4.47592	−	2.74669i	0.215848	−	0.132457i
$431$	23.7770	−	2.34183i	1.14530	−	0.112802i	0.492484	−	0.870321i	$-0.336089\pi$
$431$	23.7770	−	2.34183i	1.14530	−	0.112802i	0.652812	+	0.757520i	$0.273589\pi$
$432$	50.6054	+	14.4041i	2.43475	+	0.693020i
$433$	−1.35640	+	13.7718i	−0.0651847	+	0.661831i	0.905964	+	0.423355i	$0.139148\pi$
$433$	−1.35640	+	13.7718i	−0.0651847	+	0.661831i	−0.971148	+	0.238476i	$0.923352\pi$
$434$	−4.36997	−	1.51232i	−0.209765	−	0.0725937i
$435$	−9.06444	+	5.13494i	−0.434607	+	0.246202i
$436$	2.86897	−	11.2782i	0.137399	−	0.540128i
$437$	27.8799	+	44.0271i	1.33368	+	2.10610i
$438$	55.0475	+	0.776355i	2.63027	+	0.0370957i
$439$	−5.81287	−	12.2903i	−0.277433	−	0.586583i	0.716372	−	0.697718i	$-0.245801\pi$
$439$	−5.81287	−	12.2903i	−0.277433	−	0.586583i	−0.993805	+	0.111136i	$0.964551\pi$
$440$	3.51630	+	0.764607i	0.167633	+	0.0364512i
$441$	−18.7149	−	20.6487i	−0.891183	−	0.983269i
$442$	−10.0460	+	13.1537i	−0.477840	+	0.625656i
$443$	−13.0201	−	16.6837i	−0.618602	−	0.792666i	0.372176	−	0.928162i	$-0.378612\pi$
$443$	−13.0201	−	16.6837i	−0.618602	−	0.792666i	−0.990778	+	0.135497i	$0.956737\pi$
$444$	−25.8652	−	13.1384i	−1.22751	−	0.623520i
$445$	−1.90916	+	4.94930i	−0.0905027	+	0.234619i
$446$	9.42130	+	17.1918i	0.446111	+	0.814055i
$447$	−6.81852	−	16.4614i	−0.322505	−	0.778596i
$448$	−2.55737	+	13.8346i	−0.120824	+	0.653625i
$449$	12.1269	−	29.2769i	0.572304	−	1.38166i	−0.327285	−	0.944926i	$-0.606134\pi$
$449$	12.1269	−	29.2769i	0.572304	−	1.38166i	0.899589	−	0.436738i	$-0.143866\pi$
$450$	49.1836	−	5.36324i	2.31854	−	0.252826i
$451$	−4.99634	−	11.2716i	−0.235268	−	0.530757i
$452$	−15.7297	+	1.88163i	−0.739863	+	0.0885047i
$453$	2.17798	−	17.6586i	0.102331	−	0.829675i
$454$	−4.50110	+	16.9515i	−0.211247	+	0.795573i
$455$	2.37707	+	0.116778i	0.111439	+	0.00547463i
$456$	−4.48909	−	55.7063i	−0.210221	−	2.60869i
$457$	−9.01848	+	25.2050i	−0.421867	+	1.17904i	0.523214	+	0.852202i	$0.324733\pi$
$457$	−9.01848	+	25.2050i	−0.421867	+	1.17904i	−0.945081	+	0.326837i	$0.894017\pi$
$458$	36.0116	+	15.5150i	1.68271	+	0.724969i
$459$	34.2095	+	7.68200i	1.59676	+	0.358565i
$460$	−0.272849	+	5.16783i	−0.0127216	+	0.240951i
$461$	−21.6689	−	5.99658i	−1.00922	−	0.279289i	−0.277376	−	0.960761i	$-0.589465\pi$
$461$	−21.6689	−	5.99658i	−1.00922	−	0.279289i	−0.731844	+	0.681473i	$0.761340\pi$
$462$	1.94416	+	32.6207i	0.0904507	+	1.51765i
$463$	−4.43170	−	5.40004i	−0.205959	−	0.250961i	0.659779	−	0.751460i	$-0.270650\pi$
$463$	−4.43170	−	5.40004i	−0.205959	−	0.250961i	−0.865737	+	0.500499i	$0.833150\pi$
$464$	5.50788	−	42.1160i	0.255697	−	1.95519i
$465$	1.41009	+	1.15723i	0.0653914	+	0.0536654i
$466$	1.13970	+	7.16686i	0.0527957	+	0.331998i
$467$	5.54037	+	16.7710i	0.256378	+	0.776067i	0.994811	+	0.101740i	$0.0324411\pi$
$467$	5.54037	+	16.7710i	0.256378	+	0.776067i	−0.738433	+	0.674327i	$0.764434\pi$
$468$	44.1255	+	44.4498i	2.03970	+	2.05469i
$469$	9.73178	+	10.2216i	0.449372	+	0.471990i
$470$	−1.43392	+	1.14334i	−0.0661420	+	0.0527381i
$471$	−21.0828	−	12.6365i	−0.971442	−	0.582260i
$472$	−10.5162	+	0.0713018i	−0.484047	+	0.00328193i
$473$	7.29715	+	49.1934i	0.335523	+	2.26191i
$474$	10.4621	+	6.47302i	0.480541	+	0.297316i
$475$	−13.6895	−	27.1963i	−0.628116	−	1.24785i
$476$	−1.18168	+	9.30042i	−0.0541623	+	0.426284i
$477$	−13.6492	−	2.36836i	−0.624954	−	0.108440i
$478$	28.1531	+	27.5712i	1.28769	+	1.26108i
$479$	−11.3201	+	16.9417i	−0.517227	+	0.774085i	−0.994507	−	0.104666i	$-0.966623\pi$
$479$	−11.3201	+	16.9417i	−0.517227	+	0.774085i	0.477280	+	0.878751i	$0.341623\pi$
$480$	2.83835	−	4.76917i	0.129552	−	0.217682i
$481$	−11.1161	−	16.6364i	−0.506849	−	0.758553i
$482$	−3.35398	+	17.8327i	−0.152770	+	0.812259i
$483$	−45.8538	+	10.2968i	−2.08642	+	0.468521i
$484$	−6.99048	+	9.84892i	−0.317749	+	0.447678i
$485$	0.0225182	+	0.305271i	0.00102250	+	0.0138616i
$486$	12.7298	−	34.0555i	0.577436	−	1.54479i
$487$	−10.7474	+	6.44173i	−0.487010	+	0.291903i	−0.736455	−	0.676486i	$-0.763502\pi$
$487$	−10.7474	+	6.44173i	−0.487010	+	0.291903i	0.249445	+	0.968389i	$0.419752\pi$
$488$	8.80699	−	5.36020i	0.398674	−	0.242645i
$489$	5.84047	−	4.33159i	0.264115	−	0.195881i
$490$	−1.51316	+	0.781571i	−0.0683578	+	0.0353078i
$491$	25.2971	+	11.2134i	1.14164	+	0.506055i	0.887361	−	0.461075i	$-0.152536\pi$
$491$	25.2971	+	11.2134i	1.14164	+	0.506055i	0.254281	+	0.967130i	$0.418161\pi$
$492$	−18.9305	+	1.79453i	−0.853451	+	0.0809038i
$493$	2.08216	−	28.2272i	0.0937758	−	1.27129i
$494$	16.1152	−	35.0140i	0.725056	−	1.57535i
$495$	2.63409	−	8.68343i	0.118393	−	0.390291i
$496$	−7.22741	+	1.75423i	−0.324520	+	0.0787674i
$497$	−2.48183	+	0.752856i	−0.111325	+	0.0337702i
$498$	−19.9477	−	26.3175i	−0.893878	−	1.17932i
$499$	−27.8724	+	3.43773i	−1.24774	+	0.153894i	−0.719072	−	0.694935i	$-0.755433\pi$
$499$	−27.8724	+	3.43773i	−1.24774	+	0.153894i	−0.528667	+	0.848829i	$0.677308\pi$
$500$	0.918004	−	6.03633i	0.0410544	−	0.269953i
$501$	−9.00220	−	6.34007i	−0.402189	−	0.283253i
$502$	31.5235	+	6.73389i	1.40696	+	0.300548i
$503$	8.83461	−	0.434017i	0.393916	−	0.0193518i	0.148854	−	0.988859i	$-0.452442\pi$
$503$	8.83461	−	0.434017i	0.393916	−	0.0193518i	0.245062	+	0.969507i	$0.421192\pi$
$504$	34.2556	+	9.23024i	1.52587	+	0.411147i
$505$	0.618332	−	1.30735i	0.0275154	−	0.0581765i
$506$	−44.0025	−	21.5761i	−1.95615	−	0.959175i
$507$	5.33039	+	19.2616i	0.236731	+	0.855436i
$508$	−2.42108	+	13.6560i	−0.107418	+	0.605888i
$509$	−0.516538	−	21.0414i	−0.0228951	−	0.932644i	−0.895722	−	0.444614i	$-0.853341\pi$
$509$	−0.516538	−	21.0414i	−0.0228951	−	0.932644i	0.872827	−	0.488030i	$-0.162284\pi$
$510$	1.70921	−	3.27962i	0.0756850	−	0.145224i
$511$	21.5072			0.951423
$512$	8.57119	+	20.9412i	0.378797	+	0.925480i
$513$	−81.6513			−3.60499
$514$	−7.29829	+	14.0039i	−0.321914	+	0.617686i
$515$	−0.0525965	−	2.14254i	−0.00231768	−	0.0944117i
$516$	75.5229	+	13.3895i	3.32471	+	0.589439i
$517$	−4.63213	−	16.7384i	−0.203721	−	0.736153i
$518$	−10.1760	−	4.98969i	−0.447108	−	0.219234i
$519$	−35.5261	+	75.1136i	−1.55942	+	3.29712i
$520$	3.31755	−	1.90920i	0.145484	−	0.0837237i
$521$	17.0821	−	0.839189i	0.748380	−	0.0367655i	0.328696	−	0.944436i	$-0.393391\pi$
$521$	17.0821	−	0.839189i	0.748380	−	0.0367655i	0.419684	+	0.907670i	$0.362141\pi$
$522$	−104.744	−	22.3748i	−4.58451	−	0.979320i
$523$	−6.68053	−	4.70496i	−0.292119	−	0.205734i	0.420486	−	0.907299i	$-0.361860\pi$
$523$	−6.68053	−	4.70496i	−0.292119	−	0.205734i	−0.712605	+	0.701566i	$0.752485\pi$
$524$	−15.1931	−	2.31056i	−0.663712	−	0.100937i
$525$	27.2515	−	3.36115i	1.18935	−	0.146693i
$526$	−11.0321	−	14.5549i	−0.481020	−	0.634624i
$527$	−4.74257	+	1.43864i	−0.206590	+	0.0626683i
$528$	30.9985	+	42.4427i	1.34904	+	1.84708i
$529$	13.7823	−	45.4343i	0.599232	−	1.97540i
$530$	−0.353963	+	0.769066i	−0.0153752	+	0.0334061i
$531$	−1.95086	+	26.4471i	−0.0846599	+	1.14771i
$532$	−2.06045	−	21.7356i	−0.0893317	−	0.942356i
$533$	−11.9895	−	5.31459i	−0.519324	−	0.230200i
$534$	−68.8383	+	35.5560i	−2.97893	+	1.53866i
$535$	−1.35161	+	1.00242i	−0.0584353	+	0.0433386i
$536$	22.0555	+	5.36596i	0.952652	+	0.231774i
$537$	3.11827	−	1.86902i	0.134563	−	0.0806540i
$538$	14.4742	−	38.7224i	0.624029	−	1.66944i
$539$	−1.18647	−	16.0846i	−0.0511049	−	0.692813i
$540$	−6.61219	−	4.69314i	−0.284544	−	0.201961i
$541$	−26.9320	+	6.04778i	−1.15790	+	0.260015i	−0.755310	−	0.655367i	$-0.772514\pi$
$541$	−26.9320	+	6.04778i	−1.15790	+	0.260015i	−0.402587	+	0.915382i	$0.631889\pi$
$542$	−5.16508	+	27.4621i	−0.221859	+	1.17960i
$543$	−17.0157	−	25.4658i	−0.730214	−	1.09284i
$544$	6.48927	+	13.6104i	0.278225	+	0.583542i
$545$	−0.996365	+	1.49117i	−0.0426796	+	0.0638745i
$546$	24.8344	+	24.3211i	1.06281	+	1.04085i
$547$	−9.70067	−	1.68323i	−0.414771	−	0.0719695i	−0.0402534	−	0.999190i	$-0.512817\pi$
$547$	−9.70067	−	1.68323i	−0.414771	−	0.0719695i	−0.374517	+	0.927220i	$0.622192\pi$
$548$	−5.13555	−	0.652506i	−0.219380	−	0.0278737i
$549$	−11.6891	−	23.2223i	−0.498879	−	0.991103i
$550$	24.3497	+	15.0654i	1.03827	+	0.642391i
$551$	9.67163	+	65.2008i	0.412025	+	2.77765i
$552$	−53.0823	+	53.8070i	−2.25933	+	2.29018i
$553$	4.12243	+	2.47089i	0.175303	+	0.105073i
$554$	23.1247	−	18.4384i	0.982476	−	0.783374i
$555$	3.08279	+	3.23795i	0.130857	+	0.137443i
$556$	7.78238	−	7.72560i	0.330046	−	0.327639i
$557$	4.11556	+	12.4580i	0.174382	+	0.527862i	0.999301	−	0.0373896i	$-0.0119043\pi$
$557$	4.11556	+	12.4580i	0.174382	+	0.527862i	−0.824919	+	0.565251i	$0.808779\pi$
$558$	2.94537	+	18.5216i	0.124688	+	0.784081i
$559$	40.8918	+	33.5590i	1.72954	+	1.41940i
$560$	1.08246	−	1.87860i	0.0457422	−	0.0793851i
$561$	22.2182	+	27.0730i	0.938054	+	1.14302i
$562$	0.659064	+	11.0583i	0.0278010	+	0.466466i
$563$	−5.08598	−	1.40748i	−0.214349	−	0.0593183i	0.157884	−	0.987458i	$-0.449533\pi$
$563$	−5.08598	−	1.40748i	−0.214349	−	0.0593183i	−0.372233	+	0.928139i	$0.621408\pi$
$564$	−26.7484	−	1.41225i	−1.12631	−	0.0594665i
$565$	2.38203	+	0.534902i	0.100213	+	0.0225035i
$566$	−23.1397	−	9.96935i	−0.972633	−	0.419043i
$567$	12.1298	−	33.9005i	0.509403	−	1.42369i
$568$	−2.70302	+	3.17685i	−0.113416	+	0.133298i
$569$	23.0564	+	1.13269i	0.966577	+	0.0474849i	0.526229	−	0.850343i	$-0.323605\pi$
$569$	23.0564	+	1.13269i	0.966577	+	0.0474849i	0.440347	+	0.897828i	$0.354855\pi$
$570$	−2.21030	+	8.32414i	−0.0925791	+	0.348660i
$571$	−3.35415	+	27.1947i	−0.140367	+	1.13806i	0.742970	+	0.669325i	$0.233417\pi$
$571$	−3.35415	+	27.1947i	−0.140367	+	1.13806i	−0.883337	+	0.468739i	$0.844708\pi$
$572$	4.30543	+	35.9916i	0.180019	+	1.50489i
$573$	−21.2008	−	47.8283i	−0.885678	−	1.99806i
$574$	−7.38483	+	0.805280i	−0.308237	+	0.0336117i
$575$	−15.7582	+	38.0438i	−0.657164	+	1.58654i
$576$	54.3723	−	17.3022i	2.26551	−	0.720924i
$577$	−0.247047	−	0.596424i	−0.0102847	−	0.0248295i	0.918654	−	0.395064i	$-0.129277\pi$
$577$	−0.247047	−	0.596424i	−0.0102847	−	0.0248295i	−0.928938	+	0.370234i	$0.879277\pi$
$578$	−6.72518	−	12.2720i	−0.279731	−	0.510447i
$579$	2.31196	−	5.99354i	0.0960820	−	0.249083i
$580$	−2.96439	+	5.83592i	−0.123089	+	0.242324i
$581$	−7.93706	−	10.1704i	−0.329285	−	0.421939i
$582$	−2.71360	+	3.55303i	−0.112482	+	0.147278i
$583$	−5.38418	−	5.94052i	−0.222990	−	0.246031i
$584$	29.0977	−	18.7035i	1.20407	−	0.773956i
$585$	−4.12683	−	8.72544i	−0.170623	−	0.360753i
$586$	−29.6594	−	0.418297i	−1.22522	−	0.0172797i
$587$	3.24539	+	5.12503i	0.133952	+	0.211533i	0.905183	−	0.425022i	$-0.139734\pi$
$587$	3.24539	+	5.12503i	0.133952	+	0.211533i	−0.771231	+	0.636555i	$0.780359\pi$
$588$	−24.1068	−	6.13231i	−0.994146	−	0.252892i
$589$	10.0421	−	5.68879i	0.413779	−	0.234403i
$590$	1.53154	+	0.530022i	0.0630525	+	0.0218207i
$591$	−1.97366	+	20.0389i	−0.0811855	+	0.824291i
$592$	−18.1066	+	2.09875i	−0.744176	+	0.0862583i
$593$	−22.9091	+	2.25635i	−0.940765	+	0.0926573i	−0.556760	−	0.830674i	$-0.687956\pi$
$593$	−22.9091	+	2.25635i	−0.940765	+	0.0926573i	−0.384005	+	0.923331i	$0.625456\pi$
$594$	65.4466	−	40.1619i	2.68531	−	1.64786i
$595$	0.649592	−	1.29052i	0.0266307	−	0.0529061i
$596$	−9.28549	−	6.25366i	−0.380348	−	0.256160i
$597$	11.6066	+	0.284925i	0.475024	+	0.0116612i
$598$	−50.0930	+	14.4273i	−2.04845	+	0.589978i
$599$	5.20325	+	20.7726i	0.212599	+	0.848744i	0.978578	+	0.205878i	$0.0660049\pi$
$599$	5.20325	+	20.7726i	0.212599	+	0.848744i	−0.765979	+	0.642866i	$0.777745\pi$
$600$	33.9462	−	28.2463i	1.38585	−	1.15315i
$601$	−15.7278	−	11.6645i	−0.641551	−	0.475807i	0.225356	−	0.974277i	$-0.427646\pi$
$601$	−15.7278	−	11.6645i	−0.641551	−	0.475807i	−0.866907	+	0.498470i	$0.833896\pi$
$602$	29.5749	+	4.81420i	1.20538	+	0.196212i
$603$	17.9548	−	54.3500i	0.731177	−	2.21331i
$604$	−4.98970	−	10.0039i	−0.203028	−	0.407051i
$605$	1.52173	−	1.07172i	0.0618670	−	0.0435716i
$606$	19.4292	−	8.28656i	0.789258	−	0.336619i
$607$	−23.3104	+	4.63674i	−0.946142	+	0.188199i	−0.643967	−	0.765053i	$-0.722713\pi$
$607$	−23.3104	+	4.63674i	−0.946142	+	0.188199i	−0.302175	+	0.953253i	$0.597713\pi$
$608$	−21.6897	−	27.6148i	−0.879634	−	1.11993i
$609$	−58.3005	−	11.5967i	−2.36246	−	0.469922i
$610$	−1.55499	+	0.326221i	−0.0629596	+	0.0132083i
$611$	−15.6076	−	9.88341i	−0.631416	−	0.399840i
$612$	35.5245	−	13.5541i	1.43599	−	0.547892i
$613$	23.8820	+	20.6008i	0.964585	+	0.832057i	0.985835	−	0.167718i	$-0.0536397\pi$
$613$	23.8820	+	20.6008i	0.964585	+	0.832057i	−0.0212503	+	0.999774i	$0.506765\pi$
$614$	15.5393	−	16.6665i	0.627114	−	0.672603i
$615$	2.84258	+	0.712030i	0.114624	+	0.0287118i
$616$	12.3426	+	16.4084i	0.497299	+	0.661114i
$617$	−3.53360	+	23.8216i	−0.142257	+	0.959020i	0.794054	+	0.607848i	$0.207967\pi$
$617$	−3.53360	+	23.8216i	−0.142257	+	0.959020i	−0.936311	+	0.351173i	$0.885783\pi$
$618$	20.1972	−	23.9146i	0.812453	−	0.961986i
$619$	−9.74909	−	25.2736i	−0.391849	−	1.01583i	−0.978547	−	0.206024i	$-0.933947\pi$
$619$	−9.74909	−	25.2736i	−0.391849	−	1.01583i	0.586698	−	0.809806i	$-0.300428\pi$
$620$	1.14020	+	0.116516i	0.0457915	+	0.00467941i
$621$	72.1291	+	83.6176i	2.89444	+	3.35546i
$622$	12.2533	+	13.2390i	0.491315	+	0.530836i
$623$	−26.6941	+	14.2683i	−1.06948	+	0.571647i
$624$	54.7497	+	11.3078i	2.19174	+	0.452673i
$625$	11.1175	−	20.7993i	0.444698	−	0.831972i
$626$	22.1289	−	37.8097i	0.884451	−	1.51118i
$627$	−64.2986	−	50.1791i	−2.56784	−	2.00396i
$628$	−15.4278	+	0.701309i	−0.615636	+	0.0279853i
$629$	−11.9677	+	2.07659i	−0.477182	+	0.0827989i
$630$	−4.50264	−	3.10129i	−0.179389	−	0.123558i
$631$	36.4745	+	33.0586i	1.45203	+	1.31604i	0.860181	+	0.509989i	$0.170351\pi$
$631$	36.4745	+	33.0586i	1.45203	+	1.31604i	0.591846	+	0.806051i	$0.298399\pi$
$632$	7.72612	−	0.242090i	0.307328	−	0.00962984i
$633$	12.5320	+	35.0245i	0.498100	+	1.39210i
$634$	−8.51689	−	0.538898i	−0.338249	−	0.0214024i
$635$	1.05348	−	1.85965i	0.0418060	−	0.0737979i
$636$	−11.3227	+	4.96947i	−0.448972	+	0.197052i
$637$	−12.4249	−	11.8295i	−0.492293	−	0.468702i
$638$	−39.8226	−	47.5038i	−1.57659	−	1.88069i
$639$	7.43759	+	7.43759i	0.294226	+	0.294226i
$640$	−0.169213	−	3.48295i	−0.00668873	−	0.137676i
$641$	−7.34031	+	7.34031i	−0.289925	+	0.289925i	−0.837051	−	0.547126i	$-0.815722\pi$
$641$	−7.34031	+	7.34031i	−0.289925	+	0.289925i	0.547126	+	0.837051i	$0.315722\pi$
$642$	−24.4832	−	2.15352i	−0.966273	−	0.0849927i
$643$	16.0511	−	16.8590i	0.632992	−	0.664852i	−0.326953	−	0.945041i	$-0.606022\pi$
$643$	16.0511	−	16.8590i	0.632992	−	0.664852i	0.959945	+	0.280188i	$0.0903969\pi$
$644$	−20.4389	+	21.3108i	−0.805404	+	0.839764i
$645$	−10.2845	−	5.82612i	−0.404954	−	0.229403i
$646$	−15.4679	−	17.5575i	−0.608576	−	0.690792i
$647$	12.3364	−	4.41403i	0.484993	−	0.173533i	−0.0830282	−	0.996547i	$-0.526459\pi$
$647$	12.3364	−	4.41403i	0.484993	−	0.173533i	0.568021	+	0.823014i	$0.307709\pi$
$648$	−13.0704	−	56.4133i	−0.513455	−	2.21613i
$649$	−10.3069	+	11.3719i	−0.404580	+	0.446385i
$650$	29.9529	−	5.52008i	1.17485	−	0.216515i
$651$	1.77943	+	10.2551i	0.0697414	+	0.401930i
$652$	1.55490	−	4.29599i	0.0608944	−	0.168244i
$653$	23.5187	−	30.1365i	0.920359	−	1.17933i	−0.0630652	−	0.998009i	$-0.520088\pi$
$653$	23.5187	−	30.1365i	0.920359	−	1.17933i	0.983424	−	0.181321i	$-0.0580374\pi$
$654$	−25.3408	+	6.62948i	−0.990904	+	0.259233i
$655$	2.08864	+	1.11640i	0.0816100	+	0.0436214i
$656$	−9.29083	+	7.51161i	−0.362746	+	0.293279i
$657$	−41.1178	−	76.9260i	−1.60416	−	3.00117i
$658$	−10.4564	−	0.404300i	−0.407633	−	0.0157613i
$659$	−17.9379	+	15.4734i	−0.698762	+	0.602756i	−0.928869	−	0.370409i	$-0.879218\pi$
$659$	−17.9379	+	15.4734i	−0.698762	+	0.602756i	0.230106	+	0.973165i	$0.426093\pi$
$660$	−2.32277	−	7.75930i	−0.0904137	−	0.302030i
$661$	−27.7700	+	10.7121i	−1.08013	+	0.416652i	−0.833535	−	0.552467i	$-0.813687\pi$
$661$	−27.7700	+	10.7121i	−1.08013	+	0.416652i	−0.246595	+	0.969119i	$0.579312\pi$
$662$	−41.0444	+	3.45885i	−1.59524	+	0.134432i
$663$	36.8504	+	5.46624i	1.43115	+	0.212291i
$664$	−19.5828	−	6.85743i	−0.759961	−	0.266120i
$665$	−0.817538	+	3.26380i	−0.0317028	+	0.126565i
$666$	1.60774	+	45.9364i	0.0622986	+	1.78000i
$667$	58.2273	−	67.5016i	2.25457	−	2.61367i
$668$	−6.91541	−	0.195100i	−0.267565	−	0.00754865i
$669$	23.6068	−	37.2793i	0.912693	−	1.44130i
$670$	−2.92867	−	1.91295i	−0.113144	−	0.0739035i
$671$	2.93539	−	14.7572i	0.113320	−	0.569696i
$672$	30.0374	−	10.0270i	1.15872	−	0.386801i
$673$	−1.19777	−	6.02157i	−0.0461705	−	0.232115i	0.950809	−	0.309777i	$-0.100254\pi$
$673$	−1.19777	−	6.02157i	−0.0461705	−	0.232115i	−0.996980	+	0.0776624i	$0.975254\pi$
$674$	−16.8757	+	41.9760i	−0.650029	+	1.61685i
$675$	−37.1510	−	52.7504i	−1.42994	−	2.03036i
$676$	9.47827	+	8.23673i	0.364549	+	0.316797i
$677$	−6.01091	−	1.98574i	−0.231018	−	0.0763181i	0.195843	−	0.980635i	$-0.437256\pi$
$677$	−6.01091	−	1.98574i	−0.231018	−	0.0763181i	−0.426861	+	0.904317i	$0.640381\pi$
$678$	20.8349	+	28.9367i	0.800160	+	1.11131i
$679$	−1.04043	+	1.40285i	−0.0399279	+	0.0538365i
$680$	−0.243433	−	2.31089i	−0.00933524	−	0.0886184i
$681$	38.2938	−	9.59210i	1.46742	−	0.367570i
$682$	−5.25099	+	9.49922i	−0.201071	+	0.363744i
$683$	−0.0740497	+	3.01645i	−0.00283343	+	0.115421i	0.996615	+	0.0822109i	$0.0261981\pi$
$683$	−0.0740497	+	3.01645i	−0.00283343	+	0.115421i	−0.999448	+	0.0332103i	$0.989427\pi$
$684$	−73.8036	+	48.9241i	−2.82195	+	1.87066i
$685$	0.712605	+	0.358695i	0.0272272	+	0.0137050i
$686$	−26.3815	−	6.31624i	−1.00725	−	0.241155i
$687$	−8.65081	−	87.8332i	−0.330049	−	3.35104i
$688$	44.1993	−	19.2062i	1.68508	−	0.732230i
$689$	−8.48705	−	0.835901i	−0.323331	−	0.0318453i
$690$	10.4771	−	5.08985i	0.398858	−	0.193767i
$691$	14.8094	+	26.1422i	0.563375	+	0.994495i	0.995687	+	0.0927717i	$0.0295727\pi$
$691$	14.8094	+	26.1422i	0.563375	+	0.994495i	−0.432313	+	0.901724i	$0.642302\pi$
$692$	7.47126	+	51.6698i	0.284015	+	1.96419i
$693$	43.7429	−	27.6999i	1.66166	−	1.05223i
$694$	−5.65783	−	5.81970i	−0.214768	−	0.220913i
$695$	−1.52767	+	0.722535i	−0.0579479	+	0.0274073i
$696$	−88.9612	+	35.0109i	−3.37207	+	1.32708i
$697$	−5.89908	+	5.34661i	−0.223444	+	0.202517i
$698$	4.04023	+	30.1617i	0.152925	+	1.14164i
$699$	12.8768	−	10.0492i	0.487047	−	0.380095i
$700$	13.1046	−	11.2207i	0.495309	−	0.424104i
$701$	15.5925	+	6.01468i	0.588920	+	0.227171i	0.635961	−	0.771722i	$-0.280604\pi$
$701$	15.5925	+	6.01468i	0.588920	+	0.227171i	−0.0470408	+	0.998893i	$0.514979\pi$
$702$	22.8925	−	78.4044i	0.864023	−	2.95918i
$703$	26.1336	−	10.8249i	0.985649	−	0.408269i
$704$	30.9680	+	11.4658i	1.16715	+	0.432132i
$705$	3.81366	+	1.57967i	0.143631	+	0.0594938i
$706$	17.8683	−	22.2421i	0.672481	−	0.837093i
$707$	7.54389	−	3.34398i	0.283717	−	0.125763i
$708$	11.5917	+	20.6380i	0.435643	+	0.775625i
$709$	21.4493	+	2.64551i	0.805544	+	0.0993544i	0.514649	−	0.857401i	$-0.327922\pi$
$709$	21.4493	+	2.64551i	0.805544	+	0.0993544i	0.290895	+	0.956755i	$0.406047\pi$
$710$	0.555962	−	0.322662i	0.0208649	−	0.0121093i
$711$	0.956441	−	19.4688i	0.0358693	−	0.730137i
$712$	−23.7069	+	42.5182i	−0.888454	+	1.59344i
$713$	−14.6968	−	5.25860i	−0.550399	−	0.196936i
$714$	19.6075	−	7.79959i	0.733792	−	0.291892i
$715$	1.22393	−	5.45039i	0.0457722	−	0.203833i
$716$	0.984183	−	2.06132i	0.0367807	−	0.0770352i
$717$	23.6558	−	85.4810i	0.883441	−	3.19234i
$718$	−21.5807	+	24.3161i	−0.805383	+	0.907467i
$719$	11.5481	−	9.47728i	0.430671	−	0.353443i	−0.393946	−	0.919134i	$-0.628890\pi$
$719$	11.5481	−	9.47728i	0.430671	−	0.353443i	0.824618	+	0.565691i	$0.191390\pi$
$720$	−8.78873	−	0.280157i	−0.327537	−	0.0104408i
$721$	7.75781	−	9.45291i	0.288916	−	0.352045i
$722$	22.3570	+	16.2220i	0.832040	+	0.603720i
$723$	38.7806	−	12.8114i	1.44227	−	0.476461i
$724$	−17.7517	−	7.42924i	−0.659735	−	0.276105i
$725$	−37.7221	+	35.9144i	−1.40096	+	1.33383i
$726$	27.0133	+	3.04578i	1.00256	+	0.113040i
$727$	−13.5316	+	22.5761i	−0.501858	+	0.837299i	−0.999548	−	0.0300554i	$-0.990432\pi$
$727$	−13.5316	+	22.5761i	−0.501858	+	0.837299i	0.497690	+	0.867355i	$0.334182\pi$
$728$	21.4489	+	4.11548i	0.794950	+	0.152530i
$729$	−20.1915	+	2.99513i	−0.747835	+	0.110931i
$730$	−5.18863	+	1.22219i	−0.192040	+	0.0452353i
$731$	28.6847	−	14.4387i	1.06094	−	0.534033i
$732$	−20.1490	−	11.5119i	−0.744730	−	0.425493i
$733$	−1.46612	+	8.44946i	−0.0541524	+	0.312088i	−0.999919	−	0.0127602i	$-0.995938\pi$
$733$	−1.46612	+	8.44946i	−0.0541524	+	0.312088i	0.945766	+	0.324848i	$0.105313\pi$
$734$	0.381985	+	36.5828i	0.0140993	+	1.35030i
$735$	3.18731	+	2.12969i	0.117566	+	0.0785549i
$736$	−9.11956	+	46.6064i	−0.336151	+	1.71793i
$737$	27.5439	−	18.4042i	1.01459	−	0.677928i
$738$	16.9987	+	24.8742i	0.625732	+	0.915631i
$739$	1.23643	+	5.50606i	0.0454827	+	0.202544i	0.993174	−	0.116646i	$-0.0372143\pi$
$739$	1.23643	+	5.50606i	0.0454827	+	0.202544i	−0.947691	+	0.319190i	$0.896589\pi$
$740$	2.73852	+	0.625495i	0.100670	+	0.0229937i
$741$	−86.5215	+	6.38221i	−3.17845	+	0.234456i
$742$	−4.39554	+	2.00358i	−0.161365	+	0.0735536i
$743$	17.0049	+	28.3710i	0.623849	+	1.04083i	0.993736	+	0.111753i	$0.0356465\pi$
$743$	17.0049	+	28.3710i	0.623849	+	1.04083i	−0.369887	+	0.929077i	$0.620604\pi$
$744$	11.3257	+	12.3270i	0.415219	+	0.451928i
$745$	1.02772	+	1.38572i	0.0376528	+	0.0507690i
$746$	−3.39207	+	10.6396i	−0.124192	+	0.389545i
$747$	−21.2028	+	47.8329i	−0.775772	+	1.75011i
$748$	21.0341	+	6.46483i	0.769085	+	0.236378i
$749$	−9.57561	−	0.706339i	−0.349885	−	0.0258091i
$750$	−12.8905	+	4.76470i	−0.470695	+	0.173982i
$751$	15.8089	+	4.79557i	0.576874	+	0.174993i	0.565222	−	0.824939i	$-0.308791\pi$
$751$	15.8089	+	4.79557i	0.576874	+	0.174993i	0.0116529	+	0.999932i	$0.496291\pi$
$752$	−14.4983	+	8.54629i	−0.528700	+	0.311651i
$753$	−21.0614	−	69.4302i	−0.767521	−	2.53018i
$754$	−65.3197	−	8.99329i	−2.37880	−	0.327516i
$755$	0.210889	+	1.70984i	0.00767502	+	0.0622274i
$756$	−11.0772	−	44.9198i	−0.402874	−	1.63372i
$757$	17.9616	−	25.5035i	0.652826	−	0.926941i	−0.347115	−	0.937823i	$-0.612839\pi$
$757$	17.9616	−	25.5035i	0.652826	−	0.926941i	0.999941	+	0.0108811i	$0.00346364\pi$
$758$	−18.1575	−	28.0222i	−0.659511	−	1.01781i
$759$	5.41252	+	110.174i	0.196462	+	3.99907i
$760$	1.73225	+	5.12664i	0.0628354	+	0.185963i
$761$	23.3254	+	11.0321i	0.845545	+	0.399913i	0.800689	−	0.599081i	$-0.204467\pi$
$761$	23.3254	+	11.0321i	0.845545	+	0.399913i	0.0448559	+	0.998993i	$0.485717\pi$
$762$	29.5371	−	10.1010i	1.07002	−	0.365921i
$763$	−9.86224	+	2.72925i	−0.357037	+	0.0988055i
$764$	−27.7067	−	17.6875i	−1.00239	−	0.639912i
$765$	−5.85777	+	0.143800i	−0.211788	+	0.00519911i
$766$	−22.8451	+	7.19131i	−0.825427	+	0.259832i
$767$			16.3253i			0.589472i
$768$	31.9185	−	39.6875i	1.15176	−	1.43210i
$769$		−	26.2008i		−	0.944824i	−0.881378	−	0.472412i	$-0.843383\pi$
$769$		−	26.2008i		−	0.944824i	0.881378	−	0.472412i	$-0.156617\pi$
$770$	−0.950079	−	3.01818i	−0.0342385	−	0.108768i
$771$	35.5333	−	0.872294i	1.27970	−	0.0314149i
$772$	−0.869927	−	3.94141i	−0.0313094	−	0.141854i
$773$	3.25986	−	0.902124i	0.117249	−	0.0324471i	−0.207594	−	0.978215i	$-0.566563\pi$
$773$	3.25986	−	0.902124i	0.117249	−	0.0324471i	0.324843	+	0.945768i	$0.394688\pi$
$774$	−39.3225	−	114.986i	−1.41342	−	4.13309i
$775$	8.24433	+	3.89928i	0.296145	+	0.140066i
$776$	−0.187646	+	2.80275i	−0.00673611	+	0.100613i
$777$	1.25170	+	25.4789i	0.0449044	+	0.914049i
$778$	−5.33078	+	3.45418i	−0.191118	+	0.123838i
$779$	10.6759	−	15.1587i	0.382505	−	0.543116i
$780$	−7.37342	−	4.45623i	−0.264011	−	0.159559i
$781$	0.745165	+	6.04164i	0.0266641	+	0.216187i
$782$	−4.31635	+	31.3504i	−0.154352	+	1.12109i
$783$	40.5459	+	133.662i	1.44899	+	4.77669i
$784$	−14.7535	+	5.15733i	−0.526910	+	0.184191i
$785$	2.27751	+	0.690876i	0.0812879	+	0.0246584i
$786$	11.9924	+	32.4446i	0.427756	+	1.15726i
$787$	−29.6620	−	2.18800i	−1.05734	−	0.0779938i	−0.466290	−	0.884632i	$-0.654410\pi$
$787$	−29.6620	−	2.18800i	−1.05734	−	0.0779938i	−0.591046	+	0.806638i	$0.701285\pi$
$788$	5.92303	+	11.1795i	0.210999	+	0.398252i
$789$	−16.6585	+	37.5809i	−0.593057	+	1.33792i
$790$	−1.13495	−	0.361839i	−0.0403798	−	0.0128736i
$791$	8.29806	+	11.1886i	0.295045	+	0.397822i
$792$	35.0921	−	75.5164i	1.24694	−	2.68336i
$793$	−8.22808	−	13.7277i	−0.292188	−	0.487485i
$794$	10.0277	+	21.9991i	0.355868	+	0.780720i
$795$	1.90041	−	0.140182i	0.0674005	−	0.00497176i
$796$	6.17722	−	3.88007i	0.218946	−	0.137525i
$797$	6.86824	+	30.5857i	0.243286	+	1.08340i	0.933157	+	0.359469i	$0.117042\pi$
$797$	6.86824	+	30.5857i	0.243286	+	1.08340i	−0.689872	+	0.723932i	$0.742333\pi$
$798$	−40.5729	+	27.7270i	−1.43626	+	0.981527i
$799$	−9.32481	+	6.23064i	−0.329888	+	0.220424i
$800$	7.97164	−	26.5771i	0.281840	−	0.939643i
$801$	102.068	+	68.2000i	3.60641	+	2.40973i
$802$	−30.2698	+	0.316067i	−1.06886	+	0.0111607i
$803$	8.63036	−	49.7380i	0.304559	−	1.75522i
$804$	−13.4462	−	49.2898i	−0.474213	−	1.73832i
$805$	4.06459	−	2.04594i	0.143258	−	0.0721100i
$806$	2.64707	+	11.2377i	0.0932390	+	0.395833i
$807$	−92.0398	+	13.6528i	−3.23996	+	0.480602i
$808$	7.29828	−	11.0846i	0.256753	−	0.389955i
$809$	−11.6187	+	19.3846i	−0.408492	+	0.681527i	−0.991379	−	0.131026i	$-0.958173\pi$
$809$	−11.6187	+	19.3846i	−0.408492	+	0.681527i	0.582887	+	0.812553i	$0.301923\pi$
$810$	−0.999859	+	8.86782i	−0.0351315	+	0.311583i
$811$	−27.7849	+	26.4534i	−0.975659	+	0.928905i	−0.997486	−	0.0708572i	$-0.977427\pi$
$811$	−27.7849	+	26.4534i	−0.975659	+	0.928905i	0.0218275	+	0.999762i	$0.493052\pi$
$812$	−34.5576	+	14.1662i	−1.21273	+	0.497137i
$813$	59.7216	−	19.7293i	2.09453	−	0.691938i
$814$	−15.6226	+	21.5310i	−0.547573	+	0.754660i
$815$	−0.446660	+	0.544257i	−0.0156458	+	0.0190645i
$816$	19.7447	−	27.6037i	0.691201	−	0.966322i
$817$	−57.8108	+	47.4441i	−2.02254	+	1.65986i
$818$	−13.7871	−	12.2362i	−0.482056	−	0.427828i
$819$	14.6889	−	53.0787i	0.513270	−	1.85472i
$820$	1.73584	−	0.613932i	0.0606180	−	0.0214394i
$821$	−9.37234	+	41.7369i	−0.327097	+	1.45663i	0.485723	+	0.874113i	$0.338556\pi$
$821$	−9.37234	+	41.7369i	−0.327097	+	1.45663i	−0.812820	+	0.582515i	$0.802069\pi$
$822$	4.30682	+	10.8270i	0.150217	+	0.377634i
$823$	0.0208613	+	0.00746429i	0.000727179	+	0.000260189i	0.337253	−	0.941414i	$-0.390502\pi$
$823$	0.0208613	+	0.00746429i	0.000727179	+	0.000260189i	−0.336526	+	0.941674i	$0.609252\pi$
$824$	2.27513	−	19.5356i	0.0792578	−	0.680554i
$825$	3.16235	−	64.3710i	0.110099	−	2.24111i
$826$	4.64171	+	7.99787i	0.161506	+	0.278282i
$827$	−9.73284	−	1.20043i	−0.338444	−	0.0417431i	−0.0486038	−	0.998818i	$-0.515477\pi$
$827$	−9.73284	−	1.20043i	−0.338444	−	0.0417431i	−0.289840	+	0.957075i	$0.593602\pi$
$828$	115.299	+	32.3624i	4.00691	+	1.12467i
$829$	−35.7238	+	15.8353i	−1.24074	+	0.549982i	−0.918028	−	0.396516i	$-0.870219\pi$
$829$	−35.7238	+	15.8353i	−1.24074	+	0.549982i	−0.322711	+	0.946498i	$0.604594\pi$
$830$	2.49278	+	2.00258i	0.0865255	+	0.0695106i
$831$	−61.5024	−	25.4751i	−2.13350	−	0.883723i
$832$	32.5978	−	13.0849i	1.13012	−	0.453636i
$833$	−9.62189	+	3.98552i	−0.333379	+	0.138090i
$834$	−23.6929	−	6.91786i	−0.820418	−	0.239546i
$835$	0.994702	+	0.383699i	0.0344231	+	0.0132784i
$836$	−51.0929	−	3.95697i	−1.76709	−	0.136855i
$837$	19.2807	−	15.0468i	0.666439	−	0.520094i
$838$	3.26641	−	0.437543i	0.112836	−	0.0151147i
$839$	11.6435	−	10.5531i	0.401980	−	0.364333i	−0.445390	−	0.895337i	$-0.646935\pi$
$839$	11.6435	−	10.5531i	0.401980	−	0.364333i	0.847370	+	0.531003i	$0.178185\pi$
$840$	−4.87932	−	0.0866834i	−0.168352	−	0.00299086i
$841$	75.7144	−	35.8102i	2.61084	−	1.23484i
$842$	6.47920	−	6.29899i	0.223288	−	0.217078i
$843$	21.0659	−	13.3398i	0.725548	−	0.459448i
$844$	18.7219	+	13.9916i	0.644434	+	0.481612i
$845$	−0.953830	−	1.68375i	−0.0328128	−	0.0579226i
$846$	18.5446	+	38.1729i	0.637577	+	1.31241i
$847$	10.5688	+	1.04094i	0.363150	+	0.0357671i
$848$	−4.20445	+	6.53322i	−0.144381	+	0.224352i
$849$	5.55868	+	56.4382i	0.190773	+	1.93696i
$850$	4.30513	−	17.9815i	0.147665	−	0.616762i
$851$	−34.1715	−	17.2005i	−1.17138	−	0.589625i
$852$	9.20140	+	1.86532i	0.315235	+	0.0639048i
$853$	0.0763012	−	3.10817i	0.00261250	−	0.106422i	−0.996975	−	0.0777172i	$-0.975237\pi$
$853$	0.0763012	−	3.10817i	0.00261250	−	0.106422i	0.999588	−	0.0287043i	$-0.00913813\pi$
$854$	−7.93415	−	4.38585i	−0.271501	−	0.150081i
$855$	13.2368	−	3.31564i	0.452688	−	0.113393i
$856$	−13.5693	+	7.37168i	−0.463791	+	0.251959i
$857$	−6.18523	+	8.33981i	−0.211283	+	0.284883i	−0.896118	−	0.443816i	$-0.853624\pi$
$857$	−6.18523	+	8.33981i	−0.211283	+	0.284883i	0.684835	+	0.728699i	$0.259874\pi$
$858$	66.2111	−	47.6730i	2.26041	−	1.62753i
$859$	6.39252	+	2.11180i	0.218110	+	0.0720538i	0.420661	−	0.907218i	$-0.361798\pi$
$859$	6.39252	+	2.11180i	0.218110	+	0.0720538i	−0.202551	+	0.979272i	$0.564923\pi$
$860$	−7.40855	+	0.519223i	−0.252629	+	0.0177054i
$861$	9.62776	+	13.6704i	0.328113	+	0.465885i
$862$	−31.3497	−	12.6036i	−1.06778	−	0.429281i
$863$	−6.39347	−	32.1421i	−0.217636	−	1.09413i	−0.922857	−	0.385143i	$-0.874152\pi$
$863$	−6.39347	−	32.1421i	−0.217636	−	1.09413i	0.705221	−	0.708988i	$-0.250848\pi$
$864$	−54.0506	−	51.1400i	−1.83884	−	1.73982i
$865$	1.56960	−	7.89092i	0.0533680	−	0.268299i
$866$	10.7023	−	16.3849i	0.363679	−	0.556783i
$867$	−16.8512	+	26.6110i	−0.572297	+	0.903756i
$868$	4.49201	+	4.75282i	0.152469	+	0.161321i
$869$	7.36846	−	8.54210i	0.249958	−	0.289771i
$870$	14.7241	−	0.515331i	0.499192	−	0.0174714i
$871$	8.56184	−	34.1808i	0.290107	−	1.15817i
$872$	−10.9694	+	12.2690i	−0.371472	+	0.415482i
$873$	7.00676	+	1.03936i	0.237143	+	0.0351768i
$874$	−6.18864	−	73.4374i	−0.209334	−	2.48406i
$875$	−5.00911	+	1.93223i	−0.169339	+	0.0653212i
$876$	−68.5286	−	36.9525i	−2.31537	−	1.24851i
$877$	−19.5921	+	16.9003i	−0.661579	+	0.570682i	−0.918340	−	0.395793i	$-0.870470\pi$
$877$	−19.5921	+	16.9003i	−0.661579	+	0.570682i	0.256761	+	0.966475i	$0.417345\pi$
$878$	−0.742867	+	19.2127i	−0.0250705	+	0.648398i
$879$	31.4726	+	58.8810i	1.06154	+	1.98601i
$880$	−3.91011	−	3.25715i	−0.131810	−	0.109799i
$881$	50.0076	+	26.7296i	1.68480	+	0.900544i	0.981935	+	0.189220i	$0.0605958\pi$
$881$	50.0076	+	26.7296i	1.68480	+	0.900544i	0.702864	+	0.711324i	$0.251904\pi$
$882$	9.97473	+	38.1278i	0.335867	+	1.28383i
$883$	−25.6396	+	32.8542i	−0.862843	+	1.10563i	0.130615	+	0.991433i	$0.458305\pi$
$883$	−25.6396	+	32.8542i	−0.862843	+	1.10563i	−0.993458	+	0.114198i	$0.963570\pi$
$884$	21.1961	−	9.93019i	0.712901	−	0.333989i
$885$	−0.623637	−	3.59411i	−0.0209633	−	0.120815i
$886$	5.42430	+	29.4332i	0.182233	+	0.988827i
$887$	−17.2453	+	19.0272i	−0.579039	+	0.638871i	−0.958077	−	0.286510i	$-0.907505\pi$
$887$	−17.2453	+	19.0272i	−0.579039	+	0.638871i	0.379038	+	0.925381i	$0.376255\pi$
$888$	23.8508	+	33.3825i	0.800382	+	1.12024i
$889$	11.4823	−	4.10844i	0.385104	−	0.137792i
$890$	5.62915	−	4.95919i	0.188690	−	0.166232i
$891$	−73.5315	−	41.6551i	−2.46340	−	1.39550i
$892$	−0.578911	−	27.7183i	−0.0193834	−	0.928076i
$893$	18.0089	−	18.9153i	0.602645	−	0.632978i
$894$	−2.20787	+	25.1010i	−0.0738422	+	0.839504i
$895$	−0.248912	+	0.248912i	−0.00832023	+	0.00832023i
$896$	12.2495	−	15.6788i	0.409228	−	0.523791i
$897$	82.9672	+	82.9672i	2.77020	+	2.77020i
$898$	−34.3439	+	28.7906i	−1.14607	+	0.960755i
$899$	−14.2991	−	13.6139i	−0.476902	−	0.454049i
$900$	−65.1875	−	25.4201i	−2.17292	−	0.847338i
$901$	−2.55181	+	4.50458i	−0.0850133	+	0.150069i
$902$	−1.10106	+	17.4014i	−0.0366613	+	0.579405i
$903$	−22.7212	−	63.5014i	−0.756113	−	2.11319i
$904$	20.9567	+	7.92110i	0.697010	+	0.263452i
$905$	2.19735	+	1.99156i	0.0730423	+	0.0662017i
$906$	−14.2731	+	20.7225i	−0.474191	+	0.688458i
$907$	−25.9379	+	4.50066i	−0.861255	+	0.149442i	−0.584396	−	0.811469i	$-0.698669\pi$
$907$	−25.9379	+	4.50066i	−0.861255	+	0.149442i	−0.276859	+	0.960911i	$0.589294\pi$
$908$	16.7244	−	18.3173i	0.555017	−	0.607880i
$909$	−26.3831	−	20.5896i	−0.875073	−	0.682914i
$910$	−2.90480	−	1.70010i	−0.0962930	−	0.0563576i
$911$	−0.638760	+	1.19504i	−0.0211631	+	0.0395933i	−0.892281	−	0.451481i	$-0.850896\pi$
$911$	−0.638760	+	1.19504i	−0.0211631	+	0.0395933i	0.871118	+	0.491075i	$0.163396\pi$
$912$	−30.7796	+	72.7964i	−1.01922	+	2.41053i
$913$	−26.7052	+	14.2742i	−0.883814	+	0.472409i
$914$	27.7841	−	25.7155i	0.919017	−	0.850595i
$915$	2.33587	+	2.70792i	0.0772214	+	0.0895211i
$916$	−35.0222	−	42.9947i	−1.15717	−	1.42058i
$917$	4.86329	+	12.6076i	0.160600	+	0.416340i
$918$	−37.8818	−	31.9934i	−1.25029	−	1.05594i
$919$	−0.392757	+	2.64776i	−0.0129559	+	0.0873414i	−0.994690	−	0.102917i	$-0.967182\pi$
$919$	−0.392757	+	2.64776i	−0.0129559	+	0.0873414i	0.981734	+	0.190258i	$0.0609325\pi$
$920$	3.71986	−	6.30273i	0.122640	−	0.207795i
$921$	−49.7519	−	12.4622i	−1.63938	−	0.410644i
$922$	23.2560	+	21.6831i	0.765894	+	0.714096i
$923$	4.90306	+	4.22941i	0.161386	+	0.139213i
$924$	18.8826	−	42.1809i	0.621192	−	1.38765i
$925$	18.8841	+	11.9582i	0.620904	+	0.393183i
$926$	2.02842	+	9.66883i	0.0666581	+	0.317738i
$927$	−48.6423	−	9.67555i	−1.59762	−	0.317787i
$928$	−34.4344	+	49.2185i	−1.13036	+	1.61568i
$929$	−57.8227	+	11.5017i	−1.89710	+	0.377357i	−0.998156	−	0.0607020i	$-0.980666\pi$
$929$	−57.8227	+	11.5017i	−1.89710	+	0.377357i	−0.898946	+	0.438059i	$0.855666\pi$
$930$	−1.01206	−	2.37294i	−0.0331867	−	0.0778117i
$931$	19.8295	−	13.9655i	0.649886	−	0.457701i
$932$	3.25492	−	9.73299i	0.106618	−	0.318815i
$933$	12.7365	−	38.5538i	0.416973	−	1.26220i
$934$	4.01316	−	24.6539i	0.131315	−	0.806701i
$935$	−2.72381	−	2.02012i	−0.0890782	−	0.0660649i
$936$	−26.2863	−	84.5856i	−0.859195	−	2.76477i
$937$	−0.753343	−	3.00752i	−0.0246107	−	0.0982513i	0.956481	−	0.291794i	$-0.0942522\pi$
$937$	−0.753343	−	3.00752i	−0.0246107	−	0.0982513i	−0.981092	+	0.193543i	$0.938002\pi$
$938$	−5.52399	−	19.1798i	−0.180365	−	0.626242i
$939$	−98.5772	−	2.41993i	−3.21694	−	0.0789716i
$940$	2.54559	−	0.496668i	0.0830280	−	0.0161995i
$941$	16.7559	−	33.2882i	0.546225	−	1.08516i	−0.436433	−	0.899737i	$-0.643758\pi$
$941$	16.7559	−	33.2882i	0.546225	−	1.08516i	0.982658	−	0.185426i	$-0.0593666\pi$
$942$	18.1811	+	29.6273i	0.592371	+	0.965310i
$943$	−24.9546	+	2.45782i	−0.812635	+	0.0800375i
$944$	13.2351	+	6.78393i	0.430767	+	0.220798i
$945$	−0.698848	+	7.09552i	−0.0227335	+	0.230817i
$946$	23.0012	−	66.4637i	0.747832	−	2.16092i
$947$	30.3403	−	17.1876i	0.985927	−	0.558521i	0.0868080	−	0.996225i	$-0.472333\pi$
$947$	30.3403	−	17.1876i	0.985927	−	0.558521i	0.899119	+	0.437704i	$0.144208\pi$
$948$	−8.88998	−	14.9559i	−0.288733	−	0.485746i
$949$	−28.7276	−	45.3658i	−0.932537	−	1.47264i
$950$	−0.607217	+	43.0547i	−0.0197007	+	1.39688i
$951$	8.21261	+	17.3641i	0.266312	+	0.563069i
$952$	7.56069	−	10.8915i	0.245043	−	0.352995i
$953$	−28.6386	−	31.5978i	−0.927695	−	1.02355i	−0.999658	−	0.0261466i	$-0.991676\pi$
$953$	−28.6386	−	31.5978i	−0.927695	−	1.02355i	0.0719629	−	0.997407i	$-0.477074\pi$
$954$	15.5698	+	11.8913i	0.504090	+	0.384995i
$955$	3.11657	+	3.99351i	0.100850	+	0.129227i
$956$	−17.2868	−	52.9783i	−0.559095	−	1.71344i
$957$	−50.2134	+	130.173i	−1.62317	+	4.20791i
$958$	25.2697	−	13.8481i	0.816428	−	0.447412i
$959$	1.74200	+	4.20556i	0.0562521	+	0.135805i
$960$	−6.67674	+	4.12596i	−0.215491	+	0.133165i
$961$	10.5402	−	25.4464i	0.340007	−	0.820851i
$962$	3.06737	+	28.1294i	0.0988961	+	0.906927i
$963$	15.7804	+	35.6000i	0.508516	+	1.14719i
$964$	15.8617	−	20.1722i	0.510871	−	0.649703i
$965$	−0.0761418	+	0.617341i	−0.00245109	+	0.0198729i
$966$	64.2360	+	17.0565i	2.06676	+	0.548783i
$967$	−26.3165	−	1.29284i	−0.846280	−	0.0415751i	−0.378693	−	0.925522i	$-0.623626\pi$
$967$	−26.3165	−	1.29284i	−0.846280	−	0.0415751i	−0.467587	+	0.883947i	$0.654876\pi$
$968$	15.2041	−	7.78275i	0.488679	−	0.250147i
$969$	−17.7431	+	49.5886i	−0.569990	+	1.59302i
$970$	0.171284	−	0.397564i	0.00549959	−	0.0127650i
$971$	−56.3285	−	12.6490i	−1.80767	−	0.405925i	−0.821302	−	0.570494i	$-0.806752\pi$
$971$	−56.3285	−	12.6490i	−1.80767	−	0.405925i	−0.986366	+	0.164568i	$0.947377\pi$
$972$	−38.2233	+	34.3895i	−1.22601	+	1.10304i
$973$	−9.29315	−	2.57176i	−0.297925	−	0.0824469i
$974$	17.6888	−	1.05423i	0.566785	−	0.0337798i
$975$	−43.4901	−	52.9929i	−1.39280	−	1.69713i
$976$	−14.5484	+	0.966103i	−0.465683	+	0.0309242i
$977$	11.7993	+	9.68340i	0.377492	+	0.309799i	0.803938	−	0.594714i	$-0.202735\pi$
$977$	11.7993	+	9.68340i	0.377492	+	0.309799i	−0.426446	+	0.904513i	$0.640235\pi$
$978$	−10.1558	+	1.61501i	−0.324745	+	0.0516423i
$979$	22.2854	+	67.4589i	0.712245	+	2.15600i
$980$	2.40852	+	0.00881804i	0.0769373	+	0.000281682i
$981$	28.6166	+	30.0570i	0.913659	+	0.959646i
$982$	−24.3965	−	30.5971i	−0.778523	−	0.976392i
$983$	15.8816	+	9.51906i	0.506544	+	0.303611i	0.744451	−	0.667677i	$-0.232711\pi$
$983$	15.8816	+	9.51906i	0.506544	+	0.303611i	−0.237907	+	0.971288i	$0.576461\pi$
$984$	24.9139	+	10.1223i	0.794227	+	0.322688i
$985$	−0.286081	−	1.92860i	−0.00911530	−	0.0614504i
$986$	−21.0605	+	34.0393i	−0.670702	+	1.08403i
$987$	10.5897	+	21.0381i	0.337074	+	0.669651i
$988$	−43.0954	+	33.3788i	−1.37105	+	1.06192i
$989$	99.6555	+	17.2919i	3.16886	+	0.549849i
$990$	−8.97892	+	9.16841i	−0.285369	+	0.291391i
$991$	19.2120	−	28.7529i	0.610291	−	0.913365i	−0.389680	−	0.920950i	$-0.627415\pi$
$991$	19.2120	−	28.7529i	0.610291	−	0.913365i	0.999971	+	0.00758538i	$0.00241452\pi$
$992$	10.2106	+	2.52380i	0.324186	+	0.0801308i
$993$	51.5074	+	77.0863i	1.63454	+	2.44626i
$994$	3.60457	+	0.677949i	0.114330	+	0.0215032i
$995$	−1.09686	+	0.246307i	−0.0347727	+	0.00780847i
$996$	7.81569	+	46.0430i	0.247650	+	1.45893i
$997$	−1.14930	−	15.5807i	−0.0363987	−	0.493445i	−0.984489	−	0.175445i	$-0.943864\pi$
$997$	−1.14930	−	15.5807i	−0.0363987	−	0.493445i	0.948091	−	0.318001i	$-0.103011\pi$
$998$	37.2022	+	13.9060i	1.17761	+	0.440186i
$999$	51.4136	−	30.8161i	1.62665	−	0.974979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.117.11	✓	4032
512.477	even	128	inner	512.2.o.a.477.11	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.117.11	✓	4032	1.1	even	1	trivial
512.2.o.a.477.11	yes	4032	512.477	even	128	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25412 - 0.653597i) q^{2} +(0.0781181 + 3.18218i) q^{3} +(1.14562 + 1.63937i) q^{4} +(-0.0822049 - 0.297050i) q^{5} +(1.98189 - 4.04188i) q^{6} +(0.751910 - 1.58978i) q^{7} +(-0.365254 - 2.80474i) q^{8} +(-7.12377 + 0.349968i) q^{9} +O(q^{10})\)	\(q+(-1.25412 - 0.653597i) q^{2} +(0.0781181 + 3.18218i) q^{3} +(1.14562 + 1.63937i) q^{4} +(-0.0822049 - 0.297050i) q^{5} +(1.98189 - 4.04188i) q^{6} +(0.751910 - 1.58978i) q^{7} +(-0.365254 - 2.80474i) q^{8} +(-7.12377 + 0.349968i) q^{9} +(-0.0910565 + 0.426265i) q^{10} +(-3.37483 - 2.37683i) q^{11} +(-5.12729 + 3.77364i) q^{12} +(-4.35772 + 0.537473i) q^{13} +(-1.98206 + 1.50233i) q^{14} +(0.938845 - 0.284795i) q^{15} +(-1.37510 + 3.75621i) q^{16} +(-0.773749 + 2.55071i) q^{17} +(9.16278 + 4.21717i) q^{18} +(0.456645 - 6.19058i) q^{19} +(0.392801 - 0.475072i) q^{20} +(5.11770 + 2.26852i) q^{21} +(2.67895 + 5.18660i) q^{22} +(-6.74306 + 5.00099i) q^{23} +(8.89666 - 1.38141i) q^{24} +(4.20716 - 2.52168i) q^{25} +(5.81638 + 2.17414i) q^{26} +(-0.967658 - 13.1182i) q^{27} +(3.46765 - 0.588625i) q^{28} +(-10.3606 + 2.32656i) q^{29} +(-1.36356 - 0.256459i) q^{30} +(1.03298 + 1.54596i) q^{31} +(4.17958 - 3.81197i) q^{32} +(7.29985 - 10.9250i) q^{33} +(2.63751 - 2.69317i) q^{34} +(-0.534055 - 0.0926673i) q^{35} +(-8.73487 - 11.2776i) q^{36} +(2.04886 + 4.07038i) q^{37} +(-4.61883 + 7.46526i) q^{38} +(-2.05075 - 13.8250i) q^{39} +(-0.803124 + 0.339062i) q^{40} +(2.56194 + 1.53557i) q^{41} +(-4.93550 - 6.18991i) q^{42} +(-8.30756 - 8.72570i) q^{43} +(0.0302252 - 8.25556i) q^{44} +(0.689566 + 2.08735i) q^{45} +(11.7252 - 1.86459i) q^{46} +(3.25239 + 2.66917i) q^{47} +(-12.0603 - 4.08239i) q^{48} +(2.47872 + 3.02033i) q^{49} +(-6.92444 + 0.412690i) q^{50} +(-8.17726 - 2.26295i) q^{51} +(-5.87341 - 6.52819i) q^{52} +(1.89510 + 0.425560i) q^{53} +(-7.36047 + 17.0843i) q^{54} +(-0.428609 + 1.19788i) q^{55} +(-4.73356 - 1.52824i) q^{56} +(19.7352 + 0.969529i) q^{57} +(14.5141 + 3.85390i) q^{58} +(0.455138 - 3.69016i) q^{59} +(1.54245 + 1.21285i) q^{60} +(1.47715 + 3.33240i) q^{61} +(-0.285041 - 2.61397i) q^{62} +(-4.80006 + 11.5884i) q^{63} +(-7.73318 + 2.04889i) q^{64} +(0.517882 + 1.25028i) q^{65} +(-16.2954 + 8.93007i) q^{66} +(-2.88825 + 7.48751i) q^{67} +(-5.06799 + 1.65368i) q^{68} +(-16.4408 - 21.0669i) q^{69} +(0.609201 + 0.465273i) q^{70} +(-0.990371 - 1.09271i) q^{71} +(3.58356 + 19.8525i) q^{72} +(5.22880 + 11.0554i) q^{73} +(0.0908802 - 6.44387i) q^{74} +(8.35308 + 13.1909i) q^{75} +(10.6718 - 6.34346i) q^{76} +(-6.31620 + 3.57808i) q^{77} +(-6.46412 + 18.6786i) q^{78} +(-0.267875 + 2.71978i) q^{79} +(1.22882 + 0.0996952i) q^{80} +(20.3749 - 2.00675i) q^{81} +(-2.20933 - 3.60025i) q^{82} +(3.29826 - 6.55251i) q^{83} +(2.14399 + 10.9887i) q^{84} +(0.821295 + 0.0201617i) q^{85} +(4.71556 + 16.3728i) q^{86} +(-8.21288 - 32.7877i) q^{87} +(-5.43371 + 10.3337i) q^{88} +(-13.8242 - 10.2527i) q^{89} +(0.499486 - 3.06848i) q^{90} +(-2.42215 + 7.33194i) q^{91} +(-15.9235 - 5.32515i) q^{92} +(-4.83884 + 3.40789i) q^{93} +(-2.33432 - 5.47321i) q^{94} +(-1.87645 + 0.373250i) q^{95} +(12.4569 + 13.0024i) q^{96} +(-0.974057 - 0.193752i) q^{97} +(-1.13453 - 5.40793i) q^{98} +(24.8733 + 15.7509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

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