LMFDB - Embedded newform 600.2.b.e.251.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(251,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.b (of order $2$, degree $1$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1649659456.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{5} + 4x^{4} - 4x^{3} - 8x + 16 $ x^8 - x^7 - 2x^5 + 4x^4 - 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.5
Root			$-0.578647 + 1.29041i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.e.251.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.578647 - 1.29041i) q^{2} +(-0.751690 - 1.56044i) q^{3} +(-1.33034 - 1.49339i) q^{4} +(-2.44857 + 0.0670494i) q^{6} -4.28591i q^{7} +(-2.69688 + 0.852541i) q^{8} +(-1.86993 + 2.34593i) q^{9} +O(q^{10})$	\(q+(0.578647 - 1.29041i) q^{2} +(-0.751690 - 1.56044i) q^{3} +(-1.33034 - 1.49339i) q^{4} +(-2.44857 + 0.0670494i) q^{6} -4.28591i q^{7} +(-2.69688 + 0.852541i) q^{8} +(-1.86993 + 2.34593i) q^{9} -2.44673i q^{11} +(-1.33034 + 3.19847i) q^{12} +2.71493i q^{13} +(-5.53060 - 2.48003i) q^{14} +(-0.460411 + 3.97341i) q^{16} -1.16504i q^{17} +(1.94519 + 3.77044i) q^{18} +6.05444 q^{19} +(-6.68789 + 3.22167i) q^{21} +(-3.15729 - 1.41579i) q^{22} -7.55782 q^{23} +(3.35755 + 3.56747i) q^{24} +(3.50338 + 1.57098i) q^{26} +(5.06628 + 1.15449i) q^{27} +(-6.40052 + 5.70170i) q^{28} -0.733092 q^{29} +0.469799i q^{31} +(4.86093 + 2.89332i) q^{32} +(-3.81797 + 1.83918i) q^{33} +(-1.50338 - 0.674144i) q^{34} +(5.99101 - 0.328351i) q^{36} +1.36664i q^{37} +(3.50338 - 7.81273i) q^{38} +(4.23647 - 2.04078i) q^{39} -4.69186i q^{41} +(0.287368 + 10.4944i) q^{42} +1.50338 q^{43} +(-3.65391 + 3.25497i) q^{44} +(-4.37330 + 9.75271i) q^{46} -4.07812 q^{47} +(6.54635 - 2.26833i) q^{48} -11.3690 q^{49} +(-1.81797 + 0.875746i) q^{51} +(4.05444 - 3.61177i) q^{52} +1.00676 q^{53} +(4.42135 - 5.86955i) q^{54} +(3.65391 + 11.5586i) q^{56} +(-4.55106 - 9.44757i) q^{57} +(-0.424201 + 0.945992i) q^{58} +1.63484i q^{59} -10.9336i q^{61} +(0.606236 + 0.271848i) q^{62} +(10.0544 + 8.01433i) q^{63} +(6.54635 - 4.59841i) q^{64} +(0.164052 + 5.99099i) q^{66} +9.97632 q^{67} +(-1.73985 + 1.54989i) q^{68} +(5.68113 + 11.7935i) q^{69} -11.6359 q^{71} +(3.04297 - 7.92088i) q^{72} +9.63593 q^{73} +(1.76353 + 0.790800i) q^{74} +(-8.05444 - 9.04162i) q^{76} -10.4865 q^{77} +(-0.182034 - 6.64769i) q^{78} -3.61177i q^{79} +(-2.00676 - 8.77342i) q^{81} +(-6.05444 - 2.71493i) q^{82} -5.45095i q^{83} +(13.7084 + 5.70170i) q^{84} +(0.869925 - 1.93998i) q^{86} +(0.551058 + 1.14394i) q^{87} +(2.08594 + 6.59854i) q^{88} -7.75993i q^{89} +11.6359 q^{91} +(10.0544 + 11.2867i) q^{92} +(0.733092 - 0.353143i) q^{93} +(-2.35979 + 5.26246i) q^{94} +(0.860934 - 9.76006i) q^{96} -17.1156 q^{97} +(-6.57865 + 14.6707i) q^{98} +(5.73985 + 4.57520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{4} + q^{6} - 7 q^{8}+O(q^{10}) $ 8 * q - q^2 + q^4 + q^6 - 7 * q^8	$ 8 q - q^{2} + q^{4} + q^{6} - 7 q^{8} + q^{12} - 6 q^{14} - 7 q^{16} + 7 q^{18} - 4 q^{19} - 4 q^{21} - 14 q^{22} + 4 q^{23} - 11 q^{24} + 16 q^{26} + 12 q^{27} + 2 q^{28} - 11 q^{32} + 4 q^{33} + 13 q^{36} + 16 q^{38} + 16 q^{39} + 6 q^{42} - 30 q^{44} - 8 q^{46} - 28 q^{47} + 25 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} - 16 q^{53} + 41 q^{54} + 30 q^{56} + 4 q^{57} + 2 q^{58} + 34 q^{62} + 28 q^{63} + 25 q^{64} - 34 q^{66} + 32 q^{67} + 16 q^{68} + 20 q^{69} - 24 q^{71} + 9 q^{72} + 8 q^{73} + 32 q^{74} - 12 q^{76} - 36 q^{78} + 8 q^{81} + 4 q^{82} + 58 q^{84} - 8 q^{86} - 36 q^{87} - 14 q^{88} + 24 q^{91} + 28 q^{92} - 40 q^{94} - 43 q^{96} - 8 q^{97} - 47 q^{98} + 16 q^{99}+O(q^{100}) $ 8 * q - q^2 + q^4 + q^6 - 7 * q^8 + q^12 - 6 * q^14 - 7 * q^16 + 7 * q^18 - 4 * q^19 - 4 * q^21 - 14 * q^22 + 4 * q^23 - 11 * q^24 + 16 * q^26 + 12 * q^27 + 2 * q^28 - 11 * q^32 + 4 * q^33 + 13 * q^36 + 16 * q^38 + 16 * q^39 + 6 * q^42 - 30 * q^44 - 8 * q^46 - 28 * q^47 + 25 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 - 16 * q^53 + 41 * q^54 + 30 * q^56 + 4 * q^57 + 2 * q^58 + 34 * q^62 + 28 * q^63 + 25 * q^64 - 34 * q^66 + 32 * q^67 + 16 * q^68 + 20 * q^69 - 24 * q^71 + 9 * q^72 + 8 * q^73 + 32 * q^74 - 12 * q^76 - 36 * q^78 + 8 * q^81 + 4 * q^82 + 58 * q^84 - 8 * q^86 - 36 * q^87 - 14 * q^88 + 24 * q^91 + 28 * q^92 - 40 * q^94 - 43 * q^96 - 8 * q^97 - 47 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	0.578647	−	1.29041i	0.409165	−	0.912460i
$2$	0.578647	−	1.29041i	0.409165	−	0.912460i
$3$	−0.751690	−	1.56044i	−0.433988	−	0.900919i
$3$	−0.751690	−	1.56044i	−0.433988	−	0.900919i
$4$	−1.33034	−	1.49339i	−0.665168	−	0.746694i
$5$		0			0
$5$		0			0
$6$	−2.44857	+	0.0670494i	−0.999625	+	0.0273728i
$7$		−	4.28591i		−	1.61992i	−0.586484	−	0.809961i	$-0.699488\pi$
$7$		−	4.28591i		−	1.61992i	0.586484	−	0.809961i	$-0.300512\pi$
$8$	−2.69688	+	0.852541i	−0.953492	+	0.301419i
$9$	−1.86993	+	2.34593i	−0.623308	+	0.781976i
$10$		0			0
$11$		−	2.44673i		−	0.737717i	−0.929486	−	0.368858i	$-0.879749\pi$
$11$		−	2.44673i		−	0.737717i	0.929486	−	0.368858i	$-0.120251\pi$
$12$	−1.33034	+	3.19847i	−0.384035	+	0.923319i
$13$			2.71493i			0.752985i	0.926420	+	0.376493i	$0.122870\pi$
$13$			2.71493i			0.752985i	−0.926420	+	0.376493i	$0.877130\pi$
$14$	−5.53060	−	2.48003i	−1.47811	−	0.662815i
$15$		0			0
$16$	−0.460411	+	3.97341i	−0.115103	+	0.993354i
$17$		−	1.16504i		−	0.282563i	−0.989969	−	0.141281i	$-0.954878\pi$
$17$		−	1.16504i		−	0.282563i	0.989969	−	0.141281i	$-0.0451222\pi$
$18$	1.94519	+	3.77044i	0.458486	+	0.888701i
$19$	6.05444			1.38898			0.694492	−	0.719501i	$-0.255629\pi$
$19$	6.05444			1.38898			0.694492	+	0.719501i	$0.255629\pi$
$20$		0			0
$21$	−6.68789	+	3.22167i	−1.45942	+	0.703027i
$22$	−3.15729	−	1.41579i	−0.673137	−	0.301848i
$23$	−7.55782			−1.57591			−0.787957	−	0.615731i	$-0.788861\pi$
$23$	−7.55782			−1.57591			−0.787957	+	0.615731i	$0.788861\pi$
$24$	3.35755	+	3.56747i	0.685358	+	0.728206i
$25$		0			0
$26$	3.50338	+	1.57098i	0.687069	+	0.308095i
$27$	5.06628	+	1.15449i	0.975005	+	0.222182i
$28$	−6.40052	+	5.70170i	−1.20959	+	1.07752i
$29$	−0.733092			−0.136132			−0.0680659	−	0.997681i	$-0.521683\pi$
$29$	−0.733092			−0.136132			−0.0680659	+	0.997681i	$0.521683\pi$
$30$		0			0
$31$			0.469799i			0.0843784i	0.999110	+	0.0421892i	$0.0134332\pi$
$31$			0.469799i			0.0843784i	−0.999110	+	0.0421892i	$0.986567\pi$
$32$	4.86093	+	2.89332i	0.859300	+	0.511472i
$33$	−3.81797	+	1.83918i	−0.664623	+	0.320160i
$34$	−1.50338	−	0.674144i	−0.257827	−	0.115615i
$35$		0			0
$36$	5.99101	−	0.328351i	0.998501	−	0.0547251i
$37$			1.36664i			0.224674i	0.993670	+	0.112337i	$0.0358336\pi$
$37$			1.36664i			0.224674i	−0.993670	+	0.112337i	$0.964166\pi$
$38$	3.50338	−	7.81273i	0.568323	−	1.26739i
$39$	4.23647	−	2.04078i	0.678378	−	0.326787i
$40$		0			0
$41$		−	4.69186i		−	0.732745i	−0.930468	−	0.366372i	$-0.880600\pi$
$41$		−	4.69186i		−	0.732745i	0.930468	−	0.366372i	$-0.119400\pi$
$42$	0.287368	+	10.4944i	0.0443418	+	1.61931i
$43$	1.50338			0.229263			0.114632	−	0.993408i	$-0.463431\pi$
$43$	1.50338			0.229263			0.114632	+	0.993408i	$0.463431\pi$
$44$	−3.65391	+	3.25497i	−0.550848	+	0.490706i
$45$		0			0
$46$	−4.37330	+	9.75271i	−0.644809	+	1.43796i
$47$	−4.07812			−0.594854			−0.297427	−	0.954745i	$-0.596129\pi$
$47$	−4.07812			−0.594854			−0.297427	+	0.954745i	$0.596129\pi$
$48$	6.54635	−	2.26833i	0.944884	−	0.327406i
$49$	−11.3690			−1.62415
$50$		0			0
$51$	−1.81797	+	0.875746i	−0.254566	+	0.122629i
$52$	4.05444	−	3.61177i	0.562249	−	0.500862i
$53$	1.00676			0.138289			0.0691445	−	0.997607i	$-0.477973\pi$
$53$	1.00676			0.138289			0.0691445	+	0.997607i	$0.477973\pi$
$54$	4.42135	−	5.86955i	0.601670	−	0.798745i
$55$		0			0
$56$	3.65391	+	11.5586i	0.488275	+	1.54458i
$57$	−4.55106	−	9.44757i	−0.602802	−	1.25136i
$58$	−0.424201	+	0.945992i	−0.0557003	+	0.124215i
$59$			1.63484i			0.212837i	0.994321	+	0.106419i	$0.0339384\pi$
$59$			1.63484i			0.212837i	−0.994321	+	0.106419i	$0.966062\pi$
$60$		0			0
$61$		−	10.9336i		−	1.39990i	−0.714190	−	0.699952i	$-0.753205\pi$
$61$		−	10.9336i		−	1.39990i	0.714190	−	0.699952i	$-0.246795\pi$
$62$	0.606236	+	0.271848i	0.0769920	+	0.0345247i
$63$	10.0544	+	8.01433i	1.26674	+	1.00971i
$64$	6.54635	−	4.59841i	0.818293	−	0.574801i
$65$		0			0
$66$	0.164052	+	5.99099i	0.0201934	+	0.737440i
$67$	9.97632			1.21880			0.609401	−	0.792862i	$-0.291410\pi$
$67$	9.97632			1.21880			0.609401	+	0.792862i	$0.291410\pi$
$68$	−1.73985	+	1.54989i	−0.210988	+	0.187952i
$69$	5.68113	+	11.7935i	0.683928	+	1.41977i
$70$		0			0
$71$	−11.6359			−1.38093			−0.690465	−	0.723365i	$-0.742594\pi$
$71$	−11.6359			−1.38093			−0.690465	+	0.723365i	$0.742594\pi$
$72$	3.04297	−	7.92088i	0.358617	−	0.933485i
$73$	9.63593			1.12780			0.563900	−	0.825843i	$-0.309300\pi$
$73$	9.63593			1.12780			0.563900	+	0.825843i	$0.309300\pi$
$74$	1.76353	+	0.790800i	0.205006	+	0.0919287i
$75$		0			0
$76$	−8.05444	−	9.04162i	−0.923907	−	1.03714i
$77$	−10.4865			−1.19504
$78$	−0.182034	−	6.64769i	−0.0206113	−	0.752703i
$79$		−	3.61177i		−	0.406355i	−0.979142	−	0.203178i	$-0.934873\pi$
$79$		−	3.61177i		−	0.406355i	0.979142	−	0.203178i	$-0.0651269\pi$
$80$		0			0
$81$	−2.00676	−	8.77342i	−0.222973	−	0.974825i
$82$	−6.05444	−	2.71493i	−0.668601	−	0.299814i
$83$		−	5.45095i		−	0.598319i	−0.954203	−	0.299160i	$-0.903294\pi$
$83$		−	5.45095i		−	0.598319i	0.954203	−	0.299160i	$-0.0967063\pi$
$84$	13.7084	+	5.70170i	1.49570	+	0.622107i
$85$		0			0
$86$	0.869925	−	1.93998i	0.0938065	−	0.209194i
$87$	0.551058	+	1.14394i	0.0590796	+	0.122644i
$88$	2.08594	+	6.59854i	0.222362	+	0.703407i
$89$		−	7.75993i		−	0.822551i	−0.911511	−	0.411275i	$-0.865083\pi$
$89$		−	7.75993i		−	0.822551i	0.911511	−	0.411275i	$-0.134917\pi$
$90$		0			0
$91$	11.6359			1.21978
$92$	10.0544	+	11.2867i	1.04825	+	1.17672i
$93$	0.733092	−	0.353143i	0.0760181	−	0.0366192i
$94$	−2.35979	+	5.26246i	−0.243393	+	0.542781i
$95$		0			0
$96$	0.860934	−	9.76006i	0.0878687	−	0.996132i
$97$	−17.1156			−1.73783			−0.868915	−	0.494962i	$-0.835182\pi$
$97$	−17.1156			−1.73783			−0.868915	+	0.494962i	$0.835182\pi$
$98$	−6.57865	+	14.6707i	−0.664544	+	1.48197i
$99$	5.73985	+	4.57520i	0.576877	+	0.459825i
$100$		0			0
$101$	5.36226			0.533565			0.266783	−	0.963757i	$-0.414039\pi$
$101$	5.36226			0.533565			0.266783	+	0.963757i	$0.414039\pi$
$102$	0.0781150	+	2.85268i	0.00773454	+	0.282457i
$103$		−	13.0910i		−	1.28990i	−0.764225	−	0.644949i	$-0.776878\pi$
$103$		−	13.0910i		−	1.28990i	0.764225	−	0.644949i	$-0.223122\pi$
$104$	−2.31459	−	7.32184i	−0.226964	−	0.717965i
$105$		0			0
$106$	0.582557	−	1.29914i	0.0565830	−	0.126183i
$107$		−	8.82622i		−	0.853263i	−0.904425	−	0.426632i	$-0.859700\pi$
$107$		−	8.82622i		−	0.853263i	0.904425	−	0.426632i	$-0.140300\pi$
$108$	−5.01575	−	9.10177i	−0.482641	−	0.875818i
$109$			0.780183i			0.0747280i	0.999302	+	0.0373640i	$0.0118961\pi$
$109$			0.780183i			0.0747280i	−0.999302	+	0.0373640i	$0.988104\pi$
$110$		0			0
$111$	2.13255	−	1.02729i	0.202413	−	0.0975058i
$112$	17.0297	+	1.97328i	1.60916	+	0.186457i
$113$			2.91653i			0.274364i	0.990546	+	0.137182i	$0.0438045\pi$
$113$			2.91653i			0.274364i	−0.990546	+	0.137182i	$0.956195\pi$
$114$	−14.8247	+	0.405947i	−1.38846	+	0.0380204i
$115$		0			0
$116$	0.975259	+	1.09479i	0.0905505	+	0.101649i
$117$	−6.36902	−	5.07671i	−0.588816	−	0.469342i
$118$	2.10961	+	0.945992i	0.194206	+	0.0870856i
$119$	−4.99324			−0.457730
$120$		0			0
$121$	5.01352			0.455774
$122$	−14.1089	−	6.32669i	−1.27736	−	0.572792i
$123$	−7.32134	+	3.52682i	−0.660143	+	0.318003i
$124$	0.701592	−	0.624991i	0.0630048	−	0.0561258i
$125$		0			0
$126$	16.1598	−	8.33692i	1.43963	−	0.742712i
$127$		−	2.93762i		−	0.260672i	−0.991470	−	0.130336i	$-0.958394\pi$
$127$		−	2.93762i		−	0.260672i	0.991470	−	0.130336i	$-0.0416056\pi$
$128$	−2.14582	−	11.1083i	−0.189666	−	0.981849i
$129$	−1.13007	−	2.34593i	−0.0994975	−	0.206547i
$130$		0			0
$131$		−	7.87658i		−	0.688180i	−0.938937	−	0.344090i	$-0.888187\pi$
$131$		−	7.87658i		−	0.688180i	0.938937	−	0.344090i	$-0.111813\pi$
$132$	7.82579	+	3.25497i	0.681147	+	0.283309i
$133$		−	25.9488i		−	2.25004i
$134$	5.77276	−	12.8736i	0.498691	−	1.11211i
$135$		0			0
$136$	0.993241	+	3.14197i	0.0851697	+	0.269421i
$137$		−	2.51333i		−	0.214728i	−0.994220	−	0.107364i	$-0.965759\pi$
$137$		−	2.51333i		−	0.214728i	0.994220	−	0.107364i	$-0.0342410\pi$
$138$	18.5059	−	0.506747i	1.57532	−	0.0431372i
$139$	2.57474			0.218386			0.109193	−	0.994021i	$-0.465173\pi$
$139$	2.57474			0.218386			0.109193	+	0.994021i	$0.465173\pi$
$140$		0			0
$141$	3.06548	+	6.36364i	0.258160	+	0.535915i
$142$	−6.73309	+	15.0152i	−0.565029	+	1.26004i
$143$	6.64269			0.555490
$144$	−8.46041	−	8.51008i	−0.705034	−	0.709173i
$145$		0			0
$146$	5.57580	−	12.4343i	0.461456	−	1.02907i
$147$	8.54598	+	17.7406i	0.704860	+	1.46322i
$148$	2.04092	−	1.81809i	0.167763	−	0.149446i
$149$	−16.1224			−1.32080			−0.660399	−	0.750915i	$-0.729613\pi$
$149$	−16.1224			−1.32080			−0.660399	+	0.750915i	$0.729613\pi$
$150$		0			0
$151$		−	17.8468i		−	1.45235i	−0.687511	−	0.726174i	$-0.741297\pi$
$151$		−	17.8468i		−	1.45235i	0.687511	−	0.726174i	$-0.258703\pi$
$152$	−16.3281	+	5.16166i	−1.32438	+	0.418666i
$153$	2.73309	+	2.17853i	0.220957	+	0.176124i
$154$	−6.06795	+	13.5319i	−0.488970	+	1.09043i
$155$		0			0
$156$	−8.68361	−	3.61177i	−0.695245	−	0.289173i
$157$			23.2338i			1.85426i	0.374737	+	0.927131i	$0.377733\pi$
$157$			23.2338i			1.85426i	−0.374737	+	0.927131i	$0.622267\pi$
$158$	−4.66067	−	2.08994i	−0.370783	−	0.166266i
$159$	−0.756770	−	1.57098i	−0.0600158	−	0.124587i
$160$		0			0
$161$			32.3921i			2.55286i
$162$	−12.4825	−	2.48716i	−0.980722	−	0.195410i
$163$	−6.96956			−0.545898			−0.272949	−	0.962028i	$-0.587999\pi$
$163$	−6.96956			−0.545898			−0.272949	+	0.962028i	$0.587999\pi$
$164$	−7.00676	+	6.24175i	−0.547136	+	0.487399i
$165$		0			0
$166$	−7.03398	−	3.15417i	−0.545943	−	0.244811i
$167$	9.93540			0.768825			0.384412	−	0.923162i	$-0.374404\pi$
$167$	9.93540			0.768825			0.384412	+	0.923162i	$0.374404\pi$
$168$	15.2898	−	14.3902i	1.17964	−	1.11023i
$169$	5.62917			0.433013
$170$		0			0
$171$	−11.3213	+	14.2033i	−0.865765	+	1.08615i
$172$	−2.00000	−	2.24513i	−0.152499	−	0.171189i
$173$	−8.01352			−0.609256			−0.304628	−	0.952471i	$-0.598532\pi$
$173$	−8.01352			−0.609256			−0.304628	+	0.952471i	$0.598532\pi$
$174$	1.79503	−	0.0491534i	0.136081	−	0.00372631i
$175$		0			0
$176$	9.72187	+	1.12650i	0.732813	+	0.0849132i
$177$	2.55106	−	1.22889i	0.191749	−	0.0923690i
$178$	−10.0135	−	4.49025i	−0.750545	−	0.336559i
$179$			23.5020i			1.75663i	0.478087	+	0.878313i	$0.341330\pi$
$179$			23.5020i			1.75663i	−0.478087	+	0.878313i	$0.658670\pi$
$180$		0			0
$181$			9.92011i			0.737356i	0.929557	+	0.368678i	$0.120189\pi$
$181$			9.92011i			0.737356i	−0.929557	+	0.368678i	$0.879811\pi$
$182$	6.73309	−	15.0152i	0.499090	−	1.11300i
$183$	−17.0612	+	8.21868i	−1.26120	+	0.607542i
$184$	20.3825	−	6.44335i	1.50262	−	0.475010i
$185$		0			0
$186$	−0.0314998	−	1.15034i	−0.00230968	−	0.0843468i
$187$	−2.85053			−0.208451
$188$	5.42526	+	6.09020i	0.395678	+	0.444174i
$189$	4.94804	−	21.7136i	0.359917	−	1.57943i
$190$		0			0
$191$	22.4865			1.62706			0.813532	−	0.581521i	$-0.197542\pi$
$191$	22.4865			1.62706			0.813532	+	0.581521i	$0.197542\pi$
$192$	−12.0963	−	6.75859i	−0.872978	−	0.487759i
$193$	13.1156			0.944084			0.472042	−	0.881576i	$-0.343517\pi$
$193$	13.1156			0.944084			0.472042	+	0.881576i	$0.343517\pi$
$194$	−9.90390	+	22.0863i	−0.711059	+	1.58570i
$195$		0			0
$196$	15.1246	+	16.9784i	1.08033	+	1.21274i
$197$	24.2786			1.72978			0.864890	−	0.501961i	$-0.167388\pi$
$197$	24.2786			1.72978			0.864890	+	0.501961i	$0.167388\pi$
$198$	9.22525	−	4.75936i	0.655610	−	0.338233i
$199$			1.81809i			0.128881i	0.997922	+	0.0644404i	$0.0205262\pi$
$199$			1.81809i			0.128881i	−0.997922	+	0.0644404i	$0.979474\pi$
$200$		0			0
$201$	−7.49910	−	15.5674i	−0.528946	−	1.09804i
$202$	3.10286	−	6.91954i	0.218316	−	0.486857i
$203$			3.14197i			0.220523i
$204$	3.72633	+	1.54989i	0.260896	+	0.108514i
$205$		0			0
$206$	−16.8929	−	7.57509i	−1.17698	−	0.527781i
$207$	14.1326	−	17.7301i	0.982280	−	1.23233i
$208$	−10.7875	−	1.24998i	−0.747981	−	0.0866707i
$209$		−	14.8136i		−	1.02468i
$210$		0			0
$211$	1.06120			0.0730557			0.0365279	−	0.999333i	$-0.488370\pi$
$211$	1.06120			0.0730557			0.0365279	+	0.999333i	$0.488370\pi$
$212$	−1.33933	−	1.50348i	−0.0919854	−	0.103259i
$213$	8.74661	+	18.1571i	0.599308	+	1.24411i
$214$	−11.3895	−	5.10726i	−0.778569	−	0.349125i
$215$		0			0
$216$	−14.6474	+	1.20568i	−0.996629	+	0.0820364i
$217$	2.01352			0.136686
$218$	1.00676	+	0.451450i	0.0681863	+	0.0305761i
$219$	−7.24323	−	15.0363i	−0.489452	−	1.01606i
$220$		0			0
$221$	3.16299			0.212766
$222$	−0.0916323	−	3.34631i	−0.00614996	−	0.224590i
$223$			5.22551i			0.349926i	0.984575	+	0.174963i	$0.0559806\pi$
$223$			5.22551i			0.349926i	−0.984575	+	0.174963i	$0.944019\pi$
$224$	12.4005	−	20.8335i	0.828545	−	1.39200i
$225$		0			0
$226$	3.76353	+	1.68764i	0.250346	+	0.112260i
$227$			13.8951i			0.922248i	0.887336	+	0.461124i	$0.152554\pi$
$227$			13.8951i			0.922248i	−0.887336	+	0.461124i	$0.847446\pi$
$228$	−8.05444	+	19.3649i	−0.533418	+	1.28247i
$229$			0.233312i			0.0154177i	0.999970	+	0.00770885i	$0.00245383\pi$
$229$			0.233312i			0.0154177i	−0.999970	+	0.00770885i	$0.997546\pi$
$230$		0			0
$231$	7.88256	+	16.3635i	0.518635	+	1.07664i
$232$	1.97706	−	0.624991i	0.129801	−	0.0410327i
$233$		−	8.62188i		−	0.564838i	−0.959291	−	0.282419i	$-0.908863\pi$
$233$		−	8.62188i		−	0.564838i	0.959291	−	0.282419i	$-0.0911369\pi$
$234$	−10.2365	+	5.28106i	−0.669179	+	0.345233i
$235$		0			0
$236$	2.44144	−	2.17488i	0.158924	−	0.141573i
$237$	−5.63593	+	2.71493i	−0.366093	+	0.176353i
$238$	−2.88932	+	6.44335i	−0.187287	+	0.417660i
$239$	20.1089			1.30073			0.650367	−	0.759620i	$-0.274615\pi$
$239$	20.1089			1.30073			0.650367	+	0.759620i	$0.274615\pi$
$240$		0			0
$241$	−9.12420			−0.587741			−0.293871	−	0.955845i	$-0.594943\pi$
$241$	−9.12420			−0.587741			−0.293871	+	0.955845i	$0.594943\pi$
$242$	2.90105	−	6.46951i	0.186487	−	0.415876i
$243$	−12.1819	+	9.72631i	−0.781470	+	0.623943i
$244$	−16.3281	+	14.5454i	−1.04530	+	0.931172i
$245$		0			0
$246$	0.314586	+	11.4883i	0.0200573	+	0.732470i
$247$			16.4374i			1.04588i
$248$	−0.400523	−	1.26699i	−0.0254332	−	0.0804542i
$249$	−8.50586	+	4.09742i	−0.539037	+	0.259663i
$250$		0			0
$251$		−	13.3064i		−	0.839895i	−0.907548	−	0.419947i	$-0.862049\pi$
$251$		−	13.3064i		−	0.839895i	0.907548	−	0.419947i	$-0.137951\pi$
$252$	−1.40728	−	25.6769i	−0.0886504	−	1.61749i
$253$			18.4919i			1.16258i
$254$	−3.79075	−	1.69984i	−0.237853	−	0.106658i
$255$		0			0
$256$	−15.5760	−	3.65881i	−0.973503	−	0.228675i
$257$			30.2136i			1.88467i	0.334668	+	0.942336i	$0.391376\pi$
$257$			30.2136i			1.88467i	−0.334668	+	0.942336i	$0.608624\pi$
$258$	−3.68113	+	0.100801i	−0.229177	+	0.00627558i
$259$	5.85729			0.363954
$260$		0			0
$261$	1.37083	−	1.71978i	0.0848521	−	0.106452i
$262$	−10.1641	−	4.55776i	−0.627937	−	0.281579i
$263$	14.9286			0.920540			0.460270	−	0.887779i	$-0.347753\pi$
$263$	14.9286			0.920540			0.460270	+	0.887779i	$0.347753\pi$
$264$	8.72863	−	8.21503i	0.537210	−	0.505600i
$265$		0			0
$266$	−33.4847	−	15.0152i	−2.05308	−	0.920639i
$267$	−12.1089	+	5.83306i	−0.741051	+	0.356977i
$268$	−13.2719	−	14.8985i	−0.810708	−	0.910071i
$269$	4.85053			0.295742			0.147871	−	0.989007i	$-0.452758\pi$
$269$	4.85053			0.295742			0.147871	+	0.989007i	$0.452758\pi$
$270$		0			0
$271$			14.8802i			0.903906i	0.892042	+	0.451953i	$0.149272\pi$
$271$			14.8802i			0.903906i	−0.892042	+	0.451953i	$0.850728\pi$
$272$	4.62917	+	0.536396i	0.280685	+	0.0325238i
$273$	−8.74661	−	18.1571i	−0.529369	−	1.09892i
$274$	−3.24323	−	1.45433i	−0.195931	−	0.0878591i
$275$		0			0
$276$	10.0544	−	24.1734i	0.605206	−	1.45507i
$277$		−	19.6832i		−	1.18265i	−0.806434	−	0.591324i	$-0.798605\pi$
$277$		−	19.6832i		−	1.18265i	0.806434	−	0.591324i	$-0.201395\pi$
$278$	1.48986	−	3.32247i	0.0893560	−	0.199269i
$279$	−1.10212	−	0.878490i	−0.0659819	−	0.0525938i
$280$		0			0
$281$			2.29836i			0.137109i	0.997647	+	0.0685544i	$0.0218387\pi$
$281$			2.29836i			0.137109i	−0.997647	+	0.0685544i	$0.978161\pi$
$282$	9.98556	−	0.273435i	0.594631	−	0.0162828i
$283$	21.6123			1.28472			0.642358	−	0.766405i	$-0.277956\pi$
$283$	21.6123			1.28472			0.642358	+	0.766405i	$0.277956\pi$
$284$	15.4797	+	17.3770i	0.918551	+	1.03113i
$285$		0			0
$286$	3.84377	−	8.57182i	0.227287	−	0.506862i
$287$	−20.1089			−1.18699
$288$	−15.8771	+	5.99310i	−0.935568	+	0.353147i
$289$	15.6427			0.920158
$290$		0			0
$291$	12.8656	+	26.7079i	0.754197	+	1.56564i
$292$	−12.8190	−	14.3902i	−0.750177	−	0.842121i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$	27.8379	−	0.762287i	1.62354	−	0.0444575i
$295$		0			0
$296$	−1.16511	−	3.68566i	−0.0677209	−	0.214225i
$297$	2.82472	−	12.3958i	0.163907	−	0.719278i
$298$	−9.32917	+	20.8046i	−0.540424	+	1.20518i
$299$		−	20.5189i		−	1.18664i
$300$		0			0
$301$		−	6.44335i		−	0.371388i
$302$	−23.0297	−	10.3270i	−1.32521	−	0.594250i
$303$	−4.03076	−	8.36747i	−0.231561	−	0.480699i
$304$	−2.78753	+	24.0568i	−0.159876	+	1.37975i
$305$		0			0
$306$	4.39270	−	2.26622i	0.251114	−	0.129551i
$307$	4.98308			0.284399			0.142200	−	0.989838i	$-0.454582\pi$
$307$	4.98308			0.284399			0.142200	+	0.989838i	$0.454582\pi$
$308$	13.9505	+	15.6603i	0.794905	+	0.892331i
$309$	−20.4277	+	9.84040i	−1.16209	+	0.559801i
$310$		0			0
$311$	−11.0886			−0.628777			−0.314388	−	0.949294i	$-0.601799\pi$
$311$	−11.0886			−0.628777			−0.314388	+	0.949294i	$0.601799\pi$
$312$	−9.68541	+	9.11552i	−0.548329	+	0.516064i
$313$	−11.2583			−0.636359			−0.318180	−	0.948030i	$-0.603072\pi$
$313$	−11.2583			−0.636359			−0.318180	+	0.948030i	$0.603072\pi$
$314$	29.9813	+	13.4442i	1.69194	+	0.758699i
$315$		0			0
$316$	−5.39376	+	4.80486i	−0.303423	+	0.270295i
$317$	27.2110			1.52832			0.764161	−	0.645026i	$-0.223153\pi$
$317$	27.2110			1.52832			0.764161	+	0.645026i	$0.223153\pi$
$318$	−2.46512	+	0.0675026i	−0.138237	+	0.00378536i
$319$			1.79368i			0.100427i
$320$		0			0
$321$	−13.7728	+	6.63458i	−0.768721	+	0.370306i
$322$	41.7992	+	18.7436i	2.32938	+	1.04454i
$323$		−	7.05364i		−	0.392475i
$324$	−10.4325	+	14.6685i	−0.579581	+	0.814915i
$325$		0			0
$326$	−4.03291	+	8.99362i	−0.223362	+	0.498111i
$327$	1.21743	−	0.586455i	0.0673238	−	0.0324311i
$328$	4.00000	+	12.6534i	0.220863	+	0.698666i
$329$			17.4784i			0.963617i
$330$		0			0
$331$	−18.3195			−1.00693			−0.503467	−	0.864015i	$-0.667942\pi$
$331$	−18.3195			−1.00693			−0.503467	+	0.864015i	$0.667942\pi$
$332$	−8.14037	+	7.25159i	−0.446761	+	0.397983i
$333$	−3.20603	−	2.55551i	−0.175690	−	0.140041i
$334$	5.74909	−	12.8208i	0.314576	−	0.701522i
$335$		0			0
$336$	−9.72187	−	28.0571i	−0.530371	−	1.53064i
$337$	−2.54733			−0.138762			−0.0693810	−	0.997590i	$-0.522102\pi$
$337$	−2.54733			−0.138762			−0.0693810	+	0.997590i	$0.522102\pi$
$338$	3.25730	−	7.26396i	0.177174	−	0.395107i
$339$	4.55106	−	2.19232i	0.247180	−	0.119071i
$340$		0			0
$341$	1.14947			0.0622474
$342$	11.7770	+	22.8279i	0.636830	+	1.23439i
$343$			18.7252i			1.01107i
$344$	−4.05444	+	1.28169i	−0.218601	+	0.0691042i
$345$		0			0
$346$	−4.63699	+	10.3408i	−0.249286	+	0.555922i
$347$		−	29.3727i		−	1.57681i	−0.615156	−	0.788405i	$-0.710907\pi$
$347$		−	29.3727i		−	1.57681i	0.615156	−	0.788405i	$-0.289093\pi$
$348$	0.975259	−	2.34477i	0.0522794	−	0.125693i
$349$			23.5131i			1.25863i	0.777152	+	0.629313i	$0.216664\pi$
$349$			23.5131i			1.25863i	−0.777152	+	0.629313i	$0.783336\pi$
$350$		0			0
$351$	−3.13436	+	13.7546i	−0.167300	+	0.734165i
$352$	7.07918	−	11.8934i	0.377321	−	0.633920i
$353$			31.0677i			1.65357i	0.562522	+	0.826783i	$0.309831\pi$
$353$			31.0677i			1.65357i	−0.562522	+	0.826783i	$0.690169\pi$
$354$	−0.109615	−	4.00301i	−0.00582596	−	0.212758i
$355$		0			0
$356$	−11.5886	+	10.3233i	−0.614193	+	0.547134i
$357$	3.75337	+	7.79164i	0.198649	+	0.412377i
$358$	30.3274	+	13.5994i	1.60285	+	0.718749i
$359$	−11.3979			−0.601556			−0.300778	−	0.953694i	$-0.597246\pi$
$359$	−11.3979			−0.601556			−0.300778	+	0.953694i	$0.597246\pi$
$360$		0			0
$361$	17.6562			0.929274
$362$	12.8010	+	5.74024i	0.672808	+	0.301700i
$363$	−3.76861	−	7.82328i	−0.197801	−	0.410616i
$364$	−15.4797	−	17.3770i	−0.811357	−	0.910800i
$365$		0			0
$366$	0.733092	+	26.7717i	0.0383193	+	1.39938i
$367$			21.0209i			1.09728i	0.836059	+	0.548640i	$0.184854\pi$
$367$			21.0209i			1.09728i	−0.836059	+	0.548640i	$0.815146\pi$
$368$	3.47970	−	30.0303i	0.181392	−	1.56544i
$369$	11.0068	+	8.77342i	0.572989	+	0.456726i
$370$		0			0
$371$		−	4.31488i		−	0.224017i
$372$	−1.50264	−	0.624991i	−0.0779082	−	0.0324043i
$373$		−	10.3471i		−	0.535755i	−0.963453	−	0.267878i	$-0.913678\pi$
$373$		−	10.3471i		−	0.535755i	0.963453	−	0.267878i	$-0.0863223\pi$
$374$	−1.64945	+	3.67836i	−0.0852910	+	0.190204i
$375$		0			0
$376$	10.9982	−	3.47676i	0.567189	−	0.179300i
$377$		−	1.99029i		−	0.102505i
$378$	−25.1564	−	18.9495i	−1.29390	−	0.974658i
$379$	−17.5341			−0.900668			−0.450334	−	0.892860i	$-0.648695\pi$
$379$	−17.5341			−0.900668			−0.450334	+	0.892860i	$0.648695\pi$
$380$		0			0
$381$	−4.58397	+	2.20818i	−0.234844	+	0.113128i
$382$	13.0117	−	29.0168i	0.665737	−	1.48463i
$383$	−24.7343			−1.26386			−0.631932	−	0.775023i	$-0.717738\pi$
$383$	−24.7343			−1.26386			−0.631932	+	0.775023i	$0.717738\pi$
$384$	−15.7209	+	11.6985i	−0.802253	+	0.596984i
$385$		0			0
$386$	7.58932	−	16.9246i	0.386286	−	0.861439i
$387$	−2.81121	+	3.52682i	−0.142902	+	0.179278i
$388$	22.7695	+	25.5603i	1.15595	+	1.29763i
$389$	24.2313			1.22857			0.614287	−	0.789083i	$-0.289444\pi$
$389$	24.2313			1.22857			0.614287	+	0.789083i	$0.289444\pi$
$390$		0			0
$391$			8.80513i			0.445295i
$392$	30.6609	−	9.69256i	1.54861	−	0.489548i
$393$	−12.2909	+	5.92075i	−0.619994	+	0.298662i
$394$	14.0487	−	31.3295i	0.707765	−	1.57836i
$395$		0			0
$396$	−0.803385	−	14.6584i	−0.0403716	−	0.736611i
$397$		−	21.8856i		−	1.09840i	−0.835689	−	0.549202i	$-0.814932\pi$
$397$		−	21.8856i		−	1.09840i	0.835689	−	0.549202i	$-0.185068\pi$
$398$	2.34609	+	1.05203i	0.117599	+	0.0527335i
$399$	−40.4914	+	19.5054i	−2.02711	+	0.976493i
$400$		0			0
$401$			21.4163i			1.06948i	0.845016	+	0.534740i	$0.179591\pi$
$401$			21.4163i			1.06948i	−0.845016	+	0.534740i	$0.820409\pi$
$402$	−24.4277	+	0.668907i	−1.21835	+	0.0333620i
$403$	−1.27547			−0.0635357
$404$	−7.13362	−	8.00794i	−0.354911	−	0.398410i
$405$		0			0
$406$	4.05444	+	1.81809i	0.201218	+	0.0902302i
$407$	3.34379			0.165746
$408$	4.15623	−	3.91167i	0.205764	−	0.193657i
$409$	−21.5455			−1.06536			−0.532679	−	0.846317i	$-0.678815\pi$
$409$	−21.5455			−1.06536			−0.532679	+	0.846317i	$0.678815\pi$
$410$		0			0
$411$	−3.92188	+	1.88924i	−0.193452	+	0.0931894i
$412$	−19.5500	+	17.4155i	−0.963159	+	0.857999i
$413$	7.00676			0.344780
$414$	−14.7014	−	28.4963i	−0.722535	−	1.40052i
$415$		0			0
$416$	−7.85516	+	13.1971i	−0.385131	+	0.647040i
$417$	−1.93540	−	4.01771i	−0.0947771	−	0.196748i
$418$	−19.1156	−	8.57182i	−0.934976	−	0.419261i
$419$		−	14.6547i		−	0.715930i	−0.933735	−	0.357965i	$-0.883471\pi$
$419$		−	14.6547i		−	0.715930i	0.933735	−	0.357965i	$-0.116529\pi$
$420$		0			0
$421$			19.0967i			0.930718i	0.885122	+	0.465359i	$0.154075\pi$
$421$			19.0967i			0.930718i	−0.885122	+	0.465359i	$0.845925\pi$
$422$	0.614057	−	1.36938i	0.0298918	−	0.0666605i
$423$	7.62577	−	9.56697i	0.370778	−	0.465162i
$424$	−2.71511	+	0.858303i	−0.131857	+	0.0416829i
$425$		0			0
$426$	28.4914	−	0.780183i	1.38041	−	0.0378000i
$427$	−46.8604			−2.26774
$428$	−13.1810	+	11.7418i	−0.637126	+	0.567564i
$429$	−4.99324	−	10.3655i	−0.241076	−	0.500451i
$430$		0			0
$431$	−27.8537			−1.34166			−0.670832	−	0.741609i	$-0.734063\pi$
$431$	−27.8537			−1.34166			−0.670832	+	0.741609i	$0.734063\pi$
$432$	−6.91984	+	19.5989i	−0.332931	+	0.942951i
$433$	−24.0750			−1.15697			−0.578486	−	0.815692i	$-0.696356\pi$
$433$	−24.0750			−1.15697			−0.578486	+	0.815692i	$0.696356\pi$
$434$	1.16511	−	2.59827i	0.0559273	−	0.124721i
$435$		0			0
$436$	1.16511	−	1.03791i	0.0557989	−	0.0497067i
$437$	−45.7583			−2.18892
$438$	−23.5943	+	0.646084i	−1.12738	+	0.0308711i
$439$		−	24.6249i		−	1.17528i	−0.809122	−	0.587641i	$-0.800057\pi$
$439$		−	24.6249i		−	1.17528i	0.809122	−	0.587641i	$-0.199943\pi$
$440$		0			0
$441$	21.2592	−	26.6709i	1.01234	−	1.27004i
$442$	1.83025	−	4.08156i	0.0870562	−	0.194140i
$443$			7.61113i			0.361616i	0.983518	+	0.180808i	$0.0578712\pi$
$443$			7.61113i			0.361616i	−0.983518	+	0.180808i	$0.942129\pi$
$444$	−4.37115	−	1.81809i	−0.207446	−	0.0862826i
$445$		0			0
$446$	6.74307	+	3.02372i	0.319294	+	0.143177i
$447$	12.1190	+	25.1580i	0.573211	+	1.18993i
$448$	−19.7084	−	28.0571i	−0.931132	−	1.32557i
$449$		−	11.2946i		−	0.533026i	−0.963831	−	0.266513i	$-0.914128\pi$
$449$		−	11.2946i		−	0.533026i	0.963831	−	0.266513i	$-0.0858715\pi$
$450$		0			0
$451$	−11.4797			−0.540558
$452$	4.35551	−	3.87996i	0.204866	−	0.182498i
$453$	−27.8487	+	13.4152i	−1.30845	+	0.630302i
$454$	17.9304	+	8.04033i	0.841514	+	0.377351i
$455$		0			0
$456$	20.3281	+	21.5990i	0.951951	+	1.01147i
$457$	29.5067			1.38027			0.690133	−	0.723682i	$-0.257552\pi$
$457$	29.5067			1.38027			0.690133	+	0.723682i	$0.257552\pi$
$458$	0.301069	+	0.135005i	0.0140680	+	0.00630838i
$459$	1.34502	−	5.90240i	0.0627803	−	0.275500i
$460$		0			0
$461$	28.9508			1.34838			0.674188	−	0.738560i	$-0.264494\pi$
$461$	28.9508			1.34838			0.674188	+	0.738560i	$0.264494\pi$
$462$	25.6769	−	0.703111i	1.19460	−	0.0327117i
$463$		−	22.6025i		−	1.05043i	−0.850971	−	0.525213i	$-0.823986\pi$
$463$		−	22.6025i		−	1.05043i	0.850971	−	0.525213i	$-0.176014\pi$
$464$	0.337524	−	2.91288i	0.0156691	−	0.135227i
$465$		0			0
$466$	−11.1258	−	4.98902i	−0.515392	−	0.231112i
$467$		−	13.6141i		−	0.629984i	−0.949094	−	0.314992i	$-0.897998\pi$
$467$		−	13.6141i		−	0.629984i	0.949094	−	0.314992i	$-0.102002\pi$
$468$	0.891448	+	16.2651i	0.0412072	+	0.751857i
$469$		−	42.7576i		−	1.97436i
$470$		0			0
$471$	36.2549	−	17.4646i	1.67054	−	0.804728i
$472$	−1.39376	−	4.40896i	−0.0641532	−	0.202939i
$473$		−	3.67836i		−	0.169131i
$474$	0.242167	+	8.84367i	0.0111231	+	0.406203i
$475$		0			0
$476$	6.64269	+	7.45684i	0.304467	+	0.341784i
$477$	−1.88256	+	2.36178i	−0.0861967	+	0.108139i
$478$	11.6359	−	25.9488i	0.532215	−	1.18687i
$479$	0.411425			0.0187985			0.00939924	−	0.999956i	$-0.497008\pi$
$479$	0.411425			0.0187985			0.00939924	+	0.999956i	$0.497008\pi$
$480$		0			0
$481$	−3.71032			−0.169176
$482$	−5.27968	+	11.7740i	−0.240483	+	0.536290i
$483$	50.5459	−	24.3488i	2.29992	−	1.10791i
$484$	−6.66966	−	7.48712i	−0.303167	−	0.340324i
$485$		0			0
$486$	5.50195	+	21.3478i	0.249573	+	0.968356i
$487$		−	32.2250i		−	1.46025i	−0.683312	−	0.730126i	$-0.739461\pi$
$487$		−	32.2250i		−	1.46025i	0.683312	−	0.730126i	$-0.260539\pi$
$488$	9.32134	+	29.4866i	0.421957	+	1.33480i
$489$	5.23895	+	10.8756i	0.236913	+	0.491810i
$490$		0			0
$491$		−	14.1605i		−	0.639055i	−0.947577	−	0.319528i	$-0.896476\pi$
$491$		−	14.1605i		−	0.639055i	0.947577	−	0.319528i	$-0.103524\pi$
$492$	15.0068	+	6.24175i	0.676557	+	0.281400i
$493$			0.854079i			0.0384658i
$494$	21.2110	+	9.51142i	0.954328	+	0.427939i
$495$		0			0
$496$	−1.86671	−	0.216301i	−0.0838176	−	0.00971219i
$497$			49.8706i			2.23700i
$498$	0.365483	+	13.3470i	0.0163777	+	0.598095i
$499$	−14.6018			−0.653665			−0.326833	−	0.945082i	$-0.605981\pi$
$499$	−14.6018			−0.653665			−0.326833	+	0.945082i	$0.605981\pi$
$500$		0			0
$501$	−7.46834	−	15.5036i	−0.333661	−	0.692648i
$502$	−17.1708	−	7.69972i	−0.766371	−	0.343655i
$503$	30.2823			1.35022			0.675112	−	0.737716i	$-0.264095\pi$
$503$	30.2823			1.35022			0.675112	+	0.737716i	$0.264095\pi$
$504$	−33.9482	−	13.0419i	−1.51217	−	0.580932i
$505$		0			0
$506$	23.8622	+	10.7003i	1.06081	+	0.475686i
$507$	−4.23139	−	8.78397i	−0.187923	−	0.390110i
$508$	−4.38701	+	3.90802i	−0.194642	+	0.173391i
$509$	8.84197			0.391913			0.195957	−	0.980613i	$-0.437219\pi$
$509$	8.84197			0.391913			0.195957	+	0.980613i	$0.437219\pi$
$510$		0			0
$511$		−	41.2987i		−	1.82695i
$512$	−13.7344	+	17.9824i	−0.606980	+	0.794717i
$513$	30.6734	+	6.98979i	1.35427	+	0.308607i
$514$	38.9880	+	17.4830i	1.71969	+	0.771142i
$515$		0			0
$516$	−2.00000	+	4.80851i	−0.0880451	+	0.211683i
$517$			9.97804i			0.438834i
$518$	3.38930	−	7.55832i	0.148917	−	0.332094i
$519$	6.02368	+	12.5046i	0.264410	+	0.548890i
$520$		0			0
$521$		−	38.6076i		−	1.69143i	−0.533634	−	0.845716i	$-0.679174\pi$
$521$		−	38.6076i		−	1.69143i	0.533634	−	0.845716i	$-0.320826\pi$
$522$	−1.42601	−	2.76408i	−0.0624145	−	0.120981i
$523$	13.8674			0.606381			0.303191	−	0.952930i	$-0.401948\pi$
$523$	13.8674			0.606381			0.303191	+	0.952930i	$0.401948\pi$
$524$	−11.7628	+	10.4785i	−0.513860	+	0.457756i
$525$		0			0
$526$	8.63841	−	19.2641i	0.376653	−	0.839956i
$527$	0.547333			0.0238422
$528$	−5.54999	−	16.0171i	−0.241533	−	0.697056i
$529$	34.1206			1.48350
$530$		0			0
$531$	−3.83521	−	3.05702i	−0.166434	−	0.132663i
$532$	−38.7516	+	34.5206i	−1.68009	+	1.49666i
$533$	12.7380			0.551746
$534$	0.520299	+	19.0007i	0.0225155	+	0.822242i
$535$		0			0
$536$	−26.9050	+	8.50522i	−1.16212	+	0.367370i
$537$	36.6734	−	17.6662i	1.58258	−	0.762355i
$538$	2.80674	−	6.25919i	0.121007	−	0.269853i
$539$			27.8169i			1.19816i
$540$		0			0
$541$		−	5.19654i		−	0.223417i	−0.993741	−	0.111708i	$-0.964368\pi$
$541$		−	5.19654i		−	0.223417i	0.993741	−	0.111708i	$-0.0356323\pi$
$542$	19.2016	+	8.61036i	0.824778	+	0.369846i
$543$	15.4797	−	7.45684i	0.664298	−	0.320004i
$544$	3.37083	−	5.66317i	0.144523	−	0.242806i
$545$		0			0
$546$	−28.4914	+	0.780183i	−1.21932	+	0.0333887i
$547$	13.1393			0.561796			0.280898	−	0.959738i	$-0.409368\pi$
$547$	13.1393			0.561796			0.280898	+	0.959738i	$0.409368\pi$
$548$	−3.75337	+	3.34357i	−0.160336	+	0.142830i
$549$	25.6494	+	20.4450i	1.09469	+	0.872572i
$550$		0			0
$551$	−4.43846			−0.189085
$552$	−25.3758	−	26.9623i	−1.08007	−	1.14759i
$553$	−15.4797			−0.658264
$554$	−25.3995	−	11.3896i	−1.07912	−	0.483898i
$555$		0			0
$556$	−3.42526	−	3.84508i	−0.145264	−	0.163068i
$557$	−0.506781			−0.0214730			−0.0107365	−	0.999942i	$-0.503418\pi$
$557$	−0.506781			−0.0214730			−0.0107365	+	0.999942i	$0.503418\pi$
$558$	−1.77135	+	0.913850i	−0.0749872	+	0.0386864i
$559$			4.08156i			0.172632i
$560$		0			0
$561$	2.14271	+	4.44807i	0.0904654	+	0.187798i
$562$	2.96584	+	1.32994i	0.125106	+	0.0561001i
$563$			13.0410i			0.549612i	0.961500	+	0.274806i	$0.0886136\pi$
$563$			13.0410i			0.549612i	−0.961500	+	0.274806i	$0.911386\pi$
$564$	5.42526	−	13.0437i	0.228445	−	0.549240i
$565$		0			0
$566$	12.5059	−	27.8888i	0.525660	−	1.17225i
$567$	−37.6021	+	8.60079i	−1.57914	+	0.361199i
$568$	31.3807	−	9.92011i	1.31671	−	0.416239i
$569$			30.7683i			1.28988i	0.764235	+	0.644938i	$0.223117\pi$
$569$			30.7683i			1.28988i	−0.764235	+	0.644938i	$0.776883\pi$
$570$		0			0
$571$	27.6769			1.15824			0.579120	−	0.815242i	$-0.303396\pi$
$571$	27.6769			1.15824			0.579120	+	0.815242i	$0.303396\pi$
$572$	−8.83701	−	9.92011i	−0.369494	−	0.414781i
$573$	−16.9028	−	35.0887i	−0.706126	−	1.46585i
$574$	−11.6359	+	25.9488i	−0.485674	+	1.08308i
$575$		0			0
$576$	−1.45365	+	23.9559i	−0.0605688	+	0.998164i
$577$	33.4626			1.39307			0.696533	−	0.717525i	$-0.254725\pi$
$577$	33.4626			1.39307			0.696533	+	0.717525i	$0.254725\pi$
$578$	9.05159	−	20.1855i	0.376496	−	0.839608i
$579$	−9.85889	−	20.4661i	−0.409721	−	0.850543i
$580$		0			0
$581$	−23.3623			−0.969230
$582$	41.9089	−	1.14759i	1.73718	−	0.0475693i
$583$		−	2.46327i		−	0.102018i
$584$	−25.9870	+	8.21503i	−1.07535	+	0.339940i
$585$		0			0
$586$	3.47188	−	7.74248i	0.143422	−	0.319839i
$587$		−	28.7031i		−	1.18471i	−0.805679	−	0.592353i	$-0.798199\pi$
$587$		−	28.7031i		−	1.18471i	0.805679	−	0.592353i	$-0.201801\pi$
$588$	15.1246	−	36.3635i	0.623729	−	1.49960i
$589$			2.84437i			0.117200i
$590$		0			0
$591$	−18.2500	−	37.8853i	−0.750704	−	1.55839i
$592$	−5.43022	−	0.629215i	−0.223181	−	0.0258606i
$593$		−	44.2574i		−	1.81744i	−0.417411	−	0.908718i	$-0.637062\pi$
$593$		−	44.2574i		−	1.81744i	0.417411	−	0.908718i	$-0.362938\pi$
$594$	−14.3612	−	10.8179i	−0.589247	−	0.443862i
$595$		0			0
$596$	21.4482	+	24.0770i	0.878553	+	0.986231i
$597$	2.83701	−	1.36664i	0.116111	−	0.0559328i
$598$	−26.4779	−	11.8732i	−1.08276	−	0.485531i
$599$	24.1359			0.986166			0.493083	−	0.869982i	$-0.335870\pi$
$599$	24.1359			0.986166			0.493083	+	0.869982i	$0.335870\pi$
$600$		0			0
$601$	19.7669			0.806308			0.403154	−	0.915132i	$-0.367914\pi$
$601$	19.7669			0.806308			0.403154	+	0.915132i	$0.367914\pi$
$602$	−8.31459	−	3.72842i	−0.338877	−	0.151959i
$603$	−18.6550	+	23.4037i	−0.759689	+	0.953074i
$604$	−26.6521	+	23.7422i	−1.08446	+	0.966056i
$605$		0			0
$606$	−13.1299	+	0.359537i	−0.533365	+	0.0146052i
$607$		−	7.68877i		−	0.312078i	−0.987751	−	0.156039i	$-0.950127\pi$
$607$		−	7.68877i		−	0.312078i	0.987751	−	0.156039i	$-0.0498725\pi$
$608$	29.4302	+	17.5174i	1.19355	+	0.710426i
$609$	4.90284	−	2.36178i	0.198673	−	0.0957043i
$610$		0			0
$611$		−	11.0718i		−	0.447916i
$612$	−0.382541	−	6.97974i	−0.0154633	−	0.282139i
$613$			26.6091i			1.07473i	0.843349	+	0.537366i	$0.180581\pi$
$613$			26.6091i			1.07473i	−0.843349	+	0.537366i	$0.819419\pi$
$614$	2.88344	−	6.43024i	0.116366	−	0.259503i
$615$		0			0
$616$	28.2807	−	8.94014i	1.13946	−	0.360208i
$617$		−	25.0592i		−	1.00885i	−0.863456	−	0.504423i	$-0.831705\pi$
$617$		−	25.0592i		−	1.00885i	0.863456	−	0.504423i	$-0.168295\pi$
$618$	0.877747	+	32.0544i	0.0353082	+	1.28942i
$619$	−20.1498			−0.809889			−0.404944	−	0.914341i	$-0.632709\pi$
$619$	−20.1498			−0.809889			−0.404944	+	0.914341i	$0.632709\pi$
$620$		0			0
$621$	−38.2900	−	8.72542i	−1.53652	−	0.350139i
$622$	−6.41638	+	14.3089i	−0.257273	+	0.573734i
$623$	−33.2583			−1.33247
$624$	6.15836	+	17.7729i	0.246532	+	0.711484i
$625$		0			0
$626$	−6.51460	+	14.5279i	−0.260376	+	0.580653i
$627$	−23.1156	+	11.1352i	−0.923149	+	0.444697i
$628$	34.6971	−	30.9088i	1.38457	−	1.23340i
$629$	1.59218			0.0634845
$630$		0			0
$631$			27.8036i			1.10684i	0.832902	+	0.553421i	$0.186678\pi$
$631$			27.8036i			1.10684i	−0.832902	+	0.553421i	$0.813322\pi$
$632$	3.07918	+	9.74051i	0.122483	+	0.387457i
$633$	−0.797690	−	1.65593i	−0.0317053	−	0.0658173i
$634$	15.7455	−	35.1134i	0.625336	−	1.39453i
$635$		0			0
$636$	−1.33933	+	3.22009i	−0.0531078	+	0.127685i
$637$		−	30.8661i		−	1.22296i
$638$	2.31459	+	1.03791i	0.0916354	+	0.0410911i
$639$	21.7583	−	27.2971i	0.860746	−	1.07986i
$640$		0			0
$641$			36.3093i			1.43413i	0.697006	+	0.717065i	$0.254515\pi$
$641$			36.3093i			1.43413i	−0.697006	+	0.717065i	$0.745485\pi$
$642$	0.591793	+	21.6116i	0.0233562	+	0.852944i
$643$	−32.8571			−1.29576			−0.647878	−	0.761744i	$-0.724344\pi$
$643$	−32.8571			−1.29576			−0.647878	+	0.761744i	$0.724344\pi$
$644$	48.3740	−	43.0924i	1.90620	−	1.69808i
$645$		0			0
$646$	−9.10212	−	4.08156i	−0.358118	−	0.160587i
$647$	−17.1329			−0.673563			−0.336781	−	0.941583i	$-0.609338\pi$
$647$	−17.1329			−0.673563			−0.336781	+	0.941583i	$0.609338\pi$
$648$	12.8917	+	21.9500i	0.506434	+	0.862279i
$649$	4.00000			0.157014
$650$		0			0
$651$	−1.51354	−	3.14197i	−0.0593203	−	0.123143i
$652$	9.27186	+	10.4083i	0.363114	+	0.407619i
$653$	27.7583			1.08627			0.543134	−	0.839646i	$-0.317238\pi$
$653$	27.7583			1.08627			0.543134	+	0.839646i	$0.317238\pi$
$654$	−0.0523108	−	1.91033i	−0.00204551	−	0.0746999i
$655$		0			0
$656$	18.6427	+	2.16018i	0.727875	+	0.0843409i
$657$	−18.0185	+	22.6052i	−0.702968	+	0.881913i
$658$	22.5544	+	10.1138i	0.879263	+	0.394278i
$659$			15.3389i			0.597519i	0.954328	+	0.298760i	$0.0965729\pi$
$659$			15.3389i			0.597519i	−0.954328	+	0.298760i	$0.903427\pi$
$660$		0			0
$661$		−	38.9369i		−	1.51447i	−0.653141	−	0.757236i	$-0.726549\pi$
$661$		−	38.9369i		−	1.51447i	0.653141	−	0.757236i	$-0.273451\pi$
$662$	−10.6005	+	23.6398i	−0.412002	+	0.918787i
$663$	−2.37759	−	4.93564i	−0.0923378	−	0.191685i
$664$	4.64716	+	14.7006i	0.180345	+	0.570492i
$665$		0			0
$666$	−5.15283	+	2.65837i	−0.199668	+	0.103010i
$667$	5.54057			0.214532
$668$	−13.2174	−	14.8374i	−0.511398	−	0.574076i
$669$	8.15407	−	3.92796i	0.315255	−	0.151864i
$670$		0			0
$671$	−26.7516			−1.03273
$672$	−41.8307	−	3.68989i	−1.61366	−	0.142340i
$673$	6.78966			0.261722			0.130861	−	0.991401i	$-0.458226\pi$
$673$	6.78966			0.261722			0.130861	+	0.991401i	$0.458226\pi$
$674$	−1.47401	+	3.28711i	−0.0567766	+	0.126615i
$675$		0			0
$676$	−7.48869	−	8.40653i	−0.288027	−	0.323328i
$677$	40.6772			1.56335			0.781675	−	0.623685i	$-0.214365\pi$
$677$	40.6772			1.56335			0.781675	+	0.623685i	$0.214365\pi$
$678$	−0.195552	−	7.14133i	−0.00751011	−	0.274261i
$679$			73.3561i			2.81515i
$680$		0			0
$681$	21.6824	−	10.4448i	0.830870	−	0.400245i
$682$	0.665138	−	1.48329i	0.0254694	−	0.0567983i
$683$			8.14204i			0.311546i	0.987793	+	0.155773i	$0.0497869\pi$
$683$			8.14204i			0.311546i	−0.987793	+	0.155773i	$0.950213\pi$
$684$	36.2722	−	1.98798i	1.38690	−	0.0760123i
$685$		0			0
$686$	24.1633	+	10.8353i	0.922559	+	0.413694i
$687$	0.364069	−	0.175378i	0.0138901	−	0.00669110i
$688$	−0.692172	+	5.97355i	−0.0263888	+	0.227739i
$689$			2.73328i			0.104130i
$690$		0			0
$691$	−2.10179			−0.0799560			−0.0399780	−	0.999201i	$-0.512729\pi$
$691$	−2.10179			−0.0799560			−0.0399780	+	0.999201i	$0.512729\pi$
$692$	10.6607	+	11.9673i	0.405258	+	0.454928i
$693$	19.6089	−	24.6005i	0.744880	−	0.934495i
$694$	−37.9030	−	16.9964i	−1.43878	−	0.645176i
$695$		0			0
$696$	−2.46140	−	2.61528i	−0.0932990	−	0.0991320i
$697$	−5.46618			−0.207046
$698$	30.3416	+	13.6058i	1.14845	+	0.514986i
$699$	−13.4539	+	6.48098i	−0.508873	+	0.245133i
$700$		0			0
$701$	−20.0135			−0.755900			−0.377950	−	0.925826i	$-0.623371\pi$
$701$	−20.0135			−0.755900			−0.377950	+	0.925826i	$0.623371\pi$
$702$	15.9354	+	12.0037i	0.601443	+	0.453049i
$703$			8.27422i			0.312068i
$704$	−11.2511	−	16.0171i	−0.424040	−	0.603669i
$705$		0			0
$706$	40.0902	+	17.9772i	1.50881	+	0.676581i
$707$		−	22.9822i		−	0.864334i
$708$	−5.22897	−	2.17488i	−0.196517	−	0.0817370i
$709$		−	15.3500i		−	0.576480i	−0.957558	−	0.288240i	$-0.906930\pi$
$709$		−	15.3500i		−	0.576480i	0.957558	−	0.288240i	$-0.0930701\pi$
$710$		0			0
$711$	8.47294	+	6.75373i	0.317760	+	0.253285i
$712$	6.61566	+	20.9276i	0.247932	+	0.784295i
$713$		−	3.55066i		−	0.132973i
$714$	12.2263	−	0.334794i	0.457558	−	0.0125294i
$715$		0			0
$716$	35.0977	−	31.2656i	1.31166	−	1.16845i
$717$	−15.1156	−	31.3786i	−0.564504	−	1.17186i
$718$	−6.59533	+	14.7080i	−0.246136	+	0.548896i
$719$	5.77864			0.215507			0.107754	−	0.994178i	$-0.465634\pi$
$719$	5.77864			0.215507			0.107754	+	0.994178i	$0.465634\pi$
$720$		0			0
$721$	−56.1070			−2.08953
$722$	10.2167	−	22.7838i	0.380226	−	0.847926i
$723$	6.85856	+	14.2377i	0.255073	+	0.529507i
$724$	14.8146	−	13.1971i	0.550579	−	0.490466i
$725$		0			0
$726$	−12.2760	+	0.336154i	−0.455604	+	0.0124758i
$727$			25.0657i			0.929636i	0.885406	+	0.464818i	$0.153880\pi$
$727$			25.0657i			0.929636i	−0.885406	+	0.464818i	$0.846120\pi$
$728$	−31.3807	+	9.92011i	−1.16305	+	0.367664i
$729$	24.3343	+	11.6979i	0.901271	+	0.433257i
$730$		0			0
$731$		−	1.75149i		−	0.0647813i
$732$	34.9708	+	14.5454i	1.29256	+	0.537612i
$733$			14.9596i			0.552546i	0.961079	+	0.276273i	$0.0890994\pi$
$733$			14.9596i			0.552546i	−0.961079	+	0.276273i	$0.910901\pi$
$734$	27.1256	+	12.1636i	1.00122	+	0.448968i
$735$		0			0
$736$	−36.7380	−	21.8672i	−1.35418	−	0.806036i
$737$		−	24.4094i		−	0.899130i
$738$	17.6904	−	9.12656i	0.651191	−	0.335953i
$739$	9.76476			0.359202			0.179601	−	0.983739i	$-0.442519\pi$
$739$	9.76476			0.359202			0.179601	+	0.983739i	$0.442519\pi$
$740$		0			0
$741$	25.6494	−	12.3558i	0.942256	−	0.453901i
$742$	−5.56798	−	2.49679i	−0.204407	−	0.0916600i
$743$	13.6457			0.500613			0.250307	−	0.968167i	$-0.419469\pi$
$743$	13.6457			0.500613			0.250307	+	0.968167i	$0.419469\pi$
$744$	−1.67599	+	1.57738i	−0.0614449	+	0.0578294i
$745$		0			0
$746$	−13.3521	−	5.98734i	−0.488855	−	0.219212i
$747$	12.7875	+	10.1929i	0.467871	+	0.372937i
$748$	3.79216	+	4.25694i	0.138655	+	0.155649i
$749$	−37.8284			−1.38222
$750$		0			0
$751$			36.7841i			1.34227i	0.741335	+	0.671135i	$0.234193\pi$
$751$			36.7841i			1.34227i	−0.741335	+	0.671135i	$0.765807\pi$
$752$	1.87761	−	16.2040i	0.0684693	−	0.590901i
$753$	−20.7639	+	10.0023i	−0.756677	+	0.364504i
$754$	−2.56830	−	1.15168i	−0.0935319	−	0.0419415i
$755$		0			0
$756$	−39.0094	+	21.4971i	−1.41876	+	0.781840i
$757$			10.1994i			0.370702i	0.982672	+	0.185351i	$0.0593422\pi$
$757$			10.1994i			0.370702i	−0.982672	+	0.185351i	$0.940658\pi$
$758$	−10.1461	+	22.6263i	−0.368522	+	0.821824i
$759$	28.8555	−	13.9002i	1.04739	−	0.504545i
$760$		0			0
$761$		−	28.0668i		−	1.01742i	−0.860938	−	0.508710i	$-0.830123\pi$
$761$		−	28.0668i		−	1.01742i	0.860938	−	0.508710i	$-0.169877\pi$
$762$	0.196966	+	7.19298i	0.00713532	+	0.260574i
$763$	3.34379			0.121053
$764$	−29.9146	−	33.5810i	−1.08227	−	1.21492i
$765$		0			0
$766$	−14.3124	+	31.9175i	−0.517129	+	1.15323i
$767$	−4.43846			−0.160263
$768$	5.99901	+	27.0557i	0.216471	+	0.976289i
$769$	16.3302			0.588883			0.294442	−	0.955669i	$-0.404866\pi$
$769$	16.3302			0.588883			0.294442	+	0.955669i	$0.404866\pi$
$770$		0			0
$771$	47.1464	−	22.7112i	1.69794	−	0.817925i
$772$	−17.4482	−	19.5867i	−0.627975	−	0.704941i
$773$	−42.5099			−1.52897			−0.764487	−	0.644639i	$-0.777008\pi$
$773$	−42.5099			−1.52897			−0.764487	+	0.644639i	$0.777008\pi$
$774$	2.92436	+	5.66840i	0.105114	+	0.203747i
$775$		0			0
$776$	46.1588	−	14.5918i	1.65701	−	0.523814i
$777$	−4.40286	−	9.13993i	−0.157952	−	0.327893i
$778$	14.0213	−	31.2684i	0.502689	−	1.12103i
$779$		−	28.4065i		−	1.01777i
$780$		0			0
$781$			28.4700i			1.01874i
$782$	11.3623	+	5.09506i	0.406314	+	0.182199i
$783$	−3.71405	−	0.846347i	−0.132729	−	0.0302460i
$784$	5.23442	−	45.1738i	0.186944	−	1.61335i
$785$		0			0
$786$	0.528120	+	19.2864i	0.0188374	+	0.687922i
$787$	−27.9997			−0.998083			−0.499042	−	0.866578i	$-0.666315\pi$
$787$	−27.9997			−0.998083			−0.499042	+	0.866578i	$0.666315\pi$
$788$	−32.2987	−	36.2574i	−1.15059	−	1.29162i
$789$	−11.2217	−	23.2952i	−0.399503	−	0.829331i
$790$		0			0
$791$	12.5000			0.444448
$792$	−19.3802	−	7.44532i	−0.688647	−	0.264558i
$793$	29.6839			1.05411
$794$	−28.2414	−	12.6640i	−1.00225	−	0.449429i
$795$		0			0
$796$	2.71511	−	2.41867i	0.0962345	−	0.0857274i
$797$	−1.92561			−0.0682086			−0.0341043	−	0.999418i	$-0.510858\pi$
$797$	−1.92561			−0.0682086			−0.0341043	+	0.999418i	$0.510858\pi$
$798$	1.73985	+	63.5374i	0.0615900	+	2.24920i
$799$			4.75115i			0.168084i
$800$		0			0
$801$	18.2042	+	14.5105i	0.643215	+	0.512703i
$802$	27.6359	+	12.3925i	0.975859	+	0.437594i
$803$		−	23.5765i		−	0.831997i
$804$	−13.2719	+	31.9090i	−0.468063	+	1.12534i
$805$		0			0
$806$	−0.738047	+	1.64588i	−0.0259966	+	0.0579738i
$807$	−3.64609	−	7.56894i	−0.128349	−	0.266439i
$808$	−14.4614	+	4.57155i	−0.508750	+	0.160827i
$809$		−	30.3334i		−	1.06647i	−0.845968	−	0.533233i	$-0.820977\pi$
$809$		−	30.3334i		−	1.06647i	0.845968	−	0.533233i	$-0.179023\pi$
$810$		0			0
$811$	7.56798			0.265748			0.132874	−	0.991133i	$-0.457579\pi$
$811$	7.56798			0.265748			0.132874	+	0.991133i	$0.457579\pi$
$812$	4.69217	−	4.17987i	0.164663	−	0.146685i
$813$	23.2196	−	11.1853i	0.814345	−	0.392284i
$814$	1.93487	−	4.31488i	0.0678173	−	0.151236i
$815$		0			0
$816$	−2.64269	−	7.62673i	−0.0925127	−	0.266989i
$817$	9.10212			0.318443
$818$	−12.4672	+	27.8027i	−0.435907	+	0.972097i
$819$	−21.7583	+	27.2971i	−0.760297	+	0.953836i
$820$		0			0
$821$	28.8505			1.00689			0.503445	−	0.864027i	$-0.332066\pi$
$821$	28.8505			1.00689			0.503445	+	0.864027i	$0.332066\pi$
$822$	0.168517	+	6.15406i	0.00587771	+	0.214647i
$823$			15.3789i			0.536076i	0.963408	+	0.268038i	$0.0863752\pi$
$823$			15.3789i			0.536076i	−0.963408	+	0.268038i	$0.913625\pi$
$824$	11.1606	+	35.3050i	0.388800	+	1.22991i
$825$		0			0
$826$	4.05444	−	9.04162i	0.141072	−	0.314598i
$827$			48.0070i			1.66937i	0.550731	+	0.834683i	$0.314349\pi$
$827$			48.0070i			1.66937i	−0.550731	+	0.834683i	$0.685651\pi$
$828$	−45.2789	+	2.48161i	−1.57355	+	0.0862421i
$829$			19.0600i			0.661982i	0.943634	+	0.330991i	$0.107383\pi$
$829$			19.0600i			0.661982i	−0.943634	+	0.330991i	$0.892617\pi$
$830$		0			0
$831$	−30.7144	+	14.7956i	−1.06547	+	0.513255i
$832$	12.4843	+	17.7729i	0.432816	+	0.616163i
$833$			13.2453i			0.458923i
$834$	−6.30443	+	0.172635i	−0.218304	+	0.00597785i
$835$		0			0
$836$	−22.1224	+	19.7070i	−0.765119	+	0.681582i
$837$	−0.542379	+	2.38013i	−0.0187473	+	0.0822694i
$838$	−18.9107	−	8.47991i	−0.653258	−	0.292934i
$839$	−56.8469			−1.96257			−0.981287	−	0.192552i	$-0.938324\pi$
$839$	−56.8469			−1.96257			−0.981287	+	0.192552i	$0.938324\pi$
$840$		0			0
$841$	−28.4626			−0.981468
$842$	24.6427	+	11.0503i	0.849243	+	0.380817i
$843$	3.58645	−	1.72766i	0.123524	−	0.0595036i
$844$	−1.41175	−	1.58478i	−0.0485943	−	0.0545502i
$845$		0			0
$846$	−7.93272	−	15.3763i	−0.272733	−	0.528648i
$847$		−	21.4875i		−	0.738319i
$848$	−0.463523	+	4.00027i	−0.0159174	+	0.137370i
$849$	−16.2457	−	33.7246i	−0.557551	−	1.15742i
$850$		0			0
$851$		−	10.3288i		−	0.354067i
$852$	15.4797	−	37.2172i	0.530326	−	1.27504i
$853$			29.3057i			1.00341i	0.865039	+	0.501704i	$0.167293\pi$
$853$			29.3057i			1.00341i	−0.865039	+	0.501704i	$0.832707\pi$
$854$	−27.1156	+	60.4694i	−0.927878	+	2.06922i
$855$		0			0
$856$	7.52472	+	23.8033i	0.257190	+	0.813580i
$857$		−	30.9833i		−	1.05837i	−0.848507	−	0.529185i	$-0.822498\pi$
$857$		−	30.9833i		−	1.05837i	0.848507	−	0.529185i	$-0.177502\pi$
$858$	−16.2651	+	0.445389i	−0.555281	+	0.0152053i
$859$	−1.13559			−0.0387457			−0.0193729	−	0.999812i	$-0.506167\pi$
$859$	−1.13559			−0.0387457			−0.0193729	+	0.999812i	$0.506167\pi$
$860$		0			0
$861$	15.1156	+	31.3786i	0.515139	+	1.06938i
$862$	−16.1174	+	35.9428i	−0.548962	+	1.22422i
$863$	−12.8678			−0.438024			−0.219012	−	0.975722i	$-0.570283\pi$
$863$	−12.8678			−0.438024			−0.219012	+	0.975722i	$0.570283\pi$
$864$	21.2865	+	20.2703i	0.724182	+	0.689609i
$865$		0			0
$866$	−13.9309	+	31.0668i	−0.473393	+	1.05569i
$867$	−11.7584	−	24.4094i	−0.399338	−	0.828988i
$868$	−2.67866	−	3.00696i	−0.0909195	−	0.102063i
$869$	−8.83701			−0.299775
$870$		0			0
$871$			27.0850i			0.917740i
$872$	−0.665138	−	2.10406i	−0.0225244	−	0.0712525i
$873$	32.0050	−	40.1520i	1.08320	−	1.35894i
$874$	−26.4779	+	59.0472i	−0.895628	+	1.99730i
$875$		0			0
$876$	−12.8190	+	30.8202i	−0.433115	+	1.04132i
$877$			35.8017i			1.20894i	0.796629	+	0.604469i	$0.206615\pi$
$877$			35.8017i			1.20894i	−0.796629	+	0.604469i	$0.793385\pi$
$878$	−31.7763	−	14.2491i	−1.07240	−	0.480884i
$879$	−4.51014	−	9.36262i	−0.152123	−	0.315793i
$880$		0			0
$881$			26.0081i			0.876234i	0.898918	+	0.438117i	$0.144354\pi$
$881$			26.0081i			0.876234i	−0.898918	+	0.438117i	$0.855646\pi$
$882$	−22.1149	−	42.8662i	−0.744649	−	1.44338i
$883$	−41.3226			−1.39062			−0.695308	−	0.718712i	$-0.744732\pi$
$883$	−41.3226			−1.39062			−0.695308	+	0.718712i	$0.744732\pi$
$884$	−4.20784	−	4.72357i	−0.141525	−	0.158871i
$885$		0			0
$886$	9.82151	+	4.40415i	0.329960	+	0.147960i
$887$	−14.9286			−0.501255			−0.250627	−	0.968084i	$-0.580637\pi$
$887$	−14.9286			−0.501255			−0.250627	+	0.968084i	$0.580637\pi$
$888$	−4.87544	+	4.58856i	−0.163609	+	0.153982i
$889$	−12.5904			−0.422268
$890$		0			0
$891$	−21.4662	+	4.90999i	−0.719144	+	0.164491i
$892$	7.80371	−	6.95168i	0.261287	−	0.232760i
$893$	−24.6907			−0.826242
$894$	39.4768	−	1.08100i	1.32030	−	0.0361540i
$895$		0			0
$896$	−47.6094	+	9.19681i	−1.59052	+	0.307244i
$897$	−32.0185	+	15.4239i	−1.06907	+	0.514988i
$898$	−14.5747	−	6.53559i	−0.486365	−	0.218096i
$899$		−	0.344406i		−	0.0114866i
$900$		0			0
$901$		−	1.17291i		−	0.0390753i
$902$	−6.64269	+	14.8136i	−0.221177	+	0.493238i
$903$	−10.0544	+	4.84340i	−0.334591	+	0.161178i
$904$	−2.48646	−	7.86553i	−0.0826984	−	0.261604i
$905$		0			0
$906$	1.19661	+	43.6991i	0.0397549	+	1.45180i
$907$	39.4794			1.31089			0.655447	−	0.755241i	$-0.272480\pi$
$907$	39.4794			1.31089			0.655447	+	0.755241i	$0.272480\pi$
$908$	20.7507	−	18.4851i	0.688636	−	0.613450i
$909$	−10.0270	+	12.5795i	−0.332576	+	0.417235i
$910$		0			0
$911$	47.8266			1.58457			0.792284	−	0.610153i	$-0.208892\pi$
$911$	47.8266			1.58457			0.792284	+	0.610153i	$0.208892\pi$
$912$	39.6344	−	13.7335i	1.31243	−	0.454761i
$913$	−13.3370			−0.441390
$914$	17.0740	−	38.0759i	0.564757	−	1.25944i
$915$		0			0
$916$	0.348425	−	0.310383i	0.0115123	−	0.0102554i
$917$	−33.7583			−1.11480
$918$	−6.83824	−	5.15104i	−0.225696	−	0.170010i
$919$		−	30.2025i		−	0.996290i	−0.867094	−	0.498145i	$-0.834015\pi$
$919$		−	30.2025i		−	0.996290i	0.867094	−	0.498145i	$-0.165985\pi$
$920$		0			0
$921$	−3.74573	−	7.77578i	−0.123426	−	0.256221i
$922$	16.7523	−	37.3586i	0.551708	−	1.23034i
$923$		−	31.5907i		−	1.03982i
$924$	13.9505	−	33.5406i	0.458938	−	1.10341i
$925$		0			0
$926$	−29.1665	−	13.0788i	−0.958472	−	0.429797i
$927$	30.7106	+	24.4793i	1.00867	+	0.804005i
$928$	−3.56351	−	2.12107i	−0.116978	−	0.0696276i
$929$		−	2.81266i		−	0.0922804i	−0.998935	−	0.0461402i	$-0.985308\pi$
$929$		−	2.81266i		−	0.0922804i	0.998935	−	0.0461402i	$-0.0146921\pi$
$930$		0			0
$931$	−68.8330			−2.25591
$932$	−12.8758	+	11.4700i	−0.421761	+	0.375712i
$933$	8.33518	+	17.3031i	0.272882	+	0.566477i
$934$	−17.5678	−	7.87774i	−0.574836	−	0.257767i
$935$		0			0
$936$	21.5046	+	8.26144i	0.702900	+	0.270033i
$937$	20.7171			0.676798			0.338399	−	0.941003i	$-0.390115\pi$
$937$	20.7171			0.676798			0.338399	+	0.941003i	$0.390115\pi$
$938$	−55.1750	−	24.7415i	−1.80153	−	0.807840i
$939$	8.46278	+	17.5679i	0.276172	+	0.573308i
$940$		0			0
$941$	−41.0867			−1.33939			−0.669695	−	0.742636i	$-0.733575\pi$
$941$	−41.0867			−1.33939			−0.669695	+	0.742636i	$0.733575\pi$
$942$	−1.55782	−	56.8897i	−0.0507564	−	1.85357i
$943$			35.4602i			1.15474i
$944$	−6.49588	−	0.752696i	−0.211423	−	0.0244982i
$945$		0			0
$946$	−4.74661	−	2.12847i	−0.154326	−	0.0692026i
$947$			12.3990i			0.402913i	0.979497	+	0.201456i	$0.0645674\pi$
$947$			12.3990i			0.402913i	−0.979497	+	0.201456i	$0.935433\pi$
$948$	11.5521	+	4.80486i	0.375195	+	0.156055i
$949$			26.1608i			0.849217i
$950$		0			0
$951$	−20.4542	−	42.4610i	−0.663274	−	1.37689i
$952$	13.4662	−	4.25694i	0.436442	−	0.137968i
$953$			24.4649i			0.792496i	0.918144	+	0.396248i	$0.129688\pi$
$953$			24.4649i			0.792496i	−0.918144	+	0.396248i	$0.870312\pi$
$954$	1.95834	+	3.79592i	0.0634036	+	0.122898i
$955$		0			0
$956$	−26.7516	−	30.0303i	−0.865207	−	0.971250i
$957$	2.79892	−	1.34829i	0.0904762	−	0.0435840i
$958$	0.238070	−	0.530908i	0.00769168	−	0.0171529i
$959$	−10.7719			−0.347842
$960$		0			0
$961$	30.7793			0.992880
$962$	−2.14697	+	4.78785i	−0.0692209	+	0.154367i
$963$	20.7057	+	16.5044i	0.667232	+	0.531846i
$964$	12.1382	+	13.6260i	0.390947	+	0.438863i
$965$		0			0
$966$	−2.17187	−	79.3144i	−0.0698789	−	2.55190i
$967$		−	3.64391i		−	0.117180i	−0.998282	−	0.0585901i	$-0.981340\pi$
$967$		−	3.64391i		−	0.117180i	0.998282	−	0.0585901i	$-0.0186605\pi$
$968$	−13.5209	+	4.27423i	−0.434577	+	0.137379i
$969$	−11.0068	+	5.30215i	−0.353588	+	0.170330i
$970$		0			0
$971$			27.1170i			0.870225i	0.900376	+	0.435113i	$0.143291\pi$
$971$			27.1170i			0.870225i	−0.900376	+	0.435113i	$0.856709\pi$
$972$	30.7312	+	5.25304i	0.985703	+	0.168491i
$973$		−	11.0351i		−	0.353769i
$974$	−41.5836	−	18.6469i	−1.33242	−	0.597484i
$975$		0			0
$976$	43.4437	+	5.03395i	1.39060	+	0.161133i
$977$			41.8998i			1.34049i	0.742139	+	0.670246i	$0.233812\pi$
$977$			41.8998i			1.34049i	−0.742139	+	0.670246i	$0.766188\pi$
$978$	17.0655	−	0.467305i	0.545694	−	0.0149428i
$979$	−18.9864			−0.606809
$980$		0			0
$981$	−1.83025	−	1.45888i	−0.0584355	−	0.0465786i
$982$	−18.2729	−	8.19393i	−0.583112	−	0.261479i
$983$	−0.734322			−0.0234212			−0.0117106	−	0.999931i	$-0.503728\pi$
$983$	−0.734322			−0.0234212			−0.0117106	+	0.999931i	$0.503728\pi$
$984$	16.7380	−	15.7532i	0.533589	−	0.502193i
$985$		0			0
$986$	1.10212	+	0.494210i	0.0350985	+	0.0157388i
$987$	27.2740	−	13.1384i	0.868141	−	0.418199i
$988$	24.5473	−	21.8672i	0.780955	−	0.695689i
$989$	−11.3623			−0.361299
$990$		0			0
$991$		−	25.5433i		−	0.811408i	−0.914004	−	0.405704i	$-0.867026\pi$
$991$		−	25.5433i		−	0.811408i	0.914004	−	0.405704i	$-0.132974\pi$
$992$	−1.35928	+	2.28366i	−0.0431572	+	0.0725064i
$993$	13.7706	+	28.5865i	0.436997	+	0.907165i
$994$	64.3537	+	28.8574i	2.04117	+	0.915302i
$995$		0			0
$996$	17.4347	+	7.25159i	0.552439	+	0.229775i
$997$			23.4092i			0.741378i	0.928757	+	0.370689i	$0.120878\pi$
$997$			23.4092i			0.741378i	−0.928757	+	0.370689i	$0.879122\pi$
$998$	−8.44926	+	18.8423i	−0.267457	+	0.596443i
$999$	−1.57777	+	6.92377i	−0.0499184	+	0.219058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.b.e.251.5		8
3.2	odd	2		600.2.b.f.251.4		8
4.3	odd	2		2400.2.b.e.2351.6		8
5.2	odd	4		600.2.m.d.299.16		16
5.3	odd	4		600.2.m.d.299.1		16
5.4	even	2		120.2.b.b.11.4	yes	8
8.3	odd	2		600.2.b.f.251.3		8
8.5	even	2		2400.2.b.f.2351.6		8
12.11	even	2		2400.2.b.f.2351.5		8
15.2	even	4		600.2.m.c.299.1		16
15.8	even	4		600.2.m.c.299.16		16
15.14	odd	2		120.2.b.a.11.5	✓	8
20.3	even	4		2400.2.m.c.1199.4		16
20.7	even	4		2400.2.m.c.1199.13		16
20.19	odd	2		480.2.b.a.431.3		8
24.5	odd	2		2400.2.b.e.2351.5		8
24.11	even	2	inner	600.2.b.e.251.6		8
40.3	even	4		600.2.m.c.299.2		16
40.13	odd	4		2400.2.m.d.1199.4		16
40.19	odd	2		120.2.b.a.11.6	yes	8
40.27	even	4		600.2.m.c.299.15		16
40.29	even	2		480.2.b.b.431.3		8
40.37	odd	4		2400.2.m.d.1199.13		16
60.23	odd	4		2400.2.m.d.1199.14		16
60.47	odd	4		2400.2.m.d.1199.3		16
60.59	even	2		480.2.b.b.431.4		8
120.29	odd	2		480.2.b.a.431.4		8
120.53	even	4		2400.2.m.c.1199.14		16
120.59	even	2		120.2.b.b.11.3	yes	8
120.77	even	4		2400.2.m.c.1199.3		16
120.83	odd	4		600.2.m.d.299.15		16
120.107	odd	4		600.2.m.d.299.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.b.a.11.5	✓	8	15.14	odd	2
120.2.b.a.11.6	yes	8	40.19	odd	2
120.2.b.b.11.3	yes	8	120.59	even	2
120.2.b.b.11.4	yes	8	5.4	even	2
480.2.b.a.431.3		8	20.19	odd	2
480.2.b.a.431.4		8	120.29	odd	2
480.2.b.b.431.3		8	40.29	even	2
480.2.b.b.431.4		8	60.59	even	2
600.2.b.e.251.5		8	1.1	even	1	trivial
600.2.b.e.251.6		8	24.11	even	2	inner
600.2.b.f.251.3		8	8.3	odd	2
600.2.b.f.251.4		8	3.2	odd	2
600.2.m.c.299.1		16	15.2	even	4
600.2.m.c.299.2		16	40.3	even	4
600.2.m.c.299.15		16	40.27	even	4
600.2.m.c.299.16		16	15.8	even	4
600.2.m.d.299.1		16	5.3	odd	4
600.2.m.d.299.2		16	120.107	odd	4
600.2.m.d.299.15		16	120.83	odd	4
600.2.m.d.299.16		16	5.2	odd	4
2400.2.b.e.2351.5		8	24.5	odd	2
2400.2.b.e.2351.6		8	4.3	odd	2
2400.2.b.f.2351.5		8	12.11	even	2
2400.2.b.f.2351.6		8	8.5	even	2
2400.2.m.c.1199.3		16	120.77	even	4
2400.2.m.c.1199.4		16	20.3	even	4
2400.2.m.c.1199.13		16	20.7	even	4
2400.2.m.c.1199.14		16	120.53	even	4
2400.2.m.d.1199.3		16	60.47	odd	4
2400.2.m.d.1199.4		16	40.13	odd	4
2400.2.m.d.1199.13		16	40.37	odd	4
2400.2.m.d.1199.14		16	60.23	odd	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.578647 - 1.29041i) q^{2} +(-0.751690 - 1.56044i) q^{3} +(-1.33034 - 1.49339i) q^{4} +(-2.44857 + 0.0670494i) q^{6} -4.28591i q^{7} +(-2.69688 + 0.852541i) q^{8} +(-1.86993 + 2.34593i) q^{9} +O(q^{10})\)	\(q+(0.578647 - 1.29041i) q^{2} +(-0.751690 - 1.56044i) q^{3} +(-1.33034 - 1.49339i) q^{4} +(-2.44857 + 0.0670494i) q^{6} -4.28591i q^{7} +(-2.69688 + 0.852541i) q^{8} +(-1.86993 + 2.34593i) q^{9} -2.44673i q^{11} +(-1.33034 + 3.19847i) q^{12} +2.71493i q^{13} +(-5.53060 - 2.48003i) q^{14} +(-0.460411 + 3.97341i) q^{16} -1.16504i q^{17} +(1.94519 + 3.77044i) q^{18} +6.05444 q^{19} +(-6.68789 + 3.22167i) q^{21} +(-3.15729 - 1.41579i) q^{22} -7.55782 q^{23} +(3.35755 + 3.56747i) q^{24} +(3.50338 + 1.57098i) q^{26} +(5.06628 + 1.15449i) q^{27} +(-6.40052 + 5.70170i) q^{28} -0.733092 q^{29} +0.469799i q^{31} +(4.86093 + 2.89332i) q^{32} +(-3.81797 + 1.83918i) q^{33} +(-1.50338 - 0.674144i) q^{34} +(5.99101 - 0.328351i) q^{36} +1.36664i q^{37} +(3.50338 - 7.81273i) q^{38} +(4.23647 - 2.04078i) q^{39} -4.69186i q^{41} +(0.287368 + 10.4944i) q^{42} +1.50338 q^{43} +(-3.65391 + 3.25497i) q^{44} +(-4.37330 + 9.75271i) q^{46} -4.07812 q^{47} +(6.54635 - 2.26833i) q^{48} -11.3690 q^{49} +(-1.81797 + 0.875746i) q^{51} +(4.05444 - 3.61177i) q^{52} +1.00676 q^{53} +(4.42135 - 5.86955i) q^{54} +(3.65391 + 11.5586i) q^{56} +(-4.55106 - 9.44757i) q^{57} +(-0.424201 + 0.945992i) q^{58} +1.63484i q^{59} -10.9336i q^{61} +(0.606236 + 0.271848i) q^{62} +(10.0544 + 8.01433i) q^{63} +(6.54635 - 4.59841i) q^{64} +(0.164052 + 5.99099i) q^{66} +9.97632 q^{67} +(-1.73985 + 1.54989i) q^{68} +(5.68113 + 11.7935i) q^{69} -11.6359 q^{71} +(3.04297 - 7.92088i) q^{72} +9.63593 q^{73} +(1.76353 + 0.790800i) q^{74} +(-8.05444 - 9.04162i) q^{76} -10.4865 q^{77} +(-0.182034 - 6.64769i) q^{78} -3.61177i q^{79} +(-2.00676 - 8.77342i) q^{81} +(-6.05444 - 2.71493i) q^{82} -5.45095i q^{83} +(13.7084 + 5.70170i) q^{84} +(0.869925 - 1.93998i) q^{86} +(0.551058 + 1.14394i) q^{87} +(2.08594 + 6.59854i) q^{88} -7.75993i q^{89} +11.6359 q^{91} +(10.0544 + 11.2867i) q^{92} +(0.733092 - 0.353143i) q^{93} +(-2.35979 + 5.26246i) q^{94} +(0.860934 - 9.76006i) q^{96} -17.1156 q^{97} +(-6.57865 + 14.6707i) q^{98} +(5.73985 + 4.57520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{4} + q^{6} - 7 q^{8}+O(q^{10}) \) 8 * q - q^2 + q^4 + q^6 - 7 * q^8	\( 8 q - q^{2} + q^{4} + q^{6} - 7 q^{8} + q^{12} - 6 q^{14} - 7 q^{16} + 7 q^{18} - 4 q^{19} - 4 q^{21} - 14 q^{22} + 4 q^{23} - 11 q^{24} + 16 q^{26} + 12 q^{27} + 2 q^{28} - 11 q^{32} + 4 q^{33} + 13 q^{36} + 16 q^{38} + 16 q^{39} + 6 q^{42} - 30 q^{44} - 8 q^{46} - 28 q^{47} + 25 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} - 16 q^{53} + 41 q^{54} + 30 q^{56} + 4 q^{57} + 2 q^{58} + 34 q^{62} + 28 q^{63} + 25 q^{64} - 34 q^{66} + 32 q^{67} + 16 q^{68} + 20 q^{69} - 24 q^{71} + 9 q^{72} + 8 q^{73} + 32 q^{74} - 12 q^{76} - 36 q^{78} + 8 q^{81} + 4 q^{82} + 58 q^{84} - 8 q^{86} - 36 q^{87} - 14 q^{88} + 24 q^{91} + 28 q^{92} - 40 q^{94} - 43 q^{96} - 8 q^{97} - 47 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q - q^2 + q^4 + q^6 - 7 * q^8 + q^12 - 6 * q^14 - 7 * q^16 + 7 * q^18 - 4 * q^19 - 4 * q^21 - 14 * q^22 + 4 * q^23 - 11 * q^24 + 16 * q^26 + 12 * q^27 + 2 * q^28 - 11 * q^32 + 4 * q^33 + 13 * q^36 + 16 * q^38 + 16 * q^39 + 6 * q^42 - 30 * q^44 - 8 * q^46 - 28 * q^47 + 25 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 - 16 * q^53 + 41 * q^54 + 30 * q^56 + 4 * q^57 + 2 * q^58 + 34 * q^62 + 28 * q^63 + 25 * q^64 - 34 * q^66 + 32 * q^67 + 16 * q^68 + 20 * q^69 - 24 * q^71 + 9 * q^72 + 8 * q^73 + 32 * q^74 - 12 * q^76 - 36 * q^78 + 8 * q^81 + 4 * q^82 + 58 * q^84 - 8 * q^86 - 36 * q^87 - 14 * q^88 + 24 * q^91 + 28 * q^92 - 40 * q^94 - 43 * q^96 - 8 * q^97 - 47 * q^98 + 16 * q^99

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