LMFDB - Embedded newform 600.2.m.d.299.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(299,600)]

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, 1]))

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

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

chi := DirichletCharacter("600.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.m (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} + 4x^{12} + 12x^{10} + 16x^{8} + 48x^{6} + 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 + 4x^12 + 12x^10 + 16x^8 + 48x^6 + 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.16
Root			$1.29041 + 0.578647i$ of defining polynomial
Character	$\chi$	$=$	600.299
Dual form			600.2.m.d.299.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29041 + 0.578647i) q^{2} +(-1.56044 + 0.751690i) q^{3} +(1.33034 + 1.49339i) q^{4} +(-2.44857 + 0.0670494i) q^{6} +4.28591 q^{7} +(0.852541 + 2.69688i) q^{8} +(1.86993 - 2.34593i) q^{9} +O(q^{10})$	\(q+(1.29041 + 0.578647i) q^{2} +(-1.56044 + 0.751690i) q^{3} +(1.33034 + 1.49339i) q^{4} +(-2.44857 + 0.0670494i) q^{6} +4.28591 q^{7} +(0.852541 + 2.69688i) q^{8} +(1.86993 - 2.34593i) q^{9} -2.44673i q^{11} +(-3.19847 - 1.33034i) q^{12} +2.71493 q^{13} +(5.53060 + 2.48003i) q^{14} +(-0.460411 + 3.97341i) q^{16} +1.16504 q^{17} +(3.77044 - 1.94519i) q^{18} -6.05444 q^{19} +(-6.68789 + 3.22167i) q^{21} +(1.41579 - 3.15729i) q^{22} +7.55782i q^{23} +(-3.35755 - 3.56747i) q^{24} +(3.50338 + 1.57098i) q^{26} +(-1.15449 + 5.06628i) q^{27} +(5.70170 + 6.40052i) q^{28} +0.733092 q^{29} +0.469799i q^{31} +(-2.89332 + 4.86093i) q^{32} +(1.83918 + 3.81797i) q^{33} +(1.50338 + 0.674144i) q^{34} +(5.99101 - 0.328351i) q^{36} -1.36664 q^{37} +(-7.81273 - 3.50338i) q^{38} +(-4.23647 + 2.04078i) q^{39} -4.69186i q^{41} +(-10.4944 + 0.287368i) q^{42} -1.50338i q^{43} +(3.65391 - 3.25497i) q^{44} +(-4.37330 + 9.75271i) q^{46} -4.07812i q^{47} +(-2.26833 - 6.54635i) q^{48} +11.3690 q^{49} +(-1.81797 + 0.875746i) q^{51} +(3.61177 + 4.05444i) q^{52} -1.00676i q^{53} +(-4.42135 + 5.86955i) q^{54} +(3.65391 + 11.5586i) q^{56} +(9.44757 - 4.55106i) q^{57} +(0.945992 + 0.424201i) q^{58} -1.63484i q^{59} -10.9336i q^{61} +(-0.271848 + 0.606236i) q^{62} +(8.01433 - 10.0544i) q^{63} +(-6.54635 + 4.59841i) q^{64} +(0.164052 + 5.99099i) q^{66} +9.97632i q^{67} +(1.54989 + 1.73985i) q^{68} +(-5.68113 - 11.7935i) q^{69} -11.6359 q^{71} +(7.92088 + 3.04297i) q^{72} -9.63593i q^{73} +(-1.76353 - 0.790800i) q^{74} +(-8.05444 - 9.04162i) q^{76} -10.4865i q^{77} +(-6.64769 + 0.182034i) q^{78} +3.61177i q^{79} +(-2.00676 - 8.77342i) q^{81} +(2.71493 - 6.05444i) q^{82} -5.45095 q^{83} +(-13.7084 - 5.70170i) q^{84} +(0.869925 - 1.93998i) q^{86} +(-1.14394 + 0.551058i) q^{87} +(6.59854 - 2.08594i) q^{88} +7.75993i q^{89} +11.6359 q^{91} +(-11.2867 + 10.0544i) q^{92} +(-0.353143 - 0.733092i) q^{93} +(2.35979 - 5.26246i) q^{94} +(0.860934 - 9.76006i) q^{96} -17.1156i q^{97} +(14.6707 + 6.57865i) q^{98} +(-5.73985 - 4.57520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} + 2 q^{6}+O(q^{10}) $ 16 * q - 2 * q^4 + 2 * q^6	$ 16 q - 2 q^{4} + 2 q^{6} + 12 q^{14} - 14 q^{16} + 8 q^{19} - 8 q^{21} + 22 q^{24} + 32 q^{26} + 26 q^{36} - 32 q^{39} + 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} - 82 q^{54} + 60 q^{56} - 50 q^{64} - 68 q^{66} - 40 q^{69} - 48 q^{71} - 64 q^{74} - 24 q^{76} + 16 q^{81} - 116 q^{84} - 16 q^{86} + 48 q^{91} + 80 q^{94} - 86 q^{96} - 32 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 + 2 * q^6 + 12 * q^14 - 14 * q^16 + 8 * q^19 - 8 * q^21 + 22 * q^24 + 32 * q^26 + 26 * q^36 - 32 * q^39 + 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 - 82 * q^54 + 60 * q^56 - 50 * q^64 - 68 * q^66 - 40 * q^69 - 48 * q^71 - 64 * q^74 - 24 * q^76 + 16 * q^81 - 116 * q^84 - 16 * q^86 + 48 * q^91 + 80 * q^94 - 86 * q^96 - 32 * 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 $

$2$	1.29041	+	0.578647i	0.912460	+	0.409165i
$2$	1.29041	+	0.578647i	0.912460	+	0.409165i
$3$	−1.56044	+	0.751690i	−0.900919	+	0.433988i
$3$	−1.56044	+	0.751690i	−0.900919	+	0.433988i
$4$	1.33034	+	1.49339i	0.665168	+	0.746694i
$5$		0			0
$5$		0			0
$6$	−2.44857	+	0.0670494i	−0.999625	+	0.0273728i
$7$	4.28591			1.61992			0.809961	−	0.586484i	$-0.199488\pi$
$7$	4.28591			1.61992			0.809961	+	0.586484i	$0.199488\pi$
$8$	0.852541	+	2.69688i	0.301419	+	0.953492i
$9$	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	$-0.120251\pi$
$12$	−3.19847	−	1.33034i	−0.923319	−	0.384035i
$13$	2.71493			0.752985			0.376493	−	0.926420i	$-0.377130\pi$
$13$	2.71493			0.752985			0.376493	+	0.926420i	$0.377130\pi$
$14$	5.53060	+	2.48003i	1.47811	+	0.662815i
$15$		0			0
$16$	−0.460411	+	3.97341i	−0.115103	+	0.993354i
$17$	1.16504			0.282563			0.141281	−	0.989969i	$-0.454878\pi$
$17$	1.16504			0.282563			0.141281	+	0.989969i	$0.454878\pi$
$18$	3.77044	−	1.94519i	0.888701	−	0.458486i
$19$	−6.05444			−1.38898			−0.694492	−	0.719501i	$-0.744371\pi$
$19$	−6.05444			−1.38898			−0.694492	+	0.719501i	$0.744371\pi$
$20$		0			0
$21$	−6.68789	+	3.22167i	−1.45942	+	0.703027i
$22$	1.41579	−	3.15729i	0.301848	−	0.673137i
$23$			7.55782i			1.57591i	0.615731	+	0.787957i	$0.288861\pi$
$23$			7.55782i			1.57591i	−0.615731	+	0.787957i	$0.711139\pi$
$24$	−3.35755	−	3.56747i	−0.685358	−	0.728206i
$25$		0			0
$26$	3.50338	+	1.57098i	0.687069	+	0.308095i
$27$	−1.15449	+	5.06628i	−0.222182	+	0.975005i
$28$	5.70170	+	6.40052i	1.07752	+	1.20959i
$29$	0.733092			0.136132			0.0680659	−	0.997681i	$-0.478317\pi$
$29$	0.733092			0.136132			0.0680659	+	0.997681i	$0.478317\pi$
$30$		0			0
$31$			0.469799i			0.0843784i	0.999110	+	0.0421892i	$0.0134332\pi$
$31$			0.469799i			0.0843784i	−0.999110	+	0.0421892i	$0.986567\pi$
$32$	−2.89332	+	4.86093i	−0.511472	+	0.859300i
$33$	1.83918	+	3.81797i	0.320160	+	0.664623i
$34$	1.50338	+	0.674144i	0.257827	+	0.115615i
$35$		0			0
$36$	5.99101	−	0.328351i	0.998501	−	0.0547251i
$37$	−1.36664			−0.224674			−0.112337	−	0.993670i	$-0.535834\pi$
$37$	−1.36664			−0.224674			−0.112337	+	0.993670i	$0.535834\pi$
$38$	−7.81273	−	3.50338i	−1.26739	−	0.568323i
$39$	−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	$-0.119400\pi$
$42$	−10.4944	+	0.287368i	−1.61931	+	0.0443418i
$43$		−	1.50338i		−	0.229263i	−0.993408	−	0.114632i	$-0.963431\pi$
$43$		−	1.50338i		−	0.229263i	0.993408	−	0.114632i	$-0.0365688\pi$
$44$	3.65391	−	3.25497i	0.550848	−	0.490706i
$45$		0			0
$46$	−4.37330	+	9.75271i	−0.644809	+	1.43796i
$47$		−	4.07812i		−	0.594854i	−0.954745	−	0.297427i	$-0.903871\pi$
$47$		−	4.07812i		−	0.594854i	0.954745	−	0.297427i	$-0.0961285\pi$
$48$	−2.26833	−	6.54635i	−0.327406	−	0.944884i
$49$	11.3690			1.62415
$50$		0			0
$51$	−1.81797	+	0.875746i	−0.254566	+	0.122629i
$52$	3.61177	+	4.05444i	0.500862	+	0.562249i
$53$		−	1.00676i		−	0.138289i	−0.997607	−	0.0691445i	$-0.977973\pi$
$53$		−	1.00676i		−	0.138289i	0.997607	−	0.0691445i	$-0.0220269\pi$
$54$	−4.42135	+	5.86955i	−0.601670	+	0.798745i
$55$		0			0
$56$	3.65391	+	11.5586i	0.488275	+	1.54458i
$57$	9.44757	−	4.55106i	1.25136	−	0.602802i
$58$	0.945992	+	0.424201i	0.124215	+	0.0557003i
$59$		−	1.63484i		−	0.212837i	−0.994321	−	0.106419i	$-0.966062\pi$
$59$		−	1.63484i		−	0.212837i	0.994321	−	0.106419i	$-0.0339384\pi$
$60$		0			0
$61$		−	10.9336i		−	1.39990i	−0.714190	−	0.699952i	$-0.753205\pi$
$61$		−	10.9336i		−	1.39990i	0.714190	−	0.699952i	$-0.246795\pi$
$62$	−0.271848	+	0.606236i	−0.0345247	+	0.0769920i
$63$	8.01433	−	10.0544i	1.00971	−	1.26674i
$64$	−6.54635	+	4.59841i	−0.818293	+	0.574801i
$65$		0			0
$66$	0.164052	+	5.99099i	0.0201934	+	0.737440i
$67$			9.97632i			1.21880i	0.792862	+	0.609401i	$0.208590\pi$
$67$			9.97632i			1.21880i	−0.792862	+	0.609401i	$0.791410\pi$
$68$	1.54989	+	1.73985i	0.187952	+	0.210988i
$69$	−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	$0.742594\pi$
$72$	7.92088	+	3.04297i	0.933485	+	0.358617i
$73$		−	9.63593i		−	1.12780i	−0.825843	−	0.563900i	$-0.809300\pi$
$73$		−	9.63593i		−	1.12780i	0.825843	−	0.563900i	$-0.190700\pi$
$74$	−1.76353	−	0.790800i	−0.205006	−	0.0919287i
$75$		0			0
$76$	−8.05444	−	9.04162i	−0.923907	−	1.03714i
$77$		−	10.4865i		−	1.19504i
$78$	−6.64769	+	0.182034i	−0.752703	+	0.0206113i
$79$			3.61177i			0.406355i	0.979142	+	0.203178i	$0.0651269\pi$
$79$			3.61177i			0.406355i	−0.979142	+	0.203178i	$0.934873\pi$
$80$		0			0
$81$	−2.00676	−	8.77342i	−0.222973	−	0.974825i
$82$	2.71493	−	6.05444i	0.299814	−	0.668601i
$83$	−5.45095			−0.598319			−0.299160	−	0.954203i	$-0.596706\pi$
$83$	−5.45095			−0.598319			−0.299160	+	0.954203i	$0.596706\pi$
$84$	−13.7084	−	5.70170i	−1.49570	−	0.622107i
$85$		0			0
$86$	0.869925	−	1.93998i	0.0938065	−	0.209194i
$87$	−1.14394	+	0.551058i	−0.122644	+	0.0590796i
$88$	6.59854	−	2.08594i	0.703407	−	0.222362i
$89$			7.75993i			0.822551i	0.911511	+	0.411275i	$0.134917\pi$
$89$			7.75993i			0.822551i	−0.911511	+	0.411275i	$0.865083\pi$
$90$		0			0
$91$	11.6359			1.21978
$92$	−11.2867	+	10.0544i	−1.17672	+	1.04825i
$93$	−0.353143	−	0.733092i	−0.0366192	−	0.0760181i
$94$	2.35979	−	5.26246i	0.243393	−	0.542781i
$95$		0			0
$96$	0.860934	−	9.76006i	0.0878687	−	0.996132i
$97$		−	17.1156i		−	1.73783i	−0.494962	−	0.868915i	$-0.664818\pi$
$97$		−	17.1156i		−	1.73783i	0.494962	−	0.868915i	$-0.335182\pi$
$98$	14.6707	+	6.57865i	1.48197	+	0.664544i
$99$	−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	$0.414039\pi$
$102$	−2.85268	+	0.0781150i	−0.282457	+	0.00773454i
$103$	−13.0910			−1.28990			−0.644949	−	0.764225i	$-0.723122\pi$
$103$	−13.0910			−1.28990			−0.644949	+	0.764225i	$0.723122\pi$
$104$	2.31459	+	7.32184i	0.226964	+	0.717965i
$105$		0			0
$106$	0.582557	−	1.29914i	0.0565830	−	0.126183i
$107$	8.82622			0.853263			0.426632	−	0.904425i	$-0.359700\pi$
$107$	8.82622			0.853263			0.426632	+	0.904425i	$0.359700\pi$
$108$	−9.10177	+	5.01575i	−0.875818	+	0.482641i
$109$		−	0.780183i		−	0.0747280i	−0.999302	−	0.0373640i	$-0.988104\pi$
$109$		−	0.780183i		−	0.0747280i	0.999302	−	0.0373640i	$-0.0118961\pi$
$110$		0			0
$111$	2.13255	−	1.02729i	0.202413	−	0.0975058i
$112$	−1.97328	+	17.0297i	−0.186457	+	1.60916i
$113$	2.91653			0.274364			0.137182	−	0.990546i	$-0.456195\pi$
$113$	2.91653			0.274364			0.137182	+	0.990546i	$0.456195\pi$
$114$	14.8247	−	0.405947i	1.38846	−	0.0380204i
$115$		0			0
$116$	0.975259	+	1.09479i	0.0905505	+	0.101649i
$117$	5.07671	−	6.36902i	0.469342	−	0.588816i
$118$	0.945992	−	2.10961i	0.0870856	−	0.194206i
$119$	4.99324			0.457730
$120$		0			0
$121$	5.01352			0.455774
$122$	6.32669	−	14.1089i	0.572792	−	1.27736i
$123$	3.52682	+	7.32134i	0.318003	+	0.660143i
$124$	−0.701592	+	0.624991i	−0.0630048	+	0.0561258i
$125$		0			0
$126$	16.1598	−	8.33692i	1.43963	−	0.742712i
$127$	2.93762			0.260672			0.130336	−	0.991470i	$-0.458394\pi$
$127$	2.93762			0.260672			0.130336	+	0.991470i	$0.458394\pi$
$128$	−11.1083	+	2.14582i	−0.981849	+	0.189666i
$129$	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	$-0.111813\pi$
$132$	−3.25497	+	7.82579i	−0.283309	+	0.681147i
$133$	−25.9488			−2.25004
$134$	−5.77276	+	12.8736i	−0.498691	+	1.11211i
$135$		0			0
$136$	0.993241	+	3.14197i	0.0851697	+	0.269421i
$137$	2.51333			0.214728			0.107364	−	0.994220i	$-0.465759\pi$
$137$	2.51333			0.214728			0.107364	+	0.994220i	$0.465759\pi$
$138$	−0.506747	−	18.5059i	−0.0431372	−	1.57532i
$139$	−2.57474			−0.218386			−0.109193	−	0.994021i	$-0.534827\pi$
$139$	−2.57474			−0.218386			−0.109193	+	0.994021i	$0.534827\pi$
$140$		0			0
$141$	3.06548	+	6.36364i	0.258160	+	0.535915i
$142$	−15.0152	−	6.73309i	−1.26004	−	0.565029i
$143$		−	6.64269i		−	0.555490i
$144$	8.46041	+	8.51008i	0.705034	+	0.709173i
$145$		0			0
$146$	5.57580	−	12.4343i	0.461456	−	1.02907i
$147$	−17.7406	+	8.54598i	−1.46322	+	0.704860i
$148$	−1.81809	−	2.04092i	−0.149446	−	0.167763i
$149$	16.1224			1.32080			0.660399	−	0.750915i	$-0.270387\pi$
$149$	16.1224			1.32080			0.660399	+	0.750915i	$0.270387\pi$
$150$		0			0
$151$		−	17.8468i		−	1.45235i	−0.687511	−	0.726174i	$-0.741297\pi$
$151$		−	17.8468i		−	1.45235i	0.687511	−	0.726174i	$-0.258703\pi$
$152$	−5.16166	−	16.3281i	−0.418666	−	1.32438i
$153$	2.17853	−	2.73309i	0.176124	−	0.220957i
$154$	6.06795	−	13.5319i	0.488970	−	1.09043i
$155$		0			0
$156$	−8.68361	−	3.61177i	−0.695245	−	0.289173i
$157$	−23.2338			−1.85426			−0.927131	−	0.374737i	$-0.877733\pi$
$157$	−23.2338			−1.85426			−0.927131	+	0.374737i	$0.877733\pi$
$158$	−2.08994	+	4.66067i	−0.166266	+	0.370783i
$159$	0.756770	+	1.57098i	0.0600158	+	0.124587i
$160$		0			0
$161$			32.3921i			2.55286i
$162$	2.48716	−	12.4825i	0.195410	−	0.980722i
$163$			6.96956i			0.545898i	0.962028	+	0.272949i	$0.0879991\pi$
$163$			6.96956i			0.545898i	−0.962028	+	0.272949i	$0.912001\pi$
$164$	7.00676	−	6.24175i	0.547136	−	0.487399i
$165$		0			0
$166$	−7.03398	−	3.15417i	−0.545943	−	0.244811i
$167$			9.93540i			0.768825i	0.923162	+	0.384412i	$0.125596\pi$
$167$			9.93540i			0.768825i	−0.923162	+	0.384412i	$0.874404\pi$
$168$	−14.3902	−	15.2898i	−1.11023	−	1.17964i
$169$	−5.62917			−0.433013
$170$		0			0
$171$	−11.3213	+	14.2033i	−0.865765	+	1.08615i
$172$	2.24513	−	2.00000i	0.171189	−	0.152499i
$173$			8.01352i			0.609256i	0.952471	+	0.304628i	$0.0985322\pi$
$173$			8.01352i			0.609256i	−0.952471	+	0.304628i	$0.901468\pi$
$174$	−1.79503	+	0.0491534i	−0.136081	+	0.00372631i
$175$		0			0
$176$	9.72187	+	1.12650i	0.732813	+	0.0849132i
$177$	1.22889	+	2.55106i	0.0923690	+	0.191749i
$178$	−4.49025	+	10.0135i	−0.336559	+	0.750545i
$179$		−	23.5020i		−	1.75663i	−0.478087	−	0.878313i	$-0.658670\pi$
$179$		−	23.5020i		−	1.75663i	0.478087	−	0.878313i	$-0.341330\pi$
$180$		0			0
$181$			9.92011i			0.737356i	0.929557	+	0.368678i	$0.120189\pi$
$181$			9.92011i			0.737356i	−0.929557	+	0.368678i	$0.879811\pi$
$182$	15.0152	+	6.73309i	1.11300	+	0.499090i
$183$	8.21868	+	17.0612i	0.607542	+	1.26120i
$184$	−20.3825	+	6.44335i	−1.50262	+	0.475010i
$185$		0			0
$186$	−0.0314998	−	1.15034i	−0.00230968	−	0.0843468i
$187$		−	2.85053i		−	0.208451i
$188$	6.09020	−	5.42526i	0.444174	−	0.395678i
$189$	−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	$0.197542\pi$
$192$	6.75859	−	12.0963i	0.487759	−	0.872978i
$193$		−	13.1156i		−	0.944084i	−0.881576	−	0.472042i	$-0.843517\pi$
$193$		−	13.1156i		−	0.944084i	0.881576	−	0.472042i	$-0.156483\pi$
$194$	9.90390	−	22.0863i	0.711059	−	1.58570i
$195$		0			0
$196$	15.1246	+	16.9784i	1.08033	+	1.21274i
$197$			24.2786i			1.72978i	0.501961	+	0.864890i	$0.332612\pi$
$197$			24.2786i			1.72978i	−0.501961	+	0.864890i	$0.667388\pi$
$198$	−4.75936	−	9.22525i	−0.338233	−	0.655610i
$199$		−	1.81809i		−	0.128881i	−0.997922	−	0.0644404i	$-0.979474\pi$
$199$		−	1.81809i		−	0.128881i	0.997922	−	0.0644404i	$-0.0205262\pi$
$200$		0			0
$201$	−7.49910	−	15.5674i	−0.528946	−	1.09804i
$202$	6.91954	+	3.10286i	0.486857	+	0.218316i
$203$	3.14197			0.220523
$204$	−3.72633	−	1.54989i	−0.260896	−	0.108514i
$205$		0			0
$206$	−16.8929	−	7.57509i	−1.17698	−	0.527781i
$207$	17.7301	+	14.1326i	1.23233	+	0.982280i
$208$	−1.24998	+	10.7875i	−0.0866707	+	0.747981i
$209$			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	$0.488370\pi$
$212$	1.50348	−	1.33933i	0.103259	−	0.0919854i
$213$	18.1571	−	8.74661i	1.24411	−	0.599308i
$214$	11.3895	+	5.10726i	0.778569	+	0.349125i
$215$		0			0
$216$	−14.6474	+	1.20568i	−0.996629	+	0.0820364i
$217$			2.01352i			0.136686i
$218$	0.451450	−	1.00676i	0.0305761	−	0.0681863i
$219$	7.24323	+	15.0363i	0.489452	+	1.01606i
$220$		0			0
$221$	3.16299			0.212766
$222$	3.34631	−	0.0916323i	0.224590	−	0.00614996i
$223$	5.22551			0.349926			0.174963	−	0.984575i	$-0.444019\pi$
$223$	5.22551			0.349926			0.174963	+	0.984575i	$0.444019\pi$
$224$	−12.4005	+	20.8335i	−0.828545	+	1.39200i
$225$		0			0
$226$	3.76353	+	1.68764i	0.250346	+	0.112260i
$227$	−13.8951			−0.922248			−0.461124	−	0.887336i	$-0.652554\pi$
$227$	−13.8951			−0.922248			−0.461124	+	0.887336i	$0.652554\pi$
$228$	19.3649	+	8.05444i	1.28247	+	0.533418i
$229$		−	0.233312i		−	0.0154177i	−0.999970	−	0.00770885i	$-0.997546\pi$
$229$		−	0.233312i		−	0.0154177i	0.999970	−	0.00770885i	$-0.00245383\pi$
$230$		0			0
$231$	7.88256	+	16.3635i	0.518635	+	1.07664i
$232$	0.624991	+	1.97706i	0.0410327	+	0.129801i
$233$	−8.62188			−0.564838			−0.282419	−	0.959291i	$-0.591137\pi$
$233$	−8.62188			−0.564838			−0.282419	+	0.959291i	$0.591137\pi$
$234$	10.2365	−	5.28106i	0.669179	−	0.345233i
$235$		0			0
$236$	2.44144	−	2.17488i	0.158924	−	0.141573i
$237$	−2.71493	−	5.63593i	−0.176353	−	0.366093i
$238$	6.44335	+	2.88932i	0.417660	+	0.187287i
$239$	−20.1089			−1.30073			−0.650367	−	0.759620i	$-0.725385\pi$
$239$	−20.1089			−1.30073			−0.650367	+	0.759620i	$0.725385\pi$
$240$		0			0
$241$	−9.12420			−0.587741			−0.293871	−	0.955845i	$-0.594943\pi$
$241$	−9.12420			−0.587741			−0.293871	+	0.955845i	$0.594943\pi$
$242$	6.46951	+	2.90105i	0.415876	+	0.186487i
$243$	9.72631	+	12.1819i	0.623943	+	0.781470i
$244$	16.3281	−	14.5454i	1.04530	−	0.931172i
$245$		0			0
$246$	0.314586	+	11.4883i	0.0200573	+	0.732470i
$247$	−16.4374			−1.04588
$248$	−1.26699	+	0.400523i	−0.0804542	+	0.0254332i
$249$	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	$-0.137951\pi$
$252$	25.6769	−	1.40728i	1.61749	−	0.0886504i
$253$	18.4919			1.16258
$254$	3.79075	+	1.69984i	0.237853	+	0.106658i
$255$		0			0
$256$	−15.5760	−	3.65881i	−0.973503	−	0.228675i
$257$	−30.2136			−1.88467			−0.942336	−	0.334668i	$-0.891376\pi$
$257$	−30.2136			−1.88467			−0.942336	+	0.334668i	$0.891376\pi$
$258$	0.100801	+	3.68113i	0.00627558	+	0.229177i
$259$	−5.85729			−0.363954
$260$		0			0
$261$	1.37083	−	1.71978i	0.0848521	−	0.106452i
$262$	4.55776	−	10.1641i	0.281579	−	0.627937i
$263$		−	14.9286i		−	0.920540i	−0.887779	−	0.460270i	$-0.847753\pi$
$263$		−	14.9286i		−	0.920540i	0.887779	−	0.460270i	$-0.152247\pi$
$264$	−8.72863	+	8.21503i	−0.537210	+	0.505600i
$265$		0			0
$266$	−33.4847	−	15.0152i	−2.05308	−	0.920639i
$267$	−5.83306	−	12.1089i	−0.356977	−	0.741051i
$268$	−14.8985	+	13.2719i	−0.910071	+	0.810708i
$269$	−4.85053			−0.295742			−0.147871	−	0.989007i	$-0.547242\pi$
$269$	−4.85053			−0.295742			−0.147871	+	0.989007i	$0.547242\pi$
$270$		0			0
$271$			14.8802i			0.903906i	0.892042	+	0.451953i	$0.149272\pi$
$271$			14.8802i			0.903906i	−0.892042	+	0.451953i	$0.850728\pi$
$272$	−0.536396	+	4.62917i	−0.0325238	+	0.280685i
$273$	−18.1571	+	8.74661i	−1.09892	+	0.529369i
$274$	3.24323	+	1.45433i	0.195931	+	0.0878591i
$275$		0			0
$276$	10.0544	−	24.1734i	0.605206	−	1.45507i
$277$	19.6832			1.18265			0.591324	−	0.806434i	$-0.298605\pi$
$277$	19.6832			1.18265			0.591324	+	0.806434i	$0.298605\pi$
$278$	−3.32247	−	1.48986i	−0.199269	−	0.0893560i
$279$	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	$0.978161\pi$
$282$	0.273435	+	9.98556i	0.0162828	+	0.594631i
$283$		−	21.6123i		−	1.28472i	−0.766405	−	0.642358i	$-0.777956\pi$
$283$		−	21.6123i		−	1.28472i	0.766405	−	0.642358i	$-0.222044\pi$
$284$	−15.4797	−	17.3770i	−0.918551	−	1.03113i
$285$		0			0
$286$	3.84377	−	8.57182i	0.227287	−	0.506862i
$287$		−	20.1089i		−	1.18699i
$288$	5.99310	+	15.8771i	0.353147	+	0.935568i
$289$	−15.6427			−0.920158
$290$		0			0
$291$	12.8656	+	26.7079i	0.754197	+	1.56564i
$292$	14.3902	−	12.8190i	0.842121	−	0.750177i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$	−27.8379	+	0.762287i	−1.62354	+	0.0444575i
$295$		0			0
$296$	−1.16511	−	3.68566i	−0.0677209	−	0.214225i
$297$	12.3958	+	2.82472i	0.719278	+	0.163907i
$298$	20.8046	+	9.32917i	1.20518	+	0.540424i
$299$			20.5189i			1.18664i
$300$		0			0
$301$		−	6.44335i		−	0.371388i
$302$	10.3270	−	23.0297i	0.594250	−	1.32521i
$303$	−8.36747	+	4.03076i	−0.480699	+	0.231561i
$304$	2.78753	−	24.0568i	0.159876	−	1.37975i
$305$		0			0
$306$	4.39270	−	2.26622i	0.251114	−	0.129551i
$307$			4.98308i			0.284399i	0.989838	+	0.142200i	$0.0454175\pi$
$307$			4.98308i			0.284399i	−0.989838	+	0.142200i	$0.954582\pi$
$308$	15.6603	−	13.9505i	0.892331	−	0.794905i
$309$	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	$0.601799\pi$
$312$	−9.11552	−	9.68541i	−0.516064	−	0.548329i
$313$			11.2583i			0.636359i	0.948030	+	0.318180i	$0.103072\pi$
$313$			11.2583i			0.636359i	−0.948030	+	0.318180i	$0.896928\pi$
$314$	−29.9813	−	13.4442i	−1.69194	−	0.758699i
$315$		0			0
$316$	−5.39376	+	4.80486i	−0.303423	+	0.270295i
$317$			27.2110i			1.52832i	0.645026	+	0.764161i	$0.276847\pi$
$317$			27.2110i			1.52832i	−0.645026	+	0.764161i	$0.723153\pi$
$318$	0.0675026	+	2.46512i	0.00378536	+	0.138237i
$319$		−	1.79368i		−	0.100427i
$320$		0			0
$321$	−13.7728	+	6.63458i	−0.768721	+	0.370306i
$322$	−18.7436	+	41.7992i	−1.04454	+	2.32938i
$323$	−7.05364			−0.392475
$324$	10.4325	−	14.6685i	0.579581	−	0.814915i
$325$		0			0
$326$	−4.03291	+	8.99362i	−0.223362	+	0.498111i
$327$	0.586455	+	1.21743i	0.0324311	+	0.0673238i
$328$	12.6534	−	4.00000i	0.698666	−	0.220863i
$329$		−	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	$0.667942\pi$
$332$	−7.25159	−	8.14037i	−0.397983	−	0.446761i
$333$	−2.55551	+	3.20603i	−0.140041	+	0.175690i
$334$	−5.74909	+	12.8208i	−0.314576	+	0.701522i
$335$		0			0
$336$	−9.72187	−	28.0571i	−0.530371	−	1.53064i
$337$		−	2.54733i		−	0.138762i	−0.997590	−	0.0693810i	$-0.977898\pi$
$337$		−	2.54733i		−	0.138762i	0.997590	−	0.0693810i	$-0.0221024\pi$
$338$	−7.26396	−	3.25730i	−0.395107	−	0.177174i
$339$	−4.55106	+	2.19232i	−0.247180	+	0.119071i
$340$		0			0
$341$	1.14947			0.0622474
$342$	−22.8279	+	11.7770i	−1.23439	+	0.636830i
$343$	18.7252			1.01107
$344$	4.05444	−	1.28169i	0.218601	−	0.0691042i
$345$		0			0
$346$	−4.63699	+	10.3408i	−0.249286	+	0.555922i
$347$	29.3727			1.57681			0.788405	−	0.615156i	$-0.210907\pi$
$347$	29.3727			1.57681			0.788405	+	0.615156i	$0.210907\pi$
$348$	−2.34477	−	0.975259i	−0.125693	−	0.0522794i
$349$		−	23.5131i		−	1.25863i	−0.777152	−	0.629313i	$-0.783336\pi$
$349$		−	23.5131i		−	1.25863i	0.777152	−	0.629313i	$-0.216664\pi$
$350$		0			0
$351$	−3.13436	+	13.7546i	−0.167300	+	0.734165i
$352$	11.8934	+	7.07918i	0.633920	+	0.377321i
$353$	31.0677			1.65357			0.826783	−	0.562522i	$-0.190169\pi$
$353$	31.0677			1.65357			0.826783	+	0.562522i	$0.190169\pi$
$354$	0.109615	+	4.00301i	0.00582596	+	0.212758i
$355$		0			0
$356$	−11.5886	+	10.3233i	−0.614193	+	0.547134i
$357$	−7.79164	+	3.75337i	−0.412377	+	0.198649i
$358$	13.5994	−	30.3274i	0.718749	−	1.60285i
$359$	11.3979			0.601556			0.300778	−	0.953694i	$-0.402754\pi$
$359$	11.3979			0.601556			0.300778	+	0.953694i	$0.402754\pi$
$360$		0			0
$361$	17.6562			0.929274
$362$	−5.74024	+	12.8010i	−0.301700	+	0.672808i
$363$	−7.82328	+	3.76861i	−0.410616	+	0.197801i
$364$	15.4797	+	17.3770i	0.811357	+	0.910800i
$365$		0			0
$366$	0.733092	+	26.7717i	0.0383193	+	1.39938i
$367$	−21.0209			−1.09728			−0.548640	−	0.836059i	$-0.684854\pi$
$367$	−21.0209			−1.09728			−0.548640	+	0.836059i	$0.684854\pi$
$368$	−30.0303	−	3.47970i	−1.56544	−	0.181392i
$369$	−11.0068	−	8.77342i	−0.572989	−	0.456726i
$370$		0			0
$371$		−	4.31488i		−	0.224017i
$372$	0.624991	−	1.50264i	0.0324043	−	0.0779082i
$373$	−10.3471			−0.535755			−0.267878	−	0.963453i	$-0.586322\pi$
$373$	−10.3471			−0.535755			−0.267878	+	0.963453i	$0.586322\pi$
$374$	1.64945	−	3.67836i	0.0852910	−	0.190204i
$375$		0			0
$376$	10.9982	−	3.47676i	0.567189	−	0.179300i
$377$	1.99029			0.102505
$378$	−18.9495	+	25.1564i	−0.974658	+	1.29390i
$379$	17.5341			0.900668			0.450334	−	0.892860i	$-0.351305\pi$
$379$	17.5341			0.900668			0.450334	+	0.892860i	$0.351305\pi$
$380$		0			0
$381$	−4.58397	+	2.20818i	−0.234844	+	0.113128i
$382$	29.0168	+	13.0117i	1.48463	+	0.665737i
$383$			24.7343i			1.26386i	0.775023	+	0.631932i	$0.217738\pi$
$383$			24.7343i			1.26386i	−0.775023	+	0.631932i	$0.782262\pi$
$384$	15.7209	−	11.6985i	0.802253	−	0.596984i
$385$		0			0
$386$	7.58932	−	16.9246i	0.386286	−	0.861439i
$387$	−3.52682	−	2.81121i	−0.179278	−	0.142902i
$388$	25.5603	−	22.7695i	1.29763	−	1.15595i
$389$	−24.2313			−1.22857			−0.614287	−	0.789083i	$-0.710556\pi$
$389$	−24.2313			−1.22857			−0.614287	+	0.789083i	$0.710556\pi$
$390$		0			0
$391$			8.80513i			0.445295i
$392$	9.69256	+	30.6609i	0.489548	+	1.54861i
$393$	5.92075	+	12.2909i	0.298662	+	0.619994i
$394$	−14.0487	+	31.3295i	−0.707765	+	1.57836i
$395$		0			0
$396$	−0.803385	−	14.6584i	−0.0403716	−	0.736611i
$397$	21.8856			1.09840			0.549202	−	0.835689i	$-0.314932\pi$
$397$	21.8856			1.09840			0.549202	+	0.835689i	$0.314932\pi$
$398$	1.05203	−	2.34609i	0.0527335	−	0.117599i
$399$	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	$0.820409\pi$
$402$	−0.668907	−	24.4277i	−0.0333620	−	1.21835i
$403$			1.27547i			0.0635357i
$404$	7.13362	+	8.00794i	0.354911	+	0.398410i
$405$		0			0
$406$	4.05444	+	1.81809i	0.201218	+	0.0902302i
$407$			3.34379i			0.165746i
$408$	−3.91167	−	4.15623i	−0.193657	−	0.205764i
$409$	21.5455			1.06536			0.532679	−	0.846317i	$-0.321185\pi$
$409$	21.5455			1.06536			0.532679	+	0.846317i	$0.321185\pi$
$410$		0			0
$411$	−3.92188	+	1.88924i	−0.193452	+	0.0931894i
$412$	−17.4155	−	19.5500i	−0.857999	−	0.963159i
$413$		−	7.00676i		−	0.344780i
$414$	14.7014	+	28.4963i	0.722535	+	1.40052i
$415$		0			0
$416$	−7.85516	+	13.1971i	−0.385131	+	0.647040i
$417$	4.01771	−	1.93540i	0.196748	−	0.0947771i
$418$	−8.57182	+	19.1156i	−0.419261	+	0.934976i
$419$			14.6547i			0.715930i	0.933735	+	0.357965i	$0.116529\pi$
$419$			14.6547i			0.715930i	−0.933735	+	0.357965i	$0.883471\pi$
$420$		0			0
$421$			19.0967i			0.930718i	0.885122	+	0.465359i	$0.154075\pi$
$421$			19.0967i			0.930718i	−0.885122	+	0.465359i	$0.845925\pi$
$422$	1.36938	+	0.614057i	0.0666605	+	0.0298918i
$423$	−9.56697	−	7.62577i	−0.465162	−	0.370778i
$424$	2.71511	−	0.858303i	0.131857	−	0.0416829i
$425$		0			0
$426$	28.4914	−	0.780183i	1.38041	−	0.0378000i
$427$		−	46.8604i		−	2.26774i
$428$	11.7418	+	13.1810i	0.567564	+	0.637126i
$429$	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	$0.734063\pi$
$432$	−19.5989	−	6.91984i	−0.942951	−	0.332931i
$433$			24.0750i			1.15697i	0.815692	+	0.578486i	$0.196356\pi$
$433$			24.0750i			1.15697i	−0.815692	+	0.578486i	$0.803644\pi$
$434$	−1.16511	+	2.59827i	−0.0559273	+	0.124721i
$435$		0			0
$436$	1.16511	−	1.03791i	0.0557989	−	0.0497067i
$437$		−	45.7583i		−	2.18892i
$438$	0.646084	+	23.5943i	0.0308711	+	1.12738i
$439$			24.6249i			1.17528i	0.809122	+	0.587641i	$0.199943\pi$
$439$			24.6249i			1.17528i	−0.809122	+	0.587641i	$0.800057\pi$
$440$		0			0
$441$	21.2592	−	26.6709i	1.01234	−	1.27004i
$442$	4.08156	+	1.83025i	0.194140	+	0.0870562i
$443$	7.61113			0.361616			0.180808	−	0.983518i	$-0.442129\pi$
$443$	7.61113			0.361616			0.180808	+	0.983518i	$0.442129\pi$
$444$	4.37115	+	1.81809i	0.207446	+	0.0862826i
$445$		0			0
$446$	6.74307	+	3.02372i	0.319294	+	0.143177i
$447$	−25.1580	+	12.1190i	−1.18993	+	0.573211i
$448$	−28.0571	+	19.7084i	−1.32557	+	0.931132i
$449$			11.2946i			0.533026i	0.963831	+	0.266513i	$0.0858715\pi$
$449$			11.2946i			0.533026i	−0.963831	+	0.266513i	$0.914128\pi$
$450$		0			0
$451$	−11.4797			−0.540558
$452$	3.87996	+	4.35551i	0.182498	+	0.204866i
$453$	13.4152	+	27.8487i	0.630302	+	1.30845i
$454$	−17.9304	−	8.04033i	−0.841514	−	0.377351i
$455$		0			0
$456$	20.3281	+	21.5990i	0.951951	+	1.01147i
$457$			29.5067i			1.38027i	0.723682	+	0.690133i	$0.242448\pi$
$457$			29.5067i			1.38027i	−0.723682	+	0.690133i	$0.757552\pi$
$458$	0.135005	−	0.301069i	0.00630838	−	0.0140680i
$459$	−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	$0.264494\pi$
$462$	0.703111	+	25.6769i	0.0327117	+	1.19460i
$463$	−22.6025			−1.05043			−0.525213	−	0.850971i	$-0.676014\pi$
$463$	−22.6025			−1.05043			−0.525213	+	0.850971i	$0.676014\pi$
$464$	−0.337524	+	2.91288i	−0.0156691	+	0.135227i
$465$		0			0
$466$	−11.1258	−	4.98902i	−0.515392	−	0.231112i
$467$	13.6141			0.629984			0.314992	−	0.949094i	$-0.397998\pi$
$467$	13.6141			0.629984			0.314992	+	0.949094i	$0.397998\pi$
$468$	16.2651	−	0.891448i	0.751857	−	0.0412072i
$469$			42.7576i			1.97436i
$470$		0			0
$471$	36.2549	−	17.4646i	1.67054	−	0.804728i
$472$	4.40896	−	1.39376i	0.202939	−	0.0641532i
$473$	−3.67836			−0.169131
$474$	−0.242167	−	8.84367i	−0.0111231	−	0.406203i
$475$		0			0
$476$	6.64269	+	7.45684i	0.304467	+	0.341784i
$477$	−2.36178	−	1.88256i	−0.108139	−	0.0861967i
$478$	−25.9488	−	11.6359i	−1.18687	−	0.532215i
$479$	−0.411425			−0.0187985			−0.00939924	−	0.999956i	$-0.502992\pi$
$479$	−0.411425			−0.0187985			−0.00939924	+	0.999956i	$0.502992\pi$
$480$		0			0
$481$	−3.71032			−0.169176
$482$	−11.7740	−	5.27968i	−0.536290	−	0.240483i
$483$	−24.3488	−	50.5459i	−1.10791	−	2.29992i
$484$	6.66966	+	7.48712i	0.303167	+	0.340324i
$485$		0			0
$486$	5.50195	+	21.3478i	0.249573	+	0.968356i
$487$	32.2250			1.46025			0.730126	−	0.683312i	$-0.239461\pi$
$487$	32.2250			1.46025			0.730126	+	0.683312i	$0.239461\pi$
$488$	29.4866	−	9.32134i	1.33480	−	0.421957i
$489$	−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	$-0.103524\pi$
$492$	−6.24175	+	15.0068i	−0.281400	+	0.676557i
$493$	0.854079			0.0384658
$494$	−21.2110	−	9.51142i	−0.954328	−	0.427939i
$495$		0			0
$496$	−1.86671	−	0.216301i	−0.0838176	−	0.00971219i
$497$	−49.8706			−2.23700
$498$	13.3470	−	0.365483i	0.598095	−	0.0163777i
$499$	14.6018			0.653665			0.326833	−	0.945082i	$-0.394019\pi$
$499$	14.6018			0.653665			0.326833	+	0.945082i	$0.394019\pi$
$500$		0			0
$501$	−7.46834	−	15.5036i	−0.333661	−	0.692648i
$502$	7.69972	−	17.1708i	0.343655	−	0.766371i
$503$		−	30.2823i		−	1.35022i	−0.737716	−	0.675112i	$-0.764095\pi$
$503$		−	30.2823i		−	1.35022i	0.737716	−	0.675112i	$-0.235905\pi$
$504$	33.9482	+	13.0419i	1.51217	+	0.580932i
$505$		0			0
$506$	23.8622	+	10.7003i	1.06081	+	0.475686i
$507$	8.78397	−	4.23139i	0.390110	−	0.187923i
$508$	3.90802	+	4.38701i	0.173391	+	0.194642i
$509$	−8.84197			−0.391913			−0.195957	−	0.980613i	$-0.562781\pi$
$509$	−8.84197			−0.391913			−0.195957	+	0.980613i	$0.562781\pi$
$510$		0			0
$511$		−	41.2987i		−	1.82695i
$512$	−17.9824	−	13.7344i	−0.794717	−	0.606980i
$513$	6.98979	−	30.6734i	0.308607	−	1.35427i
$514$	−38.9880	−	17.4830i	−1.71969	−	0.771142i
$515$		0			0
$516$	−2.00000	+	4.80851i	−0.0880451	+	0.211683i
$517$	−9.97804			−0.438834
$518$	−7.55832	−	3.38930i	−0.332094	−	0.148917i
$519$	−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	$-0.320826\pi$
$522$	2.76408	−	1.42601i	0.120981	−	0.0624145i
$523$		−	13.8674i		−	0.606381i	−0.952930	−	0.303191i	$-0.901948\pi$
$523$		−	13.8674i		−	0.606381i	0.952930	−	0.303191i	$-0.0980519\pi$
$524$	11.7628	−	10.4785i	0.513860	−	0.457756i
$525$		0			0
$526$	8.63841	−	19.2641i	0.376653	−	0.839956i
$527$			0.547333i			0.0238422i
$528$	−16.0171	+	5.54999i	−0.697056	+	0.241533i
$529$	−34.1206			−1.48350
$530$		0			0
$531$	−3.83521	−	3.05702i	−0.166434	−	0.132663i
$532$	−34.5206	−	38.7516i	−1.49666	−	1.68009i
$533$		−	12.7380i		−	0.551746i
$534$	−0.520299	−	19.0007i	−0.0225155	−	0.822242i
$535$		0			0
$536$	−26.9050	+	8.50522i	−1.16212	+	0.367370i
$537$	17.6662	+	36.6734i	0.762355	+	1.58258i
$538$	−6.25919	−	2.80674i	−0.269853	−	0.121007i
$539$		−	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	$-0.0356323\pi$
$542$	−8.61036	+	19.2016i	−0.369846	+	0.824778i
$543$	−7.45684	−	15.4797i	−0.320004	−	0.664298i
$544$	−3.37083	+	5.66317i	−0.144523	+	0.242806i
$545$		0			0
$546$	−28.4914	+	0.780183i	−1.21932	+	0.0333887i
$547$			13.1393i			0.561796i	0.959738	+	0.280898i	$0.0906323\pi$
$547$			13.1393i			0.561796i	−0.959738	+	0.280898i	$0.909368\pi$
$548$	3.34357	+	3.75337i	0.142830	+	0.160336i
$549$	−25.6494	−	20.4450i	−1.09469	−	0.872572i
$550$		0			0
$551$	−4.43846			−0.189085
$552$	26.9623	−	25.3758i	1.14759	−	1.08007i
$553$			15.4797i			0.658264i
$554$	25.3995	+	11.3896i	1.07912	+	0.483898i
$555$		0			0
$556$	−3.42526	−	3.84508i	−0.145264	−	0.163068i
$557$		−	0.506781i		−	0.0214730i	−0.999942	−	0.0107365i	$-0.996582\pi$
$557$		−	0.506781i		−	0.0214730i	0.999942	−	0.0107365i	$-0.00341760\pi$
$558$	0.913850	+	1.77135i	0.0386864	+	0.0749872i
$559$		−	4.08156i		−	0.172632i
$560$		0			0
$561$	2.14271	+	4.44807i	0.0904654	+	0.187798i
$562$	−1.32994	+	2.96584i	−0.0561001	+	0.125106i
$563$	13.0410			0.549612			0.274806	−	0.961500i	$-0.411386\pi$
$563$	13.0410			0.549612			0.274806	+	0.961500i	$0.411386\pi$
$564$	−5.42526	+	13.0437i	−0.228445	+	0.549240i
$565$		0			0
$566$	12.5059	−	27.8888i	0.525660	−	1.17225i
$567$	−8.60079	−	37.6021i	−0.361199	−	1.57914i
$568$	−9.92011	−	31.3807i	−0.416239	−	1.31671i
$569$		−	30.7683i		−	1.28988i	−0.764235	−	0.644938i	$-0.776883\pi$
$569$		−	30.7683i		−	1.28988i	0.764235	−	0.644938i	$-0.223117\pi$
$570$		0			0
$571$	27.6769			1.15824			0.579120	−	0.815242i	$-0.303396\pi$
$571$	27.6769			1.15824			0.579120	+	0.815242i	$0.303396\pi$
$572$	9.92011	−	8.83701i	0.414781	−	0.369494i
$573$	−35.0887	+	16.9028i	−1.46585	+	0.706126i
$574$	11.6359	−	25.9488i	0.485674	−	1.08308i
$575$		0			0
$576$	−1.45365	+	23.9559i	−0.0605688	+	0.998164i
$577$			33.4626i			1.39307i	0.717525	+	0.696533i	$0.245275\pi$
$577$			33.4626i			1.39307i	−0.717525	+	0.696533i	$0.754725\pi$
$578$	−20.1855	−	9.05159i	−0.839608	−	0.376496i
$579$	9.85889	+	20.4661i	0.409721	+	0.850543i
$580$		0			0
$581$	−23.3623			−0.969230
$582$	1.14759	+	41.9089i	0.0475693	+	1.73718i
$583$	−2.46327			−0.102018
$584$	25.9870	−	8.21503i	1.07535	−	0.339940i
$585$		0			0
$586$	3.47188	−	7.74248i	0.143422	−	0.319839i
$587$	28.7031			1.18471			0.592353	−	0.805679i	$-0.298199\pi$
$587$	28.7031			1.18471			0.592353	+	0.805679i	$0.298199\pi$
$588$	−36.3635	−	15.1246i	−1.49960	−	0.623729i
$589$		−	2.84437i		−	0.117200i
$590$		0			0
$591$	−18.2500	−	37.8853i	−0.750704	−	1.55839i
$592$	0.629215	−	5.43022i	0.0258606	−	0.223181i
$593$	−44.2574			−1.81744			−0.908718	−	0.417411i	$-0.862938\pi$
$593$	−44.2574			−1.81744			−0.908718	+	0.417411i	$0.862938\pi$
$594$	14.3612	+	10.8179i	0.589247	+	0.443862i
$595$		0			0
$596$	21.4482	+	24.0770i	0.878553	+	0.986231i
$597$	1.36664	+	2.83701i	0.0559328	+	0.116111i
$598$	−11.8732	+	26.4779i	−0.485531	+	1.08276i
$599$	−24.1359			−0.986166			−0.493083	−	0.869982i	$-0.664130\pi$
$599$	−24.1359			−0.986166			−0.493083	+	0.869982i	$0.664130\pi$
$600$		0			0
$601$	19.7669			0.806308			0.403154	−	0.915132i	$-0.367914\pi$
$601$	19.7669			0.806308			0.403154	+	0.915132i	$0.367914\pi$
$602$	3.72842	−	8.31459i	0.151959	−	0.338877i
$603$	23.4037	+	18.6550i	0.953074	+	0.759689i
$604$	26.6521	−	23.7422i	1.08446	−	0.966056i
$605$		0			0
$606$	−13.1299	+	0.359537i	−0.533365	+	0.0146052i
$607$	7.68877			0.312078			0.156039	−	0.987751i	$-0.450127\pi$
$607$	7.68877			0.312078			0.156039	+	0.987751i	$0.450127\pi$
$608$	17.5174	−	29.4302i	0.710426	−	1.19355i
$609$	−4.90284	+	2.36178i	−0.198673	+	0.0957043i
$610$		0			0
$611$		−	11.0718i		−	0.447916i
$612$	6.97974	−	0.382541i	0.282139	−	0.0154633i
$613$	26.6091			1.07473			0.537366	−	0.843349i	$-0.319419\pi$
$613$	26.6091			1.07473			0.537366	+	0.843349i	$0.319419\pi$
$614$	−2.88344	+	6.43024i	−0.116366	+	0.259503i
$615$		0			0
$616$	28.2807	−	8.94014i	1.13946	−	0.360208i
$617$	25.0592			1.00885			0.504423	−	0.863456i	$-0.331705\pi$
$617$	25.0592			1.00885			0.504423	+	0.863456i	$0.331705\pi$
$618$	32.0544	−	0.877747i	1.28942	−	0.0353082i
$619$	20.1498			0.809889			0.404944	−	0.914341i	$-0.367291\pi$
$619$	20.1498			0.809889			0.404944	+	0.914341i	$0.367291\pi$
$620$		0			0
$621$	−38.2900	−	8.72542i	−1.53652	−	0.350139i
$622$	−14.3089	−	6.41638i	−0.573734	−	0.257273i
$623$			33.2583i			1.33247i
$624$	−6.15836	−	17.7729i	−0.246532	−	0.711484i
$625$		0			0
$626$	−6.51460	+	14.5279i	−0.260376	+	0.580653i
$627$	−11.1352	−	23.1156i	−0.444697	−	0.923149i
$628$	−30.9088	−	34.6971i	−1.23340	−	1.38457i
$629$	−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	$0.813322\pi$
$632$	−9.74051	+	3.07918i	−0.387457	+	0.122483i
$633$	−1.65593	+	0.797690i	−0.0658173	+	0.0317053i
$634$	−15.7455	+	35.1134i	−0.625336	+	1.39453i
$635$		0			0
$636$	−1.33933	+	3.22009i	−0.0531078	+	0.127685i
$637$	30.8661			1.22296
$638$	1.03791	−	2.31459i	0.0410911	−	0.0916354i
$639$	−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	$0.745485\pi$
$642$	−21.6116	+	0.591793i	−0.852944	+	0.0233562i
$643$			32.8571i			1.29576i	0.761744	+	0.647878i	$0.224344\pi$
$643$			32.8571i			1.29576i	−0.761744	+	0.647878i	$0.775656\pi$
$644$	−48.3740	+	43.0924i	−1.90620	+	1.69808i
$645$		0			0
$646$	−9.10212	−	4.08156i	−0.358118	−	0.160587i
$647$		−	17.1329i		−	0.673563i	−0.941583	−	0.336781i	$-0.890662\pi$
$647$		−	17.1329i		−	0.673563i	0.941583	−	0.336781i	$-0.109338\pi$
$648$	21.9500	−	12.8917i	0.862279	−	0.506434i
$649$	−4.00000			−0.157014
$650$		0			0
$651$	−1.51354	−	3.14197i	−0.0593203	−	0.123143i
$652$	−10.4083	+	9.27186i	−0.407619	+	0.363114i
$653$		−	27.7583i		−	1.08627i	−0.839646	−	0.543134i	$-0.817238\pi$
$653$		−	27.7583i		−	1.08627i	0.839646	−	0.543134i	$-0.182762\pi$
$654$	0.0523108	+	1.91033i	0.00204551	+	0.0746999i
$655$		0			0
$656$	18.6427	+	2.16018i	0.727875	+	0.0843409i
$657$	−22.6052	−	18.0185i	−0.881913	−	0.702968i
$658$	10.1138	−	22.5544i	0.394278	−	0.879263i
$659$		−	15.3389i		−	0.597519i	−0.954328	−	0.298760i	$-0.903427\pi$
$659$		−	15.3389i		−	0.597519i	0.954328	−	0.298760i	$-0.0965729\pi$
$660$		0			0
$661$		−	38.9369i		−	1.51447i	−0.653141	−	0.757236i	$-0.726549\pi$
$661$		−	38.9369i		−	1.51447i	0.653141	−	0.757236i	$-0.273451\pi$
$662$	−23.6398	−	10.6005i	−0.918787	−	0.412002i
$663$	−4.93564	+	2.37759i	−0.191685	+	0.0923378i
$664$	−4.64716	−	14.7006i	−0.180345	−	0.570492i
$665$		0			0
$666$	−5.15283	+	2.65837i	−0.199668	+	0.103010i
$667$			5.54057i			0.214532i
$668$	−14.8374	+	13.2174i	−0.574076	+	0.511398i
$669$	−8.15407	+	3.92796i	−0.315255	+	0.151864i
$670$		0			0
$671$	−26.7516			−1.03273
$672$	3.68989	−	41.8307i	0.142340	−	1.61366i
$673$		−	6.78966i		−	0.261722i	−0.991401	−	0.130861i	$-0.958226\pi$
$673$		−	6.78966i		−	0.261722i	0.991401	−	0.130861i	$-0.0417742\pi$
$674$	1.47401	−	3.28711i	0.0567766	−	0.126615i
$675$		0			0
$676$	−7.48869	−	8.40653i	−0.288027	−	0.323328i
$677$			40.6772i			1.56335i	0.623685	+	0.781675i	$0.285635\pi$
$677$			40.6772i			1.56335i	−0.623685	+	0.781675i	$0.714365\pi$
$678$	−7.14133	+	0.195552i	−0.274261	+	0.00751011i
$679$		−	73.3561i		−	2.81515i
$680$		0			0
$681$	21.6824	−	10.4448i	0.830870	−	0.400245i
$682$	1.48329	+	0.665138i	0.0567983	+	0.0254694i
$683$	8.14204			0.311546			0.155773	−	0.987793i	$-0.450213\pi$
$683$	8.14204			0.311546			0.155773	+	0.987793i	$0.450213\pi$
$684$	−36.2722	+	1.98798i	−1.38690	+	0.0760123i
$685$		0			0
$686$	24.1633	+	10.8353i	0.922559	+	0.413694i
$687$	0.175378	+	0.364069i	0.00669110	+	0.0138901i
$688$	5.97355	+	0.692172i	0.227739	+	0.0263888i
$689$		−	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	$0.512729\pi$
$692$	−11.9673	+	10.6607i	−0.454928	+	0.405258i
$693$	−24.6005	−	19.6089i	−0.934495	−	0.744880i
$694$	37.9030	+	16.9964i	1.43878	+	0.645176i
$695$		0			0
$696$	−2.46140	−	2.61528i	−0.0932990	−	0.0991320i
$697$		−	5.46618i		−	0.207046i
$698$	13.6058	−	30.3416i	0.514986	−	1.14845i
$699$	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	$0.623371\pi$
$702$	−12.0037	+	15.9354i	−0.453049	+	0.601443i
$703$	8.27422			0.312068
$704$	11.2511	+	16.0171i	0.424040	+	0.603669i
$705$		0			0
$706$	40.0902	+	17.9772i	1.50881	+	0.676581i
$707$	22.9822			0.864334
$708$	−2.17488	+	5.22897i	−0.0817370	+	0.196517i
$709$			15.3500i			0.576480i	0.957558	+	0.288240i	$0.0930701\pi$
$709$			15.3500i			0.576480i	−0.957558	+	0.288240i	$0.906930\pi$
$710$		0			0
$711$	8.47294	+	6.75373i	0.317760	+	0.253285i
$712$	−20.9276	+	6.61566i	−0.784295	+	0.247932i
$713$	−3.55066			−0.132973
$714$	−12.2263	+	0.334794i	−0.457558	+	0.0125294i
$715$		0			0
$716$	35.0977	−	31.2656i	1.31166	−	1.16845i
$717$	31.3786	−	15.1156i	1.17186	−	0.564504i
$718$	14.7080	+	6.59533i	0.548896	+	0.246136i
$719$	−5.77864			−0.215507			−0.107754	−	0.994178i	$-0.534366\pi$
$719$	−5.77864			−0.215507			−0.107754	+	0.994178i	$0.534366\pi$
$720$		0			0
$721$	−56.1070			−2.08953
$722$	22.7838	+	10.2167i	0.847926	+	0.380226i
$723$	14.2377	−	6.85856i	0.529507	−	0.255073i
$724$	−14.8146	+	13.1971i	−0.550579	+	0.490466i
$725$		0			0
$726$	−12.2760	+	0.336154i	−0.455604	+	0.0124758i
$727$	−25.0657			−0.929636			−0.464818	−	0.885406i	$-0.653880\pi$
$727$	−25.0657			−0.929636			−0.464818	+	0.885406i	$0.653880\pi$
$728$	9.92011	+	31.3807i	0.367664	+	1.16305i
$729$	−24.3343	−	11.6979i	−0.901271	−	0.433257i
$730$		0			0
$731$		−	1.75149i		−	0.0647813i
$732$	−14.5454	+	34.9708i	−0.537612	+	1.29256i
$733$	14.9596			0.552546			0.276273	−	0.961079i	$-0.410901\pi$
$733$	14.9596			0.552546			0.276273	+	0.961079i	$0.410901\pi$
$734$	−27.1256	−	12.1636i	−1.00122	−	0.448968i
$735$		0			0
$736$	−36.7380	−	21.8672i	−1.35418	−	0.806036i
$737$	24.4094			0.899130
$738$	−9.12656	−	17.6904i	−0.335953	−	0.651191i
$739$	−9.76476			−0.359202			−0.179601	−	0.983739i	$-0.557481\pi$
$739$	−9.76476			−0.359202			−0.179601	+	0.983739i	$0.557481\pi$
$740$		0			0
$741$	25.6494	−	12.3558i	0.942256	−	0.453901i
$742$	2.49679	−	5.56798i	0.0916600	−	0.204407i
$743$		−	13.6457i		−	0.500613i	−0.968167	−	0.250307i	$-0.919469\pi$
$743$		−	13.6457i		−	0.500613i	0.968167	−	0.250307i	$-0.0805314\pi$
$744$	1.67599	−	1.57738i	0.0614449	−	0.0578294i
$745$		0			0
$746$	−13.3521	−	5.98734i	−0.488855	−	0.219212i
$747$	−10.1929	+	12.7875i	−0.372937	+	0.467871i
$748$	4.25694	−	3.79216i	0.155649	−	0.138655i
$749$	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	$0.765807\pi$
$752$	16.2040	+	1.87761i	0.590901	+	0.0684693i
$753$	10.0023	+	20.7639i	0.364504	+	0.756677i
$754$	2.56830	+	1.15168i	0.0935319	+	0.0419415i
$755$		0			0
$756$	−39.0094	+	21.4971i	−1.41876	+	0.781840i
$757$	−10.1994			−0.370702			−0.185351	−	0.982672i	$-0.559342\pi$
$757$	−10.1994			−0.370702			−0.185351	+	0.982672i	$0.559342\pi$
$758$	22.6263	+	10.1461i	0.821824	+	0.368522i
$759$	−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	$-0.169877\pi$
$762$	−7.19298	+	0.196966i	−0.260574	+	0.00713532i
$763$		−	3.34379i		−	0.121053i
$764$	29.9146	+	33.5810i	1.08227	+	1.21492i
$765$		0			0
$766$	−14.3124	+	31.9175i	−0.517129	+	1.15323i
$767$		−	4.43846i		−	0.160263i
$768$	27.0557	−	5.99901i	0.976289	−	0.216471i
$769$	−16.3302			−0.588883			−0.294442	−	0.955669i	$-0.595134\pi$
$769$	−16.3302			−0.588883			−0.294442	+	0.955669i	$0.595134\pi$
$770$		0			0
$771$	47.1464	−	22.7112i	1.69794	−	0.817925i
$772$	19.5867	−	17.4482i	0.704941	−	0.627975i
$773$			42.5099i			1.52897i	0.644639	+	0.764487i	$0.277008\pi$
$773$			42.5099i			1.52897i	−0.644639	+	0.764487i	$0.722992\pi$
$774$	−2.92436	−	5.66840i	−0.105114	−	0.203747i
$775$		0			0
$776$	46.1588	−	14.5918i	1.65701	−	0.523814i
$777$	9.13993	−	4.40286i	0.327893	−	0.157952i
$778$	−31.2684	−	14.0213i	−1.12103	−	0.502689i
$779$			28.4065i			1.01777i
$780$		0			0
$781$			28.4700i			1.01874i
$782$	−5.09506	+	11.3623i	−0.182199	+	0.406314i
$783$	−0.846347	+	3.71405i	−0.0302460	+	0.132729i
$784$	−5.23442	+	45.1738i	−0.186944	+	1.61335i
$785$		0			0
$786$	0.528120	+	19.2864i	0.0188374	+	0.687922i
$787$		−	27.9997i		−	0.998083i	−0.866578	−	0.499042i	$-0.833685\pi$
$787$		−	27.9997i		−	0.998083i	0.866578	−	0.499042i	$-0.166315\pi$
$788$	−36.2574	+	32.2987i	−1.29162	+	1.15059i
$789$	11.2217	+	23.2952i	0.399503	+	0.829331i
$790$		0			0
$791$	12.5000			0.444448
$792$	7.44532	−	19.3802i	0.264558	−	0.688647i
$793$		−	29.6839i		−	1.05411i
$794$	28.2414	+	12.6640i	1.00225	+	0.449429i
$795$		0			0
$796$	2.71511	−	2.41867i	0.0962345	−	0.0857274i
$797$		−	1.92561i		−	0.0682086i	−0.999418	−	0.0341043i	$-0.989142\pi$
$797$		−	1.92561i		−	0.0682086i	0.999418	−	0.0341043i	$-0.0108578\pi$
$798$	63.5374	−	1.73985i	2.24920	−	0.0615900i
$799$		−	4.75115i		−	0.168084i
$800$		0			0
$801$	18.2042	+	14.5105i	0.643215	+	0.512703i
$802$	−12.3925	+	27.6359i	−0.437594	+	0.975859i
$803$	−23.5765			−0.831997
$804$	13.2719	−	31.9090i	0.468063	−	1.12534i
$805$		0			0
$806$	−0.738047	+	1.64588i	−0.0259966	+	0.0579738i
$807$	7.56894	−	3.64609i	0.266439	−	0.128349i
$808$	4.57155	+	14.4614i	0.160827	+	0.508750i
$809$			30.3334i			1.06647i	0.845968	+	0.533233i	$0.179023\pi$
$809$			30.3334i			1.06647i	−0.845968	+	0.533233i	$0.820977\pi$
$810$		0			0
$811$	7.56798			0.265748			0.132874	−	0.991133i	$-0.457579\pi$
$811$	7.56798			0.265748			0.132874	+	0.991133i	$0.457579\pi$
$812$	4.17987	+	4.69217i	0.146685	+	0.164663i
$813$	−11.1853	−	23.2196i	−0.392284	−	0.814345i
$814$	−1.93487	+	4.31488i	−0.0678173	+	0.151236i
$815$		0			0
$816$	−2.64269	−	7.62673i	−0.0925127	−	0.266989i
$817$			9.10212i			0.318443i
$818$	27.8027	+	12.4672i	0.972097	+	0.435907i
$819$	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	$0.332066\pi$
$822$	−6.15406	+	0.168517i	−0.214647	+	0.00587771i
$823$	15.3789			0.536076			0.268038	−	0.963408i	$-0.413625\pi$
$823$	15.3789			0.536076			0.268038	+	0.963408i	$0.413625\pi$
$824$	−11.1606	−	35.3050i	−0.388800	−	1.22991i
$825$		0			0
$826$	4.05444	−	9.04162i	0.141072	−	0.314598i
$827$	−48.0070			−1.66937			−0.834683	−	0.550731i	$-0.814349\pi$
$827$	−48.0070			−1.66937			−0.834683	+	0.550731i	$0.814349\pi$
$828$	2.48161	+	45.2789i	0.0862421	+	1.57355i
$829$		−	19.0600i		−	0.661982i	−0.943634	−	0.330991i	$-0.892617\pi$
$829$		−	19.0600i		−	0.661982i	0.943634	−	0.330991i	$-0.107383\pi$
$830$		0			0
$831$	−30.7144	+	14.7956i	−1.06547	+	0.513255i
$832$	−17.7729	+	12.4843i	−0.616163	+	0.432816i
$833$	13.2453			0.458923
$834$	6.30443	−	0.172635i	0.218304	−	0.00597785i
$835$		0			0
$836$	−22.1224	+	19.7070i	−0.765119	+	0.681582i
$837$	−2.38013	−	0.542379i	−0.0822694	−	0.0187473i
$838$	−8.47991	+	18.9107i	−0.292934	+	0.653258i
$839$	56.8469			1.96257			0.981287	−	0.192552i	$-0.0616763\pi$
$839$	56.8469			1.96257			0.981287	+	0.192552i	$0.0616763\pi$
$840$		0			0
$841$	−28.4626			−0.981468
$842$	−11.0503	+	24.6427i	−0.380817	+	0.849243i
$843$	−1.72766	−	3.58645i	−0.0595036	−	0.123524i
$844$	1.41175	+	1.58478i	0.0485943	+	0.0545502i
$845$		0			0
$846$	−7.93272	−	15.3763i	−0.272733	−	0.528648i
$847$	21.4875			0.738319
$848$	4.00027	+	0.463523i	0.137370	+	0.0159174i
$849$	16.2457	+	33.7246i	0.557551	+	1.15742i
$850$		0			0
$851$		−	10.3288i		−	0.354067i
$852$	37.2172	+	15.4797i	1.27504	+	0.530326i
$853$	29.3057			1.00341			0.501704	−	0.865039i	$-0.332707\pi$
$853$	29.3057			1.00341			0.501704	+	0.865039i	$0.332707\pi$
$854$	27.1156	−	60.4694i	0.927878	−	2.06922i
$855$		0			0
$856$	7.52472	+	23.8033i	0.257190	+	0.813580i
$857$	30.9833			1.05837			0.529185	−	0.848507i	$-0.322498\pi$
$857$	30.9833			1.05837			0.529185	+	0.848507i	$0.322498\pi$
$858$	0.445389	+	16.2651i	0.0152053	+	0.555281i
$859$	1.13559			0.0387457			0.0193729	−	0.999812i	$-0.493833\pi$
$859$	1.13559			0.0387457			0.0193729	+	0.999812i	$0.493833\pi$
$860$		0			0
$861$	15.1156	+	31.3786i	0.515139	+	1.06938i
$862$	−35.9428	−	16.1174i	−1.22422	−	0.548962i
$863$			12.8678i			0.438024i	0.975722	+	0.219012i	$0.0702834\pi$
$863$			12.8678i			0.438024i	−0.975722	+	0.219012i	$0.929717\pi$
$864$	−21.2865	−	20.2703i	−0.724182	−	0.689609i
$865$		0			0
$866$	−13.9309	+	31.0668i	−0.473393	+	1.05569i
$867$	24.4094	−	11.7584i	0.828988	−	0.399338i
$868$	−3.00696	+	2.67866i	−0.102063	+	0.0909195i
$869$	8.83701			0.299775
$870$		0			0
$871$			27.0850i			0.917740i
$872$	2.10406	−	0.665138i	0.0712525	−	0.0225244i
$873$	−40.1520	−	32.0050i	−1.35894	−	1.08320i
$874$	26.4779	−	59.0472i	0.895628	−	1.99730i
$875$		0			0
$876$	−12.8190	+	30.8202i	−0.433115	+	1.04132i
$877$	−35.8017			−1.20894			−0.604469	−	0.796629i	$-0.706615\pi$
$877$	−35.8017			−1.20894			−0.604469	+	0.796629i	$0.706615\pi$
$878$	−14.2491	+	31.7763i	−0.480884	+	1.07240i
$879$	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	$0.855646\pi$
$882$	42.8662	−	22.1149i	1.44338	−	0.744649i
$883$			41.3226i			1.39062i	0.718712	+	0.695308i	$0.244732\pi$
$883$			41.3226i			1.39062i	−0.718712	+	0.695308i	$0.755268\pi$
$884$	4.20784	+	4.72357i	0.141525	+	0.158871i
$885$		0			0
$886$	9.82151	+	4.40415i	0.329960	+	0.147960i
$887$		−	14.9286i		−	0.501255i	−0.968084	−	0.250627i	$-0.919363\pi$
$887$		−	14.9286i		−	0.501255i	0.968084	−	0.250627i	$-0.0806369\pi$
$888$	4.58856	+	4.87544i	0.153982	+	0.163609i
$889$	12.5904			0.422268
$890$		0			0
$891$	−21.4662	+	4.90999i	−0.719144	+	0.164491i
$892$	6.95168	+	7.80371i	0.232760	+	0.261287i
$893$			24.6907i			0.826242i
$894$	−39.4768	+	1.08100i	−1.32030	+	0.0361540i
$895$		0			0
$896$	−47.6094	+	9.19681i	−1.59052	+	0.307244i
$897$	−15.4239	−	32.0185i	−0.514988	−	1.06907i
$898$	−6.53559	+	14.5747i	−0.218096	+	0.486365i
$899$			0.344406i			0.0114866i
$900$		0			0
$901$		−	1.17291i		−	0.0390753i
$902$	−14.8136	−	6.64269i	−0.493238	−	0.221177i
$903$	4.84340	+	10.0544i	0.161178	+	0.334591i
$904$	2.48646	+	7.86553i	0.0826984	+	0.261604i
$905$		0			0
$906$	1.19661	+	43.6991i	0.0397549	+	1.45180i
$907$			39.4794i			1.31089i	0.755241	+	0.655447i	$0.227520\pi$
$907$			39.4794i			1.31089i	−0.755241	+	0.655447i	$0.772480\pi$
$908$	−18.4851	−	20.7507i	−0.613450	−	0.688636i
$909$	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	$0.208892\pi$
$912$	13.7335	+	39.6344i	0.454761	+	1.31243i
$913$			13.3370i			0.441390i
$914$	−17.0740	+	38.0759i	−0.564757	+	1.25944i
$915$		0			0
$916$	0.348425	−	0.310383i	0.0115123	−	0.0102554i
$917$		−	33.7583i		−	1.11480i
$918$	−5.15104	+	6.83824i	−0.170010	+	0.225696i
$919$			30.2025i			0.996290i	0.867094	+	0.498145i	$0.165985\pi$
$919$			30.2025i			0.996290i	−0.867094	+	0.498145i	$0.834015\pi$
$920$		0			0
$921$	−3.74573	−	7.77578i	−0.123426	−	0.256221i
$922$	37.3586	+	16.7523i	1.23034	+	0.551708i
$923$	−31.5907			−1.03982
$924$	−13.9505	+	33.5406i	−0.458938	+	1.10341i
$925$		0			0
$926$	−29.1665	−	13.0788i	−0.958472	−	0.429797i
$927$	−24.4793	+	30.7106i	−0.804005	+	1.00867i
$928$	−2.12107	+	3.56351i	−0.0696276	+	0.116978i
$929$			2.81266i			0.0922804i	0.998935	+	0.0461402i	$0.0146921\pi$
$929$			2.81266i			0.0922804i	−0.998935	+	0.0461402i	$0.985308\pi$
$930$		0			0
$931$	−68.8330			−2.25591
$932$	−11.4700	−	12.8758i	−0.375712	−	0.421761i
$933$	17.3031	−	8.33518i	0.566477	−	0.272882i
$934$	17.5678	+	7.87774i	0.574836	+	0.257767i
$935$		0			0
$936$	21.5046	+	8.26144i	0.702900	+	0.270033i
$937$			20.7171i			0.676798i	0.941003	+	0.338399i	$0.109885\pi$
$937$			20.7171i			0.676798i	−0.941003	+	0.338399i	$0.890115\pi$
$938$	−24.7415	+	55.1750i	−0.807840	+	1.80153i
$939$	−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	$0.733575\pi$
$942$	56.8897	−	1.55782i	1.85357	−	0.0507564i
$943$	35.4602			1.15474
$944$	6.49588	+	0.752696i	0.211423	+	0.0244982i
$945$		0			0
$946$	−4.74661	−	2.12847i	−0.154326	−	0.0692026i
$947$	−12.3990			−0.402913			−0.201456	−	0.979497i	$-0.564567\pi$
$947$	−12.3990			−0.402913			−0.201456	+	0.979497i	$0.564567\pi$
$948$	4.80486	−	11.5521i	0.156055	−	0.375195i
$949$		−	26.1608i		−	0.849217i
$950$		0			0
$951$	−20.4542	−	42.4610i	−0.663274	−	1.37689i
$952$	4.25694	+	13.4662i	0.137968	+	0.436442i
$953$	24.4649			0.792496			0.396248	−	0.918144i	$-0.370312\pi$
$953$	24.4649			0.792496			0.396248	+	0.918144i	$0.370312\pi$
$954$	−1.95834	−	3.79592i	−0.0634036	−	0.122898i
$955$		0			0
$956$	−26.7516	−	30.0303i	−0.865207	−	0.971250i
$957$	1.34829	+	2.79892i	0.0435840	+	0.0904762i
$958$	−0.530908	−	0.238070i	−0.0171529	−	0.00769168i
$959$	10.7719			0.347842
$960$		0			0
$961$	30.7793			0.992880
$962$	−4.78785	−	2.14697i	−0.154367	−	0.0692209i
$963$	16.5044	−	20.7057i	0.531846	−	0.667232i
$964$	−12.1382	−	13.6260i	−0.390947	−	0.438863i
$965$		0			0
$966$	−2.17187	−	79.3144i	−0.0698789	−	2.55190i
$967$	3.64391			0.117180			0.0585901	−	0.998282i	$-0.481340\pi$
$967$	3.64391			0.117180			0.0585901	+	0.998282i	$0.481340\pi$
$968$	4.27423	+	13.5209i	0.137379	+	0.434577i
$969$	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	$0.856709\pi$
$972$	−5.25304	+	30.7312i	−0.168491	+	0.985703i
$973$	−11.0351			−0.353769
$974$	41.5836	+	18.6469i	1.33242	+	0.597484i
$975$		0			0
$976$	43.4437	+	5.03395i	1.39060	+	0.161133i
$977$	−41.8998			−1.34049			−0.670246	−	0.742139i	$-0.733812\pi$
$977$	−41.8998			−1.34049			−0.670246	+	0.742139i	$0.733812\pi$
$978$	−0.467305	−	17.0655i	−0.0149428	−	0.545694i
$979$	18.9864			0.606809
$980$		0			0
$981$	−1.83025	−	1.45888i	−0.0584355	−	0.0465786i
$982$	8.19393	−	18.2729i	0.261479	−	0.583112i
$983$			0.734322i			0.0234212i	0.999931	+	0.0117106i	$0.00372769\pi$
$983$			0.734322i			0.0234212i	−0.999931	+	0.0117106i	$0.996272\pi$
$984$	−16.7380	+	15.7532i	−0.533589	+	0.502193i
$985$		0			0
$986$	1.10212	+	0.494210i	0.0350985	+	0.0157388i
$987$	13.1384	+	27.2740i	0.418199	+	0.868141i
$988$	−21.8672	−	24.5473i	−0.695689	−	0.780955i
$989$	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	$-0.132974\pi$
$992$	−2.28366	−	1.35928i	−0.0725064	−	0.0431572i
$993$	28.5865	−	13.7706i	0.907165	−	0.436997i
$994$	−64.3537	−	28.8574i	−2.04117	−	0.915302i
$995$		0			0
$996$	17.4347	+	7.25159i	0.552439	+	0.229775i
$997$	−23.4092			−0.741378			−0.370689	−	0.928757i	$-0.620878\pi$
$997$	−23.4092			−0.741378			−0.370689	+	0.928757i	$0.620878\pi$
$998$	18.8423	+	8.44926i	0.596443	+	0.267457i
$999$	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.m.d.299.16		16
3.2	odd	2		600.2.m.c.299.1		16
4.3	odd	2		2400.2.m.c.1199.13		16
5.2	odd	4		120.2.b.b.11.4	yes	8
5.3	odd	4		600.2.b.e.251.5		8
5.4	even	2	inner	600.2.m.d.299.1		16
8.3	odd	2		600.2.m.c.299.15		16
8.5	even	2		2400.2.m.d.1199.13		16
12.11	even	2		2400.2.m.d.1199.3		16
15.2	even	4		120.2.b.a.11.5	✓	8
15.8	even	4		600.2.b.f.251.4		8
15.14	odd	2		600.2.m.c.299.16		16
20.3	even	4		2400.2.b.e.2351.6		8
20.7	even	4		480.2.b.a.431.3		8
20.19	odd	2		2400.2.m.c.1199.4		16
24.5	odd	2		2400.2.m.c.1199.3		16
24.11	even	2	inner	600.2.m.d.299.2		16
40.3	even	4		600.2.b.f.251.3		8
40.13	odd	4		2400.2.b.f.2351.6		8
40.19	odd	2		600.2.m.c.299.2		16
40.27	even	4		120.2.b.a.11.6	yes	8
40.29	even	2		2400.2.m.d.1199.4		16
40.37	odd	4		480.2.b.b.431.3		8
60.23	odd	4		2400.2.b.f.2351.5		8
60.47	odd	4		480.2.b.b.431.4		8
60.59	even	2		2400.2.m.d.1199.14		16
120.29	odd	2		2400.2.m.c.1199.14		16
120.53	even	4		2400.2.b.e.2351.5		8
120.59	even	2	inner	600.2.m.d.299.15		16
120.77	even	4		480.2.b.a.431.4		8
120.83	odd	4		600.2.b.e.251.6		8
120.107	odd	4		120.2.b.b.11.3	yes	8

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

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.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.29041 + 0.578647i) q^{2} +(-1.56044 + 0.751690i) q^{3} +(1.33034 + 1.49339i) q^{4} +(-2.44857 + 0.0670494i) q^{6} +4.28591 q^{7} +(0.852541 + 2.69688i) q^{8} +(1.86993 - 2.34593i) q^{9} +O(q^{10})\)	\(q+(1.29041 + 0.578647i) q^{2} +(-1.56044 + 0.751690i) q^{3} +(1.33034 + 1.49339i) q^{4} +(-2.44857 + 0.0670494i) q^{6} +4.28591 q^{7} +(0.852541 + 2.69688i) q^{8} +(1.86993 - 2.34593i) q^{9} -2.44673i q^{11} +(-3.19847 - 1.33034i) q^{12} +2.71493 q^{13} +(5.53060 + 2.48003i) q^{14} +(-0.460411 + 3.97341i) q^{16} +1.16504 q^{17} +(3.77044 - 1.94519i) q^{18} -6.05444 q^{19} +(-6.68789 + 3.22167i) q^{21} +(1.41579 - 3.15729i) q^{22} +7.55782i q^{23} +(-3.35755 - 3.56747i) q^{24} +(3.50338 + 1.57098i) q^{26} +(-1.15449 + 5.06628i) q^{27} +(5.70170 + 6.40052i) q^{28} +0.733092 q^{29} +0.469799i q^{31} +(-2.89332 + 4.86093i) q^{32} +(1.83918 + 3.81797i) q^{33} +(1.50338 + 0.674144i) q^{34} +(5.99101 - 0.328351i) q^{36} -1.36664 q^{37} +(-7.81273 - 3.50338i) q^{38} +(-4.23647 + 2.04078i) q^{39} -4.69186i q^{41} +(-10.4944 + 0.287368i) q^{42} -1.50338i q^{43} +(3.65391 - 3.25497i) q^{44} +(-4.37330 + 9.75271i) q^{46} -4.07812i q^{47} +(-2.26833 - 6.54635i) q^{48} +11.3690 q^{49} +(-1.81797 + 0.875746i) q^{51} +(3.61177 + 4.05444i) q^{52} -1.00676i q^{53} +(-4.42135 + 5.86955i) q^{54} +(3.65391 + 11.5586i) q^{56} +(9.44757 - 4.55106i) q^{57} +(0.945992 + 0.424201i) q^{58} -1.63484i q^{59} -10.9336i q^{61} +(-0.271848 + 0.606236i) q^{62} +(8.01433 - 10.0544i) q^{63} +(-6.54635 + 4.59841i) q^{64} +(0.164052 + 5.99099i) q^{66} +9.97632i q^{67} +(1.54989 + 1.73985i) q^{68} +(-5.68113 - 11.7935i) q^{69} -11.6359 q^{71} +(7.92088 + 3.04297i) q^{72} -9.63593i q^{73} +(-1.76353 - 0.790800i) q^{74} +(-8.05444 - 9.04162i) q^{76} -10.4865i q^{77} +(-6.64769 + 0.182034i) q^{78} +3.61177i q^{79} +(-2.00676 - 8.77342i) q^{81} +(2.71493 - 6.05444i) q^{82} -5.45095 q^{83} +(-13.7084 - 5.70170i) q^{84} +(0.869925 - 1.93998i) q^{86} +(-1.14394 + 0.551058i) q^{87} +(6.59854 - 2.08594i) q^{88} +7.75993i q^{89} +11.6359 q^{91} +(-11.2867 + 10.0544i) q^{92} +(-0.353143 - 0.733092i) q^{93} +(2.35979 - 5.26246i) q^{94} +(0.860934 - 9.76006i) q^{96} -17.1156i q^{97} +(14.6707 + 6.57865i) q^{98} +(-5.73985 - 4.57520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} + 2 q^{6}+O(q^{10}) \) 16 * q - 2 * q^4 + 2 * q^6	\( 16 q - 2 q^{4} + 2 q^{6} + 12 q^{14} - 14 q^{16} + 8 q^{19} - 8 q^{21} + 22 q^{24} + 32 q^{26} + 26 q^{36} - 32 q^{39} + 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} - 82 q^{54} + 60 q^{56} - 50 q^{64} - 68 q^{66} - 40 q^{69} - 48 q^{71} - 64 q^{74} - 24 q^{76} + 16 q^{81} - 116 q^{84} - 16 q^{86} + 48 q^{91} + 80 q^{94} - 86 q^{96} - 32 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 + 2 * q^6 + 12 * q^14 - 14 * q^16 + 8 * q^19 - 8 * q^21 + 22 * q^24 + 32 * q^26 + 26 * q^36 - 32 * q^39 + 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 - 82 * q^54 + 60 * q^56 - 50 * q^64 - 68 * q^66 - 40 * q^69 - 48 * q^71 - 64 * q^74 - 24 * q^76 + 16 * q^81 - 116 * q^84 - 16 * q^86 + 48 * q^91 + 80 * q^94 - 86 * q^96 - 32 * q^99

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