LMFDB - Embedded newform 600.2.m.c.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.c.299.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29041 + 0.578647i) q^{2} +(-1.56044 - 0.751690i) q^{3} +(1.33034 + 1.49339i) q^{4} +(-1.57865 - 1.87293i) q^{6} -4.28591 q^{7} +(0.852541 + 2.69688i) q^{8} +(1.86993 + 2.34593i) q^{9} +O(q^{10})$	\(q+(1.29041 + 0.578647i) q^{2} +(-1.56044 - 0.751690i) q^{3} +(1.33034 + 1.49339i) q^{4} +(-1.57865 - 1.87293i) q^{6} -4.28591 q^{7} +(0.852541 + 2.69688i) q^{8} +(1.86993 + 2.34593i) q^{9} +2.44673i q^{11} +(-0.953342 - 3.33034i) q^{12} -2.71493 q^{13} +(-5.53060 - 2.48003i) q^{14} +(-0.460411 + 3.97341i) q^{16} +1.16504 q^{17} +(1.05551 + 4.10924i) q^{18} -6.05444 q^{19} +(6.68789 + 3.22167i) q^{21} +(-1.41579 + 3.15729i) q^{22} +7.55782i q^{23} +(0.696882 - 4.84916i) 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} +(-1.01575 + 5.91340i) q^{36} +1.36664 q^{37} +(-7.81273 - 3.50338i) q^{38} +(4.23647 + 2.04078i) q^{39} +4.69186i q^{41} +(6.76594 + 8.02722i) q^{42} +1.50338i q^{43} +(-3.65391 + 3.25497i) q^{44} +(-4.37330 + 9.75271i) q^{46} -4.07812i q^{47} +(3.70522 - 5.85418i) q^{48} +11.3690 q^{49} +(-1.81797 - 0.875746i) q^{51} +(-3.61177 - 4.05444i) q^{52} -1.00676i q^{53} +(1.44181 - 7.20563i) 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} +(4.58256 - 3.86252i) q^{66} -9.97632i q^{67} +(1.54989 + 1.73985i) q^{68} +(5.68113 - 11.7935i) q^{69} +11.6359 q^{71} +(-4.73250 + 7.04297i) q^{72} +9.63593i q^{73} +(1.76353 + 0.790800i) q^{74} +(-8.05444 - 9.04162i) q^{76} -10.4865i q^{77} +(4.28591 + 5.08487i) q^{78} +3.61177i q^{79} +(-2.00676 + 8.77342i) q^{81} +(-2.71493 + 6.05444i) q^{82} -5.45095 q^{83} +(4.08594 + 14.2735i) 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} +(8.16876 - 5.41030i) 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} - 14 q^{6}+O(q^{10}) $ 16 * q - 2 * q^4 - 14 * q^6	$ 16 q - 2 q^{4} - 14 q^{6} - 12 q^{14} - 14 q^{16} + 8 q^{19} + 8 q^{21} - 18 q^{24} - 32 q^{26} - 38 q^{36} + 32 q^{39} - 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} + 30 q^{54} - 60 q^{56} - 50 q^{64} + 36 q^{66} + 40 q^{69} + 48 q^{71} + 64 q^{74} - 24 q^{76} + 16 q^{81} + 4 q^{84} + 16 q^{86} + 48 q^{91} + 80 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 - 14 * q^6 - 12 * q^14 - 14 * q^16 + 8 * q^19 + 8 * q^21 - 18 * q^24 - 32 * q^26 - 38 * q^36 + 32 * q^39 - 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 + 30 * q^54 - 60 * q^56 - 50 * q^64 + 36 * q^66 + 40 * q^69 + 48 * q^71 + 64 * q^74 - 24 * q^76 + 16 * q^81 + 4 * q^84 + 16 * q^86 + 48 * q^91 + 80 * q^94 + 34 * 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
$6$	−1.57865	−	1.87293i	−0.644480	−	0.764621i
$7$	−4.28591			−1.61992			−0.809961	−	0.586484i	$-0.800512\pi$
$7$	−4.28591			−1.61992			−0.809961	+	0.586484i	$0.800512\pi$
$8$	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	$0.120251\pi$
$11$			2.44673i			0.737717i	−0.929486	+	0.368858i	$0.879749\pi$
$12$	−0.953342	−	3.33034i	−0.275206	−	0.961385i
$13$	−2.71493			−0.752985			−0.376493	−	0.926420i	$-0.622870\pi$
$13$	−2.71493			−0.752985			−0.376493	+	0.926420i	$0.622870\pi$
$14$	−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	$0.454878\pi$
$18$	1.05551	+	4.10924i	0.248787	+	0.968558i
$19$	−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	$0.711139\pi$
$24$	0.696882	−	4.84916i	0.142250	−	0.989831i
$25$		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	$-0.521683\pi$
$29$	−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	$0.986567\pi$
$32$	−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
$36$	−1.01575	+	5.91340i	−0.169292	+	0.985566i
$37$	1.36664			0.224674			0.112337	−	0.993670i	$-0.464166\pi$
$37$	1.36664			0.224674			0.112337	+	0.993670i	$0.464166\pi$
$38$	−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	$0.119400\pi$
$41$			4.69186i			0.732745i	−0.930468	+	0.366372i	$0.880600\pi$
$42$	6.76594	+	8.02722i	1.04401	+	1.23863i
$43$			1.50338i			0.229263i	0.993408	+	0.114632i	$0.0365688\pi$
$43$			1.50338i			0.229263i	−0.993408	+	0.114632i	$0.963431\pi$
$44$	−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	$-0.0961285\pi$
$48$	3.70522	−	5.85418i	0.534802	−	0.844977i
$49$	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	$-0.0220269\pi$
$54$	1.44181	−	7.20563i	0.196206	−	0.980563i
$55$		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	$0.0339384\pi$
$59$			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	$-0.246795\pi$
$62$	−0.271848	+	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
$66$	4.58256	−	3.86252i	0.564074	−	0.475443i
$67$		−	9.97632i		−	1.21880i	−0.792862	−	0.609401i	$-0.791410\pi$
$67$		−	9.97632i		−	1.21880i	0.792862	−	0.609401i	$-0.208590\pi$
$68$	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	$-0.257406\pi$
$71$	11.6359			1.38093			0.690465	+	0.723365i	$0.257406\pi$
$72$	−4.73250	+	7.04297i	−0.557731	+	0.830022i
$73$			9.63593i			1.12780i	0.825843	+	0.563900i	$0.190700\pi$
$73$			9.63593i			1.12780i	−0.825843	+	0.563900i	$0.809300\pi$
$74$	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
$78$	4.28591	+	5.08487i	0.485284	+	0.575749i
$79$			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	$0.596706\pi$
$84$	4.08594	+	14.2735i	0.445812	+	1.55737i
$85$		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	$-0.865083\pi$
$89$		−	7.75993i		−	0.822551i	0.911511	−	0.411275i	$-0.134917\pi$
$90$		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
$96$	8.16876	−	5.41030i	0.833721	−	0.552186i
$97$			17.1156i			1.73783i	0.494962	+	0.868915i	$0.335182\pi$
$97$			17.1156i			1.73783i	−0.494962	+	0.868915i	$0.664818\pi$
$98$	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	$-0.585961\pi$
$101$	−5.36226			−0.533565			−0.266783	+	0.963757i	$0.585961\pi$
$102$	−1.83918	−	2.18203i	−0.182106	−	0.216054i
$103$	13.0910			1.28990			0.644949	−	0.764225i	$-0.276878\pi$
$103$	13.0910			1.28990			0.644949	+	0.764225i	$0.276878\pi$
$104$	−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	$0.359700\pi$
$108$	6.03005	−	8.46395i	0.580242	−	0.814444i
$109$		−	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	$0.456195\pi$
$114$	9.55782	+	11.3395i	0.895172	+	1.06205i
$115$		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
$126$	−4.52384	−	17.6119i	−0.403016	−	1.56899i
$127$	−2.93762			−0.260672			−0.130336	−	0.991470i	$-0.541606\pi$
$127$	−2.93762			−0.260672			−0.130336	+	0.991470i	$0.541606\pi$
$128$	−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	$0.111813\pi$
$131$			7.87658i			0.688180i	−0.938937	+	0.344090i	$0.888187\pi$
$132$	8.14843	−	2.33257i	0.709230	−	0.203024i
$133$	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	$0.465759\pi$
$138$	14.1553	−	11.9311i	1.20498	−	1.01564i
$139$	−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
$144$	−10.1823	+	6.34990i	−0.848523	+	0.529158i
$145$		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	$-0.729613\pi$
$149$	−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	$-0.258703\pi$
$152$	−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
$156$	2.58825	+	9.04162i	0.207226	+	0.723909i
$157$	23.2338			1.85426			0.927131	−	0.374737i	$-0.122267\pi$
$157$	23.2338			1.85426			0.927131	+	0.374737i	$0.122267\pi$
$158$	−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
$162$	−7.66626	+	10.1601i	−0.602318	+	0.798256i
$163$		−	6.96956i		−	0.545898i	−0.962028	−	0.272949i	$-0.912001\pi$
$163$		−	6.96956i		−	0.545898i	0.962028	−	0.272949i	$-0.0879991\pi$
$164$	−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	$0.874404\pi$
$168$	−2.98677	+	20.7831i	−0.230435	+	1.60345i
$169$	−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	$0.901468\pi$
$174$	1.15729	+	1.37303i	0.0877342	+	0.104089i
$175$		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	$0.341330\pi$
$179$			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	$0.879811\pi$
$182$	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
$186$	0.879902	−	0.741647i	0.0645176	−	0.0543802i
$187$			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	$-0.802458\pi$
$191$	−22.4865			−1.62706			−0.813532	+	0.581521i	$0.802458\pi$
$192$	13.6717	−	2.25470i	0.986672	−	0.162719i
$193$			13.1156i			0.944084i	0.881576	+	0.472042i	$0.156483\pi$
$193$			13.1156i			0.944084i	−0.881576	+	0.472042i	$0.843517\pi$
$194$	−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	$0.667388\pi$
$198$	−10.0542	+	2.58256i	−0.714521	+	0.183534i
$199$		−	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
$204$	−1.11068	−	3.87996i	−0.0777630	−	0.271652i
$205$		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
$216$	12.6789	−	7.43273i	0.862690	−	0.505733i
$217$		−	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
$222$	−2.15744	−	2.55962i	−0.144798	−	0.171790i
$223$	−5.22551			−0.349926			−0.174963	−	0.984575i	$-0.555981\pi$
$223$	−5.22551			−0.349926			−0.174963	+	0.984575i	$0.555981\pi$
$224$	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	$0.652554\pi$
$228$	5.77195	+	20.1633i	0.382257	+	1.33535i
$229$		−	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	$0.591137\pi$
$234$	−2.86564	−	11.1563i	−0.187333	−	0.729310i
$235$		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	$-0.274615\pi$
$239$	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	$0.594943\pi$
$242$	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
$246$	8.78753	−	7.40678i	0.560272	−	0.472239i
$247$	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	$0.137951\pi$
$251$			13.3064i			0.839895i	−0.907548	+	0.419947i	$0.862049\pi$
$252$	4.35341	−	25.3443i	0.274239	−	1.59654i
$253$	−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	$0.891376\pi$
$258$	2.81573	−	2.37330i	0.175300	−	0.147755i
$259$	−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	$-0.152247\pi$
$264$	11.8646	+	1.70508i	0.730214	+	0.104941i
$265$		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	$-0.452758\pi$
$269$	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	$0.850728\pi$
$272$	−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
$276$	25.1701	−	7.20518i	1.51506	−	0.433701i
$277$	−19.6832			−1.18265			−0.591324	−	0.806434i	$-0.701395\pi$
$277$	−19.6832			−1.18265			−0.591324	+	0.806434i	$0.701395\pi$
$278$	−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	$-0.978161\pi$
$281$		−	2.29836i		−	0.137109i	0.997647	−	0.0685544i	$-0.0218387\pi$
$282$	−7.63803	+	6.43790i	−0.454838	+	0.383372i
$283$			21.6123i			1.28472i	0.766405	+	0.642358i	$0.222044\pi$
$283$			21.6123i			1.28472i	−0.766405	+	0.642358i	$0.777956\pi$
$284$	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
$288$	−16.8137	+	2.30205i	−0.990757	+	0.135650i
$289$	−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	$-0.0560772\pi$
$294$	−17.9477	−	21.2934i	−1.04673	−	1.24186i
$295$		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
$306$	1.22971	+	4.78742i	0.0702980	+	0.273679i
$307$		−	4.98308i		−	0.284399i	−0.989838	−	0.142200i	$-0.954582\pi$
$307$		−	4.98308i		−	0.284399i	0.989838	−	0.142200i	$-0.0454175\pi$
$308$	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	$-0.398201\pi$
$311$	11.0886			0.628777			0.314388	+	0.949294i	$0.398201\pi$
$312$	−1.89198	+	13.1651i	−0.107113	+	0.745328i
$313$		−	11.2583i		−	0.636359i	−0.948030	−	0.318180i	$-0.896928\pi$
$313$		−	11.2583i		−	0.636359i	0.948030	−	0.318180i	$-0.103072\pi$
$314$	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	$0.723153\pi$
$318$	−1.88559	+	1.58932i	−0.105739	+	0.0891244i
$319$		−	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
$324$	−15.7718	+	8.67473i	−0.876210	+	0.481930i
$325$		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
$336$	−15.8802	+	25.0905i	−0.866337	+	1.36880i
$337$			2.54733i			0.138762i	0.997590	+	0.0693810i	$0.0221024\pi$
$337$			2.54733i			0.138762i	−0.997590	+	0.0693810i	$0.977898\pi$
$338$	−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
$342$	−6.39054	−	24.8792i	−0.345561	−	1.34531i
$343$	−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	$0.210907\pi$
$348$	0.698887	+	2.44144i	0.0374643	+	0.130875i
$349$		−	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	$0.190169\pi$
$354$	3.06194	−	2.58083i	0.162740	−	0.137169i
$355$		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	$-0.597246\pi$
$359$	−11.3979			−0.601556			−0.300778	+	0.953694i	$0.597246\pi$
$360$		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
$366$	−20.4779	+	17.2603i	−1.07040	+	0.902210i
$367$	21.0209			1.09728			0.548640	−	0.836059i	$-0.315146\pi$
$367$	21.0209			1.09728			0.548640	+	0.836059i	$0.315146\pi$
$368$	−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
$372$	1.56459	−	0.447879i	0.0811202	−	0.0232215i
$373$	10.3471			0.535755			0.267878	−	0.963453i	$-0.413678\pi$
$373$	10.3471			0.535755			0.267878	+	0.963453i	$0.413678\pi$
$374$	−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
$378$	−6.17948	+	30.8827i	−0.317838	+	1.58843i
$379$	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	$0.782262\pi$
$384$	18.9469	+	5.00161i	0.966878	+	0.255237i
$385$		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	$-0.289444\pi$
$389$	24.2313			1.22857			0.614287	+	0.789083i	$0.289444\pi$
$390$		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
$396$	−14.4685	−	2.48526i	−0.727068	−	0.124889i
$397$	−21.8856			−1.09840			−0.549202	−	0.835689i	$-0.685068\pi$
$397$	−21.8856			−1.09840			−0.549202	+	0.835689i	$0.685068\pi$
$398$	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	$-0.820409\pi$
$401$		−	21.4163i		−	1.06948i	0.845016	−	0.534740i	$-0.179591\pi$
$402$	−18.6850	+	15.7491i	−0.931922	+	0.785493i
$403$		−	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
$408$	0.811893	−	5.64945i	0.0401947	−	0.279689i
$409$	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
$414$	−31.0569	+	7.97738i	−1.52636	+	0.392067i
$415$		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	$-0.883471\pi$
$419$		−	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	$0.845925\pi$
$422$	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
$426$	−18.3690	−	21.7933i	−0.889982	−	1.05589i
$427$			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	$-0.265937\pi$
$431$	27.8537			1.34166			0.670832	+	0.741609i	$0.265937\pi$
$432$	20.6620	−	2.25470i	0.994099	−	0.108479i
$433$		−	24.0750i		−	1.15697i	−0.815692	−	0.578486i	$-0.803644\pi$
$433$		−	24.0750i		−	1.15697i	0.815692	−	0.578486i	$-0.196356\pi$
$434$	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
$438$	18.0474	−	15.2117i	0.862340	−	0.726845i
$439$			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	$0.442129\pi$
$444$	−1.30287	−	4.55136i	−0.0618316	−	0.215998i
$445$		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	$-0.914128\pi$
$449$		−	11.2946i		−	0.533026i	0.963831	−	0.266513i	$-0.0858715\pi$
$450$		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
$456$	−4.21923	+	29.3589i	−0.197584	+	1.37486i
$457$		−	29.5067i		−	1.38027i	−0.723682	−	0.690133i	$-0.757552\pi$
$457$		−	29.5067i		−	1.38027i	0.723682	−	0.690133i	$-0.242448\pi$
$458$	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	$-0.735506\pi$
$461$	−28.9508			−1.34838			−0.674188	+	0.738560i	$0.735506\pi$
$462$	−19.6404	+	16.5544i	−0.913755	+	0.770181i
$463$	22.6025			1.05043			0.525213	−	0.850971i	$-0.323986\pi$
$463$	22.6025			1.05043			0.525213	+	0.850971i	$0.323986\pi$
$464$	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	$0.397998\pi$
$468$	2.75769	−	16.0544i	0.127474	−	0.742117i
$469$			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
$474$	6.76459	−	5.70170i	0.310708	−	0.261888i
$475$		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	$-0.497008\pi$
$479$	0.411425			0.0187985			0.00939924	+	0.999956i	$0.497008\pi$
$480$		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
$486$	19.6000	−	10.0916i	0.889073	−	0.457765i
$487$	−32.2250			−1.46025			−0.730126	−	0.683312i	$-0.760539\pi$
$487$	−32.2250			−1.46025			−0.730126	+	0.683312i	$0.760539\pi$
$488$	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	$0.103524\pi$
$491$			14.1605i			0.639055i	−0.947577	+	0.319528i	$0.896476\pi$
$492$	15.6255	−	4.47294i	0.704450	−	0.201656i
$493$	−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
$498$	8.60512	+	10.2093i	0.385605	+	0.457488i
$499$	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	$-0.235905\pi$
$504$	20.2831	−	30.1855i	0.903480	−	1.34457i
$505$		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	$-0.437219\pi$
$509$	8.84197			0.391913			0.195957	+	0.980613i	$0.437219\pi$
$510$		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
$516$	5.00676	−	1.43323i	0.220410	−	0.0630946i
$517$	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	$0.320826\pi$
$521$			38.6076i			1.69143i	−0.533634	+	0.845716i	$0.679174\pi$
$522$	−0.773789	−	3.01245i	−0.0338678	−	0.131852i
$523$			13.8674i			0.606381i	0.952930	+	0.303191i	$0.0980519\pi$
$523$			13.8674i			0.606381i	−0.952930	+	0.303191i	$0.901948\pi$
$524$	−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
$528$	14.3236	+	9.06566i	0.623354	+	0.394532i
$529$	−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
$534$	−14.5338	+	12.2502i	−0.628940	+	0.530117i
$535$		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
$546$	−18.3690	−	21.7933i	−0.786122	−	0.932668i
$547$		−	13.1393i		−	0.561796i	−0.959738	−	0.280898i	$-0.909368\pi$
$547$		−	13.1393i		−	0.561796i	0.959738	−	0.280898i	$-0.0906323\pi$
$548$	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
$552$	36.6491	+	5.26691i	1.55989	+	0.224174i
$553$		−	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	$-0.00341760\pi$
$558$	−1.93052	+	0.495880i	−0.0817254	+	0.0209923i
$559$		−	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	$0.411386\pi$
$564$	−13.5815	+	3.88784i	−0.571884	+	0.163707i
$565$		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	$0.223117\pi$
$569$			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	$0.303396\pi$
$572$	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
$576$	−23.0287	−	6.75859i	−0.959530	−	0.281608i
$577$		−	33.4626i		−	1.39307i	−0.717525	−	0.696533i	$-0.754725\pi$
$577$		−	33.4626i		−	1.39307i	0.717525	−	0.696533i	$-0.245275\pi$
$578$	−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
$582$	32.0564	−	27.0195i	1.32878	−	1.12000i
$583$	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	$0.298199\pi$
$588$	−10.8386	−	37.8627i	−0.446975	−	1.56143i
$589$		−	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	$0.862938\pi$
$594$	17.6302	+	3.52773i	0.723377	+	0.144744i
$595$		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	$-0.335870\pi$
$599$	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	$0.367914\pi$
$602$	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
$606$	8.46512	+	10.0432i	0.343872	+	0.407975i
$607$	−7.68877			−0.312078			−0.156039	−	0.987751i	$-0.549873\pi$
$607$	−7.68877			−0.312078			−0.156039	+	0.987751i	$0.549873\pi$
$608$	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
$612$	−1.18339	+	6.88932i	−0.0478355	+	0.278484i
$613$	−26.6091			−1.07473			−0.537366	−	0.843349i	$-0.680581\pi$
$613$	−26.6091			−1.07473			−0.537366	+	0.843349i	$0.680581\pi$
$614$	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	$0.331705\pi$
$618$	−20.6661	−	24.5186i	−0.831314	−	0.986284i
$619$	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
$624$	−10.0594	+	15.8937i	−0.402698	+	0.636256i
$625$		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
$636$	−3.35284	+	0.959785i	−0.132949	+	0.0380580i
$637$	−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	$-0.745485\pi$
$641$		−	36.3093i		−	1.43413i	0.697006	−	0.717065i	$-0.254515\pi$
$642$	−13.9335	−	16.5309i	−0.549911	−	0.652423i
$643$		−	32.8571i		−	1.29576i	−0.761744	−	0.647878i	$-0.775656\pi$
$643$		−	32.8571i		−	1.29576i	0.761744	−	0.647878i	$-0.224344\pi$
$644$	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	$-0.109338\pi$
$648$	−25.3717	+	2.06771i	−0.996696	+	0.0812273i
$649$	−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	$-0.182762\pi$
$654$	−1.46123	+	1.23163i	−0.0571386	+	0.0481607i
$655$		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	$0.0965729\pi$
$659$			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	$-0.273451\pi$
$662$	−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
$666$	1.44251	+	5.61585i	0.0558960	+	0.217610i
$667$		−	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
$672$	−35.0106	+	23.1881i	−1.35056	+	0.894499i
$673$			6.78966i			0.261722i	0.991401	+	0.130861i	$0.0417742\pi$
$673$			6.78966i			0.261722i	−0.991401	+	0.130861i	$0.958226\pi$
$674$	−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	$0.714365\pi$
$678$	−4.60417	−	5.46246i	−0.176822	−	0.209784i
$679$		−	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	$0.450213\pi$
$684$	6.14979	−	35.8023i	0.235143	−	1.36893i
$685$		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
$696$	−0.510879	+	3.55488i	−0.0193648	+	0.134747i
$697$			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	$-0.376629\pi$
$701$	20.0135			0.755900			0.377950	+	0.925826i	$0.376629\pi$
$702$	−3.91442	+	19.5628i	−0.147740	+	0.738349i
$703$	−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
$708$	5.44455	−	1.55856i	0.204619	−	0.0585742i
$709$			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
$714$	7.88256	+	9.35200i	0.294998	+	0.349990i
$715$		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	$-0.465634\pi$
$719$	5.77864			0.215507			0.107754	+	0.994178i	$0.465634\pi$
$720$		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
$726$	−7.91457	−	9.38998i	−0.293737	−	0.348495i
$727$	25.0657			0.929636			0.464818	−	0.885406i	$-0.346120\pi$
$727$	25.0657			0.929636			0.464818	+	0.885406i	$0.346120\pi$
$728$	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
$732$	−36.4126	+	10.4235i	−1.34585	+	0.385262i
$733$	−14.9596			−0.552546			−0.276273	−	0.961079i	$-0.589099\pi$
$733$	−14.9596			−0.552546			−0.276273	+	0.961079i	$0.589099\pi$
$734$	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
$738$	−19.2800	+	4.95232i	−0.709706	+	0.182297i
$739$	−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	$-0.0805314\pi$
$744$	2.27813	+	0.327395i	0.0835204	+	0.0120029i
$745$		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
$756$	−25.8443	+	36.2757i	−0.939947	+	1.31934i
$757$	10.1994			0.370702			0.185351	−	0.982672i	$-0.440658\pi$
$757$	10.1994			0.370702			0.185351	+	0.982672i	$0.440658\pi$
$758$	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	$0.169877\pi$
$761$			28.0668i			1.01742i	−0.860938	+	0.508710i	$0.830123\pi$
$762$	4.63747	+	5.50197i	0.167998	+	0.199315i
$763$			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
$768$	21.5551	+	17.4177i	0.777804	+	0.628507i
$769$	−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	$0.722992\pi$
$774$	−6.17775	+	1.58684i	−0.222055	+	0.0570377i
$775$		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
$786$	14.7523	−	12.4343i	0.526197	−	0.443518i
$787$			27.9997i			0.998083i	0.866578	+	0.499042i	$0.166315\pi$
$787$			27.9997i			0.998083i	−0.866578	+	0.499042i	$0.833685\pi$
$788$	−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
$792$	−17.2322	−	11.5792i	−0.612321	−	0.411447i
$793$			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	$-0.0108578\pi$
$798$	−40.9639	−	48.6003i	−1.45011	−	1.72043i
$799$		−	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
$804$	−33.2245	+	9.51084i	−1.17174	+	0.335422i
$805$		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	$-0.820977\pi$
$809$		−	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	$0.457579\pi$
$812$	4.17987	+	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
$816$	4.31671	−	6.82033i	0.151115	−	0.238759i
$817$		−	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	$-0.667934\pi$
$821$	−28.8505			−1.00689			−0.503445	+	0.864027i	$0.667934\pi$
$822$	−3.96765	−	4.70729i	−0.138388	−	0.164186i
$823$	−15.3789			−0.536076			−0.268038	−	0.963408i	$-0.586375\pi$
$823$	−15.3789			−0.536076			−0.268038	+	0.963408i	$0.586375\pi$
$824$	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	$0.814349\pi$
$828$	−44.6924	−	7.67685i	−1.55317	−	0.266789i
$829$		−	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
$834$	4.06460	+	4.82231i	0.140746	+	0.166983i
$835$		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	$-0.938324\pi$
$839$	−56.8469			−1.96257			−0.981287	+	0.192552i	$0.938324\pi$
$840$		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
$846$	16.7580	−	4.30451i	0.576151	−	0.147992i
$847$	−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
$852$	−11.0930	−	38.7516i	−0.380041	−	1.32761i
$853$	−29.3057			−1.00341			−0.501704	−	0.865039i	$-0.667293\pi$
$853$	−29.3057			−1.00341			−0.501704	+	0.865039i	$0.667293\pi$
$854$	−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	$0.322498\pi$
$858$	−12.4413	+	10.4865i	−0.424739	+	0.358002i
$859$	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	$0.929717\pi$
$864$	27.9671	+	9.04647i	0.951462	+	0.307767i
$865$		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
$876$	32.0909	−	9.18634i	1.08425	−	0.310378i
$877$	35.8017			1.20894			0.604469	−	0.796629i	$-0.293385\pi$
$877$	35.8017			1.20894			0.604469	+	0.796629i	$0.293385\pi$
$878$	−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	$-0.855646\pi$
$881$		−	26.0081i		−	0.876234i	0.898918	−	0.438117i	$-0.144354\pi$
$882$	12.0002	+	46.7181i	0.404067	+	1.57308i
$883$		−	41.3226i		−	1.39062i	−0.718712	−	0.695308i	$-0.755268\pi$
$883$		−	41.3226i		−	1.39062i	0.718712	−	0.695308i	$-0.244732\pi$
$884$	−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	$-0.0806369\pi$
$888$	0.952386	−	6.62705i	0.0319600	−	0.222389i
$889$	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
$894$	25.4516	+	30.1961i	0.851227	+	1.00991i
$895$		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
$906$	−33.4258	+	28.1737i	−1.11050	+	0.936009i
$907$		−	39.4794i		−	1.31089i	−0.755241	−	0.655447i	$-0.772480\pi$
$907$		−	39.4794i		−	1.31089i	0.755241	−	0.655447i	$-0.227520\pi$
$908$	−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	$-0.791108\pi$
$911$	−47.8266			−1.58457			−0.792284	+	0.610153i	$0.791108\pi$
$912$	−22.4330	+	35.4437i	−0.742831	+	1.17366i
$913$		−	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
$918$	1.67977	−	8.39483i	0.0554405	−	0.277071i
$919$			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
$924$	−34.9234	+	9.99718i	−1.14890	+	0.328883i
$925$		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	$-0.985308\pi$
$929$		−	2.81266i		−	0.0922804i	0.998935	−	0.0461402i	$-0.0146921\pi$
$930$		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
$936$	12.8484	−	19.1211i	0.419963	−	0.624994i
$937$		−	20.7171i		−	0.676798i	−0.941003	−	0.338399i	$-0.890115\pi$
$937$		−	20.7171i		−	0.676798i	0.941003	−	0.338399i	$-0.109885\pi$
$938$	−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	$-0.266425\pi$
$941$	41.0867			1.33939			0.669695	+	0.742636i	$0.266425\pi$
$942$	−36.6780	−	43.5154i	−1.19503	−	1.41781i
$943$	−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	$0.564567\pi$
$948$	12.0284	−	3.44325i	0.390664	−	0.111831i
$949$		−	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	$0.370312\pi$
$954$	4.13702	−	1.06265i	0.133941	−	0.0344045i
$955$		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
$966$	−60.6682	+	51.1357i	−1.95197	+	1.64526i
$967$	−3.64391			−0.117180			−0.0585901	−	0.998282i	$-0.518660\pi$
$967$	−3.64391			−0.117180			−0.0585901	+	0.998282i	$0.518660\pi$
$968$	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	$-0.856709\pi$
$971$		−	27.1170i		−	0.870225i	0.900376	−	0.435113i	$-0.143291\pi$
$972$	31.1316	−	1.68089i	0.998546	−	0.0539145i
$973$	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	$0.733812\pi$
$978$	−13.0535	+	11.0025i	−0.417406	+	0.351820i
$979$	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	$0.996272\pi$
$984$	22.7516	+	3.26967i	0.725293	+	0.104233i
$985$		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
$996$	5.19661	+	18.1535i	0.164661	+	0.575215i
$997$	23.4092			0.741378			0.370689	−	0.928757i	$-0.379122\pi$
$997$	23.4092			0.741378			0.370689	+	0.928757i	$0.379122\pi$
$998$	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.c.299.16		16
3.2	odd	2		600.2.m.d.299.1		16
4.3	odd	2		2400.2.m.d.1199.14		16
5.2	odd	4		600.2.b.f.251.4		8
5.3	odd	4		120.2.b.a.11.5	✓	8
5.4	even	2	inner	600.2.m.c.299.1		16
8.3	odd	2		600.2.m.d.299.15		16
8.5	even	2		2400.2.m.c.1199.14		16
12.11	even	2		2400.2.m.c.1199.4		16
15.2	even	4		600.2.b.e.251.5		8
15.8	even	4		120.2.b.b.11.4	yes	8
15.14	odd	2		600.2.m.d.299.16		16
20.3	even	4		480.2.b.b.431.4		8
20.7	even	4		2400.2.b.f.2351.5		8
20.19	odd	2		2400.2.m.d.1199.3		16
24.5	odd	2		2400.2.m.d.1199.4		16
24.11	even	2	inner	600.2.m.c.299.2		16
40.3	even	4		120.2.b.b.11.3	yes	8
40.13	odd	4		480.2.b.a.431.4		8
40.19	odd	2		600.2.m.d.299.2		16
40.27	even	4		600.2.b.e.251.6		8
40.29	even	2		2400.2.m.c.1199.3		16
40.37	odd	4		2400.2.b.e.2351.5		8
60.23	odd	4		480.2.b.a.431.3		8
60.47	odd	4		2400.2.b.e.2351.6		8
60.59	even	2		2400.2.m.c.1199.13		16
120.29	odd	2		2400.2.m.d.1199.13		16
120.53	even	4		480.2.b.b.431.3		8
120.59	even	2	inner	600.2.m.c.299.15		16
120.77	even	4		2400.2.b.f.2351.6		8
120.83	odd	4		120.2.b.a.11.6	yes	8
120.107	odd	4		600.2.b.f.251.3		8

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

\(f(q)\)	\(=\)	\(q+(1.29041 + 0.578647i) q^{2} +(-1.56044 - 0.751690i) q^{3} +(1.33034 + 1.49339i) q^{4} +(-1.57865 - 1.87293i) q^{6} -4.28591 q^{7} +(0.852541 + 2.69688i) q^{8} +(1.86993 + 2.34593i) q^{9} +O(q^{10})\)	\(q+(1.29041 + 0.578647i) q^{2} +(-1.56044 - 0.751690i) q^{3} +(1.33034 + 1.49339i) q^{4} +(-1.57865 - 1.87293i) q^{6} -4.28591 q^{7} +(0.852541 + 2.69688i) q^{8} +(1.86993 + 2.34593i) q^{9} +2.44673i q^{11} +(-0.953342 - 3.33034i) q^{12} -2.71493 q^{13} +(-5.53060 - 2.48003i) q^{14} +(-0.460411 + 3.97341i) q^{16} +1.16504 q^{17} +(1.05551 + 4.10924i) q^{18} -6.05444 q^{19} +(6.68789 + 3.22167i) q^{21} +(-1.41579 + 3.15729i) q^{22} +7.55782i q^{23} +(0.696882 - 4.84916i) 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} +(-1.01575 + 5.91340i) q^{36} +1.36664 q^{37} +(-7.81273 - 3.50338i) q^{38} +(4.23647 + 2.04078i) q^{39} +4.69186i q^{41} +(6.76594 + 8.02722i) q^{42} +1.50338i q^{43} +(-3.65391 + 3.25497i) q^{44} +(-4.37330 + 9.75271i) q^{46} -4.07812i q^{47} +(3.70522 - 5.85418i) q^{48} +11.3690 q^{49} +(-1.81797 - 0.875746i) q^{51} +(-3.61177 - 4.05444i) q^{52} -1.00676i q^{53} +(1.44181 - 7.20563i) 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} +(4.58256 - 3.86252i) q^{66} -9.97632i q^{67} +(1.54989 + 1.73985i) q^{68} +(5.68113 - 11.7935i) q^{69} +11.6359 q^{71} +(-4.73250 + 7.04297i) q^{72} +9.63593i q^{73} +(1.76353 + 0.790800i) q^{74} +(-8.05444 - 9.04162i) q^{76} -10.4865i q^{77} +(4.28591 + 5.08487i) q^{78} +3.61177i q^{79} +(-2.00676 + 8.77342i) q^{81} +(-2.71493 + 6.05444i) q^{82} -5.45095 q^{83} +(4.08594 + 14.2735i) 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} +(8.16876 - 5.41030i) q^{96} +17.1156i q^{97} +(14.6707 + 6.57865i) q^{98} +(-5.73985 + 4.57520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} - 14 q^{6}+O(q^{10}) \) 16 * q - 2 * q^4 - 14 * q^6	\( 16 q - 2 q^{4} - 14 q^{6} - 12 q^{14} - 14 q^{16} + 8 q^{19} + 8 q^{21} - 18 q^{24} - 32 q^{26} - 38 q^{36} + 32 q^{39} - 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} + 30 q^{54} - 60 q^{56} - 50 q^{64} + 36 q^{66} + 40 q^{69} + 48 q^{71} + 64 q^{74} - 24 q^{76} + 16 q^{81} + 4 q^{84} + 16 q^{86} + 48 q^{91} + 80 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 - 14 * q^6 - 12 * q^14 - 14 * q^16 + 8 * q^19 + 8 * q^21 - 18 * q^24 - 32 * q^26 - 38 * q^36 + 32 * q^39 - 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 + 30 * q^54 - 60 * q^56 - 50 * q^64 + 36 * q^66 + 40 * q^69 + 48 * q^71 + 64 * q^74 - 24 * q^76 + 16 * q^81 + 4 * q^84 + 16 * q^86 + 48 * q^91 + 80 * q^94 + 34 * q^96 - 32 * q^99

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