LMFDB - Embedded newform 76.2.k.a.51.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.4
Character	$\chi$	$=$	76.51
Dual form			76.2.k.a.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.178792 - 1.40287i) q^{2} +(1.23656 + 0.450071i) q^{3} +(-1.93607 + 0.501643i) q^{4} +(-0.503046 - 2.85292i) q^{5} +(0.410302 - 1.81520i) q^{6} +(2.71118 + 1.56530i) q^{7} +(1.04989 + 2.62635i) q^{8} +(-0.971618 - 0.815285i) q^{9} +O(q^{10})$	\(q+(-0.178792 - 1.40287i) q^{2} +(1.23656 + 0.450071i) q^{3} +(-1.93607 + 0.501643i) q^{4} +(-0.503046 - 2.85292i) q^{5} +(0.410302 - 1.81520i) q^{6} +(2.71118 + 1.56530i) q^{7} +(1.04989 + 2.62635i) q^{8} +(-0.971618 - 0.815285i) q^{9} +(-3.91232 + 1.21579i) q^{10} +(-3.30359 + 1.90733i) q^{11} +(-2.61984 - 0.251056i) q^{12} +(1.53341 + 4.21300i) q^{13} +(1.71117 - 4.08329i) q^{14} +(0.661968 - 3.75421i) q^{15} +(3.49671 - 1.94243i) q^{16} +(0.0599755 - 0.0503255i) q^{17} +(-0.970017 + 1.50882i) q^{18} +(-3.51689 + 2.57517i) q^{19} +(2.40508 + 5.27109i) q^{20} +(2.64804 + 3.15581i) q^{21} +(3.26638 + 4.29348i) q^{22} +(2.21189 + 0.390015i) q^{23} +(0.116209 + 3.72017i) q^{24} +(-3.18761 + 1.16020i) q^{25} +(5.63611 - 2.90441i) q^{26} +(-2.80841 - 4.86430i) q^{27} +(-6.03426 - 1.67048i) q^{28} +(0.332156 - 0.395848i) q^{29} +(-5.38500 - 0.257429i) q^{30} +(1.35392 - 2.34507i) q^{31} +(-3.35015 - 4.55812i) q^{32} +(-4.94351 + 0.871675i) q^{33} +(-0.0813230 - 0.0751399i) q^{34} +(3.10183 - 8.52220i) q^{35} +(2.29010 + 1.09104i) q^{36} -10.4844i q^{37} +(4.24141 + 4.47331i) q^{38} +5.89976i q^{39} +(6.96462 - 4.31643i) q^{40} +(0.203213 - 0.558324i) q^{41} +(3.95374 - 4.27908i) q^{42} +(-10.9034 + 1.92257i) q^{43} +(5.43917 - 5.34993i) q^{44} +(-1.83717 + 3.18207i) q^{45} +(0.151671 - 3.17271i) q^{46} +(-1.45618 + 1.73541i) q^{47} +(5.19812 - 0.828162i) q^{48} +(1.40035 + 2.42547i) q^{49} +(2.19752 + 4.26436i) q^{50} +(0.0968133 - 0.0352372i) q^{51} +(-5.08220 - 7.38742i) q^{52} +(0.929735 + 0.163937i) q^{53} +(-6.32184 + 4.80952i) q^{54} +(7.10330 + 8.46538i) q^{55} +(-1.26459 + 8.76392i) q^{56} +(-5.50785 + 1.60150i) q^{57} +(-0.614709 - 0.395196i) q^{58} +(6.93627 - 5.82022i) q^{59} +(0.601658 + 7.60046i) q^{60} +(-0.585413 + 3.32004i) q^{61} +(-3.53189 - 1.48010i) q^{62} +(-1.35807 - 3.73126i) q^{63} +(-5.79545 + 5.51477i) q^{64} +(11.2480 - 6.49401i) q^{65} +(2.10671 + 6.77924i) q^{66} +(1.61972 + 1.35911i) q^{67} +(-0.0908712 + 0.127520i) q^{68} +(2.55959 + 1.47778i) q^{69} +(-12.5101 - 2.82774i) q^{70} +(0.503163 + 2.85358i) q^{71} +(1.12113 - 3.40777i) q^{72} +(13.7341 + 4.99880i) q^{73} +(-14.7082 + 1.87453i) q^{74} -4.46384 q^{75} +(5.51712 - 6.74992i) q^{76} -11.9422 q^{77} +(8.27658 - 1.05483i) q^{78} +(6.53766 + 2.37952i) q^{79} +(-7.30059 - 8.99868i) q^{80} +(-0.622736 - 3.53171i) q^{81} +(-0.819587 - 0.185257i) q^{82} +(-4.69715 - 2.71190i) q^{83} +(-6.70988 - 4.78149i) q^{84} +(-0.173745 - 0.145789i) q^{85} +(4.64655 + 14.9523i) q^{86} +(0.588891 - 0.339996i) q^{87} +(-8.47772 - 6.67390i) q^{88} +(1.01763 + 2.79592i) q^{89} +(4.79249 + 2.00837i) q^{90} +(-2.43727 + 13.8225i) q^{91} +(-4.47801 + 0.354482i) q^{92} +(2.72965 - 2.29045i) q^{93} +(2.69489 + 1.73255i) q^{94} +(9.11589 + 8.73797i) q^{95} +(-2.09118 - 7.14419i) q^{96} +(-6.08391 - 7.25052i) q^{97} +(3.15224 - 2.39815i) q^{98} +(4.76484 + 0.840170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.178792	−	1.40287i	−0.126425	−	0.991976i
$2$	−0.178792	−	1.40287i	−0.126425	−	0.991976i
$3$	1.23656	+	0.450071i	0.713928	+	0.259848i	0.673346	−	0.739328i	$-0.264857\pi$
$3$	1.23656	+	0.450071i	0.713928	+	0.259848i	0.0405821	+	0.999176i	$0.487079\pi$
$4$	−1.93607	+	0.501643i	−0.968033	+	0.250822i
$5$	−0.503046	−	2.85292i	−0.224969	−	1.27586i	−0.862744	−	0.505640i	$-0.831256\pi$
$5$	−0.503046	−	2.85292i	−0.224969	−	1.27586i	0.637775	−	0.770222i	$-0.279855\pi$
$6$	0.410302	−	1.81520i	0.167505	−	0.741051i
$7$	2.71118	+	1.56530i	1.02473	+	0.591629i	0.915471	−	0.402384i	$-0.131818\pi$
$7$	2.71118	+	1.56530i	1.02473	+	0.591629i	0.109260	+	0.994013i	$0.465152\pi$
$8$	1.04989	+	2.62635i	0.371193	+	0.928556i
$9$	−0.971618	−	0.815285i	−0.323873	−	0.271762i
$10$	−3.91232	+	1.21579i	−1.23718	+	0.384465i
$11$	−3.30359	+	1.90733i	−0.996069	+	0.575081i	−0.907083	−	0.420952i	$-0.861696\pi$
$11$	−3.30359	+	1.90733i	−0.996069	+	0.575081i	−0.0889863	+	0.996033i	$0.528363\pi$
$12$	−2.61984	−	0.251056i	−0.756282	−	0.0724735i
$13$	1.53341	+	4.21300i	0.425290	+	1.16848i	0.948640	+	0.316358i	$0.102460\pi$
$13$	1.53341	+	4.21300i	0.425290	+	1.16848i	−0.523350	+	0.852118i	$0.675318\pi$
$14$	1.71117	−	4.08329i	0.457330	−	1.09131i
$15$	0.661968	−	3.75421i	0.170919	−	0.969332i
$16$	3.49671	−	1.94243i	0.874177	−	0.485607i
$17$	0.0599755	−	0.0503255i	0.0145462	−	0.0122057i	−0.635486	−	0.772113i	$-0.719200\pi$
$17$	0.0599755	−	0.0503255i	0.0145462	−	0.0122057i	0.650032	+	0.759907i	$0.274756\pi$
$18$	−0.970017	+	1.50882i	−0.228635	+	0.355632i
$19$	−3.51689	+	2.57517i	−0.806830	+	0.590784i
$19$	−3.51689	+	2.57517i	−0.806830	+	0.590784i
$20$	2.40508	+	5.27109i	0.537791	+	1.17865i
$21$	2.64804	+	3.15581i	0.577850	+	0.688655i
$22$	3.26638	+	4.29348i	0.696395	+	0.915372i
$23$	2.21189	+	0.390015i	0.461210	+	0.0813238i	0.399425	−	0.916766i	$-0.369210\pi$
$23$	2.21189	+	0.390015i	0.461210	+	0.0813238i	0.0617846	+	0.998090i	$0.480321\pi$
$24$	0.116209	+	3.72017i	0.0237210	+	0.759376i
$25$	−3.18761	+	1.16020i	−0.637522	+	0.232039i
$26$	5.63611	−	2.90441i	1.10533	−	0.569603i
$27$	−2.80841	−	4.86430i	−0.540478	−	0.936135i
$28$	−6.03426	−	1.67048i	−1.14037	−	0.315692i
$29$	0.332156	−	0.395848i	0.0616799	−	0.0735072i	−0.734322	−	0.678801i	$-0.762500\pi$
$29$	0.332156	−	0.395848i	0.0616799	−	0.0735072i	0.796002	+	0.605294i	$0.206944\pi$
$30$	−5.38500	−	0.257429i	−0.983163	−	0.0470000i
$31$	1.35392	−	2.34507i	0.243172	−	0.421186i	−0.718444	−	0.695585i	$-0.755145\pi$
$31$	1.35392	−	2.34507i	0.243172	−	0.421186i	0.961616	+	0.274398i	$0.0884787\pi$
$32$	−3.35015	−	4.55812i	−0.592229	−	0.805770i
$33$	−4.94351	+	0.871675i	−0.860555	+	0.151739i
$34$	−0.0813230	−	0.0751399i	−0.0139468	−	0.0128864i
$35$	3.10183	−	8.52220i	0.524304	−	1.44051i
$36$	2.29010	+	1.09104i	0.381683	+	0.181840i
$37$		−	10.4844i		−	1.72363i	−0.507227	−	0.861813i	$-0.669329\pi$
$37$		−	10.4844i		−	1.72363i	0.507227	−	0.861813i	$-0.330671\pi$
$38$	4.24141	+	4.47331i	0.688047	+	0.725666i
$39$			5.89976i			0.944718i
$40$	6.96462	−	4.31643i	1.10120	−	0.682487i
$41$	0.203213	−	0.558324i	0.0317366	−	0.0871956i	−0.922812	−	0.385250i	$-0.874115\pi$
$41$	0.203213	−	0.558324i	0.0317366	−	0.0871956i	0.954549	+	0.298054i	$0.0963376\pi$
$42$	3.95374	−	4.27908i	0.610075	−	0.660277i
$43$	−10.9034	+	1.92257i	−1.66276	+	0.293189i	−0.924457	−	0.381286i	$-0.875481\pi$
$43$	−10.9034	+	1.92257i	−1.66276	+	0.293189i	−0.738298	+	0.674474i	$0.764370\pi$
$44$	5.43917	−	5.34993i	0.819986	−	0.806533i
$45$	−1.83717	+	3.18207i	−0.273869	+	0.474355i
$46$	0.151671	−	3.17271i	0.0223627	−	0.467791i
$47$	−1.45618	+	1.73541i	−0.212405	+	0.253135i	−0.861719	−	0.507386i	$-0.830612\pi$
$47$	−1.45618	+	1.73541i	−0.212405	+	0.253135i	0.649314	+	0.760521i	$0.275056\pi$
$48$	5.19812	−	0.828162i	0.750284	−	0.119535i
$49$	1.40035	+	2.42547i	0.200049	+	0.346496i
$50$	2.19752	+	4.26436i	0.310776	+	0.603071i
$51$	0.0968133	−	0.0352372i	0.0135566	−	0.00493419i
$52$	−5.08220	−	7.38742i	−0.704774	−	1.02445i
$53$	0.929735	+	0.163937i	0.127709	+	0.0225185i	0.237137	−	0.971476i	$-0.423791\pi$
$53$	0.929735	+	0.163937i	0.127709	+	0.0225185i	−0.109428	+	0.993995i	$0.534902\pi$
$54$	−6.32184	+	4.80952i	−0.860294	+	0.654492i
$55$	7.10330	+	8.46538i	0.957809	+	1.14147i
$56$	−1.26459	+	8.76392i	−0.168988	+	1.17113i
$57$	−5.50785	+	1.60150i	−0.729533	+	0.212123i
$58$	−0.614709	−	0.395196i	−0.0807153	−	0.0518918i
$59$	6.93627	−	5.82022i	0.903025	−	0.757728i	−0.0677542	−	0.997702i	$-0.521583\pi$
$59$	6.93627	−	5.82022i	0.903025	−	0.757728i	0.970779	+	0.239974i	$0.0771389\pi$
$60$	0.601658	+	7.60046i	0.0776737	+	0.981216i
$61$	−0.585413	+	3.32004i	−0.0749544	+	0.425088i	0.924121	+	0.382100i	$0.124799\pi$
$61$	−0.585413	+	3.32004i	−0.0749544	+	0.425088i	−0.999076	+	0.0429882i	$0.986312\pi$
$62$	−3.53189	−	1.48010i	−0.448550	−	0.187972i
$63$	−1.35807	−	3.73126i	−0.171101	−	0.470095i
$64$	−5.79545	+	5.51477i	−0.724432	+	0.689346i
$65$	11.2480	−	6.49401i	1.39514	−	0.805483i
$66$	2.10671	+	6.77924i	0.259317	+	0.834467i
$67$	1.61972	+	1.35911i	0.197881	+	0.166042i	0.736344	−	0.676607i	$-0.236550\pi$
$67$	1.61972	+	1.35911i	0.197881	+	0.166042i	−0.538463	+	0.842649i	$0.680995\pi$
$68$	−0.0908712	+	0.127520i	−0.0110198	+	0.0154640i
$69$	2.55959	+	1.47778i	0.308139	+	0.177904i
$70$	−12.5101	−	2.82774i	−1.49524	−	0.337980i
$71$	0.503163	+	2.85358i	0.0597145	+	0.338657i	0.999998	−	0.00173334i	$-0.000551738\pi$
$71$	0.503163	+	2.85358i	0.0597145	+	0.338657i	−0.940284	+	0.340391i	$0.889441\pi$
$72$	1.12113	−	3.40777i	0.132127	−	0.401610i
$73$	13.7341	+	4.99880i	1.60745	+	0.585066i	0.980934	−	0.194340i	$-0.0622563\pi$
$73$	13.7341	+	4.99880i	1.60745	+	0.585066i	0.626520	+	0.779405i	$0.284479\pi$
$74$	−14.7082	+	1.87453i	−1.70980	+	0.217910i
$75$	−4.46384			−0.515440
$76$	5.51712	−	6.74992i	0.632857	−	0.774269i
$77$	−11.9422			−1.36094
$78$	8.27658	−	1.05483i	0.937138	−	0.119436i
$79$	6.53766	+	2.37952i	0.735545	+	0.267716i	0.682510	−	0.730876i	$-0.260888\pi$
$79$	6.53766	+	2.37952i	0.735545	+	0.267716i	0.0530348	+	0.998593i	$0.483111\pi$
$80$	−7.30059	−	8.99868i	−0.816231	−	1.00608i
$81$	−0.622736	−	3.53171i	−0.0691929	−	0.392413i
$82$	−0.819587	−	0.185257i	−0.0905083	−	0.0204582i
$83$	−4.69715	−	2.71190i	−0.515579	−	0.297670i	0.219545	−	0.975602i	$-0.429543\pi$
$83$	−4.69715	−	2.71190i	−0.515579	−	0.297670i	−0.735124	+	0.677933i	$0.762876\pi$
$84$	−6.70988	−	4.78149i	−0.732108	−	0.521704i
$85$	−0.173745	−	0.145789i	−0.0188453	−	0.0158131i
$86$	4.64655	+	14.9523i	0.501050	+	1.61235i
$87$	0.588891	−	0.339996i	0.0631357	−	0.0364514i
$88$	−8.47772	−	6.67390i	−0.903728	−	0.711440i
$89$	1.01763	+	2.79592i	0.107869	+	0.296367i	0.981870	−	0.189557i	$-0.0607053\pi$
$89$	1.01763	+	2.79592i	0.107869	+	0.296367i	−0.874001	+	0.485924i	$0.838483\pi$
$90$	4.79249	+	2.00837i	0.505173	+	0.211701i
$91$	−2.43727	+	13.8225i	−0.255496	+	1.44899i
$92$	−4.47801	+	0.354482i	−0.466864	+	0.0369573i
$93$	2.72965	−	2.29045i	0.283052	−	0.237509i
$94$	2.69489	+	1.73255i	0.277957	+	0.178698i
$95$	9.11589	+	8.73797i	0.935271	+	0.896496i
$96$	−2.09118	−	7.14419i	−0.213431	−	0.729151i
$97$	−6.08391	−	7.25052i	−0.617728	−	0.736179i	0.362950	−	0.931808i	$-0.381769\pi$
$97$	−6.08391	−	7.25052i	−0.617728	−	0.736179i	−0.980678	+	0.195629i	$0.937325\pi$
$98$	3.15224	−	2.39815i	0.318424	−	0.242250i
$99$	4.76484	+	0.840170i	0.478885	+	0.0844403i
$100$	5.58942	−	3.84526i	0.558942	−	0.384526i
$101$	−15.0894	+	5.49209i	−1.50145	+	0.546483i	−0.956435	−	0.291944i	$-0.905698\pi$
$101$	−15.0894	+	5.49209i	−1.50145	+	0.546483i	−0.545014	+	0.838427i	$0.683476\pi$
$102$	−0.0667425	−	0.129516i	−0.00660849	−	0.0128240i
$103$	−5.69920	−	9.87131i	−0.561559	−	0.972649i	−0.997361	−	0.0726061i	$-0.976868\pi$
$103$	−5.69920	−	9.87131i	−0.561559	−	0.972649i	0.435802	−	0.900043i	$-0.356465\pi$
$104$	−9.45491	+	8.45046i	−0.927130	+	0.828635i
$105$	7.67119	−	9.14216i	0.748631	−	0.892184i
$106$	0.0637528	−	1.33360i	0.00619222	−	0.129531i
$107$	−4.47937	+	7.75849i	−0.433037	+	0.750041i	−0.997133	−	0.0756674i	$-0.975891\pi$
$107$	−4.47937	+	7.75849i	−0.433037	+	0.750041i	0.564096	+	0.825709i	$0.309225\pi$
$108$	7.87740	+	8.00880i	0.758004	+	0.770647i
$109$	15.8051	−	2.78687i	1.51386	−	0.266934i	0.645841	−	0.763472i	$-0.276507\pi$
$109$	15.8051	−	2.78687i	1.51386	−	0.266934i	0.868015	+	0.496539i	$0.165396\pi$
$110$	10.6058	−	11.4785i	1.01122	−	1.09443i
$111$	4.71872	−	12.9646i	0.447881	−	1.23054i
$112$	12.5207	+	0.207126i	1.18310	+	0.0195715i
$113$			7.86582i			0.739954i	0.929041	+	0.369977i	$0.120634\pi$
$113$			7.86582i			0.739954i	−0.929041	+	0.369977i	$0.879366\pi$
$114$	3.23144	+	7.44044i	0.302653	+	0.696861i
$115$		−	6.50652i		−	0.606736i
$116$	−0.444502	+	0.933013i	−0.0412710	+	0.0866280i
$117$	1.94491	−	5.34359i	0.179807	−	0.494015i
$118$	−9.40514	−	8.69005i	−0.865813	−	0.799983i
$119$	0.241379	−	0.0425617i	0.0221272	−	0.00390162i
$120$	10.5549	−	2.20295i	0.963523	−	0.201101i
$121$	1.77579	−	3.07577i	0.161436	−	0.279615i
$122$	4.76224	+	0.227658i	0.431153	+	0.0206112i
$123$	0.502571	−	0.598941i	0.0453153	−	0.0540047i
$124$	−1.44490	+	5.21939i	−0.129756	+	0.468715i
$125$	−2.32886	−	4.03371i	−0.208300	−	0.360786i
$126$	−4.99165	+	2.57231i	−0.444692	+	0.229160i
$127$	13.7632	−	5.00938i	1.22128	−	0.444511i	0.350679	−	0.936496i	$-0.385951\pi$
$127$	13.7632	−	5.00938i	1.22128	−	0.444511i	0.870604	+	0.491985i	$0.163729\pi$
$128$	8.77267	+	7.14425i	0.775402	+	0.631468i
$129$	−14.3480	−	2.52994i	−1.26327	−	0.222749i
$130$	−11.1213	−	14.6183i	−0.975400	−	1.28211i
$131$	−12.0116	−	14.3149i	−1.04946	−	1.25070i	−0.967182	−	0.254086i	$-0.918225\pi$
$131$	−12.0116	−	14.3149i	−1.04946	−	1.25070i	−0.0822765	−	0.996610i	$-0.526219\pi$
$132$	9.13370	−	4.16750i	0.794987	−	0.362734i
$133$	−13.5659	+	1.47675i	−1.17631	+	0.128050i
$134$	1.61706	−	2.51525i	0.139692	−	0.217285i
$135$	−12.4647	+	10.4591i	−1.07279	+	0.900177i
$136$	0.195140	+	0.104681i	0.0167331	+	0.00897629i
$137$	−2.78187	+	15.7768i	−0.237671	+	1.34790i	0.599243	+	0.800568i	$0.295469\pi$
$137$	−2.78187	+	15.7768i	−0.237671	+	1.34790i	−0.836914	+	0.547334i	$0.815643\pi$
$138$	1.61549	−	3.85498i	0.137520	−	0.328158i
$139$	4.01315	+	11.0260i	0.340391	+	0.935215i	0.985281	+	0.170941i	$0.0546806\pi$
$139$	4.01315	+	11.0260i	0.340391	+	0.935215i	−0.644891	+	0.764275i	$0.723097\pi$
$140$	−1.73024	+	18.0556i	−0.146232	+	1.52597i
$141$	−2.58171	+	1.49055i	−0.217419	+	0.125527i
$142$	3.91323	−	1.21607i	0.328391	−	0.102050i
$143$	−13.1013	−	10.9933i	−1.09559	−	0.919306i
$144$	−4.98110	−	0.963513i	−0.415091	−	0.0802928i
$145$	−1.29641	−	0.748484i	−0.107661	−	0.0621582i
$146$	4.55710	−	20.1608i	0.377148	−	1.66852i
$147$	0.639977	+	3.62949i	0.0527844	+	0.299355i
$148$	5.25943	+	20.2985i	0.432322	+	1.66853i
$149$	14.4819	+	5.27097i	1.18640	+	0.431815i	0.858459	−	0.512882i	$-0.171422\pi$
$149$	14.4819	+	5.27097i	1.18640	+	0.431815i	0.327943	+	0.944697i	$0.393645\pi$
$150$	0.798100	+	6.26217i	0.0651646	+	0.511304i
$151$	−8.07351			−0.657013			−0.328506	−	0.944502i	$-0.606545\pi$
$151$	−8.07351			−0.657013			−0.328506	+	0.944502i	$0.606545\pi$
$152$	−10.4556	−	6.53295i	−0.848065	−	0.529892i
$153$	−0.0993029			−0.00802816
$154$	2.13517	+	16.7533i	0.172057	+	1.35002i
$155$	−7.37136	−	2.68296i	−0.592082	−	0.215500i
$156$	−2.95958	−	11.4223i	−0.236956	−	0.914519i
$157$	0.547741	+	3.10639i	0.0437145	+	0.247917i	0.998832	−	0.0483086i	$-0.0153831\pi$
$157$	0.547741	+	3.10639i	0.0437145	+	0.247917i	−0.955118	+	0.296226i	$0.904272\pi$
$158$	2.16926	−	9.59691i	0.172577	−	0.763489i
$159$	1.07589	+	0.621165i	0.0853236	+	0.0492616i
$160$	−11.3187	+	11.8506i	−0.894819	+	0.936876i
$161$	5.38634	+	4.51967i	0.424503	+	0.356200i
$162$	−4.84318	+	1.50506i	−0.380516	+	0.118249i
$163$	7.85954	−	4.53771i	0.615607	−	0.355421i	−0.159550	−	0.987190i	$-0.551004\pi$
$163$	7.85954	−	4.53771i	0.615607	−	0.355421i	0.775157	+	0.631769i	$0.217671\pi$
$164$	−0.113355	+	1.18289i	−0.00885156	+	0.0923685i
$165$	4.97363	+	13.6649i	0.387197	+	1.06381i
$166$	−2.96462	+	7.07434i	−0.230099	+	0.549075i
$167$	2.01187	−	11.4099i	0.155684	−	0.882925i	−0.802475	−	0.596686i	$-0.796484\pi$
$167$	2.01187	−	11.4099i	0.155684	−	0.882925i	0.958158	−	0.286239i	$-0.0924052\pi$
$168$	−5.50812	+	10.2680i	−0.424961	+	0.792190i
$169$	−5.43945	+	4.56424i	−0.418419	+	0.351095i
$170$	−0.173458	+	0.269807i	−0.0133037	+	0.0206932i
$171$	5.51657	+	0.365188i	0.421863	+	0.0279266i
$172$	20.1453	−	9.19184i	1.53606	−	0.700871i
$173$	1.95957	+	2.33532i	0.148983	+	0.177551i	0.835375	−	0.549681i	$-0.185251\pi$
$173$	1.95957	+	2.33532i	0.148983	+	0.177551i	−0.686391	+	0.727232i	$0.740806\pi$
$174$	−0.582258	−	0.765346i	−0.0441409	−	0.0580207i
$175$	−10.4583	−	1.84407i	−0.790570	−	0.139399i
$176$	−7.84684	+	13.0864i	−0.591478	+	0.986421i
$177$	11.1966	−	4.07524i	0.841589	−	0.306313i
$178$	3.74036	−	1.92749i	0.280352	−	0.144471i
$179$	2.16782	+	3.75477i	0.162030	+	0.280645i	0.935597	−	0.353070i	$-0.114862\pi$
$179$	2.16782	+	3.75477i	0.162030	+	0.280645i	−0.773566	+	0.633715i	$0.781529\pi$
$180$	1.96062	−	7.08230i	0.146136	−	0.527884i
$181$	1.29207	−	1.53983i	0.0960386	−	0.114454i	−0.715885	−	0.698219i	$-0.753976\pi$
$181$	1.29207	−	1.53983i	0.0960386	−	0.114454i	0.811923	+	0.583764i	$0.198421\pi$
$182$	19.8268	+	0.947819i	1.46966	+	0.0702570i
$183$	−2.21815	+	3.84195i	−0.163970	+	0.284005i
$184$	1.29792	+	6.21866i	0.0956841	+	0.458446i
$185$	−29.9111	+	5.27414i	−2.19911	+	0.387762i
$186$	−3.70124	−	3.41982i	−0.271388	−	0.250754i
$187$	−0.102147	+	0.280648i	−0.00746976	+	0.0205230i
$188$	1.94870	−	4.09034i	0.142124	−	0.298319i
$189$		−	17.5840i		−	1.27905i
$190$	10.6283	−	14.3507i	0.771061	−	1.04111i
$191$			7.09667i			0.513497i	0.966478	+	0.256749i	$0.0826512\pi$
$191$			7.09667i			0.513497i	−0.966478	+	0.256749i	$0.917349\pi$
$192$	−9.64846	+	4.21098i	−0.696318	+	0.303901i
$193$	−1.24224	+	3.41304i	−0.0894186	+	0.245676i	−0.976339	−	0.216247i	$-0.930618\pi$
$193$	−1.24224	+	3.41304i	−0.0894186	+	0.245676i	0.886920	+	0.461923i	$0.152840\pi$
$194$	−9.08376	+	9.83125i	−0.652176	+	0.705843i
$195$	16.8315	−	2.96785i	1.20533	−	0.212532i
$196$	−3.92788	−	3.99340i	−0.280563	−	0.285243i
$197$	8.46348	−	14.6592i	0.602998	−	1.04442i	−0.389366	−	0.921083i	$-0.627306\pi$
$197$	8.46348	−	14.6592i	0.602998	−	1.04442i	0.992364	−	0.123340i	$-0.0393607\pi$
$198$	0.326730	−	6.83465i	0.0232197	−	0.485717i
$199$	−4.24439	+	5.05827i	−0.300877	+	0.358571i	−0.895207	−	0.445650i	$-0.852973\pi$
$199$	−4.24439	+	5.05827i	−0.300877	+	0.358571i	0.594331	+	0.804221i	$0.297417\pi$
$200$	−6.39373	−	7.15371i	−0.452105	−	0.505844i
$201$	1.39119	+	2.40961i	0.0981269	+	0.169961i
$202$	10.4025	+	20.1864i	0.731919	+	1.42031i
$203$	1.52016	−	0.553293i	0.106694	−	0.0388335i
$204$	−0.169761	+	0.116787i	−0.0118856	+	0.00817674i
$205$	−1.69508	−	0.298888i	−0.118389	−	0.0208752i
$206$	−12.8291	+	9.76013i	−0.893849	+	0.680021i
$207$	−1.83113	−	2.18226i	−0.127273	−	0.151678i
$208$	13.5453	+	11.7531i	0.939199	+	0.814931i
$209$	6.70667	−	15.2151i	0.463910	−	1.05245i
$210$	−14.1968	−	9.12710i	−0.979671	−	0.629830i
$211$	1.14737	−	0.962755i	0.0789880	−	0.0662788i	−0.602439	−	0.798165i	$-0.705804\pi$
$211$	1.14737	−	0.962755i	0.0789880	−	0.0662788i	0.681427	+	0.731886i	$0.261360\pi$
$212$	−1.88227	+	0.149001i	−0.129275	+	0.0102335i
$213$	−0.662122	+	3.75508i	−0.0453678	+	0.257294i
$214$	11.6850	+	4.89679i	0.798770	+	0.334738i
$215$	10.9698	+	30.1394i	0.748137	+	2.05549i
$216$	9.82685	−	12.4829i	0.668632	−	0.849351i
$217$	7.34148	−	4.23860i	0.498372	−	0.287735i
$218$	−6.73543	−	21.6742i	−0.456181	−	1.46796i
$219$	14.7332	+	12.3626i	0.995578	+	0.835389i
$220$	−17.9991	−	12.8262i	−1.21350	−	0.864744i
$221$	0.303988	+	0.175508i	0.0204484	+	0.0118059i
$222$	−19.0313	−	4.30177i	−1.27729	−	0.288716i
$223$	−1.36458	−	7.73892i	−0.0913791	−	0.518237i	−0.995797	−	0.0915888i	$-0.970805\pi$
$223$	−1.36458	−	7.73892i	−0.0913791	−	0.518237i	0.904418	−	0.426648i	$-0.140306\pi$
$224$	−1.94804	−	17.6019i	−0.130159	−	1.17608i
$225$	4.04303	+	1.47154i	0.269535	+	0.0981028i
$226$	11.0347	−	1.40635i	0.734016	−	0.0935488i
$227$	5.35801			0.355624			0.177812	−	0.984065i	$-0.443098\pi$
$227$	5.35801			0.355624			0.177812	+	0.984065i	$0.443098\pi$
$228$	9.86019	−	5.86358i	0.653007	−	0.388325i
$229$	3.14192			0.207624			0.103812	−	0.994597i	$-0.466896\pi$
$229$	3.14192			0.207624			0.103812	+	0.994597i	$0.466896\pi$
$230$	−9.12777	+	1.16331i	−0.601868	+	0.0767067i
$231$	−14.7672	−	5.37483i	−0.971611	−	0.353638i
$232$	1.38837	+	0.456761i	0.0911506	+	0.0299879i
$233$	−2.48023	−	14.0661i	−0.162485	−	0.921500i	−0.951619	−	0.307279i	$-0.900582\pi$
$233$	−2.48023	−	14.0661i	−0.162485	−	0.921500i	0.789134	−	0.614221i	$-0.210530\pi$
$234$	−7.84407	−	1.77305i	−0.512783	−	0.115908i
$235$	5.68349	+	3.28136i	0.370750	+	0.214053i
$236$	−10.5094	+	14.7479i	−0.684104	+	0.960004i
$237$	7.01326	+	5.88482i	0.455560	+	0.382260i
$238$	−0.102865	−	0.331013i	−0.00666775	−	0.0214564i
$239$	10.7517	−	6.20747i	0.695467	−	0.401528i	−0.110190	−	0.993911i	$-0.535146\pi$
$239$	10.7517	−	6.20747i	0.695467	−	0.401528i	0.805657	+	0.592382i	$0.201813\pi$
$240$	−4.97757	−	14.4132i	−0.321301	−	0.930367i
$241$	−3.08075	−	8.46430i	−0.198449	−	0.545234i	0.800054	−	0.599928i	$-0.204804\pi$
$241$	−3.08075	−	8.46430i	−0.198449	−	0.545234i	−0.998503	+	0.0546939i	$0.982582\pi$
$242$	−4.63239	−	1.94128i	−0.297781	−	0.124790i
$243$	−2.10658	+	11.9470i	−0.135137	+	0.766400i
$244$	−0.532077	−	6.72149i	−0.0340628	−	0.430299i
$245$	6.21522	−	5.21519i	0.397076	−	0.333186i
$246$	−0.930089	−	0.597954i	−0.0593003	−	0.0381241i
$247$	−16.2420	−	10.8679i	−1.03345	−	0.691507i
$248$	7.58044	+	1.09382i	0.481359	+	0.0694575i
$249$	−4.58775	−	5.46747i	−0.290737	−	0.346487i
$250$	−5.24237	+	3.98828i	−0.331557	+	0.252241i
$251$	9.86546	+	1.73955i	0.622703	+	0.109799i	0.476093	−	0.879395i	$-0.342053\pi$
$251$	9.86546	+	1.73955i	0.622703	+	0.109799i	0.146610	+	0.989194i	$0.453164\pi$
$252$	4.50107	+	6.54271i	0.283541	+	0.412152i
$253$	−8.05104	+	2.93034i	−0.506165	+	0.184229i
$254$	−9.48824	−	18.4122i	−0.595345	−	1.15529i
$255$	−0.149230	−	0.258474i	−0.00934516	−	0.0161863i
$256$	8.45394	−	13.5842i	0.528371	−	0.849013i
$257$	0.755271	−	0.900097i	0.0471125	−	0.0561465i	−0.741974	−	0.670429i	$-0.766110\pi$
$257$	0.755271	−	0.900097i	0.0471125	−	0.0561465i	0.789086	+	0.614283i	$0.210554\pi$
$258$	−0.983857	+	20.5807i	−0.0612522	+	1.28130i
$259$	16.4113	−	28.4251i	1.01975	−	1.76625i
$260$	−18.5191	+	18.2153i	−1.14851	+	1.12966i
$261$	−0.645458	+	0.113812i	−0.0399528	+	0.00704477i
$262$	−17.9343	+	19.4100i	−1.10798	+	1.19916i
$263$	−10.0964	+	27.7395i	−0.622568	+	1.71049i	0.0780441	+	0.996950i	$0.475132\pi$
$263$	−10.0964	+	27.7395i	−0.622568	+	1.71049i	−0.700612	+	0.713542i	$0.747090\pi$
$264$	−7.47948	−	12.0682i	−0.460330	−	0.742749i
$265$		−	2.73492i		−	0.168005i
$266$	4.49715	+	18.7670i	0.275738	+	1.15068i
$267$			3.91533i			0.239614i
$268$	−3.81768	−	1.81880i	−0.233202	−	0.111101i
$269$	3.18316	−	8.74565i	0.194081	−	0.533232i	−0.804036	−	0.594581i	$-0.797318\pi$
$269$	3.18316	−	8.74565i	0.194081	−	0.533232i	0.998116	+	0.0613489i	$0.0195402\pi$
$270$	16.9013	+	15.6163i	1.02858	+	0.950376i
$271$	5.26894	−	0.929056i	0.320065	−	0.0564361i	−0.0113075	−	0.999936i	$-0.503599\pi$
$271$	5.26894	−	0.929056i	0.320065	−	0.0564361i	0.331373	+	0.943500i	$0.392488\pi$
$272$	0.111963	−	0.292472i	0.00678878	−	0.0177337i
$273$	−9.23492	+	15.9953i	−0.558923	+	0.968082i
$274$	22.6301	+	1.08183i	1.36713	+	0.0653557i
$275$	8.31768	−	9.91262i	0.501575	−	0.597754i
$276$	−5.69686	−	1.57708i	−0.342911	−	0.0949292i
$277$	7.47083	+	12.9398i	0.448878	+	0.777480i	0.998313	−	0.0580563i	$-0.0184903\pi$
$277$	7.47083	+	12.9398i	0.448878	+	0.777480i	−0.549435	+	0.835537i	$0.685157\pi$
$278$	14.7505	−	7.60127i	0.884677	−	0.455894i
$279$	−3.22739	+	1.17468i	−0.193219	+	0.0703260i
$280$	25.6389	−	0.800895i	1.53222	−	0.0478626i
$281$	19.3541	+	3.41264i	1.15457	+	0.203581i	0.717968	−	0.696076i	$-0.245072\pi$
$281$	19.3541	+	3.41264i	1.15457	+	0.203581i	0.436598	+	0.899657i	$0.356183\pi$
$282$	2.55263	+	3.35529i	0.152007	+	0.199805i
$283$	6.74711	+	8.04090i	0.401074	+	0.477982i	0.928347	−	0.371714i	$-0.121230\pi$
$283$	6.74711	+	8.04090i	0.401074	+	0.477982i	−0.527273	+	0.849696i	$0.676785\pi$
$284$	−2.40563	−	5.27231i	−0.142748	−	0.312854i
$285$	7.33963	+	14.9078i	0.434762	+	0.883062i
$286$	−13.0797	+	20.3449i	−0.773420	+	1.20302i
$287$	1.42490	−	1.19563i	0.0841089	−	0.0705758i
$288$	−0.461098	+	7.16008i	−0.0271705	+	0.421912i
$289$	−2.95095	+	16.7357i	−0.173586	+	0.984453i
$290$	−0.818234	+	1.95252i	−0.0480484	+	0.114656i
$291$	−4.25987	−	11.7039i	−0.249718	−	0.686094i
$292$	−29.0977	−	2.78840i	−1.70282	−	0.163179i
$293$	−14.0762	+	8.12692i	−0.822343	+	0.474780i	−0.851224	−	0.524803i	$-0.824139\pi$
$293$	−14.0762	+	8.12692i	−0.822343	+	0.474780i	0.0288809	+	0.999583i	$0.490806\pi$
$294$	4.97727	−	1.54673i	0.290280	−	0.0902069i
$295$	−20.0939	−	16.8608i	−1.16991	−	0.981671i
$296$	27.5357	−	11.0075i	1.60048	−	0.639797i
$297$	18.5556	+	10.7131i	1.07671	+	0.621637i
$298$	4.80522	−	21.2585i	0.278359	−	1.23147i
$299$	1.74859	+	9.91672i	0.101123	+	0.573499i
$300$	8.64229	−	2.23925i	0.498963	−	0.129283i
$301$	−32.5706	−	11.8547i	−1.87734	−	0.683295i
$302$	1.44348	+	11.3260i	0.0830629	+	0.651741i
$303$	−21.1307			−1.21393
$304$	−7.29546	+	15.8359i	−0.418424	+	0.908252i
$305$	9.76629			0.559216
$306$	0.0177546	+	0.139309i	0.00101496	+	0.00796375i
$307$	−23.4603	−	8.53887i	−1.33895	−	0.487339i	−0.429470	−	0.903081i	$-0.641300\pi$
$307$	−23.4603	−	8.53887i	−1.33895	−	0.487339i	−0.909482	+	0.415742i	$0.863522\pi$
$308$	23.1209	−	5.99071i	1.31743	−	0.341352i
$309$	−2.60461	−	14.7715i	−0.148171	−	0.840321i
$310$	−2.44589	+	10.8207i	−0.138917	+	0.614576i
$311$	−13.2821	−	7.66844i	−0.753160	−	0.434837i	0.0736742	−	0.997282i	$-0.476527\pi$
$311$	−13.2821	−	7.66844i	−0.753160	−	0.434837i	−0.826835	+	0.562445i	$0.809861\pi$
$312$	−15.4949	+	6.19411i	−0.877224	+	0.350673i
$313$	−8.05392	−	6.75804i	−0.455234	−	0.381987i	0.386140	−	0.922440i	$-0.373808\pi$
$313$	−8.05392	−	6.75804i	−0.455234	−	0.381987i	−0.841374	+	0.540453i	$0.818253\pi$
$314$	4.25992	−	1.32381i	0.240401	−	0.0747066i
$315$	−9.96181	+	5.75145i	−0.561284	+	0.324058i
$316$	−13.8510	−	1.32733i	−0.779181	−	0.0746679i
$317$	6.17206	+	16.9576i	0.346657	+	0.952433i	0.983415	+	0.181369i	$0.0580529\pi$
$317$	6.17206	+	16.9576i	0.346657	+	0.952433i	−0.636758	+	0.771064i	$0.719725\pi$
$318$	0.679051	−	1.62039i	0.0380793	−	0.0908668i
$319$	−0.342295	+	1.94125i	−0.0191648	+	0.108689i
$320$	18.6486	+	13.7598i	1.04249	+	0.769194i
$321$	−9.03087	+	7.57780i	−0.504054	+	0.422952i
$322$	5.37746	−	8.36439i	0.299674	−	0.466129i
$323$	−0.0813310	+	0.331436i	−0.00452538	+	0.0184416i
$324$	2.97732	+	6.52524i	0.165407	+	0.362513i
$325$	−9.77580	−	11.6503i	−0.542264	−	0.646245i
$326$	−7.77102	−	10.2146i	−0.430397	−	0.565733i
$327$	20.7982	+	3.66729i	1.15015	+	0.202802i
$328$	1.67971	−	0.0524699i	0.0927464	−	0.00289717i
$329$	−6.66440	+	2.42564i	−0.367420	+	0.133730i
$330$	18.2808	−	9.42052i	1.00633	−	0.518583i
$331$	11.4669	+	19.8613i	0.630278	+	1.09167i	0.987495	+	0.157652i	$0.0503925\pi$
$331$	11.4669	+	19.8613i	0.630278	+	1.09167i	−0.357216	+	0.934022i	$0.616274\pi$
$332$	10.4544	+	2.89413i	0.573760	+	0.158836i
$333$	−8.54777	+	10.1868i	−0.468415	+	0.558235i
$334$	−16.3663	−	0.782388i	−0.895523	−	0.0428104i
$335$	3.06263	−	5.30463i	0.167329	−	0.289823i
$336$	15.3894	+	5.89133i	0.839559	+	0.321398i
$337$	−8.84318	+	1.55929i	−0.481719	+	0.0849400i	−0.409234	−	0.912430i	$-0.634204\pi$
$337$	−8.84318	+	1.55929i	−0.481719	+	0.0849400i	−0.0724847	+	0.997370i	$0.523093\pi$
$338$	7.37554	+	6.81476i	0.401177	+	0.370674i
$339$	−3.54017	+	9.72655i	−0.192276	+	0.528273i
$340$	0.409516	+	0.195100i	0.0222091	+	0.0105808i
$341$			10.3295i			0.559374i
$342$	−0.474009	−	7.80430i	−0.0256315	−	0.422008i
$343$		−	13.1464i		−	0.709838i
$344$	−16.4967	−	26.6177i	−0.889445	−	1.43513i
$345$	2.92839	−	8.04569i	0.157659	−	0.433166i
$346$	2.92579	−	3.16655i	0.157291	−	0.170235i
$347$	−27.4438	+	4.83908i	−1.47326	+	0.259775i	−0.851881	−	0.523735i	$-0.824538\pi$
$347$	−27.4438	+	4.83908i	−1.47326	+	0.259775i	−0.621378	+	0.783511i	$0.713427\pi$
$348$	−0.969575	+	0.953668i	−0.0519747	+	0.0511220i
$349$	−3.63403	+	6.29433i	−0.194525	+	0.336928i	−0.946745	−	0.321985i	$-0.895650\pi$
$349$	−3.63403	+	6.29433i	−0.194525	+	0.336928i	0.752220	+	0.658913i	$0.228983\pi$
$350$	−0.717132	+	15.0012i	−0.0383323	+	0.801850i
$351$	16.1869	−	19.2908i	0.863991	−	1.02966i
$352$	19.7614	+	8.66832i	1.05328	+	0.462023i
$353$	−5.67899	−	9.83630i	−0.302262	−	0.523533i	0.674386	−	0.738379i	$-0.264408\pi$
$353$	−5.67899	−	9.83630i	−0.302262	−	0.523533i	−0.976648	+	0.214846i	$0.931075\pi$
$354$	−7.71888	−	14.9787i	−0.410254	−	0.796111i
$355$	7.88791	−	2.87096i	0.418647	−	0.152375i
$356$	−3.37276	−	4.90260i	−0.178756	−	0.259837i
$357$	0.317636	+	0.0560077i	0.0168111	+	0.00296424i
$358$	4.87985	−	3.71248i	0.257908	−	0.196211i
$359$	−10.3569	−	12.3428i	−0.546614	−	0.651429i	0.420043	−	0.907504i	$-0.362015\pi$
$359$	−10.3569	−	12.3428i	−0.546614	−	0.651429i	−0.966657	+	0.256075i	$0.917571\pi$
$360$	−10.2861	−	1.48422i	−0.542123	−	0.0782255i
$361$	5.73704	−	18.1132i	0.301949	−	0.953324i
$362$	−2.39118	−	1.53729i	−0.125678	−	0.0807981i
$363$	3.58019	−	3.00413i	0.187911	−	0.157676i
$364$	−2.21522	−	27.9838i	−0.116109	−	1.46675i
$365$	7.35228	−	41.6969i	0.384836	−	2.18251i
$366$	5.78633	+	2.42486i	0.302456	+	0.126749i
$367$	−9.70967	−	26.6771i	−0.506841	−	1.39253i	−0.884479	−	0.466580i	$-0.845486\pi$
$367$	−9.70967	−	26.6771i	−0.506841	−	1.39253i	0.377638	−	0.925953i	$-0.376736\pi$
$368$	8.49189	−	2.93266i	0.442671	−	0.152876i
$369$	−0.652639	+	0.376801i	−0.0339750	+	0.0196155i
$370$	12.7468	+	41.0183i	0.662674	+	2.13244i
$371$	2.26407	+	1.89978i	0.117545	+	0.0986317i
$372$	−4.13580	+	5.80378i	−0.214431	+	0.300912i
$373$	0.671383	+	0.387623i	0.0347629	+	0.0200704i	0.517281	−	0.855816i	$-0.326944\pi$
$373$	0.671383	+	0.387623i	0.0347629	+	0.0200704i	−0.482518	+	0.875886i	$0.660278\pi$
$374$	0.411974	+	0.0931215i	0.0213027	+	0.00481520i
$375$	−1.06432	−	6.03607i	−0.0549614	−	0.311701i
$376$	−6.08662	−	2.00245i	−0.313893	−	0.103268i
$377$	2.17704	+	0.792377i	0.112123	+	0.0408095i
$378$	−24.6680	+	3.14389i	−1.26879	+	0.161704i
$379$	8.20752			0.421592			0.210796	−	0.977530i	$-0.432394\pi$
$379$	8.20752			0.421592			0.210796	+	0.977530i	$0.432394\pi$
$380$	−22.0323	−	12.3444i	−1.13023	−	0.633252i
$381$	19.2735			0.987413
$382$	9.95568	−	1.26883i	0.509377	−	0.0649190i
$383$	28.3957	+	10.3352i	1.45095	+	0.528103i	0.942857	−	0.333198i	$-0.108128\pi$
$383$	28.3957	+	10.3352i	1.45095	+	0.528103i	0.508095	+	0.861301i	$0.330350\pi$
$384$	7.63251	+	12.7826i	0.389495	+	0.652310i
$385$	6.00747	+	34.0700i	0.306169	+	1.73637i
$386$	5.01014	+	1.13248i	0.255009	+	0.0576416i
$387$	12.1614	+	7.02139i	0.618199	+	0.356917i
$388$	15.4160	+	10.9855i	0.782630	+	0.557706i
$389$	7.57457	+	6.35582i	0.384046	+	0.322253i	0.814288	−	0.580461i	$-0.197127\pi$
$389$	7.57457	+	6.35582i	0.384046	+	0.322253i	−0.430242	+	0.902713i	$0.641572\pi$
$390$	−7.17285	−	23.0818i	−0.363211	−	1.16879i
$391$	0.152287	−	0.0879228i	0.00770147	−	0.00444645i
$392$	−4.89993	+	6.22428i	−0.247484	+	0.314374i
$393$	−8.41035	−	23.1072i	−0.424246	−	1.16561i
$394$	−22.0781	−	9.25219i	−1.11228	−	0.466118i
$395$	3.49981	−	19.8484i	0.176095	−	0.998682i
$396$	−9.64651	+	0.763624i	−0.484756	+	0.0383736i
$397$	−5.36709	+	4.50352i	−0.269367	+	0.226025i	−0.767458	−	0.641099i	$-0.778479\pi$
$397$	−5.36709	+	4.50352i	−0.269367	+	0.226025i	0.498092	+	0.867124i	$0.334034\pi$
$398$	7.85494	+	5.04993i	0.393732	+	0.253130i
$399$	−17.4396	−	4.27950i	−0.873073	−	0.214243i
$400$	−8.89255	+	10.2486i	−0.444627	+	0.512429i
$401$	12.7238	+	15.1637i	0.635397	+	0.757237i	0.983636	−	0.180169i	$-0.0576644\pi$
$401$	12.7238	+	15.1637i	0.635397	+	0.757237i	−0.348238	+	0.937406i	$0.613220\pi$
$402$	3.13163	−	2.38247i	0.156191	−	0.118827i
$403$	11.9559	+	2.10814i	0.595565	+	0.105014i
$404$	26.4590	−	18.2025i	1.31638	−	0.905609i
$405$	−9.76242	+	3.55323i	−0.485098	+	0.176561i
$406$	−1.04799	−	2.03366i	−0.0520108	−	0.100929i
$407$	19.9972	+	34.6362i	0.991224	+	1.71685i
$408$	0.194189	+	0.217271i	0.00961378	+	0.0107565i
$409$	11.1288	−	13.2628i	0.550286	−	0.655805i	−0.417175	−	0.908826i	$-0.636980\pi$
$409$	11.1288	−	13.2628i	0.550286	−	0.655805i	0.967461	+	0.253021i	$0.0814243\pi$
$410$	−0.116233	+	2.43141i	−0.00574034	+	0.120079i
$411$	−10.5406	+	18.2569i	−0.519931	+	0.900546i
$412$	15.9859	+	16.2525i	0.787569	+	0.800705i
$413$	27.9159	−	4.92233i	1.37365	−	0.242212i
$414$	−2.73403	+	2.95901i	−0.134370	+	0.145427i
$415$	−5.37394	+	14.7648i	−0.263796	+	0.724774i
$416$	14.0662	−	21.1036i	0.689653	−	1.03469i
$417$			15.4405i			0.756126i
$418$	−22.5439	−	6.68821i	−1.10266	−	0.327131i
$419$			7.36000i			0.359560i	0.983707	+	0.179780i	$0.0575385\pi$
$419$			7.36000i			0.359560i	−0.983707	+	0.179780i	$0.942461\pi$
$420$	−10.2658	+	21.5480i	−0.500921	+	1.05144i
$421$	−1.21485	+	3.33777i	−0.0592081	+	0.162673i	−0.965770	−	0.259400i	$-0.916475\pi$
$421$	−1.21485	+	3.33777i	−0.0592081	+	0.162673i	0.906562	+	0.422073i	$0.138697\pi$
$422$	−1.55576	−	1.43747i	−0.0757331	−	0.0699749i
$423$	2.82970	−	0.498952i	0.137585	−	0.0242599i
$424$	0.545564	+	2.61393i	0.0264949	+	0.126944i
$425$	−0.132791	+	0.230001i	−0.00644133	+	0.0111567i
$426$	5.38625	+	0.257489i	0.260965	+	0.0124754i
$427$	−6.78403	+	8.08490i	−0.328302	+	0.391256i
$428$	4.78036	−	17.2680i	0.231067	−	0.834680i
$429$	−11.2528	−	19.4904i	−0.543289	−	0.941005i
$430$	40.3202	−	20.7779i	1.94441	−	1.00200i
$431$	−23.3773	+	8.50864i	−1.12604	+	0.409847i	−0.836855	−	0.547425i	$-0.815608\pi$
$431$	−23.3773	+	8.50864i	−1.12604	+	0.409847i	−0.289190	+	0.957272i	$0.593386\pi$
$432$	−19.2687	−	11.5539i	−0.927068	−	0.555888i
$433$	−2.58798	−	0.456330i	−0.124370	−	0.0219298i	0.111117	−	0.993807i	$-0.464557\pi$
$433$	−2.58798	−	0.456330i	−0.124370	−	0.0219298i	−0.235487	+	0.971878i	$0.575668\pi$
$434$	−7.25879	−	9.54128i	−0.348433	−	0.457996i
$435$	−1.26622	−	1.50902i	−0.0607106	−	0.0723520i
$436$	−29.2017	+	13.3241i	−1.39851	+	0.638108i
$437$	−8.78331	+	4.32433i	−0.420163	+	0.206861i
$438$	14.7089	−	22.8791i	0.702820	−	1.09320i
$439$	−6.48906	+	5.44497i	−0.309706	+	0.259874i	−0.784370	−	0.620293i	$-0.787014\pi$
$439$	−6.48906	+	5.44497i	−0.309706	+	0.259874i	0.474665	+	0.880167i	$0.342569\pi$
$440$	−14.7754	+	27.5435i	−0.704389	+	1.31309i
$441$	0.616846	−	3.49831i	0.0293736	−	0.166586i
$442$	0.191863	−	0.457834i	0.00912599	−	0.0217769i
$443$	−5.66756	−	15.5715i	−0.269274	−	0.739824i	−0.998458	−	0.0555069i	$-0.982323\pi$
$443$	−5.66756	−	15.5715i	−0.269274	−	0.739824i	0.729184	−	0.684317i	$-0.239900\pi$
$444$	−2.63217	+	27.4674i	−0.124917	+	1.30355i
$445$	7.46461	−	4.30970i	0.353856	−	0.204299i
$446$	−10.6127	+	3.29798i	−0.502526	+	0.156164i
$447$	15.5354	+	13.0357i	0.734799	+	0.616569i
$448$	−24.3448	+	5.87992i	−1.15019	+	0.277800i
$449$	−20.3983	−	11.7770i	−0.962656	−	0.555790i	−0.0656669	−	0.997842i	$-0.520917\pi$
$449$	−20.3983	−	11.7770i	−0.962656	−	0.555790i	−0.896990	+	0.442052i	$0.854251\pi$
$450$	1.34152	−	5.93493i	0.0632396	−	0.279775i
$451$	0.393574	+	2.23207i	0.0185327	+	0.105104i
$452$	−3.94583	−	15.2287i	−0.185596	−	0.716300i
$453$	−9.98337	−	3.63365i	−0.469060	−	0.170724i
$454$	−0.957970	−	7.51657i	−0.0449598	−	0.352770i
$455$	40.6604			1.90619
$456$	−9.98874	−	12.7842i	−0.467766	−	0.598673i
$457$	−35.6608			−1.66814			−0.834070	−	0.551659i	$-0.813995\pi$
$457$	−35.6608			−1.66814			−0.834070	+	0.551659i	$0.813995\pi$
$458$	−0.561751	−	4.40769i	−0.0262489	−	0.205958i
$459$	−0.413234	−	0.150405i	−0.0192881	−	0.00702030i
$460$	3.26395	+	12.5971i	0.152182	+	0.587341i
$461$	5.18964	+	29.4319i	0.241706	+	1.37078i	0.828021	+	0.560697i	$0.189467\pi$
$461$	5.18964	+	29.4319i	0.241706	+	1.37078i	−0.586315	+	0.810083i	$0.699422\pi$
$462$	−4.89990	+	21.6774i	−0.227964	+	1.00852i
$463$	−8.24455	−	4.75999i	−0.383157	−	0.221216i	0.296034	−	0.955177i	$-0.404336\pi$
$463$	−8.24455	−	4.75999i	−0.383157	−	0.221216i	−0.679191	+	0.733962i	$0.737669\pi$
$464$	0.392546	−	2.02936i	0.0182235	−	0.0942105i
$465$	−7.90761	−	6.63527i	−0.366706	−	0.307703i
$466$	−19.2894	+	5.99434i	−0.893564	+	0.277682i
$467$	−13.8707	+	8.00827i	−0.641861	+	0.370579i	−0.785331	−	0.619076i	$-0.787507\pi$
$467$	−13.8707	+	8.00827i	−0.641861	+	0.370579i	0.143470	+	0.989655i	$0.454174\pi$
$468$	−1.08490	+	11.3212i	−0.0501493	+	0.523322i
$469$	2.26395	+	6.22016i	0.104540	+	0.287220i
$470$	3.58715	−	8.55986i	0.165463	−	0.394837i
$471$	−0.720782	+	4.08776i	−0.0332119	+	0.188354i
$472$	22.5683	+	12.1065i	1.03879	+	0.557246i
$473$	32.3534	−	27.1478i	1.48761	−	1.24825i
$474$	7.00170	−	10.8908i	0.321599	−	0.500232i
$475$	8.22278	−	12.2889i	0.377287	−	0.563854i
$476$	−0.445976	+	0.203489i	−0.0204413	+	0.00932688i
$477$	−0.769692	−	0.917283i	−0.0352418	−	0.0419995i
$478$	−10.6306	−	13.9733i	−0.486231	−	0.639124i
$479$	−11.6151	−	2.04805i	−0.530706	−	0.0935778i	−0.0981272	−	0.995174i	$-0.531285\pi$
$479$	−11.6151	−	2.04805i	−0.530706	−	0.0935778i	−0.432579	+	0.901596i	$0.642396\pi$
$480$	−19.3298	+	9.55983i	−0.882282	+	0.436345i
$481$	44.1708	−	16.0769i	2.01401	−	0.733041i
$482$	−11.3235	+	5.83524i	−0.515770	+	0.265788i
$483$	4.62635	+	8.01307i	0.210506	+	0.364608i
$484$	−1.89512	+	6.84571i	−0.0861418	+	0.311168i
$485$	−17.6246	+	21.0042i	−0.800294	+	0.953753i
$486$	17.1367	+	0.819216i	0.777335	+	0.0371604i
$487$	−10.2230	+	17.7067i	−0.463247	+	0.802367i	−0.999121	−	0.0419308i	$-0.986649\pi$
$487$	−10.2230	+	17.7067i	−0.463247	+	0.802367i	0.535873	+	0.844298i	$0.319982\pi$
$488$	−9.33422	+	1.94818i	−0.422540	+	0.0881901i
$489$	11.7611	−	2.07380i	0.531854	−	0.0937803i
$490$	−8.42745	−	7.78669i	−0.380713	−	0.351767i
$491$	12.7994	−	35.1661i	0.577630	−	1.58703i	−0.214533	−	0.976717i	$-0.568823\pi$
$491$	12.7994	−	35.1661i	0.577630	−	1.58703i	0.792163	−	0.610309i	$-0.208955\pi$
$492$	−0.672556	+	1.41170i	−0.0303212	+	0.0636444i
$493$		−	0.0404571i		−	0.00182210i
$494$	−12.3422	+	24.7284i	−0.555304	+	1.11258i
$495$		−	14.0163i		−	0.629987i
$496$	0.179155	−	10.8299i	0.00804432	−	0.486278i
$497$	−3.10255	+	8.52418i	−0.139168	+	0.382362i
$498$	−6.84988	+	7.41355i	−0.306950	+	0.332209i
$499$	36.4883	−	6.43387i	1.63344	−	0.288019i	0.719689	−	0.694296i	$-0.244284\pi$
$499$	36.4883	−	6.43387i	1.63344	−	0.288019i	0.913750	+	0.406277i	$0.133173\pi$
$500$	6.53231	+	6.64127i	0.292134	+	0.297007i
$501$	7.62307	−	13.2035i	0.340574	−	0.589891i
$502$	0.676484	−	14.1509i	0.0301930	−	0.631587i
$503$	1.85009	−	2.20485i	0.0824914	−	0.0983094i	−0.723220	−	0.690618i	$-0.757339\pi$
$503$	1.85009	−	2.20485i	0.0824914	−	0.0983094i	0.805711	+	0.592308i	$0.201783\pi$
$504$	8.37379	−	7.48419i	0.372998	−	0.333372i
$505$	23.2591	+	40.2860i	1.03502	+	1.79270i
$506$	5.55034	+	10.7706i	0.246743	+	0.478812i
$507$	−8.78043	+	3.19581i	−0.389952	+	0.141931i
$508$	−24.1335	+	16.6027i	−1.07075	+	0.736625i
$509$	−10.1796	−	1.79493i	−0.451201	−	0.0795589i	−0.0565701	−	0.998399i	$-0.518016\pi$
$509$	−10.1796	−	1.79493i	−0.451201	−	0.0795589i	−0.394631	+	0.918840i	$0.629128\pi$
$510$	−0.335924	+	0.255563i	−0.0148750	+	0.0113165i
$511$	29.4110	+	35.0507i	1.30107	+	1.55055i
$512$	−20.5683	−	9.43100i	−0.909000	−	0.416795i
$513$	22.4032	+	9.87511i	0.989127	+	0.435997i
$514$	−1.39775	−	0.898614i	−0.0616522	−	0.0396362i
$515$	−25.2950	+	21.2251i	−1.11463	+	0.935288i
$516$	29.0478	−	2.29944i	1.27876	−	0.101227i
$517$	1.50063	−	8.51047i	0.0659974	−	0.374290i
$518$	−42.8109	−	17.9406i	−1.88100	−	0.788265i
$519$	1.37206	+	3.76971i	0.0602268	+	0.165472i
$520$	28.8647	+	22.7231i	1.26580	+	0.996473i
$521$	−32.7090	+	18.8846i	−1.43301	+	0.827348i	−0.997349	−	0.0727637i	$-0.976818\pi$
$521$	−32.7090	+	18.8846i	−1.43301	+	0.827348i	−0.435659	+	0.900112i	$0.643485\pi$
$522$	0.275065	+	0.885143i	0.0120393	+	0.0387416i
$523$	−22.4623	−	18.8481i	−0.982206	−	0.824169i	0.00221480	−	0.999998i	$-0.499295\pi$
$523$	−22.4623	−	18.8481i	−0.982206	−	0.824169i	−0.984421	+	0.175829i	$0.943739\pi$
$524$	30.4362	+	21.6890i	1.32961	+	0.947488i
$525$	−12.1023	−	6.98726i	−0.528187	−	0.304949i
$526$	40.7200	+	9.20423i	1.77548	+	0.401324i
$527$	−0.0368142	−	0.208784i	−0.00160365	−	0.00909475i
$528$	−15.5929	+	12.6504i	−0.678592	+	0.550539i
$529$	−16.8726	−	6.14113i	−0.733592	−	0.267005i
$530$	−3.83673	+	0.488983i	−0.166657	+	0.0212401i
$531$	−11.4845			−0.498387
$532$	25.5236	−	9.66430i	1.10659	−	0.419001i
$533$	2.66383			0.115383
$534$	5.49268	−	0.700030i	0.237692	−	0.0302933i
$535$	24.3876	+	8.87638i	1.05437	+	0.383759i
$536$	−1.86897	+	5.68089i	−0.0807271	+	0.245377i
$537$	0.990723	+	5.61867i	0.0427529	+	0.242463i
$538$	−12.8381	−	2.90189i	−0.553490	−	0.125109i
$539$	−9.25233	−	5.34183i	−0.398526	−	0.230089i
$540$	18.8857	−	26.5024i	0.812712	−	1.14048i
$541$	1.95274	+	1.63855i	0.0839549	+	0.0704466i	0.683799	−	0.729670i	$-0.260326\pi$
$541$	1.95274	+	1.63855i	0.0839549	+	0.0704466i	−0.599844	+	0.800117i	$0.704771\pi$
$542$	−2.24539	−	7.22551i	−0.0964476	−	0.310362i
$543$	2.29075	−	1.32256i	0.0983054	−	0.0567567i
$544$	−0.430317	−	0.104778i	−0.0184497	−	0.00449232i
$545$	−15.9014	−	43.6887i	−0.681141	−	1.87142i
$546$	24.0905	+	10.0955i	1.03098	+	0.432048i
$547$	0.169432	−	0.960896i	0.00724439	−	0.0410850i	−0.980971	−	0.194153i	$-0.937804\pi$
$547$	0.169432	−	0.960896i	0.00724439	−	0.0410850i	0.988216	+	0.153068i	$0.0489153\pi$
$548$	−2.52842	−	31.9404i	−0.108009	−	1.36443i
$549$	3.27558	−	2.74854i	0.139798	−	0.117305i
$550$	−15.3932	−	9.89629i	−0.656369	−	0.421979i
$551$	−0.148782	+	2.24751i	−0.00633832	+	0.0957473i
$552$	−1.19388	+	8.27390i	−0.0508149	+	0.352161i
$553$	14.0001	+	16.6847i	0.595347	+	0.709507i
$554$	16.8172	−	12.7941i	0.714492	−	0.543570i
$555$	−39.3606	−	6.94034i	−1.67077	−	0.294601i
$556$	−13.3008	−	19.3340i	−0.564082	−	0.819942i
$557$	8.89834	−	3.23873i	0.377035	−	0.137229i	−0.146549	−	0.989203i	$-0.546817\pi$
$557$	8.89834	−	3.23873i	0.377035	−	0.137229i	0.523584	+	0.851974i	$0.324595\pi$
$558$	2.22495	+	4.31758i	0.0941894	+	0.182778i
$559$	−24.8191	−	42.9880i	−1.04974	−	1.81820i
$560$	−5.70758	−	35.8247i	−0.241189	−	1.51387i
$561$	−0.252623	+	0.301064i	−0.0106657	+	0.0127109i
$562$	1.32713	−	27.7613i	0.0559814	−	1.17104i
$563$	15.1232	−	26.1942i	0.637367	−	1.10395i	−0.348641	−	0.937256i	$-0.613357\pi$
$563$	15.1232	−	26.1942i	0.637367	−	1.10395i	0.986008	−	0.166696i	$-0.0533098\pi$
$564$	4.25063	−	4.18090i	0.178984	−	0.176047i
$565$	22.4405	−	3.95687i	0.944079	−	0.166467i
$566$	10.0740	−	10.9029i	0.423441	−	0.458285i
$567$	3.83985	−	10.5499i	0.161258	−	0.443054i
$568$	−6.96624	+	4.31743i	−0.292297	+	0.181155i
$569$			12.8421i			0.538369i	0.963089	+	0.269184i	$0.0867541\pi$
$569$			12.8421i			0.538369i	−0.963089	+	0.269184i	$0.913246\pi$
$570$	19.6014	−	12.9619i	0.821012	−	0.542915i
$571$			11.1572i			0.466915i	0.972367	+	0.233458i	$0.0750040\pi$
$571$			11.1572i			0.466915i	−0.972367	+	0.233458i	$0.924996\pi$
$572$	30.8797	+	14.7116i	1.29115	+	0.615122i
$573$	−3.19400	+	8.77545i	−0.133431	+	0.366600i
$574$	−1.93207	−	1.78517i	−0.0806430	−	0.0745115i
$575$	−7.50312	+	1.32300i	−0.312902	+	0.0551730i
$576$	10.1271	−	0.633308i	0.421962	−	0.0263878i
$577$	5.34339	−	9.25502i	0.222448	−	0.385291i	−0.733103	−	0.680118i	$-0.761929\pi$
$577$	5.34339	−	9.25502i	0.222448	−	0.385291i	0.955551	+	0.294827i	$0.0952619\pi$
$578$	24.0055	+	1.14758i	0.998499	+	0.0477331i
$579$	−3.07222	+	3.66132i	−0.127677	+	0.152159i
$580$	2.88541	+	0.798778i	0.119810	+	0.0331675i
$581$	−8.48989	−	14.7049i	−0.352220	−	0.610063i
$582$	−15.6574	+	8.06859i	−0.649018	+	0.334454i
$583$	−3.38414	+	1.23173i	−0.140157	+	0.0510129i
$584$	1.29070	+	41.3188i	0.0534094	+	1.70978i
$585$	−16.2232	−	2.86059i	−0.670746	−	0.118271i
$586$	13.9177	+	18.2941i	0.574935	+	0.755720i
$587$	−9.10535	−	10.8513i	−0.375818	−	0.447882i	0.544672	−	0.838649i	$-0.316654\pi$
$587$	−9.10535	−	10.8513i	−0.375818	−	0.447882i	−0.920490	+	0.390767i	$0.872210\pi$
$588$	−3.05975	−	6.70590i	−0.126182	−	0.276546i
$589$	1.27733	+	11.7339i	0.0526315	+	0.483488i
$590$	−20.0607	+	31.2036i	−0.825888	+	1.28463i
$591$	17.0633	−	14.3178i	0.701889	−	0.588955i
$592$	−20.3652	−	36.6609i	−0.837005	−	1.50675i
$593$	−1.39125	+	7.89016i	−0.0571317	+	0.324010i	−0.999957	−	0.00927734i	$-0.997047\pi$
$593$	−1.39125	+	7.89016i	−0.0571317	+	0.324010i	0.942825	+	0.333288i	$0.108158\pi$
$594$	11.7114	−	27.9465i	0.480526	−	1.14666i
$595$	−0.242850	−	0.667224i	−0.00995587	−	0.0273535i
$596$	−30.6820	−	2.94022i	−1.25679	−	0.120436i
$597$	−7.52502	+	4.34457i	−0.307979	+	0.177811i
$598$	13.5992	−	4.22606i	0.556113	−	0.172817i
$599$	34.0092	+	28.5371i	1.38958	+	1.16599i	0.965511	+	0.260363i	$0.0838424\pi$
$599$	34.0092	+	28.5371i	1.38958	+	1.16599i	0.424067	+	0.905631i	$0.360602\pi$
$600$	−4.68655	−	11.7236i	−0.191328	−	0.478615i
$601$	−28.8637	−	16.6645i	−1.17737	−	0.679758i	−0.221969	−	0.975054i	$-0.571248\pi$
$601$	−28.8637	−	16.6645i	−1.17737	−	0.679758i	−0.955406	+	0.295296i	$0.904582\pi$
$602$	−10.8072	+	47.8117i	−0.440469	+	1.94866i
$603$	−0.465692	−	2.64107i	−0.0189645	−	0.107553i
$604$	15.6308	−	4.05002i	0.636010	−	0.164793i
$605$	−9.66821	−	3.51894i	−0.393069	−	0.143065i
$606$	3.77801	+	29.6436i	0.153471	+	1.20419i
$607$	13.9779			0.567345			0.283672	−	0.958921i	$-0.408447\pi$
$607$	13.9779			0.567345			0.283672	+	0.958921i	$0.408447\pi$
$608$	23.5200	+	7.40322i	0.953864	+	0.300240i
$609$	2.12879			0.0862628
$610$	−1.74614	−	13.7008i	−0.0706990	−	0.554729i
$611$	−9.54417	−	3.47379i	−0.386116	−	0.140535i
$612$	0.192257	−	0.0498146i	0.00777153	−	0.00201364i
$613$	−4.97045	−	28.1888i	−0.200755	−	1.13854i	−0.903982	−	0.427571i	$-0.859369\pi$
$613$	−4.97045	−	28.1888i	−0.200755	−	1.13854i	0.703227	−	0.710965i	$-0.251742\pi$
$614$	−7.78436	+	34.4384i	−0.314151	+	1.38982i
$615$	−1.96154	−	1.13250i	−0.0790971	−	0.0456667i
$616$	−12.5380	−	31.3644i	−0.505170	−	1.26371i
$617$	−22.3135	−	18.7233i	−0.898310	−	0.753771i	0.0715497	−	0.997437i	$-0.477206\pi$
$617$	−22.3135	−	18.7233i	−0.898310	−	0.753771i	−0.969859	+	0.243666i	$0.921650\pi$
$618$	−20.2568	+	6.29495i	−0.814846	+	0.253220i
$619$	−21.0830	+	12.1723i	−0.847396	+	0.489244i	−0.859771	−	0.510679i	$-0.829394\pi$
$619$	−21.0830	+	12.1723i	−0.847396	+	0.489244i	0.0123753	+	0.999923i	$0.496061\pi$
$620$	15.6173	+	1.49659i	0.627207	+	0.0601045i
$621$	−4.31472	−	11.8546i	−0.173144	−	0.475709i
$622$	−8.38306	+	20.0041i	−0.336130	+	0.802092i
$623$	−1.61748	+	9.17316i	−0.0648028	+	0.367515i
$624$	11.4599	+	20.6298i	0.458762	+	0.825851i
$625$	−23.3291	+	19.5755i	−0.933165	+	0.783018i
$626$	−8.04064	+	12.5068i	−0.321369	+	0.499874i
$627$	15.1411	−	15.7960i	0.604677	−	0.630830i
$628$	−2.61876	−	5.73941i	−0.104500	−	0.229027i
$629$	−0.527633	−	0.628808i	−0.0210381	−	0.0250722i
$630$	9.84961	+	12.9468i	0.392418	+	0.515812i
$631$	−3.45710	−	0.609581i	−0.137625	−	0.0242670i	0.104411	−	0.994534i	$-0.466704\pi$
$631$	−3.45710	−	0.609581i	−0.137625	−	0.0242670i	−0.242036	+	0.970267i	$0.577815\pi$
$632$	0.614394	+	19.6684i	0.0244393	+	0.782369i
$633$	1.85210	−	0.674108i	0.0736142	−	0.0267934i
$634$	22.6857	−	11.6905i	0.900965	−	0.464287i
$635$	−21.2148	−	36.7452i	−0.841885	−	1.45819i
$636$	−2.39460	−	0.662904i	−0.0949519	−	0.0262859i
$637$	−8.07120	+	9.61888i	−0.319793	+	0.381114i
$638$	2.78451	+	0.133113i	0.110240	+	0.00527001i
$639$	1.83760	−	3.18281i	0.0726942	−	0.125910i
$640$	15.9689	−	28.6216i	0.631226	−	1.13137i
$641$	−3.21901	+	0.567598i	−0.127143	+	0.0224188i	−0.236858	−	0.971544i	$-0.576117\pi$
$641$	−3.21901	+	0.567598i	−0.127143	+	0.0224188i	0.109714	+	0.993963i	$0.465006\pi$
$642$	12.2453	+	11.3142i	0.483283	+	0.446538i
$643$	−12.1157	+	33.2877i	−0.477797	+	1.31274i	0.433562	+	0.901124i	$0.357257\pi$
$643$	−12.1157	+	33.2877i	−0.477797	+	1.31274i	−0.911359	+	0.411613i	$0.864966\pi$
$644$	−12.6956	−	6.04837i	−0.500275	−	0.238339i
$645$			42.2063i			1.66187i
$646$	0.479502	+	0.0548384i	0.0188657	+	0.00215759i
$647$		−	15.0857i		−	0.593078i	−0.955021	−	0.296539i	$-0.904167\pi$
$647$		−	15.0857i		−	0.593078i	0.955021	−	0.296539i	$-0.0958325\pi$
$648$	8.62172	−	5.34344i	0.338693	−	0.209910i
$649$	−11.8135	+	32.4573i	−0.463721	+	1.27406i
$650$	−14.5960	+	15.7971i	−0.572504	+	0.619615i
$651$	10.9858	−	1.93710i	0.430569	−	0.0759210i
$652$	−12.9403	+	12.7280i	−0.506781	+	0.498467i
$653$	0.273124	−	0.473065i	0.0106882	−	0.0185124i	−0.860632	−	0.509228i	$-0.829931\pi$
$653$	0.273124	−	0.473065i	0.0106882	−	0.0185124i	0.871320	+	0.490715i	$0.163264\pi$
$654$	1.42616	−	29.8328i	0.0557671	−	1.16656i
$655$	−34.7967	+	41.4691i	−1.35962	+	1.62033i
$656$	−0.373927	−	2.34702i	−0.0145994	−	0.0916359i
$657$	−9.26885	−	16.0541i	−0.361612	−	0.626331i
$658$	4.59440	+	8.91558i	0.179108	+	0.347565i
$659$	−37.6501	+	13.7035i	−1.46664	+	0.533813i	−0.947186	−	0.320686i	$-0.896087\pi$
$659$	−37.6501	+	13.7035i	−1.46664	+	0.533813i	−0.519453	+	0.854499i	$0.673864\pi$
$660$	−16.4842	−	23.9612i	−0.641647	−	0.932690i
$661$	45.3693	+	7.99983i	1.76466	+	0.311157i	0.959460	−	0.281844i	$-0.0909461\pi$
$661$	45.3693	+	7.99983i	1.76466	+	0.311157i	0.805201	+	0.593002i	$0.202057\pi$
$662$	25.8125	−	19.6376i	1.00323	−	0.763236i
$663$	0.296908	+	0.353842i	0.0115310	+	0.0137421i
$664$	2.19091	−	15.1836i	0.0850237	−	0.589237i
$665$	11.0373	+	37.9594i	0.428008	+	1.47200i
$666$	15.8190	+	10.1701i	0.612976	+	0.394082i
$667$	0.889078	−	0.746025i	0.0344252	−	0.0288862i
$668$	1.82858	+	23.0996i	0.0707498	+	0.893750i
$669$	1.79568	−	10.1838i	0.0694249	−	0.393728i
$670$	−7.98926	−	3.34803i	−0.308652	−	0.129346i
$671$	−4.39844	−	12.0846i	−0.169800	−	0.466522i
$672$	5.51324	−	22.6426i	0.212678	−	0.873456i
$673$	16.3438	−	9.43611i	0.630008	−	0.363735i	−0.150747	−	0.988572i	$-0.548168\pi$
$673$	16.3438	−	9.43611i	0.630008	−	0.363735i	0.780755	+	0.624837i	$0.214835\pi$
$674$	3.76857	+	12.1270i	0.145160	+	0.467115i
$675$	14.5956	+	12.2472i	0.561787	+	0.471395i
$676$	8.24151	−	11.5653i	0.316981	−	0.444820i
$677$	26.5149	+	15.3084i	1.01905	+	0.588349i	0.913829	−	0.406100i	$-0.133111\pi$
$677$	26.5149	+	15.3084i	1.01905	+	0.588349i	0.105222	+	0.994449i	$0.466445\pi$
$678$	14.2780	+	3.22736i	0.548343	+	0.123946i
$679$	−5.14534	−	29.1807i	−0.197460	−	1.11985i
$680$	0.200481	−	0.609378i	0.00768808	−	0.0233686i
$681$	6.62550	+	2.41148i	0.253890	+	0.0924082i
$682$	14.4909	−	1.84684i	0.554886	−	0.0707190i
$683$	47.0432			1.80006			0.900029	−	0.435829i	$-0.143545\pi$
$683$	47.0432			1.80006			0.900029	+	0.435829i	$0.143545\pi$
$684$	−10.8636	+	2.06032i	−0.415382	+	0.0787783i
$685$	46.4093			1.77321
$686$	−18.4426	+	2.35047i	−0.704142	+	0.0897414i
$687$	3.88517	+	1.41409i	0.148228	+	0.0539508i
$688$	−34.3916	+	27.9018i	−1.31117	+	1.06374i
$689$	0.734994	+	4.16836i	0.0280010	+	0.158802i
$690$	−11.8106	−	2.66964i	−0.449622	−	0.101631i
$691$	−0.680964	−	0.393155i	−0.0259051	−	0.0149563i	0.486992	−	0.873407i	$-0.338094\pi$
$691$	−0.680964	−	0.393155i	−0.0259051	−	0.0149563i	−0.512897	+	0.858450i	$0.671428\pi$
$692$	−4.96535	−	3.53834i	−0.188754	−	0.134507i
$693$	11.6032	+	9.73627i	0.440771	+	0.369850i
$694$	11.6953	+	37.6348i	0.443948	+	1.42860i
$695$	29.4375	−	16.9958i	1.11663	−	0.644686i
$696$	1.51122	+	1.18968i	0.0572827	+	0.0450945i
$697$	−0.0159101	−	0.0437126i	−0.000602638	−	0.00165573i
$698$	9.47983	+	3.97268i	0.358817	+	0.150368i
$699$	3.26378	−	18.5098i	0.123448	−	0.700106i
$700$	21.1729	−	1.67606i	0.800262	−	0.0633493i
$701$	−28.6734	+	24.0598i	−1.08298	+	0.908727i	−0.996165	−	0.0874973i	$-0.972113\pi$
$701$	−28.6734	+	24.0598i	−1.08298	+	0.908727i	−0.0868142	+	0.996225i	$0.527669\pi$
$702$	−29.9564	−	19.2590i	−1.13063	−	0.726883i
$703$	26.9991	+	36.8725i	1.01829	+	1.39067i
$704$	8.62732	−	29.2724i	0.325154	−	1.10324i
$705$	5.55113	+	6.61557i	0.209068	+	0.249157i
$706$	−12.7837	+	9.72552i	−0.481119	+	0.366025i
$707$	−49.5069	−	8.72939i	−1.86190	−	0.328303i
$708$	−19.6331	+	13.5066i	−0.737856	+	0.507610i
$709$	30.0394	−	10.9335i	1.12815	−	0.410615i	0.290533	−	0.956865i	$-0.406168\pi$
$709$	30.0394	−	10.9335i	1.12815	−	0.410615i	0.837622	+	0.546250i	$0.183945\pi$
$710$	−5.43787	−	10.5524i	−0.204080	−	0.396023i
$711$	−4.41213	−	7.64204i	−0.165468	−	0.286599i
$712$	−6.27467	+	5.60807i	−0.235153	+	0.210171i
$713$	3.90934	−	4.65897i	0.146406	−	0.174480i
$714$	0.0217806	−	0.455614i	0.000815117	−	0.0170509i
$715$	−24.7724	+	42.9071i	−0.926436	+	1.60463i
$716$	−6.08060	−	6.18202i	−0.227243	−	0.231033i
$717$	16.0889	−	2.83690i	0.600850	−	0.105946i
$718$	−15.4636	+	16.7361i	−0.577097	+	0.624585i
$719$	−0.247417	+	0.679772i	−0.00922709	+	0.0253512i	−0.944221	−	0.329313i	$-0.893183\pi$
$719$	−0.247417	+	0.679772i	−0.00922709	+	0.0253512i	0.934994	+	0.354665i	$0.115405\pi$
$720$	−0.243100	+	14.6953i	−0.00905980	+	0.547663i
$721$		−	35.6839i		−	1.32894i
$722$	−26.4361	−	4.80981i	−0.983849	−	0.179003i
$723$		−	11.8532i		−	0.440824i
$724$	−1.72909	+	3.62936i	−0.0642610	+	0.134884i
$725$	−0.599523	+	1.64718i	−0.0222657	+	0.0611746i
$726$	−4.85451	−	4.48541i	−0.180168	−	0.166469i
$727$	13.3127	−	2.34739i	0.493741	−	0.0870598i	0.0787667	−	0.996893i	$-0.474902\pi$
$727$	13.3127	−	2.34739i	0.493741	−	0.0870598i	0.414974	+	0.909833i	$0.363791\pi$
$728$	−38.8615	+	8.11095i	−1.44030	+	0.300612i
$729$	−13.3612	+	23.1423i	−0.494859	+	0.857121i
$730$	−59.8096	−	2.85919i	−2.21365	−	0.105823i
$731$	−0.557184	+	0.664026i	−0.0206082	+	0.0245599i
$732$	2.36720	−	8.55099i	0.0874943	−	0.316054i
$733$	−21.2697	−	36.8401i	−0.785613	−	1.36072i	−0.928632	−	0.371002i	$-0.879014\pi$
$733$	−21.2697	−	36.8401i	−0.785613	−	1.36072i	0.143019	−	0.989720i	$-0.454319\pi$
$734$	−35.6884	+	18.3910i	−1.31728	+	0.678825i
$735$	10.0327	−	3.65160i	0.370061	−	0.134691i
$736$	−5.63241	−	11.3887i	−0.207614	−	0.419791i
$737$	−7.94317	−	1.40060i	−0.292590	−	0.0515916i
$738$	0.645289	+	0.848196i	0.0237534	+	0.0312225i
$739$	0.408212	+	0.486488i	0.0150163	+	0.0178957i	0.773500	−	0.633796i	$-0.218504\pi$
$739$	0.408212	+	0.486488i	0.0150163	+	0.0178957i	−0.758484	+	0.651692i	$0.774060\pi$
$740$	55.2642	−	25.2158i	2.03155	−	0.926951i
$741$	−15.1929	−	20.7488i	−0.558124	−	0.762227i
$742$	2.26034	−	3.51585i	0.0829797	−	0.129071i
$743$	29.7921	−	24.9985i	1.09297	−	0.917107i	0.0960331	−	0.995378i	$-0.469385\pi$
$743$	29.7921	−	24.9985i	1.09297	−	0.917107i	0.996932	+	0.0782714i	$0.0249401\pi$
$744$	8.88137	+	4.76431i	0.325607	+	0.174668i
$745$	7.75259	−	43.9671i	0.284033	−	1.61083i
$746$	0.423745	−	1.01116i	0.0155144	−	0.0370213i
$747$	2.35286	+	6.46444i	0.0860868	+	0.236522i
$748$	0.0569792	−	0.594594i	0.00208337	−	0.0217405i
$749$	−24.2888	+	14.0231i	−0.887492	+	0.512394i
$750$	−8.27751	+	2.57230i	−0.302252	+	0.0939273i
$751$	22.5368	+	18.9106i	0.822380	+	0.690059i	0.953528	−	0.301304i	$-0.0974220\pi$
$751$	22.5368	+	18.9106i	0.822380	+	0.690059i	−0.131148	+	0.991363i	$0.541866\pi$
$752$	−1.72093	+	8.89673i	−0.0627558	+	0.324430i
$753$	11.4163	+	6.59121i	0.416034	+	0.240197i
$754$	0.722362	−	3.19576i	0.0263069	−	0.116383i
$755$	4.06135	+	23.0330i	0.147807	+	0.838258i
$756$	8.82090	+	34.0438i	0.320813	+	1.23816i
$757$	−17.9630	−	6.53799i	−0.652875	−	0.237627i	−0.00571806	−	0.999984i	$-0.501820\pi$
$757$	−17.9630	−	6.53799i	−0.652875	−	0.237627i	−0.647157	+	0.762356i	$0.724042\pi$
$758$	−1.46744	−	11.5140i	−0.0532998	−	0.418209i
$759$	−11.2745			−0.409237
$760$	−13.3783	+	33.1155i	−0.485281	+	1.20122i
$761$	−6.81878			−0.247181			−0.123590	−	0.992333i	$-0.539441\pi$
$761$	−6.81878			−0.247181			−0.123590	+	0.992333i	$0.539441\pi$
$762$	−3.44596	−	27.0382i	−0.124834	−	0.979490i
$763$	47.2129	+	17.1841i	1.70922	+	0.622105i
$764$	−3.56000	−	13.7396i	−0.128796	−	0.497082i
$765$	0.0499539	+	0.283303i	0.00180609	+	0.0102428i
$766$	9.42195	−	41.6832i	0.340429	−	1.50607i
$767$	35.1567	+	20.2977i	1.26943	+	0.732908i
$768$	16.5677	−	12.9928i	0.597834	−	0.468838i
$769$	−27.3710	−	22.9670i	−0.987022	−	0.828210i	−0.00188826	−	0.999998i	$-0.500601\pi$
$769$	−27.3710	−	22.9670i	−0.987022	−	0.828210i	−0.985134	+	0.171788i	$0.945045\pi$
$770$	46.7216	−	14.5191i	1.68373	−	0.523233i
$771$	1.33904	−	0.773098i	0.0482245	−	0.0278424i
$772$	0.692940	−	7.23103i	0.0249395	−	0.260250i
$773$	−3.45061	−	9.48048i	−0.124110	−	0.340989i	0.862041	−	0.506838i	$-0.169186\pi$
$773$	−3.45061	−	9.48048i	−0.124110	−	0.340989i	−0.986151	+	0.165849i	$0.946964\pi$
$774$	7.67570	−	18.3162i	0.275897	−	0.658362i
$775$	−1.59505	+	9.04598i	−0.0572959	+	0.324941i
$776$	12.6550	−	23.5908i	0.454287	−	0.846859i
$777$	33.0868	−	27.7631i	1.18698	−	0.995997i
$778$	7.56209	−	11.7625i	0.271114	−	0.421705i
$779$	0.723098	+	2.48687i	0.0259077	+	0.0891015i
$780$	−31.0982	+	14.1894i	−1.11349	+	0.508061i
$781$	−7.10495	−	8.46735i	−0.254235	−	0.302986i
$782$	−0.150572	−	0.197918i	−0.00538443	−	0.00707753i
$783$	−2.85836	−	0.504005i	−0.102149	−	0.0180117i
$784$	9.60790	+	5.76109i	0.343139	+	0.205753i
$785$	8.58673	−	3.12532i	0.306474	−	0.111547i
$786$	−30.9127	+	15.9300i	−1.10262	+	0.568204i
$787$	4.49406	+	7.78394i	0.160196	+	0.277468i	0.934939	−	0.354809i	$-0.115454\pi$
$787$	4.49406	+	7.78394i	0.160196	+	0.277468i	−0.774743	+	0.632276i	$0.782121\pi$
$788$	−9.03219	+	32.6268i	−0.321758	+	1.16228i
$789$	−24.9695	+	29.7575i	−0.888937	+	1.05939i
$790$	−28.4704	−	1.36102i	−1.01293	−	0.0484231i
$791$	−12.3124	+	21.3257i	−0.437778	+	0.758254i
$792$	2.79598	+	13.3962i	0.0993510	+	0.476015i
$793$	−14.8850	+	2.62463i	−0.528582	+	0.0932033i
$794$	7.27744	+	6.72411i	0.258267	+	0.238630i
$795$	1.23091	−	3.38190i	0.0436559	−	0.119943i
$796$	5.67998	−	11.9223i	0.201321	−	0.422575i
$797$		−	16.8886i		−	0.598223i	−0.954218	−	0.299112i	$-0.903310\pi$
$797$		−	16.8886i		−	0.598223i	0.954218	−	0.299112i	$-0.0966903\pi$
$798$	−2.88550	+	25.2306i	−0.102146	+	0.893153i
$799$			0.177365i			0.00627471i
$800$	15.9673	+	10.6427i	0.564529	+	0.376276i
$801$	1.29072	−	3.54623i	0.0456054	−	0.125300i
$802$	18.9977	−	20.5610i	0.670831	−	0.726033i
$803$	−54.9062	+	9.68144i	−1.93760	+	0.341650i
$804$	−3.90220	−	3.96729i	−0.137620	−	0.139915i
$805$	10.1847	−	17.6404i	0.358962	−	0.621741i
$806$	0.819826	−	17.1494i	0.0288771	−	0.604062i
$807$	7.87233	−	9.38187i	0.277119	−	0.330258i
$808$	−30.2664	−	33.8639i	−1.06477	−	1.19133i
$809$	22.3243	+	38.6668i	0.784880	+	1.35945i	0.929071	+	0.369902i	$0.120609\pi$
$809$	22.3243	+	38.6668i	0.784880	+	1.35945i	−0.144191	+	0.989550i	$0.546058\pi$
$810$	6.73015	+	13.0601i	0.236473	+	0.458884i
$811$	13.4371	−	4.89069i	0.471839	−	0.171735i	−0.0951460	−	0.995463i	$-0.530332\pi$
$811$	13.4371	−	4.89069i	0.471839	−	0.171735i	0.566985	+	0.823728i	$0.308110\pi$
$812$	−2.66557	+	1.83379i	−0.0935433	+	0.0643534i
$813$	6.93350	+	1.22256i	0.243168	+	0.0428771i
$814$	45.0145	−	34.2461i	1.57776	−	1.20032i
$815$	−16.8994	−	20.1399i	−0.591961	−	0.705471i
$816$	0.270082	−	0.311267i	0.00945477	−	0.0108965i
$817$	33.3952	−	34.8396i	1.16835	−	1.21888i
$818$	−20.5957	−	13.2410i	−0.720113	−	0.462960i
$819$	13.6373	−	11.4431i	0.476527	−	0.399854i
$820$	3.43172	−	0.271657i	0.119841	−	0.00948667i
$821$	6.15480	−	34.9056i	0.214804	−	1.21821i	−0.666442	−	0.745557i	$-0.732184\pi$
$821$	6.15480	−	34.9056i	0.214804	−	1.21821i	0.881246	−	0.472657i	$-0.156705\pi$
$822$	27.4966	+	11.5229i	0.959053	+	0.401907i
$823$	−8.58714	−	23.5930i	−0.299329	−	0.822400i	−0.994612	−	0.103664i	$-0.966943\pi$
$823$	−8.58714	−	23.5930i	−0.299329	−	0.822400i	0.695283	−	0.718736i	$-0.255279\pi$
$824$	19.9420	−	25.3319i	0.694712	−	0.882479i
$825$	14.7467	−	8.51400i	0.513414	−	0.296420i
$826$	−11.8965	−	38.2822i	−0.413933	−	1.33201i
$827$	1.24282	+	1.04285i	0.0432171	+	0.0362635i	0.664140	−	0.747608i	$-0.268798\pi$
$827$	1.24282	+	1.04285i	0.0432171	+	0.0362635i	−0.620923	+	0.783871i	$0.713242\pi$
$828$	4.63992	+	3.30643i	0.161248	+	0.114906i
$829$	−0.612854	−	0.353831i	−0.0212853	−	0.0122891i	0.489320	−	0.872105i	$-0.337245\pi$
$829$	−0.612854	−	0.353831i	−0.0212853	−	0.0122891i	−0.510605	+	0.859815i	$0.670578\pi$
$830$	21.6738	+	4.89909i	0.752309	+	0.170050i
$831$	3.41427	+	19.3633i	0.118440	+	0.671705i
$832$	−32.1205	−	15.9599i	−1.11358	−	0.553309i
$833$	0.206049	+	0.0749958i	0.00713919	+	0.00259845i
$834$	21.6610	−	2.76065i	0.750059	−	0.0955934i
$835$	−33.5636			−1.16152
$836$	−5.35199	+	32.8219i	−0.185103	+	1.13517i
$837$	−15.2095			−0.525717
$838$	10.3251	−	1.31591i	0.356675	−	0.0454574i
$839$	−34.5798	−	12.5860i	−1.19383	−	0.434518i	−0.332762	−	0.943011i	$-0.607981\pi$
$839$	−34.5798	−	12.5860i	−1.19383	−	0.434518i	−0.861066	+	0.508493i	$0.830203\pi$
$840$	32.0645	+	10.5490i	1.10633	+	0.363974i
$841$	4.98943	+	28.2965i	0.172049	+	0.975740i
$842$	4.89965	+	1.10750i	0.168853	+	0.0381671i
$843$	22.3965	+	12.9306i	0.771377	+	0.445354i
$844$	−1.73842	+	2.43953i	−0.0598389	+	0.0839720i
$845$	15.7577	+	13.2223i	0.542080	+	0.454860i
$846$	−1.20589	−	3.88048i	−0.0414594	−	0.133414i
$847$	9.62901	−	5.55931i	0.330857	−	0.191020i
$848$	3.56945	−	1.23270i	0.122575	−	0.0423312i
$849$	4.72423	+	12.9797i	0.162135	+	0.445463i
$850$	0.346403	+	0.145166i	0.0118815	+	0.00497915i
$851$	4.08908	−	23.1903i	0.140172	−	0.794953i
$852$	−0.601797	−	7.60223i	−0.0206172	−	0.260448i
$853$	−37.6785	+	31.6161i	−1.29009	+	1.08251i	−0.298321	+	0.954466i	$0.596427\pi$
$853$	−37.6785	+	31.6161i	−1.29009	+	1.08251i	−0.991768	+	0.128047i	$0.959129\pi$
$854$	12.5550	+	8.07157i	0.429622	+	0.276204i
$855$	−1.73324	−	15.9220i	−0.0592754	−	0.544521i
$856$	−25.0794	−	3.61882i	−0.857195	−	0.123689i
$857$	19.1151	+	22.7805i	0.652960	+	0.778167i	0.986357	−	0.164619i	$-0.0526396\pi$
$857$	19.1151	+	22.7805i	0.652960	+	0.778167i	−0.333398	+	0.942786i	$0.608195\pi$
$858$	−25.3305	+	19.2709i	−0.864769	+	0.657897i
$859$	1.00555	+	0.177305i	0.0343088	+	0.00604957i	0.190776	−	0.981634i	$-0.438900\pi$
$859$	1.00555	+	0.177305i	0.0343088	+	0.00604957i	−0.156467	+	0.987683i	$0.550011\pi$
$860$	−36.3576	−	52.8489i	−1.23978	−	1.80213i
$861$	2.30009	−	0.837163i	0.0783867	−	0.0285304i
$862$	16.1162	+	31.2739i	0.548918	+	1.06519i
$863$	18.1997	+	31.5228i	0.619524	+	1.07305i	0.989573	+	0.144035i	$0.0460078\pi$
$863$	18.1997	+	31.5228i	0.619524	+	1.07305i	−0.370048	+	0.929013i	$0.620659\pi$
$864$	−12.7635	+	29.0972i	−0.434223	+	0.989907i
$865$	5.67673	−	6.76526i	0.193015	−	0.230026i
$866$	−0.177460	+	3.71217i	−0.00603034	+	0.126145i
$867$	−11.1813	+	19.3665i	−0.379736	+	0.657722i
$868$	−12.0873	+	11.8890i	−0.410270	+	0.403540i
$869$	−26.1363	+	4.60853i	−0.886612	+	0.156334i
$870$	−1.89057	+	2.04614i	−0.0640962	+	0.0693706i
$871$	−3.24223	+	8.90797i	−0.109859	+	0.301835i
$872$	23.9130	+	38.5839i	0.809795	+	1.30662i
$873$			12.0049i			0.406303i
$874$	7.63685	+	11.5487i	0.258320	+	0.390639i
$875$		−	14.5815i		−	0.492945i
$876$	−34.7261	−	16.5441i	−1.17329	−	0.558972i
$877$	−14.8862	+	40.8995i	−0.502671	+	1.38108i	0.385986	+	0.922505i	$0.373861\pi$
$877$	−14.8862	+	40.8995i	−0.502671	+	1.38108i	−0.888657	+	0.458573i	$0.848361\pi$
$878$	8.79875	+	8.12976i	0.296944	+	0.274366i
$879$	−21.0638	+	3.71412i	−0.710464	+	0.125274i
$880$	41.2816	+	15.8033i	1.39160	+	0.532730i
$881$	−26.6388	+	46.1398i	−0.897486	+	1.55449i	−0.0667877	+	0.997767i	$0.521275\pi$
$881$	−26.6388	+	46.1398i	−0.897486	+	1.55449i	−0.830698	+	0.556723i	$0.812058\pi$
$882$	−5.01795	−	0.239882i	−0.168963	−	0.00807726i
$883$	9.30915	−	11.0942i	0.313278	−	0.373350i	−0.586312	−	0.810085i	$-0.699421\pi$
$883$	9.30915	−	11.0942i	0.313278	−	0.373350i	0.899590	+	0.436735i	$0.143865\pi$
$884$	−0.676583	−	0.187301i	−0.0227560	−	0.00629961i
$885$	−17.2587	−	29.8930i	−0.580145	−	1.00484i
$886$	−20.8314	+	10.7349i	−0.699845	+	0.360646i
$887$	37.1590	−	13.5248i	1.24768	−	0.454117i	0.368061	−	0.929802i	$-0.380022\pi$
$887$	37.1590	−	13.5248i	1.24768	−	0.454117i	0.879616	+	0.475684i	$0.157799\pi$
$888$	39.0037	−	1.21838i	1.30888	−	0.0408862i
$889$	45.1557	+	7.96216i	1.51447	+	0.267042i
$890$	−7.38054	−	9.70131i	−0.247396	−	0.325189i
$891$	8.79340	+	10.4796i	0.294590	+	0.351079i
$892$	6.52410	+	14.2985i	0.218443	+	0.478751i
$893$	0.652262	−	9.85313i	0.0218271	−	0.329722i
$894$	15.5098	−	24.1248i	0.518725	−	0.806853i
$895$	9.62154	−	8.07343i	0.321612	−	0.269865i
$896$	12.6014	+	33.1013i	0.420983	+	1.10584i
$897$	−2.30100	+	13.0496i	−0.0768280	+	0.435713i
$898$	−12.8745	+	30.7218i	−0.429626	+	1.02520i
$899$	−0.478576	−	1.31488i	−0.0159614	−	0.0438536i
$900$	−8.56577	−	0.820847i	−0.285526	−	0.0273616i
$901$	0.0640116	−	0.0369571i	0.00213254	−	0.00123122i
$902$	3.06092	−	0.951208i	0.101918	−	0.0316718i
$903$	−34.9400	−	29.3181i	−1.16273	−	0.975646i
$904$	−20.6584	+	8.25825i	−0.687088	+	0.274665i
$905$	−5.04296	−	2.91156i	−0.167634	−	0.0967834i
$906$	−3.31257	+	14.6550i	−0.110053	+	0.486880i
$907$	−8.61295	−	48.8464i	−0.285988	−	1.62192i	−0.701734	−	0.712439i	$-0.747591\pi$
$907$	−8.61295	−	48.8464i	−0.285988	−	1.62192i	0.415746	−	0.909481i	$-0.363520\pi$
$908$	−10.3735	+	2.68781i	−0.344255	+	0.0891980i
$909$	19.1387	+	6.96593i	0.634792	+	0.231045i
$910$	−7.26976	−	57.0411i	−0.240990	−	1.89089i
$911$	−40.7226			−1.34920			−0.674599	−	0.738184i	$-0.735684\pi$
$911$	−40.7226			−1.34920			−0.674599	+	0.738184i	$0.735684\pi$
$912$	−16.1486	+	16.2986i	−0.534732	+	0.539700i
$913$	20.6899			0.684736
$914$	6.37586	+	50.0273i	0.210895	+	1.65475i
$915$	12.0766	+	4.39552i	0.399240	+	0.145311i
$916$	−6.08297	+	1.57612i	−0.200987	+	0.0520765i
$917$	−10.1586	−	57.6120i	−0.335465	−	1.90252i
$918$	−0.137115	+	0.606603i	−0.00452547	+	0.0200209i
$919$	−23.6930	−	13.6792i	−0.781562	−	0.451235i	0.0554219	−	0.998463i	$-0.482350\pi$
$919$	−23.6930	−	13.6792i	−0.781562	−	0.451235i	−0.836983	+	0.547228i	$0.815683\pi$
$920$	17.0884	−	6.83114i	0.563388	−	0.225216i
$921$	−25.1670	−	21.1176i	−0.829281	−	0.695849i
$922$	40.3611	−	12.5426i	1.32922	−	0.413067i
$923$	−11.2506	+	6.49552i	−0.370317	+	0.213803i
$924$	31.2865	+	2.99815i	1.02925	+	0.0986319i
$925$	12.1640	+	33.4202i	0.399948	+	1.09885i
$926$	−5.20357	+	12.4171i	−0.171000	+	0.408050i
$927$	−2.51048	+	14.2376i	−0.0824548	+	0.467625i
$928$	−2.91710	−	0.187857i	−0.0957585	−	0.00616670i
$929$	20.6304	−	17.3109i	0.676860	−	0.567953i	−0.238227	−	0.971210i	$-0.576566\pi$
$929$	20.6304	−	17.3109i	0.676860	−	0.567953i	0.915087	+	0.403256i	$0.132122\pi$
$930$	−7.89458	+	12.2796i	−0.258873	+	0.402666i
$931$	−11.1708	−	4.92399i	−0.366110	−	0.161377i
$932$	11.8580	+	25.9887i	0.388423	+	0.851288i
$933$	−12.9728	−	15.4604i	−0.424710	−	0.506150i
$934$	13.7145	+	18.0270i	0.448753	+	0.589861i
$935$	0.852049	+	0.150239i	0.0278650	+	0.00491335i
$936$	16.0761	−	0.502177i	0.525463	−	0.0164142i
$937$	−39.4921	+	14.3740i	−1.29015	+	0.469577i	−0.893777	−	0.448512i	$-0.851954\pi$
$937$	−39.4921	+	14.3740i	−1.29015	+	0.469577i	−0.396375	+	0.918089i	$0.629732\pi$
$938$	8.32127	−	4.28814i	0.271699	−	0.140013i
$939$	−6.91755	−	11.9815i	−0.225746	−	0.391003i
$940$	−12.6497	−	3.50186i	−0.412587	−	0.114218i
$941$	−19.5593	+	23.3099i	−0.637615	+	0.759880i	−0.983991	−	0.178216i	$-0.942967\pi$
$941$	−19.5593	+	23.3099i	−0.637615	+	0.759880i	0.346377	+	0.938095i	$0.387412\pi$
$942$	5.86345	+	0.280301i	0.191041	+	0.00913271i
$943$	0.667240	−	1.15569i	0.0217283	−	0.0376345i
$944$	12.9487	−	33.8248i	0.421446	−	1.10090i
$945$	−50.1657	+	8.84557i	−1.63189	+	0.287747i
$946$	−43.8692	−	40.5337i	−1.42631	−	1.31787i
$947$	5.70257	−	15.6677i	0.185309	−	0.509132i	−0.811900	−	0.583797i	$-0.801567\pi$
$947$	5.70257	−	15.6677i	0.185309	−	0.509132i	0.997209	+	0.0746651i	$0.0237888\pi$
$948$	−16.5302	−	7.87526i	−0.536877	−	0.255776i
$949$			65.5269i			2.12709i
$950$	−18.7099	−	9.33830i	−0.607028	−	0.302975i
$951$			23.7469i			0.770047i
$952$	0.365204	+	0.589262i	0.0118363	+	0.0190981i
$953$	15.6863	−	43.0977i	0.508129	−	1.39607i	−0.375036	−	0.927010i	$-0.622370\pi$
$953$	15.6863	−	43.0977i	0.508129	−	1.39607i	0.883165	−	0.469062i	$-0.155408\pi$
$954$	−1.14921	+	1.24378i	−0.0372071	+	0.0402688i
$955$	20.2462	−	3.56995i	0.655152	−	0.115521i
$956$	−17.7020	+	17.4116i	−0.572523	+	0.563131i
$957$	−1.29697	+	2.24641i	−0.0419250	+	0.0726163i
$958$	−0.796456	+	16.6606i	−0.0257323	+	0.538278i
$959$	−32.2376	+	38.4193i	−1.04101	+	1.24062i
$960$	16.8672	+	25.4079i	0.544386	+	0.820037i
$961$	11.8338	+	20.4967i	0.381735	+	0.661184i
$962$	−30.4511	−	59.0913i	−0.981782	−	1.90518i
$963$	10.6776	−	3.88633i	0.344081	−	0.125235i
$964$	10.2106	+	14.8420i	0.328861	+	0.478029i
$965$	10.3620	+	1.82710i	0.333565	+	0.0588165i
$966$	10.4141	−	7.92283i	0.335069	−	0.254913i
$967$	−11.9162	−	14.2012i	−0.383200	−	0.456680i	0.539621	−	0.841908i	$-0.318567\pi$
$967$	−11.9162	−	14.2012i	−0.383200	−	0.456680i	−0.922822	+	0.385228i	$0.874123\pi$
$968$	9.94244	+	1.43464i	0.319562	+	0.0461111i
$969$	−0.249740	+	0.373236i	−0.00802282	+	0.0119901i
$970$	32.6173	+	20.9696i	1.04728	+	0.673294i
$971$	40.2577	−	33.7803i	1.29193	−	1.08406i	0.300453	−	0.953797i	$-0.402862\pi$
$971$	40.2577	−	33.7803i	1.29193	−	1.08406i	0.991479	−	0.130264i	$-0.0415824\pi$
$972$	−1.91465	−	24.1869i	−0.0614125	−	0.775796i
$973$	−6.37869	+	36.1754i	−0.204492	+	1.15973i
$974$	26.6679	+	11.1756i	0.854496	+	0.358091i
$975$	−6.84488	−	18.8061i	−0.219212	−	0.602279i
$976$	4.40193	+	12.7463i	0.140902	+	0.408000i
$977$	42.9769	−	24.8127i	1.37495	−	0.793830i	0.383407	−	0.923579i	$-0.374751\pi$
$977$	42.9769	−	24.8127i	1.37495	−	0.793830i	0.991547	+	0.129749i	$0.0414173\pi$
$978$	−5.01205	−	16.1284i	−0.160268	−	0.515731i
$979$	−8.69457	−	7.29561i	−0.277880	−	0.233169i
$980$	−9.41692	+	13.2148i	−0.300812	+	0.422131i
$981$	−17.6286	−	10.1779i	−0.562839	−	0.324955i
$982$	−51.6218	−	11.6685i	−1.64732	−	0.372355i
$983$	2.09570	+	11.8853i	0.0668425	+	0.379083i	0.999817	+	0.0191398i	$0.00609277\pi$
$983$	2.09570	+	11.8853i	0.0668425	+	0.379083i	−0.932974	+	0.359943i	$0.882796\pi$
$984$	2.10067	+	0.691105i	0.0669670	+	0.0220316i
$985$	−46.0789	−	16.7714i	−1.46820	−	0.534380i
$986$	−0.0567559	+	0.00723342i	−0.00180748	+	0.000230359i
$987$	−9.33264			−0.297061
$988$	36.8974	+	12.8933i	1.17386	+	0.410189i
$989$	−24.8669			−0.790723
$990$	−19.6630	+	2.50601i	−0.624932	+	0.0796463i
$991$	−8.02497	−	2.92085i	−0.254922	−	0.0927839i	0.211398	−	0.977400i	$-0.432198\pi$
$991$	−8.02497	−	2.92085i	−0.254922	−	0.0927839i	−0.466320	+	0.884616i	$0.654420\pi$
$992$	−15.2250	+	1.68497i	−0.483393	+	0.0534980i
$993$	5.24054	+	29.7206i	0.166303	+	0.943153i
$994$	12.5130	+	2.82840i	0.396888	+	0.0897115i
$995$	16.5659	+	9.56435i	0.525175	+	0.303210i
$996$	11.6249	+	8.28398i	0.368350	+	0.262488i
$997$	36.1681	+	30.3486i	1.14545	+	0.961150i	0.999604	−	0.0281561i	$-0.00896354\pi$
$997$	36.1681	+	30.3486i	1.14545	+	0.961150i	0.145851	+	0.989307i	$0.453408\pi$
$998$	−15.5497	−	50.0378i	−0.492216	−	1.58392i
$999$	−50.9993	+	29.4445i	−1.61355	+	0.931582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.51.4	yes	48
3.2	odd	2		684.2.cf.a.127.5		48
4.3	odd	2	inner	76.2.k.a.51.1	yes	48
12.11	even	2		684.2.cf.a.127.8		48
19.3	odd	18	inner	76.2.k.a.3.1	✓	48
57.41	even	18		684.2.cf.a.307.8		48
76.3	even	18	inner	76.2.k.a.3.4	yes	48
228.155	odd	18		684.2.cf.a.307.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.3.1	✓	48	19.3	odd	18	inner
76.2.k.a.3.4	yes	48	76.3	even	18	inner
76.2.k.a.51.1	yes	48	4.3	odd	2	inner
76.2.k.a.51.4	yes	48	1.1	even	1	trivial
684.2.cf.a.127.5		48	3.2	odd	2
684.2.cf.a.127.8		48	12.11	even	2
684.2.cf.a.307.5		48	228.155	odd	18
684.2.cf.a.307.8		48	57.41	even	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.178792 - 1.40287i) q^{2} +(1.23656 + 0.450071i) q^{3} +(-1.93607 + 0.501643i) q^{4} +(-0.503046 - 2.85292i) q^{5} +(0.410302 - 1.81520i) q^{6} +(2.71118 + 1.56530i) q^{7} +(1.04989 + 2.62635i) q^{8} +(-0.971618 - 0.815285i) q^{9} +O(q^{10})\)	\(q+(-0.178792 - 1.40287i) q^{2} +(1.23656 + 0.450071i) q^{3} +(-1.93607 + 0.501643i) q^{4} +(-0.503046 - 2.85292i) q^{5} +(0.410302 - 1.81520i) q^{6} +(2.71118 + 1.56530i) q^{7} +(1.04989 + 2.62635i) q^{8} +(-0.971618 - 0.815285i) q^{9} +(-3.91232 + 1.21579i) q^{10} +(-3.30359 + 1.90733i) q^{11} +(-2.61984 - 0.251056i) q^{12} +(1.53341 + 4.21300i) q^{13} +(1.71117 - 4.08329i) q^{14} +(0.661968 - 3.75421i) q^{15} +(3.49671 - 1.94243i) q^{16} +(0.0599755 - 0.0503255i) q^{17} +(-0.970017 + 1.50882i) q^{18} +(-3.51689 + 2.57517i) q^{19} +(2.40508 + 5.27109i) q^{20} +(2.64804 + 3.15581i) q^{21} +(3.26638 + 4.29348i) q^{22} +(2.21189 + 0.390015i) q^{23} +(0.116209 + 3.72017i) q^{24} +(-3.18761 + 1.16020i) q^{25} +(5.63611 - 2.90441i) q^{26} +(-2.80841 - 4.86430i) q^{27} +(-6.03426 - 1.67048i) q^{28} +(0.332156 - 0.395848i) q^{29} +(-5.38500 - 0.257429i) q^{30} +(1.35392 - 2.34507i) q^{31} +(-3.35015 - 4.55812i) q^{32} +(-4.94351 + 0.871675i) q^{33} +(-0.0813230 - 0.0751399i) q^{34} +(3.10183 - 8.52220i) q^{35} +(2.29010 + 1.09104i) q^{36} -10.4844i q^{37} +(4.24141 + 4.47331i) q^{38} +5.89976i q^{39} +(6.96462 - 4.31643i) q^{40} +(0.203213 - 0.558324i) q^{41} +(3.95374 - 4.27908i) q^{42} +(-10.9034 + 1.92257i) q^{43} +(5.43917 - 5.34993i) q^{44} +(-1.83717 + 3.18207i) q^{45} +(0.151671 - 3.17271i) q^{46} +(-1.45618 + 1.73541i) q^{47} +(5.19812 - 0.828162i) q^{48} +(1.40035 + 2.42547i) q^{49} +(2.19752 + 4.26436i) q^{50} +(0.0968133 - 0.0352372i) q^{51} +(-5.08220 - 7.38742i) q^{52} +(0.929735 + 0.163937i) q^{53} +(-6.32184 + 4.80952i) q^{54} +(7.10330 + 8.46538i) q^{55} +(-1.26459 + 8.76392i) q^{56} +(-5.50785 + 1.60150i) q^{57} +(-0.614709 - 0.395196i) q^{58} +(6.93627 - 5.82022i) q^{59} +(0.601658 + 7.60046i) q^{60} +(-0.585413 + 3.32004i) q^{61} +(-3.53189 - 1.48010i) q^{62} +(-1.35807 - 3.73126i) q^{63} +(-5.79545 + 5.51477i) q^{64} +(11.2480 - 6.49401i) q^{65} +(2.10671 + 6.77924i) q^{66} +(1.61972 + 1.35911i) q^{67} +(-0.0908712 + 0.127520i) q^{68} +(2.55959 + 1.47778i) q^{69} +(-12.5101 - 2.82774i) q^{70} +(0.503163 + 2.85358i) q^{71} +(1.12113 - 3.40777i) q^{72} +(13.7341 + 4.99880i) q^{73} +(-14.7082 + 1.87453i) q^{74} -4.46384 q^{75} +(5.51712 - 6.74992i) q^{76} -11.9422 q^{77} +(8.27658 - 1.05483i) q^{78} +(6.53766 + 2.37952i) q^{79} +(-7.30059 - 8.99868i) q^{80} +(-0.622736 - 3.53171i) q^{81} +(-0.819587 - 0.185257i) q^{82} +(-4.69715 - 2.71190i) q^{83} +(-6.70988 - 4.78149i) q^{84} +(-0.173745 - 0.145789i) q^{85} +(4.64655 + 14.9523i) q^{86} +(0.588891 - 0.339996i) q^{87} +(-8.47772 - 6.67390i) q^{88} +(1.01763 + 2.79592i) q^{89} +(4.79249 + 2.00837i) q^{90} +(-2.43727 + 13.8225i) q^{91} +(-4.47801 + 0.354482i) q^{92} +(2.72965 - 2.29045i) q^{93} +(2.69489 + 1.73255i) q^{94} +(9.11589 + 8.73797i) q^{95} +(-2.09118 - 7.14419i) q^{96} +(-6.08391 - 7.25052i) q^{97} +(3.15224 - 2.39815i) q^{98} +(4.76484 + 0.840170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

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