LMFDB - Embedded newform 342.2.x.b.281.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (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:	$2.73088374913$
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			281.7
Character	$\chi$	$=$	342.281
Dual form			342.2.x.b.185.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(1.40898 - 1.00736i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.759805 - 2.08755i) q^{5} +(-0.431828 + 1.67736i) q^{6} +(1.20984 + 2.09551i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.970470 - 2.83869i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(1.40898 - 1.00736i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.759805 - 2.08755i) q^{5} +(-0.431828 + 1.67736i) q^{6} +(1.20984 + 2.09551i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.970470 - 2.83869i) q^{9} +(0.759805 + 2.08755i) q^{10} +2.72097i q^{11} +(-0.747384 - 1.56250i) q^{12} +(-0.241975 - 0.664821i) q^{13} +(-2.27376 - 0.827581i) q^{14} +(-1.03235 - 3.70672i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.62169 - 4.45555i) q^{17} +(1.08125 + 2.79837i) q^{18} +(4.13839 - 1.36884i) q^{19} +(-1.92390 - 1.11076i) q^{20} +(3.81557 + 1.73380i) q^{21} +(-1.74901 - 2.08439i) q^{22} +(-7.80979 - 1.37708i) q^{23} +(1.57689 + 0.716538i) q^{24} +(0.0496682 + 0.0416766i) q^{25} +(0.612702 + 0.353744i) q^{26} +(-1.49220 - 4.97728i) q^{27} +(2.27376 - 0.827581i) q^{28} +(1.62287 - 9.20375i) q^{29} +(3.17346 + 2.17593i) q^{30} +7.01560i q^{31} +(0.939693 - 0.342020i) q^{32} +(2.74099 + 3.83381i) q^{33} +(1.62169 + 4.45555i) q^{34} +(5.29372 - 0.933426i) q^{35} +(-2.62705 - 1.44866i) q^{36} +8.40981i q^{37} +(-2.29032 + 3.70870i) q^{38} +(-1.01065 - 0.692967i) q^{39} +(2.18777 - 0.385763i) q^{40} +(-7.64614 + 6.41588i) q^{41} +(-4.03736 + 1.12444i) q^{42} +(0.243482 + 1.38085i) q^{43} +(2.67963 + 0.472492i) q^{44} +(-5.18854 - 4.18276i) q^{45} +(6.86781 - 3.96513i) q^{46} +(5.95323 + 1.04972i) q^{47} +(-1.66855 + 0.464704i) q^{48} +(0.572561 - 0.991705i) q^{49} -0.0648373 q^{50} +(-2.20339 - 7.91141i) q^{51} +(-0.696739 + 0.122854i) q^{52} +(1.98365 + 1.66448i) q^{53} +(4.34243 + 2.85365i) q^{54} +(5.68016 + 2.06741i) q^{55} +(-1.20984 + 2.09551i) q^{56} +(4.45202 - 6.09750i) q^{57} +(4.67287 + 8.09364i) q^{58} +(0.719002 + 4.07766i) q^{59} +(-3.82967 + 0.373002i) q^{60} +(-6.34757 + 2.31033i) q^{61} +(-4.50954 - 5.37426i) q^{62} +(7.12263 - 1.40075i) q^{63} +(-0.500000 + 0.866025i) q^{64} -1.57170 q^{65} +(-4.56404 - 1.17499i) q^{66} +(-0.352442 + 0.420023i) q^{67} +(-4.10626 - 2.37075i) q^{68} +(-12.3911 + 5.92695i) q^{69} +(-3.45523 + 4.11778i) q^{70} +(-3.99788 + 3.35462i) q^{71} +(2.94362 - 0.578896i) q^{72} +(-0.0490632 - 0.278251i) q^{73} +(-5.40572 - 6.44229i) q^{74} +(0.111965 + 0.00868808i) q^{75} +(-0.629420 - 4.31322i) q^{76} +(-5.70182 + 3.29195i) q^{77} +(1.21963 - 0.118790i) q^{78} +(-0.813728 + 2.23570i) q^{79} +(-1.42797 + 1.70179i) q^{80} +(-7.11638 - 5.50974i) q^{81} +(1.73324 - 9.82969i) q^{82} +(-3.28816 + 1.89842i) q^{83} +(2.37002 - 3.45653i) q^{84} +(-8.06901 - 6.77070i) q^{85} +(-1.07411 - 0.901288i) q^{86} +(-6.98485 - 14.6027i) q^{87} +(-2.35643 + 1.36049i) q^{88} +(-3.18023 + 18.0360i) q^{89} +(6.66328 - 0.130953i) q^{90} +(1.10039 - 1.31139i) q^{91} +(-2.71231 + 7.45201i) q^{92} +(7.06720 + 9.88486i) q^{93} +(-5.23519 + 3.02254i) q^{94} +(0.286852 - 9.67914i) q^{95} +(0.979476 - 1.42851i) q^{96} +(-7.49987 - 8.93800i) q^{97} +(0.198848 + 1.12773i) q^{98} +(7.72401 + 2.64062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	1.40898	−	1.00736i	0.813477	−	0.581597i
$3$	1.40898	−	1.00736i	0.813477	−	0.581597i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.759805	−	2.08755i	0.339795	−	0.933580i	−0.645657	−	0.763628i	$-0.723416\pi$
$5$	0.759805	−	2.08755i	0.339795	−	0.933580i	0.985452	−	0.169952i	$-0.0543614\pi$
$6$	−0.431828	+	1.67736i	−0.176293	+	0.684778i
$7$	1.20984	+	2.09551i	0.457278	+	0.792028i	0.998816	−	0.0486480i	$-0.0154913\pi$
$7$	1.20984	+	2.09551i	0.457278	+	0.792028i	−0.541538	+	0.840676i	$0.682158\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.970470	−	2.83869i	0.323490	−	0.946232i
$10$	0.759805	+	2.08755i	0.240272	+	0.660141i
$11$			2.72097i			0.820404i	0.911995	+	0.410202i	$0.134542\pi$
$11$			2.72097i			0.820404i	−0.911995	+	0.410202i	$0.865458\pi$
$12$	−0.747384	−	1.56250i	−0.215751	−	0.451056i
$13$	−0.241975	−	0.664821i	−0.0671118	−	0.184388i	0.901603	−	0.432564i	$-0.142391\pi$
$13$	−0.241975	−	0.664821i	−0.0671118	−	0.184388i	−0.968715	+	0.248176i	$0.920169\pi$
$14$	−2.27376	−	0.827581i	−0.607688	−	0.221180i
$15$	−1.03235	−	3.70672i	−0.266552	−	0.957070i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.62169	−	4.45555i	0.393317	−	1.08063i	−0.572160	−	0.820142i	$-0.693894\pi$
$17$	1.62169	−	4.45555i	0.393317	−	1.08063i	0.965477	−	0.260488i	$-0.0838833\pi$
$18$	1.08125	+	2.79837i	0.254854	+	0.659583i
$19$	4.13839	−	1.36884i	0.949412	−	0.314033i
$19$	4.13839	−	1.36884i	0.949412	−	0.314033i
$20$	−1.92390	−	1.11076i	−0.430196	−	0.248374i
$21$	3.81557	+	1.73380i	0.832626	+	0.378345i
$22$	−1.74901	−	2.08439i	−0.372890	−	0.444393i
$23$	−7.80979	−	1.37708i	−1.62845	−	0.287140i	−0.716547	−	0.697539i	$-0.754278\pi$
$23$	−7.80979	−	1.37708i	−1.62845	−	0.287140i	−0.911906	+	0.410399i	$0.865390\pi$
$24$	1.57689	+	0.716538i	0.321881	+	0.146263i
$25$	0.0496682	+	0.0416766i	0.00993365	+	0.00833532i
$26$	0.612702	+	0.353744i	0.120161	+	0.0693749i
$27$	−1.49220	−	4.97728i	−0.287174	−	0.957879i
$28$	2.27376	−	0.827581i	0.429700	−	0.156398i
$29$	1.62287	−	9.20375i	0.301359	−	1.70909i	−0.338806	−	0.940856i	$-0.610023\pi$
$29$	1.62287	−	9.20375i	0.301359	−	1.70909i	0.640165	−	0.768237i	$-0.278866\pi$
$30$	3.17346	+	2.17593i	0.579391	+	0.397268i
$31$			7.01560i			1.26004i	0.776580	+	0.630019i	$0.216953\pi$
$31$			7.01560i			1.26004i	−0.776580	+	0.630019i	$0.783047\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	2.74099	+	3.83381i	0.477145	+	0.667380i
$34$	1.62169	+	4.45555i	0.278117	+	0.764120i
$35$	5.29372	−	0.933426i	0.894802	−	0.157778i
$36$	−2.62705	−	1.44866i	−0.437841	−	0.241443i
$37$			8.40981i			1.38256i	0.722585	+	0.691282i	$0.242954\pi$
$37$			8.40981i			1.38256i	−0.722585	+	0.691282i	$0.757046\pi$
$38$	−2.29032	+	3.70870i	−0.371539	+	0.601630i
$39$	−1.01065	−	0.692967i	−0.161833	−	0.110963i
$40$	2.18777	−	0.385763i	0.345917	−	0.0609945i
$41$	−7.64614	+	6.41588i	−1.19413	+	1.00199i	−0.194349	+	0.980933i	$0.562259\pi$
$41$	−7.64614	+	6.41588i	−1.19413	+	1.00199i	−0.999778	+	0.0210590i	$0.993296\pi$
$42$	−4.03736	+	1.12444i	−0.622978	+	0.173504i
$43$	0.243482	+	1.38085i	0.0371306	+	0.210578i	0.997728	−	0.0673638i	$-0.0214588\pi$
$43$	0.243482	+	1.38085i	0.0371306	+	0.210578i	−0.960598	+	0.277942i	$0.910348\pi$
$44$	2.67963	+	0.472492i	0.403970	+	0.0712308i
$45$	−5.18854	−	4.18276i	−0.773463	−	0.623529i
$46$	6.86781	−	3.96513i	1.01260	−	0.584627i
$47$	5.95323	+	1.04972i	0.868368	+	0.153117i	0.590045	−	0.807371i	$-0.299110\pi$
$47$	5.95323	+	1.04972i	0.868368	+	0.153117i	0.278324	+	0.960487i	$0.410221\pi$
$48$	−1.66855	+	0.464704i	−0.240834	+	0.0670742i
$49$	0.572561	−	0.991705i	0.0817945	−	0.141672i
$50$	−0.0648373			−0.00916938
$51$	−2.20339	−	7.91141i	−0.308536	−	1.10782i
$52$	−0.696739	+	0.122854i	−0.0966203	+	0.0170368i
$53$	1.98365	+	1.66448i	0.272475	+	0.228634i	0.768778	−	0.639516i	$-0.220865\pi$
$53$	1.98365	+	1.66448i	0.272475	+	0.228634i	−0.496303	+	0.868149i	$0.665309\pi$
$54$	4.34243	+	2.85365i	0.590929	+	0.388333i
$55$	5.68016	+	2.06741i	0.765913	+	0.278769i
$56$	−1.20984	+	2.09551i	−0.161672	+	0.280024i
$57$	4.45202	−	6.09750i	0.589684	−	0.807634i
$58$	4.67287	+	8.09364i	0.613577	+	1.06275i
$59$	0.719002	+	4.07766i	0.0936061	+	0.530867i	0.995166	+	0.0982115i	$0.0313122\pi$
$59$	0.719002	+	4.07766i	0.0936061	+	0.530867i	−0.901559	+	0.432655i	$0.857577\pi$
$60$	−3.82967	+	0.373002i	−0.494408	+	0.0481543i
$61$	−6.34757	+	2.31033i	−0.812723	+	0.295807i	−0.714748	−	0.699382i	$-0.753459\pi$
$61$	−6.34757	+	2.31033i	−0.812723	+	0.295807i	−0.0979747	+	0.995189i	$0.531236\pi$
$62$	−4.50954	−	5.37426i	−0.572712	−	0.682532i
$63$	7.12263	−	1.40075i	0.897367	−	0.176477i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.57170			−0.194945
$66$	−4.56404	−	1.17499i	−0.561795	−	0.144632i
$67$	−0.352442	+	0.420023i	−0.0430576	+	0.0513140i	−0.787143	−	0.616770i	$-0.788441\pi$
$67$	−0.352442	+	0.420023i	−0.0430576	+	0.0513140i	0.744086	+	0.668084i	$0.232885\pi$
$68$	−4.10626	−	2.37075i	−0.497957	−	0.287495i
$69$	−12.3911	+	5.92695i	−1.49171	+	0.713521i
$70$	−3.45523	+	4.11778i	−0.412979	+	0.492169i
$71$	−3.99788	+	3.35462i	−0.474461	+	0.398120i	−0.848419	−	0.529326i	$-0.822445\pi$
$71$	−3.99788	+	3.35462i	−0.474461	+	0.398120i	0.373958	+	0.927446i	$0.378000\pi$
$72$	2.94362	−	0.578896i	0.346909	−	0.0682235i
$73$	−0.0490632	−	0.278251i	−0.00574241	−	0.0325668i	0.981802	−	0.189908i	$-0.0608189\pi$
$73$	−0.0490632	−	0.278251i	−0.00574241	−	0.0325668i	−0.987544	+	0.157341i	$0.949708\pi$
$74$	−5.40572	−	6.44229i	−0.628403	−	0.748901i
$75$	0.111965	+	0.00868808i	0.0129286	+	0.00100321i
$76$	−0.629420	−	4.31322i	−0.0721995	−	0.494760i
$77$	−5.70182	+	3.29195i	−0.649783	+	0.375152i
$78$	1.21963	−	0.118790i	0.138096	−	0.0134503i
$79$	−0.813728	+	2.23570i	−0.0915515	+	0.251536i	−0.977014	−	0.213175i	$-0.931620\pi$
$79$	−0.813728	+	2.23570i	−0.0915515	+	0.251536i	0.885462	+	0.464711i	$0.153842\pi$
$80$	−1.42797	+	1.70179i	−0.159652	+	0.190265i
$81$	−7.11638	−	5.50974i	−0.790709	−	0.612193i
$82$	1.73324	−	9.82969i	0.191404	−	1.08551i
$83$	−3.28816	+	1.89842i	−0.360922	+	0.208378i	−0.669485	−	0.742825i	$-0.733485\pi$
$83$	−3.28816	+	1.89842i	−0.360922	+	0.208378i	0.308563	+	0.951204i	$0.400152\pi$
$84$	2.37002	−	3.45653i	0.258591	−	0.377139i
$85$	−8.06901	−	6.77070i	−0.875207	−	0.734386i
$86$	−1.07411	−	0.901288i	−0.115825	−	0.0971884i
$87$	−6.98485	−	14.6027i	−0.748855	−	1.56558i
$88$	−2.35643	+	1.36049i	−0.251196	+	0.145028i
$89$	−3.18023	+	18.0360i	−0.337103	+	1.91181i	0.0682906	+	0.997665i	$0.478245\pi$
$89$	−3.18023	+	18.0360i	−0.337103	+	1.91181i	−0.405394	+	0.914142i	$0.632866\pi$
$90$	6.66328	−	0.130953i	0.702372	−	0.0138037i
$91$	1.10039	−	1.31139i	0.115352	−	0.137471i
$92$	−2.71231	+	7.45201i	−0.282778	+	0.776926i
$93$	7.06720	+	9.88486i	0.732835	+	1.02501i
$94$	−5.23519	+	3.02254i	−0.539968	+	0.311751i
$95$	0.286852	−	9.67914i	0.0294304	−	0.993059i
$96$	0.979476	−	1.42851i	0.0999673	−	0.145796i
$97$	−7.49987	−	8.93800i	−0.761497	−	0.907516i	0.236445	−	0.971645i	$-0.424018\pi$
$97$	−7.49987	−	8.93800i	−0.761497	−	0.907516i	−0.997942	+	0.0641285i	$0.979573\pi$
$98$	0.198848	+	1.12773i	0.0200867	+	0.113917i
$99$	7.72401	+	2.64062i	0.776292	+	0.265392i
$100$	0.0496682	−	0.0416766i	0.00496682	−	0.00416766i
$101$	−8.12730	+	9.68574i	−0.808696	+	0.963767i	−0.999842	−	0.0177950i	$-0.994335\pi$
$101$	−8.12730	+	9.68574i	−0.808696	+	0.963767i	0.191145	+	0.981562i	$0.438780\pi$
$102$	6.77325	+	4.64418i	0.670652	+	0.459842i
$103$	−6.05033	−	3.49316i	−0.596157	−	0.344191i	0.171371	−	0.985207i	$-0.445180\pi$
$103$	−6.05033	−	3.49316i	−0.596157	−	0.344191i	−0.767528	+	0.641015i	$0.778514\pi$
$104$	0.454764	−	0.541967i	0.0445933	−	0.0531442i
$105$	6.51848	−	6.64784i	0.636138	−	0.648763i
$106$	−2.58947			−0.251512
$107$	−0.382315	+	0.662189i	−0.0369598	+	0.0640162i	−0.883914	−	0.467650i	$-0.845101\pi$
$107$	−0.382315	+	0.662189i	−0.0369598	+	0.0640162i	0.846954	+	0.531666i	$0.178434\pi$
$108$	−5.16078	+	0.605233i	−0.496597	+	0.0582386i
$109$	−2.85365	−	3.40085i	−0.273330	−	0.325742i	0.611865	−	0.790962i	$-0.290420\pi$
$109$	−2.85365	−	3.40085i	−0.273330	−	0.325742i	−0.885195	+	0.465220i	$0.845975\pi$
$110$	−5.68016	+	2.06741i	−0.541582	+	0.197120i
$111$	8.47167	+	11.8493i	0.804095	+	1.12468i
$112$	−0.420174	−	2.38292i	−0.0397027	−	0.225165i
$113$	3.48694	+	6.03955i	0.328023	+	0.568153i	0.982120	−	0.188258i	$-0.0602842\pi$
$113$	3.48694	+	6.03955i	0.328023	+	0.568153i	−0.654096	+	0.756411i	$0.726951\pi$
$114$	0.508958	+	7.53266i	0.0476682	+	0.705498i
$115$	−8.80863	+	15.2570i	−0.821409	+	1.42272i
$116$	−8.78212	−	3.19643i	−0.815399	−	0.296781i
$117$	−2.12205	+	0.0417046i	−0.196184	+	0.00385559i
$118$	−3.17186	−	2.66151i	−0.291993	−	0.245012i
$119$	11.2986	−	1.99225i	1.03574	−	0.182630i
$120$	2.69394	−	2.74740i	0.245922	−	0.250802i
$121$	3.59631			0.326937
$122$	3.37747	−	5.84995i	0.305782	−	0.529630i
$123$	−4.31022	+	16.7422i	−0.388640	+	1.50960i
$124$	6.90901	+	1.21825i	0.620448	+	0.109402i
$125$	9.74422	−	5.62583i	0.871549	−	0.503189i
$126$	−4.55587	+	5.65137i	−0.405869	+	0.503464i
$127$	−0.0957048	−	0.0168753i	−0.00849242	−	0.00149744i	0.169400	−	0.985547i	$-0.445817\pi$
$127$	−0.0957048	−	0.0168753i	−0.00849242	−	0.00149744i	−0.177893	+	0.984050i	$0.556928\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	1.73407	+	1.70033i	0.152677	+	0.149705i
$130$	1.20399	−	1.01027i	0.105597	−	0.0886064i
$131$	14.8978	−	2.62688i	1.30163	−	0.229512i	0.520488	−	0.853869i	$-0.325750\pi$
$131$	14.8978	−	2.62688i	1.30163	−	0.229512i	0.781139	+	0.624357i	$0.214639\pi$
$132$	4.25153	−	2.03361i	0.370048	−	0.177003i
$133$	7.87522	+	7.01595i	0.682868	+	0.608360i
$134$		−	0.548302i		−	0.0473661i
$135$	−11.5241	−	0.666730i	−0.991837	−	0.0573830i
$136$	4.66946	−	0.823352i	0.400403	−	0.0706019i
$137$	−4.81276	−	13.2230i	−0.411182	−	1.12971i	−0.956563	−	0.291525i	$-0.905837\pi$
$137$	−4.81276	−	13.2230i	−0.411182	−	1.12971i	0.545381	−	0.838188i	$-0.316385\pi$
$138$	5.68234	−	12.5051i	0.483713	−	1.06451i
$139$	6.13295	−	2.23221i	0.520190	−	0.189334i	−0.0685630	−	0.997647i	$-0.521841\pi$
$139$	6.13295	−	2.23221i	0.520190	−	0.189334i	0.588753	+	0.808313i	$0.299619\pi$
$140$		−	5.37539i		−	0.454303i
$141$	9.44545	−	4.51799i	0.795450	−	0.380483i
$142$	0.906245	−	5.13957i	0.0760504	−	0.431303i
$143$	1.80896	−	0.658407i	0.151273	−	0.0550588i
$144$	−1.88283	+	2.33558i	−0.156903	+	0.194632i
$145$	−17.9802	−	10.3809i	−1.49318	−	0.862085i
$146$	0.216441	+	0.181616i	0.0179128	+	0.0150306i
$147$	−0.192270	−	1.97407i	−0.0158582	−	0.162818i
$148$	8.28205	+	1.46035i	0.680780	+	0.120040i
$149$	4.89923	+	5.83868i	0.401361	+	0.478323i	0.928434	−	0.371496i	$-0.121155\pi$
$149$	4.89923	+	5.83868i	0.401361	+	0.478323i	−0.527074	+	0.849820i	$0.676711\pi$
$150$	−0.0913547	+	0.0653142i	−0.00745908	+	0.00533288i
$151$	−3.72066	−	2.14813i	−0.302783	−	0.174812i	0.340909	−	0.940096i	$-0.389265\pi$
$151$	−3.72066	−	2.14813i	−0.302783	−	0.174812i	−0.643693	+	0.765284i	$0.722598\pi$
$152$	3.25465	+	2.89953i	0.263987	+	0.235183i
$153$	−11.0741	−	8.92745i	−0.895292	−	0.721742i
$154$	2.25183	−	6.18684i	0.181457	−	0.498550i
$155$	14.6454	+	5.33049i	1.17635	+	0.428155i
$156$	−0.857936	+	0.874963i	−0.0686899	+	0.0700531i
$157$	−20.0658	−	7.30336i	−1.60143	−	0.582871i	−0.621707	−	0.783250i	$-0.713561\pi$
$157$	−20.0658	−	7.30336i	−1.60143	−	0.582871i	−0.979719	+	0.200378i	$0.935783\pi$
$158$	−0.813728	−	2.23570i	−0.0647367	−	0.177863i
$159$	4.47165	+	0.346984i	0.354625	+	0.0275176i
$160$		−	2.22152i		−	0.175627i
$161$	−6.56294	−	18.0315i	−0.517232	−	1.42108i
$162$	8.99305	−	0.353617i	0.706561	−	0.0277827i
$163$	10.9025	+	18.8837i	0.853952	+	1.47909i	0.877614	+	0.479368i	$0.159134\pi$
$163$	10.9025	+	18.8837i	0.853952	+	1.47909i	−0.0236619	+	0.999720i	$0.507533\pi$
$164$	4.99067	+	8.64409i	0.389706	+	0.674990i
$165$	10.0859	−	2.80900i	0.785184	−	0.218680i
$166$	1.29859	−	3.56786i	0.100790	−	0.276920i
$167$	−2.27883	+	12.9239i	−0.176341	+	1.00008i	0.760244	+	0.649638i	$0.225079\pi$
$167$	−2.27883	+	12.9239i	−0.176341	+	1.00008i	−0.936585	+	0.350441i	$0.886032\pi$
$168$	0.406274	+	4.17128i	0.0313447	+	0.321821i
$169$	9.57514	−	8.03450i	0.736549	−	0.618038i
$170$	10.5333			0.807870
$171$	0.130464	−	13.0760i	0.00997684	−	0.999950i
$172$	1.40216			0.106913
$173$	5.38886	−	4.52179i	0.409707	−	0.343785i	−0.414524	−	0.910038i	$-0.636052\pi$
$173$	5.38886	−	4.52179i	0.409707	−	0.343785i	0.824231	+	0.566253i	$0.191608\pi$
$174$	14.7372	+	6.69657i	1.11722	+	0.507666i
$175$	−0.0272429	+	0.154502i	−0.00205937	+	0.0116793i
$176$	0.930627	−	2.55688i	0.0701487	−	0.192732i
$177$	5.12072	+	5.02107i	0.384897	+	0.377407i
$178$	−9.15710	−	15.8606i	−0.686353	−	1.18880i
$179$	1.69347	+	2.93318i	0.126576	+	0.219236i	0.922348	−	0.386360i	$-0.126268\pi$
$179$	1.69347	+	2.93318i	0.126576	+	0.219236i	−0.795772	+	0.605597i	$0.792935\pi$
$180$	−5.02019	+	4.38339i	−0.374183	+	0.326719i
$181$	6.92966	+	19.0391i	0.515077	+	1.41516i	0.875884	+	0.482523i	$0.160279\pi$
$181$	6.92966	+	19.0391i	0.515077	+	1.41516i	−0.360806	+	0.932641i	$0.617498\pi$
$182$			1.71190i			0.126894i
$183$	−6.61630	+	9.64947i	−0.489091	+	0.713309i
$184$	−2.71231	−	7.45201i	−0.199954	−	0.549370i
$185$	17.5559	+	6.38982i	1.29073	+	0.469789i
$186$	−11.7677	−	3.02953i	−0.862846	−	0.222136i
$187$	12.1234	+	4.41257i	0.886553	+	0.322679i
$188$	2.06754	−	5.68051i	0.150791	−	0.414294i
$189$	8.62462	−	9.14865i	0.627348	−	0.665466i
$190$	6.00189	+	7.59904i	0.435423	+	0.551292i
$191$	−8.58403	−	4.95599i	−0.621119	−	0.358603i	0.156186	−	0.987728i	$-0.450080\pi$
$191$	−8.58403	−	4.95599i	−0.621119	−	0.358603i	−0.777304	+	0.629125i	$0.783413\pi$
$192$	0.167904	+	1.72389i	0.0121174	+	0.124411i
$193$	−9.09660	−	10.8409i	−0.654788	−	0.780346i	0.331840	−	0.943336i	$-0.392331\pi$
$193$	−9.09660	−	10.8409i	−0.654788	−	0.780346i	−0.986628	+	0.162990i	$0.947886\pi$
$194$	11.4905	+	2.02608i	0.824968	+	0.145464i
$195$	−2.21450	+	1.58326i	−0.158584	+	0.113380i
$196$	−0.877215	−	0.736070i	−0.0626582	−	0.0525765i
$197$	−8.64271	−	4.98987i	−0.615768	−	0.355514i	0.159452	−	0.987206i	$-0.449027\pi$
$197$	−8.64271	−	4.98987i	−0.615768	−	0.355514i	−0.775219	+	0.631692i	$0.782361\pi$
$198$	−7.61429	+	2.94206i	−0.541124	+	0.209083i
$199$	17.7771	−	6.47033i	1.26018	−	0.458670i	0.376354	−	0.926476i	$-0.377178\pi$
$199$	17.7771	−	6.47033i	1.26018	−	0.458670i	0.883831	+	0.467806i	$0.154955\pi$
$200$	−0.0112589	+	0.0638523i	−0.000796123	+	0.00451504i
$201$	−0.0734714	+	0.946840i	−0.00518227	+	0.0667850i
$202$		−	12.6438i		−	0.889617i
$203$	21.2500	−	7.73435i	1.49145	−	0.542845i
$204$	−8.17383	+	0.796114i	−0.572283	+	0.0557392i
$205$	7.58387	+	20.8365i	0.529680	+	1.45529i
$206$	6.88018	−	1.21316i	0.479365	−	0.0845250i
$207$	−11.4883	+	20.8332i	−0.798489	+	1.44801i
$208$			0.707487i			0.0490554i
$209$	3.72458	+	11.2604i	0.257634	+	0.778901i
$210$	−0.720292	+	9.28254i	−0.0497049	+	0.640556i
$211$	13.0166	−	2.29518i	0.896102	−	0.158007i	0.293415	−	0.955985i	$-0.405208\pi$
$211$	13.0166	−	2.29518i	0.896102	−	0.158007i	0.602686	+	0.797978i	$0.294097\pi$
$212$	1.98365	−	1.66448i	0.136238	−	0.114317i
$213$	−2.25365	+	8.75389i	−0.154418	+	0.599806i
$214$	−0.132777	−	0.753013i	−0.00907642	−	0.0514749i
$215$	3.06760	+	0.540900i	0.209208	+	0.0368891i
$216$	3.56435	−	3.78092i	0.242524	−	0.257259i
$217$	−14.7012	+	8.48777i	−0.997986	+	0.576187i
$218$	4.37205	+	0.770910i	0.296112	+	0.0522126i
$219$	−0.349427	−	0.342627i	−0.0236121	−	0.0231526i
$220$	3.02235	−	5.23487i	0.203767	−	0.352935i
$221$	−3.35455			−0.225651
$222$	−14.1063	−	3.63160i	−0.946750	−	0.243737i
$223$	−18.0464	+	3.18207i	−1.20848	+	0.213087i	−0.741359	−	0.671108i	$-0.765818\pi$
$223$	−18.0464	+	3.18207i	−1.20848	+	0.213087i	−0.467117	+	0.884195i	$0.654707\pi$
$224$	1.85359	+	1.55534i	0.123848	+	0.103921i
$225$	0.166509	−	0.100547i	0.0111006	−	0.00670314i
$226$	−6.55330	−	2.38520i	−0.435919	−	0.158661i
$227$	0.788645	−	1.36597i	0.0523442	−	0.0906628i	−0.838666	−	0.544646i	$-0.816664\pi$
$227$	0.788645	−	1.36597i	0.0523442	−	0.0906628i	0.891010	+	0.453983i	$0.149997\pi$
$228$	−5.23178	−	5.44320i	−0.346483	−	0.360485i
$229$	−7.07034	−	12.2462i	−0.467221	−	0.809251i	0.532077	−	0.846696i	$-0.321412\pi$
$229$	−7.07034	−	12.2462i	−0.467221	−	0.809251i	−0.999299	+	0.0374448i	$0.988078\pi$
$230$	−3.05921	−	17.3496i	−0.201718	−	1.14400i
$231$	−4.71761	+	10.3821i	−0.310396	+	0.683090i
$232$	8.78212	−	3.19643i	0.576574	−	0.209856i
$233$	−7.71897	−	9.19911i	−0.505687	−	0.602654i	0.451448	−	0.892298i	$-0.350908\pi$
$233$	−7.71897	−	9.19911i	−0.505687	−	0.602654i	−0.957135	+	0.289644i	$0.906463\pi$
$234$	1.59878	−	1.39598i	0.104515	−	0.0912579i
$235$	6.71463	−	11.6301i	0.438014	−	0.758663i
$236$	4.14057			0.269528
$237$	1.10561	+	3.96978i	0.0718174	+	0.257865i
$238$	−7.37466	+	8.78877i	−0.478028	+	0.569692i
$239$	−6.31711	−	3.64718i	−0.408620	−	0.235917i	0.281577	−	0.959539i	$-0.409143\pi$
$239$	−6.31711	−	3.64718i	−0.408620	−	0.235917i	−0.690196	+	0.723622i	$0.742476\pi$
$240$	−0.297680	+	3.83626i	−0.0192152	+	0.247629i
$241$	17.1946	−	20.4917i	1.10760	−	1.31999i	0.164913	−	0.986308i	$-0.447266\pi$
$241$	17.1946	−	20.4917i	1.10760	−	1.31999i	0.942687	−	0.333678i	$-0.108290\pi$
$242$	−2.75493	+	2.31166i	−0.177094	+	0.148599i
$243$	−15.5771	−	0.594406i	−0.999273	−	0.0381312i
$244$	1.17298	+	6.65232i	0.0750926	+	0.425871i
$245$	−1.63520	−	1.94875i	−0.104469	−	0.124501i
$246$	−7.45989	−	15.5959i	−0.475625	−	0.994356i
$247$	−1.91142	−	2.42006i	−0.121621	−	0.153985i
$248$	−6.07569	+	3.50780i	−0.385806	+	0.222745i
$249$	−2.72058	+	5.98718i	−0.172410	+	0.379422i
$250$	−3.84829	+	10.5731i	−0.243387	+	0.668701i
$251$	−0.484357	+	0.577234i	−0.0305723	+	0.0364347i	−0.781114	−	0.624388i	$-0.785348\pi$
$251$	−0.484357	+	0.577234i	−0.0305723	+	0.0364347i	0.750542	+	0.660823i	$0.229793\pi$
$252$	−0.142634	−	7.25765i	−0.00898512	−	0.457189i
$253$	3.74699	−	21.2502i	0.235571	−	1.33599i
$254$	0.0841614	−	0.0485906i	0.00528075	−	0.00304884i
$255$	−18.1896	−	1.41145i	−1.13908	−	0.0883883i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−10.4830	−	8.79627i	−0.653910	−	0.548696i	0.254344	−	0.967114i	$-0.418140\pi$
$257$	−10.4830	−	8.79627i	−0.653910	−	0.548696i	−0.908255	+	0.418418i	$0.862585\pi$
$258$	−2.42133	−	0.187886i	−0.150745	−	0.0116973i
$259$	−17.6228	+	10.1746i	−1.09503	+	0.632216i
$260$	−0.272923	+	1.54782i	−0.0169259	+	0.0959918i
$261$	−24.5517	−	13.5388i	−1.51971	−	0.838030i
$262$	−9.72385	+	11.5884i	−0.600741	+	0.715936i
$263$	5.25045	−	14.4255i	0.323757	−	0.889515i	−0.665898	−	0.746043i	$-0.731951\pi$
$263$	5.25045	−	14.4255i	0.323757	−	0.889515i	0.989654	−	0.143471i	$-0.0458265\pi$
$264$	−1.94968	+	4.29067i	−0.119995	+	0.264072i
$265$	4.98187	−	2.87628i	0.306034	−	0.176689i
$266$	−10.5425	−	0.312440i	−0.646404	−	0.0191569i
$267$	13.6877	+	28.6160i	0.837676	+	1.75127i
$268$	0.352442	+	0.420023i	0.0215288	+	0.0256570i
$269$	3.84336	+	21.7968i	0.234334	+	1.32897i	0.844012	+	0.536324i	$0.180187\pi$
$269$	3.84336	+	21.7968i	0.234334	+	1.32897i	−0.609679	+	0.792649i	$0.708702\pi$
$270$	9.25654	−	6.89680i	0.563335	−	0.419726i
$271$	−10.3808	+	8.71054i	−0.630590	+	0.529128i	−0.901112	−	0.433586i	$-0.857248\pi$
$271$	−10.3808	+	8.71054i	−0.630590	+	0.529128i	0.270522	+	0.962714i	$0.412804\pi$
$272$	−3.04778	+	3.63220i	−0.184799	+	0.220234i
$273$	0.229391	−	2.95621i	0.0138834	−	0.178918i
$274$	12.1863	+	7.03579i	0.736204	+	0.425047i
$275$	−0.113401	+	0.135146i	−0.00683833	+	0.00814961i
$276$	3.68522	+	13.2320i	0.221824	+	0.796474i
$277$	−18.6780			−1.12225			−0.561127	−	0.827730i	$-0.689632\pi$
$277$	−18.6780			−1.12225			−0.561127	+	0.827730i	$0.689632\pi$
$278$	−3.26327	+	5.65215i	−0.195718	+	0.338994i
$279$	19.9151	+	6.80843i	1.19229	+	0.407610i
$280$	3.45523	+	4.11778i	0.206490	+	0.246085i
$281$	16.1968	−	5.89514i	0.966218	−	0.351675i	0.189751	−	0.981832i	$-0.439232\pi$
$281$	16.1968	−	5.89514i	0.966218	−	0.351675i	0.776467	+	0.630157i	$0.217010\pi$
$282$	−4.33152	+	9.53240i	−0.257938	+	0.567646i
$283$	−4.62374	−	26.2226i	−0.274853	−	1.55877i	−0.739428	−	0.673235i	$-0.764904\pi$
$283$	−4.62374	−	26.2226i	−0.274853	−	1.55877i	0.464575	−	0.885534i	$-0.346207\pi$
$284$	2.60943	+	4.51966i	0.154841	+	0.268193i
$285$	−9.34617	−	13.9267i	−0.553619	−	0.824947i
$286$	−0.962527	+	1.66715i	−0.0569154	+	0.0985804i
$287$	−22.6952	−	8.26036i	−1.33965	−	0.487594i
$288$	−0.0589475	−	2.99942i	−0.00347351	−	0.176743i
$289$	−4.19929	−	3.52362i	−0.247017	−	0.207272i
$290$	20.4463	−	3.60524i	1.20065	−	0.211707i
$291$	−19.5709	−	5.03846i	−1.14727	−	0.295360i
$292$	−0.282544			−0.0165346
$293$	−14.3734	+	24.8954i	−0.839701	+	1.45440i	0.0504440	+	0.998727i	$0.483936\pi$
$293$	−14.3734	+	24.8954i	−0.839701	+	1.45440i	−0.890145	+	0.455678i	$0.849397\pi$
$294$	1.41619	+	1.38864i	0.0825941	+	0.0809869i
$295$	9.05862	+	1.59728i	0.527414	+	0.0929972i
$296$	−7.28311	+	4.20491i	−0.423322	+	0.244405i
$297$	13.5430	−	4.06023i	0.785847	−	0.235599i
$298$	−7.50606	−	1.32352i	−0.434814	−	0.0766695i
$299$	0.974264	+	5.52533i	0.0563431	+	0.319538i
$300$	0.0279986	−	0.108755i	0.00161650	−	0.00627899i
$301$	−2.59902	+	2.18083i	−0.149805	+	0.125701i
$302$	4.23098	−	0.746036i	0.243466	−	0.0429296i
$303$	−1.69425	+	21.8341i	−0.0973321	+	1.25434i
$304$	−4.35699	−	0.129124i	−0.249890	−	0.00740577i
$305$			15.0063i			0.859256i
$306$	14.2217	−	0.279499i	0.813003	−	0.0159779i
$307$	−20.5632	+	3.62584i	−1.17360	+	0.206938i	−0.726256	−	0.687424i	$-0.758741\pi$
$307$	−20.5632	+	3.62584i	−1.17360	+	0.206938i	−0.447345	+	0.894362i	$0.647630\pi$
$308$	2.25183	+	6.18684i	0.128310	+	0.352528i
$309$	−12.0437	+	1.17303i	−0.685141	+	0.0667313i
$310$	−14.6454	+	5.33049i	−0.831803	+	0.302751i
$311$		−	9.45035i		−	0.535880i	−0.963436	−	0.267940i	$-0.913657\pi$
$311$		−	9.45035i		−	0.535880i	0.963436	−	0.267940i	$-0.0863429\pi$
$312$	0.0948020	−	1.22173i	0.00536711	−	0.0691669i
$313$	2.27679	−	12.9123i	0.128692	−	0.729848i	−0.850354	−	0.526210i	$-0.823612\pi$
$313$	2.27679	−	12.9123i	0.128692	−	0.729848i	0.979046	−	0.203638i	$-0.0652765\pi$
$314$	20.0658	−	7.30336i	1.13238	−	0.412152i
$315$	2.48769	−	15.9331i	0.140165	−	0.897730i
$316$	2.06043	+	1.18959i	0.115908	+	0.0669197i
$317$	4.52011	+	3.79283i	0.253875	+	0.213026i	0.760839	−	0.648941i	$-0.224788\pi$
$317$	4.52011	+	3.79283i	0.253875	+	0.213026i	−0.506964	+	0.861967i	$0.669232\pi$
$318$	−3.64852	+	2.60852i	−0.204599	+	0.146278i
$319$	25.0432	+	4.41578i	1.40215	+	0.247236i
$320$	1.42797	+	1.70179i	0.0798258	+	0.0951327i
$321$	0.128384	+	1.31814i	0.00716570	+	0.0735714i
$322$	16.6179	+	9.59437i	0.926082	+	0.534674i
$323$	0.612241	−	20.6586i	0.0340660	−	1.14948i
$324$	−6.66178	+	6.05151i	−0.370099	+	0.336195i
$325$	0.0156890	−	0.0431052i	0.000870269	−	0.00239104i
$326$	−20.4901	−	7.45777i	−1.13484	−	0.413048i
$327$	−7.44661	−	1.91710i	−0.411798	−	0.106016i
$328$	−9.37938	−	3.41382i	−0.517890	−	0.188496i
$329$	5.00279	+	13.7450i	0.275813	+	0.757789i
$330$	−5.92064	+	8.63489i	−0.325920	+	0.475335i
$331$			5.02188i			0.276028i	0.990430	+	0.138014i	$0.0440718\pi$
$331$			5.02188i			0.276028i	−0.990430	+	0.138014i	$0.955928\pi$
$332$	1.29859	+	3.56786i	0.0712696	+	0.195812i
$333$	23.8729	+	8.16147i	1.30823	+	0.447246i
$334$	−6.56162	−	11.3651i	−0.359036	−	0.621868i
$335$	0.609032	+	1.05487i	0.0332750	+	0.0576340i
$336$	−2.99247	−	2.93424i	−0.163253	−	0.160076i
$337$	4.07843	−	11.2054i	0.222166	−	0.610397i	−0.777667	−	0.628677i	$-0.783597\pi$
$337$	4.07843	−	11.2054i	0.222166	−	0.610397i	0.999833	+	0.0182800i	$0.00581903\pi$
$338$	−2.17051	+	12.3096i	−0.118060	+	0.669552i
$339$	10.9970	+	4.99704i	0.597276	+	0.271402i
$340$	−8.06901	+	6.77070i	−0.437603	+	0.367193i
$341$	−19.0892			−1.03374
$342$	8.30518	+	10.1007i	0.449093	+	0.546183i
$343$	19.7086			1.06417
$344$	−1.07411	+	0.901288i	−0.0579123	+	0.0485942i
$345$	2.95800	+	30.3703i	0.159254	+	1.63508i
$346$	−1.22155	+	6.92778i	−0.0656712	+	0.372440i
$347$	12.4134	−	34.1054i	0.666384	−	1.83088i	0.121070	−	0.992644i	$-0.461367\pi$
$347$	12.4134	−	34.1054i	0.666384	−	1.83088i	0.545314	−	0.838232i	$-0.316410\pi$
$348$	−15.5938	+	4.34300i	−0.835915	+	0.232809i
$349$	−14.4521	−	25.0317i	−0.773602	−	1.33992i	−0.935577	−	0.353124i	$-0.885120\pi$
$349$	−14.4521	−	25.0317i	−0.773602	−	1.33992i	0.161974	−	0.986795i	$-0.448214\pi$
$350$	−0.0784429	−	0.135867i	−0.00419295	−	0.00726240i
$351$	−2.94793	+	2.19642i	−0.157349	+	0.117236i
$352$	0.930627	+	2.55688i	0.0496026	+	0.136282i
$353$		−	14.1474i		−	0.752989i	−0.926419	−	0.376494i	$-0.877129\pi$
$353$		−	14.1474i		−	0.752989i	0.926419	−	0.376494i	$-0.122871\pi$
$354$	−7.15018	−	0.554829i	−0.380028	−	0.0294888i
$355$	3.96532	+	10.8946i	0.210457	+	0.578226i
$356$	17.2097	+	6.26382i	0.912113	+	0.331982i
$357$	13.9127	−	14.1888i	0.736337	−	0.750950i
$358$	−3.18269	−	1.15840i	−0.168210	−	0.0612236i
$359$	2.03698	−	5.59655i	0.107508	−	0.295375i	−0.874261	−	0.485457i	$-0.838653\pi$
$359$	2.03698	−	5.59655i	0.107508	−	0.295375i	0.981768	+	0.190082i	$0.0608755\pi$
$360$	1.02810	−	6.58479i	0.0541858	−	0.347049i
$361$	15.2526	−	11.3296i	0.802766	−	0.596294i
$362$	−17.5465	−	10.1305i	−0.922224	−	0.532446i
$363$	5.06714	−	3.62276i	0.265956	−	0.190146i
$364$	−1.10039	−	1.31139i	−0.0576759	−	0.0687355i
$365$	−0.618141	−	0.108995i	−0.0323550	−	0.00570506i
$366$	−1.13418	−	11.6448i	−0.0592845	−	0.608683i
$367$	19.8612	+	16.6655i	1.03675	+	0.869933i	0.991638	−	0.129050i	$-0.0411926\pi$
$367$	19.8612	+	16.6655i	1.03675	+	0.869933i	0.0451071	+	0.998982i	$0.485637\pi$
$368$	6.86781	+	3.96513i	0.358009	+	0.206697i
$369$	10.7924	+	27.9315i	0.561828	+	1.45405i
$370$	−17.5559	+	6.38982i	−0.912687	+	0.332191i
$371$	−1.08803	+	6.17051i	−0.0564876	+	0.320357i
$372$	10.9619	−	5.24335i	0.568348	−	0.271855i
$373$			13.7506i			0.711977i	0.934490	+	0.355989i	$0.115856\pi$
$373$			13.7506i			0.711977i	−0.934490	+	0.355989i	$0.884144\pi$
$374$	−12.1234	+	4.41257i	−0.626887	+	0.228168i
$375$	8.06223	−	17.7426i	0.416332	−	0.916223i
$376$	2.06754	+	5.68051i	0.106625	+	0.292950i
$377$	−6.51154	+	1.14816i	−0.335361	+	0.0591332i
$378$	−0.726203	+	12.5521i	−0.0373518	+	0.645609i
$379$		−	31.9051i		−	1.63885i	−0.573184	−	0.819426i	$-0.694292\pi$
$379$		−	31.9051i		−	1.63885i	0.573184	−	0.819426i	$-0.305708\pi$
$380$	−9.48228	−	1.96326i	−0.486431	−	0.100713i
$381$	−0.151846	+	0.0726316i	−0.00777930	+	0.00372103i
$382$	9.76140	−	1.72120i	0.499437	−	0.0880641i
$383$	−1.37055	+	1.15003i	−0.0700317	+	0.0587636i	−0.677132	−	0.735862i	$-0.736777\pi$
$383$	−1.37055	+	1.15003i	−0.0700317	+	0.0587636i	0.607100	+	0.794626i	$0.292333\pi$
$384$	−1.23672	−	1.21265i	−0.0631110	−	0.0618829i
$385$	2.53983	+	14.4041i	0.129442	+	0.734099i
$386$	13.9368	+	2.45743i	0.709365	+	0.125080i
$387$	4.15611	+	0.648906i	0.211267	+	0.0329858i
$388$	−10.1046	+	5.83386i	−0.512981	+	0.296170i
$389$	20.6635	+	3.64353i	1.04768	+	0.184734i	0.670885	−	0.741562i	$-0.265915\pi$
$389$	20.6635	+	3.64353i	1.04768	+	0.184734i	0.376796	+	0.926296i	$0.377026\pi$
$390$	0.678705	−	2.63630i	0.0343675	−	0.133494i
$391$	−18.8007	+	32.5637i	−0.950790	+	1.64682i
$392$	1.14512			0.0578374
$393$	18.3445	−	18.7086i	0.925360	−	0.943725i
$394$	9.82813	−	1.73296i	0.495134	−	0.0873055i
$395$	4.04885	+	3.39739i	0.203720	+	0.170941i
$396$	3.94177	−	7.14813i	0.198081	−	0.359207i
$397$	11.5484	+	4.20328i	0.579598	+	0.210956i	0.615148	−	0.788411i	$-0.289096\pi$
$397$	11.5484	+	4.20328i	0.579598	+	0.210956i	−0.0355501	+	0.999368i	$0.511318\pi$
$398$	−9.45900	+	16.3835i	−0.474137	+	0.821229i
$399$	18.1636	+	1.95222i	0.909318	+	0.0977332i
$400$	−0.0324186	−	0.0561507i	−0.00162093	−	0.00280754i
$401$	1.07618	+	6.10333i	0.0537419	+	0.304786i	0.999816	−	0.0191637i	$-0.00610038\pi$
$401$	1.07618	+	6.10333i	0.0537419	+	0.304786i	−0.946074	+	0.323949i	$0.894989\pi$
$402$	−0.552335	−	0.772548i	−0.0275480	−	0.0385312i
$403$	4.66411	−	1.69760i	0.232336	−	0.0845634i
$404$	8.12730	+	9.68574i	0.404348	+	0.481883i
$405$	−16.9089	+	10.6695i	−0.840210	+	0.530169i
$406$	−11.3069	+	19.5841i	−0.561150	+	0.971941i
$407$	−22.8829			−1.13426
$408$	5.74979	−	5.86390i	0.284657	−	0.290306i
$409$	−12.0503	+	14.3609i	−0.595847	+	0.710103i	−0.976719	−	0.214525i	$-0.931180\pi$
$409$	−12.0503	+	14.3609i	−0.595847	+	0.710103i	0.380871	+	0.924628i	$0.375624\pi$
$410$	−19.2030	−	11.0869i	−0.948370	−	0.547542i
$411$	−20.1013	−	13.7828i	−0.991525	−	0.679853i
$412$	−4.49072	+	5.35183i	−0.221242	+	0.263666i
$413$	−7.67490	+	6.44001i	−0.377657	+	0.316892i
$414$	−4.59080	−	23.3437i	−0.225625	−	1.14728i
$415$	1.46468	+	8.30661i	0.0718983	+	0.407756i
$416$	−0.454764	−	0.541967i	−0.0222966	−	0.0265721i
$417$	6.39259	−	9.32320i	0.313047	−	0.456559i
$418$	−10.0913	−	6.23189i	−0.493580	−	0.304812i
$419$	10.7621	−	6.21351i	0.525764	−	0.303550i	−0.213526	−	0.976937i	$-0.568495\pi$
$419$	10.7621	−	6.21351i	0.525764	−	0.303550i	0.739290	+	0.673388i	$0.235161\pi$
$420$	−5.41492	−	7.57383i	−0.264221	−	0.369565i
$421$	−1.20837	+	3.31996i	−0.0588923	+	0.161805i	−0.965650	−	0.259848i	$-0.916328\pi$
$421$	−1.20837	+	3.31996i	−0.0588923	+	0.161805i	0.906757	+	0.421653i	$0.138550\pi$
$422$	−8.49600	+	10.1251i	−0.413579	+	0.492884i
$423$	8.75726	−	15.8807i	0.425792	−	0.772146i
$424$	−0.449657	+	2.55013i	−0.0218373	+	0.123845i
$425$	0.266238	−	0.153713i	0.0129145	−	0.00745617i
$426$	−3.90049	−	8.15449i	−0.188979	−	0.395086i
$427$	−12.5209	−	10.5063i	−0.605927	−	0.508433i
$428$	0.585740	+	0.491494i	0.0283128	+	0.0237573i
$429$	1.88554	−	2.74995i	0.0910349	−	0.132769i
$430$	−2.69760	+	1.55746i	−0.130090	+	0.0751074i
$431$	3.48779	−	19.7802i	0.168001	−	0.952781i	−0.777915	−	0.628369i	$-0.783723\pi$
$431$	3.48779	−	19.7802i	0.168001	−	0.952781i	0.945916	−	0.324411i	$-0.105166\pi$
$432$	−0.300123	+	5.18748i	−0.0144397	+	0.249583i
$433$	14.7894	−	17.6253i	0.710732	−	0.847017i	−0.282963	−	0.959131i	$-0.591317\pi$
$433$	14.7894	−	17.6253i	0.710732	−	0.847017i	0.993695	+	0.112113i	$0.0357619\pi$
$434$	5.80598	−	15.9518i	0.278696	−	0.765710i
$435$	−35.7911	+	3.48597i	−1.71605	+	0.167140i
$436$	−3.84471	+	2.21975i	−0.184128	+	0.106307i
$437$	−34.2049	+	4.99147i	−1.63624	+	0.238774i
$438$	0.487913	+	0.0378603i	0.0233134	+	0.00180904i
$439$	2.48796	+	2.96504i	0.118744	+	0.141514i	0.822142	−	0.569283i	$-0.192779\pi$
$439$	2.48796	+	2.96504i	0.118744	+	0.141514i	−0.703398	+	0.710797i	$0.748335\pi$
$440$	1.04965	+	5.95287i	0.0500402	+	0.283792i
$441$	−2.25949	−	2.58775i	−0.107595	−	0.123226i
$442$	2.56973	−	2.15626i	0.122230	−	0.102563i
$443$	−12.8955	+	15.3682i	−0.612682	+	0.730165i	−0.979794	−	0.200011i	$-0.935902\pi$
$443$	−12.8955	+	15.3682i	−0.612682	+	0.730165i	0.367112	+	0.930177i	$0.380347\pi$
$444$	13.1404	−	6.28536i	0.623614	−	0.298290i
$445$	35.2346	+	20.3427i	1.67028	+	0.964336i
$446$	11.7790	−	14.0376i	0.557749	−	0.664700i
$447$	12.7846	+	3.29133i	0.604689	+	0.155675i
$448$	−2.41969			−0.114319
$449$	14.4457	−	25.0207i	0.681735	−	1.18080i	−0.292716	−	0.956200i	$-0.594559\pi$
$449$	14.4457	−	25.0207i	0.681735	−	1.18080i	0.974451	−	0.224601i	$-0.0721077\pi$
$450$	−0.0629226	+	0.184053i	−0.00296620	+	0.00867635i
$451$	−17.4574	−	20.8049i	−0.822038	−	0.979667i
$452$	6.55330	−	2.38520i	0.308241	−	0.112191i
$453$	−7.40628	+	0.721356i	−0.347977	+	0.0338923i
$454$	0.273893	+	1.55333i	0.0128545	+	0.0729012i
$455$	−1.90151	−	3.29351i	−0.0891441	−	0.154402i
$456$	7.50660	+	0.806807i	0.351529	+	0.0377822i
$457$	13.6445	−	23.6330i	0.638264	−	1.10551i	−0.347549	−	0.937662i	$-0.612986\pi$
$457$	13.6445	−	23.6330i	0.638264	−	1.10551i	0.985814	−	0.167844i	$-0.0536806\pi$
$458$	13.2879	+	4.83640i	0.620902	+	0.225990i
$459$	−24.5964	−	1.42303i	−1.14806	−	0.0664214i
$460$	13.4956	+	11.3242i	0.629236	+	0.527992i
$461$	15.3256	−	2.70232i	0.713785	−	0.125859i	0.195048	−	0.980794i	$-0.437514\pi$
$461$	15.3256	−	2.70232i	0.713785	−	0.125859i	0.518736	+	0.854934i	$0.326403\pi$
$462$	−3.05956	−	10.9855i	−0.142344	−	0.511094i
$463$	−10.6919			−0.496896			−0.248448	−	0.968645i	$-0.579920\pi$
$463$	−10.6919			−0.496896			−0.248448	+	0.968645i	$0.579920\pi$
$464$	−4.67287	+	8.09364i	−0.216932	+	0.375738i
$465$	26.0048	−	7.24255i	1.20594	−	0.335865i
$466$	11.8262	+	2.08527i	0.547836	+	0.0965983i
$467$	−23.5493	+	13.5962i	−1.08973	+	0.629156i	−0.933505	−	0.358565i	$-0.883266\pi$
$467$	−23.5493	+	13.5962i	−1.08973	+	0.629156i	−0.156226	+	0.987721i	$0.549933\pi$
$468$	−0.327420	+	2.09706i	−0.0151350	+	0.0969364i
$469$	−1.30656	−	0.230382i	−0.0603314	−	0.0106381i
$470$	2.33197	+	13.2252i	0.107566	+	0.610035i
$471$	−35.6295	+	9.92309i	−1.64172	+	0.457232i
$472$	−3.17186	+	2.66151i	−0.145997	+	0.122506i
$473$	−3.75726	+	0.662507i	−0.172759	+	0.0304621i
$474$	−3.39867	−	2.33035i	−0.156106	−	0.107037i
$475$	0.262595	+	0.104486i	0.0120487	+	0.00479415i
$476$		−	11.4729i		−	0.525861i
$477$	6.65002	−	4.01565i	0.304483	−	0.183864i
$478$	7.18355	−	1.26665i	0.328568	−	0.0579354i
$479$	−10.5704	−	29.0420i	−0.482975	−	1.32696i	−0.906930	−	0.421281i	$-0.861581\pi$
$479$	−10.5704	−	29.0420i	−0.482975	−	1.32696i	0.423955	−	0.905683i	$-0.360642\pi$
$480$	−2.23786	−	3.13009i	−0.102144	−	0.142868i
$481$	5.59102	−	2.03496i	0.254928	−	0.0927864i
$482$			26.7500i			1.21843i
$483$	−27.4112	−	18.7949i	−1.24725	−	0.855198i
$484$	0.624492	−	3.54167i	0.0283860	−	0.160985i
$485$	−24.3570	+	8.86520i	−1.10599	+	0.402548i
$486$	12.3148	−	9.55744i	0.558613	−	0.433534i
$487$	2.16318	+	1.24891i	0.0980230	+	0.0565936i	0.548210	−	0.836341i	$-0.315309\pi$
$487$	2.16318	+	1.24891i	0.0980230	+	0.0565936i	−0.450187	+	0.892934i	$0.648643\pi$
$488$	−5.17459	−	4.34199i	−0.234242	−	0.196553i
$489$	34.3841	+	15.6242i	1.55490	+	0.706549i
$490$	2.50527	+	0.441746i	0.113176	+	0.0199561i
$491$	24.6041	+	29.3220i	1.11037	+	1.32328i	0.941259	+	0.337684i	$0.109644\pi$
$491$	24.6041	+	29.3220i	1.11037	+	1.32328i	0.169106	+	0.985598i	$0.445912\pi$
$492$	15.7394	+	7.15200i	0.709588	+	0.322437i
$493$	−38.3760	−	22.1564i	−1.72837	−	0.997873i
$494$	3.01982	+	0.625239i	0.135868	+	0.0281308i
$495$	11.3812	−	14.1179i	0.511546	−	0.634552i
$496$	2.39948	−	6.59250i	0.107740	−	0.296012i
$497$	−11.8664	−	4.31903i	−0.532282	−	0.193735i
$498$	−1.76440	−	6.33520i	−0.0790648	−	0.283887i
$499$	26.3243	+	9.58126i	1.17844	+	0.428916i	0.855650	−	0.517555i	$-0.173158\pi$
$499$	26.3243	+	9.58126i	1.17844	+	0.428916i	0.322788	+	0.946471i	$0.395380\pi$
$500$	−3.84829	−	10.5731i	−0.172101	−	0.472843i
$501$	9.80810	+	20.5051i	0.438193	+	0.916100i
$502$		−	0.753526i		−	0.0336315i
$503$	−8.33024	−	22.8872i	−0.371427	−	1.02049i	−0.974810	−	0.223036i	$-0.928403\pi$
$503$	−8.33024	−	22.8872i	−0.371427	−	1.02049i	0.603383	−	0.797452i	$-0.293819\pi$
$504$	4.77439	+	5.46800i	0.212668	+	0.243564i
$505$	14.0443	+	24.3254i	0.624962	+	1.08247i
$506$	10.7890	+	18.6871i	0.479630	+	0.830744i
$507$	5.39762	−	20.9661i	0.239717	−	0.931135i
$508$	−0.0332379	+	0.0913204i	−0.00147469	+	0.00405169i
$509$	−6.88038	+	39.0206i	−0.304968	+	1.72956i	0.318689	+	0.947859i	$0.396757\pi$
$509$	−6.88038	+	39.0206i	−0.304968	+	1.72956i	−0.623657	+	0.781698i	$0.714354\pi$
$510$	14.8413	−	10.6108i	0.657184	−	0.469855i
$511$	0.523719	−	0.439453i	0.0231680	−	0.0194402i
$512$	−1.00000			−0.0441942
$513$	−12.9884	−	18.5554i	−0.573452	−	0.819239i
$514$	13.6846			0.603600
$515$	−11.8892	+	9.97624i	−0.523901	+	0.439606i
$516$	1.97561	−	1.41247i	0.0869715	−	0.0621805i
$517$	−2.85625	+	16.1986i	−0.125618	+	0.712413i
$518$	6.95980	−	19.1219i	0.305796	−	0.840168i
$519$	3.03776	−	11.7996i	0.133343	−	0.517946i
$520$	−0.785850	−	1.36113i	−0.0344618	−	0.0596896i
$521$	4.68512	+	8.11486i	0.205259	+	0.355519i	0.950215	−	0.311595i	$-0.100863\pi$
$521$	4.68512	+	8.11486i	0.205259	+	0.355519i	−0.744956	+	0.667113i	$0.767530\pi$
$522$	27.5103	−	5.41021i	1.20409	−	0.236798i
$523$	−0.966637	−	2.65581i	−0.0422681	−	0.116131i	0.916763	−	0.399432i	$-0.130793\pi$
$523$	−0.966637	−	2.65581i	−0.0422681	−	0.116131i	−0.959031	+	0.283301i	$0.908570\pi$
$524$		−	15.1276i		−	0.660853i
$525$	0.117254	+	0.245135i	0.00511738	+	0.0106986i
$526$	5.25045	+	14.4255i	0.228931	+	0.628982i
$527$	31.2583	+	11.3771i	1.36163	+	0.495594i
$528$	−1.26445	−	4.54007i	−0.0550280	−	0.197581i
$529$	37.4835	+	13.6429i	1.62972	+	0.593169i
$530$	−1.96749	+	5.40564i	−0.0854624	+	0.234806i
$531$	12.2730	+	1.91622i	0.532604	+	0.0831570i
$532$	8.27688	−	6.53727i	0.358848	−	0.283427i
$533$	6.11558	+	3.53083i	0.264895	+	0.152937i
$534$	−28.8794	−	13.1228i	−1.24973	−	0.567880i
$535$	1.09187	+	1.30124i	0.0472055	+	0.0562573i
$536$	−0.539972	−	0.0952116i	−0.0233232	−	0.00411251i
$537$	5.34083	+	2.42688i	0.230474	+	0.104727i
$538$	−16.9549	−	14.2268i	−0.730977	−	0.613362i
$539$	2.69840	+	1.55792i	0.116228	+	0.0671045i
$540$	−2.65774	+	11.2332i	−0.114371	+	0.483402i
$541$	−4.53832	+	1.65181i	−0.195118	+	0.0710170i	−0.437731	−	0.899106i	$-0.644218\pi$
$541$	−4.53832	+	1.65181i	−0.195118	+	0.0710170i	0.242613	+	0.970123i	$0.421995\pi$
$542$	2.35314	−	13.3453i	0.101076	−	0.573231i
$543$	28.9429	+	19.8451i	1.24206	+	0.851636i
$544$		−	4.74150i		−	0.203290i
$545$	−9.26765	+	3.37315i	−0.396983	+	0.144490i
$546$	1.72449	+	2.41203i	0.0738013	+	0.103226i
$547$	−12.8933	−	35.4241i	−0.551279	−	1.51463i	−0.831966	−	0.554827i	$-0.812785\pi$
$547$	−12.8933	−	35.4241i	−0.551279	−	1.51463i	0.280687	−	0.959799i	$-0.409438\pi$
$548$	−13.8578	+	2.44350i	−0.591976	+	0.104381i
$549$	0.398187	+	20.2609i	0.0169942	+	0.864715i
$550$		−	0.176420i		−	0.00752259i
$551$	−5.88239	−	40.3102i	−0.250598	−	1.71727i
$552$	−11.3284	−	7.76750i	−0.482170	−	0.330607i
$553$	−5.66941	+	0.999670i	−0.241088	+	0.0425103i
$554$	14.3082	−	12.0060i	0.607897	−	0.510086i
$555$	31.1728	−	8.68187i	1.32321	−	0.368525i
$556$	−1.13332	−	6.42739i	−0.0480636	−	0.272582i
$557$	−22.2059	−	3.91550i	−0.940894	−	0.165905i	−0.317893	−	0.948127i	$-0.602975\pi$
$557$	−22.2059	−	3.91550i	−0.940894	−	0.165905i	−0.623000	+	0.782222i	$0.714086\pi$
$558$	−19.6323	+	7.58565i	−0.831100	+	0.321126i
$559$	0.859103	−	0.496004i	0.0363362	−	0.0209787i
$560$	−5.29372	−	0.933426i	−0.223701	−	0.0394444i
$561$	21.5267	−	5.99537i	0.908859	−	0.253125i
$562$	−8.61812	+	14.9270i	−0.363534	+	0.629659i
$563$	−15.6527			−0.659682			−0.329841	−	0.944036i	$-0.606995\pi$
$563$	−15.6527			−0.659682			−0.329841	+	0.944036i	$0.606995\pi$
$564$	−2.80917	−	10.0865i	−0.118287	−	0.424718i
$565$	15.2572	−	2.69026i	0.641877	−	0.113180i
$566$	20.3975	+	17.1156i	0.857372	+	0.719420i
$567$	2.93600	−	21.5783i	0.123301	−	0.906205i
$568$	−4.90412	−	1.78496i	−0.205772	−	0.0748951i
$569$	−20.7950	+	36.0179i	−0.871770	+	1.50995i	−0.0116060	+	0.999933i	$0.503694\pi$
$569$	−20.7950	+	36.0179i	−0.871770	+	1.50995i	−0.860164	+	0.510017i	$0.829639\pi$
$570$	16.1115	+	4.66088i	0.674836	+	0.195223i
$571$	15.5016	+	26.8496i	0.648723	+	1.12362i	0.983428	+	0.181298i	$0.0580298\pi$
$571$	15.5016	+	26.8496i	0.648723	+	1.12362i	−0.334706	+	0.942323i	$0.608637\pi$
$572$	−0.334282	−	1.89581i	−0.0139770	−	0.0792677i
$573$	−17.0872	+	1.66426i	−0.713828	+	0.0695254i
$574$	22.6952	−	8.26036i	0.947278	−	0.344781i
$575$	−0.330507	−	0.393882i	−0.0137831	−	0.0164260i
$576$	1.97315	+	2.25980i	0.0822145	+	0.0941583i
$577$	−10.6373	+	18.4244i	−0.442837	+	0.767017i	−0.997899	−	0.0647926i	$-0.979361\pi$
$577$	−10.6373	+	18.4244i	−0.442837	+	0.767017i	0.555061	+	0.831809i	$0.312695\pi$
$578$	5.48179			0.228012
$579$	−23.7376	−	6.11115i	−0.986501	−	0.253971i
$580$	−13.3454	+	15.9044i	−0.554138	+	0.660396i
$581$	−7.95630	−	4.59357i	−0.330083	−	0.190574i
$582$	18.2309	−	8.72027i	0.755694	−	0.361467i
$583$	−4.52900	+	5.39745i	−0.187572	+	0.223540i
$584$	0.216441	−	0.181616i	0.00895639	−	0.00751531i
$585$	−1.52529	+	4.46157i	−0.0630628	+	0.184463i
$586$	−4.99182	−	28.3100i	−0.206210	−	1.16948i
$587$	2.62498	+	3.12833i	0.108344	+	0.129120i	0.817491	−	0.575941i	$-0.195364\pi$
$587$	2.62498	+	3.12833i	0.108344	+	0.129120i	−0.709147	+	0.705061i	$0.750920\pi$
$588$	−1.97747	−	0.153444i	−0.0815493	−	0.00632794i
$589$	9.60323	+	29.0333i	0.395694	+	1.19630i
$590$	−7.96602	+	4.59918i	−0.327956	+	0.189345i
$591$	−17.2040	+	1.67564i	−0.707679	+	0.0689264i
$592$	2.87633	−	7.90264i	0.118216	−	0.324796i
$593$	−6.73046	+	8.02105i	−0.276387	+	0.329385i	−0.886325	−	0.463064i	$-0.846750\pi$
$593$	−6.73046	+	8.02105i	−0.276387	+	0.329385i	0.609938	+	0.792449i	$0.291194\pi$
$594$	−7.76471	+	11.8156i	−0.318590	+	0.484801i
$595$	4.42584	−	25.1002i	0.181442	−	1.02901i
$596$	6.60072	−	3.81093i	0.270376	−	0.156102i
$597$	18.5297	−	27.0245i	0.758371	−	1.10604i
$598$	−4.29794	−	3.60640i	−0.175756	−	0.147477i
$599$	−23.5732	−	19.7802i	−0.963173	−	0.808198i	0.0182934	−	0.999833i	$-0.494177\pi$
$599$	−23.5732	−	19.7802i	−0.963173	−	0.808198i	−0.981466	+	0.191635i	$0.938621\pi$
$600$	0.0484584	+	0.101308i	0.00197830	+	0.00413590i
$601$	1.73100	−	0.999396i	0.0706091	−	0.0407662i	−0.464280	−	0.885689i	$-0.653687\pi$
$601$	1.73100	−	0.999396i	0.0706091	−	0.0407662i	0.534889	+	0.844922i	$0.320353\pi$
$602$	0.589149	−	3.34123i	0.0240119	−	0.136178i
$603$	0.850285	+	1.40809i	0.0346263	+	0.0573420i
$604$	−2.76158	+	3.29112i	−0.112367	+	0.133914i
$605$	2.73249	−	7.50747i	0.111092	−	0.305222i
$606$	−12.7368	−	17.8150i	−0.517398	−	0.723683i
$607$	37.0207	−	21.3739i	1.50262	−	0.867541i	0.502629	−	0.864502i	$-0.332366\pi$
$607$	37.0207	−	21.3739i	1.50262	−	0.867541i	0.999995	−	0.00303888i	$-0.000967308\pi$
$608$	3.42064	−	2.70170i	0.138725	−	0.109568i
$609$	22.1496	−	32.3038i	0.897547	−	1.30902i
$610$	−9.64583	−	11.4955i	−0.390548	−	0.465437i
$611$	−0.742661	−	4.21184i	−0.0300448	−	0.170393i
$612$	−10.7148	+	9.35567i	−0.433121	+	0.378180i
$613$	7.55686	−	6.34096i	0.305219	−	0.256109i	−0.477294	−	0.878744i	$-0.658382\pi$
$613$	7.55686	−	6.34096i	0.305219	−	0.256109i	0.782513	+	0.622635i	$0.213938\pi$
$614$	13.4216	−	15.9953i	0.541654	−	0.645518i
$615$	31.6753	+	21.7187i	1.27727	+	0.875781i
$616$	−5.70182	−	3.29195i	−0.229733	−	0.132636i
$617$	−7.85014	+	9.35543i	−0.316035	+	0.376636i	−0.900554	−	0.434744i	$-0.856839\pi$
$617$	−7.85014	+	9.35543i	−0.316035	+	0.376636i	0.584519	+	0.811380i	$0.301283\pi$
$618$	8.47198	−	8.64012i	0.340793	−	0.347556i
$619$	−39.4613			−1.58608			−0.793042	−	0.609167i	$-0.791504\pi$
$619$	−39.4613			−1.58608			−0.793042	+	0.609167i	$0.791504\pi$
$620$	7.79265	−	13.4973i	0.312961	−	0.542064i
$621$	4.79966	+	40.9264i	0.192604	+	1.64232i
$622$	6.07457	+	7.23939i	0.243568	+	0.290273i
$623$	−41.6421	+	15.1565i	−1.66835	+	0.607232i
$624$	0.712691	+	0.996838i	0.0285305	+	0.0399055i
$625$	−4.28418	−	24.2968i	−0.171367	−	0.971872i
$626$	6.55576	+	11.3549i	0.262021	+	0.453834i
$627$	16.5911	+	12.1138i	0.662586	+	0.483779i
$628$	−10.6768	+	18.4927i	−0.426050	+	0.737941i
$629$	37.4703	+	13.6381i	1.49404	+	0.543786i
$630$	8.33594	+	13.8045i	0.332112	+	0.549986i
$631$	−13.6437	−	11.4484i	−0.543145	−	0.455753i	0.329467	−	0.944167i	$-0.393131\pi$
$631$	−13.6437	−	11.4484i	−0.543145	−	0.455753i	−0.872612	+	0.488414i	$0.837576\pi$
$632$	−2.34304	+	0.413140i	−0.0932010	+	0.0164338i
$633$	16.0282	−	16.3463i	0.637062	−	0.649705i
$634$	−5.90059			−0.234342
$635$	−0.107945	+	0.186966i	−0.00428367	+	0.00741953i
$636$	1.11821	−	4.34346i	0.0443398	−	0.172230i
$637$	−0.797852	−	0.140683i	−0.0316120	−	0.00557405i
$638$	−22.0226	+	12.7147i	−0.871882	+	0.503381i
$639$	5.64292	+	14.6043i	0.223230	+	0.577738i
$640$	−2.18777	−	0.385763i	−0.0864793	−	0.0152486i
$641$	1.67580	+	9.50396i	0.0661903	+	0.375384i	0.999852	+	0.0172267i	$0.00548370\pi$
$641$	1.67580	+	9.50396i	0.0661903	+	0.375384i	−0.933661	+	0.358157i	$0.883405\pi$
$642$	−0.945632	−	0.927230i	−0.0373211	−	0.0365948i
$643$	−18.2426	+	15.3074i	−0.719418	+	0.603663i	−0.927224	−	0.374507i	$-0.877812\pi$
$643$	−18.2426	+	15.3074i	−0.719418	+	0.603663i	0.207806	+	0.978170i	$0.433368\pi$
$644$	−18.8972	+	3.33209i	−0.744655	+	0.131303i
$645$	4.86707	−	2.32804i	0.191641	−	0.0916665i
$646$	12.8101	+	16.2190i	0.504007	+	0.638127i
$647$			34.9679i			1.37473i	0.726312	+	0.687365i	$0.241233\pi$
$647$			34.9679i			1.37473i	−0.726312	+	0.687365i	$0.758767\pi$
$648$	1.21338	−	8.91783i	0.0476662	−	0.350325i
$649$	−11.0952	+	1.95639i	−0.435525	+	0.0767948i
$650$	0.0156890	+	0.0431052i	0.000615373	+	0.00169072i
$651$	−12.1636	+	26.7685i	−0.476730	+	1.04914i
$652$	20.4901	−	7.45777i	0.802452	−	0.292069i
$653$		−	21.7829i		−	0.852429i	−0.904622	−	0.426215i	$-0.859847\pi$
$653$		−	21.7829i		−	0.852429i	0.904622	−	0.426215i	$-0.140153\pi$
$654$	6.93672	−	3.31801i	0.271247	−	0.129744i
$655$	5.83568	−	33.0958i	0.228019	−	1.29316i
$656$	9.37938	−	3.41382i	0.366203	−	0.133287i
$657$	−0.837485	−	0.130759i	−0.0326734	−	0.00510139i
$658$	−12.6675	−	7.31359i	−0.493831	−	0.285113i
$659$	9.96031	+	8.35769i	0.387999	+	0.325569i	0.815833	−	0.578288i	$-0.196279\pi$
$659$	9.96031	+	8.35769i	0.387999	+	0.325569i	−0.427834	+	0.903857i	$0.640723\pi$
$660$	−1.01493	−	10.4204i	−0.0395060	−	0.405614i
$661$	25.6775	+	4.52764i	0.998741	+	0.176105i	0.649038	−	0.760756i	$-0.275172\pi$
$661$	25.6775	+	4.52764i	0.998741	+	0.176105i	0.349703	+	0.936861i	$0.386283\pi$
$662$	−3.22800	−	3.84698i	−0.125460	−	0.149517i
$663$	−4.72650	+	3.37922i	−0.183562	+	0.131238i
$664$	−3.28816	−	1.89842i	−0.127605	−	0.0736729i
$665$	20.6298	−	11.1091i	0.799988	−	0.430794i
$666$	−23.5338	+	9.09315i	−0.911916	+	0.352352i
$667$	−25.3485	+	69.6445i	−0.981499	+	2.69665i
$668$	12.3318	+	4.48841i	0.477132	+	0.173662i
$669$	−22.2216	+	22.6626i	−0.859137	+	0.876187i
$670$	−1.14461	−	0.416603i	−0.0442200	−	0.0160948i
$671$	−6.28633	−	17.2716i	−0.242681	−	0.666761i
$672$	4.17846	+	0.324233i	0.161187	+	0.0125076i
$673$			23.6078i			0.910013i	0.890488	+	0.455006i	$0.150363\pi$
$673$			23.6078i			0.910013i	−0.890488	+	0.455006i	$0.849637\pi$
$674$	4.07843	+	11.2054i	0.157095	+	0.431616i
$675$	0.133321	−	0.309403i	0.00513154	−	0.0119089i
$676$	−6.24973	−	10.8249i	−0.240374	−	0.416340i
$677$	3.35551	+	5.81192i	0.128963	+	0.223370i	0.923275	−	0.384140i	$-0.125502\pi$
$677$	3.35551	+	5.81192i	0.128963	+	0.223370i	−0.794312	+	0.607510i	$0.792169\pi$
$678$	−11.6362	+	3.24078i	−0.446887	+	0.124462i
$679$	9.65599	−	26.5296i	0.370563	−	1.01811i
$680$	1.82910	−	10.3733i	0.0701426	−	0.397799i
$681$	−0.264833	−	2.71908i	−0.0101484	−	0.104195i
$682$	14.6232	−	12.2703i	0.559952	−	0.469855i
$683$	21.1763			0.810288			0.405144	−	0.914253i	$-0.367221\pi$
$683$	21.1763			0.810288			0.405144	+	0.914253i	$0.367221\pi$
$684$	−12.8547	−	2.39911i	−0.491513	−	0.0917324i
$685$	−31.2603			−1.19440
$686$	−15.0977	+	12.6685i	−0.576432	+	0.483684i
$687$	−22.2983	−	10.1323i	−0.850732	−	0.386573i
$688$	0.243482	−	1.38085i	0.00928265	−	0.0526445i
$689$	0.626587	−	1.72153i	0.0238711	−	0.0655852i
$690$	−21.7876	−	21.3636i	−0.829440	−	0.813299i
$691$	12.9744	+	22.4723i	0.493569	+	0.854886i	0.999973	−	0.00741014i	$-0.00235874\pi$
$691$	12.9744	+	22.4723i	0.493569	+	0.854886i	−0.506404	+	0.862297i	$0.669025\pi$
$692$	−3.51733	−	6.09219i	−0.133709	−	0.231590i
$693$	3.81139	+	19.3805i	0.144783	+	0.736203i
$694$	12.4134	+	34.1054i	0.471205	+	1.29462i
$695$		−	14.4989i		−	0.549973i
$696$	9.15392	−	13.3504i	0.346978	−	0.506047i
$697$	16.1866	+	44.4723i	0.613111	+	1.68451i
$698$	27.1610	+	9.88581i	1.02806	+	0.374183i
$699$	−20.1427	−	5.18565i	−0.761866	−	0.196139i
$700$	0.147424	+	0.0536581i	0.00557212	+	0.00202809i
$701$	−4.81377	+	13.2257i	−0.181814	+	0.499529i	−0.996799	−	0.0799534i	$-0.974523\pi$
$701$	−4.81377	+	13.2257i	−0.181814	+	0.499529i	0.814985	+	0.579482i	$0.196745\pi$
$702$	0.846409	−	3.57745i	0.0319457	−	0.135022i
$703$	11.5117	+	34.8031i	0.434172	+	1.31262i
$704$	−2.35643	−	1.36049i	−0.0888113	−	0.0512753i
$705$	−2.25482	−	23.1506i	−0.0849215	−	0.871903i
$706$	9.09375	+	10.8375i	0.342248	+	0.407875i
$707$	−30.1293	−	5.31261i	−1.13313	−	0.199801i
$708$	5.83399	−	4.17103i	0.219255	−	0.156757i
$709$	−3.24458	−	2.72253i	−0.121853	−	0.102247i	0.579825	−	0.814741i	$-0.303121\pi$
$709$	−3.24458	−	2.72253i	−0.121853	−	0.102247i	−0.701678	+	0.712494i	$0.747565\pi$
$710$	−10.0405	−	5.79691i	−0.376815	−	0.217554i
$711$	5.55677	+	4.47960i	0.208395	+	0.167998i
$712$	−17.2097	+	6.26382i	−0.644961	+	0.234747i
$713$	9.66101	−	54.7903i	0.361808	−	2.05191i
$714$	−1.53735	+	19.8121i	−0.0575339	+	0.741451i
$715$		−	4.27655i		−	0.159934i
$716$	3.18269	−	1.15840i	0.118943	−	0.0432916i
$717$	−12.5747	+	1.22475i	−0.469611	+	0.0457391i
$718$	2.03698	+	5.59655i	0.0760193	+	0.208861i
$719$	−12.1693	+	2.14577i	−0.453837	+	0.0800237i	−0.395894	−	0.918296i	$-0.629565\pi$
$719$	−12.1693	+	2.14577i	−0.453837	+	0.0800237i	−0.0579428	+	0.998320i	$0.518454\pi$
$720$	3.44505	+	5.70509i	0.128389	+	0.212616i
$721$		−	16.9047i		−	0.629564i
$722$	−4.40161	+	18.4831i	−0.163811	+	0.687871i
$723$	3.58445	−	46.1935i	0.133307	−	1.71796i
$724$	19.9532	−	3.51828i	0.741553	−	0.130756i
$725$	0.464186	−	0.389498i	0.0172394	−	0.0144656i
$726$	−1.55299	+	6.03229i	−0.0576368	+	0.223879i
$727$	1.76356	+	10.0017i	0.0654070	+	0.370941i	0.999889	+	0.0149299i	$0.00475251\pi$
$727$	1.76356	+	10.0017i	0.0654070	+	0.370941i	−0.934482	+	0.356012i	$0.884136\pi$
$728$	1.68589	+	0.297268i	0.0624832	+	0.0110175i
$729$	−22.5467	+	14.8542i	−0.835062	+	0.550155i
$730$	0.543584	−	0.313839i	0.0201190	−	0.0116157i
$731$	6.54731	+	1.15447i	0.242161	+	0.0426995i
$732$	8.35396	+	8.19140i	0.308771	+	0.302763i
$733$	21.7492	−	37.6708i	0.803327	−	1.39140i	−0.114088	−	0.993471i	$-0.536395\pi$
$733$	21.7492	−	37.6708i	0.803327	−	1.39140i	0.917415	−	0.397932i	$-0.130272\pi$
$734$	−25.9269			−0.956981
$735$	−4.26705	−	1.09853i	−0.157393	−	0.0405201i
$736$	−7.80979	+	1.37708i	−0.287873	+	0.0507597i
$737$	−1.14287	−	0.958984i	−0.0420982	−	0.0353246i
$738$	−26.2214	−	14.4596i	−0.965225	−	0.532264i
$739$	−20.7892	−	7.56666i	−0.764744	−	0.278344i	−0.0699479	−	0.997551i	$-0.522283\pi$
$739$	−20.7892	−	7.56666i	−0.764744	−	0.278344i	−0.694796	+	0.719206i	$0.744506\pi$
$740$	9.34129	−	16.1796i	0.343393	−	0.594774i
$741$	−5.13102	−	1.48435i	−0.188493	−	0.0545289i
$742$	−3.13285	−	5.42626i	−0.115011	−	0.199204i
$743$	2.49107	+	14.1276i	0.0913885	+	0.518290i	0.995794	+	0.0916167i	$0.0292035\pi$
$743$	2.49107	+	14.1276i	0.0913885	+	0.518290i	−0.904406	+	0.426673i	$0.859685\pi$
$744$	−5.02694	+	11.0628i	−0.184297	+	0.405582i
$745$	15.9110	−	5.79113i	0.582934	−	0.212170i
$746$	−8.83869	−	10.5335i	−0.323608	−	0.385660i
$747$	2.19797	+	11.1764i	0.0804196	+	0.408924i
$748$	6.45074	−	11.1730i	0.235862	−	0.408526i
$749$	−1.85016			−0.0676035
$750$	5.22868	+	18.7739i	0.190925	+	0.685526i
$751$	−19.2162	+	22.9009i	−0.701208	+	0.835667i	−0.992663	−	0.120918i	$-0.961416\pi$
$751$	−19.2162	+	22.9009i	−0.701208	+	0.835667i	0.291455	+	0.956585i	$0.405861\pi$
$752$	−5.23519	−	3.02254i	−0.190908	−	0.110221i
$753$	−0.100971	+	1.30123i	−0.00367959	+	0.0474196i
$754$	4.25010	−	5.06508i	0.154780	−	0.184459i
$755$	−7.31130	+	6.13491i	−0.266085	+	0.223272i
$756$	−7.51201	−	10.0822i	−0.273209	−	0.366687i
$757$	3.87775	+	21.9918i	0.140939	+	0.799307i	0.970538	+	0.240947i	$0.0774580\pi$
$757$	3.87775	+	21.9918i	0.140939	+	0.799307i	−0.829599	+	0.558360i	$0.811431\pi$
$758$	20.5082	+	24.4407i	0.744891	+	0.887726i
$759$	−16.1271	−	33.7158i	−0.585376	−	1.22380i
$760$	8.52581	−	4.59115i	0.309264	−	0.166539i
$761$	4.46023	−	2.57511i	0.161683	−	0.0933478i	−0.416975	−	0.908918i	$-0.636910\pi$
$761$	4.46023	−	2.57511i	0.161683	−	0.0933478i	0.578658	+	0.815570i	$0.303576\pi$
$762$	0.0696340	−	0.153244i	0.00252257	−	0.00555143i
$763$	3.67404	−	10.0943i	0.133009	−	0.365440i
$764$	−6.37130	+	7.59302i	−0.230506	+	0.274706i
$765$	−27.0507	+	16.3347i	−0.978019	+	0.590582i
$766$	0.310678	−	1.76194i	0.0112253	−	0.0636616i
$767$	2.53694	−	1.46470i	0.0916034	−	0.0528873i
$768$	1.72686	+	0.133998i	0.0623127	+	0.00483524i
$769$	12.3995	+	10.4044i	0.447138	+	0.375193i	0.838373	−	0.545098i	$-0.183507\pi$
$769$	12.3995	+	10.4044i	0.447138	+	0.375193i	−0.391234	+	0.920291i	$0.627952\pi$
$770$	−11.2044	−	9.40159i	−0.403778	−	0.338810i
$771$	−23.6313	−	1.83371i	−0.851061	−	0.0660393i
$772$	−12.2558	+	7.07590i	−0.441097	+	0.254667i
$773$	8.28337	−	46.9773i	0.297932	−	1.68966i	−0.357109	−	0.934063i	$-0.616238\pi$
$773$	8.28337	−	46.9773i	0.297932	−	1.68966i	0.655041	−	0.755593i	$-0.272651\pi$
$774$	−3.60088	+	2.17441i	−0.129431	+	0.0781574i
$775$	−0.292386	+	0.348452i	−0.0105028	+	0.0125168i
$776$	3.99060	−	10.9641i	0.143254	−	0.393588i
$777$	−14.5809	+	32.0882i	−0.523087	+	1.15116i
$778$	−18.1712	+	10.4911i	−0.651468	+	0.376125i
$779$	−22.8604	+	37.0177i	−0.819060	+	1.32630i
$780$	1.17466	+	2.45579i	0.0420597	+	0.0879312i
$781$	−9.12782	−	10.8781i	−0.326619	−	0.389250i
$782$	−6.52940	−	37.0301i	−0.233491	−	1.32419i
$783$	−48.2313	+	5.65634i	−1.72365	+	0.202141i
$784$	−0.877215	+	0.736070i	−0.0313291	+	0.0262882i
$785$	−30.4922	+	36.3392i	−1.08831	+	1.29700i
$786$	−2.02707	+	26.1233i	−0.0723033	+	0.931787i
$787$	39.5344	+	22.8252i	1.40925	+	0.813630i	0.995316	−	0.0966776i	$-0.0308216\pi$
$787$	39.5344	+	22.8252i	1.40925	+	0.813630i	0.413933	+	0.910308i	$0.364155\pi$
$788$	−6.41486	+	7.64493i	−0.228520	+	0.272339i
$789$	−7.13381	−	25.6144i	−0.253970	−	0.911896i
$790$	−5.28540			−0.188046
$791$	−8.43729	+	14.6138i	−0.299995	+	0.519607i
$792$	1.57516	+	8.00950i	0.0559709	+	0.284605i
$793$	3.07191	+	3.66095i	0.109087	+	0.130004i
$794$	−11.5484	+	4.20328i	−0.409838	+	0.149169i
$795$	4.12193	−	9.07115i	0.146190	−	0.321720i
$796$	−3.28507	−	18.6306i	−0.116436	−	0.660344i
$797$	−11.0400	−	19.1218i	−0.391056	−	0.677328i	0.601533	−	0.798848i	$-0.294557\pi$
$797$	−11.0400	−	19.1218i	−0.391056	−	0.677328i	−0.992589	+	0.121519i	$0.961223\pi$
$798$	−15.1690	+	10.1799i	−0.536977	+	0.360363i
$799$	14.3313	−	24.8226i	0.507006	−	0.878161i
$800$	0.0609271	+	0.0221757i	0.00215410	+	0.000784028i
$801$	48.1123	+	26.5310i	1.69996	+	0.937428i
$802$	−4.74755	−	3.98366i	−0.167642	−	0.140668i
$803$	0.757114	−	0.133500i	0.0267180	−	0.00471110i
$804$	0.919697	+	0.236772i	0.0324352	+	0.00835031i
$805$	−42.6282			−1.50245
$806$	−2.48172	+	4.29847i	−0.0874150	+	0.151407i
$807$	27.3723	+	26.8397i	0.963551	+	0.944801i
$808$	−12.4517	−	2.19558i	−0.438051	−	0.0772402i
$809$	24.3814	−	14.0766i	0.857203	−	0.494906i	−0.00587175	−	0.999983i	$-0.501869\pi$
$809$	24.3814	−	14.0766i	0.857203	−	0.494906i	0.863075	+	0.505076i	$0.168536\pi$
$810$	6.09478	−	19.0421i	0.214149	−	0.669071i
$811$	−9.49909	−	1.67495i	−0.333558	−	0.0588153i	0.00436094	−	0.999990i	$-0.498612\pi$
$811$	−9.49909	−	1.67495i	−0.333558	−	0.0588153i	−0.337919	+	0.941175i	$0.609723\pi$
$812$	−3.92683	−	22.2702i	−0.137805	−	0.781530i
$813$	−5.85179	+	22.7302i	−0.205231	+	0.797183i
$814$	17.5293	−	14.7088i	0.614401	−	0.515544i
$815$	47.7045	−	8.41159i	1.67102	−	0.294645i
$816$	−0.635352	+	8.18790i	−0.0222418	+	0.286634i
$817$	2.89779	+	5.38122i	0.101381	+	0.188265i
$818$		−	18.7469i		−	0.655470i
$819$	−2.65474	−	4.39632i	−0.0927642	−	0.153620i
$820$	21.8369	−	3.85043i	0.762577	−	0.134463i
$821$	10.9275	+	30.0231i	0.381372	+	1.04781i	0.970779	+	0.239975i	$0.0771394\pi$
$821$	10.9275	+	30.0231i	0.381372	+	1.04781i	−0.589407	+	0.807837i	$0.700638\pi$
$822$	24.2579	−	2.36267i	0.846091	−	0.0824075i
$823$	−15.7280	+	5.72453i	−0.548244	+	0.199545i	−0.601266	−	0.799049i	$-0.705337\pi$
$823$	−15.7280	+	5.72453i	−0.548244	+	0.199545i	0.0530221	+	0.998593i	$0.483115\pi$
$824$		−	6.98632i		−	0.243380i
$825$	−0.0236400	+	0.304653i	−0.000823040	+	0.0106067i
$826$	1.73976	−	9.86667i	0.0605340	−	0.343305i
$827$	−14.0633	+	5.11864i	−0.489030	+	0.177992i	−0.574754	−	0.818327i	$-0.694902\pi$
$827$	−14.0633	+	5.11864i	−0.489030	+	0.177992i	0.0857234	+	0.996319i	$0.472680\pi$
$828$	18.5218	+	14.9314i	0.643676	+	0.518901i
$829$	−47.3954	−	27.3638i	−1.64611	−	0.950382i	−0.978597	−	0.205785i	$-0.934025\pi$
$829$	−47.3954	−	27.3638i	−1.64611	−	0.950382i	−0.667514	−	0.744598i	$-0.732641\pi$
$830$	−6.46140	−	5.42176i	−0.224278	−	0.188192i
$831$	−26.3170	+	18.8154i	−0.912928	+	0.652699i
$832$	0.696739	+	0.122854i	0.0241551	+	0.00425919i
$833$	−3.49008	−	4.15931i	−0.120924	−	0.144112i
$834$	1.09583	+	11.2511i	0.0379455	+	0.389593i
$835$	25.2477	+	14.5768i	0.873733	+	0.504450i
$836$	11.7361	−	1.71264i	0.405903	−	0.0592327i
$837$	34.9186	−	10.4687i	1.20696	−	0.361850i
$838$	−4.25029	+	11.6776i	−0.146824	+	0.403395i
$839$	−12.7286	−	4.63283i	−0.439440	−	0.159943i	0.112819	−	0.993616i	$-0.464012\pi$
$839$	−12.7286	−	4.63283i	−0.439440	−	0.159943i	−0.552259	+	0.833673i	$0.686234\pi$
$840$	9.01644	+	2.32124i	0.311097	+	0.0800905i
$841$	−54.8242	−	19.9544i	−1.89049	−	0.688083i
$842$	−1.20837	−	3.31996i	−0.0416431	−	0.114414i
$843$	16.8825	−	24.6221i	0.581464	−	0.848029i
$844$		−	13.2174i		−	0.454963i
$845$	−9.49716	−	26.0932i	−0.326712	−	0.897634i
$846$	3.49947	+	17.7944i	0.120314	+	0.611783i
$847$	4.35097	+	7.53610i	0.149501	+	0.258943i
$848$	−1.29473	−	2.24255i	−0.0444614	−	0.0770094i
$849$	−32.9302	−	32.2894i	−1.13016	−	1.10817i
$850$	−0.105146	+	0.288886i	−0.00360647	+	0.00990870i
$851$	11.5810	−	65.6788i	0.396990	−	2.25144i
$852$	8.22955	+	3.73951i	0.281940	+	0.128114i
$853$	22.4305	−	18.8214i	0.768004	−	0.644432i	−0.172193	−	0.985063i	$-0.555085\pi$
$853$	22.4305	−	18.8214i	0.768004	−	0.644432i	0.940197	+	0.340631i	$0.110641\pi$
$854$	16.3448			0.559309
$855$	−27.1978	−	10.2076i	−0.930143	−	0.349093i
$856$	−0.764630			−0.0261345
$857$	39.7280	−	33.3358i	1.35708	−	1.13873i	0.380212	−	0.924899i	$-0.375851\pi$
$857$	39.7280	−	33.3358i	1.35708	−	1.13873i	0.976871	−	0.213828i	$-0.0685934\pi$
$858$	0.323224	+	3.31859i	0.0110347	+	0.113295i
$859$	−6.92548	+	39.2763i	−0.236294	+	1.34009i	0.603577	+	0.797305i	$0.293742\pi$
$859$	−6.92548	+	39.2763i	−0.236294	+	1.34009i	−0.839871	+	0.542786i	$0.817369\pi$
$860$	1.06537	−	2.92707i	0.0363287	−	0.0998122i
$861$	−40.2982	+	11.2234i	−1.37336	+	0.382492i
$862$	10.0427	+	17.3945i	0.342055	+	0.592457i
$863$	26.6811	+	46.2130i	0.908235	+	1.57311i	0.816515	+	0.577324i	$0.195903\pi$
$863$	26.6811	+	46.2130i	0.908235	+	1.57311i	0.0917200	+	0.995785i	$0.470764\pi$
$864$	−3.10454	−	4.16675i	−0.105619	−	0.141756i
$865$	−5.34497	−	14.6852i	−0.181734	−	0.499311i
$866$			23.0082i			0.781850i
$867$	−9.46628	−	0.734549i	−0.321492	−	0.0249466i
$868$	5.80598	+	15.9518i	0.197068	+	0.541439i
$869$	−6.08328	−	2.21413i	−0.206361	−	0.0751093i
$870$	25.1768	−	25.6765i	0.853573	−	0.870514i
$871$	0.364522	+	0.132675i	0.0123514	+	0.00449553i
$872$	1.51840	−	4.17176i	0.0514194	−	0.141274i
$873$	−32.6507	+	12.6158i	−1.10506	+	0.426980i
$874$	22.9941	−	25.8102i	0.777785	−	0.873043i
$875$	23.5779	+	13.6127i	0.797080	+	0.460194i
$876$	−0.398099	+	0.284622i	−0.0134505	+	0.00961648i
$877$	−29.3001	−	34.9185i	−0.989395	−	1.17912i	−0.983825	−	0.179131i	$-0.942672\pi$
$877$	−29.3001	−	34.9185i	−0.989395	−	1.17912i	−0.00556975	−	0.999984i	$-0.501773\pi$
$878$	−3.81178	−	0.672120i	−0.128641	−	0.0226829i
$879$	4.82668	+	49.5563i	0.162800	+	1.67149i
$880$	−4.63051	−	3.88546i	−0.156094	−	0.130979i
$881$	11.2839	+	6.51477i	0.380165	+	0.219488i	0.677890	−	0.735163i	$-0.262895\pi$
$881$	11.2839	+	6.51477i	0.380165	+	0.219488i	−0.297725	+	0.954652i	$0.596228\pi$
$882$	3.39424	+	0.529953i	0.114290	+	0.0178445i
$883$	−54.9495	+	20.0000i	−1.84920	+	0.673053i	−0.863542	+	0.504277i	$0.831759\pi$
$883$	−54.9495	+	20.0000i	−1.84920	+	0.673053i	−0.985654	+	0.168776i	$0.946019\pi$
$884$	−0.582511	+	3.30359i	−0.0195920	+	0.111112i
$885$	14.3725	−	6.87471i	0.483126	−	0.231091i
$886$		−	20.0618i		−	0.673988i
$887$	12.0239	−	4.37634i	0.403723	−	0.146943i	−0.132174	−	0.991227i	$-0.542196\pi$
$887$	12.0239	−	4.37634i	0.403723	−	0.146943i	0.535897	+	0.844283i	$0.319974\pi$
$888$	−6.02595	+	13.2613i	−0.202218	+	0.445021i
$889$	−0.0804253	−	0.220967i	−0.00269738	−	0.00741098i
$890$	−40.0673	+	7.06494i	−1.34306	+	0.236817i
$891$	14.9918	−	19.3635i	0.502245	−	0.648700i
$892$			18.3248i			0.613559i
$893$	26.0737	−	3.80489i	0.872523	−	0.127326i
$894$	−11.9092	+	5.69645i	−0.398302	+	0.190518i
$895$	7.40987	−	1.30656i	0.247685	−	0.0436735i
$896$	1.85359	−	1.55534i	0.0619240	−	0.0519604i
$897$	6.93869	+	6.80366i	0.231676	+	0.227168i
$898$	5.01694	+	28.4525i	0.167418	+	0.949472i
$899$	64.5698	+	11.3854i	2.15352	+	0.379724i
$900$	−0.0701056	−	0.181439i	−0.00233685	−	0.00604796i
$901$	10.6330	−	6.13898i	0.354237	−	0.204519i
$902$	26.7463	+	4.71610i	0.890555	+	0.157029i
$903$	−1.46510	+	5.69089i	−0.0487554	+	0.189381i
$904$	−3.48694	+	6.03955i	−0.115974	+	0.200872i
$905$	45.0102			1.49619
$906$	5.20986	−	5.31326i	0.173086	−	0.176521i
$907$	−12.4014	+	2.18669i	−0.411780	+	0.0726080i	−0.375701	−	0.926741i	$-0.622598\pi$
$907$	−12.4014	+	2.18669i	−0.411780	+	0.0726080i	−0.0360793	+	0.999349i	$0.511487\pi$
$908$	−1.20827	−	1.01386i	−0.0400980	−	0.0336462i
$909$	19.6076	+	32.4706i	0.650341	+	1.07698i
$910$	3.57367	+	1.30071i	0.118466	+	0.0431181i
$911$	−11.2821	+	19.5412i	−0.373792	+	0.647427i	−0.990145	−	0.140042i	$-0.955276\pi$
$911$	−11.2821	+	19.5412i	−0.373792	+	0.647427i	0.616353	+	0.787470i	$0.288609\pi$
$912$	−6.26900	+	4.20710i	−0.207587	+	0.139311i
$913$	−5.16554	−	8.94698i	−0.170955	−	0.296102i
$914$	4.73870	+	26.8745i	0.156742	+	0.888929i
$915$	15.1166	+	21.1436i	0.499740	+	0.698985i
$916$	−13.2879	+	4.83640i	−0.439044	+	0.159799i
$917$	23.5287	+	28.0404i	0.776985	+	0.925974i
$918$	19.7566	−	14.7202i	0.652067	−	0.485838i
$919$	15.9735	−	27.6670i	0.526919	−	0.912650i	−0.472589	−	0.881283i	$-0.656681\pi$
$919$	15.9735	−	27.6670i	0.526919	−	0.912650i	0.999508	−	0.0313671i	$-0.00998609\pi$
$920$	−17.6173			−0.580824
$921$	−25.3206	+	25.8232i	−0.834343	+	0.850902i
$922$	−10.0031	+	11.9212i	−0.329434	+	0.392604i
$923$	3.19761	+	1.84614i	0.105250	+	0.0607664i
$924$	9.40513	+	6.44877i	0.309406	+	0.212149i
$925$	−0.350492	+	0.417701i	−0.0115241	+	0.0137339i
$926$	8.19049	−	6.87263i	0.269156	−	0.225849i
$927$	−15.7877	+	13.7850i	−0.518535	+	0.452760i
$928$	−1.62287	−	9.20375i	−0.0532733	−	0.302128i
$929$	10.0497	+	11.9768i	0.329721	+	0.392946i	0.905281	−	0.424814i	$-0.139660\pi$
$929$	10.0497	+	11.9768i	0.329721	+	0.392946i	−0.575560	+	0.817759i	$0.695216\pi$
$930$	−15.2654	+	22.2637i	−0.500573	+	0.730055i
$931$	1.01200	−	4.88781i	0.0331668	−	0.160191i
$932$	−10.3997	+	6.00430i	−0.340655	+	0.196677i
$933$	−9.51986	−	13.3154i	−0.311666	−	0.435926i
$934$	9.30033	−	25.5525i	0.304316	−	0.836102i
$935$	18.4229	−	21.9555i	0.602493	−	0.718023i
$936$	−1.09714	−	1.81690i	−0.0358613	−	0.0593872i
$937$	−0.569539	+	3.23001i	−0.0186060	+	0.105520i	−0.992696	−	0.120639i	$-0.961506\pi$
$937$	−0.569539	+	3.23001i	−0.0186060	+	0.105520i	0.974090	+	0.226159i	$0.0726168\pi$
$938$	1.14897	−	0.663359i	0.0375152	−	0.0216594i
$939$	−9.79934	−	20.4868i	−0.319790	−	0.668562i
$940$	−10.2874	−	8.63216i	−0.335538	−	0.281550i
$941$	−33.4005	−	28.0263i	−1.08882	−	0.913632i	−0.0922014	−	0.995740i	$-0.529390\pi$
$941$	−33.4005	−	28.0263i	−1.08882	−	0.913632i	−0.996623	+	0.0821079i	$0.973835\pi$
$942$	20.9153	−	30.5037i	0.681458	−	0.993865i
$943$	68.5499	−	39.5773i	2.23229	−	1.28881i
$944$	0.719002	−	4.07766i	0.0234015	−	0.132717i
$945$	−12.5452	−	24.9555i	−0.408096	−	0.811802i
$946$	2.45238	−	2.92263i	0.0797337	−	0.0950230i
$947$	−6.46807	+	17.7709i	−0.210184	+	0.577476i	−0.999325	−	0.0367365i	$-0.988304\pi$
$947$	−6.46807	+	17.7709i	−0.210184	+	0.577476i	0.789141	+	0.614212i	$0.210526\pi$
$948$	4.10145	−	0.399473i	0.133209	−	0.0129743i
$949$	−0.173115	+	0.0999480i	−0.00561955	+	0.00324445i
$950$	−0.268322	+	0.0887519i	−0.00870552	+	0.00287949i
$951$	10.1895	+	0.790668i	0.330417	+	0.0256392i
$952$	7.37466	+	8.78877i	0.239014	+	0.284846i
$953$	−7.81368	−	44.3136i	−0.253110	−	1.43546i	−0.800878	−	0.598827i	$-0.795634\pi$
$953$	−7.81368	−	44.3136i	−0.253110	−	1.43546i	0.547769	−	0.836630i	$-0.315477\pi$
$954$	−2.51300	+	7.35071i	−0.0813615	+	0.237988i
$955$	−16.8681	+	14.1540i	−0.545838	+	0.458012i
$956$	−4.68873	+	5.58781i	−0.151644	+	0.180723i
$957$	39.7337	−	19.0056i	1.28441	−	0.614364i
$958$	26.7653	+	15.4529i	0.864747	+	0.499262i
$959$	21.8861	−	26.0829i	0.706740	−	0.842260i
$960$	3.72628	+	0.959317i	0.120265	+	0.0309618i
$961$	−18.2186			−0.587697
$962$	−2.97492	+	5.15271i	−0.0959152	+	0.166130i
$963$	1.50873	+	1.72791i	0.0486180	+	0.0556811i
$964$	−17.1946	−	20.4917i	−0.553800	−	0.659993i
$965$	−29.5426	+	10.7526i	−0.951009	+	0.346139i
$966$	33.0794	−	3.22186i	1.06431	−	0.103662i
$967$	−0.336492	−	1.90834i	−0.0108209	−	0.0613682i	0.978919	−	0.204248i	$-0.0654749\pi$
$967$	−0.336492	−	1.90834i	−0.0108209	−	0.0613682i	−0.989740	+	0.142880i	$0.954364\pi$
$968$	1.79815	+	3.11449i	0.0577949	+	0.100104i
$969$	−19.9479	−	29.7244i	−0.640820	−	0.954886i
$970$	12.9601	−	22.4475i	0.416123	−	0.720745i
$971$	−4.16555	−	1.51614i	−0.133679	−	0.0486551i	0.274314	−	0.961640i	$-0.411549\pi$
$971$	−4.16555	−	1.51614i	−0.133679	−	0.0486551i	−0.407993	+	0.912985i	$0.633771\pi$
$972$	−3.29031	+	15.2373i	−0.105537	+	0.488735i
$973$	12.0975	+	10.1510i	0.387828	+	0.325427i
$974$	−2.45988	+	0.433743i	−0.0788195	+	0.0138980i
$975$	−0.0213167	−	0.0765389i	−0.000682680	−	0.00245121i
$976$	6.75494			0.216220
$977$	4.57419	−	7.92272i	0.146341	−	0.253470i	−0.783531	−	0.621352i	$-0.786584\pi$
$977$	4.57419	−	7.92272i	0.146341	−	0.253470i	0.929873	+	0.367882i	$0.119917\pi$
$978$	−36.3828	+	10.1329i	−1.16339	+	0.324014i
$979$	−49.0753	−	8.65331i	−1.56845	−	0.276561i
$980$	−2.20310	+	1.27196i	−0.0703753	+	0.0406312i
$981$	−12.4234	+	4.80022i	−0.396647	+	0.153259i
$982$	−37.6956	−	6.64675i	−1.20292	−	0.212106i
$983$	2.57344	+	14.5947i	0.0820799	+	0.465498i	0.997949	+	0.0640203i	$0.0203923\pi$
$983$	2.57344	+	14.5947i	0.0820799	+	0.465498i	−0.915869	+	0.401478i	$0.868497\pi$
$984$	−16.6543	+	4.63836i	−0.530920	+	0.147866i
$985$	−16.9834	+	14.2507i	−0.541136	+	0.454067i
$986$	43.6396	−	7.69483i	1.38977	−	0.245053i
$987$	20.8950	+	14.3270i	0.665095	+	0.456032i
$988$	−2.71521	+	1.46214i	−0.0863824	+	0.0465169i
$989$		−	11.1195i		−	0.353578i
$990$	0.356320	+	18.1306i	0.0113246	+	0.576228i
$991$	22.0288	−	3.88428i	0.699769	−	0.123388i	0.187565	−	0.982252i	$-0.439940\pi$
$991$	22.0288	−	3.88428i	0.699769	−	0.123388i	0.512204	+	0.858864i	$0.328829\pi$
$992$	2.39948	+	6.59250i	0.0761834	+	0.209312i
$993$	5.05882	+	7.07575i	0.160537	+	0.224542i
$994$	11.8664	−	4.31903i	0.376381	−	0.136991i
$995$		−	42.0267i		−	1.33234i
$996$	5.42380	+	3.71891i	0.171860	+	0.117838i
$997$	−8.43692	+	47.8481i	−0.267200	+	1.51537i	0.495497	+	0.868610i	$0.334986\pi$
$997$	−8.43692	+	47.8481i	−0.267200	+	1.51537i	−0.762697	+	0.646756i	$0.776125\pi$
$998$	−26.3243	+	9.58126i	−0.833281	+	0.303290i
$999$	41.8580	−	12.5491i	1.32433	−	0.397036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.b.281.7	yes	48
9.5	odd	6		342.2.bf.b.167.8	yes	48
19.14	odd	18		342.2.bf.b.299.8	yes	48
171.14	even	18	inner	342.2.x.b.185.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.b.185.7	✓	48	171.14	even	18	inner
342.2.x.b.281.7	yes	48	1.1	even	1	trivial
342.2.bf.b.167.8	yes	48	9.5	odd	6
342.2.bf.b.299.8	yes	48	19.14	odd	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.40898 - 1.00736i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.759805 - 2.08755i) q^{5} +(-0.431828 + 1.67736i) q^{6} +(1.20984 + 2.09551i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.970470 - 2.83869i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.40898 - 1.00736i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.759805 - 2.08755i) q^{5} +(-0.431828 + 1.67736i) q^{6} +(1.20984 + 2.09551i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.970470 - 2.83869i) q^{9} +(0.759805 + 2.08755i) q^{10} +2.72097i q^{11} +(-0.747384 - 1.56250i) q^{12} +(-0.241975 - 0.664821i) q^{13} +(-2.27376 - 0.827581i) q^{14} +(-1.03235 - 3.70672i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.62169 - 4.45555i) q^{17} +(1.08125 + 2.79837i) q^{18} +(4.13839 - 1.36884i) q^{19} +(-1.92390 - 1.11076i) q^{20} +(3.81557 + 1.73380i) q^{21} +(-1.74901 - 2.08439i) q^{22} +(-7.80979 - 1.37708i) q^{23} +(1.57689 + 0.716538i) q^{24} +(0.0496682 + 0.0416766i) q^{25} +(0.612702 + 0.353744i) q^{26} +(-1.49220 - 4.97728i) q^{27} +(2.27376 - 0.827581i) q^{28} +(1.62287 - 9.20375i) q^{29} +(3.17346 + 2.17593i) q^{30} +7.01560i q^{31} +(0.939693 - 0.342020i) q^{32} +(2.74099 + 3.83381i) q^{33} +(1.62169 + 4.45555i) q^{34} +(5.29372 - 0.933426i) q^{35} +(-2.62705 - 1.44866i) q^{36} +8.40981i q^{37} +(-2.29032 + 3.70870i) q^{38} +(-1.01065 - 0.692967i) q^{39} +(2.18777 - 0.385763i) q^{40} +(-7.64614 + 6.41588i) q^{41} +(-4.03736 + 1.12444i) q^{42} +(0.243482 + 1.38085i) q^{43} +(2.67963 + 0.472492i) q^{44} +(-5.18854 - 4.18276i) q^{45} +(6.86781 - 3.96513i) q^{46} +(5.95323 + 1.04972i) q^{47} +(-1.66855 + 0.464704i) q^{48} +(0.572561 - 0.991705i) q^{49} -0.0648373 q^{50} +(-2.20339 - 7.91141i) q^{51} +(-0.696739 + 0.122854i) q^{52} +(1.98365 + 1.66448i) q^{53} +(4.34243 + 2.85365i) q^{54} +(5.68016 + 2.06741i) q^{55} +(-1.20984 + 2.09551i) q^{56} +(4.45202 - 6.09750i) q^{57} +(4.67287 + 8.09364i) q^{58} +(0.719002 + 4.07766i) q^{59} +(-3.82967 + 0.373002i) q^{60} +(-6.34757 + 2.31033i) q^{61} +(-4.50954 - 5.37426i) q^{62} +(7.12263 - 1.40075i) q^{63} +(-0.500000 + 0.866025i) q^{64} -1.57170 q^{65} +(-4.56404 - 1.17499i) q^{66} +(-0.352442 + 0.420023i) q^{67} +(-4.10626 - 2.37075i) q^{68} +(-12.3911 + 5.92695i) q^{69} +(-3.45523 + 4.11778i) q^{70} +(-3.99788 + 3.35462i) q^{71} +(2.94362 - 0.578896i) q^{72} +(-0.0490632 - 0.278251i) q^{73} +(-5.40572 - 6.44229i) q^{74} +(0.111965 + 0.00868808i) q^{75} +(-0.629420 - 4.31322i) q^{76} +(-5.70182 + 3.29195i) q^{77} +(1.21963 - 0.118790i) q^{78} +(-0.813728 + 2.23570i) q^{79} +(-1.42797 + 1.70179i) q^{80} +(-7.11638 - 5.50974i) q^{81} +(1.73324 - 9.82969i) q^{82} +(-3.28816 + 1.89842i) q^{83} +(2.37002 - 3.45653i) q^{84} +(-8.06901 - 6.77070i) q^{85} +(-1.07411 - 0.901288i) q^{86} +(-6.98485 - 14.6027i) q^{87} +(-2.35643 + 1.36049i) q^{88} +(-3.18023 + 18.0360i) q^{89} +(6.66328 - 0.130953i) q^{90} +(1.10039 - 1.31139i) q^{91} +(-2.71231 + 7.45201i) q^{92} +(7.06720 + 9.88486i) q^{93} +(-5.23519 + 3.02254i) q^{94} +(0.286852 - 9.67914i) q^{95} +(0.979476 - 1.42851i) q^{96} +(-7.49987 - 8.93800i) q^{97} +(0.198848 + 1.12773i) q^{98} +(7.72401 + 2.64062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

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