LMFDB - Embedded newform 196.2.j.a.111.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(27,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("196.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.5
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25414 - 0.653556i) q^{2} +(-0.635719 - 0.797166i) q^{3} +(1.14573 + 1.63930i) q^{4} +(-0.726306 + 0.579209i) q^{5} +(0.276287 + 1.41524i) q^{6} +(-2.60326 + 0.472259i) q^{7} +(-0.365526 - 2.80471i) q^{8} +(0.436227 - 1.91124i) q^{9} +O(q^{10})$	\(q+(-1.25414 - 0.653556i) q^{2} +(-0.635719 - 0.797166i) q^{3} +(1.14573 + 1.63930i) q^{4} +(-0.726306 + 0.579209i) q^{5} +(0.276287 + 1.41524i) q^{6} +(-2.60326 + 0.472259i) q^{7} +(-0.365526 - 2.80471i) q^{8} +(0.436227 - 1.91124i) q^{9} +(1.28943 - 0.251727i) q^{10} +(-5.04868 + 1.15233i) q^{11} +(0.578434 - 1.95547i) q^{12} +(-2.71007 + 0.618555i) q^{13} +(3.57350 + 1.10910i) q^{14} +(0.923453 + 0.210772i) q^{15} +(-1.37461 + 3.75639i) q^{16} +(-2.67586 + 5.55648i) q^{17} +(-1.79619 + 2.11186i) q^{18} +5.31475 q^{19} +(-1.78165 - 0.527017i) q^{20} +(2.03141 + 1.77501i) q^{21} +(7.08486 + 1.85442i) q^{22} +(-2.67158 - 5.54759i) q^{23} +(-2.00345 + 2.07439i) q^{24} +(-0.920568 + 4.03327i) q^{25} +(3.80306 + 0.995428i) q^{26} +(-4.55681 + 2.19445i) q^{27} +(-3.75681 - 3.72645i) q^{28} +(-6.99898 - 3.37053i) q^{29} +(-1.02039 - 0.867866i) q^{30} +2.80797 q^{31} +(4.17897 - 3.81264i) q^{32} +(4.12814 + 3.29208i) q^{33} +(6.98737 - 5.21977i) q^{34} +(1.61723 - 1.85084i) q^{35} +(3.63289 - 1.47465i) q^{36} +(-5.03268 - 2.42361i) q^{37} +(-6.66544 - 3.47349i) q^{38} +(2.21593 + 1.76715i) q^{39} +(1.89000 + 1.82536i) q^{40} +(8.64941 - 6.89767i) q^{41} +(-1.38760 - 3.55375i) q^{42} +(1.76174 + 1.40494i) q^{43} +(-7.67343 - 6.95606i) q^{44} +(0.790172 + 1.64081i) q^{45} +(-0.275133 + 8.70347i) q^{46} +(-1.31376 - 5.75595i) q^{47} +(3.86833 - 1.29221i) q^{48} +(6.55394 - 2.45883i) q^{49} +(3.79049 - 4.45664i) q^{50} +(6.13053 - 1.39925i) q^{51} +(-4.11900 - 3.73392i) q^{52} +(3.53549 - 1.70260i) q^{53} +(7.14907 + 0.225995i) q^{54} +(2.99945 - 3.76119i) q^{55} +(2.27611 + 7.12877i) q^{56} +(-3.37869 - 4.23674i) q^{57} +(6.57486 + 8.80135i) q^{58} +(-3.63089 + 4.55299i) q^{59} +(0.712507 + 1.75530i) q^{60} +(-2.83755 + 5.89224i) q^{61} +(-3.52158 - 1.83516i) q^{62} +(-0.233014 + 5.18146i) q^{63} +(-7.73278 + 2.05039i) q^{64} +(1.61006 - 2.01896i) q^{65} +(-3.02570 - 6.82670i) q^{66} -7.05842i q^{67} +(-12.1745 + 1.97967i) q^{68} +(-2.72398 + 5.65640i) q^{69} +(-3.23785 + 1.26426i) q^{70} +(-0.607747 - 1.26200i) q^{71} +(-5.51991 - 0.524883i) q^{72} +(-4.23286 - 0.966123i) q^{73} +(4.72771 + 6.32868i) q^{74} +(3.80041 - 1.83018i) q^{75} +(6.08926 + 8.71248i) q^{76} +(12.5988 - 5.38410i) q^{77} +(-1.62416 - 3.66449i) q^{78} +1.47889i q^{79} +(-1.17734 - 3.52447i) q^{80} +(-0.652553 - 0.314253i) q^{81} +(-15.3556 + 2.99776i) q^{82} +(-2.36598 + 10.3660i) q^{83} +(-0.582327 + 5.36377i) q^{84} +(-1.27487 - 5.58558i) q^{85} +(-1.29126 - 2.91339i) q^{86} +(1.76251 + 7.72207i) q^{87} +(5.07738 + 13.7389i) q^{88} +(8.05318 + 1.83809i) q^{89} +(0.0813759 - 2.57422i) q^{90} +(6.76290 - 2.89012i) q^{91} +(6.03326 - 10.7355i) q^{92} +(-1.78508 - 2.23842i) q^{93} +(-2.11420 + 8.07738i) q^{94} +(-3.86013 + 3.07835i) q^{95} +(-5.69596 - 0.907564i) q^{96} -11.4703i q^{97} +(-9.82654 - 1.19966i) q^{98} +10.1519i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

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 $

$2$	−1.25414	−	0.653556i	−0.886810	−	0.462134i
$2$	−1.25414	−	0.653556i	−0.886810	−	0.462134i
$3$	−0.635719	−	0.797166i	−0.367033	−	0.460244i	0.563681	−	0.825992i	$-0.309385\pi$
$3$	−0.635719	−	0.797166i	−0.367033	−	0.460244i	−0.930714	+	0.365748i	$0.880813\pi$
$4$	1.14573	+	1.63930i	0.572864	+	0.819650i
$5$	−0.726306	+	0.579209i	−0.324814	+	0.259030i	−0.772297	−	0.635262i	$-0.780892\pi$
$5$	−0.726306	+	0.579209i	−0.324814	+	0.259030i	0.447483	+	0.894293i	$0.352321\pi$
$6$	0.276287	+	1.41524i	0.112794	+	0.577767i
$7$	−2.60326	+	0.472259i	−0.983940	+	0.178497i
$7$	−2.60326	+	0.472259i	−0.983940	+	0.178497i
$8$	−0.365526	−	2.80471i	−0.129233	−	0.991614i
$9$	0.436227	−	1.91124i	0.145409	−	0.637079i
$10$	1.28943	−	0.251727i	0.407755	−	0.0796032i
$11$	−5.04868	+	1.15233i	−1.52224	+	0.347440i	−0.900175	−	0.435529i	$-0.856561\pi$
$11$	−5.04868	+	1.15233i	−1.52224	+	0.347440i	−0.622061	+	0.782969i	$0.713704\pi$
$12$	0.578434	−	1.95547i	0.166980	−	0.564496i
$13$	−2.71007	+	0.618555i	−0.751638	+	0.171556i	−0.581142	−	0.813802i	$-0.697394\pi$
$13$	−2.71007	+	0.618555i	−0.751638	+	0.171556i	−0.170495	+	0.985358i	$0.554537\pi$
$14$	3.57350	+	1.10910i	0.955058	+	0.296419i
$15$	0.923453	+	0.210772i	0.238434	+	0.0544211i
$16$	−1.37461	+	3.75639i	−0.343654	+	0.939096i
$17$	−2.67586	+	5.55648i	−0.648991	+	1.34764i	0.273593	+	0.961846i	$0.411788\pi$
$17$	−2.67586	+	5.55648i	−0.648991	+	1.34764i	−0.922583	+	0.385798i	$0.873926\pi$
$18$	−1.79619	+	2.11186i	−0.423366	+	0.497769i
$19$	5.31475			1.21929			0.609644	−	0.792675i	$-0.291312\pi$
$19$	5.31475			1.21929			0.609644	+	0.792675i	$0.291312\pi$
$20$	−1.78165	−	0.527017i	−0.398388	−	0.117845i
$21$	2.03141	+	1.77501i	0.443290	+	0.387339i
$22$	7.08486	+	1.85442i	1.51050	+	0.395363i
$23$	−2.67158	−	5.54759i	−0.557062	−	1.15675i	−0.969347	−	0.245697i	$-0.920983\pi$
$23$	−2.67158	−	5.54759i	−0.557062	−	1.15675i	0.412284	−	0.911055i	$-0.364731\pi$
$24$	−2.00345	+	2.07439i	−0.408952	+	0.423433i
$25$	−0.920568	+	4.03327i	−0.184114	+	0.806655i
$26$	3.80306	+	0.995428i	0.745842	+	0.195219i
$27$	−4.55681	+	2.19445i	−0.876959	+	0.422321i
$28$	−3.75681	−	3.72645i	−0.709969	−	0.704232i
$29$	−6.99898	−	3.37053i	−1.29968	−	0.625892i	−0.349307	−	0.937008i	$-0.613583\pi$
$29$	−6.99898	−	3.37053i	−1.29968	−	0.625892i	−0.950372	+	0.311116i	$0.899297\pi$
$30$	−1.02039	−	0.867866i	−0.186296	−	0.158450i
$31$	2.80797			0.504326			0.252163	−	0.967685i	$-0.418858\pi$
$31$	2.80797			0.504326			0.252163	+	0.967685i	$0.418858\pi$
$32$	4.17897	−	3.81264i	0.738744	−	0.673986i
$33$	4.12814	+	3.29208i	0.718617	+	0.573078i
$34$	6.98737	−	5.21977i	1.19832	−	0.895183i
$35$	1.61723	−	1.85084i	0.273361	−	0.312849i
$36$	3.63289	−	1.47465i	0.605481	−	0.245775i
$37$	−5.03268	−	2.42361i	−0.827367	−	0.398439i	−0.0282401	−	0.999601i	$-0.508990\pi$
$37$	−5.03268	−	2.42361i	−0.827367	−	0.398439i	−0.799127	+	0.601162i	$0.794705\pi$
$38$	−6.66544	−	3.47349i	−1.08128	−	0.563475i
$39$	2.21593	+	1.76715i	0.354833	+	0.282970i
$40$	1.89000	+	1.82536i	0.298835	+	0.288615i
$41$	8.64941	−	6.89767i	1.35081	−	1.07724i	0.361351	−	0.932430i	$-0.382316\pi$
$41$	8.64941	−	6.89767i	1.35081	−	1.07724i	0.989460	−	0.144805i	$-0.0462556\pi$
$42$	−1.38760	−	3.55375i	−0.214112	−	0.548355i
$43$	1.76174	+	1.40494i	0.268663	+	0.214252i	0.748549	−	0.663079i	$-0.230751\pi$
$43$	1.76174	+	1.40494i	0.268663	+	0.214252i	−0.479886	+	0.877331i	$0.659322\pi$
$44$	−7.67343	−	6.95606i	−1.15681	−	1.04866i
$45$	0.790172	+	1.64081i	0.117792	+	0.244597i
$46$	−0.275133	+	8.70347i	−0.0405661	+	1.28326i
$47$	−1.31376	−	5.75595i	−0.191631	−	0.839592i	−0.975734	−	0.218960i	$-0.929733\pi$
$47$	−1.31376	−	5.75595i	−0.191631	−	0.839592i	0.784102	−	0.620631i	$-0.213124\pi$
$48$	3.86833	−	1.29221i	0.558346	−	0.186514i
$49$	6.55394	−	2.45883i	0.936277	−	0.351261i
$50$	3.79049	−	4.45664i	0.536057	−	0.630264i
$51$	6.13053	−	1.39925i	0.858446	−	0.195935i
$52$	−4.11900	−	3.73392i	−0.571202	−	0.517802i
$53$	3.53549	−	1.70260i	0.485636	−	0.233870i	−0.175011	−	0.984566i	$-0.555996\pi$
$53$	3.53549	−	1.70260i	0.485636	−	0.233870i	0.660647	+	0.750696i	$0.270282\pi$
$54$	7.14907	+	0.225995i	0.972865	+	0.0307540i
$55$	2.99945	−	3.76119i	0.404445	−	0.507159i
$56$	2.27611	+	7.12877i	0.304158	+	0.952622i
$57$	−3.37869	−	4.23674i	−0.447518	−	0.561170i
$58$	6.57486	+	8.80135i	0.863322	+	1.15567i
$59$	−3.63089	+	4.55299i	−0.472701	+	0.592749i	−0.959830	−	0.280581i	$-0.909473\pi$
$59$	−3.63089	+	4.55299i	−0.472701	+	0.592749i	0.487129	+	0.873330i	$0.338044\pi$
$60$	0.712507	+	1.75530i	0.0919842	+	0.226609i
$61$	−2.83755	+	5.89224i	−0.363311	+	0.754424i	−0.999859	−	0.0168139i	$-0.994648\pi$
$61$	−2.83755	+	5.89224i	−0.363311	+	0.754424i	0.636547	+	0.771238i	$0.280362\pi$
$62$	−3.52158	−	1.83516i	−0.447241	−	0.233066i
$63$	−0.233014	+	5.18146i	−0.0293570	+	0.652803i
$64$	−7.73278	+	2.05039i	−0.966598	+	0.256299i
$65$	1.61006	−	2.01896i	0.199704	−	0.250421i
$66$	−3.02570	−	6.82670i	−0.372438	−	0.840309i
$67$		−	7.05842i		−	0.862324i	−0.902275	−	0.431162i	$-0.858104\pi$
$67$		−	7.05842i		−	0.862324i	0.902275	−	0.431162i	$-0.141896\pi$
$68$	−12.1745	+	1.97967i	−1.47638	+	0.240071i
$69$	−2.72398	+	5.65640i	−0.327928	+	0.680950i
$70$	−3.23785	+	1.26426i	−0.386998	+	0.151108i
$71$	−0.607747	−	1.26200i	−0.0721264	−	0.149772i	0.861788	−	0.507268i	$-0.169345\pi$
$71$	−0.607747	−	1.26200i	−0.0721264	−	0.149772i	−0.933914	+	0.357496i	$0.883630\pi$
$72$	−5.51991	−	0.524883i	−0.650528	−	0.0618580i
$73$	−4.23286	−	0.966123i	−0.495419	−	0.113076i	−0.0324911	−	0.999472i	$-0.510344\pi$
$73$	−4.23286	−	0.966123i	−0.495419	−	0.113076i	−0.462928	+	0.886396i	$0.653201\pi$
$74$	4.72771	+	6.32868i	0.549585	+	0.735694i
$75$	3.80041	−	1.83018i	0.438834	−	0.211331i
$76$	6.08926	+	8.71248i	0.698486	+	0.999390i
$77$	12.5988	−	5.38410i	1.43577	−	0.613575i
$78$	−1.62416	−	3.66449i	−0.183900	−	0.414921i
$79$			1.47889i			0.166388i	0.996533	+	0.0831942i	$0.0265122\pi$
$79$			1.47889i			0.166388i	−0.996533	+	0.0831942i	$0.973488\pi$
$80$	−1.17734	−	3.52447i	−0.131631	−	0.394048i
$81$	−0.652553	−	0.314253i	−0.0725058	−	0.0349170i
$82$	−15.3556	+	2.99776i	−1.69574	+	0.331048i
$83$	−2.36598	+	10.3660i	−0.259700	+	1.13782i	0.661873	+	0.749616i	$0.269762\pi$
$83$	−2.36598	+	10.3660i	−0.259700	+	1.13782i	−0.921573	+	0.388205i	$0.873095\pi$
$84$	−0.582327	+	5.36377i	−0.0635371	+	0.585236i
$85$	−1.27487	−	5.58558i	−0.138279	−	0.605841i
$86$	−1.29126	−	2.91339i	−0.139240	−	0.314159i
$87$	1.76251	+	7.72207i	0.188961	+	0.827892i
$88$	5.07738	+	13.7389i	0.541250	+	1.46457i
$89$	8.05318	+	1.83809i	0.853636	+	0.194837i	0.626881	−	0.779115i	$-0.284331\pi$
$89$	8.05318	+	1.83809i	0.853636	+	0.194837i	0.226755	+	0.973952i	$0.427188\pi$
$90$	0.0813759	−	2.57422i	0.00857777	−	0.271347i
$91$	6.76290	−	2.89012i	0.708944	−	0.302967i
$92$	6.03326	−	10.7355i	0.629011	−	1.11926i
$93$	−1.78508	−	2.23842i	−0.185104	−	0.232113i
$94$	−2.11420	+	8.07738i	−0.218063	+	0.833118i
$95$	−3.86013	+	3.07835i	−0.396041	+	0.315833i
$96$	−5.69596	−	0.907564i	−0.581341	−	0.0926279i
$97$		−	11.4703i		−	1.16463i	−0.812963	−	0.582316i	$-0.802147\pi$
$97$		−	11.4703i		−	1.16463i	0.812963	−	0.582316i	$-0.197853\pi$
$98$	−9.82654	−	1.19966i	−0.992630	−	0.121184i
$99$			10.1519i			1.02030i
$100$	−7.66647	+	3.11195i	−0.766647	+	0.311195i
$101$	−11.8837	+	9.47693i	−1.18247	+	0.942989i	−0.999197	−	0.0400725i	$-0.987241\pi$
$101$	−11.8837	+	9.47693i	−1.18247	+	0.942989i	−0.183274	+	0.983062i	$0.558670\pi$
$102$	−8.60303	−	2.25179i	−0.851826	−	0.222960i
$103$	6.06708	+	7.60788i	0.597808	+	0.749627i	0.985034	−	0.172357i	$-0.0551384\pi$
$103$	6.06708	+	7.60788i	0.597808	+	0.749627i	−0.387227	+	0.921984i	$0.626567\pi$
$104$	2.72547	+	7.37485i	0.267254	+	0.723164i
$105$	−2.50353	−	0.112586i	−0.244319	−	0.0109872i
$106$	−5.54673	−	0.175342i	−0.538747	−	0.0170308i
$107$	−4.09741	−	0.935207i	−0.396111	−	0.0904098i	0.0198252	−	0.999803i	$-0.493689\pi$
$107$	−4.09741	−	0.935207i	−0.396111	−	0.0904098i	−0.415937	+	0.909394i	$0.636546\pi$
$108$	−8.81822	−	4.95575i	−0.848534	−	0.476867i
$109$	−1.62349	−	7.11295i	−0.155502	−	0.681297i	−0.991229	−	0.132153i	$-0.957811\pi$
$109$	−1.62349	−	7.11295i	−0.155502	−	0.681297i	0.835728	−	0.549144i	$-0.185046\pi$
$110$	−6.21987	+	2.75674i	−0.593042	+	0.262845i
$111$	1.26735	+	5.55262i	0.120291	+	0.527031i
$112$	1.80449	−	10.4280i	0.170508	−	0.985356i
$113$	−1.59142	+	6.97247i	−0.149708	+	0.655915i	0.843257	+	0.537510i	$0.180635\pi$
$113$	−1.59142	+	6.97247i	−0.149708	+	0.655915i	−0.992965	+	0.118404i	$0.962222\pi$
$114$	1.46839	+	7.52163i	0.137528	+	0.704465i
$115$	5.15360	+	2.48184i	0.480575	+	0.231433i
$116$	−2.49361	−	15.3352i	−0.231526	−	1.42383i
$117$			5.44941i			0.503798i
$118$	7.52927	−	3.33709i	0.693125	−	0.307204i
$119$	4.34186	−	15.7287i	0.398018	−	1.44184i
$120$	0.253608	−	2.66706i	0.0231511	−	0.243468i
$121$	14.2507	−	6.86277i	1.29552	−	0.623888i
$122$	7.40959	−	5.53518i	0.670833	−	0.501132i
$123$	−10.9972	−	2.51004i	−0.991583	−	0.226322i
$124$	3.21717	+	4.60310i	0.288910	+	0.413371i
$125$	−3.68284	−	7.64750i	−0.329403	−	0.684013i
$126$	3.67861	−	6.34598i	0.327716	−	0.565345i
$127$	−2.83208	+	5.88087i	−0.251306	+	0.521843i	−0.988013	−	0.154369i	$-0.950665\pi$
$127$	−2.83208	+	5.88087i	−0.251306	+	0.521843i	0.736707	+	0.676212i	$0.236380\pi$
$128$	11.0380	+	2.48233i	0.975633	+	0.219409i
$129$		−	2.29755i		−	0.202288i
$130$	−3.33875	+	1.47978i	−0.292827	+	0.129786i
$131$	−9.72960	+	12.2005i	−0.850080	+	1.06597i	0.146965	+	0.989142i	$0.453049\pi$
$131$	−9.72960	+	12.2005i	−0.850080	+	1.06597i	−0.997045	+	0.0768243i	$0.975522\pi$
$132$	−0.666987	+	10.5391i	−0.0580538	+	0.917311i
$133$	−13.8357	+	2.50994i	−1.19971	+	0.217640i
$134$	−4.61308	+	8.85224i	−0.398509	+	0.764717i
$135$	2.03860	−	4.23319i	0.175454	−	0.364335i
$136$	16.5624	+	5.47396i	1.42021	+	0.469388i
$137$	1.56347	−	1.96053i	0.133576	−	0.167500i	−0.710545	−	0.703652i	$-0.751551\pi$
$137$	1.56347	−	1.96053i	0.133576	−	0.167500i	0.844121	+	0.536153i	$0.180123\pi$
$138$	7.11302	−	5.31364i	0.605501	−	0.452327i
$139$	−2.50048	−	3.13550i	−0.212088	−	0.265950i	0.664396	−	0.747380i	$-0.268689\pi$
$139$	−2.50048	−	3.13550i	−0.212088	−	0.265950i	−0.876484	+	0.481431i	$0.840117\pi$
$140$	4.88698	+	0.530563i	0.413025	+	0.0448408i
$141$	−3.75327	+	4.70645i	−0.316082	+	0.396355i
$142$	−0.0625889	+	1.97992i	−0.00525235	+	0.166151i
$143$	12.9695	−	6.24578i	1.08456	−	0.522298i
$144$	6.57970	+	4.26585i	0.548308	+	0.355488i
$145$	7.03565	−	1.60584i	0.584279	−	0.133358i
$146$	4.67718	+	3.97807i	0.387086	+	0.329227i
$147$	−6.12656	−	3.66146i	−0.505310	−	0.301992i
$148$	−1.79305	−	11.0269i	−0.147388	−	0.906403i
$149$	0.452330	+	1.98179i	0.0370563	+	0.162354i	0.990071	−	0.140571i	$-0.0448938\pi$
$149$	0.452330	+	1.98179i	0.0370563	+	0.162354i	−0.953014	+	0.302925i	$0.902037\pi$
$150$	−5.96237	−	0.188481i	−0.486826	−	0.0153894i
$151$	1.45269	+	3.01654i	0.118218	+	0.245483i	0.951678	−	0.307097i	$-0.0993577\pi$
$151$	1.45269	+	3.01654i	0.118218	+	0.245483i	−0.833460	+	0.552580i	$0.813643\pi$
$152$	−1.94268	−	14.9063i	−0.157572	−	1.20906i
$153$	9.45246	+	7.53808i	0.764186	+	0.609418i
$154$	−19.3195	−	1.48165i	−1.55681	−	0.119394i
$155$	−2.03944	+	1.62640i	−0.163812	+	0.130636i
$156$	−0.358030	+	5.65725i	−0.0286653	+	0.452943i
$157$	−0.749519	−	0.597722i	−0.0598181	−	0.0477034i	0.593124	−	0.805111i	$-0.297894\pi$
$157$	−0.749519	−	0.597722i	−0.0598181	−	0.0477034i	−0.652942	+	0.757407i	$0.726466\pi$
$158$	0.966540	−	1.85474i	0.0768938	−	0.147555i
$159$	−3.60483	−	1.73600i	−0.285882	−	0.137673i
$160$	−0.826890	+	5.18964i	−0.0653714	+	0.410277i
$161$	9.57472	+	13.1801i	0.754593	+	1.03874i
$162$	0.613010	+	0.820596i	0.0481626	+	0.0644721i
$163$	−8.79053	−	7.01022i	−0.688528	−	0.549082i	0.215528	−	0.976498i	$-0.430853\pi$
$163$	−8.79053	−	7.01022i	−0.688528	−	0.549082i	−0.904055	+	0.427415i	$0.859424\pi$
$164$	21.2172	+	6.27612i	1.65679	+	0.490083i
$165$	−4.90510			−0.381861
$166$	9.74207	−	11.4542i	0.756131	−	0.889015i
$167$	2.46446	+	1.18682i	0.190706	+	0.0918390i	0.526800	−	0.849989i	$-0.323392\pi$
$167$	2.46446	+	1.18682i	0.190706	+	0.0918390i	−0.336094	+	0.941828i	$0.609106\pi$
$168$	4.23585	−	6.34633i	0.326803	−	0.489630i
$169$	−4.75074	+	2.28784i	−0.365441	+	0.175987i
$170$	−2.05163	+	7.83830i	−0.157353	+	0.601170i
$171$	2.31844	−	10.1577i	0.177295	−	0.776782i
$172$	−0.284646	+	4.49770i	−0.0217040	+	0.342947i
$173$	5.47431	+	11.3675i	0.416204	+	0.864257i	0.998678	+	0.0514072i	$0.0163706\pi$
$173$	5.47431	+	11.3675i	0.416204	+	0.864257i	−0.582474	+	0.812850i	$0.697915\pi$
$174$	2.83637	−	10.8364i	0.215025	−	0.821509i
$175$	0.491729	−	10.9344i	0.0371712	−	0.826564i
$176$	2.61140	−	20.5488i	0.196842	−	1.54893i
$177$	5.93771			0.446306
$178$	−8.89852	−	7.56842i	−0.666972	−	0.567277i
$179$	4.51082	−	9.36681i	0.337154	−	0.700108i	−0.661608	−	0.749850i	$-0.730126\pi$
$179$	4.51082	−	9.36681i	0.337154	−	0.700108i	0.998762	+	0.0497418i	$0.0158399\pi$
$180$	−1.78446	+	3.17525i	−0.133006	+	0.236669i
$181$	−8.90161	−	2.03174i	−0.661652	−	0.151018i	−0.121508	−	0.992590i	$-0.538773\pi$
$181$	−8.90161	−	2.03174i	−0.661652	−	0.151018i	−0.540144	+	0.841573i	$0.681630\pi$
$182$	−10.3705	−	0.795328i	−0.768710	−	0.0589536i
$183$	6.50098	−	1.48381i	0.480566	−	0.109686i
$184$	−14.5828	+	9.52079i	−1.07506	+	0.701882i
$185$	5.05904	−	1.15469i	0.371948	−	0.0848947i
$186$	0.775804	+	3.97393i	0.0568847	+	0.291383i
$187$	7.10667	−	31.1364i	0.519691	−	2.27692i
$188$	7.93053	−	8.74840i	0.578393	−	0.638043i
$189$	10.8262	−	7.86471i	0.787492	−	0.572074i
$190$	6.85302	−	1.33787i	0.497171	−	0.0970592i
$191$	−13.2051	+	10.5307i	−0.955486	+	0.761975i	−0.971290	−	0.237900i	$-0.923541\pi$
$191$	−13.2051	+	10.5307i	−0.955486	+	0.761975i	0.0158035	+	0.999875i	$0.494969\pi$
$192$	6.55038	+	4.86084i	0.472733	+	0.350801i
$193$	−6.54666	−	8.20926i	−0.471239	−	0.590915i	0.488235	−	0.872712i	$-0.337641\pi$
$193$	−6.54666	−	8.20926i	−0.471239	−	0.590915i	−0.959474	+	0.281797i	$0.909070\pi$
$194$	−7.49648	+	14.3853i	−0.538216	+	1.03281i
$195$	−2.63299			−0.188553
$196$	11.5398	+	7.92673i	0.824271	+	0.566195i
$197$	−11.8054			−0.841099			−0.420550	−	0.907269i	$-0.638163\pi$
$197$	−11.8054			−0.841099			−0.420550	+	0.907269i	$0.638163\pi$
$198$	6.63484	−	12.7319i	0.471518	−	0.904817i
$199$	−0.317945	−	0.398690i	−0.0225385	−	0.0282624i	0.770435	−	0.637519i	$-0.220039\pi$
$199$	−0.317945	−	0.398690i	−0.0225385	−	0.0282624i	−0.792973	+	0.609257i	$0.791468\pi$
$200$	11.6486	+	1.10766i	0.823684	+	0.0783232i
$201$	−5.62674	+	4.48717i	−0.396880	+	0.316501i
$202$	21.0975	−	4.11872i	1.48441	−	0.289792i
$203$	19.8120	+	5.46904i	1.39053	+	0.383852i
$204$	9.31772	+	8.44662i	0.652371	+	0.591382i
$205$	−2.28692	+	10.0196i	−0.159725	+	0.699802i
$206$	−2.63678	−	13.5065i	−0.183714	−	0.941044i
$207$	−11.7682	+	2.68601i	−0.817944	+	0.186690i
$208$	1.40177	−	11.0303i	0.0971950	−	0.764816i
$209$	−26.8325	+	6.12434i	−1.85604	+	0.423630i
$210$	3.06619	+	1.77739i	0.211587	+	0.122652i
$211$	0.438590	+	0.100105i	0.0301938	+	0.00689154i	0.237591	−	0.971365i	$-0.423642\pi$
$211$	0.438590	+	0.100105i	0.0301938	+	0.00689154i	−0.207397	+	0.978257i	$0.566499\pi$
$212$	6.84178	+	3.84501i	0.469895	+	0.264076i
$213$	−0.619668	+	1.28675i	−0.0424589	+	0.0881669i
$214$	4.52751	+	3.85077i	0.309494	+	0.263233i
$215$	−2.09332			−0.142763
$216$	7.82042	+	11.9784i	0.532112	+	0.815027i
$217$	−7.30987	+	1.32609i	−0.496226	+	0.0900208i
$218$	−2.61264	+	9.98167i	−0.176950	+	0.676044i
$219$	1.92075	+	3.98848i	0.129792	+	0.269516i
$220$	9.60227	+	0.607698i	0.647385	+	0.0409710i
$221$	3.81477	−	16.7136i	0.256609	−	1.12428i
$222$	2.03952	−	7.79204i	0.136883	−	0.522967i
$223$	−19.5719	+	9.42534i	−1.31063	+	0.631167i	−0.953078	−	0.302725i	$-0.902104\pi$
$223$	−19.5719	+	9.42534i	−1.31063	+	0.631167i	−0.357555	+	0.933892i	$0.616389\pi$
$224$	−9.07839	+	11.8989i	−0.606575	+	0.795026i
$225$	7.30696	+	3.51885i	0.487131	+	0.234590i
$226$	6.55276	−	7.70436i	0.435883	−	0.512486i
$227$	1.22521			0.0813200			0.0406600	−	0.999173i	$-0.487054\pi$
$227$	1.22521			0.0813200			0.0406600	+	0.999173i	$0.487054\pi$
$228$	3.07424	−	10.3928i	0.203596	−	0.688283i
$229$	−15.2692	−	12.1768i	−1.00902	−	0.804667i	−0.0282040	−	0.999602i	$-0.508979\pi$
$229$	−15.2692	−	12.1768i	−1.00902	−	0.804667i	−0.980816	+	0.194936i	$0.937550\pi$
$230$	−4.84130	−	6.48074i	−0.319226	−	0.427327i
$231$	−12.3014	−	6.62060i	−0.809370	−	0.435604i
$232$	−6.89505	+	20.8621i	−0.452682	+	1.36967i
$233$	20.5149	+	9.87944i	1.34397	+	0.647224i	0.961003	−	0.276537i	$-0.0891868\pi$
$233$	20.5149	+	9.87944i	1.34397	+	0.647224i	0.382970	+	0.923761i	$0.374901\pi$
$234$	3.56150	−	6.83432i	0.232822	−	0.446773i
$235$	4.28809	+	3.41964i	0.279724	+	0.223073i
$236$	−11.6237	−	0.735630i	−0.756640	−	0.0478854i
$237$	1.17892	−	0.940160i	0.0765793	−	0.0610700i
$238$	−15.7249	+	16.8883i	−1.01929	+	1.09470i
$239$	−3.76316	−	3.00102i	−0.243419	−	0.194120i	0.494179	−	0.869360i	$-0.335469\pi$
$239$	−3.76316	−	3.00102i	−0.243419	−	0.194120i	−0.737598	+	0.675240i	$0.764040\pi$
$240$	−2.06113	+	3.17911i	−0.133046	+	0.205211i
$241$	3.87499	+	8.04649i	0.249610	+	0.518320i	0.987696	−	0.156386i	$-0.0499845\pi$
$241$	3.87499	+	8.04649i	0.249610	+	0.518320i	−0.738086	+	0.674707i	$0.764270\pi$
$242$	−22.3576	−	0.706763i	−1.43720	−	0.0454325i
$243$	3.54065	+	15.5126i	0.227133	+	0.995133i
$244$	−12.9102	+	2.09930i	−0.826492	+	0.134394i
$245$	−3.33599	+	5.58197i	−0.213128	+	0.356619i
$246$	12.1515	+	10.3352i	0.774754	+	0.658949i
$247$	−14.4033	+	3.28747i	−0.916463	+	0.209177i
$248$	−1.02639	−	7.87553i	−0.0651756	−	0.500096i
$249$	9.76756	−	4.70381i	0.618994	−	0.298092i
$250$	−0.379278	+	11.9980i	−0.0239876	+	0.758818i
$251$	3.20226	−	4.01551i	0.202125	−	0.253457i	−0.670430	−	0.741973i	$-0.733890\pi$
$251$	3.20226	−	4.01551i	0.202125	−	0.253457i	0.872555	+	0.488516i	$0.162462\pi$
$252$	−8.76094	+	5.55456i	−0.551887	+	0.349905i
$253$	19.8806	+	24.9295i	1.24988	+	1.56730i
$254$	7.39530	−	5.52450i	0.464022	−	0.346638i
$255$	−3.64218	+	4.56715i	−0.228082	+	0.286006i
$256$	−12.2209	−	10.3272i	−0.763804	−	0.645448i
$257$	−4.89436	+	10.1632i	−0.305302	+	0.633966i	−0.996017	−	0.0891610i	$-0.971581\pi$
$257$	−4.89436	+	10.1632i	−0.305302	+	0.633966i	0.690715	+	0.723127i	$0.257296\pi$
$258$	−1.50158	+	2.88144i	−0.0934841	+	0.179391i
$259$	14.2459	+	3.93256i	0.885200	+	0.244357i
$260$	5.15437	+	0.326204i	0.319661	+	0.0202303i
$261$	−9.49503	+	11.9064i	−0.587728	+	0.736987i
$262$	20.1760	−	8.94232i	1.24648	−	0.552459i
$263$		−	8.81724i		−	0.543695i	−0.962340	−	0.271847i	$-0.912365\pi$
$263$		−	8.81724i		−	0.543695i	0.962340	−	0.271847i	$-0.0876346\pi$
$264$	7.72439	−	12.7816i	0.475403	−	0.786652i
$265$	−1.58168	+	3.28439i	−0.0971619	+	0.201759i
$266$	18.9923	+	5.89459i	1.16449	+	0.361420i
$267$	−3.65430	−	7.58823i	−0.223640	−	0.464392i
$268$	11.5709	−	8.08704i	0.706804	−	0.493994i
$269$	−7.18151	−	1.63913i	−0.437865	−	0.0999397i	−0.00209460	−	0.999998i	$-0.500667\pi$
$269$	−7.18151	−	1.63913i	−0.437865	−	0.0999397i	−0.435770	+	0.900058i	$0.643524\pi$
$270$	−5.32331	+	3.97667i	−0.323966	+	0.242012i
$271$	3.66069	−	1.76290i	0.222371	−	0.107088i	−0.319382	−	0.947626i	$-0.603475\pi$
$271$	3.66069	−	1.76290i	0.222371	−	0.107088i	0.541753	+	0.840538i	$0.317761\pi$
$272$	−17.1940	−	17.6896i	−1.04254	−	1.07259i
$273$	−6.60321	−	3.55385i	−0.399644	−	0.215089i
$274$	−3.24213	+	1.43696i	−0.195864	+	0.0868100i
$275$		−	21.4235i		−	1.29189i
$276$	−12.3935	+	2.01528i	−0.746000	+	0.121305i
$277$	7.24493	+	3.48897i	0.435305	+	0.209632i	0.638686	−	0.769468i	$-0.279478\pi$
$277$	7.24493	+	3.48897i	0.435305	+	0.209632i	−0.203380	+	0.979100i	$0.565193\pi$
$278$	1.08672	+	5.56655i	0.0651771	+	0.333860i
$279$	1.22491	−	5.36669i	0.0733335	−	0.321295i
$280$	−5.78220	−	3.85932i	−0.345553	−	0.230638i
$281$	−4.29563	−	18.8204i	−0.256256	−	1.12273i	−0.925219	−	0.379434i	$-0.876119\pi$
$281$	−4.29563	−	18.8204i	−0.256256	−	1.12273i	0.668963	−	0.743295i	$-0.266738\pi$
$282$	7.78305	−	3.44957i	0.463474	−	0.205419i
$283$	6.17237	+	27.0429i	0.366909	+	1.60753i	0.735218	+	0.677831i	$0.237080\pi$
$283$	6.17237	+	27.0429i	0.366909	+	1.60753i	−0.368309	+	0.929704i	$0.620063\pi$
$284$	1.37249	−	2.44219i	0.0814420	−	0.144917i
$285$	4.90792	+	1.12020i	0.290720	+	0.0663550i
$286$	−20.3475	−	0.643222i	−1.20317	−	0.0380345i
$287$	−19.2592	+	22.0412i	−1.13683	+	1.30105i
$288$	−5.46388	−	9.65017i	−0.321962	−	0.568642i
$289$	−13.1149	−	16.4455i	−0.771464	−	0.967385i
$290$	−9.87318	−	2.58424i	−0.579773	−	0.151752i
$291$	−9.14373	+	7.29188i	−0.536015	+	0.427458i
$292$	−3.26594	−	8.04585i	−0.191125	−	0.470848i
$293$		−	0.497423i		−	0.0290598i	−0.999894	−	0.0145299i	$-0.995375\pi$
$293$		−	0.497423i		−	0.0290598i	0.999894	−	0.0145299i	$-0.00462517\pi$
$294$	5.29059	+	8.59603i	0.308553	+	0.501331i
$295$		−	5.40990i		−	0.314977i
$296$	−4.95794	+	15.0011i	−0.288175	+	0.871921i
$297$	20.4772	−	16.3300i	1.18821	−	0.947563i
$298$	0.727925	−	2.78106i	0.0421676	−	0.161103i
$299$	10.6716	+	13.3818i	0.617157	+	0.773891i
$300$	7.35446	+	4.13313i	0.424610	+	0.238626i
$301$	−5.24977	−	2.82543i	−0.302592	−	0.162855i
$302$	0.149605	−	4.73258i	0.00860883	−	0.272329i
$303$	15.1094	+	3.44862i	0.868011	+	0.198118i
$304$	−7.30574	+	19.9643i	−0.419013	+	1.14503i
$305$	−1.35191	−	5.92310i	−0.0774101	−	0.339156i
$306$	−6.92813	−	15.6315i	−0.396055	−	0.893594i
$307$	−5.29958	−	23.2190i	−0.302463	−	1.32518i	−0.866397	−	0.499357i	$-0.833570\pi$
$307$	−5.29958	−	23.2190i	−0.302463	−	1.32518i	0.563934	−	0.825820i	$-0.309287\pi$
$308$	23.2610	+	14.4846i	1.32542	+	0.825336i
$309$	2.20779	−	9.67295i	0.125597	−	0.550275i
$310$	3.62069	−	0.706842i	0.205641	−	0.0401459i
$311$	−21.9549	−	10.5729i	−1.24495	−	0.599534i	−0.308793	−	0.951129i	$-0.599925\pi$
$311$	−21.9549	−	10.5729i	−1.24495	−	0.599534i	−0.936152	+	0.351595i	$0.885639\pi$
$312$	4.14635	−	6.86099i	0.234741	−	0.388427i
$313$		−	23.6603i		−	1.33736i	−0.743550	−	0.668680i	$-0.766859\pi$
$313$		−	23.6603i		−	1.33736i	0.743550	−	0.668680i	$-0.233141\pi$
$314$	0.549356	+	1.23948i	0.0310020	+	0.0699478i
$315$	−2.83191	−	3.89829i	−0.159560	−	0.219644i
$316$	−2.42435	+	1.69441i	−0.136380	+	0.0953180i
$317$	13.4108	−	6.45831i	0.753227	−	0.362735i	−0.0175451	−	0.999846i	$-0.505585\pi$
$317$	13.4108	−	6.45831i	0.753227	−	0.362735i	0.770772	+	0.637111i	$0.219871\pi$
$318$	3.38639	+	4.53314i	0.189899	+	0.254206i
$319$	39.2196	+	8.95162i	2.19588	+	0.501195i
$320$	4.42876	−	5.96811i	0.247575	−	0.333627i
$321$	1.85928	+	3.86084i	0.103775	+	0.215491i
$322$	−3.39405	−	22.7873i	−0.189143	−	1.26989i
$323$	−14.2215	+	29.5313i	−0.791307	+	1.64317i
$324$	−0.232493	−	1.42978i	−0.0129163	−	0.0794321i
$325$		−	11.4999i		−	0.637898i
$326$	6.44298	+	14.5369i	0.356843	+	0.805124i
$327$	−4.63813	+	5.81603i	−0.256489	+	0.321627i
$328$	−22.5076	−	21.7378i	−1.24277	−	1.20027i
$329$	6.13836	+	14.3638i	0.338419	+	0.791903i
$330$	6.15168	+	3.20576i	0.338639	+	0.176471i
$331$	0.975324	−	2.02528i	0.0536087	−	0.111320i	−0.872444	−	0.488715i	$-0.837466\pi$
$331$	0.975324	−	2.02528i	0.0536087	−	0.111320i	0.926052	+	0.377395i	$0.123180\pi$
$332$	−19.7038	+	7.99811i	−1.08139	+	0.438953i
$333$	−6.82748	+	8.56139i	−0.374144	+	0.469161i
$334$	−2.31512	−	3.09910i	−0.126678	−	0.169575i
$335$	4.08831	+	5.12657i	0.223368	+	0.280095i
$336$	−9.46003	+	5.19082i	−0.516087	+	0.283182i
$337$	−8.07365	+	10.1240i	−0.439800	+	0.551491i	−0.951490	−	0.307678i	$-0.900448\pi$
$337$	−8.07365	+	10.1240i	−0.439800	+	0.551491i	0.511691	+	0.859170i	$0.329019\pi$
$338$	7.45331	+	0.235613i	0.405407	+	0.0128157i
$339$	6.56991	−	3.16390i	0.356829	−	0.171840i
$340$	7.69579	−	8.48946i	0.417363	−	0.460405i
$341$	−14.1765	+	3.23570i	−0.767702	+	0.175223i
$342$	−9.54630	+	11.2240i	−0.516205	+	0.606924i
$343$	−15.9004	+	9.49614i	−0.858542	+	0.512743i
$344$	3.29649	−	5.45471i	0.177735	−	0.294098i
$345$	−1.29780	−	5.68603i	−0.0698711	−	0.306125i
$346$	0.563772	−	17.8342i	0.0303086	−	0.958774i
$347$	0.157351	+	0.326743i	0.00844706	+	0.0175405i	0.905150	−	0.425093i	$-0.139759\pi$
$347$	0.157351	+	0.326743i	0.00844706	+	0.0175405i	−0.896703	+	0.442633i	$0.854044\pi$
$348$	−10.6394	+	11.7367i	−0.570333	+	0.629152i
$349$	−19.8892	−	15.8611i	−1.06464	−	0.849026i	−0.0756735	−	0.997133i	$-0.524111\pi$
$349$	−19.8892	−	15.8611i	−1.06464	−	0.849026i	−0.988971	+	0.148107i	$0.952682\pi$
$350$	−7.76295	+	13.3919i	−0.414947	+	0.715827i
$351$	10.9919	−	8.76574i	0.586703	−	0.467880i
$352$	−16.7049	+	24.0644i	−0.890372	+	1.28264i
$353$	16.5145	+	13.1699i	0.878981	+	0.700964i	0.955147	−	0.296131i	$-0.0956966\pi$
$353$	16.5145	+	13.1699i	0.878981	+	0.700964i	−0.0761665	+	0.997095i	$0.524268\pi$
$354$	−7.44672	−	3.88063i	−0.395788	−	0.206253i
$355$	1.17237	+	0.564585i	0.0622231	+	0.0299651i
$356$	6.21358	+	15.3075i	0.329319	+	0.811298i
$357$	−15.2986	+	6.53782i	−0.809686	+	0.346018i
$358$	−11.7789	+	8.79921i	−0.622536	+	0.465052i
$359$	29.2037	+	23.2892i	1.54131	+	1.22916i	0.875695	+	0.482864i	$0.160404\pi$
$359$	29.2037	+	23.2892i	1.54131	+	1.22916i	0.665618	+	0.746292i	$0.268168\pi$
$360$	4.31316	−	2.81596i	0.227324	−	0.148414i
$361$	9.24659			0.486663
$362$	9.83601	+	8.36579i	0.516969	+	0.439696i
$363$	−14.5302	−	6.99738i	−0.762638	−	0.367267i
$364$	12.4862	+	7.77514i	0.654455	+	0.407528i
$365$	3.63394	−	1.75001i	0.190209	−	0.0915999i
$366$	−9.12288	−	2.38786i	−0.476861	−	0.124815i
$367$	7.26281	−	31.8205i	0.379116	−	1.66102i	−0.321071	−	0.947055i	$-0.604043\pi$
$367$	7.26281	−	31.8205i	0.379116	−	1.66102i	0.700187	−	0.713960i	$-0.253100\pi$
$368$	24.5113	−	2.40968i	1.27774	−	0.125613i
$369$	−9.40997	−	19.5400i	−0.489864	−	1.01721i
$370$	−7.09940	−	1.85822i	−0.369080	−	0.0966044i
$371$	−8.39973	+	6.10198i	−0.436092	+	0.316799i
$372$	1.62422	−	5.49090i	0.0842121	−	0.284690i
$373$	17.4750			0.904820			0.452410	−	0.891810i	$-0.350564\pi$
$373$	17.4750			0.904820			0.452410	+	0.891810i	$0.350564\pi$
$374$	−29.2621	+	34.4047i	−1.51311	+	1.77903i
$375$	−3.75508	+	7.79750i	−0.193911	+	0.402661i
$376$	−15.6636	+	5.78866i	−0.807786	+	0.298527i
$377$	21.0526	+	4.80511i	1.08426	+	0.247476i
$378$	−18.7176	+	2.78789i	−0.962731	+	0.143394i
$379$	1.61455	−	0.368510i	0.0829337	−	0.0189291i	−0.180853	−	0.983510i	$-0.557886\pi$
$379$	1.61455	−	0.368510i	0.0829337	−	0.0189291i	0.263786	+	0.964581i	$0.415029\pi$
$380$	−9.46901	−	2.80096i	−0.485750	−	0.143686i
$381$	6.48844	−	1.48094i	0.332413	−	0.0758710i
$382$	23.4434	−	4.57669i	1.19947	−	0.234164i
$383$	0.707587	−	3.10014i	0.0361560	−	0.158410i	−0.953627	−	0.300990i	$-0.902683\pi$
$383$	0.707587	−	3.10014i	0.0361560	−	0.158410i	0.989783	+	0.142580i	$0.0455400\pi$
$384$	−5.03825	−	10.3772i	−0.257107	−	0.529560i
$385$	−6.03209	+	11.2079i	−0.307424	+	0.571206i
$386$	2.84521	+	14.5742i	0.144818	+	0.741805i
$387$	3.45369	−	2.75423i	0.175561	−	0.140005i
$388$	18.8032	−	13.1418i	0.954590	−	0.667175i
$389$	9.34855	+	11.7227i	0.473990	+	0.594365i	0.960143	−	0.279509i	$-0.0901717\pi$
$389$	9.34855	+	11.7227i	0.473990	+	0.594365i	−0.486153	+	0.873874i	$0.661600\pi$
$390$	3.30214	+	1.72081i	0.167210	+	0.0871366i
$391$	37.9738			1.92042
$392$	−9.29194	−	17.4831i	−0.469314	−	0.883031i
$393$	15.9112			0.802612
$394$	14.8056	+	7.71549i	0.745895	+	0.388701i
$395$	−0.856589	−	1.07413i	−0.0430997	−	0.0540453i
$396$	−16.6420	+	11.6313i	−0.836293	+	0.584496i
$397$	21.8016	−	17.3862i	1.09419	−	0.872587i	0.101688	−	0.994816i	$-0.467576\pi$
$397$	21.8016	−	17.3862i	1.09419	−	0.872587i	0.992502	+	0.122229i	$0.0390043\pi$
$398$	0.138180	+	0.707808i	0.00692636	+	0.0354792i
$399$	10.7965	+	9.43373i	0.540499	+	0.472277i
$400$	−13.8851	−	9.00221i	−0.694255	−	0.450110i
$401$	−0.731013	+	3.20278i	−0.0365051	+	0.159939i	−0.989895	−	0.141802i	$-0.954711\pi$
$401$	−0.731013	+	3.20278i	−0.0365051	+	0.159939i	0.953390	+	0.301741i	$0.0975677\pi$
$402$	9.98933	−	1.95015i	0.498223	−	0.0972646i
$403$	−7.60978	+	1.73688i	−0.379070	+	0.0865203i
$404$	−29.1510	−	8.62296i	−1.45032	−	0.429008i
$405$	0.655971	−	0.149721i	0.0325955	−	0.00743970i
$406$	−21.2726	−	19.8072i	−1.05574	−	0.983013i
$407$	28.2012	+	6.43674i	1.39788	+	0.319057i
$408$	−6.16537	−	16.6829i	−0.305231	−	0.825926i
$409$	−12.4942	+	25.9445i	−0.617800	+	1.28288i	0.323795	+	0.946127i	$0.395041\pi$
$409$	−12.4942	+	25.9445i	−0.617800	+	1.28288i	−0.941595	+	0.336748i	$0.890673\pi$
$410$	9.41651	−	11.0714i	0.465048	−	0.546777i
$411$	−2.55680			−0.126118
$412$	−5.52038	+	18.6623i	−0.271970	+	0.919428i
$413$	7.30196	−	13.5673i	0.359306	−	0.667605i
$414$	16.5144	+	4.32253i	0.811637	+	0.212441i
$415$	−4.28569	−	8.89932i	−0.210376	−	0.436850i
$416$	−8.96696	+	12.9174i	−0.439641	+	0.633330i
$417$	−0.909914	+	3.98659i	−0.0445587	+	0.195224i
$418$	37.6543	+	9.85578i	1.84173	+	0.482062i
$419$	17.7821	−	8.56341i	0.868713	−	0.418350i	0.0542237	−	0.998529i	$-0.482732\pi$
$419$	17.7821	−	8.56341i	0.868713	−	0.418350i	0.814489	+	0.580179i	$0.197017\pi$
$420$	−2.68380	−	4.23303i	−0.130956	−	0.206551i
$421$	32.0152	+	15.4177i	1.56032	+	0.751412i	0.997187	−	0.0749514i	$-0.0238802\pi$
$421$	32.0152	+	15.4177i	1.56032	+	0.751412i	0.563137	+	0.826364i	$0.309594\pi$
$422$	−0.484629	−	0.412190i	−0.0235913	−	0.0200651i
$423$	−11.5741			−0.562751
$424$	−6.06761	−	9.29366i	−0.294669	−	0.451340i
$425$	−19.9475	−	15.9076i	−0.967595	−	0.771631i
$426$	1.61812	−	1.20878i	0.0783980	−	0.0585656i
$427$	4.60423	−	16.6791i	0.222814	−	0.807158i
$428$	−3.16143	−	7.78838i	−0.152813	−	0.376465i
$429$	−13.2239	−	6.36829i	−0.638455	−	0.307464i
$430$	2.62531	+	1.36810i	0.126604	+	0.0659757i
$431$	18.4581	+	14.7199i	0.889097	+	0.709031i	0.957440	−	0.288631i	$-0.0932001\pi$
$431$	18.4581	+	14.7199i	0.889097	+	0.709031i	−0.0683439	+	0.997662i	$0.521772\pi$
$432$	−1.97932	−	20.1337i	−0.0952302	−	0.968681i
$433$	−4.61587	+	3.68104i	−0.221825	+	0.176899i	−0.728096	−	0.685475i	$-0.759595\pi$
$433$	−4.61587	+	3.68104i	−0.221825	+	0.176899i	0.506272	+	0.862374i	$0.331023\pi$
$434$	10.0343	+	3.11431i	0.481660	+	0.149492i
$435$	−5.75282	−	4.58772i	−0.275826	−	0.219964i
$436$	9.80020	−	10.8109i	0.469344	−	0.517748i
$437$	−14.1988	−	29.4841i	−0.679219	−	1.41041i
$438$	0.197809	−	6.25743i	0.00945166	−	0.298991i
$439$	−4.87444	−	21.3563i	−0.232644	−	1.01928i	−0.947436	−	0.319944i	$-0.896336\pi$
$439$	−4.87444	−	21.3563i	−0.232644	−	1.01928i	0.714792	−	0.699337i	$-0.246521\pi$
$440$	−11.6454	−	7.03776i	−0.555173	−	0.335512i
$441$	−1.84040	−	13.5987i	−0.0876379	−	0.647559i
$442$	−15.7075	+	18.4680i	−0.747131	+	0.878433i
$443$	20.9084	−	4.77220i	0.993387	−	0.226734i	0.305216	−	0.952283i	$-0.401271\pi$
$443$	20.9084	−	4.77220i	0.993387	−	0.226734i	0.688170	+	0.725549i	$0.258414\pi$
$444$	−7.65037	+	8.43935i	−0.363071	+	0.400514i
$445$	−6.91371	+	3.32947i	−0.327741	+	0.157832i
$446$	30.7059	+	0.970669i	1.45397	+	0.0459625i
$447$	1.29226	−	1.62044i	0.0611218	−	0.0766443i
$448$	19.1621	−	8.98958i	0.905326	−	0.424718i
$449$	−11.6549	−	14.6148i	−0.550029	−	0.689714i	0.426651	−	0.904416i	$-0.359693\pi$
$449$	−11.6549	−	14.6148i	−0.550029	−	0.689714i	−0.976680	+	0.214702i	$0.931122\pi$
$450$	−6.86418	−	9.18863i	−0.323580	−	0.433156i
$451$	−35.7197	+	44.7911i	−1.68198	+	2.10913i
$452$	−13.2533	+	5.37974i	−0.623383	+	0.253042i
$453$	1.48118	−	3.07571i	0.0695921	−	0.144509i
$454$	−1.53658	−	0.800743i	−0.0721154	−	0.0375807i
$455$	−3.23795	+	6.01624i	−0.151797	+	0.282046i
$456$	−10.6478	+	11.0249i	−0.498630	+	0.516287i
$457$	−13.2680	+	16.6376i	−0.620652	+	0.778273i	−0.988436	−	0.151638i	$-0.951545\pi$
$457$	−13.2680	+	16.6376i	−0.620652	+	0.778273i	0.367784	+	0.929911i	$0.380117\pi$
$458$	11.1915	+	25.2507i	0.522945	+	1.17989i
$459$		−	31.1918i		−	1.45591i
$460$	1.83614	+	11.2918i	0.0856103	+	0.526483i
$461$	−1.12831	+	2.34296i	−0.0525506	+	0.109122i	−0.925591	−	0.378526i	$-0.876431\pi$
$461$	−1.12831	+	2.34296i	−0.0525506	+	0.109122i	0.873040	+	0.487649i	$0.162145\pi$
$462$	11.1007	+	16.3428i	0.516450	+	0.760335i
$463$	−16.5778	−	34.4242i	−0.770436	−	1.59983i	−0.799806	−	0.600258i	$-0.795064\pi$
$463$	−16.5778	−	34.4242i	−0.770436	−	1.59983i	0.0293703	−	0.999569i	$-0.490650\pi$
$464$	22.2819	−	21.6577i	1.03441	−	1.00543i
$465$	2.59302	+	0.591841i	0.120249	+	0.0274460i
$466$	−19.2717	−	25.7978i	−0.892745	−	1.19506i
$467$	19.5231	−	9.40182i	0.903421	−	0.435064i	0.0762975	−	0.997085i	$-0.475690\pi$
$467$	19.5231	−	9.40182i	0.903421	−	0.435064i	0.827123	+	0.562021i	$0.189976\pi$
$468$	−8.93322	+	6.24354i	−0.412938	+	0.288608i
$469$	3.33341	+	18.3749i	0.153922	+	0.848475i
$470$	−3.14293	−	7.09121i	−0.144973	−	0.327093i
$471$			0.977474i			0.0450396i
$472$	14.0970	+	8.51934i	0.648867	+	0.392134i
$473$	−10.5134	−	5.06300i	−0.483408	−	0.232797i
$474$	−2.09298	+	0.408598i	−0.0961338	+	0.0187675i
$475$	−4.89259	+	21.4358i	−0.224488	+	0.983544i
$476$	30.7586	−	10.9032i	1.40982	−	0.499745i
$477$	−1.71180	−	7.49987i	−0.0783778	−	0.343395i
$478$	2.75819	+	6.22314i	0.126157	+	0.284640i
$479$	−3.29653	−	14.4430i	−0.150622	−	0.659919i	−0.992705	−	0.120571i	$-0.961528\pi$
$479$	−3.29653	−	14.4430i	−0.150622	−	0.659919i	0.842082	−	0.539349i	$-0.181330\pi$
$480$	4.66268	−	2.63998i	0.212821	−	0.120498i
$481$	15.1380	+	3.45516i	0.690235	+	0.157542i
$482$	0.399066	−	12.6239i	0.0181770	−	0.575005i
$483$	4.41994	−	16.0115i	0.201114	−	0.728549i
$484$	27.5776	+	15.4983i	1.25353	+	0.704468i
$485$	6.64370	+	8.33093i	0.301675	+	0.378288i
$486$	5.69789	−	21.7690i	0.258462	−	0.987460i
$487$	−15.1969	+	12.1192i	−0.688639	+	0.549172i	−0.904089	−	0.427343i	$-0.859450\pi$
$487$	−15.1969	+	12.1192i	−0.688639	+	0.549172i	0.215450	+	0.976515i	$0.430878\pi$
$488$	17.5632	+	5.80474i	0.795049	+	0.262768i
$489$			11.4640i			0.518422i
$490$	7.83192	−	4.82030i	0.353810	−	0.217759i
$491$			10.0146i			0.451952i	0.974133	+	0.225976i	$0.0725571\pi$
$491$			10.0146i			0.451952i	−0.974133	+	0.225976i	$0.927443\pi$
$492$	−8.48508	−	20.9035i	−0.382537	−	0.942403i
$493$	37.4566	−	29.8706i	1.68696	−	1.34530i
$494$	20.2123	+	5.29045i	0.909396	+	0.238029i
$495$	−5.88008	−	7.37339i	−0.264290	−	0.331409i
$496$	−3.85987	+	10.5478i	−0.173313	+	0.473610i
$497$	2.17812	+	2.99830i	0.0977019	+	0.134492i
$498$	−15.3241	−	0.484422i	−0.686689	−	0.0217075i
$499$	−12.4803	−	2.84855i	−0.558696	−	0.127519i	−0.0661570	−	0.997809i	$-0.521074\pi$
$499$	−12.4803	−	2.84855i	−0.558696	−	0.127519i	−0.492539	+	0.870291i	$0.663931\pi$
$500$	8.31702	−	14.7992i	0.371948	−	0.661842i
$501$	−0.620610	−	2.71907i	−0.0277268	−	0.121479i
$502$	−6.64044	+	2.94315i	−0.296377	+	0.131359i
$503$	2.26568	+	9.92658i	0.101022	+	0.442605i	0.999989	+	0.00458995i	$0.00146103\pi$
$503$	2.26568	+	9.92658i	0.101022	+	0.442605i	−0.898968	+	0.438015i	$0.855682\pi$
$504$	14.6177	−	1.24042i	0.651122	−	0.0552529i
$505$	3.14207	−	13.7663i	0.139820	−	0.612592i
$506$	−8.64021	−	44.2581i	−0.384104	−	1.96751i
$507$	4.84392	+	2.33271i	0.215126	+	0.103599i
$508$	−12.8853	+	2.09525i	−0.571693	+	0.0929617i
$509$			9.97627i			0.442190i	0.975252	+	0.221095i	$0.0709631\pi$
$509$			9.97627i			0.442190i	−0.975252	+	0.221095i	$0.929037\pi$
$510$	7.55268	−	3.34747i	0.334438	−	0.148228i
$511$	11.4755	+	0.516063i	0.507647	+	0.0228293i
$512$	8.57728	+	20.9387i	0.379066	+	0.925370i
$513$	−24.2183	+	11.6629i	−1.06927	+	0.514931i
$514$	12.7805	−	9.54738i	0.563722	−	0.421117i
$515$	−8.81312	−	2.01154i	−0.388352	−	0.0886389i
$516$	3.76637	−	2.63237i	0.165805	−	0.115883i
$517$	13.2655	+	27.5461i	0.583416	+	1.21148i
$518$	−15.2962	−	14.2425i	−0.672079	−	0.625780i
$519$	5.58168	−	11.5905i	0.245009	−	0.508766i
$520$	−6.25111	−	3.77778i	−0.274129	−	0.165667i
$521$		−	16.0983i		−	0.705280i	−0.935759	−	0.352640i	$-0.885284\pi$
$521$		−	16.0983i		−	0.705280i	0.935759	−	0.352640i	$-0.114716\pi$
$522$	19.6896	−	8.72673i	0.861790	−	0.381959i
$523$	−18.6524	+	23.3893i	−0.815612	+	1.02274i	0.183598	+	0.983001i	$0.441226\pi$
$523$	−18.6524	+	23.3893i	−0.815612	+	1.02274i	−0.999210	+	0.0397435i	$0.987346\pi$
$524$	−31.1478	−	1.97125i	−1.36070	−	0.0861145i
$525$	−9.02915	+	6.55922i	−0.394064	+	0.286268i
$526$	−5.76257	+	11.0580i	−0.251260	+	0.482154i
$527$	−7.51372	+	15.6024i	−0.327303	+	0.679651i
$528$	−18.0409	+	10.9816i	−0.785131	+	0.477911i
$529$	−9.29814	+	11.6595i	−0.404267	+	0.506935i
$530$	4.13018	−	3.08537i	0.179404	−	0.134020i
$531$	7.11794	+	8.92562i	0.308892	+	0.387339i
$532$	−19.9665	−	19.8051i	−0.865657	−	0.858662i
$533$	−19.1739	+	24.0433i	−0.830513	+	1.04143i
$534$	−0.376338	+	11.9050i	−0.0162858	+	0.515179i
$535$	3.51765	−	1.69401i	0.152081	−	0.0732385i
$536$	−19.7968	+	2.58004i	−0.855093	+	0.111441i
$537$	−10.3345	+	2.35879i	−0.445967	+	0.101789i
$538$	7.93535	+	6.74922i	0.342117	+	0.290980i
$539$	−30.2554	+	19.9662i	−1.30319	+	0.860003i
$540$	9.27514	−	1.50821i	0.399139	−	0.0649030i
$541$	−2.64693	−	11.5970i	−0.113801	−	0.498593i	−0.999416	−	0.0341733i	$-0.989120\pi$
$541$	−2.64693	−	11.5970i	−0.113801	−	0.498593i	0.885615	−	0.464419i	$-0.153737\pi$
$542$	−5.74317	−	0.181552i	−0.246690	−	0.00779833i
$543$	4.03929	+	8.38768i	0.173343	+	0.359950i
$544$	10.0025	+	33.4224i	0.428855	+	1.43297i
$545$	5.29904	+	4.22584i	0.226986	+	0.181015i
$546$	5.95869	+	8.77259i	0.255009	+	0.375432i
$547$	−0.697519	+	0.556253i	−0.0298237	+	0.0237836i	−0.638288	−	0.769797i	$-0.720357\pi$
$547$	−0.697519	+	0.556253i	−0.0298237	+	0.0237836i	0.608465	+	0.793581i	$0.291786\pi$
$548$	5.00521	+	0.316765i	0.213812	+	0.0135315i
$549$	10.0236	+	7.99359i	0.427799	+	0.341158i
$550$	−14.0015	+	26.8681i	−0.597025	+	1.14566i
$551$	−37.1979	−	17.9135i	−1.58468	−	0.763143i
$552$	16.8602	+	5.57240i	0.717619	+	0.237177i
$553$	−0.698421	−	3.84994i	−0.0296999	−	0.163716i
$554$	−6.80590	−	9.11062i	−0.289155	−	0.387073i
$555$	−4.13661	−	3.29884i	−0.175589	−	0.140028i
$556$	2.27516	−	7.69146i	0.0964882	−	0.326191i
$557$	5.08127			0.215300			0.107650	−	0.994189i	$-0.465667\pi$
$557$	5.08127			0.215300			0.107650	+	0.994189i	$0.465667\pi$
$558$	−5.04364	+	5.93002i	−0.213514	+	0.251038i
$559$	−5.64347	−	2.71775i	−0.238693	−	0.114949i
$560$	4.72940	+	8.61912i	0.199854	+	0.364224i
$561$	−29.3387	+	14.1288i	−1.23868	+	0.596517i
$562$	−6.91286	+	26.4108i	−0.291601	+	1.11407i
$563$	2.45358	−	10.7498i	0.103406	−	0.453052i	−0.896543	−	0.442957i	$-0.853929\pi$
$563$	2.45358	−	10.7498i	0.103406	−	0.453052i	0.999949	−	0.0100951i	$-0.00321343\pi$
$564$	−12.0155	−	0.760425i	−0.505944	−	0.0320197i
$565$	−2.88266	−	5.98591i	−0.121275	−	0.251829i
$566$	9.93306	−	37.9496i	0.417518	−	1.59514i
$567$	1.84717	+	0.509908i	0.0775740	+	0.0214141i
$568$	−3.31740	+	2.16585i	−0.139195	+	0.0908770i
$569$	−29.8693			−1.25219			−0.626093	−	0.779748i	$-0.715347\pi$
$569$	−29.8693			−1.25219			−0.626093	+	0.779748i	$0.715347\pi$
$570$	−5.42310	−	4.61249i	−0.227149	−	0.193196i
$571$	12.1074	−	25.1413i	0.506680	−	1.05213i	−0.478097	−	0.878307i	$-0.658673\pi$
$571$	12.1074	−	25.1413i	0.506680	−	1.05213i	0.984777	−	0.173825i	$-0.0556126\pi$
$572$	25.0982	+	14.1049i	1.04941	+	0.589757i
$573$	16.7894	+	3.83208i	0.701389	+	0.160087i
$574$	38.5589	−	15.0558i	1.60942	−	0.628416i
$575$	24.8343	−	5.66827i	1.03566	−	0.236383i
$576$	0.545531	+	15.6736i	0.0227304	+	0.653067i
$577$	−21.1227	+	4.82112i	−0.879349	+	0.200706i	−0.638282	−	0.769803i	$-0.720355\pi$
$577$	−21.1227	+	4.82112i	−0.879349	+	0.200706i	−0.241067	+	0.970508i	$0.577497\pi$
$578$	5.69979	+	29.1963i	0.237080	+	1.21441i
$579$	−2.38231	+	10.4376i	−0.0990052	+	0.433770i
$580$	10.6934	+	9.69368i	0.444019	+	0.402508i
$581$	1.26381	−	28.1029i	0.0524316	−	1.16590i
$582$	16.2332	−	3.16909i	0.672886	−	0.131363i
$583$	−15.8876	+	12.6699i	−0.657997	+	0.524735i
$584$	−1.16247	+	12.2251i	−0.0481034	+	0.505878i
$585$	−3.15635	−	3.95794i	−0.130499	−	0.163641i
$586$	−0.325094	+	0.623838i	−0.0134295	+	0.0257705i
$587$	−22.0575			−0.910410			−0.455205	−	0.890387i	$-0.650434\pi$
$587$	−22.0575			−0.910410			−0.455205	+	0.890387i	$0.650434\pi$
$588$	−1.01714	−	14.2383i	−0.0419463	−	0.587178i
$589$	14.9236			0.614918
$590$	−3.53568	+	6.78477i	−0.145562	+	0.279325i
$591$	7.50491	+	9.41086i	0.308711	+	0.387111i
$592$	16.0220	−	15.5732i	0.658500	−	0.640053i
$593$	−29.3534	+	23.4085i	−1.20540	+	0.961274i	−0.999849	−	0.0173730i	$-0.994470\pi$
$593$	−29.3534	+	23.4085i	−1.20540	+	0.961274i	−0.205550	+	0.978647i	$0.565898\pi$
$594$	−36.3538	+	7.09710i	−1.49162	+	0.291198i
$595$	5.95667	+	13.9387i	0.244200	+	0.571429i
$596$	−2.73050	+	3.01210i	−0.111846	+	0.123380i
$597$	−0.115699	+	0.506910i	−0.00473524	+	0.0207465i
$598$	−4.63795	−	23.7572i	−0.189660	−	0.971503i
$599$	−18.4439	+	4.20970i	−0.753597	+	0.172004i	−0.582028	−	0.813168i	$-0.697741\pi$
$599$	−18.4439	+	4.20970i	−0.753597	+	0.172004i	−0.171569	+	0.985172i	$0.554884\pi$
$600$	−6.52228	−	9.99007i	−0.266271	−	0.407843i
$601$	38.9502	−	8.89012i	1.58881	−	0.362636i	0.665411	−	0.746477i	$-0.268256\pi$
$601$	38.9502	−	8.89012i	1.58881	−	0.362636i	0.923399	+	0.383842i	$0.125399\pi$
$602$	4.73736	+	6.97450i	0.193080	+	0.284259i
$603$	−13.4903	−	3.07908i	−0.549368	−	0.125390i
$604$	−3.28063	+	5.83754i	−0.133487	+	0.237526i
$605$	−6.37538	+	13.2386i	−0.259196	+	0.538226i
$606$	−16.6954	−	14.1999i	−0.678204	−	0.576830i
$607$	−19.3766			−0.786472			−0.393236	−	0.919438i	$-0.628644\pi$
$607$	−19.3766			−0.786472			−0.393236	+	0.919438i	$0.628644\pi$
$608$	22.2102	−	20.2632i	0.900742	−	0.821783i
$609$	−8.23510	−	19.2702i	−0.333703	−	0.780868i
$610$	−2.17560	+	8.31194i	−0.0880874	+	0.336541i
$611$	7.12075	+	14.7864i	0.288075	+	0.598193i
$612$	−1.52724	+	24.1320i	−0.0617350	+	0.975479i
$613$	−10.5186	+	46.0851i	−0.424843	+	1.86136i	0.0779593	+	0.996957i	$0.475160\pi$
$613$	−10.5186	+	46.0851i	−0.424843	+	1.86136i	−0.502802	+	0.864402i	$0.667698\pi$
$614$	−8.52850	+	32.5834i	−0.344182	+	1.31496i
$615$	9.44116	−	4.54662i	0.380704	−	0.183337i
$616$	−19.7061	−	33.3681i	−0.793979	−	1.34444i
$617$	23.7284	+	11.4270i	0.955268	+	0.460033i	0.845530	−	0.533928i	$-0.179285\pi$
$617$	23.7284	+	11.4270i	0.955268	+	0.460033i	0.109738	+	0.993961i	$0.464999\pi$
$618$	−9.09069	+	10.6883i	−0.365681	+	0.429947i
$619$	12.4492			0.500376			0.250188	−	0.968197i	$-0.419508\pi$
$619$	12.4492			0.500376			0.250188	+	0.968197i	$0.419508\pi$
$620$	−5.00281	−	1.47985i	−0.200918	−	0.0594320i
$621$	24.3478	+	19.4167i	0.977042	+	0.779165i
$622$	20.6244	+	27.6086i	0.826965	+	1.10700i
$623$	−21.8326	−	0.981828i	−0.874704	−	0.0393361i
$624$	−9.68414	+	5.89475i	−0.387676	+	0.235979i
$625$	−11.5322	−	5.55359i	−0.461286	−	0.222144i
$626$	−15.4634	+	29.6733i	−0.618040	+	1.18599i
$627$	21.9401	+	17.4966i	0.876201	+	0.698747i
$628$	0.121100	−	1.91351i	0.00483243	−	0.0763575i
$629$	26.9335	−	21.4787i	1.07391	−	0.856413i
$630$	1.00386	+	6.73981i	0.0399947	+	0.268520i
$631$	−31.6136	−	25.2110i	−1.25852	−	1.00363i	−0.999285	−	0.0378184i	$-0.987959\pi$
$631$	−31.6136	−	25.2110i	−1.25852	−	1.00363i	−0.259232	−	0.965815i	$-0.583469\pi$
$632$	4.14786	−	0.540574i	0.164993	−	0.0215029i
$633$	−0.199020	−	0.413268i	−0.00791032	−	0.0164259i
$634$	−21.0399	−	0.665110i	−0.835601	−	0.0264149i
$635$	−1.34930	−	5.91168i	−0.0535454	−	0.234598i
$636$	−1.28434	−	7.89838i	−0.0509273	−	0.313191i
$637$	−16.2407	+	10.7176i	−0.643480	+	0.424646i
$638$	−43.3365	−	36.8588i	−1.71571	−	1.45925i
$639$	−2.67710	+	0.611030i	−0.105904	+	0.0241720i
$640$	−9.45477	+	4.59040i	−0.373733	+	0.181451i
$641$	−41.3677	+	19.9216i	−1.63393	+	0.786857i	−0.634017	+	0.773319i	$0.718595\pi$
$641$	−41.3677	+	19.9216i	−1.63393	+	0.786857i	−0.999908	+	0.0135385i	$0.995690\pi$
$642$	0.191479	−	6.05718i	0.00755706	−	0.239058i
$643$	8.61176	−	10.7988i	0.339614	−	0.425863i	−0.582470	−	0.812852i	$-0.697914\pi$
$643$	8.61176	−	10.7988i	0.339614	−	0.425863i	0.922084	+	0.386989i	$0.126485\pi$
$644$	−10.6362	+	30.7967i	−0.419125	+	1.21356i
$645$	1.33076	+	1.66872i	0.0523987	+	0.0657059i
$646$	37.1361	−	27.7418i	1.46110	−	1.09149i
$647$	10.1662	−	12.7480i	0.399673	−	0.501174i	−0.540749	−	0.841184i	$-0.681859\pi$
$647$	10.1662	−	12.7480i	0.399673	−	0.501174i	0.940422	+	0.340010i	$0.110430\pi$
$648$	−0.642862	+	1.94509i	−0.0252540	+	0.0764103i
$649$	13.0847	−	27.1706i	0.513618	−	1.06654i
$650$	−7.51581	+	14.4224i	−0.294794	+	0.565694i
$651$	5.70414	+	4.98416i	0.223563	+	0.195345i
$652$	1.42029	−	22.4421i	0.0556230	−	0.878902i
$653$	7.90068	−	9.90714i	0.309177	−	0.387696i	−0.602830	−	0.797870i	$-0.705960\pi$
$653$	7.90068	−	9.90714i	0.309177	−	0.387696i	0.912008	+	0.410173i	$0.134532\pi$
$654$	9.61796	−	4.26283i	0.376092	−	0.166690i
$655$		−	14.4968i		−	0.566437i
$656$	14.0207	+	41.9722i	0.547417	+	1.63874i
$657$	−3.69298	+	7.66855i	−0.144077	+	0.299179i
$658$	1.68921	−	22.0260i	0.0658522	−	0.858662i
$659$	−20.1815	−	41.9073i	−0.786159	−	1.63248i	−0.774525	−	0.632543i	$-0.782011\pi$
$659$	−20.1815	−	41.9073i	−0.786159	−	1.63248i	−0.0116331	−	0.999932i	$-0.503703\pi$
$660$	−5.61991	−	8.04093i	−0.218755	−	0.312993i
$661$	−15.1941	−	3.46795i	−0.590981	−	0.134887i	−0.0834363	−	0.996513i	$-0.526590\pi$
$661$	−15.1941	−	3.46795i	−0.590981	−	0.134887i	−0.507544	+	0.861626i	$0.669447\pi$
$662$	−2.54683	+	1.90255i	−0.0989853	+	0.0739449i
$663$	−15.7486	+	7.58414i	−0.611626	+	0.294544i
$664$	29.9386	+	2.84683i	1.16184	+	0.110478i
$665$	8.59516	−	9.83675i	0.333306	−	0.381453i
$666$	14.1580	−	6.27503i	0.548610	−	0.243152i
$667$			47.8321i			1.85207i
$668$	0.878043	+	5.39976i	0.0339725	+	0.208923i
$669$	19.9558	+	9.61021i	0.771536	+	0.371552i
$670$	−1.77680	−	9.10137i	−0.0686437	−	0.351617i
$671$	7.53611	−	33.0178i	0.290928	−	1.27464i
$672$	15.2567	−	0.327344i	0.588539	−	0.0126276i
$673$	−6.37705	−	27.9397i	−0.245817	−	1.07700i	−0.935623	−	0.353001i	$-0.885161\pi$
$673$	−6.37705	−	27.9397i	−0.245817	−	1.07700i	0.689805	−	0.723995i	$-0.257696\pi$
$674$	16.7421	−	7.42036i	0.644882	−	0.285822i
$675$	−4.65594	−	20.3990i	−0.179207	−	0.785158i
$676$	−9.19350	−	5.16665i	−0.353596	−	0.198717i
$677$	0.0287922	+	0.00657164i	0.00110658	+	0.000252569i	0.223074	−	0.974801i	$-0.428391\pi$
$677$	0.0287922	+	0.00657164i	0.00110658	+	0.000252569i	−0.221968	+	0.975054i	$0.571248\pi$
$678$	−10.3074	−	0.325835i	−0.395852	−	0.0125136i
$679$	5.41695	+	29.8602i	0.207883	+	1.14593i
$680$	−15.1999	+	5.61732i	−0.582891	+	0.215415i
$681$	−0.778889	−	0.976695i	−0.0298471	−	0.0374270i
$682$	19.8941	+	5.20715i	0.761783	+	0.199392i
$683$	9.04267	−	7.21129i	0.346008	−	0.275932i	−0.435030	−	0.900416i	$-0.643262\pi$
$683$	9.04267	−	7.21129i	0.346008	−	0.275932i	0.781038	+	0.624484i	$0.214691\pi$
$684$	19.3079	−	7.83740i	0.738256	−	0.299670i
$685$			2.32952i			0.0890065i
$686$	26.1476	−	1.51765i	0.998320	−	0.0579443i
$687$			19.9132i			0.759734i
$688$	−7.69921	+	4.68652i	−0.293530	+	0.178672i
$689$	−8.52825	+	6.80105i	−0.324901	+	0.259100i
$690$	−2.08852	+	7.97925i	−0.0795086	+	0.303765i
$691$	15.6042	+	19.5671i	0.593613	+	0.744368i	0.984367	−	0.176128i	$-0.0563571\pi$
$691$	15.6042	+	19.5671i	0.593613	+	0.744368i	−0.390754	+	0.920495i	$0.627786\pi$
$692$	−12.3627	+	21.9981i	−0.469960	+	0.836243i
$693$	−4.79433	−	26.4281i	−0.182122	−	1.00392i
$694$	0.0162048	−	0.512619i	0.000615127	−	0.0194588i
$695$	3.63222	+	0.829031i	0.137778	+	0.0314469i
$696$	21.0139	−	7.76595i	0.796530	−	0.294368i
$697$	15.1822	+	66.5174i	0.575066	+	2.51953i
$698$	14.5777	+	32.8908i	0.551774	+	1.24493i
$699$	−5.16613	−	22.6343i	−0.195401	−	0.856108i
$700$	18.4882	−	11.7218i	0.698788	−	0.443041i
$701$	9.79183	−	42.9008i	0.369832	−	1.62034i	−0.357402	−	0.933951i	$-0.616337\pi$
$701$	9.79183	−	42.9008i	0.369832	−	1.62034i	0.727234	−	0.686390i	$-0.240806\pi$
$702$	−19.5143	+	3.80963i	−0.736518	+	0.143785i
$703$	−26.7474	−	12.8809i	−1.00880	−	0.485812i
$704$	36.6776	−	19.2625i	1.38234	−	0.725982i
$705$		−	5.59225i		−	0.210616i
$706$	−12.1043	−	27.3101i	−0.455550	−	1.02783i
$707$	26.4608	−	30.2831i	0.995160	−	1.13891i
$708$	6.80300	+	9.73370i	0.255673	+	0.365815i
$709$	−28.0827	+	13.5239i	−1.05467	+	0.507900i	−0.879135	−	0.476573i	$-0.841879\pi$
$709$	−28.0827	+	13.5239i	−1.05467	+	0.507900i	−0.175531	+	0.984474i	$0.556164\pi$
$710$	−1.10133	−	1.47428i	−0.0413322	−	0.0553287i
$711$	2.82651	+	0.645133i	0.106003	+	0.0241944i
$712$	2.21165	−	23.2587i	0.0828849	−	0.871657i
$713$	−7.50170	−	15.5774i	−0.280941	−	0.583380i
$714$	23.4594	+	1.79914i	0.877944	+	0.0673310i
$715$	−5.80220	+	12.0484i	−0.216990	+	0.450585i
$716$	20.5232	−	3.33723i	0.766988	−	0.124718i
$717$			4.90767i			0.183280i
$718$	−21.4047	−	48.2942i	−0.798817	−	1.80232i
$719$	−11.6224	+	14.5740i	−0.433441	+	0.543518i	−0.949801	−	0.312854i	$-0.898715\pi$
$719$	−11.6224	+	14.5740i	−0.433441	+	0.543518i	0.516360	+	0.856371i	$0.327287\pi$
$720$	−7.24969	+	0.712711i	−0.270180	+	0.0265612i
$721$	−19.3871	−	16.9401i	−0.722013	−	0.630881i
$722$	−11.5965	−	6.04317i	−0.431577	−	0.224903i
$723$	3.95099	−	8.20432i	0.146939	−	0.305122i
$724$	−6.86820	−	16.9202i	−0.255255	−	0.628836i
$725$	20.0373	−	25.1260i	0.744167	−	0.933157i
$726$	13.6497	+	18.2720i	0.506588	+	0.678137i
$727$	18.2390	+	22.8710i	0.676447	+	0.848237i	0.995022	−	0.0996604i	$-0.0317756\pi$
$727$	18.2390	+	22.8710i	0.676447	+	0.848237i	−0.318575	+	0.947898i	$0.603204\pi$
$728$	−10.5780	−	17.9115i	−0.392045	−	0.663846i
$729$	8.76052	−	10.9853i	0.324464	−	0.406865i
$730$	−5.70120	−	0.180225i	−0.211011	−	0.00667044i
$731$	−12.5207	+	6.02965i	−0.463094	+	0.223014i
$732$	9.88076	+	8.95702i	0.365203	+	0.331061i
$733$	27.4010	−	6.25409i	1.01208	−	0.231000i	0.315841	−	0.948812i	$-0.397713\pi$
$733$	27.4010	−	6.25409i	1.01208	−	0.231000i	0.696237	+	0.717812i	$0.254856\pi$
$734$	−29.9050	+	35.1606i	−1.10382	+	1.29780i
$735$	6.57051	−	0.889225i	0.242357	−	0.0327996i
$736$	−32.3154	−	12.9974i	−1.19116	−	0.479091i
$737$	8.13363	+	35.6358i	0.299606	+	1.31266i
$738$	−0.969087	+	30.6558i	−0.0356726	+	1.12846i
$739$	−10.2252	−	21.2329i	−0.376142	−	0.781066i	0.623858	−	0.781538i	$-0.285564\pi$
$739$	−10.2252	−	21.2329i	−0.376142	−	0.781066i	−1.00000		0.000471178i	$0.999850\pi$
$740$	7.68917	+	6.97032i	0.282660	+	0.256234i
$741$	11.7771	+	9.39195i	0.432644	+	0.345022i
$742$	14.5224	−	2.16304i	0.533134	−	0.0794075i
$743$	−2.49935	+	1.99316i	−0.0916922	+	0.0731221i	−0.668263	−	0.743925i	$-0.732962\pi$
$743$	−2.49935	+	1.99316i	−0.0916922	+	0.0731221i	0.576571	+	0.817047i	$0.304390\pi$
$744$	−5.62561	+	5.82482i	−0.206245	+	0.213548i
$745$	−1.47640	−	1.17739i	−0.0540911	−	0.0431362i
$746$	−21.9160	−	11.4209i	−0.802403	−	0.418148i
$747$	18.7799	+	9.04390i	0.687119	+	0.330899i
$748$	59.1842	−	24.0238i	2.16399	−	0.878398i
$749$	11.1083	+	0.499548i	0.405888	+	0.0182531i
$750$	9.80549	−	7.32499i	0.358046	−	0.267471i
$751$	−2.87328	−	2.29137i	−0.104848	−	0.0836132i	0.569663	−	0.821879i	$-0.307074\pi$
$751$	−2.87328	−	2.29137i	−0.104848	−	0.0836132i	−0.674510	+	0.738265i	$0.735645\pi$
$752$	23.4275	+	2.97723i	0.854312	+	0.108568i
$753$	−5.23676			−0.190838
$754$	−23.2624	−	19.7853i	−0.847168	−	0.720539i
$755$	−2.80231	−	1.34952i	−0.101986	−	0.0491141i
$756$	25.2965	+	8.73662i	0.920026	+	0.317748i
$757$	17.6860	−	8.51712i	0.642808	−	0.309560i	−0.0839331	−	0.996471i	$-0.526748\pi$
$757$	17.6860	−	8.51712i	0.642808	−	0.309560i	0.726741	+	0.686911i	$0.241034\pi$
$758$	−2.26571	−	0.593035i	−0.0822942	−	0.0215400i
$759$	7.23447	−	31.6963i	0.262595	−	1.15050i
$760$	10.0449	+	9.70133i	0.364366	+	0.351904i
$761$	7.92651	+	16.4596i	0.287336	+	0.596659i	0.993812	−	0.111078i	$-0.0354304\pi$
$761$	7.92651	+	16.4596i	0.287336	+	0.596659i	−0.706476	+	0.707737i	$0.749716\pi$
$762$	−9.10528	−	2.38325i	−0.329850	−	0.0863361i
$763$	7.58552	+	17.7502i	0.274614	+	0.642599i
$764$	−32.3924	−	9.58178i	−1.17192	−	0.346657i
$765$	−11.2315			−0.406076
$766$	−2.91353	+	3.42556i	−0.105270	+	0.123771i
$767$	7.02367	−	14.5848i	0.253610	−	0.526627i

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25414 - 0.653556i) q^{2} +(-0.635719 - 0.797166i) q^{3} +(1.14573 + 1.63930i) q^{4} +(-0.726306 + 0.579209i) q^{5} +(0.276287 + 1.41524i) q^{6} +(-2.60326 + 0.472259i) q^{7} +(-0.365526 - 2.80471i) q^{8} +(0.436227 - 1.91124i) q^{9} +O(q^{10})\)	\(q+(-1.25414 - 0.653556i) q^{2} +(-0.635719 - 0.797166i) q^{3} +(1.14573 + 1.63930i) q^{4} +(-0.726306 + 0.579209i) q^{5} +(0.276287 + 1.41524i) q^{6} +(-2.60326 + 0.472259i) q^{7} +(-0.365526 - 2.80471i) q^{8} +(0.436227 - 1.91124i) q^{9} +(1.28943 - 0.251727i) q^{10} +(-5.04868 + 1.15233i) q^{11} +(0.578434 - 1.95547i) q^{12} +(-2.71007 + 0.618555i) q^{13} +(3.57350 + 1.10910i) q^{14} +(0.923453 + 0.210772i) q^{15} +(-1.37461 + 3.75639i) q^{16} +(-2.67586 + 5.55648i) q^{17} +(-1.79619 + 2.11186i) q^{18} +5.31475 q^{19} +(-1.78165 - 0.527017i) q^{20} +(2.03141 + 1.77501i) q^{21} +(7.08486 + 1.85442i) q^{22} +(-2.67158 - 5.54759i) q^{23} +(-2.00345 + 2.07439i) q^{24} +(-0.920568 + 4.03327i) q^{25} +(3.80306 + 0.995428i) q^{26} +(-4.55681 + 2.19445i) q^{27} +(-3.75681 - 3.72645i) q^{28} +(-6.99898 - 3.37053i) q^{29} +(-1.02039 - 0.867866i) q^{30} +2.80797 q^{31} +(4.17897 - 3.81264i) q^{32} +(4.12814 + 3.29208i) q^{33} +(6.98737 - 5.21977i) q^{34} +(1.61723 - 1.85084i) q^{35} +(3.63289 - 1.47465i) q^{36} +(-5.03268 - 2.42361i) q^{37} +(-6.66544 - 3.47349i) q^{38} +(2.21593 + 1.76715i) q^{39} +(1.89000 + 1.82536i) q^{40} +(8.64941 - 6.89767i) q^{41} +(-1.38760 - 3.55375i) q^{42} +(1.76174 + 1.40494i) q^{43} +(-7.67343 - 6.95606i) q^{44} +(0.790172 + 1.64081i) q^{45} +(-0.275133 + 8.70347i) q^{46} +(-1.31376 - 5.75595i) q^{47} +(3.86833 - 1.29221i) q^{48} +(6.55394 - 2.45883i) q^{49} +(3.79049 - 4.45664i) q^{50} +(6.13053 - 1.39925i) q^{51} +(-4.11900 - 3.73392i) q^{52} +(3.53549 - 1.70260i) q^{53} +(7.14907 + 0.225995i) q^{54} +(2.99945 - 3.76119i) q^{55} +(2.27611 + 7.12877i) q^{56} +(-3.37869 - 4.23674i) q^{57} +(6.57486 + 8.80135i) q^{58} +(-3.63089 + 4.55299i) q^{59} +(0.712507 + 1.75530i) q^{60} +(-2.83755 + 5.89224i) q^{61} +(-3.52158 - 1.83516i) q^{62} +(-0.233014 + 5.18146i) q^{63} +(-7.73278 + 2.05039i) q^{64} +(1.61006 - 2.01896i) q^{65} +(-3.02570 - 6.82670i) q^{66} -7.05842i q^{67} +(-12.1745 + 1.97967i) q^{68} +(-2.72398 + 5.65640i) q^{69} +(-3.23785 + 1.26426i) q^{70} +(-0.607747 - 1.26200i) q^{71} +(-5.51991 - 0.524883i) q^{72} +(-4.23286 - 0.966123i) q^{73} +(4.72771 + 6.32868i) q^{74} +(3.80041 - 1.83018i) q^{75} +(6.08926 + 8.71248i) q^{76} +(12.5988 - 5.38410i) q^{77} +(-1.62416 - 3.66449i) q^{78} +1.47889i q^{79} +(-1.17734 - 3.52447i) q^{80} +(-0.652553 - 0.314253i) q^{81} +(-15.3556 + 2.99776i) q^{82} +(-2.36598 + 10.3660i) q^{83} +(-0.582327 + 5.36377i) q^{84} +(-1.27487 - 5.58558i) q^{85} +(-1.29126 - 2.91339i) q^{86} +(1.76251 + 7.72207i) q^{87} +(5.07738 + 13.7389i) q^{88} +(8.05318 + 1.83809i) q^{89} +(0.0813759 - 2.57422i) q^{90} +(6.76290 - 2.89012i) q^{91} +(6.03326 - 10.7355i) q^{92} +(-1.78508 - 2.23842i) q^{93} +(-2.11420 + 8.07738i) q^{94} +(-3.86013 + 3.07835i) q^{95} +(-5.69596 - 0.907564i) q^{96} -11.4703i q^{97} +(-9.82654 - 1.19966i) q^{98} +10.1519i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9}+O(q^{10}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26} + 42 q^{28} - 30 q^{29} - 4 q^{30} - 5 q^{32} - 14 q^{33} + 77 q^{34} - 11 q^{36} + 10 q^{37} - 21 q^{38} - 63 q^{40} - 14 q^{41} - 7 q^{42} - 55 q^{44} - 14 q^{45} - 19 q^{46} - 132 q^{50} - 7 q^{52} - 2 q^{53} + 14 q^{54} - 70 q^{56} - 64 q^{57} - 3 q^{58} - 107 q^{60} + 14 q^{61} - 21 q^{62} - 11 q^{64} - 22 q^{65} + 161 q^{66} - 70 q^{69} - 77 q^{70} + 114 q^{72} - 14 q^{73} + 5 q^{74} + 70 q^{76} - 42 q^{77} + 61 q^{78} + 92 q^{81} - 42 q^{82} + 70 q^{84} - 6 q^{85} + 47 q^{86} + 65 q^{88} - 14 q^{89} + 112 q^{90} - 70 q^{92} - 48 q^{93} - 28 q^{94} + 238 q^{96} + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

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