LMFDB - Embedded newform 378.2.w.b.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	378.25
Dual form			378.2.w.b.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-0.902405 + 1.47840i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.70320 - 1.34785i) q^{5} +(-0.342341 + 1.69788i) q^{6} +(-0.207321 + 2.63762i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.37133 - 2.66823i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-0.902405 + 1.47840i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.70320 - 1.34785i) q^{5} +(-0.342341 + 1.69788i) q^{6} +(-0.207321 + 2.63762i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.37133 - 2.66823i) q^{9} -3.94086 q^{10} +(-3.21532 + 1.17028i) q^{11} +(0.259015 + 1.71257i) q^{12} +(-0.849585 - 4.81824i) q^{13} +(0.707299 + 2.54946i) q^{14} +(5.33445 - 4.25849i) q^{15} +(0.173648 - 0.984808i) q^{16} -7.47519 q^{17} +(-2.20122 - 2.03829i) q^{18} +0.401606 q^{19} +(-3.70320 + 1.34785i) q^{20} +(-3.71236 - 2.68670i) q^{21} +(-2.62115 + 2.19941i) q^{22} +(0.809905 + 4.59320i) q^{23} +(0.829129 + 1.52071i) q^{24} +(8.06673 + 6.76879i) q^{25} +(-2.44628 - 4.23709i) q^{26} +(5.18221 + 0.380448i) q^{27} +(1.53661 + 2.15379i) q^{28} +(-0.196696 + 1.11552i) q^{29} +(3.55625 - 5.82616i) q^{30} +(-3.94095 + 3.30685i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(1.17138 - 5.80959i) q^{33} +(-7.02438 + 2.55666i) q^{34} +(4.32287 - 9.48817i) q^{35} +(-2.76561 - 1.16251i) q^{36} +(1.59639 - 2.76503i) q^{37} +(0.377386 - 0.137357i) q^{38} +(7.88995 + 3.09197i) q^{39} +(-3.01887 + 2.53314i) q^{40} +(0.523747 + 2.97031i) q^{41} +(-4.40739 - 1.25497i) q^{42} +(-3.03657 - 2.54798i) q^{43} +(-1.71083 + 2.96325i) q^{44} +(1.48193 + 11.7293i) q^{45} +(2.33203 + 4.03919i) q^{46} +(0.854241 + 0.716794i) q^{47} +(1.29924 + 1.14542i) q^{48} +(-6.91404 - 1.09367i) q^{49} +(9.89531 + 3.60160i) q^{50} +(6.74564 - 11.0513i) q^{51} +(-3.74792 - 3.14488i) q^{52} +(5.46677 - 9.46872i) q^{53} +(4.99980 - 1.41491i) q^{54} +13.4843 q^{55} +(2.18058 + 1.49835i) q^{56} +(-0.362411 + 0.593734i) q^{57} +(0.196696 + 1.11552i) q^{58} +(0.596467 + 3.38273i) q^{59} +(1.34912 - 6.69111i) q^{60} +(7.90237 + 6.63088i) q^{61} +(-2.57227 + 4.45531i) q^{62} +(7.32207 - 3.06386i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.34810 + 18.9880i) q^{65} +(-0.886263 - 5.85986i) q^{66} +(-1.99857 - 0.727420i) q^{67} +(-5.72632 + 4.80496i) q^{68} +(-7.52145 - 2.94756i) q^{69} +(0.817025 - 10.3945i) q^{70} +(-1.71767 - 2.97510i) q^{71} +(-2.99642 - 0.146507i) q^{72} +(1.09956 + 1.90449i) q^{73} +(0.554420 - 3.14427i) q^{74} +(-17.2864 + 5.81766i) q^{75} +(0.307648 - 0.258147i) q^{76} +(-2.42014 - 8.72340i) q^{77} +(8.47165 + 0.206983i) q^{78} +(-15.2674 + 5.55686i) q^{79} +(-1.97043 + 3.41288i) q^{80} +(-5.23890 + 7.31805i) q^{81} +(1.50807 + 2.61205i) q^{82} +(-0.188556 + 1.06935i) q^{83} +(-4.57081 + 0.328128i) q^{84} +(27.6821 + 10.0755i) q^{85} +(-3.72490 - 1.35575i) q^{86} +(-1.47168 - 1.29744i) q^{87} +(-0.594167 + 3.36969i) q^{88} +3.30103 q^{89} +(5.40422 + 10.5151i) q^{90} +(12.8848 - 1.24196i) q^{91} +(3.57287 + 2.99800i) q^{92} +(-1.33251 - 8.81042i) q^{93} +(1.04788 + 0.381398i) q^{94} +(-1.48723 - 0.541306i) q^{95} +(1.61264 + 0.631974i) q^{96} +(-10.4530 - 8.77109i) q^{97} +(-6.87113 + 1.33703i) q^{98} +(7.53184 + 6.97436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−0.902405	+	1.47840i	−0.521004	+	0.853554i
$3$	−0.902405	+	1.47840i	−0.521004	+	0.853554i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−3.70320	−	1.34785i	−1.65612	−	0.602778i	−0.666374	−	0.745618i	$-0.732154\pi$
$5$	−3.70320	−	1.34785i	−1.65612	−	0.602778i	−0.989746	+	0.142840i	$0.954377\pi$
$6$	−0.342341	+	1.69788i	−0.139760	+	0.693157i
$7$	−0.207321	+	2.63762i	−0.0783602	+	0.996925i
$7$	−0.207321	+	2.63762i	−0.0783602	+	0.996925i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−1.37133	−	2.66823i	−0.457110	−	0.889410i
$10$	−3.94086			−1.24621
$11$	−3.21532	+	1.17028i	−0.969455	+	0.352853i	−0.777732	−	0.628596i	$-0.783630\pi$
$11$	−3.21532	+	1.17028i	−0.969455	+	0.352853i	−0.191723	+	0.981449i	$0.561408\pi$
$12$	0.259015	+	1.71257i	0.0747711	+	0.494378i
$13$	−0.849585	−	4.81824i	−0.235633	−	1.33634i	−0.841277	−	0.540604i	$-0.818196\pi$
$13$	−0.849585	−	4.81824i	−0.235633	−	1.33634i	0.605645	−	0.795735i	$-0.292915\pi$
$14$	0.707299	+	2.54946i	0.189034	+	0.681371i
$15$	5.33445	−	4.25849i	1.37735	−	1.09954i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−7.47519			−1.81300			−0.906499	−	0.422207i	$-0.861256\pi$
$17$	−7.47519			−1.81300			−0.906499	+	0.422207i	$0.861256\pi$
$18$	−2.20122	−	2.03829i	−0.518832	−	0.480430i
$19$	0.401606			0.0921348			0.0460674	−	0.998938i	$-0.485331\pi$
$19$	0.401606			0.0921348			0.0460674	+	0.998938i	$0.485331\pi$
$20$	−3.70320	+	1.34785i	−0.828060	+	0.301389i
$21$	−3.71236	−	2.68670i	−0.810104	−	0.586286i
$22$	−2.62115	+	2.19941i	−0.558831	+	0.468915i
$23$	0.809905	+	4.59320i	0.168877	+	0.957748i	0.944977	+	0.327138i	$0.106084\pi$
$23$	0.809905	+	4.59320i	0.168877	+	0.957748i	−0.776100	+	0.630610i	$0.782805\pi$
$24$	0.829129	+	1.52071i	0.169245	+	0.310413i
$25$	8.06673	+	6.76879i	1.61335	+	1.35376i
$26$	−2.44628	−	4.23709i	−0.479756	−	0.830961i
$27$	5.18221	+	0.380448i	0.997316	+	0.0732172i
$28$	1.53661	+	2.15379i	0.290392	+	0.407029i
$29$	−0.196696	+	1.11552i	−0.0365255	+	0.207147i	−0.997609	−	0.0691119i	$-0.977983\pi$
$29$	−0.196696	+	1.11552i	−0.0365255	+	0.207147i	0.961083	+	0.276258i	$0.0890946\pi$
$30$	3.55625	−	5.82616i	0.649279	−	1.06371i
$31$	−3.94095	+	3.30685i	−0.707816	+	0.593928i	−0.923985	−	0.382428i	$-0.875088\pi$
$31$	−3.94095	+	3.30685i	−0.707816	+	0.593928i	0.216169	+	0.976356i	$0.430644\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	1.17138	−	5.80959i	0.203910	−	1.01132i
$34$	−7.02438	+	2.55666i	−1.20467	+	0.438464i
$35$	4.32287	−	9.48817i	0.730699	−	1.60379i
$36$	−2.76561	−	1.16251i	−0.460934	−	0.193751i
$37$	1.59639	−	2.76503i	0.262445	−	0.454568i	−0.704446	−	0.709757i	$-0.748805\pi$
$37$	1.59639	−	2.76503i	0.262445	−	0.454568i	0.966891	+	0.255190i	$0.0821379\pi$
$38$	0.377386	−	0.137357i	0.0612201	−	0.0222823i
$39$	7.88995	+	3.09197i	1.26340	+	0.495112i
$40$	−3.01887	+	2.53314i	−0.477326	+	0.400524i
$41$	0.523747	+	2.97031i	0.0817955	+	0.463885i	0.998002	+	0.0631792i	$0.0201240\pi$
$41$	0.523747	+	2.97031i	0.0817955	+	0.463885i	−0.916207	+	0.400706i	$0.868765\pi$
$42$	−4.40739	−	1.25497i	−0.680074	−	0.193646i
$43$	−3.03657	−	2.54798i	−0.463072	−	0.388564i	0.381188	−	0.924498i	$-0.375515\pi$
$43$	−3.03657	−	2.54798i	−0.463072	−	0.388564i	−0.844260	+	0.535934i	$0.819960\pi$
$44$	−1.71083	+	2.96325i	−0.257918	+	0.446727i
$45$	1.48193	+	11.7293i	0.220913	+	1.74851i
$46$	2.33203	+	4.03919i	0.343839	+	0.595546i
$47$	0.854241	+	0.716794i	0.124604	+	0.104555i	0.702960	−	0.711229i	$-0.251861\pi$
$47$	0.854241	+	0.716794i	0.124604	+	0.104555i	−0.578356	+	0.815784i	$0.696306\pi$
$48$	1.29924	+	1.14542i	0.187529	+	0.165327i
$49$	−6.91404	−	1.09367i	−0.987719	−	0.156238i
$50$	9.89531	+	3.60160i	1.39941	+	0.509343i
$51$	6.74564	−	11.0513i	0.944579	−	1.54749i
$52$	−3.74792	−	3.14488i	−0.519744	−	0.436117i
$53$	5.46677	−	9.46872i	0.750918	−	1.30063i	−0.196460	−	0.980512i	$-0.562945\pi$
$53$	5.46677	−	9.46872i	0.750918	−	1.30063i	0.947378	−	0.320117i	$-0.103722\pi$
$54$	4.99980	−	1.41491i	0.680387	−	0.192546i
$55$	13.4843			1.81822
$56$	2.18058	+	1.49835i	0.291392	+	0.200226i
$57$	−0.362411	+	0.593734i	−0.0480025	+	0.0786420i
$58$	0.196696	+	1.11552i	0.0258274	+	0.146475i
$59$	0.596467	+	3.38273i	0.0776534	+	0.440394i	0.998701	+	0.0509454i	$0.0162234\pi$
$59$	0.596467	+	3.38273i	0.0776534	+	0.440394i	−0.921048	+	0.389449i	$0.872665\pi$
$60$	1.34912	−	6.69111i	0.174170	−	0.863819i
$61$	7.90237	+	6.63088i	1.01180	+	0.848997i	0.988574	−	0.150733i	$-0.0481635\pi$
$61$	7.90237	+	6.63088i	1.01180	+	0.848997i	0.0232207	+	0.999730i	$0.492608\pi$
$62$	−2.57227	+	4.45531i	−0.326679	+	0.565825i
$63$	7.32207	−	3.06386i	0.922494	−	0.386011i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−3.34810	+	18.9880i	−0.415280	+	2.35517i
$66$	−0.886263	−	5.85986i	−0.109091	−	0.721299i
$67$	−1.99857	−	0.727420i	−0.244164	−	0.0888685i	0.217039	−	0.976163i	$-0.430360\pi$
$67$	−1.99857	−	0.727420i	−0.244164	−	0.0888685i	−0.461204	+	0.887294i	$0.652582\pi$
$68$	−5.72632	+	4.80496i	−0.694419	+	0.582687i
$69$	−7.52145	−	2.94756i	−0.905476	−	0.354845i
$70$	0.817025	−	10.3945i	0.0976531	−	1.24238i
$71$	−1.71767	−	2.97510i	−0.203850	−	0.353079i	0.745915	−	0.666041i	$-0.232012\pi$
$71$	−1.71767	−	2.97510i	−0.203850	−	0.353079i	−0.949766	+	0.312961i	$0.898679\pi$
$72$	−2.99642	−	0.146507i	−0.353132	−	0.0172660i
$73$	1.09956	+	1.90449i	0.128694	+	0.222904i	0.923171	−	0.384390i	$-0.125588\pi$
$73$	1.09956	+	1.90449i	0.128694	+	0.222904i	−0.794477	+	0.607294i	$0.792255\pi$
$74$	0.554420	−	3.14427i	0.0644501	−	0.365514i
$75$	−17.2864	+	5.81766i	−1.99607	+	0.671766i
$76$	0.307648	−	0.258147i	0.0352897	−	0.0296115i
$77$	−2.42014	−	8.72340i	−0.275801	−	0.994123i
$78$	8.47165	+	0.206983i	0.959225	+	0.0234362i
$79$	−15.2674	+	5.55686i	−1.71771	+	0.625196i	−0.997637	−	0.0687006i	$-0.978115\pi$
$79$	−15.2674	+	5.55686i	−1.71771	+	0.625196i	−0.720075	+	0.693897i	$0.755892\pi$
$80$	−1.97043	+	3.41288i	−0.220301	+	0.381572i
$81$	−5.23890	+	7.31805i	−0.582100	+	0.813117i
$82$	1.50807	+	2.61205i	0.166538	+	0.288453i
$83$	−0.188556	+	1.06935i	−0.0206967	+	0.117377i	−0.993406	−	0.114651i	$-0.963425\pi$
$83$	−0.188556	+	1.06935i	−0.0206967	+	0.117377i	0.972709	+	0.232028i	$0.0745361\pi$
$84$	−4.57081	+	0.328128i	−0.498717	+	0.0358017i
$85$	27.6821	+	10.0755i	3.00254	+	1.09284i
$86$	−3.72490	−	1.35575i	−0.401667	−	0.146195i
$87$	−1.47168	−	1.29744i	−0.157781	−	0.139101i
$88$	−0.594167	+	3.36969i	−0.0633384	+	0.359210i
$89$	3.30103			0.349909			0.174954	−	0.984577i	$-0.444022\pi$
$89$	3.30103			0.349909			0.174954	+	0.984577i	$0.444022\pi$
$90$	5.40422	+	10.5151i	0.569655	+	1.10839i
$91$	12.8848	−	1.24196i	1.35069	−	0.130192i
$92$	3.57287	+	2.99800i	0.372498	+	0.312563i
$93$	−1.33251	−	8.81042i	−0.138175	−	0.913598i
$94$	1.04788	+	0.381398i	0.108081	+	0.0393382i
$95$	−1.48723	−	0.541306i	−0.152586	−	0.0555368i
$96$	1.61264	+	0.631974i	0.164589	+	0.0645006i
$97$	−10.4530	−	8.77109i	−1.06134	−	0.890569i	−0.0670992	−	0.997746i	$-0.521374\pi$
$97$	−10.4530	−	8.77109i	−1.06134	−	0.890569i	−0.994240	+	0.107177i	$0.965819\pi$
$98$	−6.87113	+	1.33703i	−0.694088	+	0.135060i
$99$	7.53184	+	6.97436i	0.756978	+	0.700950i
$100$	10.5304			1.05304
$101$	0.226498	−	1.28454i	0.0225374	−	0.127816i	−0.971463	−	0.237190i	$-0.923774\pi$
$101$	0.226498	−	1.28454i	0.0225374	−	0.127816i	0.994001	+	0.109374i	$0.0348846\pi$
$102$	2.55906	−	12.6920i	0.253385	−	1.25669i
$103$	7.68981	+	2.79886i	0.757700	+	0.275780i	0.691842	−	0.722049i	$-0.256799\pi$
$103$	7.68981	+	2.79886i	0.757700	+	0.275780i	0.0658578	+	0.997829i	$0.479022\pi$
$104$	−4.59751	−	1.67336i	−0.450823	−	0.164086i
$105$	10.1263	+	14.9531i	0.988228	+	1.45927i
$106$	1.89859	−	10.7674i	0.184407	−	1.04583i
$107$	−7.15354	−	12.3903i	−0.691559	−	1.19781i	−0.971327	−	0.237747i	$-0.923591\pi$
$107$	−7.15354	−	12.3903i	−0.691559	−	1.19781i	0.279768	−	0.960068i	$-0.409742\pi$
$108$	4.21435	−	3.03962i	0.405526	−	0.292487i
$109$	−4.67627	+	8.09953i	−0.447905	+	0.775794i	−0.998249	−	0.0591435i	$-0.981163\pi$
$109$	−4.67627	+	8.09953i	−0.447905	+	0.775794i	0.550345	+	0.834938i	$0.314496\pi$
$110$	12.6711	−	4.61191i	1.20814	−	0.439728i
$111$	2.64723	+	4.85528i	0.251264	+	0.460843i
$112$	2.56154	+	0.662189i	0.242043	+	0.0625710i
$113$	−4.30835	+	3.61514i	−0.405296	+	0.340084i	−0.822536	−	0.568713i	$-0.807442\pi$
$113$	−4.30835	+	3.61514i	−0.405296	+	0.340084i	0.417241	+	0.908796i	$0.362997\pi$
$114$	−0.137486	+	0.681880i	−0.0128768	+	0.0638639i
$115$	3.19172	−	18.1011i	0.297629	−	1.68794i
$116$	0.566363	+	0.980970i	0.0525855	+	0.0910808i
$117$	−11.6911	+	8.87429i	−1.08084	+	0.820428i
$118$	1.71746	+	2.97473i	0.158105	+	0.273846i
$119$	1.54977	−	19.7167i	0.142067	−	1.80742i
$120$	−1.02074	−	6.74901i	−0.0931805	−	0.616098i
$121$	0.542222	−	0.454978i	0.0492929	−	0.0413617i
$122$	9.69369	+	3.52822i	0.877626	+	0.319430i
$123$	−4.86394	−	1.90612i	−0.438567	−	0.171869i
$124$	−0.893342	+	5.06639i	−0.0802245	+	0.454975i
$125$	−10.8972	−	18.8745i	−0.974675	−	1.68819i
$126$	5.83259	−	5.38339i	0.519609	−	0.479590i
$127$	0.680921	−	1.17939i	0.0604220	−	0.104654i	−0.834232	−	0.551413i	$-0.814089\pi$
$127$	0.680921	−	1.17939i	0.0604220	−	0.104654i	0.894654	+	0.446760i	$0.147422\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	6.50715	−	2.18995i	0.572923	−	0.192814i
$130$	3.34810	+	18.9880i	0.293647	+	1.66536i
$131$	−3.11469	−	17.6643i	−0.272132	−	1.54334i	−0.747927	−	0.663781i	$-0.768951\pi$
$131$	−3.11469	−	17.6643i	−0.272132	−	1.54334i	0.475795	−	0.879556i	$-0.342160\pi$
$132$	−2.83701	−	5.20335i	−0.246930	−	0.452894i
$133$	−0.0832616	+	1.05928i	−0.00721969	+	0.0918515i
$134$	−2.12683			−0.183730
$135$	−18.6779	−	8.39373i	−1.60754	−	0.722417i
$136$	−3.73759	+	6.47370i	−0.320496	+	0.555115i
$137$	−9.37983	−	7.87061i	−0.801373	−	0.672432i	0.147159	−	0.989113i	$-0.452987\pi$
$137$	−9.37983	−	7.87061i	−0.801373	−	0.672432i	−0.948532	+	0.316681i	$0.897432\pi$
$138$	−8.07597	−	0.197316i	−0.687472	−	0.0167966i
$139$	−5.24500	−	1.90902i	−0.444875	−	0.161921i	0.109862	−	0.993947i	$-0.464959\pi$
$139$	−5.24500	−	1.90902i	−0.444875	−	0.161921i	−0.554737	+	0.832026i	$0.687181\pi$
$140$	−2.78737	−	10.0470i	−0.235575	−	0.849130i
$141$	−1.83058	+	0.616072i	−0.154163	+	0.0518826i
$142$	−2.63163	−	2.20820i	−0.220841	−	0.185308i
$143$	8.37037	+	14.4979i	0.699966	+	1.21238i
$144$	−2.86582	+	0.887164i	−0.238819	+	0.0739304i
$145$	2.23196	−	3.86587i	0.185354	−	0.321043i
$146$	1.68462	+	1.41357i	0.139420	+	0.116988i
$147$	7.85614	−	9.23478i	0.647963	−	0.761671i
$148$	−0.554420	−	3.14427i	−0.0455731	−	0.258458i
$149$	−12.5034	+	10.4916i	−1.02432	+	0.859503i	−0.990164	−	0.139914i	$-0.955318\pi$
$149$	−12.5034	+	10.4916i	−1.02432	+	0.859503i	−0.0341521	+	0.999417i	$0.510873\pi$
$150$	−14.2542	+	11.3791i	−1.16385	+	0.929101i
$151$	−10.3687	+	3.77391i	−0.843796	+	0.307117i	−0.727508	−	0.686099i	$-0.759322\pi$
$151$	−10.3687	+	3.77391i	−0.843796	+	0.307117i	−0.116288	+	0.993216i	$0.537100\pi$
$152$	0.200803	−	0.347801i	0.0162873	−	0.0282104i
$153$	10.2510	+	19.9455i	0.828741	+	1.61250i
$154$	−5.25777	−	7.36957i	−0.423683	−	0.593857i
$155$	19.0513	−	6.93410i	1.53024	−	0.556960i
$156$	8.03154	−	2.70297i	0.643038	−	0.216411i
$157$	−2.34598	−	13.3047i	−0.187229	−	1.06183i	−0.923058	−	0.384662i	$-0.874318\pi$
$157$	−2.34598	−	13.3047i	−0.187229	−	1.06183i	0.735828	−	0.677168i	$-0.236793\pi$
$158$	−12.4461	+	10.4435i	−0.990156	+	0.830839i
$159$	9.06531	+	16.6267i	0.718926	+	1.31858i
$160$	−0.684323	+	3.88099i	−0.0541005	+	0.306819i
$161$	−12.2830	+	1.18395i	−0.968036	+	0.0933083i
$162$	−2.42004	+	8.66853i	−0.190136	+	0.681064i
$163$	−2.08224	−	3.60655i	−0.163094	−	0.282487i	0.772883	−	0.634549i	$-0.218814\pi$
$163$	−2.08224	−	3.60655i	−0.163094	−	0.282487i	−0.935977	+	0.352062i	$0.885481\pi$
$164$	2.31049	+	1.93873i	0.180419	+	0.151390i
$165$	−12.1683	+	19.9352i	−0.947302	+	1.55195i
$166$	0.188556	+	1.06935i	0.0146348	+	0.0829979i
$167$	12.0596	−	10.1192i	0.933203	−	0.783050i	−0.0431868	−	0.999067i	$-0.513751\pi$
$167$	12.0596	−	10.1192i	0.933203	−	0.783050i	0.976390	+	0.216017i	$0.0693066\pi$
$168$	−4.18293	+	1.87165i	−0.322720	+	0.144401i
$169$	−10.2776	+	3.74075i	−0.790587	+	0.287750i
$170$	29.4587			2.25938
$171$	−0.550735	−	1.07158i	−0.0421158	−	0.0819456i
$172$	−3.96396			−0.302249
$173$	−4.15976	+	23.5912i	−0.316261	+	1.79360i	0.248800	+	0.968555i	$0.419964\pi$
$173$	−4.15976	+	23.5912i	−0.316261	+	1.79360i	−0.565061	+	0.825049i	$0.691147\pi$
$174$	−1.82668	−	0.715854i	−0.138480	−	0.0542687i
$175$	−19.5259	+	19.8736i	−1.47602	+	1.50230i
$176$	0.594167	+	3.36969i	0.0447870	+	0.254000i
$177$	−5.53929	−	2.17078i	−0.416358	−	0.163166i
$178$	3.10196	−	1.12902i	0.232501	−	0.0846236i
$179$	11.0034			0.822430			0.411215	−	0.911538i	$-0.365105\pi$
$179$	11.0034			0.822430			0.411215	+	0.911538i	$0.365105\pi$
$180$	8.67469	+	8.03262i	0.646573	+	0.598717i
$181$	0.501923	−	0.869356i	0.0373076	−	0.0646187i	−0.846769	−	0.531961i	$-0.821455\pi$
$181$	0.501923	−	0.869356i	0.0373076	−	0.0646187i	0.884076	+	0.467343i	$0.154789\pi$
$182$	11.6830	−	5.57392i	0.866000	−	0.413166i
$183$	−16.9342	+	5.69913i	−1.25181	+	0.421292i
$184$	4.38278	+	1.59520i	0.323103	+	0.117600i
$185$	−9.63860	+	8.08774i	−0.708644	+	0.594623i
$186$	−4.26550	−	7.82334i	−0.312761	−	0.573635i
$187$	24.0351	−	8.74806i	1.75762	−	0.639721i
$188$	1.11513			0.0813294
$189$	−2.07786	+	13.5898i	−0.151142	+	0.988512i
$190$	−1.58267			−0.114819
$191$	1.44470	−	0.525827i	0.104535	−	0.0380475i	−0.289223	−	0.957262i	$-0.593397\pi$
$191$	1.44470	−	0.525827i	0.104535	−	0.0380475i	0.393758	+	0.919214i	$0.371175\pi$
$192$	1.73153	+	0.0423056i	0.124963	+	0.00305315i
$193$	13.8997	−	11.6632i	1.00052	−	0.839536i	0.0134641	−	0.999909i	$-0.495714\pi$
$193$	13.8997	−	11.6632i	1.00052	−	0.839536i	0.987057	+	0.160373i	$0.0512697\pi$
$194$	−12.8225	−	4.66700i	−0.920600	−	0.335071i
$195$	−25.0505	−	22.0847i	−1.79390	−	1.58152i
$196$	−5.99946	+	3.60646i	−0.428533	+	0.257604i
$197$	−6.04304	+	10.4669i	−0.430549	+	0.745732i	−0.996921	−	0.0784176i	$-0.975013\pi$
$197$	−6.04304	+	10.4669i	−0.430549	+	0.745732i	0.566372	+	0.824150i	$0.308347\pi$
$198$	9.46299	+	3.97772i	0.672505	+	0.282684i
$199$	0.954423			0.0676573			0.0338286	−	0.999428i	$-0.489230\pi$
$199$	0.954423			0.0676573			0.0338286	+	0.999428i	$0.489230\pi$
$200$	9.89531	−	3.60160i	0.699704	−	0.254671i
$201$	2.87894	−	2.29826i	0.203065	−	0.162107i
$202$	−0.226498	−	1.28454i	−0.0159364	−	0.0903797i
$203$	−2.90153	−	0.750079i	−0.203647	−	0.0526452i
$204$	−1.93618	−	12.8018i	−0.135560	−	0.896306i
$205$	2.06401	−	11.7056i	0.144157	−	0.817554i
$206$	8.18333			0.570160
$207$	11.1451	−	8.45981i	0.774635	−	0.587997i
$208$	−4.89257			−0.339239
$209$	−1.29129	+	0.469992i	−0.0893205	+	0.0325100i
$210$	14.6299	+	10.5879i	1.00956	+	0.730635i
$211$	−12.1201	+	10.1700i	−0.834383	+	0.700131i	−0.956293	−	0.292411i	$-0.905543\pi$
$211$	−12.1201	+	10.1700i	−0.834383	+	0.700131i	0.121910	+	0.992541i	$0.461098\pi$
$212$	−1.89859	−	10.7674i	−0.130396	−	0.739510i
$213$	5.94842	+	0.145335i	0.407579	+	0.00995816i
$214$	−10.9599	−	9.19641i	−0.749200	−	0.628654i
$215$	7.81070	+	13.5285i	0.532685	+	0.922638i
$216$	2.92058	−	4.29770i	0.198720	−	0.292421i
$217$	−7.90516	−	11.0803i	−0.536637	−	0.752180i
$218$	−1.62405	+	9.21044i	−0.109995	+	0.623810i
$219$	−3.80785	−	0.0930351i	−0.257310	−	0.00628673i
$220$	10.3296	−	8.66755i	0.696420	−	0.584366i
$221$	6.35081	+	36.0172i	0.427202	+	2.42278i
$222$	4.14818	+	3.65706i	0.278408	+	0.245446i
$223$	−11.7347	+	4.27109i	−0.785816	+	0.286014i	−0.703596	−	0.710601i	$-0.748423\pi$
$223$	−11.7347	+	4.27109i	−0.785816	+	0.286014i	−0.0822204	+	0.996614i	$0.526201\pi$
$224$	2.63355	−	0.253845i	0.175961	−	0.0169608i
$225$	6.99853	−	30.8061i	0.466569	−	2.05374i
$226$	−2.81208	+	4.87066i	−0.187057	+	0.323992i
$227$	−21.2608	+	7.73829i	−1.41113	+	0.513608i	−0.931461	−	0.363842i	$-0.881465\pi$
$227$	−21.2608	+	7.73829i	−1.41113	+	0.513608i	−0.479667	+	0.877451i	$0.659242\pi$
$228$	0.104022	+	0.687780i	0.00688902	+	0.0455494i
$229$	−10.0990	+	8.47403i	−0.667357	+	0.559979i	−0.912282	−	0.409563i	$-0.865681\pi$
$229$	−10.0990	+	8.47403i	−0.667357	+	0.559979i	0.244925	+	0.969542i	$0.421237\pi$
$230$	−3.19172	−	18.1011i	−0.210456	−	1.19355i
$231$	15.0806	+	4.29409i	0.992232	+	0.282531i
$232$	0.867719	+	0.728103i	0.0569686	+	0.0478023i
$233$	6.26126	−	10.8448i	0.410189	−	0.710468i	−0.584721	−	0.811234i	$-0.698796\pi$
$233$	6.26126	−	10.8448i	0.410189	−	0.710468i	0.994910	+	0.100766i	$0.0321294\pi$
$234$	−7.95086	+	12.3377i	−0.519764	+	0.806541i
$235$	−2.19729	−	3.80582i	−0.143335	−	0.248264i
$236$	2.63130	+	2.20792i	0.171283	+	0.143724i
$237$	5.56207	−	27.5858i	0.361295	−	1.79189i
$238$	−5.28719	−	19.0577i	−0.342718	−	1.23532i
$239$	21.3504	+	7.77092i	1.38104	+	0.502659i	0.922495	−	0.386010i	$-0.126147\pi$
$239$	21.3504	+	7.77092i	1.38104	+	0.502659i	0.458549	+	0.888669i	$0.348369\pi$
$240$	−3.26748	−	5.99288i	−0.210915	−	0.386839i
$241$	−1.17639	−	0.987112i	−0.0757782	−	0.0635855i	0.604112	−	0.796900i	$-0.293528\pi$
$241$	−1.17639	−	0.987112i	−0.0757782	−	0.0635855i	−0.679890	+	0.733314i	$0.737972\pi$
$242$	0.353910	−	0.612991i	0.0227502	−	0.0394045i
$243$	−6.09140	−	14.3490i	−0.390763	−	0.920491i
$244$	10.3158			0.660402
$245$	24.1299	+	13.3692i	1.54160	+	0.854125i
$246$	−5.22254	−	0.127600i	−0.332977	−	0.00813545i
$247$	−0.341199	−	1.93503i	−0.0217100	−	0.123123i
$248$	0.893342	+	5.06639i	0.0567273	+	0.321716i
$249$	−1.41078	−	1.24375i	−0.0894044	−	0.0788195i
$250$	−16.6955	−	14.0092i	−1.05591	−	0.886018i
$251$	−4.33773	+	7.51317i	−0.273795	+	0.474227i	−0.969830	−	0.243781i	$-0.921612\pi$
$251$	−4.33773	+	7.51317i	−0.273795	+	0.474227i	0.696035	+	0.718007i	$0.254946\pi$
$252$	3.63962	−	7.05359i	0.229274	−	0.444335i
$253$	−7.97943	−	13.8208i	−0.501662	−	0.868905i
$254$	0.236481	−	1.34115i	0.0148382	−	0.0841514i
$255$	−39.8760	+	31.8330i	−2.49713	+	1.99346i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	8.65283	−	7.26059i	0.539749	−	0.452903i	−0.331703	−	0.943384i	$-0.607623\pi$
$257$	8.65283	−	7.26059i	0.539749	−	0.452903i	0.871452	+	0.490481i	$0.163179\pi$
$258$	5.36571	−	4.28346i	0.334055	−	0.266676i
$259$	6.96212	+	4.78391i	0.432605	+	0.297258i
$260$	9.64046	+	16.6978i	0.597876	+	1.03555i
$261$	3.24619	−	1.00491i	0.200934	−	0.0622027i
$262$	−8.96840	−	15.5337i	−0.554070	−	0.959677i
$263$	−1.42830	+	8.10028i	−0.0880726	+	0.499485i	0.908579	+	0.417714i	$0.137169\pi$
$263$	−1.42830	+	8.10028i	−0.0880726	+	0.499485i	−0.996651	+	0.0817706i	$0.973943\pi$
$264$	−4.44556	−	3.91924i	−0.273606	−	0.241212i
$265$	−33.0070	+	27.6961i	−2.02760	+	1.70136i
$266$	0.284056	+	1.02388i	0.0174166	+	0.0627779i
$267$	−2.97887	+	4.88025i	−0.182304	+	0.298666i
$268$	−1.99857	+	0.727420i	−0.122082	+	0.0444343i
$269$	13.8246	−	23.9449i	0.842901	−	1.45995i	−0.0445311	−	0.999008i	$-0.514179\pi$
$269$	13.8246	−	23.9449i	0.842901	−	1.45995i	0.887432	−	0.460939i	$-0.152487\pi$
$270$	−20.4223	−	1.49929i	−1.24286	−	0.0912439i
$271$	8.35025	+	14.4631i	0.507242	+	0.878568i	0.999965	+	0.00838234i	$0.00266821\pi$
$271$	8.35025	+	14.4631i	0.507242	+	0.878568i	−0.492723	+	0.870186i	$0.663998\pi$
$272$	−1.29805	+	7.36162i	−0.0787060	+	0.446364i
$273$	−9.79120	+	20.1696i	−0.592590	+	1.22072i
$274$	−11.5061	−	4.18787i	−0.695107	−	0.252998i
$275$	−33.8585	−	12.3235i	−2.04174	−	0.743134i
$276$	−7.65642	+	2.57673i	−0.460862	+	0.155101i
$277$	4.46825	−	25.3407i	0.268471	−	1.52258i	−0.490494	−	0.871445i	$-0.663183\pi$
$277$	4.46825	−	25.3407i	0.268471	−	1.52258i	0.758965	−	0.651132i	$-0.225705\pi$
$278$	−5.58161			−0.334763
$279$	14.2278	+	5.98058i	0.851796	+	0.358048i
$280$	−6.05556	−	8.48780i	−0.361889	−	0.507243i
$281$	−1.53256	−	1.28597i	−0.0914249	−	0.0767146i	0.595930	−	0.803037i	$-0.296784\pi$
$281$	−1.53256	−	1.28597i	−0.0914249	−	0.0767146i	−0.687355	+	0.726322i	$0.741228\pi$
$282$	−1.50947	+	1.20501i	−0.0898878	+	0.0717575i
$283$	−25.0437	−	9.11517i	−1.48869	−	0.541841i	−0.535589	−	0.844479i	$-0.679910\pi$
$283$	−25.0437	−	9.11517i	−1.48869	−	0.541841i	−0.953106	+	0.302638i	$0.902133\pi$
$284$	−3.22817	−	1.17496i	−0.191557	−	0.0697209i
$285$	2.14235	−	1.71024i	0.126902	−	0.101306i
$286$	12.8242	+	10.7607i	0.758308	+	0.636296i
$287$	−7.94313	+	0.765632i	−0.468868	+	0.0451938i
$288$	−2.38956	+	1.81383i	−0.140806	+	0.106881i
$289$	38.8784			2.28697
$290$	0.775151	−	4.39610i	0.0455184	−	0.258148i
$291$	22.4000	−	7.53861i	1.31311	−	0.441921i
$292$	2.06649	+	0.752143i	0.120932	+	0.0440158i
$293$	20.0174	+	7.28576i	1.16943	+	0.425638i	0.852458	−	0.522796i	$-0.175111\pi$
$293$	20.0174	+	7.28576i	1.16943	+	0.425638i	0.316974	+	0.948434i	$0.397333\pi$
$294$	4.22388	−	11.3648i	0.246341	−	0.662809i
$295$	2.35059	−	13.3309i	0.136857	−	0.776154i
$296$	−1.59639	−	2.76503i	−0.0927883	−	0.160714i
$297$	−17.1077	+	4.84137i	−0.992688	+	0.280925i
$298$	−8.16099	+	14.1353i	−0.472754	+	0.818833i
$299$	21.4430	−	7.80463i	1.24008	−	0.451353i
$300$	−9.50265	+	15.5681i	−0.548636	+	0.898824i
$301$	7.35015	−	7.48105i	0.423655	−	0.431200i
$302$	−8.45268	+	7.09264i	−0.486397	+	0.408135i
$303$	1.69467	+	1.49403i	0.0973560	+	0.0858296i
$304$	0.0697382	−	0.395505i	0.00399976	−	0.0226838i
$305$	−20.3266	−	35.2067i	−1.16390	−	2.01593i
$306$	16.4545	+	15.2366i	0.940642	+	0.871020i
$307$	6.56172	+	11.3652i	0.374497	+	0.648648i	0.990252	−	0.139290i	$-0.0444820\pi$
$307$	6.56172	+	11.3652i	0.374497	+	0.648648i	−0.615754	+	0.787938i	$0.711149\pi$
$308$	−7.46123	−	5.12687i	−0.425143	−	0.292131i
$309$	−11.0772	+	8.84291i	−0.630158	+	0.503056i
$310$	15.5307	−	13.0318i	0.882087	−	0.740159i
$311$	22.1261	+	8.05326i	1.25466	+	0.456658i	0.881973	−	0.471300i	$-0.156215\pi$
$311$	22.1261	+	8.05326i	1.25466	+	0.456658i	0.372685	+	0.927958i	$0.378437\pi$
$312$	6.62270	−	5.28691i	0.374937	−	0.299312i
$313$	0.500193	−	2.83674i	0.0282726	−	0.160342i	−0.967403	−	0.253243i	$-0.918503\pi$
$313$	0.500193	−	2.83674i	0.0282726	−	0.160342i	0.995675	+	0.0929009i	$0.0296140\pi$
$314$	−6.75497	−	11.7000i	−0.381205	−	0.660266i
$315$	−31.2447	+	1.47701i	−1.76044	+	0.0832201i
$316$	−8.12359	+	14.0705i	−0.456988	+	0.791526i
$317$	−0.766578	−	0.643236i	−0.0430553	−	0.0361277i	0.621006	−	0.783806i	$-0.286724\pi$
$317$	−0.766578	−	0.643236i	−0.0430553	−	0.0361277i	−0.664061	+	0.747678i	$0.731169\pi$
$318$	14.2053	+	12.5235i	0.796592	+	0.702280i
$319$	−0.673029	−	3.81693i	−0.0376824	−	0.213707i
$320$	0.684323	+	3.88099i	0.0382548	+	0.216954i
$321$	24.7732	+	0.605270i	1.38270	+	0.0337829i
$322$	−11.1373	+	5.31358i	−0.620658	+	0.296114i
$323$	−3.00208			−0.167040
$324$	0.690723	+	8.97346i	0.0383735	+	0.498525i
$325$	25.7603	−	44.6181i	1.42892	−	2.47497i
$326$	−3.19018	−	2.67688i	−0.176688	−	0.148259i
$327$	−7.75446	−	14.2224i	−0.428822	−	0.786503i
$328$	2.83424	+	1.03158i	0.156495	+	0.0569594i
$329$	−2.06773	+	2.10455i	−0.113998	+	0.116028i
$330$	−4.61623	+	22.8948i	−0.254115	+	1.26032i
$331$	−5.66595	−	4.75430i	−0.311429	−	0.261320i	0.473654	−	0.880711i	$-0.342935\pi$
$331$	−5.66595	−	4.75430i	−0.311429	−	0.261320i	−0.785082	+	0.619392i	$0.787379\pi$
$332$	0.542925	+	0.940374i	0.0297969	+	0.0516097i
$333$	−9.56691	−	0.467765i	−0.524263	−	0.0256334i
$334$	7.87137	−	13.6336i	0.430702	−	0.745998i
$335$	6.42064	+	5.38756i	0.350797	+	0.294354i
$336$	−3.29053	+	3.18942i	−0.179513	+	0.173997i
$337$	0.107710	+	0.610855i	0.00586734	+	0.0332754i	0.987601	−	0.156986i	$-0.0501777\pi$
$337$	0.107710	+	0.610855i	0.00586734	+	0.0332754i	−0.981734	+	0.190261i	$0.939067\pi$
$338$	−8.37840	+	7.03031i	−0.455725	+	0.382398i
$339$	−1.45674	−	9.63179i	−0.0791192	−	0.523127i
$340$	27.6821	−	10.0755i	1.50127	−	0.546418i
$341$	8.80147	−	15.2446i	0.476627	−	0.825541i
$342$	−0.884023	−	0.818591i	−0.0478025	−	0.0442643i
$343$	4.31811	−	18.0098i	0.233156	−	0.972439i
$344$	−3.72490	+	1.35575i	−0.200833	+	0.0730973i
$345$	23.8805	+	21.0532i	1.28568	+	1.13347i
$346$	4.15976	+	23.5912i	0.223630	+	1.26827i
$347$	−4.03981	+	3.38980i	−0.216868	+	0.181974i	−0.744750	−	0.667344i	$-0.767431\pi$
$347$	−4.03981	+	3.38980i	−0.216868	+	0.181974i	0.527881	+	0.849318i	$0.322987\pi$
$348$	−1.96136	−	0.0479207i	−0.105140	−	0.00256882i
$349$	−4.38282	+	24.8562i	−0.234607	+	1.33052i	0.608833	+	0.793298i	$0.291638\pi$
$349$	−4.38282	+	24.8562i	−0.234607	+	1.33052i	−0.843440	+	0.537224i	$0.819473\pi$
$350$	−11.5511	+	25.3533i	−0.617435	+	1.35519i
$351$	−2.56964	−	25.2923i	−0.137157	−	1.35000i
$352$	1.71083	+	2.96325i	0.0911878	+	0.157942i
$353$	−1.83786	−	1.54215i	−0.0978196	−	0.0820804i	0.592566	−	0.805522i	$-0.298115\pi$
$353$	−1.83786	−	1.54215i	−0.0978196	−	0.0820804i	−0.690386	+	0.723441i	$0.742559\pi$
$354$	−5.94768	−	0.145316i	−0.316115	−	0.00772348i
$355$	2.35089	+	13.3325i	0.124772	+	0.707618i
$356$	2.52874	−	2.12186i	0.134023	−	0.112459i
$357$	27.7506	+	20.0836i	1.46872	+	1.06294i
$358$	10.3398	−	3.76337i	0.546474	−	0.198900i
$359$	−16.6016			−0.876201			−0.438101	−	0.898926i	$-0.644349\pi$
$359$	−16.6016			−0.876201			−0.438101	+	0.898926i	$0.644349\pi$
$360$	10.8989	+	4.58128i	0.574420	+	0.241455i
$361$	−18.8387			−0.991511
$362$	0.174316	−	0.988595i	0.00916184	−	0.0519594i
$363$	0.183336	+	1.21220i	0.00962265	+	0.0636238i
$364$	9.07202	−	9.23358i	0.475503	−	0.483971i
$365$	−1.50491	−	8.53475i	−0.0787704	−	0.446729i
$366$	−13.9638	+	11.1473i	−0.729897	+	0.582677i
$367$	−8.81224	+	3.20739i	−0.459995	+	0.167425i	−0.561615	−	0.827399i	$-0.689820\pi$
$367$	−8.81224	+	3.20739i	−0.459995	+	0.167425i	0.101620	+	0.994823i	$0.467598\pi$
$368$	4.66406			0.243131
$369$	7.20725	−	5.47076i	0.375194	−	0.284796i
$370$	−6.29115	+	10.8966i	−0.327061	+	0.566487i
$371$	23.8415	+	16.3823i	1.23779	+	0.850527i
$372$	−6.68400	−	5.89265i	−0.346549	−	0.305520i
$373$	24.7784	+	9.01860i	1.28298	+	0.466966i	0.891416	−	0.453186i	$-0.149713\pi$
$373$	24.7784	+	9.01860i	1.28298	+	0.466966i	0.391561	+	0.920152i	$0.371935\pi$
$374$	19.5936	−	16.4410i	1.01316	−	0.850143i
$375$	37.7377	+	0.922026i	1.94877	+	0.0476132i
$376$	1.04788	−	0.381398i	0.0540404	−	0.0196691i
$377$	5.54194			0.285425
$378$	2.69544	+	13.4809i	0.138638	+	0.693383i
$379$	21.8385			1.12177			0.560883	−	0.827895i	$-0.310462\pi$
$379$	21.8385			1.12177			0.560883	+	0.827895i	$0.310462\pi$
$380$	−1.48723	+	0.541306i	−0.0762931	+	0.0277684i
$381$	1.12914	+	2.07096i	0.0578478	+	0.106099i
$382$	1.17773	−	0.988232i	0.0602579	−	0.0505624i
$383$	36.2901	+	13.2085i	1.85434	+	0.674923i	0.982823	+	0.184550i	$0.0590828\pi$
$383$	36.2901	+	13.2085i	1.85434	+	0.674923i	0.871513	+	0.490373i	$0.163139\pi$
$384$	1.64158	−	0.552465i	0.0837715	−	0.0281929i
$385$	−2.79559	+	35.5664i	−0.142476	+	1.81263i
$386$	9.07237	−	15.7138i	0.461771	−	0.799812i
$387$	−2.63446	+	11.5964i	−0.133917	+	0.589478i
$388$	−13.6454			−0.692740
$389$	16.3454	−	5.94922i	0.828742	−	0.301638i	0.107400	−	0.994216i	$-0.465748\pi$
$389$	16.3454	−	5.94922i	0.828742	−	0.301638i	0.721343	+	0.692578i	$0.243525\pi$
$390$	−31.0932	−	12.1850i	−1.57446	−	0.617013i
$391$	−6.05419	−	34.3350i	−0.306174	−	1.73640i
$392$	−4.40416	+	5.44090i	−0.222444	+	0.274807i
$393$	28.9256	+	11.3356i	1.45910	+	0.571805i
$394$	−2.09873	+	11.9025i	−0.105732	+	0.599637i
$395$	64.0279			3.22159
$396$	10.2528	+	0.501299i	0.515221	+	0.0251912i
$397$	−26.6310			−1.33657			−0.668285	−	0.743905i	$-0.732971\pi$
$397$	−26.6310			−1.33657			−0.668285	+	0.743905i	$0.732971\pi$
$398$	0.896864	−	0.326432i	0.0449558	−	0.0163626i
$399$	−1.49091	−	1.07900i	−0.0746387	−	0.0540173i
$400$	8.06673	−	6.76879i	0.403336	−	0.338440i
$401$	3.51981	+	19.9619i	0.175771	+	0.996848i	0.937250	+	0.348658i	$0.113363\pi$
$401$	3.51981	+	19.9619i	0.175771	+	0.996848i	−0.761479	+	0.648190i	$0.775526\pi$
$402$	1.91927	−	3.14431i	0.0957243	−	0.156824i
$403$	19.2814	+	16.1790i	0.960474	+	0.805934i
$404$	−0.652176	−	1.12960i	−0.0324470	−	0.0561998i
$405$	29.2643	−	20.0389i	1.45416	−	0.995742i
$406$	−2.98309	+	0.287538i	−0.148048	+	0.0142702i
$407$	−1.89704	+	10.7587i	−0.0940329	+	0.533287i
$408$	−6.19790	−	11.3676i	−0.306842	−	0.562778i
$409$	−0.475135	+	0.398686i	−0.0234939	+	0.0197137i	−0.654459	−	0.756098i	$-0.727104\pi$
$409$	−0.475135	+	0.398686i	−0.0234939	+	0.0197137i	0.630965	+	0.775811i	$0.282659\pi$
$410$	−2.06401	−	11.7056i	−0.101934	−	0.578098i
$411$	20.1003	−	6.76466i	0.991475	−	0.333676i
$412$	7.68981	−	2.79886i	0.378850	−	0.137890i
$413$	−9.04601	+	0.871938i	−0.445125	+	0.0429053i
$414$	7.57951	−	11.7615i	0.372512	−	0.578044i
$415$	2.13959	−	3.70588i	0.105028	−	0.181914i
$416$	−4.59751	+	1.67336i	−0.225411	+	0.0820431i
$417$	7.55541	−	6.03149i	0.369990	−	0.295363i
$418$	−1.05267	+	0.883295i	−0.0514878	+	0.0432034i
$419$	1.34242	+	7.61322i	0.0655813	+	0.371930i	0.999881	+	0.0154409i	$0.00491518\pi$
$419$	1.34242	+	7.61322i	0.0655813	+	0.371930i	−0.934300	+	0.356489i	$0.883974\pi$
$420$	17.3689	+	4.94566i	0.847515	+	0.241324i
$421$	−0.346722	−	0.290934i	−0.0168982	−	0.0141793i	0.634299	−	0.773087i	$-0.281289\pi$
$421$	−0.346722	−	0.290934i	−0.0168982	−	0.0141793i	−0.651198	+	0.758908i	$0.725733\pi$
$422$	−7.91084	+	13.7020i	−0.385094	+	0.667002i
$423$	0.741122	−	3.26227i	0.0360346	−	0.158617i
$424$	−5.46677	−	9.46872i	−0.265490	−	0.459842i
$425$	−60.3003	−	50.5980i	−2.92499	−	2.45436i
$426$	5.63939	−	1.89791i	0.273230	−	0.0919540i
$427$	−19.1280	+	19.4687i	−0.925671	+	0.942156i
$428$	−13.4443	−	4.89331i	−0.649853	−	0.236527i
$429$	−28.9872	−	0.708228i	−1.39951	−	0.0341936i
$430$	11.9667	+	10.0412i	0.577085	+	0.484232i
$431$	−18.4614	+	31.9760i	−0.889253	+	1.54023i	−0.0484934	+	0.998824i	$0.515442\pi$
$431$	−18.4614	+	31.9760i	−0.889253	+	1.54023i	−0.840760	+	0.541408i	$0.817891\pi$
$432$	1.27455	−	5.03741i	0.0613217	−	0.242363i
$433$	−36.6719			−1.76234			−0.881169	−	0.472801i	$-0.843243\pi$
$433$	−36.6719			−1.76234			−0.881169	+	0.472801i	$0.843243\pi$
$434$	−11.2181	−	7.70836i	−0.538487	−	0.370013i
$435$	3.70116	+	6.78830i	0.177457	+	0.325474i
$436$	1.62405	+	9.21044i	0.0777779	+	0.441100i
$437$	0.325263	+	1.84466i	0.0155594	+	0.0882419i
$438$	−3.61003	+	1.21494i	−0.172494	+	0.0580519i
$439$	16.9717	+	14.2409i	0.810015	+	0.679683i	0.950611	−	0.310384i	$-0.100458\pi$
$439$	16.9717	+	14.2409i	0.810015	+	0.679683i	−0.140596	+	0.990067i	$0.544902\pi$
$440$	6.74216	−	11.6778i	0.321420	−	0.556715i
$441$	6.56327	+	19.9480i	0.312537	+	0.949906i
$442$	18.2864	+	31.6730i	0.869797	+	1.50653i
$443$	−4.65340	+	26.3907i	−0.221090	+	1.25386i	0.648931	+	0.760847i	$0.275216\pi$
$443$	−4.65340	+	26.3907i	−0.221090	+	1.25386i	−0.870021	+	0.493015i	$0.835895\pi$
$444$	5.14881	+	2.01775i	0.244352	+	0.0957583i
$445$	−12.2244	−	4.44931i	−0.579491	−	0.210917i
$446$	−9.56624	+	8.02703i	−0.452975	+	0.380091i
$447$	−4.22764	−	27.9526i	−0.199960	−	1.32211i
$448$	2.38790	−	1.13926i	0.112818	−	0.0538251i
$449$	−4.09017	−	7.08439i	−0.193027	−	0.334333i	0.753225	−	0.657763i	$-0.228497\pi$
$449$	−4.09017	−	7.08439i	−0.193027	−	0.334333i	−0.946252	+	0.323430i	$0.895164\pi$
$450$	−3.95986	−	31.3419i	−0.186669	−	1.47747i
$451$	−5.16011	−	8.93757i	−0.242980	−	0.420854i
$452$	−0.976624	+	5.53871i	−0.0459366	+	0.260519i
$453$	3.77745	−	18.7347i	0.177480	−	0.880235i
$454$	−17.3319	+	14.5432i	−0.813428	+	0.682548i
$455$	−49.3889	−	12.7676i	−2.31539	−	0.598555i
$456$	0.332983	+	0.610725i	0.0155934	+	0.0285998i
$457$	1.74311	−	0.634441i	0.0815394	−	0.0296779i	−0.300928	−	0.953647i	$-0.597297\pi$
$457$	1.74311	−	0.634441i	0.0815394	−	0.0296779i	0.382468	+	0.923969i	$0.375074\pi$
$458$	−6.59162	+	11.4170i	−0.308006	+	0.533482i
$459$	−38.7380	−	2.84392i	−1.80813	−	0.132743i
$460$	−9.19019	−	15.9179i	−0.428495	−	0.742175i
$461$	5.89233	−	33.4171i	0.274433	−	1.55639i	−0.466323	−	0.884614i	$-0.654422\pi$
$461$	5.89233	−	33.4171i	0.274433	−	1.55639i	0.740757	−	0.671774i	$-0.234467\pi$
$462$	15.6398	−	1.12275i	0.727630	−	0.0522349i
$463$	1.39988	+	0.509514i	0.0650578	+	0.0236791i	0.374344	−	0.927290i	$-0.377868\pi$
$463$	1.39988	+	0.509514i	0.0650578	+	0.0236791i	−0.309286	+	0.950969i	$0.600090\pi$
$464$	1.06442	+	0.387415i	0.0494142	+	0.0179853i
$465$	−6.94060	+	34.4228i	−0.321862	+	1.59632i
$466$	2.17451	−	12.3323i	0.100732	−	0.571282i
$467$	−23.9827			−1.10979			−0.554894	−	0.831921i	$-0.687241\pi$
$467$	−23.9827			−1.10979			−0.554894	+	0.831921i	$0.687241\pi$
$468$	−3.25162	+	14.3130i	−0.150306	+	0.661619i
$469$	2.33300	−	5.12065i	0.107728	−	0.236450i
$470$	−3.36644	−	2.82478i	−0.155283	−	0.130297i
$471$	21.7867	+	8.53793i	1.00388	+	0.393407i
$472$	3.22777	+	1.17481i	0.148570	+	0.0540751i
$473$	12.7454	+	4.63894i	0.586033	+	0.213299i
$474$	−4.20826	−	27.8245i	−0.193292	−	1.27802i
$475$	3.23965	+	2.71839i	0.148645	+	0.124728i
$476$	−11.4864	−	16.1000i	−0.526480	−	0.737943i
$477$	−32.7615	−	1.60184i	−1.50004	−	0.0733433i
$478$	22.7206			1.03922
$479$	2.17803	−	12.3522i	0.0995168	−	0.564388i	−0.893753	−	0.448560i	$-0.851937\pi$
$479$	2.17803	−	12.3522i	0.0995168	−	0.564388i	0.993269	−	0.115827i	$-0.0369520\pi$
$480$	−5.12012	−	4.51393i	−0.233700	−	0.206032i
$481$	−14.6788	−	5.34266i	−0.669297	−	0.243604i
$482$	−1.44306	−	0.525231i	−0.0657296	−	0.0239236i
$483$	9.33389	−	19.2276i	0.424707	−	0.874886i
$484$	0.122912	−	0.697067i	0.00558690	−	0.0316849i
$485$	26.8873	+	46.5701i	1.22089	+	2.11464i
$486$	−10.6317	−	11.4003i	−0.482264	−	0.517128i
$487$	−8.44716	+	14.6309i	−0.382777	+	0.662990i	−0.991458	−	0.130425i	$-0.958366\pi$
$487$	−8.44716	+	14.6309i	−0.382777	+	0.662990i	0.608681	+	0.793415i	$0.291699\pi$
$488$	9.69369	−	3.52822i	0.438813	−	0.159715i
$489$	7.21095	+	0.176181i	0.326090	+	0.00796719i
$490$	27.2472	+	4.30999i	1.23090	+	0.194706i
$491$	−1.49431	+	1.25388i	−0.0674373	+	0.0565866i	−0.675883	−	0.737009i	$-0.736238\pi$
$491$	−1.49431	+	1.25388i	−0.0674373	+	0.0565866i	0.608446	+	0.793595i	$0.291793\pi$
$492$	−4.95123	+	1.66631i	−0.223219	+	0.0751231i
$493$	1.47034	−	8.33871i	0.0662207	−	0.375556i
$494$	−0.982443	−	1.70164i	−0.0442022	−	0.0765604i
$495$	−18.4915	−	35.9793i	−0.831129	−	1.61715i
$496$	2.57227	+	4.45531i	0.115499	+	0.200049i
$497$	8.20328	−	3.91376i	0.367967	−	0.175556i
$498$	−1.75109	−	0.686229i	−0.0784680	−	0.0307506i
$499$	−3.07558	+	2.58071i	−0.137682	+	0.115529i	−0.709028	−	0.705181i	$-0.750866\pi$
$499$	−3.07558	+	2.58071i	−0.137682	+	0.115529i	0.571346	+	0.820709i	$0.306421\pi$
$500$	−20.4800	−	7.45412i	−0.915895	−	0.333359i
$501$	4.07760	+	26.9606i	0.182174	+	1.20451i
$502$	−1.50648	+	8.54366i	−0.0672374	+	0.381322i
$503$	11.6682	+	20.2098i	0.520257	+	0.901112i	0.999723	+	0.0235513i	$0.00749732\pi$
$503$	11.6682	+	20.2098i	0.520257	+	0.901112i	−0.479465	+	0.877561i	$0.659169\pi$
$504$	1.00765	−	7.87303i	0.0448844	−	0.350693i
$505$	−2.57013	+	4.45160i	−0.114369	+	0.198094i
$506$	−12.2252	−	10.2582i	−0.543476	−	0.456031i
$507$	3.74425	−	18.5701i	0.166288	−	0.824727i
$508$	−0.236481	−	1.34115i	−0.0104922	−	0.0595040i
$509$	1.79317	+	10.1696i	0.0794808	+	0.450758i	0.998412	+	0.0563393i	$0.0179429\pi$
$509$	1.79317	+	10.1696i	0.0794808	+	0.450758i	−0.918931	+	0.394419i	$0.870946\pi$
$510$	−26.5836	+	43.5517i	−1.17714	+	1.92850i
$511$	−5.25128	+	2.50537i	−0.232303	+	0.110831i
$512$	−1.00000			−0.0441942
$513$	2.08121	+	0.152790i	0.0918875	+	0.00674585i
$514$	5.64773	−	9.78216i	0.249111	−	0.431473i
$515$	−24.7044	−	20.7295i	−1.08861	−	0.913450i
$516$	3.57709	−	5.86031i	0.157473	−	0.257986i
$517$	−3.58551	−	1.30502i	−0.157690	−	0.0573946i
$518$	8.17844	+	2.11422i	0.359340	+	0.0928937i
$519$	−31.1234	−	27.4386i	−1.36617	−	1.20442i
$520$	14.7700	+	12.3935i	0.647709	+	0.543492i
$521$	−3.91764	−	6.78555i	−0.171635	−	0.297280i	0.767357	−	0.641220i	$-0.221572\pi$
$521$	−3.91764	−	6.78555i	−0.171635	−	0.297280i	−0.938992	+	0.343940i	$0.888238\pi$
$522$	2.70672	−	2.05458i	0.118470	−	0.0899263i
$523$	−0.560714	+	0.971185i	−0.0245183	+	0.0424670i	−0.878024	−	0.478616i	$-0.841139\pi$
$523$	−0.560714	+	0.971185i	−0.0245183	+	0.0424670i	0.853506	+	0.521083i	$0.174472\pi$
$524$	−13.7404	−	11.5296i	−0.600252	−	0.503671i
$525$	−11.7609	−	46.8011i	−0.513288	−	2.04257i
$526$	1.42830	+	8.10028i	0.0622767	+	0.353189i
$527$	29.4594	−	24.7193i	1.28327	−	1.07679i
$528$	−5.51792	−	2.16241i	−0.240137	−	0.0941066i
$529$	1.17140	−	0.426356i	0.0509306	−	0.0185372i
$530$	−21.5438	+	37.3149i	−0.935801	+	1.62086i
$531$	8.20796	−	6.23036i	0.356195	−	0.270375i
$532$	0.617112	+	0.864977i	0.0267552	+	0.0375015i
$533$	13.8667	−	5.04707i	0.600634	−	0.218613i
$534$	−1.13008	+	5.60476i	−0.0489032	+	0.242542i
$535$	9.79066	+	55.5256i	0.423287	+	2.40058i
$536$	−1.62925	+	1.36710i	−0.0703729	+	0.0590498i
$537$	−9.92949	+	16.2674i	−0.428489	+	0.701989i
$538$	4.80123	−	27.2291i	0.206996	−	1.17393i
$539$	23.5107	−	4.57486i	1.01268	−	0.197053i
$540$	−19.7035	+	5.57598i	−0.847904	+	0.239952i
$541$	−9.55597	−	16.5514i	−0.410843	−	0.711602i	0.584139	−	0.811654i	$-0.301432\pi$
$541$	−9.55597	−	16.5514i	−0.410843	−	0.711602i	−0.994982	+	0.100052i	$0.968099\pi$
$542$	12.7933	+	10.7349i	0.549521	+	0.461103i
$543$	0.832318	+	1.52655i	0.0357182	+	0.0655107i
$544$	1.29805	+	7.36162i	0.0556535	+	0.315627i
$545$	28.2341	−	23.6912i	1.20942	−	1.01482i
$546$	−2.30230	+	22.3020i	−0.0985292	+	0.954439i
$547$	8.34510	−	3.03737i	0.356811	−	0.129868i	−0.157394	−	0.987536i	$-0.550309\pi$
$547$	8.34510	−	3.03737i	0.356811	−	0.129868i	0.514205	+	0.857667i	$0.328087\pi$
$548$	−12.2445			−0.523059
$549$	6.85594	−	30.1785i	0.292604	−	1.28799i
$550$	−36.0314			−1.53639
$551$	−0.0789943	+	0.447999i	−0.00336527	+	0.0190854i
$552$	−6.31339	+	5.03998i	−0.268716	+	0.214516i
$553$	−11.4916	−	41.4215i	−0.488673	−	1.76142i
$554$	−4.46825	−	25.3407i	−0.189838	−	1.07662i
$555$	−3.25900	−	21.5481i	−0.138337	−	0.914667i
$556$	−5.24500	+	1.90902i	−0.222437	+	0.0809606i
$557$	−27.6007			−1.16948			−0.584739	−	0.811222i	$-0.698803\pi$
$557$	−27.6007			−1.16948			−0.584739	+	0.811222i	$0.698803\pi$
$558$	15.4152	+	0.753714i	0.652579	+	0.0319073i
$559$	−9.69697	+	16.7956i	−0.410138	+	0.710380i
$560$	−8.59336	−	5.90480i	−0.363136	−	0.249523i
$561$	−8.75626	+	43.4278i	−0.369689	+	1.83352i
$562$	−1.87996	−	0.684251i	−0.0793015	−	0.0288634i
$563$	15.4294	−	12.9468i	0.650273	−	0.545643i	−0.256881	−	0.966443i	$-0.582695\pi$
$563$	15.4294	−	12.9468i	0.650273	−	0.545643i	0.907154	+	0.420800i	$0.138250\pi$
$564$	−1.00630	+	1.64861i	−0.0423729	+	0.0694191i
$565$	20.8274	−	7.58054i	0.876213	−	0.318916i
$566$	−26.6510			−1.12022
$567$	−18.2161	−	15.3354i	−0.765003	−	0.644026i
$568$	−3.43535			−0.144144
$569$	−32.8736	+	11.9650i	−1.37813	+	0.501599i	−0.921612	−	0.388113i	$-0.873127\pi$
$569$	−32.8736	+	11.9650i	−1.37813	+	0.501599i	−0.456521	+	0.889713i	$0.650905\pi$
$570$	1.42821	−	2.33982i	0.0598212	−	0.0980044i
$571$	20.7076	−	17.3757i	0.866586	−	0.727152i	−0.0967906	−	0.995305i	$-0.530858\pi$
$571$	20.7076	−	17.3757i	0.866586	−	0.727152i	0.963376	+	0.268153i	$0.0864133\pi$
$572$	15.7312	+	5.72567i	0.657753	+	0.239402i
$573$	−0.526320	+	2.61035i	−0.0219873	+	0.109049i
$574$	−7.20224	+	3.43617i	−0.300616	+	0.143423i
$575$	−24.5571	+	42.5342i	−1.02410	+	1.77380i
$576$	−1.62509	+	2.52172i	−0.0677121	+	0.105072i
$577$	−13.2951			−0.553483			−0.276741	−	0.960944i	$-0.589255\pi$
$577$	−13.2951			−0.553483			−0.276741	+	0.960944i	$0.589255\pi$
$578$	36.5338	−	13.2972i	1.51960	−	0.553091i
$579$	4.69976	+	31.0742i	0.195315	+	1.29140i
$580$	−0.775151	−	4.39610i	−0.0321864	−	0.182538i
$581$	−2.78145	−	0.719038i	−0.115394	−	0.0298307i
$582$	18.4708	−	14.7452i	0.765637	−	0.611209i
$583$	−6.49634	+	36.8426i	−0.269051	+	1.52586i
$584$	2.19912			0.0910001
$585$	55.2557	−	17.1053i	2.28454	−	0.707219i
$586$	21.3021			0.879983
$587$	−32.7194	+	11.9089i	−1.35047	+	0.491533i	−0.913096	−	0.407745i	$-0.866315\pi$
$587$	−32.7194	+	11.9089i	−1.35047	+	0.491533i	−0.437379	+	0.899277i	$0.644093\pi$
$588$	0.0821516	−	12.1241i	0.00338788	−	0.499989i
$589$	−1.58271	+	1.32805i	−0.0652145	+	0.0547214i
$590$	−2.35059	−	13.3309i	−0.0967724	−	0.548823i
$591$	−10.0209	−	18.3794i	−0.412206	−	0.756026i
$592$	−2.44581	−	2.05228i	−0.100522	−	0.0843482i
$593$	−0.406959	−	0.704873i	−0.0167118	−	0.0289457i	0.857549	−	0.514403i	$-0.171986\pi$
$593$	−0.406959	−	0.704873i	−0.0167118	−	0.0289457i	−0.874260	+	0.485457i	$0.838653\pi$
$594$	−14.4201	+	10.4006i	−0.591664	+	0.426740i
$595$	−32.3143	+	70.9258i	−1.32476	+	2.90768i
$596$	−2.83428	+	16.0740i	−0.116097	+	0.658418i
$597$	−0.861276	+	1.41102i	−0.0352497	+	0.0577492i
$598$	17.4805	−	14.6679i	0.714832	−	0.599815i
$599$	−1.32762	−	7.52930i	−0.0542451	−	0.307639i	0.945598	−	0.325336i	$-0.105478\pi$
$599$	−1.32762	−	7.52930i	−0.0542451	−	0.307639i	−0.999843	+	0.0176974i	$0.994366\pi$
$600$	−3.60497	+	17.8793i	−0.147172	+	0.729920i
$601$	30.4980	−	11.1004i	1.24404	−	0.452793i	0.365656	−	0.930750i	$-0.380845\pi$
$601$	30.4980	−	11.1004i	1.24404	−	0.452793i	0.878383	+	0.477957i	$0.158622\pi$
$602$	4.34821	−	9.54378i	0.177220	−	0.388976i
$603$	0.799778	+	6.33018i	0.0325695	+	0.257785i
$604$	−5.51709	+	9.55589i	−0.224487	+	0.388823i
$605$	−2.62120	+	0.954038i	−0.106567	+	0.0387872i
$606$	2.10345	+	0.824317i	0.0854469	+	0.0334856i
$607$	33.8652	−	28.4163i	1.37455	−	1.15338i	0.403367	−	0.915038i	$-0.367840\pi$
$607$	33.8652	−	28.4163i	1.37455	−	1.15338i	0.971181	−	0.238344i	$-0.0766045\pi$
$608$	−0.0697382	−	0.395505i	−0.00282826	−	0.0160398i
$609$	3.72727	−	3.61275i	0.151037	−	0.146396i
$610$	−31.1421	−	26.1314i	−1.26091	−	1.05803i
$611$	2.72793	−	4.72492i	0.110360	−	0.191150i
$612$	20.6734	+	8.68996i	0.835673	+	0.351271i
$613$	16.3949	+	28.3967i	0.662182	+	1.14693i	0.980041	+	0.198795i	$0.0637028\pi$
$613$	16.3949	+	28.3967i	0.662182	+	1.14693i	−0.317859	+	0.948138i	$0.602964\pi$
$614$	10.0531	+	8.43559i	0.405712	+	0.340433i
$615$	15.4430	+	13.6146i	0.622720	+	0.548994i
$616$	−8.76476	−	2.26579i	−0.353142	−	0.0912914i
$617$	−6.94319	−	2.52711i	−0.279522	−	0.101738i	0.198455	−	0.980110i	$-0.436408\pi$
$617$	−6.94319	−	2.52711i	−0.279522	−	0.101738i	−0.477977	+	0.878372i	$0.658630\pi$
$618$	−7.38468	+	12.0982i	−0.297055	+	0.486662i
$619$	−35.4916	−	29.7810i	−1.42653	−	1.19700i	−0.947729	−	0.319076i	$-0.896627\pi$
$619$	−35.4916	−	29.7810i	−1.42653	−	1.19700i	−0.478800	−	0.877924i	$-0.658928\pi$
$620$	10.1370	−	17.5578i	0.407111	−	0.705136i
$621$	2.44962	+	24.1110i	0.0982999	+	0.967542i
$622$	23.5461			0.944114
$623$	−0.684375	+	8.70686i	−0.0274189	+	0.348833i
$624$	4.41508	−	7.23317i	0.176745	−	0.289559i
$625$	5.77151	+	32.7319i	0.230860	+	1.30927i
$626$	−0.500193	−	2.83674i	−0.0199917	−	0.113379i
$627$	0.470432	−	2.33317i	0.0187872	−	0.0931777i
$628$	−10.3492	−	8.68402i	−0.412979	−	0.346530i
$629$	−11.9333	+	20.6691i	−0.475812	+	0.824131i
$630$	−28.8553	+	12.0743i	−1.14962	+	0.481050i
$631$	−4.12433	−	7.14355i	−0.164187	−	0.284380i	0.772179	−	0.635405i	$-0.219167\pi$
$631$	−4.12433	−	7.14355i	−0.164187	−	0.284380i	−0.936366	+	0.351025i	$0.885833\pi$
$632$	−2.82129	+	16.0004i	−0.112225	+	0.636460i
$633$	−4.09805	−	27.0958i	−0.162883	−	1.07696i
$634$	−0.940348	−	0.342259i	−0.0373460	−	0.0135928i
$635$	−4.11123	+	3.44973i	−0.163149	+	0.136898i
$636$	17.6319	+	6.90971i	0.699149	+	0.273988i
$637$	0.604507	+	34.2426i	0.0239514	+	1.35674i
$638$	−1.93791	−	3.35656i	−0.0767225	−	0.132887i
$639$	−5.58275	+	8.66299i	−0.220850	+	0.342703i
$640$	1.97043	+	3.41288i	0.0778881	+	0.134906i
$641$	−3.71840	+	21.0881i	−0.146868	+	0.832930i	0.818980	+	0.573822i	$0.194540\pi$
$641$	−3.71840	+	21.0881i	−0.146868	+	0.832930i	−0.965848	+	0.259108i	$0.916571\pi$
$642$	23.4862	−	7.90416i	0.926926	−	0.311952i
$643$	16.9584	−	14.2298i	0.668775	−	0.561169i	−0.243928	−	0.969793i	$-0.578436\pi$
$643$	16.9584	−	14.2298i	0.668775	−	0.561169i	0.912703	+	0.408625i	$0.133991\pi$
$644$	−8.64830	+	8.80232i	−0.340791	+	0.346860i
$645$	−27.0490	−	0.660873i	−1.06505	−	0.0260218i
$646$	−2.82103	+	1.02677i	−0.110992	+	0.0403978i
$647$	9.06473	−	15.7006i	0.356371	−	0.617253i	−0.630980	−	0.775799i	$-0.717347\pi$
$647$	9.06473	−	15.7006i	0.356371	−	0.617253i	0.987352	+	0.158546i	$0.0506805\pi$
$648$	3.71817	+	8.19605i	0.146064	+	0.321971i
$649$	−5.87658	−	10.1785i	−0.230676	−	0.399542i
$650$	8.94645	−	50.7378i	0.350909	−	1.99010i
$651$	23.5148	−	1.68807i	0.921617	−	0.0661607i
$652$	−3.91334	−	1.42434i	−0.153258	−	0.0557814i
$653$	−32.3114	−	11.7604i	−1.26444	−	0.460219i	−0.379185	−	0.925321i	$-0.623796\pi$
$653$	−32.3114	−	11.7604i	−1.26444	−	0.460219i	−0.885257	+	0.465102i	$0.846018\pi$
$654$	−12.1512	−	10.7125i	−0.475148	−	0.418894i
$655$	−12.2746	+	69.6125i	−0.479607	+	2.71999i
$656$	3.01614			0.117760
$657$	3.57376	−	5.54556i	0.139426	−	0.216353i
$658$	−1.22323	+	2.68484i	−0.0476865	+	0.104666i
$659$	−23.6717	−	19.8629i	−0.922120	−	0.773751i	0.0522658	−	0.998633i	$-0.483356\pi$
$659$	−23.6717	−	19.8629i	−0.922120	−	0.773751i	−0.974386	+	0.224883i	$0.927800\pi$
$660$	3.49264	+	23.0929i	0.135951	+	0.898890i
$661$	6.41894	+	2.33630i	0.249668	+	0.0908716i	0.463823	−	0.885928i	$-0.346477\pi$
$661$	6.41894	+	2.33630i	0.249668	+	0.0908716i	−0.214155	+	0.976800i	$0.568700\pi$
$662$	−6.95032	−	2.52971i	−0.270132	−	0.0983199i
$663$	−58.9789	−	23.1131i	−2.29055	−	0.897638i
$664$	0.831809	+	0.697971i	0.0322805	+	0.0270865i
$665$	1.73609	−	3.81051i	0.0673227	−	0.147765i
$666$	−9.14994	+	2.83252i	−0.354553	+	0.109758i
$667$	−5.28310			−0.204563
$668$	2.73370	−	15.5036i	0.105770	−	0.599851i
$669$	4.27510	−	21.2029i	0.165285	−	0.819751i
$670$	7.87608	+	2.86666i	0.304280	+	0.110749i
$671$	−33.1686	−	12.0724i	−1.28046	−	0.466049i
$672$	−2.00124	+	4.12250i	−0.0771995	+	0.159029i
$673$	5.04760	−	28.6264i	0.194571	−	1.10347i	−0.718458	−	0.695570i	$-0.755152\pi$
$673$	5.04760	−	28.6264i	0.194571	−	1.10347i	0.913029	−	0.407895i	$-0.133737\pi$
$674$	0.310139	+	0.537176i	0.0119461	+	0.0206913i
$675$	39.2283	+	38.1462i	1.50990	+	1.46825i
$676$	−5.46861	+	9.47191i	−0.210331	+	0.364304i
$677$	−31.8021	+	11.5750i	−1.22225	+	0.444864i	−0.870938	−	0.491393i	$-0.836488\pi$
$677$	−31.8021	+	11.5750i	−1.22225	+	0.444864i	−0.351315	+	0.936257i	$0.614265\pi$
$678$	−4.66315	−	8.55268i	−0.179087	−	0.328464i
$679$	25.3019	−	25.7525i	0.970998	−	0.988291i
$680$	22.5666	−	18.9357i	0.865391	−	0.726149i
$681$	7.74554	−	38.4150i	0.296810	−	1.47207i
$682$	3.05672	−	17.3355i	0.117048	−	0.663811i
$683$	−3.77078	−	6.53117i	−0.144285	−	0.249908i	0.784821	−	0.619722i	$-0.212755\pi$
$683$	−3.77078	−	6.53117i	−0.144285	−	0.249908i	−0.929106	+	0.369814i	$0.879421\pi$
$684$	−1.11068	−	0.466870i	−0.0424681	−	0.0178512i
$685$	24.1269	+	41.7890i	0.921842	+	1.59668i
$686$	−2.10203	−	18.4006i	−0.0802559	−	0.702538i
$687$	−3.41466	−	22.5773i	−0.130277	−	0.861377i
$688$	−3.03657	+	2.54798i	−0.115768	+	0.0971409i
$689$	−50.2670	−	18.2957i	−1.91502	−	0.697011i
$690$	29.6410	+	11.6159i	1.12841	+	0.442211i
$691$	−2.81871	+	15.9857i	−0.107229	+	0.608124i	0.883078	+	0.469226i	$0.155467\pi$
$691$	−2.81871	+	15.9857i	−0.107229	+	0.608124i	−0.990307	+	0.138898i	$0.955644\pi$
$692$	11.9776	+	20.7457i	0.455318	+	0.788634i
$693$	−19.9572	+	18.4202i	−0.758112	+	0.699724i
$694$	−2.63680	+	4.56707i	−0.100091	+	0.173363i
$695$	16.8502	+	14.1390i	0.639163	+	0.536322i
$696$	−1.85946	+	0.625792i	−0.0704827	+	0.0237206i
$697$	−3.91510	−	22.2037i	−0.148295	−	0.841023i
$698$	4.38282	+	24.8562i	0.165892	+	0.940821i
$699$	10.3828	+	19.0431i	0.392713	+	0.720275i
$700$	−2.18317	+	27.7751i	−0.0825161	+	1.04980i
$701$	−22.5406			−0.851348			−0.425674	−	0.904877i	$-0.639963\pi$
$701$	−22.5406			−0.851348			−0.425674	+	0.904877i	$0.639963\pi$
$702$	−11.0652	−	22.8881i	−0.417627	−	0.863857i
$703$	0.641120	−	1.11045i	0.0241803	−	0.0418815i
$704$	2.62115	+	2.19941i	0.0987883	+	0.0828933i
$705$	7.60937	+	0.185916i	0.286585	+	0.00700198i
$706$	−2.25447	−	0.820562i	−0.0848483	−	0.0308822i
$707$	3.34116	+	0.863728i	0.125657	+	0.0324838i
$708$	−5.63869	+	1.89767i	−0.211915	+	0.0713189i
$709$	16.6662	+	13.9846i	0.625911	+	0.525202i	0.899655	−	0.436601i	$-0.143818\pi$
$709$	16.6662	+	13.9846i	0.625911	+	0.525202i	−0.273744	+	0.961802i	$0.588262\pi$
$710$	6.76911	+	11.7244i	0.254040	+	0.440010i
$711$	35.7636	+	33.1165i	1.34124	+	1.24197i
$712$	1.65052	−	2.85878i	0.0618557	−	0.107137i
$713$	−18.3808	−	15.4233i	−0.688367	−	0.577609i
$714$	32.9460	+	9.38114i	1.23297	+	0.351080i
$715$	−11.4561	−	64.9707i	−0.428433	−	2.42976i
$716$	8.42906	−	7.07282i	0.315009	−	0.264324i
$717$	−30.7552	+	24.5519i	−1.14858	+	0.916909i
$718$	−15.6004	+	5.67810i	−0.582203	+	0.211905i
$719$	−5.30431	+	9.18734i	−0.197817	+	0.342630i	−0.947820	−	0.318805i	$-0.896719\pi$
$719$	−5.30431	+	9.18734i	−0.197817	+	0.342630i	0.750003	+	0.661434i	$0.230052\pi$
$720$	11.8085	+	0.577364i	0.440076	+	0.0215171i
$721$	−8.97659	+	19.7025i	−0.334306	+	0.733760i
$722$	−17.7026	+	6.44322i	−0.658823	+	0.239792i
$723$	2.52093	−	0.848406i	0.0937544	−	0.0315526i
$724$	−0.174316	−	0.988595i	−0.00647840	−	0.0367408i
$725$	−9.13740	+	7.66719i	−0.339355	+	0.284752i
$726$	0.586875	+	1.07639i	0.0217810	+	0.0399484i
$727$	−2.40713	+	13.6515i	−0.0892755	+	0.506306i	0.907076	+	0.420966i	$0.138309\pi$
$727$	−2.40713	+	13.6515i	−0.0892755	+	0.506306i	−0.996352	+	0.0853404i	$0.972802\pi$
$728$	5.36683	−	11.7795i	0.198908	−	0.436579i
$729$	26.7105	+	3.94312i	0.989278	+	0.146041i
$730$	−4.33321	−	7.50533i	−0.160379	−	0.277785i
$731$	22.6989	+	19.0466i	0.839550	+	0.704466i
$732$	−9.30904	+	15.2509i	−0.344072	+	0.563689i
$733$	−3.36988	−	19.1115i	−0.124469	−	0.705901i	−0.981622	−	0.190838i	$-0.938880\pi$
$733$	−3.36988	−	19.1115i	−0.124469	−	0.705901i	0.857152	−	0.515063i	$-0.172232\pi$
$734$	−7.18380	+	6.02793i	−0.265159	+	0.222495i
$735$	−41.5399	+	23.6093i	−1.53222	+	0.870841i
$736$	4.38278	−	1.59520i	0.161551	−	0.0587999i
$737$	7.27732			0.268064
$738$	4.90149	−	7.60586i	0.180426	−	0.279976i
$739$	39.3044			1.44584			0.722918	−	0.690934i	$-0.242801\pi$
$739$	39.3044			1.44584			0.722918	+	0.690934i	$0.242801\pi$
$740$	−2.18489	+	12.3911i	−0.0803182	+	0.455507i
$741$	3.16865	+	1.24176i	0.116403	+	0.0456170i
$742$	28.0067	+	7.24007i	1.02816	+	0.265791i
$743$	−1.64288	−	9.31724i	−0.0602715	−	0.341816i	0.939729	−	0.341921i	$-0.111078\pi$
$743$	−1.64288	−	9.31724i	−0.0602715	−	0.341816i	−1.00000		0.000104995i	$0.999967\pi$
$744$	−8.29631	−	3.25122i	−0.304157	−	0.119196i
$745$	60.4435	−	21.9996i	2.21448	−	0.806005i
$746$	26.3686			0.965424
$747$	3.11185	−	0.963327i	0.113857	−	0.0352463i
$748$	12.7888	−	22.1509i	0.467605	−	0.809916i
$749$	34.1639	−	16.2995i	1.24832	−	0.595571i
$750$	35.7772	−	12.0406i	1.30640	−	0.439662i
$751$	8.38650	+	3.05244i	0.306028	+	0.111385i	0.490469	−	0.871459i	$-0.336825\pi$
$751$	8.38650	+	3.05244i	0.306028	+	0.111385i	−0.184441	+	0.982843i	$0.559048\pi$
$752$	0.854241	−	0.716794i	0.0311510	−	0.0261388i
$753$	−7.19308	−	13.1928i	−0.262130	−	0.480773i
$754$	5.20772	−	1.89546i	0.189654	−	0.0690284i
$755$	43.4842			1.58255
$756$	7.14362	+	11.7460i	0.259811	+	0.427198i
$757$	−46.7158			−1.69791			−0.848957	−	0.528462i	$-0.822769\pi$
$757$	−46.7158			−1.69791			−0.848957	+	0.528462i	$0.822769\pi$
$758$	20.5214	−	7.46919i	0.745372	−	0.271293i
$759$	27.6333	+	0.675149i	1.00303	+	0.0245064i
$760$	−1.21240	+	1.01732i	−0.0439783	+	0.0369022i
$761$	−4.28236	−	1.55865i	−0.155235	−	0.0565010i	0.263234	−	0.964732i	$-0.415211\pi$
$761$	−4.28236	−	1.55865i	−0.155235	−	0.0565010i	−0.418469	+	0.908231i	$0.637433\pi$
$762$	1.76936	+	1.55988i	0.0640971	+	0.0565084i
$763$	−20.3940	−	14.0134i	−0.738311	−	0.507319i
$764$	0.768708	−	1.33144i	0.0278109	−	0.0481699i
$765$	−11.0777	−	87.6789i	−0.400514	−	3.17004i
$766$	38.6191			1.39536
$767$	15.7921	−	5.74784i	0.570219	−	0.207543i
$768$	1.35363	−	1.08060i	0.0488448	−	0.0389928i
$769$	4.65375	+	26.3927i	0.167818	+	0.951745i	0.946111	+	0.323843i	$0.104975\pi$
$769$	4.65375	+	26.3927i	0.167818	+	0.951745i	−0.778292	+	0.627902i	$0.783914\pi$
$770$	9.53745	+	34.3777i	0.343706	+	1.23889i
$771$	2.92569	+	19.3443i	0.105366	+	0.696669i
$772$	3.15080	−	17.8691i	0.113400	−	0.643122i
$773$	−7.09931			−0.255345			−0.127672	−	0.991816i	$-0.540751\pi$
$773$	−7.09931			−0.255345			−0.127672	+	0.991816i	$0.540751\pi$
$774$	1.49061	+	11.7981i	0.0535790	+	0.424073i
$775$	−54.1740			−1.94599
$776$	−12.8225	+	4.66700i	−0.460300	+	0.167536i
$777$	−13.3552	+	5.97577i	−0.479115	+	0.214379i
$778$	13.3249	−	11.1809i	0.477719	−	0.400854i
$779$	0.210340	+	1.19290i	0.00753621	+	0.0427399i
$780$	−33.3856	−	0.815691i	−1.19540	−	0.0292064i
$781$	9.00456	+	7.55573i	0.322209	+	0.270365i
$782$	−17.4323	−	30.1937i	−0.623379	−	1.07972i
$783$	−1.44372	+	5.70601i	−0.0515942	+	0.203916i
$784$	−2.27766	+	6.61908i	−0.0813451	+	0.236396i
$785$	−9.24516	+	52.4319i	−0.329974	+	1.87138i
$786$	31.0582	+	0.758828i	1.10781	+	0.0270665i
$787$	−17.8834	+	15.0059i	−0.637473	+	0.534904i	−0.903241	−	0.429133i	$-0.858819\pi$
$787$	−17.8834	+	15.0059i	−0.637473	+	0.534904i	0.265768	+	0.964037i	$0.414375\pi$
$788$	2.09873	+	11.9025i	0.0747640	+	0.424008i
$789$	−10.6865	−	9.42133i	−0.380451	−	0.335408i
$790$	60.1665	−	21.8988i	2.14063	−	0.779125i
$791$	−8.64213	−	12.1133i	−0.307279	−	0.430699i
$792$	9.80590	−	3.03558i	0.348437	−	0.107865i
$793$	25.2354	−	43.7090i	0.896136	−	1.55215i
$794$	−25.0249	+	9.10833i	−0.888102	+	0.323243i
$795$	−11.1603	−	73.7906i	−0.395815	−	2.61708i
$796$	0.731131	−	0.613491i	0.0259142	−	0.0217446i
$797$	3.31354	+	18.7920i	0.117372	+	0.665648i	0.985549	+	0.169393i	$0.0541807\pi$
$797$	3.31354	+	18.7920i	0.117372	+	0.665648i	−0.868177	+	0.496255i	$0.834708\pi$
$798$	−1.77003	−	0.504004i	−0.0626585	−	0.0178415i
$799$	−6.38561	−	5.35817i	−0.225907	−	0.189558i
$800$	5.26518	−	9.11957i	0.186152	−	0.322425i
$801$	−4.52681	−	8.80791i	−0.159947	−	0.311212i
$802$	10.1349	+	17.5542i	0.357876	+	0.619859i
$803$	−5.76422	−	4.83675i	−0.203415	−	0.170685i
$804$	0.728102	−	3.61111i	0.0256782	−	0.127354i
$805$	47.0822	+	12.1713i	1.65943	+	0.428982i
$806$	23.6521	+	8.60867i	0.833110	+	0.303227i
$807$	22.9248	+	42.0463i	0.806990	+	1.48010i
$808$	−0.999192	−	0.838422i	−0.0351515	−	0.0294956i
$809$	6.30348	−	10.9179i	0.221619	−	0.383855i	−0.733681	−	0.679494i	$-0.762199\pi$
$809$	6.30348	−	10.9179i	0.221619	−	0.383855i	0.955300	+	0.295639i	$0.0955327\pi$
$810$	20.6458	−	28.8394i	0.725418	−	1.01331i
$811$	−28.3161			−0.994311			−0.497156	−	0.867661i	$-0.665622\pi$
$811$	−28.3161			−0.994311			−0.497156	+	0.867661i	$0.665622\pi$
$812$	−2.70484	+	1.29047i	−0.0949214	+	0.0452867i
$813$	−28.9175	−	0.706525i	−1.01418	−	0.0247789i
$814$	1.89704	+	10.7587i	0.0664913	+	0.377091i
$815$	2.84985	+	16.1623i	0.0998260	+	0.566141i
$816$	−9.71205	−	8.56220i	−0.339990	−	0.299737i
$817$	−1.21950	−	1.02329i	−0.0426651	−	0.0358002i
$818$	−0.310122	+	0.537148i	−0.0108432	+	0.0187809i
$819$	−20.9832	−	32.6765i	−0.733211	−	1.14181i
$820$	−5.94308	−	10.2937i	−0.207541	−	0.359472i
$821$	2.09357	−	11.8732i	0.0730660	−	0.414378i	−0.926233	−	0.376951i	$-0.876973\pi$
$821$	2.09357	−	11.8732i	0.0730660	−	0.414378i	0.999299	−	0.0374272i	$-0.0119162\pi$
$822$	16.5745	−	13.2314i	0.578101	−	0.461499i
$823$	13.1414	+	4.78306i	0.458079	+	0.166727i	0.560745	−	0.827989i	$-0.310515\pi$
$823$	13.1414	+	4.78306i	0.458079	+	0.166727i	−0.102666	+	0.994716i	$0.532737\pi$
$824$	6.26879	−	5.26014i	0.218384	−	0.183246i
$825$	48.7731	−	38.9356i	1.69806	−	1.35556i
$826$	−8.20225	+	3.91327i	−0.285393	+	0.136160i
$827$	−5.96830	−	10.3374i	−0.207538	−	0.359467i	0.743400	−	0.668847i	$-0.233212\pi$
$827$	−5.96830	−	10.3374i	−0.207538	−	0.359467i	−0.950938	+	0.309380i	$0.899878\pi$
$828$	3.09975	−	13.6445i	0.107724	−	0.474179i
$829$	2.25857	+	3.91197i	0.0784435	+	0.135868i	0.902579	−	0.430525i	$-0.141672\pi$
$829$	2.25857	+	3.91197i	0.0784435	+	0.135868i	−0.824135	+	0.566393i	$0.808338\pi$
$830$	0.743072	−	4.21417i	0.0257924	−	0.146276i
$831$	33.4315	+	29.4735i	1.15973	+	1.02242i
$832$	−3.74792	+	3.14488i	−0.129936	+	0.109029i
$833$	51.6837	+	8.17538i	1.79073	+	0.283260i
$834$	5.03687	−	8.25185i	0.174413	−	0.285738i
$835$	−58.2984	+	21.2189i	−2.01750	+	0.734310i
$836$	−0.687082	+	1.19006i	−0.0237632	+	0.0411591i
$837$	−21.6809	+	15.6375i	−0.749402	+	0.540510i
$838$	3.86533	+	6.69495i	0.133526	+	0.231273i
$839$	−1.41516	+	8.02576i	−0.0488567	+	0.277080i	−0.999443	−	0.0333813i	$-0.989372\pi$
$839$	−1.41516	+	8.02576i	−0.0488567	+	0.277080i	0.950586	+	0.310461i	$0.100484\pi$
$840$	18.0129	−	1.29311i	0.621505	−	0.0446164i
$841$	26.0454	+	9.47975i	0.898117	+	0.326888i
$842$	−0.425317	−	0.154803i	−0.0146574	−	0.00533486i
$843$	3.28417	−	1.10527i	0.113113	−	0.0380676i
$844$	−2.74741	+	15.5813i	−0.0945697	+	0.536331i
$845$	43.1020			1.48276
$846$	−0.419336	−	3.31901i	−0.0144171	−	0.114110i
$847$	1.08764	+	1.52450i	0.0373719	+	0.0523824i
$848$	−8.37557	−	7.02794i	−0.287618	−	0.241340i
$849$	36.0754	−	28.7991i	1.23811	−	0.988381i
$850$	−73.9693	−	26.9226i	−2.53713	−	0.923438i
$851$	13.9932	+	5.09313i	0.479682	+	0.174590i
$852$	4.65017	−	3.71224i	0.159312	−	0.127179i
$853$	−26.4820	−	22.2210i	−0.906725	−	0.760833i	0.0647678	−	0.997900i	$-0.479369\pi$
$853$	−26.4820	−	22.2210i	−0.906725	−	0.760833i	−0.971493	+	0.237067i	$0.923814\pi$
$854$	−11.3158	+	24.8368i	−0.387218	+	0.849897i
$855$	0.595151	+	4.71057i	0.0203537	+	0.161098i
$856$	−14.3071			−0.489006
$857$	−5.80775	+	32.9374i	−0.198389	+	1.12512i	0.709120	+	0.705088i	$0.249092\pi$
$857$	−5.80775	+	32.9374i	−0.198389	+	1.12512i	−0.907509	+	0.420033i	$0.862019\pi$
$858$	−27.4813	+	9.24868i	−0.938195	+	0.315745i
$859$	−34.3394	−	12.4985i	−1.17164	−	0.426444i	−0.318401	−	0.947956i	$-0.603146\pi$
$859$	−34.3394	−	12.4985i	−1.17164	−	0.426444i	−0.853244	+	0.521512i	$0.825368\pi$
$860$	14.6793	+	5.34283i	0.500560	+	0.182189i
$861$	6.03601	−	12.4340i	0.205707	−	0.423751i
$862$	−6.41157	+	36.3618i	−0.218379	+	1.23849i
$863$	16.3210	+	28.2688i	0.555574	+	0.962282i	0.997859	+	0.0654076i	$0.0208348\pi$
$863$	16.3210	+	28.2688i	0.555574	+	0.962282i	−0.442285	+	0.896875i	$0.645832\pi$
$864$	−0.525213	−	5.16954i	−0.0178681	−	0.175871i
$865$	47.2018	−	81.7560i	1.60491	−	2.77979i
$866$	−34.4603	+	12.5425i	−1.17101	+	0.426212i
$867$	−35.0841	+	57.4778i	−1.19152	+	1.95205i
$868$	−13.1780	−	3.40666i	−0.447290	−	0.115630i
$869$	42.5863	−	35.7342i	1.44464	−	1.21220i
$870$	5.79969	+	5.11304i	0.196628	+	0.173348i
$871$	−1.80693	+	10.2476i	−0.0612254	+	0.347227i
$872$	4.67627	+	8.09953i	0.158358	+	0.274285i
$873$	−9.06879	+	39.9190i	−0.306932	+	1.35105i
$874$	0.936557	+	1.62216i	0.0316795	+	0.0548705i
$875$	52.0429	−	24.8295i	1.75937	−	0.839392i
$876$	−2.97678	+	2.37637i	−0.100576	+	0.0802900i
$877$	−36.5767	+	30.6915i	−1.23511	+	1.03638i	−0.237217	+	0.971457i	$0.576235\pi$
$877$	−36.5767	+	30.6915i	−1.23511	+	1.03638i	−0.997890	+	0.0649210i	$0.979320\pi$
$878$	20.8189	+	7.57745i	0.702603	+	0.255727i
$879$	−28.8351	+	23.0191i	−0.972584	+	0.776415i
$880$	2.34153	−	13.2795i	0.0789329	−	0.447650i
$881$	22.9571	+	39.7629i	0.773445	+	1.33965i	0.935665	+	0.352891i	$0.114801\pi$
$881$	22.9571	+	39.7629i	0.773445	+	1.33965i	−0.162220	+	0.986755i	$0.551865\pi$
$882$	12.9901	+	16.5002i	0.437399	+	0.555592i
$883$	−2.48770	+	4.30882i	−0.0837178	+	0.145003i	−0.904844	−	0.425743i	$-0.860013\pi$
$883$	−2.48770	+	4.30882i	−0.0837178	+	0.145003i	0.821126	+	0.570747i	$0.193346\pi$
$884$	28.0164	+	23.5086i	0.942295	+	0.790679i
$885$	17.5872	+	15.5050i	0.591186	+	0.521194i
$886$	4.65340	+	26.3907i	0.156334	+	0.886614i
$887$	2.50163	+	14.1874i	0.0839964	+	0.476367i	0.997569	+	0.0696907i	$0.0222012\pi$
$887$	2.50163	+	14.1874i	0.0839964	+	0.476367i	−0.913572	+	0.406676i	$0.866688\pi$
$888$	5.52841	+	0.135073i	0.185521	+	0.00453274i
$889$	2.96961	+	2.04052i	0.0995974	+	0.0684369i
$890$	−13.0089			−0.436059
$891$	8.28056	−	29.6608i	0.277409	−	0.993676i
$892$	−6.24392	+	10.8148i	−0.209062	+	0.362106i
$893$	0.343069	+	0.287869i	0.0114804	+	0.00963316i
$894$	−13.5330	−	24.8209i	−0.452612	−	0.830136i
$895$	−40.7476	−	14.8309i	−1.36204	−	0.495743i
$896$	1.85424	−	1.88727i	0.0619460	−	0.0630492i
$897$	−7.81194	+	38.7443i	−0.260833	+	1.29364i
$898$	−6.26651	−	5.25823i	−0.209116	−	0.175469i
$899$	−2.91369	−	5.04665i	−0.0971768	−	0.168315i
$900$	−14.4406	−	28.0974i	−0.481354	−	0.936581i
$901$	−40.8651	+	70.7804i	−1.36141	+	2.35804i
$902$	−7.90575	−	6.63371i	−0.263233	−	0.220878i
$903$	4.42717	+	17.6174i	0.147327	+	0.586270i
$904$	0.976624	+	5.53871i	0.0324820	+	0.184215i
$905$	−3.03048	+	2.54288i	−0.100737	+	0.0845281i
$906$	−2.85802	−	18.8969i	−0.0949513	−	0.627806i
$907$	13.1176	−	4.77441i	0.435562	−	0.158532i	−0.114927	−	0.993374i	$-0.536663\pi$
$907$	13.1176	−	4.77441i	0.435562	−	0.158532i	0.550489	+	0.834842i	$0.314441\pi$
$908$	−11.3126	+	19.5940i	−0.375423	+	0.650251i
$909$	−3.73804	+	1.15718i	−0.123983	+	0.0383811i
$910$	−50.7772	+	4.89437i	−1.68325	+	0.162247i
$911$	6.67210	−	2.42845i	0.221057	−	0.0804580i	−0.229118	−	0.973399i	$-0.573584\pi$
$911$	6.67210	−	2.42845i	0.221057	−	0.0804580i	0.450174	+	0.892941i	$0.351362\pi$
$912$	0.521782	+	0.460006i	0.0172779	+	0.0152323i
$913$	−0.645176	−	3.65897i	−0.0213522	−	0.121094i
$914$	1.42100	−	1.19236i	0.0470025	−	0.0394398i
$915$	70.3923	+	1.71986i	2.32710	+	0.0568567i
$916$	−2.28925	+	12.9830i	−0.0756388	+	0.428969i
$917$	47.2374	−	4.55318i	1.55992	−	0.150359i
$918$	−37.3744	+	10.5768i	−1.23354	+	0.349085i
$919$	−26.5199	−	45.9338i	−0.874811	−	1.51522i	−0.856964	−	0.515376i	$-0.827652\pi$
$919$	−26.5199	−	45.9338i	−0.874811	−	1.51522i	−0.0178467	−	0.999841i	$-0.505681\pi$
$920$	−14.0802	−	11.8147i	−0.464210	−	0.389519i
$921$	−22.7237	−	0.555195i	−0.748771	−	0.0182943i
$922$	−5.89233	−	33.4171i	−0.194054	−	1.10053i
$923$	−12.8754	+	10.8038i	−0.423800	+	0.355610i
$924$	14.3126	−	6.40417i	0.470850	−	0.210682i
$925$	31.5935	−	11.4991i	1.03879	−	0.378088i
$926$	1.48972			0.0489552
$927$	−3.07727	−	24.3564i	−0.101071	−	0.799968i
$928$	1.13273			0.0371836
$929$	−1.41364	+	8.01714i	−0.0463800	+	0.263034i	−0.999176	−	0.0405758i	$-0.987081\pi$
$929$	−1.41364	+	8.01714i	−0.0463800	+	0.263034i	0.952797	+	0.303610i	$0.0981919\pi$
$930$	5.25125	+	34.7206i	0.172195	+	1.13853i
$931$	−2.77672	−	0.439224i	−0.0910033	−	0.0143950i
$932$	−2.17451	−	12.3323i	−0.0712286	−	0.403957i
$933$	−31.8727	+	25.4440i	−1.04346	+	0.832999i
$934$	−22.5364	+	8.20257i	−0.737413	+	0.268396i
$935$	−100.798			−3.29644
$936$	1.83981	+	14.5619i	0.0601360	+	0.475972i
$937$	10.4893	−	18.1680i	0.342670	−	0.593522i	−0.642258	−	0.766489i	$-0.722002\pi$
$937$	10.4893	−	18.1680i	0.342670	−	0.593522i	0.984928	+	0.172967i	$0.0553354\pi$
$938$	0.440938	−	5.60977i	0.0143971	−	0.183166i
$939$	3.74246	+	3.29937i	0.122130	+	0.107671i
$940$	−4.12956	−	1.50304i	−0.134691	−	0.0490236i
$941$	40.6165	−	34.0813i	1.32406	−	1.11102i	0.338632	−	0.940919i	$-0.390036\pi$
$941$	40.6165	−	34.0813i	1.32406	−	1.11102i	0.985427	−	0.170099i	$-0.0544087\pi$
$942$	23.3929	+	0.571546i	0.762183	+	0.0186220i
$943$	−13.2191	+	4.81134i	−0.430472	+	0.156679i
$944$	3.43492			0.111797
$945$	26.0118	−	47.5250i	0.846163	−	1.54599i
$946$	13.5634			0.440983
$947$	−10.3158	+	3.75466i	−0.335220	+	0.122010i	−0.504145	−	0.863619i	$-0.668192\pi$
$947$	−10.3158	+	3.75466i	−0.335220	+	0.122010i	0.168926	+	0.985629i	$0.445970\pi$
$948$	−13.4710	−	24.7072i	−0.437518	−	0.802452i
$949$	8.24213	−	6.91597i	0.267551	−	0.224502i
$950$	3.97402	+	1.44642i	0.128934	+	0.0469282i
$951$	1.64272	−	0.552850i	0.0532690	−	0.0179274i
$952$	−16.3003	−	11.2005i	−0.528294	−	0.363009i
$953$	1.34851	−	2.33569i	0.0436825	−	0.0756603i	−0.843358	−	0.537353i	$-0.819424\pi$
$953$	1.34851	−	2.33569i	0.0436825	−	0.0756603i	0.887040	+	0.461693i	$0.152758\pi$
$954$	−31.3336	+	9.69984i	−1.01446	+	0.314044i
$955$	−6.05874			−0.196056
$956$	21.3504	−	7.77092i	0.690522	−	0.251329i
$957$	6.25030	+	2.44941i	0.202043	+	0.0791783i
$958$	−2.17803	−	12.3522i	−0.0703690	−	0.399082i
$959$	22.7043	−	23.1086i	0.733160	−	0.746217i
$960$	−6.35519	−	2.49052i	−0.205113	−	0.0803812i
$961$	−0.787252	+	4.46473i	−0.0253952	+	0.144024i
$962$	−15.6209			−0.503638
$963$	−23.2503	+	36.0785i	−0.749230	+	1.16261i
$964$	−1.53567			−0.0494607
$965$	−67.1935	+	24.4564i	−2.16304	+	0.787281i
$966$	2.19477	−	21.2604i	0.0706154	−	0.684042i
$967$	12.4689	−	10.4626i	0.400972	−	0.336456i	−0.419897	−	0.907572i	$-0.637934\pi$
$967$	12.4689	−	10.4626i	0.400972	−	0.336456i	0.820869	+	0.571116i	$0.193489\pi$
$968$	−0.122912	−	0.697067i	−0.00395053	−	0.0224046i
$969$	2.70909	−	4.43827i	0.0870286	−	0.142578i
$970$	41.1937	+	34.5656i	1.32265	+	1.10984i
$971$	−10.8061	−	18.7167i	−0.346783	−	0.600646i	0.638893	−	0.769296i	$-0.279393\pi$
$971$	−10.8061	−	18.7167i	−0.346783	−	0.600646i	−0.985676	+	0.168650i	$0.946059\pi$
$972$	−13.8897	−	7.07652i	−0.445511	−	0.226980i
$973$	6.12267	−	13.4385i	0.196284	−	0.430819i
$974$	−2.93367	+	16.6377i	−0.0940008	+	0.533105i
$975$	42.7172	+	78.3476i	1.36804	+	2.50913i
$976$	7.90237	−	6.63088i	0.252949	−	0.212249i
$977$	−4.65609	−	26.4060i	−0.148961	−	0.844802i	−0.964101	−	0.265537i	$-0.914451\pi$
$977$	−4.65609	−	26.4060i	−0.148961	−	0.844802i	0.815139	−	0.579265i	$-0.196660\pi$
$978$	6.83633	−	2.30073i	0.218602	−	0.0735693i
$979$	−10.6139	+	3.86313i	−0.339221	+	0.123466i
$980$	27.0781	−	5.26903i	0.864979	−	0.168313i
$981$	28.0241	+	1.37021i	0.894741	+	0.0437476i
$982$	−0.975342	+	1.68934i	−0.0311244	+	0.0539091i
$983$	4.04741	−	1.47314i	0.129092	−	0.0469858i	−0.276666	−	0.960966i	$-0.589230\pi$
$983$	4.04741	−	1.47314i	0.129092	−	0.0469858i	0.405759	+	0.913980i	$0.367007\pi$
$984$	−4.08272	+	3.25924i	−0.130152	+	0.103901i
$985$	36.4863	−	30.6157i	1.16255	−	0.975496i
$986$	−1.47034	−	8.33871i	−0.0468251	−	0.265559i
$987$	−1.24544	−	4.95609i	−0.0396429	−	0.157754i
$988$	−1.50519	−	1.26300i	−0.0478865	−	0.0401815i
$989$	9.24406	−	16.0112i	0.293944	−	0.509126i
$990$	−29.6819	−	27.4850i	−0.943353	−	0.873530i
$991$	−21.2812	−	36.8602i	−0.676020	−	1.17090i	−0.976170	−	0.217009i	$-0.930370\pi$
$991$	−21.2812	−	36.8602i	−0.676020	−	1.17090i	0.300149	−	0.953892i	$-0.402964\pi$
$992$	3.94095	+	3.30685i	0.125125	+	0.104993i
$993$	12.1417	−	4.08624i	0.385306	−	0.129673i
$994$	6.36997	−	6.48342i	0.202043	−	0.205642i
$995$	−3.53442	−	1.28642i	−0.112049	−	0.0407823i
$996$	−1.88019	−	0.0459376i	−0.0595760	−	0.00145559i
$997$	−20.8192	−	17.4694i	−0.659350	−	0.553260i	0.250542	−	0.968106i	$-0.419391\pi$
$997$	−20.8192	−	17.4694i	−0.659350	−	0.553260i	−0.909892	+	0.414845i	$0.863836\pi$
$998$	−2.00744	+	3.47699i	−0.0635444	+	0.110062i
$999$	9.32477	−	13.7216i	0.295023	−	0.434132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.25.5	yes	72
7.2	even	3		378.2.v.a.79.5	yes	72
27.13	even	9		378.2.v.a.67.5	✓	72
189.121	even	9	inner	378.2.w.b.121.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.5	✓	72	27.13	even	9
378.2.v.a.79.5	yes	72	7.2	even	3
378.2.w.b.25.5	yes	72	1.1	even	1	trivial
378.2.w.b.121.5	yes	72	189.121	even	9	inner

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.902405 + 1.47840i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.70320 - 1.34785i) q^{5} +(-0.342341 + 1.69788i) q^{6} +(-0.207321 + 2.63762i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.37133 - 2.66823i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.902405 + 1.47840i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.70320 - 1.34785i) q^{5} +(-0.342341 + 1.69788i) q^{6} +(-0.207321 + 2.63762i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.37133 - 2.66823i) q^{9} -3.94086 q^{10} +(-3.21532 + 1.17028i) q^{11} +(0.259015 + 1.71257i) q^{12} +(-0.849585 - 4.81824i) q^{13} +(0.707299 + 2.54946i) q^{14} +(5.33445 - 4.25849i) q^{15} +(0.173648 - 0.984808i) q^{16} -7.47519 q^{17} +(-2.20122 - 2.03829i) q^{18} +0.401606 q^{19} +(-3.70320 + 1.34785i) q^{20} +(-3.71236 - 2.68670i) q^{21} +(-2.62115 + 2.19941i) q^{22} +(0.809905 + 4.59320i) q^{23} +(0.829129 + 1.52071i) q^{24} +(8.06673 + 6.76879i) q^{25} +(-2.44628 - 4.23709i) q^{26} +(5.18221 + 0.380448i) q^{27} +(1.53661 + 2.15379i) q^{28} +(-0.196696 + 1.11552i) q^{29} +(3.55625 - 5.82616i) q^{30} +(-3.94095 + 3.30685i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(1.17138 - 5.80959i) q^{33} +(-7.02438 + 2.55666i) q^{34} +(4.32287 - 9.48817i) q^{35} +(-2.76561 - 1.16251i) q^{36} +(1.59639 - 2.76503i) q^{37} +(0.377386 - 0.137357i) q^{38} +(7.88995 + 3.09197i) q^{39} +(-3.01887 + 2.53314i) q^{40} +(0.523747 + 2.97031i) q^{41} +(-4.40739 - 1.25497i) q^{42} +(-3.03657 - 2.54798i) q^{43} +(-1.71083 + 2.96325i) q^{44} +(1.48193 + 11.7293i) q^{45} +(2.33203 + 4.03919i) q^{46} +(0.854241 + 0.716794i) q^{47} +(1.29924 + 1.14542i) q^{48} +(-6.91404 - 1.09367i) q^{49} +(9.89531 + 3.60160i) q^{50} +(6.74564 - 11.0513i) q^{51} +(-3.74792 - 3.14488i) q^{52} +(5.46677 - 9.46872i) q^{53} +(4.99980 - 1.41491i) q^{54} +13.4843 q^{55} +(2.18058 + 1.49835i) q^{56} +(-0.362411 + 0.593734i) q^{57} +(0.196696 + 1.11552i) q^{58} +(0.596467 + 3.38273i) q^{59} +(1.34912 - 6.69111i) q^{60} +(7.90237 + 6.63088i) q^{61} +(-2.57227 + 4.45531i) q^{62} +(7.32207 - 3.06386i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.34810 + 18.9880i) q^{65} +(-0.886263 - 5.85986i) q^{66} +(-1.99857 - 0.727420i) q^{67} +(-5.72632 + 4.80496i) q^{68} +(-7.52145 - 2.94756i) q^{69} +(0.817025 - 10.3945i) q^{70} +(-1.71767 - 2.97510i) q^{71} +(-2.99642 - 0.146507i) q^{72} +(1.09956 + 1.90449i) q^{73} +(0.554420 - 3.14427i) q^{74} +(-17.2864 + 5.81766i) q^{75} +(0.307648 - 0.258147i) q^{76} +(-2.42014 - 8.72340i) q^{77} +(8.47165 + 0.206983i) q^{78} +(-15.2674 + 5.55686i) q^{79} +(-1.97043 + 3.41288i) q^{80} +(-5.23890 + 7.31805i) q^{81} +(1.50807 + 2.61205i) q^{82} +(-0.188556 + 1.06935i) q^{83} +(-4.57081 + 0.328128i) q^{84} +(27.6821 + 10.0755i) q^{85} +(-3.72490 - 1.35575i) q^{86} +(-1.47168 - 1.29744i) q^{87} +(-0.594167 + 3.36969i) q^{88} +3.30103 q^{89} +(5.40422 + 10.5151i) q^{90} +(12.8848 - 1.24196i) q^{91} +(3.57287 + 2.99800i) q^{92} +(-1.33251 - 8.81042i) q^{93} +(1.04788 + 0.381398i) q^{94} +(-1.48723 - 0.541306i) q^{95} +(1.61264 + 0.631974i) q^{96} +(-10.4530 - 8.77109i) q^{97} +(-6.87113 + 1.33703i) q^{98} +(7.53184 + 6.97436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

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