LMFDB - Embedded newform 380.2.be.b.231.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(51,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 5]))

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

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

chi := DirichletCharacter("380.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			231.10
Character	$\chi$	$=$	380.231
Dual form			380.2.be.b.51.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0889099 - 1.41142i) q^{2} +(-1.86185 + 0.677657i) q^{3} +(-1.98419 - 0.250978i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.790919 + 2.68809i) q^{6} +(1.89621 - 1.09478i) q^{7} +(-0.530648 + 2.77820i) q^{8} +(0.709122 - 0.595024i) q^{9} +O(q^{10})$	\(q+(0.0889099 - 1.41142i) q^{2} +(-1.86185 + 0.677657i) q^{3} +(-1.98419 - 0.250978i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.790919 + 2.68809i) q^{6} +(1.89621 - 1.09478i) q^{7} +(-0.530648 + 2.77820i) q^{8} +(0.709122 - 0.595024i) q^{9} +(1.37453 + 0.332649i) q^{10} +(1.11884 + 0.645961i) q^{11} +(3.86434 - 0.877318i) q^{12} +(1.54509 - 4.24510i) q^{13} +(-1.37660 - 2.77368i) q^{14} +(-0.344055 - 1.95124i) q^{15} +(3.87402 + 0.995975i) q^{16} +(3.21680 + 2.69921i) q^{17} +(-0.776779 - 1.05377i) q^{18} +(0.583643 - 4.31965i) q^{19} +(0.591716 - 1.91046i) q^{20} +(-2.78857 + 3.32329i) q^{21} +(1.01120 - 1.52171i) q^{22} +(7.68844 - 1.35568i) q^{23} +(-0.894683 - 5.53219i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-5.85422 - 2.55819i) q^{26} +(2.05495 - 3.55928i) q^{27} +(-4.03721 + 1.69634i) q^{28} +(-5.00853 - 5.96893i) q^{29} +(-2.78459 + 0.312121i) q^{30} +(0.801118 + 1.38758i) q^{31} +(1.75017 - 5.37930i) q^{32} +(-2.52084 - 0.444493i) q^{33} +(4.09572 - 4.30025i) q^{34} +(0.748873 + 2.05751i) q^{35} +(-1.55637 + 1.00267i) q^{36} +0.916035i q^{37} +(-6.04493 - 1.20782i) q^{38} +8.95076i q^{39} +(-2.64385 - 1.00502i) q^{40} +(3.58454 + 9.84843i) q^{41} +(4.44262 + 4.23131i) q^{42} +(3.96610 + 0.699331i) q^{43} +(-2.05786 - 1.56251i) q^{44} +(0.462847 + 0.801674i) q^{45} +(-1.22985 - 10.9721i) q^{46} +(-0.117552 - 0.140092i) q^{47} +(-7.88776 + 0.770903i) q^{48} +(-1.10292 + 1.91031i) q^{49} +(-0.566281 + 1.29589i) q^{50} +(-7.81833 - 2.84564i) q^{51} +(-4.13117 + 8.03529i) q^{52} +(11.2420 - 1.98226i) q^{53} +(-4.84091 - 3.21684i) q^{54} +(-0.830431 + 0.989670i) q^{55} +(2.03530 + 5.84901i) q^{56} +(1.84059 + 8.43803i) q^{57} +(-8.86996 + 6.53842i) q^{58} +(5.65551 + 4.74554i) q^{59} +(0.192955 + 3.95797i) q^{60} +(-0.489472 - 2.77593i) q^{61} +(2.02968 - 1.00734i) q^{62} +(0.693227 - 1.90462i) q^{63} +(-7.43682 - 2.94850i) q^{64} +(3.91230 + 2.25877i) q^{65} +(-0.851492 + 3.51844i) q^{66} +(-7.03072 + 5.89947i) q^{67} +(-5.70530 - 6.16310i) q^{68} +(-13.3960 + 7.73419i) q^{69} +(2.97059 - 0.874038i) q^{70} +(0.824318 - 4.67494i) q^{71} +(1.27680 + 2.28583i) q^{72} +(2.41720 - 0.879790i) q^{73} +(1.29291 + 0.0814446i) q^{74} +1.98134 q^{75} +(-2.24219 + 8.42452i) q^{76} +2.82874 q^{77} +(12.6332 + 0.795811i) q^{78} +(-10.9331 + 3.97931i) q^{79} +(-1.65356 + 3.64222i) q^{80} +(-1.89627 + 10.7543i) q^{81} +(14.2189 - 4.18365i) q^{82} +(4.79084 - 2.76600i) q^{83} +(6.36713 - 5.89417i) q^{84} +(-3.21680 + 2.69921i) q^{85} +(1.33967 - 5.53564i) q^{86} +(13.3700 + 7.71918i) q^{87} +(-2.38832 + 2.76558i) q^{88} +(5.59996 - 15.3858i) q^{89} +(1.17265 - 0.581993i) q^{90} +(-1.71762 - 9.74113i) q^{91} +(-15.5956 + 0.760298i) q^{92} +(-2.43186 - 2.04057i) q^{93} +(-0.208180 + 0.153458i) q^{94} +(4.15267 + 1.32487i) q^{95} +(0.386765 + 11.2015i) q^{96} +(3.27224 - 3.89970i) q^{97} +(2.59818 + 1.72652i) q^{98} +(1.17776 - 0.207670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.0889099	−	1.41142i	0.0628688	−	0.998022i
$2$	0.0889099	−	1.41142i	0.0628688	−	0.998022i
$3$	−1.86185	+	0.677657i	−1.07494	+	0.391245i	−0.818021	−	0.575188i	$-0.804929\pi$
$3$	−1.86185	+	0.677657i	−1.07494	+	0.391245i	−0.256917	+	0.966434i	$0.582707\pi$
$4$	−1.98419	−	0.250978i	−0.992095	−	0.125489i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$5$	−0.173648	+	0.984808i	−0.0776578	+	0.440419i
$6$	0.790919	+	2.68809i	0.322891	+	1.09741i
$7$	1.89621	−	1.09478i	0.716701	−	0.413787i	−0.0968363	−	0.995300i	$-0.530872\pi$
$7$	1.89621	−	1.09478i	0.716701	−	0.413787i	0.813537	+	0.581513i	$0.197539\pi$
$8$	−0.530648	+	2.77820i	−0.187612	+	0.982243i
$9$	0.709122	−	0.595024i	0.236374	−	0.198341i
$10$	1.37453	+	0.332649i	0.434666	+	0.105193i
$11$	1.11884	+	0.645961i	0.337342	+	0.194765i	0.659096	−	0.752059i	$-0.270939\pi$
$11$	1.11884	+	0.645961i	0.337342	+	0.194765i	−0.321754	+	0.946823i	$0.604272\pi$
$12$	3.86434	−	0.877318i	1.11554	−	0.253260i
$13$	1.54509	−	4.24510i	0.428530	−	1.17738i	−0.518174	−	0.855275i	$-0.673388\pi$
$13$	1.54509	−	4.24510i	0.428530	−	1.17738i	0.946705	−	0.322103i	$-0.104390\pi$
$14$	−1.37660	−	2.77368i	−0.367911	−	0.741297i
$15$	−0.344055	−	1.95124i	−0.0888347	−	0.503807i
$16$	3.87402	+	0.995975i	0.968505	+	0.248994i
$17$	3.21680	+	2.69921i	0.780188	+	0.654656i	0.943296	−	0.331953i	$-0.107707\pi$
$17$	3.21680	+	2.69921i	0.780188	+	0.654656i	−0.163108	+	0.986608i	$0.552152\pi$
$18$	−0.776779	−	1.05377i	−0.183089	−	0.248376i
$19$	0.583643	−	4.31965i	0.133897	−	0.990995i
$19$	0.583643	−	4.31965i	0.133897	−	0.990995i
$20$	0.591716	−	1.91046i	0.132312	−	0.427193i
$21$	−2.78857	+	3.32329i	−0.608517	+	0.725202i
$22$	1.01120	−	1.52171i	0.215588	−	0.324430i
$23$	7.68844	−	1.35568i	1.60315	−	0.282679i	0.700694	−	0.713461i	$-0.252874\pi$
$23$	7.68844	−	1.35568i	1.60315	−	0.282679i	0.902456	+	0.430783i	$0.141763\pi$
$24$	−0.894683	−	5.53219i	−0.182626	−	1.12925i
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	−5.85422	−	2.55819i	−1.14811	−	0.501703i
$27$	2.05495	−	3.55928i	0.395475	−	0.684983i
$28$	−4.03721	+	1.69634i	−0.762961	+	0.320579i
$29$	−5.00853	−	5.96893i	−0.930061	−	1.10840i	−0.993883	−	0.110442i	$-0.964773\pi$
$29$	−5.00853	−	5.96893i	−0.930061	−	1.10840i	0.0638218	−	0.997961i	$-0.479671\pi$
$30$	−2.78459	+	0.312121i	−0.508395	+	0.0569853i
$31$	0.801118	+	1.38758i	0.143885	+	0.249216i	0.928956	−	0.370189i	$-0.120707\pi$
$31$	0.801118	+	1.38758i	0.143885	+	0.249216i	−0.785071	+	0.619405i	$0.787374\pi$
$32$	1.75017	−	5.37930i	0.309390	−	0.950935i
$33$	−2.52084	−	0.444493i	−0.438823	−	0.0773763i
$34$	4.09572	−	4.30025i	0.702410	−	0.737487i
$35$	0.748873	+	2.05751i	0.126583	+	0.347783i
$36$	−1.55637	+	1.00267i	−0.259395	+	0.167111i
$37$			0.916035i			0.150595i	0.997161	+	0.0752976i	$0.0239907\pi$
$37$			0.916035i			0.150595i	−0.997161	+	0.0752976i	$0.976009\pi$
$38$	−6.04493	−	1.20782i	−0.980617	−	0.195935i
$39$			8.95076i			1.43327i
$40$	−2.64385	−	1.00502i	−0.418029	−	0.158907i
$41$	3.58454	+	9.84843i	0.559811	+	1.53807i	0.819914	+	0.572486i	$0.194021\pi$
$41$	3.58454	+	9.84843i	0.559811	+	1.53807i	−0.260104	+	0.965581i	$0.583757\pi$
$42$	4.44262	+	4.23131i	0.685511	+	0.652905i
$43$	3.96610	+	0.699331i	0.604825	+	0.106647i	0.467671	−	0.883903i	$-0.345093\pi$
$43$	3.96610	+	0.699331i	0.604825	+	0.106647i	0.137154	+	0.990550i	$0.456204\pi$
$44$	−2.05786	−	1.56251i	−0.310235	−	0.235558i
$45$	0.462847	+	0.801674i	0.0689971	+	0.119507i
$46$	−1.22985	−	10.9721i	−0.181331	−	1.61775i
$47$	−0.117552	−	0.140092i	−0.0171467	−	0.0204346i	0.757403	−	0.652948i	$-0.226468\pi$
$47$	−0.117552	−	0.140092i	−0.0171467	−	0.0204346i	−0.774550	+	0.632513i	$0.782023\pi$
$48$	−7.88776	+	0.770903i	−1.13850	+	0.111270i
$49$	−1.10292	+	1.91031i	−0.157560	+	0.272902i
$50$	−0.566281	+	1.29589i	−0.0800842	+	0.183266i
$51$	−7.81833	−	2.84564i	−1.09478	−	0.398469i
$52$	−4.13117	+	8.03529i	−0.572891	+	1.11429i
$53$	11.2420	−	1.98226i	1.54420	−	0.272284i	0.664310	−	0.747458i	$-0.268726\pi$
$53$	11.2420	−	1.98226i	1.54420	−	0.272284i	0.879892	+	0.475173i	$0.157615\pi$
$54$	−4.84091	−	3.21684i	−0.658765	−	0.437757i
$55$	−0.830431	+	0.989670i	−0.111975	+	0.133447i
$56$	2.03530	+	5.84901i	0.271978	+	0.781606i
$57$	1.84059	+	8.43803i	0.243792	+	1.11764i
$58$	−8.86996	+	6.53842i	−1.16468	+	0.858537i
$59$	5.65551	+	4.74554i	0.736285	+	0.617817i	0.931837	−	0.362877i	$-0.118205\pi$
$59$	5.65551	+	4.74554i	0.736285	+	0.617817i	−0.195552	+	0.980693i	$0.562650\pi$
$60$	0.192955	+	3.95797i	0.0249103	+	0.510972i
$61$	−0.489472	−	2.77593i	−0.0626705	−	0.355422i	−0.999976	−	0.00691341i	$-0.997799\pi$
$61$	−0.489472	−	2.77593i	−0.0626705	−	0.355422i	0.937306	−	0.348508i	$-0.113312\pi$
$62$	2.02968	−	1.00734i	0.257769	−	0.127932i
$63$	0.693227	−	1.90462i	0.0873384	−	0.239960i
$64$	−7.43682	−	2.94850i	−0.929603	−	0.368562i
$65$	3.91230	+	2.25877i	0.485261	+	0.280166i
$66$	−0.851492	+	3.51844i	−0.104811	+	0.433090i
$67$	−7.03072	+	5.89947i	−0.858939	+	0.720735i	−0.961739	−	0.273967i	$-0.911664\pi$
$67$	−7.03072	+	5.89947i	−0.858939	+	0.720735i	0.102800	+	0.994702i	$0.467220\pi$
$68$	−5.70530	−	6.16310i	−0.691869	−	0.747385i
$69$	−13.3960	+	7.73419i	−1.61269	+	0.931087i
$70$	2.97059	−	0.874038i	0.355053	−	0.104468i
$71$	0.824318	−	4.67494i	0.0978286	−	0.554813i	−0.896015	−	0.444023i	$-0.853551\pi$
$71$	0.824318	−	4.67494i	0.0978286	−	0.554813i	0.993844	−	0.110790i	$-0.0353381\pi$
$72$	1.27680	+	2.28583i	0.150473	+	0.269388i
$73$	2.41720	−	0.879790i	0.282912	−	0.102972i	−0.196667	−	0.980470i	$-0.563012\pi$
$73$	2.41720	−	0.879790i	0.282912	−	0.102972i	0.479579	+	0.877499i	$0.340789\pi$
$74$	1.29291	+	0.0814446i	0.150297	+	0.00946774i
$75$	1.98134			0.228785
$76$	−2.24219	+	8.42452i	−0.257197	+	0.966359i
$77$	2.82874			0.322365
$78$	12.6332	+	0.795811i	1.43043	+	0.0901079i
$79$	−10.9331	+	3.97931i	−1.23006	+	0.447707i	−0.873620	−	0.486610i	$-0.838233\pi$
$79$	−10.9331	+	3.97931i	−1.23006	+	0.447707i	−0.356445	+	0.934316i	$0.616011\pi$
$80$	−1.65356	+	3.64222i	−0.184874	+	0.407212i
$81$	−1.89627	+	10.7543i	−0.210696	+	1.19492i
$82$	14.2189	−	4.18365i	1.57022	−	0.462007i
$83$	4.79084	−	2.76600i	0.525864	−	0.303607i	−0.213467	−	0.976950i	$-0.568476\pi$
$83$	4.79084	−	2.76600i	0.525864	−	0.303607i	0.739330	+	0.673343i	$0.235142\pi$
$84$	6.36713	−	5.89417i	0.694711	−	0.643107i
$85$	−3.21680	+	2.69921i	−0.348911	+	0.292771i
$86$	1.33967	−	5.53564i	0.144461	−	0.596924i
$87$	13.3700	+	7.71918i	1.43342	+	0.827583i
$88$	−2.38832	+	2.76558i	−0.254596	+	0.294812i
$89$	5.59996	−	15.3858i	0.593594	−	1.63089i	−0.170187	−	0.985412i	$-0.554437\pi$
$89$	5.59996	−	15.3858i	0.593594	−	1.63089i	0.763781	−	0.645475i	$-0.223341\pi$
$90$	1.17265	−	0.581993i	0.123608	−	0.0613474i
$91$	−1.71762	−	9.74113i	−0.180056	−	1.02115i
$92$	−15.5956	+	0.760298i	−1.62595	+	0.0792665i
$93$	−2.43186	−	2.04057i	−0.252172	−	0.211598i
$94$	−0.208180	+	0.153458i	−0.0214721	+	0.0158280i
$95$	4.15267	+	1.32487i	0.426055	+	0.135929i
$96$	0.386765	+	11.2015i	0.0394740	+	1.14324i
$97$	3.27224	−	3.89970i	0.332245	−	0.395955i	−0.573897	−	0.818928i	$-0.694569\pi$
$97$	3.27224	−	3.89970i	0.332245	−	0.395955i	0.906142	+	0.422973i	$0.139013\pi$
$98$	2.59818	+	1.72652i	0.262456	+	0.174405i
$99$	1.17776	−	0.207670i	0.118369	−	0.0208716i
$100$	1.77869	+	0.914475i	0.177869	+	0.0914475i
$101$	−5.56628	−	2.02596i	−0.553866	−	0.201591i	0.0498975	−	0.998754i	$-0.484111\pi$
$101$	−5.56628	−	2.02596i	−0.553866	−	0.201591i	−0.603763	+	0.797164i	$0.706333\pi$
$102$	−4.71151	+	10.7819i	−0.466509	+	1.06757i
$103$	−2.90093	+	5.02455i	−0.285837	+	0.495084i	−0.972812	−	0.231597i	$-0.925605\pi$
$103$	−2.90093	+	5.02455i	−0.285837	+	0.495084i	0.686975	+	0.726681i	$0.258938\pi$
$104$	10.9738	+	6.54522i	1.07607	+	0.641812i
$105$	−2.78857	−	3.32329i	−0.272137	−	0.324320i
$106$	−1.79827	−	16.0433i	−0.174664	−	1.55827i
$107$	−8.14346	−	14.1049i	−0.787258	−	1.36357i	−0.927641	−	0.373474i	$-0.878167\pi$
$107$	−8.14346	−	14.1049i	−0.787258	−	1.36357i	0.140383	−	0.990097i	$-0.455167\pi$
$108$	−4.97071	+	6.54653i	−0.478307	+	0.629941i
$109$	−4.65630	−	0.821031i	−0.445992	−	0.0786405i	−0.0538583	−	0.998549i	$-0.517152\pi$
$109$	−4.65630	−	0.821031i	−0.445992	−	0.0786405i	−0.392134	+	0.919908i	$0.628263\pi$
$110$	1.32300	+	1.26008i	0.126143	+	0.120143i
$111$	−0.620758	−	1.70552i	−0.0589197	−	0.161881i
$112$	8.43634	−	2.35261i	0.797159	−	0.222301i
$113$			2.91511i			0.274231i	0.990555	+	0.137115i	$0.0437831\pi$
$113$			2.91511i			0.274231i	−0.990555	+	0.137115i	$0.956217\pi$
$114$	12.0732	−	1.84761i	1.13076	−	0.173044i
$115$			7.80704i			0.728011i
$116$	8.43981	+	13.1005i	0.783616	+	1.21635i
$117$	−1.43028	−	3.92966i	−0.132229	−	0.363297i
$118$	7.20076	−	7.56036i	0.662884	−	0.695987i
$119$	9.05477	+	1.59660i	0.830050	+	0.146360i
$120$	5.60350	+	0.0795636i	0.511527	+	0.00726313i
$121$	−4.66547	−	8.08083i	−0.424134	−	0.734621i
$122$	−3.96152	+	0.444041i	−0.358659	+	0.0402015i
$123$	−13.3477	−	15.9072i	−1.20352	−	1.43430i
$124$	−1.24132	−	2.95428i	−0.111474	−	0.265302i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	−2.62658	−	1.14777i	−0.233995	−	0.102252i
$127$	1.25704	+	0.457526i	0.111545	+	0.0405989i	0.397189	−	0.917737i	$-0.369986\pi$
$127$	1.25704	+	0.457526i	0.111545	+	0.0405989i	−0.285645	+	0.958336i	$0.592208\pi$
$128$	−4.82276	+	10.2343i	−0.426276	+	0.904593i
$129$	−7.85818	+	1.38561i	−0.691874	+	0.121996i
$130$	3.53590	−	5.32106i	0.310119	−	0.466688i
$131$	−3.15773	+	3.76323i	−0.275892	+	0.328795i	−0.886142	−	0.463414i	$-0.846624\pi$
$131$	−3.15773	+	3.76323i	−0.275892	+	0.328795i	0.610250	+	0.792209i	$0.291069\pi$
$132$	4.89028	+	1.51463i	0.425644	+	0.131832i
$133$	−3.62235	−	8.82993i	−0.314097	−	0.765652i
$134$	7.70151	+	10.4478i	0.665309	+	0.902551i
$135$	3.14837	+	2.64179i	0.270968	+	0.227369i
$136$	−9.20595	+	7.50459i	−0.789404	+	0.643513i
$137$	3.80659	+	21.5882i	0.325219	+	1.84441i	0.508134	+	0.861278i	$0.330335\pi$
$137$	3.80659	+	21.5882i	0.325219	+	1.84441i	−0.182916	+	0.983129i	$0.558553\pi$
$138$	9.72512	+	19.5950i	0.827857	+	1.66804i
$139$	−3.72398	+	10.2316i	−0.315864	+	0.867830i	0.675579	+	0.737288i	$0.263894\pi$
$139$	−3.72398	+	10.2316i	−0.315864	+	0.867830i	−0.991443	+	0.130542i	$0.958328\pi$
$140$	−0.969516	−	4.27044i	−0.0819391	−	0.360918i
$141$	0.313798	+	0.181171i	0.0264265	+	0.0152574i
$142$	−6.52500	−	1.57910i	−0.547565	−	0.132516i
$143$	4.47087	−	3.75150i	0.373873	−	0.313717i
$144$	3.33978	−	1.59887i	0.278315	−	0.133239i
$145$	6.74798	−	3.89595i	0.560389	−	0.323541i
$146$	−1.02684	−	3.48990i	−0.0849815	−	0.288826i
$147$	0.758930	−	4.30411i	0.0625955	−	0.354997i
$148$	0.229904	−	1.81759i	0.0188980	−	0.149405i
$149$	−12.8628	+	4.68167i	−1.05376	+	0.383538i	−0.810081	−	0.586318i	$-0.800577\pi$
$149$	−12.8628	+	4.68167i	−1.05376	+	0.383538i	−0.243680	+	0.969856i	$0.578355\pi$
$150$	0.176160	−	2.79649i	0.0143834	−	0.228332i
$151$	3.10658			0.252810			0.126405	−	0.991979i	$-0.459656\pi$
$151$	3.10658			0.252810			0.126405	+	0.991979i	$0.459656\pi$
$152$	11.6912	+	3.91369i	0.948278	+	0.317442i
$153$	3.88720			0.314262
$154$	0.251503	−	3.99253i	0.0202667	−	0.321727i
$155$	−1.50561	+	0.547997i	−0.120933	+	0.0440162i
$156$	2.24644	−	17.7600i	0.179859	−	1.42194i
$157$	1.97079	−	11.1769i	0.157286	−	0.892016i	−0.799379	−	0.600827i	$-0.794838\pi$
$157$	1.97079	−	11.1769i	0.157286	−	0.892016i	0.956666	−	0.291189i	$-0.0940508\pi$
$158$	4.64440	+	15.7849i	0.369489	+	1.25578i
$159$	−19.5875	+	11.3089i	−1.55339	+	0.896851i
$160$	4.99366	+	2.65769i	0.394784	+	0.210109i
$161$	13.0947	−	10.9878i	1.03201	−	0.865959i
$162$	15.0102	+	3.63258i	1.17931	+	0.285403i
$163$	−12.7994	−	7.38973i	−1.00253	−	0.578808i	−0.0935307	−	0.995616i	$-0.529815\pi$
$163$	−12.7994	−	7.38973i	−1.00253	−	0.578808i	−0.908994	+	0.416808i	$0.863149\pi$
$164$	−4.64066	−	20.4408i	−0.362375	−	1.59616i
$165$	0.875480	−	2.40536i	0.0681560	−	0.187257i
$166$	−3.47802	−	7.00780i	−0.269946	−	0.543911i
$167$	−2.06323	−	11.7012i	−0.159658	−	0.905463i	−0.954403	−	0.298520i	$-0.903507\pi$
$167$	−2.06323	−	11.7012i	−0.159658	−	0.905463i	0.794746	−	0.606943i	$-0.207604\pi$
$168$	−7.75303	−	9.51072i	−0.598159	−	0.733768i
$169$	−5.67496	−	4.76186i	−0.436536	−	0.366297i
$170$	3.52371	+	4.78023i	0.270256	+	0.366627i
$171$	−2.15642	−	3.41044i	−0.164906	−	0.260803i
$172$	−7.69399	−	2.38301i	−0.586661	−	0.181703i
$173$	4.31273	−	5.13971i	0.327891	−	0.390765i	−0.576764	−	0.816911i	$-0.695685\pi$
$173$	4.31273	−	5.13971i	0.327891	−	0.390765i	0.904654	+	0.426146i	$0.140129\pi$
$174$	12.0837	−	18.1843i	0.916063	−	1.37855i
$175$	−2.15629	+	0.380213i	−0.163000	+	0.0287414i
$176$	3.69104	+	3.61680i	0.278222	+	0.272627i
$177$	−13.7456	−	5.00297i	−1.03318	−	0.376046i
$178$	−21.2178	−	9.27182i	−1.59034	−	0.694952i
$179$	−9.28011	+	16.0736i	−0.693628	+	1.20140i	0.277013	+	0.960866i	$0.410655\pi$
$179$	−9.28011	+	16.0736i	−0.693628	+	1.20140i	−0.970641	+	0.240532i	$0.922678\pi$
$180$	−0.717174	−	1.70684i	−0.0534550	−	0.127220i
$181$	−0.226799	−	0.270289i	−0.0168579	−	0.0200904i	0.757550	−	0.652778i	$-0.226396\pi$
$181$	−0.226799	−	0.270289i	−0.0168579	−	0.0200904i	−0.774408	+	0.632687i	$0.781952\pi$
$182$	−13.9015	+	1.55820i	−1.03045	+	0.115501i
$183$	2.79245	+	4.83667i	0.206424	+	0.357537i
$184$	−0.313504	+	22.0794i	−0.0231118	+	1.62772i
$185$	−0.902119	−	0.159068i	−0.0663251	−	0.0116949i
$186$	−3.09631	+	3.25094i	−0.227033	+	0.238370i
$187$	1.85549	+	5.09791i	0.135687	+	0.372796i
$188$	0.198084	+	0.307473i	0.0144468	+	0.0224248i
$189$		−	8.99886i		−	0.654571i
$190$	2.23916	−	5.74336i	0.162446	−	0.416667i
$191$		−	3.47946i		−	0.251765i	−0.992045	−	0.125882i	$-0.959824\pi$
$191$		−	3.47946i		−	0.251765i	0.992045	−	0.125882i	$-0.0401762\pi$
$192$	15.8443	+	0.450035i	1.14346	+	0.0324784i
$193$	−4.59149	−	12.6150i	−0.330503	−	0.908050i	−0.987981	−	0.154576i	$-0.950599\pi$
$193$	−4.59149	−	12.6150i	−0.330503	−	0.908050i	0.657478	−	0.753474i	$-0.271623\pi$
$194$	−5.21317	−	4.96521i	−0.374284	−	0.356481i
$195$	−8.81478	−	1.55428i	−0.631239	−	0.111305i
$196$	2.66785	−	3.51361i	0.190560	−	0.250972i
$197$	10.1224	+	17.5325i	0.721192	+	1.24914i	0.960522	+	0.278203i	$0.0897387\pi$
$197$	10.1224	+	17.5325i	0.721192	+	1.24914i	−0.239330	+	0.970938i	$0.576928\pi$
$198$	−0.188395	−	1.68077i	−0.0133886	−	0.119447i
$199$	1.34495	+	1.60284i	0.0953406	+	0.113623i	0.811605	−	0.584206i	$-0.198594\pi$
$199$	1.34495	+	1.60284i	0.0953406	+	0.113623i	−0.716265	+	0.697829i	$0.754150\pi$
$200$	1.44885	−	2.42916i	0.102449	−	0.171768i
$201$	9.09230	−	15.7483i	0.641321	−	1.11080i
$202$	−3.35437	+	7.67621i	−0.236013	+	0.540096i
$203$	−16.0319	−	5.83513i	−1.12522	−	0.409546i
$204$	14.7989	+	7.60851i	1.03613	+	0.532702i
$205$	−10.3213	+	1.81992i	−0.720868	+	0.127109i
$206$	6.83382	+	4.54115i	0.476134	+	0.316397i
$207$	4.64538	−	5.53615i	0.322876	−	0.384789i
$208$	10.2137	−	14.9067i	0.708194	−	1.03359i
$209$	3.44333	−	4.45597i	0.238180	−	0.308226i
$210$	−4.93848	+	3.64036i	−0.340787	+	0.251209i
$211$	4.51259	+	3.78651i	0.310659	+	0.260674i	0.784764	−	0.619794i	$-0.212784\pi$
$211$	4.51259	+	3.78651i	0.310659	+	0.260674i	−0.474105	+	0.880468i	$0.657228\pi$
$212$	−22.8037	+	1.11170i	−1.56616	+	0.0763519i
$213$	1.63325	+	9.26263i	0.111909	+	0.634665i
$214$	−20.6319	+	10.2397i	−1.41037	+	0.699975i
$215$	−1.37741	+	3.78441i	−0.0939388	+	0.258095i
$216$	8.79794	+	7.59779i	0.598624	+	0.516964i
$217$	3.03818	+	1.75409i	0.206245	+	0.119076i
$218$	−1.57281	+	6.49897i	−0.106524	+	0.440166i
$219$	−3.90427	+	3.27607i	−0.263826	+	0.221376i
$220$	1.89612	−	1.75527i	0.127836	−	0.118340i
$221$	16.4287	−	9.48509i	1.10511	−	0.638036i
$222$	−2.46239	+	0.724510i	−0.165265	+	0.0486259i
$223$	3.74352	−	21.2306i	0.250685	−	1.42170i	−0.556226	−	0.831031i	$-0.687751\pi$
$223$	3.74352	−	21.2306i	0.250685	−	1.42170i	0.806911	−	0.590673i	$-0.201138\pi$
$224$	−2.57044	−	12.1164i	−0.171745	−	0.809558i
$225$	−0.869867	+	0.316606i	−0.0579912	+	0.0211071i
$226$	4.11444	+	0.259182i	0.273688	+	0.0172406i
$227$	−13.0082			−0.863387			−0.431693	−	0.902020i	$-0.642084\pi$
$227$	−13.0082			−0.863387			−0.431693	+	0.902020i	$0.642084\pi$
$228$	−1.53431	−	17.2046i	−0.101612	−	1.13940i
$229$	12.4762			0.824449			0.412225	−	0.911082i	$-0.364752\pi$
$229$	12.4762			0.824449			0.412225	+	0.911082i	$0.364752\pi$
$230$	11.0190	+	0.694124i	0.726570	+	0.0457692i
$231$	−5.26668	+	1.91691i	−0.346522	+	0.126124i
$232$	19.2407	−	10.7473i	1.26321	−	0.705596i
$233$	−3.93848	+	22.3362i	−0.258018	+	1.46329i	0.530186	+	0.847881i	$0.322122\pi$
$233$	−3.93848	+	22.3362i	−0.258018	+	1.46329i	−0.788205	+	0.615413i	$0.788989\pi$
$234$	−5.67355	+	1.66933i	−0.370891	+	0.109128i
$235$	0.158377	−	0.0914389i	0.0103314	−	0.00596481i
$236$	−10.0306	−	10.8355i	−0.652936	−	0.705328i
$237$	17.6591	−	14.8177i	1.14708	−	0.962514i
$238$	3.05853	−	12.6381i	0.198255	−	0.819206i
$239$	24.7712	+	14.3017i	1.60232	+	0.925097i	0.991023	+	0.133692i	$0.0426833\pi$
$239$	24.7712	+	14.3017i	1.60232	+	0.925097i	0.611292	+	0.791405i	$0.290650\pi$
$240$	0.610504	−	7.90180i	0.0394079	−	0.510059i
$241$	8.91259	−	24.4871i	0.574110	−	1.57736i	−0.223836	−	0.974627i	$-0.571858\pi$
$241$	8.91259	−	24.4871i	0.574110	−	1.57736i	0.797946	−	0.602728i	$-0.205920\pi$
$242$	−11.8202	+	5.86645i	−0.759832	+	0.377110i
$243$	−1.61612	−	9.16545i	−0.103674	−	0.587964i
$244$	0.274508	+	5.63083i	0.0175736	+	0.360477i
$245$	−1.68977	−	1.41789i	−0.107955	−	0.0905854i
$246$	−23.6384	+	17.4249i	−1.50713	+	1.11097i
$247$	−17.4355	−	9.15186i	−1.10940	−	0.582319i
$248$	−4.28008	+	1.48935i	−0.271785	+	0.0945740i
$249$	−7.04542	+	8.39641i	−0.446486	+	0.532101i
$250$	−1.17787	−	0.782706i	−0.0744949	−	0.0495027i
$251$	10.7702	−	1.89908i	0.679809	−	0.119869i	0.176927	−	0.984224i	$-0.443384\pi$
$251$	10.7702	−	1.89908i	0.679809	−	0.119869i	0.502882	+	0.864355i	$0.332273\pi$
$252$	−1.85351	+	3.60515i	−0.116760	+	0.227103i
$253$	9.47783	+	3.44965i	0.595866	+	0.216877i
$254$	0.757523	−	1.73353i	0.0475312	−	0.108771i
$255$	4.16004	−	7.20541i	0.260512	−	0.451220i
$256$	14.0161	+	7.71686i	0.876004	+	0.482303i
$257$	−17.5407	−	20.9042i	−1.09416	−	1.30397i	−0.949251	−	0.314521i	$-0.898156\pi$
$257$	−17.5407	−	20.9042i	−1.09416	−	1.30397i	−0.144907	−	0.989445i	$-0.546288\pi$
$258$	1.25700	+	11.2144i	0.0782575	+	0.698176i
$259$	1.00286	+	1.73700i	0.0623144	+	0.107932i
$260$	−7.19585	−	5.46373i	−0.446268	−	0.338846i
$261$	−7.10332	−	1.25251i	−0.439685	−	0.0775283i
$262$	5.03073	+	4.79146i	0.310800	+	0.296017i
$263$	−0.0231579	−	0.0636259i	−0.00142798	−	0.00392334i	0.938977	−	0.343981i	$-0.111776\pi$
$263$	−0.0231579	−	0.0636259i	−0.00142798	−	0.00392334i	−0.940405	+	0.340058i	$0.889553\pi$
$264$	2.57257	−	6.76755i	0.158331	−	0.416514i
$265$			11.4154i			0.701242i
$266$	−12.7848	+	4.32757i	−0.783884	+	0.265340i
$267$			32.4408i			1.98534i
$268$	15.4309	−	9.94112i	0.942593	−	0.607250i
$269$	8.21093	+	22.5593i	0.500629	+	1.37547i	0.890662	+	0.454667i	$0.150242\pi$
$269$	8.21093	+	22.5593i	0.500629	+	1.37547i	−0.390032	+	0.920801i	$0.627536\pi$
$270$	4.00859	−	4.20877i	0.243955	−	0.256138i
$271$	28.6082	+	5.04439i	1.73782	+	0.306425i	0.950640	−	0.310296i	$-0.100428\pi$
$271$	28.6082	+	5.04439i	1.73782	+	0.306425i	0.787182	+	0.616721i	$0.211539\pi$
$272$	9.77359	+	13.6607i	0.592611	+	0.828299i
$273$	9.79910	+	16.9725i	0.593069	+	1.02722i
$274$	30.8084	−	3.45327i	1.86120	−	0.208620i
$275$	−0.830431	−	0.989670i	−0.0500769	−	0.0596793i
$276$	28.5213	−	11.9840i	1.71678	−	0.721352i
$277$	2.89701	−	5.01778i	0.174065	−	0.301489i	−0.765772	−	0.643112i	$-0.777643\pi$
$277$	2.89701	−	5.01778i	0.174065	−	0.301489i	0.939837	+	0.341623i	$0.110976\pi$
$278$	14.1099	+	6.16578i	0.846255	+	0.369799i
$279$	1.39373	+	0.507277i	0.0834406	+	0.0303699i
$280$	−6.11357	+	0.988706i	−0.365356	+	0.0590865i
$281$	−18.1992	+	3.20900i	−1.08567	+	0.191433i	−0.687722	−	0.725974i	$-0.741389\pi$
$281$	−18.1992	+	3.20900i	−1.08567	+	0.191433i	−0.397949	+	0.917408i	$0.630278\pi$
$282$	0.283608	−	0.426791i	0.0168886	−	0.0254150i
$283$	−8.16320	+	9.72852i	−0.485252	+	0.578301i	−0.952003	−	0.306088i	$-0.900980\pi$
$283$	−8.16320	+	9.72852i	−0.485252	+	0.578301i	0.466751	+	0.884389i	$0.345424\pi$
$284$	−2.80891	+	9.06909i	−0.166678	+	0.538151i
$285$	−8.62946	+	0.347374i	−0.511165	+	0.0205767i
$286$	−4.89743	−	6.64380i	−0.289591	−	0.392856i
$287$	17.5789	+	14.7504i	1.03765	+	0.870691i
$288$	−1.95973	−	4.85598i	−0.115478	−	0.286141i
$289$	0.110014	+	0.623920i	0.00647141	+	0.0367012i
$290$	−4.89884	−	9.87059i	−0.287670	−	0.579621i
$291$	−3.44975	+	9.47810i	−0.202228	+	0.555616i
$292$	−5.01700	+	1.13901i	−0.293597	+	0.0666553i
$293$	16.7147	+	9.65026i	0.976486	+	0.563774i	0.901207	−	0.433388i	$-0.142682\pi$
$293$	16.7147	+	9.65026i	0.976486	+	0.563774i	0.0752785	+	0.997163i	$0.476015\pi$
$294$	−6.00741	−	1.45384i	−0.350359	−	0.0847899i
$295$	−5.65551	+	4.74554i	−0.329277	+	0.276296i
$296$	−2.54493	−	0.486092i	−0.147921	−	0.0282536i
$297$	4.59831	−	2.65483i	0.266821	−	0.154049i
$298$	5.46416	+	18.5710i	0.316530	+	1.07579i
$299$	6.12433	−	34.7328i	0.354179	−	2.00865i
$300$	−3.93135	−	0.497271i	−0.226976	−	0.0287100i
$301$	8.28619	−	3.01593i	0.477608	−	0.173835i
$302$	0.276206	−	4.38468i	0.0158939	−	0.252310i
$303$	11.7365			0.674243
$304$	6.56331	−	16.1531i	0.376431	−	0.926444i
$305$	2.81876			0.161402
$306$	0.345611	−	5.48646i	0.0197573	−	0.313640i
$307$	−11.2786	+	4.10507i	−0.643702	+	0.234289i	−0.643184	−	0.765711i	$-0.722387\pi$
$307$	−11.2786	+	4.10507i	−0.643702	+	0.234289i	−0.000518029		1.00000i	$0.500165\pi$
$308$	−5.61275	−	0.709950i	−0.319816	−	0.0404532i
$309$	1.99616	−	11.3208i	0.113558	−	0.644017i
$310$	0.639588	+	2.17376i	0.0363262	+	0.123461i
$311$	−8.04275	+	4.64348i	−0.456062	+	0.263308i	−0.710387	−	0.703811i	$-0.751480\pi$
$311$	−8.04275	+	4.64348i	−0.456062	+	0.263308i	0.254325	+	0.967119i	$0.418147\pi$
$312$	−24.8670	−	4.74970i	−1.40782	−	0.268899i
$313$	−14.5905	+	12.2429i	−0.824705	+	0.692010i	−0.954069	−	0.299587i	$-0.903151\pi$
$313$	−14.5905	+	12.2429i	−0.824705	+	0.692010i	0.129364	+	0.991597i	$0.458707\pi$
$314$	−15.6001	−	3.77535i	−0.880363	−	0.213055i
$315$	1.75531	+	1.01343i	0.0989006	+	0.0571003i
$316$	22.6920	−	5.15175i	1.27652	−	0.289808i
$317$	−8.89622	+	24.4422i	−0.499662	+	1.37281i	0.391941	+	0.919990i	$0.371804\pi$
$317$	−8.89622	+	24.4422i	−0.499662	+	1.37281i	−0.891603	+	0.452819i	$0.850419\pi$
$318$	14.2200	+	28.6516i	0.797417	+	1.60670i
$319$	−1.74803	−	9.91358i	−0.0978710	−	0.555054i
$320$	4.19509	−	6.81184i	0.234513	−	0.380794i
$321$	24.7202	+	20.7427i	1.37974	+	1.15774i
$322$	−14.3441	−	19.4591i	−0.799365	−	1.08441i
$323$	13.5371	−	12.3201i	0.753225	−	0.685506i
$324$	6.46164	−	20.8626i	0.358980	−	1.15903i
$325$	−2.90382	+	3.46063i	−0.161075	+	0.191961i
$326$	−11.5680	+	17.4082i	−0.640691	+	0.964153i
$327$	9.22569	−	1.62674i	0.510182	−	0.0899588i
$328$	−29.2631	+	4.73252i	−1.61578	+	0.261310i
$329$	−0.376273	−	0.136952i	−0.0207446	−	0.00755042i
$330$	−3.31713	−	1.44953i	−0.182602	−	0.0797938i
$331$	−8.29050	+	14.3596i	−0.455687	+	0.789273i	−0.998727	−	0.0504337i	$-0.983940\pi$
$331$	−8.29050	+	14.3596i	−0.455687	+	0.789273i	0.543041	+	0.839706i	$0.317273\pi$
$332$	−10.2001	+	4.28587i	−0.559806	+	0.235217i
$333$	0.545063	+	0.649581i	0.0298693	+	0.0355968i
$334$	−16.6986	+	1.87173i	−0.913709	+	0.102416i
$335$	−4.58897	−	7.94834i	−0.250722	−	0.434264i
$336$	−14.1129	+	10.0972i	−0.769922	+	0.550845i
$337$	−1.74633	−	0.307926i	−0.0951289	−	0.0167738i	0.125881	−	0.992045i	$-0.459824\pi$
$337$	−1.74633	−	0.307926i	−0.0951289	−	0.0167738i	−0.221010	+	0.975272i	$0.570935\pi$
$338$	−7.22553	+	7.58636i	−0.393017	+	0.412643i
$339$	−1.97545	−	5.42749i	−0.107291	−	0.294781i
$340$	7.06018	−	4.54841i	0.382892	−	0.246672i
$341$			2.06996i			0.112095i
$342$	−5.00528	+	2.74039i	−0.270654	+	0.148183i
$343$			20.1567i			1.08836i
$344$	−4.04749	+	10.6475i	−0.218226	+	0.574077i
$345$	−5.29050	−	14.5355i	−0.284831	−	0.782566i
$346$	−6.87083	−	6.54403i	−0.369378	−	0.351809i
$347$	7.38708	+	1.30254i	0.396559	+	0.0699241i	0.368372	−	0.929679i	$-0.379915\pi$
$347$	7.38708	+	1.30254i	0.396559	+	0.0699241i	0.0281873	+	0.999603i	$0.491027\pi$
$348$	−24.5913	−	18.6719i	−1.31823	−	1.00092i
$349$	−1.46884	−	2.54411i	−0.0786253	−	0.136183i	0.824032	−	0.566544i	$-0.191720\pi$
$349$	−1.46884	−	2.54411i	−0.0786253	−	0.136183i	−0.902657	+	0.430361i	$0.858386\pi$
$350$	0.344922	+	3.07723i	0.0184369	+	0.164485i
$351$	−11.9344	−	14.2229i	−0.637011	−	0.759160i
$352$	5.43298	−	4.88802i	0.289579	−	0.260532i
$353$	4.66770	−	8.08470i	0.248437	−	0.430305i	−0.714655	−	0.699477i	$-0.753417\pi$
$353$	4.66770	−	8.08470i	0.248437	−	0.430305i	0.963092	+	0.269171i	$0.0867498\pi$
$354$	−8.28339	+	18.9559i	−0.440257	+	1.00749i
$355$	4.46078	+	1.62359i	0.236753	+	0.0861712i
$356$	−14.9729	+	29.1228i	−0.793560	+	1.54351i
$357$	−17.9406	+	3.16340i	−0.949515	+	0.167425i
$358$	21.8615	+	14.5272i	1.15541	+	0.767786i
$359$	5.98924	−	7.13770i	0.316100	−	0.376713i	−0.584477	−	0.811411i	$-0.698700\pi$
$359$	5.98924	−	7.13770i	0.316100	−	0.376713i	0.900577	+	0.434697i	$0.143145\pi$
$360$	−2.47282	+	0.860475i	−0.130329	+	0.0453510i
$361$	−18.3187	−	5.04226i	−0.964143	−	0.265382i
$362$	−0.401655	+	0.296077i	−0.0211105	+	0.0155615i
$363$	14.1624	+	11.8837i	0.743334	+	0.623732i
$364$	0.963286	+	19.7593i	0.0504899	+	1.03567i
$365$	0.446681	+	2.53325i	0.0233803	+	0.132597i
$366$	7.07483	−	3.51128i	0.369807	−	0.183538i
$367$	3.80625	−	10.4576i	0.198685	−	0.545881i	−0.799838	−	0.600216i	$-0.795081\pi$
$367$	3.80625	−	10.4576i	0.198685	−	0.545881i	0.998523	+	0.0543343i	$0.0173037\pi$
$368$	31.1354	+	2.40556i	1.62304	+	0.125399i
$369$	8.40193	+	4.85086i	0.437387	+	0.252526i
$370$	−0.304718	+	1.25912i	−0.0158415	+	0.0654586i
$371$	19.1470	−	16.0662i	0.994063	−	0.834118i
$372$	4.31313	+	4.65923i	0.223626	+	0.241570i
$373$	−25.9924	+	15.0067i	−1.34583	+	0.777017i	−0.987656	−	0.156636i	$-0.949935\pi$
$373$	−25.9924	+	15.0067i	−1.34583	+	0.777017i	−0.358177	+	0.933654i	$0.616602\pi$
$374$	7.36024	−	2.16561i	0.380589	−	0.111981i
$375$	−0.344055	+	1.95124i	−0.0177669	+	0.100761i
$376$	0.451584	−	0.252242i	0.0232887	−	0.0130084i
$377$	−33.0773	+	12.0392i	−1.70357	+	0.620048i
$378$	−12.7011	−	0.800088i	−0.653276	−	0.0411521i
$379$	−5.04463			−0.259125			−0.129563	−	0.991571i	$-0.541357\pi$
$379$	−5.04463			−0.259125			−0.129563	+	0.991571i	$0.541357\pi$
$380$	−7.90718	−	3.67103i	−0.405630	−	0.188320i
$381$	−2.65047			−0.135788
$382$	−4.91096	−	0.309358i	−0.251267	−	0.0158281i
$383$	−6.88904	+	2.50740i	−0.352013	+	0.128122i	−0.511974	−	0.859001i	$-0.671086\pi$
$383$	−6.88904	+	2.50740i	−0.352013	+	0.128122i	0.159960	+	0.987123i	$0.448863\pi$
$384$	2.04390	−	22.3229i	0.104302	−	1.13916i
$385$	−0.491205	+	2.78576i	−0.0250341	+	0.141976i
$386$	−18.2133	+	5.35891i	−0.927032	+	0.272761i
$387$	3.22857	−	1.86402i	0.164118	−	0.0947533i
$388$	−7.47148	+	6.91649i	−0.379307	+	0.351132i
$389$	−20.2543	+	16.9954i	−1.02694	+	0.861701i	−0.990483	−	0.137634i	$-0.956050\pi$
$389$	−20.2543	+	16.9954i	−1.02694	+	0.861701i	−0.0364526	+	0.999335i	$0.511606\pi$
$390$	−2.97746	+	12.3031i	−0.150770	+	0.622993i
$391$	28.3914	+	16.3918i	1.43582	+	0.828969i
$392$	−4.72197	−	4.07784i	−0.238496	−	0.205962i
$393$	3.32903	−	9.14642i	0.167927	−	0.461376i
$394$	25.6457	−	12.7281i	1.29201	−	0.641233i
$395$	−2.02035	−	11.4580i	−0.101655	−	0.576512i
$396$	−2.38901	+	0.116466i	−0.120052	+	0.00585266i
$397$	−7.44283	−	6.24527i	−0.373545	−	0.313441i	0.436617	−	0.899647i	$-0.356176\pi$
$397$	−7.44283	−	6.24527i	−0.373545	−	0.313441i	−0.810162	+	0.586206i	$0.800621\pi$
$398$	2.38186	−	1.75577i	0.119392	−	0.0880087i
$399$	12.7279	+	13.9853i	0.637193	+	0.700139i
$400$	−3.29974	−	2.26090i	−0.164987	−	0.113045i
$401$	−23.8773	+	28.4559i	−1.19238	+	1.42102i	−0.309830	+	0.950792i	$0.600272\pi$
$401$	−23.8773	+	28.4559i	−1.19238	+	1.42102i	−0.882546	+	0.470226i	$0.844172\pi$
$402$	−21.4190	−	14.2332i	−1.06828	−	0.709888i
$403$	7.12820	−	1.25689i	0.355081	−	0.0626103i
$404$	10.5361	+	5.41690i	0.524190	+	0.269501i
$405$	−10.2616	−	3.73492i	−0.509903	−	0.185590i
$406$	−9.66120	+	22.1089i	−0.479477	+	1.09725i
$407$	−0.591723	+	1.02489i	−0.0293306	+	0.0508021i
$408$	12.0545	−	20.2109i	0.596789	−	1.00059i
$409$	4.06396	+	4.84324i	0.200950	+	0.239483i	0.857103	−	0.515145i	$-0.172262\pi$
$409$	4.06396	+	4.84324i	0.200950	+	0.239483i	−0.656153	+	0.754628i	$0.727818\pi$
$410$	1.65100	+	14.7294i	0.0815369	+	0.727433i
$411$	−21.7167	−	37.6144i	−1.07121	−	1.85538i
$412$	7.01704	−	9.24160i	0.345705	−	0.455301i
$413$	15.9194	+	2.80702i	0.783341	+	0.138124i
$414$	−7.40079	−	7.04878i	−0.363729	−	0.346429i
$415$	1.89205	+	5.19837i	0.0928772	+	0.255178i
$416$	−20.1315	−	15.7412i	−0.987027	−	0.771774i
$417$		−	21.5732i		−	1.05644i
$418$	−5.98309	−	5.25614i	−0.292642	−	0.257086i
$419$		−	25.9110i		−	1.26583i	−0.774220	−	0.632917i	$-0.781857\pi$
$419$		−	25.9110i		−	1.26583i	0.774220	−	0.632917i	$-0.218143\pi$
$420$	4.69899	+	7.29391i	0.229287	+	0.355907i
$421$	8.49411	+	23.3374i	0.413978	+	1.13739i	0.955057	+	0.296423i	$0.0957937\pi$
$421$	8.49411	+	23.3374i	0.413978	+	1.13739i	−0.541079	+	0.840972i	$0.681984\pi$
$422$	5.74555	−	6.03248i	0.279689	−	0.293656i
$423$	−0.166717	−	0.0293967i	−0.00810605	−	0.00142932i
$424$	−0.458403	+	32.2843i	−0.0222620	+	1.56787i
$425$	−2.09962	−	3.63664i	−0.101846	−	0.176403i
$426$	13.2186	−	1.48166i	0.640445	−	0.0717865i
$427$	−3.96718	−	4.72790i	−0.191985	−	0.228799i
$428$	12.6182	+	30.0306i	0.609922	+	1.45158i
$429$	−5.78184	+	10.0144i	−0.279150	+	0.483502i
$430$	5.21891	+	2.28057i	0.251678	+	0.109979i
$431$	17.7777	+	6.47056i	0.856322	+	0.311676i	0.732615	−	0.680643i	$-0.238299\pi$
$431$	17.7777	+	6.47056i	0.856322	+	0.311676i	0.123707	+	0.992319i	$0.460522\pi$
$432$	11.5059	−	11.7420i	0.553576	−	0.564939i
$433$	−3.37452	+	0.595018i	−0.162169	+	0.0285948i	−0.254143	−	0.967167i	$-0.581793\pi$
$433$	−3.37452	+	0.595018i	−0.162169	+	0.0285948i	0.0919741	+	0.995761i	$0.470682\pi$
$434$	2.74588	−	4.13218i	0.131806	−	0.198351i
$435$	−9.92358	+	11.8265i	−0.475799	+	0.567036i
$436$	9.03292	+	2.79771i	0.432598	+	0.133986i
$437$	−1.36876	−	34.0026i	−0.0654764	−	1.62656i
$438$	4.27677	+	5.80182i	0.204352	+	0.277222i
$439$	23.6939	+	19.8816i	1.13085	+	0.948895i	0.999101	−	0.0423886i	$-0.0134968\pi$
$439$	23.6939	+	19.8816i	1.13085	+	0.948895i	0.131747	+	0.991283i	$0.457941\pi$
$440$	−2.30884	−	2.83227i	−0.110069	−	0.135023i
$441$	0.354577	+	2.01091i	0.0168846	+	0.0957575i
$442$	−11.9267	−	24.0310i	−0.567297	−	1.14304i
$443$	7.87237	−	21.6292i	0.374028	−	1.02763i	−0.599761	−	0.800179i	$-0.704738\pi$
$443$	7.87237	−	21.6292i	0.374028	−	1.02763i	0.973789	−	0.227454i	$-0.0730400\pi$
$444$	0.803654	+	3.53987i	0.0381397	+	0.167995i
$445$	14.1796	+	8.18659i	0.672177	+	0.388082i
$446$	−29.6323	−	7.17128i	−1.40313	−	0.339570i
$447$	20.7760	−	17.4331i	0.982670	−	0.824558i
$448$	−17.3298	+	2.55070i	−0.818754	+	0.120509i
$449$	−13.6870	+	7.90217i	−0.645928	+	0.372926i	−0.786894	−	0.617088i	$-0.788312\pi$
$449$	−13.6870	+	7.90217i	−0.645928	+	0.372926i	0.140967	+	0.990014i	$0.454979\pi$
$450$	0.369523	+	1.25589i	0.0174195	+	0.0592034i
$451$	−2.35119	+	13.3343i	−0.110713	+	0.627886i
$452$	0.731628	−	5.78414i	0.0344129	−	0.272063i
$453$	−5.78398	+	2.10520i	−0.271755	+	0.0989107i
$454$	−1.15656	+	18.3600i	−0.0542801	+	0.861679i
$455$	9.89141			0.463716
$456$	−24.4193	+	0.635894i	−1.14354	+	0.0297785i
$457$	22.5800			1.05625			0.528125	−	0.849167i	$-0.322895\pi$
$457$	22.5800			1.05625			0.528125	+	0.849167i	$0.322895\pi$
$458$	1.10926	−	17.6091i	0.0518321	−	0.822818i
$459$	16.2176	−	5.90273i	0.756973	−	0.275516i
$460$	1.95939	−	15.4907i	0.0913572	−	0.722256i
$461$	0.325413	−	1.84551i	0.0151560	−	0.0859538i	−0.976292	−	0.216460i	$-0.930549\pi$
$461$	0.325413	−	1.84551i	0.0151560	−	0.0859538i	0.991448	+	0.130506i	$0.0416601\pi$
$462$	2.23730	+	7.60390i	0.104089	+	0.353766i
$463$	−19.0509	+	10.9990i	−0.885369	+	0.511168i	−0.872425	−	0.488748i	$-0.837454\pi$
$463$	−19.0509	+	10.9990i	−0.885369	+	0.511168i	−0.0129441	+	0.999916i	$0.504120\pi$
$464$	−13.4582	−	28.1121i	−0.624783	−	1.30507i
$465$	2.43186	−	2.04057i	0.112775	−	0.0946293i
$466$	31.1755	+	7.54474i	1.44418	+	0.349503i
$467$	1.02822	+	0.593642i	0.0475802	+	0.0274705i	0.523601	−	0.851963i	$-0.324588\pi$
$467$	1.02822	+	0.593642i	0.0475802	+	0.0274705i	−0.476021	+	0.879434i	$0.657921\pi$
$468$	1.85169	+	8.15616i	0.0855943	+	0.377018i
$469$	−6.87312	+	18.8837i	−0.317371	+	0.871970i
$470$	−0.114977	−	0.231665i	−0.00530349	−	0.0106859i
$471$	3.90480	+	22.1452i	0.179924	+	1.02040i
$472$	−16.1852	+	13.1940i	−0.744982	+	0.607301i
$473$	3.98568	+	3.34439i	0.183262	+	0.153775i
$474$	−19.3439	−	26.2417i	−0.888495	−	1.20532i
$475$	−2.02585	+	3.85952i	−0.0929524	+	0.177087i
$476$	−17.5657	−	5.44051i	−0.805122	−	0.249365i
$477$	6.79243	−	8.09491i	0.311004	−	0.370640i
$478$	22.3880	−	33.6909i	1.02400	−	1.54099i
$479$	−13.8408	+	2.44051i	−0.632404	+	0.111510i	−0.480656	−	0.876909i	$-0.659601\pi$
$479$	−13.8408	+	2.44051i	−0.632404	+	0.111510i	−0.151748	+	0.988419i	$0.548490\pi$
$480$	−11.0984	−	1.56422i	−0.506572	−	0.0713967i
$481$	3.88866	+	1.41536i	0.177308	+	0.0645347i
$482$	−33.7691	−	14.7565i	−1.53814	−	0.672141i
$483$	−16.9345	+	29.3313i	−0.770544	+	1.33462i
$484$	7.22907	+	17.2048i	0.328594	+	0.782038i
$485$	3.27224	+	3.89970i	0.148585	+	0.177076i
$486$	−13.0799	+	1.46611i	−0.593318	+	0.0665042i
$487$	−21.3490	−	36.9775i	−0.967414	−	1.67561i	−0.702983	−	0.711207i	$-0.748149\pi$
$487$	−21.3490	−	36.9775i	−0.967414	−	1.67561i	−0.264431	−	0.964405i	$-0.585184\pi$
$488$	7.97184	+	0.113192i	0.360868	+	0.00512394i
$489$	28.8382	+	5.08495i	1.30411	+	0.229950i
$490$	−2.15146	+	2.25890i	−0.0971932	+	0.102047i
$491$	−10.4057	−	28.5895i	−0.469603	−	1.29022i	−0.918068	−	0.396424i	$-0.870251\pi$
$491$	−10.4057	−	28.5895i	−0.469603	−	1.29022i	0.448464	−	0.893801i	$-0.351971\pi$
$492$	22.4921	+	34.9129i	1.01402	+	1.57399i
$493$		−	32.7200i		−	1.47363i
$494$	−14.4673	+	23.7951i	−0.650913	+	1.07059i
$495$			1.19592i			0.0537528i
$496$	1.72155	+	6.17339i	0.0773001	+	0.277194i
$497$	−3.55494	−	9.76713i	−0.159461	−	0.438116i
$498$	11.2244	+	10.6905i	0.502978	+	0.479055i
$499$	−37.0657	−	6.53568i	−1.65929	−	0.292577i	−0.736085	−	0.676889i	$-0.763328\pi$
$499$	−37.0657	−	6.53568i	−1.65929	−	0.292577i	−0.923203	+	0.384312i	$0.874439\pi$
$500$	−1.20945	+	1.59287i	−0.0540882	+	0.0712353i
$501$	11.7708	+	20.3876i	0.525880	+	0.910851i
$502$	−1.72281	−	15.3701i	−0.0768928	−	0.686000i
$503$	2.75267	+	3.28050i	0.122735	+	0.146270i	0.823913	−	0.566716i	$-0.191786\pi$
$503$	2.75267	+	3.28050i	0.122735	+	0.146270i	−0.701178	+	0.712987i	$0.747342\pi$
$504$	4.92357	+	2.93661i	0.219313	+	0.130807i
$505$	2.96176	−	5.12991i	0.131796	−	0.228278i
$506$	5.71156	−	13.0704i	0.253910	−	0.581052i
$507$	13.7928	+	5.02018i	0.612561	+	0.222954i
$508$	−2.37938	−	1.22331i	−0.105568	−	0.0542756i
$509$	23.2550	−	4.10048i	1.03076	−	0.181751i	0.367409	−	0.930060i	$-0.380245\pi$
$509$	23.2550	−	4.10048i	1.03076	−	0.181751i	0.663350	+	0.748309i	$0.269134\pi$
$510$	−9.79996	−	6.51219i	−0.433950	−	0.288364i
$511$	3.62035	−	4.31457i	0.160155	−	0.190865i
$512$	12.1379	−	19.0964i	0.536423	−	0.843949i
$513$	−14.1755	−	10.9540i	−0.625862	−	0.483631i
$514$	−31.0640	+	22.8986i	−1.37017	+	1.01001i
$515$	−4.44448	−	3.72936i	−0.195847	−	0.164335i
$516$	15.9399	−	0.777084i	0.701714	−	0.0342092i
$517$	−0.0410268	−	0.232674i	−0.00180435	−	0.0102330i
$518$	2.54079	−	1.26101i	0.111636	−	0.0554056i
$519$	−4.54668	+	12.4919i	−0.199577	+	0.548334i
$520$	−8.35137	+	9.67056i	−0.366232	+	0.424082i
$521$	11.2260	+	6.48134i	0.491821	+	0.283953i	0.725329	−	0.688402i	$-0.241687\pi$
$521$	11.2260	+	6.48134i	0.491821	+	0.283953i	−0.233509	+	0.972355i	$0.575021\pi$
$522$	−2.39936	+	9.91438i	−0.105017	+	0.433941i
$523$	21.5486	−	18.0814i	0.942255	−	0.790646i	−0.0357214	−	0.999362i	$-0.511373\pi$
$523$	21.5486	−	18.0814i	0.942255	−	0.790646i	0.977976	+	0.208716i	$0.0669284\pi$
$524$	7.21002	−	6.67445i	0.314971	−	0.291575i
$525$	3.75703	−	2.16912i	0.163970	−	0.0946684i
$526$	−0.0918615	+	0.0270285i	−0.00400535	+	0.00117850i
$527$	−1.16833	+	6.62594i	−0.0508934	+	0.288631i
$528$	−9.32310	−	4.23267i	−0.405736	−	0.184203i
$529$	35.6613	−	12.9796i	1.55049	−	0.564332i
$530$	16.1119	+	1.01494i	0.699854	+	0.0440862i
$531$	6.83416			0.296577
$532$	4.97131	+	18.4294i	0.215534	+	0.799015i
$533$	47.3460			2.05078
$534$	45.7874	+	2.88431i	1.98142	+	0.124816i
$535$	15.3047	−	5.57045i	0.661680	−	0.240832i
$536$	−12.6591	−	22.6633i	−0.546790	−	0.978906i
$537$	6.38574	−	36.2153i	0.275565	−	1.56281i
$538$	32.5707	−	9.58329i	1.40422	−	0.413165i
$539$	−2.46797	+	1.42488i	−0.106303	+	0.0613741i
$540$	−5.58392	−	6.03199i	−0.240294	−	0.259575i
$541$	−15.4251	+	12.9432i	−0.663176	+	0.556471i	−0.911037	−	0.412325i	$-0.864717\pi$
$541$	−15.4251	+	12.9432i	−0.663176	+	0.556471i	0.247861	+	0.968796i	$0.420272\pi$
$542$	9.66328	−	39.9295i	0.415073	−	1.71512i
$543$	0.605429	+	0.349545i	0.0259815	+	0.0150004i
$544$	20.1498	−	12.5800i	0.863917	−	0.539364i
$545$	1.61711	−	4.44299i	0.0692696	−	0.190317i
$546$	24.8266	−	12.3216i	1.06248	−	0.527315i
$547$	3.81947	+	21.6613i	0.163309	+	0.926171i	0.950791	+	0.309833i	$0.100273\pi$
$547$	3.81947	+	21.6613i	0.163309	+	0.926171i	−0.787482	+	0.616338i	$0.788616\pi$
$548$	−2.13483	−	43.7905i	−0.0911953	−	1.87064i
$549$	−1.99884	−	1.67723i	−0.0853086	−	0.0715824i
$550$	−1.47067	+	1.08409i	−0.0627095	+	0.0462259i
$551$	−28.7069	+	18.1514i	−1.22295	+	0.773274i
$552$	−14.3786	−	41.3210i	−0.611993	−	1.75874i
$553$	−16.3749	+	19.5149i	−0.696333	+	0.829857i
$554$	−6.82460	−	4.53502i	−0.289949	−	0.192675i
$555$	1.78740	−	0.315167i	0.0758709	−	0.0133781i
$556$	9.95699	−	19.3667i	0.422270	−	0.821332i
$557$	22.9155	+	8.34058i	0.970963	+	0.353402i	0.778320	−	0.627867i	$-0.216072\pi$
$557$	22.9155	+	8.34058i	0.970963	+	0.353402i	0.192643	+	0.981269i	$0.438294\pi$
$558$	0.839896	−	1.92203i	0.0355556	−	0.0813662i
$559$	9.09671	−	15.7560i	0.384750	−	0.666406i
$560$	0.851918	+	8.71670i	0.0360001	+	0.368348i
$561$	−6.90926	−	8.23414i	−0.291709	−	0.347646i
$562$	2.91115	+	25.9719i	0.122800	+	1.09556i
$563$	13.8351	+	23.9630i	0.583078	+	1.00992i	0.995112	+	0.0987526i	$0.0314852\pi$
$563$	13.8351	+	23.9630i	0.583078	+	1.00992i	−0.412034	+	0.911169i	$0.635181\pi$
$564$	−0.577164	−	0.438234i	−0.0243030	−	0.0184530i
$565$	−2.87082	−	0.506204i	−0.120777	−	0.0212962i
$566$	13.0052	+	12.3866i	0.546649	+	0.520649i
$567$	8.17782	+	22.4684i	0.343436	+	0.943583i
$568$	12.5505	+	4.77087i	0.526608	+	0.200181i
$569$		−	25.6287i		−	1.07441i	−0.843452	−	0.537204i	$-0.819480\pi$
$569$		−	25.6287i		−	1.07441i	0.843452	−	0.537204i	$-0.180520\pi$
$570$	−0.276955	+	12.2106i	−0.0116004	+	0.511447i
$571$		−	2.53311i		−	0.106007i	−0.998594	−	0.0530037i	$-0.983120\pi$
$571$		−	2.53311i		−	0.106007i	0.998594	−	0.0530037i	$-0.0168795\pi$
$572$	−9.81260	+	6.32161i	−0.410285	+	0.264320i
$573$	2.35788	+	6.47821i	0.0985017	+	0.270631i
$574$	22.3820	−	23.4997i	0.934205	−	0.980858i
$575$	−7.68844	−	1.35568i	−0.320630	−	0.0565357i
$576$	−7.02805	+	2.33425i	−0.292835	+	0.0972603i
$577$	5.13545	+	8.89487i	0.213792	+	0.370298i	0.952898	−	0.303291i	$-0.0980853\pi$
$577$	5.13545	+	8.89487i	0.213792	+	0.370298i	−0.739106	+	0.673589i	$0.764752\pi$
$578$	0.890392	−	0.0998028i	0.0370354	−	0.00415125i
$579$	17.0973	+	20.3758i	0.710540	+	0.846789i
$580$	−14.3671	+	6.03670i	−0.596560	+	0.250660i
$581$	6.05631	−	10.4898i	0.251258	−	0.435191i
$582$	13.0708	+	5.71173i	0.541803	+	0.236759i
$583$	13.8584	+	5.04404i	0.573956	+	0.208903i
$584$	1.16155	+	7.18234i	0.0480653	+	0.297207i
$585$	4.11832	−	0.726171i	0.170272	−	0.0300235i
$586$	15.1066	−	22.7335i	0.624050	−	0.939110i
$587$	−30.0628	+	35.8275i	−1.24083	+	1.47876i	−0.420056	+	0.907498i	$0.637990\pi$
$587$	−30.0628	+	35.8275i	−1.24083	+	1.47876i	−0.820769	+	0.571260i	$0.806455\pi$
$588$	−2.58610	+	8.34969i	−0.106649	+	0.344336i
$589$	6.46141	−	2.65070i	0.266238	−	0.109220i
$590$	6.19510	+	8.40421i	0.255048	+	0.345996i
$591$	−30.7274	−	25.7834i	−1.26396	−	1.06059i
$592$	−0.912348	+	3.54874i	−0.0374973	+	0.145852i
$593$	0.217227	+	1.23195i	0.00892044	+	0.0505903i	0.988943	−	0.148296i	$-0.0473787\pi$
$593$	0.217227	+	1.23195i	0.00892044	+	0.0505903i	−0.980023	+	0.198886i	$0.936268\pi$
$594$	−3.33824	−	6.72617i	−0.136970	−	0.275978i
$595$	−3.14469	+	8.63997i	−0.128920	+	0.354204i
$596$	26.6972	−	6.06106i	1.09356	−	0.248271i
$597$	−3.59026	−	2.07284i	−0.146940	−	0.0848356i
$598$	−48.4779	−	11.7321i	−1.98241	−	0.479760i
$599$	−11.6153	+	9.74643i	−0.474590	+	0.398228i	−0.848466	−	0.529251i	$-0.822473\pi$
$599$	−11.6153	+	9.74643i	−0.474590	+	0.398228i	0.373876	+	0.927479i	$0.378029\pi$
$600$	−1.05139	+	5.50455i	−0.0429229	+	0.224723i
$601$	−38.0644	+	21.9765i	−1.55268	+	0.896440i	−0.554756	+	0.832013i	$0.687189\pi$
$601$	−38.0644	+	21.9765i	−1.55268	+	0.896440i	−0.997922	+	0.0644268i	$0.979478\pi$
$602$	−3.52000	−	11.9634i	−0.143465	−	0.487592i
$603$	−1.47531	+	8.36689i	−0.0600792	+	0.340726i
$604$	−6.16404	−	0.779682i	−0.250811	−	0.0317248i
$605$	8.76821	−	3.19137i	0.356479	−	0.129748i
$606$	1.04349	−	16.5650i	0.0423888	−	0.672909i
$607$	25.7674			1.04587			0.522934	−	0.852373i	$-0.324838\pi$
$607$	25.7674			1.04587			0.522934	+	0.852373i	$0.324838\pi$
$608$	−22.2152	−	10.6997i	−0.900946	−	0.433931i
$609$	33.8032			1.36977
$610$	0.250615	−	3.97844i	0.0101471	−	0.161082i
$611$	−0.776333	+	0.282562i	−0.0314071	+	0.0114312i
$612$	−7.71295	−	0.975601i	−0.311777	−	0.0394363i
$613$	3.48096	−	19.7415i	0.140595	−	0.797352i	−0.830205	−	0.557459i	$-0.811776\pi$
$613$	3.48096	−	19.7415i	0.140595	−	0.797352i	0.970799	−	0.239893i	$-0.0771125\pi$
$614$	4.79118	+	16.2837i	0.193356	+	0.657158i
$615$	17.9833	−	10.3827i	0.725158	−	0.418670i
$616$	−1.50106	+	7.85881i	−0.0604796	+	0.316640i
$617$	0.897505	−	0.753096i	0.0361322	−	0.0303185i	−0.624543	−	0.780991i	$-0.714715\pi$
$617$	0.897505	−	0.753096i	0.0361322	−	0.0303185i	0.660675	+	0.750672i	$0.270270\pi$
$618$	−15.8009	−	3.82394i	−0.635604	−	0.153822i
$619$	−3.68904	−	2.12987i	−0.148275	−	0.0856067i	0.424027	−	0.905650i	$-0.360616\pi$
$619$	−3.68904	−	2.12987i	−0.148275	−	0.0856067i	−0.572302	+	0.820043i	$0.693950\pi$
$620$	3.12495	−	0.709456i	0.125501	−	0.0284924i
$621$	10.9741	−	30.1511i	0.440376	−	1.20992i
$622$	5.83880	+	11.7645i	0.234115	+	0.471714i
$623$	−6.22529	−	35.3054i	−0.249411	−	1.41448i
$624$	−8.91473	+	34.6754i	−0.356875	+	1.38813i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	15.9826	+	21.6818i	0.638793	+	0.866580i
$627$	−3.39132	+	10.6297i	−0.135436	+	0.424511i
$628$	−6.71559	+	21.6825i	−0.267981	+	0.865227i
$629$	−2.47258	+	2.94670i	−0.0985880	+	0.117493i
$630$	1.58644	−	2.38737i	0.0632051	−	0.0951151i
$631$	−40.0594	+	7.06355i	−1.59474	+	0.281196i	−0.899281	−	0.437371i	$-0.855910\pi$
$631$	−40.0594	+	7.06355i	−1.59474	+	0.281196i	−0.695458	+	0.718566i	$0.744799\pi$
$632$	−5.25371	−	32.4859i	−0.208982	−	1.29222i
$633$	−10.9677	−	3.99192i	−0.435927	−	0.158664i
$634$	33.7071	+	14.7294i	1.33868	+	0.584980i
$635$	−0.668859	+	1.15850i	−0.0265428	+	0.0459736i
$636$	41.7036	−	17.5229i	1.65366	−	0.694828i
$637$	6.40535	+	7.63360i	0.253789	+	0.302454i
$638$	−14.1476	+	1.58578i	−0.560109	+	0.0627818i
$639$	−2.19716	−	3.80559i	−0.0869183	−	0.150547i
$640$	−9.24136	−	6.52666i	−0.365297	−	0.257989i
$641$	−29.4624	−	5.19502i	−1.16370	−	0.205191i	−0.441749	−	0.897139i	$-0.645642\pi$
$641$	−29.4624	−	5.19502i	−1.16370	−	0.205191i	−0.721948	+	0.691948i	$0.756753\pi$
$642$	31.4744	−	33.0462i	1.24220	−	1.30423i
$643$	−12.0728	−	33.1698i	−0.476106	−	1.30809i	−0.912773	−	0.408467i	$-0.866063\pi$
$643$	−12.0728	−	33.1698i	−0.476106	−	1.30809i	0.436667	−	0.899623i	$-0.356159\pi$
$644$	−28.7402	+	18.5154i	−1.13252	+	0.729608i
$645$		−	7.97941i		−	0.314189i
$646$	−16.1851	−	20.2019i	−0.636796	−	0.794832i
$647$			3.28925i			0.129314i	0.997908	+	0.0646568i	$0.0205953\pi$
$647$			3.28925i			0.129314i	−0.997908	+	0.0646568i	$0.979405\pi$
$648$	−28.8713	−	10.9750i	−1.13417	−	0.431137i
$649$	3.26217	+	8.96273i	0.128051	+	0.351818i
$650$	4.62622	+	4.40618i	0.181455	+	0.172825i
$651$	−6.84530	−	1.20701i	−0.268288	−	0.0473065i
$652$	23.5418	+	17.8750i	0.921966	+	0.700039i
$653$	−15.9137	−	27.5634i	−0.622753	−	1.07864i	−0.988971	−	0.148110i	$-0.952681\pi$
$653$	−15.9137	−	27.5634i	−0.622753	−	1.07864i	0.366218	−	0.930529i	$-0.380652\pi$
$654$	−1.47575	−	13.1659i	−0.0577063	−	0.514828i
$655$	−3.15773	−	3.76323i	−0.123383	−	0.147042i
$656$	4.07777	+	41.7231i	0.159210	+	1.62901i
$657$	1.19060	−	2.06217i	0.0464496	−	0.0804530i
$658$	−0.226751	+	0.518901i	−0.00883967	+	0.0202289i
$659$	0.310492	+	0.113010i	0.0120950	+	0.00440224i	0.348061	−	0.937472i	$-0.386840\pi$
$659$	0.310492	+	0.113010i	0.0120950	+	0.00440224i	−0.335966	+	0.941874i	$0.609063\pi$
$660$	−2.34081	+	4.55297i	−0.0911159	+	0.177224i
$661$	−9.26849	+	1.63428i	−0.360502	+	0.0635663i	−0.350966	−	0.936388i	$-0.614147\pi$
$661$	−9.26849	+	1.63428i	−0.360502	+	0.0635663i	−0.00953646	+	0.999955i	$0.503036\pi$
$662$	19.5302	+	12.9780i	0.759063	+	0.504406i
$663$	−24.1600	+	28.7928i	−0.938297	+	1.11822i
$664$	5.14224	+	14.7777i	0.199558	+	0.573486i
$665$	9.32480	−	2.03402i	0.361600	−	0.0788757i
$666$	0.965291	−	0.711557i	0.0374043	−	0.0275723i
$667$	−46.5997	−	39.1018i	−1.80435	−	1.51403i
$668$	1.15711	+	23.7351i	0.0447699	+	0.918340i
$669$	7.41718	+	42.0649i	0.286765	+	1.62632i
$670$	−11.6264	+	5.77027i	−0.449168	+	0.222925i
$671$	1.24551	−	3.42200i	0.0480822	−	0.132105i
$672$	12.9965	+	20.8169i	0.501351	+	0.803030i
$673$	−25.3526	−	14.6374i	−0.977273	−	0.564229i	−0.0758271	−	0.997121i	$-0.524160\pi$
$673$	−25.3526	−	14.6374i	−0.977273	−	0.564229i	−0.901446	+	0.432892i	$0.857493\pi$
$674$	−0.589878	+	2.43743i	−0.0227213	+	0.0938862i
$675$	−3.14837	+	2.64179i	−0.121181	+	0.101683i
$676$	10.0651	+	10.8727i	0.387119	+	0.418182i
$677$	−1.08122	+	0.624242i	−0.0415546	+	0.0239916i	−0.520633	−	0.853780i	$-0.674304\pi$
$677$	−1.08122	+	0.624242i	−0.0415546	+	0.0239916i	0.479079	+	0.877772i	$0.340971\pi$
$678$	−7.83609	+	2.30562i	−0.300943	+	0.0885467i
$679$	1.93555	−	10.9770i	0.0742795	−	0.421260i
$680$	−5.79198	−	10.3693i	−0.222112	−	0.397643i
$681$	24.2193	−	8.81512i	0.928087	−	0.337796i
$682$	2.92158	+	0.184040i	0.111873	+	0.00704727i
$683$	35.6390			1.36369			0.681844	−	0.731498i	$-0.261178\pi$
$683$	35.6390			1.36369			0.681844	+	0.731498i	$0.261178\pi$
$684$	3.42281	+	7.30818i	0.130874	+	0.279435i
$685$	−21.9213			−0.837568
$686$	28.4495	+	1.79213i	1.08621	+	0.0684239i
$687$	−23.2287	+	8.45457i	−0.886232	+	0.322562i
$688$	14.6682	+	6.65936i	0.559222	+	0.253886i
$689$	8.95494	−	50.7860i	0.341156	−	1.93479i
$690$	−20.9860	+	6.17474i	−0.798925	+	0.235068i
$691$	−40.9046	+	23.6163i	−1.55608	+	0.898405i	−0.558457	+	0.829533i	$0.688607\pi$
$691$	−40.9046	+	23.6163i	−1.55608	+	0.898405i	−0.997626	+	0.0688718i	$0.978060\pi$
$692$	−9.84723	+	9.11576i	−0.374335	+	0.346529i
$693$	2.00592	−	1.68317i	0.0761986	−	0.0639383i
$694$	2.49521	−	10.3104i	0.0947169	−	0.391378i
$695$	−9.42946	−	5.44410i	−0.357680	−	0.206506i
$696$	−28.5402	+	33.0484i	−1.08181	+	1.25270i
$697$	−15.0523	+	41.3558i	−0.570146	+	1.56646i
$698$	−3.72139	+	1.84695i	−0.140857	+	0.0699081i
$699$	−7.80345	−	44.2556i	−0.295154	−	1.67390i
$700$	4.37392	−	0.213233i	0.165319	−	0.00805943i
$701$	−5.47588	−	4.59481i	−0.206821	−	0.173544i	0.533493	−	0.845804i	$-0.320879\pi$
$701$	−5.47588	−	4.59481i	−0.206821	−	0.173544i	−0.740315	+	0.672261i	$0.765323\pi$
$702$	−21.1355	+	15.5798i	−0.797706	+	0.588023i
$703$	3.95695	+	0.534637i	0.149239	+	0.0201642i
$704$	−6.41598	−	8.10279i	−0.241811	−	0.305385i
$705$	−0.232909	+	0.277570i	−0.00877186	+	0.0104539i
$706$	−10.9959	−	7.30688i	−0.413835	−	0.274998i
$707$	−12.7728	+	2.25219i	−0.480372	+	0.0847025i
$708$	26.0182	+	13.3767i	0.977822	+	0.502726i
$709$	−11.5660	−	4.20970i	−0.434372	−	0.158099i	0.115574	−	0.993299i	$-0.463129\pi$
$709$	−11.5660	−	4.20970i	−0.434372	−	0.158099i	−0.549946	+	0.835200i	$0.685352\pi$
$710$	2.68817	−	6.15166i	0.100885	−	0.230868i
$711$	−5.38509	+	9.32725i	−0.201957	+	0.349799i
$712$	39.7732	+	23.7222i	1.49056	+	0.889029i
$713$	8.04045	+	9.58224i	0.301117	+	0.358858i
$714$	2.86979	+	25.6028i	0.107399	+	0.958162i
$715$	2.91815	+	5.05439i	0.109133	+	0.189023i
$716$	22.4476	−	29.5640i	0.838907	−	1.10486i
$717$	−55.8118	−	9.84112i	−2.08433	−	0.367523i
$718$	−9.54176	−	9.08792i	−0.356095	−	0.339158i
$719$	−9.31093	−	25.5816i	−0.347239	−	0.954031i	−0.983236	−	0.182339i	$-0.941633\pi$
$719$	−9.31093	−	25.5816i	−0.347239	−	0.954031i	0.635997	−	0.771692i	$-0.280589\pi$
$720$	0.994630	+	3.56669i	0.0370677	+	0.132923i
$721$			12.7035i			0.473103i
$722$	−8.74545	+	25.4070i	−0.325472	+	0.945552i
$723$			51.6310i			1.92018i
$724$	0.382177	+	0.593227i	0.0142035	+	0.0220471i
$725$	2.66498	+	7.32198i	0.0989750	+	0.271932i
$726$	18.0320	−	18.9325i	0.669230	−	0.702651i
$727$	15.2599	+	2.69073i	0.565959	+	0.0997938i	0.449304	−	0.893379i	$-0.351672\pi$
$727$	15.2599	+	2.69073i	0.565959	+	0.0997938i	0.116654	+	0.993173i	$0.462783\pi$
$728$	27.9743	+	0.397205i	1.03680	+	0.0147214i
$729$	−7.16027	−	12.4020i	−0.265195	−	0.459332i
$730$	3.61519	−	0.405221i	0.133804	−	0.0149979i
$731$	10.8705	+	12.9550i	0.402060	+	0.479157i
$732$	−4.32686	−	10.2977i	−0.159925	−	0.380615i
$733$	19.2675	−	33.3722i	0.711660	−	1.23263i	−0.252574	−	0.967578i	$-0.581277\pi$
$733$	19.2675	−	33.3722i	0.711660	−	1.23263i	0.964234	−	0.265053i	$-0.0853895\pi$
$734$	−14.4216	−	6.30198i	−0.532310	−	0.232610i
$735$	4.10693	+	1.49480i	0.151486	+	0.0551366i
$736$	6.16350	−	43.7311i	0.227190	−	1.61195i
$737$	−11.6771	+	2.05898i	−0.430130	+	0.0758435i
$738$	7.59359	−	11.4273i	0.279524	−	0.420646i
$739$	24.2525	−	28.9029i	0.892141	−	1.06321i	−0.105490	−	0.994420i	$-0.533641\pi$
$739$	24.2525	−	28.9029i	0.892141	−	1.06321i	0.997631	−	0.0687918i	$-0.0219144\pi$
$740$	1.75005	+	0.542033i	0.0643332	+	0.0199255i
$741$	38.6641	+	5.22405i	1.42036	+	0.191910i
$742$	−20.9738	−	28.4528i	−0.769972	−	1.04454i
$743$	−6.59531	−	5.53412i	−0.241958	−	0.203027i	0.513742	−	0.857945i	$-0.328259\pi$
$743$	−6.59531	−	5.53412i	−0.241958	−	0.203027i	−0.755700	+	0.654918i	$0.772703\pi$
$744$	6.95959	−	5.67337i	0.255151	−	0.207996i
$745$	−2.37695	−	13.4803i	−0.0870846	−	0.493882i
$746$	18.8697	+	38.0203i	0.690869	+	1.39202i
$747$	1.75146	−	4.81210i	0.0640826	−	0.176065i
$748$	−2.40218	−	10.5809i	−0.0878323	−	0.386876i
$749$	−30.8835	−	17.8306i	−1.12846	−	0.651515i
$750$	2.72341	+	0.659090i	0.0994450	+	0.0240665i
$751$	34.7067	−	29.1224i	1.26646	−	1.06269i	0.271503	−	0.962438i	$-0.412479\pi$
$751$	34.7067	−	29.1224i	1.26646	−	1.06269i	0.994962	−	0.100252i	$-0.0319650\pi$
$752$	−0.315868	−	0.659799i	−0.0115185	−	0.0240604i
$753$	−18.7655	+	10.8343i	−0.683854	+	0.394824i
$754$	14.0514	+	47.7563i	0.511720	+	1.73918i
$755$	−0.539452	+	3.05938i	−0.0196327	+	0.111342i
$756$	−2.25851	+	17.8554i	−0.0821413	+	0.649396i
$757$	−2.24560	+	0.817332i	−0.0816178	+	0.0297064i	−0.382506	−	0.923953i	$-0.624939\pi$
$757$	−2.24560	+	0.817332i	−0.0816178	+	0.0297064i	0.300889	+	0.953659i	$0.402717\pi$
$758$	−0.448517	+	7.12007i	−0.0162909	+	0.258613i
$759$	−19.9839			−0.725371
$760$	−5.88438	+	10.8339i	−0.213449	+	0.392988i
$761$	−34.1499			−1.23793			−0.618967	−	0.785417i	$-0.712449\pi$
$761$	−34.1499			−1.23793			−0.618967	+	0.785417i	$0.712449\pi$
$762$	−0.235653	+	3.74091i	−0.00853680	+	0.135519i
$763$	−9.72818	+	3.54077i	−0.352184	+	0.128184i
$764$	−0.873266	+	6.90390i	−0.0315937	+	0.249774i
$765$	−0.675005	+	3.82815i	−0.0244049	+	0.138407i
$766$	2.92649	+	9.94623i	0.105738	+	0.359372i
$767$	28.8835	−	16.6759i	1.04292	−	0.602133i
$768$	−31.3252	−	4.86952i	−1.13035	−	0.175714i
$769$	−11.4917	+	9.64269i	−0.414401	+	0.347724i	−0.826029	−	0.563628i	$-0.809405\pi$
$769$	−11.4917	+	9.64269i	−0.414401	+	0.347724i	0.411627	+	0.911352i	$0.364961\pi$
$770$	3.88820	+	0.940977i	0.140121	+	0.0339104i
$771$	46.8239	+	27.0338i	1.68632	+	0.973598i
$772$	5.94431	+	26.1830i	0.213940	+	0.942346i
$773$	−1.44066	+	3.95817i	−0.0518168	+	0.142365i	−0.962901	−	0.269855i	$-0.913024\pi$
$773$	−1.44066	+	3.95817i	−0.0518168	+	0.142365i	0.911084	+	0.412220i	$0.135247\pi$
$774$	−2.34385	−	4.72259i	−0.0842480	−	0.169750i
$775$	−0.278225	−	1.57789i	−0.00999415	−	0.0566796i
$776$	9.09776	+	11.1603i	0.326590	+	0.400632i
$777$	−3.04425	−	2.55443i	−0.109212	−	0.0916397i
$778$	22.1868	+	30.0984i	0.795435	+	1.07908i
$779$	44.6339	−	9.73597i	1.59917	−	0.348827i
$780$	17.1001	+	5.29631i	0.612282	+	0.189638i
$781$	3.94211	−	4.69802i	0.141060	−	0.168108i
$782$	25.6599	−	38.6147i	0.917597	−	1.38086i
$783$	−31.5374	+	5.56089i	−1.12705	+	0.198730i
$784$	−6.17535	+	6.30211i	−0.220548	+	0.225075i
$785$	10.6649	+	3.88171i	0.380647	+	0.138544i
$786$	−12.6134	−	5.51185i	−0.449906	−	0.196601i
$787$	−0.0582833	+	0.100950i	−0.00207758	+	0.00359847i	−0.867062	−	0.498200i	$-0.833995\pi$
$787$	−0.0582833	+	0.100950i	−0.00207758	+	0.00359847i	0.864985	+	0.501798i	$0.167328\pi$
$788$	−15.6845	−	37.3284i	−0.558738	−	1.32977i
$789$	0.0862330	+	0.102769i	0.00306998	+	0.00365866i
$790$	−16.3516	+	1.83282i	−0.581763	+	0.0652089i
$791$	3.19140	+	5.52767i	0.113473	+	0.196541i
$792$	−0.0480242	+	3.38224i	−0.00170646	+	0.120183i
$793$	−12.5404	−	2.21121i	−0.445322	−	0.0785223i
$794$	−9.47642	+	9.94966i	−0.336305	+	0.353100i
$795$	−7.73571	−	21.2537i	−0.274358	−	0.753791i
$796$	−2.26635	−	3.51790i	−0.0803286	−	0.124689i
$797$			51.6825i			1.83069i	0.402673	+	0.915344i	$0.368081\pi$
$797$			51.6825i			1.83069i	−0.402673	+	0.915344i	$0.631919\pi$
$798$	20.8707	−	16.7210i	0.738814	−	0.591916i
$799$		−	0.767946i		−	0.0271680i
$800$	−3.48446	+	4.45630i	−0.123194	+	0.157554i
$801$	−5.18385	−	14.2425i	−0.183162	−	0.503234i
$802$	38.0401	+	36.2308i	1.34324	+	1.27935i
$803$	3.27277	+	0.577077i	0.115493	+	0.0203646i
$804$	−21.9933	+	28.9657i	−0.775645	+	1.02154i
$805$	8.54699	+	14.8038i	0.301242	+	0.521766i
$806$	−1.14023	−	10.1726i	−0.0401630	−	0.358315i
$807$	−30.5750	−	36.4379i	−1.07629	−	1.28267i
$808$	8.58227	−	14.3892i	0.301923	−	0.506210i
$809$	1.18083	−	2.04525i	0.0415156	−	0.0719071i	−0.844521	−	0.535522i	$-0.820115\pi$
$809$	1.18083	−	2.04525i	0.0415156	−	0.0719071i	0.886037	+	0.463615i	$0.153448\pi$
$810$	−6.18388	+	14.1513i	−0.217279	+	0.497227i
$811$	14.7579	+	5.37144i	0.518220	+	0.188617i	0.587871	−	0.808955i	$-0.299966\pi$
$811$	14.7579	+	5.37144i	0.518220	+	0.188617i	−0.0696508	+	0.997571i	$0.522189\pi$
$812$	30.3458	+	15.6017i	1.06493	+	0.547511i
$813$	−56.6824	+	9.99463i	−1.98794	+	0.350527i
$814$	1.39394	+	0.926291i	0.0488576	+	0.0324665i
$815$	9.50005	−	11.3217i	0.332772	−	0.396583i
$816$	−27.4542	−	18.8109i	−0.961088	−	0.658514i
$817$	5.33565	−	16.7240i	0.186671	−	0.585099i
$818$	7.19715	−	5.30532i	0.251642	−	0.185496i
$819$	−7.01422	−	5.88563i	−0.245097	−	0.205660i
$820$	20.9361	−	1.02065i	0.731120	−	0.0356428i
$821$	−5.05077	−	28.6443i	−0.176273	−	0.999694i	−0.936664	−	0.350228i	$-0.886104\pi$
$821$	−5.05077	−	28.6443i	−0.176273	−	0.999694i	0.760391	−	0.649465i	$-0.225007\pi$
$822$	−55.0204	+	27.3070i	−1.91906	+	0.952441i
$823$	−0.122761	+	0.337284i	−0.00427920	+	0.0117570i	−0.941814	−	0.336135i	$-0.890880\pi$
$823$	−0.122761	+	0.337284i	−0.00427920	+	0.0117570i	0.937535	+	0.347892i	$0.113102\pi$
$824$	−12.4199	−	10.7256i	−0.432666	−	0.373645i
$825$	2.21679	+	1.27987i	0.0771788	+	0.0445592i
$826$	5.37726	−	22.2193i	0.187099	−	0.773108i
$827$	−21.1504	+	17.7473i	−0.735472	+	0.617134i	−0.931617	−	0.363441i	$-0.881602\pi$
$827$	−21.1504	+	17.7473i	−0.735472	+	0.617134i	0.196146	+	0.980575i	$0.437157\pi$
$828$	−10.6068	+	9.81889i	−0.368611	+	0.341230i
$829$	3.78214	−	2.18362i	0.131359	−	0.0758403i	−0.432880	−	0.901451i	$-0.642503\pi$
$829$	3.78214	−	2.18362i	0.131359	−	0.0758403i	0.564240	+	0.825611i	$0.309169\pi$
$830$	7.50529	−	2.20829i	0.260512	−	0.0766507i
$831$	−1.99347	+	11.3055i	−0.0691526	+	0.392184i
$832$	−24.0072	+	27.0143i	−0.832300	+	0.936554i
$833$	−8.70421	+	3.16807i	−0.301583	+	0.109767i
$834$	−30.4487	−	1.91807i	−1.05435	−	0.0664173i
$835$	11.8817			0.411182
$836$	−7.95056	+	7.97730i	−0.274976	+	0.275901i
$837$	6.58503			0.227612
$838$	−36.5712	−	2.30374i	−1.26333	−	0.0795815i
$839$	−32.7249	+	11.9109i	−1.12979	+	0.411210i	−0.838216	−	0.545338i	$-0.816401\pi$
$839$	−32.7249	+	11.9109i	−1.12979	+	0.411210i	−0.291574	+	0.956548i	$0.594179\pi$
$840$	10.7125	−	5.98372i	0.369617	−	0.206458i
$841$	−5.50700	+	31.2318i	−0.189897	+	1.07696i
$842$	33.6940	−	9.91380i	1.16117	−	0.341652i
$843$	31.7094	−	18.3075i	1.09213	−	0.630542i
$844$	−8.00350	−	8.64571i	−0.275492	−	0.297598i
$845$	5.67496	−	4.76186i	0.195225	−	0.163813i
$846$	−0.0563137	+	0.232693i	−0.00193611	+	0.00800016i
$847$	−17.6934	−	10.2153i	−0.607954	−	0.351002i
$848$	45.5259	+	3.51739i	1.56336	+	0.120788i
$849$	8.60603	−	23.6449i	0.295358	−	0.811490i
$850$	−5.31949	+	2.64010i	−0.182457	+	0.0905546i
$851$	1.24185	+	7.04288i	0.0425701	+	0.241427i
$852$	−0.915967	−	18.7887i	−0.0313805	−	0.643691i
$853$	−12.3783	−	10.3866i	−0.423823	−	0.355630i	0.405792	−	0.913965i	$-0.366996\pi$
$853$	−12.3783	−	10.3866i	−0.423823	−	0.355630i	−0.829615	+	0.558336i	$0.811440\pi$
$854$	−7.02575	+	5.17898i	−0.240416	+	0.177221i
$855$	3.73309	−	1.53144i	0.127669	−	0.0523743i
$856$	43.5076	−	15.1395i	1.48706	−	0.517456i
$857$	15.5585	−	18.5419i	0.531467	−	0.633378i	−0.431785	−	0.901976i	$-0.642116\pi$
$857$	15.5585	−	18.5419i	0.531467	−	0.633378i	0.963252	+	0.268599i	$0.0865606\pi$
$858$	13.6205	+	9.05097i	0.464996	+	0.308995i
$859$	0.572651	−	0.100974i	0.0195386	−	0.00344518i	−0.163870	−	0.986482i	$-0.552398\pi$
$859$	0.572651	−	0.100974i	0.0195386	−	0.00344518i	0.183409	+	0.983037i	$0.441287\pi$
$860$	3.68285	−	7.16329i	0.125584	−	0.244266i
$861$	−42.7250	−	15.5506i	−1.45606	−	0.529964i
$862$	10.7133	−	24.5165i	0.364895	−	0.835034i
$863$	−25.1829	+	43.6180i	−0.857235	+	1.48477i	0.0173211	+	0.999850i	$0.494486\pi$
$863$	−25.1829	+	43.6180i	−0.857235	+	1.48477i	−0.874556	+	0.484924i	$0.838847\pi$
$864$	−15.5499	−	17.2835i	−0.529019	−	0.587998i
$865$	4.31273	+	5.13971i	0.146637	+	0.174755i
$866$	0.539790	+	4.81575i	0.0183428	+	0.163646i
$867$	−0.627633	−	1.08709i	−0.0213155	−	0.0369196i
$868$	−5.58809	−	4.24297i	−0.189672	−	0.144016i
$869$	−14.8028	−	2.61013i	−0.502150	−	0.0885426i
$870$	15.8098	+	15.0578i	0.536001	+	0.510507i
$871$	14.1807	+	38.9613i	0.480496	+	1.32015i
$872$	4.75185	−	12.5005i	0.160918	−	0.423319i
$873$		−	4.71243i		−	0.159492i
$874$	−48.1135	−	1.09128i	−1.62746	−	0.0369132i
$875$		−	2.18956i		−	0.0740206i
$876$	8.56902	−	5.52046i	0.289520	−	0.186519i
$877$	10.3316	+	28.3858i	0.348873	+	0.958522i	0.982726	+	0.185068i	$0.0592505\pi$
$877$	10.3316	+	28.3858i	0.348873	+	0.958522i	−0.633852	+	0.773454i	$0.718527\pi$
$878$	30.1678	−	31.6743i	1.01811	−	1.06896i
$879$	−37.6599	−	6.64045i	−1.27024	−	0.223977i
$880$	−4.20279	+	3.00691i	−0.141676	+	0.101363i
$881$	6.99092	+	12.1086i	0.235530	+	0.407950i	0.959427	−	0.281958i	$-0.0909840\pi$
$881$	6.99092	+	12.1086i	0.235530	+	0.407950i	−0.723897	+	0.689909i	$0.757651\pi$
$882$	2.86975	−	0.321666i	0.0966296	−	0.0108311i
$883$	3.37021	+	4.01646i	0.113417	+	0.135165i	0.819766	−	0.572699i	$-0.194104\pi$
$883$	3.37021	+	4.01646i	0.113417	+	0.135165i	−0.706349	+	0.707864i	$0.749659\pi$
$884$	−34.9781	+	14.6970i	−1.17644	+	0.494313i
$885$	7.31386	−	12.6680i	0.245853	−	0.425829i
$886$	−29.8278	−	13.0342i	−1.00209	−	0.437894i
$887$	55.9468	+	20.3630i	1.87851	+	0.683722i	0.949691	+	0.313188i	$0.101397\pi$
$887$	55.9468	+	20.3630i	1.87851	+	0.683722i	0.928819	+	0.370534i	$0.120825\pi$
$888$	5.06768	−	0.819561i	0.170060	−	0.0275027i
$889$	2.88451	−	0.508617i	0.0967434	−	0.0170585i
$890$	12.8154	−	19.2854i	0.429573	−	0.646449i
$891$	−9.06845	+	10.8074i	−0.303805	+	0.362060i
$892$	−12.7563	+	41.1859i	−0.427111	+	1.37901i
$893$	−0.673758	+	0.426017i	−0.0225465	+	0.0142561i
$894$	−22.7582	−	30.8735i	−0.761148	−	1.03257i
$895$	−14.2179	−	11.9303i	−0.475254	−	0.398785i
$896$	2.05931	+	24.6863i	0.0687969	+	0.824710i
$897$	12.1344	+	68.8174i	0.405154	+	2.29774i
$898$	9.93634	+	20.0206i	0.331580	+	0.668095i
$899$	4.26993	−	11.7315i	0.142410	−	0.391269i
$900$	1.80544	−	0.409889i	0.0601814	−	0.0136630i
$901$	41.5137	+	23.9679i	1.38302	+	0.798487i
$902$	18.6111	+	4.50406i	0.619683	+	0.149969i
$903$	−13.3838	+	11.2304i	−0.445387	+	0.373724i
$904$	−8.09877	−	1.54690i	−0.269361	−	0.0514491i
$905$	0.305566	−	0.176419i	0.0101574	−	0.00586436i
$906$	2.45705	+	8.35077i	0.0816301	+	0.277436i
$907$	2.96464	−	16.8133i	0.0984391	−	0.558276i	−0.895200	−	0.445665i	$-0.852967\pi$
$907$	2.96464	−	16.8133i	0.0984391	−	0.558276i	0.993639	−	0.112611i	$-0.0359215\pi$
$908$	25.8108	+	3.26478i	0.856562	+	0.108345i
$909$	−5.15267	+	1.87542i	−0.170903	+	0.0622037i
$910$	0.879444	−	13.9609i	0.0291533	−	0.462799i
$911$	−38.8521			−1.28723			−0.643613	−	0.765351i	$-0.722565\pi$
$911$	−38.8521			−1.28723			−0.643613	+	0.765351i	$0.722565\pi$
$912$	−1.27361	+	34.5223i	−0.0421733	+	1.14315i
$913$	7.14690			0.236528
$914$	2.00759	−	31.8698i	0.0664051	−	1.05416i
$915$	−5.24809	+	1.91015i	−0.173497	+	0.0631476i
$916$	−24.7551	−	3.13124i	−0.817932	−	0.103459i
$917$	−1.86781	+	10.5929i	−0.0616807	+	0.349809i
$918$	−6.88930	−	23.4146i	−0.227381	−	0.772797i
$919$	−40.0921	+	23.1472i	−1.32252	+	0.763556i	−0.984130	−	0.177451i	$-0.943215\pi$
$919$	−40.0921	+	23.1472i	−1.32252	+	0.763556i	−0.338387	+	0.941007i	$0.609881\pi$
$920$	−21.6896	−	4.14279i	−0.715083	−	0.136584i
$921$	18.2172	−	15.2860i	0.600276	−	0.503691i
$922$	−2.57585	−	0.623377i	−0.0848310	−	0.0205298i
$923$	−18.5719	−	10.7225i	−0.611302	−	0.352936i
$924$	10.9312	−	2.48170i	0.359610	−	0.0816420i
$925$	0.313303	−	0.860792i	0.0103013	−	0.0283027i
$926$	13.8304	+	27.8666i	0.454495	+	0.915754i
$927$	0.932619	+	5.28915i	0.0306312	+	0.173718i
$928$	−40.8745	+	16.4957i	−1.34177	+	0.541499i
$929$	40.2400	+	33.7654i	1.32023	+	1.10781i	0.986256	+	0.165224i	$0.0528348\pi$
$929$	40.2400	+	33.7654i	1.32023	+	1.10781i	0.333976	+	0.942582i	$0.391610\pi$
$930$	−2.66388	−	3.61379i	−0.0873521	−	0.118501i
$931$	7.60816	+	5.87916i	0.249347	+	0.192682i
$932$	13.4206	−	43.3308i	0.439606	−	1.41935i
$933$	11.8277	−	14.0957i	0.387221	−	0.461472i
$934$	0.929294	−	1.39846i	0.0304074	−	0.0457591i
$935$	−5.34266	+	0.942055i	−0.174724	+	0.0308085i
$936$	11.6764	−	1.88834i	0.381654	−	0.0617223i
$937$	34.5874	+	12.5888i	1.12992	+	0.411258i	0.838264	−	0.545265i	$-0.183571\pi$
$937$	34.5874	+	12.5888i	1.12992	+	0.411258i	0.291657	+	0.956523i	$0.405793\pi$
$938$	26.0417	+	11.3798i	0.850292	+	0.371563i
$939$	18.8688	−	32.6818i	0.615761	−	1.06653i
$940$	−0.337199	+	0.141683i	−0.0109982	+	0.00462119i
$941$	−23.4769	−	27.9787i	−0.765327	−	0.912081i	0.232846	−	0.972514i	$-0.425196\pi$
$941$	−23.4769	−	27.9787i	−0.765327	−	0.912081i	−0.998172	+	0.0604331i	$0.980752\pi$
$942$	31.6033	−	3.54237i	1.02969	−	0.115417i
$943$	40.9108	+	70.8596i	1.33224	+	2.30751i
$944$	17.1831	+	24.0171i	0.559263	+	0.781689i
$945$	8.86215	+	1.56264i	0.288286	+	0.0508325i
$946$	5.07469	−	5.32811i	0.164992	−	0.173232i
$947$	9.51078	+	26.1307i	0.309059	+	0.849132i	0.992841	+	0.119446i	$0.0381118\pi$
$947$	9.51078	+	26.1307i	0.309059	+	0.849132i	−0.683782	+	0.729686i	$0.739666\pi$
$948$	−38.7579	+	24.9691i	−1.25880	+	0.810960i
$949$		−	11.6206i		−	0.377221i
$950$	5.26728	+	3.20247i	0.170893	+	0.103902i
$951$		−	51.5362i		−	1.67117i
$952$	−9.24058	+	24.3088i	−0.299489	+	0.787852i
$953$	3.45241	+	9.48542i	0.111835	+	0.307263i	0.982966	−	0.183787i	$-0.0588356\pi$
$953$	3.45241	+	9.48542i	0.111835	+	0.307263i	−0.871132	+	0.491050i	$0.836613\pi$
$954$	−10.8214	−	10.3067i	−0.350355	−	0.333691i
$955$	3.42660	+	0.604201i	0.110882	+	0.0195515i
$956$	−45.5614	−	34.5942i	−1.47356	−	1.11886i
$957$	9.97257	+	17.2730i	0.322368	+	0.558357i
$958$	2.21399	+	19.7522i	0.0715308	+	0.638164i
$959$	30.8524	+	36.7685i	0.996277	+	1.18732i
$960$	−3.19453	+	15.5254i	−0.103103	+	0.501081i
$961$	14.2164	−	24.6236i	0.458594	−	0.794308i
$962$	2.34340	−	5.36267i	0.0755541	−	0.172900i
$963$	−14.1675	−	5.15653i	−0.456540	−	0.166167i
$964$	−23.8300	+	46.3503i	−0.767513	+	1.49284i
$965$	13.2207	−	2.33116i	0.425589	−	0.0750428i
$966$	39.8931	+	26.5094i	1.28354	+	0.852926i
$967$	19.1468	−	22.8183i	0.615720	−	0.733787i	−0.364608	−	0.931161i	$-0.618797\pi$
$967$	19.1468	−	22.8183i	0.615720	−	0.733787i	0.980328	+	0.197374i	$0.0632415\pi$
$968$	24.9259	−	8.67354i	0.801149	−	0.278778i
$969$	−16.8553	+	32.1116i	−0.541469	+	1.03157i
$970$	5.79504	−	4.27177i	0.186067	−	0.137158i
$971$	−5.20283	−	4.36569i	−0.166967	−	0.140102i	0.555476	−	0.831533i	$-0.312536\pi$
$971$	−5.20283	−	4.36569i	−0.166967	−	0.140102i	−0.722443	+	0.691431i	$0.756981\pi$
$972$	0.906357	+	18.5916i	0.0290714	+	0.596326i
$973$	4.13983	+	23.4782i	0.132717	+	0.752675i
$974$	−54.0888	+	26.8446i	−1.73312	+	0.860157i
$975$	3.06134	−	8.41096i	0.0980413	−	0.269366i
$976$	0.868536	−	11.2415i	0.0278012	−	0.359832i
$977$	10.2026	+	5.89048i	0.326410	+	0.188453i	0.654246	−	0.756282i	$-0.272986\pi$
$977$	10.2026	+	5.89048i	0.326410	+	0.188453i	−0.327836	+	0.944735i	$0.606319\pi$
$978$	9.74099	−	40.2506i	0.311482	−	1.28707i
$979$	16.2040	−	13.5968i	0.517883	−	0.434556i
$980$	2.99697	+	3.23745i	0.0957346	+	0.103416i
$981$	−3.79042	+	2.18840i	−0.121019	+	0.0698702i
$982$	−41.2768	+	12.1449i	−1.31720	+	0.387560i
$983$	−7.75067	+	43.9562i	−0.247208	+	1.40199i	0.568101	+	0.822959i	$0.307678\pi$
$983$	−7.75067	+	43.9562i	−0.247208	+	1.40199i	−0.815309	+	0.579027i	$0.803433\pi$
$984$	51.2763	−	28.6415i	1.63463	−	0.913059i
$985$	−19.0239	+	6.92414i	−0.606152	+	0.220621i
$986$	−46.1815	−	2.90913i	−1.47072	−	0.0926455i
$987$	0.793369			0.0252532
$988$	32.2985	+	22.5350i	1.02755	+	0.716933i
$989$	31.4412			0.999772
$990$	1.68795	+	0.106329i	0.0536464	+	0.00337937i
$991$	51.3219	−	18.6796i	1.63029	−	0.593378i	0.644989	−	0.764192i	$-0.276862\pi$
$991$	51.3219	−	18.6796i	1.63029	−	0.593378i	0.985303	+	0.170814i	$0.0546396\pi$
$992$	8.86629	−	1.88095i	0.281505	−	0.0597203i
$993$	5.70478	−	32.3534i	0.181036	−	1.02670i
$994$	−14.1015	+	4.14911i	−0.447274	+	0.131602i
$995$	−1.81204	+	1.04618i	−0.0574455	+	0.0331662i
$996$	16.0868	−	14.8918i	0.509729	−	0.471866i
$997$	−7.88491	+	6.61622i	−0.249718	+	0.209538i	−0.759051	−	0.651032i	$-0.774337\pi$
$997$	−7.88491	+	6.61622i	−0.249718	+	0.209538i	0.509333	+	0.860569i	$0.329892\pi$
$998$	−12.5201	+	51.7340i	−0.396316	+	1.63761i
$999$	3.26042	+	1.88241i	0.103155	+	0.0595567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.be.b.231.10	yes	120
4.3	odd	2	inner	380.2.be.b.231.19	yes	120
19.13	odd	18	inner	380.2.be.b.51.19	yes	120
76.51	even	18	inner	380.2.be.b.51.10	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.be.b.51.10	✓	120	76.51	even	18	inner
380.2.be.b.51.19	yes	120	19.13	odd	18	inner
380.2.be.b.231.10	yes	120	1.1	even	1	trivial
380.2.be.b.231.19	yes	120	4.3	odd	2	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0889099 - 1.41142i) q^{2} +(-1.86185 + 0.677657i) q^{3} +(-1.98419 - 0.250978i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.790919 + 2.68809i) q^{6} +(1.89621 - 1.09478i) q^{7} +(-0.530648 + 2.77820i) q^{8} +(0.709122 - 0.595024i) q^{9} +O(q^{10})\)	\(q+(0.0889099 - 1.41142i) q^{2} +(-1.86185 + 0.677657i) q^{3} +(-1.98419 - 0.250978i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.790919 + 2.68809i) q^{6} +(1.89621 - 1.09478i) q^{7} +(-0.530648 + 2.77820i) q^{8} +(0.709122 - 0.595024i) q^{9} +(1.37453 + 0.332649i) q^{10} +(1.11884 + 0.645961i) q^{11} +(3.86434 - 0.877318i) q^{12} +(1.54509 - 4.24510i) q^{13} +(-1.37660 - 2.77368i) q^{14} +(-0.344055 - 1.95124i) q^{15} +(3.87402 + 0.995975i) q^{16} +(3.21680 + 2.69921i) q^{17} +(-0.776779 - 1.05377i) q^{18} +(0.583643 - 4.31965i) q^{19} +(0.591716 - 1.91046i) q^{20} +(-2.78857 + 3.32329i) q^{21} +(1.01120 - 1.52171i) q^{22} +(7.68844 - 1.35568i) q^{23} +(-0.894683 - 5.53219i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-5.85422 - 2.55819i) q^{26} +(2.05495 - 3.55928i) q^{27} +(-4.03721 + 1.69634i) q^{28} +(-5.00853 - 5.96893i) q^{29} +(-2.78459 + 0.312121i) q^{30} +(0.801118 + 1.38758i) q^{31} +(1.75017 - 5.37930i) q^{32} +(-2.52084 - 0.444493i) q^{33} +(4.09572 - 4.30025i) q^{34} +(0.748873 + 2.05751i) q^{35} +(-1.55637 + 1.00267i) q^{36} +0.916035i q^{37} +(-6.04493 - 1.20782i) q^{38} +8.95076i q^{39} +(-2.64385 - 1.00502i) q^{40} +(3.58454 + 9.84843i) q^{41} +(4.44262 + 4.23131i) q^{42} +(3.96610 + 0.699331i) q^{43} +(-2.05786 - 1.56251i) q^{44} +(0.462847 + 0.801674i) q^{45} +(-1.22985 - 10.9721i) q^{46} +(-0.117552 - 0.140092i) q^{47} +(-7.88776 + 0.770903i) q^{48} +(-1.10292 + 1.91031i) q^{49} +(-0.566281 + 1.29589i) q^{50} +(-7.81833 - 2.84564i) q^{51} +(-4.13117 + 8.03529i) q^{52} +(11.2420 - 1.98226i) q^{53} +(-4.84091 - 3.21684i) q^{54} +(-0.830431 + 0.989670i) q^{55} +(2.03530 + 5.84901i) q^{56} +(1.84059 + 8.43803i) q^{57} +(-8.86996 + 6.53842i) q^{58} +(5.65551 + 4.74554i) q^{59} +(0.192955 + 3.95797i) q^{60} +(-0.489472 - 2.77593i) q^{61} +(2.02968 - 1.00734i) q^{62} +(0.693227 - 1.90462i) q^{63} +(-7.43682 - 2.94850i) q^{64} +(3.91230 + 2.25877i) q^{65} +(-0.851492 + 3.51844i) q^{66} +(-7.03072 + 5.89947i) q^{67} +(-5.70530 - 6.16310i) q^{68} +(-13.3960 + 7.73419i) q^{69} +(2.97059 - 0.874038i) q^{70} +(0.824318 - 4.67494i) q^{71} +(1.27680 + 2.28583i) q^{72} +(2.41720 - 0.879790i) q^{73} +(1.29291 + 0.0814446i) q^{74} +1.98134 q^{75} +(-2.24219 + 8.42452i) q^{76} +2.82874 q^{77} +(12.6332 + 0.795811i) q^{78} +(-10.9331 + 3.97931i) q^{79} +(-1.65356 + 3.64222i) q^{80} +(-1.89627 + 10.7543i) q^{81} +(14.2189 - 4.18365i) q^{82} +(4.79084 - 2.76600i) q^{83} +(6.36713 - 5.89417i) q^{84} +(-3.21680 + 2.69921i) q^{85} +(1.33967 - 5.53564i) q^{86} +(13.3700 + 7.71918i) q^{87} +(-2.38832 + 2.76558i) q^{88} +(5.59996 - 15.3858i) q^{89} +(1.17265 - 0.581993i) q^{90} +(-1.71762 - 9.74113i) q^{91} +(-15.5956 + 0.760298i) q^{92} +(-2.43186 - 2.04057i) q^{93} +(-0.208180 + 0.153458i) q^{94} +(4.15267 + 1.32487i) q^{95} +(0.386765 + 11.2015i) q^{96} +(3.27224 - 3.89970i) q^{97} +(2.59818 + 1.72652i) q^{98} +(1.17776 - 0.207670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

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