LMFDB - Embedded newform 370.2.o.b.231.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 25 x^{15} + 132 x^{14} - 135 x^{13} + 666 x^{12} - 297 x^{11} + 1845 x^{10} + \cdots + 9 $ x^18 - 3x^17 + 18x^16 - 25x^15 + 132x^14 - 135x^13 + 666x^12 - 297x^11 + 1845x^10 - 382x^9 + 3810x^8 - 63x^7 + 3325x^6 - 1329x^5 + 1332x^4 - 192x^3 + 117x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			231.3
Root			$-1.09918 - 1.90384i$ of defining polynomial
Character	$\chi$	$=$	370.231
Dual form			370.2.o.b.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(0.381743 - 2.16497i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{5} -2.19837 q^{6} +(-2.80439 - 2.35316i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.72229 - 0.626862i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(0.381743 - 2.16497i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{5} -2.19837 q^{6} +(-2.80439 - 2.35316i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.72229 - 0.626862i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.760664 + 1.31751i) q^{11} +(0.381743 + 2.16497i) q^{12} +(-0.396939 + 0.144474i) q^{13} +(-1.83043 + 3.17041i) q^{14} +(-1.68405 + 1.41308i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-3.43528 - 1.25034i) q^{17} +(-0.318266 + 1.80498i) q^{18} +(-0.280874 + 1.59292i) q^{19} +(0.939693 + 0.342020i) q^{20} +(-6.16508 + 5.17311i) q^{21} +(1.16540 - 0.977891i) q^{22} +(1.58767 - 2.74993i) q^{23} +(2.06579 - 0.751886i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.211207 + 0.365821i) q^{26} +(1.28294 - 2.22212i) q^{27} +(3.44009 + 1.25209i) q^{28} +(-1.06893 - 1.85144i) q^{29} +(1.68405 + 1.41308i) q^{30} +3.91727 q^{31} +(-0.766044 - 0.642788i) q^{32} +(3.14274 - 1.14387i) q^{33} +(-0.634814 + 3.60021i) q^{34} +(0.635703 + 3.60525i) q^{35} +1.83282 q^{36} +(-4.81875 - 3.71210i) q^{37} +1.61749 q^{38} +(0.161253 + 0.914512i) q^{39} +(0.173648 - 0.984808i) q^{40} +(-3.94285 + 1.43508i) q^{41} +(6.16508 + 5.17311i) q^{42} +1.06506 q^{43} +(-1.16540 - 0.977891i) q^{44} +(0.916411 + 1.58727i) q^{45} +(-2.98385 - 1.08603i) q^{46} +(1.17275 - 2.03126i) q^{47} +(-1.09918 - 1.90384i) q^{48} +(1.11169 + 6.30470i) q^{49} +(0.939693 - 0.342020i) q^{50} +(-4.01834 + 6.95997i) q^{51} +(0.323587 - 0.271522i) q^{52} +(2.03625 - 1.70861i) q^{53} +(-2.41115 - 0.877585i) q^{54} +(0.264176 - 1.49822i) q^{55} +(0.635703 - 3.60525i) q^{56} +(3.34139 + 1.21617i) q^{57} +(-1.63769 + 1.37419i) q^{58} +(10.3613 - 8.69413i) q^{59} +(1.09918 - 1.90384i) q^{60} +(-11.3270 + 4.12269i) q^{61} +(-0.680226 - 3.85775i) q^{62} +(3.35486 + 5.81079i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.396939 + 0.144474i) q^{65} +(-1.67222 - 2.89637i) q^{66} +(-9.69452 - 8.13466i) q^{67} +3.65575 q^{68} +(-5.34743 - 4.48703i) q^{69} +(3.44009 - 1.25209i) q^{70} +(2.80510 - 15.9085i) q^{71} +(-0.318266 - 1.80498i) q^{72} +11.7958 q^{73} +(-2.81894 + 5.39014i) q^{74} +2.19837 q^{75} +(-0.280874 - 1.59292i) q^{76} +(0.967113 - 5.48477i) q^{77} +(0.872617 - 0.317607i) q^{78} +(1.70308 + 1.42905i) q^{79} -1.00000 q^{80} +(-8.53315 - 7.16016i) q^{81} +(2.09795 + 3.63375i) q^{82} +(12.2075 + 4.44316i) q^{83} +(4.02397 - 6.96972i) q^{84} +(1.82787 + 3.16597i) q^{85} +(-0.184945 - 1.04888i) q^{86} +(-4.41637 + 1.60743i) q^{87} +(-0.760664 + 1.31751i) q^{88} +(2.42826 - 2.03755i) q^{89} +(1.40402 - 1.17811i) q^{90} +(1.45314 + 0.528900i) q^{91} +(-0.551393 + 3.12710i) q^{92} +(1.49539 - 8.48076i) q^{93} +(-2.20404 - 0.802206i) q^{94} +(1.23907 - 1.03970i) q^{95} +(-1.68405 + 1.41308i) q^{96} +(-7.19146 + 12.4560i) q^{97} +(6.01587 - 2.18960i) q^{98} +(-0.484187 - 2.74596i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	0.381743	−	2.16497i	0.220399	−	1.24995i	−0.650889	−	0.759173i	$-0.725603\pi$
$3$	0.381743	−	2.16497i	0.220399	−	1.24995i	0.871288	−	0.490773i	$-0.163285\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$6$	−2.19837			−0.897480
$7$	−2.80439	−	2.35316i	−1.05996	−	0.889411i	−0.0658536	−	0.997829i	$-0.520977\pi$
$7$	−2.80439	−	2.35316i	−1.05996	−	0.889411i	−0.994105	+	0.108418i	$0.965421\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.72229	−	0.626862i	−0.574096	−	0.208954i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	0.760664	+	1.31751i	0.229349	+	0.397244i	0.957615	−	0.288050i	$-0.0930070\pi$
$11$	0.760664	+	1.31751i	0.229349	+	0.397244i	−0.728266	+	0.685294i	$0.759674\pi$
$12$	0.381743	+	2.16497i	0.110200	+	0.624973i
$13$	−0.396939	+	0.144474i	−0.110091	+	0.0400699i	−0.396478	−	0.918044i	$-0.629768\pi$
$13$	−0.396939	+	0.144474i	−0.110091	+	0.0400699i	0.286387	+	0.958114i	$0.407546\pi$
$14$	−1.83043	+	3.17041i	−0.489204	+	0.847326i
$15$	−1.68405	+	1.41308i	−0.434819	+	0.364857i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−3.43528	−	1.25034i	−0.833178	−	0.303252i	−0.110015	−	0.993930i	$-0.535090\pi$
$17$	−3.43528	−	1.25034i	−0.833178	−	0.303252i	−0.723163	+	0.690678i	$0.757312\pi$
$18$	−0.318266	+	1.80498i	−0.0750160	+	0.425437i
$19$	−0.280874	+	1.59292i	−0.0644369	+	0.365440i	0.935490	+	0.353353i	$0.114959\pi$
$19$	−0.280874	+	1.59292i	−0.0644369	+	0.365440i	−0.999927	+	0.0120869i	$0.996153\pi$
$20$	0.939693	+	0.342020i	0.210122	+	0.0764780i
$21$	−6.16508	+	5.17311i	−1.34533	+	1.12887i
$22$	1.16540	−	0.977891i	0.248465	−	0.208487i
$23$	1.58767	−	2.74993i	0.331052	−	0.573400i	−0.651666	−	0.758506i	$-0.725930\pi$
$23$	1.58767	−	2.74993i	0.331052	−	0.573400i	0.982718	+	0.185106i	$0.0592630\pi$
$24$	2.06579	−	0.751886i	0.421678	−	0.153478i
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	0.211207	+	0.365821i	0.0414210	+	0.0717434i
$27$	1.28294	−	2.22212i	0.246903	−	0.427648i
$28$	3.44009	+	1.25209i	0.650116	+	0.236623i
$29$	−1.06893	−	1.85144i	−0.198495	−	0.343804i	0.749546	−	0.661953i	$-0.230272\pi$
$29$	−1.06893	−	1.85144i	−0.198495	−	0.343804i	−0.948041	+	0.318149i	$0.896939\pi$
$30$	1.68405	+	1.41308i	0.307464	+	0.257993i
$31$	3.91727			0.703562			0.351781	−	0.936082i	$-0.385576\pi$
$31$	3.91727			0.703562			0.351781	+	0.936082i	$0.385576\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	3.14274	−	1.14387i	0.547082	−	0.199121i
$34$	−0.634814	+	3.60021i	−0.108870	+	0.617431i
$35$	0.635703	+	3.60525i	0.107453	+	0.609399i
$36$	1.83282			0.305470
$37$	−4.81875	−	3.71210i	−0.792197	−	0.610266i
$37$	−4.81875	−	3.71210i	−0.792197	−	0.610266i
$38$	1.61749			0.262391
$39$	0.161253	+	0.914512i	0.0258212	+	0.146439i
$40$	0.173648	−	0.984808i	0.0274562	−	0.155712i
$41$	−3.94285	+	1.43508i	−0.615770	+	0.224122i	−0.631026	−	0.775762i	$-0.717366\pi$
$41$	−3.94285	+	1.43508i	−0.615770	+	0.224122i	0.0152559	+	0.999884i	$0.495144\pi$
$42$	6.16508	+	5.17311i	0.951292	+	0.798229i
$43$	1.06506			0.162420			0.0812099	−	0.996697i	$-0.474122\pi$
$43$	1.06506			0.162420			0.0812099	+	0.996697i	$0.474122\pi$
$44$	−1.16540	−	0.977891i	−0.175691	−	0.147423i
$45$	0.916411	+	1.58727i	0.136610	+	0.236616i
$46$	−2.98385	−	1.08603i	−0.439944	−	0.160127i
$47$	1.17275	−	2.03126i	0.171063	−	0.296289i	−0.767729	−	0.640775i	$-0.778613\pi$
$47$	1.17275	−	2.03126i	0.171063	−	0.296289i	0.938792	+	0.344485i	$0.111947\pi$
$48$	−1.09918	−	1.90384i	−0.158654	−	0.274796i
$49$	1.11169	+	6.30470i	0.158813	+	0.900671i
$50$	0.939693	−	0.342020i	0.132893	−	0.0483690i
$51$	−4.01834	+	6.95997i	−0.562680	+	0.974591i
$52$	0.323587	−	0.271522i	0.0448735	−	0.0376533i
$53$	2.03625	−	1.70861i	0.279700	−	0.234696i	−0.492135	−	0.870519i	$-0.663783\pi$
$53$	2.03625	−	1.70861i	0.279700	−	0.234696i	0.771835	+	0.635823i	$0.219339\pi$
$54$	−2.41115	−	0.877585i	−0.328115	−	0.119424i
$55$	0.264176	−	1.49822i	0.0356215	−	0.202019i
$56$	0.635703	−	3.60525i	0.0849494	−	0.481772i
$57$	3.34139	+	1.21617i	0.442578	+	0.161085i
$58$	−1.63769	+	1.37419i	−0.215040	+	0.180440i
$59$	10.3613	−	8.69413i	1.34892	−	1.13188i	0.369685	−	0.929157i	$-0.379466\pi$
$59$	10.3613	−	8.69413i	1.34892	−	1.13188i	0.979236	−	0.202722i	$-0.0649789\pi$
$60$	1.09918	−	1.90384i	0.141904	−	0.245785i
$61$	−11.3270	+	4.12269i	−1.45027	+	0.527856i	−0.942668	−	0.333733i	$-0.891692\pi$
$61$	−11.3270	+	4.12269i	−1.45027	+	0.527856i	−0.507606	+	0.861589i	$0.669469\pi$
$62$	−0.680226	−	3.85775i	−0.0863888	−	0.489935i
$63$	3.35486	+	5.81079i	0.422672	+	0.732090i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.396939	+	0.144474i	0.0492342	+	0.0179198i
$66$	−1.67222	−	2.89637i	−0.205836	−	0.356518i
$67$	−9.69452	−	8.13466i	−1.18437	−	0.993807i	−0.999940	−	0.0109624i	$-0.996510\pi$
$67$	−9.69452	−	8.13466i	−1.18437	−	0.993807i	−0.184434	−	0.982845i	$-0.559045\pi$
$68$	3.65575			0.443325
$69$	−5.34743	−	4.48703i	−0.643755	−	0.540174i
$70$	3.44009	−	1.25209i	0.411170	−	0.149653i
$71$	2.80510	−	15.9085i	0.332904	−	1.88799i	−0.114116	−	0.993467i	$-0.536403\pi$
$71$	2.80510	−	15.9085i	0.332904	−	1.88799i	0.447020	−	0.894524i	$-0.352485\pi$
$72$	−0.318266	−	1.80498i	−0.0375080	−	0.212719i
$73$	11.7958			1.38060			0.690300	−	0.723524i	$-0.257479\pi$
$73$	11.7958			1.38060			0.690300	+	0.723524i	$0.257479\pi$
$74$	−2.81894	+	5.39014i	−0.327695	+	0.626591i
$75$	2.19837			0.253846
$76$	−0.280874	−	1.59292i	−0.0322185	−	0.182720i
$77$	0.967113	−	5.48477i	0.110213	−	0.625048i
$78$	0.872617	−	0.317607i	0.0988045	−	0.0359619i
$79$	1.70308	+	1.42905i	0.191611	+	0.160781i	0.733546	−	0.679639i	$-0.237864\pi$
$79$	1.70308	+	1.42905i	0.191611	+	0.160781i	−0.541935	+	0.840420i	$0.682308\pi$
$80$	−1.00000			−0.111803
$81$	−8.53315	−	7.16016i	−0.948127	−	0.795573i
$82$	2.09795	+	3.63375i	0.231680	+	0.401281i
$83$	12.2075	+	4.44316i	1.33994	+	0.487700i	0.909795	−	0.415058i	$-0.136239\pi$
$83$	12.2075	+	4.44316i	1.33994	+	0.487700i	0.430149	+	0.902758i	$0.358461\pi$
$84$	4.02397	−	6.96972i	0.439051	−	0.760458i
$85$	1.82787	+	3.16597i	0.198261	+	0.343398i
$86$	−0.184945	−	1.04888i	−0.0199432	−	0.113103i
$87$	−4.41637	+	1.60743i	−0.473484	+	0.172334i
$88$	−0.760664	+	1.31751i	−0.0810871	+	0.140447i
$89$	2.42826	−	2.03755i	0.257395	−	0.215980i	−0.504954	−	0.863146i	$-0.668490\pi$
$89$	2.42826	−	2.03755i	0.257395	−	0.215980i	0.762349	+	0.647166i	$0.224046\pi$
$90$	1.40402	−	1.17811i	0.147997	−	0.124184i
$91$	1.45314	+	0.528900i	0.152331	+	0.0554438i
$92$	−0.551393	+	3.12710i	−0.0574867	+	0.326023i
$93$	1.49539	−	8.48076i	0.155064	−	0.879414i
$94$	−2.20404	−	0.802206i	−0.227330	−	0.0827412i
$95$	1.23907	−	1.03970i	0.127126	−	0.106671i
$96$	−1.68405	+	1.41308i	−0.171877	+	0.144222i
$97$	−7.19146	+	12.4560i	−0.730183	+	1.26471i	0.226622	+	0.973983i	$0.427232\pi$
$97$	−7.19146	+	12.4560i	−0.730183	+	1.26471i	−0.956805	+	0.290731i	$0.906102\pi$
$98$	6.01587	−	2.18960i	0.607695	−	0.221183i
$99$	−0.484187	−	2.74596i	−0.0486626	−	0.275980i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	5.69466	−	9.86344i	0.566640	−	0.981449i	−0.430255	−	0.902707i	$-0.641576\pi$
$101$	5.69466	−	9.86344i	0.566640	−	0.981449i	0.996895	−	0.0787417i	$-0.0250902\pi$
$102$	7.55201	+	2.74871i	0.747761	+	0.272163i
$103$	2.91240	+	5.04442i	0.286967	+	0.497042i	0.973084	−	0.230449i	$-0.0740196\pi$
$103$	2.91240	+	5.04442i	0.286967	+	0.497042i	−0.686117	+	0.727491i	$0.740686\pi$
$104$	−0.323587	−	0.271522i	−0.0317304	−	0.0266249i
$105$	8.04794			0.785398
$106$	−2.03625	−	1.70861i	−0.197778	−	0.165955i
$107$	4.42669	−	1.61119i	0.427945	−	0.155759i	−0.119063	−	0.992887i	$-0.537989\pi$
$107$	4.42669	−	1.61119i	0.427945	−	0.155759i	0.547008	+	0.837128i	$0.315767\pi$
$108$	−0.445562	+	2.52691i	−0.0428742	+	0.243152i
$109$	0.168787	+	0.957238i	0.0161668	+	0.0916868i	0.991824	−	0.127617i	$-0.0407327\pi$
$109$	0.168787	+	0.957238i	0.0161668	+	0.0916868i	−0.975657	+	0.219303i	$0.929622\pi$
$110$	−1.52133			−0.145053
$111$	−9.87611	+	9.01537i	−0.937398	+	0.855701i
$112$	−3.66087			−0.345920
$113$	−1.37046	−	7.77229i	−0.128922	−	0.731156i	−0.978900	−	0.204338i	$-0.934496\pi$
$113$	−1.37046	−	7.77229i	−0.128922	−	0.731156i	0.849978	−	0.526818i	$-0.176615\pi$
$114$	0.617465	−	3.50182i	0.0578309	−	0.327975i
$115$	−2.98385	+	1.08603i	−0.278245	+	0.101273i
$116$	1.63769	+	1.37419i	0.152056	+	0.127590i
$117$	0.774208			0.0715756
$118$	−10.3613	−	8.69413i	−0.953831	−	0.800360i
$119$	6.69161	+	11.5902i	0.613419	+	1.06247i
$120$	−2.06579	−	0.751886i	−0.188580	−	0.0686375i
$121$	4.34278	−	7.52192i	0.394798	−	0.683811i
$122$	6.02697	+	10.4390i	0.545656	+	0.945104i
$123$	1.60175	+	9.08399i	0.144425	+	0.819076i
$124$	−3.68103	+	1.33978i	−0.330566	+	0.120316i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	5.13994	−	4.31292i	0.457902	−	0.384226i
$127$	−1.93109	+	1.62038i	−0.171357	+	0.143785i	−0.724433	−	0.689345i	$-0.757898\pi$
$127$	−1.93109	+	1.62038i	−0.171357	+	0.143785i	0.553076	+	0.833131i	$0.313454\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	0.406578	−	2.30582i	0.0357972	−	0.203016i
$130$	0.0733513	−	0.415996i	0.00643334	−	0.0364853i
$131$	19.6703	+	7.15940i	1.71860	+	0.625519i	0.997717	−	0.0675367i	$-0.0215140\pi$
$131$	19.6703	+	7.15940i	1.71860	+	0.625519i	0.720884	+	0.693056i	$0.243736\pi$
$132$	−2.56199	+	2.14976i	−0.222992	+	0.187113i
$133$	4.53607	−	3.80621i	0.393327	−	0.330040i
$134$	−6.32765	+	10.9598i	−0.546625	+	0.946783i
$135$	−2.41115	+	0.877585i	−0.207518	+	0.0755305i
$136$	−0.634814	−	3.60021i	−0.0544349	−	0.308716i
$137$	6.73170	+	11.6596i	0.575128	+	0.996150i	0.996028	+	0.0890432i	$0.0283809\pi$
$137$	6.73170	+	11.6596i	0.575128	+	0.996150i	−0.420900	+	0.907107i	$0.638286\pi$
$138$	−3.49029	+	6.04535i	−0.297113	+	0.514615i
$139$	−1.40070	−	0.509811i	−0.118805	−	0.0432416i	0.281933	−	0.959434i	$-0.409024\pi$
$139$	−1.40070	−	0.509811i	−0.118805	−	0.0432416i	−0.400739	+	0.916192i	$0.631247\pi$
$140$	−1.83043	−	3.17041i	−0.154700	−	0.267948i
$141$	−3.94992	−	3.31438i	−0.332643	−	0.279121i
$142$	−16.1539			−1.35561
$143$	−0.492283	−	0.413074i	−0.0411667	−	0.0345430i
$144$	−1.72229	+	0.626862i	−0.143524	+	0.0522385i
$145$	−0.371235	+	2.10538i	−0.0308294	+	0.174842i
$146$	−2.04833	−	11.6166i	−0.169521	−	0.961400i
$147$	14.0739			1.16079
$148$	5.79775	+	1.84013i	0.476572	+	0.151257i
$149$	−14.9618			−1.22572			−0.612859	−	0.790192i	$-0.709981\pi$
$149$	−14.9618			−1.22572			−0.612859	+	0.790192i	$0.709981\pi$
$150$	−0.381743	−	2.16497i	−0.0311692	−	0.176769i
$151$	−1.73093	+	9.81659i	−0.140861	+	0.798863i	0.829737	+	0.558155i	$0.188491\pi$
$151$	−1.73093	+	9.81659i	−0.140861	+	0.798863i	−0.970598	+	0.240708i	$0.922620\pi$
$152$	−1.51994	+	0.553214i	−0.123284	+	0.0448716i
$153$	5.13276	+	4.30689i	0.414959	+	0.348192i
$154$	−5.56938			−0.448794
$155$	−3.00080	−	2.51797i	−0.241030	−	0.202248i
$156$	−0.464310	−	0.804209i	−0.0371746	−	0.0643882i
$157$	7.85917	+	2.86050i	0.627230	+	0.228293i	0.636025	−	0.771668i	$-0.280577\pi$
$157$	7.85917	+	2.86050i	0.627230	+	0.228293i	−0.00879509	+	0.999961i	$0.502800\pi$
$158$	1.11161	−	1.92536i	0.0884347	−	0.153173i
$159$	−2.92177	−	5.06066i	−0.231712	−	0.401336i
$160$	0.173648	+	0.984808i	0.0137281	+	0.0778559i
$161$	−10.9235	+	3.97582i	−0.860890	+	0.313338i
$162$	−5.56961	+	9.64686i	−0.437590	+	0.757929i
$163$	−9.61747	+	8.07001i	−0.753298	+	0.632092i	−0.936373	−	0.351007i	$-0.885839\pi$
$163$	−9.61747	+	8.07001i	−0.753298	+	0.632092i	0.183075	+	0.983099i	$0.441395\pi$
$164$	3.21424	−	2.69707i	0.250990	−	0.210606i
$165$	−3.14274	−	1.14387i	−0.244662	−	0.0890498i
$166$	2.25585	−	12.7936i	0.175088	−	0.992973i
$167$	−0.521597	+	2.95813i	−0.0403624	+	0.228907i	−0.998316	−	0.0580181i	$-0.981522\pi$
$167$	−0.521597	+	2.95813i	−0.0403624	+	0.228907i	0.957953	+	0.286925i	$0.0926330\pi$
$168$	−7.56259	−	2.75256i	−0.583466	−	0.212364i
$169$	−9.82189	+	8.24154i	−0.755530	+	0.633965i
$170$	2.80047	−	2.34987i	0.214786	−	0.180227i
$171$	1.48228	−	2.56739i	0.113353	−	0.196333i
$172$	−1.00083	+	0.364271i	−0.0763123	+	0.0277754i
$173$	−2.04477	−	11.5964i	−0.155461	−	0.881661i	−0.958363	−	0.285551i	$-0.907823\pi$
$173$	−2.04477	−	11.5964i	−0.155461	−	0.881661i	0.802903	−	0.596110i	$-0.203288\pi$
$174$	2.34990	+	4.07015i	0.178145	+	0.308557i
$175$	1.83043	−	3.17041i	0.138368	−	0.239660i
$176$	1.42958	+	0.520325i	0.107759	+	0.0392210i
$177$	−14.8672	−	25.7507i	−1.11749	−	1.93554i
$178$	−2.42826	−	2.03755i	−0.182006	−	0.152721i
$179$	3.69510			0.276185			0.138092	−	0.990419i	$-0.455903\pi$
$179$	3.69510			0.276185			0.138092	+	0.990419i	$0.455903\pi$
$180$	−1.40402	−	1.17811i	−0.104650	−	0.0878115i
$181$	11.4143	−	4.15448i	0.848421	−	0.308800i	0.119024	−	0.992891i	$-0.462023\pi$
$181$	11.4143	−	4.15448i	0.848421	−	0.308800i	0.729396	+	0.684091i	$0.239801\pi$
$182$	0.268530	−	1.52291i	0.0199047	−	0.112885i
$183$	4.60150	+	26.0964i	0.340153	+	1.92910i
$184$	3.17534			0.234089
$185$	1.30528	+	5.94106i	0.0959662	+	0.436796i
$186$	−8.61159			−0.631433
$187$	−0.965761	−	5.47710i	−0.0706234	−	0.400525i
$188$	−0.407291	+	2.30986i	−0.0297047	+	0.168464i
$189$	−8.82689	+	3.21272i	−0.642062	+	0.233691i
$190$	−1.23907	−	1.03970i	−0.0898915	−	0.0754279i
$191$	−8.26542			−0.598065			−0.299033	−	0.954243i	$-0.596664\pi$
$191$	−8.26542			−0.598065			−0.299033	+	0.954243i	$0.596664\pi$
$192$	1.68405	+	1.41308i	0.121536	+	0.101981i
$193$	10.1808	+	17.6336i	0.732829	+	1.26930i	0.955669	+	0.294442i	$0.0951337\pi$
$193$	10.1808	+	17.6336i	0.732829	+	1.26930i	−0.222841	+	0.974855i	$0.571533\pi$
$194$	13.5155	+	4.91925i	0.970359	+	0.353182i
$195$	0.464310	−	0.804209i	0.0332499	−	0.0575906i
$196$	−3.20098	−	5.54426i	−0.228641	−	0.396018i
$197$	1.01392	+	5.75022i	0.0722387	+	0.409686i	0.999388	+	0.0349928i	$0.0111408\pi$
$197$	1.01392	+	5.75022i	0.0722387	+	0.409686i	−0.927149	+	0.374693i	$0.877748\pi$
$198$	−2.62017	+	0.953662i	−0.186207	+	0.0677738i
$199$	5.05362	−	8.75313i	0.358242	−	0.620493i	−0.629425	−	0.777061i	$-0.716710\pi$
$199$	5.05362	−	8.75313i	0.358242	−	0.620493i	0.987667	+	0.156568i	$0.0500430\pi$
$200$	−0.766044	+	0.642788i	−0.0541675	+	0.0454519i
$201$	−21.3121	+	17.8830i	−1.50324	+	1.26137i
$202$	−10.7025	−	3.89538i	−0.753022	−	0.274078i
$203$	−1.35904	+	7.70752i	−0.0953861	+	0.540962i
$204$	1.39556	−	7.91459i	0.0977084	−	0.554132i
$205$	3.94285	+	1.43508i	0.275381	+	0.100230i
$206$	4.46205	−	3.74411i	0.310886	−	0.260864i
$207$	−4.45825	+	3.74092i	−0.309870	+	0.260012i
$208$	−0.211207	+	0.365821i	−0.0146446	+	0.0253651i
$209$	−2.31233	+	0.841620i	−0.159947	+	0.0582161i
$210$	−1.39751	−	7.92567i	−0.0964373	−	0.546923i
$211$	8.56783	+	14.8399i	0.589834	+	1.02162i	0.994254	+	0.107049i	$0.0341401\pi$
$211$	8.56783	+	14.8399i	0.589834	+	1.02162i	−0.404420	+	0.914573i	$0.632527\pi$
$212$	−1.32906	+	2.30201i	−0.0912806	+	0.158103i
$213$	−33.3706	−	12.1459i	−2.28652	−	0.832224i
$214$	−2.35540	−	4.07966i	−0.161011	−	0.278880i
$215$	−0.815881	−	0.684606i	−0.0556426	−	0.0466897i
$216$	2.56589			0.174587
$217$	−10.9855	−	9.21796i	−0.745747	−	0.625756i
$218$	0.913386	−	0.332445i	0.0618623	−	0.0225160i
$219$	4.50298	−	25.5377i	0.304283	−	1.72567i
$220$	0.264176	+	1.49822i	0.0178107	+	0.101010i
$221$	1.54424			0.103877
$222$	10.5934	+	8.16056i	0.710981	+	0.547701i
$223$	−26.8907			−1.80073			−0.900366	−	0.435134i	$-0.856701\pi$
$223$	−26.8907			−1.80073			−0.900366	+	0.435134i	$0.856701\pi$
$224$	0.635703	+	3.60525i	0.0424747	+	0.240886i
$225$	0.318266	−	1.80498i	0.0212177	−	0.120332i
$226$	−7.41623	+	2.69929i	−0.493321	+	0.179554i
$227$	15.3463	+	12.8771i	1.01857	+	0.854681i	0.989447	−	0.144895i	$-0.0462844\pi$
$227$	15.3463	+	12.8771i	1.01857	+	0.854681i	0.0291221	+	0.999576i	$0.490729\pi$
$228$	−3.55584			−0.235491
$229$	18.9495	+	15.9005i	1.25222	+	1.05073i	0.996467	+	0.0839906i	$0.0267666\pi$
$229$	18.9495	+	15.9005i	1.25222	+	1.05073i	0.255749	+	0.966743i	$0.417678\pi$
$230$	1.58767	+	2.74993i	0.104688	+	0.181325i
$231$	−11.5052	−	4.18754i	−0.756985	−	0.275520i
$232$	1.06893	−	1.85144i	0.0701786	−	0.121553i
$233$	−3.17546	−	5.50006i	−0.208031	−	0.360321i	0.743063	−	0.669222i	$-0.233372\pi$
$233$	−3.17546	−	5.50006i	−0.208031	−	0.360321i	−0.951094	+	0.308901i	$0.900039\pi$
$234$	−0.134440	−	0.762446i	−0.00878861	−	0.0498427i
$235$	−2.20404	+	0.802206i	−0.143776	+	0.0523301i
$236$	−6.76283	+	11.7136i	−0.440223	+	0.762489i
$237$	3.74400	−	3.14159i	0.243199	−	0.204068i
$238$	10.2521	−	8.60257i	0.664548	−	0.557622i
$239$	−12.0572	−	4.38845i	−0.779914	−	0.283865i	−0.0787770	−	0.996892i	$-0.525101\pi$
$239$	−12.0572	−	4.38845i	−0.779914	−	0.283865i	−0.701137	+	0.713027i	$0.747324\pi$
$240$	−0.381743	+	2.16497i	−0.0246414	+	0.139748i
$241$	−3.30959	+	18.7696i	−0.213189	+	1.20906i	0.670832	+	0.741609i	$0.265937\pi$
$241$	−3.30959	+	18.7696i	−0.213189	+	1.20906i	−0.884021	+	0.467447i	$0.845174\pi$
$242$	−8.16176	−	2.97064i	−0.524658	−	0.190960i
$243$	−12.8622	+	10.7927i	−0.825113	+	0.692352i
$244$	9.23386	−	7.74812i	0.591137	−	0.496023i
$245$	3.20098	−	5.54426i	0.204503	−	0.354210i
$246$	8.66784	−	3.15484i	0.552641	−	0.201145i
$247$	−0.118645	−	0.672869i	−0.00754920	−	0.0428136i
$248$	1.95863	+	3.39245i	0.124373	+	0.215421i
$249$	14.2794	−	24.7327i	0.904921	−	1.56737i
$250$	−0.939693	−	0.342020i	−0.0594314	−	0.0216313i
$251$	13.2540	+	22.9565i	0.836583	+	1.44900i	0.892735	+	0.450582i	$0.148784\pi$
$251$	13.2540	+	22.9565i	0.836583	+	1.44900i	−0.0561519	+	0.998422i	$0.517883\pi$
$252$	−5.13994	−	4.31292i	−0.323786	−	0.271689i
$253$	4.83074			0.303706
$254$	1.93109	+	1.62038i	0.121167	+	0.101672i
$255$	7.55201	−	2.74871i	0.472925	−	0.172131i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.66726	+	9.45551i	0.104001	+	0.589818i	0.991615	+	0.129230i	$0.0412505\pi$
$257$	1.66726	+	9.45551i	0.104001	+	0.589818i	−0.887614	+	0.460588i	$0.847638\pi$
$258$	−2.34139			−0.145768
$259$	4.77846	+	21.7495i	0.296919	+	1.35145i
$260$	−0.422413			−0.0261970
$261$	0.680408	+	3.85878i	0.0421162	+	0.238853i
$262$	3.63492	−	20.6147i	0.224566	−	1.27358i
$263$	−9.24331	+	3.36429i	−0.569967	+	0.207451i	−0.610896	−	0.791711i	$-0.709191\pi$
$263$	−9.24331	+	3.36429i	−0.569967	+	0.207451i	0.0409287	+	0.999162i	$0.486968\pi$
$264$	2.56199	+	2.14976i	0.157680	+	0.132309i
$265$	−2.65813			−0.163288
$266$	−4.53607	−	3.80621i	−0.278124	−	0.233374i
$267$	−3.48427	−	6.03494i	−0.213234	−	0.369332i
$268$	11.8921	+	4.32836i	0.726425	+	0.264397i
$269$	6.48109	−	11.2256i	0.395159	−	0.684436i	−0.597962	−	0.801524i	$-0.704023\pi$
$269$	6.48109	−	11.2256i	0.395159	−	0.684436i	0.993121	+	0.117089i	$0.0373561\pi$
$270$	1.28294	+	2.22212i	0.0780775	+	0.135234i
$271$	−0.255888	−	1.45121i	−0.0155441	−	0.0881548i	0.976049	−	0.217552i	$-0.0698070\pi$
$271$	−0.255888	−	1.45121i	−0.0155441	−	0.0881548i	−0.991593	+	0.129397i	$0.958696\pi$
$272$	−3.43528	+	1.25034i	−0.208295	+	0.0758130i
$273$	1.69978	−	2.94410i	0.102875	−	0.178185i
$274$	10.3136	−	8.65410i	0.623065	−	0.522813i
$275$	−1.16540	+	0.977891i	−0.0702766	+	0.0589690i
$276$	6.55959	+	2.38750i	0.394841	+	0.143710i
$277$	4.86734	−	27.6041i	0.292450	−	1.65857i	−0.384938	−	0.922943i	$-0.625777\pi$
$277$	4.86734	−	27.6041i	0.292450	−	1.65857i	0.677388	−	0.735626i	$-0.263112\pi$
$278$	−0.258838	+	1.46794i	−0.0155241	+	0.0880414i
$279$	−6.74666	−	2.45559i	−0.403912	−	0.147012i
$280$	−2.80439	+	2.35316i	−0.167594	+	0.140628i
$281$	−7.88230	+	6.61404i	−0.470219	+	0.394560i	−0.846874	−	0.531793i	$-0.821518\pi$
$281$	−7.88230	+	6.61404i	−0.470219	+	0.394560i	0.376656	+	0.926353i	$0.377074\pi$
$282$	−2.57813	+	4.46545i	−0.153525	+	0.265914i
$283$	31.2403	−	11.3705i	1.85704	−	0.675908i	0.875938	−	0.482423i	$-0.160243\pi$
$283$	31.2403	−	11.3705i	1.85704	−	0.675908i	0.981103	−	0.193484i	$-0.0619789\pi$
$284$	2.80510	+	15.9085i	0.166452	+	0.943996i
$285$	−1.77792	−	3.07944i	−0.105315	−	0.182411i
$286$	−0.321315	+	0.556533i	−0.0189997	+	0.0329085i
$287$	14.4343	+	5.25364i	0.852028	+	0.310113i
$288$	0.916411	+	1.58727i	0.0540000	+	0.0935308i
$289$	−2.78495	−	2.33685i	−0.163821	−	0.137462i
$290$	2.13786			0.125539
$291$	24.2215	+	20.3243i	1.41989	+	1.19143i
$292$	−11.0845	+	4.03442i	−0.648670	+	0.236096i
$293$	4.26594	−	24.1934i	0.249219	−	1.41339i	−0.561268	−	0.827634i	$-0.689686\pi$
$293$	4.26594	−	24.1934i	0.249219	−	1.41339i	0.810487	−	0.585757i	$-0.199203\pi$
$294$	−2.44390	−	13.8600i	−0.142531	−	0.808334i
$295$	−13.5257			−0.787495
$296$	0.805400	−	6.02921i	0.0468129	−	0.350441i
$297$	3.90356			0.226507
$298$	2.59809	+	14.7345i	0.150503	+	0.853546i
$299$	−0.232916	+	1.32093i	−0.0134699	+	0.0763914i
$300$	−2.06579	+	0.751886i	−0.119268	+	0.0434102i
$301$	−2.98683	−	2.50625i	−0.172158	−	0.144458i
$302$	9.96803			0.573596
$303$	−19.1802	−	16.0941i	−1.10187	−	0.924580i
$304$	0.808745	+	1.40079i	0.0463847	+	0.0803406i
$305$	11.3270	+	4.12269i	0.648582	+	0.236065i
$306$	3.35017	−	5.80266i	0.191516	−	0.331716i
$307$	1.64958	+	2.85715i	0.0941465	+	0.163066i	0.909252	−	0.416246i	$-0.136654\pi$
$307$	1.64958	+	2.85715i	0.0941465	+	0.163066i	−0.815106	+	0.579312i	$0.803321\pi$
$308$	0.967113	+	5.48477i	0.0551064	+	0.312524i
$309$	12.0328	−	4.37958i	0.684523	−	0.249146i
$310$	−1.95863	+	3.39245i	−0.111243	+	0.192678i
$311$	22.2513	−	18.6710i	1.26175	−	1.05874i	0.266261	−	0.963901i	$-0.414212\pi$
$311$	22.2513	−	18.6710i	1.26175	−	1.05874i	0.995493	−	0.0948366i	$-0.0302329\pi$
$312$	−0.711364	+	0.596906i	−0.0402731	+	0.0337931i
$313$	−13.2012	−	4.80483i	−0.746174	−	0.271585i	−0.0591791	−	0.998247i	$-0.518848\pi$
$313$	−13.2012	−	4.80483i	−0.746174	−	0.271585i	−0.686995	+	0.726662i	$0.741071\pi$
$314$	1.45232	−	8.23650i	0.0819590	−	0.464812i
$315$	1.16513	−	6.60778i	0.0656477	−	0.372306i
$316$	−2.08914	−	0.760384i	−0.117523	−	0.0427749i
$317$	1.43671	−	1.20554i	0.0806937	−	0.0677101i	−0.601549	−	0.798836i	$-0.705449\pi$
$317$	1.43671	−	1.20554i	0.0806937	−	0.0677101i	0.682242	+	0.731126i	$0.261005\pi$
$318$	−4.47642	+	3.75616i	−0.251025	+	0.210635i
$319$	1.62619	−	2.81665i	0.0910493	−	0.157702i
$320$	0.939693	−	0.342020i	0.0525304	−	0.0191195i
$321$	−1.79831	−	10.1987i	−0.100372	−	0.569237i
$322$	5.81226	+	10.0671i	0.323904	+	0.561019i
$323$	2.95657	−	5.12093i	0.164508	−	0.284936i
$324$	10.4675	+	3.80984i	0.581525	+	0.211658i
$325$	−0.211207	−	0.365821i	−0.0117156	−	0.0202921i
$326$	9.61747	+	8.07001i	0.532662	+	0.446957i
$327$	2.13682			0.118167
$328$	−3.21424	−	2.69707i	−0.177477	−	0.148921i
$329$	−8.06871	+	2.93677i	−0.444842	+	0.161909i
$330$	−0.580756	+	3.29363i	−0.0319695	+	0.181308i
$331$	−2.37140	−	13.4489i	−0.130344	−	0.739218i	−0.977989	−	0.208655i	$-0.933092\pi$
$331$	−2.37140	−	13.4489i	−0.130344	−	0.739218i	0.847645	−	0.530563i	$-0.178020\pi$
$332$	−12.9909			−0.712969
$333$	5.97230	+	9.41400i	0.327280	+	0.515884i
$334$	3.00376			0.164358
$335$	2.19757	+	12.4630i	0.120066	+	0.680928i
$336$	−1.39751	+	7.92567i	−0.0762404	+	0.432381i
$337$	−20.8652	+	7.59430i	−1.13660	+	0.413688i	−0.840684	−	0.541527i	$-0.817847\pi$
$337$	−20.8652	+	7.59430i	−1.13660	+	0.413688i	−0.295915	+	0.955214i	$0.595624\pi$
$338$	9.82189	+	8.24154i	0.534240	+	0.448281i
$339$	−17.3499			−0.942319
$340$	−2.80047	−	2.34987i	−0.151877	−	0.127440i
$341$	2.97972	+	5.16103i	0.161361	+	0.279486i
$342$	−2.78578	−	1.01394i	−0.150638	−	0.0548277i
$343$	−1.09468	+	1.89604i	−0.0591070	+	0.102376i
$344$	0.532529	+	0.922367i	0.0287120	+	0.0497307i
$345$	1.21216	+	6.87452i	0.0652607	+	0.370112i
$346$	−11.0652	+	4.02740i	−0.594869	+	0.216514i
$347$	11.4115	−	19.7653i	0.612601	−	1.06106i	−0.378199	−	0.925724i	$-0.623456\pi$
$347$	11.4115	−	19.7653i	0.612601	−	1.06106i	0.990800	−	0.135332i	$-0.0432102\pi$
$348$	3.60025	−	3.02097i	0.192994	−	0.161941i
$349$	4.21369	−	3.53570i	0.225554	−	0.189262i	−0.523007	−	0.852328i	$-0.675190\pi$
$349$	4.21369	−	3.53570i	0.225554	−	0.189262i	0.748560	+	0.663067i	$0.230745\pi$
$350$	−3.44009	−	1.25209i	−0.183881	−	0.0669271i
$351$	−0.188211	+	1.06740i	−0.0100460	+	0.0569736i
$352$	0.264176	−	1.49822i	0.0140806	−	0.0798552i
$353$	1.73359	+	0.630977i	0.0922699	+	0.0335835i	0.387743	−	0.921768i	$-0.373255\pi$
$353$	1.73359	+	0.630977i	0.0922699	+	0.0335835i	−0.295473	+	0.955351i	$0.595477\pi$
$354$	−22.7779	+	19.1129i	−1.21063	+	1.01584i
$355$	−12.3746	+	10.3835i	−0.656776	+	0.551101i
$356$	−1.58494	+	2.74519i	−0.0840014	+	0.145495i
$357$	27.6469	−	10.0627i	1.46323	−	0.532572i
$358$	−0.641647	−	3.63896i	−0.0339121	−	0.192325i
$359$	−4.97550	−	8.61782i	−0.262597	−	0.454831i	0.704334	−	0.709868i	$-0.251246\pi$
$359$	−4.97550	−	8.61782i	−0.262597	−	0.454831i	−0.966931	+	0.255037i	$0.917912\pi$
$360$	−0.916411	+	1.58727i	−0.0482991	+	0.0836565i
$361$	15.3957	+	5.60357i	0.810298	+	0.294924i
$362$	−6.07344	−	10.5195i	−0.319213	−	0.552893i
$363$	−14.6269	−	12.2734i	−0.767713	−	0.644188i
$364$	−1.54640			−0.0810534
$365$	−9.03614	−	7.58222i	−0.472973	−	0.396872i
$366$	24.9009	−	9.06319i	1.30159	−	0.473741i
$367$	5.36011	−	30.3987i	0.279795	−	1.58680i	−0.443510	−	0.896269i	$-0.646267\pi$
$367$	5.36011	−	30.3987i	0.279795	−	1.58680i	0.723305	−	0.690528i	$-0.242622\pi$
$368$	−0.551393	−	3.12710i	−0.0287433	−	0.163012i
$369$	7.69033			0.400343
$370$	5.62415	−	2.31711i	0.292385	−	0.120461i
$371$	−9.73106			−0.505212
$372$	1.49539	+	8.48076i	0.0775322	+	0.439707i
$373$	1.21019	−	6.86331i	0.0626611	−	0.355369i	−0.937315	−	0.348483i	$-0.886697\pi$
$373$	1.21019	−	6.86331i	0.0626611	−	0.355369i	0.999976	−	0.00688610i	$-0.00219193\pi$
$374$	−5.22619	+	1.90218i	−0.270240	+	0.0983593i
$375$	−1.68405	−	1.41308i	−0.0869638	−	0.0729713i
$376$	2.34549			0.120960
$377$	0.691784	+	0.580476i	0.0356287	+	0.0298960i
$378$	4.69669	+	8.13490i	0.241572	+	0.418414i
$379$	−22.4525	−	8.17205i	−1.15331	−	0.419770i	−0.306606	−	0.951836i	$-0.599194\pi$
$379$	−22.4525	−	8.17205i	−1.15331	−	0.419770i	−0.846703	+	0.532066i	$0.821416\pi$
$380$	−0.808745	+	1.40079i	−0.0414877	+	0.0718588i
$381$	2.77089	+	4.79932i	0.141957	+	0.245877i
$382$	1.43528	+	8.13985i	0.0734351	+	0.416471i
$383$	1.85800	−	0.676255i	0.0949392	−	0.0345550i	−0.294114	−	0.955770i	$-0.595024\pi$
$383$	1.85800	−	0.676255i	0.0949392	−	0.0345550i	0.389053	+	0.921215i	$0.372802\pi$
$384$	1.09918	−	1.90384i	0.0560925	−	0.0971551i
$385$	−4.26639	+	3.57993i	−0.217436	+	0.182450i
$386$	15.5979	−	13.0882i	0.793910	−	0.666170i
$387$	−1.83434	−	0.667644i	−0.0932446	−	0.0339382i
$388$	2.49757	−	14.1644i	0.126795	−	0.719089i
$389$	−5.79376	+	32.8581i	−0.293755	+	1.66597i	0.378463	+	0.925616i	$0.376453\pi$
$389$	−5.79376	+	32.8581i	−0.293755	+	1.66597i	−0.672218	+	0.740353i	$0.734658\pi$
$390$	−0.872617	−	0.317607i	−0.0441867	−	0.0160826i
$391$	−8.89244	+	7.46165i	−0.449710	+	0.377352i
$392$	−4.90418	+	4.11510i	−0.247699	+	0.207844i
$393$	23.0089	−	39.8525i	1.16064	−	2.01029i
$394$	5.48679	−	1.99703i	0.276421	−	0.100609i
$395$	−0.386057	−	2.18944i	−0.0194246	−	0.110163i
$396$	1.39416	+	2.41476i	0.0700592	+	0.121346i
$397$	15.1943	−	26.3174i	0.762582	−	1.32083i	−0.178934	−	0.983861i	$-0.557265\pi$
$397$	15.1943	−	26.3174i	0.762582	−	1.32083i	0.941516	−	0.336969i	$-0.109402\pi$
$398$	−9.49771	−	3.45688i	−0.476077	−	0.173278i
$399$	−6.50872	−	11.2734i	−0.325844	−	0.564378i
$400$	0.766044	+	0.642788i	0.0383022	+	0.0321394i
$401$	22.0012			1.09869			0.549343	−	0.835597i	$-0.314878\pi$
$401$	22.0012			1.09869			0.549343	+	0.835597i	$0.314878\pi$
$402$	21.3121	+	17.8830i	1.06295	+	0.891922i
$403$	−1.55492	+	0.565943i	−0.0774558	+	0.0281916i
$404$	−1.97773	+	11.2163i	−0.0983960	+	0.558031i
$405$	1.93431	+	10.9700i	0.0961165	+	0.545104i
$406$	7.82642			0.388419
$407$	1.22528	−	9.17240i	0.0607348	−	0.454659i
$408$	−8.03668			−0.397875
$409$	4.37133	+	24.7911i	0.216148	+	1.22584i	0.878902	+	0.477002i	$0.158276\pi$
$409$	4.37133	+	24.7911i	0.216148	+	1.22584i	−0.662754	+	0.748837i	$0.730612\pi$
$410$	0.728610	−	4.13215i	0.0359835	−	0.204072i
$411$	27.8125	−	10.1229i	1.37189	−	0.499328i
$412$	−4.46205	−	3.74411i	−0.219830	−	0.184459i
$413$	−49.5157			−2.43651
$414$	4.45825	+	3.74092i	0.219111	+	0.183856i
$415$	−6.49546	−	11.2505i	−0.318850	−	0.552264i
$416$	0.396939	+	0.144474i	0.0194615	+	0.00708342i
$417$	−1.63843	+	2.83785i	−0.0802343	+	0.138970i
$418$	1.23037	+	2.13106i	0.0601792	+	0.104233i
$419$	−5.81810	−	32.9961i	−0.284233	−	1.61196i	−0.708013	−	0.706200i	$-0.750408\pi$
$419$	−5.81810	−	32.9961i	−0.284233	−	1.61196i	0.423780	−	0.905765i	$-0.360703\pi$
$420$	−7.56259	+	2.75256i	−0.369016	+	0.134311i
$421$	−0.811520	+	1.40559i	−0.0395510	+	0.0685044i	−0.885123	−	0.465357i	$-0.845926\pi$
$421$	−0.811520	+	1.40559i	−0.0395510	+	0.0685044i	0.845572	+	0.533861i	$0.179259\pi$
$422$	13.1267	−	11.0146i	0.638997	−	0.536182i
$423$	−3.29313	+	2.76326i	−0.160117	+	0.134354i
$424$	2.49782	+	0.909134i	0.121305	+	0.0441514i
$425$	0.634814	−	3.60021i	0.0307930	−	0.174636i
$426$	−6.16664	+	34.9727i	−0.298775	+	1.69443i
$427$	41.4667	+	15.0926i	2.00671	+	0.730384i
$428$	−3.60867	+	3.02804i	−0.174432	+	0.146366i
$429$	−1.08222	+	0.908089i	−0.0522500	+	0.0438430i
$430$	−0.532529	+	0.922367i	−0.0256808	+	0.0444805i
$431$	−11.1419	+	4.05531i	−0.536685	+	0.195337i	−0.596121	−	0.802895i	$-0.703292\pi$
$431$	−11.1419	+	4.05531i	−0.536685	+	0.195337i	0.0594357	+	0.998232i	$0.481070\pi$
$432$	−0.445562	−	2.52691i	−0.0214371	−	0.121576i
$433$	−0.225709	−	0.390940i	−0.0108469	−	0.0187874i	0.860551	−	0.509364i	$-0.170119\pi$
$433$	−0.225709	−	0.390940i	−0.0108469	−	0.0187874i	−0.871398	+	0.490577i	$0.836786\pi$
$434$	−7.17030	+	12.4193i	−0.344185	+	0.596147i
$435$	4.41637	+	1.60743i	0.211749	+	0.0770702i
$436$	−0.486002	−	0.841781i	−0.0232753	−	0.0403140i
$437$	3.93447	+	3.30141i	0.188211	+	0.157928i
$438$	−25.9316			−1.23906
$439$	10.9031	+	9.14880i	0.520377	+	0.436648i	0.864763	−	0.502180i	$-0.167468\pi$
$439$	10.9031	+	9.14880i	0.520377	+	0.436648i	−0.344386	+	0.938828i	$0.611913\pi$
$440$	1.42958	−	0.520325i	0.0681526	−	0.0248055i
$441$	2.03753	−	11.5554i	0.0970250	−	0.550256i
$442$	−0.268154	−	1.52078i	−0.0127548	−	0.0723360i
$443$	−32.3338			−1.53622			−0.768112	−	0.640316i	$-0.778804\pi$
$443$	−32.3338			−1.53622			−0.768112	+	0.640316i	$0.778804\pi$
$444$	6.19706	−	11.8495i	0.294100	−	0.562353i
$445$	−3.16987			−0.150266
$446$	4.66951	+	26.4821i	0.221108	+	1.25397i
$447$	−5.71156	+	32.3918i	−0.270147	+	1.53208i
$448$	3.44009	−	1.25209i	0.162529	−	0.0591557i
$449$	8.59289	+	7.21029i	0.405523	+	0.340274i	0.822624	−	0.568586i	$-0.192509\pi$
$449$	8.59289	+	7.21029i	0.405523	+	0.340274i	−0.417101	+	0.908860i	$0.636954\pi$
$450$	−1.83282			−0.0864000
$451$	−4.88992	−	4.10313i	−0.230257	−	0.193209i
$452$	3.94610	+	6.83484i	0.185609	+	0.321484i
$453$	20.5919	+	7.49482i	0.967490	+	0.352137i
$454$	10.0166	−	17.3492i	0.470101	−	0.814240i
$455$	−0.773200	−	1.33922i	−0.0362482	−	0.0627837i
$456$	0.617465	+	3.50182i	0.0289154	+	0.163988i
$457$	−7.27593	+	2.64822i	−0.340354	+	0.123879i	−0.506542	−	0.862215i	$-0.669076\pi$
$457$	−7.27593	+	2.64822i	−0.340354	+	0.123879i	0.166188	+	0.986094i	$0.446854\pi$
$458$	12.3684	−	21.4227i	0.577937	−	1.00102i
$459$	−7.18568	+	6.02951i	−0.335399	+	0.281433i
$460$	2.43245	−	2.04107i	0.113414	−	0.0951654i
$461$	31.4616	+	11.4511i	1.46531	+	0.533330i	0.946824	−	0.321753i	$-0.104272\pi$
$461$	31.4616	+	11.4511i	1.46531	+	0.533330i	0.518490	+	0.855084i	$0.326494\pi$
$462$	−2.12607	+	12.0575i	−0.0989137	+	0.560968i
$463$	1.38675	−	7.86465i	0.0644478	−	0.365501i	−0.935479	−	0.353383i	$-0.885031\pi$
$463$	1.38675	−	7.86465i	0.0644478	−	0.365501i	0.999927	−	0.0121186i	$-0.00385756\pi$
$464$	−2.00893	−	0.731191i	−0.0932622	−	0.0339447i
$465$	−6.59686	+	5.53543i	−0.305922	+	0.256699i
$466$	−4.86509	+	4.08230i	−0.225371	+	0.189109i
$467$	−12.3958	+	21.4701i	−0.573607	+	0.993517i	0.422584	+	0.906324i	$0.361123\pi$
$467$	−12.3958	+	21.4701i	−0.573607	+	0.993517i	−0.996191	+	0.0871932i	$0.972210\pi$
$468$	−0.727518	+	0.264795i	−0.0336295	+	0.0122401i
$469$	8.04501	+	45.6255i	0.371484	+	2.10679i
$470$	1.17275	+	2.03126i	0.0540948	+	0.0936949i
$471$	9.19309	−	15.9229i	0.423595	−	0.733688i
$472$	12.7100	+	4.62605i	0.585024	+	0.212931i
$473$	0.810151	+	1.40322i	0.0372508	+	0.0645202i
$474$	−3.74400	−	3.14159i	−0.171967	−	0.144298i
$475$	−1.61749			−0.0742155
$476$	−10.2521	−	8.60257i	−0.469906	−	0.394298i
$477$	−4.57807	+	1.66628i	−0.209615	+	0.0762937i
$478$	−2.22808	+	12.6360i	−0.101910	+	0.577959i
$479$	−2.86332	−	16.2387i	−0.130828	−	0.741964i	−0.977674	−	0.210126i	$-0.932613\pi$
$479$	−2.86332	−	16.2387i	−0.130828	−	0.741964i	0.846846	−	0.531838i	$-0.178499\pi$
$480$	2.19837			0.100341
$481$	2.44905	+	0.777294i	0.111667	+	0.0354415i
$482$	19.0591			0.868120
$483$	4.43757	+	25.1667i	0.201917	+	1.14513i
$484$	−1.50823	+	8.55361i	−0.0685560	+	0.388800i
$485$	13.5155	−	4.91925i	0.613709	−	0.223372i
$486$	12.8622	+	10.7927i	0.583443	+	0.489567i
$487$	6.21076			0.281436			0.140718	−	0.990050i	$-0.455059\pi$
$487$	6.21076			0.281436			0.140718	+	0.990050i	$0.455059\pi$
$488$	−9.23386	−	7.74812i	−0.417997	−	0.350741i
$489$	13.7999	+	23.9022i	0.624055	+	1.08089i
$490$	−6.01587	−	2.18960i	−0.271769	−	0.0989160i
$491$	10.2832	−	17.8110i	0.464074	−	0.803800i	−0.535085	−	0.844798i	$-0.679720\pi$
$491$	10.2832	−	17.8110i	0.464074	−	0.803800i	0.999159	+	0.0409980i	$0.0130537\pi$
$492$	−4.61206	−	7.98833i	−0.207928	−	0.360142i
$493$	1.35714	+	7.69674i	0.0611226	+	0.346644i
$494$	−0.642044	+	0.233685i	−0.0288869	+	0.0105140i
$495$	−1.39416	+	2.41476i	−0.0626629	+	0.108535i
$496$	3.00080	−	2.51797i	0.134740	−	0.113060i
$497$	−45.3018	+	38.0128i	−2.03207	+	1.70511i
$498$	−26.8365	−	9.76769i	−1.20257	−	0.437701i
$499$	1.38131	−	7.83381i	0.0618360	−	0.350690i	−0.938154	−	0.346218i	$-0.887466\pi$
$499$	1.38131	−	7.83381i	0.0618360	−	0.350690i	0.999990	−	0.00447124i	$-0.00142325\pi$
$500$	−0.173648	+	0.984808i	−0.00776578	+	0.0440419i
$501$	6.20514	+	2.25849i	0.277225	+	0.100902i
$502$	20.3063	−	17.0390i	0.906313	−	0.760487i
$503$	−10.4804	+	8.79406i	−0.467296	+	0.392108i	−0.845807	−	0.533489i	$-0.820881\pi$
$503$	−10.4804	+	8.79406i	−0.467296	+	0.392108i	0.378511	+	0.925597i	$0.376436\pi$
$504$	−3.35486	+	5.81079i	−0.149437	+	0.258833i
$505$	−10.7025	+	3.89538i	−0.476253	+	0.173342i
$506$	−0.838849	−	4.75735i	−0.0372914	−	0.211490i
$507$	14.0933	+	24.4102i	0.625904	+	1.08410i
$508$	1.26043	−	2.18313i	0.0559225	−	0.0968607i
$509$	−36.8225	−	13.4023i	−1.63213	−	0.594047i	−0.646493	−	0.762920i	$-0.723765\pi$
$509$	−36.8225	−	13.4023i	−1.63213	−	0.594047i	−0.985638	+	0.168873i	$0.945987\pi$
$510$	−4.01834	−	6.95997i	−0.177935	−	0.308193i
$511$	−33.0801	−	27.7575i	−1.46338	−	1.22792i
$512$	−1.00000			−0.0441942
$513$	3.17931	+	2.66776i	0.140370	+	0.117784i
$514$	9.02234	−	3.28386i	0.397958	−	0.144845i
$515$	1.01147	−	5.73631i	0.0445705	−	0.252772i
$516$	0.406578	+	2.30582i	0.0178986	+	0.101508i
$517$	3.56826			0.156932
$518$	20.5893	−	8.48262i	0.904640	−	0.372705i
$519$	−25.8865			−1.13629
$520$	0.0733513	+	0.415996i	0.00321667	+	0.0182426i
$521$	4.21192	−	23.8870i	0.184527	−	1.04651i	−0.742034	−	0.670363i	$-0.766139\pi$
$521$	4.21192	−	23.8870i	0.184527	−	1.04651i	0.926561	−	0.376144i	$-0.122750\pi$
$522$	3.68201	−	1.34014i	0.161157	−	0.0586564i
$523$	−21.4648	−	18.0111i	−0.938590	−	0.787570i	0.0387495	−	0.999249i	$-0.487663\pi$
$523$	−21.4648	−	18.0111i	−0.938590	−	0.787570i	−0.977339	+	0.211679i	$0.932107\pi$
$524$	−20.9327			−0.914448
$525$	−6.16508	−	5.17311i	−0.269066	−	0.225773i
$526$	4.91826	+	8.51868i	0.214447	+	0.371432i
$527$	−13.4569	−	4.89792i	−0.586192	−	0.213357i
$528$	1.67222	−	2.89637i	0.0727740	−	0.126048i
$529$	6.45860	+	11.1866i	0.280809	+	0.486375i
$530$	0.461579	+	2.61775i	0.0200497	+	0.113708i
$531$	−23.2951	+	8.47872i	−1.01092	+	0.367945i
$532$	−2.96071	+	5.12810i	−0.128363	+	0.222331i
$533$	1.35774	−	1.13928i	0.0588102	−	0.0493476i
$534$	−5.33821	+	4.47929i	−0.231007	+	0.193838i
$535$	−4.42669	−	1.61119i	−0.191383	−	0.0696576i
$536$	2.19757	−	12.4630i	0.0949205	−	0.538321i
$537$	1.41058	−	7.99977i	0.0608708	−	0.345216i
$538$	−12.1805	−	4.43333i	−0.525137	−	0.191134i
$539$	−7.46087	+	6.26042i	−0.321363	+	0.269655i
$540$	1.96558	−	1.64932i	0.0845853	−	0.0709755i
$541$	−11.4683	+	19.8636i	−0.493060	+	0.854005i	−0.999968	−	0.00799519i	$-0.997455\pi$
$541$	−11.4683	+	19.8636i	−0.493060	+	0.854005i	0.506908	+	0.862000i	$0.330788\pi$
$542$	−1.38473	+	0.504000i	−0.0594792	+	0.0216487i
$543$	−4.63698	−	26.2976i	−0.198992	−	1.12854i
$544$	1.82787	+	3.16597i	0.0783695	+	0.135740i
$545$	0.486002	−	0.841781i	0.0208181	−	0.0360579i
$546$	−3.19454	−	1.16272i	−0.136714	−	0.0497597i
$547$	−15.6882	−	27.1728i	−0.670779	−	1.16182i	−0.977684	−	0.210083i	$-0.932627\pi$
$547$	−15.6882	−	27.1728i	−0.670779	−	1.16182i	0.306905	−	0.951740i	$-0.400707\pi$
$548$	−10.3136	−	8.65410i	−0.440573	−	0.369685i
$549$	22.0927			0.942894
$550$	1.16540	+	0.977891i	0.0496930	+	0.0416974i
$551$	3.24942	−	1.18269i	0.138430	−	0.0503844i
$552$	1.21216	−	6.87452i	0.0515931	−	0.292599i
$553$	−1.41330	−	8.01524i	−0.0600998	−	0.340843i
$554$	−28.0299			−1.19088
$555$	13.3605	−	0.557937i	0.567122	−	0.0236831i
$556$	1.49059			0.0632150
$557$	−0.0936074	−	0.530874i	−0.00396627	−	0.0224939i	0.982760	−	0.184884i	$-0.0591909\pi$
$557$	−0.0936074	−	0.530874i	−0.00396627	−	0.0224939i	−0.986727	+	0.162390i	$0.948080\pi$
$558$	−1.24673	+	7.07058i	−0.0527784	+	0.299321i
$559$	−0.422763	+	0.153873i	−0.0178810	+	0.00650813i
$560$	2.80439	+	2.35316i	0.118507	+	0.0994392i
$561$	−12.2264			−0.516200
$562$	7.88230	+	6.61404i	0.332495	+	0.278996i
$563$	18.6099	+	32.2332i	0.784312	+	1.35847i	0.929409	+	0.369051i	$0.120317\pi$
$563$	18.6099	+	32.2332i	0.784312	+	1.35847i	−0.145097	+	0.989417i	$0.546350\pi$
$564$	4.84530	+	1.76354i	0.204024	+	0.0742586i
$565$	−3.94610	+	6.83484i	−0.166013	+	0.287544i
$566$	−16.6226	−	28.7912i	−0.698700	−	1.21018i
$567$	7.08124	+	40.1597i	0.297384	+	1.68655i
$568$	15.1797	−	5.52496i	0.636927	−	0.231822i
$569$	5.11977	−	8.86771i	0.214632	−	0.371754i	−0.738527	−	0.674224i	$-0.764478\pi$
$569$	5.11977	−	8.86771i	0.214632	−	0.371754i	0.953159	+	0.302471i	$0.0978114\pi$
$570$	−2.72393	+	2.28565i	−0.114093	+	0.0957352i
$571$	32.9612	−	27.6578i	1.37938	−	1.15744i	0.409945	−	0.912110i	$-0.365548\pi$
$571$	32.9612	−	27.6578i	1.37938	−	1.15744i	0.969439	−	0.245331i	$-0.0788967\pi$
$572$	0.603874	+	0.219792i	0.0252492	+	0.00918997i
$573$	−3.15526	+	17.8944i	−0.131813	+	0.747549i
$574$	2.66734	−	15.1273i	0.111333	−	0.631400i
$575$	2.98385	+	1.08603i	0.124435	+	0.0452906i
$576$	1.40402	−	1.17811i	0.0585009	−	0.0490881i
$577$	−26.5217	+	22.2544i	−1.10411	+	0.926462i	−0.997695	−	0.0678595i	$-0.978383\pi$
$577$	−26.5217	+	22.2544i	−1.10411	+	0.926462i	−0.106419	+	0.994321i	$0.533939\pi$
$578$	−1.81775	+	3.14843i	−0.0756083	+	0.130957i
$579$	42.0627	−	15.3096i	1.74807	−	0.636244i
$580$	−0.371235	−	2.10538i	−0.0154147	−	0.0874211i
$581$	−23.7790	−	41.1865i	−0.986520	−	1.70870i
$582$	15.8095	−	27.3828i	0.655324	−	1.13505i
$583$	3.80001	+	1.38309i	0.157380	+	0.0572818i
$584$	5.89792	+	10.2155i	0.244058	+	0.422721i
$585$	−0.593078	−	0.497652i	−0.0245208	−	0.0205754i
$586$	−24.5666			−1.01484
$587$	−25.1954	−	21.1414i	−1.03993	−	0.872601i	−0.0479267	−	0.998851i	$-0.515261\pi$
$587$	−25.1954	−	21.1414i	−1.03993	−	0.872601i	−0.991998	+	0.126250i	$0.959706\pi$
$588$	−13.2251	+	4.81354i	−0.545394	+	0.198507i
$589$	−1.10026	+	6.23988i	−0.0453354	+	0.257110i
$590$	2.34871	+	13.3202i	0.0966948	+	0.548383i
$591$	12.8361			0.528007
$592$	−6.07747	+	0.253796i	−0.249782	+	0.0104310i
$593$	−30.3849			−1.24776			−0.623878	−	0.781521i	$-0.714444\pi$
$593$	−30.3849			−1.24776			−0.623878	+	0.781521i	$0.714444\pi$
$594$	−0.677846	−	3.84425i	−0.0278123	−	0.157732i
$595$	2.32397	−	13.1799i	0.0952735	−	0.540323i
$596$	14.0595	−	5.11724i	0.575899	−	0.209610i
$597$	−17.0211	−	14.2824i	−0.696627	−	0.584539i
$598$	1.34131			0.0548502
$599$	−24.9091	−	20.9012i	−1.01776	−	0.854000i	−0.0284138	−	0.999596i	$-0.509046\pi$
$599$	−24.9091	−	20.9012i	−1.01776	−	0.854000i	−0.989344	+	0.145596i	$0.953490\pi$
$600$	1.09918	+	1.90384i	0.0448740	+	0.0777240i
$601$	−23.1059	−	8.40986i	−0.942509	−	0.343045i	−0.175353	−	0.984506i	$-0.556107\pi$
$601$	−23.1059	−	8.40986i	−0.942509	−	0.343045i	−0.767156	+	0.641460i	$0.778329\pi$
$602$	−1.94952	+	3.37666i	−0.0794564	+	0.137623i
$603$	11.5974	+	20.0874i	0.472284	+	0.818021i
$604$	−1.73093	−	9.81659i	−0.0704305	−	0.399431i
$605$	−8.16176	+	2.97064i	−0.331823	+	0.120774i
$606$	−12.5190	+	21.6835i	−0.508548	+	0.880831i
$607$	−16.2047	+	13.5974i	−0.657730	+	0.551901i	−0.909406	−	0.415910i	$-0.863463\pi$
$607$	−16.2047	+	13.5974i	−0.657730	+	0.551901i	0.251675	+	0.967812i	$0.419019\pi$
$608$	1.23907	−	1.03970i	0.0502509	−	0.0421655i
$609$	16.1677	+	5.88457i	0.655150	+	0.238455i
$610$	2.09315	−	11.8708i	0.0847490	−	0.480635i
$611$	−0.172045	+	0.975716i	−0.00696020	+	0.0394732i
$612$	−6.29626	−	2.29165i	−0.254511	−	0.0926345i
$613$	−14.5146	+	12.1792i	−0.586240	+	0.491913i	−0.886989	−	0.461790i	$-0.847208\pi$
$613$	−14.5146	+	12.1792i	−0.586240	+	0.491913i	0.300750	+	0.953703i	$0.402763\pi$
$614$	2.52730	−	2.12066i	0.101994	−	0.0855828i
$615$	4.61206	−	7.98833i	0.185976	−	0.322120i
$616$	5.23351	−	1.90484i	0.210864	−	0.0767482i
$617$	2.65957	+	15.0832i	0.107070	+	0.607225i	0.990373	+	0.138423i	$0.0442032\pi$
$617$	2.65957	+	15.0832i	0.107070	+	0.607225i	−0.883303	+	0.468802i	$0.844686\pi$
$618$	−6.40252	−	11.0895i	−0.257547	−	0.446085i
$619$	−0.577898	+	1.00095i	−0.0232277	+	0.0402316i	−0.877406	−	0.479749i	$-0.840728\pi$
$619$	−0.577898	+	1.00095i	−0.0232277	+	0.0402316i	0.854178	+	0.519981i	$0.174061\pi$
$620$	3.68103	+	1.33978i	0.147834	+	0.0538070i
$621$	−4.07379	−	7.05601i	−0.163475	−	0.283148i
$622$	−22.2513	−	18.6710i	−0.892195	−	0.748640i
$623$	−11.6045			−0.464924
$624$	0.711364	+	0.596906i	0.0284774	+	0.0238953i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	−2.43948	+	13.8350i	−0.0975011	+	0.552956i
$627$	0.939366	+	5.32741i	0.0375147	+	0.212756i
$628$	−8.36356			−0.333742
$629$	11.9124	+	18.7772i	0.474977	+	0.748695i
$630$	−6.70972			−0.267322
$631$	4.19876	+	23.8124i	0.167150	+	0.947955i	0.946820	+	0.321764i	$0.104276\pi$
$631$	4.19876	+	23.8124i	0.167150	+	0.947955i	−0.779670	+	0.626191i	$0.784613\pi$
$632$	−0.386057	+	2.18944i	−0.0153565	+	0.0870911i
$633$	35.3987	−	12.8841i	1.40697	−	0.512096i
$634$	−1.43671	−	1.20554i	−0.0570591	−	0.0478783i
$635$	2.52086			0.100037
$636$	4.47642	+	3.75616i	0.177501	+	0.148941i
$637$	−1.35214	−	2.34197i	−0.0535736	−	0.0927922i
$638$	−3.05624	−	1.11238i	−0.120998	−	0.0440396i
$639$	−14.8036	+	25.6406i	−0.585622	+	1.01433i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	0.0931463	+	0.528259i	0.00367906	+	0.0208650i	0.986592	−	0.163206i	$-0.0521835\pi$
$641$	0.0931463	+	0.528259i	0.00367906	+	0.0208650i	−0.982913	+	0.184071i	$0.941072\pi$
$642$	−9.73150	+	3.54198i	−0.384072	+	0.139791i
$643$	17.3974	−	30.1332i	0.686087	−	1.18834i	−0.287007	−	0.957929i	$-0.592660\pi$
$643$	17.3974	−	30.1332i	0.686087	−	1.18834i	0.973094	−	0.230409i	$-0.0740064\pi$
$644$	8.90489	−	7.47209i	0.350902	−	0.294442i
$645$	−1.79361	+	1.50502i	−0.0706232	+	0.0592599i
$646$	−5.55653	−	2.02241i	−0.218619	−	0.0795707i
$647$	−2.80043	+	15.8820i	−0.110096	+	0.624387i	0.878966	+	0.476885i	$0.158234\pi$
$647$	−2.80043	+	15.8820i	−0.110096	+	0.624387i	−0.989062	+	0.147502i	$0.952877\pi$
$648$	1.93431	−	10.9700i	0.0759868	−	0.430942i
$649$	19.3360	+	7.03774i	0.759006	+	0.276255i
$650$	−0.323587	+	0.271522i	−0.0126921	+	0.0106500i
$651$	−24.1502	+	20.2645i	−0.946523	+	0.794227i
$652$	6.27736	−	10.8727i	0.245840	−	0.425808i
$653$	−29.0127	+	10.5598i	−1.13535	+	0.413235i	−0.840233	−	0.542225i	$-0.817582\pi$
$653$	−29.0127	+	10.5598i	−1.13535	+	0.413235i	−0.295121	+	0.955460i	$0.595360\pi$
$654$	−0.371056	−	2.10436i	−0.0145094	−	0.0822870i
$655$	−10.4663	−	18.1282i	−0.408954	−	0.708329i
$656$	−2.09795	+	3.63375i	−0.0819111	+	0.141874i
$657$	−20.3159	−	7.39437i	−0.792597	−	0.288482i
$658$	4.29327	+	7.43616i	0.167369	+	0.289892i
$659$	−8.51746	−	7.14700i	−0.331793	−	0.278407i	0.461637	−	0.887069i	$-0.347262\pi$
$659$	−8.51746	−	7.14700i	−0.331793	−	0.278407i	−0.793430	+	0.608662i	$0.791707\pi$
$660$	3.34444			0.130182
$661$	22.9362	+	19.2457i	0.892114	+	0.748572i	0.968633	−	0.248496i	$-0.0799362\pi$
$661$	22.9362	+	19.2457i	0.892114	+	0.748572i	−0.0765192	+	0.997068i	$0.524381\pi$
$662$	−12.8328	+	4.67075i	−0.498760	+	0.181534i
$663$	0.589501	−	3.34323i	0.0228943	−	0.129840i
$664$	2.25585	+	12.7936i	0.0875439	+	0.496486i
$665$	−5.92142			−0.229623
$666$	8.23390	−	7.51629i	0.319057	−	0.291250i
$667$	−6.78843			−0.262849
$668$	−0.521597	−	2.95813i	−0.0201812	−	0.114453i
$669$	−10.2653	+	58.2175i	−0.396880	+	2.25082i
$670$	11.8921	−	4.32836i	0.459431	−	0.167219i
$671$	−14.0477	−	11.7874i	−0.542306	−	0.455049i
$672$	8.04794			0.310456
$673$	13.2758	+	11.1397i	0.511745	+	0.429405i	0.861743	−	0.507346i	$-0.169373\pi$
$673$	13.2758	+	11.1397i	0.511745	+	0.429405i	−0.349998	+	0.936750i	$0.613818\pi$
$674$	11.1021	+	19.2294i	0.427638	+	0.740690i
$675$	2.41115	+	0.877585i	0.0928051	+	0.0337783i
$676$	6.41078	−	11.1038i	0.246569	−	0.427069i
$677$	23.4313	+	40.5842i	0.900538	+	1.55978i	0.826798	+	0.562500i	$0.190160\pi$
$677$	23.4313	+	40.5842i	0.900538	+	1.55978i	0.0737403	+	0.997277i	$0.476506\pi$
$678$	3.01279	+	17.0864i	0.115705	+	0.656198i
$679$	49.4786	−	18.0087i	1.89881	−	0.691112i
$680$	−1.82787	+	3.16597i	−0.0700958	+	0.121409i
$681$	33.7368	−	28.3085i	1.29280	−	1.08479i
$682$	4.56520	−	3.83066i	0.174811	−	0.146684i
$683$	32.9556	+	11.9949i	1.26101	+	0.458970i	0.884108	−	0.467282i	$-0.154767\pi$
$683$	32.9556	+	11.9949i	1.26101	+	0.458970i	0.376903	+	0.926253i	$0.376989\pi$
$684$	−0.514792	+	2.91953i	−0.0196836	+	0.111631i
$685$	2.33789	−	13.2589i	0.0893263	−	0.506595i
$686$	2.05732	+	0.748804i	0.0785489	+	0.0285895i
$687$	41.6579	−	34.9551i	1.58935	−	1.33362i
$688$	0.815881	−	0.684606i	0.0311052	−	0.0261003i
$689$	−0.561415	+	0.972399i	−0.0213882	+	0.0370455i
$690$	6.55959	−	2.38750i	0.249719	−	0.0908904i
$691$	−0.446075	−	2.52982i	−0.0169695	−	0.0962387i	0.975147	−	0.221560i	$-0.0711149\pi$
$691$	−0.446075	−	2.52982i	−0.0169695	−	0.0962387i	−0.992116	+	0.125321i	$0.960004\pi$
$692$	5.88767	+	10.1977i	0.223816	+	0.387660i
$693$	−5.10384	+	8.84011i	−0.193879	+	0.335808i
$694$	−21.4466	−	7.80593i	−0.814102	−	0.296309i
$695$	0.745294	+	1.29089i	0.0282706	+	0.0489662i
$696$	−3.60025	−	3.02097i	−0.136467	−	0.114510i
$697$	15.3391			0.581012
$698$	−4.21369	−	3.53570i	−0.159490	−	0.133828i
$699$	−13.1197	+	4.77517i	−0.496232	+	0.180614i
$700$	−0.635703	+	3.60525i	−0.0240273	+	0.136266i
$701$	−2.11891	−	12.0169i	−0.0800302	−	0.453874i	−0.998319	−	0.0579622i	$-0.981540\pi$
$701$	−2.11891	−	12.0169i	−0.0800302	−	0.453874i	0.918289	−	0.395912i	$-0.129571\pi$
$702$	1.08387			0.0409079
$703$	7.26652	−	6.63322i	0.274062	−	0.250177i
$704$	−1.52133			−0.0573372
$705$	0.895375	+	5.07792i	0.0337218	+	0.191246i
$706$	0.320355	−	1.81682i	0.0120567	−	0.0683771i
$707$	−39.1803	+	14.2605i	−1.47353	+	0.536320i
$708$	22.7779	+	19.1129i	0.856045	+	0.718307i
$709$	16.1474			0.606430			0.303215	−	0.952922i	$-0.401940\pi$
$709$	16.1474			0.606430			0.303215	+	0.952922i	$0.401940\pi$
$710$	12.3746	+	10.3835i	0.464411	+	0.389687i
$711$	−2.03738	−	3.52884i	−0.0764076	−	0.132342i
$712$	2.97871	+	1.08416i	0.111632	+	0.0406306i
$713$	6.21933	−	10.7722i	0.232916	−	0.403422i
$714$	−14.7106	−	25.4795i	−0.550531	−	0.953548i
$715$	0.111591	+	0.632866i	0.00417328	+	0.0236679i
$716$	−3.47226	+	1.26380i	−0.129764	+	0.0472303i
$717$	−14.1036	+	24.4282i	−0.526709	+	0.912286i
$718$	−7.62291	+	6.39638i	−0.284484	+	0.238711i
$719$	20.8221	−	17.4718i	0.776533	−	0.651589i	−0.165840	−	0.986153i	$-0.553034\pi$
$719$	20.8221	−	17.4718i	0.776533	−	0.651589i	0.942373	+	0.334564i	$0.108589\pi$
$720$	1.72229	+	0.626862i	0.0641859	+	0.0233618i
$721$	3.70284	−	20.9999i	0.137901	−	0.782076i
$722$	2.84500	−	16.1348i	0.105880	−	0.600476i
$723$	39.3722	+	14.3303i	1.46427	+	0.532950i
$724$	−9.30505	+	7.80786i	−0.345819	+	0.290177i
$725$	1.63769	−	1.37419i	0.0608224	−	0.0510361i
$726$	−9.54703	+	16.5359i	−0.354323	+	0.613706i
$727$	11.7709	−	4.28425i	0.436558	−	0.158894i	−0.114386	−	0.993436i	$-0.536490\pi$
$727$	11.7709	−	4.28425i	0.436558	−	0.158894i	0.550944	+	0.834542i	$0.314268\pi$
$728$	0.268530	+	1.52291i	0.00995237	+	0.0564427i
$729$	1.74696	+	3.02582i	0.0647022	+	0.112068i
$730$	−5.89792	+	10.2155i	−0.218292	+	0.378093i
$731$	−3.65877	−	1.33168i	−0.135325	−	0.0492541i
$732$	−13.2495	−	22.9488i	−0.489716	−	0.848212i
$733$	19.0358	+	15.9729i	0.703103	+	0.589973i	0.922655	−	0.385628i	$-0.126015\pi$
$733$	19.0358	+	15.9729i	0.703103	+	0.589973i	−0.219552	+	0.975601i	$0.570459\pi$
$734$	−30.8676			−1.13934
$735$	−10.7812	−	9.04650i	−0.397671	−	0.333685i
$736$	−2.98385	+	1.08603i	−0.109986	+	0.0400316i
$737$	3.34322	−	18.9604i	0.123149	−	0.698414i
$738$	−1.33541	−	7.57350i	−0.0491572	−	0.278784i
$739$	33.7671			1.24214			0.621072	−	0.783754i	$-0.286698\pi$
$739$	33.7671			1.24214			0.621072	+	0.783754i	$0.286698\pi$
$740$	−3.25853	−	5.13634i	−0.119786	−	0.188816i
$741$	−1.50203			−0.0551786
$742$	1.68978	+	9.58323i	0.0620338	+	0.351811i
$743$	−4.14031	+	23.4809i	−0.151893	+	0.861430i	0.809678	+	0.586874i	$0.199642\pi$
$743$	−4.14031	+	23.4809i	−0.151893	+	0.861430i	−0.961571	+	0.274555i	$0.911469\pi$
$744$	8.09225	−	2.94534i	0.296676	−	0.107981i
$745$	11.4614	+	9.61726i	0.419913	+	0.352349i
$746$	−6.96919			−0.255160
$747$	−18.2395	−	15.3048i	−0.667350	−	0.559973i
$748$	2.78080	+	4.81648i	0.101676	+	0.176108i
$749$	−16.2055	−	5.89834i	−0.592138	−	0.215521i
$750$	−1.09918	+	1.90384i	−0.0401365	+	0.0695185i
$751$	10.1621	+	17.6013i	0.370821	+	0.642280i	0.989692	−	0.143212i	$-0.0457431\pi$
$751$	10.1621	+	17.6013i	0.370821	+	0.642280i	−0.618871	+	0.785492i	$0.712410\pi$
$752$	−0.407291	−	2.30986i	−0.0148524	−	0.0842319i
$753$	54.7598	−	19.9309i	1.99556	−	0.726324i
$754$	0.451530	−	0.782073i	0.0164438	−	0.0284814i
$755$	7.63595	−	6.40733i	0.277901	−	0.233186i
$756$	7.19575	−	6.03795i	0.261707	−	0.219598i
$757$	10.1089	+	3.67933i	0.367414	+	0.133728i	0.519128	−	0.854697i	$-0.326257\pi$
$757$	10.1089	+	3.67933i	0.367414	+	0.133728i	−0.151714	+	0.988424i	$0.548479\pi$
$758$	−4.14906	+	23.5305i	−0.150701	+	0.854666i
$759$	1.84410	−	10.4584i	0.0669365	−	0.379616i
$760$	1.51994	+	0.553214i	0.0551341	+	0.0200672i
$761$	−1.55481	+	1.30464i	−0.0563619	+	0.0472932i	−0.670533	−	0.741879i	$-0.733935\pi$
$761$	−1.55481	+	1.30464i	−0.0563619	+	0.0472932i	0.614172	+	0.789173i	$0.289490\pi$
$762$	4.24525	−	3.56219i	0.153789	−	0.129044i
$763$	1.77919	−	3.08165i	0.0644110	−	0.111563i
$764$	7.76696	−	2.82694i	0.280999	−	0.102275i
$765$	−1.16350	−	6.59854i	−0.0420665	−	0.238571i
$766$	−0.988619	−	1.71234i	−0.0357203	−	0.0618693i
$767$	−2.85671	+	4.94797i	−0.103150	+	0.178661i
$768$	−2.06579	−	0.751886i	−0.0745428	−	0.0271314i
$769$	−12.2272	−	21.1782i	−0.440926	−	0.763706i	0.556833	−	0.830625i	$-0.312016\pi$
$769$	−12.2272	−	21.1782i	−0.440926	−	0.763706i	−0.997758	+	0.0669191i	$0.978683\pi$
$770$	4.26639	+	3.57993i	0.153750	+	0.129012i
$771$	21.1073			0.760163
$772$	−15.5979	−	13.0882i	−0.561379	−	0.471053i
$773$	−5.04909	+	1.83772i	−0.181603	+	0.0660981i	−0.431221	−	0.902246i	$-0.641917\pi$
$773$	−5.04909	+	1.83772i	−0.181603	+	0.0660981i	0.249618	+	0.968344i	$0.419695\pi$
$774$	−0.338972	+	1.92240i	−0.0121841	+	0.0690994i
$775$	0.680226	+	3.85775i	0.0244344	+	0.138575i
$776$	−14.3829			−0.516317
$777$	48.9111	−	2.04253i	1.75467	−	0.0732755i
$778$	33.3649			1.19619
$779$	−1.17852	−	6.68371i	−0.0422248	−	0.239469i
$780$	−0.161253	+	0.914512i	−0.00577379	+	0.0327448i
$781$	23.0933	−	8.40528i	0.826344	−	0.300765i
$782$	8.89244	+	7.46165i	0.317993	+	0.266828i
$783$	−5.48551			−0.196036
$784$	4.90418	+	4.11510i	0.175149	+	0.146968i
$785$	−4.18178	−	7.24305i	−0.149254	−	0.258516i
$786$	−43.2425	−	15.7390i	−1.54241	−	0.561391i
$787$	−25.4345	+	44.0538i	−0.906641	+	1.57035i	−0.0879413	+	0.996126i	$0.528029\pi$
$787$	−25.4345	+	44.0538i	−0.906641	+	1.57035i	−0.818699	+	0.574222i	$0.805305\pi$
$788$	−2.91946	−	5.05666i	−0.104002	−	0.180136i
$789$	3.75502	+	21.2958i	0.133682	+	0.758150i
$790$	−2.08914	+	0.760384i	−0.0743282	+	0.0270532i
$791$	−14.4461	+	25.0214i	−0.513646	+	0.889660i
$792$	2.13598	−	1.79230i	0.0758987	−	0.0636866i
$793$	3.90050	−	3.27291i	0.138511	−	0.116225i
$794$	−28.5560	−	10.3935i	−1.01341	−	0.368853i
$795$	−1.01472	+	5.75477i	−0.0359885	+	0.204101i
$796$	−1.75511	+	9.95370i	−0.0622081	+	0.352799i
$797$	51.9345	+	18.9026i	1.83961	+	0.669565i	0.989797	+	0.142488i	$0.0455101\pi$
$797$	51.9345	+	18.9026i	1.83961	+	0.669565i	0.849817	+	0.527077i	$0.176712\pi$
$798$	−9.97194	+	8.36746i	−0.353003	+	0.296205i
$799$	−6.56848	+	5.51161i	−0.232376	+	0.194987i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−5.45943	+	1.98707i	−0.192900	+	0.0702097i
$802$	−3.82046	−	21.6669i	−0.134905	−	0.765086i
$803$	8.97268	+	15.5411i	0.316639	+	0.548435i
$804$	13.9105	−	24.0937i	0.490585	−	0.849719i
$805$	10.9235	+	3.97582i	0.385002	+	0.140129i
$806$	0.827353	+	1.43302i	0.0291423	+	0.0504759i
$807$	−21.8289	−	18.3166i	−0.768415	−	0.644777i
$808$	11.3893			0.400675
$809$	8.89437	+	7.46326i	0.312709	+	0.262394i	0.785611	−	0.618721i	$-0.212349\pi$
$809$	8.89437	+	7.46326i	0.312709	+	0.262394i	−0.472901	+	0.881115i	$0.656793\pi$
$810$	10.4675	−	3.80984i	0.367789	−	0.133864i
$811$	−4.86130	+	27.5698i	−0.170703	+	0.968107i	0.772284	+	0.635278i	$0.219114\pi$
$811$	−4.86130	+	27.5698i	−0.170703	+	0.968107i	−0.942987	+	0.332829i	$0.891997\pi$
$812$	−1.35904	−	7.70752i	−0.0476931	−	0.270481i
$813$	−3.23951			−0.113615
$814$	−9.24582	+	0.386107i	−0.324066	+	0.0135330i
$815$	12.5547			0.439772
$816$	1.39556	+	7.91459i	0.0488542	+	0.277066i
$817$	−0.299147	+	1.69655i	−0.0104658	+	0.0593547i
$818$	23.6553	−	8.60984i	0.827090	−	0.301036i
$819$	−2.17118	−	1.82184i	−0.0758672	−	0.0636601i
$820$	−4.19590			−0.146527
$821$	27.5361	+	23.1055i	0.961017	+	0.806389i	0.981118	−	0.193409i	$-0.0619543\pi$
$821$	27.5361	+	23.1055i	0.961017	+	0.806389i	−0.0201010	+	0.999798i	$0.506399\pi$
$822$	−14.7987	−	25.6322i	−0.516165	−	0.894025i
$823$	21.6145	+	7.86703i	0.753434	+	0.274228i	0.690050	−	0.723762i	$-0.257589\pi$
$823$	21.6145	+	7.86703i	0.753434	+	0.274228i	0.0633839	+	0.997989i	$0.479811\pi$
$824$	−2.91240	+	5.04442i	−0.101458	+	0.175731i
$825$	1.67222	+	2.89637i	0.0582192	+	0.100839i
$826$	8.59831	+	48.7634i	0.299173	+	1.69670i
$827$	28.1210	−	10.2352i	0.977863	−	0.355913i	0.196854	−	0.980433i	$-0.436928\pi$
$827$	28.1210	−	10.2352i	0.977863	−	0.355913i	0.781009	+	0.624520i	$0.214705\pi$
$828$	2.90992	−	5.04013i	0.101127	−	0.175157i
$829$	−5.62083	+	4.71644i	−0.195219	+	0.163809i	−0.735158	−	0.677896i	$-0.762892\pi$
$829$	−5.62083	+	4.71644i	−0.195219	+	0.163809i	0.539938	+	0.841705i	$0.318448\pi$
$830$	−9.95162	+	8.35040i	−0.345426	+	0.289847i
$831$	−57.9039	−	21.0753i	−2.00866	−	0.731094i
$832$	0.0733513	−	0.415996i	0.00254300	−	0.0144221i
$833$	4.06405	−	23.0484i	0.140811	−	0.798580i
$834$	3.07924	+	1.12075i	0.106625	+	0.0388085i
$835$	2.30101	−	1.93078i	0.0796299	−	0.0668174i
$836$	1.88503	−	1.58173i	0.0651951	−	0.0547052i
$837$	5.02563	−	8.70465i	0.173711	−	0.300877i
$838$	−31.4845	+	11.4594i	−1.08761	+	0.395859i
$839$	3.22039	+	18.2637i	0.111180	+	0.630534i	0.988571	+	0.150757i	$0.0481712\pi$
$839$	3.22039	+	18.2637i	0.111180	+	0.630534i	−0.877391	+	0.479777i	$0.840718\pi$
$840$	4.02397	+	6.96972i	0.138840	+	0.240478i
$841$	12.2148	−	21.1566i	0.421199	−	0.729539i
$842$	1.52516	+	0.555112i	0.0525604	+	0.0191304i
$843$	11.3102	+	19.5898i	0.389543	+	0.674709i
$844$	−13.1267	−	11.0146i	−0.451839	−	0.379138i
$845$	12.8216			0.441075
$846$	3.29313	+	2.76326i	0.113220	+	0.0950028i
$847$	−29.8791	+	10.8751i	−1.02666	+	0.373673i
$848$	0.461579	−	2.61775i	0.0158507	−	0.0898938i
$849$	−12.6911	−	71.9749i	−0.435558	−	2.47017i
$850$	−3.65575			−0.125391
$851$	−17.8586	+	7.35761i	−0.612185	+	0.252216i
$852$	35.5122			1.21663
$853$	−1.83151	−	10.3870i	−0.0627097	−	0.355644i	−0.999975	−	0.00702814i	$-0.997763\pi$
$853$	−1.83151	−	10.3870i	−0.0627097	−	0.355644i	0.937266	−	0.348616i	$-0.113348\pi$
$854$	7.66273	−	43.4575i	0.262213	−	1.48708i
$855$	−2.78578	+	1.01394i	−0.0952718	+	0.0346761i
$856$	3.60867	+	3.02804i	0.123342	+	0.103496i
$857$	−1.19774			−0.0409141			−0.0204570	−	0.999791i	$-0.506512\pi$
$857$	−1.19774			−0.0409141			−0.0204570	+	0.999791i	$0.506512\pi$
$858$	1.08222	+	0.908089i	0.0369463	+	0.0310016i
$859$	−4.64701	−	8.04886i	−0.158554	−	0.274624i	0.775793	−	0.630987i	$-0.217350\pi$
$859$	−4.64701	−	8.04886i	−0.158554	−	0.274624i	−0.934347	+	0.356363i	$0.884017\pi$
$860$	1.00083	+	0.364271i	0.0341279	+	0.0124215i
$861$	16.8842	−	29.2442i	0.575410	−	0.996640i
$862$	5.92847	+	10.2684i	0.201924	+	0.349743i
$863$	−2.65814	−	15.0750i	−0.0904840	−	0.513161i	−0.996038	−	0.0889293i	$-0.971655\pi$
$863$	−2.65814	−	15.0750i	−0.0904840	−	0.513161i	0.905554	−	0.424231i	$-0.139456\pi$
$864$	−2.41115	+	0.877585i	−0.0820289	+	0.0298561i
$865$	−5.88767	+	10.1977i	−0.200187	+	0.346734i
$866$	−0.345806	+	0.290166i	−0.0117510	+	0.00986024i
$867$	−6.12234	+	5.13726i	−0.207926	+	0.174470i
$868$	13.4758	+	4.90477i	0.457397	+	0.166479i
$869$	−0.587319	+	3.33085i	−0.0199234	+	0.112991i
$870$	0.816112	−	4.62840i	0.0276688	−	0.156917i
$871$	5.02338	+	1.82836i	0.170211	+	0.0619516i
$872$	−0.744599	+	0.624793i	−0.0252153	+	0.0211581i
$873$	20.1940	−	16.9447i	0.683462	−	0.573493i
$874$	2.56804	−	4.44798i	0.0868653	−	0.150455i
$875$	−3.44009	+	1.25209i	−0.116296	+	0.0423284i
$876$	4.50298	+	25.5377i	0.152141	+	0.862837i
$877$	1.85636	+	3.21532i	0.0626849	+	0.108574i	0.895665	−	0.444730i	$-0.146700\pi$
$877$	1.85636	+	3.21532i	0.0626849	+	0.108574i	−0.832980	+	0.553303i	$0.813367\pi$
$878$	7.11650	−	12.3261i	0.240170	−	0.415987i
$879$	−50.7494	−	18.4713i	−1.71173	−	0.623020i
$880$	−0.760664	−	1.31751i	−0.0256420	−	0.0444132i
$881$	−9.37099	−	7.86319i	−0.315717	−	0.264918i	0.471133	−	0.882062i	$-0.343845\pi$
$881$	−9.37099	−	7.86319i	−0.315717	−	0.264918i	−0.786850	+	0.617144i	$0.788289\pi$
$882$	−11.7336			−0.395092
$883$	−13.1155	−	11.0052i	−0.441370	−	0.370354i	0.394852	−	0.918745i	$-0.370796\pi$
$883$	−13.1155	−	11.0052i	−0.441370	−	0.370354i	−0.836222	+	0.548391i	$0.815240\pi$
$884$	−1.45111	+	0.528160i	−0.0488061	+	0.0177640i
$885$	−5.16332	+	29.2827i	−0.173563	+	0.984326i
$886$	5.61470	+	31.8425i	0.188630	+	1.06977i
$887$	−14.8978			−0.500218			−0.250109	−	0.968218i	$-0.580466\pi$
$887$	−14.8978			−0.500218			−0.250109	+	0.968218i	$0.580466\pi$
$888$	−12.7456	−	4.04527i	−0.427714	−	0.135750i
$889$	9.22854			0.309515
$890$	0.550442	+	3.12171i	0.0184509	+	0.104640i
$891$	2.94272	−	16.6890i	0.0985847	−	0.559101i
$892$	25.2690	−	9.19715i	0.846067	−	0.307943i
$893$	2.90623	+	2.43861i	0.0972532	+	0.0816051i
$894$	32.8915			1.10006
$895$	−2.83061	−	2.37516i	−0.0946168	−	0.0793929i
$896$	−1.83043	−	3.17041i	−0.0611505	−	0.105916i
$897$	2.77086	+	1.00851i	0.0925163	+	0.0336732i
$898$	5.60861	−	9.71439i	0.187162	−	0.324174i
$899$	−4.18728	−	7.25258i	−0.139654	−	0.241887i
$900$	0.318266	+	1.80498i	0.0106089	+	0.0601659i
$901$	−9.13142	+	3.32357i	−0.304212	+	0.110724i
$902$	−3.19167	+	5.52813i	−0.106271	+	0.184067i
$903$	−6.56616	+	5.50966i	−0.218508	+	0.183350i
$904$	6.04577	−	5.07300i	0.201079	−	0.168726i
$905$	−11.4143	−	4.15448i	−0.379425	−	0.138099i
$906$	3.80522	−	21.5805i	0.126420	−	0.716963i
$907$	8.45365	−	47.9431i	0.280699	−	1.59192i	−0.439557	−	0.898215i	$-0.644865\pi$
$907$	8.45365	−	47.9431i	0.280699	−	1.59192i	0.720256	−	0.693708i	$-0.244024\pi$
$908$	−18.8250	−	6.85174i	−0.624730	−	0.227383i
$909$	−15.9909	+	13.4179i	−0.530383	+	0.445045i
$910$	−1.18461	+	0.994007i	−0.0392695	+	0.0329510i
$911$	−16.5689	+	28.6982i	−0.548953	+	0.950814i	0.449394	+	0.893334i	$0.351640\pi$
$911$	−16.5689	+	28.6982i	−0.548953	+	0.950814i	−0.998347	+	0.0574801i	$0.981693\pi$
$912$	3.34139	−	1.21617i	0.110645	−	0.0402713i
$913$	3.43189	+	19.4632i	0.113579	+	0.644138i
$914$	3.87144	+	6.70553i	0.128056	+	0.221799i
$915$	13.2495	−	22.9488i	0.438015	−	0.758664i
$916$	−23.2450	−	8.46047i	−0.768035	−	0.279542i
$917$	−38.3159	−	66.3651i	−1.26530	−	2.19157i
$918$	7.18568	+	6.02951i	0.237163	+	0.199003i
$919$	16.5218			0.545005			0.272503	−	0.962155i	$-0.412149\pi$
$919$	16.5218			0.545005			0.272503	+	0.962155i	$0.412149\pi$
$920$	−2.43245	−	2.04107i	−0.0801956	−	0.0672921i
$921$	6.81537	−	2.48059i	0.224574	−	0.0817383i
$922$	5.81387	−	32.9721i	0.191470	−	1.08588i
$923$	1.18491	+	6.71996i	0.0390018	+	0.221190i
$924$	12.2435			0.402783
$925$	2.81894	−	5.39014i	0.0926861	−	0.177227i
$926$	−7.98598			−0.262435
$927$	−1.85384	−	10.5136i	−0.0608879	−	0.345313i
$928$	−0.371235	+	2.10538i	−0.0121864	+	0.0691125i
$929$	41.9234	−	15.2589i	1.37546	−	0.500627i	0.454662	−	0.890664i	$-0.349760\pi$
$929$	41.9234	−	15.2589i	1.37546	−	0.500627i	0.920799	+	0.390038i	$0.127538\pi$
$930$	6.59686	+	5.53543i	0.216320	+	0.181514i
$931$	−10.3551			−0.339375
$932$	4.86509	+	4.08230i	0.159361	+	0.133720i
$933$	−31.9280	−	55.3009i	−1.04527	−	1.81047i
$934$	23.2964	+	8.47920i	0.762282	+	0.277448i
$935$	−2.78080	+	4.81648i	−0.0909418	+	0.157516i
$936$	0.387104	+	0.670484i	0.0126529	+	0.0219155i
$937$	4.94854	+	28.0646i	0.161662	+	0.916830i	0.952440	+	0.304727i	$0.0985651\pi$
$937$	4.94854	+	28.0646i	0.161662	+	0.916830i	−0.790778	+	0.612103i	$0.790324\pi$
$938$	43.5354	−	15.8456i	1.42148	−	0.517376i
$939$	−15.4418	+	26.7459i	−0.503923	+	0.872820i
$940$	1.79675	−	1.50765i	0.0586036	−	0.0491743i
$941$	−17.6990	+	14.8512i	−0.576972	+	0.484137i	−0.883951	−	0.467580i	$-0.845126\pi$
$941$	−17.6990	+	14.8512i	−0.576972	+	0.484137i	0.306979	+	0.951716i	$0.400682\pi$
$942$	−17.2774	−	6.28844i	−0.562927	−	0.204889i
$943$	−2.31359	+	13.1210i	−0.0753407	+	0.427279i
$944$	2.34871	−	13.3202i	0.0764439	−	0.433535i
$945$	8.82689	+	3.21272i	0.287139	+	0.104510i
$946$	1.24122	−	1.04151i	0.0403556	−	0.0338624i
$947$	−12.7645	+	10.7107i	−0.414791	+	0.348051i	−0.826178	−	0.563410i	$-0.809489\pi$
$947$	−12.7645	+	10.7107i	−0.414791	+	0.348051i	0.411386	+	0.911461i	$0.365045\pi$
$948$	−2.44372	+	4.23265i	−0.0793683	+	0.137470i
$949$	−4.68223	+	1.70419i	−0.151992	+	0.0553204i
$950$	0.280874	+	1.59292i	0.00911276	+	0.0516810i
$951$	−2.06151	−	3.57064i	−0.0668491	−	0.115786i
$952$	−6.69161	+	11.5902i	−0.216876	+	0.375641i
$953$	−33.2955	−	12.1186i	−1.07855	−	0.392559i	−0.259180	−	0.965829i	$-0.583452\pi$
$953$	−33.2955	−	12.1186i	−1.07855	−	0.392559i	−0.819367	+	0.573270i	$0.805675\pi$
$954$	2.43594	+	4.21917i	0.0788664	+	0.136601i
$955$	6.33168	+	5.31291i	0.204888	+	0.171922i
$956$	12.8310			0.414983
$957$	−5.47717	−	4.59589i	−0.177052	−	0.148564i
$958$	−15.4948	+	5.63964i	−0.500613	+	0.182208i
$959$	8.55872	−	48.5389i	0.276375	−	1.56740i
$960$	−0.381743	−	2.16497i	−0.0123207	−	0.0698741i
$961$	−15.6550			−0.505001
$962$	0.340212	−	2.54682i	0.0109689	−	0.0821127i
$963$	−8.63404			−0.278228
$964$	−3.30959	−	18.7696i	−0.106595	−	0.604528i
$965$	3.53575	−	20.0522i	0.113820	−	0.645504i
$966$	24.0138	−	8.74031i	0.772632	−	0.281215i
$967$	−36.3612	−	30.5106i	−1.16930	−	0.981156i	−0.169306	−	0.985563i	$-0.554153\pi$
$967$	−36.3612	−	30.5106i	−1.16930	−	0.981156i	−0.999990	+	0.00440724i	$0.998597\pi$
$968$	8.68556			0.279165
$969$	−9.95800	−	8.35576i	−0.319897	−	0.268426i
$970$	−7.19146	−	12.4560i	−0.230904	−	0.399937i
$971$	−33.4353	−	12.1694i	−1.07299	−	0.390536i	−0.255695	−	0.966758i	$-0.582304\pi$
$971$	−33.4353	−	12.1694i	−1.07299	−	0.390536i	−0.817293	+	0.576222i	$0.804526\pi$
$972$	8.39523	−	14.5410i	0.269277	−	0.466402i
$973$	2.72842	+	4.72577i	0.0874693	+	0.151501i
$974$	−1.07849	−	6.11640i	−0.0345570	−	0.195982i
$975$	−0.872617	+	0.317607i	−0.0279461	+	0.0101716i
$976$	−6.02697	+	10.4390i	−0.192919	+	0.334145i
$977$	27.6487	−	23.2000i	0.884559	−	0.742233i	−0.0825525	−	0.996587i	$-0.526307\pi$
$977$	27.6487	−	23.2000i	0.884559	−	0.742233i	0.967111	+	0.254354i	$0.0818628\pi$
$978$	21.1427	−	17.7409i	0.676070	−	0.567290i
$979$	4.53159	+	1.64936i	0.144830	+	0.0527139i
$980$	−1.11169	+	6.30470i	−0.0355116	+	0.201396i
$981$	0.309356	−	1.75445i	0.00987698	−	0.0560152i
$982$	−19.3261	−	7.03412i	−0.616720	−	0.224468i
$983$	−4.49942	+	3.77546i	−0.143509	+	0.120419i	−0.711716	−	0.702467i	$-0.752082\pi$
$983$	−4.49942	+	3.77546i	−0.143509	+	0.120419i	0.568207	+	0.822886i	$0.307637\pi$
$984$	−7.06609	+	5.92915i	−0.225259	+	0.189014i
$985$	2.91946	−	5.05666i	0.0930218	−	0.161118i
$986$	7.34414	−	2.67305i	0.233885	−	0.0851273i
$987$	3.27785	+	18.5896i	0.104335	+	0.591714i
$988$	0.341625	+	0.591711i	0.0108685	+	0.0188248i
$989$	1.69096	−	2.92883i	0.0537694	−	0.0931314i
$990$	2.62017	+	0.953662i	0.0832743	+	0.0303094i
$991$	12.8003	+	22.1707i	0.406614	+	0.704277i	0.994508	−	0.104662i	$-0.0333760\pi$
$991$	12.8003	+	22.1707i	0.406614	+	0.704277i	−0.587894	+	0.808938i	$0.700043\pi$
$992$	−3.00080	−	2.51797i	−0.0952755	−	0.0799456i
$993$	−30.0217			−0.952710
$994$	45.3018	+	38.0128i	1.43689	+	1.20569i
$995$	−9.49771	+	3.45688i	−0.301098	+	0.109591i
$996$	−4.95919	+	28.1249i	−0.157138	+	0.891173i
$997$	4.64136	+	26.3225i	0.146993	+	0.833641i	0.965745	+	0.259493i	$0.0835555\pi$
$997$	4.64136	+	26.3225i	0.146993	+	0.833641i	−0.818752	+	0.574148i	$0.805333\pi$
$998$	−7.95466			−0.251800
$999$	−14.4309	+	5.94543i	−0.456574	+	0.188105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.b.231.3	yes	18
37.33	even	9	inner	370.2.o.b.181.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.b.181.3	✓	18	37.33	even	9	inner
370.2.o.b.231.3	yes	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.381743 - 2.16497i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{5} -2.19837 q^{6} +(-2.80439 - 2.35316i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.72229 - 0.626862i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.381743 - 2.16497i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{5} -2.19837 q^{6} +(-2.80439 - 2.35316i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.72229 - 0.626862i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.760664 + 1.31751i) q^{11} +(0.381743 + 2.16497i) q^{12} +(-0.396939 + 0.144474i) q^{13} +(-1.83043 + 3.17041i) q^{14} +(-1.68405 + 1.41308i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-3.43528 - 1.25034i) q^{17} +(-0.318266 + 1.80498i) q^{18} +(-0.280874 + 1.59292i) q^{19} +(0.939693 + 0.342020i) q^{20} +(-6.16508 + 5.17311i) q^{21} +(1.16540 - 0.977891i) q^{22} +(1.58767 - 2.74993i) q^{23} +(2.06579 - 0.751886i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.211207 + 0.365821i) q^{26} +(1.28294 - 2.22212i) q^{27} +(3.44009 + 1.25209i) q^{28} +(-1.06893 - 1.85144i) q^{29} +(1.68405 + 1.41308i) q^{30} +3.91727 q^{31} +(-0.766044 - 0.642788i) q^{32} +(3.14274 - 1.14387i) q^{33} +(-0.634814 + 3.60021i) q^{34} +(0.635703 + 3.60525i) q^{35} +1.83282 q^{36} +(-4.81875 - 3.71210i) q^{37} +1.61749 q^{38} +(0.161253 + 0.914512i) q^{39} +(0.173648 - 0.984808i) q^{40} +(-3.94285 + 1.43508i) q^{41} +(6.16508 + 5.17311i) q^{42} +1.06506 q^{43} +(-1.16540 - 0.977891i) q^{44} +(0.916411 + 1.58727i) q^{45} +(-2.98385 - 1.08603i) q^{46} +(1.17275 - 2.03126i) q^{47} +(-1.09918 - 1.90384i) q^{48} +(1.11169 + 6.30470i) q^{49} +(0.939693 - 0.342020i) q^{50} +(-4.01834 + 6.95997i) q^{51} +(0.323587 - 0.271522i) q^{52} +(2.03625 - 1.70861i) q^{53} +(-2.41115 - 0.877585i) q^{54} +(0.264176 - 1.49822i) q^{55} +(0.635703 - 3.60525i) q^{56} +(3.34139 + 1.21617i) q^{57} +(-1.63769 + 1.37419i) q^{58} +(10.3613 - 8.69413i) q^{59} +(1.09918 - 1.90384i) q^{60} +(-11.3270 + 4.12269i) q^{61} +(-0.680226 - 3.85775i) q^{62} +(3.35486 + 5.81079i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.396939 + 0.144474i) q^{65} +(-1.67222 - 2.89637i) q^{66} +(-9.69452 - 8.13466i) q^{67} +3.65575 q^{68} +(-5.34743 - 4.48703i) q^{69} +(3.44009 - 1.25209i) q^{70} +(2.80510 - 15.9085i) q^{71} +(-0.318266 - 1.80498i) q^{72} +11.7958 q^{73} +(-2.81894 + 5.39014i) q^{74} +2.19837 q^{75} +(-0.280874 - 1.59292i) q^{76} +(0.967113 - 5.48477i) q^{77} +(0.872617 - 0.317607i) q^{78} +(1.70308 + 1.42905i) q^{79} -1.00000 q^{80} +(-8.53315 - 7.16016i) q^{81} +(2.09795 + 3.63375i) q^{82} +(12.2075 + 4.44316i) q^{83} +(4.02397 - 6.96972i) q^{84} +(1.82787 + 3.16597i) q^{85} +(-0.184945 - 1.04888i) q^{86} +(-4.41637 + 1.60743i) q^{87} +(-0.760664 + 1.31751i) q^{88} +(2.42826 - 2.03755i) q^{89} +(1.40402 - 1.17811i) q^{90} +(1.45314 + 0.528900i) q^{91} +(-0.551393 + 3.12710i) q^{92} +(1.49539 - 8.48076i) q^{93} +(-2.20404 - 0.802206i) q^{94} +(1.23907 - 1.03970i) q^{95} +(-1.68405 + 1.41308i) q^{96} +(-7.19146 + 12.4560i) q^{97} +(6.01587 - 2.18960i) q^{98} +(-0.484187 - 2.74596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Introduction

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