LMFDB - Embedded newform 370.2.o.b.271.2

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			271.2
Root			$-0.132544 - 0.229572i$ of defining polynomial
Character	$\chi$	$=$	370.271
Dual form			370.2.o.b.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.203068 + 0.170395i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} -0.265087 q^{6} +(1.72587 - 0.628164i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.508742 - 2.88522i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.203068 + 0.170395i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} -0.265087 q^{6} +(1.72587 - 0.628164i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.508742 - 2.88522i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.26403 - 2.18936i) q^{11} +(0.203068 - 0.170395i) q^{12} +(0.483973 - 2.74475i) q^{13} +(-0.918315 + 1.59057i) q^{14} +(0.249100 + 0.0906651i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.786329 + 4.45949i) q^{17} +(2.24430 + 1.88319i) q^{18} +(-1.19894 - 1.00603i) q^{19} +(-0.173648 - 0.984808i) q^{20} +(0.457505 + 0.166518i) q^{21} +(2.37560 + 0.864647i) q^{22} +(3.64922 - 6.32064i) q^{23} +(-0.0460319 + 0.261060i) q^{24} +(0.766044 - 0.642788i) q^{25} +(1.39355 + 2.41369i) q^{26} +(0.785947 - 1.36130i) q^{27} +(-0.318927 - 1.80873i) q^{28} +(3.63847 + 6.30201i) q^{29} +(-0.249100 + 0.0906651i) q^{30} +1.29267 q^{31} +(0.939693 - 0.342020i) q^{32} +(0.116371 - 0.659974i) q^{33} +(-3.46887 - 2.91073i) q^{34} +(1.40694 - 1.18056i) q^{35} -2.92973 q^{36} +(0.599814 - 6.05312i) q^{37} +1.56511 q^{38} +(0.565970 - 0.474906i) q^{39} +(0.766044 + 0.642788i) q^{40} +(-0.798833 + 4.53041i) q^{41} +(-0.457505 + 0.166518i) q^{42} +12.0813 q^{43} +(-2.37560 + 0.864647i) q^{44} +(-1.46486 - 2.53722i) q^{45} +(1.26736 + 7.18757i) q^{46} +(-6.06083 + 10.4977i) q^{47} +(-0.132544 - 0.229572i) q^{48} +(-2.77829 + 2.33126i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(-0.600195 + 1.03957i) q^{51} +(-2.61901 - 0.953241i) q^{52} +(11.0668 + 4.02800i) q^{53} +(0.272957 + 1.54801i) q^{54} +(-1.93660 - 1.62500i) q^{55} +(1.40694 + 1.18056i) q^{56} +(-0.0720450 - 0.408587i) q^{57} +(-6.83808 - 2.48886i) q^{58} +(-13.1207 - 4.77556i) q^{59} +(0.132544 - 0.229572i) q^{60} +(0.624562 - 3.54207i) q^{61} +(-0.990246 + 0.830915i) q^{62} +(-2.69041 - 4.65993i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.483973 - 2.74475i) q^{65} +(0.335078 + 0.580372i) q^{66} +(-6.15138 + 2.23892i) q^{67} +4.52829 q^{68} +(1.81805 - 0.661714i) q^{69} +(-0.318927 + 1.80873i) q^{70} +(-5.94694 - 4.99007i) q^{71} +(2.24430 - 1.88319i) q^{72} +2.00763 q^{73} +(3.43138 + 5.02251i) q^{74} +0.265087 q^{75} +(-1.19894 + 1.00603i) q^{76} +(-3.55682 - 2.98453i) q^{77} +(-0.128295 + 0.727597i) q^{78} +(-7.63395 + 2.77853i) q^{79} -1.00000 q^{80} +(-7.86757 + 2.86356i) q^{81} +(-2.30015 - 3.98397i) q^{82} +(-0.0889045 - 0.504202i) q^{83} +(0.243433 - 0.421639i) q^{84} +(2.26414 + 3.92161i) q^{85} +(-9.25478 + 7.76568i) q^{86} +(-0.334971 + 1.89971i) q^{87} +(1.26403 - 2.18936i) q^{88} +(7.93627 + 2.88857i) q^{89} +(2.75304 + 1.00203i) q^{90} +(-0.888880 - 5.04109i) q^{91} +(-5.59093 - 4.69135i) q^{92} +(0.262501 + 0.220265i) q^{93} +(-2.10490 - 11.9375i) q^{94} +(-1.47072 - 0.535299i) q^{95} +(0.249100 + 0.0906651i) q^{96} +(0.127750 - 0.221269i) q^{97} +(0.629786 - 3.57169i) q^{98} +(-5.67373 + 4.76082i) 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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	0.203068	+	0.170395i	0.117242	+	0.0983774i	0.699524	−	0.714609i	$-0.253396\pi$
$3$	0.203068	+	0.170395i	0.117242	+	0.0983774i	−0.582282	+	0.812987i	$0.697840\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$6$	−0.265087			−0.108221
$7$	1.72587	−	0.628164i	0.652316	−	0.237424i	0.00540081	−	0.999985i	$-0.498281\pi$
$7$	1.72587	−	0.628164i	0.652316	−	0.237424i	0.646915	+	0.762562i	$0.276059\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.508742	−	2.88522i	−0.169581	−	0.961740i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−1.26403	−	2.18936i	−0.381119	−	0.660118i	0.610103	−	0.792322i	$-0.291128\pi$
$11$	−1.26403	−	2.18936i	−0.381119	−	0.660118i	−0.991223	+	0.132204i	$0.957795\pi$
$12$	0.203068	−	0.170395i	0.0586208	−	0.0491887i
$13$	0.483973	−	2.74475i	0.134230	−	0.761257i	−0.841163	−	0.540782i	$-0.818128\pi$
$13$	0.483973	−	2.74475i	0.134230	−	0.761257i	0.975393	−	0.220474i	$-0.0707605\pi$
$14$	−0.918315	+	1.59057i	−0.245430	+	0.425097i
$15$	0.249100	+	0.0906651i	0.0643174	+	0.0234096i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.786329	+	4.45949i	0.190713	+	1.08159i	0.918393	+	0.395669i	$0.129487\pi$
$17$	0.786329	+	4.45949i	0.190713	+	1.08159i	−0.727680	+	0.685917i	$0.759401\pi$
$18$	2.24430	+	1.88319i	0.528987	+	0.443873i
$19$	−1.19894	−	1.00603i	−0.275057	−	0.230800i	0.494816	−	0.868998i	$-0.335236\pi$
$19$	−1.19894	−	1.00603i	−0.275057	−	0.230800i	−0.769872	+	0.638198i	$0.779680\pi$
$20$	−0.173648	−	0.984808i	−0.0388289	−	0.220210i
$21$	0.457505	+	0.166518i	0.0998357	+	0.0363372i
$22$	2.37560	+	0.864647i	0.506479	+	0.184343i
$23$	3.64922	−	6.32064i	0.760916	−	1.31794i	−0.181463	−	0.983398i	$-0.558083\pi$
$23$	3.64922	−	6.32064i	0.760916	−	1.31794i	0.942379	−	0.334547i	$-0.108583\pi$
$24$	−0.0460319	+	0.261060i	−0.00939622	+	0.0532886i
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	1.39355	+	2.41369i	0.273297	+	0.473364i
$27$	0.785947	−	1.36130i	0.151256	−	0.261982i
$28$	−0.318927	−	1.80873i	−0.0602716	−	0.341817i
$29$	3.63847	+	6.30201i	0.675646	+	1.17025i	0.976280	+	0.216514i	$0.0694686\pi$
$29$	3.63847	+	6.30201i	0.675646	+	1.17025i	−0.300633	+	0.953740i	$0.597198\pi$
$30$	−0.249100	+	0.0906651i	−0.0454793	+	0.0165531i
$31$	1.29267			0.232171			0.116086	−	0.993239i	$-0.462965\pi$
$31$	1.29267			0.232171			0.116086	+	0.993239i	$0.462965\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.116371	−	0.659974i	0.0202576	−	0.114887i
$34$	−3.46887	−	2.91073i	−0.594906	−	0.499186i
$35$	1.40694	−	1.18056i	0.237816	−	0.199551i
$36$	−2.92973			−0.488288
$37$	0.599814	−	6.05312i	0.0986088	−	0.995126i
$37$	0.599814	−	6.05312i	0.0986088	−	0.995126i
$38$	1.56511			0.253894
$39$	0.565970	−	0.474906i	0.0906278	−	0.0760457i
$40$	0.766044	+	0.642788i	0.121122	+	0.101634i
$41$	−0.798833	+	4.53041i	−0.124757	+	0.707531i	0.856695	+	0.515823i	$0.172514\pi$
$41$	−0.798833	+	4.53041i	−0.124757	+	0.707531i	−0.981452	+	0.191708i	$0.938597\pi$
$42$	−0.457505	+	0.166518i	−0.0705945	+	0.0256943i
$43$	12.0813			1.84237			0.921187	−	0.389121i	$-0.127221\pi$
$43$	12.0813			1.84237			0.921187	+	0.389121i	$0.127221\pi$
$44$	−2.37560	+	0.864647i	−0.358135	+	0.130350i
$45$	−1.46486	−	2.53722i	−0.218369	−	0.378226i
$46$	1.26736	+	7.18757i	0.186862	+	1.05975i
$47$	−6.06083	+	10.4977i	−0.884062	+	1.53124i	−0.0372777	+	0.999305i	$0.511869\pi$
$47$	−6.06083	+	10.4977i	−0.884062	+	1.53124i	−0.846785	+	0.531936i	$0.821465\pi$
$48$	−0.132544	−	0.229572i	−0.0191310	−	0.0331359i
$49$	−2.77829	+	2.33126i	−0.396898	+	0.333037i
$50$	−0.173648	+	0.984808i	−0.0245576	+	0.139273i
$51$	−0.600195	+	1.03957i	−0.0840441	+	0.145569i
$52$	−2.61901	−	0.953241i	−0.363191	−	0.132191i
$53$	11.0668	+	4.02800i	1.52015	+	0.553289i	0.961185	−	0.275904i	$-0.0889772\pi$
$53$	11.0668	+	4.02800i	1.52015	+	0.553289i	0.558963	+	0.829193i	$0.311199\pi$
$54$	0.272957	+	1.54801i	0.0371447	+	0.210658i
$55$	−1.93660	−	1.62500i	−0.261132	−	0.219116i
$56$	1.40694	+	1.18056i	0.188010	+	0.157759i
$57$	−0.0720450	−	0.408587i	−0.00954259	−	0.0541187i
$58$	−6.83808	−	2.48886i	−0.897884	−	0.326803i
$59$	−13.1207	−	4.77556i	−1.70817	−	0.621724i	−0.711460	−	0.702727i	$-0.751966\pi$
$59$	−13.1207	−	4.77556i	−1.70817	−	0.621724i	−0.996714	+	0.0810023i	$0.974188\pi$
$60$	0.132544	−	0.229572i	0.0171113	−	0.0296376i
$61$	0.624562	−	3.54207i	0.0799670	−	0.453515i	−0.918363	−	0.395740i	$-0.870488\pi$
$61$	0.624562	−	3.54207i	0.0799670	−	0.453515i	0.998330	−	0.0577753i	$-0.0184007\pi$
$62$	−0.990246	+	0.830915i	−0.125761	+	0.105526i
$63$	−2.69041	−	4.65993i	−0.338960	−	0.587096i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.483973	−	2.74475i	−0.0600295	−	0.340444i
$66$	0.335078	+	0.580372i	0.0412452	+	0.0714388i
$67$	−6.15138	+	2.23892i	−0.751511	+	0.273528i	−0.689241	−	0.724532i	$-0.742056\pi$
$67$	−6.15138	+	2.23892i	−0.751511	+	0.273528i	−0.0622696	+	0.998059i	$0.519834\pi$
$68$	4.52829			0.549136
$69$	1.81805	−	0.661714i	0.218867	−	0.0796611i
$70$	−0.318927	+	1.80873i	−0.0381191	+	0.216184i
$71$	−5.94694	−	4.99007i	−0.705771	−	0.592212i	0.217638	−	0.976030i	$-0.430165\pi$
$71$	−5.94694	−	4.99007i	−0.705771	−	0.592212i	−0.923409	+	0.383817i	$0.874609\pi$
$72$	2.24430	−	1.88319i	0.264494	−	0.221936i
$73$	2.00763			0.234975			0.117488	−	0.993074i	$-0.462516\pi$
$73$	2.00763			0.234975			0.117488	+	0.993074i	$0.462516\pi$
$74$	3.43138	+	5.02251i	0.398890	+	0.583855i
$75$	0.265087			0.0306096
$76$	−1.19894	+	1.00603i	−0.137528	+	0.115400i
$77$	−3.55682	−	2.98453i	−0.405338	−	0.340119i
$78$	−0.128295	+	0.727597i	−0.0145266	+	0.0823842i
$79$	−7.63395	+	2.77853i	−0.858887	+	0.312609i	−0.733658	−	0.679519i	$-0.762189\pi$
$79$	−7.63395	+	2.77853i	−0.858887	+	0.312609i	−0.125229	+	0.992128i	$0.539966\pi$
$80$	−1.00000			−0.111803
$81$	−7.86757	+	2.86356i	−0.874175	+	0.318174i
$82$	−2.30015	−	3.98397i	−0.254009	−	0.439956i
$83$	−0.0889045	−	0.504202i	−0.00975853	−	0.0553434i	0.979540	−	0.201251i	$-0.0645008\pi$
$83$	−0.0889045	−	0.504202i	−0.00975853	−	0.0553434i	−0.989298	+	0.145908i	$0.953390\pi$
$84$	0.243433	−	0.421639i	0.0265607	−	0.0460046i
$85$	2.26414	+	3.92161i	0.245581	+	0.425359i
$86$	−9.25478	+	7.76568i	−0.997968	+	0.837395i
$87$	−0.334971	+	1.89971i	−0.0359126	+	0.203671i
$88$	1.26403	−	2.18936i	0.134746	−	0.233387i
$89$	7.93627	+	2.88857i	0.841243	+	0.306187i	0.726465	−	0.687204i	$-0.241162\pi$
$89$	7.93627	+	2.88857i	0.841243	+	0.306187i	0.114778	+	0.993391i	$0.463384\pi$
$90$	2.75304	+	1.00203i	0.290196	+	0.105623i
$91$	−0.888880	−	5.04109i	−0.0931799	−	0.528449i
$92$	−5.59093	−	4.69135i	−0.582895	−	0.489107i
$93$	0.262501	+	0.220265i	0.0272201	+	0.0228404i
$94$	−2.10490	−	11.9375i	−0.217104	−	1.23126i
$95$	−1.47072	−	0.535299i	−0.150893	−	0.0549205i
$96$	0.249100	+	0.0906651i	0.0254237	+	0.00925347i
$97$	0.127750	−	0.221269i	0.0129710	−	0.0224665i	−0.859467	−	0.511191i	$-0.829204\pi$
$97$	0.127750	−	0.221269i	0.0129710	−	0.0224665i	0.872438	+	0.488725i	$0.162538\pi$
$98$	0.629786	−	3.57169i	0.0636180	−	0.360796i
$99$	−5.67373	+	4.76082i	−0.570231	+	0.478481i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−4.90298	+	8.49222i	−0.487865	+	0.845007i	−0.999903	−	0.0139560i	$-0.995558\pi$
$101$	−4.90298	+	8.49222i	−0.487865	+	0.845007i	0.512038	+	0.858963i	$0.328891\pi$
$102$	−0.208446	−	1.18215i	−0.0206392	−	0.117051i
$103$	−4.70664	−	8.15214i	−0.463759	−	0.803255i	0.535385	−	0.844608i	$-0.320166\pi$
$103$	−4.70664	−	8.15214i	−0.463759	−	0.803255i	−0.999145	+	0.0413533i	$0.986833\pi$
$104$	2.61901	−	0.953241i	0.256815	−	0.0934730i
$105$	0.486867			0.0475133
$106$	−11.0668	+	4.02800i	−1.07491	+	0.391234i
$107$	−1.44116	+	8.17321i	−0.139322	+	0.790134i	0.832430	+	0.554130i	$0.186949\pi$
$107$	−1.44116	+	8.17321i	−0.139322	+	0.790134i	−0.971752	+	0.236004i	$0.924162\pi$
$108$	−1.20414	−	1.01039i	−0.115869	−	0.0972252i
$109$	−5.38953	+	4.52236i	−0.516224	+	0.433163i	−0.863313	−	0.504669i	$-0.831615\pi$
$109$	−5.38953	+	4.52236i	−0.516224	+	0.433163i	0.347089	+	0.937832i	$0.387170\pi$
$110$	2.52806			0.241041
$111$	1.15322	−	1.12699i	0.109459	−	0.106969i
$112$	−1.83663			−0.173545
$113$	−8.65013	+	7.25832i	−0.813736	+	0.682805i	−0.951496	−	0.307660i	$-0.900454\pi$
$113$	−8.65013	+	7.25832i	−0.813736	+	0.682805i	0.137761	+	0.990466i	$0.456010\pi$
$114$	0.317824	+	0.266686i	0.0297670	+	0.0249775i
$115$	1.26736	−	7.18757i	0.118182	−	0.670244i
$116$	6.83808	−	2.48886i	0.634900	−	0.231085i
$117$	−8.16542			−0.754894
$118$	13.1207	−	4.77556i	1.20786	−	0.439626i
$119$	4.15839	+	7.20255i	0.381199	+	0.660256i
$120$	0.0460319	+	0.261060i	0.00420212	+	0.0238314i
$121$	2.30446	−	3.99144i	0.209496	−	0.362859i
$122$	1.79835	+	3.11484i	0.162815	+	0.282004i
$123$	−0.934175	+	0.783866i	−0.0842317	+	0.0706788i
$124$	0.224471	−	1.27304i	0.0201580	−	0.114322i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	5.05632	+	1.84035i	0.450453	+	0.163951i
$127$	0.498789	+	0.181544i	0.0442604	+	0.0161095i	0.364055	−	0.931377i	$-0.381392\pi$
$127$	0.498789	+	0.181544i	0.0442604	+	0.0161095i	−0.319795	+	0.947487i	$0.603614\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	2.45332	+	2.05858i	0.216003	+	0.181248i
$130$	2.13504	+	1.79151i	0.187255	+	0.157126i
$131$	0.623527	+	3.53620i	0.0544778	+	0.308959i	0.999855	−	0.0170191i	$-0.00541760\pi$
$131$	0.623527	+	3.53620i	0.0544778	+	0.308959i	−0.945377	+	0.325978i	$0.894306\pi$
$132$	−0.629740	−	0.229207i	−0.0548118	−	0.0199499i
$133$	−2.70117	−	0.983146i	−0.234221	−	0.0852496i
$134$	3.27308	−	5.66915i	0.282751	−	0.489740i
$135$	0.272957	−	1.54801i	0.0234924	−	0.133232i
$136$	−3.46887	+	2.91073i	−0.297453	+	0.249593i
$137$	9.33481	+	16.1684i	0.797526	+	1.38136i	0.921223	+	0.389036i	$0.127192\pi$
$137$	9.33481	+	16.1684i	0.797526	+	1.38136i	−0.123696	+	0.992320i	$0.539475\pi$
$138$	−0.967362	+	1.67552i	−0.0823473	+	0.142630i
$139$	−2.97484	−	16.8712i	−0.252323	−	1.43099i	−0.802852	−	0.596178i	$-0.796685\pi$
$139$	−2.97484	−	16.8712i	−0.252323	−	1.43099i	0.550529	−	0.834816i	$-0.314426\pi$
$140$	−0.918315	−	1.59057i	−0.0776117	−	0.134427i
$141$	−3.01951	+	1.09901i	−0.254288	+	0.0925534i
$142$	7.76317			0.651471
$143$	−6.62101	+	2.40985i	−0.553677	+	0.201522i
$144$	−0.508742	+	2.88522i	−0.0423952	+	0.240435i
$145$	5.57445	+	4.67752i	0.462933	+	0.388447i
$146$	−1.53793	+	1.29048i	−0.127280	+	0.106801i
$147$	−0.961416			−0.0792963
$148$	−5.85700	−	1.64181i	−0.481442	−	0.134956i
$149$	21.8530			1.79026			0.895132	−	0.445801i	$-0.147081\pi$
$149$	21.8530			1.79026			0.895132	+	0.445801i	$0.147081\pi$
$150$	−0.203068	+	0.170395i	−0.0165805	+	0.0139127i
$151$	−3.64906	−	3.06193i	−0.296957	−	0.249176i	0.482120	−	0.876105i	$-0.339867\pi$
$151$	−3.64906	−	3.06193i	−0.296957	−	0.249176i	−0.779076	+	0.626929i	$0.784311\pi$
$152$	0.271778	−	1.54133i	0.0220441	−	0.125019i
$153$	12.4666	−	4.53746i	1.00786	−	0.366832i
$154$	4.64310			0.374152
$155$	1.21472	−	0.442121i	0.0975684	−	0.0355120i
$156$	−0.369411	−	0.639838i	−0.0295765	−	0.0512281i
$157$	1.88655	+	10.6992i	0.150563	+	0.853886i	0.962731	+	0.270462i	$0.0871763\pi$
$157$	1.88655	+	10.6992i	0.150563	+	0.853886i	−0.812168	+	0.583424i	$0.801713\pi$
$158$	4.06194	−	7.03549i	0.323151	−	0.559713i
$159$	1.56098	+	2.70369i	0.123794	+	0.214417i
$160$	0.766044	−	0.642788i	0.0605611	−	0.0508168i
$161$	2.32767	−	13.2009i	0.183446	−	1.04038i
$162$	4.18625	−	7.25080i	0.328903	−	0.569676i
$163$	11.2153	+	4.08202i	0.878447	+	0.319729i	0.741583	−	0.670861i	$-0.234075\pi$
$163$	11.2153	+	4.08202i	0.878447	+	0.319729i	0.136864	+	0.990590i	$0.456298\pi$
$164$	4.32287	+	1.57339i	0.337559	+	0.122861i
$165$	−0.116371	−	0.659974i	−0.00905949	−	0.0513789i
$166$	0.392200	+	0.329095i	0.0304406	+	0.0255427i
$167$	−2.46102	−	2.06504i	−0.190439	−	0.159797i	0.542583	−	0.840002i	$-0.317446\pi$
$167$	−2.46102	−	2.06504i	−0.190439	−	0.159797i	−0.733022	+	0.680205i	$0.761891\pi$
$168$	0.0845435	+	0.479470i	0.00652267	+	0.0369919i
$169$	4.91658	+	1.78949i	0.378199	+	0.137653i
$170$	−4.25520	−	1.54877i	−0.326359	−	0.118785i
$171$	−2.29267	+	3.97103i	−0.175325	+	0.303672i
$172$	2.09789	−	11.8977i	0.159962	−	0.907192i
$173$	−6.61783	+	5.55302i	−0.503144	+	0.422188i	−0.858709	−	0.512463i	$-0.828733\pi$
$173$	−6.61783	+	5.55302i	−0.503144	+	0.422188i	0.355565	+	0.934652i	$0.384289\pi$
$174$	−0.964510	−	1.67058i	−0.0731193	−	0.126646i
$175$	0.918315	−	1.59057i	0.0694181	−	0.120236i
$176$	0.438993	+	2.48965i	0.0330903	+	0.187665i
$177$	−1.85068	−	3.20547i	−0.139105	−	0.240938i
$178$	−7.93627	+	2.88857i	−0.594849	+	0.216507i
$179$	6.50585			0.486270			0.243135	−	0.969992i	$-0.421824\pi$
$179$	6.50585			0.486270			0.243135	+	0.969992i	$0.421824\pi$
$180$	−2.75304	+	1.00203i	−0.205200	+	0.0746866i
$181$	−1.07092	+	6.07349i	−0.0796009	+	0.451439i	0.918791	+	0.394745i	$0.129167\pi$
$181$	−1.07092	+	6.07349i	−0.0796009	+	0.451439i	−0.998392	+	0.0566941i	$0.981944\pi$
$182$	3.92127	+	3.29034i	0.290664	+	0.243896i
$183$	0.730378	−	0.612860i	0.0539911	−	0.0453039i
$184$	7.29845			0.538049
$185$	−1.50665	−	5.89322i	−0.110771	−	0.433278i
$186$	−0.342671			−0.0251259
$187$	8.76950	−	7.35849i	0.641290	−	0.538106i
$188$	9.28572	+	7.79165i	0.677231	+	0.568264i
$189$	0.501320	−	2.84313i	0.0364657	−	0.206807i
$190$	1.47072	−	0.535299i	0.106697	−	0.0388347i
$191$	12.2028			0.882965			0.441483	−	0.897270i	$-0.354453\pi$
$191$	12.2028			0.882965			0.441483	+	0.897270i	$0.354453\pi$
$192$	−0.249100	+	0.0906651i	−0.0179773	+	0.00654319i
$193$	−5.34756	−	9.26224i	−0.384926	−	0.666711i	0.606833	−	0.794829i	$-0.292440\pi$
$193$	−5.34756	−	9.26224i	−0.384926	−	0.666711i	−0.991759	+	0.128118i	$0.959106\pi$
$194$	0.0443671	+	0.251618i	0.00318537	+	0.0180651i
$195$	0.369411	−	0.639838i	0.0264541	−	0.0458198i
$196$	1.81340	+	3.14090i	0.129528	+	0.224350i
$197$	−2.85941	+	2.39933i	−0.203725	+	0.170945i	−0.738942	−	0.673769i	$-0.764674\pi$
$197$	−2.85941	+	2.39933i	−0.203725	+	0.170945i	0.535217	+	0.844715i	$0.320230\pi$
$198$	1.28613	−	7.29400i	0.0914012	−	0.518362i
$199$	−9.01993	+	15.6230i	−0.639406	+	1.10748i	0.346158	+	0.938176i	$0.387486\pi$
$199$	−9.01993	+	15.6230i	−0.639406	+	1.10748i	−0.985563	+	0.169307i	$0.945847\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	−1.63065	−	0.593509i	−0.115017	−	0.0418629i
$202$	−1.70279	−	9.65699i	−0.119808	−	0.679464i
$203$	10.2382	+	8.59087i	0.718581	+	0.602961i
$204$	0.919552	+	0.771596i	0.0643815	+	0.0540225i
$205$	0.798833	+	4.53041i	0.0557929	+	0.316417i
$206$	8.84560	+	3.21953i	0.616302	+	0.224316i
$207$	−20.0929	−	7.31324i	−1.39656	−	0.508305i
$208$	−1.39355	+	2.41369i	−0.0966250	+	0.167359i
$209$	−0.687072	+	3.89658i	−0.0475258	+	0.269532i
$210$	−0.372961	+	0.312952i	−0.0257368	+	0.0215957i
$211$	2.19430	+	3.80063i	0.151062	+	0.261647i	0.931618	−	0.363439i	$-0.118397\pi$
$211$	2.19430	+	3.80063i	0.151062	+	0.261647i	−0.780556	+	0.625085i	$0.785064\pi$
$212$	5.88854	−	10.1993i	0.404427	−	0.700488i
$213$	−0.357353	−	2.02665i	−0.0244855	−	0.138864i
$214$	−4.14965	−	7.18740i	−0.283664	−	0.491320i
$215$	11.3527	−	4.13203i	0.774245	−	0.281802i
$216$	1.57189			0.106954
$217$	2.23098	−	0.812011i	0.151449	−	0.0551229i
$218$	1.22171	−	6.92865i	0.0827445	−	0.469267i
$219$	0.407686	+	0.342089i	0.0275489	+	0.0231162i
$220$	−1.93660	+	1.62500i	−0.130566	+	0.109558i
$221$	12.6208			0.848964
$222$	−0.159003	+	1.60460i	−0.0106716	+	0.107694i
$223$	−9.97461			−0.667949			−0.333975	−	0.942582i	$-0.608390\pi$
$223$	−9.97461			−0.667949			−0.333975	+	0.942582i	$0.608390\pi$
$224$	1.40694	−	1.18056i	0.0940051	−	0.0788796i
$225$	−2.24430	−	1.88319i	−0.149620	−	0.125546i
$226$	1.96083	−	11.1204i	0.130432	−	0.739717i
$227$	20.9434	−	7.62277i	1.39006	−	0.505941i	0.464849	−	0.885390i	$-0.346109\pi$
$227$	20.9434	−	7.62277i	1.39006	−	0.505941i	0.925213	+	0.379449i	$0.123886\pi$
$228$	−0.414890			−0.0274768
$229$	19.4478	−	7.07842i	1.28515	−	0.467755i	0.393016	−	0.919532i	$-0.371432\pi$
$229$	19.4478	−	7.07842i	1.28515	−	0.467755i	0.892131	+	0.451777i	$0.149210\pi$
$230$	3.64922	+	6.32064i	0.240623	+	0.416771i
$231$	−0.213731	−	1.21213i	−0.0140625	−	0.0797522i
$232$	−3.63847	+	6.30201i	−0.238877	+	0.413747i
$233$	−1.39764	−	2.42078i	−0.0915624	−	0.158591i	0.816606	−	0.577195i	$-0.195853\pi$
$233$	−1.39764	−	2.42078i	−0.0915624	−	0.158591i	−0.908169	+	0.418604i	$0.862519\pi$
$234$	6.25508	−	5.24863i	0.408907	−	0.343114i
$235$	−2.10490	+	11.9375i	−0.137309	+	0.778716i
$236$	−6.98140	+	12.0921i	−0.454450	+	0.787131i
$237$	−2.02366	−	0.736553i	−0.131451	−	0.0478442i
$238$	−7.81522	−	2.84451i	−0.506586	−	0.184382i
$239$	0.352937	+	2.00160i	0.0228296	+	0.129473i	0.994093	−	0.108536i	$-0.0346163\pi$
$239$	0.352937	+	2.00160i	0.0228296	+	0.129473i	−0.971263	+	0.238009i	$0.923505\pi$
$240$	−0.203068	−	0.170395i	−0.0131080	−	0.0109989i
$241$	3.95670	+	3.32007i	0.254874	+	0.213864i	0.761268	−	0.648438i	$-0.224577\pi$
$241$	3.95670	+	3.32007i	0.254874	+	0.213864i	−0.506394	+	0.862302i	$0.669022\pi$
$242$	0.800331	+	4.53890i	0.0514472	+	0.291772i
$243$	−6.51688	−	2.37195i	−0.418058	−	0.152161i
$244$	−3.37980	−	1.23015i	−0.216370	−	0.0787521i
$245$	−1.81340	+	3.14090i	−0.115854	+	0.200664i
$246$	0.211760	−	1.20095i	0.0135013	−	0.0765699i
$247$	−3.34157	+	2.80391i	−0.212619	+	0.178408i
$248$	0.646337	+	1.11949i	0.0410424	+	0.0710876i
$249$	0.0678597	−	0.117536i	0.00430043	−	0.00744857i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	−13.1083	−	22.7042i	−0.827386	−	1.43308i	−0.900082	−	0.435721i	$-0.856493\pi$
$251$	−13.1083	−	22.7042i	−0.827386	−	1.43308i	0.0726956	−	0.997354i	$-0.476840\pi$
$252$	−5.05632	+	1.84035i	−0.318518	+	0.115931i
$253$	−18.4509			−1.16000
$254$	−0.498789	+	0.181544i	−0.0312968	+	0.0113911i
$255$	−0.208446	+	1.18215i	−0.0130534	+	0.0740293i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−5.97491	+	5.01354i	−0.372705	+	0.312736i	−0.809830	−	0.586664i	$-0.800441\pi$
$257$	−5.97491	+	5.01354i	−0.372705	+	0.312736i	0.437126	+	0.899400i	$0.355996\pi$
$258$	−3.20258			−0.199384
$259$	−2.76715	−	10.8237i	−0.171942	−	0.672549i
$260$	−2.78709			−0.172848
$261$	16.3316	−	13.7039i	1.01090	−	0.848248i
$262$	−2.75067	−	2.30809i	−0.169937	−	0.142594i
$263$	−1.97911	+	11.2241i	−0.122037	+	0.692108i	0.860986	+	0.508628i	$0.169847\pi$
$263$	−1.97911	+	11.2241i	−0.122037	+	0.692108i	−0.983023	+	0.183480i	$0.941264\pi$
$264$	0.629740	−	0.229207i	0.0387578	−	0.0141067i
$265$	11.7771			0.723461
$266$	2.70117	−	0.983146i	0.165619	−	0.0602805i
$267$	1.11941	+	1.93887i	0.0685068	+	0.118657i
$268$	1.13673	+	6.44671i	0.0694368	+	0.393796i
$269$	−9.87347	+	17.1014i	−0.601996	+	1.04269i	0.390522	+	0.920594i	$0.372295\pi$
$269$	−9.87347	+	17.1014i	−0.601996	+	1.04269i	−0.992518	+	0.122095i	$0.961039\pi$
$270$	0.785947	+	1.36130i	0.0478312	+	0.0828461i
$271$	−8.50697	+	7.13819i	−0.516762	+	0.433614i	−0.863501	−	0.504347i	$-0.831733\pi$
$271$	−8.50697	+	7.13819i	−0.516762	+	0.433614i	0.346740	+	0.937961i	$0.387289\pi$
$272$	0.786329	−	4.45949i	0.0476782	−	0.270396i
$273$	0.678471	−	1.17515i	0.0410629	−	0.0711231i
$274$	−17.5437	−	6.38538i	−1.05985	−	0.385755i
$275$	−2.37560	−	0.864647i	−0.143254	−	0.0521402i
$276$	−0.335961	−	1.90533i	−0.0202225	−	0.114687i
$277$	23.5373	+	19.7501i	1.41422	+	1.18667i	0.954353	+	0.298680i	$0.0965462\pi$
$277$	23.5373	+	19.7501i	1.41422	+	1.18667i	0.459864	+	0.887989i	$0.347898\pi$
$278$	13.1234	+	11.0119i	0.787092	+	0.660448i
$279$	−0.657638	−	3.72965i	−0.0393717	−	0.223288i
$280$	1.72587	+	0.628164i	0.103140	+	0.0375400i
$281$	−29.4772	−	10.7288i	−1.75846	−	0.640028i	−0.758529	−	0.651640i	$-0.774081\pi$
$281$	−29.4772	−	10.7288i	−1.75846	−	0.640028i	−0.999933	+	0.0116120i	$0.996304\pi$
$282$	1.60665	−	2.78279i	0.0956744	−	0.165713i
$283$	0.193059	−	1.09489i	0.0114762	−	0.0650846i	−0.978532	−	0.206096i	$-0.933924\pi$
$283$	0.193059	−	1.09489i	0.0114762	−	0.0650846i	0.990008	+	0.141011i	$0.0450353\pi$
$284$	−5.94694	+	4.99007i	−0.352886	+	0.296106i
$285$	−0.207445	−	0.359306i	−0.0122880	−	0.0212834i
$286$	3.52296	−	6.10195i	0.208317	−	0.360816i
$287$	1.46716	+	8.32068i	0.0866037	+	0.491154i
$288$	−1.46486	−	2.53722i	−0.0863180	−	0.149507i
$289$	−3.29399	+	1.19891i	−0.193764	+	0.0705244i
$290$	−7.27693			−0.427316
$291$	0.0636451	−	0.0231649i	0.00373094	−	0.00135795i
$292$	0.348621	−	1.97713i	0.0204015	−	0.115703i
$293$	−2.30659	−	1.93546i	−0.134753	−	0.113071i	0.572920	−	0.819611i	$-0.305810\pi$
$293$	−2.30659	−	1.93546i	−0.134753	−	0.113071i	−0.707673	+	0.706540i	$0.750255\pi$
$294$	0.736487	−	0.617986i	0.0429528	−	0.0360417i
$295$	−13.9628			−0.812945
$296$	5.54206	−	2.50710i	0.322126	−	0.145722i
$297$	−3.97384			−0.230586
$298$	−16.7403	+	14.0468i	−0.969742	+	0.813710i
$299$	−15.5824	−	13.0752i	−0.901156	−	0.756160i
$300$	0.0460319	−	0.261060i	0.00265765	−	0.0150723i
$301$	20.8506	−	7.58901i	1.20181	−	0.437423i
$302$	4.76351			0.274109
$303$	−2.44267	+	0.889059i	−0.140328	+	0.0510751i
$304$	0.782555	+	1.35542i	0.0448826	+	0.0777390i
$305$	−0.624562	−	3.54207i	−0.0357623	−	0.202818i
$306$	−6.63333	+	11.4893i	−0.379202	+	0.656797i
$307$	10.1927	+	17.6542i	0.581725	+	1.00758i	0.995275	+	0.0970962i	$0.0309555\pi$
$307$	10.1927	+	17.6542i	0.581725	+	1.00758i	−0.413550	+	0.910482i	$0.635711\pi$
$308$	−3.55682	+	2.98453i	−0.202669	+	0.170059i
$309$	0.433311	−	2.45743i	0.0246502	−	0.139798i
$310$	−0.646337	+	1.11949i	−0.0367095	+	0.0635827i
$311$	−11.2225	−	4.08465i	−0.636368	−	0.231619i	0.00363255	−	0.999993i	$-0.498844\pi$
$311$	−11.2225	−	4.08465i	−0.636368	−	0.231619i	−0.640001	+	0.768374i	$0.721066\pi$
$312$	0.694265	+	0.252692i	0.0393050	+	0.0143059i
$313$	1.07393	+	6.09057i	0.0607022	+	0.344259i	0.999999	+	0.00115447i	$0.000367479\pi$
$313$	1.07393	+	6.09057i	0.0607022	+	0.344259i	−0.939297	+	0.343105i	$0.888521\pi$
$314$	−8.32247	−	6.98338i	−0.469664	−	0.394095i
$315$	−4.12195	−	3.45873i	−0.232246	−	0.194877i
$316$	1.41070	+	8.00046i	0.0793579	+	0.450061i
$317$	−22.9568	−	8.35559i	−1.28938	−	0.469297i	−0.395858	−	0.918312i	$-0.629553\pi$
$317$	−22.9568	−	8.35559i	−1.28938	−	0.469297i	−0.893524	+	0.449015i	$0.851775\pi$
$318$	−2.93368	−	1.06777i	−0.164512	−	0.0598776i
$319$	9.19825	−	15.9318i	0.515003	−	0.892012i
$320$	−0.173648	+	0.984808i	−0.00970723	+	0.0550524i
$321$	−1.68532	+	1.41415i	−0.0940656	+	0.0789304i
$322$	6.70227	+	11.6087i	0.373503	+	0.646926i
$323$	3.54363	−	6.13775i	0.197173	−	0.341514i
$324$	1.45387	+	8.24530i	0.0807705	+	0.458072i
$325$	−1.39355	−	2.41369i	−0.0773000	−	0.133888i
$326$	−11.2153	+	4.08202i	−0.621156	+	0.226082i
$327$	−1.86503			−0.103136
$328$	−4.32287	+	1.57339i	−0.238690	+	0.0868762i
$329$	−3.86593	+	21.9248i	−0.213135	+	1.20875i
$330$	0.513369	+	0.430768i	0.0282600	+	0.0237130i
$331$	10.8995	−	9.14575i	0.599090	−	0.502696i	−0.292063	−	0.956399i	$-0.594342\pi$
$331$	10.8995	−	9.14575i	0.599090	−	0.502696i	0.891153	+	0.453703i	$0.149897\pi$
$332$	−0.511980			−0.0280986
$333$	−17.7697	+	1.34888i	−0.973775	+	0.0739182i
$334$	3.21263			0.175787
$335$	−5.01465	+	4.20779i	−0.273980	+	0.229896i
$336$	−0.372961	−	0.312952i	−0.0203467	−	0.0170729i
$337$	−0.826468	+	4.68713i	−0.0450206	+	0.255324i	−0.999008	−	0.0445207i	$-0.985824\pi$
$337$	−0.826468	+	4.68713i	−0.0450206	+	0.255324i	0.953988	+	0.299845i	$0.0969350\pi$
$338$	−4.91658	+	1.78949i	−0.267427	+	0.0973355i
$339$	−2.99335			−0.162576
$340$	4.25520	−	1.54877i	0.230771	−	0.0839936i
$341$	−1.63398	−	2.83013i	−0.0884849	−	0.153260i
$342$	−0.796237	−	4.51569i	−0.0430556	−	0.244180i
$343$	−9.75874	+	16.9026i	−0.526922	+	0.912656i
$344$	6.04063	+	10.4627i	0.325689	+	0.564109i
$345$	1.48208	−	1.24362i	0.0797927	−	0.0669541i
$346$	1.50014	−	8.50772i	0.0806481	−	0.457378i
$347$	3.13016	−	5.42159i	0.168036	−	0.291046i	−0.769694	−	0.638414i	$-0.779591\pi$
$347$	3.13016	−	5.42159i	0.168036	−	0.291046i	0.937729	+	0.347367i	$0.112924\pi$
$348$	1.81269	+	0.659764i	0.0971702	+	0.0353671i
$349$	−6.26986	−	2.28204i	−0.335618	−	0.122155i	0.168713	−	0.985665i	$-0.446039\pi$
$349$	−6.26986	−	2.28204i	−0.335618	−	0.122155i	−0.504331	+	0.863510i	$0.668261\pi$
$350$	0.318927	+	1.80873i	0.0170474	+	0.0966805i
$351$	−3.35605	−	2.81606i	−0.179133	−	0.150310i
$352$	−1.93660	−	1.62500i	−0.103221	−	0.0866130i
$353$	−4.26655	−	24.1968i	−0.227085	−	1.28787i	−0.858658	−	0.512549i	$-0.828701\pi$
$353$	−4.26655	−	24.1968i	−0.227085	−	1.28787i	0.631573	−	0.775316i	$-0.282410\pi$
$354$	3.47814	+	1.26594i	0.184861	+	0.0672838i
$355$	−7.29500	−	2.65516i	−0.387178	−	0.140921i
$356$	4.22280	−	7.31411i	0.223808	−	0.387647i
$357$	−0.382837	+	2.17118i	−0.0202619	+	0.114911i
$358$	−4.98377	+	4.18188i	−0.263400	+	0.221019i
$359$	1.54185	+	2.67057i	0.0813759	+	0.140947i	0.903841	−	0.427868i	$-0.140735\pi$
$359$	1.54185	+	2.67057i	0.0813759	+	0.140947i	−0.822465	+	0.568815i	$0.807402\pi$
$360$	1.46486	−	2.53722i	0.0772051	−	0.133723i
$361$	−2.87395	−	16.2990i	−0.151261	−	0.857842i
$362$	−3.08359	−	5.34094i	−0.162070	−	0.280714i
$363$	1.14808	−	0.417868i	0.0602588	−	0.0219324i
$364$	−5.11885			−0.268301
$365$	1.88655	−	0.686649i	0.0987467	−	0.0359409i
$366$	−0.165563	+	0.938956i	−0.00865413	+	0.0490800i
$367$	4.50569	+	3.78072i	0.235195	+	0.197352i	0.752766	−	0.658288i	$-0.228719\pi$
$367$	4.50569	+	3.78072i	0.235195	+	0.197352i	−0.517571	+	0.855640i	$0.673164\pi$
$368$	−5.59093	+	4.69135i	−0.291448	+	0.244554i
$369$	13.4776			0.701617
$370$	4.94225	+	3.54601i	0.256935	+	0.184348i
$371$	21.6301			1.12298
$372$	0.262501	−	0.220265i	0.0136101	−	0.0114202i
$373$	2.45064	+	2.05633i	0.126889	+	0.106473i	0.704024	−	0.710176i	$-0.251385\pi$
$373$	2.45064	+	2.05633i	0.126889	+	0.106473i	−0.577135	+	0.816649i	$0.695829\pi$
$374$	−1.98789	+	11.2739i	−0.102791	+	0.582957i
$375$	0.249100	−	0.0906651i	0.0128635	−	0.00468193i
$376$	−12.1217			−0.625126
$377$	19.0584	−	6.93667i	0.981555	−	0.357257i
$378$	1.44349	+	2.50020i	0.0742453	+	0.128597i
$379$	−3.70807	−	21.0295i	−0.190471	−	1.08021i	−0.918722	−	0.394904i	$-0.870778\pi$
$379$	−3.70807	−	21.0295i	−0.190471	−	1.08021i	0.728251	−	0.685310i	$-0.240333\pi$
$380$	−0.782555	+	1.35542i	−0.0401442	+	0.0695318i
$381$	0.0703542	+	0.121857i	0.00360435	+	0.00624292i
$382$	−9.34790	+	7.84382i	−0.478280	+	0.401325i
$383$	−5.26719	+	29.8717i	−0.269141	+	1.52637i	0.487837	+	0.872935i	$0.337786\pi$
$383$	−5.26719	+	29.8717i	−0.269141	+	1.52637i	−0.756978	+	0.653440i	$0.773325\pi$
$384$	0.132544	−	0.229572i	0.00676383	−	0.0117153i
$385$	−4.36309	−	1.58804i	−0.222364	−	0.0809338i
$386$	10.0501	+	3.65795i	0.511538	+	0.186185i
$387$	−6.14624	−	34.8571i	−0.312431	−	1.77188i
$388$	−0.195724	−	0.164232i	−0.00993639	−	0.00833762i
$389$	−2.90943	−	2.44131i	−0.147514	−	0.123779i	0.566044	−	0.824375i	$-0.308473\pi$
$389$	−2.90943	−	2.44131i	−0.147514	−	0.123779i	−0.713558	+	0.700596i	$0.752918\pi$
$390$	0.128295	+	0.727597i	0.00649647	+	0.0368433i
$391$	31.0563	+	11.3036i	1.57059	+	0.571647i
$392$	−3.40807	−	1.24044i	−0.172134	−	0.0626515i
$393$	−0.475930	+	0.824335i	−0.0240075	+	0.0415822i
$394$	0.648176	−	3.67599i	0.0326547	−	0.185194i
$395$	−6.22326	+	5.22193i	−0.313126	+	0.262744i
$396$	3.70326	+	6.41424i	0.186096	+	0.322328i
$397$	3.29455	−	5.70633i	0.165349	−	0.286393i	−0.771430	−	0.636314i	$-0.780458\pi$
$397$	3.29455	−	5.70633i	0.165349	−	0.286393i	0.936779	+	0.349921i	$0.113792\pi$
$398$	−3.13259	−	17.7658i	−0.157022	−	0.890519i
$399$	−0.381000	−	0.659911i	−0.0190738	−	0.0330369i
$400$	−0.939693	+	0.342020i	−0.0469846	+	0.0171010i
$401$	32.1958			1.60778			0.803891	−	0.594777i	$-0.202760\pi$
$401$	32.1958			1.60778			0.803891	+	0.594777i	$0.202760\pi$
$402$	1.63065	−	0.593509i	0.0813295	−	0.0296015i
$403$	0.625620	−	3.54807i	0.0311643	−	0.176742i
$404$	7.51181	+	6.30315i	0.373726	+	0.313594i
$405$	−6.41371	+	5.38174i	−0.318700	+	0.267421i
$406$	−13.3650			−0.663295
$407$	−14.0106	+	6.33811i	−0.694482	+	0.314168i
$408$	−1.20039			−0.0594282
$409$	−8.98171	+	7.53655i	−0.444117	+	0.372658i	−0.837247	−	0.546824i	$-0.815837\pi$
$409$	−8.98171	+	7.53655i	−0.444117	+	0.372658i	0.393130	+	0.919483i	$0.371392\pi$
$410$	−3.52403	−	2.95701i	−0.174040	−	0.146037i
$411$	−0.859397	+	4.87388i	−0.0423909	+	0.240411i
$412$	−8.84560	+	3.21953i	−0.435791	+	0.158615i
$413$	−25.6445			−1.26188
$414$	20.0929	−	7.31324i	0.987515	−	0.359426i
$415$	−0.255990	−	0.443388i	−0.0125661	−	0.0217651i
$416$	−0.483973	−	2.74475i	−0.0237287	−	0.134572i
$417$	2.27066	−	3.93290i	0.111195	−	0.192595i
$418$	−1.97834	−	3.42659i	−0.0967640	−	0.167600i
$419$	6.28642	−	5.27493i	0.307112	−	0.257697i	−0.476185	−	0.879345i	$-0.657981\pi$
$419$	6.28642	−	5.27493i	0.307112	−	0.257697i	0.783297	+	0.621648i	$0.213536\pi$
$420$	0.0845435	−	0.479470i	0.00412530	−	0.0233957i
$421$	−15.2363	+	26.3901i	−0.742572	+	1.28617i	0.208748	+	0.977969i	$0.433061\pi$
$421$	−15.2363	+	26.3901i	−0.742572	+	1.28617i	−0.951320	+	0.308203i	$0.900272\pi$
$422$	−4.12393	−	1.50099i	−0.200750	−	0.0730670i
$423$	33.3714	+	12.1462i	1.62258	+	0.590569i
$424$	2.04507	+	11.5982i	0.0993174	+	0.563257i
$425$	3.46887	+	2.91073i	0.168265	+	0.141191i
$426$	1.57646	+	1.32280i	0.0763795	+	0.0640900i
$427$	−1.14709	−	6.50546i	−0.0555115	−	0.314821i
$428$	7.79878	+	2.83852i	0.376968	+	0.137205i
$429$	−1.75514	−	0.638820i	−0.0847391	−	0.0308425i
$430$	−6.04063	+	10.4627i	−0.291305	+	0.504555i
$431$	0.107636	−	0.610434i	0.00518464	−	0.0294036i	−0.982106	−	0.188331i	$-0.939692\pi$
$431$	0.107636	−	0.610434i	0.00518464	−	0.0294036i	0.987290	+	0.158927i	$0.0508035\pi$
$432$	−1.20414	+	1.01039i	−0.0579343	+	0.0486126i
$433$	18.8017	+	32.5656i	0.903554	+	1.56500i	0.822847	+	0.568263i	$0.192384\pi$
$433$	18.8017	+	32.5656i	0.903554	+	1.56500i	0.0807067	+	0.996738i	$0.474282\pi$
$434$	−1.18708	+	2.05609i	−0.0569817	+	0.0986953i
$435$	0.334971	+	1.89971i	0.0160606	+	0.0910843i
$436$	3.51777	+	6.09295i	0.168471	+	0.291800i
$437$	−10.7340	+	3.90685i	−0.513476	+	0.186890i
$438$	−0.532196			−0.0254293
$439$	−9.96101	+	3.62551i	−0.475413	+	0.173036i	−0.568603	−	0.822612i	$-0.692516\pi$
$439$	−9.96101	+	3.62551i	−0.475413	+	0.173036i	0.0931899	+	0.995648i	$0.470294\pi$
$440$	0.438993	−	2.48965i	0.0209282	−	0.118689i
$441$	8.13962	+	6.82995i	0.387601	+	0.325236i
$442$	−9.66806	+	8.11246i	−0.459863	+	0.385871i
$443$	−8.87063			−0.421456			−0.210728	−	0.977545i	$-0.567584\pi$
$443$	−8.87063			−0.421456			−0.210728	+	0.977545i	$0.567584\pi$
$444$	−0.909615	−	1.33140i	−0.0431684	−	0.0631855i
$445$	8.44560			0.400360
$446$	7.64099	−	6.41156i	0.361812	−	0.303596i
$447$	4.43765	+	3.72363i	0.209893	+	0.176122i
$448$	−0.318927	+	1.80873i	−0.0150679	+	0.0854543i
$449$	25.4664	−	9.26901i	1.20183	−	0.437431i	0.337969	−	0.941157i	$-0.390260\pi$
$449$	25.4664	−	9.26901i	1.20183	−	0.437431i	0.863864	+	0.503726i	$0.168038\pi$
$450$	2.92973			0.138109
$451$	10.9285	−	3.97763i	0.514601	−	0.187299i
$452$	5.64597	+	9.77911i	0.265564	+	0.459971i
$453$	−0.219273	−	1.24356i	−0.0103024	−	0.0584276i
$454$	−11.1437	+	19.3015i	−0.523002	+	0.905866i
$455$	−2.55943	−	4.43306i	−0.119988	−	0.207825i
$456$	0.317824	−	0.266686i	0.0148835	−	0.0124887i
$457$	0.705269	−	3.99978i	0.0329911	−	0.187102i	−0.963859	−	0.266414i	$-0.914161\pi$
$457$	0.705269	−	3.99978i	0.0329911	−	0.187102i	0.996850	+	0.0793120i	$0.0252723\pi$
$458$	−10.3480	+	17.9232i	−0.483528	+	0.837496i
$459$	6.68872	+	2.43450i	0.312203	+	0.113633i
$460$	−6.85830	−	2.49622i	−0.319770	−	0.116387i
$461$	−7.39956	−	41.9650i	−0.344632	−	1.95451i	−0.294068	−	0.955785i	$-0.595009\pi$
$461$	−7.39956	−	41.9650i	−0.344632	−	1.95451i	−0.0505642	−	0.998721i	$-0.516102\pi$
$462$	0.942868	+	0.791160i	0.0438662	+	0.0368081i
$463$	4.79264	+	4.02150i	0.222733	+	0.186895i	0.747325	−	0.664459i	$-0.231338\pi$
$463$	4.79264	+	4.02150i	0.222733	+	0.186895i	−0.524592	+	0.851354i	$0.675782\pi$
$464$	−1.26363	−	7.16638i	−0.0586624	−	0.332691i
$465$	0.322006	+	0.117200i	0.0149326	+	0.00543504i
$466$	2.62670	+	0.956041i	0.121680	+	0.0442878i
$467$	19.9452	−	34.5461i	0.922953	−	1.59860i	0.128132	−	0.991757i	$-0.459102\pi$
$467$	19.9452	−	34.5461i	0.922953	−	1.59860i	0.794821	−	0.606844i	$-0.207565\pi$
$468$	−1.41791	+	8.04137i	−0.0655429	+	0.371713i
$469$	−9.21006	+	7.72816i	−0.425281	+	0.356853i
$470$	−6.06083	−	10.4977i	−0.279565	−	0.484221i
$471$	−1.43998	+	2.49412i	−0.0663508	+	0.114923i
$472$	−2.42461	−	13.7507i	−0.111602	−	0.632926i
$473$	−15.2711	−	26.4502i	−0.702164	−	1.21618i
$474$	2.02366	−	0.736553i	0.0929499	−	0.0338310i
$475$	−1.56511			−0.0718122
$476$	7.81522	−	2.84451i	0.358210	−	0.130378i
$477$	5.99150	−	33.9795i	0.274332	−	1.55581i
$478$	−1.55697	−	1.30645i	−0.0712142	−	0.0597558i
$479$	−30.4396	+	25.5418i	−1.39082	+	1.16704i	−0.425813	+	0.904811i	$0.640012\pi$
$479$	−30.4396	+	25.5418i	−1.39082	+	1.16704i	−0.965007	+	0.262226i	$0.915544\pi$
$480$	0.265087			0.0120995
$481$	−16.3240	−	4.57589i	−0.744310	−	0.208642i
$482$	−5.16511			−0.235264
$483$	2.72204	−	2.28406i	0.123857	−	0.103928i
$484$	−3.53064	−	2.96256i	−0.160484	−	0.134662i
$485$	0.0443671	−	0.251618i	0.00201461	−	0.0114254i
$486$	6.51688	−	2.37195i	0.295612	−	0.107594i
$487$	−2.42924			−0.110079			−0.0550397	−	0.998484i	$-0.517529\pi$
$487$	−2.42924			−0.110079			−0.0550397	+	0.998484i	$0.517529\pi$
$488$	3.37980	−	1.23015i	0.152996	−	0.0556861i
$489$	1.58191	+	2.73995i	0.0715365	+	0.123905i
$490$	−0.629786	−	3.57169i	−0.0284508	−	0.161353i
$491$	7.86035	−	13.6145i	0.354733	−	0.614415i	−0.632340	−	0.774691i	$-0.717905\pi$
$491$	7.86035	−	13.6145i	0.354733	−	0.614415i	0.987072	+	0.160276i	$0.0512386\pi$
$492$	0.609740	+	1.05610i	0.0274892	+	0.0476127i
$493$	−25.2427	+	21.1812i	−1.13688	+	0.953952i
$494$	0.757472	−	4.29583i	0.0340803	−	0.193279i
$495$	−3.70326	+	6.41424i	−0.166449	+	0.288299i
$496$	−1.21472	−	0.442121i	−0.0545424	−	0.0198518i
$497$	−13.3982	−	4.87655i	−0.600991	−	0.218743i
$498$	0.0235674	+	0.133657i	0.00105608	+	0.00598933i
$499$	14.2312	+	11.9414i	0.637076	+	0.534570i	0.903119	−	0.429391i	$-0.141272\pi$
$499$	14.2312	+	11.9414i	0.637076	+	0.534570i	−0.266043	+	0.963961i	$0.585716\pi$
$500$	−0.766044	−	0.642788i	−0.0342585	−	0.0287463i
$501$	−0.147883	−	0.838688i	−0.00660694	−	0.0374698i
$502$	24.6355	+	8.96658i	1.09954	+	0.400198i
$503$	15.6012	+	5.67838i	0.695624	+	0.253186i	0.665541	−	0.746361i	$-0.268201\pi$
$503$	15.6012	+	5.67838i	0.695624	+	0.253186i	0.0300827	+	0.999547i	$0.490423\pi$
$504$	2.69041	−	4.65993i	0.119840	−	0.207570i
$505$	−1.70279	+	9.65699i	−0.0757731	+	0.429730i
$506$	14.1342	−	11.8600i	0.628342	−	0.527242i
$507$	0.693484	+	1.20115i	0.0307987	+	0.0533449i
$508$	0.265400	−	0.459687i	0.0117752	−	0.0203953i
$509$	−1.18550	−	6.72330i	−0.0525463	−	0.298005i	0.947197	−	0.320652i	$-0.103902\pi$
$509$	−1.18550	−	6.72330i	−0.0525463	−	0.298005i	−0.999744	+	0.0226465i	$0.992791\pi$
$510$	−0.600195	−	1.03957i	−0.0265771	−	0.0460329i
$511$	3.46490	−	1.26112i	0.153278	−	0.0557887i
$512$	−1.00000			−0.0441942
$513$	−2.31182	+	0.841434i	−0.102069	+	0.0371502i
$514$	1.35440	−	7.68119i	0.0597401	−	0.338803i
$515$	−7.21100	−	6.05074i	−0.317754	−	0.266628i
$516$	2.45332	−	2.05858i	0.108001	−	0.0906240i
$517$	30.6442			1.34773
$518$	9.07707	+	6.51271i	0.398824	+	0.286152i
$519$	−2.29008			−0.100523
$520$	2.13504	−	1.79151i	0.0936275	−	0.0785628i
$521$	2.40152	+	2.01511i	0.105212	+	0.0882836i	0.693876	−	0.720094i	$-0.255901\pi$
$521$	2.40152	+	2.01511i	0.105212	+	0.0882836i	−0.588664	+	0.808378i	$0.700346\pi$
$522$	−3.70208	+	20.9955i	−0.162036	+	0.918950i
$523$	38.9959	−	14.1933i	1.70517	−	0.620631i	0.708772	−	0.705437i	$-0.249249\pi$
$523$	38.9959	−	14.1933i	1.70517	−	0.620631i	0.996397	+	0.0848063i	$0.0270271\pi$
$524$	3.59075			0.156863
$525$	0.457505	−	0.166518i	0.0199671	−	0.00726745i
$526$	−5.69863	−	9.87031i	−0.248472	−	0.430366i
$527$	1.01647	+	5.76467i	0.0442780	+	0.251113i
$528$	−0.335078	+	0.580372i	−0.0145824	+	0.0252574i
$529$	−15.1337	−	26.2123i	−0.657985	−	1.13966i
$530$	−9.02177	+	7.57017i	−0.391881	+	0.328827i
$531$	−7.10346	+	40.2857i	−0.308264	+	1.74825i
$532$	−1.43726	+	2.48941i	−0.0623133	+	0.107930i
$533$	12.0482	+	4.38519i	0.521866	+	0.189944i
$534$	−2.10380	−	0.765721i	−0.0910404	−	0.0331360i
$535$	1.44116	+	8.17321i	0.0623066	+	0.353359i
$536$	−5.01465	−	4.20779i	−0.216600	−	0.181749i
$537$	1.32113	+	1.10856i	0.0570111	+	0.0478380i
$538$	−3.42902	−	19.4469i	−0.147836	−	0.838417i
$539$	8.61580	+	3.13590i	0.371109	+	0.135073i
$540$	−1.47710	−	0.537619i	−0.0635641	−	0.0231355i
$541$	13.5122	−	23.4039i	0.580937	−	1.00621i	−0.414432	−	0.910080i	$-0.636020\pi$
$541$	13.5122	−	23.4039i	0.580937	−	1.00621i	0.995369	−	0.0961315i	$-0.0306469\pi$
$542$	1.92837	−	10.9363i	0.0828307	−	0.469756i
$543$	−1.25236	+	1.05086i	−0.0537439	+	0.0450965i
$544$	2.26414	+	3.92161i	0.0970744	+	0.168138i
$545$	−3.51777	+	6.09295i	−0.150685	+	0.260993i
$546$	0.235630	+	1.33633i	0.0100841	+	0.0571895i
$547$	6.55974	+	11.3618i	0.280474	+	0.485796i	0.971502	−	0.237033i	$-0.0761749\pi$
$547$	6.55974	+	11.3618i	0.280474	+	0.485796i	−0.691027	+	0.722829i	$0.742842\pi$
$548$	17.5437	−	6.38538i	0.749430	−	0.272770i
$549$	−10.5374			−0.449725
$550$	2.37560	−	0.864647i	0.101296	−	0.0368687i
$551$	1.97771	−	11.2162i	0.0842534	−	0.477825i
$552$	1.48208	+	1.24362i	0.0630817	+	0.0529318i
$553$	−11.4298	+	9.59075i	−0.486045	+	0.407840i
$554$	−30.7257			−1.30541
$555$	0.698220	−	1.45345i	0.0296378	−	0.0616956i
$556$	−17.1314			−0.726535
$557$	20.6130	−	17.2964i	0.873403	−	0.732872i	−0.0914092	−	0.995813i	$-0.529137\pi$
$557$	20.6130	−	17.2964i	0.873403	−	0.732872i	0.964812	+	0.262942i	$0.0846927\pi$
$558$	2.90115	+	2.43436i	0.122816	+	0.103054i
$559$	5.84700	−	33.1600i	0.247302	−	1.40252i
$560$	−1.72587	+	0.628164i	−0.0729312	+	0.0265448i
$561$	3.03466			0.128123
$562$	29.4772	−	10.7288i	1.24342	−	0.452568i
$563$	8.15416	+	14.1234i	0.343657	+	0.595231i	0.985109	−	0.171932i	$-0.0550010\pi$
$563$	8.15416	+	14.1234i	0.343657	+	0.595231i	−0.641452	+	0.767163i	$0.721668\pi$
$564$	0.557982	+	3.16448i	0.0234953	+	0.133248i
$565$	−5.64597	+	9.77911i	−0.237528	+	0.411410i
$566$	0.555892	+	0.962833i	0.0233659	+	0.0404709i
$567$	−11.7796	+	9.88426i	−0.494697	+	0.415100i
$568$	1.34806	−	7.64523i	0.0565634	−	0.320787i
$569$	20.6395	−	35.7486i	0.865251	−	1.49866i	−0.00154631	−	0.999999i	$-0.500492\pi$
$569$	20.6395	−	35.7486i	0.865251	−	1.49866i	0.866798	−	0.498660i	$-0.166174\pi$
$570$	0.389869	+	0.141901i	0.0163298	+	0.00594357i
$571$	35.9755	+	13.0940i	1.50553	+	0.547968i	0.957485	−	0.288482i	$-0.0931506\pi$
$571$	35.9755	+	13.0940i	1.50553	+	0.547968i	0.548043	+	0.836450i	$0.315373\pi$
$572$	1.22351	+	6.93889i	0.0511576	+	0.290129i
$573$	2.47801	+	2.07930i	0.103520	+	0.0868638i
$574$	−6.47234	−	5.43094i	−0.270150	−	0.226683i
$575$	−1.26736	−	7.18757i	−0.0528526	−	0.299742i
$576$	2.75304	+	1.00203i	0.114710	+	0.0417511i
$577$	−10.3860	−	3.78020i	−0.432376	−	0.157372i	0.116658	−	0.993172i	$-0.462782\pi$
$577$	−10.3860	−	3.78020i	−0.432376	−	0.157372i	−0.549034	+	0.835800i	$0.685004\pi$
$578$	1.75270	−	3.03576i	0.0729026	−	0.126271i
$579$	0.492316	−	2.79206i	0.0204600	−	0.116034i
$580$	5.57445	−	4.67752i	0.231467	−	0.194224i
$581$	−0.470159	−	0.814339i	−0.0195055	−	0.0337845i
$582$	−0.0338649	+	0.0586556i	−0.00140374	+	0.00243135i
$583$	−5.17006	−	29.3208i	−0.214122	−	1.21435i
$584$	1.00381	+	1.73866i	0.0415381	+	0.0719461i
$585$	−7.67299	+	2.79274i	−0.317239	+	0.115466i
$586$	3.01105			0.124385
$587$	−12.3824	+	4.50682i	−0.511076	+	0.186016i	−0.584669	−	0.811272i	$-0.698776\pi$
$587$	−12.3824	+	4.50682i	−0.511076	+	0.186016i	0.0735931	+	0.997288i	$0.476553\pi$
$588$	−0.166948	+	0.946810i	−0.00688483	+	0.0390458i
$589$	−1.54984	−	1.30047i	−0.0638602	−	0.0535851i
$590$	10.6961	−	8.97511i	0.440352	−	0.369499i
$591$	−0.989490			−0.0407022
$592$	−2.63393	+	5.48292i	−0.108254	+	0.225347i
$593$	−30.0008			−1.23199			−0.615993	−	0.787752i	$-0.711245\pi$
$593$	−30.0008			−1.23199			−0.615993	+	0.787752i	$0.711245\pi$
$594$	3.04414	−	2.55434i	0.124902	−	0.104806i
$595$	6.37103	+	5.34593i	0.261187	+	0.219162i
$596$	3.79473	−	21.5210i	0.155438	−	0.881533i
$597$	−4.49373	+	1.63559i	−0.183916	+	0.0669401i
$598$	20.3414			0.831823
$599$	−36.9289	+	13.4410i	−1.50887	+	0.549185i	−0.958340	−	0.285629i	$-0.907798\pi$
$599$	−36.9289	+	13.4410i	−1.50887	+	0.549185i	−0.550533	+	0.834814i	$0.685575\pi$
$600$	0.132544	+	0.229572i	0.00541107	+	0.00937224i
$601$	1.03805	+	5.88707i	0.0423429	+	0.240139i	0.998632	−	0.0522834i	$-0.0166499\pi$
$601$	1.03805	+	5.88707i	0.0423429	+	0.240139i	−0.956289	+	0.292422i	$0.905539\pi$
$602$	−11.0944	+	19.2160i	−0.452174	+	0.783188i
$603$	9.58924	+	16.6091i	0.390504	+	0.676373i
$604$	−3.64906	+	3.06193i	−0.148478	+	0.124588i
$605$	0.800331	−	4.53890i	0.0325381	−	0.184533i
$606$	1.29972	−	2.25118i	0.0527974	−	0.0914478i
$607$	26.0973	+	9.49864i	1.05926	+	0.385538i	0.812149	−	0.583450i	$-0.198298\pi$
$607$	26.0973	+	9.49864i	1.05926	+	0.385538i	0.247108	+	0.968988i	$0.420520\pi$
$608$	−1.47072	−	0.535299i	−0.0596457	−	0.0217092i
$609$	0.615217	+	3.48907i	0.0249299	+	0.141384i
$610$	2.75524	+	2.31192i	0.111556	+	0.0936069i
$611$	25.8802	+	21.7160i	1.04700	+	0.878537i
$612$	−2.30373	−	13.0651i	−0.0931228	−	0.528126i
$613$	−37.7584	−	13.7429i	−1.52505	−	0.555071i	−0.562644	−	0.826700i	$-0.690216\pi$
$613$	−37.7584	−	13.7429i	−1.52505	−	0.555071i	−0.962402	+	0.271628i	$0.912438\pi$
$614$	−19.1559	−	6.97218i	−0.773070	−	0.281374i
$615$	−0.609740	+	1.05610i	−0.0245871	+	0.0425861i
$616$	0.806267	−	4.57257i	0.0324854	−	0.184234i
$617$	−22.0527	+	18.5044i	−0.887808	+	0.744959i	−0.967769	−	0.251839i	$-0.918965\pi$
$617$	−22.0527	+	18.5044i	−0.887808	+	0.744959i	0.0799615	+	0.996798i	$0.474520\pi$
$618$	1.24767	+	2.16103i	0.0501886	+	0.0869293i
$619$	−8.67414	+	15.0240i	−0.348643	+	0.603867i	−0.986009	−	0.166694i	$-0.946691\pi$
$619$	−8.67414	+	15.0240i	−0.348643	+	0.603867i	0.637366	+	0.770561i	$0.280024\pi$
$620$	−0.224471	−	1.27304i	−0.00901495	−	0.0511263i
$621$	−5.73619	−	9.93538i	−0.230185	−	0.398693i
$622$	11.2225	−	4.08465i	0.449980	−	0.163779i
$623$	15.5114			0.621453
$624$	−0.694265	+	0.252692i	−0.0277929	+	0.0101158i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	−4.73762	−	3.97534i	−0.189353	−	0.158886i
$627$	−0.803479	+	0.674199i	−0.0320878	+	0.0269249i
$628$	10.8642			0.433529
$629$	27.4655	−	2.08487i	1.09512	−	0.0831294i
$630$	5.38083			0.214377
$631$	5.41588	−	4.54446i	0.215603	−	0.180912i	−0.528590	−	0.848877i	$-0.677279\pi$
$631$	5.41588	−	4.54446i	0.215603	−	0.180912i	0.744192	+	0.667965i	$0.232835\pi$
$632$	−6.22326	−	5.22193i	−0.247548	−	0.207717i
$633$	−0.202015	+	1.14569i	−0.00802939	+	0.0455369i
$634$	22.9568	−	8.35559i	0.911731	−	0.331843i
$635$	0.530801			0.0210642
$636$	2.93368	−	1.06777i	0.116328	−	0.0423399i
$637$	5.05410	+	8.75396i	0.200251	+	0.346845i
$638$	3.19452	+	18.1170i	0.126472	+	0.717260i
$639$	−11.3720	+	19.6969i	−0.449869	+	0.779196i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−35.8501	+	30.0818i	−1.41599	+	1.18816i	−0.462549	+	0.886594i	$0.653065\pi$
$641$	−35.8501	+	30.0818i	−1.41599	+	1.18816i	−0.953445	+	0.301566i	$0.902490\pi$
$642$	0.382032	−	2.16661i	0.0150776	−	0.0855093i
$643$	14.7191	−	25.4942i	0.580464	−	1.00539i	−0.414960	−	0.909840i	$-0.636205\pi$
$643$	14.7191	−	25.4942i	0.580464	−	1.00539i	0.995424	−	0.0955537i	$-0.0304622\pi$
$644$	−12.5961	−	4.58462i	−0.496358	−	0.180659i
$645$	3.00944	+	1.09535i	0.118497	+	0.0431293i
$646$	1.23069	+	6.97960i	0.0484209	+	0.274609i
$647$	−22.2138	−	18.6396i	−0.873315	−	0.732799i	0.0914782	−	0.995807i	$-0.470841\pi$
$647$	−22.2138	−	18.6396i	−0.873315	−	0.732799i	−0.964793	+	0.263009i	$0.915285\pi$
$648$	−6.41371	−	5.38174i	−0.251954	−	0.211415i
$649$	6.12956	+	34.7625i	0.240606	+	1.36455i
$650$	2.61901	+	0.953241i	0.102726	+	0.0373892i
$651$	0.591405	+	0.215254i	0.0231790	+	0.00843646i
$652$	5.96752	−	10.3360i	0.233706	−	0.404791i
$653$	5.47769	−	31.0655i	0.214359	−	1.21569i	−0.667657	−	0.744469i	$-0.732703\pi$
$653$	5.47769	−	31.0655i	0.214359	−	1.21569i	0.882016	−	0.471220i	$-0.156186\pi$
$654$	1.42870	−	1.19882i	0.0558664	−	0.0468775i
$655$	1.79537	+	3.10968i	0.0701511	+	0.121505i
$656$	2.30015	−	3.98397i	0.0898057	−	0.155548i
$657$	−1.02136	−	5.79245i	−0.0398472	−	0.225985i
$658$	−11.1315	−	19.2803i	−0.433951	−	0.751624i
$659$	17.1358	−	6.23694i	0.667518	−	0.242957i	0.0140390	−	0.999901i	$-0.495531\pi$
$659$	17.1358	−	6.23694i	0.667518	−	0.242957i	0.653479	+	0.756945i	$0.273309\pi$
$660$	−0.670155			−0.0260858
$661$	−35.0863	+	12.7704i	−1.36470	+	0.496709i	−0.917503	−	0.397728i	$-0.869799\pi$
$661$	−35.0863	+	12.7704i	−1.36470	+	0.496709i	−0.447194	+	0.894437i	$0.647577\pi$
$662$	−2.47071	+	14.0121i	−0.0960269	+	0.544596i
$663$	2.56288	+	2.15051i	0.0995339	+	0.0835188i
$664$	0.392200	−	0.329095i	0.0152203	−	0.0127713i
$665$	−2.87453			−0.111469
$666$	12.7454	−	12.4555i	0.493872	−	0.482639i
$667$	53.1103			2.05644
$668$	−2.46102	+	2.06504i	−0.0952196	+	0.0798987i
$669$	−2.02553	−	1.69962i	−0.0783115	−	0.0657111i
$670$	1.13673	−	6.44671i	0.0439157	−	0.249058i
$671$	−8.54433	+	3.10988i	−0.329850	+	0.120056i
$672$	0.486867			0.0187813
$673$	1.68715	−	0.614073i	0.0650349	−	0.0236708i	−0.309298	−	0.950965i	$-0.600094\pi$
$673$	1.68715	−	0.614073i	0.0650349	−	0.0236708i	0.374333	+	0.927294i	$0.377872\pi$
$674$	−2.37972	−	4.12180i	−0.0916634	−	0.158766i
$675$	−0.272957	−	1.54801i	−0.0105061	−	0.0595831i
$676$	2.61606	−	4.53115i	0.100618	−	0.174275i
$677$	−23.8150	−	41.2488i	−0.915286	−	1.58532i	−0.806482	−	0.591258i	$-0.798631\pi$
$677$	−23.8150	−	41.2488i	−0.915286	−	1.58532i	−0.108804	−	0.994063i	$-0.534702\pi$
$678$	2.29304	−	1.92409i	0.0880636	−	0.0738941i
$679$	0.0814859	−	0.462129i	0.00312714	−	0.0177349i
$680$	−2.26414	+	3.92161i	−0.0868260	+	0.150387i
$681$	5.55182	+	2.02070i	0.212746	+	0.0774333i
$682$	3.07087	+	1.11771i	0.117590	+	0.0427992i
$683$	2.01948	+	11.4530i	0.0772731	+	0.438238i	0.998758	+	0.0498235i	$0.0158659\pi$
$683$	2.01948	+	11.4530i	0.0772731	+	0.438238i	−0.921485	+	0.388414i	$0.873023\pi$
$684$	3.51258	+	2.94740i	0.134307	+	0.112697i
$685$	14.3018	+	12.0006i	0.546442	+	0.458519i
$686$	−3.38917	−	19.2210i	−0.129399	−	0.733860i
$687$	5.15536	+	1.87640i	0.196689	+	0.0715890i
$688$	−11.3527	−	4.13203i	−0.432816	−	0.157532i
$689$	16.4119	−	28.4263i	0.625244	−	1.08295i
$690$	−0.335961	+	1.90533i	−0.0127898	+	0.0725347i
$691$	−32.7367	+	27.4693i	−1.24536	+	1.04498i	−0.248277	+	0.968689i	$0.579864\pi$
$691$	−32.7367	+	27.4693i	−1.24536	+	1.04498i	−0.997085	+	0.0762942i	$0.975691\pi$
$692$	4.31948	+	7.48156i	0.164202	+	0.284406i
$693$	−6.80152	+	11.7806i	−0.258368	+	0.447507i
$694$	1.08709	+	6.16520i	0.0412654	+	0.234028i
$695$	−8.56572	−	14.8363i	−0.324916	−	0.562771i
$696$	−1.81269	+	0.659764i	−0.0687097	+	0.0250083i
$697$	−20.8315			−0.789048
$698$	6.26986	−	2.28204i	0.237318	−	0.0863766i
$699$	0.128672	−	0.729734i	0.00486682	−	0.0276011i
$700$	−1.40694	−	1.18056i	−0.0531773	−	0.0446211i
$701$	−12.0899	+	10.1446i	−0.456628	+	0.383156i	−0.841889	−	0.539651i	$-0.818556\pi$
$701$	−12.0899	+	10.1446i	−0.456628	+	0.383156i	0.385261	+	0.922808i	$0.374112\pi$
$702$	4.38101			0.165351
$703$	−6.80878	+	6.65391i	−0.256798	+	0.250957i
$704$	2.52806			0.0952798
$705$	−2.46152	+	2.06546i	−0.0927064	+	0.0777899i
$706$	18.8218	+	15.7933i	0.708366	+	0.594390i
$707$	−3.12739	+	17.7363i	−0.117618	+	0.667043i
$708$	−3.47814	+	1.26594i	−0.130716	+	0.0475769i
$709$	−9.40905			−0.353364			−0.176682	−	0.984268i	$-0.556536\pi$
$709$	−9.40905			−0.353364			−0.176682	+	0.984268i	$0.556536\pi$
$710$	7.29500	−	2.65516i	0.273776	−	0.0996464i
$711$	11.9004	+	20.6121i	0.446299	+	0.773013i
$712$	1.46656	+	8.31729i	0.0549618	+	0.311704i
$713$	4.71726	−	8.17053i	0.176663	−	0.305989i
$714$	−1.10234	−	1.90930i	−0.0412539	−	0.0714538i
$715$	−5.39750	+	4.52904i	−0.201855	+	0.169376i
$716$	1.12973	−	6.40701i	0.0422199	−	0.239441i
$717$	−0.269392	+	0.466601i	−0.0100606	+	0.0174255i
$718$	−2.89773	−	1.05469i	−0.108142	−	0.0393606i
$719$	26.5250	+	9.65432i	0.989216	+	0.360045i	0.785417	−	0.618967i	$-0.212449\pi$
$719$	26.5250	+	9.65432i	0.989216	+	0.360045i	0.203800	+	0.979013i	$0.434671\pi$
$720$	0.508742	+	2.88522i	0.0189597	+	0.107526i
$721$	−13.2439	−	11.1130i	−0.493229	−	0.413869i
$722$	12.6784	+	10.6384i	0.471840	+	0.395921i
$723$	0.237760	+	1.34840i	0.00884237	+	0.0501476i
$724$	5.79526	+	2.10930i	0.215379	+	0.0783916i
$725$	6.83808	+	2.48886i	0.253960	+	0.0924338i
$726$	−0.610883	+	1.05808i	−0.0226720	+	0.0392690i
$727$	−5.68599	+	32.2469i	−0.210882	+	1.19597i	0.677030	+	0.735956i	$0.263267\pi$
$727$	−5.68599	+	32.2469i	−0.210882	+	1.19597i	−0.887912	+	0.460014i	$0.847844\pi$
$728$	3.92127	−	3.29034i	0.145332	−	0.121948i
$729$	11.6395	+	20.1603i	0.431094	+	0.746677i
$730$	−1.00381	+	1.73866i	−0.0371528	+	0.0643506i
$731$	9.49984	+	53.8763i	0.351364	+	1.99269i
$732$	−0.476720	−	0.825704i	−0.0176201	−	0.0305189i
$733$	34.0169	−	12.3811i	1.25644	−	0.457308i	0.373869	−	0.927481i	$-0.378031\pi$
$733$	34.0169	−	12.3811i	1.25644	−	0.457308i	0.882574	+	0.470173i	$0.155809\pi$
$734$	−5.88175			−0.217100
$735$	−0.903436	+	0.328824i	−0.0333237	+	0.0121288i
$736$	1.26736	−	7.18757i	0.0467156	−	0.264937i
$737$	12.6773	+	10.6375i	0.466976	+	0.391839i
$738$	−10.3245	+	8.66325i	−0.380049	+	0.318899i
$739$	−2.25546			−0.0829686			−0.0414843	−	0.999139i	$-0.513209\pi$
$739$	−2.25546			−0.0829686			−0.0414843	+	0.999139i	$0.513209\pi$
$740$	−6.06531	+	0.460411i	−0.222965	+	0.0169251i
$741$	−1.15634			−0.0424791
$742$	−16.5697	+	13.9036i	−0.608291	+	0.510417i
$743$	−29.0300	−	24.3591i	−1.06501	−	0.893648i	−0.0704177	−	0.997518i	$-0.522433\pi$
$743$	−29.0300	−	24.3591i	−1.06501	−	0.893648i	−0.994591	+	0.103869i	$0.966878\pi$
$744$	−0.0595042	+	0.337465i	−0.00218153	+	0.0123721i
$745$	20.5351	−	7.47415i	0.752347	−	0.273832i
$746$	−3.19908			−0.117127
$747$	−1.40950	+	0.513018i	−0.0515711	+	0.0187703i
$748$	−5.72389	−	9.91406i	−0.209286	−	0.362494i
$749$	2.64687	+	15.0111i	0.0967145	+	0.548495i
$750$	−0.132544	+	0.229572i	−0.00483980	+	0.00838279i
$751$	−25.9988	−	45.0313i	−0.948710	−	1.64321i	−0.748147	−	0.663533i	$-0.769056\pi$
$751$	−25.9988	−	45.0313i	−0.948710	−	1.64321i	−0.200563	−	0.979681i	$-0.564277\pi$
$752$	9.28572	−	7.79165i	0.338616	−	0.284132i
$753$	1.20680	−	6.84408i	0.0439781	−	0.249412i
$754$	−10.1407	+	17.5643i	−0.369304	+	0.639653i
$755$	−4.47624	−	1.62922i	−0.162907	−	0.0592933i
$756$	−2.71288	−	0.987408i	−0.0986665	−	0.0359117i
$757$	5.14835	+	29.1977i	0.187120	+	1.06121i	0.923201	+	0.384317i	$0.125563\pi$
$757$	5.14835	+	29.1977i	0.187120	+	1.06121i	−0.736081	+	0.676893i	$0.763326\pi$
$758$	16.3581	+	13.7260i	0.594152	+	0.498552i
$759$	−3.74680	−	3.14393i	−0.136000	−	0.114118i
$760$	−0.271778	−	1.54133i	−0.00985844	−	0.0559100i
$761$	8.27732	+	3.01270i	0.300053	+	0.109210i	0.487659	−	0.873034i	$-0.337851\pi$
$761$	8.27732	+	3.01270i	0.300053	+	0.109210i	−0.187607	+	0.982244i	$0.560073\pi$
$762$	−0.132223	−	0.0481251i	−0.00478992	−	0.00174339i
$763$	−6.46083	+	11.1905i	−0.233898	+	0.405123i
$764$	2.11900	−	12.0174i	0.0766626	−	0.434775i
$765$	10.1628	−	8.52764i	0.367439	−	0.308318i
$766$	−15.1663	−	26.2688i	−0.547980	−	0.949129i
$767$	−19.4578	+	33.7019i	−0.702580	+	1.21690i
$768$	0.0460319	+	0.261060i	0.00166103	+	0.00942018i
$769$	−11.2014	−	19.4013i	−0.403932	−	0.699630i	0.590265	−	0.807210i	$-0.299023\pi$
$769$	−11.2014	−	19.4013i	−0.403932	−	0.699630i	−0.994196	+	0.107580i	$0.965690\pi$
$770$	4.36309	−	1.58804i	0.157235	−	0.0572288i
$771$	−2.06760			−0.0744627
$772$	−10.0501	+	3.65795i	−0.361712	+	0.131652i
$773$	−5.90803	+	33.5061i	−0.212497	+	1.20513i	0.672700	+	0.739915i	$0.265134\pi$
$773$	−5.90803	+	33.5061i	−0.212497	+	1.20513i	−0.885197	+	0.465216i	$0.845977\pi$
$774$	27.1140	+	22.7513i	0.974592	+	0.817780i
$775$	0.990246	−	0.830915i	0.0355707	−	0.0298473i
$776$	0.255500			0.00917191
$777$	1.28237	−	2.66945i	0.0460048	−	0.0957660i
$778$	3.79800			0.136165
$779$	5.51550	−	4.62805i	0.197613	−	0.165817i
$780$	−0.565970	−	0.474906i	−0.0202650	−	0.0170043i
$781$	−3.40798	+	19.3276i	−0.121947	+	0.691596i
$782$	−31.0563	+	11.3036i	−1.11057	+	0.404215i
$783$	11.4386			0.408781
$784$	3.40807	−	1.24044i	0.121717	−	0.0443013i
$785$	5.43210	+	9.40868i	0.193880	+	0.335810i
$786$	−0.165289	−	0.937400i	−0.00589566	−	0.0334359i
$787$	10.4653	−	18.1265i	0.373049	−	0.646140i	−0.616984	−	0.786976i	$-0.711646\pi$
$787$	10.4653	−	18.1265i	0.373049	−	0.646140i	0.990033	+	0.140836i	$0.0449789\pi$
$788$	1.86635	+	3.23261i	0.0664860	+	0.115157i
$789$	−2.31442	+	1.94203i	−0.0823957	+	0.0691382i
$790$	1.41070	−	8.00046i	0.0501904	−	0.284644i
$791$	−10.3696	+	17.9606i	−0.368699	+	0.638605i
$792$	−6.95986	−	2.53318i	−0.247308	−	0.0900127i
$793$	−9.41982	−	3.42853i	−0.334507	−	0.121751i
$794$	1.14419	+	6.48900i	0.0406056	+	0.230286i
$795$	2.39156	+	2.00675i	0.0848197	+	0.0711722i
$796$	13.8193	+	11.5958i	0.489813	+	0.411002i
$797$	−4.37095	−	24.7889i	−0.154827	−	0.878067i	−0.958944	−	0.283596i	$-0.908473\pi$
$797$	−4.37095	−	24.7889i	−0.154827	−	0.878067i	0.804117	−	0.594471i	$-0.202639\pi$
$798$	0.716045	+	0.260619i	0.0253477	+	0.00922582i
$799$	−51.5800	−	18.7736i	−1.82477	−	0.664162i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	4.29663	−	24.3674i	0.151814	−	0.860980i
$802$	−24.6634	+	20.6951i	−0.870896	+	0.730768i
$803$	−2.53770	−	4.39543i	−0.0895535	−	0.155111i
$804$	−0.867652	+	1.50282i	−0.0305997	+	0.0530003i
$805$	−2.32767	−	13.2009i	−0.0820397	−	0.465270i
$806$	1.80140	+	3.12012i	0.0634516	+	0.109901i
$807$	−4.91897	+	1.79036i	−0.173156	+	0.0630236i
$808$	−9.80597			−0.344973
$809$	22.0943	−	8.04166i	0.776794	−	0.282730i	0.0769587	−	0.997034i	$-0.475479\pi$
$809$	22.0943	−	8.04166i	0.776794	−	0.282730i	0.699835	+	0.714304i	$0.253257\pi$
$810$	1.45387	−	8.24530i	0.0510837	−	0.289710i
$811$	−11.0257	−	9.25166i	−0.387165	−	0.324870i	0.428343	−	0.903616i	$-0.359098\pi$
$811$	−11.0257	−	9.25166i	−0.387165	−	0.324870i	−0.815507	+	0.578747i	$0.803542\pi$
$812$	10.2382	−	8.59087i	0.359290	−	0.301481i
$813$	−2.94381			−0.103244
$814$	6.65872	−	13.8611i	0.233388	−	0.485833i
$815$	11.9350			0.418066
$816$	0.919552	−	0.771596i	0.0321908	−	0.0270113i
$817$	−14.4847	−	12.1541i	−0.506757	−	0.425220i
$818$	2.03599	−	11.5467i	0.0711866	−	0.403720i
$819$	−14.0924	+	5.12923i	−0.492429	+	0.179230i
$820$	4.60030			0.160649
$821$	−33.9730	+	12.3652i	−1.18567	+	0.431548i	−0.858200	−	0.513315i	$-0.828417\pi$
$821$	−33.9730	+	12.3652i	−1.18567	+	0.431548i	−0.327467	+	0.944863i	$0.606195\pi$
$822$	−2.47454	−	4.28602i	−0.0863094	−	0.149492i
$823$	2.44793	+	13.8829i	0.0853296	+	0.483928i	0.997285	+	0.0736387i	$0.0234612\pi$
$823$	2.44793	+	13.8829i	0.0853296	+	0.483928i	−0.911955	+	0.410289i	$0.865428\pi$
$824$	4.70664	−	8.15214i	0.163964	−	0.283993i
$825$	−0.335078	−	0.580372i	−0.0116659	−	0.0202059i
$826$	19.6448	−	16.4839i	0.683530	−	0.573550i
$827$	8.48506	−	48.1212i	0.295055	−	1.67334i	−0.371926	−	0.928262i	$-0.621302\pi$
$827$	8.48506	−	48.1212i	0.295055	−	1.67334i	0.666981	−	0.745075i	$-0.267586\pi$
$828$	−10.6912	+	18.5178i	−0.371546	+	0.643537i
$829$	−5.23376	−	1.90493i	−0.181776	−	0.0661611i	0.249529	−	0.968367i	$-0.419724\pi$
$829$	−5.23376	−	1.90493i	−0.181776	−	0.0661611i	−0.431305	+	0.902206i	$0.641947\pi$
$830$	0.481104	+	0.175108i	0.0166994	+	0.00607807i
$831$	1.41436	+	8.02125i	0.0490637	+	0.278254i
$832$	2.13504	+	1.79151i	0.0740191	+	0.0621094i
$833$	−12.5809	−	10.5566i	−0.435902	−	0.365765i
$834$	0.788592	+	4.47233i	0.0273067	+	0.154864i
$835$	−3.01888	−	1.09878i	−0.104473	−	0.0380250i
$836$	3.71807	+	1.35327i	0.128592	+	0.0468037i
$837$	1.01597	−	1.75972i	0.0351172	−	0.0608247i
$838$	−1.42502	+	8.08166i	−0.0492263	+	0.279176i
$839$	−2.11459	+	1.77435i	−0.0730038	+	0.0612575i	−0.678559	−	0.734546i	$-0.737395\pi$
$839$	−2.11459	+	1.77435i	−0.0730038	+	0.0612575i	0.605556	+	0.795803i	$0.292951\pi$
$840$	0.243433	+	0.421639i	0.00839925	+	0.0145479i
$841$	−11.9769	+	20.7445i	−0.412995	+	0.715329i
$842$	−5.29151	−	30.0097i	−0.182358	−	1.03420i
$843$	−4.15775	−	7.20144i	−0.143201	−	0.248031i
$844$	4.12393	−	1.50099i	0.141952	−	0.0516661i
$845$	5.23212			0.179990
$846$	−33.3714	+	12.1462i	−1.14733	+	0.417595i
$847$	1.46991	−	8.33628i	0.0505067	−	0.286438i
$848$	−9.02177	−	7.57017i	−0.309809	−	0.259961i
$849$	0.225768	−	0.189442i	0.00774834	−	0.00650163i
$850$	−4.52829			−0.155319
$851$	−36.0707	−	25.8804i	−1.23649	−	0.887168i
$852$	−2.05792			−0.0705031
$853$	15.0752	−	12.6496i	0.516165	−	0.433114i	−0.347128	−	0.937818i	$-0.612843\pi$
$853$	15.0752	−	12.6496i	0.516165	−	0.433114i	0.863292	+	0.504704i	$0.168398\pi$
$854$	5.06035	+	4.24614i	0.173162	+	0.145300i
$855$	−0.796237	+	4.51569i	−0.0272307	+	0.154433i
$856$	−7.79878	+	2.83852i	−0.266557	+	0.0970188i
$857$	−41.2694			−1.40974			−0.704869	−	0.709338i	$-0.748994\pi$
$857$	−41.2694			−1.40974			−0.704869	+	0.709338i	$0.748994\pi$
$858$	1.75514	−	0.638820i	0.0599196	−	0.0218090i
$859$	−5.91755	−	10.2495i	−0.201904	−	0.349708i	0.747238	−	0.664557i	$-0.231380\pi$
$859$	−5.91755	−	10.2495i	−0.201904	−	0.349708i	−0.949142	+	0.314848i	$0.898046\pi$
$860$	−2.09789	−	11.8977i	−0.0715374	−	0.405709i
$861$	−1.11987	+	1.93966i	−0.0381649	+	0.0661036i
$862$	0.309925	+	0.536806i	0.0105561	+	0.0182837i
$863$	−29.1091	+	24.4255i	−0.990887	+	0.831453i	−0.985696	−	0.168534i	$-0.946097\pi$
$863$	−29.1091	+	24.4255i	−0.990887	+	0.831453i	−0.00519081	+	0.999987i	$0.501652\pi$
$864$	0.272957	−	1.54801i	0.00928617	−	0.0526645i
$865$	−4.31948	+	7.48156i	−0.146867	+	0.254381i
$866$	−35.3357	−	12.8611i	−1.20076	−	0.437039i
$867$	−0.873194	−	0.317817i	−0.0296552	−	0.0107936i
$868$	−0.412269	−	2.33809i	−0.0139933	−	0.0793601i
$869$	15.7328	+	13.2013i	0.533697	+	0.447825i
$870$	−1.47772	−	1.23995i	−0.0500992	−	0.0420383i
$871$	3.16817	+	17.9676i	0.107349	+	0.608808i
$872$	−6.61124	−	2.40629i	−0.223885	−	0.0814874i
$873$	−0.703403	−	0.256018i	−0.0238066	−	0.00866488i
$874$	5.71144	−	9.89250i	0.193192	−	0.334619i
$875$	0.318927	−	1.80873i	0.0107817	−	0.0611461i
$876$	0.407686	−	0.342089i	0.0137744	−	0.0115581i
$877$	−2.05132	−	3.55299i	−0.0692682	−	0.119976i	0.829311	−	0.558787i	$-0.188733\pi$
$877$	−2.05132	−	3.55299i	−0.0692682	−	0.119976i	−0.898579	+	0.438811i	$0.855400\pi$
$878$	5.30014	−	9.18011i	0.178871	−	0.309814i
$879$	−0.138604	−	0.786063i	−0.00467500	−	0.0265132i
$880$	1.26403	+	2.18936i	0.0426104	+	0.0738034i
$881$	−30.4724	+	11.0911i	−1.02664	+	0.373667i	−0.799802	−	0.600265i	$-0.795062\pi$
$881$	−30.4724	+	11.0911i	−1.02664	+	0.373667i	−0.226841	+	0.973932i	$0.572840\pi$
$882$	−10.6255			−0.357780
$883$	30.1132	−	10.9603i	1.01339	−	0.368844i	0.218657	−	0.975802i	$-0.429832\pi$
$883$	30.1132	−	10.9603i	1.01339	−	0.368844i	0.794734	+	0.606958i	$0.207610\pi$
$884$	2.19157	−	12.4290i	0.0737105	−	0.418033i
$885$	−2.83540	−	2.37918i	−0.0953110	−	0.0799754i
$886$	6.79530	−	5.70193i	0.228292	−	0.191560i
$887$	14.2695			0.479124			0.239562	−	0.970881i	$-0.422996\pi$
$887$	14.2695			0.479124			0.239562	+	0.970881i	$0.422996\pi$
$888$	1.55261	+	0.435224i	0.0521023	+	0.0146051i
$889$	0.974884			0.0326965
$890$	−6.46971	+	5.42873i	−0.216865	+	0.181971i
$891$	16.2142	+	13.6053i	0.543197	+	0.455796i
$892$	−1.73207	+	9.82307i	−0.0579941	+	0.328901i
$893$	17.8276	−	6.48871i	0.596577	−	0.217136i
$894$	−5.79294			−0.193745
$895$	6.11350	−	2.22513i	0.204352	−	0.0743779i
$896$	−0.918315	−	1.59057i	−0.0306787	−	0.0531371i
$897$	−0.936355	−	5.31033i	−0.0312640	−	0.177307i
$898$	−13.5504	+	23.4699i	−0.452182	+	0.783202i
$899$	4.70335	+	8.14644i	0.156866	+	0.271699i
$900$	−2.24430	+	1.88319i	−0.0748101	+	0.0627731i
$901$	−9.26067	+	52.5199i	−0.308518	+	1.74969i
$902$	−5.81491	+	10.0717i	−0.193615	+	0.335352i
$903$	5.52723	+	2.01175i	0.183935	+	0.0669468i
$904$	−10.6110	−	3.86207i	−0.352915	−	0.128451i
$905$	1.07092	+	6.07349i	0.0355986	+	0.201890i
$906$	0.967319	+	0.811677i	0.0321370	+	0.0269662i
$907$	−7.88205	−	6.61383i	−0.261719	−	0.219609i	0.502480	−	0.864589i	$-0.332421\pi$
$907$	−7.88205	−	6.61383i	−0.261719	−	0.219609i	−0.764199	+	0.644980i	$0.776866\pi$
$908$	−3.87018	−	21.9489i	−0.128437	−	0.728400i
$909$	26.9963	+	9.82584i	0.895409	+	0.325902i
$910$	4.81015	+	1.75075i	0.159455	+	0.0580368i
$911$	2.04960	−	3.55001i	0.0679062	−	0.117617i	−0.830073	−	0.557654i	$-0.811701\pi$
$911$	2.04960	−	3.55001i	0.0679062	−	0.117617i	0.897979	+	0.440037i	$0.145035\pi$
$912$	−0.0720450	+	0.408587i	−0.00238565	+	0.0135297i
$913$	−0.991504	+	0.831970i	−0.0328140	+	0.0275342i
$914$	2.03074	+	3.51735i	0.0671710	+	0.116344i
$915$	0.476720	−	0.825704i	0.0157599	−	0.0272969i
$916$	−3.59381	−	20.3815i	−0.118743	−	0.673424i
$917$	3.29744	+	5.71133i	0.108891	+	0.188605i
$918$	−6.68872	+	2.43450i	−0.220761	+	0.0803503i
$919$	−32.3626			−1.06754			−0.533772	−	0.845628i	$-0.679226\pi$
$919$	−32.3626			−1.06754			−0.533772	+	0.845628i	$0.679226\pi$
$920$	6.85830	−	2.49622i	0.226111	−	0.0822978i
$921$	−0.938374	+	5.32178i	−0.0309205	+	0.175359i
$922$	32.6430	+	27.3907i	1.07504	+	0.902065i
$923$	−16.5747	+	13.9078i	−0.545561	+	0.457780i
$924$	−1.23083			−0.0404912
$925$	−3.43138	−	5.02251i	−0.112823	−	0.165139i
$926$	−6.25634			−0.205596
$927$	−21.1263	+	17.7270i	−0.693877	+	0.582232i
$928$	5.57445	+	4.67752i	0.182990	+	0.153547i
$929$	−8.20216	+	46.5167i	−0.269104	+	1.52617i	0.487984	+	0.872852i	$0.337732\pi$
$929$	−8.20216	+	46.5167i	−0.269104	+	1.52617i	−0.757088	+	0.653313i	$0.773379\pi$
$930$	−0.322006	+	0.117200i	−0.0105590	+	0.00384315i
$931$	5.67633			0.186034
$932$	−2.62670	+	0.956041i	−0.0860405	+	0.0313162i
$933$	−1.58293	−	2.74171i	−0.0518227	−	0.0897596i
$934$	6.92689	+	39.2843i	0.226655	+	1.28542i
$935$	5.72389	−	9.91406i	0.187191	−	0.324225i
$936$	−4.08271	−	7.07146i	−0.133448	−	0.231138i
$937$	8.97552	−	7.53136i	0.293218	−	0.246039i	−0.484297	−	0.874904i	$-0.660925\pi$
$937$	8.97552	−	7.53136i	0.293218	−	0.246039i	0.777515	+	0.628865i	$0.216480\pi$
$938$	2.08775	−	11.8402i	0.0681675	−	0.386597i
$939$	−0.819719	+	1.41979i	−0.0267505	+	0.0463332i
$940$	11.3906	+	4.14585i	0.371521	+	0.135223i
$941$	8.31461	+	3.02627i	0.271049	+	0.0986536i	0.473969	−	0.880542i	$-0.342821\pi$
$941$	8.31461	+	3.02627i	0.271049	+	0.0986536i	−0.202920	+	0.979195i	$0.565043\pi$
$942$	−0.500100	−	2.83621i	−0.0162941	−	0.0924086i
$943$	25.7200	+	21.5816i	0.837557	+	0.702794i
$944$	10.6961	+	8.97511i	0.348129	+	0.292115i
$945$	−0.501320	−	2.84313i	−0.0163079	−	0.0924869i
$946$	28.7002	+	10.4460i	0.933124	+	0.339629i
$947$	−28.7628	−	10.4688i	−0.934664	−	0.340190i	−0.170607	−	0.985339i	$-0.554573\pi$
$947$	−28.7628	−	10.4688i	−0.934664	−	0.340190i	−0.764057	+	0.645149i	$0.776795\pi$
$948$	−1.07677	+	1.86502i	−0.0349718	+	0.0605729i
$949$	0.971639	−	5.51044i	0.0315407	−	0.178876i
$950$	1.19894	−	1.00603i	0.0388989	−	0.0326400i
$951$	−3.23805	−	5.60847i	−0.105001	−	0.181867i
$952$	−4.15839	+	7.20255i	−0.134774	+	0.233436i
$953$	−9.40120	−	53.3168i	−0.304535	−	1.72710i	−0.625687	−	0.780074i	$-0.715181\pi$
$953$	−9.40120	−	53.3168i	−0.304535	−	1.72710i	0.321152	−	0.947028i	$-0.395930\pi$
$954$	17.2518	+	29.8811i	0.558549	+	0.967435i
$955$	11.4669	−	4.17361i	0.371060	−	0.135055i
$956$	2.03248			0.0657351
$957$	4.58258	−	1.66792i	0.148134	−	0.0539162i
$958$	6.90009	−	39.1324i	0.222932	−	1.26431i
$959$	26.2670	+	22.0406i	0.848206	+	0.711730i
$960$	−0.203068	+	0.170395i	−0.00655401	+	0.00549946i
$961$	−29.3290			−0.946097
$962$	15.4462	−	6.98753i	0.498006	−	0.225287i
$963$	24.3147			0.783529
$964$	3.95670	−	3.32007i	0.127437	−	0.106932i
$965$	−8.19293	−	6.87469i	−0.263740	−	0.221304i
$966$	−0.617036	+	3.49939i	−0.0198528	+	0.112591i
$967$	5.24834	−	1.91024i	0.168775	−	0.0614292i	−0.256251	−	0.966610i	$-0.582487\pi$
$967$	5.24834	−	1.91024i	0.168775	−	0.0614292i	0.425026	+	0.905181i	$0.360265\pi$
$968$	4.60892			0.148136
$969$	1.76544	−	0.642568i	0.0567141	−	0.0206423i
$970$	0.127750	+	0.221269i	0.00410180	+	0.00710453i
$971$	−0.362111	−	2.05363i	−0.0116207	−	0.0659042i	0.978446	−	0.206503i	$-0.0662083\pi$
$971$	−0.362111	−	2.05363i	−0.0116207	−	0.0659042i	−0.990067	+	0.140599i	$0.955097\pi$
$972$	−3.46756	+	6.00599i	−0.111222	+	0.192642i
$973$	−15.7320	−	27.2487i	−0.504346	−	0.873553i
$974$	1.86090	−	1.56148i	0.0596272	−	0.0500332i
$975$	0.128295	−	0.727597i	0.00410873	−	0.0233018i
$976$	−1.79835	+	3.11484i	−0.0575639	+	0.0997036i
$977$	8.14143	+	2.96324i	0.260467	+	0.0948023i	0.468953	−	0.883223i	$-0.344631\pi$
$977$	8.14143	+	2.96324i	0.260467	+	0.0948023i	−0.208486	+	0.978025i	$0.566854\pi$
$978$	−2.97302	−	1.08209i	−0.0950667	−	0.0346015i
$979$	−3.70756	−	21.0266i	−0.118494	−	0.672013i
$980$	2.77829	+	2.33126i	0.0887491	+	0.0744693i
$981$	15.7899	+	13.2493i	0.504132	+	0.423017i
$982$	2.72987	+	15.4819i	0.0871137	+	0.494046i
$983$	32.3863	+	11.7877i	1.03296	+	0.375968i	0.802208	−	0.597044i	$-0.203658\pi$
$983$	32.3863	+	11.7877i	1.03296	+	0.375968i	0.230754	+	0.973012i	$0.425881\pi$
$984$	−1.14594	−	0.417086i	−0.0365311	−	0.0132962i
$985$	−1.86635	+	3.23261i	−0.0594668	+	0.103000i
$986$	5.72206	−	32.4514i	0.182228	−	1.03346i
$987$	−4.52091	+	3.79349i	−0.143902	+	0.120748i
$988$	2.18105	+	3.77769i	0.0693885	+	0.120184i
$989$	44.0872	−	76.3612i	1.40189	−	2.42815i
$990$	−1.28613	−	7.29400i	−0.0408759	−	0.231819i
$991$	−8.67821	−	15.0311i	−0.275673	−	0.477479i	0.694632	−	0.719365i	$-0.255567\pi$
$991$	−8.67821	−	15.0311i	−0.275673	−	0.477479i	−0.970305	+	0.241886i	$0.922234\pi$
$992$	1.21472	−	0.442121i	0.0385673	−	0.0140373i
$993$	3.77173			0.119692
$994$	13.3982	−	4.87655i	0.424965	−	0.154675i
$995$	−3.13259	+	17.7658i	−0.0993097	+	0.563213i
$996$	−0.103967	−	0.0872387i	−0.00329432	−	0.00276426i
$997$	−23.7802	+	19.9540i	−0.753127	+	0.631949i	−0.936328	−	0.351127i	$-0.885799\pi$
$997$	−23.7802	+	19.9540i	−0.753127	+	0.631949i	0.183201	+	0.983075i	$0.441354\pi$
$998$	−18.5775			−0.588061
$999$	−7.76869	−	5.57396i	−0.245790	−	0.176352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.b.271.2	yes	18
37.34	even	9	inner	370.2.o.b.71.2	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.b.71.2	✓	18	37.34	even	9	inner
370.2.o.b.271.2	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)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.203068 + 0.170395i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} -0.265087 q^{6} +(1.72587 - 0.628164i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.508742 - 2.88522i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.203068 + 0.170395i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} -0.265087 q^{6} +(1.72587 - 0.628164i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.508742 - 2.88522i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.26403 - 2.18936i) q^{11} +(0.203068 - 0.170395i) q^{12} +(0.483973 - 2.74475i) q^{13} +(-0.918315 + 1.59057i) q^{14} +(0.249100 + 0.0906651i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.786329 + 4.45949i) q^{17} +(2.24430 + 1.88319i) q^{18} +(-1.19894 - 1.00603i) q^{19} +(-0.173648 - 0.984808i) q^{20} +(0.457505 + 0.166518i) q^{21} +(2.37560 + 0.864647i) q^{22} +(3.64922 - 6.32064i) q^{23} +(-0.0460319 + 0.261060i) q^{24} +(0.766044 - 0.642788i) q^{25} +(1.39355 + 2.41369i) q^{26} +(0.785947 - 1.36130i) q^{27} +(-0.318927 - 1.80873i) q^{28} +(3.63847 + 6.30201i) q^{29} +(-0.249100 + 0.0906651i) q^{30} +1.29267 q^{31} +(0.939693 - 0.342020i) q^{32} +(0.116371 - 0.659974i) q^{33} +(-3.46887 - 2.91073i) q^{34} +(1.40694 - 1.18056i) q^{35} -2.92973 q^{36} +(0.599814 - 6.05312i) q^{37} +1.56511 q^{38} +(0.565970 - 0.474906i) q^{39} +(0.766044 + 0.642788i) q^{40} +(-0.798833 + 4.53041i) q^{41} +(-0.457505 + 0.166518i) q^{42} +12.0813 q^{43} +(-2.37560 + 0.864647i) q^{44} +(-1.46486 - 2.53722i) q^{45} +(1.26736 + 7.18757i) q^{46} +(-6.06083 + 10.4977i) q^{47} +(-0.132544 - 0.229572i) q^{48} +(-2.77829 + 2.33126i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(-0.600195 + 1.03957i) q^{51} +(-2.61901 - 0.953241i) q^{52} +(11.0668 + 4.02800i) q^{53} +(0.272957 + 1.54801i) q^{54} +(-1.93660 - 1.62500i) q^{55} +(1.40694 + 1.18056i) q^{56} +(-0.0720450 - 0.408587i) q^{57} +(-6.83808 - 2.48886i) q^{58} +(-13.1207 - 4.77556i) q^{59} +(0.132544 - 0.229572i) q^{60} +(0.624562 - 3.54207i) q^{61} +(-0.990246 + 0.830915i) q^{62} +(-2.69041 - 4.65993i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.483973 - 2.74475i) q^{65} +(0.335078 + 0.580372i) q^{66} +(-6.15138 + 2.23892i) q^{67} +4.52829 q^{68} +(1.81805 - 0.661714i) q^{69} +(-0.318927 + 1.80873i) q^{70} +(-5.94694 - 4.99007i) q^{71} +(2.24430 - 1.88319i) q^{72} +2.00763 q^{73} +(3.43138 + 5.02251i) q^{74} +0.265087 q^{75} +(-1.19894 + 1.00603i) q^{76} +(-3.55682 - 2.98453i) q^{77} +(-0.128295 + 0.727597i) q^{78} +(-7.63395 + 2.77853i) q^{79} -1.00000 q^{80} +(-7.86757 + 2.86356i) q^{81} +(-2.30015 - 3.98397i) q^{82} +(-0.0889045 - 0.504202i) q^{83} +(0.243433 - 0.421639i) q^{84} +(2.26414 + 3.92161i) q^{85} +(-9.25478 + 7.76568i) q^{86} +(-0.334971 + 1.89971i) q^{87} +(1.26403 - 2.18936i) q^{88} +(7.93627 + 2.88857i) q^{89} +(2.75304 + 1.00203i) q^{90} +(-0.888880 - 5.04109i) q^{91} +(-5.59093 - 4.69135i) q^{92} +(0.262501 + 0.220265i) q^{93} +(-2.10490 - 11.9375i) q^{94} +(-1.47072 - 0.535299i) q^{95} +(0.249100 + 0.0906651i) q^{96} +(0.127750 - 0.221269i) q^{97} +(0.629786 - 3.57169i) q^{98} +(-5.67373 + 4.76082i) 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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