LMFDB - Embedded newform 342.2.w.b.175.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(43,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([12, 16]))

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

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

chi := DirichletCharacter("342.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.w (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			175.5
Character	$\chi$	$=$	342.175
Dual form			342.2.w.b.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-0.908677 - 1.47455i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.355621 - 2.01683i) q^{5} +(1.29436 - 1.15093i) q^{6} -1.40682 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.34861 + 2.67978i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-0.908677 - 1.47455i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.355621 - 2.01683i) q^{5} +(1.29436 - 1.15093i) q^{6} -1.40682 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.34861 + 2.67978i) q^{9} +(1.92444 - 0.700437i) q^{10} +(-2.09120 + 3.62207i) q^{11} +(1.35820 + 1.07484i) q^{12} +(-1.63442 - 1.37144i) q^{13} +(-0.244291 - 1.38544i) q^{14} +(-2.65078 + 2.35703i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-6.80180 - 2.47565i) q^{17} +(-2.87326 - 0.862786i) q^{18} +(-4.20921 + 1.13250i) q^{19} +(1.02397 + 1.77357i) q^{20} +(1.27834 + 2.07442i) q^{21} +(-3.93018 - 1.43047i) q^{22} +(3.81755 - 1.38947i) q^{23} +(-0.822662 + 1.52421i) q^{24} +(0.757329 - 0.275645i) q^{25} +(1.06679 - 1.84773i) q^{26} +(5.17694 - 0.446454i) q^{27} +(1.32197 - 0.481159i) q^{28} +(-7.00883 - 5.88111i) q^{29} +(-2.78152 - 2.20121i) q^{30} +(1.84668 + 3.19854i) q^{31} +(0.766044 + 0.642788i) q^{32} +(7.24116 - 0.207700i) q^{33} +(1.25692 - 7.12835i) q^{34} +(0.500294 + 2.83731i) q^{35} +(0.350743 - 2.97943i) q^{36} +8.68625 q^{37} +(-1.84621 - 3.94861i) q^{38} +(-0.537103 + 3.65623i) q^{39} +(-1.56881 + 1.31639i) q^{40} +(-10.1379 - 3.68991i) q^{41} +(-1.82093 + 1.61914i) q^{42} +(5.99376 + 2.18155i) q^{43} +(0.726267 - 4.11887i) q^{44} +(5.88426 + 1.76694i) q^{45} +(2.03128 + 3.51827i) q^{46} +(-6.92744 - 5.81281i) q^{47} +(-1.64391 - 0.545487i) q^{48} -5.02087 q^{49} +(0.402967 + 0.697959i) q^{50} +(2.53015 + 12.2792i) q^{51} +(2.00491 + 0.729728i) q^{52} +(4.42019 + 3.70898i) q^{53} +(1.33864 + 5.02076i) q^{54} +(8.04877 + 2.92951i) q^{55} +(0.703408 + 1.21834i) q^{56} +(5.49474 + 5.17763i) q^{57} +(4.57469 - 7.92359i) q^{58} +(8.27066 - 6.93991i) q^{59} +(1.68476 - 3.12150i) q^{60} +(0.196697 - 1.11552i) q^{61} +(-2.82928 + 2.37404i) q^{62} +(1.89725 - 3.76996i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.18472 + 3.78405i) q^{65} +(1.46196 + 7.09509i) q^{66} +(-0.666967 + 3.78256i) q^{67} +7.23832 q^{68} +(-5.51777 - 4.36660i) q^{69} +(-2.70733 + 0.985387i) q^{70} +(-3.85529 + 3.23497i) q^{71} +(2.99507 - 0.171958i) q^{72} +(-1.09776 - 6.22570i) q^{73} +(1.50835 + 8.55429i) q^{74} +(-1.09462 - 0.866250i) q^{75} +(3.56803 - 2.50383i) q^{76} +(2.94194 - 5.09559i) q^{77} +(-3.69395 + 0.105954i) q^{78} +(1.01508 - 0.851754i) q^{79} +(-1.56881 - 1.31639i) q^{80} +(-5.36248 - 7.22799i) q^{81} +(1.87342 - 10.6247i) q^{82} +2.51338 q^{83} +(-1.91074 - 1.51210i) q^{84} +(-2.57410 + 14.5985i) q^{85} +(-1.10760 + 6.28152i) q^{86} +(-2.30324 + 15.6789i) q^{87} +4.18241 q^{88} +(-0.623365 + 3.53528i) q^{89} +(-0.718300 + 6.10169i) q^{90} +(2.29932 + 1.92936i) q^{91} +(-3.11210 + 2.61136i) q^{92} +(3.03839 - 5.62946i) q^{93} +(4.52157 - 7.83158i) q^{94} +(3.78094 + 8.08652i) q^{95} +(0.251738 - 1.71366i) q^{96} +(-1.01208 - 5.73980i) q^{97} +(-0.871865 - 4.94459i) q^{98} +(-6.88614 - 10.4887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 3 q^{3} - 3 q^{6} + 24 q^{7} - 33 q^{8} - 3 q^{9}+O(q^{10}) $ 66 * q - 3 * q^3 - 3 * q^6 + 24 * q^7 - 33 * q^8 - 3 * q^9	$ 66 q - 3 q^{3} - 3 q^{6} + 24 q^{7} - 33 q^{8} - 3 q^{9} - 3 q^{13} - 3 q^{14} - 30 q^{15} + 9 q^{17} + 6 q^{18} - 21 q^{19} + 6 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{25} + 30 q^{27} - 3 q^{28} + 9 q^{29} + 18 q^{33} - 18 q^{34} - 18 q^{35} - 3 q^{36} + 6 q^{37} + 6 q^{38} + 12 q^{39} + 6 q^{41} + 6 q^{43} - 12 q^{44} - 18 q^{45} - 18 q^{47} - 3 q^{48} + 114 q^{49} - 63 q^{50} - 63 q^{51} - 3 q^{52} - 24 q^{53} + 18 q^{54} + 36 q^{55} - 12 q^{56} - 60 q^{57} - 18 q^{58} + 78 q^{59} - 3 q^{60} - 21 q^{62} - 27 q^{63} - 33 q^{64} - 12 q^{65} + 45 q^{66} - 3 q^{67} + 12 q^{68} - 24 q^{69} - 18 q^{70} - 24 q^{71} - 3 q^{72} - 15 q^{73} - 3 q^{74} + 15 q^{78} + 12 q^{79} - 87 q^{81} + 6 q^{82} - 24 q^{83} - 15 q^{84} + 72 q^{85} - 3 q^{86} + 66 q^{87} + 9 q^{89} - 6 q^{90} + 27 q^{91} + 6 q^{92} - 45 q^{93} - 6 q^{94} - 30 q^{95} + 87 q^{97} + 24 q^{98} - 96 q^{99}+O(q^{100}) $ 66 * q - 3 * q^3 - 3 * q^6 + 24 * q^7 - 33 * q^8 - 3 * q^9 - 3 * q^13 - 3 * q^14 - 30 * q^15 + 9 * q^17 + 6 * q^18 - 21 * q^19 + 6 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^25 + 30 * q^27 - 3 * q^28 + 9 * q^29 + 18 * q^33 - 18 * q^34 - 18 * q^35 - 3 * q^36 + 6 * q^37 + 6 * q^38 + 12 * q^39 + 6 * q^41 + 6 * q^43 - 12 * q^44 - 18 * q^45 - 18 * q^47 - 3 * q^48 + 114 * q^49 - 63 * q^50 - 63 * q^51 - 3 * q^52 - 24 * q^53 + 18 * q^54 + 36 * q^55 - 12 * q^56 - 60 * q^57 - 18 * q^58 + 78 * q^59 - 3 * q^60 - 21 * q^62 - 27 * q^63 - 33 * q^64 - 12 * q^65 + 45 * q^66 - 3 * q^67 + 12 * q^68 - 24 * q^69 - 18 * q^70 - 24 * q^71 - 3 * q^72 - 15 * q^73 - 3 * q^74 + 15 * q^78 + 12 * q^79 - 87 * q^81 + 6 * q^82 - 24 * q^83 - 15 * q^84 + 72 * q^85 - 3 * q^86 + 66 * q^87 + 9 * q^89 - 6 * q^90 + 27 * q^91 + 6 * q^92 - 45 * q^93 - 6 * q^94 - 30 * q^95 + 87 * q^97 + 24 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−0.908677	−	1.47455i	−0.524625	−	0.851334i
$3$	−0.908677	−	1.47455i	−0.524625	−	0.851334i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.355621	−	2.01683i	−0.159039	−	0.901953i	−0.955000	−	0.296606i	$-0.904145\pi$
$5$	−0.355621	−	2.01683i	−0.159039	−	0.901953i	0.795961	−	0.605348i	$-0.206966\pi$
$6$	1.29436	−	1.15093i	0.528421	−	0.469863i
$7$	−1.40682			−0.531726			−0.265863	−	0.964011i	$-0.585657\pi$
$7$	−1.40682			−0.531726			−0.265863	+	0.964011i	$0.585657\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−1.34861	+	2.67978i	−0.449538	+	0.893261i
$10$	1.92444	−	0.700437i	0.608560	−	0.221498i
$11$	−2.09120	+	3.62207i	−0.630522	+	1.09210i	0.356924	+	0.934134i	$0.383826\pi$
$11$	−2.09120	+	3.62207i	−0.630522	+	1.09210i	−0.987445	+	0.157962i	$0.949508\pi$
$12$	1.35820	+	1.07484i	0.392080	+	0.310280i
$13$	−1.63442	−	1.37144i	−0.453306	−	0.380369i	0.387355	−	0.921931i	$-0.373389\pi$
$13$	−1.63442	−	1.37144i	−0.453306	−	0.380369i	−0.840661	+	0.541562i	$0.817833\pi$
$14$	−0.244291	−	1.38544i	−0.0652895	−	0.370275i
$15$	−2.65078	+	2.35703i	−0.684428	+	0.608582i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−6.80180	−	2.47565i	−1.64968	−	0.600434i	−0.660986	−	0.750398i	$-0.729862\pi$
$17$	−6.80180	−	2.47565i	−1.64968	−	0.600434i	−0.988691	+	0.149964i	$0.952084\pi$
$18$	−2.87326	−	0.862786i	−0.677233	−	0.203361i
$19$	−4.20921	+	1.13250i	−0.965659	+	0.259812i
$19$	−4.20921	+	1.13250i	−0.965659	+	0.259812i
$20$	1.02397	+	1.77357i	0.228967	+	0.396582i
$21$	1.27834	+	2.07442i	0.278957	+	0.452677i
$22$	−3.93018	−	1.43047i	−0.837916	−	0.304977i
$23$	3.81755	−	1.38947i	0.796014	−	0.289726i	0.0881805	−	0.996105i	$-0.471895\pi$
$23$	3.81755	−	1.38947i	0.796014	−	0.289726i	0.707834	+	0.706379i	$0.249673\pi$
$24$	−0.822662	+	1.52421i	−0.167925	+	0.311129i
$25$	0.757329	−	0.275645i	0.151466	−	0.0551291i
$26$	1.06679	−	1.84773i	0.209215	−	0.362371i
$27$	5.17694	−	0.446454i	0.996302	−	0.0859200i
$28$	1.32197	−	0.481159i	0.249830	−	0.0909306i
$29$	−7.00883	−	5.88111i	−1.30151	−	1.09209i	−0.989883	−	0.141889i	$-0.954683\pi$
$29$	−7.00883	−	5.88111i	−1.30151	−	1.09209i	−0.311624	−	0.950205i	$-0.600873\pi$
$30$	−2.78152	−	2.20121i	−0.507834	−	0.401885i
$31$	1.84668	+	3.19854i	0.331673	+	0.574475i	0.982840	−	0.184460i	$-0.0590535\pi$
$31$	1.84668	+	3.19854i	0.331673	+	0.574475i	−0.651167	+	0.758935i	$0.725720\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	7.24116	−	0.207700i	1.26052	−	0.0361559i
$34$	1.25692	−	7.12835i	0.215560	−	1.22250i
$35$	0.500294	+	2.83731i	0.0845651	+	0.479593i
$36$	0.350743	−	2.97943i	0.0584571	−	0.496571i
$37$	8.68625			1.42801			0.714005	−	0.700140i	$-0.246879\pi$
$37$	8.68625			1.42801			0.714005	+	0.700140i	$0.246879\pi$
$38$	−1.84621	−	3.94861i	−0.299495	−	0.640549i
$39$	−0.537103	+	3.65623i	−0.0860053	+	0.585465i
$40$	−1.56881	+	1.31639i	−0.248051	+	0.208140i
$41$	−10.1379	−	3.68991i	−1.58328	−	0.576267i	−0.607367	−	0.794421i	$-0.707774\pi$
$41$	−10.1379	−	3.68991i	−1.58328	−	0.576267i	−0.975914	+	0.218154i	$0.929996\pi$
$42$	−1.82093	+	1.61914i	−0.280975	+	0.249839i
$43$	5.99376	+	2.18155i	0.914039	+	0.332683i	0.755865	−	0.654728i	$-0.227217\pi$
$43$	5.99376	+	2.18155i	0.914039	+	0.332683i	0.158175	+	0.987411i	$0.449439\pi$
$44$	0.726267	−	4.11887i	0.109489	−	0.620942i
$45$	5.88426	+	1.76694i	0.877174	+	0.263399i
$46$	2.03128	+	3.51827i	0.299495	+	0.518741i
$47$	−6.92744	−	5.81281i	−1.01047	−	0.847886i	−0.0220709	−	0.999756i	$-0.507026\pi$
$47$	−6.92744	−	5.81281i	−1.01047	−	0.847886i	−0.988400	+	0.151870i	$0.951470\pi$
$48$	−1.64391	−	0.545487i	−0.237278	−	0.0787343i
$49$	−5.02087			−0.717267
$50$	0.402967	+	0.697959i	0.0569881	+	0.0987062i
$51$	2.53015	+	12.2792i	0.354292	+	1.71943i
$52$	2.00491	+	0.729728i	0.278031	+	0.101195i
$53$	4.42019	+	3.70898i	0.607160	+	0.509468i	0.893738	−	0.448589i	$-0.148073\pi$
$53$	4.42019	+	3.70898i	0.607160	+	0.509468i	−0.286578	+	0.958057i	$0.592518\pi$
$54$	1.33864	+	5.02076i	0.182165	+	0.683239i
$55$	8.04877	+	2.92951i	1.08530	+	0.395016i
$56$	0.703408	+	1.21834i	0.0939968	+	0.162807i
$57$	5.49474	+	5.17763i	0.727795	+	0.685794i
$58$	4.57469	−	7.92359i	0.600686	−	1.04042i
$59$	8.27066	−	6.93991i	1.07675	−	0.903499i	0.0811016	−	0.996706i	$-0.474156\pi$
$59$	8.27066	−	6.93991i	1.07675	−	0.903499i	0.995647	+	0.0932066i	$0.0297117\pi$
$60$	1.68476	−	3.12150i	0.217502	−	0.402984i
$61$	0.196697	−	1.11552i	0.0251844	−	0.142828i	−0.969623	−	0.244605i	$-0.921342\pi$
$61$	0.196697	−	1.11552i	0.0251844	−	0.142828i	0.994807	+	0.101777i	$0.0324528\pi$
$62$	−2.82928	+	2.37404i	−0.359318	+	0.301504i
$63$	1.89725	−	3.76996i	0.239031	−	0.474971i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.18472	+	3.78405i	−0.270982	+	0.469354i
$66$	1.46196	+	7.09509i	0.179955	+	0.873345i
$67$	−0.666967	+	3.78256i	−0.0814829	+	0.462113i	0.916577	+	0.399858i	$0.130940\pi$
$67$	−0.666967	+	3.78256i	−0.0814829	+	0.462113i	−0.998060	+	0.0622552i	$0.980171\pi$
$68$	7.23832			0.877775
$69$	−5.51777	−	4.36660i	−0.664262	−	0.525677i
$70$	−2.70733	+	0.985387i	−0.323588	+	0.117776i
$71$	−3.85529	+	3.23497i	−0.457539	+	0.383920i	−0.842224	−	0.539127i	$-0.818754\pi$
$71$	−3.85529	+	3.23497i	−0.457539	+	0.383920i	0.384686	+	0.923048i	$0.374310\pi$
$72$	2.99507	−	0.171958i	0.352972	−	0.0202654i
$73$	−1.09776	−	6.22570i	−0.128483	−	0.728663i	−0.979178	−	0.203003i	$-0.934930\pi$
$73$	−1.09776	−	6.22570i	−0.128483	−	0.728663i	0.850695	−	0.525659i	$-0.176181\pi$
$74$	1.50835	+	8.55429i	0.175342	+	0.994416i
$75$	−1.09462	−	0.866250i	−0.126396	−	0.100026i
$76$	3.56803	−	2.50383i	0.409281	−	0.287209i
$77$	2.94194	−	5.09559i	0.335265	−	0.580696i
$78$	−3.69395	+	0.105954i	−0.418258	+	0.0119970i
$79$	1.01508	−	0.851754i	0.114206	−	0.0958298i	−0.583897	−	0.811828i	$-0.698473\pi$
$79$	1.01508	−	0.851754i	0.114206	−	0.0958298i	0.698102	+	0.715998i	$0.254028\pi$
$80$	−1.56881	−	1.31639i	−0.175399	−	0.147177i
$81$	−5.36248	−	7.22799i	−0.595831	−	0.803110i
$82$	1.87342	−	10.6247i	0.206884	−	1.17330i
$83$	2.51338			0.275879			0.137940	−	0.990441i	$-0.455952\pi$
$83$	2.51338			0.275879			0.137940	+	0.990441i	$0.455952\pi$
$84$	−1.91074	−	1.51210i	−0.208479	−	0.164984i
$85$	−2.57410	+	14.5985i	−0.279200	+	1.58342i
$86$	−1.10760	+	6.28152i	−0.119436	+	0.677354i
$87$	−2.30324	+	15.6789i	−0.246934	+	1.68096i
$88$	4.18241			0.445846
$89$	−0.623365	+	3.53528i	−0.0660765	+	0.374739i	0.933781	+	0.357846i	$0.116489\pi$
$89$	−0.623365	+	3.53528i	−0.0660765	+	0.374739i	−0.999857	+	0.0168930i	$0.994623\pi$
$90$	−0.718300	+	6.10169i	−0.0757155	+	0.643175i
$91$	2.29932	+	1.92936i	0.241035	+	0.202252i
$92$	−3.11210	+	2.61136i	−0.324458	+	0.272253i
$93$	3.03839	−	5.62946i	0.315066	−	0.583748i
$94$	4.52157	−	7.83158i	0.466364	−	0.807766i
$95$	3.78094	+	8.08652i	0.387916	+	0.829659i
$96$	0.251738	−	1.71366i	0.0256929	−	0.174900i
$97$	−1.01208	−	5.73980i	−0.102761	−	0.582788i	−0.992091	−	0.125521i	$-0.959940\pi$
$97$	−1.01208	−	5.73980i	−0.102761	−	0.582788i	0.889330	−	0.457267i	$-0.151171\pi$
$98$	−0.871865	−	4.94459i	−0.0880716	−	0.499479i
$99$	−6.88614	−	10.4887i	−0.692083	−	1.05416i
$100$	−0.617381	+	0.518044i	−0.0617381	+	0.0518044i
$101$	7.65633	−	2.78667i	0.761833	−	0.277284i	0.0682567	−	0.997668i	$-0.478256\pi$
$101$	7.65633	−	2.78667i	0.761833	−	0.277284i	0.693576	+	0.720383i	$0.256034\pi$
$102$	−11.6533	+	4.62397i	−1.15385	+	0.457841i
$103$	−3.36110			−0.331179			−0.165590	−	0.986195i	$-0.552953\pi$
$103$	−3.36110			−0.331179			−0.165590	+	0.986195i	$0.552953\pi$
$104$	−0.370492	+	2.10117i	−0.0363298	+	0.206036i
$105$	3.72916	−	3.31590i	0.363928	−	0.323599i
$106$	−2.88508	+	4.99710i	−0.280223	+	0.485361i
$107$	−5.80019	+	10.0462i	−0.560726	+	0.971205i	0.436708	+	0.899603i	$0.356144\pi$
$107$	−5.80019	+	10.0462i	−0.560726	+	0.971205i	−0.997433	+	0.0716018i	$0.977189\pi$
$108$	−4.71203	+	2.19015i	−0.453416	+	0.210747i
$109$	7.31555	−	6.13848i	0.700703	−	0.587960i	−0.221271	−	0.975212i	$-0.571020\pi$
$109$	7.31555	−	6.13848i	0.700703	−	0.587960i	0.921974	+	0.387253i	$0.126576\pi$
$110$	−1.48735	+	8.43520i	−0.141814	+	0.804265i
$111$	−7.89299	−	12.8083i	−0.749170	−	1.21571i
$112$	−1.07768	+	0.904284i	−0.101832	+	0.0854468i
$113$	−5.25828	+	9.10760i	−0.494657	+	0.856771i	−0.999981	−	0.00615871i	$-0.998040\pi$
$113$	−5.25828	+	9.10760i	−0.494657	+	0.856771i	0.505324	+	0.862930i	$0.331373\pi$
$114$	−4.14482	+	6.31034i	−0.388198	+	0.591018i
$115$	−4.15994	−	7.20522i	−0.387916	−	0.671890i
$116$	8.59760	+	3.12927i	0.798267	+	0.290546i
$117$	5.87936	−	2.53034i	0.543547	−	0.233930i
$118$	8.27066	+	6.93991i	0.761376	+	0.638870i
$119$	9.56887	+	3.48279i	0.877177	+	0.319266i
$120$	3.36663	+	1.11713i	0.307330	+	0.101979i
$121$	−3.24626	−	5.62269i	−0.295115	−	0.511154i
$122$	1.13273			0.102553
$123$	3.77114	+	18.3019i	0.340033	+	1.65022i
$124$	−2.82928	−	2.37404i	−0.254076	−	0.213195i
$125$	−5.94511	−	10.2972i	−0.531747	−	0.921012i
$126$	4.04214	+	1.21378i	0.360103	+	0.108132i
$127$	−1.66002	+	9.41447i	−0.147303	+	0.835399i	0.818185	+	0.574954i	$0.194980\pi$
$127$	−1.66002	+	9.41447i	−0.147303	+	0.835399i	−0.965489	+	0.260445i	$0.916131\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−2.22958	−	10.8204i	−0.196303	−	0.952686i
$130$	−4.10594	−	1.49444i	−0.360115	−	0.131071i
$131$	8.65957	−	7.26624i	0.756590	−	0.634855i	−0.180647	−	0.983548i	$-0.557819\pi$
$131$	8.65957	−	7.26624i	0.756590	−	0.634855i	0.937237	+	0.348693i	$0.113375\pi$
$132$	−6.73343	+	2.67180i	−0.586070	+	0.232550i
$133$	5.92158	−	1.59321i	0.513467	−	0.138149i
$134$	−3.84091			−0.331804
$135$	−2.74145	−	10.2822i	−0.235946	−	0.884953i
$136$	1.25692	+	7.12835i	0.107780	+	0.611251i
$137$	1.55580	−	8.82341i	0.132921	−	0.753835i	−0.843363	−	0.537344i	$-0.819428\pi$
$137$	1.55580	−	8.82341i	0.132921	−	0.753835i	0.976285	−	0.216491i	$-0.0694611\pi$
$138$	3.34211	−	6.19220i	0.284499	−	0.527115i
$139$	−9.74953	−	8.18083i	−0.826945	−	0.693889i	0.127643	−	0.991820i	$-0.459259\pi$
$139$	−9.74953	−	8.18083i	−0.826945	−	0.693889i	−0.954587	+	0.297931i	$0.903703\pi$
$140$	−1.44054	−	2.49509i	−0.121748	−	0.210873i
$141$	−2.27650	+	15.4968i	−0.191716	+	1.30507i
$142$	−3.85529	−	3.23497i	−0.323529	−	0.271473i
$143$	8.38535	−	3.05202i	0.701218	−	0.255223i
$144$	0.689434	+	2.91971i	0.0574528	+	0.243309i
$145$	−9.36870	+	16.2271i	−0.778028	+	1.34758i
$146$	5.94049	−	2.16216i	0.491639	−	0.178942i
$147$	4.56235	+	7.40354i	0.376296	+	0.610634i
$148$	−8.16241	+	2.97087i	−0.670946	+	0.244204i
$149$	−10.8700	−	3.95637i	−0.890508	−	0.324118i	−0.144065	−	0.989568i	$-0.546018\pi$
$149$	−10.8700	−	3.95637i	−0.890508	−	0.324118i	−0.746443	+	0.665450i	$0.768240\pi$
$150$	0.663011	−	1.22841i	0.0541346	−	0.100300i
$151$	1.47754	+	2.55918i	0.120241	+	0.208263i	0.919863	−	0.392241i	$-0.128300\pi$
$151$	1.47754	+	2.55918i	0.120241	+	0.208263i	−0.799622	+	0.600504i	$0.794967\pi$
$152$	3.08538	+	3.07904i	0.250257	+	0.249743i
$153$	15.8072	−	14.8886i	1.27794	−	1.20368i
$154$	5.52904	+	2.01240i	0.445542	+	0.162164i
$155$	5.79419	−	4.86190i	0.465401	−	0.390518i
$156$	−0.745793	−	3.61943i	−0.0597112	−	0.289787i
$157$	1.80792	+	10.2532i	0.144288	+	0.818296i	0.967936	+	0.251196i	$0.0808238\pi$
$157$	1.80792	+	10.2532i	0.144288	+	0.818296i	−0.823649	+	0.567101i	$0.808065\pi$
$158$	1.01508	+	0.851754i	0.0807555	+	0.0677619i
$159$	1.45257	−	9.88807i	0.115196	−	0.784175i
$160$	1.02397	−	1.77357i	0.0809520	−	0.140213i
$161$	−5.37059	+	1.95474i	−0.423262	+	0.154055i
$162$	6.18699	−	6.53614i	0.486096	−	0.513528i
$163$	−9.24296	−	16.0093i	−0.723964	−	1.25394i	−0.959399	−	0.282053i	$-0.908985\pi$
$163$	−9.24296	−	16.0093i	−0.723964	−	1.25394i	0.235435	−	0.971890i	$-0.424349\pi$
$164$	10.7886			0.842446
$165$	−2.99401	−	14.5303i	−0.233083	−	1.13118i
$166$	0.436444	+	2.47520i	0.0338746	+	0.192113i
$167$	−22.0088	+	8.01056i	−1.70309	+	0.619876i	−0.996172	−	0.0874151i	$-0.972139\pi$
$167$	−22.0088	+	8.01056i	−1.70309	+	0.619876i	−0.706923	+	0.707291i	$0.749917\pi$
$168$	1.15733	−	2.14429i	0.0892903	−	0.165435i
$169$	−1.46695	−	8.31949i	−0.112842	−	0.639961i
$170$	−14.8237			−1.13692
$171$	2.64176	−	12.8071i	0.202020	−	0.979381i
$172$	−6.37842			−0.486350
$173$	0.0512064	+	0.290406i	0.00389315	+	0.0220792i	0.986692	−	0.162598i	$-0.0519873\pi$
$173$	0.0512064	+	0.290406i	0.00389315	+	0.0220792i	−0.982799	+	0.184677i	$0.940876\pi$
$174$	−15.8407	+	0.454362i	−1.20088	+	0.0344451i
$175$	−1.06542	+	0.387782i	−0.0805384	+	0.0293136i
$176$	0.726267	+	4.11887i	0.0547445	+	0.310471i
$177$	−17.7486	−	5.88940i	−1.33407	−	0.442674i
$178$	−3.58981			−0.269068
$179$	6.57989	+	11.3967i	0.491804	+	0.851830i	0.999955	−	0.00943785i	$-0.00300420\pi$
$179$	6.57989	+	11.3967i	0.491804	+	0.851830i	−0.508151	+	0.861268i	$0.669671\pi$
$180$	−6.13373	+	0.352160i	−0.457181	+	0.0262484i
$181$	14.7097	−	5.35391i	1.09337	−	0.397953i	0.268500	−	0.963280i	$-0.413472\pi$
$181$	14.7097	−	5.35391i	1.09337	−	0.397953i	0.824867	+	0.565327i	$0.191250\pi$
$182$	−1.50078	+	2.59942i	−0.111245	+	0.192682i
$183$	−1.82363	+	0.723609i	−0.134807	+	0.0534907i
$184$	−3.11210	−	2.61136i	−0.229427	−	0.192512i
$185$	−3.08902	−	17.5187i	−0.227109	−	1.28800i
$186$	6.07155	+	2.01468i	0.445188	+	0.147723i
$187$	23.1909	−	19.4595i	1.69589	−	1.42302i
$188$	8.49777	+	3.09293i	0.619763	+	0.225575i
$189$	−7.28300	+	0.628078i	−0.529760	+	0.0456860i
$190$	−7.30711	+	5.12770i	−0.530114	+	0.372003i
$191$	−2.83824	−	4.91597i	−0.205368	−	0.355707i	0.744882	−	0.667196i	$-0.232506\pi$
$191$	−2.83824	−	4.91597i	−0.205368	−	0.355707i	−0.950250	+	0.311489i	$0.899172\pi$
$192$	1.73134	−	0.0496604i	0.124949	−	0.00358393i
$193$	−7.79808	−	2.83827i	−0.561318	−	0.204303i	0.0457500	−	0.998953i	$-0.485432\pi$
$193$	−7.79808	−	2.83827i	−0.561318	−	0.204303i	−0.607068	+	0.794650i	$0.707654\pi$
$194$	5.47685	−	1.99341i	0.393215	−	0.143119i
$195$	7.56500	−	0.216989i	0.541741	−	0.0155389i
$196$	4.71807	−	1.71724i	0.337005	−	0.122660i
$197$	2.79959	−	4.84903i	0.199463	−	0.345479i	−0.748892	−	0.662692i	$-0.769414\pi$
$197$	2.79959	−	4.84903i	0.199463	−	0.345479i	0.948354	+	0.317213i	$0.102747\pi$
$198$	9.13363	−	8.60288i	0.649099	−	0.611380i
$199$	−18.5256	+	6.74276i	−1.31324	+	0.477982i	−0.901287	−	0.433222i	$-0.857377\pi$
$199$	−18.5256	+	6.74276i	−1.31324	+	0.477982i	−0.411957	+	0.911203i	$0.635155\pi$
$200$	−0.617381	−	0.518044i	−0.0436554	−	0.0366312i
$201$	6.18364	−	2.45364i	0.436160	−	0.173067i
$202$	4.07385	+	7.05611i	0.286635	+	0.496466i
$203$	9.86013	+	8.27363i	0.692046	+	0.580695i
$204$	−6.57729	−	10.6733i	−0.460502	−	0.747280i
$205$	−3.83665	+	21.7587i	−0.267963	+	1.51969i
$206$	−0.583649	−	3.31004i	−0.0406648	−	0.230621i
$207$	−1.42491	+	12.1041i	−0.0990381	+	0.841291i
$208$	−2.13358			−0.147937
$209$	4.70034	−	17.6143i	0.325129	−	1.21841i
$210$	3.91309	+	3.09670i	0.270029	+	0.213693i
$211$	0.361802	−	0.303588i	0.0249075	−	0.0208999i	−0.630249	−	0.776393i	$-0.717047\pi$
$211$	0.361802	−	0.303588i	0.0249075	−	0.0208999i	0.655156	+	0.755493i	$0.272603\pi$
$212$	−5.42217	−	1.97351i	−0.372396	−	0.135541i
$213$	8.27335	+	2.74529i	0.566880	+	0.188104i
$214$	−10.9008	−	3.96756i	−0.745163	−	0.271217i
$215$	2.26830	−	12.8642i	0.154697	−	0.877330i
$216$	−2.97511	−	4.26013i	−0.202431	−	0.289865i
$217$	−2.59794	−	4.49976i	−0.176359	−	0.305463i
$218$	7.31555	+	6.13848i	0.495472	+	0.415750i
$219$	−8.18261	+	7.27585i	−0.552930	+	0.491656i
$220$	−8.56533			−0.577474
$221$	7.72177	+	13.3745i	0.519422	+	0.899666i
$222$	11.2431	−	9.99723i	0.754591	−	0.670970i
$223$	−7.33109	−	2.66830i	−0.490926	−	0.178682i	0.0846824	−	0.996408i	$-0.473012\pi$
$223$	−7.33109	−	2.66830i	−0.490926	−	0.178682i	−0.575608	+	0.817726i	$0.695235\pi$
$224$	−1.07768	−	0.904284i	−0.0720058	−	0.0604200i
$225$	−0.282675	+	2.40122i	−0.0188450	+	0.160081i
$226$	−9.88232	−	3.59687i	−0.657362	−	0.239260i
$227$	10.1380	+	17.5596i	0.672885	+	1.16547i	0.977082	+	0.212862i	$0.0682785\pi$
$227$	10.1380	+	17.5596i	0.672885	+	1.16547i	−0.304197	+	0.952609i	$0.598388\pi$
$228$	−6.93422	−	2.98607i	−0.459230	−	0.197758i
$229$	−12.3117	+	21.3245i	−0.813581	+	1.40916i	0.0967619	+	0.995308i	$0.469151\pi$
$229$	−12.3117	+	21.3245i	−0.813581	+	1.40916i	−0.910343	+	0.413856i	$0.864182\pi$
$230$	6.37339	−	5.34791i	0.420249	−	0.352631i
$231$	−10.1870	+	0.292196i	−0.670254	+	0.0192251i
$232$	−1.58877	+	9.01038i	−0.104308	+	0.591560i
$233$	18.3529	−	15.3999i	1.20234	−	1.00888i	0.202781	−	0.979224i	$-0.435002\pi$
$233$	18.3529	−	15.3999i	1.20234	−	1.00888i	0.999560	−	0.0296598i	$-0.00944241\pi$
$234$	3.51284	+	5.35065i	0.229642	+	0.349783i
$235$	−9.25991	+	16.0386i	−0.604050	+	1.04624i
$236$	−5.39829	+	9.35011i	−0.351399	+	0.608641i
$237$	−2.17834	−	0.722822i	−0.141498	−	0.0469523i
$238$	−1.76826	+	10.0283i	−0.114619	+	0.650037i
$239$	−17.4873			−1.13116			−0.565579	−	0.824694i	$-0.691347\pi$
$239$	−17.4873			−1.13116			−0.565579	+	0.824694i	$0.691347\pi$
$240$	−0.515545	+	3.50947i	−0.0332783	+	0.226536i
$241$	−12.9984	+	4.73104i	−0.837302	+	0.304753i	−0.724852	−	0.688904i	$-0.758092\pi$
$241$	−12.9984	+	4.73104i	−0.837302	+	0.304753i	−0.112450	+	0.993657i	$0.535870\pi$
$242$	4.97356	−	4.17332i	0.319713	−	0.268271i
$243$	−5.78529	+	14.4752i	−0.371127	+	0.928582i
$244$	0.196697	+	1.11552i	0.0125922	+	0.0714140i
$245$	1.78553	+	10.1262i	0.114073	+	0.646941i
$246$	−17.3690	+	6.89194i	−1.10741	+	0.439414i
$247$	8.43276	+	3.92171i	0.536563	+	0.249532i
$248$	1.84668	−	3.19854i	0.117264	−	0.203108i
$249$	−2.28385	−	3.70611i	−0.144733	−	0.234865i
$250$	9.10843	−	7.64288i	0.576068	−	0.483378i
$251$	−11.3840	−	9.55233i	−0.718554	−	0.602938i	0.208431	−	0.978037i	$-0.433164\pi$
$251$	−11.3840	−	9.55233i	−0.718554	−	0.602938i	−0.926985	+	0.375099i	$0.877609\pi$
$252$	−0.493430	+	4.19150i	−0.0310832	+	0.264040i
$253$	−2.95050	+	16.7331i	−0.185496	+	1.05200i
$254$	−9.55970			−0.599829
$255$	23.8652	−	9.46962i	1.49450	−	0.593011i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−2.23159	+	12.6560i	−0.139202	+	0.789457i	0.832638	+	0.553817i	$0.186829\pi$
$257$	−2.23159	+	12.6560i	−0.139202	+	0.789457i	−0.971841	+	0.235639i	$0.924282\pi$
$258$	10.2689	−	4.07465i	0.639313	−	0.253677i
$259$	−12.2200			−0.759311
$260$	0.758747	−	4.30307i	0.0470555	−	0.266865i
$261$	25.2123	−	10.8508i	1.56060	−	0.671648i
$262$	8.65957	+	7.26624i	0.534990	+	0.448910i
$263$	−6.66704	+	5.59431i	−0.411107	+	0.344960i	−0.824768	−	0.565471i	$-0.808694\pi$
$263$	−6.66704	+	5.59431i	−0.411107	+	0.344960i	0.413661	+	0.910431i	$0.364250\pi$
$264$	−3.80045	−	6.16718i	−0.233902	−	0.379564i
$265$	5.90847	−	10.2338i	0.362954	−	0.628655i
$266$	2.59728	+	5.55496i	0.159249	+	0.340597i
$267$	5.77939	−	2.29324i	0.353693	−	0.140344i
$268$	−0.666967	−	3.78256i	−0.0407415	−	0.231056i
$269$	4.29203	+	24.3413i	0.261690	+	1.48412i	0.778299	+	0.627894i	$0.216083\pi$
$269$	4.29203	+	24.3413i	0.261690	+	1.48412i	−0.516609	+	0.856221i	$0.672806\pi$
$270$	9.64997	−	4.48529i	0.587279	−	0.272966i
$271$	−19.5526	+	16.4066i	−1.18773	+	0.996628i	−0.187839	+	0.982200i	$0.560148\pi$
$271$	−19.5526	+	16.4066i	−1.18773	+	0.996628i	−0.999896	+	0.0144276i	$0.995407\pi$
$272$	−6.80180	+	2.47565i	−0.412419	+	0.150108i
$273$	0.755605	−	5.14364i	0.0457313	−	0.311307i
$274$	8.95952			0.541265
$275$	−0.585323	+	3.31953i	−0.0352963	+	0.200175i
$276$	6.67848	+	2.21607i	0.401997	+	0.133392i
$277$	4.81472	−	8.33934i	0.289288	−	0.501062i	−0.684352	−	0.729152i	$-0.739915\pi$
$277$	4.81472	−	8.33934i	0.289288	−	0.501062i	0.973640	+	0.228090i	$0.0732480\pi$
$278$	6.36356	−	11.0220i	0.381661	−	0.661056i
$279$	−11.0619	+	0.635102i	−0.662256	+	0.0380226i
$280$	2.20703	−	1.85192i	0.131895	−	0.110673i
$281$	0.857875	−	4.86525i	0.0511765	−	0.290237i	−0.948469	−	0.316871i	$-0.897368\pi$
$281$	0.857875	−	4.86525i	0.0511765	−	0.290237i	0.999645	+	0.0266343i	$0.00847895\pi$
$282$	−15.6567	+	0.449086i	−0.932345	+	0.0267427i
$283$	2.97611	−	2.49725i	0.176911	−	0.148446i	−0.550032	−	0.835143i	$-0.685385\pi$
$283$	2.97611	−	2.49725i	0.176911	−	0.148446i	0.726943	+	0.686697i	$0.240940\pi$
$284$	2.51636	−	4.35846i	0.149319	−	0.258627i
$285$	8.48836	−	12.9232i	0.502807	−	0.765506i
$286$	4.46175	+	7.72798i	0.263829	+	0.456965i
$287$	14.2622	+	5.19103i	0.841873	+	0.306417i
$288$	−2.75563	+	1.18596i	−0.162377	+	0.0698834i
$289$	27.1128	+	22.7504i	1.59487	+	1.33826i
$290$	−17.6074	−	6.40857i	−1.03394	−	0.376324i
$291$	−7.54398	+	6.70798i	−0.442236	+	0.393229i
$292$	3.16087	+	5.47479i	0.184976	+	0.320388i
$293$	−11.5290			−0.673531			−0.336766	−	0.941589i	$-0.609333\pi$
$293$	−11.5290			−0.673531			−0.336766	+	0.941589i	$0.609333\pi$
$294$	−6.49882	+	5.77864i	−0.379019	+	0.337017i
$295$	−16.9378	−	14.2125i	−0.986159	−	0.827486i
$296$	−4.34313	−	7.52251i	−0.252439	−	0.437237i
$297$	−9.20894	+	19.6849i	−0.534357	+	1.14223i
$298$	2.00870	−	11.3919i	0.116361	−	0.659916i
$299$	−8.14505	−	2.96456i	−0.471041	−	0.171445i
$300$	1.32488	+	0.439626i	0.0764921	+	0.0253818i
$301$	−8.43211	−	3.06904i	−0.486019	−	0.176896i
$302$	−2.26373	+	1.89949i	−0.130263	+	0.109304i
$303$	−11.0662	−	8.75747i	−0.635738	−	0.503104i
$304$	−2.49649	+	3.57317i	−0.143183	+	0.204935i
$305$	−2.31977			−0.132829
$306$	17.4073	+	12.9817i	0.995112	+	0.742113i
$307$	−0.650952	−	3.69173i	−0.0371518	−	0.210698i	0.960581	−	0.278001i	$-0.0896718\pi$
$307$	−0.650952	−	3.69173i	−0.0371518	−	0.210698i	−0.997733	+	0.0673026i	$0.978561\pi$
$308$	−1.02172	+	5.79449i	−0.0582182	+	0.330172i
$309$	3.05416	+	4.95613i	0.173745	+	0.281944i
$310$	5.79419	+	4.86190i	0.329088	+	0.276138i
$311$	−2.52569	−	4.37462i	−0.143219	−	0.248062i	0.785488	−	0.618876i	$-0.212412\pi$
$311$	−2.52569	−	4.37462i	−0.143219	−	0.248062i	−0.928707	+	0.370815i	$0.879079\pi$
$312$	3.43494	−	1.36297i	0.194465	−	0.0771630i
$313$	21.5031	+	18.0433i	1.21543	+	1.01987i	0.999051	+	0.0435555i	$0.0138685\pi$
$313$	21.5031	+	18.0433i	1.21543	+	1.01987i	0.216377	+	0.976310i	$0.430576\pi$
$314$	−9.78351	+	3.56091i	−0.552116	+	0.200954i
$315$	−8.27807	−	2.48575i	−0.466417	−	0.140056i
$316$	−0.662547	+	1.14757i	−0.0372712	+	0.0645556i
$317$	17.9231	−	6.52349i	1.00666	−	0.366396i	0.214513	−	0.976721i	$-0.431183\pi$
$317$	17.9231	−	6.52349i	1.00666	−	0.366396i	0.792151	+	0.610325i	$0.208961\pi$
$318$	9.99009	−	0.286548i	0.560216	−	0.0160688i
$319$	35.9587	−	13.0879i	2.01330	−	0.732781i
$320$	1.92444	+	0.700437i	0.107579	+	0.0391556i
$321$	20.0842	−	0.576079i	1.12099	−	0.0321536i
$322$	−2.85763	−	4.94956i	−0.159250	−	0.275828i
$323$	31.4339	+	2.71754i	1.74903	+	0.151208i
$324$	7.51120	+	4.95801i	0.417289	+	0.275445i
$325$	−1.61582	−	0.588112i	−0.0896297	−	0.0326226i
$326$	14.1610	−	11.8825i	0.784307	−	0.658112i
$327$	−15.6990	−	5.20928i	−0.868156	−	0.288074i
$328$	1.87342	+	10.6247i	0.103442	+	0.586650i
$329$	9.74564	+	8.17756i	0.537294	+	0.450843i
$330$	13.7897	−	5.47169i	0.759097	−	0.301206i
$331$	5.45925	−	9.45569i	0.300067	−	0.519732i	−0.676084	−	0.736825i	$-0.736324\pi$
$331$	5.45925	−	9.45569i	0.300067	−	0.519732i	0.976151	+	0.217093i	$0.0696575\pi$
$332$	−2.36181	+	0.859627i	−0.129621	+	0.0471782i
$333$	−11.7144	+	23.2773i	−0.641945	+	1.27559i
$334$	−11.7107	−	20.2835i	−0.640779	−	1.10986i
$335$	7.86596			0.429763
$336$	2.31268	+	0.767400i	0.126167	+	0.0418651i
$337$	−4.49994	−	25.5204i	−0.245127	−	1.39019i	−0.820197	−	0.572081i	$-0.806136\pi$
$337$	−4.49994	−	25.5204i	−0.245127	−	1.39019i	0.575070	−	0.818104i	$-0.304975\pi$
$338$	7.93837	−	2.88933i	0.431790	−	0.157159i
$339$	18.2077	−	0.522256i	0.988907	−	0.0283651i
$340$	−2.57410	−	14.5985i	−0.139600	−	0.791712i
$341$	−15.4471			−0.836508
$342$	13.0712	+	0.377699i	0.706812	+	0.0204236i
$343$	16.9112			0.913116
$344$	−1.10760	−	6.28152i	−0.0597179	−	0.338677i
$345$	−6.84445	+	12.6813i	−0.368493	+	0.682736i
$346$	−0.277102	+	0.100857i	−0.0148971	+	0.00542211i
$347$	0.155187	+	0.880107i	0.00833086	+	0.0472466i	0.988690	−	0.149975i	$-0.0479193\pi$
$347$	0.155187	+	0.880107i	0.00833086	+	0.0472466i	−0.980359	+	0.197222i	$0.936808\pi$
$348$	−3.19816	−	15.5211i	−0.171440	−	0.832019i
$349$	−14.3389			−0.767545			−0.383773	−	0.923428i	$-0.625375\pi$
$349$	−14.3389			−0.767545			−0.383773	+	0.923428i	$0.625375\pi$
$350$	−0.566900	−	0.981899i	−0.0303021	−	0.0524847i
$351$	−9.07356	−	6.37016i	−0.484311	−	0.340014i
$352$	−3.93018	+	1.43047i	−0.209479	+	0.0762442i
$353$	7.67879	−	13.3001i	0.408701	−	0.707891i	−0.586044	−	0.810280i	$-0.699315\pi$
$353$	7.67879	−	13.3001i	0.408701	−	0.707891i	0.994744	+	0.102389i	$0.0326486\pi$
$354$	2.71791	−	18.5017i	0.144455	−	0.983352i
$355$	7.89541	+	6.62503i	0.419045	+	0.351620i
$356$	−0.623365	−	3.53528i	−0.0330383	−	0.187369i
$357$	−3.55946	−	17.2745i	−0.188387	−	0.914266i
$358$	−10.0810	+	8.45895i	−0.532796	+	0.447069i
$359$	25.1271	+	9.14550i	1.32616	+	0.482681i	0.905426	−	0.424505i	$-0.139552\pi$
$359$	25.1271	+	9.14550i	1.32616	+	0.482681i	0.420730	+	0.907186i	$0.361774\pi$
$360$	−1.41192	−	5.97939i	−0.0744147	−	0.315141i
$361$	16.4349	−	9.53382i	0.864995	−	0.501780i
$362$	7.82689	+	13.5566i	0.411372	+	0.712518i
$363$	−5.34116	+	9.89600i	−0.280338	+	0.519405i
$364$	−2.82054	−	1.02659i	−0.147836	−	0.0538081i
$365$	−12.1658	+	4.42798i	−0.636786	+	0.231771i
$366$	−1.02929	−	1.67027i	−0.0538016	−	0.0873065i
$367$	9.84220	−	3.58227i	0.513759	−	0.186993i	−0.0721134	−	0.997396i	$-0.522974\pi$
$367$	9.84220	−	3.58227i	0.513759	−	0.186993i	0.585872	+	0.810404i	$0.300752\pi$
$368$	2.03128	−	3.51827i	0.105888	−	0.183403i
$369$	23.5603	−	22.1912i	1.22650	−	1.15523i
$370$	16.7161	−	6.08418i	0.869031	−	0.316301i
$371$	−6.21840	−	5.21786i	−0.322843	−	0.270898i
$372$	−0.929758	+	6.32915i	−0.0482057	+	0.328151i
$373$	1.54981	+	2.68435i	0.0802462	+	0.138991i	0.903356	−	0.428892i	$-0.141096\pi$
$373$	1.54981	+	2.68435i	0.0802462	+	0.138991i	−0.823109	+	0.567883i	$0.807763\pi$
$374$	23.1909	+	19.4595i	1.19917	+	1.00623i
$375$	−9.78163	+	18.1232i	−0.505121	+	0.935879i
$376$	−1.57032	+	8.90575i	−0.0809833	+	0.459279i
$377$	3.38977	+	19.2244i	0.174582	+	0.990105i
$378$	−1.88322	−	7.06329i	−0.0968622	−	0.363296i
$379$	−3.65811			−0.187905			−0.0939523	−	0.995577i	$-0.529950\pi$
$379$	−3.65811			−0.187905			−0.0939523	+	0.995577i	$0.529950\pi$
$380$	−6.31867	−	6.30569i	−0.324141	−	0.323475i
$381$	15.3906	−	6.10691i	0.788482	−	0.312867i
$382$	4.34843	−	3.64877i	0.222485	−	0.186687i
$383$	19.7639	+	7.19349i	1.00989	+	0.367570i	0.793391	−	0.608713i	$-0.208314\pi$
$383$	19.7639	+	7.19349i	1.00989	+	0.367570i	0.216500	+	0.976283i	$0.430536\pi$
$384$	0.349550	+	1.69641i	0.0178379	+	0.0865697i
$385$	−11.3231	−	4.12129i	−0.577081	−	0.210040i
$386$	1.44103	−	8.17247i	0.0733463	−	0.415968i
$387$	−13.9293	+	13.1199i	−0.708068	+	0.666922i
$388$	2.91417	+	5.04749i	0.147945	+	0.256248i
$389$	−5.67617	−	4.76287i	−0.287793	−	0.241487i	0.487449	−	0.873152i	$-0.337928\pi$
$389$	−5.67617	−	4.76287i	−0.287793	−	0.241487i	−0.775242	+	0.631664i	$0.782372\pi$
$390$	1.52734	+	7.41239i	0.0773399	+	0.375341i
$391$	−29.4061			−1.48713
$392$	2.51043	+	4.34820i	0.126796	+	0.219617i
$393$	−18.5832	−	6.16633i	−0.937399	−	0.311050i
$394$	5.26151	+	1.91503i	0.265071	+	0.0964779i
$395$	−2.07883	−	1.74434i	−0.104597	−	0.0877674i
$396$	10.0582	+	7.50100i	0.505444	+	0.376939i
$397$	−17.6292	−	6.41651i	−0.884785	−	0.322036i	−0.140646	−	0.990060i	$-0.544918\pi$
$397$	−17.6292	−	6.41651i	−0.884785	−	0.322036i	−0.744139	+	0.668024i	$0.767140\pi$
$398$	−9.85726	−	17.0733i	−0.494100	−	0.855806i
$399$	−7.73008	−	7.28398i	−0.386988	−	0.364655i
$400$	0.402967	−	0.697959i	0.0201483	−	0.0348979i
$401$	17.2966	−	14.5136i	0.863750	−	0.724772i	−0.0990226	−	0.995085i	$-0.531572\pi$
$401$	17.2966	−	14.5136i	0.863750	−	0.724772i	0.962773	+	0.270313i	$0.0871272\pi$
$402$	3.49014	+	5.66362i	0.174073	+	0.282476i
$403$	1.36836	−	7.76036i	0.0681629	−	0.386571i
$404$	−6.24149	+	5.23724i	−0.310526	+	0.260562i
$405$	−12.6706	+	13.3856i	−0.629607	+	0.665138i
$406$	−6.43574	+	11.1470i	−0.319401	+	0.553218i
$407$	−18.1647	+	31.4622i	−0.900392	+	1.55952i
$408$	9.36900	−	8.33076i	0.463835	−	0.412434i
$409$	−3.57339	+	20.2657i	−0.176693	+	1.00207i	0.759479	+	0.650532i	$0.225454\pi$
$409$	−3.57339	+	20.2657i	−0.176693	+	1.00207i	−0.936172	+	0.351543i	$0.885657\pi$
$410$	−22.0944			−1.09116
$411$	−14.4243	+	5.72351i	−0.711499	+	0.282320i
$412$	3.15840	−	1.14956i	0.155603	−	0.0566350i
$413$	−11.6353	+	9.76317i	−0.572536	+	0.480414i
$414$	−12.1676	+	0.698588i	−0.598006	+	0.0343337i
$415$	−0.893812	−	5.06906i	−0.0438755	−	0.248830i
$416$	−0.370492	−	2.10117i	−0.0181649	−	0.103018i
$417$	−3.20390	+	21.8099i	−0.156895	+	1.06804i
$418$	18.1629	+	1.57023i	0.888378	+	0.0768025i
$419$	4.10584	−	7.11153i	0.200584	−	0.347421i	−0.748133	−	0.663549i	$-0.769049\pi$
$419$	4.10584	−	7.11153i	0.200584	−	0.347421i	0.948717	+	0.316128i	$0.102383\pi$
$420$	−2.37015	+	4.39138i	−0.115652	+	0.214277i
$421$	−14.8054	+	12.4232i	−0.721572	+	0.605471i	−0.927820	−	0.373029i	$-0.878319\pi$
$421$	−14.8054	+	12.4232i	−0.721572	+	0.605471i	0.206248	+	0.978500i	$0.433875\pi$
$422$	0.361802	+	0.303588i	0.0176123	+	0.0147784i
$423$	24.9195	−	10.7248i	1.21163	−	0.521458i
$424$	1.00198	−	5.68249i	0.0486603	−	0.275966i
$425$	−5.83360			−0.282971
$426$	−1.26693	+	8.62437i	−0.0613828	+	0.417852i
$427$	−0.276716	+	1.56933i	−0.0133912	+	0.0759454i
$428$	2.01439	−	11.4241i	0.0973690	−	0.552207i
$429$	−12.1199	−	9.59135i	−0.585156	−	0.463075i
$430$	13.0626			0.629936
$431$	2.30835	−	13.0913i	0.111189	−	0.630586i	−0.877377	−	0.479801i	$-0.840709\pi$
$431$	2.30835	−	13.0913i	0.111189	−	0.630586i	0.988567	−	0.150785i	$-0.0481801\pi$
$432$	3.67879	−	3.66967i	0.176996	−	0.176557i
$433$	−7.71664	−	6.47503i	−0.370838	−	0.311170i	0.438255	−	0.898851i	$-0.355597\pi$
$433$	−7.71664	−	6.47503i	−0.370838	−	0.311170i	−0.809093	+	0.587681i	$0.800041\pi$
$434$	3.98027	−	3.33984i	0.191059	−	0.160318i
$435$	32.4408	−	0.930506i	1.55542	−	0.0446144i
$436$	−4.77489	+	8.27035i	−0.228676	+	0.396078i
$437$	−14.4953	+	10.1720i	−0.693404	+	0.486590i
$438$	−8.58621	−	6.79486i	−0.410265	−	0.324671i
$439$	3.70792	+	21.0287i	0.176969	+	1.00364i	0.935846	+	0.352409i	$0.114637\pi$
$439$	3.70792	+	21.0287i	0.176969	+	1.00364i	−0.758877	+	0.651234i	$0.774251\pi$
$440$	−1.48735	−	8.43520i	−0.0709068	−	0.402132i
$441$	6.77121	−	13.4548i	0.322439	−	0.640707i
$442$	−11.8304	+	9.92691i	−0.562716	+	0.472175i
$443$	−16.8872	+	6.14643i	−0.802334	+	0.292026i	−0.710453	−	0.703744i	$-0.751510\pi$
$443$	−16.8872	+	6.14643i	−0.802334	+	0.292026i	−0.0918809	+	0.995770i	$0.529288\pi$
$444$	11.7977	+	9.33634i	0.559894	+	0.443083i
$445$	7.35173			0.348505
$446$	1.35473	−	7.68306i	0.0641483	−	0.363803i
$447$	4.04347	+	19.6235i	0.191250	+	0.928160i
$448$	0.703408	−	1.21834i	0.0332329	−	0.0575611i
$449$	−18.7575	+	32.4890i	−0.885221	+	1.53325i	−0.0397619	+	0.999209i	$0.512660\pi$
$449$	−18.7575	+	32.4890i	−0.885221	+	1.53325i	−0.845460	+	0.534039i	$0.820673\pi$
$450$	−2.41382	+	0.138587i	−0.113789	+	0.00653303i
$451$	34.5656	−	29.0040i	1.62763	−	1.36575i
$452$	1.82618	−	10.3568i	0.0858963	−	0.487142i
$453$	2.43104	−	4.50418i	0.114220	−	0.211625i
$454$	−15.5324	+	13.0332i	−0.728970	+	0.611679i
$455$	3.07351	−	5.32347i	0.144088	−	0.249568i
$456$	1.73659	−	7.34740i	0.0813235	−	0.344073i
$457$	−15.3316	−	26.5551i	−0.717182	−	1.24220i	−0.962112	−	0.272655i	$-0.912098\pi$
$457$	−15.3316	−	26.5551i	−0.717182	−	1.24220i	0.244930	−	0.969541i	$-0.421235\pi$
$458$	−23.1384	−	8.42171i	−1.08119	−	0.393520i
$459$	−36.3177	−	9.77960i	−1.69517	−	0.456473i
$460$	6.37339	+	5.34791i	0.297161	+	0.249348i
$461$	23.2215	+	8.45192i	1.08153	+	0.393645i	0.820477	−	0.571679i	$-0.193708\pi$
$461$	23.2215	+	8.45192i	1.08153	+	0.393645i	0.261054	+	0.965324i	$0.415930\pi$
$462$	−2.05671	−	9.98148i	−0.0956867	−	0.464381i
$463$	−5.28090	−	9.14679i	−0.245424	−	0.425087i	0.716826	−	0.697252i	$-0.245594\pi$
$463$	−5.28090	−	9.14679i	−0.245424	−	0.425087i	−0.962251	+	0.272164i	$0.912261\pi$
$464$	−9.14938			−0.424749
$465$	−12.4342	−	4.12595i	−0.576621	−	0.191336i
$466$	18.3529	+	15.3999i	0.850184	+	0.713389i
$467$	3.05559	+	5.29244i	0.141396	+	0.244905i	0.928023	−	0.372524i	$-0.121508\pi$
$467$	3.05559	+	5.29244i	0.141396	+	0.244905i	−0.786627	+	0.617429i	$0.788174\pi$
$468$	−4.65936	+	4.38860i	−0.215379	+	0.202863i
$469$	0.938299	−	5.32136i	0.0433266	−	0.245718i
$470$	−17.4029	−	6.33415i	−0.802737	−	0.292173i
$471$	13.4761	−	11.9827i	0.620946	−	0.552135i
$472$	−10.1455	−	3.69265i	−0.466983	−	0.169968i
$473$	−20.4359	+	17.1477i	−0.939643	+	0.788454i
$474$	0.333576	−	2.27076i	0.0153217	−	0.104299i
$475$	−2.87559	+	2.01792i	−0.131941	+	0.0925886i
$476$	−10.1830			−0.466736
$477$	−15.9004	+	6.84318i	−0.728029	+	0.313327i
$478$	−3.03663	−	17.2216i	−0.138892	−	0.787698i
$479$	6.47862	−	36.7421i	0.296015	−	1.67879i	−0.367031	−	0.930209i	$-0.619626\pi$
$479$	6.47862	−	36.7421i	0.296015	−	1.67879i	0.663046	−	0.748578i	$-0.269263\pi$
$480$	−3.54568	+	0.101702i	−0.161837	+	0.00464202i
$481$	−14.1970	−	11.9127i	−0.647326	−	0.543171i
$482$	−6.91632	−	11.9794i	−0.315030	−	0.545648i
$483$	7.76249	+	6.14300i	0.353206	+	0.279516i
$484$	4.97356	+	4.17332i	0.226071	+	0.189696i
$485$	−11.2163	+	4.08239i	−0.509305	+	0.185372i
$486$	−15.2599	−	3.18381i	−0.692201	−	0.144421i
$487$	20.3942	−	35.3238i	0.924151	−	1.60068i	0.131230	−	0.991352i	$-0.458107\pi$
$487$	20.3942	−	35.3238i	0.924151	−	1.60068i	0.792921	−	0.609324i	$-0.208559\pi$
$488$	−1.06442	+	0.387417i	−0.0481840	+	0.0175375i
$489$	−15.2077	+	28.1765i	−0.687714	+	1.27418i
$490$	−9.66234	+	3.51680i	−0.436500	+	0.158873i
$491$	−25.0199	−	9.10652i	−1.12913	−	0.410971i	−0.291157	−	0.956675i	$-0.594040\pi$
$491$	−25.0199	−	9.10652i	−1.12913	−	0.410971i	−0.837978	+	0.545704i	$0.816262\pi$
$492$	−9.80333	−	15.9083i	−0.441968	−	0.717203i
$493$	33.1131	+	57.3535i	1.49134	+	2.58307i
$494$	−2.39779	+	8.98564i	−0.107882	+	0.404283i
$495$	−18.7052	+	17.6182i	−0.840734	+	0.791879i
$496$	3.47062	+	1.26320i	0.155835	+	0.0567195i
$497$	5.42368	−	4.55101i	0.243285	−	0.204141i
$498$	3.25322	−	2.89271i	0.145780	−	0.129626i
$499$	−4.75671	−	26.9767i	−0.212940	−	1.20764i	−0.884446	−	0.466642i	$-0.845464\pi$
$499$	−4.75671	−	26.9767i	−0.212940	−	1.20764i	0.671506	−	0.740999i	$-0.265648\pi$
$500$	9.10843	+	7.64288i	0.407342	+	0.341800i
$501$	31.8109	+	25.1742i	1.42121	+	1.12470i
$502$	7.43040	−	12.8698i	0.331635	−	0.574408i
$503$	−5.41852	+	1.97218i	−0.241600	+	0.0879352i	−0.459982	−	0.887928i	$-0.652144\pi$
$503$	−5.41852	+	1.97218i	−0.241600	+	0.0879352i	0.218382	+	0.975863i	$0.429922\pi$
$504$	−4.21351	+	0.241913i	−0.187685	+	0.0107757i
$505$	−8.34300	−	14.4505i	−0.371259	−	0.643039i
$506$	−16.9912			−0.755353
$507$	−10.9346	+	9.72283i	−0.485620	+	0.431806i
$508$	−1.66002	−	9.41447i	−0.0736517	−	0.417699i
$509$	−5.54563	+	2.01844i	−0.245806	+	0.0894659i	−0.461985	−	0.886888i	$-0.652863\pi$
$509$	−5.54563	+	2.01844i	−0.245806	+	0.0894659i	0.216179	+	0.976354i	$0.430640\pi$
$510$	13.4699	+	21.8583i	0.596458	+	0.967901i
$511$	1.54434	+	8.75841i	0.0683178	+	0.387449i
$512$	1.00000			0.0441942
$513$	−21.2852	+	7.74207i	−0.939765	+	0.341821i
$514$	−12.8512			−0.566842
$515$	1.19528	+	6.77877i	0.0526703	+	0.298708i
$516$	5.79592	+	9.40532i	0.255151	+	0.414046i
$517$	35.5411	−	12.9359i	1.56310	−	0.568921i
$518$	−2.12197	−	12.0343i	−0.0932342	−	0.528757i
$519$	0.381689	−	0.339392i	0.0167543	−	0.0148976i
$520$	4.36945			0.191613
$521$	−14.5847	−	25.2615i	−0.638969	−	1.10673i	−0.985659	−	0.168748i	$-0.946028\pi$
$521$	−14.5847	−	25.2615i	−0.638969	−	1.10673i	0.346690	−	0.937980i	$-0.387306\pi$
$522$	15.0640	+	22.9450i	0.659335	+	1.00428i
$523$	20.8643	−	7.59399i	0.912333	−	0.332062i	0.157149	−	0.987575i	$-0.449770\pi$
$523$	20.8643	−	7.59399i	0.912333	−	0.332062i	0.755184	+	0.655513i	$0.227547\pi$
$524$	−5.65213	+	9.78978i	−0.246915	+	0.427669i
$525$	1.53993	+	1.21865i	0.0672081	+	0.0531864i
$526$	−6.66704	−	5.59431i	−0.290697	−	0.243923i
$527$	−4.64226	−	26.3275i	−0.202220	−	1.14685i
$528$	5.41355	−	4.81364i	0.235594	−	0.209487i
$529$	−4.97597	+	4.17533i	−0.216346	+	0.181536i
$530$	11.1043	+	4.04163i	0.482339	+	0.175557i
$531$	7.44353	+	31.5228i	0.323021	+	1.36797i
$532$	−5.01956	+	3.52243i	−0.217625	+	0.152717i
$533$	11.5091	+	19.9344i	0.498517	+	0.863456i
$534$	3.26198	+	5.29337i	0.141160	+	0.229067i
$535$	22.3242	+	8.12534i	0.965159	+	0.351289i
$536$	3.60927	−	1.31367i	0.155897	−	0.0567418i
$537$	10.8261	−	20.0583i	0.467179	−	0.865581i
$538$	−23.2262	+	8.45365i	−1.00135	+	0.364463i
$539$	10.4997	−	18.1859i	0.452252	−	0.783324i
$540$	6.09285	+	8.72450i	0.262195	+	0.375443i
$541$	−31.7280	+	11.5481i	−1.36410	+	0.496490i	−0.917318	−	0.398155i	$-0.869650\pi$
$541$	−31.7280	+	11.5481i	−1.36410	+	0.496490i	−0.446777	+	0.894645i	$0.647428\pi$
$542$	−19.5526	−	16.4066i	−0.839855	−	0.704722i
$543$	−21.2610	−	16.8253i	−0.912398	−	0.722044i
$544$	−3.61916	−	6.26857i	−0.155170	−	0.268763i
$545$	−14.9818	−	12.5712i	−0.641751	−	0.538493i
$546$	5.19671	−	0.149058i	0.222399	−	0.00637911i
$547$	4.75655	−	26.9757i	0.203375	−	1.15340i	−0.696600	−	0.717459i	$-0.745305\pi$
$547$	4.75655	−	26.9757i	0.203375	−	1.15340i	0.899976	−	0.435940i	$-0.143584\pi$
$548$	1.55580	+	8.82341i	0.0664607	+	0.376917i
$549$	2.72409	+	2.03151i	0.116261	+	0.0867028i
$550$	−3.37074			−0.143729
$551$	36.1620	+	16.8173i	1.54055	+	0.716443i
$552$	−1.02270	+	6.96183i	−0.0435289	+	0.296315i
$553$	−1.42803	+	1.19826i	−0.0607261	+	0.0509552i
$554$	9.04871	+	3.29346i	0.384443	+	0.139926i
$555$	−23.0253	+	20.4737i	−0.977370	+	0.869062i
$556$	11.9596	+	4.35293i	0.507199	+	0.184605i
$557$	1.23359	−	6.99603i	0.0522689	−	0.296431i	−0.947456	−	0.319886i	$-0.896355\pi$
$557$	1.23359	−	6.99603i	0.0522689	−	0.296431i	0.999725	+	0.0234546i	$0.00746650\pi$
$558$	−2.54632	−	10.7835i	−0.107794	−	0.456503i
$559$	−6.80444	−	11.7856i	−0.287797	−	0.498479i
$560$	2.20703	+	1.85192i	0.0932642	+	0.0782579i
$561$	−49.7671	−	16.5139i	−2.10117	−	0.697216i
$562$	4.94031			0.208394
$563$	8.01427	+	13.8811i	0.337761	+	0.585020i	0.984011	−	0.178106i	$-0.0569970\pi$
$563$	8.01427	+	13.8811i	0.337761	+	0.585020i	−0.646250	+	0.763126i	$0.723664\pi$
$564$	−3.16103	−	15.3409i	−0.133103	−	0.645968i
$565$	20.2384	+	7.36619i	0.851437	+	0.309898i
$566$	2.97611	+	2.49725i	0.125095	+	0.104967i
$567$	7.54402	+	10.1684i	0.316819	+	0.427035i
$568$	4.72921	+	1.72129i	0.198433	+	0.0722238i
$569$	−18.9076	−	32.7490i	−0.792649	−	1.37291i	−0.924321	−	0.381616i	$-0.875368\pi$
$569$	−18.9076	−	32.7490i	−0.792649	−	1.37291i	0.131672	−	0.991293i	$-0.457966\pi$
$570$	14.2009	+	6.11531i	0.594809	+	0.256142i
$571$	9.25405	−	16.0285i	0.387270	−	0.670771i	−0.604811	−	0.796369i	$-0.706752\pi$
$571$	9.25405	−	16.0285i	0.387270	−	0.670771i	0.992081	+	0.125598i	$0.0400849\pi$
$572$	−6.83580	+	5.73592i	−0.285819	+	0.239831i
$573$	−4.66982	+	8.65217i	−0.195085	+	0.361449i
$574$	−2.63555	+	14.9470i	−0.110006	+	0.623874i
$575$	2.50814	−	2.10458i	0.104597	−	0.0877671i
$576$	−1.64645	−	2.50783i	−0.0686022	−	0.104493i
$577$	14.6098	−	25.3049i	0.608213	−	1.05346i	−0.383321	−	0.923615i	$-0.625220\pi$
$577$	14.6098	−	25.3049i	0.608213	−	1.05346i	0.991535	−	0.129842i	$-0.0414469\pi$
$578$	−17.6966	+	30.6515i	−0.736083	+	1.27493i
$579$	2.90075	+	14.0778i	0.120551	+	0.585051i
$580$	3.25371	−	18.4527i	0.135103	−	0.766208i
$581$	−3.53586			−0.146692
$582$	−7.91607	−	6.26454i	−0.328132	−	0.259674i
$583$	−22.6777	+	8.25401i	−0.939215	+	0.341846i
$584$	−4.84273	+	4.06354i	−0.200394	+	0.168150i
$585$	−7.19410	−	10.9578i	−0.297439	−	0.453050i
$586$	−2.00199	−	11.3538i	−0.0827014	−	0.469023i
$587$	−2.52370	−	14.3126i	−0.104164	−	0.590745i	−0.991551	−	0.129719i	$-0.958593\pi$
$587$	−2.52370	−	14.3126i	−0.104164	−	0.590745i	0.887387	−	0.461026i	$-0.152519\pi$
$588$	−6.81936	−	5.39664i	−0.281226	−	0.222554i
$589$	−11.3954	−	11.3720i	−0.469539	−	0.468574i
$590$	11.0554	−	19.1485i	0.455143	−	0.788331i
$591$	−9.69408	+	0.278057i	−0.398761	+	0.0114378i
$592$	6.65405	−	5.58341i	0.273480	−	0.229477i
$593$	26.4073	+	22.1584i	1.08442	+	0.909936i	0.996280	−	0.0861720i	$-0.0274634\pi$
$593$	26.4073	+	22.1584i	1.08442	+	0.909936i	0.0881394	+	0.996108i	$0.471908\pi$
$594$	−20.9849	−	5.65080i	−0.861022	−	0.231855i
$595$	3.62129	−	20.5373i	0.148458	−	0.841949i
$596$	11.5677			0.473830
$597$	26.7763	+	21.1900i	1.09588	+	0.867248i
$598$	1.50514	−	8.53610i	0.0615499	−	0.349067i
$599$	−5.38210	+	30.5234i	−0.219907	+	1.24715i	0.652279	+	0.757979i	$0.273813\pi$
$599$	−5.38210	+	30.5234i	−0.219907	+	1.24715i	−0.872186	+	0.489174i	$0.837298\pi$
$600$	−0.202884	+	1.38109i	−0.00828270	+	0.0563830i
$601$	19.1175			0.779820			0.389910	−	0.920853i	$-0.372506\pi$
$601$	19.1175			0.779820			0.389910	+	0.920853i	$0.372506\pi$
$602$	1.55819	−	8.83694i	0.0635071	−	0.360167i
$603$	−9.23695	−	6.88853i	−0.376158	−	0.280523i
$604$	−2.26373	−	1.89949i	−0.0921098	−	0.0772893i
$605$	−10.1856	+	8.54671i	−0.414102	+	0.347473i
$606$	6.70280	−	12.4188i	0.272283	−	0.504480i
$607$	15.0369	−	26.0446i	0.610327	−	1.05712i	−0.380858	−	0.924634i	$-0.624371\pi$
$607$	15.0369	−	26.0446i	0.610327	−	1.05712i	0.991185	−	0.132484i	$-0.0422953\pi$
$608$	−3.95240	−	1.83809i	−0.160291	−	0.0745443i
$609$	3.24024	−	22.0573i	0.131301	−	0.893809i
$610$	−0.402823	−	2.28452i	−0.0163098	−	0.0924977i
$611$	3.35041	+	19.0011i	0.135543	+	0.768703i
$612$	−9.76170	+	19.3971i	−0.394593	+	0.784082i
$613$	23.0106	−	19.3082i	0.929389	−	0.779850i	−0.0463186	−	0.998927i	$-0.514749\pi$
$613$	23.0106	−	19.3082i	0.929389	−	0.779850i	0.975708	+	0.219077i	$0.0703045\pi$
$614$	3.52261	−	1.28212i	0.142161	−	0.0517423i
$615$	35.5707	−	14.1143i	1.43435	−	0.569143i
$616$	−5.88388			−0.237068
$617$	5.00463	−	28.3827i	0.201479	−	1.14264i	−0.701407	−	0.712761i	$-0.747444\pi$
$617$	5.00463	−	28.3827i	0.201479	−	1.14264i	0.902885	−	0.429882i	$-0.141445\pi$
$618$	−4.35048	+	3.86838i	−0.175002	+	0.155609i
$619$	11.7165	−	20.2936i	0.470926	−	0.815668i	−0.528521	−	0.848920i	$-0.677253\pi$
$619$	11.7165	−	20.2936i	0.470926	−	0.815668i	0.999447	+	0.0332526i	$0.0105866\pi$
$620$	−3.78189	+	6.55043i	−0.151884	+	0.263071i
$621$	19.1429	−	8.89758i	0.768178	−	0.357048i
$622$	3.86958	−	3.24696i	0.155156	−	0.130191i
$623$	0.876959	−	4.97348i	0.0351346	−	0.199258i
$624$	1.93873	+	3.14608i	0.0776115	+	0.125944i
$625$	−15.5666	+	13.0620i	−0.622666	+	0.522478i
$626$	−14.0352	+	24.3096i	−0.560958	+	0.971608i
$627$	−30.2444	+	9.07484i	−1.20784	+	0.362414i
$628$	−5.20570	−	9.01653i	−0.207730	−	0.359799i
$629$	−59.0821	−	21.5041i	−2.35576	−	0.857426i
$630$	1.01052	−	8.58396i	0.0402599	−	0.341993i
$631$	28.7487	+	24.1230i	1.14447	+	0.960321i	0.999576	−	0.0291263i	$-0.00927249\pi$
$631$	28.7487	+	24.1230i	1.14447	+	0.960321i	0.144891	+	0.989448i	$0.453717\pi$
$632$	−1.24518	−	0.453209i	−0.0495306	−	0.0180277i
$633$	−0.776418	−	0.257633i	−0.0308598	−	0.0102400i
$634$	9.53671	+	16.5181i	0.378751	+	0.656016i
$635$	19.5777			0.776918
$636$	2.01696	+	9.78856i	0.0799775	+	0.388142i
$637$	8.20620	+	6.88582i	0.325141	+	0.272826i
$638$	19.1332	+	33.1397i	0.757491	+	1.31201i
$639$	−3.46973	−	14.6941i	−0.137260	−	0.581288i
$640$	−0.355621	+	2.01683i	−0.0140572	+	0.0797222i
$641$	−38.8669	−	14.1464i	−1.53515	−	0.558749i	−0.570274	−	0.821455i	$-0.693163\pi$
$641$	−38.8669	−	14.1464i	−1.53515	−	0.558749i	−0.964876	+	0.262706i	$0.915385\pi$
$642$	4.05491	+	19.6790i	0.160035	+	0.776669i
$643$	−7.05961	−	2.56949i	−0.278404	−	0.101331i	0.199045	−	0.979990i	$-0.436216\pi$
$643$	−7.05961	−	2.56949i	−0.278404	−	0.101331i	−0.477449	+	0.878660i	$0.658438\pi$
$644$	4.37815	−	3.67370i	0.172523	−	0.144764i
$645$	−21.0301	+	8.34465i	−0.828059	+	0.328570i
$646$	2.78218	+	31.4282i	0.109463	+	1.23653i
$647$	15.4302			0.606625			0.303312	−	0.952891i	$-0.401907\pi$
$647$	15.4302			0.606625			0.303312	+	0.952891i	$0.401907\pi$
$648$	−3.57838	+	8.25804i	−0.140572	+	0.324406i
$649$	7.84120	+	44.4697i	0.307794	+	1.74559i
$650$	0.298592	−	1.69340i	0.0117117	−	0.0664206i
$651$	−4.27445	+	7.91962i	−0.167529	+	0.310394i
$652$	14.1610	+	11.8825i	0.554589	+	0.465355i
$653$	−0.811874	−	1.40621i	−0.0317711	−	0.0550291i	0.849703	−	0.527262i	$-0.176781\pi$
$653$	−0.811874	−	1.40621i	−0.0317711	−	0.0550291i	−0.881474	+	0.472233i	$0.843448\pi$
$654$	2.40404	−	16.3651i	0.0940054	−	0.639925i
$655$	−17.7343	−	14.8808i	−0.692937	−	0.581443i
$656$	−10.1379	+	3.68991i	−0.395820	+	0.144067i
$657$	18.1640	+	5.45431i	0.708644	+	0.212793i
$658$	−6.36101	+	11.0176i	−0.247978	+	0.429511i
$659$	−15.5300	+	5.65246i	−0.604963	+	0.220189i	−0.626298	−	0.779584i	$-0.715431\pi$
$659$	−15.5300	+	5.65246i	−0.604963	+	0.220189i	0.0213348	+	0.999772i	$0.493208\pi$
$660$	7.78311	+	12.6300i	0.302957	+	0.491623i
$661$	32.4049	−	11.7944i	1.26041	−	0.458750i	0.376500	−	0.926417i	$-0.377127\pi$
$661$	32.4049	−	11.7944i	1.26041	−	0.458750i	0.883905	+	0.467667i	$0.154905\pi$
$662$	10.2600	+	3.73435i	0.398767	+	0.145139i
$663$	12.7048	−	23.5392i	0.493414	−	0.914189i
$664$	−1.25669	−	2.17665i	−0.0487691	−	0.0844705i
$665$	−5.31908	−	11.3762i	−0.206265	−	0.441152i
$666$	−24.9578	−	7.49438i	−0.967096	−	0.290401i
$667$	−34.9282	−	12.7128i	−1.35243	−	0.492243i
$668$	17.9418	−	15.0549i	0.694188	−	0.582493i
$669$	2.72704	+	13.2347i	0.105433	+	0.511683i
$670$	1.36591	+	7.74646i	0.0527697	+	0.299272i
$671$	3.62917	+	3.04523i	0.140102	+	0.117560i
$672$	−0.354149	+	2.41080i	−0.0136616	+	0.0929988i
$673$	−9.90758	+	17.1604i	−0.381909	+	0.661486i	−0.991335	−	0.131357i	$-0.958067\pi$
$673$	−9.90758	+	17.1604i	−0.381909	+	0.661486i	0.609426	+	0.792843i	$0.291400\pi$
$674$	24.3513	−	8.86314i	0.937977	−	0.341396i
$675$	3.79758	−	1.76511i	0.146169	−	0.0679392i
$676$	4.22392	+	7.31604i	0.162458	+	0.281386i
$677$	42.8855			1.64822			0.824111	−	0.566428i	$-0.191675\pi$
$677$	42.8855			1.64822			0.824111	+	0.566428i	$0.191675\pi$
$678$	3.67606	+	17.8404i	0.141178	+	0.685157i
$679$	1.42381	+	8.07484i	0.0546409	+	0.309884i
$680$	13.9297	−	5.06999i	0.534179	−	0.194425i
$681$	16.6804	−	30.9051i	0.639193	−	1.18428i
$682$	−2.68236	−	15.2124i	−0.102713	−	0.582515i
$683$	−17.3519			−0.663953			−0.331976	−	0.943288i	$-0.607715\pi$
$683$	−17.3519			−0.663953			−0.331976	+	0.943288i	$0.607715\pi$
$684$	1.89784	+	12.9382i	0.0725656	+	0.494706i
$685$	−18.3486			−0.701063
$686$	2.93659	+	16.6542i	0.112120	+	0.635862i
$687$	42.6315	−	1.22281i	1.62649	−	0.0466531i
$688$	5.99376	−	2.18155i	0.228510	−	0.0831708i
$689$	−2.13780	−	12.1241i	−0.0814436	−	0.461890i
$690$	−13.6771	−	4.53838i	−0.520679	−	0.172773i
$691$	11.0701			0.421126			0.210563	−	0.977580i	$-0.432470\pi$
$691$	11.0701			0.421126			0.210563	+	0.977580i	$0.432470\pi$
$692$	−0.147443	−	0.255379i	−0.00560494	−	0.00970805i
$693$	9.68753	+	14.7557i	0.367999	+	0.560524i
$694$	−0.839789	+	0.305658i	−0.0318779	+	0.0116026i
$695$	−13.0322	+	22.5724i	−0.494339	+	0.856221i
$696$	14.7300	−	5.84479i	0.558338	−	0.221546i
$697$	59.8213	+	50.1960i	2.26589	+	1.90131i
$698$	−2.48993	−	14.1211i	−0.0942452	−	0.534491i
$699$	−39.3849	−	13.0688i	−1.48967	−	0.494308i
$700$	0.868541	−	0.728792i	0.0328278	−	0.0275458i
$701$	24.2791	+	8.83689i	0.917011	+	0.333765i	0.757049	−	0.653359i	$-0.226641\pi$
$701$	24.2791	+	8.83689i	0.917011	+	0.333765i	0.159962	+	0.987123i	$0.448863\pi$
$702$	4.69778	−	10.0419i	0.177306	−	0.379006i
$703$	−36.5623	+	9.83714i	−1.37897	+	0.371015i
$704$	−2.09120	−	3.62207i	−0.0788152	−	0.136512i
$705$	32.0641	−	0.919701i	1.20760	−	0.0346379i
$706$	14.4314	+	5.25260i	0.543133	+	0.197684i
$707$	−10.7710	+	3.92034i	−0.405087	+	0.147439i
$708$	18.6925	−	0.536162i	0.702509	−	0.0201502i
$709$	−20.7773	+	7.56231i	−0.780307	+	0.284008i	−0.701301	−	0.712866i	$-0.747397\pi$
$709$	−20.7773	+	7.56231i	−0.780307	+	0.284008i	−0.0790061	+	0.996874i	$0.525175\pi$
$710$	−5.15336	+	8.92588i	−0.193402	+	0.334982i
$711$	0.913564	+	3.86888i	0.0342613	+	0.145094i
$712$	3.37332	−	1.22779i	0.126421	−	0.0460133i
$713$	11.4941	+	9.64468i	0.430457	+	0.361196i
$714$	16.3940	−	6.50508i	0.613530	−	0.243446i
$715$	−9.13741	−	15.8265i	−0.341720	−	0.591876i
$716$	−10.0810	−	8.45895i	−0.376744	−	0.316126i
$717$	15.8903	+	25.7859i	0.593433	+	0.962993i
$718$	−4.64329	+	26.3334i	−0.173286	+	0.982755i
$719$	−4.88647	−	27.7125i	−0.182234	−	1.03350i	−0.929457	−	0.368930i	$-0.879724\pi$
$719$	−4.88647	−	27.7125i	−0.182234	−	1.03350i	0.747223	−	0.664574i	$-0.231387\pi$
$720$	5.64337	−	2.42878i	0.210316	−	0.0905153i
$721$	4.72845			0.176097
$722$	12.2429	+	14.5297i	0.455633	+	0.540739i
$723$	18.7875	+	14.8679i	0.698716	+	0.552943i
$724$	−11.9915	+	10.0621i	−0.445660	+	0.373953i
$725$	−6.92909	−	2.52198i	−0.257340	−	0.0936641i
$726$	−10.6731	−	3.54159i	−0.396117	−	0.131441i
$727$	−26.5160	−	9.65103i	−0.983424	−	0.357937i	−0.200253	−	0.979744i	$-0.564177\pi$
$727$	−26.5160	−	9.65103i	−0.983424	−	0.357937i	−0.783170	+	0.621807i	$0.786399\pi$
$728$	0.521215	−	2.95595i	0.0193175	−	0.109555i
$729$	26.6014	−	4.62252i	0.985235	−	0.171205i
$730$	−6.47328	−	11.2120i	−0.239587	−	0.414976i
$731$	−35.3675	−	29.6769i	−1.30812	−	1.09764i
$732$	1.46616	−	1.30369i	0.0541909	−	0.0481857i
$733$	7.79669			0.287977			0.143989	−	0.989579i	$-0.454007\pi$
$733$	7.79669			0.287977			0.143989	+	0.989579i	$0.454007\pi$
$734$	5.23692	+	9.07062i	0.193298	+	0.334803i
$735$	13.3092	−	11.8343i	0.490917	−	0.436516i
$736$	3.81755	+	1.38947i	0.140717	+	0.0512167i
$737$	−12.3059	−	10.3259i	−0.453294	−	0.380359i
$738$	25.9453	+	19.3489i	0.955060	+	0.712244i
$739$	−40.5662	−	14.7649i	−1.49225	−	0.543136i	−0.538211	−	0.842810i	$-0.680900\pi$
$739$	−40.5662	−	14.7649i	−1.49225	−	0.543136i	−0.954042	+	0.299674i	$0.903122\pi$
$740$	8.89447	+	15.4057i	0.326967	+	0.566324i
$741$	−1.87988	−	15.9981i	−0.0690592	−	0.587705i
$742$	4.05877	−	7.03000i	0.149002	−	0.258079i
$743$	29.2193	−	24.5179i	1.07195	−	0.899475i	0.0767244	−	0.997052i	$-0.475554\pi$
$743$	29.2193	−	24.5179i	1.07195	−	0.899475i	0.995228	+	0.0975775i	$0.0311094\pi$
$744$	−6.39445	+	0.183414i	−0.234432	+	0.00672427i
$745$	−4.11370	+	23.3300i	−0.150714	+	0.854744i
$746$	−2.37445	+	1.99240i	−0.0869348	+	0.0729469i
$747$	−3.38958	+	6.73532i	−0.124018	+	0.246432i
$748$	−15.1368	+	26.2177i	−0.553456	+	0.958614i
$749$	8.15980	−	14.1332i	0.298153	−	0.516416i
$750$	−19.5465	−	6.48596i	−0.713736	−	0.236834i
$751$	1.96943	−	11.1692i	0.0718654	−	0.407569i	−0.927560	−	0.373674i	$-0.878098\pi$
$751$	1.96943	−	11.1692i	0.0718654	−	0.407569i	0.999425	−	0.0338946i	$-0.0107911\pi$
$752$	−9.04313			−0.329769
$753$	−3.74103	+	25.4663i	−0.136331	+	0.928045i
$754$	−18.3437	+	6.67655i	−0.668037	+	0.243146i
$755$	4.63598	−	3.89005i	0.168721	−	0.141574i
$756$	6.62896	−	3.08113i	0.241093	−	0.112060i
$757$	−6.12290	−	34.7247i	−0.222541	−	1.26209i	−0.867331	−	0.497731i	$-0.834167\pi$
$757$	−6.12290	−	34.7247i	−0.222541	−	1.26209i	0.644791	−	0.764359i	$-0.276945\pi$
$758$	−0.635225	−	3.60254i	−0.0230724	−	0.130850i
$759$	27.3549	−	10.8543i	0.992920	−	0.393987i
$760$	5.11266	−	7.31765i	0.185456	−	0.265439i
$761$	−7.92202	+	13.7213i	−0.287173	+	0.497398i	−0.973134	−	0.230240i	$-0.926049\pi$
$761$	−7.92202	+	13.7213i	−0.287173	+	0.497398i	0.685961	+	0.727638i	$0.259382\pi$
$762$	8.68668	+	14.0963i	0.314685	+	0.510655i
$763$	−10.2916	+	8.63571i	−0.372582	+	0.312634i
$764$	4.34843	+	3.64877i	0.157321	+	0.132008i
$765$	−35.6492	−	26.5857i	−1.28890	−	0.961208i
$766$	−3.65223	+	20.7128i	−0.131960	+	0.748385i
$767$	−23.0354			−0.831759
$768$	−1.60994	+	0.638818i	−0.0580938	+	0.0230514i
$769$	6.21036	−	35.2207i	0.223951	−	1.27009i	−0.640729	−	0.767767i	$-0.721368\pi$
$769$	6.21036	−	35.2207i	0.223951	−	1.27009i	0.864680	−	0.502323i	$-0.167521\pi$
$770$	2.09243	−	11.8668i	0.0754060	−	0.427649i
$771$	20.6897	−	8.20957i	0.745120	−	0.295661i
$772$	8.29854			0.298671
$773$	−3.58808	+	20.3490i	−0.129054	+	0.731903i	0.849763	+	0.527166i	$0.176745\pi$
$773$	−3.58808	+	20.3490i	−0.129054	+	0.731903i	−0.978817	+	0.204738i	$0.934366\pi$
$774$	−15.3394	−	11.4395i	−0.551363	−	0.411184i
$775$	2.28021	+	1.91332i	0.0819074	+	0.0687285i
$776$	−4.46477	+	3.74639i	−0.160276	+	0.134487i
$777$	11.1040	+	18.0190i	0.398353	+	0.646427i
$778$	3.70486	−	6.41700i	0.132826	−	0.230061i
$779$	46.8516	+	4.05043i	1.67863	+	0.145122i
$780$	−7.03456	+	2.79128i	−0.251878	+	0.0999440i
$781$	−3.65510	−	20.7291i	−0.130790	−	0.741746i
$782$	−5.10631	−	28.9593i	−0.182601	−	1.03558i
$783$	−38.9099	−	27.3170i	−1.39053	−	0.976230i
$784$	−3.84621	+	3.22735i	−0.137365	+	0.115263i
$785$	20.0361	−	7.29253i	0.715118	−	0.260282i
$786$	2.84571	−	19.3717i	0.101503	−	0.690964i
$787$	−38.2871			−1.36479			−0.682394	−	0.730985i	$-0.739061\pi$
$787$	−38.2871			−1.36479			−0.682394	+	0.730985i	$0.739061\pi$
$788$	−0.972287	+	5.51412i	−0.0346363	+	0.196432i
$789$	14.3073	+	4.74748i	0.509353	+	0.169015i
$790$	1.35686	−	2.35015i	0.0482748	−	0.0836145i
$791$	7.39743	−	12.8127i	0.263022	−	0.455568i
$792$	−5.64045	+	11.2079i	−0.200425	+	0.398257i
$793$	−1.85135	+	1.55347i	−0.0657435	+	0.0551654i
$794$	3.25775	−	18.4756i	0.115613	−	0.655675i
$795$	−20.4591	+	0.586834i	−0.725610	+	0.0208128i
$796$	15.1022	−	12.6722i	0.535283	−	0.449156i
$797$	12.8470	−	22.2516i	0.455063	−	0.788192i	−0.543629	−	0.839326i	$-0.682950\pi$
$797$	12.8470	−	22.2516i	0.455063	−	0.788192i	0.998692	+	0.0511334i	$0.0162834\pi$
$798$	5.83100	−	8.87749i	0.206415	−	0.314260i
$799$	32.7285	+	56.6875i	1.15785	+	2.00546i
$800$	0.757329	+	0.275645i	0.0267756	+	0.00974554i
$801$	−8.63310	−	6.43821i	−0.305036	−	0.227483i
$802$	17.2966	+	14.5136i	0.610763	+	0.512491i
$803$	24.8456	+	9.04304i	0.876780	+	0.319122i
$804$	−4.97152	+	4.42060i	−0.175332	+	0.155902i
$805$	5.85227	+	10.1364i	0.206265	+	0.357262i
$806$	7.88007			0.277564
$807$	31.9925	−	28.4472i	1.12619	−	1.00139i
$808$	−6.24149	−	5.23724i	−0.219575	−	0.184245i
$809$	21.3817	+	37.0341i	0.751739	+	1.30205i	0.946979	+	0.321294i	$0.104118\pi$
$809$	21.3817	+	37.0341i	0.751739	+	1.30205i	−0.195240	+	0.980755i	$0.562549\pi$
$810$	−15.3825	−	10.1537i	−0.540486	−	0.356765i
$811$	−2.67702	+	15.1821i	−0.0940027	+	0.533116i	0.901046	+	0.433724i	$0.142801\pi$
$811$	−2.67702	+	15.1821i	−0.0940027	+	0.533116i	−0.995048	+	0.0993917i	$0.968310\pi$
$812$	−12.0952	−	4.40231i	−0.424460	−	0.154491i
$813$	41.9593	+	13.9231i	1.47158	+	0.488303i
$814$	−34.1385	−	12.4254i	−1.19655	−	0.435510i
$815$	−29.0010	+	24.3347i	−1.01586	+	0.852407i
$816$	9.83111	+	7.78004i	0.344158	+	0.272356i
$817$	−27.6996	−	2.39470i	−0.969086	−	0.0837799i
$818$	−20.5783			−0.719504
$819$	−8.27117	+	3.55973i	−0.289018	+	0.124387i
$820$	−3.83665	−	21.7587i	−0.133982	−	0.759847i
$821$	−0.527969	+	2.99426i	−0.0184262	+	0.104500i	−0.992634	−	0.121153i	$-0.961341\pi$
$821$	−0.527969	+	2.99426i	−0.0184262	+	0.104500i	0.974208	+	0.225654i	$0.0724518\pi$
$822$	−8.14131	−	13.2113i	−0.283961	−	0.460797i
$823$	37.7857	+	31.7060i	1.31713	+	1.10520i	0.986906	+	0.161297i	$0.0515677\pi$
$823$	37.7857	+	31.7060i	1.31713	+	1.10520i	0.330221	+	0.943904i	$0.392877\pi$
$824$	1.68055	+	2.91080i	0.0585448	+	0.101403i
$825$	5.42669	−	2.15329i	0.188933	−	0.0749679i
$826$	−11.6353	−	9.76317i	−0.404844	−	0.339704i
$827$	18.9351	−	6.89180i	0.658437	−	0.239651i	0.00887563	−	0.999961i	$-0.497175\pi$
$827$	18.9351	−	6.89180i	0.658437	−	0.239651i	0.649561	+	0.760309i	$0.274953\pi$
$828$	−2.80086	−	11.8615i	−0.0973366	−	0.412214i
$829$	−24.6333	+	42.6661i	−0.855550	+	1.48186i	0.0205846	+	0.999788i	$0.493447\pi$
$829$	−24.6333	+	42.6661i	−0.855550	+	1.48186i	−0.876134	+	0.482067i	$0.839886\pi$
$830$	4.83684	−	1.76047i	0.167889	−	0.0611067i
$831$	−16.6718	+	0.478202i	−0.578339	+	0.0165886i
$832$	2.00491	−	0.729728i	0.0695077	−	0.0252987i
$833$	34.1509	+	12.4299i	1.18326	+	0.430671i
$834$	−22.0349	+	0.632033i	−0.763008	+	0.0218855i
$835$	23.9827	+	41.5393i	0.829957	+	1.43753i
$836$	1.60759	+	18.1597i	0.0555995	+	0.628065i
$837$	10.9881	+	15.7342i	0.379806	+	0.543853i
$838$	7.71646	+	2.80856i	0.266561	+	0.0970202i
$839$	−26.9085	+	22.5789i	−0.928985	+	0.779511i	−0.975635	−	0.219400i	$-0.929590\pi$
$839$	−26.9085	+	22.5789i	−0.928985	+	0.779511i	0.0466501	+	0.998911i	$0.485145\pi$
$840$	−4.73624	−	1.57159i	−0.163416	−	0.0542250i
$841$	9.50048	+	53.8799i	0.327603	+	1.85793i
$842$	−14.8054	−	12.4232i	−0.510229	−	0.428133i
$843$	−7.95360	+	3.15596i	−0.273937	+	0.108697i
$844$	−0.236150	+	0.409023i	−0.00812860	+	0.0140792i
$845$	−16.2573	+	5.91718i	−0.559269	+	0.203557i
$846$	14.8891	+	22.6786i	0.511898	+	0.779706i
$847$	4.56689	+	7.91009i	0.156920	+	0.271794i
$848$	5.77015			0.198148
$849$	−6.38664	−	2.11923i	−0.219189	−	0.0727319i
$850$	−1.01299	−	5.74498i	−0.0347454	−	0.197051i
$851$	33.1602	−	12.0693i	1.13672	−	0.413731i
$852$	−8.71335	+	0.249927i	−0.298514	+	0.00856235i
$853$	0.0839631	+	0.476178i	0.00287484	+	0.0163040i	0.986211	−	0.165490i	$-0.0529206\pi$
$853$	0.0839631	+	0.476178i	0.00287484	+	0.0163040i	−0.983337	+	0.181794i	$0.941810\pi$
$854$	−1.59354			−0.0545299
$855$	−26.7691	−	0.773505i	−0.915485	−	0.0264533i
$856$	11.6004			0.396493
$857$	4.63393	+	26.2803i	0.158292	+	0.897718i	0.955714	+	0.294297i	$0.0950853\pi$
$857$	4.63393	+	26.2803i	0.158292	+	0.897718i	−0.797422	+	0.603422i	$0.793804\pi$
$858$	7.34103	−	13.6013i	0.250619	−	0.464341i
$859$	−41.8616	+	15.2364i	−1.42830	+	0.519858i	−0.936443	−	0.350819i	$-0.885903\pi$
$859$	−41.8616	+	15.2364i	−1.42830	+	0.519858i	−0.491855	+	0.870677i	$0.663681\pi$
$860$	2.26830	+	12.8642i	0.0773485	+	0.438665i
$861$	−5.30531	−	25.7474i	−0.180804	−	0.877468i
$862$	13.2933			0.452770
$863$	1.78209	+	3.08667i	0.0606630	+	0.105071i	0.894762	−	0.446543i	$-0.147345\pi$
$863$	1.78209	+	3.08667i	0.0606630	+	0.105071i	−0.834099	+	0.551615i	$0.814012\pi$
$864$	4.25274	+	2.98567i	0.144681	+	0.101574i
$865$	0.567490	−	0.206549i	0.0192952	−	0.00702289i
$866$	5.03668	−	8.72379i	0.171153	−	0.296446i
$867$	8.90983	−	60.6520i	0.302594	−	2.05985i
$868$	3.98027	+	3.33984i	0.135099	+	0.113362i
$869$	0.962372	+	5.45789i	0.0326462	+	0.185146i
$870$	6.54965	+	31.7863i	0.222054	+	1.07766i
$871$	6.27765	−	5.26757i	0.212710	−	0.178485i
$872$	−8.97386	−	3.26622i	−0.303893	−	0.110608i
$873$	16.7463	+	5.02861i	0.566777	+	0.170193i
$874$	−12.5345	−	12.5087i	−0.423986	−	0.423115i
$875$	8.36367	+	14.4863i	0.282744	+	0.489726i
$876$	5.20066	−	9.63568i	0.175714	−	0.325559i
$877$	−6.40858	−	2.33253i	−0.216402	−	0.0787640i	0.231544	−	0.972824i	$-0.425622\pi$
$877$	−6.40858	−	2.33253i	−0.216402	−	0.0787640i	−0.447946	+	0.894060i	$0.647844\pi$
$878$	−20.0653	+	7.30318i	−0.677172	+	0.246470i
$879$	10.4761	+	17.0001i	0.353351	+	0.573400i
$880$	8.04877	−	2.92951i	0.271324	−	0.0987539i
$881$	7.74997	−	13.4233i	0.261103	−	0.452244i	−0.705432	−	0.708777i	$-0.749247\pi$
$881$	7.74997	−	13.4233i	0.261103	−	0.452244i	0.966535	+	0.256534i	$0.0825804\pi$
$882$	14.4262	+	4.33193i	0.485757	+	0.145864i
$883$	−14.3585	+	5.22606i	−0.483201	+	0.175871i	−0.572123	−	0.820168i	$-0.693880\pi$
$883$	−14.3585	+	5.22606i	−0.483201	+	0.175871i	0.0889220	+	0.996039i	$0.471658\pi$
$884$	−11.8304	−	9.92691i	−0.397901	−	0.333878i
$885$	−5.56612	+	37.8903i	−0.187103	+	1.27367i
$886$	−8.98548	−	15.5633i	−0.301873	−	0.522860i
$887$	−7.82826	−	6.56869i	−0.262847	−	0.220555i	0.501834	−	0.864964i	$-0.332659\pi$
$887$	−7.82826	−	6.56869i	−0.262847	−	0.220555i	−0.764681	+	0.644409i	$0.777103\pi$
$888$	−7.14585	+	13.2397i	−0.239799	+	0.444295i
$889$	2.33535	−	13.2444i	0.0783251	−	0.444204i
$890$	1.27661	+	7.24004i	0.0427922	+	0.242687i
$891$	37.3943	−	4.30809i	1.25276	−	0.144327i
$892$	7.80158			0.261216
$893$	35.7420	+	16.6221i	1.19606	+	0.556236i
$894$	−18.6232	+	7.38963i	−0.622854	+	0.247146i
$895$	20.6453	−	17.3234i	0.690095	−	0.579059i
$896$	1.32197	+	0.481159i	0.0441641	+	0.0160744i
$897$	3.02982	+	14.7041i	0.101163	+	0.490957i
$898$	−35.2526	−	12.8309i	−1.17639	−	0.428172i
$899$	5.86790	−	33.2785i	0.195706	−	1.10990i
$900$	−0.555637	−	2.35309i	−0.0185212	−	0.0784363i
$901$	−20.8831	−	36.1706i	−0.695717	−	1.20502i
$902$	34.5656	+	29.0040i	1.15091	+	0.965728i
$903$	3.13660	+	15.2224i	0.104380	+	0.506568i
$904$	10.5166			0.349775
$905$	−16.0290	−	27.7631i	−0.532823	−	0.922876i
$906$	4.85790	+	1.61196i	0.161393	+	0.0535539i
$907$	−1.10628	−	0.402651i	−0.0367333	−	0.0133698i	0.323588	−	0.946198i	$-0.395111\pi$
$907$	−1.10628	−	0.402651i	−0.0367333	−	0.0133698i	−0.360321	+	0.932828i	$0.617333\pi$
$908$	−15.5324	−	13.0332i	−0.515460	−	0.432522i
$909$	−2.85774	+	24.2754i	−0.0947853	+	0.805166i
$910$	5.77630	+	2.10240i	0.191483	+	0.0696939i
$911$	−4.02033	−	6.96341i	−0.133199	−	0.230708i	0.791709	−	0.610899i	$-0.209192\pi$
$911$	−4.02033	−	6.96341i	−0.133199	−	0.230708i	−0.924908	+	0.380191i	$0.875858\pi$
$912$	7.53733	+	0.434349i	0.249586	+	0.0143827i
$913$	−5.25599	+	9.10364i	−0.173948	+	0.301287i
$914$	23.4894	−	19.7099i	0.776959	−	0.651946i
$915$	2.10792	+	3.42062i	0.0696856	+	0.113082i
$916$	4.27581	−	24.2493i	0.141277	−	0.801221i
$917$	−12.1824	+	10.2223i	−0.402299	+	0.337569i
$918$	3.32452	−	37.4642i	0.109726	−	1.23650i
$919$	−18.9164	+	32.7642i	−0.623996	+	1.08079i	0.364738	+	0.931110i	$0.381158\pi$
$919$	−18.9164	+	32.7642i	−0.623996	+	1.08079i	−0.988734	+	0.149683i	$0.952175\pi$
$920$	−4.15994	+	7.20522i	−0.137149	+	0.237549i
$921$	−4.85215	+	4.31445i	−0.159884	+	0.142166i
$922$	−4.29115	+	24.3363i	−0.141322	+	0.801474i
$923$	10.7377			0.353436
$924$	9.47270	−	3.75873i	0.311629	−	0.123653i
$925$	6.57835	−	2.39432i	0.216295	−	0.0787249i
$926$	8.09081	−	6.78900i	0.265881	−	0.223100i
$927$	4.53283	−	9.00703i	0.148878	−	0.295830i
$928$	−1.58877	−	9.01038i	−0.0521540	−	0.295780i
$929$	8.98778	+	50.9723i	0.294880	+	1.67235i	0.667691	+	0.744438i	$0.267283\pi$
$929$	8.98778	+	50.9723i	0.294880	+	1.67235i	−0.372812	+	0.927907i	$0.621606\pi$
$930$	1.90409	−	12.9617i	0.0624376	−	0.425032i
$931$	21.1339	−	5.68611i	0.692635	−	0.186355i
$932$	−11.9790	+	20.7483i	−0.392386	+	0.679633i
$933$	−4.15557	+	7.69937i	−0.136047	+	0.252066i
$934$	−4.68144	+	3.92819i	−0.153181	+	0.128534i
$935$	−47.4937	−	39.8519i	−1.55321	−	1.30330i
$936$	−5.13102	−	3.82650i	−0.167713	−	0.125073i
$937$	−3.02674	+	17.1655i	−0.0988794	+	0.560773i	0.894610	+	0.446848i	$0.147453\pi$
$937$	−3.02674	+	17.1655i	−0.0988794	+	0.560773i	−0.993489	+	0.113925i	$0.963658\pi$
$938$	5.40345			0.176429
$939$	7.06637	−	48.1030i	0.230602	−	1.56978i
$940$	3.21593	−	18.2385i	0.104892	−	0.594873i
$941$	4.38861	−	24.8890i	0.143065	−	0.811359i	−0.825836	−	0.563910i	$-0.809296\pi$
$941$	4.38861	−	24.8890i	0.143065	−	0.811359i	0.968901	−	0.247449i	$-0.0795924\pi$
$942$	14.1408	+	11.1906i	0.460732	+	0.364609i
$943$	−43.8292			−1.42727
$944$	1.87481	−	10.6326i	0.0610198	−	0.346060i
$945$	3.85672	+	14.4652i	0.125459	+	0.470553i
$946$	−20.4359	−	17.1477i	−0.664428	−	0.557521i
$947$	−25.0112	+	20.9869i	−0.812754	+	0.681982i	−0.951264	−	0.308379i	$-0.900213\pi$
$947$	−25.0112	+	20.9869i	−0.812754	+	0.681982i	0.138509	+	0.990361i	$0.455769\pi$
$948$	2.29419	−	0.0658047i	0.0745117	−	0.00213724i
$949$	−6.74397	+	11.6809i	−0.218919	+	0.379178i
$950$	−2.48661	−	2.48150i	−0.0806761	−	0.0805104i
$951$	−25.9056	−	20.5009i	−0.840046	−	0.664787i
$952$	−1.76826	−	10.0283i	−0.0573095	−	0.325018i
$953$	−8.23069	−	46.6786i	−0.266618	−	1.51207i	−0.764387	−	0.644758i	$-0.776958\pi$
$953$	−8.23069	−	46.6786i	−0.266618	−	1.51207i	0.497769	−	0.867310i	$-0.334153\pi$
$954$	−9.50029	−	14.4705i	−0.307583	−	0.468501i
$955$	−8.90534	+	7.47247i	−0.288170	+	0.241803i
$956$	16.4327	−	5.98100i	0.531470	−	0.193439i
$957$	−51.9736	−	41.1303i	−1.68007	−	1.32955i
$958$	37.3089			1.20539
$959$	−2.18873	+	12.4129i	−0.0706778	+	0.400834i
$960$	−0.715858	−	3.47415i	−0.0231042	−	0.112128i
$961$	8.67956	−	15.0334i	0.279986	−	0.484950i
$962$	9.26641	−	16.0499i	0.298761	−	0.517469i
$963$	−19.0995	−	29.0917i	−0.615473	−	0.937468i
$964$	10.5964	−	8.89145i	0.341288	−	0.286374i
$965$	−2.95114	+	16.7367i	−0.0950006	+	0.538775i
$966$	−4.70173	+	8.71128i	−0.151276	+	0.280281i
$967$	−8.03082	+	6.73866i	−0.258254	+	0.216701i	−0.762717	−	0.646733i	$-0.776135\pi$
$967$	−8.03082	+	6.73866i	−0.258254	+	0.216701i	0.504463	+	0.863433i	$0.331691\pi$
$968$	−3.24626	+	5.62269i	−0.104339	+	0.180720i
$969$	−24.5561	−	48.8202i	−0.788854	−	1.56833i
$970$	−5.96805	−	10.3370i	−0.191623	−	0.331900i
$971$	−4.83606	−	1.76018i	−0.155196	−	0.0564869i	0.263254	−	0.964727i	$-0.415204\pi$
$971$	−4.83606	−	1.76018i	−0.155196	−	0.0564869i	−0.418450	+	0.908240i	$0.637427\pi$
$972$	0.485597	−	15.5809i	0.0155755	−	0.499757i
$973$	13.7158	+	11.5089i	0.439708	+	0.368959i
$974$	38.3286	+	13.9505i	1.22813	+	0.447002i
$975$	0.601059	+	2.91702i	0.0192493	+	0.0934194i
$976$	−0.566365	−	0.980973i	−0.0181289	−	0.0314002i
$977$	−33.4995			−1.07174			−0.535872	−	0.844300i	$-0.680017\pi$
$977$	−33.4995			−1.07174			−0.535872	+	0.844300i	$0.680017\pi$
$978$	−30.3892	−	10.0838i	−0.971739	−	0.322445i
$979$	−11.5014	−	9.65085i	−0.367588	−	0.308443i
$980$	−5.14122	−	8.90486i	−0.164230	−	0.284455i
$981$	6.58394	+	27.8825i	0.210209	+	0.890221i
$982$	4.62350	−	26.2212i	0.147542	−	0.836751i
$983$	−26.9278	−	9.80093i	−0.858865	−	0.312601i	−0.125215	−	0.992130i	$-0.539962\pi$
$983$	−26.9278	−	9.80093i	−0.858865	−	0.312601i	−0.733649	+	0.679528i	$0.762184\pi$
$984$	13.9643	−	12.4168i	0.445166	−	0.395835i
$985$	−10.7753	−	3.92188i	−0.343328	−	0.124961i
$986$	−50.7321	+	42.5693i	−1.61564	+	1.35568i
$987$	3.20262	−	21.8012i	0.101940	−	0.693940i
$988$	−9.26550	−	0.801026i	−0.294775	−	0.0254840i
$989$	25.9127			0.823975
$990$	−20.5986	−	15.3616i	−0.654668	−	0.488224i
$991$	3.00174	+	17.0237i	0.0953535	+	0.540777i	0.994638	+	0.103413i	$0.0329765\pi$
$991$	3.00174	+	17.0237i	0.0953535	+	0.540777i	−0.899285	+	0.437363i	$0.855912\pi$
$992$	−0.641345	+	3.63725i	−0.0203627	+	0.115483i
$993$	−18.9036	+	0.542217i	−0.599888	+	0.0172067i
$994$	5.42368	+	4.55101i	0.172029	+	0.144349i
$995$	20.1871	+	34.9651i	0.639974	+	1.10847i
$996$	3.41368	+	2.70149i	0.108167	+	0.0855998i
$997$	20.7307	+	17.3951i	0.656547	+	0.550909i	0.909050	−	0.416688i	$-0.136809\pi$
$997$	20.7307	+	17.3951i	0.656547	+	0.550909i	−0.252502	+	0.967596i	$0.581254\pi$
$998$	25.7408	−	9.36890i	0.814812	−	0.296567i
$999$	44.9682	−	3.87801i	1.42273	−	0.122695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.w.b.175.5	yes	66
9.7	even	3		342.2.v.b.61.6	✓	66
19.5	even	9		342.2.v.b.157.6	yes	66
171.43	even	9	inner	342.2.w.b.43.5	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.v.b.61.6	✓	66	9.7	even	3
342.2.v.b.157.6	yes	66	19.5	even	9
342.2.w.b.43.5	yes	66	171.43	even	9	inner
342.2.w.b.175.5	yes	66	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.908677 - 1.47455i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.355621 - 2.01683i) q^{5} +(1.29436 - 1.15093i) q^{6} -1.40682 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.34861 + 2.67978i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-0.908677 - 1.47455i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.355621 - 2.01683i) q^{5} +(1.29436 - 1.15093i) q^{6} -1.40682 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.34861 + 2.67978i) q^{9} +(1.92444 - 0.700437i) q^{10} +(-2.09120 + 3.62207i) q^{11} +(1.35820 + 1.07484i) q^{12} +(-1.63442 - 1.37144i) q^{13} +(-0.244291 - 1.38544i) q^{14} +(-2.65078 + 2.35703i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-6.80180 - 2.47565i) q^{17} +(-2.87326 - 0.862786i) q^{18} +(-4.20921 + 1.13250i) q^{19} +(1.02397 + 1.77357i) q^{20} +(1.27834 + 2.07442i) q^{21} +(-3.93018 - 1.43047i) q^{22} +(3.81755 - 1.38947i) q^{23} +(-0.822662 + 1.52421i) q^{24} +(0.757329 - 0.275645i) q^{25} +(1.06679 - 1.84773i) q^{26} +(5.17694 - 0.446454i) q^{27} +(1.32197 - 0.481159i) q^{28} +(-7.00883 - 5.88111i) q^{29} +(-2.78152 - 2.20121i) q^{30} +(1.84668 + 3.19854i) q^{31} +(0.766044 + 0.642788i) q^{32} +(7.24116 - 0.207700i) q^{33} +(1.25692 - 7.12835i) q^{34} +(0.500294 + 2.83731i) q^{35} +(0.350743 - 2.97943i) q^{36} +8.68625 q^{37} +(-1.84621 - 3.94861i) q^{38} +(-0.537103 + 3.65623i) q^{39} +(-1.56881 + 1.31639i) q^{40} +(-10.1379 - 3.68991i) q^{41} +(-1.82093 + 1.61914i) q^{42} +(5.99376 + 2.18155i) q^{43} +(0.726267 - 4.11887i) q^{44} +(5.88426 + 1.76694i) q^{45} +(2.03128 + 3.51827i) q^{46} +(-6.92744 - 5.81281i) q^{47} +(-1.64391 - 0.545487i) q^{48} -5.02087 q^{49} +(0.402967 + 0.697959i) q^{50} +(2.53015 + 12.2792i) q^{51} +(2.00491 + 0.729728i) q^{52} +(4.42019 + 3.70898i) q^{53} +(1.33864 + 5.02076i) q^{54} +(8.04877 + 2.92951i) q^{55} +(0.703408 + 1.21834i) q^{56} +(5.49474 + 5.17763i) q^{57} +(4.57469 - 7.92359i) q^{58} +(8.27066 - 6.93991i) q^{59} +(1.68476 - 3.12150i) q^{60} +(0.196697 - 1.11552i) q^{61} +(-2.82928 + 2.37404i) q^{62} +(1.89725 - 3.76996i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.18472 + 3.78405i) q^{65} +(1.46196 + 7.09509i) q^{66} +(-0.666967 + 3.78256i) q^{67} +7.23832 q^{68} +(-5.51777 - 4.36660i) q^{69} +(-2.70733 + 0.985387i) q^{70} +(-3.85529 + 3.23497i) q^{71} +(2.99507 - 0.171958i) q^{72} +(-1.09776 - 6.22570i) q^{73} +(1.50835 + 8.55429i) q^{74} +(-1.09462 - 0.866250i) q^{75} +(3.56803 - 2.50383i) q^{76} +(2.94194 - 5.09559i) q^{77} +(-3.69395 + 0.105954i) q^{78} +(1.01508 - 0.851754i) q^{79} +(-1.56881 - 1.31639i) q^{80} +(-5.36248 - 7.22799i) q^{81} +(1.87342 - 10.6247i) q^{82} +2.51338 q^{83} +(-1.91074 - 1.51210i) q^{84} +(-2.57410 + 14.5985i) q^{85} +(-1.10760 + 6.28152i) q^{86} +(-2.30324 + 15.6789i) q^{87} +4.18241 q^{88} +(-0.623365 + 3.53528i) q^{89} +(-0.718300 + 6.10169i) q^{90} +(2.29932 + 1.92936i) q^{91} +(-3.11210 + 2.61136i) q^{92} +(3.03839 - 5.62946i) q^{93} +(4.52157 - 7.83158i) q^{94} +(3.78094 + 8.08652i) q^{95} +(0.251738 - 1.71366i) q^{96} +(-1.01208 - 5.73980i) q^{97} +(-0.871865 - 4.94459i) q^{98} +(-6.88614 - 10.4887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 3 q^{3} - 3 q^{6} + 24 q^{7} - 33 q^{8} - 3 q^{9}+O(q^{10}) \) 66 * q - 3 * q^3 - 3 * q^6 + 24 * q^7 - 33 * q^8 - 3 * q^9	\( 66 q - 3 q^{3} - 3 q^{6} + 24 q^{7} - 33 q^{8} - 3 q^{9} - 3 q^{13} - 3 q^{14} - 30 q^{15} + 9 q^{17} + 6 q^{18} - 21 q^{19} + 6 q^{22} - 12 q^{23} + 6 q^{24} + 6 q^{25} + 30 q^{27} - 3 q^{28} + 9 q^{29} + 18 q^{33} - 18 q^{34} - 18 q^{35} - 3 q^{36} + 6 q^{37} + 6 q^{38} + 12 q^{39} + 6 q^{41} + 6 q^{43} - 12 q^{44} - 18 q^{45} - 18 q^{47} - 3 q^{48} + 114 q^{49} - 63 q^{50} - 63 q^{51} - 3 q^{52} - 24 q^{53} + 18 q^{54} + 36 q^{55} - 12 q^{56} - 60 q^{57} - 18 q^{58} + 78 q^{59} - 3 q^{60} - 21 q^{62} - 27 q^{63} - 33 q^{64} - 12 q^{65} + 45 q^{66} - 3 q^{67} + 12 q^{68} - 24 q^{69} - 18 q^{70} - 24 q^{71} - 3 q^{72} - 15 q^{73} - 3 q^{74} + 15 q^{78} + 12 q^{79} - 87 q^{81} + 6 q^{82} - 24 q^{83} - 15 q^{84} + 72 q^{85} - 3 q^{86} + 66 q^{87} + 9 q^{89} - 6 q^{90} + 27 q^{91} + 6 q^{92} - 45 q^{93} - 6 q^{94} - 30 q^{95} + 87 q^{97} + 24 q^{98} - 96 q^{99}+O(q^{100}) \) 66 * q - 3 * q^3 - 3 * q^6 + 24 * q^7 - 33 * q^8 - 3 * q^9 - 3 * q^13 - 3 * q^14 - 30 * q^15 + 9 * q^17 + 6 * q^18 - 21 * q^19 + 6 * q^22 - 12 * q^23 + 6 * q^24 + 6 * q^25 + 30 * q^27 - 3 * q^28 + 9 * q^29 + 18 * q^33 - 18 * q^34 - 18 * q^35 - 3 * q^36 + 6 * q^37 + 6 * q^38 + 12 * q^39 + 6 * q^41 + 6 * q^43 - 12 * q^44 - 18 * q^45 - 18 * q^47 - 3 * q^48 + 114 * q^49 - 63 * q^50 - 63 * q^51 - 3 * q^52 - 24 * q^53 + 18 * q^54 + 36 * q^55 - 12 * q^56 - 60 * q^57 - 18 * q^58 + 78 * q^59 - 3 * q^60 - 21 * q^62 - 27 * q^63 - 33 * q^64 - 12 * q^65 + 45 * q^66 - 3 * q^67 + 12 * q^68 - 24 * q^69 - 18 * q^70 - 24 * q^71 - 3 * q^72 - 15 * q^73 - 3 * q^74 + 15 * q^78 + 12 * q^79 - 87 * q^81 + 6 * q^82 - 24 * q^83 - 15 * q^84 + 72 * q^85 - 3 * q^86 + 66 * q^87 + 9 * q^89 - 6 * q^90 + 27 * q^91 + 6 * q^92 - 45 * q^93 - 6 * q^94 - 30 * q^95 + 87 * q^97 + 24 * q^98 - 96 * q^99

Introduction

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