LMFDB - Embedded newform 342.2.x.a.281.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			281.2
Root			$0.500000 - 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	342.281
Dual form			342.2.x.a.185.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(1.68842 + 0.386327i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.944822 + 2.59588i) q^{5} +(-1.54173 + 0.789350i) q^{6} +(-1.67878 - 2.90773i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.70150 + 1.30456i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(1.68842 + 0.386327i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.944822 + 2.59588i) q^{5} +(-1.54173 + 0.789350i) q^{6} +(-1.67878 - 2.90773i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.70150 + 1.30456i) q^{9} +(-0.944822 - 2.59588i) q^{10} +6.01766i q^{11} +(0.673648 - 1.59568i) q^{12} +(1.37321 + 3.77286i) q^{13} +(3.15507 + 1.14835i) q^{14} +(-2.59811 + 4.01791i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.08905 - 2.99214i) q^{17} +(-2.90803 + 0.737141i) q^{18} +(-1.90379 + 3.92117i) q^{19} +(2.39237 + 1.38124i) q^{20} +(-1.71114 - 5.55801i) q^{21} +(-3.86808 - 4.60980i) q^{22} +(1.67285 + 0.294969i) q^{23} +(0.509640 + 1.65538i) q^{24} +(-2.01566 - 1.69134i) q^{25} +(-3.47709 - 2.00750i) q^{26} +(4.05728 + 3.24631i) q^{27} +(-3.15507 + 1.14835i) q^{28} +(1.20810 - 6.85149i) q^{29} +(-0.592396 - 4.74793i) q^{30} +1.49449i q^{31} +(0.939693 - 0.342020i) q^{32} +(-2.32479 + 10.1603i) q^{33} +(1.08905 + 2.99214i) q^{34} +(9.13425 - 1.61061i) q^{35} +(1.75385 - 2.43393i) q^{36} -9.47475i q^{37} +(-1.06209 - 4.22752i) q^{38} +(0.860992 + 6.90067i) q^{39} +(-2.72051 + 0.479699i) q^{40} +(-4.60084 + 3.86056i) q^{41} +(4.88343 + 3.15778i) q^{42} +(-0.275475 - 1.56230i) q^{43} +(5.92624 + 1.04496i) q^{44} +(-5.93892 + 5.78019i) q^{45} +(-1.47108 + 0.849329i) q^{46} +(-1.70951 - 0.301432i) q^{47} +(-1.45446 - 0.940501i) q^{48} +(-2.13659 + 3.70068i) q^{49} +2.63126 q^{50} +(2.99471 - 4.63124i) q^{51} +(3.95400 - 0.697197i) q^{52} +(1.37731 + 1.15570i) q^{53} +(-5.19474 + 0.121152i) q^{54} +(-15.6211 - 5.68562i) q^{55} +(1.67878 - 2.90773i) q^{56} +(-4.72925 + 5.88508i) q^{57} +(3.47859 + 6.02510i) q^{58} +(0.982040 + 5.56942i) q^{59} +(3.50571 + 3.25634i) q^{60} +(12.3749 - 4.50411i) q^{61} +(-0.960637 - 1.14484i) q^{62} +(-0.741913 - 10.0453i) q^{63} +(-0.500000 + 0.866025i) q^{64} -11.0913 q^{65} +(-4.75004 - 9.27760i) q^{66} +(6.43126 - 7.66447i) q^{67} +(-2.75757 - 1.59208i) q^{68} +(2.71052 + 1.14430i) q^{69} +(-5.96196 + 7.10518i) q^{70} +(-6.75349 + 5.66685i) q^{71} +(0.220968 + 2.99185i) q^{72} +(-1.28887 - 7.30952i) q^{73} +(6.09025 + 7.25808i) q^{74} +(-2.74987 - 3.63440i) q^{75} +(3.53101 + 2.55577i) q^{76} +(17.4977 - 10.1023i) q^{77} +(-5.09522 - 4.73279i) q^{78} +(2.75141 - 7.55942i) q^{79} +(1.77568 - 2.11618i) q^{80} +(5.59624 + 7.04855i) q^{81} +(1.04293 - 5.91472i) q^{82} +(1.22480 - 0.707141i) q^{83} +(-5.77071 + 0.720008i) q^{84} +(6.73826 + 5.65407i) q^{85} +(1.21525 + 1.01972i) q^{86} +(4.68670 - 11.1015i) q^{87} +(-5.21145 + 3.00883i) q^{88} +(2.88817 - 16.3796i) q^{89} +(0.834042 - 8.24535i) q^{90} +(8.66514 - 10.3267i) q^{91} +(0.580975 - 1.59622i) q^{92} +(-0.577360 + 2.52332i) q^{93} +(1.50332 - 0.867940i) q^{94} +(-8.38013 - 8.64682i) q^{95} +(1.71872 - 0.214444i) q^{96} +(6.43776 + 7.67222i) q^{97} +(-0.742029 - 4.20825i) q^{98} +(-7.85041 + 16.2567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 9 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^3 + 9 * q^5 + 3 * q^6 - 9 * q^7 + 6 * q^8	$ 12 q + 6 q^{3} + 9 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{10} + 6 q^{12} - 12 q^{13} + 3 q^{14} + 9 q^{15} - 9 q^{18} + 15 q^{19} + 9 q^{20} + 15 q^{21} - 27 q^{22} + 18 q^{23} + 3 q^{24} + 9 q^{25} - 18 q^{26} + 9 q^{27} - 3 q^{28} - 45 q^{29} - 9 q^{33} + 18 q^{35} + 9 q^{36} - 9 q^{38} - 36 q^{41} + 3 q^{42} + 12 q^{43} + 18 q^{44} - 18 q^{45} - 27 q^{46} + 27 q^{47} + 6 q^{48} + 3 q^{49} - 6 q^{50} + 36 q^{51} - 15 q^{52} - 27 q^{54} - 9 q^{55} + 9 q^{56} - 42 q^{57} + 9 q^{58} - 36 q^{59} + 9 q^{60} - 3 q^{61} + 6 q^{62} - 9 q^{63} - 6 q^{64} - 54 q^{65} + 30 q^{67} - 27 q^{68} + 9 q^{69} - 9 q^{71} + 9 q^{72} - 24 q^{73} + 21 q^{74} - 24 q^{75} + 27 q^{77} - 54 q^{78} + 6 q^{79} + 9 q^{80} + 36 q^{81} + 45 q^{83} - 12 q^{84} - 18 q^{85} + 33 q^{86} - 36 q^{87} - 9 q^{88} - 9 q^{89} - 18 q^{90} + 6 q^{91} + 18 q^{92} + 9 q^{93} + 36 q^{94} + 3 q^{96} + 45 q^{97} + 6 q^{98} - 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 9 * q^5 + 3 * q^6 - 9 * q^7 + 6 * q^8 + 9 * q^10 + 6 * q^12 - 12 * q^13 + 3 * q^14 + 9 * q^15 - 9 * q^18 + 15 * q^19 + 9 * q^20 + 15 * q^21 - 27 * q^22 + 18 * q^23 + 3 * q^24 + 9 * q^25 - 18 * q^26 + 9 * q^27 - 3 * q^28 - 45 * q^29 - 9 * q^33 + 18 * q^35 + 9 * q^36 - 9 * q^38 - 36 * q^41 + 3 * q^42 + 12 * q^43 + 18 * q^44 - 18 * q^45 - 27 * q^46 + 27 * q^47 + 6 * q^48 + 3 * q^49 - 6 * q^50 + 36 * q^51 - 15 * q^52 - 27 * q^54 - 9 * q^55 + 9 * q^56 - 42 * q^57 + 9 * q^58 - 36 * q^59 + 9 * q^60 - 3 * q^61 + 6 * q^62 - 9 * q^63 - 6 * q^64 - 54 * q^65 + 30 * q^67 - 27 * q^68 + 9 * q^69 - 9 * q^71 + 9 * q^72 - 24 * q^73 + 21 * q^74 - 24 * q^75 + 27 * q^77 - 54 * q^78 + 6 * q^79 + 9 * q^80 + 36 * q^81 + 45 * q^83 - 12 * q^84 - 18 * q^85 + 33 * q^86 - 36 * q^87 - 9 * q^88 - 9 * q^89 - 18 * q^90 + 6 * q^91 + 18 * q^92 + 9 * q^93 + 36 * q^94 + 3 * q^96 + 45 * q^97 + 6 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	1.68842	+	0.386327i	0.974808	+	0.223046i
$3$	1.68842	+	0.386327i	0.974808	+	0.223046i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.944822	+	2.59588i	−0.422537	+	1.16091i	0.527713	+	0.849423i	$0.323050\pi$
$5$	−0.944822	+	2.59588i	−0.422537	+	1.16091i	−0.950250	+	0.311488i	$0.899173\pi$
$6$	−1.54173	+	0.789350i	−0.629408	+	0.322251i
$7$	−1.67878	−	2.90773i	−0.634518	−	1.09902i	−0.986617	−	0.163055i	$-0.947865\pi$
$7$	−1.67878	−	2.90773i	−0.634518	−	1.09902i	0.352099	−	0.935963i	$-0.385468\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.70150	+	1.30456i	0.900501	+	0.434854i
$10$	−0.944822	−	2.59588i	−0.298779	−	0.820888i
$11$			6.01766i			1.81439i	0.420706	+	0.907197i	$0.361782\pi$
$11$			6.01766i			1.81439i	−0.420706	+	0.907197i	$0.638218\pi$
$12$	0.673648	−	1.59568i	0.194465	−	0.460633i
$13$	1.37321	+	3.77286i	0.380860	+	1.04640i	0.970995	+	0.239099i	$0.0768521\pi$
$13$	1.37321	+	3.77286i	0.380860	+	1.04640i	−0.590135	+	0.807304i	$0.700926\pi$
$14$	3.15507	+	1.14835i	0.843228	+	0.306910i
$15$	−2.59811	+	4.01791i	−0.670829	+	1.03742i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.08905	−	2.99214i	0.264133	−	0.725700i	−0.734745	−	0.678343i	$-0.762698\pi$
$17$	1.08905	−	2.99214i	0.264133	−	0.725700i	0.998878	−	0.0473562i	$-0.0150796\pi$
$18$	−2.90803	+	0.737141i	−0.685429	+	0.173746i
$19$	−1.90379	+	3.92117i	−0.436760	+	0.899578i
$19$	−1.90379	+	3.92117i	−0.436760	+	0.899578i
$20$	2.39237	+	1.38124i	0.534951	+	0.308854i
$21$	−1.71114	−	5.55801i	−0.373402	−	1.21286i
$22$	−3.86808	−	4.60980i	−0.824677	−	0.982812i
$23$	1.67285	+	0.294969i	0.348814	+	0.0615053i	0.345310	−	0.938489i	$-0.387774\pi$
$23$	1.67285	+	0.294969i	0.348814	+	0.0615053i	0.00350348	+	0.999994i	$0.498885\pi$
$24$	0.509640	+	1.65538i	0.104030	+	0.337902i
$25$	−2.01566	−	1.69134i	−0.403133	−	0.338269i
$26$	−3.47709	−	2.00750i	−0.681913	−	0.393703i
$27$	4.05728	+	3.24631i	0.780823	+	0.624752i
$28$	−3.15507	+	1.14835i	−0.596252	+	0.217018i
$29$	1.20810	−	6.85149i	0.224339	−	1.27229i	−0.639606	−	0.768703i	$-0.720902\pi$
$29$	1.20810	−	6.85149i	0.224339	−	1.27229i	0.863945	−	0.503587i	$-0.167987\pi$
$30$	−0.592396	−	4.74793i	−0.108156	−	0.866850i
$31$			1.49449i			0.268418i	0.990953	+	0.134209i	$0.0428493\pi$
$31$			1.49449i			0.268418i	−0.990953	+	0.134209i	$0.957151\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−2.32479	+	10.1603i	−0.404693	+	1.76869i
$34$	1.08905	+	2.99214i	0.186770	+	0.513147i
$35$	9.13425	−	1.61061i	1.54397	−	0.272243i
$36$	1.75385	−	2.43393i	0.292309	−	0.405654i
$37$		−	9.47475i		−	1.55764i	−0.627248	−	0.778820i	$-0.715819\pi$
$37$		−	9.47475i		−	1.55764i	0.627248	−	0.778820i	$-0.284181\pi$
$38$	−1.06209	−	4.22752i	−0.172294	−	0.685795i
$39$	0.860992	+	6.90067i	0.137869	+	1.10499i
$40$	−2.72051	+	0.479699i	−0.430150	+	0.0758470i
$41$	−4.60084	+	3.86056i	−0.718530	+	0.602919i	−0.926978	−	0.375115i	$-0.877603\pi$
$41$	−4.60084	+	3.86056i	−0.718530	+	0.602919i	0.208448	+	0.978033i	$0.433159\pi$
$42$	4.88343	+	3.15778i	0.753530	+	0.487257i
$43$	−0.275475	−	1.56230i	−0.0420096	−	0.238248i	0.956572	−	0.291497i	$-0.0941534\pi$
$43$	−0.275475	−	1.56230i	−0.0420096	−	0.238248i	−0.998581	+	0.0532491i	$0.983042\pi$
$44$	5.92624	+	1.04496i	0.893415	+	0.157533i
$45$	−5.93892	+	5.78019i	−0.885322	+	0.861660i
$46$	−1.47108	+	0.849329i	−0.216899	+	0.125227i
$47$	−1.70951	−	0.301432i	−0.249357	−	0.0439684i	0.0475722	−	0.998868i	$-0.484852\pi$
$47$	−1.70951	−	0.301432i	−0.249357	−	0.0439684i	−0.296930	+	0.954899i	$0.595963\pi$
$48$	−1.45446	−	0.940501i	−0.209933	−	0.135750i
$49$	−2.13659	+	3.70068i	−0.305227	+	0.528668i
$50$	2.63126			0.372117
$51$	2.99471	−	4.63124i	0.419343	−	0.648504i
$52$	3.95400	−	0.697197i	0.548321	−	0.0966838i
$53$	1.37731	+	1.15570i	0.189187	+	0.158747i	0.732462	−	0.680808i	$-0.238371\pi$
$53$	1.37731	+	1.15570i	0.189187	+	0.158747i	−0.543274	+	0.839555i	$0.682816\pi$
$54$	−5.19474	+	0.121152i	−0.706915	+	0.0164867i
$55$	−15.6211	−	5.68562i	−2.10635	−	0.766649i
$56$	1.67878	−	2.90773i	0.224336	−	0.388561i
$57$	−4.72925	+	5.88508i	−0.626404	+	0.779498i
$58$	3.47859	+	6.02510i	0.456762	+	0.791134i
$59$	0.982040	+	5.56942i	0.127851	+	0.725077i	0.979574	+	0.201085i	$0.0644468\pi$
$59$	0.982040	+	5.56942i	0.127851	+	0.725077i	−0.851723	+	0.523992i	$0.824442\pi$
$60$	3.50571	+	3.25634i	0.452586	+	0.420392i
$61$	12.3749	−	4.50411i	1.58445	−	0.576692i	0.608282	−	0.793721i	$-0.291859\pi$
$61$	12.3749	−	4.50411i	1.58445	−	0.576692i	0.976165	+	0.217029i	$0.0696368\pi$
$62$	−0.960637	−	1.14484i	−0.122001	−	0.145395i
$63$	−0.741913	−	10.0453i	−0.0934722	−	1.26559i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−11.0913			−1.37571
$66$	−4.75004	−	9.27760i	−0.584690	−	1.14199i
$67$	6.43126	−	7.66447i	0.785703	−	0.936364i	−0.213473	−	0.976949i	$-0.568478\pi$
$67$	6.43126	−	7.66447i	0.785703	−	0.936364i	0.999176	+	0.0405846i	$0.0129220\pi$
$68$	−2.75757	−	1.59208i	−0.334404	−	0.193068i
$69$	2.71052	+	1.14430i	0.326308	+	0.137757i
$70$	−5.96196	+	7.10518i	−0.712590	+	0.849232i
$71$	−6.75349	+	5.66685i	−0.801492	+	0.672531i	−0.948561	−	0.316595i	$-0.897460\pi$
$71$	−6.75349	+	5.66685i	−0.801492	+	0.672531i	0.147069	+	0.989126i	$0.453016\pi$
$72$	0.220968	+	2.99185i	0.0260413	+	0.352593i
$73$	−1.28887	−	7.30952i	−0.150850	−	0.855515i	−0.962482	−	0.271346i	$-0.912531\pi$
$73$	−1.28887	−	7.30952i	−0.150850	−	0.855515i	0.811632	−	0.584170i	$-0.198580\pi$
$74$	6.09025	+	7.25808i	0.707977	+	0.843735i
$75$	−2.74987	−	3.63440i	−0.317528	−	0.419664i
$76$	3.53101	+	2.55577i	0.405034	+	0.293167i
$77$	17.4977	−	10.1023i	1.99405	−	1.15127i
$78$	−5.09522	−	4.73279i	−0.576921	−	0.535882i
$79$	2.75141	−	7.55942i	0.309557	−	0.850502i	−0.683185	−	0.730245i	$-0.739406\pi$
$79$	2.75141	−	7.55942i	0.309557	−	0.850502i	0.992743	−	0.120257i	$-0.0383718\pi$
$80$	1.77568	−	2.11618i	0.198528	−	0.236596i
$81$	5.59624	+	7.04855i	0.621804	+	0.783173i
$82$	1.04293	−	5.91472i	0.115172	−	0.653172i
$83$	1.22480	−	0.707141i	0.134440	−	0.0776188i	−0.431272	−	0.902222i	$-0.641935\pi$
$83$	1.22480	−	0.707141i	0.134440	−	0.0776188i	0.565711	+	0.824603i	$0.308602\pi$
$84$	−5.77071	+	0.720008i	−0.629636	+	0.0785593i
$85$	6.73826	+	5.65407i	0.730867	+	0.613270i
$86$	1.21525	+	1.01972i	0.131044	+	0.109959i
$87$	4.68670	−	11.1015i	0.502467	−	1.19020i
$88$	−5.21145	+	3.00883i	−0.555542	+	0.320743i
$89$	2.88817	−	16.3796i	0.306145	−	1.73624i	−0.311918	−	0.950109i	$-0.600972\pi$
$89$	2.88817	−	16.3796i	0.306145	−	1.73624i	0.618064	−	0.786128i	$-0.287917\pi$
$90$	0.834042	−	8.24535i	0.0879157	−	0.869136i
$91$	8.66514	−	10.3267i	0.908354	−	1.08253i
$92$	0.580975	−	1.59622i	0.0605709	−	0.166417i
$93$	−0.577360	+	2.52332i	−0.0598695	+	0.261656i
$94$	1.50332	−	0.867940i	0.155055	−	0.0895212i
$95$	−8.38013	−	8.64682i	−0.859783	−	0.887145i
$96$	1.71872	−	0.214444i	0.175417	−	0.0218866i
$97$	6.43776	+	7.67222i	0.653655	+	0.778996i	0.986460	−	0.163999i	$-0.0524395\pi$
$97$	6.43776	+	7.67222i	0.653655	+	0.778996i	−0.332805	+	0.942996i	$0.607995\pi$
$98$	−0.742029	−	4.20825i	−0.0749562	−	0.425098i
$99$	−7.85041	+	16.2567i	−0.788996	+	1.63386i
$100$	−2.01566	+	1.69134i	−0.201566	+	0.169134i
$101$	9.24276	−	11.0151i	0.919689	−	1.09604i	−0.0754094	−	0.997153i	$-0.524026\pi$
$101$	9.24276	−	11.0151i	0.919689	−	1.09604i	0.995098	−	0.0988900i	$-0.0315292\pi$
$102$	0.682825	+	5.47270i	0.0676098	+	0.541878i
$103$	3.05208	+	1.76212i	0.300731	+	0.173627i	0.642771	−	0.766058i	$-0.277785\pi$
$103$	3.05208	+	1.76212i	0.300731	+	0.173627i	−0.342040	+	0.939685i	$0.611118\pi$
$104$	−2.58079	+	3.07567i	−0.253067	+	0.301594i
$105$	16.0446	+	0.809417i	1.56580	+	0.0789910i
$106$	−1.79794			−0.174632
$107$	−0.933767	+	1.61733i	−0.0902707	+	0.156353i	−0.907625	−	0.419782i	$-0.862107\pi$
$107$	−0.933767	+	1.61733i	−0.0902707	+	0.156353i	0.817354	+	0.576135i	$0.195440\pi$
$108$	3.90153	−	3.43192i	0.375425	−	0.330237i
$109$	−7.84099	−	9.34452i	−0.751030	−	0.895043i	0.246215	−	0.969215i	$-0.420813\pi$
$109$	−7.84099	−	9.34452i	−0.751030	−	0.895043i	−0.997245	+	0.0741722i	$0.976369\pi$
$110$	15.6211	−	5.68562i	1.48941	−	0.542103i
$111$	3.66035	−	15.9973i	0.347425	−	1.51840i
$112$	0.583033	+	3.30655i	0.0550915	+	0.312439i
$113$	8.53824	+	14.7887i	0.803210	+	1.39120i	0.917493	+	0.397752i	$0.130209\pi$
$113$	8.53824	+	14.7887i	0.803210	+	1.39120i	−0.114284	+	0.993448i	$0.536457\pi$
$114$	−0.160042	−	7.54814i	−0.0149893	−	0.706948i
$115$	−2.34625	+	4.06382i	−0.218789	+	0.378954i
$116$	−6.53762	−	2.37950i	−0.607002	−	0.220931i
$117$	−1.21220	+	11.9838i	−0.112068	+	1.10791i
$118$	−4.33224	−	3.63518i	−0.398815	−	0.334646i
$119$	−10.5286	+	1.85647i	−0.965154	+	0.170183i
$120$	−4.77867	−	0.241073i	−0.436231	−	0.0220069i
$121$	−25.2123			−2.29203
$122$	−6.58456	+	11.4048i	−0.596138	+	1.03254i
$123$	−9.25957	+	4.74081i	−0.834908	+	0.427465i
$124$	1.47178	+	0.259515i	0.132170	+	0.0233051i
$125$	−5.66690	+	3.27179i	−0.506863	+	0.292638i
$126$	7.02533	+	7.21826i	0.625867	+	0.643053i
$127$	8.20417	+	1.44662i	0.728002	+	0.128366i	0.525352	−	0.850885i	$-0.323934\pi$
$127$	8.20417	+	1.44662i	0.728002	+	0.128366i	0.202650	+	0.979251i	$0.435045\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	0.138440	−	2.74423i	0.0121890	−	0.241616i
$130$	8.49644	−	7.12936i	0.745188	−	0.625287i
$131$	−5.99705	+	1.05744i	−0.523965	+	0.0923891i	−0.429373	−	0.903127i	$-0.641266\pi$
$131$	−5.99705	+	1.05744i	−0.523965	+	0.0923891i	−0.0945913	+	0.995516i	$0.530154\pi$
$132$	9.60227	+	4.05379i	0.835771	+	0.352837i
$133$	14.5977	−	1.04706i	1.26578	−	0.0907914i
$134$			10.0053i			0.864323i
$135$	−12.2604	+	7.46501i	−1.05521	+	0.642485i
$136$	3.13579	−	0.552924i	0.268892	−	0.0474129i
$137$	0.999186	+	2.74524i	0.0853663	+	0.234542i	0.975029	−	0.222075i	$-0.0712831\pi$
$137$	0.999186	+	2.74524i	0.0853663	+	0.234542i	−0.889663	+	0.456617i	$0.849061\pi$
$138$	−2.81192	+	0.865704i	−0.239366	+	0.0736936i
$139$	−11.9051	+	4.33311i	−1.00978	+	0.367529i	−0.793348	−	0.608768i	$-0.791664\pi$
$139$	−11.9051	+	4.33311i	−1.00978	+	0.367529i	−0.216431	+	0.976298i	$0.569442\pi$
$140$		−	9.27516i		−	0.783894i
$141$	−2.76991	−	1.16937i	−0.233269	−	0.0984789i
$142$	1.53089	−	8.68212i	0.128470	−	0.728587i
$143$	−22.7038	+	8.26351i	−1.89859	+	0.691030i
$144$	−2.09240	−	2.14986i	−0.174366	−	0.179155i
$145$	16.6442	+	9.60952i	1.38222	+	0.798027i
$146$	5.68580	+	4.77095i	0.470560	+	0.394847i
$147$	−5.03712	+	5.42286i	−0.415455	+	0.447270i
$148$	−9.33081	−	1.64527i	−0.766988	−	0.135241i
$149$	−9.16454	−	10.9219i	−0.750789	−	0.894755i	0.246440	−	0.969158i	$-0.420739\pi$
$149$	−9.16454	−	10.9219i	−0.750789	−	0.894755i	−0.997228	+	0.0744031i	$0.976295\pi$
$150$	4.44267	+	1.01653i	0.362742	+	0.0829991i
$151$	−2.33272	−	1.34680i	−0.189834	−	0.109601i	0.402071	−	0.915609i	$-0.368291\pi$
$151$	−2.33272	−	1.34680i	−0.189834	−	0.109601i	−0.591905	+	0.806008i	$0.701624\pi$
$152$	−4.34773	+	0.311851i	−0.352647	+	0.0252945i
$153$	6.84549	−	6.66253i	0.553425	−	0.538634i
$154$	−6.91039	+	18.9861i	−0.556855	+	1.52995i
$155$	−3.87950	−	1.41202i	−0.311609	−	0.113416i
$156$	6.94534	+	0.350377i	0.556073	+	0.0280526i
$157$	−7.66777	−	2.79084i	−0.611955	−	0.222733i	0.0174034	−	0.999849i	$-0.494460\pi$
$157$	−7.66777	−	2.79084i	−0.611955	−	0.222733i	−0.629358	+	0.777115i	$0.716682\pi$
$158$	2.75141	+	7.55942i	0.218890	+	0.601396i
$159$	1.87899	+	2.48339i	0.149014	+	0.196945i
$160$			2.76247i			0.218393i
$161$	−1.95066	−	5.35938i	−0.153733	−	0.422379i
$162$	−8.81769	−	1.80231i	−0.692783	−	0.141603i
$163$	1.15041	+	1.99257i	0.0901072	+	0.156070i	0.907556	−	0.419931i	$-0.137946\pi$
$163$	1.15041	+	1.99257i	0.0901072	+	0.156070i	−0.817449	+	0.576001i	$0.804612\pi$
$164$	3.00298	+	5.20132i	0.234494	+	0.406155i
$165$	−24.1784	−	15.6346i	−1.88229	−	1.21715i
$166$	−0.483713	+	1.32899i	−0.0375434	+	0.103150i
$167$	0.351502	−	1.99347i	0.0272001	−	0.154259i	−0.968183	−	0.250244i	$-0.919489\pi$
$167$	0.351502	−	1.99347i	0.0272001	−	0.154259i	0.995383	+	0.0959852i	$0.0306001\pi$
$168$	3.95781	−	4.26090i	0.305352	−	0.328736i
$169$	−2.39020	+	2.00562i	−0.183862	+	0.154278i
$170$	−8.79617			−0.674636
$171$	−10.2585	+	8.10944i	−0.784488	+	0.620144i
$172$	−1.58640			−0.120962
$173$	3.70889	−	3.11212i	0.281981	−	0.236610i	−0.490816	−	0.871263i	$-0.663301\pi$
$173$	3.70889	−	3.11212i	0.281981	−	0.236610i	0.772797	+	0.634653i	$0.218857\pi$
$174$	3.54566	+	11.5168i	0.268796	+	0.873083i
$175$	−1.53411	+	8.70039i	−0.115968	+	0.657688i
$176$	2.05816	−	5.65476i	0.155140	−	0.426243i
$177$	−0.493526	+	9.78290i	−0.0370956	+	0.735328i
$178$	8.31615	+	14.4040i	0.623322	+	1.07963i
$179$	3.04231	+	5.26944i	0.227393	+	0.393856i	0.957035	−	0.289973i	$-0.0936464\pi$
$179$	3.04231	+	5.26944i	0.227393	+	0.393856i	−0.729642	+	0.683830i	$0.760313\pi$
$180$	4.66109	+	6.85241i	0.347417	+	0.510749i
$181$	7.93889	+	21.8119i	0.590093	+	1.62127i	0.770331	+	0.637644i	$0.220091\pi$
$181$	7.93889	+	21.8119i	0.590093	+	1.62127i	−0.180238	+	0.983623i	$0.557687\pi$
$182$			13.4806i			0.999246i
$183$	22.6341	−	2.82404i	1.67316	−	0.208759i
$184$	0.580975	+	1.59622i	0.0428301	+	0.117675i
$185$	24.5953	+	8.95195i	1.80828	+	0.658160i
$186$	−1.17967	−	2.30409i	−0.0864978	−	0.168944i
$187$	18.0057	+	6.55353i	1.31671	+	0.479241i
$188$	−0.593706	+	1.63119i	−0.0433005	+	0.118967i
$189$	2.62811	−	17.2473i	0.191167	−	1.25456i
$190$	11.9776	+	1.23721i	0.868948	+	0.0897564i
$191$	1.18916	+	0.686561i	0.0860445	+	0.0496778i	0.542405	−	0.840117i	$-0.317514\pi$
$191$	1.18916	+	0.686561i	0.0860445	+	0.0496778i	−0.456360	+	0.889795i	$0.650847\pi$
$192$	−1.17878	+	1.26905i	−0.0850709	+	0.0915857i
$193$	14.5842	+	17.3807i	1.04979	+	1.25109i	0.967068	+	0.254519i	$0.0819171\pi$
$193$	14.5842	+	17.3807i	1.04979	+	1.25109i	0.0827227	+	0.996573i	$0.473638\pi$
$194$	−9.86322	−	1.73915i	−0.708138	−	0.124864i
$195$	−18.7268	−	4.28487i	−1.34105	−	0.306846i
$196$	3.27344	+	2.74674i	0.233817	+	0.196196i
$197$	16.3700	+	9.45125i	1.16632	+	0.673374i	0.952810	−	0.303568i	$-0.0981778\pi$
$197$	16.3700	+	9.45125i	1.16632	+	0.673374i	0.213508	+	0.976941i	$0.431511\pi$
$198$	−4.43587	−	17.4995i	−0.315243	−	1.24364i
$199$	−17.7306	+	6.45339i	−1.25689	+	0.457469i	−0.882723	−	0.469894i	$-0.844292\pi$
$199$	−17.7306	+	6.45339i	−1.25689	+	0.457469i	−0.374163	+	0.927363i	$0.622070\pi$
$200$	0.456914	−	2.59129i	0.0323087	−	0.183232i
$201$	13.8196	−	10.4563i	0.974762	−	0.737528i
$202$			14.3792i			1.01172i
$203$	−21.9504	+	7.98929i	−1.54062	+	0.560738i
$204$	−4.04086	−	3.75342i	−0.282917	−	0.262792i
$205$	−5.67457	−	15.5908i	−0.396329	−	1.08891i
$206$	−3.47070	+	0.611978i	−0.241815	+	0.0426385i
$207$	4.13441	+	2.97920i	0.287361	+	0.207069i
$208$		−	4.01500i		−	0.278390i
$209$	−23.5963	−	11.4564i	−1.63219	−	0.792455i
$210$	−12.8112	+	9.69325i	−0.884056	+	0.668898i
$211$	17.3756	−	3.06378i	1.19618	−	0.210919i	0.460136	−	0.887849i	$-0.347801\pi$
$211$	17.3756	−	3.06378i	1.19618	−	0.210919i	0.736048	+	0.676929i	$0.236690\pi$
$212$	1.37731	−	1.15570i	0.0945937	−	0.0793736i
$213$	−13.5920	+	6.95895i	−0.931306	+	0.476820i
$214$	−0.324294	−	1.83916i	−0.0221683	−	0.125723i
$215$	4.31581	+	0.760993i	0.294336	+	0.0518993i
$216$	−0.782746	+	5.13686i	−0.0532591	+	0.349519i
$217$	4.34556	−	2.50891i	0.294996	−	0.170316i
$218$	12.0131	+	2.11823i	0.813629	+	0.143465i
$219$	0.647722	−	12.8394i	0.0437690	−	0.867609i
$220$	−8.31182	+	14.3965i	−0.560383	+	0.970612i
$221$	12.7844			0.859972
$222$	7.47889	+	14.6075i	0.501950	+	0.980391i
$223$	4.65165	−	0.820212i	0.311498	−	0.0549255i	−0.0157139	−	0.999877i	$-0.505002\pi$
$223$	4.65165	−	0.820212i	0.311498	−	0.0549255i	0.327212	+	0.944951i	$0.393891\pi$
$224$	−2.57204	−	2.15819i	−0.171851	−	0.144200i
$225$	−3.23886	−	7.19873i	−0.215924	−	0.479915i
$226$	−16.0466	−	5.84050i	−1.06741	−	0.388504i
$227$	−3.48821	+	6.04176i	−0.231521	+	0.401006i	−0.958256	−	0.285912i	$-0.907703\pi$
$227$	−3.48821	+	6.04176i	−0.231521	+	0.401006i	0.726735	+	0.686918i	$0.241037\pi$
$228$	4.97445	+	5.67934i	0.329441	+	0.376123i
$229$	0.781310	+	1.35327i	0.0516304	+	0.0894265i	0.890686	−	0.454620i	$-0.150225\pi$
$229$	0.781310	+	1.35327i	0.0516304	+	0.0894265i	−0.839055	+	0.544046i	$0.816892\pi$
$230$	−0.814844	−	4.62121i	−0.0537292	−	0.304714i
$231$	33.4463	−	10.2971i	2.20060	−	0.677498i
$232$	6.53762	−	2.37950i	0.429216	−	0.156222i
$233$	−13.7636	−	16.4029i	−0.901686	−	1.07459i	−0.996865	−	0.0791274i	$-0.974787\pi$
$233$	−13.7636	−	16.4029i	−0.901686	−	1.07459i	0.0951784	−	0.995460i	$-0.469658\pi$
$234$	−6.77446	−	9.95934i	−0.442860	−	0.651062i
$235$	2.39766	−	4.15287i	0.156406	−	0.270904i
$236$	5.65534			0.368131
$237$	7.56593	−	11.7005i	0.491460	−	0.760030i
$238$	6.87205	−	8.18979i	0.445449	−	0.530865i
$239$	−23.7929	−	13.7368i	−1.53903	−	0.888562i	−0.998896	−	0.0469865i	$-0.985038\pi$
$239$	−23.7929	−	13.7368i	−1.53903	−	0.888562i	−0.540139	−	0.841576i	$-0.681628\pi$
$240$	3.81563	−	2.88700i	0.246298	−	0.186355i
$241$	12.5141	−	14.9138i	0.806106	−	0.960680i	−0.193686	−	0.981064i	$-0.562044\pi$
$241$	12.5141	−	14.9138i	0.806106	−	0.960680i	0.999792	+	0.0203839i	$0.00648885\pi$
$242$	19.3137	−	16.2061i	1.24153	−	1.04177i
$243$	6.72574	+	14.0629i	0.431456	+	0.902134i
$244$	−2.28679	−	12.9691i	−0.146397	−	0.830259i
$245$	−7.58780	−	9.04279i	−0.484767	−	0.577723i
$246$	4.04591	−	9.58361i	0.257958	−	0.611029i
$247$	−17.4083	−	1.79816i	−1.10767	−	0.114414i
$248$	−1.29426	+	0.747243i	−0.0821858	+	0.0474500i
$249$	2.34117	−	0.720774i	0.148366	−	0.0456772i
$250$	2.23803	−	6.14895i	0.141546	−	0.388894i
$251$	−15.7987	+	18.8281i	−0.997202	+	1.18842i	−0.0151357	+	0.999885i	$0.504818\pi$
$251$	−15.7987	+	18.8281i	−0.997202	+	1.18842i	−0.982067	+	0.188534i	$0.939626\pi$
$252$	−10.0215	−	1.01371i	−0.631297	−	0.0638576i
$253$	−1.77502	+	10.0667i	−0.111595	+	0.632886i
$254$	−7.21462	+	4.16536i	−0.452686	+	0.261358i
$255$	9.19267	+	12.1496i	0.575667	+	0.760837i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−18.7399	−	15.7246i	−1.16896	−	0.980876i	−0.168973	−	0.985621i	$-0.554045\pi$
$257$	−18.7399	−	15.7246i	−1.16896	−	0.980876i	−0.999989	+	0.00474486i	$0.998490\pi$
$258$	1.65791	+	2.19119i	0.103217	+	0.136418i
$259$	−27.5500	+	15.9060i	−1.71187	+	0.988350i
$260$	−1.92599	+	10.9228i	−0.119445	+	0.677404i
$261$	12.2019	−	16.9333i	0.755278	−	1.04814i
$262$	3.91430	−	4.66488i	0.241826	−	0.288197i
$263$	−2.21491	+	6.08541i	−0.136577	+	0.375243i	−0.989060	−	0.147512i	$-0.952873\pi$
$263$	−2.21491	+	6.08541i	−0.136577	+	0.375243i	0.852483	+	0.522755i	$0.175096\pi$
$264$	−9.96149	+	3.06684i	−0.613088	+	0.188751i
$265$	−4.30135	+	2.48339i	−0.264230	+	0.152553i
$266$	−10.5095	+	10.1853i	−0.644378	+	0.624503i
$267$	11.2043	−	26.5399i	0.685693	−	1.62421i
$268$	−6.43126	−	7.66447i	−0.392851	−	0.468182i
$269$	3.11694	+	17.6771i	0.190043	+	1.07779i	0.919302	+	0.393552i	$0.128754\pi$
$269$	3.11694	+	17.6771i	0.190043	+	1.07779i	−0.729259	+	0.684238i	$0.760135\pi$
$270$	4.59361	−	13.5994i	0.279558	−	0.827631i
$271$	−12.0388	+	10.1017i	−0.731302	+	0.613635i	−0.930486	−	0.366327i	$-0.880615\pi$
$271$	−12.0388	+	10.1017i	−0.731302	+	0.613635i	0.199184	+	0.979962i	$0.436171\pi$
$272$	−2.04674	+	2.43921i	−0.124102	+	0.147899i
$273$	18.6199	−	14.0882i	1.12693	−	0.852658i
$274$	−2.53003	−	1.46071i	−0.152845	−	0.0882449i
$275$	10.1779	−	12.1296i	0.613753	−	0.731442i
$276$	1.59759	−	2.47063i	0.0961636	−	0.148715i
$277$	−9.21954			−0.553949			−0.276974	−	0.960877i	$-0.589332\pi$
$277$	−9.21954			−0.553949			−0.276974	+	0.960877i	$0.589332\pi$
$278$	6.33458	−	10.9718i	0.379923	−	0.658046i
$279$	−1.94965	+	4.03736i	−0.116722	+	0.241710i
$280$	5.96196	+	7.10518i	0.356295	+	0.424616i
$281$	−3.02918	+	1.10253i	−0.180706	+	0.0657714i	−0.430788	−	0.902453i	$-0.641764\pi$
$281$	−3.02918	+	1.10253i	−0.180706	+	0.0657714i	0.250083	+	0.968224i	$0.419542\pi$
$282$	2.87353	−	0.884673i	0.171116	−	0.0526815i
$283$	−4.12569	−	23.3980i	−0.245247	−	1.39087i	−0.819918	−	0.572481i	$-0.805981\pi$
$283$	−4.12569	−	23.3980i	−0.245247	−	1.39087i	0.574671	−	0.818384i	$-0.305130\pi$
$284$	4.40803	+	7.63493i	0.261568	+	0.453050i
$285$	−10.8086	−	17.8369i	−0.640249	−	1.05657i
$286$	12.0804	−	20.9240i	0.714332	−	1.23726i
$287$	18.9492	+	6.89696i	1.11854	+	0.407115i
$288$	2.98477	+	0.301918i	0.175879	+	0.0177907i
$289$	5.25590	+	4.41023i	0.309171	+	0.259425i
$290$	−18.9271	+	3.33735i	−1.11144	+	0.195976i
$291$	7.90564	+	15.4410i	0.463437	+	0.905167i
$292$	−7.42229			−0.434356
$293$	3.50138	−	6.06457i	0.204553	−	0.354296i	−0.745437	−	0.666576i	$-0.767759\pi$
$293$	3.50138	−	6.06457i	0.204553	−	0.354296i	0.949990	+	0.312280i	$0.101093\pi$
$294$	0.372908	−	7.39195i	0.0217484	−	0.431107i
$295$	−15.3854	−	2.71286i	−0.895772	−	0.157949i
$296$	8.20537	−	4.73737i	0.476928	−	0.275354i
$297$	−19.5352	+	24.4153i	−1.13355	+	1.41672i
$298$	14.0409	+	2.47579i	0.813367	+	0.143419i
$299$	1.18430	+	6.71649i	0.0684898	+	0.388425i
$300$	−4.05669	+	2.07699i	−0.234213	+	0.119915i
$301$	−4.08027	+	3.42376i	−0.235183	+	0.197342i
$302$	2.65267	−	0.467737i	0.152644	−	0.0269152i
$303$	19.8611	−	15.0273i	1.14099	−	0.863298i
$304$	3.13010	−	3.03356i	0.179524	−	0.173987i
$305$			36.3794i			2.08308i
$306$	−0.961358	+	9.50400i	−0.0549572	+	0.543307i
$307$	6.88301	−	1.21366i	0.392834	−	0.0692673i	0.0262577	−	0.999655i	$-0.491641\pi$
$307$	6.88301	−	1.21366i	0.392834	−	0.0692673i	0.366576	+	0.930388i	$0.380530\pi$
$308$	−6.91039	−	18.9861i	−0.393756	−	1.08184i
$309$	4.47243	+	4.15430i	0.254428	+	0.236330i
$310$	3.87950	−	1.41202i	0.220341	−	0.0801975i
$311$		−	2.60330i		−	0.147620i	−0.997272	−	0.0738098i	$-0.976484\pi$
$311$		−	2.60330i		−	0.147620i	0.997272	−	0.0738098i	$-0.0235158\pi$
$312$	−5.54566	+	4.19598i	−0.313961	+	0.237550i
$313$	1.91675	−	10.8705i	0.108341	−	0.614434i	−0.881492	−	0.472200i	$-0.843460\pi$
$313$	1.91675	−	10.8705i	0.108341	−	0.614434i	0.989833	−	0.142235i	$-0.0454288\pi$
$314$	7.66777	−	2.79084i	0.432718	−	0.157496i
$315$	26.7773	+	7.56511i	1.50873	+	0.426246i
$316$	−6.96680	−	4.02229i	−0.391913	−	0.226271i
$317$	−4.08021	−	3.42370i	−0.229167	−	0.192294i	0.520972	−	0.853573i	$-0.325569\pi$
$317$	−4.08021	−	3.42370i	−0.229167	−	0.192294i	−0.750140	+	0.661279i	$0.770014\pi$
$318$	−3.03568	−	0.694594i	−0.170232	−	0.0389509i
$319$	41.2300	+	7.26996i	2.30844	+	0.407039i
$320$	−1.77568	−	2.11618i	−0.0992638	−	0.118298i
$321$	−2.20141	+	2.36999i	−0.122871	+	0.132280i
$322$	4.93924	+	2.85167i	0.275253	+	0.158917i
$323$	9.65935	+	9.96675i	0.537461	+	0.554565i
$324$	7.91325	−	4.28725i	0.439625	−	0.238181i
$325$	3.61327	−	9.92739i	0.200428	−	0.550672i
$326$	−2.16207	−	0.786928i	−0.119746	−	0.0435839i
$327$	−9.62881	−	18.8066i	−0.532475	−	1.04001i
$328$	−5.64376	−	2.05416i	−0.311625	−	0.113422i
$329$	1.99340	+	5.47682i	0.109900	+	0.301947i
$330$	28.5715	−	3.56484i	1.57281	−	0.196238i
$331$		−	14.3736i		−	0.790043i	−0.918672	−	0.395022i	$-0.870737\pi$
$331$		−	14.3736i		−	0.790043i	0.918672	−	0.395022i	$-0.129263\pi$
$332$	−0.483713	−	1.32899i	−0.0265472	−	0.0729378i
$333$	12.3604	−	25.5961i	0.677345	−	1.40266i
$334$	1.01211	+	1.75303i	0.0553802	+	0.0959213i
$335$	13.8196	+	23.9363i	0.755047	+	1.30778i
$336$	−0.293004	+	5.80807i	−0.0159847	+	0.316856i
$337$	−6.36444	+	17.4862i	−0.346693	+	0.952532i	0.636711	+	0.771103i	$0.280295\pi$
$337$	−6.36444	+	17.4862i	−0.346693	+	0.952532i	−0.983404	+	0.181429i	$0.941928\pi$
$338$	0.541815	−	3.07279i	0.0294709	−	0.167138i
$339$	8.70285	+	28.2680i	0.472674	+	1.53531i
$340$	6.73826	−	5.65407i	0.365433	−	0.306635i
$341$	−8.99332			−0.487015
$342$	2.64583	−	12.8062i	0.143070	−	0.692482i
$343$	−9.15547			−0.494349
$344$	1.21525	−	1.01972i	0.0655220	−	0.0549795i
$345$	−5.53141	+	5.95501i	−0.297801	+	0.320607i
$346$	−0.840736	+	4.76805i	−0.0451982	+	0.256332i
$347$	7.68491	−	21.1141i	0.412548	−	1.13347i	−0.543284	−	0.839549i	$-0.682819\pi$
$347$	7.68491	−	21.1141i	0.412548	−	1.13347i	0.955831	−	0.293916i	$-0.0949586\pi$
$348$	−10.1190	−	6.54324i	−0.542433	−	0.350755i
$349$	12.1069	+	20.9697i	0.648065	+	1.12248i	0.983584	+	0.180448i	$0.0577548\pi$
$349$	12.1069	+	20.9697i	0.648065	+	1.12248i	−0.335520	+	0.942033i	$0.608912\pi$
$350$	−4.41730	−	7.65099i	−0.236115	−	0.408963i
$351$	−6.67638	+	19.7654i	−0.356359	+	1.05500i
$352$	2.05816	+	5.65476i	0.109700	+	0.301399i
$353$			32.1419i			1.71074i	0.518016	+	0.855371i	$0.326671\pi$
$353$			32.1419i			1.71074i	−0.518016	+	0.855371i	$0.673329\pi$
$354$	−5.91026	−	7.81137i	−0.314127	−	0.415169i
$355$	−8.32960	−	22.8854i	−0.442089	−	1.21463i
$356$	−15.6293	−	5.68858i	−0.828349	−	0.301494i
$357$	−18.4938	−	0.932974i	−0.978798	−	0.0493782i
$358$	−5.71768	−	2.08106i	−0.302189	−	0.109988i
$359$	9.44729	−	25.9562i	0.498609	−	1.36992i	−0.394010	−	0.919106i	$-0.628913\pi$
$359$	9.44729	−	25.9562i	0.498609	−	1.36992i	0.892619	−	0.450811i	$-0.148865\pi$
$360$	−7.97525	−	2.25316i	−0.420333	−	0.118752i
$361$	−11.7511	−	14.9302i	−0.618481	−	0.785800i
$362$	−20.1020	−	11.6059i	−1.05654	−	0.609991i
$363$	−42.5689	−	9.74018i	−2.23429	−	0.511227i
$364$	−8.66514	−	10.3267i	−0.454177	−	0.541267i
$365$	20.1924	+	3.56046i	1.05692	+	0.186363i
$366$	−15.5235	+	16.7123i	−0.811424	+	0.873564i
$367$	−6.98736	−	5.86309i	−0.364737	−	0.306051i	0.441938	−	0.897045i	$-0.354291\pi$
$367$	−6.98736	−	5.86309i	−0.364737	−	0.306051i	−0.806676	+	0.590995i	$0.798735\pi$
$368$	−1.47108	−	0.849329i	−0.0766854	−	0.0442743i
$369$	−17.4655	+	4.42724i	−0.909219	+	0.230473i
$370$	−24.5953	+	8.95195i	−1.27865	+	0.465390i
$371$	1.04826	−	5.94499i	0.0544230	−	0.308648i
$372$	2.38472	+	1.00676i	0.123642	+	0.0521980i
$373$		−	3.43306i		−	0.177757i	−0.996042	−	0.0888787i	$-0.971672\pi$
$373$		−	3.43306i		−	0.177757i	0.996042	−	0.0888787i	$-0.0283283\pi$
$374$	−18.0057	+	6.55353i	−0.931051	+	0.338875i
$375$	−10.8321	+	3.33487i	−0.559366	+	0.172212i
$376$	−0.593706	−	1.63119i	−0.0306181	−	0.0841224i
$377$	27.5087	−	4.85053i	1.41677	−	0.249815i
$378$	9.07309	+	14.9015i	0.466669	+	0.766451i
$379$		−	1.12304i		−	0.0576865i	−0.999584	−	0.0288432i	$-0.990818\pi$
$379$		−	1.12304i		−	0.0576865i	0.999584	−	0.0288432i	$-0.00918236\pi$
$380$	−9.97065	+	6.75131i	−0.511483	+	0.346335i
$381$	13.2932	+	5.61198i	0.681031	+	0.287510i
$382$	−1.35226	+	0.238440i	−0.0691877	+	0.0121997i
$383$	14.0390	−	11.7801i	0.717361	−	0.601937i	−0.209293	−	0.977853i	$-0.567116\pi$
$383$	14.0390	−	11.7801i	0.717361	−	0.601937i	0.926654	+	0.375916i	$0.122672\pi$
$384$	0.0872671	−	1.72985i	0.00445333	−	0.0882761i
$385$	9.69214	+	54.9668i	0.493957	+	2.80137i
$386$	−22.3442	−	3.93989i	−1.13729	−	0.200535i
$387$	1.29392	−	4.57993i	0.0657734	−	0.232811i
$388$	8.67357	−	5.00769i	0.440334	−	0.254227i
$389$	−27.4916	−	4.84751i	−1.39388	−	0.245778i	−0.574253	−	0.818678i	$-0.694707\pi$
$389$	−27.4916	−	4.84751i	−1.39388	−	0.245778i	−0.819626	+	0.572900i	$0.805818\pi$
$390$	17.0998	−	8.75493i	0.865882	−	0.443323i
$391$	2.70440	−	4.68416i	0.136768	−	0.236888i
$392$	−4.27317			−0.215828
$393$	−10.5340	−	0.531419i	−0.531372	−	0.0268065i
$394$	−18.6153	+	3.28239i	−0.937827	+	0.165364i
$395$	17.0237	+	14.2846i	0.856558	+	0.718737i
$396$	14.6466	+	10.5541i	0.736017	+	0.530364i
$397$	16.4411	+	5.98408i	0.825156	+	0.300332i	0.719869	−	0.694110i	$-0.244202\pi$
$397$	16.4411	+	5.98408i	0.825156	+	0.300332i	0.105287	+	0.994442i	$0.466424\pi$
$398$	9.43423	−	16.3406i	0.472895	−	0.819079i
$399$	25.0516	+	3.87163i	1.25415	+	0.193824i
$400$	1.31563	+	2.27874i	0.0657816	+	0.113937i
$401$	−4.51042	−	25.5799i	−0.225240	−	1.27740i	−0.862227	−	0.506523i	$-0.830931\pi$
$401$	−4.51042	−	25.5799i	−0.225240	−	1.27740i	0.636987	−	0.770874i	$-0.280180\pi$
$402$	−3.86530	+	16.8930i	−0.192784	+	0.842549i
$403$	−5.63849	+	2.05224i	−0.280873	+	0.102229i
$404$	−9.24276	−	11.0151i	−0.459845	−	0.548021i
$405$	−23.5846	+	7.86752i	−1.17193	+	0.390940i
$406$	11.6796	−	20.2296i	0.579647	−	1.00398i
$407$	57.0159			2.82617
$408$	5.50813	+	0.277873i	0.272693	+	0.0137568i
$409$	−5.81978	+	6.93574i	−0.287769	+	0.342950i	−0.890491	−	0.455002i	$-0.849639\pi$
$409$	−5.81978	+	6.93574i	−0.287769	+	0.342950i	0.602721	+	0.797952i	$0.294083\pi$
$410$	14.3685	+	8.29567i	0.709610	+	0.409694i
$411$	0.626483	+	5.02113i	0.0309021	+	0.247674i
$412$	2.26534	−	2.69973i	0.111605	−	0.133006i
$413$	14.5457	−	12.2053i	0.715749	−	0.600585i
$414$	−5.08213	+	0.375349i	−0.249773	+	0.0184474i
$415$	0.678429	+	3.84756i	0.0333028	+	0.188869i
$416$	2.58079	+	3.07567i	0.126534	+	0.150797i
$417$	−21.7748	+	2.71683i	−1.06632	+	0.133044i
$418$	25.4398	−	6.39129i	1.24430	−	0.312608i
$419$	−21.0196	+	12.1357i	−1.02687	+	0.592866i	−0.916088	−	0.400978i	$-0.868670\pi$
$419$	−21.0196	+	12.1357i	−1.02687	+	0.592866i	−0.110787	+	0.993844i	$0.535337\pi$
$420$	3.58324	−	15.6603i	0.174844	−	0.764146i
$421$	−3.01312	+	8.27847i	−0.146850	+	0.403468i	−0.991208	−	0.132312i	$-0.957760\pi$
$421$	−3.01312	+	8.27847i	−0.146850	+	0.403468i	0.844358	+	0.535780i	$0.179982\pi$
$422$	−11.3411	+	13.5158i	−0.552076	+	0.657939i
$423$	−4.22501	−	3.04448i	−0.205427	−	0.148028i
$424$	−0.312210	+	1.77063i	−0.0151622	+	0.0859894i
$425$	−7.25588	+	4.18919i	−0.351962	+	0.203205i
$426$	5.93892	−	14.0676i	0.287742	−	0.681578i
$427$	−33.8715	−	28.4215i	−1.63915	−	1.37541i
$428$	1.43061	+	1.20043i	0.0691514	+	0.0580249i
$429$	−41.5259	+	5.18116i	−2.00489	+	0.250149i
$430$	−3.79526	+	2.19119i	−0.183023	+	0.105669i
$431$	2.31721	−	13.1416i	0.111616	−	0.633007i	−0.876754	−	0.480939i	$-0.840296\pi$
$431$	2.31721	−	13.1416i	0.111616	−	0.633007i	0.988370	−	0.152068i	$-0.0485932\pi$
$432$	−2.70229	−	4.43820i	−0.130014	−	0.213533i
$433$	14.3916	−	17.1512i	0.691614	−	0.824234i	−0.299935	−	0.953959i	$-0.596965\pi$
$433$	14.3916	−	17.1512i	0.691614	−	0.824234i	0.991550	+	0.129725i	$0.0414096\pi$
$434$	−1.71620	+	4.71521i	−0.0823800	+	0.226337i
$435$	24.3899	+	22.6550i	1.16941	+	1.08622i
$436$	−10.5641	+	6.09920i	−0.505930	+	0.292099i
$437$	−4.34139	+	5.99798i	−0.207677	+	0.286922i
$438$	7.75685	+	10.2519i	0.370637	+	0.489856i
$439$	17.0431	+	20.3112i	0.813423	+	0.969399i	0.999915	−	0.0130572i	$-0.00415637\pi$
$439$	17.0431	+	20.3112i	0.813423	+	0.969399i	−0.186492	+	0.982456i	$0.559712\pi$
$440$	−2.88667	−	16.3711i	−0.137616	−	0.780461i
$441$	−10.5998	+	7.21008i	−0.504750	+	0.343337i
$442$	−9.79342	+	8.21766i	−0.465826	+	0.390874i
$443$	2.45155	−	2.92164i	0.116477	−	0.138811i	−0.704655	−	0.709550i	$-0.748898\pi$
$443$	2.45155	−	2.92164i	0.116477	−	0.138811i	0.821132	+	0.570738i	$0.193343\pi$
$444$	−15.1187	−	6.38265i	−0.717501	−	0.302907i
$445$	39.7907	+	22.9732i	1.88626	+	1.08903i
$446$	−3.03615	+	3.61834i	−0.143766	+	0.171334i
$447$	−11.2542	−	21.9812i	−0.532303	−	1.03967i
$448$	3.35755			0.158630
$449$	0.123310	−	0.213580i	0.00581937	−	0.0100794i	−0.863101	−	0.505031i	$-0.831481\pi$
$449$	0.123310	−	0.213580i	0.00581937	−	0.0100794i	0.868920	+	0.494952i	$0.164814\pi$
$450$	7.10836	+	3.43264i	0.335091	+	0.161816i
$451$	−23.2316	−	27.6863i	−1.09393	−	1.30370i
$452$	16.0466	−	5.84050i	0.754770	−	0.274714i
$453$	−3.41830	−	3.17514i	−0.160606	−	0.149181i
$454$	−1.21144	−	6.87043i	−0.0568558	−	0.322445i
$455$	18.6199	+	32.2505i	0.872912	+	1.51193i
$456$	−7.46126	−	1.15311i	−0.349405	−	0.0539993i
$457$	9.28341	−	16.0793i	0.434260	−	0.752160i	−0.562975	−	0.826474i	$-0.690343\pi$
$457$	9.28341	−	16.0793i	0.434260	−	0.752160i	0.997235	+	0.0743139i	$0.0236767\pi$
$458$	−1.46838	−	0.534447i	−0.0686130	−	0.0249731i
$459$	14.1320	−	8.60454i	0.659624	−	0.401625i
$460$	3.59466	+	3.01628i	0.167602	+	0.140635i
$461$	4.81815	−	0.849570i	0.224404	−	0.0395684i	−0.0603157	−	0.998179i	$-0.519211\pi$
$461$	4.81815	−	0.849570i	0.224404	−	0.0395684i	0.284719	+	0.958611i	$0.408100\pi$
$462$	−19.0025	+	29.3869i	−0.884076	+	1.36720i
$463$	−36.9096			−1.71534			−0.857668	−	0.514204i	$-0.828088\pi$
$463$	−36.9096			−1.71534			−0.857668	+	0.514204i	$0.828088\pi$
$464$	−3.47859	+	6.02510i	−0.161490	+	0.279708i
$465$	−6.00471	−	3.88284i	−0.278462	−	0.180062i
$466$	21.0871	+	3.71823i	0.976842	+	0.172244i
$467$	18.1011	−	10.4507i	0.837619	−	0.483600i	−0.0188350	−	0.999823i	$-0.505996\pi$
$467$	18.1011	−	10.4507i	0.837619	−	0.483600i	0.856454	+	0.516223i	$0.172662\pi$
$468$	11.5913	+	3.27476i	0.535807	+	0.151376i
$469$	−33.0828	−	5.83340i	−1.52762	−	0.269361i
$470$	0.832699	+	4.72247i	0.0384096	+	0.217831i
$471$	−11.8682	−	7.67437i	−0.546859	−	0.353616i
$472$	−4.33224	+	3.63518i	−0.199408	+	0.167323i
$473$	9.40138	−	1.65772i	0.432276	−	0.0762219i
$474$	1.72511	+	13.8264i	0.0792370	+	0.635068i
$475$	10.4694	−	4.68379i	0.480371	−	0.214907i
$476$			10.6910i			0.490021i
$477$	2.21312	+	4.91890i	0.101332	+	0.225221i
$478$	27.0563	−	4.77075i	1.23753	−	0.218209i
$479$	−5.47743	−	15.0491i	−0.250270	−	0.687611i	−0.999675	−	0.0254993i	$-0.991882\pi$
$479$	−5.47743	−	15.0491i	−0.250270	−	0.687611i	0.749405	−	0.662112i	$-0.230340\pi$
$480$	−1.06722	+	4.66421i	−0.0487116	+	0.212891i
$481$	35.7469	−	13.0108i	1.62992	−	0.593242i
$482$			19.4685i			0.886767i
$483$	−1.22305	−	9.80247i	−0.0556506	−	0.446028i
$484$	−4.37807	+	24.8293i	−0.199003	+	1.12860i
$485$	−25.9987	+	9.46275i	−1.18054	+	0.429681i
$486$	−14.1917	−	6.44957i	−0.643747	−	0.292558i
$487$	−4.73675	−	2.73477i	−0.214643	−	0.123924i	0.388824	−	0.921312i	$-0.372881\pi$
$487$	−4.73675	−	2.73477i	−0.214643	−	0.123924i	−0.603467	+	0.797388i	$0.706215\pi$
$488$	10.0881	+	8.46495i	0.456668	+	0.383190i
$489$	1.17259	+	3.80873i	0.0530264	+	0.172237i
$490$	11.6252	+	2.04983i	0.525173	+	0.0926021i
$491$	−16.3048	−	19.4313i	−0.735826	−	0.876923i	0.260239	−	0.965544i	$-0.416199\pi$
$491$	−16.3048	−	19.4313i	−0.735826	−	0.876923i	−0.996065	+	0.0886208i	$0.971754\pi$
$492$	3.06088	+	9.94213i	0.137995	+	0.448226i
$493$	−19.1849	−	11.0764i	−0.864045	−	0.498857i
$494$	14.4914	−	9.81239i	0.651999	−	0.441480i
$495$	−34.7832	−	35.7384i	−1.56339	−	1.60632i
$496$	0.511144	−	1.40436i	0.0229511	−	0.0630575i
$497$	27.8153	+	10.1239i	1.24769	+	0.454120i
$498$	−1.33013	+	2.05702i	−0.0596047	+	0.0921772i
$499$	32.1152	+	11.6890i	1.43767	+	0.523270i	0.939120	−	0.343589i	$-0.111643\pi$
$499$	32.1152	+	11.6890i	1.43767	+	0.523270i	0.498553	+	0.866859i	$0.333865\pi$
$500$	2.23803	+	6.14895i	0.100088	+	0.274989i
$501$	1.36361	−	3.23001i	0.0609217	−	0.144306i
$502$		−	24.5783i		−	1.09699i
$503$	−0.991012	−	2.72278i	−0.0441871	−	0.121403i	0.915636	−	0.402007i	$-0.131687\pi$
$503$	−0.991012	−	2.72278i	−0.0441871	−	0.121403i	−0.959824	+	0.280604i	$0.909465\pi$
$504$	8.32853	−	5.66517i	0.370982	−	0.252347i
$505$	19.8611	+	34.4004i	0.883805	+	1.53080i
$506$	−5.11098	−	8.85247i	−0.227211	−	0.393540i
$507$	−4.81049	+	2.46292i	−0.213641	+	0.109382i
$508$	2.84928	−	7.82833i	0.126416	−	0.347326i
$509$	−0.948700	+	5.38034i	−0.0420504	+	0.238480i	−0.998588	−	0.0531308i	$-0.983080\pi$
$509$	−0.948700	+	5.38034i	−0.0420504	+	0.238480i	0.956537	+	0.291610i	$0.0941911\pi$
$510$	−14.8516	−	3.39820i	−0.657640	−	0.150475i
$511$	−19.0904	+	16.0187i	−0.844509	+	0.708627i
$512$	−1.00000			−0.0441942
$513$	−20.4535	+	9.72897i	−0.903046	+	0.429545i
$514$	24.4632			1.07902
$515$	−7.45792	+	6.25794i	−0.328635	+	0.275758i
$516$	−2.67850	−	0.612868i	−0.117914	−	0.0269800i
$517$	1.81392	−	10.2872i	0.0797761	−	0.452433i
$518$	10.8803	−	29.8935i	0.478055	−	1.31344i
$519$	7.46444	−	3.82172i	0.327653	−	0.167755i
$520$	−5.54566	−	9.60537i	−0.243193	−	0.421223i
$521$	4.88541	+	8.46178i	0.214034	+	0.370717i	0.952973	−	0.303054i	$-0.0980064\pi$
$521$	4.88541	+	8.46178i	0.214034	+	0.370717i	−0.738939	+	0.673772i	$0.764673\pi$
$522$	1.53732	+	20.8149i	0.0672865	+	0.911042i
$523$	9.34910	+	25.6864i	0.408808	+	1.12319i	0.957818	+	0.287374i	$0.0927824\pi$
$523$	9.34910	+	25.6864i	0.408808	+	1.12319i	−0.549011	+	0.835815i	$0.684995\pi$
$524$			6.08956i			0.266024i
$525$	−5.95142	+	14.0972i	−0.259741	+	0.615253i
$526$	−2.21491	−	6.08541i	−0.0965746	−	0.265337i
$527$	4.47171	+	1.62757i	0.194791	+	0.0708980i
$528$	5.65962	−	8.75246i	0.246303	−	0.380902i
$529$	−18.9015	−	6.87958i	−0.821805	−	0.299112i
$530$	1.69874	−	4.66724i	0.0737884	−	0.202732i
$531$	−4.61267	+	16.3269i	−0.200173	+	0.708529i
$532$	1.50372	−	14.5578i	0.0651945	−	0.631160i
$533$	−20.8833	−	12.0570i	−0.904555	−	0.522245i
$534$	8.47648	+	27.5327i	0.366813	+	1.19146i
$535$	−3.31615	−	3.95203i	−0.143370	−	0.170861i
$536$	9.85326	+	1.73739i	0.425596	+	0.0750440i
$537$	3.10097	+	10.0723i	0.133817	+	0.434654i
$538$	−13.7503	−	11.5379i	−0.592818	−	0.497434i
$539$	−22.2694	−	12.8573i	−0.959212	−	0.553801i
$540$	5.22260	+	13.3704i	0.224745	+	0.575372i
$541$	−24.9424	+	9.07830i	−1.07236	+	0.390307i	−0.817058	−	0.576555i	$-0.804397\pi$
$541$	−24.9424	+	9.07830i	−1.07236	+	0.390307i	−0.255300	+	0.966862i	$0.582174\pi$
$542$	2.72896	−	15.4767i	0.117219	−	0.664782i
$543$	4.97762	+	39.8946i	0.213610	+	1.71204i
$544$		−	3.18416i		−	0.136520i
$545$	31.6656	−	11.5253i	1.35640	−	0.493691i
$546$	−5.20790	+	22.7608i	−0.222878	+	0.974073i
$547$	1.07867	+	2.96362i	0.0461206	+	0.126715i	0.960615	−	0.277884i	$-0.0896331\pi$
$547$	1.07867	+	2.96362i	0.0461206	+	0.126715i	−0.914494	+	0.404600i	$0.867411\pi$
$548$	2.87704	−	0.507300i	0.122901	−	0.0216708i
$549$	39.3068	+	3.97600i	1.67757	+	0.169692i
$550$			15.8341i			0.675166i
$551$	24.5659	+	17.7810i	1.04654	+	0.757496i
$552$	0.364267	+	2.91953i	0.0155042	+	0.124263i
$553$	−26.5997	+	4.69025i	−1.13114	+	0.199450i
$554$	7.06258	−	5.92621i	0.300060	−	0.251780i
$555$	38.0687	+	24.6164i	1.61593	+	1.04491i
$556$	2.19998	+	12.4767i	0.0932998	+	0.529129i
$557$	−6.73127	−	1.18690i	−0.285213	−	0.0502907i	0.0292114	−	0.999573i	$-0.490700\pi$
$557$	−6.73127	−	1.18690i	−0.285213	−	0.0502907i	−0.314424	+	0.949283i	$0.601811\pi$
$558$	−1.10165	−	4.34601i	−0.0466364	−	0.183981i
$559$	5.51605	−	3.18469i	0.233304	−	0.134698i
$560$	−9.13425	−	1.61061i	−0.385992	−	0.0680609i
$561$	27.8693	+	18.0212i	1.17664	+	0.760854i
$562$	1.61179	−	2.79170i	0.0679893	−	0.117761i
$563$	35.5375			1.49773			0.748864	−	0.662724i	$-0.230600\pi$
$563$	35.5375			1.49773			0.748864	+	0.662724i	$0.230600\pi$
$564$	−1.63260	+	2.52477i	−0.0687448	+	0.106312i
$565$	−46.4566	+	8.19156i	−1.95445	+	0.344621i
$566$	18.2004	+	15.2719i	0.765020	+	0.641928i
$567$	11.1004	−	28.1053i	0.466175	−	1.18031i
$568$	−8.28438	−	3.01527i	−0.347605	−	0.126518i
$569$	−9.30185	+	16.1113i	−0.389954	+	0.675420i	−0.992443	−	0.122707i	$-0.960842\pi$
$569$	−9.30185	+	16.1113i	−0.389954	+	0.675420i	0.602489	+	0.798127i	$0.294176\pi$
$570$	19.7452	+	6.71620i	0.827037	+	0.281310i
$571$	11.5490	+	20.0034i	0.483309	+	0.837116i	0.999816	−	0.0191672i	$-0.00610148\pi$
$571$	11.5490	+	20.0034i	0.483309	+	0.837116i	−0.516507	+	0.856283i	$0.672768\pi$
$572$	4.19550	+	23.7938i	0.175422	+	0.994870i
$573$	1.74256	+	1.61861i	0.0727965	+	0.0676182i
$574$	−18.9492	+	6.89696i	−0.790926	+	0.287874i
$575$	−2.87301	−	3.42392i	−0.119813	−	0.142788i
$576$	−2.48053	+	1.68729i	−0.103356	+	0.0703037i
$577$	−6.90632	+	11.9621i	−0.287514	+	0.497988i	−0.973216	−	0.229894i	$-0.926162\pi$
$577$	−6.90632	+	11.9621i	−0.287514	+	0.497988i	0.685702	+	0.727882i	$0.259495\pi$
$578$	−6.86110			−0.285384
$579$	17.9095	+	34.9802i	0.744293	+	1.45373i
$580$	12.3538	−	14.7226i	0.512962	−	0.611324i
$581$	−4.11235	−	2.37427i	−0.170609	−	0.0985011i
$582$	−15.9813	−	6.74684i	−0.662448	−	0.279666i
$583$	−6.95459	+	8.28816i	−0.288030	+	0.343261i
$584$	5.68580	−	4.77095i	0.235280	−	0.197423i
$585$	−29.9632	−	14.4693i	−1.23883	−	0.598232i
$586$	1.21602	+	6.89637i	0.0502332	+	0.284887i
$587$	−3.93954	−	4.69496i	−0.162602	−	0.193782i	0.678591	−	0.734516i	$-0.262591\pi$
$587$	−3.93954	−	4.69496i	−0.162602	−	0.193782i	−0.841193	+	0.540734i	$0.818146\pi$
$588$	4.46579	+	5.90226i	0.184166	+	0.243405i
$589$	−5.86013	−	2.84519i	−0.241463	−	0.117234i
$590$	13.5297	−	7.81137i	0.557008	−	0.321589i
$591$	23.9882	+	22.2818i	0.986742	+	0.916552i
$592$	−3.24056	+	8.90335i	−0.133186	+	0.365926i
$593$	15.8738	−	18.9176i	0.651857	−	0.776853i	−0.334336	−	0.942454i	$-0.608512\pi$
$593$	15.8738	−	18.9176i	0.651857	−	0.776853i	0.986193	+	0.165601i	$0.0529563\pi$
$594$	−0.729050	−	31.2602i	−0.0299133	−	1.28262i
$595$	5.12846	−	29.0849i	0.210246	−	1.19237i
$596$	−12.3474	+	7.12875i	−0.505767	+	0.292005i
$597$	−32.4297	+	4.04623i	−1.32726	+	0.165601i
$598$	−5.22450	−	4.38388i	−0.213646	−	0.179270i
$599$	3.70017	+	3.10481i	0.151185	+	0.126859i	0.715243	−	0.698876i	$-0.246316\pi$
$599$	3.70017	+	3.10481i	0.151185	+	0.126859i	−0.564058	+	0.825735i	$0.690761\pi$
$600$	1.77255	−	4.19866i	0.0723639	−	0.171409i
$601$	−10.3486	+	5.97477i	−0.422129	+	0.243716i	−0.695988	−	0.718054i	$-0.745033\pi$
$601$	−10.3486	+	5.97477i	−0.422129	+	0.243716i	0.273859	+	0.961770i	$0.411700\pi$
$602$	0.924923	−	5.24550i	0.0376970	−	0.213791i
$603$	27.3728	−	12.3156i	1.11471	−	0.501531i
$604$	−1.73141	+	2.06341i	−0.0704499	+	0.0839590i
$605$	23.8211	−	65.4480i	0.968466	−	2.66084i
$606$	−5.55506	+	24.2781i	−0.225659	+	0.986229i
$607$	−33.0615	+	19.0881i	−1.34193	+	0.774761i	−0.987090	−	0.160168i	$-0.948796\pi$
$607$	−33.0615	+	19.0881i	−1.34193	+	0.774761i	−0.354835	+	0.934929i	$0.615463\pi$
$608$	−0.447862	+	4.33583i	−0.0181632	+	0.175841i
$609$	−40.1479	+	5.00923i	−1.62688	+	0.202984i
$610$	−23.3842	−	27.8682i	−0.946799	−	1.12835i
$611$	−1.21025	−	6.86367i	−0.0489615	−	0.277674i
$612$	−5.37261	−	7.89843i	−0.217175	−	0.319275i
$613$	8.49157	−	7.12527i	0.342971	−	0.287787i	−0.454989	−	0.890497i	$-0.650357\pi$
$613$	8.49157	−	7.12527i	0.342971	−	0.287787i	0.797960	+	0.602710i	$0.205912\pi$
$614$	−4.49257	+	5.35403i	−0.181305	+	0.216071i
$615$	−3.55791	−	28.5159i	−0.143469	−	1.14987i
$616$	17.4977	+	10.1023i	0.705004	+	0.407034i
$617$	14.0987	−	16.8022i	0.567594	−	0.676432i	−0.403542	−	0.914961i	$-0.632221\pi$
$617$	14.0987	−	16.8022i	0.567594	−	0.676432i	0.971135	+	0.238530i	$0.0766654\pi$
$618$	−6.09641	−	0.307551i	−0.245234	−	0.0123715i
$619$	23.5538			0.946707			0.473353	−	0.880873i	$-0.343043\pi$
$619$	23.5538			0.946707			0.473353	+	0.880873i	$0.343043\pi$
$620$	−2.06424	+	3.57537i	−0.0829019	+	0.143590i
$621$	5.82966	+	6.62736i	0.233936	+	0.265947i
$622$	1.67337	+	1.99424i	0.0670960	+	0.0799619i
$623$	−52.4761	+	19.0997i	−2.10241	+	0.765215i
$624$	1.55110	−	6.77899i	0.0620937	−	0.271377i
$625$	−5.42351	−	30.7583i	−0.216941	−	1.23033i
$626$	5.51907	+	9.55932i	0.220587	+	0.382067i
$627$	−35.4145	−	28.4590i	−1.41432	−	1.13654i
$628$	−4.07994	+	7.06666i	−0.162807	+	0.281990i
$629$	−28.3497	−	10.3185i	−1.13038	−	0.411424i
$630$	−25.3754	+	11.4169i	−1.01098	+	0.454862i
$631$	−19.6357	−	16.4763i	−0.781684	−	0.655910i	0.161988	−	0.986793i	$-0.448209\pi$
$631$	−19.6357	−	16.4763i	−0.781684	−	0.655910i	−0.943672	+	0.330882i	$0.892654\pi$
$632$	7.92236	−	1.39693i	0.315134	−	0.0555667i
$633$	30.5208	+	1.53971i	1.21309	+	0.0611979i
$634$	5.32634			0.211536
$635$	−11.5067	+	19.9302i	−0.456630	+	0.790906i
$636$	2.77194	−	1.41921i	0.109915	−	0.0562752i
$637$	−16.8961	−	2.97924i	−0.669449	−	0.118042i
$638$	−36.2570	+	20.9330i	−1.43543	+	0.828746i
$639$	−25.6373	+	6.49867i	−1.01420	+	0.257084i
$640$	2.72051	+	0.479699i	0.107537	+	0.0189618i
$641$	−1.79503	−	10.1801i	−0.0708996	−	0.402092i	−0.999518	−	0.0310546i	$-0.990113\pi$
$641$	−1.79503	−	10.1801i	−0.0708996	−	0.402092i	0.928618	−	0.371037i	$-0.120998\pi$
$642$	0.162974	−	3.23056i	0.00643209	−	0.127500i
$643$	28.0456	−	23.5330i	1.10601	−	0.928052i	0.108195	−	0.994130i	$-0.465493\pi$
$643$	28.0456	−	23.5330i	1.10601	−	0.928052i	0.997814	+	0.0660777i	$0.0210485\pi$
$644$	−5.61669	+	0.990374i	−0.221329	+	0.0390262i
$645$	6.99289	+	2.95218i	0.275345	+	0.116242i
$646$	−13.8060	−	1.42607i	−0.543190	−	0.0561078i
$647$			5.28544i			0.207792i	0.994588	+	0.103896i	$0.0331309\pi$
$647$			5.28544i			0.207792i	−0.994588	+	0.103896i	$0.966869\pi$
$648$	−3.30611	+	8.37076i	−0.129876	+	0.328835i
$649$	−33.5149	+	5.90959i	−1.31558	+	0.231972i
$650$	3.61327	+	9.92739i	0.141724	+	0.389384i
$651$	8.30637	−	2.55728i	0.325552	−	0.100228i
$652$	2.16207	−	0.786928i	0.0846731	−	0.0308185i
$653$		−	16.9561i		−	0.663544i	−0.943360	−	0.331772i	$-0.892354\pi$
$653$		−	16.9561i		−	0.663544i	0.943360	−	0.331772i	$-0.107646\pi$
$654$	19.4648	+	8.21744i	0.761133	+	0.321327i
$655$	2.92116	−	16.5667i	0.114139	−	0.647314i
$656$	5.64376	−	2.05416i	0.220352	−	0.0802016i
$657$	6.05385	−	21.4281i	0.236183	−	0.835990i
$658$	−5.04747	−	2.91416i	−0.196771	−	0.113606i
$659$	10.8105	+	9.07108i	0.421117	+	0.353359i	0.828588	−	0.559859i	$-0.189145\pi$
$659$	10.8105	+	9.07108i	0.421117	+	0.353359i	−0.407471	+	0.913218i	$0.633589\pi$
$660$	−19.5956	+	21.0962i	−0.762757	+	0.821169i
$661$	18.7804	+	3.31150i	0.730474	+	0.128802i	0.526501	−	0.850174i	$-0.323503\pi$
$661$	18.7804	+	3.31150i	0.730474	+	0.128802i	0.203973	+	0.978977i	$0.434615\pi$
$662$	9.23916	+	11.0108i	0.359090	+	0.427947i
$663$	21.5854	+	4.93896i	0.838308	+	0.191813i
$664$	1.22480	+	0.707141i	0.0475316	+	0.0274424i
$665$	−11.0742	+	38.8832i	−0.429440	+	1.50783i
$666$	6.98422	+	27.5528i	0.270633	+	1.06765i
$667$	4.04195	−	11.1052i	0.156505	−	0.429994i
$668$	−1.90215	−	0.692324i	−0.0735962	−	0.0267868i
$669$	8.17080	+	0.412199i	0.315901	+	0.0159365i
$670$	−25.9724	−	9.45319i	−1.00340	−	0.365208i
$671$	27.1042	+	74.4682i	1.04635	+	2.87481i
$672$	−3.50890	−	4.63758i	−0.135359	−	0.178898i
$673$		−	6.57266i		−	0.253358i	−0.991944	−	0.126679i	$-0.959568\pi$
$673$		−	6.57266i		−	0.253358i	0.991944	−	0.126679i	$-0.0404317\pi$
$674$	−6.36444	−	17.4862i	−0.245149	−	0.673542i
$675$	−2.68749	−	13.4057i	−0.103441	−	0.515986i
$676$	1.56010	+	2.70216i	0.0600037	+	0.103929i
$677$	−7.00831	−	12.1388i	−0.269351	−	0.466530i	0.699343	−	0.714786i	$-0.253476\pi$
$677$	−7.00831	−	12.1388i	−0.269351	−	0.466530i	−0.968694	+	0.248256i	$0.920143\pi$
$678$	−24.8371	−	16.0604i	−0.953862	−	0.616797i
$679$	11.5012	−	31.5992i	0.441374	−	1.21267i
$680$	−1.52744	+	8.66254i	−0.0585746	+	0.332193i
$681$	−8.22365	+	8.85342i	−0.315131	+	0.339264i
$682$	6.88928	−	5.78079i	0.263804	−	0.221358i
$683$	4.06453			0.155525			0.0777625	−	0.996972i	$-0.475222\pi$
$683$	4.06453			0.155525			0.0777625	+	0.996972i	$0.475222\pi$
$684$	6.20486	+	11.5108i	0.237249	+	0.440128i
$685$	−8.07036			−0.308353
$686$	7.01350	−	5.88502i	0.267777	−	0.224691i
$687$	0.796373	+	2.58672i	0.0303835	+	0.0986896i
$688$	−0.275475	+	1.56230i	−0.0105024	+	0.0595620i
$689$	−2.46895	+	6.78340i	−0.0940597	+	0.258427i
$690$	0.409501	−	8.11732i	0.0155894	−	0.309021i
$691$	−4.41696	−	7.65039i	−0.168029	−	0.291035i	0.769698	−	0.638408i	$-0.220407\pi$
$691$	−4.41696	−	7.65039i	−0.168029	−	0.291035i	−0.937727	+	0.347374i	$0.887074\pi$
$692$	−2.42080	−	4.19295i	−0.0920251	−	0.159392i
$693$	60.4493	−	4.46458i	2.29628	−	0.169595i
$694$	7.68491	+	21.1141i	0.291715	+	0.801481i
$695$		−	34.9982i		−	1.32756i
$696$	11.9575	−	1.49193i	0.453247	−	0.0565514i
$697$	6.54079	+	17.9707i	0.247750	+	0.680688i
$698$	−22.7534	−	8.28157i	−0.861230	−	0.313462i
$699$	−16.9019	−	33.0121i	−0.639288	−	1.24863i
$700$	8.30182	+	3.02161i	0.313779	+	0.114206i
$701$	−0.225040	+	0.618292i	−0.00849964	+	0.0233526i	−0.943870	−	0.330317i	$-0.892844\pi$
$701$	−0.225040	+	0.618292i	−0.00849964	+	0.0233526i	0.935370	+	0.353670i	$0.115066\pi$
$702$	−7.59055	−	19.4327i	−0.286487	−	0.733439i
$703$	37.1521	+	18.0380i	1.40122	+	0.680315i
$704$	−5.21145	−	3.00883i	−0.196414	−	0.113400i
$705$	5.65262	−	6.08550i	0.212890	−	0.229193i
$706$	−20.6604	−	24.6221i	−0.777565	−	0.926666i
$707$	−47.5454	−	8.38354i	−1.78813	−	0.315296i
$708$	9.54857	+	2.18481i	0.358857	+	0.0821102i
$709$	−4.75612	−	3.99086i	−0.178620	−	0.149880i	0.549094	−	0.835760i	$-0.314973\pi$
$709$	−4.75612	−	3.99086i	−0.178620	−	0.149880i	−0.727714	+	0.685881i	$0.759417\pi$
$710$	21.0913	+	12.1771i	0.791542	+	0.456997i
$711$	17.2947	−	16.8324i	0.648601	−	0.631266i
$712$	15.6293	−	5.68858i	0.585731	−	0.213189i
$713$	−0.440827	+	2.50005i	−0.0165091	+	0.0936278i
$714$	14.7668	−	11.1729i	0.552634	−	0.418136i
$715$		−	66.7439i		−	2.49608i
$716$	5.71768	−	2.08106i	0.213680	−	0.0777730i
$717$	−34.8654	−	32.3853i	−1.30207	−	1.20945i
$718$	9.44729	+	25.9562i	0.352570	+	0.968678i
$719$	−28.0129	+	4.93943i	−1.04470	+	0.184210i	−0.669561	−	0.742757i	$-0.733518\pi$
$719$	−28.0129	+	4.93943i	−1.04470	+	0.184210i	−0.375144	+	0.926967i	$0.622407\pi$
$720$	7.55770	−	3.40037i	0.281659	−	0.126724i
$721$		−	11.8328i		−	0.440678i
$722$	18.5988	+	3.88370i	0.692177	+	0.144537i
$723$	26.8907	−	20.3461i	1.00007	−	0.756679i
$724$	22.8591	−	4.03068i	0.849552	−	0.149799i
$725$	−14.0233	+	11.7670i	−0.520814	+	0.437015i
$726$	38.8705	−	19.9013i	1.44262	−	0.738607i
$727$	−5.87084	−	33.2952i	−0.217738	−	1.23485i	−0.876092	−	0.482143i	$-0.839859\pi$
$727$	−5.87084	−	33.2952i	−0.217738	−	1.23485i	0.658355	−	0.752708i	$-0.271253\pi$
$728$	13.2758	+	2.34088i	0.492033	+	0.0867586i
$729$	5.92298	+	26.3423i	0.219370	+	0.975642i
$730$	−17.7569	+	10.2519i	−0.657211	+	0.379441i
$731$	−4.97461	−	0.877158i	−0.183993	−	0.0324429i
$732$	1.14923	−	22.7806i	0.0424768	−	0.841996i
$733$	7.64098	−	13.2346i	0.282226	−	0.488830i	−0.689707	−	0.724089i	$-0.742261\pi$
$733$	7.64098	−	13.2346i	0.282226	−	0.488830i	0.971933	+	0.235259i	$0.0755939\pi$
$734$	9.12135			0.336675
$735$	−9.31790	−	18.1994i	−0.343696	−	0.671294i
$736$	1.67285	−	0.294969i	0.0616621	−	0.0108727i
$737$	46.1222	+	38.7011i	1.69893	+	1.42557i
$738$	10.5336	−	14.6181i	0.387747	−	0.538099i
$739$	18.3433	+	6.67640i	0.674768	+	0.245595i	0.656599	−	0.754240i	$-0.271994\pi$
$739$	18.3433	+	6.67640i	0.674768	+	0.245595i	0.0181685	+	0.999835i	$0.494216\pi$
$740$	13.0869	−	22.6671i	0.481083	−	0.833260i
$741$	−28.6979	−	9.76136i	−1.05424	−	0.358592i
$742$	3.01835	+	5.22793i	0.110807	+	0.191923i
$743$	8.09041	+	45.8830i	0.296808	+	1.68328i	0.659760	+	0.751476i	$0.270658\pi$
$743$	8.09041	+	45.8830i	0.296808	+	1.68328i	−0.362952	+	0.931808i	$0.618231\pi$
$744$	−2.47394	+	0.761649i	−0.0906989	+	0.0279234i
$745$	37.0107	−	13.4708i	1.35597	−	0.493532i
$746$	2.20673	+	2.62988i	0.0807942	+	0.0962867i
$747$	4.23132	−	0.312511i	0.154816	−	0.0114342i
$748$	9.58062	−	16.5941i	0.350302	−	0.606741i
$749$	6.27035			0.229114
$750$	6.15424	−	9.51738i	0.224721	−	0.347526i
$751$	1.93034	−	2.30049i	0.0704392	−	0.0839461i	−0.729674	−	0.683795i	$-0.760328\pi$
$751$	1.93034	−	2.30049i	0.0704392	−	0.0839461i	0.800113	+	0.599849i	$0.204773\pi$
$752$	1.50332	+	0.867940i	0.0548203	+	0.0316505i
$753$	−33.9485	+	25.6862i	−1.23715	+	0.936059i
$754$	−17.9550	+	21.3980i	−0.653884	+	0.779268i
$755$	5.70012	−	4.78297i	0.207449	−	0.174070i
$756$	−16.5289	−	5.58314i	−0.601150	−	0.203057i
$757$	0.0994676	+	0.564109i	0.00361521	+	0.0205029i	0.986562	−	0.163387i	$-0.0522420\pi$
$757$	0.0994676	+	0.564109i	0.00361521	+	0.0205029i	−0.982947	+	0.183890i	$0.941131\pi$
$758$	0.721873	+	0.860295i	0.0262196	+	0.0312473i
$759$	−6.88600	+	16.3110i	−0.249946	+	0.592051i
$760$	3.29830	−	11.5808i	0.119642	−	0.420080i
$761$	−19.9412	+	11.5130i	−0.722867	+	0.417348i	−0.815807	−	0.578324i	$-0.803707\pi$
$761$	−19.9412	+	11.5130i	−0.722867	+	0.417348i	0.0929398	+	0.995672i	$0.470374\pi$
$762$	−13.7905	+	4.24567i	−0.499577	+	0.153804i
$763$	−14.0081	+	38.4868i	−0.507126	+	1.39332i
$764$	0.882626	−	1.05187i	0.0319323	−	0.0380554i
$765$	10.8273	+	24.0650i	0.391463	+	0.870071i
$766$	−3.18239	+	18.0482i	−0.114984	+	0.652109i
$767$	−19.6641	+	11.3531i	−0.710030	+	0.409936i
$768$	1.04508	+	1.38124i	0.0377109	+	0.0498411i
$769$	6.71340	+	5.63321i	0.242092	+	0.203139i	0.755758	−	0.654851i	$-0.227269\pi$
$769$	6.71340	+	5.63321i	0.242092	+	0.203139i	−0.513666	+	0.857990i	$0.671713\pi$
$770$	−42.7566	−	35.8771i	−1.54084	−	1.29292i
$771$	−25.5659	−	33.7895i	−0.920733	−	1.21690i
$772$	19.6492	−	11.3445i	0.707189	−	0.408296i
$773$	6.64191	−	37.6682i	0.238893	−	1.35483i	−0.595365	−	0.803455i	$-0.702992\pi$
$773$	6.64191	−	37.6682i	0.238893	−	1.35483i	0.834258	−	0.551374i	$-0.185896\pi$
$774$	1.95272	+	4.34014i	0.0701892	+	0.156003i
$775$	2.52769	−	3.01238i	0.0907972	−	0.108208i
$776$	−3.42546	+	9.41138i	−0.122967	+	0.337849i
$777$	−52.6608	+	16.2126i	−1.88919	+	0.581626i
$778$	24.1757	−	13.9578i	0.866740	−	0.500413i
$779$	−6.37887	−	25.3904i	−0.228547	−	0.909705i
$780$	−7.47165	+	17.6982i	−0.267528	+	0.633698i
$781$	−34.1012	−	40.6402i	−1.22024	−	1.45422i
$782$	0.939230	+	5.32664i	0.0335868	+	0.190480i
$783$	27.1436	−	23.8765i	0.970035	−	0.853277i
$784$	3.27344	−	2.74674i	0.116909	−	0.0980979i
$785$	14.4894	−	17.2677i	0.517147	−	0.616312i
$786$	8.41113	−	6.36406i	0.300015	−	0.226998i
$787$	21.3744	+	12.3405i	0.761916	+	0.439893i	0.829983	−	0.557788i	$-0.188350\pi$
$787$	21.3744	+	12.3405i	0.761916	+	0.439893i	−0.0680669	+	0.997681i	$0.521683\pi$
$788$	12.1503	−	14.4802i	0.432836	−	0.515834i
$789$	−6.09065	+	9.41904i	−0.216833	+	0.335327i
$790$	−22.2229			−0.790656
$791$	28.6676	−	49.6537i	1.01930	−	1.76548i
$792$	−18.0040	+	1.32971i	−0.639743	+	0.0472493i
$793$	33.9867	+	40.5038i	1.20690	+	1.43833i
$794$	−16.4411	+	5.98408i	−0.583474	+	0.212367i
$795$	−8.22188	+	2.53126i	−0.291600	+	0.0897747i
$796$	3.27647	+	18.5818i	0.116132	+	0.658615i
$797$	−11.1134	−	19.2489i	−0.393655	−	0.681831i	0.599273	−	0.800545i	$-0.295456\pi$
$797$	−11.1134	−	19.2489i	−0.393655	−	0.681831i	−0.992929	+	0.118714i	$0.962123\pi$
$798$	−21.6793	+	13.1370i	−0.767437	+	0.465045i
$799$	−2.76366	+	4.78681i	−0.0977714	+	0.169345i
$800$	−2.47258	−	0.899945i	−0.0874188	−	0.0318179i
$801$	29.1706	−	40.4818i	1.03069	−	1.43035i
$802$	19.8976	+	16.6961i	0.702609	+	0.589559i
$803$	43.9863	−	7.75597i	1.55224	−	0.273702i
$804$	−7.89765	−	15.4254i	−0.278529	−	0.544012i
$805$	15.7553			0.555302
$806$	3.00018	−	5.19646i	0.105677	−	0.183038i
$807$	−1.56642	+	31.0504i	−0.0551408	+	1.09303i
$808$	14.1607	+	2.49692i	0.498173	+	0.0878413i
$809$	−5.97016	+	3.44688i	−0.209900	+	0.121186i	−0.601265	−	0.799050i	$-0.705336\pi$
$809$	−5.97016	+	3.44688i	−0.209900	+	0.121186i	0.391365	+	0.920236i	$0.372003\pi$
$810$	13.0097	−	21.1868i	0.457115	−	0.744427i
$811$	−18.8568	−	3.32497i	−0.662153	−	0.116756i	−0.167536	−	0.985866i	$-0.553581\pi$
$811$	−18.8568	−	3.32497i	−0.662153	−	0.116756i	−0.494618	+	0.869111i	$0.664692\pi$
$812$	4.05627	+	23.0043i	0.142347	+	0.807291i
$813$	−24.2290	+	12.4050i	−0.849748	+	0.435063i
$814$	−43.6767	+	36.6491i	−1.53087	+	1.28455i
$815$	−6.25940	+	1.10370i	−0.219257	+	0.0386610i
$816$	−4.39809	+	3.32769i	−0.153964	+	0.116493i
$817$	6.65048	+	1.89411i	0.232671	+	0.0662664i
$818$		−	9.05397i		−	0.316564i
$819$	36.8807	−	16.5934i	1.28872	−	0.579822i
$820$	−16.3393	+	2.88105i	−0.570592	+	0.100611i
$821$	4.55550	+	12.5161i	0.158988	+	0.436816i	0.993453	−	0.114246i	$-0.0364452\pi$
$821$	4.55550	+	12.5161i	0.158988	+	0.436816i	−0.834465	+	0.551062i	$0.814223\pi$
$822$	−3.70743	−	3.44371i	−0.129311	−	0.120113i
$823$	−43.5171	+	15.8389i	−1.51691	+	0.552110i	−0.960374	−	0.278713i	$-0.910092\pi$
$823$	−43.5171	+	15.8389i	−1.51691	+	0.552110i	−0.556536	+	0.830823i	$0.687870\pi$
$824$			3.52424i			0.122773i
$825$	21.8706	−	16.5478i	0.761436	−	0.576120i
$826$	−3.29725	+	18.6996i	−0.114726	+	0.650644i
$827$	−38.3602	+	13.9620i	−1.33391	+	0.485505i	−0.907890	−	0.419208i	$-0.862308\pi$
$827$	−38.3602	+	13.9620i	−1.33391	+	0.485505i	−0.426023	+	0.904712i	$0.640086\pi$
$828$	3.65187	−	3.55427i	0.126911	−	0.123519i
$829$	19.2367	+	11.1063i	0.668118	+	0.385738i	0.795363	−	0.606133i	$-0.207280\pi$
$829$	19.2367	+	11.1063i	0.668118	+	0.385738i	−0.127245	+	0.991871i	$0.540614\pi$
$830$	−2.99287	−	2.51132i	−0.103884	−	0.0871691i
$831$	−15.5664	−	3.56176i	−0.539994	−	0.123556i
$832$	−3.95400	−	0.697197i	−0.137080	−	0.0241709i
$833$	8.74608	+	10.4232i	0.303034	+	0.361142i
$834$	14.9341	−	16.0778i	0.517126	−	0.556728i
$835$	4.84269	+	2.79593i	0.167588	+	0.0967571i
$836$	−15.3798	+	21.2484i	−0.531921	+	0.734892i
$837$	−4.85156	+	6.06354i	−0.167694	+	0.209587i
$838$	8.30128	−	22.8076i	0.286763	−	0.787875i
$839$	31.9524	+	11.6297i	1.10312	+	0.401503i	0.828466	−	0.560040i	$-0.189214\pi$
$839$	31.9524	+	11.6297i	1.10312	+	0.401503i	0.274655	+	0.961543i	$0.411436\pi$
$840$	7.32134	+	14.2998i	0.252610	+	0.493389i
$841$	−18.2323	−	6.63602i	−0.628701	−	0.228828i
$842$	−3.01312	−	8.27847i	−0.103839	−	0.285295i
$843$	−5.54045	+	0.691278i	−0.190823	+	0.0238089i
$844$		−	17.6436i		−	0.607318i
$845$	−2.94802	−	8.09963i	−0.101415	−	0.278636i
$846$	5.19350	−	0.383574i	0.178556	−	0.0131876i
$847$	42.3258	+	73.3105i	1.45433	+	2.51898i
$848$	−0.898972	−	1.55707i	−0.0308708	−	0.0534698i
$849$	2.07337	−	41.0994i	0.0711580	−	1.41053i
$850$	2.86557	−	7.87310i	0.0982883	−	0.270045i
$851$	2.79476	−	15.8499i	0.0958030	−	0.543326i
$852$	4.49301	+	14.5939i	0.153928	+	0.499978i
$853$	−17.4731	+	14.6617i	−0.598268	+	0.502007i	−0.890888	−	0.454222i	$-0.849917\pi$
$853$	−17.4731	+	14.6617i	−0.598268	+	0.502007i	0.292620	+	0.956229i	$0.405473\pi$
$854$	44.2160			1.51304
$855$	−11.3586	−	34.2918i	−0.388457	−	1.17275i
$856$	−1.86753			−0.0638310
$857$	−5.60404	+	4.70235i	−0.191430	+	0.160629i	−0.733466	−	0.679727i	$-0.762098\pi$
$857$	−5.60404	+	4.70235i	−0.191430	+	0.160629i	0.542035	+	0.840356i	$0.317654\pi$
$858$	28.4803	−	30.6614i	0.972302	−	1.04676i
$859$	−4.63482	+	26.2854i	−0.158138	+	0.896845i	0.797723	+	0.603025i	$0.206038\pi$
$859$	−4.63482	+	26.2854i	−0.158138	+	0.896845i	−0.955861	+	0.293821i	$0.905073\pi$
$860$	1.49886	−	4.11809i	0.0511108	−	0.140426i
$861$	29.3297	+	18.9655i	0.999555	+	0.646344i
$862$	6.67215	+	11.5565i	0.227254	+	0.393616i
$863$	−7.69847	−	13.3341i	−0.262059	−	0.453900i	0.704730	−	0.709476i	$-0.251068\pi$
$863$	−7.69847	−	13.3341i	−0.262059	−	0.453900i	−0.966789	+	0.255576i	$0.917735\pi$
$864$	4.92290	+	1.66286i	0.167480	+	0.0565717i
$865$	4.57445	+	12.5682i	0.155536	+	0.427332i
$866$			22.3893i			0.760819i
$867$	7.17037	+	9.47680i	0.243518	+	0.321849i
$868$	−1.71620	−	4.71521i	−0.0582515	−	0.160045i
$869$	45.4901	+	16.5570i	1.54315	+	0.561659i
$870$	−33.2461	−	1.67719i	−1.12715	−	0.0568621i
$871$	37.7485	+	13.7393i	1.27906	+	0.465539i
$872$	4.17210	−	11.4628i	0.141285	−	0.388178i
$873$	7.38274	+	29.1250i	0.249868	+	0.985732i
$874$	−0.529729	−	7.38531i	−0.0179183	−	0.249812i
$875$	19.0269	+	10.9852i	0.643228	+	0.371368i
$876$	−12.5319	−	2.86743i	−0.423414	−	0.0968814i
$877$	−35.2710	−	42.0343i	−1.19102	−	1.41940i	−0.883868	−	0.467737i	$-0.845070\pi$
$877$	−35.2710	−	42.0343i	−1.19102	−	1.41940i	−0.307149	−	0.951662i	$-0.599375\pi$
$878$	−26.1115	−	4.60417i	−0.881222	−	0.155383i
$879$	8.25470	−	8.88684i	0.278424	−	0.299746i
$880$	12.7344	+	10.6855i	0.429278	+	0.360207i
$881$	−26.7129	−	15.4227i	−0.899980	−	0.519604i	−0.0227864	−	0.999740i	$-0.507254\pi$
$881$	−26.7129	−	15.4227i	−0.899980	−	0.519604i	−0.877194	+	0.480137i	$0.840587\pi$
$882$	3.48533	−	12.3366i	0.117357	−	0.415396i
$883$	−9.20055	+	3.34873i	−0.309623	+	0.112694i	−0.492158	−	0.870506i	$-0.663792\pi$
$883$	−9.20055	+	3.34873i	−0.309623	+	0.112694i	0.182535	+	0.983199i	$0.441570\pi$
$884$	2.21999	−	12.5902i	0.0746663	−	0.423454i
$885$	−24.9289	−	10.5242i	−0.837976	−	0.353768i
$886$			3.81393i			0.128132i
$887$	−5.74930	+	2.09257i	−0.193043	+	0.0702617i	−0.436732	−	0.899591i	$-0.643864\pi$
$887$	−5.74930	+	2.09257i	−0.193043	+	0.0702617i	0.243690	+	0.969853i	$0.421642\pi$
$888$	15.6843	−	4.82871i	0.526330	−	0.162041i
$889$	−9.56660	−	26.2840i	−0.320854	−	0.881538i
$890$	−45.2483	+	7.97849i	−1.51673	+	0.267440i
$891$	−42.4158	+	33.6763i	−1.42098	+	1.12820i
$892$		−	4.72341i		−	0.158152i
$893$	4.43652	−	6.12941i	0.148462	−	0.205113i
$894$	22.7504	+	9.60454i	0.760888	+	0.321224i
$895$	−16.5533	+	2.91879i	−0.553314	+	0.0975643i
$896$	−2.57204	+	2.15819i	−0.0859257	+	0.0721002i
$897$	−0.595171	+	11.7978i	−0.0198722	+	0.393916i
$898$	0.0428252	+	0.242874i	0.00142910	+	0.00810481i
$899$	10.2395	+	1.80549i	0.341505	+	0.0602166i
$900$	−7.65178	+	1.93961i	−0.255059	+	0.0646537i
$901$	4.95795	−	2.86248i	0.165173	−	0.0953629i
$902$	35.5928	+	6.27598i	1.18511	+	0.208967i
$903$	−8.21189	+	4.20441i	−0.273275	+	0.139914i
$904$	−8.53824	+	14.7887i	−0.283977	+	0.491863i
$905$	−64.1219			−2.13148
$906$	4.65951	+	0.235062i	0.154802	+	0.00780941i
$907$	−17.7707	+	3.13346i	−0.590067	+	0.104045i	−0.460706	−	0.887553i	$-0.652404\pi$
$907$	−17.7707	+	3.13346i	−0.590067	+	0.104045i	−0.129361	+	0.991598i	$0.541293\pi$
$908$	5.34425	+	4.48436i	0.177355	+	0.148819i
$909$	39.3392	−	17.6996i	1.30480	−	0.587057i
$910$	−34.9939	−	12.7367i	−1.16004	−	0.422219i
$911$	2.38906	−	4.13797i	0.0791531	−	0.137097i	−0.823732	−	0.566980i	$-0.808112\pi$
$911$	2.38906	−	4.13797i	0.0791531	−	0.137097i	0.902885	+	0.429883i	$0.141445\pi$
$912$	6.45686	−	3.91267i	0.213808	−	0.129561i
$913$	4.25534	+	7.37046i	0.140831	+	0.243927i
$914$	3.22410	+	18.2848i	0.106644	+	0.604806i
$915$	−14.0543	+	61.4235i	−0.464622	+	2.03060i
$916$	1.46838	−	0.534447i	0.0485167	−	0.0176586i
$917$	13.1425	+	15.6626i	0.434002	+	0.517224i
$918$	−5.29482	+	15.6753i	−0.174755	+	0.517362i
$919$	−2.46699	+	4.27296i	−0.0813786	+	0.140952i	−0.903842	−	0.427866i	$-0.859266\pi$
$919$	−2.46699	+	4.27296i	−0.0813786	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$920$	−4.69250			−0.154707
$921$	12.0903	+	0.609927i	0.398388	+	0.0200978i
$922$	−3.14482	+	3.74786i	−0.103569	+	0.123429i
$923$	−30.6542	−	17.6982i	−1.00900	−	0.582544i
$924$	−4.33277	−	34.7262i	−0.142538	−	1.14241i
$925$	−16.0250	+	19.0979i	−0.526900	+	0.627935i
$926$	28.2744	−	23.7251i	0.929155	−	0.779654i
$927$	5.94642	+	8.74200i	0.195306	+	0.287125i
$928$	−1.20810	−	6.85149i	−0.0396579	−	0.224911i
$929$	−24.2067	−	28.8484i	−0.794195	−	0.946485i	0.205286	−	0.978702i	$-0.434188\pi$
$929$	−24.2067	−	28.8484i	−0.794195	−	0.946485i	−0.999481	+	0.0322175i	$0.989743\pi$
$930$	7.09572	−	0.885328i	0.232678	−	0.0290310i
$931$	−10.4434	−	15.4232i	−0.342267	−	0.505476i
$932$	−18.5437	+	10.7062i	−0.607419	+	0.350694i
$933$	1.00572	−	4.39546i	0.0329259	−	0.143901i
$934$	−7.14868	+	19.6408i	−0.233912	+	0.642668i
$935$	−34.0243	+	40.5486i	−1.11271	+	1.32608i
$936$	−10.9844	+	4.94212i	−0.359037	+	0.161538i
$937$	10.0234	−	56.8457i	0.327451	−	1.85707i	−0.164407	−	0.986393i	$-0.552571\pi$
$937$	10.0234	−	56.8457i	0.327451	−	1.85707i	0.491858	−	0.870675i	$-0.336318\pi$
$938$	29.0926	−	16.7966i	0.949906	−	0.548428i
$939$	7.43583	−	17.6134i	0.242659	−	0.574790i
$940$	−3.67343	−	3.08238i	−0.119814	−	0.100536i
$941$	−27.6380	−	23.1910i	−0.900972	−	0.756005i	0.0694084	−	0.997588i	$-0.477889\pi$
$941$	−27.6380	−	23.1910i	−0.900972	−	0.756005i	−0.970380	+	0.241583i	$0.922333\pi$
$942$	14.0246	−	1.74984i	0.456945	−	0.0570128i
$943$	−8.83527	+	5.10104i	−0.287716	+	0.166113i
$944$	0.982040	−	5.56942i	0.0319627	−	0.181269i
$945$	42.2887	+	23.1179i	1.37565	+	0.752024i
$946$	−6.13632	+	7.31298i	−0.199509	+	0.237765i
$947$	−14.3989	+	39.5607i	−0.467902	+	1.28555i	0.451513	+	0.892264i	$0.350884\pi$
$947$	−14.3989	+	39.5607i	−0.467902	+	1.28555i	−0.919416	+	0.393287i	$0.871338\pi$
$948$	−10.2090	−	9.48276i	−0.331571	−	0.307986i
$949$	25.8079	−	14.9002i	0.837761	−	0.483682i
$950$	−5.00938	+	10.3176i	−0.162526	+	0.334748i
$951$	−5.56643	−	7.35693i	−0.180504	−	0.238565i
$952$	−6.87205	−	8.18979i	−0.222724	−	0.265433i
$953$	−8.26753	−	46.8875i	−0.267812	−	1.51883i	−0.760908	−	0.648860i	$-0.775246\pi$
$953$	−8.26753	−	46.8875i	−0.267812	−	1.51883i	0.493096	−	0.869975i	$-0.335865\pi$
$954$	−4.85715	−	2.34553i	−0.157256	−	0.0759393i
$955$	−2.90577	+	2.43823i	−0.0940286	+	0.0788993i
$956$	−17.6597	+	21.0461i	−0.571157	+	0.680678i
$957$	66.8048	+	28.2030i	2.15949	+	0.911672i
$958$	13.8693	+	8.00747i	0.448098	+	0.258709i
$959$	6.30500	−	7.51401i	0.203599	−	0.242640i
$960$	−2.18056	−	4.25898i	−0.0703772	−	0.137458i
$961$	28.7665			0.927952
$962$	−19.0205	+	32.9445i	−0.613247	+	1.06217i
$963$	−4.63248	+	3.15107i	−0.149280	+	0.101542i
$964$	−12.5141	−	14.9138i	−0.403053	−	0.480340i
$965$	−58.8976	+	21.4370i	−1.89598	+	0.690081i
$966$	7.23781	+	6.72297i	0.232873	+	0.216308i
$967$	5.31043	+	30.1169i	0.170772	+	0.968495i	0.942912	+	0.333043i	$0.108075\pi$
$967$	5.31043	+	30.1169i	0.170772	+	0.968495i	−0.772140	+	0.635453i	$0.780814\pi$
$968$	−12.6061	−	21.8345i	−0.405177	−	0.701787i
$969$	12.4586	+	20.5597i	0.400227	+	0.660473i
$970$	13.8336	−	23.9605i	0.444170	−	0.769326i
$971$	−17.5799	−	6.39858i	−0.564167	−	0.205340i	0.0441627	−	0.999024i	$-0.485938\pi$
$971$	−17.5799	−	6.39858i	−0.564167	−	0.205340i	−0.608330	+	0.793684i	$0.708160\pi$
$972$	15.0171	−	4.18157i	0.481675	−	0.134124i
$973$	32.5855	+	27.3425i	1.04464	+	0.876561i
$974$	5.38644	−	0.949774i	0.172593	−	0.0304327i
$975$	9.93593	−	15.3657i	0.318204	−	0.492095i
$976$	−13.1691			−0.421533
$977$	−7.25243	+	12.5616i	−0.232026	+	0.401881i	−0.958404	−	0.285415i	$-0.907869\pi$
$977$	−7.25243	+	12.5616i	−0.232026	+	0.401881i	0.726378	+	0.687295i	$0.241202\pi$
$978$	−3.34646	−	2.16393i	−0.107008	−	0.0691947i
$979$	98.5671	+	17.3800i	3.15022	+	0.555468i
$980$	−10.2230	+	5.90226i	−0.326562	+	0.188541i
$981$	−8.99194	−	35.4733i	−0.287091	−	1.13258i
$982$	24.9804	+	4.40472i	0.797157	+	0.140560i
$983$	0.103547	+	0.587242i	0.00330263	+	0.0187301i	0.986415	−	0.164275i	$-0.0525285\pi$
$983$	0.103547	+	0.587242i	0.00330263	+	0.0187301i	−0.983112	+	0.183005i	$0.941417\pi$
$984$	−8.73545	−	5.64862i	−0.278476	−	0.180071i
$985$	−40.0011	+	33.5649i	−1.27454	+	1.06947i
$986$	21.8163	−	3.84680i	0.694772	−	0.122507i
$987$	1.24985	+	10.0173i	0.0397831	+	0.318853i
$988$	−4.79377	+	16.8316i	−0.152510	+	0.535485i
$989$		−	2.69475i		−	0.0856880i
$990$	49.6177	+	5.01898i	1.57695	+	0.159514i
$991$	−26.4619	+	4.66594i	−0.840589	+	0.148219i	−0.577334	−	0.816508i	$-0.695907\pi$
$991$	−26.4619	+	4.66594i	−0.840589	+	0.148219i	−0.263255	+	0.964726i	$0.584796\pi$
$992$	0.511144	+	1.40436i	0.0162288	+	0.0445884i
$993$	5.55290	−	24.2686i	0.176216	−	0.770140i
$994$	−27.8153	+	10.1239i	−0.882247	+	0.321112i
$995$		−	52.1236i		−	1.65243i
$996$	−0.303285	−	2.43076i	−0.00960994	−	0.0770216i
$997$	2.43597	−	13.8151i	0.0771481	−	0.437528i	−0.921628	−	0.388074i	$-0.873141\pi$
$997$	2.43597	−	13.8151i	0.0771481	−	0.437528i	0.998776	−	0.0494546i	$-0.0157483\pi$
$998$	−32.1152	+	11.6890i	−1.01659	+	0.370008i
$999$	30.7579	−	38.4417i	0.973138	−	1.21624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.a.281.2	yes	12
9.5	odd	6		342.2.bf.a.167.2	yes	12
19.14	odd	18		342.2.bf.a.299.2	yes	12
171.14	even	18	inner	342.2.x.a.185.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.a.185.2	✓	12	171.14	even	18	inner
342.2.x.a.281.2	yes	12	1.1	even	1	trivial
342.2.bf.a.167.2	yes	12	9.5	odd	6
342.2.bf.a.299.2	yes	12	19.14	odd	18

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.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.68842 + 0.386327i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.944822 + 2.59588i) q^{5} +(-1.54173 + 0.789350i) q^{6} +(-1.67878 - 2.90773i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.70150 + 1.30456i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.68842 + 0.386327i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.944822 + 2.59588i) q^{5} +(-1.54173 + 0.789350i) q^{6} +(-1.67878 - 2.90773i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.70150 + 1.30456i) q^{9} +(-0.944822 - 2.59588i) q^{10} +6.01766i q^{11} +(0.673648 - 1.59568i) q^{12} +(1.37321 + 3.77286i) q^{13} +(3.15507 + 1.14835i) q^{14} +(-2.59811 + 4.01791i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.08905 - 2.99214i) q^{17} +(-2.90803 + 0.737141i) q^{18} +(-1.90379 + 3.92117i) q^{19} +(2.39237 + 1.38124i) q^{20} +(-1.71114 - 5.55801i) q^{21} +(-3.86808 - 4.60980i) q^{22} +(1.67285 + 0.294969i) q^{23} +(0.509640 + 1.65538i) q^{24} +(-2.01566 - 1.69134i) q^{25} +(-3.47709 - 2.00750i) q^{26} +(4.05728 + 3.24631i) q^{27} +(-3.15507 + 1.14835i) q^{28} +(1.20810 - 6.85149i) q^{29} +(-0.592396 - 4.74793i) q^{30} +1.49449i q^{31} +(0.939693 - 0.342020i) q^{32} +(-2.32479 + 10.1603i) q^{33} +(1.08905 + 2.99214i) q^{34} +(9.13425 - 1.61061i) q^{35} +(1.75385 - 2.43393i) q^{36} -9.47475i q^{37} +(-1.06209 - 4.22752i) q^{38} +(0.860992 + 6.90067i) q^{39} +(-2.72051 + 0.479699i) q^{40} +(-4.60084 + 3.86056i) q^{41} +(4.88343 + 3.15778i) q^{42} +(-0.275475 - 1.56230i) q^{43} +(5.92624 + 1.04496i) q^{44} +(-5.93892 + 5.78019i) q^{45} +(-1.47108 + 0.849329i) q^{46} +(-1.70951 - 0.301432i) q^{47} +(-1.45446 - 0.940501i) q^{48} +(-2.13659 + 3.70068i) q^{49} +2.63126 q^{50} +(2.99471 - 4.63124i) q^{51} +(3.95400 - 0.697197i) q^{52} +(1.37731 + 1.15570i) q^{53} +(-5.19474 + 0.121152i) q^{54} +(-15.6211 - 5.68562i) q^{55} +(1.67878 - 2.90773i) q^{56} +(-4.72925 + 5.88508i) q^{57} +(3.47859 + 6.02510i) q^{58} +(0.982040 + 5.56942i) q^{59} +(3.50571 + 3.25634i) q^{60} +(12.3749 - 4.50411i) q^{61} +(-0.960637 - 1.14484i) q^{62} +(-0.741913 - 10.0453i) q^{63} +(-0.500000 + 0.866025i) q^{64} -11.0913 q^{65} +(-4.75004 - 9.27760i) q^{66} +(6.43126 - 7.66447i) q^{67} +(-2.75757 - 1.59208i) q^{68} +(2.71052 + 1.14430i) q^{69} +(-5.96196 + 7.10518i) q^{70} +(-6.75349 + 5.66685i) q^{71} +(0.220968 + 2.99185i) q^{72} +(-1.28887 - 7.30952i) q^{73} +(6.09025 + 7.25808i) q^{74} +(-2.74987 - 3.63440i) q^{75} +(3.53101 + 2.55577i) q^{76} +(17.4977 - 10.1023i) q^{77} +(-5.09522 - 4.73279i) q^{78} +(2.75141 - 7.55942i) q^{79} +(1.77568 - 2.11618i) q^{80} +(5.59624 + 7.04855i) q^{81} +(1.04293 - 5.91472i) q^{82} +(1.22480 - 0.707141i) q^{83} +(-5.77071 + 0.720008i) q^{84} +(6.73826 + 5.65407i) q^{85} +(1.21525 + 1.01972i) q^{86} +(4.68670 - 11.1015i) q^{87} +(-5.21145 + 3.00883i) q^{88} +(2.88817 - 16.3796i) q^{89} +(0.834042 - 8.24535i) q^{90} +(8.66514 - 10.3267i) q^{91} +(0.580975 - 1.59622i) q^{92} +(-0.577360 + 2.52332i) q^{93} +(1.50332 - 0.867940i) q^{94} +(-8.38013 - 8.64682i) q^{95} +(1.71872 - 0.214444i) q^{96} +(6.43776 + 7.67222i) q^{97} +(-0.742029 - 4.20825i) q^{98} +(-7.85041 + 16.2567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 9 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^3 + 9 * q^5 + 3 * q^6 - 9 * q^7 + 6 * q^8	\( 12 q + 6 q^{3} + 9 q^{5} + 3 q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{10} + 6 q^{12} - 12 q^{13} + 3 q^{14} + 9 q^{15} - 9 q^{18} + 15 q^{19} + 9 q^{20} + 15 q^{21} - 27 q^{22} + 18 q^{23} + 3 q^{24} + 9 q^{25} - 18 q^{26} + 9 q^{27} - 3 q^{28} - 45 q^{29} - 9 q^{33} + 18 q^{35} + 9 q^{36} - 9 q^{38} - 36 q^{41} + 3 q^{42} + 12 q^{43} + 18 q^{44} - 18 q^{45} - 27 q^{46} + 27 q^{47} + 6 q^{48} + 3 q^{49} - 6 q^{50} + 36 q^{51} - 15 q^{52} - 27 q^{54} - 9 q^{55} + 9 q^{56} - 42 q^{57} + 9 q^{58} - 36 q^{59} + 9 q^{60} - 3 q^{61} + 6 q^{62} - 9 q^{63} - 6 q^{64} - 54 q^{65} + 30 q^{67} - 27 q^{68} + 9 q^{69} - 9 q^{71} + 9 q^{72} - 24 q^{73} + 21 q^{74} - 24 q^{75} + 27 q^{77} - 54 q^{78} + 6 q^{79} + 9 q^{80} + 36 q^{81} + 45 q^{83} - 12 q^{84} - 18 q^{85} + 33 q^{86} - 36 q^{87} - 9 q^{88} - 9 q^{89} - 18 q^{90} + 6 q^{91} + 18 q^{92} + 9 q^{93} + 36 q^{94} + 3 q^{96} + 45 q^{97} + 6 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 9 * q^5 + 3 * q^6 - 9 * q^7 + 6 * q^8 + 9 * q^10 + 6 * q^12 - 12 * q^13 + 3 * q^14 + 9 * q^15 - 9 * q^18 + 15 * q^19 + 9 * q^20 + 15 * q^21 - 27 * q^22 + 18 * q^23 + 3 * q^24 + 9 * q^25 - 18 * q^26 + 9 * q^27 - 3 * q^28 - 45 * q^29 - 9 * q^33 + 18 * q^35 + 9 * q^36 - 9 * q^38 - 36 * q^41 + 3 * q^42 + 12 * q^43 + 18 * q^44 - 18 * q^45 - 27 * q^46 + 27 * q^47 + 6 * q^48 + 3 * q^49 - 6 * q^50 + 36 * q^51 - 15 * q^52 - 27 * q^54 - 9 * q^55 + 9 * q^56 - 42 * q^57 + 9 * q^58 - 36 * q^59 + 9 * q^60 - 3 * q^61 + 6 * q^62 - 9 * q^63 - 6 * q^64 - 54 * q^65 + 30 * q^67 - 27 * q^68 + 9 * q^69 - 9 * q^71 + 9 * q^72 - 24 * q^73 + 21 * q^74 - 24 * q^75 + 27 * q^77 - 54 * q^78 + 6 * q^79 + 9 * q^80 + 36 * q^81 + 45 * q^83 - 12 * q^84 - 18 * q^85 + 33 * q^86 - 36 * q^87 - 9 * q^88 - 9 * q^89 - 18 * q^90 + 6 * q^91 + 18 * q^92 + 9 * q^93 + 36 * q^94 + 3 * q^96 + 45 * q^97 + 6 * q^98 - 27 * q^99

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