LMFDB - Embedded newform 228.2.v.a.23.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(23,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 2]))

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

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

chi := DirichletCharacter("228.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.v (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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.20
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.245722 + 1.39270i) q^{2} +(1.12016 - 1.32107i) q^{3} +(-1.87924 + 0.684435i) q^{4} +(0.218260 + 0.260112i) q^{5} +(2.11511 + 1.23544i) q^{6} +(3.52551 + 2.03545i) q^{7} +(-1.41498 - 2.44904i) q^{8} +(-0.490465 - 2.95964i) q^{9} +O(q^{10})$	\(q+(0.245722 + 1.39270i) q^{2} +(1.12016 - 1.32107i) q^{3} +(-1.87924 + 0.684435i) q^{4} +(0.218260 + 0.260112i) q^{5} +(2.11511 + 1.23544i) q^{6} +(3.52551 + 2.03545i) q^{7} +(-1.41498 - 2.44904i) q^{8} +(-0.490465 - 2.95964i) q^{9} +(-0.308628 + 0.367887i) q^{10} +(1.08725 + 1.88317i) q^{11} +(-1.20087 + 3.24929i) q^{12} +(0.347438 - 1.97042i) q^{13} +(-1.96849 + 5.41014i) q^{14} +(0.588114 + 0.00303100i) q^{15} +(3.06310 - 2.57244i) q^{16} +(-0.940649 + 2.58441i) q^{17} +(4.00137 - 1.41032i) q^{18} +(-2.64686 + 3.46326i) q^{19} +(-0.588193 - 0.339429i) q^{20} +(6.63813 - 2.37741i) q^{21} +(-2.35553 + 1.97695i) q^{22} +(1.64563 + 1.38085i) q^{23} +(-4.82038 - 0.874034i) q^{24} +(0.848220 - 4.81049i) q^{25} +(2.82958 - 0.000297014i) q^{26} +(-4.45929 - 2.66734i) q^{27} +(-8.01842 - 1.41213i) q^{28} +(-1.84632 - 5.07272i) q^{29} +(0.140291 + 0.819813i) q^{30} +(-3.62030 - 2.09018i) q^{31} +(4.33531 + 3.63388i) q^{32} +(3.70569 + 0.673124i) q^{33} +(-3.83046 - 0.674998i) q^{34} +(0.240031 + 1.36129i) q^{35} +(2.94738 + 5.22618i) q^{36} -9.21054 q^{37} +(-5.47368 - 2.83529i) q^{38} +(-2.21388 - 2.66618i) q^{39} +(0.328192 - 0.902583i) q^{40} +(-11.0765 + 1.95309i) q^{41} +(4.94216 + 8.66076i) q^{42} +(-2.45526 - 2.92607i) q^{43} +(-3.33210 - 2.79478i) q^{44} +(0.662789 - 0.773546i) q^{45} +(-1.51874 + 2.63118i) q^{46} +(11.9828 - 4.36138i) q^{47} +(0.0327969 - 6.92813i) q^{48} +(4.78614 + 8.28983i) q^{49} +(6.90801 - 0.000725118i) q^{50} +(2.36051 + 4.13763i) q^{51} +(0.695703 + 3.94069i) q^{52} +(3.14955 - 3.75349i) q^{53} +(2.61906 - 6.86589i) q^{54} +(-0.252532 + 0.693826i) q^{55} +(-0.00362587 - 11.5143i) q^{56} +(1.61030 + 7.37611i) q^{57} +(6.61111 - 3.81785i) q^{58} +(0.0500092 + 0.0182019i) q^{59} +(-1.10728 + 0.396830i) q^{60} +(-5.42537 - 4.55243i) q^{61} +(2.02141 - 5.55560i) q^{62} +(4.29506 - 11.4325i) q^{63} +(-3.99564 + 6.93072i) q^{64} +(0.588362 - 0.339691i) q^{65} +(-0.0268915 + 5.32633i) q^{66} +(1.18364 + 3.25203i) q^{67} +(-0.00115476 - 5.50055i) q^{68} +(3.66757 - 0.627220i) q^{69} +(-1.83689 + 0.668790i) q^{70} +(-3.65424 + 3.06627i) q^{71} +(-6.55428 + 5.38901i) q^{72} +(0.198992 + 1.12854i) q^{73} +(-2.26323 - 12.8275i) q^{74} +(-5.40487 - 6.50910i) q^{75} +(2.60371 - 8.31990i) q^{76} +8.85216i q^{77} +(3.16920 - 3.73841i) q^{78} +(0.357871 - 0.0631023i) q^{79} +(1.33767 + 0.235289i) q^{80} +(-8.51889 + 2.90320i) q^{81} +(-5.44182 - 14.9464i) q^{82} +(-5.84559 + 10.1249i) q^{83} +(-10.8475 + 9.01109i) q^{84} +(-0.877544 + 0.319400i) q^{85} +(3.47183 - 4.13845i) q^{86} +(-8.76961 - 3.24316i) q^{87} +(3.07352 - 5.32737i) q^{88} +(11.7753 + 2.07631i) q^{89} +(1.24018 + 0.732990i) q^{90} +(5.23559 - 6.23953i) q^{91} +(-4.03763 - 1.46862i) q^{92} +(-6.81661 + 2.44133i) q^{93} +(9.01854 + 15.6168i) q^{94} +(-1.47854 + 0.0674103i) q^{95} +(9.65688 - 1.65672i) q^{96} +(13.6314 + 4.96143i) q^{97} +(-10.3692 + 8.70266i) q^{98} +(5.04023 - 4.14148i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.245722	+	1.39270i	0.173752	+	0.984790i
$2$	0.245722	+	1.39270i	0.173752	+	0.984790i
$3$	1.12016	−	1.32107i	0.646727	−	0.762722i
$3$	1.12016	−	1.32107i	0.646727	−	0.762722i
$4$	−1.87924	+	0.684435i	−0.939621	+	0.342217i
$5$	0.218260	+	0.260112i	0.0976089	+	0.116326i	0.812638	−	0.582769i	$-0.198031\pi$
$5$	0.218260	+	0.260112i	0.0976089	+	0.116326i	−0.715029	+	0.699095i	$0.753586\pi$
$6$	2.11511	+	1.23544i	0.863490	+	0.504366i
$7$	3.52551	+	2.03545i	1.33252	+	0.769329i	0.985685	−	0.168599i	$-0.0539241\pi$
$7$	3.52551	+	2.03545i	1.33252	+	0.769329i	0.346832	+	0.937927i	$0.387257\pi$
$8$	−1.41498	−	2.44904i	−0.500273	−	0.865868i
$9$	−0.490465	−	2.95964i	−0.163488	−	0.986545i
$10$	−0.308628	+	0.367887i	−0.0975967	+	0.116336i
$11$	1.08725	+	1.88317i	0.327817	+	0.567796i	0.982078	−	0.188473i	$-0.0603537\pi$
$11$	1.08725	+	1.88317i	0.327817	+	0.567796i	−0.654261	+	0.756269i	$0.727020\pi$
$12$	−1.20087	+	3.24929i	−0.346662	+	0.937990i
$13$	0.347438	−	1.97042i	0.0963619	−	0.546496i	−0.897960	−	0.440078i	$-0.854951\pi$
$13$	0.347438	−	1.97042i	0.0963619	−	0.546496i	0.994322	−	0.106418i	$-0.0339381\pi$
$14$	−1.96849	+	5.41014i	−0.526100	+	1.44592i
$15$	0.588114	+	0.00303100i	0.151850	+	0.000782600i
$16$	3.06310	−	2.57244i	0.765774	−	0.643109i
$17$	−0.940649	+	2.58441i	−0.228141	+	0.626812i	−0.999959	−	0.00903105i	$-0.997125\pi$
$17$	−0.940649	+	2.58441i	−0.228141	+	0.626812i	0.771818	+	0.635843i	$0.219348\pi$
$18$	4.00137	−	1.41032i	0.943133	−	0.332415i
$19$	−2.64686	+	3.46326i	−0.607231	+	0.794525i
$19$	−2.64686	+	3.46326i	−0.607231	+	0.794525i
$20$	−0.588193	−	0.339429i	−0.131524	−	0.0758986i
$21$	6.63813	−	2.37741i	1.44856	−	0.518793i
$22$	−2.35553	+	1.97695i	−0.502201	+	0.421486i
$23$	1.64563	+	1.38085i	0.343137	+	0.287926i	0.798027	−	0.602621i	$-0.205877\pi$
$23$	1.64563	+	1.38085i	0.343137	+	0.287926i	−0.454890	+	0.890548i	$0.650321\pi$
$24$	−4.82038	−	0.874034i	−0.983956	−	0.178411i
$25$	0.848220	−	4.81049i	0.169644	−	0.962099i
$26$	2.82958		0.000297014i	0.554926		5.82493e-5i
$27$	−4.45929	−	2.66734i	−0.858192	−	0.513329i
$28$	−8.01842	−	1.41213i	−1.51534	−	0.266867i
$29$	−1.84632	−	5.07272i	−0.342853	−	0.941980i	−0.984563	−	0.175033i	$-0.943997\pi$
$29$	−1.84632	−	5.07272i	−0.342853	−	0.941980i	0.641710	−	0.766948i	$-0.278225\pi$
$30$	0.140291	+	0.819813i	0.0256136	+	0.149677i
$31$	−3.62030	−	2.09018i	−0.650225	−	0.375408i	0.138317	−	0.990388i	$-0.455831\pi$
$31$	−3.62030	−	2.09018i	−0.650225	−	0.375408i	−0.788542	+	0.614980i	$0.789164\pi$
$32$	4.33531	+	3.63388i	0.766382	+	0.642385i
$33$	3.70569	+	0.673124i	0.645078	+	0.117176i
$34$	−3.83046	−	0.674998i	−0.656918	−	0.115761i
$35$	0.240031	+	1.36129i	0.0405727	+	0.230099i
$36$	2.94738	+	5.22618i	0.491230	+	0.871030i
$37$	−9.21054			−1.51420			−0.757102	−	0.653297i	$-0.773385\pi$
$37$	−9.21054			−1.51420			−0.757102	+	0.653297i	$0.773385\pi$
$38$	−5.47368	−	2.83529i	−0.887948	−	0.459945i
$39$	−2.21388	−	2.66618i	−0.354504	−	0.426931i
$40$	0.328192	−	0.902583i	0.0518917	−	0.142711i
$41$	−11.0765	+	1.95309i	−1.72986	+	0.305022i	−0.947963	−	0.318381i	$-0.896861\pi$
$41$	−11.0765	+	1.95309i	−1.72986	+	0.305022i	−0.781901	+	0.623403i	$0.785750\pi$
$42$	4.94216	+	8.66076i	0.762592	+	1.33638i
$43$	−2.45526	−	2.92607i	−0.374424	−	0.446221i	0.545622	−	0.838031i	$-0.316293\pi$
$43$	−2.45526	−	2.92607i	−0.374424	−	0.446221i	−0.920046	+	0.391810i	$0.871849\pi$
$44$	−3.33210	−	2.79478i	−0.502334	−	0.421328i
$45$	0.662789	−	0.773546i	0.0988027	−	0.115313i
$46$	−1.51874	+	2.63118i	−0.223926	+	0.387946i
$47$	11.9828	−	4.36138i	1.74787	−	0.636173i	0.748242	−	0.663426i	$-0.230898\pi$
$47$	11.9828	−	4.36138i	1.74787	−	0.636173i	0.999629	+	0.0272526i	$0.00867586\pi$
$48$	0.0327969	−	6.92813i	0.00473382	−	0.999989i
$49$	4.78614	+	8.28983i	0.683734	+	1.18426i
$50$	6.90801		0.000725118i	0.976941		0.000102547i
$51$	2.36051	+	4.13763i	0.330538	+	0.579384i
$52$	0.695703	+	3.94069i	0.0964767	+	0.546475i
$53$	3.14955	−	3.75349i	0.432624	−	0.515581i	−0.505053	−	0.863088i	$-0.668527\pi$
$53$	3.14955	−	3.75349i	0.432624	−	0.515581i	0.937677	+	0.347507i	$0.112972\pi$
$54$	2.61906	−	6.86589i	0.356409	−	0.934330i
$55$	−0.252532	+	0.693826i	−0.0340514	+	0.0935555i
$56$	−0.00362587	−	11.5143i	−0.000484528	−	1.53866i
$57$	1.61030	+	7.37611i	0.213289	+	0.976989i
$58$	6.61111	−	3.81785i	0.868081	−	0.501308i
$59$	0.0500092	+	0.0182019i	0.00651065	+	0.00236968i	0.345273	−	0.938502i	$-0.387786\pi$
$59$	0.0500092	+	0.0182019i	0.00651065	+	0.00236968i	−0.338763	+	0.940872i	$0.610008\pi$
$60$	−1.10728	+	0.396830i	−0.142950	+	0.0512305i
$61$	−5.42537	−	4.55243i	−0.694648	−	0.582879i	0.225597	−	0.974221i	$-0.427567\pi$
$61$	−5.42537	−	4.55243i	−0.694648	−	0.582879i	−0.920245	+	0.391342i	$0.872011\pi$
$62$	2.02141	−	5.55560i	0.256720	−	0.705562i
$63$	4.29506	−	11.4325i	0.541127	−	1.44036i
$64$	−3.99564	+	6.93072i	−0.499454	+	0.866340i
$65$	0.588362	−	0.339691i	0.0729773	−	0.0421335i
$66$	−0.0268915	+	5.32633i	−0.00331011	+	0.655626i
$67$	1.18364	+	3.25203i	0.144605	+	0.397299i	0.990758	−	0.135641i	$-0.0433093\pi$
$67$	1.18364	+	3.25203i	0.144605	+	0.397299i	−0.846153	+	0.532940i	$0.821087\pi$
$68$	−0.00115476	−	5.50055i	−0.000140035	−	0.667040i
$69$	3.66757	−	0.627220i	0.441524	−	0.0755084i
$70$	−1.83689	+	0.668790i	−0.219550	+	0.0799357i
$71$	−3.65424	+	3.06627i	−0.433679	+	0.363900i	−0.833338	−	0.552764i	$-0.813573\pi$
$71$	−3.65424	+	3.06627i	−0.433679	+	0.363900i	0.399659	+	0.916664i	$0.369129\pi$
$72$	−6.55428	+	5.38901i	−0.772429	+	0.635101i
$73$	0.198992	+	1.12854i	0.0232903	+	0.132086i	0.994236	−	0.107214i	$-0.0341931\pi$
$73$	0.198992	+	1.12854i	0.0232903	+	0.132086i	−0.970946	+	0.239300i	$0.923082\pi$
$74$	−2.26323	−	12.8275i	−0.263095	−	1.49117i
$75$	−5.40487	−	6.50910i	−0.624100	−	0.751606i
$76$	2.60371	−	8.31990i	0.298666	−	0.954358i
$77$			8.85216i			1.00880i
$78$	3.16920	−	3.73841i	0.358841	−	0.423292i
$79$	0.357871	−	0.0631023i	0.0402636	−	0.00709956i	−0.153480	−	0.988152i	$-0.549048\pi$
$79$	0.357871	−	0.0631023i	0.0402636	−	0.00709956i	0.193744	+	0.981052i	$0.437937\pi$
$80$	1.33767	+	0.235289i	0.149557	+	0.0263061i
$81$	−8.51889	+	2.90320i	−0.946543	+	0.322577i
$82$	−5.44182	−	14.9464i	−0.600949	−	1.65055i
$83$	−5.84559	+	10.1249i	−0.641637	+	1.11135i	0.343430	+	0.939178i	$0.388411\pi$
$83$	−5.84559	+	10.1249i	−0.641637	+	1.11135i	−0.985067	+	0.172170i	$0.944922\pi$
$84$	−10.8475	+	9.01109i	−1.18356	+	0.983191i
$85$	−0.877544	+	0.319400i	−0.0951830	+	0.0346438i
$86$	3.47183	−	4.13845i	0.374377	−	0.446260i
$87$	−8.76961	−	3.24316i	−0.940201	−	0.347703i
$88$	3.07352	−	5.32737i	0.327638	−	0.567899i
$89$	11.7753	+	2.07631i	1.24818	+	0.220088i	0.758419	−	0.651767i	$-0.225972\pi$
$89$	11.7753	+	2.07631i	1.24818	+	0.220088i	0.489763	+	0.871855i	$0.337083\pi$
$90$	1.24018	+	0.732990i	0.130727	+	0.0772640i
$91$	5.23559	−	6.23953i	0.548839	−	0.654081i
$92$	−4.03763	−	1.46862i	−0.420952	−	0.153114i
$93$	−6.81661	+	2.44133i	−0.706849	+	0.253154i
$94$	9.01854	+	15.6168i	0.930192	+	1.61075i
$95$	−1.47854	+	0.0674103i	−0.151695	+	0.00691615i
$96$	9.65688	−	1.65672i	0.985601	−	0.169088i
$97$	13.6314	+	4.96143i	1.38406	+	0.503757i	0.923407	−	0.383823i	$-0.125393\pi$
$97$	13.6314	+	4.96143i	1.38406	+	0.503757i	0.460654	+	0.887580i	$0.347615\pi$
$98$	−10.3692	+	8.70266i	−1.04745	+	0.879101i
$99$	5.04023	−	4.14148i	0.506562	−	0.416234i
$100$	1.69846	+	9.62063i	0.169846	+	0.962063i
$101$	4.63308	+	0.816937i	0.461008	+	0.0812882i	0.399329	−	0.916808i	$-0.369243\pi$
$101$	4.63308	+	0.816937i	0.461008	+	0.0812882i	0.0616796	+	0.998096i	$0.480354\pi$
$102$	−5.18246	+	4.30420i	−0.513140	+	0.426180i
$103$	8.26145	−	4.76975i	0.814025	−	0.469977i	−0.0343270	−	0.999411i	$-0.510929\pi$
$103$	8.26145	−	4.76975i	0.814025	−	0.469977i	0.848352	+	0.529433i	$0.177595\pi$
$104$	−5.31726	+	1.93722i	−0.521400	+	0.189960i
$105$	2.06723	+	1.20776i	0.201741	+	0.117866i
$106$	6.00141	+	3.46407i	0.582908	+	0.336461i
$107$	−3.10251	+	5.37371i	−0.299931	+	0.519497i	−0.976120	−	0.217232i	$-0.930297\pi$
$107$	−3.10251	+	5.37371i	−0.299931	+	0.519497i	0.676189	+	0.736729i	$0.263630\pi$
$108$	10.2057	+	1.96048i	0.982045	+	0.188647i
$109$	−5.45985	+	4.58136i	−0.522959	+	0.438815i	−0.865662	−	0.500629i	$-0.833102\pi$
$109$	−5.45985	+	4.58136i	−0.522959	+	0.438815i	0.342703	+	0.939444i	$0.388658\pi$
$110$	−1.02835	−	0.181214i	−0.0980490	−	0.0172781i
$111$	−10.3173	+	12.1678i	−0.979276	+	1.15492i
$112$	16.0350	−	2.83435i	1.51517	−	0.267821i
$113$			6.44736i			0.606516i	0.952908	+	0.303258i	$0.0980745\pi$
$113$			6.44736i			0.606516i	−0.952908	+	0.303258i	$0.901926\pi$
$114$	−9.87704	+	4.05513i	−0.925069	+	0.379798i
$115$			0.729432i			0.0680199i
$116$	6.94163	+	8.26918i	0.644514	+	0.767774i
$117$	−6.00213	−	0.0618686i	−0.554897	−	0.00571975i
$118$	−0.0130614	+	0.0741206i	−0.00120240	+	0.00682335i
$119$	−8.57672	+	7.19672i	−0.786226	+	0.659722i
$120$	−0.824750	−	1.44461i	−0.0752890	−	0.131874i
$121$	3.13579	−	5.43135i	0.285072	−	0.493759i
$122$	5.00705	−	8.67456i	0.453317	−	0.785358i
$123$	−9.82736	+	16.8207i	−0.886103	+	1.51667i
$124$	8.23401	+	1.45010i	0.739436	+	0.130222i
$125$	2.90671	−	1.67819i	0.259984	−	0.150102i
$126$	16.9775	+	3.17252i	1.51248	+	0.282631i
$127$	−7.92303	−	1.39704i	−0.703055	−	0.123968i	−0.189319	−	0.981916i	$-0.560628\pi$
$127$	−7.92303	−	1.39704i	−0.703055	−	0.123968i	−0.513736	+	0.857948i	$0.671739\pi$
$128$	−10.6342	−	3.86170i	−0.939944	−	0.341330i
$129$	−6.61584	−	0.0340964i	−0.582492	−	0.00300202i
$130$	0.617662	+	0.735943i	0.0541725	+	0.0645465i
$131$	15.1562	+	5.51641i	1.32420	+	0.481971i	0.904803	−	0.425831i	$-0.140018\pi$
$131$	15.1562	+	5.51641i	1.32420	+	0.481971i	0.419401	+	0.907801i	$0.362240\pi$
$132$	−7.42460	+	1.27134i	−0.646229	+	0.110656i
$133$	−16.3808	+	6.82218i	−1.42040	+	0.591558i
$134$	−4.23827	+	2.44756i	−0.366131	+	0.211437i
$135$	−0.279479	−	1.74209i	−0.0240537	−	0.149935i
$136$	7.66035	−	1.35321i	0.656869	−	0.116037i
$137$	−8.59034	+	10.2376i	−0.733922	+	0.874654i	−0.995904	−	0.0904185i	$-0.971180\pi$
$137$	−8.59034	+	10.2376i	−0.733922	+	0.874654i	0.261982	+	0.965073i	$0.415624\pi$
$138$	1.77473	+	4.95372i	0.151075	+	0.421688i
$139$	−10.3451	−	1.82411i	−0.877456	−	0.154719i	−0.283264	−	0.959042i	$-0.591417\pi$
$139$	−10.3451	−	1.82411i	−0.877456	−	0.154719i	−0.594193	+	0.804323i	$0.702528\pi$
$140$	−1.38279	−	2.39390i	−0.116867	−	0.202321i
$141$	7.66100	−	20.7156i	0.645172	−	1.74457i
$142$	−5.16834	−	4.33582i	−0.433717	−	0.363854i
$143$	4.08838	−	1.48805i	0.341887	−	0.124437i
$144$	−9.11582	−	7.80396i	−0.759652	−	0.650330i
$145$	0.916499	−	1.58742i	0.0761111	−	0.131828i
$146$	−1.52283	+	0.554445i	−0.126030	+	0.0458862i
$147$	16.3127	+	2.96314i	1.34545	+	0.244395i
$148$	17.3088	−	6.30402i	1.42278	−	0.518187i
$149$	−6.72165	+	1.18521i	−0.550659	+	0.0970961i	−0.442053	−	0.896989i	$-0.645750\pi$
$149$	−6.72165	+	1.18521i	−0.550659	+	0.0970961i	−0.108606	+	0.994085i	$0.534639\pi$
$150$	7.73715	−	9.12680i	0.631736	−	0.745200i
$151$			14.9895i			1.21983i	0.792468	+	0.609914i	$0.208796\pi$
$151$			14.9895i			1.21983i	−0.792468	+	0.609914i	$0.791204\pi$
$152$	12.2269	+	1.58182i	0.991735	+	0.128302i
$153$	8.11028	+	1.51642i	0.655677	+	0.122595i
$154$	−12.3284	+	2.17517i	−0.993453	+	0.175280i
$155$	−0.246485	−	1.39789i	−0.0197982	−	0.112281i
$156$	5.98524	+	3.49515i	0.479203	+	0.279836i
$157$	12.6382	−	10.6047i	1.00864	−	0.846349i	0.0204816	−	0.999790i	$-0.493480\pi$
$157$	12.6382	−	10.6047i	1.00864	−	0.846349i	0.988158	+	0.153441i	$0.0490356\pi$
$158$	0.175819	+	0.482902i	0.0139874	+	0.0384176i
$159$	−1.43062	−	8.36531i	−0.113455	−	0.663412i
$160$	0.00100811	+	1.92080i	7.96979e−5	+	0.151852i
$161$	2.99103	+	8.21778i	0.235726	+	0.647652i
$162$	−6.13656	−	11.1509i	−0.482134	−	0.876097i
$163$	2.03794	−	1.17661i	0.159624	−	0.0921589i	−0.418060	−	0.908419i	$-0.637290\pi$
$163$	2.03794	−	1.17661i	0.159624	−	0.0921589i	0.577684	+	0.816260i	$0.303957\pi$
$164$	19.4787	−	11.2515i	1.52103	−	0.878594i
$165$	0.633717	+	1.11081i	0.0493348	+	0.0864766i
$166$	−15.5373	−	5.65327i	−1.20593	−	0.438779i
$167$	−14.0716	−	11.8075i	−1.08889	−	0.913688i	−0.0922628	−	0.995735i	$-0.529410\pi$
$167$	−14.0716	−	11.8075i	−1.08889	−	0.913688i	−0.996629	+	0.0820464i	$0.973854\pi$
$168$	−15.2152	−	12.8931i	−1.17388	−	0.994722i
$169$	8.45417	+	3.07707i	0.650321	+	0.236697i
$170$	−0.660460	−	1.14367i	−0.0506550	−	0.0877158i
$171$	11.5482	+	6.13513i	0.883110	+	0.469165i
$172$	6.61673	+	3.81832i	0.504521	+	0.291144i
$173$	7.23020	−	19.8648i	0.549702	−	1.51029i	−0.284412	−	0.958702i	$-0.591798\pi$
$173$	7.23020	−	19.8648i	0.549702	−	1.51029i	0.834114	−	0.551592i	$-0.185979\pi$
$174$	2.36187	−	13.0104i	0.179053	−	0.986314i
$175$	12.7819	−	15.2329i	0.966224	−	1.15150i
$176$	8.17467	+	2.97145i	0.616189	+	0.223981i
$177$	0.0800645	−	0.0456767i	0.00601802	−	0.00343327i
$178$	0.00177497	+	16.9097i	0.000133040	+	1.26744i
$179$	−9.20951	−	15.9513i	−0.688351	−	1.19226i	−0.972371	−	0.233441i	$-0.925002\pi$
$179$	−9.20951	−	15.9513i	−0.688351	−	1.19226i	0.284020	−	0.958818i	$-0.408332\pi$
$180$	−0.716098	+	1.90732i	−0.0533748	+	0.142163i
$181$	−0.604112	+	0.219879i	−0.0449033	+	0.0163435i	−0.364374	−	0.931253i	$-0.618717\pi$
$181$	−0.604112	+	0.219879i	−0.0449033	+	0.0163435i	0.319471	+	0.947596i	$0.396495\pi$
$182$	9.97631	+	5.75843i	0.739493	+	0.426843i
$183$	−12.0914	+	2.06784i	−0.893822	+	0.152859i
$184$	1.05321	−	5.98409i	0.0776440	−	0.441153i
$185$	−2.01029	−	2.39577i	−0.147800	−	0.176141i
$186$	−5.07504	−	8.89362i	−0.372120	−	0.652112i
$187$	−5.88960	+	1.03849i	−0.430690	+	0.0759423i
$188$	−19.5335	+	16.3975i	−1.42463	+	1.19591i
$189$	−10.2920	−	18.4804i	−0.748635	−	1.34425i
$190$	−0.457192	−	2.04260i	−0.0331682	−	0.148186i
$191$	11.8385			0.856602			0.428301	−	0.903636i	$-0.359112\pi$
$191$	11.8385			0.856602			0.428301	+	0.903636i	$0.359112\pi$
$192$	4.68022	+	13.0421i	0.337766	+	0.941230i
$193$	3.66793	+	20.8019i	0.264024	+	1.49735i	0.771801	+	0.635864i	$0.219356\pi$
$193$	3.66793	+	20.8019i	0.264024	+	1.49735i	−0.507777	+	0.861488i	$0.669533\pi$
$194$	−3.56026	+	20.2036i	−0.255612	+	1.45054i
$195$	0.210305	−	1.15778i	0.0150603	−	0.0829102i
$196$	−14.6682	−	12.3028i	−1.04773	−	0.878771i
$197$	−12.0504	−	6.95731i	−0.858557	−	0.495688i	0.00497203	−	0.999988i	$-0.498417\pi$
$197$	−12.0504	−	6.95731i	−0.858557	−	0.495688i	−0.863529	+	0.504300i	$0.831751\pi$
$198$	7.00635	+	6.00189i	0.497919	+	0.426536i
$199$	2.30041	+	6.32032i	0.163072	+	0.448036i	0.994136	−	0.108141i	$-0.0344898\pi$
$199$	2.30041	+	6.32032i	0.163072	+	0.448036i	−0.831064	+	0.556177i	$0.812268\pi$
$200$	−12.9813	+	4.72945i	−0.917919	+	0.334423i
$201$	5.62205	+	2.07913i	0.396549	+	0.146651i
$202$	0.000698375		6.65324i	4.91375e−5		0.468120i
$203$	3.81607	−	21.6420i	0.267836	−	1.51897i
$204$	−7.26792	−	6.15999i	−0.508856	−	0.431286i
$205$	−2.92559	−	2.45486i	−0.204332	−	0.171455i
$206$	8.67286	+	10.3337i	0.604267	+	0.719984i
$207$	3.27968	−	5.54772i	0.227953	−	0.385593i
$208$	−4.00454	−	6.92935i	−0.277665	−	0.480464i
$209$	−9.39967	−	1.21906i	−0.650189	−	0.0843242i
$210$	−1.17409	+	3.17581i	−0.0810201	+	0.219152i
$211$	6.23878	−	17.1409i	0.429495	−	1.18003i	−0.516624	−	0.856212i	$-0.672812\pi$
$211$	6.23878	−	17.1409i	0.429495	−	1.18003i	0.946120	−	0.323817i	$-0.104966\pi$
$212$	−3.34975	+	9.20937i	−0.230062	+	0.632502i
$213$	−0.0425816	+	8.26225i	−0.00291764	+	0.566120i
$214$	−8.24634	−	3.00044i	−0.563708	−	0.205106i
$215$	0.225220	−	1.27729i	0.0153599	−	0.0871102i
$216$	−0.222595	+	14.6953i	−0.0151456	+	0.999885i
$217$	−8.50893	−	14.7379i	−0.577624	−	1.00047i
$218$	−7.72208	−	6.47821i	−0.523005	−	0.438760i
$219$	1.71379	+	1.00127i	0.115807	+	0.0676595i
$220$	−0.000310013	−	1.47671i	−2.09011e−5	−	0.0995597i
$221$	4.76556	+	2.75140i	0.320566	+	0.185079i
$222$	−19.4813	−	11.3791i	−1.30750	−	0.763713i
$223$	6.14678	+	7.32545i	0.411619	+	0.490548i	0.931526	−	0.363674i	$-0.118478\pi$
$223$	6.14678	+	7.32545i	0.411619	+	0.490548i	−0.519907	+	0.854223i	$0.674033\pi$
$224$	7.88757	+	21.6356i	0.527011	+	1.44559i
$225$	−14.6533	−	0.151043i	−0.976889	−	0.0100696i
$226$	−8.97925	+	1.58426i	−0.597291	+	0.105383i
$227$	11.5941			0.769529			0.384765	−	0.923015i	$-0.374283\pi$
$227$	11.5941			0.769529			0.384765	+	0.923015i	$0.374283\pi$
$228$	−8.07460	−	12.7593i	−0.534753	−	0.845008i
$229$	28.2430			1.86635			0.933176	−	0.359420i	$-0.117025\pi$
$229$	28.2430			1.86635			0.933176	+	0.359420i	$0.117025\pi$
$230$	−1.01588	+	0.179237i	−0.0669852	+	0.0118186i
$231$	11.6943	+	9.91587i	0.769431	+	0.652416i
$232$	−9.81080	+	11.6995i	−0.644111	+	0.768112i
$233$	−11.6686	−	13.9061i	−0.764438	−	0.911021i	0.233682	−	0.972313i	$-0.424922\pi$
$233$	−11.6686	−	13.9061i	−0.764438	−	0.911021i	−0.998120	+	0.0612917i	$0.980478\pi$
$234$	−1.38869	−	8.37438i	−0.0907814	−	0.547450i
$235$	3.74982	+	2.16496i	0.244611	+	0.141226i
$236$	−0.106437		2.23450e-5i	−0.00692849		1.45453e-6i
$237$	0.317511	−	0.543458i	0.0206246	−	0.0353014i
$238$	−12.1304	−	10.1764i	−0.786296	−	0.659640i
$239$	12.0529	+	20.8763i	0.779638	+	1.35037i	0.932151	+	0.362071i	$0.117930\pi$
$239$	12.0529	+	20.8763i	0.779638	+	1.35037i	−0.152513	+	0.988302i	$0.548736\pi$
$240$	1.80925	−	1.50360i	0.116786	−	0.0970571i
$241$	−0.585666	+	3.32147i	−0.0377260	+	0.213955i	−0.997843	−	0.0656431i	$-0.979090\pi$
$241$	−0.585666	+	3.32147i	−0.0377260	+	0.213955i	0.960117	+	0.279598i	$0.0902012\pi$
$242$	8.33478	+	3.03262i	0.535780	+	0.194944i
$243$	−5.70722	+	14.5061i	−0.366118	+	0.930568i
$244$	13.3114	+	4.84180i	0.852177	+	0.309964i
$245$	−1.11166	+	3.05427i	−0.0710216	+	0.195130i
$246$	−25.8410	−	9.55338i	−1.64756	−	0.609101i
$247$	5.90444	+	6.41868i	0.375691	+	0.408411i
$248$	0.00372336	+	11.8238i	0.000236434	+	0.750815i
$249$	6.82765	+	19.0640i	0.432685	+	1.20813i
$250$	3.05146	+	3.63581i	0.192991	+	0.229949i
$251$	−13.0099	−	10.9166i	−0.821175	−	0.689047i	0.132072	−	0.991240i	$-0.457837\pi$
$251$	−13.0099	−	10.9166i	−0.821175	−	0.689047i	−0.953247	+	0.302193i	$0.902281\pi$
$252$	−0.246631	+	24.4242i	−0.0155363	+	1.53858i
$253$	−0.811159	+	4.60031i	−0.0509971	+	0.289219i
$254$	−0.00119429	−	11.3777i	−7.49365e−5	−	0.713901i
$255$	−0.561043	+	1.51708i	−0.0351338	+	0.0950032i
$256$	2.76514	−	15.7593i	0.172821	−	0.984953i
$257$	−1.82086	−	5.00277i	−0.113582	−	0.312064i	0.869857	−	0.493304i	$-0.164211\pi$
$257$	−1.82086	−	5.00277i	−0.113582	−	0.312064i	−0.983439	+	0.181240i	$0.941989\pi$
$258$	−1.57817	−	9.22228i	−0.0982526	−	0.574154i
$259$	−32.4718	−	18.7476i	−2.01770	−	1.16492i
$260$	−0.873178	+	1.04106i	−0.0541522	+	0.0645636i
$261$	−14.1078	+	7.95242i	−0.873254	+	0.492243i
$262$	−3.95850	+	22.4636i	−0.244557	+	1.38780i
$263$	0.915009	+	5.18927i	0.0564219	+	0.319984i	0.999936	−	0.0113491i	$-0.00361261\pi$
$263$	0.915009	+	5.18927i	0.0564219	+	0.319984i	−0.943514	+	0.331333i	$0.892502\pi$
$264$	−3.59499	−	10.0279i	−0.221256	−	0.617173i
$265$	1.66375			0.102203
$266$	−13.5264	−	21.1372i	−0.829356	−	1.29601i
$267$	15.9333	−	13.2303i	0.975099	−	0.809679i
$268$	−4.45016	−	5.30123i	−0.271837	−	0.323824i
$269$	27.2401	−	4.80317i	1.66086	−	0.292854i	0.737088	−	0.675797i	$-0.236200\pi$
$269$	27.2401	−	4.80317i	1.66086	−	0.292854i	0.923772	+	0.382943i	$0.125089\pi$
$270$	2.35754	−	0.817300i	0.143475	−	0.0497393i
$271$	10.6710	+	12.7172i	0.648216	+	0.772514i	0.985644	−	0.168837i	$-0.0540013\pi$
$271$	10.6710	+	12.7172i	0.648216	+	0.772514i	−0.337428	+	0.941351i	$0.609557\pi$
$272$	3.76694	+	10.3361i	0.228404	+	0.626716i
$273$	−2.37815	−	13.9059i	−0.143932	−	0.841623i
$274$	−16.3687	−	9.44819i	−0.988870	−	0.570786i
$275$	9.98119	−	3.63285i	0.601888	−	0.219069i
$276$	−6.46296	+	3.68891i	−0.389025	+	0.222046i
$277$	−10.8499	−	18.7926i	−0.651908	−	1.12914i	−0.982659	−	0.185420i	$-0.940635\pi$
$277$	−10.8499	−	18.7926i	−0.651908	−	1.12914i	0.330751	−	0.943718i	$-0.392698\pi$
$278$	−0.00155938	−	14.8558i	−9.35254e−5	−	0.890993i
$279$	−4.41054	+	11.7399i	−0.264052	+	0.702851i
$280$	2.99421	−	2.51405i	0.178938	−	0.150243i
$281$	10.5420	−	12.5635i	0.628882	−	0.749473i	−0.353688	−	0.935363i	$-0.615073\pi$
$281$	10.5420	−	12.5635i	0.628882	−	0.749473i	0.982570	+	0.185891i	$0.0595170\pi$
$282$	30.7332	+	5.57922i	1.83013	+	0.332238i
$283$	−10.1982	+	28.0192i	−0.606217	+	1.66557i	0.132199	+	0.991223i	$0.457796\pi$
$283$	−10.1982	+	28.0192i	−0.606217	+	1.66557i	−0.738416	+	0.674345i	$0.764426\pi$
$284$	4.76854	−	8.26336i	0.282961	−	0.490340i
$285$	−1.56715	+	2.02877i	−0.0928301	+	0.120174i
$286$	3.07701	+	5.32825i	0.181947	+	0.315066i
$287$	−43.0258	−	15.6601i	−2.53973	−	0.924387i
$288$	8.62865	−	14.6132i	0.508448	−	0.861093i
$289$	7.22839	+	6.06534i	0.425199	+	0.356785i
$290$	2.43601	+	0.886346i	0.143047	+	0.0520480i
$291$	21.8238	−	12.4505i	1.27934	−	0.729860i
$292$	−1.14637	−	1.98461i	−0.0670862	−	0.116140i
$293$	8.06932	−	4.65883i	0.471415	−	0.272172i	−0.245417	−	0.969418i	$-0.578925\pi$
$293$	8.06932	−	4.65883i	0.471415	−	0.272172i	0.716832	+	0.697246i	$0.245592\pi$
$294$	−0.118378	+	23.4469i	−0.00690396	+	1.36745i
$295$	0.00618049	+	0.0169808i	0.000359842	+	0.000988658i
$296$	13.0328	+	22.5570i	0.757515	+	1.31110i
$297$	0.174688	−	11.2976i	0.0101364	−	0.655556i
$298$	−3.30230	−	9.07003i	−0.191297	−	0.525413i
$299$	3.29260	−	2.76282i	0.190416	−	0.159778i
$300$	14.6121	+	8.53290i	0.843630	+	0.492647i
$301$	−2.70017	−	15.3134i	−0.155635	−	0.882652i
$302$	−20.8759	+	3.68325i	−1.20127	+	0.211947i
$303$	6.26904	−	5.20553i	0.360147	−	0.299050i
$304$	0.801420	+	17.4172i	0.0459646	+	0.998943i
$305$		−	2.40482i		−	0.137700i
$306$	−0.119044	+	11.6678i	−0.00680532	+	0.667005i
$307$	−10.4998	+	1.85140i	−0.599257	+	0.105665i	−0.465044	−	0.885287i	$-0.653962\pi$
$307$	−10.4998	+	1.85140i	−0.599257	+	0.105665i	−0.134213	+	0.990953i	$0.542850\pi$
$308$	−6.05872	−	16.6353i	−0.345228	−	0.947886i
$309$	2.95299	−	16.2569i	0.167990	−	0.924821i
$310$	1.88627	−	0.686772i	0.107133	−	0.0390060i
$311$	−0.599347	+	1.03810i	−0.0339859	+	0.0588653i	−0.882518	−	0.470279i	$-0.844153\pi$
$311$	−0.599347	+	1.03810i	−0.0339859	+	0.0588653i	0.848532	+	0.529144i	$0.177487\pi$
$312$	−3.39699	+	9.19449i	−0.192317	+	0.520536i
$313$	−14.8764	+	5.41456i	−0.840863	+	0.306049i	−0.726309	−	0.687368i	$-0.758766\pi$
$313$	−14.8764	+	5.41456i	−0.840863	+	0.306049i	−0.114554	+	0.993417i	$0.536544\pi$
$314$	17.8747	+	14.9955i	1.00873	+	0.846243i
$315$	3.91118	−	1.37807i	0.220370	−	0.0776454i
$316$	−0.629336	+	0.363524i	−0.0354029	+	0.0204498i
$317$	−24.8359	−	4.37924i	−1.39492	−	0.245963i	−0.574868	−	0.818246i	$-0.694947\pi$
$317$	−24.8359	−	4.37924i	−1.39492	−	0.245963i	−0.820056	+	0.572283i	$0.806058\pi$
$318$	11.2989	−	4.04796i	0.633608	−	0.226998i
$319$	7.54537	−	8.99222i	0.422460	−	0.503468i
$320$	−2.67485	+	0.473386i	−0.149529	+	0.0264631i
$321$	3.62374	+	10.1181i	0.202257	+	0.564737i
$322$	−10.7100	+	6.18490i	−0.596843	+	0.344671i
$323$	−6.46072	−	10.0983i	−0.359484	−	0.561884i
$324$	14.0220	−	11.2864i	0.779000	−	0.627024i
$325$	−9.18398	−	3.34270i	−0.509436	−	0.185419i
$326$	2.13943	+	2.54913i	0.118492	+	0.141183i
$327$	−0.0636217	+	12.3447i	−0.00351829	+	0.682665i
$328$	20.4563	+	24.3633i	1.12951	+	1.34524i
$329$	51.1228	+	9.01434i	2.81849	+	0.496976i
$330$	−1.39131	+	1.15553i	−0.0765893	+	0.0636099i
$331$	8.10526	−	4.67957i	0.445505	−	0.257213i	−0.260425	−	0.965494i	$-0.583863\pi$
$331$	8.10526	−	4.67957i	0.445505	−	0.257213i	0.705930	+	0.708282i	$0.250529\pi$
$332$	4.05547	−	23.0280i	0.222573	−	1.26382i
$333$	4.51745	+	27.2598i	0.247555	+	1.49383i
$334$	12.9866	−	22.4989i	0.710594	−	1.23108i
$335$	−0.587552	+	1.01767i	−0.0321014	+	0.0556012i
$336$	14.2175	−	24.3584i	0.775628	−	1.32886i
$337$	4.14592	−	3.47884i	0.225843	−	0.189504i	−0.522844	−	0.852428i	$-0.675129\pi$
$337$	4.14592	−	3.47884i	0.225843	−	0.189504i	0.748687	+	0.662924i	$0.230685\pi$
$338$	−2.20806	+	12.5302i	−0.120103	+	0.681556i
$339$	8.51743	+	7.22210i	0.462603	+	0.392251i
$340$	1.43051	−	1.20085i	0.0775802	−	0.0651253i
$341$		−	9.09017i		−	0.492260i
$342$	−5.70678	+	17.5907i	−0.308587	+	0.951196i
$343$			10.4715i			0.565406i
$344$	−3.69191	+	10.1534i	−0.199054	+	0.547434i
$345$	0.963632	+	0.817083i	0.0518802	+	0.0439903i
$346$	29.4424	+	5.18830i	1.58283	+	0.278925i
$347$	−24.6949	+	20.7215i	−1.32569	+	1.11239i	−0.340627	+	0.940199i	$0.610639\pi$
$347$	−24.6949	+	20.7215i	−1.32569	+	1.11239i	−0.985064	+	0.172188i	$0.944916\pi$
$348$	18.6999	+	0.0924490i	1.00242	+	0.00495579i
$349$	−3.76866	+	6.52751i	−0.201732	+	0.349409i	−0.949086	−	0.315016i	$-0.897990\pi$
$349$	−3.76866	+	6.52751i	−0.201732	+	0.349409i	0.747355	+	0.664425i	$0.231324\pi$
$350$	24.3557	+	14.0584i	1.30187	+	0.751452i
$351$	−6.80510	+	7.85994i	−0.363229	+	0.419533i
$352$	−2.12965	+	12.1150i	−0.113511	+	0.645733i
$353$	−14.0533	+	8.11369i	−0.747983	+	0.431848i	−0.824965	−	0.565185i	$-0.808805\pi$
$353$	−14.0533	+	8.11369i	−0.747983	+	0.431848i	0.0769819	+	0.997032i	$0.475472\pi$
$354$	0.0832877	+	0.100282i	0.00442669	+	0.00532995i
$355$	−1.59515	−	0.281268i	−0.0846618	−	0.0149282i
$356$	−23.5498	+	4.15756i	−1.24814	+	0.220350i
$357$	−0.0999414	+	19.3920i	−0.00528946	+	1.02633i
$358$	19.9525	−	16.7457i	1.05452	−	0.885038i
$359$	5.02034	+	1.82725i	0.264963	+	0.0964387i	0.471086	−	0.882087i	$-0.343862\pi$
$359$	5.02034	+	1.82725i	0.264963	+	0.0964387i	−0.206122	+	0.978526i	$0.566085\pi$
$360$	−2.83228	−	0.528642i	−0.149275	−	0.0278619i
$361$	−4.98828	−	18.3335i	−0.262541	−	0.964921i
$362$	−0.454670	−	0.787320i	−0.0238969	−	0.0413806i
$363$	−3.66260	−	10.2266i	−0.192237	−	0.536758i
$364$	−5.56838	+	15.3090i	−0.291863	+	0.802410i
$365$	−0.250116	+	0.298076i	−0.0130916	+	0.0156020i
$366$	−5.85101	−	16.3316i	−0.305837	−	0.853667i
$367$	22.5439	+	3.97509i	1.17678	+	0.207498i	0.727637	−	0.685962i	$-0.240618\pi$
$367$	22.5439	+	3.97509i	1.17678	+	0.207498i	0.449143	+	0.893460i	$0.351729\pi$
$368$	8.59286	−	0.00360789i	0.447934	−	0.000188074i
$369$	11.2131	+	31.8246i	0.583730	+	1.65672i
$370$	2.84263	−	3.38844i	0.147781	−	0.176156i
$371$	18.7438	−	6.82219i	0.973130	−	0.354190i
$372$	11.1391	−	9.25338i	0.577537	−	0.479765i
$373$	0.359410	−	0.622516i	0.0186095	−	0.0322327i	−0.856571	−	0.516030i	$-0.827409\pi$
$373$	0.359410	−	0.622516i	0.0186095	−	0.0322327i	0.875180	+	0.483797i	$0.160743\pi$
$374$	−2.89352	−	7.94728i	−0.149620	−	0.410944i
$375$	1.03898	−	5.71981i	0.0536527	−	0.295370i
$376$	−27.6367	−	23.1751i	−1.42525	−	1.19517i
$377$	−10.6369	+	1.87557i	−0.547826	+	0.0965965i
$378$	23.2087	−	18.8748i	1.19373	−	0.970814i
$379$			13.9549i			0.716814i	0.933565	+	0.358407i	$0.116680\pi$
$379$			13.9549i			0.716814i	−0.933565	+	0.358407i	$0.883320\pi$
$380$	2.73239	−	1.13864i	0.140169	−	0.0584112i
$381$	−10.7207	+	8.90198i	−0.549237	+	0.456062i
$382$	2.90897	+	16.4875i	0.148836	+	0.843573i
$383$	2.43522	+	13.8108i	0.124434	+	0.705700i	0.981642	+	0.190731i	$0.0610857\pi$
$383$	2.43522	+	13.8108i	0.124434	+	0.705700i	−0.857208	+	0.514970i	$0.827803\pi$
$384$	−17.0137	+	9.72287i	−0.868226	+	0.496168i
$385$	−2.30255	+	1.93207i	−0.117349	+	0.0984675i
$386$	−28.0696	+	10.2198i	−1.42870	+	0.520175i
$387$	−7.45587	+	8.70181i	−0.379003	+	0.442338i
$388$	−29.0125	+	0.00609075i	−1.47289	+	0.000309211i
$389$	3.78838	+	10.4085i	0.192078	+	0.527731i	0.997925	−	0.0643938i	$-0.0205114\pi$
$389$	3.78838	+	10.4085i	0.192078	+	0.527731i	−0.805846	+	0.592125i	$0.798289\pi$
$390$	1.66412	+	0.00840177i	0.0842658	+	0.000425440i
$391$	−5.11664	+	2.95409i	−0.258759	+	0.149395i
$392$	13.5299	−	23.4514i	0.683361	−	1.18448i
$393$	24.2650	−	13.8432i	1.22401	−	0.698295i
$394$	6.72842	−	18.4922i	0.338973	−	0.931624i
$395$	0.0945226	+	0.0793139i	0.00475595	+	0.00399071i
$396$	−6.63724	+	11.2326i	−0.333534	+	0.564457i
$397$	−6.13237	−	2.23200i	−0.307775	−	0.112021i	0.183515	−	0.983017i	$-0.441252\pi$
$397$	−6.13237	−	2.23200i	−0.307775	−	0.112021i	−0.491290	+	0.870996i	$0.663475\pi$
$398$	−8.23707	+	4.75683i	−0.412887	+	0.238438i
$399$	−9.33660	+	29.2822i	−0.467415	+	1.46594i
$400$	−9.77651	−	16.9170i	−0.488826	−	0.845850i
$401$	−3.45492	+	9.49233i	−0.172531	+	0.474024i	−0.995577	−	0.0939503i	$-0.970051\pi$
$401$	−3.45492	+	9.49233i	−0.172531	+	0.474024i	0.823046	+	0.567974i	$0.192273\pi$
$402$	−1.51415	+	8.34073i	−0.0755192	+	0.415998i
$403$	−5.37636	+	6.40729i	−0.267816	+	0.319170i
$404$	−9.26581	+	1.63582i	−0.460991	+	0.0813850i
$405$	−2.61449	−	1.58222i	−0.129915	−	0.0786209i
$406$	31.0786	−	0.00326224i	1.54240	−	0.000161902i
$407$	−10.0141	−	17.3450i	−0.496382	−	0.859759i
$408$	6.79315	−	11.6357i	0.336311	−	0.576053i
$409$	−23.6560	+	8.61008i	−1.16971	+	0.425741i	−0.852558	−	0.522633i	$-0.824950\pi$
$409$	−23.6560	+	8.61008i	−1.16971	+	0.425741i	−0.317156	+	0.948374i	$0.602728\pi$
$410$	2.70001	−	4.67769i	0.133344	−	0.231014i
$411$	3.90198	+	22.8162i	0.192470	+	1.12544i
$412$	−12.2607	+	14.6179i	−0.604040	+	0.720174i
$413$	0.139259	+	0.165962i	0.00685248	+	0.00816647i
$414$	8.53221	+	3.20442i	0.419335	+	0.157489i
$415$	−3.90946	+	0.689343i	−0.191908	+	0.0338385i
$416$	8.66652	−	7.27982i	0.424911	−	0.356923i
$417$	−13.9979	+	11.6233i	−0.685482	+	0.569194i
$418$	−0.611915	−	13.3905i	−0.0299297	−	0.654951i
$419$	−5.77923			−0.282334			−0.141167	−	0.989986i	$-0.545085\pi$
$419$	−5.77923			−0.282334			−0.141167	+	0.989986i	$0.545085\pi$
$420$	−4.71146	−	0.854796i	−0.229896	−	0.0417098i
$421$	1.93681	+	10.9842i	0.0943942	+	0.535336i	0.994931	+	0.100557i	$0.0320624\pi$
$421$	1.93681	+	10.9842i	0.0943942	+	0.535336i	−0.900537	+	0.434779i	$0.856826\pi$
$422$	25.4052	+	4.47687i	1.23671	+	0.217931i
$423$	−18.7852	−	33.3256i	−0.913370	−	1.62035i
$424$	−13.6490	−	2.40226i	−0.662855	−	0.116664i
$425$	11.6344	+	6.71714i	0.564353	+	0.325829i
$426$	−11.5173	+	1.97091i	−0.558016	+	0.0954910i
$427$	−9.86094	−	27.0927i	−0.477204	−	1.31111i
$428$	2.15242	−	12.2220i	0.104041	−	0.590771i
$429$	2.61383	−	7.06790i	0.126197	−	0.341241i
$430$	1.83422		0.000192534i	0.0884540		9.28481e-6i
$431$	2.55507	−	14.4905i	0.123073	−	0.697984i	−0.859360	−	0.511371i	$-0.829138\pi$
$431$	2.55507	−	14.4905i	0.123073	−	0.697984i	0.982434	−	0.186613i	$-0.0597510\pi$
$432$	−20.5208	+	3.30094i	−0.987308	+	0.158816i
$433$	0.265598	+	0.222863i	0.0127638	+	0.0107101i	0.649147	−	0.760663i	$-0.275126\pi$
$433$	0.265598	+	0.222863i	0.0127638	+	0.0107101i	−0.636383	+	0.771373i	$0.719570\pi$
$434$	18.4347	−	15.4718i	0.884893	−	0.742672i
$435$	−1.07047	−	2.98893i	−0.0513252	−	0.143308i
$436$	7.12474	−	12.3464i	0.341213	−	0.591285i
$437$	−9.13797	+	2.04433i	−0.437128	+	0.0977935i
$438$	−0.973355	+	2.63283i	−0.0465087	+	0.125802i
$439$	9.04226	−	24.8434i	0.431563	−	1.18571i	−0.513289	−	0.858216i	$-0.671573\pi$
$439$	9.04226	−	24.8434i	0.431563	−	1.18571i	0.944853	−	0.327495i	$-0.106205\pi$
$440$	2.05654	−	0.363291i	0.0980417	−	0.0173192i
$441$	22.1874	−	18.2311i	1.05655	−	0.868147i
$442$	−2.66087	+	7.31308i	−0.126565	+	0.347848i
$443$	−1.24252	+	7.04669i	−0.0590340	+	0.334798i	−0.999993	−	0.00372195i	$-0.998815\pi$
$443$	−1.24252	+	7.04669i	−0.0590340	+	0.334798i	0.940959	+	0.338520i	$0.109926\pi$
$444$	11.0607	−	29.9278i	0.524916	−	1.42031i
$445$	2.03001	+	3.51608i	0.0962318	+	0.166678i
$446$	−8.69178	+	10.3607i	−0.411567	+	0.490592i
$447$	−5.96361	+	10.2074i	−0.282069	+	0.482794i
$448$	−28.1938	+	16.3014i	−1.33203	+	0.770168i
$449$	−16.1424	−	9.31983i	−0.761808	−	0.439830i	0.0681366	−	0.997676i	$-0.478295\pi$
$449$	−16.1424	−	9.31983i	−0.761808	−	0.439830i	−0.829944	+	0.557846i	$0.811628\pi$
$450$	−3.39029	−	20.4449i	−0.159820	−	0.963780i
$451$	−15.7209	−	18.7355i	−0.740269	−	0.882218i
$452$	−4.41280	−	12.1161i	−0.207560	−	0.569895i
$453$	19.8022	+	16.7907i	0.930389	+	0.788896i
$454$	2.84893	+	16.1472i	0.133707	+	0.757824i
$455$	2.76570			0.129658
$456$	15.7859	−	14.3808i	0.739241	−	0.673441i
$457$	−24.2994			−1.13668			−0.568338	−	0.822795i	$-0.692413\pi$
$457$	−24.2994			−1.13668			−0.568338	+	0.822795i	$0.692413\pi$
$458$	6.93993	+	39.3341i	0.324282	+	1.83796i
$459$	11.0881	−	9.01563i	0.517550	−	0.420813i
$460$	−0.499248	−	1.37078i	−0.0232776	−	0.0639129i
$461$	19.2482	+	22.9391i	0.896479	+	1.06838i	0.997297	+	0.0734767i	$0.0234095\pi$
$461$	19.2482	+	22.9391i	0.896479	+	1.06838i	−0.100818	+	0.994905i	$0.532146\pi$
$462$	−10.9363	+	18.7233i	−0.508803	+	0.871086i
$463$	−19.2507	−	11.1144i	−0.894656	−	0.516530i	−0.0191936	−	0.999816i	$-0.506110\pi$
$463$	−19.2507	−	11.1144i	−0.894656	−	0.516530i	−0.875463	+	0.483286i	$0.839443\pi$
$464$	−18.7047	−	10.7887i	−0.868344	−	0.500853i
$465$	−2.12281	−	1.24024i	−0.0984431	−	0.0575147i
$466$	16.4999	−	19.6680i	0.764342	−	0.911102i
$467$	−8.21437	−	14.2277i	−0.380116	−	0.658380i	0.610963	−	0.791659i	$-0.290783\pi$
$467$	−8.21437	−	14.2277i	−0.380116	−	0.658380i	−0.991078	+	0.133280i	$0.957449\pi$
$468$	11.3218	−	3.99180i	0.523350	−	0.184521i
$469$	−2.44642	+	13.8743i	−0.112965	+	0.640657i
$470$	−2.09373	+	5.75435i	−0.0965766	+	0.265429i
$471$	0.147269	−	28.5750i	0.00678578	−	1.31667i
$472$	−0.0261851	−	0.148230i	−0.00120527	−	0.00682285i
$473$	2.84079	−	7.80502i	0.130620	−	0.358875i
$474$	0.834895	+	0.308659i	0.0383480	+	0.0141772i
$475$	14.4149	+	15.6703i	0.661399	+	0.719003i
$476$	11.1920	−	19.3946i	0.512986	−	0.888949i
$477$	−12.6537	−	7.48057i	−0.579373	−	0.342512i
$478$	−26.1127	+	21.9159i	−1.19437	+	1.00241i
$479$	−11.0402	−	9.26381i	−0.504439	−	0.423274i	0.354728	−	0.934969i	$-0.384573\pi$
$479$	−11.0402	−	9.26381i	−0.504439	−	0.423274i	−0.859167	+	0.511695i	$0.829018\pi$
$480$	2.53864	+	2.15028i	0.115873	+	0.0981463i
$481$	−3.20009	+	18.1486i	−0.145912	+	0.827506i
$482$	−4.76974		0.000500668i	−0.217256		2.28048e-5i
$483$	14.2067	+	5.25390i	0.646429	+	0.239061i
$484$	−2.17550	+	12.3531i	−0.0988865	+	0.561503i
$485$	1.68467	+	4.62858i	0.0764967	+	0.210173i
$486$	−21.6051	−	4.38399i	−0.980028	−	0.198862i
$487$	0.808031	+	0.466517i	0.0366154	+	0.0211399i	0.518196	−	0.855262i	$-0.326604\pi$
$487$	0.808031	+	0.466517i	0.0366154	+	0.0211399i	−0.481581	+	0.876402i	$0.659937\pi$
$488$	−3.47228	+	19.7286i	−0.157183	+	0.893072i
$489$	0.728447	−	4.01026i	0.0329415	−	0.181350i
$490$	−4.52685	−	0.797716i	−0.204502	−	0.0360371i
$491$	5.34346	+	30.3043i	0.241147	+	1.36761i	0.829274	+	0.558843i	$0.188755\pi$
$491$	5.34346	+	30.3043i	0.241147	+	1.36761i	−0.588127	+	0.808769i	$0.700134\pi$
$492$	6.95532	−	38.3363i	0.313570	−	1.72833i
$493$	14.8467			0.668664
$494$	−7.48847	+	9.80034i	−0.336922	+	0.440938i
$495$	2.17733	+	0.407106i	0.0978637	+	0.0182980i
$496$	−16.4662	+	2.91056i	−0.739354	+	0.130688i
$497$	−19.1243	+	3.37213i	−0.857843	+	0.151261i
$498$	−24.8727	+	14.1933i	−1.11457	+	0.636018i
$499$	−4.81036	−	5.73276i	−0.215341	−	0.256634i	0.647550	−	0.762023i	$-0.275793\pi$
$499$	−4.81036	−	5.73276i	−0.215341	−	0.256634i	−0.862892	+	0.505389i	$0.831349\pi$
$500$	−4.31379	+	5.14317i	−0.192919	+	0.230010i
$501$	−31.3610	+	5.36329i	−1.40111	+	0.239614i
$502$	12.0067	−	20.8013i	0.535886	−	0.928407i
$503$	2.59975	−	0.946231i	0.115917	−	0.0421904i	−0.283410	−	0.958999i	$-0.591466\pi$
$503$	2.59975	−	0.946231i	0.115917	−	0.0421904i	0.399328	+	0.916808i	$0.369244\pi$
$504$	−34.0762	+	5.65807i	−1.51788	+	0.252031i
$505$	0.798721	+	1.38342i	0.0355426	+	0.0615616i
$506$	−6.60619		0.000693436i	−0.293681		3.08270e-5i
$507$	13.5351	−	7.72175i	0.601114	−	0.342935i
$508$	15.8455	−	2.79741i	0.703029	−	0.124115i
$509$	11.8481	−	14.1200i	0.525159	−	0.625860i	−0.436634	−	0.899639i	$-0.643829\pi$
$509$	11.8481	−	14.1200i	0.525159	−	0.625860i	0.961792	+	0.273780i	$0.0882739\pi$
$510$	−2.25070	−	0.408586i	−0.0996627	−	0.0180925i
$511$	−1.59555	+	4.38372i	−0.0705828	+	0.193925i
$512$	22.6274	−	0.0213763i	1.00000	−	0.000944708i
$513$	21.0408	−	8.38361i	0.928974	−	0.370146i
$514$	6.51995	−	3.76521i	0.287583	−	0.166076i
$515$	3.04381	+	1.10786i	0.134126	+	0.0488180i
$516$	12.4561	−	4.46404i	0.548349	−	0.196518i
$517$	21.2415	+	17.8237i	0.934199	+	0.783886i
$518$	18.1308	−	49.8303i	0.796623	−	2.18942i
$519$	−18.1439	−	31.8035i	−0.796427	−	1.39602i
$520$	−1.66444	−	0.960266i	−0.0729905	−	0.0421105i
$521$	4.83770	−	2.79305i	0.211944	−	0.122366i	−0.390271	−	0.920700i	$-0.627619\pi$
$521$	4.83770	−	2.79305i	0.211944	−	0.122366i	0.602214	+	0.798334i	$0.294285\pi$
$522$	−14.5420	−	17.6940i	−0.636485	−	0.774443i
$523$	6.84216	+	18.7987i	0.299187	+	0.822009i	0.994636	+	0.103434i	$0.0329830\pi$
$523$	6.84216	+	18.7987i	0.299187	+	0.822009i	−0.695450	+	0.718575i	$0.744795\pi$
$524$	−32.2578	+	0.00677205i	−1.40919	+	0.000295838i
$525$	−5.80593	−	33.9492i	−0.253391	−	1.48167i
$526$	−7.00228	+	2.54945i	−0.305314	+	0.111161i
$527$	8.80732	−	7.39022i	0.383653	−	0.321923i
$528$	13.0825	−	7.47082i	0.569341	−	0.325126i
$529$	−3.19255	−	18.1059i	−0.138807	−	0.787211i
$530$	0.408820	+	2.31711i	0.0177580	+	0.100649i
$531$	0.0293431	−	0.156937i	0.00127338	−	0.00681046i
$532$	26.1142	−	24.0321i	1.13219	−	1.04192i
$533$			22.5040i			0.974755i
$534$	22.3410	+	18.9393i	0.966788	+	0.819585i
$535$	−2.07492	+	0.365865i	−0.0897068	+	0.0158177i
$536$	6.28954	−	7.50038i	0.271667	−	0.323967i
$537$	−31.3890	−	5.70169i	−1.35454	−	0.246046i
$538$	13.3829	+	36.7572i	0.576977	+	1.58471i
$539$	−10.4074	+	18.0262i	−0.448279	+	0.776443i
$540$	1.71756	+	3.08252i	0.0739118	+	0.132651i
$541$	5.29466	−	1.92710i	0.227635	−	0.0828524i	−0.225685	−	0.974200i	$-0.572462\pi$
$541$	5.29466	−	1.92710i	0.227635	−	0.0828524i	0.453320	+	0.891348i	$0.350240\pi$
$542$	−15.0892	+	17.9864i	−0.648135	+	0.772582i
$543$	−0.386229	+	1.04438i	−0.0165747	+	0.0448185i
$544$	−13.4695	+	7.78602i	−0.577498	+	0.333823i
$545$	−2.38334	−	0.420246i	−0.102091	−	0.0180014i
$546$	18.7824	−	6.72904i	0.803813	−	0.287976i
$547$	5.26148	−	6.27039i	0.224965	−	0.268103i	−0.641742	−	0.766921i	$-0.721788\pi$
$547$	5.26148	−	6.27039i	0.224965	−	0.268103i	0.866707	+	0.498818i	$0.166232\pi$
$548$	9.13637	−	25.1184i	0.390287	−	1.07300i
$549$	−10.8126	+	18.2899i	−0.461470	+	0.780596i
$550$	7.51208	+	13.0082i	0.320316	+	0.554669i
$551$	22.4551	+	7.03250i	0.956618	+	0.299594i
$552$	−6.72565	−	8.09454i	−0.286263	−	0.344526i
$553$	1.39012	+	0.505962i	0.0591138	+	0.0215157i
$554$	23.5064	−	19.7285i	0.998693	−	0.838182i
$555$	−5.41685	−	0.0279171i	−0.229932	−	0.00118502i
$556$	20.6893	−	3.65257i	0.877424	−	0.154903i
$557$	−4.08608	−	0.720485i	−0.173133	−	0.0305279i	0.0864097	−	0.996260i	$-0.472461\pi$
$557$	−4.08608	−	0.720485i	−0.173133	−	0.0305279i	−0.259542	+	0.965732i	$0.583572\pi$
$558$	−17.4340	−	3.25782i	−0.738040	−	0.137915i
$559$	−6.61862	+	3.82126i	−0.279938	+	0.161622i
$560$	4.23706	+	3.55229i	0.179049	+	0.150111i
$561$	−5.22539	+	8.94387i	−0.220616	+	0.377610i
$562$	20.0875	+	11.5947i	0.847342	+	0.489095i
$563$	−5.04252	+	8.73390i	−0.212517	+	0.368090i	−0.952502	−	0.304534i	$-0.901499\pi$
$563$	−5.04252	+	8.73390i	−0.212517	+	0.368090i	0.739985	+	0.672624i	$0.234833\pi$
$564$	−0.218384	+	44.1731i	−0.00919560	+	1.86002i
$565$	−1.67704	+	1.40720i	−0.0705535	+	0.0592014i
$566$	−41.5283	−	7.31807i	−1.74557	−	0.307601i
$567$	−35.9427	−	7.10456i	−1.50945	−	0.298363i
$568$	12.6801	+	4.61067i	0.532047	+	0.193460i
$569$			45.1026i			1.89080i	0.325914	+	0.945399i	$0.394328\pi$
$569$			45.1026i			1.89080i	−0.325914	+	0.945399i	$0.605672\pi$
$570$	−3.21055	−	1.68406i	−0.134475	−	0.0705377i
$571$		−	10.9495i		−	0.458221i	−0.973400	−	0.229110i	$-0.926418\pi$
$571$		−	10.9495i		−	0.458221i	0.973400	−	0.229110i	$-0.0735817\pi$
$572$	−6.66457	+	5.59463i	−0.278660	+	0.233923i
$573$	13.2610	−	15.6395i	0.553988	−	0.653349i
$574$	11.2375	−	63.7702i	0.469044	−	2.66172i
$575$	8.03841	−	6.74503i	0.335225	−	0.281287i
$576$	22.4721	+	8.42635i	0.936339	+	0.351098i
$577$	4.03497	−	6.98877i	0.167978	−	0.290946i	−0.769731	−	0.638369i	$-0.779610\pi$
$577$	4.03497	−	6.98877i	0.167978	−	0.290946i	0.937709	+	0.347422i	$0.112943\pi$
$578$	−6.67104	+	11.5574i	−0.277479	+	0.480724i
$579$	31.5895	+	18.4559i	1.31281	+	0.767002i
$580$	−0.635835	+	3.61043i	−0.0264016	+	0.149915i
$581$	−41.2174	+	23.7969i	−1.70998	+	0.987260i
$582$	22.7024	+	27.3348i	0.941045	+	1.13306i
$583$	10.4928	+	1.85016i	0.434567	+	0.0766258i
$584$	2.48228	−	2.08421i	0.102717	−	0.0862453i
$585$	−1.29393	−	1.57473i	−0.0534975	−	0.0651071i
$586$	8.47117	+	10.0934i	0.349941	+	0.416954i
$587$	17.8900	+	6.51145i	0.738401	+	0.268756i	0.683717	−	0.729748i	$-0.260362\pi$
$587$	17.8900	+	6.51145i	0.738401	+	0.268756i	0.0546847	+	0.998504i	$0.482585\pi$
$588$	−32.6836	+	5.59654i	−1.34785	+	0.230798i
$589$	16.8212	−	7.00561i	0.693107	−	0.288661i
$590$	−0.0221305	+	0.0127801i	−0.000911097	+	0.000526149i
$591$	−22.6896	+	8.12614i	−0.933324	+	0.334265i
$592$	−28.2128	+	23.6935i	−1.15954	+	0.973798i
$593$	20.4598	−	24.3830i	0.840183	−	1.00129i	−0.159718	−	0.987163i	$-0.551058\pi$
$593$	20.4598	−	24.3830i	0.840183	−	1.00129i	0.999900	−	0.0141280i	$-0.00449722\pi$
$594$	15.7772	−	2.53279i	0.647346	−	0.103922i
$595$	−3.74391	−	0.660152i	−0.153485	−	0.0270636i
$596$	11.8204	−	6.82783i	0.484183	−	0.279679i
$597$	10.9264	+	4.04079i	0.447190	+	0.165379i
$598$	4.65685	+	3.90673i	0.190433	+	0.159758i
$599$	20.2669	−	7.37654i	0.828083	−	0.301397i	0.107011	−	0.994258i	$-0.465872\pi$
$599$	20.2669	−	7.37654i	0.828083	−	0.301397i	0.721072	+	0.692860i	$0.243650\pi$
$600$	−8.29328	+	22.4470i	−0.338572	+	0.916397i
$601$	20.5858	−	35.6556i	0.839711	−	1.45442i	−0.0504255	−	0.998728i	$-0.516058\pi$
$601$	20.5858	−	35.6556i	0.839711	−	1.45442i	0.890136	−	0.455694i	$-0.150609\pi$
$602$	20.6636	−	7.52338i	0.842184	−	0.306630i
$603$	9.04430	−	5.09816i	0.368312	−	0.207613i
$604$	−10.2593	−	28.1689i	−0.417446	−	1.14618i
$605$	2.09718	−	0.369789i	0.0852624	−	0.0150341i
$606$	8.79019	+	7.45180i	0.357077	+	0.302709i
$607$			18.5930i			0.754668i	0.926077	+	0.377334i	$0.123159\pi$
$607$			18.5930i			0.754668i	−0.926077	+	0.377334i	$0.876841\pi$
$608$	−24.0600	+	5.39592i	−0.975762	+	0.218833i
$609$	−24.3160	−	29.2839i	−0.985335	−	1.18664i
$610$	3.34920	−	0.590917i	0.135605	−	0.0239255i
$611$	−4.43047	−	25.1264i	−0.179238	−	1.01651i
$612$	−16.2791	+	2.70124i	−0.658042	+	0.109191i
$613$	−4.87384	+	4.08963i	−0.196852	+	0.165179i	−0.735886	−	0.677106i	$-0.763234\pi$
$613$	−4.87384	+	4.08963i	−0.196852	+	0.165179i	0.539034	+	0.842284i	$0.318790\pi$
$614$	−5.15849	−	14.1682i	−0.208180	−	0.571782i
$615$	−6.52018	+	1.11507i	−0.262919	+	0.0449639i
$616$	21.6793	−	12.5257i	0.873485	−	0.504673i
$617$	−12.5561	−	34.4977i	−0.505490	−	1.38882i	−0.885844	−	0.463982i	$-0.846420\pi$
$617$	−12.5561	−	34.4977i	−0.505490	−	1.38882i	0.380354	−	0.924841i	$-0.375802\pi$
$618$	23.3666	+	0.117973i	0.939943	+	0.00474557i
$619$	−7.50762	+	4.33452i	−0.301757	+	0.174219i	−0.643232	−	0.765672i	$-0.722407\pi$
$619$	−7.50762	+	4.33452i	−0.301757	+	0.174219i	0.341475	+	0.939891i	$0.389073\pi$
$620$	1.41997	+	2.45826i	0.0570273	+	0.0987263i
$621$	−3.65516	−	10.5470i	−0.146676	−	0.423238i
$622$	−1.59304	−	0.579629i	−0.0638750	−	0.0232410i
$623$	37.2878	+	31.2882i	1.49390	+	1.25353i
$624$	−13.6399	−	2.47172i	−0.546033	−	0.0989479i
$625$	−21.8797	−	7.96355i	−0.875187	−	0.318542i
$626$	−11.1963	−	19.3879i	−0.447495	−	0.774897i
$627$	−12.1396	+	11.0521i	−0.484811	+	0.441378i
$628$	−16.4920	+	28.5789i	−0.658103	+	1.14042i
$629$	8.66389	−	23.8038i	0.345452	−	0.949121i
$630$	2.88030	+	5.10849i	0.114754	+	0.203527i
$631$	7.54580	−	8.99273i	0.300394	−	0.357995i	−0.594641	−	0.803991i	$-0.702706\pi$
$631$	7.54580	−	8.99273i	0.300394	−	0.357995i	0.895035	+	0.445996i	$0.147150\pi$
$632$	−0.660922	−	0.787153i	−0.0262901	−	0.0313113i
$633$	−15.6559	−	27.4425i	−0.622267	−	1.09074i
$634$	−0.00374368	−	35.6651i	−0.000148681	−	1.41644i
$635$	−1.36589	−	2.36580i	−0.0542038	−	0.0938837i
$636$	8.41398	+	14.7413i	0.333636	+	0.584529i
$637$	17.9973	−	6.55049i	0.713080	−	0.259540i
$638$	14.3776	+	8.29887i	0.569213	+	0.328556i
$639$	10.8673	+	9.31133i	0.429905	+	0.368351i
$640$	−1.31656	−	3.60895i	−0.0520414	−	0.142656i
$641$	5.54434	+	6.60749i	0.218988	+	0.260980i	0.864343	−	0.502903i	$-0.167735\pi$
$641$	5.54434	+	6.60749i	0.218988	+	0.260980i	−0.645354	+	0.763883i	$0.723290\pi$
$642$	−13.2011	+	7.53303i	−0.521004	+	0.297305i
$643$	1.50608	−	0.265563i	0.0593942	−	0.0104728i	−0.143872	−	0.989596i	$-0.545955\pi$
$643$	1.50608	−	0.265563i	0.0593942	−	0.0104728i	0.203266	+	0.979123i	$0.434844\pi$
$644$	−11.2454	−	13.3960i	−0.443131	−	0.527878i
$645$	−1.43510	−	1.72830i	−0.0565072	−	0.0680518i
$646$	12.4764	−	11.4792i	0.490876	−	0.451644i
$647$	−34.8365			−1.36956			−0.684781	−	0.728749i	$-0.740102\pi$
$647$	−34.8365			−1.36956			−0.684781	+	0.728749i	$0.740102\pi$
$648$	19.1642	+	16.7552i	0.752839	+	0.658205i
$649$	0.0200952	+	0.113966i	0.000788806	+	0.00447354i
$650$	2.39868	−	13.6119i	0.0940839	−	0.533904i
$651$	−29.0012	−	5.26795i	−1.13665	−	0.206467i
$652$	−3.02447	+	3.60596i	−0.118448	+	0.141220i
$653$	8.90940	+	5.14384i	0.348652	+	0.201294i	0.664091	−	0.747652i	$-0.268819\pi$
$653$	8.90940	+	5.14384i	0.348652	+	0.201294i	−0.315440	+	0.948946i	$0.602152\pi$
$654$	−17.2082	+	2.94476i	−0.672893	+	0.115149i
$655$	1.87311	+	5.14632i	0.0731884	+	0.201084i
$656$	−28.9043	+	34.4762i	−1.12852	+	1.34607i
$657$	3.24248	−	1.14246i	0.126501	−	0.0445714i
$658$	0.00770608	+	73.4139i	0.000300414	+	2.86197i
$659$	−8.77745	+	49.7794i	−0.341921	+	1.93913i	0.00163545	+	0.999999i	$0.499479\pi$
$659$	−8.77745	+	49.7794i	−0.341921	+	1.93913i	−0.343557	+	0.939132i	$0.611632\pi$
$660$	−1.95119	−	1.65375i	−0.0759498	−	0.0643720i
$661$	22.0456	+	18.4985i	0.857476	+	0.719508i	0.961423	−	0.275075i	$-0.0887026\pi$
$661$	22.0456	+	18.4985i	0.857476	+	0.719508i	−0.103946	+	0.994583i	$0.533147\pi$
$662$	8.50889	+	10.1383i	0.330707	+	0.394038i
$663$	8.97300	−	3.21363i	0.348482	−	0.124807i
$664$	33.0677	−	0.0104131i	1.28327	−	0.000404107i
$665$	−5.34981	−	2.77184i	−0.207457	−	0.107487i
$666$	−36.8548	+	12.9898i	−1.42810	+	0.503345i
$667$	3.96629	−	10.8973i	0.153575	−	0.421945i
$668$	34.5253	+	12.5580i	1.33582	+	0.485883i
$669$	16.5629	+	0.0853609i	0.640357	+	0.00330024i
$670$	−1.56169	−	0.568221i	−0.0603332	−	0.0219523i
$671$	2.67426	−	15.1665i	0.103239	−	0.585496i
$672$	37.4176	+	13.8154i	1.44341	+	0.532939i
$673$	22.2008	+	38.4530i	0.855780	+	1.48225i	0.875920	+	0.482457i	$0.160255\pi$
$673$	22.2008	+	38.4530i	0.855780	+	1.48225i	−0.0201402	+	0.999797i	$0.506411\pi$
$674$	5.86373	+	4.91921i	0.225862	+	0.189481i
$675$	−16.6137	+	19.1889i	−0.639461	+	0.738582i
$676$	−17.9935	+	0.00377746i	−0.692057	+	0.000145287i
$677$	−2.35032	−	1.35696i	−0.0903302	−	0.0521522i	0.454154	−	0.890923i	$-0.349941\pi$
$677$	−2.35032	−	1.35696i	−0.0903302	−	0.0521522i	−0.544485	+	0.838771i	$0.683275\pi$
$678$	−7.96532	+	13.6369i	−0.305906	+	0.523721i
$679$	37.9589	+	45.2377i	1.45673	+	1.73606i
$680$	2.02393	+	1.69720i	0.0776144	+	0.0650845i
$681$	12.9873	−	15.3167i	0.497675	−	0.586936i
$682$	12.6599	−	2.23365i	0.484773	−	0.0855310i
$683$	−21.1047			−0.807550			−0.403775	−	0.914858i	$-0.632302\pi$
$683$	−21.1047			−0.807550			−0.403775	+	0.914858i	$0.632302\pi$
$684$	−25.9009	−	3.62543i	−0.990345	−	0.138622i
$685$	−4.53784			−0.173382
$686$	−14.5837	+	2.57307i	−0.556806	+	0.0982403i
$687$	31.6368	−	37.3111i	1.20702	−	1.42351i
$688$	−15.0478	−	2.64682i	−0.573693	−	0.100909i
$689$	−6.30167	−	7.51004i	−0.240074	−	0.286110i
$690$	−0.901169	+	1.54283i	−0.0343069	+	0.0587345i
$691$	−9.17049	−	5.29459i	−0.348862	−	0.201416i	0.315322	−	0.948985i	$-0.397887\pi$
$691$	−9.17049	−	5.29459i	−0.348862	−	0.201416i	−0.664184	+	0.747569i	$0.731221\pi$
$692$	0.00887593	+	42.2794i	0.000337412	+	1.60722i
$693$	26.1992	−	4.34167i	0.995224	−	0.164926i
$694$	−34.9269	−	29.3009i	−1.32581	−	1.11225i
$695$	−1.78344	−	3.08901i	−0.0676497	−	0.117173i
$696$	4.46623	+	26.0662i	0.169292	+	0.988036i
$697$	5.37154	−	30.4635i	0.203461	−	1.15389i
$698$	−10.0169	−	3.64467i	−0.379146	−	0.137953i
$699$	−31.4418	−	0.162043i	−1.18924	−	0.00612904i
$700$	−13.5944	+	37.3747i	−0.513820	+	1.41263i
$701$	11.2547	−	30.9221i	0.425085	−	1.16791i	−0.523676	−	0.851917i	$-0.675440\pi$
$701$	11.2547	−	30.9221i	0.425085	−	1.16791i	0.948761	−	0.315994i	$-0.102338\pi$
$702$	−12.6187	−	7.54612i	−0.476263	−	0.284810i
$703$	24.3790	−	31.8985i	0.919471	−	1.20307i
$704$	−17.3959	+	0.0109561i	−0.655634	+	0.000412922i
$705$	7.06047	−	2.52867i	0.265913	−	0.0952353i
$706$	−14.7532	−	17.5784i	−0.555242	−	0.661571i
$707$	14.6711	+	12.3105i	0.551764	+	0.462985i
$708$	−0.119198	+	0.140637i	−0.00447973	+	0.00528545i
$709$	−2.16937	+	12.3031i	−0.0814726	+	0.462054i	0.916590	+	0.399829i	$0.130931\pi$
$709$	−2.16937	+	12.3031i	−0.0814726	+	0.462054i	−0.998062	+	0.0622245i	$0.980181\pi$
$710$	−0.000240448	−	2.29068i	−9.02384e−6	−	0.0859679i
$711$	−0.362283	−	1.02822i	−0.0135867	−	0.0385612i
$712$	−11.5769	−	31.7763i	−0.433864	−	1.19087i
$713$	−3.07145	−	8.43874i	−0.115027	−	0.316033i
$714$	−27.0318	+	4.62584i	−1.01164	+	0.173118i
$715$	1.27939	+	0.738655i	0.0478464	+	0.0276241i
$716$	28.2245	+	23.6731i	1.05480	+	0.884706i
$717$	41.0803	+	7.46206i	1.53417	+	0.278676i
$718$	−1.31121	+	7.44083i	−0.0489341	+	0.277689i
$719$	2.27158	+	12.8828i	0.0847157	+	0.480446i	0.997418	+	0.0718204i	$0.0228808\pi$
$719$	2.27158	+	12.8828i	0.0847157	+	0.480446i	−0.912702	+	0.408626i	$0.866008\pi$
$720$	0.0402874	−	4.07443i	0.00150142	−	0.151845i
$721$	38.8344			1.44627
$722$	24.3074	−	11.4521i	0.904627	−	0.426204i
$723$	3.73187	+	4.49430i	0.138790	+	0.167145i
$724$	0.984780	−	0.826681i	0.0365991	−	0.0307234i
$725$	−25.9684	+	4.57893i	−0.964441	+	0.170057i
$726$	13.3426	−	7.61382i	0.495192	−	0.282575i
$727$	−0.0279308	−	0.0332867i	−0.00103590	−	0.00123453i	0.765526	−	0.643405i	$-0.222479\pi$
$727$	−0.0279308	−	0.0332867i	−0.00103590	−	0.00123453i	−0.766562	+	0.642170i	$0.778034\pi$
$728$	−22.6892	−	3.99335i	−0.840916	−	0.148003i
$729$	12.7706	+	23.7889i	0.472986	+	0.881070i
$730$	−0.476590	−	0.275093i	−0.0176394	−	0.0101816i
$731$	9.87170	−	3.59301i	0.365118	−	0.132892i
$732$	21.3074	−	12.1618i	0.787543	−	0.449511i
$733$	−5.70905	−	9.88836i	−0.210868	−	0.365235i	0.741118	−	0.671375i	$-0.234296\pi$
$733$	−5.70905	−	9.88836i	−0.210868	−	0.365235i	−0.951987	+	0.306140i	$0.900962\pi$
$734$	0.00339819	+	32.3737i	0.000125429	+	1.19493i
$735$	2.78967	+	4.88987i	0.102898	+	0.180366i
$736$	2.11648	+	11.9664i	0.0780144	+	0.441088i
$737$	−4.83721	+	5.76476i	−0.178181	+	0.212348i
$738$	−41.5669	+	23.4365i	−1.53010	+	0.862709i
$739$	1.00831	−	2.77031i	0.0370913	−	0.101908i	−0.919764	−	0.392471i	$-0.871620\pi$
$739$	1.00831	−	2.77031i	0.0370913	−	0.101908i	0.956856	+	0.290563i	$0.0938427\pi$
$740$	5.41758	+	3.12632i	0.199154	+	0.114926i
$741$	15.0935	−	0.610218i	0.554473	−	0.0224169i
$742$	14.1070	+	24.4282i	0.517886	+	0.896787i
$743$	40.2105	+	14.6354i	1.47518	+	0.536922i	0.949502	−	0.313761i	$-0.101589\pi$
$743$	40.2105	+	14.6354i	1.47518	+	0.536922i	0.525679	+	0.850683i	$0.323811\pi$
$744$	15.6243	+	13.2397i	0.572816	+	0.485392i
$745$	−1.77536	−	1.48970i	−0.0650440	−	0.0545784i
$746$	0.955295	+	0.347585i	0.0349758	+	0.0127260i
$747$	32.8330	+	12.3349i	1.20130	+	0.451312i
$748$	10.3572	−	5.98263i	0.378696	−	0.218747i
$749$	−21.8759	+	12.6300i	−0.799327	+	0.461492i
$750$	8.22130	+	0.0415076i	0.300199	+	0.00151564i
$751$	−11.2827	−	30.9990i	−0.411711	−	1.13117i	−0.956280	−	0.292452i	$-0.905529\pi$
$751$	−11.2827	−	30.9990i	−0.411711	−	1.13117i	0.544569	−	0.838716i	$-0.316693\pi$
$752$	25.4851	−	44.1843i	0.929346	−	1.61124i
$753$	−28.9947	+	4.95862i	−1.05663	+	0.180702i
$754$	−5.22581	−	14.3531i	−0.190313	−	0.522710i
$755$	−3.89895	+	3.27161i	−0.141897	+	0.119066i
$756$	31.9899	+	27.6849i	1.16346	+	1.00689i
$757$	0.0272321	+	0.154441i	0.000989768	+	0.00561325i	0.985299	−	0.170841i	$-0.0546484\pi$
$757$	0.0272321	+	0.154441i	0.000989768	+	0.00561325i	−0.984309	+	0.176454i	$0.943537\pi$
$758$	−19.4350	+	3.42902i	−0.705911	+	0.124548i
$759$	5.16871	+	6.22470i	0.187612	+	0.225942i
$760$	2.25720	+	3.52562i	0.0818773	+	0.127888i
$761$		−	26.0234i		−	0.943347i	−0.881773	−	0.471673i	$-0.843650\pi$
$761$		−	26.0234i		−	0.943347i	0.881773	−	0.471673i	$-0.156350\pi$
$762$	−15.0321	−	12.7433i	−0.544556	−	0.461642i
$763$	−28.5739	+	5.03835i	−1.03444	+	0.182400i
$764$	−22.2474	+	8.10267i	−0.804881	+	0.293144i
$765$	1.37571	+	2.44055i	0.0497389	+	0.0882384i
$766$	−18.6360	+	6.78516i	−0.673346	+	0.245158i
$767$	0.0532404	−	0.0922151i	0.00192240	−	0.00332969i
$768$	−17.7217	−	21.3059i	−0.639477	−	0.768810i
$769$	−17.5452	+	6.38594i	−0.632697	+	0.230283i	−0.638405	−	0.769701i	$-0.720405\pi$
$769$	−17.5452	+	6.38594i	−0.632697	+	0.230283i	0.00570751	+	0.999984i	$0.498183\pi$
$770$	−3.25659	−	2.73202i	−0.117359	−	0.0984552i
$771$	−8.64869	−	3.19844i	−0.311475	−	0.115189i
$772$	−21.1305	−	36.5813i	−0.760502	−	1.31659i
$773$	−42.3125	−	7.46083i	−1.52187	−	0.268347i	−0.650704	−	0.759331i	$-0.725526\pi$
$773$	−42.3125	−	7.46083i	−1.52187	−	0.268347i	−0.871169	+	0.490984i	$0.836637\pi$
$774$	−13.9511	−	8.24559i	−0.501462	−	0.296381i
$775$	−13.1256	+	15.6425i	−0.471486	+	0.561895i
$776$	−7.13749	−	40.4043i	−0.256221	−	1.45043i
$777$	−61.1408	+	21.8972i	−2.19341	+	0.785559i
$778$	−13.5650	+	7.83368i	−0.486330	+	0.280851i
$779$	22.5540	−	43.5304i	0.808079	−	1.55964i
$780$	0.397209	+	2.31968i	0.0142224	+	0.0830580i
$781$	−9.74737	−	3.54775i	−0.348788	−	0.126949i
$782$	−5.37144	−	6.40007i	−0.192082	−	0.228866i
$783$	−5.29738	+	27.5455i	−0.189313	+	0.984396i
$784$	35.9855	+	13.0805i	1.28520	+	0.467162i
$785$	5.51684	+	0.972767i	0.196904	+	0.0347195i
$786$	25.2418	+	30.3924i	0.900347	+	1.08406i
$787$	15.7694	−	9.10449i	0.562120	−	0.324540i	−0.191876	−	0.981419i	$-0.561457\pi$
$787$	15.7694	−	9.10449i	0.562120	−	0.324540i	0.753996	+	0.656879i	$0.228124\pi$
$788$	27.4075	+	4.82674i	0.976351	+	0.171946i
$789$	7.88037	+	4.60404i	0.280548	+	0.163908i
$790$	−0.0872344	+	0.151131i	−0.00310366	+	0.00537700i
$791$	−13.1233	+	22.7302i	−0.466611	+	0.808193i
$792$	−17.2745	−	6.48361i	−0.613823	−	0.230385i
$793$	−10.8552	+	9.10857i	−0.385478	+	0.323455i
$794$	1.60166	−	9.08902i	0.0568406	−	0.322557i
$795$	1.86367	−	2.19793i	0.0660976	−	0.0779527i
$796$	−8.64888	−	10.3029i	−0.306551	−	0.365178i
$797$			13.7014i			0.485330i	0.970110	+	0.242665i	$0.0780215\pi$
$797$			13.7014i			0.485330i	−0.970110	+	0.242665i	$0.921978\pi$
$798$	−43.0756	−	5.80784i	−1.52486	−	0.205595i
$799$			35.0710i			1.24072i
$800$	21.1581	−	17.7727i	0.748050	−	0.628358i
$801$	0.369730	−	35.8690i	0.0130638	−	1.26737i
$802$	−14.0689	−	2.47921i	−0.496791	−	0.0875440i
$803$	−1.90888	+	1.60174i	−0.0673629	+	0.0565242i
$804$	−11.9882	−	0.0592675i	−0.422792	−	0.00209020i
$805$	−1.48472	+	2.57162i	−0.0523296	+	0.0906376i
$806$	−10.2445	−	5.91326i	−0.360849	−	0.208286i
$807$	24.1681	−	41.3665i	0.850757	−	1.45617i
$808$	−4.55502	−	12.5026i	−0.160245	−	0.439839i
$809$	35.8537	−	20.7001i	1.26055	−	0.727777i	0.287367	−	0.957821i	$-0.407220\pi$
$809$	35.8537	−	20.7001i	1.26055	−	0.727777i	0.973180	+	0.230043i	$0.0738867\pi$
$810$	1.56112	−	4.02999i	0.0548521	−	0.141599i
$811$	−3.95845	−	0.697981i	−0.139000	−	0.0245094i	0.103715	−	0.994607i	$-0.466927\pi$
$811$	−3.95845	−	0.697981i	−0.139000	−	0.0245094i	−0.242715	+	0.970098i	$0.578038\pi$
$812$	7.64123	+	43.2824i	0.268154	+	1.51891i
$813$	28.7536	+	0.148189i	1.00843	+	0.00519721i
$814$	21.6957	−	18.2087i	0.760434	−	0.638216i
$815$	0.750851	+	0.273287i	0.0263012	+	0.00957284i
$816$	17.8743	+	6.60170i	0.625725	+	0.231106i
$817$	16.6324	−	0.758314i	0.581895	−	0.0265301i
$818$	−17.8041	−	30.8301i	−0.622505	−	1.07795i
$819$	−21.0346	−	12.4352i	−0.735009	−	0.434520i
$820$	7.17808	+	2.61090i	0.250669	+	0.0911766i
$821$	−9.71713	+	11.5804i	−0.339130	+	0.404160i	−0.908475	−	0.417939i	$-0.862752\pi$
$821$	−9.71713	+	11.5804i	−0.339130	+	0.404160i	0.569345	+	0.822099i	$0.307197\pi$
$822$	−30.8174	+	11.0407i	−1.07488	+	0.385090i
$823$	41.5345	+	7.32365i	1.44780	+	0.255286i	0.841633	−	0.540050i	$-0.181595\pi$
$823$	41.5345	+	7.32365i	1.44780	+	0.255286i	0.606168	+	0.795337i	$0.292706\pi$
$824$	−23.3711	−	13.4835i	−0.814172	−	0.469721i
$825$	6.38130	−	17.2553i	0.222168	−	0.600751i
$826$	−0.196917	+	0.234727i	−0.00685162	+	0.00816719i
$827$	22.6630	−	8.24867i	0.788071	−	0.286834i	0.0835370	−	0.996505i	$-0.473378\pi$
$827$	22.6630	−	8.24867i	0.788071	−	0.286834i	0.704534	+	0.709670i	$0.251156\pi$
$828$	−2.36626	+	12.6702i	−0.0822332	+	0.440321i
$829$	−15.4300	+	26.7255i	−0.535905	+	0.928215i	0.463214	+	0.886247i	$0.346696\pi$
$829$	−15.4300	+	26.7255i	−0.535905	+	0.928215i	−0.999119	+	0.0419684i	$0.986637\pi$
$830$	−1.92069	−	5.27533i	−0.0666681	−	0.183109i
$831$	−36.9801	−	6.71727i	−1.28282	−	0.233020i
$832$	12.2682	+	10.2811i	0.425323	+	0.356432i
$833$	−25.9264	+	4.57153i	−0.898297	+	0.158394i
$834$	−19.6274	−	16.6389i	−0.679640	−	0.576158i
$835$		−	6.23728i		−	0.215850i
$836$	18.4986	−	4.14255i	0.639788	−	0.143273i
$837$	10.5688	+	18.9773i	0.365310	+	0.655951i
$838$	−1.42008	−	8.04875i	−0.0490559	−	0.278039i
$839$	0.0334751	+	0.189847i	0.00115569	+	0.00655423i	0.985380	−	0.170370i	$-0.0544963\pi$
$839$	0.0334751	+	0.189847i	0.00115569	+	0.00655423i	−0.984224	+	0.176924i	$0.943385\pi$
$840$	0.0327672	−	6.77171i	0.00113058	−	0.233646i
$841$	−0.108304	+	0.0908775i	−0.00373461	+	0.00313371i
$842$	−14.8218	+	5.39645i	−0.510792	+	0.185974i
$843$	−4.78847	−	27.9999i	−0.164924	−	0.964366i
$844$	0.00765885	+	36.4820i	0.000263628	+	1.25576i
$845$	1.04483	+	2.87063i	0.0359431	+	0.0987528i
$846$	41.7967	−	34.3511i	1.43700	−	1.18101i
$847$	22.1105	−	12.7655i	0.759726	−	0.438628i
$848$	−0.00822918	−	19.5993i	−0.000282591	−	0.673044i
$849$	25.5918	+	44.8586i	0.878308	+	1.53954i
$850$	−6.49615	+	17.8538i	−0.222816	+	0.612382i
$851$	−15.1571	−	12.7183i	−0.519580	−	0.435979i
$852$	−5.57495	−	15.5559i	−0.190995	−	0.532937i
$853$	26.8776	+	9.78266i	0.920272	+	0.334952i	0.758347	−	0.651851i	$-0.226007\pi$
$853$	26.8776	+	9.78266i	0.920272	+	0.334952i	0.161926	+	0.986803i	$0.448230\pi$
$854$	35.3091	−	20.3906i	1.20825	−	0.697753i
$855$	0.924681	+	4.34287i	0.0316234	+	0.148523i
$856$	17.5505	−	0.00552669i	0.599863	−	0.000188899i
$857$	6.44591	−	17.7100i	0.220188	−	0.604962i	−0.779584	−	0.626297i	$-0.784570\pi$
$857$	6.44591	−	17.7100i	0.220188	−	0.604962i	0.999772	+	0.0213354i	$0.00679177\pi$
$858$	10.4858	+	1.90356i	0.357978	+	0.0649863i
$859$	−16.5228	+	19.6911i	−0.563750	+	0.671851i	−0.970336	−	0.241762i	$-0.922275\pi$
$859$	−16.5228	+	19.6911i	−0.563750	+	0.671851i	0.406586	+	0.913613i	$0.366719\pi$
$860$	0.450976	+	2.55448i	0.0153782	+	0.0871070i
$861$	−68.8841	+	39.2983i	−2.34756	+	1.33928i
$862$	20.8088	−	0.00218425i	0.708751	−	7.43959e-5i
$863$	−6.25339	−	10.8312i	−0.212868	−	0.368698i	0.739743	−	0.672889i	$-0.234947\pi$
$863$	−6.25339	−	10.8312i	−0.212868	−	0.368698i	−0.952611	+	0.304192i	$0.901614\pi$
$864$	−9.63963	−	27.7683i	−0.327947	−	0.944696i
$865$	6.74515	−	2.45503i	0.229342	−	0.0834736i
$866$	−0.245119	+	0.424661i	−0.00832947	+	0.0144306i
$867$	16.1097	−	2.75505i	0.547115	−	0.0935664i
$868$	26.0775	+	21.8723i	0.885127	+	0.742393i
$869$	0.507926	+	0.605323i	0.0172302	+	0.0205342i
$870$	3.89966	−	2.22529i	0.132211	−	0.0754445i
$871$	6.81911	−	1.20239i	0.231057	−	0.0407415i
$872$	18.9456	+	6.88886i	0.641578	+	0.233286i
$873$	7.99829	−	42.7774i	0.270701	−	1.44780i
$874$	−5.09254	−	12.2241i	−0.172258	−	0.413488i
$875$	13.6635			0.461910
$876$	−3.90593	−	0.708649i	−0.131969	−	0.0239430i
$877$	−9.86431	−	55.9433i	−0.333094	−	1.88907i	−0.445292	−	0.895385i	$-0.646900\pi$
$877$	−9.86431	−	55.9433i	−0.333094	−	1.88907i	0.112198	−	0.993686i	$-0.464211\pi$
$878$	36.8214	+	6.48861i	1.24266	+	0.218980i
$879$	2.88432	−	15.8788i	0.0972857	−	0.535579i
$880$	1.01129	+	2.77488i	0.0340907	+	0.0935412i
$881$	17.2332	+	9.94959i	0.580601	+	0.335210i	0.761372	−	0.648315i	$-0.224526\pi$
$881$	17.2332	+	9.94959i	0.580601	+	0.335210i	−0.180771	+	0.983525i	$0.557859\pi$
$882$	30.8424	+	26.4207i	1.03852	+	0.889633i
$883$	−2.63850	−	7.24921i	−0.0887925	−	0.243955i	0.887346	−	0.461104i	$-0.152547\pi$
$883$	−2.63850	−	7.24921i	−0.0887925	−	0.243955i	−0.976139	+	0.217149i	$0.930324\pi$
$884$	−10.8388	−	1.90882i	−0.364548	−	0.0642007i
$885$	0.0293560	+	0.0108564i	0.000986790	+	0.000364932i
$886$	−10.1193	+	0.00106219i	−0.339963	+	3.56851e-5i
$887$	4.12020	−	23.3668i	0.138343	−	0.784580i	−0.834131	−	0.551567i	$-0.814030\pi$
$887$	4.12020	−	23.3668i	0.138343	−	0.784580i	0.972473	−	0.233014i	$-0.0748587\pi$
$888$	44.3983	+	8.05033i	1.48991	+	0.270151i
$889$	−25.0891	−	21.0522i	−0.841461	−	0.706069i
$890$	−4.39804	+	3.69118i	−0.147423	+	0.123729i
$891$	−14.7293	−	12.8860i	−0.493451	−	0.431697i
$892$	−16.5651	−	9.55922i	−0.554640	−	0.320066i
$893$	−16.6122	+	53.0435i	−0.555906	+	1.77503i
$894$	−15.6813	−	5.79735i	−0.524461	−	0.193892i
$895$	2.13907	−	5.87705i	0.0715012	−	0.196448i
$896$	−29.6308	−	35.2600i	−0.989896	−	1.17795i
$897$	0.0383675	−	7.44457i	0.00128105	−	0.248567i
$898$	9.01321	−	24.7717i	0.300775	−	0.826642i
$899$	−3.91867	+	22.2239i	−0.130695	+	0.741209i
$900$	27.6405	−	9.74541i	0.921351	−	0.324847i
$901$	6.73794	+	11.6705i	0.224473	+	0.388799i
$902$	22.2299	−	26.4983i	0.740176	−	0.882296i
$903$	−23.2548	−	13.5864i	−0.773871	−	0.452128i
$904$	15.7899	−	9.12291i	0.525163	−	0.303424i
$905$	−0.189047	−	0.109146i	−0.00628413	−	0.00362814i
$906$	−18.5186	+	31.7044i	−0.615240	+	1.05331i
$907$	−20.0741	−	23.9234i	−0.666550	−	0.794363i	0.321760	−	0.946821i	$-0.395725\pi$
$907$	−20.0741	−	23.9234i	−0.666550	−	0.794363i	−0.988310	+	0.152458i	$0.951281\pi$
$908$	−21.7882	+	7.93542i	−0.723065	+	0.263346i
$909$	0.145473	−	14.1129i	0.00482503	−	0.468095i
$910$	0.679592	+	3.85180i	0.0225283	+	0.127686i
$911$	0.0767253			0.00254202			0.00127101	−	0.999999i	$-0.499595\pi$
$911$	0.0767253			0.00254202			0.00127101	+	0.999999i	$0.499595\pi$
$912$	23.9071	+	18.4514i	0.791642	+	0.610985i
$913$	−25.4224			−0.841359
$914$	−5.97088	−	33.8418i	−0.197499	−	1.11939i
$915$	−3.17694	−	2.69379i	−0.105026	−	0.0890540i
$916$	−53.0755	+	19.3305i	−1.75366	+	0.638698i
$917$	42.2049	+	50.2979i	1.39373	+	1.66098i
$918$	15.2807	+	13.2271i	0.504338	+	0.436561i
$919$	−21.1113	−	12.1886i	−0.696398	−	0.402066i	0.109606	−	0.993975i	$-0.465041\pi$
$919$	−21.1113	−	12.1886i	−0.696398	−	0.402066i	−0.806005	+	0.591909i	$0.798374\pi$
$920$	1.78641	−	1.03213i	0.0588962	−	0.0340285i
$921$	−9.31569	+	15.9449i	−0.306962	+	0.525403i
$922$	−27.2177	+	32.4437i	−0.896366	+	1.06848i
$923$	4.77222	+	8.26573i	0.157080	+	0.272070i
$924$	−28.7633	−	10.6303i	−0.946242	−	0.349711i
$925$	−7.81257	+	44.3073i	−0.256876	+	1.45681i
$926$	10.7487	−	29.5416i	0.353225	−	0.970796i
$927$	−18.1687	−	22.1115i	−0.596737	−	0.726236i
$928$	10.4293	−	28.7011i	0.342358	−	0.942160i
$929$	13.7548	−	37.7911i	0.451281	−	1.23989i	−0.480542	−	0.876972i	$-0.659560\pi$
$929$	13.7548	−	37.7911i	0.451281	−	1.23989i	0.931823	−	0.362913i	$-0.118218\pi$
$930$	1.20566	−	3.26120i	0.0395352	−	0.106939i
$931$	−41.3780	−	5.36639i	−1.35611	−	0.175876i
$932$	31.4460	+	18.1466i	1.03005	+	0.594411i
$933$	0.700038	+	1.95462i	0.0229182	+	0.0639915i
$934$	17.7965	−	14.9362i	0.582320	−	0.488729i
$935$	−1.55559	−	1.30529i	−0.0508732	−	0.0426877i
$936$	8.34140	+	14.7870i	0.272647	+	0.483329i
$937$	−0.524061	+	2.97210i	−0.0171203	+	0.0970942i	−0.992171	−	0.124890i	$-0.960142\pi$
$937$	−0.524061	+	2.97210i	−0.0171203	+	0.0970942i	0.975050	+	0.221984i	$0.0712533\pi$
$938$	−19.9239	+	0.00209137i	−0.650540	+	6.82856e-5i
$939$	−9.51096	+	25.7180i	−0.310379	+	0.839275i
$940$	−8.52858	−	1.50197i	−0.278172	−	0.0489890i
$941$	−1.23392	−	3.39016i	−0.0402245	−	0.110516i	0.917954	−	0.396686i	$-0.129840\pi$
$941$	−1.23392	−	3.39016i	−0.0402245	−	0.110516i	−0.958179	+	0.286170i	$0.907618\pi$
$942$	39.8327	−	6.81641i	1.29782	−	0.222090i
$943$	−20.9248	−	12.0809i	−0.681404	−	0.393409i
$944$	0.200006	−	0.0728915i	0.00650965	−	0.00237242i
$945$	2.56064	−	6.71062i	0.0832976	−	0.218296i
$946$	11.5681	+	2.03852i	0.376112	+	0.0662780i
$947$	−0.302599	−	1.71613i	−0.00983316	−	0.0557666i	0.979496	−	0.201462i	$-0.0645692\pi$
$947$	−0.302599	−	1.71613i	−0.00983316	−	0.0557666i	−0.989330	+	0.145695i	$0.953458\pi$
$948$	−0.224719	+	1.23861i	−0.00729853	+	0.0402280i
$949$	2.29284			0.0744287
$950$	−18.2820	+	23.9261i	−0.593147	+	0.776267i
$951$	−33.6056	+	27.9046i	−1.08974	+	0.904868i
$952$	29.7610	+	10.8215i	0.964560	+	0.350727i
$953$	33.3454	−	5.87970i	1.08016	−	0.190462i	0.394877	−	0.918734i	$-0.370787\pi$
$953$	33.3454	−	5.87970i	1.08016	−	0.190462i	0.685288	+	0.728272i	$0.259676\pi$
$954$	7.30892	−	19.4610i	0.236635	−	0.630073i
$955$	2.58387	+	3.07933i	0.0836120	+	0.0996449i
$956$	−36.9388	−	30.9821i	−1.19468	−	1.00203i
$957$	−3.42732	−	20.0407i	−0.110790	−	0.647825i
$958$	10.1889	−	17.6520i	0.329189	−	0.570311i
$959$	−51.1234	+	18.6074i	−1.65086	+	0.600864i
$960$	−2.37090	+	4.06394i	−0.0765204	+	0.131163i
$961$	−6.76229	−	11.7126i	−0.218138	−	0.377827i
$962$	−26.0620	+	0.00273566i	−0.840271	+	8.82013e-5i
$963$	17.4259	+	6.54670i	0.561542	+	0.210964i
$964$	−1.17273	−	6.64270i	−0.0377710	−	0.213947i
$965$	−4.61026	+	5.49430i	−0.148410	+	0.176868i
$966$	−3.82622	+	21.0767i	−0.123107	+	0.678133i
$967$	−8.36352	+	22.9786i	−0.268953	+	0.738941i	0.729534	+	0.683945i	$0.239737\pi$
$967$	−8.36352	+	22.9786i	−0.268953	+	0.738941i	−0.998487	+	0.0549967i	$0.982485\pi$
$968$	−17.7387	+	0.00558597i	−0.570144	+	0.000179540i
$969$	−20.5776	−	2.77666i	−0.661049	−	0.0891991i
$970$	−6.03228	+	3.48358i	−0.193685	+	0.111851i
$971$	3.12091	+	1.13592i	0.100155	+	0.0364534i	0.391612	−	0.920131i	$-0.371918\pi$
$971$	3.12091	+	1.13592i	0.100155	+	0.0364534i	−0.291457	+	0.956584i	$0.594140\pi$
$972$	0.796752	−	31.1667i	0.0255558	−	0.999673i
$973$	−32.7587	−	27.4878i	−1.05020	−	0.881218i
$974$	−0.451169	+	1.23998i	−0.0144564	+	0.0397315i
$975$	−14.7035	+	8.38834i	−0.470889	+	0.268642i
$976$	−28.3293	+	0.0118946i	−0.906798	+	0.000380738i
$977$	−22.8654	+	13.2013i	−0.731529	+	0.422349i	−0.818981	−	0.573820i	$-0.805461\pi$
$977$	−22.8654	+	13.2013i	−0.731529	+	0.422349i	0.0874521	+	0.996169i	$0.472128\pi$
$978$	5.76409	+	0.0291017i	0.184315	+	0.000930569i
$979$	8.89265	+	24.4324i	0.284210	+	0.780862i
$980$	−0.00136470	−	6.50058i	−4.35937e−5	−	0.207653i
$981$	16.2370	+	13.9122i	0.518408	+	0.444182i
$982$	−40.8918	+	14.8883i	−1.30491	+	0.475104i
$983$	−11.4614	+	9.61725i	−0.365562	+	0.306743i	−0.807003	−	0.590548i	$-0.798912\pi$
$983$	−11.4614	+	9.61725i	−0.365562	+	0.306743i	0.441441	+	0.897290i	$0.354467\pi$
$984$	55.1002	+	0.266621i	1.75653	+	0.00849957i
$985$	−0.820443	−	4.65296i	−0.0261415	−	0.148256i
$986$	3.64817	+	20.6771i	0.116181	+	0.658493i
$987$	69.1746	−	57.4394i	2.20185	−	1.82832i
$988$	−15.4890	−	8.02105i	−0.492772	−	0.255184i
$989$		−	8.20555i		−	0.260921i
$990$	−0.0319594	+	3.13241i	−0.00101573	+	0.0995545i
$991$	−51.9670	+	9.16319i	−1.65079	+	0.291078i	−0.920114	−	0.391650i	$-0.871904\pi$
$991$	−51.9670	+	9.16319i	−1.65079	+	0.291078i	−0.730672	+	0.682728i	$0.760793\pi$
$992$	−8.09965	−	22.2173i	−0.257164	−	0.705400i
$993$	2.89716	−	15.9495i	0.0919387	−	0.506143i
$994$	−9.39564	−	25.8059i	−0.298012	−	0.818513i
$995$	−1.14191	+	1.97784i	−0.0362009	+	0.0627017i
$996$	−25.8788	−	31.1527i	−0.820003	−	0.987111i
$997$	−39.1439	+	14.2472i	−1.23970	+	0.451213i	−0.876908	−	0.480657i	$-0.840398\pi$
$997$	−39.1439	+	14.2472i	−1.23970	+	0.451213i	−0.362790	+	0.931871i	$0.618176\pi$
$998$	6.80202	−	8.10806i	0.215314	−	0.256656i
$999$	41.0725	+	24.5676i	1.29948	+	0.777285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.v.a.23.20	yes	216
3.2	odd	2	inner	228.2.v.a.23.17	yes	216
4.3	odd	2	inner	228.2.v.a.23.10	✓	216
12.11	even	2	inner	228.2.v.a.23.27	yes	216
19.5	even	9	inner	228.2.v.a.119.27	yes	216
57.5	odd	18	inner	228.2.v.a.119.10	yes	216
76.43	odd	18	inner	228.2.v.a.119.17	yes	216
228.119	even	18	inner	228.2.v.a.119.20	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.v.a.23.10	✓	216	4.3	odd	2	inner
228.2.v.a.23.17	yes	216	3.2	odd	2	inner
228.2.v.a.23.20	yes	216	1.1	even	1	trivial
228.2.v.a.23.27	yes	216	12.11	even	2	inner
228.2.v.a.119.10	yes	216	57.5	odd	18	inner
228.2.v.a.119.17	yes	216	76.43	odd	18	inner
228.2.v.a.119.20	yes	216	228.119	even	18	inner
228.2.v.a.119.27	yes	216	19.5	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.245722 + 1.39270i) q^{2} +(1.12016 - 1.32107i) q^{3} +(-1.87924 + 0.684435i) q^{4} +(0.218260 + 0.260112i) q^{5} +(2.11511 + 1.23544i) q^{6} +(3.52551 + 2.03545i) q^{7} +(-1.41498 - 2.44904i) q^{8} +(-0.490465 - 2.95964i) q^{9} +O(q^{10})\)	\(q+(0.245722 + 1.39270i) q^{2} +(1.12016 - 1.32107i) q^{3} +(-1.87924 + 0.684435i) q^{4} +(0.218260 + 0.260112i) q^{5} +(2.11511 + 1.23544i) q^{6} +(3.52551 + 2.03545i) q^{7} +(-1.41498 - 2.44904i) q^{8} +(-0.490465 - 2.95964i) q^{9} +(-0.308628 + 0.367887i) q^{10} +(1.08725 + 1.88317i) q^{11} +(-1.20087 + 3.24929i) q^{12} +(0.347438 - 1.97042i) q^{13} +(-1.96849 + 5.41014i) q^{14} +(0.588114 + 0.00303100i) q^{15} +(3.06310 - 2.57244i) q^{16} +(-0.940649 + 2.58441i) q^{17} +(4.00137 - 1.41032i) q^{18} +(-2.64686 + 3.46326i) q^{19} +(-0.588193 - 0.339429i) q^{20} +(6.63813 - 2.37741i) q^{21} +(-2.35553 + 1.97695i) q^{22} +(1.64563 + 1.38085i) q^{23} +(-4.82038 - 0.874034i) q^{24} +(0.848220 - 4.81049i) q^{25} +(2.82958 - 0.000297014i) q^{26} +(-4.45929 - 2.66734i) q^{27} +(-8.01842 - 1.41213i) q^{28} +(-1.84632 - 5.07272i) q^{29} +(0.140291 + 0.819813i) q^{30} +(-3.62030 - 2.09018i) q^{31} +(4.33531 + 3.63388i) q^{32} +(3.70569 + 0.673124i) q^{33} +(-3.83046 - 0.674998i) q^{34} +(0.240031 + 1.36129i) q^{35} +(2.94738 + 5.22618i) q^{36} -9.21054 q^{37} +(-5.47368 - 2.83529i) q^{38} +(-2.21388 - 2.66618i) q^{39} +(0.328192 - 0.902583i) q^{40} +(-11.0765 + 1.95309i) q^{41} +(4.94216 + 8.66076i) q^{42} +(-2.45526 - 2.92607i) q^{43} +(-3.33210 - 2.79478i) q^{44} +(0.662789 - 0.773546i) q^{45} +(-1.51874 + 2.63118i) q^{46} +(11.9828 - 4.36138i) q^{47} +(0.0327969 - 6.92813i) q^{48} +(4.78614 + 8.28983i) q^{49} +(6.90801 - 0.000725118i) q^{50} +(2.36051 + 4.13763i) q^{51} +(0.695703 + 3.94069i) q^{52} +(3.14955 - 3.75349i) q^{53} +(2.61906 - 6.86589i) q^{54} +(-0.252532 + 0.693826i) q^{55} +(-0.00362587 - 11.5143i) q^{56} +(1.61030 + 7.37611i) q^{57} +(6.61111 - 3.81785i) q^{58} +(0.0500092 + 0.0182019i) q^{59} +(-1.10728 + 0.396830i) q^{60} +(-5.42537 - 4.55243i) q^{61} +(2.02141 - 5.55560i) q^{62} +(4.29506 - 11.4325i) q^{63} +(-3.99564 + 6.93072i) q^{64} +(0.588362 - 0.339691i) q^{65} +(-0.0268915 + 5.32633i) q^{66} +(1.18364 + 3.25203i) q^{67} +(-0.00115476 - 5.50055i) q^{68} +(3.66757 - 0.627220i) q^{69} +(-1.83689 + 0.668790i) q^{70} +(-3.65424 + 3.06627i) q^{71} +(-6.55428 + 5.38901i) q^{72} +(0.198992 + 1.12854i) q^{73} +(-2.26323 - 12.8275i) q^{74} +(-5.40487 - 6.50910i) q^{75} +(2.60371 - 8.31990i) q^{76} +8.85216i q^{77} +(3.16920 - 3.73841i) q^{78} +(0.357871 - 0.0631023i) q^{79} +(1.33767 + 0.235289i) q^{80} +(-8.51889 + 2.90320i) q^{81} +(-5.44182 - 14.9464i) q^{82} +(-5.84559 + 10.1249i) q^{83} +(-10.8475 + 9.01109i) q^{84} +(-0.877544 + 0.319400i) q^{85} +(3.47183 - 4.13845i) q^{86} +(-8.76961 - 3.24316i) q^{87} +(3.07352 - 5.32737i) q^{88} +(11.7753 + 2.07631i) q^{89} +(1.24018 + 0.732990i) q^{90} +(5.23559 - 6.23953i) q^{91} +(-4.03763 - 1.46862i) q^{92} +(-6.81661 + 2.44133i) q^{93} +(9.01854 + 15.6168i) q^{94} +(-1.47854 + 0.0674103i) q^{95} +(9.65688 - 1.65672i) q^{96} +(13.6314 + 4.96143i) q^{97} +(-10.3692 + 8.70266i) q^{98} +(5.04023 - 4.14148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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