LMFDB - Embedded newform 228.2.v.a.23.17

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			23.17
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.245722 - 1.39270i) q^{2} +(1.50444 + 0.858283i) q^{3} +(-1.87924 + 0.684435i) q^{4} +(-0.218260 - 0.260112i) q^{5} +(0.825659 - 2.30614i) q^{6} +(3.52551 + 2.03545i) q^{7} +(1.41498 + 2.44904i) q^{8} +(1.52670 + 2.58248i) q^{9} +O(q^{10})$	\(q+(-0.245722 - 1.39270i) q^{2} +(1.50444 + 0.858283i) q^{3} +(-1.87924 + 0.684435i) q^{4} +(-0.218260 - 0.260112i) q^{5} +(0.825659 - 2.30614i) q^{6} +(3.52551 + 2.03545i) q^{7} +(1.41498 + 2.44904i) q^{8} +(1.52670 + 2.58248i) q^{9} +(-0.308628 + 0.367887i) q^{10} +(-1.08725 - 1.88317i) q^{11} +(-3.41465 - 0.583228i) q^{12} +(0.347438 - 1.97042i) q^{13} +(1.96849 - 5.41014i) q^{14} +(-0.105110 - 0.578653i) q^{15} +(3.06310 - 2.57244i) q^{16} +(0.940649 - 2.58441i) q^{17} +(3.22148 - 2.76081i) q^{18} +(-2.64686 + 3.46326i) q^{19} +(0.588193 + 0.339429i) q^{20} +(3.55693 + 6.08811i) q^{21} +(-2.35553 + 1.97695i) q^{22} +(-1.64563 - 1.38085i) q^{23} +(0.0267905 + 4.89891i) q^{24} +(0.848220 - 4.81049i) q^{25} +(-2.82958 + 0.000297014i) q^{26} +(0.0803352 + 5.19553i) q^{27} +(-8.01842 - 1.41213i) q^{28} +(1.84632 + 5.07272i) q^{29} +(-0.780064 + 0.288575i) q^{30} +(-3.62030 - 2.09018i) q^{31} +(-4.33531 - 3.63388i) q^{32} +(-0.0194105 - 3.76628i) q^{33} +(-3.83046 - 0.674998i) q^{34} +(-0.240031 - 1.36129i) q^{35} +(-4.63657 - 3.80817i) 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} +(7.60491 - 6.44973i) q^{42} +(-2.45526 - 2.92607i) q^{43} +(3.33210 + 2.79478i) q^{44} +(0.338516 - 0.960765i) q^{45} +(-1.51874 + 2.63118i) q^{46} +(-11.9828 + 4.36138i) q^{47} +(6.81614 - 1.24108i) q^{48} +(4.78614 + 8.28983i) q^{49} +(-6.90801 + 0.000725118i) q^{50} +(3.63331 - 3.08076i) q^{51} +(0.695703 + 3.94069i) q^{52} +(-3.14955 + 3.75349i) q^{53} +(7.21609 - 1.38854i) q^{54} +(-0.252532 + 0.693826i) q^{55} +(0.00362587 + 11.5143i) q^{56} +(-6.95450 + 2.93852i) q^{57} +(6.61111 - 3.81785i) q^{58} +(-0.0500092 - 0.0182019i) q^{59} +(0.593577 + 1.01549i) q^{60} +(-5.42537 - 4.55243i) q^{61} +(-2.02141 + 5.55560i) q^{62} +(0.125879 + 12.2121i) q^{63} +(-3.99564 + 6.93072i) q^{64} +(-0.588362 + 0.339691i) q^{65} +(-5.24054 + 0.952491i) q^{66} +(1.18364 + 3.25203i) q^{67} +(0.00115476 + 5.50055i) q^{68} +(-1.29060 - 3.48982i) q^{69} +(-1.83689 + 0.668790i) q^{70} +(3.65424 - 3.06627i) q^{71} +(-4.16435 + 7.39312i) 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} +(-4.25720 - 2.42813i) q^{78} +(0.357871 - 0.0631023i) q^{79} +(-1.33767 - 0.235289i) q^{80} +(-4.33838 + 7.88533i) q^{81} +(-5.44182 - 14.9464i) q^{82} +(5.84559 - 10.1249i) q^{83} +(-10.8512 - 9.00654i) q^{84} +(-0.877544 + 0.319400i) q^{85} +(-3.47183 + 4.13845i) q^{86} +(-1.57615 + 9.21628i) q^{87} +(3.07352 - 5.32737i) q^{88} +(-11.7753 - 2.07631i) q^{89} +(-1.42124 - 0.235372i) q^{90} +(5.23559 - 6.23953i) q^{91} +(4.03763 + 1.46862i) q^{92} +(-3.65257 - 6.25180i) q^{93} +(9.01854 + 15.6168i) q^{94} +(1.47854 - 0.0674103i) q^{95} +(-3.40333 - 9.18789i) q^{96} +(13.6314 + 4.96143i) q^{97} +(10.3692 - 8.70266i) q^{98} +(3.20334 - 5.68282i) 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
$3$	1.50444	+	0.858283i	0.868591	+	0.495530i
$3$	1.50444	+	0.858283i	0.868591	+	0.495530i
$4$	−1.87924	+	0.684435i	−0.939621	+	0.342217i
$5$	−0.218260	−	0.260112i	−0.0976089	−	0.116326i	0.715029	−	0.699095i	$-0.246414\pi$
$5$	−0.218260	−	0.260112i	−0.0976089	−	0.116326i	−0.812638	+	0.582769i	$0.801969\pi$
$6$	0.825659	−	2.30614i	0.337074	−	0.941478i
$7$	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
$9$	1.52670	+	2.58248i	0.508900	+	0.860826i
$10$	−0.308628	+	0.367887i	−0.0975967	+	0.116336i
$11$	−1.08725	−	1.88317i	−0.327817	−	0.567796i	0.654261	−	0.756269i	$-0.272980\pi$
$11$	−1.08725	−	1.88317i	−0.327817	−	0.567796i	−0.982078	+	0.188473i	$0.939646\pi$
$12$	−3.41465	−	0.583228i	−0.985725	−	0.168364i
$13$	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
$15$	−0.105110	−	0.578653i	−0.0271393	−	0.149408i
$16$	3.06310	−	2.57244i	0.765774	−	0.643109i
$17$	0.940649	−	2.58441i	0.228141	−	0.626812i	−0.771818	−	0.635843i	$-0.780652\pi$
$17$	0.940649	−	2.58441i	0.228141	−	0.626812i	0.999959	+	0.00903105i	$0.00287471\pi$
$18$	3.22148	−	2.76081i	0.759310	−	0.650729i
$19$	−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
$21$	3.55693	+	6.08811i	0.776186	+	1.32853i
$22$	−2.35553	+	1.97695i	−0.502201	+	0.421486i
$23$	−1.64563	−	1.38085i	−0.343137	−	0.287926i	0.454890	−	0.890548i	$-0.349679\pi$
$23$	−1.64563	−	1.38085i	−0.343137	−	0.287926i	−0.798027	+	0.602621i	$0.794123\pi$
$24$	0.0267905	+	4.89891i	0.00546858	+	0.999985i
$25$	0.848220	−	4.81049i	0.169644	−	0.962099i
$26$	−2.82958		0.000297014i	−0.554926		5.82493e-5i
$27$	0.0803352	+	5.19553i	0.0154605	+	0.999880i
$28$	−8.01842	−	1.41213i	−1.51534	−	0.266867i
$29$	1.84632	+	5.07272i	0.342853	+	0.941980i	0.984563	+	0.175033i	$0.0560032\pi$
$29$	1.84632	+	5.07272i	0.342853	+	0.941980i	−0.641710	+	0.766948i	$0.721775\pi$
$30$	−0.780064	+	0.288575i	−0.142420	+	0.0526863i
$31$	−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
$33$	−0.0194105	−	3.76628i	−0.00337893	−	0.655626i
$34$	−3.83046	−	0.674998i	−0.656918	−	0.115761i
$35$	−0.240031	−	1.36129i	−0.0405727	−	0.230099i
$36$	−4.63657	−	3.80817i	−0.772762	−	0.634695i
$37$	−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	0.781901	−	0.623403i	$-0.214250\pi$
$41$	11.0765	−	1.95309i	1.72986	−	0.305022i	0.947963	+	0.318381i	$0.103139\pi$
$42$	7.60491	−	6.44973i	1.17346	−	0.995215i
$43$	−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
$45$	0.338516	−	0.960765i	0.0504630	−	0.143222i
$46$	−1.51874	+	2.63118i	−0.223926	+	0.387946i
$47$	−11.9828	+	4.36138i	−1.74787	+	0.636173i	−0.999629	−	0.0272526i	$-0.991324\pi$
$47$	−11.9828	+	4.36138i	−1.74787	+	0.636173i	−0.748242	+	0.663426i	$0.769102\pi$
$48$	6.81614	−	1.24108i	0.983825	−	0.179134i
$49$	4.78614	+	8.28983i	0.683734	+	1.18426i
$50$	−6.90801		0.000725118i	−0.976941		0.000102547i
$51$	3.63331	−	3.08076i	0.508765	−	0.431393i
$52$	0.695703	+	3.94069i	0.0964767	+	0.546475i
$53$	−3.14955	+	3.75349i	−0.432624	+	0.515581i	−0.937677	−	0.347507i	$-0.887028\pi$
$53$	−3.14955	+	3.75349i	−0.432624	+	0.515581i	0.505053	+	0.863088i	$0.331473\pi$
$54$	7.21609	−	1.38854i	0.981986	−	0.188956i
$55$	−0.252532	+	0.693826i	−0.0340514	+	0.0935555i
$56$	0.00362587	+	11.5143i	0.000484528	+	1.53866i
$57$	−6.95450	+	2.93852i	−0.921146	+	0.389216i
$58$	6.61111	−	3.81785i	0.868081	−	0.501308i
$59$	−0.0500092	−	0.0182019i	−0.00651065	−	0.00236968i	0.338763	−	0.940872i	$-0.389992\pi$
$59$	−0.0500092	−	0.0182019i	−0.00651065	−	0.00236968i	−0.345273	+	0.938502i	$0.612214\pi$
$60$	0.593577	+	1.01549i	0.0766305	+	0.131099i
$61$	−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
$63$	0.125879	+	12.2121i	0.0158593	+	1.53858i
$64$	−3.99564	+	6.93072i	−0.499454	+	0.866340i
$65$	−0.588362	+	0.339691i	−0.0729773	+	0.0421335i
$66$	−5.24054	+	0.952491i	−0.645066	+	0.117244i
$67$	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
$69$	−1.29060	−	3.48982i	−0.155370	−	0.420125i
$70$	−1.83689	+	0.668790i	−0.219550	+	0.0799357i
$71$	3.65424	−	3.06627i	0.433679	−	0.363900i	−0.399659	−	0.916664i	$-0.630871\pi$
$71$	3.65424	−	3.06627i	0.433679	−	0.363900i	0.833338	+	0.552764i	$0.186427\pi$
$72$	−4.16435	+	7.39312i	−0.490773	+	0.871288i
$73$	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
$78$	−4.25720	−	2.42813i	−0.482033	−	0.274932i
$79$	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
$81$	−4.33838	+	7.88533i	−0.482042	+	0.876148i
$82$	−5.44182	−	14.9464i	−0.600949	−	1.65055i
$83$	5.84559	−	10.1249i	0.641637	−	1.11135i	−0.343430	−	0.939178i	$-0.611589\pi$
$83$	5.84559	−	10.1249i	0.641637	−	1.11135i	0.985067	−	0.172170i	$-0.0550778\pi$
$84$	−10.8512	−	9.00654i	−1.18397	−	0.982694i
$85$	−0.877544	+	0.319400i	−0.0951830	+	0.0346438i
$86$	−3.47183	+	4.13845i	−0.374377	+	0.446260i
$87$	−1.57615	+	9.21628i	−0.168981	+	0.988089i
$88$	3.07352	−	5.32737i	0.327638	−	0.567899i
$89$	−11.7753	−	2.07631i	−1.24818	−	0.220088i	−0.489763	−	0.871855i	$-0.662917\pi$
$89$	−11.7753	−	2.07631i	−1.24818	−	0.220088i	−0.758419	+	0.651767i	$0.774028\pi$
$90$	−1.42124	−	0.235372i	−0.149812	−	0.0248104i
$91$	5.23559	−	6.23953i	0.548839	−	0.654081i
$92$	4.03763	+	1.46862i	0.420952	+	0.153114i
$93$	−3.65257	−	6.25180i	−0.378754	−	0.648282i
$94$	9.01854	+	15.6168i	0.930192	+	1.61075i
$95$	1.47854	−	0.0674103i	0.151695	−	0.00691615i
$96$	−3.40333	−	9.18789i	−0.347351	−	0.937735i
$97$	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
$99$	3.20334	−	5.68282i	0.321947	−	0.571145i
$100$	1.69846	+	9.62063i	0.169846	+	0.962063i
$101$	−4.63308	−	0.816937i	−0.461008	−	0.0812882i	−0.0616796	−	0.998096i	$-0.519646\pi$
$101$	−4.63308	−	0.816937i	−0.461008	−	0.0812882i	−0.399329	+	0.916808i	$0.630757\pi$
$102$	−5.18337	−	4.30311i	−0.513230	−	0.426072i
$103$	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
$105$	0.807255	−	2.25399i	0.0787800	−	0.219967i
$106$	6.00141	+	3.46407i	0.582908	+	0.336461i
$107$	3.10251	−	5.37371i	0.299931	−	0.519497i	−0.676189	−	0.736729i	$-0.736370\pi$
$107$	3.10251	−	5.37371i	0.299931	−	0.519497i	0.976120	+	0.217232i	$0.0697029\pi$
$108$	−3.70697	−	9.70867i	−0.356704	−	0.934218i
$109$	−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
$111$	−13.8567	−	7.90525i	−1.31522	−	0.750334i
$112$	16.0350	−	2.83435i	1.51517	−	0.267821i
$113$		−	6.44736i		−	0.606516i	−0.952908	−	0.303258i	$-0.901926\pi$
$113$		−	6.44736i		−	0.606516i	0.952908	−	0.303258i	$-0.0980745\pi$
$114$	5.80135	+	8.96350i	0.543347	+	0.839508i
$115$			0.729432i			0.0680199i
$116$	−6.94163	−	8.26918i	−0.644514	−	0.767774i
$117$	5.61899	−	2.11099i	0.519476	−	0.195161i
$118$	−0.0130614	+	0.0741206i	−0.00120240	+	0.00682335i
$119$	8.57672	−	7.19672i	0.786226	−	0.659722i
$120$	1.26842	−	1.07620i	0.115790	−	0.0982435i
$121$	3.13579	−	5.43135i	0.285072	−	0.493759i
$122$	−5.00705	+	8.67456i	−0.453317	+	0.785358i
$123$	18.3403	+	6.56849i	1.65369	+	0.592261i
$124$	8.23401	+	1.45010i	0.739436	+	0.130222i
$125$	−2.90671	+	1.67819i	−0.259984	+	0.150102i
$126$	16.9768	−	3.17608i	1.51242	−	0.282948i
$127$	−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
$129$	−1.18241	−	6.50941i	−0.104105	−	0.573122i
$130$	0.617662	+	0.735943i	0.0541725	+	0.0645465i
$131$	−15.1562	−	5.51641i	−1.32420	−	0.481971i	−0.419401	−	0.907801i	$-0.637760\pi$
$131$	−15.1562	−	5.51641i	−1.32420	−	0.481971i	−0.904803	+	0.425831i	$0.859982\pi$
$132$	2.61425	+	7.06447i	0.227541	+	0.614883i
$133$	−16.3808	+	6.82218i	−1.42040	+	0.591558i
$134$	4.23827	−	2.44756i	0.366131	−	0.211437i
$135$	1.33389	−	1.15487i	0.114803	−	0.0993957i
$136$	7.66035	−	1.35321i	0.656869	−	0.116037i
$137$	8.59034	−	10.2376i	0.733922	−	0.874654i	−0.261982	−	0.965073i	$-0.584376\pi$
$137$	8.59034	−	10.2376i	0.733922	−	0.874654i	0.995904	+	0.0904185i	$0.0288205\pi$
$138$	−4.54315	+	2.65494i	−0.386739	+	0.226004i
$139$	−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
$141$	−21.7707	−	3.72318i	−1.83343	−	0.313549i
$142$	−5.16834	−	4.33582i	−0.433717	−	0.363854i
$143$	−4.08838	+	1.48805i	−0.341887	+	0.124437i
$144$	11.3197	+	3.98304i	0.943307	+	0.331920i
$145$	0.916499	−	1.58742i	0.0761111	−	0.131828i
$146$	1.52283	−	0.554445i	0.126030	−	0.0458862i
$147$	0.0854464	+	16.5794i	0.00704750	+	1.36745i
$148$	17.3088	−	6.30402i	1.42278	−	0.518187i
$149$	6.72165	−	1.18521i	0.550659	−	0.0970961i	0.108606	−	0.994085i	$-0.465361\pi$
$149$	6.72165	−	1.18521i	0.550659	−	0.0970961i	0.442053	+	0.896989i	$0.354250\pi$
$150$	−10.3933	−	5.92794i	−0.848613	−	0.484015i
$151$			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
$156$	−2.33558	+	6.52566i	−0.186996	+	0.522471i
$157$	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
$159$	−7.95988	+	2.94370i	−0.631259	+	0.233451i
$160$	0.00100811	+	1.92080i	7.96979e−5	+	0.151852i
$161$	−2.99103	−	8.21778i	−0.235726	−	0.647652i
$162$	12.0480	+	4.10447i	0.946577	+	0.322478i
$163$	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
$165$	−0.975420	+	0.827078i	−0.0759363	+	0.0643879i
$166$	−15.5373	−	5.65327i	−1.20593	−	0.438779i
$167$	14.0716	+	11.8075i	1.08889	+	0.913688i	0.996629	−	0.0820464i	$-0.0261456\pi$
$167$	14.0716	+	11.8075i	1.08889	+	0.913688i	0.0922628	+	0.995735i	$0.470590\pi$
$168$	−9.87704	+	17.3257i	−0.762030	+	1.33670i
$169$	8.45417	+	3.07707i	0.650321	+	0.236697i
$170$	0.660460	+	1.14367i	0.0506550	+	0.0877158i
$171$	−12.9847	−	1.54810i	−0.992968	−	0.118386i
$172$	6.61673	+	3.81832i	0.504521	+	0.291144i
$173$	−7.23020	+	19.8648i	−0.549702	+	1.51029i	0.284412	+	0.958702i	$0.408202\pi$
$173$	−7.23020	+	19.8648i	−0.549702	+	1.51029i	−0.834114	+	0.551592i	$0.814021\pi$
$174$	13.2228	−	0.0695353i	1.00242	−	0.00527145i
$175$	12.7819	−	15.2329i	0.966224	−	1.15150i
$176$	−8.17467	−	2.97145i	−0.616189	−	0.223981i
$177$	−0.0596137	−	0.0703058i	−0.00448084	−	0.00528451i
$178$	0.00177497	+	16.9097i	0.000133040	+	1.26744i
$179$	9.20951	+	15.9513i	0.688351	+	1.19226i	0.972371	+	0.233441i	$0.0749985\pi$
$179$	9.20951	+	15.9513i	0.688351	+	1.19226i	−0.284020	+	0.958818i	$0.591668\pi$
$180$	0.0214268	+	2.03720i	0.00159706	+	0.151844i
$181$	−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
$183$	−4.25489	−	11.5054i	−0.314531	−	0.850502i
$184$	1.05321	−	5.98409i	0.0776440	−	0.441153i
$185$	2.01029	+	2.39577i	0.147800	+	0.176141i
$186$	−7.80938	+	6.62314i	−0.572612	+	0.485632i
$187$	−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	$-0.640888\pi$
$191$	−11.8385			−0.856602			−0.428301	+	0.903636i	$0.640888\pi$
$192$	−11.9597	+	6.99749i	−0.863119	+	0.505000i
$193$	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
$195$	−1.17671	+	0.00606446i	−0.0842658	+	0.000434285i
$196$	−14.6682	−	12.3028i	−1.04773	−	0.878771i
$197$	12.0504	+	6.95731i	0.858557	+	0.495688i	0.863529	−	0.504300i	$-0.168249\pi$
$197$	12.0504	+	6.95731i	0.858557	+	0.495688i	−0.00497203	+	0.999988i	$0.501583\pi$
$198$	−8.70161	−	3.06490i	−0.618396	−	0.217813i
$199$	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
$201$	−1.01044	+	5.90840i	−0.0712711	+	0.416747i
$202$	0.000698375		6.65324i	4.91375e−5		0.468120i
$203$	−3.81607	+	21.6420i	−0.267836	+	1.51897i
$204$	−4.71929	+	8.27626i	−0.330417	+	0.579454i
$205$	−2.92559	−	2.45486i	−0.204332	−	0.171455i
$206$	−8.67286	−	10.3337i	−0.604267	−	0.719984i
$207$	1.05362	−	6.35794i	0.0732320	−	0.441907i
$208$	−4.00454	−	6.92935i	−0.277665	−	0.480464i
$209$	9.39967	+	1.21906i	0.650189	+	0.0843242i
$210$	−3.33750	−	0.570412i	−0.230309	−	0.0393621i
$211$	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
$213$	8.12933	−	1.47666i	0.557013	−	0.101179i
$214$	−8.24634	−	3.00044i	−0.563708	−	0.205106i
$215$	−0.225220	+	1.27729i	−0.0153599	+	0.0871102i
$216$	−12.6104	+	7.54834i	−0.858030	+	0.513600i
$217$	−8.50893	−	14.7379i	−0.577624	−	1.00047i
$218$	7.72208	+	6.47821i	0.523005	+	0.438760i
$219$	−0.669236	+	1.86862i	−0.0452228	+	0.126270i
$220$	−0.000310013	−	1.47671i	−2.09011e−5	−	0.0995597i
$221$	−4.76556	−	2.75140i	−0.320566	−	0.185079i
$222$	−7.60477	+	21.2408i	−0.510399	+	1.42559i
$223$	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
$225$	13.7180	−	5.15367i	0.914531	−	0.343578i
$226$	−8.97925	+	1.58426i	−0.597291	+	0.105383i
$227$	−11.5941			−0.769529			−0.384765	−	0.923015i	$-0.625717\pi$
$227$	−11.5941			−0.769529			−0.384765	+	0.923015i	$0.625717\pi$
$228$	11.0580	−	10.2821i	0.732332	−	0.680948i
$229$	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
$231$	7.59766	−	13.3176i	0.499889	−	0.876232i
$232$	−9.81080	+	11.6995i	−0.644111	+	0.768112i
$233$	11.6686	+	13.9061i	0.764438	+	0.911021i	0.998120	−	0.0612917i	$-0.0195220\pi$
$233$	11.6686	+	13.9061i	0.764438	+	0.911021i	−0.233682	+	0.972313i	$0.575078\pi$
$234$	−4.32068	−	7.30687i	−0.282452	−	0.477665i
$235$	3.74982	+	2.16496i	0.244611	+	0.141226i
$236$	0.106437		2.23450e-5i	0.00692849		1.45453e-6i
$237$	0.592556	+	0.212221i	0.0384907	+	0.0137852i
$238$	−12.1304	−	10.1764i	−0.786296	−	0.659640i
$239$	−12.0529	−	20.8763i	−0.779638	−	1.35037i	−0.932151	−	0.362071i	$-0.882070\pi$
$239$	−12.0529	−	20.8763i	−0.779638	−	1.35037i	0.152513	−	0.988302i	$-0.451264\pi$
$240$	−1.81051	−	1.50208i	−0.116868	−	0.0969590i
$241$	−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
$243$	−13.2947	+	8.13948i	−0.852855	+	0.522148i
$244$	13.3114	+	4.84180i	0.852177	+	0.309964i
$245$	1.11166	−	3.05427i	0.0710216	−	0.195130i
$246$	4.64133	−	27.1566i	0.295921	−	1.73144i
$247$	5.90444	+	6.41868i	0.375691	+	0.408411i
$248$	−0.00372336	−	11.8238i	−0.000236434	−	0.750815i
$249$	17.4844	−	10.2151i	1.10803	−	0.647356i
$250$	3.05146	+	3.63581i	0.192991	+	0.229949i
$251$	13.0099	+	10.9166i	0.821175	+	0.689047i	0.953247	−	0.302193i	$-0.0977186\pi$
$251$	13.0099	+	10.9166i	0.821175	+	0.689047i	−0.132072	+	0.991240i	$0.542163\pi$
$252$	−8.59492	−	22.8633i	−0.541429	−	1.44025i
$253$	−0.811159	+	4.60031i	−0.0509971	+	0.289219i
$254$	0.00119429	+	11.3777i	7.49365e−5	+	0.713901i
$255$	−1.59435	−	0.272662i	−0.0998421	−	0.0170748i
$256$	2.76514	−	15.7593i	0.172821	−	0.984953i
$257$	1.82086	+	5.00277i	0.113582	+	0.312064i	0.983439	−	0.181240i	$-0.0580111\pi$
$257$	1.82086	+	5.00277i	0.113582	+	0.312064i	−0.869857	+	0.493304i	$0.835789\pi$
$258$	−8.77513	+	3.24624i	−0.546316	+	0.202102i
$259$	−32.4718	−	18.7476i	−2.01770	−	1.16492i
$260$	0.873178	−	1.04106i	0.0541522	−	0.0645636i
$261$	−10.2814	+	12.5126i	−0.636403	+	0.774510i
$262$	−3.95850	+	22.4636i	−0.244557	+	1.38780i
$263$	−0.915009	−	5.18927i	−0.0564219	−	0.319984i	0.943514	−	0.331333i	$-0.107498\pi$
$263$	−0.915009	−	5.18927i	−0.0564219	−	0.319984i	−0.999936	+	0.0113491i	$0.996387\pi$
$264$	9.19633	−	5.37677i	0.565995	−	0.330917i
$265$	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	−0.923772	−	0.382943i	$-0.874911\pi$
$269$	−27.2401	+	4.80317i	−1.66086	+	0.292854i	−0.737088	+	0.675797i	$0.763800\pi$
$270$	−1.93616	−	1.57393i	−0.117831	−	0.0957864i
$271$	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
$273$	13.2319	−	4.89340i	0.800833	−	0.296162i
$274$	−16.3687	−	9.44819i	−0.988870	−	0.570786i
$275$	−9.98119	+	3.63285i	−0.601888	+	0.219069i
$276$	4.81390	+	5.67489i	0.289763	+	0.341588i
$277$	−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
$279$	−0.129264	−	12.5404i	−0.00773883	−	0.750775i
$280$	2.99421	−	2.51405i	0.178938	−	0.150243i
$281$	−10.5420	+	12.5635i	−0.628882	+	0.749473i	−0.982570	−	0.185891i	$-0.940483\pi$
$281$	−10.5420	+	12.5635i	−0.628882	+	0.749473i	0.353688	+	0.935363i	$0.384927\pi$
$282$	0.164256	+	31.2350i	0.00978133	+	1.86002i
$283$	−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
$285$	2.28223	+	1.16759i	0.135188	+	0.0691621i
$286$	3.07701	+	5.32825i	0.181947	+	0.315066i
$287$	43.0258	+	15.6601i	2.53973	+	0.924387i
$288$	2.76570	−	16.7437i	0.162971	−	0.986631i
$289$	7.22839	+	6.06534i	0.425199	+	0.356785i
$290$	−2.43601	−	0.886346i	−0.143047	−	0.0520480i
$291$	16.2494	+	19.1638i	0.952556	+	1.12340i
$292$	−1.14637	−	1.98461i	−0.0670862	−	0.116140i
$293$	−8.06932	+	4.65883i	−0.471415	+	0.272172i	−0.716832	−	0.697246i	$-0.754408\pi$
$293$	−8.06932	+	4.65883i	−0.471415	+	0.272172i	0.245417	+	0.969418i	$0.421075\pi$
$294$	23.0692	−	4.19293i	1.34543	−	0.244537i
$295$	0.00618049	+	0.0169808i	0.000359842	+	0.000988658i
$296$	−13.0328	−	22.5570i	−0.757515	−	1.31110i
$297$	9.69671	−	5.80011i	0.562660	−	0.336556i
$298$	−3.30230	−	9.07003i	−0.191297	−	0.525413i
$299$	−3.29260	+	2.76282i	−0.190416	+	0.159778i
$300$	−5.70199	+	15.9315i	−0.329205	+	0.919803i
$301$	−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
$306$	−4.10479	−	10.9226i	−0.234655	−	0.624403i
$307$	−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
$309$	16.5227	−	0.0851538i	0.939942	−	0.00484423i
$310$	1.88627	−	0.686772i	0.107133	−	0.0390060i
$311$	0.599347	−	1.03810i	0.0339859	−	0.0588653i	−0.848532	−	0.529144i	$-0.822513\pi$
$311$	0.599347	−	1.03810i	0.0339859	−	0.0588653i	0.882518	+	0.470279i	$0.155847\pi$
$312$	9.66220	+	1.64928i	0.547014	+	0.0933719i
$313$	−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
$315$	3.14903	−	2.69815i	0.177428	−	0.152024i
$316$	−0.629336	+	0.363524i	−0.0354029	+	0.0204498i
$317$	24.8359	+	4.37924i	1.39492	+	0.245963i	0.820056	−	0.572283i	$-0.193942\pi$
$317$	24.8359	+	4.37924i	1.39492	+	0.245963i	0.574868	+	0.818246i	$0.305053\pi$
$318$	6.05562	+	10.3624i	0.339582	+	0.581095i
$319$	7.54537	−	8.99222i	0.422460	−	0.503468i
$320$	2.67485	−	0.473386i	0.149529	−	0.0264631i
$321$	9.27973	−	5.42161i	0.517944	−	0.302605i
$322$	−10.7100	+	6.18490i	−0.596843	+	0.344671i
$323$	6.46072	+	10.0983i	0.359484	+	0.561884i
$324$	2.75587	−	17.7878i	0.153104	−	0.988210i
$325$	−9.18398	−	3.34270i	−0.509436	−	0.185419i
$326$	−2.13943	−	2.54913i	−0.118492	−	0.141183i
$327$	−12.1461	+	2.20630i	−0.671683	+	0.122008i
$328$	20.4563	+	24.3633i	1.12951	+	1.34524i
$329$	−51.1228	−	9.01434i	−2.81849	−	0.496976i
$330$	1.39156	+	1.15524i	0.0766026	+	0.0635938i
$331$	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
$333$	−14.0617	−	23.7860i	−0.770578	−	1.30347i
$334$	12.9866	−	22.4989i	0.710594	−	1.23108i
$335$	0.587552	−	1.01767i	0.0321014	−	0.0556012i
$336$	26.5565	+	9.49849i	1.44878	+	0.518185i
$337$	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
$339$	5.53366	−	9.69968i	0.300547	−	0.526815i
$340$	1.43051	−	1.20085i	0.0775802	−	0.0651253i
$341$			9.09017i			0.492260i
$342$	1.03459	+	18.4643i	0.0559441	+	0.998434i
$343$			10.4715i			0.565406i
$344$	3.69191	−	10.1534i	0.199054	−	0.547434i
$345$	−0.626059	+	1.09739i	−0.0337059	+	0.0590814i
$346$	29.4424	+	5.18830i	1.58283	+	0.278925i
$347$	24.6949	−	20.7215i	1.32569	−	1.11239i	0.340627	−	0.940199i	$-0.389361\pi$
$347$	24.6949	−	20.7215i	1.32569	−	1.11239i	0.985064	−	0.172188i	$-0.0550837\pi$
$348$	−3.34598	−	18.3984i	−0.179363	−	0.986258i
$349$	−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
$351$	10.2653	+	1.64683i	0.547920	+	0.0879013i
$352$	−2.12965	+	12.1150i	−0.113511	+	0.645733i
$353$	14.0533	−	8.11369i	0.747983	−	0.431848i	−0.0769819	−	0.997032i	$-0.524528\pi$
$353$	14.0533	−	8.11369i	0.747983	−	0.431848i	0.824965	+	0.565185i	$0.191195\pi$
$354$	−0.0832667	+	0.100300i	−0.00442557	+	0.00533088i
$355$	−1.59515	−	0.281268i	−0.0846618	−	0.0149282i
$356$	23.5498	−	4.15756i	1.24814	−	0.220350i
$357$	19.0800	−	3.46580i	1.00982	−	0.183430i
$358$	19.9525	−	16.7457i	1.05452	−	0.885038i
$359$	−5.02034	−	1.82725i	−0.264963	−	0.0964387i	0.206122	−	0.978526i	$-0.433915\pi$
$359$	−5.02034	−	1.82725i	−0.264963	−	0.0964387i	−0.471086	+	0.882087i	$0.656138\pi$
$360$	2.83195	−	0.530426i	0.149257	−	0.0279559i
$361$	−4.98828	−	18.3335i	−0.262541	−	0.964921i
$362$	0.454670	+	0.787320i	0.0238969	+	0.0413806i
$363$	9.37925	−	5.47976i	0.492283	−	0.287613i
$364$	−5.56838	+	15.3090i	−0.291863	+	0.802410i
$365$	0.250116	−	0.298076i	0.0130916	−	0.0156020i
$366$	−14.9781	+	8.75292i	−0.782915	+	0.457523i
$367$	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
$369$	21.9543	+	25.6231i	1.14290	+	1.33389i
$370$	2.84263	−	3.38844i	0.147781	−	0.176156i
$371$	−18.7438	+	6.82219i	−0.973130	+	0.354190i
$372$	11.1430	+	9.24870i	0.577738	+	0.479523i
$373$	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
$375$	−5.81333	+	0.0299605i	−0.300199	+	0.00154715i
$376$	−27.6367	−	23.1751i	−1.42525	−	1.19517i
$377$	10.6369	−	1.87557i	0.547826	−	0.0965965i
$378$	28.2667	+	9.79271i	1.45388	+	0.503683i
$379$			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	$-0.938914\pi$
$383$	−2.43522	−	13.8108i	−0.124434	−	0.705700i	0.857208	−	0.514970i	$-0.172197\pi$
$384$	12.6842	+	14.9369i	0.647287	+	0.762246i
$385$	−2.30255	+	1.93207i	−0.117349	+	0.0984675i
$386$	28.0696	−	10.2198i	1.42870	−	0.520175i
$387$	3.80805	−	10.8079i	0.193574	−	0.549395i
$388$	−29.0125	+	0.00609075i	−1.47289	+	0.000309211i
$389$	−3.78838	−	10.4085i	−0.192078	−	0.527731i	0.805846	−	0.592125i	$-0.201711\pi$
$389$	−3.78838	−	10.4085i	−0.192078	−	0.527731i	−0.997925	+	0.0643938i	$0.979489\pi$
$390$	0.297589	+	1.63731i	0.0150690	+	0.0829086i
$391$	−5.11664	+	2.95409i	−0.258759	+	0.149395i
$392$	−13.5299	+	23.4514i	−0.683361	+	1.18448i
$393$	−18.0670	−	21.3074i	−0.911360	−	1.07482i
$394$	6.72842	−	18.4922i	0.338973	−	0.931624i
$395$	−0.0945226	−	0.0793139i	−0.00475595	−	0.00399071i
$396$	−2.13032	+	12.8719i	−0.107053	+	0.646835i
$397$	−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
$399$	−30.4994	−	3.79580i	−1.52688	−	0.190028i
$400$	−9.77651	−	16.9170i	−0.488826	−	0.845850i
$401$	3.45492	−	9.49233i	0.172531	−	0.474024i	−0.823046	−	0.567974i	$-0.807727\pi$
$401$	3.45492	−	9.49233i	0.172531	−	0.474024i	0.995577	+	0.0939503i	$0.0299495\pi$
$402$	8.47694	−	0.0445779i	0.422791	−	0.00222334i
$403$	−5.37636	+	6.40729i	−0.267816	+	0.319170i
$404$	9.26581	−	1.63582i	0.460991	−	0.0813850i
$405$	2.99797	−	0.592588i	0.148970	−	0.0294459i
$406$	31.0786	−	0.00326224i	1.54240	−	0.000161902i
$407$	10.0141	+	17.3450i	0.496382	+	0.859759i
$408$	12.6860	+	4.53892i	0.628050	+	0.224710i
$409$	−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
$411$	21.7104	−	8.02889i	1.07090	−	0.396036i
$412$	−12.2607	+	14.6179i	−0.604040	+	0.720174i
$413$	−0.139259	−	0.165962i	−0.00685248	−	0.00816647i
$414$	−9.11361	+	0.0948979i	−0.447910	+	0.00466398i
$415$	−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	$-0.454915\pi$
$419$	5.77923			0.282334			0.141167	+	0.989986i	$0.454915\pi$
$420$	0.0256830	+	4.78831i	0.00125320	+	0.233646i
$421$	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
$423$	−29.5573	−	24.2868i	−1.43713	−	1.18086i
$424$	−13.6490	−	2.40226i	−0.662855	−	0.116664i
$425$	−11.6344	−	6.71714i	−0.564353	−	0.325829i
$426$	−4.05410	−	10.9589i	−0.196422	−	0.530960i
$427$	−9.86094	−	27.0927i	−0.477204	−	1.31111i
$428$	−2.15242	+	12.2220i	−0.104041	+	0.590771i
$429$	−7.42790	−	1.27030i	−0.358622	−	0.0613308i
$430$	1.83422		0.000192534i	0.0884540		9.28481e-6i
$431$	−2.55507	+	14.4905i	−0.123073	+	0.697984i	0.859360	+	0.511371i	$0.170862\pi$
$431$	−2.55507	+	14.4905i	−0.123073	+	0.697984i	−0.982434	+	0.186613i	$0.940249\pi$
$432$	13.6113	+	15.7078i	0.654872	+	0.755740i
$433$	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
$435$	2.74128	−	1.60157i	0.131434	−	0.0767895i
$436$	7.12474	−	12.3464i	0.341213	−	0.591285i
$437$	9.13797	−	2.04433i	0.437128	−	0.0977935i
$438$	2.76688	+	0.472887i	0.132207	+	0.0225954i
$439$	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
$441$	−14.1013	+	25.0162i	−0.671491	+	1.19125i
$442$	−2.66087	+	7.31308i	−0.126565	+	0.347848i
$443$	1.24252	−	7.04669i	0.0590340	−	0.334798i	−0.940959	−	0.338520i	$-0.890074\pi$
$443$	1.24252	−	7.04669i	0.0590340	−	0.334798i	0.999993	+	0.00372195i	$0.00118474\pi$
$444$	31.4508	+	5.37185i	1.49259	+	0.254937i
$445$	2.03001	+	3.51608i	0.0962318	+	0.166678i
$446$	8.69178	−	10.3607i	0.411567	−	0.490592i
$447$	11.1296	+	3.98600i	0.526412	+	0.188532i
$448$	−28.1938	+	16.3014i	−1.33203	+	0.770168i
$449$	16.1424	+	9.31983i	0.761808	+	0.439830i	0.829944	−	0.557846i	$-0.188372\pi$
$449$	16.1424	+	9.31983i	0.761808	+	0.439830i	−0.0681366	+	0.997676i	$0.521705\pi$
$450$	−10.5483	−	17.8387i	−0.497253	−	0.840924i
$451$	−15.7209	−	18.7355i	−0.740269	−	0.882218i
$452$	4.41280	+	12.1161i	0.207560	+	0.569895i
$453$	−12.8652	+	22.5509i	−0.604462	+	1.05953i
$454$	2.84893	+	16.1472i	0.133707	+	0.757824i
$455$	−2.76570			−0.129658
$456$	−17.0371	−	12.8739i	−0.797834	−	0.602877i
$457$	−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
$459$	13.5030	+	4.67955i	0.630264	+	0.218423i
$460$	−0.499248	−	1.37078i	−0.0232776	−	0.0639129i
$461$	−19.2482	−	22.9391i	−0.896479	−	1.06838i	−0.997297	−	0.0734767i	$-0.976591\pi$
$461$	−19.2482	−	22.9391i	−0.896479	−	1.06838i	0.100818	−	0.994905i	$-0.467854\pi$
$462$	−20.4143	−	7.30886i	−0.949760	−	0.340039i
$463$	−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
$465$	−0.828960	+	2.31460i	−0.0384421	+	0.107337i
$466$	16.4999	−	19.6680i	0.764342	−	0.911102i
$467$	8.21437	+	14.2277i	0.380116	+	0.658380i	0.991078	−	0.133280i	$-0.0425508\pi$
$467$	8.21437	+	14.2277i	0.380116	+	0.658380i	−0.610963	+	0.791659i	$0.709217\pi$
$468$	−9.11461	+	7.81289i	−0.421323	+	0.361151i
$469$	−2.44642	+	13.8743i	−0.112965	+	0.640657i
$470$	2.09373	−	5.75435i	0.0965766	−	0.265429i
$471$	28.1153	−	5.10703i	1.29549	−	0.235320i
$472$	−0.0261851	−	0.148230i	−0.00120527	−	0.00682285i
$473$	−2.84079	+	7.80502i	−0.130620	+	0.358875i
$474$	0.149957	−	0.877402i	0.00688773	−	0.0403004i
$475$	14.4149	+	15.6703i	0.661399	+	0.719003i
$476$	−11.1920	+	19.3946i	−0.512986	+	0.888949i
$477$	−14.5017	−	2.40320i	−0.663988	−	0.110035i
$478$	−26.1127	+	21.9159i	−1.19437	+	1.00241i
$479$	11.0402	+	9.26381i	0.504439	+	0.423274i	0.859167	−	0.511695i	$-0.170982\pi$
$479$	11.0402	+	9.26381i	0.504439	+	0.423274i	−0.354728	+	0.934969i	$0.615427\pi$
$480$	−1.64707	+	2.89060i	−0.0751782	+	0.131937i
$481$	−3.20009	+	18.1486i	−0.145912	+	0.827506i
$482$	4.76974		0.000500668i	0.217256		2.28048e-5i
$483$	2.55335	−	14.9303i	0.116182	−	0.679354i
$484$	−2.17550	+	12.3531i	−0.0988865	+	0.561503i
$485$	−1.68467	−	4.62858i	−0.0764967	−	0.210173i
$486$	14.6027	+	16.5155i	0.662391	+	0.749159i
$487$	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
$489$	4.07583	−	0.0210058i	0.184315	−	0.000949916i
$490$	−4.52685	−	0.797716i	−0.204502	−	0.0360371i
$491$	−5.34346	−	30.3043i	−0.241147	−	1.36761i	−0.829274	−	0.558843i	$-0.811245\pi$
$491$	−5.34346	−	30.3043i	−0.241147	−	1.36761i	0.588127	−	0.808769i	$-0.299866\pi$
$492$	−38.9616	+	0.208978i	−1.75652	+	0.00942146i
$493$	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
$498$	−18.5229	−	21.8404i	−0.830031	−	0.978694i
$499$	−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
$501$	11.0357	+	29.8410i	0.493041	+	1.33320i
$502$	12.0067	−	20.8013i	0.535886	−	0.928407i
$503$	−2.59975	+	0.946231i	−0.115917	+	0.0421904i	−0.399328	−	0.916808i	$-0.630756\pi$
$503$	−2.59975	+	0.946231i	−0.115917	+	0.0421904i	0.283410	+	0.958999i	$0.408534\pi$
$504$	−29.7298	+	17.5882i	−1.32427	+	0.783440i
$505$	0.798721	+	1.38342i	0.0355426	+	0.0615616i
$506$	6.60619		0.000693436i	0.293681		3.08270e-5i
$507$	10.0778	+	11.8853i	0.447572	+	0.527847i
$508$	15.8455	−	2.79741i	0.703029	−	0.124115i
$509$	−11.8481	+	14.1200i	−0.525159	+	0.625860i	−0.961792	−	0.273780i	$-0.911726\pi$
$509$	−11.8481	+	14.1200i	−0.525159	+	0.625860i	0.436634	+	0.899639i	$0.356171\pi$
$510$	0.0120291	+	2.28745i	0.000532657	+	0.101290i
$511$	−1.59555	+	4.38372i	−0.0705828	+	0.193925i
$512$	−22.6274	+	0.0213763i	−1.00000	+	0.000944708i
$513$	−18.2061	−	13.4736i	−0.803819	−	0.594875i
$514$	6.51995	−	3.76521i	0.287583	−	0.166076i
$515$	−3.04381	−	1.10786i	−0.134126	−	0.0488180i
$516$	6.67729	+	11.4235i	0.293952	+	0.502890i
$517$	21.2415	+	17.8237i	0.934199	+	0.783886i
$518$	−18.1308	+	49.8303i	−0.796623	+	2.18942i
$519$	−27.9271	+	23.6799i	−1.22586	+	1.03943i
$520$	−1.66444	−	0.960266i	−0.0729905	−	0.0421105i
$521$	−4.83770	+	2.79305i	−0.211944	+	0.122366i	−0.602214	−	0.798334i	$-0.705715\pi$
$521$	−4.83770	+	2.79305i	−0.211944	+	0.122366i	0.390271	+	0.920700i	$0.372381\pi$
$522$	19.9527	+	11.2443i	0.873306	+	0.492151i
$523$	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
$525$	32.3039	−	11.9465i	1.40986	−	0.521390i
$526$	−7.00228	+	2.54945i	−0.305314	+	0.111161i
$527$	−8.80732	+	7.39022i	−0.383653	+	0.321923i
$528$	−9.74798	−	11.4866i	−0.424226	−	0.499888i
$529$	−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
$534$	−14.5107	+	25.4413i	−0.627938	+	1.10095i
$535$	−2.07492	+	0.365865i	−0.0897068	+	0.0158177i
$536$	−6.28954	+	7.50038i	−0.271667	+	0.323967i
$537$	0.164416	+	31.9023i	0.00709509	+	1.37668i
$538$	13.3829	+	36.7572i	0.576977	+	1.58471i
$539$	10.4074	−	18.0262i	0.448279	−	0.776443i
$540$	−1.71626	+	3.08324i	−0.0738561	+	0.132682i
$541$	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
$543$	−1.09757	−	0.187704i	−0.0471013	−	0.00805516i
$544$	−13.4695	+	7.78602i	−0.577498	+	0.333823i
$545$	2.38334	+	0.420246i	0.102091	+	0.0180014i
$546$	−10.0664	−	17.2257i	−0.430803	−	0.737193i
$547$	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
$549$	3.47363	−	20.9611i	0.148251	−	0.894598i
$550$	7.51208	+	13.0082i	0.320316	+	0.554669i
$551$	−22.4551	−	7.03250i	−0.956618	−	0.299594i
$552$	6.72055	−	8.09877i	0.286046	−	0.344707i
$553$	1.39012	+	0.505962i	0.0591138	+	0.0215157i
$554$	−23.5064	+	19.7285i	−0.998693	+	0.838182i
$555$	0.968119	+	5.32971i	0.0410944	+	0.226234i
$556$	20.6893	−	3.65257i	0.877424	−	0.154903i
$557$	4.08608	+	0.720485i	0.173133	+	0.0305279i	0.259542	−	0.965732i	$-0.416428\pi$
$557$	4.08608	+	0.720485i	0.173133	+	0.0305279i	−0.0864097	+	0.996260i	$0.527539\pi$
$558$	−17.4333	+	3.26148i	−0.738011	+	0.138069i
$559$	−6.61862	+	3.82126i	−0.279938	+	0.161622i
$560$	−4.23706	−	3.55229i	−0.179049	−	0.150111i
$561$	−9.75189	−	3.49259i	−0.411725	−	0.147457i
$562$	20.0875	+	11.5947i	0.847342	+	0.489095i
$563$	5.04252	−	8.73390i	0.212517	−	0.368090i	−0.739985	−	0.672624i	$-0.765167\pi$
$563$	5.04252	−	8.73390i	0.212517	−	0.368090i	0.952502	+	0.304534i	$0.0985006\pi$
$564$	43.4608	−	7.90389i	1.83003	−	0.332814i
$565$	−1.67704	+	1.40720i	−0.0705535	+	0.0592014i
$566$	41.5283	+	7.31807i	1.74557	+	0.307601i
$567$	−31.3452	+	18.9692i	−1.31638	+	0.796633i
$568$	12.6801	+	4.61067i	0.532047	+	0.193460i
$569$		−	45.1026i		−	1.89080i	−0.325914	−	0.945399i	$-0.605672\pi$
$569$		−	45.1026i		−	1.89080i	0.325914	−	0.945399i	$-0.394328\pi$
$570$	1.06531	−	3.46538i	0.0446210	−	0.145149i
$571$		−	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
$573$	−17.8103	−	10.1608i	−0.744037	−	0.424472i
$574$	11.2375	−	63.7702i	0.469044	−	2.66172i
$575$	−8.03841	+	6.74503i	−0.335225	+	0.281287i
$576$	−23.9986	+	0.262488i	−0.999940	+	0.0109370i
$577$	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
$579$	−12.3357	+	34.4434i	−0.512655	+	1.43142i
$580$	−0.635835	+	3.61043i	−0.0264016	+	0.149915i
$581$	41.2174	−	23.7969i	1.70998	−	0.987260i
$582$	22.6967	−	27.3395i	0.940807	−	1.13326i
$583$	10.4928	+	1.85016i	0.434567	+	0.0766258i
$584$	−2.48228	+	2.08421i	−0.102717	+	0.0862453i
$585$	−1.77550	−	1.00083i	−0.0734077	−	0.0413790i
$586$	8.47117	+	10.0934i	0.349941	+	0.416954i
$587$	−17.8900	−	6.51145i	−0.738401	−	0.268756i	−0.0546847	−	0.998504i	$-0.517415\pi$
$587$	−17.8900	−	6.51145i	−0.738401	−	0.268756i	−0.683717	+	0.729748i	$0.739638\pi$
$588$	−11.5081	−	31.0983i	−0.474587	−	1.28247i
$589$	16.8212	−	7.00561i	0.693107	−	0.288661i
$590$	0.0221305	−	0.0127801i	0.000911097	−	0.000526149i
$591$	12.1578	+	20.8096i	0.500106	+	0.855991i
$592$	−28.2128	+	23.6935i	−1.15954	+	0.973798i
$593$	−20.4598	+	24.3830i	−0.840183	+	1.00129i	0.159718	+	0.987163i	$0.448942\pi$
$593$	−20.4598	+	24.3830i	−0.840183	+	1.00129i	−0.999900	+	0.0141280i	$0.995503\pi$
$594$	−10.4605	−	12.0794i	−0.429200	−	0.495624i
$595$	−3.74391	−	0.660152i	−0.153485	−	0.0270636i
$596$	−11.8204	+	6.82783i	−0.484183	+	0.279679i
$597$	−1.96379	+	11.4830i	−0.0803727	+	0.469967i
$598$	4.65685	+	3.90673i	0.190433	+	0.159758i
$599$	−20.2669	+	7.37654i	−0.828083	+	0.301397i	−0.721072	−	0.692860i	$-0.756350\pi$
$599$	−20.2669	+	7.37654i	−0.828083	+	0.301397i	−0.107011	+	0.994258i	$0.534128\pi$
$600$	23.5889	+	4.02647i	0.963012	+	0.164380i
$601$	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
$603$	−6.59124	+	8.02161i	−0.268416	+	0.326665i
$604$	−10.2593	−	28.1689i	−0.417446	−	1.14618i
$605$	−2.09718	+	0.369789i	−0.0852624	+	0.0150341i
$606$	−5.70931	+	10.0100i	−0.231925	+	0.406629i
$607$			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
$612$	−14.2033	+	8.40067i	−0.574134	+	0.339577i
$613$	−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
$615$	−2.29442	−	6.20418i	−0.0925198	−	0.250177i
$616$	21.6793	−	12.5257i	0.873485	−	0.504673i
$617$	12.5561	+	34.4977i	0.505490	+	1.38882i	0.885844	+	0.463982i	$0.153580\pi$
$617$	12.5561	+	34.4977i	0.505490	+	1.38882i	−0.380354	+	0.924841i	$0.624198\pi$
$618$	−4.17858	−	22.9902i	−0.168087	−	0.924803i
$619$	−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
$621$	7.04203	−	8.66085i	0.282587	−	0.347548i
$622$	−1.59304	−	0.579629i	−0.0638750	−	0.0232410i
$623$	−37.2878	−	31.2882i	−1.49390	−	1.25353i
$624$	−0.0772608	−	13.8618i	−0.00309291	−	0.554918i
$625$	−21.8797	−	7.96355i	−0.875187	−	0.318542i
$626$	11.1963	+	19.3879i	0.447495	+	0.774897i
$627$	13.0950	+	9.90159i	0.522963	+	0.395432i
$628$	−16.4920	+	28.5789i	−0.658103	+	1.14042i
$629$	−8.66389	+	23.8038i	−0.345452	+	0.949121i
$630$	−4.53151	−	3.72267i	−0.180540	−	0.148315i
$631$	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
$633$	24.0977	−	20.4329i	0.957796	−	0.812134i
$634$	−0.00374368	−	35.6651i	−0.000148681	−	1.41644i
$635$	1.36589	+	2.36580i	0.0542038	+	0.0938837i
$636$	12.9438	−	10.9799i	0.513253	−	0.435383i
$637$	17.9973	−	6.55049i	0.713080	−	0.259540i
$638$	−14.3776	−	8.29887i	−0.569213	−	0.328556i
$639$	13.4975	+	4.75572i	0.533953	+	0.188133i
$640$	−1.31656	−	3.60895i	−0.0520414	−	0.142656i
$641$	−5.54434	−	6.60749i	−0.218988	−	0.260980i	0.645354	−	0.763883i	$-0.276710\pi$
$641$	−5.54434	−	6.60749i	−0.218988	−	0.260980i	−0.864343	+	0.502903i	$0.832265\pi$
$642$	−9.83092	−	11.5917i	−0.387996	−	0.457488i
$643$	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	$-0.259898\pi$
$647$	34.8365			1.36956			0.684781	+	0.728749i	$0.259898\pi$
$648$	−25.4503	+	0.532745i	−0.999781	+	0.0209282i
$649$	0.0200952	+	0.113966i	0.000788806	+	0.00447354i
$650$	−2.39868	+	13.6119i	−0.0940839	+	0.533904i
$651$	−0.151909	−	29.4754i	−0.00595378	−	1.15523i
$652$	−3.02447	+	3.60596i	−0.118448	+	0.141220i
$653$	−8.90940	−	5.14384i	−0.348652	−	0.201294i	0.315440	−	0.948946i	$-0.397848\pi$
$653$	−8.90940	−	5.14384i	−0.348652	−	0.201294i	−0.664091	+	0.747652i	$0.731181\pi$
$654$	6.05729	+	16.3738i	0.236859	+	0.640267i
$655$	1.87311	+	5.14632i	0.0731884	+	0.201084i
$656$	28.9043	−	34.4762i	1.12852	−	1.34607i
$657$	−2.61063	+	2.23684i	−0.101851	+	0.0872674i
$658$	0.00770608	+	73.4139i	0.000300414	+	2.86197i
$659$	8.77745	−	49.7794i	0.341921	−	1.93913i	−0.00163545	−	0.999999i	$-0.500521\pi$
$659$	8.77745	−	49.7794i	0.341921	−	1.93913i	0.343557	−	0.939132i	$-0.388368\pi$
$660$	1.26697	−	2.22189i	0.0493167	−	0.0864870i
$661$	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
$663$	−4.80803	−	8.22952i	−0.186729	−	0.319608i
$664$	33.0677	−	0.0104131i	1.28327	−	0.000404107i
$665$	5.34981	+	2.77184i	0.207457	+	0.107487i
$666$	−29.6716	+	25.4285i	−1.14975	+	0.985336i
$667$	3.96629	−	10.8973i	0.153575	−	0.421945i
$668$	−34.5253	−	12.5580i	−1.33582	−	0.485883i
$669$	2.96017	+	16.2964i	0.114447	+	0.630055i
$670$	−1.56169	−	0.568221i	−0.0603332	−	0.0219523i
$671$	−2.67426	+	15.1665i	−0.103239	+	0.585496i
$672$	6.70306	−	39.3193i	0.258576	−	1.51677i
$673$	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
$675$	25.0612	+	4.02050i	0.964607	+	0.154749i
$676$	−17.9935	+	0.00377746i	−0.692057	+	0.000145287i
$677$	2.35032	+	1.35696i	0.0903302	+	0.0521522i	0.544485	−	0.838771i	$-0.316725\pi$
$677$	2.35032	+	1.35696i	0.0903302	+	0.0521522i	−0.454154	+	0.890923i	$0.650059\pi$
$678$	−14.8685	−	5.32332i	−0.571022	−	0.204441i
$679$	37.9589	+	45.2377i	1.45673	+	1.73606i
$680$	−2.02393	−	1.69720i	−0.0776144	−	0.0650845i
$681$	−17.4427	−	9.95104i	−0.668406	−	0.381325i
$682$	12.6599	−	2.23365i	0.484773	−	0.0855310i
$683$	21.1047			0.807550			0.403775	−	0.914858i	$-0.367698\pi$
$683$	21.1047			0.807550			0.403775	+	0.914858i	$0.367698\pi$
$684$	25.4610	−	5.97795i	0.973527	−	0.228573i
$685$	−4.53784			−0.173382
$686$	14.5837	−	2.57307i	0.556806	−	0.0982403i
$687$	42.4900	+	24.2405i	1.62110	+	0.924834i
$688$	−15.0478	−	2.64682i	−0.573693	−	0.100909i
$689$	6.30167	+	7.51004i	0.240074	+	0.286110i
$690$	1.68217	+	0.602262i	0.0640392	+	0.0229277i
$691$	−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
$693$	22.8605	−	13.5146i	0.868398	−	0.513376i
$694$	−34.9269	−	29.3009i	−1.32581	−	1.11225i
$695$	1.78344	+	3.08901i	0.0676497	+	0.117173i
$696$	−24.8013	+	9.18084i	−0.940091	+	0.347999i
$697$	5.37154	−	30.4635i	0.203461	−	1.15389i
$698$	10.0169	+	3.64467i	0.379146	+	0.137953i
$699$	5.61939	+	30.9360i	0.212545	+	1.17011i
$700$	−13.5944	+	37.3747i	−0.513820	+	1.41263i
$701$	−11.2547	+	30.9221i	−0.425085	+	1.16791i	0.523676	+	0.851917i	$0.324560\pi$
$701$	−11.2547	+	30.9221i	−0.425085	+	1.16791i	−0.948761	+	0.315994i	$0.897662\pi$
$702$	−0.228858	−	14.7011i	−0.00863768	−	0.554859i
$703$	24.3790	−	31.8985i	0.919471	−	1.20307i
$704$	17.3959	−	0.0109561i	0.655634	−	0.000412922i
$705$	3.78324	+	6.47546i	0.142485	+	0.243880i
$706$	−14.7532	−	17.5784i	−0.555242	−	0.661571i
$707$	−14.6711	−	12.3105i	−0.551764	−	0.462985i
$708$	0.160148	+	0.0913199i	0.00601874	+	0.00343201i
$709$	−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
$711$	0.709321	+	0.827855i	0.0266016	+	0.0310470i
$712$	−11.5769	−	31.7763i	−0.433864	−	1.19087i
$713$	3.07145	+	8.43874i	0.115027	+	0.316033i
$714$	−9.51521	−	25.7212i	−0.356098	−	0.962590i
$715$	1.27939	+	0.738655i	0.0478464	+	0.0276241i
$716$	−28.2245	−	23.6731i	−1.05480	−	0.884706i
$717$	−0.215179	−	41.7519i	−0.00803602	−	1.55926i
$718$	−1.31121	+	7.44083i	−0.0489341	+	0.277689i
$719$	−2.27158	−	12.8828i	−0.0847157	−	0.480446i	−0.997418	−	0.0718204i	$-0.977119\pi$
$719$	−2.27158	−	12.8828i	−0.0847157	−	0.480446i	0.912702	−	0.408626i	$-0.133992\pi$
$720$	−1.43460	−	3.81373i	−0.0534643	−	0.142129i
$721$	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
$726$	−9.93636	−	11.7160i	−0.368773	−	0.434822i
$727$	−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
$729$	−26.9871	+	0.834768i	−0.999522	+	0.0309173i
$730$	−0.476590	−	0.275093i	−0.0176394	−	0.0101816i
$731$	−9.87170	+	3.59301i	−0.365118	+	0.132892i
$732$	15.8707	+	18.7092i	0.586596	+	0.691512i
$733$	−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
$735$	4.29387	−	3.64086i	0.158382	−	0.134295i
$736$	2.11648	+	11.9664i	0.0780144	+	0.441088i
$737$	4.83721	−	5.76476i	0.178181	−	0.212348i
$738$	30.2907	−	36.8720i	1.11502	−	1.35728i
$739$	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
$741$	3.37385	+	14.7242i	0.123941	+	0.540908i
$742$	14.1070	+	24.4282i	0.517886	+	0.896787i
$743$	−40.2105	−	14.6354i	−1.47518	−	0.536922i	−0.525679	−	0.850683i	$-0.676189\pi$
$743$	−40.2105	−	14.6354i	−1.47518	−	0.536922i	−0.949502	+	0.313761i	$0.898411\pi$
$744$	10.1426	−	17.7915i	0.371846	−	0.652268i
$745$	−1.77536	−	1.48970i	−0.0650440	−	0.0545784i
$746$	−0.955295	−	0.347585i	−0.0349758	−	0.0127260i
$747$	35.0717	−	0.361511i	1.28321	−	0.0132270i
$748$	10.3572	−	5.98263i	0.378696	−	0.218747i
$749$	21.8759	−	12.6300i	0.799327	−	0.461492i
$750$	1.47019	+	8.08889i	0.0536837	+	0.295364i
$751$	−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
$753$	10.2031	+	27.5895i	0.371821	+	1.00542i
$754$	−5.22581	−	14.3531i	−0.190313	−	0.522710i
$755$	3.89895	−	3.27161i	0.141897	−	0.119066i
$756$	6.69259	−	41.7734i	0.243407	−	1.51928i
$757$	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	$0.156350\pi$
$761$			26.0234i			0.943347i	−0.881773	+	0.471673i	$0.843650\pi$
$762$	−9.76350	+	17.1181i	−0.353694	+	0.620125i
$763$	−28.5739	+	5.03835i	−1.03444	+	0.182400i
$764$	22.2474	−	8.10267i	0.804881	−	0.293144i
$765$	−2.16459	−	1.77861i	−0.0782608	−	0.0643057i
$766$	−18.6360	+	6.78516i	−0.673346	+	0.245158i
$767$	−0.0532404	+	0.0922151i	−0.00192240	+	0.00332969i
$768$	17.6859	−	21.3356i	0.638185	−	0.769883i
$769$	−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
$771$	−1.55442	+	9.08920i	−0.0559809	+	0.327340i
$772$	−21.1305	−	36.5813i	−0.760502	−	1.31659i
$773$	42.3125	+	7.46083i	1.52187	+	0.268347i	0.871169	−	0.490984i	$-0.163363\pi$
$773$	42.3125	+	7.46083i	1.52187	+	0.268347i	0.650704	+	0.759331i	$0.274474\pi$
$774$	−15.9879	−	2.64776i	−0.574673	−	0.0951716i
$775$	−13.1256	+	15.6425i	−0.471486	+	0.561895i
$776$	7.13749	+	40.4043i	0.256221	+	1.45043i
$777$	−32.7613	−	56.0748i	−1.17530	−	2.01167i
$778$	−13.5650	+	7.83368i	−0.486330	+	0.280851i
$779$	−22.5540	+	43.5304i	−0.808079	+	1.55964i
$780$	2.20717	−	0.816776i	0.0790293	−	0.0292453i
$781$	−9.74737	−	3.54775i	−0.348788	−	0.126949i
$782$	5.37144	+	6.40007i	0.192082	+	0.228866i
$783$	−26.2072	+	10.0001i	−0.936567	+	0.357375i
$784$	35.9855	+	13.0805i	1.28520	+	0.467162i
$785$	−5.51684	−	0.972767i	−0.196904	−	0.0347195i
$786$	−25.2355	+	30.3977i	−0.900119	+	1.08425i
$787$	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
$789$	3.07729	−	8.59231i	0.109554	−	0.305894i
$790$	−0.0872344	+	0.151131i	−0.00310366	+	0.00537700i
$791$	13.1233	−	22.7302i	0.466611	−	0.808193i
$792$	18.4501	−	0.195991i	0.655597	−	0.00696423i
$793$	−10.8552	+	9.10857i	−0.385478	+	0.323455i
$794$	−1.60166	+	9.08902i	−0.0568406	+	0.322557i
$795$	2.50302	+	1.42797i	0.0887729	+	0.0506448i
$796$	−8.64888	−	10.3029i	−0.306551	−	0.365178i
$797$		−	13.7014i		−	0.485330i	−0.970110	−	0.242665i	$-0.921978\pi$
$797$		−	13.7014i		−	0.485330i	0.970110	−	0.242665i	$-0.0780215\pi$
$798$	2.20794	+	43.4093i	0.0781603	+	1.53667i
$799$			35.0710i			1.24072i
$800$	−21.1581	+	17.7727i	−0.748050	+	0.628358i
$801$	−12.6154	−	33.5794i	−0.445742	−	1.18647i
$802$	−14.0689	−	2.47921i	−0.496791	−	0.0875440i
$803$	1.90888	−	1.60174i	0.0673629	−	0.0565242i
$804$	−2.14505	−	11.7949i	−0.0756502	−	0.415974i
$805$	−1.48472	+	2.57162i	−0.0523296	+	0.0906376i
$806$	10.2445	+	5.91326i	0.360849	+	0.208286i
$807$	−45.1037	−	16.1537i	−1.58773	−	0.568636i
$808$	−4.55502	−	12.5026i	−0.160245	−	0.439839i
$809$	−35.8537	+	20.7001i	−1.26055	+	0.727777i	−0.973180	−	0.230043i	$-0.926113\pi$
$809$	−35.8537	+	20.7001i	−1.26055	+	0.727777i	−0.287367	+	0.957821i	$0.592780\pi$
$810$	−1.56196	−	4.02966i	−0.0548818	−	0.141588i
$811$	−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
$813$	5.13894	+	28.2910i	0.180231	+	0.992209i
$814$	21.6957	−	18.2087i	0.760434	−	0.638216i
$815$	−0.750851	−	0.273287i	−0.0263012	−	0.00957284i
$816$	3.20413	−	18.7831i	0.112167	−	0.657541i
$817$	16.6324	−	0.758314i	0.581895	−	0.0265301i
$818$	17.8041	+	30.8301i	0.622505	+	1.07795i
$819$	24.1066	+	3.99490i	0.842353	+	0.139593i
$820$	7.17808	+	2.61090i	0.250669	+	0.0911766i
$821$	9.71713	−	11.5804i	0.339130	−	0.404160i	−0.569345	−	0.822099i	$-0.692803\pi$
$821$	9.71713	−	11.5804i	0.339130	−	0.404160i	0.908475	+	0.417939i	$0.137248\pi$
$822$	−16.5166	−	28.2633i	−0.576082	−	0.985795i
$823$	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
$825$	−18.1341	−	3.10126i	−0.631350	−	0.107972i
$826$	−0.196917	+	0.234727i	−0.00685162	+	0.00816719i
$827$	−22.6630	+	8.24867i	−0.788071	+	0.286834i	−0.704534	−	0.709670i	$-0.748844\pi$
$827$	−22.6630	+	8.24867i	−0.788071	+	0.286834i	−0.0835370	+	0.996505i	$0.526622\pi$
$828$	2.37158	+	12.6692i	0.0824180	+	0.440286i
$829$	−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
$831$	−0.193702	−	37.5847i	−0.00671946	−	1.30380i
$832$	12.2682	+	10.2811i	0.425323	+	0.356432i
$833$	25.9264	−	4.57153i	0.898297	−	0.158394i
$834$	−12.7482	+	22.3511i	−0.441432	+	0.773954i
$835$		−	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	0.984224	−	0.176924i	$-0.0566148\pi$
$839$	−0.0334751	−	0.189847i	−0.00115569	−	0.00655423i	−0.985380	+	0.170370i	$0.945504\pi$
$840$	6.66238	−	1.21236i	0.229874	−	0.0418304i
$841$	−0.108304	+	0.0908775i	−0.00373461	+	0.00313371i
$842$	14.8218	−	5.39645i	0.510792	−	0.185974i
$843$	−26.6428	+	9.85299i	−0.917628	+	0.339355i
$844$	0.00765885	+	36.4820i	0.000263628	+	1.25576i
$845$	−1.04483	−	2.87063i	−0.0359431	−	0.0987528i
$846$	−26.5614	+	47.1323i	−0.913200	+	1.62044i
$847$	22.1105	−	12.7655i	0.759726	−	0.438628i
$848$	0.00822918	+	19.5993i	0.000282591	+	0.673044i
$849$	−39.3910	+	33.4004i	−1.35189	+	1.14630i
$850$	−6.49615	+	17.8538i	−0.222816	+	0.612382i
$851$	15.1571	+	12.7183i	0.519580	+	0.435979i
$852$	−14.2663	+	8.33900i	−0.488756	+	0.285689i
$853$	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
$855$	2.43137	+	3.71538i	0.0831511	+	0.127063i
$856$	17.5505	−	0.00552669i	0.599863	−	0.000188899i
$857$	−6.44591	+	17.7100i	−0.220188	+	0.604962i	−0.999772	−	0.0213354i	$-0.993208\pi$
$857$	−6.44591	+	17.7100i	−0.220188	+	0.604962i	0.779584	+	0.626297i	$0.215430\pi$
$858$	0.0560422	+	10.6570i	0.00191325	+	0.363824i
$859$	−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
$861$	51.2891	+	60.4881i	1.74793	+	2.06143i
$862$	20.8088	−	0.00218425i	0.708751	−	7.43959e-5i
$863$	6.25339	+	10.8312i	0.212868	+	0.368698i	0.952611	−	0.304192i	$-0.0983863\pi$
$863$	6.25339	+	10.8312i	0.212868	+	0.368698i	−0.739743	+	0.672889i	$0.765053\pi$
$864$	18.5317	−	22.8162i	0.630460	−	0.776222i
$865$	6.74515	−	2.45503i	0.229342	−	0.0834736i
$866$	0.245119	−	0.424661i	0.00832947	−	0.0144306i
$867$	5.66892	+	15.3290i	0.192527	+	0.520599i
$868$	26.0775	+	21.8723i	0.885127	+	0.742393i
$869$	−0.507926	−	0.605323i	−0.0172302	−	0.0205342i
$870$	−2.90410	−	3.42425i	−0.0984584	−	0.116093i
$871$	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
$876$	−0.0212919	−	3.96964i	−0.000719387	−	0.134122i
$877$	−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
$879$	−16.1384	+	0.0831735i	−0.544336	+	0.00280537i
$880$	1.01129	+	2.77488i	0.0340907	+	0.0935412i
$881$	−17.2332	−	9.94959i	−0.580601	−	0.335210i	0.180771	−	0.983525i	$-0.442141\pi$
$881$	−17.2332	−	9.94959i	−0.580601	−	0.335210i	−0.761372	+	0.648315i	$0.775474\pi$
$882$	38.3051	+	13.4919i	1.28980	+	0.454296i
$883$	−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
$885$	−0.00527610	+	0.0308512i	−0.000177354	+	0.00103705i
$886$	−10.1193	+	0.00106219i	−0.339963	+	3.56851e-5i
$887$	−4.12020	+	23.3668i	−0.138343	+	0.784580i	0.834131	+	0.551567i	$0.185970\pi$
$887$	−4.12020	+	23.3668i	−0.138343	+	0.784580i	−0.972473	+	0.233014i	$0.925141\pi$
$888$	−0.246755	−	45.1216i	−0.00828055	−	1.51418i
$889$	−25.0891	−	21.0522i	−0.841461	−	0.706069i
$890$	4.39804	−	3.69118i	0.147423	−	0.123729i
$891$	19.5663	−	0.403413i	0.655495	−	0.0135148i
$892$	−16.5651	−	9.55922i	−0.554640	−	0.320066i
$893$	16.6122	−	53.0435i	0.555906	−	1.77503i
$894$	2.81654	−	16.4797i	0.0941990	−	0.551162i
$895$	2.13907	−	5.87705i	0.0715012	−	0.196448i
$896$	29.6308	+	35.2600i	0.989896	+	1.17795i
$897$	−7.32481	+	1.33052i	−0.244568	+	0.0444248i
$898$	9.01321	−	24.7717i	0.300775	−	0.826642i
$899$	3.91867	−	22.2239i	0.130695	−	0.741209i
$900$	−22.2520	+	19.0740i	−0.741734	+	0.635802i
$901$	6.73794	+	11.6705i	0.224473	+	0.388799i
$902$	−22.2299	+	26.4983i	−0.740176	+	0.882296i
$903$	9.08101	−	25.3557i	0.302197	−	0.843785i
$904$	15.7899	−	9.12291i	0.525163	−	0.303424i
$905$	0.189047	+	0.109146i	0.00628413	+	0.00362814i
$906$	34.5679	+	12.3762i	1.14844	+	0.411172i
$907$	−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
$909$	−4.96360	−	13.2120i	−0.164632	−	0.438216i
$910$	0.679592	+	3.85180i	0.0225283	+	0.127686i
$911$	−0.0767253			−0.00254202			−0.00127101	−	0.999999i	$-0.500405\pi$
$911$	−0.0767253			−0.00254202			−0.00127101	+	0.999999i	$0.500405\pi$
$912$	−13.7432	+	26.8910i	−0.455082	+	0.890450i
$913$	−25.4224			−0.841359
$914$	5.97088	+	33.8418i	0.197499	+	1.11939i
$915$	−2.06402	+	3.61792i	−0.0682343	+	0.119605i
$916$	−53.0755	+	19.3305i	−1.75366	+	0.638698i
$917$	−42.2049	−	50.2979i	−1.39373	−	1.66098i
$918$	3.19925	−	19.9555i	0.105591	−	0.658629i
$919$	−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
$921$	−17.3854	−	6.22650i	−0.572869	−	0.205170i
$922$	−27.2177	+	32.4437i	−0.896366	+	1.06848i
$923$	−4.77222	−	8.26573i	−0.157080	−	0.272070i
$924$	−5.16283	+	30.2270i	−0.169845	+	0.994396i
$925$	−7.81257	+	44.3073i	−0.256876	+	1.45681i
$926$	−10.7487	+	29.5416i	−0.353225	+	0.970796i
$927$	24.9305	+	14.0530i	0.818825	+	0.461562i
$928$	10.4293	−	28.7011i	0.342358	−	0.942160i
$929$	−13.7548	+	37.7911i	−0.451281	+	1.23989i	0.480542	+	0.876972i	$0.340440\pi$
$929$	−13.7548	+	37.7911i	−0.451281	+	1.23989i	−0.931823	+	0.362913i	$0.881782\pi$
$930$	3.42724	+	0.585748i	0.112384	+	0.0192074i
$931$	−41.3780	−	5.36639i	−1.35611	−	0.175876i
$932$	−31.4460	−	18.1466i	−1.03005	−	0.594411i
$933$	1.79267	−	1.04735i	0.0586893	−	0.0342888i
$934$	17.7965	−	14.9362i	0.582320	−	0.488729i
$935$	1.55559	+	1.30529i	0.0508732	+	0.0426877i
$936$	13.1207	+	10.7742i	0.428863	+	0.352164i
$937$	−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
$939$	−27.0279	−	4.62225i	−0.882022	−	0.150842i
$940$	−8.52858	−	1.50197i	−0.278172	−	0.0489890i
$941$	1.23392	+	3.39016i	0.0402245	+	0.110516i	0.958179	−	0.286170i	$-0.0923823\pi$
$941$	1.23392	+	3.39016i	0.0402245	+	0.110516i	−0.917954	+	0.396686i	$0.870160\pi$
$942$	−14.0211	−	37.9014i	−0.456833	−	1.23489i
$943$	−20.9248	−	12.0809i	−0.681404	−	0.393409i
$944$	−0.200006	+	0.0728915i	−0.00650965	+	0.00237242i
$945$	7.05332	−	1.35645i	0.229445	−	0.0441253i
$946$	11.5681	+	2.03852i	0.376112	+	0.0662780i
$947$	0.302599	+	1.71613i	0.00983316	+	0.0557666i	0.989330	−	0.145695i	$-0.0465419\pi$
$947$	0.302599	+	1.71613i	0.00983316	+	0.0557666i	−0.979496	+	0.201462i	$0.935431\pi$
$948$	−1.25881	+	0.00675186i	−0.0408842	+	0.000219290i
$949$	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	−0.685288	−	0.728272i	$-0.740324\pi$
$953$	−33.3454	+	5.87970i	−1.08016	+	0.190462i	−0.394877	+	0.918734i	$0.629213\pi$
$954$	0.216451	+	20.7871i	0.00700786	+	0.673007i
$955$	2.58387	+	3.07933i	0.0836120	+	0.0996449i
$956$	36.9388	+	30.9821i	1.19468	+	1.00203i
$957$	19.0695	−	7.05222i	0.616428	−	0.227966i
$958$	10.1889	−	17.6520i	0.329189	−	0.570311i
$959$	51.1234	−	18.6074i	1.65086	−	0.600864i
$960$	4.43046	+	1.58360i	0.142993	+	0.0511105i
$961$	−6.76229	−	11.7126i	−0.218138	−	0.377827i
$962$	26.0620	−	0.00273566i	0.840271	−	8.82013e-5i
$963$	18.6141	−	0.191870i	0.599831	−	0.00618293i
$964$	−1.17273	−	6.64270i	−0.0377710	−	0.213947i
$965$	4.61026	−	5.49430i	0.148410	−	0.176868i
$966$	−21.4209	+	0.112647i	−0.689207	+	0.00362435i
$967$	−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
$969$	1.05259	+	20.7374i	0.0338142	+	0.666182i
$970$	−6.03228	+	3.48358i	−0.193685	+	0.111851i
$971$	−3.12091	−	1.13592i	−0.100155	−	0.0364534i	0.291457	−	0.956584i	$-0.405860\pi$
$971$	−3.12091	−	1.13592i	−0.100155	−	0.0364534i	−0.391612	+	0.920131i	$0.628082\pi$
$972$	19.4130	−	24.3954i	0.622672	−	0.782483i
$973$	−32.7587	−	27.4878i	−1.05020	−	0.881218i
$974$	0.451169	−	1.23998i	0.0144564	−	0.0397315i
$975$	−10.9478	−	12.9114i	−0.350610	−	0.413494i
$976$	−28.3293	+	0.0118946i	−0.906798	+	0.000380738i
$977$	22.8654	−	13.2013i	0.731529	−	0.422349i	−0.0874521	−	0.996169i	$-0.527872\pi$
$977$	22.8654	−	13.2013i	0.731529	−	0.422349i	0.818981	+	0.573820i	$0.194539\pi$
$978$	−1.03077	−	5.67126i	−0.0329605	−	0.181347i
$979$	8.89265	+	24.4324i	0.284210	+	0.780862i
$980$	0.00136470	+	6.50058i	4.35937e−5	+	0.207653i
$981$	−20.1668	−	7.10558i	−0.643877	−	0.226864i
$982$	−40.8918	+	14.8883i	−1.30491	+	0.475104i
$983$	11.4614	−	9.61725i	0.365562	−	0.306743i	−0.441441	−	0.897290i	$-0.645533\pi$
$983$	11.4614	−	9.61725i	0.365562	−	0.306743i	0.807003	+	0.590548i	$0.201088\pi$
$984$	9.86476	+	54.2106i	0.314477	+	1.72817i
$985$	−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
$990$	1.10199	+	2.93234i	0.0350237	+	0.0931959i
$991$	−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
$993$	16.2103	−	0.0835439i	0.514418	−	0.00265118i
$994$	−9.39564	−	25.8059i	−0.298012	−	0.818513i
$995$	1.14191	−	1.97784i	0.0362009	−	0.0627017i
$996$	−25.8658	+	31.1636i	−0.819588	+	0.987455i
$997$	−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
$999$	−0.739930	−	47.8537i	−0.0234104	−	1.51402i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.245722 - 1.39270i) q^{2} +(1.50444 + 0.858283i) q^{3} +(-1.87924 + 0.684435i) q^{4} +(-0.218260 - 0.260112i) q^{5} +(0.825659 - 2.30614i) q^{6} +(3.52551 + 2.03545i) q^{7} +(1.41498 + 2.44904i) q^{8} +(1.52670 + 2.58248i) q^{9} +O(q^{10})\)	\(q+(-0.245722 - 1.39270i) q^{2} +(1.50444 + 0.858283i) q^{3} +(-1.87924 + 0.684435i) q^{4} +(-0.218260 - 0.260112i) q^{5} +(0.825659 - 2.30614i) q^{6} +(3.52551 + 2.03545i) q^{7} +(1.41498 + 2.44904i) q^{8} +(1.52670 + 2.58248i) q^{9} +(-0.308628 + 0.367887i) q^{10} +(-1.08725 - 1.88317i) q^{11} +(-3.41465 - 0.583228i) q^{12} +(0.347438 - 1.97042i) q^{13} +(1.96849 - 5.41014i) q^{14} +(-0.105110 - 0.578653i) q^{15} +(3.06310 - 2.57244i) q^{16} +(0.940649 - 2.58441i) q^{17} +(3.22148 - 2.76081i) q^{18} +(-2.64686 + 3.46326i) q^{19} +(0.588193 + 0.339429i) q^{20} +(3.55693 + 6.08811i) q^{21} +(-2.35553 + 1.97695i) q^{22} +(-1.64563 - 1.38085i) q^{23} +(0.0267905 + 4.89891i) q^{24} +(0.848220 - 4.81049i) q^{25} +(-2.82958 + 0.000297014i) q^{26} +(0.0803352 + 5.19553i) q^{27} +(-8.01842 - 1.41213i) q^{28} +(1.84632 + 5.07272i) q^{29} +(-0.780064 + 0.288575i) q^{30} +(-3.62030 - 2.09018i) q^{31} +(-4.33531 - 3.63388i) q^{32} +(-0.0194105 - 3.76628i) q^{33} +(-3.83046 - 0.674998i) q^{34} +(-0.240031 - 1.36129i) q^{35} +(-4.63657 - 3.80817i) 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} +(7.60491 - 6.44973i) q^{42} +(-2.45526 - 2.92607i) q^{43} +(3.33210 + 2.79478i) q^{44} +(0.338516 - 0.960765i) q^{45} +(-1.51874 + 2.63118i) q^{46} +(-11.9828 + 4.36138i) q^{47} +(6.81614 - 1.24108i) q^{48} +(4.78614 + 8.28983i) q^{49} +(-6.90801 + 0.000725118i) q^{50} +(3.63331 - 3.08076i) q^{51} +(0.695703 + 3.94069i) q^{52} +(-3.14955 + 3.75349i) q^{53} +(7.21609 - 1.38854i) q^{54} +(-0.252532 + 0.693826i) q^{55} +(0.00362587 + 11.5143i) q^{56} +(-6.95450 + 2.93852i) q^{57} +(6.61111 - 3.81785i) q^{58} +(-0.0500092 - 0.0182019i) q^{59} +(0.593577 + 1.01549i) q^{60} +(-5.42537 - 4.55243i) q^{61} +(-2.02141 + 5.55560i) q^{62} +(0.125879 + 12.2121i) q^{63} +(-3.99564 + 6.93072i) q^{64} +(-0.588362 + 0.339691i) q^{65} +(-5.24054 + 0.952491i) q^{66} +(1.18364 + 3.25203i) q^{67} +(0.00115476 + 5.50055i) q^{68} +(-1.29060 - 3.48982i) q^{69} +(-1.83689 + 0.668790i) q^{70} +(3.65424 - 3.06627i) q^{71} +(-4.16435 + 7.39312i) 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} +(-4.25720 - 2.42813i) q^{78} +(0.357871 - 0.0631023i) q^{79} +(-1.33767 - 0.235289i) q^{80} +(-4.33838 + 7.88533i) q^{81} +(-5.44182 - 14.9464i) q^{82} +(5.84559 - 10.1249i) q^{83} +(-10.8512 - 9.00654i) q^{84} +(-0.877544 + 0.319400i) q^{85} +(-3.47183 + 4.13845i) q^{86} +(-1.57615 + 9.21628i) q^{87} +(3.07352 - 5.32737i) q^{88} +(-11.7753 - 2.07631i) q^{89} +(-1.42124 - 0.235372i) q^{90} +(5.23559 - 6.23953i) q^{91} +(4.03763 + 1.46862i) q^{92} +(-3.65257 - 6.25180i) q^{93} +(9.01854 + 15.6168i) q^{94} +(1.47854 - 0.0674103i) q^{95} +(-3.40333 - 9.18789i) q^{96} +(13.6314 + 4.96143i) q^{97} +(10.3692 - 8.70266i) q^{98} +(3.20334 - 5.68282i) 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

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