LMFDB - Embedded newform 27.2.e.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,2,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.215596085457$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.2
Root			$0.500000 + 1.00210i$ of defining polynomial
Character	$\chi$	$=$	27.13
Dual form			27.2.e.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.183082 + 1.03831i) q^{2} +(-1.72962 - 0.0916693i) q^{3} +(0.834822 - 0.303850i) q^{4} +(-1.33735 - 1.12217i) q^{5} +(-0.221481 - 1.81266i) q^{6} +(-2.31094 - 0.841112i) q^{7} +(1.52266 + 2.63732i) q^{8} +(2.98319 + 0.317107i) q^{9} +O(q^{10})$	\(q+(0.183082 + 1.03831i) q^{2} +(-1.72962 - 0.0916693i) q^{3} +(0.834822 - 0.303850i) q^{4} +(-1.33735 - 1.12217i) q^{5} +(-0.221481 - 1.81266i) q^{6} +(-2.31094 - 0.841112i) q^{7} +(1.52266 + 2.63732i) q^{8} +(2.98319 + 0.317107i) q^{9} +(0.920313 - 1.59403i) q^{10} +(-0.960783 + 0.806193i) q^{11} +(-1.47178 + 0.449019i) q^{12} +(-0.789931 + 4.47992i) q^{13} +(0.450243 - 2.55345i) q^{14} +(2.21024 + 2.06353i) q^{15} +(-1.09847 + 0.921724i) q^{16} +(3.32358 - 5.75662i) q^{17} +(0.216914 + 3.15553i) q^{18} +(-0.124578 - 0.215776i) q^{19} +(-1.45742 - 0.530458i) q^{20} +(3.91994 + 1.66665i) q^{21} +(-1.01298 - 0.849989i) q^{22} +(-0.791222 + 0.287981i) q^{23} +(-2.39186 - 4.70115i) q^{24} +(-0.339001 - 1.92257i) q^{25} -4.79615 q^{26} +(-5.13073 - 0.821942i) q^{27} -2.18479 q^{28} +(-0.0889744 - 0.504599i) q^{29} +(-1.73792 + 2.67271i) q^{30} +(0.770551 - 0.280458i) q^{31} +(3.50754 + 2.94318i) q^{32} +(1.73570 - 1.30634i) q^{33} +(6.58563 + 2.39697i) q^{34} +(2.14666 + 3.71812i) q^{35} +(2.58679 - 0.641717i) q^{36} +(-1.30403 + 2.25865i) q^{37} +(0.201233 - 0.168855i) q^{38} +(1.77695 - 7.67616i) q^{39} +(0.923194 - 5.23570i) q^{40} +(-1.41572 + 8.02895i) q^{41} +(-1.01282 + 4.37524i) q^{42} +(3.31478 - 2.78143i) q^{43} +(-0.557121 + 0.964962i) q^{44} +(-3.63373 - 3.77173i) q^{45} +(-0.443871 - 0.768808i) q^{46} +(4.98256 + 1.81351i) q^{47} +(1.98443 - 1.49354i) q^{48} +(-0.729356 - 0.612002i) q^{49} +(1.93415 - 0.703974i) q^{50} +(-6.27625 + 9.65211i) q^{51} +(0.701774 + 3.97996i) q^{52} -10.4841 q^{53} +(-0.0859140 - 5.47776i) q^{54} +2.18959 q^{55} +(-1.30048 - 7.37539i) q^{56} +(0.195693 + 0.384630i) q^{57} +(0.507639 - 0.184765i) q^{58} +(-2.30289 - 1.93235i) q^{59} +(2.47216 + 1.05109i) q^{60} +(-2.70930 - 0.986103i) q^{61} +(0.432275 + 0.748722i) q^{62} +(-6.62725 - 3.24201i) q^{63} +(-3.84771 + 6.66442i) q^{64} +(6.08365 - 5.10479i) q^{65} +(1.67415 + 1.56302i) q^{66} +(1.75146 - 9.93303i) q^{67} +(1.02545 - 5.81562i) q^{68} +(1.39492 - 0.425568i) q^{69} +(-3.46754 + 2.90961i) q^{70} +(-0.0447378 + 0.0774882i) q^{71} +(3.70607 + 8.35047i) q^{72} +(2.66057 + 4.60824i) q^{73} +(-2.58391 - 0.940468i) q^{74} +(0.410103 + 3.35640i) q^{75} +(-0.169564 - 0.142281i) q^{76} +(2.89841 - 1.05493i) q^{77} +(8.29554 + 0.439660i) q^{78} +(0.829503 + 4.70435i) q^{79} +2.50337 q^{80} +(8.79889 + 1.89198i) q^{81} -8.59571 q^{82} +(1.39625 + 7.91851i) q^{83} +(3.77887 + 0.200278i) q^{84} +(-10.9047 + 3.96899i) q^{85} +(3.49486 + 2.93254i) q^{86} +(0.107636 + 0.880922i) q^{87} +(-3.58913 - 1.30634i) q^{88} +(-3.35189 - 5.80564i) q^{89} +(3.25095 - 4.46346i) q^{90} +(5.59359 - 9.68839i) q^{91} +(-0.573026 + 0.480826i) q^{92} +(-1.35847 + 0.414450i) q^{93} +(-0.970760 + 5.50545i) q^{94} +(-0.0755324 + 0.428365i) q^{95} +(-5.79693 - 5.41213i) q^{96} +(4.20603 - 3.52928i) q^{97} +(0.501915 - 0.869342i) q^{98} +(-3.12185 + 2.10036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.183082	+	1.03831i	0.129458	+	0.734194i	0.978560	+	0.205964i	$0.0660330\pi$
$2$	0.183082	+	1.03831i	0.129458	+	0.734194i	−0.849101	+	0.528230i	$0.822856\pi$
$3$	−1.72962	−	0.0916693i	−0.998598	−	0.0529253i
$3$	−1.72962	−	0.0916693i	−0.998598	−	0.0529253i
$4$	0.834822	−	0.303850i	0.417411	−	0.151925i
$5$	−1.33735	−	1.12217i	−0.598081	−	0.501850i	0.292747	−	0.956190i	$-0.405431\pi$
$5$	−1.33735	−	1.12217i	−0.598081	−	0.501850i	−0.890828	+	0.454340i	$0.849875\pi$
$6$	−0.221481	−	1.81266i	−0.0904194	−	0.740017i
$7$	−2.31094	−	0.841112i	−0.873452	−	0.317910i	−0.133888	−	0.990997i	$-0.542746\pi$
$7$	−2.31094	−	0.841112i	−0.873452	−	0.317910i	−0.739564	+	0.673086i	$0.764968\pi$
$8$	1.52266	+	2.63732i	0.538340	+	0.932432i
$9$	2.98319	+	0.317107i	0.994398	+	0.105702i
$10$	0.920313	−	1.59403i	0.291029	−	0.504076i
$11$	−0.960783	+	0.806193i	−0.289687	+	0.243076i	−0.776036	−	0.630688i	$-0.782773\pi$
$11$	−0.960783	+	0.806193i	−0.289687	+	0.243076i	0.486349	+	0.873764i	$0.338328\pi$
$12$	−1.47178	+	0.449019i	−0.424867	+	0.129621i
$13$	−0.789931	+	4.47992i	−0.219087	+	1.24251i	0.654584	+	0.755989i	$0.272844\pi$
$13$	−0.789931	+	4.47992i	−0.219087	+	1.24251i	−0.873671	+	0.486517i	$0.838267\pi$
$14$	0.450243	−	2.55345i	0.120332	−	0.682439i
$15$	2.21024	+	2.06353i	0.570683	+	0.532800i
$16$	−1.09847	+	0.921724i	−0.274617	+	0.230431i
$17$	3.32358	−	5.75662i	0.806088	−	1.39618i	−0.109467	−	0.993990i	$-0.534914\pi$
$17$	3.32358	−	5.75662i	0.806088	−	1.39618i	0.915554	−	0.402194i	$-0.131752\pi$
$18$	0.216914	+	3.15553i	0.0511270	+	0.743765i
$19$	−0.124578	−	0.215776i	−0.0285802	−	0.0495023i	0.851382	−	0.524547i	$-0.175765\pi$
$19$	−0.124578	−	0.215776i	−0.0285802	−	0.0495023i	−0.879962	+	0.475045i	$0.842432\pi$
$20$	−1.45742	−	0.530458i	−0.325889	−	0.118614i
$21$	3.91994	+	1.66665i	0.855402	+	0.363693i
$22$	−1.01298	−	0.849989i	−0.215967	−	0.181218i
$23$	−0.791222	+	0.287981i	−0.164981	+	0.0600483i	−0.423190	−	0.906041i	$-0.639090\pi$
$23$	−0.791222	+	0.287981i	−0.164981	+	0.0600483i	0.258209	+	0.966089i	$0.416868\pi$
$24$	−2.39186	−	4.70115i	−0.488236	−	0.959617i
$25$	−0.339001	−	1.92257i	−0.0678002	−	0.384514i
$26$	−4.79615			−0.940603
$27$	−5.13073	−	0.821942i	−0.987410	−	0.158183i
$28$	−2.18479			−0.412887
$29$	−0.0889744	−	0.504599i	−0.0165221	−	0.0937016i	0.975432	−	0.220302i	$-0.0707044\pi$
$29$	−0.0889744	−	0.504599i	−0.0165221	−	0.0937016i	−0.991954	+	0.126601i	$0.959593\pi$
$30$	−1.73792	+	2.67271i	−0.317299	+	0.487967i
$31$	0.770551	−	0.280458i	0.138395	−	0.0503717i	−0.271894	−	0.962327i	$-0.587650\pi$
$31$	0.770551	−	0.280458i	0.138395	−	0.0503717i	0.410289	+	0.911956i	$0.365428\pi$
$32$	3.50754	+	2.94318i	0.620052	+	0.520286i
$33$	1.73570	−	1.30634i	0.302146	−	0.227404i
$34$	6.58563	+	2.39697i	1.12943	+	0.411077i
$35$	2.14666	+	3.71812i	0.362852	+	0.628478i
$36$	2.58679	−	0.641717i	0.431131	−	0.106953i
$37$	−1.30403	+	2.25865i	−0.214381	+	0.371319i	−0.953081	−	0.302715i	$-0.902107\pi$
$37$	−1.30403	+	2.25865i	−0.214381	+	0.371319i	0.738700	+	0.674035i	$0.235440\pi$
$38$	0.201233	−	0.168855i	0.0326444	−	0.0273919i
$39$	1.77695	−	7.67616i	0.284540	−	1.22917i
$40$	0.923194	−	5.23570i	0.145970	−	0.827836i
$41$	−1.41572	+	8.02895i	−0.221099	+	1.25391i	0.648906	+	0.760869i	$0.275227\pi$
$41$	−1.41572	+	8.02895i	−0.221099	+	1.25391i	−0.870005	+	0.493044i	$0.835884\pi$
$42$	−1.01282	+	4.37524i	−0.156282	+	0.675114i
$43$	3.31478	−	2.78143i	0.505500	−	0.424165i	−0.354042	−	0.935229i	$-0.615193\pi$
$43$	3.31478	−	2.78143i	0.505500	−	0.424165i	0.859542	+	0.511065i	$0.170749\pi$
$44$	−0.557121	+	0.964962i	−0.0839891	+	0.145473i
$45$	−3.63373	−	3.77173i	−0.541684	−	0.562257i
$46$	−0.443871	−	0.768808i	−0.0654452	−	0.113354i
$47$	4.98256	+	1.81351i	0.726782	+	0.264527i	0.678802	−	0.734321i	$-0.262499\pi$
$47$	4.98256	+	1.81351i	0.726782	+	0.264527i	0.0479798	+	0.998848i	$0.484722\pi$
$48$	1.98443	−	1.49354i	0.286428	−	0.215574i
$49$	−0.729356	−	0.612002i	−0.104194	−	0.0874289i
$50$	1.93415	−	0.703974i	0.273530	−	0.0995569i
$51$	−6.27625	+	9.65211i	−0.878851	+	1.35157i
$52$	0.701774	+	3.97996i	0.0973185	+	0.551921i
$53$	−10.4841			−1.44010			−0.720052	−	0.693920i	$-0.755882\pi$
$53$	−10.4841			−1.44010			−0.720052	+	0.693920i	$0.755882\pi$
$54$	−0.0859140	−	5.47776i	−0.0116914	−	0.745429i
$55$	2.18959			0.295244
$56$	−1.30048	−	7.37539i	−0.173784	−	0.985578i
$57$	0.195693	+	0.384630i	0.0259202	+	0.0509456i
$58$	0.507639	−	0.184765i	0.0666563	−	0.0242609i
$59$	−2.30289	−	1.93235i	−0.299810	−	0.251571i	0.480455	−	0.877019i	$-0.340471\pi$
$59$	−2.30289	−	1.93235i	−0.299810	−	0.251571i	−0.780265	+	0.625449i	$0.784916\pi$
$60$	2.47216	+	1.05109i	0.319155	+	0.135696i
$61$	−2.70930	−	0.986103i	−0.346890	−	0.126258i	0.162699	−	0.986676i	$-0.447980\pi$
$61$	−2.70930	−	0.986103i	−0.346890	−	0.126258i	−0.509589	+	0.860418i	$0.670202\pi$
$62$	0.432275	+	0.748722i	0.0548990	+	0.0950878i
$63$	−6.62725	−	3.24201i	−0.834955	−	0.408455i
$64$	−3.84771	+	6.66442i	−0.480963	+	0.833053i
$65$	6.08365	−	5.10479i	0.754584	−	0.633171i
$66$	1.67415	+	1.56302i	0.206074	+	0.192394i
$67$	1.75146	−	9.93303i	0.213975	−	1.21351i	−0.668701	−	0.743531i	$-0.733149\pi$
$67$	1.75146	−	9.93303i	0.213975	−	1.21351i	0.882676	−	0.469982i	$-0.155739\pi$
$68$	1.02545	−	5.81562i	0.124354	−	0.705248i
$69$	1.39492	−	0.425568i	0.167928	−	0.0512324i
$70$	−3.46754	+	2.90961i	−0.414451	+	0.347765i
$71$	−0.0447378	+	0.0774882i	−0.00530940	+	0.00919615i	−0.868668	−	0.495395i	$-0.835023\pi$
$71$	−0.0447378	+	0.0774882i	−0.00530940	+	0.00919615i	0.863358	+	0.504591i	$0.168357\pi$
$72$	3.70607	+	8.35047i	0.436764	+	0.984112i
$73$	2.66057	+	4.60824i	0.311396	+	0.539354i	0.978665	−	0.205463i	$-0.0658701\pi$
$73$	2.66057	+	4.60824i	0.311396	+	0.539354i	−0.667269	+	0.744817i	$0.732537\pi$
$74$	−2.58391	−	0.940468i	−0.300374	−	0.109327i
$75$	0.410103	+	3.35640i	0.0473546	+	0.387563i
$76$	−0.169564	−	0.142281i	−0.0194503	−	0.0163208i
$77$	2.89841	−	1.05493i	0.330304	−	0.120221i
$78$	8.29554	+	0.439660i	0.939285	+	0.0497817i
$79$	0.829503	+	4.70435i	0.0933264	+	0.529280i	0.995247	+	0.0973792i	$0.0310460\pi$
$79$	0.829503	+	4.70435i	0.0933264	+	0.529280i	−0.901921	+	0.431901i	$0.857843\pi$
$80$	2.50337			0.279885
$81$	8.79889	+	1.89198i	0.977654	+	0.210220i
$82$	−8.59571			−0.949238
$83$	1.39625	+	7.91851i	0.153258	+	0.869169i	0.960361	+	0.278759i	$0.0899229\pi$
$83$	1.39625	+	7.91851i	0.153258	+	0.869169i	−0.807103	+	0.590410i	$0.798966\pi$
$84$	3.77887	+	0.200278i	0.412308	+	0.0218522i
$85$	−10.9047	+	3.96899i	−1.18278	+	0.430497i
$86$	3.49486	+	2.93254i	0.376860	+	0.316223i
$87$	0.107636	+	0.880922i	0.0115398	+	0.0944448i
$88$	−3.58913	−	1.30634i	−0.382602	−	0.139256i
$89$	−3.35189	−	5.80564i	−0.355299	−	0.615396i	0.631870	−	0.775074i	$-0.282288\pi$
$89$	−3.35189	−	5.80564i	−0.355299	−	0.615396i	−0.987169	+	0.159678i	$0.948954\pi$
$90$	3.25095	−	4.46346i	0.342680	−	0.470490i
$91$	5.59359	−	9.68839i	0.586368	−	1.01562i
$92$	−0.573026	+	0.480826i	−0.0597421	+	0.0501296i
$93$	−1.35847	+	0.414450i	−0.140867	+	0.0429765i
$94$	−0.970760	+	5.50545i	−0.100126	+	0.567844i
$95$	−0.0755324	+	0.428365i	−0.00774946	+	0.0439494i
$96$	−5.79693	−	5.41213i	−0.591647	−	0.552373i
$97$	4.20603	−	3.52928i	0.427057	−	0.358344i	−0.403783	−	0.914855i	$-0.632305\pi$
$97$	4.20603	−	3.52928i	0.427057	−	0.358344i	0.830840	+	0.556511i	$0.187860\pi$
$98$	0.501915	−	0.869342i	0.0507010	−	0.0878168i
$99$	−3.12185	+	2.10036i	−0.313758	+	0.211094i
$100$	−0.867179	−	1.50200i	−0.0867179	−	0.150200i
$101$	−4.70360	−	1.71197i	−0.468025	−	0.170347i	0.0972322	−	0.995262i	$-0.469001\pi$
$101$	−4.70360	−	1.71197i	−0.468025	−	0.170347i	−0.565258	+	0.824914i	$0.691223\pi$
$102$	−11.1709	−	4.74956i	−1.10609	−	0.470276i
$103$	8.90079	+	7.46865i	0.877021	+	0.735908i	0.965564	−	0.260164i	$-0.0837767\pi$
$103$	8.90079	+	7.46865i	0.877021	+	0.735908i	−0.0885431	+	0.996072i	$0.528221\pi$
$104$	−13.0178	+	4.73808i	−1.27650	+	0.464607i
$105$	−3.37208	−	6.62774i	−0.329081	−	0.646801i
$106$	−1.91945	−	10.8857i	−0.186433	−	1.05732i
$107$	19.4581			1.88109			0.940544	−	0.339673i	$-0.110316\pi$
$107$	19.4581			1.88109			0.940544	+	0.339673i	$0.110316\pi$
$108$	−4.53300	+	0.872799i	−0.436188	+	0.0839852i
$109$	6.31515			0.604881			0.302441	−	0.953168i	$-0.402199\pi$
$109$	6.31515			0.604881			0.302441	+	0.953168i	$0.402199\pi$
$110$	0.400873	+	2.27347i	0.0382218	+	0.216766i
$111$	2.46253	−	3.78707i	0.233733	−	0.359453i
$112$	3.31376	−	1.20611i	0.313121	−	0.113967i
$113$	−5.29775	−	4.44534i	−0.498371	−	0.418183i	0.358644	−	0.933474i	$-0.383239\pi$
$113$	−5.29775	−	4.44534i	−0.498371	−	0.418183i	−0.857015	+	0.515292i	$0.827684\pi$
$114$	−0.363537	+	0.273608i	−0.0340483	+	0.0256258i
$115$	1.38131	+	0.502754i	0.128807	+	0.0468821i
$116$	−0.227600	−	0.394215i	−0.0211322	−	0.0366020i
$117$	−3.77713	+	13.1140i	−0.349196	+	1.21239i
$118$	1.58476	−	2.74488i	0.145889	−	0.252687i
$119$	−12.5226	+	10.5077i	−1.14794	+	0.963236i
$120$	−2.07673	+	8.97115i	−0.189579	+	0.818950i
$121$	−1.63697	+	9.28373i	−0.148816	+	0.843976i
$122$	0.527856	−	2.99362i	0.0477898	−	0.271030i
$123$	3.18467	−	13.7573i	0.287152	−	1.24045i
$124$	0.558056	−	0.468265i	0.0501149	−	0.0420514i
$125$	−6.06855	+	10.5110i	−0.542788	+	0.940136i
$126$	2.15288	−	7.47467i	0.191794	−	0.665897i
$127$	−6.01162	−	10.4124i	−0.533445	−	0.923954i	−0.999237	−	0.0390598i	$-0.987564\pi$
$127$	−6.01162	−	10.4124i	−0.533445	−	0.923954i	0.465792	−	0.884894i	$-0.345770\pi$
$128$	0.981117	+	0.357098i	0.0867194	+	0.0315633i
$129$	−5.98830	+	4.50697i	−0.527240	+	0.396817i
$130$	6.41414	+	5.38210i	0.562557	+	0.472042i
$131$	13.2354	−	4.81728i	1.15638	−	0.420888i	0.308577	−	0.951199i	$-0.400147\pi$
$131$	13.2354	−	4.81728i	1.15638	−	0.420888i	0.847803	+	0.530311i	$0.177925\pi$
$132$	1.05207	−	1.61795i	0.0915706	−	0.140824i
$133$	0.106401	+	0.603428i	0.00922610	+	0.0523238i
$134$	10.6342			0.918655
$135$	5.93923	+	6.85678i	0.511167	+	0.590138i
$136$	20.2427			1.73580
$137$	0.392122	+	2.22383i	0.0335012	+	0.189995i	0.996966	−	0.0778409i	$-0.0248026\pi$
$137$	0.392122	+	2.22383i	0.0335012	+	0.189995i	−0.963465	+	0.267836i	$0.913692\pi$
$138$	0.697254	+	1.37044i	0.0593542	+	0.116659i
$139$	7.49414	−	2.72764i	0.635644	−	0.231356i	−0.00404179	−	0.999992i	$-0.501287\pi$
$139$	7.49414	−	2.72764i	0.635644	−	0.231356i	0.639686	+	0.768636i	$0.279064\pi$
$140$	2.92183	+	2.45171i	0.246940	+	0.207207i
$141$	−8.45172	−	3.59343i	−0.711763	−	0.302621i
$142$	−0.0886472	−	0.0322649i	−0.00743911	−	0.00270761i
$143$	−2.85273	−	4.94107i	−0.238557	−	0.413193i
$144$	−3.56923	+	2.40135i	−0.297436	+	0.200113i
$145$	−0.447256	+	0.774670i	−0.0371426	+	0.0643328i
$146$	−4.29767	+	3.60617i	−0.355678	+	0.298449i
$147$	1.20541	+	1.12539i	0.0994204	+	0.0928208i
$148$	−0.402343	+	2.28180i	−0.0330724	+	0.187563i
$149$	−0.0185697	+	0.105314i	−0.00152129	+	0.00862764i	−0.985559	−	0.169333i	$-0.945839\pi$
$149$	−0.0185697	+	0.105314i	−0.00152129	+	0.00862764i	0.984038	+	0.177960i	$0.0569499\pi$
$150$	−3.40989	+	1.04031i	−0.278416	+	0.0849407i
$151$	−15.5196	+	13.0225i	−1.26297	+	1.05976i	−0.267609	+	0.963528i	$0.586233\pi$
$151$	−15.5196	+	13.0225i	−1.26297	+	1.05976i	−0.995359	+	0.0962282i	$0.969322\pi$
$152$	0.379379	−	0.657104i	0.0307717	−	0.0532982i
$153$	11.7404	−	16.1192i	0.949152	−	1.30316i
$154$	1.62599	+	2.81630i	0.131026	+	0.226944i
$155$	−1.34522	−	0.489620i	−0.108051	−	0.0393272i
$156$	−0.848964	−	6.94816i	−0.0679716	−	0.556298i
$157$	−15.8953	−	13.3377i	−1.26858	−	1.06447i	−0.994712	−	0.102701i	$-0.967252\pi$
$157$	−15.8953	−	13.3377i	−1.26858	−	1.06447i	−0.273871	−	0.961767i	$-0.588304\pi$
$158$	−4.73269	+	1.72256i	−0.376513	+	0.137039i
$159$	18.1336	+	0.961071i	1.43809	+	0.0762179i
$160$	−1.38807	−	7.87212i	−0.109736	−	0.622346i
$161$	2.07069			0.163193
$162$	−0.353543	+	9.48234i	−0.0277770	+	0.745003i
$163$	−20.1346			−1.57706			−0.788531	−	0.614995i	$-0.789158\pi$
$163$	−20.1346			−1.57706			−0.788531	+	0.614995i	$0.789158\pi$
$164$	1.25773	+	7.13292i	0.0982119	+	0.556987i
$165$	−3.78716	−	0.200718i	−0.294830	−	0.0156259i
$166$	−7.96622	+	2.89947i	−0.618298	+	0.225042i
$167$	−15.2156	−	12.7674i	−1.17742	−	0.987974i	−0.999993	−	0.00383999i	$-0.998778\pi$
$167$	−15.2156	−	12.7674i	−1.17742	−	0.987974i	−0.177429	−	0.984134i	$-0.556778\pi$
$168$	1.57325	+	12.8759i	0.121378	+	0.993395i
$169$	−7.22968	−	2.63139i	−0.556130	−	0.202415i
$170$	−6.11748	−	10.5958i	−0.469189	−	0.812660i
$171$	−0.303217	−	0.683205i	−0.0231876	−	0.0522460i
$172$	1.92212	−	3.32920i	0.146560	−	0.253849i
$173$	14.4975	−	12.1648i	1.10222	−	0.924875i	0.104650	−	0.994509i	$-0.466628\pi$
$173$	14.4975	−	12.1648i	1.10222	−	0.924875i	0.997573	+	0.0696342i	$0.0221832\pi$
$174$	−0.894962	+	0.273040i	−0.0678469	+	0.0206991i
$175$	−0.833686	+	4.72807i	−0.0630208	+	0.357409i
$176$	0.312302	−	1.77115i	0.0235407	−	0.133506i
$177$	3.80599	+	3.55334i	0.286075	+	0.267085i
$178$	5.41436	−	4.54319i	0.405824	−	0.340527i
$179$	−5.45683	+	9.45151i	−0.407863	+	0.706439i	−0.994650	−	0.103302i	$-0.967059\pi$
$179$	−5.45683	+	9.45151i	−0.407863	+	0.706439i	0.586787	+	0.809741i	$0.300392\pi$
$180$	−4.17956	−	2.04462i	−0.311526	−	0.152397i
$181$	8.97393	+	15.5433i	0.667027	+	1.15532i	0.978731	+	0.205146i	$0.0657668\pi$
$181$	8.97393	+	15.5433i	0.667027	+	1.15532i	−0.311704	+	0.950179i	$0.600900\pi$
$182$	11.0836	+	4.03410i	0.821572	+	0.299028i
$183$	4.59567	+	1.95395i	0.339721	+	0.144440i
$184$	−1.96426	−	1.64821i	−0.144807	−	0.121507i
$185$	4.27853	−	1.55726i	0.314564	−	0.114492i
$186$	−0.679038	−	1.33463i	−0.0497895	−	0.0978601i
$187$	1.44770	+	8.21031i	0.105866	+	0.600397i
$188$	4.71059			0.343555
$189$	11.1654	+	6.21498i	0.812167	+	0.452073i
$190$	−0.458604			−0.0332706
$191$	−4.68261	−	26.5564i	−0.338822	−	1.92155i	−0.385641	−	0.922649i	$-0.626020\pi$
$191$	−4.68261	−	26.5564i	−0.338822	−	1.92155i	0.0468192	−	0.998903i	$-0.485092\pi$
$192$	7.26601	−	11.1742i	0.524379	−	0.806430i
$193$	16.1202	−	5.86729i	1.16036	−	0.422337i	0.311135	−	0.950366i	$-0.399291\pi$
$193$	16.1202	−	5.86729i	1.16036	−	0.422337i	0.849226	+	0.528029i	$0.177069\pi$
$194$	4.43452	+	3.72100i	0.318380	+	0.267152i
$195$	−10.9904	+	8.27167i	−0.787037	+	0.592347i
$196$	−0.794839	−	0.289298i	−0.0567742	−	0.0206641i
$197$	−1.25612	−	2.17567i	−0.0894951	−	0.155010i	0.817803	−	0.575499i	$-0.195192\pi$
$197$	−1.25612	−	2.17567i	−0.0894951	−	0.155010i	−0.907298	+	0.420489i	$0.861859\pi$
$198$	−2.75237	−	2.85690i	−0.195602	−	0.203031i
$199$	−9.26942	+	16.0551i	−0.657092	+	1.13812i	0.324273	+	0.945964i	$0.394880\pi$
$199$	−9.26942	+	16.0551i	−0.657092	+	1.13812i	−0.981365	+	0.192153i	$0.938453\pi$
$200$	4.55424	−	3.82146i	0.322033	−	0.270218i
$201$	−3.93992	+	17.0198i	−0.277901	+	1.20049i
$202$	0.916408	−	5.19721i	0.0644783	−	0.365674i
$203$	−0.218810	+	1.24093i	−0.0153574	+	0.0870964i
$204$	−2.30676	+	9.96484i	−0.161505	+	0.697678i
$205$	10.9032	−	9.14885i	0.761510	−	0.638983i
$206$	−6.12519	+	10.6091i	−0.426762	+	0.739173i
$207$	−2.45169	+	0.608202i	−0.170404	+	0.0422730i
$208$	−3.26154	−	5.64915i	−0.226147	−	0.391698i
$209$	0.293649	+	0.106880i	0.0203121	+	0.00739301i
$210$	6.26426	−	4.71467i	0.432275	−	0.325343i
$211$	−2.82761	−	2.37264i	−0.194661	−	0.163340i	0.540248	−	0.841506i	$-0.318330\pi$
$211$	−2.82761	−	2.37264i	−0.194661	−	0.163340i	−0.734908	+	0.678166i	$0.762775\pi$
$212$	−8.75237	+	3.18560i	−0.601115	+	0.218788i
$213$	0.0844829	−	0.129924i	0.00578867	−	0.00890226i
$214$	3.56242	+	20.2035i	0.243522	+	1.38108i
$215$	−7.55427			−0.515197
$216$	−5.64462	−	14.7829i	−0.384067	−	1.00585i
$217$	−2.01659			−0.136895
$218$	1.15619	+	6.55706i	0.0783069	+	0.444100i
$219$	−4.17935	−	8.21441i	−0.282414	−	0.555079i
$220$	1.82792	−	0.665307i	0.123238	−	0.0448550i
$221$	23.1638	+	19.4367i	1.55816	+	1.30746i
$222$	4.38299	+	1.86352i	0.294167	+	0.125071i
$223$	19.9601	+	7.26487i	1.33662	+	0.486491i	0.908748	−	0.417346i	$-0.137040\pi$
$223$	19.9601	+	7.26487i	1.33662	+	0.486491i	0.427876	+	0.903837i	$0.359262\pi$
$224$	−5.63017	−	9.75174i	−0.376181	−	0.651565i
$225$	−0.401646	−	5.84289i	−0.0267764	−	0.389526i
$226$	3.64571	−	6.31456i	0.242509	−	0.420038i
$227$	−10.9851	+	9.21761i	−0.729108	+	0.611794i	−0.929888	−	0.367842i	$-0.880097\pi$
$227$	−10.9851	+	9.21761i	−0.729108	+	0.611794i	0.200781	+	0.979636i	$0.435652\pi$
$228$	0.280239	+	0.261637i	0.0185593	+	0.0173273i
$229$	2.93219	−	16.6293i	0.193765	−	1.09889i	−0.720403	−	0.693556i	$-0.756043\pi$
$229$	2.93219	−	16.6293i	0.193765	−	1.09889i	0.914167	−	0.405337i	$-0.132846\pi$
$230$	−0.269122	+	1.52626i	−0.0177454	+	0.100639i
$231$	−5.10985	+	1.55894i	−0.336204	+	0.102571i
$232$	1.19531	−	1.00298i	0.0784759	−	0.0658491i
$233$	−2.79972	+	4.84926i	−0.183416	+	0.317686i	−0.943042	−	0.332675i	$-0.892049\pi$
$233$	−2.79972	+	4.84926i	−0.183416	+	0.317686i	0.759626	+	0.650361i	$0.225382\pi$
$234$	−14.3079	−	1.52089i	−0.935334	−	0.0994238i
$235$	−4.62837	−	8.01658i	−0.301922	−	0.522944i
$236$	−2.50964	−	0.913436i	−0.163364	−	0.0594596i
$237$	−1.00348	−	8.21279i	−0.0651833	−	0.533478i
$238$	−13.2028	−	11.0785i	−0.855813	−	0.718112i
$239$	4.95620	−	1.80391i	0.320590	−	0.116685i	−0.176712	−	0.984263i	$-0.556546\pi$
$239$	4.95620	−	1.80391i	0.320590	−	0.116685i	0.497302	+	0.867577i	$0.334324\pi$
$240$	−4.32989	−	0.229482i	−0.279493	−	0.0148130i
$241$	−1.54590	−	8.76723i	−0.0995801	−	0.564747i	−0.993247	−	0.116017i	$-0.962987\pi$
$241$	−1.54590	−	8.76723i	−0.0995801	−	0.564747i	0.893667	−	0.448730i	$-0.148124\pi$
$242$	−9.93907			−0.638907
$243$	−15.0453	−	4.07900i	−0.965158	−	0.261668i
$244$	−2.56141			−0.163977
$245$	0.288634	+	1.63692i	0.0184401	+	0.104579i
$246$	14.8673	+	0.787963i	0.947908	+	0.0502387i
$247$	1.06507	−	0.387652i	0.0677685	−	0.0246657i
$248$	1.91294	+	1.60515i	0.121472	+	0.101927i
$249$	−1.68910	−	13.8240i	−0.107042	−	0.876062i
$250$	−12.0247	−	4.37665i	−0.760511	−	0.276803i
$251$	3.89010	+	6.73786i	0.245541	+	0.425290i	0.962284	−	0.272048i	$-0.0877010\pi$
$251$	3.89010	+	6.73786i	0.245541	+	0.425290i	−0.716742	+	0.697338i	$0.754368\pi$
$252$	−6.51766	−	0.692812i	−0.410574	−	0.0436431i
$253$	0.528024	−	0.914565i	0.0331966	−	0.0574982i
$254$	9.71069	−	8.14824i	0.609303	−	0.511266i
$255$	19.2249	−	5.86523i	1.20391	−	0.367295i
$256$	−2.86374	+	16.2411i	−0.178984	+	1.01507i
$257$	−3.54877	+	20.1261i	−0.221366	+	1.25543i	0.648145	+	0.761517i	$0.275545\pi$
$257$	−3.54877	+	20.1261i	−0.221366	+	1.25543i	−0.869511	+	0.493913i	$0.835566\pi$
$258$	−5.77597	−	5.39255i	−0.359596	−	0.335726i
$259$	4.91331	−	4.12275i	0.305298	−	0.256175i
$260$	3.52767	−	6.11011i	0.218777	−	0.378933i
$261$	−0.105416	−	1.53353i	−0.00652510	−	0.0949231i
$262$	7.42498	+	12.8604i	0.458717	+	0.794520i
$263$	−10.5996	−	3.85792i	−0.653596	−	0.237890i	−0.00612723	−	0.999981i	$-0.501950\pi$
$263$	−10.5996	−	3.85792i	−0.653596	−	0.237890i	−0.647469	+	0.762092i	$0.724173\pi$
$264$	6.08809	+	2.58848i	0.374696	+	0.159310i
$265$	14.0209	+	11.7650i	0.861299	+	0.722716i
$266$	−0.607063	+	0.220953i	−0.0372214	+	0.0135475i
$267$	5.26530	+	10.3488i	0.322231	+	0.633338i
$268$	−1.55600	−	8.82450i	−0.0950476	−	0.539042i
$269$	−0.307761			−0.0187645			−0.00938226	−	0.999956i	$-0.502987\pi$
$269$	−0.307761			−0.0187645			−0.00938226	+	0.999956i	$0.502987\pi$
$270$	−6.03208	+	7.42209i	−0.367101	+	0.451694i
$271$	−2.22251			−0.135008			−0.0675040	−	0.997719i	$-0.521504\pi$
$271$	−2.22251			−0.135008			−0.0675040	+	0.997719i	$0.521504\pi$
$272$	1.65516	+	9.38689i	0.100359	+	0.569164i
$273$	−10.5629	+	16.2445i	−0.639298	+	0.983162i
$274$	−2.23723	+	0.814286i	−0.135156	+	0.0491928i
$275$	1.87567	+	1.57387i	0.113107	+	0.0949080i
$276$	1.03520	−	0.779119i	0.0623115	−	0.0468975i
$277$	21.9228	+	7.97924i	1.31721	+	0.479426i	0.902564	−	0.430556i	$-0.141683\pi$
$277$	21.9228	+	7.97924i	1.31721	+	0.479426i	0.414648	+	0.909982i	$0.363905\pi$
$278$	4.20417	+	7.28184i	0.252149	+	0.436735i
$279$	2.38764	−	0.592313i	0.142944	−	0.0354608i
$280$	−6.53725	+	11.3228i	−0.390675	+	0.676670i
$281$	5.53502	−	4.64443i	0.330192	−	0.277064i	−0.462586	−	0.886574i	$-0.653078\pi$
$281$	5.53502	−	4.64443i	0.330192	−	0.277064i	0.792778	+	0.609511i	$0.208634\pi$
$282$	2.18373	−	9.43337i	0.130039	−	0.561749i
$283$	1.23643	−	7.01212i	0.0734979	−	0.416827i	−0.925753	−	0.378129i	$-0.876568\pi$
$283$	1.23643	−	7.01212i	0.0734979	−	0.416827i	0.999251	−	0.0386985i	$-0.0123212\pi$
$284$	−0.0138033	+	0.0782824i	−0.000819076	+	0.00464521i
$285$	0.169911	−	0.733987i	0.0100646	−	0.0434776i
$286$	4.60806	−	3.86662i	0.272480	−	0.228638i
$287$	10.0249	−	17.3636i	0.591751	−	1.02494i
$288$	9.53038	+	9.89234i	0.561583	+	0.582912i
$289$	−13.5924	−	23.5428i	−0.799555	−	1.38487i
$290$	−0.886230	−	0.322561i	−0.0520412	−	0.0189414i
$291$	−7.59837	+	5.71875i	−0.445424	+	0.335239i
$292$	3.62132	+	3.03865i	0.211922	+	0.177823i
$293$	−0.519166	+	0.188961i	−0.0303300	+	0.0110392i	−0.357141	−	0.934051i	$-0.616248\pi$
$293$	−0.519166	+	0.188961i	−0.0303300	+	0.0110392i	0.326811	+	0.945090i	$0.394026\pi$
$294$	−0.947815	+	1.45762i	−0.0552777	+	0.0850103i
$295$	0.911339	+	5.16846i	0.0530602	+	0.300919i
$296$	−7.94236			−0.461640
$297$	5.59216	−	3.34665i	0.324490	−	0.194192i
$298$	−0.112748			−0.00653131
$299$	−0.665122	−	3.77210i	−0.0384650	−	0.218146i
$300$	1.36221	+	2.67738i	0.0786470	+	0.154579i
$301$	−9.99975	+	3.63961i	−0.576376	+	0.209784i
$302$	−16.3627	−	13.7299i	−0.941568	−	0.790069i
$303$	7.97852	+	3.39224i	0.458354	+	0.194879i
$304$	0.335731	+	0.122196i	0.0192555	+	0.00700842i
$305$	2.51670	+	4.35906i	0.144106	+	0.249599i
$306$	18.8861	+	9.23898i	1.07965	+	0.528157i
$307$	−3.36438	+	5.82728i	−0.192015	+	0.332580i	−0.945918	−	0.324406i	$-0.894836\pi$
$307$	−3.36438	+	5.82728i	−0.192015	+	0.332580i	0.753903	+	0.656986i	$0.228169\pi$
$308$	2.09911	−	1.76136i	0.119608	−	0.100363i
$309$	−14.7104	−	13.7339i	−0.836844	−	0.781293i
$310$	0.262091	−	1.48639i	0.0148858	−	0.0844213i
$311$	2.67825	−	15.1891i	0.151870	−	0.861297i	−0.809722	−	0.586814i	$-0.800382\pi$
$311$	2.67825	−	15.1891i	0.151870	−	0.861297i	0.961592	−	0.274483i	$-0.0885068\pi$
$312$	22.9502	−	7.00176i	1.29930	−	0.396397i
$313$	−18.0487	+	15.1446i	−1.02017	+	0.856025i	−0.989649	−	0.143509i	$-0.954162\pi$
$313$	−18.0487	+	15.1446i	−1.02017	+	0.856025i	−0.0305223	+	0.999534i	$0.509717\pi$
$314$	10.9385	−	18.9461i	0.617297	−	1.06919i
$315$	5.22486	+	11.7726i	0.294388	+	0.663311i
$316$	2.12191	+	3.67525i	0.119367	+	0.206749i
$317$	−6.81469	−	2.48034i	−0.382751	−	0.139310i	0.143477	−	0.989654i	$-0.454172\pi$
$317$	−6.81469	−	2.48034i	−0.382751	−	0.139310i	−0.526228	+	0.850344i	$0.676394\pi$
$318$	2.32204	+	19.0042i	0.130213	+	1.06570i
$319$	0.492289	+	0.413079i	0.0275629	+	0.0231280i
$320$	12.6243	−	4.59489i	0.705723	−	0.256862i
$321$	−33.6552	−	1.78371i	−1.87845	−	0.0995571i
$322$	0.379105	+	2.15001i	0.0211267	+	0.119815i
$323$	−1.65618			−0.0921525
$324$	7.92038	−	1.09408i	0.440021	−	0.0607821i
$325$	8.88074			0.492615
$326$	−3.68627	−	20.9059i	−0.204164	−	1.15787i
$327$	−10.9228	−	0.578905i	−0.604034	−	0.0320135i
$328$	−23.3306	+	8.49163i	−1.28821	+	0.468872i
$329$	−9.98903	−	8.38179i	−0.550713	−	0.462103i
$330$	−0.484953	−	3.96899i	−0.0266958	−	0.218486i
$331$	−27.2835	−	9.93037i	−1.49964	−	0.545823i	−0.543669	−	0.839300i	$-0.682965\pi$
$331$	−27.2835	−	9.93037i	−1.49964	−	0.545823i	−0.955966	+	0.293477i	$0.905188\pi$
$332$	3.57166	+	6.18629i	0.196020	+	0.339517i
$333$	−4.60641	+	6.32447i	−0.252430	+	0.346579i
$334$	10.4708	−	18.1360i	0.572938	−	0.992357i
$335$	−13.4889	+	11.3185i	−0.736976	+	0.618396i
$336$	−5.84213	+	1.78235i	−0.318714	+	0.0972351i
$337$	−0.201275	+	1.14149i	−0.0109641	+	0.0621807i	−0.989799	−	0.142471i	$-0.954495\pi$
$337$	−0.201275	+	1.14149i	−0.0109641	+	0.0621807i	0.978835	+	0.204652i	$0.0656063\pi$
$338$	1.40857	−	7.98839i	0.0766161	−	0.434511i
$339$	8.75561	+	8.17441i	0.475540	+	0.443973i
$340$	−7.89751	+	6.62680i	−0.428303	+	0.359389i
$341$	−0.514230	+	0.890672i	−0.0278471	+	0.0482326i
$342$	0.653863	−	0.439914i	0.0353569	−	0.0237878i
$343$	9.77810	+	16.9362i	0.527968	+	0.914467i
$344$	12.3828	+	4.50697i	0.667636	+	0.243000i
$345$	−2.34305	−	0.996198i	−0.126146	−	0.0536335i
$346$	15.2851	+	12.8257i	0.821730	+	0.689513i
$347$	−5.53452	+	2.01440i	−0.297108	+	0.108139i	−0.486273	−	0.873807i	$-0.661644\pi$
$347$	−5.53452	+	2.01440i	−0.297108	+	0.108139i	0.189165	+	0.981945i	$0.439422\pi$
$348$	0.357525	+	0.702708i	0.0191654	+	0.0376691i
$349$	−5.31237	−	30.1279i	−0.284364	−	1.61271i	−0.707547	−	0.706666i	$-0.750198\pi$
$349$	−5.31237	−	30.1279i	−0.284364	−	1.61271i	0.423183	−	0.906044i	$-0.360913\pi$
$350$	−5.06182			−0.270566
$351$	7.73516	−	22.3360i	0.412872	−	1.19221i
$352$	−5.74276			−0.306090
$353$	6.41826	+	36.3997i	0.341609	+	1.93736i	0.348294	+	0.937385i	$0.386761\pi$
$353$	6.41826	+	36.3997i	0.341609	+	1.93736i	−0.00668455	+	0.999978i	$0.502128\pi$
$354$	−2.99265	+	4.60233i	−0.159058	+	0.244611i
$355$	0.146785	−	0.0534254i	0.00779054	−	0.00283553i
$356$	−4.56227	−	3.82820i	−0.241800	−	0.202894i
$357$	22.6225	−	17.0264i	1.19731	−	0.901131i
$358$	−10.8126	−	3.93547i	−0.571464	−	0.207996i
$359$	13.1880	+	22.8423i	0.696037	+	1.20557i	0.969830	+	0.243783i	$0.0783886\pi$
$359$	13.1880	+	22.8423i	0.696037	+	1.20557i	−0.273792	+	0.961789i	$0.588278\pi$
$360$	4.41434	−	15.3263i	0.232656	−	0.807769i
$361$	9.46896	−	16.4007i	0.498366	−	0.863196i
$362$	−14.4958	+	12.1634i	−0.761881	+	0.639294i
$363$	3.68238	−	15.9073i	0.193275	−	0.834917i
$364$	1.72583	−	9.78769i	0.0904583	−	0.513015i
$365$	1.61312	−	9.14845i	0.0844345	−	0.478852i
$366$	−1.18741	+	5.12944i	−0.0620671	+	0.268120i
$367$	−8.66636	+	7.27194i	−0.452380	+	0.379592i	−0.840318	−	0.542093i	$-0.817632\pi$
$367$	−8.66636	+	7.27194i	−0.452380	+	0.379592i	0.387938	+	0.921685i	$0.373187\pi$
$368$	0.603693	−	1.04563i	0.0314697	−	0.0545071i
$369$	−6.76941	+	23.5030i	−0.352401	+	1.22352i
$370$	2.40023	+	4.15733i	0.124782	+	0.216129i
$371$	24.2281	+	8.81831i	1.25786	+	0.457824i
$372$	−1.00815	+	0.758765i	−0.0522703	+	0.0393401i
$373$	4.47682	+	3.75650i	0.231801	+	0.194504i	0.751289	−	0.659974i	$-0.229433\pi$
$373$	4.47682	+	3.75650i	0.231801	+	0.194504i	−0.519487	+	0.854478i	$0.673877\pi$
$374$	−8.25978	+	3.00631i	−0.427103	+	0.155453i
$375$	11.4599	−	17.6238i	0.591784	−	0.910092i
$376$	2.80394	+	15.9019i	0.144602	+	0.820080i
$377$	2.33085			0.120045
$378$	−4.40887	+	12.7310i	−0.226768	+	0.654813i
$379$	24.3265			1.24957			0.624783	−	0.780798i	$-0.285187\pi$
$379$	24.3265			1.24957			0.624783	+	0.780798i	$0.285187\pi$
$380$	0.0671029	+	0.380559i	0.00344231	+	0.0195223i
$381$	9.44334	+	18.5607i	0.483797	+	0.950892i
$382$	26.7164	−	9.72397i	1.36693	−	0.497522i
$383$	−2.92326	−	2.45291i	−0.149372	−	0.125338i	0.565039	−	0.825064i	$-0.308861\pi$
$383$	−2.92326	−	2.45291i	−0.149372	−	0.125338i	−0.714411	+	0.699726i	$0.753305\pi$
$384$	−1.66423	−	0.707583i	−0.0849273	−	0.0361087i
$385$	−5.06000	−	1.84169i	−0.257881	−	0.0938612i
$386$	9.04337	+	15.6636i	0.460295	+	0.797255i
$387$	10.7707	−	7.24642i	0.547503	−	0.368356i
$388$	2.43891	−	4.22432i	0.123817	−	0.214457i
$389$	8.30534	−	6.96901i	0.421097	−	0.353343i	−0.407483	−	0.913213i	$-0.633593\pi$
$389$	8.30534	−	6.96901i	0.421097	−	0.353343i	0.828580	+	0.559870i	$0.189149\pi$
$390$	−10.6007	−	9.89699i	−0.536786	−	0.501154i
$391$	−0.971896	+	5.51189i	−0.0491509	+	0.278748i
$392$	0.503486	−	2.85541i	0.0254299	−	0.144220i
$393$	−23.3338	+	7.11881i	−1.17704	+	0.359096i
$394$	2.02904	−	1.70257i	0.102222	−	0.0857741i
$395$	4.16974	−	7.22221i	0.209802	−	0.363389i
$396$	−1.96799	+	2.70200i	−0.0988955	+	0.135781i
$397$	5.25461	+	9.10124i	0.263721	+	0.456778i	0.967228	−	0.253910i	$-0.0817168\pi$
$397$	5.25461	+	9.10124i	0.263721	+	0.456778i	−0.703507	+	0.710689i	$0.748383\pi$
$398$	−18.3672	−	6.68511i	−0.920665	−	0.335094i
$399$	−0.128717	−	1.05346i	−0.00644392	−	0.0527388i
$400$	2.14446	+	1.79942i	0.107223	+	0.0899708i
$401$	−13.4992	+	4.91332i	−0.674119	+	0.245359i	−0.656320	−	0.754482i	$-0.727888\pi$
$401$	−13.4992	+	4.91332i	−0.674119	+	0.245359i	−0.0177987	+	0.999842i	$0.505666\pi$
$402$	−18.3932	−	0.974829i	−0.917367	−	0.0486201i
$403$	0.647746	+	3.67355i	0.0322665	+	0.182993i
$404$	−4.44685			−0.221239
$405$	−9.64407	−	12.4041i	−0.479218	−	0.616364i
$406$	−1.32853			−0.0659338
$407$	−0.568014	−	3.22137i	−0.0281554	−	0.159677i
$408$	−35.0122	−	1.85563i	−1.73336	−	0.0918675i
$409$	−16.6159	+	6.04769i	−0.821603	+	0.299039i	−0.718408	−	0.695622i	$-0.755129\pi$
$409$	−16.6159	+	6.04769i	−0.821603	+	0.299039i	−0.103195	+	0.994661i	$0.532907\pi$
$410$	11.4955	+	9.64586i	0.567721	+	0.476375i
$411$	−0.474366	−	3.88234i	−0.0233988	−	0.191502i
$412$	9.69993	+	3.53049i	0.477881	+	0.173935i
$413$	3.69650	+	6.40252i	0.181893	+	0.315047i
$414$	−1.08036	−	2.43426i	−0.0530968	−	0.119637i
$415$	7.01864	−	12.1566i	0.344532	−	0.596746i
$416$	−15.9559	+	13.3886i	−0.782303	+	0.656431i
$417$	−13.2121	+	4.03081i	−0.646998	+	0.197390i
$418$	−0.0572121	+	0.324466i	−0.00279833	+	0.0158701i
$419$	1.58606	−	8.99500i	0.0774842	−	0.439435i	−0.921243	−	0.388988i	$-0.872825\pi$
$419$	1.58606	−	8.99500i	0.0774842	−	0.439435i	0.998727	−	0.0504461i	$-0.0160643\pi$
$420$	−4.82892	−	4.50838i	−0.235627	−	0.219986i
$421$	18.5344	−	15.5522i	0.903310	−	0.757967i	−0.0675243	−	0.997718i	$-0.521510\pi$
$421$	18.5344	−	15.5522i	0.903310	−	0.757967i	0.970835	+	0.239750i	$0.0770656\pi$
$422$	1.94585	−	3.37031i	0.0947226	−	0.164064i
$423$	14.2889	+	6.99004i	0.694749	+	0.339867i
$424$	−15.9637	−	27.6499i	−0.775265	−	1.34280i
$425$	−12.1942	−	4.43832i	−0.591505	−	0.215290i
$426$	0.150369	+	0.0639324i	0.00728538	+	0.00309754i
$427$	5.43159	+	4.55764i	0.262853	+	0.220560i
$428$	16.2441	−	5.91236i	0.785187	−	0.285785i
$429$	4.48120	+	8.80769i	0.216354	+	0.425239i
$430$	−1.38305	−	7.84366i	−0.0666965	−	0.378255i
$431$	−29.5332			−1.42256			−0.711282	−	0.702907i	$-0.751885\pi$
$431$	−29.5332			−1.42256			−0.711282	+	0.702907i	$0.751885\pi$
$432$	6.39355	−	3.82624i	0.307610	−	0.184090i
$433$	0.669754			0.0321863			0.0160932	−	0.999870i	$-0.494877\pi$
$433$	0.669754			0.0321863			0.0160932	+	0.999870i	$0.494877\pi$
$434$	−0.369201	−	2.09384i	−0.0177222	−	0.100508i
$435$	0.844598	−	1.29889i	0.0404954	−	0.0622769i
$436$	5.27203	−	1.91886i	0.252484	−	0.0918967i
$437$	0.160708	+	0.134850i	0.00768772	+	0.00645076i
$438$	7.76392	−	5.84336i	0.370975	−	0.279206i
$439$	5.96599	+	2.17144i	0.284741	+	0.103637i	0.480442	−	0.877026i	$-0.340476\pi$
$439$	5.96599	+	2.17144i	0.284741	+	0.103637i	−0.195701	+	0.980664i	$0.562698\pi$
$440$	3.33399	+	5.77464i	0.158942	+	0.275295i
$441$	−1.98174	−	2.05700i	−0.0943685	−	0.0979526i
$442$	−15.9404	+	27.6096i	−0.758209	+	1.31326i
$443$	11.7618	−	9.86931i	0.558819	−	0.468905i	−0.319095	−	0.947723i	$-0.603379\pi$
$443$	11.7618	−	9.86931i	0.558819	−	0.468905i	0.877914	+	0.478818i	$0.158934\pi$
$444$	0.905072	−	3.90977i	0.0429528	−	0.185550i
$445$	−2.03227	+	11.5256i	−0.0963387	+	0.546364i
$446$	−3.88884	+	22.0547i	−0.184142	+	1.04432i
$447$	0.0417726	−	0.180451i	0.00197577	−	0.00853503i
$448$	14.4973	−	12.1647i	0.684934	−	0.574728i
$449$	16.0199	−	27.7473i	0.756027	−	1.30948i	−0.188836	−	0.982009i	$-0.560471\pi$
$449$	16.0199	−	27.7473i	0.756027	−	1.30948i	0.944862	−	0.327468i	$-0.106195\pi$
$450$	5.99319	−	1.48676i	0.282521	−	0.0700864i
$451$	−5.11268	−	8.85543i	−0.240747	−	0.416986i
$452$	−5.77340	−	2.10135i	−0.271558	−	0.0988390i
$453$	28.0368	−	21.1013i	1.31729	−	0.991428i
$454$	−11.5819	−	9.71835i	−0.543565	−	0.456105i
$455$	−18.3526	+	6.67980i	−0.860384	+	0.313154i
$456$	−0.716419	+	1.10176i	−0.0335494	+	0.0515949i
$457$	3.32849	+	18.8768i	0.155700	+	0.883021i	0.958143	+	0.286291i	$0.0924225\pi$
$457$	3.32849	+	18.8768i	0.155700	+	0.883021i	−0.802442	+	0.596730i	$0.796466\pi$
$458$	17.8031			0.831886
$459$	−21.7840	+	26.8039i	−1.01679	+	1.25110i
$460$	1.30591			0.0608882
$461$	−0.906494	−	5.14098i	−0.0422196	−	0.239440i	0.956394	−	0.292080i	$-0.0943474\pi$
$461$	−0.906494	−	5.14098i	−0.0422196	−	0.239440i	−0.998614	+	0.0526405i	$0.983236\pi$
$462$	−2.55418	−	5.02019i	−0.118831	−	0.233560i
$463$	−1.59502	+	0.580541i	−0.0741271	+	0.0269800i	−0.378818	−	0.925471i	$-0.623669\pi$
$463$	−1.59502	+	0.580541i	−0.0741271	+	0.0269800i	0.304690	+	0.952451i	$0.401447\pi$
$464$	0.562837	+	0.472276i	0.0261290	+	0.0219249i
$465$	2.28184	+	0.970173i	0.105818	+	0.0449907i
$466$	−5.54760	−	2.01916i	−0.256988	−	0.0935359i
$467$	−9.84136	−	17.0457i	−0.455404	−	0.788783i	0.543307	−	0.839534i	$-0.317172\pi$
$467$	−9.84136	−	17.0457i	−0.455404	−	0.788783i	−0.998711	+	0.0507511i	$0.983838\pi$
$468$	0.831456	+	12.0955i	0.0384341	+	0.559115i
$469$	−12.4023	+	21.4814i	−0.572685	+	0.991920i
$470$	7.47630	−	6.27336i	0.344856	−	0.289369i
$471$	26.2702	+	24.5264i	1.21047	+	1.13012i
$472$	1.58972	−	9.01574i	0.0731727	−	0.414983i
$473$	−0.942416	+	5.34471i	−0.0433324	+	0.245750i
$474$	8.34368	−	2.54554i	0.383238	−	0.116920i
$475$	−0.372611	+	0.312658i	−0.0170966	+	0.0143457i
$476$	−7.26134	+	12.5770i	−0.332823	+	0.576467i
$477$	−31.2761	−	3.32458i	−1.43204	−	0.152222i
$478$	2.78040	+	4.81579i	0.127173	+	0.220269i
$479$	27.4892	+	10.0053i	1.25601	+	0.457152i	0.882430	−	0.470444i	$-0.155906\pi$
$479$	27.4892	+	10.0053i	1.25601	+	0.457152i	0.373585	+	0.927596i	$0.378128\pi$
$480$	1.67920	+	13.7431i	0.0766448	+	0.627282i
$481$	−9.08847	−	7.62613i	−0.414398	−	0.347722i
$482$	8.82005	−	3.21024i	0.401742	−	0.146222i
$483$	−3.58151	−	0.189818i	−0.162964	−	0.00863704i
$484$	1.45429	+	8.24766i	0.0661039	+	0.374894i
$485$	−9.58538			−0.435250
$486$	1.48074	−	16.3685i	0.0671675	−	0.742488i
$487$	−20.5056			−0.929199			−0.464600	−	0.885521i	$-0.653802\pi$
$487$	−20.5056			−0.929199			−0.464600	+	0.885521i	$0.653802\pi$
$488$	−1.52466	−	8.64677i	−0.0690180	−	0.391421i
$489$	34.8252	+	1.84572i	1.57485	+	0.0834664i
$490$	−1.64679	+	0.599381i	−0.0743942	+	0.0270773i
$491$	13.4265	+	11.2661i	0.605927	+	0.508433i	0.893345	−	0.449372i	$-0.148352\pi$
$491$	13.4265	+	11.2661i	0.605927	+	0.508433i	−0.287417	+	0.957805i	$0.592797\pi$
$492$	−1.52152	−	12.4526i	−0.0685955	−	0.561404i
$493$	−3.20050	−	1.16489i	−0.144143	−	0.0524638i
$494$	0.597496	+	1.03489i	0.0268826	+	0.0465620i
$495$	6.53197	+	0.694333i	0.293590	+	0.0312080i
$496$	−0.587922	+	1.01831i	−0.0263985	+	0.0457235i
$497$	0.168562	−	0.141441i	0.00756106	−	0.00634448i
$498$	14.0443	−	4.28473i	0.629342	−	0.192003i
$499$	−3.31772	+	18.8157i	−0.148522	+	0.842307i	0.815950	+	0.578122i	$0.196214\pi$
$499$	−3.31772	+	18.8157i	−0.148522	+	0.842307i	−0.964472	+	0.264185i	$0.914897\pi$
$500$	−1.87238	+	10.6188i	−0.0837353	+	0.474887i
$501$	25.1469	+	23.4777i	1.12348	+	1.04890i
$502$	−6.28376	+	5.27270i	−0.280458	+	0.235332i
$503$	5.48381	−	9.49824i	0.244511	−	0.423506i	−0.717483	−	0.696576i	$-0.754706\pi$
$503$	5.48381	−	9.49824i	0.244511	−	0.423506i	0.961994	+	0.273070i	$0.0880392\pi$
$504$	−1.54080	−	22.4146i	−0.0686327	−	0.998426i
$505$	4.36924	+	7.56774i	0.194429	+	0.336760i
$506$	1.04627	+	0.380811i	0.0465124	+	0.0169291i
$507$	12.2634	+	5.21405i	0.544637	+	0.231564i
$508$	−8.18246	−	6.86590i	−0.363038	−	0.304625i
$509$	18.6993	−	6.80598i	0.828831	−	0.301670i	0.107452	−	0.994210i	$-0.465731\pi$
$509$	18.6993	−	6.80598i	0.828831	−	0.301670i	0.721379	+	0.692540i	$0.243509\pi$
$510$	9.60963	+	18.8875i	0.425521	+	0.836353i
$511$	−2.27236	−	12.8872i	−0.100523	−	0.570096i
$512$	−15.2994			−0.676143
$513$	0.461822	+	1.20948i	0.0203899	+	0.0534000i
$514$	−21.5468			−0.950387
$515$	−3.52238	−	19.9764i	−0.155215	−	0.880266i
$516$	−3.62972	+	5.58207i	−0.159790	+	0.245737i
$517$	−6.24920	+	2.27452i	−0.274839	+	0.100033i
$518$	5.18022	+	4.34672i	0.227606	+	0.190984i
$519$	−26.1903	+	19.7116i	−1.14963	+	0.865243i
$520$	22.7262	+	8.27167i	0.996611	+	0.362737i
$521$	−17.5583	−	30.4119i	−0.769244	−	1.33237i	−0.937973	−	0.346708i	$-0.887300\pi$
$521$	−17.5583	−	30.4119i	−0.769244	−	1.33237i	0.168729	−	0.985662i	$-0.446034\pi$
$522$	1.57298	−	0.390216i	0.0688473	−	0.0170793i
$523$	7.12269	−	12.3369i	0.311453	−	0.539453i	−0.667224	−	0.744857i	$-0.732518\pi$
$523$	7.12269	−	12.3369i	0.311453	−	0.539453i	0.978677	+	0.205404i	$0.0658509\pi$
$524$	9.58545	−	8.04315i	0.418742	−	0.351367i
$525$	1.87538	−	8.10136i	0.0818484	−	0.353572i
$526$	2.06513	−	11.7119i	0.0900437	−	0.510663i
$527$	0.946505	−	5.36789i	0.0412304	−	0.233829i
$528$	−0.702526	+	3.03480i	−0.0305735	+	0.132073i
$529$	−17.0759	+	14.3284i	−0.742431	+	0.622974i
$530$	−9.64867	+	16.7120i	−0.419111	+	0.725922i
$531$	−6.25719	−	6.49483i	−0.271539	−	0.281852i
$532$	0.272177	+	0.471425i	0.0118004	+	0.0204389i
$533$	−34.8507	−	12.6846i	−1.50955	−	0.549433i
$534$	−9.78128	+	7.36168i	−0.423277	+	0.318571i
$535$	−26.0223	−	21.8353i	−1.12504	−	0.944023i
$536$	28.8634	−	10.5054i	1.24671	−	0.453765i
$537$	10.3047	−	15.8473i	0.444679	−	0.683862i
$538$	−0.0563454	−	0.319550i	−0.00242922	−	0.0137768i
$539$	1.19414			0.0514354
$540$	7.04163	+	3.91955i	0.303024	+	0.168671i
$541$	−13.2368			−0.569094			−0.284547	−	0.958662i	$-0.591843\pi$
$541$	−13.2368			−0.569094			−0.284547	+	0.958662i	$0.591843\pi$
$542$	−0.406901	−	2.30765i	−0.0174779	−	0.0991222i
$543$	−14.0967	−	27.7067i	−0.604946	−	1.18901i
$544$	28.6004	−	10.4097i	1.22623	−	0.446312i
$545$	−8.44557	−	7.08667i	−0.361768	−	0.303560i
$546$	−18.8007	−	7.99350i	−0.804594	−	0.342090i
$547$	15.3216	+	5.57661i	0.655105	+	0.238439i	0.648121	−	0.761537i	$-0.275555\pi$
$547$	15.3216	+	5.57661i	0.655105	+	0.238439i	0.00698326	+	0.999976i	$0.497777\pi$
$548$	1.00306	+	1.73736i	0.0428488	+	0.0742163i
$549$	−7.76965	−	3.80087i	−0.331601	−	0.162217i
$550$	−1.29076	+	2.23567i	−0.0550383	+	0.0953291i
$551$	−0.0977958	+	0.0820605i	−0.00416624	+	0.00349589i
$552$	3.24633	+	3.03084i	0.138173	+	0.129001i
$553$	2.03995	−	11.5692i	0.0867476	−	0.491970i
$554$	−4.27124	+	24.2234i	−0.181468	+	1.02915i
$555$	−7.54300	+	2.30126i	−0.320183	+	0.0976831i
$556$	5.42748	−	4.55419i	0.230176	−	0.193141i
$557$	−15.4486	+	26.7577i	−0.654577	+	1.13376i	0.327422	+	0.944878i	$0.393820\pi$
$557$	−15.4486	+	26.7577i	−0.654577	+	1.13376i	−0.982000	+	0.188883i	$0.939513\pi$
$558$	1.05214	+	2.37066i	0.0445404	+	0.100358i
$559$	9.84215	+	17.0471i	0.416279	+	0.721016i
$560$	−5.78513	−	2.10561i	−0.244466	−	0.0889784i
$561$	−1.75134	−	14.3335i	−0.0739417	−	0.605159i
$562$	5.83571	+	4.89674i	0.246165	+	0.206557i
$563$	−25.1612	+	9.15791i	−1.06042	+	0.385960i	−0.812585	−	0.582843i	$-0.801940\pi$
$563$	−25.1612	+	9.15791i	−1.06042	+	0.385960i	−0.247832	+	0.968803i	$0.579718\pi$
$564$	−8.14755	−	0.431816i	−0.343074	−	0.0181827i
$565$	2.09652	+	11.8900i	0.0882013	+	0.500214i
$566$	7.50710			0.315547
$567$	−18.7423	−	11.7731i	−0.787102	−	0.494423i
$568$	−0.272481			−0.0114331
$569$	3.30985	+	18.7711i	0.138756	+	0.786924i	0.972170	+	0.234275i	$0.0752717\pi$
$569$	3.30985	+	18.7711i	0.138756	+	0.786924i	−0.833414	+	0.552649i	$0.813617\pi$
$570$	0.793211	+	0.0420399i	0.0332240	+	0.00176086i
$571$	17.6420	−	6.42116i	0.738294	−	0.268717i	0.0546227	−	0.998507i	$-0.482604\pi$
$571$	17.6420	−	6.42116i	0.738294	−	0.268717i	0.683671	+	0.729790i	$0.260382\pi$
$572$	−3.88286	−	3.25811i	−0.162351	−	0.136228i
$573$	5.66474	+	46.3618i	0.236648	+	1.93679i
$574$	19.8641	+	7.22996i	0.829113	+	0.301773i
$575$	0.821889	+	1.42355i	0.0342751	+	0.0593663i
$576$	−13.5918	+	18.6611i	−0.566324	+	0.777547i
$577$	2.42981	−	4.20856i	0.101154	−	0.175204i	−0.811006	−	0.585038i	$-0.801080\pi$
$577$	2.42981	−	4.20856i	0.101154	−	0.175204i	0.912161	+	0.409833i	$0.134413\pi$
$578$	21.9561	−	18.4234i	0.913254	−	0.766311i
$579$	−28.4198	+	8.67047i	−1.18109	+	0.360332i
$580$	−0.137995	+	0.782610i	−0.00572994	+	0.0324961i
$581$	3.43371	−	19.4736i	0.142454	−	0.807899i
$582$	−7.32894	−	6.84244i	−0.303795	−	0.283628i
$583$	10.0730	−	8.45221i	0.417179	−	0.350055i
$584$	−8.10226	+	14.0335i	−0.335274	+	0.580712i
$585$	19.7675	−	13.2994i	0.817284	−	0.549862i
$586$	−0.291249	−	0.504459i	−0.0120314	−	0.0208390i
$587$	30.8194	+	11.2174i	1.27205	+	0.462990i	0.887796	−	0.460236i	$-0.152235\pi$
$587$	30.8194	+	11.2174i	1.27205	+	0.462990i	0.384257	+	0.923226i	$0.374458\pi$
$588$	1.34825	+	0.573239i	0.0556010	+	0.0236400i
$589$	−0.156510	−	0.131327i	−0.00644887	−	0.00541125i
$590$	−5.19960	+	1.89250i	−0.214064	+	0.0779130i
$591$	1.97318	+	3.87824i	0.0811657	+	0.159529i
$592$	−0.649414	−	3.68301i	−0.0266908	−	0.151371i
$593$	17.3446			0.712258			0.356129	−	0.934437i	$-0.384096\pi$
$593$	17.3446			0.712258			0.356129	+	0.934437i	$0.384096\pi$
$594$	4.49867	+	5.19367i	0.184583	+	0.213099i
$595$	28.5384			1.16996
$596$	0.0164973	+	0.0935607i	0.000675754	+	0.00383239i
$597$	17.5044	−	26.9196i	0.716406	−	1.10174i
$598$	3.79482	−	1.38120i	0.155182	−	0.0564816i
$599$	18.6975	+	15.6891i	0.763961	+	0.641039i	0.939155	−	0.343495i	$-0.111611\pi$
$599$	18.6975	+	15.6891i	0.763961	+	0.641039i	−0.175194	+	0.984534i	$0.556055\pi$
$600$	−8.22743	+	6.19221i	−0.335884	+	0.252796i
$601$	−7.39563	−	2.69179i	−0.301674	−	0.109800i	0.186748	−	0.982408i	$-0.440205\pi$
$601$	−7.39563	−	2.69179i	−0.301674	−	0.109800i	−0.488422	+	0.872607i	$0.662427\pi$
$602$	−5.60981	−	9.71647i	−0.228639	−	0.396014i
$603$	8.37478	−	29.0768i	0.341047	−	1.18410i
$604$	−8.99922	+	15.5871i	−0.366173	+	0.634230i
$605$	12.6071	−	10.5786i	0.512553	−	0.430083i
$606$	−2.06147	+	8.90521i	−0.0837413	+	0.361749i
$607$	−1.77772	+	10.0819i	−0.0721553	+	0.409213i	0.927241	+	0.374466i	$0.122174\pi$
$607$	−1.77772	+	10.0819i	−0.0721553	+	0.409213i	−0.999396	+	0.0347476i	$0.988937\pi$
$608$	0.198103	−	1.12350i	0.00803414	−	0.0455639i
$609$	0.492214	−	2.12629i	0.0199455	−	0.0861615i
$610$	−4.06528	+	3.41117i	−0.164598	+	0.138114i
$611$	−12.0602	+	20.8889i	−0.487905	+	0.845076i
$612$	4.90329	−	17.0240i	0.198204	−	0.688153i
$613$	−1.11753	−	1.93563i	−0.0451368	−	0.0781792i	0.842574	−	0.538580i	$-0.181039\pi$
$613$	−1.11753	−	1.93563i	−0.0451368	−	0.0781792i	−0.887711	+	0.460401i	$0.847706\pi$
$614$	−6.66646	−	2.42639i	−0.269036	−	0.0979213i
$615$	−19.6970	+	14.8246i	−0.794262	+	0.597784i
$616$	7.19547	+	6.03771i	0.289914	+	0.243266i
$617$	−31.9267	+	11.6204i	−1.28532	+	0.467818i	−0.892188	−	0.451664i	$-0.850831\pi$
$617$	−31.9267	+	11.6204i	−1.28532	+	0.467818i	−0.393132	+	0.919482i	$0.628609\pi$
$618$	11.5668	−	17.7883i	0.465285	−	0.715551i
$619$	−5.01079	−	28.4176i	−0.201401	−	1.14220i	−0.903004	−	0.429632i	$-0.858643\pi$
$619$	−5.01079	−	28.4176i	−0.201401	−	1.14220i	0.701604	−	0.712567i	$-0.252468\pi$
$620$	−1.27179			−0.0510763
$621$	4.29625	−	0.827216i	0.172403	−	0.0331950i
$622$	16.2613			0.652020
$623$	2.86280	+	16.2358i	0.114696	+	0.650472i
$624$	5.12338	+	10.0699i	0.205099	+	0.403118i
$625$	10.7385	−	3.90849i	0.429540	−	0.156340i
$626$	−19.0292	−	15.9674i	−0.760558	−	0.638184i
$627$	−0.498105	−	0.211780i	−0.0198924	−	0.00845768i
$628$	−17.3224	−	6.30485i	−0.691240	−	0.251591i
$629$	8.66811	+	15.0136i	0.345620	+	0.598632i
$630$	−11.2670	+	7.58036i	−0.448888	+	0.302009i
$631$	1.57039	−	2.71999i	0.0625162	−	0.108281i	−0.833073	−	0.553163i	$-0.813421\pi$
$631$	1.57039	−	2.71999i	0.0625162	−	0.108281i	0.895590	+	0.444881i	$0.146754\pi$
$632$	−11.1438	+	9.35076i	−0.443277	+	0.371953i
$633$	4.67320	+	4.36299i	0.185743	+	0.173413i
$634$	1.32772	−	7.52985i	0.0527303	−	0.299049i
$635$	−3.64488	+	20.6711i	−0.144643	+	0.820309i
$636$	15.4303	−	4.70757i	0.611852	−	0.186667i
$637$	3.31786	−	2.78402i	0.131458	−	0.110307i
$638$	−0.338774	+	0.586774i	−0.0134122	+	0.0232306i
$639$	−0.158034	+	0.216976i	−0.00625171	+	0.00858342i
$640$	−0.911374	−	1.57855i	−0.0360252	−	0.0623975i
$641$	29.9034	+	10.8839i	1.18111	+	0.429890i	0.856595	−	0.515989i	$-0.172576\pi$
$641$	29.9034	+	10.8839i	1.18111	+	0.429890i	0.324518	+	0.945879i	$0.394798\pi$
$642$	−4.30961	−	35.2710i	−0.170087	−	1.39204i
$643$	−9.84142	−	8.25794i	−0.388108	−	0.325661i	0.427768	−	0.903889i	$-0.359300\pi$
$643$	−9.84142	−	8.25794i	−0.388108	−	0.325661i	−0.815876	+	0.578228i	$0.803745\pi$
$644$	1.72866	−	0.629179i	0.0681186	−	0.0247931i
$645$	13.0660	+	0.692495i	0.514475	+	0.0272669i
$646$	−0.303217	−	1.71963i	−0.0119299	−	0.0676578i
$647$	28.2444			1.11040			0.555200	−	0.831717i	$-0.312642\pi$
$647$	28.2444			1.11040			0.555200	+	0.831717i	$0.312642\pi$
$648$	8.40792	+	26.0863i	0.330294	+	1.02477i
$649$	3.77042			0.148002
$650$	1.62590	+	9.22094i	0.0637730	+	0.361675i
$651$	3.48794	+	0.184859i	0.136703	+	0.00724521i
$652$	−16.8088	+	6.11790i	−0.658283	+	0.239595i
$653$	19.9099	+	16.7064i	0.779134	+	0.653771i	0.943030	−	0.332707i	$-0.107962\pi$
$653$	19.9099	+	16.7064i	0.779134	+	0.653771i	−0.163897	+	0.986477i	$0.552406\pi$
$654$	−1.39869	−	11.4472i	−0.0546930	−	0.447622i
$655$	−23.1062	−	8.40995i	−0.902832	−	0.328604i
$656$	−5.84536	−	10.1245i	−0.228223	−	0.395294i
$657$	6.47569	+	14.5910i	0.252641	+	0.569248i
$658$	6.87407	−	11.9062i	0.267979	−	0.464153i
$659$	−36.4774	+	30.6081i	−1.42096	+	1.19232i	−0.470131	+	0.882597i	$0.655793\pi$
$659$	−36.4774	+	30.6081i	−1.42096	+	1.19232i	−0.950826	+	0.309727i	$0.899762\pi$
$660$	−3.22260	+	0.983167i	−0.125439	+	0.0382697i
$661$	−0.152204	+	0.863192i	−0.00592005	+	0.0335743i	−0.987625	−	0.156836i	$-0.949871\pi$
$661$	−0.152204	+	0.863192i	−0.00592005	+	0.0335743i	0.981705	+	0.190410i	$0.0609818\pi$
$662$	5.31568	−	30.1467i	0.206600	−	1.17168i
$663$	−38.2829	−	35.7416i	−1.48678	−	1.38809i
$664$	−18.7576	+	15.7395i	−0.727936	+	0.610811i
$665$	0.534854	−	0.926394i	0.0207407	−	0.0359240i
$666$	−7.41009	−	3.62497i	−0.287135	−	0.140465i
$667$	0.215714	+	0.373627i	0.00835246	+	0.0144669i
$668$	−16.5817	−	6.03526i	−0.641567	−	0.233511i
$669$	−33.8574	−	14.3952i	−1.30900	−	0.556551i
$670$	−14.2217	−	11.9334i	−0.549430	−	0.461027i
$671$	3.39803	−	1.23678i	0.131180	−	0.0477455i
$672$	8.84413	+	17.3829i	0.341170	+	0.670562i
$673$	6.48393	+	36.7722i	0.249937	+	1.41746i	0.808742	+	0.588164i	$0.200149\pi$
$673$	6.48393	+	36.7722i	0.249937	+	1.41746i	−0.558805	+	0.829299i	$0.688740\pi$
$674$	−1.22206			−0.0470721
$675$	0.159082	+	10.1428i	0.00612306	+	0.390397i
$676$	−6.83505			−0.262886
$677$	−2.38231	−	13.5107i	−0.0915596	−	0.519260i	−0.995747	−	0.0921251i	$-0.970634\pi$
$677$	−2.38231	−	13.5107i	−0.0915596	−	0.519260i	0.904188	−	0.427135i	$-0.140477\pi$
$678$	−6.88456	+	10.5876i	−0.264400	+	0.406614i
$679$	−12.6884	+	4.61819i	−0.486935	+	0.177230i
$680$	−27.0716	−	22.7158i	−1.03815	−	0.871109i
$681$	19.8451	−	14.9360i	0.760465	−	0.572348i
$682$	−1.01894	−	0.370863i	−0.0390171	−	0.0142011i
$683$	−24.9943	−	43.2914i	−0.956381	−	1.65650i	−0.731175	−	0.682190i	$-0.761028\pi$
$683$	−24.9943	−	43.2914i	−0.956381	−	1.65650i	−0.225206	−	0.974311i	$-0.572306\pi$
$684$	−0.460724	−	0.478222i	−0.0176162	−	0.0182853i
$685$	1.97112	−	3.41407i	0.0753125	−	0.130445i
$686$	−15.7947	+	13.2534i	−0.603046	+	0.506016i
$687$	−6.59598	+	28.4936i	−0.251652	+	1.08710i
$688$	−1.07747	+	6.11064i	−0.0410782	+	0.232966i
$689$	8.28172	−	46.9680i	0.315509	−	1.78934i
$690$	0.605391	−	2.61519i	0.0230468	−	0.0995587i
$691$	18.2434	−	15.3080i	0.694011	−	0.582345i	−0.226052	−	0.974115i	$-0.572582\pi$
$691$	18.2434	−	15.3080i	0.694011	−	0.582345i	0.920063	+	0.391771i	$0.128137\pi$
$692$	8.40653	−	14.5605i	0.319568	−	0.553508i
$693$	8.98103	−	2.22797i	0.341161	−	0.0846335i
$694$	−3.10483	−	5.37773i	−0.117858	−	0.204136i
$695$	−13.0832	−	4.76188i	−0.496273	−	0.180629i
$696$	−2.15938	+	1.62521i	−0.0818510	+	0.0616035i
$697$	41.5144	+	34.8347i	1.57247	+	1.31946i
$698$	30.3094	−	11.0317i	1.14723	−	0.417557i
$699$	5.28700	−	8.13075i	0.199973	−	0.307533i
$700$	0.740646	+	4.20041i	0.0279938	+	0.158761i
$701$	34.4493			1.30113			0.650565	−	0.759450i	$-0.274532\pi$
$701$	34.4493			1.30113			0.650565	+	0.759450i	$0.274532\pi$
$702$	24.6078	+	3.94216i	0.928761	+	0.148787i
$703$	0.649815			0.0245082
$704$	−1.67600	−	9.50506i	−0.0631665	−	0.358235i
$705$	7.27047	+	14.2899i	0.273822	+	0.538190i
$706$	−36.6191	+	13.3282i	−1.37818	+	0.501615i
$707$	9.42975	+	7.91250i	0.354642	+	0.297580i
$708$	4.25701	+	1.80996i	0.159988	+	0.0680224i
$709$	−14.5871	−	5.30927i	−0.547830	−	0.199394i	0.0532520	−	0.998581i	$-0.483041\pi$
$709$	−14.5871	−	5.30927i	−0.547830	−	0.199394i	−0.601082	+	0.799187i	$0.705264\pi$
$710$	0.0823456	+	0.142627i	0.00309038	+	0.00535269i
$711$	0.982789	+	14.2970i	0.0368575	+	0.536180i
$712$	10.2075	−	17.6800i	0.382543	−	0.662585i
$713$	−0.528911	+	0.443809i	−0.0198079	+	0.0166208i
$714$	21.8204	+	20.3719i	0.816607	+	0.762400i
$715$	−1.72962	+	9.80918i	−0.0646842	+	0.366843i
$716$	−1.68364	+	9.54839i	−0.0629205	+	0.356840i
$717$	−8.73772	+	2.66575i	−0.326316	+	0.0995543i
$718$	−21.3029	+	17.8752i	−0.795016	+	0.667098i
$719$	−6.02686	+	10.4388i	−0.224764	+	0.389303i	−0.956249	−	0.292555i	$-0.905494\pi$
$719$	−6.02686	+	10.4388i	−0.224764	+	0.389303i	0.731485	+	0.681858i	$0.238828\pi$
$720$	7.46803	+	0.793835i	0.278317	+	0.0295845i
$721$	−14.2872	−	24.7461i	−0.532083	−	0.921594i
$722$	18.7626	+	6.82902i	0.698271	+	0.254150i
$723$	1.87014	+	15.3057i	0.0695512	+	0.569226i
$724$	12.2145	+	10.2492i	0.453947	+	0.380907i
$725$	−0.939963	+	0.342119i	−0.0349094	+	0.0127060i
$726$	17.1908	+	0.911107i	0.638012	+	0.0338144i
$727$	−5.49253	−	31.1497i	−0.203707	−	1.15528i	−0.899462	−	0.437000i	$-0.856041\pi$
$727$	−5.49253	−	31.1497i	−0.203707	−	1.15528i	0.695755	−	0.718279i	$-0.255070\pi$
$728$	34.0685			1.26266
$729$	25.6488	+	8.43433i	0.949956	+	0.312383i
$730$	9.79423			0.362501
$731$	−4.99469	−	28.3263i	−0.184735	−	1.04769i
$732$	4.43027	+	0.234802i	0.163748	+	0.00867855i
$733$	17.8831	−	6.50891i	0.660527	−	0.240412i	0.0100630	−	0.999949i	$-0.496797\pi$
$733$	17.8831	−	6.50891i	0.660527	−	0.240412i	0.650464	+	0.759537i	$0.274575\pi$
$734$	−9.13716	−	7.66699i	−0.337259	−	0.282994i
$735$	−0.349172	−	2.85772i	−0.0128794	−	0.105409i
$736$	−3.62283	−	1.31860i	−0.133539	−	0.0486043i
$737$	6.32516	+	10.9555i	0.232990	+	0.403551i
$738$	−25.6427	−	2.72576i	−0.943920	−	0.100337i
$739$	−8.30036	+	14.3767i	−0.305334	+	0.528854i	−0.977336	−	0.211696i	$-0.932101\pi$
$739$	−8.30036	+	14.3767i	−0.305334	+	0.528854i	0.672002	+	0.740550i	$0.265435\pi$
$740$	3.09864	−	2.60007i	0.113908	−	0.0955804i
$741$	−1.87770	+	0.572858i	−0.0689789	+	0.0210445i
$742$	−4.72040	+	26.7707i	−0.173291	+	0.982783i
$743$	−5.78310	+	32.7976i	−0.212161	+	1.20323i	0.673604	+	0.739093i	$0.264745\pi$
$743$	−5.78310	+	32.7976i	−0.212161	+	1.20323i	−0.885765	+	0.464134i	$0.846366\pi$
$744$	−3.16152	−	2.95166i	−0.115907	−	0.108213i
$745$	0.143014	−	0.120003i	0.00523963	−	0.00439657i
$746$	−3.08078	+	5.33606i	−0.112795	+	0.195367i
$747$	1.65426	+	24.0652i	0.0605263	+	0.880499i
$748$	3.70328	+	6.41426i	0.135405	+	0.234529i
$749$	−44.9665	−	16.3665i	−1.64304	−	0.598017i
$750$	20.3971	+	8.67225i	0.744795	+	0.316666i
$751$	21.2819	+	17.8577i	0.776589	+	0.651636i	0.942387	−	0.334524i	$-0.108576\pi$
$751$	21.2819	+	17.8577i	0.776589	+	0.651636i	−0.165798	+	0.986160i	$0.553020\pi$
$752$	−7.14474	+	2.60047i	−0.260542	+	0.0948295i
$753$	−6.11076	−	12.0106i	−0.222688	−	0.437689i
$754$	0.426735	+	2.42013i	0.0155408	+	0.0881361i
$755$	35.3686			1.28720
$756$	11.2096	+	1.79577i	0.407689	+	0.0653116i
$757$	−3.12036			−0.113411			−0.0567057	−	0.998391i	$-0.518060\pi$
$757$	−3.12036			−0.113411			−0.0567057	+	0.998391i	$0.518060\pi$
$758$	4.45373	+	25.2583i	0.161767	+	0.917424i
$759$	−0.997121	+	1.53345i	−0.0361932	+	0.0556607i
$760$	−1.24475	+	0.453050i	−0.0451517	+	0.0164339i
$761$	−33.6747	−	28.2564i	−1.22071	−	1.02429i	−0.998787	−	0.0492297i	$-0.984323\pi$
$761$	−33.6747	−	28.2564i	−1.22071	−	1.02429i	−0.221919	−	0.975065i	$-0.571232\pi$
$762$	−17.5428	+	13.2032i	−0.635508	+	0.478302i
$763$	−14.5939	−	5.31175i	−0.528335	−	0.192298i
$764$	−11.9783	−	20.7470i	−0.433360	−	0.750602i
$765$	−33.7894	+	8.38230i	−1.22166	+	0.303063i
$766$	2.01168	−	3.48433i	0.0726849	−	0.125894i
$767$	10.4759	−	8.79032i	0.378263	−	0.317400i
$768$	6.44200	−	27.8284i	0.232456	−	1.00417i
$769$	0.644731	−	3.65645i	0.0232496	−	0.131855i	−0.970974	−	0.239186i	$-0.923119\pi$
$769$	0.644731	−	3.65645i	0.0232496	−	0.131855i	0.994223	+	0.107331i	$0.0342305\pi$
$770$	0.985846	−	5.59101i	0.0355274	−	0.201486i
$771$	7.98298	−	34.4852i	0.287500	−	1.24195i
$772$	11.6748	−	9.79629i	0.420184	−	0.352576i
$773$	4.48452	−	7.76741i	0.161297	−	0.279374i	−0.774037	−	0.633140i	$-0.781766\pi$
$773$	4.48452	−	7.76741i	0.161297	−	0.279374i	0.935334	+	0.353766i	$0.115099\pi$
$774$	9.49592	+	9.85656i	0.341324	+	0.354287i
$775$	−0.800417	−	1.38636i	−0.0287518	−	0.0497996i
$776$	15.7121	+	5.71875i	0.564033	+	0.205291i
$777$	−8.87610	+	6.68041i	−0.318428	+	0.239658i
$778$	8.75652	+	7.34760i	0.313937	+	0.263424i
$779$	1.90882	−	0.694754i	0.0683906	−	0.0248921i
$780$	−6.66165	+	10.2448i	−0.238525	+	0.366823i
$781$	−0.0194871	−	0.110517i	−0.000697302	−	0.00395459i
$782$	−5.90098			−0.211018
$783$	0.0417527	+	2.66209i	0.00149212	+	0.0951354i
$784$	1.36527			0.0487597
$785$	6.29037	+	35.6745i	0.224513	+	1.27328i
$786$	−11.6635	−	22.9243i	−0.416023	−	0.817684i
$787$	−41.2069	+	14.9981i	−1.46887	+	0.534624i	−0.947792	−	0.318888i	$-0.896691\pi$
$787$	−41.2069	+	14.9981i	−1.46887	+	0.534624i	−0.521074	+	0.853512i	$0.674468\pi$
$788$	−1.70972	−	1.43462i	−0.0609062	−	0.0511063i
$789$	17.9796	+	7.64441i	0.640090	+	0.272148i
$790$	8.26227	+	3.00722i	0.293958	+	0.106992i
$791$	8.50374	+	14.7289i	0.302358	+	0.523699i
$792$	−10.2928	−	5.03519i	−0.365739	−	0.178918i
$793$	6.55782	−	11.3585i	0.232875	−	0.403351i
$794$	−8.48787	+	7.12217i	−0.301223	+	0.252756i
$795$	−23.1724	−	21.6342i	−0.821842	−	0.767287i
$796$	−2.85997	+	16.2197i	−0.101369	+	0.574891i
$797$	2.08656	−	11.8335i	0.0739097	−	0.419163i	−0.925294	−	0.379252i	$-0.876181\pi$
$797$	2.08656	−	11.8335i	0.0739097	−	0.419163i	0.999203	−	0.0399111i	$-0.0127075\pi$
$798$	1.07025	−	0.326516i	0.0378863	−	0.0115586i
$799$	26.9996	−	22.6554i	0.955178	−	0.801490i
$800$	4.46940	−	7.74124i	0.158017	−	0.273694i
$801$	−8.15832	−	18.3822i	−0.288260	−	0.649504i
$802$	−7.57299	−	13.1168i	−0.267412	−	0.463171i
$803$	−6.27136	−	2.28259i	−0.221311	−	0.0805508i
$804$	1.88235	+	15.4057i	0.0663855	+	0.543317i
$805$	−2.76924	−	2.32366i	−0.0976027	−	0.0818984i
$806$	−3.69568	+	1.34512i	−0.130175	+	0.0473798i
$807$	0.532311	+	0.0282122i	0.0187382	+	0.000993117i
$808$	−2.64695	−	15.0116i	−0.0931195	−	0.528107i
$809$	−8.02937			−0.282298			−0.141149	−	0.989988i	$-0.545080\pi$
$809$	−8.02937			−0.282298			−0.141149	+	0.989988i	$0.545080\pi$
$810$	11.1136	−	12.2845i	0.390492	−	0.431632i
$811$	−12.8345			−0.450681			−0.225341	−	0.974280i	$-0.572349\pi$
$811$	−12.8345			−0.450681			−0.225341	+	0.974280i	$0.572349\pi$
$812$	0.194391	+	1.10244i	0.00682177	+	0.0386882i
$813$	3.84411	+	0.203736i	0.134819	+	0.00714534i
$814$	3.24078	−	1.17955i	0.113589	−	0.0413431i
$815$	26.9270	+	22.5944i	0.943211	+	0.791448i
$816$	−2.00232	−	16.3875i	−0.0700951	−	0.573678i
$817$	−1.01312	−	0.368744i	−0.0354444	−	0.0129007i
$818$	−9.32142	−	16.1452i	−0.325916	−	0.564503i
$819$	19.7590	−	27.1286i	0.690436	−	0.947949i
$820$	6.32233	−	10.9506i	0.220785	−	0.382411i
$821$	−22.7250	+	19.0685i	−0.793108	+	0.665497i	−0.946513	−	0.322667i	$-0.895421\pi$
$821$	−22.7250	+	19.0685i	−0.793108	+	0.665497i	0.153404	+	0.988163i	$0.450976\pi$
$822$	3.94422	−	1.20332i	0.137570	−	0.0419707i
$823$	8.60266	−	48.7881i	0.299870	−	1.70065i	−0.346852	−	0.937920i	$-0.612749\pi$
$823$	8.60266	−	48.7881i	0.299870	−	1.70065i	0.646722	−	0.762726i	$-0.276139\pi$
$824$	−6.14436	+	34.8464i	−0.214049	+	1.21393i
$825$	−3.09992	−	2.89415i	−0.107925	−	0.100761i
$826$	−5.97102	+	5.01028i	−0.207758	+	0.174330i
$827$	−20.4215	+	35.3711i	−0.710126	+	1.22997i	0.254683	+	0.967025i	$0.418029\pi$
$827$	−20.4215	+	35.3711i	−0.710126	+	1.22997i	−0.964809	+	0.262950i	$0.915305\pi$
$828$	−1.86192	+	1.25269i	−0.0647063	+	0.0435339i
$829$	4.72638	+	8.18633i	0.164154	+	0.284323i	0.936355	−	0.351056i	$-0.114177\pi$
$829$	4.72638	+	8.18633i	0.164154	+	0.284323i	−0.772201	+	0.635379i	$0.780844\pi$
$830$	13.9073	+	5.06185i	0.482730	+	0.175699i
$831$	−37.1867	−	15.8107i	−1.28999	−	0.548468i
$832$	−26.8167	−	22.5018i	−0.929700	−	0.780111i
$833$	−5.94714	+	2.16458i	−0.206056	+	0.0749983i
$834$	−6.60411	−	12.9802i	−0.228682	−	0.449468i
$835$	6.02140	+	34.1491i	0.208379	+	1.18178i
$836$	0.277620			0.00960170
$837$	−4.18401	+	0.805605i	−0.144621	+	0.0278458i
$838$	9.62995			0.332661
$839$	−2.13360	−	12.1002i	−0.0736599	−	0.417746i	−0.999232	−	0.0391756i	$-0.987527\pi$
$839$	−2.13360	−	12.1002i	−0.0736599	−	0.417746i	0.925572	−	0.378571i	$-0.123584\pi$
$840$	12.3449	−	18.9850i	0.425941	−	0.655045i
$841$	27.0044	−	9.82879i	0.931186	−	0.338924i
$842$	19.5413	+	16.3971i	0.673436	+	0.565080i
$843$	−9.99925	+	7.52573i	−0.344392	+	0.259200i
$844$	−3.08148	−	1.12157i	−0.106069	−	0.0386059i
$845$	6.71575	+	11.6320i	0.231029	+	0.400154i
$846$	−4.64178	+	16.1160i	−0.159588	+	0.554079i
$847$	11.5916	−	20.0772i	0.398292	−	0.689862i
$848$	11.5165	−	9.66346i	0.395477	−	0.331845i
$849$	−2.78135	+	12.0150i	−0.0954556	+	0.412353i
$850$	2.37581	−	13.4739i	0.0814896	−	0.462151i
$851$	0.381330	−	2.16263i	0.0130718	−	0.0741339i
$852$	0.0310506	−	0.134134i	0.00106378	−	0.00459535i
$853$	−23.6446	+	19.8402i	−0.809576	+	0.679315i	−0.950507	−	0.310704i	$-0.899435\pi$
$853$	−23.6446	+	19.8402i	−0.809576	+	0.679315i	0.140930	+	0.990020i	$0.454991\pi$
$854$	−3.73781	+	6.47408i	−0.127905	+	0.221538i
$855$	−0.361165	+	1.25395i	−0.0123516	+	0.0428840i
$856$	29.6280	+	51.3172i	1.01266	+	1.75399i
$857$	−10.4738	−	3.81217i	−0.357780	−	0.130221i	0.156876	−	0.987618i	$-0.449858\pi$
$857$	−10.4738	−	3.81217i	−0.357780	−	0.130221i	−0.514655	+	0.857397i	$0.672080\pi$
$858$	−8.32466	+	6.26539i	−0.284199	+	0.213897i
$859$	3.17807	+	2.66672i	0.108434	+	0.0909872i	0.695393	−	0.718630i	$-0.255230\pi$
$859$	3.17807	+	2.66672i	0.108434	+	0.0909872i	−0.586958	+	0.809617i	$0.699675\pi$
$860$	−6.30647	+	2.29537i	−0.215049	+	0.0782714i
$861$	−18.9310	+	29.1135i	−0.645167	+	0.992187i
$862$	−5.40698	−	30.6645i	−0.184163	−	1.04444i
$863$	−47.2534			−1.60852			−0.804262	−	0.594275i	$-0.797439\pi$
$863$	−47.2534			−1.60852			−0.804262	+	0.594275i	$0.797439\pi$
$864$	−15.5771	−	17.9837i	−0.529945	−	0.611817i
$865$	−33.0392			−1.12337
$866$	0.122620	+	0.695411i	0.00416678	+	0.0236310i
$867$	21.3516	+	41.9662i	0.725140	+	1.42525i
$868$	−1.68349	+	0.612742i	−0.0571415	+	0.0207978i
$869$	−4.58958	−	3.85112i	−0.155691	−	0.130640i
$870$	1.50327	+	0.639149i	0.0509658	+	0.0216692i
$871$	43.1156	+	15.6928i	1.46092	+	0.531731i
$872$	9.61579	+	16.6550i	0.325632	+	0.564011i
$873$	13.6665	−	9.19475i	0.462543	−	0.311195i
$874$	−0.110593	+	0.191553i	−0.00374087	+	0.00647938i
$875$	22.8650	−	19.1860i	0.772978	−	0.648606i
$876$	−5.98497	−	5.58768i	−0.202213	−	0.188790i
$877$	6.10381	−	34.6164i	0.206111	−	1.16891i	−0.689571	−	0.724218i	$-0.742201\pi$
$877$	6.10381	−	34.6164i	0.206111	−	1.16891i	0.895682	−	0.444695i	$-0.146688\pi$
$878$	−1.16236	+	6.59208i	−0.0392278	+	0.222472i
$879$	0.915284	−	0.279240i	0.0308718	−	0.00941852i
$880$	−2.40519	+	2.01820i	−0.0810791	+	0.0680334i
$881$	9.67981	−	16.7659i	0.326121	−	0.564858i	−0.655618	−	0.755093i	$-0.727592\pi$
$881$	9.67981	−	16.7659i	0.326121	−	0.564858i	0.981739	+	0.190235i	$0.0609250\pi$
$882$	1.77298	−	2.43425i	0.0596994	−	0.0819656i
$883$	6.89302	+	11.9391i	0.231969	+	0.401781i	0.958387	−	0.285471i	$-0.0921500\pi$
$883$	6.89302	+	11.9391i	0.231969	+	0.401781i	−0.726419	+	0.687252i	$0.758817\pi$
$884$	25.2435	+	9.18788i	0.849031	+	0.309022i
$885$	−1.10248	−	9.02303i	−0.0370596	−	0.303306i
$886$	12.4007	+	10.4055i	0.416611	+	0.349578i
$887$	28.0192	−	10.1982i	0.940794	−	0.342421i	0.174315	−	0.984690i	$-0.444229\pi$
$887$	28.0192	−	10.1982i	0.940794	−	0.342421i	0.766479	+	0.642269i	$0.222007\pi$
$888$	13.7373	+	0.728070i	0.460993	+	0.0244324i
$889$	5.13445	+	29.1189i	0.172204	+	0.976617i
$890$	−12.3391			−0.413609
$891$	−9.97912	+	5.27581i	−0.334313	+	0.176746i
$892$	18.8705			0.631832
$893$	−0.229408	−	1.30104i	−0.00767685	−	0.0435376i
$894$	0.195011	+	0.0103355i	0.00652215	+	0.000345671i
$895$	17.9039	−	6.51649i	0.598461	−	0.217822i
$896$	−1.96694	−	1.65046i	−0.0657109	−	0.0551380i
$897$	0.804626	+	6.58528i	0.0268657	+	0.219876i
$898$	31.7432	+	11.5536i	1.05928	+	0.385548i
$899$	−0.210078	−	0.363866i	−0.00700649	−	0.0121356i
$900$	−2.11067	−	4.75574i	−0.0703556	−	0.158525i
$901$	−34.8448	+	60.3530i	−1.16085	+	2.01065i
$902$	8.25862	−	6.92980i	0.274982	−	0.230737i
$903$	17.6294	−	5.37849i	0.586671	−	0.178985i
$904$	3.65712	−	20.7406i	0.121634	−	0.689821i
$905$	5.44094	−	30.8571i	0.180863	−	1.02573i
$906$	27.0427	+	25.2476i	0.898434	+	0.838795i
$907$	−4.77366	+	4.00558i	−0.158507	+	0.133003i	−0.718592	−	0.695432i	$-0.755213\pi$
$907$	−4.77366	+	4.00558i	−0.158507	+	0.133003i	0.560085	+	0.828435i	$0.310769\pi$
$908$	−6.36984	+	11.0329i	−0.211391	+	0.366139i
$909$	−13.4889	−	6.59868i	−0.447397	−	0.218864i
$910$	−10.2957	−	17.8327i	−0.341300	−	0.591148i
$911$	29.7314	+	10.8213i	0.985044	+	0.358527i	0.783799	−	0.621014i	$-0.213279\pi$
$911$	29.7314	+	10.8213i	0.985044	+	0.358527i	0.201245	+	0.979541i	$0.435501\pi$
$912$	−0.569486	−	0.242129i	−0.0188576	−	0.00801770i
$913$	−7.72533	−	6.48232i	−0.255671	−	0.214534i
$914$	−18.9906	+	6.91200i	−0.628152	+	0.228629i
$915$	−3.95336	−	7.77023i	−0.130694	−	0.256876i
$916$	−2.60496	−	14.7734i	−0.0860701	−	0.488128i
$917$	−34.6380			−1.14385
$918$	−31.8189	−	17.7112i	−1.05018	−	0.584557i
$919$	36.0031			1.18763			0.593816	−	0.804601i	$-0.297621\pi$
$919$	36.0031			1.18763			0.593816	+	0.804601i	$0.297621\pi$
$920$	0.777331	+	4.40846i	0.0256278	+	0.145343i
$921$	6.35329	−	9.77058i	0.209348	−	0.321952i
$922$	5.17196	−	1.88244i	0.170329	−	0.0619948i
$923$	−0.311801	−	0.261632i	−0.0102631	−	0.00861173i
$924$	−3.79213	+	2.85407i	−0.124752	+	0.0938921i
$925$	4.78447	+	1.74141i	0.157313	+	0.0572571i
$926$	−0.894800	−	1.54984i	−0.0294049	−	0.0509309i
$927$	24.1844	+	25.1029i	0.794321	+	0.824489i
$928$	1.17304	−	2.03177i	0.0385070	−	0.0666961i
$929$	19.4941	−	16.3575i	0.639580	−	0.536672i	−0.264309	−	0.964438i	$-0.585144\pi$
$929$	19.4941	−	16.3575i	0.639580	−	0.536672i	0.903889	+	0.427767i	$0.140699\pi$
$930$	−0.589575	+	2.54687i	−0.0193329	+	0.0835152i
$931$	−0.0411934	+	0.233619i	−0.00135006	+	0.00765656i
$932$	−0.863820	+	4.89897i	−0.0282954	+	0.160471i
$933$	−6.02475	+	26.0260i	−0.197241	+	0.852052i
$934$	15.8969	−	13.3391i	0.520164	−	0.436469i
$935$	7.27728	−	12.6046i	0.237993	−	0.412215i
$936$	−40.3370	+	10.0066i	−1.31846	+	0.327075i
$937$	−14.1524	−	24.5127i	−0.462338	−	0.800794i	0.536739	−	0.843749i	$-0.319656\pi$
$937$	−14.1524	−	24.5127i	−0.462338	−	0.800794i	−0.999077	+	0.0429549i	$0.986323\pi$
$938$	−24.5750	−	8.94455i	−0.802401	−	0.292050i
$939$	32.6057	−	24.5400i	1.06405	−	0.800833i
$940$	−6.29971	−	5.28608i	−0.205474	−	0.172413i
$941$	−7.79422	+	2.83687i	−0.254084	+	0.0924792i	−0.465922	−	0.884826i	$-0.654277\pi$
$941$	−7.79422	+	2.83687i	−0.254084	+	0.0924792i	0.211838	+	0.977305i	$0.432055\pi$
$942$	−20.6563	+	31.7669i	−0.673019	+	1.03502i
$943$	−1.19204	−	6.76039i	−0.0388181	−	0.220149i
$944$	4.31074			0.140303
$945$	−7.95786	−	20.8411i	−0.258869	−	0.677962i
$946$	−5.72199			−0.186038
$947$	−7.71877	−	43.7753i	−0.250826	−	1.42251i	−0.806563	−	0.591148i	$-0.798675\pi$
$947$	−7.71877	−	43.7753i	−0.250826	−	1.42251i	0.555737	−	0.831358i	$-0.312436\pi$
$948$	−3.33319	−	6.55131i	−0.108257	−	0.212777i
$949$	−22.7462	+	8.27895i	−0.738373	+	0.268746i
$950$	−0.392853	−	0.329643i	−0.0127458	−	0.0106950i
$951$	11.5595	+	4.91476i	0.374842	+	0.159372i
$952$	−46.7796	−	17.0264i	−1.51613	−	0.551828i
$953$	4.83574	+	8.37576i	0.156645	+	0.271317i	0.933657	−	0.358169i	$-0.116599\pi$
$953$	4.83574	+	8.37576i	0.156645	+	0.271317i	−0.777012	+	0.629486i	$0.783265\pi$
$954$	−2.27415	−	33.0829i	−0.0736283	−	1.07110i
$955$	−23.5385	+	40.7699i	−0.761688	+	1.31928i
$956$	3.58942	−	3.01188i	0.116090	−	0.0974113i
$957$	−0.813608	−	0.759599i	−0.0263002	−	0.0245544i
$958$	−5.35576	+	30.3740i	−0.173037	+	0.981341i
$959$	0.964325	−	5.46896i	0.0311397	−	0.176602i
$960$	−22.2566	+	6.79016i	−0.718328	+	0.219151i
$961$	−23.2323	+	19.4942i	−0.749429	+	0.628845i
$962$	6.25433	−	10.8328i	0.201648	−	0.349264i
$963$	58.0473	+	6.17030i	1.87055	+	0.198835i
$964$	−3.95448	−	6.84936i	−0.127365	−	0.220603i
$965$	−28.1425	−	10.2430i	−0.905940	−	0.329735i
$966$	−0.458619	−	3.75346i	−0.0147558	−	0.120766i
$967$	−25.3676	−	21.2860i	−0.815768	−	0.684510i	0.136209	−	0.990680i	$-0.456508\pi$
$967$	−25.3676	−	21.2860i	−0.815768	−	0.684510i	−0.951977	+	0.306170i	$0.900953\pi$
$968$	−26.9767	+	9.81871i	−0.867064	+	0.315585i
$969$	2.86457	+	0.151821i	0.0920234	+	0.00487720i
$970$	−1.75491	−	9.95257i	−0.0563466	−	0.319558i
$971$	−27.4309			−0.880298			−0.440149	−	0.897925i	$-0.645074\pi$
$971$	−27.4309			−0.880298			−0.440149	+	0.897925i	$0.645074\pi$
$972$	−13.7996	+	1.16629i	−0.442622	+	0.0374087i
$973$	−19.6127			−0.628755
$974$	−3.75420	−	21.2912i	−0.120292	−	0.682213i
$975$	−15.3603	−	0.814091i	−0.491924	−	0.0260718i
$976$	3.88499	−	1.41402i	0.124356	−	0.0452617i
$977$	27.8668	+	23.3831i	0.891539	+	0.748090i	0.968518	−	0.248943i	$-0.0800830\pi$
$977$	27.8668	+	23.3831i	0.891539	+	0.748090i	−0.0769792	+	0.997033i	$0.524527\pi$
$978$	4.45943	+	36.4972i	0.142597	+	1.16705i
$979$	7.90089	+	2.87569i	0.252514	+	0.0919075i
$980$	0.738337	+	1.27884i	0.0235853	+	0.0408510i
$981$	18.8393	+	2.00258i	0.601493	+	0.0639373i
$982$	−9.23957	+	16.0034i	−0.294847	+	0.510689i
$983$	32.2790	−	27.0853i	1.02954	−	0.863886i	0.0387434	−	0.999249i	$-0.487665\pi$
$983$	32.2790	−	27.0853i	1.02954	−	0.863886i	0.990796	+	0.135363i	$0.0432201\pi$
$984$	41.1315	−	12.5486i	1.31122	−	0.400035i
$985$	−0.761595	+	4.31922i	−0.0242664	+	0.137622i
$986$	0.623557	−	3.53637i	0.0198581	−	0.112621i
$987$	16.5089	+	15.4130i	0.525484	+	0.490602i
$988$	0.771352	−	0.647241i	0.0245400	−	0.0205915i
$989$	−1.82173	+	3.15533i	−0.0579276	+	0.100334i
$990$	0.474952	+	6.90931i	0.0150950	+	0.219592i
$991$	−12.7705	−	22.1191i	−0.405667	−	0.702635i	0.588732	−	0.808328i	$-0.299627\pi$
$991$	−12.7705	−	22.1191i	−0.405667	−	0.702635i	−0.994399	+	0.105693i	$0.966294\pi$
$992$	3.52818	+	1.28415i	0.112020	+	0.0407719i
$993$	46.2798	+	19.6769i	1.46865	+	0.624426i
$994$	0.177720	+	0.149124i	0.00563692	+	0.00472994i
$995$	30.4130	−	11.0694i	0.964158	−	0.350925i
$996$	−5.61053	−	11.0274i	−0.177776	−	0.349416i
$997$	4.08644	+	23.1754i	0.129419	+	0.733971i	0.978585	+	0.205845i	$0.0659942\pi$
$997$	4.08644	+	23.1754i	0.129419	+	0.733971i	−0.849166	+	0.528126i	$0.822895\pi$
$998$	−20.1439			−0.637644
$999$	8.54711	−	10.5167i	0.270419	−	0.332733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.2.e.a.13.2	✓	12
3.2	odd	2		81.2.e.a.10.1		12
4.3	odd	2		432.2.u.c.337.2		12
5.2	odd	4		675.2.u.b.499.2		24
5.3	odd	4		675.2.u.b.499.3		24
5.4	even	2		675.2.l.c.526.1		12
9.2	odd	6		243.2.e.b.109.1		12
9.4	even	3		243.2.e.d.190.1		12
9.5	odd	6		243.2.e.a.190.2		12
9.7	even	3		243.2.e.c.109.2		12
27.2	odd	18		81.2.e.a.73.1		12
27.4	even	9		729.2.c.e.487.2		12
27.5	odd	18		729.2.a.d.1.2		6
27.7	even	9		243.2.e.c.136.2		12
27.11	odd	18		243.2.e.a.55.2		12
27.13	even	9		729.2.c.e.244.2		12
27.14	odd	18		729.2.c.b.244.5		12
27.16	even	9		243.2.e.d.55.1		12
27.20	odd	18		243.2.e.b.136.1		12
27.22	even	9		729.2.a.a.1.5		6
27.23	odd	18		729.2.c.b.487.5		12
27.25	even	9	inner	27.2.e.a.25.2	yes	12
108.79	odd	18		432.2.u.c.241.2		12
135.52	odd	36		675.2.u.b.349.3		24
135.79	even	18		675.2.l.c.376.1		12
135.133	odd	36		675.2.u.b.349.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.2	✓	12	1.1	even	1	trivial
27.2.e.a.25.2	yes	12	27.25	even	9	inner
81.2.e.a.10.1		12	3.2	odd	2
81.2.e.a.73.1		12	27.2	odd	18
243.2.e.a.55.2		12	27.11	odd	18
243.2.e.a.190.2		12	9.5	odd	6
243.2.e.b.109.1		12	9.2	odd	6
243.2.e.b.136.1		12	27.20	odd	18
243.2.e.c.109.2		12	9.7	even	3
243.2.e.c.136.2		12	27.7	even	9
243.2.e.d.55.1		12	27.16	even	9
243.2.e.d.190.1		12	9.4	even	3
432.2.u.c.241.2		12	108.79	odd	18
432.2.u.c.337.2		12	4.3	odd	2
675.2.l.c.376.1		12	135.79	even	18
675.2.l.c.526.1		12	5.4	even	2
675.2.u.b.349.2		24	135.133	odd	36
675.2.u.b.349.3		24	135.52	odd	36
675.2.u.b.499.2		24	5.2	odd	4
675.2.u.b.499.3		24	5.3	odd	4
729.2.a.a.1.5		6	27.22	even	9
729.2.a.d.1.2		6	27.5	odd	18
729.2.c.b.244.5		12	27.14	odd	18
729.2.c.b.487.5		12	27.23	odd	18
729.2.c.e.244.2		12	27.13	even	9
729.2.c.e.487.2		12	27.4	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.183082 + 1.03831i) q^{2} +(-1.72962 - 0.0916693i) q^{3} +(0.834822 - 0.303850i) q^{4} +(-1.33735 - 1.12217i) q^{5} +(-0.221481 - 1.81266i) q^{6} +(-2.31094 - 0.841112i) q^{7} +(1.52266 + 2.63732i) q^{8} +(2.98319 + 0.317107i) q^{9} +O(q^{10})\)	\(q+(0.183082 + 1.03831i) q^{2} +(-1.72962 - 0.0916693i) q^{3} +(0.834822 - 0.303850i) q^{4} +(-1.33735 - 1.12217i) q^{5} +(-0.221481 - 1.81266i) q^{6} +(-2.31094 - 0.841112i) q^{7} +(1.52266 + 2.63732i) q^{8} +(2.98319 + 0.317107i) q^{9} +(0.920313 - 1.59403i) q^{10} +(-0.960783 + 0.806193i) q^{11} +(-1.47178 + 0.449019i) q^{12} +(-0.789931 + 4.47992i) q^{13} +(0.450243 - 2.55345i) q^{14} +(2.21024 + 2.06353i) q^{15} +(-1.09847 + 0.921724i) q^{16} +(3.32358 - 5.75662i) q^{17} +(0.216914 + 3.15553i) q^{18} +(-0.124578 - 0.215776i) q^{19} +(-1.45742 - 0.530458i) q^{20} +(3.91994 + 1.66665i) q^{21} +(-1.01298 - 0.849989i) q^{22} +(-0.791222 + 0.287981i) q^{23} +(-2.39186 - 4.70115i) q^{24} +(-0.339001 - 1.92257i) q^{25} -4.79615 q^{26} +(-5.13073 - 0.821942i) q^{27} -2.18479 q^{28} +(-0.0889744 - 0.504599i) q^{29} +(-1.73792 + 2.67271i) q^{30} +(0.770551 - 0.280458i) q^{31} +(3.50754 + 2.94318i) q^{32} +(1.73570 - 1.30634i) q^{33} +(6.58563 + 2.39697i) q^{34} +(2.14666 + 3.71812i) q^{35} +(2.58679 - 0.641717i) q^{36} +(-1.30403 + 2.25865i) q^{37} +(0.201233 - 0.168855i) q^{38} +(1.77695 - 7.67616i) q^{39} +(0.923194 - 5.23570i) q^{40} +(-1.41572 + 8.02895i) q^{41} +(-1.01282 + 4.37524i) q^{42} +(3.31478 - 2.78143i) q^{43} +(-0.557121 + 0.964962i) q^{44} +(-3.63373 - 3.77173i) q^{45} +(-0.443871 - 0.768808i) q^{46} +(4.98256 + 1.81351i) q^{47} +(1.98443 - 1.49354i) q^{48} +(-0.729356 - 0.612002i) q^{49} +(1.93415 - 0.703974i) q^{50} +(-6.27625 + 9.65211i) q^{51} +(0.701774 + 3.97996i) q^{52} -10.4841 q^{53} +(-0.0859140 - 5.47776i) q^{54} +2.18959 q^{55} +(-1.30048 - 7.37539i) q^{56} +(0.195693 + 0.384630i) q^{57} +(0.507639 - 0.184765i) q^{58} +(-2.30289 - 1.93235i) q^{59} +(2.47216 + 1.05109i) q^{60} +(-2.70930 - 0.986103i) q^{61} +(0.432275 + 0.748722i) q^{62} +(-6.62725 - 3.24201i) q^{63} +(-3.84771 + 6.66442i) q^{64} +(6.08365 - 5.10479i) q^{65} +(1.67415 + 1.56302i) q^{66} +(1.75146 - 9.93303i) q^{67} +(1.02545 - 5.81562i) q^{68} +(1.39492 - 0.425568i) q^{69} +(-3.46754 + 2.90961i) q^{70} +(-0.0447378 + 0.0774882i) q^{71} +(3.70607 + 8.35047i) q^{72} +(2.66057 + 4.60824i) q^{73} +(-2.58391 - 0.940468i) q^{74} +(0.410103 + 3.35640i) q^{75} +(-0.169564 - 0.142281i) q^{76} +(2.89841 - 1.05493i) q^{77} +(8.29554 + 0.439660i) q^{78} +(0.829503 + 4.70435i) q^{79} +2.50337 q^{80} +(8.79889 + 1.89198i) q^{81} -8.59571 q^{82} +(1.39625 + 7.91851i) q^{83} +(3.77887 + 0.200278i) q^{84} +(-10.9047 + 3.96899i) q^{85} +(3.49486 + 2.93254i) q^{86} +(0.107636 + 0.880922i) q^{87} +(-3.58913 - 1.30634i) q^{88} +(-3.35189 - 5.80564i) q^{89} +(3.25095 - 4.46346i) q^{90} +(5.59359 - 9.68839i) q^{91} +(-0.573026 + 0.480826i) q^{92} +(-1.35847 + 0.414450i) q^{93} +(-0.970760 + 5.50545i) q^{94} +(-0.0755324 + 0.428365i) q^{95} +(-5.79693 - 5.41213i) q^{96} +(4.20603 - 3.52928i) q^{97} +(0.501915 - 0.869342i) q^{98} +(-3.12185 + 2.10036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23} - 18 q^{24} + 3 q^{25} - 30 q^{26} - 9 q^{27} - 12 q^{28} - 6 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{34} + 12 q^{35} + 18 q^{36} - 3 q^{37} + 42 q^{38} + 33 q^{39} + 21 q^{40} + 15 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 9 q^{45} - 3 q^{46} - 15 q^{47} - 15 q^{48} + 12 q^{49} - 33 q^{50} - 18 q^{51} + 9 q^{52} - 18 q^{53} - 54 q^{54} - 12 q^{55} - 33 q^{56} - 3 q^{57} + 21 q^{58} - 12 q^{59} + 12 q^{61} - 12 q^{62} + 9 q^{63} + 12 q^{64} + 3 q^{65} - 9 q^{66} - 15 q^{67} + 9 q^{68} + 9 q^{69} - 15 q^{70} + 27 q^{71} + 18 q^{72} + 6 q^{73} + 33 q^{74} + 39 q^{75} - 48 q^{76} + 15 q^{77} + 18 q^{78} - 42 q^{79} + 42 q^{80} + 36 q^{81} - 12 q^{82} + 39 q^{83} + 6 q^{84} - 27 q^{85} + 51 q^{86} + 9 q^{87} - 30 q^{88} + 9 q^{89} + 18 q^{90} + 6 q^{91} - 39 q^{92} - 39 q^{93} - 15 q^{94} - 33 q^{95} + 3 q^{97} - 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Introduction

L-functions

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