LMFDB - Embedded newform 847.2.f.x.372.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.4
Root			$0.751051 - 2.31150i$ of defining polynomial
Character	$\chi$	$=$	847.372
Dual form			847.2.f.x.148.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.751051 - 2.31150i) q^{2} +(-1.16030 + 0.843005i) q^{3} +(-3.16091 - 2.29654i) q^{4} +(0.388938 + 1.19703i) q^{5} +(1.07716 + 3.31516i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-3.74989 + 2.72445i) q^{8} +(-0.291419 + 0.896896i) q^{9} +O(q^{10})$	\(q+(0.751051 - 2.31150i) q^{2} +(-1.16030 + 0.843005i) q^{3} +(-3.16091 - 2.29654i) q^{4} +(0.388938 + 1.19703i) q^{5} +(1.07716 + 3.31516i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-3.74989 + 2.72445i) q^{8} +(-0.291419 + 0.896896i) q^{9} +3.05904 q^{10} +5.60359 q^{12} +(0.982152 - 3.02275i) q^{13} +(1.96628 - 1.42858i) q^{14} +(-1.46039 - 1.06103i) q^{15} +(1.06649 + 3.28231i) q^{16} +(-1.83067 - 5.63423i) q^{17} +(1.85430 + 1.34723i) q^{18} +(2.31558 - 1.68237i) q^{19} +(1.51962 - 4.67691i) q^{20} -1.43421 q^{21} +6.76343 q^{23} +(2.05426 - 6.32235i) q^{24} +(2.76348 - 2.00778i) q^{25} +(-6.24944 - 4.54048i) q^{26} +(-1.74754 - 5.37837i) q^{27} +(-1.20736 - 3.71587i) q^{28} +(3.63693 + 2.64238i) q^{29} +(-3.54940 + 2.57879i) q^{30} +(3.00597 - 9.25141i) q^{31} -0.882184 q^{32} -14.3984 q^{34} +(-0.388938 + 1.19703i) q^{35} +(2.98090 - 2.16575i) q^{36} +(4.41315 + 3.20634i) q^{37} +(-2.14967 - 6.61601i) q^{38} +(1.40861 + 4.33525i) q^{39} +(-4.71972 - 3.42908i) q^{40} +(-0.254423 + 0.184849i) q^{41} +(-1.07716 + 3.31516i) q^{42} +0.132562 q^{43} -1.18696 q^{45} +(5.07968 - 15.6337i) q^{46} +(-7.58458 + 5.51052i) q^{47} +(-4.00445 - 2.90940i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-2.56548 - 7.89572i) q^{50} +(6.87381 + 4.99412i) q^{51} +(-10.0463 + 7.29910i) q^{52} +(1.34482 - 4.13893i) q^{53} -13.7446 q^{54} -4.63512 q^{56} +(-1.26852 + 3.90410i) q^{57} +(8.83939 - 6.42219i) q^{58} +(5.62012 + 4.08326i) q^{59} +(2.17945 + 6.70766i) q^{60} +(0.757757 + 2.33214i) q^{61} +(-19.1270 - 13.8966i) q^{62} +(-0.762946 + 0.554312i) q^{63} +(-2.79554 + 8.60379i) q^{64} +4.00032 q^{65} -9.41987 q^{67} +(-7.15262 + 22.0135i) q^{68} +(-7.84759 + 5.70161i) q^{69} +(2.47482 + 1.79806i) q^{70} +(-0.0360345 - 0.110903i) q^{71} +(-1.35076 - 4.15722i) q^{72} +(0.497571 + 0.361506i) q^{73} +(10.7260 - 7.79286i) q^{74} +(-1.51388 + 4.65925i) q^{75} -11.1830 q^{76} +11.0789 q^{78} +(-2.63569 + 8.11183i) q^{79} +(-3.51423 + 2.55324i) q^{80} +(4.27282 + 3.10438i) q^{81} +(0.236194 + 0.726930i) q^{82} +(-0.293731 - 0.904010i) q^{83} +(4.53340 + 3.29371i) q^{84} +(6.03232 - 4.38274i) q^{85} +(0.0995608 - 0.306417i) q^{86} -6.44746 q^{87} +10.0552 q^{89} +(-0.891464 + 2.74364i) q^{90} +(2.57131 - 1.86816i) q^{91} +(-21.3786 - 15.5325i) q^{92} +(4.31118 + 13.2684i) q^{93} +(7.04114 + 21.6704i) q^{94} +(2.91446 + 2.11748i) q^{95} +(1.02360 - 0.743685i) q^{96} +(5.43159 - 16.7167i) q^{97} +2.43045 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.751051	−	2.31150i	0.531073	−	1.63448i	−0.220910	−	0.975294i	$-0.570903\pi$
$2$	0.751051	−	2.31150i	0.531073	−	1.63448i	0.751984	−	0.659182i	$-0.229097\pi$
$3$	−1.16030	+	0.843005i	−0.669898	+	0.486709i	−0.869991	−	0.493068i	$-0.835876\pi$
$3$	−1.16030	+	0.843005i	−0.669898	+	0.486709i	0.200093	+	0.979777i	$0.435876\pi$
$4$	−3.16091	−	2.29654i	−1.58046	−	1.14827i
$5$	0.388938	+	1.19703i	0.173939	+	0.535328i	0.999583	−	0.0288624i	$-0.00918846\pi$
$5$	0.388938	+	1.19703i	0.173939	+	0.535328i	−0.825645	+	0.564190i	$0.809188\pi$
$6$	1.07716	+	3.31516i	0.439750	+	1.35341i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−3.74989	+	2.72445i	−1.32579	+	0.963239i
$9$	−0.291419	+	0.896896i	−0.0971398	+	0.298965i
$10$	3.05904			0.967354
$11$		0			0
$11$		0			0
$12$	5.60359			1.61762
$13$	0.982152	−	3.02275i	0.272400	−	0.838361i	−0.717496	−	0.696563i	$-0.754712\pi$
$13$	0.982152	−	3.02275i	0.272400	−	0.838361i	0.989896	−	0.141798i	$-0.0452882\pi$
$14$	1.96628	−	1.42858i	0.525510	−	0.381805i
$15$	−1.46039	−	1.06103i	−0.377070	−	0.273957i
$16$	1.06649	+	3.28231i	0.266622	+	0.820578i
$17$	−1.83067	−	5.63423i	−0.444003	−	1.36650i	−0.883573	−	0.468293i	$-0.844869\pi$
$17$	−1.83067	−	5.63423i	−0.444003	−	1.36650i	0.439570	−	0.898208i	$-0.355131\pi$
$18$	1.85430	+	1.34723i	0.437063	+	0.317545i
$19$	2.31558	−	1.68237i	0.531231	−	0.385962i	−0.289587	−	0.957152i	$-0.593518\pi$
$19$	2.31558	−	1.68237i	0.531231	−	0.385962i	0.820818	+	0.571190i	$0.193518\pi$
$20$	1.51962	−	4.67691i	0.339798	−	1.04579i
$21$	−1.43421			−0.312969
$22$		0			0
$23$	6.76343			1.41027			0.705136	−	0.709072i	$-0.250886\pi$
$23$	6.76343			1.41027			0.705136	+	0.709072i	$0.250886\pi$
$24$	2.05426	−	6.32235i	0.419323	−	1.29054i
$25$	2.76348	−	2.00778i	0.552696	−	0.401557i
$26$	−6.24944	−	4.54048i	−1.22562	−	0.890462i
$27$	−1.74754	−	5.37837i	−0.336314	−	1.03507i
$28$	−1.20736	−	3.71587i	−0.228170	−	0.702234i
$29$	3.63693	+	2.64238i	0.675361	+	0.490678i	0.871815	−	0.489834i	$-0.162943\pi$
$29$	3.63693	+	2.64238i	0.675361	+	0.490678i	−0.196454	+	0.980513i	$0.562943\pi$
$30$	−3.54940	+	2.57879i	−0.648029	+	0.470820i
$31$	3.00597	−	9.25141i	0.539888	−	1.66160i	−0.192957	−	0.981207i	$-0.561808\pi$
$31$	3.00597	−	9.25141i	0.539888	−	1.66160i	0.732845	−	0.680396i	$-0.238192\pi$
$32$	−0.882184			−0.155950
$33$		0			0
$34$	−14.3984			−2.46931
$35$	−0.388938	+	1.19703i	−0.0657426	+	0.202335i
$36$	2.98090	−	2.16575i	0.496817	−	0.360959i
$37$	4.41315	+	3.20634i	0.725517	+	0.527119i	0.888142	−	0.459569i	$-0.151996\pi$
$37$	4.41315	+	3.20634i	0.725517	+	0.527119i	−0.162625	+	0.986688i	$0.551996\pi$
$38$	−2.14967	−	6.61601i	−0.348723	−	1.07326i
$39$	1.40861	+	4.33525i	0.225558	+	0.694195i
$40$	−4.71972	−	3.42908i	−0.746254	−	0.542185i
$41$	−0.254423	+	0.184849i	−0.0397342	+	0.0288686i	−0.607475	−	0.794339i	$-0.707818\pi$
$41$	−0.254423	+	0.184849i	−0.0397342	+	0.0288686i	0.567741	+	0.823207i	$0.307818\pi$
$42$	−1.07716	+	3.31516i	−0.166210	+	0.511541i
$43$	0.132562			0.0202155			0.0101078	−	0.999949i	$-0.496783\pi$
$43$	0.132562			0.0202155			0.0101078	+	0.999949i	$0.496783\pi$
$44$		0			0
$45$	−1.18696			−0.176941
$46$	5.07968	−	15.6337i	0.748958	−	2.30506i
$47$	−7.58458	+	5.51052i	−1.10632	+	0.803791i	−0.982081	−	0.188460i	$-0.939650\pi$
$47$	−7.58458	+	5.51052i	−1.10632	+	0.803791i	−0.124243	+	0.992252i	$0.539650\pi$
$48$	−4.00445	−	2.90940i	−0.577993	−	0.419936i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−2.56548	−	7.89572i	−0.362813	−	1.11662i
$51$	6.87381	+	4.99412i	0.962526	+	0.699316i
$52$	−10.0463	+	7.29910i	−1.39318	+	1.01220i
$53$	1.34482	−	4.13893i	0.184725	−	0.568525i	−0.815219	−	0.579153i	$-0.803383\pi$
$53$	1.34482	−	4.13893i	0.184725	−	0.568525i	0.999944	+	0.0106284i	$0.00338319\pi$
$54$	−13.7446			−1.87040
$55$		0			0
$56$	−4.63512			−0.619393
$57$	−1.26852	+	3.90410i	−0.168019	+	0.517110i
$58$	8.83939	−	6.42219i	1.16067	−	0.843275i
$59$	5.62012	+	4.08326i	0.731678	+	0.531595i	0.890094	−	0.455778i	$-0.150639\pi$
$59$	5.62012	+	4.08326i	0.731678	+	0.531595i	−0.158416	+	0.987372i	$0.550639\pi$
$60$	2.17945	+	6.70766i	0.281366	+	0.865955i
$61$	0.757757	+	2.33214i	0.0970209	+	0.298600i	0.987775	−	0.155886i	$-0.0498232\pi$
$61$	0.757757	+	2.33214i	0.0970209	+	0.298600i	−0.890754	+	0.454485i	$0.849823\pi$
$62$	−19.1270	−	13.8966i	−2.42913	−	1.76487i
$63$	−0.762946	+	0.554312i	−0.0961221	+	0.0698368i
$64$	−2.79554	+	8.60379i	−0.349443	+	1.07547i
$65$	4.00032			0.496179
$66$		0			0
$67$	−9.41987			−1.15082			−0.575410	−	0.817865i	$-0.695158\pi$
$67$	−9.41987			−1.15082			−0.575410	+	0.817865i	$0.695158\pi$
$68$	−7.15262	+	22.0135i	−0.867383	+	2.66953i
$69$	−7.84759	+	5.70161i	−0.944739	+	0.686393i
$70$	2.47482	+	1.79806i	0.295797	+	0.214909i
$71$	−0.0360345	−	0.110903i	−0.00427651	−	0.0131617i	0.948895	−	0.315590i	$-0.102203\pi$
$71$	−0.0360345	−	0.110903i	−0.00427651	−	0.0131617i	−0.953172	+	0.302429i	$0.902203\pi$
$72$	−1.35076	−	4.15722i	−0.159189	−	0.489933i
$73$	0.497571	+	0.361506i	0.0582363	+	0.0423111i	0.616523	−	0.787337i	$-0.288541\pi$
$73$	0.497571	+	0.361506i	0.0582363	+	0.0423111i	−0.558286	+	0.829648i	$0.688541\pi$
$74$	10.7260	−	7.79286i	1.24687	−	0.905902i
$75$	−1.51388	+	4.65925i	−0.174808	+	0.538004i
$76$	−11.1830			−1.28277
$77$		0			0
$78$	11.0789			1.25443
$79$	−2.63569	+	8.11183i	−0.296539	+	0.912652i	0.686162	+	0.727449i	$0.259294\pi$
$79$	−2.63569	+	8.11183i	−0.296539	+	0.912652i	−0.982700	+	0.185203i	$0.940706\pi$
$80$	−3.51423	+	2.55324i	−0.392903	+	0.285460i
$81$	4.27282	+	3.10438i	0.474758	+	0.344932i
$82$	0.236194	+	0.726930i	0.0260832	+	0.0802760i
$83$	−0.293731	−	0.904010i	−0.0322411	−	0.0992280i	0.933641	−	0.358210i	$-0.116613\pi$
$83$	−0.293731	−	0.904010i	−0.0322411	−	0.0992280i	−0.965882	+	0.258982i	$0.916613\pi$
$84$	4.53340	+	3.29371i	0.494634	+	0.359373i
$85$	6.03232	−	4.38274i	0.654297	−	0.475375i
$86$	0.0995608	−	0.306417i	0.0107359	−	0.0330418i
$87$	−6.44746			−0.691241
$88$		0			0
$89$	10.0552			1.06585			0.532923	−	0.846164i	$-0.321094\pi$
$89$	10.0552			1.06585			0.532923	+	0.846164i	$0.321094\pi$
$90$	−0.891464	+	2.74364i	−0.0939686	+	0.289206i
$91$	2.57131	−	1.86816i	0.269546	−	0.195837i
$92$	−21.3786	−	15.5325i	−2.22887	−	1.61937i
$93$	4.31118	+	13.2684i	0.447048	+	1.37587i
$94$	7.04114	+	21.6704i	0.726238	+	2.23513i
$95$	2.91446	+	2.11748i	0.299018	+	0.217249i
$96$	1.02360	−	0.743685i	0.104470	−	0.0759021i
$97$	5.43159	−	16.7167i	0.551495	−	1.69733i	−0.153530	−	0.988144i	$-0.549064\pi$
$97$	5.43159	−	16.7167i	0.551495	−	1.69733i	0.705025	−	0.709182i	$-0.250936\pi$
$98$	2.43045			0.245513
$99$		0			0
$100$	−13.3461			−1.33461
$101$	3.85534	−	11.8655i	0.383621	−	1.18066i	−0.553855	−	0.832613i	$-0.686844\pi$
$101$	3.85534	−	11.8655i	0.383621	−	1.18066i	0.937476	−	0.348050i	$-0.113156\pi$
$102$	16.7065	−	12.1380i	1.65419	−	1.20184i
$103$	−6.64852	−	4.83043i	−0.655098	−	0.475957i	0.209906	−	0.977722i	$-0.432684\pi$
$103$	−6.64852	−	4.83043i	−0.655098	−	0.475957i	−0.865004	+	0.501765i	$0.832684\pi$
$104$	4.55239	+	14.0108i	0.446398	+	1.37387i
$105$	−0.557818	−	1.71679i	−0.0544375	−	0.167541i
$106$	−8.55709	−	6.21709i	−0.831138	−	0.603857i
$107$	9.86072	−	7.16423i	0.953272	−	0.692593i	0.00169340	−	0.999999i	$-0.499461\pi$
$107$	9.86072	−	7.16423i	0.953272	−	0.692593i	0.951578	+	0.307406i	$0.0994610\pi$
$108$	−6.82780	+	21.0138i	−0.657006	+	2.02206i
$109$	−0.886088			−0.0848718			−0.0424359	−	0.999099i	$-0.513512\pi$
$109$	−0.886088			−0.0848718			−0.0424359	+	0.999099i	$0.513512\pi$
$110$		0			0
$111$	−7.82353			−0.742577
$112$	−1.06649	+	3.28231i	−0.100774	+	0.310149i
$113$	−3.67700	+	2.67149i	−0.345903	+	0.251313i	−0.747148	−	0.664658i	$-0.768577\pi$
$113$	−3.67700	+	2.67149i	−0.345903	+	0.251313i	0.401245	+	0.915971i	$0.368577\pi$
$114$	8.07159	+	5.86435i	0.755974	+	0.549247i
$115$	2.63056	+	8.09602i	0.245301	+	0.754958i
$116$	−5.42768	−	16.7047i	−0.503947	−	1.55099i
$117$	2.42488	+	1.76178i	0.224180	+	0.162876i
$118$	13.6594	−	9.92416i	1.25745	−	0.913593i
$119$	1.83067	−	5.63423i	0.167817	−	0.516489i
$120$	8.36702			0.763801
$121$		0			0
$122$	5.95984			0.539579
$123$	0.139378	−	0.428960i	0.0125673	−	0.0386780i
$124$	−30.7478	+	22.3396i	−2.76123	+	2.00615i
$125$	8.56947	+	6.22608i	0.766477	+	0.556878i
$126$	0.708281	+	2.17986i	0.0630987	+	0.194198i
$127$	2.48072	+	7.63488i	0.220129	+	0.677486i	0.998750	+	0.0499916i	$0.0159195\pi$
$127$	2.48072	+	7.63488i	0.220129	+	0.677486i	−0.778621	+	0.627494i	$0.784081\pi$
$128$	16.3606	+	11.8867i	1.44609	+	1.05065i
$129$	−0.153811	+	0.111750i	−0.0135423	+	0.00983908i
$130$	3.00444	−	9.24673i	0.263507	−	0.810992i
$131$	−0.101461			−0.00886466			−0.00443233	−	0.999990i	$-0.501411\pi$
$131$	−0.101461			−0.00886466			−0.00443233	+	0.999990i	$0.501411\pi$
$132$		0			0
$133$	2.86222			0.248186
$134$	−7.07480	+	21.7740i	−0.611170	+	1.88099i
$135$	5.75838	−	4.18371i	0.495602	−	0.360076i
$136$	22.2150	+	16.1401i	1.90492	+	1.38401i
$137$	−1.41038	−	4.34071i	−0.120497	−	0.370852i	0.872557	−	0.488513i	$-0.162460\pi$
$137$	−1.41038	−	4.34071i	−0.120497	−	0.370852i	−0.993054	+	0.117661i	$0.962460\pi$
$138$	7.28531	+	22.4219i	0.620167	+	1.90868i
$139$	−3.09475	−	2.24847i	−0.262494	−	0.190713i	0.448752	−	0.893656i	$-0.351869\pi$
$139$	−3.09475	−	2.24847i	−0.262494	−	0.190713i	−0.711246	+	0.702944i	$0.751869\pi$
$140$	3.97842	−	2.89049i	0.336238	−	0.244291i
$141$	4.15497	−	12.7877i	0.349911	−	1.07692i
$142$	−0.283415			−0.0237837
$143$		0			0
$144$	−3.25469			−0.271224
$145$	−1.74847	+	5.38124i	−0.145203	+	0.446887i
$146$	1.20932	−	0.878624i	0.100084	−	0.0727155i
$147$	−1.16030	−	0.843005i	−0.0956997	−	0.0695299i
$148$	−6.58609	−	20.2699i	−0.541374	−	1.66618i
$149$	1.50560	+	4.63377i	0.123344	+	0.379613i	0.993596	−	0.112994i	$-0.0360440\pi$
$149$	1.50560	+	4.63377i	0.123344	+	0.379613i	−0.870252	+	0.492607i	$0.836044\pi$
$150$	9.63285	+	6.99868i	0.786519	+	0.571440i
$151$	−13.7321	+	9.97699i	−1.11751	+	0.811916i	−0.983829	−	0.179109i	$-0.942678\pi$
$151$	−13.7321	+	9.97699i	−1.11751	+	0.811916i	−0.133677	+	0.991025i	$0.542678\pi$
$152$	−4.09964	+	12.6174i	−0.332525	+	1.02341i
$153$	5.58681			0.451667
$154$		0			0
$155$	12.2434			0.983410
$156$	5.50357	−	16.9383i	0.440638	−	1.35615i
$157$	−1.81611	+	1.31948i	−0.144941	+	0.105306i	−0.657893	−	0.753112i	$-0.728552\pi$
$157$	−1.81611	+	1.31948i	−0.144941	+	0.105306i	0.512952	+	0.858417i	$0.328552\pi$
$158$	16.7709	+	12.1848i	1.33422	+	0.969371i
$159$	1.92875	+	5.93607i	0.152960	+	0.470761i
$160$	−0.343115	−	1.05600i	−0.0271256	−	0.0834841i
$161$	5.47173	+	3.97544i	0.431233	+	0.313309i
$162$	10.3849	−	7.54506i	0.815913	−	0.592796i
$163$	−4.89398	+	15.0621i	−0.383326	+	1.17976i	0.554361	+	0.832276i	$0.312963\pi$
$163$	−4.89398	+	15.0621i	−0.383326	+	1.17976i	−0.937687	+	0.347480i	$0.887037\pi$
$164$	1.22872			0.0959470
$165$		0			0
$166$	−2.31022			−0.179308
$167$	−6.40950	+	19.7264i	−0.495982	+	1.52647i	0.319440	+	0.947607i	$0.396505\pi$
$167$	−6.40950	+	19.7264i	−0.495982	+	1.52647i	−0.815421	+	0.578868i	$0.803495\pi$
$168$	5.37811	−	3.90743i	0.414930	−	0.301464i
$169$	2.34481	+	1.70361i	0.180370	+	0.131047i
$170$	−5.60011	−	17.2354i	−0.429509	−	1.32189i
$171$	0.834105	+	2.56711i	0.0637856	+	0.196312i
$172$	−0.419017	−	0.304433i	−0.0319497	−	0.0232128i
$173$	−17.4387	+	12.6700i	−1.32584	+	0.963279i	−0.326000	+	0.945370i	$0.605701\pi$
$173$	−17.4387	+	12.6700i	−1.32584	+	0.963279i	−0.999840	+	0.0179090i	$0.994299\pi$
$174$	−4.84238	+	14.9033i	−0.367100	+	1.12982i
$175$	3.41585			0.258214
$176$		0			0
$177$	−9.96322			−0.748881
$178$	7.55194	−	23.2425i	0.566042	−	1.74210i
$179$	−3.86840	+	2.81056i	−0.289138	+	0.210071i	−0.722893	−	0.690960i	$-0.757188\pi$
$179$	−3.86840	+	2.81056i	−0.289138	+	0.210071i	0.433755	+	0.901031i	$0.357188\pi$
$180$	3.75186	+	2.72589i	0.279647	+	0.203175i
$181$	−2.42666	−	7.46850i	−0.180372	−	0.555129i	0.819466	−	0.573128i	$-0.194270\pi$
$181$	−2.42666	−	7.46850i	−0.180372	−	0.555129i	−0.999838	+	0.0179992i	$0.994270\pi$
$182$	−2.38707	−	7.34665i	−0.176942	−	0.544570i
$183$	−2.84523	−	2.06718i	−0.210325	−	0.152810i
$184$	−25.3621	+	18.4266i	−1.86972	+	1.35843i
$185$	−2.12164	+	6.52974i	−0.155986	+	0.480076i
$186$	33.9079			2.48625
$187$		0			0
$188$	36.6293			2.67146
$189$	1.74754	−	5.37837i	0.127115	−	0.391219i
$190$	7.08347	−	5.14644i	0.513889	−	0.373362i
$191$	7.14385	+	5.19031i	0.516911	+	0.375558i	0.815439	−	0.578843i	$-0.196496\pi$
$191$	7.14385	+	5.19031i	0.516911	+	0.375558i	−0.298528	+	0.954401i	$0.596496\pi$
$192$	−4.00938	−	12.3396i	−0.289352	−	0.890535i
$193$	−7.91153	−	24.3492i	−0.569485	−	1.75269i	−0.654235	−	0.756292i	$-0.727009\pi$
$193$	−7.91153	−	24.3492i	−0.569485	−	1.75269i	0.0847500	−	0.996402i	$-0.472991\pi$
$194$	−34.5613	−	25.1102i	−2.48135	−	1.80281i
$195$	−4.64156	+	3.37229i	−0.332389	+	0.241495i
$196$	1.20736	−	3.71587i	0.0862400	−	0.265419i
$197$	11.1977			0.797802			0.398901	−	0.916994i	$-0.369392\pi$
$197$	11.1977			0.797802			0.398901	+	0.916994i	$0.369392\pi$
$198$		0			0
$199$	−12.2503			−0.868400			−0.434200	−	0.900817i	$-0.642969\pi$
$199$	−12.2503			−0.868400			−0.434200	+	0.900817i	$0.642969\pi$
$200$	−4.89262	+	15.0579i	−0.345960	+	1.06476i
$201$	10.9298	−	7.94100i	0.770932	−	0.560115i
$202$	−24.5316	−	17.8232i	−1.72603	−	1.25404i
$203$	1.38918	+	4.27547i	0.0975016	+	0.300079i
$204$	−10.2583	−	31.5719i	−0.718227	−	2.21048i
$205$	−0.320225	−	0.232657i	−0.0223655	−	0.0162495i
$206$	−16.1589	+	11.7401i	−1.12585	+	0.817974i
$207$	−1.97099	+	6.06609i	−0.136994	+	0.421623i
$208$	10.9691			0.760568
$209$		0			0
$210$	−4.38730			−0.302752
$211$	4.40769	−	13.5655i	0.303438	−	0.933887i	−0.676817	−	0.736151i	$-0.736641\pi$
$211$	4.40769	−	13.5655i	0.303438	−	0.933887i	0.980255	−	0.197736i	$-0.0633587\pi$
$212$	−13.7560	+	9.99435i	−0.944769	+	0.686415i
$213$	0.135302	+	0.0983030i	0.00927077	+	0.00673561i
$214$	−9.15420	−	28.1737i	−0.625768	−	1.92592i
$215$	0.0515585	+	0.158681i	0.00351626	+	0.0108219i
$216$	21.2062	+	15.4072i	1.44290	+	1.04833i
$217$	7.86972	−	5.71769i	0.534232	−	0.388142i
$218$	−0.665497	+	2.04819i	−0.0450732	+	0.138721i
$219$	−0.882082			−0.0596056
$220$		0			0
$221$	−18.8289			−1.26657
$222$	−5.87587	+	18.0841i	−0.394363	+	1.21372i
$223$	2.39793	−	1.74220i	0.160577	−	0.116666i	−0.504595	−	0.863356i	$-0.668358\pi$
$223$	2.39793	−	1.74220i	0.160577	−	0.116666i	0.665172	+	0.746690i	$0.268358\pi$
$224$	−0.713702	−	0.518535i	−0.0476862	−	0.0346460i
$225$	0.995444	+	3.06366i	0.0663629	+	0.204244i
$226$	3.41354	+	10.5058i	0.227065	+	0.698835i
$227$	6.67929	+	4.85279i	0.443320	+	0.322091i	0.786953	−	0.617013i	$-0.211658\pi$
$227$	6.67929	+	4.85279i	0.443320	+	0.322091i	−0.343633	+	0.939104i	$0.611658\pi$
$228$	12.9756	−	9.42730i	0.859328	−	0.624338i
$229$	4.05063	−	12.4666i	0.267673	−	0.823813i	−0.723392	−	0.690437i	$-0.757418\pi$
$229$	4.05063	−	12.4666i	0.267673	−	0.823813i	0.991066	−	0.133376i	$-0.0425818\pi$
$230$	20.6896			1.36423
$231$		0			0
$232$	−20.8371			−1.36802
$233$	3.96397	−	12.1998i	0.259688	−	0.799239i	−0.733181	−	0.680033i	$-0.761965\pi$
$233$	3.96397	−	12.1998i	0.259688	−	0.799239i	0.992870	−	0.119205i	$-0.0380347\pi$
$234$	5.89355	−	4.28191i	0.385273	−	0.279917i
$235$	−9.54618	−	6.93571i	−0.622724	−	0.452436i
$236$	−8.38735	−	25.8136i	−0.545970	−	1.68032i
$237$	−3.78013	−	11.6340i	−0.245546	−	0.755712i
$238$	−11.6486	−	8.46319i	−0.755065	−	0.548587i
$239$	−4.02979	+	2.92781i	−0.260665	+	0.189384i	−0.710440	−	0.703758i	$-0.751504\pi$
$239$	−4.02979	+	2.92781i	−0.260665	+	0.189384i	0.449775	+	0.893142i	$0.351504\pi$
$240$	1.92516	−	5.92502i	0.124268	−	0.382459i
$241$	2.62686			0.169211			0.0846053	−	0.996415i	$-0.473037\pi$
$241$	2.62686			0.169211			0.0846053	+	0.996415i	$0.473037\pi$
$242$		0			0
$243$	9.39070			0.602414
$244$	2.96063	−	9.11189i	0.189535	−	0.583329i
$245$	−1.01825	+	0.739805i	−0.0650539	+	0.0472644i
$246$	−0.886861	−	0.644342i	−0.0565442	−	0.0410818i
$247$	−2.81113	−	8.65177i	−0.178868	−	0.550499i
$248$	13.9330	+	42.8814i	0.884747	+	2.72297i
$249$	1.10290	+	0.801303i	0.0698934	+	0.0507805i
$250$	20.8277	−	15.1322i	1.31726	−	0.957045i
$251$	−8.10332	+	24.9395i	−0.511477	+	1.57417i	0.278124	+	0.960545i	$0.410287\pi$
$251$	−8.10332	+	24.9395i	−0.511477	+	1.57417i	−0.789601	+	0.613620i	$0.789713\pi$
$252$	3.68460			0.232108
$253$		0			0
$254$	19.5112			1.22424
$255$	−3.30461	+	10.1706i	−0.206943	+	0.636905i
$256$	25.1261	−	18.2552i	1.57038	−	1.14095i
$257$	−24.2315	−	17.6052i	−1.51152	−	1.09818i	−0.965497	−	0.260413i	$-0.916141\pi$
$257$	−24.2315	−	17.6052i	−1.51152	−	1.09818i	−0.546022	−	0.837771i	$-0.683859\pi$
$258$	0.142791	+	0.439465i	0.00888977	+	0.0273599i
$259$	1.68567	+	5.18797i	0.104743	+	0.322365i
$260$	−12.6446	−	9.18688i	−0.784188	−	0.569746i
$261$	−3.42982	+	2.49191i	−0.212300	+	0.154245i
$262$	−0.0762022	+	0.234526i	−0.00470779	+	0.0144891i
$263$	−3.33709			−0.205774			−0.102887	−	0.994693i	$-0.532808\pi$
$263$	−3.33709			−0.205774			−0.102887	+	0.994693i	$0.532808\pi$
$264$		0			0
$265$	5.47747			0.336478
$266$	2.14967	−	6.61601i	0.131805	−	0.405654i
$267$	−11.6670	+	8.47656i	−0.714008	+	0.518757i
$268$	29.7754	+	21.6331i	1.81882	+	1.32145i
$269$	−0.536395	−	1.65086i	−0.0327046	−	0.100654i	0.933372	−	0.358911i	$-0.116852\pi$
$269$	−0.536395	−	1.65086i	−0.0327046	−	0.100654i	−0.966076	+	0.258257i	$0.916852\pi$
$270$	−5.34579	−	16.4527i	−0.325335	−	1.00128i
$271$	−2.00309	−	1.45533i	−0.121679	−	0.0884051i	0.525281	−	0.850929i	$-0.323960\pi$
$271$	−2.00309	−	1.45533i	−0.121679	−	0.0884051i	−0.646960	+	0.762524i	$0.723960\pi$
$272$	16.5409	−	12.0177i	1.00294	−	0.728679i
$273$	−1.40861	+	4.33525i	−0.0852528	+	0.262381i
$274$	−11.0928			−0.670141
$275$		0			0
$276$	37.8995			2.28128
$277$	−1.59320	+	4.90337i	−0.0957262	+	0.294615i	−0.987442	−	0.157980i	$-0.949502\pi$
$277$	−1.59320	+	4.90337i	−0.0957262	+	0.294615i	0.891716	+	0.452595i	$0.149502\pi$
$278$	−7.52165	+	5.46480i	−0.451119	+	0.327757i
$279$	7.42156	+	5.39208i	0.444317	+	0.322815i
$280$	−1.80277	−	5.54837i	−0.107736	−	0.331578i
$281$	6.97467	+	21.4658i	0.416074	+	1.28054i	0.911287	+	0.411772i	$0.135090\pi$
$281$	6.97467	+	21.4658i	0.416074	+	1.28054i	−0.495213	+	0.868772i	$0.664910\pi$
$282$	−26.4381	−	19.2084i	−1.57437	−	1.14384i
$283$	−6.86659	+	4.98887i	−0.408176	+	0.296557i	−0.772863	−	0.634573i	$-0.781176\pi$
$283$	−6.86659	+	4.98887i	−0.408176	+	0.296557i	0.364687	+	0.931130i	$0.381176\pi$
$284$	−0.140790	+	0.433309i	−0.00835438	+	0.0257121i
$285$	−5.16669			−0.306049
$286$		0			0
$287$	−0.314484			−0.0185634
$288$	0.257085	−	0.791227i	0.0151489	−	0.0466235i
$289$	−14.6399	+	10.6365i	−0.861171	+	0.625677i
$290$	11.1255	+	8.08317i	0.653313	+	0.474660i
$291$	7.79002	+	23.9752i	0.456659	+	1.40545i
$292$	−0.742565	−	2.28538i	−0.0434553	−	0.133742i
$293$	19.9229	+	14.4749i	1.16391	+	0.845630i	0.990267	−	0.139178i	$-0.0444462\pi$
$293$	19.9229	+	14.4749i	1.16391	+	0.845630i	0.173643	+	0.984809i	$0.444446\pi$
$294$	−2.82005	+	2.04888i	−0.164468	+	0.119493i
$295$	−2.70190	+	8.31559i	−0.157311	+	0.484152i
$296$	−25.2843			−1.46962
$297$		0			0
$298$	11.8417			0.685973
$299$	6.64271	−	20.4442i	0.384158	−	1.18232i
$300$	15.4854	−	11.2508i	0.894050	−	0.649565i
$301$	0.107245	+	0.0779180i	0.00618149	+	0.00449112i
$302$	12.7482	+	39.2351i	0.733579	+	2.25772i
$303$	5.52935	+	17.0176i	0.317653	+	0.977636i
$304$	7.99160	+	5.80624i	0.458350	+	0.333011i
$305$	−2.49692	+	1.81412i	−0.142973	+	0.103876i
$306$	4.19598	−	12.9139i	0.239868	−	0.738239i
$307$	−4.59391			−0.262188			−0.131094	−	0.991370i	$-0.541849\pi$
$307$	−4.59391			−0.262188			−0.131094	+	0.991370i	$0.541849\pi$
$308$		0			0
$309$	11.7863			0.670502
$310$	9.19538	−	28.3005i	0.522263	−	1.60736i
$311$	1.78852	−	1.29944i	0.101418	−	0.0736843i	−0.535921	−	0.844268i	$-0.680035\pi$
$311$	1.78852	−	1.29944i	0.101418	−	0.0736843i	0.637338	+	0.770584i	$0.280035\pi$
$312$	−17.0933	−	12.4190i	−0.967718	−	0.703088i
$313$	−2.99724	−	9.22457i	−0.169414	−	0.521403i	0.829920	−	0.557882i	$-0.188386\pi$
$313$	−2.99724	−	9.22457i	−0.169414	−	0.521403i	−0.999334	+	0.0364788i	$0.988386\pi$
$314$	1.68598	+	5.18892i	0.0951455	+	0.292828i
$315$	−0.960267	−	0.697675i	−0.0541049	−	0.0393095i
$316$	26.9603	−	19.5878i	1.51664	−	1.10190i
$317$	1.99483	−	6.13944i	0.112041	−	0.344826i	−0.879278	−	0.476310i	$-0.841974\pi$
$317$	1.99483	−	6.13944i	0.112041	−	0.344826i	0.991318	+	0.131484i	$0.0419742\pi$
$318$	15.1698			0.850680
$319$		0			0
$320$	−11.3863			−0.636513
$321$	−5.40188	+	16.6253i	−0.301504	+	0.927933i
$322$	13.2988	−	9.66213i	0.741112	−	0.538449i
$323$	−13.7179	−	9.96666i	−0.763286	−	0.554560i
$324$	−6.37667	−	19.6254i	−0.354259	−	1.09030i
$325$	−3.35488	−	10.3253i	−0.186095	−	0.572742i
$326$	31.1404	+	22.6248i	1.72471	+	1.25307i
$327$	1.02813	−	0.746977i	0.0568555	−	0.0413079i
$328$	0.450445	−	1.38633i	0.0248717	−	0.0765471i
$329$	−9.37505			−0.516863
$330$		0			0
$331$	3.62076			0.199015			0.0995075	−	0.995037i	$-0.468273\pi$
$331$	3.62076			0.199015			0.0995075	+	0.995037i	$0.468273\pi$
$332$	−1.14763	+	3.53206i	−0.0629846	+	0.193847i
$333$	−4.16183	+	3.02375i	−0.228067	+	0.165700i
$334$	40.7837	+	29.6311i	2.23158	+	1.62134i
$335$	−3.66375	−	11.2759i	−0.200172	−	0.616066i
$336$	−1.52956	−	4.70751i	−0.0834446	−	0.256816i
$337$	−5.18183	−	3.76482i	−0.282272	−	0.205083i	0.437636	−	0.899152i	$-0.355816\pi$
$337$	−5.18183	−	3.76482i	−0.282272	−	0.205083i	−0.719908	+	0.694070i	$0.755816\pi$
$338$	5.69896	−	4.14054i	0.309983	−	0.225215i
$339$	2.01433	−	6.19946i	0.109403	−	0.336708i
$340$	−29.1327			−1.57994
$341$		0			0
$342$	6.56033			0.354742
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−0.497093	+	0.361159i	−0.0268014	+	0.0194724i
$345$	−9.87722	−	7.17622i	−0.531772	−	0.386355i
$346$	16.1892	+	49.8253i	0.870338	+	2.67862i
$347$	5.39544	+	16.6054i	0.289642	+	0.891427i	0.984969	+	0.172733i	$0.0552598\pi$
$347$	5.39544	+	16.6054i	0.289642	+	0.891427i	−0.695327	+	0.718694i	$0.744740\pi$
$348$	20.3799	+	14.8068i	1.09247	+	0.793729i
$349$	−17.4949	+	12.7108i	−0.936481	+	0.680393i	−0.947571	−	0.319545i	$-0.896470\pi$
$349$	−17.4949	+	12.7108i	−0.936481	+	0.680393i	0.0110900	+	0.999939i	$0.496470\pi$
$350$	2.56548	−	7.89572i	0.137130	−	0.422044i
$351$	−17.9738			−0.959371
$352$		0			0
$353$	4.40150			0.234268			0.117134	−	0.993116i	$-0.462629\pi$
$353$	4.40150			0.234268			0.117134	+	0.993116i	$0.462629\pi$
$354$	−7.48289	+	23.0300i	−0.397711	+	1.22403i
$355$	0.118739	−	0.0862688i	0.00630200	−	0.00457867i
$356$	−31.7835	−	23.0920i	−1.68452	−	1.22388i
$357$	2.62556	+	8.08065i	0.138959	+	0.427673i
$358$	3.59123	+	11.0527i	0.189802	+	0.584152i
$359$	−8.64170	−	6.27857i	−0.456092	−	0.331370i	0.335904	−	0.941896i	$-0.390958\pi$
$359$	−8.64170	−	6.27857i	−0.456092	−	0.331370i	−0.791996	+	0.610526i	$0.790958\pi$
$360$	4.45095	−	3.23380i	0.234586	−	0.170436i
$361$	−3.33977	+	10.2787i	−0.175777	+	0.540986i
$362$	−19.0860			−1.00314
$363$		0			0
$364$	−12.4180			−0.650879
$365$	−0.239209	+	0.736211i	−0.0125208	+	0.0385350i
$366$	−6.91519	+	5.02418i	−0.361463	+	0.262618i
$367$	−8.26552	−	6.00525i	−0.431456	−	0.313471i	0.350775	−	0.936460i	$-0.385918\pi$
$367$	−8.26552	−	6.00525i	−0.431456	−	0.313471i	−0.782231	+	0.622988i	$0.785918\pi$
$368$	7.21312	+	22.1997i	0.376010	+	1.15724i
$369$	−0.0916468	−	0.282060i	−0.00477094	−	0.0146835i
$370$	13.5000	+	9.80834i	0.701833	+	0.509911i
$371$	3.52078	−	2.55800i	0.182790	−	0.132805i
$372$	16.8442	−	51.8411i	0.873331	−	2.68784i
$373$	27.8851			1.44383			0.721917	−	0.691980i	$-0.243261\pi$
$373$	27.8851			1.44383			0.721917	+	0.691980i	$0.243261\pi$
$374$		0			0
$375$	−15.1918			−0.784499
$376$	13.4282	−	41.3276i	0.692504	−	2.13131i
$377$	11.5593	−	8.39832i	0.595334	−	0.432535i
$378$	−11.1196	−	8.07886i	−0.571930	−	0.415532i
$379$	0.354761	+	1.09184i	0.0182228	+	0.0560841i	0.959754	−	0.280841i	$-0.0906132\pi$
$379$	0.354761	+	1.09184i	0.0182228	+	0.0560841i	−0.941532	+	0.336925i	$0.890613\pi$
$380$	−4.34949	−	13.3863i	−0.223124	−	0.686705i
$381$	−9.31462	−	6.76747i	−0.477202	−	0.346708i
$382$	17.3628	−	12.6148i	0.888358	−	0.645430i
$383$	−6.16539	+	18.9751i	−0.315037	+	0.969583i	0.660703	+	0.750648i	$0.270258\pi$
$383$	−6.16539	+	18.9751i	−0.315037	+	0.969583i	−0.975739	+	0.218936i	$0.929742\pi$
$384$	−29.0038			−1.48009
$385$		0			0
$386$	−62.2251			−3.16717
$387$	−0.0386311	+	0.118894i	−0.00196373	+	0.00604374i
$388$	−55.5593	+	40.3662i	−2.82060	+	2.04928i
$389$	−2.10345	−	1.52824i	−0.106649	−	0.0774850i	0.533183	−	0.846000i	$-0.320996\pi$
$389$	−2.10345	−	1.52824i	−0.106649	−	0.0774850i	−0.639832	+	0.768515i	$0.720996\pi$
$390$	4.30899	+	13.2617i	0.218194	+	0.671533i
$391$	−12.3816	−	38.1067i	−0.626166	−	1.92714i
$392$	−3.74989	−	2.72445i	−0.189398	−	0.137606i
$393$	0.117725	−	0.0855319i	0.00593842	−	0.00431451i
$394$	8.41003	−	25.8834i	0.423691	−	1.30399i
$395$	−10.7352			−0.540148
$396$		0			0
$397$	8.77237			0.440272			0.220136	−	0.975469i	$-0.429350\pi$
$397$	8.77237			0.440272			0.220136	+	0.975469i	$0.429350\pi$
$398$	−9.20059	+	28.3165i	−0.461184	+	1.41938i
$399$	−3.32102	+	2.41286i	−0.166259	+	0.120794i
$400$	9.53740	+	6.92932i	0.476870	+	0.346466i
$401$	8.76171	+	26.9658i	0.437539	+	1.34661i	0.890462	+	0.455057i	$0.150381\pi$
$401$	8.76171	+	26.9658i	0.437539	+	1.34661i	−0.452923	+	0.891549i	$0.649619\pi$
$402$	−10.1467	−	31.2284i	−0.506073	−	1.55753i
$403$	−25.0124	−	18.1726i	−1.24596	−	0.905241i
$404$	−39.4360	+	28.6519i	−1.96201	+	1.42549i
$405$	−2.05418	+	6.32210i	−0.102073	+	0.314148i
$406$	10.9261			0.542252
$407$		0			0
$408$	−39.3822			−1.94971
$409$	−6.15114	+	18.9313i	−0.304154	+	0.936091i	0.675837	+	0.737051i	$0.263782\pi$
$409$	−6.15114	+	18.9313i	−0.304154	+	0.936091i	−0.979991	+	0.199040i	$0.936218\pi$
$410$	−0.778292	+	0.565462i	−0.0384371	+	0.0279262i
$411$	5.29570	+	3.84755i	0.261218	+	0.189786i
$412$	9.92212	+	30.5371i	0.488828	+	1.50446i
$413$	2.14670	+	6.60685i	0.105632	+	0.325102i
$414$	12.5414	+	9.11189i	0.616379	+	0.447825i
$415$	0.967883	−	0.703208i	0.0475115	−	0.0345191i
$416$	−0.866438	+	2.66662i	−0.0424806	+	0.130742i
$417$	5.48631			0.268666
$418$		0			0
$419$	−30.8957			−1.50935			−0.754676	−	0.656097i	$-0.772206\pi$
$419$	−30.8957			−1.50935			−0.754676	+	0.656097i	$0.772206\pi$
$420$	−2.17945	+	6.70766i	−0.106346	+	0.327300i
$421$	19.5727	−	14.2204i	0.953913	−	0.693058i	0.00218371	−	0.999998i	$-0.499305\pi$
$421$	19.5727	−	14.2204i	0.953913	−	0.693058i	0.951729	+	0.306939i	$0.0993049\pi$
$422$	−28.0462	−	20.3767i	−1.36527	−	0.991925i
$423$	−2.73207	−	8.40845i	−0.132838	−	0.408833i
$424$	6.23339	+	19.1844i	0.302720	+	0.931677i
$425$	−16.3713	−	11.8945i	−0.794127	−	0.576967i
$426$	0.328846	−	0.238921i	0.0159326	−	0.0115757i
$427$	−0.757757	+	2.33214i	−0.0366704	+	0.112860i
$428$	−47.6218			−2.30188
$429$		0			0
$430$	0.405513			0.0195556
$431$	−5.99495	+	18.4506i	−0.288766	+	0.888732i	0.696478	+	0.717578i	$0.254749\pi$
$431$	−5.99495	+	18.4506i	−0.288766	+	0.888732i	−0.985244	+	0.171154i	$0.945251\pi$
$432$	15.7898	−	11.4719i	0.759685	−	0.551944i
$433$	17.3030	+	12.5714i	0.831530	+	0.604142i	0.919992	−	0.391937i	$-0.128195\pi$
$433$	17.3030	+	12.5714i	0.831530	+	0.604142i	−0.0884616	+	0.996080i	$0.528195\pi$
$434$	−7.30586	−	22.4851i	−0.350692	−	1.07932i
$435$	−2.50767	−	7.71780i	−0.120233	−	0.370040i
$436$	2.80084	+	2.03493i	0.134136	+	0.0974556i
$437$	15.6613	−	11.3786i	0.749181	−	0.544312i
$438$	−0.662489	+	2.03893i	−0.0316549	+	0.0974239i
$439$	31.7315			1.51446			0.757232	−	0.653146i	$-0.226551\pi$
$439$	31.7315			1.51446			0.757232	+	0.653146i	$0.226551\pi$
$440$		0			0
$441$	−0.943053			−0.0449073
$442$	−14.1415	+	43.5229i	−0.672640	+	2.07017i
$443$	1.34791	−	0.979312i	0.0640410	−	0.0465285i	−0.555304	−	0.831647i	$-0.687398\pi$
$443$	1.34791	−	0.979312i	0.0640410	−	0.0465285i	0.619345	+	0.785119i	$0.287398\pi$
$444$	24.7295	+	17.9670i	1.17361	+	0.852677i
$445$	3.91084	+	12.0363i	0.185392	+	0.570577i
$446$	−2.22612	−	6.85128i	−0.105410	−	0.324417i
$447$	−5.65324	−	4.10732i	−0.267389	−	0.194270i
$448$	−7.31882	+	5.31744i	−0.345782	+	0.251225i
$449$	−5.31070	+	16.3447i	−0.250627	+	0.771352i	0.744032	+	0.668144i	$0.232911\pi$
$449$	−5.31070	+	16.3447i	−0.250627	+	0.771352i	−0.994660	+	0.103208i	$0.967089\pi$
$450$	7.82927			0.369076
$451$		0			0
$452$	17.7578			0.835258
$453$	7.52272	−	23.1525i	0.353448	−	1.08780i
$454$	16.2337	−	11.7945i	0.761885	−	0.553542i
$455$	3.23633	+	2.35133i	0.151721	+	0.110232i
$456$	−5.87973	−	18.0959i	−0.275343	−	0.847420i
$457$	−3.15835	−	9.72041i	−0.147741	−	0.454701i	0.849612	−	0.527408i	$-0.176836\pi$
$457$	−3.15835	−	9.72041i	−0.147741	−	0.454701i	−0.997353	+	0.0727070i	$0.976836\pi$
$458$	−25.7742	−	18.7260i	−1.20435	−	0.875010i
$459$	−27.1038	+	19.6921i	−1.26510	+	0.919147i
$460$	10.2779	−	31.6320i	0.479207	−	1.47485i
$461$	22.1160			1.03004			0.515022	−	0.857177i	$-0.327784\pi$
$461$	22.1160			1.03004			0.515022	+	0.857177i	$0.327784\pi$
$462$		0			0
$463$	−30.3717			−1.41149			−0.705747	−	0.708464i	$-0.749389\pi$
$463$	−30.3717			−1.41149			−0.705747	+	0.708464i	$0.749389\pi$
$464$	−4.79439	+	14.7556i	−0.222574	+	0.685012i
$465$	−14.2059	+	10.3212i	−0.658784	+	0.478635i
$466$	−25.2228	−	18.3254i	−1.16842	−	0.848909i
$467$	7.78441	+	23.9580i	0.360220	+	1.10864i	0.952921	+	0.303220i	$0.0980615\pi$
$467$	7.78441	+	23.9580i	0.360220	+	1.10864i	−0.592701	+	0.805422i	$0.701938\pi$
$468$	−3.61884	−	11.1376i	−0.167281	−	0.514837i
$469$	−7.62083	−	5.53686i	−0.351897	−	0.255668i
$470$	−23.2015	+	16.8569i	−1.07021	+	0.777551i
$471$	0.994895	−	3.06197i	0.0458424	−	0.141088i
$472$	−32.1995			−1.48210
$473$		0			0
$474$	−29.7311			−1.36560
$475$	3.02123	−	9.29838i	0.138623	−	0.426639i
$476$	−18.7258	+	13.6051i	−0.858296	+	0.623588i
$477$	3.32028	+	2.41233i	0.152025	+	0.110453i
$478$	3.74105	+	11.5138i	0.171112	+	0.526628i
$479$	6.55239	+	20.1662i	0.299386	+	0.921417i	0.981713	+	0.190369i	$0.0609684\pi$
$479$	6.55239	+	20.1662i	0.299386	+	0.921417i	−0.682326	+	0.731048i	$0.739032\pi$
$480$	1.28833	+	0.936026i	0.0588039	+	0.0427235i
$481$	14.0264	−	10.1907i	0.639547	−	0.464658i
$482$	1.97290	−	6.07197i	0.0898633	−	0.276571i
$483$	−9.70015			−0.441372
$484$		0			0
$485$	22.1230			1.00455
$486$	7.05290	−	21.7066i	0.319926	−	0.984631i
$487$	13.6075	−	9.88641i	0.616613	−	0.447996i	−0.235123	−	0.971966i	$-0.575549\pi$
$487$	13.6075	−	9.88641i	0.616613	−	0.447996i	0.851737	+	0.523970i	$0.175549\pi$
$488$	−9.19530	−	6.68078i	−0.416252	−	0.302425i
$489$	−7.01897	−	21.6022i	−0.317409	−	0.976884i
$490$	0.945296	+	2.90932i	0.0427041	+	0.131430i
$491$	3.91406	+	2.84373i	0.176639	+	0.128336i	0.672592	−	0.740014i	$-0.265181\pi$
$491$	3.91406	+	2.84373i	0.176639	+	0.128336i	−0.495953	+	0.868350i	$0.665181\pi$
$492$	−1.42568	+	1.03582i	−0.0642747	+	0.0466983i
$493$	8.22978	−	25.3286i	0.370650	−	1.14074i
$494$	−22.1099			−0.994770
$495$		0			0
$496$	33.5719			1.50742
$497$	0.0360345	−	0.110903i	0.00161637	−	0.00497467i
$498$	2.68055	−	1.94753i	0.120118	−	0.0872709i
$499$	−24.7426	−	17.9766i	−1.10763	−	0.804742i	−0.125343	−	0.992114i	$-0.540003\pi$
$499$	−24.7426	−	17.9766i	−1.10763	−	0.804742i	−0.982289	+	0.187372i	$0.940003\pi$
$500$	−12.7889	−	39.3602i	−0.571937	−	1.76024i
$501$	−9.19254	−	28.2917i	−0.410692	−	1.26398i
$502$	51.5615	+	37.4616i	2.30130	+	1.67199i
$503$	−22.8472	+	16.5994i	−1.01871	+	0.740133i	−0.966017	−	0.258478i	$-0.916779\pi$
$503$	−22.8472	+	16.5994i	−1.01871	+	0.740133i	−0.0526880	+	0.998611i	$0.516779\pi$
$504$	1.35076	−	4.15722i	0.0601677	−	0.185177i
$505$	15.7029			0.698768
$506$		0			0
$507$	−4.15683			−0.184611
$508$	9.69243	−	29.8302i	0.430032	−	1.32350i
$509$	3.39839	−	2.46908i	0.150631	−	0.109440i	−0.509917	−	0.860224i	$-0.670324\pi$
$509$	3.39839	−	2.46908i	0.150631	−	0.109440i	0.660548	+	0.750784i	$0.270324\pi$
$510$	21.0273	+	15.2772i	0.931104	+	0.676486i
$511$	0.190055	+	0.584930i	0.00840755	+	0.0258758i
$512$	−10.8274	−	33.3234i	−0.478509	−	1.47270i
$513$	−13.0950	−	9.51405i	−0.578157	−	0.420056i
$514$	−58.8935	+	42.7886i	−2.59768	+	1.88733i
$515$	3.19631	−	9.83722i	0.140846	−	0.433480i
$516$	0.742823			0.0327009
$517$		0			0
$518$	13.2580			0.582523
$519$	9.55323	−	29.4018i	0.419340	−	1.29060i
$520$	−15.0007	+	10.8987i	−0.657826	+	0.477939i
$521$	16.7037	+	12.1360i	0.731804	+	0.531687i	0.890134	−	0.455700i	$-0.150611\pi$
$521$	16.7037	+	12.1360i	0.731804	+	0.531687i	−0.158330	+	0.987386i	$0.550611\pi$
$522$	3.18407	+	9.79956i	0.139363	+	0.428915i
$523$	6.99431	+	21.5263i	0.305840	+	0.941278i	0.979362	+	0.202112i	$0.0647804\pi$
$523$	6.99431	+	21.5263i	0.305840	+	0.941278i	−0.673523	+	0.739167i	$0.735220\pi$
$524$	0.320708	+	0.233008i	0.0140102	+	0.0101790i
$525$	−3.96340	+	2.87958i	−0.172977	+	0.125675i
$526$	−2.50632	+	7.71367i	−0.109281	+	0.336332i
$527$	−57.6275			−2.51030
$528$		0			0
$529$	22.7440			0.988869
$530$	4.11386	−	12.6612i	0.178695	−	0.549965i
$531$	−5.30007	+	3.85073i	−0.230003	+	0.167107i
$532$	−9.04721	−	6.57318i	−0.392246	−	0.284984i
$533$	0.308871	+	0.950608i	0.0133787	+	0.0411754i
$534$	10.8310	+	33.3345i	0.468705	+	1.44253i
$535$	12.4110	+	9.01713i	0.536575	+	0.389844i
$536$	35.3234	−	25.6640i	1.52574	−	1.10852i
$537$	2.11918	−	6.52216i	0.0914494	−	0.281452i
$538$	−4.21881			−0.181886
$539$		0			0
$540$	−27.8098			−1.19674
$541$	−13.2001	+	40.6256i	−0.567515	+	1.74663i	0.0928437	+	0.995681i	$0.470404\pi$
$541$	−13.2001	+	40.6256i	−0.567515	+	1.74663i	−0.660359	+	0.750950i	$0.729596\pi$
$542$	−4.86842	+	3.53711i	−0.209117	+	0.151932i
$543$	9.11163	+	6.61999i	0.391018	+	0.284091i
$544$	1.61499	+	4.97043i	0.0692421	+	0.213105i
$545$	−0.344634	−	1.06067i	−0.0147625	−	0.0454343i
$546$	8.96298	+	6.51199i	0.383580	+	0.278687i
$547$	35.9873	−	26.1463i	1.53870	−	1.11793i	0.587563	−	0.809178i	$-0.300087\pi$
$547$	35.9873	−	26.1463i	1.53870	−	1.11793i	0.951141	−	0.308756i	$-0.0999127\pi$
$548$	−5.51050	+	16.9596i	−0.235397	+	0.724477i
$549$	−2.31251			−0.0986955
$550$		0			0
$551$	12.8671			0.548156
$552$	13.8938	−	42.7608i	0.591360	−	1.82002i
$553$	−6.90033	+	5.01339i	−0.293432	+	0.213191i
$554$	10.1376	+	7.36536i	0.430703	+	0.312924i
$555$	−3.04287	−	9.36499i	−0.129163	−	0.397522i
$556$	4.61855	+	14.2144i	0.195870	+	0.602826i
$557$	−20.2182	−	14.6894i	−0.856674	−	0.622410i	0.0703041	−	0.997526i	$-0.477603\pi$
$557$	−20.2182	−	14.6894i	−0.856674	−	0.622410i	−0.926978	+	0.375116i	$0.877603\pi$
$558$	18.0378	−	13.1052i	0.763599	−	0.554787i
$559$	0.130196	−	0.400702i	0.00550670	−	0.0169479i
$560$	−4.34382			−0.183560
$561$		0			0
$562$	54.8565			2.31398
$563$	−2.78426	+	8.56907i	−0.117343	+	0.361143i	−0.992428	−	0.122824i	$-0.960805\pi$
$563$	−2.78426	+	8.56907i	−0.117343	+	0.361143i	0.875086	+	0.483968i	$0.160805\pi$
$564$	−42.5008	+	30.8787i	−1.78961	+	1.30023i
$565$	−4.62798	−	3.36243i	−0.194701	−	0.141458i
$566$	6.37460	+	19.6190i	0.267944	+	0.824648i
$567$	1.63207	+	5.02300i	0.0685406	+	0.210946i
$568$	0.437275	+	0.317699i	0.0183476	+	0.0133303i
$569$	23.6021	−	17.1480i	0.989453	−	0.718880i	0.0296519	−	0.999560i	$-0.490560\pi$
$569$	23.6021	−	17.1480i	0.989453	−	0.718880i	0.959801	+	0.280681i	$0.0905601\pi$
$570$	−3.88045	+	11.9428i	−0.162534	+	0.500229i
$571$	−1.78994			−0.0749067			−0.0374533	−	0.999298i	$-0.511925\pi$
$571$	−1.78994			−0.0749067			−0.0374533	+	0.999298i	$0.511925\pi$
$572$		0			0
$573$	−12.6645			−0.529065
$574$	−0.236194	+	0.726930i	−0.00985854	+	0.0303415i
$575$	18.6906	−	13.5795i	0.779452	−	0.566305i
$576$	−6.90203	−	5.01462i	−0.287585	−	0.208943i
$577$	−6.67012	−	20.5285i	−0.277681	−	0.854614i	−0.988498	−	0.151236i	$-0.951675\pi$
$577$	−6.67012	−	20.5285i	−0.277681	−	0.854614i	0.710817	−	0.703377i	$-0.248325\pi$
$578$	13.5910	+	41.8287i	0.565309	+	1.73984i
$579$	29.7062	+	21.5828i	1.23455	+	0.896952i
$580$	17.8850	−	12.9942i	0.742633	−	0.539554i
$581$	0.293731	−	0.904010i	0.0121860	−	0.0375046i
$582$	61.2694			2.53970
$583$		0			0
$584$	−2.85074			−0.117965
$585$	−1.16577	+	3.58787i	−0.0481987	+	0.148340i
$586$	48.4217	−	35.1805i	2.00028	−	1.45329i
$587$	−4.46865	−	3.24666i	−0.184441	−	0.134004i	0.491734	−	0.870746i	$-0.336363\pi$
$587$	−4.46865	−	3.24666i	−0.184441	−	0.134004i	−0.676174	+	0.736742i	$0.736363\pi$
$588$	1.73160	+	5.32933i	0.0714101	+	0.219778i
$589$	−8.60373	−	26.4796i	−0.354511	−	1.09107i
$590$	17.1922	+	12.4909i	0.707792	+	0.514241i
$591$	−12.9926	+	9.43971i	−0.534446	+	0.388298i
$592$	−5.81764	+	17.9049i	−0.239104	+	0.735886i
$593$	40.7867			1.67491			0.837454	−	0.546508i	$-0.184043\pi$
$593$	40.7867			1.67491			0.837454	+	0.546508i	$0.184043\pi$
$594$		0			0
$595$	7.45636			0.305681
$596$	5.88254	−	18.1046i	0.240958	−	0.741593i
$597$	14.2140	−	10.3271i	0.581739	−	0.422658i
$598$	−42.2676	−	30.7092i	−1.72845	−	1.25579i
$599$	−8.19356	−	25.2172i	−0.334780	−	1.03035i	−0.966830	−	0.255419i	$-0.917787\pi$
$599$	−8.19356	−	25.2172i	−0.334780	−	1.03035i	0.632051	−	0.774927i	$-0.282213\pi$
$600$	−7.01702	−	21.5962i	−0.286469	−	0.881660i
$601$	−30.5565	−	22.2006i	−1.24643	−	0.905581i	−0.248417	−	0.968653i	$-0.579910\pi$
$601$	−30.5565	−	22.2006i	−1.24643	−	0.905581i	−0.998009	+	0.0630720i	$0.979910\pi$
$602$	0.260654	−	0.189376i	0.0106235	−	0.00771839i
$603$	2.74513	−	8.44864i	0.111790	−	0.344055i
$604$	66.3186			2.69847
$605$		0			0
$606$	43.4890			1.76662
$607$	8.56730	−	26.3674i	0.347736	−	1.07022i	−0.612367	−	0.790574i	$-0.709782\pi$
$607$	8.56730	−	26.3674i	0.347736	−	1.07022i	0.960103	−	0.279647i	$-0.0902176\pi$
$608$	−2.04277	+	1.48416i	−0.0828452	+	0.0601906i
$609$	−5.21611	−	3.78972i	−0.211367	−	0.153567i
$610$	2.31801	+	7.13411i	0.0938536	+	0.288852i
$611$	9.20772	+	28.3385i	0.372505	+	1.14645i
$612$	−17.6594	−	12.8303i	−0.713840	−	0.518635i
$613$	29.3078	−	21.2934i	1.18373	−	0.860031i	0.191144	−	0.981562i	$-0.438780\pi$
$613$	29.3078	−	21.2934i	1.18373	−	0.860031i	0.992588	+	0.121531i	$0.0387804\pi$
$614$	−3.45026	+	10.6188i	−0.139241	+	0.428540i
$615$	0.567687			0.0228914
$616$		0			0
$617$	41.1920			1.65833			0.829163	−	0.559007i	$-0.188817\pi$
$617$	41.1920			1.65833			0.829163	+	0.559007i	$0.188817\pi$
$618$	8.85215	−	27.2441i	0.356086	−	1.09592i
$619$	28.9139	−	21.0072i	1.16215	−	0.844349i	0.172099	−	0.985080i	$-0.444945\pi$
$619$	28.9139	−	21.0072i	1.16215	−	0.844349i	0.990048	+	0.140730i	$0.0449450\pi$
$620$	−38.7001	−	28.1173i	−1.55423	−	1.12922i
$621$	−11.8193	−	36.3762i	−0.474294	−	1.45973i
$622$	−1.66037	−	5.11010i	−0.0665749	−	0.204897i
$623$	8.13480	+	5.91028i	0.325914	+	0.236790i
$624$	−12.7274	+	9.24698i	−0.509503	+	0.370176i
$625$	1.15796	−	3.56385i	0.0463186	−	0.142554i
$626$	−23.5736			−0.942192
$627$		0			0
$628$	8.77077			0.349992
$629$	9.98623	−	30.7345i	0.398177	−	1.22546i
$630$	−2.33388	+	1.69567i	−0.0929841	+	0.0675569i
$631$	−2.23700	−	1.62527i	−0.0890534	−	0.0647011i	0.542368	−	0.840141i	$-0.317528\pi$
$631$	−2.23700	−	1.62527i	−0.0890534	−	0.0647011i	−0.631421	+	0.775440i	$0.717528\pi$
$632$	−12.2167	−	37.5993i	−0.485956	−	1.49562i
$633$	6.32154	+	19.4557i	0.251259	+	0.773295i
$634$	−12.6931	−	9.22207i	−0.504107	−	0.366255i
$635$	−8.17433	+	5.93900i	−0.324388	+	0.235682i
$636$	7.53581	−	23.1928i	0.298814	−	0.919655i
$637$	3.17831			0.125929
$638$		0			0
$639$	0.109970			0.00435033
$640$	−7.86545	+	24.2074i	−0.310909	+	0.956880i
$641$	−31.1362	+	22.6218i	−1.22981	+	0.893506i	−0.996876	−	0.0789878i	$-0.974831\pi$
$641$	−31.1362	+	22.6218i	−1.22981	+	0.893506i	−0.232930	+	0.972494i	$0.574831\pi$
$642$	34.3722	+	24.9729i	1.35656	+	0.985601i
$643$	−8.15130	−	25.0871i	−0.321456	−	0.989339i	−0.973015	−	0.230741i	$-0.925885\pi$
$643$	−8.15130	−	25.0871i	−0.321456	−	0.989339i	0.651559	−	0.758598i	$-0.274115\pi$
$644$	−8.16590	−	25.1320i	−0.321781	−	0.990341i
$645$	−0.193592	−	0.140653i	−0.00762267	−	0.00553819i
$646$	−33.3408	+	24.2235i	−1.31178	+	0.953061i
$647$	−8.44268	+	25.9839i	−0.331916	+	1.02153i	0.636305	+	0.771437i	$0.280462\pi$
$647$	−8.44268	+	25.9839i	−0.331916	+	1.02153i	−0.968221	+	0.250095i	$0.919538\pi$
$648$	−24.4803			−0.961678
$649$		0			0
$650$	−26.3865			−1.03496
$651$	−4.31118	+	13.2684i	−0.168968	+	0.520031i
$652$	50.0601	−	36.3708i	1.96051	−	1.42439i
$653$	6.84562	+	4.97364i	0.267890	+	0.194633i	0.713618	−	0.700535i	$-0.247055\pi$
$653$	6.84562	+	4.97364i	0.267890	+	0.194633i	−0.445728	+	0.895168i	$0.647055\pi$
$654$	−0.954460	−	2.93753i	−0.0373224	−	0.114866i
$655$	−0.0394620	−	0.121451i	−0.00154191	−	0.00474550i
$656$	−0.878073	−	0.637957i	−0.0342830	−	0.0249080i
$657$	−0.469236	+	0.340920i	−0.0183066	+	0.0133005i
$658$	−7.04114	+	21.6704i	−0.274492	+	0.844800i
$659$	5.29247			0.206165			0.103083	−	0.994673i	$-0.467129\pi$
$659$	5.29247			0.206165			0.103083	+	0.994673i	$0.467129\pi$
$660$		0			0
$661$	−19.2700			−0.749517			−0.374759	−	0.927122i	$-0.622274\pi$
$661$	−19.2700			−0.749517			−0.374759	+	0.927122i	$0.622274\pi$
$662$	2.71938	−	8.36938i	0.105692	−	0.325285i
$663$	21.8471	−	15.8728i	0.848471	−	0.616450i
$664$	3.56439	+	2.58968i	0.138325	+	0.100499i
$665$	1.11323	+	3.42616i	0.0431691	+	0.132861i
$666$	3.86364	+	11.8911i	0.149713	+	0.460769i
$667$	24.5981	+	17.8716i	0.952443	+	0.691990i
$668$	65.5622	−	47.6337i	2.53668	−	1.84300i
$669$	−1.31363	+	4.04293i	−0.0507878	+	0.156309i
$670$	−28.8158			−1.11325
$671$		0			0
$672$	1.26523			0.0488074
$673$	5.86892	−	18.0627i	0.226230	−	0.696265i	−0.771934	−	0.635702i	$-0.780711\pi$
$673$	5.86892	−	18.0627i	0.226230	−	0.696265i	0.998164	−	0.0605625i	$-0.0192894\pi$
$674$	−12.5942	+	9.15022i	−0.485110	+	0.352453i
$675$	−15.6279	−	11.3543i	−0.601518	−	0.437028i
$676$	−3.49935	−	10.7699i	−0.134590	−	0.414227i
$677$	−10.0189	−	30.8350i	−0.385058	−	1.18509i	−0.936438	−	0.350833i	$-0.885899\pi$
$677$	−10.0189	−	30.8350i	−0.385058	−	1.18509i	0.551380	−	0.834254i	$-0.314101\pi$
$678$	−12.8172	−	9.31222i	−0.492240	−	0.357633i
$679$	14.2201	−	10.3315i	0.545717	−	0.396487i
$680$	−10.6800	+	32.8695i	−0.409558	+	1.26049i
$681$	−11.8409			−0.453744
$682$		0			0
$683$	15.1260			0.578779			0.289389	−	0.957211i	$-0.406548\pi$
$683$	15.1260			0.578779			0.289389	+	0.957211i	$0.406548\pi$
$684$	3.25893	−	10.0300i	0.124608	−	0.383505i
$685$	4.64740	−	3.37654i	0.177568	−	0.129011i
$686$	1.96628	+	1.42858i	0.0750728	+	0.0545436i
$687$	5.80944	+	17.8796i	0.221644	+	0.682150i
$688$	0.141376	+	0.435110i	0.00538990	+	0.0165884i
$689$	−11.1901	−	8.13010i	−0.426310	−	0.309732i
$690$	−24.0061	+	17.4415i	−0.913897	+	0.663985i
$691$	−9.70646	+	29.8734i	−0.369251	+	1.13644i	0.578025	+	0.816019i	$0.303824\pi$
$691$	−9.70646	+	29.8734i	−0.369251	+	1.13644i	−0.947276	+	0.320419i	$0.896176\pi$
$692$	84.2192			3.20153
$693$		0			0
$694$	42.4357			1.61084
$695$	1.48782	−	4.57903i	0.0564361	−	0.173692i
$696$	24.1773	−	17.5658i	0.916437	−	0.665830i
$697$	1.50725	+	1.09508i	0.0570911	+	0.0414791i
$698$	16.2414	+	49.9859i	0.614746	+	1.89199i
$699$	5.68515	+	17.4971i	0.215032	+	0.661801i
$700$	−10.7972	−	7.84462i	−0.408095	−	0.296499i
$701$	−12.9966	+	9.44259i	−0.490875	+	0.356642i	−0.805521	−	0.592568i	$-0.798114\pi$
$701$	−12.9966	+	9.44259i	−0.490875	+	0.356642i	0.314646	+	0.949209i	$0.398114\pi$
$702$	−13.4993	+	41.5464i	−0.509497	+	1.56807i
$703$	15.6133			0.588865
$704$		0			0
$705$	16.9232			0.637366
$706$	3.30575	−	10.1741i	0.124414	−	0.382906i
$707$	10.0934	−	7.33330i	0.379602	−	0.275797i
$708$	31.4928	+	22.8809i	1.18357	+	0.859916i
$709$	12.2673	+	37.7548i	0.460708	+	1.41791i	0.864301	+	0.502974i	$0.167761\pi$
$709$	12.2673	+	37.7548i	0.460708	+	1.41791i	−0.403594	+	0.914938i	$0.632239\pi$
$710$	−0.110231	−	0.339257i	−0.00413690	−	0.0127321i
$711$	−6.50738	−	4.72789i	−0.244046	−	0.177310i
$712$	−37.7057	+	27.3948i	−1.41308	+	1.02666i
$713$	20.3306	−	62.5713i	0.761389	−	2.34331i
$714$	20.6503			0.772819
$715$		0			0
$716$	18.6822			0.698187
$717$	2.20759	−	6.79426i	0.0824439	−	0.253736i
$718$	−21.0033	+	15.2598i	−0.783834	+	0.569489i
$719$	7.97885	+	5.79698i	0.297561	+	0.216191i	0.726541	−	0.687123i	$-0.241127\pi$
$719$	7.97885	+	5.79698i	0.297561	+	0.216191i	−0.428980	+	0.903314i	$0.641127\pi$
$720$	−1.26587	−	3.89596i	−0.0471763	−	0.145194i
$721$	−2.53951	−	7.81581i	−0.0945763	−	0.291076i
$722$	21.2510	+	15.4397i	0.790879	+	0.574607i
$723$	−3.04793	+	2.21445i	−0.113354	+	0.0823564i
$724$	−9.48121	+	29.1802i	−0.352366	+	1.08447i
$725$	15.3559			0.570305
$726$		0			0
$727$	−31.5764			−1.17111			−0.585553	−	0.810634i	$-0.699122\pi$
$727$	−31.5764			−1.17111			−0.585553	+	0.810634i	$0.699122\pi$
$728$	−4.55239	+	14.0108i	−0.168723	+	0.519275i
$729$	−23.7145	+	17.2296i	−0.878313	+	0.638132i
$730$	1.52209	+	1.10586i	0.0563351	+	0.0409299i
$731$	−0.242678	−	0.746885i	−0.00897576	−	0.0276245i
$732$	4.24616	+	13.0683i	0.156943	+	0.483019i
$733$	33.4064	+	24.2712i	1.23389	+	0.896476i	0.997176	−	0.0751027i	$-0.0239285\pi$
$733$	33.4064	+	24.2712i	1.23389	+	0.896476i	0.236717	+	0.971579i	$0.423928\pi$
$734$	−20.0889	+	14.5955i	−0.741496	+	0.538729i
$735$	0.557818	−	1.71679i	0.0205754	−	0.0633246i
$736$	−5.96659			−0.219931
$737$		0			0
$738$	−0.720812			−0.0265335
$739$	−10.9422	+	33.6765i	−0.402514	+	1.23881i	0.520440	+	0.853898i	$0.325768\pi$
$739$	−10.9422	+	33.6765i	−0.402514	+	1.23881i	−0.922954	+	0.384911i	$0.874232\pi$
$740$	21.7021	−	15.7675i	0.797785	−	0.579625i
$741$	10.5552	+	7.66883i	0.387756	+	0.281722i
$742$	−3.26852	−	10.0595i	−0.119991	−	0.369294i
$743$	1.24351	+	3.82713i	0.0456200	+	0.140404i	0.971272	−	0.237972i	$-0.0764827\pi$
$743$	1.24351	+	3.82713i	0.0456200	+	0.140404i	−0.925652	+	0.378376i	$0.876483\pi$
$744$	−52.3156	−	38.0095i	−1.91798	−	1.39350i
$745$	−4.96117	+	3.60450i	−0.181763	+	0.132059i
$746$	20.9431	−	64.4562i	0.766781	−	2.35991i
$747$	0.896402			0.0327976
$748$		0			0
$749$	12.1885			0.445359
$750$	−11.4098	+	35.1157i	−0.416626	+	1.28224i
$751$	−19.7554	+	14.3531i	−0.720884	+	0.523753i	−0.886666	−	0.462410i	$-0.846985\pi$
$751$	−19.7554	+	14.3531i	−0.720884	+	0.523753i	0.165783	+	0.986162i	$0.446985\pi$
$752$	−26.1761	−	19.0181i	−0.954544	−	0.693517i
$753$	−11.6218	−	35.7683i	−0.423523	−	1.30347i
$754$	−10.7311	−	33.0268i	−0.390803	−	1.20277i
$755$	−17.2837	−	12.5573i	−0.629019	−	0.457009i
$756$	−17.8754	+	12.9873i	−0.650123	+	0.472342i
$757$	−0.407046	+	1.25276i	−0.0147943	+	0.0455323i	−0.958181	−	0.286162i	$-0.907620\pi$
$757$	−0.407046	+	1.25276i	−0.0147943	+	0.0455323i	0.943387	+	0.331695i	$0.107620\pi$
$758$	2.79023			0.101346
$759$		0			0
$760$	−16.6979			−0.605696
$761$	2.23853	−	6.88949i	0.0811467	−	0.249744i	−0.902250	−	0.431214i	$-0.858085\pi$
$761$	2.23853	−	6.88949i	0.0811467	−	0.249744i	0.983397	+	0.181470i	$0.0580855\pi$
$762$	−22.6387	+	16.4480i	−0.820115	+	0.595848i
$763$	−0.716860	−	0.520829i	−0.0259521	−	0.0188553i
$764$	−10.6613	−	32.8122i	−0.385714	−	1.18710i
$765$	2.17293	+	6.68758i	0.0785623	+	0.241790i
$766$	39.2304	+	28.5026i	1.41745	+	1.02984i
$767$	17.8625	−	12.9779i	0.644977	−	0.468603i
$768$	−13.7645	+	42.3629i	−0.496685	+	1.52864i
$769$	−44.3139			−1.59800			−0.798999	−	0.601332i	$-0.794637\pi$
$769$	−44.3139			−1.59800			−0.798999	+	0.601332i	$0.794637\pi$
$770$		0			0
$771$	42.9570			1.54706
$772$	−30.9112	+	95.1348i	−1.11252	+	3.42397i
$773$	−15.4166	+	11.2008i	−0.554496	+	0.402865i	−0.829440	−	0.558595i	$-0.811341\pi$
$773$	−15.4166	+	11.2008i	−0.554496	+	0.402865i	0.274944	+	0.961460i	$0.411341\pi$
$774$	0.245810	+	0.178591i	0.00883546	+	0.00641934i
$775$	−10.2679	−	31.6014i	−0.368835	−	1.13516i
$776$	25.1761	+	77.4839i	0.903768	+	2.78151i
$777$	−6.32937	−	4.59856i	−0.227065	−	0.164972i
$778$	−5.11232	+	3.71432i	−0.183286	+	0.133165i
$779$	−0.278153	+	0.856068i	−0.00996587	+	0.0306718i
$780$	22.4161			0.802626
$781$		0			0
$782$	−97.3828			−3.48240
$783$	7.85604	−	24.1784i	0.280752	−	0.864066i
$784$	−2.79210	+	2.02858i	−0.0997179	+	0.0724493i
$785$	−2.28581	−	1.66074i	−0.0815840	−	0.0592742i
$786$	−0.109290	−	0.336359i	−0.00389823	−	0.0119975i
$787$	−9.72168	−	29.9203i	−0.346540	−	1.06654i	−0.960754	−	0.277402i	$-0.910527\pi$
$787$	−9.72168	−	29.9203i	−0.346540	−	1.06654i	0.614213	−	0.789140i	$-0.289473\pi$
$788$	−35.3949	−	25.7159i	−1.26089	−	0.916090i
$789$	3.87201	−	2.81318i	0.137847	−	0.100152i
$790$	−8.06270	+	24.8144i	−0.286858	+	0.882858i
$791$	−4.54502			−0.161602
$792$		0			0
$793$	7.79370			0.276763
$794$	6.58850	−	20.2773i	0.233817	−	0.719615i
$795$	−6.35549	+	4.61753i	−0.225406	+	0.163767i
$796$	38.7220	+	28.1332i	1.37247	+	0.997155i
$797$	−3.87670	−	11.9313i	−0.137320	−	0.422627i	0.858624	−	0.512606i	$-0.171320\pi$
$797$	−3.87670	−	11.9313i	−0.137320	−	0.422627i	−0.995944	+	0.0899793i	$0.971320\pi$
$798$	3.08307	+	9.48872i	0.109140	+	0.335897i
$799$	44.9324	+	32.6453i	1.58959	+	1.15491i
$800$	−2.43790	+	1.77123i	−0.0861926	+	0.0626226i
$801$	−2.93027	+	9.01844i	−0.103536	+	0.318651i
$802$	68.9118			2.43336
$803$		0			0
$804$	−52.7850			−1.86159
$805$	−2.63056	+	8.09602i	−0.0927150	+	0.285347i
$806$	−60.7915	+	44.1676i	−2.14129	+	1.55574i
$807$	2.01406	+	1.46330i	0.0708982	+	0.0515106i
$808$	17.8700	+	54.9981i	0.628663	+	1.93482i
$809$	1.66259	+	5.11691i	0.0584534	+	0.179901i	0.976020	−	0.217681i	$-0.0698493\pi$
$809$	1.66259	+	5.11691i	0.0584534	+	0.179901i	−0.917567	+	0.397582i	$0.869849\pi$
$810$	13.0707	+	9.49645i	0.459259	+	0.333671i
$811$	11.0835	−	8.05262i	0.389194	−	0.282766i	−0.375931	−	0.926647i	$-0.622677\pi$
$811$	11.0835	−	8.05262i	0.389194	−	0.282766i	0.765125	+	0.643882i	$0.222677\pi$
$812$	5.42768	−	16.7047i	0.190474	−	0.586219i
$813$	3.55103			0.124540
$814$		0			0
$815$	−19.9333			−0.698231
$816$	−9.06141	+	27.8882i	−0.317213	+	0.976281i
$817$	0.306958	−	0.223018i	0.0107391	−	0.00780242i
$818$	39.1398	+	28.4367i	1.36849	+	0.994266i
$819$	0.926221	+	2.85061i	0.0323648	+	0.0996085i
$820$	0.477897	+	1.47082i	0.0166889	+	0.0513631i
$821$	−7.46816	−	5.42594i	−0.260641	−	0.189367i	0.449789	−	0.893135i	$-0.351499\pi$
$821$	−7.46816	−	5.42594i	−0.260641	−	0.189367i	−0.710429	+	0.703768i	$0.751499\pi$
$822$	12.8710	−	9.35129i	0.448926	−	0.326164i
$823$	−3.84500	+	11.8337i	−0.134028	+	0.412496i	−0.995438	−	0.0954150i	$-0.969582\pi$
$823$	−3.84500	+	11.8337i	−0.134028	+	0.412496i	0.861409	+	0.507911i	$0.169582\pi$
$824$	38.0915			1.32698
$825$		0			0
$826$	16.8840			0.587469
$827$	1.38559	−	4.26441i	0.0481817	−	0.148288i	−0.924071	−	0.382221i	$-0.875159\pi$
$827$	1.38559	−	4.26441i	0.0481817	−	0.148288i	0.972253	+	0.233932i	$0.0751595\pi$
$828$	20.1611	−	14.6479i	0.700648	−	0.509051i
$829$	29.8346	+	21.6761i	1.03620	+	0.752842i	0.969540	−	0.244934i	$-0.0787664\pi$
$829$	29.8346	+	21.6761i	1.03620	+	0.752842i	0.0666578	+	0.997776i	$0.478766\pi$
$830$	−0.898534	−	2.76540i	−0.0311886	−	0.0959886i
$831$	−2.28498	−	7.03244i	−0.0792650	−	0.243953i
$832$	23.2615	+	16.9005i	0.806447	+	0.585918i
$833$	4.79276	−	3.48215i	0.166059	−	0.120649i
$834$	4.12050	−	12.6816i	0.142681	−	0.439127i
$835$	−26.1060			−0.903435
$836$		0			0
$837$	−55.0105			−1.90144
$838$	−23.2042	+	71.4153i	−0.801577	+	2.46700i
$839$	−7.41389	+	5.38651i	−0.255956	+	0.185963i	−0.708362	−	0.705849i	$-0.750566\pi$
$839$	−7.41389	+	5.38651i	−0.255956	+	0.185963i	0.452406	+	0.891812i	$0.350566\pi$
$840$	6.76906	+	4.91801i	0.233555	+	0.169687i
$841$	−2.71643	−	8.36030i	−0.0936699	−	0.288286i
$842$	−18.1703	−	55.9224i	−0.626189	−	1.92721i
$843$	−26.1885	−	19.0271i	−0.901980	−	0.655326i
$844$	−45.0859	+	32.7569i	−1.55192	+	1.12754i
$845$	−1.12728	+	3.46941i	−0.0387796	+	0.119351i
$846$	−21.4880			−0.738774
$847$		0			0
$848$	15.0195			0.515771
$849$	3.76164	−	11.5771i	0.129099	−	0.397326i
$850$	−39.7898	+	28.9090i	−1.36478	+	0.991570i
$851$	29.8480	+	21.6859i	1.02318	+	0.743382i
$852$	−0.201923	−	0.621454i	−0.00691775	−	0.0212907i
$853$	−2.01494	−	6.20135i	−0.0689903	−	0.212330i	0.910617	−	0.413251i	$-0.135607\pi$
$853$	−2.01494	−	6.20135i	−0.0689903	−	0.212330i	−0.979608	+	0.200921i	$0.935607\pi$
$854$	4.82162	+	3.50311i	0.164992	+	0.119874i
$855$	−2.74849	+	1.99690i	−0.0939965	+	0.0682924i
$856$	−17.4580	+	53.7301i	−0.596701	+	1.83646i
$857$	−48.0736			−1.64216			−0.821082	−	0.570810i	$-0.806629\pi$
$857$	−48.0736			−1.64216			−0.821082	+	0.570810i	$0.806629\pi$
$858$		0			0
$859$	−0.316298			−0.0107920			−0.00539598	−	0.999985i	$-0.501718\pi$
$859$	−0.316298			−0.0107920			−0.00539598	+	0.999985i	$0.501718\pi$
$860$	0.201444	−	0.619981i	0.00686918	−	0.0211412i
$861$	0.364895	−	0.265112i	0.0124356	−	0.00903499i
$862$	38.1459	+	27.7146i	1.29925	+	0.943963i
$863$	1.12078	+	3.44942i	0.0381519	+	0.117419i	0.968319	−	0.249718i	$-0.0803379\pi$
$863$	1.12078	+	3.44942i	0.0381519	+	0.117419i	−0.930167	+	0.367137i	$0.880338\pi$
$864$	1.54165	+	4.74471i	0.0524480	+	0.161418i
$865$	−21.9489	−	15.9468i	−0.746285	−	0.542207i
$866$	42.0542	−	30.5542i	1.42906	−	1.03827i
$867$	8.02000	−	24.6830i	0.272374	−	0.838280i
$868$	−38.0064			−1.29002
$869$		0			0
$870$	−19.7231			−0.668675
$871$	−9.25174	+	28.4739i	−0.313483	+	0.964802i
$872$	3.32273	−	2.41410i	0.112522	−	0.0817519i
$873$	13.4103	+	9.74315i	0.453870	+	0.329756i
$874$	−14.5392	−	44.7469i	−0.491794	−	1.51359i
$875$	3.27325	+	10.0740i	0.110656	+	0.340564i
$876$	2.78818	+	2.02573i	0.0942039	+	0.0684432i
$877$	21.6069	−	15.6983i	0.729614	−	0.530095i	−0.159828	−	0.987145i	$-0.551094\pi$
$877$	21.6069	−	15.6983i	0.729614	−	0.530095i	0.889441	+	0.457050i	$0.151094\pi$
$878$	23.8320	−	73.3474i	0.804291	−	2.47535i
$879$	−35.3189			−1.19128
$880$		0			0
$881$	2.91937			0.0983560			0.0491780	−	0.998790i	$-0.484340\pi$
$881$	2.91937			0.0983560			0.0491780	+	0.998790i	$0.484340\pi$
$882$	−0.708281	+	2.17986i	−0.0238491	+	0.0733998i
$883$	36.5331	−	26.5429i	1.22944	−	0.893238i	0.232589	−	0.972575i	$-0.425280\pi$
$883$	36.5331	−	26.5429i	1.22944	−	0.893238i	0.996848	+	0.0793369i	$0.0252803\pi$
$884$	59.5164	+	43.2412i	2.00175	+	1.45436i
$885$	−3.87508	−	11.9263i	−0.130259	−	0.400897i
$886$	−1.25133	−	3.85120i	−0.0420392	−	0.129383i
$887$	−19.4365	−	14.1215i	−0.652614	−	0.474152i	0.211546	−	0.977368i	$-0.432150\pi$
$887$	−19.4365	−	14.1215i	−0.652614	−	0.474152i	−0.864161	+	0.503216i	$0.832150\pi$
$888$	29.3373	−	21.3148i	0.984497	−	0.715279i
$889$	−2.48072	+	7.63488i	−0.0832008	+	0.256066i
$890$	30.7592			1.03105
$891$		0			0
$892$	−11.5806			−0.387749
$893$	−8.29199	+	25.5201i	−0.277481	+	0.853998i
$894$	−13.7399	+	9.98264i	−0.459532	+	0.333870i
$895$	−4.86889	−	3.53746i	−0.162749	−	0.118244i
$896$	6.24921	+	19.2331i	0.208772	+	0.642533i
$897$	9.52702	+	29.3212i	0.318098	+	0.979005i
$898$	33.7920	+	24.5513i	1.12765	+	0.819289i
$899$	35.3783	−	25.7038i	1.17993	−	0.857271i
$900$	3.88930	−	11.9700i	0.129643	−	0.399001i
$901$	−25.7816			−0.858909
$902$		0			0
$903$	−0.190121			−0.00632684
$904$	6.50996	−	20.0356i	0.216518	−	0.666374i
$905$	7.99619	−	5.80957i	0.265802	−	0.193117i
$906$	−47.8671	−	34.7775i	−1.59028	−	1.15540i
$907$	−4.95260	−	15.2425i	−0.164448	−	0.506120i	0.834547	−	0.550937i	$-0.185730\pi$
$907$	−4.95260	−	15.2425i	−0.164448	−	0.506120i	−0.998995	+	0.0448168i	$0.985730\pi$
$908$	−9.96803	−	30.6784i	−0.330801	−	1.01810i
$909$	9.51862	+	6.91568i	0.315713	+	0.229379i
$910$	7.86574	−	5.71479i	0.260747	−	0.189444i
$911$	−5.06922	+	15.6014i	−0.167951	+	0.516899i	−0.999242	−	0.0389385i	$-0.987602\pi$
$911$	−5.06922	+	15.6014i	−0.167951	+	0.516899i	0.831291	+	0.555838i	$0.187602\pi$
$912$	−14.1673			−0.469127
$913$		0			0
$914$	−24.8408			−0.821660
$915$	1.36786	−	4.20983i	0.0452199	−	0.139173i
$916$	−41.4336	+	30.1032i	−1.36900	+	0.994639i
$917$	−0.0820834	−	0.0596371i	−0.00271063	−	0.00196939i
$918$	25.1618	+	77.4401i	0.830464	+	2.55590i
$919$	−9.98747	−	30.7383i	−0.329456	−	1.01396i	−0.969389	−	0.245531i	$-0.921038\pi$
$919$	−9.98747	−	30.7383i	−0.329456	−	1.01396i	0.639933	−	0.768431i	$-0.278962\pi$
$920$	−31.9215	−	23.1923i	−1.05242	−	0.764629i
$921$	5.33030	−	3.87269i	0.175639	−	0.127609i
$922$	16.6102	−	51.1210i	0.547029	−	1.68358i
$923$	−0.370623			−0.0121992
$924$		0			0
$925$	18.6333			0.612659
$926$	−22.8107	+	70.2042i	−0.749607	+	2.30705i
$927$	6.26991	−	4.55535i	0.205931	−	0.149617i
$928$	−3.20844	−	2.33107i	−0.105322	−	0.0765211i
$929$	−2.53249	−	7.79420i	−0.0830883	−	0.255720i	0.900878	−	0.434071i	$-0.142923\pi$
$929$	−2.53249	−	7.79420i	−0.0830883	−	0.255720i	−0.983967	+	0.178352i	$0.942923\pi$
$930$	13.1881	+	40.5887i	0.432454	+	1.33096i
$931$	2.31558	+	1.68237i	0.0758902	+	0.0551374i
$932$	−40.5471	+	29.4592i	−1.32817	+	0.964969i
$933$	−0.979784	+	3.01546i	−0.0320767	+	0.0987219i
$934$	61.2253			2.00335
$935$		0			0
$936$	−13.8929			−0.454103
$937$	−10.5490	+	32.4666i	−0.344622	+	1.06064i	0.617164	+	0.786835i	$0.288282\pi$
$937$	−10.5490	+	32.4666i	−0.344622	+	1.06064i	−0.961786	+	0.273803i	$0.911718\pi$
$938$	−18.5221	+	13.4571i	−0.604767	+	0.439389i
$939$	11.2541	+	8.17655i	0.367262	+	0.266831i
$940$	14.2465	+	43.8463i	0.464670	+	1.43011i
$941$	−0.302642	−	0.931437i	−0.00986585	−	0.0303640i	0.946002	−	0.324160i	$-0.105081\pi$
$941$	−0.302642	−	0.931437i	−0.00986585	−	0.0303640i	−0.955868	+	0.293796i	$0.905081\pi$
$942$	−6.33053	−	4.59940i	−0.206260	−	0.149856i
$943$	−1.72077	+	1.25022i	−0.0560361	+	0.0407126i
$944$	−7.40874	+	22.8017i	−0.241134	+	0.742134i
$945$	7.11775			0.231540
$946$		0			0
$947$	0.935599			0.0304029			0.0152014	−	0.999884i	$-0.495161\pi$
$947$	0.935599			0.0304029			0.0152014	+	0.999884i	$0.495161\pi$
$948$	−14.7693	+	45.4553i	−0.479686	+	1.47632i
$949$	1.58143	−	1.14898i	0.0513355	−	0.0372974i
$950$	−19.2241	−	13.9671i	−0.623712	−	0.453153i
$951$	2.86099	+	8.80523i	0.0927740	+	0.285529i
$952$	8.48538	+	26.1153i	0.275013	+	0.846402i
$953$	13.5365	+	9.83486i	0.438491	+	0.318582i	0.785035	−	0.619451i	$-0.212645\pi$
$953$	13.5365	+	9.83486i	0.438491	+	0.318582i	−0.346544	+	0.938034i	$0.612645\pi$
$954$	8.06978	−	5.86304i	0.261269	−	0.189823i
$955$	−3.43444	+	10.5701i	−0.111136	+	0.342041i
$956$	19.4616			0.629434
$957$		0			0
$958$	51.5353			1.66503
$959$	1.41038	−	4.34071i	0.0455436	−	0.140169i
$960$	13.2115	−	9.59870i	0.426399	−	0.309797i
$961$	−51.4733	−	37.3975i	−1.66043	−	1.20637i
$962$	−13.0214	−	40.0757i	−0.419826	−	1.29209i
$963$	3.55197	+	10.9318i	0.114461	+	0.352274i
$964$	−8.30326	−	6.03267i	−0.267430	−	0.194299i
$965$	26.0696	−	18.9407i	0.839210	−	0.609722i
$966$	−7.28531	+	22.4219i	−0.234401	+	0.721412i
$967$	−36.4439			−1.17196			−0.585978	−	0.810327i	$-0.699290\pi$
$967$	−36.4439			−1.17196			−0.585978	+	0.810327i	$0.699290\pi$
$968$		0			0
$969$	24.3188			0.781233
$970$	16.6155	−	51.1372i	0.533491	−	1.64192i
$971$	26.8931	−	19.5390i	0.863042	−	0.627036i	−0.0656691	−	0.997841i	$-0.520918\pi$
$971$	26.8931	−	19.5390i	0.863042	−	0.627036i	0.928711	+	0.370805i	$0.120918\pi$
$972$	−29.6832	−	21.5661i	−0.952088	−	0.691732i
$973$	−1.18209	−	3.63810i	−0.0378961	−	0.116632i
$974$	−12.6325	−	38.8788i	−0.404771	−	1.24576i
$975$	12.5969	+	9.15219i	0.403424	+	0.293105i
$976$	−6.84667	+	4.97439i	−0.219156	+	0.159226i
$977$	6.97347	−	21.4621i	0.223101	−	0.686634i	−0.775378	−	0.631498i	$-0.782441\pi$
$977$	6.97347	−	21.4621i	0.223101	−	0.686634i	0.998479	−	0.0551366i	$-0.0175594\pi$
$978$	−55.2050			−1.76526
$979$		0			0
$980$	4.91760			0.157087
$981$	0.258223	−	0.794729i	0.00824443	−	0.0253737i
$982$	9.51294	−	6.91155i	0.303570	−	0.220557i
$983$	12.2200	+	8.87836i	0.389758	+	0.283176i	0.765356	−	0.643607i	$-0.222563\pi$
$983$	12.2200	+	8.87836i	0.389758	+	0.283176i	−0.375598	+	0.926783i	$0.622563\pi$
$984$	0.646031	+	1.98828i	0.0205947	+	0.0633840i
$985$	4.35521	+	13.4040i	0.138769	+	0.427086i
$986$	−52.3661	−	38.0462i	−1.66768	−	1.21164i
$987$	10.8778	−	7.90322i	0.346246	−	0.251562i
$988$	−10.9834	+	33.8033i	−0.349428	+	1.07543i
$989$	0.896574			0.0285094
$990$		0			0
$991$	−55.1534			−1.75201			−0.876003	−	0.482305i	$-0.839800\pi$
$991$	−55.1534			−1.75201			−0.876003	+	0.482305i	$0.839800\pi$
$992$	−2.65181	+	8.16145i	−0.0841952	+	0.259126i
$993$	−4.20116	+	3.05232i	−0.133320	+	0.0968624i
$994$	−0.229288	−	0.166587i	−0.00727257	−	0.00528383i
$995$	−4.76461	−	14.6639i	−0.151048	−	0.464878i
$996$	−1.64594	−	5.06570i	−0.0521537	−	0.160513i
$997$	40.2120	+	29.2157i	1.27353	+	0.925272i	0.999337	−	0.0364038i	$-0.0115902\pi$
$997$	40.2120	+	29.2157i	1.27353	+	0.925272i	0.274190	+	0.961676i	$0.411590\pi$
$998$	−60.1358	+	43.6912i	−1.90356	+	1.38302i
$999$	9.53274	−	29.3387i	0.301602	−	0.928237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.x.372.4		16
11.2	odd	10		847.2.f.w.729.4		16
11.3	even	5		847.2.f.v.323.1		16
11.4	even	5		847.2.a.o.1.8		8
11.5	even	5	inner	847.2.f.x.148.4		16
11.6	odd	10		77.2.f.b.71.1	yes	16
11.7	odd	10		847.2.a.p.1.1		8
11.8	odd	10		847.2.f.w.323.4		16
11.9	even	5		847.2.f.v.729.1		16
11.10	odd	2		77.2.f.b.64.1	✓	16
33.17	even	10		693.2.m.i.379.4		16
33.26	odd	10		7623.2.a.cw.1.1		8
33.29	even	10		7623.2.a.ct.1.8		8
33.32	even	2		693.2.m.i.64.4		16
77.6	even	10		539.2.f.e.148.1		16
77.10	even	6		539.2.q.f.471.1		32
77.17	even	30		539.2.q.f.324.4		32
77.32	odd	6		539.2.q.g.471.1		32
77.39	odd	30		539.2.q.g.324.4		32
77.48	odd	10		5929.2.a.bs.1.8		8
77.54	even	6		539.2.q.f.361.4		32
77.61	even	30		539.2.q.f.214.1		32
77.62	even	10		5929.2.a.bt.1.1		8
77.65	odd	6		539.2.q.g.361.4		32
77.72	odd	30		539.2.q.g.214.1		32
77.76	even	2		539.2.f.e.295.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.1	✓	16	11.10	odd	2
77.2.f.b.71.1	yes	16	11.6	odd	10
539.2.f.e.148.1		16	77.6	even	10
539.2.f.e.295.1		16	77.76	even	2
539.2.q.f.214.1		32	77.61	even	30
539.2.q.f.324.4		32	77.17	even	30
539.2.q.f.361.4		32	77.54	even	6
539.2.q.f.471.1		32	77.10	even	6
539.2.q.g.214.1		32	77.72	odd	30
539.2.q.g.324.4		32	77.39	odd	30
539.2.q.g.361.4		32	77.65	odd	6
539.2.q.g.471.1		32	77.32	odd	6
693.2.m.i.64.4		16	33.32	even	2
693.2.m.i.379.4		16	33.17	even	10
847.2.a.o.1.8		8	11.4	even	5
847.2.a.p.1.1		8	11.7	odd	10
847.2.f.v.323.1		16	11.3	even	5
847.2.f.v.729.1		16	11.9	even	5
847.2.f.w.323.4		16	11.8	odd	10
847.2.f.w.729.4		16	11.2	odd	10
847.2.f.x.148.4		16	11.5	even	5	inner
847.2.f.x.372.4		16	1.1	even	1	trivial
5929.2.a.bs.1.8		8	77.48	odd	10
5929.2.a.bt.1.1		8	77.62	even	10
7623.2.a.ct.1.8		8	33.29	even	10
7623.2.a.cw.1.1		8	33.26	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.751051 - 2.31150i) q^{2} +(-1.16030 + 0.843005i) q^{3} +(-3.16091 - 2.29654i) q^{4} +(0.388938 + 1.19703i) q^{5} +(1.07716 + 3.31516i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-3.74989 + 2.72445i) q^{8} +(-0.291419 + 0.896896i) q^{9} +O(q^{10})\)	\(q+(0.751051 - 2.31150i) q^{2} +(-1.16030 + 0.843005i) q^{3} +(-3.16091 - 2.29654i) q^{4} +(0.388938 + 1.19703i) q^{5} +(1.07716 + 3.31516i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-3.74989 + 2.72445i) q^{8} +(-0.291419 + 0.896896i) q^{9} +3.05904 q^{10} +5.60359 q^{12} +(0.982152 - 3.02275i) q^{13} +(1.96628 - 1.42858i) q^{14} +(-1.46039 - 1.06103i) q^{15} +(1.06649 + 3.28231i) q^{16} +(-1.83067 - 5.63423i) q^{17} +(1.85430 + 1.34723i) q^{18} +(2.31558 - 1.68237i) q^{19} +(1.51962 - 4.67691i) q^{20} -1.43421 q^{21} +6.76343 q^{23} +(2.05426 - 6.32235i) q^{24} +(2.76348 - 2.00778i) q^{25} +(-6.24944 - 4.54048i) q^{26} +(-1.74754 - 5.37837i) q^{27} +(-1.20736 - 3.71587i) q^{28} +(3.63693 + 2.64238i) q^{29} +(-3.54940 + 2.57879i) q^{30} +(3.00597 - 9.25141i) q^{31} -0.882184 q^{32} -14.3984 q^{34} +(-0.388938 + 1.19703i) q^{35} +(2.98090 - 2.16575i) q^{36} +(4.41315 + 3.20634i) q^{37} +(-2.14967 - 6.61601i) q^{38} +(1.40861 + 4.33525i) q^{39} +(-4.71972 - 3.42908i) q^{40} +(-0.254423 + 0.184849i) q^{41} +(-1.07716 + 3.31516i) q^{42} +0.132562 q^{43} -1.18696 q^{45} +(5.07968 - 15.6337i) q^{46} +(-7.58458 + 5.51052i) q^{47} +(-4.00445 - 2.90940i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-2.56548 - 7.89572i) q^{50} +(6.87381 + 4.99412i) q^{51} +(-10.0463 + 7.29910i) q^{52} +(1.34482 - 4.13893i) q^{53} -13.7446 q^{54} -4.63512 q^{56} +(-1.26852 + 3.90410i) q^{57} +(8.83939 - 6.42219i) q^{58} +(5.62012 + 4.08326i) q^{59} +(2.17945 + 6.70766i) q^{60} +(0.757757 + 2.33214i) q^{61} +(-19.1270 - 13.8966i) q^{62} +(-0.762946 + 0.554312i) q^{63} +(-2.79554 + 8.60379i) q^{64} +4.00032 q^{65} -9.41987 q^{67} +(-7.15262 + 22.0135i) q^{68} +(-7.84759 + 5.70161i) q^{69} +(2.47482 + 1.79806i) q^{70} +(-0.0360345 - 0.110903i) q^{71} +(-1.35076 - 4.15722i) q^{72} +(0.497571 + 0.361506i) q^{73} +(10.7260 - 7.79286i) q^{74} +(-1.51388 + 4.65925i) q^{75} -11.1830 q^{76} +11.0789 q^{78} +(-2.63569 + 8.11183i) q^{79} +(-3.51423 + 2.55324i) q^{80} +(4.27282 + 3.10438i) q^{81} +(0.236194 + 0.726930i) q^{82} +(-0.293731 - 0.904010i) q^{83} +(4.53340 + 3.29371i) q^{84} +(6.03232 - 4.38274i) q^{85} +(0.0995608 - 0.306417i) q^{86} -6.44746 q^{87} +10.0552 q^{89} +(-0.891464 + 2.74364i) q^{90} +(2.57131 - 1.86816i) q^{91} +(-21.3786 - 15.5325i) q^{92} +(4.31118 + 13.2684i) q^{93} +(7.04114 + 21.6704i) q^{94} +(2.91446 + 2.11748i) q^{95} +(1.02360 - 0.743685i) q^{96} +(5.43159 - 16.7167i) q^{97} +2.43045 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 3 q^{6} + 4 q^{7} + 5 q^{8} - 12 q^{9} - 12 q^{10} + 18 q^{12} + 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} + 5 q^{17} - 11 q^{18} - 19 q^{19} + q^{20} - 8 q^{21} + 32 q^{23} + 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} - 4 q^{28} - 3 q^{29} + 2 q^{30} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} - 11 q^{39} + 10 q^{40} + 10 q^{41} + 3 q^{42} + 8 q^{43} + 70 q^{45} + 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} - 52 q^{50} + 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 2 q^{63} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} + 35 q^{73} + 29 q^{74} + 9 q^{75} - 52 q^{76} - 58 q^{78} - 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} - 5 q^{83} - 8 q^{84} - 6 q^{85} - 52 q^{86} + 72 q^{87} + 74 q^{89} + 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} + 24 q^{94} - 32 q^{95} + 42 q^{96} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 3 * q^6 + 4 * q^7 + 5 * q^8 - 12 * q^9 - 12 * q^10 + 18 * q^12 + 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 + 5 * q^17 - 11 * q^18 - 19 * q^19 + q^20 - 8 * q^21 + 32 * q^23 + 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 - 4 * q^28 - 3 * q^29 + 2 * q^30 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 - 11 * q^39 + 10 * q^40 + 10 * q^41 + 3 * q^42 + 8 * q^43 + 70 * q^45 + 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 - 52 * q^50 + 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 2 * q^63 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 + 35 * q^73 + 29 * q^74 + 9 * q^75 - 52 * q^76 - 58 * q^78 - 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 - 5 * q^83 - 8 * q^84 - 6 * q^85 - 52 * q^86 + 72 * q^87 + 74 * q^89 + 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 + 24 * q^94 - 32 * q^95 + 42 * q^96 + 20 * q^97 - 2 * q^98

Introduction

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