LMFDB - Embedded newform 150.2.h.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(19,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("150.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.h (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Root			$-1.80334 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	150.19
Dual form			150.2.h.b.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.73558 + 1.40988i) q^{5} +(-0.809017 - 0.587785i) q^{6} +2.61995i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.73558 + 1.40988i) q^{5} +(-0.809017 - 0.587785i) q^{6} +2.61995i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.21496 - 1.87720i) q^{10} +(-0.0883198 - 0.271820i) q^{11} +(0.951057 + 0.309017i) q^{12} +(2.66799 + 0.866884i) q^{13} +(-0.809610 - 2.49172i) q^{14} +(-2.16076 - 0.575410i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.81615 + 5.25248i) q^{17} -1.00000i q^{18} +(-0.358647 - 0.260572i) q^{19} +(-0.575410 + 2.16076i) q^{20} +(-2.11959 + 1.53997i) q^{21} +(0.167994 + 0.231224i) q^{22} +(6.20562 - 2.01633i) q^{23} -1.00000 q^{24} +(1.02449 - 4.89392i) q^{25} -2.80530 q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.53997 + 2.11959i) q^{28} +(5.87052 - 4.26518i) q^{29} +(2.23282 - 0.120465i) q^{30} +(-2.93409 - 2.13174i) q^{31} +1.00000i q^{32} +(0.167994 - 0.231224i) q^{33} +(2.00627 - 6.17466i) q^{34} +(-3.69381 - 4.54714i) q^{35} +(0.309017 + 0.951057i) q^{36} +(4.31691 + 1.40265i) q^{37} +(0.421615 + 0.136991i) q^{38} +(0.866884 + 2.66799i) q^{39} +(-0.120465 - 2.23282i) q^{40} +(1.64523 - 5.06349i) q^{41} +(1.53997 - 2.11959i) q^{42} -8.05390i q^{43} +(-0.231224 - 0.167994i) q^{44} +(-0.804549 - 2.08631i) q^{45} +(-5.27882 + 3.83529i) q^{46} +(-5.28799 - 7.27829i) q^{47} +(0.951057 - 0.309017i) q^{48} +0.135854 q^{49} +(0.537954 + 4.97098i) q^{50} -6.49242 q^{51} +(2.66799 - 0.866884i) q^{52} +(8.17947 + 11.2581i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.536520 + 0.347247i) q^{55} +(-2.11959 - 1.53997i) q^{56} -0.443312i q^{57} +(-4.26518 + 5.87052i) q^{58} +(1.15784 - 3.56347i) q^{59} +(-2.08631 + 0.804549i) q^{60} +(4.02308 + 12.3818i) q^{61} +(3.44923 + 1.12072i) q^{62} +(-2.49172 - 0.809610i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-5.85272 + 2.25700i) q^{65} +(-0.0883198 + 0.271820i) q^{66} +(-6.01453 + 8.27829i) q^{67} +6.49242i q^{68} +(5.27882 + 3.83529i) q^{69} +(4.91817 + 3.18314i) q^{70} +(3.89771 - 2.83185i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-11.2098 + 3.64230i) q^{73} -4.53906 q^{74} +(4.56144 - 2.04774i) q^{75} -0.443312 q^{76} +(0.712156 - 0.231394i) q^{77} +(-1.64891 - 2.26953i) q^{78} +(-6.32216 + 4.59332i) q^{79} +(0.804549 + 2.08631i) q^{80} +(-0.809017 - 0.587785i) q^{81} +5.32407i q^{82} +(3.03407 - 4.17604i) q^{83} +(-0.809610 + 2.49172i) q^{84} +(-0.782111 - 14.4964i) q^{85} +(2.48879 + 7.65972i) q^{86} +(6.90121 + 2.24234i) q^{87} +(0.271820 + 0.0883198i) q^{88} +(1.90527 + 5.86383i) q^{89} +(1.40988 + 1.73558i) q^{90} +(-2.27119 + 6.99002i) q^{91} +(3.83529 - 5.27882i) q^{92} -3.62674i q^{93} +(7.27829 + 5.28799i) q^{94} +(0.989836 - 0.0534036i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-3.20367 - 4.40947i) q^{97} +(-0.129205 + 0.0419811i) q^{98} +0.285809 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9} + 2 q^{10} + 2 q^{11} + 20 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 30 q^{17} - 4 q^{20} - 2 q^{21} - 20 q^{22} - 10 q^{23} - 16 q^{24} + 24 q^{25} + 4 q^{26} - 10 q^{29} - 6 q^{30} - 18 q^{31} - 20 q^{33} + 12 q^{34} - 34 q^{35} - 4 q^{36} + 20 q^{37} + 10 q^{38} - 4 q^{39} - 2 q^{40} + 22 q^{41} + 8 q^{44} - 4 q^{45} - 6 q^{46} - 50 q^{47} - 52 q^{49} + 12 q^{50} + 28 q^{51} + 20 q^{52} + 30 q^{53} + 4 q^{54} + 18 q^{55} - 2 q^{56} - 30 q^{58} + 20 q^{59} + 2 q^{60} + 12 q^{61} + 50 q^{62} + 10 q^{63} + 4 q^{64} - 8 q^{65} + 2 q^{66} - 50 q^{67} + 6 q^{69} - 12 q^{70} - 28 q^{71} + 20 q^{73} + 12 q^{74} + 28 q^{75} + 20 q^{76} + 100 q^{77} - 20 q^{79} + 4 q^{80} - 4 q^{81} - 30 q^{83} + 2 q^{84} - 4 q^{85} - 6 q^{86} + 10 q^{87} + 70 q^{89} + 8 q^{90} + 12 q^{91} - 30 q^{92} + 2 q^{94} - 30 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} - 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9 + 2 * q^10 + 2 * q^11 + 20 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 30 * q^17 - 4 * q^20 - 2 * q^21 - 20 * q^22 - 10 * q^23 - 16 * q^24 + 24 * q^25 + 4 * q^26 - 10 * q^29 - 6 * q^30 - 18 * q^31 - 20 * q^33 + 12 * q^34 - 34 * q^35 - 4 * q^36 + 20 * q^37 + 10 * q^38 - 4 * q^39 - 2 * q^40 + 22 * q^41 + 8 * q^44 - 4 * q^45 - 6 * q^46 - 50 * q^47 - 52 * q^49 + 12 * q^50 + 28 * q^51 + 20 * q^52 + 30 * q^53 + 4 * q^54 + 18 * q^55 - 2 * q^56 - 30 * q^58 + 20 * q^59 + 2 * q^60 + 12 * q^61 + 50 * q^62 + 10 * q^63 + 4 * q^64 - 8 * q^65 + 2 * q^66 - 50 * q^67 + 6 * q^69 - 12 * q^70 - 28 * q^71 + 20 * q^73 + 12 * q^74 + 28 * q^75 + 20 * q^76 + 100 * q^77 - 20 * q^79 + 4 * q^80 - 4 * q^81 - 30 * q^83 + 2 * q^84 - 4 * q^85 - 6 * q^86 + 10 * q^87 + 70 * q^89 + 8 * q^90 + 12 * q^91 - 30 * q^92 + 2 * q^94 - 30 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−1.73558	+	1.40988i	−0.776176	+	0.630516i
$5$	−1.73558	+	1.40988i	−0.776176	+	0.630516i
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$			2.61995i			0.990249i	0.868822	+	0.495124i	$0.164877\pi$
$7$			2.61995i			0.990249i	−0.868822	+	0.495124i	$0.835123\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	1.21496	−	1.87720i	0.384204	−	0.593622i
$11$	−0.0883198	−	0.271820i	−0.0266294	−	0.0819569i	0.936859	−	0.349708i	$-0.113719\pi$
$11$	−0.0883198	−	0.271820i	−0.0266294	−	0.0819569i	−0.963488	+	0.267752i	$0.913719\pi$
$12$	0.951057	+	0.309017i	0.274546	+	0.0892055i
$13$	2.66799	+	0.866884i	0.739968	+	0.240430i	0.654659	−	0.755924i	$-0.272812\pi$
$13$	2.66799	+	0.866884i	0.739968	+	0.240430i	0.0853093	+	0.996355i	$0.472812\pi$
$14$	−0.809610	−	2.49172i	−0.216377	−	0.665941i
$15$	−2.16076	−	0.575410i	−0.557907	−	0.148570i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−3.81615	+	5.25248i	−0.925553	+	1.27391i	0.0360165	+	0.999351i	$0.488533\pi$
$17$	−3.81615	+	5.25248i	−0.925553	+	1.27391i	−0.961569	+	0.274563i	$0.911467\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−0.358647	−	0.260572i	−0.0822792	−	0.0597794i	0.545885	−	0.837860i	$-0.316193\pi$
$19$	−0.358647	−	0.260572i	−0.0822792	−	0.0597794i	−0.628164	+	0.778081i	$0.716193\pi$
$20$	−0.575410	+	2.16076i	−0.128666	+	0.483162i
$21$	−2.11959	+	1.53997i	−0.462531	+	0.336049i
$22$	0.167994	+	0.231224i	0.0358165	+	0.0492972i
$23$	6.20562	−	2.01633i	1.29396	−	0.420434i	0.420485	−	0.907299i	$-0.361860\pi$
$23$	6.20562	−	2.01633i	1.29396	−	0.420434i	0.873477	+	0.486866i	$0.161860\pi$
$24$	−1.00000			−0.204124
$25$	1.02449	−	4.89392i	0.204898	−	0.978783i
$26$	−2.80530			−0.550164
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	1.53997	+	2.11959i	0.291027	+	0.400564i
$29$	5.87052	−	4.26518i	1.09013	−	0.792024i	0.110707	−	0.993853i	$-0.464689\pi$
$29$	5.87052	−	4.26518i	1.09013	−	0.792024i	0.979421	+	0.201829i	$0.0646886\pi$
$30$	2.23282	−	0.120465i	0.407655	−	0.0219938i
$31$	−2.93409	−	2.13174i	−0.526979	−	0.382872i	0.292248	−	0.956343i	$-0.405597\pi$
$31$	−2.93409	−	2.13174i	−0.526979	−	0.382872i	−0.819226	+	0.573470i	$0.805597\pi$
$32$			1.00000i			0.176777i
$33$	0.167994	−	0.231224i	0.0292440	−	0.0402510i
$34$	2.00627	−	6.17466i	0.344072	−	1.05895i
$35$	−3.69381	−	4.54714i	−0.624368	−	0.768607i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	4.31691	+	1.40265i	0.709695	+	0.230594i	0.641550	−	0.767082i	$-0.278292\pi$
$37$	4.31691	+	1.40265i	0.709695	+	0.230594i	0.0681453	+	0.997675i	$0.478292\pi$
$38$	0.421615	+	0.136991i	0.0683949	+	0.0222229i
$39$	0.866884	+	2.66799i	0.138813	+	0.427221i
$40$	−0.120465	−	2.23282i	−0.0190472	−	0.353040i
$41$	1.64523	−	5.06349i	0.256941	−	0.790784i	−0.736500	−	0.676438i	$-0.763523\pi$
$41$	1.64523	−	5.06349i	0.256941	−	0.790784i	0.993441	−	0.114346i	$-0.0364774\pi$
$42$	1.53997	−	2.11959i	0.237622	−	0.327059i
$43$		−	8.05390i		−	1.22821i	−0.789225	−	0.614104i	$-0.789517\pi$
$43$		−	8.05390i		−	1.22821i	0.789225	−	0.614104i	$-0.210483\pi$
$44$	−0.231224	−	0.167994i	−0.0348584	−	0.0253261i
$45$	−0.804549	−	2.08631i	−0.119935	−	0.311009i
$46$	−5.27882	+	3.83529i	−0.778319	+	0.565482i
$47$	−5.28799	−	7.27829i	−0.771332	−	1.06165i	−0.996186	−	0.0872549i	$-0.972191\pi$
$47$	−5.28799	−	7.27829i	−0.771332	−	1.06165i	0.224854	−	0.974392i	$-0.427809\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	0.135854			0.0194077
$50$	0.537954	+	4.97098i	0.0760782	+	0.703002i
$51$	−6.49242			−0.909121
$52$	2.66799	−	0.866884i	0.369984	−	0.120215i
$53$	8.17947	+	11.2581i	1.12354	+	1.54642i	0.799797	+	0.600270i	$0.204940\pi$
$53$	8.17947	+	11.2581i	1.12354	+	1.54642i	0.323740	+	0.946146i	$0.395060\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	0.536520	+	0.347247i	0.0723443	+	0.0468227i
$56$	−2.11959	−	1.53997i	−0.283242	−	0.205787i
$57$		−	0.443312i		−	0.0587181i
$58$	−4.26518	+	5.87052i	−0.560046	+	0.770837i
$59$	1.15784	−	3.56347i	0.150738	−	0.463924i	−0.846966	−	0.531647i	$-0.821573\pi$
$59$	1.15784	−	3.56347i	0.150738	−	0.463924i	0.997704	+	0.0677230i	$0.0215734\pi$
$60$	−2.08631	+	0.804549i	−0.269342	+	0.103867i
$61$	4.02308	+	12.3818i	0.515102	+	1.58532i	0.783096	+	0.621901i	$0.213639\pi$
$61$	4.02308	+	12.3818i	0.515102	+	1.58532i	−0.267994	+	0.963421i	$0.586361\pi$
$62$	3.44923	+	1.12072i	0.438053	+	0.142332i
$63$	−2.49172	−	0.809610i	−0.313927	−	0.102001i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−5.85272	+	2.25700i	−0.725941	+	0.279946i
$66$	−0.0883198	+	0.271820i	−0.0108714	+	0.0334588i
$67$	−6.01453	+	8.27829i	−0.734792	+	1.01135i	0.264110	+	0.964493i	$0.414922\pi$
$67$	−6.01453	+	8.27829i	−0.734792	+	1.01135i	−0.998901	+	0.0468612i	$0.985078\pi$
$68$			6.49242i			0.787322i
$69$	5.27882	+	3.83529i	0.635495	+	0.461714i
$70$	4.91817	+	3.18314i	0.587833	+	0.380458i
$71$	3.89771	−	2.83185i	0.462573	−	0.336079i	−0.331967	−	0.943291i	$-0.607712\pi$
$71$	3.89771	−	2.83185i	0.462573	−	0.336079i	0.794540	+	0.607212i	$0.207712\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	−11.2098	+	3.64230i	−1.31201	+	0.426298i	−0.879744	−	0.475447i	$-0.842286\pi$
$73$	−11.2098	+	3.64230i	−1.31201	+	0.426298i	−0.432267	+	0.901745i	$0.642286\pi$
$74$	−4.53906			−0.527655
$75$	4.56144	−	2.04774i	0.526710	−	0.236453i
$76$	−0.443312			−0.0508514
$77$	0.712156	−	0.231394i	0.0811577	−	0.0263698i
$78$	−1.64891	−	2.26953i	−0.186702	−	0.256974i
$79$	−6.32216	+	4.59332i	−0.711299	+	0.516789i	−0.883592	−	0.468257i	$-0.844882\pi$
$79$	−6.32216	+	4.59332i	−0.711299	+	0.516789i	0.172294	+	0.985046i	$0.444882\pi$
$80$	0.804549	+	2.08631i	0.0899513	+	0.233257i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$			5.32407i			0.587945i
$83$	3.03407	−	4.17604i	0.333032	−	0.458380i	−0.609358	−	0.792895i	$-0.708573\pi$
$83$	3.03407	−	4.17604i	0.333032	−	0.458380i	0.942390	+	0.334516i	$0.108573\pi$
$84$	−0.809610	+	2.49172i	−0.0883356	+	0.271869i
$85$	−0.782111	−	14.4964i	−0.0848318	−	1.57236i
$86$	2.48879	+	7.65972i	0.268373	+	0.825968i
$87$	6.90121	+	2.24234i	0.739887	+	0.240404i
$88$	0.271820	+	0.0883198i	0.0289762	+	0.00941492i
$89$	1.90527	+	5.86383i	0.201959	+	0.621565i	0.999825	+	0.0187300i	$0.00596230\pi$
$89$	1.90527	+	5.86383i	0.201959	+	0.621565i	−0.797866	+	0.602835i	$0.794038\pi$
$90$	1.40988	+	1.73558i	0.148614	+	0.182946i
$91$	−2.27119	+	6.99002i	−0.238086	+	0.732753i
$92$	3.83529	−	5.27882i	0.399856	−	0.550355i
$93$		−	3.62674i		−	0.376075i
$94$	7.27829	+	5.28799i	0.750698	+	0.545414i
$95$	0.989836	−	0.0534036i	0.101555	−	0.00547910i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−3.20367	−	4.40947i	−0.325283	−	0.447714i	0.614788	−	0.788692i	$-0.289242\pi$
$97$	−3.20367	−	4.40947i	−0.325283	−	0.447714i	−0.940071	+	0.340979i	$0.889242\pi$
$98$	−0.129205	+	0.0419811i	−0.0130516	+	0.00424073i
$99$	0.285809			0.0287249
$100$	−2.04774	−	4.56144i	−0.204774	−	0.456144i
$101$	10.7765			1.07230			0.536152	−	0.844121i	$-0.319877\pi$
$101$	10.7765			1.07230			0.536152	+	0.844121i	$0.319877\pi$
$102$	6.17466	−	2.00627i	0.611383	−	0.198650i
$103$	−10.5308	−	14.4945i	−1.03763	−	1.42818i	−0.899058	−	0.437829i	$-0.855748\pi$
$103$	−10.5308	−	14.4945i	−1.03763	−	1.42818i	−0.138576	−	0.990352i	$-0.544252\pi$
$104$	−2.26953	+	1.64891i	−0.222546	+	0.161689i
$105$	1.50755	−	5.66110i	0.147122	−	0.552467i
$106$	−11.2581	−	8.17947i	−1.09348	−	0.794461i
$107$			3.81291i			0.368608i	0.982869	+	0.184304i	$0.0590030\pi$
$107$			3.81291i			0.368608i	−0.982869	+	0.184304i	$0.940997\pi$
$108$	−0.587785	+	0.809017i	−0.0565597	+	0.0778477i
$109$	−2.46160	+	7.57602i	−0.235778	+	0.725651i	0.761239	+	0.648472i	$0.224591\pi$
$109$	−2.46160	+	7.57602i	−0.235778	+	0.725651i	−0.997017	+	0.0771796i	$0.975409\pi$
$110$	−0.617566	−	0.164457i	−0.0588826	−	0.0156804i
$111$	1.40265	+	4.31691i	0.133133	+	0.409743i
$112$	2.49172	+	0.809610i	0.235446	+	0.0765009i
$113$	−4.99319	−	1.62239i	−0.469720	−	0.152621i	0.0645865	−	0.997912i	$-0.479427\pi$
$113$	−4.99319	−	1.62239i	−0.469720	−	0.152621i	−0.534306	+	0.845291i	$0.679427\pi$
$114$	0.136991	+	0.421615i	0.0128304	+	0.0394878i
$115$	−7.92759	+	12.2487i	−0.739252	+	1.14219i
$116$	2.24234	−	6.90121i	0.208196	−	0.640761i
$117$	−1.64891	+	2.26953i	−0.152442	+	0.209818i
$118$			3.74685i			0.344926i
$119$	−13.7612	−	9.99813i	−1.26149	−	0.916527i
$120$	1.73558	−	1.40988i	0.158436	−	0.128704i
$121$	8.83310	−	6.41762i	0.803009	−	0.583420i
$122$	−7.65235	−	10.5326i	−0.692811	−	0.953572i
$123$	5.06349	−	1.64523i	0.456560	−	0.148345i
$124$	−3.62674			−0.325691
$125$	5.12173	+	9.93820i	0.458102	+	0.888900i
$126$	2.61995			0.233404
$127$	17.7838	−	5.77832i	1.57806	−	0.512743i	0.616505	−	0.787351i	$-0.288548\pi$
$127$	17.7838	−	5.77832i	1.57806	−	0.512743i	0.961556	+	0.274608i	$0.0885481\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	6.51574	−	4.73397i	0.573679	−	0.416802i
$130$	4.86882	−	3.95512i	0.427024	−	0.346887i
$131$	−3.68219	−	2.67527i	−0.321714	−	0.233739i	0.415192	−	0.909734i	$-0.363714\pi$
$131$	−3.68219	−	2.67527i	−0.321714	−	0.233739i	−0.736907	+	0.675995i	$0.763714\pi$
$132$		−	0.285809i		−	0.0248765i
$133$	0.682687	−	0.939637i	0.0591964	−	0.0814769i
$134$	3.16202	−	9.73171i	0.273157	−	0.840692i
$135$	1.21496	−	1.87720i	0.104567	−	0.161563i
$136$	−2.00627	−	6.17466i	−0.172036	−	0.529473i
$137$	−14.7832	−	4.80334i	−1.26301	−	0.410377i	−0.400444	−	0.916321i	$-0.631144\pi$
$137$	−14.7832	−	4.80334i	−1.26301	−	0.410377i	−0.862566	+	0.505944i	$0.831144\pi$
$138$	−6.20562	−	2.01633i	−0.528258	−	0.171641i
$139$	2.78145	+	8.56041i	0.235919	+	0.726085i	0.996998	+	0.0774254i	$0.0246700\pi$
$139$	2.78145	+	8.56041i	0.235919	+	0.726085i	−0.761079	+	0.648659i	$0.775330\pi$
$140$	−5.66110	−	1.50755i	−0.478450	−	0.127411i
$141$	2.78006	−	8.55614i	0.234123	−	0.720557i
$142$	−2.83185	+	3.89771i	−0.237644	+	0.327089i
$143$		−	0.801778i		−	0.0670481i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	−4.17538	+	15.6793i	−0.346747	+	1.30209i
$146$	9.53565	−	6.92806i	0.789176	−	0.573370i
$147$	0.0798529	+	0.109908i	0.00658615	+	0.00906506i
$148$	4.31691	−	1.40265i	0.354847	−	0.115297i
$149$	7.87441			0.645097			0.322548	−	0.946553i	$-0.395460\pi$
$149$	7.87441			0.645097			0.322548	+	0.946553i	$0.395460\pi$
$150$	−3.70540	+	3.35708i	−0.302545	+	0.274104i
$151$	17.7660			1.44578			0.722888	−	0.690965i	$-0.242814\pi$
$151$	17.7660			1.44578			0.722888	+	0.690965i	$0.242814\pi$
$152$	0.421615	−	0.136991i	0.0341975	−	0.0111114i
$153$	−3.81615	−	5.25248i	−0.308518	−	0.424638i
$154$	−0.605796	+	0.440137i	−0.0488165	+	0.0354672i
$155$	8.09786	−	0.436896i	0.650435	−	0.0350923i
$156$	2.26953	+	1.64891i	0.181708	+	0.132019i
$157$		−	20.1191i		−	1.60568i	−0.596194	−	0.802840i	$-0.703321\pi$
$157$		−	20.1191i		−	1.60568i	0.596194	−	0.802840i	$-0.296679\pi$
$158$	4.59332	−	6.32216i	0.365425	−	0.502964i
$159$	−4.30020	+	13.2347i	−0.341028	+	1.04958i
$160$	−1.40988	−	1.73558i	−0.111461	−	0.137210i
$161$	5.28269	+	16.2584i	0.416334	+	1.28134i
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	−2.01084	−	0.653363i	−0.157501	−	0.0511753i	0.229205	−	0.973378i	$-0.426387\pi$
$163$	−2.01084	−	0.653363i	−0.157501	−	0.0511753i	−0.386707	+	0.922203i	$0.626387\pi$
$164$	−1.64523	−	5.06349i	−0.128471	−	0.395392i
$165$	0.0344300	+	0.638160i	0.00268037	+	0.0496807i
$166$	−1.59510	+	4.90923i	−0.123804	+	0.381030i
$167$	−11.4476	+	15.7563i	−0.885844	+	1.21926i	0.0889243	+	0.996038i	$0.471657\pi$
$167$	−11.4476	+	15.7563i	−0.885844	+	1.21926i	−0.974768	+	0.223221i	$0.928343\pi$
$168$		−	2.61995i		−	0.202134i
$169$	−4.15052	−	3.01553i	−0.319270	−	0.231964i
$170$	5.22347	+	13.5452i	0.400622	+	1.03887i
$171$	0.358647	−	0.260572i	0.0274264	−	0.0199265i
$172$	−4.73397	−	6.51574i	−0.360961	−	0.496821i
$173$	−3.14874	+	1.02309i	−0.239394	+	0.0777838i	−0.426257	−	0.904602i	$-0.640168\pi$
$173$	−3.14874	+	1.02309i	−0.239394	+	0.0777838i	0.186863	+	0.982386i	$0.440168\pi$
$174$	−7.25636			−0.550103
$175$	12.8218	+	2.68412i	0.969239	+	0.202900i
$176$	−0.285809			−0.0215437
$177$	3.56347	−	1.15784i	0.267847	−	0.0870286i
$178$	−3.62405	−	4.98807i	−0.271634	−	0.373872i
$179$	−10.0806	+	7.32398i	−0.753459	+	0.547420i	−0.896897	−	0.442239i	$-0.854184\pi$
$179$	−10.0806	+	7.32398i	−0.753459	+	0.547420i	0.143438	+	0.989659i	$0.454184\pi$
$180$	−1.87720	−	1.21496i	−0.139918	−	0.0905578i
$181$	−4.90060	−	3.56050i	−0.364259	−	0.264650i	0.390567	−	0.920574i	$-0.372279\pi$
$181$	−4.90060	−	3.56050i	−0.364259	−	0.264650i	−0.754826	+	0.655925i	$0.772279\pi$
$182$		−	7.34974i		−	0.544799i
$183$	−7.65235	+	10.5326i	−0.565678	+	0.778589i
$184$	−2.01633	+	6.20562i	−0.148646	+	0.457485i
$185$	−9.46991	+	3.65190i	−0.696241	+	0.268493i
$186$	1.12072	+	3.44923i	0.0821754	+	0.252910i
$187$	1.76477	+	0.573410i	0.129053	+	0.0419319i
$188$	−8.55614	−	2.78006i	−0.624021	−	0.202757i
$189$	−0.809610	−	2.49172i	−0.0588904	−	0.181246i
$190$	−0.924887	+	0.356666i	−0.0670984	+	0.0258753i
$191$	7.22123	−	22.2247i	0.522510	−	1.60812i	−0.246678	−	0.969098i	$-0.579339\pi$
$191$	7.22123	−	22.2247i	0.522510	−	1.60812i	0.769188	−	0.639023i	$-0.220661\pi$
$192$	0.587785	−	0.809017i	0.0424197	−	0.0583858i
$193$			2.13291i			0.153530i	0.997049	+	0.0767650i	$0.0244591\pi$
$193$			2.13291i			0.153530i	−0.997049	+	0.0767650i	$0.975541\pi$
$194$	4.40947	+	3.20367i	0.316581	+	0.230010i
$195$	−5.26609	−	3.40832i	−0.377113	−	0.244075i
$196$	0.109908	−	0.0798529i	0.00785057	−	0.00570378i
$197$	−9.67275	−	13.3134i	−0.689155	−	0.948540i	0.310843	−	0.950461i	$-0.399389\pi$
$197$	−9.67275	−	13.3134i	−0.689155	−	0.948540i	−0.999998	+	0.00192101i	$0.999389\pi$
$198$	−0.271820	+	0.0883198i	−0.0193174	+	0.00627662i
$199$	−1.66552			−0.118065			−0.0590327	−	0.998256i	$-0.518802\pi$
$199$	−1.66552			−0.118065			−0.0590327	+	0.998256i	$0.518802\pi$
$200$	3.35708	+	3.70540i	0.237381	+	0.262012i
$201$	−10.2325			−0.721747
$202$	−10.2491	+	3.33013i	−0.721123	+	0.234307i
$203$	11.1746	+	15.3805i	0.784301	+	1.07950i
$204$	−5.25248	+	3.81615i	−0.367747	+	0.267184i
$205$	4.28347	+	11.1077i	0.299171	+	0.775794i
$206$	14.4945	+	10.5308i	1.00988	+	0.733718i
$207$			6.52498i			0.453517i
$208$	1.64891	−	2.26953i	0.114331	−	0.157364i
$209$	−0.0391532	+	0.120501i	−0.00270829	+	0.00833525i
$210$	0.315613	+	5.84988i	0.0217794	+	0.403680i
$211$	−3.63522	−	11.1881i	−0.250259	−	0.770218i	−0.994727	−	0.102559i	$-0.967297\pi$
$211$	−3.63522	−	11.1881i	−0.250259	−	0.770218i	0.744468	−	0.667658i	$-0.232703\pi$
$212$	13.2347	+	4.30020i	0.908961	+	0.295339i
$213$	4.58203	+	1.48879i	0.313956	+	0.102010i
$214$	−1.17825	−	3.62629i	−0.0805437	−	0.247888i
$215$	11.3550	+	13.9782i	0.774406	+	0.953306i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	5.58506	−	7.68718i	0.379139	−	0.521840i
$218$		−	7.96590i		−	0.539519i
$219$	−9.53565	−	6.92806i	−0.644360	−	0.468155i
$220$	0.638160	−	0.0344300i	0.0430247	−	0.00232127i
$221$	−14.7348	+	10.7054i	−0.991167	+	0.720125i
$222$	−2.66799	−	3.67218i	−0.179064	−	0.246461i
$223$	9.05554	−	2.94232i	0.606404	−	0.197033i	0.0103094	−	0.999947i	$-0.496718\pi$
$223$	9.05554	−	2.94232i	0.606404	−	0.197033i	0.596095	+	0.802914i	$0.296718\pi$
$224$	−2.61995			−0.175053
$225$	4.33781	+	2.48665i	0.289187	+	0.165777i
$226$	5.25015			0.349235
$227$	15.5187	−	5.04232i	1.03001	−	0.334671i	0.255216	−	0.966884i	$-0.417853\pi$
$227$	15.5187	−	5.04232i	1.03001	−	0.334671i	0.774794	+	0.632213i	$0.217853\pi$
$228$	−0.260572	−	0.358647i	−0.0172568	−	0.0237520i
$229$	−0.431759	+	0.313691i	−0.0285314	+	0.0207293i	−0.601960	−	0.798527i	$-0.705613\pi$
$229$	−0.431759	+	0.313691i	−0.0285314	+	0.0207293i	0.573428	+	0.819256i	$0.305613\pi$
$230$	3.75454	−	14.0989i	0.247567	−	0.929657i
$231$	0.605796	+	0.440137i	0.0398585	+	0.0289589i
$232$			7.25636i			0.476403i
$233$	−6.43141	+	8.85208i	−0.421336	+	0.579919i	−0.965937	−	0.258776i	$-0.916681\pi$
$233$	−6.43141	+	8.85208i	−0.421336	+	0.579919i	0.544602	+	0.838695i	$0.316681\pi$
$234$	0.866884	−	2.66799i	0.0566700	−	0.174412i
$235$	19.4392	+	5.17666i	1.26808	+	0.337688i
$236$	−1.15784	−	3.56347i	−0.0753690	−	0.231962i
$237$	−7.43215	−	2.41485i	−0.482770	−	0.156861i
$238$	16.1773	+	5.25633i	1.04862	+	0.340717i
$239$	−1.86591	−	5.74268i	−0.120696	−	0.371463i	0.872397	−	0.488798i	$-0.162565\pi$
$239$	−1.86591	−	5.74268i	−0.120696	−	0.371463i	−0.993092	+	0.117336i	$0.962565\pi$
$240$	−1.21496	+	1.87720i	−0.0784254	+	0.121173i
$241$	0.682003	−	2.09899i	0.0439317	−	0.135208i	−0.926685	−	0.375839i	$-0.877354\pi$
$241$	0.682003	−	2.09899i	0.0439317	−	0.135208i	0.970617	+	0.240631i	$0.0773545\pi$
$242$	−6.41762	+	8.83310i	−0.412540	+	0.567813i
$243$		−	1.00000i		−	0.0641500i
$244$	10.5326	+	7.65235i	0.674277	+	0.489891i
$245$	−0.235785	+	0.191537i	−0.0150638	+	0.0122369i
$246$	−4.30726	+	3.12941i	−0.274621	+	0.199524i
$247$	−0.730982	−	1.00611i	−0.0465113	−	0.0640173i
$248$	3.44923	−	1.12072i	0.219027	−	0.0711660i
$249$	5.16187			0.327120
$250$	−7.94213	−	7.86909i	−0.502304	−	0.497685i
$251$	−0.151651			−0.00957211			−0.00478606	−	0.999989i	$-0.501523\pi$
$251$	−0.151651			−0.00957211			−0.00478606	+	0.999989i	$0.501523\pi$
$252$	−2.49172	+	0.809610i	−0.156964	+	0.0510006i
$253$	−1.09616	−	1.50873i	−0.0689149	−	0.0948533i
$254$	−15.1278	+	10.9910i	−0.949205	+	0.689638i
$255$	11.2681	−	9.15352i	0.705638	−	0.573216i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			10.4462i			0.651614i	0.945436	+	0.325807i	$0.105636\pi$
$257$			10.4462i			0.651614i	−0.945436	+	0.325807i	$0.894364\pi$
$258$	−4.73397	+	6.51574i	−0.294724	+	0.405652i
$259$	−3.67487	+	11.3101i	−0.228345	+	0.702774i
$260$	−3.40832	+	5.26609i	−0.211375	+	0.326589i
$261$	2.24234	+	6.90121i	0.138797	+	0.427174i
$262$	4.32867	+	1.40647i	0.267426	+	0.0868920i
$263$	−20.8854	−	6.78608i	−1.28785	−	0.418448i	−0.416511	−	0.909131i	$-0.636747\pi$
$263$	−20.8854	−	6.78608i	−1.28785	−	0.418448i	−0.871338	+	0.490683i	$0.836747\pi$
$264$	0.0883198	+	0.271820i	0.00543571	+	0.0167294i
$265$	−30.0687	−	8.00727i	−1.84710	−	0.491883i
$266$	−0.358910	+	1.10461i	−0.0220062	+	0.0677280i
$267$	−3.62405	+	4.98807i	−0.221788	+	0.305265i
$268$			10.2325i			0.625051i
$269$	−11.4313	−	8.30535i	−0.696981	−	0.506386i	0.181967	−	0.983305i	$-0.441754\pi$
$269$	−11.4313	−	8.30535i	−0.696981	−	0.506386i	−0.878948	+	0.476918i	$0.841754\pi$
$270$	−0.575410	+	2.16076i	−0.0350184	+	0.131500i
$271$	−22.2714	+	16.1811i	−1.35289	+	0.982934i	−0.354031	+	0.935234i	$0.615189\pi$
$271$	−22.2714	+	16.1811i	−1.35289	+	0.982934i	−0.998862	+	0.0477007i	$0.984811\pi$
$272$	3.81615	+	5.25248i	0.231388	+	0.318478i
$273$	−6.99002	+	2.27119i	−0.423055	+	0.137459i
$274$	15.5439			0.939043
$275$	−1.42075	+	0.153752i	−0.0856744	+	0.00927160i
$276$	6.52498			0.392758
$277$	22.4411	−	7.29155i	1.34835	−	0.438107i	0.456216	−	0.889869i	$-0.349205\pi$
$277$	22.4411	−	7.29155i	1.34835	−	0.438107i	0.892138	+	0.451763i	$0.149205\pi$
$278$	−5.29063	−	7.28192i	−0.317311	−	0.436741i
$279$	2.93409	−	2.13174i	0.175660	−	0.127624i
$280$	5.84988	−	0.315613i	0.349597	−	0.0188615i
$281$	−5.80174	−	4.21521i	−0.346103	−	0.251458i	0.401130	−	0.916021i	$-0.368618\pi$
$281$	−5.80174	−	4.21521i	−0.346103	−	0.251458i	−0.747232	+	0.664563i	$0.768618\pi$
$282$			8.99646i			0.535731i
$283$	13.5380	−	18.6334i	0.804748	−	1.10764i	−0.187365	−	0.982290i	$-0.559995\pi$
$283$	13.5380	−	18.6334i	0.804748	−	1.10764i	0.992113	−	0.125350i	$-0.0400054\pi$
$284$	1.48879	−	4.58203i	0.0883436	−	0.271894i
$285$	0.625015	+	0.769404i	0.0370227	+	0.0455756i
$286$	0.247763	+	0.762537i	0.0146505	+	0.0450897i
$287$	13.2661	+	4.31042i	0.783073	+	0.254436i
$288$	−0.951057	−	0.309017i	−0.0560415	−	0.0182090i
$289$	−7.77227	−	23.9206i	−0.457192	−	1.40709i
$290$	−0.874138	−	16.2021i	−0.0513312	−	0.951423i
$291$	1.68427	−	5.18364i	0.0987335	−	0.303871i
$292$	−6.92806	+	9.53565i	−0.405434	+	0.558032i
$293$			16.3851i			0.957230i	0.878025	+	0.478615i	$0.158861\pi$
$293$			16.3851i			0.957230i	−0.878025	+	0.478615i	$0.841139\pi$
$294$	−0.109908	−	0.0798529i	−0.00640997	−	0.00465711i
$295$	3.01452	+	7.81710i	0.175512	+	0.455129i
$296$	−3.67218	+	2.66799i	−0.213441	+	0.155074i
$297$	0.167994	+	0.231224i	0.00974802	+	0.0134170i
$298$	−7.48901	+	2.43333i	−0.433827	+	0.140959i
$299$	18.3045			1.05858
$300$	2.48665	−	4.33781i	0.143567	−	0.250443i
$301$	21.1008			1.21623
$302$	−16.8965	+	5.48999i	−0.972282	+	0.315914i
$303$	6.33428	+	8.71839i	0.363895	+	0.500858i
$304$	−0.358647	+	0.260572i	−0.0205698	+	0.0149448i
$305$	−24.4391	−	15.8175i	−1.39938	−	0.905708i
$306$	5.25248	+	3.81615i	0.300264	+	0.218155i
$307$		−	18.6027i		−	1.06171i	−0.847461	−	0.530857i	$-0.821870\pi$
$307$		−	18.6027i		−	1.06171i	0.847461	−	0.530857i	$-0.178130\pi$
$308$	0.440137	−	0.605796i	0.0250791	−	0.0345185i
$309$	5.53639	−	17.0392i	0.314954	−	0.969329i
$310$	−7.56651	+	2.91789i	−0.429749	+	0.165725i
$311$	−4.30073	−	13.2363i	−0.243872	−	0.750561i	−0.995820	−	0.0913384i	$-0.970886\pi$
$311$	−4.30073	−	13.2363i	−0.243872	−	0.750561i	0.751948	−	0.659223i	$-0.229114\pi$
$312$	−2.66799	−	0.866884i	−0.151045	−	0.0490776i
$313$	14.6277	+	4.75282i	0.826805	+	0.268645i	0.691699	−	0.722186i	$-0.256863\pi$
$313$	14.6277	+	4.75282i	0.826805	+	0.268645i	0.135106	+	0.990831i	$0.456863\pi$
$314$	6.21715	+	19.1344i	0.350854	+	1.07982i
$315$	5.46604	−	2.10788i	0.307976	−	0.118766i
$316$	−2.41485	+	7.43215i	−0.135846	+	0.418091i
$317$	3.77620	−	5.19749i	0.212092	−	0.291920i	−0.689695	−	0.724100i	$-0.742255\pi$
$317$	3.77620	−	5.19749i	0.212092	−	0.291920i	0.901787	+	0.432180i	$0.142255\pi$
$318$		−	13.9158i		−	0.780357i
$319$	−1.67785	−	1.21903i	−0.0939413	−	0.0682524i
$320$	1.87720	+	1.21496i	0.104939	+	0.0679184i
$321$	−3.08471	+	2.24117i	−0.172172	+	0.125090i
$322$	−10.0483	−	13.8303i	−0.559968	−	0.770730i
$323$	2.73730	−	0.889403i	0.152308	−	0.0494877i
$324$	−1.00000			−0.0555556
$325$	6.97579	−	12.1688i	0.386947	−	0.675005i
$326$	2.11433			0.117102
$327$	−7.57602	+	2.46160i	−0.418955	+	0.136127i
$328$	3.12941	+	4.30726i	0.172793	+	0.237829i
$329$	19.0688	−	13.8543i	1.05129	−	0.763810i
$330$	−0.229947	−	0.596287i	−0.0126582	−	0.0328245i
$331$	−14.6979	−	10.6786i	−0.807868	−	0.586951i	0.105344	−	0.994436i	$-0.466406\pi$
$331$	−14.6979	−	10.6786i	−0.807868	−	0.586951i	−0.913212	+	0.407485i	$0.866406\pi$
$332$		−	5.16187i		−	0.283294i
$333$	−2.66799	+	3.67218i	−0.146205	+	0.201234i
$334$	6.01837	−	18.5226i	0.329311	−	1.01351i
$335$	−1.23266	−	22.8474i	−0.0673476	−	1.24829i
$336$	0.809610	+	2.49172i	0.0441678	+	0.135935i
$337$	−2.26995	−	0.737552i	−0.123652	−	0.0401770i	0.246537	−	0.969133i	$-0.420707\pi$
$337$	−2.26995	−	0.737552i	−0.123652	−	0.0401770i	−0.370189	+	0.928956i	$0.620707\pi$
$338$	4.87922	+	1.58536i	0.265395	+	0.0862320i
$339$	−1.62239	−	4.99319i	−0.0881159	−	0.271193i
$340$	−9.15352	−	11.2681i	−0.496419	−	0.611101i
$341$	−0.320313	+	0.985821i	−0.0173459	+	0.0533852i
$342$	−0.260572	+	0.358647i	−0.0140901	+	0.0193934i
$343$			18.6956i			1.00947i
$344$	6.51574	+	4.73397i	0.351305	+	0.255238i
$345$	−14.5691	+	0.786033i	−0.784374	+	0.0423186i
$346$	2.67848	−	1.94603i	0.143996	−	0.104619i
$347$	15.2463	+	20.9848i	0.818466	+	1.12652i	0.989961	+	0.141337i	$0.0451403\pi$
$347$	15.2463	+	20.9848i	0.818466	+	1.12652i	−0.171495	+	0.985185i	$0.554860\pi$
$348$	6.90121	−	2.24234i	0.369943	−	0.120202i
$349$	−0.246770			−0.0132093			−0.00660463	−	0.999978i	$-0.502102\pi$
$349$	−0.246770			−0.0132093			−0.00660463	+	0.999978i	$0.502102\pi$
$350$	−13.0237	+	1.40941i	−0.696147	+	0.0753363i
$351$	−2.80530			−0.149736
$352$	0.271820	−	0.0883198i	0.0144881	−	0.00470746i
$353$	−11.2868	−	15.5350i	−0.600738	−	0.826844i	0.395038	−	0.918665i	$-0.370731\pi$
$353$	−11.2868	−	15.5350i	−0.600738	−	0.826844i	−0.995776	+	0.0918205i	$0.970731\pi$
$354$	−3.03127	+	2.20234i	−0.161110	+	0.117053i
$355$	−2.77223	+	10.4102i	−0.147135	+	0.552516i
$356$	4.98807	+	3.62405i	0.264367	+	0.192074i
$357$		−	17.0098i		−	0.900256i
$358$	7.32398	−	10.0806i	0.387084	−	0.532776i
$359$	−4.77188	+	14.6863i	−0.251850	+	0.775116i	0.742584	+	0.669753i	$0.233600\pi$
$359$	−4.77188	+	14.6863i	−0.251850	+	0.775116i	−0.994434	+	0.105362i	$0.966400\pi$
$360$	2.16076	+	0.575410i	0.113882	+	0.0303268i
$361$	−5.81059	−	17.8832i	−0.305821	−	0.941219i
$362$	5.76100	+	1.87186i	0.302792	+	0.0983830i
$363$	10.3839	+	3.37394i	0.545015	+	0.177086i
$364$	2.27119	+	6.99002i	0.119043	+	0.366376i
$365$	14.3204	−	22.1260i	0.749564	−	1.15813i
$366$	4.02308	−	12.3818i	0.210290	−	0.647205i
$367$	−14.6775	+	20.2019i	−0.766160	+	1.05453i	0.230516	+	0.973068i	$0.425959\pi$
$367$	−14.6775	+	20.2019i	−0.766160	+	1.05453i	−0.996677	+	0.0814607i	$0.974041\pi$
$368$		−	6.52498i		−	0.340138i
$369$	4.30726	+	3.12941i	0.224227	+	0.162911i
$370$	7.87792	−	6.39952i	0.409553	−	0.332695i
$371$	−29.4956	+	21.4298i	−1.53134	+	1.11258i
$372$	−2.13174	−	2.93409i	−0.110526	−	0.152126i
$373$	−17.7509	+	5.76763i	−0.919109	+	0.298637i	−0.730101	−	0.683339i	$-0.760527\pi$
$373$	−17.7509	+	5.76763i	−0.919109	+	0.298637i	−0.189008	+	0.981976i	$0.560527\pi$
$374$	−1.85559			−0.0959504
$375$	−5.02969	+	9.98510i	−0.259732	+	0.515628i
$376$	8.99646			0.463957
$377$	19.3599	−	6.29042i	0.997087	−	0.323973i
$378$	1.53997	+	2.11959i	0.0792075	+	0.109020i
$379$	23.6622	−	17.1916i	1.21545	−	0.883073i	0.219732	−	0.975560i	$-0.429482\pi$
$379$	23.6622	−	17.1916i	1.21545	−	0.883073i	0.995714	+	0.0924869i	$0.0294816\pi$
$380$	0.769404	−	0.625015i	0.0394696	−	0.0320626i
$381$	15.1278	+	10.9910i	0.775023	+	0.563087i
$382$			23.3684i			1.19563i
$383$	6.09627	−	8.39079i	0.311505	−	0.428750i	−0.624345	−	0.781149i	$-0.714634\pi$
$383$	6.09627	−	8.39079i	0.311505	−	0.428750i	0.935850	+	0.352399i	$0.114634\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	−0.909769	+	1.40566i	−0.0463661	+	0.0716389i
$386$	−0.659104	−	2.02851i	−0.0335475	−	0.103249i
$387$	7.65972	+	2.48879i	0.389365	+	0.126512i
$388$	−5.18364	−	1.68427i	−0.263160	−	0.0855057i
$389$	2.82831	+	8.70463i	0.143401	+	0.441342i	0.996802	−	0.0799126i	$-0.0254641\pi$
$389$	2.82831	+	8.70463i	0.143401	+	0.441342i	−0.853401	+	0.521255i	$0.825464\pi$
$390$	6.06158	+	1.61420i	0.306940	+	0.0817380i
$391$	−13.0909	+	40.2895i	−0.662034	+	2.03753i
$392$	−0.0798529	+	0.109908i	−0.00403318	+	0.00555119i
$393$		−	4.55143i		−	0.229589i
$394$	13.3134	+	9.67275i	0.670719	+	0.487306i
$395$	4.49662	−	16.8856i	0.226249	−	0.849605i
$396$	0.231224	−	0.167994i	0.0116195	−	0.00844203i
$397$	9.48983	+	13.0616i	0.476281	+	0.655544i	0.977785	−	0.209611i	$-0.0672198\pi$
$397$	9.48983	+	13.0616i	0.476281	+	0.655544i	−0.501504	+	0.865155i	$0.667220\pi$
$398$	1.58400	−	0.514674i	0.0793989	−	0.0257983i
$399$	1.16146			0.0581455
$400$	−4.33781	−	2.48665i	−0.216890	−	0.124333i
$401$	−25.9388			−1.29532			−0.647662	−	0.761928i	$-0.724253\pi$
$401$	−25.9388			−1.29532			−0.647662	+	0.761928i	$0.724253\pi$
$402$	9.73171	−	3.16202i	0.485374	−	0.157707i
$403$	−5.98017	−	8.23100i	−0.297893	−	0.410015i
$404$	8.71839	−	6.33428i	0.433756	−	0.315142i
$405$	2.23282	−	0.120465i	0.110950	−	0.00598596i
$406$	−15.3805	−	11.1746i	−0.763320	−	0.554584i
$407$		−	1.29730i		−	0.0643050i
$408$	3.81615	−	5.25248i	0.188928	−	0.260037i
$409$	−5.27338	+	16.2298i	−0.260752	+	0.802512i	0.731890	+	0.681423i	$0.238639\pi$
$409$	−5.27338	+	16.2298i	−0.260752	+	0.802512i	−0.992642	+	0.121089i	$0.961361\pi$
$410$	−7.50629	−	9.24036i	−0.370709	−	0.456349i
$411$	−4.80334	−	14.7832i	−0.236931	−	0.729199i
$412$	−17.0392	−	5.53639i	−0.839464	−	0.272758i
$413$	9.33611	+	3.03349i	0.459400	+	0.149268i
$414$	−2.01633	−	6.20562i	−0.0990972	−	0.304990i
$415$	0.621825	+	11.5255i	0.0305242	+	0.565766i
$416$	−0.866884	+	2.66799i	−0.0425025	+	0.130809i
$417$	−5.29063	+	7.28192i	−0.259083	+	0.356597i
$418$		−	0.126703i		−	0.00619722i
$419$	11.1748	+	8.11899i	0.545926	+	0.396639i	0.826281	−	0.563258i	$-0.190452\pi$
$419$	11.1748	+	8.11899i	0.545926	+	0.396639i	−0.280355	+	0.959896i	$0.590452\pi$
$420$	−2.10788	−	5.46604i	−0.102854	−	0.266715i
$421$	1.68679	−	1.22553i	0.0822093	−	0.0597286i	−0.545921	−	0.837836i	$-0.683820\pi$
$421$	1.68679	−	1.22553i	0.0822093	−	0.0597286i	0.628131	+	0.778108i	$0.283820\pi$
$422$	6.91460	+	9.51713i	0.336597	+	0.463287i
$423$	8.55614	−	2.78006i	0.416014	−	0.135171i
$424$	−13.9158			−0.675809
$425$	21.7956	+	24.0570i	1.05724	+	1.16694i
$426$	−4.81783			−0.233425
$427$	−32.4396	+	10.5403i	−1.56986	+	0.510079i
$428$	2.24117	+	3.08471i	0.108331	+	0.149105i
$429$	0.648652	−	0.471274i	0.0313172	−	0.0227533i
$430$	−15.1188	−	9.78517i	−0.729092	−	0.471883i
$431$	−7.55310	−	5.48765i	−0.363820	−	0.264331i	0.390824	−	0.920466i	$-0.372190\pi$
$431$	−7.55310	−	5.48765i	−0.363820	−	0.264331i	−0.754644	+	0.656135i	$0.772190\pi$
$432$			1.00000i			0.0481125i
$433$	−6.88534	+	9.47685i	−0.330888	+	0.455429i	−0.941752	−	0.336307i	$-0.890822\pi$
$433$	−6.88534	+	9.47685i	−0.330888	+	0.455429i	0.610864	+	0.791735i	$0.290822\pi$
$434$	−2.93624	+	9.03682i	−0.140944	+	0.433781i
$435$	−15.1390	+	5.83809i	−0.725861	+	0.279915i
$436$	2.46160	+	7.57602i	0.117889	+	0.362826i
$437$	−2.75103	−	0.893863i	−0.131599	−	0.0427593i
$438$	11.2098	+	3.64230i	0.535627	+	0.174036i
$439$	−0.952391	−	2.93116i	−0.0454552	−	0.139897i	0.925753	−	0.378128i	$-0.123432\pi$
$439$	−0.952391	−	2.93116i	−0.0454552	−	0.139897i	−0.971208	+	0.238232i	$0.923432\pi$
$440$	−0.596287	+	0.229947i	−0.0284269	+	0.0109623i
$441$	−0.0419811	+	0.129205i	−0.00199910	+	0.00615260i
$442$	10.7054	−	14.7348i	0.509205	−	0.700861i
$443$		−	10.6355i		−	0.505309i	−0.967557	−	0.252654i	$-0.918696\pi$
$443$		−	10.6355i		−	0.505309i	0.967557	−	0.252654i	$-0.0813035\pi$
$444$	3.67218	+	2.66799i	0.174274	+	0.126617i
$445$	−11.5740	−	7.49096i	−0.548662	−	0.355106i
$446$	−7.70310	+	5.59663i	−0.364753	+	0.265008i
$447$	4.62846	+	6.37053i	0.218919	+	0.301316i
$448$	2.49172	−	0.809610i	0.117723	−	0.0382505i
$449$	22.8276			1.07730			0.538651	−	0.842529i	$-0.318934\pi$
$449$	22.8276			1.07730			0.538651	+	0.842529i	$0.318934\pi$
$450$	−4.89392	−	1.02449i	−0.230701	−	0.0482950i
$451$	−1.52167			−0.0716525
$452$	−4.99319	+	1.62239i	−0.234860	+	0.0763106i
$453$	10.4426	+	14.3730i	0.490635	+	0.675302i
$454$	−13.2010	+	9.59107i	−0.619552	+	0.450131i
$455$	−5.91322	−	15.3339i	−0.277216	−	0.718862i
$456$	0.358647	+	0.260572i	0.0167952	+	0.0122024i
$457$			25.7628i			1.20513i	0.798068	+	0.602567i	$0.205855\pi$
$457$			25.7628i			1.20513i	−0.798068	+	0.602567i	$0.794145\pi$
$458$	0.313691	−	0.431759i	0.0146578	−	0.0201748i
$459$	2.00627	−	6.17466i	0.0936446	−	0.288209i
$460$	0.786033	+	14.5691i	0.0366490	+	0.679288i
$461$	10.0189	+	30.8349i	0.466626	+	1.43613i	0.856926	+	0.515439i	$0.172371\pi$
$461$	10.0189	+	30.8349i	0.466626	+	1.43613i	−0.390301	+	0.920688i	$0.627629\pi$
$462$	−0.712156	−	0.231394i	−0.0331325	−	0.0107654i
$463$	17.8584	+	5.80256i	0.829952	+	0.269668i	0.693025	−	0.720914i	$-0.256278\pi$
$463$	17.8584	+	5.80256i	0.829952	+	0.269668i	0.136927	+	0.990581i	$0.456278\pi$
$464$	−2.24234	−	6.90121i	−0.104098	−	0.320380i
$465$	5.11326	+	6.29450i	0.237122	+	0.291901i
$466$	3.38119	−	10.4062i	0.156631	−	0.482060i
$467$	−1.15330	+	1.58739i	−0.0533686	+	0.0734555i	−0.834867	−	0.550451i	$-0.814456\pi$
$467$	−1.15330	+	1.58739i	−0.0533686	+	0.0734555i	0.781499	+	0.623907i	$0.214456\pi$
$468$			2.80530i			0.129675i
$469$	−21.6887	−	15.7578i	−1.00149	−	0.727626i
$470$	−20.0875	+	1.08376i	−0.926566	+	0.0499901i
$471$	16.2767	−	11.8257i	0.749991	−	0.544900i
$472$	2.20234	+	3.03127i	0.101371	+	0.139525i
$473$	−2.18922	+	0.711319i	−0.100660	+	0.0327065i
$474$	7.81462			0.358938
$475$	−1.64265	+	1.48823i	−0.0753699	+	0.0682849i
$476$	−17.0098			−0.779645
$477$	−13.2347	+	4.30020i	−0.605974	+	0.196893i
$478$	3.54917	+	4.88501i	0.162335	+	0.223435i
$479$	−5.45583	+	3.96389i	−0.249283	+	0.181115i	−0.705409	−	0.708800i	$-0.749237\pi$
$479$	−5.45583	+	3.96389i	−0.249283	+	0.181115i	0.456126	+	0.889915i	$0.349237\pi$
$480$	0.575410	−	2.16076i	0.0262638	−	0.0986250i
$481$	10.3015	+	7.48451i	0.469710	+	0.341264i
$482$			2.20701i			0.100526i
$483$	−10.0483	+	13.8303i	−0.457212	+	0.629298i
$484$	3.37394	−	10.3839i	0.153361	−	0.471997i
$485$	11.7770	+	3.13622i	0.534768	+	0.142408i
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	1.10709	+	0.359717i	0.0501672	+	0.0163003i	0.333993	−	0.942576i	$-0.391604\pi$
$487$	1.10709	+	0.359717i	0.0501672	+	0.0163003i	−0.283826	+	0.958876i	$0.591604\pi$
$488$	−12.3818	−	4.02308i	−0.560496	−	0.182116i
$489$	−0.653363	−	2.01084i	−0.0295461	−	0.0909335i
$490$	0.165057	−	0.255024i	0.00745652	−	0.0115208i
$491$	−2.59179	+	7.97671i	−0.116966	+	0.359984i	−0.992352	−	0.123441i	$-0.960607\pi$
$491$	−2.59179	+	7.97671i	−0.116966	+	0.359984i	0.875386	+	0.483424i	$0.160607\pi$
$492$	3.12941	−	4.30726i	0.141085	−	0.194186i
$493$			47.1113i			2.12179i
$494$	1.00611	+	0.730982i	0.0452670	+	0.0328884i
$495$	−0.496045	+	0.402956i	−0.0222956	+	0.0181115i
$496$	−2.93409	+	2.13174i	−0.131745	+	0.0957181i
$497$	7.41931	+	10.2118i	0.332802	+	0.458062i
$498$	−4.90923	+	1.59510i	−0.219988	+	0.0714783i
$499$	−17.2590			−0.772620			−0.386310	−	0.922369i	$-0.626251\pi$
$499$	−17.2590			−0.772620			−0.386310	+	0.922369i	$0.626251\pi$
$500$	9.98510	+	5.02969i	0.446547	+	0.224935i
$501$	−19.4759			−0.870117
$502$	0.144228	−	0.0468627i	0.00643723	−	0.00209158i
$503$	5.18659	+	7.13873i	0.231259	+	0.318300i	0.908838	−	0.417150i	$-0.136971\pi$
$503$	5.18659	+	7.13873i	0.231259	+	0.318300i	−0.677579	+	0.735450i	$0.736971\pi$
$504$	2.11959	−	1.53997i	0.0944138	−	0.0685957i
$505$	−18.7035	+	15.1936i	−0.832297	+	0.676105i
$506$	1.50873	+	1.09616i	0.0670714	+	0.0487302i
$507$		−	5.13032i		−	0.227845i
$508$	10.9910	−	15.1278i	0.487648	−	0.671189i
$509$	4.21361	−	12.9682i	0.186765	−	0.574804i	−0.813209	−	0.581971i	$-0.802282\pi$
$509$	4.21361	−	12.9682i	0.186765	−	0.574804i	0.999974	+	0.00716772i	$0.00228158\pi$
$510$	−7.88804	+	12.1876i	−0.349288	+	0.539674i
$511$	−9.54264	−	29.3692i	−0.422141	−	1.29922i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	0.421615	+	0.136991i	0.0186147	+	0.00604830i
$514$	−3.22805	−	9.93490i	−0.142383	−	0.438210i
$515$	38.7125	+	10.3091i	1.70588	+	0.454274i
$516$	2.48879	−	7.65972i	0.109563	−	0.337200i
$517$	−1.51135	+	2.08020i	−0.0664692	+	0.0914871i
$518$		−	11.8921i		−	0.522510i
$519$	−2.67848	−	1.94603i	−0.117572	−	0.0854211i
$520$	1.61420	−	6.06158i	0.0707872	−	0.265818i
$521$	10.9134	−	7.92905i	0.478125	−	0.347378i	−0.322474	−	0.946578i	$-0.604515\pi$
$521$	10.9134	−	7.92905i	0.478125	−	0.347378i	0.800599	+	0.599200i	$0.204515\pi$
$522$	−4.26518	−	5.87052i	−0.186682	−	0.256946i
$523$	−9.68125	+	3.14563i	−0.423332	+	0.137549i	−0.512932	−	0.858429i	$-0.671441\pi$
$523$	−9.68125	+	3.14563i	−0.423332	+	0.137549i	0.0896008	+	0.995978i	$0.471441\pi$
$524$	−4.55143			−0.198830
$525$	5.36498	+	11.9508i	0.234147	+	0.521574i
$526$	21.9602			0.957511
$527$	22.3939	−	7.27621i	0.975493	−	0.316957i
$528$	−0.167994	−	0.231224i	−0.00731101	−	0.0100627i
$529$	15.8368	−	11.5061i	0.688556	−	0.500266i
$530$	31.0714	−	1.67636i	1.34965	−	0.0728166i
$531$	3.03127	+	2.20234i	0.131546	+	0.0955736i
$532$		−	1.16146i		−	0.0503555i
$533$	8.77892	−	12.0831i	0.380257	−	0.523379i
$534$	1.90527	−	5.86383i	0.0824493	−	0.253753i
$535$	−5.37573	−	6.61761i	−0.232413	−	0.286104i
$536$	−3.16202	−	9.73171i	−0.136579	−	0.420346i
$537$	−11.8504	−	3.85044i	−0.511385	−	0.166159i
$538$	13.4383	+	4.36638i	0.579368	+	0.188248i
$539$	−0.0119986	−	0.0369278i	−0.000516816	−	0.00159059i
$540$	−0.120465	−	2.23282i	−0.00518400	−	0.0960853i
$541$	−3.58842	+	11.0440i	−0.154278	+	0.474819i	−0.998087	−	0.0618246i	$-0.980308\pi$
$541$	−3.58842	+	11.0440i	−0.154278	+	0.474819i	0.843809	+	0.536644i	$0.180308\pi$
$542$	16.1811	−	22.2714i	0.695039	−	0.956640i
$543$		−	6.05748i		−	0.259951i
$544$	−5.25248	−	3.81615i	−0.225198	−	0.163616i
$545$	−6.40896	−	16.6194i	−0.274529	−	0.711895i
$546$	5.94606	−	4.32007i	0.254468	−	0.184882i
$547$	−11.8352	−	16.2897i	−0.506035	−	0.696497i	0.477210	−	0.878789i	$-0.341648\pi$
$547$	−11.8352	−	16.2897i	−0.506035	−	0.696497i	−0.983244	+	0.182293i	$0.941648\pi$
$548$	−14.7832	+	4.80334i	−0.631505	+	0.205188i
$549$	−13.0189			−0.555635
$550$	1.30370	−	0.585263i	0.0555900	−	0.0249557i
$551$	−3.21683			−0.137042
$552$	−6.20562	+	2.01633i	−0.264129	+	0.0858207i
$553$	−12.0343	−	16.5638i	−0.511750	−	0.704363i
$554$	−19.0895	+	13.8693i	−0.811036	+	0.589252i
$555$	−8.52072	−	5.51478i	−0.361684	−	0.234090i
$556$	7.28192	+	5.29063i	0.308822	+	0.224373i
$557$		−	8.99374i		−	0.381077i	−0.981680	−	0.190539i	$-0.938977\pi$
$557$		−	8.99374i		−	0.381077i	0.981680	−	0.190539i	$-0.0610234\pi$
$558$	−2.13174	+	2.93409i	−0.0902439	+	0.124210i
$559$	6.98180	−	21.4878i	0.295299	−	0.908836i
$560$	−5.46604	+	2.10788i	−0.230982	+	0.0890741i
$561$	0.573410	+	1.76477i	0.0242094	+	0.0745088i
$562$	6.82035	+	2.21607i	0.287699	+	0.0934791i
$563$	−0.442435	−	0.143756i	−0.0186464	−	0.00605858i	0.299679	−	0.954040i	$-0.403120\pi$
$563$	−0.442435	−	0.143756i	−0.0186464	−	0.00605858i	−0.318325	+	0.947982i	$0.603120\pi$
$564$	−2.78006	−	8.55614i	−0.117062	−	0.360278i
$565$	10.9535	−	4.22400i	0.460815	−	0.177705i
$566$	−7.11732	+	21.9049i	−0.299163	+	0.920730i
$567$	1.53997	−	2.11959i	0.0646726	−	0.0890142i
$568$			4.81783i			0.202152i
$569$	−4.12851	−	2.99954i	−0.173076	−	0.125747i	0.497875	−	0.867249i	$-0.334114\pi$
$569$	−4.12851	−	2.99954i	−0.173076	−	0.125747i	−0.670951	+	0.741502i	$0.734114\pi$
$570$	−0.832184	−	0.538607i	−0.0348564	−	0.0225597i
$571$	34.9562	−	25.3971i	1.46287	−	1.06284i	0.480266	−	0.877123i	$-0.340540\pi$
$571$	34.9562	−	25.3971i	1.46287	−	1.06284i	0.982604	−	0.185714i	$-0.0594597\pi$
$572$	−0.471274	−	0.648652i	−0.0197049	−	0.0271215i
$573$	22.2247	−	7.22123i	0.928449	−	0.301671i
$574$	−13.9488			−0.582212
$575$	−3.51014	−	32.4355i	−0.146383	−	1.35265i
$576$	1.00000			0.0416667
$577$	−14.6870	+	4.77209i	−0.611427	+	0.198665i	−0.598330	−	0.801249i	$-0.704169\pi$
$577$	−14.6870	+	4.77209i	−0.611427	+	0.198665i	−0.0130969	+	0.999914i	$0.504169\pi$
$578$	14.7837	+	20.3481i	0.614922	+	0.846367i
$579$	−1.72556	+	1.25369i	−0.0717117	+	0.0521016i
$580$	5.83809	+	15.1390i	0.242414	+	0.628614i
$581$	10.9410	+	7.94911i	0.453910	+	0.329785i
$582$			5.45040i			0.225927i
$583$	2.33777	−	3.21766i	0.0968204	−	0.133262i
$584$	3.64230	−	11.2098i	0.150719	−	0.463866i
$585$	−0.337940	−	6.26372i	−0.0139721	−	0.258973i
$586$	−5.06328	−	15.5832i	−0.209162	−	0.643735i
$587$	−27.1662	−	8.82684i	−1.12127	−	0.364323i	−0.311018	−	0.950404i	$-0.600670\pi$
$587$	−27.1662	−	8.82684i	−1.12127	−	0.364323i	−0.810252	+	0.586081i	$0.800670\pi$
$588$	0.129205	+	0.0419811i	0.00532831	+	0.00173127i
$589$	0.496830	+	1.52909i	0.0204715	+	0.0630049i
$590$	−5.28260	−	6.50297i	−0.217481	−	0.267723i
$591$	5.08526	−	15.6508i	0.209180	−	0.643789i
$592$	2.66799	−	3.67218i	0.109654	−	0.150926i
$593$		−	31.6123i		−	1.29816i	−0.760720	−	0.649080i	$-0.775154\pi$
$593$		−	31.6123i		−	1.29816i	0.760720	−	0.649080i	$-0.224846\pi$
$594$	−0.231224	−	0.167994i	−0.00948725	−	0.00689289i
$595$	37.9799	−	2.04909i	1.55702	−	0.0840046i
$596$	6.37053	−	4.62846i	0.260947	−	0.189589i
$597$	−0.978967	−	1.34743i	−0.0400665	−	0.0551468i
$598$	−17.4086	+	5.65640i	−0.711891	+	0.231307i
$599$	−36.7361			−1.50099			−0.750497	−	0.660873i	$-0.770186\pi$
$599$	−36.7361			−1.50099			−0.750497	+	0.660873i	$0.770186\pi$
$600$	−1.02449	+	4.89392i	−0.0418247	+	0.199793i
$601$	45.3145			1.84842			0.924209	−	0.381887i	$-0.124726\pi$
$601$	45.3145			1.84842			0.924209	+	0.381887i	$0.124726\pi$
$602$	−20.0681	+	6.52052i	−0.817914	+	0.265756i
$603$	−6.01453	−	8.27829i	−0.244931	−	0.337118i
$604$	14.3730	−	10.4426i	0.584829	−	0.424903i
$605$	−6.28251	+	23.5919i	−0.255420	+	0.959147i
$606$	−8.71839	−	6.33428i	−0.354160	−	0.257313i
$607$		−	3.15730i		−	0.128151i	−0.997945	−	0.0640754i	$-0.979590\pi$
$607$		−	3.15730i		−	0.128151i	0.997945	−	0.0640754i	$-0.0204098\pi$
$608$	0.260572	−	0.358647i	0.0105676	−	0.0145451i
$609$	−5.87482	+	18.0808i	−0.238060	+	0.732672i
$610$	28.1309	+	7.49124i	1.13899	+	0.303311i
$611$	−7.79888	−	24.0025i	−0.315509	−	0.971037i
$612$	−6.17466	−	2.00627i	−0.249596	−	0.0810986i
$613$	19.9336	+	6.47683i	0.805111	+	0.261596i	0.682526	−	0.730861i	$-0.260881\pi$
$613$	19.9336	+	6.47683i	0.805111	+	0.261596i	0.122585	+	0.992458i	$0.460881\pi$
$614$	5.74856	+	17.6923i	0.231993	+	0.714002i
$615$	−6.46854	+	9.99433i	−0.260837	+	0.403010i
$616$	−0.231394	+	0.712156i	−0.00932311	+	0.0286936i
$617$	21.5952	−	29.7233i	0.869391	−	1.19661i	−0.109856	−	0.993947i	$-0.535039\pi$
$617$	21.5952	−	29.7233i	0.869391	−	1.19661i	0.979248	−	0.202667i	$-0.0649609\pi$
$618$			17.9161i			0.720692i
$619$	−9.41595	−	6.84109i	−0.378459	−	0.274967i	0.382251	−	0.924059i	$-0.375149\pi$
$619$	−9.41595	−	6.84109i	−0.378459	−	0.274967i	−0.760710	+	0.649092i	$0.775149\pi$
$620$	6.29450	−	5.11326i	0.252793	−	0.205353i
$621$	−5.27882	+	3.83529i	−0.211832	+	0.153905i
$622$	8.18047	+	11.2595i	0.328007	+	0.451463i
$623$	−15.3630	+	4.99173i	−0.615504	+	0.199989i
$624$	2.80530			0.112302
$625$	−22.9008	−	10.0275i	−0.916033	−	0.401102i
$626$	−15.3804			−0.614726
$627$	−0.120501	+	0.0391532i	−0.00481236	+	0.00156363i
$628$	−11.8257	−	16.2767i	−0.471898	−	0.649511i
$629$	−23.8413	+	17.3218i	−0.950617	+	0.690663i
$630$	−4.54714	+	3.69381i	−0.181162	+	0.147165i
$631$	−3.73919	−	2.71668i	−0.148855	−	0.108149i	0.510865	−	0.859661i	$-0.329325\pi$
$631$	−3.73919	−	2.71668i	−0.148855	−	0.108149i	−0.659720	+	0.751511i	$0.729325\pi$
$632$		−	7.81462i		−	0.310849i
$633$	6.91460	−	9.51713i	0.274831	−	0.378272i
$634$	−1.98526	+	6.11001i	−0.0788449	+	0.242660i
$635$	−22.7186	+	35.1018i	−0.901560	+	1.39297i
$636$	4.30020	+	13.2347i	0.170514	+	0.524789i
$637$	0.362457	+	0.117769i	0.0143611	+	0.00466620i
$638$	1.97243	+	0.640880i	0.0780891	+	0.0253727i
$639$	1.48879	+	4.58203i	0.0588957	+	0.181262i
$640$	−2.16076	−	0.575410i	−0.0854117	−	0.0227451i
$641$	7.85079	−	24.1623i	0.310088	−	0.954352i	−0.667642	−	0.744483i	$-0.732696\pi$
$641$	7.85079	−	24.1623i	0.310088	−	0.954352i	0.977730	−	0.209869i	$-0.0673037\pi$
$642$	2.24117	−	3.08471i	0.0884520	−	0.121744i
$643$		−	41.3338i		−	1.63005i	−0.579429	−	0.815023i	$-0.696724\pi$
$643$		−	41.3338i		−	1.63005i	0.579429	−	0.815023i	$-0.303276\pi$
$644$	13.8303	+	10.0483i	0.544988	+	0.395957i
$645$	−4.63430	+	17.4026i	−0.182475	+	0.685226i
$646$	−2.32849	+	1.69175i	−0.0916131	+	0.0665608i
$647$	−3.20446	−	4.41055i	−0.125980	−	0.173397i	0.741368	−	0.671099i	$-0.234177\pi$
$647$	−3.20446	−	4.41055i	−0.125980	−	0.173397i	−0.867348	+	0.497702i	$0.834177\pi$
$648$	0.951057	−	0.309017i	0.0373610	−	0.0121393i
$649$	−1.07088			−0.0420358
$650$	−2.87400	+	13.7289i	−0.112728	+	0.538491i
$651$	9.50188			0.372408
$652$	−2.01084	+	0.653363i	−0.0787507	+	0.0255877i
$653$	−16.1526	−	22.2322i	−0.632101	−	0.870013i	0.366062	−	0.930590i	$-0.380706\pi$
$653$	−16.1526	−	22.2322i	−0.632101	−	0.870013i	−0.998163	+	0.0605775i	$0.980706\pi$
$654$	6.44455	−	4.68224i	0.252002	−	0.183090i
$655$	10.1625	−	0.548289i	0.397083	−	0.0214234i
$656$	−4.30726	−	3.12941i	−0.168170	−	0.122183i
$657$		−	11.7867i		−	0.459844i
$658$	−13.8543	+	19.0688i	−0.540096	+	0.743378i
$659$	−13.0534	+	40.1743i	−0.508489	+	1.56497i	0.286336	+	0.958129i	$0.407563\pi$
$659$	−13.0534	+	40.1743i	−0.508489	+	1.56497i	−0.794825	+	0.606839i	$0.792437\pi$
$660$	0.402956	+	0.496045i	0.0156850	+	0.0193085i
$661$	1.96478	+	6.04696i	0.0764210	+	0.235200i	0.981968	−	0.189046i	$-0.0605394\pi$
$661$	1.96478	+	6.04696i	0.0764210	+	0.235200i	−0.905547	+	0.424245i	$0.860539\pi$
$662$	17.2784	+	5.61409i	0.671544	+	0.218198i
$663$	−17.3218	−	5.62818i	−0.672721	−	0.218580i
$664$	1.59510	+	4.90923i	0.0619021	+	0.190515i
$665$	0.139915	+	2.59332i	0.00542567	+	0.100565i
$666$	1.40265	−	4.31691i	0.0543515	−	0.167277i
$667$	27.8302	−	38.3050i	1.07759	−	1.48318i
$668$			19.4759i			0.753544i
$669$	7.70310	+	5.59663i	0.297819	+	0.216378i
$670$	8.23257	+	21.3483i	0.318052	+	0.824755i
$671$	3.01030	−	2.18711i	0.116211	−	0.0844324i
$672$	−1.53997	−	2.11959i	−0.0594056	−	0.0817648i
$673$	−19.3775	+	6.29612i	−0.746947	+	0.242698i	−0.657667	−	0.753309i	$-0.728457\pi$
$673$	−19.3775	+	6.29612i	−0.746947	+	0.242698i	−0.0892798	+	0.996007i	$0.528457\pi$
$674$	2.38677			0.0919349
$675$	0.537954	+	4.97098i	0.0207059	+	0.191333i
$676$	−5.13032			−0.197320
$677$	−5.99042	+	1.94641i	−0.230231	+	0.0748065i	−0.421860	−	0.906661i	$-0.638623\pi$
$677$	−5.99042	+	1.94641i	−0.230231	+	0.0748065i	0.191630	+	0.981467i	$0.438623\pi$
$678$	3.08596	+	4.24746i	0.118516	+	0.163123i
$679$	11.5526	−	8.39345i	0.443348	−	0.322111i
$680$	12.1876	+	7.88804i	0.467372	+	0.302493i
$681$	13.2010	+	9.59107i	0.505862	+	0.367530i
$682$		−	1.03655i		−	0.0396917i
$683$	−11.5797	+	15.9381i	−0.443085	+	0.609855i	−0.970894	−	0.239508i	$-0.923014\pi$
$683$	−11.5797	+	15.9381i	−0.443085	+	0.609855i	0.527809	+	0.849363i	$0.323014\pi$
$684$	0.136991	−	0.421615i	0.00523798	−	0.0161208i
$685$	32.4295	−	12.5058i	1.23907	−	0.477824i
$686$	−5.77726	−	17.7806i	−0.220577	−	0.678865i
$687$	−0.507563	−	0.164917i	−0.0193647	−	0.00629199i
$688$	−7.65972	−	2.48879i	−0.292024	−	0.0948843i
$689$	12.0633	+	37.1272i	0.459577	+	1.41443i
$690$	13.6131	−	5.24966i	0.518244	−	0.199851i
$691$	−15.0733	+	46.3909i	−0.573416	+	1.76479i	0.0680955	+	0.997679i	$0.478308\pi$
$691$	−15.0733	+	46.3909i	−0.573416	+	1.76479i	−0.641511	+	0.767114i	$0.721692\pi$
$692$	−1.94603	+	2.67848i	−0.0739768	+	0.101820i
$693$			0.748806i			0.0284448i
$694$	−20.9848	−	15.2463i	−0.796572	−	0.578743i
$695$	−16.8966	−	10.9358i	−0.640923	−	0.414819i
$696$	−5.87052	+	4.26518i	−0.222521	+	0.161671i
$697$	20.3175	+	27.9646i	0.769578	+	1.05923i
$698$	0.234692	−	0.0762560i	0.00888321	−	0.00288633i
$699$	−10.9418			−0.413856
$700$	11.9508	−	5.36498i	0.451696	−	0.202777i
$701$	−43.3213			−1.63622			−0.818111	−	0.575061i	$-0.804978\pi$
$701$	−43.3213			−1.63622			−0.818111	+	0.575061i	$0.804978\pi$
$702$	2.66799	−	0.866884i	0.100697	−	0.0327184i
$703$	−1.18275	−	1.62792i	−0.0446084	−	0.0613982i
$704$	−0.231224	+	0.167994i	−0.00871459	+	0.00633152i
$705$	7.23809	+	18.7694i	0.272602	+	0.706898i
$706$	15.5350	+	11.2868i	0.584667	+	0.424786i
$707$			28.2340i			1.06185i
$708$	2.20234	−	3.03127i	0.0827691	−	0.113922i
$709$	−4.95136	+	15.2387i	−0.185952	+	0.572302i	−0.999963	−	0.00854727i	$-0.997279\pi$
$709$	−4.95136	+	15.2387i	−0.185952	+	0.572302i	0.814011	+	0.580849i	$0.197279\pi$
$710$	−0.580381	−	10.7574i	−0.0217813	−	0.403717i
$711$	−2.41485	−	7.43215i	−0.0905640	−	0.278727i
$712$	−5.86383	−	1.90527i	−0.219756	−	0.0714032i
$713$	−22.5062	−	7.31270i	−0.842863	−	0.273863i
$714$	5.25633	+	16.1773i	0.196713	+	0.605421i
$715$	1.13041	+	1.39155i	0.0422749	+	0.0520411i
$716$	−3.85044	+	11.8504i	−0.143898	+	0.442872i
$717$	3.54917	−	4.88501i	0.132546	−	0.182434i
$718$		−	15.4421i		−	0.576296i
$719$	22.4469	+	16.3087i	0.837130	+	0.608210i	0.921567	−	0.388218i	$-0.126909\pi$
$719$	22.4469	+	16.3087i	0.837130	+	0.608210i	−0.0844377	+	0.996429i	$0.526909\pi$
$720$	−2.23282	+	0.120465i	−0.0832123	+	0.00448947i
$721$	37.9748	−	27.5903i	1.41425	−	1.02752i
$722$	11.0524	+	15.2123i	0.411328	+	0.566144i
$723$	2.09899	−	0.682003i	0.0780623	−	0.0253640i
$724$	−6.05748			−0.225124
$725$	−14.8591	−	33.0995i	−0.551855	−	1.22928i
$726$	−10.9183			−0.405217
$727$	−43.2427	+	14.0504i	−1.60378	+	0.521101i	−0.968039	−	0.250799i	$-0.919307\pi$
$727$	−43.2427	+	14.0504i	−1.60378	+	0.521101i	−0.635744	+	0.771900i	$0.719307\pi$
$728$	−4.32007	−	5.94606i	−0.160112	−	0.220376i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−6.78220	+	25.4683i	−0.251020	+	0.942625i
$731$	42.3030	+	30.7349i	1.56463	+	1.13677i
$732$			13.0189i			0.481194i
$733$	18.4749	−	25.4285i	0.682385	−	0.939223i	−0.317574	−	0.948233i	$-0.602868\pi$
$733$	18.4749	−	25.4285i	0.682385	−	0.939223i	0.999959	+	0.00901080i	$0.00286826\pi$
$734$	7.71643	−	23.7487i	0.284819	−	0.876581i
$735$	−0.293548	−	0.0781717i	−0.0108277	−	0.00288341i
$736$	2.01633	+	6.20562i	0.0743229	+	0.228742i
$737$	2.78141	+	0.903735i	0.102455	+	0.0332895i
$738$	−5.06349	−	1.64523i	−0.186390	−	0.0605617i
$739$	5.26372	+	16.2001i	0.193629	+	0.595929i	0.999990	+	0.00450517i	$0.00143405\pi$
$739$	5.26372	+	16.2001i	0.193629	+	0.595929i	−0.806361	+	0.591424i	$0.798566\pi$
$740$	−5.51478	+	8.52072i	−0.202727	+	0.313228i
$741$	0.384300	−	1.18275i	0.0141176	−	0.0434495i
$742$	21.4298	−	29.4956i	0.786714	−	1.08282i
$743$		−	1.44429i		−	0.0529858i	−0.999649	−	0.0264929i	$-0.991566\pi$
$743$		−	1.44429i		−	0.0529858i	0.999649	−	0.0264929i	$-0.00843393\pi$
$744$	2.93409	+	2.13174i	0.107569	+	0.0781535i
$745$	−13.6667	+	11.1020i	−0.500709	+	0.406744i
$746$	15.0999	−	10.9707i	0.552845	−	0.401665i
$747$	3.03407	+	4.17604i	0.111011	+	0.152793i
$748$	1.76477	−	0.573410i	0.0645265	−	0.0209659i
$749$	−9.98963			−0.365013
$750$	1.69796	−	11.0507i	0.0620007	−	0.403513i
$751$	22.1167			0.807051			0.403526	−	0.914968i	$-0.367785\pi$
$751$	22.1167			0.807051			0.403526	+	0.914968i	$0.367785\pi$
$752$	−8.55614	+	2.78006i	−0.312010	+	0.101378i
$753$	−0.0891381	−	0.122688i	−0.00324837	−	0.00447100i
$754$	−16.4685	+	11.9651i	−0.599748	+	0.435743i
$755$	−30.8343	+	25.0479i	−1.12218	+	0.911585i
$756$	−2.11959	−	1.53997i	−0.0770886	−	0.0560081i
$757$		−	18.0645i		−	0.656565i	−0.944580	−	0.328283i	$-0.893530\pi$
$757$		−	18.0645i		−	0.656565i	0.944580	−	0.328283i	$-0.106470\pi$
$758$	−17.1916	+	23.6622i	−0.624427	+	0.859450i
$759$	0.576285	−	1.77362i	0.0209178	−	0.0643784i
$760$	−0.538607	+	0.832184i	−0.0195373	+	0.0301865i
$761$	4.42227	+	13.6103i	0.160307	+	0.493375i	0.998660	−	0.0517535i	$-0.0164810\pi$
$761$	4.42227	+	13.6103i	0.160307	+	0.493375i	−0.838353	+	0.545128i	$0.816481\pi$
$762$	−17.7838	−	5.77832i	−0.644241	−	0.209326i
$763$	−19.8488	−	6.44927i	−0.718575	−	0.233479i
$764$	−7.22123	−	22.2247i	−0.261255	−	0.804060i
$765$	14.0286	+	3.73581i	0.507205	+	0.135068i
$766$	−3.20500	+	9.86397i	−0.115801	+	0.356400i
$767$	6.17822	−	8.50359i	0.223083	−	0.307047i
$768$		−	1.00000i		−	0.0360844i
$769$	27.8453	+	20.2308i	1.00413	+	0.729541i	0.962969	−	0.269612i	$-0.0868954\pi$
$769$	27.8453	+	20.2308i	1.00413	+	0.729541i	0.0411578	+	0.999153i	$0.486895\pi$
$770$	0.430870	−	1.61799i	0.0155275	−	0.0583084i
$771$	−8.45113	+	6.14011i	−0.304360	+	0.221131i
$772$	1.25369	+	1.72556i	0.0451213	+	0.0621042i
$773$	30.5888	−	9.93889i	1.10020	−	0.357477i	0.298021	−	0.954559i	$-0.403673\pi$
$773$	30.5888	−	9.93889i	1.10020	−	0.357477i	0.802180	+	0.597082i	$0.203673\pi$
$774$	−8.05390			−0.289492
$775$	−13.4385	+	12.1753i	−0.482726	+	0.437348i
$776$	5.45040			0.195658
$777$	−11.3101	+	3.67487i	−0.405747	+	0.131835i
$778$	−5.37976	−	7.40460i	−0.192874	−	0.265468i
$779$	−1.90946	+	1.38730i	−0.0684135	+	0.0497053i
$780$	−6.26372	+	0.337940i	−0.224277	+	0.0121002i
$781$	−1.11400	−	0.809369i	−0.0398621	−	0.0289615i
$782$		−	42.3629i		−	1.51490i
$783$	−4.26518	+	5.87052i	−0.152425	+	0.209795i
$784$	0.0419811	−	0.129205i	0.00149933	−	0.00461445i
$785$	28.3655	+	34.9184i	1.01241	+	1.24629i
$786$	1.40647	+	4.32867i	0.0501671	+	0.154399i
$787$	−30.0132	−	9.75188i	−1.06985	−	0.347617i	−0.279424	−	0.960168i	$-0.590143\pi$
$787$	−30.0132	−	9.75188i	−1.06985	−	0.347617i	−0.790431	+	0.612551i	$0.790143\pi$
$788$	−15.6508	−	5.08526i	−0.557538	−	0.181155i
$789$	−6.78608	−	20.8854i	−0.241591	−	0.743540i
$790$	0.941390	+	17.4487i	0.0334931	+	0.620795i
$791$	4.25057	−	13.0819i	0.151133	−	0.465139i
$792$	−0.167994	+	0.231224i	−0.00596942	+	0.00821620i
$793$			36.5220i			1.29693i
$794$	−13.0616	−	9.48983i	−0.463540	−	0.336781i
$795$	−11.1959	−	29.0326i	−0.397078	−	1.02968i
$796$	−1.34743	+	0.978967i	−0.0477585	+	0.0346986i
$797$	−16.0150	−	22.0428i	−0.567281	−	0.780796i	0.424948	−	0.905218i	$-0.360292\pi$
$797$	−16.0150	−	22.0428i	−0.567281	−	0.780796i	−0.992229	+	0.124422i	$0.960292\pi$
$798$	−1.10461	+	0.358910i	−0.0391028	+	0.0127053i
$799$	58.4088			2.06636
$800$	4.89392	+	1.02449i	0.173026	+	0.0362212i
$801$	−6.16560			−0.217851
$802$	24.6693	−	8.01554i	0.871103	−	0.283039i
$803$	1.98010	+	2.72537i	0.0698762	+	0.0961764i
$804$	−8.27829	+	6.01453i	−0.291953	+	0.212116i
$805$	−32.0909	−	20.7699i	−1.13106	−	0.732043i
$806$	8.23100	+	5.98017i	0.289924	+	0.210642i
$807$		−	14.1299i		−	0.497396i
$808$	−6.33428	+	8.71839i	−0.222839	+	0.306712i
$809$	−4.84894	+	14.9235i	−0.170480	+	0.524682i	−0.999398	−	0.0346871i	$-0.988957\pi$
$809$	−4.84894	+	14.9235i	−0.170480	+	0.524682i	0.828919	+	0.559369i	$0.188957\pi$
$810$	−2.08631	+	0.804549i	−0.0733056	+	0.0282690i
$811$	−7.11528	−	21.8986i	−0.249851	−	0.768963i	−0.994801	−	0.101842i	$-0.967526\pi$
$811$	−7.11528	−	21.8986i	−0.249851	−	0.768963i	0.744949	−	0.667121i	$-0.232474\pi$
$812$	18.0808	+	5.87482i	0.634513	+	0.206166i
$813$	−26.1816	−	8.50693i	−0.918230	−	0.298351i
$814$	0.400889	+	1.23381i	0.0140512	+	0.0432450i
$815$	4.41115	−	1.70108i	0.154516	−	0.0595862i
$816$	−2.00627	+	6.17466i	−0.0702335	+	0.216156i
$817$	−2.09862	+	2.88851i	−0.0734215	+	0.101056i
$818$		−	17.0650i		−	0.596665i
$819$	−5.94606	−	4.32007i	−0.207772	−	0.150955i
$820$	9.99433	+	6.46854i	0.349017	+	0.225891i
$821$	8.97939	−	6.52391i	0.313383	−	0.227686i	−0.419964	−	0.907541i	$-0.637957\pi$
$821$	8.97939	−	6.52391i	0.313383	−	0.227686i	0.733347	+	0.679855i	$0.237957\pi$
$822$	9.13649	+	12.5753i	0.318672	+	0.438614i
$823$	42.1285	−	13.6884i	1.46851	−	0.477146i	0.537849	−	0.843041i	$-0.319237\pi$
$823$	42.1285	−	13.6884i	1.46851	−	0.477146i	0.930656	+	0.365894i	$0.119237\pi$
$824$	17.9161			0.624138
$825$	−0.959484	−	1.05904i	−0.0334049	−	0.0368709i
$826$	−9.81657			−0.341562
$827$	9.82358	−	3.19188i	0.341599	−	0.110992i	−0.133193	−	0.991090i	$-0.542523\pi$
$827$	9.82358	−	3.19188i	0.341599	−	0.110992i	0.474793	+	0.880098i	$0.342523\pi$
$828$	3.83529	+	5.27882i	0.133285	+	0.183452i
$829$	−38.9949	+	28.3315i	−1.35435	+	0.983992i	−0.355567	+	0.934651i	$0.615712\pi$
$829$	−38.9949	+	28.3315i	−1.35435	+	0.983992i	−0.998782	+	0.0493418i	$0.984288\pi$
$830$	−4.15297	−	10.7693i	−0.144152	−	0.373807i
$831$	19.0895	+	13.8693i	0.662208	+	0.481122i
$832$		−	2.80530i		−	0.0972561i
$833$	−0.518439	+	0.713570i	−0.0179628	+	0.0247237i
$834$	2.78145	−	8.56041i	0.0963136	−	0.296423i
$835$	−2.34616	−	43.4861i	−0.0811923	−	1.50490i
$836$	0.0391532	+	0.120501i	0.00135414	+	0.00416762i
$837$	3.44923	+	1.12072i	0.119223	+	0.0387379i
$838$	−13.1368	−	4.26840i	−0.453803	−	0.147450i
$839$	−0.808745	−	2.48906i	−0.0279210	−	0.0859320i	0.936125	−	0.351667i	$-0.114385\pi$
$839$	−0.808745	−	2.48906i	−0.0279210	−	0.0859320i	−0.964046	+	0.265736i	$0.914385\pi$
$840$	3.69381	+	4.54714i	0.127449	+	0.156891i
$841$	7.30971	−	22.4970i	0.252059	−	0.775758i
$842$	−1.22553	+	1.68679i	−0.0422345	+	0.0581308i
$843$		−	7.17134i		−	0.246994i
$844$	−9.51713	−	6.91460i	−0.327593	−	0.238010i
$845$	11.4551	−	0.618025i	0.394067	−	0.0212607i
$846$	−7.27829	+	5.28799i	−0.250233	+	0.181805i
$847$	16.8139	+	23.1423i	0.577731	+	0.795179i
$848$	13.2347	−	4.30020i	0.454480	−	0.147670i
$849$	23.0321			0.790461
$850$	−28.1629	−	16.1444i	−0.965979	−	0.553748i
$851$	29.6173			1.01527
$852$	4.58203	−	1.48879i	0.156978	−	0.0510052i
$853$	8.93777	+	12.3018i	0.306023	+	0.421205i	0.934136	−	0.356917i	$-0.116172\pi$
$853$	8.93777	+	12.3018i	0.306023	+	0.421205i	−0.628113	+	0.778123i	$0.716172\pi$
$854$	27.5948	−	20.0488i	0.944274	−	0.686055i
$855$	−0.255086	+	0.957893i	−0.00872377	+	0.0327592i
$856$	−3.08471	−	2.24117i	−0.105433	−	0.0766016i
$857$			26.1596i			0.893595i	0.894635	+	0.446797i	$0.147436\pi$
$857$			26.1596i			0.893595i	−0.894635	+	0.446797i	$0.852564\pi$
$858$	−0.471274	+	0.648652i	−0.0160890	+	0.0221446i
$859$	−2.21938	+	6.83054i	−0.0757241	+	0.233055i	−0.981753	−	0.190161i	$-0.939099\pi$
$859$	−2.21938	+	6.83054i	−0.0757241	+	0.233055i	0.906029	+	0.423216i	$0.139099\pi$
$860$	17.4026	+	4.63430i	0.593423	+	0.158028i
$861$	4.31042	+	13.2661i	0.146899	+	0.452108i
$862$	8.87920	+	2.88503i	0.302427	+	0.0982644i
$863$	−34.9141	−	11.3443i	−1.18849	−	0.386164i	−0.352977	−	0.935632i	$-0.614830\pi$
$863$	−34.9141	−	11.3443i	−1.18849	−	0.386164i	−0.835515	+	0.549468i	$0.814830\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	4.02246	−	6.21498i	0.136768	−	0.211316i
$866$	3.61984	−	11.1407i	0.123007	−	0.378577i
$867$	14.7837	−	20.3481i	0.502082	−	0.691056i
$868$		−	9.50188i		−	0.322515i
$869$	1.80693	+	1.31281i	0.0612959	+	0.0445341i
$870$	12.5940	−	10.2306i	0.426977	−	0.346849i
$871$	−23.2230	+	16.8725i	−0.786883	+	0.571704i
$872$	−4.68224	−	6.44455i	−0.158561	−	0.218240i
$873$	5.18364	−	1.68427i	0.175440	−	0.0570038i
$874$	2.89260			0.0978437
$875$	−26.0376	+	13.4187i	−0.880232	+	0.453635i
$876$	−11.7867			−0.398236
$877$	−17.1289	+	5.56551i	−0.578401	+	0.187934i	−0.583584	−	0.812053i	$-0.698350\pi$
$877$	−17.1289	+	5.56551i	−0.578401	+	0.187934i	0.00518298	+	0.999987i	$0.498350\pi$
$878$	1.81156	+	2.49339i	0.0611371	+	0.0841479i
$879$	−13.2558	+	9.63094i	−0.447109	+	0.324844i
$880$	0.496045	−	0.402956i	0.0167217	−	0.0135836i
$881$	2.31663	+	1.68313i	0.0780491	+	0.0567060i	0.626126	−	0.779722i	$-0.284640\pi$
$881$	2.31663	+	1.68313i	0.0780491	+	0.0567060i	−0.548076	+	0.836428i	$0.684640\pi$
$882$		−	0.135854i		−	0.00457444i
$883$	−26.9383	+	37.0773i	−0.906545	+	1.24775i	0.0617883	+	0.998089i	$0.480320\pi$
$883$	−26.9383	+	37.0773i	−0.906545	+	1.24775i	−0.968333	+	0.249662i	$0.919680\pi$
$884$	−5.62818	+	17.3218i	−0.189296	+	0.582594i
$885$	−4.55228	+	7.03358i	−0.153023	+	0.236431i
$886$	3.28656	+	10.1150i	0.110414	+	0.339819i
$887$	−14.1264	−	4.58995i	−0.474319	−	0.154116i	0.0620957	−	0.998070i	$-0.480222\pi$
$887$	−14.1264	−	4.58995i	−0.474319	−	0.154116i	−0.536414	+	0.843955i	$0.680222\pi$
$888$	−4.31691	−	1.40265i	−0.144866	−	0.0470698i
$889$	15.1389	+	46.5928i	0.507743	+	1.56267i
$890$	13.3224	+	3.54775i	0.446568	+	0.118921i
$891$	−0.0883198	+	0.271820i	−0.00295883	+	0.00910633i
$892$	5.59663	−	7.70310i	0.187389	−	0.257919i
$893$			3.98824i			0.133461i
$894$	−6.37053	−	4.62846i	−0.213062	−	0.154799i
$895$	7.16978	−	26.9238i	0.239659	−	0.899962i
$896$	−2.11959	+	1.53997i	−0.0708104	+	0.0514467i
$897$	10.7591	+	14.8086i	0.359236	+	0.494446i
$898$	−21.7104	+	7.05412i	−0.724484	+	0.235399i
$899$	−26.3169			−0.877718
$900$	4.97098	−	0.537954i	0.165699	−	0.0179318i
$901$	−90.3470			−3.00989
$902$	1.44719	−	0.470221i	0.0481862	−	0.0156566i
$903$	12.4028	+	17.0709i	0.412738	+	0.568085i
$904$	4.24746	−	3.08596i	0.141268	−	0.102638i
$905$	13.5253	−	0.729715i	0.449595	−	0.0242565i
$906$	−14.3730	−	10.4426i	−0.477510	−	0.346932i
$907$		−	38.6577i		−	1.28361i	−0.766869	−	0.641804i	$-0.778186\pi$
$907$		−	38.6577i		−	1.28361i	0.766869	−	0.641804i	$-0.221814\pi$
$908$	9.59107	−	13.2010i	0.318291	−	0.438090i
$909$	−3.33013	+	10.2491i	−0.110453	+	0.339941i
$910$	10.3622	+	12.7561i	0.343505	+	0.422860i
$911$	15.0057	+	46.1829i	0.497162	+	1.53011i	0.813560	+	0.581481i	$0.197526\pi$
$911$	15.0057	+	46.1829i	0.497162	+	1.53011i	−0.316398	+	0.948627i	$0.602474\pi$
$912$	−0.421615	−	0.136991i	−0.0139611	−	0.00453622i
$913$	−1.40310	−	0.455895i	−0.0464359	−	0.0150879i
$914$	−7.96115	−	24.5019i	−0.263331	−	0.810451i
$915$	−1.56833	−	29.0690i	−0.0518474	−	0.960991i
$916$	−0.164917	+	0.507563i	−0.00544902	+	0.0167704i
$917$	7.00907	−	9.64715i	0.231460	−	0.318577i
$918$			6.49242i			0.214282i
$919$	−23.7760	−	17.2743i	−0.784298	−	0.569826i	0.121968	−	0.992534i	$-0.461080\pi$
$919$	−23.7760	−	17.2743i	−0.784298	−	0.569826i	−0.906266	+	0.422708i	$0.861080\pi$
$920$	−5.24966	−	13.6131i	−0.173076	−	0.448812i
$921$	15.0499	−	10.9344i	0.495912	−	0.360301i
$922$	−19.0570	−	26.2298i	−0.627610	−	0.863831i
$923$	12.8540	−	4.17650i	0.423093	−	0.137471i
$924$	0.748806			0.0246339
$925$	11.2871	−	19.6896i	0.371117	−	0.647389i
$926$	−18.7775			−0.617066
$927$	17.0392	−	5.53639i	0.559642	−	0.181839i
$928$	4.26518	+	5.87052i	0.140011	+	0.192709i
$929$	38.3191	−	27.8405i	1.25721	−	0.913416i	0.258592	−	0.965987i	$-0.416741\pi$
$929$	38.3191	−	27.8405i	1.25721	−	0.913416i	0.998617	+	0.0525705i	$0.0167414\pi$
$930$	−6.80810	−	4.40634i	−0.223247	−	0.144490i
$931$	−0.0487235	−	0.0353997i	−0.00159685	−	0.00116018i
$932$			10.9418i			0.358410i
$933$	8.18047	−	11.2595i	0.267817	−	0.368618i
$934$	0.606328	−	1.86609i	0.0198397	−	0.0610602i
$935$	−3.87135	+	1.49291i	−0.126607	+	0.0488235i
$936$	−0.866884	−	2.66799i	−0.0283350	−	0.0872061i
$937$	23.1496	+	7.52176i	0.756264	+	0.245725i	0.661675	−	0.749791i	$-0.269846\pi$
$937$	23.1496	+	7.52176i	0.756264	+	0.245725i	0.0945898	+	0.995516i	$0.469846\pi$
$938$	25.4966	+	8.28435i	0.832494	+	0.270494i
$939$	4.75282	+	14.6277i	0.155102	+	0.477356i
$940$	18.7694	−	7.23809i	0.612191	−	0.236080i
$941$	6.04638	−	18.6088i	0.197106	−	0.606631i	−0.802839	−	0.596196i	$-0.796678\pi$
$941$	6.04638	−	18.6088i	0.197106	−	0.606631i	0.999946	−	0.0104355i	$-0.00332177\pi$
$942$	−11.8257	+	16.2767i	−0.385303	+	0.530324i
$943$		−	34.7394i		−	1.13127i
$944$	−3.03127	−	2.20234i	−0.0986593	−	0.0716802i
$945$	4.91817	+	3.18314i	0.159988	+	0.103547i
$946$	1.86226	−	1.35301i	0.0605472	−	0.0439901i
$947$	26.9916	+	37.1508i	0.877110	+	1.20724i	0.977213	+	0.212261i	$0.0680827\pi$
$947$	26.9916	+	37.1508i	0.877110	+	1.20724i	−0.100103	+	0.994977i	$0.531917\pi$
$948$	−7.43215	+	2.41485i	−0.241385	+	0.0784307i
$949$	−33.0652			−1.07334
$950$	1.10236	−	1.92300i	0.0357654	−	0.0623904i
$951$	6.42445			0.208327
$952$	16.1773	−	5.25633i	0.524310	−	0.170359i
$953$	−11.6259	−	16.0017i	−0.376600	−	0.518346i	0.578080	−	0.815980i	$-0.303802\pi$
$953$	−11.6259	−	16.0017i	−0.376600	−	0.518346i	−0.954680	+	0.297635i	$0.903802\pi$
$954$	11.2581	−	8.17947i	0.364494	−	0.264820i
$955$	18.8010	+	48.7538i	0.608386	+	1.57764i
$956$	−4.88501	−	3.54917i	−0.157993	−	0.114788i
$957$		−	2.07393i		−	0.0670407i
$958$	3.96389	−	5.45583i	0.128068	−	0.176270i
$959$	12.5845	−	38.7311i	0.406375	−	1.25069i
$960$	0.120465	+	2.23282i	0.00388800	+	0.0720640i
$961$	−5.51496	−	16.9733i	−0.177902	−	0.547525i
$962$	−12.1102	−	3.93484i	−0.390448	−	0.126864i
$963$	−3.62629	−	1.17825i	−0.116856	−	0.0379687i
$964$	−0.682003	−	2.09899i	−0.0219658	−	0.0676039i
$965$	−3.00714	−	3.70183i	−0.0968031	−	0.119166i
$966$	5.28269	−	16.2584i	0.169968	−	0.523107i
$967$	−12.4205	+	17.0954i	−0.399417	+	0.549750i	−0.960598	−	0.277943i	$-0.910347\pi$
$967$	−12.4205	+	17.0954i	−0.399417	+	0.549750i	0.561181	+	0.827693i	$0.310347\pi$
$968$			10.9183i			0.350928i
$969$	2.32849	+	1.69175i	0.0748018	+	0.0543467i
$970$	−12.1698	+	0.656584i	−0.390748	+	0.0210816i
$971$	38.9629	−	28.3082i	1.25038	−	0.908454i	0.252136	−	0.967692i	$-0.418867\pi$
$971$	38.9629	−	28.3082i	1.25038	−	0.908454i	0.998244	+	0.0592379i	$0.0188671\pi$
$972$	−0.587785	−	0.809017i	−0.0188532	−	0.0259492i
$973$	−22.4279	+	7.28726i	−0.719004	+	0.233619i
$974$	−1.16407			−0.0372991
$975$	13.9451	−	1.50912i	0.446599	−	0.0483305i
$976$	13.0189			0.416726
$977$	−48.0847	+	15.6237i	−1.53837	+	0.499846i	−0.950925	−	0.309421i	$-0.899865\pi$
$977$	−48.0847	+	15.6237i	−1.53837	+	0.499846i	−0.587441	+	0.809267i	$0.699865\pi$
$978$	1.24277	+	1.71053i	0.0397394	+	0.0546966i
$979$	1.42564	−	1.03579i	0.0455635	−	0.0331038i
$980$	−0.0781717	+	0.293548i	−0.00249710	+	0.00937705i
$981$	−6.44455	−	4.68224i	−0.205759	−	0.149492i
$982$		−	8.38720i		−	0.267646i
$983$	−19.9304	+	27.4319i	−0.635683	+	0.874942i	−0.998376	−	0.0569664i	$-0.981857\pi$
$983$	−19.9304	+	27.4319i	−0.635683	+	0.874942i	0.362693	+	0.931908i	$0.381857\pi$
$984$	−1.64523	+	5.06349i	−0.0524480	+	0.161418i
$985$	35.5581	+	9.46910i	1.13298	+	0.301711i
$986$	−14.5582	−	44.8056i	−0.463628	−	1.42690i
$987$	22.4167	+	7.28362i	0.713531	+	0.231840i
$988$	−1.18275	−	0.384300i	−0.0376284	−	0.0122262i
$989$	−16.2393	−	49.9795i	−0.516380	−	1.58926i
$990$	0.347247	−	0.536520i	0.0110362	−	0.0170517i
$991$	−15.9403	+	49.0592i	−0.506360	+	1.55842i	0.292111	+	0.956384i	$0.405642\pi$
$991$	−15.9403	+	49.0592i	−0.506360	+	1.55842i	−0.798472	+	0.602033i	$0.794358\pi$
$992$	2.13174	−	2.93409i	0.0676829	−	0.0931575i
$993$		−	18.1676i		−	0.576530i
$994$	−10.2118	−	7.41931i	−0.323899	−	0.235326i
$995$	2.89064	−	2.34818i	0.0916396	−	0.0744422i
$996$	4.17604	−	3.03407i	0.132323	−	0.0961381i
$997$	20.1177	+	27.6896i	0.637134	+	0.876940i	0.998459	−	0.0555003i	$-0.0176754\pi$
$997$	20.1177	+	27.6896i	0.637134	+	0.876940i	−0.361325	+	0.932440i	$0.617675\pi$
$998$	16.4143	−	5.33333i	0.519586	−	0.168824i
$999$	−4.53906			−0.143610

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.h.b.19.1	✓	16
3.2	odd	2		450.2.l.c.19.4		16
5.2	odd	4		750.2.g.g.151.2		16
5.3	odd	4		750.2.g.f.151.3		16
5.4	even	2		750.2.h.d.349.3		16
25.2	odd	20		3750.2.a.u.1.4		8
25.3	odd	20		750.2.g.f.601.3		16
25.4	even	10	inner	150.2.h.b.79.1	yes	16
25.11	even	5		3750.2.c.k.1249.13		16
25.14	even	10		3750.2.c.k.1249.4		16
25.21	even	5		750.2.h.d.649.4		16
25.22	odd	20		750.2.g.g.601.2		16
25.23	odd	20		3750.2.a.v.1.5		8
75.29	odd	10		450.2.l.c.379.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.1	✓	16	1.1	even	1	trivial
150.2.h.b.79.1	yes	16	25.4	even	10	inner
450.2.l.c.19.4		16	3.2	odd	2
450.2.l.c.379.4		16	75.29	odd	10
750.2.g.f.151.3		16	5.3	odd	4
750.2.g.f.601.3		16	25.3	odd	20
750.2.g.g.151.2		16	5.2	odd	4
750.2.g.g.601.2		16	25.22	odd	20
750.2.h.d.349.3		16	5.4	even	2
750.2.h.d.649.4		16	25.21	even	5
3750.2.a.u.1.4		8	25.2	odd	20
3750.2.a.v.1.5		8	25.23	odd	20
3750.2.c.k.1249.4		16	25.14	even	10
3750.2.c.k.1249.13		16	25.11	even	5

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.73558 + 1.40988i) q^{5} +(-0.809017 - 0.587785i) q^{6} +2.61995i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-1.73558 + 1.40988i) q^{5} +(-0.809017 - 0.587785i) q^{6} +2.61995i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.21496 - 1.87720i) q^{10} +(-0.0883198 - 0.271820i) q^{11} +(0.951057 + 0.309017i) q^{12} +(2.66799 + 0.866884i) q^{13} +(-0.809610 - 2.49172i) q^{14} +(-2.16076 - 0.575410i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.81615 + 5.25248i) q^{17} -1.00000i q^{18} +(-0.358647 - 0.260572i) q^{19} +(-0.575410 + 2.16076i) q^{20} +(-2.11959 + 1.53997i) q^{21} +(0.167994 + 0.231224i) q^{22} +(6.20562 - 2.01633i) q^{23} -1.00000 q^{24} +(1.02449 - 4.89392i) q^{25} -2.80530 q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.53997 + 2.11959i) q^{28} +(5.87052 - 4.26518i) q^{29} +(2.23282 - 0.120465i) q^{30} +(-2.93409 - 2.13174i) q^{31} +1.00000i q^{32} +(0.167994 - 0.231224i) q^{33} +(2.00627 - 6.17466i) q^{34} +(-3.69381 - 4.54714i) q^{35} +(0.309017 + 0.951057i) q^{36} +(4.31691 + 1.40265i) q^{37} +(0.421615 + 0.136991i) q^{38} +(0.866884 + 2.66799i) q^{39} +(-0.120465 - 2.23282i) q^{40} +(1.64523 - 5.06349i) q^{41} +(1.53997 - 2.11959i) q^{42} -8.05390i q^{43} +(-0.231224 - 0.167994i) q^{44} +(-0.804549 - 2.08631i) q^{45} +(-5.27882 + 3.83529i) q^{46} +(-5.28799 - 7.27829i) q^{47} +(0.951057 - 0.309017i) q^{48} +0.135854 q^{49} +(0.537954 + 4.97098i) q^{50} -6.49242 q^{51} +(2.66799 - 0.866884i) q^{52} +(8.17947 + 11.2581i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.536520 + 0.347247i) q^{55} +(-2.11959 - 1.53997i) q^{56} -0.443312i q^{57} +(-4.26518 + 5.87052i) q^{58} +(1.15784 - 3.56347i) q^{59} +(-2.08631 + 0.804549i) q^{60} +(4.02308 + 12.3818i) q^{61} +(3.44923 + 1.12072i) q^{62} +(-2.49172 - 0.809610i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-5.85272 + 2.25700i) q^{65} +(-0.0883198 + 0.271820i) q^{66} +(-6.01453 + 8.27829i) q^{67} +6.49242i q^{68} +(5.27882 + 3.83529i) q^{69} +(4.91817 + 3.18314i) q^{70} +(3.89771 - 2.83185i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-11.2098 + 3.64230i) q^{73} -4.53906 q^{74} +(4.56144 - 2.04774i) q^{75} -0.443312 q^{76} +(0.712156 - 0.231394i) q^{77} +(-1.64891 - 2.26953i) q^{78} +(-6.32216 + 4.59332i) q^{79} +(0.804549 + 2.08631i) q^{80} +(-0.809017 - 0.587785i) q^{81} +5.32407i q^{82} +(3.03407 - 4.17604i) q^{83} +(-0.809610 + 2.49172i) q^{84} +(-0.782111 - 14.4964i) q^{85} +(2.48879 + 7.65972i) q^{86} +(6.90121 + 2.24234i) q^{87} +(0.271820 + 0.0883198i) q^{88} +(1.90527 + 5.86383i) q^{89} +(1.40988 + 1.73558i) q^{90} +(-2.27119 + 6.99002i) q^{91} +(3.83529 - 5.27882i) q^{92} -3.62674i q^{93} +(7.27829 + 5.28799i) q^{94} +(0.989836 - 0.0534036i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-3.20367 - 4.40947i) q^{97} +(-0.129205 + 0.0419811i) q^{98} +0.285809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{9} + 2 q^{10} + 2 q^{11} + 20 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 30 q^{17} - 4 q^{20} - 2 q^{21} - 20 q^{22} - 10 q^{23} - 16 q^{24} + 24 q^{25} + 4 q^{26} - 10 q^{29} - 6 q^{30} - 18 q^{31} - 20 q^{33} + 12 q^{34} - 34 q^{35} - 4 q^{36} + 20 q^{37} + 10 q^{38} - 4 q^{39} - 2 q^{40} + 22 q^{41} + 8 q^{44} - 4 q^{45} - 6 q^{46} - 50 q^{47} - 52 q^{49} + 12 q^{50} + 28 q^{51} + 20 q^{52} + 30 q^{53} + 4 q^{54} + 18 q^{55} - 2 q^{56} - 30 q^{58} + 20 q^{59} + 2 q^{60} + 12 q^{61} + 50 q^{62} + 10 q^{63} + 4 q^{64} - 8 q^{65} + 2 q^{66} - 50 q^{67} + 6 q^{69} - 12 q^{70} - 28 q^{71} + 20 q^{73} + 12 q^{74} + 28 q^{75} + 20 q^{76} + 100 q^{77} - 20 q^{79} + 4 q^{80} - 4 q^{81} - 30 q^{83} + 2 q^{84} - 4 q^{85} - 6 q^{86} + 10 q^{87} + 70 q^{89} + 8 q^{90} + 12 q^{91} - 30 q^{92} + 2 q^{94} - 30 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} - 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^9 + 2 * q^10 + 2 * q^11 + 20 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 30 * q^17 - 4 * q^20 - 2 * q^21 - 20 * q^22 - 10 * q^23 - 16 * q^24 + 24 * q^25 + 4 * q^26 - 10 * q^29 - 6 * q^30 - 18 * q^31 - 20 * q^33 + 12 * q^34 - 34 * q^35 - 4 * q^36 + 20 * q^37 + 10 * q^38 - 4 * q^39 - 2 * q^40 + 22 * q^41 + 8 * q^44 - 4 * q^45 - 6 * q^46 - 50 * q^47 - 52 * q^49 + 12 * q^50 + 28 * q^51 + 20 * q^52 + 30 * q^53 + 4 * q^54 + 18 * q^55 - 2 * q^56 - 30 * q^58 + 20 * q^59 + 2 * q^60 + 12 * q^61 + 50 * q^62 + 10 * q^63 + 4 * q^64 - 8 * q^65 + 2 * q^66 - 50 * q^67 + 6 * q^69 - 12 * q^70 - 28 * q^71 + 20 * q^73 + 12 * q^74 + 28 * q^75 + 20 * q^76 + 100 * q^77 - 20 * q^79 + 4 * q^80 - 4 * q^81 - 30 * q^83 + 2 * q^84 - 4 * q^85 - 6 * q^86 + 10 * q^87 + 70 * q^89 + 8 * q^90 + 12 * q^91 - 30 * q^92 + 2 * q^94 - 30 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 - 12 * q^99

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