LMFDB - Embedded newform 150.2.h.b.139.2

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			139.2
Root			$-2.79002 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	150.139
Dual form			150.2.h.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.03938 + 0.917020i) q^{5} +(0.309017 + 0.951057i) q^{6} -4.80694i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.03938 + 0.917020i) q^{5} +(0.309017 + 0.951057i) q^{6} -4.80694i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.456833 - 2.18890i) q^{10} +(0.714027 - 0.518771i) q^{11} +(0.587785 - 0.809017i) q^{12} +(1.66061 - 2.28564i) q^{13} +(-3.88890 + 2.82545i) q^{14} +(-1.65619 - 1.50234i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.57666 + 0.512289i) q^{17} -1.00000i q^{18} +(-1.66217 - 5.11563i) q^{19} +(-1.50234 + 1.65619i) q^{20} +(-1.48543 + 4.57167i) q^{21} +(-0.839389 - 0.272734i) q^{22} +(3.44056 + 4.73553i) q^{23} -1.00000 q^{24} +(3.31815 + 3.74031i) q^{25} -2.82520 q^{26} +(-0.587785 - 0.809017i) q^{27} +(4.57167 + 1.48543i) q^{28} +(-1.10574 + 3.40313i) q^{29} +(-0.241934 + 2.22294i) q^{30} +(3.22681 + 9.93109i) q^{31} +1.00000i q^{32} +(-0.839389 + 0.272734i) q^{33} +(1.34119 + 0.974432i) q^{34} +(4.40806 - 9.80318i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-1.02631 + 1.41260i) q^{37} +(-3.16163 + 4.35161i) q^{38} +(-2.28564 + 1.66061i) q^{39} +(2.22294 + 0.241934i) q^{40} +(1.40381 + 1.01993i) q^{41} +(4.57167 - 1.48543i) q^{42} -2.27151i q^{43} +(0.272734 + 0.839389i) q^{44} +(1.11088 + 1.94060i) q^{45} +(1.80881 - 5.56695i) q^{46} +(-8.29746 - 2.69601i) q^{47} +(0.587785 + 0.809017i) q^{48} -16.1067 q^{49} +(1.07561 - 4.88294i) q^{50} +1.65780 q^{51} +(1.66061 + 2.28564i) q^{52} +(-3.37565 - 1.09681i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.93190 - 0.403195i) q^{55} +(-1.48543 - 4.57167i) q^{56} +5.37889i q^{57} +(3.40313 - 1.10574i) q^{58} +(8.37628 + 6.08572i) q^{59} +(1.94060 - 1.11088i) q^{60} +(0.0697810 - 0.0506988i) q^{61} +(6.13775 - 8.44789i) q^{62} +(2.82545 - 3.88890i) q^{63} +(0.809017 - 0.587785i) q^{64} +(5.48259 - 3.13847i) q^{65} +(0.714027 + 0.518771i) q^{66} +(-11.3751 + 3.69601i) q^{67} -1.65780i q^{68} +(-1.80881 - 5.56695i) q^{69} +(-10.5219 + 2.19597i) q^{70} +(-1.08390 + 3.33591i) q^{71} +(0.951057 + 0.309017i) q^{72} +(4.24851 + 5.84757i) q^{73} +1.74607 q^{74} +(-1.99993 - 4.58261i) q^{75} +5.37889 q^{76} +(-2.49370 - 3.43228i) q^{77} +(2.68693 + 0.873035i) q^{78} +(3.88627 - 11.9607i) q^{79} +(-1.11088 - 1.94060i) q^{80} +(0.309017 + 0.951057i) q^{81} -1.73520i q^{82} +(-12.6244 + 4.10192i) q^{83} +(-3.88890 - 2.82545i) q^{84} +(-3.68520 - 0.401079i) q^{85} +(-1.83769 + 1.33516i) q^{86} +(2.10325 - 2.89488i) q^{87} +(0.518771 - 0.714027i) q^{88} +(15.1178 - 10.9837i) q^{89} +(0.917020 - 2.03938i) q^{90} +(-10.9869 - 7.98246i) q^{91} +(-5.56695 + 1.80881i) q^{92} -10.4422i q^{93} +(2.69601 + 8.29746i) q^{94} +(1.30134 - 11.9570i) q^{95} +(0.309017 - 0.951057i) q^{96} +(17.3764 + 5.64593i) q^{97} +(9.46727 + 13.0306i) q^{98} +0.882586 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	2.03938	+	0.917020i	0.912039	+	0.410104i
$5$	2.03938	+	0.917020i	0.912039	+	0.410104i
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$		−	4.80694i		−	1.81685i	−0.418045	−	0.908426i	$-0.637284\pi$
$7$		−	4.80694i		−	1.81685i	0.418045	−	0.908426i	$-0.362716\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−0.456833	−	2.18890i	−0.144463	−	0.692192i
$11$	0.714027	−	0.518771i	0.215287	−	0.156415i	−0.474915	−	0.880031i	$-0.657521\pi$
$11$	0.714027	−	0.518771i	0.215287	−	0.156415i	0.690203	+	0.723616i	$0.257521\pi$
$12$	0.587785	−	0.809017i	0.169679	−	0.233543i
$13$	1.66061	−	2.28564i	0.460571	−	0.633921i	−0.514056	−	0.857756i	$-0.671858\pi$
$13$	1.66061	−	2.28564i	0.460571	−	0.633921i	0.974627	+	0.223835i	$0.0718578\pi$
$14$	−3.88890	+	2.82545i	−1.03935	+	0.755133i
$15$	−1.65619	−	1.50234i	−0.427627	−	0.387903i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.57666	+	0.512289i	−0.382397	+	0.124248i	−0.493907	−	0.869515i	$-0.664432\pi$
$17$	−1.57666	+	0.512289i	−0.382397	+	0.124248i	0.111509	+	0.993763i	$0.464432\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.66217	−	5.11563i	−0.381327	−	1.17361i	−0.939110	−	0.343618i	$-0.888348\pi$
$19$	−1.66217	−	5.11563i	−0.381327	−	1.17361i	0.557782	−	0.829987i	$-0.311652\pi$
$20$	−1.50234	+	1.65619i	−0.335934	+	0.370336i
$21$	−1.48543	+	4.57167i	−0.324147	+	0.997621i
$22$	−0.839389	−	0.272734i	−0.178958	−	0.0581471i
$23$	3.44056	+	4.73553i	0.717407	+	0.987426i	0.999606	+	0.0280705i	$0.00893629\pi$
$23$	3.44056	+	4.73553i	0.717407	+	0.987426i	−0.282199	+	0.959356i	$0.591064\pi$
$24$	−1.00000			−0.204124
$25$	3.31815	+	3.74031i	0.663630	+	0.748061i
$26$	−2.82520			−0.554067
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	4.57167	+	1.48543i	0.863965	+	0.280719i
$29$	−1.10574	+	3.40313i	−0.205332	+	0.631946i	0.794368	+	0.607437i	$0.207802\pi$
$29$	−1.10574	+	3.40313i	−0.205332	+	0.631946i	−0.999700	+	0.0245090i	$0.992198\pi$
$30$	−0.241934	+	2.22294i	−0.0441710	+	0.405852i
$31$	3.22681	+	9.93109i	0.579551	+	1.78368i	0.620130	+	0.784499i	$0.287080\pi$
$31$	3.22681	+	9.93109i	0.579551	+	1.78368i	−0.0405785	+	0.999176i	$0.512920\pi$
$32$			1.00000i			0.176777i
$33$	−0.839389	+	0.272734i	−0.146119	+	0.0474769i
$34$	1.34119	+	0.974432i	0.230012	+	0.167114i
$35$	4.40806	−	9.80318i	0.745098	−	1.65704i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−1.02631	+	1.41260i	−0.168725	+	0.232230i	−0.885003	−	0.465585i	$-0.845844\pi$
$37$	−1.02631	+	1.41260i	−0.168725	+	0.232230i	0.716278	+	0.697815i	$0.245844\pi$
$38$	−3.16163	+	4.35161i	−0.512884	+	0.705925i
$39$	−2.28564	+	1.66061i	−0.365995	+	0.265911i
$40$	2.22294	+	0.241934i	0.351478	+	0.0382532i
$41$	1.40381	+	1.01993i	0.219238	+	0.159286i	0.691984	−	0.721913i	$-0.256737\pi$
$41$	1.40381	+	1.01993i	0.219238	+	0.159286i	−0.472746	+	0.881199i	$0.656737\pi$
$42$	4.57167	−	1.48543i	0.705424	−	0.229206i
$43$		−	2.27151i		−	0.346403i	−0.984886	−	0.173201i	$-0.944589\pi$
$43$		−	2.27151i		−	0.346403i	0.984886	−	0.173201i	$-0.0554111\pi$
$44$	0.272734	+	0.839389i	0.0411162	+	0.126543i
$45$	1.11088	+	1.94060i	0.165601	+	0.289288i
$46$	1.80881	−	5.56695i	0.266695	−	0.820802i
$47$	−8.29746	−	2.69601i	−1.21031	−	0.393253i	−0.366765	−	0.930314i	$-0.619535\pi$
$47$	−8.29746	−	2.69601i	−1.21031	−	0.393253i	−0.843544	+	0.537060i	$0.819535\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	−16.1067			−2.30095
$50$	1.07561	−	4.88294i	0.152114	−	0.690551i
$51$	1.65780			0.232139
$52$	1.66061	+	2.28564i	0.230285	+	0.316961i
$53$	−3.37565	−	1.09681i	−0.463681	−	0.150659i	0.0678545	−	0.997695i	$-0.478385\pi$
$53$	−3.37565	−	1.09681i	−0.463681	−	0.150659i	−0.531535	+	0.847036i	$0.678385\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	1.93190	−	0.403195i	0.260497	−	0.0543667i
$56$	−1.48543	−	4.57167i	−0.198498	−	0.610915i
$57$			5.37889i			0.712451i
$58$	3.40313	−	1.10574i	0.446853	−	0.145191i
$59$	8.37628	+	6.08572i	1.09050	+	0.792293i	0.979483	−	0.201525i	$-0.0645898\pi$
$59$	8.37628	+	6.08572i	1.09050	+	0.792293i	0.111015	+	0.993819i	$0.464590\pi$
$60$	1.94060	−	1.11088i	0.250531	−	0.143414i
$61$	0.0697810	−	0.0506988i	0.00893454	−	0.00649132i	−0.583309	−	0.812250i	$-0.698242\pi$
$61$	0.0697810	−	0.0506988i	0.00893454	−	0.00649132i	0.592244	+	0.805759i	$0.298242\pi$
$62$	6.13775	−	8.44789i	0.779495	−	1.07288i
$63$	2.82545	−	3.88890i	0.355973	−	0.489955i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	5.48259	−	3.13847i	0.680032	−	0.389279i
$66$	0.714027	+	0.518771i	0.0878906	+	0.0638563i
$67$	−11.3751	+	3.69601i	−1.38969	+	0.451539i	−0.905844	−	0.423611i	$-0.860762\pi$
$67$	−11.3751	+	3.69601i	−1.38969	+	0.451539i	−0.483851	+	0.875150i	$0.660762\pi$
$68$		−	1.65780i		−	0.201038i
$69$	−1.80881	−	5.56695i	−0.217755	−	0.670182i
$70$	−10.5219	+	2.19597i	−1.25761	+	0.262469i
$71$	−1.08390	+	3.33591i	−0.128636	+	0.395900i	−0.994546	−	0.104300i	$-0.966740\pi$
$71$	−1.08390	+	3.33591i	−0.128636	+	0.395900i	0.865910	+	0.500199i	$0.166740\pi$
$72$	0.951057	+	0.309017i	0.112083	+	0.0364180i
$73$	4.24851	+	5.84757i	0.497251	+	0.684407i	0.981705	−	0.190410i	$-0.0609817\pi$
$73$	4.24851	+	5.84757i	0.497251	+	0.684407i	−0.484454	+	0.874817i	$0.660982\pi$
$74$	1.74607			0.202977
$75$	−1.99993	−	4.58261i	−0.230932	−	0.529154i
$76$	5.37889			0.617001
$77$	−2.49370	−	3.43228i	−0.284184	−	0.391145i
$78$	2.68693	+	0.873035i	0.304234	+	0.0988518i
$79$	3.88627	−	11.9607i	0.437240	−	1.34569i	−0.453533	−	0.891239i	$-0.649837\pi$
$79$	3.88627	−	11.9607i	0.437240	−	1.34569i	0.890774	−	0.454447i	$-0.150163\pi$
$80$	−1.11088	−	1.94060i	−0.124201	−	0.216966i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	1.73520i		−	0.191621i
$83$	−12.6244	+	4.10192i	−1.38571	+	0.450244i	−0.904541	−	0.426386i	$-0.859787\pi$
$83$	−12.6244	+	4.10192i	−1.38571	+	0.450244i	−0.481166	+	0.876629i	$0.659787\pi$
$84$	−3.88890	−	2.82545i	−0.424313	−	0.308282i
$85$	−3.68520	−	0.401079i	−0.399716	−	0.0435032i
$86$	−1.83769	+	1.33516i	−0.198164	+	0.143974i
$87$	2.10325	−	2.89488i	0.225492	−	0.310363i
$88$	0.518771	−	0.714027i	0.0553011	−	0.0761155i
$89$	15.1178	−	10.9837i	1.60248	−	1.16427i	0.719939	−	0.694037i	$-0.244170\pi$
$89$	15.1178	−	10.9837i	1.60248	−	1.16427i	0.882542	−	0.470233i	$-0.155830\pi$
$90$	0.917020	−	2.03938i	0.0966624	−	0.214970i
$91$	−10.9869	−	7.98246i	−1.15174	−	0.836789i
$92$	−5.56695	+	1.80881i	−0.580395	+	0.188582i
$93$		−	10.4422i		−	1.08280i
$94$	2.69601	+	8.29746i	0.278072	+	0.855818i
$95$	1.30134	−	11.9570i	0.133514	−	1.22676i
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	17.3764	+	5.64593i	1.76430	+	0.573257i	0.997632	−	0.0687822i	$-0.0219114\pi$
$97$	17.3764	+	5.64593i	1.76430	+	0.573257i	0.766672	+	0.642039i	$0.221911\pi$
$98$	9.46727	+	13.0306i	0.956339	+	1.31629i
$99$	0.882586			0.0887032
$100$	−4.58261	+	1.99993i	−0.458261	+	0.199993i
$101$	−5.46110			−0.543400			−0.271700	−	0.962382i	$-0.587586\pi$
$101$	−5.46110			−0.543400			−0.271700	+	0.962382i	$0.587586\pi$
$102$	−0.974432	−	1.34119i	−0.0964831	−	0.132798i
$103$	6.31725	+	2.05260i	0.622457	+	0.202248i	0.603231	−	0.797567i	$-0.293880\pi$
$103$	6.31725	+	2.05260i	0.622457	+	0.202248i	0.0192260	+	0.999815i	$0.493880\pi$
$104$	0.873035	−	2.68693i	0.0856081	−	0.263475i
$105$	−7.22166	+	7.96122i	−0.704762	+	0.776935i
$106$	1.09681	+	3.37565i	0.106532	+	0.327872i
$107$			14.5245i			1.40414i	0.712108	+	0.702070i	$0.247741\pi$
$107$			14.5245i			1.40414i	−0.712108	+	0.702070i	$0.752259\pi$
$108$	0.951057	−	0.309017i	0.0915155	−	0.0297352i
$109$	3.85954	+	2.80412i	0.369676	+	0.268586i	0.757077	−	0.653326i	$-0.226627\pi$
$109$	3.85954	+	2.80412i	0.369676	+	0.268586i	−0.387400	+	0.921912i	$0.626627\pi$
$110$	−1.46173	−	1.32594i	−0.139371	−	0.126424i
$111$	1.41260	−	1.02631i	0.134078	−	0.0974134i
$112$	−2.82545	+	3.88890i	−0.266980	+	0.367466i
$113$	2.84228	−	3.91206i	0.267379	−	0.368016i	−0.654124	−	0.756388i	$-0.726962\pi$
$113$	2.84228	−	3.91206i	0.267379	−	0.368016i	0.921503	+	0.388372i	$0.126962\pi$
$114$	4.35161	−	3.16163i	0.407566	−	0.296114i
$115$	2.67405	+	12.8126i	0.249356	+	1.19478i
$116$	−2.89488	−	2.10325i	−0.268783	−	0.195282i
$117$	2.68693	−	0.873035i	0.248406	−	0.0807121i
$118$		−	10.3536i		−	0.953131i
$119$	2.46254	+	7.57893i	0.225741	+	0.694759i
$120$	−2.03938	−	0.917020i	−0.186169	−	0.0837121i
$121$	−3.15848	+	9.72079i	−0.287134	+	0.883708i
$122$	−0.0820324	−	0.0266540i	−0.00742687	−	0.00241314i
$123$	−1.01993	−	1.40381i	−0.0919637	−	0.126577i
$124$	−10.4422			−0.937734
$125$	3.33704	+	10.6707i	0.298474	+	0.954418i
$126$	−4.80694			−0.428236
$127$	1.05908	+	1.45769i	0.0939779	+	0.129349i	0.853417	−	0.521229i	$-0.174526\pi$
$127$	1.05908	+	1.45769i	0.0939779	+	0.129349i	−0.759439	+	0.650579i	$0.774526\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	−0.701936	+	2.16034i	−0.0618021	+	0.190207i
$130$	−5.76166	−	2.59077i	−0.505331	−	0.227225i
$131$	−4.95400	−	15.2468i	−0.432833	−	1.33212i	−0.895291	−	0.445481i	$-0.853033\pi$
$131$	−4.95400	−	15.2468i	−0.432833	−	1.33212i	0.462459	−	0.886641i	$-0.346967\pi$
$132$		−	0.882586i		−	0.0768192i
$133$	−24.5905	+	7.98994i	−2.13227	+	0.692816i
$134$	9.67628	+	7.03023i	0.835903	+	0.607319i
$135$	−0.456833	−	2.18890i	−0.0393180	−	0.188391i
$136$	−1.34119	+	0.974432i	−0.115006	+	0.0835569i
$137$	−1.03872	+	1.42968i	−0.0887443	+	0.122146i	−0.851081	−	0.525035i	$-0.824052\pi$
$137$	−1.03872	+	1.42968i	−0.0887443	+	0.122146i	0.762336	+	0.647181i	$0.224052\pi$
$138$	−3.44056	+	4.73553i	−0.292880	+	0.403115i
$139$	8.89636	−	6.46359i	0.754580	−	0.548234i	−0.142663	−	0.989771i	$-0.545567\pi$
$139$	8.89636	−	6.46359i	0.754580	−	0.548234i	0.897243	+	0.441537i	$0.145567\pi$
$140$	7.96122	+	7.22166i	0.672846	+	0.610342i
$141$	7.05824	+	5.12811i	0.594411	+	0.431865i
$142$	3.33591	−	1.08390i	0.279943	−	0.0909591i
$143$		−	2.49348i		−	0.208515i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$	−5.37577	+	5.92629i	−0.446434	+	0.492152i
$146$	2.23357	−	6.87424i	0.184852	−	0.568916i
$147$	15.3184	+	4.97724i	1.26344	+	0.410516i
$148$	−1.02631	−	1.41260i	−0.0843625	−	0.116115i
$149$	−2.90948			−0.238354			−0.119177	−	0.992873i	$-0.538026\pi$
$149$	−2.90948			−0.238354			−0.119177	+	0.992873i	$0.538026\pi$
$150$	−2.53188	+	4.31157i	−0.206727	+	0.352038i
$151$	−1.34184			−0.109197			−0.0545986	−	0.998508i	$-0.517388\pi$
$151$	−1.34184			−0.109197			−0.0545986	+	0.998508i	$0.517388\pi$
$152$	−3.16163	−	4.35161i	−0.256442	−	0.352962i
$153$	−1.57666	−	0.512289i	−0.127466	−	0.0414161i
$154$	−1.31102	+	4.03489i	−0.105645	+	0.325141i
$155$	−2.52632	+	23.2123i	−0.202919	+	1.86446i
$156$	−0.873035	−	2.68693i	−0.0698987	−	0.215126i
$157$		−	8.31169i		−	0.663345i	−0.943395	−	0.331673i	$-0.892387\pi$
$157$		−	8.31169i		−	0.663345i	0.943395	−	0.331673i	$-0.107613\pi$
$158$	−11.9607	+	3.88627i	−0.951544	+	0.309175i
$159$	2.87150	+	2.08626i	0.227724	+	0.165451i
$160$	−0.917020	+	2.03938i	−0.0724968	+	0.161227i
$161$	22.7634	−	16.5386i	1.79401	−	1.30342i
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	3.66704	−	5.04724i	0.287225	−	0.395331i	−0.640886	−	0.767636i	$-0.721433\pi$
$163$	3.66704	−	5.04724i	0.287225	−	0.395331i	0.928110	+	0.372306i	$0.121433\pi$
$164$	−1.40381	+	1.01993i	−0.109619	+	0.0796429i
$165$	−1.96194	−	0.213528i	−0.152736	−	0.0166231i
$166$	10.7390	+	7.80231i	0.833505	+	0.605576i
$167$	−14.1107	+	4.58483i	−1.09192	+	0.354785i	−0.798986	−	0.601349i	$-0.794630\pi$
$167$	−14.1107	+	4.58483i	−1.09192	+	0.354785i	−0.292929	+	0.956134i	$0.594630\pi$
$168$			4.80694i			0.370864i
$169$	1.55072	+	4.77263i	0.119286	+	0.367125i
$170$	1.84163	+	3.21714i	0.141246	+	0.246743i
$171$	1.66217	−	5.11563i	0.127109	−	0.391202i
$172$	2.16034	+	0.701936i	0.164724	+	0.0535221i
$173$	−9.42623	−	12.9741i	−0.716663	−	0.986402i	−0.999628	−	0.0272719i	$-0.991318\pi$
$173$	−9.42623	−	12.9741i	−0.716663	−	0.986402i	0.282965	−	0.959130i	$-0.408682\pi$
$174$	−3.57827			−0.271268
$175$	17.9794	−	15.9501i	1.35912	−	1.20572i
$176$	−0.882586			−0.0665274
$177$	−6.08572	−	8.37628i	−0.457431	−	0.629600i
$178$	−17.7720	−	5.77448i	−1.33207	−	0.432815i
$179$	−3.63061	+	11.1739i	−0.271365	+	0.835174i	0.718794	+	0.695223i	$0.244694\pi$
$179$	−3.63061	+	11.1739i	−0.271365	+	0.835174i	−0.990158	+	0.139951i	$0.955306\pi$
$180$	−2.18890	+	0.456833i	−0.163151	+	0.0340504i
$181$	−1.24658	−	3.83658i	−0.0926577	−	0.285171i	0.893979	−	0.448110i	$-0.147903\pi$
$181$	−1.24658	−	3.83658i	−0.0926577	−	0.285171i	−0.986636	+	0.162939i	$0.947903\pi$
$182$			13.5806i			1.00666i
$183$	−0.0820324	+	0.0266540i	−0.00606401	+	0.00197032i
$184$	4.73553	+	3.44056i	0.349108	+	0.253642i
$185$	−3.38843	+	1.93968i	−0.249122	+	0.142608i
$186$	−8.44789	+	6.13775i	−0.619429	+	0.450042i
$187$	−0.860020	+	1.18372i	−0.0628909	+	0.0865618i
$188$	5.12811	−	7.05824i	0.374006	−	0.514775i
$189$	−3.88890	+	2.82545i	−0.282876	+	0.205521i
$190$	−10.4383	+	5.97532i	−0.757273	+	0.433495i
$191$	−9.64472	−	7.00730i	−0.697867	−	0.507030i	0.181370	−	0.983415i	$-0.441947\pi$
$191$	−9.64472	−	7.00730i	−0.697867	−	0.507030i	−0.879237	+	0.476385i	$0.841947\pi$
$192$	−0.951057	+	0.309017i	−0.0686366	+	0.0223014i
$193$		−	11.8088i		−	0.850019i	−0.905189	−	0.425009i	$-0.860271\pi$
$193$		−	11.8088i		−	0.850019i	0.905189	−	0.425009i	$-0.139729\pi$
$194$	−5.64593	−	17.3764i	−0.405354	−	1.24755i
$195$	−6.18409	+	1.29065i	−0.442852	+	0.0924251i
$196$	4.97724	−	15.3184i	0.355517	−	1.09417i
$197$	−6.92219	−	2.24916i	−0.493186	−	0.160246i	0.0518562	−	0.998655i	$-0.483486\pi$
$197$	−6.92219	−	2.24916i	−0.493186	−	0.160246i	−0.545042	+	0.838409i	$0.683486\pi$
$198$	−0.518771	−	0.714027i	−0.0368674	−	0.0507437i
$199$	−2.27949			−0.161589			−0.0807944	−	0.996731i	$-0.525746\pi$
$199$	−2.27949			−0.161589			−0.0807944	+	0.996731i	$0.525746\pi$
$200$	4.31157	+	2.53188i	0.304874	+	0.179031i
$201$	11.9605			0.843631
$202$	3.20996	+	4.41813i	0.225852	+	0.310858i
$203$	16.3587	+	5.31525i	1.14815	+	0.373057i
$204$	−0.512289	+	1.57666i	−0.0358674	+	0.110389i
$205$	1.92761	+	3.36734i	0.134630	+	0.235185i
$206$	−2.05260	−	6.31725i	−0.143011	−	0.440143i
$207$			5.85344i			0.406842i
$208$	−2.68693	+	0.873035i	−0.186305	+	0.0605341i
$209$	−3.84067	−	2.79041i	−0.265665	−	0.193017i
$210$	10.6855	+	1.16296i	0.737373	+	0.0802521i
$211$	1.01062	−	0.734260i	0.0695741	−	0.0505485i	−0.552455	−	0.833543i	$-0.686309\pi$
$211$	1.01062	−	0.734260i	0.0695741	−	0.0505485i	0.622029	+	0.782994i	$0.286309\pi$
$212$	2.08626	−	2.87150i	0.143285	−	0.197215i
$213$	2.06170	−	2.83769i	0.141266	−	0.194436i
$214$	11.7506	−	8.53731i	0.803255	−	0.583599i
$215$	2.08302	−	4.63248i	0.142061	−	0.315933i
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	47.7381	−	15.5111i	3.24068	−	1.05296i
$218$		−	4.77065i		−	0.323109i
$219$	−2.23357	−	6.87424i	−0.150931	−	0.464518i
$220$	−0.213528	+	1.96194i	−0.0143960	+	0.132274i
$221$	−1.44732	+	4.45439i	−0.0973573	+	0.299635i
$222$	−1.66061	−	0.539565i	−0.111453	−	0.0362133i
$223$	5.19727	+	7.15343i	0.348035	+	0.479029i	0.946767	−	0.321921i	$-0.104328\pi$
$223$	5.19727	+	7.15343i	0.348035	+	0.479029i	−0.598732	+	0.800950i	$0.704328\pi$
$224$	4.80694			0.321177
$225$	0.485943	+	4.97633i	0.0323962	+	0.331755i
$226$	−4.83558			−0.321658
$227$	10.4019	+	14.3170i	0.690398	+	0.950251i	1.00000		0.000615300i	$-0.000195856\pi$
$227$	10.4019	+	14.3170i	0.690398	+	0.950251i	−0.309602	+	0.950866i	$0.600196\pi$
$228$	−5.11563	−	1.66217i	−0.338791	−	0.110080i
$229$	2.75446	−	8.47737i	0.182020	−	0.560200i	−0.817864	−	0.575411i	$-0.804842\pi$
$229$	2.75446	−	8.47737i	0.182020	−	0.560200i	0.999884	+	0.0152110i	$0.00484200\pi$
$230$	8.79386	−	9.69442i	0.579850	−	0.639231i
$231$	1.31102	+	4.03489i	0.0862585	+	0.265476i
$232$			3.57827i			0.234925i
$233$	−9.12123	+	2.96367i	−0.597551	+	0.194156i	−0.592148	−	0.805829i	$-0.701720\pi$
$233$	−9.12123	+	2.96367i	−0.597551	+	0.194156i	−0.00540335	+	0.999985i	$0.501720\pi$
$234$	−2.28564	−	1.66061i	−0.149417	−	0.108558i
$235$	−14.4494	−	13.1071i	−0.942574	−	0.855014i
$236$	−8.37628	+	6.08572i	−0.545249	+	0.396147i
$237$	−7.39213	+	10.1744i	−0.480171	+	0.660898i
$238$	4.68404	−	6.44702i	0.303621	−	0.417898i
$239$	−7.41301	+	5.38587i	−0.479508	+	0.348383i	−0.801135	−	0.598483i	$-0.795770\pi$
$239$	−7.41301	+	5.38587i	−0.479508	+	0.348383i	0.321627	+	0.946866i	$0.395770\pi$
$240$	0.456833	+	2.18890i	0.0294885	+	0.141293i
$241$	2.01891	+	1.46682i	0.130049	+	0.0944864i	0.650908	−	0.759156i	$-0.274388\pi$
$241$	2.01891	+	1.46682i	0.130049	+	0.0944864i	−0.520859	+	0.853643i	$0.674388\pi$
$242$	9.72079	−	3.15848i	0.624876	−	0.203035i
$243$		−	1.00000i		−	0.0641500i
$244$	0.0266540	+	0.0820324i	0.00170634	+	0.00525159i
$245$	−32.8477	−	14.7701i	−2.09856	−	0.943630i
$246$	−0.536207	+	1.65028i	−0.0341873	+	0.105218i
$247$	−14.4527	−	4.69596i	−0.919601	−	0.298797i
$248$	6.13775	+	8.44789i	0.389747	+	0.536441i
$249$	13.2741			0.841211
$250$	6.67133	−	8.97181i	0.421932	−	0.567427i
$251$	8.71262			0.549936			0.274968	−	0.961453i	$-0.411333\pi$
$251$	8.71262			0.549936			0.274968	+	0.961453i	$0.411333\pi$
$252$	2.82545	+	3.88890i	0.177987	+	0.244977i
$253$	4.91331	+	1.59643i	0.308897	+	0.100367i
$254$	0.556790	−	1.71362i	0.0349361	−	0.107522i
$255$	3.38089	+	1.52024i	0.211720	+	0.0952010i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	19.7871i		−	1.23429i	−0.786851	−	0.617143i	$-0.788290\pi$
$257$		−	19.7871i		−	1.23429i	0.786851	−	0.617143i	$-0.211710\pi$
$258$	2.16034	−	0.701936i	0.134497	−	0.0437007i
$259$	6.79029	+	4.93343i	0.421928	+	0.306549i
$260$	1.29065	+	6.18409i	0.0800425	+	0.383521i
$261$	−2.89488	+	2.10325i	−0.179188	+	0.130188i
$262$	−9.42306	+	12.9697i	−0.582159	+	0.801272i
$263$	−15.0258	+	20.6813i	−0.926532	+	1.27526i	0.0346651	+	0.999399i	$0.488964\pi$
$263$	−15.0258	+	20.6813i	−0.926532	+	1.27526i	−0.961197	+	0.275863i	$0.911036\pi$
$264$	−0.714027	+	0.518771i	−0.0439453	+	0.0319281i
$265$	−5.87843	−	5.33236i	−0.361109	−	0.327564i
$266$	20.9179	+	15.1978i	1.28256	+	0.931835i
$267$	−17.7720	+	5.77448i	−1.08763	+	0.353392i
$268$		−	11.9605i		−	0.730606i
$269$	−7.54447	−	23.2195i	−0.459994	−	1.41572i	−0.865170	−	0.501478i	$-0.832790\pi$
$269$	−7.54447	−	23.2195i	−0.459994	−	1.41572i	0.405176	−	0.914239i	$-0.367210\pi$
$270$	−1.50234	+	1.65619i	−0.0914296	+	0.100793i
$271$	0.848720	−	2.61209i	0.0515561	−	0.158673i	−0.921964	−	0.387277i	$-0.873416\pi$
$271$	0.848720	−	2.61209i	0.0515561	−	0.158673i	0.973520	+	0.228603i	$0.0734159\pi$
$272$	1.57666	+	0.512289i	0.0955993	+	0.0310621i
$273$	7.98246	+	10.9869i	0.483120	+	0.664958i
$274$	1.76718			0.106760
$275$	4.30961	+	0.949319i	0.259879	+	0.0572461i
$276$	5.85344			0.352336
$277$	−1.75206	−	2.41151i	−0.105271	−	0.144893i	0.753131	−	0.657870i	$-0.228543\pi$
$277$	−1.75206	−	2.41151i	−0.105271	−	0.144893i	−0.858402	+	0.512977i	$0.828543\pi$
$278$	−10.4583	−	3.39811i	−0.627247	−	0.203805i
$279$	−3.22681	+	9.93109i	−0.193184	+	0.594559i
$280$	1.16296	−	10.6855i	0.0695004	−	0.638584i
$281$	1.19334	+	3.67274i	0.0711890	+	0.219097i	0.980321	−	0.197412i	$-0.0632535\pi$
$281$	1.19334	+	3.67274i	0.0711890	+	0.219097i	−0.909132	+	0.416509i	$0.863254\pi$
$282$		−	8.72447i		−	0.519534i
$283$	−15.8844	+	5.16117i	−0.944232	+	0.306800i	−0.740370	−	0.672200i	$-0.765350\pi$
$283$	−15.8844	+	5.16117i	−0.944232	+	0.306800i	−0.203863	+	0.979000i	$0.565350\pi$
$284$	−2.83769	−	2.06170i	−0.168386	−	0.122340i
$285$	−4.93255	+	10.9696i	−0.292179	+	0.649783i
$286$	−2.01727	+	1.46563i	−0.119284	+	0.0866646i
$287$	4.90273	−	6.74802i	0.289399	−	0.398323i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	−11.5299	+	8.37693i	−0.678227	+	0.492761i
$290$	7.95427	+	0.865705i	0.467091	+	0.0508360i
$291$	−14.7812	−	10.7392i	−0.866491	−	0.629542i
$292$	−6.87424	+	2.23357i	−0.402284	+	0.130710i
$293$			0.503153i			0.0293945i	0.999892	+	0.0146972i	$0.00467845\pi$
$293$			0.503153i			0.0293945i	−0.999892	+	0.0146972i	$0.995322\pi$
$294$	−4.97724	−	15.3184i	−0.290278	−	0.893385i
$295$	11.5017	+	20.0923i	0.669654	+	1.16982i
$296$	−0.539565	+	1.66061i	−0.0313616	+	0.0965211i
$297$	−0.839389	−	0.272734i	−0.0487063	−	0.0158256i
$298$	1.71015	+	2.35382i	0.0990664	+	0.136353i
$299$	16.5371			0.956367
$300$	4.97633	−	0.485943i	0.287309	−	0.0280559i
$301$	−10.9190			−0.629363
$302$	0.788713	+	1.08557i	0.0453853	+	0.0624675i
$303$	5.19382	+	1.68757i	0.298377	+	0.0969486i
$304$	−1.66217	+	5.11563i	−0.0953319	+	0.293401i
$305$	0.188802	−	0.0394037i	0.0108108	−	0.00225625i
$306$	0.512289	+	1.57666i	0.0292856	+	0.0901319i
$307$		−	8.63375i		−	0.492754i	−0.969174	−	0.246377i	$-0.920760\pi$
$307$		−	8.63375i		−	0.492754i	0.969174	−	0.246377i	$-0.0792402\pi$
$308$	4.03489	−	1.31102i	0.229909	−	0.0747021i
$309$	−5.37377	−	3.90427i	−0.305703	−	0.222106i
$310$	20.2641	−	11.6000i	1.15092	−	0.658837i
$311$	−16.3967	+	11.9129i	−0.929771	+	0.675518i	−0.945937	−	0.324351i	$-0.894854\pi$
$311$	−16.3967	+	11.9129i	−0.929771	+	0.675518i	0.0161660	+	0.999869i	$0.494854\pi$
$312$	−1.66061	+	2.28564i	−0.0940136	+	0.129399i
$313$	10.0101	−	13.7777i	0.565805	−	0.778763i	−0.426245	−	0.904608i	$-0.640164\pi$
$313$	10.0101	−	13.7777i	0.565805	−	0.778763i	0.992050	+	0.125844i	$0.0401640\pi$
$314$	−6.72430	+	4.88549i	−0.379474	+	0.275704i
$315$	9.32836	−	5.33995i	0.525594	−	0.300872i
$316$	10.1744	+	7.39213i	0.572355	+	0.415840i
$317$	2.68347	−	0.871912i	0.150719	−	0.0489715i	−0.232686	−	0.972552i	$-0.574751\pi$
$317$	2.68347	−	0.871912i	0.150719	−	0.0489715i	0.383405	+	0.923580i	$0.374751\pi$
$318$		−	3.54936i		−	0.199038i
$319$	0.975914	+	3.00356i	0.0546407	+	0.168167i
$320$	2.18890	−	0.456833i	0.122363	−	0.0255378i
$321$	4.48833	−	13.8137i	0.250514	−	0.771003i
$322$	−26.7600	−	8.69485i	−1.49128	−	0.484545i
$323$	5.24136	+	7.21411i	0.291637	+	0.401404i
$324$	−1.00000			−0.0555556
$325$	14.0591	−	1.37289i	0.779860	−	0.0761540i
$326$	−6.23874			−0.345532
$327$	−2.80412	−	3.85954i	−0.155068	−	0.213433i
$328$	1.65028	+	0.536207i	0.0911212	+	0.0296071i
$329$	−12.9596	+	39.8854i	−0.714483	+	2.19895i
$330$	0.980449	+	1.71275i	0.0539720	+	0.0942837i
$331$	−1.25862	−	3.87364i	−0.0691802	−	0.212915i	0.910489	−	0.413532i	$-0.135705\pi$
$331$	−1.25862	−	3.87364i	−0.0691802	−	0.212915i	−0.979670	+	0.200618i	$0.935705\pi$
$332$		−	13.2741i		−	0.728510i
$333$	−1.66061	+	0.539565i	−0.0910009	+	0.0295680i
$334$	12.0032	+	8.72086i	0.656788	+	0.477184i
$335$	−26.5876	−	2.89366i	−1.45263	−	0.158098i
$336$	3.88890	−	2.82545i	0.212157	−	0.154141i
$337$	−5.31818	+	7.31984i	−0.289700	+	0.398737i	−0.928917	−	0.370289i	$-0.879259\pi$
$337$	−5.31818	+	7.31984i	−0.289700	+	0.398737i	0.639217	+	0.769026i	$0.279259\pi$
$338$	2.94965	−	4.05984i	0.160440	−	0.220826i
$339$	−3.91206	+	2.84228i	−0.212474	+	0.154371i
$340$	1.52024	−	3.38089i	0.0824465	−	0.183355i
$341$	7.45598	+	5.41709i	0.403764	+	0.293352i
$342$	−5.11563	+	1.66217i	−0.276621	+	0.0898797i
$343$			43.7753i			2.36364i
$344$	−0.701936	−	2.16034i	−0.0378459	−	0.116478i
$345$	1.41615	−	13.0118i	0.0762428	−	0.700534i
$346$	−4.95566	+	15.2520i	−0.266418	+	0.819951i
$347$	8.26141	+	2.68429i	0.443495	+	0.144100i	0.522248	−	0.852794i	$-0.325094\pi$
$347$	8.26141	+	2.68429i	0.443495	+	0.144100i	−0.0787523	+	0.996894i	$0.525094\pi$
$348$	2.10325	+	2.89488i	0.112746	+	0.155182i
$349$	−26.8305			−1.43620			−0.718101	−	0.695938i	$-0.754989\pi$
$349$	−26.8305			−1.43620			−0.718101	+	0.695938i	$0.754989\pi$
$350$	−23.4720	−	5.17040i	−1.25463	−	0.276370i
$351$	−2.82520			−0.150798
$352$	0.518771	+	0.714027i	0.0276506	+	0.0380577i
$353$	26.9623	+	8.76060i	1.43506	+	0.466279i	0.920354	−	0.391087i	$-0.127901\pi$
$353$	26.9623	+	8.76060i	1.43506	+	0.466279i	0.514707	+	0.857366i	$0.327901\pi$
$354$	−3.19945	+	9.84690i	−0.170049	+	0.523357i
$355$	−5.26958	+	5.80923i	−0.279680	+	0.308322i
$356$	5.77448	+	17.7720i	0.306047	+	0.941915i
$357$		−	7.96896i		−	0.421762i
$358$	11.1739	−	3.63061i	0.590557	−	0.191884i
$359$	7.02898	+	5.10686i	0.370976	+	0.269530i	0.757615	−	0.652701i	$-0.226364\pi$
$359$	7.02898	+	5.10686i	0.370976	+	0.269530i	−0.386640	+	0.922231i	$0.626364\pi$
$360$	1.65619	+	1.50234i	0.0872890	+	0.0791803i
$361$	−8.03551	+	5.83814i	−0.422921	+	0.307270i
$362$	−2.37114	+	3.26359i	−0.124624	+	0.171531i
$363$	6.00778	−	8.26900i	0.315327	−	0.434010i
$364$	10.9869	−	7.98246i	0.575871	−	0.418395i
$365$	3.30199	+	15.8214i	0.172834	+	0.828130i
$366$	0.0697810	+	0.0506988i	0.00364751	+	0.00265007i
$367$	11.8609	−	3.85385i	0.619136	−	0.201170i	0.0173794	−	0.999849i	$-0.494468\pi$
$367$	11.8609	−	3.85385i	0.619136	−	0.201170i	0.601757	+	0.798679i	$0.294468\pi$
$368$		−	5.85344i		−	0.305132i
$369$	0.536207	+	1.65028i	0.0279138	+	0.0859099i
$370$	3.56090	+	1.60118i	0.185122	+	0.0832414i
$371$	−5.27232	+	16.2265i	−0.273725	+	0.842439i
$372$	9.93109	+	3.22681i	0.514903	+	0.167302i
$373$	−7.64048	−	10.5162i	−0.395609	−	0.544509i	0.564026	−	0.825757i	$-0.309252\pi$
$373$	−7.64048	−	10.5162i	−0.395609	−	0.544509i	−0.959635	+	0.281248i	$0.909252\pi$
$374$	1.46315			0.0756578
$375$	0.123723	−	11.1797i	0.00638904	−	0.577315i
$376$	−8.72447			−0.449930
$377$	5.94211	+	8.17861i	0.306034	+	0.421220i
$378$	4.57167	+	1.48543i	0.235141	+	0.0764021i
$379$	−0.541481	+	1.66651i	−0.0278140	+	0.0856027i	−0.964000	−	0.265903i	$-0.914330\pi$
$379$	−0.541481	+	1.66651i	−0.0278140	+	0.0856027i	0.936186	+	0.351505i	$0.114330\pi$
$380$	10.9696	+	4.93255i	0.562729	+	0.253034i
$381$	−0.556790	−	1.71362i	−0.0285252	−	0.0877915i
$382$			11.9215i			0.609958i
$383$	32.4652	−	10.5486i	1.65889	−	0.539007i	0.678252	−	0.734829i	$-0.262738\pi$
$383$	32.4652	−	10.5486i	1.65889	−	0.539007i	0.980639	+	0.195822i	$0.0627376\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$	−1.93813	−	9.28651i	−0.0987764	−	0.473284i
$386$	−9.55355	+	6.94106i	−0.486263	+	0.353291i
$387$	1.33516	−	1.83769i	0.0678701	−	0.0934152i
$388$	−10.7392	+	14.7812i	−0.545200	+	0.750403i
$389$	5.54704	−	4.03016i	0.281246	−	0.204337i	−0.438215	−	0.898870i	$-0.644389\pi$
$389$	5.54704	−	4.03016i	0.281246	−	0.204337i	0.719461	+	0.694533i	$0.244389\pi$
$390$	4.67907	+	4.24442i	0.236934	+	0.214924i
$391$	−7.85058	−	5.70378i	−0.397021	−	0.288452i
$392$	−15.3184	+	4.97724i	−0.773694	+	0.251388i
$393$			16.0315i			0.808680i
$394$	2.24916	+	6.92219i	0.113311	+	0.348735i
$395$	18.8938	−	20.8287i	0.950651	−	1.04800i
$396$	−0.272734	+	0.839389i	−0.0137054	+	0.0421809i
$397$	−31.5358	−	10.2466i	−1.58274	−	0.514262i	−0.619976	−	0.784621i	$-0.712858\pi$
$397$	−31.5358	−	10.2466i	−1.58274	−	0.514262i	−0.962760	+	0.270359i	$0.912858\pi$
$398$	1.33985	+	1.84415i	0.0671607	+	0.0924387i
$399$	25.8560			1.29442
$400$	−0.485943	−	4.97633i	−0.0242971	−	0.248816i
$401$	3.51432			0.175497			0.0877483	−	0.996143i	$-0.472033\pi$
$401$	3.51432			0.175497			0.0877483	+	0.996143i	$0.472033\pi$
$402$	−7.03023	−	9.67628i	−0.350636	−	0.482609i
$403$	28.0573	+	9.11637i	1.39763	+	0.454119i
$404$	1.68757	−	5.19382i	0.0839599	−	0.258402i
$405$	−0.241934	+	2.22294i	−0.0120218	+	0.110459i
$406$	−5.31525	−	16.3587i	−0.263791	−	0.811866i
$407$			1.54106i			0.0763873i
$408$	1.57666	−	0.512289i	0.0780565	−	0.0253621i
$409$	−13.1746	−	9.57194i	−0.651444	−	0.473302i	0.212318	−	0.977201i	$-0.431899\pi$
$409$	−13.1746	−	9.57194i	−0.651444	−	0.473302i	−0.863763	+	0.503898i	$0.831899\pi$
$410$	1.59122	−	3.53874i	0.0785845	−	0.174766i
$411$	1.42968	−	1.03872i	0.0705210	−	0.0512365i
$412$	−3.90427	+	5.37377i	−0.192350	+	0.264747i
$413$	29.2537	−	40.2643i	1.43948	−	1.98128i
$414$	4.73553	−	3.44056i	0.232739	−	0.169095i
$415$	−29.5075	−	3.21146i	−1.44847	−	0.157644i
$416$	2.28564	+	1.66061i	0.112062	+	0.0814182i
$417$	−10.4583	+	3.39811i	−0.512145	+	0.166406i
$418$			4.74733i			0.232199i
$419$	−8.18528	−	25.1917i	−0.399877	−	1.23070i	−0.925098	−	0.379730i	$-0.876017\pi$
$419$	−8.18528	−	25.1917i	−0.399877	−	1.23070i	0.525220	−	0.850966i	$-0.323983\pi$
$420$	−5.33995	−	9.32836i	−0.260563	−	0.455177i
$421$	−9.56476	+	29.4373i	−0.466158	+	1.43469i	0.391362	+	0.920237i	$0.372004\pi$
$421$	−9.56476	+	29.4373i	−0.466158	+	1.43469i	−0.857520	+	0.514450i	$0.827996\pi$
$422$	−1.18806	−	0.386023i	−0.0578337	−	0.0187913i
$423$	−5.12811	−	7.05824i	−0.249337	−	0.343183i
$424$	−3.54936			−0.172372
$425$	−7.14772	−	4.19735i	−0.346716	−	0.203602i
$426$	−3.50758			−0.169943
$427$	−0.243706	−	0.335433i	−0.0117938	−	0.0162327i
$428$	−13.8137	−	4.48833i	−0.667708	−	0.216952i
$429$	−0.770528	+	2.37144i	−0.0372014	+	0.114494i
$430$	−4.97213	+	1.03770i	−0.239777	+	0.0500425i
$431$	−0.532381	−	1.63850i	−0.0256439	−	0.0789238i	0.937416	−	0.348213i	$-0.113211\pi$
$431$	−0.532381	−	1.63850i	−0.0256439	−	0.0789238i	−0.963059	+	0.269289i	$0.913211\pi$
$432$			1.00000i			0.0481125i
$433$	22.9568	−	7.45911i	1.10323	−	0.358462i	0.299886	−	0.953975i	$-0.403051\pi$
$433$	22.9568	−	7.45911i	1.10323	−	0.358462i	0.803346	+	0.595513i	$0.203051\pi$
$434$	−40.6085	−	29.5038i	−1.94927	−	1.41623i
$435$	6.94399	−	3.97503i	0.332939	−	0.190588i
$436$	−3.85954	+	2.80412i	−0.184838	+	0.134293i
$437$	18.5064	−	25.4719i	0.885282	−	1.21849i
$438$	−4.24851	+	5.84757i	−0.203002	+	0.279408i
$439$	6.66899	−	4.84531i	0.318294	−	0.231254i	−0.417153	−	0.908836i	$-0.636972\pi$
$439$	6.66899	−	4.84531i	0.318294	−	0.231254i	0.735447	+	0.677582i	$0.236972\pi$
$440$	1.71275	−	0.980449i	0.0816520	−	0.0467411i
$441$	−13.0306	−	9.46727i	−0.620504	−	0.450822i
$442$	4.45439	−	1.44732i	0.211874	−	0.0688420i
$443$		−	22.4652i		−	1.06735i	−0.845689	−	0.533676i	$-0.820810\pi$
$443$		−	22.4652i		−	1.06735i	0.845689	−	0.533676i	$-0.179190\pi$
$444$	0.539565	+	1.66061i	0.0256066	+	0.0788091i
$445$	40.9032	−	8.53666i	1.93900	−	0.404677i
$446$	2.73237	−	8.40936i	0.129381	−	0.398195i
$447$	2.76708	+	0.899079i	0.130878	+	0.0425250i
$448$	−2.82545	−	3.88890i	−0.133490	−	0.183733i
$449$	−30.4988			−1.43933			−0.719663	−	0.694323i	$-0.755704\pi$
$449$	−30.4988			−1.43933			−0.719663	+	0.694323i	$0.755704\pi$
$450$	3.74031	−	3.31815i	0.176320	−	0.156419i
$451$	1.53146			0.0721139
$452$	2.84228	+	3.91206i	0.133690	+	0.184008i
$453$	1.27616	+	0.414651i	0.0599594	+	0.0194820i
$454$	5.46860	−	16.8306i	0.256654	−	0.789900i
$455$	−15.0864	−	26.3545i	−0.707263	−	1.23552i
$456$	1.66217	+	5.11563i	0.0778381	+	0.239561i
$457$		−	6.65272i		−	0.311201i	−0.987820	−	0.155601i	$-0.950269\pi$
$457$		−	6.65272i		−	0.311201i	0.987820	−	0.155601i	$-0.0497313\pi$
$458$	−8.47737	+	2.75446i	−0.396121	+	0.128708i
$459$	1.34119	+	0.974432i	0.0626014	+	0.0454826i
$460$	−13.0118	−	1.41615i	−0.606681	−	0.0660282i
$461$	19.1479	−	13.9118i	0.891808	−	0.647936i	−0.0445410	−	0.999008i	$-0.514183\pi$
$461$	19.1479	−	13.9118i	0.891808	−	0.647936i	0.936349	+	0.351071i	$0.114183\pi$
$462$	2.49370	−	3.43228i	0.116017	−	0.159684i
$463$	−15.3328	+	21.1038i	−0.712575	+	0.980775i	0.287163	+	0.957882i	$0.407288\pi$
$463$	−15.3328	+	21.1038i	−0.712575	+	0.980775i	−0.999738	+	0.0228935i	$0.992712\pi$
$464$	2.89488	−	2.10325i	0.134391	−	0.0976410i
$465$	9.57567	−	21.2955i	0.444061	−	0.987557i
$466$	7.75898	+	5.63723i	0.359428	+	0.261140i
$467$	1.40340	−	0.455993i	0.0649417	−	0.0211008i	−0.276366	−	0.961052i	$-0.589130\pi$
$467$	1.40340	−	0.455993i	0.0649417	−	0.0211008i	0.341308	+	0.939952i	$0.389130\pi$
$468$			2.82520i			0.130595i
$469$	17.7665	+	54.6796i	0.820380	+	2.52487i
$470$	−2.11075	+	19.3940i	−0.0973615	+	0.894577i
$471$	−2.56845	+	7.90489i	−0.118348	+	0.364238i
$472$	9.84690	+	3.19945i	0.453240	+	0.147267i
$473$	−1.17839	−	1.62192i	−0.0541827	−	0.0745760i
$474$	12.5762			0.577646
$475$	13.6187	−	23.1914i	0.624868	−	1.06410i
$476$	−7.96896			−0.365257
$477$	−2.08626	−	2.87150i	−0.0955235	−	0.131477i
$478$	8.71452	+	2.83152i	0.398593	+	0.129511i
$479$	4.14388	−	12.7536i	0.189339	−	0.582725i	−0.810657	−	0.585521i	$-0.800890\pi$
$479$	4.14388	−	12.7536i	0.189339	−	0.582725i	0.999996	+	0.00279598i	$0.000889988\pi$
$480$	1.50234	−	1.65619i	0.0685722	−	0.0755945i
$481$	1.52438	+	4.69156i	0.0695058	+	0.213917i
$482$		−	2.49551i		−	0.113667i
$483$	−26.7600	+	8.69485i	−1.21762	+	0.395629i
$484$	−8.26900	−	6.00778i	−0.375864	−	0.273081i
$485$	30.2596	+	27.4487i	1.37402	+	1.24638i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−1.24615	+	1.71518i	−0.0564686	+	0.0777224i	−0.836317	−	0.548246i	$-0.815296\pi$
$487$	−1.24615	+	1.71518i	−0.0564686	+	0.0777224i	0.779849	+	0.625968i	$0.215296\pi$
$488$	0.0506988	−	0.0697810i	0.00229503	−	0.00315884i
$489$	−5.04724	+	3.66704i	−0.228244	+	0.165829i
$490$	7.35807	+	35.2560i	0.332404	+	1.59270i
$491$	1.79947	+	1.30739i	0.0812091	+	0.0590019i	0.627649	−	0.778496i	$-0.284017\pi$
$491$	1.79947	+	1.30739i	0.0812091	+	0.0590019i	−0.546440	+	0.837498i	$0.684017\pi$
$492$	1.65028	−	0.536207i	0.0744002	−	0.0241741i
$493$		−	5.93206i		−	0.267166i
$494$	4.69596	+	14.4527i	0.211281	+	0.650256i
$495$	1.79993	+	0.809348i	0.0809007	+	0.0363775i
$496$	3.22681	−	9.93109i	0.144888	−	0.445919i
$497$	16.0355	+	5.21025i	0.719291	+	0.233712i
$498$	−7.80231	−	10.7390i	−0.349630	−	0.481224i
$499$	−14.5582			−0.651715			−0.325858	−	0.945419i	$-0.605653\pi$
$499$	−14.5582			−0.651715			−0.325858	+	0.945419i	$0.605653\pi$
$500$	−11.1797	−	0.123723i	−0.499969	−	0.00553307i
$501$	14.8368			0.662860
$502$	−5.12115	−	7.04866i	−0.228568	−	0.314597i
$503$	−22.6744	−	7.36734i	−1.01100	−	0.328494i	−0.243747	−	0.969839i	$-0.578377\pi$
$503$	−22.6744	−	7.36734i	−1.01100	−	0.328494i	−0.767252	+	0.641345i	$0.778377\pi$
$504$	1.48543	−	4.57167i	0.0661662	−	0.203638i
$505$	−11.1373	−	5.00794i	−0.495602	−	0.222850i
$506$	−1.59643	−	4.91331i	−0.0709700	−	0.218423i
$507$		−	5.01824i		−	0.222868i
$508$	−1.71362	+	0.556790i	−0.0760297	+	0.0247035i
$509$	−28.1543	−	20.4553i	−1.24792	−	0.906664i	−0.249817	−	0.968293i	$-0.580370\pi$
$509$	−28.1543	−	20.4553i	−1.24792	−	0.906664i	−0.998099	+	0.0616289i	$0.980370\pi$
$510$	−0.757340	−	3.62877i	−0.0335356	−	0.160685i
$511$	28.1089	−	20.4223i	1.24347	−	0.903431i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−3.16163	+	4.35161i	−0.139589	+	0.192128i
$514$	−16.0081	+	11.6306i	−0.706088	+	0.513003i
$515$	11.0010	+	9.97907i	0.484762	+	0.439730i
$516$	−1.83769	−	1.33516i	−0.0808999	−	0.0587772i
$517$	−7.32322	+	2.37946i	−0.322075	+	0.104648i
$518$		−	8.39326i		−	0.368778i
$519$	4.95566	+	15.2520i	0.217529	+	0.669487i
$520$	4.24442	−	4.67907i	0.186130	−	0.205191i
$521$	−2.68575	+	8.26589i	−0.117665	+	0.362135i	−0.992494	−	0.122297i	$-0.960974\pi$
$521$	−2.68575	+	8.26589i	−0.117665	+	0.362135i	0.874829	+	0.484433i	$0.160974\pi$
$522$	3.40313	+	1.10574i	0.148951	+	0.0483971i
$523$	19.0655	+	26.2414i	0.833676	+	1.14746i	0.987228	+	0.159317i	$0.0509290\pi$
$523$	19.0655	+	26.2414i	0.833676	+	1.14746i	−0.153551	+	0.988141i	$0.549071\pi$
$524$	16.0315			0.700338
$525$	−22.0283	+	9.61354i	−0.961395	+	0.419569i
$526$	25.5635			1.11462
$527$	−10.1752	−	14.0049i	−0.443238	−	0.610064i
$528$	0.839389	+	0.272734i	0.0365297	+	0.0118692i
$529$	−3.48038	+	10.7115i	−0.151321	+	0.465717i
$530$	−0.858713	+	7.89003i	−0.0373001	+	0.342721i
$531$	3.19945	+	9.84690i	0.138844	+	0.427319i
$532$		−	25.8560i		−	1.12100i
$533$	4.66236	−	1.51489i	0.201949	−	0.0656173i
$534$	15.1178	+	10.9837i	0.654210	+	0.475312i
$535$	−13.3193	+	29.6211i	−0.575843	+	1.28063i
$536$	−9.67628	+	7.03023i	−0.417951	+	0.303659i
$537$	6.90583	−	9.50506i	0.298009	−	0.410174i
$538$	−14.3504	+	19.7517i	−0.618691	+	0.851555i
$539$	−11.5006	+	8.35567i	−0.495366	+	0.359904i
$540$	2.22294	+	0.241934i	0.0956602	+	0.0104112i
$541$	−25.0000	−	18.1636i	−1.07483	−	0.780913i	−0.0980596	−	0.995181i	$-0.531264\pi$
$541$	−25.0000	−	18.1636i	−1.07483	−	0.780913i	−0.976775	+	0.214268i	$0.931264\pi$
$542$	−2.61209	+	0.848720i	−0.112199	+	0.0364557i
$543$			4.03402i			0.173116i
$544$	−0.512289	−	1.57666i	−0.0219642	−	0.0675989i
$545$	5.29963	+	9.25793i	0.227011	+	0.396566i
$546$	4.19663	−	12.9159i	0.179599	−	0.552749i
$547$	−29.7315	−	9.66035i	−1.27123	−	0.413047i	−0.405745	−	0.913986i	$-0.632988\pi$
$547$	−29.7315	−	9.66035i	−1.27123	−	0.413047i	−0.865482	+	0.500940i	$0.832988\pi$
$548$	−1.03872	−	1.42968i	−0.0443721	−	0.0610730i
$549$	0.0862540			0.00368123
$550$	−1.76511	−	4.04454i	−0.0752645	−	0.172460i
$551$	19.2471			0.819953
$552$	−3.44056	−	4.73553i	−0.146440	−	0.201558i
$553$	−57.4945	−	18.6811i	−2.44491	−	0.794401i
$554$	−0.921114	+	2.83490i	−0.0391344	+	0.120443i
$555$	3.82198	−	0.797663i	0.162234	−	0.0338589i
$556$	3.39811	+	10.4583i	0.144112	+	0.443531i
$557$			34.8113i			1.47500i	0.675347	+	0.737500i	$0.263994\pi$
$557$			34.8113i			1.47500i	−0.675347	+	0.737500i	$0.736006\pi$
$558$	9.93109	−	3.22681i	0.420416	−	0.136602i
$559$	−5.19185	−	3.77210i	−0.219592	−	0.159543i
$560$	−9.32836	+	5.33995i	−0.394195	+	0.225654i
$561$	1.18372	−	0.860020i	0.0499765	−	0.0363101i
$562$	2.26988	−	3.12422i	0.0957490	−	0.131787i
$563$	−2.87518	+	3.95734i	−0.121174	+	0.166782i	−0.865295	−	0.501263i	$-0.832869\pi$
$563$	−2.87518	+	3.95734i	−0.121174	+	0.166782i	0.744121	+	0.668045i	$0.232869\pi$
$564$	−7.05824	+	5.12811i	−0.297206	+	0.215932i
$565$	9.38393	−	5.37176i	0.394785	−	0.225992i
$566$	13.5121	+	9.81713i	0.567957	+	0.412645i
$567$	4.57167	−	1.48543i	0.191992	−	0.0623820i
$568$			3.50758i			0.147175i
$569$	0.906980	+	2.79140i	0.0380226	+	0.117021i	0.968266	−	0.249921i	$-0.0804046\pi$
$569$	0.906980	+	2.79140i	0.0380226	+	0.117021i	−0.930244	+	0.366942i	$0.880405\pi$
$570$	11.7739	−	2.45726i	0.493153	−	0.102923i
$571$	9.85310	−	30.3247i	0.412339	−	1.26905i	−0.502270	−	0.864711i	$-0.667501\pi$
$571$	9.85310	−	30.3247i	0.412339	−	1.26905i	0.914609	−	0.404339i	$-0.132499\pi$
$572$	2.37144	+	0.770528i	0.0991550	+	0.0322174i
$573$	7.00730	+	9.64472i	0.292734	+	0.402914i
$574$	−8.34102			−0.348147
$575$	−6.29603	+	28.5820i	−0.262562	+	1.19195i
$576$	1.00000			0.0416667
$577$	21.7254	+	29.9024i	0.904439	+	1.24485i	0.969030	+	0.246942i	$0.0794256\pi$
$577$	21.7254	+	29.9024i	0.904439	+	1.24485i	−0.0645913	+	0.997912i	$0.520574\pi$
$578$	13.5542	+	4.40401i	0.563779	+	0.183183i
$579$	−3.64913	+	11.2309i	−0.151653	+	0.466739i
$580$	−3.97503	−	6.94399i	−0.165054	−	0.288334i
$581$	19.7177	+	60.6847i	0.818027	+	2.51763i
$582$			18.2706i			0.757341i
$583$	−2.97930	+	0.968032i	−0.123390	+	0.0400918i
$584$	5.84757	+	4.24851i	0.241974	+	0.175805i
$585$	6.28026	+	0.683513i	0.259657	+	0.0282598i
$586$	0.407059	−	0.295746i	0.0168155	−	0.0122171i
$587$	16.4935	−	22.7014i	0.680761	−	0.936988i	−0.319181	−	0.947694i	$-0.603408\pi$
$587$	16.4935	−	22.7014i	0.680761	−	0.936988i	0.999943	+	0.0107059i	$0.00340786\pi$
$588$	−9.46727	+	13.0306i	−0.390424	+	0.537372i
$589$	45.4402	−	33.0143i	1.87233	−	1.36033i
$590$	9.49450	−	21.1150i	0.390882	−	0.869292i
$591$	5.88837	+	4.27815i	0.242215	+	0.175980i
$592$	1.66061	−	0.539565i	0.0682507	−	0.0221760i
$593$			40.6263i			1.66832i	0.551521	+	0.834161i	$0.314048\pi$
$593$			40.6263i			1.66832i	−0.551521	+	0.834161i	$0.685952\pi$
$594$	0.272734	+	0.839389i	0.0111904	+	0.0344405i
$595$	−1.92796	+	17.7145i	−0.0790389	+	0.726225i
$596$	0.899079	−	2.76708i	0.0368277	−	0.113344i
$597$	2.16792	+	0.704401i	0.0887272	+	0.0288292i
$598$	−9.72029	−	13.3788i	−0.397492	−	0.547101i
$599$	22.6989			0.927451			0.463725	−	0.885979i	$-0.346512\pi$
$599$	22.6989			0.927451			0.463725	+	0.885979i	$0.346512\pi$
$600$	−3.31815	−	3.74031i	−0.135463	−	0.152697i
$601$	32.9640			1.34463			0.672316	−	0.740265i	$-0.265300\pi$
$601$	32.9640			1.34463			0.672316	+	0.740265i	$0.265300\pi$
$602$	6.41805	+	8.83368i	0.261580	+	0.360034i
$603$	−11.3751	−	3.69601i	−0.463232	−	0.150513i
$604$	0.414651	−	1.27616i	0.0168719	−	0.0519264i
$605$	−15.3555	+	16.9280i	−0.624290	+	0.688221i
$606$	−1.68757	−	5.19382i	−0.0685530	−	0.210984i
$607$			8.32854i			0.338045i	0.985612	+	0.169023i	$0.0540611\pi$
$607$			8.32854i			0.338045i	−0.985612	+	0.169023i	$0.945939\pi$
$608$	5.11563	−	1.66217i	0.207466	−	0.0674098i
$609$	−13.9155	−	10.1102i	−0.563885	−	0.409686i
$610$	−0.142853	−	0.129583i	−0.00578396	−	0.00524666i
$611$	−19.9409	+	14.4879i	−0.806724	+	0.586120i
$612$	0.974432	−	1.34119i	0.0393891	−	0.0542144i
$613$	4.33351	−	5.96457i	0.175029	−	0.240907i	−0.712485	−	0.701687i	$-0.752430\pi$
$613$	4.33351	−	5.96457i	0.175029	−	0.240907i	0.887514	+	0.460780i	$0.152430\pi$
$614$	−6.98485	+	5.07479i	−0.281886	+	0.204802i
$615$	−0.792698	−	3.79819i	−0.0319647	−	0.153158i
$616$	−3.43228	−	2.49370i	−0.138291	−	0.100474i
$617$	8.43210	−	2.73975i	0.339463	−	0.110298i	−0.134324	−	0.990937i	$-0.542886\pi$
$617$	8.43210	−	2.73975i	0.339463	−	0.110298i	0.473788	+	0.880639i	$0.342886\pi$
$618$			6.64235i			0.267194i
$619$	0.139486	+	0.429292i	0.00560640	+	0.0172547i	0.953821	−	0.300377i	$-0.0971125\pi$
$619$	0.139486	+	0.429292i	0.00560640	+	0.0172547i	−0.948214	+	0.317632i	$0.897112\pi$
$620$	−21.2955	−	9.57567i	−0.855250	−	0.384568i
$621$	1.80881	−	5.56695i	0.0725851	−	0.223394i
$622$	19.2755	+	6.26298i	0.772875	+	0.251122i
$623$	−52.7980	−	72.6703i	−2.11531	−	2.91147i
$624$	2.82520			0.113099
$625$	−2.97977	+	24.8218i	−0.119191	+	0.992871i
$626$	−17.0302			−0.680664
$627$	2.79041	+	3.84067i	0.111438	+	0.153382i
$628$	7.90489	+	2.56845i	0.315439	+	0.102492i
$629$	0.894493	−	2.75297i	0.0356658	−	0.109768i
$630$	−9.80318	−	4.40806i	−0.390568	−	0.175621i
$631$	−9.74952	−	30.0059i	−0.388122	−	1.19452i	−0.934190	−	0.356776i	$-0.883876\pi$
$631$	−9.74952	−	30.0059i	−0.388122	−	1.19452i	0.546068	−	0.837741i	$-0.316124\pi$
$632$		−	12.5762i		−	0.500256i
$633$	−1.18806	+	0.386023i	−0.0472210	+	0.0153430i
$634$	−2.28270	−	1.65848i	−0.0906575	−	0.0658665i
$635$	0.823127	+	3.94399i	0.0326648	+	0.156512i
$636$	−2.87150	+	2.08626i	−0.113862	+	0.0827257i
$637$	−26.7469	+	36.8140i	−1.05975	+	1.45862i
$638$	1.85630	−	2.55498i	0.0734916	−	0.101153i
$639$	−2.83769	+	2.06170i	−0.112257	+	0.0815598i
$640$	−1.65619	−	1.50234i	−0.0654667	−	0.0593852i
$641$	−15.1110	−	10.9788i	−0.596848	−	0.433635i	0.247911	−	0.968783i	$-0.420256\pi$
$641$	−15.1110	−	10.9788i	−0.596848	−	0.433635i	−0.844759	+	0.535147i	$0.820256\pi$
$642$	−13.8137	+	4.48833i	−0.545182	+	0.177140i
$643$		−	15.5969i		−	0.615083i	−0.951535	−	0.307541i	$-0.900494\pi$
$643$		−	15.5969i		−	0.615083i	0.951535	−	0.307541i	$-0.0995063\pi$
$644$	8.69485	+	26.7600i	0.342625	+	1.05449i
$645$	−3.41259	+	3.76206i	−0.134371	+	0.148131i
$646$	2.75555	−	8.48070i	0.108416	−	0.333669i
$647$	25.0683	+	8.14520i	0.985538	+	0.320221i	0.757072	−	0.653331i	$-0.226629\pi$
$647$	25.0683	+	8.14520i	0.985538	+	0.320221i	0.228466	+	0.973552i	$0.426629\pi$
$648$	0.587785	+	0.809017i	0.0230904	+	0.0317812i
$649$	9.13798			0.358697
$650$	−9.37444	−	10.5671i	−0.367696	−	0.414476i
$651$	−50.1948			−1.96729
$652$	3.66704	+	5.04724i	0.143612	+	0.197665i
$653$	−18.6583	−	6.06245i	−0.730156	−	0.237242i	−0.0797351	−	0.996816i	$-0.525407\pi$
$653$	−18.6583	−	6.06245i	−0.730156	−	0.237242i	−0.650421	+	0.759574i	$0.725407\pi$
$654$	−1.47421	+	4.53716i	−0.0576462	+	0.177417i
$655$	3.87856	−	35.6370i	0.151548	−	1.39245i
$656$	−0.536207	−	1.65028i	−0.0209354	−	0.0644324i
$657$			7.22800i			0.281991i
$658$	39.8854	−	12.9596i	1.55489	−	0.505216i
$659$	18.7179	+	13.5993i	0.729145	+	0.529755i	0.889293	−	0.457338i	$-0.151197\pi$
$659$	18.7179	+	13.5993i	0.729145	+	0.529755i	−0.160148	+	0.987093i	$0.551197\pi$
$660$	0.809348	−	1.79993i	0.0315038	−	0.0700621i
$661$	−14.1554	+	10.2845i	−0.550581	+	0.400021i	−0.828000	−	0.560729i	$-0.810521\pi$
$661$	−14.1554	+	10.2845i	−0.550581	+	0.400021i	0.277419	+	0.960749i	$0.410521\pi$
$662$	−2.39404	+	3.29512i	−0.0930472	+	0.128068i
$663$	2.75297	−	3.78913i	0.106916	−	0.147158i
$664$	−10.7390	+	7.80231i	−0.416752	+	0.302788i
$665$	−57.4764	−	6.25545i	−2.22884	−	0.242576i
$666$	1.41260	+	1.02631i	0.0547372	+	0.0397689i
$667$	−19.9200	+	6.47241i	−0.771306	+	0.250613i
$668$		−	14.8368i		−	0.574054i
$669$	−2.73237	−	8.40936i	−0.105639	−	0.325125i
$670$	13.2868	+	23.2106i	0.513312	+	0.896705i
$671$	0.0235244	−	0.0724006i	0.000908149	−	0.00279500i
$672$	−4.57167	−	1.48543i	−0.176356	−	0.0573016i
$673$	0.608086	+	0.836959i	0.0234400	+	0.0322624i	0.820576	−	0.571537i	$-0.193653\pi$
$673$	0.608086	+	0.836959i	0.0234400	+	0.0322624i	−0.797136	+	0.603800i	$0.793653\pi$
$674$	9.04782			0.348509
$675$	1.07561	−	4.88294i	0.0414003	−	0.187944i
$676$	−5.01824			−0.193009
$677$	5.53353	+	7.61625i	0.212671	+	0.292716i	0.902004	−	0.431729i	$-0.142096\pi$
$677$	5.53353	+	7.61625i	0.212671	+	0.292716i	−0.689333	+	0.724445i	$0.742096\pi$
$678$	4.59891	+	1.49428i	0.176620	+	0.0573873i
$679$	27.1396	−	83.5272i	1.04152	−	3.20548i
$680$	−3.62877	+	0.757340i	−0.139157	+	0.0290427i
$681$	−5.46860	−	16.8306i	−0.209557	−	0.644950i
$682$		−	9.21610i		−	0.352903i
$683$	13.1823	−	4.28318i	0.504405	−	0.163891i	−0.0457510	−	0.998953i	$-0.514568\pi$
$683$	13.1823	−	4.28318i	0.504405	−	0.163891i	0.550156	+	0.835062i	$0.314568\pi$
$684$	4.35161	+	3.16163i	0.166388	+	0.120888i
$685$	−3.42940	+	1.96314i	−0.131031	+	0.0750075i
$686$	35.4149	−	25.7305i	1.35215	−	0.982394i
$687$	−5.23930	+	7.21128i	−0.199892	+	0.275128i
$688$	−1.33516	+	1.83769i	−0.0509026	+	0.0700614i
$689$	−8.11255	+	5.89411i	−0.309064	+	0.224548i
$690$	−11.3592	+	6.50249i	−0.432437	+	0.247545i
$691$	7.36726	+	5.35263i	0.280264	+	0.203624i	0.719032	−	0.694977i	$-0.244585\pi$
$691$	7.36726	+	5.35263i	0.280264	+	0.203624i	−0.438769	+	0.898600i	$0.644585\pi$
$692$	15.2520	−	4.95566i	0.579793	−	0.188386i
$693$		−	4.24254i		−	0.161161i
$694$	−2.68429	−	8.26141i	−0.101894	−	0.313599i
$695$	24.0703	−	5.02357i	0.913039	−	0.190555i
$696$	1.10574	−	3.40313i	0.0419131	−	0.128995i
$697$	−2.73583	−	0.888926i	−0.103627	−	0.0336705i
$698$	15.7706	+	21.7063i	0.596925	+	0.821596i
$699$	9.59063			0.362751
$700$	9.61354	+	22.0283i	0.363358	+	0.832592i
$701$	−22.6848			−0.856791			−0.428396	−	0.903591i	$-0.640921\pi$
$701$	−22.6848			−0.856791			−0.428396	+	0.903591i	$0.640921\pi$
$702$	1.66061	+	2.28564i	0.0626757	+	0.0862657i
$703$	8.93224	+	2.90226i	0.336886	+	0.109461i
$704$	0.272734	−	0.839389i	0.0102790	−	0.0316357i
$705$	9.69186	+	16.9307i	0.365017	+	0.637648i
$706$	−8.76060	−	26.9623i	−0.329709	−	1.01474i
$707$			26.2512i			0.987278i
$708$	9.84690	−	3.19945i	0.370069	−	0.120243i
$709$	18.1615	+	13.1951i	0.682069	+	0.495552i	0.874043	−	0.485848i	$-0.161489\pi$
$709$	18.1615	+	13.1951i	0.682069	+	0.495552i	−0.191974	+	0.981400i	$0.561489\pi$
$710$	7.79715	+	0.848604i	0.292622	+	0.0318476i
$711$	10.1744	−	7.39213i	0.381570	−	0.277227i
$712$	10.9837	−	15.1178i	0.411632	−	0.566563i
$713$	−35.9269	+	49.4492i	−1.34547	+	1.85189i
$714$	−6.44702	+	4.68404i	−0.241274	+	0.175296i
$715$	2.28657	−	5.08516i	0.0855129	−	0.190174i
$716$	−9.50506	−	6.90583i	−0.355221	−	0.258083i
$717$	8.71452	−	2.83152i	0.325450	−	0.105745i
$718$		−	8.68830i		−	0.324245i
$719$	−14.1238	−	43.4684i	−0.526727	−	1.62110i	−0.760875	−	0.648898i	$-0.775230\pi$
$719$	−14.1238	−	43.4684i	−0.526727	−	1.62110i	0.234148	−	0.972201i	$-0.424770\pi$
$720$	0.241934	−	2.22294i	0.00901636	−	0.0828441i
$721$	9.86672	−	30.3666i	0.367456	−	1.13091i
$722$	9.44630	+	3.06929i	0.351555	+	0.114227i
$723$	−1.46682	−	2.01891i	−0.0545517	−	0.0750840i
$724$	4.03402			0.149923
$725$	−16.3978	+	7.15628i	−0.608998	+	0.265777i
$726$	−10.2210			−0.379338
$727$	−1.28973	−	1.77517i	−0.0478336	−	0.0658373i	0.784430	−	0.620217i	$-0.212956\pi$
$727$	−1.28973	−	1.77517i	−0.0478336	−	0.0658373i	−0.832264	+	0.554380i	$0.812956\pi$
$728$	−12.9159	−	4.19663i	−0.478695	−	0.155537i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	10.8589	−	11.9710i	0.401907	−	0.443065i
$731$	1.16367	+	3.58141i	0.0430400	+	0.132463i
$732$		−	0.0862540i		−	0.00318804i
$733$	8.72887	−	2.83618i	0.322408	−	0.104757i	−0.143342	−	0.989673i	$-0.545785\pi$
$733$	8.72887	−	2.83618i	0.322408	−	0.104757i	0.465750	+	0.884917i	$0.345785\pi$
$734$	−10.0895	−	7.33046i	−0.372411	−	0.270572i
$735$	26.6758	+	24.1977i	0.983950	+	0.892547i
$736$	−4.73553	+	3.44056i	−0.174554	+	0.126821i
$737$	−6.20478	+	8.54014i	−0.228556	+	0.314580i
$738$	1.01993	−	1.40381i	0.0375440	−	0.0516749i
$739$	−35.2025	+	25.5761i	−1.29495	+	0.940833i	−0.999893	−	0.0146478i	$-0.995337\pi$
$739$	−35.2025	+	25.5761i	−1.29495	+	0.940833i	−0.295053	+	0.955481i	$0.595337\pi$
$740$	−0.797663	−	3.82198i	−0.0293227	−	0.140499i
$741$	12.2942	+	8.93224i	0.451638	+	0.328134i
$742$	16.2265	−	5.27232i	0.595695	−	0.193553i
$743$			8.61668i			0.316115i	0.987430	+	0.158058i	$0.0505232\pi$
$743$			8.61668i			0.316115i	−0.987430	+	0.158058i	$0.949477\pi$
$744$	−3.22681	−	9.93109i	−0.118300	−	0.364091i
$745$	−5.93354	−	2.66805i	−0.217388	−	0.0977499i
$746$	−4.01684	+	12.3626i	−0.147067	+	0.452625i
$747$	−12.6244	−	4.10192i	−0.461903	−	0.150081i
$748$	−0.860020	−	1.18372i	−0.0314454	−	0.0432809i
$749$	69.8186			2.55112
$750$	−9.11725	+	6.47114i	−0.332915	+	0.236293i
$751$	1.11603			0.0407245			0.0203623	−	0.999793i	$-0.493518\pi$
$751$	1.11603			0.0407245			0.0203623	+	0.999793i	$0.493518\pi$
$752$	5.12811	+	7.05824i	0.187003	+	0.257388i
$753$	−8.28619	−	2.69235i	−0.301966	−	0.0981146i
$754$	3.12395	−	9.61453i	0.113768	−	0.350141i
$755$	−2.73652	−	1.23049i	−0.0995921	−	0.0447822i
$756$	−1.48543	−	4.57167i	−0.0540244	−	0.166270i
$757$		−	37.2729i		−	1.35471i	−0.735658	−	0.677354i	$-0.763127\pi$
$757$		−	37.2729i		−	1.35471i	0.735658	−	0.677354i	$-0.236873\pi$
$758$	1.66651	−	0.541481i	0.0605302	−	0.0196675i
$759$	−4.17951	−	3.03659i	−0.151707	−	0.110221i
$760$	−2.45726	−	11.7739i	−0.0891340	−	0.427083i
$761$	16.1999	−	11.7699i	0.587245	−	0.426659i	−0.254084	−	0.967182i	$-0.581774\pi$
$761$	16.1999	−	11.7699i	0.587245	−	0.426659i	0.841329	+	0.540524i	$0.181774\pi$
$762$	−1.05908	+	1.45769i	−0.0383663	+	0.0528067i
$763$	13.4792	−	18.5526i	0.487981	−	0.671648i
$764$	9.64472	−	7.00730i	0.348934	−	0.253515i
$765$	−2.74564	−	2.49059i	−0.0992688	−	0.0900473i
$766$	−27.6165	−	20.0646i	−0.997825	−	0.724962i
$767$	27.8195	−	9.03910i	1.00450	−	0.326383i
$768$		−	1.00000i		−	0.0360844i
$769$	4.78043	+	14.7126i	0.172387	+	0.530552i	0.999504	−	0.0314770i	$-0.0100211\pi$
$769$	4.78043	+	14.7126i	0.172387	+	0.530552i	−0.827118	+	0.562029i	$0.810021\pi$
$770$	−6.37374	+	7.02645i	−0.229694	+	0.253216i
$771$	−6.11455	+	18.8187i	−0.220210	+	0.677738i
$772$	11.2309	+	3.64913i	0.404208	+	0.131335i
$773$	−14.1408	−	19.4632i	−0.508610	−	0.700042i	0.475074	−	0.879946i	$-0.342421\pi$
$773$	−14.1408	−	19.4632i	−0.508610	−	0.700042i	−0.983684	+	0.179904i	$0.942421\pi$
$774$	−2.27151			−0.0816479
$775$	−26.4383	+	45.0221i	−0.949691	+	1.61724i
$776$	18.2706			0.655876
$777$	−4.93343	−	6.79029i	−0.176986	−	0.243600i
$778$	−6.52094	−	2.11878i	−0.233787	−	0.0759620i
$779$	2.88420	−	8.87665i	0.103337	−	0.318039i
$780$	0.683513	−	6.28026i	0.0244737	−	0.224869i
$781$	0.956637	+	2.94422i	0.0342311	+	0.105353i
$782$			9.70385i			0.347009i
$783$	3.40313	−	1.10574i	0.121618	−	0.0395161i
$784$	13.0306	+	9.46727i	0.465378	+	0.338117i
$785$	7.62199	−	16.9507i	0.272040	−	0.604997i
$786$	12.9697	−	9.42306i	0.462615	−	0.336109i
$787$	−19.6062	+	26.9857i	−0.698887	+	0.961935i	0.301079	+	0.953599i	$0.402653\pi$
$787$	−19.6062	+	26.9857i	−0.698887	+	0.961935i	−0.999965	+	0.00833555i	$0.997347\pi$
$788$	4.27815	−	5.88837i	0.152403	−	0.209764i
$789$	20.6813	−	15.0258i	0.736273	−	0.534933i
$790$	−27.9563	−	3.04263i	−0.994639	−	0.108252i
$791$	−18.8051	−	13.6627i	−0.668631	−	0.485789i
$792$	0.839389	−	0.272734i	0.0298264	−	0.00969118i
$793$		−	0.243685i		−	0.00865350i
$794$	10.2466	+	31.5358i	0.363638	+	1.11916i
$795$	3.94293	+	6.88791i	0.139841	+	0.244289i
$796$	0.704401	−	2.16792i	0.0249668	−	0.0768400i
$797$	−31.0587	−	10.0916i	−1.10016	−	0.357462i	−0.297993	−	0.954568i	$-0.596317\pi$
$797$	−31.0587	−	10.0916i	−1.10016	−	0.357462i	−0.802162	+	0.597106i	$0.796317\pi$
$798$	−15.1978	−	20.9179i	−0.537995	−	0.740487i
$799$	14.4634			0.511680
$800$	−3.74031	+	3.31815i	−0.132240	+	0.117314i
$801$	18.6866			0.660259
$802$	−2.06566	−	2.84314i	−0.0729411	−	0.100395i
$803$	6.06710	+	1.97132i	0.214103	+	0.0695664i
$804$	−3.69601	+	11.3751i	−0.130348	+	0.401170i
$805$	61.5895	−	12.8540i	2.17074	−	0.453043i
$806$	−9.11637	−	28.0573i	−0.321111	−	0.988277i
$807$			24.4144i			0.859428i
$808$	−5.19382	+	1.68757i	−0.182718	+	0.0593686i
$809$	8.36995	+	6.08113i	0.294272	+	0.213801i	0.725118	−	0.688624i	$-0.241785\pi$
$809$	8.36995	+	6.08113i	0.294272	+	0.213801i	−0.430847	+	0.902425i	$0.641785\pi$
$810$	1.94060	−	1.11088i	0.0681858	−	0.0390325i
$811$	30.7731	−	22.3580i	1.08059	−	0.785094i	0.102804	−	0.994702i	$-0.467219\pi$
$811$	30.7731	−	22.3580i	1.08059	−	0.785094i	0.977786	+	0.209607i	$0.0672186\pi$
$812$	−10.1102	+	13.9155i	−0.354799	+	0.488338i
$813$	−1.61436	+	2.22198i	−0.0566181	+	0.0779282i
$814$	1.24674	−	0.905810i	0.0436982	−	0.0317486i
$815$	12.1069	−	6.93051i	0.424087	−	0.242765i
$816$	−1.34119	−	0.974432i	−0.0469511	−	0.0341119i
$817$	−11.6202	+	3.77564i	−0.406540	+	0.132093i
$818$			16.2848i			0.569383i
$819$	−4.19663	−	12.9159i	−0.146642	−	0.451318i
$820$	−3.79819	+	0.792698i	−0.132639	+	0.0276822i
$821$	−6.18062	+	19.0220i	−0.215705	+	0.663872i	0.783398	+	0.621521i	$0.213485\pi$
$821$	−6.18062	+	19.0220i	−0.215705	+	0.663872i	−0.999103	+	0.0423510i	$0.986515\pi$
$822$	−1.68069	−	0.546090i	−0.0586209	−	0.0190471i
$823$	−23.0591	−	31.7381i	−0.803790	−	1.10632i	−0.992252	−	0.124242i	$-0.960350\pi$
$823$	−23.0591	−	31.7381i	−0.803790	−	1.10632i	0.188462	−	0.982080i	$-0.439650\pi$
$824$	6.64235			0.231397
$825$	−3.80533	−	2.23460i	−0.132484	−	0.0777987i
$826$	−49.7694			−1.73170
$827$	−32.2736	−	44.4208i	−1.12226	−	1.54466i	−0.801991	−	0.597336i	$-0.796226\pi$
$827$	−32.2736	−	44.4208i	−1.12226	−	1.54466i	−0.320271	−	0.947326i	$-0.603774\pi$
$828$	−5.56695	−	1.80881i	−0.193465	−	0.0628606i
$829$	2.01553	−	6.20315i	0.0700021	−	0.215444i	−0.909935	−	0.414751i	$-0.863869\pi$
$829$	2.01553	−	6.20315i	0.0700021	−	0.215444i	0.979937	+	0.199306i	$0.0638689\pi$
$830$	14.7459	+	25.7597i	0.511839	+	0.894133i
$831$	0.921114	+	2.83490i	0.0319531	+	0.0983415i
$832$		−	2.82520i		−	0.0979462i
$833$	25.3948	−	8.25128i	0.879879	−	0.285890i
$834$	8.89636	+	6.46359i	0.308056	+	0.223816i
$835$	−32.9814	−	3.58954i	−1.14137	−	0.124221i
$836$	3.84067	−	2.79041i	0.132832	−	0.0965083i
$837$	6.13775	−	8.44789i	0.212152	−	0.292002i
$838$	−15.5693	+	21.4294i	−0.537834	+	0.740265i
$839$	−35.1557	+	25.5421i	−1.21371	+	0.881811i	−0.995562	−	0.0941047i	$-0.970001\pi$
$839$	−35.1557	+	25.5421i	−1.21371	+	0.881811i	−0.218147	+	0.975916i	$0.570001\pi$
$840$	−4.40806	+	9.80318i	−0.152093	+	0.338242i
$841$	13.1029	+	9.51978i	0.451823	+	0.328268i
$842$	29.4373	−	9.56476i	1.01448	−	0.329624i
$843$		−	3.86174i		−	0.133006i
$844$	0.386023	+	1.18806i	0.0132875	+	0.0408946i
$845$	−1.21408	+	11.1553i	−0.0417658	+	0.383752i
$846$	−2.69601	+	8.29746i	−0.0926907	+	0.285273i
$847$	46.7273	+	15.1826i	1.60557	+	0.521681i
$848$	2.08626	+	2.87150i	0.0716426	+	0.0986076i
$849$	16.7019			0.573208
$850$	0.805597	+	8.24977i	0.0276317	+	0.282965i
$851$	−10.2205			−0.350355
$852$	2.06170	+	2.83769i	0.0706328	+	0.0972178i
$853$	−19.8410	−	6.44673i	−0.679343	−	0.220732i	−0.0510350	−	0.998697i	$-0.516252\pi$
$853$	−19.8410	−	6.44673i	−0.679343	−	0.220732i	−0.628307	+	0.777965i	$0.716252\pi$
$854$	−0.128124	+	0.394325i	−0.00438431	+	0.0134935i
$855$	8.08092	−	8.90847i	0.276362	−	0.304663i
$856$	4.48833	+	13.8137i	0.153408	+	0.472141i
$857$		−	10.2125i		−	0.348854i	−0.984670	−	0.174427i	$-0.944193\pi$
$857$		−	10.2125i		−	0.348854i	0.984670	−	0.174427i	$-0.0558073\pi$
$858$	2.37144	−	0.770528i	0.0809597	−	0.0263054i
$859$	2.14672	+	1.55969i	0.0732453	+	0.0532158i	0.623805	−	0.781580i	$-0.285586\pi$
$859$	2.14672	+	1.55969i	0.0732453	+	0.0532158i	−0.550560	+	0.834796i	$0.685586\pi$
$860$	3.76206	+	3.41259i	0.128285	+	0.116368i
$861$	−6.74802	+	4.90273i	−0.229972	+	0.167084i
$862$	−1.01265	+	1.39379i	−0.0344910	+	0.0474727i
$863$	−1.31766	+	1.81361i	−0.0448538	+	0.0617360i	−0.830855	−	0.556489i	$-0.812148\pi$
$863$	−1.31766	+	1.81361i	−0.0448538	+	0.0617360i	0.786001	+	0.618225i	$0.212148\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	−7.32618	−	35.1032i	−0.249097	−	1.19354i
$866$	−19.5282	−	14.1881i	−0.663595	−	0.482130i
$867$	13.5542	−	4.40401i	0.460323	−	0.149568i
$868$			50.1948i			1.70372i
$869$	−3.42997	−	10.5564i	−0.116354	−	0.358100i
$870$	−7.29745	−	3.28134i	−0.247407	−	0.111248i
$871$	−10.4420	+	32.1371i	−0.353812	+	1.08892i
$872$	4.53716	+	1.47421i	0.153648	+	0.0499231i
$873$	10.7392	+	14.7812i	0.363467	+	0.500269i
$874$	−31.4850			−1.06500
$875$	51.2935	−	16.0409i	1.73404	−	0.542283i
$876$	7.22800			0.244211
$877$	30.0466	+	41.3556i	1.01460	+	1.39648i	0.915921	+	0.401359i	$0.131462\pi$
$877$	30.0466	+	41.3556i	1.01460	+	1.39648i	0.0986803	+	0.995119i	$0.468538\pi$
$878$	−7.83987	−	2.54733i	−0.264583	−	0.0859682i
$879$	0.155483	−	0.478527i	0.00524430	−	0.0161403i
$880$	−1.79993	−	0.809348i	−0.0606756	−	0.0272831i
$881$	−14.5343	−	44.7321i	−0.489674	−	1.50706i	−0.825096	−	0.564993i	$-0.808879\pi$
$881$	−14.5343	−	44.7321i	−0.489674	−	1.50706i	0.335422	−	0.942068i	$-0.391121\pi$
$882$			16.1067i			0.542340i
$883$	25.2883	−	8.21666i	0.851018	−	0.276513i	0.149146	−	0.988815i	$-0.452348\pi$
$883$	25.2883	−	8.21666i	0.851018	−	0.276513i	0.701873	+	0.712303i	$0.252348\pi$
$884$	−3.78913	−	2.75297i	−0.127442	−	0.0925923i
$885$	−4.72989	−	22.6631i	−0.158994	−	0.761813i
$886$	−18.1747	+	13.2047i	−0.610591	+	0.443621i
$887$	−28.1751	+	38.7797i	−0.946027	+	1.30209i	0.00724276	+	0.999974i	$0.497695\pi$
$887$	−28.1751	+	38.7797i	−0.946027	+	1.30209i	−0.953270	+	0.302121i	$0.902305\pi$
$888$	1.02631	−	1.41260i	0.0344409	−	0.0474038i
$889$	7.00705	−	5.09092i	0.235009	−	0.170744i
$890$	−30.9486	−	28.0736i	−1.03740	−	0.941031i
$891$	0.714027	+	0.518771i	0.0239208	+	0.0173795i
$892$	−8.40936	+	2.73237i	−0.281566	+	0.0914864i
$893$			46.9279i			1.57038i
$894$	−0.899079	−	2.76708i	−0.0300697	−	0.0925451i
$895$	−17.6509	+	19.4584i	−0.590003	+	0.650424i
$896$	−1.48543	+	4.57167i	−0.0496246	+	0.152729i
$897$	−15.7278	−	5.11026i	−0.525134	−	0.170627i
$898$	17.9267	+	24.6740i	0.598223	+	0.823383i
$899$	−37.3648			−1.24619
$900$	−4.88294	−	1.07561i	−0.162765	−	0.0358537i
$901$	5.88415			0.196029
$902$	−0.900172	−	1.23898i	−0.0299725	−	0.0412536i
$903$	10.3846	+	3.37417i	0.345578	+	0.112285i
$904$	1.49428	−	4.59891i	0.0496989	−	0.152957i
$905$	0.975968	−	8.96739i	0.0324423	−	0.298086i
$906$	−0.414651	−	1.27616i	−0.0137759	−	0.0423977i
$907$			5.35392i			0.177774i	0.996042	+	0.0888870i	$0.0283310\pi$
$907$			5.35392i			0.177774i	−0.996042	+	0.0888870i	$0.971669\pi$
$908$	−16.8306	+	5.46860i	−0.558543	+	0.181482i
$909$	−4.41813	−	3.20996i	−0.146540	−	0.106468i
$910$	−12.4537	+	27.6960i	−0.412835	+	0.918112i
$911$	10.9464	−	7.95304i	0.362671	−	0.263496i	−0.391494	−	0.920181i	$-0.628042\pi$
$911$	10.9464	−	7.95304i	0.362671	−	0.263496i	0.754165	+	0.656685i	$0.228042\pi$
$912$	3.16163	−	4.35161i	0.104692	−	0.144096i
$913$	−6.88620	+	9.47805i	−0.227900	+	0.313678i
$914$	−5.38217	+	3.91037i	−0.178026	+	0.129344i
$915$	−0.191738	−	0.0208678i	−0.00633865	−	0.000689868i
$916$	7.21128	+	5.23930i	0.238267	+	0.173111i
$917$	−73.2906	+	23.8136i	−2.42027	+	0.786393i
$918$		−	1.65780i		−	0.0547156i
$919$	17.2285	+	53.0240i	0.568317	+	1.74910i	0.657884	+	0.753119i	$0.271452\pi$
$919$	17.2285	+	53.0240i	0.568317	+	1.74910i	−0.0895666	+	0.995981i	$0.528548\pi$
$920$	6.50249	+	11.3592i	0.214381	+	0.374502i
$921$	−2.66798	+	8.21118i	−0.0879128	+	0.270568i
$922$	−22.5097	−	7.31386i	−0.741319	−	0.240869i
$923$	5.82473	+	8.01705i	0.191723	+	0.263885i
$924$	−4.24254			−0.139569
$925$	−8.68902	+	0.848490i	−0.285693	+	0.0278982i
$926$	26.0857			0.857229
$927$	3.90427	+	5.37377i	0.128233	+	0.176498i
$928$	−3.40313	−	1.10574i	−0.111713	−	0.0362979i
$929$	16.0123	−	49.2807i	0.525346	−	1.61685i	−0.238284	−	0.971195i	$-0.576585\pi$
$929$	16.0123	−	49.2807i	0.525346	−	1.61685i	0.763631	−	0.645653i	$-0.223415\pi$
$930$	−22.8569	+	4.77033i	−0.749507	+	0.156425i
$931$	26.7720	+	82.3958i	0.877417	+	2.70041i
$932$		−	9.59063i		−	0.314151i
$933$	19.2755	−	6.26298i	0.631050	−	0.205041i
$934$	−1.19380	−	0.867350i	−0.0390625	−	0.0283805i
$935$	−2.83940	+	1.62539i	−0.0928582	+	0.0531560i
$936$	2.28564	−	1.66061i	0.0747083	−	0.0542788i
$937$	23.4907	−	32.3322i	0.767409	−	1.05625i	−0.229152	−	0.973391i	$-0.573595\pi$
$937$	23.4907	−	32.3322i	0.767409	−	1.05625i	0.996561	−	0.0828575i	$-0.0264046\pi$
$938$	33.7939	−	46.5133i	1.10341	−	1.51871i
$939$	−13.7777	+	10.0101i	−0.449619	+	0.326667i
$940$	16.9307	−	9.69186i	0.552219	−	0.316114i
$941$	12.2262	+	8.88288i	0.398564	+	0.289574i	0.768956	−	0.639302i	$-0.220777\pi$
$941$	12.2262	+	8.88288i	0.398564	+	0.289574i	−0.370392	+	0.928876i	$0.620777\pi$
$942$	7.90489	−	2.56845i	0.257555	−	0.0836848i
$943$			10.1569i			0.330754i
$944$	−3.19945	−	9.84690i	−0.104133	−	0.320489i
$945$	−10.5219	+	2.19597i	−0.342279	+	0.0714349i
$946$	−0.619519	+	1.90668i	−0.0201423	+	0.0619916i
$947$	32.3992	+	10.5272i	1.05283	+	0.342087i	0.783780	−	0.621039i	$-0.213289\pi$
$947$	32.3992	+	10.5272i	1.05283	+	0.342087i	0.269054	+	0.963125i	$0.413289\pi$
$948$	−7.39213	−	10.1744i	−0.240085	−	0.330449i
$949$	20.4205			0.662879
$950$	−26.7671	+	2.61383i	−0.868440	+	0.0848039i
$951$	−2.82157			−0.0914956
$952$	4.68404	+	6.44702i	0.151811	+	0.208949i
$953$	31.7376	+	10.3122i	1.02808	+	0.334044i	0.774031	−	0.633147i	$-0.218237\pi$
$953$	31.7376	+	10.3122i	1.02808	+	0.334044i	0.254050	+	0.967191i	$0.418237\pi$
$954$	−1.09681	+	3.37565i	−0.0355107	+	0.109291i
$955$	−13.2434	−	23.1349i	−0.428547	−	0.748629i
$956$	−2.83152	−	8.71452i	−0.0915779	−	0.281848i
$957$		−	3.15813i		−	0.102088i
$958$	−12.7536	+	4.14388i	−0.412049	+	0.133883i
$959$	6.87240	+	4.99309i	0.221921	+	0.161235i
$960$	−2.22294	−	0.241934i	−0.0717451	−	0.00780840i
$961$	−63.1347	+	45.8700i	−2.03660	+	1.47968i
$962$	2.89954	−	3.99088i	0.0934850	−	0.128671i
$963$	−8.53731	+	11.7506i	−0.275111	+	0.378658i
$964$	−2.01891	+	1.46682i	−0.0650247	+	0.0472432i
$965$	10.8289	−	24.0827i	0.348596	−	0.775250i
$966$	22.7634	+	16.5386i	0.732401	+	0.532120i
$967$	−25.1661	+	8.17697i	−0.809288	+	0.262954i	−0.684296	−	0.729204i	$-0.739890\pi$
$967$	−25.1661	+	8.17697i	−0.809288	+	0.262954i	−0.124992	+	0.992158i	$0.539890\pi$
$968$			10.2210i			0.328517i
$969$	−2.75555	−	8.48070i	−0.0885209	−	0.272439i
$970$	4.42029	−	40.6145i	0.141927	−	1.30405i
$971$	9.76352	−	30.0490i	0.313326	−	0.964319i	−0.663112	−	0.748520i	$-0.730765\pi$
$971$	9.76352	−	30.0490i	0.313326	−	0.964319i	0.976438	−	0.215798i	$-0.0692354\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	−31.0701	−	42.7643i	−0.996061	−	1.37096i
$974$	2.12008			0.0679318
$975$	−13.7953	−	3.03882i	−0.441802	−	0.0973201i
$976$	−0.0862540			−0.00276092
$977$	2.72764	+	3.75428i	0.0872650	+	0.120110i	0.850417	−	0.526109i	$-0.176349\pi$
$977$	2.72764	+	3.75428i	0.0872650	+	0.120110i	−0.763152	+	0.646219i	$0.776349\pi$
$978$	5.93339	+	1.92788i	0.189729	+	0.0616467i
$979$	5.09647	−	15.6853i	0.162884	−	0.501305i
$980$	24.1977	−	26.6758i	0.772968	−	0.852126i
$981$	1.47421	+	4.53716i	0.0470679	+	0.144860i
$982$		−	2.22427i		−	0.0709793i
$983$	32.3253	−	10.5031i	1.03102	−	0.334998i	0.255825	−	0.966723i	$-0.417653\pi$
$983$	32.3253	−	10.5031i	1.03102	−	0.334998i	0.775192	+	0.631725i	$0.217653\pi$
$984$	−1.40381	−	1.01993i	−0.0447518	−	0.0325141i
$985$	−12.0545	−	10.9347i	−0.384087	−	0.348408i
$986$	−4.79914	+	3.48678i	−0.152836	+	0.111042i
$987$	24.6505	−	33.9285i	0.784635	−	1.07996i
$988$	8.93224	−	12.2942i	0.284172	−	0.391130i
$989$	10.7568	−	7.81529i	0.342047	−	0.248512i
$990$	−0.403195	−	1.93190i	−0.0128144	−	0.0613997i
$991$	44.5440	+	32.3631i	1.41499	+	1.02805i	0.992574	+	0.121643i	$0.0388162\pi$
$991$	44.5440	+	32.3631i	1.41499	+	1.02805i	0.422411	+	0.906404i	$0.361184\pi$
$992$	−9.93109	+	3.22681i	−0.315312	+	0.102451i
$993$			4.07299i			0.129252i
$994$	−5.21025	−	16.0355i	−0.165259	−	0.508616i
$995$	−4.64875	−	2.09034i	−0.147375	−	0.0662682i
$996$	−4.10192	+	12.6244i	−0.129974	+	0.400019i
$997$	−0.695101	−	0.225852i	−0.0220141	−	0.00715280i	0.297989	−	0.954569i	$-0.403684\pi$
$997$	−0.695101	−	0.225852i	−0.0220141	−	0.00715280i	−0.320003	+	0.947416i	$0.603684\pi$
$998$	8.55710	+	11.7778i	0.270870	+	0.372821i
$999$	1.74607			0.0552432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.h.b.139.2	yes	16
3.2	odd	2		450.2.l.c.289.3		16
5.2	odd	4		750.2.g.g.301.4		16
5.3	odd	4		750.2.g.f.301.1		16
5.4	even	2		750.2.h.d.199.4		16
25.3	odd	20		3750.2.a.v.1.1		8
25.4	even	10		3750.2.c.k.1249.8		16
25.9	even	10	inner	150.2.h.b.109.2	✓	16
25.12	odd	20		750.2.g.g.451.4		16
25.13	odd	20		750.2.g.f.451.1		16
25.16	even	5		750.2.h.d.49.3		16
25.21	even	5		3750.2.c.k.1249.9		16
25.22	odd	20		3750.2.a.u.1.8		8
75.59	odd	10		450.2.l.c.109.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.2	✓	16	25.9	even	10	inner
150.2.h.b.139.2	yes	16	1.1	even	1	trivial
450.2.l.c.109.3		16	75.59	odd	10
450.2.l.c.289.3		16	3.2	odd	2
750.2.g.f.301.1		16	5.3	odd	4
750.2.g.f.451.1		16	25.13	odd	20
750.2.g.g.301.4		16	5.2	odd	4
750.2.g.g.451.4		16	25.12	odd	20
750.2.h.d.49.3		16	25.16	even	5
750.2.h.d.199.4		16	5.4	even	2
3750.2.a.u.1.8		8	25.22	odd	20
3750.2.a.v.1.1		8	25.3	odd	20
3750.2.c.k.1249.8		16	25.4	even	10
3750.2.c.k.1249.9		16	25.21	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)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.03938 + 0.917020i) q^{5} +(0.309017 + 0.951057i) q^{6} -4.80694i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.03938 + 0.917020i) q^{5} +(0.309017 + 0.951057i) q^{6} -4.80694i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.456833 - 2.18890i) q^{10} +(0.714027 - 0.518771i) q^{11} +(0.587785 - 0.809017i) q^{12} +(1.66061 - 2.28564i) q^{13} +(-3.88890 + 2.82545i) q^{14} +(-1.65619 - 1.50234i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.57666 + 0.512289i) q^{17} -1.00000i q^{18} +(-1.66217 - 5.11563i) q^{19} +(-1.50234 + 1.65619i) q^{20} +(-1.48543 + 4.57167i) q^{21} +(-0.839389 - 0.272734i) q^{22} +(3.44056 + 4.73553i) q^{23} -1.00000 q^{24} +(3.31815 + 3.74031i) q^{25} -2.82520 q^{26} +(-0.587785 - 0.809017i) q^{27} +(4.57167 + 1.48543i) q^{28} +(-1.10574 + 3.40313i) q^{29} +(-0.241934 + 2.22294i) q^{30} +(3.22681 + 9.93109i) q^{31} +1.00000i q^{32} +(-0.839389 + 0.272734i) q^{33} +(1.34119 + 0.974432i) q^{34} +(4.40806 - 9.80318i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-1.02631 + 1.41260i) q^{37} +(-3.16163 + 4.35161i) q^{38} +(-2.28564 + 1.66061i) q^{39} +(2.22294 + 0.241934i) q^{40} +(1.40381 + 1.01993i) q^{41} +(4.57167 - 1.48543i) q^{42} -2.27151i q^{43} +(0.272734 + 0.839389i) q^{44} +(1.11088 + 1.94060i) q^{45} +(1.80881 - 5.56695i) q^{46} +(-8.29746 - 2.69601i) q^{47} +(0.587785 + 0.809017i) q^{48} -16.1067 q^{49} +(1.07561 - 4.88294i) q^{50} +1.65780 q^{51} +(1.66061 + 2.28564i) q^{52} +(-3.37565 - 1.09681i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.93190 - 0.403195i) q^{55} +(-1.48543 - 4.57167i) q^{56} +5.37889i q^{57} +(3.40313 - 1.10574i) q^{58} +(8.37628 + 6.08572i) q^{59} +(1.94060 - 1.11088i) q^{60} +(0.0697810 - 0.0506988i) q^{61} +(6.13775 - 8.44789i) q^{62} +(2.82545 - 3.88890i) q^{63} +(0.809017 - 0.587785i) q^{64} +(5.48259 - 3.13847i) q^{65} +(0.714027 + 0.518771i) q^{66} +(-11.3751 + 3.69601i) q^{67} -1.65780i q^{68} +(-1.80881 - 5.56695i) q^{69} +(-10.5219 + 2.19597i) q^{70} +(-1.08390 + 3.33591i) q^{71} +(0.951057 + 0.309017i) q^{72} +(4.24851 + 5.84757i) q^{73} +1.74607 q^{74} +(-1.99993 - 4.58261i) q^{75} +5.37889 q^{76} +(-2.49370 - 3.43228i) q^{77} +(2.68693 + 0.873035i) q^{78} +(3.88627 - 11.9607i) q^{79} +(-1.11088 - 1.94060i) q^{80} +(0.309017 + 0.951057i) q^{81} -1.73520i q^{82} +(-12.6244 + 4.10192i) q^{83} +(-3.88890 - 2.82545i) q^{84} +(-3.68520 - 0.401079i) q^{85} +(-1.83769 + 1.33516i) q^{86} +(2.10325 - 2.89488i) q^{87} +(0.518771 - 0.714027i) q^{88} +(15.1178 - 10.9837i) q^{89} +(0.917020 - 2.03938i) q^{90} +(-10.9869 - 7.98246i) q^{91} +(-5.56695 + 1.80881i) q^{92} -10.4422i q^{93} +(2.69601 + 8.29746i) q^{94} +(1.30134 - 11.9570i) q^{95} +(0.309017 - 0.951057i) q^{96} +(17.3764 + 5.64593i) q^{97} +(9.46727 + 13.0306i) q^{98} +0.882586 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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