LMFDB - Embedded newform 114.2.l.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(29,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17]))

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

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

chi := DirichletCharacter("114.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.1
Root			$-0.442647 - 1.67453i$ of defining polynomial
Character	$\chi$	$=$	114.89
Dual form			114.2.l.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-1.67151 - 0.453924i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.96615 - 0.346685i) q^{5} +(1.57223 - 0.726702i) q^{6} +(0.910931 - 1.57778i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.58791 + 1.51748i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.67151 - 0.453924i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.96615 - 0.346685i) q^{5} +(1.57223 - 0.726702i) q^{6} +(0.910931 - 1.57778i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.58791 + 1.51748i) q^{9} +(-1.28331 + 1.52939i) q^{10} +(4.10844 - 2.37201i) q^{11} +(-0.737283 + 1.56730i) q^{12} +(0.151321 + 0.415752i) q^{13} +(0.316363 + 1.79418i) q^{14} +(-3.44381 - 0.312993i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.07476 + 1.28085i) q^{17} +(-2.95787 + 0.501018i) q^{18} +(-3.58212 - 2.48363i) q^{19} -1.99648i q^{20} +(-2.23882 + 2.22378i) q^{21} +(-1.62255 + 4.45791i) q^{22} +(-5.93571 - 1.04663i) q^{23} +(-0.442647 - 1.67453i) q^{24} +(-0.952914 + 0.346832i) q^{25} +(-0.383159 - 0.221217i) q^{26} +(-3.63690 - 3.71120i) q^{27} +(-1.39563 - 1.17107i) q^{28} +(4.91935 + 4.12783i) q^{29} +(2.83930 - 1.97387i) q^{30} +(4.88683 + 2.82141i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-7.94401 + 2.09992i) q^{33} +(-1.64663 - 0.290345i) q^{34} +(1.24403 - 3.41795i) q^{35} +(1.94381 - 2.28508i) q^{36} -5.80180i q^{37} +(4.34051 - 0.399967i) q^{38} +(-0.0642158 - 0.763624i) q^{39} +(1.28331 + 1.52939i) q^{40} +(-3.75563 - 1.36694i) q^{41} +(0.285618 - 3.14260i) q^{42} +(2.15807 + 12.2390i) q^{43} +(-1.62255 - 4.45791i) q^{44} +(5.61430 + 2.08640i) q^{45} +(5.21978 - 3.01364i) q^{46} +(-6.92588 + 8.25394i) q^{47} +(1.41546 + 0.998240i) q^{48} +(1.84041 + 3.18768i) q^{49} +(0.507035 - 0.878210i) q^{50} +(-1.21507 - 2.62881i) q^{51} +(0.435713 - 0.0768279i) q^{52} +(-0.424873 + 2.40957i) q^{53} +(5.17154 + 0.505189i) q^{54} +(7.25545 - 6.08805i) q^{55} +1.82186 q^{56} +(4.86017 + 5.77743i) q^{57} -6.42176 q^{58} +(-3.87172 + 3.24876i) q^{59} +(-0.906250 + 3.33714i) q^{60} +(1.80210 - 10.2202i) q^{61} +(-5.55710 + 0.979866i) q^{62} +(4.75165 - 2.70083i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.441656 + 0.764970i) q^{65} +(4.73566 - 6.71494i) q^{66} +(5.27060 - 6.28126i) q^{67} +(1.44802 - 0.836015i) q^{68} +(9.44653 + 4.44381i) q^{69} +(1.24403 + 3.41795i) q^{70} +(-0.897109 - 5.08776i) q^{71} +(-0.0202217 + 2.99993i) q^{72} +(-13.5869 - 4.94524i) q^{73} +(3.72933 + 4.44444i) q^{74} +(1.75024 - 0.147184i) q^{75} +(-3.06793 + 3.09642i) q^{76} -8.64294i q^{77} +(0.540040 + 0.543692i) q^{78} +(-3.23544 + 8.88931i) q^{79} +(-1.96615 - 0.346685i) q^{80} +(4.39452 + 7.85418i) q^{81} +(3.75563 - 1.36694i) q^{82} +(0.523324 + 0.302141i) q^{83} +(1.80123 + 2.59097i) q^{84} +(2.55719 + 2.14574i) q^{85} +(-9.52025 - 7.98844i) q^{86} +(-6.34904 - 9.13273i) q^{87} +(4.10844 + 2.37201i) q^{88} +(-4.07161 + 1.48195i) q^{89} +(-5.64191 + 2.01052i) q^{90} +(0.793809 + 0.139970i) q^{91} +(-2.06145 + 5.66379i) q^{92} +(-6.88769 - 6.93427i) q^{93} -10.7748i q^{94} +(-7.90401 - 3.64132i) q^{95} +(-1.72596 + 0.145142i) q^{96} +(1.64505 + 1.96049i) q^{97} +(-3.45884 - 1.25891i) q^{98} +(14.2317 + 0.0959322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) $ 18 * q + 3 * q^6 + 9 * q^8	$ 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) $ 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−1.67151	−	0.453924i	−0.965048	−	0.262073i
$3$	−1.67151	−	0.453924i	−0.965048	−	0.262073i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	1.96615	−	0.346685i	0.879288	−	0.155042i	0.284260	−	0.958747i	$-0.408252\pi$
$5$	1.96615	−	0.346685i	0.879288	−	0.155042i	0.595028	+	0.803705i	$0.297141\pi$
$6$	1.57223	−	0.726702i	0.641860	−	0.296675i
$7$	0.910931	−	1.57778i	0.344300	−	0.596344i	−0.640927	−	0.767602i	$-0.721450\pi$
$7$	0.910931	−	1.57778i	0.344300	−	0.596344i	0.985226	+	0.171258i	$0.0547831\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.58791	+	1.51748i	0.862635	+	0.505826i
$10$	−1.28331	+	1.52939i	−0.405819	+	0.483636i
$11$	4.10844	−	2.37201i	1.23874	−	0.715187i	0.269903	−	0.962887i	$-0.413008\pi$
$11$	4.10844	−	2.37201i	1.23874	−	0.715187i	0.968837	+	0.247701i	$0.0796749\pi$
$12$	−0.737283	+	1.56730i	−0.212835	+	0.452439i
$13$	0.151321	+	0.415752i	0.0419690	+	0.115309i	0.958907	−	0.283721i	$-0.0915691\pi$
$13$	0.151321	+	0.415752i	0.0419690	+	0.115309i	−0.916938	+	0.399030i	$0.869347\pi$
$14$	0.316363	+	1.79418i	0.0845516	+	0.479516i
$15$	−3.44381	−	0.312993i	−0.889188	−	0.0808145i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.07476	+	1.28085i	0.260668	+	0.310652i	0.880466	−	0.474110i	$-0.157230\pi$
$17$	1.07476	+	1.28085i	0.260668	+	0.310652i	−0.619798	+	0.784761i	$0.712786\pi$
$18$	−2.95787	+	0.501018i	−0.697176	+	0.118091i
$19$	−3.58212	−	2.48363i	−0.821794	−	0.569785i
$19$	−3.58212	−	2.48363i	−0.821794	−	0.569785i
$20$		−	1.99648i		−	0.446426i
$21$	−2.23882	+	2.22378i	−0.488551	+	0.485269i
$22$	−1.62255	+	4.45791i	−0.345928	+	0.950430i
$23$	−5.93571	−	1.04663i	−1.23768	−	0.218237i	−0.483760	−	0.875201i	$-0.660729\pi$
$23$	−5.93571	−	1.04663i	−1.23768	−	0.218237i	−0.753922	+	0.656964i	$0.771840\pi$
$24$	−0.442647	−	1.67453i	−0.0903548	−	0.341813i
$25$	−0.952914	+	0.346832i	−0.190583	+	0.0693665i
$26$	−0.383159	−	0.221217i	−0.0751437	−	0.0433843i
$27$	−3.63690	−	3.71120i	−0.699921	−	0.714220i
$28$	−1.39563	−	1.17107i	−0.263749	−	0.221311i
$29$	4.91935	+	4.12783i	0.913501	+	0.766518i	0.972782	−	0.231723i	$-0.0744363\pi$
$29$	4.91935	+	4.12783i	0.913501	+	0.766518i	−0.0592808	+	0.998241i	$0.518881\pi$
$30$	2.83930	−	1.97387i	0.518383	−	0.360378i
$31$	4.88683	+	2.82141i	0.877700	+	0.506741i	0.869899	−	0.493229i	$-0.164184\pi$
$31$	4.88683	+	2.82141i	0.877700	+	0.506741i	0.00780088	+	0.999970i	$0.497517\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−7.94401	+	2.09992i	−1.38287	+	0.365549i
$34$	−1.64663	−	0.290345i	−0.282394	−	0.0497938i
$35$	1.24403	−	3.41795i	0.210280	−	0.577740i
$36$	1.94381	−	2.28508i	0.323968	−	0.380847i
$37$		−	5.80180i		−	0.953811i	−0.878955	−	0.476905i	$-0.841758\pi$
$37$		−	5.80180i		−	0.953811i	0.878955	−	0.476905i	$-0.158242\pi$
$38$	4.34051	−	0.399967i	0.704124	−	0.0648833i
$39$	−0.0642158	−	0.763624i	−0.0102828	−	0.122278i
$40$	1.28331	+	1.52939i	0.202909	+	0.241818i
$41$	−3.75563	−	1.36694i	−0.586530	−	0.213480i	0.0316723	−	0.999498i	$-0.489917\pi$
$41$	−3.75563	−	1.36694i	−0.586530	−	0.213480i	−0.618203	+	0.786019i	$0.712139\pi$
$42$	0.285618	−	3.14260i	0.0440718	−	0.484914i
$43$	2.15807	+	12.2390i	0.329102	+	1.86643i	0.479125	+	0.877747i	$0.340954\pi$
$43$	2.15807	+	12.2390i	0.329102	+	1.86643i	−0.150023	+	0.988683i	$0.547935\pi$
$44$	−1.62255	−	4.45791i	−0.244608	−	0.672056i
$45$	5.61430	+	2.08640i	0.836930	+	0.311022i
$46$	5.21978	−	3.01364i	0.769614	−	0.444337i
$47$	−6.92588	+	8.25394i	−1.01024	+	1.20396i	−0.0313665	+	0.999508i	$0.509986\pi$
$47$	−6.92588	+	8.25394i	−1.01024	+	1.20396i	−0.978876	+	0.204453i	$0.934459\pi$
$48$	1.41546	+	0.998240i	0.204304	+	0.144083i
$49$	1.84041	+	3.18768i	0.262916	+	0.455383i
$50$	0.507035	−	0.878210i	0.0717056	−	0.124198i
$51$	−1.21507	−	2.62881i	−0.170143	−	0.368108i
$52$	0.435713	−	0.0768279i	0.0604225	−	0.0106541i
$53$	−0.424873	+	2.40957i	−0.0583608	+	0.330981i	−0.999984	−	0.00568857i	$-0.998189\pi$
$53$	−0.424873	+	2.40957i	−0.0583608	+	0.330981i	0.941623	+	0.336669i	$0.109300\pi$
$54$	5.17154	+	0.505189i	0.703757	+	0.0687475i
$55$	7.25545	−	6.08805i	0.978325	−	0.820912i
$56$	1.82186			0.243457
$57$	4.86017	+	5.77743i	0.643746	+	0.765240i
$58$	−6.42176			−0.843218
$59$	−3.87172	+	3.24876i	−0.504055	+	0.422952i	−0.859031	−	0.511923i	$-0.828933\pi$
$59$	−3.87172	+	3.24876i	−0.504055	+	0.422952i	0.354977	+	0.934875i	$0.384489\pi$
$60$	−0.906250	+	3.33714i	−0.116996	+	0.430823i
$61$	1.80210	−	10.2202i	0.230735	−	1.30856i	−0.620677	−	0.784067i	$-0.713142\pi$
$61$	1.80210	−	10.2202i	0.230735	−	1.30856i	0.851412	−	0.524498i	$-0.175747\pi$
$62$	−5.55710	+	0.979866i	−0.705752	+	0.124443i
$63$	4.75165	−	2.70083i	0.598652	−	0.340272i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.441656	+	0.764970i	0.0547806	+	0.0948828i
$66$	4.73566	−	6.71494i	0.582920	−	0.826552i
$67$	5.27060	−	6.28126i	0.643906	−	0.767378i	−0.341075	−	0.940036i	$-0.610791\pi$
$67$	5.27060	−	6.28126i	0.643906	−	0.767378i	0.984982	+	0.172658i	$0.0552356\pi$
$68$	1.44802	−	0.836015i	0.175598	−	0.101382i
$69$	9.44653	+	4.44381i	1.13723	+	0.534972i
$70$	1.24403	+	3.41795i	0.148690	+	0.408524i
$71$	−0.897109	−	5.08776i	−0.106467	−	0.603806i	−0.990624	−	0.136616i	$-0.956377\pi$
$71$	−0.897109	−	5.08776i	−0.106467	−	0.603806i	0.884157	−	0.467190i	$-0.154734\pi$
$72$	−0.0202217	+	2.99993i	−0.00238316	+	0.353545i
$73$	−13.5869	−	4.94524i	−1.59023	−	0.578796i	−0.612834	−	0.790212i	$-0.709971\pi$
$73$	−13.5869	−	4.94524i	−1.59023	−	0.578796i	−0.977396	+	0.211415i	$0.932193\pi$
$74$	3.72933	+	4.44444i	0.433526	+	0.516656i
$75$	1.75024	−	0.147184i	0.202101	−	0.0169954i
$76$	−3.06793	+	3.09642i	−0.351916	+	0.355184i
$77$		−	8.64294i		−	0.984954i
$78$	0.540040	+	0.543692i	0.0611475	+	0.0615610i
$79$	−3.23544	+	8.88931i	−0.364016	+	1.00013i	0.613580	+	0.789633i	$0.289729\pi$
$79$	−3.23544	+	8.88931i	−0.364016	+	1.00013i	−0.977595	+	0.210493i	$0.932493\pi$
$80$	−1.96615	−	0.346685i	−0.219822	−	0.0387606i
$81$	4.39452	+	7.85418i	0.488280	+	0.872687i
$82$	3.75563	−	1.36694i	0.414740	−	0.150953i
$83$	0.523324	+	0.302141i	0.0574423	+	0.0331643i	0.528446	−	0.848967i	$-0.322775\pi$
$83$	0.523324	+	0.302141i	0.0574423	+	0.0331643i	−0.471004	+	0.882131i	$0.656108\pi$
$84$	1.80123	+	2.59097i	0.196530	+	0.282698i
$85$	2.55719	+	2.14574i	0.277366	+	0.232738i
$86$	−9.52025	−	7.98844i	−1.02659	−	0.861415i
$87$	−6.34904	−	9.13273i	−0.680689	−	0.979131i
$88$	4.10844	+	2.37201i	0.437961	+	0.252857i
$89$	−4.07161	+	1.48195i	−0.431590	+	0.157086i	−0.548675	−	0.836036i	$-0.684867\pi$
$89$	−4.07161	+	1.48195i	−0.431590	+	0.157086i	0.117084	+	0.993122i	$0.462645\pi$
$90$	−5.64191	+	2.01052i	−0.594710	+	0.211928i
$91$	0.793809	+	0.139970i	0.0832137	+	0.0146728i
$92$	−2.06145	+	5.66379i	−0.214921	+	0.590491i
$93$	−6.88769	−	6.93427i	−0.714220	−	0.719051i
$94$		−	10.7748i		−	1.11133i
$95$	−7.90401	−	3.64132i	−0.810935	−	0.373592i
$96$	−1.72596	+	0.145142i	−0.176155	+	0.0148135i
$97$	1.64505	+	1.96049i	0.167029	+	0.199057i	0.843066	−	0.537810i	$-0.180748\pi$
$97$	1.64505	+	1.96049i	0.167029	+	0.199057i	−0.676037	+	0.736868i	$0.736304\pi$
$98$	−3.45884	−	1.25891i	−0.349395	−	0.127170i
$99$	14.2317	+	0.0959322i	1.43034	+	0.00964155i
$100$	0.176091	+	0.998664i	0.0176091	+	0.0998664i
$101$	2.72562	+	7.48859i	0.271210	+	0.745142i	0.998283	+	0.0585821i	$0.0186579\pi$
$101$	2.72562	+	7.48859i	0.271210	+	0.745142i	−0.727073	+	0.686560i	$0.759120\pi$
$102$	2.62056	+	1.23276i	0.259475	+	0.122061i
$103$	−13.3041	+	7.68115i	−1.31090	+	0.756846i	−0.982245	−	0.187605i	$-0.939927\pi$
$103$	−13.3041	+	7.68115i	−1.31090	+	0.756846i	−0.328651	+	0.944451i	$0.606594\pi$
$104$	−0.284391	+	0.338924i	−0.0278869	+	0.0332343i
$105$	−3.63091	+	5.14845i	−0.354340	+	0.502438i
$106$	−1.22337	−	2.11894i	−0.118825	−	0.205810i
$107$	9.34857	−	16.1922i	0.903760	−	1.56536i	0.0811876	−	0.996699i	$-0.474129\pi$
$107$	9.34857	−	16.1922i	0.903760	−	1.56536i	0.822573	−	0.568660i	$-0.192538\pi$
$108$	−4.28636	+	2.93720i	−0.412455	+	0.282632i
$109$	−11.2420	+	1.98227i	−1.07679	+	0.189867i	−0.683795	−	0.729674i	$-0.739672\pi$
$109$	−11.2420	+	1.98227i	−1.07679	+	0.189867i	−0.392994	+	0.919541i	$0.628561\pi$
$110$	−1.64468	+	9.32743i	−0.156814	+	0.889336i
$111$	−2.63358	+	9.69779i	−0.249968	+	0.920473i
$112$	−1.39563	+	1.17107i	−0.131874	+	0.110656i
$113$	0.594179			0.0558957			0.0279478	−	0.999609i	$-0.491103\pi$
$113$	0.594179			0.0558957			0.0279478	+	0.999609i	$0.491103\pi$
$114$	−7.43677	−	1.30171i	−0.696517	−	0.121916i
$115$	−12.0333			−1.12212
$116$	4.91935	−	4.12783i	0.456751	−	0.383259i
$117$	−0.239289	+	1.30556i	−0.0221223	+	0.120699i
$118$	0.877647	−	4.97738i	0.0807940	−	0.458205i
$119$	2.99993	−	0.528968i	0.275003	−	0.0484905i
$120$	−1.45084	−	3.13892i	−0.132443	−	0.286543i
$121$	5.75283	−	9.96419i	0.522984	−	0.905835i
$122$	5.18894	+	8.98751i	0.469784	+	0.813691i
$123$	5.65709	+	3.98962i	0.510083	+	0.359732i
$124$	3.62714	−	4.32265i	0.325727	−	0.388186i
$125$	−10.3983	+	6.00348i	−0.930056	+	0.536968i
$126$	−1.90392	+	5.12325i	−0.169614	+	0.456416i
$127$	4.51501	+	12.4049i	0.400642	+	1.10076i	0.961968	+	0.273161i	$0.0880691\pi$
$127$	4.51501	+	12.4049i	0.400642	+	1.10076i	−0.561326	+	0.827595i	$0.689709\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	1.94834	−	21.4372i	0.171542	−	1.88744i
$130$	−0.830041	−	0.302110i	−0.0727994	−	0.0264968i
$131$	4.54726	+	5.41921i	0.397296	+	0.473479i	0.927193	−	0.374583i	$-0.122214\pi$
$131$	4.54726	+	5.41921i	0.397296	+	0.473479i	−0.529898	+	0.848062i	$0.677770\pi$
$132$	0.688555	+	8.18797i	0.0599311	+	0.712671i
$133$	−7.18169	+	3.38937i	−0.622731	+	0.293896i
$134$			8.19960i			0.708337i
$135$	−8.43730	−	6.03590i	−0.726167	−	0.519488i
$136$	−0.571868	+	1.57119i	−0.0490373	+	0.134729i
$137$	9.23589	+	1.62854i	0.789075	+	0.139135i	0.553641	−	0.832755i	$-0.313238\pi$
$137$	9.23589	+	1.62854i	0.789075	+	0.139135i	0.235434	+	0.971890i	$0.424349\pi$
$138$	−10.0929	+	2.66796i	−0.859164	+	0.227111i
$139$	10.1792	−	3.70494i	0.863392	−	0.314249i	0.127904	−	0.991787i	$-0.459175\pi$
$139$	10.1792	−	3.70494i	0.863392	−	0.314249i	0.735488	+	0.677538i	$0.236953\pi$
$140$	−3.15000	−	1.81865i	−0.266224	−	0.153704i
$141$	15.3233	−	10.6527i	1.29046	−	0.897122i
$142$	3.95758	+	3.32080i	0.332112	+	0.278675i
$143$	1.60786	+	1.34916i	0.134456	+	0.112822i
$144$	−1.91283	−	2.31108i	−0.159402	−	0.192590i
$145$	11.1032	+	6.41046i	0.922074	+	0.532359i
$146$	13.5869	−	4.94524i	1.12446	−	0.409271i
$147$	−1.62930	−	6.16366i	−0.134383	−	0.508370i
$148$	−5.71366	−	1.00747i	−0.469660	−	0.0828137i
$149$	3.85231	−	10.5841i	0.315594	−	0.867086i	−0.675907	−	0.736987i	$-0.736248\pi$
$149$	3.85231	−	10.5841i	0.315594	−	0.867086i	0.991501	−	0.130100i	$-0.0415297\pi$
$150$	−1.24616	+	1.23778i	−0.101748	+	0.101065i
$151$		−	3.54669i		−	0.288625i	−0.989532	−	0.144313i	$-0.953903\pi$
$151$		−	3.54669i		−	0.288625i	0.989532	−	0.144313i	$-0.0460971\pi$
$152$	0.359831	−	4.34402i	0.0291861	−	0.352347i
$153$	0.837717	+	4.94564i	0.0677254	+	0.399832i
$154$	5.55557	+	6.62087i	0.447681	+	0.533525i
$155$	10.5864	+	3.85312i	0.850318	+	0.309490i
$156$	−0.763173	−	0.0693616i	−0.0611028	−	0.00555337i
$157$	−0.0548481	−	0.311059i	−0.00437736	−	0.0248252i	0.982541	−	0.186047i	$-0.0595677\pi$
$157$	−0.0548481	−	0.311059i	−0.00437736	−	0.0248252i	−0.986918	+	0.161222i	$0.948457\pi$
$158$	−3.23544	−	8.88931i	−0.257398	−	0.707196i
$159$	1.80394	−	3.83477i	0.143062	−	0.304117i
$160$	1.72900	−	0.998240i	0.136690	−	0.0789178i
$161$	−7.05837	+	8.41184i	−0.556277	+	0.662946i
$162$	−8.41497	−	3.19191i	−0.661142	−	0.250780i
$163$	0.624535	+	1.08173i	0.0489174	+	0.0847274i	0.889447	−	0.457038i	$-0.151090\pi$
$163$	0.624535	+	1.08173i	0.0489174	+	0.0847274i	−0.840530	+	0.541765i	$0.817756\pi$
$164$	−1.99833	+	3.46120i	−0.156043	+	0.270275i
$165$	−14.8911	+	6.88283i	−1.15927	+	0.535827i
$166$	−0.595102	+	0.104933i	−0.0461889	+	0.00814435i
$167$	−0.177553	+	1.00695i	−0.0137395	+	0.0779205i	−0.990907	−	0.134552i	$-0.957040\pi$
$167$	−0.177553	+	1.00695i	−0.0137395	+	0.0779205i	0.977167	+	0.212472i	$0.0681516\pi$
$168$	−3.04526	−	0.826987i	−0.234947	−	0.0638034i
$169$	9.80863	−	8.23041i	0.754510	−	0.633109i
$170$	−3.33817			−0.256026
$171$	−5.50132	−	11.8632i	−0.420697	−	0.907201i
$172$	12.4278			0.947611
$173$	11.5762	−	9.71361i	0.880124	−	0.738512i	−0.0860802	−	0.996288i	$-0.527434\pi$
$173$	11.5762	−	9.71361i	0.880124	−	0.738512i	0.966205	+	0.257776i	$0.0829897\pi$
$174$	10.7341	+	2.91499i	0.813746	+	0.220985i
$175$	−0.320814	+	1.81943i	−0.0242513	+	0.137536i
$176$	−4.67194	+	0.823789i	−0.352161	+	0.0620954i
$177$	7.94631	−	3.67287i	0.597281	−	0.276070i
$178$	2.16646	−	3.75242i	0.162383	−	0.281256i
$179$	−2.97218	−	5.14797i	−0.222151	−	0.384777i	0.733310	−	0.679895i	$-0.237974\pi$
$179$	−2.97218	−	5.14797i	−0.222151	−	0.384777i	−0.955461	+	0.295118i	$0.904641\pi$
$180$	3.02961	−	5.16670i	0.225814	−	0.385103i
$181$	−4.17230	+	4.97236i	−0.310125	+	0.369593i	−0.898483	−	0.439008i	$-0.855330\pi$
$181$	−4.17230	+	4.97236i	−0.310125	+	0.369593i	0.588358	+	0.808600i	$0.299774\pi$
$182$	−0.698064	+	0.403027i	−0.0517439	+	0.0298744i
$183$	−7.65143	+	16.2652i	−0.565610	+	1.20236i
$184$	−2.06145	−	5.66379i	−0.151972	−	0.417540i
$185$	−2.01140	−	11.4072i	−0.147881	−	0.838675i
$186$	9.73354	+	0.884640i	0.713698	+	0.0648650i
$187$	7.45377	+	2.71295i	0.545073	+	0.198390i
$188$	6.92588	+	8.25394i	0.505121	+	0.601980i
$189$	−9.16841	+	2.35758i	−0.666904	+	0.171488i
$190$	8.39542	−	2.29119i	0.609068	−	0.166220i
$191$			23.8639i			1.72673i	0.504577	+	0.863367i	$0.331648\pi$
$191$			23.8639i			1.72673i	−0.504577	+	0.863367i	$0.668352\pi$
$192$	1.22887	−	1.22061i	0.0886857	−	0.0880899i
$193$	−0.726280	+	1.99544i	−0.0522788	+	0.143635i	−0.963084	−	0.269202i	$-0.913240\pi$
$193$	−0.726280	+	1.99544i	−0.0522788	+	0.143635i	0.910805	+	0.412837i	$0.135462\pi$
$194$	−2.52036	−	0.444407i	−0.180951	−	0.0319065i
$195$	−0.390995	−	1.47913i	−0.0279997	−	0.105923i
$196$	3.45884	−	1.25891i	0.247060	−	0.0899225i
$197$	−3.27574	−	1.89125i	−0.233387	−	0.134746i	0.378747	−	0.925500i	$-0.376355\pi$
$197$	−3.27574	−	1.89125i	−0.233387	−	0.134746i	−0.612133	+	0.790755i	$0.709688\pi$
$198$	−10.9638	+	9.07448i	−0.779163	+	0.644895i
$199$	−10.5692	−	8.86860i	−0.749230	−	0.628679i	0.186069	−	0.982537i	$-0.440425\pi$
$199$	−10.5692	−	8.86860i	−0.749230	−	0.628679i	−0.935299	+	0.353858i	$0.884870\pi$
$200$	−0.776823	−	0.651831i	−0.0549296	−	0.0460914i
$201$	−11.6611	+	8.10675i	−0.822510	+	0.571806i
$202$	−6.90152	−	3.98459i	−0.485589	−	0.280355i
$203$	10.9940	−	4.00149i	0.771627	−	0.280849i
$204$	−2.79987	+	0.740118i	−0.196030	+	0.0518186i
$205$	−7.85802	−	1.38558i	−0.548828	−	0.0967731i
$206$	5.25422	−	14.4358i	0.366079	−	1.00579i
$207$	−13.7728	−	11.7159i	−0.957278	−	0.814311i
$208$		−	0.442434i		−	0.0306773i
$209$	−20.6081	−	1.70704i	−1.42549	−	0.118078i
$210$	−0.527926	−	6.27785i	−0.0364304	−	0.433213i
$211$	10.3613	+	12.3481i	0.713299	+	0.850077i	0.993961	−	0.109730i	$-0.0349985\pi$
$211$	10.3613	+	12.3481i	0.713299	+	0.850077i	−0.280662	+	0.959807i	$0.590554\pi$
$212$	2.29919	+	0.836837i	0.157909	+	0.0574742i
$213$	−0.809926	+	8.91147i	−0.0554952	+	0.610604i
$214$	3.24672	+	18.4131i	0.221941	+	1.25869i
$215$	8.48615	+	23.3155i	0.578751	+	1.59010i
$216$	1.39554	−	5.00524i	0.0949546	−	0.340564i
$217$	8.90313	−	5.14022i	0.604384	−	0.348941i
$218$	7.33769	−	8.74472i	0.496971	−	0.592267i
$219$	20.4660	+	14.4335i	1.38296	+	0.975323i
$220$	−4.73566	−	8.20241i	−0.319278	−	0.553006i
$221$	−0.369882	+	0.640654i	−0.0248809	+	0.0430951i
$222$	−4.21618	−	9.12177i	−0.282971	−	0.612213i
$223$	1.05803	−	0.186559i	0.0708508	−	0.0124929i	−0.138110	−	0.990417i	$-0.544103\pi$
$223$	1.05803	−	0.186559i	0.0708508	−	0.0124929i	0.208961	+	0.977924i	$0.432992\pi$
$224$	0.316363	−	1.79418i	0.0211379	−	0.119879i
$225$	−2.99236	−	0.548457i	−0.199491	−	0.0365638i
$226$	−0.455168	+	0.381931i	−0.0302773	+	0.0254057i
$227$	18.7633			1.24536			0.622682	−	0.782475i	$-0.286043\pi$
$227$	18.7633			1.24536			0.622682	+	0.782475i	$0.286043\pi$
$228$	6.53362	−	3.78310i	0.432700	−	0.250542i
$229$	−11.6264			−0.768296			−0.384148	−	0.923271i	$-0.625505\pi$
$229$	−11.6264			−0.768296			−0.384148	+	0.923271i	$0.625505\pi$
$230$	9.21808	−	7.73488i	0.607822	−	0.510023i
$231$	−3.92323	+	14.4468i	−0.258130	+	0.950528i
$232$	−1.11513	+	6.32420i	−0.0732117	+	0.415204i
$233$	16.0133	−	2.82357i	1.04907	−	0.184979i	0.377565	−	0.925983i	$-0.376761\pi$
$233$	16.0133	−	2.82357i	1.04907	−	0.184979i	0.671500	+	0.741004i	$0.265650\pi$
$234$	−0.655888	−	1.15393i	−0.0428768	−	0.0754345i
$235$	−10.7558	+	18.6296i	−0.701630	+	1.21526i
$236$	2.52708	+	4.37704i	0.164499	+	0.284921i
$237$	9.44315	−	13.3899i	0.613399	−	0.869770i
$238$	−1.95806	+	2.33353i	−0.126922	+	0.151260i
$239$	−5.90043	+	3.40661i	−0.381667	+	0.220356i	−0.678543	−	0.734560i	$-0.737388\pi$
$239$	−5.90043	+	3.40661i	−0.381667	+	0.220356i	0.296876	+	0.954916i	$0.404055\pi$
$240$	3.12907	+	1.47197i	0.201981	+	0.0950152i
$241$	−6.63839	−	18.2388i	−0.427616	−	1.17487i	−0.947255	−	0.320480i	$-0.896156\pi$
$241$	−6.63839	−	18.2388i	−0.427616	−	1.17487i	0.519639	−	0.854386i	$-0.326066\pi$
$242$	1.99794	+	11.3309i	0.128432	+	0.728375i
$243$	−3.78029	−	15.1231i	−0.242506	−	0.970150i
$244$	−9.75201	−	3.54944i	−0.624309	−	0.227230i
$245$	4.72364	+	5.62942i	0.301782	+	0.359650i
$246$	−6.89806	+	0.580082i	−0.439804	+	0.0369847i
$247$	0.490525	−	1.86510i	0.0312114	−	0.118674i
$248$			5.64282i			0.358320i
$249$	−0.737593	−	0.742582i	−0.0467431	−	0.0470592i
$250$	4.10662	−	11.2829i	0.259726	−	0.713591i
$251$	−16.8226	−	2.96628i	−1.06183	−	0.187230i	−0.384664	−	0.923057i	$-0.625683\pi$
$251$	−16.8226	−	2.96628i	−1.06183	−	0.187230i	−0.677170	+	0.735827i	$0.736794\pi$
$252$	−1.83468	−	5.14845i	−0.115574	−	0.324322i
$253$	−26.8691	+	9.77955i	−1.68925	+	0.614835i
$254$	−11.4324	−	6.60050i	−0.717333	−	0.414152i
$255$	−3.30037	−	4.74739i	−0.206677	−	0.297293i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−12.1113	−	10.1626i	−0.755485	−	0.633927i	0.181462	−	0.983398i	$-0.441917\pi$
$257$	−12.1113	−	10.1626i	−0.755485	−	0.633927i	−0.936947	+	0.349471i	$0.886361\pi$
$258$	12.2871	+	17.6742i	0.764960	+	1.10035i
$259$	−9.15396	−	5.28504i	−0.568800	−	0.328397i
$260$	0.830041	−	0.302110i	0.0514770	−	0.0187361i
$261$	6.46694	+	18.1474i	0.400293	+	1.12330i
$262$	−6.96680	−	1.22844i	−0.430410	−	0.0758930i
$263$	−0.888930	+	2.44232i	−0.0548138	+	0.150600i	−0.964078	−	0.265620i	$-0.914423\pi$
$263$	−0.888930	+	2.44232i	−0.0548138	+	0.150600i	0.909264	+	0.416220i	$0.136645\pi$
$264$	−5.79059	−	5.82975i	−0.356386	−	0.358797i
$265$			4.88488i			0.300076i
$266$	3.32284	−	7.21271i	0.203737	−	0.442239i
$267$	7.47844	−	0.628889i	0.457673	−	0.0384874i
$268$	−5.27060	−	6.28126i	−0.321953	−	0.383689i
$269$	−29.9875	−	10.9146i	−1.82837	−	0.665473i	−0.993333	−	0.115281i	$-0.963223\pi$
$269$	−29.9875	−	10.9146i	−1.82837	−	0.665473i	−0.835039	−	0.550191i	$-0.814555\pi$
$270$	10.3431	−	0.799618i	0.629464	−	0.0486632i
$271$	−3.48942	−	19.7895i	−0.211967	−	1.20212i	−0.886093	−	0.463508i	$-0.846590\pi$
$271$	−3.48942	−	19.7895i	−0.211967	−	1.20212i	0.674126	−	0.738617i	$-0.264521\pi$
$272$	−0.571868	−	1.57119i	−0.0346746	−	0.0952676i
$273$	−1.26333	−	0.594290i	−0.0764599	−	0.0359681i
$274$	−8.12190	+	4.68918i	−0.490662	+	0.283284i
$275$	−3.09230	+	3.68526i	−0.186473	+	0.222229i
$276$	6.01667	−	8.53136i	0.362161	−	0.513527i
$277$	4.04017	+	6.99778i	0.242750	+	0.420456i	0.961497	−	0.274816i	$-0.0886171\pi$
$277$	4.04017	+	6.99778i	0.242750	+	0.420456i	−0.718746	+	0.695272i	$0.755284\pi$
$278$	−5.41626	+	9.38124i	−0.324846	+	0.562649i
$279$	8.36522	+	14.7172i	0.500813	+	0.881096i
$280$	3.58205	−	0.631612i	0.214068	−	0.0377460i
$281$	−2.05091	+	11.6313i	−0.122347	+	0.693866i	0.860501	+	0.509449i	$0.170151\pi$
$281$	−2.05091	+	11.6313i	−0.122347	+	0.693866i	−0.982848	+	0.184417i	$0.940960\pi$
$282$	−4.89092	+	18.0101i	−0.291250	+	1.07249i
$283$	11.0055	−	9.23472i	0.654210	−	0.548947i	−0.254135	−	0.967169i	$-0.581791\pi$
$283$	11.0055	−	9.23472i	0.654210	−	0.548947i	0.908345	+	0.418221i	$0.137346\pi$
$284$	−5.16625			−0.306560
$285$	11.5588	+	9.67434i	0.684682	+	0.573058i
$286$	−2.09891			−0.124111
$287$	−5.57784	+	4.68036i	−0.329249	+	0.276273i
$288$	2.95084	+	0.540847i	0.173880	+	0.0318697i
$289$	2.46655	−	13.9885i	0.145091	−	0.822854i
$290$	−12.6261	+	2.22633i	−0.741432	+	0.130734i
$291$	−1.85980	−	4.02371i	−0.109023	−	0.235874i
$292$	−7.22946	+	12.5218i	−0.423072	+	0.732782i
$293$	0.00324263	+	0.00561639i	0.000189436	+	0.000328113i	0.866120	−	0.499836i	$-0.166606\pi$
$293$	0.00324263	+	0.00561639i	0.000189436	+	0.000328113i	−0.865931	+	0.500164i	$0.833273\pi$
$294$	5.21004	+	3.67434i	0.303856	+	0.214292i
$295$	−6.48608	+	7.72981i	−0.377634	+	0.450047i
$296$	5.02451	−	2.90090i	0.292044	−	0.168611i
$297$	−23.7449	−	6.62047i	−1.37782	−	0.384158i
$298$	3.85231	+	10.5841i	0.223158	+	0.613122i
$299$	−0.463063	−	2.62616i	−0.0267797	−	0.151875i
$300$	0.158978	−	1.74921i	0.00917862	−	0.100991i
$301$	21.2763	+	7.74393i	1.22634	+	0.446353i
$302$	2.27977	+	2.71692i	0.131186	+	0.156341i
$303$	−1.15666	−	13.7545i	−0.0664486	−	0.790175i
$304$	2.51664	+	3.55901i	0.144339	+	0.204123i
$305$		−	20.7192i		−	1.18638i
$306$	−3.82073	−	3.25011i	−0.218416	−	0.185796i
$307$	4.66013	−	12.8036i	0.265968	−	0.730741i	−0.732768	−	0.680478i	$-0.761772\pi$
$307$	4.66013	−	12.8036i	0.265968	−	0.730741i	0.998736	−	0.0502623i	$-0.0160057\pi$
$308$	−8.51163	−	1.50083i	−0.484995	−	0.0855177i
$309$	25.7247	−	6.80007i	1.46343	−	0.386842i
$310$	−10.5864	+	3.85312i	−0.601266	+	0.218843i
$311$	−10.1422	−	5.85560i	−0.575111	−	0.332041i	0.184077	−	0.982912i	$-0.441070\pi$
$311$	−10.1422	−	5.85560i	−0.575111	−	0.332041i	−0.759188	+	0.650871i	$0.774404\pi$
$312$	0.629209	−	0.437424i	0.0356220	−	0.0247643i
$313$	1.34587	+	1.12932i	0.0760730	+	0.0638328i	0.680031	−	0.733183i	$-0.261966\pi$
$313$	1.34587	+	1.12932i	0.0760730	+	0.0638328i	−0.603958	+	0.797016i	$0.706411\pi$
$314$	0.241961	+	0.203030i	0.0136547	+	0.0114576i
$315$	8.40611	−	6.95755i	0.473631	−	0.392013i
$316$	8.19243	+	4.72990i	0.460860	+	0.266078i
$317$	6.59148	−	2.39910i	0.370214	−	0.134747i	−0.150211	−	0.988654i	$-0.547995\pi$
$317$	6.59148	−	2.39910i	0.370214	−	0.134747i	0.520426	+	0.853907i	$0.325773\pi$
$318$	1.08304	+	4.09716i	0.0607341	+	0.229757i
$319$	30.0021	+	5.29018i	1.67979	+	0.296193i
$320$	−0.682836	+	1.87608i	−0.0381717	+	0.104876i
$321$	−22.9763	+	22.8219i	−1.28241	+	1.27380i
$322$		−	10.9809i		−	0.611940i
$323$	−0.668758	−	7.25746i	−0.0372107	−	0.403816i
$324$	8.49796	−	2.96389i	0.472109	−	0.164661i
$325$	−0.288393	−	0.343693i	−0.0159971	−	0.0190647i
$326$	−1.17374	−	0.427207i	−0.0650076	−	0.0236608i
$327$	19.6909	+	1.78963i	1.08891	+	0.0989666i
$328$	−0.694012	−	3.93594i	−0.0383204	−	0.217326i
$329$	6.71389	+	18.4463i	0.370149	+	1.01698i
$330$	6.98304	−	14.8444i	0.384404	−	0.817155i
$331$	−1.36720	+	0.789353i	−0.0751481	+	0.0433868i	−0.537103	−	0.843517i	$-0.680481\pi$
$331$	−1.36720	+	0.789353i	−0.0751481	+	0.0433868i	0.461955	+	0.886903i	$0.347148\pi$
$332$	0.388425	−	0.462907i	0.0213176	−	0.0254053i
$333$	8.80411	−	15.0145i	0.482462	−	0.822791i
$334$	−0.511244	−	0.885501i	−0.0279740	−	0.0484525i
$335$	8.18517	−	14.1771i	0.447203	−	0.774579i
$336$	2.86438	−	1.32395i	0.156265	−	0.0722274i
$337$	32.2083	−	5.67918i	1.75450	−	0.309365i	0.798336	−	0.602212i	$-0.205714\pi$
$337$	32.2083	−	5.67918i	1.75450	−	0.309365i	0.956159	+	0.292847i	$0.0946028\pi$
$338$	−2.22343	+	12.6097i	−0.120939	+	0.685879i
$339$	−0.993178	−	0.269712i	−0.0539420	−	0.0146488i
$340$	2.55719	−	2.14574i	0.138683	−	0.116369i
$341$	26.7696			1.44966
$342$	11.8398	+	5.55155i	0.640222	+	0.300194i
$343$	19.4590			1.05069
$344$	−9.52025	+	7.98844i	−0.513297	+	0.430708i
$345$	20.1139	+	5.46222i	1.08289	+	0.294076i
$346$	−2.62412	+	14.8821i	−0.141073	+	0.800067i
$347$	−2.28496	+	0.402900i	−0.122663	+	0.0216288i	−0.234643	−	0.972082i	$-0.575392\pi$
$347$	−2.28496	+	0.402900i	−0.122663	+	0.0216288i	0.111980	+	0.993711i	$0.464281\pi$
$348$	−10.0965	+	4.66670i	−0.541228	+	0.250162i
$349$	6.90604	−	11.9616i	0.369672	−	0.640291i	−0.619842	−	0.784727i	$-0.712803\pi$
$349$	6.90604	−	11.9616i	0.369672	−	0.640291i	0.989514	+	0.144436i	$0.0461367\pi$
$350$	−0.923748	−	1.59998i	−0.0493764	−	0.0855224i
$351$	0.992598	−	2.07363i	0.0529809	−	0.110682i
$352$	3.04939	−	3.63412i	0.162533	−	0.193699i
$353$	12.6233	−	7.28806i	0.671870	−	0.387904i	−0.124915	−	0.992167i	$-0.539866\pi$
$353$	12.6233	−	7.28806i	0.671870	−	0.387904i	0.796785	+	0.604263i	$0.206532\pi$
$354$	−3.72635	+	7.92137i	−0.198053	+	0.421016i
$355$	−3.52770	−	9.69228i	−0.187231	−	0.514413i
$356$	0.752404	+	4.26709i	0.0398773	+	0.226156i
$357$	−5.25453	−	0.477562i	−0.278099	−	0.0252753i
$358$	5.58587	+	2.03309i	0.295222	+	0.107452i
$359$	−12.4925	−	14.8880i	−0.659331	−	0.785760i	0.327959	−	0.944692i	$-0.393639\pi$
$359$	−12.4925	−	14.8880i	−0.659331	−	0.785760i	−0.987290	+	0.158932i	$0.949195\pi$
$360$	1.00027	+	5.90532i	0.0527190	+	0.311238i
$361$	6.66313	+	17.7933i	0.350691	+	0.936491i
$362$		−	6.49095i		−	0.341157i
$363$	−14.1389	+	14.0439i	−0.742100	+	0.737115i
$364$	0.275687	−	0.757443i	0.0144499	−	0.0397008i
$365$	−28.4284	−	5.01269i	−1.48801	−	0.262376i
$366$	−4.59373	−	17.3781i	−0.240118	−	0.908368i
$367$	−7.10474	+	2.58591i	−0.370865	+	0.134984i	−0.520727	−	0.853723i	$-0.674339\pi$
$367$	−7.10474	+	2.58591i	−0.370865	+	0.134984i	0.149863	+	0.988707i	$0.452117\pi$
$368$	5.21978	+	3.01364i	0.272100	+	0.157097i
$369$	−7.64491	−	9.23659i	−0.397978	−	0.480837i
$370$	8.87323	+	7.44553i	0.461297	+	0.387074i
$371$	3.41475	+	2.86531i	0.177285	+	0.148760i
$372$	−8.02496	+	5.57892i	−0.416075	+	0.289254i
$373$	−5.00566	−	2.89002i	−0.259183	−	0.149640i	0.364779	−	0.931094i	$-0.381145\pi$
$373$	−5.00566	−	2.89002i	−0.259183	−	0.149640i	−0.623962	+	0.781455i	$0.714478\pi$
$374$	−7.45377	+	2.71295i	−0.385425	+	0.140283i
$375$	20.1061	−	5.31484i	1.03827	−	0.274457i
$376$	−10.6111	−	1.87102i	−0.547224	−	0.0964903i
$377$	−0.971750	+	2.66986i	−0.0500477	+	0.137505i
$378$	5.50799	−	7.69935i	0.283300	−	0.396012i
$379$			31.0884i			1.59690i	0.602058	+	0.798452i	$0.294347\pi$
$379$			31.0884i			1.59690i	−0.602058	+	0.798452i	$0.705653\pi$
$380$	−4.95852	+	7.15162i	−0.254367	+	0.366871i
$381$	−1.91602	−	22.7844i	−0.0981607	−	1.16728i
$382$	−15.3394	−	18.2808i	−0.784834	−	0.935329i
$383$	6.29971	+	2.29291i	0.321900	+	0.117162i	0.497916	−	0.867225i	$-0.334099\pi$
$383$	6.29971	+	2.29291i	0.321900	+	0.117162i	−0.176016	+	0.984387i	$0.556321\pi$
$384$	−0.156773	+	1.72494i	−0.00800027	+	0.0880255i
$385$	−2.99638	−	16.9933i	−0.152709	−	0.866058i
$386$	−0.726280	−	1.99544i	−0.0369667	−	0.101565i
$387$	−12.9875	+	34.9482i	−0.660194	+	1.77652i
$388$	2.21636	−	1.27962i	0.112519	−	0.0649628i
$389$	−22.9366	+	27.3348i	−1.16293	+	1.38593i	−0.254933	+	0.966959i	$0.582053\pi$
$389$	−22.9366	+	27.3348i	−1.16293	+	1.38593i	−0.908000	+	0.418971i	$0.862391\pi$
$390$	1.25029	+	0.881756i	0.0633108	+	0.0446495i
$391$	−5.03890	−	8.72763i	−0.254828	−	0.441375i
$392$	−1.84041	+	3.18768i	−0.0929547	+	0.161002i
$393$	−5.14089	−	11.1224i	−0.259323	−	0.561050i
$394$	3.72503	−	0.656824i	0.187664	−	0.0330903i
$395$	−3.27957	+	18.5994i	−0.165013	+	0.935837i
$396$	2.56579	−	13.9988i	0.128936	−	0.703468i
$397$	−23.1763	+	19.4472i	−1.16319	+	0.976029i	−0.999944	−	0.0105571i	$-0.996640\pi$
$397$	−23.1763	+	19.4472i	−1.16319	+	0.976029i	−0.163242	+	0.986586i	$0.552195\pi$
$398$	13.7971			0.691586
$399$	13.5428	−	2.40544i	0.677988	−	0.120422i
$400$	1.01407			0.0507035
$401$	14.3394	−	12.0322i	0.716074	−	0.600858i	−0.210222	−	0.977654i	$-0.567419\pi$
$401$	14.3394	−	12.0322i	0.716074	−	0.600858i	0.926296	+	0.376796i	$0.122974\pi$
$402$	3.72199	−	13.7057i	0.185636	−	0.683580i
$403$	−0.433526	+	2.45865i	−0.0215955	+	0.122474i
$404$	7.84812	−	1.38383i	0.390458	−	0.0688484i
$405$	11.3632	+	13.9190i	0.564642	+	0.691640i
$406$	−5.84978	+	10.1321i	−0.290320	+	0.502848i
$407$	−13.7619	−	23.8363i	−0.682153	−	1.18152i
$408$	1.66909	−	2.36669i	0.0826321	−	0.117168i
$409$	−9.76955	+	11.6429i	−0.483073	+	0.575704i	−0.951442	−	0.307829i	$-0.900398\pi$
$409$	−9.76955	+	11.6429i	−0.483073	+	0.575704i	0.468369	+	0.883533i	$0.344842\pi$
$410$	6.91022	−	3.98962i	0.341272	−	0.197033i
$411$	−14.6987	−	6.91451i	−0.725032	−	0.341067i
$412$	5.25422	+	14.4358i	0.258857	+	0.711203i
$413$	1.59895	+	9.06811i	0.0786793	+	0.446212i
$414$	18.0814	+	0.121882i	0.888654	+	0.00599018i
$415$	1.13368	+	0.412626i	0.0556502	+	0.0202550i
$416$	0.284391	+	0.338924i	0.0139434	+	0.0166171i
$417$	−18.6965	+	1.57225i	−0.915571	+	0.0769936i
$418$	16.8840	−	11.9390i	0.825822	−	0.583953i
$419$			6.74268i			0.329402i	0.986344	+	0.164701i	$0.0526659\pi$
$419$			6.74268i			0.329402i	−0.986344	+	0.164701i	$0.947334\pi$
$420$	4.43974	+	4.46977i	0.216637	+	0.218102i
$421$	5.11036	−	14.0406i	0.249064	−	0.684297i	−0.750658	−	0.660691i	$-0.770263\pi$
$421$	5.11036	−	14.0406i	0.249064	−	0.684297i	0.999721	−	0.0236056i	$-0.00751459\pi$
$422$	−15.8744	−	2.79908i	−0.772753	−	0.136257i
$423$	−30.4487	+	10.8506i	−1.48047	+	0.527572i
$424$	−2.29919	+	0.836837i	−0.111659	+	0.0406404i
$425$	−1.46839	−	0.847778i	−0.0712276	−	0.0411233i
$426$	−5.10775	−	7.34720i	−0.247471	−	0.355973i
$427$	−14.4836	−	12.1532i	−0.700913	−	0.588136i
$428$	−14.3228	−	12.0183i	−0.692321	−	0.580926i
$429$	−2.07515	−	2.98498i	−0.100189	−	0.144116i
$430$	−21.4877	−	12.4059i	−1.03623	−	0.598267i
$431$	12.6508	−	4.60452i	0.609368	−	0.221792i	−0.0188586	−	0.999822i	$-0.506003\pi$
$431$	12.6508	−	4.60452i	0.609368	−	0.221792i	0.628227	+	0.778030i	$0.283781\pi$
$432$	2.14826	+	4.73128i	0.103358	+	0.227634i
$433$	16.6663	+	2.93872i	0.800933	+	0.141226i	0.559109	−	0.829094i	$-0.311143\pi$
$433$	16.6663	+	2.93872i	0.800933	+	0.141226i	0.241824	+	0.970320i	$0.422254\pi$
$434$	−3.51612	+	9.66046i	−0.168779	+	0.463717i
$435$	−15.6493	−	15.7552i	−0.750328	−	0.755403i
$436$			11.4154i			0.546700i
$437$	18.6630	+	18.4913i	0.892772	+	0.884558i
$438$	−24.9555	+	2.09860i	−1.19242	+	0.100275i
$439$	−9.65722	−	11.5090i	−0.460914	−	0.549296i	0.484660	−	0.874702i	$-0.338943\pi$
$439$	−9.65722	−	11.5090i	−0.460914	−	0.549296i	−0.945574	+	0.325407i	$0.894499\pi$
$440$	8.90013	+	3.23938i	0.424297	+	0.154432i
$441$	−0.0744326	+	11.0422i	−0.00354441	+	0.525819i
$442$	−0.128459	−	0.728525i	−0.00611015	−	0.0346524i
$443$	−12.6699	−	34.8103i	−0.601966	−	1.65389i	−0.747286	−	0.664503i	$-0.768643\pi$
$443$	−12.6699	−	34.8103i	−0.601966	−	1.65389i	0.145320	−	0.989385i	$-0.453579\pi$
$444$	9.09314	+	4.27757i	0.431541	+	0.203004i
$445$	−7.49163	+	4.32529i	−0.355137	+	0.205039i
$446$	−0.690579	+	0.823000i	−0.0326999	+	0.0389702i
$447$	−11.2436	+	15.9429i	−0.531803	+	0.754071i
$448$	0.910931	+	1.57778i	0.0430374	+	0.0745430i
$449$	5.81501	−	10.0719i	0.274427	−	0.475322i	−0.695563	−	0.718465i	$-0.744845\pi$
$449$	5.81501	−	10.0719i	0.274427	−	0.475322i	0.969991	+	0.243143i	$0.0781784\pi$
$450$	2.64482	−	1.50331i	0.124678	−	0.0708668i
$451$	−18.6721	+	3.29240i	−0.879236	+	0.155033i
$452$	0.103178	−	0.585152i	0.00485309	−	0.0275233i
$453$	−1.60993	+	5.92833i	−0.0756409	+	0.278537i
$454$	−14.3735	+	12.0608i	−0.674583	+	0.566042i
$455$	1.60927			0.0754438
$456$	−2.57332	+	7.09775i	−0.120507	+	0.332383i
$457$	15.7379			0.736189			0.368094	−	0.929788i	$-0.380010\pi$
$457$	15.7379			0.736189			0.368094	+	0.929788i	$0.380010\pi$
$458$	8.90636	−	7.47333i	0.416167	−	0.349206i
$459$	0.844691	−	8.64696i	0.0394268	−	0.403606i
$460$	−2.08957	+	11.8505i	−0.0974266	+	0.552534i
$461$	5.96078	−	1.05105i	0.277621	−	0.0489521i	−0.0331039	−	0.999452i	$-0.510539\pi$
$461$	5.96078	−	1.05105i	0.277621	−	0.0489521i	0.310725	+	0.950500i	$0.399428\pi$
$462$	−6.28083	−	13.5887i	−0.292211	−	0.632202i
$463$	4.59401	−	7.95705i	0.213502	−	0.369796i	−0.739306	−	0.673369i	$-0.764846\pi$
$463$	4.59401	−	7.95705i	0.213502	−	0.369796i	0.952808	+	0.303574i	$0.0981798\pi$
$464$	−3.21088	−	5.56141i	−0.149061	−	0.258182i
$465$	−15.9462	−	11.2460i	−0.739489	−	0.521518i
$466$	−10.4519	+	12.4561i	−0.484176	+	0.577019i
$467$	−0.179338	+	0.103541i	−0.00829879	+	0.00479131i	−0.504144	−	0.863620i	$-0.668192\pi$
$467$	−0.179338	+	0.103541i	−0.00829879	+	0.00479131i	0.495845	+	0.868411i	$0.334858\pi$
$468$	1.24417	+	0.462361i	0.0575117	+	0.0213727i
$469$	−5.10928	−	14.0376i	−0.235925	−	0.648198i
$470$	−3.73544	−	21.1848i	−0.172303	−	0.977180i
$471$	−0.0495179	+	0.544836i	−0.00228166	+	0.0251047i
$472$	−4.74937	−	1.72863i	−0.218607	−	0.0795665i
$473$	37.8972	+	45.1642i	1.74252	+	2.07665i
$474$	1.37302	+	16.3272i	0.0630647	+	0.749935i
$475$	4.27485	+	1.12429i	0.196144	+	0.0515862i
$476$		−	3.04621i		−	0.139623i
$477$	−4.75601	+	5.59102i	−0.217763	+	0.255995i
$478$	2.33026	−	6.40234i	0.106584	−	0.292836i
$479$	−4.92232	−	0.867938i	−0.224907	−	0.0396571i	0.0600591	−	0.998195i	$-0.480871\pi$
$479$	−4.92232	−	0.867938i	−0.224907	−	0.0396571i	−0.284966	+	0.958538i	$0.591982\pi$
$480$	−3.34317	+	0.883735i	−0.152594	+	0.0403368i
$481$	2.41211	−	0.877937i	0.109983	−	0.0400305i
$482$	16.8090	+	9.70467i	0.765628	+	0.442036i
$483$	15.6165	−	10.8565i	0.710575	−	0.493989i
$484$	−8.81384	−	7.39569i	−0.400629	−	0.336168i
$485$	3.91408	+	3.28430i	0.177729	+	0.149132i
$486$	12.6168	+	9.15508i	0.572311	+	0.415283i
$487$	−23.4422	−	13.5344i	−1.06227	−	0.613300i	−0.136209	−	0.990680i	$-0.543492\pi$
$487$	−23.4422	−	13.5344i	−1.06227	−	0.613300i	−0.926059	+	0.377380i	$0.876825\pi$
$488$	9.75201	−	3.54944i	0.441453	−	0.160676i
$489$	−0.552897	−	2.09161i	−0.0250029	−	0.0945859i
$490$	−7.23704	−	1.27608i	−0.326936	−	0.0576476i
$491$	−2.14701	+	5.89886i	−0.0968931	+	0.266212i	−0.978664	−	0.205466i	$-0.934129\pi$
$491$	−2.14701	+	5.89886i	−0.0968931	+	0.266212i	0.881771	+	0.471677i	$0.156351\pi$
$492$	4.91135	−	4.87836i	0.221421	−	0.219933i
$493$			10.7374i			0.483587i
$494$	0.823100	+	1.74405i	0.0370330	+	0.0784687i
$495$	28.0149	−	4.74531i	1.25918	−	0.213286i
$496$	−3.62714	−	4.32265i	−0.162863	−	0.194093i
$497$	−8.84457	−	3.21916i	−0.396733	−	0.144399i
$498$	1.04235	+	0.0947350i	0.0467089	+	0.00424518i
$499$	−3.81949	−	21.6614i	−0.170984	−	0.969699i	−0.942678	−	0.333704i	$-0.891701\pi$
$499$	−3.81949	−	21.6614i	−0.170984	−	0.969699i	0.771694	−	0.635994i	$-0.219410\pi$
$500$	4.10662	+	11.2829i	0.183654	+	0.504585i
$501$	0.753863	−	1.60254i	0.0336801	−	0.0715963i
$502$	14.7935	−	8.54106i	0.660268	−	0.381206i
$503$	6.51623	−	7.76574i	0.290544	−	0.346257i	−0.600952	−	0.799285i	$-0.705212\pi$
$503$	6.51623	−	7.76574i	0.290544	−	0.346257i	0.891496	+	0.453028i	$0.149656\pi$
$504$	4.71481	+	2.76464i	0.210014	+	0.123147i
$505$	7.95516	+	13.7787i	0.354000	+	0.613146i
$506$	14.2967	−	24.7627i	0.635568	−	1.10084i
$507$	−20.1312	+	9.30487i	−0.894059	+	0.413244i
$508$	13.0005	−	2.29233i	0.576802	−	0.101706i
$509$	1.94826	−	11.0492i	0.0863553	−	0.489745i	−0.910701	−	0.413067i	$-0.864457\pi$
$509$	1.94826	−	11.0492i	0.0863553	−	0.489745i	0.997056	−	0.0766782i	$-0.0244314\pi$
$510$	5.57980	+	1.51528i	0.247078	+	0.0670976i
$511$	−20.1793	+	16.9324i	−0.892678	+	0.749045i
$512$	−1.00000			−0.0441942
$513$	3.81054	+	22.3267i	0.168240	+	0.985746i
$514$	15.8102			0.697360
$515$	−23.4950	+	19.7146i	−1.03531	+	0.868730i
$516$	−20.7732	−	5.64128i	−0.914490	−	0.248343i
$517$	−8.87612	+	50.3390i	−0.390371	+	2.21391i
$518$	10.4095	−	1.83548i	0.457367	−	0.0806462i
$519$	−23.7590	+	10.9817i	−1.04291	+	0.482043i
$520$	−0.441656	+	0.764970i	−0.0193679	+	0.0335461i
$521$	22.3984	+	38.7951i	0.981290	+	1.69964i	0.657386	+	0.753554i	$0.271662\pi$
$521$	22.3984	+	38.7951i	0.981290	+	1.69964i	0.323904	+	0.946090i	$0.395005\pi$
$522$	−16.6189	−	9.74488i	−0.727390	−	0.426522i
$523$	25.4174	−	30.2913i	1.11143	−	1.32455i	0.170721	−	0.985319i	$-0.445390\pi$
$523$	25.4174	−	30.2913i	1.11143	−	1.32455i	0.940705	−	0.339226i	$-0.110165\pi$
$524$	6.12650	−	3.53714i	0.267638	−	0.154521i
$525$	1.36213	−	2.89557i	0.0594481	−	0.126373i
$526$	−0.888930	−	2.44232i	−0.0387592	−	0.106490i
$527$	1.63837	+	9.29163i	0.0713683	+	0.404750i
$528$	8.18314	+	0.743731i	0.356126	+	0.0323668i
$529$	12.5243	+	4.55849i	0.544536	+	0.198195i
$530$	−3.13994	−	3.74203i	−0.136390	−	0.162544i
$531$	−14.9496	+	2.53223i	−0.648756	+	0.109889i
$532$	2.09079	+	7.66114i	0.0906473	+	0.332152i
$533$		−	1.76826i		−	0.0765917i
$534$	−5.32458	+	5.28881i	−0.230417	+	0.228869i
$535$	12.7671	−	35.0773i	0.551969	−	1.51652i
$536$	8.07503	+	1.42385i	0.348788	+	0.0615008i
$537$	2.63125	+	9.95403i	0.113547	+	0.429548i
$538$	29.9875	−	10.9146i	1.29285	−	0.470560i
$539$	15.1224	+	8.73093i	0.651368	+	0.376068i
$540$	−7.40933	+	7.26099i	−0.318847	+	0.312463i
$541$	9.00083	+	7.55259i	0.386976	+	0.324711i	0.815434	−	0.578850i	$-0.196499\pi$
$541$	9.00083	+	7.55259i	0.386976	+	0.324711i	−0.428458	+	0.903562i	$0.640943\pi$
$542$	15.3935	+	12.9167i	0.661207	+	0.554818i
$543$	9.23113	−	6.41745i	0.396146	−	0.275399i
$544$	1.44802	+	0.836015i	0.0620834	+	0.0358438i
$545$	−21.4162	+	7.79487i	−0.917370	+	0.333895i
$546$	1.34977	−	0.356797i	0.0577646	−	0.0152695i
$547$	3.60851	+	0.636278i	0.154289	+	0.0272053i	0.250259	−	0.968179i	$-0.419484\pi$
$547$	3.60851	+	0.636278i	0.154289	+	0.0272053i	−0.0959702	+	0.995384i	$0.530595\pi$
$548$	3.20759	−	8.81278i	0.137021	−	0.376463i
$549$	20.1726	−	23.7143i	0.860946	−	1.01210i
$550$		−	4.81076i		−	0.205131i
$551$	−7.36969	−	27.0042i	−0.313959	−	1.15042i
$552$	0.874812	+	10.4028i	0.0372345	+	0.442774i
$553$	11.0781	+	13.2024i	0.471089	+	0.561422i
$554$	−7.59304	−	2.76364i	−0.322597	−	0.117416i
$555$	−1.81593	+	19.9803i	−0.0770818	+	0.848117i
$556$	−1.88105	−	10.6679i	−0.0797742	−	0.452422i
$557$	−4.53013	−	12.4464i	−0.191948	−	0.527372i	0.805964	−	0.591965i	$-0.201647\pi$
$557$	−4.53013	−	12.4464i	−0.191948	−	0.527372i	−0.997912	+	0.0645925i	$0.979425\pi$
$558$	−15.8682	−	5.89697i	−0.671753	−	0.249639i
$559$	−4.76183	+	2.74924i	−0.201404	+	0.116281i
$560$	−2.33802	+	2.78634i	−0.0987993	+	0.117744i
$561$	−11.2276	−	7.91817i	−0.474029	−	0.334305i
$562$	−5.90537	−	10.2284i	−0.249103	−	0.431459i
$563$	2.30395	−	3.99056i	0.0970999	−	0.168182i	−0.813383	−	0.581728i	$-0.802377\pi$
$563$	2.30395	−	3.99056i	0.0970999	−	0.168182i	0.910483	+	0.413546i	$0.135710\pi$
$564$	−7.83003	−	16.9404i	−0.329704	−	0.713319i
$565$	1.16824	−	0.205993i	0.0491484	−	0.00866619i
$566$	−2.49475	+	14.1484i	−0.104862	+	0.594702i
$567$	16.3953	+	0.221042i	0.688536	+	0.00928290i
$568$	3.95758	−	3.32080i	0.166056	−	0.139338i
$569$	−24.3659			−1.02147			−0.510736	−	0.859738i	$-0.670627\pi$
$569$	−24.3659			−1.02147			−0.510736	+	0.859738i	$0.670627\pi$
$570$	−15.0731	+	0.0188610i	−0.631342	+	0.000789999i
$571$	−20.9944			−0.878589			−0.439294	−	0.898343i	$-0.644772\pi$
$571$	−20.9944			−0.878589			−0.439294	+	0.898343i	$0.644772\pi$
$572$	1.60786	−	1.34916i	0.0672281	−	0.0564110i
$573$	10.8324	−	39.8888i	0.452530	−	1.66638i
$574$	1.26439	−	7.17073i	0.0527748	−	0.299301i
$575$	6.01923	−	1.06135i	0.251019	−	0.0442614i
$576$	−2.60813	+	1.48245i	−0.108672	+	0.0617689i
$577$	−2.59042	+	4.48675i	−0.107841	+	0.186786i	−0.914895	−	0.403691i	$-0.867727\pi$
$577$	−2.59042	+	4.48675i	−0.107841	+	0.186786i	0.807055	+	0.590477i	$0.201060\pi$
$578$	7.10216	+	12.3013i	0.295411	+	0.511667i
$579$	2.11976	−	3.00572i	0.0880943	−	0.124914i
$580$	8.24112	−	9.82139i	0.342194	−	0.407811i
$581$	0.953424	−	0.550460i	0.0395547	−	0.0228369i
$582$	4.01108	+	1.88688i	0.166265	+	0.0782137i
$583$	3.96996	+	10.9074i	0.164419	+	0.451738i
$584$	−2.51076	−	14.2392i	−0.103896	−	0.589224i
$585$	−0.0178621	+	2.64987i	−0.000738507	+	0.109559i
$586$	−0.00609414	−	0.00221809i	−0.000251747	−	9.16283e-5i
$587$	−19.9370	−	23.7599i	−0.822887	−	0.980678i	0.177107	−	0.984192i	$-0.443326\pi$
$587$	−19.9370	−	23.7599i	−0.822887	−	0.980678i	−0.999994	+	0.00351357i	$0.998882\pi$
$588$	−6.35294	+	0.534241i	−0.261991	+	0.0220317i
$589$	−10.4978	−	22.2437i	−0.432556	−	0.916536i
$590$		−	10.0905i		−	0.415421i
$591$	4.61695	+	4.64818i	0.189916	+	0.191201i
$592$	−1.98433	+	5.45191i	−0.0815556	+	0.224072i
$593$	19.0316	+	3.35579i	0.781536	+	0.137806i	0.550161	−	0.835059i	$-0.314566\pi$
$593$	19.0316	+	3.35579i	0.781536	+	0.137806i	0.231375	+	0.972865i	$0.425678\pi$
$594$	22.4452	−	10.1914i	0.920939	−	0.418157i
$595$	5.71492	−	2.08006i	0.234289	−	0.0852742i
$596$	−9.75439	−	5.63170i	−0.399555	−	0.230683i
$597$	13.6409	+	19.6216i	0.558283	+	0.803058i
$598$	2.04279	+	1.71411i	0.0835360	+	0.0700950i
$599$	14.4631	+	12.1360i	0.590946	+	0.495863i	0.888521	−	0.458836i	$-0.151733\pi$
$599$	14.4631	+	12.1360i	0.590946	+	0.495863i	−0.297575	+	0.954698i	$0.596178\pi$
$600$	1.00259	+	1.44216i	0.0409304	+	0.0588760i
$601$	−9.35958	−	5.40376i	−0.381785	−	0.220424i	0.296809	−	0.954937i	$-0.404077\pi$
$601$	−9.35958	−	5.40376i	−0.381785	−	0.220424i	−0.678595	+	0.734513i	$0.737411\pi$
$602$	−21.2763	+	7.74393i	−0.867156	+	0.315619i
$603$	23.1715	−	8.25728i	0.943616	−	0.336263i
$604$	−3.49280	−	0.615876i	−0.142120	−	0.0250596i
$605$	7.85648	−	21.5855i	0.319411	−	0.877575i
$606$	9.72727	+	9.79306i	0.395143	+	0.397816i
$607$			7.06408i			0.286722i	0.989670	+	0.143361i	$0.0457910\pi$
$607$			7.06408i			0.286722i	−0.989670	+	0.143361i	$0.954209\pi$
$608$	−4.21554	−	1.10870i	−0.170963	−	0.0449635i
$609$	−20.1930	+	1.69810i	−0.818260	+	0.0688104i
$610$	13.3181	+	15.8718i	0.539232	+	0.642632i
$611$	−4.47963	−	1.63045i	−0.181226	−	0.0659610i
$612$	5.01598	+	0.0338114i	0.202759	+	0.00136674i
$613$	−5.48141	−	31.0866i	−0.221392	−	1.25558i	−0.869463	−	0.493998i	$-0.835535\pi$
$613$	−5.48141	−	31.0866i	−0.221392	−	1.25558i	0.648071	−	0.761580i	$-0.275576\pi$
$614$	4.66013	+	12.8036i	0.188068	+	0.516712i
$615$	12.5058	+	5.88296i	0.504283	+	0.237224i
$616$	7.48500	−	4.32147i	0.301579	−	0.174117i
$617$	19.6647	−	23.4355i	0.791672	−	0.943478i	−0.207725	−	0.978187i	$-0.566606\pi$
$617$	19.6647	−	23.4355i	0.791672	−	0.943478i	0.999397	+	0.0347092i	$0.0110505\pi$
$618$	−15.3353	+	21.7447i	−0.616874	+	0.874699i
$619$	21.8906	+	37.9157i	0.879859	+	1.52396i	0.851494	+	0.524364i	$0.175697\pi$
$619$	21.8906	+	37.9157i	0.879859	+	1.52396i	0.0283650	+	0.999598i	$0.490970\pi$
$620$	5.63289	−	9.75645i	0.226222	−	0.391829i
$621$	17.7033	+	25.8351i	0.710411	+	1.03673i
$622$	11.5333	−	2.03363i	0.462442	−	0.0815411i
$623$	−1.37078	+	7.77406i	−0.0549190	+	0.311461i
$624$	−0.200832	+	0.739534i	−0.00803969	+	0.0296051i
$625$	−14.4792	+	12.1495i	−0.579170	+	0.485981i
$626$	−1.75691			−0.0702201
$627$	33.6718	+	12.2078i	1.34472	+	0.487534i
$628$	−0.315858			−0.0126041
$629$	7.43124	−	6.23555i	0.296303	−	0.248628i
$630$	−1.96723	+	10.7331i	−0.0783763	+	0.427618i
$631$	0.0934107	−	0.529758i	0.00371862	−	0.0210893i	−0.982892	−	0.184183i	$-0.941036\pi$
$631$	0.0934107	−	0.529758i	0.00371862	−	0.0210893i	0.986611	+	0.163094i	$0.0521472\pi$
$632$	−9.31609	+	1.64268i	−0.370574	+	0.0653422i
$633$	−11.7139	−	25.3432i	−0.465586	−	1.00730i
$634$	−3.50725	+	6.07474i	−0.139291	+	0.241259i
$635$	13.1778	+	22.8246i	0.522944	+	0.905765i
$636$	−3.46326	−	2.44244i	−0.137327	−	0.0968490i
$637$	−1.04679	+	1.24752i	−0.0414755	+	0.0494285i
$638$	−26.3834	+	15.2325i	−1.04453	+	0.603059i
$639$	5.39893	−	14.5280i	0.213578	−	0.574719i
$640$	−0.682836	−	1.87608i	−0.0269915	−	0.0741585i
$641$	−4.01897	−	22.7927i	−0.158740	−	0.900259i	−0.955287	−	0.295682i	$-0.904453\pi$
$641$	−4.01897	−	22.7927i	−0.158740	−	0.900259i	0.796547	−	0.604577i	$-0.206658\pi$
$642$	2.93120	−	32.2515i	0.115685	−	1.27286i
$643$	−8.18931	−	2.98066i	−0.322955	−	0.117546i	0.175455	−	0.984487i	$-0.443860\pi$
$643$	−8.18931	−	2.98066i	−0.322955	−	0.117546i	−0.498410	+	0.866941i	$0.666083\pi$
$644$	7.05837	+	8.41184i	0.278139	+	0.331473i
$645$	−3.60124	−	42.8242i	−0.141799	−	1.68620i
$646$	5.17731	+	5.12967i	0.203698	+	0.201824i
$647$			39.9441i			1.57037i	0.619264	+	0.785183i	$0.287431\pi$
$647$			39.9441i			1.57037i	−0.619264	+	0.785183i	$0.712569\pi$
$648$	−4.60466	+	7.73286i	−0.180888	+	0.303775i
$649$	−8.20063	+	22.5310i	−0.321903	+	0.884421i
$650$	0.441843	+	0.0779089i	0.0173305	+	0.00305584i
$651$	−17.2150	+	4.55060i	−0.674707	+	0.178352i
$652$	1.17374	−	0.427207i	0.0459673	−	0.0167307i
$653$	−1.49337	−	0.862200i	−0.0584402	−	0.0337405i	0.470495	−	0.882403i	$-0.344075\pi$
$653$	−1.49337	−	0.862200i	−0.0584402	−	0.0337405i	−0.528935	+	0.848662i	$0.677409\pi$
$654$	−16.2345	+	11.2862i	−0.634819	+	0.441324i
$655$	10.8193	+	9.07851i	0.422747	+	0.354727i
$656$	3.06162	+	2.56900i	0.119536	+	0.100303i
$657$	−27.6574	−	33.4157i	−1.07902	−	1.30367i
$658$	−17.0002	−	9.81505i	−0.662736	−	0.382631i
$659$	22.0705	−	8.03300i	0.859744	−	0.312921i	0.125737	−	0.992064i	$-0.459870\pi$
$659$	22.0705	−	8.03300i	0.859744	−	0.312921i	0.734006	+	0.679142i	$0.237648\pi$
$660$	4.19245	+	15.8601i	0.163191	+	0.617352i
$661$	10.0686	+	1.77536i	0.391622	+	0.0690535i	0.365992	−	0.930618i	$-0.380730\pi$
$661$	10.0686	+	1.77536i	0.391622	+	0.0690535i	0.0256300	+	0.999671i	$0.491841\pi$
$662$	0.539949	−	1.48350i	0.0209857	−	0.0576578i
$663$	0.909070	−	0.902963i	0.0353054	−	0.0350682i
$664$			0.604283i			0.0234507i
$665$	−12.9452	+	9.15379i	−0.501994	+	0.354969i
$666$	2.90681	+	17.1610i	0.112637	+	0.664974i
$667$	−24.8796	−	29.6503i	−0.963341	−	1.14807i
$668$	0.960825	+	0.349712i	0.0371754	+	0.0135307i
$669$	−1.85319	−	0.168429i	−0.0716485	−	0.00651183i
$670$	2.84268	+	16.1216i	0.109822	+	0.622833i
$671$	−16.8386	−	46.2637i	−0.650047	−	1.78599i
$672$	−1.34323	+	2.85540i	−0.0518161	+	0.110149i
$673$	−32.9000	+	18.9948i	−1.26820	+	0.732197i	−0.974648	−	0.223745i	$-0.928172\pi$
$673$	−32.9000	+	18.9948i	−1.26820	+	0.732197i	−0.293555	+	0.955942i	$0.594838\pi$
$674$	−21.0224	+	25.0536i	−0.809754	+	0.965028i
$675$	4.75281	+	2.27506i	0.182936	+	0.0875670i
$676$	−6.40213	−	11.0888i	−0.246236	−	0.426493i
$677$	−16.1698	+	28.0070i	−0.621457	+	1.07640i	0.367757	+	0.929922i	$0.380126\pi$
$677$	−16.1698	+	28.0070i	−0.621457	+	1.07640i	−0.989215	+	0.146474i	$0.953208\pi$
$678$	0.934186	−	0.431791i	0.0358772	−	0.0165828i
$679$	4.59174	−	0.809648i	0.176215	−	0.0310714i
$680$	−0.579668	+	3.28746i	−0.0222292	+	0.126068i
$681$	−31.3631	−	8.51711i	−1.20184	−	0.326376i
$682$	−20.5067	+	17.2072i	−0.785243	+	0.658897i
$683$	−27.4952			−1.05208			−0.526038	−	0.850461i	$-0.676323\pi$
$683$	−27.4952			−1.05208			−0.526038	+	0.850461i	$0.676323\pi$
$684$	−12.6383	+	3.35773i	−0.483236	+	0.128386i
$685$	18.7237			0.715396
$686$	−14.9064	+	12.5080i	−0.569131	+	0.477557i
$687$	19.4337	+	5.27751i	0.741443	+	0.201350i
$688$	2.15807	−	12.2390i	0.0822755	−	0.466607i
$689$	−1.06608	+	0.187978i	−0.0406144	+	0.00716141i
$690$	−18.9192	+	8.74465i	−0.720241	+	0.332903i
$691$	8.55714	−	14.8214i	0.325529	−	0.563833i	−0.656090	−	0.754682i	$-0.727791\pi$
$691$	8.55714	−	14.8214i	0.325529	−	0.563833i	0.981619	+	0.190850i	$0.0611243\pi$
$692$	−7.55585	−	13.0871i	−0.287230	−	0.497497i
$693$	13.1155	−	22.3671i	0.498215	−	0.849656i
$694$	1.49140	−	1.77738i	0.0566128	−	0.0674685i
$695$	18.7294	−	10.8134i	0.710448	−	0.410178i
$696$	4.73465	−	10.0648i	0.179467	−	0.381505i
$697$	−2.28556	−	6.27952i	−0.0865717	−	0.237854i
$698$	2.39844	+	13.6023i	0.0907824	+	0.514853i
$699$	−28.0481	−	2.54917i	−1.06088	−	0.0964186i
$700$	1.73608	+	0.631881i	0.0656176	+	0.0238828i
$701$	24.3781	+	29.0527i	0.920748	+	1.09730i	0.994981	+	0.100064i	$0.0319046\pi$
$701$	24.3781	+	29.0527i	0.920748	+	1.09730i	−0.0742333	+	0.997241i	$0.523651\pi$
$702$	0.572531	+	2.22652i	0.0216088	+	0.0840347i
$703$	−14.4096	+	20.7827i	−0.543467	+	0.783836i
$704$			4.74401i			0.178797i
$705$	26.4348	−	26.2572i	0.995593	−	0.988905i
$706$	−4.98533	+	13.6971i	−0.187625	+	0.515496i
$707$	14.2982	+	2.52116i	0.537739	+	0.0948178i
$708$	−2.23721	−	8.46338i	−0.0840795	−	0.318073i
$709$	−18.3247	+	6.66963i	−0.688197	+	0.250483i	−0.662363	−	0.749183i	$-0.730446\pi$
$709$	−18.3247	+	6.66963i	−0.688197	+	0.250483i	−0.0258338	+	0.999666i	$0.508224\pi$
$710$	8.93245	+	5.15715i	0.335229	+	0.193545i
$711$	−21.8624	+	18.0950i	−0.819903	+	0.678615i
$712$	−3.31921	−	2.78515i	−0.124393	−	0.104378i
$713$	−26.0539	−	21.8618i	−0.975724	−	0.818730i
$714$	4.33217	−	3.01171i	0.162128	−	0.112711i
$715$	3.62903	+	2.09522i	0.135718	+	0.0783568i
$716$	−5.58587	+	2.03309i	−0.208754	+	0.0759802i
$717$	11.4090	−	3.01585i	0.426076	−	0.112629i
$718$	19.1397	+	3.37484i	0.714287	+	0.125948i
$719$	0.618865	−	1.70032i	0.0230798	−	0.0634111i	−0.927618	−	0.373531i	$-0.878147\pi$
$719$	0.618865	−	1.70032i	0.0230798	−	0.0634111i	0.950697	+	0.310120i	$0.100369\pi$
$720$	−4.56212	−	3.88078i	−0.170020	−	0.144628i
$721$			27.9880i			1.04233i
$722$	−16.5416	−	9.34750i	−0.615614	−	0.347878i
$723$	2.81711	+	33.4997i	0.104769	+	1.24587i
$724$	4.17230	+	4.97236i	0.155062	+	0.184796i
$725$	−6.11938	−	2.22727i	−0.227268	−	0.0827189i
$726$	1.80377	−	19.8466i	0.0669443	−	0.736576i
$727$	2.39063	+	13.5580i	0.0886637	+	0.502837i	0.996506	+	0.0835244i	$0.0266177\pi$
$727$	2.39063	+	13.5580i	0.0886637	+	0.502837i	−0.907842	+	0.419312i	$0.862271\pi$
$728$	0.275687	+	0.757443i	0.0102176	+	0.0280727i
$729$	−0.545954	+	26.9945i	−0.0202205	+	0.999796i
$730$	24.9995	−	14.4335i	0.925273	−	0.534206i
$731$	−13.3569	+	15.9181i	−0.494023	+	0.588754i
$732$	14.6894	+	10.3596i	0.542937	+	0.382902i
$733$	3.00825	+	5.21044i	0.111112	+	0.192452i	0.916219	−	0.400678i	$-0.131225\pi$
$733$	3.00825	+	5.21044i	0.111112	+	0.192452i	−0.805107	+	0.593130i	$0.797892\pi$
$734$	3.78035	−	6.54777i	0.139535	−	0.241682i
$735$	−5.34030	−	11.5538i	−0.196980	−	0.426169i
$736$	−5.93571	+	1.04663i	−0.218793	+	0.0385792i
$737$	6.75474	−	38.3080i	0.248814	−	1.41109i
$738$	11.7935	+	2.16158i	0.434125	+	0.0795688i
$739$	16.5397	−	13.8784i	0.608421	−	0.510526i	−0.285719	−	0.958313i	$-0.592232\pi$
$739$	16.5397	−	13.8784i	0.608421	−	0.510526i	0.894140	+	0.447788i	$0.147788\pi$
$740$	−11.5832			−0.425806
$741$	−1.66653	+	2.89488i	−0.0612216	+	0.106346i
$742$	−4.45763			−0.163645
$743$	18.9259	−	15.8807i	0.694322	−	0.582606i	−0.225830	−	0.974167i	$-0.572509\pi$
$743$	18.9259	−	15.8807i	0.694322	−	0.582606i	0.920152	+	0.391561i	$0.128065\pi$
$744$	2.56141	−	9.43205i	0.0939059	−	0.345796i
$745$	3.90485	−	22.1455i	0.143063	−	0.811349i
$746$	5.69223	−	1.00369i	0.208407	−	0.0367478i
$747$	0.895821	+	1.57605i	0.0327764	+	0.0576645i
$748$	3.96607	−	6.86943i	0.145014	−	0.251171i
$749$	−17.0318	−	29.4999i	−0.622329	−	1.07790i
$750$	−11.9858	+	16.9953i	−0.437661	+	0.620582i
$751$	−14.8918	+	17.7473i	−0.543409	+	0.647609i	−0.965948	−	0.258735i	$-0.916694\pi$
$751$	−14.8918	+	17.7473i	−0.543409	+	0.647609i	0.422540	+	0.906344i	$0.361139\pi$
$752$	9.33121	−	5.38738i	0.340274	−	0.196457i
$753$	26.7727	+	12.5943i	0.975652	+	0.458964i
$754$	−0.971750	−	2.66986i	−0.0353891	−	0.0972306i
$755$	−1.22958	−	6.97331i	−0.0447491	−	0.253785i
$756$	0.729681	+	9.43851i	0.0265383	+	0.343275i
$757$	−11.1562	−	4.06054i	−0.405480	−	0.147583i	0.131225	−	0.991353i	$-0.458109\pi$
$757$	−11.1562	−	4.06054i	−0.405480	−	0.147583i	−0.536705	+	0.843770i	$0.680331\pi$
$758$	−19.9832	−	23.8151i	−0.725824	−	0.865003i
$759$	49.3512	−	4.15012i	1.79134	−	0.150640i
$760$	−0.798527	−	8.66574i	−0.0289656	−	0.314339i
$761$		−	6.51835i		−	0.236290i	−0.992996	−	0.118145i	$-0.962305\pi$
$761$		−	6.51835i		−	0.236290i	0.992996	−	0.118145i	$-0.0376948\pi$
$762$	16.1133	+	16.2223i	0.583722	+	0.587670i
$763$	−7.11311	+	19.5431i	−0.257512	+	0.707508i
$764$	23.5014	+	4.14393i	0.850250	+	0.149922i
$765$	3.36166	+	9.43345i	0.121541	+	0.341067i
$766$	−6.29971	+	2.29291i	−0.227618	+	0.0828461i
$767$	−1.93655	−	1.11807i	−0.0699249	−	0.0403711i
$768$	−0.988676	−	1.42215i	−0.0356758	−	0.0513175i
$769$	6.42301	+	5.38954i	0.231620	+	0.194352i	0.751209	−	0.660064i	$-0.229471\pi$
$769$	6.42301	+	5.38954i	0.231620	+	0.194352i	−0.519590	+	0.854416i	$0.673915\pi$
$770$	13.2184	+	11.0916i	0.476359	+	0.399713i
$771$	15.6312	+	22.4846i	0.562944	+	0.809763i
$772$	1.83900	+	1.06175i	0.0661872	+	0.0382132i
$773$	−15.1689	+	5.52103i	−0.545588	+	0.198578i	−0.600085	−	0.799936i	$-0.704867\pi$
$773$	−15.1689	+	5.52103i	−0.545588	+	0.198578i	0.0544971	+	0.998514i	$0.482644\pi$
$774$	−12.5152	−	35.1201i	−0.449851	−	1.26237i
$775$	−5.63528	−	0.993653i	−0.202425	−	0.0356931i
$776$	−0.875310	+	2.40490i	−0.0314218	+	0.0863307i
$777$	12.9020	+	12.9892i	0.462855	+	0.465985i
$778$		−	35.6830i		−	1.27930i
$779$	10.0581	+	14.2241i	0.360370	+	0.509632i
$780$	−1.52456	+	0.128206i	−0.0545880	+	0.00459049i
$781$	−15.7539	−	18.7748i	−0.563719	−	0.671815i
$782$	9.47003	+	3.44681i	0.338648	+	0.123258i
$783$	−2.57201	−	33.2692i	−0.0919160	−	1.18894i
$784$	−0.639168	−	3.62490i	−0.0228274	−	0.129461i
$785$	−0.215679	−	0.592574i	−0.00769792	−	0.0211499i
$786$	11.0875	+	5.21574i	0.395477	+	0.186039i
$787$	19.4065	−	11.2044i	0.691768	−	0.399392i	−0.112506	−	0.993651i	$-0.535888\pi$
$787$	19.4065	−	11.2044i	0.691768	−	0.399392i	0.804274	+	0.594259i	$0.202554\pi$
$788$	−2.43134	+	2.89756i	−0.0866130	+	0.103221i
$789$	2.59448	−	3.67885i	0.0923661	−	0.130971i
$790$	−9.44315	−	16.3560i	−0.335972	−	0.581921i
$791$	0.541256	−	0.937483i	0.0192449	−	0.0333331i
$792$	7.03278	+	12.3730i	0.249899	+	0.439655i
$793$	4.52177	−	0.797311i	0.160573	−	0.0283133i
$794$	5.25364	−	29.7949i	0.186445	−	1.05738i
$795$	2.21736	−	8.16513i	0.0786418	−	0.289587i
$796$	−10.5692	+	8.86860i	−0.374615	+	0.314339i
$797$	−33.1888			−1.17561			−0.587804	−	0.809003i	$-0.700007\pi$
$797$	−33.1888			−1.17561			−0.587804	+	0.809003i	$0.700007\pi$
$798$	−8.82819	+	10.5478i	−0.312515	+	0.373388i
$799$	−18.0157			−0.637350
$800$	−0.776823	+	0.651831i	−0.0274648	+	0.0230457i
$801$	−12.7858	−	2.34345i	−0.451763	−	0.0828017i
$802$	−3.25047	+	18.4344i	−0.114778	+	0.650940i
$803$	−67.5512	+	11.9111i	−2.38383	+	0.420333i
$804$	5.95866	+	12.8916i	0.210146	+	0.454653i
$805$	−10.9615	+	18.9860i	−0.386344	+	0.669167i
$806$	−1.24829	−	2.16210i	−0.0439691	−	0.0761568i
$807$	45.1701	+	31.8559i	1.59006	+	1.12138i
$808$	−5.12250	+	6.10475i	−0.180209	+	0.214764i
$809$	−35.2784	+	20.3680i	−1.24032	+	0.716101i	−0.969160	−	0.246432i	$-0.920742\pi$
$809$	−35.2784	+	20.3680i	−1.24032	+	0.716101i	−0.271164	+	0.962533i	$0.587409\pi$
$810$	−17.6517	−	3.35843i	−0.620216	−	0.118003i
$811$	−6.36968	−	17.5006i	−0.223670	−	0.614528i	0.776203	−	0.630483i	$-0.217143\pi$
$811$	−6.36968	−	17.5006i	−0.223670	−	0.614528i	−0.999873	+	0.0159555i	$0.994921\pi$
$812$	−2.03161	−	11.5218i	−0.0712954	−	0.404337i
$813$	−3.15031	+	34.6623i	−0.110486	+	1.21566i
$814$	25.8639	+	9.41370i	0.906531	+	0.329950i
$815$	1.60295	+	1.91032i	0.0561488	+	0.0669155i
$816$	0.242682	+	2.88586i	0.00849556	+	0.101025i
$817$	22.6667	−	49.2014i	0.793009	−	1.72134i
$818$		−	15.1987i		−	0.531411i
$819$	1.84190	+	1.56682i	0.0643612	+	0.0547490i
$820$	−2.72906	+	7.49803i	−0.0953029	+	0.261843i
$821$	−17.1780	−	3.02894i	−0.599515	−	0.105711i	−0.134349	−	0.990934i	$-0.542894\pi$
$821$	−17.1780	−	3.02894i	−0.599515	−	0.105711i	−0.465166	+	0.885223i	$0.654005\pi$
$822$	15.7044	−	4.15130i	0.547754	−	0.144793i
$823$	13.0772	−	4.75972i	0.455844	−	0.165914i	−0.103885	−	0.994589i	$-0.533127\pi$
$823$	13.0772	−	4.75972i	0.455844	−	0.165914i	0.559729	+	0.828676i	$0.310905\pi$
$824$	−13.3041	−	7.68115i	−0.463472	−	0.267586i
$825$	6.84164	−	4.75628i	0.238195	−	0.165593i
$826$	−7.05374	−	5.91879i	−0.245431	−	0.205941i
$827$	−3.80513	−	3.19288i	−0.132317	−	0.111027i	0.574227	−	0.818696i	$-0.305303\pi$
$827$	−3.80513	−	3.19288i	−0.132317	−	0.111027i	−0.706545	+	0.707669i	$0.749747\pi$
$828$	−13.9295	+	11.5292i	−0.484084	+	0.400666i
$829$	36.2878	+	20.9508i	1.26033	+	0.727650i	0.973138	−	0.230224i	$-0.0739460\pi$
$829$	36.2878	+	20.9508i	1.26033	+	0.727650i	0.287189	+	0.957874i	$0.407279\pi$
$830$	−1.13368	+	0.412626i	−0.0393506	+	0.0143225i
$831$	−3.57674	−	13.5308i	−0.124076	−	0.469379i
$832$	−0.435713	−	0.0768279i	−0.0151056	−	0.00266353i
$833$	−2.10494	+	5.78328i	−0.0729319	+	0.200379i
$834$	13.3117	−	13.2223i	0.460947	−	0.457850i
$835$			2.04138i			0.0706448i
$836$	−5.25966	+	19.9986i	−0.181909	+	0.691665i
$837$	−7.30208	−	28.3972i	−0.252397	−	0.981550i
$838$	−4.33411	−	5.16519i	−0.149719	−	0.178429i
$839$	37.7944	+	13.7560i	1.30481	+	0.474912i	0.898560	−	0.438851i	$-0.144614\pi$
$839$	37.7944	+	13.7560i	1.30481	+	0.474912i	0.406249	+	0.913763i	$0.366837\pi$
$840$	−6.27415	−	0.570231i	−0.216479	−	0.0196748i
$841$	2.12528	+	12.0531i	0.0732855	+	0.415623i
$842$	5.11036	+	14.0406i	0.176115	+	0.483871i
$843$	8.70786	−	18.5109i	0.299915	−	0.637550i
$844$	13.9597	−	8.05964i	0.480513	−	0.277424i
$845$	16.4319	−	19.5827i	0.565273	−	0.673666i
$846$	16.3505	−	27.8840i	0.562140	−	0.958673i
$847$	−10.4809	−	18.1534i	−0.360126	−	0.623757i
$848$	1.22337	−	2.11894i	0.0420108	−	0.0727648i
$849$	−22.5877	+	10.4403i	−0.775208	+	0.358310i
$850$	1.66980	−	0.294430i	0.0572735	−	0.0100989i
$851$	−6.07232	+	34.4378i	−0.208156	+	1.18051i
$852$	8.63545	+	2.34508i	0.295846	+	0.0803412i
$853$	25.6859	−	21.5531i	0.879470	−	0.737963i	−0.0866001	−	0.996243i	$-0.527600\pi$
$853$	25.6859	−	21.5531i	0.879470	−	0.737963i	0.966070	+	0.258280i	$0.0831558\pi$
$854$	18.9071			0.646986
$855$	−14.9292	−	21.4176i	−0.510568	−	0.732466i
$856$	18.6971			0.639055
$857$	−0.680362	+	0.570892i	−0.0232407	+	0.0195013i	−0.654334	−	0.756206i	$-0.727051\pi$
$857$	−0.680362	+	0.570892i	−0.0232407	+	0.0195013i	0.631093	+	0.775707i	$0.282607\pi$
$858$	3.50836	+	0.952747i	0.119773	+	0.0325263i
$859$	−0.641169	+	3.63625i	−0.0218764	+	0.124067i	−0.993790	−	0.111270i	$-0.964508\pi$
$859$	−0.641169	+	3.63625i	−0.0218764	+	0.124067i	0.971914	+	0.235337i	$0.0756194\pi$
$860$	24.4349	−	4.30853i	0.833223	−	0.146920i
$861$	11.4480	−	5.29137i	0.390145	−	0.180329i
$862$	−6.73136	+	11.6591i	−0.229271	+	0.397109i
$863$	9.90600	+	17.1577i	0.337204	+	0.584055i	0.983906	−	0.178688i	$-0.0571854\pi$
$863$	9.90600	+	17.1577i	0.337204	+	0.584055i	−0.646701	+	0.762743i	$0.723852\pi$
$864$	−4.68687	−	2.24349i	−0.159451	−	0.0763251i
$865$	19.3930	−	23.1117i	0.659383	−	0.785822i
$866$	−14.6561	+	8.46172i	−0.498035	+	0.287541i
$867$	−10.4726	+	22.2624i	−0.355668	+	0.756069i
$868$	−3.51612	−	9.66046i	−0.119345	−	0.327897i
$869$	7.79289	+	44.1957i	0.264356	+	1.49923i
$870$	22.1153	+	2.00997i	0.749780	+	0.0681443i
$871$	3.40900	+	1.24078i	0.115510	+	0.0420421i
$872$	−7.33769	−	8.74472i	−0.248486	−	0.296134i
$873$	1.28222	+	7.56988i	0.0433967	+	0.256202i
$874$	−26.1826	−	2.16880i	−0.885641	−	0.0733608i
$875$			21.8750i			0.739511i
$876$	17.7681	−	17.6487i	0.600327	−	0.596294i
$877$	−11.7852	+	32.3795i	−0.397958	+	1.09338i	0.565320	+	0.824872i	$0.308753\pi$
$877$	−11.7852	+	32.3795i	−0.397958	+	1.09338i	−0.963278	+	0.268508i	$0.913470\pi$
$878$	14.7957	+	2.60888i	0.499331	+	0.0880456i
$879$	−0.00287067	−	0.0108598i	−9.68254e−5	−	0.000366291i
$880$	−8.90013	+	3.23938i	−0.300023	+	0.109200i
$881$	−18.5560	−	10.7133i	−0.625166	−	0.360940i	0.153711	−	0.988116i	$-0.450877\pi$
$881$	−18.5560	−	10.7133i	−0.625166	−	0.360940i	−0.778878	+	0.627176i	$0.784211\pi$
$882$	−7.04078	−	8.50667i	−0.237075	−	0.286434i
$883$	−26.4524	−	22.1962i	−0.890193	−	0.746960i	0.0780562	−	0.996949i	$-0.475129\pi$
$883$	−26.4524	−	22.1962i	−0.890193	−	0.746960i	−0.968249	+	0.249989i	$0.919573\pi$
$884$	0.566692	+	0.475511i	0.0190599	+	0.0159932i
$885$	14.3503	−	9.97628i	0.482380	−	0.335349i
$886$	32.0813	+	18.5222i	1.07779	+	0.622265i
$887$	28.3275	−	10.3104i	0.951145	−	0.346189i	0.180588	−	0.983559i	$-0.442200\pi$
$887$	28.3275	−	10.3104i	0.951145	−	0.346189i	0.770558	+	0.637370i	$0.219978\pi$
$888$	−9.71532	+	2.56815i	−0.326025	+	0.0861814i
$889$	23.6850	+	4.17631i	0.794370	+	0.140069i
$890$	2.95868	−	8.12889i	0.0991750	−	0.272481i
$891$	36.6848	+	21.8446i	1.22899	+	0.731821i
$892$		−	1.07435i		−	0.0359719i
$893$	45.3091	−	12.3652i	1.51621	−	0.413787i
$894$	−1.63479	−	19.4402i	−0.0546756	−	0.650176i
$895$	−7.62847	−	9.09125i	−0.254992	−	0.303887i
$896$	−1.71199	−	0.623113i	−0.0571936	−	0.0208168i
$897$	−0.418062	+	4.59986i	−0.0139587	+	0.153585i
$898$	2.01953	+	11.4533i	0.0673927	+	0.382203i
$899$	12.3937	+	34.0515i	0.413354	+	1.13568i
$900$	−1.05974	+	2.85166i	−0.0353248	+	0.0950554i
$901$	−3.54294	+	2.04552i	−0.118032	+	0.0681460i
$902$	12.1874	−	14.5243i	0.405795	−	0.483608i
$903$	−32.0484	−	22.6019i	−1.06650	−	0.752144i
$904$	0.297090	+	0.514574i	0.00988105	+	0.0171145i
$905$	−6.47953	+	11.2229i	−0.215387	+	0.373061i
$906$	−2.57738	−	5.57621i	−0.0856278	−	0.185257i
$907$	−56.6712	+	9.99267i	−1.88174	+	0.331801i	−0.992159	−	0.124981i	$-0.960113\pi$
$907$	−56.6712	+	9.99267i	−1.88174	+	0.331801i	−0.889579	+	0.456782i	$0.849002\pi$
$908$	3.25821	−	18.4782i	0.108128	−	0.613222i
$909$	−4.31011	+	23.5158i	−0.142957	+	0.779971i
$910$	−1.23277	+	1.03442i	−0.0408660	+	0.0342907i
$911$	38.7915			1.28522			0.642610	−	0.766194i	$-0.277852\pi$
$911$	38.7915			1.28522			0.642610	+	0.766194i	$0.277852\pi$
$912$	−2.59107	−	7.09129i	−0.0857989	−	0.234816i
$913$	2.86672			0.0948747
$914$	−12.0559	+	10.1161i	−0.398775	+	0.334612i
$915$	−9.40495	+	34.6324i	−0.310918	+	1.14491i
$916$	−2.01891	+	11.4498i	−0.0667066	+	0.378312i
$917$	12.6926	−	2.23804i	0.419145	−	0.0739066i
$918$	4.91109	+	7.16692i	0.162090	+	0.236543i
$919$	28.1669	−	48.7865i	0.929141	−	1.60932i	0.144379	−	0.989522i	$-0.453882\pi$
$919$	28.1669	−	48.7865i	0.929141	−	1.60932i	0.784762	−	0.619797i	$-0.212785\pi$
$920$	−6.01667	−	10.4212i	−0.198364	−	0.343576i
$921$	−13.6013	+	19.2860i	−0.448179	+	0.635497i
$922$	−3.89062	+	4.63666i	−0.128131	+	0.152700i
$923$	1.97950	−	1.14286i	0.0651559	−	0.0376178i
$924$	13.5460	+	6.37229i	0.445632	+	0.209633i
$925$	2.01225	+	5.52862i	0.0661625	+	0.181780i
$926$	1.59548	+	9.04843i	0.0524308	+	0.297350i
$927$	−46.0858	−	0.310652i	−1.51366	−	0.0102032i
$928$	6.03448	+	2.19637i	0.198092	+	0.0720994i
$929$	−31.8205	−	37.9221i	−1.04400	−	1.24418i	−0.969016	−	0.247000i	$-0.920555\pi$
$929$	−31.8205	−	37.9221i	−1.04400	−	1.24418i	−0.0749796	−	0.997185i	$-0.523889\pi$
$930$	19.4443	−	1.63514i	0.637603	−	0.0536183i
$931$	1.32447	−	15.9896i	0.0434078	−	0.524037i
$932$		−	16.2603i		−	0.532624i
$933$	14.2948	+	14.3915i	0.467991	+	0.471156i
$934$	0.0708263	−	0.194594i	0.00231751	−	0.00636730i
$935$	15.5957	+	2.74995i	0.510035	+	0.0899330i
$936$	−1.25029	+	0.445547i	−0.0408670	+	0.0145632i
$937$	21.2381	−	7.73002i	0.693817	−	0.252529i	0.0290486	−	0.999578i	$-0.490752\pi$
$937$	21.2381	−	7.73002i	0.693817	−	0.252529i	0.664769	+	0.747049i	$0.268530\pi$
$938$	12.9372	+	7.46927i	0.422413	+	0.243880i
$939$	−1.73701	−	2.49859i	−0.0566853	−	0.0815385i
$940$	16.4788	+	13.8274i	0.537480	+	0.450999i
$941$	−40.2199	−	33.7485i	−1.31113	−	1.10017i	−0.988105	−	0.153778i	$-0.950856\pi$
$941$	−40.2199	−	33.7485i	−1.31113	−	1.10017i	−0.323024	−	0.946391i	$-0.604700\pi$
$942$	−0.312281	−	0.449198i	−0.0101747	−	0.0146357i
$943$	20.8617	+	12.0445i	0.679349	+	0.392222i
$944$	4.74937	−	1.72863i	0.154579	−	0.0562620i
$945$	−17.2091	+	7.81389i	−0.559813	+	0.254186i
$946$	−58.0619	−	10.2379i	−1.88776	−	0.332862i
$947$	−9.84314	+	27.0438i	−0.319859	+	0.878805i	0.670701	+	0.741728i	$0.265993\pi$
$947$	−9.84314	+	27.0438i	−0.319859	+	0.878805i	−0.990560	+	0.137078i	$0.956229\pi$
$948$	−11.5467	−	11.6248i	−0.375021	−	0.377557i
$949$		−	6.39712i		−	0.207659i
$950$	−3.99741	+	1.88656i	−0.129693	+	0.0612082i
$951$	−12.1067	+	1.01810i	−0.392588	+	0.0330141i
$952$	1.95806	+	2.33353i	0.0634612	+	0.0756302i
$953$	1.95076	+	0.710020i	0.0631914	+	0.0229998i	0.373422	−	0.927661i	$-0.378184\pi$
$953$	1.95076	+	0.710020i	0.0631914	+	0.0229998i	−0.310231	+	0.950661i	$0.600406\pi$
$954$	0.0494775	−	7.34007i	0.00160189	−	0.237644i
$955$	8.27327	+	46.9200i	0.267717	+	1.51830i
$956$	2.33026	+	6.40234i	0.0753660	+	0.207066i
$957$	−47.7475	−	22.4613i	−1.54346	−	0.726069i
$958$	4.32862	−	2.49913i	0.139851	−	0.0807432i
$959$	10.9827	−	13.0887i	0.354651	−	0.422656i
$960$	1.99297	−	2.82593i	0.0643227	−	0.0912065i
$961$	0.420731	+	0.728727i	0.0135720	+	0.0235073i
$962$	−1.28346	+	2.22302i	−0.0413804	+	0.0716729i
$963$	48.7645	−	27.7176i	1.57142	−	0.893188i
$964$	−19.1145	+	3.37040i	−0.615636	+	0.108553i
$965$	−0.736186	+	4.17512i	−0.0236987	+	0.134402i
$966$	−4.98448	+	18.3547i	−0.160373	+	0.590552i
$967$	−2.18110	+	1.83016i	−0.0701395	+	0.0588540i	−0.677183	−	0.735814i	$-0.736800\pi$
$967$	−2.18110	+	1.83016i	−0.0701395	+	0.0588540i	0.607044	+	0.794668i	$0.292355\pi$
$968$	11.5057			0.369806
$969$	−2.17650	+	12.4345i	−0.0699192	+	0.399454i
$970$	−5.10946			−0.164055
$971$	−0.796470	+	0.668318i	−0.0255599	+	0.0214473i	−0.655478	−	0.755214i	$-0.727533\pi$
$971$	−0.796470	+	0.668318i	−0.0255599	+	0.0214473i	0.629918	+	0.776661i	$0.283088\pi$
$972$	−15.5498	+	1.09675i	−0.498761	+	0.0351784i
$973$	3.42701	−	19.4355i	0.109865	−	0.623074i
$974$	26.6575	−	4.70043i	0.854161	−	0.150612i
$975$	0.326041	+	0.705395i	0.0104417	+	0.0225907i
$976$	−5.18894	+	8.98751i	−0.166094	+	0.287683i
$977$	17.5242	+	30.3529i	0.560650	+	0.971074i	0.997440	+	0.0715108i	$0.0227820\pi$
$977$	17.5242	+	30.3529i	0.560650	+	0.971074i	−0.436790	+	0.899564i	$0.643885\pi$
$978$	1.76801	+	1.24687i	0.0565346	+	0.0398706i
$979$	−13.2128	+	15.7464i	−0.422282	+	0.503256i
$980$	6.36414	−	3.67434i	0.203295	−	0.117372i
$981$	−32.1013	−	11.9296i	−1.02492	−	0.380882i
$982$	−2.14701	−	5.89886i	−0.0685138	−	0.188240i
$983$	3.51109	+	19.9124i	0.111986	+	0.635106i	0.988198	+	0.153180i	$0.0489515\pi$
$983$	3.51109	+	19.9124i	0.111986	+	0.635106i	−0.876212	+	0.481926i	$0.839937\pi$
$984$	−0.626566	+	6.89399i	−0.0199742	+	0.219773i
$985$	−7.09625	−	2.58283i	−0.226105	−	0.0822957i
$986$	−6.90185	−	8.22531i	−0.219800	−	0.261947i
$987$	−2.84915	−	33.8808i	−0.0906895	−	1.07844i
$988$	−1.75159	−	0.806944i	−0.0557254	−	0.0256723i
$989$		−	74.9059i		−	2.38187i
$990$	−18.4105	+	21.6428i	−0.585123	+	0.687852i
$991$	4.51355	−	12.4009i	0.143378	−	0.393926i	−0.847130	−	0.531386i	$-0.821671\pi$
$991$	4.51355	−	12.4009i	0.143378	−	0.393926i	0.990507	+	0.137459i	$0.0438937\pi$
$992$	5.55710	+	0.979866i	0.176438	+	0.0311108i
$993$	2.64360	−	0.698809i	0.0838920	−	0.0221760i
$994$	8.84457	−	3.21916i	0.280533	−	0.102106i
$995$	−23.8552	−	13.7728i	−0.756261	−	0.436627i
$996$	−0.859382	+	0.597440i	−0.0272306	+	0.0189306i
$997$	20.9990	+	17.6202i	0.665045	+	0.558039i	0.911594	−	0.411091i	$-0.134852\pi$
$997$	20.9990	+	17.6202i	0.665045	+	0.558039i	−0.246549	+	0.969130i	$0.579297\pi$
$998$	16.8496	+	14.1385i	0.533365	+	0.447546i
$999$	−21.5316	+	21.1006i	−0.681231	+	0.667592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.a.89.1	yes	18
3.2	odd	2		114.2.l.b.89.3	yes	18
4.3	odd	2		912.2.cc.d.545.3		18
12.11	even	2		912.2.cc.c.545.1		18
19.3	odd	18		114.2.l.b.41.3	yes	18
57.41	even	18	inner	114.2.l.a.41.1	✓	18
76.3	even	18		912.2.cc.c.497.1		18
228.155	odd	18		912.2.cc.d.497.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.41.1	✓	18	57.41	even	18	inner
114.2.l.a.89.1	yes	18	1.1	even	1	trivial
114.2.l.b.41.3	yes	18	19.3	odd	18
114.2.l.b.89.3	yes	18	3.2	odd	2
912.2.cc.c.497.1		18	76.3	even	18
912.2.cc.c.545.1		18	12.11	even	2
912.2.cc.d.497.3		18	228.155	odd	18
912.2.cc.d.545.3		18	4.3	odd	2

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.67151 - 0.453924i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.96615 - 0.346685i) q^{5} +(1.57223 - 0.726702i) q^{6} +(0.910931 - 1.57778i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.58791 + 1.51748i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.67151 - 0.453924i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.96615 - 0.346685i) q^{5} +(1.57223 - 0.726702i) q^{6} +(0.910931 - 1.57778i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.58791 + 1.51748i) q^{9} +(-1.28331 + 1.52939i) q^{10} +(4.10844 - 2.37201i) q^{11} +(-0.737283 + 1.56730i) q^{12} +(0.151321 + 0.415752i) q^{13} +(0.316363 + 1.79418i) q^{14} +(-3.44381 - 0.312993i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.07476 + 1.28085i) q^{17} +(-2.95787 + 0.501018i) q^{18} +(-3.58212 - 2.48363i) q^{19} -1.99648i q^{20} +(-2.23882 + 2.22378i) q^{21} +(-1.62255 + 4.45791i) q^{22} +(-5.93571 - 1.04663i) q^{23} +(-0.442647 - 1.67453i) q^{24} +(-0.952914 + 0.346832i) q^{25} +(-0.383159 - 0.221217i) q^{26} +(-3.63690 - 3.71120i) q^{27} +(-1.39563 - 1.17107i) q^{28} +(4.91935 + 4.12783i) q^{29} +(2.83930 - 1.97387i) q^{30} +(4.88683 + 2.82141i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-7.94401 + 2.09992i) q^{33} +(-1.64663 - 0.290345i) q^{34} +(1.24403 - 3.41795i) q^{35} +(1.94381 - 2.28508i) q^{36} -5.80180i q^{37} +(4.34051 - 0.399967i) q^{38} +(-0.0642158 - 0.763624i) q^{39} +(1.28331 + 1.52939i) q^{40} +(-3.75563 - 1.36694i) q^{41} +(0.285618 - 3.14260i) q^{42} +(2.15807 + 12.2390i) q^{43} +(-1.62255 - 4.45791i) q^{44} +(5.61430 + 2.08640i) q^{45} +(5.21978 - 3.01364i) q^{46} +(-6.92588 + 8.25394i) q^{47} +(1.41546 + 0.998240i) q^{48} +(1.84041 + 3.18768i) q^{49} +(0.507035 - 0.878210i) q^{50} +(-1.21507 - 2.62881i) q^{51} +(0.435713 - 0.0768279i) q^{52} +(-0.424873 + 2.40957i) q^{53} +(5.17154 + 0.505189i) q^{54} +(7.25545 - 6.08805i) q^{55} +1.82186 q^{56} +(4.86017 + 5.77743i) q^{57} -6.42176 q^{58} +(-3.87172 + 3.24876i) q^{59} +(-0.906250 + 3.33714i) q^{60} +(1.80210 - 10.2202i) q^{61} +(-5.55710 + 0.979866i) q^{62} +(4.75165 - 2.70083i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.441656 + 0.764970i) q^{65} +(4.73566 - 6.71494i) q^{66} +(5.27060 - 6.28126i) q^{67} +(1.44802 - 0.836015i) q^{68} +(9.44653 + 4.44381i) q^{69} +(1.24403 + 3.41795i) q^{70} +(-0.897109 - 5.08776i) q^{71} +(-0.0202217 + 2.99993i) q^{72} +(-13.5869 - 4.94524i) q^{73} +(3.72933 + 4.44444i) q^{74} +(1.75024 - 0.147184i) q^{75} +(-3.06793 + 3.09642i) q^{76} -8.64294i q^{77} +(0.540040 + 0.543692i) q^{78} +(-3.23544 + 8.88931i) q^{79} +(-1.96615 - 0.346685i) q^{80} +(4.39452 + 7.85418i) q^{81} +(3.75563 - 1.36694i) q^{82} +(0.523324 + 0.302141i) q^{83} +(1.80123 + 2.59097i) q^{84} +(2.55719 + 2.14574i) q^{85} +(-9.52025 - 7.98844i) q^{86} +(-6.34904 - 9.13273i) q^{87} +(4.10844 + 2.37201i) q^{88} +(-4.07161 + 1.48195i) q^{89} +(-5.64191 + 2.01052i) q^{90} +(0.793809 + 0.139970i) q^{91} +(-2.06145 + 5.66379i) q^{92} +(-6.88769 - 6.93427i) q^{93} -10.7748i q^{94} +(-7.90401 - 3.64132i) q^{95} +(-1.72596 + 0.145142i) q^{96} +(1.64505 + 1.96049i) q^{97} +(-3.45884 - 1.25891i) q^{98} +(14.2317 + 0.0959322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) \) 18 * q + 3 * q^6 + 9 * q^8	\( 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) \) 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

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