LMFDB - Embedded newform 114.2.l.b.41.3

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			41.3
Root			$-0.442647 - 1.67453i$ of defining polynomial
Character	$\chi$	$=$	114.41
Dual form			114.2.l.b.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(1.57223 - 0.726702i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.96615 - 0.346685i) q^{5} +(1.67151 + 0.453924i) q^{6} +(0.910931 + 1.57778i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.94381 - 2.28508i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(1.57223 - 0.726702i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.96615 - 0.346685i) q^{5} +(1.67151 + 0.453924i) q^{6} +(0.910931 + 1.57778i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.94381 - 2.28508i) q^{9} +(-1.28331 - 1.52939i) q^{10} +(-4.10844 - 2.37201i) q^{11} +(0.988676 + 1.42215i) q^{12} +(0.151321 - 0.415752i) q^{13} +(-0.316363 + 1.79418i) q^{14} +(-3.34317 + 0.883735i) 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} +(2.57877 + 1.81865i) q^{21} +(-1.62255 - 4.45791i) q^{22} +(5.93571 - 1.04663i) q^{23} +(-0.156773 + 1.72494i) q^{24} +(-0.952914 - 0.346832i) q^{25} +(0.383159 - 0.221217i) q^{26} +(1.39554 - 5.00524i) q^{27} +(-1.39563 + 1.17107i) q^{28} +(-4.91935 + 4.12783i) q^{29} +(-3.12907 - 1.47197i) q^{30} +(4.88683 - 2.82141i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-8.18314 - 0.743731i) q^{33} +(-1.64663 + 0.290345i) q^{34} +(-1.24403 - 3.41795i) q^{35} +(2.58791 + 1.51748i) 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} +(0.806441 + 3.05077i) q^{42} +(2.15807 - 12.2390i) q^{43} +(1.62255 - 4.45791i) q^{44} +(-4.61402 + 3.81892i) q^{45} +(5.21978 + 3.01364i) q^{46} +(6.92588 + 8.25394i) q^{47} +(-1.22887 + 1.22061i) q^{48} +(1.84041 - 3.18768i) q^{49} +(-0.507035 - 0.878210i) q^{50} +(-0.758974 + 2.79482i) q^{51} +(0.435713 + 0.0768279i) q^{52} +(0.424873 + 2.40957i) q^{53} +(4.28636 - 2.93720i) q^{54} +(7.25545 + 6.08805i) q^{55} -1.82186 q^{56} +(-3.82705 + 6.50797i) q^{57} -6.42176 q^{58} +(3.87172 + 3.24876i) q^{59} +(-1.45084 - 3.13892i) q^{60} +(1.80210 + 10.2202i) q^{61} +(5.55710 + 0.979866i) q^{62} +(5.37603 + 0.985349i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.441656 + 0.764970i) q^{65} +(-5.79059 - 5.82975i) q^{66} +(5.27060 + 6.28126i) q^{67} +(-1.44802 - 0.836015i) q^{68} +(8.57172 - 5.95903i) q^{69} +(1.24403 - 3.41795i) q^{70} +(0.897109 - 5.08776i) q^{71} +(1.00703 + 2.82593i) 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} +(0.441656 - 0.626247i) q^{78} +(-3.23544 - 8.88931i) q^{79} +(1.96615 - 0.346685i) q^{80} +(-1.44321 - 8.88353i) q^{81} +(3.75563 + 1.36694i) q^{82} +(-0.523324 + 0.302141i) q^{83} +(-1.34323 + 2.85540i) q^{84} +(2.55719 - 2.14574i) q^{85} +(9.52025 - 7.98844i) q^{86} +(-4.73465 + 10.0648i) q^{87} +(4.10844 - 2.37201i) q^{88} +(4.07161 + 1.48195i) q^{89} +(-5.98930 - 0.0403723i) q^{90} +(0.793809 - 0.139970i) q^{91} +(2.06145 + 5.66379i) q^{92} +(5.63289 - 7.98717i) 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} +(-13.4062 + 4.77739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35} + 3 q^{38} + 6 q^{39} + 3 q^{41} - 6 q^{43} + 24 q^{44} - 54 q^{45} + 18 q^{46} + 30 q^{47} + 21 q^{49} + 3 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 54 q^{54} + 30 q^{55} + 12 q^{57} + 12 q^{58} + 3 q^{59} + 24 q^{60} + 54 q^{61} + 6 q^{62} - 18 q^{63} - 9 q^{64} + 24 q^{65} - 27 q^{66} - 15 q^{67} - 27 q^{68} + 30 q^{69} + 24 q^{70} + 36 q^{71} + 6 q^{72} - 42 q^{73} + 6 q^{74} - 24 q^{78} - 6 q^{79} - 3 q^{81} + 3 q^{82} + 36 q^{83} - 30 q^{84} - 6 q^{86} - 60 q^{89} - 18 q^{91} - 66 q^{93} + 6 q^{95} + 9 q^{97} + 12 q^{98} - 102 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

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
$3$	1.57223	−	0.726702i	0.907727	−	0.419561i
$3$	1.57223	−	0.726702i	0.907727	−	0.419561i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−1.96615	−	0.346685i	−0.879288	−	0.155042i	−0.284260	−	0.958747i	$-0.591748\pi$
$5$	−1.96615	−	0.346685i	−0.879288	−	0.155042i	−0.595028	+	0.803705i	$0.702859\pi$
$6$	1.67151	+	0.453924i	0.682392	+	0.185314i
$7$	0.910931	+	1.57778i	0.344300	+	0.596344i	0.985226	−	0.171258i	$-0.0547831\pi$
$7$	0.910931	+	1.57778i	0.344300	+	0.596344i	−0.640927	+	0.767602i	$0.721450\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.94381	−	2.28508i	0.647937	−	0.761694i
$10$	−1.28331	−	1.52939i	−0.405819	−	0.483636i
$11$	−4.10844	−	2.37201i	−1.23874	−	0.715187i	−0.269903	−	0.962887i	$-0.586992\pi$
$11$	−4.10844	−	2.37201i	−1.23874	−	0.715187i	−0.968837	+	0.247701i	$0.920325\pi$
$12$	0.988676	+	1.42215i	0.285406	+	0.410540i
$13$	0.151321	−	0.415752i	0.0419690	−	0.115309i	−0.916938	−	0.399030i	$-0.869347\pi$
$13$	0.151321	−	0.415752i	0.0419690	−	0.115309i	0.958907	+	0.283721i	$0.0915691\pi$
$14$	−0.316363	+	1.79418i	−0.0845516	+	0.479516i
$15$	−3.34317	+	0.883735i	−0.863203	+	0.228179i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−1.07476	+	1.28085i	−0.260668	+	0.310652i	−0.880466	−	0.474110i	$-0.842770\pi$
$17$	−1.07476	+	1.28085i	−0.260668	+	0.310652i	0.619798	+	0.784761i	$0.287214\pi$
$18$	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
$21$	2.57877	+	1.81865i	0.562733	+	0.396863i
$22$	−1.62255	−	4.45791i	−0.345928	−	0.950430i
$23$	5.93571	−	1.04663i	1.23768	−	0.218237i	0.483760	−	0.875201i	$-0.339271\pi$
$23$	5.93571	−	1.04663i	1.23768	−	0.218237i	0.753922	+	0.656964i	$0.228160\pi$
$24$	−0.156773	+	1.72494i	−0.0320011	+	0.352102i
$25$	−0.952914	−	0.346832i	−0.190583	−	0.0693665i
$26$	0.383159	−	0.221217i	0.0751437	−	0.0433843i
$27$	1.39554	−	5.00524i	0.268572	−	0.963260i
$28$	−1.39563	+	1.17107i	−0.263749	+	0.221311i
$29$	−4.91935	+	4.12783i	−0.913501	+	0.766518i	−0.972782	−	0.231723i	$-0.925564\pi$
$29$	−4.91935	+	4.12783i	−0.913501	+	0.766518i	0.0592808	+	0.998241i	$0.481119\pi$
$30$	−3.12907	−	1.47197i	−0.571288	−	0.268744i
$31$	4.88683	−	2.82141i	0.877700	−	0.506741i	0.00780088	−	0.999970i	$-0.497517\pi$
$31$	4.88683	−	2.82141i	0.877700	−	0.506741i	0.869899	+	0.493229i	$0.164184\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	−8.18314	−	0.743731i	−1.42450	−	0.129467i
$34$	−1.64663	+	0.290345i	−0.282394	+	0.0497938i
$35$	−1.24403	−	3.41795i	−0.210280	−	0.577740i
$36$	2.58791	+	1.51748i	0.431318	+	0.252913i
$37$			5.80180i			0.953811i	0.878955	+	0.476905i	$0.158242\pi$
$37$			5.80180i			0.953811i	−0.878955	+	0.476905i	$0.841758\pi$
$38$	−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	$-0.510083\pi$
$41$	3.75563	−	1.36694i	0.586530	−	0.213480i	0.618203	+	0.786019i	$0.287861\pi$
$42$	0.806441	+	3.05077i	0.124437	+	0.470744i
$43$	2.15807	−	12.2390i	0.329102	−	1.86643i	−0.150023	−	0.988683i	$-0.547935\pi$
$43$	2.15807	−	12.2390i	0.329102	−	1.86643i	0.479125	−	0.877747i	$-0.340954\pi$
$44$	1.62255	−	4.45791i	0.244608	−	0.672056i
$45$	−4.61402	+	3.81892i	−0.687818	+	0.569291i
$46$	5.21978	+	3.01364i	0.769614	+	0.444337i
$47$	6.92588	+	8.25394i	1.01024	+	1.20396i	0.978876	+	0.204453i	$0.0655414\pi$
$47$	6.92588	+	8.25394i	1.01024	+	1.20396i	0.0313665	+	0.999508i	$0.490014\pi$
$48$	−1.22887	+	1.22061i	−0.177371	+	0.176180i
$49$	1.84041	−	3.18768i	0.262916	−	0.455383i
$50$	−0.507035	−	0.878210i	−0.0717056	−	0.124198i
$51$	−0.758974	+	2.79482i	−0.106278	+	0.391353i
$52$	0.435713	+	0.0768279i	0.0604225	+	0.0106541i
$53$	0.424873	+	2.40957i	0.0583608	+	0.330981i	0.999984	−	0.00568857i	$-0.00181074\pi$
$53$	0.424873	+	2.40957i	0.0583608	+	0.330981i	−0.941623	+	0.336669i	$0.890700\pi$
$54$	4.28636	−	2.93720i	0.583299	−	0.399703i
$55$	7.25545	+	6.08805i	0.978325	+	0.820912i
$56$	−1.82186			−0.243457
$57$	−3.82705	+	6.50797i	−0.506905	+	0.862002i
$58$	−6.42176			−0.843218
$59$	3.87172	+	3.24876i	0.504055	+	0.422952i	0.859031	−	0.511923i	$-0.171067\pi$
$59$	3.87172	+	3.24876i	0.504055	+	0.422952i	−0.354977	+	0.934875i	$0.615511\pi$
$60$	−1.45084	−	3.13892i	−0.187303	−	0.405233i
$61$	1.80210	+	10.2202i	0.230735	+	1.30856i	0.851412	+	0.524498i	$0.175747\pi$
$61$	1.80210	+	10.2202i	0.230735	+	1.30856i	−0.620677	+	0.784067i	$0.713142\pi$
$62$	5.55710	+	0.979866i	0.705752	+	0.124443i
$63$	5.37603	+	0.985349i	0.677316	+	0.124142i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.441656	+	0.764970i	−0.0547806	+	0.0948828i
$66$	−5.79059	−	5.82975i	−0.712772	−	0.717593i
$67$	5.27060	+	6.28126i	0.643906	+	0.767378i	0.984982	−	0.172658i	$-0.0552356\pi$
$67$	5.27060	+	6.28126i	0.643906	+	0.767378i	−0.341075	+	0.940036i	$0.610791\pi$
$68$	−1.44802	−	0.836015i	−0.175598	−	0.101382i
$69$	8.57172	−	5.95903i	1.03191	−	0.717383i
$70$	1.24403	−	3.41795i	0.148690	−	0.408524i
$71$	0.897109	−	5.08776i	0.106467	−	0.603806i	−0.884157	−	0.467190i	$-0.845266\pi$
$71$	0.897109	−	5.08776i	0.106467	−	0.603806i	0.990624	−	0.136616i	$-0.0436226\pi$
$72$	1.00703	+	2.82593i	0.118680	+	0.333039i
$73$	−13.5869	+	4.94524i	−1.59023	+	0.578796i	−0.977396	−	0.211415i	$-0.932193\pi$
$73$	−13.5869	+	4.94524i	−1.59023	+	0.578796i	−0.612834	+	0.790212i	$0.709971\pi$
$74$	−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
$78$	0.441656	−	0.626247i	0.0500076	−	0.0709085i
$79$	−3.23544	−	8.88931i	−0.364016	−	1.00013i	−0.977595	−	0.210493i	$-0.932493\pi$
$79$	−3.23544	−	8.88931i	−0.364016	−	1.00013i	0.613580	−	0.789633i	$-0.289729\pi$
$80$	1.96615	−	0.346685i	0.219822	−	0.0387606i
$81$	−1.44321	−	8.88353i	−0.160356	−	0.987059i
$82$	3.75563	+	1.36694i	0.414740	+	0.150953i
$83$	−0.523324	+	0.302141i	−0.0574423	+	0.0331643i	−0.528446	−	0.848967i	$-0.677225\pi$
$83$	−0.523324	+	0.302141i	−0.0574423	+	0.0331643i	0.471004	+	0.882131i	$0.343892\pi$
$84$	−1.34323	+	2.85540i	−0.146558	+	0.311549i
$85$	2.55719	−	2.14574i	0.277366	−	0.232738i
$86$	9.52025	−	7.98844i	1.02659	−	0.861415i
$87$	−4.73465	+	10.0648i	−0.507608	+	1.07906i
$88$	4.10844	−	2.37201i	0.437961	−	0.252857i
$89$	4.07161	+	1.48195i	0.431590	+	0.157086i	0.548675	−	0.836036i	$-0.315133\pi$
$89$	4.07161	+	1.48195i	0.431590	+	0.157086i	−0.117084	+	0.993122i	$0.537355\pi$
$90$	−5.98930	−	0.0403723i	−0.631328	−	0.00425561i
$91$	0.793809	−	0.139970i	0.0832137	−	0.0146728i
$92$	2.06145	+	5.66379i	0.214921	+	0.590491i
$93$	5.63289	−	7.98717i	0.584104	−	0.828231i
$94$			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	−0.676037	−	0.736868i	$-0.736304\pi$
$97$	1.64505	−	1.96049i	0.167029	−	0.199057i	0.843066	+	0.537810i	$0.180748\pi$
$98$	3.45884	−	1.25891i	0.349395	−	0.127170i
$99$	−13.4062	+	4.77739i	−1.34738	+	0.480145i
$100$	0.176091	−	0.998664i	0.0176091	−	0.0998664i
$101$	−2.72562	+	7.48859i	−0.271210	+	0.745142i	0.727073	+	0.686560i	$0.240880\pi$
$101$	−2.72562	+	7.48859i	−0.271210	+	0.745142i	−0.998283	+	0.0585821i	$0.981342\pi$
$102$	−2.37788	+	1.65310i	−0.235445	+	0.163681i
$103$	−13.3041	−	7.68115i	−1.31090	−	0.756846i	−0.328651	−	0.944451i	$-0.606594\pi$
$103$	−13.3041	−	7.68115i	−1.31090	−	0.756846i	−0.982245	+	0.187605i	$0.939927\pi$
$104$	0.284391	+	0.338924i	0.0278869	+	0.0332343i
$105$	−4.43974	−	4.46977i	−0.433274	−	0.436204i
$106$	−1.22337	+	2.11894i	−0.118825	+	0.205810i
$107$	−9.34857	−	16.1922i	−0.903760	−	1.56536i	−0.822573	−	0.568660i	$-0.807462\pi$
$107$	−9.34857	−	16.1922i	−0.903760	−	1.56536i	−0.0811876	−	0.996699i	$-0.525871\pi$
$108$	5.17154	+	0.505189i	0.497631	+	0.0486118i
$109$	−11.2420	−	1.98227i	−1.07679	−	0.189867i	−0.392994	−	0.919541i	$-0.628561\pi$
$109$	−11.2420	−	1.98227i	−1.07679	−	0.189867i	−0.683795	+	0.729674i	$0.739672\pi$
$110$	1.64468	+	9.32743i	0.156814	+	0.889336i
$111$	4.21618	+	9.12177i	0.400182	+	0.865800i
$112$	−1.39563	−	1.17107i	−0.131874	−	0.110656i
$113$	−0.594179			−0.0558957			−0.0279478	−	0.999609i	$-0.508897\pi$
$113$	−0.594179			−0.0558957			−0.0279478	+	0.999609i	$0.508897\pi$
$114$	−7.11493	+	2.52541i	−0.666375	+	0.236527i
$115$	−12.0333			−1.12212
$116$	−4.91935	−	4.12783i	−0.456751	−	0.383259i
$117$	−0.655888	−	1.15393i	−0.0606369	−	0.106680i
$118$	0.877647	+	4.97738i	0.0807940	+	0.458205i
$119$	−2.99993	−	0.528968i	−0.275003	−	0.0484905i
$120$	0.906250	−	3.33714i	0.0827289	−	0.304638i
$121$	5.75283	+	9.96419i	0.522984	+	0.905835i
$122$	−5.18894	+	8.98751i	−0.469784	+	0.813691i
$123$	4.91135	−	4.87836i	0.442842	−	0.439867i
$124$	3.62714	+	4.32265i	0.325727	+	0.388186i
$125$	10.3983	+	6.00348i	0.930056	+	0.536968i
$126$	3.48491	+	4.21047i	0.310460	+	0.375098i
$127$	4.51501	−	12.4049i	0.400642	−	1.10076i	−0.561326	−	0.827595i	$-0.689709\pi$
$127$	4.51501	−	12.4049i	0.400642	−	1.10076i	0.961968	−	0.273161i	$-0.0880691\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−5.50112	−	20.8108i	−0.484347	−	1.83229i
$130$	−0.830041	+	0.302110i	−0.0727994	+	0.0264968i
$131$	−4.54726	+	5.41921i	−0.397296	+	0.473479i	−0.927193	−	0.374583i	$-0.877786\pi$
$131$	−4.54726	+	5.41921i	−0.397296	+	0.473479i	0.529898	+	0.848062i	$0.322230\pi$
$132$	−0.688555	−	8.18797i	−0.0599311	−	0.712671i
$133$	−7.18169	−	3.38937i	−0.622731	−	0.293896i
$134$			8.19960i			0.708337i
$135$	−4.47908	+	9.35724i	−0.385498	+	0.805343i
$136$	−0.571868	−	1.57119i	−0.0490373	−	0.134729i
$137$	−9.23589	+	1.62854i	−0.789075	+	0.139135i	−0.553641	−	0.832755i	$-0.686762\pi$
$137$	−9.23589	+	1.62854i	−0.789075	+	0.139135i	−0.235434	+	0.971890i	$0.575651\pi$
$138$	10.3967	+	0.944913i	0.885026	+	0.0804363i
$139$	10.1792	+	3.70494i	0.863392	+	0.314249i	0.735488	−	0.677538i	$-0.236953\pi$
$139$	10.1792	+	3.70494i	0.863392	+	0.314249i	0.127904	+	0.991787i	$0.459175\pi$
$140$	3.15000	−	1.81865i	0.266224	−	0.153704i
$141$	16.8872	+	7.94404i	1.42216	+	0.669009i
$142$	3.95758	−	3.32080i	0.332112	−	0.278675i
$143$	−1.60786	+	1.34916i	−0.134456	+	0.112822i
$144$	−1.04504	+	2.81210i	−0.0870866	+	0.234341i
$145$	11.1032	−	6.41046i	0.922074	−	0.532359i
$146$	−13.5869	−	4.94524i	−1.12446	−	0.409271i
$147$	0.577052	−	6.34920i	0.0475944	−	0.523673i
$148$	−5.71366	+	1.00747i	−0.469660	+	0.0828137i
$149$	−3.85231	−	10.5841i	−0.315594	−	0.867086i	−0.991501	−	0.130100i	$-0.958470\pi$
$149$	−3.85231	−	10.5841i	−0.315594	−	0.867086i	0.675907	−	0.736987i	$-0.263752\pi$
$150$	−1.43537	−	1.01228i	−0.117198	−	0.0826527i
$151$			3.54669i			0.288625i	0.989532	+	0.144313i	$0.0460971\pi$
$151$			3.54669i			0.288625i	−0.989532	+	0.144313i	$0.953903\pi$
$152$	−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
$156$	0.740871	−	0.195842i	0.0593172	−	0.0156799i
$157$	−0.0548481	+	0.311059i	−0.00437736	+	0.0248252i	−0.986918	−	0.161222i	$-0.948457\pi$
$157$	−0.0548481	+	0.311059i	−0.00437736	+	0.0248252i	0.982541	+	0.186047i	$0.0595677\pi$
$158$	3.23544	−	8.88931i	0.257398	−	0.707196i
$159$	2.41904	+	3.47965i	0.191842	+	0.275954i
$160$	1.72900	+	0.998240i	0.136690	+	0.0789178i
$161$	7.05837	+	8.41184i	0.556277	+	0.662946i
$162$	4.60466	−	7.73286i	0.361777	−	0.607551i
$163$	0.624535	−	1.08173i	0.0489174	−	0.0847274i	−0.840530	−	0.541765i	$-0.817756\pi$
$163$	0.624535	−	1.08173i	0.0489174	−	0.0847274i	0.889447	+	0.457038i	$0.151090\pi$
$164$	1.99833	+	3.46120i	0.156043	+	0.270275i
$165$	15.8314	+	4.29926i	1.23248	+	0.334697i
$166$	−0.595102	−	0.104933i	−0.0461889	−	0.00814435i
$167$	0.177553	+	1.00695i	0.0137395	+	0.0779205i	0.990907	−	0.134552i	$-0.0429595\pi$
$167$	0.177553	+	1.00695i	0.0137395	+	0.0779205i	−0.977167	+	0.212472i	$0.931848\pi$
$168$	−2.86438	+	1.32395i	−0.220992	+	0.102145i
$169$	9.80863	+	8.23041i	0.754510	+	0.633109i
$170$	3.33817			0.256026
$171$	−1.28765	+	13.0131i	−0.0984689	+	0.995140i
$172$	12.4278			0.947611
$173$	−11.5762	−	9.71361i	−0.880124	−	0.738512i	0.0860802	−	0.996288i	$-0.472566\pi$
$173$	−11.5762	−	9.71361i	−0.880124	−	0.738512i	−0.966205	+	0.257776i	$0.917010\pi$
$174$	−10.0965	+	4.66670i	−0.765412	+	0.353782i
$175$	−0.320814	−	1.81943i	−0.0242513	−	0.137536i
$176$	4.67194	+	0.823789i	0.352161	+	0.0620954i
$177$	8.44811	+	2.29421i	0.634998	+	0.172443i
$178$	2.16646	+	3.75242i	0.162383	+	0.281256i
$179$	2.97218	−	5.14797i	0.222151	−	0.384777i	−0.733310	−	0.679895i	$-0.762026\pi$
$179$	2.97218	−	5.14797i	0.222151	−	0.384777i	0.955461	+	0.295118i	$0.0953588\pi$
$180$	−4.56212	−	3.88078i	−0.340040	−	0.289256i
$181$	−4.17230	−	4.97236i	−0.310125	−	0.369593i	0.588358	−	0.808600i	$-0.299774\pi$
$181$	−4.17230	−	4.97236i	−0.310125	−	0.369593i	−0.898483	+	0.439008i	$0.855330\pi$
$182$	0.698064	+	0.403027i	0.0517439	+	0.0298744i
$183$	10.2604	+	14.7589i	0.758468	+	1.09101i
$184$	−2.06145	+	5.66379i	−0.151972	+	0.417540i
$185$	2.01140	−	11.4072i	0.147881	−	0.838675i
$186$	9.44910	−	2.49778i	0.692842	−	0.183146i
$187$	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	$0.668352\pi$
$192$	−1.41546	−	0.998240i	−0.102152	−	0.0720417i
$193$	−0.726280	−	1.99544i	−0.0522788	−	0.143635i	0.910805	−	0.412837i	$-0.135462\pi$
$193$	−0.726280	−	1.99544i	−0.0522788	−	0.143635i	−0.963084	+	0.269202i	$0.913240\pi$
$194$	2.52036	−	0.444407i	0.180951	−	0.0319065i
$195$	−0.138479	+	1.52366i	−0.00991669	+	0.109112i
$196$	3.45884	+	1.25891i	0.247060	+	0.0899225i
$197$	3.27574	−	1.89125i	0.233387	−	0.134746i	−0.378747	−	0.925500i	$-0.623645\pi$
$197$	3.27574	−	1.89125i	0.233387	−	0.134746i	0.612133	+	0.790755i	$0.290312\pi$
$198$	−13.3406	−	4.95768i	−0.948077	−	0.352327i
$199$	−10.5692	+	8.86860i	−0.749230	+	0.628679i	−0.935299	−	0.353858i	$-0.884870\pi$
$199$	−10.5692	+	8.86860i	−0.749230	+	0.628679i	0.186069	+	0.982537i	$0.440425\pi$
$200$	0.776823	−	0.651831i	0.0549296	−	0.0460914i
$201$	12.8512	+	6.04542i	0.906453	+	0.426411i
$202$	−6.90152	+	3.98459i	−0.485589	+	0.280355i
$203$	−10.9940	−	4.00149i	−0.771627	−	0.280849i
$204$	−2.88415	−	0.262129i	−0.201931	−	0.0183527i
$205$	−7.85802	+	1.38558i	−0.548828	+	0.0967731i
$206$	−5.25422	−	14.4358i	−0.366079	−	1.00579i
$207$	9.14627	−	15.5980i	0.635710	−	1.08414i
$208$			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	−0.280662	−	0.959807i	$-0.590554\pi$
$211$	10.3613	−	12.3481i	0.713299	−	0.850077i	0.993961	+	0.109730i	$0.0349985\pi$
$212$	−2.29919	+	0.836837i	−0.157909	+	0.0574742i
$213$	−2.28682	−	8.65106i	−0.156690	−	0.592761i
$214$	3.24672	−	18.4131i	0.221941	−	1.25869i
$215$	−8.48615	+	23.3155i	−0.578751	+	1.59010i
$216$	3.63690	+	3.71120i	0.247460	+	0.252515i
$217$	8.90313	+	5.14022i	0.604384	+	0.348941i
$218$	−7.33769	−	8.74472i	−0.496971	−	0.592267i
$219$	−17.7681	+	17.6487i	−1.20065	+	1.19259i
$220$	−4.73566	+	8.20241i	−0.319278	+	0.553006i
$221$	0.369882	+	0.640654i	0.0248809	+	0.0430951i
$222$	−2.63358	+	9.69779i	−0.176754	+	0.650873i
$223$	1.05803	+	0.186559i	0.0708508	+	0.0124929i	0.208961	−	0.977924i	$-0.432992\pi$
$223$	1.05803	+	0.186559i	0.0708508	+	0.0124929i	−0.138110	+	0.990417i	$0.544103\pi$
$224$	−0.316363	−	1.79418i	−0.0211379	−	0.119879i
$225$	−2.64482	+	1.50331i	−0.176322	+	0.100221i
$226$	−0.455168	−	0.381931i	−0.0302773	−	0.0254057i
$227$	−18.7633			−1.24536			−0.622682	−	0.782475i	$-0.713957\pi$
$227$	−18.7633			−1.24536			−0.622682	+	0.782475i	$0.713957\pi$
$228$	−7.07366	−	2.63881i	−0.468465	−	0.174760i
$229$	−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
$231$	−6.28083	−	13.5887i	−0.413249	−	0.894069i
$232$	−1.11513	−	6.32420i	−0.0732117	−	0.415204i
$233$	−16.0133	−	2.82357i	−1.04907	−	0.184979i	−0.377565	−	0.925983i	$-0.623239\pi$
$233$	−16.0133	−	2.82357i	−1.04907	−	0.184979i	−0.671500	+	0.741004i	$0.734350\pi$
$234$	0.239289	−	1.30556i	0.0156428	−	0.0853468i
$235$	−10.7558	−	18.6296i	−0.701630	−	1.21526i
$236$	−2.52708	+	4.37704i	−0.164499	+	0.284921i
$237$	−11.5467	−	11.6248i	−0.750041	−	0.755114i
$238$	−1.95806	−	2.33353i	−0.126922	−	0.151260i
$239$	5.90043	+	3.40661i	0.381667	+	0.220356i	0.678543	−	0.734560i	$-0.262612\pi$
$239$	5.90043	+	3.40661i	0.381667	+	0.220356i	−0.296876	+	0.954916i	$0.595945\pi$
$240$	2.83930	−	1.97387i	0.183276	−	0.127413i
$241$	−6.63839	+	18.2388i	−0.427616	+	1.17487i	0.519639	+	0.854386i	$0.326066\pi$
$241$	−6.63839	+	18.2388i	−0.427616	+	1.17487i	−0.947255	+	0.320480i	$0.896156\pi$
$242$	−1.99794	+	11.3309i	−0.128432	+	0.728375i
$243$	−8.72473	−	12.9182i	−0.559692	−	0.828701i
$244$	−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
$249$	−0.603219	+	0.855336i	−0.0382274	+	0.0542047i
$250$	4.10662	+	11.2829i	0.259726	+	0.713591i
$251$	16.8226	−	2.96628i	1.06183	−	0.187230i	0.384664	−	0.923057i	$-0.374317\pi$
$251$	16.8226	−	2.96628i	1.06183	−	0.187230i	0.677170	+	0.735827i	$0.263206\pi$
$252$	−0.0368412	+	5.46546i	−0.00232078	+	0.344292i
$253$	−26.8691	−	9.77955i	−1.68925	−	0.614835i
$254$	11.4324	−	6.60050i	0.717333	−	0.414152i
$255$	2.46118	−	5.23190i	0.154125	−	0.327635i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	12.1113	−	10.1626i	0.755485	−	0.633927i	−0.181462	−	0.983398i	$-0.558083\pi$
$257$	12.1113	−	10.1626i	0.755485	−	0.633927i	0.936947	+	0.349471i	$0.113639\pi$
$258$	9.16280	−	19.4780i	0.570451	−	1.21265i
$259$	−9.15396	+	5.28504i	−0.568800	+	0.328397i
$260$	−0.830041	−	0.302110i	−0.0514770	−	0.0187361i
$261$	−0.129859	+	19.2648i	−0.00803808	+	1.19246i
$262$	−6.96680	+	1.22844i	−0.430410	+	0.0758930i
$263$	0.888930	+	2.44232i	0.0548138	+	0.150600i	0.964078	−	0.265620i	$-0.0855768\pi$
$263$	0.888930	+	2.44232i	0.0548138	+	0.150600i	−0.909264	+	0.416220i	$0.863355\pi$
$264$	4.73566	−	6.71494i	0.291460	−	0.413276i
$265$		−	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	0.835039	−	0.550191i	$-0.185445\pi$
$269$	29.9875	−	10.9146i	1.82837	−	0.665473i	0.993333	−	0.115281i	$-0.0367769\pi$
$270$	−9.44589	+	4.28896i	−0.574859	+	0.261018i
$271$	−3.48942	+	19.7895i	−0.211967	+	1.20212i	0.674126	+	0.738617i	$0.264521\pi$
$271$	−3.48942	+	19.7895i	−0.211967	+	1.20212i	−0.886093	+	0.463508i	$0.846590\pi$
$272$	0.571868	−	1.57119i	0.0346746	−	0.0952676i
$273$	1.14633	−	0.796927i	0.0693792	−	0.0482322i
$274$	−8.12190	−	4.68918i	−0.490662	−	0.283284i
$275$	3.09230	+	3.68526i	0.186473	+	0.222229i
$276$	7.35696	+	7.40672i	0.442837	+	0.445832i
$277$	4.04017	−	6.99778i	0.242750	−	0.420456i	−0.718746	−	0.695272i	$-0.755284\pi$
$277$	4.04017	−	6.99778i	0.242750	−	0.420456i	0.961497	+	0.274816i	$0.0886171\pi$
$278$	5.41626	+	9.38124i	0.324846	+	0.562649i
$279$	3.05191	−	16.6511i	0.182713	−	0.996875i
$280$	3.58205	+	0.631612i	0.214068	+	0.0377460i
$281$	2.05091	+	11.6313i	0.122347	+	0.693866i	0.982848	+	0.184417i	$0.0590396\pi$
$281$	2.05091	+	11.6313i	0.122347	+	0.693866i	−0.860501	+	0.509449i	$0.829849\pi$
$282$	7.83003	+	16.9404i	0.466271	+	1.00878i
$283$	11.0055	+	9.23472i	0.654210	+	0.548947i	0.908345	−	0.418221i	$-0.137346\pi$
$283$	11.0055	+	9.23472i	0.654210	+	0.548947i	−0.254135	+	0.967169i	$0.581791\pi$
$284$	5.16625			0.306560
$285$	9.78076	−	11.4689i	0.579363	−	0.679356i
$286$	−2.09891			−0.124111
$287$	5.57784	+	4.68036i	0.329249	+	0.276273i
$288$	−2.60813	+	1.48245i	−0.153685	+	0.0873544i
$289$	2.46655	+	13.9885i	0.145091	+	0.822854i
$290$	12.6261	+	2.22633i	0.741432	+	0.130734i
$291$	1.16170	−	4.27779i	0.0681000	−	0.250769i
$292$	−7.22946	−	12.5218i	−0.423072	−	0.732782i
$293$	−0.00324263	+	0.00561639i	−0.000189436	+	0.000328113i	−0.866120	−	0.499836i	$-0.833394\pi$
$293$	−0.00324263	+	0.00561639i	−0.000189436	+	0.000328113i	0.865931	+	0.500164i	$0.166727\pi$
$294$	4.52323	−	4.49285i	0.263800	−	0.262028i
$295$	−6.48608	−	7.72981i	−0.377634	−	0.450047i
$296$	−5.02451	−	2.90090i	−0.292044	−	0.168611i
$297$	−17.6060	+	17.2535i	−1.02160	+	1.00115i
$298$	3.85231	−	10.5841i	0.223158	−	0.613122i
$299$	0.463063	−	2.62616i	0.0267797	−	0.151875i
$300$	−0.448874	−	1.69809i	−0.0259158	−	0.0980395i
$301$	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
$306$	−2.53727	+	4.32706i	−0.145046	+	0.247361i
$307$	4.66013	+	12.8036i	0.265968	+	0.730741i	0.998736	+	0.0502623i	$0.0160057\pi$
$307$	4.66013	+	12.8036i	0.265968	+	0.730741i	−0.732768	+	0.680478i	$0.761772\pi$
$308$	8.51163	−	1.50083i	0.484995	−	0.0855177i
$309$	−26.4991	−	2.40839i	−1.50748	−	0.137008i
$310$	−10.5864	−	3.85312i	−0.601266	−	0.218843i
$311$	10.1422	−	5.85560i	0.575111	−	0.332041i	−0.184077	−	0.982912i	$-0.558930\pi$
$311$	10.1422	−	5.85560i	0.575111	−	0.332041i	0.759188	+	0.650871i	$0.225596\pi$
$312$	0.693425	+	0.326199i	0.0392575	+	0.0184674i
$313$	1.34587	−	1.12932i	0.0760730	−	0.0638328i	−0.603958	−	0.797016i	$-0.706411\pi$
$313$	1.34587	−	1.12932i	0.0760730	−	0.0638328i	0.680031	+	0.733183i	$0.261966\pi$
$314$	−0.241961	+	0.203030i	−0.0136547	+	0.0114576i
$315$	−10.2285	−	3.80113i	−0.576309	−	0.214170i
$316$	8.19243	−	4.72990i	0.460860	−	0.266078i
$317$	−6.59148	−	2.39910i	−0.370214	−	0.134747i	0.150211	−	0.988654i	$-0.452005\pi$
$317$	−6.59148	−	2.39910i	−0.370214	−	0.134747i	−0.520426	+	0.853907i	$0.674227\pi$
$318$	−0.383583	+	4.22049i	−0.0215103	+	0.236674i
$319$	30.0021	−	5.29018i	1.67979	−	0.296193i
$320$	0.682836	+	1.87608i	0.0381717	+	0.104876i
$321$	−26.4650	−	18.6642i	−1.47713	−	1.04174i
$322$			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
$327$	−19.1155	+	5.05300i	−1.05709	+	0.279431i
$328$	−0.694012	+	3.93594i	−0.0383204	+	0.217326i
$329$	−6.71389	+	18.4463i	−0.370149	+	1.01698i
$330$	9.36407	+	13.4697i	0.515475	+	0.741481i
$331$	−1.36720	−	0.789353i	−0.0751481	−	0.0433868i	0.461955	−	0.886903i	$-0.347148\pi$
$331$	−1.36720	−	0.789353i	−0.0751481	−	0.0433868i	−0.537103	+	0.843517i	$0.680481\pi$
$332$	−0.388425	−	0.462907i	−0.0213176	−	0.0254053i
$333$	13.2576	+	11.2776i	0.726512	+	0.618009i
$334$	−0.511244	+	0.885501i	−0.0279740	+	0.0484525i
$335$	−8.18517	−	14.1771i	−0.447203	−	0.774579i
$336$	−3.04526	−	0.826987i	−0.166133	−	0.0451158i
$337$	32.2083	+	5.67918i	1.75450	+	0.309365i	0.956159	−	0.292847i	$-0.0946028\pi$
$337$	32.2083	+	5.67918i	1.75450	+	0.309365i	0.798336	+	0.602212i	$0.205714\pi$
$338$	2.22343	+	12.6097i	0.120939	+	0.685879i
$339$	−0.934186	+	0.431791i	−0.0507380	+	0.0234517i
$340$	2.55719	+	2.14574i	0.138683	+	0.116369i
$341$	−26.7696			−1.44966
$342$	−9.35108	+	9.14096i	−0.505649	+	0.494287i
$343$	19.4590			1.05069
$344$	9.52025	+	7.98844i	0.513297	+	0.430708i
$345$	−18.9192	+	8.74465i	−1.01857	+	0.470796i
$346$	−2.62412	−	14.8821i	−0.141073	−	0.800067i
$347$	2.28496	+	0.402900i	0.122663	+	0.0216288i	0.234643	−	0.972082i	$-0.424608\pi$
$347$	2.28496	+	0.402900i	0.122663	+	0.0216288i	−0.111980	+	0.993711i	$0.535719\pi$
$348$	−10.7341	−	2.91499i	−0.575406	−	0.156260i
$349$	6.90604	+	11.9616i	0.369672	+	0.640291i	0.989514	−	0.144436i	$-0.0461367\pi$
$349$	6.90604	+	11.9616i	0.369672	+	0.640291i	−0.619842	+	0.784727i	$0.712803\pi$
$350$	0.923748	−	1.59998i	0.0493764	−	0.0855224i
$351$	−1.86977	−	1.33760i	−0.0998007	−	0.0713958i
$352$	3.04939	+	3.63412i	0.162533	+	0.193699i
$353$	−12.6233	−	7.28806i	−0.671870	−	0.387904i	0.124915	−	0.992167i	$-0.460134\pi$
$353$	−12.6233	−	7.28806i	−0.671870	−	0.387904i	−0.796785	+	0.604263i	$0.793468\pi$
$354$	4.99694	+	7.18780i	0.265584	+	0.382027i
$355$	−3.52770	+	9.69228i	−0.187231	+	0.514413i
$356$	−0.752404	+	4.26709i	−0.0398773	+	0.226156i
$357$	−5.10098	+	1.34839i	−0.269972	+	0.0713645i
$358$	5.58587	−	2.03309i	0.295222	−	0.107452i
$359$	12.4925	−	14.8880i	0.659331	−	0.785760i	−0.327959	−	0.944692i	$-0.606361\pi$
$359$	12.4925	−	14.8880i	0.659331	−	0.785760i	0.987290	+	0.158932i	$0.0508051\pi$
$360$	−1.00027	−	5.90532i	−0.0527190	−	0.311238i
$361$	6.66313	−	17.7933i	0.350691	−	0.936491i
$362$		−	6.49095i		−	0.341157i
$363$	16.2858	+	11.4854i	0.854780	+	0.602827i
$364$	0.275687	+	0.757443i	0.0144499	+	0.0397008i
$365$	28.4284	−	5.01269i	1.48801	−	0.262376i
$366$	−1.62697	+	17.9012i	−0.0850429	+	0.935712i
$367$	−7.10474	−	2.58591i	−0.370865	−	0.134984i	0.149863	−	0.988707i	$-0.452117\pi$
$367$	−7.10474	−	2.58591i	−0.370865	−	0.134984i	−0.520727	+	0.853723i	$0.674339\pi$
$368$	−5.21978	+	3.01364i	−0.272100	+	0.157097i
$369$	4.17666	−	11.2390i	0.217428	−	0.585078i
$370$	8.87323	−	7.44553i	0.461297	−	0.387074i
$371$	−3.41475	+	2.86531i	−0.177285	+	0.148760i
$372$	8.84397	+	4.16036i	0.458539	+	0.215704i
$373$	−5.00566	+	2.89002i	−0.259183	+	0.149640i	−0.623962	−	0.781455i	$-0.714478\pi$
$373$	−5.00566	+	2.89002i	−0.259183	+	0.149640i	0.364779	+	0.931094i	$0.381145\pi$
$374$	7.45377	+	2.71295i	0.385425	+	0.140283i
$375$	20.7113	+	1.88236i	1.06953	+	0.0972049i
$376$	−10.6111	+	1.87102i	−0.547224	+	0.0964903i
$377$	0.971750	+	2.66986i	0.0500477	+	0.137505i
$378$	8.53883	+	4.08733i	0.439190	+	0.210230i
$379$		−	31.0884i		−	1.59690i	−0.602058	−	0.798452i	$-0.705653\pi$
$379$		−	31.0884i		−	1.59690i	0.602058	−	0.798452i	$-0.294347\pi$
$380$	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	$-0.665901\pi$
$383$	−6.29971	+	2.29291i	−0.321900	+	0.117162i	0.176016	+	0.984387i	$0.443679\pi$
$384$	−0.442647	−	1.67453i	−0.0225887	−	0.0854532i
$385$	−2.99638	+	16.9933i	−0.152709	+	0.866058i
$386$	0.726280	−	1.99544i	0.0369667	−	0.101565i
$387$	−23.7722	−	28.7216i	−1.20841	−	1.46000i
$388$	2.21636	+	1.27962i	0.112519	+	0.0649628i
$389$	22.9366	+	27.3348i	1.16293	+	1.38593i	0.908000	+	0.418971i	$0.137609\pi$
$389$	22.9366	+	27.3348i	1.16293	+	1.38593i	0.254933	+	0.966959i	$0.417947\pi$
$390$	−1.08547	+	1.07818i	−0.0549649	+	0.0545957i
$391$	−5.03890	+	8.72763i	−0.254828	+	0.441375i
$392$	1.84041	+	3.18768i	0.0929547	+	0.161002i
$393$	−3.21118	+	11.8247i	−0.161983	+	0.596479i
$394$	3.72503	+	0.656824i	0.187664	+	0.0330903i
$395$	3.27957	+	18.5994i	0.165013	+	0.935837i
$396$	−7.03278	−	12.3730i	−0.353410	−	0.621766i
$397$	−23.1763	−	19.4472i	−1.16319	−	0.976029i	−0.163242	−	0.986586i	$-0.552195\pi$
$397$	−23.1763	−	19.4472i	−1.16319	−	0.976029i	−0.999944	+	0.0105571i	$0.996640\pi$
$398$	−13.7971			−0.691586
$399$	−13.7543	−	0.109926i	−0.688577	−	0.00550318i
$400$	1.01407			0.0507035
$401$	−14.3394	−	12.0322i	−0.716074	−	0.600858i	0.210222	−	0.977654i	$-0.432581\pi$
$401$	−14.3394	−	12.0322i	−0.716074	−	0.600858i	−0.926296	+	0.376796i	$0.877026\pi$
$402$	5.95866	+	12.8916i	0.297191	+	0.642977i
$403$	−0.433526	−	2.45865i	−0.0215955	−	0.122474i
$404$	−7.84812	−	1.38383i	−0.390458	−	0.0688484i
$405$	−0.242228	+	17.9667i	−0.0120364	+	0.892772i
$406$	−5.84978	−	10.1321i	−0.290320	−	0.502848i
$407$	13.7619	−	23.8363i	0.682153	−	1.18152i
$408$	−2.04090	−	2.05470i	−0.101039	−	0.101723i
$409$	−9.76955	−	11.6429i	−0.483073	−	0.575704i	0.468369	−	0.883533i	$-0.344842\pi$
$409$	−9.76955	−	11.6429i	−0.483073	−	0.575704i	−0.951442	+	0.307829i	$0.900398\pi$
$410$	−6.91022	−	3.98962i	−0.341272	−	0.197033i
$411$	−13.3375	+	9.27216i	−0.657889	+	0.457362i
$412$	5.25422	−	14.4358i	0.258857	−	0.711203i
$413$	−1.59895	+	9.06811i	−0.0786793	+	0.446212i
$414$	17.0327	−	6.06968i	0.837110	−	0.298309i
$415$	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	$0.947334\pi$
$420$	3.63091	−	5.14845i	0.177170	−	0.251219i
$421$	5.11036	+	14.0406i	0.249064	+	0.684297i	0.999721	+	0.0236056i	$0.00751459\pi$
$421$	5.11036	+	14.0406i	0.249064	+	0.684297i	−0.750658	+	0.660691i	$0.770263\pi$
$422$	15.8744	−	2.79908i	0.772753	−	0.136257i
$423$	32.3235	+	0.217884i	1.57162	+	0.0105939i
$424$	−2.29919	−	0.836837i	−0.111659	−	0.0406404i
$425$	1.46839	−	0.847778i	0.0712276	−	0.0411233i
$426$	3.80899	−	8.09703i	0.184546	−	0.392303i
$427$	−14.4836	+	12.1532i	−0.700913	+	0.588136i
$428$	14.3228	−	12.0183i	0.692321	−	0.580926i
$429$	−1.54749	+	3.28962i	−0.0747137	+	0.158824i
$430$	−21.4877	+	12.4059i	−1.03623	+	0.598267i
$431$	−12.6508	−	4.60452i	−0.609368	−	0.221792i	0.0188586	−	0.999822i	$-0.493997\pi$
$431$	−12.6508	−	4.60452i	−0.609368	−	0.221792i	−0.628227	+	0.778030i	$0.716219\pi$
$432$	0.400514	+	5.18069i	0.0192697	+	0.249256i
$433$	16.6663	−	2.93872i	0.800933	−	0.141226i	0.241824	−	0.970320i	$-0.422254\pi$
$433$	16.6663	−	2.93872i	0.800933	−	0.141226i	0.559109	+	0.829094i	$0.311143\pi$
$434$	3.51612	+	9.66046i	0.168779	+	0.463717i
$435$	12.7983	−	18.1474i	0.613634	−	0.870103i
$436$		−	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	−0.945574	−	0.325407i	$-0.894499\pi$
$439$	−9.65722	+	11.5090i	−0.460914	+	0.549296i	0.484660	+	0.874702i	$0.338943\pi$
$440$	−8.90013	+	3.23938i	−0.424297	+	0.154432i
$441$	−3.70671	−	10.4017i	−0.176510	−	0.495321i
$442$	−0.128459	+	0.728525i	−0.00611015	+	0.0346524i
$443$	12.6699	−	34.8103i	0.601966	−	1.65389i	−0.145320	−	0.989385i	$-0.546421\pi$
$443$	12.6699	−	34.8103i	0.601966	−	1.65389i	0.747286	−	0.664503i	$-0.231357\pi$
$444$	−8.25105	+	5.73610i	−0.391578	+	0.272223i
$445$	−7.49163	−	4.32529i	−0.355137	−	0.205039i
$446$	0.690579	+	0.823000i	0.0326999	+	0.0389702i
$447$	−13.7482	−	13.8412i	−0.650269	−	0.654667i
$448$	0.910931	−	1.57778i	0.0430374	−	0.0745430i
$449$	−5.81501	−	10.0719i	−0.274427	−	0.475322i	0.695563	−	0.718465i	$-0.255155\pi$
$449$	−5.81501	−	10.0719i	−0.274427	−	0.475322i	−0.969991	+	0.243143i	$0.921822\pi$
$450$	−2.99236	−	0.548457i	−0.141061	−	0.0258545i
$451$	−18.6721	−	3.29240i	−0.879236	−	0.155033i
$452$	−0.103178	−	0.585152i	−0.00485309	−	0.0275233i
$453$	2.57738	+	5.57621i	0.121096	+	0.261993i
$454$	−14.3735	−	12.0608i	−0.674583	−	0.566042i
$455$	−1.60927			−0.0754438
$456$	−3.72254	−	6.56831i	−0.174324	−	0.307589i
$457$	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
$459$	4.91109	+	7.16692i	0.229230	+	0.334523i
$460$	−2.08957	−	11.8505i	−0.0974266	−	0.552534i
$461$	−5.96078	−	1.05105i	−0.277621	−	0.0489521i	0.0331039	−	0.999452i	$-0.489461\pi$
$461$	−5.96078	−	1.05105i	−0.277621	−	0.0489521i	−0.310725	+	0.950500i	$0.600572\pi$
$462$	3.92323	−	14.4468i	0.182525	−	0.672125i
$463$	4.59401	+	7.95705i	0.213502	+	0.369796i	0.952808	−	0.303574i	$-0.0981798\pi$
$463$	4.59401	+	7.95705i	0.213502	+	0.369796i	−0.739306	+	0.673369i	$0.764846\pi$
$464$	3.21088	−	5.56141i	0.149061	−	0.258182i
$465$	−13.8441	+	13.7511i	−0.642006	+	0.637693i
$466$	−10.4519	−	12.4561i	−0.484176	−	0.577019i
$467$	0.179338	+	0.103541i	0.00829879	+	0.00479131i	0.504144	−	0.863620i	$-0.331808\pi$
$467$	0.179338	+	0.103541i	0.00829879	+	0.00479131i	−0.495845	+	0.868411i	$0.665142\pi$
$468$	1.02250	−	0.846301i	0.0472651	−	0.0391203i
$469$	−5.10928	+	14.0376i	−0.235925	+	0.648198i
$470$	3.73544	−	21.1848i	0.172303	−	0.977180i
$471$	0.139813	+	0.528915i	0.00644226	+	0.0243711i
$472$	−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
$477$	6.33195	+	3.71288i	0.289920	+	0.170001i
$478$	2.33026	+	6.40234i	0.106584	+	0.292836i
$479$	4.92232	−	0.867938i	0.224907	−	0.0396571i	−0.0600591	−	0.998195i	$-0.519129\pi$
$479$	4.92232	−	0.867938i	0.224907	−	0.0396571i	0.284966	+	0.958538i	$0.408018\pi$
$480$	3.44381	+	0.312993i	0.157188	+	0.0142861i
$481$	2.41211	+	0.877937i	0.109983	+	0.0400305i
$482$	−16.8090	+	9.70467i	−0.765628	+	0.442036i
$483$	17.2103	+	8.09601i	0.783094	+	0.368381i
$484$	−8.81384	+	7.39569i	−0.400629	+	0.336168i
$485$	−3.91408	+	3.28430i	−0.177729	+	0.149132i
$486$	1.62011	−	15.5040i	0.0734896	−	0.703278i
$487$	−23.4422	+	13.5344i	−1.06227	+	0.613300i	−0.926059	−	0.377380i	$-0.876825\pi$
$487$	−23.4422	+	13.5344i	−1.06227	+	0.613300i	−0.136209	+	0.990680i	$0.543492\pi$
$488$	−9.75201	−	3.54944i	−0.441453	−	0.160676i
$489$	0.195820	−	2.15457i	0.00885529	−	0.0974332i
$490$	−7.23704	+	1.27608i	−0.326936	+	0.0576476i
$491$	2.14701	+	5.89886i	0.0968931	+	0.266212i	0.978664	−	0.205466i	$-0.0658709\pi$
$491$	2.14701	+	5.89886i	0.0968931	+	0.266212i	−0.881771	+	0.471677i	$0.843649\pi$
$492$	5.65709	+	3.98962i	0.255041	+	0.179866i
$493$		−	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
$498$	−1.01189	+	0.267484i	−0.0453440	+	0.0119862i
$499$	−3.81949	+	21.6614i	−0.170984	+	0.969699i	0.771694	+	0.635994i	$0.219410\pi$
$499$	−3.81949	+	21.6614i	−0.170984	+	0.969699i	−0.942678	+	0.333704i	$0.891701\pi$
$500$	−4.10662	+	11.2829i	−0.183654	+	0.504585i
$501$	1.01091	+	1.45414i	0.0451641	+	0.0649660i
$502$	14.7935	+	8.54106i	0.660268	+	0.381206i
$503$	−6.51623	−	7.76574i	−0.290544	−	0.346257i	0.600952	−	0.799285i	$-0.294788\pi$
$503$	−6.51623	−	7.76574i	−0.290544	−	0.346257i	−0.891496	+	0.453028i	$0.850344\pi$
$504$	−3.54135	+	4.16311i	−0.157744	+	0.185439i
$505$	7.95516	−	13.7787i	0.354000	−	0.613146i
$506$	−14.2967	−	24.7627i	−0.635568	−	1.10084i
$507$	21.4025	+	5.81216i	0.950517	+	0.258127i
$508$	13.0005	+	2.29233i	0.576802	+	0.101706i
$509$	−1.94826	−	11.0492i	−0.0863553	−	0.489745i	−0.997056	−	0.0766782i	$-0.975569\pi$
$509$	−1.94826	−	11.0492i	−0.0863553	−	0.489745i	0.910701	−	0.413067i	$-0.135543\pi$
$510$	5.24837	−	2.42586i	0.232402	−	0.107419i
$511$	−20.1793	−	16.9324i	−0.892678	−	0.749045i
$512$	1.00000			0.0441942
$513$	7.43220	+	21.3954i	0.328139	+	0.944629i
$514$	15.8102			0.697360
$515$	23.4950	+	19.7146i	1.03531	+	0.868730i
$516$	19.5394	−	9.03130i	0.860172	−	0.397581i
$517$	−8.87612	−	50.3390i	−0.390371	−	2.21391i
$518$	−10.4095	−	1.83548i	−0.457367	−	0.0806462i
$519$	−25.2594	−	6.85956i	−1.10876	−	0.301101i
$520$	−0.441656	−	0.764970i	−0.0193679	−	0.0335461i
$521$	−22.3984	+	38.7951i	−0.981290	+	1.69964i	−0.323904	+	0.946090i	$0.604995\pi$
$521$	−22.3984	+	38.7951i	−0.981290	+	1.69964i	−0.657386	+	0.753554i	$0.728338\pi$
$522$	−12.4827	+	14.6743i	−0.546352	+	0.642275i
$523$	25.4174	+	30.2913i	1.11143	+	1.32455i	0.940705	+	0.339226i	$0.110165\pi$
$523$	25.4174	+	30.2913i	1.11143	+	1.32455i	0.170721	+	0.985319i	$0.445390\pi$
$524$	−6.12650	−	3.53714i	−0.267638	−	0.154521i
$525$	−1.82657	−	2.62742i	−0.0797182	−	0.114670i
$526$	−0.888930	+	2.44232i	−0.0387592	+	0.106490i
$527$	−1.63837	+	9.29163i	−0.0713683	+	0.404750i
$528$	7.94401	−	2.09992i	0.345719	−	0.0913873i
$529$	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
$534$	6.13306	+	4.32529i	0.265404	+	0.187174i
$535$	12.7671	+	35.0773i	0.551969	+	1.51652i
$536$	−8.07503	+	1.42385i	−0.348788	+	0.0615008i
$537$	0.931913	−	10.2537i	0.0402150	−	0.442479i
$538$	29.9875	+	10.9146i	1.29285	+	0.470560i
$539$	−15.1224	+	8.73093i	−0.651368	+	0.376068i
$540$	−9.99287	−	2.78617i	−0.430024	−	0.119898i
$541$	9.00083	−	7.55259i	0.386976	−	0.324711i	−0.428458	−	0.903562i	$-0.640943\pi$
$541$	9.00083	−	7.55259i	0.386976	−	0.324711i	0.815434	+	0.578850i	$0.196499\pi$
$542$	−15.3935	+	12.9167i	−0.661207	+	0.554818i
$543$	−10.1732	−	4.78567i	−0.436576	−	0.205373i
$544$	1.44802	−	0.836015i	0.0620834	−	0.0358438i
$545$	21.4162	+	7.79487i	0.917370	+	0.333895i
$546$	1.39040	+	0.126367i	0.0595035	+	0.00540802i
$547$	3.60851	−	0.636278i	0.154289	−	0.0272053i	−0.0959702	−	0.995384i	$-0.530595\pi$
$547$	3.60851	−	0.636278i	0.154289	−	0.0272053i	0.250259	+	0.968179i	$0.419484\pi$
$548$	−3.20759	−	8.81278i	−0.137021	−	0.376463i
$549$	26.8570	+	15.7482i	1.14623	+	0.672117i
$550$			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
$555$	−5.12726	−	19.3964i	−0.217640	−	0.823333i
$556$	−1.88105	+	10.6679i	−0.0797742	+	0.452422i
$557$	4.53013	−	12.4464i	0.191948	−	0.527372i	−0.805964	−	0.591965i	$-0.798353\pi$
$557$	4.53013	−	12.4464i	0.191948	−	0.527372i	0.997912	+	0.0645925i	$0.0205747\pi$
$558$	13.0410	−	10.7938i	0.552070	−	0.456936i
$559$	−4.76183	−	2.74924i	−0.201404	−	0.116281i
$560$	2.33802	+	2.78634i	0.0987993	+	0.117744i
$561$	9.74752	−	9.68204i	0.411541	−	0.408776i
$562$	−5.90537	+	10.2284i	−0.249103	+	0.431459i
$563$	−2.30395	−	3.99056i	−0.0970999	−	0.168182i	0.813383	−	0.581728i	$-0.197623\pi$
$563$	−2.30395	−	3.99056i	−0.0970999	−	0.168182i	−0.910483	+	0.413546i	$0.864290\pi$
$564$	−4.89092	+	18.0101i	−0.205945	+	0.758363i
$565$	1.16824	+	0.205993i	0.0491484	+	0.00866619i
$566$	2.49475	+	14.1484i	0.104862	+	0.594702i
$567$	12.7016	−	10.3693i	0.533416	−	0.435472i
$568$	3.95758	+	3.32080i	0.166056	+	0.139338i
$569$	24.3659			1.02147			0.510736	−	0.859738i	$-0.329373\pi$
$569$	24.3659			1.02147			0.510736	+	0.859738i	$0.329373\pi$
$570$	14.8645	−	2.49870i	0.622607	−	0.104659i
$571$	−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
$573$	17.3420	+	37.5196i	0.724470	+	1.56740i
$574$	1.26439	+	7.17073i	0.0527748	+	0.299301i
$575$	−6.01923	−	1.06135i	−0.251019	−	0.0442614i
$576$	−2.95084	−	0.540847i	−0.122952	−	0.0225353i
$577$	−2.59042	−	4.48675i	−0.107841	−	0.186786i	0.807055	−	0.590477i	$-0.201060\pi$
$577$	−2.59042	−	4.48675i	−0.107841	−	0.186786i	−0.914895	+	0.403691i	$0.867727\pi$
$578$	−7.10216	+	12.3013i	−0.295411	+	0.511667i
$579$	−2.59197	−	2.60950i	−0.107718	−	0.108447i
$580$	8.24112	+	9.82139i	0.342194	+	0.407811i
$581$	−0.953424	−	0.550460i	−0.0395547	−	0.0228369i
$582$	3.63963	−	2.53026i	0.150867	−	0.104882i
$583$	3.96996	−	10.9074i	0.164419	−	0.451738i
$584$	2.51076	−	14.2392i	0.103896	−	0.589224i
$585$	0.889525	+	2.49618i	0.0367773	+	0.103204i
$586$	−0.00609414	+	0.00221809i	−0.000251747	+	9.16283e-5i
$587$	19.9370	−	23.7599i	0.822887	−	0.980678i	−0.177107	−	0.984192i	$-0.556674\pi$
$587$	19.9370	−	23.7599i	0.822887	−	0.980678i	0.999994	+	0.00351357i	$0.00111841\pi$
$588$	6.35294	−	0.534241i	0.261991	−	0.0220317i
$589$	−10.4978	+	22.2437i	−0.432556	+	0.916536i
$590$		−	10.0905i		−	0.415421i
$591$	3.77584	−	5.35396i	0.155317	−	0.220232i
$592$	−1.98433	−	5.45191i	−0.0815556	−	0.224072i
$593$	−19.0316	+	3.35579i	−0.781536	+	0.137806i	−0.550161	−	0.835059i	$-0.685434\pi$
$593$	−19.0316	+	3.35579i	−0.781536	+	0.137806i	−0.231375	+	0.972865i	$0.574322\pi$
$594$	−24.5773	+	1.90004i	−1.00842	+	0.0779598i
$595$	5.71492	+	2.08006i	0.234289	+	0.0852742i
$596$	9.75439	−	5.63170i	0.399555	−	0.230683i
$597$	−10.1724	+	21.6241i	−0.416327	+	0.885016i
$598$	2.04279	−	1.71411i	0.0835360	−	0.0700950i
$599$	−14.4631	+	12.1360i	−0.590946	+	0.495863i	−0.888521	−	0.458836i	$-0.848267\pi$
$599$	−14.4631	+	12.1360i	−0.590946	+	0.495863i	0.297575	+	0.954698i	$0.403822\pi$
$600$	0.747656	−	1.58935i	0.0305229	−	0.0648848i
$601$	−9.35958	+	5.40376i	−0.381785	+	0.220424i	−0.678595	−	0.734513i	$-0.737411\pi$
$601$	−9.35958	+	5.40376i	−0.381785	+	0.220424i	0.296809	+	0.954937i	$0.404077\pi$
$602$	21.2763	+	7.74393i	0.867156	+	0.315619i
$603$	24.5982	+	0.165810i	1.00172	+	0.00675231i
$604$	−3.49280	+	0.615876i	−0.142120	+	0.0250596i
$605$	−7.85648	−	21.5855i	−0.319411	−	0.877575i
$606$	−7.95516	+	11.2800i	−0.323156	+	0.458220i
$607$		−	7.06408i		−	0.286722i	−0.989670	−	0.143361i	$-0.954209\pi$
$607$		−	7.06408i		−	0.286722i	0.989670	−	0.143361i	$-0.0457910\pi$
$608$	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
$612$	−4.72504	+	1.68379i	−0.190998	+	0.0680633i
$613$	−5.48141	+	31.0866i	−0.221392	+	1.25558i	0.648071	+	0.761580i	$0.275576\pi$
$613$	−5.48141	+	31.0866i	−0.221392	+	1.25558i	−0.869463	+	0.493998i	$0.835535\pi$
$614$	−4.66013	+	12.8036i	−0.188068	+	0.516712i
$615$	−11.3477	+	7.88888i	−0.457583	+	0.318110i
$616$	7.48500	+	4.32147i	0.301579	+	0.174117i
$617$	−19.6647	−	23.4355i	−0.791672	−	0.943478i	0.207725	−	0.978187i	$-0.433394\pi$
$617$	−19.6647	−	23.4355i	−0.791672	−	0.943478i	−0.999397	+	0.0347092i	$0.988950\pi$
$618$	−18.7514	−	18.8782i	−0.754291	−	0.759393i
$619$	21.8906	−	37.9157i	0.879859	−	1.52396i	0.0283650	−	0.999598i	$-0.490970\pi$
$619$	21.8906	−	37.9157i	0.879859	−	1.52396i	0.851494	−	0.524364i	$-0.175697\pi$
$620$	−5.63289	−	9.75645i	−0.226222	−	0.391829i
$621$	3.04491	−	31.1703i	0.122188	−	1.25082i
$622$	11.5333	+	2.03363i	0.462442	+	0.0815411i
$623$	1.37078	+	7.77406i	0.0549190	+	0.311461i
$624$	0.321518	+	0.695608i	0.0128710	+	0.0278466i
$625$	−14.4792	−	12.1495i	−0.579170	−	0.485981i
$626$	1.75691			0.0702201
$627$	31.1601	−	17.6598i	1.24442	−	0.705264i
$628$	−0.315858			−0.0126041
$629$	−7.43124	−	6.23555i	−0.296303	−	0.248628i
$630$	−5.39214	−	9.48657i	−0.214828	−	0.377954i
$631$	0.0934107	+	0.529758i	0.00371862	+	0.0210893i	0.986611	−	0.163094i	$-0.0521472\pi$
$631$	0.0934107	+	0.529758i	0.00371862	+	0.0210893i	−0.982892	+	0.184183i	$0.941036\pi$
$632$	9.31609	+	1.64268i	0.370574	+	0.0653422i
$633$	7.31692	−	26.9436i	0.290822	−	1.07091i
$634$	−3.50725	−	6.07474i	−0.139291	−	0.241259i
$635$	−13.1778	+	22.8246i	−0.522944	+	0.905765i
$636$	−3.00672	+	2.98652i	−0.119224	+	0.118423i
$637$	−1.04679	−	1.24752i	−0.0414755	−	0.0494285i
$638$	26.3834	+	15.2325i	1.04453	+	0.603059i
$639$	−9.88214	−	11.9396i	−0.390932	−	0.472324i
$640$	−0.682836	+	1.87608i	−0.0269915	+	0.0741585i
$641$	4.01897	−	22.7927i	0.158740	−	0.900259i	−0.796547	−	0.604577i	$-0.793342\pi$
$641$	4.01897	−	22.7927i	0.158740	−	0.900259i	0.955287	−	0.295682i	$-0.0955467\pi$
$642$	−8.27622	−	31.3090i	−0.326637	−	1.23567i
$643$	−8.18931	+	2.98066i	−0.322955	+	0.117546i	−0.498410	−	0.866941i	$-0.666083\pi$
$643$	−8.18931	+	2.98066i	−0.322955	+	0.117546i	0.175455	+	0.984487i	$0.443860\pi$
$644$	−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	$0.712569\pi$
$648$	8.41497	+	3.19191i	0.330571	+	0.125390i
$649$	−8.20063	−	22.5310i	−0.321903	−	0.884421i
$650$	−0.441843	+	0.0779089i	−0.0173305	+	0.00305584i
$651$	17.7332	+	1.61169i	0.695018	+	0.0631672i
$652$	1.17374	+	0.427207i	0.0459673	+	0.0167307i
$653$	1.49337	−	0.862200i	0.0584402	−	0.0337405i	−0.470495	−	0.882403i	$-0.655925\pi$
$653$	1.49337	−	0.862200i	0.0584402	−	0.0337405i	0.528935	+	0.848662i	$0.322591\pi$
$654$	−17.8913	−	8.41640i	−0.699607	−	0.329107i
$655$	10.8193	−	9.07851i	0.422747	−	0.354727i
$656$	−3.06162	+	2.56900i	−0.119536	+	0.100303i
$657$	−15.1101	+	40.6599i	−0.589502	+	1.58629i
$658$	−17.0002	+	9.81505i	−0.662736	+	0.382631i
$659$	−22.0705	−	8.03300i	−0.859744	−	0.312921i	−0.125737	−	0.992064i	$-0.540130\pi$
$659$	−22.0705	−	8.03300i	−0.859744	−	0.312921i	−0.734006	+	0.679142i	$0.762352\pi$
$660$	−1.48484	+	16.3375i	−0.0577975	+	0.635935i
$661$	10.0686	−	1.77536i	0.391622	−	0.0690535i	0.0256300	−	0.999671i	$-0.491841\pi$
$661$	10.0686	−	1.77536i	0.391622	−	0.0690535i	0.365992	+	0.930618i	$0.380730\pi$
$662$	−0.539949	−	1.48350i	−0.0209857	−	0.0576578i
$663$	1.04710	+	0.738461i	0.0406661	+	0.0286795i
$664$		−	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
$669$	1.79904	−	0.475558i	0.0695548	−	0.0183861i
$670$	2.84268	−	16.1216i	0.109822	−	0.622833i
$671$	16.8386	−	46.2637i	0.650047	−	1.78599i
$672$	−1.80123	−	2.59097i	−0.0694840	−	0.0999487i
$673$	−32.9000	−	18.9948i	−1.26820	−	0.732197i	−0.293555	−	0.955942i	$-0.594838\pi$
$673$	−32.9000	−	18.9948i	−1.26820	−	0.732197i	−0.974648	+	0.223745i	$0.928172\pi$
$674$	21.0224	+	25.0536i	0.809754	+	0.965028i
$675$	−3.06581	+	4.28555i	−0.118003	+	0.164951i
$676$	−6.40213	+	11.0888i	−0.246236	+	0.426493i
$677$	16.1698	+	28.0070i	0.621457	+	1.07640i	0.989215	+	0.146474i	$0.0467925\pi$
$677$	16.1698	+	28.0070i	0.621457	+	1.07640i	−0.367757	+	0.929922i	$0.619874\pi$
$678$	−0.993178	−	0.269712i	−0.0381428	−	0.0103582i
$679$	4.59174	+	0.809648i	0.176215	+	0.0310714i
$680$	0.579668	+	3.28746i	0.0222292	+	0.126068i
$681$	−29.5002	+	13.6353i	−1.13045	+	0.522506i
$682$	−20.5067	−	17.2072i	−0.785243	−	0.658897i
$683$	27.4952			1.05208			0.526038	−	0.850461i	$-0.323677\pi$
$683$	27.4952			1.05208			0.526038	+	0.850461i	$0.323677\pi$
$684$	−13.0390	+	0.991624i	−0.498560	+	0.0379157i
$685$	18.7237			0.715396
$686$	14.9064	+	12.5080i	0.569131	+	0.477557i
$687$	−18.2794	+	8.44895i	−0.697403	+	0.322347i
$688$	2.15807	+	12.2390i	0.0822755	+	0.466607i
$689$	1.06608	+	0.187978i	0.0406144	+	0.00716141i
$690$	−20.1139	−	5.46222i	−0.765722	−	0.207943i
$691$	8.55714	+	14.8214i	0.325529	+	0.563833i	0.981619	−	0.190850i	$-0.0611243\pi$
$691$	8.55714	+	14.8214i	0.325529	+	0.563833i	−0.656090	+	0.754682i	$0.727791\pi$
$692$	7.55585	−	13.0871i	0.287230	−	0.497497i
$693$	−19.7498	−	16.8002i	−0.750234	−	0.638188i
$694$	1.49140	+	1.77738i	0.0566128	+	0.0674685i
$695$	−18.7294	−	10.8134i	−0.710448	−	0.410178i
$696$	−6.34904	−	9.13273i	−0.240660	−	0.346175i
$697$	−2.28556	+	6.27952i	−0.0865717	+	0.237854i
$698$	−2.39844	+	13.6023i	−0.0907824	+	0.514853i
$699$	−27.2285	+	7.19757i	−1.02987	+	0.272237i
$700$	1.73608	−	0.631881i	0.0656176	−	0.0238828i
$701$	−24.3781	+	29.0527i	−0.920748	+	1.09730i	0.0742333	+	0.997241i	$0.476349\pi$
$701$	−24.3781	+	29.0527i	−0.920748	+	1.09730i	−0.994981	+	0.100064i	$0.968095\pi$
$702$	−0.572531	−	2.22652i	−0.0216088	−	0.0840347i
$703$	−14.4096	−	20.7827i	−0.543467	−	0.783836i
$704$			4.74401i			0.178797i
$705$	−30.4487	−	21.4737i	−1.14676	−	0.808746i
$706$	−4.98533	−	13.6971i	−0.187625	−	0.515496i
$707$	−14.2982	+	2.52116i	−0.537739	+	0.0948178i
$708$	−0.792355	+	8.71814i	−0.0297785	+	0.327648i
$709$	−18.3247	−	6.66963i	−0.688197	−	0.250483i	−0.0258338	−	0.999666i	$-0.508224\pi$
$709$	−18.3247	−	6.66963i	−0.688197	−	0.250483i	−0.662363	+	0.749183i	$0.730446\pi$
$710$	−8.93245	+	5.15715i	−0.335229	+	0.193545i
$711$	−26.6019	−	9.88587i	−0.997649	−	0.370749i
$712$	−3.31921	+	2.78515i	−0.124393	+	0.104378i
$713$	26.0539	−	21.8618i	0.975724	−	0.818730i
$714$	−4.77431	−	2.24592i	−0.178674	−	0.0840513i
$715$	3.62903	−	2.09522i	0.135718	−	0.0783568i
$716$	5.58587	+	2.03309i	0.208754	+	0.0759802i
$717$	11.7524	+	1.06813i	0.438902	+	0.0398900i
$718$	19.1397	−	3.37484i	0.714287	−	0.125948i
$719$	−0.618865	−	1.70032i	−0.0230798	−	0.0634111i	0.927618	−	0.373531i	$-0.121853\pi$
$719$	−0.618865	−	1.70032i	−0.0230798	−	0.0634111i	−0.950697	+	0.310120i	$0.899631\pi$
$720$	3.02961	−	5.16670i	0.112907	−	0.192552i
$721$		−	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
$726$	5.09294	+	19.2666i	0.189017	+	0.715051i
$727$	2.39063	−	13.5580i	0.0886637	−	0.502837i	−0.907842	−	0.419312i	$-0.862271\pi$
$727$	2.39063	−	13.5580i	0.0886637	−	0.502837i	0.996506	−	0.0835244i	$-0.0266177\pi$
$728$	−0.275687	+	0.757443i	−0.0102176	+	0.0280727i
$729$	−23.1049	−	13.9700i	−0.855738	−	0.517409i
$730$	24.9995	+	14.4335i	0.925273	+	0.534206i
$731$	13.3569	+	15.9181i	0.494023	+	0.588754i
$732$	−12.7530	+	12.6673i	−0.471365	+	0.468198i
$733$	3.00825	−	5.21044i	0.111112	−	0.192452i	−0.805107	−	0.593130i	$-0.797892\pi$
$733$	3.00825	−	5.21044i	0.111112	−	0.192452i	0.916219	+	0.400678i	$0.131225\pi$
$734$	−3.78035	−	6.54777i	−0.139535	−	0.241682i
$735$	−3.33574	+	12.2834i	−0.123041	+	0.453080i
$736$	−5.93571	−	1.04663i	−0.218793	−	0.0385792i
$737$	−6.75474	−	38.3080i	−0.248814	−	1.41109i
$738$	10.4238	−	5.92485i	0.383705	−	0.218097i
$739$	16.5397	+	13.8784i	0.608421	+	0.510526i	0.894140	−	0.447788i	$-0.147788\pi$
$739$	16.5397	+	13.8784i	0.608421	+	0.510526i	−0.285719	+	0.958313i	$0.592232\pi$
$740$	11.5832			0.425806
$741$	2.12659	+	2.57590i	0.0781222	+	0.0946281i
$742$	−4.45763			−0.163645
$743$	−18.9259	−	15.8807i	−0.694322	−	0.582606i	0.225830	−	0.974167i	$-0.427491\pi$
$743$	−18.9259	−	15.8807i	−0.694322	−	0.582606i	−0.920152	+	0.391561i	$0.871935\pi$
$744$	4.10065	+	8.87181i	0.150337	+	0.325256i
$745$	3.90485	+	22.1455i	0.143063	+	0.811349i
$746$	−5.69223	−	1.00369i	−0.208407	−	0.0367478i
$747$	−0.326825	+	1.78314i	−0.0119579	+	0.0652418i
$748$	3.96607	+	6.86943i	0.145014	+	0.251171i
$749$	17.0318	−	29.4999i	0.622329	−	1.07790i
$750$	14.6558	+	14.7549i	0.535155	+	0.538775i
$751$	−14.8918	−	17.7473i	−0.543409	−	0.647609i	0.422540	−	0.906344i	$-0.361139\pi$
$751$	−14.8918	−	17.7473i	−0.543409	−	0.647609i	−0.965948	+	0.258735i	$0.916694\pi$
$752$	−9.33121	−	5.38738i	−0.340274	−	0.196457i
$753$	24.2934	−	16.8887i	0.885300	−	0.615458i
$754$	−0.971750	+	2.66986i	−0.0353891	+	0.0972306i
$755$	1.22958	−	6.97331i	0.0447491	−	0.253785i
$756$	3.91384	+	8.61973i	0.142345	+	0.313497i
$757$	−11.1562	+	4.06054i	−0.405480	+	0.147583i	−0.536705	−	0.843770i	$-0.680331\pi$
$757$	−11.1562	+	4.06054i	−0.405480	+	0.147583i	0.131225	+	0.991353i	$0.458109\pi$
$758$	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	$-0.0376948\pi$
$762$	13.1778	−	18.6854i	0.477380	−	0.676902i
$763$	−7.11311	−	19.5431i	−0.257512	−	0.707508i
$764$	−23.5014	+	4.14393i	−0.850250	+	0.149922i
$765$	0.0675037	−	10.0143i	0.00244060	−	0.362068i
$766$	−6.29971	−	2.29291i	−0.227618	−	0.0828461i
$767$	1.93655	−	1.11807i	0.0699249	−	0.0403711i
$768$	0.737283	−	1.56730i	0.0266044	−	0.0565549i
$769$	6.42301	−	5.38954i	0.231620	−	0.194352i	−0.519590	−	0.854416i	$-0.673915\pi$
$769$	6.42301	−	5.38954i	0.231620	−	0.194352i	0.751209	+	0.660064i	$0.229471\pi$
$770$	−13.2184	+	11.0916i	−0.476359	+	0.399713i
$771$	11.6566	−	24.7793i	0.419803	−	0.892405i
$772$	1.83900	−	1.06175i	0.0661872	−	0.0382132i
$773$	15.1689	+	5.52103i	0.545588	+	0.198578i	0.600085	−	0.799936i	$-0.295133\pi$
$773$	15.1689	+	5.52103i	0.545588	+	0.198578i	−0.0544971	+	0.998514i	$0.517356\pi$
$774$	0.251312	−	37.2826i	0.00903322	−	1.34009i
$775$	−5.63528	+	0.993653i	−0.202425	+	0.0356931i
$776$	0.875310	+	2.40490i	0.0314218	+	0.0863307i
$777$	−10.5515	+	14.9615i	−0.378532	+	0.536741i
$778$			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
$783$	13.7956	+	30.3831i	0.493015	+	1.08580i
$784$	−0.639168	+	3.62490i	−0.0228274	+	0.129461i
$785$	0.215679	−	0.592574i	0.00769792	−	0.0211499i
$786$	−10.0607	+	6.99417i	−0.358853	+	0.249474i
$787$	19.4065	+	11.2044i	0.691768	+	0.399392i	0.804274	−	0.594259i	$-0.202554\pi$
$787$	19.4065	+	11.2044i	0.691768	+	0.399392i	−0.112506	+	0.993651i	$0.535888\pi$
$788$	2.43134	+	2.89756i	0.0866130	+	0.103221i
$789$	3.17244	+	3.19389i	0.112942	+	0.113706i
$790$	−9.44315	+	16.3560i	−0.335972	+	0.581921i
$791$	−0.541256	−	0.937483i	−0.0192449	−	0.0333331i
$792$	2.56579	−	13.9988i	0.0911712	−	0.497427i
$793$	4.52177	+	0.797311i	0.160573	+	0.0283133i
$794$	−5.25364	−	29.7949i	−0.186445	−	1.05738i
$795$	−3.54985	−	7.68015i	−0.125900	−	0.272387i
$796$	−10.5692	−	8.86860i	−0.374615	−	0.314339i
$797$	33.1888			1.17561			0.587804	−	0.809003i	$-0.299993\pi$
$797$	33.1888			1.17561			0.587804	+	0.809003i	$0.299993\pi$
$798$	−10.4658	−	8.92531i	−0.370484	−	0.315953i
$799$	−18.0157			−0.637350
$800$	0.776823	+	0.651831i	0.0274648	+	0.0230457i
$801$	11.3008	−	6.42335i	0.399295	−	0.226958i
$802$	−3.25047	−	18.4344i	−0.114778	−	0.650940i
$803$	67.5512	+	11.9111i	2.38383	+	0.420333i
$804$	−3.72199	+	13.7057i	−0.131265	+	0.483364i
$805$	−10.9615	−	18.9860i	−0.386344	−	0.669167i
$806$	1.24829	−	2.16210i	0.0439691	−	0.0761568i
$807$	39.2156	−	38.9522i	1.38046	−	1.37118i
$808$	−5.12250	−	6.10475i	−0.180209	−	0.214764i
$809$	35.2784	+	20.3680i	1.24032	+	0.716101i	0.969160	−	0.246432i	$-0.0792581\pi$
$809$	35.2784	+	20.3680i	1.24032	+	0.716101i	0.271164	+	0.962533i	$0.412591\pi$
$810$	−11.7343	+	13.6076i	−0.412302	+	0.478121i
$811$	−6.36968	+	17.5006i	−0.223670	+	0.614528i	−0.999873	−	0.0159555i	$-0.994921\pi$
$811$	−6.36968	+	17.5006i	−0.223670	+	0.614528i	0.776203	+	0.630483i	$0.217143\pi$
$812$	2.03161	−	11.5218i	0.0712954	−	0.404337i
$813$	8.89488	+	33.6494i	0.311957	+	1.18013i
$814$	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
$819$	1.22317	−	2.08599i	0.0427410	−	0.0728905i
$820$	−2.72906	−	7.49803i	−0.0953029	−	0.261843i
$821$	17.1780	−	3.02894i	0.599515	−	0.105711i	0.134349	−	0.990934i	$-0.457106\pi$
$821$	17.1780	−	3.02894i	0.599515	−	0.105711i	0.465166	+	0.885223i	$0.345995\pi$
$822$	−16.1771	−	1.47027i	−0.564242	−	0.0512816i
$823$	13.0772	+	4.75972i	0.455844	+	0.165914i	0.559729	−	0.828676i	$-0.310905\pi$
$823$	13.0772	+	4.75972i	0.455844	+	0.165914i	−0.103885	+	0.994589i	$0.533127\pi$
$824$	13.3041	−	7.68115i	0.463472	−	0.267586i
$825$	7.53988	+	3.54689i	0.262505	+	0.123487i
$826$	−7.05374	+	5.91879i	−0.245431	+	0.205941i
$827$	3.80513	−	3.19288i	0.132317	−	0.111027i	−0.574227	−	0.818696i	$-0.694697\pi$
$827$	3.80513	−	3.19288i	0.132317	−	0.111027i	0.706545	+	0.707669i	$0.250253\pi$
$828$	16.9493	+	6.29875i	0.589029	+	0.218897i
$829$	36.2878	−	20.9508i	1.26033	−	0.727650i	0.287189	−	0.957874i	$-0.407279\pi$
$829$	36.2878	−	20.9508i	1.26033	−	0.727650i	0.973138	+	0.230224i	$0.0739460\pi$
$830$	1.13368	+	0.412626i	0.0393506	+	0.0143225i
$831$	1.26678	−	13.9381i	0.0439440	−	0.483508i
$832$	−0.435713	+	0.0768279i	−0.0151056	+	0.00266353i
$833$	2.10494	+	5.78328i	0.0729319	+	0.200379i
$834$	15.3330	+	10.8134i	0.530937	+	0.374439i
$835$		−	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	$-0.855386\pi$
$839$	−37.7944	+	13.7560i	−1.30481	+	0.474912i	−0.406249	+	0.913763i	$0.633163\pi$
$840$	6.09080	−	1.61004i	0.210153	−	0.0555517i
$841$	2.12528	−	12.0531i	0.0732855	−	0.415623i
$842$	−5.11036	+	14.0406i	−0.176115	+	0.483871i
$843$	11.6770	+	16.7967i	0.402177	+	0.578509i
$844$	13.9597	+	8.05964i	0.480513	+	0.277424i
$845$	−16.4319	−	19.5827i	−0.565273	−	0.673666i
$846$	24.6212	+	20.9441i	0.846494	+	0.720072i
$847$	−10.4809	+	18.1534i	−0.360126	+	0.623757i
$848$	−1.22337	−	2.11894i	−0.0420108	−	0.0727648i
$849$	24.0141	+	6.52138i	0.824161	+	0.223813i
$850$	1.66980	+	0.294430i	0.0572735	+	0.0100989i
$851$	6.07232	+	34.4378i	0.208156	+	1.18051i
$852$	8.12253	−	3.75432i	0.278273	−	0.128621i
$853$	25.6859	+	21.5531i	0.879470	+	0.737963i	0.966070	−	0.258280i	$-0.0831558\pi$
$853$	25.6859	+	21.5531i	0.879470	+	0.737963i	−0.0866001	+	0.996243i	$0.527600\pi$
$854$	−18.9071			−0.646986
$855$	7.04317	−	25.1394i	0.240871	−	0.859748i
$856$	18.6971			0.639055
$857$	0.680362	+	0.570892i	0.0232407	+	0.0195013i	0.654334	−	0.756206i	$-0.272949\pi$
$857$	0.680362	+	0.570892i	0.0232407	+	0.0195013i	−0.631093	+	0.775707i	$0.717393\pi$
$858$	−3.29997	+	1.52528i	−0.112659	+	0.0520723i
$859$	−0.641169	−	3.63625i	−0.0218764	−	0.124067i	0.971914	−	0.235337i	$-0.0756194\pi$
$859$	−0.641169	−	3.63625i	−0.0218764	−	0.124067i	−0.993790	+	0.111270i	$0.964508\pi$
$860$	−24.4349	−	4.30853i	−0.833223	−	0.146920i
$861$	12.1709	+	3.30518i	0.414782	+	0.112640i
$862$	−6.73136	−	11.6591i	−0.229271	−	0.397109i
$863$	−9.90600	+	17.1577i	−0.337204	+	0.584055i	−0.983906	−	0.178688i	$-0.942815\pi$
$863$	−9.90600	+	17.1577i	−0.337204	+	0.584055i	0.646701	+	0.762743i	$0.276148\pi$
$864$	−3.02327	+	4.22609i	−0.102854	+	0.143774i
$865$	19.3930	+	23.1117i	0.659383	+	0.785822i
$866$	14.6561	+	8.46172i	0.498035	+	0.287541i
$867$	14.0435	+	20.2007i	0.476941	+	0.686052i
$868$	−3.51612	+	9.66046i	−0.119345	+	0.327897i
$869$	−7.79289	+	44.1957i	−0.264356	+	1.49923i
$870$	21.4691	−	5.67513i	0.727869	−	0.192405i
$871$	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
$876$	−20.4660	−	14.4335i	−0.691481	−	0.487661i
$877$	−11.7852	−	32.3795i	−0.397958	−	1.09338i	−0.963278	−	0.268508i	$-0.913470\pi$
$877$	−11.7852	−	32.3795i	−0.397958	−	1.09338i	0.565320	−	0.824872i	$-0.308753\pi$
$878$	−14.7957	+	2.60888i	−0.499331	+	0.0880456i
$879$	−0.00101671	+	0.0111867i	−3.42928e−5	+	0.000377317i
$880$	−8.90013	−	3.23938i	−0.300023	−	0.109200i
$881$	18.5560	−	10.7133i	0.625166	−	0.360940i	−0.153711	−	0.988116i	$-0.549123\pi$
$881$	18.5560	−	10.7133i	0.625166	−	0.360940i	0.778878	+	0.627176i	$0.215789\pi$
$882$	3.84660	−	10.3508i	0.129522	−	0.348530i
$883$	−26.4524	+	22.1962i	−0.890193	+	0.746960i	−0.968249	−	0.249989i	$-0.919573\pi$
$883$	−26.4524	+	22.1962i	−0.890193	+	0.746960i	0.0780562	+	0.996949i	$0.475129\pi$
$884$	−0.566692	+	0.475511i	−0.0190599	+	0.0159932i
$885$	−15.8149	−	7.43958i	−0.531611	−	0.250079i
$886$	32.0813	−	18.5222i	1.07779	−	0.622265i
$887$	−28.3275	−	10.3104i	−0.951145	−	0.346189i	−0.180588	−	0.983559i	$-0.557800\pi$
$887$	−28.3275	−	10.3104i	−0.951145	−	0.346189i	−0.770558	+	0.637370i	$0.780022\pi$
$888$	−10.0078	−	0.909564i	−0.335839	−	0.0305230i
$889$	23.6850	−	4.17631i	0.794370	−	0.140069i
$890$	−2.95868	−	8.12889i	−0.0991750	−	0.272481i
$891$	−15.1425	+	39.9207i	−0.507292	+	1.33739i
$892$			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
$897$	−1.18040	−	4.46544i	−0.0394122	−	0.149097i
$898$	2.01953	−	11.4533i	0.0673927	−	0.382203i
$899$	−12.3937	+	34.0515i	−0.413354	+	1.13568i
$900$	−1.93974	−	2.34360i	−0.0646580	−	0.0781199i
$901$	−3.54294	−	2.04552i	−0.118032	−	0.0681460i
$902$	−12.1874	−	14.5243i	−0.405795	−	0.483608i
$903$	27.8237	−	27.6367i	0.925913	−	0.919693i
$904$	0.297090	−	0.514574i	0.00988105	−	0.0171145i
$905$	6.47953	+	11.2229i	0.215387	+	0.373061i
$906$	−1.60993	+	5.92833i	−0.0534862	+	0.196956i
$907$	−56.6712	−	9.99267i	−1.88174	−	0.331801i	−0.889579	−	0.456782i	$-0.849002\pi$
$907$	−56.6712	−	9.99267i	−1.88174	−	0.331801i	−0.992159	+	0.124981i	$0.960113\pi$
$908$	−3.25821	−	18.4782i	−0.108128	−	0.613222i
$909$	11.8139	+	20.7847i	0.391844	+	0.689384i
$910$	−1.23277	−	1.03442i	−0.0408660	−	0.0342907i
$911$	−38.7915			−1.28522			−0.642610	−	0.766194i	$-0.722148\pi$
$911$	−38.7915			−1.28522			−0.642610	+	0.766194i	$0.722148\pi$
$912$	1.37039	−	7.42442i	0.0453783	−	0.245847i
$913$	2.86672			0.0948747
$914$	12.0559	+	10.1161i	0.398775	+	0.334612i
$915$	−15.0567	−	32.5754i	−0.497759	−	1.07691i
$916$	−2.01891	−	11.4498i	−0.0667066	−	0.378312i
$917$	−12.6926	−	2.23804i	−0.419145	−	0.0739066i
$918$	−0.844691	+	8.64696i	−0.0278789	+	0.285392i
$919$	28.1669	+	48.7865i	0.929141	+	1.60932i	0.784762	+	0.619797i	$0.212785\pi$
$919$	28.1669	+	48.7865i	0.929141	+	1.60932i	0.144379	+	0.989522i	$0.453882\pi$
$920$	6.01667	−	10.4212i	0.198364	−	0.343576i
$921$	16.6312	+	16.7437i	0.548017	+	0.551723i
$922$	−3.89062	−	4.63666i	−0.128131	−	0.152700i
$923$	−1.97950	−	1.14286i	−0.0651559	−	0.0376178i
$924$	12.2916	−	8.54506i	0.404363	−	0.281112i
$925$	2.01225	−	5.52862i	0.0661625	−	0.181780i
$926$	−1.59548	+	9.04843i	−0.0524308	+	0.297350i
$927$	−43.4128	+	15.4704i	−1.42586	+	0.508114i
$928$	6.03448	−	2.19637i	0.198092	−	0.0720994i
$929$	31.8205	−	37.9221i	1.04400	−	1.24418i	0.0749796	−	0.997185i	$-0.476111\pi$
$929$	31.8205	−	37.9221i	1.04400	−	1.24418i	0.969016	−	0.247000i	$-0.0794447\pi$
$930$	−19.4443	+	1.63514i	−0.637603	+	0.0536183i
$931$	1.32447	+	15.9896i	0.0434078	+	0.524037i
$932$		−	16.2603i		−	0.532624i
$933$	11.6906	−	16.5767i	0.382733	−	0.542697i
$934$	0.0708263	+	0.194594i	0.00231751	+	0.00636730i
$935$	−15.5957	+	2.74995i	−0.510035	+	0.0899330i
$936$	1.32727	+	0.00894679i	0.0433833	+	0.000292435i
$937$	21.2381	+	7.73002i	0.693817	+	0.252529i	0.664769	−	0.747049i	$-0.268530\pi$
$937$	21.2381	+	7.73002i	0.693817	+	0.252529i	0.0290486	+	0.999578i	$0.490752\pi$
$938$	−12.9372	+	7.46927i	−0.422413	+	0.243880i
$939$	1.29534	−	2.75359i	0.0422717	−	0.0898601i
$940$	16.4788	−	13.8274i	0.537480	−	0.450999i
$941$	40.2199	−	33.7485i	1.31113	−	1.10017i	0.323024	−	0.946391i	$-0.395300\pi$
$941$	40.2199	−	33.7485i	1.31113	−	1.10017i	0.988105	−	0.153778i	$-0.0491440\pi$
$942$	−0.232877	+	0.495042i	−0.00758753	+	0.0161294i
$943$	20.8617	−	12.0445i	0.679349	−	0.392222i
$944$	−4.74937	−	1.72863i	−0.154579	−	0.0562620i
$945$	−18.8438	+	1.45679i	−0.612988	+	0.0473895i
$946$	−58.0619	+	10.2379i	−1.88776	+	0.332862i
$947$	9.84314	+	27.0438i	0.319859	+	0.878805i	0.990560	+	0.137078i	$0.0437710\pi$
$947$	9.84314	+	27.0438i	0.319859	+	0.878805i	−0.670701	+	0.741728i	$0.734007\pi$
$948$	9.44315	−	13.3899i	0.306699	−	0.434885i
$949$			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	$-0.621816\pi$
$953$	−1.95076	+	0.710020i	−0.0631914	+	0.0229998i	0.310231	+	0.950661i	$0.399594\pi$
$954$	2.46396	+	6.91433i	0.0797736	+	0.223860i
$955$	8.27327	−	46.9200i	0.267717	−	1.51830i
$956$	−2.33026	+	6.40234i	−0.0753660	+	0.207066i
$957$	43.3258	−	30.1199i	1.40052	−	0.973639i
$958$	4.32862	+	2.49913i	0.139851	+	0.0807432i
$959$	−10.9827	−	13.0887i	−0.354651	−	0.422656i
$960$	2.43692	+	2.45341i	0.0786514	+	0.0791833i
$961$	0.420731	−	0.728727i	0.0135720	−	0.0235073i
$962$	1.28346	+	2.22302i	0.0413804	+	0.0716729i
$963$	−55.1724	−	10.1123i	−1.77790	−	0.325864i
$964$	−19.1145	−	3.37040i	−0.615636	−	0.108553i
$965$	0.736186	+	4.17512i	0.0236987	+	0.134402i
$966$	7.97982	+	17.2645i	0.256746	+	0.555475i
$967$	−2.18110	−	1.83016i	−0.0701395	−	0.0588540i	0.607044	−	0.794668i	$-0.292355\pi$
$967$	−2.18110	−	1.83016i	−0.0701395	−	0.0588540i	−0.677183	+	0.735814i	$0.736800\pi$
$968$	−11.5057			−0.369806
$969$	−4.22257	−	11.8964i	−0.135648	−	0.382167i
$970$	−5.10946			−0.164055
$971$	0.796470	+	0.668318i	0.0255599	+	0.0214473i	0.655478	−	0.755214i	$-0.272467\pi$
$971$	0.796470	+	0.668318i	0.0255599	+	0.0214473i	−0.629918	+	0.776661i	$0.716912\pi$
$972$	11.2069	−	10.8354i	0.359461	−	0.347546i
$973$	3.42701	+	19.4355i	0.109865	+	0.623074i
$974$	−26.6575	−	4.70043i	−0.854161	−	0.150612i
$975$	−0.203657	+	0.749940i	−0.00652225	+	0.0240173i
$976$	−5.18894	−	8.98751i	−0.166094	−	0.287683i
$977$	−17.5242	+	30.3529i	−0.560650	+	0.971074i	0.436790	+	0.899564i	$0.356115\pi$
$977$	−17.5242	+	30.3529i	−0.560650	+	0.971074i	−0.997440	+	0.0715108i	$0.977218\pi$
$978$	1.53494	−	1.52463i	0.0490820	−	0.0487522i
$979$	−13.2128	−	15.7464i	−0.422282	−	0.503256i
$980$	−6.36414	−	3.67434i	−0.203295	−	0.117372i
$981$	−26.3820	+	21.8357i	−0.842311	+	0.697162i
$982$	−2.14701	+	5.89886i	−0.0685138	+	0.188240i
$983$	−3.51109	+	19.9124i	−0.111986	+	0.635106i	0.876212	+	0.481926i	$0.160063\pi$
$983$	−3.51109	+	19.9124i	−0.111986	+	0.635106i	−0.988198	+	0.153180i	$0.951048\pi$
$984$	1.76911	+	6.69253i	0.0563970	+	0.213350i
$985$	−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
$990$	24.5109	+	14.3725i	0.779007	+	0.456789i
$991$	4.51355	+	12.4009i	0.143378	+	0.393926i	0.990507	−	0.137459i	$-0.0438937\pi$
$991$	4.51355	+	12.4009i	0.143378	+	0.393926i	−0.847130	+	0.531386i	$0.821671\pi$
$992$	−5.55710	+	0.979866i	−0.176438	+	0.0311108i
$993$	−2.72317	−	0.247498i	−0.0864173	−	0.00785411i
$994$	8.84457	+	3.21916i	0.280533	+	0.102106i
$995$	23.8552	−	13.7728i	0.756261	−	0.436627i
$996$	−0.947089	−	0.445527i	−0.0300097	−	0.0141171i
$997$	20.9990	−	17.6202i	0.665045	−	0.558039i	−0.246549	−	0.969130i	$-0.579297\pi$
$997$	20.9990	−	17.6202i	0.665045	−	0.558039i	0.911594	+	0.411091i	$0.134852\pi$
$998$	−16.8496	+	14.1385i	−0.533365	+	0.447546i
$999$	29.0394	+	8.09666i	0.918767	+	0.256167i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.41.1	✓	18	3.2	odd	2
114.2.l.a.89.1	yes	18	19.13	odd	18
114.2.l.b.41.3	yes	18	1.1	even	1	trivial
114.2.l.b.89.3	yes	18	57.32	even	18	inner
912.2.cc.c.497.1		18	4.3	odd	2
912.2.cc.c.545.1		18	228.203	odd	18
912.2.cc.d.497.3		18	12.11	even	2
912.2.cc.d.545.3		18	76.51	even	18

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)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.57223 - 0.726702i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.96615 - 0.346685i) q^{5} +(1.67151 + 0.453924i) q^{6} +(0.910931 + 1.57778i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.94381 - 2.28508i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.57223 - 0.726702i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-1.96615 - 0.346685i) q^{5} +(1.67151 + 0.453924i) q^{6} +(0.910931 + 1.57778i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.94381 - 2.28508i) q^{9} +(-1.28331 - 1.52939i) q^{10} +(-4.10844 - 2.37201i) q^{11} +(0.988676 + 1.42215i) q^{12} +(0.151321 - 0.415752i) q^{13} +(-0.316363 + 1.79418i) q^{14} +(-3.34317 + 0.883735i) 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} +(2.57877 + 1.81865i) q^{21} +(-1.62255 - 4.45791i) q^{22} +(5.93571 - 1.04663i) q^{23} +(-0.156773 + 1.72494i) q^{24} +(-0.952914 - 0.346832i) q^{25} +(0.383159 - 0.221217i) q^{26} +(1.39554 - 5.00524i) q^{27} +(-1.39563 + 1.17107i) q^{28} +(-4.91935 + 4.12783i) q^{29} +(-3.12907 - 1.47197i) q^{30} +(4.88683 - 2.82141i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-8.18314 - 0.743731i) q^{33} +(-1.64663 + 0.290345i) q^{34} +(-1.24403 - 3.41795i) q^{35} +(2.58791 + 1.51748i) 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} +(0.806441 + 3.05077i) q^{42} +(2.15807 - 12.2390i) q^{43} +(1.62255 - 4.45791i) q^{44} +(-4.61402 + 3.81892i) q^{45} +(5.21978 + 3.01364i) q^{46} +(6.92588 + 8.25394i) q^{47} +(-1.22887 + 1.22061i) q^{48} +(1.84041 - 3.18768i) q^{49} +(-0.507035 - 0.878210i) q^{50} +(-0.758974 + 2.79482i) q^{51} +(0.435713 + 0.0768279i) q^{52} +(0.424873 + 2.40957i) q^{53} +(4.28636 - 2.93720i) q^{54} +(7.25545 + 6.08805i) q^{55} -1.82186 q^{56} +(-3.82705 + 6.50797i) q^{57} -6.42176 q^{58} +(3.87172 + 3.24876i) q^{59} +(-1.45084 - 3.13892i) q^{60} +(1.80210 + 10.2202i) q^{61} +(5.55710 + 0.979866i) q^{62} +(5.37603 + 0.985349i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.441656 + 0.764970i) q^{65} +(-5.79059 - 5.82975i) q^{66} +(5.27060 + 6.28126i) q^{67} +(-1.44802 - 0.836015i) q^{68} +(8.57172 - 5.95903i) q^{69} +(1.24403 - 3.41795i) q^{70} +(0.897109 - 5.08776i) q^{71} +(1.00703 + 2.82593i) 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} +(0.441656 - 0.626247i) q^{78} +(-3.23544 - 8.88931i) q^{79} +(1.96615 - 0.346685i) q^{80} +(-1.44321 - 8.88353i) q^{81} +(3.75563 + 1.36694i) q^{82} +(-0.523324 + 0.302141i) q^{83} +(-1.34323 + 2.85540i) q^{84} +(2.55719 - 2.14574i) q^{85} +(9.52025 - 7.98844i) q^{86} +(-4.73465 + 10.0648i) q^{87} +(4.10844 - 2.37201i) q^{88} +(4.07161 + 1.48195i) q^{89} +(-5.98930 - 0.0403723i) q^{90} +(0.793809 - 0.139970i) q^{91} +(2.06145 + 5.66379i) q^{92} +(5.63289 - 7.98717i) 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} +(-13.4062 + 4.77739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35} + 3 q^{38} + 6 q^{39} + 3 q^{41} - 6 q^{43} + 24 q^{44} - 54 q^{45} + 18 q^{46} + 30 q^{47} + 21 q^{49} + 3 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 54 q^{54} + 30 q^{55} + 12 q^{57} + 12 q^{58} + 3 q^{59} + 24 q^{60} + 54 q^{61} + 6 q^{62} - 18 q^{63} - 9 q^{64} + 24 q^{65} - 27 q^{66} - 15 q^{67} - 27 q^{68} + 30 q^{69} + 24 q^{70} + 36 q^{71} + 6 q^{72} - 42 q^{73} + 6 q^{74} - 24 q^{78} - 6 q^{79} - 3 q^{81} + 3 q^{82} + 36 q^{83} - 30 q^{84} - 6 q^{86} - 60 q^{89} - 18 q^{91} - 66 q^{93} + 6 q^{95} + 9 q^{97} + 12 q^{98} - 102 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

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