LMFDB - Embedded newform 378.2.u.c.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			211.1
Character	$\chi$	$=$	378.211
Dual form			378.2.u.c.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-1.71357 - 0.252371i) q^{3} +(0.173648 - 0.984808i) q^{4} +(3.65119 - 1.32893i) q^{5} +(1.47489 - 0.908132i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.87262 + 0.864908i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.71357 - 0.252371i) q^{3} +(0.173648 - 0.984808i) q^{4} +(3.65119 - 1.32893i) q^{5} +(1.47489 - 0.908132i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.87262 + 0.864908i) q^{9} +(-1.94276 + 3.36496i) q^{10} +(-4.96921 - 1.80865i) q^{11} +(-0.546094 + 1.64371i) q^{12} +(-2.09826 - 1.76065i) q^{13} +(0.766044 + 0.642788i) q^{14} +(-6.59194 + 1.35575i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.996396 - 1.72581i) q^{17} +(-2.75651 + 1.18393i) q^{18} +(2.45170 + 4.24647i) q^{19} +(-0.674713 - 3.82649i) q^{20} +(0.0490210 + 1.73136i) q^{21} +(4.96921 - 1.80865i) q^{22} +(1.56862 - 8.89609i) q^{23} +(-0.638224 - 1.61018i) q^{24} +(7.73494 - 6.49039i) q^{25} +2.73909 q^{26} +(-4.70414 - 2.20704i) q^{27} -1.00000 q^{28} +(0.710566 - 0.596236i) q^{29} +(4.17826 - 5.27578i) q^{30} +(0.0593042 - 0.336331i) q^{31} +(0.939693 - 0.342020i) q^{32} +(8.05863 + 4.35332i) q^{33} +(0.346045 + 1.96252i) q^{34} +(-1.94276 - 3.36496i) q^{35} +(1.35059 - 2.67879i) q^{36} +(0.894687 - 1.54964i) q^{37} +(-4.60769 - 1.67706i) q^{38} +(3.15118 + 3.54654i) q^{39} +(2.97648 + 2.49756i) q^{40} +(-5.82323 - 4.88627i) q^{41} +(-1.15045 - 1.29479i) q^{42} +(9.69659 + 3.52927i) q^{43} +(-2.64406 + 4.57965i) q^{44} +(11.6379 - 0.659550i) q^{45} +(4.51666 + 7.82309i) q^{46} +(-1.07446 - 6.09358i) q^{47} +(1.52391 + 0.823225i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(-1.75337 + 9.94385i) q^{50} +(-2.14293 + 2.70582i) q^{51} +(-2.09826 + 1.76065i) q^{52} -1.39692 q^{53} +(5.02224 - 1.33307i) q^{54} -20.5471 q^{55} +(0.766044 - 0.642788i) q^{56} +(-3.12947 - 7.89534i) q^{57} +(-0.161072 + 0.913486i) q^{58} +(-2.72721 + 0.992623i) q^{59} +(0.190472 + 6.72722i) q^{60} +(0.411160 + 2.33180i) q^{61} +(0.170760 + 0.295765i) q^{62} +(0.352943 - 2.97917i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-10.0009 - 3.64005i) q^{65} +(-8.97152 + 1.84515i) q^{66} +(4.34776 + 3.64821i) q^{67} +(-1.52657 - 1.28094i) q^{68} +(-4.93305 + 14.8482i) q^{69} +(3.65119 + 1.32893i) q^{70} +(-1.95946 + 3.39388i) q^{71} +(0.687277 + 2.92021i) q^{72} +(2.43337 + 4.21473i) q^{73} +(0.310722 + 1.76219i) q^{74} +(-14.8923 + 9.16963i) q^{75} +(4.60769 - 1.67706i) q^{76} +(-0.918273 + 5.20779i) q^{77} +(-4.69361 - 0.691266i) q^{78} +(1.54919 - 1.29992i) q^{79} -3.88552 q^{80} +(7.50387 + 4.96910i) q^{81} +7.60169 q^{82} +(10.1028 - 8.47729i) q^{83} +(1.71357 + 0.252371i) q^{84} +(1.34456 - 7.62539i) q^{85} +(-9.69659 + 3.52927i) q^{86} +(-1.36807 + 0.842363i) q^{87} +(-0.918273 - 5.20779i) q^{88} +(0.103636 + 0.179503i) q^{89} +(-8.49118 + 7.98593i) q^{90} +(-1.36955 + 2.37212i) q^{91} +(-8.48855 - 3.08958i) q^{92} +(-0.186502 + 0.561359i) q^{93} +(4.73996 + 3.97730i) q^{94} +(14.5949 + 12.2465i) q^{95} +(-1.69654 + 0.348923i) q^{96} +(-5.71088 - 2.07859i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-12.7103 - 9.49346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	$ 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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
$3$	−1.71357	−	0.252371i	−0.989328	−	0.145706i
$3$	−1.71357	−	0.252371i	−0.989328	−	0.145706i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	3.65119	−	1.32893i	1.63286	−	0.594313i	0.647093	−	0.762411i	$-0.275985\pi$
$5$	3.65119	−	1.32893i	1.63286	−	0.594313i	0.985770	+	0.168098i	$0.0537625\pi$
$6$	1.47489	−	0.908132i	0.602121	−	0.370743i
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.87262	+	0.864908i	0.957539	+	0.288303i
$10$	−1.94276	+	3.36496i	−0.614354	+	1.06409i
$11$	−4.96921	−	1.80865i	−1.49827	−	0.545327i	−0.542661	−	0.839952i	$-0.682583\pi$
$11$	−4.96921	−	1.80865i	−1.49827	−	0.545327i	−0.955613	+	0.294625i	$0.904805\pi$
$12$	−0.546094	+	1.64371i	−0.157644	+	0.474498i
$13$	−2.09826	−	1.76065i	−0.581954	−	0.488317i	0.303634	−	0.952789i	$-0.401800\pi$
$13$	−2.09826	−	1.76065i	−0.581954	−	0.488317i	−0.885588	+	0.464471i	$0.846244\pi$
$14$	0.766044	+	0.642788i	0.204734	+	0.171792i
$15$	−6.59194	+	1.35575i	−1.70203	+	0.350053i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.996396	−	1.72581i	0.241661	−	0.418570i	−0.719526	−	0.694465i	$-0.755641\pi$
$17$	0.996396	−	1.72581i	0.241661	−	0.418570i	0.961188	+	0.275895i	$0.0889743\pi$
$18$	−2.75651	+	1.18393i	−0.649714	+	0.279054i
$19$	2.45170	+	4.24647i	0.562459	+	0.974207i	0.997281	+	0.0736907i	$0.0234778\pi$
$19$	2.45170	+	4.24647i	0.562459	+	0.974207i	−0.434823	+	0.900516i	$0.643189\pi$
$20$	−0.674713	−	3.82649i	−0.150870	−	0.855629i
$21$	0.0490210	+	1.73136i	0.0106973	+	0.377813i
$22$	4.96921	−	1.80865i	1.05944	−	0.385605i
$23$	1.56862	−	8.89609i	0.327080	−	1.85496i	−0.167557	−	0.985862i	$-0.553588\pi$
$23$	1.56862	−	8.89609i	0.327080	−	1.85496i	0.494637	−	0.869100i	$-0.335301\pi$
$24$	−0.638224	−	1.61018i	−0.130277	−	0.328676i
$25$	7.73494	−	6.49039i	1.54699	−	1.29808i
$26$	2.73909			0.537180
$27$	−4.70414	−	2.20704i	−0.905313	−	0.424745i
$28$	−1.00000			−0.188982
$29$	0.710566	−	0.596236i	0.131949	−	0.110718i	−0.574425	−	0.818557i	$-0.694774\pi$
$29$	0.710566	−	0.596236i	0.131949	−	0.110718i	0.706374	+	0.707839i	$0.250330\pi$
$30$	4.17826	−	5.27578i	0.762843	−	0.963221i
$31$	0.0593042	−	0.336331i	0.0106514	−	0.0604068i	−0.979019	−	0.203770i	$-0.934681\pi$
$31$	0.0593042	−	0.336331i	0.0106514	−	0.0604068i	0.989670	+	0.143363i	$0.0457917\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	8.05863	+	4.35332i	1.40283	+	0.757815i
$34$	0.346045	+	1.96252i	0.0593462	+	0.336569i
$35$	−1.94276	−	3.36496i	−0.328386	−	0.568782i
$36$	1.35059	−	2.67879i	0.225099	−	0.446464i
$37$	0.894687	−	1.54964i	0.147086	−	0.254760i	−0.783063	−	0.621942i	$-0.786344\pi$
$37$	0.894687	−	1.54964i	0.147086	−	0.254760i	0.930149	+	0.367182i	$0.119677\pi$
$38$	−4.60769	−	1.67706i	−0.747466	−	0.272055i
$39$	3.15118	+	3.54654i	0.504592	+	0.567900i
$40$	2.97648	+	2.49756i	0.470623	+	0.394899i
$41$	−5.82323	−	4.88627i	−0.909436	−	0.763107i	0.0625757	−	0.998040i	$-0.480069\pi$
$41$	−5.82323	−	4.88627i	−0.909436	−	0.763107i	−0.972012	+	0.234933i	$0.924513\pi$
$42$	−1.15045	−	1.29479i	−0.177518	−	0.199790i
$43$	9.69659	+	3.52927i	1.47872	+	0.538209i	0.950452	−	0.310871i	$-0.100621\pi$
$43$	9.69659	+	3.52927i	1.47872	+	0.538209i	0.528265	+	0.849080i	$0.322843\pi$
$44$	−2.64406	+	4.57965i	−0.398608	+	0.690408i
$45$	11.6379	−	0.659550i	1.73487	−	0.0983199i
$46$	4.51666	+	7.82309i	0.665945	+	1.15345i
$47$	−1.07446	−	6.09358i	−0.156726	−	0.888840i	−0.957190	−	0.289459i	$-0.906525\pi$
$47$	−1.07446	−	6.09358i	−0.156726	−	0.888840i	0.800464	−	0.599381i	$-0.204586\pi$
$48$	1.52391	+	0.823225i	0.219957	+	0.118822i
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	−1.75337	+	9.94385i	−0.247964	+	1.40627i
$51$	−2.14293	+	2.70582i	−0.300071	+	0.378891i
$52$	−2.09826	+	1.76065i	−0.290977	+	0.244159i
$53$	−1.39692			−0.191882			−0.0959408	−	0.995387i	$-0.530586\pi$
$53$	−1.39692			−0.191882			−0.0959408	+	0.995387i	$0.530586\pi$
$54$	5.02224	−	1.33307i	0.683441	−	0.181408i
$55$	−20.5471			−2.77057
$56$	0.766044	−	0.642788i	0.102367	−	0.0858961i
$57$	−3.12947	−	7.89534i	−0.414508	−	1.04576i
$58$	−0.161072	+	0.913486i	−0.0211498	+	0.119947i
$59$	−2.72721	+	0.992623i	−0.355052	+	0.129228i	−0.513387	−	0.858157i	$-0.671610\pi$
$59$	−2.72721	+	0.992623i	−0.355052	+	0.129228i	0.158335	+	0.987385i	$0.449387\pi$
$60$	0.190472	+	6.72722i	0.0245898	+	0.868480i
$61$	0.411160	+	2.33180i	0.0526436	+	0.298557i	0.999750	−	0.0223633i	$-0.00711905\pi$
$61$	0.411160	+	2.33180i	0.0526436	+	0.298557i	−0.947106	+	0.320920i	$0.896008\pi$
$62$	0.170760	+	0.295765i	0.0216865	+	0.0375621i
$63$	0.352943	−	2.97917i	0.0444666	−	0.375340i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−10.0009	−	3.64005i	−1.24046	−	0.451492i
$66$	−8.97152	+	1.84515i	−1.10432	+	0.227122i
$67$	4.34776	+	3.64821i	0.531164	+	0.445699i	0.868503	−	0.495684i	$-0.165082\pi$
$67$	4.34776	+	3.64821i	0.531164	+	0.445699i	−0.337339	+	0.941383i	$0.609527\pi$
$68$	−1.52657	−	1.28094i	−0.185123	−	0.155337i
$69$	−4.93305	+	14.8482i	−0.593869	+	1.78751i
$70$	3.65119	+	1.32893i	0.436401	+	0.158837i
$71$	−1.95946	+	3.39388i	−0.232545	+	0.402779i	−0.958556	−	0.284903i	$-0.908038\pi$
$71$	−1.95946	+	3.39388i	−0.232545	+	0.402779i	0.726012	+	0.687682i	$0.241372\pi$
$72$	0.687277	+	2.92021i	0.0809964	+	0.344151i
$73$	2.43337	+	4.21473i	0.284805	+	0.493296i	0.972562	−	0.232645i	$-0.0747379\pi$
$73$	2.43337	+	4.21473i	0.284805	+	0.493296i	−0.687757	+	0.725941i	$0.741405\pi$
$74$	0.310722	+	1.76219i	0.0361207	+	0.204850i
$75$	−14.8923	+	9.16963i	−1.71962	+	1.05882i
$76$	4.60769	−	1.67706i	0.528538	−	0.192372i
$77$	−0.918273	+	5.20779i	−0.104647	+	0.593482i
$78$	−4.69361	−	0.691266i	−0.531447	−	0.0782705i
$79$	1.54919	−	1.29992i	0.174297	−	0.146253i	−0.551466	−	0.834197i	$-0.685931\pi$
$79$	1.54919	−	1.29992i	0.174297	−	0.146253i	0.725763	+	0.687945i	$0.241487\pi$
$80$	−3.88552			−0.434414
$81$	7.50387	+	4.96910i	0.833763	+	0.552122i
$82$	7.60169			0.839466
$83$	10.1028	−	8.47729i	1.10893	−	0.930503i	0.110937	−	0.993827i	$-0.464615\pi$
$83$	10.1028	−	8.47729i	1.10893	−	0.930503i	0.997993	+	0.0633242i	$0.0201702\pi$
$84$	1.71357	+	0.252371i	0.186965	+	0.0275359i
$85$	1.34456	−	7.62539i	0.145838	−	0.827090i
$86$	−9.69659	+	3.52927i	−1.04561	+	0.380571i
$87$	−1.36807	+	0.842363i	−0.146673	+	0.0903108i
$88$	−0.918273	−	5.20779i	−0.0978883	−	0.555152i
$89$	0.103636	+	0.179503i	0.0109854	+	0.0190273i	0.871466	−	0.490456i	$-0.163170\pi$
$89$	0.103636	+	0.179503i	0.0109854	+	0.0190273i	−0.860480	+	0.509483i	$0.829837\pi$
$90$	−8.49118	+	7.98593i	−0.895049	+	0.841791i
$91$	−1.36955	+	2.37212i	−0.143567	+	0.248666i
$92$	−8.48855	−	3.08958i	−0.884992	−	0.322111i
$93$	−0.186502	+	0.561359i	−0.0193393	+	0.0582102i
$94$	4.73996	+	3.97730i	0.488890	+	0.410227i
$95$	14.5949	+	12.2465i	1.49740	+	1.25647i
$96$	−1.69654	+	0.348923i	−0.173153	+	0.0356118i
$97$	−5.71088	−	2.07859i	−0.579852	−	0.211049i	0.0354082	−	0.999373i	$-0.488727\pi$
$97$	−5.71088	−	2.07859i	−0.579852	−	0.211049i	−0.615260	+	0.788324i	$0.710949\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	−12.7103	−	9.49346i	−1.27744	−	0.954129i
$100$	−5.04862	−	8.74447i	−0.504862	−	0.874447i
$101$	3.04732	+	17.2822i	0.303220	+	1.71964i	0.631768	+	0.775157i	$0.282329\pi$
$101$	3.04732	+	17.2822i	0.303220	+	1.71964i	−0.328548	+	0.944487i	$0.606559\pi$
$102$	−0.0976887	−	3.45023i	−0.00967262	−	0.341624i
$103$	−14.1508	+	5.15048i	−1.39432	+	0.507491i	−0.926488	−	0.376325i	$-0.877188\pi$
$103$	−14.1508	+	5.15048i	−1.39432	+	0.507491i	−0.467834	+	0.883817i	$0.654965\pi$
$104$	0.475638	−	2.69748i	0.0466401	−	0.264509i
$105$	2.47983	+	6.25637i	0.242007	+	0.610559i
$106$	1.07010	−	0.897922i	0.103937	−	0.0872139i
$107$	20.1535			1.94831			0.974155	−	0.225880i	$-0.0725258\pi$
$107$	20.1535			1.94831			0.974155	+	0.225880i	$0.0725258\pi$
$108$	−2.99038	+	4.24943i	−0.287749	+	0.408901i
$109$	−13.4345			−1.28679			−0.643396	−	0.765534i	$-0.722475\pi$
$109$	−13.4345			−1.28679			−0.643396	+	0.765534i	$0.722475\pi$
$110$	15.7400	−	13.2074i	1.50075	−	1.25928i
$111$	−1.92419	+	2.42962i	−0.182636	+	0.230610i
$112$	−0.173648	+	0.984808i	−0.0164082	+	0.0930556i
$113$	0.336862	−	0.122608i	0.0316893	−	0.0115340i	−0.326127	−	0.945326i	$-0.605744\pi$
$113$	0.336862	−	0.122608i	0.0316893	−	0.0115340i	0.357816	+	0.933792i	$0.383521\pi$
$114$	7.47234	+	4.03660i	0.699849	+	0.378062i
$115$	−6.09490	−	34.5659i	−0.568352	−	3.22329i
$116$	−0.463789	−	0.803306i	−0.0430617	−	0.0745851i
$117$	−4.50471	−	6.87249i	−0.416461	−	0.635362i
$118$	1.45112	−	2.51341i	0.133586	−	0.231378i
$119$	−1.87261	−	0.681575i	−0.171662	−	0.0624799i
$120$	−4.47008	−	5.03091i	−0.408061	−	0.459258i
$121$	12.9954	+	10.9044i	1.18140	+	0.991312i
$122$	−1.81382	−	1.52198i	−0.164216	−	0.137793i
$123$	8.74534	+	9.84256i	0.788541	+	0.887474i
$124$	−0.320923	−	0.116807i	−0.0288198	−	0.0104895i
$125$	9.90272	−	17.1520i	0.885726	−	1.53412i
$126$	1.64460	+	2.50904i	0.146513	+	0.223523i
$127$	5.70505	+	9.88144i	0.506242	+	0.876836i	0.999974	+	0.00722231i	$0.00229895\pi$
$127$	5.70505	+	9.88144i	0.506242	+	0.876836i	−0.493732	+	0.869614i	$0.664368\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−15.7251	−	8.49478i	−1.38452	−	0.747923i
$130$	10.0009	−	3.64005i	0.877141	−	0.319253i
$131$	−2.14911	+	12.1882i	−0.187769	+	1.06489i	0.734577	+	0.678525i	$0.237381\pi$
$131$	−2.14911	+	12.1882i	−0.187769	+	1.06489i	−0.922346	+	0.386365i	$0.873731\pi$
$132$	5.68655	−	7.18025i	0.494950	−	0.624961i
$133$	3.75622	−	3.15185i	0.325706	−	0.273300i
$134$	−5.67560			−0.490297
$135$	−20.1087	−	1.80688i	−1.73068	−	0.155511i
$136$	1.99279			0.170880
$137$	6.98871	−	5.86422i	0.597085	−	0.501014i	−0.293422	−	0.955983i	$-0.594794\pi$
$137$	6.98871	−	5.86422i	0.597085	−	0.501014i	0.890507	+	0.454969i	$0.150350\pi$
$138$	−5.76528	−	14.5453i	−0.490773	−	1.23817i
$139$	−0.976843	+	5.53995i	−0.0828547	+	0.469892i	0.914944	+	0.403580i	$0.132234\pi$
$139$	−0.976843	+	5.53995i	−0.0828547	+	0.469892i	−0.997799	+	0.0663121i	$0.978877\pi$
$140$	−3.65119	+	1.32893i	−0.308582	+	0.112315i
$141$	0.303322	+	10.7129i	0.0255443	+	0.902190i
$142$	−0.680512	−	3.85937i	−0.0571073	−	0.323871i
$143$	7.24233	+	12.5441i	0.605634	+	1.04899i
$144$	−2.40356	−	1.79524i	−0.200297	−	0.149603i
$145$	1.80206	−	3.12126i	0.149653	−	0.259207i
$146$	−4.57325	−	1.66453i	−0.378485	−	0.137757i
$147$	1.69654	−	0.348923i	0.139928	−	0.0287787i
$148$	−1.37074	−	1.15019i	−0.112674	−	0.0945448i
$149$	14.8936	+	12.4972i	1.22013	+	1.02381i	0.998818	+	0.0486113i	$0.0154796\pi$
$149$	14.8936	+	12.4972i	1.22013	+	1.02381i	0.221316	+	0.975202i	$0.428965\pi$
$150$	5.51405	−	16.5969i	0.450220	−	1.35513i
$151$	8.87558	+	3.23045i	0.722285	+	0.262890i	0.676895	−	0.736079i	$-0.263325\pi$
$151$	8.87558	+	3.23045i	0.722285	+	0.262890i	0.0453893	+	0.998969i	$0.485547\pi$
$152$	−2.45170	+	4.24647i	−0.198859	+	0.344434i
$153$	4.35493	−	4.09580i	0.352075	−	0.331126i
$154$	−2.64406	−	4.57965i	−0.213065	−	0.369039i
$155$	−0.230428	−	1.30682i	−0.0185084	−	0.104966i
$156$	4.03985	−	2.48746i	0.323447	−	0.199156i
$157$	−13.8740	+	5.04971i	−1.10726	+	0.403011i	−0.829989	−	0.557780i	$-0.811653\pi$
$157$	−13.8740	+	5.04971i	−1.10726	+	0.403011i	−0.277275	+	0.960791i	$0.589431\pi$
$158$	−0.351172	+	1.99159i	−0.0279377	+	0.158443i
$159$	2.39371	+	0.352541i	0.189834	+	0.0279583i
$160$	2.97648	−	2.49756i	0.235311	−	0.197450i
$161$	−9.03332			−0.711926
$162$	−8.94237	+	1.01684i	−0.702579	+	0.0798907i
$163$	7.02448			0.550200			0.275100	−	0.961416i	$-0.411289\pi$
$163$	7.02448			0.550200			0.275100	+	0.961416i	$0.411289\pi$
$164$	−5.82323	+	4.88627i	−0.454718	+	0.381554i
$165$	35.2088	+	5.18549i	2.74100	+	0.403690i
$166$	−2.29013	+	12.9880i	−0.177748	+	1.00806i
$167$	−18.8011	+	6.84306i	−1.45488	+	0.529532i	−0.943949	−	0.330092i	$-0.892920\pi$
$167$	−18.8011	+	6.84306i	−1.45488	+	0.529532i	−0.510928	+	0.859624i	$0.670698\pi$
$168$	−1.47489	+	0.908132i	−0.113790	+	0.0700639i
$169$	−0.954611	−	5.41387i	−0.0734316	−	0.416451i
$170$	3.87151	+	6.70566i	0.296931	+	0.514300i
$171$	3.36999	+	14.3190i	0.257710	+	1.09500i
$172$	5.15945	−	8.93643i	0.393404	−	0.681396i
$173$	2.95664	+	1.07613i	0.224789	+	0.0818166i	0.451959	−	0.892038i	$-0.350725\pi$
$173$	2.95664	+	1.07613i	0.224789	+	0.0818166i	−0.227170	+	0.973855i	$0.572947\pi$
$174$	0.506545	−	1.52467i	0.0384011	−	0.115585i
$175$	−7.73494	−	6.49039i	−0.584707	−	0.490627i
$176$	4.05094	+	3.39914i	0.305351	+	0.256220i
$177$	4.92376	−	1.01266i	0.370093	−	0.0761160i
$178$	−0.194772	−	0.0708912i	−0.0145988	−	0.00531352i
$179$	−1.50907	+	2.61379i	−0.112793	+	0.195364i	−0.916895	−	0.399127i	$-0.869313\pi$
$179$	−1.50907	+	2.61379i	−0.112793	+	0.195364i	0.804102	+	0.594491i	$0.202646\pi$
$180$	1.37137	−	11.5756i	0.102216	−	0.862794i
$181$	8.11666	+	14.0585i	0.603307	+	1.04496i	0.992317	+	0.123724i	$0.0394838\pi$
$181$	8.11666	+	14.0585i	0.603307	+	1.04496i	−0.389010	+	0.921233i	$0.627183\pi$
$182$	−0.475638	−	2.69748i	−0.0352566	−	0.199950i
$183$	−0.116071	−	4.09946i	−0.00858019	−	0.303041i
$184$	8.48855	−	3.08958i	0.625784	−	0.227767i
$185$	1.20731	−	6.84702i	0.0887635	−	0.503403i
$186$	−0.217966	−	0.549907i	−0.0159820	−	0.0403211i
$187$	−8.07268	+	6.77378i	−0.590333	+	0.495348i
$188$	−6.18758			−0.451276
$189$	−1.35665	+	5.01593i	−0.0986814	+	0.364855i
$190$	−19.0522			−1.38220
$191$	−18.6278	+	15.6306i	−1.34786	+	1.13099i	−0.368331	+	0.929695i	$0.620071\pi$
$191$	−18.6278	+	15.6306i	−1.34786	+	1.13099i	−0.979531	+	0.201295i	$0.935485\pi$
$192$	1.07534	−	1.35781i	0.0776062	−	0.0979912i
$193$	−0.0499695	+	0.283391i	−0.00359688	+	0.0203989i	−0.986553	−	0.163439i	$-0.947741\pi$
$193$	−0.0499695	+	0.283391i	−0.00359688	+	0.0203989i	0.982956	+	0.183838i	$0.0588523\pi$
$194$	5.71088	−	2.07859i	0.410017	−	0.149234i
$195$	16.2186	+	8.76141i	1.16144	+	0.627417i
$196$	0.173648	+	0.984808i	0.0124034	+	0.0703434i
$197$	−10.5272	−	18.2337i	−0.750033	−	1.29910i	−0.947806	−	0.318848i	$-0.896704\pi$
$197$	−10.5272	−	18.2337i	−0.750033	−	1.29910i	0.197773	−	0.980248i	$-0.436629\pi$
$198$	15.8390	−	0.897637i	1.12563	−	0.0637923i
$199$	11.3557	−	19.6687i	0.804984	−	1.39427i	−0.111317	−	0.993785i	$-0.535507\pi$
$199$	11.3557	−	19.6687i	0.804984	−	1.39427i	0.916302	−	0.400489i	$-0.131160\pi$
$200$	9.48831	+	3.45346i	0.670925	+	0.244197i
$201$	−6.52948	−	7.34869i	−0.460554	−	0.518337i
$202$	−13.4432	−	11.2802i	−0.945859	−	0.793670i
$203$	−0.710566	−	0.596236i	−0.0498720	−	0.0418475i
$204$	2.29260	+	2.58024i	0.160514	+	0.180653i
$205$	−27.7552	−	10.1021i	−1.93851	−	0.705560i
$206$	7.52949	−	13.0415i	0.524605	−	0.908642i
$207$	12.2003	−	24.1983i	0.847982	−	1.68190i
$208$	1.36955	+	2.37212i	0.0949609	+	0.164477i
$209$	−4.50266	−	25.5359i	−0.311456	−	1.76635i
$210$	−5.92118	−	3.19866i	−0.408600	−	0.220728i
$211$	18.6851	−	6.80084i	1.28634	−	0.468189i	0.393815	−	0.919190i	$-0.371155\pi$
$211$	18.6851	−	6.80084i	1.28634	−	0.468189i	0.892524	+	0.451001i	$0.148933\pi$
$212$	−0.242572	+	1.37570i	−0.0166599	+	0.0944832i
$213$	4.21417	−	5.32112i	0.288750	−	0.364597i
$214$	−15.4385	+	12.9544i	−1.05535	+	0.885545i
$215$	40.0943			2.73441
$216$	−0.440718	−	5.17743i	−0.0299871	−	0.352279i
$217$	−0.341519			−0.0231839
$218$	10.2914	−	8.63553i	0.697023	−	0.584872i
$219$	−3.10607	−	7.83632i	−0.209889	−	0.529530i
$220$	−3.56797	+	20.2350i	−0.240552	+	1.36424i
$221$	−5.12925	+	1.86689i	−0.345031	+	0.125581i
$222$	−0.0877170	−	3.09805i	−0.00588718	−	0.207927i
$223$	2.49375	+	14.1427i	0.166994	+	0.947068i	0.946985	+	0.321278i	$0.104112\pi$
$223$	2.49375	+	14.1427i	0.166994	+	0.947068i	−0.779991	+	0.625790i	$0.784777\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	27.8331	−	11.9544i	1.85554	−	0.796959i
$226$	−0.179240	+	0.310453i	−0.0119229	+	0.0206510i
$227$	−10.5959	−	3.85659i	−0.703274	−	0.255971i	−0.0344659	−	0.999406i	$-0.510973\pi$
$227$	−10.5959	−	3.85659i	−0.703274	−	0.255971i	−0.668808	+	0.743435i	$0.733195\pi$
$228$	−8.31882	+	1.71091i	−0.550927	+	0.113308i
$229$	8.49566	+	7.12871i	0.561409	+	0.471078i	0.878782	−	0.477223i	$-0.158356\pi$
$229$	8.49566	+	7.12871i	0.561409	+	0.471078i	−0.317373	+	0.948301i	$0.602801\pi$
$230$	26.8875	+	22.5613i	1.77291	+	1.48765i
$231$	2.88782	−	8.69214i	0.190004	−	0.571901i
$232$	0.871638	+	0.317250i	0.0572259	+	0.0208285i
$233$	1.60547	−	2.78076i	0.105178	−	0.182173i	−0.808633	−	0.588313i	$-0.799792\pi$
$233$	1.60547	−	2.78076i	0.105178	−	0.182173i	0.913811	+	0.406140i	$0.133125\pi$
$234$	7.86836	+	2.36906i	0.514371	+	0.154870i
$235$	−12.0210	−	20.8209i	−0.784162	−	1.35821i
$236$	0.503968	+	2.85814i	0.0328055	+	0.186049i
$237$	−2.98269	+	1.83653i	−0.193747	+	0.119296i
$238$	1.87261	−	0.681575i	0.121383	−	0.0441799i
$239$	4.20916	−	23.8714i	0.272268	−	1.54411i	−0.475239	−	0.879857i	$-0.657639\pi$
$239$	4.20916	−	23.8714i	0.272268	−	1.54411i	0.747508	−	0.664253i	$-0.231250\pi$
$240$	6.65809	+	0.980591i	0.429778	+	0.0632969i
$241$	3.61479	−	3.03317i	0.232849	−	0.195384i	−0.518896	−	0.854837i	$-0.673657\pi$
$241$	3.61479	−	3.03317i	0.232849	−	0.195384i	0.751745	+	0.659454i	$0.229212\pi$
$242$	−16.9643			−1.09051
$243$	−11.6043	−	10.4086i	−0.744418	−	0.667714i
$244$	2.36777			0.151581
$245$	−2.97648	+	2.49756i	−0.190160	+	0.159563i
$246$	−13.0260	−	1.91844i	−0.830507	−	0.122315i
$247$	2.33224	−	13.2268i	0.148397	−	0.841602i
$248$	0.320923	−	0.116807i	0.0203787	−	0.00741722i
$249$	−19.4513	+	11.9767i	−1.23268	+	0.758995i
$250$	3.43918	+	19.5046i	0.217513	+	1.23358i
$251$	14.9083	+	25.8219i	0.941004	+	1.62987i	0.763561	+	0.645735i	$0.223449\pi$
$251$	14.9083	+	25.8219i	0.941004	+	1.62987i	0.177443	+	0.984131i	$0.443218\pi$
$252$	−2.87262	−	0.864908i	−0.180958	−	0.0544841i
$253$	−23.8847	+	41.3695i	−1.50162	+	2.60088i
$254$	−10.7220	−	3.90249i	−0.672758	−	0.244864i
$255$	−4.22842	+	12.7273i	−0.264794	+	0.797014i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−8.94838	−	7.50859i	−0.558185	−	0.468373i	0.319516	−	0.947581i	$-0.396480\pi$
$257$	−8.94838	−	7.50859i	−0.558185	−	0.468373i	−0.877701	+	0.479208i	$0.840924\pi$
$258$	17.5064	−	3.60050i	1.08990	−	0.224158i
$259$	−1.68146	−	0.612002i	−0.104481	−	0.0380280i
$260$	−5.32139	+	9.21692i	−0.330019	+	0.571609i
$261$	2.55687	−	1.09818i	0.158267	−	0.0679758i
$262$	−6.18812	−	10.7181i	−0.382304	−	0.662169i
$263$	−2.37708	−	13.4811i	−0.146577	−	0.831281i	−0.966087	−	0.258216i	$-0.916865\pi$
$263$	−2.37708	−	13.4811i	−0.146577	−	0.831281i	0.819510	−	0.573065i	$-0.194246\pi$
$264$	0.259229	+	9.15563i	0.0159545	+	0.563490i
$265$	−5.10042	+	1.85640i	−0.313316	+	0.114038i
$266$	−0.851467	+	4.82891i	−0.0522068	+	0.296079i
$267$	−0.132286	−	0.333745i	−0.00809576	−	0.0204248i
$268$	4.34776	−	3.64821i	0.265582	−	0.222850i
$269$	8.76727			0.534550			0.267275	−	0.963620i	$-0.413877\pi$
$269$	8.76727			0.534550			0.267275	+	0.963620i	$0.413877\pi$
$270$	16.5656	−	11.5415i	1.00815	−	0.702393i
$271$	0.309464			0.0187986			0.00939930	−	0.999956i	$-0.497008\pi$
$271$	0.309464			0.0187986			0.00939930	+	0.999956i	$0.497008\pi$
$272$	−1.52657	+	1.28094i	−0.0925617	+	0.0776685i
$273$	2.94546	−	3.71915i	0.178267	−	0.225093i
$274$	−1.58421	+	8.98451i	−0.0957057	+	0.542774i
$275$	−50.1754	+	18.2623i	−3.02569	+	1.10126i
$276$	13.7660	+	7.43646i	0.828614	+	0.447622i
$277$	−2.61544	−	14.8329i	−0.157146	−	0.891221i	−0.956797	−	0.290756i	$-0.906093\pi$
$277$	−2.61544	−	14.8329i	−0.157146	−	0.891221i	0.799651	−	0.600465i	$-0.205018\pi$
$278$	−2.81271	−	4.87175i	−0.168695	−	0.292188i
$279$	0.461254	−	0.914858i	0.0276145	−	0.0547711i
$280$	1.94276	−	3.36496i	0.116102	−	0.201095i
$281$	30.0647	+	10.9426i	1.79351	+	0.652783i	0.998961	+	0.0455812i	$0.0145140\pi$
$281$	30.0647	+	10.9426i	1.79351	+	0.652783i	0.794547	+	0.607202i	$0.207708\pi$
$282$	−7.11849	−	8.01160i	−0.423900	−	0.477084i
$283$	−1.94220	−	1.62970i	−0.115452	−	0.0968754i	0.583234	−	0.812304i	$-0.301787\pi$
$283$	−1.94220	−	1.62970i	−0.115452	−	0.0968754i	−0.698686	+	0.715429i	$0.746231\pi$
$284$	3.00206	+	2.51903i	0.178139	+	0.149477i
$285$	−21.9186	−	24.6686i	−1.29835	−	1.46124i
$286$	−13.6111	−	4.95404i	−0.804843	−	0.292939i
$287$	−3.80084	+	6.58326i	−0.224357	+	0.388597i
$288$	2.99519	−	0.169746i	0.176493	−	0.0100024i
$289$	6.51439	+	11.2833i	0.383199	+	0.663721i
$290$	0.625849	+	3.54937i	0.0367511	+	0.208426i
$291$	9.26140	+	5.00306i	0.542913	+	0.293285i
$292$	4.57325	−	1.66453i	0.267629	−	0.0974090i
$293$	−1.13917	+	6.46056i	−0.0665511	+	0.377430i	0.933282	+	0.359145i	$0.116932\pi$
$293$	−1.13917	+	6.46056i	−0.0665511	+	0.377430i	−0.999833	+	0.0182849i	$0.994179\pi$
$294$	−1.07534	+	1.35781i	−0.0627152	+	0.0791889i
$295$	−8.63844	+	7.24851i	−0.502950	+	0.422025i
$296$	1.78937			0.104005
$297$	19.3841	+	19.4754i	1.12478	+	1.13008i
$298$	−19.4422			−1.12626
$299$	−18.9543	+	15.9045i	−1.09616	+	0.919784i
$300$	6.44430	+	16.2584i	0.372062	+	0.938677i
$301$	1.79186	−	10.1621i	0.103281	−	0.585736i
$302$	−8.87558	+	3.23045i	−0.510732	+	0.185891i
$303$	−0.860261	−	30.3833i	−0.0494207	−	1.74547i
$304$	−0.851467	−	4.82891i	−0.0488350	−	0.276957i
$305$	4.60001	+	7.96746i	0.263396	+	0.456215i
$306$	−0.703342	+	5.93686i	−0.0402074	+	0.339387i
$307$	−2.33913	+	4.05149i	−0.133501	+	0.231231i	−0.925024	−	0.379909i	$-0.875955\pi$
$307$	−2.33913	+	4.05149i	−0.133501	+	0.231231i	0.791523	+	0.611140i	$0.209289\pi$
$308$	4.96921	+	1.80865i	0.283147	+	0.103057i
$309$	25.5482	−	5.25443i	1.45339	−	0.298914i
$310$	1.01653	+	0.852966i	0.0577348	+	0.0484452i
$311$	−22.9718	−	19.2756i	−1.30261	−	1.09302i	−0.989688	−	0.143240i	$-0.954248\pi$
$311$	−22.9718	−	19.2756i	−1.30261	−	1.09302i	−0.312922	−	0.949779i	$-0.601308\pi$
$312$	−1.49580	+	4.50227i	−0.0846831	+	0.254891i
$313$	21.7693	+	7.92338i	1.23047	+	0.447856i	0.873760	−	0.486357i	$-0.161675\pi$
$313$	21.7693	+	7.92338i	1.23047	+	0.447856i	0.356715	+	0.934213i	$0.383897\pi$
$314$	7.38219	−	12.7863i	0.416601	−	0.721574i
$315$	−2.67043	−	11.3465i	−0.150461	−	0.639305i
$316$	−1.01116	−	1.75138i	−0.0568821	−	0.0985227i
$317$	1.31799	+	7.47468i	0.0740255	+	0.419820i	0.999190	+	0.0402521i	$0.0128161\pi$
$317$	1.31799	+	7.47468i	0.0740255	+	0.419820i	−0.925164	+	0.379568i	$0.876073\pi$
$318$	−2.06030	+	1.26859i	−0.115536	+	0.0711388i
$319$	−4.60933	+	1.67766i	−0.258073	+	0.0939309i
$320$	−0.674713	+	3.82649i	−0.0377176	+	0.213907i
$321$	−34.5343	−	5.08615i	−1.92752	−	0.283881i
$322$	6.91993	−	5.80651i	0.385632	−	0.323584i
$323$	9.77145			0.543698
$324$	6.19664	−	6.52699i	0.344258	−	0.362611i
$325$	−27.6573			−1.53415
$326$	−5.38106	+	4.51525i	−0.298029	+	0.250076i
$327$	23.0209	+	3.39047i	1.27306	+	0.187494i
$328$	1.32002	−	7.48620i	0.0728859	−	0.413356i
$329$	−5.81442	+	2.11628i	−0.320560	+	0.116674i
$330$	−30.3047	+	18.6595i	−1.66822	+	1.02717i
$331$	0.338982	+	1.92246i	0.0186321	+	0.105668i	0.992706	−	0.120564i	$-0.0384703\pi$
$331$	0.338982	+	1.92246i	0.0186321	+	0.105668i	−0.974073	+	0.226232i	$0.927359\pi$
$332$	−6.59416	−	11.4214i	−0.361901	−	0.626832i
$333$	3.91039	−	3.67771i	0.214288	−	0.201537i
$334$	10.0039	−	17.3272i	0.547388	−	0.948104i
$335$	20.7227	+	7.54245i	1.13220	+	0.412088i
$336$	0.546094	−	1.64371i	0.0297919	−	0.0896717i
$337$	6.13056	+	5.14415i	0.333953	+	0.280220i	0.794308	−	0.607515i	$-0.207834\pi$
$337$	6.13056	+	5.14415i	0.333953	+	0.280220i	−0.460355	+	0.887735i	$0.652278\pi$
$338$	4.21124	+	3.53365i	0.229061	+	0.192205i
$339$	−0.608177	+	0.125082i	−0.0330317	+	0.00679353i
$340$	−7.27606	−	2.64827i	−0.394600	−	0.143623i
$341$	−0.902999	+	1.56404i	−0.0489001	+	0.0846975i
$342$	−11.7856	−	8.80278i	−0.637294	−	0.476000i
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$	1.79186	+	10.1621i	0.0966105	+	0.547905i
$345$	1.72060	+	60.7691i	0.0926338	+	3.27170i
$346$	−2.95664	+	1.07613i	−0.158950	+	0.0578530i
$347$	−0.869896	+	4.93343i	−0.0466985	+	0.264840i	−0.999214	−	0.0396511i	$-0.987375\pi$
$347$	−0.869896	+	4.93343i	−0.0466985	+	0.264840i	0.952515	+	0.304491i	$0.0984865\pi$
$348$	0.592002	+	1.49357i	0.0317347	+	0.0800635i
$349$	15.8306	−	13.2834i	0.847392	−	0.711047i	−0.111821	−	0.993728i	$-0.535668\pi$
$349$	15.8306	−	13.2834i	0.847392	−	0.711047i	0.959214	+	0.282682i	$0.0912240\pi$
$350$	10.0972			0.539721
$351$	5.98470	+	12.9133i	0.319440	+	0.689262i
$352$	−5.28813			−0.281858
$353$	−19.2203	+	16.1277i	−1.02299	+	0.858391i	−0.990000	−	0.141064i	$-0.954948\pi$
$353$	−19.2203	+	16.1277i	−1.02299	+	0.858391i	−0.0329905	+	0.999456i	$0.510503\pi$
$354$	−3.12090	+	3.94067i	−0.165874	+	0.209444i
$355$	−2.64414	+	14.9957i	−0.140336	+	0.795887i
$356$	0.194772	−	0.0708912i	0.0103229	−	0.00375723i
$357$	3.03683	+	1.64052i	0.160726	+	0.0868253i
$358$	−0.524095	−	2.97229i	−0.0276993	−	0.157090i
$359$	10.2552	+	17.7624i	0.541246	+	0.937466i	0.998833	+	0.0483010i	$0.0153807\pi$
$359$	10.2552	+	17.7624i	0.541246	+	0.937466i	−0.457586	+	0.889165i	$0.651286\pi$
$360$	6.39013	+	9.74892i	0.336789	+	0.513813i
$361$	−2.52167	+	4.36766i	−0.132719	+	0.229877i
$362$	−15.2543	−	5.55212i	−0.801750	−	0.291813i
$363$	−19.5165	−	21.9651i	−1.02435	−	1.15287i
$364$	2.09826	+	1.76065i	0.109979	+	0.0922833i
$365$	14.4858	+	12.1550i	0.758220	+	0.636222i
$366$	2.72400	+	3.06576i	0.142386	+	0.160250i
$367$	−3.23123	−	1.17607i	−0.168669	−	0.0613904i	0.256306	−	0.966596i	$-0.417495\pi$
$367$	−3.23123	−	1.17607i	−0.168669	−	0.0613904i	−0.424974	+	0.905205i	$0.639717\pi$
$368$	−4.51666	+	7.82309i	−0.235447	+	0.407807i
$369$	−12.5017	−	19.0729i	−0.650815	−	0.992898i
$370$	3.47632	+	6.02117i	0.180725	+	0.313026i
$371$	0.242572	+	1.37570i	0.0125937	+	0.0714226i
$372$	0.520445	+	0.281147i	0.0269838	+	0.0145768i
$373$	−12.1040	+	4.40550i	−0.626722	+	0.228108i	−0.635804	−	0.771851i	$-0.719331\pi$
$373$	−12.1040	+	4.40550i	−0.626722	+	0.228108i	0.00908215	+	0.999959i	$0.497109\pi$
$374$	1.82993	−	10.3780i	0.0946233	−	0.536635i
$375$	−21.2976	+	26.8920i	−1.09981	+	1.38869i
$376$	4.73996	−	3.97730i	0.244445	−	0.205114i
$377$	−2.54072			−0.130854
$378$	−2.18492	−	4.71446i	−0.112380	−	0.242486i
$379$	−23.9767			−1.23160			−0.615800	−	0.787902i	$-0.711167\pi$
$379$	−23.9767			−1.23160			−0.615800	+	0.787902i	$0.711167\pi$
$380$	14.5949	−	12.2465i	0.748701	−	0.628235i
$381$	−7.28220	−	18.3723i	−0.373078	−	0.941241i
$382$	4.22258	−	23.9475i	0.216046	−	1.22526i
$383$	24.1854	−	8.80278i	1.23582	−	0.449801i	0.360232	−	0.932863i	$-0.382698\pi$
$383$	24.1854	−	8.80278i	1.23582	−	0.449801i	0.875586	+	0.483062i	$0.160475\pi$
$384$	0.0490210	+	1.73136i	0.00250159	+	0.0883529i
$385$	3.56797	+	20.2350i	0.181840	+	1.03127i
$386$	−0.143881	−	0.249210i	−0.00732337	−	0.0126845i
$387$	24.8021	+	18.5249i	1.26076	+	0.941674i
$388$	−3.03870	+	5.26318i	−0.154266	+	0.267197i
$389$	−17.3392	−	6.31096i	−0.879134	−	0.319979i	−0.137274	−	0.990533i	$-0.543834\pi$
$389$	−17.3392	−	6.31096i	−0.879134	−	0.319979i	−0.741860	+	0.670555i	$0.766056\pi$
$390$	−18.0559	+	3.71351i	−0.914297	+	0.188041i
$391$	−13.7900	−	11.5712i	−0.697389	−	0.585179i
$392$	−0.766044	−	0.642788i	−0.0386911	−	0.0324657i
$393$	6.75860	−	20.3430i	0.340926	−	1.02617i
$394$	19.7847	+	7.20104i	0.996739	+	0.362783i
$395$	3.92888	−	6.80501i	0.197683	−	0.342397i
$396$	−11.5564	+	10.8687i	−0.580729	+	0.546174i
$397$	5.38025	+	9.31887i	0.270027	+	0.467701i	0.968868	−	0.247576i	$-0.0796340\pi$
$397$	5.38025	+	9.31887i	0.270027	+	0.467701i	−0.698841	+	0.715277i	$0.746301\pi$
$398$	3.94379	+	22.3664i	0.197685	+	1.12112i
$399$	−7.23197	+	4.45293i	−0.362051	+	0.222926i
$400$	−9.48831	+	3.45346i	−0.474415	+	0.172673i
$401$	2.21558	−	12.5652i	0.110641	−	0.627476i	−0.878176	−	0.478338i	$-0.841239\pi$
$401$	2.21558	−	12.5652i	0.110641	−	0.627476i	0.988817	−	0.149137i	$-0.0476496\pi$
$402$	9.72552	+	1.43236i	0.485065	+	0.0714394i
$403$	−0.716598	+	0.601297i	−0.0356963	+	0.0299528i
$404$	17.5488			0.873086
$405$	34.0016	+	8.17106i	1.68955	+	0.406023i
$406$	0.927578			0.0460349
$407$	−7.24865	+	6.08234i	−0.359302	+	0.301490i
$408$	−3.41478	−	0.502922i	−0.169057	−	0.0248984i
$409$	0.546532	−	3.09953i	0.0270242	−	0.153262i	−0.968310	−	0.249753i	$-0.919651\pi$
$409$	0.546532	−	3.09953i	0.0270242	−	0.153262i	0.995334	+	0.0964906i	$0.0307618\pi$
$410$	27.7552	−	10.1021i	1.37073	−	0.498906i
$411$	−13.4556	+	8.28499i	−0.663714	+	0.408668i
$412$	2.61497	+	14.8302i	0.128830	+	0.730632i
$413$	1.45112	+	2.51341i	0.0714048	+	0.123677i
$414$	6.20839	+	26.3792i	0.305126	+	1.29647i
$415$	25.6217	−	44.3781i	1.25772	−	2.17844i
$416$	−2.57390	−	0.936824i	−0.126196	−	0.0459316i
$417$	3.07201	−	9.24654i	0.150437	−	0.452805i
$418$	19.8634	+	16.6674i	0.971550	+	0.815227i
$419$	−3.62254	−	3.03968i	−0.176973	−	0.148498i	0.549999	−	0.835166i	$-0.314628\pi$
$419$	−3.62254	−	3.03968i	−0.176973	−	0.148498i	−0.726971	+	0.686668i	$0.759073\pi$
$420$	6.59194	−	1.35575i	0.321654	−	0.0661537i
$421$	−15.4225	−	5.61334i	−0.751648	−	0.273577i	−0.0623487	−	0.998054i	$-0.519859\pi$
$421$	−15.4225	−	5.61334i	−0.751648	−	0.273577i	−0.689299	+	0.724477i	$0.742081\pi$
$422$	−9.94216	+	17.2203i	−0.483977	+	0.838272i
$423$	2.18386	−	18.4338i	0.106183	−	0.896284i
$424$	−0.698459	−	1.20977i	−0.0339202	−	0.0587515i
$425$	−3.49410	−	19.8160i	−0.169489	−	0.961218i
$426$	0.192109	+	6.78503i	0.00930771	+	0.328736i
$427$	2.22498	−	0.809826i	0.107674	−	0.0391902i
$428$	3.49961	−	19.8473i	0.169160	−	0.959355i
$429$	−9.24445	−	23.3229i	−0.446326	−	1.12604i
$430$	−30.7140	+	25.7721i	−1.48116	+	1.24284i
$431$	−28.7804			−1.38631			−0.693153	−	0.720791i	$-0.743779\pi$
$431$	−28.7804			−1.38631			−0.693153	+	0.720791i	$0.743779\pi$
$432$	3.66560	+	3.68285i	0.176361	+	0.177191i
$433$	−1.63216			−0.0784365			−0.0392182	−	0.999231i	$-0.512487\pi$
$433$	−1.63216			−0.0784365			−0.0392182	+	0.999231i	$0.512487\pi$
$434$	0.261619	−	0.219524i	0.0125581	−	0.0105375i
$435$	−3.87566	+	4.89370i	−0.185824	+	0.234635i
$436$	−2.33288	+	13.2304i	−0.111725	+	0.633621i
$437$	41.6227	−	15.1494i	1.99109	−	0.724696i
$438$	7.41648	+	4.00643i	0.354373	+	0.191435i
$439$	0.621095	+	3.52241i	0.0296433	+	0.168115i	0.996035	−	0.0889569i	$-0.0283533\pi$
$439$	0.621095	+	3.52241i	0.0296433	+	0.168115i	−0.966392	+	0.257072i	$0.917242\pi$
$440$	−10.2736	−	17.7943i	−0.489772	−	0.848311i
$441$	−2.99519	+	0.169746i	−0.142628	+	0.00808313i
$442$	2.72922	−	4.72714i	0.129816	−	0.224847i
$443$	17.9895	+	6.54763i	0.854706	+	0.311087i	0.731957	−	0.681350i	$-0.238607\pi$
$443$	17.9895	+	6.54763i	0.854706	+	0.311087i	0.122748	+	0.992438i	$0.460829\pi$
$444$	2.05858	+	2.31686i	0.0976959	+	0.109953i
$445$	0.616941	+	0.517675i	0.0292458	+	0.0245401i
$446$	−11.0011	−	9.23102i	−0.520917	−	0.437101i
$447$	−22.3673	−	25.1736i	−1.05794	−	1.19067i
$448$	0.939693	+	0.342020i	0.0443963	+	0.0161589i
$449$	5.43726	−	9.41761i	0.256600	−	0.444444i	−0.708729	−	0.705481i	$-0.750731\pi$
$449$	5.43726	−	9.41761i	0.256600	−	0.444444i	0.965329	+	0.261037i	$0.0840643\pi$
$450$	−13.6373	+	27.0484i	−0.642867	+	1.27507i
$451$	20.0993	+	34.8131i	0.946441	+	1.63928i
$452$	−0.0622495	−	0.353035i	−0.00292797	−	0.0166053i
$453$	−14.3936	−	7.77552i	−0.676272	−	0.365326i
$454$	10.5959	−	3.85659i	0.497290	−	0.180999i
$455$	−1.84810	+	10.4811i	−0.0866403	+	0.491361i
$456$	5.27284	−	6.65787i	0.246923	−	0.311783i
$457$	8.75541	−	7.34666i	0.409561	−	0.343662i	−0.414614	−	0.909997i	$-0.636084\pi$
$457$	8.75541	−	7.34666i	0.409561	−	0.343662i	0.824175	+	0.566335i	$0.191639\pi$
$458$	−11.0903			−0.518216
$459$	−8.49612	+	5.91936i	−0.396565	+	0.276292i
$460$	−35.0991			−1.63651
$461$	−3.65515	+	3.06703i	−0.170237	+	0.142846i	−0.723926	−	0.689878i	$-0.757664\pi$
$461$	−3.65515	+	3.06703i	−0.170237	+	0.142846i	0.553689	+	0.832724i	$0.313220\pi$
$462$	3.37501	+	8.51482i	0.157020	+	0.396145i
$463$	3.63174	−	20.5966i	0.168781	−	0.957207i	−0.776298	−	0.630366i	$-0.782905\pi$
$463$	3.63174	−	20.5966i	0.168781	−	0.957207i	0.945079	−	0.326841i	$-0.105984\pi$
$464$	−0.871638	+	0.317250i	−0.0404648	+	0.0147280i
$465$	0.0650499	+	2.29748i	0.00301662	+	0.106543i
$466$	0.557574	+	3.16216i	0.0258291	+	0.146484i
$467$	−0.594718	−	1.03008i	−0.0275203	−	0.0476665i	0.851937	−	0.523644i	$-0.175428\pi$
$467$	−0.594718	−	1.03008i	−0.0275203	−	0.0476665i	−0.879458	+	0.475977i	$0.842094\pi$
$468$	−7.55032	+	3.24288i	−0.349013	+	0.149902i
$469$	2.83780	−	4.91522i	0.131038	−	0.226964i
$470$	22.5921	+	8.22283i	1.04209	+	0.379291i
$471$	25.0484	−	5.15163i	1.15417	−	0.237375i
$472$	−2.22324	−	1.86552i	−0.102333	−	0.0858675i
$473$	−41.8012	−	35.0754i	−1.92202	−	1.61277i
$474$	1.10438	−	3.32410i	0.0507257	−	0.152681i
$475$	46.5250	+	16.9337i	2.13471	+	0.776972i
$476$	−0.996396	+	1.72581i	−0.0456697	+	0.0791023i
$477$	−4.01281	−	1.20821i	−0.183734	−	0.0553199i
$478$	12.1198	+	20.9921i	0.554347	+	0.960157i
$479$	1.80442	+	10.2334i	0.0824459	+	0.467574i	0.997879	+	0.0651028i	$0.0207375\pi$
$479$	1.80442	+	10.2334i	0.0824459	+	0.467574i	−0.915433	+	0.402471i	$0.868151\pi$
$480$	−5.73071	+	3.52856i	−0.261570	+	0.161056i
$481$	−4.60568	+	1.67633i	−0.210001	+	0.0764340i
$482$	−0.819407	+	4.64709i	−0.0373230	+	0.211669i
$483$	15.4792	+	2.27975i	0.704328	+	0.103732i
$484$	12.9954	−	10.9044i	0.590700	−	0.495656i
$485$	−23.6138			−1.07225
$486$	15.5800	+	0.514365i	0.706722	+	0.0233321i
$487$	33.9850			1.54001			0.770004	−	0.638039i	$-0.220254\pi$
$487$	33.9850			1.54001			0.770004	+	0.638039i	$0.220254\pi$
$488$	−1.81382	+	1.52198i	−0.0821078	+	0.0688966i
$489$	−12.0369	−	1.77277i	−0.544328	−	0.0801675i
$490$	0.674713	−	3.82649i	0.0304804	−	0.172863i
$491$	27.1846	−	9.89439i	1.22682	−	0.446527i	0.354315	−	0.935126i	$-0.384714\pi$
$491$	27.1846	−	9.89439i	1.22682	−	0.446527i	0.872509	+	0.488599i	$0.162492\pi$
$492$	11.2116	−	6.90334i	0.505460	−	0.311226i
$493$	−0.320983	−	1.82039i	−0.0144564	−	0.0819861i
$494$	6.71543	+	11.6315i	0.302141	+	0.523324i
$495$	−59.0240	−	17.7714i	−2.65293	−	0.798763i
$496$	−0.170760	+	0.295765i	−0.00766734	+	0.0132802i
$497$	3.68257	+	1.34035i	0.165186	+	0.0601228i
$498$	7.20206	−	21.6778i	0.322732	−	0.971404i
$499$	−15.1031	−	12.6730i	−0.676107	−	0.567321i	0.238759	−	0.971079i	$-0.423259\pi$
$499$	−15.1031	−	12.6730i	−0.676107	−	0.567321i	−0.914866	+	0.403758i	$0.867704\pi$
$500$	−15.1719	−	12.7307i	−0.678506	−	0.569334i
$501$	33.9440	−	6.98117i	1.51651	−	0.311896i
$502$	−28.0184	−	10.1979i	−1.25052	−	0.455154i
$503$	8.09160	−	14.0151i	0.360786	−	0.624901i	−0.627304	−	0.778774i	$-0.715842\pi$
$503$	8.09160	−	14.0151i	0.360786	−	0.624901i	0.988090	+	0.153874i	$0.0491750\pi$
$504$	2.75651	−	1.18393i	0.122784	−	0.0527362i
$505$	34.0931	+	59.0510i	1.51712	+	2.62774i
$506$	−8.29506	−	47.0436i	−0.368760	−	2.09134i
$507$	0.269487	+	9.51794i	0.0119684	+	0.422706i
$508$	10.7220	−	3.90249i	0.475712	−	0.173145i
$509$	5.11966	−	29.0350i	0.226925	−	1.28696i	−0.632046	−	0.774931i	$-0.717785\pi$
$509$	5.11966	−	29.0350i	0.226925	−	1.28696i	0.858971	−	0.512024i	$-0.171104\pi$
$510$	−4.94178	−	12.4676i	−0.218826	−	0.552077i
$511$	3.72814	−	3.12828i	0.164923	−	0.138387i
$512$	−1.00000			−0.0441942
$513$	−2.16102	−	25.3870i	−0.0954112	−	1.12086i
$514$	11.6813			0.515239
$515$	−44.8228	+	37.6108i	−1.97513	+	1.65733i
$516$	−11.0964	+	14.0111i	−0.488490	+	0.616803i
$517$	−5.68189	+	32.2236i	−0.249889	+	1.41719i
$518$	1.68146	−	0.612002i	0.0738792	−	0.0268898i
$519$	−4.79481	−	2.59019i	−0.210469	−	0.113697i
$520$	−1.84810	−	10.4811i	−0.0810445	−	0.459626i
$521$	−2.16668	−	3.75280i	−0.0949239	−	0.164413i	0.814653	−	0.579949i	$-0.196927\pi$
$521$	−2.16668	−	3.75280i	−0.0949239	−	0.164413i	−0.909577	+	0.415536i	$0.863594\pi$
$522$	−1.25278	+	2.48478i	−0.0548327	+	0.108756i
$523$	8.73785	−	15.1344i	0.382080	−	0.661781i	−0.609280	−	0.792955i	$-0.708541\pi$
$523$	8.73785	−	15.1344i	0.382080	−	0.661781i	0.991359	+	0.131174i	$0.0418746\pi$
$524$	11.6299	+	4.23293i	0.508053	+	0.184916i
$525$	11.6163	+	13.0738i	0.506979	+	0.570586i
$526$	10.4864	+	8.79917i	0.457231	+	0.383662i
$527$	−0.521352	−	0.437466i	−0.0227105	−	0.0190563i
$528$	−6.08371	−	6.84699i	−0.264759	−	0.297977i
$529$	−55.0669	−	20.0427i	−2.39421	−	0.871422i
$530$	2.71388	−	4.70057i	0.117883	−	0.204180i
$531$	−8.69276	+	0.492642i	−0.377233	+	0.0213788i
$532$	−2.45170	−	4.24647i	−0.106295	−	0.184108i
$533$	3.61565	+	20.5054i	0.156611	+	0.888187i
$534$	0.315864	+	0.170631i	0.0136688	+	0.00738395i
$535$	73.5842	−	26.7825i	3.18132	−	1.15791i
$536$	−0.985558	+	5.58938i	−0.0425696	+	0.241424i
$537$	3.24554	−	4.09805i	0.140055	−	0.176844i
$538$	−6.71612	+	5.63550i	−0.289553	+	0.242963i
$539$	5.28813			0.227776
$540$	−5.27127	+	19.4895i	−0.226839	+	0.838693i
$541$	11.3431			0.487678			0.243839	−	0.969816i	$-0.421593\pi$
$541$	11.3431			0.487678			0.243839	+	0.969816i	$0.421593\pi$
$542$	−0.237063	+	0.198920i	−0.0101827	+	0.00854433i
$543$	−10.3605	−	26.1385i	−0.444611	−	1.12171i
$544$	0.346045	−	1.96252i	0.0148365	−	0.0841422i
$545$	−49.0519	+	17.8534i	−2.10115	+	0.764758i
$546$	0.134273	+	4.74234i	0.00574635	+	0.202954i
$547$	−2.81811	−	15.9823i	−0.120494	−	0.683354i	−0.983883	−	0.178815i	$-0.942774\pi$
$547$	−2.81811	−	15.9823i	−0.120494	−	0.683354i	0.863389	−	0.504539i	$-0.168338\pi$
$548$	−4.56155	−	7.90084i	−0.194860	−	0.337507i
$549$	−0.835689	+	7.05399i	−0.0356664	+	0.301057i
$550$	26.6978	−	46.2419i	1.13840	−	1.97176i
$551$	4.27399	+	1.55561i	0.182078	+	0.0662710i
$552$	−15.3254	+	3.15194i	−0.652293	+	0.134155i
$553$	−1.54919	−	1.29992i	−0.0658781	−	0.0552783i
$554$	11.5379	+	9.68147i	0.490199	+	0.411326i
$555$	−3.79680	+	11.4281i	−0.161165	+	0.485097i
$556$	5.28616	+	1.92400i	0.224183	+	0.0815960i
$557$	−1.91271	+	3.31291i	−0.0810442	+	0.140373i	−0.903699	−	0.428169i	$-0.859159\pi$
$557$	−1.91271	+	3.31291i	−0.0810442	+	0.140373i	0.822655	+	0.568542i	$0.192492\pi$
$558$	0.234718	+	0.997310i	0.00993642	+	0.0422195i
$559$	−14.1322	−	24.4777i	−0.597728	−	1.03530i
$560$	0.674713	+	3.82649i	0.0285118	+	0.161699i
$561$	15.5426	−	9.57001i	0.656208	−	0.404046i
$562$	−30.0647	+	10.9426i	−1.26820	+	0.461588i
$563$	−6.20803	+	35.2075i	−0.261637	+	1.48382i	0.516805	+	0.856103i	$0.327121\pi$
$563$	−6.20803	+	35.2075i	−0.261637	+	1.48382i	−0.778442	+	0.627716i	$0.783990\pi$
$564$	10.6028	+	1.56156i	0.446460	+	0.0657537i
$565$	1.06701	−	0.895328i	0.0448895	−	0.0376667i
$566$	2.53536			0.106569
$567$	3.59057	−	8.25274i	0.150790	−	0.346583i
$568$	−3.91891			−0.164434
$569$	12.8444	−	10.7778i	0.538467	−	0.451827i	−0.332546	−	0.943087i	$-0.607908\pi$
$569$	12.8444	−	10.7778i	0.538467	−	0.451827i	0.871013	+	0.491260i	$0.163463\pi$
$570$	32.6473	+	4.80823i	1.36744	+	0.201395i
$571$	−3.79138	+	21.5020i	−0.158664	+	0.899829i	0.796695	+	0.604382i	$0.206580\pi$
$571$	−3.79138	+	21.5020i	−0.158664	+	0.899829i	−0.955359	+	0.295447i	$0.904531\pi$
$572$	13.6111	−	4.95404i	0.569110	−	0.207139i
$573$	35.8647	−	22.0829i	1.49827	−	0.922528i
$574$	−1.32002	−	7.48620i	−0.0550965	−	0.312468i
$575$	−45.6059	−	78.9917i	−1.90190	−	3.29418i
$576$	−2.18534	+	2.05531i	−0.0910559	+	0.0856378i
$577$	11.8807	−	20.5779i	0.494599	−	0.856671i	−0.505381	−	0.862896i	$-0.668648\pi$
$577$	11.8807	−	20.5779i	0.494599	−	0.856671i	0.999981	+	0.00622509i	$0.00198152\pi$
$578$	−12.2431	−	4.45611i	−0.509244	−	0.185350i
$579$	0.157146	−	0.472999i	0.00653075	−	0.0196571i
$580$	−2.76092	−	2.31668i	−0.114641	−	0.0961951i
$581$	−10.1028	−	8.47729i	−0.419136	−	0.351697i
$582$	−10.3105	+	2.12054i	−0.427386	+	0.0878994i
$583$	6.94159	+	2.52653i	0.287491	+	0.104638i
$584$	−2.43337	+	4.21473i	−0.100694	+	0.174407i
$585$	−25.5806	−	19.1064i	−1.05763	−	0.789951i
$586$	−3.28011	−	5.68132i	−0.135500	−	0.234693i
$587$	−0.633502	−	3.59277i	−0.0261474	−	0.148289i	0.968939	−	0.247300i	$-0.0795433\pi$
$587$	−0.633502	−	3.59277i	−0.0261474	−	0.148289i	−0.995086	+	0.0990106i	$0.968432\pi$
$588$	−0.0490210	−	1.73136i	−0.00202159	−	0.0714000i
$589$	1.57362	−	0.572749i	0.0648397	−	0.0235997i
$590$	1.95818	−	11.1054i	0.0806168	−	0.457201i
$591$	13.4374	+	33.9014i	0.552742	+	1.39452i
$592$	−1.37074	+	1.15019i	−0.0563371	+	0.0472724i
$593$	−20.2008			−0.829547			−0.414773	−	0.909925i	$-0.636139\pi$
$593$	−20.2008			−0.829547			−0.414773	+	0.909925i	$0.636139\pi$
$594$	−27.3676	−	2.45913i	−1.12291	−	0.100899i
$595$	−7.74303			−0.317433
$596$	14.8936	−	12.4972i	0.610067	−	0.511907i
$597$	−24.4225	+	30.8377i	−0.999548	+	1.26210i
$598$	4.29659	−	24.3672i	0.175701	−	0.996448i
$599$	29.0993	−	10.5913i	1.18896	−	0.432747i	0.329604	−	0.944119i	$-0.393085\pi$
$599$	29.0993	−	10.5913i	1.18896	−	0.432747i	0.859359	+	0.511372i	$0.170863\pi$
$600$	−15.3873	−	8.31231i	−0.628184	−	0.339349i
$601$	4.21362	+	23.8966i	0.171877	+	0.974763i	0.941687	+	0.336490i	$0.109240\pi$
$601$	4.21362	+	23.8966i	0.171877	+	0.974763i	−0.769810	+	0.638273i	$0.779649\pi$
$602$	5.15945	+	8.93643i	0.210283	+	0.364222i
$603$	9.33410	+	14.2403i	0.380114	+	0.579911i
$604$	4.72260	−	8.17978i	0.192160	−	0.332831i
$605$	61.9398	+	22.5443i	2.51821	+	0.916554i
$606$	20.1890	+	22.7220i	0.820122	+	0.923017i
$607$	−3.83935	−	3.22159i	−0.155834	−	0.130760i	0.561537	−	0.827452i	$-0.310210\pi$
$607$	−3.83935	−	3.22159i	−0.155834	−	0.130760i	−0.717371	+	0.696691i	$0.754655\pi$
$608$	3.75622	+	3.15185i	0.152335	+	0.127824i
$609$	1.06713	+	1.20102i	0.0432423	+	0.0486676i
$610$	−8.64520	−	3.14659i	−0.350034	−	0.127402i
$611$	−8.47417	+	14.6777i	−0.342828	+	0.593796i
$612$	−3.27735	−	5.00000i	−0.132479	−	0.202113i
$613$	−2.19176	−	3.79624i	−0.0885243	−	0.153329i	0.818363	−	0.574701i	$-0.194882\pi$
$613$	−2.19176	−	3.79624i	−0.0885243	−	0.153329i	−0.906888	+	0.421373i	$0.861548\pi$
$614$	−0.812371	−	4.60718i	−0.0327846	−	0.185931i
$615$	45.0109	+	24.3152i	1.81502	+	0.980483i
$616$	−4.96921	+	1.80865i	−0.200215	+	0.0728724i
$617$	1.07156	−	6.07709i	0.0431392	−	0.244655i	−0.955611	−	0.294631i	$-0.904803\pi$
$617$	1.07156	−	6.07709i	0.0431392	−	0.244655i	0.998750	+	0.0499760i	$0.0159145\pi$
$618$	−16.1936	+	20.4472i	−0.651401	+	0.822506i
$619$	12.2473	−	10.2767i	0.492259	−	0.413054i	−0.362576	−	0.931954i	$-0.618103\pi$
$619$	12.2473	−	10.2767i	0.492259	−	0.413054i	0.854835	+	0.518900i	$0.173658\pi$
$620$	−1.32698			−0.0532928
$621$	−27.0130	+	38.3865i	−1.08400	+	1.54040i
$622$	29.9875			1.20239
$623$	0.158780	−	0.133232i	0.00636137	−	0.00533782i
$624$	−1.74815	−	4.41042i	−0.0699821	−	0.176558i
$625$	4.59615	−	26.0661i	0.183846	−	1.04264i
$626$	−21.7693	+	7.92338i	−0.870077	+	0.316682i
$627$	1.27111	+	44.8937i	0.0507631	+	1.79288i
$628$	2.56381	+	14.5401i	0.102307	+	0.580212i
$629$	−1.78292	−	3.08812i	−0.0710899	−	0.123131i
$630$	9.33908	+	6.97544i	0.372078	+	0.277908i
$631$	20.5836	−	35.6519i	0.819422	−	1.41928i	−0.0866875	−	0.996236i	$-0.527628\pi$
$631$	20.5836	−	35.6519i	0.819422	−	1.41928i	0.906109	−	0.423044i	$-0.139039\pi$
$632$	1.90036	+	0.691673i	0.0755921	+	0.0275133i
$633$	−33.7346	+	6.93810i	−1.34083	+	0.275765i
$634$	−5.81427	−	4.87875i	−0.230914	−	0.193760i
$635$	33.9619	+	28.4975i	1.34774	+	1.13089i
$636$	0.762849	−	2.29613i	0.0302489	−	0.0910474i
$637$	2.57390	+	0.936824i	0.101982	+	0.0371183i
$638$	2.45257	−	4.24798i	0.0970984	−	0.168179i
$639$	−8.56416	+	8.05456i	−0.338793	+	0.318634i
$640$	−1.94276	−	3.36496i	−0.0767943	−	0.133012i
$641$	−4.55099	−	25.8099i	−0.179753	−	1.01943i	−0.932513	−	0.361136i	$-0.882389\pi$
$641$	−4.55099	−	25.8099i	−0.179753	−	1.01943i	0.752760	−	0.658295i	$-0.228722\pi$
$642$	29.7241	−	18.3020i	1.17312	−	0.722323i
$643$	−25.1102	+	9.13935i	−0.990248	+	0.360421i	−0.785816	−	0.618460i	$-0.787757\pi$
$643$	−25.1102	+	9.13935i	−0.990248	+	0.360421i	−0.204432	+	0.978881i	$0.565535\pi$
$644$	−1.56862	+	8.89609i	−0.0618123	+	0.350555i
$645$	−68.7042	−	10.1186i	−2.70522	−	0.398420i
$646$	−7.48537	+	6.28097i	−0.294508	+	0.247121i
$647$	−18.1894			−0.715099			−0.357550	−	0.933894i	$-0.616388\pi$
$647$	−18.1894			−0.715099			−0.357550	+	0.933894i	$0.616388\pi$
$648$	−0.551432	+	8.98309i	−0.0216623	+	0.352889i
$649$	15.3474			0.602438
$650$	21.1867	−	17.7778i	0.831011	−	0.697301i
$651$	0.585216	+	0.0861895i	0.0229364	+	0.00337803i
$652$	1.21979	−	6.91776i	0.0477706	−	0.270920i
$653$	−30.9631	+	11.2696i	−1.21168	+	0.441015i	−0.867286	−	0.497811i	$-0.834137\pi$
$653$	−30.9631	+	11.2696i	−1.21168	+	0.441015i	−0.344393	+	0.938826i	$0.611915\pi$
$654$	−19.8144	+	12.2003i	−0.774804	+	0.477069i
$655$	8.35042	+	47.3576i	0.326278	+	1.85041i
$656$	3.80084	+	6.58326i	0.148398	+	0.257033i
$657$	3.34480	+	14.2119i	0.130493	+	0.554461i
$658$	3.09379	−	5.35860i	0.120609	−	0.208900i
$659$	11.4085	+	4.15237i	0.444414	+	0.161753i	0.554527	−	0.832166i	$-0.312899\pi$
$659$	11.4085	+	4.15237i	0.444414	+	0.161753i	−0.110113	+	0.993919i	$0.535121\pi$
$660$	11.2207	−	33.7735i	0.436764	−	1.31463i
$661$	−19.4967	−	16.3597i	−0.758333	−	0.636317i	0.179359	−	0.983784i	$-0.442597\pi$
$661$	−19.4967	−	16.3597i	−0.758333	−	0.636317i	−0.937692	+	0.347467i	$0.887042\pi$
$662$	−1.49541	−	1.25480i	−0.0581207	−	0.0487691i
$663$	9.26046	−	1.90457i	0.359646	−	0.0739676i
$664$	12.3930	+	4.51067i	0.480940	+	0.175048i
$665$	9.52612	−	16.4997i	0.369407	−	0.639832i
$666$	−0.631547	+	5.33084i	−0.0244720	+	0.206566i
$667$	−4.18956	−	7.25652i	−0.162220	−	0.280974i
$668$	3.47431	+	19.7038i	0.134425	+	0.762363i
$669$	−0.703987	−	24.8639i	−0.0272177	−	0.961293i
$670$	−20.7227	+	7.54245i	−0.800588	+	0.291390i
$671$	2.17426	−	12.3309i	0.0839365	−	0.476028i
$672$	0.638224	+	1.61018i	0.0246200	+	0.0621139i
$673$	−15.7947	+	13.2533i	−0.608842	+	0.510879i	−0.894274	−	0.447520i	$-0.852307\pi$
$673$	−15.7947	+	13.2533i	−0.608842	+	0.510879i	0.285432	+	0.958399i	$0.407863\pi$
$674$	−8.00288			−0.308259
$675$	−50.7108	+	13.4604i	−1.95186	+	0.518090i
$676$	−5.49739			−0.211438
$677$	17.9909	−	15.0962i	0.691447	−	0.580193i	−0.227879	−	0.973689i	$-0.573179\pi$
$677$	17.9909	−	15.0962i	0.691447	−	0.580193i	0.919326	+	0.393497i	$0.128735\pi$
$678$	0.385489	−	0.486747i	0.0148046	−	0.0186934i
$679$	−1.05533	+	5.98506i	−0.0404998	+	0.229686i
$680$	7.27606	−	2.64827i	0.279024	−	0.101557i
$681$	17.1835	+	9.28261i	0.658472	+	0.355710i
$682$	−0.313608	−	1.77856i	−0.0120087	−	0.0681046i
$683$	17.2450	+	29.8692i	0.659862	+	1.14291i	0.980651	+	0.195764i	$0.0627186\pi$
$683$	17.2450	+	29.8692i	0.659862	+	1.14291i	−0.320789	+	0.947151i	$0.603948\pi$
$684$	14.6866	−	0.832332i	0.561558	−	0.0318250i
$685$	17.7240	−	30.6989i	0.677199	−	1.17294i
$686$	−0.939693	−	0.342020i	−0.0358776	−	0.0130584i
$687$	−12.7588	−	14.3596i	−0.486779	−	0.547852i
$688$	−7.90474	−	6.63286i	−0.301365	−	0.252875i
$689$	2.93111	+	2.45949i	0.111666	+	0.0936991i
$690$	−40.3797	−	45.4459i	−1.53723	−	1.73010i
$691$	7.52017	+	2.73712i	0.286081	+	0.104125i	0.481075	−	0.876680i	$-0.340247\pi$
$691$	7.52017	+	2.73712i	0.286081	+	0.104125i	−0.194994	+	0.980804i	$0.562469\pi$
$692$	1.57320	−	2.72485i	0.0598039	−	0.103583i
$693$	−7.14211	+	14.1658i	−0.271306	+	0.538113i
$694$	−2.50477	−	4.33838i	−0.0950796	−	0.164683i
$695$	3.79554	+	21.5256i	0.143973	+	0.816511i
$696$	−1.41355	−	0.763605i	−0.0535803	−	0.0289444i
$697$	−14.2350	+	5.18112i	−0.539189	+	0.196249i
$698$	−3.58851	+	20.3514i	−0.135827	+	0.770313i
$699$	−3.45286	+	4.35984i	−0.130599	+	0.164904i
$700$	−7.73494	+	6.49039i	−0.292353	+	0.245314i
$701$	−27.5575			−1.04083			−0.520415	−	0.853913i	$-0.674223\pi$
$701$	−27.5575			−1.04083			−0.520415	+	0.853913i	$0.674223\pi$
$702$	−12.8851	−	6.04529i	−0.486316	−	0.228165i
$703$	8.77402			0.330918
$704$	4.05094	−	3.39914i	0.152676	−	0.128110i
$705$	15.3441	+	38.7118i	0.577894	+	1.45797i
$706$	4.35688	−	24.7091i	0.163973	−	0.929939i
$707$	16.4905	−	6.00205i	0.620189	−	0.225730i
$708$	−0.142271	−	5.02480i	−0.00534685	−	0.188844i
$709$	−1.80536	−	10.2387i	−0.0678018	−	0.384523i	−0.999759	−	0.0219548i	$-0.993011\pi$
$709$	−1.80536	−	10.2387i	−0.0678018	−	0.384523i	0.931957	−	0.362568i	$-0.118100\pi$
$710$	−7.61350	−	13.1870i	−0.285730	−	0.494898i
$711$	5.57453	−	2.39427i	0.209061	−	0.0897923i
$712$	−0.103636	+	0.179503i	−0.00388392	+	0.00672715i
$713$	−2.89900	−	1.05515i	−0.108569	−	0.0395157i
$714$	−3.38085	+	0.695331i	−0.126525	+	0.0260221i
$715$	43.1133	+	36.1763i	1.61234	+	1.35292i
$716$	2.31203	+	1.94002i	0.0864047	+	0.0725021i
$717$	−13.2371	+	39.8429i	−0.494349	+	1.48796i
$718$	−19.2734	−	7.01494i	−0.719276	−	0.261795i
$719$	−2.44683	+	4.23803i	−0.0912513	+	0.158052i	−0.908038	−	0.418888i	$-0.862420\pi$
$719$	−2.44683	+	4.23803i	−0.0912513	+	0.158052i	0.816787	+	0.576940i	$0.195753\pi$
$720$	−11.1616	−	3.36061i	−0.415969	−	0.125243i
$721$	7.52949	+	13.0415i	0.280413	+	0.485689i
$722$	−0.875766	−	4.96672i	−0.0325926	−	0.184842i
$723$	−6.95967	+	4.28527i	−0.258833	+	0.159371i
$724$	15.2543	−	5.55212i	0.566923	−	0.206343i
$725$	1.62639	−	9.22369i	0.0604025	−	0.342559i
$726$	29.0694	+	4.28129i	1.07887	+	0.158893i
$727$	16.4959	−	13.8417i	0.611800	−	0.513361i	−0.283414	−	0.958998i	$-0.591467\pi$
$727$	16.4959	−	13.8417i	0.611800	−	0.513361i	0.895214	+	0.445636i	$0.147023\pi$
$728$	−2.73909			−0.101517
$729$	17.2579	+	20.7645i	0.639183	+	0.769055i
$730$	−18.9098			−0.699884
$731$	15.7525	−	13.2179i	0.582627	−	0.488882i
$732$	−4.05734	−	0.597557i	−0.149964	−	0.0220863i
$733$	−4.56323	+	25.8794i	−0.168547	+	0.955877i	0.776785	+	0.629766i	$0.216849\pi$
$733$	−4.56323	+	25.8794i	−0.168547	+	0.955877i	−0.945332	+	0.326111i	$0.894262\pi$
$734$	3.23123	−	1.17607i	0.119267	−	0.0434096i
$735$	5.73071	−	3.52856i	0.211380	−	0.130153i
$736$	−1.56862	−	8.89609i	−0.0578201	−	0.327914i
$737$	−15.0067	−	25.9923i	−0.552777	−	0.957438i
$738$	21.8367	+	6.57476i	0.803822	+	0.242020i
$739$	−7.55318	+	13.0825i	−0.277848	+	0.481247i	−0.970850	−	0.239689i	$-0.922955\pi$
$739$	−7.55318	+	13.0825i	−0.277848	+	0.481247i	0.693002	+	0.720936i	$0.256288\pi$
$740$	−6.53335	−	2.37794i	−0.240171	−	0.0874150i
$741$	−7.33451	+	22.0764i	−0.269440	+	0.810998i
$742$	−1.07010	−	0.897922i	−0.0392847	−	0.0329638i
$743$	−6.09227	−	5.11202i	−0.223504	−	0.187542i	0.524159	−	0.851620i	$-0.324380\pi$
$743$	−6.09227	−	5.11202i	−0.223504	−	0.187542i	−0.747663	+	0.664078i	$0.768824\pi$
$744$	−0.579402	+	0.119164i	−0.0212419	+	0.00436877i
$745$	70.9874	+	25.8373i	2.60078	+	0.946605i
$746$	6.44041	−	11.1551i	0.235800	−	0.408418i
$747$	36.3537	−	15.6140i	1.33011	−	0.571286i
$748$	5.26907	+	9.12629i	0.192656	+	0.333690i
$749$	−3.49961	−	19.8473i	−0.127873	−	0.725205i
$750$	−0.970883	−	34.2903i	−0.0354516	−	1.25210i
$751$	1.49135	−	0.542806i	0.0544200	−	0.0198073i	−0.314667	−	0.949202i	$-0.601893\pi$
$751$	1.49135	−	0.542806i	0.0544200	−	0.0198073i	0.369087	+	0.929395i	$0.379671\pi$
$752$	−1.07446	+	6.09358i	−0.0391816	+	0.222210i
$753$	−19.0297	−	48.0100i	−0.693480	−	1.74958i
$754$	1.94630	−	1.63314i	0.0708802	−	0.0594756i
$755$	36.6995			1.33563
$756$	4.70414	+	2.20704i	0.171088	+	0.0802693i
$757$	−6.82756			−0.248152			−0.124076	−	0.992273i	$-0.539597\pi$
$757$	−6.82756			−0.248152			−0.124076	+	0.992273i	$0.539597\pi$
$758$	18.3672	−	15.4119i	0.667128	−	0.559786i
$759$	51.3684	−	64.8615i	1.86456	−	2.35432i
$760$	−3.30839	+	18.7628i	−0.120008	+	0.680598i
$761$	1.45977	−	0.531312i	0.0529165	−	0.0192600i	−0.315426	−	0.948950i	$-0.602147\pi$
$761$	1.45977	−	0.531312i	0.0529165	−	0.0192600i	0.368343	+	0.929690i	$0.379925\pi$
$762$	17.3880	+	9.39309i	0.629900	+	0.340276i
$763$	2.33288	+	13.2304i	0.0844558	+	0.478973i
$764$	12.1584	+	21.0590i	0.439877	+	0.761889i
$765$	10.4577	−	20.7419i	0.378098	−	0.749926i
$766$	−12.8688	+	22.2894i	−0.464969	+	0.805350i
$767$	7.47007	+	2.71888i	0.269729	+	0.0981732i
$768$	−1.15045	−	1.29479i	−0.0415132	−	0.0467216i
$769$	−2.79210	−	2.34285i	−0.100686	−	0.0844854i	0.591055	−	0.806631i	$-0.298712\pi$
$769$	−2.79210	−	2.34285i	−0.100686	−	0.0844854i	−0.691741	+	0.722146i	$0.743156\pi$
$770$	−15.7400	−	13.2074i	−0.567230	−	0.475963i
$771$	13.4387	+	15.1248i	0.483983	+	0.544705i
$772$	0.270409	+	0.0984207i	0.00973222	+	0.00354224i
$773$	−21.5946	+	37.4030i	−0.776705	+	1.34529i	0.157127	+	0.987578i	$0.449777\pi$
$773$	−21.5946	+	37.4030i	−0.776705	+	1.34529i	−0.933831	+	0.357713i	$0.883557\pi$
$774$	−30.9071	+	1.75159i	−1.11093	+	0.0629596i
$775$	−1.72420	−	2.98641i	−0.0619352	−	0.107275i
$776$	−1.05533	−	5.98506i	−0.0378841	−	0.214851i
$777$	2.72684	+	1.47306i	0.0978250	+	0.0528457i
$778$	17.3392	−	6.31096i	0.621641	−	0.226259i
$779$	6.47258	−	36.7078i	0.231904	−	1.31520i
$780$	11.4446	−	14.4508i	0.409784	−	0.517423i
$781$	15.8753	−	13.3209i	0.568062	−	0.476661i
$782$	18.0015			0.643733
$783$	−4.65852	+	1.23653i	−0.166482	+	0.0441900i
$784$	1.00000			0.0357143
$785$	−43.9459	+	36.8749i	−1.56849	+	1.31612i
$786$	7.89881	+	19.9280i	0.281741	+	0.710806i
$787$	4.62023	−	26.2026i	0.164693	−	0.934023i	−0.784687	−	0.619893i	$-0.787176\pi$
$787$	4.62023	−	26.2026i	0.164693	−	0.934023i	0.949380	−	0.314130i	$-0.101713\pi$
$788$	−19.7847	+	7.20104i	−0.704801	+	0.256526i
$789$	0.671053	+	23.7007i	0.0238901	+	0.843766i
$790$	1.36448	+	7.73837i	0.0485462	+	0.275319i
$791$	−0.179240	−	0.310453i	−0.00637305	−	0.0110385i
$792$	1.86641	−	15.7542i	0.0663199	−	0.559801i
$793$	3.24277	−	5.61665i	0.115154	−	0.199453i
$794$	−10.1116	−	3.68031i	−0.358846	−	0.130609i
$795$	9.20841	−	1.89387i	0.326589	−	0.0671686i
$796$	−17.3979	−	14.5986i	−0.616654	−	0.517434i
$797$	3.75261	+	3.14882i	0.132924	+	0.111537i	0.706826	−	0.707387i	$-0.250126\pi$
$797$	3.75261	+	3.14882i	0.132924	+	0.111537i	−0.573902	+	0.818924i	$0.694571\pi$
$798$	2.67772	−	8.05977i	0.0947902	−	0.285313i
$799$	−11.5869	−	4.21730i	−0.409916	−	0.149197i
$800$	5.04862	−	8.74447i	0.178496	−	0.309164i
$801$	0.142453	+	0.605279i	0.00503334	+	0.0213865i
$802$	6.37951	+	11.0496i	0.225268	+	0.390176i
$803$	−4.46900	−	25.3450i	−0.157708	−	0.894405i
$804$	−8.37088	+	5.15420i	−0.295218	+	0.181774i
$805$	−32.9824	+	12.0046i	−1.16248	+	0.423107i
$806$	0.162440	−	0.921241i	0.00572169	−	0.0324493i
$807$	−15.0233	−	2.21260i	−0.528845	−	0.0778873i
$808$	−13.4432	+	11.2802i	−0.472929	+	0.396835i
$809$	−39.5210			−1.38948			−0.694742	−	0.719259i	$-0.744481\pi$
$809$	−39.5210			−1.38948			−0.694742	+	0.719259i	$0.744481\pi$
$810$	−31.2990	+	15.5964i	−1.09974	+	0.548003i
$811$	4.35620			0.152967			0.0764834	−	0.997071i	$-0.475631\pi$
$811$	4.35620			0.152967			0.0764834	+	0.997071i	$0.475631\pi$
$812$	−0.710566	+	0.596236i	−0.0249360	+	0.0209238i
$813$	−0.530287	−	0.0780997i	−0.0185980	−	0.00273908i
$814$	1.64313	−	9.31868i	0.0575919	−	0.326620i
$815$	25.6477	−	9.33501i	0.898400	−	0.326991i
$816$	2.93915	−	1.80972i	0.102891	−	0.0633528i
$817$	8.78620	+	49.8290i	0.307390	+	1.74330i
$818$	1.57367	+	2.72568i	0.0550223	+	0.0953013i
$819$	−5.98585	+	5.62967i	−0.209162	+	0.196717i
$820$	−14.7682	+	25.5794i	−0.515730	+	0.893270i
$821$	−25.5355	−	9.29416i	−0.891195	−	0.324368i	−0.144476	−	0.989508i	$-0.546150\pi$
$821$	−25.5355	−	9.29416i	−0.891195	−	0.324368i	−0.746719	+	0.665140i	$0.768372\pi$
$822$	4.98208	−	14.9957i	0.173770	−	0.523036i
$823$	0.540289	+	0.453356i	0.0188333	+	0.0158030i	0.652156	−	0.758085i	$-0.273865\pi$
$823$	0.540289	+	0.453356i	0.0188333	+	0.0158030i	−0.633322	+	0.773888i	$0.718309\pi$
$824$	−11.5359	−	9.67973i	−0.401870	−	0.337209i
$825$	90.5877	−	18.6309i	3.15386	−	0.648646i
$826$	−2.72721	−	0.992623i	−0.0948917	−	0.0345378i
$827$	−19.1588	+	33.1840i	−0.666216	+	1.15392i	0.312738	+	0.949839i	$0.398754\pi$
$827$	−19.1588	+	33.1840i	−0.666216	+	1.15392i	−0.978954	+	0.204080i	$0.934580\pi$
$828$	−21.7122	−	16.2170i	−0.754549	−	0.563579i
$829$	−4.54847	−	7.87817i	−0.157975	−	0.273620i	0.776163	−	0.630532i	$-0.217163\pi$
$829$	−4.54847	−	7.87817i	−0.157975	−	0.273620i	−0.934138	+	0.356911i	$0.883830\pi$
$830$	8.89833	+	50.4649i	0.308866	+	1.75166i
$831$	0.738339	+	26.0772i	0.0256127	+	0.904607i
$832$	2.57390	−	0.936824i	0.0892340	−	0.0324785i
$833$	−0.346045	+	1.96252i	−0.0119897	+	0.0679972i
$834$	3.59027	+	9.05791i	0.124321	+	0.313650i
$835$	−59.5527	+	49.9706i	−2.06091	+	1.72931i
$836$	−25.9298			−0.896801
$837$	−1.02127	+	1.45126i	−0.0353003	+	0.0501630i
$838$	4.72890			0.163357
$839$	−14.8652	+	12.4734i	−0.513204	+	0.430629i	−0.862255	−	0.506475i	$-0.830948\pi$
$839$	−14.8652	+	12.4734i	−0.513204	+	0.430629i	0.349051	+	0.937104i	$0.386504\pi$
$840$	−4.17826	+	5.27578i	−0.144164	+	0.182032i
$841$	−4.88639	+	27.7121i	−0.168496	+	0.955589i
$842$	15.4225	−	5.61334i	0.531495	−	0.193448i
$843$	−48.7562	−	26.3384i	−1.67925	−	0.907142i
$844$	−3.45288	−	19.5822i	−0.118853	−	0.674048i
$845$	−10.6801	−	18.4985i	−0.367406	−	0.636367i
$846$	10.1761	+	15.5249i	0.349862	+	0.533757i
$847$	8.48214	−	14.6915i	0.291450	−	0.504806i
$848$	1.31267	+	0.477774i	0.0450774	+	0.0164068i
$849$	2.91679	+	3.28275i	0.100104	+	0.112664i
$850$	15.4141	+	12.9340i	0.528700	+	0.443632i
$851$	−12.3823	−	10.3900i	−0.424461	−	0.356165i
$852$	−4.50850	−	5.07415i	−0.154459	−	0.173838i
$853$	−11.7181	−	4.26505i	−0.401221	−	0.146033i	0.133525	−	0.991045i	$-0.457370\pi$
$853$	−11.7181	−	4.26505i	−0.401221	−	0.146033i	−0.534746	+	0.845013i	$0.679593\pi$
$854$	−1.18389	+	2.05055i	−0.0405118	+	0.0701685i
$855$	31.3333	+	47.8029i	1.07158	+	1.63482i
$856$	10.0767	+	17.4534i	0.344416	+	0.596546i
$857$	0.862365	+	4.89072i	0.0294578	+	0.167064i	0.995988	−	0.0894906i	$-0.0285239\pi$
$857$	0.862365	+	4.89072i	0.0294578	+	0.167064i	−0.966530	+	0.256554i	$0.917413\pi$
$858$	22.0733	+	11.9241i	0.753570	+	0.407083i
$859$	−29.3782	+	10.6928i	−1.00237	+	0.364834i	−0.790499	−	0.612464i	$-0.790179\pi$
$859$	−29.3782	+	10.6928i	−1.00237	+	0.364834i	−0.211873	+	0.977297i	$0.567956\pi$
$860$	6.96230	−	39.4851i	0.237412	−	1.34643i
$861$	8.17442	−	10.3216i	0.278583	−	0.351760i
$862$	22.0471	−	18.4997i	0.750927	−	0.630103i
$863$	3.56388			0.121316			0.0606580	−	0.998159i	$-0.480680\pi$
$863$	3.56388			0.121316			0.0606580	+	0.998159i	$0.480680\pi$
$864$	−5.17530	−	0.465029i	−0.176067	−	0.0158206i
$865$	12.2254			0.415675
$866$	1.25030	−	1.04913i	0.0424871	−	0.0356509i
$867$	−8.31528	−	20.9786i	−0.282402	−	0.712472i
$868$	−0.0593042	+	0.336331i	−0.00201292	+	0.0114158i
$869$	−10.0493	+	3.65766i	−0.340900	+	0.124077i
$870$	−0.176678	−	6.24002i	−0.00598993	−	0.211556i
$871$	−2.69953	−	15.3098i	−0.0914702	−	0.518753i
$872$	−6.71725	−	11.6346i	−0.227475	−	0.393998i
$873$	−14.6074	−	10.9104i	−0.494385	−	0.369261i
$874$	−22.1470	+	38.3597i	−0.749133	+	1.29754i
$875$	−18.6110	−	6.77386i	−0.629168	−	0.228998i
$876$	−8.25664	+	1.69812i	−0.278966	+	0.0573742i
$877$	−42.7782	−	35.8952i	−1.44452	−	1.21209i	−0.936461	−	0.350771i	$-0.885920\pi$
$877$	−42.7782	−	35.8952i	−1.44452	−	1.21209i	−0.508057	−	0.861324i	$-0.669636\pi$
$878$	−2.73994	−	2.29909i	−0.0924687	−	0.0775904i
$879$	3.58250	−	10.7831i	0.120835	−	0.363705i
$880$	19.3080	+	7.02752i	0.650871	+	0.236898i
$881$	−20.6004	+	35.6809i	−0.694045	+	1.20212i	0.276457	+	0.961026i	$0.410840\pi$
$881$	−20.6004	+	35.6809i	−0.694045	+	1.20212i	−0.970502	+	0.241095i	$0.922494\pi$
$882$	2.18534	−	2.05531i	0.0735843	−	0.0692058i
$883$	−0.622497	−	1.07820i	−0.0209487	−	0.0362842i	0.855361	−	0.518032i	$-0.173335\pi$
$883$	−0.622497	−	1.07820i	−0.0209487	−	0.0362842i	−0.876310	+	0.481748i	$0.840002\pi$
$884$	0.947847	+	5.37551i	0.0318796	+	0.180798i
$885$	16.6319	−	10.2407i	0.559074	−	0.344238i
$886$	−17.9895	+	6.54763i	−0.604368	+	0.219972i
$887$	1.55194	−	8.80151i	0.0521092	−	0.295526i	−0.947605	−	0.319445i	$-0.896503\pi$
$887$	1.55194	−	8.80151i	0.0521092	−	0.295526i	0.999714	+	0.0239195i	$0.00761455\pi$
$888$	−3.06621	−	0.451586i	−0.102895	−	0.0151542i
$889$	8.74065	−	7.33428i	0.293152	−	0.245984i
$890$	−0.805359			−0.0269957
$891$	−28.3010	−	38.2644i	−0.948119	−	1.28190i
$892$	14.3609			0.480839
$893$	23.2419	−	19.5023i	0.777762	−	0.652620i
$894$	33.3156	+	4.90665i	1.11424	+	0.164103i
$895$	−2.03638	+	11.5489i	−0.0680687	+	0.386037i
$896$	−0.939693	+	0.342020i	−0.0313929	+	0.0114261i
$897$	36.4933	−	22.4700i	1.21848	−	0.750251i
$898$	1.88834	+	10.7093i	0.0630147	+	0.357374i
$899$	−0.158393	−	0.274345i	−0.00528270	−	0.00914991i
$900$	−6.93961	−	29.4861i	−0.231320	−	0.982871i
$901$	−1.39188	+	2.41081i	−0.0463704	+	0.0803158i
$902$	−37.7744	−	13.7488i	−1.25775	−	0.457784i
$903$	−5.63509	+	16.9613i	−0.187524	+	0.564436i
$904$	0.274612	+	0.230427i	0.00913346	+	0.00766389i
$905$	48.3181	+	40.5437i	1.60615	+	1.34772i
$906$	16.0242	−	3.29565i	0.532367	−	0.109491i
$907$	−4.87855	−	1.77565i	−0.161990	−	0.0589594i	0.259752	−	0.965675i	$-0.416359\pi$
$907$	−4.87855	−	1.77565i	−0.161990	−	0.0589594i	−0.421742	+	0.906716i	$0.638581\pi$
$908$	−5.63796	+	9.76523i	−0.187102	+	0.324070i
$909$	−6.19373	+	52.2809i	−0.205433	+	1.73405i
$910$	−5.32139	−	9.21692i	−0.176402	−	0.305538i
$911$	8.58915	+	48.7115i	0.284571	+	1.61388i	0.706813	+	0.707400i	$0.250132\pi$
$911$	8.58915	+	48.7115i	0.284571	+	1.61388i	−0.422242	+	0.906483i	$0.638757\pi$
$912$	0.240370	+	8.48954i	0.00795944	+	0.281117i
$913$	−65.5356	+	23.8530i	−2.16891	+	0.789419i
$914$	−1.98469	+	11.2557i	−0.0656477	+	0.372307i
$915$	−5.87168	−	14.8137i	−0.194112	−	0.489725i
$916$	8.49566	−	7.12871i	0.280705	−	0.235539i
$917$	12.3762			0.408700
$918$	2.70351	−	9.99569i	0.0892292	−	0.329907i
$919$	−33.2187			−1.09578			−0.547892	−	0.836549i	$-0.684570\pi$
$919$	−33.2187			−1.09578			−0.547892	+	0.836549i	$0.684570\pi$
$920$	26.8875	−	22.5613i	0.886455	−	0.743824i
$921$	5.03073	−	6.35217i	0.165768	−	0.209311i
$922$	0.828555	−	4.69897i	0.0272870	−	0.154752i
$923$	10.0869	−	3.67133i	0.332014	−	0.120843i
$924$	−8.05863	−	4.35332i	−0.265109	−	0.143214i
$925$	−3.13743	−	17.7933i	−0.103158	−	0.585039i
$926$	10.4572	+	18.1124i	0.343645	+	0.595210i
$927$	−45.1046	+	2.55620i	−1.48143	+	0.0839566i
$928$	0.463789	−	0.803306i	0.0152246	−	0.0263698i
$929$	−17.3203	−	6.30406i	−0.568259	−	0.206829i	0.0418814	−	0.999123i	$-0.486665\pi$
$929$	−17.3203	−	6.30406i	−0.568259	−	0.206829i	−0.610141	+	0.792293i	$0.708887\pi$
$930$	−1.52662	−	1.71816i	−0.0500598	−	0.0563405i
$931$	−3.75622	−	3.15185i	−0.123105	−	0.103298i
$932$	−2.45972	−	2.06395i	−0.0805709	−	0.0676071i
$933$	34.4991	+	38.8274i	1.12945	+	1.27115i
$934$	1.11770	+	0.406811i	0.0365724	+	0.0133113i
$935$	−20.4730	+	35.4604i	−0.669540	+	1.15968i
$936$	3.69940	−	7.33744i	0.120919	−	0.239832i
$937$	21.8105	+	37.7768i	0.712517	+	1.23411i	0.963910	+	0.266230i	$0.0857780\pi$
$937$	21.8105	+	37.7768i	0.712517	+	1.23411i	−0.251393	+	0.967885i	$0.580889\pi$
$938$	0.985558	+	5.58938i	0.0321796	+	0.182500i
$939$	−35.3035	−	19.0712i	−1.15209	−	0.622365i
$940$	−22.5921	+	8.22283i	−0.736871	+	0.268199i
$941$	−8.29985	+	47.0708i	−0.270568	+	1.53446i	0.482131	+	0.876099i	$0.339863\pi$
$941$	−8.29985	+	47.0708i	−0.270568	+	1.53446i	−0.752698	+	0.658366i	$0.771248\pi$
$942$	−15.8768	+	20.0472i	−0.517293	+	0.653172i
$943$	−52.6031	+	44.1393i	−1.71299	+	1.43737i
$944$	2.90223			0.0944597
$945$	1.71242	+	20.1170i	0.0557049	+	0.654406i
$946$	54.5676			1.77415
$947$	−13.6055	+	11.4164i	−0.442120	+	0.370983i	−0.836502	−	0.547964i	$-0.815403\pi$
$947$	−13.6055	+	11.4164i	−0.442120	+	0.370983i	0.394382	+	0.918947i	$0.370959\pi$
$948$	1.29069	+	3.25629i	0.0419197	+	0.105759i
$949$	2.31481	−	13.1279i	0.0751419	−	0.426151i
$950$	−46.5250	+	16.9337i	−1.50947	+	0.549402i
$951$	−0.372069	−	13.1410i	−0.0120652	−	0.426125i
$952$	−0.346045	−	1.96252i	−0.0112154	−	0.0636055i
$953$	27.3415	+	47.3568i	0.885677	+	1.53404i	0.844936	+	0.534867i	$0.179638\pi$
$953$	27.3415	+	47.3568i	0.885677	+	1.53404i	0.0407402	+	0.999170i	$0.487028\pi$
$954$	3.85061	−	1.65385i	0.124668	−	0.0535453i
$955$	−47.2419	+	81.8253i	−1.52871	+	2.64780i
$956$	−22.7778	−	8.29044i	−0.736686	−	0.268132i
$957$	8.32179	−	1.71152i	0.269005	−	0.0553256i
$958$	−7.96014	−	6.67935i	−0.257180	−	0.215800i
$959$	−6.98871	−	5.86422i	−0.225677	−	0.189366i
$960$	2.12186	−	6.38666i	0.0684827	−	0.206129i
$961$	29.0209	+	10.5627i	0.936157	+	0.340733i
$962$	2.45063	−	4.24461i	0.0790114	−	0.136852i
$963$	57.8932	+	17.4309i	1.86558	+	0.561703i
$964$	−2.35939	−	4.08658i	−0.0759908	−	0.131620i
$965$	0.194157	+	1.10112i	0.00625015	+	0.0354463i
$966$	−13.3231	+	8.20345i	−0.428665	+	0.263942i
$967$	−14.2894	+	5.20090i	−0.459515	+	0.167250i	−0.561397	−	0.827547i	$-0.689736\pi$
$967$	−14.2894	+	5.20090i	−0.459515	+	0.167250i	0.101882	+	0.994796i	$0.467514\pi$
$968$	−2.94582	+	16.7066i	−0.0946821	+	0.536969i
$969$	−16.7440	−	2.46603i	−0.537896	−	0.0792203i
$970$	18.0892	−	15.1787i	0.580810	−	0.487358i
$971$	42.4902			1.36358			0.681788	−	0.731550i	$-0.261203\pi$
$971$	42.4902			1.36358			0.681788	+	0.731550i	$0.261203\pi$
$972$	−12.2656	+	9.62058i	−0.393419	+	0.308580i
$973$	5.62541			0.180342
$974$	−26.0340	+	21.8452i	−0.834185	+	0.699964i
$975$	47.3926	+	6.97988i	1.51778	+	0.223535i
$976$	0.411160	−	2.33180i	0.0131609	−	0.0746392i
$977$	54.2371	−	19.7407i	1.73520	−	0.631560i	0.736219	−	0.676743i	$-0.236609\pi$
$977$	54.2371	−	19.7407i	1.73520	−	0.631560i	0.998979	+	0.0451824i	$0.0143869\pi$
$978$	10.3603	−	6.37915i	0.331287	−	0.203983i
$979$	−0.190332	−	1.07943i	−0.00608305	−	0.0344987i
$980$	1.94276	+	3.36496i	0.0620592	+	0.107490i
$981$	−38.5922	−	11.6196i	−1.23215	−	0.370985i
$982$	−14.4646	+	25.0535i	−0.461585	+	0.799488i
$983$	10.8971	+	3.96622i	0.347563	+	0.126503i	0.509902	−	0.860232i	$-0.329682\pi$
$983$	10.8971	+	3.96622i	0.347563	+	0.126503i	−0.162339	+	0.986735i	$0.551904\pi$
$984$	−4.15124	+	12.4950i	−0.132337	+	0.398325i
$985$	−62.6681	−	52.5848i	−1.99677	−	1.67549i
$986$	1.41601	+	1.18817i	0.0450949	+	0.0378391i
$987$	10.4975	−	2.15899i	0.334139	−	0.0687214i
$988$	−12.6209	−	4.59362i	−0.401524	−	0.146143i
$989$	46.6070	−	80.7256i	1.48202	−	2.56693i
$990$	56.6382	−	24.3262i	1.80008	−	0.773139i
$991$	8.90657	+	15.4266i	0.282927	+	0.490043i	0.972104	−	0.234549i	$-0.0753614\pi$
$991$	8.90657	+	15.4266i	0.282927	+	0.490043i	−0.689178	+	0.724592i	$0.742028\pi$
$992$	−0.0593042	−	0.336331i	−0.00188291	−	0.0106785i
$993$	−0.0956948	−	3.37981i	−0.00303678	−	0.107255i
$994$	−3.68257	+	1.34035i	−0.116804	+	0.0425132i
$995$	15.3237	−	86.9049i	0.485793	−	2.75507i
$996$	8.41710	+	21.2355i	0.266706	+	0.672873i
$997$	31.4300	−	26.3729i	0.995397	−	0.835237i	0.00905678	−	0.999959i	$-0.497117\pi$
$997$	31.4300	−	26.3729i	0.995397	−	0.835237i	0.986340	+	0.164722i	$0.0526727\pi$
$998$	19.7157			0.624089
$999$	−7.62886	+	5.31513i	−0.241367	+	0.168163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.c.211.1	yes	24
27.16	even	9	inner	378.2.u.c.43.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.c.43.1	✓	24	27.16	even	9	inner
378.2.u.c.211.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.71357 - 0.252371i) q^{3} +(0.173648 - 0.984808i) q^{4} +(3.65119 - 1.32893i) q^{5} +(1.47489 - 0.908132i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.87262 + 0.864908i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.71357 - 0.252371i) q^{3} +(0.173648 - 0.984808i) q^{4} +(3.65119 - 1.32893i) q^{5} +(1.47489 - 0.908132i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.87262 + 0.864908i) q^{9} +(-1.94276 + 3.36496i) q^{10} +(-4.96921 - 1.80865i) q^{11} +(-0.546094 + 1.64371i) q^{12} +(-2.09826 - 1.76065i) q^{13} +(0.766044 + 0.642788i) q^{14} +(-6.59194 + 1.35575i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.996396 - 1.72581i) q^{17} +(-2.75651 + 1.18393i) q^{18} +(2.45170 + 4.24647i) q^{19} +(-0.674713 - 3.82649i) q^{20} +(0.0490210 + 1.73136i) q^{21} +(4.96921 - 1.80865i) q^{22} +(1.56862 - 8.89609i) q^{23} +(-0.638224 - 1.61018i) q^{24} +(7.73494 - 6.49039i) q^{25} +2.73909 q^{26} +(-4.70414 - 2.20704i) q^{27} -1.00000 q^{28} +(0.710566 - 0.596236i) q^{29} +(4.17826 - 5.27578i) q^{30} +(0.0593042 - 0.336331i) q^{31} +(0.939693 - 0.342020i) q^{32} +(8.05863 + 4.35332i) q^{33} +(0.346045 + 1.96252i) q^{34} +(-1.94276 - 3.36496i) q^{35} +(1.35059 - 2.67879i) q^{36} +(0.894687 - 1.54964i) q^{37} +(-4.60769 - 1.67706i) q^{38} +(3.15118 + 3.54654i) q^{39} +(2.97648 + 2.49756i) q^{40} +(-5.82323 - 4.88627i) q^{41} +(-1.15045 - 1.29479i) q^{42} +(9.69659 + 3.52927i) q^{43} +(-2.64406 + 4.57965i) q^{44} +(11.6379 - 0.659550i) q^{45} +(4.51666 + 7.82309i) q^{46} +(-1.07446 - 6.09358i) q^{47} +(1.52391 + 0.823225i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(-1.75337 + 9.94385i) q^{50} +(-2.14293 + 2.70582i) q^{51} +(-2.09826 + 1.76065i) q^{52} -1.39692 q^{53} +(5.02224 - 1.33307i) q^{54} -20.5471 q^{55} +(0.766044 - 0.642788i) q^{56} +(-3.12947 - 7.89534i) q^{57} +(-0.161072 + 0.913486i) q^{58} +(-2.72721 + 0.992623i) q^{59} +(0.190472 + 6.72722i) q^{60} +(0.411160 + 2.33180i) q^{61} +(0.170760 + 0.295765i) q^{62} +(0.352943 - 2.97917i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-10.0009 - 3.64005i) q^{65} +(-8.97152 + 1.84515i) q^{66} +(4.34776 + 3.64821i) q^{67} +(-1.52657 - 1.28094i) q^{68} +(-4.93305 + 14.8482i) q^{69} +(3.65119 + 1.32893i) q^{70} +(-1.95946 + 3.39388i) q^{71} +(0.687277 + 2.92021i) q^{72} +(2.43337 + 4.21473i) q^{73} +(0.310722 + 1.76219i) q^{74} +(-14.8923 + 9.16963i) q^{75} +(4.60769 - 1.67706i) q^{76} +(-0.918273 + 5.20779i) q^{77} +(-4.69361 - 0.691266i) q^{78} +(1.54919 - 1.29992i) q^{79} -3.88552 q^{80} +(7.50387 + 4.96910i) q^{81} +7.60169 q^{82} +(10.1028 - 8.47729i) q^{83} +(1.71357 + 0.252371i) q^{84} +(1.34456 - 7.62539i) q^{85} +(-9.69659 + 3.52927i) q^{86} +(-1.36807 + 0.842363i) q^{87} +(-0.918273 - 5.20779i) q^{88} +(0.103636 + 0.179503i) q^{89} +(-8.49118 + 7.98593i) q^{90} +(-1.36955 + 2.37212i) q^{91} +(-8.48855 - 3.08958i) q^{92} +(-0.186502 + 0.561359i) q^{93} +(4.73996 + 3.97730i) q^{94} +(14.5949 + 12.2465i) q^{95} +(-1.69654 + 0.348923i) q^{96} +(-5.71088 - 2.07859i) q^{97} +(0.500000 - 0.866025i) q^{98} +(-12.7103 - 9.49346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9	\( 24 q - 3 q^{3} + 3 q^{5} + 6 q^{6} + 12 q^{8} - 3 q^{9} + 3 q^{10} - 9 q^{13} - 6 q^{18} + 15 q^{19} - 6 q^{20} - 3 q^{21} + 6 q^{23} + 3 q^{24} + 33 q^{25} + 18 q^{26} - 18 q^{27} - 24 q^{28} - 30 q^{29} + 15 q^{30} - 6 q^{33} - 3 q^{34} + 3 q^{35} - 12 q^{36} - 3 q^{37} + 15 q^{38} - 18 q^{39} - 3 q^{40} + 27 q^{41} + 18 q^{43} - 3 q^{44} + 12 q^{45} + 15 q^{46} + 3 q^{48} + 3 q^{50} + 24 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} - 66 q^{55} - 6 q^{57} + 3 q^{58} - 30 q^{59} - 30 q^{60} - 57 q^{61} - 18 q^{62} + 12 q^{63} - 12 q^{64} + 24 q^{65} - 54 q^{66} + 39 q^{67} + 3 q^{68} + 36 q^{69} + 3 q^{70} - 24 q^{71} - 6 q^{72} + 36 q^{73} - 12 q^{74} + 15 q^{75} - 15 q^{76} - 9 q^{77} + 18 q^{78} - 33 q^{79} + 6 q^{80} + 9 q^{81} - 15 q^{83} + 3 q^{84} + 36 q^{85} - 18 q^{86} - 84 q^{87} - 9 q^{88} - 3 q^{89} - 30 q^{90} - 9 q^{91} - 30 q^{92} - 45 q^{93} + 45 q^{94} + 63 q^{95} - 30 q^{97} + 12 q^{98} - 57 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 + 3 * q^5 + 6 * q^6 + 12 * q^8 - 3 * q^9 + 3 * q^10 - 9 * q^13 - 6 * q^18 + 15 * q^19 - 6 * q^20 - 3 * q^21 + 6 * q^23 + 3 * q^24 + 33 * q^25 + 18 * q^26 - 18 * q^27 - 24 * q^28 - 30 * q^29 + 15 * q^30 - 6 * q^33 - 3 * q^34 + 3 * q^35 - 12 * q^36 - 3 * q^37 + 15 * q^38 - 18 * q^39 - 3 * q^40 + 27 * q^41 + 18 * q^43 - 3 * q^44 + 12 * q^45 + 15 * q^46 + 3 * q^48 + 3 * q^50 + 24 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 - 66 * q^55 - 6 * q^57 + 3 * q^58 - 30 * q^59 - 30 * q^60 - 57 * q^61 - 18 * q^62 + 12 * q^63 - 12 * q^64 + 24 * q^65 - 54 * q^66 + 39 * q^67 + 3 * q^68 + 36 * q^69 + 3 * q^70 - 24 * q^71 - 6 * q^72 + 36 * q^73 - 12 * q^74 + 15 * q^75 - 15 * q^76 - 9 * q^77 + 18 * q^78 - 33 * q^79 + 6 * q^80 + 9 * q^81 - 15 * q^83 + 3 * q^84 + 36 * q^85 - 18 * q^86 - 84 * q^87 - 9 * q^88 - 3 * q^89 - 30 * q^90 - 9 * q^91 - 30 * q^92 - 45 * q^93 + 45 * q^94 + 63 * q^95 - 30 * q^97 + 12 * q^98 - 57 * q^99

Introduction

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