LMFDB - Embedded newform 684.2.cc.a.535.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(211,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 6, 1]))

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

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

chi := DirichletCharacter("684.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.cc (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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$696$
Relative dimension:	$116$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			535.43
Character	$\chi$	$=$	684.535
Dual form			684.2.cc.a.583.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.535268 - 1.30900i) q^{2} +(1.73199 + 0.0149747i) q^{3} +(-1.42698 + 1.40134i) q^{4} +(-0.784523 - 0.658293i) q^{5} +(-0.907475 - 2.27519i) q^{6} +(-0.920724 - 0.531580i) q^{7} +(2.59817 + 1.11783i) q^{8} +(2.99955 + 0.0518718i) q^{9} +O(q^{10})$	\(q+(-0.535268 - 1.30900i) q^{2} +(1.73199 + 0.0149747i) q^{3} +(-1.42698 + 1.40134i) q^{4} +(-0.784523 - 0.658293i) q^{5} +(-0.907475 - 2.27519i) q^{6} +(-0.920724 - 0.531580i) q^{7} +(2.59817 + 1.11783i) q^{8} +(2.99955 + 0.0518718i) q^{9} +(-0.441777 + 1.37931i) q^{10} -1.95319i q^{11} +(-2.49249 + 2.40572i) q^{12} +(-3.18171 - 3.79182i) q^{13} +(-0.203006 + 1.48977i) q^{14} +(-1.34893 - 1.15190i) q^{15} +(0.0725201 - 3.99934i) q^{16} +(2.18769 + 1.83569i) q^{17} +(-1.53766 - 3.95419i) q^{18} +(2.84681 - 3.30086i) q^{19} +(2.04199 - 0.160011i) q^{20} +(-1.58672 - 0.934477i) q^{21} +(-2.55673 + 1.04548i) q^{22} +(0.416325 - 1.14384i) q^{23} +(4.48325 + 1.97496i) q^{24} +(-0.686114 - 3.89115i) q^{25} +(-3.26043 + 6.19451i) q^{26} +(5.19440 + 0.134759i) q^{27} +(2.05877 - 0.531690i) q^{28} +(0.544417 - 1.49577i) q^{29} +(-0.785806 + 2.38232i) q^{30} -3.11708 q^{31} +(-5.27397 + 2.04579i) q^{32} +(0.0292484 - 3.38290i) q^{33} +(1.23192 - 3.84628i) q^{34} +(0.372394 + 1.02314i) q^{35} +(-4.35298 + 4.12936i) q^{36} -8.94457i q^{37} +(-5.84464 - 1.95965i) q^{38} +(-5.45390 - 6.61502i) q^{39} +(-1.30247 - 2.58731i) q^{40} +(-1.61617 - 0.284974i) q^{41} +(-0.373912 + 2.57722i) q^{42} +(2.23734 + 6.14703i) q^{43} +(2.73707 + 2.78715i) q^{44} +(-2.31907 - 2.01528i) q^{45} +(-1.72014 + 0.0672927i) q^{46} +(-1.96833 + 5.40795i) q^{47} +(0.185493 - 6.92572i) q^{48} +(-2.93485 - 5.08330i) q^{49} +(-4.72627 + 2.98093i) q^{50} +(3.76156 + 3.21215i) q^{51} +(9.85383 + 0.952186i) q^{52} +(1.47345 - 0.259809i) q^{53} +(-2.60400 - 6.87162i) q^{54} +(-1.28577 + 1.53232i) q^{55} +(-1.79798 - 2.41034i) q^{56} +(4.98007 - 5.67441i) q^{57} +(-2.24938 + 0.0879967i) q^{58} +(9.74014 - 3.54512i) q^{59} +(3.53909 - 0.246560i) q^{60} +(5.18261 - 4.34872i) q^{61} +(1.66848 + 4.08027i) q^{62} +(-2.73418 - 1.64226i) q^{63} +(5.50093 + 5.80859i) q^{64} +5.06927i q^{65} +(-4.44388 + 1.77247i) q^{66} +(1.37693 + 7.80899i) q^{67} +(-5.69420 + 0.446202i) q^{68} +(0.738199 - 1.97489i) q^{69} +(1.13997 - 1.03512i) q^{70} +(-1.76325 + 9.99987i) q^{71} +(7.73535 + 3.48775i) q^{72} +(-2.87516 + 1.04647i) q^{73} +(-11.7085 + 4.78775i) q^{74} +(-1.13007 - 6.74969i) q^{75} +(0.563268 + 8.69958i) q^{76} +(-1.03828 + 1.79835i) q^{77} +(-5.73978 + 10.6800i) q^{78} +(0.624534 + 0.524047i) q^{79} +(-2.68963 + 3.08984i) q^{80} +(8.99462 + 0.311185i) q^{81} +(0.492052 + 2.26811i) q^{82} +(-2.89850 - 1.67345i) q^{83} +(3.57373 - 0.890051i) q^{84} +(-0.507872 - 2.88029i) q^{85} +(6.84891 - 6.21899i) q^{86} +(0.965321 - 2.58251i) q^{87} +(2.18332 - 5.07471i) q^{88} +(-2.89294 + 7.94828i) q^{89} +(-1.39668 + 4.11438i) q^{90} +(0.913824 + 5.18255i) q^{91} +(1.00882 + 2.21565i) q^{92} +(-5.39875 - 0.0466773i) q^{93} +(8.13260 - 0.318151i) q^{94} +(-4.40632 + 0.715559i) q^{95} +(-9.16507 + 3.46431i) q^{96} +(-8.30734 - 1.46481i) q^{97} +(-5.08313 + 6.56265i) q^{98} +(0.101316 - 5.85869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8}+O(q^{10}) $ 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8	$ 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 15 q^{14} - 3 q^{16} - 24 q^{17} - 6 q^{20} - 30 q^{21} + 21 q^{22} + 24 q^{24} - 6 q^{25} - 30 q^{26} - 6 q^{29} - 21 q^{30} - 3 q^{32} + 36 q^{33} + 33 q^{34} + 54 q^{36} - 3 q^{38} - 33 q^{40} + 54 q^{41} - 87 q^{42} - 33 q^{44} - 6 q^{45} - 18 q^{46} + 6 q^{48} + 282 q^{49} - 3 q^{52} - 24 q^{53} - 51 q^{54} - 63 q^{56} - 12 q^{57} - 6 q^{58} - 27 q^{60} - 6 q^{61} - 18 q^{62} - 24 q^{64} - 30 q^{66} + 3 q^{68} - 18 q^{69} - 45 q^{70} + 12 q^{72} - 60 q^{73} + 3 q^{74} - 3 q^{76} + 72 q^{77} - 81 q^{78} - 12 q^{80} - 72 q^{81} - 12 q^{82} - 9 q^{84} - 6 q^{85} - 57 q^{86} - 9 q^{88} - 24 q^{89} + 39 q^{90} + 81 q^{92} - 48 q^{93} + 15 q^{96} + 30 q^{97} - 63 q^{98}+O(q^{100}) $ 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 15 * q^14 - 3 * q^16 - 24 * q^17 - 6 * q^20 - 30 * q^21 + 21 * q^22 + 24 * q^24 - 6 * q^25 - 30 * q^26 - 6 * q^29 - 21 * q^30 - 3 * q^32 + 36 * q^33 + 33 * q^34 + 54 * q^36 - 3 * q^38 - 33 * q^40 + 54 * q^41 - 87 * q^42 - 33 * q^44 - 6 * q^45 - 18 * q^46 + 6 * q^48 + 282 * q^49 - 3 * q^52 - 24 * q^53 - 51 * q^54 - 63 * q^56 - 12 * q^57 - 6 * q^58 - 27 * q^60 - 6 * q^61 - 18 * q^62 - 24 * q^64 - 30 * q^66 + 3 * q^68 - 18 * q^69 - 45 * q^70 + 12 * q^72 - 60 * q^73 + 3 * q^74 - 3 * q^76 + 72 * q^77 - 81 * q^78 - 12 * q^80 - 72 * q^81 - 12 * q^82 - 9 * q^84 - 6 * q^85 - 57 * q^86 - 9 * q^88 - 24 * q^89 + 39 * q^90 + 81 * q^92 - 48 * q^93 + 15 * q^96 + 30 * q^97 - 63 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.535268	−	1.30900i	−0.378492	−	0.925605i
$2$	−0.535268	−	1.30900i	−0.378492	−	0.925605i
$3$	1.73199	+	0.0149747i	0.999963	+	0.00864563i
$3$	1.73199	+	0.0149747i	0.999963	+	0.00864563i
$4$	−1.42698	+	1.40134i	−0.713488	+	0.700668i
$5$	−0.784523	−	0.658293i	−0.350849	−	0.294398i	0.450282	−	0.892887i	$-0.351324\pi$
$5$	−0.784523	−	0.658293i	−0.350849	−	0.294398i	−0.801131	+	0.598489i	$0.795768\pi$
$6$	−0.907475	−	2.27519i	−0.370475	−	0.928842i
$7$	−0.920724	−	0.531580i	−0.348001	−	0.200918i	0.315804	−	0.948825i	$-0.397726\pi$
$7$	−0.920724	−	0.531580i	−0.348001	−	0.200918i	−0.663804	+	0.747906i	$0.731059\pi$
$8$	2.59817	+	1.11783i	0.918590	+	0.395211i
$9$	2.99955	+	0.0518718i	0.999851	+	0.0172906i
$10$	−0.441777	+	1.37931i	−0.139702	+	0.436175i
$11$		−	1.95319i		−	0.588909i	−0.955666	−	0.294454i	$-0.904862\pi$
$11$		−	1.95319i		−	0.588909i	0.955666	−	0.294454i	$-0.0951379\pi$
$12$	−2.49249	+	2.40572i	−0.719519	+	0.694473i
$13$	−3.18171	−	3.79182i	−0.882448	−	1.05166i	−0.998294	−	0.0583936i	$-0.981402\pi$
$13$	−3.18171	−	3.79182i	−0.882448	−	1.05166i	0.115845	−	0.993267i	$-0.463042\pi$
$14$	−0.203006	+	1.48977i	−0.0542555	+	0.398157i
$15$	−1.34893	−	1.15190i	−0.348291	−	0.297420i
$16$	0.0725201	−	3.99934i	0.0181300	−	0.999836i
$17$	2.18769	+	1.83569i	0.530593	+	0.445221i	0.868306	−	0.496029i	$-0.165209\pi$
$17$	2.18769	+	1.83569i	0.530593	+	0.445221i	−0.337713	+	0.941249i	$0.609653\pi$
$18$	−1.53766	−	3.95419i	−0.362431	−	0.932011i
$19$	2.84681	−	3.30086i	0.653104	−	0.757268i
$19$	2.84681	−	3.30086i	0.653104	−	0.757268i
$20$	2.04199	−	0.160011i	0.456602	−	0.0357797i
$21$	−1.58672	−	0.934477i	−0.346251	−	0.203920i
$22$	−2.55673	+	1.04548i	−0.545097	+	0.222897i
$23$	0.416325	−	1.14384i	0.0868099	−	0.238508i	−0.888690	−	0.458509i	$-0.848384\pi$
$23$	0.416325	−	1.14384i	0.0868099	−	0.238508i	0.975500	+	0.220001i	$0.0706060\pi$
$24$	4.48325	+	1.97496i	0.915139	+	0.403138i
$25$	−0.686114	−	3.89115i	−0.137223	−	0.778229i
$26$	−3.26043	+	6.19451i	−0.639423	+	1.21484i
$27$	5.19440	+	0.134759i	0.999664	+	0.0259343i
$28$	2.05877	−	0.531690i	0.389071	−	0.100480i
$29$	0.544417	−	1.49577i	0.101096	−	0.277758i	−0.878826	−	0.477143i	$-0.841672\pi$
$29$	0.544417	−	1.49577i	0.101096	−	0.277758i	0.979921	+	0.199385i	$0.0638945\pi$
$30$	−0.785806	+	2.38232i	−0.143468	+	0.434951i
$31$	−3.11708			−0.559845			−0.279922	−	0.960023i	$-0.590309\pi$
$31$	−3.11708			−0.559845			−0.279922	+	0.960023i	$0.590309\pi$
$32$	−5.27397	+	2.04579i	−0.932315	+	0.361648i
$33$	0.0292484	−	3.38290i	0.00509149	−	0.588887i
$34$	1.23192	−	3.84628i	0.211273	−	0.659632i
$35$	0.372394	+	1.02314i	0.0629460	+	0.172943i
$36$	−4.35298	+	4.12936i	−0.725496	+	0.688226i
$37$		−	8.94457i		−	1.47048i	−0.677807	−	0.735239i	$-0.737070\pi$
$37$		−	8.94457i		−	1.47048i	0.677807	−	0.735239i	$-0.262930\pi$
$38$	−5.84464	−	1.95965i	−0.948125	−	0.317896i
$39$	−5.45390	−	6.61502i	−0.873323	−	1.05925i
$40$	−1.30247	−	2.58731i	−0.205938	−	0.409090i
$41$	−1.61617	−	0.284974i	−0.252403	−	0.0445055i	0.0460149	−	0.998941i	$-0.485348\pi$
$41$	−1.61617	−	0.284974i	−0.252403	−	0.0445055i	−0.298418	+	0.954435i	$0.596459\pi$
$42$	−0.373912	+	2.57722i	−0.0576958	+	0.397673i
$43$	2.23734	+	6.14703i	0.341191	+	0.937414i	0.985050	+	0.172270i	$0.0551100\pi$
$43$	2.23734	+	6.14703i	0.341191	+	0.937414i	−0.643859	+	0.765144i	$0.722668\pi$
$44$	2.73707	+	2.78715i	0.412629	+	0.420179i
$45$	−2.31907	−	2.01528i	−0.345707	−	0.300420i
$46$	−1.72014	+	0.0672927i	−0.253621	+	0.00992176i
$47$	−1.96833	+	5.40795i	−0.287111	+	0.788830i	0.709357	+	0.704850i	$0.248986\pi$
$47$	−1.96833	+	5.40795i	−0.287111	+	0.788830i	−0.996467	+	0.0839803i	$0.973237\pi$
$48$	0.185493	−	6.92572i	0.0267736	−	0.999642i
$49$	−2.93485	−	5.08330i	−0.419264	−	0.726186i
$50$	−4.72627	+	2.98093i	−0.668395	+	0.421567i
$51$	3.76156	+	3.21215i	0.526724	+	0.449791i
$52$	9.85383	+	0.952186i	1.36648	+	0.132044i
$53$	1.47345	−	0.259809i	0.202394	−	0.0356875i	−0.0715321	−	0.997438i	$-0.522789\pi$
$53$	1.47345	−	0.259809i	0.202394	−	0.0356875i	0.273926	+	0.961751i	$0.411678\pi$
$54$	−2.60400	−	6.87162i	−0.354360	−	0.935109i
$55$	−1.28577	+	1.53232i	−0.173373	+	0.206618i
$56$	−1.79798	−	2.41034i	−0.240265	−	0.322095i
$57$	4.98007	−	5.67441i	0.659627	−	0.751593i
$58$	−2.24938	+	0.0879967i	−0.295358	+	0.0115545i
$59$	9.74014	−	3.54512i	1.26806	−	0.461536i	0.381593	−	0.924330i	$-0.375376\pi$
$59$	9.74014	−	3.54512i	1.26806	−	0.461536i	0.886465	+	0.462795i	$0.153153\pi$
$60$	3.53909	−	0.246560i	0.456894	−	0.0318307i
$61$	5.18261	−	4.34872i	0.663565	−	0.556797i	−0.247588	−	0.968865i	$-0.579638\pi$
$61$	5.18261	−	4.34872i	0.663565	−	0.556797i	0.911153	+	0.412068i	$0.135193\pi$
$62$	1.66848	+	4.08027i	0.211897	+	0.518195i
$63$	−2.73418	−	1.64226i	−0.344475	−	0.206905i
$64$	5.50093	+	5.80859i	0.687617	+	0.726074i
$65$			5.06927i			0.628765i
$66$	−4.44388	+	1.77247i	−0.547003	+	0.218176i
$67$	1.37693	+	7.80899i	0.168219	+	0.954019i	0.945683	+	0.325091i	$0.105395\pi$
$67$	1.37693	+	7.80899i	0.168219	+	0.954019i	−0.777463	+	0.628928i	$0.783494\pi$
$68$	−5.69420	+	0.446202i	−0.690523	+	0.0541099i
$69$	0.738199	−	1.97489i	0.0888687	−	0.237749i
$70$	1.13997	−	1.03512i	0.136252	−	0.123721i
$71$	−1.76325	+	9.99987i	−0.209259	+	1.18677i	0.681337	+	0.731970i	$0.261399\pi$
$71$	−1.76325	+	9.99987i	−0.209259	+	1.18677i	−0.890596	+	0.454796i	$0.849712\pi$
$72$	7.73535	+	3.48775i	0.911620	+	0.411035i
$73$	−2.87516	+	1.04647i	−0.336513	+	0.122481i	−0.504749	−	0.863266i	$-0.668415\pi$
$73$	−2.87516	+	1.04647i	−0.336513	+	0.122481i	0.168237	+	0.985747i	$0.446193\pi$
$74$	−11.7085	+	4.78775i	−1.36108	+	0.556564i
$75$	−1.13007	−	6.74969i	−0.130489	−	0.779387i
$76$	0.563268	+	8.69958i	0.0646113	+	0.997911i
$77$	−1.03828	+	1.79835i	−0.118323	+	0.204941i
$78$	−5.73978	+	10.6800i	−0.649902	+	1.20927i
$79$	0.624534	+	0.524047i	0.0702656	+	0.0589599i	0.677244	−	0.735758i	$-0.263174\pi$
$79$	0.624534	+	0.524047i	0.0702656	+	0.0589599i	−0.606978	+	0.794718i	$0.707619\pi$
$80$	−2.68963	+	3.08984i	−0.300710	+	0.345454i
$81$	8.99462	+	0.311185i	0.999402	+	0.0345761i
$82$	0.492052	+	2.26811i	0.0543380	+	0.250470i
$83$	−2.89850	−	1.67345i	−0.318151	−	0.183685i	0.332417	−	0.943133i	$-0.392136\pi$
$83$	−2.89850	−	1.67345i	−0.318151	−	0.183685i	−0.650568	+	0.759448i	$0.725469\pi$
$84$	3.57373	−	0.890051i	0.389926	−	0.0971125i
$85$	−0.507872	−	2.88029i	−0.0550865	−	0.312411i
$86$	6.84891	−	6.21899i	0.738537	−	0.670611i
$87$	0.965321	−	2.58251i	0.103493	−	0.276874i
$88$	2.18332	−	5.07471i	0.232743	−	0.540966i
$89$	−2.89294	+	7.94828i	−0.306651	+	0.842516i	0.686653	+	0.726985i	$0.259079\pi$
$89$	−2.89294	+	7.94828i	−0.306651	+	0.842516i	−0.993304	+	0.115531i	$0.963143\pi$
$90$	−1.39668	+	4.11438i	−0.147223	+	0.433694i
$91$	0.913824	+	5.18255i	0.0957947	+	0.543279i
$92$	1.00882	+	2.21565i	0.105177	+	0.230998i
$93$	−5.39875	−	0.0466773i	−0.559824	−	0.00484021i
$94$	8.13260	−	0.318151i	0.838814	−	0.0328147i
$95$	−4.40632	+	0.715559i	−0.452079	+	0.0734148i
$96$	−9.16507	+	3.46431i	−0.935406	+	0.353574i
$97$	−8.30734	−	1.46481i	−0.843483	−	0.148729i	−0.264822	−	0.964297i	$-0.585313\pi$
$97$	−8.30734	−	1.46481i	−0.843483	−	0.148729i	−0.578661	+	0.815568i	$0.696424\pi$
$98$	−5.08313	+	6.56265i	−0.513473	+	0.662928i
$99$	0.101316	−	5.85869i	0.0101826	−	0.588821i
$100$	6.43187	+	4.59110i	0.643187	+	0.459110i
$101$	0.567375	+	3.21774i	0.0564559	+	0.320177i	0.999937	−	0.0112498i	$-0.00358098\pi$
$101$	0.567375	+	3.21774i	0.0564559	+	0.320177i	−0.943481	+	0.331427i	$0.892470\pi$
$102$	2.19127	−	6.64326i	0.216968	−	0.657781i
$103$	2.32938	+	4.03461i	0.229521	+	0.397542i	0.957666	−	0.287881i	$-0.0929507\pi$
$103$	2.32938	+	4.03461i	0.229521	+	0.397542i	−0.728145	+	0.685423i	$0.759617\pi$
$104$	−4.02803	−	13.4084i	−0.394981	−	1.31480i
$105$	0.629659	+	1.77765i	0.0614485	+	0.173480i
$106$	−1.12878	−	1.78968i	−0.109637	−	0.173829i
$107$	8.70285	+	15.0738i	0.841336	+	1.45724i	0.888766	+	0.458362i	$0.151564\pi$
$107$	8.70285	+	15.0738i	0.841336	+	1.45724i	−0.0474299	+	0.998875i	$0.515103\pi$
$108$	−7.60113	+	7.08680i	−0.731419	+	0.681928i
$109$	−9.82328	−	1.73211i	−0.940899	−	0.165906i	−0.317896	−	0.948125i	$-0.602976\pi$
$109$	−9.82328	−	1.73211i	−0.940899	−	0.165906i	−0.623003	+	0.782220i	$0.714088\pi$
$110$	2.69405	+	0.862874i	0.256867	+	0.0822718i
$111$	0.133942	−	15.4919i	0.0127132	−	1.47042i
$112$	−2.19274	+	3.64374i	−0.207195	+	0.344301i
$113$	−9.98397	−	5.76425i	−0.939213	−	0.542255i	−0.0494996	−	0.998774i	$-0.515763\pi$
$113$	−9.98397	−	5.76425i	−0.939213	−	0.542255i	−0.889714	+	0.456519i	$0.849096\pi$
$114$	−10.0935	−	3.48160i	−0.945342	−	0.326082i
$115$	−1.07960	+	0.623309i	−0.100673	+	0.0581238i
$116$	1.31921	+	2.89734i	0.122486	+	0.269011i
$117$	−9.34702	−	11.5388i	−0.864132	−	1.06676i
$118$	−9.85416	−	10.8523i	−0.907149	−	0.999033i
$119$	−1.03844	−	2.85310i	−0.0951939	−	0.261543i
$120$	−2.21711	−	4.50070i	−0.202393	−	0.410856i
$121$	7.18505			0.653186
$122$	−8.46658	−	4.45631i	−0.766528	−	0.403456i
$123$	−2.79491	−	0.517773i	−0.252009	−	0.0466860i
$124$	4.44800	−	4.36808i	0.399443	−	0.392265i
$125$	−4.58355	+	7.93894i	−0.409965	+	0.710080i
$126$	−0.686203	+	4.45810i	−0.0611318	+	0.397160i
$127$	11.3156	+	4.11852i	1.00409	+	0.365460i	0.791162	−	0.611607i	$-0.209477\pi$
$127$	11.3156	+	4.11852i	1.00409	+	0.365460i	0.212931	+	0.977067i	$0.431699\pi$
$128$	4.65898	−	10.3099i	0.411800	−	0.911274i
$129$	3.78299	+	10.6801i	0.333073	+	0.940328i
$130$	6.63569	−	2.71342i	0.581988	−	0.237983i
$131$	3.89202	+	10.6932i	0.340047	+	0.934272i	0.985380	+	0.170371i	$0.0544965\pi$
$131$	3.89202	+	10.6932i	0.340047	+	0.934272i	−0.645333	+	0.763902i	$0.723281\pi$
$132$	4.69884	+	4.86830i	0.408981	+	0.423731i
$133$	−4.37580	+	1.52587i	−0.379430	+	0.132309i
$134$	9.48495	−	5.98231i	0.819375	−	0.516793i
$135$	−3.98642	−	3.52516i	−0.343096	−	0.303398i
$136$	3.63201	+	7.21489i	0.311442	+	0.618672i
$137$	16.7039	−	14.0162i	1.42711	−	1.19749i	0.479714	−	0.877425i	$-0.340741\pi$
$137$	16.7039	−	14.0162i	1.42711	−	1.19749i	0.947396	−	0.320062i	$-0.103704\pi$
$138$	−2.98027	+	0.0907914i	−0.253697	+	0.00772868i
$139$	−9.20402	−	10.9689i	−0.780675	−	0.930372i	0.218289	−	0.975884i	$-0.429952\pi$
$139$	−9.20402	−	10.9689i	−0.780675	−	0.930372i	−0.998964	+	0.0455124i	$0.985508\pi$
$140$	−1.96516	−	0.938152i	−0.166087	−	0.0792883i
$141$	−3.49010	+	9.33701i	−0.293920	+	0.786318i
$142$	14.0337	−	3.04452i	1.17768	−	0.255490i
$143$	−7.40614	+	6.21449i	−0.619332	+	0.519682i
$144$	0.424981	−	11.9925i	0.0354151	−	0.999373i
$145$	−1.41176	+	0.815083i	−0.117241	+	0.0676889i
$146$	2.90882	+	3.20345i	0.240736	+	0.265120i
$147$	−5.00699	−	8.84816i	−0.412970	−	0.729784i
$148$	12.5343	+	12.7637i	1.03032	+	1.04917i
$149$	−2.49651	+	14.1584i	−0.204522	+	1.15990i	0.693667	+	0.720296i	$0.255994\pi$
$149$	−2.49651	+	14.1584i	−0.204522	+	1.15990i	−0.898190	+	0.439608i	$0.855117\pi$
$150$	−8.23046	+	5.09216i	−0.672015	+	0.415773i
$151$	−2.23007	−	3.86259i	−0.181480	−	0.314333i	0.760905	−	0.648864i	$-0.224755\pi$
$151$	−2.23007	−	3.86259i	−0.181480	−	0.314333i	−0.942385	+	0.334531i	$0.891422\pi$
$152$	11.0863	−	5.39393i	0.899216	−	0.437505i
$153$	6.46687	+	5.61973i	0.522816	+	0.454328i
$154$	2.90980	+	0.396508i	0.234478	+	0.0319516i
$155$	2.44543	+	2.05196i	0.196421	+	0.164817i
$156$	17.0524	+	1.79673i	1.36529	+	0.143854i
$157$	15.7929	+	13.2518i	1.26041	+	1.05761i	0.995638	+	0.0933003i	$0.0297417\pi$
$157$	15.7929	+	13.2518i	1.26041	+	1.05761i	0.264774	+	0.964311i	$0.414703\pi$
$158$	0.351685	−	1.09802i	0.0279786	−	0.0873540i
$159$	2.55588	−	0.427921i	0.202695	−	0.0339363i
$160$	5.48428	+	1.86685i	0.433570	+	0.147587i
$161$	−0.991366	+	0.831855i	−0.0781306	+	0.0655593i
$162$	−4.40719	−	11.9405i	−0.346262	−	0.938138i
$163$	14.8021	+	8.54603i	1.15939	+	0.669376i	0.951159	−	0.308702i	$-0.0998947\pi$
$163$	14.8021	+	8.54603i	1.15939	+	0.669376i	0.208235	+	0.978079i	$0.433228\pi$
$164$	2.70558	−	1.85814i	0.211270	−	0.145097i
$165$	−2.24988	+	2.63471i	−0.175153	+	0.205112i
$166$	−0.639074	+	4.68988i	−0.0496018	+	0.364006i
$167$	13.3361	+	4.85396i	1.03198	+	0.375610i	0.801835	−	0.597546i	$-0.203857\pi$
$167$	13.3361	+	4.85396i	1.03198	+	0.375610i	0.230146	+	0.973156i	$0.426080\pi$
$168$	−3.07798	−	4.20160i	−0.237471	−	0.324161i
$169$	−1.99716	+	11.3264i	−0.153627	+	0.871265i
$170$	−3.49845	+	2.20653i	−0.268319	+	0.169233i
$171$	8.71039	−	9.75342i	0.666100	−	0.745862i
$172$	−11.8067	−	5.63641i	−0.900251	−	0.429772i
$173$	12.3705	+	2.18125i	0.940512	+	0.165838i	0.622828	−	0.782359i	$-0.285984\pi$
$173$	12.3705	+	2.18125i	0.940512	+	0.165838i	0.317684	+	0.948197i	$0.397095\pi$
$174$	−3.89721	+	0.118725i	−0.295447	+	0.00900054i
$175$	−1.43673	+	3.94739i	−0.108607	+	0.298395i
$176$	−7.81147	−	0.141646i	−0.588812	−	0.0106769i
$177$	16.9229	−	5.99425i	1.27200	−	0.450555i
$178$	11.9528	−	0.467599i	0.895902	−	0.0350480i
$179$	0.761463	−	1.31889i	0.0569144	−	0.0985787i	−0.836164	−	0.548479i	$-0.815207\pi$
$179$	0.761463	−	1.31889i	0.0569144	−	0.0985787i	0.893079	+	0.449900i	$0.148540\pi$
$180$	6.13334	−	0.374041i	0.457152	−	0.0278794i
$181$	2.79975	+	3.33662i	0.208104	+	0.248009i	0.859993	−	0.510306i	$-0.170468\pi$
$181$	2.79975	+	3.33662i	0.208104	+	0.248009i	−0.651889	+	0.758314i	$0.726023\pi$
$182$	6.29483	−	3.97025i	0.466604	−	0.294295i
$183$	9.04133	−	7.45432i	0.668354	−	0.551039i
$184$	2.36030	−	2.50652i	0.174004	−	0.184783i
$185$	−5.88815	+	7.01723i	−0.432906	+	0.515917i
$186$	2.82868	+	7.09196i	0.207409	+	0.520008i
$187$	3.58545	−	4.27298i	0.262194	−	0.312471i
$188$	−4.76958	−	10.4753i	−0.347858	−	0.763990i
$189$	−4.71098	−	2.88532i	−0.342673	−	0.209876i
$190$	3.29523	+	5.38487i	0.239061	+	0.390660i
$191$	5.72943	−	3.30789i	0.414567	−	0.239350i	−0.278183	−	0.960528i	$-0.589732\pi$
$191$	5.72943	−	3.30789i	0.414567	−	0.239350i	0.692750	+	0.721178i	$0.256399\pi$
$192$	9.44056	+	10.1428i	0.681314	+	0.731992i
$193$	16.5659	+	2.92102i	1.19244	+	0.210259i	0.734428	−	0.678687i	$-0.237451\pi$
$193$	16.5659	+	2.92102i	1.19244	+	0.210259i	0.458012	+	0.888946i	$0.348562\pi$
$194$	2.52922	+	11.6584i	0.181587	+	0.837024i
$195$	−0.0759106	+	8.77990i	−0.00543607	+	0.628742i
$196$	11.3114	+	3.14105i	0.807954	+	0.224360i
$197$	−10.0699	−	17.4416i	−0.717452	−	1.24266i	−0.962006	−	0.273027i	$-0.911975\pi$
$197$	−10.0699	−	17.4416i	−0.717452	−	1.24266i	0.244555	−	0.969636i	$-0.421358\pi$
$198$	−7.72327	+	3.00335i	−0.548869	+	0.213439i
$199$	−8.71880	−	10.3907i	−0.618059	−	0.736574i	0.362676	−	0.931915i	$-0.381863\pi$
$199$	−8.71880	−	10.3907i	−0.618059	−	0.736574i	−0.980735	+	0.195341i	$0.937419\pi$
$200$	2.56698	−	10.8768i	0.181513	−	0.769106i
$201$	2.26789	+	13.5457i	0.159965	+	0.955438i
$202$	3.90834	−	2.46505i	0.274990	−	0.173440i
$203$	−1.29638	+	1.08779i	−0.0909881	+	0.0763481i
$204$	−9.86896	+	0.687547i	−0.690965	+	0.0481379i
$205$	1.08033	+	1.28748i	0.0754532	+	0.0899216i
$206$	4.03447	−	5.20877i	0.281095	−	0.362912i
$207$	1.30812	−	3.40943i	0.0909208	−	0.236971i
$208$	−15.3955	+	12.4498i	−1.06749	+	0.863237i
$209$	−6.44720	−	5.56037i	−0.445962	−	0.384619i
$210$	1.98991	−	1.77574i	0.137317	−	0.122538i
$211$	−17.8830	+	6.50886i	−1.23111	+	0.448089i	−0.873979	−	0.485964i	$-0.838468\pi$
$211$	−17.8830	+	6.50886i	−1.23111	+	0.448089i	−0.357135	+	0.934053i	$0.616246\pi$
$212$	−1.73850	+	2.43553i	−0.119400	+	0.167273i
$213$	−3.20366	+	17.2932i	−0.219511	+	1.18491i
$214$	15.0732	−	19.4606i	1.03039	−	1.33030i
$215$	2.29131	−	6.29531i	0.156266	−	0.429337i
$216$	13.3453	+	6.15656i	0.908032	+	0.418901i
$217$	2.86997	+	1.65698i	0.194827	+	0.112483i
$218$	2.99075	+	13.7858i	0.202559	+	0.933695i
$219$	−4.99541	+	1.76942i	−0.337559	+	0.119567i
$220$	−0.312533	−	3.98838i	−0.0210710	−	0.268897i
$221$		−	14.1360i		−	0.950888i
$222$	−20.3506	+	8.11698i	−1.36584	+	0.544776i
$223$	2.92427	−	1.06435i	0.195824	−	0.0712740i	−0.242247	−	0.970215i	$-0.577884\pi$
$223$	2.92427	−	1.06435i	0.195824	−	0.0712740i	0.438070	+	0.898941i	$0.355662\pi$
$224$	5.94337	+	0.919927i	0.397108	+	0.0614652i
$225$	−1.85619	−	11.7073i	−0.123746	−	0.780486i
$226$	−2.20131	+	16.1545i	−0.146429	+	1.07458i
$227$	−9.79197	−	16.9602i	−0.649916	−	1.12569i	−0.983143	−	0.182841i	$-0.941471\pi$
$227$	−9.79197	−	16.9602i	−0.649916	−	1.12569i	0.333227	−	0.942847i	$-0.391863\pi$
$228$	0.845299	+	15.0760i	0.0559813	+	0.998432i
$229$	11.6124	−	20.1133i	0.767372	−	1.32913i	−0.171611	−	0.985165i	$-0.554897\pi$
$229$	11.6124	−	20.1133i	0.767372	−	1.32913i	0.938983	−	0.343962i	$-0.111769\pi$
$230$	1.39379	+	1.07956i	0.0919038	+	0.0711844i
$231$	−1.82521	+	3.09917i	−0.120090	+	0.203910i
$232$	3.08650	−	3.27770i	0.202638	−	0.215192i
$233$	−3.53919	+	20.0718i	−0.231860	+	1.31494i	0.617266	+	0.786755i	$0.288240\pi$
$233$	−3.53919	+	20.0718i	−0.231860	+	1.31494i	−0.849126	+	0.528190i	$0.822871\pi$
$234$	−10.1011	+	18.4116i	−0.660333	+	1.20361i
$235$	5.10422	−	2.94692i	0.332962	−	0.192236i
$236$	−8.93104	+	18.7080i	−0.581361	+	1.21779i
$237$	1.07384	+	0.916994i	0.0697532	+	0.0595651i
$238$	−3.17887	+	2.88650i	−0.206055	+	0.187104i
$239$	6.95747	−	4.01690i	0.450041	−	0.259831i	−0.257806	−	0.966197i	$-0.583000\pi$
$239$	6.95747	−	4.01690i	0.450041	−	0.259831i	0.707848	+	0.706365i	$0.249666\pi$
$240$	−4.70468	+	5.31128i	−0.303686	+	0.342842i
$241$	−25.0080	+	4.40958i	−1.61091	+	0.284046i	−0.905369	−	0.424626i	$-0.860405\pi$
$241$	−25.0080	+	4.40958i	−1.61091	+	0.284046i	−0.705537	+	0.708673i	$0.749294\pi$
$242$	−3.84593	−	9.40525i	−0.247226	−	0.604592i
$243$	15.5739	+	0.673659i	0.999066	+	0.0432152i
$244$	−1.30144	+	13.4681i	−0.0833159	+	0.862207i
$245$	−1.04385	+	5.91996i	−0.0666890	+	0.378212i
$246$	0.818263	+	3.93570i	0.0521705	+	0.250931i
$247$	−21.5740	−	0.292229i	−1.37272	−	0.0185941i
$248$	−8.09870	−	3.48436i	−0.514268	−	0.221257i
$249$	−4.99510	−	2.94179i	−0.316551	−	0.186429i
$250$	12.8455	+	1.75042i	0.812422	+	0.110706i
$251$	8.39510	−	1.48028i	0.529894	−	0.0934346i	0.0977012	−	0.995216i	$-0.468851\pi$
$251$	8.39510	−	1.48028i	0.529894	−	0.0934346i	0.432193	+	0.901781i	$0.357740\pi$
$252$	6.20297	−	1.48804i	0.390751	−	0.0937377i
$253$	−2.23415	−	0.813163i	−0.140460	−	0.0511231i
$254$	−0.665697	−	17.0166i	−0.0417695	−	1.06772i
$255$	−0.836496	−	4.99622i	−0.0523834	−	0.312875i
$256$	−15.9895	−	0.580065i	−0.999343	−	0.0362541i
$257$	20.7324	−	3.65569i	1.29325	−	0.228035i	0.515655	−	0.856797i	$-0.327549\pi$
$257$	20.7324	−	3.65569i	1.29325	−	0.228035i	0.777598	+	0.628761i	$0.216438\pi$
$258$	11.9553	−	10.6686i	0.744307	−	0.664201i
$259$	−4.75476	+	8.23548i	−0.295446	+	0.511728i
$260$	−7.10374	−	7.23372i	−0.440555	−	0.448616i
$261$	1.71059	−	4.45841i	0.105883	−	0.275969i
$262$	11.9142	−	10.8184i	0.736062	−	0.668364i
$263$	1.50399	−	1.79239i	0.0927401	−	0.110523i	−0.717679	−	0.696375i	$-0.754795\pi$
$263$	1.50399	−	1.79239i	0.0927401	−	0.110523i	0.810419	+	0.585851i	$0.199240\pi$
$264$	3.85748	−	8.75663i	0.237411	−	0.538934i
$265$	−1.32698	−	0.766135i	−0.0815160	−	0.0470633i
$266$	4.33959	+	4.91118i	0.266077	+	0.301124i
$267$	−5.12955	+	13.7230i	−0.313923	+	0.839833i
$268$	−12.9079	−	9.21369i	−0.788473	−	0.562815i
$269$	4.56715	+	12.5481i	0.278464	+	0.765074i	0.997537	+	0.0701395i	$0.0223444\pi$
$269$	4.56715	+	12.5481i	0.278464	+	0.765074i	−0.719073	+	0.694934i	$0.755433\pi$
$270$	−2.48064	+	7.10514i	−0.150967	+	0.432405i
$271$	−25.5657	−	4.50793i	−1.55301	−	0.273837i	−0.669700	−	0.742632i	$-0.733577\pi$
$271$	−25.5657	−	4.50793i	−1.55301	−	0.273837i	−0.883307	+	0.468795i	$0.844688\pi$
$272$	7.50021	−	8.61620i	0.454767	−	0.522434i
$273$	1.50512	+	8.98979i	0.0910942	+	0.544087i
$274$	−27.2883	−	14.3630i	−1.64855	−	0.867700i
$275$	−7.60015	+	1.34011i	−0.458306	+	0.0808117i
$276$	1.71409	+	3.85258i	0.103176	+	0.231898i
$277$	−6.78657			−0.407766			−0.203883	−	0.978995i	$-0.565356\pi$
$277$	−6.78657			−0.407766			−0.203883	+	0.978995i	$0.565356\pi$
$278$	−9.43173	+	17.9194i	−0.565677	+	1.07473i
$279$	−9.34986	−	0.161689i	−0.559761	−	0.00968006i
$280$	−0.176154	+	3.07457i	−0.0105272	+	0.183740i
$281$	6.82595	+	8.13485i	0.407202	+	0.485285i	0.930202	−	0.367048i	$-0.119632\pi$
$281$	6.82595	+	8.13485i	0.407202	+	0.485285i	−0.523000	+	0.852333i	$0.675187\pi$
$282$	14.0903	−	0.429250i	0.839066	−	0.0255614i
$283$	4.63961	+	12.7472i	0.275796	+	0.757744i	0.997827	+	0.0658832i	$0.0209865\pi$
$283$	4.63961	+	12.7472i	0.275796	+	0.757744i	−0.722031	+	0.691861i	$0.756791\pi$
$284$	−11.4971	−	16.7405i	−0.682225	−	0.993364i
$285$	−7.64241	+	1.17335i	−0.452697	+	0.0695035i
$286$	12.0991	+	6.36824i	0.715432	+	0.376562i
$287$	1.33656	+	1.12151i	0.0788945	+	0.0662004i
$288$	−15.9257	+	5.86289i	−0.938428	+	0.345474i
$289$	−1.53579	−	8.70988i	−0.0903404	−	0.512346i
$290$	1.82262	+	1.41172i	0.107028	+	0.0828988i
$291$	−14.3663	−	2.66143i	−0.842166	−	0.156016i
$292$	2.63633	−	5.52236i	0.154279	−	0.323172i
$293$	−20.0831	+	11.5950i	−1.17327	+	0.677387i	−0.954448	−	0.298378i	$-0.903554\pi$
$293$	−20.0831	+	11.5950i	−1.17327	+	0.677387i	−0.218821	+	0.975765i	$0.570221\pi$
$294$	−8.90218	+	11.2903i	−0.519185	+	0.658464i
$295$	−9.97510	−	3.63064i	−0.580773	−	0.211384i
$296$	9.99847	−	23.2395i	0.581149	−	1.35077i
$297$	0.263209	−	10.1457i	0.0152729	−	0.588711i
$298$	19.8697	−	4.31062i	1.15102	−	0.249707i
$299$	−5.66188	+	2.06076i	−0.327435	+	0.119177i
$300$	11.0712	+	8.04803i	0.639193	+	0.464653i
$301$	1.20767	−	6.84904i	0.0696090	−	0.394772i
$302$	−3.86245	+	4.98668i	−0.222259	+	0.286951i
$303$	0.934501	+	5.58158i	0.0536857	+	0.320654i
$304$	−12.9948	−	11.6248i	−0.745303	−	0.666726i
$305$	−6.92861			−0.396731
$306$	3.89473	−	11.4732i	0.222647	−	0.655880i
$307$	6.57093	−	2.39162i	0.375023	−	0.136497i	−0.147630	−	0.989043i	$-0.547165\pi$
$307$	6.57093	−	2.39162i	0.375023	−	0.136497i	0.522653	+	0.852545i	$0.324942\pi$
$308$	−1.03849	−	4.02117i	−0.0591736	−	0.229128i
$309$	3.97404	+	7.02277i	0.226075	+	0.399511i
$310$	1.37706	−	4.29941i	0.0782116	−	0.244190i
$311$			23.1353i			1.31188i	0.754811	+	0.655942i	$0.227729\pi$
$311$			23.1353i			1.31188i	−0.754811	+	0.655942i	$0.772271\pi$
$312$	−6.77570	−	23.2834i	−0.383599	−	1.31816i
$313$	16.2910	+	5.92943i	0.920820	+	0.335151i	0.758565	−	0.651598i	$-0.225901\pi$
$313$	16.2910	+	5.92943i	0.920820	+	0.335151i	0.162255	+	0.986749i	$0.448123\pi$
$314$	8.89323	−	27.7662i	0.501874	−	1.56694i
$315$	1.06394	+	3.08829i	0.0599463	+	0.174005i
$316$	−1.62556	+	0.127380i	−0.0914449	+	0.00716569i
$317$	18.4311	−	3.24990i	1.03519	−	0.182533i	0.369867	−	0.929085i	$-0.379403\pi$
$317$	18.4311	−	3.24990i	1.03519	−	0.182533i	0.665327	+	0.746552i	$0.268292\pi$
$318$	−1.92823	−	3.11660i	−0.108130	−	0.174770i
$319$	−2.92153	−	1.06335i	−0.163574	−	0.0595361i
$320$	−0.491856	−	8.17820i	−0.0274956	−	0.457175i
$321$	14.8475	+	26.2379i	0.828706	+	1.46446i
$322$	1.61955	+	0.852435i	0.0902538	+	0.0475044i
$323$	12.2873	−	1.99538i	0.683684	−	0.111026i
$324$	−13.2712	+	12.1604i	−0.737288	+	0.675579i
$325$	−12.5715	+	14.9821i	−0.697341	+	0.831059i
$326$	3.26365	−	23.9505i	0.180757	−	1.32649i
$327$	−16.9878	−	3.14709i	−0.939430	−	0.174034i
$328$	−3.88052	−	2.54700i	−0.214266	−	0.140635i
$329$	4.68705	−	3.93290i	0.258405	−	0.216828i
$330$	4.65313	+	1.53483i	0.256146	+	0.0844896i
$331$	−35.6558			−1.95982			−0.979910	−	0.199438i	$-0.936088\pi$
$331$	−35.6558			−1.95982			−0.979910	+	0.199438i	$0.936088\pi$
$332$	6.48115	−	1.67380i	0.355699	−	0.0918614i
$333$	0.463972	−	26.8297i	0.0254255	−	1.47026i
$334$	−0.784568	−	20.0552i	−0.0429296	−	1.09737i
$335$	4.06036	−	7.03276i	0.221841	−	0.384241i
$336$	−3.85236	+	6.27807i	−0.210164	+	0.342497i
$337$	−6.52425	+	7.77530i	−0.355399	+	0.423547i	−0.913889	−	0.405963i	$-0.866936\pi$
$337$	−6.52425	+	7.77530i	−0.355399	+	0.423547i	0.558491	+	0.829511i	$0.311381\pi$
$338$	15.8954	−	3.44840i	0.864594	−	0.187568i
$339$	−17.2058	−	10.1331i	−0.934490	−	0.550355i
$340$	4.76097	+	3.39840i	0.258200	+	0.184304i
$341$			6.08826i			0.329698i
$342$	−17.4296	−	6.18123i	−0.942487	−	0.334243i
$343$			13.6825i			0.738788i
$344$	−1.05833	+	18.4720i	−0.0570615	+	0.995941i
$345$	−1.87919	+	1.06340i	−0.101172	+	0.0572513i
$346$	−3.76627	−	17.3606i	−0.202476	−	0.933311i
$347$	−3.18430	+	3.79490i	−0.170942	+	0.203721i	−0.844713	−	0.535219i	$-0.820229\pi$
$347$	−3.18430	+	3.79490i	−0.170942	+	0.203721i	0.673771	+	0.738940i	$0.264673\pi$
$348$	2.24147	+	5.03791i	0.120155	+	0.270060i
$349$	−3.33288	+	5.77271i	−0.178405	+	0.309006i	−0.941334	−	0.337475i	$-0.890427\pi$
$349$	−3.33288	+	5.77271i	−0.178405	+	0.309006i	0.762930	+	0.646482i	$0.223760\pi$
$350$	5.93619	−	0.232226i	0.317303	−	0.0124130i
$351$	−16.0161	−	20.1250i	−0.854877	−	1.07419i
$352$	3.99582	+	10.3011i	0.212978	+	0.549048i
$353$	−27.0106			−1.43763			−0.718813	−	0.695203i	$-0.755314\pi$
$353$	−27.0106			−1.43763			−0.718813	+	0.695203i	$0.755314\pi$
$354$	−16.9048	−	18.9436i	−0.898478	−	1.00684i
$355$	7.96616	−	6.68440i	0.422800	−	0.354771i
$356$	−7.01005	−	15.3960i	−0.371532	−	0.815985i
$357$	−1.75584	−	4.95708i	−0.0929291	−	0.262356i
$358$	−2.13402	−	0.290796i	−0.112787	−	0.0153690i
$359$	12.9128	−	15.3889i	0.681513	−	0.812195i	−0.308789	−	0.951131i	$-0.599924\pi$
$359$	12.9128	−	15.3889i	0.681513	−	0.812195i	0.990301	+	0.138935i	$0.0443680\pi$
$360$	−3.77260	−	7.82835i	−0.198834	−	0.412590i
$361$	−2.79129	−	18.7938i	−0.146910	−	0.989150i
$362$	2.86902	−	5.45087i	0.150792	−	0.286491i
$363$	12.4444	+	0.107594i	0.653162	+	0.00564721i
$364$	−8.56649	−	6.11480i	−0.449006	−	0.320503i
$365$	2.94452	+	1.07172i	0.154123	+	0.0560963i
$366$	−14.5973	−	7.84506i	−0.763011	−	0.410068i
$367$	−24.4255	+	4.30687i	−1.27500	+	0.224817i	−0.769855	−	0.638219i	$-0.779671\pi$
$367$	−24.4255	+	4.30687i	−1.27500	+	0.224817i	−0.505143	+	0.863036i	$0.668560\pi$
$368$	−4.54444	−	1.74798i	−0.236895	−	0.0911198i
$369$	−4.83300	−	0.938628i	−0.251596	−	0.0488630i
$370$	12.3373	+	3.95151i	0.641386	+	0.205429i
$371$	−1.49475	−	0.544044i	−0.0776034	−	0.0282453i
$372$	7.76929	−	7.49885i	0.402819	−	0.388797i
$373$		−	21.6447i		−	1.12072i	−0.828250	−	0.560359i	$-0.810663\pi$
$373$		−	21.6447i		−	1.12072i	0.828250	−	0.560359i	$-0.189337\pi$
$374$	−7.51252	−	2.40618i	−0.388463	−	0.124421i
$375$	−8.05753	+	13.6815i	−0.416089	+	0.706509i
$376$	−11.1592	+	11.8505i	−0.575491	+	0.611142i
$377$	−7.40387	+	2.69479i	−0.381319	+	0.138789i
$378$	−1.25525	+	7.71110i	−0.0645632	+	0.396616i
$379$	17.8984			0.919378			0.459689	−	0.888080i	$-0.347961\pi$
$379$	17.8984			0.919378			0.459689	+	0.888080i	$0.347961\pi$
$380$	5.28498	−	7.19582i	0.271114	−	0.369138i
$381$	19.5367	+	7.30267i	1.00090	+	0.374127i
$382$	−7.39681	−	5.72923i	−0.378454	−	0.293133i
$383$	2.99127	−	16.9643i	0.152847	−	0.866837i	−0.807881	−	0.589345i	$-0.799386\pi$
$383$	2.99127	−	16.9643i	0.152847	−	0.866837i	0.960728	−	0.277492i	$-0.0895031\pi$
$384$	8.22368	−	17.7868i	0.419663	−	0.907680i
$385$	1.99839	−	0.727355i	0.101847	−	0.0370695i
$386$	−5.04359	−	23.2483i	−0.256712	−	1.18331i
$387$	6.39215	+	18.5544i	0.324931	+	0.943173i
$388$	13.9071	−	9.55113i	0.706024	−	0.484885i
$389$	2.27788	+	0.829080i	0.115493	+	0.0420360i	0.399120	−	0.916899i	$-0.369316\pi$
$389$	2.27788	+	0.829080i	0.115493	+	0.0420360i	−0.283627	+	0.958935i	$0.591538\pi$
$390$	11.5335	−	4.60024i	0.584024	−	0.232942i
$391$	3.01054	−	1.73813i	0.152249	−	0.0879013i
$392$	−1.94297	−	16.4879i	−0.0981350	−	0.832765i
$393$	6.58079	+	18.5788i	0.331957	+	0.937177i
$394$	−17.4410	+	22.5175i	−0.878665	+	1.13441i
$395$	−0.144985	−	0.822253i	−0.00729501	−	0.0413721i
$396$	8.06542	+	8.50219i	0.405302	+	0.427251i
$397$	13.0376	+	10.9398i	0.654337	+	0.549054i	0.908384	−	0.418138i	$-0.137317\pi$
$397$	13.0376	+	10.9398i	0.654337	+	0.549054i	−0.254046	+	0.967192i	$0.581762\pi$
$398$	−8.93450	+	16.9747i	−0.447846	+	0.850866i
$399$	−7.60167	+	2.57725i	−0.380560	+	0.129024i
$400$	−15.6118	+	2.46182i	−0.780589	+	0.123091i
$401$	−10.8095	−	29.6988i	−0.539800	−	1.48309i	−0.847077	−	0.531469i	$-0.821640\pi$
$401$	−10.8095	−	29.6988i	−0.539800	−	1.48309i	0.307277	−	0.951620i	$-0.400582\pi$
$402$	16.5174	−	10.2192i	0.823813	−	0.509690i
$403$	9.91767	+	11.8194i	0.494034	+	0.588767i
$404$	−5.31877	−	3.79656i	−0.264619	−	0.188886i
$405$	−6.85164	−	6.16523i	−0.340461	−	0.306353i
$406$	2.11783	+	1.11470i	0.105106	+	0.0553219i
$407$	−17.4704			−0.865978
$408$	6.18254	+	12.5505i	0.306081	+	0.621341i
$409$	7.08449	−	1.24919i	0.350305	−	0.0617683i	0.00427303	−	0.999991i	$-0.498640\pi$
$409$	7.08449	−	1.24919i	0.350305	−	0.0617683i	0.346032	+	0.938223i	$0.387529\pi$
$410$	1.10705	−	2.10330i	0.0546734	−	0.103874i
$411$	29.1408	−	24.0258i	1.43741	−	1.18510i
$412$	−8.97781	−	2.49304i	−0.442305	−	0.122823i
$413$	−10.8525	−	1.91359i	−0.534016	−	0.0941615i
$414$	−5.16314	+	0.112621i	−0.253755	+	0.00553501i
$415$	1.17232	+	3.22092i	0.0575469	+	0.158109i
$416$	24.5375	+	13.4888i	1.20305	+	0.661343i
$417$	−15.7770	−	19.1358i	−0.772602	−	0.937086i
$418$	−3.82756	+	11.4157i	−0.187212	+	0.558359i
$419$	8.45961	+	4.88416i	0.413279	+	0.238607i	0.692198	−	0.721708i	$-0.256643\pi$
$419$	8.45961	+	4.88416i	0.413279	+	0.238607i	−0.278919	+	0.960315i	$0.589976\pi$
$420$	−3.38959	−	1.65429i	−0.165395	−	0.0807213i
$421$	−6.68041	+	7.96140i	−0.325583	+	0.388015i	−0.903862	−	0.427824i	$-0.859280\pi$
$421$	−6.68041	+	7.96140i	−0.325583	+	0.388015i	0.578279	+	0.815839i	$0.303725\pi$
$422$	18.0923	+	19.9248i	0.880719	+	0.969926i
$423$	−6.18463	+	16.1193i	−0.300707	+	0.783748i
$424$	4.11868	+	0.972031i	0.200021	+	0.0472060i
$425$	5.64194	−	9.77212i	0.273674	−	0.474018i
$426$	24.3517	−	5.06291i	1.17984	−	0.245299i
$427$	−7.08345	+	1.24900i	−0.342792	+	0.0604435i
$428$	−33.5422	−	9.31430i	−1.62132	−	0.450224i
$429$	−12.9204	+	10.6525i	−0.623802	+	0.514308i
$430$	−9.46705	+	0.370355i	−0.456541	+	0.0178601i
$431$	−36.6636	−	13.3445i	−1.76602	−	0.642781i	−0.766025	−	0.642811i	$-0.777768\pi$
$431$	−36.6636	−	13.3445i	−1.76602	−	0.642781i	−1.00000		3.03679e-5i	$0.999990\pi$
$432$	0.915645	−	20.7644i	0.0440540	−	0.999029i
$433$	−27.2793	+	4.81008i	−1.31096	+	0.231158i	−0.785077	−	0.619399i	$-0.787376\pi$
$433$	−27.2793	+	4.81008i	−1.31096	+	0.231158i	−0.525884	+	0.850556i	$0.676265\pi$
$434$	0.632786	−	4.64373i	0.0303747	−	0.222906i
$435$	−2.45736	+	1.39057i	−0.117822	+	0.0666728i
$436$	16.4448	−	11.2940i	0.787565	−	0.540886i
$437$	−2.59046	−	4.63054i	−0.123919	−	0.221509i
$438$	4.99007	+	5.59189i	0.238435	+	0.267191i
$439$	0.826273	−	4.68603i	0.0394358	−	0.223652i	−0.958720	−	0.284351i	$-0.908222\pi$
$439$	0.826273	−	4.68603i	0.0394358	−	0.223652i	0.998156	+	0.0606992i	$0.0193330\pi$
$440$	−5.05352	+	2.54396i	−0.240917	+	0.121279i
$441$	−8.53954	−	15.3999i	−0.406645	−	0.733327i
$442$	−18.5040	+	7.56654i	−0.880147	+	0.359903i
$443$	18.1310	−	3.19698i	0.861428	−	0.151893i	0.274554	−	0.961572i	$-0.411470\pi$
$443$	18.1310	−	3.19698i	0.861428	−	0.151893i	0.586873	+	0.809679i	$0.300359\pi$
$444$	21.5182	+	22.2942i	1.02121	+	1.05804i
$445$	7.50188	−	4.33121i	0.355623	−	0.205319i
$446$	−2.95851	−	3.25817i	−0.140089	−	0.154279i
$447$	−4.53595	+	24.4848i	−0.214543	+	1.15809i
$448$	−1.97711	−	8.27229i	−0.0934097	−	0.390829i
$449$	1.50388	−	0.868265i	0.0709724	−	0.0409759i	−0.464094	−	0.885786i	$-0.653620\pi$
$449$	1.50388	−	0.868265i	0.0709724	−	0.0409759i	0.535066	+	0.844810i	$0.320287\pi$
$450$	−14.3313	+	8.69630i	−0.675584	+	0.409947i
$451$	−0.556608	+	3.15668i	−0.0262097	+	0.148642i
$452$	22.3245	−	5.76545i	1.05006	−	0.271184i
$453$	−3.80460	−	6.72334i	−0.178756	−	0.315890i
$454$	−16.9596	+	21.8960i	−0.795954	+	1.02763i
$455$	2.69472	−	4.66740i	0.126331	−	0.218811i
$456$	19.2820	−	9.17620i	0.902965	−	0.429715i
$457$	4.52709	+	7.84115i	0.211768	+	0.366793i	0.952268	−	0.305263i	$-0.0987445\pi$
$457$	4.52709	+	7.84115i	0.211768	+	0.366793i	−0.740500	+	0.672057i	$0.765411\pi$
$458$	−32.5442	−	4.43469i	−1.52069	−	0.207219i
$459$	11.1164	+	9.83013i	0.518868	+	0.458831i
$460$	0.667102	−	2.40233i	0.0311038	−	0.112009i
$461$	−15.1060	+	5.49812i	−0.703555	+	0.256073i	−0.668928	−	0.743327i	$-0.733247\pi$
$461$	−15.1060	+	5.49812i	−0.703555	+	0.256073i	−0.0346271	+	0.999400i	$0.511024\pi$
$462$	5.03379	+	0.730320i	0.234193	+	0.0339776i
$463$			21.8355i			1.01478i	0.861716	+	0.507391i	$0.169390\pi$
$463$			21.8355i			1.01478i	−0.861716	+	0.507391i	$0.830610\pi$
$464$	−5.94263	−	2.28578i	−0.275880	−	0.106115i
$465$	4.20472	+	3.59058i	0.194989	+	0.166509i
$466$	28.1684	−	6.11096i	1.30488	−	0.283085i
$467$	33.7722	+	19.4984i	1.56279	+	0.902278i	0.996973	+	0.0777470i	$0.0247726\pi$
$467$	33.7722	+	19.4984i	1.56279	+	0.902278i	0.565817	+	0.824531i	$0.308561\pi$
$468$	29.5077	+	3.36727i	1.36399	+	0.155652i
$469$	2.88332	−	7.92187i	0.133140	−	0.365798i
$470$	−6.58965	−	5.10404i	−0.303958	−	0.235432i
$471$	27.1547	+	23.1885i	1.25122	+	1.06847i
$472$	29.2693	+	1.67696i	1.34723	+	0.0771883i
$473$	12.0063	−	4.36994i	0.552051	−	0.200930i
$474$	0.625556	−	1.89649i	0.0287327	−	0.0871088i
$475$	−14.7974	−	8.81261i	−0.678949	−	0.404350i
$476$	5.47998	+	2.61610i	0.251174	+	0.119909i
$477$	4.43316	−	0.702879i	0.202980	−	0.0321826i
$478$	−8.98224	−	6.95723i	−0.410838	−	0.318216i
$479$	22.0231	+	26.2461i	1.00626	+	1.19921i	0.979885	+	0.199562i	$0.0639519\pi$
$479$	22.0231	+	26.2461i	1.00626	+	1.19921i	0.0263750	+	0.999652i	$0.491604\pi$
$480$	9.47074	+	3.31548i	0.432278	+	0.151330i
$481$	−33.9162	+	28.4591i	−1.54645	+	1.29762i
$482$	19.1581	+	30.3752i	0.872629	+	1.38355i
$483$	−1.72949	+	1.42592i	−0.0786945	+	0.0648814i
$484$	−10.2529	+	10.0687i	−0.466041	+	0.457667i
$485$	5.55303	+	6.61784i	0.252150	+	0.300501i
$486$	−7.45439	−	20.7469i	−0.338138	−	0.941097i
$487$	−15.5273	−	26.8940i	−0.703607	−	1.21868i	−0.967192	−	0.254047i	$-0.918238\pi$
$487$	−15.5273	−	26.8940i	−0.703607	−	1.21868i	0.263584	−	0.964636i	$-0.415095\pi$
$488$	18.3264	−	5.50546i	0.829597	−	0.249220i
$489$	25.5091	+	15.0233i	1.15356	+	0.679375i
$490$	8.30798	−	1.80236i	0.375316	−	0.0814225i
$491$	−14.5877	−	2.57220i	−0.658331	−	0.116082i	−0.165505	−	0.986209i	$-0.552925\pi$
$491$	−14.5877	−	2.57220i	−0.658331	−	0.116082i	−0.492827	+	0.870127i	$0.664036\pi$
$492$	4.71385	−	3.17776i	0.212517	−	0.143265i
$493$	3.93679	−	2.27291i	0.177304	−	0.102367i
$494$	11.1653	+	28.3968i	0.502352	+	1.27763i
$495$	−3.93622	+	4.52959i	−0.176920	+	0.203590i
$496$	−0.226051	+	12.4663i	−0.0101500	+	0.559753i
$497$	6.93920	−	8.26981i	0.311265	−	0.370952i
$498$	−1.17710	+	8.11324i	−0.0527470	+	0.363563i
$499$	14.9492	−	17.8158i	0.669219	−	0.797544i	−0.319459	−	0.947600i	$-0.603501\pi$
$499$	14.9492	−	17.8158i	0.669219	−	0.797544i	0.988677	+	0.150056i	$0.0479455\pi$
$500$	−4.58450	−	17.7518i	−0.205025	−	0.793883i
$501$	23.0253	+	8.60669i	1.02869	+	0.384518i
$502$	−6.43133	−	10.1969i	−0.287044	−	0.455108i
$503$	−8.29825	−	9.88947i	−0.370001	−	0.440950i	0.548631	−	0.836065i	$-0.315149\pi$
$503$	−8.29825	−	9.88947i	−0.370001	−	0.440950i	−0.918632	+	0.395115i	$0.870705\pi$
$504$	−5.26810	−	7.32321i	−0.234660	−	0.326202i
$505$	1.67310	−	2.89789i	0.0744520	−	0.128955i
$506$	0.131435	+	3.35976i	0.00584301	+	0.149360i
$507$	−3.62866	+	19.5873i	−0.161154	+	0.869904i
$508$	−21.9185	+	9.97985i	−0.972474	+	0.442784i
$509$	−2.66991	+	7.33553i	−0.118342	+	0.325142i	−0.984694	−	0.174292i	$-0.944236\pi$
$509$	−2.66991	+	7.33553i	−0.118342	+	0.325142i	0.866352	+	0.499434i	$0.166459\pi$
$510$	−6.09231	+	3.76929i	−0.269772	+	0.166907i
$511$	3.20352	+	0.564866i	0.141715	+	0.0249882i
$512$	7.79935	+	21.2408i	0.344686	+	0.938718i
$513$	15.2323	−	16.7623i	0.672524	−	0.740076i
$514$	−15.8827	−	25.1820i	−0.700556	−	1.11073i
$515$	0.828501	−	4.69866i	0.0365081	−	0.207048i
$516$	−20.3646	−	9.93898i	−0.896501	−	0.437539i
$517$	10.5627	+	3.84452i	0.464549	+	0.169082i
$518$	13.3253	+	1.81580i	0.585482	+	0.0797816i
$519$	21.3929	+	3.96315i	0.939043	+	0.173963i
$520$	−5.66655	+	13.1708i	−0.248495	+	0.577578i
$521$	2.55268	+	1.47379i	0.111835	+	0.0645678i	0.554874	−	0.831934i	$-0.312766\pi$
$521$	2.55268	+	1.47379i	0.111835	+	0.0645678i	−0.443039	+	0.896502i	$0.646100\pi$
$522$	−6.75169	+	0.147271i	−0.295514	+	0.00644588i
$523$	−16.2436	+	13.6300i	−0.710285	+	0.596000i	−0.924679	−	0.380747i	$-0.875667\pi$
$523$	−16.2436	+	13.6300i	−0.710285	+	0.596000i	0.214394	+	0.976747i	$0.431222\pi$
$524$	−20.5386	−	9.80496i	−0.897234	−	0.428332i
$525$	−2.54751	+	6.81532i	−0.111183	+	0.297445i
$526$	−3.15128	−	1.00932i	−0.137402	−	0.0440085i
$527$	−6.81922	−	5.72201i	−0.297050	−	0.249254i
$528$	−13.5272	−	0.362302i	−0.588698	−	0.0157672i
$529$	16.4840	+	13.8317i	0.716694	+	0.601378i
$530$	−0.292580	+	2.14711i	−0.0127089	+	0.0932647i
$531$	29.3999	−	10.1285i	1.27585	−	0.439541i
$532$	4.10591	−	8.30933i	0.178014	−	0.360255i
$533$	4.06161	+	7.03492i	0.175928	+	0.304716i
$534$	20.7091	−	0.630886i	0.896171	−	0.0273011i
$535$	3.09538	−	17.5547i	0.133825	−	0.758958i
$536$	−5.15157	+	21.8282i	−0.222514	+	0.942835i
$537$	1.33859	−	2.27290i	0.0577646	−	0.0980829i
$538$	13.9809	−	12.6950i	0.602760	−	0.547322i
$539$	−9.92865	+	5.73231i	−0.427657	+	0.246908i
$540$	10.6285	−	0.555989i	0.457376	−	0.0239260i
$541$	7.52521	−	6.31440i	0.323534	−	0.271477i	−0.466525	−	0.884508i	$-0.654494\pi$
$541$	7.52521	−	6.31440i	0.323534	−	0.271477i	0.790059	+	0.613031i	$0.210050\pi$
$542$	7.78363	+	35.8785i	0.334336	+	1.54112i
$543$	4.79917	+	5.82090i	0.205952	+	0.249799i
$544$	−15.2933	−	5.20581i	−0.655693	−	0.223197i
$545$	6.56635	+	7.82548i	0.281272	+	0.335207i
$546$	10.9620	−	6.78216i	0.469131	−	0.290250i
$547$	3.16811	−	2.65836i	0.135459	−	0.113663i	−0.572541	−	0.819876i	$-0.694042\pi$
$547$	3.16811	−	2.65836i	0.135459	−	0.113663i	0.708000	+	0.706213i	$0.249598\pi$
$548$	−4.19462	+	43.4086i	−0.179185	+	1.85432i
$549$	15.7711	−	12.7754i	0.673093	−	0.545240i
$550$	5.82233	+	9.23129i	0.248265	+	0.393624i
$551$	−3.38748	−	6.05523i	−0.144311	−	0.257961i
$552$	4.12554	−	4.30591i	0.175595	−	0.183272i
$553$	−0.296451	−	0.814492i	−0.0126064	−	0.0346357i
$554$	3.63264	+	8.88364i	0.154336	+	0.377430i
$555$	−10.3033	+	12.0656i	−0.437350	+	0.512155i
$556$	28.5050	+	2.75447i	1.20888	+	0.116816i
$557$	−10.0801	−	3.66886i	−0.427108	−	0.155454i	0.119517	−	0.992832i	$-0.461865\pi$
$557$	−10.0801	−	3.66886i	−0.427108	−	0.155454i	−0.546625	+	0.837378i	$0.684088\pi$
$558$	4.79303	+	12.3255i	0.202905	+	0.521781i
$559$	16.1899	−	28.0417i	0.684758	−	1.18604i
$560$	4.11891	−	1.41513i	0.174056	−	0.0598002i
$561$	6.27394	−	7.34705i	0.264886	−	0.310192i
$562$	6.99483	−	13.2895i	0.295059	−	0.560585i
$563$	−25.1912			−1.06168			−0.530840	−	0.847472i	$-0.678124\pi$
$563$	−25.1912			−1.06168			−0.530840	+	0.847472i	$0.678124\pi$
$564$	−8.10399	−	18.2145i	−0.341239	−	0.766969i
$565$	4.03809	+	11.0946i	0.169884	+	0.466752i
$566$	14.2027	−	12.8964i	0.596985	−	0.542078i
$567$	−8.11614	−	5.06787i	−0.340846	−	0.212831i
$568$	−15.7593	+	24.0103i	−0.661246	+	1.00745i
$569$	−9.25376	+	5.34266i	−0.387938	+	0.223976i	−0.681266	−	0.732036i	$-0.738570\pi$
$569$	−9.25376	+	5.34266i	−0.387938	+	0.223976i	0.293329	+	0.956012i	$0.405237\pi$
$570$	5.62666	+	9.37587i	0.235675	+	0.392712i
$571$	20.3258	+	11.7351i	0.850606	+	0.491098i	0.860855	−	0.508850i	$-0.169929\pi$
$571$	20.3258	+	11.7351i	0.850606	+	0.491098i	−0.0102491	+	0.999947i	$0.503262\pi$
$572$	1.85980	−	19.2464i	0.0777622	−	0.804733i
$573$	9.97282	−	5.64342i	0.416621	−	0.235757i
$574$	0.752636	−	2.34986i	0.0314144	−	0.0980814i
$575$	−4.73651	−	0.835175i	−0.197526	−	0.0348292i
$576$	16.1990	+	17.7085i	0.674960	+	0.737855i
$577$	−14.9268	−	25.8539i	−0.621409	−	1.07631i	−0.989224	−	0.146413i	$-0.953227\pi$
$577$	−14.9268	−	25.8539i	−0.621409	−	1.07631i	0.367815	−	0.929899i	$-0.380106\pi$
$578$	−10.5792	+	6.67247i	−0.440036	+	0.277538i
$579$	28.6482	+	5.30723i	1.19058	+	0.220561i
$580$	0.872350	−	3.14146i	0.0362224	−	0.130442i
$581$	1.77914	+	3.08157i	0.0738113	+	0.127845i
$582$	4.20599	+	20.2301i	0.174344	+	0.838563i
$583$	−0.507455	−	2.87792i	−0.0210167	−	0.119191i
$584$	−8.63993	−	0.495017i	−0.357523	−	0.0204839i
$585$	−0.262952	+	15.2055i	−0.0108717	+	0.628671i
$586$	25.9277	+	20.0824i	1.07106	+	0.829597i
$587$	24.2062	+	4.26821i	0.999098	+	0.176168i	0.649198	−	0.760619i	$-0.275104\pi$
$587$	24.2062	+	4.26821i	0.999098	+	0.176168i	0.349900	+	0.936787i	$0.386216\pi$
$588$	19.5441	+	5.60963i	0.805984	+	0.231337i
$589$	−8.87376	+	10.2890i	−0.365637	+	0.423953i
$590$	0.586837	+	15.0008i	0.0241597	+	0.617573i
$591$	−17.1798	−	30.3594i	−0.706681	−	1.24882i
$592$	−35.7724	−	0.648661i	−1.47024	−	0.0266598i
$593$	−1.39673	−	7.92125i	−0.0573569	−	0.325287i	0.942606	−	0.333907i	$-0.108367\pi$
$593$	−1.39673	−	7.92125i	−0.0573569	−	0.325287i	−0.999963	+	0.00862021i	$0.997256\pi$
$594$	−13.4216	+	5.08611i	−0.550694	+	0.208685i
$595$	−1.06349	+	2.92192i	−0.0435989	+	0.119787i
$596$	−16.2782	−	23.7022i	−0.666783	−	0.970880i
$597$	−14.9452	−	18.1270i	−0.611668	−	0.741890i
$598$	5.72816	+	6.30836i	0.234242	+	0.257968i
$599$	0.861663	+	4.88674i	0.0352066	+	0.199667i	0.997338	−	0.0729203i	$-0.0232319\pi$
$599$	0.861663	+	4.88674i	0.0352066	+	0.199667i	−0.962131	+	0.272587i	$0.912121\pi$
$600$	4.60885	−	18.8000i	0.188156	−	0.767508i
$601$	−17.1551	−	9.90450i	−0.699771	−	0.404013i	0.107491	−	0.994206i	$-0.465718\pi$
$601$	−17.1551	−	9.90450i	−0.699771	−	0.404013i	−0.807262	+	0.590193i	$0.799052\pi$
$602$	−9.61184	+	2.08523i	−0.391749	+	0.0849876i
$603$	3.72512	+	23.4949i	0.151699	+	0.956785i
$604$	8.59503	+	2.38675i	0.349727	+	0.0971155i
$605$	−5.63684	−	4.72987i	−0.229170	−	0.192297i
$606$	6.80610	−	4.21091i	0.276479	−	0.171056i
$607$	14.8341	−	25.6934i	0.602098	−	1.04286i	−0.390405	−	0.920643i	$-0.627665\pi$
$607$	14.8341	−	25.6934i	0.602098	−	1.04286i	0.992503	−	0.122221i	$-0.0390016\pi$
$608$	−8.26115	+	23.2326i	−0.335034	+	0.942206i
$609$	−2.26160	+	1.86463i	−0.0916447	+	0.0755585i
$610$	3.70867	+	9.06957i	0.150160	+	0.367216i
$611$	26.7686	−	9.74298i	1.08294	−	0.394159i
$612$	−17.1032	+	1.04304i	−0.691356	+	0.0421623i
$613$	0.255725	−	1.45029i	0.0103286	−	0.0585767i	−0.979208	−	0.202860i	$-0.934976\pi$
$613$	0.255725	−	1.45029i	0.0103286	−	0.0585767i	0.989536	+	0.144283i	$0.0460876\pi$
$614$	−6.64785	−	7.32121i	−0.268285	−	0.295460i
$615$	1.85183	+	2.24608i	0.0746729	+	0.0905706i
$616$	−4.70785	+	3.51179i	−0.189685	+	0.141494i
$617$	6.18003	+	35.0487i	0.248799	+	1.41101i	0.811503	+	0.584348i	$0.198650\pi$
$617$	6.18003	+	35.0487i	0.248799	+	1.41101i	−0.562704	+	0.826658i	$0.690239\pi$
$618$	7.06564	−	8.96110i	0.284222	−	0.360468i
$619$		−	0.431684i		−	0.0173508i	−0.999962	−	0.00867542i	$-0.997238\pi$
$619$		−	0.431684i		−	0.0173508i	0.999962	−	0.00867542i	$-0.00276151\pi$
$620$	−6.36504	+	0.498769i	−0.255626	+	0.0200311i
$621$	2.31671	−	5.88549i	0.0929662	−	0.236177i
$622$	30.2842	−	12.3836i	1.21429	−	0.496537i
$623$	6.88874	−	5.78034i	0.275992	−	0.231585i
$624$	−26.8512	+	21.3323i	−1.07491	+	0.853975i
$625$	−9.74239	+	3.54594i	−0.389696	+	0.141838i
$626$	−0.958401	−	24.4987i	−0.0383054	−	0.979167i
$627$	−11.0832	−	9.72703i	−0.442620	−	0.388460i
$628$	−41.1064	+	3.22112i	−1.64032	+	0.128537i
$629$	16.4195	−	19.5680i	0.654687	−	0.780226i
$630$	3.47308	−	3.04576i	0.138371	−	0.121346i
$631$	26.2905	−	4.63573i	1.04661	−	0.184546i	0.376202	−	0.926538i	$-0.377230\pi$
$631$	26.2905	−	4.63573i	1.04661	−	0.184546i	0.670409	+	0.741992i	$0.266119\pi$
$632$	1.03685	+	2.05968i	0.0412438	+	0.0819297i
$633$	−31.0705	+	11.0055i	−1.23494	+	0.437428i
$634$	−14.1197	−	22.3868i	−0.560766	−	0.889094i
$635$	−6.16612	−	10.6800i	−0.244695	−	0.423824i
$636$	−3.04752	+	4.19228i	−0.120842	+	0.166235i
$637$	−9.93712	+	27.3020i	−0.393723	+	1.08174i
$638$	0.171874	+	4.39346i	0.00680456	+	0.173939i
$639$	−5.80766	+	29.9037i	−0.229748	+	1.18297i
$640$	−10.4420	+	5.02137i	−0.412757	+	0.198487i
$641$	−10.3934	−	28.5556i	−0.410515	−	1.12788i	−0.956918	−	0.290358i	$-0.906226\pi$
$641$	−10.3934	−	28.5556i	−0.410515	−	1.12788i	0.546403	−	0.837522i	$-0.315997\pi$
$642$	26.3981	−	33.4797i	1.04185	−	1.32134i
$643$	24.6639	+	4.34890i	0.972647	+	0.171504i	0.637321	−	0.770598i	$-0.280042\pi$
$643$	24.6639	+	4.34890i	0.972647	+	0.171504i	0.335326	+	0.942102i	$0.391154\pi$
$644$	0.248948	−	2.57627i	0.00980992	−	0.101519i
$645$	4.06278	−	10.8691i	0.159972	−	0.427970i
$646$	−9.18896	−	15.0161i	−0.361535	−	0.590799i
$647$		−	18.5229i		−	0.728209i	−0.931358	−	0.364105i	$-0.881375\pi$
$647$		−	18.5229i		−	0.728209i	0.931358	−	0.364105i	$-0.118625\pi$
$648$	23.0217	+	10.8629i	0.904376	+	0.426736i
$649$	−6.92429	−	19.0243i	−0.271802	−	0.746771i
$650$	26.3408	+	8.43667i	1.03317	+	0.330913i
$651$	4.94594	+	2.91284i	0.193847	+	0.114163i
$652$	−33.0982	+	8.54780i	−1.29622	+	0.334758i
$653$	−14.6728			−0.574192			−0.287096	−	0.957902i	$-0.592690\pi$
$653$	−14.6728			−0.574192			−0.287096	+	0.957902i	$0.592690\pi$
$654$	4.97350	+	23.9217i	0.194479	+	0.935411i
$655$	3.98590	−	10.9512i	0.155742	−	0.427898i
$656$	−1.25691	+	6.44294i	−0.0490742	+	0.251555i
$657$	−8.67849	+	2.98981i	−0.338580	+	0.116644i
$658$	−7.65700	−	4.03020i	−0.298501	−	0.157114i
$659$	−1.92494	−	10.9169i	−0.0749850	−	0.425261i	−0.999072	−	0.0430781i	$-0.986284\pi$
$659$	−1.92494	−	10.9169i	−0.0749850	−	0.425261i	0.924087	−	0.382183i	$-0.124828\pi$
$660$	−0.481578	−	6.91250i	−0.0187454	−	0.269069i
$661$	15.8730	−	43.6107i	0.617387	−	1.69626i	−0.0959045	−	0.995391i	$-0.530574\pi$
$661$	15.8730	−	43.6107i	0.617387	−	1.69626i	0.713292	−	0.700867i	$-0.247203\pi$
$662$	19.0854	+	46.6736i	0.741776	+	1.81402i
$663$	0.211681	−	24.4833i	0.00822103	−	0.950853i
$664$	−5.66015	−	7.58791i	−0.219657	−	0.294468i
$665$	4.43738	+	1.68348i	0.172074	+	0.0652826i
$666$	−35.3685	+	13.7538i	−1.37050	+	0.532947i
$667$	−1.48428	−	1.24546i	−0.0574715	−	0.0482243i
$668$	−25.8324	+	11.7619i	−0.999484	+	0.455082i
$669$	5.08074	−	1.79965i	0.196433	−	0.0695784i
$670$	−11.3793	−	1.55062i	−0.439620	−	0.0599055i
$671$	−8.49388	−	10.1226i	−0.327903	−	0.390779i
$672$	10.2801	+	1.68230i	0.396562	+	0.0648962i
$673$			15.1133i			0.582575i	0.956636	+	0.291287i	$0.0940836\pi$
$673$			15.1133i			0.582575i	−0.956636	+	0.291287i	$0.905916\pi$
$674$	13.6701	+	4.37839i	0.526553	+	0.168649i
$675$	−3.03959	−	20.3046i	−0.116994	−	0.781526i
$676$	−13.0222	−	18.9612i	−0.500856	−	0.729279i
$677$	29.0386	+	16.7654i	1.11604	+	0.644348i	0.940388	−	0.340104i	$-0.110462\pi$
$677$	29.0386	+	16.7654i	1.11604	+	0.644348i	0.175655	+	0.984452i	$0.443796\pi$
$678$	−4.05455	+	27.9463i	−0.155714	+	1.07327i
$679$	6.87011	+	5.76470i	0.263650	+	0.221229i
$680$	1.90012	−	8.05117i	0.0728662	−	0.308748i
$681$	−16.7056	−	29.5214i	−0.640159	−	1.13126i
$682$	7.96954	−	3.25885i	0.305170	−	0.124788i
$683$	21.1907			0.810838			0.405419	−	0.914131i	$-0.367126\pi$
$683$	21.1907			0.810838			0.405419	+	0.914131i	$0.367126\pi$
$684$	1.23829	+	26.1241i	0.0473472	+	0.998878i
$685$	−22.3314			−0.853238
$686$	17.9105	−	7.32383i	0.683825	−	0.279625i
$687$	20.4138	−	34.6621i	0.778834	−	1.32244i
$688$	24.7463	−	8.50209i	0.943445	−	0.324139i
$689$	−5.67323	−	4.76041i	−0.216133	−	0.181357i
$690$	2.39786	+	1.89066i	0.0912849	+	0.0719763i
$691$	−13.1930	−	7.61700i	−0.501887	−	0.289764i	0.227606	−	0.973753i	$-0.426910\pi$
$691$	−13.1930	−	7.61700i	−0.501887	−	0.289764i	−0.729492	+	0.683989i	$0.760244\pi$
$692$	−20.7091	+	14.2226i	−0.787241	+	0.540663i
$693$	−3.20765	+	5.34038i	−0.121848	+	0.202864i
$694$	6.67198	+	2.13696i	0.253265	+	0.0811181i
$695$			14.6643i			0.556249i
$696$	5.39485	−	5.63072i	0.204491	−	0.213432i
$697$	−3.01255	−	3.59022i	−0.114109	−	0.135989i
$698$	9.34048	+	1.27280i	0.353542	+	0.0481760i
$699$	−6.43040	+	34.7110i	−0.243220	+	1.31289i
$700$	−3.48144	−	7.64618i	−0.131586	−	0.288999i
$701$	27.3975	+	22.9893i	1.03479	+	0.868292i	0.991413	−	0.130767i	$-0.0417438\pi$
$701$	27.3975	+	22.9893i	1.03479	+	0.868292i	0.0433771	+	0.999059i	$0.486188\pi$
$702$	−17.7708	+	31.7374i	−0.670714	+	1.19785i
$703$	−29.5247	−	25.4635i	−1.11355	−	0.960376i
$704$	11.3453	−	10.7444i	0.427591	−	0.404944i
$705$	8.88456	−	5.02759i	0.334612	−	0.189350i
$706$	14.4579	+	35.3569i	0.544130	+	1.33067i
$707$	1.18809	−	3.26426i	0.0446828	−	0.122765i
$708$	−15.7486	+	32.2683i	−0.591868	+	1.21272i
$709$	3.09170	+	17.5339i	0.116111	+	0.658499i	0.986194	+	0.165594i	$0.0529541\pi$
$709$	3.09170	+	17.5339i	0.116111	+	0.658499i	−0.870083	+	0.492906i	$0.835935\pi$
$710$	−13.0139	−	6.84977i	−0.488404	−	0.257067i
$711$	1.84614	+	1.60430i	0.0692357	+	0.0601660i
$712$	−16.4011	+	17.4172i	−0.614658	+	0.652736i
$713$	−1.29772	+	3.56546i	−0.0486001	+	0.133528i
$714$	−5.54898	+	4.95177i	−0.207665	+	0.185315i
$715$	9.90124			0.370285
$716$	0.761621	+	2.94909i	0.0284631	+	0.110213i
$717$	12.1104	−	6.85302i	0.452271	−	0.255931i
$718$	−27.0559	−	8.66573i	−1.00972	−	0.323402i
$719$	−16.8293	−	46.2380i	−0.627625	−	1.72439i	−0.687504	−	0.726180i	$-0.741294\pi$
$719$	−16.8293	−	46.2380i	−0.627625	−	1.72439i	0.0598792	−	0.998206i	$-0.480928\pi$
$720$	−8.22797	+	9.12861i	−0.306638	+	0.340203i
$721$		−	4.95301i		−	0.184460i
$722$	−23.1071	+	13.7136i	−0.859957	+	0.510366i
$723$	−43.3795	+	7.26285i	−1.61330	+	0.270108i
$724$	−8.67090	−	0.837878i	−0.322251	−	0.0311395i
$725$	−6.19380	−	1.09213i	−0.230032	−	0.0405609i
$726$	−6.52026	−	16.3474i	−0.241989	−	0.606707i
$727$	11.7248	+	32.2137i	0.434850	+	1.19474i	0.942802	+	0.333354i	$0.108181\pi$
$727$	11.7248	+	32.2137i	0.434850	+	1.19474i	−0.507952	+	0.861385i	$0.669597\pi$
$728$	−3.41892	+	14.4866i	−0.126714	+	0.536910i
$729$	26.9637	+	1.39998i	0.998655	+	0.0518512i
$730$	−0.173227	−	4.42804i	−0.00641141	−	0.163889i
$731$	−6.38945	+	17.5549i	−0.236322	+	0.649290i
$732$	−2.45575	+	23.3071i	−0.0907671	+	0.861454i
$733$	26.5717	+	46.0235i	0.981446	+	1.69991i	0.656772	+	0.754089i	$0.271921\pi$
$733$	26.5717	+	46.0235i	0.981446	+	1.69991i	0.324674	+	0.945826i	$0.394745\pi$
$734$	18.7119	+	29.6677i	0.690668	+	1.09505i
$735$	−1.89658	+	10.2377i	−0.0699564	+	0.377621i
$736$	0.144382	+	6.88432i	0.00532197	+	0.253759i
$737$	15.2524	−	2.68941i	0.561830	−	0.0990659i
$738$	1.35828	+	6.82882i	0.0499991	+	0.251372i
$739$	19.9421	−	23.7661i	0.733583	−	0.874250i	−0.262292	−	0.964989i	$-0.584478\pi$
$739$	19.9421	−	23.7661i	0.733583	−	0.874250i	0.995875	+	0.0907384i	$0.0289227\pi$
$740$	−1.43123	−	18.2647i	−0.0526132	−	0.671423i
$741$	−37.3615	−	0.829200i	−1.37251	−	0.0304614i
$742$	0.0879363	+	2.24784i	0.00322824	+	0.0825207i
$743$	16.9856	−	6.18227i	0.623143	−	0.226806i	−0.0111010	−	0.999938i	$-0.503534\pi$
$743$	16.9856	−	6.18227i	0.623143	−	0.226806i	0.634244	+	0.773133i	$0.281311\pi$
$744$	−13.9747	−	6.15613i	−0.512336	−	0.225695i
$745$	11.2790	−	9.46418i	0.413230	−	0.346741i
$746$	−28.3329	+	11.5857i	−1.03734	+	0.424183i
$747$	−8.60738	−	5.16994i	−0.314928	−	0.189158i
$748$	0.871517	+	11.1219i	0.0318658	+	0.406655i
$749$		−	18.5050i		−	0.676159i
$750$	22.2220	+	3.22405i	0.811435	+	0.117726i
$751$	4.11570	+	23.3413i	0.150184	+	0.851735i	0.963058	+	0.269295i	$0.0867907\pi$
$751$	4.11570	+	23.3413i	0.150184	+	0.851735i	−0.812874	+	0.582440i	$0.802098\pi$
$752$	21.4855	+	8.26422i	0.783495	+	0.301365i
$753$	14.5624	−	2.43812i	0.530682	−	0.0888499i
$754$	7.49055	+	8.24926i	0.272790	+	0.300420i
$755$	−0.793176	+	4.49833i	−0.0288666	+	0.163711i
$756$	10.7657	−	2.48438i	0.391546	−	0.0903560i
$757$	35.5239	−	12.9296i	1.29114	−	0.469936i	0.397038	−	0.917802i	$-0.370038\pi$
$757$	35.5239	−	12.9296i	1.29114	−	0.469936i	0.894101	+	0.447866i	$0.147816\pi$
$758$	−9.58044	−	23.4290i	−0.347977	−	0.850981i
$759$	−3.85733	−	1.44184i	−0.140012	−	0.0523355i
$760$	−12.2482	−	3.06636i	−0.444290	−	0.111228i
$761$	6.90847	−	11.9658i	0.250432	−	0.433761i	−0.713213	−	0.700947i	$-0.752761\pi$
$761$	6.90847	−	11.9658i	0.250432	−	0.433761i	0.963645	+	0.267187i	$0.0860941\pi$
$762$	−0.898159	−	29.4825i	−0.0325369	−	1.06804i
$763$	8.12377	+	6.81665i	0.294100	+	0.246779i
$764$	−3.54030	+	12.7491i	−0.128083	+	0.461247i
$765$	−1.37398	−	8.66591i	−0.0496764	−	0.313317i
$766$	−23.8075	+	5.16489i	−0.860200	+	0.186615i
$767$	−44.4328	−	25.6533i	−1.60437	−	0.926286i
$768$	−27.6849	−	1.24410i	−0.998992	−	0.0448927i
$769$	−1.27520	−	7.23201i	−0.0459848	−	0.260793i	0.953144	−	0.302516i	$-0.0978265\pi$
$769$	−1.27520	−	7.23201i	−0.0459848	−	0.260793i	−0.999129	+	0.0417228i	$0.986715\pi$
$770$	−2.02179	−	2.22657i	−0.0728601	−	0.0802400i
$771$	35.9630	−	6.02114i	1.29518	−	0.216846i
$772$	−27.7325	+	19.0462i	−0.998113	+	0.685486i
$773$	3.16481	−	8.69525i	0.113830	−	0.312746i	−0.869675	−	0.493624i	$-0.835672\pi$
$773$	3.16481	−	8.69525i	0.113830	−	0.312746i	0.983506	+	0.180878i	$0.0578940\pi$
$774$	20.8662	−	18.2989i	0.750021	−	0.657741i
$775$	2.13868	+	12.1290i	0.0768235	+	0.435688i
$776$	−19.9465	−	13.0920i	−0.716036	−	0.469975i
$777$	−8.35850	+	14.1925i	−0.299859	+	0.509154i
$778$	−0.134008	−	3.42553i	−0.00480443	−	0.122811i
$779$	−5.54159	+	4.52347i	−0.198548	+	0.162070i
$780$	−12.1953	−	12.6351i	−0.436660	−	0.452409i
$781$	19.5316	+	3.44396i	0.698897	+	0.123234i
$782$	−3.88667	−	3.01043i	−0.138987	−	0.107653i
$783$	3.02949	−	7.69628i	0.108265	−	0.275043i
$784$	−20.5427	+	11.3688i	−0.733668	+	0.406029i
$785$	−3.66632	−	20.7927i	−0.130857	−	0.742124i
$786$	20.7972	−	18.5589i	0.741812	−	0.661975i
$787$	−9.09002	−	15.7444i	−0.324024	−	0.561227i	0.657290	−	0.753638i	$-0.271703\pi$
$787$	−9.09002	−	15.7444i	−0.324024	−	0.561227i	−0.981314	+	0.192411i	$0.938369\pi$
$788$	38.8111	+	10.7774i	1.38259	+	0.383930i
$789$	2.63173	−	3.08187i	0.0936922	−	0.109717i
$790$	−0.998726	+	0.629913i	−0.0355331	+	0.0224113i
$791$	6.12832	+	10.6146i	0.217898	+	0.377410i
$792$	6.81223	−	15.1086i	0.242062	−	0.536861i
$793$	−32.9791	−	5.81511i	−1.17112	−	0.206501i
$794$	7.34166	−	22.9220i	0.260546	−	0.813470i
$795$	−2.28685	−	1.34681i	−0.0811061	−	0.0477663i
$796$	27.0023	+	2.60926i	0.957071	+	0.0924828i
$797$	−9.81028	−	5.66397i	−0.347498	−	0.200628i	0.316085	−	0.948731i	$-0.397632\pi$
$797$	−9.81028	−	5.66397i	−0.347498	−	0.200628i	−0.663583	+	0.748103i	$0.730965\pi$
$798$	7.44256	+	8.57109i	0.263464	+	0.303413i
$799$	−14.2334	+	8.21767i	−0.503542	+	0.290720i
$800$	11.5790	+	19.1181i	0.409380	+	0.675928i
$801$	−9.08981	+	23.6912i	−0.321173	+	0.837088i
$802$	−33.0899	+	30.0465i	−1.16844	+	1.06098i
$803$	2.04396	+	5.61574i	0.0721299	+	0.198175i
$804$	−22.2183	−	16.1513i	−0.783578	−	0.569611i
$805$	1.32535			0.0467126
$806$	10.1630	−	19.3088i	0.357978	−	0.680124i
$807$	7.72234	+	21.8016i	0.271839	+	0.767453i
$808$	−2.12274	+	8.99446i	−0.0746777	+	0.316424i
$809$	23.2455	−	40.2624i	0.817269	−	1.41555i	−0.0904181	−	0.995904i	$-0.528820\pi$
$809$	23.2455	−	40.2624i	0.817269	−	1.41555i	0.907687	−	0.419648i	$-0.137846\pi$
$810$	−4.40284	+	12.2689i	−0.154700	+	0.431084i
$811$	17.7019	+	6.44295i	0.621597	+	0.226243i	0.633570	−	0.773686i	$-0.281589\pi$
$811$	17.7019	+	6.44295i	0.621597	+	0.226243i	−0.0119730	+	0.999928i	$0.503811\pi$
$812$	0.325542	−	3.36892i	0.0114243	−	0.118226i
$813$	−44.2120	−	8.19050i	−1.55058	−	0.287254i
$814$	9.35138	+	22.8689i	0.327766	+	0.801553i
$815$	−5.98684	−	16.4487i	−0.209710	−	0.576173i
$816$	13.1193	−	14.8108i	0.459267	−	0.518483i
$817$	26.6597	+	10.1143i	0.932706	+	0.353856i
$818$	−5.42729	−	8.60496i	−0.189761	−	0.300865i
$819$	2.47223	+	15.5927i	0.0863868	+	0.544854i
$820$	−3.34579	−	0.323307i	−0.116840	−	0.0112904i
$821$	−26.6929	+	22.3980i	−0.931588	+	0.781695i	−0.976102	−	0.217314i	$-0.930271\pi$
$821$	−26.6929	+	22.3980i	−0.931588	+	0.781695i	0.0445140	+	0.999009i	$0.485826\pi$
$822$	−47.0480	−	25.2851i	−1.64099	−	0.881921i
$823$	25.7619	+	30.7018i	0.898004	+	1.07020i	0.997174	+	0.0751286i	$0.0239367\pi$
$823$	25.7619	+	30.7018i	0.898004	+	1.07020i	−0.0991702	+	0.995070i	$0.531619\pi$
$824$	1.54214	+	13.0864i	0.0537229	+	0.455887i
$825$	−13.1834	+	2.20724i	−0.458988	+	0.0768464i
$826$	3.30410	+	15.2302i	0.114964	+	0.529927i
$827$	−30.9479	+	25.9684i	−1.07616	+	0.903009i	−0.995597	−	0.0937399i	$-0.970118\pi$
$827$	−30.9479	+	25.9684i	−1.07616	+	0.903009i	−0.0805678	+	0.996749i	$0.525673\pi$
$828$	2.91109	+	6.69829i	0.101167	+	0.232782i
$829$	41.8555	−	24.1653i	1.45370	−	0.839295i	0.455012	−	0.890485i	$-0.349635\pi$
$829$	41.8555	−	24.1653i	1.45370	−	0.839295i	0.998689	+	0.0511903i	$0.0163015\pi$
$830$	3.58869	−	3.25862i	0.124565	−	0.113108i
$831$	−11.7542	−	0.101627i	−0.407750	−	0.00352539i
$832$	4.52272	−	39.3398i	0.156797	−	1.36386i
$833$	2.91084	−	16.5082i	0.100854	−	0.571974i
$834$	−16.6040	+	30.8949i	−0.574948	+	1.06980i
$835$	−7.26718	−	12.5871i	−0.251491	−	0.435595i
$836$	16.9919	−	1.10017i	0.587678	−	0.0380502i
$837$	−16.1914	−	0.420054i	−0.559657	−	0.0145192i
$838$	1.86521	−	13.6880i	0.0644328	−	0.472843i
$839$	18.7107	+	15.7001i	0.645964	+	0.542028i	0.905843	−	0.423613i	$-0.139238\pi$
$839$	18.7107	+	15.7001i	0.645964	+	0.542028i	−0.259880	+	0.965641i	$0.583683\pi$
$840$	−0.351138	+	5.32247i	−0.0121154	+	0.183643i
$841$	20.2743	+	17.0122i	0.699115	+	0.586627i
$842$	13.9973	+	4.48319i	0.482379	+	0.154501i
$843$	11.7006	+	14.1917i	0.402991	+	0.488787i
$844$	16.3974	−	34.3480i	0.564423	−	1.18231i
$845$	9.02294	−	7.57114i	0.310398	−	0.260455i
$846$	24.4107	−	0.532456i	0.839256	−	0.0183062i
$847$	−6.61545	−	3.81943i	−0.227309	−	0.131237i
$848$	−0.932209	−	5.91166i	−0.0320122	−	0.203007i
$849$	7.84485	+	22.1475i	0.269235	+	0.760100i
$850$	−15.8117	−	2.15460i	−0.542336	−	0.0739023i
$851$	−10.2312	−	3.72385i	−0.350721	−	0.127652i
$852$	−19.6621	−	29.1664i	−0.673611	−	0.999226i
$853$	3.39698	−	19.2652i	0.116310	−	0.659628i	−0.869783	−	0.493435i	$-0.835741\pi$
$853$	3.39698	−	19.2652i	0.116310	−	0.659628i	0.986093	−	0.166194i	$-0.0531476\pi$
$854$	5.42649	+	8.60370i	0.185691	+	0.294412i
$855$	−13.2541	+	1.91779i	−0.453281	+	0.0655871i
$856$	5.76160	+	48.8924i	0.196927	+	1.67111i
$857$	1.15299	+	0.203302i	0.0393852	+	0.00694468i	0.193306	−	0.981139i	$-0.438079\pi$
$857$	1.15299	+	0.203302i	0.0393852	+	0.00694468i	−0.153921	+	0.988083i	$0.549190\pi$
$858$	20.8600	+	11.2109i	0.712149	+	0.382733i
$859$	−7.49126	+	20.5821i	−0.255599	+	0.702252i	0.743827	+	0.668372i	$0.233009\pi$
$859$	−7.49126	+	20.5821i	−0.255599	+	0.702252i	−0.999426	+	0.0338796i	$0.989214\pi$
$860$	5.55220	+	12.1941i	0.189329	+	0.415817i
$861$	2.29811	+	1.96245i	0.0783192	+	0.0668800i
$862$	2.15693	+	55.1357i	0.0734653	+	1.87793i
$863$	−19.7962	+	34.2880i	−0.673871	+	1.16718i	0.302927	+	0.953014i	$0.402036\pi$
$863$	−19.7962	+	34.2880i	−0.673871	+	1.16718i	−0.976798	+	0.214164i	$0.931297\pi$
$864$	−27.6708	+	9.91596i	−0.941380	+	0.337348i
$865$	−8.26905	−	9.85466i	−0.281156	−	0.335069i
$866$	20.8982	+	33.1340i	0.710148	+	1.12594i
$867$	−2.52953	−	15.1084i	−0.0859074	−	0.513108i
$868$	−6.41737	+	1.65732i	−0.217820	+	0.0562532i
$869$	1.02356	−	1.21983i	0.0347220	−	0.0413800i
$870$	3.13561	+	2.47237i	0.106307	+	0.0838210i
$871$	25.2292	−	30.0670i	0.854860	−	1.01878i
$872$	−23.5863	−	15.4810i	−0.798733	−	0.524253i
$873$	−24.8423	−	4.82469i	−0.840785	−	0.163291i
$874$	−4.67480	+	5.86951i	−0.158128	+	0.198539i
$875$	8.44036	−	4.87305i	0.285336	−	0.164739i
$876$	4.64878	−	9.52518i	0.157068	−	0.321826i
$877$	36.7997	+	6.48878i	1.24264	+	0.219111i	0.756046	−	0.654519i	$-0.227129\pi$
$877$	36.7997	+	6.48878i	1.24264	+	0.219111i	0.486592	+	0.873629i	$0.338240\pi$
$878$	−6.57630	+	1.42669i	−0.221939	+	0.0481484i
$879$	−34.9573	+	19.7816i	−1.17908	+	0.667218i
$880$	6.03504	+	5.25336i	0.203441	+	0.177091i
$881$	−27.1854	−	47.0865i	−0.915899	−	1.58638i	−0.805580	−	0.592487i	$-0.798146\pi$
$881$	−27.1854	−	47.0865i	−0.915899	−	1.58638i	−0.110319	−	0.993896i	$-0.535187\pi$
$882$	−15.5875	+	19.4213i	−0.524859	+	0.653950i
$883$	−0.766124	−	0.913031i	−0.0257821	−	0.0307259i	0.752999	−	0.658021i	$-0.228606\pi$
$883$	−0.766124	−	0.913031i	−0.0257821	−	0.0307259i	−0.778781	+	0.627295i	$0.784162\pi$
$884$	19.8092	+	20.1717i	0.666257	+	0.678447i
$885$	−17.2224	−	6.43759i	−0.578923	−	0.216397i
$886$	−13.8898	−	22.0222i	−0.466636	−	0.739851i
$887$	−39.0845	+	32.7958i	−1.31233	+	1.10117i	−0.324456	+	0.945901i	$0.605181\pi$
$887$	−39.0845	+	32.7958i	−1.31233	+	1.10117i	−0.987872	+	0.155273i	$0.950374\pi$
$888$	17.6652	−	40.1007i	0.592806	−	1.34569i
$889$	−8.22917	−	9.80714i	−0.275998	−	0.328921i
$890$	−9.68508	−	7.50162i	−0.324645	−	0.251455i
$891$	0.607802	−	17.5682i	0.0203621	−	0.588557i
$892$	−2.68136	+	5.61669i	−0.0897785	+	0.188061i
$893$	12.2474	+	21.8926i	0.409843	+	0.732608i
$894$	34.4787	−	7.16839i	1.15314	−	0.239747i
$895$	−1.46560	+	0.533436i	−0.0489897	+	0.0178308i
$896$	−9.77017	+	7.01594i	−0.326398	+	0.234386i
$897$	−9.83715	+	3.48441i	−0.328453	+	0.116341i
$898$	−1.94154	−	1.50383i	−0.0647900	−	0.0501833i
$899$	−1.69699	+	4.66245i	−0.0565979	+	0.155501i
$900$	19.0546	+	14.1049i	0.635152	+	0.470162i
$901$	3.70038	+	2.13641i	0.123277	+	0.0711743i
$902$	4.43004	−	0.961070i	0.147504	−	0.0320001i
$903$	2.19423	−	11.8444i	0.0730194	−	0.394156i
$904$	−19.4966	−	26.1368i	−0.648447	−	0.869297i
$905$		−	4.46071i		−	0.148279i
$906$	−6.76439	+	8.57903i	−0.224732	+	0.285019i
$907$	35.5996	−	12.9572i	1.18206	−	0.430236i	0.325134	−	0.945668i	$-0.394591\pi$
$907$	35.5996	−	12.9572i	1.18206	−	0.430236i	0.856931	+	0.515432i	$0.172368\pi$
$908$	37.7398	+	10.4800i	1.25244	+	0.347789i
$909$	1.53496	+	9.68122i	0.0509114	+	0.321106i
$910$	−7.55203	−	1.02909i	−0.250347	−	0.0341140i
$911$	−8.09799	−	14.0261i	−0.268298	−	0.464707i	0.700124	−	0.714021i	$-0.253128\pi$
$911$	−8.09799	−	14.0261i	−0.268298	−	0.464707i	−0.968423	+	0.249315i	$0.919795\pi$
$912$	−22.3327	−	20.3285i	−0.739511	−	0.673145i
$913$	−3.26856	+	5.66131i	−0.108174	+	0.187362i
$914$	7.84087	−	10.1231i	0.259353	−	0.334842i
$915$	−12.0003	−	0.103754i	−0.396716	−	0.00342999i
$916$	11.6149	+	44.9742i	0.383766	+	1.48599i
$917$	2.10084	−	11.9144i	0.0693757	−	0.393449i
$918$	6.91743	−	19.8131i	0.228309	−	0.653931i
$919$	23.8060	−	13.7444i	0.785288	−	0.453386i	−0.0530133	−	0.998594i	$-0.516883\pi$
$919$	23.8060	−	13.7444i	0.785288	−	0.453386i	0.838301	+	0.545208i	$0.183549\pi$
$920$	−3.50174	+	0.412653i	−0.115449	+	0.0136048i
$921$	11.4166	−	4.04386i	0.376189	−	0.133250i
$922$	15.2828	+	16.8308i	0.503312	+	0.554292i
$923$	43.5278	−	25.1308i	1.43274	−	0.827190i
$924$	−1.73844	−	6.98017i	−0.0571904	−	0.229631i
$925$	−34.8046	+	6.13700i	−1.14437	+	0.201783i
$926$	28.5827	−	11.6879i	0.939287	−	0.384087i
$927$	6.77782	+	12.2228i	0.222613	+	0.401451i
$928$	0.188804	+	9.00242i	0.00619778	+	0.295519i
$929$	2.64253	−	14.9866i	0.0866987	−	0.491693i	−0.910278	−	0.413997i	$-0.864132\pi$
$929$	2.64253	−	14.9866i	0.0866987	−	0.491693i	0.996977	−	0.0776961i	$-0.0247564\pi$
$930$	2.44943	−	7.42591i	0.0803198	−	0.243505i
$931$	−25.1342	−	4.78372i	−0.823740	−	0.156780i
$932$	−23.0769	−	33.6015i	−0.755910	−	1.10065i
$933$	−0.346444	+	40.0701i	−0.0113421	+	1.31184i
$934$	7.44625	−	54.6447i	0.243649	−	1.78803i
$935$	−5.62574	+	0.991970i	−0.183981	+	0.0324409i
$936$	−11.3868	−	40.4280i	−0.372188	−	1.32143i
$937$	9.31026	+	3.38866i	0.304153	+	0.110703i	0.489588	−	0.871954i	$-0.337147\pi$
$937$	9.31026	+	3.38866i	0.304153	+	0.110703i	−0.185435	+	0.982657i	$0.559369\pi$
$938$	−11.9131	+	0.466045i	−0.388976	+	0.0152169i
$939$	28.1269	+	10.5136i	0.917888	+	0.343100i
$940$	−3.15397	+	11.3579i	−0.102871	+	0.370454i
$941$	−20.0766	+	3.54005i	−0.654478	+	0.115402i	−0.491020	−	0.871148i	$-0.663376\pi$
$941$	−20.0766	+	3.54005i	−0.654478	+	0.115402i	−0.163458	+	0.986550i	$0.552265\pi$
$942$	15.8187	−	47.9576i	0.515403	−	1.56254i
$943$	−0.998818	+	1.73000i	−0.0325260	+	0.0563367i
$944$	−13.4718	−	39.2113i	−0.438470	−	1.27622i
$945$	1.79649	+	5.36480i	0.0584397	+	0.174517i
$946$	−12.1469	−	13.3772i	−0.394929	−	0.434931i
$947$	−11.4374	+	13.6305i	−0.371665	+	0.442933i	−0.919165	−	0.393873i	$-0.871135\pi$
$947$	−11.4374	+	13.6305i	−0.371665	+	0.442933i	0.547500	+	0.836805i	$0.315579\pi$
$948$	−2.81736	+	0.196278i	−0.0915035	+	0.00637483i
$949$	13.1160	+	7.57252i	0.425763	+	0.245814i
$950$	−3.61518	+	24.0869i	−0.117292	+	0.781482i
$951$	31.9711	−	5.35279i	1.03673	−	0.173576i
$952$	0.491218	−	8.57362i	0.0159205	−	0.277873i
$953$	11.7613	+	32.3138i	0.380985	+	1.04675i	0.970942	+	0.239313i	$0.0769223\pi$
$953$	11.7613	+	32.3138i	0.380985	+	1.04675i	−0.589958	+	0.807434i	$0.700856\pi$
$954$	−3.29300	−	5.42679i	−0.106615	−	0.175699i
$955$	−6.67243	−	1.17653i	−0.215915	−	0.0380716i
$956$	−4.29912	+	15.4818i	−0.139044	+	0.500716i
$957$	−5.04412	−	1.88545i	−0.163053	−	0.0609481i
$958$	22.5679	−	42.8770i	0.729137	−	1.38529i
$959$	−22.8304	+	4.02562i	−0.737233	+	0.129994i
$960$	−0.729421	−	14.1719i	−0.0235420	−	0.457396i
$961$	−21.2838			−0.686574
$962$	55.4072	+	29.1632i	1.78640	+	0.940258i
$963$	25.3227	+	45.6660i	0.816014	+	1.47157i
$964$	29.5065	−	41.3369i	0.950340	−	1.33137i
$965$	−11.0735	−	13.1968i	−0.356467	−	0.424821i
$966$	2.79227	+	1.50066i	0.0898397	+	0.0482829i
$967$	20.2702	+	55.6918i	0.651844	+	1.79093i	0.610820	+	0.791769i	$0.290840\pi$
$967$	20.2702	+	55.6918i	0.651844	+	1.79093i	0.0410243	+	0.999158i	$0.486938\pi$
$968$	18.6680	+	8.03163i	0.600011	+	0.258146i
$969$	21.3113	−	3.27197i	0.684618	−	0.105111i
$970$	5.69042	−	10.8113i	0.182708	−	0.347128i
$971$	−28.0033	−	23.4976i	−0.898669	−	0.754073i	0.0712610	−	0.997458i	$-0.477298\pi$
$971$	−28.0033	−	23.4976i	−0.898669	−	0.754073i	−0.969930	+	0.243385i	$0.921742\pi$
$972$	−23.1676	+	20.8629i	−0.743101	+	0.669179i
$973$	2.64350	+	14.9920i	0.0847466	+	0.480622i
$974$	−26.8931	+	34.7207i	−0.861710	+	1.11252i
$975$	−21.9980	+	25.7606i	−0.704500	+	0.824999i
$976$	−17.0162	−	21.0424i	−0.544675	−	0.673551i
$977$	34.6590	−	20.0104i	1.10884	−	0.640189i	0.170311	−	0.985390i	$-0.445523\pi$
$977$	34.6590	−	20.0104i	1.10884	−	0.640189i	0.938528	+	0.345202i	$0.112190\pi$
$978$	6.01125	−	41.4330i	0.192218	−	1.32488i
$979$	15.5245	+	5.65046i	0.496165	+	0.180589i
$980$	−6.80630	−	9.91042i	−0.217419	−	0.316577i
$981$	−29.3756	−	5.70510i	−0.937890	−	0.182150i
$982$	4.44129	+	20.4721i	0.141727	+	0.653291i
$983$	−0.506634	+	0.184400i	−0.0161591	+	0.00588144i	−0.350087	−	0.936717i	$-0.613848\pi$
$983$	−0.506634	+	0.184400i	−0.0161591	+	0.00588144i	0.333928	+	0.942599i	$0.391626\pi$
$984$	−6.68287	−	4.46948i	−0.213042	−	0.142482i
$985$	−3.58161	+	20.3123i	−0.114119	+	0.647204i
$986$	−5.08248	−	3.93666i	−0.161859	−	0.125369i
$987$	8.17679	−	6.74154i	0.260270	−	0.214585i
$988$	31.1951	−	29.8154i	0.992447	−	0.948554i
$989$	7.96271			0.253199
$990$	8.03617	+	2.72798i	0.255406	+	0.0867009i
$991$	19.7156	−	7.17591i	0.626288	−	0.227950i	−0.00932695	−	0.999957i	$-0.502969\pi$
$991$	19.7156	−	7.17591i	0.626288	−	0.227950i	0.635615	+	0.772006i	$0.280747\pi$
$992$	16.4394	−	6.37691i	0.521952	−	0.202467i
$993$	−61.7554	−	0.533934i	−1.95975	−	0.0169439i
$994$	−14.5395	−	4.65686i	−0.461166	−	0.147707i
$995$			13.8912i			0.440382i
$996$	11.2503	−	2.80194i	0.356480	−	0.0887828i
$997$	−42.6239	−	15.5138i	−1.34991	−	0.491328i	−0.436991	−	0.899466i	$-0.643956\pi$
$997$	−42.6239	−	15.5138i	−1.34991	−	0.491328i	−0.912920	+	0.408138i	$0.866178\pi$
$998$	−31.3227	−	10.0323i	−0.991504	−	0.317568i
$999$	1.20536	−	46.4617i	0.0381359	−	1.46998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cc.a.535.43	yes	696
4.3	odd	2	inner	684.2.cc.a.535.31	yes	696
9.7	even	3		684.2.bt.a.79.33	✓	696
19.13	odd	18		684.2.bt.a.355.107	yes	696
36.7	odd	6		684.2.bt.a.79.107	yes	696
76.51	even	18		684.2.bt.a.355.33	yes	696
171.70	odd	18	inner	684.2.cc.a.583.31	yes	696
684.583	even	18	inner	684.2.cc.a.583.43	yes	696

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.bt.a.79.33	✓	696	9.7	even	3
684.2.bt.a.79.107	yes	696	36.7	odd	6
684.2.bt.a.355.33	yes	696	76.51	even	18
684.2.bt.a.355.107	yes	696	19.13	odd	18
684.2.cc.a.535.31	yes	696	4.3	odd	2	inner
684.2.cc.a.535.43	yes	696	1.1	even	1	trivial
684.2.cc.a.583.31	yes	696	171.70	odd	18	inner
684.2.cc.a.583.43	yes	696	684.583	even	18	inner

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.535268 - 1.30900i) q^{2} +(1.73199 + 0.0149747i) q^{3} +(-1.42698 + 1.40134i) q^{4} +(-0.784523 - 0.658293i) q^{5} +(-0.907475 - 2.27519i) q^{6} +(-0.920724 - 0.531580i) q^{7} +(2.59817 + 1.11783i) q^{8} +(2.99955 + 0.0518718i) q^{9} +O(q^{10})\)	\(q+(-0.535268 - 1.30900i) q^{2} +(1.73199 + 0.0149747i) q^{3} +(-1.42698 + 1.40134i) q^{4} +(-0.784523 - 0.658293i) q^{5} +(-0.907475 - 2.27519i) q^{6} +(-0.920724 - 0.531580i) q^{7} +(2.59817 + 1.11783i) q^{8} +(2.99955 + 0.0518718i) q^{9} +(-0.441777 + 1.37931i) q^{10} -1.95319i q^{11} +(-2.49249 + 2.40572i) q^{12} +(-3.18171 - 3.79182i) q^{13} +(-0.203006 + 1.48977i) q^{14} +(-1.34893 - 1.15190i) q^{15} +(0.0725201 - 3.99934i) q^{16} +(2.18769 + 1.83569i) q^{17} +(-1.53766 - 3.95419i) q^{18} +(2.84681 - 3.30086i) q^{19} +(2.04199 - 0.160011i) q^{20} +(-1.58672 - 0.934477i) q^{21} +(-2.55673 + 1.04548i) q^{22} +(0.416325 - 1.14384i) q^{23} +(4.48325 + 1.97496i) q^{24} +(-0.686114 - 3.89115i) q^{25} +(-3.26043 + 6.19451i) q^{26} +(5.19440 + 0.134759i) q^{27} +(2.05877 - 0.531690i) q^{28} +(0.544417 - 1.49577i) q^{29} +(-0.785806 + 2.38232i) q^{30} -3.11708 q^{31} +(-5.27397 + 2.04579i) q^{32} +(0.0292484 - 3.38290i) q^{33} +(1.23192 - 3.84628i) q^{34} +(0.372394 + 1.02314i) q^{35} +(-4.35298 + 4.12936i) q^{36} -8.94457i q^{37} +(-5.84464 - 1.95965i) q^{38} +(-5.45390 - 6.61502i) q^{39} +(-1.30247 - 2.58731i) q^{40} +(-1.61617 - 0.284974i) q^{41} +(-0.373912 + 2.57722i) q^{42} +(2.23734 + 6.14703i) q^{43} +(2.73707 + 2.78715i) q^{44} +(-2.31907 - 2.01528i) q^{45} +(-1.72014 + 0.0672927i) q^{46} +(-1.96833 + 5.40795i) q^{47} +(0.185493 - 6.92572i) q^{48} +(-2.93485 - 5.08330i) q^{49} +(-4.72627 + 2.98093i) q^{50} +(3.76156 + 3.21215i) q^{51} +(9.85383 + 0.952186i) q^{52} +(1.47345 - 0.259809i) q^{53} +(-2.60400 - 6.87162i) q^{54} +(-1.28577 + 1.53232i) q^{55} +(-1.79798 - 2.41034i) q^{56} +(4.98007 - 5.67441i) q^{57} +(-2.24938 + 0.0879967i) q^{58} +(9.74014 - 3.54512i) q^{59} +(3.53909 - 0.246560i) q^{60} +(5.18261 - 4.34872i) q^{61} +(1.66848 + 4.08027i) q^{62} +(-2.73418 - 1.64226i) q^{63} +(5.50093 + 5.80859i) q^{64} +5.06927i q^{65} +(-4.44388 + 1.77247i) q^{66} +(1.37693 + 7.80899i) q^{67} +(-5.69420 + 0.446202i) q^{68} +(0.738199 - 1.97489i) q^{69} +(1.13997 - 1.03512i) q^{70} +(-1.76325 + 9.99987i) q^{71} +(7.73535 + 3.48775i) q^{72} +(-2.87516 + 1.04647i) q^{73} +(-11.7085 + 4.78775i) q^{74} +(-1.13007 - 6.74969i) q^{75} +(0.563268 + 8.69958i) q^{76} +(-1.03828 + 1.79835i) q^{77} +(-5.73978 + 10.6800i) q^{78} +(0.624534 + 0.524047i) q^{79} +(-2.68963 + 3.08984i) q^{80} +(8.99462 + 0.311185i) q^{81} +(0.492052 + 2.26811i) q^{82} +(-2.89850 - 1.67345i) q^{83} +(3.57373 - 0.890051i) q^{84} +(-0.507872 - 2.88029i) q^{85} +(6.84891 - 6.21899i) q^{86} +(0.965321 - 2.58251i) q^{87} +(2.18332 - 5.07471i) q^{88} +(-2.89294 + 7.94828i) q^{89} +(-1.39668 + 4.11438i) q^{90} +(0.913824 + 5.18255i) q^{91} +(1.00882 + 2.21565i) q^{92} +(-5.39875 - 0.0466773i) q^{93} +(8.13260 - 0.318151i) q^{94} +(-4.40632 + 0.715559i) q^{95} +(-9.16507 + 3.46431i) q^{96} +(-8.30734 - 1.46481i) q^{97} +(-5.08313 + 6.56265i) q^{98} +(0.101316 - 5.85869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8}+O(q^{10}) \) 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8	\( 696 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} - 18 q^{8} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 15 q^{14} - 3 q^{16} - 24 q^{17} - 6 q^{20} - 30 q^{21} + 21 q^{22} + 24 q^{24} - 6 q^{25} - 30 q^{26} - 6 q^{29} - 21 q^{30} - 3 q^{32} + 36 q^{33} + 33 q^{34} + 54 q^{36} - 3 q^{38} - 33 q^{40} + 54 q^{41} - 87 q^{42} - 33 q^{44} - 6 q^{45} - 18 q^{46} + 6 q^{48} + 282 q^{49} - 3 q^{52} - 24 q^{53} - 51 q^{54} - 63 q^{56} - 12 q^{57} - 6 q^{58} - 27 q^{60} - 6 q^{61} - 18 q^{62} - 24 q^{64} - 30 q^{66} + 3 q^{68} - 18 q^{69} - 45 q^{70} + 12 q^{72} - 60 q^{73} + 3 q^{74} - 3 q^{76} + 72 q^{77} - 81 q^{78} - 12 q^{80} - 72 q^{81} - 12 q^{82} - 9 q^{84} - 6 q^{85} - 57 q^{86} - 9 q^{88} - 24 q^{89} + 39 q^{90} + 81 q^{92} - 48 q^{93} + 15 q^{96} + 30 q^{97} - 63 q^{98}+O(q^{100}) \) 696 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 - 18 * q^8 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 15 * q^14 - 3 * q^16 - 24 * q^17 - 6 * q^20 - 30 * q^21 + 21 * q^22 + 24 * q^24 - 6 * q^25 - 30 * q^26 - 6 * q^29 - 21 * q^30 - 3 * q^32 + 36 * q^33 + 33 * q^34 + 54 * q^36 - 3 * q^38 - 33 * q^40 + 54 * q^41 - 87 * q^42 - 33 * q^44 - 6 * q^45 - 18 * q^46 + 6 * q^48 + 282 * q^49 - 3 * q^52 - 24 * q^53 - 51 * q^54 - 63 * q^56 - 12 * q^57 - 6 * q^58 - 27 * q^60 - 6 * q^61 - 18 * q^62 - 24 * q^64 - 30 * q^66 + 3 * q^68 - 18 * q^69 - 45 * q^70 + 12 * q^72 - 60 * q^73 + 3 * q^74 - 3 * q^76 + 72 * q^77 - 81 * q^78 - 12 * q^80 - 72 * q^81 - 12 * q^82 - 9 * q^84 - 6 * q^85 - 57 * q^86 - 9 * q^88 - 24 * q^89 + 39 * q^90 + 81 * q^92 - 48 * q^93 + 15 * q^96 + 30 * q^97 - 63 * q^98

Introduction

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