LMFDB - Embedded newform 336.2.bq.b.109.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.11
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.687104 - 1.23608i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.05578 + 1.69863i) q^{4} +(0.137710 + 0.0368993i) q^{5} +(-0.983612 - 1.01612i) q^{6} +(-2.08565 - 1.62790i) q^{7} +(2.82506 + 0.137888i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.687104 - 1.23608i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.05578 + 1.69863i) q^{4} +(0.137710 + 0.0368993i) q^{5} +(-0.983612 - 1.01612i) q^{6} +(-2.08565 - 1.62790i) q^{7} +(2.82506 + 0.137888i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.0490107 - 0.195574i) q^{10} +(-1.29326 - 4.82651i) q^{11} +(-0.580165 + 1.91400i) q^{12} +(-0.0957679 - 0.0957679i) q^{13} +(-0.579159 + 3.69656i) q^{14} +0.142568 q^{15} +(-1.77067 - 3.58674i) q^{16} +(2.58943 - 4.48502i) q^{17} +(-1.21309 - 0.726923i) q^{18} +(0.638013 - 2.38110i) q^{19} +(-0.208069 + 0.194961i) q^{20} +(-2.43591 - 1.03263i) q^{21} +(-5.07734 + 4.91489i) q^{22} +(4.16740 - 2.40605i) q^{23} +(2.76449 - 0.597991i) q^{24} +(-4.31252 - 2.48984i) q^{25} +(-0.0525741 + 0.184179i) q^{26} +(0.707107 - 0.707107i) q^{27} +(4.96718 - 1.82404i) q^{28} +(6.22873 + 6.22873i) q^{29} +(-0.0979589 - 0.176225i) q^{30} +(-2.44044 + 4.22696i) q^{31} +(-3.21686 + 4.65315i) q^{32} +(-2.49839 - 4.32733i) q^{33} +(-7.32303 - 0.119059i) q^{34} +(-0.227146 - 0.301137i) q^{35} +(-0.0650154 + 1.99894i) q^{36} +(-5.01001 - 1.34243i) q^{37} +(-3.38160 + 0.847427i) q^{38} +(-0.117291 - 0.0677181i) q^{39} +(0.383951 + 0.123231i) q^{40} +5.89239i q^{41} +(0.397316 + 3.72050i) q^{42} +(-0.390746 + 0.390746i) q^{43} +(9.56384 + 2.89895i) q^{44} +(0.137710 - 0.0368993i) q^{45} +(-5.83750 - 3.49802i) q^{46} +(1.18744 + 2.05670i) q^{47} +(-2.63866 - 3.00624i) q^{48} +(1.69986 + 6.79047i) q^{49} +(-0.114480 + 7.04139i) q^{50} +(1.34039 - 5.00239i) q^{51} +(0.263784 - 0.0615645i) q^{52} +(0.658095 + 2.45604i) q^{53} +(-1.35989 - 0.388183i) q^{54} -0.712379i q^{55} +(-5.66762 - 4.88652i) q^{56} -2.46509i q^{57} +(3.41941 - 11.9790i) q^{58} +(-2.09440 - 7.81641i) q^{59} +(-0.150520 + 0.242170i) q^{60} +(-1.17785 + 4.39581i) q^{61} +(6.90169 + 0.112209i) q^{62} +(-2.62018 - 0.366982i) q^{63} +(7.96197 + 0.779085i) q^{64} +(-0.00965443 - 0.0167220i) q^{65} +(-3.63227 + 6.06153i) q^{66} +(0.284860 - 0.0763279i) q^{67} +(4.88452 + 9.13364i) q^{68} +(3.40267 - 3.40267i) q^{69} +(-0.216156 + 0.487683i) q^{70} -9.82085i q^{71} +(2.51552 - 1.29312i) q^{72} +(12.3493 + 7.12989i) q^{73} +(1.78305 + 7.11515i) q^{74} +(-4.81000 - 1.28883i) q^{75} +(3.37100 + 3.59765i) q^{76} +(-5.15981 + 12.1717i) q^{77} +(-0.00311360 + 0.191511i) q^{78} +(5.01195 + 8.68095i) q^{79} +(-0.111491 - 0.559266i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.28345 - 4.04868i) q^{82} +(-1.66074 - 1.66074i) q^{83} +(4.32583 - 3.04749i) q^{84} +(0.522083 - 0.522083i) q^{85} +(0.751475 + 0.214509i) q^{86} +(7.62861 + 4.40438i) q^{87} +(-2.98802 - 13.8135i) q^{88} +(10.5430 - 6.08701i) q^{89} +(-0.140231 - 0.144867i) q^{90} +(0.0438372 + 0.355639i) q^{91} +(-0.312860 + 9.61910i) q^{92} +(-1.26326 + 4.71457i) q^{93} +(1.72635 - 2.88093i) q^{94} +(0.175721 - 0.304358i) q^{95} +(-1.90292 + 5.32718i) q^{96} +12.5887 q^{97} +(7.22557 - 6.76692i) q^{98} +(-3.53325 - 3.53325i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.687104	−	1.23608i	−0.485856	−	0.874039i
$2$	−0.687104	−	1.23608i	−0.485856	−	0.874039i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−1.05578	+	1.69863i	−0.527888	+	0.849314i
$5$	0.137710	+	0.0368993i	0.0615857	+	0.0165019i	0.289480	−	0.957184i	$-0.406518\pi$
$5$	0.137710	+	0.0368993i	0.0615857	+	0.0165019i	−0.227895	+	0.973686i	$0.573184\pi$
$6$	−0.983612	−	1.01612i	−0.401558	−	0.414831i
$7$	−2.08565	−	1.62790i	−0.788301	−	0.615290i
$7$	−2.08565	−	1.62790i	−0.788301	−	0.615290i
$8$	2.82506	+	0.137888i	0.998811	+	0.0487508i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−0.0490107	−	0.195574i	−0.0154985	−	0.0618459i
$11$	−1.29326	−	4.82651i	−0.389933	−	1.45525i	−0.830242	−	0.557402i	$-0.811798\pi$
$11$	−1.29326	−	4.82651i	−0.389933	−	1.45525i	0.440310	−	0.897846i	$-0.354869\pi$
$12$	−0.580165	+	1.91400i	−0.167479	+	0.552525i
$13$	−0.0957679	−	0.0957679i	−0.0265612	−	0.0265612i	0.693701	−	0.720263i	$-0.255979\pi$
$13$	−0.0957679	−	0.0957679i	−0.0265612	−	0.0265612i	−0.720263	+	0.693701i	$0.755979\pi$
$14$	−0.579159	+	3.69656i	−0.154787	+	0.987948i
$15$	0.142568			0.0368108
$16$	−1.77067	−	3.58674i	−0.442668	−	0.896686i
$17$	2.58943	−	4.48502i	0.628028	−	1.08778i	−0.359919	−	0.932984i	$-0.617196\pi$
$17$	2.58943	−	4.48502i	0.628028	−	1.08778i	0.987947	−	0.154793i	$-0.0494710\pi$
$18$	−1.21309	−	0.726923i	−0.285928	−	0.171337i
$19$	0.638013	−	2.38110i	0.146370	−	0.546261i	−0.853320	−	0.521387i	$-0.825415\pi$
$19$	0.638013	−	2.38110i	0.146370	−	0.546261i	0.999691	−	0.0248740i	$-0.00791845\pi$
$20$	−0.208069	+	0.194961i	−0.0465256	+	0.0435945i
$21$	−2.43591	−	1.03263i	−0.531560	−	0.225338i
$22$	−5.07734	+	4.91489i	−1.08249	+	1.04786i
$23$	4.16740	−	2.40605i	0.868962	−	0.501696i	0.00195903	−	0.999998i	$-0.499376\pi$
$23$	4.16740	−	2.40605i	0.868962	−	0.501696i	0.867003	+	0.498302i	$0.166043\pi$
$24$	2.76449	−	0.597991i	0.564299	−	0.122064i
$25$	−4.31252	−	2.48984i	−0.862505	−	0.497967i
$26$	−0.0525741	+	0.184179i	−0.0103106	+	0.0361205i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	4.96718	−	1.82404i	0.938709	−	0.344711i
$29$	6.22873	+	6.22873i	1.15665	+	1.15665i	0.985192	+	0.171455i	$0.0548468\pi$
$29$	6.22873	+	6.22873i	1.15665	+	1.15665i	0.171455	+	0.985192i	$0.445153\pi$
$30$	−0.0979589	−	0.176225i	−0.0178848	−	0.0321741i
$31$	−2.44044	+	4.22696i	−0.438316	+	0.759185i	−0.997560	−	0.0698179i	$-0.977758\pi$
$31$	−2.44044	+	4.22696i	−0.438316	+	0.759185i	0.559244	+	0.829003i	$0.311092\pi$
$32$	−3.21686	+	4.65315i	−0.568665	+	0.822569i
$33$	−2.49839	−	4.32733i	−0.434913	−	0.753292i
$34$	−7.32303	−	0.119059i	−1.25589	−	0.0204184i
$35$	−0.227146	−	0.301137i	−0.0383947	−	0.0509015i
$36$	−0.0650154	+	1.99894i	−0.0108359	+	0.333157i
$37$	−5.01001	−	1.34243i	−0.823640	−	0.220694i	−0.177703	−	0.984084i	$-0.556867\pi$
$37$	−5.01001	−	1.34243i	−0.823640	−	0.220694i	−0.645937	+	0.763390i	$0.723533\pi$
$38$	−3.38160	+	0.847427i	−0.548568	+	0.137471i
$39$	−0.117291	−	0.0677181i	−0.0187816	−	0.0108436i
$40$	0.383951	+	0.123231i	0.0607080	+	0.0194846i
$41$			5.89239i			0.920237i	0.887858	+	0.460118i	$0.152193\pi$
$41$			5.89239i			0.920237i	−0.887858	+	0.460118i	$0.847807\pi$
$42$	0.397316	+	3.72050i	0.0613073	+	0.574086i
$43$	−0.390746	+	0.390746i	−0.0595882	+	0.0595882i	−0.736273	−	0.676685i	$-0.763416\pi$
$43$	−0.390746	+	0.390746i	−0.0595882	+	0.0595882i	0.676685	+	0.736273i	$0.263416\pi$
$44$	9.56384	+	2.89895i	1.44180	+	0.437033i
$45$	0.137710	−	0.0368993i	0.0205286	−	0.00550062i
$46$	−5.83750	−	3.49802i	−0.860692	−	0.515755i
$47$	1.18744	+	2.05670i	0.173205	+	0.300000i	0.939539	−	0.342443i	$-0.111254\pi$
$47$	1.18744	+	2.05670i	0.173205	+	0.300000i	−0.766333	+	0.642443i	$0.777921\pi$
$48$	−2.63866	−	3.00624i	−0.380857	−	0.433914i
$49$	1.69986	+	6.79047i	0.242837	+	0.970067i
$50$	−0.114480	+	7.04139i	−0.0161899	+	0.995803i
$51$	1.34039	−	5.00239i	0.187691	−	0.700474i
$52$	0.263784	−	0.0615645i	0.0365802	−	0.00853746i
$53$	0.658095	+	2.45604i	0.0903963	+	0.337363i	0.996281	−	0.0861602i	$-0.0274597\pi$
$53$	0.658095	+	2.45604i	0.0903963	+	0.337363i	−0.905885	+	0.423524i	$0.860793\pi$
$54$	−1.35989	−	0.388183i	−0.185058	−	0.0528250i
$55$		−	0.712379i		−	0.0960572i
$56$	−5.66762	−	4.88652i	−0.757368	−	0.652989i
$57$		−	2.46509i		−	0.326509i
$58$	3.41941	−	11.9790i	0.448991	−	1.57292i
$59$	−2.09440	−	7.81641i	−0.272668	−	1.01761i	−0.957388	−	0.288804i	$-0.906742\pi$
$59$	−2.09440	−	7.81641i	−0.272668	−	1.01761i	0.684721	−	0.728806i	$-0.259924\pi$
$60$	−0.150520	+	0.242170i	−0.0194320	+	0.0312640i
$61$	−1.17785	+	4.39581i	−0.150809	+	0.562826i	0.848619	+	0.529004i	$0.177434\pi$
$61$	−1.17785	+	4.39581i	−0.150809	+	0.562826i	−0.999428	+	0.0338216i	$0.989232\pi$
$62$	6.90169	+	0.112209i	0.876516	+	0.0142505i
$63$	−2.62018	−	0.366982i	−0.330111	−	0.0462354i
$64$	7.96197	+	0.779085i	0.995247	+	0.0973856i
$65$	−0.00965443	−	0.0167220i	−0.00119748	−	0.00207410i
$66$	−3.63227	+	6.06153i	−0.447101	+	0.746122i
$67$	0.284860	−	0.0763279i	0.0348011	−	0.00932494i	−0.241376	−	0.970432i	$-0.577599\pi$
$67$	0.284860	−	0.0763279i	0.0348011	−	0.00932494i	0.276178	+	0.961107i	$0.410932\pi$
$68$	4.88452	+	9.13364i	0.592335	+	1.10762i
$69$	3.40267	−	3.40267i	0.409633	−	0.409633i
$70$	−0.216156	+	0.487683i	−0.0258356	+	0.0582892i
$71$		−	9.82085i		−	1.16552i	−0.812644	−	0.582760i	$-0.801973\pi$
$71$		−	9.82085i		−	1.16552i	0.812644	−	0.582760i	$-0.198027\pi$
$72$	2.51552	−	1.29312i	0.296457	−	0.152395i
$73$	12.3493	+	7.12989i	1.44538	+	0.834491i	0.998201	−	0.0599535i	$-0.0190952\pi$
$73$	12.3493	+	7.12989i	1.44538	+	0.834491i	0.447179	+	0.894444i	$0.352429\pi$
$74$	1.78305	+	7.11515i	0.207275	+	0.827119i
$75$	−4.81000	−	1.28883i	−0.555411	−	0.148822i
$76$	3.37100	+	3.59765i	0.386680	+	0.412679i
$77$	−5.15981	+	12.1717i	−0.588015	+	1.38710i
$78$	−0.00311360	+	0.191511i	−0.000352546	+	0.0216843i
$79$	5.01195	+	8.68095i	0.563888	+	0.976683i	0.997152	+	0.0754162i	$0.0240285\pi$
$79$	5.01195	+	8.68095i	0.563888	+	0.976683i	−0.433264	+	0.901267i	$0.642638\pi$
$80$	−0.111491	−	0.559266i	−0.0124651	−	0.0625279i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	7.28345	−	4.04868i	0.804323	−	0.447102i
$83$	−1.66074	−	1.66074i	−0.182290	−	0.182290i	0.610063	−	0.792353i	$-0.291144\pi$
$83$	−1.66074	−	1.66074i	−0.182290	−	0.182290i	−0.792353	+	0.610063i	$0.791144\pi$
$84$	4.32583	−	3.04749i	0.471987	−	0.332508i
$85$	0.522083	−	0.522083i	0.0566279	−	0.0566279i
$86$	0.751475	+	0.214509i	0.0810336	+	0.0231311i
$87$	7.62861	+	4.40438i	0.817873	+	0.472199i
$88$	−2.98802	−	13.8135i	−0.318524	−	1.47253i
$89$	10.5430	−	6.08701i	1.11756	−	0.645222i	0.176781	−	0.984250i	$-0.443431\pi$
$89$	10.5430	−	6.08701i	1.11756	−	0.645222i	0.940776	+	0.339028i	$0.110098\pi$
$90$	−0.140231	−	0.144867i	−0.0147817	−	0.0152703i
$91$	0.0438372	+	0.355639i	0.00459539	+	0.0372811i
$92$	−0.312860	+	9.61910i	−0.0326179	+	1.00286i
$93$	−1.26326	+	4.71457i	−0.130994	+	0.488878i
$94$	1.72635	−	2.88093i	0.178059	−	0.297145i
$95$	0.175721	−	0.304358i	0.0180286	−	0.0312265i
$96$	−1.90292	+	5.32718i	−0.194216	+	0.543703i
$97$	12.5887			1.27819			0.639093	−	0.769130i	$-0.279310\pi$
$97$	12.5887			1.27819			0.639093	+	0.769130i	$0.279310\pi$
$98$	7.22557	−	6.76692i	0.729893	−	0.683562i
$99$	−3.53325	−	3.53325i	−0.355105	−	0.355105i
$100$	8.78237	−	4.69666i	0.878237	−	0.469666i
$101$	2.02206	+	7.54643i	0.201203	+	0.750898i	0.990574	+	0.136982i	$0.0437402\pi$
$101$	2.02206	+	7.54643i	0.201203	+	0.750898i	−0.789371	+	0.613916i	$0.789593\pi$
$102$	−7.10432	+	1.78034i	−0.703433	+	0.176280i
$103$	15.5354	−	8.96935i	1.53075	−	0.883776i	0.531418	−	0.847110i	$-0.321660\pi$
$103$	15.5354	−	8.96935i	1.53075	−	0.883776i	0.999328	−	0.0366662i	$-0.0116738\pi$
$104$	−0.257345	−	0.283756i	−0.0252348	−	0.0278245i
$105$	−0.297346	−	0.232087i	−0.0290180	−	0.0226493i
$106$	2.58368	−	2.50101i	0.250949	−	0.242920i
$107$	2.17380	+	0.582469i	0.210149	+	0.0563094i	0.362358	−	0.932039i	$-0.381972\pi$
$107$	2.17380	+	0.582469i	0.210149	+	0.0563094i	−0.152208	+	0.988348i	$0.548639\pi$
$108$	0.454564	+	1.94766i	0.0437405	+	0.187413i
$109$	−19.1681	+	5.13607i	−1.83597	+	0.491946i	−0.998511	−	0.0545581i	$-0.982625\pi$
$109$	−19.1681	+	5.13607i	−1.83597	+	0.491946i	−0.837456	+	0.546504i	$0.815958\pi$
$110$	−0.880556	+	0.489478i	−0.0839577	+	0.0466699i
$111$	−5.18674			−0.492304
$112$	−2.14587	+	10.3632i	−0.202766	+	0.979227i
$113$	−9.33529			−0.878190			−0.439095	−	0.898441i	$-0.644701\pi$
$113$	−9.33529			−0.878190			−0.439095	+	0.898441i	$0.644701\pi$
$114$	−3.04704	+	1.69377i	−0.285382	+	0.158636i
$115$	0.662673	−	0.177563i	0.0617946	−	0.0165578i
$116$	−17.1565	+	4.00415i	−1.59294	+	0.371776i
$117$	−0.130821	−	0.0350535i	−0.0120944	−	0.00324070i
$118$	−8.22262	+	7.95952i	−0.756953	+	0.732734i
$119$	−12.7018	+	5.13883i	−1.16437	+	0.471076i
$120$	0.402763	+	0.0196584i	0.0367671	+	0.00179456i
$121$	−12.0964	+	6.98387i	−1.09967	+	0.634898i
$122$	6.24287	−	1.56446i	0.565203	−	0.141640i
$123$	1.52506	+	5.69161i	0.137510	+	0.513195i
$124$	−4.60348	−	8.60813i	−0.413405	−	0.773033i
$125$	−1.00606	−	1.00606i	−0.0899845	−	0.0899845i
$126$	1.34672	+	3.49090i	0.119975	+	0.310994i
$127$	0.499655			0.0443372			0.0221686	−	0.999754i	$-0.492943\pi$
$127$	0.499655			0.0443372			0.0221686	+	0.999754i	$0.492943\pi$
$128$	−4.50769	−	10.3769i	−0.398428	−	0.917200i
$129$	−0.276299	+	0.478564i	−0.0243268	+	0.0421352i
$130$	−0.0140360	+	0.0234233i	−0.00123104	+	0.00205436i
$131$	5.63421	−	21.0272i	0.492264	−	1.83715i	−0.0525820	−	0.998617i	$-0.516745\pi$
$131$	5.63421	−	21.0272i	0.492264	−	1.83715i	0.544846	−	0.838536i	$-0.316588\pi$
$132$	9.98827	+	0.324867i	0.869367	+	0.0282761i
$133$	−5.20686	+	3.92750i	−0.451492	+	0.340558i
$134$	−0.290075	−	0.299663i	−0.0250587	−	0.0258870i
$135$	0.123467	−	0.0712839i	0.0106264	−	0.00613514i
$136$	7.93372	−	12.3134i	0.680311	−	1.05587i
$137$	18.9386	+	10.9342i	1.61803	+	0.934170i	0.987429	+	0.158064i	$0.0505251\pi$
$137$	18.9386	+	10.9342i	1.61803	+	0.934170i	0.630602	+	0.776107i	$0.282808\pi$
$138$	−6.54394	−	1.86797i	−0.557057	−	0.159013i
$139$	−13.4424	+	13.4424i	−1.14017	+	1.14017i	−0.151750	+	0.988419i	$0.548491\pi$
$139$	−13.4424	+	13.4424i	−1.14017	+	1.14017i	−0.988419	+	0.151750i	$0.951509\pi$
$140$	0.751336	−	0.0679027i	0.0634995	−	0.00573883i
$141$	1.67929	+	1.67929i	0.141421	+	0.141421i
$142$	−12.1393	+	6.74795i	−1.01871	+	0.566275i
$143$	−0.338372	+	0.586078i	−0.0282961	+	0.0490103i
$144$	−3.32682	−	2.22087i	−0.277235	−	0.185073i
$145$	0.627923	+	1.08759i	0.0521462	+	0.0903198i
$146$	0.327825	−	20.1637i	0.0271310	−	1.66876i
$147$	3.39944	+	6.11913i	0.280381	+	0.504698i
$148$	7.56973	−	7.09284i	0.622228	−	0.583027i
$149$	−14.4299	−	3.86649i	−1.18215	−	0.316755i	−0.386368	−	0.922345i	$-0.626271\pi$
$149$	−14.4299	−	3.86649i	−1.18215	−	0.316755i	−0.795777	+	0.605590i	$0.792937\pi$
$150$	1.71187	+	6.83109i	0.139773	+	0.557756i
$151$	−7.48900	−	4.32378i	−0.609446	−	0.351864i	0.163303	−	0.986576i	$-0.447785\pi$
$151$	−7.48900	−	4.32378i	−0.609446	−	0.351864i	−0.772749	+	0.634712i	$0.781119\pi$
$152$	2.13075	−	6.63877i	0.172827	−	0.538476i
$153$		−	5.17885i		−	0.418685i
$154$	18.5905	−	1.98530i	1.49807	−	0.159980i
$155$	−0.492045	+	0.492045i	−0.0395220	+	0.0395220i
$156$	0.238861	−	0.127739i	0.0191242	−	0.0102273i
$157$	5.28857	−	1.41707i	0.422074	−	0.113094i	−0.0415292	−	0.999137i	$-0.513223\pi$
$157$	5.28857	−	1.41707i	0.422074	−	0.113094i	0.463603	+	0.886043i	$0.346556\pi$
$158$	7.28660	−	12.1599i	0.579691	−	0.967388i
$159$	1.27134	+	2.20203i	0.100824	+	0.174632i
$160$	−0.614691	+	0.522086i	−0.0485956	+	0.0412745i
$161$	−12.6085	−	1.76595i	−0.993692	−	0.139177i
$162$	−1.41403	−	0.0229894i	−0.111096	−	0.00180622i
$163$	−3.11628	+	11.6301i	−0.244086	+	0.910940i	0.729755	+	0.683709i	$0.239634\pi$
$163$	−3.11628	+	11.6301i	−0.244086	+	0.910940i	−0.973841	+	0.227231i	$0.927033\pi$
$164$	−10.0090	−	6.22105i	−0.781570	−	0.485782i
$165$	−0.184377	−	0.688105i	−0.0143537	−	0.0535689i
$166$	−0.911702	+	3.19390i	−0.0707618	+	0.247895i
$167$			8.87082i			0.686444i	0.939254	+	0.343222i	$0.111518\pi$
$167$			8.87082i			0.686444i	−0.939254	+	0.343222i	$0.888482\pi$
$168$	−6.73923	−	3.25313i	−0.519943	−	0.250984i
$169$		−	12.9817i		−	0.998589i
$170$	−1.00406	−	0.286610i	−0.0770080	−	0.0219820i
$171$	−0.638013	−	2.38110i	−0.0487900	−	0.182087i
$172$	−0.251191	−	1.07627i	−0.0191532	−	0.0820649i
$173$	2.72147	−	10.1567i	0.206910	−	0.772197i	−0.781949	−	0.623342i	$-0.785775\pi$
$173$	2.72147	−	10.1567i	0.206910	−	0.772197i	0.988859	−	0.148855i	$-0.0475588\pi$
$174$	0.202509	−	12.4558i	0.0153521	−	0.944274i
$175$	4.94119	+	12.2133i	0.373519	+	0.923239i
$176$	−15.0215	+	13.1848i	−1.13229	+	0.993839i
$177$	−4.04607	−	7.00800i	−0.304121	−	0.526753i
$178$	−14.7682	−	8.84958i	−1.10692	−	0.663304i
$179$	−14.7300	+	3.94689i	−1.10097	+	0.295005i	−0.763161	−	0.646209i	$-0.776354\pi$
$179$	−14.7300	+	3.94689i	−1.10097	+	0.295005i	−0.337812	+	0.941214i	$0.609687\pi$
$180$	−0.0827128	+	0.272875i	−0.00616505	+	0.0203389i
$181$	8.14761	−	8.14761i	0.605607	−	0.605607i	−0.336188	−	0.941795i	$-0.609138\pi$
$181$	8.14761	−	8.14761i	0.605607	−	0.605607i	0.941795	+	0.336188i	$0.109138\pi$
$182$	0.409477	−	0.298547i	0.0303524	−	0.0221298i
$183$			4.55088i			0.336411i
$184$	12.1049	−	6.22260i	0.892387	−	0.458736i
$185$	−0.640393	−	0.369731i	−0.0470826	−	0.0271832i
$186$	6.69556	−	1.67790i	0.490943	−	0.123030i
$187$	−24.9958	−	6.69760i	−1.82787	−	0.489777i
$188$	−4.74723	−	0.154403i	−0.346227	−	0.0112610i
$189$	−2.62588	+	0.323674i	−0.191005	+	0.0235438i
$190$	−0.496949	−	0.00807947i	−0.0360525	−	0.000586146i
$191$	5.29941	+	9.17886i	0.383452	+	0.664159i	0.991553	−	0.129701i	$-0.0414018\pi$
$191$	5.29941	+	9.17886i	0.383452	+	0.664159i	−0.608101	+	0.793860i	$0.708068\pi$
$192$	7.89232	−	1.30817i	0.569579	−	0.0944092i
$193$	3.18069	−	5.50912i	0.228951	−	0.396555i	−0.728546	−	0.684996i	$-0.759804\pi$
$193$	3.18069	−	5.50912i	0.228951	−	0.396555i	0.957498	+	0.288441i	$0.0931371\pi$
$194$	−8.64972	−	15.5606i	−0.621014	−	1.11718i
$195$	−0.0136534	−	0.0136534i	−0.000977742	−	0.000977742i
$196$	−13.3292	−	4.28179i	−0.952082	−	0.305842i
$197$	−6.69371	+	6.69371i	−0.476907	+	0.476907i	−0.904141	−	0.427234i	$-0.859488\pi$
$197$	−6.69371	+	6.69371i	−0.476907	+	0.476907i	0.427234	+	0.904141i	$0.359488\pi$
$198$	−1.93966	+	6.79509i	−0.137846	+	0.482906i
$199$	17.8398	+	10.2998i	1.26463	+	0.730133i	0.973966	−	0.226693i	$-0.0727915\pi$
$199$	17.8398	+	10.2998i	1.26463	+	0.730133i	0.290661	+	0.956826i	$0.406125\pi$
$200$	−11.8398	−	7.62860i	−0.837203	−	0.539423i
$201$	0.255398	−	0.147454i	0.0180144	−	0.0104006i
$202$	7.93861	−	7.68461i	0.558559	−	0.540687i
$203$	−2.85117	−	23.1307i	−0.200113	−	1.62346i
$204$	7.08204	+	7.55822i	0.495842	+	0.529181i
$205$	−0.217425	+	0.811440i	−0.0151856	+	0.0566735i
$206$	−21.7612	−	13.0400i	−1.51618	−	0.908543i
$207$	2.40605	−	4.16740i	0.167232	−	0.289654i
$208$	−0.173921	+	0.513068i	−0.0120593	+	0.0355749i
$209$	−12.3175			−0.852020
$210$	−0.0825694	+	0.527011i	−0.00569783	+	0.0363672i
$211$	0.464512	+	0.464512i	0.0319783	+	0.0319783i	0.722915	−	0.690937i	$-0.242802\pi$
$211$	0.464512	+	0.464512i	0.0319783	+	0.0319783i	−0.690937	+	0.722915i	$0.742802\pi$
$212$	−4.86670	−	1.47517i	−0.334247	−	0.101315i
$213$	−2.54182	−	9.48622i	−0.174163	−	0.649985i
$214$	−0.773652	−	3.08721i	−0.0528857	−	0.211037i
$215$	−0.0682278	+	0.0393913i	−0.00465310	+	0.00268647i
$216$	2.09512	−	1.90012i	0.142555	−	0.129287i
$217$	11.9710	−	4.84316i	0.812644	−	0.328775i
$218$	19.5190	+	20.1642i	1.32200	+	1.36569i
$219$	13.7739	+	3.69070i	0.930754	+	0.249395i
$220$	1.21007	+	0.752113i	0.0815827	+	0.0507074i
$221$	−0.677504	+	0.181537i	−0.0455739	+	0.0122115i
$222$	3.56383	+	6.41122i	0.239189	+	0.430293i
$223$	−8.48668			−0.568310			−0.284155	−	0.958778i	$-0.591713\pi$
$223$	−8.48668			−0.568310			−0.284155	+	0.958778i	$0.591713\pi$
$224$	14.2841	−	4.46811i	0.954398	−	0.298538i
$225$	−4.97967			−0.331978
$226$	6.41431	+	11.5391i	0.426674	+	0.767572i
$227$	7.77334	−	2.08286i	0.515935	−	0.138244i	0.00854926	−	0.999963i	$-0.497279\pi$
$227$	7.77334	−	2.08286i	0.515935	−	0.138244i	0.507386	+	0.861719i	$0.330612\pi$
$228$	4.18727	+	2.60259i	0.277309	+	0.172360i
$229$	−0.774442	−	0.207511i	−0.0511766	−	0.0137127i	0.233140	−	0.972443i	$-0.425100\pi$
$229$	−0.774442	−	0.207511i	−0.0511766	−	0.0137127i	−0.284316	+	0.958730i	$0.591767\pi$
$230$	−0.674807	−	0.697112i	−0.0444954	−	0.0459662i
$231$	−1.83373	+	13.0924i	−0.120650	+	0.861419i
$232$	16.7377	+	18.4554i	1.09888	+	1.21166i
$233$	1.53596	−	0.886785i	0.100624	−	0.0580952i	−0.448844	−	0.893610i	$-0.648164\pi$
$233$	1.53596	−	0.886785i	0.100624	−	0.0580952i	0.549467	+	0.835515i	$0.314831\pi$
$234$	0.0465591	+	0.185791i	0.00304366	+	0.0121455i
$235$	0.0876310	+	0.327043i	0.00571641	+	0.0213339i
$236$	15.4884	+	4.69477i	1.00821	+	0.305604i
$237$	7.08797	+	7.08797i	0.460413	+	0.460413i
$238$	15.0795	+	12.1695i	0.977456	+	0.788832i
$239$	−14.1393			−0.914593			−0.457296	−	0.889314i	$-0.651182\pi$
$239$	−14.1393			−0.914593			−0.457296	+	0.889314i	$0.651182\pi$
$240$	−0.252441	−	0.511354i	−0.0162950	−	0.0330078i
$241$	0.181691	−	0.314699i	0.0117038	−	0.0202715i	−0.860114	−	0.510102i	$-0.829608\pi$
$241$	0.181691	−	0.314699i	0.0117038	−	0.0202715i	0.871818	+	0.489830i	$0.162941\pi$
$242$	16.9441	+	10.1535i	1.08921	+	0.652690i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−6.22329	−	6.64173i	−0.398406	−	0.425193i
$245$	−0.0164760	+	0.997839i	−0.00105262	+	0.0637496i
$246$	5.98740	−	5.79582i	0.381743	−	0.369528i
$247$	−0.289134	+	0.166931i	−0.0183971	+	0.0106216i
$248$	−7.47724	+	11.6049i	−0.474806	+	0.736914i
$249$	−2.03398	−	1.17432i	−0.128898	−	0.0744195i
$250$	−0.552299	+	1.93483i	−0.0349305	+	0.122369i
$251$	4.00610	−	4.00610i	0.252863	−	0.252863i	−0.569281	−	0.822143i	$-0.692778\pi$
$251$	4.00610	−	4.00610i	0.252863	−	0.252863i	0.822143	+	0.569281i	$0.192778\pi$
$252$	3.38969	−	4.06325i	0.213530	−	0.255961i
$253$	−17.0023	−	17.0023i	−1.06893	−	1.06893i
$254$	−0.343315	−	0.617612i	−0.0215415	−	0.0387524i
$255$	0.369169	−	0.639419i	0.0231182	−	0.0400420i
$256$	−9.72944	+	12.7019i	−0.608090	+	0.793868i
$257$	8.58831	+	14.8754i	0.535724	+	0.927901i	0.999128	+	0.0417538i	$0.0132945\pi$
$257$	8.58831	+	14.8754i	0.535724	+	0.927901i	−0.463404	+	0.886147i	$0.653372\pi$
$258$	0.781388	+	0.0127039i	0.0486471	+	0.000790911i
$259$	8.26377	+	10.9556i	0.513486	+	0.680751i
$260$	0.0385973	+	0.00125537i	0.00239370	+	7.78549e-5i
$261$	8.50861	+	2.27988i	0.526670	+	0.141121i
$262$	−29.8625	+	7.48353i	−1.84491	+	0.462334i
$263$	6.78844	+	3.91931i	0.418593	+	0.241675i	0.694475	−	0.719517i	$-0.255637\pi$
$263$	6.78844	+	3.91931i	0.418593	+	0.241675i	−0.275882	+	0.961191i	$0.588970\pi$
$264$	−6.46142	−	12.5695i	−0.397673	−	0.773599i
$265$			0.362505i			0.0222685i
$266$	8.43236	+	3.73749i	0.517021	+	0.229160i
$267$	8.60834	−	8.60834i	0.526822	−	0.526822i
$268$	−0.171095	+	0.564456i	−0.0104513	+	0.0344796i
$269$	11.0926	−	2.97226i	0.676329	−	0.181222i	0.0957252	−	0.995408i	$-0.469483\pi$
$269$	11.0926	−	2.97226i	0.676329	−	0.181222i	0.580604	+	0.814186i	$0.302816\pi$
$270$	−0.172947	−	0.103636i	−0.0105252	−	0.00630707i
$271$	13.5380	+	23.4486i	0.822378	+	1.42440i	0.903907	+	0.427729i	$0.140686\pi$
$271$	13.5380	+	23.4486i	0.822378	+	1.42440i	−0.0815293	+	0.996671i	$0.525980\pi$
$272$	−20.6716	−	1.34611i	−1.25340	−	0.0816198i
$273$	0.134390	+	0.332175i	0.00813363	+	0.0201042i
$274$	0.502742	−	30.9225i	0.0303717	−	1.86809i
$275$	−6.44001	+	24.0345i	−0.388347	+	1.44933i
$276$	2.18741	+	9.37232i	0.131666	+	0.564147i
$277$	−1.09562	−	4.08893i	−0.0658297	−	0.245680i	0.925168	−	0.379557i	$-0.123924\pi$
$277$	−1.09562	−	4.08893i	−0.0658297	−	0.245680i	−0.990998	+	0.133878i	$0.957257\pi$
$278$	25.8522	+	7.37952i	1.55051	+	0.442594i
$279$			4.88088i			0.292211i
$280$	−0.600179	−	0.882053i	−0.0358675	−	0.0527128i
$281$		−	10.0464i		−	0.599316i	−0.954047	−	0.299658i	$-0.903127\pi$
$281$		−	10.0464i		−	0.599316i	0.954047	−	0.299658i	$-0.0968726\pi$
$282$	0.921885	−	3.22957i	0.0548974	−	0.192318i
$283$	5.86368	+	21.8836i	0.348560	+	1.30084i	0.888398	+	0.459074i	$0.151819\pi$
$283$	5.86368	+	21.8836i	0.348560	+	1.30084i	−0.539838	+	0.841769i	$0.681515\pi$
$284$	16.6820	+	10.3686i	0.989893	+	0.615265i
$285$	0.0909600	−	0.339468i	0.00538801	−	0.0201083i
$286$	0.956935	+	0.0155580i	0.0565847	+	0.000919962i
$287$	9.59224	−	12.2895i	0.566212	−	0.725423i
$288$	−0.459303	+	5.63818i	−0.0270647	+	0.332233i
$289$	−4.91025	−	8.50480i	−0.288838	−	0.500282i
$290$	0.912903	−	1.52345i	0.0536075	−	0.0894602i
$291$	12.1597	−	3.25819i	0.712815	−	0.190998i
$292$	−25.1492	+	13.4494i	−1.47174	+	0.787064i
$293$	16.5560	−	16.5560i	0.967212	−	0.967212i	−0.0322669	−	0.999479i	$-0.510273\pi$
$293$	16.5560	−	16.5560i	0.967212	−	0.967212i	0.999479	+	0.0322669i	$0.0102727\pi$
$294$	5.22796	−	8.40645i	0.304901	−	0.490274i
$295$		−	1.15368i		−	0.0671698i
$296$	−13.9685	−	4.48326i	−0.811902	−	0.260584i
$297$	−4.32733	−	2.49839i	−0.251097	−	0.144971i
$298$	5.13558	+	20.4932i	0.297496	+	1.18714i
$299$	−0.629525	−	0.168681i	−0.0364064	−	0.00975506i
$300$	7.26753	−	6.80967i	0.419591	−	0.393157i
$301$	1.45105	−	0.178862i	0.0836374	−	0.0103094i
$302$	−0.198802	+	12.2279i	−0.0114398	+	0.703635i
$303$	3.90632	+	6.76595i	0.224412	+	0.388694i
$304$	−9.67009	+	1.92775i	−0.554618	+	0.110564i
$305$	−0.324404	+	0.561885i	−0.0185753	+	0.0321734i
$306$	−6.40146	+	3.55841i	−0.365947	+	0.203421i
$307$	9.64846	+	9.64846i	0.550667	+	0.550667i	0.926633	−	0.375966i	$-0.122689\pi$
$307$	9.64846	+	9.64846i	0.550667	+	0.550667i	−0.375966	+	0.926633i	$0.622689\pi$
$308$	−15.2276	−	21.6152i	−0.867673	−	1.23164i
$309$	12.6846	−	12.6846i	0.721600	−	0.721600i
$310$	0.946291	+	0.270120i	0.0537457	+	0.0153418i
$311$	−24.9628	−	14.4123i	−1.41551	−	0.817246i	−0.419612	−	0.907704i	$-0.637834\pi$
$311$	−24.9628	−	14.4123i	−1.41551	−	0.817246i	−0.995900	+	0.0904575i	$0.971167\pi$
$312$	−0.322018	−	0.207481i	−0.0182307	−	0.0117463i
$313$	0.297274	−	0.171631i	0.0168029	−	0.00970118i	−0.491575	−	0.870835i	$-0.663579\pi$
$313$	0.297274	−	0.171631i	0.0168029	−	0.00970118i	0.508378	+	0.861134i	$0.330245\pi$
$314$	−5.38541	−	5.56341i	−0.303916	−	0.313962i
$315$	−0.347283	−	0.147220i	−0.0195672	−	0.00829489i
$316$	−20.0372	−	0.651708i	−1.12718	−	0.0366614i
$317$	−0.124691	+	0.465352i	−0.00700332	+	0.0261368i	−0.969339	−	0.245727i	$-0.920973\pi$
$317$	−0.124691	+	0.465352i	−0.00700332	+	0.0261368i	0.962336	+	0.271864i	$0.0876400\pi$
$318$	1.84833	−	3.08450i	0.103649	−	0.172970i
$319$	22.0077	−	38.1184i	1.23219	−	2.13422i
$320$	1.06770	+	0.401079i	0.0596860	+	0.0224210i
$321$	2.25049			0.125610
$322$	6.48052	+	16.7985i	0.361145	+	0.936145i
$323$	−9.02717	−	9.02717i	−0.502285	−	0.502285i
$324$	0.943167	+	1.76364i	0.0523981	+	0.0979802i
$325$	0.174555	+	0.651448i	0.00968257	+	0.0361358i
$326$	16.5169	−	4.13913i	0.914787	−	0.229245i
$327$	−17.1856	+	9.92212i	−0.950366	+	0.548694i
$328$	−0.812490	+	16.6464i	−0.0448623	+	0.919142i
$329$	0.871535	−	6.22258i	0.0480493	−	0.343062i
$330$	−0.723865	+	0.700704i	−0.0398475	+	0.0385725i
$331$	−18.4365	−	4.94005i	−1.01336	−	0.271530i	−0.286329	−	0.958131i	$-0.592435\pi$
$331$	−18.4365	−	4.94005i	−1.01336	−	0.271530i	−0.727034	+	0.686601i	$0.759102\pi$
$332$	4.57435	−	1.06761i	0.251050	−	0.0585926i
$333$	−5.01001	+	1.34243i	−0.274547	+	0.0735646i
$334$	10.9650	−	6.09517i	0.599979	−	0.333513i
$335$	0.0420444			0.00229713
$336$	0.609432	+	10.5654i	0.0332472	+	0.576392i
$337$	16.2089			0.882953			0.441477	−	0.897273i	$-0.354455\pi$
$337$	16.2089			0.882953			0.441477	+	0.897273i	$0.354455\pi$
$338$	−16.0463	+	8.91975i	−0.872806	+	0.485170i
$339$	−9.01720	+	2.41615i	−0.489747	+	0.131227i
$340$	0.335622	+	1.43803i	0.0182017	+	0.0779880i
$341$	23.5576	+	6.31225i	1.27572	+	0.341827i
$342$	−2.50484	+	2.42469i	−0.135446	+	0.131112i
$343$	7.50893	−	16.9297i	0.405444	−	0.914120i
$344$	−1.15776	+	1.05000i	−0.0624223	+	0.0566123i
$345$	0.594137	−	0.343025i	0.0319872	−	0.0184678i
$346$	−14.4244	+	3.61474i	−0.775458	+	0.194329i
$347$	4.88289	+	18.2232i	0.262127	+	0.978272i	0.963985	+	0.265955i	$0.0856874\pi$
$347$	4.88289	+	18.2232i	0.262127	+	0.978272i	−0.701858	+	0.712317i	$0.747646\pi$
$348$	−15.5355	+	8.30813i	−0.832791	+	0.445362i
$349$	−20.0607	−	20.0607i	−1.07382	−	1.07382i	−0.997048	−	0.0767754i	$-0.975538\pi$
$349$	−20.0607	−	20.0607i	−1.07382	−	1.07382i	−0.0767754	−	0.997048i	$-0.524462\pi$
$350$	11.7015	−	14.4995i	0.625470	−	0.775031i
$351$	−0.135436			−0.00722905
$352$	26.6187	+	9.50846i	1.41878	+	0.506803i
$353$	7.06919	−	12.2442i	0.376255	−	0.651693i	−0.614259	−	0.789104i	$-0.710545\pi$
$353$	7.06919	−	12.2442i	0.376255	−	0.651693i	0.990514	+	0.137412i	$0.0438784\pi$
$354$	−5.88236	+	9.81648i	−0.312644	+	0.521740i
$355$	0.362382	−	1.35243i	0.0192333	−	0.0717795i
$356$	−0.791499	+	24.3352i	−0.0419494	+	1.28976i
$357$	−10.9390	+	8.25120i	−0.578952	+	0.436700i
$358$	14.9997	+	15.4955i	0.792760	+	0.818963i
$359$	−1.38470	+	0.799455i	−0.0730815	+	0.0421936i	−0.536095	−	0.844157i	$-0.680101\pi$
$359$	−1.38470	+	0.799455i	−0.0730815	+	0.0421936i	0.463014	+	0.886351i	$0.346768\pi$
$360$	0.394127	−	0.0852542i	0.0207723	−	0.00449329i
$361$	11.1919	+	6.46166i	0.589049	+	0.340087i
$362$	−15.6693	−	4.47282i	−0.823562	−	0.235086i
$363$	−9.87669	+	9.87669i	−0.518392	+	0.518392i
$364$	−0.650381	−	0.301012i	−0.0340892	−	0.0157773i
$365$	1.43754	+	1.43754i	0.0752442	+	0.0752442i
$366$	5.62524	−	3.12693i	0.294036	−	0.163447i
$367$	3.74278	−	6.48269i	0.195372	−	0.338393i	−0.751651	−	0.659561i	$-0.770742\pi$
$367$	3.74278	−	6.48269i	0.195372	−	0.338393i	0.947022	+	0.321168i	$0.104075\pi$
$368$	−16.0090	−	10.6871i	−0.834525	−	0.557101i
$369$	2.94619	+	5.10296i	0.153373	+	0.265649i
$370$	−0.0169998	+	1.04562i	−0.000883779	+	0.0543592i
$371$	2.62565	−	6.19376i	0.136317	−	0.321564i
$372$	−6.67457	−	7.12334i	−0.346060	−	0.369328i
$373$	−17.1872	−	4.60530i	−0.889919	−	0.238453i	−0.215237	−	0.976562i	$-0.569053\pi$
$373$	−17.1872	−	4.60530i	−0.889919	−	0.238453i	−0.674682	+	0.738109i	$0.735719\pi$
$374$	8.89595	+	35.4987i	0.459998	+	1.83559i
$375$	−1.23216	−	0.711390i	−0.0636287	−	0.0367360i
$376$	3.07099	+	5.97404i	0.158374	+	0.308087i
$377$		−	1.19303i		−	0.0614440i
$378$	2.20434	+	3.02339i	0.113379	+	0.155506i
$379$	4.84387	−	4.84387i	0.248813	−	0.248813i	−0.571670	−	0.820483i	$-0.693704\pi$
$379$	4.84387	−	4.84387i	0.248813	−	0.248813i	0.820483	+	0.571670i	$0.193704\pi$
$380$	0.331469	+	0.619819i	0.0170040	+	0.0317961i
$381$	0.482629	−	0.129320i	0.0247259	−	0.00662527i
$382$	7.70453	−	12.8573i	0.394198	−	0.657838i
$383$	−4.43857	−	7.68783i	−0.226800	−	0.392830i	0.730058	−	0.683385i	$-0.239493\pi$
$383$	−4.43857	−	7.68783i	−0.226800	−	0.392830i	−0.956858	+	0.290556i	$0.906160\pi$
$384$	−7.03984	−	8.85667i	−0.359251	−	0.451965i
$385$	−1.15968	+	1.48577i	−0.0591030	+	0.0757220i
$386$	−8.99516	−	0.146245i	−0.457842	−	0.00744365i
$387$	−0.143023	+	0.533769i	−0.00727026	+	0.0271330i
$388$	−13.2908	+	21.3835i	−0.674739	+	1.08558i
$389$	5.90777	+	22.0481i	0.299536	+	1.11788i	0.937548	+	0.347856i	$0.113090\pi$
$389$	5.90777	+	22.0481i	0.299536	+	1.11788i	−0.638012	+	0.770026i	$0.720243\pi$
$390$	−0.00749537	+	0.0262580i	−0.000379543	+	0.00132963i
$391$		−	24.9211i		−	1.26032i
$392$	3.86588	+	19.4179i	0.195257	+	0.980752i
$393$		−	21.7689i		−	1.09810i
$394$	12.8732	+	3.67467i	0.648544	+	0.185127i
$395$	0.369874	+	1.38039i	0.0186104	+	0.0694550i
$396$	9.73201	−	2.27136i	0.489052	−	0.114140i
$397$	9.09376	−	33.9384i	0.456403	−	1.70332i	−0.227528	−	0.973772i	$-0.573064\pi$
$397$	9.09376	−	33.9384i	0.456403	−	1.70332i	0.683931	−	0.729547i	$-0.260269\pi$
$398$	0.473573	−	29.1284i	0.0237381	−	1.46007i
$399$	−4.01293	+	5.14131i	−0.200898	+	0.257388i
$400$	−1.29434	+	19.8766i	−0.0647169	+	0.993830i
$401$	−13.0918	−	22.6757i	−0.653774	−	1.13237i	−0.982200	−	0.187841i	$-0.939851\pi$
$401$	−13.0918	−	22.6757i	−0.653774	−	1.13237i	0.328425	−	0.944530i	$-0.393482\pi$
$402$	−0.357750	−	0.214376i	−0.0178429	−	0.0106921i
$403$	0.638523	−	0.171092i	0.0318071	−	0.00852269i
$404$	−14.9534	−	4.53262i	−0.743961	−	0.225506i
$405$	0.100811	−	0.100811i	0.00500932	−	0.00500932i
$406$	−26.6323	+	19.4175i	−1.32174	+	0.963673i
$407$			25.9170i			1.28466i
$408$	4.47644	−	13.9472i	0.221617	−	0.690491i
$409$	−18.0697	−	10.4326i	−0.893490	−	0.515857i	−0.0184074	−	0.999831i	$-0.505860\pi$
$409$	−18.0697	−	10.4326i	−0.893490	−	0.515857i	−0.875082	+	0.483974i	$0.839193\pi$
$410$	1.15240	−	0.288790i	0.0569128	−	0.0142623i
$411$	21.1232	+	5.65995i	1.04193	+	0.279185i
$412$	−1.16629	+	35.8584i	−0.0574590	+	1.76662i
$413$	−8.35618	+	19.7118i	−0.411181	+	0.969952i
$414$	−6.80443	−	0.110627i	−0.334420	−	0.00543704i
$415$	−0.167420	−	0.289980i	−0.00821833	−	0.0142346i
$416$	0.753694	−	0.137551i	0.0369529	−	0.00674400i
$417$	−9.50520	+	16.4635i	−0.465472	+	0.806221i
$418$	8.46340	+	15.2254i	0.413959	+	0.744698i
$419$	10.9118	+	10.9118i	0.533076	+	0.533076i	0.921487	−	0.388410i	$-0.126976\pi$
$419$	10.9118	+	10.9118i	0.533076	+	0.533076i	−0.388410	+	0.921487i	$0.626976\pi$
$420$	0.708160	−	0.260049i	0.0345547	−	0.0126891i
$421$	−10.8119	+	10.8119i	−0.526938	+	0.526938i	−0.919658	−	0.392720i	$-0.871534\pi$
$421$	−10.8119	+	10.8119i	−0.526938	+	0.526938i	0.392720	+	0.919658i	$0.371534\pi$
$422$	0.255005	−	0.893341i	0.0124134	−	0.0434872i
$423$	2.05670	+	1.18744i	0.100000	+	0.0577351i
$424$	1.52050	+	7.02922i	0.0738420	+	0.341369i
$425$	−22.3339	+	12.8945i	−1.08335	+	0.625475i
$426$	−9.97920	+	9.65991i	−0.483494	+	0.468024i
$427$	9.61255	−	7.25068i	0.465184	−	0.350885i
$428$	−3.28445	+	3.07752i	−0.158760	+	0.148758i
$429$	−0.175154	+	0.653685i	−0.00845653	+	0.0315602i
$430$	0.0955703	+	0.0572689i	0.00460881	+	0.00276175i
$431$	17.1278	−	29.6661i	0.825015	−	1.42897i	−0.0768926	−	0.997039i	$-0.524500\pi$
$431$	17.1278	−	29.6661i	0.825015	−	1.42897i	0.901908	−	0.431929i	$-0.142167\pi$
$432$	−3.78826	−	1.28416i	−0.182263	−	0.0617840i
$433$	33.8838			1.62835			0.814175	−	0.580620i	$-0.197190\pi$
$433$	33.8838			1.62835			0.814175	+	0.580620i	$0.197190\pi$
$434$	−14.2118	−	11.4693i	−0.682190	−	0.550545i
$435$	0.888017	+	0.888017i	0.0425772	+	0.0425772i
$436$	11.5129	−	37.9819i	0.551369	−	1.81900i
$437$	−3.07018	−	11.4581i	−0.146867	−	0.548113i
$438$	−4.90210	−	19.5615i	−0.234231	−	0.934685i
$439$	−18.7950	+	10.8513i	−0.897037	+	0.517904i	−0.876238	−	0.481879i	$-0.839954\pi$
$439$	−18.7950	+	10.8513i	−0.897037	+	0.517904i	−0.0207991	+	0.999784i	$0.506621\pi$
$440$	0.0982286	−	2.01252i	0.00468286	−	0.0959429i
$441$	4.86736	+	5.03079i	0.231779	+	0.239561i
$442$	0.689910	+	0.712714i	0.0328156	+	0.0339003i
$443$	19.0104	+	5.09383i	0.903213	+	0.242015i	0.680396	−	0.732845i	$-0.261808\pi$
$443$	19.0104	+	5.09383i	0.903213	+	0.242015i	0.222817	+	0.974860i	$0.428475\pi$
$444$	5.47604	−	8.81034i	0.259881	−	0.418120i
$445$	1.67648	−	0.449213i	0.0794730	−	0.0212947i
$446$	5.83123	+	10.4902i	0.276117	+	0.496725i
$447$	−14.9390			−0.706588
$448$	−15.3376	−	14.5862i	−0.724634	−	0.689134i
$449$	7.82130			0.369110			0.184555	−	0.982822i	$-0.440916\pi$
$449$	7.82130			0.369110			0.184555	+	0.982822i	$0.440916\pi$
$450$	3.42155	+	6.15526i	0.161294	+	0.290162i
$451$	28.4397	−	7.62039i	1.33917	−	0.358830i
$452$	9.85598	−	15.8572i	0.463586	−	0.745859i
$453$	−8.35289	−	2.23815i	−0.392453	−	0.105158i
$454$	−7.91567	−	8.17731i	−0.371501	−	0.383780i
$455$	−0.00708600	+	0.0505926i	−0.000332197	+	0.00237182i
$456$	0.339907	−	6.96404i	0.0159176	−	0.326121i
$457$	−28.5156	+	16.4635i	−1.33391	+	0.770131i	−0.985896	−	0.167360i	$-0.946476\pi$
$457$	−28.5156	+	16.4635i	−1.33391	+	0.770131i	−0.348010	+	0.937491i	$0.613142\pi$
$458$	0.275622	+	1.09985i	0.0128790	+	0.0513927i
$459$	−1.34039	−	5.00239i	−0.0625638	−	0.233491i
$460$	−0.398022	+	1.31310i	−0.0185579	+	0.0612237i
$461$	4.44057	+	4.44057i	0.206818	+	0.206818i	0.802914	−	0.596096i	$-0.203282\pi$
$461$	4.44057	+	4.44057i	0.206818	+	0.206818i	−0.596096	+	0.802914i	$0.703282\pi$
$462$	17.4432	−	6.72923i	0.811532	−	0.313072i
$463$	−26.8244			−1.24664			−0.623319	−	0.781968i	$-0.714216\pi$
$463$	−26.8244			−1.24664			−0.623319	+	0.781968i	$0.714216\pi$
$464$	11.3118	−	33.3699i	0.525138	−	1.54916i
$465$	−0.347928	+	0.602629i	−0.0161348	+	0.0279463i
$466$	−2.15150	−	1.28925i	−0.0996662	−	0.0597233i
$467$	−4.89634	+	18.2734i	−0.226576	+	0.845592i	0.755191	+	0.655504i	$0.227544\pi$
$467$	−4.89634	+	18.2734i	−0.226576	+	0.845592i	−0.981767	+	0.190088i	$0.939123\pi$
$468$	0.197661	−	0.185208i	0.00913688	−	0.00856125i
$469$	−0.718371	−	0.304531i	−0.0331713	−	0.0140619i
$470$	0.344039	−	0.333031i	0.0158693	−	0.0153616i
$471$	4.74161	−	2.73757i	0.218482	−	0.126140i
$472$	−4.83902	−	22.3706i	−0.222734	−	1.02969i
$473$	2.39128	+	1.38060i	0.109951	+	0.0634802i
$474$	3.89111	−	13.6314i	0.178725	−	0.626113i
$475$	−8.67998	+	8.67998i	−0.398265	+	0.398265i
$476$	4.68131	−	27.0011i	0.214567	−	1.23759i
$477$	1.79795	+	1.79795i	0.0823224	+	0.0823224i
$478$	9.71514	+	17.4772i	0.444360	+	0.799389i
$479$	−10.5124	+	18.2081i	−0.480326	+	0.831949i	−0.999745	−	0.0225705i	$-0.992815\pi$
$479$	−10.5124	+	18.2081i	−0.480326	+	0.831949i	0.519419	+	0.854520i	$0.326148\pi$
$480$	−0.458620	+	0.663390i	−0.0209331	+	0.0302795i
$481$	0.351237	+	0.608360i	0.0160150	+	0.0277388i
$482$	−0.513833	−	0.00835397i	−0.0234044	−	0.000380513i
$483$	−12.6360	+	1.55755i	−0.574957	+	0.0708710i
$484$	0.908118	−	27.9207i	0.0412781	−	1.26912i
$485$	1.73358	+	0.464512i	0.0787180	+	0.0210924i
$486$	−1.37180	+	0.343771i	−0.0622259	+	0.0155938i
$487$	−1.07317	−	0.619594i	−0.0486299	−	0.0280765i	0.475488	−	0.879722i	$-0.342272\pi$
$487$	−1.07317	−	0.619594i	−0.0486299	−	0.0280765i	−0.524118	+	0.851646i	$0.675605\pi$
$488$	−3.93364	+	12.2560i	−0.178068	+	0.554805i
$489$			12.0404i			0.544484i
$490$	1.24473	−	0.665253i	0.0562310	−	0.0300531i
$491$	17.0854	−	17.0854i	0.771053	−	0.771053i	−0.207238	−	0.978291i	$-0.566447\pi$
$491$	17.0854	−	17.0854i	0.771053	−	0.771053i	0.978291	+	0.207238i	$0.0664473\pi$
$492$	−11.2781	−	3.41856i	−0.508454	−	0.154120i
$493$	44.0648	−	11.8071i	1.98458	−	0.531767i
$494$	0.405005	+	0.242692i	0.0182220	+	0.0109193i
$495$	−0.356189	−	0.616938i	−0.0160095	−	0.0277293i
$496$	19.4822	+	1.26866i	0.874779	+	0.0569644i
$497$	−15.9874	+	20.4828i	−0.717133	+	0.918781i
$498$	−0.0539939	+	3.32104i	−0.00241953	+	0.148819i
$499$	3.53169	−	13.1804i	0.158100	−	0.590038i	−0.840720	−	0.541471i	$-0.817868\pi$
$499$	3.53169	−	13.1804i	0.158100	−	0.590038i	0.998820	−	0.0485674i	$-0.0154656\pi$
$500$	2.77109	−	0.646745i	0.123927	−	0.0289233i
$501$	2.29594	+	8.56855i	0.102575	+	0.382815i
$502$	−7.70446	−	2.19924i	−0.343867	−	0.0981571i
$503$			25.2848i			1.12739i	0.825982	+	0.563697i	$0.190621\pi$
$503$			25.2848i			1.12739i	−0.825982	+	0.563697i	$0.809379\pi$
$504$	−7.35156	−	1.39804i	−0.327465	−	0.0622736i
$505$			1.11383i			0.0495648i
$506$	−9.33384	+	32.6986i	−0.414940	+	1.45363i
$507$	−3.35990	−	12.5393i	−0.149218	−	0.556891i
$508$	−0.527524	+	0.848727i	−0.0234051	+	0.0376562i
$509$	−1.59906	+	5.96776i	−0.0708769	+	0.264516i	−0.992267	−	0.124123i	$-0.960388\pi$
$509$	−1.59906	+	5.96776i	−0.0708769	+	0.264516i	0.921390	+	0.388640i	$0.127055\pi$
$510$	−1.04403	−	0.0169740i	−0.0462304	−	0.000751620i
$511$	−14.1496	−	34.9740i	−0.625941	−	1.54716i
$512$	22.3857	+	3.29883i	0.989316	+	0.145789i
$513$	−1.23255	−	2.13483i	−0.0544182	−	0.0942551i
$514$	12.4861	−	20.8367i	0.550737	−	0.919070i
$515$	2.47034	−	0.661925i	0.108856	−	0.0291679i
$516$	−0.521192	−	0.974586i	−0.0229442	−	0.0429037i
$517$	8.39102	−	8.39102i	0.369036	−	0.369036i
$518$	7.86396	−	17.7423i	0.345522	−	0.779553i
$519$		−	10.5150i		−	0.461555i
$520$	−0.0249686	−	0.0485718i	−0.00109495	−	0.00213002i
$521$	−25.7063	−	14.8415i	−1.12621	−	0.650220i	−0.183234	−	0.983069i	$-0.558657\pi$
$521$	−25.7063	−	14.8415i	−1.12621	−	0.650220i	−0.942980	+	0.332850i	$0.891990\pi$
$522$	−3.02820	−	12.0838i	−0.132541	−	0.528894i
$523$	−28.1158	−	7.53361i	−1.22942	−	0.329422i	−0.415066	−	0.909791i	$-0.636241\pi$
$523$	−28.1158	−	7.53361i	−1.22942	−	0.329422i	−0.814353	+	0.580370i	$0.802908\pi$
$524$	29.7689	+	31.7704i	1.30046	+	1.38790i
$525$	7.93386	+	10.5183i	0.346262	+	0.459055i
$526$	0.180205	−	11.0840i	0.00785732	−	0.483286i
$527$	12.6387	+	21.8908i	0.550549	+	0.953579i
$528$	−11.0972	+	16.6234i	−0.482944	+	0.723439i
$529$	0.0781302	−	0.135326i	0.00339697	−	0.00588372i
$530$	0.448084	−	0.249078i	0.0194635	−	0.0108193i
$531$	−5.72201	−	5.72201i	−0.248314	−	0.248314i
$532$	−1.17408	−	12.9911i	−0.0509030	−	0.563235i
$533$	0.564302	−	0.564302i	0.0244426	−	0.0244426i
$534$	−16.5554	−	4.72575i	−0.716422	−	0.204503i
$535$	0.277861	+	0.160423i	0.0120130	+	0.00693571i
$536$	0.815271	−	0.176352i	0.0352144	−	0.00761727i
$537$	−13.2066	+	7.62481i	−0.569905	+	0.329035i
$538$	−11.2957	−	11.6691i	−0.486994	−	0.503091i
$539$	30.5759	−	16.9862i	1.31700	−	0.731649i
$540$	−0.00926910	+	0.284985i	−0.000398878	+	0.0122638i
$541$	8.77264	−	32.7400i	0.377165	−	1.40760i	−0.472990	−	0.881068i	$-0.656825\pi$
$541$	8.77264	−	32.7400i	0.377165	−	1.40760i	0.850155	−	0.526533i	$-0.176508\pi$
$542$	19.6822	−	32.8457i	0.845424	−	1.41084i
$543$	5.76123	−	9.97874i	0.247238	−	0.428229i
$544$	12.5397	+	26.4766i	0.537633	+	1.13518i
$545$	−2.82915			−0.121187
$546$	0.318255	−	0.394355i	0.0136200	−	0.0168768i
$547$	−11.8854	−	11.8854i	−0.508185	−	0.508185i	0.405784	−	0.913969i	$-0.366998\pi$
$547$	−11.8854	−	11.8854i	−0.508185	−	0.508185i	−0.913969	+	0.405784i	$0.866998\pi$
$548$	−38.5680	+	20.6255i	−1.64754	+	0.881078i
$549$	1.17785	+	4.39581i	0.0502696	+	0.187609i
$550$	34.1334	−	8.55381i	1.45545	−	0.364736i
$551$	18.8052	−	10.8572i	0.801129	−	0.462532i
$552$	10.0819	−	9.14356i	0.429116	−	0.389176i
$553$	3.67859	−	26.2644i	0.156430	−	1.11688i
$554$	−4.30142	+	4.16380i	−0.182750	+	0.176903i
$555$	−0.714266	−	0.191387i	−0.0303189	−	0.00812392i
$556$	−8.64146	−	37.0258i	−0.366479	−	1.57024i
$557$	9.45494	−	2.53344i	0.400619	−	0.107345i	−0.0528834	−	0.998601i	$-0.516841\pi$
$557$	9.45494	−	2.53344i	0.400619	−	0.107345i	0.453502	+	0.891255i	$0.350175\pi$
$558$	6.03315	−	3.35367i	0.255403	−	0.141972i
$559$	0.0748418			0.00316547
$560$	−0.677901	+	1.34793i	−0.0286465	+	0.0569604i
$561$	−25.8775			−1.09255
$562$	−12.4181	+	6.90290i	−0.523826	+	0.291181i
$563$	−14.6498	+	3.92540i	−0.617415	+	0.165436i	−0.553953	−	0.832548i	$-0.686881\pi$
$563$	−14.6498	+	3.92540i	−0.617415	+	0.165436i	−0.0634629	+	0.997984i	$0.520214\pi$
$564$	−4.62543	+	1.07953i	−0.194766	+	0.0454565i
$565$	−1.28556	−	0.344465i	−0.0540840	−	0.0144918i
$566$	23.0208	−	22.2842i	0.967637	−	0.936677i
$567$	−2.45263	+	0.992272i	−0.103001	+	0.0416715i
$568$	1.35418	−	27.7445i	0.0568201	−	1.16414i
$569$	−14.5222	+	8.38437i	−0.608800	+	0.351491i	−0.772496	−	0.635020i	$-0.780992\pi$
$569$	−14.5222	+	8.38437i	−0.608800	+	0.351491i	0.163695	+	0.986511i	$0.447659\pi$
$570$	−0.482107	+	0.120816i	−0.0201933	+	0.00506042i
$571$	3.08681	+	11.5201i	0.129179	+	0.482102i	0.999954	−	0.00957925i	$-0.00304922\pi$
$571$	3.08681	+	11.5201i	0.129179	+	0.482102i	−0.870775	+	0.491681i	$0.836383\pi$
$572$	−0.638283	−	1.19354i	−0.0266879	−	0.0499042i
$573$	7.49450	+	7.49450i	0.313087	+	0.313087i
$574$	−21.7816	−	3.41263i	−0.909146	−	0.142440i
$575$	−23.9627			−0.999312
$576$	7.28481	−	3.30628i	0.303534	−	0.137762i
$577$	−12.5849	+	21.7976i	−0.523915	+	0.907447i	0.475698	+	0.879609i	$0.342196\pi$
$577$	−12.5849	+	21.7976i	−0.523915	+	0.907447i	−0.999612	+	0.0278382i	$0.991138\pi$
$578$	−7.13874	+	11.9131i	−0.296932	+	0.495521i
$579$	1.64645	−	6.14462i	0.0684240	−	0.255362i
$580$	−2.51036	−	0.0816493i	−0.104237	−	0.00339030i
$581$	0.760194	+	6.16724i	0.0315382	+	0.255860i
$582$	−12.3824	−	12.7916i	−0.513265	−	0.530231i
$583$	11.0030	−	6.35261i	0.455699	−	0.263098i
$584$	33.9045	+	21.8452i	1.40298	+	0.903962i
$585$	−0.0167220	−	0.00965443i	−0.000691368	−	0.000399161i
$586$	−31.8402	−	9.08882i	−1.31531	−	0.375456i
$587$	−23.0438	+	23.0438i	−0.951118	+	0.951118i	−0.998860	−	0.0477416i	$-0.984798\pi$
$587$	−23.0438	+	23.0438i	−0.951118	+	0.951118i	0.0477416	+	0.998860i	$0.484798\pi$
$588$	−13.9832	−	0.686056i	−0.576657	−	0.0282925i
$589$	8.50777	+	8.50777i	0.350557	+	0.350557i
$590$	−1.42604	+	0.792697i	−0.0587090	+	0.0326348i
$591$	−4.73317	+	8.19809i	−0.194697	+	0.337224i
$592$	4.05614	+	20.3466i	0.166706	+	0.836240i
$593$	18.9664	+	32.8508i	0.778858	+	1.34902i	0.932600	+	0.360911i	$0.117534\pi$
$593$	18.9664	+	32.8508i	0.778858	+	1.34902i	−0.153742	+	0.988111i	$0.549133\pi$
$594$	−0.114873	+	7.06557i	−0.00471330	+	0.289904i
$595$	−1.93878	+	0.238981i	−0.0794824	+	0.00979725i
$596$	21.8025	−	20.4289i	0.893065	−	0.836801i
$597$	19.8977	+	5.33156i	0.814357	+	0.218206i
$598$	0.224047	+	0.894043i	0.00916195	+	0.0365601i
$599$	−35.4478	−	20.4658i	−1.44836	−	0.836210i	−0.449975	−	0.893041i	$-0.648567\pi$
$599$	−35.4478	−	20.4658i	−1.44836	−	0.836210i	−0.998384	+	0.0568307i	$0.981900\pi$
$600$	−13.4108	−	4.30428i	−0.547495	−	0.175722i
$601$			37.1917i			1.51708i	0.651625	+	0.758541i	$0.274088\pi$
$601$			37.1917i			1.51708i	−0.651625	+	0.758541i	$0.725912\pi$
$602$	−1.21811	−	1.67072i	−0.0496466	−	0.0680935i
$603$	0.208532	−	0.208532i	0.00849207	−	0.00849207i
$604$	15.2512	−	8.15608i	0.620562	−	0.331866i
$605$	−1.92350	+	0.515399i	−0.0782013	+	0.0209540i
$606$	5.67919	−	9.47743i	0.230701	−	0.384994i
$607$	−5.19794	−	9.00310i	−0.210978	−	0.365424i	0.741043	−	0.671458i	$-0.234331\pi$
$607$	−5.19794	−	9.00310i	−0.210978	−	0.365424i	−0.952021	+	0.306033i	$0.900998\pi$
$608$	9.02721	+	10.6284i	0.366102	+	0.431039i
$609$	−8.74069	−	21.6046i	−0.354191	−	0.875464i
$610$	0.917433	+	0.0149157i	0.0371458	+	0.000603921i
$611$	0.0832475	−	0.310684i	0.00336783	−	0.0125689i
$612$	8.79694	+	5.46771i	0.355595	+	0.221019i
$613$	5.85588	+	21.8544i	0.236517	+	0.882693i	0.977459	+	0.211124i	$0.0677124\pi$
$613$	5.85588	+	21.8544i	0.236517	+	0.882693i	−0.740942	+	0.671568i	$0.765621\pi$
$614$	5.29675	−	18.5557i	0.213760	−	0.748849i
$615$			0.840065i			0.0338747i
$616$	−16.2551	+	33.6744i	−0.654938	+	1.35678i
$617$		−	18.1714i		−	0.731555i	−0.930702	−	0.365777i	$-0.880803\pi$
$617$		−	18.1714i		−	0.731555i	0.930702	−	0.365777i	$-0.119197\pi$
$618$	−24.3947	−	6.96350i	−0.981300	−	0.280113i
$619$	6.88682	+	25.7020i	0.276805	+	1.03305i	0.954622	+	0.297819i	$0.0962592\pi$
$619$	6.88682	+	25.7020i	0.276805	+	1.03305i	−0.677818	+	0.735230i	$0.737074\pi$
$620$	−0.316311	−	1.35529i	−0.0127034	−	0.0544297i
$621$	1.24546	−	4.64813i	0.0499787	−	0.186523i
$622$	−0.662661	+	40.7587i	−0.0265703	+	1.63428i
$623$	−31.8981	−	4.46765i	−1.27797	−	0.178993i
$624$	−0.0352031	+	0.540600i	−0.00140925	+	0.0216413i
$625$	12.3478	+	21.3870i	0.493911	+	0.855478i
$626$	−0.416408	−	0.249526i	−0.0166430	−	0.00997304i
$627$	−11.8978	+	3.18800i	−0.475152	+	0.127317i
$628$	−3.17648	+	10.4794i	−0.126755	+	0.418175i
$629$	−18.9939	+	18.9939i	−0.757334	+	0.757334i
$630$	0.0566445	+	0.530424i	0.00225677	+	0.0211326i
$631$			4.93700i			0.196539i	0.995160	+	0.0982694i	$0.0313307\pi$
$631$			4.93700i			0.196539i	−0.995160	+	0.0982694i	$0.968669\pi$
$632$	12.9621	+	25.2153i	0.515604	+	1.00301i
$633$	0.568909	+	0.328460i	0.0226121	+	0.0130551i
$634$	0.660886	−	0.165618i	0.0262471	−	0.00657752i
$635$	0.0688074	+	0.0184369i	0.00273054	+	0.000731646i
$636$	−5.08268	−	0.165313i	−0.201541	−	0.00655511i
$637$	0.487517	−	0.813101i	0.0193161	−	0.0322162i
$638$	−62.2389	−	1.01189i	−2.46406	−	0.0400611i
$639$	−4.91043	−	8.50511i	−0.194253	−	0.336457i
$640$	−0.237853	−	1.59534i	−0.00940197	−	0.0630612i
$641$	4.01060	−	6.94657i	0.158409	−	0.274373i	−0.775886	−	0.630873i	$-0.782697\pi$
$641$	4.01060	−	6.94657i	0.158409	−	0.274373i	0.934295	+	0.356500i	$0.116030\pi$
$642$	−1.54632	−	2.78178i	−0.0610283	−	0.109788i
$643$	−25.2361	−	25.2361i	−0.995215	−	0.995215i	0.00477361	−	0.999989i	$-0.498481\pi$
$643$	−25.2361	−	25.2361i	−0.995215	−	0.995215i	−0.999989	+	0.00477361i	$0.998481\pi$
$644$	16.3115	−	19.5528i	0.642763	−	0.770487i
$645$	−0.0557078	+	0.0557078i	−0.00219349	+	0.00219349i
$646$	−4.95568	+	17.3609i	−0.194979	+	0.683055i
$647$	30.8905	+	17.8346i	1.21443	+	0.701152i	0.963721	−	0.266910i	$-0.0860027\pi$
$647$	30.8905	+	17.8346i	1.21443	+	0.701152i	0.250710	+	0.968062i	$0.419336\pi$
$648$	1.53195	−	2.37763i	0.0601805	−	0.0934023i
$649$	−35.0174	+	20.2173i	−1.37455	+	0.793598i
$650$	0.685303	−	0.663376i	0.0268798	−	0.0260197i
$651$	10.3096	−	7.77645i	0.404065	−	0.304783i
$652$	−16.4651	−	17.5722i	−0.644824	−	0.688180i
$653$	8.65629	−	32.3057i	0.338747	−	1.26422i	−0.561003	−	0.827814i	$-0.689584\pi$
$653$	8.65629	−	32.3057i	0.338747	−	1.26422i	0.899750	−	0.436406i	$-0.143749\pi$
$654$	24.0728	+	14.4252i	0.941321	+	0.564071i
$655$	1.55177	−	2.68775i	0.0606328	−	0.105019i
$656$	21.1345	−	10.4335i	0.825163	−	0.407359i
$657$	14.2598			0.556327
$658$	−8.29043	+	3.19827i	−0.323194	+	0.124682i
$659$	13.6657	+	13.6657i	0.532340	+	0.532340i	0.921268	−	0.388928i	$-0.127155\pi$
$659$	13.6657	+	13.6657i	0.532340	+	0.532340i	−0.388928	+	0.921268i	$0.627155\pi$
$660$	1.36350	+	0.413297i	0.0530740	+	0.0160876i
$661$	9.28075	+	34.6362i	0.360979	+	1.34719i	0.872790	+	0.488095i	$0.162308\pi$
$661$	9.28075	+	34.6362i	0.360979	+	1.34719i	−0.511811	+	0.859098i	$0.671025\pi$
$662$	6.56152	+	26.1833i	0.255021	+	1.01764i
$663$	−0.607434	+	0.350702i	−0.0235908	+	0.0136201i
$664$	−4.46270	−	4.92069i	−0.173186	−	0.190960i
$665$	−0.861959	+	0.348727i	−0.0334253	+	0.0135230i
$666$	5.10174	+	5.27037i	0.197688	+	0.204223i
$667$	40.9442	+	10.9710i	1.58537	+	0.424798i
$668$	−15.0682	−	9.36560i	−0.583007	−	0.362366i
$669$	−8.19750	+	2.19651i	−0.316934	+	0.0849222i
$670$	−0.0288889	−	0.0519702i	−0.00111608	−	0.00200778i
$671$	22.7397			0.877857
$672$	12.6410	−	8.01286i	0.487636	−	0.309103i
$673$	8.54935			0.329553			0.164777	−	0.986331i	$-0.447310\pi$
$673$	8.54935			0.329553			0.164777	+	0.986331i	$0.447310\pi$
$674$	−11.1372	−	20.0354i	−0.428988	−	0.771735i
$675$	−4.81000	+	1.28883i	−0.185137	+	0.0496073i
$676$	22.0510	+	13.7057i	0.848115	+	0.527143i
$677$	11.5242	+	3.08790i	0.442910	+	0.118677i	0.473380	−	0.880858i	$-0.343034\pi$
$677$	11.5242	+	3.08790i	0.442910	+	0.118677i	−0.0304699	+	0.999536i	$0.509700\pi$
$678$	9.18230	+	9.48581i	0.352644	+	0.364300i
$679$	−26.2555	−	20.4931i	−1.00759	−	0.786454i
$680$	1.54691	−	1.40293i	0.0593212	−	0.0537999i
$681$	6.96939	−	4.02378i	0.267068	−	0.154192i
$682$	−8.38411	−	33.4562i	−0.321044	−	1.28110i
$683$	13.3090	+	49.6698i	0.509255	+	1.90056i	0.427766	+	0.903889i	$0.359301\pi$
$683$	13.3090	+	49.6698i	0.509255	+	1.90056i	0.0814882	+	0.996674i	$0.474033\pi$
$684$	4.71819	+	1.43016i	0.180405	+	0.0546835i
$685$	2.20456	+	2.20456i	0.0842321	+	0.0842321i
$686$	−26.0859	+	2.35087i	−0.995964	+	0.0897567i
$687$	−0.801761			−0.0305891
$688$	2.09339	+	0.709622i	0.0798096	+	0.0270541i
$689$	0.172186	−	0.298234i	0.00655975	−	0.0113618i
$690$	−0.832239	−	0.498705i	−0.0316828	−	0.0189854i
$691$	−10.0762	+	37.6049i	−0.383317	+	1.43056i	0.457487	+	0.889217i	$0.348750\pi$
$691$	−10.0762	+	37.6049i	−0.383317	+	1.43056i	−0.840803	+	0.541341i	$0.817917\pi$
$692$	14.3791	+	15.3459i	0.546612	+	0.583365i
$693$	1.61733	+	13.1209i	0.0614372	+	0.498422i
$694$	19.1702	−	18.5569i	0.727692	−	0.704409i
$695$	−2.34716	+	1.35514i	−0.0890330	+	0.0514032i
$696$	20.9440	+	13.4946i	0.793880	+	0.511510i
$697$	26.4275	+	15.2579i	1.00101	+	0.577934i
$698$	−11.0128	+	38.5803i	−0.416840	+	1.46029i
$699$	1.25410	−	1.25410i	0.0474345	−	0.0474345i
$700$	−25.9626	−	4.50127i	−0.981296	−	0.170132i
$701$	26.5728	+	26.5728i	1.00364	+	1.00364i	0.999993	+	0.00364808i	$0.00116122\pi$
$701$	26.5728	+	26.5728i	1.00364	+	1.00364i	0.00364808	+	0.999993i	$0.498839\pi$
$702$	0.0930588	+	0.167410i	0.00351228	+	0.00631847i
$703$	−6.39290	+	11.0728i	−0.241113	+	0.417619i
$704$	−6.53664	−	39.4361i	−0.246359	−	1.48630i
$705$	0.169290	+	0.293219i	0.00637583	+	0.0110433i
$706$	−19.9920	−	0.325033i	−0.752410	−	0.0122328i
$707$	8.06756	−	19.0309i	0.303412	−	0.715732i
$708$	16.1757	+	0.526113i	0.607921	+	0.0197726i
$709$	−15.0987	−	4.04567i	−0.567042	−	0.151938i	−0.0361025	−	0.999348i	$-0.511494\pi$
$709$	−15.0987	−	4.04567i	−0.567042	−	0.151938i	−0.530940	+	0.847410i	$0.678161\pi$
$710$	−1.92070	+	0.481327i	−0.0720826	+	0.0180639i
$711$	8.68095	+	5.01195i	0.325561	+	0.187963i
$712$	30.6240	−	15.7425i	1.14768	−	0.589973i
$713$			23.4873i			0.879604i
$714$	17.7153	+	7.85199i	0.662980	+	0.293853i
$715$	−0.0682230	+	0.0682230i	−0.00255140	+	0.00255140i
$716$	8.84729	−	29.1878i	0.330639	−	1.09080i
$717$	−13.6575	+	3.65951i	−0.510048	+	0.136667i
$718$	1.93962	+	1.16228i	0.0723859	+	0.0433761i
$719$	2.02122	+	3.50085i	0.0753788	+	0.130560i	0.901251	−	0.433298i	$-0.142650\pi$
$719$	2.02122	+	3.50085i	0.0753788	+	0.130560i	−0.825872	+	0.563857i	$0.809317\pi$
$720$	−0.376187	−	0.428593i	−0.0140197	−	0.0159727i
$721$	−47.0025	−	6.58318i	−1.75047	−	0.245170i
$722$	0.297100	−	18.2739i	0.0110569	−	0.680085i
$723$	0.0940504	−	0.351001i	0.00349777	−	0.0130539i
$724$	5.23770	+	22.4418i	0.194658	+	0.834043i
$725$	−11.3530	−	42.3701i	−0.421641	−	1.57359i
$726$	18.9947	+	5.42204i	0.704958	+	0.201231i
$727$		−	31.6328i		−	1.17320i	−0.809879	−	0.586598i	$-0.800467\pi$
$727$		−	31.6328i		−	1.17320i	0.809879	−	0.586598i	$-0.199533\pi$
$728$	0.0748046	+	1.01075i	0.00277244	+	0.0374608i
$729$		−	1.00000i		−	0.0370370i
$730$	0.789171	−	2.76465i	0.0292085	−	0.102324i
$731$	0.740694	+	2.76431i	0.0273956	+	0.102242i
$732$	−7.73025	−	4.80471i	−0.285718	−	0.177587i
$733$	−0.292365	+	1.09112i	−0.0107988	+	0.0403015i	−0.971115	−	0.238612i	$-0.923308\pi$
$733$	−0.292365	+	1.09112i	−0.0107988	+	0.0403015i	0.960316	+	0.278913i	$0.0899743\pi$
$734$	−10.5848	−	0.172089i	−0.390691	−	0.00635192i
$735$	0.242345	+	0.968102i	0.00893903	+	0.0357090i
$736$	−2.21021	+	27.1314i	−0.0814694	+	1.00008i
$737$	−0.736795	−	1.27617i	−0.0271402	−	0.0470082i
$738$	4.28331	−	7.14799i	0.157671	−	0.263121i
$739$	−16.5235	+	4.42747i	−0.607828	+	0.162867i	−0.549589	−	0.835436i	$-0.685215\pi$
$739$	−16.5235	+	4.42747i	−0.607828	+	0.162867i	−0.0582399	+	0.998303i	$0.518549\pi$
$740$	1.30415	−	0.697436i	0.0479414	−	0.0256383i
$741$	−0.236077	+	0.236077i	−0.00867249	+	0.00867249i
$742$	−9.46006	+	1.01025i	−0.347290	+	0.0370874i
$743$		−	6.36981i		−	0.233686i	−0.993150	−	0.116843i	$-0.962723\pi$
$743$		−	6.36981i		−	0.233686i	0.993150	−	0.116843i	$-0.0372774\pi$
$744$	−4.21888	+	13.1448i	−0.154672	+	0.481910i
$745$	−1.84447	−	1.06491i	−0.0675762	−	0.0390152i
$746$	6.11689	+	24.4090i	0.223955	+	0.893678i
$747$	−2.26861	−	0.607873i	−0.0830042	−	0.0222409i
$748$	37.7667	−	35.3874i	1.38089	−	1.29389i
$749$	−3.58558	−	4.75357i	−0.131014	−	0.173692i
$750$	−0.0327089	+	2.01185i	−0.00119436	+	0.0734623i
$751$	−6.47389	−	11.2131i	−0.236236	−	0.409172i	0.723395	−	0.690434i	$-0.242580\pi$
$751$	−6.47389	−	11.2131i	−0.236236	−	0.409172i	−0.959631	+	0.281262i	$0.909247\pi$
$752$	5.27429	−	7.90076i	0.192333	−	0.288111i
$753$	2.83274	−	4.90645i	0.103231	−	0.178801i
$754$	−1.47467	+	0.819733i	−0.0537044	+	0.0298529i
$755$	−0.871765	−	0.871765i	−0.0317268	−	0.0317268i
$756$	2.22254	−	4.80212i	0.0808329	−	0.174651i
$757$	−24.1962	+	24.1962i	−0.879425	+	0.879425i	−0.993475	−	0.114050i	$-0.963617\pi$
$757$	−24.1962	+	24.1962i	−0.879425	+	0.879425i	0.114050	+	0.993475i	$0.463617\pi$
$758$	−9.31564	−	2.65916i	−0.338359	−	0.0965850i
$759$	−20.8235	−	12.0225i	−0.755847	−	0.436388i
$760$	0.538391	−	0.835602i	0.0195295	−	0.0303105i
$761$	−10.6629	+	6.15624i	−0.386530	+	0.223163i	−0.680656	−	0.732603i	$-0.738305\pi$
$761$	−10.6629	+	6.15624i	−0.386530	+	0.223163i	0.294125	+	0.955767i	$0.404972\pi$
$762$	−0.491466	−	0.507711i	−0.0178039	−	0.0183924i
$763$	48.3389	+	20.4917i	1.74998	+	0.741850i
$764$	−21.1865	−	0.689087i	−0.766499	−	0.0249303i
$765$	0.191096	−	0.713179i	0.00690908	−	0.0257850i
$766$	−6.45299	+	10.7688i	−0.233156	+	0.389091i
$767$	−0.547985	+	0.949137i	−0.0197866	+	0.0342714i
$768$	−6.11043	+	14.7872i	−0.220491	+	0.533589i
$769$	35.1091			1.26607			0.633033	−	0.774125i	$-0.281810\pi$
$769$	35.1091			1.26607			0.633033	+	0.774125i	$0.281810\pi$
$770$	2.63335	+	0.412580i	0.0948995	+	0.0148684i
$771$	12.1457	+	12.1457i	0.437417	+	0.437417i
$772$	5.99984	+	11.2192i	0.215939	+	0.403788i
$773$	−12.0142	−	44.8375i	−0.432120	−	1.61269i	−0.747866	−	0.663850i	$-0.768921\pi$
$773$	−12.0142	−	44.8375i	−0.432120	−	1.61269i	0.315746	−	0.948844i	$-0.397745\pi$
$774$	0.758051	−	0.189967i	0.0272476	−	0.00682823i
$775$	21.0489	−	12.1526i	0.756099	−	0.436534i
$776$	35.5638	+	1.73583i	1.27667	+	0.0623125i
$777$	10.8177	+	8.44352i	0.388084	+	0.302910i
$778$	23.1939	−	22.4518i	0.831542	−	0.804936i
$779$	14.0303	+	3.75942i	0.502689	+	0.134695i
$780$	0.0376070	−	0.00877712i	0.00134655	−	0.000314271i
$781$	−47.4005	+	12.7009i	−1.69612	+	0.454475i
$782$	−30.8044	+	17.1234i	−1.10156	+	0.612332i
$783$	8.80876			0.314799
$784$	21.3458	−	18.1206i	0.762349	−	0.647166i
$785$	0.780578			0.0278600
$786$	−26.9081	+	14.9575i	−0.959780	+	0.533517i
$787$	−29.7555	+	7.97296i	−1.06067	+	0.284205i	−0.746654	−	0.665213i	$-0.768341\pi$
$787$	−29.7555	+	7.97296i	−1.06067	+	0.284205i	−0.314015	+	0.949418i	$0.601674\pi$
$788$	−4.30306	−	18.4372i	−0.153290	−	0.656798i
$789$	7.57152	+	2.02878i	0.269553	+	0.0722265i
$790$	1.45213	−	1.40567i	0.0516644	−	0.0500113i
$791$	19.4701	+	15.1970i	0.692278	+	0.540341i
$792$	−9.49447	−	10.4689i	−0.337371	−	0.371995i
$793$	0.533778	−	0.308177i	0.0189550	−	0.0109437i
$794$	−48.1988	+	12.0786i	−1.71051	+	0.428653i
$795$	0.0938231	+	0.350153i	0.00332756	+	0.0124186i
$796$	−36.3303	+	19.4288i	−1.28769	+	0.688637i
$797$	−13.9401	−	13.9401i	−0.493783	−	0.493783i	0.415713	−	0.909496i	$-0.363532\pi$
$797$	−13.9401	−	13.9401i	−0.493783	−	0.493783i	−0.909496	+	0.415713i	$0.863532\pi$
$798$	9.11236	+	1.42768i	0.322574	+	0.0505393i
$799$	12.2991			0.435111
$800$	25.4584	−	12.0574i	0.900089	−	0.426293i
$801$	6.08701	−	10.5430i	0.215074	−	0.372519i
$802$	−19.0335	+	31.7631i	−0.672096	+	1.12159i
$803$	18.4416	−	68.8250i	0.650790	−	2.42878i
$804$	−0.0191736	+	0.589505i	−0.000676200	+	0.0207902i
$805$	−1.67116	−	0.708435i	−0.0589006	−	0.0249690i
$806$	−0.650215	−	0.671707i	−0.0229028	−	0.0236599i
$807$	9.94538	−	5.74197i	0.350094	−	0.202127i
$808$	4.67189	+	21.5980i	0.164356	+	0.759814i
$809$	20.2704	+	11.7031i	0.712668	+	0.411459i	0.812048	−	0.583591i	$-0.198353\pi$
$809$	20.2704	+	11.7031i	0.712668	+	0.411459i	−0.0993802	+	0.995050i	$0.531686\pi$
$810$	−0.193877	−	0.0553424i	−0.00681215	−	0.00194453i
$811$	17.2887	−	17.2887i	0.607088	−	0.607088i	−0.335096	−	0.942184i	$-0.608769\pi$
$811$	17.2887	−	17.2887i	0.607088	−	0.607088i	0.942184	+	0.335096i	$0.108769\pi$
$812$	42.3007	+	19.5778i	1.48446	+	0.687046i
$813$	19.1457	+	19.1457i	0.671469	+	0.671469i
$814$	32.0354	−	17.8077i	1.12284	−	0.624158i
$815$	−0.858284	+	1.48659i	−0.0300644	+	0.0520731i
$816$	−20.3156	+	4.04997i	−0.711190	+	0.141777i
$817$	0.681102	+	1.17970i	0.0238287	+	0.0412726i
$818$	−0.479677	+	29.5038i	−0.0167715	+	1.03158i
$819$	0.215784	+	0.286074i	0.00754009	+	0.00999623i
$820$	−1.14878	−	1.22602i	−0.0401172	−	0.0428146i
$821$	24.2646	+	6.50167i	0.846839	+	0.226910i	0.656047	−	0.754720i	$-0.272227\pi$
$821$	24.2646	+	6.50167i	0.846839	+	0.226910i	0.190793	+	0.981630i	$0.438894\pi$
$822$	−7.51771	−	29.9989i	−0.262210	−	1.04633i
$823$	−4.41178	−	2.54714i	−0.153785	−	0.0887879i	0.421133	−	0.906999i	$-0.361633\pi$
$823$	−4.41178	−	2.54714i	−0.153785	−	0.0887879i	−0.574918	+	0.818211i	$0.694966\pi$
$824$	45.1252	−	23.1968i	1.57201	−	0.808100i
$825$			24.8823i			0.866291i
$826$	30.1068	−	3.21514i	1.04755	−	0.111869i
$827$	−19.8436	+	19.8436i	−0.690030	+	0.690030i	−0.962238	−	0.272208i	$-0.912246\pi$
$827$	−19.8436	+	19.8436i	−0.690030	+	0.690030i	0.272208	+	0.962238i	$0.412246\pi$
$828$	4.53861	+	8.48682i	0.157728	+	0.294937i
$829$	−19.5877	+	5.24851i	−0.680309	+	0.182288i	−0.582394	−	0.812907i	$-0.697884\pi$
$829$	−19.5877	+	5.24851i	−0.680309	+	0.182288i	−0.0979148	+	0.995195i	$0.531217\pi$
$830$	−0.243403	+	0.406191i	−0.00844865	+	0.0140991i
$831$	−2.11658	−	3.66603i	−0.0734235	−	0.127173i
$832$	−0.687890	−	0.837113i	−0.0238483	−	0.0290217i
$833$	34.8570	+	9.95952i	1.20772	+	0.345077i
$834$	26.8812	+	0.437039i	0.930821	+	0.0151334i
$835$	−0.327327	+	1.22160i	−0.0113276	+	0.0422752i
$836$	13.0045	−	20.9229i	0.449771	−	0.723632i
$837$	1.26326	+	4.71457i	0.0436648	+	0.162959i
$838$	5.99029	−	20.9854i	0.206931	−	0.724928i
$839$		−	3.06714i		−	0.105889i	−0.998597	−	0.0529447i	$-0.983139\pi$
$839$		−	3.06714i		−	0.105889i	0.998597	−	0.0529447i	$-0.0168607\pi$
$840$	−0.808020	−	0.696660i	−0.0278793	−	0.0240371i
$841$			48.5943i			1.67566i
$842$	20.7932	+	5.93543i	0.716580	+	0.204548i
$843$	−2.60019	−	9.70405i	−0.0895553	−	0.334225i
$844$	−1.27945	+	0.298612i	−0.0440406	+	0.0102787i
$845$	0.479014	−	1.78770i	0.0164786	−	0.0614988i
$846$	0.0545969	−	3.35813i	0.00187708	−	0.115455i
$847$	36.5980	+	5.12591i	1.25752	+	0.176128i
$848$	7.64392	−	6.70926i	0.262493	−	0.230397i
$849$	11.3278	+	19.6203i	0.388768	+	0.673366i
$850$	31.2843	+	18.7466i	1.07304	+	0.643003i
$851$	−24.1086	+	6.45989i	−0.826433	+	0.221442i
$852$	18.7971	+	5.69771i	0.643980	+	0.195200i
$853$	31.2169	−	31.2169i	1.06885	−	1.06885i	0.0713978	−	0.997448i	$-0.477254\pi$
$853$	31.2169	−	31.2169i	1.06885	−	1.06885i	0.997448	−	0.0713978i	$-0.0227460\pi$
$854$	−15.5672	−	6.89988i	−0.532699	−	0.236109i
$855$		−	0.351443i		−	0.0120191i
$856$	6.06082	+	1.94525i	0.207154	+	0.0664874i
$857$	−27.1179	−	15.6565i	−0.926330	−	0.534817i	−0.0406811	−	0.999172i	$-0.512953\pi$
$857$	−27.1179	−	15.6565i	−0.926330	−	0.534817i	−0.885649	+	0.464355i	$0.846286\pi$
$858$	0.928355	−	0.232645i	0.0316935	−	0.00794237i
$859$	−42.0363	−	11.2636i	−1.43426	−	0.384309i	−0.543741	−	0.839253i	$-0.682993\pi$
$859$	−42.0363	−	11.2636i	−1.43426	−	0.384309i	−0.890520	+	0.454944i	$0.849659\pi$
$860$	0.00512208	−	0.157482i	0.000174662	−	0.00537009i
$861$	6.08465	−	14.3534i	0.207364	−	0.489161i
$862$	−48.4382	−	0.787515i	−1.64981	−	0.0268229i
$863$	−18.3075	−	31.7095i	−0.623195	−	1.07941i	−0.988887	−	0.148669i	$-0.952501\pi$
$863$	−18.3075	−	31.7095i	−0.623195	−	1.07941i	0.365692	−	0.930736i	$-0.380832\pi$
$864$	1.01562	+	5.56494i	0.0345519	+	0.189323i
$865$	0.749547	−	1.29825i	0.0254854	−	0.0441419i
$866$	−23.2817	−	41.8830i	−0.791143	−	1.42324i
$867$	−6.94414	−	6.94414i	−0.235835	−	0.235835i
$868$	−4.41196	+	25.4476i	−0.149752	+	0.863746i
$869$	35.4170	−	35.4170i	1.20144	−	1.20144i
$870$	0.487498	−	1.70782i	0.0165277	−	0.0579005i
$871$	−0.0345902	−	0.0199706i	−0.00117204	−	0.000676680i
$872$	−54.8592	+	11.8667i	−1.85777	+	0.401856i
$873$	10.9021	−	6.29433i	0.368980	−	0.213031i
$874$	−12.0535	+	11.6679i	−0.407716	+	0.394671i
$875$	0.460517	+	3.73605i	0.0155683	+	0.126301i
$876$	−20.8113	+	19.5002i	−0.703148	+	0.658849i
$877$	−0.494557	+	1.84571i	−0.0167000	+	0.0623252i	−0.973773	−	0.227522i	$-0.926938\pi$
$877$	−0.494557	+	1.84571i	−0.0167000	+	0.0623252i	0.957073	+	0.289847i	$0.0936044\pi$
$878$	26.3272	+	15.7761i	0.888499	+	0.532418i
$879$	11.7069	−	20.2769i	0.394863	−	0.683922i
$880$	−2.55512	+	1.26139i	−0.0861331	+	0.0425214i
$881$	−33.9062			−1.14233			−0.571164	−	0.820836i	$-0.693508\pi$
$881$	−33.9062			−1.14233			−0.571164	+	0.820836i	$0.693508\pi$
$882$	2.87407	−	9.47311i	0.0967750	−	0.318976i
$883$	35.2802	+	35.2802i	1.18727	+	1.18727i	0.977818	+	0.209455i	$0.0671689\pi$
$883$	35.2802	+	35.2802i	1.18727	+	1.18727i	0.209455	+	0.977818i	$0.432831\pi$
$884$	0.406930	−	1.34249i	0.0136865	−	0.0451528i
$885$	−0.298594	−	1.11437i	−0.0100371	−	0.0374591i
$886$	−6.76577	−	26.9984i	−0.227301	−	0.907028i
$887$	−10.1685	+	5.87076i	−0.341423	+	0.197121i	−0.660901	−	0.750473i	$-0.729826\pi$
$887$	−10.1685	+	5.87076i	−0.341423	+	0.197121i	0.319478	+	0.947594i	$0.396492\pi$
$888$	−14.6529	−	0.715190i	−0.491718	−	0.0240002i
$889$	−1.04210	−	0.813390i	−0.0349510	−	0.0272802i
$890$	−1.70718	−	1.76361i	−0.0572248	−	0.0591163i
$891$	−4.82651	−	1.29326i	−0.161694	−	0.0433258i
$892$	8.96004	−	14.4157i	0.300004	−	0.482674i
$893$	5.65479	−	1.51520i	0.189230	−	0.0507041i
$894$	10.2646	+	18.4657i	0.343300	+	0.617586i
$895$	−2.17411			−0.0726724
$896$	−7.49118	+	28.9807i	−0.250263	+	0.968178i
$897$	−0.651732			−0.0217607
$898$	−5.37404	−	9.66773i	−0.179334	−	0.322616i
$899$	−41.5295	+	11.1278i	−1.38509	+	0.371133i
$900$	5.25742	−	8.45861i	0.175247	−	0.281954i
$901$	12.7195	+	3.40817i	0.423747	+	0.113543i
$902$	−28.9604	−	29.9177i	−0.964277	−	0.996149i
$903$	1.35532	−	0.548328i	0.0451022	−	0.0182472i
$904$	−26.3728	−	1.28722i	−0.877146	−	0.0428125i
$905$	1.42265	−	0.821365i	0.0472904	−	0.0273031i
$906$	2.97278	+	11.8627i	0.0987639	+	0.394111i
$907$	−12.9212	−	48.2227i	−0.429043	−	1.60121i	−0.754933	−	0.655802i	$-0.772331\pi$
$907$	−12.9212	−	48.2227i	−0.429043	−	1.60121i	0.325890	−	0.945408i	$-0.394336\pi$
$908$	−4.66891	+	15.4031i	−0.154943	+	0.511168i
$909$	5.52437	+	5.52437i	0.183232	+	0.183232i
$910$	0.0674052	−	0.0260035i	0.00223446	−	0.000862008i
$911$	0.183986			0.00609572			0.00304786	−	0.999995i	$-0.499030\pi$
$911$	0.183986			0.00609572			0.00304786	+	0.999995i	$0.499030\pi$
$912$	−8.84165	+	4.36487i	−0.292776	+	0.144535i
$913$	−5.86781	+	10.1633i	−0.194196	+	0.336358i
$914$	39.9434	+	23.9354i	1.32121	+	0.791713i
$915$	−0.167924	+	0.626701i	−0.00555140	+	0.0207181i
$916$	1.17012	−	1.09640i	0.0386619	−	0.0362262i
$917$	−45.9812	+	34.6833i	−1.51843	+	1.14534i
$918$	−5.26235	+	5.09398i	−0.173684	+	0.168126i
$919$	−35.0067	+	20.2112i	−1.15477	+	0.666704i	−0.950044	−	0.312116i	$-0.898962\pi$
$919$	−35.0067	+	20.2112i	−1.15477	+	0.666704i	−0.204722	+	0.978820i	$0.565629\pi$
$920$	1.89658	−	0.410251i	0.0625283	−	0.0135256i
$921$	11.8169	+	6.82249i	0.389380	+	0.224809i
$922$	2.43776	−	8.54003i	0.0802833	−	0.281251i
$923$	−0.940523	+	0.940523i	−0.0309577	+	0.0309577i
$924$	−20.3032	−	16.9375i	−0.667925	−	0.557203i
$925$	18.2634	+	18.2634i	0.600495	+	0.600495i
$926$	18.4312	+	33.1571i	0.605686	+	1.08961i
$927$	8.96935	−	15.5354i	0.294592	−	0.510248i
$928$	−49.0202	+	8.94631i	−1.60917	+	0.293677i
$929$	−1.81799	−	3.14886i	−0.0596465	−	0.103311i	0.834660	−	0.550765i	$-0.185664\pi$
$929$	−1.81799	−	3.14886i	−0.0596465	−	0.103311i	−0.894307	+	0.447454i	$0.852331\pi$
$930$	0.983959	+	0.0159973i	0.0322653	+	0.000524574i
$931$	17.2533	+	0.284882i	0.565454	+	0.00933661i
$932$	−0.115309	+	3.54526i	−0.00377708	+	0.116129i
$933$	−27.8424	−	7.46035i	−0.911520	−	0.244241i
$934$	25.9516	−	6.50346i	0.849164	−	0.212800i
$935$	−3.19503	−	1.84465i	−0.104489	−	0.0603266i
$936$	−0.364745	−	0.117067i	−0.0119221	−	0.00382646i
$937$		−	56.0184i		−	1.83004i	−0.403405	−	0.915021i	$-0.632174\pi$
$937$		−	56.0184i		−	1.83004i	0.403405	−	0.915021i	$-0.367826\pi$
$938$	0.117172	+	1.09721i	0.00382580	+	0.0358251i
$939$	0.242723	−	0.242723i	0.00792098	−	0.00792098i
$940$	−0.648043	−	0.196432i	−0.0211368	−	0.00640691i
$941$	−35.4523	+	9.49941i	−1.15571	+	0.309672i	−0.785252	−	0.619176i	$-0.787467\pi$
$941$	−35.4523	+	9.49941i	−1.15571	+	0.309672i	−0.370460	+	0.928848i	$0.620800\pi$
$942$	−6.64182	−	3.98000i	−0.216402	−	0.129675i
$943$	14.1774	+	24.5559i	0.461679	+	0.799651i
$944$	−24.3269	+	21.3524i	−0.791774	+	0.694960i
$945$	−0.373553	−	0.0523198i	−0.0121517	−	0.00170196i
$946$	0.0634786	−	3.90442i	0.00206387	−	0.126944i
$947$	8.77905	−	32.7639i	0.285281	−	1.06468i	−0.663353	−	0.748307i	$-0.730867\pi$
$947$	8.77905	−	32.7639i	0.285281	−	1.06468i	0.948634	−	0.316376i	$-0.102466\pi$
$948$	−19.5231	+	4.55651i	−0.634082	+	0.147989i
$949$	−0.499855	−	1.86549i	−0.0162260	−	0.0605562i
$950$	16.6932	+	4.76508i	0.541599	+	0.154600i
$951$			0.481767i			0.0156224i
$952$	−36.5920	+	12.7661i	−1.18595	+	0.413752i
$953$		−	17.4729i		−	0.566003i	−0.959119	−	0.283002i	$-0.908670\pi$
$953$		−	17.4729i		−	0.566003i	0.959119	−	0.283002i	$-0.0913302\pi$
$954$	0.987027	−	3.45778i	0.0319562	−	0.111950i
$955$	0.391089	+	1.45956i	0.0126553	+	0.0472304i
$956$	14.9279	−	24.0173i	0.482803	−	0.776776i
$957$	11.3920	−	42.5156i	0.368252	−	1.37433i
$958$	29.7298	+	0.483351i	0.960525	+	0.0156164i
$959$	−21.6994	−	53.6350i	−0.700710	−	1.73197i
$960$	1.13512	+	0.111072i	0.0366359	+	0.00358485i
$961$	3.58851	+	6.21549i	0.115759	+	0.200500i
$962$	0.510644	−	0.852162i	0.0164638	−	0.0274748i
$963$	2.17380	−	0.582469i	0.0700498	−	0.0187698i
$964$	0.342730	+	0.640877i	0.0110386	+	0.0206413i
$965$	0.641295	−	0.641295i	0.0206440	−	0.0206440i
$966$	10.6075	+	14.5488i	0.341290	+	0.468102i
$967$			43.2766i			1.39168i	0.718196	+	0.695841i	$0.244968\pi$
$967$			43.2766i			1.39168i	−0.718196	+	0.695841i	$0.755032\pi$
$968$	−35.1362	+	18.0619i	−1.12932	+	0.580533i
$969$	−11.0560	−	6.38317i	−0.355169	−	0.205057i
$970$	−0.616979	−	2.46201i	−0.0198100	−	0.0790505i
$971$	−26.7945	−	7.17957i	−0.859877	−	0.230403i	−0.198172	−	0.980167i	$-0.563500\pi$
$971$	−26.7945	−	7.17957i	−0.859877	−	0.230403i	−0.661705	+	0.749764i	$0.730167\pi$
$972$	1.36749	+	1.45944i	0.0438624	+	0.0468115i
$973$	49.9190	−	6.15318i	1.60033	−	0.197262i
$974$	−0.0284882	+	1.75224i	−0.000912822	+	0.0561455i
$975$	0.337214	+	0.584072i	0.0107995	+	0.0187053i
$976$	17.8522	−	3.55888i	0.571436	−	0.113917i
$977$	14.5770	−	25.2481i	0.466360	−	0.807759i	−0.532902	−	0.846177i	$-0.678899\pi$
$977$	14.5770	−	25.2481i	0.466360	−	0.807759i	0.999262	+	0.0384182i	$0.0122319\pi$
$978$	14.8828	−	8.27298i	0.475900	−	0.264541i
$979$	−43.0139	−	43.0139i	−1.37473	−	1.37473i
$980$	−1.67756	−	1.08148i	−0.0535877	−	0.0345466i
$981$	−14.0320	+	14.0320i	−0.448007	+	0.448007i
$982$	−32.8583	−	9.37944i	−1.04855	−	0.299310i
$983$	16.3548	+	9.44247i	0.521638	+	0.301168i	0.737605	−	0.675233i	$-0.235957\pi$
$983$	16.3548	+	9.44247i	0.521638	+	0.301168i	−0.215966	+	0.976401i	$0.569290\pi$
$984$	3.52359	+	16.2895i	0.112328	+	0.519289i
$985$	−1.16878	+	0.674798i	−0.0372405	+	0.0215008i
$986$	−44.8716	−	46.3548i	−1.42900	−	1.47624i
$987$	−0.768684	−	6.23612i	−0.0244675	−	0.198498i
$988$	0.0217062	−	0.667373i	0.000690567	−	0.0212320i
$989$	−0.688240	+	2.56855i	−0.0218847	+	0.0816750i
$990$	−0.517845	+	0.864179i	−0.0164582	+	0.0274654i
$991$	16.1545	−	27.9805i	0.513165	−	0.888829i	−0.486718	−	0.873559i	$-0.661806\pi$
$991$	16.1545	−	27.9805i	0.513165	−	0.888829i	0.999883	−	0.0152695i	$-0.00486061\pi$
$992$	−11.8182	−	24.9533i	−0.375227	−	0.792267i
$993$	−19.0869			−0.605704
$994$	36.3034	+	5.68783i	1.15147	+	0.180407i
$995$	2.07666	+	2.07666i	0.0658345	+	0.0658345i
$996$	4.14216	−	2.21516i	0.131249	−	0.0701900i
$997$	−4.91856	−	18.3563i	−0.155772	−	0.581350i	−0.999038	−	0.0438531i	$-0.986037\pi$
$997$	−4.91856	−	18.3563i	−0.155772	−	0.581350i	0.843266	−	0.537497i	$-0.180630\pi$
$998$	−18.7187	+	4.69089i	−0.592530	+	0.148488i
$999$	−4.49185	+	2.59337i	−0.142116	+	0.0820506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.11	yes	120
7.2	even	3	inner	336.2.bq.b.205.10	yes	120
16.5	even	4	inner	336.2.bq.b.277.10	yes	120
112.37	even	12	inner	336.2.bq.b.37.11	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.11	✓	120	112.37	even	12	inner
336.2.bq.b.109.11	yes	120	1.1	even	1	trivial
336.2.bq.b.205.10	yes	120	7.2	even	3	inner
336.2.bq.b.277.10	yes	120	16.5	even	4	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.687104 - 1.23608i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.05578 + 1.69863i) q^{4} +(0.137710 + 0.0368993i) q^{5} +(-0.983612 - 1.01612i) q^{6} +(-2.08565 - 1.62790i) q^{7} +(2.82506 + 0.137888i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.687104 - 1.23608i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.05578 + 1.69863i) q^{4} +(0.137710 + 0.0368993i) q^{5} +(-0.983612 - 1.01612i) q^{6} +(-2.08565 - 1.62790i) q^{7} +(2.82506 + 0.137888i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.0490107 - 0.195574i) q^{10} +(-1.29326 - 4.82651i) q^{11} +(-0.580165 + 1.91400i) q^{12} +(-0.0957679 - 0.0957679i) q^{13} +(-0.579159 + 3.69656i) q^{14} +0.142568 q^{15} +(-1.77067 - 3.58674i) q^{16} +(2.58943 - 4.48502i) q^{17} +(-1.21309 - 0.726923i) q^{18} +(0.638013 - 2.38110i) q^{19} +(-0.208069 + 0.194961i) q^{20} +(-2.43591 - 1.03263i) q^{21} +(-5.07734 + 4.91489i) q^{22} +(4.16740 - 2.40605i) q^{23} +(2.76449 - 0.597991i) q^{24} +(-4.31252 - 2.48984i) q^{25} +(-0.0525741 + 0.184179i) q^{26} +(0.707107 - 0.707107i) q^{27} +(4.96718 - 1.82404i) q^{28} +(6.22873 + 6.22873i) q^{29} +(-0.0979589 - 0.176225i) q^{30} +(-2.44044 + 4.22696i) q^{31} +(-3.21686 + 4.65315i) q^{32} +(-2.49839 - 4.32733i) q^{33} +(-7.32303 - 0.119059i) q^{34} +(-0.227146 - 0.301137i) q^{35} +(-0.0650154 + 1.99894i) q^{36} +(-5.01001 - 1.34243i) q^{37} +(-3.38160 + 0.847427i) q^{38} +(-0.117291 - 0.0677181i) q^{39} +(0.383951 + 0.123231i) q^{40} +5.89239i q^{41} +(0.397316 + 3.72050i) q^{42} +(-0.390746 + 0.390746i) q^{43} +(9.56384 + 2.89895i) q^{44} +(0.137710 - 0.0368993i) q^{45} +(-5.83750 - 3.49802i) q^{46} +(1.18744 + 2.05670i) q^{47} +(-2.63866 - 3.00624i) q^{48} +(1.69986 + 6.79047i) q^{49} +(-0.114480 + 7.04139i) q^{50} +(1.34039 - 5.00239i) q^{51} +(0.263784 - 0.0615645i) q^{52} +(0.658095 + 2.45604i) q^{53} +(-1.35989 - 0.388183i) q^{54} -0.712379i q^{55} +(-5.66762 - 4.88652i) q^{56} -2.46509i q^{57} +(3.41941 - 11.9790i) q^{58} +(-2.09440 - 7.81641i) q^{59} +(-0.150520 + 0.242170i) q^{60} +(-1.17785 + 4.39581i) q^{61} +(6.90169 + 0.112209i) q^{62} +(-2.62018 - 0.366982i) q^{63} +(7.96197 + 0.779085i) q^{64} +(-0.00965443 - 0.0167220i) q^{65} +(-3.63227 + 6.06153i) q^{66} +(0.284860 - 0.0763279i) q^{67} +(4.88452 + 9.13364i) q^{68} +(3.40267 - 3.40267i) q^{69} +(-0.216156 + 0.487683i) q^{70} -9.82085i q^{71} +(2.51552 - 1.29312i) q^{72} +(12.3493 + 7.12989i) q^{73} +(1.78305 + 7.11515i) q^{74} +(-4.81000 - 1.28883i) q^{75} +(3.37100 + 3.59765i) q^{76} +(-5.15981 + 12.1717i) q^{77} +(-0.00311360 + 0.191511i) q^{78} +(5.01195 + 8.68095i) q^{79} +(-0.111491 - 0.559266i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.28345 - 4.04868i) q^{82} +(-1.66074 - 1.66074i) q^{83} +(4.32583 - 3.04749i) q^{84} +(0.522083 - 0.522083i) q^{85} +(0.751475 + 0.214509i) q^{86} +(7.62861 + 4.40438i) q^{87} +(-2.98802 - 13.8135i) q^{88} +(10.5430 - 6.08701i) q^{89} +(-0.140231 - 0.144867i) q^{90} +(0.0438372 + 0.355639i) q^{91} +(-0.312860 + 9.61910i) q^{92} +(-1.26326 + 4.71457i) q^{93} +(1.72635 - 2.88093i) q^{94} +(0.175721 - 0.304358i) q^{95} +(-1.90292 + 5.32718i) q^{96} +12.5887 q^{97} +(7.22557 - 6.76692i) q^{98} +(-3.53325 - 3.53325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Introduction

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