LMFDB - Embedded newform 68.2.i.b.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [68,2,Mod(3,68)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(68, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 1]))

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

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

chi := DirichletCharacter("68.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 68 = 2^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	68.i (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.542982733745$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	68.3
Dual form			68.2.i.b.23.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.368108 + 1.36547i) q^{2} +(0.563072 - 2.83076i) q^{3} +(-1.72899 + 1.00528i) q^{4} +(0.991762 + 1.48428i) q^{5} +(4.07257 - 0.273169i) q^{6} +(1.11612 + 0.745767i) q^{7} +(-2.00913 - 1.99083i) q^{8} +(-4.92449 - 2.03979i) q^{9} +O(q^{10})$	\(q+(0.368108 + 1.36547i) q^{2} +(0.563072 - 2.83076i) q^{3} +(-1.72899 + 1.00528i) q^{4} +(0.991762 + 1.48428i) q^{5} +(4.07257 - 0.273169i) q^{6} +(1.11612 + 0.745767i) q^{7} +(-2.00913 - 1.99083i) q^{8} +(-4.92449 - 2.03979i) q^{9} +(-1.66165 + 1.90059i) q^{10} +(-4.92539 + 0.979720i) q^{11} +(1.87215 + 5.46040i) q^{12} +(-1.71621 - 1.71621i) q^{13} +(-0.607467 + 1.79855i) q^{14} +(4.76006 - 1.97168i) q^{15} +(1.97883 - 3.47624i) q^{16} +(1.47922 + 3.84862i) q^{17} +(0.972518 - 7.47509i) q^{18} +(-0.320260 - 0.773176i) q^{19} +(-3.20686 - 1.56931i) q^{20} +(2.73954 - 2.73954i) q^{21} +(-3.15085 - 6.36480i) q^{22} +(0.843557 + 4.24085i) q^{23} +(-6.76684 + 4.56638i) q^{24} +(0.693933 - 1.67530i) q^{25} +(1.71167 - 2.97517i) q^{26} +(-3.73651 + 5.59209i) q^{27} +(-2.67947 - 0.167415i) q^{28} +(7.26771 - 4.85613i) q^{29} +(4.44448 + 5.77390i) q^{30} +(0.974564 + 0.193853i) q^{31} +(5.47511 + 1.42239i) q^{32} +14.4942i q^{33} +(-4.71065 + 3.43654i) q^{34} +2.39625i q^{35} +(10.5650 - 1.42370i) q^{36} +(-2.82219 - 0.561369i) q^{37} +(0.937854 - 0.721916i) q^{38} +(-5.82451 + 3.89182i) q^{39} +(0.962361 - 4.95653i) q^{40} +(-2.39752 + 3.58815i) q^{41} +(4.74920 + 2.73230i) q^{42} +(2.09905 - 5.06756i) q^{43} +(7.53106 - 6.64531i) q^{44} +(-1.85631 - 9.33229i) q^{45} +(-5.48021 + 2.71294i) q^{46} +(1.58763 - 1.58763i) q^{47} +(-8.72616 - 7.55896i) q^{48} +(-1.98923 - 4.80243i) q^{49} +(2.54301 + 0.330849i) q^{50} +(11.7274 - 2.02026i) q^{51} +(4.69258 + 1.24204i) q^{52} +(-5.72685 + 2.37214i) q^{53} +(-9.01125 - 3.04359i) q^{54} +(-6.33898 - 6.33898i) q^{55} +(-0.757735 - 3.72035i) q^{56} +(-2.36900 + 0.471224i) q^{57} +(9.30618 + 8.13623i) q^{58} +(1.85609 + 0.768817i) q^{59} +(-6.24802 + 8.19420i) q^{60} +(4.99961 + 3.34063i) q^{61} +(0.0940458 + 1.40209i) q^{62} +(-3.97511 - 5.94918i) q^{63} +(0.0732056 + 7.99967i) q^{64} +(0.845257 - 4.24939i) q^{65} +(-19.7914 + 5.33544i) q^{66} +0.290815 q^{67} +(-6.42650 - 5.16721i) q^{68} +12.4798 q^{69} +(-3.27200 + 0.882081i) q^{70} +(-1.91314 + 9.61800i) q^{71} +(5.83307 + 13.9020i) q^{72} +(-1.60357 - 2.39991i) q^{73} +(-0.272343 - 4.06025i) q^{74} +(-4.35164 - 2.90767i) q^{75} +(1.33098 + 1.01486i) q^{76} +(-6.22796 - 2.57971i) q^{77} +(-7.45819 - 6.52056i) q^{78} +(8.76636 - 1.74374i) q^{79} +(7.12222 - 0.510469i) q^{80} +(2.41878 + 2.41878i) q^{81} +(-5.78204 - 1.95291i) q^{82} +(-1.69169 + 0.700723i) q^{83} +(-1.98264 + 7.49065i) q^{84} +(-4.24539 + 6.01249i) q^{85} +(7.69225 + 1.00077i) q^{86} +(-9.65427 - 23.3075i) q^{87} +(11.8462 + 7.83721i) q^{88} +(-3.02367 + 3.02367i) q^{89} +(12.0596 - 5.97002i) q^{90} +(-0.635601 - 3.19538i) q^{91} +(-5.72174 - 6.48438i) q^{92} +(1.09750 - 2.64960i) q^{93} +(2.75227 + 1.58343i) q^{94} +(0.829985 - 1.24216i) q^{95} +(7.10933 - 14.6978i) q^{96} +(-8.76227 + 5.85476i) q^{97} +(5.82530 - 4.48404i) q^{98} +(26.2534 + 5.22214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/68\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	0.368108	+	1.36547i	0.260292	+	0.965530i
$2$	0.368108	+	1.36547i	0.260292	+	0.965530i
$3$	0.563072	−	2.83076i	0.325090	−	1.63434i	−0.379834	−	0.925055i	$-0.624019\pi$
$3$	0.563072	−	2.83076i	0.325090	−	1.63434i	0.704924	−	0.709283i	$-0.250981\pi$
$4$	−1.72899	+	1.00528i	−0.864496	+	0.502639i
$5$	0.991762	+	1.48428i	0.443529	+	0.663788i	0.984121	−	0.177496i	$-0.0567998\pi$
$5$	0.991762	+	1.48428i	0.443529	+	0.663788i	−0.540592	+	0.841285i	$0.681800\pi$
$6$	4.07257	−	0.273169i	1.66262	−	0.111521i
$7$	1.11612	+	0.745767i	0.421854	+	0.281874i	0.748323	−	0.663334i	$-0.230859\pi$
$7$	1.11612	+	0.745767i	0.421854	+	0.281874i	−0.326470	+	0.945208i	$0.605859\pi$
$8$	−2.00913	−	1.99083i	−0.710335	−	0.703864i
$9$	−4.92449	−	2.03979i	−1.64150	−	0.679930i
$10$	−1.66165	+	1.90059i	−0.525461	+	0.601020i
$11$	−4.92539	+	0.979720i	−1.48506	+	0.295397i	−0.869987	−	0.493074i	$-0.835873\pi$
$11$	−4.92539	+	0.979720i	−1.48506	+	0.295397i	−0.615072	+	0.788471i	$0.710873\pi$
$12$	1.87215	+	5.46040i	0.540443	+	1.57628i
$13$	−1.71621	−	1.71621i	−0.475990	−	0.475990i	0.427856	−	0.903847i	$-0.359269\pi$
$13$	−1.71621	−	1.71621i	−0.475990	−	0.475990i	−0.903847	+	0.427856i	$0.859269\pi$
$14$	−0.607467	+	1.79855i	−0.162352	+	0.480682i
$15$	4.76006	−	1.97168i	1.22904	−	0.509086i
$16$	1.97883	−	3.47624i	0.494707	−	0.869060i
$17$	1.47922	+	3.84862i	0.358764	+	0.933428i
$17$	1.47922	+	3.84862i	0.358764	+	0.933428i
$18$	0.972518	−	7.47509i	0.229225	−	1.76190i
$19$	−0.320260	−	0.773176i	−0.0734726	−	0.177379i	0.882876	−	0.469605i	$-0.155604\pi$
$19$	−0.320260	−	0.773176i	−0.0734726	−	0.177379i	−0.956349	+	0.292227i	$0.905604\pi$
$20$	−3.20686	−	1.56931i	−0.717075	−	0.350907i
$21$	2.73954	−	2.73954i	0.597817	−	0.597817i
$22$	−3.15085	−	6.36480i	−0.671763	−	1.35698i
$23$	0.843557	+	4.24085i	0.175894	+	0.884278i	0.963420	+	0.267997i	$0.0863616\pi$
$23$	0.843557	+	4.24085i	0.175894	+	0.884278i	−0.787526	+	0.616281i	$0.788638\pi$
$24$	−6.76684	+	4.56638i	−1.38127	+	0.932108i
$25$	0.693933	−	1.67530i	0.138787	−	0.335060i
$26$	1.71167	−	2.97517i	0.335686	−	0.583479i
$27$	−3.73651	+	5.59209i	−0.719092	+	1.07620i
$28$	−2.67947	−	0.167415i	−0.506371	−	0.0316384i
$29$	7.26771	−	4.85613i	1.34958	−	0.901761i	0.350190	−	0.936679i	$-0.386117\pi$
$29$	7.26771	−	4.85613i	1.34958	−	0.901761i	0.999390	+	0.0349181i	$0.0111170\pi$
$30$	4.44448	+	5.77390i	0.811447	+	1.05417i
$31$	0.974564	+	0.193853i	0.175037	+	0.0348170i	0.281830	−	0.959464i	$-0.409058\pi$
$31$	0.974564	+	0.193853i	0.175037	+	0.0348170i	−0.106794	+	0.994281i	$0.534058\pi$
$32$	5.47511	+	1.42239i	0.967871	+	0.251446i
$33$			14.4942i			2.52312i
$34$	−4.71065	+	3.43654i	−0.807870	+	0.589361i
$35$			2.39625i			0.405041i
$36$	10.5650	−	1.42370i	1.76083	−	0.237284i
$37$	−2.82219	−	0.561369i	−0.463966	−	0.0922885i	−0.0424283	−	0.999100i	$-0.513509\pi$
$37$	−2.82219	−	0.561369i	−0.463966	−	0.0922885i	−0.421537	+	0.906811i	$0.638509\pi$
$38$	0.937854	−	0.721916i	0.152140	−	0.117110i
$39$	−5.82451	+	3.89182i	−0.932669	+	0.623189i
$40$	0.962361	−	4.95653i	0.152163	−	0.783696i
$41$	−2.39752	+	3.58815i	−0.374430	+	0.560375i	−0.970054	−	0.242889i	$-0.921905\pi$
$41$	−2.39752	+	3.58815i	−0.374430	+	0.560375i	0.595624	+	0.803264i	$0.296905\pi$
$42$	4.74920	+	2.73230i	0.732817	+	0.421603i
$43$	2.09905	−	5.06756i	0.320102	−	0.772795i	−0.679145	−	0.734004i	$-0.737649\pi$
$43$	2.09905	−	5.06756i	0.320102	−	0.772795i	0.999247	−	0.0387911i	$-0.0123507\pi$
$44$	7.53106	−	6.64531i	1.13535	−	1.00182i
$45$	−1.85631	−	9.33229i	−0.276722	−	1.39118i
$46$	−5.48021	+	2.71294i	−0.808013	+	0.400001i
$47$	1.58763	−	1.58763i	0.231579	−	0.231579i	−0.581772	−	0.813352i	$-0.697641\pi$
$47$	1.58763	−	1.58763i	0.231579	−	0.231579i	0.813352	+	0.581772i	$0.197641\pi$
$48$	−8.72616	−	7.55896i	−1.25951	−	1.09104i
$49$	−1.98923	−	4.80243i	−0.284176	−	0.686061i
$50$	2.54301	+	0.330849i	0.359636	+	0.0467891i
$51$	11.7274	−	2.02026i	1.64217	−	0.282893i
$52$	4.69258	+	1.24204i	0.650743	+	0.172240i
$53$	−5.72685	+	2.37214i	−0.786643	+	0.325838i	−0.739593	−	0.673054i	$-0.764982\pi$
$53$	−5.72685	+	2.37214i	−0.786643	+	0.325838i	−0.0470499	+	0.998893i	$0.514982\pi$
$54$	−9.01125	−	3.04359i	−1.22628	−	0.414180i
$55$	−6.33898	−	6.33898i	−0.854748	−	0.854748i
$56$	−0.757735	−	3.72035i	−0.101257	−	0.497152i
$57$	−2.36900	+	0.471224i	−0.313782	+	0.0624151i
$58$	9.30618	+	8.13623i	1.22196	+	1.06834i
$59$	1.85609	+	0.768817i	0.241642	+	0.100091i	0.500218	−	0.865899i	$-0.333253\pi$
$59$	1.85609	+	0.768817i	0.241642	+	0.100091i	−0.258576	+	0.965991i	$0.583253\pi$
$60$	−6.24802	+	8.19420i	−0.806615	+	1.05787i
$61$	4.99961	+	3.34063i	0.640135	+	0.427724i	0.832826	−	0.553535i	$-0.186722\pi$
$61$	4.99961	+	3.34063i	0.640135	+	0.427724i	−0.192691	+	0.981259i	$0.561722\pi$
$62$	0.0940458	+	1.40209i	0.0119438	+	0.178066i
$63$	−3.97511	−	5.94918i	−0.500817	−	0.749526i
$64$	0.0732056	+	7.99967i	0.00915070	+	0.999958i
$65$	0.845257	−	4.24939i	0.104841	−	0.527072i
$66$	−19.7914	+	5.33544i	−2.43615	+	0.656748i
$67$	0.290815			0.0355287			0.0177643	−	0.999842i	$-0.494345\pi$
$67$	0.290815			0.0355287			0.0177643	+	0.999842i	$0.494345\pi$
$68$	−6.42650	−	5.16721i	−0.779328	−	0.626617i
$69$	12.4798			1.50239
$70$	−3.27200	+	0.882081i	−0.391079	+	0.105429i
$71$	−1.91314	+	9.61800i	−0.227048	+	1.14145i	0.684107	+	0.729382i	$0.260192\pi$
$71$	−1.91314	+	9.61800i	−0.227048	+	1.14145i	−0.911155	+	0.412065i	$0.864808\pi$
$72$	5.83307	+	13.9020i	0.687434	+	1.63837i
$73$	−1.60357	−	2.39991i	−0.187683	−	0.280888i	0.725681	−	0.688031i	$-0.241525\pi$
$73$	−1.60357	−	2.39991i	−0.187683	−	0.280888i	−0.913364	+	0.407143i	$0.866525\pi$
$74$	−0.272343	−	4.06025i	−0.0316592	−	0.471995i
$75$	−4.35164	−	2.90767i	−0.502484	−	0.335749i
$76$	1.33098	+	1.01486i	0.152674	+	0.116413i
$77$	−6.22796	−	2.57971i	−0.709742	−	0.293985i
$78$	−7.45819	−	6.52056i	−0.844474	−	0.738308i
$79$	8.76636	−	1.74374i	0.986292	−	0.196186i	0.324510	−	0.945882i	$-0.394801\pi$
$79$	8.76636	−	1.74374i	0.986292	−	0.196186i	0.661782	+	0.749696i	$0.269801\pi$
$80$	7.12222	−	0.510469i	0.796289	−	0.0570722i
$81$	2.41878	+	2.41878i	0.268754	+	0.268754i
$82$	−5.78204	−	1.95291i	−0.638520	−	0.215663i
$83$	−1.69169	+	0.700723i	−0.185688	+	0.0769143i	−0.473590	−	0.880745i	$-0.657042\pi$
$83$	−1.69169	+	0.700723i	−0.185688	+	0.0769143i	0.287902	+	0.957660i	$0.407042\pi$
$84$	−1.98264	+	7.49065i	−0.216324	+	0.817297i
$85$	−4.24539	+	6.01249i	−0.460477	+	0.652146i
$86$	7.69225	+	1.00077i	0.829477	+	0.107916i
$87$	−9.65427	−	23.3075i	−1.03505	−	2.49882i
$88$	11.8462	+	7.83721i	1.26281	+	0.835450i
$89$	−3.02367	+	3.02367i	−0.320508	+	0.320508i	−0.848962	−	0.528454i	$-0.822772\pi$
$89$	−3.02367	+	3.02367i	−0.320508	+	0.320508i	0.528454	+	0.848962i	$0.322772\pi$
$90$	12.0596	−	5.97002i	1.27119	−	0.629295i
$91$	−0.635601	−	3.19538i	−0.0666291	−	0.334967i
$92$	−5.72174	−	6.48438i	−0.596532	−	0.676044i
$93$	1.09750	−	2.64960i	0.113805	−	0.274751i
$94$	2.75227	+	1.58343i	0.283875	+	0.163319i
$95$	0.829985	−	1.24216i	0.0851546	−	0.127443i
$96$	7.10933	−	14.6978i	0.725593	−	1.50009i
$97$	−8.76227	+	5.85476i	−0.889674	+	0.594461i	−0.914211	−	0.405238i	$-0.867189\pi$
$97$	−8.76227	+	5.85476i	−0.889674	+	0.594461i	0.0245374	+	0.999699i	$0.492189\pi$
$98$	5.82530	−	4.48404i	0.588444	−	0.452956i
$99$	26.2534	+	5.22214i	2.63857	+	0.524844i
$100$	0.484341	+	3.59418i	0.0484341	+	0.359418i
$101$		−	14.5118i		−	1.44398i	−0.691906	−	0.721988i	$-0.743229\pi$
$101$		−	14.5118i		−	1.44398i	0.691906	−	0.721988i	$-0.256771\pi$
$102$	7.07556	+	15.2697i	0.700584	+	1.51193i
$103$			14.0628i			1.38564i	0.721109	+	0.692822i	$0.243633\pi$
$103$			14.0628i			1.38564i	−0.721109	+	0.692822i	$0.756367\pi$
$104$	0.0314093	+	6.86476i	0.00307994	+	0.673145i
$105$	6.78321	+	1.34926i	0.661973	+	0.131675i
$106$	−5.34717	−	6.94661i	−0.519363	−	0.674714i
$107$	−8.79162	+	5.87437i	−0.849918	+	0.567897i	−0.902485	−	0.430720i	$-0.858259\pi$
$107$	−8.79162	+	5.87437i	−0.849918	+	0.567897i	0.0525677	+	0.998617i	$0.483259\pi$
$108$	0.838798	−	13.4249i	0.0807134	−	1.29181i
$109$	−2.34403	+	3.50808i	−0.224517	+	0.336013i	−0.926578	−	0.376104i	$-0.877264\pi$
$109$	−2.34403	+	3.50808i	−0.224517	+	0.336013i	0.702061	+	0.712117i	$0.252264\pi$
$110$	6.32223	−	10.9891i	0.602801	−	1.04777i
$111$	−3.17820	+	7.67285i	−0.301661	+	0.728275i
$112$	4.80108	−	2.40415i	0.453659	−	0.227171i
$113$	1.53979	+	7.74105i	0.144851	+	0.728217i	0.983120	+	0.182960i	$0.0585679\pi$
$113$	1.53979	+	7.74105i	0.144851	+	0.728217i	−0.838269	+	0.545257i	$0.816432\pi$
$114$	−1.51549	−	3.06133i	−0.141939	−	0.286720i
$115$	−5.45798	+	5.45798i	−0.508959	+	0.508959i
$116$	−7.68406	+	15.7023i	−0.713447	+	1.45792i
$117$	4.95074	+	11.9522i	0.457696	+	1.10498i
$118$	−0.366552	+	2.81743i	−0.0337438	+	0.259366i
$119$	−1.21919	+	5.39868i	−0.111763	+	0.494896i
$120$	−13.4888	−	5.51509i	−1.23136	−	0.503457i
$121$	13.1369	−	5.44148i	1.19426	−	0.494680i
$122$	−2.72112	+	8.05651i	−0.246359	+	0.729403i
$123$	8.80720	+	8.80720i	0.794118	+	0.794118i
$124$	−1.87989	+	0.644538i	−0.168819	+	0.0578812i
$125$	11.9289	−	2.37281i	1.06696	−	0.212231i
$126$	6.66012	−	7.61782i	0.593331	−	0.678649i
$127$	−4.00607	−	1.65937i	−0.355481	−	0.147245i	0.197794	−	0.980244i	$-0.436622\pi$
$127$	−4.00607	−	1.65937i	−0.355481	−	0.147245i	−0.553275	+	0.832998i	$0.686622\pi$
$128$	−10.8963	+	3.04470i	−0.963108	+	0.269116i
$129$	−13.1631	−	8.79530i	−1.15895	−	0.774383i
$130$	6.11355	−	0.410068i	0.536193	−	0.0359653i
$131$	−10.5322	−	15.7626i	−0.920203	−	1.37718i	−0.926132	−	0.377198i	$-0.876887\pi$
$131$	−10.5322	−	15.7626i	−0.920203	−	1.37718i	0.00592968	−	0.999982i	$-0.498113\pi$
$132$	−14.5707	−	25.0604i	−1.26822	−	2.18123i
$133$	0.219161	−	1.10180i	0.0190036	−	0.0955378i
$134$	0.107051	+	0.397098i	0.00924783	+	0.0343040i
$135$	−12.0059			−1.03331
$136$	4.69000	−	10.6773i	0.402164	−	0.915567i
$137$	−10.4761			−0.895035			−0.447518	−	0.894275i	$-0.647692\pi$
$137$	−10.4761			−0.895035			−0.447518	+	0.894275i	$0.647692\pi$
$138$	4.59391	+	17.0407i	0.391060	+	1.45060i
$139$	−0.649633	+	3.26593i	−0.0551012	+	0.277012i	−0.998507	−	0.0546290i	$-0.982602\pi$
$139$	−0.649633	+	3.26593i	−0.0551012	+	0.277012i	0.943406	+	0.331641i	$0.107602\pi$
$140$	−2.40890	−	4.14310i	−0.203589	−	0.350156i
$141$	−3.60024	−	5.38814i	−0.303195	−	0.453763i
$142$	−13.8373	+	0.928141i	−1.16120	+	0.0778878i
$143$	10.1344	+	6.77158i	0.847480	+	0.566268i
$144$	−16.8355	+	13.0823i	−1.40296	+	1.09019i
$145$	14.4157	+	5.97117i	1.19716	+	0.495878i
$146$	2.68671	−	3.07304i	0.222353	−	0.254327i
$147$	−14.7146	+	2.92691i	−1.21364	+	0.241408i
$148$	5.44388	−	1.86649i	0.447484	−	0.153424i
$149$	4.40652	+	4.40652i	0.360996	+	0.360996i	0.864180	−	0.503183i	$-0.167838\pi$
$149$	4.40652	+	4.40652i	0.360996	+	0.360996i	−0.503183	+	0.864180i	$0.667838\pi$
$150$	2.36845	−	7.01235i	0.193383	−	0.572556i
$151$	21.8610	−	9.05512i	1.77902	−	0.736895i	0.786104	−	0.618094i	$-0.212095\pi$
$151$	21.8610	−	9.05512i	1.77902	−	0.736895i	0.992918	−	0.118802i	$-0.0379052\pi$
$152$	−0.895816	+	2.19099i	−0.0726603	+	0.177713i
$153$	0.565981	−	21.9698i	0.0457568	−	1.77615i
$154$	1.22994	−	9.45368i	0.0991110	−	0.761799i
$155$	0.678804	+	1.63878i	0.0545228	+	0.131630i
$156$	6.15818	−	12.5842i	0.493049	−	1.00754i
$157$	−3.59587	+	3.59587i	−0.286982	+	0.286982i	−0.835886	−	0.548904i	$-0.815045\pi$
$157$	−3.59587	+	3.59587i	−0.286982	+	0.286982i	0.548904	+	0.835886i	$0.315045\pi$
$158$	5.60798	+	11.3283i	0.446147	+	0.901229i
$159$	3.49031	+	17.5470i	0.276800	+	1.39157i
$160$	3.31878	+	9.53724i	0.262372	+	0.753985i
$161$	−2.22117	+	5.36239i	−0.175053	+	0.422616i
$162$	−2.41239	+	4.19314i	−0.189535	+	0.329444i
$163$	−2.48983	+	3.72630i	−0.195019	+	0.291866i	−0.916072	−	0.401013i	$-0.868658\pi$
$163$	−2.48983	+	3.72630i	−0.195019	+	0.291866i	0.721054	+	0.692879i	$0.243658\pi$
$164$	0.538213	−	8.61406i	0.0420273	−	0.672645i
$165$	−21.5134	+	14.3748i	−1.67482	+	1.11908i
$166$	−1.57954	−	2.05201i	−0.122596	−	0.159267i
$167$	−2.10583	−	0.418875i	−0.162954	−	0.0324135i	0.112939	−	0.993602i	$-0.463973\pi$
$167$	−2.10583	−	0.418875i	−0.162954	−	0.0324135i	−0.275893	+	0.961188i	$0.588973\pi$
$168$	−10.9581	+	0.0501379i	−0.845432	+	0.00386823i
$169$		−	7.10927i		−	0.546867i
$170$	−9.77261	−	3.58368i	−0.749525	−	0.274856i
$171$			4.46076i			0.341123i
$172$	1.46506	+	10.8719i	0.111710	+	0.828974i
$173$	−17.4295	−	3.46694i	−1.32514	−	0.263586i	−0.518726	−	0.854940i	$-0.673594\pi$
$173$	−17.4295	−	3.46694i	−1.32514	−	0.263586i	−0.806412	+	0.591354i	$0.798594\pi$
$174$	28.2717	−	21.7622i	2.14327	−	1.64979i
$175$	2.02390	−	1.35232i	0.152992	−	0.102226i
$176$	−6.34076	+	19.0605i	−0.477953	+	1.43674i
$177$	3.22145	−	4.82124i	0.242139	−	0.362386i
$178$	−5.24175	−	3.01568i	−0.392886	−	0.226034i
$179$	5.89728	−	14.2373i	0.440783	−	1.06414i	−0.534891	−	0.844921i	$-0.679648\pi$
$179$	5.89728	−	14.2373i	0.440783	−	1.06414i	0.975675	−	0.219224i	$-0.0703525\pi$
$180$	12.5911	+	14.2694i	0.938485	+	1.06357i
$181$	1.43459	+	7.21218i	0.106632	+	0.536077i	0.996765	+	0.0803750i	$0.0256118\pi$
$181$	1.43459	+	7.21218i	0.106632	+	0.536077i	−0.890132	+	0.455702i	$0.849388\pi$
$182$	4.12922	−	2.04414i	0.306078	−	0.151522i
$183$	12.2717	−	12.2717i	0.907148	−	0.907148i
$184$	6.74798	−	10.1998i	0.497468	−	0.751939i
$185$	−1.96572	−	4.74566i	−0.144522	−	0.348908i
$186$	4.02194	+	0.523259i	0.294903	+	0.0383672i
$187$	−11.0563	−	17.5067i	−0.808517	−	1.28022i
$188$	−1.14899	+	4.34101i	−0.0837986	+	0.316600i
$189$	−8.34079	+	3.45487i	−0.606703	+	0.251305i
$190$	2.00165	+	0.676066i	0.145215	+	0.0490470i
$191$	−9.92044	−	9.92044i	−0.717818	−	0.717818i	0.250340	−	0.968158i	$-0.419458\pi$
$191$	−9.92044	−	9.92044i	−0.717818	−	0.717818i	−0.968158	+	0.250340i	$0.919458\pi$
$192$	22.6863	+	4.29716i	1.63724	+	0.310121i
$193$	18.9416	−	3.76772i	1.36345	−	0.271206i	0.541466	−	0.840722i	$-0.317869\pi$
$193$	18.9416	−	3.76772i	1.36345	−	0.271206i	0.821980	+	0.569516i	$0.192869\pi$
$194$	−11.2199	−	9.80939i	−0.805545	−	0.704273i
$195$	−11.5531	−	4.78543i	−0.827332	−	0.342692i
$196$	8.26714	+	6.30363i	0.590510	+	0.450259i
$197$	13.9350	+	9.31106i	0.992826	+	0.663385i	0.942102	−	0.335327i	$-0.108847\pi$
$197$	13.9350	+	9.31106i	0.992826	+	0.663385i	0.0507247	+	0.998713i	$0.483847\pi$
$198$	2.53347	+	37.7705i	0.180046	+	2.68423i
$199$	8.39407	+	12.5626i	0.595040	+	0.890540i	0.999714	−	0.0239212i	$-0.00761507\pi$
$199$	8.39407	+	12.5626i	0.595040	+	0.890540i	−0.404674	+	0.914461i	$0.632615\pi$
$200$	−4.72944	+	1.98440i	−0.334422	+	0.140318i
$201$	0.163750	−	0.823226i	0.0115500	−	0.0580659i
$202$	19.8153	−	5.34190i	1.39420	−	0.375855i
$203$	11.7332			0.823508
$204$	−18.2457	+	15.2823i	−1.27745	+	1.06998i
$205$	−7.70358			−0.538041
$206$	−19.2022	+	5.17662i	−1.33788	+	0.360672i
$207$	4.49635	−	22.6047i	0.312518	−	1.57114i
$208$	−9.36203	+	2.56986i	−0.649140	+	0.178188i
$209$	2.33490	+	3.49442i	0.161508	+	0.241714i
$210$	0.654582	+	9.75891i	0.0451704	+	0.673429i
$211$	−10.0842	−	6.73807i	−0.694227	−	0.463868i	0.157728	−	0.987483i	$-0.449583\pi$
$211$	−10.0842	−	6.73807i	−0.694227	−	0.463868i	−0.851955	+	0.523615i	$0.824583\pi$
$212$	7.51702	−	9.85848i	0.516271	−	0.677083i
$213$	26.1490	+	10.8313i	1.79170	+	0.742146i
$214$	−11.2575	−	9.84225i	−0.769548	−	0.672802i
$215$	9.60341	−	1.91024i	0.654947	−	0.130277i
$216$	18.6400	−	3.79647i	1.26829	−	0.258317i
$217$	0.943161	+	0.943161i	0.0640259	+	0.0640259i
$218$	−5.65302	−	1.90933i	−0.382871	−	0.129316i
$219$	−7.69648	+	3.18799i	−0.520080	+	0.215424i
$220$	17.3325	+	4.58761i	1.16856	+	0.309297i
$221$	4.06639	−	9.14368i	0.273535	−	0.615071i
$222$	−11.6469	−	1.51528i	−0.781691	−	0.101699i
$223$	3.21585	+	7.76376i	0.215350	+	0.519900i	0.994230	−	0.107273i	$-0.0342119\pi$
$223$	3.21585	+	7.76376i	0.215350	+	0.519900i	−0.778880	+	0.627173i	$0.784212\pi$
$224$	5.05010	+	5.67071i	0.337424	+	0.378891i
$225$	−6.83453	+	6.83453i	−0.455636	+	0.455636i
$226$	−10.0033	+	4.95208i	−0.665412	+	0.329407i
$227$	−0.0555394	−	0.279215i	−0.00368628	−	0.0185322i	0.978898	−	0.204348i	$-0.0655073\pi$
$227$	−0.0555394	−	0.279215i	−0.00368628	−	0.0185322i	−0.982585	+	0.185816i	$0.940507\pi$
$228$	3.62227	−	3.19625i	0.239891	−	0.211677i
$229$	−8.51435	+	20.5555i	−0.562644	+	1.35834i	0.345001	+	0.938602i	$0.387879\pi$
$229$	−8.51435	+	20.5555i	−0.562644	+	1.35834i	−0.907644	+	0.419740i	$0.862121\pi$
$230$	−9.46181	−	5.44356i	−0.623894	−	0.358937i
$231$	−10.8093	+	16.1773i	−0.711201	+	1.06439i
$232$	−24.2695	−	4.71217i	−1.59337	−	0.309369i
$233$	14.0954	−	9.41822i	0.923418	−	0.617008i	−0.000333628	−	1.00000i	$-0.500106\pi$
$233$	14.0954	−	9.41822i	0.923418	−	0.617008i	0.923752	+	0.382992i	$0.125106\pi$
$234$	−14.4978	+	11.1598i	−0.947754	+	0.729536i
$235$	3.93103	+	0.781930i	0.256432	+	0.0510075i
$236$	−3.98204	+	0.536607i	−0.259209	+	0.0349302i
$237$		−	25.7973i		−	1.67571i
$238$	−7.82050	+	0.322536i	−0.506928	+	0.0209069i
$239$		−	13.9613i		−	0.903081i	−0.892251	−	0.451541i	$-0.850875\pi$
$239$		−	13.9613i		−	0.903081i	0.892251	−	0.451541i	$-0.149125\pi$
$240$	2.56531	−	20.4487i	0.165590	−	1.31996i
$241$	5.79160	+	1.15202i	0.373070	+	0.0742082i	0.378064	−	0.925779i	$-0.376590\pi$
$241$	5.79160	+	1.15202i	0.373070	+	0.0742082i	−0.00499442	+	0.999988i	$0.501590\pi$
$242$	12.2660	+	15.9349i	0.788486	+	1.02434i
$243$	−8.56733	+	5.72451i	−0.549595	+	0.367227i
$244$	−12.0026	−	0.749928i	−0.768385	−	0.0480092i
$245$	5.15528	−	7.71543i	0.329359	−	0.492921i
$246$	−8.78392	+	15.2679i	−0.560042	+	0.973447i
$247$	−0.777297	+	1.87656i	−0.0494582	+	0.119403i
$248$	−1.57210	−	2.32967i	−0.0998283	−	0.147934i
$249$	1.03103	+	5.18333i	0.0653388	+	0.328480i
$250$	7.63114	+	15.4151i	0.482636	+	0.974937i
$251$	13.8365	−	13.8365i	0.873353	−	0.873353i	−0.119484	−	0.992836i	$-0.538124\pi$
$251$	13.8365	−	13.8365i	0.873353	−	0.873353i	0.992836	+	0.119484i	$0.0381239\pi$
$252$	12.8535	+	6.28998i	0.809695	+	0.396232i
$253$	−8.30969	−	20.0614i	−0.522426	−	1.26125i
$254$	0.791143	−	6.08098i	0.0496407	−	0.381554i
$255$	14.6294	+	15.4031i	0.916130	+	0.964581i
$256$	−8.16846	−	13.7578i	−0.510529	−	0.859861i
$257$	8.22800	−	3.40815i	0.513249	−	0.212595i	−0.111000	−	0.993820i	$-0.535405\pi$
$257$	8.22800	−	3.40815i	0.513249	−	0.212595i	0.624249	+	0.781226i	$0.285405\pi$
$258$	7.16423	−	21.2114i	0.446026	−	1.32056i
$259$	−2.73125	−	2.73125i	−0.169712	−	0.169712i
$260$	2.81038	+	8.19689i	0.174292	+	0.508349i
$261$	−45.6953	+	9.08936i	−2.82847	+	0.562617i
$262$	17.6462	−	20.1837i	1.09019	−	1.24695i
$263$	12.6108	+	5.22356i	0.777614	+	0.322098i	0.735952	−	0.677033i	$-0.236735\pi$
$263$	12.6108	+	5.22356i	0.777614	+	0.322098i	0.0416618	+	0.999132i	$0.486735\pi$
$264$	28.8555	−	29.1208i	1.77593	−	1.79226i
$265$	−9.20057	−	6.14763i	−0.565187	−	0.377646i
$266$	1.58514	−	0.106324i	0.0971911	−	0.00651912i
$267$	6.85672	+	10.2618i	0.419624	+	0.628012i
$268$	−0.502817	+	0.292350i	−0.0307144	+	0.0178581i
$269$	−4.83460	+	24.3052i	−0.294771	+	1.48191i	0.495206	+	0.868776i	$0.335093\pi$
$269$	−4.83460	+	24.3052i	−0.294771	+	1.48191i	−0.789976	+	0.613137i	$0.789907\pi$
$270$	−4.41948	−	16.3937i	−0.268961	−	0.997688i
$271$	−25.5812			−1.55395			−0.776975	−	0.629532i	$-0.783247\pi$
$271$	−25.5812			−1.55395			−0.776975	+	0.629532i	$0.783247\pi$
$272$	16.3059	+	2.47365i	0.988688	+	0.149987i
$273$	−9.40324			−0.569110
$274$	−3.85635	−	14.3048i	−0.232970	−	0.864183i
$275$	−1.77656	+	8.93137i	−0.107131	+	0.538582i
$276$	−21.5775	+	12.5457i	−1.29881	+	0.755160i
$277$	2.18357	+	3.26795i	0.131198	+	0.196352i	0.891252	−	0.453508i	$-0.149828\pi$
$277$	2.18357	+	3.26795i	0.131198	+	0.196352i	−0.760054	+	0.649860i	$0.774828\pi$
$278$	−4.69865	+	0.315163i	−0.281806	+	0.0189022i
$279$	−4.40381	−	2.94253i	−0.263649	−	0.176165i
$280$	4.77053	−	4.81438i	0.285094	−	0.287714i
$281$	−16.9165	−	7.00705i	−1.00915	−	0.418005i	−0.184008	−	0.982925i	$-0.558907\pi$
$281$	−16.9165	−	7.00705i	−1.00915	−	0.418005i	−0.825146	+	0.564919i	$0.808907\pi$
$282$	6.03204	−	6.89942i	0.359203	−	0.410855i
$283$	−8.25526	+	1.64207i	−0.490724	+	0.0976111i	−0.434249	−	0.900793i	$-0.642986\pi$
$283$	−8.25526	+	1.64207i	−0.490724	+	0.0976111i	−0.0564751	+	0.998404i	$0.517986\pi$
$284$	−6.36097	−	18.5527i	−0.377454	−	1.10090i
$285$	−3.04891	−	3.04891i	−0.180602	−	0.180602i
$286$	−5.51581	+	16.3308i	−0.326157	+	0.965662i
$287$	−5.35185	+	2.21681i	−0.315910	+	0.130854i
$288$	−24.0607	−	18.1726i	−1.41779	−	1.07083i
$289$	−12.6238	+	11.3859i	−0.742577	+	0.669760i
$290$	−2.84689	+	21.8821i	−0.167175	+	1.28496i
$291$	11.6396	+	28.1005i	0.682326	+	1.64728i
$292$	5.18513	+	2.53739i	0.303437	+	0.148490i
$293$	1.10042	−	1.10042i	0.0642871	−	0.0642871i	−0.674232	−	0.738519i	$-0.735525\pi$
$293$	1.10042	−	1.10042i	0.0642871	−	0.0642871i	0.738519	+	0.674232i	$0.235525\pi$
$294$	−9.41316	−	19.0148i	−0.548986	−	1.10897i
$295$	0.699661	+	3.51743i	0.0407358	+	0.204793i
$296$	4.55256	+	6.74637i	0.264612	+	0.392125i
$297$	12.9251	−	31.2039i	0.749990	−	1.81064i
$298$	−4.39488	+	7.63903i	−0.254588	+	0.442517i
$299$	5.83045	−	8.72589i	0.337184	−	0.504631i
$300$	10.4470	+	0.652734i	0.603156	+	0.0376856i
$301$	6.12201	−	4.09060i	0.352867	−	0.235778i
$302$	20.4117	+	26.5172i	1.17456	+	1.52589i
$303$	−41.0793	−	8.17118i	−2.35994	−	0.469422i
$304$	−3.32148	−	0.416684i	−0.190500	−	0.0238984i
$305$			10.7339i			0.614622i
$306$	30.2074	−	7.31445i	1.72684	−	0.418139i
$307$			22.6712i			1.29391i	0.762528	+	0.646955i	$0.223958\pi$
$307$			22.6712i			1.29391i	−0.762528	+	0.646955i	$0.776042\pi$
$308$	13.3614	−	1.80054i	0.761338	−	0.102596i
$309$	39.8082	+	7.91835i	2.26461	+	0.450459i
$310$	−1.98782	+	1.53013i	−0.112901	+	0.0869056i
$311$	14.0183	−	9.36670i	0.794903	−	0.531137i	−0.0905359	−	0.995893i	$-0.528858\pi$
$311$	14.0183	−	9.36670i	0.794903	−	0.531137i	0.885439	+	0.464756i	$0.153858\pi$
$312$	19.4501	+	3.77644i	1.10115	+	0.213799i
$313$	12.4969	−	18.7029i	0.706366	−	1.05715i	−0.288650	−	0.957435i	$-0.593206\pi$
$313$	12.4969	−	18.7029i	0.706366	−	1.05715i	0.995016	−	0.0997165i	$-0.0317936\pi$
$314$	−6.23371	−	3.58637i	−0.351789	−	0.202391i
$315$	4.88786	−	11.8003i	0.275399	−	0.664873i
$316$	−13.4040	+	11.8275i	−0.754035	+	0.665351i
$317$	4.76163	+	23.9383i	0.267440	+	1.34451i	0.847872	+	0.530202i	$0.177884\pi$
$317$	4.76163	+	23.9383i	0.267440	+	1.34451i	−0.580432	+	0.814309i	$0.697116\pi$
$318$	−22.6750	+	11.2251i	−1.27155	+	0.629472i
$319$	−31.0386	+	31.0386i	−1.73783	+	1.73783i
$320$	−11.8011	+	8.04242i	−0.659702	+	0.449585i
$321$	11.6786	+	28.1946i	0.651836	+	1.57367i
$322$	−8.13979	−	1.05900i	−0.453613	−	0.0590156i
$323$	2.50193	−	2.37626i	0.139211	−	0.132218i
$324$	−6.61360	−	1.75051i	−0.367422	−	0.0972503i
$325$	−4.06610	+	1.68423i	−0.225547	+	0.0934244i
$326$	−6.00466	−	2.02810i	−0.332567	−	0.112326i
$327$	8.61067	+	8.61067i	0.476171	+	0.476171i
$328$	11.9603	−	2.43600i	0.660399	−	0.134505i
$329$	2.95598	−	0.587982i	0.162969	−	0.0324165i
$330$	−27.5476	−	24.0844i	−1.51644	−	1.32580i
$331$	26.8372	+	11.1163i	1.47510	+	0.611008i	0.968017	−	0.250886i	$-0.0807220\pi$
$331$	26.8372	+	11.1163i	1.47510	+	0.611008i	0.507088	+	0.861894i	$0.330722\pi$
$332$	2.22050	−	2.91217i	0.121866	−	0.159826i
$333$	12.7528	+	8.52114i	0.698849	+	0.466956i
$334$	−0.203213	−	3.02962i	−0.0111193	−	0.165774i
$335$	0.288419	+	0.431649i	0.0157580	+	0.0235835i
$336$	−4.10221	−	14.9444i	−0.223794	−	0.815283i
$337$	4.98342	−	25.0534i	0.271464	−	1.36474i	−0.568759	−	0.822504i	$-0.692576\pi$
$337$	4.98342	−	25.0534i	0.271464	−	1.36474i	0.840224	−	0.542240i	$-0.182424\pi$
$338$	9.70746	−	2.61698i	0.528016	−	0.142345i
$339$	22.7800			1.23724
$340$	1.29601	−	14.6633i	0.0702863	−	0.795231i
$341$	−4.99003			−0.270225
$342$	−6.09101	+	1.64204i	−0.329364	+	0.0887915i
$343$	3.19442	−	16.0595i	0.172483	−	0.867129i
$344$	−14.3059	+	6.00253i	−0.771322	+	0.323635i
$345$	12.3770	+	18.5235i	0.666354	+	0.997269i
$346$	−1.68195	−	25.0756i	−0.0904222	−	1.34807i
$347$	4.13565	+	2.76335i	0.222013	+	0.148344i	0.661603	−	0.749854i	$-0.269876\pi$
$347$	4.13565	+	2.76335i	0.222013	+	0.148344i	−0.439590	+	0.898198i	$0.644876\pi$
$348$	40.1227	+	30.5932i	2.15080	+	1.63997i
$349$	−21.0451	−	8.71718i	−1.12652	−	0.466620i	−0.259924	−	0.965629i	$-0.583697\pi$
$349$	−21.0451	−	8.71718i	−1.12652	−	0.466620i	−0.866597	+	0.499009i	$0.833697\pi$
$350$	2.59157	+	2.26576i	0.138525	+	0.121110i
$351$	16.0098	−	3.18455i	0.854541	−	0.169979i
$352$	−28.3606	−	1.64176i	−1.51162	−	0.0875059i
$353$	−10.3536	−	10.3536i	−0.551065	−	0.551065i	0.375683	−	0.926748i	$-0.377408\pi$
$353$	−10.3536	−	10.3536i	−0.551065	−	0.551065i	−0.926748	+	0.375683i	$0.877408\pi$
$354$	7.76907	+	2.62404i	0.412922	+	0.139466i
$355$	−16.1731	+	6.69914i	−0.858382	+	0.355553i
$356$	2.18827	−	8.26753i	0.115978	−	0.438178i
$357$	14.5958	+	6.49108i	0.772494	+	0.343544i
$358$	21.6114	+	2.81166i	1.14220	+	0.148601i
$359$	−13.1255	−	31.6878i	−0.692739	−	1.67242i	−0.739187	−	0.673500i	$-0.764790\pi$
$359$	−13.1255	−	31.6878i	−0.692739	−	1.67242i	0.0464482	−	0.998921i	$-0.485210\pi$
$360$	−14.8494	+	22.4454i	−0.782633	+	1.18298i
$361$	12.9398	−	12.9398i	0.681042	−	0.681042i
$362$	−9.31990	+	4.61375i	−0.489843	+	0.242493i
$363$	−8.00648	−	40.2513i	−0.420231	−	2.11265i
$364$	4.31120	+	4.88584i	0.225968	+	0.256087i
$365$	1.97177	−	4.76027i	0.103207	−	0.249164i
$366$	21.2738	+	12.2392i	1.11200	+	0.639755i
$367$	11.5996	−	17.3600i	0.605494	−	0.906185i	−0.394425	−	0.918928i	$-0.629056\pi$
$367$	11.5996	−	17.3600i	0.605494	−	0.906185i	0.999919	+	0.0127429i	$0.00405629\pi$
$368$	16.4115	+	5.45951i	0.855506	+	0.284597i
$369$	19.1257	−	12.7794i	0.995642	−	0.665267i
$370$	5.75644	−	4.43103i	0.299263	−	0.230358i
$371$	−8.16091	−	1.62331i	−0.423693	−	0.0842778i
$372$	0.766016	+	5.68443i	0.0397161	+	0.294724i
$373$			25.7729i			1.33447i	0.744848	+	0.667234i	$0.232522\pi$
$373$			25.7729i			1.33447i	−0.744848	+	0.667234i	$0.767478\pi$
$374$	19.8349	−	21.5414i	1.02564	−	1.11388i
$375$		−	35.1040i		−	1.81276i
$376$	−6.35045	+	0.0290561i	−0.327499	+	0.00149845i
$377$	−20.8070	−	4.13877i	−1.07162	−	0.213158i
$378$	−7.78782	−	10.1173i	−0.400562	−	0.520378i
$379$	24.4242	−	16.3197i	1.25459	−	0.838288i	0.262633	−	0.964896i	$-0.415409\pi$
$379$	24.4242	−	16.3197i	1.25459	−	0.838288i	0.991953	+	0.126608i	$0.0404090\pi$
$380$	−0.186321	+	2.98205i	−0.00955804	+	0.152976i
$381$	−6.95297	+	10.4059i	−0.356212	+	0.533108i
$382$	9.89422	−	17.1978i	0.506232	−	0.879917i
$383$	−11.1858	+	27.0049i	−0.571566	+	1.37988i	0.328655	+	0.944450i	$0.393405\pi$
$383$	−11.1858	+	27.0049i	−0.571566	+	1.37988i	−0.900221	+	0.435433i	$0.856595\pi$
$384$	2.48340	+	32.5592i	0.126730	+	1.66153i
$385$	−2.34766	−	11.8025i	−0.119648	−	0.601510i
$386$	12.1173	+	24.4772i	0.616752	+	1.24586i
$387$	−20.6735	+	20.6735i	−1.05089	+	1.05089i
$388$	9.26423	−	18.9314i	0.470320	−	0.961094i
$389$	−9.60055	−	23.1778i	−0.486767	−	1.17516i	−0.956338	−	0.292265i	$-0.905591\pi$
$389$	−9.60055	−	23.1778i	−0.486767	−	1.17516i	0.469571	−	0.882895i	$-0.344409\pi$
$390$	2.28157	−	17.5369i	0.115532	−	0.888013i
$391$	−15.0736	+	9.51968i	−0.762306	+	0.481431i
$392$	−5.56418	+	13.6089i	−0.281034	+	0.687354i
$393$	−50.5503	+	20.9386i	−2.54993	+	1.05621i
$394$	−7.58435	+	22.4552i	−0.382094	+	1.13128i
$395$	11.2823	+	11.2823i	0.567675	+	0.567675i
$396$	−50.6417	+	17.3630i	−2.54484	+	0.872523i
$397$	−18.0161	+	3.58363i	−0.904203	+	0.179857i	−0.625229	−	0.780441i	$-0.714994\pi$
$397$	−18.0161	+	3.58363i	−0.904203	+	0.179857i	−0.278974	+	0.960299i	$0.589994\pi$
$398$	−14.0639	+	16.0862i	−0.704959	+	0.806329i
$399$	−2.99551	−	1.24078i	−0.149963	−	0.0621168i
$400$	−4.45057	−	5.72741i	−0.222529	−	0.286371i
$401$	−3.03812	−	2.03001i	−0.151717	−	0.101374i	0.477395	−	0.878689i	$-0.341581\pi$
$401$	−3.03812	−	2.03001i	−0.151717	−	0.101374i	−0.629112	+	0.777315i	$0.716581\pi$
$402$	1.18436	−	0.0794416i	0.0590707	−	0.00396219i
$403$	−1.33986	−	2.00525i	−0.0667433	−	0.0998884i
$404$	14.5884	+	25.0907i	0.725799	+	1.24831i
$405$	−1.19128	+	5.98899i	−0.0591954	+	0.297595i
$406$	4.31908	+	16.0212i	0.214352	+	0.795121i
$407$	14.4504			0.716279
$408$	−27.5839	−	19.2883i	−1.36561	−	0.954914i
$409$	−8.84736			−0.437474			−0.218737	−	0.975784i	$-0.570194\pi$
$409$	−8.84736			−0.437474			−0.218737	+	0.975784i	$0.570194\pi$
$410$	−2.83575	−	10.5190i	−0.140048	−	0.519495i
$411$	−5.89881	+	29.6553i	−0.290967	+	1.46279i
$412$	−14.1370	−	24.3144i	−0.696479	−	1.19788i
$413$	1.49826	+	2.24230i	0.0737245	+	0.110336i
$414$	32.5211	−	2.18136i	1.59832	−	0.107208i
$415$	−2.71782	−	1.81599i	−0.133413	−	0.0891435i
$416$	−6.95530	−	11.8375i	−0.341012	−	0.580383i
$417$	8.87925	+	3.67791i	0.434819	+	0.180108i
$418$	−3.91202	+	4.47455i	−0.191343	+	0.218857i
$419$	−9.33540	+	1.85693i	−0.456064	+	0.0907168i	−0.417776	−	0.908550i	$-0.637190\pi$
$419$	−9.33540	+	1.85693i	−0.456064	+	0.0907168i	−0.0382879	+	0.999267i	$0.512190\pi$
$420$	−13.0845	+	4.48615i	−0.638458	+	0.218901i
$421$	−18.2677	−	18.2677i	−0.890312	−	0.890312i	0.104240	−	0.994552i	$-0.466759\pi$
$421$	−18.2677	−	18.2677i	−0.890312	−	0.890312i	−0.994552	+	0.104240i	$0.966759\pi$
$422$	5.48851	−	16.2500i	0.267176	−	0.791038i
$423$	−11.0567	+	4.57983i	−0.537595	+	0.222679i
$424$	16.2285	+	6.63524i	0.788125	+	0.322236i
$425$	7.47409	+	0.192545i	0.362547	+	0.00933983i
$426$	−5.16406	+	39.6926i	−0.250199	+	1.92311i
$427$	3.08883	+	7.45709i	0.149479	+	0.360874i
$428$	9.29526	−	18.9948i	0.449303	−	0.918147i
$429$	24.8751	−	24.8751i	1.20098	−	1.20098i
$430$	6.14346	+	12.4100i	0.296264	+	0.598461i
$431$	−1.45038	−	7.29157i	−0.0698626	−	0.351223i	0.930004	−	0.367549i	$-0.119803\pi$
$431$	−1.45038	−	7.29157i	−0.0698626	−	0.351223i	−0.999867	+	0.0163262i	$0.994803\pi$
$432$	12.0455	+	24.0548i	0.579540	+	1.15734i
$433$	−9.40065	+	22.6952i	−0.451766	+	1.09066i	0.519884	+	0.854237i	$0.325975\pi$
$433$	−9.40065	+	22.6952i	−0.451766	+	1.09066i	−0.971650	+	0.236423i	$0.924025\pi$
$434$	−0.940668	+	1.63504i	−0.0451535	+	0.0784844i
$435$	25.0200	−	37.4451i	1.19962	−	1.79535i
$436$	0.526203	−	8.42185i	0.0252006	−	0.403333i
$437$	3.00876	−	2.01039i	0.143929	−	0.0961700i
$438$	−7.18622	−	9.33575i	−0.343371	−	0.446080i
$439$	12.1200	+	2.41082i	0.578456	+	0.115062i	0.475643	−	0.879639i	$-0.342216\pi$
$439$	12.1200	+	2.41082i	0.578456	+	0.115062i	0.102813	+	0.994701i	$0.467216\pi$
$440$	0.116013	+	25.3557i	0.00553072	+	1.20878i
$441$			27.7071i			1.31939i
$442$	13.9823	+	2.18665i	0.665068	+	0.104008i
$443$		−	9.04955i		−	0.429957i	−0.976619	−	0.214979i	$-0.931032\pi$
$443$		−	9.04955i		−	0.429957i	0.976619	−	0.214979i	$-0.0689682\pi$
$444$	−2.21827	−	16.4613i	−0.105274	−	0.781218i
$445$	−7.48671	−	1.48920i	−0.354904	−	0.0705948i
$446$	−9.41736	+	7.24904i	−0.445925	+	0.343252i
$447$	14.9550	−	9.99260i	0.707346	−	0.472634i
$448$	−5.88418	+	8.98318i	−0.278001	+	0.424415i
$449$	0.419431	−	0.627722i	0.0197942	−	0.0296240i	−0.821441	−	0.570294i	$-0.806829\pi$
$449$	0.419431	−	0.627722i	0.0197942	−	0.0296240i	0.841235	+	0.540670i	$0.181829\pi$
$450$	−11.8482	−	6.81647i	−0.558528	−	0.321332i
$451$	8.29335	−	20.0219i	0.390519	−	0.942796i
$452$	−10.4442	−	11.8363i	−0.491254	−	0.556733i
$453$	−13.3235	−	66.9818i	−0.625993	−	3.14708i
$454$	0.360814	−	0.178619i	0.0169339	−	0.00838298i
$455$	4.11247	−	4.11247i	0.192795	−	0.192795i
$456$	5.69776	+	3.76953i	0.266822	+	0.176524i
$457$	8.16305	+	19.7073i	0.381851	+	0.921871i	0.991608	+	0.129282i	$0.0412672\pi$
$457$	8.16305	+	19.7073i	0.381851	+	0.921871i	−0.609756	+	0.792589i	$0.708733\pi$
$458$	−31.2020	−	4.05941i	−1.45797	−	0.189684i
$459$	−27.0490	−	6.10851i	−1.26254	−	0.285121i
$460$	3.95002	−	14.9236i	0.184170	−	0.695816i
$461$	34.9014	−	14.4566i	1.62552	−	0.673313i	0.630802	−	0.775944i	$-0.282726\pi$
$461$	34.9014	−	14.4566i	1.62552	−	0.673313i	0.994720	+	0.102630i	$0.0327259\pi$
$462$	−26.0685	−	8.80475i	−1.21282	−	0.409634i
$463$	−4.48309	−	4.48309i	−0.208347	−	0.208347i	0.595218	−	0.803565i	$-0.297066\pi$
$463$	−4.48309	−	4.48309i	−0.208347	−	0.208347i	−0.803565	+	0.595218i	$0.797066\pi$
$464$	−2.49950	−	34.8738i	−0.116036	−	1.61897i
$465$	5.02120	−	0.998778i	0.232852	−	0.0463172i
$466$	18.0489	+	15.7798i	0.836098	+	0.730986i
$467$	−26.0189	−	10.7774i	−1.20401	−	0.498718i	−0.311719	−	0.950174i	$-0.600905\pi$
$467$	−26.0189	−	10.7774i	−1.20401	−	0.498718i	−0.892293	+	0.451456i	$0.850905\pi$
$468$	−20.5750	−	15.6883i	−0.951082	−	0.725192i
$469$	0.324584	+	0.216880i	0.0149879	+	0.0100146i
$470$	0.379346	+	5.65552i	0.0174979	+	0.260870i
$471$	8.15431	+	12.2038i	0.375731	+	0.562321i
$472$	−2.19854	−	5.23981i	−0.101196	−	0.241182i
$473$	−5.37385	+	27.0162i	−0.247090	+	1.24220i
$474$	35.2253	−	9.49619i	1.61795	−	0.436174i
$475$	−1.51754			−0.0696296
$476$	−3.31920	−	10.5599i	−0.152135	−	0.484012i
$477$	33.0405			1.51282
$478$	19.0637	−	5.13927i	0.871952	−	0.235065i
$479$	−1.12114	+	5.63635i	−0.0512262	+	0.257532i	−0.997909	−	0.0646359i	$-0.979411\pi$
$479$	−1.12114	+	5.63635i	−0.0512262	+	0.257532i	0.946683	+	0.322167i	$0.104411\pi$
$480$	28.8663	−	4.02449i	1.31756	−	0.183692i
$481$	3.88004	+	5.80689i	0.176915	+	0.264772i
$482$	0.558892	+	8.33230i	0.0254568	+	0.379526i
$483$	13.9289	+	9.30702i	0.633789	+	0.423484i
$484$	−17.2434	+	22.6145i	−0.783791	+	1.02793i
$485$	−17.3802	−	7.19910i	−0.789193	−	0.326894i
$486$	−10.9703	−	9.59116i	−0.497624	−	0.435064i
$487$	28.1838	−	5.60611i	1.27713	−	0.254037i	0.490489	−	0.871447i	$-0.336818\pi$
$487$	28.1838	−	5.60611i	1.27713	−	0.254037i	0.786641	+	0.617410i	$0.211818\pi$
$488$	−3.39424	−	16.6651i	−0.153650	−	0.754395i
$489$	9.14628	+	9.14628i	0.413609	+	0.413609i
$490$	12.4329	+	4.19925i	0.561659	+	0.189703i
$491$	−13.7267	+	5.68577i	−0.619476	+	0.256595i	−0.670274	−	0.742114i	$-0.733823\pi$
$491$	−13.7267	+	5.68577i	−0.619476	+	0.256595i	0.0507983	+	0.998709i	$0.483823\pi$
$492$	−24.0813	−	6.37389i	−1.08567	−	0.287357i
$493$	29.4400	+	20.7874i	1.32591	+	0.936218i
$494$	−2.84851	−	0.370595i	−0.128161	−	0.0166738i
$495$	18.2861	+	44.1465i	0.821898	+	1.98424i
$496$	2.60238	−	3.00421i	0.116850	−	0.134893i
$497$	−9.30808	+	9.30808i	−0.417525	+	0.417525i
$498$	−6.69813	+	3.31586i	−0.300150	+	0.148587i
$499$	1.89929	+	9.54836i	0.0850237	+	0.427443i	0.999728	+	0.0233195i	$0.00742350\pi$
$499$	1.89929	+	9.54836i	0.0850237	+	0.427443i	−0.914704	+	0.404124i	$0.867577\pi$
$500$	−18.2397	+	16.0945i	−0.815705	+	0.719767i
$501$	−2.37147	+	5.72522i	−0.105949	+	0.255784i
$502$	23.9866	+	13.7999i	1.07057	+	0.615922i
$503$	−8.29120	+	12.4087i	−0.369686	+	0.553275i	−0.968944	−	0.247282i	$-0.920463\pi$
$503$	−8.29120	+	12.4087i	−0.369686	+	0.553275i	0.599257	+	0.800556i	$0.295463\pi$
$504$	−3.85727	+	19.8664i	−0.171816	+	0.884921i
$505$	21.5395	−	14.3922i	0.958494	−	0.640445i
$506$	24.3342	−	18.7313i	1.08179	−	0.832710i
$507$	−20.1246	−	4.00303i	−0.893765	−	0.177781i
$508$	8.59459	−	1.15818i	0.381323	−	0.0513859i
$509$			2.75472i			0.122101i	0.998135	+	0.0610504i	$0.0194450\pi$
$509$			2.75472i			0.122101i	−0.998135	+	0.0610504i	$0.980555\pi$
$510$	−15.6472	+	25.6460i	−0.692870	+	1.13562i
$511$		−	3.87447i		−	0.171397i
$512$	15.7789	−	16.2181i	0.697335	−	0.716746i
$513$	5.52032	+	1.09806i	0.243728	+	0.0484805i
$514$	7.68251	+	9.98049i	0.338861	+	0.440220i
$515$	−20.8730	+	13.9469i	−0.919774	+	0.614574i
$516$	31.6006	+	1.97443i	1.39114	+	0.0869194i
$517$	−6.26425	+	9.37511i	−0.275501	+	0.412317i
$518$	2.72404	−	4.73483i	0.119687	−	0.208037i
$519$	−19.6281	+	47.3865i	−0.861579	+	2.08003i
$520$	−10.1580	+	6.85482i	−0.445460	+	0.300604i
$521$	5.32582	+	26.7747i	0.233329	+	1.17302i	0.902759	+	0.430147i	$0.141538\pi$
$521$	5.32582	+	26.7747i	0.233329	+	1.17302i	−0.669430	+	0.742875i	$0.733462\pi$
$522$	−29.2320	−	59.0495i	−1.27945	−	2.58452i
$523$	22.8232	−	22.8232i	0.997987	−	0.997987i	−0.00201122	−	0.999998i	$-0.500640\pi$
$523$	22.8232	−	22.8232i	0.997987	−	0.997987i	0.999998	+	0.00201122i	$0.000640191\pi$
$524$	34.0559	+	16.6655i	1.48774	+	0.728038i
$525$	−2.68850	−	6.49062i	−0.117336	−	0.283274i
$526$	−2.49045	+	19.1424i	−0.108589	+	0.834649i
$527$	0.695528	+	4.03748i	0.0302977	+	0.175875i
$528$	50.3854	+	28.6816i	2.19274	+	1.24821i
$529$	3.97603	−	1.64693i	0.172871	−	0.0716054i
$530$	5.00756	−	14.8261i	0.217515	−	0.644003i
$531$	−7.57207	−	7.57207i	−0.328600	−	0.328600i
$532$	0.728684	+	2.12531i	0.0315925	+	0.0921440i
$533$	10.2727	−	2.04336i	0.444958	−	0.0885077i
$534$	−11.4881	+	13.1401i	−0.497140	+	0.568627i
$535$	−17.4384	−	7.22321i	−0.753927	−	0.312287i
$536$	−0.584285	−	0.578962i	−0.0252373	−	0.0250074i
$537$	−36.9817	−	24.7104i	−1.59588	−	1.06633i
$538$	−34.9675	+	2.34546i	−1.50756	+	0.101120i
$539$	14.5028	+	21.7049i	0.624678	+	0.934897i
$540$	20.7582	−	12.0693i	0.893289	−	0.519380i
$541$	2.79175	−	14.0351i	0.120027	−	0.603415i	−0.873214	−	0.487338i	$-0.837968\pi$
$541$	2.79175	−	14.0351i	0.120027	−	0.603415i	0.993240	−	0.116077i	$-0.0370319\pi$
$542$	−9.41667	−	34.9303i	−0.404481	−	1.50038i
$543$	21.2237			0.910796
$544$	2.62464	+	23.1757i	0.112530	+	0.993648i
$545$	−7.53168			−0.322622
$546$	−3.46141	−	12.8398i	−0.148135	−	0.549493i
$547$	3.66488	−	18.4246i	0.156699	−	0.787779i	−0.819866	−	0.572555i	$-0.805952\pi$
$547$	3.66488	−	18.4246i	0.156699	−	0.787779i	0.976565	−	0.215223i	$-0.0690479\pi$
$548$	18.1131	−	10.5314i	0.773754	−	0.449880i
$549$	−17.8064	−	26.6491i	−0.759957	−	1.13736i
$550$	−12.8494	+	0.861880i	−0.547902	+	0.0367507i
$551$	−6.08220	−	4.06399i	−0.259110	−	0.173132i
$552$	−25.0735	−	24.8451i	−1.06720	−	1.05748i
$553$	11.0847	+	4.59144i	0.471370	+	0.195248i
$554$	−3.65848	+	4.18455i	−0.155434	+	0.177784i
$555$	−14.5406	+	2.89231i	−0.617216	+	0.122772i
$556$	−2.15996	−	6.29983i	−0.0916025	−	0.267172i
$557$	7.58955	+	7.58955i	0.321580	+	0.321580i	0.849373	−	0.527793i	$-0.176980\pi$
$557$	7.58955	+	7.58955i	0.321580	+	0.321580i	−0.527793	+	0.849373i	$0.676980\pi$
$558$	2.39685	−	7.09643i	0.101467	−	0.300416i
$559$	−12.2994	+	5.09457i	−0.520208	+	0.215477i
$560$	8.32994	+	4.74178i	0.352004	+	0.200377i
$561$	−55.7828	+	21.4401i	−2.35515	+	0.905204i
$562$	3.34077	−	25.6783i	0.140922	−	1.08317i
$563$	15.9024	+	38.3917i	0.670205	+	1.61802i	0.781261	+	0.624205i	$0.214577\pi$
$563$	15.9024	+	38.3917i	0.670205	+	1.61802i	−0.111055	+	0.993814i	$0.535423\pi$
$564$	11.6414	+	5.69681i	0.490190	+	0.239879i
$565$	−9.96275	+	9.96275i	−0.419136	+	0.419136i
$566$	−5.28102	−	10.6678i	−0.221978	−	0.448401i
$567$	0.895801	+	4.50350i	0.0376201	+	0.189129i
$568$	22.9915	−	15.5151i	0.964703	−	0.650998i
$569$	9.02237	−	21.7819i	0.378237	−	0.913146i	−0.614059	−	0.789260i	$-0.710464\pi$
$569$	9.02237	−	21.7819i	0.378237	−	0.913146i	0.992296	−	0.123886i	$-0.0395357\pi$
$570$	3.04085	−	5.28551i	0.127367	−	0.221386i
$571$	−23.2762	+	34.8353i	−0.974078	+	1.45781i	−0.0869905	+	0.996209i	$0.527725\pi$
$571$	−23.2762	+	34.8353i	−0.974078	+	1.45781i	−0.887087	+	0.461601i	$0.847275\pi$
$572$	−24.3296	−	1.52013i	−1.01727	−	0.0635598i
$573$	−33.6683	+	22.4964i	−1.40651	+	0.939801i
$574$	−4.99703	−	6.49174i	−0.208572	−	0.270960i
$575$	7.69007	+	1.52965i	0.320698	+	0.0637908i
$576$	15.9571	−	39.5436i	0.664881	−	1.64765i
$577$		−	1.51084i		−	0.0628972i	−0.999505	−	0.0314486i	$-0.989988\pi$
$577$		−	1.51084i		−	0.0628972i	0.999505	−	0.0314486i	$-0.0100120\pi$
$578$	−20.1940	−	13.0461i	−0.839961	−	0.542647i
$579$		−	55.7406i		−	2.31650i
$580$	−30.9273	+	4.16766i	−1.28419	+	0.173053i
$581$	−2.41071	−	0.479520i	−0.100013	−	0.0198938i
$582$	−34.0856	+	26.2375i	−1.41290	+	1.08758i
$583$	25.8829	−	17.2944i	1.07196	−	0.716261i
$584$	−1.55603	+	8.01415i	−0.0643890	+	0.331628i
$585$	−12.8303	+	19.2020i	−0.530469	+	0.793903i
$586$	1.90766	+	1.09751i	0.0788045	+	0.0453377i
$587$	−12.3602	+	29.8402i	−0.510160	+	1.23164i	0.433630	+	0.901091i	$0.357232\pi$
$587$	−12.3602	+	29.8402i	−0.510160	+	1.23164i	−0.943790	+	0.330545i	$0.892768\pi$
$588$	22.4990	−	19.8529i	0.927845	−	0.818718i
$589$	−0.162231	−	0.815592i	−0.00668463	−	0.0336059i
$590$	−4.54538	+	2.25016i	−0.187130	+	0.0926376i
$591$	34.2037	−	34.2037i	1.40695	−	1.40695i
$592$	−7.53609	+	8.69976i	−0.309732	+	0.357558i
$593$	−7.23989	−	17.4786i	−0.297307	−	0.717761i	−0.999980	−	0.00624946i	$-0.998011\pi$
$593$	−7.23989	−	17.4786i	−0.297307	−	0.717761i	0.702674	−	0.711512i	$-0.251989\pi$
$594$	47.3657	+	6.16234i	1.94344	+	0.252844i
$595$	−9.22227	+	3.54459i	−0.378076	+	0.145314i
$596$	−12.0486	−	3.18906i	−0.493531	−	0.130629i
$597$	40.2882	−	16.6879i	1.64888	−	0.682990i
$598$	14.0611	+	4.74921i	0.575003	+	0.194210i
$599$	10.2655	+	10.2655i	0.419438	+	0.419438i	0.885010	−	0.465572i	$-0.154151\pi$
$599$	10.2655	+	10.2655i	0.419438	+	0.419438i	−0.465572	+	0.885010i	$0.654151\pi$
$600$	2.95433	+	14.5053i	0.120610	+	0.592174i
$601$	28.6294	−	5.69474i	1.16782	−	0.232293i	0.427160	−	0.904176i	$-0.359514\pi$
$601$	28.6294	−	5.69474i	1.16782	−	0.232293i	0.740658	+	0.671883i	$0.234514\pi$
$602$	7.83913	+	6.85361i	0.319499	+	0.279332i
$603$	−1.43211	−	0.593201i	−0.0583202	−	0.0241570i
$604$	−28.6946	+	37.6326i	−1.16757	+	1.53125i
$605$	21.1053	+	14.1021i	0.858054	+	0.573333i
$606$	−3.96417	−	59.1002i	−0.161033	−	2.40078i
$607$	−10.7489	−	16.0869i	−0.436285	−	0.652947i	0.546551	−	0.837426i	$-0.315940\pi$
$607$	−10.7489	−	16.0869i	−0.436285	−	0.652947i	−0.982836	+	0.184479i	$0.940940\pi$
$608$	−0.653698	−	4.68875i	−0.0265110	−	0.190154i
$609$	6.60663	−	33.2138i	0.267714	−	1.34589i
$610$	−14.6568	+	3.95124i	−0.593436	+	0.159981i
$611$	−5.44940			−0.220459
$612$	21.1072	+	38.5546i	0.853208	+	1.55848i
$613$	36.7642			1.48489			0.742446	−	0.669906i	$-0.233666\pi$
$613$	36.7642			1.48489			0.742446	+	0.669906i	$0.233666\pi$
$614$	−30.9567	+	8.34544i	−1.24931	+	0.336795i
$615$	−4.33767	+	21.8069i	−0.174912	+	0.879341i
$616$	7.37703	+	17.5818i	0.297229	+	0.708390i
$617$	−8.09289	−	12.1119i	−0.325807	−	0.487605i	0.632019	−	0.774953i	$-0.282226\pi$
$617$	−8.09289	−	12.1119i	−0.325807	−	0.487605i	−0.957826	+	0.287348i	$0.907226\pi$
$618$	3.84151	+	57.2716i	0.154528	+	2.30380i
$619$	−30.0086	−	20.0511i	−1.20615	−	0.805921i	−0.220606	−	0.975363i	$-0.570804\pi$
$619$	−30.0086	−	20.0511i	−1.20615	−	0.805921i	−0.985540	+	0.169442i	$0.945804\pi$
$620$	−2.82108	−	2.15105i	−0.113297	−	0.0863881i
$621$	−26.8672	−	11.1287i	−1.07814	−	0.446581i
$622$	17.9502	+	15.6935i	0.719736	+	0.629252i
$623$	−5.62973	+	1.11982i	−0.225550	+	0.0448647i
$624$	2.00316	+	27.9486i	0.0801904	+	1.11884i
$625$	8.94147	+	8.94147i	0.357659	+	0.357659i
$626$	30.1384	+	10.1794i	1.20457	+	0.406849i
$627$	11.2066	−	4.64192i	0.447548	−	0.185380i
$628$	2.60238	−	9.83210i	0.103846	−	0.392343i
$629$	−2.01415	−	11.6920i	−0.0803093	−	0.466189i
$630$	17.9122	+	2.33040i	0.713639	+	0.0928453i
$631$	5.84136	+	14.1023i	0.232541	+	0.561403i	0.996475	−	0.0838910i	$-0.0267348\pi$
$631$	5.84136	+	14.1023i	0.232541	+	0.561403i	−0.763934	+	0.645294i	$0.776735\pi$
$632$	−21.0842	−	13.9489i	−0.838686	−	0.554858i
$633$	−24.7520	+	24.7520i	−0.983803	+	0.983803i
$634$	−30.9342	+	15.3137i	−1.22855	+	0.608186i
$635$	−1.51010	−	7.59181i	−0.0599267	−	0.301272i
$636$	−23.6743	−	26.8299i	−0.938749	−	1.06387i
$637$	−4.82803	+	11.6559i	−0.191293	+	0.461823i
$638$	−53.8078	−	30.9566i	−2.13027	−	1.22558i
$639$	29.0400	−	43.4614i	1.14880	−	1.71931i
$640$	−15.3257	−	13.1535i	−0.605803	−	0.519939i
$641$	0.00674020	−	0.00450366i	0.000266222	−	0.000177884i	−0.555437	−	0.831559i	$-0.687449\pi$
$641$	0.00674020	−	0.00450366i	0.000266222	−	0.000177884i	0.555703	+	0.831381i	$0.312449\pi$
$642$	−34.1998	+	26.3254i	−1.34976	+	1.03898i
$643$	−17.9589	−	3.57225i	−0.708230	−	0.140876i	−0.172184	−	0.985065i	$-0.555082\pi$
$643$	−17.9589	−	3.57225i	−0.708230	−	0.140876i	−0.536046	+	0.844189i	$0.680082\pi$
$644$	−1.55030	−	11.5044i	−0.0610904	−	0.453338i
$645$		−	28.2605i		−	1.11276i
$646$	4.16568	+	2.54158i	0.163896	+	0.0999970i
$647$		−	3.14632i		−	0.123694i	−0.998086	−	0.0618472i	$-0.980301\pi$
$647$		−	3.14632i		−	0.123694i	0.998086	−	0.0618472i	$-0.0196992\pi$
$648$	−0.0442675	−	9.67503i	−0.00173899	−	0.380071i
$649$	−9.89518	−	1.96827i	−0.388420	−	0.0772615i
$650$	−3.79653	−	4.93214i	−0.148912	−	0.193454i
$651$	3.20093	−	2.13879i	0.125454	−	0.0838258i
$652$	0.558934	−	8.94571i	0.0218895	−	0.350341i
$653$	−7.56661	+	11.3242i	−0.296104	+	0.443151i	−0.949455	−	0.313904i	$-0.898363\pi$
$653$	−7.56661	+	11.3242i	−0.296104	+	0.443151i	0.653350	+	0.757056i	$0.273363\pi$
$654$	−8.58792	+	14.9272i	−0.335814	+	0.583701i
$655$	12.9505	−	31.2654i	0.506020	−	1.22164i
$656$	7.72897	+	15.4347i	0.301765	+	0.602624i
$657$	3.00144	+	15.0893i	0.117097	+	0.588688i
$658$	1.89099	+	3.81985i	0.0737185	+	0.148913i
$659$	−5.18140	+	5.18140i	−0.201839	+	0.201839i	−0.800787	−	0.598949i	$-0.795585\pi$
$659$	−5.18140	+	5.18140i	−0.201839	+	0.201839i	0.598949	+	0.800787i	$0.295585\pi$
$660$	22.7459	−	46.4809i	0.885381	−	1.80927i
$661$	7.89415	+	19.0582i	0.307047	+	0.741276i	0.999798	+	0.0200998i	$0.00639840\pi$
$661$	7.89415	+	19.0582i	0.307047	+	0.741276i	−0.692751	+	0.721177i	$0.743602\pi$
$662$	−5.29997	+	40.7372i	−0.205989	+	1.58330i
$663$	−23.5939	−	16.6595i	−0.916310	−	0.647002i
$664$	4.79385	+	1.96003i	0.186038	+	0.0760639i
$665$	1.85272	−	0.767423i	0.0718456	−	0.0297594i
$666$	−6.94092	+	20.5502i	−0.268955	+	0.796304i
$667$	26.7248	+	26.7248i	1.03479	+	1.03479i
$668$	4.06204	−	1.39271i	0.157165	−	0.0538856i
$669$	23.7881	−	4.73174i	0.919700	−	0.182940i
$670$	−0.483233	+	0.552720i	−0.0186689	+	0.0213534i
$671$	−27.8979	−	11.5557i	−1.07699	−	0.446103i
$672$	18.8960	−	11.1026i	0.728928	−	0.428291i
$673$	14.1796	+	9.47450i	0.546583	+	0.365215i	0.797994	−	0.602665i	$-0.205895\pi$
$673$	14.1796	+	9.47450i	0.546583	+	0.365215i	−0.251411	+	0.967880i	$0.580895\pi$
$674$	36.0440	−	2.41766i	1.38836	−	0.0931247i
$675$	6.77555	+	10.1403i	0.260791	+	0.390301i
$676$	7.14679	+	12.2919i	0.274877	+	0.472764i
$677$	2.45339	−	12.3340i	0.0942915	−	0.474035i	−0.904570	−	0.426326i	$-0.859808\pi$
$677$	2.45339	−	12.3340i	0.0942915	−	0.474035i	0.998861	−	0.0477097i	$-0.0151922\pi$
$678$	8.38552	+	31.1054i	0.322044	+	1.19459i
$679$	−14.1460			−0.542875
$680$	20.4994	−	3.62804i	0.786115	−	0.139129i
$681$	−0.821663			−0.0314862
$682$	−1.83687	−	6.81371i	−0.0703374	−	0.260910i
$683$	5.09935	−	25.6362i	0.195121	−	0.980941i	−0.751779	−	0.659415i	$-0.770804\pi$
$683$	5.09935	−	25.6362i	0.195121	−	0.980941i	0.946901	−	0.321526i	$-0.104196\pi$
$684$	−4.48431	−	7.71262i	−0.171462	−	0.294899i
$685$	−10.3898	−	15.5494i	−0.396974	−	0.594114i
$686$	23.1045	−	1.54974i	0.882135	−	0.0591695i
$687$	53.3933	+	35.6762i	2.03708	+	1.36113i
$688$	−13.4624	−	17.3246i	−0.513248	−	0.660495i
$689$	13.8995	+	5.75738i	0.529530	+	0.219339i
$690$	−20.7371	+	23.7190i	−0.789447	+	0.902966i
$691$	36.2752	−	7.21558i	1.37997	−	0.274494i	0.551337	−	0.834283i	$-0.314118\pi$
$691$	36.2752	−	7.21558i	1.37997	−	0.274494i	0.828635	+	0.559789i	$0.189118\pi$
$692$	33.6207	−	11.5272i	1.27807	−	0.438197i
$693$	25.4075	+	25.4075i	0.965151	+	0.965151i
$694$	−2.25090	+	6.66430i	−0.0854428	+	0.252973i
$695$	−5.49182	+	2.27479i	−0.208317	+	0.0862876i
$696$	−27.0045	+	66.0477i	−1.02360	+	2.50353i
$697$	−17.3559	−	3.91951i	−0.657402	−	0.148462i
$698$	4.15612	−	31.9453i	0.157311	−	1.20915i
$699$	−18.7240	−	45.2037i	−0.708206	−	1.70976i
$700$	−2.13984	+	4.37274i	−0.0808783	+	0.165274i
$701$	9.40213	−	9.40213i	0.355114	−	0.355114i	−0.506895	−	0.862008i	$-0.669207\pi$
$701$	9.40213	−	9.40213i	0.355114	−	0.355114i	0.862008	+	0.506895i	$0.169207\pi$
$702$	10.2417	+	20.6886i	0.386550	+	0.780840i
$703$	0.469798	+	2.36184i	0.0177188	+	0.0890783i
$704$	−8.19800	−	39.3297i	−0.308974	−	1.48229i
$705$	4.42691	−	10.6875i	0.166727	−	0.402514i
$706$	10.3262	−	17.9487i	0.388632	−	0.675508i
$707$	10.8224	−	16.1969i	0.407018	−	0.609146i
$708$	−0.723172	+	11.5743i	−0.0271785	+	0.434990i
$709$	−38.4032	+	25.6602i	−1.44226	+	0.963689i	−0.444573	+	0.895743i	$0.646645\pi$
$709$	−38.4032	+	25.6602i	−1.44226	+	0.963689i	−0.997689	+	0.0679461i	$0.978355\pi$
$710$	−15.1009	−	19.6179i	−0.566727	−	0.736246i
$711$	−46.7267	−	9.29452i	−1.75239	−	0.348572i
$712$	12.0945	−	0.0553379i	0.453262	−	0.00207388i
$713$			4.29650i			0.160905i
$714$	−3.49049	+	22.3196i	−0.130628	+	0.835288i
$715$			21.7580i			0.813704i
$716$	4.11609	+	30.5446i	0.153826	+	1.14150i
$717$	−39.5210	−	7.86122i	−1.47594	−	0.293583i
$718$	38.4370	−	29.5870i	1.43446	−	1.10418i
$719$	−24.7601	+	16.5441i	−0.923394	+	0.616992i	−0.923745	−	0.383008i	$-0.874888\pi$
$719$	−24.7601	+	16.5441i	−0.923394	+	0.616992i	0.000350873		1.00000i	$0.499888\pi$
$720$	−36.1146	−	12.0140i	−1.34591	−	0.447737i
$721$	−10.4875	+	15.6957i	−0.390576	+	0.584539i
$722$	22.4321	+	12.9056i	0.834836	+	0.480297i
$723$	6.52218	−	15.7459i	0.242563	−	0.585598i
$724$	−9.73065	−	11.0276i	−0.361637	−	0.409839i
$725$	−3.09218	−	15.5454i	−0.114841	−	0.577343i
$726$	52.0145	−	25.7494i	1.93044	−	0.955651i
$727$	−9.13024	+	9.13024i	−0.338622	+	0.338622i	−0.855848	−	0.517227i	$-0.826964\pi$
$727$	−9.13024	+	9.13024i	−0.338622	+	0.338622i	0.517227	+	0.855848i	$0.326964\pi$
$728$	−5.08445	+	7.68531i	−0.188442	+	0.284837i
$729$	15.3078	+	36.9562i	0.566954	+	1.36875i
$730$	7.22581	+	0.940087i	0.267439	+	0.0347942i
$731$	22.6081	+	0.582423i	0.836190	+	0.0215417i
$732$	−8.88118	+	33.5541i	−0.328258	+	1.24019i
$733$	−6.43823	+	2.66680i	−0.237802	+	0.0985006i	−0.498402	−	0.866946i	$-0.666080\pi$
$733$	−6.43823	+	2.66680i	−0.237802	+	0.0985006i	0.260600	+	0.965447i	$0.416080\pi$
$734$	27.9744	+	9.44847i	1.03255	+	0.348750i
$735$	−18.9377	−	18.9377i	−0.698527	−	0.698527i
$736$	−1.41358	+	24.4190i	−0.0521053	+	0.900095i
$737$	−1.43238	+	0.284917i	−0.0527622	+	0.0104951i
$738$	24.4901	+	21.4112i	0.901493	+	0.788159i
$739$	34.6109	+	14.3363i	1.27318	+	0.527369i	0.913930	−	0.405872i	$-0.133032\pi$
$739$	34.6109	+	14.3363i	1.27318	+	0.527369i	0.359251	+	0.933241i	$0.383032\pi$
$740$	8.16942	+	6.22912i	0.300314	+	0.228987i
$741$	4.87441	+	3.25698i	0.179066	+	0.119648i
$742$	−0.787530	−	11.7410i	−0.0289112	−	0.431025i
$743$	−4.14388	−	6.20175i	−0.152024	−	0.227520i	0.747639	−	0.664106i	$-0.231188\pi$
$743$	−4.14388	−	6.20175i	−0.152024	−	0.227520i	−0.899663	+	0.436586i	$0.856188\pi$
$744$	−7.47992	+	3.13846i	−0.274227	+	0.115061i
$745$	−2.17028	+	10.9107i	−0.0795128	+	0.399738i
$746$	−35.1920	+	9.48721i	−1.28847	+	0.347351i
$747$	9.76006			0.357102
$748$	36.7154	+	19.1543i	1.34245	+	0.700352i
$749$	−14.1934			−0.518616
$750$	47.9333	−	12.9221i	1.75028	−	0.471847i
$751$	4.12190	−	20.7222i	0.150410	−	0.756163i	−0.829778	−	0.558094i	$-0.811533\pi$
$751$	4.12190	−	20.7222i	0.150410	−	0.756163i	0.980188	−	0.198069i	$-0.0634671\pi$
$752$	−2.37733	−	8.66062i	−0.0866922	−	0.315820i
$753$	−31.3768	−	46.9587i	−1.14344	−	1.71127i
$754$	−2.00789	−	29.9348i	−0.0731229	−	1.09016i
$755$	35.1212	+	23.4672i	1.27819	+	0.854060i
$756$	10.9481	−	14.3583i	0.398177	−	0.522205i
$757$	30.9238	+	12.8091i	1.12395	+	0.465553i	0.865719	−	0.500531i	$-0.166862\pi$
$757$	30.9238	+	12.8091i	1.12395	+	0.465553i	0.258227	+	0.966084i	$0.416862\pi$
$758$	31.2748	+	27.3430i	1.13595	+	0.993141i
$759$	−61.4678	+	12.2267i	−2.23114	+	0.443801i
$760$	−4.14047	+	0.843303i	−0.150191	+	0.0305898i
$761$	16.3926	+	16.3926i	0.594233	+	0.594233i	0.938772	−	0.344539i	$-0.111965\pi$
$761$	16.3926	+	16.3926i	0.594233	+	0.594233i	−0.344539	+	0.938772i	$0.611965\pi$
$762$	−16.7683	−	5.66356i	−0.607451	−	0.205169i
$763$	−5.23243	+	2.16734i	−0.189427	+	0.0784631i
$764$	27.1252	+	7.17956i	0.981354	+	0.259747i
$765$	33.1706	−	20.9487i	1.19929	−	0.757404i
$766$	−40.9918	−	5.33308i	−1.48109	−	0.192692i
$767$	−1.86598	−	4.50488i	−0.0673768	−	0.162662i
$768$	−43.5443	+	15.3763i	−1.57127	+	0.554845i
$769$	−0.934932	+	0.934932i	−0.0337145	+	0.0337145i	−0.723763	−	0.690049i	$-0.757589\pi$
$769$	−0.934932	+	0.934932i	−0.0337145	+	0.0337145i	0.690049	+	0.723763i	$0.257589\pi$
$770$	15.2517	−	7.55023i	0.549632	−	0.272091i
$771$	−5.01468	−	25.2105i	−0.180599	−	0.907934i
$772$	−28.9623	+	25.5559i	−1.04238	+	0.919779i
$773$	−1.07317	+	2.59086i	−0.0385993	+	0.0931868i	−0.942004	−	0.335603i	$-0.891060\pi$
$773$	−1.07317	+	2.59086i	−0.0385993	+	0.0931868i	0.903404	+	0.428790i	$0.141060\pi$
$774$	−35.8391	−	20.6189i	−1.28821	−	0.741130i
$775$	1.00104	−	1.49817i	0.0359586	−	0.0538158i
$776$	29.2604	+	5.68120i	1.05039	+	0.203943i
$777$	−9.26941	+	6.19362i	−0.332538	+	0.222195i
$778$	28.1144	−	21.6411i	1.00795	−	0.775873i
$779$	3.54210	+	0.704568i	0.126909	+	0.0252438i
$780$	24.7858	−	3.34006i	0.887475	−	0.119593i
$781$		−	49.2467i		−	1.76219i
$782$	−18.5475	−	17.0782i	−0.663258	−	0.610716i
$783$			58.7867i			2.10086i
$784$	−20.6307	−	2.58815i	−0.736812	−	0.0924338i
$785$	−8.90352	−	1.77102i	−0.317780	−	0.0632104i
$786$	−47.1990	−	61.3171i	−1.68353	−	2.18711i
$787$	14.0349	−	9.37781i	0.500289	−	0.334283i	−0.279687	−	0.960091i	$-0.590231\pi$
$787$	14.0349	−	9.37781i	0.500289	−	0.334283i	0.779977	+	0.625808i	$0.215231\pi$
$788$	−33.4537	−	2.09021i	−1.19174	−	0.0744606i
$789$	21.8874	−	32.7568i	0.779212	−	1.16617i
$790$	−11.2525	+	19.5587i	−0.400346	+	0.695869i
$791$	−4.05443	+	9.78826i	−0.144159	+	0.348031i
$792$	−42.3502	−	62.7581i	−1.50485	−	2.23001i
$793$	−2.84715	−	14.3136i	−0.101105	−	0.508291i
$794$	−11.5252	−	23.2812i	−0.409014	−	0.826220i
$795$	−22.5830	+	22.5830i	−0.800937	+	0.800937i
$796$	−27.1422	−	13.2823i	−0.962030	−	0.470778i
$797$	2.57967	+	6.22789i	0.0913768	+	0.220603i	0.962960	−	0.269645i	$-0.0869063\pi$
$797$	2.57967	+	6.22789i	0.0913768	+	0.220603i	−0.871583	+	0.490248i	$0.836906\pi$
$798$	0.591572	−	4.54701i	0.0209414	−	0.160962i
$799$	8.45864	+	3.76173i	0.299245	+	0.133081i
$800$	6.18229	−	8.18541i	0.218577	−	0.289398i
$801$	21.0577	−	8.72237i	0.744036	−	0.308190i
$802$	1.65355	−	4.89572i	0.0583888	−	0.172874i
$803$	10.2494	+	10.2494i	0.361694	+	0.361694i
$804$	0.544449	+	1.58797i	0.0192012	+	0.0560032i
$805$	−10.1621	+	2.02138i	−0.358168	+	0.0712441i
$806$	2.24488	−	2.56768i	0.0790725	−	0.0904428i
$807$	66.0798	+	27.3712i	2.32612	+	0.963510i
$808$	−28.8904	+	29.1560i	−1.01636	+	1.02571i
$809$	0.552433	+	0.369124i	0.0194225	+	0.0129777i	0.565244	−	0.824924i	$-0.308782\pi$
$809$	0.552433	+	0.369124i	0.0194225	+	0.0129777i	−0.545821	+	0.837902i	$0.683782\pi$
$810$	−8.61629	+	0.577940i	−0.302745	+	0.0203067i
$811$	4.63426	+	6.93566i	0.162731	+	0.243544i	0.903870	−	0.427808i	$-0.140714\pi$
$811$	4.63426	+	6.93566i	0.162731	+	0.243544i	−0.741139	+	0.671352i	$0.765714\pi$
$812$	−20.2866	+	11.7951i	−0.711919	+	0.413927i
$813$	−14.4041	+	72.4143i	−0.505173	+	2.53968i
$814$	5.31930	+	19.7315i	0.186442	+	0.691588i
$815$	−8.00017			−0.280234
$816$	16.1837	−	44.7651i	0.566542	−	1.56709i
$817$	−4.59035			−0.160596
$818$	−3.25679	−	12.0808i	−0.113871	−	0.422394i
$819$	−3.38790	+	17.0321i	−0.118383	+	0.595151i
$820$	13.3194	−	7.74424i	0.465135	−	0.270441i
$821$	5.24884	+	7.85544i	0.183186	+	0.274157i	0.911685	−	0.410890i	$-0.134782\pi$
$821$	5.24884	+	7.85544i	0.183186	+	0.274157i	−0.728499	+	0.685047i	$0.759782\pi$
$822$	−42.6647	+	2.86175i	−1.48810	+	0.0998150i
$823$	−44.0744	−	29.4495i	−1.53634	−	1.02655i	−0.980791	−	0.195059i	$-0.937510\pi$
$823$	−44.0744	−	29.4495i	−1.53634	−	1.02655i	−0.555544	−	0.831487i	$-0.687490\pi$
$824$	27.9965	−	28.2539i	0.975305	−	0.984271i
$825$	24.2822	+	10.0580i	0.845398	+	0.350175i
$826$	−2.51027	+	2.87123i	−0.0873433	+	0.0999029i
$827$	−15.9515	+	3.17294i	−0.554687	+	0.110334i	−0.464471	−	0.885588i	$-0.653756\pi$
$827$	−15.9515	+	3.17294i	−0.554687	+	0.110334i	−0.0902155	+	0.995922i	$0.528756\pi$
$828$	14.9499	+	43.6034i	0.519543	+	1.51532i
$829$	−6.95676	−	6.95676i	−0.241618	−	0.241618i	0.575901	−	0.817519i	$-0.304651\pi$
$829$	−6.95676	−	6.95676i	−0.241618	−	0.241618i	−0.817519	+	0.575901i	$0.804651\pi$
$830$	1.47922	−	4.37957i	0.0513445	−	0.152017i
$831$	10.4803	−	4.34107i	0.363556	−	0.150590i
$832$	13.6034	−	13.8547i	0.471615	−	0.480326i
$833$	15.5402	−	14.7596i	0.538437	−	0.511391i
$834$	−1.75353	+	13.4782i	−0.0607197	+	0.466711i
$835$	−1.46675	−	3.54105i	−0.0507590	−	0.122543i
$836$	−7.54989	−	3.69461i	−0.261118	−	0.127781i
$837$	−4.72551	+	4.72551i	−0.163338	+	0.163338i
$838$	−5.97201	−	12.0636i	−0.206300	−	0.416731i
$839$	−8.45967	−	42.5296i	−0.292060	−	1.46829i	−0.796395	−	0.604777i	$-0.793262\pi$
$839$	−8.45967	−	42.5296i	−0.292060	−	1.46829i	0.504335	−	0.863508i	$-0.331738\pi$
$840$	−10.9422	−	16.2150i	−0.377541	−	0.559472i
$841$	18.1398	−	43.7934i	0.625511	−	1.51012i
$842$	18.2194	−	31.6684i	0.627882	−	1.09136i
$843$	−29.3605	+	43.9410i	−1.01123	+	1.51341i
$844$	24.2092	+	1.51261i	0.833315	+	0.0520661i
$845$	10.5521	−	7.05070i	0.363004	−	0.242551i
$846$	−10.3237	−	13.4117i	−0.354935	−	0.461102i
$847$	18.7204	+	3.72373i	0.643242	+	0.127949i
$848$	−3.08634	+	24.6019i	−0.105985	+	0.844834i
$849$			24.2932i			0.833741i
$850$	2.48836	+	10.2765i	0.0853500	+	0.352481i
$851$		−	12.4420i		−	0.426508i
$852$	−56.0998	+	7.55984i	−1.92195	+	0.258996i
$853$	−15.3622	−	3.05574i	−0.525993	−	0.104626i	−0.0750507	−	0.997180i	$-0.523912\pi$
$853$	−15.3622	−	3.05574i	−0.525993	−	0.104626i	−0.450942	+	0.892553i	$0.648912\pi$
$854$	−9.04538	+	6.96271i	−0.309527	+	0.238259i
$855$	−6.62100	+	4.42401i	−0.226433	+	0.151298i
$856$	29.3584	+	5.70023i	1.00345	+	0.194830i
$857$	−31.7696	+	47.5466i	−1.08523	+	1.62416i	−0.364099	+	0.931360i	$0.618623\pi$
$857$	−31.7696	+	47.5466i	−1.08523	+	1.62416i	−0.721130	+	0.692800i	$0.756377\pi$
$858$	43.1228	+	24.8093i	1.47219	+	0.846977i
$859$	−3.99736	+	9.65048i	−0.136388	+	0.329270i	−0.977286	−	0.211923i	$-0.932027\pi$
$859$	−3.99736	+	9.65048i	−0.136388	+	0.329270i	0.840898	+	0.541193i	$0.182027\pi$
$860$	−14.6839	+	12.9569i	−0.500717	+	0.441826i
$861$	3.26176	+	16.3980i	0.111161	+	0.558842i
$862$	9.42249	−	4.66454i	0.320931	−	0.158875i
$863$	−30.3784	+	30.3784i	−1.03409	+	1.03409i	−0.0346932	+	0.999398i	$0.511045\pi$
$863$	−30.3784	+	30.3784i	−1.03409	+	1.03409i	−0.999398	+	0.0346932i	$0.988955\pi$
$864$	−28.4120	+	25.3025i	−0.966594	+	0.860808i
$865$	−12.1400	−	29.3085i	−0.412772	−	0.996520i
$866$	−34.4499	−	4.48198i	−1.17066	−	0.152304i
$867$	25.1227	+	42.1460i	0.853210	+	1.43135i
$868$	−2.57886	−	0.682579i	−0.0875321	−	0.0231682i
$869$	−41.4693	+	17.1772i	−1.40675	+	0.582695i
$870$	60.3400	+	20.3801i	2.04572	+	0.690950i
$871$	−0.499098	−	0.499098i	−0.0169113	−	0.0169113i
$872$	11.6934	−	2.38164i	0.395990	−	0.0806525i
$873$	55.0922	−	10.9585i	1.86459	−	0.370890i
$874$	3.85267	+	3.36832i	0.130319	+	0.113935i
$875$	15.0837	+	6.24787i	0.509922	+	0.211217i
$876$	10.1023	−	13.2491i	0.341326	−	0.447646i
$877$	−28.0286	−	18.7281i	−0.946458	−	0.632403i	−0.0164198	−	0.999865i	$-0.505227\pi$
$877$	−28.0286	−	18.7281i	−0.946458	−	0.632403i	−0.930039	+	0.367462i	$0.880227\pi$
$878$	1.16958	+	17.4369i	0.0394716	+	0.588467i
$879$	−2.49540	−	3.73463i	−0.0841678	−	0.125966i
$880$	−34.5796	+	9.49205i	−1.16568	+	0.319977i
$881$	5.59819	−	28.1440i	0.188608	−	0.948196i	−0.764283	−	0.644881i	$-0.776907\pi$
$881$	5.59819	−	28.1440i	0.188608	−	0.948196i	0.952891	−	0.303314i	$-0.0980932\pi$
$882$	−37.8331	+	10.1992i	−1.27391	+	0.343426i
$883$	−53.5921			−1.80352			−0.901759	−	0.432239i	$-0.857724\pi$
$883$	−53.5921			−1.80352			−0.901759	+	0.432239i	$0.857724\pi$
$884$	2.16120	+	19.8972i	0.0726889	+	0.669216i
$885$	10.3510			0.347943
$886$	12.3569	−	3.33122i	0.415137	−	0.111914i
$887$	−8.00373	+	40.2375i	−0.268739	+	1.35104i	0.576694	+	0.816960i	$0.304342\pi$
$887$	−8.00373	+	40.2375i	−0.268739	+	1.35104i	−0.845433	+	0.534081i	$0.820658\pi$
$888$	21.6607	−	9.08850i	0.726887	−	0.304990i
$889$	−3.23375	−	4.83965i	−0.108456	−	0.162317i
$890$	−0.722471	−	10.7710i	−0.0242173	−	0.361046i
$891$	−14.2832	−	9.54370i	−0.478504	−	0.319726i
$892$	−13.3649	−	10.1907i	−0.447491	−	0.341208i
$893$	−1.73597	−	0.719062i	−0.0580920	−	0.0240625i
$894$	19.1496	+	16.7422i	0.640459	+	0.559941i
$895$	26.9807	−	5.36680i	0.901867	−	0.179392i
$896$	−14.4322	−	4.72787i	−0.482147	−	0.157947i
$897$	−21.4179	−	21.4179i	−0.715123	−	0.715123i
$898$	1.01153	+	0.341648i	0.0337552	+	0.0114010i
$899$	8.02422	−	3.32374i	0.267623	−	0.110853i
$900$	4.94625	−	18.6875i	0.164875	−	0.622916i
$901$	−17.6007	−	18.5316i	−0.586365	−	0.617376i
$902$	30.3921	+	3.95405i	1.01195	+	0.131655i
$903$	−8.13234	−	19.6332i	−0.270627	−	0.653352i
$904$	12.3175	−	18.6182i	0.409673	−	0.619233i
$905$	−9.28209	+	9.28209i	−0.308547	+	0.308547i
$906$	86.5569	−	42.8494i	2.87566	−	1.42358i
$907$	8.01518	+	40.2950i	0.266140	+	1.33797i	0.850284	+	0.526324i	$0.176430\pi$
$907$	8.01518	+	40.2950i	0.266140	+	1.33797i	−0.584144	+	0.811650i	$0.698570\pi$
$908$	0.376716	+	0.426929i	0.0125018	+	0.0141681i
$909$	−29.6010	+	71.4631i	−0.981803	+	2.37028i
$910$	7.12926	+	4.10160i	0.236333	+	0.135967i
$911$	−5.67087	+	8.48705i	−0.187884	+	0.281189i	−0.913439	−	0.406976i	$-0.866583\pi$
$911$	−5.67087	+	8.48705i	−0.187884	+	0.281189i	0.725555	+	0.688165i	$0.241583\pi$
$912$	−3.04977	+	9.16768i	−0.100988	+	0.303572i
$913$	7.64573	−	5.10872i	0.253037	−	0.169074i
$914$	−23.9048	+	18.4008i	−0.790701	+	0.608644i
$915$	30.3851	+	6.04397i	1.00450	+	0.199808i
$916$	−5.94271	−	44.0995i	−0.196353	−	1.45709i
$917$		−	25.4475i		−	0.840349i
$918$	−1.61600	−	39.1830i	−0.0533359	−	1.29323i
$919$		−	6.22948i		−	0.205491i	−0.994708	−	0.102746i	$-0.967237\pi$
$919$		−	6.22948i		−	0.205491i	0.994708	−	0.102746i	$-0.0327628\pi$
$920$	21.8317	−	0.0998897i	0.719770	−	0.00329327i
$921$	64.1765	+	12.7655i	2.11469	+	0.420638i
$922$	32.5876	+	42.3351i	1.07321	+	1.39423i
$923$	19.7898	−	13.2231i	0.651390	−	0.435245i
$924$	2.42655	−	38.8368i	0.0798276	−	1.27764i
$925$	−2.89888	+	4.33847i	−0.0953144	+	0.142648i
$926$	4.47124	−	7.77177i	0.146934	−	0.255396i
$927$	28.6851	−	69.2519i	0.942142	−	2.27453i
$928$	46.6988	−	16.2503i	1.53296	−	0.533442i
$929$	5.58447	+	28.0750i	0.183220	+	0.921112i	0.957536	+	0.288312i	$0.0930941\pi$
$929$	5.58447	+	28.0750i	0.183220	+	0.921112i	−0.774316	+	0.632799i	$0.781906\pi$
$930$	3.21214	+	6.48861i	0.105330	+	0.212770i
$931$	−3.07605	+	3.07605i	−0.100813	+	0.100813i
$932$	−14.9028	+	30.4538i	−0.488159	+	0.997548i
$933$	−18.6216	−	44.9564i	−0.609642	−	1.47181i
$934$	5.13837	−	39.4952i	0.168133	−	1.29232i
$935$	15.0196	−	33.7731i	0.491194	−	1.10450i
$936$	13.8480	−	33.8695i	0.452636	−	1.10706i
$937$	4.79158	−	1.98474i	0.156534	−	0.0648386i	−0.303041	−	0.952978i	$-0.598002\pi$
$937$	4.79158	−	1.98474i	0.156534	−	0.0648386i	0.459575	+	0.888139i	$0.348002\pi$
$938$	−0.176660	+	0.523044i	−0.00576816	+	0.0170780i
$939$	−45.9067	−	45.9067i	−1.49811	−	1.49811i
$940$	−7.58277	+	2.59983i	−0.247323	+	0.0847970i
$941$	−32.1838	+	6.40175i	−1.04916	+	0.208691i	−0.689421	−	0.724361i	$-0.742135\pi$
$941$	−32.1838	+	6.40175i	−1.04916	+	0.208691i	−0.359741	+	0.933052i	$0.617135\pi$
$942$	−13.6622	+	15.6267i	−0.445138	+	0.509147i
$943$	−17.2392	−	7.14073i	−0.561387	−	0.232534i
$944$	6.34548	−	4.93085i	0.206528	−	0.160485i
$945$	−13.4001	−	8.95363i	−0.435904	−	0.291262i
$946$	−38.8678	+	2.60707i	−1.26370	+	0.0847631i
$947$	−1.12055	−	1.67702i	−0.0364129	−	0.0544957i	0.812817	−	0.582520i	$-0.197933\pi$
$947$	−1.12055	−	1.67702i	−0.0364129	−	0.0544957i	−0.849229	+	0.528024i	$0.822933\pi$
$948$	25.9334	+	44.6033i	0.842279	+	1.44865i
$949$	−1.36669	+	6.87079i	−0.0443645	+	0.223035i
$950$	−0.558620	−	2.07215i	−0.0181240	−	0.0672295i
$951$	70.4447			2.28433
$952$	13.1974	−	8.41945i	0.427729	−	0.272876i
$953$	−23.3127			−0.755173			−0.377587	−	0.925974i	$-0.623246\pi$
$953$	−23.3127			−0.755173			−0.377587	+	0.925974i	$0.623246\pi$
$954$	12.1625	+	45.1156i	0.393775	+	1.46067i
$955$	4.88596	−	24.5634i	0.158106	−	0.794852i
$956$	14.0350	+	24.1390i	0.453924	+	0.780710i
$957$	70.3858	+	105.340i	2.27525	+	3.40515i
$958$	−8.10895	+	0.543910i	−0.261988	+	0.0175729i
$959$	−11.6926	−	7.81274i	−0.377574	−	0.252287i
$960$	16.1212	+	37.9345i	0.520311	+	1.22433i
$961$	−27.7281	−	11.4853i	−0.894454	−	0.370495i
$962$	−6.50084	+	7.43563i	−0.209595	+	0.239734i
$963$	55.2767	−	10.9952i	1.78127	−	0.354316i
$964$	−11.1717	+	3.83034i	−0.359818	+	0.123367i
$965$	24.3779	+	24.3779i	0.784752	+	0.784752i
$966$	−7.58105	+	22.4455i	−0.243916	+	0.722171i
$967$	−13.8345	+	5.73043i	−0.444887	+	0.184278i	−0.593869	−	0.804562i	$-0.702400\pi$
$967$	−13.8345	+	5.73043i	−0.444887	+	0.184278i	0.148982	+	0.988840i	$0.452400\pi$
$968$	−37.2268	−	15.2207i	−1.19651	−	0.489211i
$969$	−5.31784	−	8.42035i	−0.170834	−	0.270501i
$970$	3.43234	−	26.3821i	0.110206	−	0.847077i
$971$	−14.9871	−	36.1822i	−0.480960	−	1.16114i	−0.959153	−	0.282886i	$-0.908708\pi$
$971$	−14.9871	−	36.1822i	−0.480960	−	1.16114i	0.478193	−	0.878255i	$-0.341292\pi$
$972$	9.05813	−	18.5102i	0.290540	−	0.593715i
$973$	−3.16069	+	3.16069i	−0.101327	+	0.101327i
$974$	18.0296	+	36.4204i	0.577707	+	1.16698i
$975$	2.47815	+	12.4585i	0.0793642	+	0.398991i
$976$	21.5062	−	10.7693i	0.688397	−	0.344717i
$977$	17.5831	−	42.4494i	0.562534	−	1.35808i	−0.345199	−	0.938530i	$-0.612188\pi$
$977$	17.5831	−	42.4494i	0.562534	−	1.35808i	0.907733	−	0.419548i	$-0.137812\pi$
$978$	−9.12211	+	15.8557i	−0.291693	+	0.507011i
$979$	11.9304	−	17.8551i	0.381297	−	0.570651i
$980$	−1.15729	+	18.5224i	−0.0369684	+	0.591677i
$981$	18.6989	−	12.4942i	0.597010	−	0.398909i
$982$	−12.8166	−	16.6503i	−0.408995	−	0.531333i
$983$	20.3659	+	4.05103i	0.649572	+	0.129208i	0.508869	−	0.860844i	$-0.330064\pi$
$983$	20.3659	+	4.05103i	0.649572	+	0.129208i	0.140703	+	0.990052i	$0.455064\pi$
$984$	−0.161186	−	35.2284i	−0.00513841	−	1.12304i
$985$			29.9177i			0.953257i
$986$	−17.5474	+	47.8513i	−0.558823	+	1.52389i
$987$		−	8.69875i		−	0.276884i
$988$	−0.542526	−	4.02596i	−0.0172601	−	0.128083i
$989$	23.2614	+	4.62698i	0.739670	+	0.147129i
$990$	−53.5492	+	41.2197i	−1.70191	+	1.31005i
$991$	−46.0024	+	30.7378i	−1.46131	+	0.976419i	−0.465497	+	0.885049i	$0.654124\pi$
$991$	−46.0024	+	30.7378i	−1.46131	+	0.976419i	−0.995817	+	0.0913695i	$0.970876\pi$
$992$	5.06011	+	2.44758i	0.160659	+	0.0777106i
$993$	46.5789	−	69.7102i	1.47814	−	2.21219i
$994$	−16.1363	−	9.28348i	−0.511811	−	0.294454i
$995$	−10.3215	+	24.9182i	−0.327212	+	0.789961i
$996$	−6.99333	−	7.92547i	−0.221592	−	0.251128i
$997$	0.696168	+	3.49987i	0.0220479	+	0.110842i	0.990242	−	0.139358i	$-0.0445037\pi$
$997$	0.696168	+	3.49987i	0.0220479	+	0.110842i	−0.968194	+	0.250200i	$0.919504\pi$
$998$	−12.3388	+	6.10824i	−0.390578	+	0.193353i
$999$	13.6844	−	13.6844i	0.432955	−	0.432955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	68.2.i.b.3.5	yes	48
3.2	odd	2		612.2.bd.d.343.2		48
4.3	odd	2	inner	68.2.i.b.3.2	✓	48
12.11	even	2		612.2.bd.d.343.5		48
17.6	odd	16	inner	68.2.i.b.23.2	yes	48
51.23	even	16		612.2.bd.d.91.5		48
68.23	even	16	inner	68.2.i.b.23.5	yes	48
204.23	odd	16		612.2.bd.d.91.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.i.b.3.2	✓	48	4.3	odd	2	inner
68.2.i.b.3.5	yes	48	1.1	even	1	trivial
68.2.i.b.23.2	yes	48	17.6	odd	16	inner
68.2.i.b.23.5	yes	48	68.23	even	16	inner
612.2.bd.d.91.2		48	204.23	odd	16
612.2.bd.d.91.5		48	51.23	even	16
612.2.bd.d.343.2		48	3.2	odd	2
612.2.bd.d.343.5		48	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	68.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.368108 + 1.36547i) q^{2} +(0.563072 - 2.83076i) q^{3} +(-1.72899 + 1.00528i) q^{4} +(0.991762 + 1.48428i) q^{5} +(4.07257 - 0.273169i) q^{6} +(1.11612 + 0.745767i) q^{7} +(-2.00913 - 1.99083i) q^{8} +(-4.92449 - 2.03979i) q^{9} +O(q^{10})\)	\(q+(0.368108 + 1.36547i) q^{2} +(0.563072 - 2.83076i) q^{3} +(-1.72899 + 1.00528i) q^{4} +(0.991762 + 1.48428i) q^{5} +(4.07257 - 0.273169i) q^{6} +(1.11612 + 0.745767i) q^{7} +(-2.00913 - 1.99083i) q^{8} +(-4.92449 - 2.03979i) q^{9} +(-1.66165 + 1.90059i) q^{10} +(-4.92539 + 0.979720i) q^{11} +(1.87215 + 5.46040i) q^{12} +(-1.71621 - 1.71621i) q^{13} +(-0.607467 + 1.79855i) q^{14} +(4.76006 - 1.97168i) q^{15} +(1.97883 - 3.47624i) q^{16} +(1.47922 + 3.84862i) q^{17} +(0.972518 - 7.47509i) q^{18} +(-0.320260 - 0.773176i) q^{19} +(-3.20686 - 1.56931i) q^{20} +(2.73954 - 2.73954i) q^{21} +(-3.15085 - 6.36480i) q^{22} +(0.843557 + 4.24085i) q^{23} +(-6.76684 + 4.56638i) q^{24} +(0.693933 - 1.67530i) q^{25} +(1.71167 - 2.97517i) q^{26} +(-3.73651 + 5.59209i) q^{27} +(-2.67947 - 0.167415i) q^{28} +(7.26771 - 4.85613i) q^{29} +(4.44448 + 5.77390i) q^{30} +(0.974564 + 0.193853i) q^{31} +(5.47511 + 1.42239i) q^{32} +14.4942i q^{33} +(-4.71065 + 3.43654i) q^{34} +2.39625i q^{35} +(10.5650 - 1.42370i) q^{36} +(-2.82219 - 0.561369i) q^{37} +(0.937854 - 0.721916i) q^{38} +(-5.82451 + 3.89182i) q^{39} +(0.962361 - 4.95653i) q^{40} +(-2.39752 + 3.58815i) q^{41} +(4.74920 + 2.73230i) q^{42} +(2.09905 - 5.06756i) q^{43} +(7.53106 - 6.64531i) q^{44} +(-1.85631 - 9.33229i) q^{45} +(-5.48021 + 2.71294i) q^{46} +(1.58763 - 1.58763i) q^{47} +(-8.72616 - 7.55896i) q^{48} +(-1.98923 - 4.80243i) q^{49} +(2.54301 + 0.330849i) q^{50} +(11.7274 - 2.02026i) q^{51} +(4.69258 + 1.24204i) q^{52} +(-5.72685 + 2.37214i) q^{53} +(-9.01125 - 3.04359i) q^{54} +(-6.33898 - 6.33898i) q^{55} +(-0.757735 - 3.72035i) q^{56} +(-2.36900 + 0.471224i) q^{57} +(9.30618 + 8.13623i) q^{58} +(1.85609 + 0.768817i) q^{59} +(-6.24802 + 8.19420i) q^{60} +(4.99961 + 3.34063i) q^{61} +(0.0940458 + 1.40209i) q^{62} +(-3.97511 - 5.94918i) q^{63} +(0.0732056 + 7.99967i) q^{64} +(0.845257 - 4.24939i) q^{65} +(-19.7914 + 5.33544i) q^{66} +0.290815 q^{67} +(-6.42650 - 5.16721i) q^{68} +12.4798 q^{69} +(-3.27200 + 0.882081i) q^{70} +(-1.91314 + 9.61800i) q^{71} +(5.83307 + 13.9020i) q^{72} +(-1.60357 - 2.39991i) q^{73} +(-0.272343 - 4.06025i) q^{74} +(-4.35164 - 2.90767i) q^{75} +(1.33098 + 1.01486i) q^{76} +(-6.22796 - 2.57971i) q^{77} +(-7.45819 - 6.52056i) q^{78} +(8.76636 - 1.74374i) q^{79} +(7.12222 - 0.510469i) q^{80} +(2.41878 + 2.41878i) q^{81} +(-5.78204 - 1.95291i) q^{82} +(-1.69169 + 0.700723i) q^{83} +(-1.98264 + 7.49065i) q^{84} +(-4.24539 + 6.01249i) q^{85} +(7.69225 + 1.00077i) q^{86} +(-9.65427 - 23.3075i) q^{87} +(11.8462 + 7.83721i) q^{88} +(-3.02367 + 3.02367i) q^{89} +(12.0596 - 5.97002i) q^{90} +(-0.635601 - 3.19538i) q^{91} +(-5.72174 - 6.48438i) q^{92} +(1.09750 - 2.64960i) q^{93} +(2.75227 + 1.58343i) q^{94} +(0.829985 - 1.24216i) q^{95} +(7.10933 - 14.6978i) q^{96} +(-8.76227 + 5.85476i) q^{97} +(5.82530 - 4.48404i) q^{98} +(26.2534 + 5.22214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

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